LMFDB - Embedded newform 1320.2.bw.f.1081.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1320,2,Mod(361,1320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1320, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 6]))

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

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

chi := DirichletCharacter("1320.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1320.bw (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$10.5402530668$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 7 x^{10} + 15 x^{9} + 51 x^{8} + 175 x^{7} + 1103 x^{6} + 2884 x^{5} + 5561 x^{4} + \cdots + 25 $ x^12 - 2x^11 + 7x^10 + 15x^9 + 51x^8 + 175x^7 + 1103x^6 + 2884x^5 + 5561x^4 + 5670x^3 + 2840x^2 - 125*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			1081.3
Root			$3.14116 - 2.28219i$ of defining polynomial
Character	$\chi$	$=$	1320.1081
Dual form			1320.2.bw.f.961.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(1.50883 - 4.64371i) q^{7} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(1.50883 - 4.64371i) q^{7} +(-0.809017 + 0.587785i) q^{9} +(0.881611 - 3.19731i) q^{11} +(2.56857 - 1.86617i) q^{13} +(-0.309017 + 0.951057i) q^{15} +(1.69666 + 1.23270i) q^{17} +(-0.0706444 - 0.217421i) q^{19} -4.88269 q^{21} -2.62434 q^{23} +(0.309017 + 0.951057i) q^{25} +(0.809017 + 0.587785i) q^{27} +(-1.67173 + 5.14507i) q^{29} +(1.23874 - 0.899998i) q^{31} +(-3.31325 + 0.149559i) q^{33} +(-3.95018 + 2.86997i) q^{35} +(-0.370827 + 1.14129i) q^{37} +(-2.56857 - 1.86617i) q^{39} +(-0.0371365 - 0.114294i) q^{41} +5.02859 q^{43} +1.00000 q^{45} +(-3.27087 - 10.0667i) q^{47} +(-13.6244 - 9.89869i) q^{49} +(0.648067 - 1.99455i) q^{51} +(-1.82247 + 1.32411i) q^{53} +(-2.59257 + 2.06848i) q^{55} +(-0.184950 + 0.134374i) q^{57} +(-3.41557 + 10.5120i) q^{59} +(-6.83461 - 4.96564i) q^{61} +(1.50883 + 4.64371i) q^{63} -3.17492 q^{65} +2.63570 q^{67} +(0.810967 + 2.49590i) q^{69} +(-5.10191 - 3.70675i) q^{71} +(2.37226 - 7.30107i) q^{73} +(0.809017 - 0.587785i) q^{75} +(-13.5172 - 8.91816i) q^{77} +(8.45580 - 6.14350i) q^{79} +(0.309017 - 0.951057i) q^{81} +(12.5129 + 9.09115i) q^{83} +(-0.648067 - 1.99455i) q^{85} +5.40985 q^{87} -1.53633 q^{89} +(-4.79043 - 14.7434i) q^{91} +(-1.23874 - 0.899998i) q^{93} +(-0.0706444 + 0.217421i) q^{95} +(-2.29322 + 1.66612i) q^{97} +(1.16609 + 3.10487i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{3} - 3 q^{5} - 3 q^{9}+O(q^{10}) $ 12 * q + 3 * q^3 - 3 * q^5 - 3 * q^9	$ 12 q + 3 q^{3} - 3 q^{5} - 3 q^{9} - 4 q^{11} + 3 q^{13} + 3 q^{15} + 12 q^{17} - 4 q^{19} - 10 q^{21} - 12 q^{23} - 3 q^{25} + 3 q^{27} + 16 q^{29} + 3 q^{31} + 4 q^{33} - 5 q^{35} - 19 q^{37} - 3 q^{39} + 22 q^{41} + 52 q^{43} + 12 q^{45} + 25 q^{47} - 11 q^{49} + 8 q^{51} - q^{53} - 4 q^{55} + 4 q^{57} - 9 q^{59} + 21 q^{61} - 12 q^{65} - 18 q^{67} - 8 q^{69} + 17 q^{71} + 37 q^{73} + 3 q^{75} - 13 q^{77} - 18 q^{79} - 3 q^{81} + 19 q^{83} - 8 q^{85} + 14 q^{87} + 2 q^{89} - 30 q^{91} - 3 q^{93} - 4 q^{95} + q^{97} + 6 q^{99}+O(q^{100}) $ 12 * q + 3 * q^3 - 3 * q^5 - 3 * q^9 - 4 * q^11 + 3 * q^13 + 3 * q^15 + 12 * q^17 - 4 * q^19 - 10 * q^21 - 12 * q^23 - 3 * q^25 + 3 * q^27 + 16 * q^29 + 3 * q^31 + 4 * q^33 - 5 * q^35 - 19 * q^37 - 3 * q^39 + 22 * q^41 + 52 * q^43 + 12 * q^45 + 25 * q^47 - 11 * q^49 + 8 * q^51 - q^53 - 4 * q^55 + 4 * q^57 - 9 * q^59 + 21 * q^61 - 12 * q^65 - 18 * q^67 - 8 * q^69 + 17 * q^71 + 37 * q^73 + 3 * q^75 - 13 * q^77 - 18 * q^79 - 3 * q^81 + 19 * q^83 - 8 * q^85 + 14 * q^87 + 2 * q^89 - 30 * q^91 - 3 * q^93 - 4 * q^95 + q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1320\mathbb{Z}\right)^\times$.

$n$	$661$	$881$	$991$	$1057$	$1201$
$\chi(n)$	$1$	$1$	$1$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$		0			0
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$6$		0			0
$7$	1.50883	−	4.64371i	0.570286	−	1.75516i	−0.0814123	−	0.996681i	$-0.525943\pi$
$7$	1.50883	−	4.64371i	0.570286	−	1.75516i	0.651698	−	0.758479i	$-0.274057\pi$
$8$		0			0
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$		0			0
$11$	0.881611	−	3.19731i	0.265816	−	0.964024i
$11$	0.881611	−	3.19731i	0.265816	−	0.964024i
$12$		0			0
$13$	2.56857	−	1.86617i	0.712393	−	0.517583i	−0.171552	−	0.985175i	$-0.554878\pi$
$13$	2.56857	−	1.86617i	0.712393	−	0.517583i	0.883945	+	0.467592i	$0.154878\pi$
$14$		0			0
$15$	−0.309017	+	0.951057i	−0.0797878	+	0.245562i
$16$		0			0
$17$	1.69666	+	1.23270i	0.411501	+	0.298973i	0.774209	−	0.632930i	$-0.218148\pi$
$17$	1.69666	+	1.23270i	0.411501	+	0.298973i	−0.362708	+	0.931903i	$0.618148\pi$
$18$		0			0
$19$	−0.0706444	−	0.217421i	−0.0162069	−	0.0498798i	0.942626	−	0.333851i	$-0.108348\pi$
$19$	−0.0706444	−	0.217421i	−0.0162069	−	0.0498798i	−0.958833	+	0.283971i	$0.908348\pi$
$20$		0			0
$21$	−4.88269			−1.06549
$22$		0			0
$23$	−2.62434			−0.547214			−0.273607	−	0.961842i	$-0.588217\pi$
$23$	−2.62434			−0.547214			−0.273607	+	0.961842i	$0.588217\pi$
$24$		0			0
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$		0			0
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$		0			0
$29$	−1.67173	+	5.14507i	−0.310433	+	0.955415i	0.667160	+	0.744914i	$0.267510\pi$
$29$	−1.67173	+	5.14507i	−0.310433	+	0.955415i	−0.977594	+	0.210501i	$0.932490\pi$
$30$		0			0
$31$	1.23874	−	0.899998i	0.222485	−	0.161644i	−0.470960	−	0.882155i	$-0.656092\pi$
$31$	1.23874	−	0.899998i	0.222485	−	0.161644i	0.693444	+	0.720510i	$0.256092\pi$
$32$		0			0
$33$	−3.31325	+	0.149559i	−0.576763	+	0.0260349i
$34$		0			0
$35$	−3.95018	+	2.86997i	−0.667702	+	0.485114i
$36$		0			0
$37$	−0.370827	+	1.14129i	−0.0609636	+	0.187627i	−0.976900	−	0.213697i	$-0.931450\pi$
$37$	−0.370827	+	1.14129i	−0.0609636	+	0.187627i	0.915936	+	0.401323i	$0.131450\pi$
$38$		0			0
$39$	−2.56857	−	1.86617i	−0.411300	−	0.298827i
$40$		0			0
$41$	−0.0371365	−	0.114294i	−0.00579975	−	0.0178498i	0.948115	−	0.317928i	$-0.102987\pi$
$41$	−0.0371365	−	0.114294i	−0.00579975	−	0.0178498i	−0.953915	+	0.300078i	$0.902987\pi$
$42$		0			0
$43$	5.02859			0.766853			0.383426	−	0.923571i	$-0.374744\pi$
$43$	5.02859			0.766853			0.383426	+	0.923571i	$0.374744\pi$
$44$		0			0
$45$	1.00000			0.149071
$46$		0			0
$47$	−3.27087	−	10.0667i	−0.477106	−	1.46838i	−0.843096	−	0.537763i	$-0.819270\pi$
$47$	−3.27087	−	10.0667i	−0.477106	−	1.46838i	0.365990	−	0.930619i	$-0.380730\pi$
$48$		0			0
$49$	−13.6244	−	9.89869i	−1.94634	−	1.41410i
$50$		0			0
$51$	0.648067	−	1.99455i	0.0907476	−	0.279292i
$52$		0			0
$53$	−1.82247	+	1.32411i	−0.250336	+	0.181880i	−0.705876	−	0.708336i	$-0.749446\pi$
$53$	−1.82247	+	1.32411i	−0.250336	+	0.181880i	0.455540	+	0.890216i	$0.349446\pi$
$54$		0			0
$55$	−2.59257	+	2.06848i	−0.349582	+	0.278913i
$56$		0			0
$57$	−0.184950	+	0.134374i	−0.0244972	+	0.0177982i
$58$		0			0
