LMFDB - Embedded newform 768.2.o.a.95.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [768,2,Mod(95,768)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(768, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 3, 4]))

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

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

chi := DirichletCharacter("768.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 768 = 2^{8} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	768.o (of order $8$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.13251087523$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 96)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			95.14
Character	$\chi$	$=$	768.95
Dual form			768.2.o.a.671.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.72928 + 0.0979076i) q^{3} +(0.180206 - 0.0746437i) q^{5} +(0.289055 + 0.289055i) q^{7} +(2.98083 + 0.338620i) q^{9} +O(q^{10})$	\(q+(1.72928 + 0.0979076i) q^{3} +(0.180206 - 0.0746437i) q^{5} +(0.289055 + 0.289055i) q^{7} +(2.98083 + 0.338620i) q^{9} +(3.10859 - 1.28762i) q^{11} +(1.27981 - 3.08973i) q^{13} +(0.318935 - 0.111436i) q^{15} -0.806332 q^{17} +(-5.57935 - 2.31104i) q^{19} +(0.471557 + 0.528159i) q^{21} +(5.03681 + 5.03681i) q^{23} +(-3.50863 + 3.50863i) q^{25} +(5.12154 + 0.877415i) q^{27} +(3.64020 - 8.78822i) q^{29} +7.48336i q^{31} +(5.50170 - 1.92230i) q^{33} +(0.0736656 + 0.0305133i) q^{35} +(1.47112 + 3.55159i) q^{37} +(2.51565 - 5.21770i) q^{39} +(2.62513 - 2.62513i) q^{41} +(2.84744 + 6.87432i) q^{43} +(0.562438 - 0.161479i) q^{45} -0.399772i q^{47} -6.83289i q^{49} +(-1.39438 - 0.0789461i) q^{51} +(-1.42173 - 3.43237i) q^{53} +(0.464073 - 0.464073i) q^{55} +(-9.42200 - 4.54271i) q^{57} +(0.918629 + 2.21777i) q^{59} +(-8.81133 - 3.64977i) q^{61} +(0.763745 + 0.959504i) q^{63} -0.652316i q^{65} +(-3.76613 + 9.09225i) q^{67} +(8.21692 + 9.20321i) q^{69} +(-2.86762 + 2.86762i) q^{71} +(-6.97993 - 6.97993i) q^{73} +(-6.41093 + 5.72389i) q^{75} +(1.27075 + 0.526361i) q^{77} -8.01674 q^{79} +(8.77067 + 2.01873i) q^{81} +(2.47115 - 5.96589i) q^{83} +(-0.145306 + 0.0601876i) q^{85} +(7.15536 - 14.8409i) q^{87} +(5.43308 + 5.43308i) q^{89} +(1.26304 - 0.523167i) q^{91} +(-0.732678 + 12.9408i) q^{93} -1.17794 q^{95} +2.61408 q^{97} +(9.70219 - 2.78555i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 4 q^{3} + 8 q^{7} - 4 q^{9}+O(q^{10}) $ 56 * q - 4 * q^3 + 8 * q^7 - 4 * q^9	$ 56 q - 4 q^{3} + 8 q^{7} - 4 q^{9} + 8 q^{13} + 8 q^{15} - 8 q^{19} + 4 q^{21} - 8 q^{25} - 28 q^{27} - 8 q^{33} + 8 q^{37} + 28 q^{39} - 8 q^{43} + 4 q^{45} - 16 q^{51} - 24 q^{55} - 4 q^{57} + 40 q^{61} + 56 q^{67} + 4 q^{69} - 8 q^{73} + 16 q^{75} - 16 q^{79} + 48 q^{85} - 52 q^{87} + 40 q^{91} - 8 q^{93} - 16 q^{97} + 60 q^{99}+O(q^{100}) $ 56 * q - 4 * q^3 + 8 * q^7 - 4 * q^9 + 8 * q^13 + 8 * q^15 - 8 * q^19 + 4 * q^21 - 8 * q^25 - 28 * q^27 - 8 * q^33 + 8 * q^37 + 28 * q^39 - 8 * q^43 + 4 * q^45 - 16 * q^51 - 24 * q^55 - 4 * q^57 + 40 * q^61 + 56 * q^67 + 4 * q^69 - 8 * q^73 + 16 * q^75 - 16 * q^79 + 48 * q^85 - 52 * q^87 + 40 * q^91 - 8 * q^93 - 16 * q^97 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{8}\right)$

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
$3$	1.72928	+	0.0979076i	0.998401	+	0.0565270i
$3$	1.72928	+	0.0979076i	0.998401	+	0.0565270i
$4$		0			0
$5$	0.180206	−	0.0746437i	0.0805904	−	0.0333817i	−0.342024	−	0.939691i	$-0.611112\pi$
$5$	0.180206	−	0.0746437i	0.0805904	−	0.0333817i	0.422614	+	0.906310i	$0.361112\pi$
$6$		0			0
$7$	0.289055	+	0.289055i	0.109253	+	0.109253i	0.759620	−	0.650367i	$-0.225385\pi$
$7$	0.289055	+	0.289055i	0.109253	+	0.109253i	−0.650367	+	0.759620i	$0.725385\pi$
$8$		0			0
$9$	2.98083	+	0.338620i	0.993609	+	0.112873i
$10$		0			0
$11$	3.10859	−	1.28762i	0.937276	−	0.388232i	0.138842	−	0.990315i	$-0.455662\pi$
$11$	3.10859	−	1.28762i	0.937276	−	0.388232i	0.798434	+	0.602082i	$0.205662\pi$
$12$		0			0
$13$	1.27981	−	3.08973i	0.354954	−	0.856936i	−0.641039	−	0.767508i	$-0.721496\pi$
$13$	1.27981	−	3.08973i	0.354954	−	0.856936i	0.995993	−	0.0894273i	$-0.0285037\pi$
$14$		0			0
$15$	0.318935	−	0.111436i	0.0823486	−	0.0287727i
$16$		0			0
$17$	−0.806332			−0.195564			−0.0977822	−	0.995208i	$-0.531175\pi$
$17$	−0.806332			−0.195564			−0.0977822	+	0.995208i	$0.531175\pi$
$18$		0			0
$19$	−5.57935	−	2.31104i	−1.27999	−	0.530190i	−0.364004	−	0.931397i	$-0.618591\pi$
$19$	−5.57935	−	2.31104i	−1.27999	−	0.530190i	−0.915987	+	0.401208i	$0.868591\pi$
$20$		0			0
$21$	0.471557	+	0.528159i	0.102902	+	0.115254i
$22$		0			0
$23$	5.03681	+	5.03681i	1.05025	+	1.05025i	0.998669	+	0.0515792i	$0.0164254\pi$
$23$	5.03681	+	5.03681i	1.05025	+	1.05025i	0.0515792	+	0.998669i	$0.483575\pi$
$24$		0			0
$25$	−3.50863	+	3.50863i	−0.701726	+	0.701726i
$26$		0			0
$27$	5.12154	+	0.877415i	0.985640	+	0.168859i
$28$		0			0
$29$	3.64020	−	8.78822i	0.675968	−	1.63193i	−0.0953212	−	0.995447i	$-0.530388\pi$
$29$	3.64020	−	8.78822i	0.675968	−	1.63193i	0.771289	−	0.636485i	$-0.219612\pi$
$30$		0			0
$31$			7.48336i			1.34405i	0.740528	+	0.672026i	$0.234576\pi$
$31$			7.48336i			1.34405i	−0.740528	+	0.672026i	$0.765424\pi$
$32$		0			0
$33$	5.50170	−	1.92230i	0.957723	−	0.334630i
$34$		0			0
$35$	0.0736656	+	0.0305133i	0.0124518	+	0.00515769i
$36$		0			0
$37$	1.47112	+	3.55159i	0.241850	+	0.583878i	0.997467	−	0.0711364i	$-0.0226626\pi$
$37$	1.47112	+	3.55159i	0.241850	+	0.583878i	−0.755616	+	0.655014i	$0.772663\pi$
$38$		0			0
$39$	2.51565	−	5.21770i	0.402827	−	0.835501i
$40$		0			0
$41$	2.62513	−	2.62513i	0.409976	−	0.409976i	−0.471754	−	0.881730i	$-0.656379\pi$
$41$	2.62513	−	2.62513i	0.409976	−	0.409976i	0.881730	+	0.471754i	$0.156379\pi$
$42$		0			0
$43$	2.84744	+	6.87432i	0.434230	+	1.04832i	0.977909	+	0.209031i	$0.0670310\pi$
$43$	2.84744	+	6.87432i	0.434230	+	1.04832i	−0.543679	+	0.839293i	$0.682969\pi$
$44$		0			0
$45$	0.562438	−	0.161479i	0.0838433	−	0.0240718i
$46$		0			0
$47$		−	0.399772i		−	0.0583127i	−0.999575	−	0.0291564i	$-0.990718\pi$
$47$		−	0.399772i		−	0.0583127i	0.999575	−	0.0291564i	$-0.00928208\pi$
$48$		0			0
$49$		−	6.83289i		−	0.976128i
$50$		0			0
$51$	−1.39438	−	0.0789461i	−0.195252	−	0.0110547i
$52$		0			0
$53$	−1.42173	−	3.43237i	−0.195290	−	0.471472i	0.795653	−	0.605752i	$-0.207128\pi$
$53$	−1.42173	−	3.43237i	−0.195290	−	0.471472i	−0.990943	+	0.134280i	$0.957128\pi$
$54$		0			0
$55$	0.464073	−	0.464073i	0.0625756	−	0.0625756i
$56$		0			0
$57$	−9.42200	−	4.54271i	−1.24797	−	0.601696i
$58$		0			0
$59$	0.918629	+	2.21777i	0.119595	+	0.288729i	0.972328	−	0.233618i	$-0.0750566\pi$
$59$	0.918629	+	2.21777i	0.119595	+	0.288729i	−0.852733	+	0.522347i	$0.825057\pi$
$60$		0			0
$61$	−8.81133	−	3.64977i	−1.12818	−	0.467306i	−0.261015	−	0.965335i	$-0.584057\pi$
$61$	−8.81133	−	3.64977i	−1.12818	−	0.467306i	−0.867160	+	0.498029i	$0.834057\pi$
$62$		0			0
$63$	0.763745	+	0.959504i	0.0962228	+	0.120886i
$64$		0			0
