LMFDB - Embedded newform 512.2.g.h.65.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [512,2,Mod(65,512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(512, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("512.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.g (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:	$4.08834058349$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{8})$
Coefficient field:	8.0.18939904.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 $ x^8 - 4x^7 + 14x^6 - 28x^5 + 43x^4 - 44x^3 + 30x^2 - 12*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			65.2
Root			$0.500000 + 1.44392i$ of defining polynomial
Character	$\chi$	$=$	512.65
Dual form			512.2.g.h.449.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.529706 - 1.27882i) q^{3} +(1.70711 - 0.707107i) q^{5} +(2.74912 - 2.74912i) q^{7} +(0.766519 + 0.766519i) q^{9} +O(q^{10})$	\(q+(0.529706 - 1.27882i) q^{3} +(1.70711 - 0.707107i) q^{5} +(2.74912 - 2.74912i) q^{7} +(0.766519 + 0.766519i) q^{9} +(0.0560803 + 0.135390i) q^{11} +(-2.85054 - 1.18073i) q^{13} -2.55765i q^{15} +6.44549i q^{17} +(-1.94392 - 0.805198i) q^{19} +(-2.05941 - 4.97186i) q^{21} +(-0.749118 - 0.749118i) q^{23} +(-1.12132 + 1.12132i) q^{25} +(5.22274 - 2.16333i) q^{27} +(1.79113 - 4.32417i) q^{29} +1.17157 q^{31} +0.202846 q^{33} +(2.74912 - 6.63696i) q^{35} +(-4.18073 + 1.73172i) q^{37} +(-3.01990 + 3.01990i) q^{39} +(2.49824 + 2.49824i) q^{41} +(-2.52971 - 6.10725i) q^{43} +(1.85054 + 0.766519i) q^{45} -2.66981i q^{47} -8.11529i q^{49} +(8.24264 + 3.41421i) q^{51} +(0.682497 + 1.64769i) q^{53} +(0.191470 + 0.191470i) q^{55} +(-2.05941 + 2.05941i) q^{57} +(-3.47029 + 1.43744i) q^{59} +(-1.43633 + 3.46760i) q^{61} +4.21450 q^{63} -5.70108 q^{65} +(-5.83176 + 14.0791i) q^{67} +(-1.35480 + 0.561177i) q^{69} +(3.40950 - 3.40950i) q^{71} +(0.442353 + 0.442353i) q^{73} +(0.840001 + 2.02794i) q^{75} +(0.526374 + 0.218031i) q^{77} +7.07550i q^{79} -4.57283i q^{81} +(-7.23931 - 2.99862i) q^{83} +(4.55765 + 11.0031i) q^{85} +(-4.58107 - 4.58107i) q^{87} +(4.21803 - 4.21803i) q^{89} +(-11.0824 + 4.59050i) q^{91} +(0.620589 - 1.49824i) q^{93} -3.88784 q^{95} +10.3267 q^{97} +(-0.0607923 + 0.146766i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} + 8 q^{5} + 8 q^{7}+O(q^{10}) $ 8 * q + 4 * q^3 + 8 * q^5 + 8 * q^7	$ 8 q + 4 q^{3} + 8 q^{5} + 8 q^{7} + 12 q^{11} - 4 q^{19} - 16 q^{21} + 8 q^{23} + 8 q^{25} + 16 q^{27} - 8 q^{29} + 32 q^{31} - 16 q^{33} + 8 q^{35} - 16 q^{37} - 16 q^{39} - 8 q^{41} - 20 q^{43} - 8 q^{45} + 32 q^{51} + 16 q^{53} + 16 q^{55} - 16 q^{57} - 28 q^{59} - 40 q^{63} - 12 q^{67} + 24 q^{71} + 32 q^{73} + 20 q^{75} + 16 q^{77} - 36 q^{83} + 8 q^{85} - 56 q^{87} + 16 q^{89} + 32 q^{93} - 8 q^{95} + 32 q^{97} - 4 q^{99}+O(q^{100}) $ 8 * q + 4 * q^3 + 8 * q^5 + 8 * q^7 + 12 * q^11 - 4 * q^19 - 16 * q^21 + 8 * q^23 + 8 * q^25 + 16 * q^27 - 8 * q^29 + 32 * q^31 - 16 * q^33 + 8 * q^35 - 16 * q^37 - 16 * q^39 - 8 * q^41 - 20 * q^43 - 8 * q^45 + 32 * q^51 + 16 * q^53 + 16 * q^55 - 16 * q^57 - 28 * q^59 - 40 * q^63 - 12 * q^67 + 24 * q^71 + 32 * q^73 + 20 * q^75 + 16 * q^77 - 36 * q^83 + 8 * q^85 - 56 * q^87 + 16 * q^89 + 32 * q^93 - 8 * q^95 + 32 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.529706	−	1.27882i	0.305826	−	0.738329i	−0.694005	−	0.719970i	$-0.744156\pi$
$3$	0.529706	−	1.27882i	0.305826	−	0.738329i	0.999831	−	0.0183595i	$-0.00584433\pi$
$4$		0			0
$5$	1.70711	−	0.707107i	0.763441	−	0.316228i	0.0332288	−	0.999448i	$-0.489421\pi$
$5$	1.70711	−	0.707107i	0.763441	−	0.316228i	0.730213	+	0.683220i	$0.239421\pi$
$6$		0			0
$7$	2.74912	−	2.74912i	1.03907	−	1.03907i	0.0398636	−	0.999205i	$-0.487308\pi$
$7$	2.74912	−	2.74912i	1.03907	−	1.03907i	0.999205	−	0.0398636i	$-0.0126924\pi$
$8$		0			0
$9$	0.766519	+	0.766519i	0.255506	+	0.255506i
$10$		0			0
$11$	0.0560803	+	0.135390i	0.0169089	+	0.0408216i	0.932108	−	0.362179i	$-0.117967\pi$
$11$	0.0560803	+	0.135390i	0.0169089	+	0.0408216i	−0.915200	+	0.403001i	$0.867967\pi$
$12$		0			0
$13$	−2.85054	−	1.18073i	−0.790598	−	0.327476i	−0.0494138	−	0.998778i	$-0.515735\pi$
$13$	−2.85054	−	1.18073i	−0.790598	−	0.327476i	−0.741184	+	0.671302i	$0.765735\pi$