$59$	−3.41557	+	10.5120i	−0.444669	+	1.36855i	0.438178	+	0.898888i	$0.355624\pi$
$59$	−3.41557	+	10.5120i	−0.444669	+	1.36855i	−0.882846	+	0.469662i	$0.844376\pi$
$60$		0			0
$61$	−6.83461	−	4.96564i	−0.875083	−	0.635785i	0.0568632	−	0.998382i	$-0.481890\pi$
$61$	−6.83461	−	4.96564i	−0.875083	−	0.635785i	−0.931946	+	0.362597i	$0.881890\pi$
$62$		0			0
$63$	1.50883	+	4.64371i	0.190095	+	0.585053i
$64$		0			0
$65$	−3.17492			−0.393801
$66$		0			0
$67$	2.63570			0.322002			0.161001	−	0.986954i	$-0.448528\pi$
$67$	2.63570			0.322002			0.161001	+	0.986954i	$0.448528\pi$
$68$		0			0
$69$	0.810967	+	2.49590i	0.0976290	+	0.300471i
$70$		0			0
$71$	−5.10191	−	3.70675i	−0.605485	−	0.439911i	0.242337	−	0.970192i	$-0.422086\pi$
$71$	−5.10191	−	3.70675i	−0.605485	−	0.439911i	−0.847822	+	0.530282i	$0.822086\pi$
$72$		0			0
$73$	2.37226	−	7.30107i	0.277652	−	0.854525i	−0.710853	−	0.703340i	$-0.751691\pi$
$73$	2.37226	−	7.30107i	0.277652	−	0.854525i	0.988505	−	0.151185i	$-0.0483089\pi$
$74$		0			0
$75$	0.809017	−	0.587785i	0.0934172	−	0.0678716i
$76$		0			0
$77$	−13.5172	−	8.91816i	−1.54042	−	1.01632i
$78$		0			0
$79$	8.45580	−	6.14350i	0.951352	−	0.691198i	0.000225975	−	1.00000i	$-0.499928\pi$
$79$	8.45580	−	6.14350i	0.951352	−	0.691198i	0.951126	+	0.308802i	$0.0999281\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$		0			0
$83$	12.5129	+	9.09115i	1.37347	+	0.997884i	0.997457	+	0.0712689i	$0.0227049\pi$
$83$	12.5129	+	9.09115i	1.37347	+	0.997884i	0.376012	+	0.926615i	$0.377295\pi$
$84$		0			0
$85$	−0.648067	−	1.99455i	−0.0702928	−	0.216339i
$86$		0			0
$87$	5.40985			0.579996
$88$		0			0
$89$	−1.53633			−0.162851			−0.0814254	−	0.996679i	$-0.525947\pi$
$89$	−1.53633			−0.162851			−0.0814254	+	0.996679i	$0.525947\pi$
$90$		0			0
$91$	−4.79043	−	14.7434i	−0.502174	−	1.54553i
$92$		0			0
$93$	−1.23874	−	0.899998i	−0.128452	−	0.0933255i
$94$		0			0
$95$	−0.0706444	+	0.217421i	−0.00724797	+	0.0223069i
$96$		0			0
$97$	−2.29322	+	1.66612i	−0.232841	+	0.169169i	−0.698088	−	0.716012i	$-0.745966\pi$
$97$	−2.29322	+	1.66612i	−0.232841	+	0.169169i	0.465247	+	0.885181i	$0.345966\pi$
$98$		0			0
$99$	1.16609	+	3.10487i	0.117196	+	0.312051i
$100$		0			0
$101$	0.758118	−	0.550805i	0.0754355	−	0.0548071i	−0.549428	−	0.835541i	$-0.685154\pi$
$101$	0.758118	−	0.550805i	0.0754355	−	0.0548071i	0.624864	+	0.780734i	$0.285154\pi$
$102$		0			0
$103$	−4.32899	+	13.3233i	−0.426548	+	1.31278i	0.474956	+	0.880010i	$0.342464\pi$
$103$	−4.32899	+	13.3233i	−0.426548	+	1.31278i	−0.901504	+	0.432770i	$0.857536\pi$
$104$		0			0
$105$	3.95018	+	2.86997i	0.385498	+	0.280081i
$106$		0			0
$107$	−0.417884	−	1.28611i	−0.0403984	−	0.124333i	0.928823	−	0.370523i	$-0.120821\pi$
$107$	−0.417884	−	1.28611i	−0.0403984	−	0.124333i	−0.969222	+	0.246189i	$0.920821\pi$
$108$		0			0
$109$	−17.1322			−1.64096			−0.820482	−	0.571673i	$-0.806295\pi$
$109$	−17.1322			−1.64096			−0.820482	+	0.571673i	$0.806295\pi$
$110$		0			0
$111$	1.20002			0.113901
$112$		0			0
$113$	0.169565	+	0.521867i	0.0159513	+	0.0490931i	0.958715	−	0.284367i	$-0.0917836\pi$
$113$	0.169565	+	0.521867i	0.0159513	+	0.0490931i	−0.942764	+	0.333461i	$0.891784\pi$
$114$		0			0
$115$	2.12314	+	1.54255i	0.197984	+	0.143844i
$116$		0			0
$117$	−0.981106	+	3.01953i	−0.0907032	+	0.279156i
$118$		0			0
$119$	8.28427	−	6.01888i	0.759418	−	0.551750i
$120$		0			0
$121$	−9.44552	−	5.63756i	−0.858684	−	0.512506i
$122$		0			0
$123$	−0.0972246	+	0.0706378i	−0.00876645	+	0.00636920i
$124$		0			0
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$		0			0
$127$	13.1382	+	9.54548i	1.16583	+	0.847025i	0.990504	−	0.137486i	$-0.0439022\pi$
$127$	13.1382	+	9.54548i	1.16583	+	0.847025i	0.175326	+	0.984511i	$0.443902\pi$
$128$		0			0
$129$	−1.55392	−	4.78247i	−0.136815	−	0.421073i
$130$		0			0
$131$	−8.45080			−0.738350			−0.369175	−	0.929360i	$-0.620360\pi$
$131$	−8.45080			−0.738350			−0.369175	+	0.929360i	$0.620360\pi$
$132$		0			0
$133$	−1.11623			−0.0967897
$134$		0			0
$135$	−0.309017	−	0.951057i	−0.0265959	−	0.0818539i
$136$		0			0
$137$	5.24262	+	3.80899i	0.447907	+	0.325424i	0.788769	−	0.614690i	$-0.210719\pi$
$137$	5.24262	+	3.80899i	0.447907	+	0.325424i	−0.340862	+	0.940113i	$0.610719\pi$
$138$		0			0
$139$	5.81607	−	17.9000i	0.493313	−	1.51826i	−0.326257	−	0.945281i	$-0.605787\pi$
$139$	5.81607	−	17.9000i	0.493313	−	1.51826i	0.819570	−	0.572980i	$-0.194213\pi$
$140$		0			0
$141$	−8.56326	+	6.22157i	−0.721156	+	0.523951i
$142$		0			0
$143$	−3.70225	−	9.85774i	−0.309598	−	0.824345i
$144$		0			0
$145$	4.37666	−	3.17983i	0.363462	−	0.264070i
$146$		0			0
$147$	−5.20405	+	16.0164i	−0.429223	+	1.32101i
$148$		0			0
$149$	15.9056	+	11.5561i	1.30304	+	0.946715i	0.999980	−	0.00625611i	$-0.00199140\pi$
$149$	15.9056	+	11.5561i	1.30304	+	0.946715i	0.303061	+	0.952971i	$0.401991\pi$
$150$		0			0
$151$	−4.68044	−	14.4049i	−0.380889	−	1.17226i	−0.939419	−	0.342771i	$-0.888634\pi$
$151$	−4.68044	−	14.4049i	−0.380889	−	1.17226i	0.558530	−	0.829484i	$-0.311366\pi$
$152$		0			0
$153$	−2.09719			−0.169548
$154$		0			0
$155$	−1.53117			−0.122986
$156$		0			0
$157$	−5.19898	−	16.0008i	−0.414924	−	1.27700i	−0.912319	−	0.409480i	$-0.865710\pi$
$157$	−5.19898	−	16.0008i	−0.414924	−	1.27700i	0.497395	−	0.867524i	$-0.334290\pi$
$158$		0			0
$159$	1.82247	+	1.32411i	0.144532	+	0.105008i
$160$		0			0
$161$	−3.95970	+	12.1867i	−0.312068	+	0.960447i
$162$		0			0
$163$	−9.06938	+	6.58929i	−0.710369	+	0.516113i	−0.883293	−	0.468822i	$-0.844679\pi$
$163$	−9.06938	+	6.58929i	−0.710369	+	0.516113i	0.172924	+	0.984935i	$0.444679\pi$
$164$		0			0
$165$	2.76839	+	1.82648i	0.215518	+	0.142192i
$166$		0			0
$167$	−1.23273	+	0.895629i	−0.0953913	+	0.0693058i	−0.634459	−	0.772957i	$-0.718777\pi$
$167$	−1.23273	+	0.895629i	−0.0953913	+	0.0693058i	0.539067	+	0.842263i	$0.318777\pi$
$168$		0			0
$169$	−0.902285	+	2.77695i	−0.0694065	+	0.213611i
$170$		0			0
$171$	0.184950	+	0.134374i	0.0141434	+	0.0102758i
$172$		0			0
$173$	4.47541	+	13.7739i	0.340259	+	1.04721i	0.964073	+	0.265638i	$0.0855825\pi$
$173$	4.47541	+	13.7739i	0.340259	+	1.04721i	−0.623813	+	0.781573i	$0.714417\pi$
$174$		0			0
$175$	4.88269			0.369097
$176$		0			0
$177$	11.0530			0.830795
$178$		0			0
$179$	3.57716	+	11.0094i	0.267370	+	0.822879i	0.991138	+	0.132836i	$0.0424084\pi$
$179$	3.57716	+	11.0094i	0.267370	+	0.822879i	−0.723768	+	0.690043i	$0.757592\pi$
$180$		0			0
$181$	15.4932	+	11.2565i	1.15160	+	0.836686i	0.988693	−	0.149955i	$-0.0479130\pi$
$181$	15.4932	+	11.2565i	1.15160	+	0.836686i	0.162907	+	0.986641i	$0.447913\pi$
$182$		0			0
$183$	−2.61059	+	8.03457i	−0.192980	+	0.593933i
$184$		0			0
$185$	0.970838	−	0.705355i	0.0713774	−	0.0518587i
$186$		0			0
$187$	5.43711	−	4.33799i	0.397601	−	0.317225i
$188$		0			0
$189$	3.95018	−	2.86997i	0.287333	−	0.208760i
$190$		0			0