$65$		−	0.652316i		−	0.0809098i
$66$		0			0
$67$	−3.76613	+	9.09225i	−0.460107	+	1.11080i	0.508247	+	0.861212i	$0.330294\pi$
$67$	−3.76613	+	9.09225i	−0.460107	+	1.11080i	−0.968353	+	0.249584i	$0.919706\pi$
$68$		0			0
$69$	8.21692	+	9.20321i	0.989201	+	1.10794i
$70$		0			0
$71$	−2.86762	+	2.86762i	−0.340324	+	0.340324i	−0.856489	−	0.516165i	$-0.827359\pi$
$71$	−2.86762	+	2.86762i	−0.340324	+	0.340324i	0.516165	+	0.856489i	$0.327359\pi$
$72$		0			0
$73$	−6.97993	−	6.97993i	−0.816939	−	0.816939i	0.168725	−	0.985663i	$-0.446035\pi$
$73$	−6.97993	−	6.97993i	−0.816939	−	0.816939i	−0.985663	+	0.168725i	$0.946035\pi$
$74$		0			0
$75$	−6.41093	+	5.72389i	−0.740271	+	0.660938i
$76$		0			0
$77$	1.27075	+	0.526361i	0.144815	+	0.0599845i
$78$		0			0
$79$	−8.01674			−0.901954			−0.450977	−	0.892536i	$-0.648924\pi$
$79$	−8.01674			−0.901954			−0.450977	+	0.892536i	$0.648924\pi$
$80$		0			0
$81$	8.77067	+	2.01873i	0.974519	+	0.224304i
$82$		0			0
$83$	2.47115	−	5.96589i	0.271244	−	0.654841i	−0.728293	−	0.685266i	$-0.759686\pi$
$83$	2.47115	−	5.96589i	0.271244	−	0.654841i	0.999537	+	0.0304247i	$0.00968596\pi$
$84$		0			0
$85$	−0.145306	+	0.0601876i	−0.0157606	+	0.00652826i
$86$		0			0
$87$	7.15536	−	14.8409i	0.767135	−	1.59111i
$88$		0			0
$89$	5.43308	+	5.43308i	0.575905	+	0.575905i	0.933773	−	0.357867i	$-0.116496\pi$
$89$	5.43308	+	5.43308i	0.575905	+	0.575905i	−0.357867	+	0.933773i	$0.616496\pi$
$90$		0			0
$91$	1.26304	−	0.523167i	0.132402	−	0.0548428i
$92$		0			0
$93$	−0.732678	+	12.9408i	−0.0759752	+	1.34190i
$94$		0			0
$95$	−1.17794			−0.120854
$96$		0			0
$97$	2.61408			0.265419			0.132710	−	0.991155i	$-0.457632\pi$
$97$	2.61408			0.265419			0.132710	+	0.991155i	$0.457632\pi$
$98$		0			0
$99$	9.70219	−	2.78555i	0.975107	−	0.279958i
$100$		0			0
$101$	−12.1420	+	5.02940i	−1.20818	+	0.500444i	−0.893633	−	0.448798i	$-0.851852\pi$
$101$	−12.1420	+	5.02940i	−1.20818	+	0.500444i	−0.314546	+	0.949242i	$0.601852\pi$
$102$		0			0
$103$	−8.46981	−	8.46981i	−0.834555	−	0.834555i	0.153581	−	0.988136i	$-0.450919\pi$
$103$	−8.46981	−	8.46981i	−0.834555	−	0.834555i	−0.988136	+	0.153581i	$0.950919\pi$
$104$		0			0
$105$	0.124401	+	0.0599785i	0.0121403	+	0.00585330i
$106$		0			0
$107$	1.03423	−	0.428394i	0.0999833	−	0.0414144i	−0.332131	−	0.943233i	$-0.607768\pi$
$107$	1.03423	−	0.428394i	0.0999833	−	0.0414144i	0.432114	+	0.901819i	$0.357768\pi$
$108$		0			0
$109$	0.703211	−	1.69770i	0.0673554	−	0.162610i	−0.886617	−	0.462504i	$-0.846951\pi$
$109$	0.703211	−	1.69770i	0.0673554	−	0.162610i	0.953973	+	0.299894i	$0.0969512\pi$
$110$		0			0
$111$	2.19625	+	6.28573i	0.208459	+	0.596616i
$112$		0			0
$113$	−1.39540			−0.131268			−0.0656339	−	0.997844i	$-0.520907\pi$
$113$	−1.39540			−0.131268			−0.0656339	+	0.997844i	$0.520907\pi$
$114$		0			0
$115$	1.28363	+	0.531696i	0.119699	+	0.0495809i
$116$		0			0
$117$	4.86112	−	8.77657i	0.449411	−	0.811394i
$118$		0			0
$119$	−0.233075	−	0.233075i	−0.0213659	−	0.0213659i
$120$		0			0
$121$	0.227201	−	0.227201i	0.0206547	−	0.0206547i
$122$		0			0
$123$	4.79661	−	4.28257i	0.432495	−	0.386146i
$124$		0			0
$125$	−0.743597	+	1.79520i	−0.0665093	+	0.160568i
$126$		0			0
$127$			6.87310i			0.609889i	0.952370	+	0.304944i	$0.0986379\pi$
$127$			6.87310i			0.609889i	−0.952370	+	0.304944i	$0.901362\pi$
$128$		0			0
$129$	4.25097	+	12.1664i	0.374277	+	1.07119i
$130$		0			0
$131$	−16.0581	−	6.65149i	−1.40300	−	0.581143i	−0.452474	−	0.891778i	$-0.649458\pi$
$131$	−16.0581	−	6.65149i	−1.40300	−	0.581143i	−0.950529	+	0.310635i	$0.899458\pi$
$132$		0			0
$133$	−0.944722	−	2.28076i	−0.0819178	−	0.197767i
$134$		0			0
$135$	0.988424	−	0.224175i	0.0850700	−	0.0192939i
$136$		0			0
$137$	−10.7787	+	10.7787i	−0.920890	+	0.920890i	−0.997092	−	0.0762022i	$-0.975721\pi$
$137$	−10.7787	+	10.7787i	−0.920890	+	0.920890i	0.0762022	+	0.997092i	$0.475721\pi$
$138$		0			0
$139$	−1.41183	−	3.40847i	−0.119750	−	0.289102i	0.852626	−	0.522521i	$-0.175009\pi$
$139$	−1.41183	−	3.40847i	−0.119750	−	0.289102i	−0.972376	+	0.233419i	$0.925009\pi$
$140$		0			0
$141$	0.0391407	−	0.691318i	0.00329624	−	0.0582195i
$142$		0			0
$143$		−	11.2526i		−	0.940990i
$144$		0			0
$145$		−	1.85541i		−	0.154083i
$146$		0			0
$147$	0.668992	−	11.8160i	0.0551776	−	0.974567i
$148$		0			0
$149$	6.49923	+	15.6905i	0.532438	+	1.28542i	0.929904	+	0.367802i	$0.119889\pi$
$149$	6.49923	+	15.6905i	0.532438	+	1.28542i	−0.397466	+	0.917617i	$0.630111\pi$
$150$		0			0
$151$	1.50166	−	1.50166i	0.122204	−	0.122204i	−0.643360	−	0.765564i	$-0.722460\pi$
$151$	1.50166	−	1.50166i	0.122204	−	0.122204i	0.765564	+	0.643360i	$0.222460\pi$
$152$		0			0
$153$	−2.40354	−	0.273040i	−0.194315	−	0.0220740i
$154$		0			0
$155$	0.558586	+	1.34855i	0.0448667	+	0.108318i
$156$		0			0
$157$	−12.7594	−	5.28511i	−1.01831	−	0.421798i	−0.189830	−	0.981817i	$-0.560794\pi$
$157$	−12.7594	−	5.28511i	−1.01831	−	0.421798i	−0.828480	+	0.560019i	$0.810794\pi$
$158$		0			0
$159$	−2.12252	−	6.07473i	−0.168327	−	0.481757i
$160$		0			0
$161$			2.91184i			0.229485i
$162$		0			0
$163$	3.02496	−	7.30291i	0.236933	−	0.572008i	−0.760029	−	0.649889i	$-0.774815\pi$
$163$	3.02496	−	7.30291i	0.236933	−	0.572008i	0.996963	+	0.0778809i	$0.0248154\pi$
$164$		0			0
$165$	0.847950	−	0.757077i	0.0660128	−	0.0589384i
$166$		0			0
$167$	−1.65109	+	1.65109i	−0.127765	+	0.127765i	−0.768098	−	0.640333i	$-0.778797\pi$
$167$	−1.65109	+	1.65109i	−0.127765	+	0.127765i	0.640333	+	0.768098i	$0.278797\pi$
$168$		0			0
$169$	1.28389	+	1.28389i	0.0987607	+	0.0987607i
$170$		0			0
$171$	−15.8485	−	8.77810i	−1.21197	−	0.671278i
$172$		0			0
$173$	9.81571	+	4.06580i	0.746275	+	0.309117i	0.723221	−	0.690617i	$-0.242661\pi$
$173$	9.81571	+	4.06580i	0.746275	+	0.309117i	0.0230541	+	0.999734i	$0.492661\pi$
$174$		0			0
$175$	−2.02838			−0.153331
$176$		0			0
$177$	1.37143	+	3.92508i	0.103083	+	0.295027i
$178$		0			0
$179$	−6.28126	+	15.1643i	−0.469484	+	1.13343i	0.494906	+	0.868947i	$0.335203\pi$
$179$	−6.28126	+	15.1643i	−0.469484	+	1.13343i	−0.964389	+	0.264487i	$0.914797\pi$
$180$		0			0
$181$	−4.93385	+	2.04367i	−0.366730	+	0.151905i	−0.558436	−	0.829548i	$-0.688598\pi$
$181$	−4.93385	+	2.04367i	−0.366730	+	0.151905i	0.191705	+	0.981453i	$0.438598\pi$
$182$		0			0
$183$	−14.8799	−	7.17418i	−1.09996	−	0.530331i
$184$		0			0
$185$	0.530208	+	0.530208i	0.0389816	+	0.0389816i
$186$		0			0
$187$	−2.50656	+	1.03825i	−0.183298	+	0.0759244i
$188$		0			0
$189$	1.22679	+	1.73403i	0.0892356	+	0.126132i
$190$		0			0
$191$	−11.6455			−0.842637			−0.421318	−	0.906913i	$-0.638433\pi$
$191$	−11.6455			−0.842637			−0.421318	+	0.906913i	$0.638433\pi$
$192$		0			0
$193$	−6.03220			−0.434207			−0.217104	−	0.976149i	$-0.569661\pi$
$193$	−6.03220			−0.434207			−0.217104	+	0.976149i	$0.569661\pi$
$194$		0			0
$195$	0.0638667	−	1.12804i	0.00457359	−	0.0807804i
$196$		0			0
$197$	0.581435	−	0.240838i	0.0414255	−	0.0171590i	−0.361874	−	0.932227i	$-0.617863\pi$