$14$		0			0
$15$		−	2.55765i		−	0.660382i
$16$		0			0
$17$			6.44549i			1.56326i	0.623742	+	0.781630i	$0.285611\pi$
$17$			6.44549i			1.56326i	−0.623742	+	0.781630i	$0.714389\pi$
$18$		0			0
$19$	−1.94392	−	0.805198i	−0.445966	−	0.184725i	0.148387	−	0.988929i	$-0.452592\pi$
$19$	−1.94392	−	0.805198i	−0.445966	−	0.184725i	−0.594353	+	0.804204i	$0.702592\pi$
$20$		0			0
$21$	−2.05941	−	4.97186i	−0.449401	−	1.08495i
$22$		0			0
$23$	−0.749118	−	0.749118i	−0.156202	−	0.156202i	0.624679	−	0.780881i	$-0.285230\pi$
$23$	−0.749118	−	0.749118i	−0.156202	−	0.156202i	−0.780881	+	0.624679i	$0.785230\pi$
$24$		0			0
$25$	−1.12132	+	1.12132i	−0.224264	+	0.224264i
$26$		0			0
$27$	5.22274	−	2.16333i	1.00512	−	0.416333i
$28$		0			0
$29$	1.79113	−	4.32417i	0.332604	−	0.802978i	−0.665780	−	0.746148i	$-0.731901\pi$
$29$	1.79113	−	4.32417i	0.332604	−	0.802978i	0.998384	−	0.0568292i	$-0.0180990\pi$
$30$		0			0
$31$	1.17157			0.210421			0.105210	−	0.994450i	$-0.466448\pi$
$31$	1.17157			0.210421			0.105210	+	0.994450i	$0.466448\pi$
$32$		0			0
$33$	0.202846			0.0353109
$34$		0			0
$35$	2.74912	−	6.63696i	0.464686	−	1.12185i
$36$		0			0
$37$	−4.18073	+	1.73172i	−0.687308	+	0.284692i	−0.698878	−	0.715241i	$-0.746317\pi$
$37$	−4.18073	+	1.73172i	−0.687308	+	0.284692i	0.0115700	+	0.999933i	$0.496317\pi$
$38$		0			0
$39$	−3.01990	+	3.01990i	−0.483571	+	0.483571i
$40$		0			0
$41$	2.49824	+	2.49824i	0.390159	+	0.390159i	0.874744	−	0.484585i	$-0.161029\pi$
$41$	2.49824	+	2.49824i	0.390159	+	0.390159i	−0.484585	+	0.874744i	$0.661029\pi$
$42$		0			0
$43$	−2.52971	−	6.10725i	−0.385777	−	0.931347i	−0.990824	−	0.135158i	$-0.956846\pi$
$43$	−2.52971	−	6.10725i	−0.385777	−	0.931347i	0.605048	−	0.796189i	$-0.293154\pi$
$44$		0			0
$45$	1.85054	+	0.766519i	0.275862	+	0.114266i
$46$		0			0
$47$		−	2.66981i		−	0.389432i	−0.980860	−	0.194716i	$-0.937622\pi$
$47$		−	2.66981i		−	0.389432i	0.980860	−	0.194716i	$-0.0623784\pi$
$48$		0			0
$49$		−	8.11529i		−	1.15933i
$50$		0			0
$51$	8.24264	+	3.41421i	1.15420	+	0.478086i
$52$		0			0
$53$	0.682497	+	1.64769i	0.0937482	+	0.226328i	0.963797	−	0.266638i	$-0.0859127\pi$
$53$	0.682497	+	1.64769i	0.0937482	+	0.226328i	−0.870049	+	0.492966i	$0.835913\pi$
$54$		0			0
$55$	0.191470	+	0.191470i	0.0258178	+	0.0258178i
$56$		0			0
$57$	−2.05941	+	2.05941i	−0.272776	+	0.272776i
$58$		0			0
$59$	−3.47029	+	1.43744i	−0.451794	+	0.187139i	−0.596965	−	0.802267i	$-0.703627\pi$
$59$	−3.47029	+	1.43744i	−0.451794	+	0.187139i	0.145171	+	0.989407i	$0.453627\pi$
$60$		0			0
$61$	−1.43633	+	3.46760i	−0.183903	+	0.443981i	−0.988764	−	0.149482i	$-0.952239\pi$
$61$	−1.43633	+	3.46760i	−0.183903	+	0.443981i	0.804862	+	0.593462i	$0.202239\pi$
$62$		0			0
$63$	4.21450			0.530977
$64$		0			0
$65$	−5.70108			−0.707132
$66$		0			0
$67$	−5.83176	+	14.0791i	−0.712463	+	1.72004i	−0.0187090	+	0.999825i	$0.505956\pi$
$67$	−5.83176	+	14.0791i	−0.712463	+	1.72004i	−0.693754	+	0.720212i	$0.744044\pi$
$68$		0			0
$69$	−1.35480	+	0.561177i	−0.163099	+	0.0675578i
$70$		0			0
$71$	3.40950	−	3.40950i	0.404633	−	0.404633i	−0.475229	−	0.879862i	$-0.657635\pi$
$71$	3.40950	−	3.40950i	0.404633	−	0.404633i	0.879862	+	0.475229i	$0.157635\pi$
$72$		0			0
$73$	0.442353	+	0.442353i	0.0517735	+	0.0517735i	0.732520	−	0.680746i	$-0.238344\pi$
$73$	0.442353	+	0.442353i	0.0517735	+	0.0517735i	−0.680746	+	0.732520i	$0.738344\pi$
$74$		0			0
$75$	0.840001	+	2.02794i	0.0969949	+	0.234166i
$76$		0			0
$77$	0.526374	+	0.218031i	0.0599859	+	0.0248470i
$78$		0			0
$79$			7.07550i			0.796056i	0.917373	+	0.398028i	$0.130305\pi$
$79$			7.07550i			0.796056i	−0.917373	+	0.398028i	$0.869695\pi$
$80$		0			0
$81$		−	4.57283i		−	0.508093i
$82$		0			0
$83$	−7.23931	−	2.99862i	−0.794617	−	0.329141i	−0.0518190	−	0.998656i	$-0.516502\pi$
$83$	−7.23931	−	2.99862i	−0.794617	−	0.329141i	−0.742798	+	0.669515i	$0.766502\pi$
$84$		0			0
$85$	4.55765	+	11.0031i	0.494346	+	1.19346i
$86$		0			0
$87$	−4.58107	−	4.58107i	−0.491143	−	0.491143i
$88$		0			0
$89$	4.21803	−	4.21803i	0.447110	−	0.447110i	−0.447282	−	0.894393i	$-0.647608\pi$
$89$	4.21803	−	4.21803i	0.447110	−	0.447110i	0.894393	+	0.447282i	$0.147608\pi$
$90$		0			0