$191$	8.16748	−	25.1369i	0.590978	−	1.81884i	0.0171723	−	0.999853i	$-0.494534\pi$
$191$	8.16748	−	25.1369i	0.590978	−	1.81884i	0.573806	−	0.818991i	$-0.305466\pi$
$192$		0			0
$193$	9.99387	+	7.26097i	0.719375	+	0.522656i	0.886184	−	0.463333i	$-0.153347\pi$
$193$	9.99387	+	7.26097i	0.719375	+	0.522656i	−0.166810	+	0.985989i	$0.553347\pi$
$194$		0			0
$195$	0.981106	+	3.01953i	0.0702584	+	0.216233i
$196$		0			0
$197$	−17.8792			−1.27384			−0.636921	−	0.770929i	$-0.719792\pi$
$197$	−17.8792			−1.27384			−0.636921	+	0.770929i	$0.719792\pi$
$198$		0			0
$199$	26.6850			1.89165			0.945824	−	0.324681i	$-0.105257\pi$
$199$	26.6850			1.89165			0.945824	+	0.324681i	$0.105257\pi$
$200$		0			0
$201$	−0.814477	−	2.50670i	−0.0574488	−	0.176809i
$202$		0			0
$203$	21.3699	+	15.5261i	1.49987	+	1.08972i
$204$		0			0
$205$	−0.0371365	+	0.114294i	−0.00259373	+	0.00798267i
$206$		0			0
$207$	2.12314	−	1.54255i	0.147568	−	0.107215i
$208$		0			0
$209$	−0.757443	+	0.0341908i	−0.0523934	+	0.00236503i
$210$		0			0
$211$	−18.9702	+	13.7827i	−1.30596	+	0.948837i	−0.999995	−	0.00320462i	$-0.998980\pi$
$211$	−18.9702	+	13.7827i	−1.30596	+	0.948837i	−0.305968	+	0.952042i	$0.598980\pi$
$212$		0			0
$213$	−1.94876	+	5.99765i	−0.133526	+	0.410952i
$214$		0			0
$215$	−4.06821	−	2.95573i	−0.277450	−	0.201579i
$216$		0			0
$217$	−2.31028	−	7.11031i	−0.156832	−	0.482679i
$218$		0			0
$219$	−7.67680			−0.518750
$220$		0			0
$221$	6.65842			0.447894
$222$		0			0
$223$	−1.79876	−	5.53602i	−0.120454	−	0.370720i	0.872591	−	0.488451i	$-0.162438\pi$
$223$	−1.79876	−	5.53602i	−0.120454	−	0.370720i	−0.993045	+	0.117731i	$0.962438\pi$
$224$		0			0
$225$	−0.809017	−	0.587785i	−0.0539345	−	0.0391857i
$226$		0			0
$227$	−3.91004	+	12.0339i	−0.259518	+	0.798715i	0.733387	+	0.679811i	$0.237938\pi$
$227$	−3.91004	+	12.0339i	−0.259518	+	0.798715i	−0.992906	+	0.118904i	$0.962062\pi$
$228$		0			0
$229$	22.0670	−	16.0326i	1.45823	−	1.05947i	0.474411	−	0.880304i	$-0.342661\pi$
$229$	22.0670	−	16.0326i	1.45823	−	1.05947i	0.983819	−	0.179163i	$-0.0573388\pi$
$230$		0			0
$231$	−4.30464	+	15.6115i	−0.283224	+	1.02716i
$232$		0			0
$233$	−21.1403	+	15.3594i	−1.38495	+	1.00622i	−0.388552	+	0.921427i	$0.627024\pi$
$233$	−21.1403	+	15.3594i	−1.38495	+	1.00622i	−0.996398	+	0.0847980i	$0.972976\pi$
$234$		0			0
$235$	−3.27087	+	10.0667i	−0.213368	+	0.656680i
$236$		0			0
$237$	−8.45580	−	6.14350i	−0.549264	−	0.399063i
$238$		0			0
$239$	−5.67703	−	17.4721i	−0.367217	−	1.13018i	−0.948581	−	0.316534i	$-0.897481\pi$
$239$	−5.67703	−	17.4721i	−0.367217	−	1.13018i	0.581365	−	0.813643i	$-0.302519\pi$
$240$		0			0
$241$	7.02543			0.452548			0.226274	−	0.974064i	$-0.427346\pi$
$241$	7.02543			0.452548			0.226274	+	0.974064i	$0.427346\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	5.20405	+	16.0164i	0.332475	+	1.02325i
$246$		0			0
$247$	−0.587201	−	0.426626i	−0.0373627	−	0.0271456i
$248$		0			0
$249$	4.77950	−	14.7098i	0.302889	−	0.932195i
$250$		0			0
$251$	−0.509913	+	0.370473i	−0.0321854	+	0.0233841i	−0.603762	−	0.797165i	$-0.706332\pi$
$251$	−0.509913	+	0.370473i	−0.0321854	+	0.0233841i	0.571576	+	0.820549i	$0.306332\pi$
$252$		0			0
$253$	−2.31365	+	8.39083i	−0.145458	+	0.527527i
$254$		0			0
$255$	−1.69666	+	1.23270i	−0.106249	+	0.0771945i
$256$		0			0
$257$	4.12698	−	12.7015i	0.257434	−	0.792301i	−0.735906	−	0.677084i	$-0.763244\pi$
$257$	4.12698	−	12.7015i	0.257434	−	0.792301i	0.993340	−	0.115217i	$-0.0367564\pi$
$258$		0			0
$259$	4.74030	+	3.44403i	0.294548	+	0.214002i
$260$		0			0
$261$	−1.67173	−	5.14507i	−0.103478	−	0.318472i
$262$		0			0
$263$	31.7536			1.95801			0.979005	−	0.203838i	$-0.0653416\pi$
$263$	31.7536			1.95801			0.979005	+	0.203838i	$0.0653416\pi$
$264$		0			0
$265$	2.25270			0.138382
$266$		0			0
$267$	0.474753	+	1.46114i	0.0290544	+	0.0894202i
$268$		0			0
$269$	10.8602	+	7.89040i	0.662159	+	0.481086i	0.867391	−	0.497627i	$-0.165795\pi$
$269$	10.8602	+	7.89040i	0.662159	+	0.481086i	−0.205233	+	0.978713i	$0.565795\pi$
$270$		0			0
$271$	4.94014	−	15.2042i	0.300092	−	0.923589i	−0.681371	−	0.731938i	$-0.738616\pi$
$271$	4.94014	−	15.2042i	0.300092	−	0.923589i	0.981463	−	0.191651i	$-0.0613840\pi$
$272$		0			0
$273$	−12.5415	+	9.11195i	−0.759047	+	0.551480i
$274$		0			0
$275$	3.31325	−	0.149559i	0.199797	−	0.00901877i
$276$		0			0
$277$	19.2284	−	13.9702i	1.15532	−	0.839389i	0.166141	−	0.986102i	$-0.446869\pi$
$277$	19.2284	−	13.9702i	1.15532	−	0.839389i	0.989179	+	0.146712i	$0.0468692\pi$
$278$		0			0
$279$	−0.473157	+	1.45623i	−0.0283272	+	0.0871821i
$280$		0			0
$281$	1.09701	+	0.797021i	0.0654419	+	0.0475463i	0.620025	−	0.784582i	$-0.287122\pi$
$281$	1.09701	+	0.797021i	0.0654419	+	0.0475463i	−0.554583	+	0.832128i	$0.687122\pi$
$282$		0			0
$283$	4.24649	+	13.0693i	0.252427	+	0.776892i	0.994326	+	0.106379i	$0.0339257\pi$
$283$	4.24649	+	13.0693i	0.252427	+	0.776892i	−0.741898	+	0.670512i	$0.766074\pi$
$284$		0			0
$285$	0.228610			0.0135417
$286$		0			0
$287$	−0.586783			−0.0346367
$288$		0			0
$289$	−3.89417	−	11.9850i	−0.229069	−	0.705001i
$290$		0			0
$291$	2.29322	+	1.66612i	0.134431	+	0.0976698i
$292$		0			0
$293$	−4.62995	+	14.2495i	−0.270485	+	0.832467i	0.719894	+	0.694084i	$0.244190\pi$
$293$	−4.62995	+	14.2495i	−0.270485	+	0.832467i	−0.990379	+	0.138383i	$0.955810\pi$
$294$		0			0
$295$	8.94207	−	6.49679i	0.520627	−	0.378258i
$296$		0			0
$297$	2.59257	−	2.06848i	0.150436	−	0.120025i
$298$		0			0
$299$	−6.74081	+	4.89748i	−0.389831	+	0.283229i
$300$		0			0
$301$	7.58731	−	23.3513i	0.437325	−	1.34595i
$302$		0			0
$303$	−0.758118	−	0.550805i	−0.0435527	−	0.0316429i
$304$		0			0
$305$	2.61059	+	8.03457i	0.149482	+	0.460058i
$306$		0			0
$307$	11.4006			0.650669			0.325335	−	0.945599i	$-0.394523\pi$
$307$	11.4006			0.650669			0.325335	+	0.945599i	$0.394523\pi$
$308$		0			0
$309$	14.0089			0.796939
$310$		0			0
$311$	−5.72785	−	17.6285i	−0.324797	−	0.999622i	−0.971532	−	0.236907i	$-0.923866\pi$
$311$	−5.72785	−	17.6285i	−0.324797	−	0.999622i	0.646735	−	0.762714i	$-0.276134\pi$
$312$		0			0
$313$	5.05732	+	3.67436i	0.285856	+	0.207687i	0.721468	−	0.692448i	$-0.243468\pi$
$313$	5.05732	+	3.67436i	0.285856	+	0.207687i	−0.435611	+	0.900135i	$0.643468\pi$
$314$		0			0
$315$	1.50883	−	4.64371i	0.0850132	−	0.261644i
$316$		0			0
$317$	23.8996	−	17.3641i	1.34234	−	0.975264i	0.342981	−	0.939342i	$-0.388563\pi$
$317$	23.8996	−	17.3641i	1.34234	−	0.975264i	0.999355	−	0.0359220i	$-0.0114368\pi$
$318$		0			0
$319$	14.9765	+	9.88100i	0.838525	+	0.553230i
$320$		0			0
$321$	−1.09403	+	0.794862i	−0.0610630	+	0.0443649i
$322$		0			0
$323$	0.148155	−	0.455973i	0.00824355	−	0.0253710i
$324$		0			0
$325$	2.56857	+	1.86617i	0.142479	+	0.103517i
$326$		0			0
$327$	5.29413	+	16.2937i	0.292766	+	0.901041i
$328$		0			0
$329$	−51.6822			−2.84933
$330$		0			0
$331$	14.2910			0.785502			0.392751	−	0.919645i	$-0.371523\pi$