$197$	0.581435	−	0.240838i	0.0414255	−	0.0171590i	0.403300	+	0.915068i	$0.367863\pi$
$198$		0			0
$199$	13.6071	+	13.6071i	0.964583	+	0.964583i	0.999394	−	0.0348110i	$-0.0110829\pi$
$199$	13.6071	+	13.6071i	0.964583	+	0.964583i	−0.0348110	+	0.999394i	$0.511083\pi$
$200$		0			0
$201$	−7.40291	+	15.3543i	−0.522161	+	1.08301i
$202$		0			0
$203$	3.59250	−	1.48806i	0.252144	−	0.104442i
$204$		0			0
$205$	0.277114	−	0.669012i	0.0193545	−	0.0467259i
$206$		0			0
$207$	13.3083	+	16.7194i	0.924991	+	1.16208i
$208$		0			0
$209$	−20.3197			−1.40554
$210$		0			0
$211$	−6.94196	−	2.87545i	−0.477904	−	0.197954i	0.130710	−	0.991421i	$-0.458274\pi$
$211$	−6.94196	−	2.87545i	−0.477904	−	0.197954i	−0.608614	+	0.793466i	$0.708274\pi$
$212$		0			0
$213$	−5.23969	+	4.67816i	−0.359017	+	0.320542i
$214$		0			0
$215$	1.02625	+	1.02625i	0.0699896	+	0.0699896i
$216$		0			0
$217$	−2.16311	+	2.16311i	−0.146841	+	0.146841i
$218$		0			0
$219$	−11.3869	−	12.7536i	−0.769453	−	0.861811i
$220$		0			0
$221$	−1.03195	+	2.49135i	−0.0694164	+	0.167586i
$222$		0			0
$223$		−	6.45182i		−	0.432046i	−0.976388	−	0.216023i	$-0.930691\pi$
$223$		−	6.45182i		−	0.432046i	0.976388	−	0.216023i	$-0.0693086\pi$
$224$		0			0
$225$	−11.6467	+	9.27054i	−0.776448	+	0.618036i
$226$		0			0
$227$	−3.16606	−	1.31143i	−0.210139	−	0.0870424i	0.275131	−	0.961407i	$-0.411279\pi$
$227$	−3.16606	−	1.31143i	−0.210139	−	0.0870424i	−0.485270	+	0.874364i	$0.661279\pi$
$228$		0			0
$229$	−8.63723	−	20.8521i	−0.570764	−	1.37795i	−0.900905	−	0.434015i	$-0.857096\pi$
$229$	−8.63723	−	20.8521i	−0.570764	−	1.37795i	0.330141	−	0.943932i	$-0.392904\pi$
$230$		0			0
$231$	2.14595	+	1.03464i	0.141193	+	0.0680745i
$232$		0			0
$233$	15.5223	−	15.5223i	1.01690	−	1.01690i	0.0170465	−	0.999855i	$-0.494574\pi$
$233$	15.5223	−	15.5223i	1.01690	−	1.01690i	0.999855	−	0.0170465i	$-0.00542634\pi$
$234$		0			0
$235$	−0.0298404	−	0.0720412i	−0.00194658	−	0.00469945i
$236$		0			0
$237$	−13.8632	−	0.784900i	−0.900512	−	0.0509847i
$238$		0			0
$239$		−	22.3335i		−	1.44463i	−0.691563	−	0.722316i	$-0.743078\pi$
$239$		−	22.3335i		−	1.44463i	0.691563	−	0.722316i	$-0.256922\pi$
$240$		0			0
$241$			10.0345i			0.646380i	0.946334	+	0.323190i	$0.104755\pi$
$241$			10.0345i			0.646380i	−0.946334	+	0.323190i	$0.895245\pi$
$242$		0			0
$243$	14.9693	+	4.34968i	0.960282	+	0.279032i
$244$		0			0
$245$	−0.510032	−	1.23133i	−0.0325848	−	0.0786666i
$246$		0			0
$247$	−14.2810	+	14.2810i	−0.908677	+	0.908677i
$248$		0			0
$249$	4.85742	−	10.0748i	0.307827	−	0.638462i
$250$		0			0
$251$	−1.23078	−	2.97137i	−0.0776862	−	0.187551i	0.880265	−	0.474483i	$-0.157365\pi$
$251$	−1.23078	−	2.97137i	−0.0776862	−	0.187551i	−0.957951	+	0.286931i	$0.907365\pi$
$252$		0			0
$253$	22.1429	+	9.17189i	1.39211	+	0.576632i
$254$		0			0
$255$	−0.257167	+	0.0898547i	−0.0161044	+	0.00562692i
$256$		0			0
$257$		−	22.7842i		−	1.42124i	−0.703576	−	0.710620i	$-0.748415\pi$
$257$		−	22.7842i		−	1.42124i	0.703576	−	0.710620i	$-0.251585\pi$
$258$		0			0
$259$	−0.601372	+	1.45184i	−0.0373675	+	0.0902130i
$260$		0			0
$261$	13.8267	−	24.9635i	0.855850	−	1.54520i
$262$		0			0
$263$	−12.8553	+	12.8553i	−0.792690	+	0.792690i	−0.981931	−	0.189241i	$-0.939397\pi$
$263$	−12.8553	+	12.8553i	−0.792690	+	0.792690i	0.189241	+	0.981931i	$0.439397\pi$
$264$		0			0
$265$	−0.512409	−	0.512409i	−0.0314770	−	0.0314770i
$266$		0			0
$267$	8.86338	+	9.92726i	0.542430	+	0.607539i
$268$		0			0
$269$	−11.7742	−	4.87704i	−0.717886	−	0.297358i	−0.00632279	−	0.999980i	$-0.502013\pi$
$269$	−11.7742	−	4.87704i	−0.717886	−	0.297358i	−0.711564	+	0.702622i	$0.752013\pi$
$270$		0			0
$271$	11.6627			0.708457			0.354228	−	0.935159i	$-0.384744\pi$
$271$	11.6627			0.708457			0.354228	+	0.935159i	$0.384744\pi$
$272$		0			0
$273$	2.23537	−	0.781042i	0.135291	−	0.0472708i
$274$		0			0
$275$	−6.38912	+	15.4247i	−0.385278	+	0.930144i
$276$		0			0
$277$	−8.48904	+	3.51628i	−0.510057	+	0.211273i	−0.622843	−	0.782347i	$-0.714023\pi$
$277$	−8.48904	+	3.51628i	−0.510057	+	0.211273i	0.112786	+	0.993619i	$0.464023\pi$
$278$		0			0
$279$	−2.53401	+	22.3066i	−0.151707	+	1.33546i
$280$		0			0
$281$	22.3102	+	22.3102i	1.33091	+	1.33091i	0.904553	+	0.426362i	$0.140205\pi$
$281$	22.3102	+	22.3102i	1.33091	+	1.33091i	0.426362	+	0.904553i	$0.359795\pi$
$282$		0			0
$283$	−9.95203	+	4.12227i	−0.591587	+	0.245043i	−0.658333	−	0.752727i	$-0.728738\pi$
$283$	−9.95203	+	4.12227i	−0.591587	+	0.245043i	0.0667462	+	0.997770i	$0.478738\pi$
$284$		0			0
$285$	−2.03698	−	0.115329i	−0.120660	−	0.00683150i
$286$		0			0
$287$	1.51762			0.0895820
$288$		0			0
$289$	−16.3498			−0.961755
$290$		0			0
$291$	4.52048	+	0.255938i	0.264995	+	0.0150034i
$292$		0			0
$293$	−23.2108	+	9.61422i	−1.35599	+	0.561669i	−0.937953	−	0.346762i	$-0.887281\pi$
$293$	−23.2108	+	9.61422i	−1.35599	+	0.561669i	−0.418035	+	0.908431i	$0.637281\pi$
$294$		0			0
$295$	0.331084	+	0.331084i	0.0192765	+	0.0192765i
$296$		0			0
$297$	17.0505	−	3.86707i	0.989373	−	0.224390i
$298$		0			0
$299$	22.0085	−	9.11622i	1.27279	−	0.527205i
$300$		0			0
$301$	−1.16399	+	2.81013i	−0.0670914	+	0.161973i
$302$		0			0
$303$	−21.4894	+	7.50845i	−1.23454	+	0.431349i
$304$		0			0
$305$	−1.86029			−0.106520
$306$		0			0
$307$	18.3982	+	7.62077i	1.05004	+	0.434940i	0.839906	−	0.542733i	$-0.182610\pi$
$307$	18.3982	+	7.62077i	1.05004	+	0.434940i	0.210133	+	0.977673i	$0.432610\pi$
$308$		0			0
$309$	−13.8174	−	15.4759i	−0.786046	−	0.880395i
$310$		0			0
$311$	0.938468	+	0.938468i	0.0532157	+	0.0532157i	0.733214	−	0.679998i	$-0.238019\pi$
$311$	0.938468	+	0.938468i	0.0532157	+	0.0532157i	−0.679998	+	0.733214i	$0.738019\pi$
$312$		0			0
$313$	11.2850	−	11.2850i	0.637867	−	0.637867i	−0.312162	−	0.950029i	$-0.601053\pi$
$313$	11.2850	−	11.2850i	0.637867	−	0.637867i	0.950029	+	0.312162i	$0.101053\pi$
$314$		0			0
$315$	0.209252	+	0.115899i	0.0117900	+	0.00653020i
$316$		0			0
$317$	7.57388	−	18.2850i	0.425391	−	1.02699i	−0.555340	−	0.831623i	$-0.687412\pi$
$317$	7.57388	−	18.2850i	0.425391	−	1.02699i	0.980731	−	0.195362i	$-0.0625881\pi$
$318$		0			0
$319$		−	32.0062i		−	1.79200i
$320$		0			0
$321$	1.83043	−	0.639555i	0.102164	−	0.0356965i
$322$		0			0
$323$	4.49881	+	1.86347i	0.250321	+	0.103686i
$324$		0			0
$325$	6.35034	+	15.3311i	0.352253	+	0.850415i
$326$		0			0
$327$	1.38227	−	2.86695i	0.0764395	−	0.158543i
$328$		0			0
$329$	0.115556	−	0.115556i	0.00637082	−	0.00637082i
$330$		0			0
$331$	−4.79305	−	11.5714i	−0.263450	−	0.636024i	0.735698	−	0.677310i	$-0.236855\pi$
$331$	−4.79305	−	11.5714i	−0.263450	−	0.636024i	−0.999147	+	0.0412860i	$0.986855\pi$
$332$		0			0
$333$	3.18251	+	11.0848i	0.174400	+	0.607445i
$334$		0			0
$335$			1.91959i			0.104879i
$336$		0			0
$337$		−	7.03034i		−	0.382967i	−0.981496	−	0.191484i	$-0.938670\pi$
$337$		−	7.03034i		−	0.382967i	0.981496	−	0.191484i	$-0.0613299\pi$
$338$		0			0
$339$	−2.41303	−	0.136620i	−0.131058	−	0.00742018i
$340$		0			0