$91$	−11.0824	+	4.59050i	−1.16176	+	0.481215i
$92$		0			0
$93$	0.620589	−	1.49824i	0.0643521	−	0.155360i
$94$		0			0
$95$	−3.88784			−0.398884
$96$		0			0
$97$	10.3267			1.04851			0.524257	−	0.851560i	$-0.324343\pi$
$97$	10.3267			1.04851			0.524257	+	0.851560i	$0.324343\pi$
$98$		0			0
$99$	−0.0607923	+	0.146766i	−0.00610986	+	0.0147505i
$100$		0			0
$101$	10.4234	−	4.31750i	1.03716	−	0.429608i	0.201871	−	0.979412i	$-0.435298\pi$
$101$	10.4234	−	4.31750i	1.03716	−	0.429608i	0.835293	+	0.549805i	$0.185298\pi$
$102$		0			0
$103$	−13.3134	+	13.3134i	−1.31181	+	1.31181i	−0.391732	+	0.920080i	$0.628124\pi$
$103$	−13.3134	+	13.3134i	−1.31181	+	1.31181i	−0.920080	+	0.391732i	$0.871876\pi$
$104$		0			0
$105$	−7.03127	−	7.03127i	−0.686182	−	0.686182i
$106$		0			0
$107$	5.48861	+	13.2507i	0.530604	+	1.28099i	0.931124	+	0.364704i	$0.118830\pi$
$107$	5.48861	+	13.2507i	0.530604	+	1.28099i	−0.400519	+	0.916288i	$0.631170\pi$
$108$		0			0
$109$	11.7697	+	4.87515i	1.12733	+	0.466955i	0.866872	−	0.498531i	$-0.166127\pi$
$109$	11.7697	+	4.87515i	1.12733	+	0.466955i	0.260456	+	0.965486i	$0.416127\pi$
$110$		0			0
$111$			6.26372i			0.594526i
$112$		0			0
$113$			5.88118i			0.553254i	0.960977	+	0.276627i	$0.0892167\pi$
$113$			5.88118i			0.553254i	−0.960977	+	0.276627i	$0.910783\pi$
$114$		0			0
$115$	−1.80853	−	0.749118i	−0.168646	−	0.0698556i
$116$		0			0
$117$	−1.27994	−	3.09005i	−0.118330	−	0.285675i
$118$		0			0
$119$	17.7194	+	17.7194i	1.62433	+	1.62433i
$120$		0			0
$121$	7.76299	−	7.76299i	0.705726	−	0.705726i
$122$		0			0
$123$	4.51813	−	1.87147i	0.407386	−	0.168745i
$124$		0			0
$125$	−4.65685	+	11.2426i	−0.416522	+	1.00557i
$126$		0			0
$127$	−15.4022			−1.36672			−0.683360	−	0.730081i	$-0.739482\pi$
$127$	−15.4022			−1.36672			−0.683360	+	0.730081i	$0.739482\pi$
$128$		0			0
$129$	−9.15010			−0.805621
$130$		0			0
$131$	−1.22765	+	2.96382i	−0.107261	+	0.258950i	−0.968392	−	0.249432i	$-0.919756\pi$
$131$	−1.22765	+	2.96382i	−0.107261	+	0.258950i	0.861132	+	0.508382i	$0.169756\pi$
$132$		0			0
$133$	−7.55765	+	3.13048i	−0.655331	+	0.271447i
$134$		0			0
$135$	7.38607	−	7.38607i	0.635692	−	0.635692i
$136$		0			0
$137$	−10.7757	−	10.7757i	−0.920628	−	0.920628i	0.0764454	−	0.997074i	$-0.475643\pi$
$137$	−10.7757	−	10.7757i	−0.920628	−	0.920628i	−0.997074	+	0.0764454i	$0.975643\pi$
$138$		0			0
$139$	1.98148	+	4.78372i	0.168067	+	0.405750i	0.985363	−	0.170468i	$-0.0545279\pi$
$139$	1.98148	+	4.78372i	0.168067	+	0.405750i	−0.817296	+	0.576218i	$0.804528\pi$
$140$		0			0
$141$	−3.41421	−	1.41421i	−0.287529	−	0.119098i
$142$		0			0
$143$		−	0.452150i		−	0.0378107i
$144$		0			0
$145$		−	8.64833i		−	0.718205i
$146$		0			0
$147$	−10.3780	−	4.29872i	−0.855966	−	0.354553i
$148$		0			0
$149$	1.79113	+	4.32417i	0.146735	+	0.354250i	0.980109	−	0.198460i	$-0.0635940\pi$
$149$	1.79113	+	4.32417i	0.146735	+	0.354250i	−0.833374	+	0.552709i	$0.813594\pi$
$150$		0			0
$151$	−13.2344	−	13.2344i	−1.07700	−	1.07700i	−0.996777	−	0.0802232i	$-0.974437\pi$
$151$	−13.2344	−	13.2344i	−1.07700	−	1.07700i	−0.0802232	−	0.996777i	$-0.525563\pi$
$152$		0			0
$153$	−4.94059	+	4.94059i	−0.399423	+	0.399423i
$154$		0			0
$155$	2.00000	−	0.828427i	0.160644	−	0.0665409i
$156$		0			0
$157$	−6.60790	+	15.9529i	−0.527368	+	1.27318i	0.405874	+	0.913929i	$0.366967\pi$
$157$	−6.60790	+	15.9529i	−0.527368	+	1.27318i	−0.933242	+	0.359249i	$0.883033\pi$
$158$		0			0
$159$	2.46863			0.195775
$160$		0			0
$161$	−4.11882			−0.324609
$162$		0			0
$163$	4.41088	−	10.6488i	0.345487	−	0.834079i	−0.651654	−	0.758516i	$-0.725925\pi$
$163$	4.41088	−	10.6488i	0.345487	−	0.834079i	0.997141	−	0.0755629i	$-0.0240754\pi$
$164$		0			0
$165$	0.346280	−	0.143434i	0.0269578	−	0.0111663i
$166$		0			0
$167$	2.98677	−	2.98677i	0.231123	−	0.231123i	−0.582038	−	0.813161i	$-0.697745\pi$
$167$	2.98677	−	2.98677i	0.231123	−	0.231123i	0.813161	+	0.582038i	$0.197745\pi$
$168$		0			0
$169$	−2.46094	−	2.46094i	−0.189303	−	0.189303i
$170$		0			0
$171$	−0.872852	−	2.10725i	−0.0667486	−	0.161145i
$172$		0			0
$173$	−18.9529	−	7.85054i	−1.44096	−	0.596866i	−0.480930	−	0.876759i	$-0.659701\pi$
$173$	−18.9529	−	7.85054i	−1.44096	−	0.596866i	−0.960031	+	0.279894i	$0.909701\pi$