$331$	14.2910			0.785502			0.392751	+	0.919645i	$0.371523\pi$
$332$		0			0
$333$	−0.370827	−	1.14129i	−0.0203212	−	0.0625422i
$334$		0			0
$335$	−2.13233	−	1.54923i	−0.116502	−	0.0846433i
$336$		0			0
$337$	1.87368	−	5.76661i	0.102066	−	0.314127i	−0.886965	−	0.461837i	$-0.847190\pi$
$337$	1.87368	−	5.76661i	0.102066	−	0.314127i	0.989031	+	0.147710i	$0.0471903\pi$
$338$		0			0
$339$	0.443927	−	0.322532i	0.0241108	−	0.0175175i
$340$		0			0
$341$	−1.78548	−	4.75408i	−0.0966892	−	0.257448i
$342$		0			0
$343$	−38.8724	+	28.2424i	−2.09891	+	1.52495i
$344$		0			0
$345$	0.810967	−	2.49590i	0.0436610	−	0.134375i
$346$		0			0
$347$	−14.1125	−	10.2533i	−0.757597	−	0.550426i	0.140576	−	0.990070i	$-0.455105\pi$
$347$	−14.1125	−	10.2533i	−0.757597	−	0.550426i	−0.898172	+	0.439644i	$0.855105\pi$
$348$		0			0
$349$	3.11016	+	9.57210i	0.166483	+	0.512383i	0.999143	−	0.0414028i	$-0.0131827\pi$
$349$	3.11016	+	9.57210i	0.166483	+	0.512383i	−0.832659	+	0.553786i	$0.813183\pi$
$350$		0			0
$351$	3.17492			0.169465
$352$		0			0
$353$	8.53660			0.454358			0.227179	−	0.973853i	$-0.427050\pi$
$353$	8.53660			0.454358			0.227179	+	0.973853i	$0.427050\pi$
$354$		0			0
$355$	1.94876	+	5.99765i	0.103429	+	0.318322i
$356$		0			0
$357$	−8.28427	−	6.01888i	−0.438450	−	0.318553i
$358$		0			0
$359$	−0.504545	+	1.55283i	−0.0266289	+	0.0819552i	−0.963488	−	0.267752i	$-0.913719\pi$
$359$	−0.504545	+	1.55283i	−0.0266289	+	0.0819552i	0.936859	+	0.349708i	$0.113719\pi$
$360$		0			0
$361$	15.3290	−	11.1372i	0.806792	−	0.586168i
$362$		0			0
$363$	−2.44281	+	10.7253i	−0.128214	+	0.562934i
$364$		0			0
$365$	−6.21066	+	4.51231i	−0.325081	+	0.236185i
$366$		0			0
$367$	1.60632	−	4.94374i	0.0838491	−	0.258061i	−0.900339	−	0.435190i	$-0.856681\pi$
$367$	1.60632	−	4.94374i	0.0838491	−	0.258061i	0.984188	+	0.177129i	$0.0566811\pi$
$368$		0			0
$369$	0.0972246	+	0.0706378i	0.00506131	+	0.00367726i
$370$		0			0
$371$	3.39896	+	10.4609i	0.176465	+	0.543103i
$372$		0			0
$373$	19.9771			1.03437			0.517187	−	0.855873i	$-0.326979\pi$
$373$	19.9771			1.03437			0.517187	+	0.855873i	$0.326979\pi$
$374$		0			0
$375$	−1.00000			−0.0516398
$376$		0			0
$377$	5.30763	+	16.3352i	0.273357	+	0.841306i
$378$		0			0
$379$	15.3496	+	11.1521i	0.788455	+	0.572846i	0.907505	−	0.420042i	$-0.137985\pi$
$379$	15.3496	+	11.1521i	0.788455	+	0.572846i	−0.119049	+	0.992888i	$0.537985\pi$
$380$		0			0
$381$	5.01836	−	15.4449i	0.257098	−	0.791267i
$382$		0			0
$383$	13.8498	−	10.0624i	0.707690	−	0.514167i	−0.174738	−	0.984615i	$-0.555908\pi$
$383$	13.8498	−	10.0624i	0.707690	−	0.514167i	0.882428	+	0.470448i	$0.155908\pi$
$384$		0			0
$385$	5.69366	+	15.1601i	0.290176	+	0.772632i
$386$		0			0
$387$	−4.06821	+	2.95573i	−0.206799	+	0.150248i
$388$		0			0
$389$	−7.81305	+	24.0461i	−0.396137	+	1.21918i	0.531935	+	0.846785i	$0.321465\pi$
$389$	−7.81305	+	24.0461i	−0.396137	+	1.21918i	−0.928072	+	0.372400i	$0.878535\pi$
$390$		0			0
$391$	−4.45263	−	3.23502i	−0.225179	−	0.163602i
$392$		0			0
$393$	2.61144	+	8.03719i	0.131730	+	0.405422i
$394$		0			0
$395$	−10.4519			−0.525895
$396$		0			0
$397$	−17.4575			−0.876166			−0.438083	−	0.898935i	$-0.644342\pi$
$397$	−17.4575			−0.876166			−0.438083	+	0.898935i	$0.644342\pi$
$398$		0			0
$399$	0.344935	+	1.06160i	0.0172683	+	0.0531465i
$400$		0			0
$401$	9.68733	+	7.03825i	0.483762	+	0.351474i	0.802780	−	0.596275i	$-0.203353\pi$
$401$	9.68733	+	7.03825i	0.483762	+	0.351474i	−0.319018	+	0.947749i	$0.603353\pi$
$402$		0			0
$403$	1.50224	−	4.62341i	0.0748318	−	0.230309i
$404$		0			0
$405$	−0.809017	+	0.587785i	−0.0402004	+	0.0292073i
$406$		0			0
$407$	3.32212	+	2.19182i	0.164672	+	0.108645i
$408$		0			0
$409$	−13.9260	+	10.1179i	−0.688599	+	0.500296i	−0.876199	−	0.481949i	$-0.839929\pi$
$409$	−13.9260	+	10.1179i	−0.688599	+	0.500296i	0.187601	+	0.982245i	$0.439929\pi$
$410$		0			0
$411$	2.00250	−	6.16307i	0.0987761	−	0.304002i
$412$		0			0
$413$	43.6614	+	31.7218i	2.14843	+	1.56093i
$414$		0			0
$415$	−4.77950	−	14.7098i	−0.234617	−	0.722075i
$416$		0			0
$417$	−18.8212			−0.921678
$418$		0			0
$419$	−29.0101			−1.41724			−0.708619	−	0.705591i	$-0.750682\pi$
$419$	−29.0101			−1.41724			−0.708619	+	0.705591i	$0.750682\pi$
$420$		0			0
$421$	5.40635	+	16.6390i	0.263489	+	0.810937i	0.992038	+	0.125942i	$0.0401954\pi$
$421$	5.40635	+	16.6390i	0.263489	+	0.810937i	−0.728548	+	0.684994i	$0.759805\pi$
$422$		0			0
$423$	8.56326	+	6.22157i	0.416360	+	0.302503i
$424$		0			0
$425$	−0.648067	+	1.99455i	−0.0314359	+	0.0967497i
$426$		0			0
$427$	−33.3713	+	24.2457i	−1.61495	+	1.17333i
$428$		0			0
$429$	−8.23121	+	6.56726i	−0.397406	+	0.317070i
$430$		0			0
$431$	−24.0987	+	17.5087i	−1.16079	+	0.843365i	−0.989878	−	0.141921i	$-0.954672\pi$
$431$	−24.0987	+	17.5087i	−1.16079	+	0.843365i	−0.170914	+	0.985286i	$0.554672\pi$
$432$		0			0
$433$	0.462167	−	1.42240i	0.0222103	−	0.0683564i	−0.939337	−	0.342996i	$-0.888558\pi$
$433$	0.462167	−	1.42240i	0.0222103	−	0.0683564i	0.961547	+	0.274639i	$0.0885584\pi$
$434$		0			0
$435$	−4.37666	−	3.17983i	−0.209845	−	0.152461i
$436$		0			0
$437$	0.185395	+	0.570588i	0.00886866	+	0.0272949i
$438$		0			0
$439$	−24.9028			−1.18855			−0.594273	−	0.804263i	$-0.702560\pi$
$439$	−24.9028			−1.18855			−0.594273	+	0.804263i	$0.702560\pi$
$440$		0			0
$441$	16.8407			0.801936
$442$		0			0
$443$	−5.38856	−	16.5843i	−0.256018	−	0.787943i	−0.993627	−	0.112715i	$-0.964045\pi$
$443$	−5.38856	−	16.5843i	−0.256018	−	0.787943i	0.737609	−	0.675228i	$-0.235955\pi$
$444$		0			0
$445$	1.24292	+	0.903033i	0.0589200	+	0.0428079i
$446$		0			0
$447$	6.07542	−	18.6982i	0.287357	−	0.884395i
$448$		0			0
$449$	−4.77626	+	3.47016i	−0.225406	+	0.163767i	−0.694757	−	0.719245i	$-0.744488\pi$
$449$	−4.77626	+	3.47016i	−0.225406	+	0.163767i	0.469351	+	0.883012i	$0.344488\pi$
$450$		0			0
$451$	−0.398174	+	0.0179735i	−0.0187493	+	0.000846338i
$452$		0			0
$453$	−12.2536	+	8.90273i	−0.575722	+	0.418287i
$454$		0			0
$455$	−4.79043	+	14.7434i	−0.224579	+	0.691183i
$456$		0			0
$457$	−1.87431	−	1.36176i	−0.0876764	−	0.0637006i	0.543083	−	0.839679i	$-0.317257\pi$
$457$	−1.87431	−	1.36176i	−0.0876764	−	0.0637006i	−0.630760	+	0.775978i	$0.717257\pi$
$458$		0			0
$459$	0.648067	+	1.99455i	0.0302492	+	0.0930974i
$460$		0			0
$461$	24.8206			1.15601			0.578005	−	0.816033i	$-0.303832\pi$
$461$	24.8206			1.15601			0.578005	+	0.816033i	$0.303832\pi$
$462$		0			0
$463$	27.6837			1.28657			0.643286	−	0.765626i	$-0.277570\pi$
$463$	27.6837			1.28657			0.643286	+	0.765626i	$0.277570\pi$
$464$		0			0
$465$	0.473157	+	1.45623i	0.0219421	+	0.0675310i
$466$		0			0
$467$	31.3492	+	22.7765i	1.45067	+	1.05397i	0.985675	+	0.168658i	$0.0539432\pi$
$467$	31.3492	+	22.7765i	1.45067	+	1.05397i	0.464993	+	0.885314i	$0.346057\pi$
$468$		0			0
$469$	3.97684	−	12.2394i	0.183633	−	0.565165i
$470$		0			0