$341$	9.63574	+	23.2627i	0.521804	+	1.25975i
$342$		0			0
$343$	3.99847	−	3.99847i	0.215897	−	0.215897i
$344$		0			0
$345$	2.16770	+	1.04513i	0.116705	+	0.0562679i
$346$		0			0
$347$	4.70857	+	11.3675i	0.252769	+	0.610240i	0.998426	−	0.0560914i	$-0.0178638\pi$
$347$	4.70857	+	11.3675i	0.252769	+	0.610240i	−0.745656	+	0.666331i	$0.767864\pi$
$348$		0			0
$349$	29.2204	+	12.1035i	1.56413	+	0.647885i	0.985801	−	0.167917i	$-0.0537039\pi$
$349$	29.2204	+	12.1035i	1.56413	+	0.647885i	0.578332	+	0.815802i	$0.303704\pi$
$350$		0			0
$351$	9.26554	−	14.7012i	0.494558	−	0.784693i
$352$		0			0
$353$		−	14.9632i		−	0.796411i	−0.917296	−	0.398206i	$-0.869633\pi$
$353$		−	14.9632i		−	0.796411i	0.917296	−	0.398206i	$-0.130367\pi$
$354$		0			0
$355$	−0.302712	+	0.730811i	−0.0160663	+	0.0387874i
$356$		0			0
$357$	−0.380232	−	0.425872i	−0.0201240	−	0.0225395i
$358$		0			0
$359$	19.5707	−	19.5707i	1.03290	−	1.03290i	0.0334594	−	0.999440i	$-0.489348\pi$
$359$	19.5707	−	19.5707i	1.03290	−	1.03290i	0.999440	−	0.0334594i	$-0.0106524\pi$
$360$		0			0
$361$	12.3532	+	12.3532i	0.650170	+	0.650170i
$362$		0			0
$363$	0.415140	−	0.370650i	0.0217892	−	0.0194541i
$364$		0			0
$365$	−1.77883	−	0.736815i	−0.0931082	−	0.0385667i
$366$		0			0
$367$	21.5484			1.12482			0.562410	−	0.826859i	$-0.309874\pi$
$367$	21.5484			1.12482			0.562410	+	0.826859i	$0.309874\pi$
$368$		0			0
$369$	8.71398	−	6.93614i	0.453632	−	0.361081i
$370$		0			0
$371$	0.581184	−	1.40310i	0.0301736	−	0.0728455i
$372$		0			0
$373$	27.1858	−	11.2607i	1.40763	−	0.583059i	0.455910	−	0.890026i	$-0.349314\pi$
$373$	27.1858	−	11.2607i	1.40763	−	0.583059i	0.951720	+	0.306967i	$0.0993141\pi$
$374$		0			0
$375$	−1.46165	+	3.03160i	−0.0754794	+	0.156551i
$376$		0			0
$377$	−22.4944	−	22.4944i	−1.15852	−	1.15852i
$378$		0			0
$379$	−11.5245	+	4.77361i	−0.591975	+	0.245204i	−0.658500	−	0.752581i	$-0.728809\pi$
$379$	−11.5245	+	4.77361i	−0.591975	+	0.245204i	0.0665251	+	0.997785i	$0.478809\pi$
$380$		0			0
$381$	−0.672929	+	11.8855i	−0.0344752	+	0.608914i
$382$		0			0
$383$	33.6911			1.72154			0.860768	−	0.508998i	$-0.169984\pi$
$383$	33.6911			1.72154			0.860768	+	0.508998i	$0.169984\pi$
$384$		0			0
$385$	0.268286			0.0136731
$386$		0			0
$387$	6.15994	+	21.4554i	0.313127	+	1.09064i
$388$		0			0
$389$	34.0564	−	14.1066i	1.72673	−	0.715233i	0.727139	−	0.686490i	$-0.240849\pi$
$389$	34.0564	−	14.1066i	1.72673	−	0.715233i	0.999587	−	0.0287433i	$-0.00915052\pi$
$390$		0			0
$391$	−4.06135	−	4.06135i	−0.205391	−	0.205391i
$392$		0			0
$393$	−27.1178	−	13.0745i	−1.36791	−	0.659521i
$394$		0			0
$395$	−1.44466	+	0.598399i	−0.0726889	+	0.0301087i
$396$		0			0
$397$	−11.3891	+	27.4958i	−0.571604	+	1.37997i	0.328586	+	0.944474i	$0.393428\pi$
$397$	−11.3891	+	27.4958i	−0.571604	+	1.37997i	−0.900189	+	0.435499i	$0.856572\pi$
$398$		0			0
$399$	−1.41039	−	4.03657i	−0.0706077	−	0.202081i
$400$		0			0
$401$	9.31753			0.465295			0.232648	−	0.972561i	$-0.425261\pi$
$401$	9.31753			0.465295			0.232648	+	0.972561i	$0.425261\pi$
$402$		0			0
$403$	23.1215	+	9.57726i	1.15177	+	0.477077i
$404$		0			0
$405$	1.73121	−	0.290888i	0.0860246	−	0.0144543i
$406$		0			0
$407$	9.14621	+	9.14621i	0.453361	+	0.453361i
$408$		0			0
$409$	17.7916	−	17.7916i	0.879736	−	0.879736i	−0.113771	−	0.993507i	$-0.536293\pi$
$409$	17.7916	−	17.7916i	0.879736	−	0.879736i	0.993507	+	0.113771i	$0.0362930\pi$
$410$		0			0
$411$	−19.6948	+	17.5842i	−0.971473	+	0.867363i
$412$		0			0
$413$	−0.375523	+	0.906592i	−0.0184783	+	0.0446105i
$414$		0			0
$415$		−	1.25954i		−	0.0618285i
$416$		0			0
$417$	−2.10774	−	6.03242i	−0.103217	−	0.295409i
$418$		0			0
$419$	9.75715	+	4.04154i	0.476668	+	0.197442i	0.608065	−	0.793888i	$-0.291946\pi$
$419$	9.75715	+	4.04154i	0.476668	+	0.197442i	−0.131397	+	0.991330i	$0.541946\pi$
$420$		0			0
$421$	−1.73340	−	4.18479i	−0.0844806	−	0.203954i	0.875994	−	0.482322i	$-0.160207\pi$
$421$	−1.73340	−	4.18479i	−0.0844806	−	0.203954i	−0.960474	+	0.278368i	$0.910207\pi$
$422$		0			0
$423$	0.135371	−	1.19165i	0.00658195	−	0.0579401i
$424$		0			0
$425$	2.82912	−	2.82912i	0.137233	−	0.137233i
$426$		0			0
$427$	−1.49198	−	3.60195i	−0.0722018	−	0.174311i
$428$		0			0
$429$	1.10172	−	19.4589i	0.0531913	−	0.939485i
$430$		0			0
$431$			24.2865i			1.16984i	0.811092	+	0.584919i	$0.198874\pi$
$431$			24.2865i			1.16984i	−0.811092	+	0.584919i	$0.801126\pi$
$432$		0			0
$433$			21.4987i			1.03316i	0.856239	+	0.516580i	$0.172795\pi$
$433$			21.4987i			1.03316i	−0.856239	+	0.516580i	$0.827205\pi$
$434$		0			0
$435$	0.181658	−	3.20852i	0.00870985	−	0.153837i
$436$		0			0
$437$	−16.4619	−	39.7424i	−0.787478	−	1.90114i
$438$		0			0
$439$	1.71247	−	1.71247i	0.0817316	−	0.0817316i	−0.665059	−	0.746791i	$-0.731594\pi$
$439$	1.71247	−	1.71247i	0.0817316	−	0.0817316i	0.746791	+	0.665059i	$0.231594\pi$
$440$		0			0
$441$	2.31375	−	20.3677i	0.110179	−	0.969890i
$442$		0			0
$443$	1.69988	+	4.10388i	0.0807639	+	0.194981i	0.959103	−	0.283056i	$-0.0913483\pi$
$443$	1.69988	+	4.10388i	0.0807639	+	0.194981i	−0.878339	+	0.478037i	$0.841348\pi$
$444$		0			0
$445$	1.38462	+	0.573527i	0.0656371	+	0.0271878i
$446$		0			0
$447$	9.70278	+	27.7697i	0.458926	+	1.31346i
$448$		0			0
$449$			6.34782i			0.299572i	0.988718	+	0.149786i	$0.0478585\pi$
$449$			6.34782i			0.299572i	−0.988718	+	0.149786i	$0.952142\pi$
$450$		0			0
$451$	4.78028	−	11.5406i	0.225095	−	0.543427i
$452$		0			0
$453$	2.74382	−	2.44977i	0.128916	−	0.115100i
$454$		0			0
$455$	0.188555	−	0.188555i	0.00883961	−	0.00883961i
$456$		0			0
$457$	10.0211	+	10.0211i	0.468765	+	0.468765i	0.901514	−	0.432749i	$-0.142456\pi$
$457$	10.0211	+	10.0211i	0.468765	+	0.468765i	−0.432749	+	0.901514i	$0.642456\pi$
$458$		0			0
$459$	−4.12966	−	0.707488i	−0.192756	−	0.0330227i
$460$		0			0
$461$	19.1656	+	7.93865i	0.892631	+	0.369740i	0.781382	−	0.624053i	$-0.214515\pi$
$461$	19.1656	+	7.93865i	0.892631	+	0.369740i	0.111249	+	0.993793i	$0.464515\pi$
$462$		0			0
$463$	−30.9634			−1.43899			−0.719496	−	0.694496i	$-0.755627\pi$
$463$	−30.9634			−1.43899			−0.719496	+	0.694496i	$0.755627\pi$
$464$		0			0
$465$	0.833919	+	2.38670i	0.0386721	+	0.110681i
$466$		0			0
$467$	2.87599	−	6.94326i	0.133085	−	0.321296i	−0.843263	−	0.537502i	$-0.819368\pi$
$467$	2.87599	−	6.94326i	0.133085	−	0.321296i	0.976348	+	0.216206i	$0.0693682\pi$
$468$		0			0
$469$	−3.71679	+	1.53954i	−0.171625	+	0.0710895i
$470$		0			0
$471$	−21.5471	−	10.3887i	−0.992839	−	0.478685i
$472$		0			0
$473$	17.7030	+	17.7030i	0.813987	+	0.813987i
$474$		0			0
$475$	27.6845	−	11.4673i	1.27025	−	0.526155i
$476$		0			0
$477$	−3.07567	−	10.7127i	−0.140825	−	0.490502i
$478$		0			0
$479$	12.3852			0.565894			0.282947	−	0.959136i	$-0.408688\pi$
$479$	12.3852			0.565894			0.282947	+	0.959136i	$0.408688\pi$
$480$		0			0
$481$	12.8562			0.586192
$482$		0			0
$483$	−0.285091	+	5.03538i	−0.0129721	+	0.229118i
$484$		0			0
$485$	0.471072	−	0.195124i	0.0213903	−	0.00886014i