$174$		0			0
$175$			6.16528i			0.466052i
$176$		0			0
$177$			5.19932i			0.390805i
$178$		0			0
$179$	23.1897	+	9.60549i	1.73328	+	0.717948i	0.999246	+	0.0388344i	$0.0123645\pi$
$179$	23.1897	+	9.60549i	1.73328	+	0.717948i	0.734033	+	0.679113i	$0.237636\pi$
$180$		0			0
$181$	0.778175	+	1.87868i	0.0578413	+	0.139641i	0.950158	−	0.311768i	$-0.100921\pi$
$181$	0.778175	+	1.87868i	0.0578413	+	0.139641i	−0.892317	+	0.451410i	$0.850921\pi$
$182$		0			0
$183$	3.67362	+	3.67362i	0.271562	+	0.271562i
$184$		0			0
$185$	−5.91245	+	5.91245i	−0.434692	+	0.434692i
$186$		0			0
$187$	−0.872654	+	0.361465i	−0.0638148	+	0.0264329i
$188$		0			0
$189$	8.41068	−	20.3052i	0.611787	−	1.47699i
$190$		0			0
$191$	9.05902			0.655487			0.327744	−	0.944767i	$-0.393712\pi$
$191$	9.05902			0.655487			0.327744	+	0.944767i	$0.393712\pi$
$192$		0			0
$193$	6.24707			0.449674			0.224837	−	0.974396i	$-0.427815\pi$
$193$	6.24707			0.449674			0.224837	+	0.974396i	$0.427815\pi$
$194$		0			0
$195$	−3.01990	+	7.29068i	−0.216259	+	0.522096i
$196$		0			0
$197$	4.37691	−	1.81298i	0.311842	−	0.129169i	−0.221273	−	0.975212i	$-0.571021\pi$
$197$	4.37691	−	1.81298i	0.311842	−	0.129169i	0.533115	+	0.846043i	$0.321021\pi$
$198$		0			0
$199$	−6.14186	+	6.14186i	−0.435385	+	0.435385i	−0.890455	−	0.455071i	$-0.849614\pi$
$199$	−6.14186	+	6.14186i	−0.435385	+	0.435385i	0.455071	+	0.890455i	$0.349614\pi$
$200$		0			0
$201$	14.9156	+	14.9156i	1.05206	+	1.05206i
$202$		0			0
$203$	−6.96362	−	16.8117i	−0.488750	−	1.17995i
$204$		0			0
$205$	6.03127	+	2.49824i	0.421242	+	0.174484i
$206$		0			0
$207$		−	1.14843i		−	0.0798211i
$208$		0			0
$209$		−	0.308343i		−	0.0213285i
$210$		0			0
$211$	−12.5923	−	5.21588i	−0.866886	−	0.359076i	−0.0954895	−	0.995430i	$-0.530442\pi$
$211$	−12.5923	−	5.21588i	−0.866886	−	0.359076i	−0.771397	+	0.636354i	$0.780442\pi$
$212$		0			0
$213$	−2.55412	−	6.16619i	−0.175005	−	0.422500i
$214$		0			0
$215$	−8.63696	−	8.63696i	−0.589036	−	0.589036i
$216$		0			0
$217$	3.22079	−	3.22079i	0.218642	−	0.218642i
$218$		0			0
$219$	0.800008	−	0.331374i	0.0540595	−	0.0223922i
$220$		0			0
$221$	7.61040	−	18.3731i	0.511931	−	1.23591i
$222$		0			0
$223$	−0.960579			−0.0643251			−0.0321626	−	0.999483i	$-0.510239\pi$
$223$	−0.960579			−0.0643251			−0.0321626	+	0.999483i	$0.510239\pi$
$224$		0			0
$225$	−1.71903			−0.114602
$226$		0			0
$227$	5.86932	−	14.1698i	0.389561	−	0.940482i	−0.600472	−	0.799646i	$-0.705021\pi$
$227$	5.86932	−	14.1698i	0.389561	−	0.940482i	0.990033	−	0.140837i	$-0.0449793\pi$
$228$		0			0
$229$	−4.35544	+	1.80408i	−0.287816	+	0.119217i	−0.521920	−	0.852994i	$-0.674784\pi$
$229$	−4.35544	+	1.80408i	−0.287816	+	0.119217i	0.234105	+	0.972211i	$0.424784\pi$
$230$		0			0
$231$	0.557647	−	0.557647i	0.0366905	−	0.0366905i
$232$		0			0
$233$	16.7918	+	16.7918i	1.10007	+	1.10007i	0.994402	+	0.105663i	$0.0336965\pi$
$233$	16.7918	+	16.7918i	1.10007	+	1.10007i	0.105663	+	0.994402i	$0.466303\pi$
$234$		0			0
$235$	−1.88784	−	4.55765i	−0.123149	−	0.297308i
$236$		0			0
$237$	9.04832	+	3.74794i	0.587751	+	0.243455i
$238$		0			0
$239$		−	15.8414i		−	1.02469i	−0.858779	−	0.512347i	$-0.828776\pi$
$239$		−	15.8414i		−	1.02469i	0.858779	−	0.512347i	$-0.171224\pi$
$240$		0			0
$241$		−	0.313335i		−	0.0201837i	−0.999949	−	0.0100918i	$-0.996788\pi$
$241$		−	0.313335i		−	0.0201837i	0.999949	−	0.0100918i	$-0.00321239\pi$
$242$		0			0
$243$	9.82038	+	4.06774i	0.629978	+	0.260945i
$244$		0			0
$245$	−5.73838	−	13.8537i	−0.366612	−	0.885079i
$246$		0			0
$247$	4.59050	+	4.59050i	0.292086	+	0.292086i
$248$		0			0
$249$	−7.66941	+	7.66941i	−0.486029	+	0.486029i
$250$		0			0
$251$	8.59225	−	3.55903i	0.542338	−	0.224644i	−0.0946593	−	0.995510i	$-0.530176\pi$
$251$	8.59225	−	3.55903i	0.542338	−	0.224644i	0.636997	+	0.770866i	$0.280176\pi$
$252$		0			0
$253$	0.0594122	−	0.143434i	0.00373521	−	0.00901760i
$254$		0			0
$255$	16.4853			1.03235
$256$		0			0
$257$	18.9043			1.17922			0.589609	−	0.807689i	$-0.299282\pi$
$257$	18.9043			1.17922			0.589609	+	0.807689i	$0.299282\pi$
$258$		0			0
$259$	−6.73263	+	16.2540i	−0.418346	+	1.00998i
$260$		0			0
$261$	4.68749	−	1.94162i	0.290148	−	0.120183i
$262$		0			0