$471$	−13.6111	+	9.88905i	−0.627167	+	0.455663i
$472$		0			0
$473$	4.43326	−	16.0779i	0.203842	−	0.739264i
$474$		0			0
$475$	0.184950	−	0.134374i	0.00848607	−	0.00616549i
$476$		0			0
$477$	0.696123	−	2.14245i	0.0318733	−	0.0980959i
$478$		0			0
$479$	0.874488	+	0.635352i	0.0399564	+	0.0290300i	0.607584	−	0.794255i	$-0.292139\pi$
$479$	0.874488	+	0.635352i	0.0399564	+	0.0290300i	−0.567628	+	0.823285i	$0.692139\pi$
$480$		0			0
$481$	1.17735	+	3.62351i	0.0536825	+	0.165218i
$482$		0			0
$483$	12.8139			0.583051
$484$		0			0
$485$	2.83458			0.128712
$486$		0			0
$487$	−2.13272	−	6.56385i	−0.0966430	−	0.297437i	0.891035	−	0.453934i	$-0.149980\pi$
$487$	−2.13272	−	6.56385i	−0.0966430	−	0.297437i	−0.987678	+	0.156497i	$0.949980\pi$
$488$		0			0
$489$	9.06938	+	6.58929i	0.410132	+	0.297978i
$490$		0			0
$491$	12.5700	−	38.6866i	0.567278	−	1.74590i	−0.0938056	−	0.995591i	$-0.529903\pi$
$491$	12.5700	−	38.6866i	0.567278	−	1.74590i	0.661084	−	0.750312i	$-0.270097\pi$
$492$		0			0
$493$	−9.17868	+	6.66870i	−0.413387	+	0.300343i
$494$		0			0
$495$	0.881611	−	3.19731i	0.0396255	−	0.143708i
$496$		0			0
$497$	−24.9110	+	18.0989i	−1.11741	+	0.811848i
$498$		0			0
$499$	−3.83643	+	11.8073i	−0.171742	+	0.528568i	−0.999470	−	0.0325624i	$-0.989633\pi$
$499$	−3.83643	+	11.8073i	−0.171742	+	0.528568i	0.827728	+	0.561130i	$0.189633\pi$
$500$		0			0
$501$	1.23273	+	0.895629i	0.0550742	+	0.0400137i
$502$		0			0
$503$	−9.21013	−	28.3459i	−0.410660	−	1.26388i	−0.916076	−	0.401005i	$-0.868661\pi$
$503$	−9.21013	−	28.3459i	−0.410660	−	1.26388i	0.505416	−	0.862876i	$-0.331339\pi$
$504$		0			0
$505$	−0.937085			−0.0416997
$506$		0			0
$507$	2.91985			0.129675
$508$		0			0
$509$	−1.08377	−	3.33549i	−0.0480372	−	0.147843i	0.924161	−	0.382004i	$-0.124766\pi$
$509$	−1.08377	−	3.33549i	−0.0480372	−	0.147843i	−0.972198	+	0.234161i	$0.924766\pi$
$510$		0			0
$511$	−30.3247	−	22.0322i	−1.34149	−	0.974647i
$512$		0			0
$513$	0.0706444	−	0.217421i	0.00311903	−	0.00959938i
$514$		0			0
$515$	11.3334	−	8.23423i	0.499411	−	0.362843i
$516$		0			0
$517$	−35.0700	+	1.58305i	−1.54238	+	0.0696225i
$518$		0			0
$519$	11.7168	−	8.51274i	0.514310	−	0.373668i
$520$		0			0
$521$	5.37607	−	16.5458i	0.235530	−	0.724886i	−0.761521	−	0.648140i	$-0.775547\pi$
$521$	5.37607	−	16.5458i	0.235530	−	0.724886i	0.997051	−	0.0767458i	$-0.0244530\pi$
$522$		0			0
$523$	−26.6652	−	19.3734i	−1.16599	−	0.847139i	−0.175464	−	0.984486i	$-0.556143\pi$
$523$	−26.6652	−	19.3734i	−1.16599	−	0.847139i	−0.990523	+	0.137347i	$0.956143\pi$
$524$		0			0
$525$	−1.50883	−	4.64371i	−0.0658509	−	0.202668i
$526$		0			0
$527$	3.21115			0.139880
$528$		0			0
$529$	−16.1128			−0.700557
$530$		0			0
$531$	−3.41557	−	10.5120i	−0.148223	−	0.456183i
$532$		0			0
$533$	−0.308681	−	0.224270i	−0.0133704	−	0.00971420i
$534$		0			0
$535$	−0.417884	+	1.28611i	−0.0180667	+	0.0556036i
$536$		0			0
$537$	9.36513	−	6.80417i	0.404135	−	0.293621i
$538$		0			0
$539$	−43.6606	+	34.8345i	−1.88059	+	1.50043i
$540$		0			0
$541$	−8.70707	+	6.32606i	−0.374346	+	0.271978i	−0.759011	−	0.651078i	$-0.774317\pi$
$541$	−8.70707	+	6.32606i	−0.374346	+	0.271978i	0.384665	+	0.923056i	$0.374317\pi$
$542$		0			0
$543$	5.91787	−	18.2133i	0.253960	−	0.781609i
$544$		0			0
$545$	13.8602	+	10.0700i	0.593706	+	0.431353i
$546$		0			0
$547$	−10.1218	−	31.1516i	−0.432775	−	1.33195i	−0.895349	−	0.445365i	$-0.853074\pi$
$547$	−10.1218	−	31.1516i	−0.432775	−	1.33195i	0.462574	−	0.886581i	$-0.346926\pi$
$548$		0			0
$549$	8.44805			0.360554
$550$		0			0
$551$	1.23675			0.0526871
$552$		0			0
$553$	−15.7703	−	48.5359i	−0.670620	−	2.06395i
$554$		0			0
$555$	−0.970838	−	0.705355i	−0.0412098	−	0.0299407i
$556$		0			0
$557$	5.89811	−	18.1525i	0.249911	−	0.769147i	−0.744879	−	0.667200i	$-0.767493\pi$
$557$	5.89811	−	18.1525i	0.249911	−	0.769147i	0.994790	−	0.101947i	$-0.0325073\pi$
$558$		0			0
$559$	12.9163	−	9.38422i	0.546300	−	0.396910i
$560$		0			0
$561$	−5.80583	−	3.83048i	−0.245122	−	0.161723i
$562$		0			0
$563$	17.5446	−	12.7469i	0.739415	−	0.537216i	−0.153113	−	0.988209i	$-0.548930\pi$
$563$	17.5446	−	12.7469i	0.739415	−	0.537216i	0.892528	+	0.450992i	$0.148930\pi$
$564$		0			0
$565$	0.169565	−	0.521867i	0.00713365	−	0.0219551i
$566$		0			0
$567$	−3.95018	−	2.86997i	−0.165892	−	0.120528i
$568$		0			0
$569$	−9.19823	−	28.3092i	−0.385610	−	1.18679i	−0.936037	−	0.351902i	$-0.885535\pi$
$569$	−9.19823	−	28.3092i	−0.385610	−	1.18679i	0.550427	−	0.834883i	$-0.314465\pi$
$570$		0			0
$571$	−15.8058			−0.661452			−0.330726	−	0.943727i	$-0.607294\pi$
$571$	−15.8058			−0.661452			−0.330726	+	0.943727i	$0.607294\pi$
$572$		0			0
$573$	−26.4305			−1.10415
$574$		0			0
$575$	−0.810967	−	2.49590i	−0.0338197	−	0.104086i
$576$		0			0
$577$	22.3731	+	16.2550i	0.931404	+	0.676704i	0.946336	−	0.323184i	$-0.104753\pi$
$577$	22.3731	+	16.2550i	0.931404	+	0.676704i	−0.0149324	+	0.999889i	$0.504753\pi$
$578$		0			0
$579$	3.81732	−	11.7485i	0.158642	−	0.488251i
$580$		0			0
$581$	61.0966	−	44.3893i	2.53471	−	1.84158i
$582$		0			0
$583$	2.62685	+	6.99435i	0.108793	+	0.289677i
$584$		0			0
$585$	2.56857	−	1.86617i	0.106197	−	0.0771568i
$586$		0			0
$587$	0.0549832	−	0.169221i	0.00226940	−	0.00698450i	−0.949915	−	0.312507i	$-0.898831\pi$
$587$	0.0549832	−	0.169221i	0.00226940	−	0.00698450i	0.952185	+	0.305523i	$0.0988312\pi$
$588$		0			0
$589$	−0.283189	−	0.205749i	−0.0116686	−	0.00847773i
$590$		0			0
$591$	5.52499	+	17.0042i	0.227268	+	0.699458i
$592$		0			0
$593$	24.1592			0.992099			0.496049	−	0.868294i	$-0.334783\pi$
$593$	24.1592			0.992099			0.496049	+	0.868294i	$0.334783\pi$
$594$		0			0
$595$	−10.2399			−0.419796
$596$		0			0
$597$	−8.24611	−	25.3789i	−0.337491	−	1.03869i
$598$		0			0
$599$	−29.2030	−	21.2172i	−1.19320	−	0.866911i	−0.199602	−	0.979877i	$-0.563965\pi$
$599$	−29.2030	−	21.2172i	−1.19320	−	0.866911i	−0.993599	+	0.112966i	$0.963965\pi$
$600$		0			0
$601$	−9.21848	+	28.3716i	−0.376030	+	1.15730i	0.566752	+	0.823889i	$0.308200\pi$
$601$	−9.21848	+	28.3716i	−0.376030	+	1.15730i	−0.942781	+	0.333412i	$0.891800\pi$
$602$		0			0
$603$	−2.13233	+	1.54923i	−0.0868351	+	0.0630894i
$604$		0			0
$605$	4.32791	+	10.1128i	0.175955	+	0.411145i
$606$		0			0
$607$	−20.3077	+	14.7544i	−0.824264	+	0.598863i	−0.917931	−	0.396741i	$-0.870141\pi$
$607$	−20.3077	+	14.7544i	−0.824264	+	0.598863i	0.0936668	+	0.995604i	$0.470141\pi$
$608$		0			0
$609$	8.16256	−	25.1218i	0.330764	−	1.01799i
$610$		0			0
$611$	−27.1877	−	19.7530i	−1.09990	−	0.799122i
$612$		0			0
$613$	10.4343	+	32.1135i	0.421437	+	1.29705i	0.906365	+	0.422496i	$0.138846\pi$
$613$	10.4343	+	32.1135i	0.421437	+	1.29705i	−0.484927	+	0.874555i	$0.661154\pi$
$614$		0			0
$615$	0.120176			0.00484597
$616$		0			0
$617$	10.4022			0.418775			0.209388	−	0.977833i	$-0.432853\pi$
$617$	10.4022			0.418775			0.209388	+	0.977833i	$0.432853\pi$