$486$		0			0
$487$	8.82766	+	8.82766i	0.400019	+	0.400019i	0.878240	−	0.478220i	$-0.158718\pi$
$487$	8.82766	+	8.82766i	0.400019	+	0.400019i	−0.478220	+	0.878240i	$0.658718\pi$
$488$		0			0
$489$	5.94602	−	12.3326i	0.268889	−	0.557700i
$490$		0			0
$491$	−9.13225	+	3.78270i	−0.412133	+	0.170711i	−0.579109	−	0.815250i	$-0.696600\pi$
$491$	−9.13225	+	3.78270i	−0.412133	+	0.170711i	0.166977	+	0.985961i	$0.446600\pi$
$492$		0			0
$493$	−2.93521	+	7.08623i	−0.132195	+	0.319148i
$494$		0			0
$495$	1.54047	−	1.22618i	0.0692389	−	0.0551126i
$496$		0			0
$497$	−1.65780			−0.0743626
$498$		0			0
$499$	−4.86758	−	2.01622i	−0.217903	−	0.0902583i	0.271062	−	0.962562i	$-0.412625\pi$
$499$	−4.86758	−	2.01622i	−0.217903	−	0.0902583i	−0.488965	+	0.872304i	$0.662625\pi$
$500$		0			0
$501$	−3.01685	+	2.69354i	−0.134783	+	0.120339i
$502$		0			0
$503$	0.926311	+	0.926311i	0.0413022	+	0.0413022i	0.727456	−	0.686154i	$-0.240702\pi$
$503$	0.926311	+	0.926311i	0.0413022	+	0.0413022i	−0.686154	+	0.727456i	$0.740702\pi$
$504$		0			0
$505$	−1.81265	+	1.81265i	−0.0806620	+	0.0806620i
$506$		0			0
$507$	2.09450	+	2.34591i	0.0930201	+	0.104185i
$508$		0			0
$509$	−1.79808	+	4.34096i	−0.0796987	+	0.192410i	−0.958706	−	0.284398i	$-0.908206\pi$
$509$	−1.79808	+	4.34096i	−0.0796987	+	0.192410i	0.879008	+	0.476808i	$0.158206\pi$
$510$		0			0
$511$		−	4.03517i		−	0.178505i
$512$		0			0
$513$	−26.5471	−	16.7315i	−1.17208	−	0.738714i
$514$		0			0
$515$	−2.15853	−	0.894090i	−0.0951160	−	0.0393983i
$516$		0			0
$517$	−0.514755	−	1.24273i	−0.0226389	−	0.0546551i
$518$		0			0
$519$	16.5761	+	7.99195i	0.727608	+	0.350807i
$520$		0			0
$521$	−12.3969	+	12.3969i	−0.543120	+	0.543120i	−0.924442	−	0.381322i	$-0.875469\pi$
$521$	−12.3969	+	12.3969i	−0.543120	+	0.543120i	0.381322	+	0.924442i	$0.375469\pi$
$522$		0			0
$523$	−5.71533	−	13.7980i	−0.249914	−	0.603346i	0.748282	−	0.663380i	$-0.230879\pi$
$523$	−5.71533	−	13.7980i	−0.249914	−	0.603346i	−0.998196	+	0.0600346i	$0.980879\pi$
$524$		0			0
$525$	−3.50764	−	0.198594i	−0.153086	−	0.00866734i
$526$		0			0
$527$		−	6.03408i		−	0.262849i
$528$		0			0
$529$			27.7390i			1.20604i
$530$		0			0
$531$	1.98730	+	6.92184i	0.0862413	+	0.300382i
$532$		0			0
$533$	−4.75127	−	11.4706i	−0.205800	−	0.496846i
$534$		0			0
$535$	0.154398	−	0.154398i	0.00667521	−	0.00667521i
$536$		0			0
$537$	−12.3468	+	25.6084i	−0.532802	+	1.10508i
$538$		0			0
$539$	−8.79818	−	21.2407i	−0.378964	−	0.914901i
$540$		0			0
$541$	−16.5235	−	6.84424i	−0.710399	−	0.294257i	−0.00192927	−	0.999998i	$-0.500614\pi$
$541$	−16.5235	−	6.84424i	−0.710399	−	0.294257i	−0.708470	+	0.705741i	$0.750614\pi$
$542$		0			0
$543$	−8.73211	+	3.05102i	−0.374731	+	0.130932i
$544$		0			0
$545$		−	0.358426i		−	0.0153533i
$546$		0			0
$547$	2.24912	−	5.42985i	0.0961654	−	0.232164i	−0.868475	−	0.495733i	$-0.834900\pi$
$547$	2.24912	−	5.42985i	0.0961654	−	0.232164i	0.964641	+	0.263569i	$0.0848996\pi$
$548$		0			0
$549$	−25.0292	−	13.8630i	−1.06822	−	0.591660i
$550$		0			0
$551$	−40.6199	+	40.6199i	−1.73047	+	1.73047i
$552$		0			0
$553$	−2.31728	−	2.31728i	−0.0985409	−	0.0985409i
$554$		0			0
$555$	0.864967	+	0.968789i	0.0367158	+	0.0411228i
$556$		0			0
$557$	−17.5896	−	7.28584i	−0.745294	−	0.308711i	−0.0224743	−	0.999747i	$-0.507154\pi$
$557$	−17.5896	−	7.28584i	−0.745294	−	0.308711i	−0.722820	+	0.691036i	$0.757154\pi$
$558$		0			0
$559$	24.8839			1.05248
$560$		0			0
$561$	−4.43620	+	1.55002i	−0.187296	+	0.0654417i
$562$		0			0
$563$	7.04761	−	17.0144i	0.297021	−	0.717073i	−0.702962	−	0.711228i	$-0.748139\pi$
$563$	7.04761	−	17.0144i	0.297021	−	0.717073i	0.999983	−	0.00584493i	$-0.00186051\pi$
$564$		0			0
$565$	−0.251458	+	0.104157i	−0.0105789	+	0.00438194i
$566$		0			0
$567$	1.95168	+	3.11874i	0.0819630	+	0.130975i
$568$		0			0
$569$	−15.9856	−	15.9856i	−0.670152	−	0.670152i	0.287599	−	0.957751i	$-0.407143\pi$
$569$	−15.9856	−	15.9856i	−0.670152	−	0.670152i	−0.957751	+	0.287599i	$0.907143\pi$
$570$		0			0
$571$	−21.2300	+	8.79375i	−0.888447	+	0.368007i	−0.779767	−	0.626070i	$-0.784663\pi$
$571$	−21.2300	+	8.79375i	−0.888447	+	0.368007i	−0.108680	+	0.994077i	$0.534663\pi$
$572$		0			0
$573$	−20.1383	−	1.14018i	−0.841290	−	0.0476317i
$574$		0			0
$575$	−35.3446			−1.47397
$576$		0			0
$577$	21.1703			0.881332			0.440666	−	0.897671i	$-0.354742\pi$
$577$	21.1703			0.881332			0.440666	+	0.897671i	$0.354742\pi$
$578$		0			0
$579$	−10.4314	−	0.590599i	−0.433513	−	0.0245444i
$580$		0			0
$581$	2.43877	−	1.01017i	0.101177	−	0.0419090i
$582$		0			0
$583$	−8.83917	−	8.83917i	−0.366081	−	0.366081i
$584$		0			0
$585$	0.220887	−	1.94444i	0.00913255	−	0.0803927i
$586$		0			0
$587$	14.4081	−	5.96803i	0.594686	−	0.246327i	−0.0649791	−	0.997887i	$-0.520698\pi$
$587$	14.4081	−	5.96803i	0.594686	−	0.246327i	0.659665	+	0.751560i	$0.270698\pi$
$588$		0			0
$589$	17.2944	−	41.7523i	0.712603	−	1.72037i
$590$		0			0
$591$	1.02905	−	0.359550i	0.0423293	−	0.0147899i
$592$		0			0
$593$	20.5777			0.845025			0.422512	−	0.906357i	$-0.361148\pi$
$593$	20.5777			0.845025			0.422512	+	0.906357i	$0.361148\pi$
$594$		0			0
$595$	−0.0593989	−	0.0246038i	−0.00243512	−	0.00100866i
$596$		0			0
$597$	22.1983	+	24.8628i	0.908516	+	1.01757i
$598$		0			0
$599$	−14.6016	−	14.6016i	−0.596604	−	0.596604i	0.342803	−	0.939407i	$-0.388624\pi$
$599$	−14.6016	−	14.6016i	−0.596604	−	0.596604i	−0.939407	+	0.342803i	$0.888624\pi$
$600$		0			0
$601$	−22.7394	+	22.7394i	−0.927561	+	0.927561i	−0.997548	−	0.0699869i	$-0.977704\pi$
$601$	−22.7394	+	22.7394i	−0.927561	+	0.927561i	0.0699869	+	0.997548i	$0.477704\pi$
$602$		0			0
$603$	−14.3050	+	25.8272i	−0.582545	+	1.05176i
$604$		0			0
$605$	0.0239839	−	0.0579021i	0.000975082	−	0.00235406i
$606$		0			0
$607$			40.2640i			1.63426i	0.576451	+	0.817132i	$0.304437\pi$
$607$			40.2640i			1.63426i	−0.576451	+	0.817132i	$0.695563\pi$
$608$		0			0
$609$	6.35814	−	2.22155i	0.257645	−	0.0900216i
$610$		0			0
$611$	−1.23519	−	0.511631i	−0.0499703	−	0.0206984i
$612$		0			0
$613$	6.76173	+	16.3243i	0.273104	+	0.659331i	0.999613	−	0.0278260i	$-0.00885845\pi$
$613$	6.76173	+	16.3243i	0.273104	+	0.659331i	−0.726509	+	0.687157i	$0.758858\pi$
$614$		0			0
$615$	0.544710	−	1.12978i	0.0219648	−	0.0455571i
$616$		0			0
$617$	5.19834	−	5.19834i	0.209277	−	0.209277i	−0.594683	−	0.803960i	$-0.702722\pi$
$617$	5.19834	−	5.19834i	0.209277	−	0.209277i	0.803960	+	0.594683i	$0.202722\pi$
$618$		0			0
$619$	8.07299	+	19.4899i	0.324481	+	0.783366i	0.998983	+	0.0450932i	$0.0143585\pi$
$619$	8.07299	+	19.4899i	0.324481	+	0.783366i	−0.674502	+	0.738273i	$0.735642\pi$
$620$		0			0
$621$	21.3769	+	30.2156i	0.857824	+	1.21251i
$622$		0			0
$623$			3.14092i			0.125838i
$624$		0			0
$625$		−	24.4308i		−	0.977230i
$626$		0			0
$627$	−35.1384	−	1.98945i	−1.40329	−	0.0794510i
$628$		0			0
$629$	−1.18621	−	2.86376i	−0.0472973	−	0.114186i
$630$		0			0
$631$	22.5327	−	22.5327i	0.897012	−	0.897012i	−0.0981592	−	0.995171i	$-0.531295\pi$