$263$	16.6366	−	16.6366i	1.02585	−	1.02585i	0.0261975	−	0.999657i	$-0.491660\pi$
$263$	16.6366	−	16.6366i	1.02585	−	1.02585i	0.999657	−	0.0261975i	$-0.00833988\pi$
$264$		0			0
$265$	2.33019	+	2.33019i	0.143143	+	0.143143i
$266$		0			0
$267$	−3.15980	−	7.62844i	−0.193377	−	0.466853i
$268$		0			0
$269$	12.0963	+	5.01046i	0.737525	+	0.305493i	0.719640	−	0.694347i	$-0.244307\pi$
$269$	12.0963	+	5.01046i	0.737525	+	0.305493i	0.0178850	+	0.999840i	$0.494307\pi$
$270$		0			0
$271$		−	28.2141i		−	1.71388i	−0.515412	−	0.856942i	$-0.672361\pi$
$271$		−	28.2141i		−	1.71388i	0.515412	−	0.856942i	$-0.327639\pi$
$272$		0			0
$273$			16.6041i			1.00493i
$274$		0			0
$275$	−0.214699	−	0.0889314i	−0.0129469	−	0.00536277i
$276$		0			0
$277$	−9.04006	−	21.8246i	−0.543165	−	1.31132i	−0.922479	−	0.386047i	$-0.873840\pi$
$277$	−9.04006	−	21.8246i	−0.543165	−	1.31132i	0.379314	−	0.925268i	$-0.376160\pi$
$278$		0			0
$279$	0.898033	+	0.898033i	0.0537638	+	0.0537638i
$280$		0			0
$281$	−3.00666	+	3.00666i	−0.179363	+	0.179363i	−0.791078	−	0.611715i	$-0.790480\pi$
$281$	−3.00666	+	3.00666i	−0.179363	+	0.179363i	0.611715	+	0.791078i	$0.290480\pi$
$282$		0			0
$283$	−1.71293	+	0.709521i	−0.101823	+	0.0421766i	−0.433014	−	0.901387i	$-0.642550\pi$
$283$	−1.71293	+	0.709521i	−0.101823	+	0.0421766i	0.331190	+	0.943564i	$0.392550\pi$
$284$		0			0
$285$	−2.05941	+	4.97186i	−0.121989	+	0.294508i
$286$		0			0
$287$	13.7359			0.810804
$288$		0			0
$289$	−24.5443			−1.44378
$290$		0			0
$291$	5.47010	−	13.2060i	0.320663	−	0.774148i
$292$		0			0
$293$	−25.3917	+	10.5176i	−1.48340	+	0.614444i	−0.969869	−	0.243627i	$-0.921663\pi$
$293$	−25.3917	+	10.5176i	−1.48340	+	0.614444i	−0.513530	+	0.858071i	$0.671663\pi$
$294$		0			0
$295$	−4.90774	+	4.90774i	−0.285739	+	0.285739i
$296$		0			0
$297$	0.585786	+	0.585786i	0.0339908	+	0.0339908i
$298$		0			0
$299$	1.25088	+	3.01990i	0.0723404	+	0.174645i
$300$		0			0
$301$	−23.7440	−	9.83509i	−1.36858	−	0.566885i
$302$		0			0
$303$		−	15.6167i		−	0.897154i
$304$		0			0
$305$			6.93520i			0.397108i
$306$		0			0
$307$	−14.0065	−	5.80167i	−0.799391	−	0.331119i	−0.0546786	−	0.998504i	$-0.517413\pi$
$307$	−14.0065	−	5.80167i	−0.799391	−	0.331119i	−0.744713	+	0.667385i	$0.767413\pi$
$308$		0			0
$309$	9.97332	+	24.0777i	0.567363	+	1.36973i
$310$		0			0
$311$	−7.15481	−	7.15481i	−0.405712	−	0.405712i	0.474528	−	0.880240i	$-0.342619\pi$
$311$	−7.15481	−	7.15481i	−0.405712	−	0.405712i	−0.880240	+	0.474528i	$0.842619\pi$
$312$		0			0
$313$	11.8512	−	11.8512i	0.669868	−	0.669868i	−0.287817	−	0.957685i	$-0.592930\pi$
$313$	11.8512	−	11.8512i	0.669868	−	0.669868i	0.957685	+	0.287817i	$0.0929295\pi$
$314$		0			0
$315$	7.19460	−	2.98010i	0.405370	−	0.167910i
$316$		0			0
$317$	7.84425	−	18.9377i	0.440577	−	1.06365i	−0.535170	−	0.844745i	$-0.679752\pi$
$317$	7.84425	−	18.9377i	0.440577	−	1.06365i	0.975747	−	0.218902i	$-0.0702476\pi$
$318$		0			0
$319$	0.685896			0.0384028
$320$		0			0
$321$	19.8526			1.10807
$322$		0			0
$323$	5.18989	−	12.5295i	0.288773	−	0.697160i
$324$		0			0
$325$	4.52035	−	1.87239i	0.250744	−	0.103861i
$326$		0			0
$327$	12.4689	−	12.4689i	0.689533	−	0.689533i
$328$		0			0
$329$	−7.33962	−	7.33962i	−0.404646	−	0.404646i
$330$		0			0
$331$	4.10530	+	9.91107i	0.225648	+	0.544762i	0.995639	−	0.0932931i	$-0.0297394\pi$
$331$	4.10530	+	9.91107i	0.225648	+	0.544762i	−0.769991	+	0.638055i	$0.779739\pi$
$332$		0			0
$333$	−4.53200	−	1.87722i	−0.248352	−	0.102871i
$334$		0			0
$335$			28.1582i			1.53845i
$336$		0			0
$337$		−	3.23412i		−	0.176174i	−0.996113	−	0.0880868i	$-0.971925\pi$
$337$		−	3.23412i		−	0.176174i	0.996113	−	0.0880868i	$-0.0280753\pi$
$338$		0			0
$339$	7.52099	+	3.11529i	0.408484	+	0.169200i
$340$		0			0
$341$	0.0657022	+	0.158619i	0.00355797	+	0.00858971i
$342$		0			0
$343$	−3.06608	−	3.06608i	−0.165553	−	0.165553i
$344$		0			0
$345$	−1.91598	+	1.91598i	−0.103153	+	0.103153i
$346$		0			0
$347$	23.7246	−	9.82705i	1.27360	−	0.527544i	0.359545	−	0.933128i	$-0.382932\pi$
$347$	23.7246	−	9.82705i	1.27360	−	0.527544i	0.914058	+	0.405584i	$0.132932\pi$
$348$		0			0
$349$	−5.20925	+	12.5762i	−0.278845	+	0.673190i	−0.999804	−	0.0197868i	$-0.993701\pi$