$618$		0			0
$619$	1.88608	+	5.80475i	0.0758079	+	0.233313i	0.981779	−	0.190027i	$-0.0608576\pi$
$619$	1.88608	+	5.80475i	0.0758079	+	0.233313i	−0.905971	+	0.423340i	$0.860858\pi$
$620$		0			0
$621$	−2.12314	−	1.54255i	−0.0851986	−	0.0619004i
$622$		0			0
$623$	−2.31807	+	7.13429i	−0.0928715	+	0.285829i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$		0			0
$627$	0.266580	+	0.709806i	0.0106462	+	0.0283469i
$628$		0			0
$629$	−2.03603	+	1.47926i	−0.0811819	+	0.0589821i
$630$		0			0
$631$	11.7659	−	36.2118i	0.468394	−	1.44157i	−0.386271	−	0.922386i	$-0.626237\pi$
$631$	11.7659	−	36.2118i	0.468394	−	1.44157i	0.854664	−	0.519181i	$-0.173763\pi$
$632$		0			0
$633$	18.9702	+	13.7827i	0.753998	+	0.547811i
$634$		0			0
$635$	−5.01836	−	15.4449i	−0.199147	−	0.612913i
$636$		0			0
$637$	−53.4678			−2.11847
$638$		0			0
$639$	6.30630			0.249474
$640$		0			0
$641$	−0.478424	−	1.47244i	−0.0188966	−	0.0581578i	0.941164	−	0.337951i	$-0.109734\pi$
$641$	−0.478424	−	1.47244i	−0.0188966	−	0.0581578i	−0.960060	+	0.279794i	$0.909734\pi$
$642$		0			0
$643$	31.2737	+	22.7217i	1.23331	+	0.896055i	0.997134	−	0.0756537i	$-0.0241044\pi$
$643$	31.2737	+	22.7217i	1.23331	+	0.896055i	0.236180	+	0.971709i	$0.424104\pi$
$644$		0			0
$645$	−1.55392	+	4.78247i	−0.0611855	+	0.188310i
$646$		0			0
$647$	22.0327	−	16.0077i	0.866194	−	0.629326i	−0.0633693	−	0.997990i	$-0.520185\pi$
$647$	22.0327	−	16.0077i	0.866194	−	0.629326i	0.929563	+	0.368664i	$0.120185\pi$
$648$		0			0
$649$	30.5990	+	20.1881i	1.20111	+	0.792454i
$650$		0			0
$651$	−6.04839	+	4.39441i	−0.237055	+	0.172231i
$652$		0			0
$653$	8.23709	−	25.3512i	0.322342	−	0.992068i	−0.650284	−	0.759692i	$-0.725350\pi$
$653$	8.23709	−	25.3512i	0.322342	−	0.992068i	0.972626	−	0.232376i	$-0.0746501\pi$
$654$		0			0
$655$	6.83684	+	4.96725i	0.267137	+	0.194087i
$656$		0			0
$657$	2.37226	+	7.30107i	0.0925507	+	0.284842i
$658$		0			0
$659$	−31.0531			−1.20966			−0.604828	−	0.796356i	$-0.706758\pi$
$659$	−31.0531			−1.20966			−0.604828	+	0.796356i	$0.706758\pi$
$660$		0			0
$661$	−30.3744			−1.18143			−0.590713	−	0.806882i	$-0.701153\pi$
$661$	−30.3744			−1.18143			−0.590713	+	0.806882i	$0.701153\pi$
$662$		0			0
$663$	−2.05756	−	6.33253i	−0.0799092	−	0.245935i
$664$		0			0
$665$	0.903051	+	0.656105i	0.0350188	+	0.0254427i
$666$		0			0
$667$	4.38721	−	13.5024i	0.169873	−	0.522816i
$668$		0			0
$669$	−4.70922	+	3.42145i	−0.182069	+	0.132281i
$670$		0			0
$671$	−21.9021	+	17.4746i	−0.845523	+	0.674599i
$672$		0			0
$673$	−20.3844	+	14.8101i	−0.785761	+	0.570889i	−0.906703	−	0.421771i	$-0.861409\pi$
$673$	−20.3844	+	14.8101i	−0.785761	+	0.570889i	0.120941	+	0.992660i	$0.461409\pi$
$674$		0			0
$675$	−0.309017	+	0.951057i	−0.0118941	+	0.0366062i
$676$		0			0
$677$	6.63602	+	4.82135i	0.255043	+	0.185300i	0.707959	−	0.706254i	$-0.249616\pi$
$677$	6.63602	+	4.82135i	0.255043	+	0.185300i	−0.452916	+	0.891553i	$0.649616\pi$
$678$		0			0
$679$	4.27691	+	13.1630i	0.164133	+	0.505148i
$680$		0			0
$681$	12.6531			0.484870
$682$		0			0
$683$	−24.1927			−0.925707			−0.462854	−	0.886435i	$-0.653174\pi$
$683$	−24.1927			−0.925707			−0.462854	+	0.886435i	$0.653174\pi$
$684$		0			0
$685$	−2.00250	−	6.16307i	−0.0765117	−	0.235479i
$686$		0			0
$687$	−22.0670	−	16.0326i	−0.841910	−	0.611683i
$688$		0			0
$689$	−2.21014	+	6.80211i	−0.0841996	+	0.259140i
$690$		0			0
$691$	−33.3683	+	24.2435i	−1.26939	+	0.922267i	−0.999178	−	0.0405340i	$-0.987094\pi$
$691$	−33.3683	+	24.2435i	−1.26939	+	0.922267i	−0.270213	+	0.962801i	$0.587094\pi$
$692$		0			0
$693$	16.1776	−	0.730252i	0.614535	−	0.0277400i
$694$		0			0
$695$	−15.2267	+	11.0628i	−0.577581	+	0.419637i
$696$		0			0
$697$	0.0778823	−	0.239697i	0.00295000	−	0.00907917i
$698$		0			0
$699$	21.1403	+	15.3594i	0.799601	+	0.580944i
$700$		0			0
$701$	−3.55609	−	10.9445i	−0.134312	−	0.413369i	0.861171	−	0.508316i	$-0.169732\pi$
$701$	−3.55609	−	10.9445i	−0.134312	−	0.413369i	−0.995482	+	0.0949472i	$0.969732\pi$
$702$		0			0
$703$	0.274337			0.0103468
$704$		0			0
$705$	10.5848			0.398645
$706$		0			0
$707$	−1.41391	−	4.35155i	−0.0531754	−	0.163657i
$708$		0			0
$709$	−32.3165	−	23.4793i	−1.21367	−	0.881785i	−0.218113	−	0.975923i	$-0.569990\pi$
$709$	−32.3165	−	23.4793i	−1.21367	−	0.881785i	−0.995559	+	0.0941389i	$0.969990\pi$
$710$		0			0
$711$	−3.22983	+	9.94039i	−0.121128	+	0.372794i
$712$		0			0
$713$	−3.25088	+	2.36191i	−0.121747	+	0.0884541i
$714$		0			0
$715$	−2.79905	+	10.1512i	−0.104679	+	0.379633i
$716$		0			0
$717$	−14.8627	+	10.7984i	−0.555056	+	0.403272i
$718$		0			0
$719$	9.44067	−	29.0554i	0.352078	−	1.08358i	−0.605607	−	0.795764i	$-0.707070\pi$
$719$	9.44067	−	29.0554i	0.352078	−	1.08358i	0.957685	−	0.287819i	$-0.0929303\pi$
$720$		0			0
$721$	55.3377	+	40.2052i	2.06088	+	1.49732i
$722$		0			0
$723$	−2.17098	−	6.68158i	−0.0807395	−	0.248491i
$724$		0			0
$725$	−5.40985			−0.200917
$726$		0			0
$727$	20.4646			0.758991			0.379496	−	0.925193i	$-0.376098\pi$
$727$	20.4646			0.758991			0.379496	+	0.925193i	$0.376098\pi$
$728$		0			0
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		0			0
$731$	8.53181	+	6.19873i	0.315561	+	0.229268i
$732$		0			0
$733$	2.55892	−	7.87554i	0.0945158	−	0.290890i	−0.892611	−	0.450827i	$-0.851129\pi$
$733$	2.55892	−	7.87554i	0.0945158	−	0.290890i	0.987127	+	0.159937i	$0.0511292\pi$
$734$		0			0
$735$	13.6244	−	9.89869i	0.502543	−	0.365119i
$736$		0			0
$737$	2.32367	−	8.42715i	0.0855933	−	0.310418i
$738$		0			0
$739$	−3.25215	+	2.36282i	−0.119632	+	0.0869178i	−0.645993	−	0.763344i	$-0.723556\pi$
$739$	−3.25215	+	2.36282i	−0.119632	+	0.0869178i	0.526360	+	0.850262i	$0.323556\pi$
$740$		0			0
$741$	−0.224291	+	0.690296i	−0.00823953	+	0.0253587i
$742$		0			0
$743$	−40.5893	−	29.4898i	−1.48908	−	1.08188i	−0.974488	−	0.224440i	$-0.927945\pi$
$743$	−40.5893	−	29.4898i	−1.48908	−	1.08188i	−0.514588	−	0.857437i	$-0.672055\pi$
$744$		0			0
$745$	−6.07542	−	18.6982i	−0.222586	−	0.685049i
$746$		0			0
$747$	−15.4668			−0.565900
$748$		0			0
$749$	−6.60287			−0.241263
$750$		0			0
$751$	−10.4866	−	32.2745i	−0.382662	−	1.17771i	−0.938162	−	0.346196i	$-0.887473\pi$
$751$	−10.4866	−	32.2745i	−0.382662	−	1.17771i	0.555500	−	0.831516i	$-0.312527\pi$
$752$		0			0
$753$	0.509913	+	0.370473i	0.0185823	+	0.0135008i
$754$		0			0
$755$	−4.68044	+	14.4049i	−0.170339	+	0.524249i
$756$		0			0
$757$	20.0780	−	14.5875i	0.729746	−	0.530191i	−0.159737	−	0.987160i	$-0.551065\pi$
$757$	20.0780	−	14.5875i	0.729746	−	0.530191i	0.889483	+	0.456968i	$0.151065\pi$
$758$		0			0
$759$	8.69511	−	0.392495i	0.315613	−	0.0142467i
$760$		0			0
$761$	−1.77615	+	1.29045i	−0.0643852	+	0.0467786i	−0.619512	−	0.784987i	$-0.712670\pi$
$761$	−1.77615	+	1.29045i	−0.0643852	+	0.0467786i	0.555127	+	0.831766i	$0.312670\pi$
$762$		0			0
$763$	−25.8496	+	79.5569i	−0.935818	+	2.88015i