$631$	22.5327	−	22.5327i	0.897012	−	0.897012i	0.995171	+	0.0981592i	$0.0312954\pi$
$632$		0			0
$633$	−11.7231	−	5.65214i	−0.465950	−	0.224652i
$634$		0			0
$635$	0.513033	+	1.23857i	0.0203591	+	0.0491512i
$636$		0			0
$637$	−21.1118	−	8.74478i	−0.836479	−	0.346481i
$638$		0			0
$639$	−9.51892	+	7.57685i	−0.376563	+	0.299736i
$640$		0			0
$641$			41.6012i			1.64315i	0.570100	+	0.821575i	$0.306904\pi$
$641$			41.6012i			1.64315i	−0.570100	+	0.821575i	$0.693096\pi$
$642$		0			0
$643$	7.11746	−	17.1831i	0.280685	−	0.677634i	−0.719167	−	0.694837i	$-0.755476\pi$
$643$	7.11746	−	17.1831i	0.280685	−	0.677634i	0.999852	+	0.0172036i	$0.00547635\pi$
$644$		0			0
$645$	1.67420	+	1.87515i	0.0659214	+	0.0738340i
$646$		0			0
$647$	31.4452	−	31.4452i	1.23624	−	1.23624i	0.274714	−	0.961526i	$-0.411417\pi$
$647$	31.4452	−	31.4452i	1.23624	−	1.23624i	0.961526	−	0.274714i	$-0.0885833\pi$
$648$		0			0
$649$	5.71128	+	5.71128i	0.224187	+	0.224187i
$650$		0			0
$651$	−3.95240	+	3.52884i	−0.154907	+	0.138306i
$652$		0			0
$653$	−5.38622	−	2.23104i	−0.210779	−	0.0873075i	0.274796	−	0.961503i	$-0.411390\pi$
$653$	−5.38622	−	2.23104i	−0.210779	−	0.0873075i	−0.485575	+	0.874195i	$0.661390\pi$
$654$		0			0
$655$	−3.39025			−0.132468
$656$		0			0
$657$	−18.4424	−	23.1695i	−0.719507	−	0.903928i
$658$		0			0
$659$	7.05977	−	17.0438i	0.275010	−	0.663932i	−0.724674	−	0.689092i	$-0.758010\pi$
$659$	7.05977	−	17.0438i	0.275010	−	0.663932i	0.999683	+	0.0251602i	$0.00800958\pi$
$660$		0			0
$661$	−25.7857	+	10.6808i	−1.00295	+	0.415435i	−0.822878	−	0.568219i	$-0.807633\pi$
$661$	−25.7857	+	10.6808i	−1.00295	+	0.415435i	−0.180071	+	0.983654i	$0.557633\pi$
$662$		0			0
$663$	−2.02845	+	4.20720i	−0.0787786	+	0.163394i
$664$		0			0
$665$	−0.340489	−	0.340489i	−0.0132036	−	0.0132036i
$666$		0			0
$667$	62.5996	−	25.9296i	2.42387	−	1.00400i
$668$		0			0
$669$	0.631682	−	11.1570i	0.0244222	−	0.431355i
$670$		0			0
$671$	−32.0904			−1.23883
$672$		0			0
$673$	18.5829			0.716319			0.358160	−	0.933660i	$-0.383404\pi$
$673$	18.5829			0.716319			0.358160	+	0.933660i	$0.383404\pi$
$674$		0			0
$675$	−21.0481	+	14.8911i	−0.810142	+	0.573157i
$676$		0			0
$677$	−22.9138	+	9.49122i	−0.880650	+	0.364777i	−0.776749	−	0.629810i	$-0.783133\pi$
$677$	−22.9138	+	9.49122i	−0.880650	+	0.364777i	−0.103901	+	0.994588i	$0.533133\pi$
$678$		0			0
$679$	0.755613	+	0.755613i	0.0289978	+	0.0289978i
$680$		0			0
$681$	−5.34661	−	2.57781i	−0.204883	−	0.0987817i
$682$		0			0
$683$	−34.5480	+	14.3103i	−1.32194	+	0.547567i	−0.928346	−	0.371717i	$-0.878769\pi$
$683$	−34.5480	+	14.3103i	−1.32194	+	0.547567i	−0.393597	+	0.919283i	$0.628769\pi$
$684$		0			0
$685$	−1.13783	+	2.74696i	−0.0434741	+	0.104956i
$686$		0			0
$687$	−12.8946	−	36.9048i	−0.491960	−	1.40801i
$688$		0			0
$689$	−12.4246			−0.473340
$690$		0			0
$691$	−29.9717	−	12.4147i	−1.14018	−	0.472277i	−0.268948	−	0.963155i	$-0.586676\pi$
$691$	−29.9717	−	12.4147i	−1.14018	−	0.472277i	−0.871228	+	0.490878i	$0.836676\pi$
$692$		0			0
$693$	3.60965	+	1.99929i	0.137119	+	0.0759469i
$694$		0			0
$695$	−0.508841	−	0.508841i	−0.0193014	−	0.0193014i
$696$		0			0
$697$	−2.11673	+	2.11673i	−0.0801767	+	0.0801767i
$698$		0			0
$699$	28.3622	−	25.3227i	1.07276	−	0.957793i
$700$		0			0
$701$	−6.56454	+	15.8482i	−0.247939	+	0.598578i	−0.998029	−	0.0627582i	$-0.980010\pi$
$701$	−6.56454	+	15.8482i	−0.247939	+	0.598578i	0.750090	+	0.661336i	$0.230010\pi$
$702$		0			0
$703$		−	23.2154i		−	0.875585i
$704$		0			0
$705$	−0.0445491	−	0.127501i	−0.00167782	−	0.00480197i
$706$		0			0
$707$	−4.96350	−	2.05595i	−0.186672	−	0.0773219i
$708$		0			0
$709$	11.6861	+	28.2128i	0.438882	+	1.05955i	0.976336	+	0.216261i	$0.0693863\pi$
$709$	11.6861	+	28.2128i	0.438882	+	1.05955i	−0.537454	+	0.843293i	$0.680614\pi$
$710$		0			0
$711$	−23.8965	−	2.71463i	−0.896190	−	0.101806i
$712$		0			0
$713$	−37.6923	+	37.6923i	−1.41159	+	1.41159i
$714$		0			0
$715$	−0.839935	−	2.02778i	−0.0314118	−	0.0758348i
$716$		0			0
$717$	2.18662	−	38.6208i	0.0816607	−	1.44232i
$718$		0			0
$719$			32.6392i			1.21724i	0.793463	+	0.608619i	$0.208276\pi$
$719$			32.6392i			1.21724i	−0.793463	+	0.608619i	$0.791724\pi$
$720$		0			0
$721$		−	4.89649i		−	0.182355i
$722$		0			0
$723$	−0.982456	+	17.3525i	−0.0365379	+	0.645347i
$724$		0			0
$725$	18.0625	+	43.6067i	0.670825	+	1.61951i
$726$		0			0
$727$	11.8938	−	11.8938i	0.441118	−	0.441118i	−0.451270	−	0.892388i	$-0.649029\pi$
$727$	11.8938	−	11.8938i	0.441118	−	0.441118i	0.892388	+	0.451270i	$0.149029\pi$
$728$		0			0
$729$	25.4603	+	8.98742i	0.942974	+	0.332867i
$730$		0			0
$731$	−2.29598	−	5.54299i	−0.0849199	−	0.205015i
$732$		0			0
$733$	14.2498	+	5.90246i	0.526328	+	0.218012i	0.629994	−	0.776600i	$-0.283057\pi$
$733$	14.2498	+	5.90246i	0.526328	+	0.218012i	−0.103666	+	0.994612i	$0.533057\pi$
$734$		0			0
$735$	−0.761433	−	2.17925i	−0.0280859	−	0.0803827i
$736$		0			0
$737$			33.1135i			1.21975i
$738$		0			0
$739$	−1.65560	+	3.99698i	−0.0609024	+	0.147031i	−0.951401	−	0.307954i	$-0.900356\pi$
$739$	−1.65560	+	3.99698i	−0.0609024	+	0.147031i	0.890499	+	0.454986i	$0.150356\pi$
$740$		0			0
$741$	−26.0940	+	23.2976i	−0.958589	+	0.855859i
$742$		0			0
$743$	15.0005	−	15.0005i	0.550313	−	0.550313i	−0.376218	−	0.926531i	$-0.622776\pi$
$743$	15.0005	−	15.0005i	0.550313	−	0.550313i	0.926531	+	0.376218i	$0.122776\pi$
$744$		0			0
$745$	2.34240	+	2.34240i	0.0858188	+	0.0858188i
$746$		0			0
$747$	9.38625	−	16.9465i	0.343425	−	0.620040i
$748$		0			0
$749$	0.422781	+	0.175122i	0.0154481	+	0.00639880i
$750$		0			0
$751$	−10.9267			−0.398720			−0.199360	−	0.979926i	$-0.563886\pi$
$751$	−10.9267			−0.398720			−0.199360	+	0.979926i	$0.563886\pi$
$752$		0			0
$753$	−1.83745	−	5.25884i	−0.0669603	−	0.191643i
$754$		0			0
$755$	0.158519	−	0.382698i	0.00576908	−	0.0139278i
$756$		0			0
$757$	19.8634	−	8.22770i	0.721948	−	0.299041i	0.00870961	−	0.999962i	$-0.497228\pi$
$757$	19.8634	−	8.22770i	0.721948	−	0.299041i	0.713239	+	0.700921i	$0.247228\pi$
$758$		0			0
$759$	37.3933	+	18.0287i	1.35729	+	0.654402i
$760$		0			0
$761$	8.07215	+	8.07215i	0.292615	+	0.292615i	0.838112	−	0.545497i	$-0.183659\pi$
$761$	8.07215	+	8.07215i	0.292615	+	0.292615i	−0.545497	+	0.838112i	$0.683659\pi$
$762$		0			0
$763$	0.693996	−	0.287463i	0.0251243	−	0.0104068i
$764$		0			0
$765$	−0.453512	+	0.130206i	−0.0163968	+	0.00470759i
$766$		0			0
$767$	8.02795			0.289873
$768$		0			0
$769$	−7.21321			−0.260115			−0.130057	−	0.991506i	$-0.541516\pi$
$769$	−7.21321			−0.260115			−0.130057	+	0.991506i	$0.541516\pi$
$770$		0			0
$771$	2.23075	−	39.4003i	0.0803384	−	1.41897i
$772$		0			0
$773$	29.1506	−	12.0746i	1.04848	−	0.434293i	0.209128	−	0.977888i	$-0.432937\pi$
$773$	29.1506	−	12.0746i	1.04848	−	0.434293i	0.839347	+	0.543595i	$0.182937\pi$
$774$		0			0
$775$	−26.2564	−	26.2564i	−0.943157	−	0.943157i
$776$		0			0
$777$	−1.18209	+	2.45176i	−0.0424072	+	0.0879565i
$778$		0			0