$349$	−5.20925	+	12.5762i	−0.278845	+	0.673190i	0.720960	+	0.692977i	$0.243701\pi$
$350$		0			0
$351$	−17.4420			−0.930983
$352$		0			0
$353$	−8.67371			−0.461655			−0.230828	−	0.972995i	$-0.574143\pi$
$353$	−8.67371			−0.461655			−0.230828	+	0.972995i	$0.574143\pi$
$354$		0			0
$355$	3.40950	−	8.23127i	0.180958	−	0.436870i
$356$		0			0
$357$	32.0461	−	13.2739i	1.69606	−	0.702530i
$358$		0			0
$359$	−13.6307	+	13.6307i	−0.719399	+	0.719399i	−0.968482	−	0.249083i	$-0.919871\pi$
$359$	−13.6307	+	13.6307i	−0.719399	+	0.719399i	0.249083	+	0.968482i	$0.419871\pi$
$360$		0			0
$361$	−10.3045	−	10.3045i	−0.542345	−	0.542345i
$362$		0			0
$363$	−5.81539	−	14.0396i	−0.305229	−	0.736888i
$364$		0			0
$365$	1.06793	+	0.442353i	0.0558982	+	0.0231538i
$366$		0			0
$367$			28.9800i			1.51274i	0.654142	+	0.756371i	$0.273030\pi$
$367$			28.9800i			1.51274i	−0.654142	+	0.756371i	$0.726970\pi$
$368$		0			0
$369$			3.82989i			0.199376i
$370$		0			0
$371$	6.40597	+	2.65344i	0.332581	+	0.137760i
$372$		0			0
$373$	−2.30455	−	5.56367i	−0.119325	−	0.288076i	0.852920	−	0.522042i	$-0.174830\pi$
$373$	−2.30455	−	5.56367i	−0.119325	−	0.288076i	−0.972245	+	0.233966i	$0.924830\pi$
$374$		0			0
$375$	11.9106	+	11.9106i	0.615060	+	0.615060i
$376$		0			0
$377$	−10.2114	+	10.2114i	−0.525912	+	0.525912i
$378$		0			0
$379$	−20.6481	+	8.55274i	−1.06062	+	0.439325i	−0.843673	−	0.536858i	$-0.819611\pi$
$379$	−20.6481	+	8.55274i	−1.06062	+	0.439325i	−0.216951	+	0.976183i	$0.569611\pi$
$380$		0			0
$381$	−8.15862	+	19.6966i	−0.417979	+	1.00909i
$382$		0			0
$383$	−30.5667			−1.56188			−0.780942	−	0.624603i	$-0.785261\pi$
$383$	−30.5667			−1.56188			−0.780942	+	0.624603i	$0.785261\pi$
$384$		0			0
$385$	1.05275			0.0536530
$386$		0			0
$387$	2.74226	−	6.62039i	0.139397	−	0.336533i
$388$		0			0
$389$	17.0597	−	7.06634i	0.864959	−	0.358278i	0.0943139	−	0.995543i	$-0.469934\pi$
$389$	17.0597	−	7.06634i	0.864959	−	0.358278i	0.770645	+	0.637265i	$0.219934\pi$
$390$		0			0
$391$	4.82843	−	4.82843i	0.244184	−	0.244184i
$392$		0			0
$393$	3.13990	+	3.13990i	0.158387	+	0.158387i
$394$		0			0
$395$	5.00313	+	12.0786i	0.251735	+	0.607742i
$396$		0			0
$397$	−17.2799	−	7.15759i	−0.867255	−	0.359229i	−0.0957146	−	0.995409i	$-0.530514\pi$
$397$	−17.2799	−	7.15759i	−0.867255	−	0.359229i	−0.771541	+	0.636180i	$0.780514\pi$
$398$		0			0
$399$			11.3231i			0.566866i
$400$		0			0
$401$		−	11.0004i		−	0.549332i	−0.961540	−	0.274666i	$-0.911433\pi$
$401$		−	11.0004i		−	0.549332i	0.961540	−	0.274666i	$-0.0885674\pi$
$402$		0			0
$403$	−3.33962	−	1.38331i	−0.166358	−	0.0689078i
$404$		0			0
$405$	−3.23348	−	7.80631i	−0.160673	−	0.387899i
$406$		0			0
$407$	−0.468914	−	0.468914i	−0.0232432	−	0.0232432i
$408$		0			0
$409$	1.15862	−	1.15862i	0.0572900	−	0.0572900i	−0.677881	−	0.735171i	$-0.737102\pi$
$409$	1.15862	−	1.15862i	0.0572900	−	0.0572900i	0.735171	+	0.677881i	$0.237102\pi$
$410$		0			0
$411$	−19.4881	+	8.07225i	−0.961279	+	0.398175i
$412$		0			0
$413$	−5.58855	+	13.4919i	−0.274994	+	0.663895i
$414$		0			0
$415$	−14.4786			−0.710727
$416$		0			0
$417$	7.16714			0.350976
$418$		0			0
$419$	−13.2698	+	32.0362i	−0.648273	+	1.56507i	0.166978	+	0.985961i	$0.446599\pi$
$419$	−13.2698	+	32.0362i	−0.648273	+	1.56507i	−0.815251	+	0.579108i	$0.803401\pi$
$420$		0			0
$421$	−22.5633	+	9.34602i	−1.09967	+	0.455497i	−0.857368	−	0.514705i	$-0.827902\pi$
$421$	−22.5633	+	9.34602i	−1.09967	+	0.455497i	−0.242299	+	0.970202i	$0.577902\pi$
$422$		0			0
$423$	2.04646	−	2.04646i	0.0995022	−	0.0995022i
$424$		0			0
$425$	−7.22746	−	7.22746i	−0.350583	−	0.350583i
$426$		0			0
$427$	5.58421	+	13.4815i	0.270239	+	0.652414i
$428$		0			0
$429$	−0.578221	−	0.239507i	−0.0279168	−	0.0115635i
$430$		0			0
$431$		−	4.47586i		−	0.215594i	−0.994173	−	0.107797i	$-0.965620\pi$
$431$		−	4.47586i		−	0.215594i	0.994173	−	0.107797i	$-0.0343797\pi$
$432$		0			0
$433$		−	1.44196i		−	0.0692960i	−0.999400	−	0.0346480i	$-0.988969\pi$
$433$		−	1.44196i		−	0.0692960i	0.999400	−	0.0346480i	$-0.0110310\pi$
$434$		0			0
$435$	−11.0597	−	4.58107i	−0.530272	−	0.219646i
$436$		0			0
$437$	0.853036	+	2.05941i	0.0408063	+	0.0985150i
$438$		0			0
$439$	−0.854615	−	0.854615i	−0.0407885	−	0.0407885i	0.686418	−	0.727207i	$-0.259182\pi$