$764$		0			0
$765$	1.69666	+	1.23270i	0.0613429	+	0.0445683i
$766$		0			0
$767$	10.8442	+	33.3749i	0.391560	+	1.20510i
$768$		0			0
$769$	38.2966			1.38101			0.690505	−	0.723328i	$-0.257388\pi$
$769$	38.2966			1.38101			0.690505	+	0.723328i	$0.257388\pi$
$770$		0			0
$771$	−13.3552			−0.480976
$772$		0			0
$773$	−12.8063	−	39.4137i	−0.460610	−	1.41761i	−0.864421	−	0.502769i	$-0.832315\pi$
$773$	−12.8063	−	39.4137i	−0.460610	−	1.41761i	0.403811	−	0.914842i	$-0.367685\pi$
$774$		0			0
$775$	1.23874	+	0.899998i	0.0444969	+	0.0323289i
$776$		0			0
$777$	1.81063	−	5.57256i	0.0649561	−	0.199914i
$778$		0			0
$779$	−0.0222265	+	0.0161485i	−0.000796348	+	0.000578581i
$780$		0			0
$781$	−16.3495	+	13.0444i	−0.585032	+	0.466767i
$782$		0			0
$783$	−4.37666	+	3.17983i	−0.156409	+	0.113638i
$784$		0			0
$785$	−5.19898	+	16.0008i	−0.185560	+	0.571094i
$786$		0			0
$787$	19.0373	+	13.8314i	0.678607	+	0.493037i	0.872895	−	0.487908i	$-0.162240\pi$
$787$	19.0373	+	13.8314i	0.678607	+	0.493037i	−0.194289	+	0.980944i	$0.562240\pi$
$788$		0			0
$789$	−9.81239	−	30.1994i	−0.349330	−	1.07513i
$790$		0			0
$791$	2.67925			0.0952631
$792$		0			0
$793$	−26.8219			−0.952474
$794$		0			0
$795$	−0.696123	−	2.14245i	−0.0246890	−	0.0759848i
$796$		0			0
$797$	−19.0344	−	13.8293i	−0.674234	−	0.489860i	0.197206	−	0.980362i	$-0.436813\pi$
$797$	−19.0344	−	13.8293i	−0.674234	−	0.489860i	−0.871440	+	0.490503i	$0.836813\pi$
$798$		0			0
$799$	6.85964	−	21.1118i	0.242677	−	0.746882i
$800$		0			0
$801$	1.24292	−	0.903033i	0.0439164	−	0.0319071i
$802$		0			0
$803$	−21.2523	−	14.0215i	−0.749978	−	0.494810i
$804$		0			0
$805$	10.3666	−	7.53180i	0.365376	−	0.265461i
$806$		0			0
$807$	4.14823	−	12.7669i	0.146025	−	0.449418i
$808$		0			0
$809$	−24.1988	−	17.5815i	−0.850784	−	0.618131i	0.0745779	−	0.997215i	$-0.476239\pi$
$809$	−24.1988	−	17.5815i	−0.850784	−	0.618131i	−0.925362	+	0.379084i	$0.876239\pi$
$810$		0			0
$811$	10.8580	+	33.4174i	0.381275	+	1.17344i	0.939147	+	0.343517i	$0.111618\pi$
$811$	10.8580	+	33.4174i	0.381275	+	1.17344i	−0.557871	+	0.829927i	$0.688382\pi$
$812$		0			0
$813$	−15.9866			−0.560676
$814$		0			0
$815$	11.2104			0.392682
$816$		0			0
$817$	−0.355242	−	1.09332i	−0.0124283	−	0.0382505i
$818$		0			0
$819$	12.5415	+	9.11195i	0.438236	+	0.318397i
$820$		0			0
$821$	−14.5266	+	44.7082i	−0.506981	+	1.56033i	0.290433	+	0.956895i	$0.406201\pi$
$821$	−14.5266	+	44.7082i	−0.506981	+	1.56033i	−0.797414	+	0.603432i	$0.793799\pi$
$822$		0			0
$823$	−18.2447	+	13.2556i	−0.635970	+	0.462060i	−0.858463	−	0.512875i	$-0.828581\pi$
$823$	−18.2447	+	13.2556i	−0.635970	+	0.462060i	0.222493	+	0.974934i	$0.428581\pi$
$824$		0			0
$825$	−1.16609	−	3.10487i	−0.0405981	−	0.108098i
$826$		0			0
$827$	24.2083	−	17.5884i	0.841805	−	0.611607i	−0.0810692	−	0.996708i	$-0.525833\pi$
$827$	24.2083	−	17.5884i	0.841805	−	0.611607i	0.922874	+	0.385101i	$0.125833\pi$
$828$		0			0
$829$	−1.56179	+	4.80668i	−0.0542430	+	0.166943i	−0.974508	−	0.224353i	$-0.927973\pi$
$829$	−1.56179	+	4.80668i	−0.0542430	+	0.166943i	0.920265	+	0.391296i	$0.127973\pi$
$830$		0			0
$831$	−19.2284	−	13.9702i	−0.667025	−	0.484622i
$832$		0			0
$833$	−10.9139	−	33.5895i	−0.378144	−	1.16381i
$834$		0			0
$835$	1.52373			0.0527310
$836$		0			0
$837$	1.53117			0.0529249
$838$		0			0
$839$	8.14549	+	25.0692i	0.281214	+	0.865486i	0.987508	+	0.157568i	$0.0503654\pi$
$839$	8.14549	+	25.0692i	0.281214	+	0.865486i	−0.706295	+	0.707918i	$0.749635\pi$
$840$		0			0
$841$	−0.215543	−	0.156601i	−0.00743250	−	0.00540003i
$842$		0			0
$843$	0.419019	−	1.28961i	0.0144318	−	0.0444164i
$844$		0			0
$845$	2.36221	−	1.71625i	0.0812626	−	0.0590407i
$846$		0			0
$847$	−40.4310	+	35.3562i	−1.38922	+	1.21485i
$848$		0			0
$849$	11.1174	−	8.07730i	0.381550	−	0.277212i
$850$		0			0
$851$	0.973178	−	2.99513i	0.0333601	−	0.102672i
$852$		0			0
$853$	27.9688	+	20.3206i	0.957635	+	0.695763i	0.952600	−	0.304225i	$-0.0983974\pi$
$853$	27.9688	+	20.3206i	0.957635	+	0.695763i	0.00503470	+	0.999987i	$0.498397\pi$
$854$		0			0
$855$	−0.0706444	−	0.217421i	−0.00241599	−	0.00743565i
$856$		0			0
$857$	−10.3371			−0.353109			−0.176555	−	0.984291i	$-0.556495\pi$
$857$	−10.3371			−0.353109			−0.176555	+	0.984291i	$0.556495\pi$
$858$		0			0
$859$	10.1886			0.347629			0.173815	−	0.984778i	$-0.444391\pi$
$859$	10.1886			0.347629			0.173815	+	0.984778i	$0.444391\pi$
$860$		0			0
$861$	0.181326	+	0.558064i	0.00617957	+	0.0190188i
$862$		0			0
$863$	22.3169	+	16.2142i	0.759676	+	0.551937i	0.898811	−	0.438336i	$-0.144432\pi$
$863$	22.3169	+	16.2142i	0.759676	+	0.551937i	−0.139135	+	0.990273i	$0.544432\pi$
$864$		0			0
$865$	4.47541	−	13.7739i	0.152169	−	0.468327i
$866$		0			0
$867$	−10.1951	+	7.40715i	−0.346243	+	0.251560i
$868$		0			0
$869$	−12.1879	−	32.4520i	−0.413447	−	1.10086i
$870$		0			0
$871$	6.76998	−	4.91868i	0.229392	−	0.166663i
$872$		0			0
$873$	0.875933	−	2.69584i	0.0296458	−	0.0912405i
$874$		0			0
$875$	−3.95018	−	2.86997i	−0.133540	−	0.0970228i
$876$		0			0
$877$	2.44003	+	7.50965i	0.0823941	+	0.253583i	0.983764	−	0.179467i	$-0.0574374\pi$
$877$	2.44003	+	7.50965i	0.0823941	+	0.253583i	−0.901370	+	0.433050i	$0.857437\pi$
$878$		0			0
$879$	14.9828			0.505359
$880$		0			0
$881$	25.7284			0.866811			0.433406	−	0.901199i	$-0.357312\pi$
$881$	25.7284			0.866811			0.433406	+	0.901199i	$0.357312\pi$
$882$		0			0
$883$	−4.03772	−	12.4268i	−0.135880	−	0.418196i	0.859846	−	0.510554i	$-0.170560\pi$
$883$	−4.03772	−	12.4268i	−0.135880	−	0.418196i	−0.995726	+	0.0923580i	$0.970560\pi$
$884$		0			0
$885$	−8.94207	−	6.49679i	−0.300584	−	0.218387i
$886$		0			0
$887$	9.80806	−	30.1861i	0.329322	−	1.01355i	−0.640129	−	0.768267i	$-0.721119\pi$
$887$	9.80806	−	30.1861i	0.329322	−	1.01355i	0.969452	−	0.245283i	$-0.0788808\pi$
$888$		0			0
$889$	64.1499	−	46.6076i	2.15152	−	1.56317i
$890$		0			0
$891$	−2.76839	−	1.82648i	−0.0927444	−	0.0611895i
$892$		0			0
$893$	−1.95765	+	1.42231i	−0.0655102	+	0.0475959i
$894$		0			0
$895$	3.57716	−	11.0094i	0.119571	−	0.368003i
$896$		0			0
$897$	6.74081	+	4.89748i	0.225069	+	0.163522i
$898$		0			0
$899$	2.55971	+	7.87797i	0.0853710	+	0.262745i
$900$		0			0
$901$	−4.72434			−0.157391
$902$		0			0
$903$	−24.5530			−0.817074
$904$		0			0
$905$	−5.91787	−	18.2133i	−0.196717	−	0.605432i
$906$		0			0
$907$	43.0077	+	31.2469i	1.42805	+	1.03754i	0.990376	+	0.138403i	$0.0441968\pi$
$907$	43.0077	+	31.2469i	1.42805	+	1.03754i	0.437672	+	0.899135i	$0.355803\pi$
$908$		0			0
$909$	−0.289575	+	0.891221i	−0.00960460	+	0.0295599i
$910$		0			0
$911$	5.23907	−	3.80641i	0.173578	−	0.126112i	−0.497604	−	0.867404i	$-0.665787\pi$
$911$	5.23907	−	3.80641i	0.173578	−	0.126112i	0.671182	+	0.741292i	$0.265787\pi$
$912$		0			0
$913$	40.0987	−	31.9927i	1.32707	−	1.05880i
$914$		0			0
$915$	6.83461	−	4.96564i	0.225945	−	0.164159i