$779$	−20.7133	+	8.57973i	−0.742131	+	0.307401i
$780$		0			0
$781$	−5.22185	+	12.6067i	−0.186853	+	0.451102i
$782$		0			0
$783$	26.3543	−	41.8152i	0.941827	−	1.49435i
$784$		0			0
$785$	−2.69382			−0.0961464
$786$		0			0
$787$	−34.5666	−	14.3179i	−1.23217	−	0.510380i	−0.330908	−	0.943663i	$-0.607355\pi$
$787$	−34.5666	−	14.3179i	−1.23217	−	0.510380i	−0.901258	+	0.433283i	$0.857355\pi$
$788$		0			0
$789$	−23.4890	+	20.9718i	−0.836231	+	0.746614i
$790$		0			0
$791$	−0.403347	−	0.403347i	−0.0143414	−	0.0143414i
$792$		0			0
$793$	−22.5536	+	22.5536i	−0.800902	+	0.800902i
$794$		0			0
$795$	−0.835930	−	0.936268i	−0.0296474	−	0.0332060i
$796$		0			0
$797$	0.403632	−	0.974454i	0.0142974	−	0.0345169i	−0.916570	−	0.399875i	$-0.869053\pi$
$797$	0.403632	−	0.974454i	0.0142974	−	0.0345169i	0.930867	+	0.365358i	$0.119053\pi$
$798$		0			0
$799$			0.322349i			0.0114039i
$800$		0			0
$801$	14.3553	+	18.0348i	0.507221	+	0.637229i
$802$		0			0
$803$	−30.6852	−	12.7102i	−1.08286	−	0.448535i
$804$		0			0
$805$	0.217350	+	0.524729i	0.00766058	+	0.0184943i
$806$		0			0
$807$	−19.8834	−	9.58656i	−0.699930	−	0.337463i
$808$		0			0
$809$	34.9129	−	34.9129i	1.22747	−	1.22747i	0.262555	−	0.964917i	$-0.415435\pi$
$809$	34.9129	−	34.9129i	1.22747	−	1.22747i	0.964917	−	0.262555i	$-0.0845653\pi$
$810$		0			0
$811$	13.0178	+	31.4278i	0.457117	+	1.10358i	0.969559	+	0.244857i	$0.0787411\pi$
$811$	13.0178	+	31.4278i	0.457117	+	1.10358i	−0.512442	+	0.858722i	$0.671259\pi$
$812$		0			0
$813$	20.1680	+	1.14186i	0.707324	+	0.0400469i
$814$		0			0
$815$		−	1.54182i		−	0.0540076i
$816$		0			0
$817$		−	44.9348i		−	1.57207i
$818$		0			0
$819$	3.94205	−	1.13178i	0.137746	−	0.0395476i
$820$		0			0
$821$	−3.16275	−	7.63556i	−0.110381	−	0.266483i	0.859031	−	0.511924i	$-0.171067\pi$
$821$	−3.16275	−	7.63556i	−0.110381	−	0.266483i	−0.969411	+	0.245441i	$0.921067\pi$
$822$		0			0
$823$	11.3941	−	11.3941i	0.397173	−	0.397173i	−0.480062	−	0.877235i	$-0.659386\pi$
$823$	11.3941	−	11.3941i	0.397173	−	0.397173i	0.877235	+	0.480062i	$0.159386\pi$
$824$		0			0
$825$	−12.5588	+	26.0481i	−0.437240	+	0.906878i
$826$		0			0
$827$	−8.32108	−	20.0889i	−0.289352	−	0.698558i	0.710635	−	0.703561i	$-0.248408\pi$
$827$	−8.32108	−	20.0889i	−0.289352	−	0.698558i	−0.999987	+	0.00500239i	$0.998408\pi$
$828$		0			0
$829$	7.00953	+	2.90344i	0.243451	+	0.100841i	0.501073	−	0.865405i	$-0.332939\pi$
$829$	7.00953	+	2.90344i	0.243451	+	0.100841i	−0.257622	+	0.966246i	$0.582939\pi$
$830$		0			0
$831$	−15.0242	+	5.24949i	−0.521184	+	0.182103i
$832$		0			0
$833$			5.50958i			0.190896i
$834$		0			0
$835$	−0.174292	+	0.420779i	−0.00603163	+	0.0145617i
$836$		0			0
$837$	−6.56601	+	38.3263i	−0.226955	+	1.32475i
$838$		0			0
$839$	−4.15538	+	4.15538i	−0.143460	+	0.143460i	−0.775189	−	0.631729i	$-0.782345\pi$
$839$	−4.15538	+	4.15538i	−0.143460	+	0.143460i	0.631729	+	0.775189i	$0.282345\pi$
$840$		0			0
$841$	−43.4756	−	43.4756i	−1.49916	−	1.49916i
$842$		0			0
$843$	36.3963	+	40.7649i	1.25355	+	1.40402i
$844$		0			0
$845$	0.327198	+	0.135530i	0.0112560	+	0.00466237i
$846$		0			0
$847$	0.131348			0.00451316
$848$		0			0
$849$	−17.6135	+	6.15418i	−0.604493	+	0.211211i
$850$		0			0
$851$	−10.4790	+	25.2984i	−0.359214	+	0.867219i
$852$		0			0
$853$	24.9124	−	10.3191i	0.852986	−	0.353318i	0.0870255	−	0.996206i	$-0.472264\pi$
$853$	24.9124	−	10.3191i	0.852986	−	0.353318i	0.765960	+	0.642888i	$0.222264\pi$
$854$		0			0
$855$	−3.51122	−	0.398872i	−0.120081	−	0.0136411i
$856$		0			0
$857$	−9.13231	−	9.13231i	−0.311954	−	0.311954i	0.533712	−	0.845666i	$-0.320797\pi$
$857$	−9.13231	−	9.13231i	−0.311954	−	0.311954i	−0.845666	+	0.533712i	$0.820797\pi$
$858$		0			0
$859$	−20.1392	+	8.34191i	−0.687139	+	0.284622i	−0.698808	−	0.715310i	$-0.746286\pi$
$859$	−20.1392	+	8.34191i	−0.687139	+	0.284622i	0.0116685	+	0.999932i	$0.496286\pi$
$860$		0			0
$861$	2.62438	+	0.148586i	0.0894388	+	0.00506380i
$862$		0			0
$863$	14.2708			0.485784			0.242892	−	0.970053i	$-0.421904\pi$
$863$	14.2708			0.485784			0.242892	+	0.970053i	$0.421904\pi$
$864$		0			0
$865$	2.07233			0.0704614
$866$		0			0
$867$	−28.2735	−	1.60077i	−0.960217	−	0.0543651i
$868$		0			0
$869$	−24.9208	+	10.3225i	−0.845380	+	0.350168i
$870$		0			0
$871$	23.2726	+	23.2726i	0.788563	+	0.788563i
$872$		0			0
$873$	7.79212	+	0.885178i	0.263723	+	0.0299587i
$874$		0			0
$875$	−0.733853	+	0.303972i	−0.0248088	+	0.0102761i
$876$		0			0
$877$	10.3328	−	24.9457i	0.348915	−	0.842355i	−0.647834	−	0.761782i	$-0.724325\pi$
$877$	10.3328	−	24.9457i	0.348915	−	0.842355i	0.996749	−	0.0805736i	$-0.0256752\pi$
$878$		0			0
$879$	−41.0793	+	14.3532i	−1.38557	+	0.484121i
$880$		0			0
$881$	3.06465			0.103251			0.0516254	−	0.998667i	$-0.483560\pi$
$881$	3.06465			0.103251			0.0516254	+	0.998667i	$0.483560\pi$
$882$		0			0
$883$	0.883537	+	0.365973i	0.0297334	+	0.0123160i	0.397501	−	0.917602i	$-0.369878\pi$
$883$	0.883537	+	0.365973i	0.0297334	+	0.0123160i	−0.367767	+	0.929918i	$0.619878\pi$
$884$		0			0
$885$	0.540122	+	0.604954i	0.0181560	+	0.0203353i
$886$		0			0
$887$	5.90816	+	5.90816i	0.198377	+	0.198377i	0.799304	−	0.600927i	$-0.205202\pi$
$887$	5.90816	+	5.90816i	0.198377	+	0.198377i	−0.600927	+	0.799304i	$0.705202\pi$
$888$		0			0
$889$	−1.98671	+	1.98671i	−0.0666320	+	0.0666320i
$890$		0			0
$891$	29.8638	−	5.01788i	1.00048	−	0.168105i
$892$		0			0
$893$	−0.923891	+	2.23047i	−0.0309168	+	0.0746398i
$894$		0			0
$895$			3.20155i			0.107016i
$896$		0			0
$897$	38.9515	−	13.6097i	1.30055	−	0.454415i
$898$		0			0
$899$	65.7654	+	27.2409i	2.19340	+	0.908536i
$900$		0			0
$901$	1.14639	+	2.76763i	0.0381918	+	0.0922031i
$902$		0			0
$903$	−2.28800	+	4.74554i	−0.0761400	+	0.157922i
$904$		0			0
$905$	−0.736562	+	0.736562i	−0.0244841	+	0.0244841i
$906$		0			0
$907$	−1.83330	−	4.42597i	−0.0608736	−	0.146962i	0.890516	−	0.454952i	$-0.150344\pi$
$907$	−1.83330	−	4.42597i	−0.0608736	−	0.146962i	−0.951390	+	0.307990i	$0.900344\pi$
$908$		0			0
$909$	−37.8964	+	10.8802i	−1.25694	+	0.360875i
$910$		0			0
$911$		−	29.4647i		−	0.976208i	−0.872786	−	0.488104i	$-0.837689\pi$
$911$		−	29.4647i		−	0.976208i	0.872786	−	0.488104i	$-0.162311\pi$
$912$		0			0
$913$		−	21.7274i		−	0.719073i
$914$		0			0
$915$	−3.21696	−	0.182136i	−0.106349	−	0.00602123i
$916$		0			0
$917$	−2.71903	−	6.56433i	−0.0897904	−	0.216773i
$918$		0			0
$919$	−14.4648	+	14.4648i	−0.477149	+	0.477149i	−0.904219	−	0.427070i	$-0.859546\pi$
$919$	−14.4648	+	14.4648i	−0.477149	+	0.477149i	0.427070	+	0.904219i	$0.359546\pi$
$920$		0			0
$921$	31.0695	+	14.9798i	1.02377	+	0.493600i
$922$		0			0
$923$	5.19016	+	12.5302i	0.170836	+	0.412435i
$924$		0			0
$925$	−17.6228	−	7.29962i	−0.579435	−	0.240010i
$926$		0			0
$927$	−22.3790	−	28.1151i	−0.735023	−	0.923421i
$928$		0			0
$929$		−	30.4237i		−	0.998170i	−0.866553	−	0.499085i	$-0.833670\pi$
$929$		−	30.4237i		−	0.998170i	0.866553	−	0.499085i	$-0.166330\pi$
$930$		0			0