$439$	−0.854615	−	0.854615i	−0.0407885	−	0.0407885i	−0.727207	+	0.686418i	$0.759182\pi$
$440$		0			0
$441$	6.22053	−	6.22053i	0.296216	−	0.296216i
$442$		0			0
$443$	−11.3206	+	4.68913i	−0.537857	+	0.222787i	−0.635040	−	0.772479i	$-0.719017\pi$
$443$	−11.3206	+	4.68913i	−0.537857	+	0.222787i	0.0971838	+	0.995266i	$0.469017\pi$
$444$		0			0
$445$	4.21803	−	10.1832i	0.199954	−	0.482731i
$446$		0			0
$447$	6.47862			0.306428
$448$		0			0
$449$	−24.5573			−1.15893			−0.579464	−	0.814998i	$-0.696738\pi$
$449$	−24.5573			−1.15893			−0.579464	+	0.814998i	$0.696738\pi$
$450$		0			0
$451$	−0.198134	+	0.478338i	−0.00932976	+	0.0225240i
$452$		0			0
$453$	−23.9348	+	9.91412i	−1.12456	+	0.465806i
$454$		0			0
$455$	−15.6729	+	15.6729i	−0.734759	+	0.734759i
$456$		0			0
$457$	−14.1684	−	14.1684i	−0.662771	−	0.662771i	0.293262	−	0.956032i	$-0.405259\pi$
$457$	−14.1684	−	14.1684i	−0.662771	−	0.662771i	−0.956032	+	0.293262i	$0.905259\pi$
$458$		0			0
$459$	13.9437	+	33.6631i	0.650837	+	1.57126i
$460$		0			0
$461$	28.4793	+	11.7965i	1.32641	+	0.549417i	0.929630	−	0.368496i	$-0.120127\pi$
$461$	28.4793	+	11.7965i	1.32641	+	0.549417i	0.396782	+	0.917913i	$0.370127\pi$
$462$		0			0
$463$		−	14.8190i		−	0.688697i	−0.938842	−	0.344349i	$-0.888100\pi$
$463$		−	14.8190i		−	0.688697i	0.938842	−	0.344349i	$-0.111900\pi$
$464$		0			0
$465$		−	2.99647i		−	0.138958i
$466$		0			0
$467$	−13.1218	−	5.43521i	−0.607203	−	0.251512i	0.0578293	−	0.998326i	$-0.481582\pi$
$467$	−13.1218	−	5.43521i	−0.607203	−	0.251512i	−0.665032	+	0.746815i	$0.731582\pi$
$468$		0			0
$469$	22.6729	+	54.7373i	1.04694	+	2.52753i
$470$		0			0
$471$	16.9007	+	16.9007i	0.778742	+	0.778742i
$472$		0			0
$473$	0.684993	−	0.684993i	0.0314960	−	0.0314960i
$474$		0			0
$475$	3.08264	−	1.27687i	0.141441	−	0.0585869i
$476$		0			0
$477$	−0.739842	+	1.78614i	−0.0338750	+	0.0817816i
$478$		0			0
$479$	32.3727			1.47915			0.739574	−	0.673076i	$-0.235027\pi$
$479$	32.3727			1.47915			0.739574	+	0.673076i	$0.235027\pi$
$480$		0			0
$481$	13.9620			0.636614
$482$		0			0
$483$	−2.18177	+	5.26725i	−0.0992738	+	0.239668i
$484$		0			0
$485$	17.6287	−	7.30205i	0.800479	−	0.331569i
$486$		0			0
$487$	1.89478	−	1.89478i	0.0858608	−	0.0858608i	−0.662872	−	0.748733i	$-0.730663\pi$
$487$	1.89478	−	1.89478i	0.0858608	−	0.0858608i	0.748733	+	0.662872i	$0.230663\pi$
$488$		0			0
$489$	−11.2815	−	11.2815i	−0.510166	−	0.510166i
$490$		0			0
$491$	−7.57539	−	18.2886i	−0.341873	−	0.825354i	−0.997526	−	0.0702922i	$-0.977607\pi$
$491$	−7.57539	−	18.2886i	−0.341873	−	0.825354i	0.655654	−	0.755062i	$-0.272393\pi$
$492$		0			0
$493$	27.8714	+	11.5447i	1.25526	+	0.519947i
$494$		0			0
$495$			0.293531i			0.0131932i
$496$		0			0
$497$		−	18.7462i		−	0.840884i
$498$		0			0
$499$	23.0538	+	9.54921i	1.03203	+	0.427481i	0.833445	−	0.552602i	$-0.186365\pi$
$499$	23.0538	+	9.54921i	1.03203	+	0.427481i	0.198586	+	0.980083i	$0.436365\pi$
$500$		0			0
$501$	−2.23744	−	5.40166i	−0.0999614	−	0.241328i
$502$		0			0
$503$	−22.6436	−	22.6436i	−1.00963	−	1.00963i	−0.999953	−	0.00967595i	$-0.996920\pi$
$503$	−22.6436	−	22.6436i	−1.00963	−	1.00963i	−0.00967595	−	0.999953i	$-0.503080\pi$
$504$		0			0
$505$	14.7409	−	14.7409i	0.655960	−	0.655960i
$506$		0			0
$507$	−4.45068	+	1.84353i	−0.197661	+	0.0818741i
$508$		0			0
$509$	−8.85238	+	21.3715i	−0.392375	+	0.947276i	0.597047	+	0.802206i	$0.296341\pi$
$509$	−8.85238	+	21.3715i	−0.392375	+	0.947276i	−0.989421	+	0.145070i	$0.953659\pi$
$510$		0			0
$511$	2.43216			0.107592
$512$		0			0
$513$	−11.8945			−0.525155
$514$		0			0
$515$	−13.3134	+	32.1415i	−0.586660	+	1.41632i
$516$		0			0
$517$	0.361465	−	0.149724i	0.0158972	−	0.00658484i
$518$		0			0
$519$	−20.0789	+	20.0789i	−0.881366	+	0.881366i
$520$		0			0
$521$	9.76588	+	9.76588i	0.427851	+	0.427851i	0.887896	−	0.460045i	$-0.152167\pi$
$521$	9.76588	+	9.76588i	0.427851	+	0.427851i	−0.460045	+	0.887896i	$0.652167\pi$
$522$		0			0
$523$	−7.01552	−	16.9370i	−0.306767	−	0.740601i	−0.999806	−	0.0197010i	$-0.993729\pi$
$523$	−7.01552	−	16.9370i	−0.306767	−	0.740601i	0.693039	−	0.720900i	$-0.256271\pi$
$524$		0			0
$525$	7.88431	+	3.26579i	0.344099	+	0.142531i
$526$		0			0