$916$		0			0
$917$	−12.7509	+	39.2431i	−0.421070	+	1.29592i
$918$		0			0
$919$	−20.3442	−	14.7809i	−0.671092	−	0.487577i	0.199298	−	0.979939i	$-0.436134\pi$
$919$	−20.3442	−	14.7809i	−0.671092	−	0.487577i	−0.870391	+	0.492362i	$0.836134\pi$
$920$		0			0
$921$	−3.52299	−	10.8427i	−0.116087	−	0.357278i
$922$		0			0
$923$	−20.0220			−0.659033
$924$		0			0
$925$	−1.20002			−0.0394565
$926$		0			0
$927$	−4.32899	−	13.3233i	−0.142183	−	0.437593i
$928$		0			0
$929$	30.1735	+	21.9224i	0.989961	+	0.719249i	0.959913	−	0.280299i	$-0.0904338\pi$
$929$	30.1735	+	21.9224i	0.989961	+	0.719249i	0.0300487	+	0.999548i	$0.490434\pi$
$930$		0			0
$931$	−1.18970	+	3.66152i	−0.0389908	+	0.120001i
$932$		0			0
$933$	−14.9957	+	10.8950i	−0.490938	+	0.356687i
$934$		0			0
$935$	−6.94852	+	0.313654i	−0.227241	+	0.0102576i
$936$		0			0
$937$	2.54139	−	1.84643i	0.0830236	−	0.0603202i	−0.545499	−	0.838111i	$-0.683660\pi$
$937$	2.54139	−	1.84643i	0.0830236	−	0.0603202i	0.628523	+	0.777791i	$0.283660\pi$
$938$		0			0
$939$	1.93172	−	5.94523i	0.0630394	−	0.194015i
$940$		0			0
$941$	−4.21104	−	3.05950i	−0.137276	−	0.0997369i	0.517028	−	0.855969i	$-0.327038\pi$
$941$	−4.21104	−	3.05950i	−0.137276	−	0.0997369i	−0.654304	+	0.756232i	$0.727038\pi$
$942$		0			0
$943$	0.0974590	+	0.299948i	0.00317370	+	0.00976765i
$944$		0			0
$945$	−4.88269			−0.158834
$946$		0			0
$947$	−9.54468			−0.310160			−0.155080	−	0.987902i	$-0.549564\pi$
$947$	−9.54468			−0.310160			−0.155080	+	0.987902i	$0.549564\pi$
$948$		0			0
$949$	−7.53175	−	23.1803i	−0.244491	−	0.752466i
$950$		0			0
$951$	−23.8996	−	17.3641i	−0.774998	−	0.563069i
$952$		0			0
$953$	0.831892	−	2.56030i	0.0269476	−	0.0829363i	−0.936678	−	0.350191i	$-0.886117\pi$
$953$	0.831892	−	2.56030i	0.0269476	−	0.0829363i	0.963626	+	0.267255i	$0.0861166\pi$
$954$		0			0
$955$	−21.3827	+	15.5355i	−0.691929	+	0.502716i
$956$		0			0
$957$	4.76938	−	17.2969i	0.154172	−	0.559130i
$958$		0			0
$959$	25.5981	−	18.5981i	0.826605	−	0.600564i
$960$		0			0
$961$	−8.85504	+	27.2530i	−0.285647	+	0.879130i
$962$		0			0
$963$	1.09403	+	0.794862i	0.0352548	+	0.0256141i
$964$		0			0
$965$	−3.81732	−	11.7485i	−0.122884	−	0.378198i
$966$		0			0
$967$	16.4794			0.529943			0.264971	−	0.964256i	$-0.414637\pi$
$967$	16.4794			0.529943			0.264971	+	0.964256i	$0.414637\pi$
$968$		0			0
$969$	−0.479439			−0.0154018
$970$		0			0
$971$	−7.81840	−	24.0626i	−0.250905	−	0.772205i	−0.994609	−	0.103696i	$-0.966933\pi$
$971$	−7.81840	−	24.0626i	−0.250905	−	0.772205i	0.743704	−	0.668509i	$-0.233067\pi$
$972$		0			0
$973$	−74.3471	−	54.0164i	−2.38346	−	1.73168i
$974$		0			0
$975$	0.981106	−	3.01953i	0.0314205	−	0.0967024i
$976$		0			0
$977$	26.0190	−	18.9039i	0.832423	−	0.604791i	−0.0878207	−	0.996136i	$-0.527990\pi$
$977$	26.0190	−	18.9039i	0.832423	−	0.604791i	0.920244	+	0.391345i	$0.127990\pi$
$978$		0			0
$979$	−1.35445	+	4.91212i	−0.0432883	+	0.156992i
$980$		0			0
$981$	13.8602	−	10.0700i	0.442522	−	0.321511i
$982$		0			0
$983$	−16.6822	+	51.3424i	−0.532078	+	1.63757i	0.217801	+	0.975993i	$0.430112\pi$
$983$	−16.6822	+	51.3424i	−0.532078	+	1.63757i	−0.749879	+	0.661575i	$0.769888\pi$
$984$		0			0
$985$	14.4646	+	10.5091i	0.460880	+	0.334849i
$986$		0			0
$987$	15.9707	+	49.1526i	0.508352	+	1.56455i
$988$		0			0
$989$	−13.1967			−0.419632
$990$		0			0
$991$	56.6237			1.79871			0.899356	−	0.437218i	$-0.144036\pi$
$991$	56.6237			1.79871			0.899356	+	0.437218i	$0.144036\pi$
$992$		0			0
$993$	−4.41615	−	13.5915i	−0.140142	−	0.431313i
$994$		0			0
$995$	−21.5886	−	15.6850i	−0.684404	−	0.497249i
$996$		0			0
$997$	−10.4845	+	32.2681i	−0.332048	+	1.02194i	0.636109	+	0.771599i	$0.280543\pi$
$997$	−10.4845	+	32.2681i	−0.332048	+	1.02194i	−0.968158	+	0.250341i	$0.919457\pi$
$998$		0			0
$999$	−0.970838	+	0.705355i	−0.0307160	+	0.0223165i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1320.2.bw.f.1081.3	yes	12
11.4	even	5	inner	1320.2.bw.f.961.3	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1320.2.bw.f.961.3	✓	12	11.4	even	5	inner
1320.2.bw.f.1081.3	yes	12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1320.bw (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(1.50883 - 4.64371i) q^{7} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(1.50883 - 4.64371i) q^{7} +(-0.809017 + 0.587785i) q^{9} +(0.881611 - 3.19731i) q^{11} +(2.56857 - 1.86617i) q^{13} +(-0.309017 + 0.951057i) q^{15} +(1.69666 + 1.23270i) q^{17} +(-0.0706444 - 0.217421i) q^{19} -4.88269 q^{21} -2.62434 q^{23} +(0.309017 + 0.951057i) q^{25} +(0.809017 + 0.587785i) q^{27} +(-1.67173 + 5.14507i) q^{29} +(1.23874 - 0.899998i) q^{31} +(-3.31325 + 0.149559i) q^{33} +(-3.95018 + 2.86997i) q^{35} +(-0.370827 + 1.14129i) q^{37} +(-2.56857 - 1.86617i) q^{39} +(-0.0371365 - 0.114294i) q^{41} +5.02859 q^{43} +1.00000 q^{45} +(-3.27087 - 10.0667i) q^{47} +(-13.6244 - 9.89869i) q^{49} +(0.648067 - 1.99455i) q^{51} +(-1.82247 + 1.32411i) q^{53} +(-2.59257 + 2.06848i) q^{55} +(-0.184950 + 0.134374i) q^{57} +(-3.41557 + 10.5120i) q^{59} +(-6.83461 - 4.96564i) q^{61} +(1.50883 + 4.64371i) q^{63} -3.17492 q^{65} +2.63570 q^{67} +(0.810967 + 2.49590i) q^{69} +(-5.10191 - 3.70675i) q^{71} +(2.37226 - 7.30107i) q^{73} +(0.809017 - 0.587785i) q^{75} +(-13.5172 - 8.91816i) q^{77} +(8.45580 - 6.14350i) q^{79} +(0.309017 - 0.951057i) q^{81} +(12.5129 + 9.09115i) q^{83} +(-0.648067 - 1.99455i) q^{85} +5.40985 q^{87} -1.53633 q^{89} +(-4.79043 - 14.7434i) q^{91} +(-1.23874 - 0.899998i) q^{93} +(-0.0706444 + 0.217421i) q^{95} +(-2.29322 + 1.66612i) q^{97} +(1.16609 + 3.10487i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{3} - 3 q^{5} - 3 q^{9}+O(q^{10}) \) 12 * q + 3 * q^3 - 3 * q^5 - 3 * q^9	\( 12 q + 3 q^{3} - 3 q^{5} - 3 q^{9} - 4 q^{11} + 3 q^{13} + 3 q^{15} + 12 q^{17} - 4 q^{19} - 10 q^{21} - 12 q^{23} - 3 q^{25} + 3 q^{27} + 16 q^{29} + 3 q^{31} + 4 q^{33} - 5 q^{35} - 19 q^{37} - 3 q^{39} + 22 q^{41} + 52 q^{43} + 12 q^{45} + 25 q^{47} - 11 q^{49} + 8 q^{51} - q^{53} - 4 q^{55} + 4 q^{57} - 9 q^{59} + 21 q^{61} - 12 q^{65} - 18 q^{67} - 8 q^{69} + 17 q^{71} + 37 q^{73} + 3 q^{75} - 13 q^{77} - 18 q^{79} - 3 q^{81} + 19 q^{83} - 8 q^{85} + 14 q^{87} + 2 q^{89} - 30 q^{91} - 3 q^{93} - 4 q^{95} + q^{97} + 6 q^{99}+O(q^{100}) \) 12 * q + 3 * q^3 - 3 * q^5 - 3 * q^9 - 4 * q^11 + 3 * q^13 + 3 * q^15 + 12 * q^17 - 4 * q^19 - 10 * q^21 - 12 * q^23 - 3 * q^25 + 3 * q^27 + 16 * q^29 + 3 * q^31 + 4 * q^33 - 5 * q^35 - 19 * q^37 - 3 * q^39 + 22 * q^41 + 52 * q^43 + 12 * q^45 + 25 * q^47 - 11 * q^49 + 8 * q^51 - q^53 - 4 * q^55 + 4 * q^57 - 9 * q^59 + 21 * q^61 - 12 * q^65 - 18 * q^67 - 8 * q^69 + 17 * q^71 + 37 * q^73 + 3 * q^75 - 13 * q^77 - 18 * q^79 - 3 * q^81 + 19 * q^83 - 8 * q^85 + 14 * q^87 + 2 * q^89 - 30 * q^91 - 3 * q^93 - 4 * q^95 + q^97 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more