$931$	−15.7911	+	38.1231i	−0.517533	+	1.24943i
$932$		0			0
$933$	1.53099	+	1.71476i	0.0501225	+	0.0561387i
$934$		0			0
$935$	−0.374197	+	0.374197i	−0.0122376	+	0.0122376i
$936$		0			0
$937$	17.7838	+	17.7838i	0.580972	+	0.580972i	0.935170	−	0.354199i	$-0.115246\pi$
$937$	17.7838	+	17.7838i	0.580972	+	0.580972i	−0.354199	+	0.935170i	$0.615246\pi$
$938$		0			0
$939$	20.6199	−	18.4101i	0.672903	−	0.600790i
$940$		0			0
$941$	11.2523	+	4.66086i	0.366815	+	0.151940i	0.558474	−	0.829522i	$-0.311387\pi$
$941$	11.2523	+	4.66086i	0.366815	+	0.151940i	−0.191660	+	0.981461i	$0.561387\pi$
$942$		0			0
$943$	26.4446			0.861154
$944$		0			0
$945$	0.350508	+	0.220910i	0.0114020	+	0.00718621i
$946$		0			0
$947$	15.4459	−	37.2898i	0.501925	−	1.21175i	−0.446509	−	0.894779i	$-0.647333\pi$
$947$	15.4459	−	37.2898i	0.501925	−	1.21175i	0.948434	−	0.316975i	$-0.102667\pi$
$948$		0			0
$949$	−30.4990	+	12.6331i	−0.990040	+	0.410088i
$950$		0			0
$951$	14.8876	−	30.8783i	0.482763	−	1.00130i
$952$		0			0
$953$	−35.9782	−	35.9782i	−1.16545	−	1.16545i	−0.983264	−	0.182184i	$-0.941683\pi$
$953$	−35.9782	−	35.9782i	−1.16545	−	1.16545i	−0.182184	−	0.983264i	$-0.558317\pi$
$954$		0			0
$955$	−2.09858	+	0.869261i	−0.0679085	+	0.0281286i
$956$		0			0
$957$	3.13365	−	55.3477i	0.101297	−	1.78914i
$958$		0			0
$959$	−6.23131			−0.201219
$960$		0			0
$961$	−25.0007			−0.806476
$962$		0			0
$963$	3.22794	−	0.926757i	0.104019	−	0.0298643i
$964$		0			0
$965$	−1.08704	+	0.450266i	−0.0349930	+	0.0144946i
$966$		0			0
$967$	−23.1751	−	23.1751i	−0.745262	−	0.745262i	0.228324	−	0.973585i	$-0.426676\pi$
$967$	−23.1751	−	23.1751i	−0.745262	−	0.745262i	−0.973585	+	0.228324i	$0.926676\pi$
$968$		0			0
$969$	7.59726	+	3.66293i	0.244059	+	0.117670i
$970$		0			0
$971$	−33.6938	+	13.9564i	−1.08128	+	0.447883i	−0.850960	−	0.525231i	$-0.823979\pi$
$971$	−33.6938	+	13.9564i	−1.08128	+	0.447883i	−0.230325	+	0.973114i	$0.573979\pi$
$972$		0			0
$973$	0.577137	−	1.39333i	0.0185022	−	0.0446682i
$974$		0			0
$975$	9.48049	+	27.1335i	0.303619	+	0.868967i
$976$		0			0
$977$	42.1411			1.34821			0.674106	−	0.738635i	$-0.264529\pi$
$977$	42.1411			1.34821			0.674106	+	0.738635i	$0.264529\pi$
$978$		0			0
$979$	23.8850	+	9.89348i	0.763367	+	0.316197i
$980$		0			0
$981$	2.67102	−	4.82243i	0.0852792	−	0.153968i
$982$		0			0
$983$	−27.4787	−	27.4787i	−0.876436	−	0.876436i	0.116728	−	0.993164i	$-0.462759\pi$
$983$	−27.4787	−	27.4787i	−0.876436	−	0.876436i	−0.993164	+	0.116728i	$0.962759\pi$
$984$		0			0
$985$	0.0868009	−	0.0868009i	0.00276571	−	0.00276571i
$986$		0			0
$987$	0.211143	−	0.188515i	0.00672076	−	0.00600051i
$988$		0			0
$989$	−20.2827	+	48.9667i	−0.644951	+	1.55705i
$990$		0			0
$991$			42.6090i			1.35352i	0.736204	+	0.676760i	$0.236616\pi$
$991$			42.6090i			1.35352i	−0.736204	+	0.676760i	$0.763384\pi$
$992$		0			0
$993$	−7.15560	−	20.4796i	−0.227076	−	0.649899i
$994$		0			0
$995$	3.46777	+	1.43640i	0.109936	+	0.0455368i
$996$		0			0
$997$	5.53889	+	13.3721i	0.175418	+	0.423497i	0.986995	−	0.160748i	$-0.0513906\pi$
$997$	5.53889	+	13.3721i	0.175418	+	0.423497i	−0.811577	+	0.584245i	$0.801391\pi$
$998$		0			0
$999$	4.41816	+	19.4804i	0.139785	+	0.616332i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.o.a.95.14		56
3.2	odd	2	inner	768.2.o.a.95.4		56
4.3	odd	2		768.2.o.b.95.1		56
8.3	odd	2		96.2.o.a.35.1	yes	56
8.5	even	2		384.2.o.a.47.1		56
12.11	even	2		768.2.o.b.95.11		56
24.5	odd	2		384.2.o.a.47.11		56
24.11	even	2		96.2.o.a.35.14	yes	56
32.5	even	8		96.2.o.a.11.14	yes	56
32.11	odd	8	inner	768.2.o.a.671.4		56
32.21	even	8		768.2.o.b.671.11		56
32.27	odd	8		384.2.o.a.335.11		56
96.5	odd	8		96.2.o.a.11.1	✓	56
96.11	even	8	inner	768.2.o.a.671.14		56
96.53	odd	8		768.2.o.b.671.1		56
96.59	even	8		384.2.o.a.335.1		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.o.a.11.1	✓	56	96.5	odd	8
96.2.o.a.11.14	yes	56	32.5	even	8
96.2.o.a.35.1	yes	56	8.3	odd	2
96.2.o.a.35.14	yes	56	24.11	even	2
384.2.o.a.47.1		56	8.5	even	2
384.2.o.a.47.11		56	24.5	odd	2
384.2.o.a.335.1		56	96.59	even	8
384.2.o.a.335.11		56	32.27	odd	8
768.2.o.a.95.4		56	3.2	odd	2	inner
768.2.o.a.95.14		56	1.1	even	1	trivial
768.2.o.a.671.4		56	32.11	odd	8	inner
768.2.o.a.671.14		56	96.11	even	8	inner
768.2.o.b.95.1		56	4.3	odd	2
768.2.o.b.95.11		56	12.11	even	2
768.2.o.b.671.1		56	96.53	odd	8
768.2.o.b.671.11		56	32.21	even	8

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:	\( N \)	\(=\)	\( 768 = 2^{8} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	768.o (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.72928 + 0.0979076i) q^{3} +(0.180206 - 0.0746437i) q^{5} +(0.289055 + 0.289055i) q^{7} +(2.98083 + 0.338620i) q^{9} +O(q^{10})\)	\(q+(1.72928 + 0.0979076i) q^{3} +(0.180206 - 0.0746437i) q^{5} +(0.289055 + 0.289055i) q^{7} +(2.98083 + 0.338620i) q^{9} +(3.10859 - 1.28762i) q^{11} +(1.27981 - 3.08973i) q^{13} +(0.318935 - 0.111436i) q^{15} -0.806332 q^{17} +(-5.57935 - 2.31104i) q^{19} +(0.471557 + 0.528159i) q^{21} +(5.03681 + 5.03681i) q^{23} +(-3.50863 + 3.50863i) q^{25} +(5.12154 + 0.877415i) q^{27} +(3.64020 - 8.78822i) q^{29} +7.48336i q^{31} +(5.50170 - 1.92230i) q^{33} +(0.0736656 + 0.0305133i) q^{35} +(1.47112 + 3.55159i) q^{37} +(2.51565 - 5.21770i) q^{39} +(2.62513 - 2.62513i) q^{41} +(2.84744 + 6.87432i) q^{43} +(0.562438 - 0.161479i) q^{45} -0.399772i q^{47} -6.83289i q^{49} +(-1.39438 - 0.0789461i) q^{51} +(-1.42173 - 3.43237i) q^{53} +(0.464073 - 0.464073i) q^{55} +(-9.42200 - 4.54271i) q^{57} +(0.918629 + 2.21777i) q^{59} +(-8.81133 - 3.64977i) q^{61} +(0.763745 + 0.959504i) q^{63} -0.652316i q^{65} +(-3.76613 + 9.09225i) q^{67} +(8.21692 + 9.20321i) q^{69} +(-2.86762 + 2.86762i) q^{71} +(-6.97993 - 6.97993i) q^{73} +(-6.41093 + 5.72389i) q^{75} +(1.27075 + 0.526361i) q^{77} -8.01674 q^{79} +(8.77067 + 2.01873i) q^{81} +(2.47115 - 5.96589i) q^{83} +(-0.145306 + 0.0601876i) q^{85} +(7.15536 - 14.8409i) q^{87} +(5.43308 + 5.43308i) q^{89} +(1.26304 - 0.523167i) q^{91} +(-0.732678 + 12.9408i) q^{93} -1.17794 q^{95} +2.61408 q^{97} +(9.70219 - 2.78555i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 4 q^{3} + 8 q^{7} - 4 q^{9}+O(q^{10}) \) 56 * q - 4 * q^3 + 8 * q^7 - 4 * q^9	\( 56 q - 4 q^{3} + 8 q^{7} - 4 q^{9} + 8 q^{13} + 8 q^{15} - 8 q^{19} + 4 q^{21} - 8 q^{25} - 28 q^{27} - 8 q^{33} + 8 q^{37} + 28 q^{39} - 8 q^{43} + 4 q^{45} - 16 q^{51} - 24 q^{55} - 4 q^{57} + 40 q^{61} + 56 q^{67} + 4 q^{69} - 8 q^{73} + 16 q^{75} - 16 q^{79} + 48 q^{85} - 52 q^{87} + 40 q^{91} - 8 q^{93} - 16 q^{97} + 60 q^{99}+O(q^{100}) \) 56 * q - 4 * q^3 + 8 * q^7 - 4 * q^9 + 8 * q^13 + 8 * q^15 - 8 * q^19 + 4 * q^21 - 8 * q^25 - 28 * q^27 - 8 * q^33 + 8 * q^37 + 28 * q^39 - 8 * q^43 + 4 * q^45 - 16 * q^51 - 24 * q^55 - 4 * q^57 + 40 * q^61 + 56 * q^67 + 4 * q^69 - 8 * q^73 + 16 * q^75 - 16 * q^79 + 48 * q^85 - 52 * q^87 + 40 * q^91 - 8 * q^93 - 16 * q^97 + 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more