$527$			7.55136i			0.328942i
$528$		0			0
$529$		−	21.8776i		−	0.951202i
$530$		0			0
$531$	−3.76187	−	1.55822i	−0.163251	−	0.0676209i
$532$		0			0
$533$	−4.17157	−	10.0711i	−0.180691	−	0.436226i
$534$		0			0
$535$	18.7393	+	18.7393i	0.810170	+	0.810170i
$536$		0			0
$537$	24.5674	−	24.5674i	1.06016	−	1.06016i
$538$		0			0
$539$	1.09873	−	0.455108i	0.0473256	−	0.0196029i
$540$		0			0
$541$	5.89071	−	14.2214i	0.253261	−	0.611427i	−0.745202	−	0.666839i	$-0.767647\pi$
$541$	5.89071	−	14.2214i	0.253261	−	0.611427i	0.998464	+	0.0554115i	$0.0176471\pi$
$542$		0			0
$543$	2.81470			0.120791
$544$		0			0
$545$	23.5393			1.00831
$546$		0			0
$547$	−4.00686	+	9.67342i	−0.171321	+	0.413606i	−0.986097	−	0.166170i	$-0.946860\pi$
$547$	−4.00686	+	9.67342i	−0.171321	+	0.413606i	0.814776	+	0.579776i	$0.196860\pi$
$548$		0			0
$549$	−3.75895	+	1.55701i	−0.160428	+	0.0664515i
$550$		0			0
$551$	−6.96362	+	6.96362i	−0.296660	+	0.296660i
$552$		0			0
$553$	19.4514	+	19.4514i	0.827157	+	0.827157i
$554$		0			0
$555$	4.42912	+	10.6928i	0.188006	+	0.453886i
$556$		0			0
$557$	7.45908	+	3.08965i	0.316051	+	0.130913i	0.535070	−	0.844808i	$-0.320285\pi$
$557$	7.45908	+	3.08965i	0.316051	+	0.130913i	−0.219018	+	0.975721i	$0.570285\pi$
$558$		0			0
$559$			20.3959i			0.862653i
$560$		0			0
$561$			1.30744i			0.0552002i
$562$		0			0
$563$	−24.5802	−	10.1815i	−1.03593	−	0.429097i	−0.201082	−	0.979574i	$-0.564446\pi$
$563$	−24.5802	−	10.1815i	−1.03593	−	0.429097i	−0.834850	+	0.550477i	$0.814446\pi$
$564$		0			0
$565$	4.15862	+	10.0398i	0.174954	+	0.422377i
$566$		0			0
$567$	−12.5713	−	12.5713i	−0.527943	−	0.527943i
$568$		0			0
$569$	−8.12862	+	8.12862i	−0.340770	+	0.340770i	−0.856657	−	0.515887i	$-0.827462\pi$
$569$	−8.12862	+	8.12862i	−0.340770	+	0.340770i	0.515887	+	0.856657i	$0.327462\pi$
$570$		0			0
$571$	17.8876	−	7.40930i	0.748574	−	0.310070i	0.0244147	−	0.999702i	$-0.492228\pi$
$571$	17.8876	−	7.40930i	0.748574	−	0.310070i	0.724160	+	0.689632i	$0.242228\pi$
$572$		0			0
$573$	4.79862	−	11.5849i	0.200465	−	0.483965i
$574$		0			0
$575$	1.68000			0.0700609
$576$		0			0
$577$	−11.9134			−0.495959			−0.247980	−	0.968765i	$-0.579767\pi$
$577$	−11.9134			−0.495959			−0.247980	+	0.968765i	$0.579767\pi$
$578$		0			0
$579$	3.30911	−	7.98890i	0.137522	−	0.332008i
$580$		0			0
$581$	−28.1453	+	11.6582i	−1.16766	+	0.483662i
$582$		0			0
$583$	−0.184807	+	0.184807i	−0.00765391	+	0.00765391i
$584$		0			0
$585$	−4.36999	−	4.36999i	−0.180677	−	0.180677i
$586$		0			0
$587$	−9.77588	−	23.6011i	−0.403494	−	0.974120i	−0.986811	−	0.161876i	$-0.948246\pi$
$587$	−9.77588	−	23.6011i	−0.403494	−	0.974120i	0.583318	−	0.812244i	$-0.301754\pi$
$588$		0			0
$589$	−2.27744	−	0.943348i	−0.0938404	−	0.0388700i
$590$		0			0
$591$		−	6.55765i		−	0.269746i
$592$		0			0
$593$		−	12.5549i		−	0.515567i	−0.966203	−	0.257784i	$-0.917008\pi$
$593$		−	12.5549i		−	0.515567i	0.966203	−	0.257784i	$-0.0829922\pi$
$594$		0			0
$595$	42.7784	+	17.7194i	1.75374	+	0.726425i
$596$		0			0
$597$	4.60097	+	11.1077i	0.188305	+	0.454609i
$598$		0			0
$599$	6.66010	+	6.66010i	0.272124	+	0.272124i	0.829955	−	0.557830i	$-0.188366\pi$
$599$	6.66010	+	6.66010i	0.272124	+	0.272124i	−0.557830	+	0.829955i	$0.688366\pi$
$600$		0			0
$601$	−27.4318	+	27.4318i	−1.11896	+	1.11896i	−0.127071	+	0.991894i	$0.540558\pi$
$601$	−27.4318	+	27.4318i	−1.11896	+	1.11896i	−0.991894	+	0.127071i	$0.959442\pi$
$602$		0			0
$603$	−15.2621	+	6.32175i	−0.621519	+	0.257442i
$604$		0			0
$605$	7.76299	−	18.7415i	0.315610	−	0.761951i
$606$		0			0
$607$	−20.3361			−0.825416			−0.412708	−	0.910863i	$-0.635417\pi$
$607$	−20.3361			−0.825416			−0.412708	+	0.910863i	$0.635417\pi$
$608$		0			0
$609$	−25.1878			−1.02066
$610$		0			0
$611$	−3.15233	+	7.61040i	−0.127530	+	0.307884i
$612$		0			0
$613$	32.1759	−	13.3277i	1.29957	−	0.538301i	0.377748	−	0.925908i	$-0.376699\pi$
$613$	32.1759	−	13.3277i	1.29957	−	0.538301i	0.921824	+	0.387608i	$0.126699\pi$
$614$		0			0
$615$	6.38960	−	6.38960i	0.257654	−	0.257654i
$616$		0			0
$617$	11.3168	+	11.3168i	0.455599	+	0.455599i	0.897208	−	0.441609i	$-0.145592\pi$
$617$	11.3168	+	11.3168i	0.455599	+	0.455599i	−0.441609	+	0.897208i	$0.645592\pi$
$618$		0			0
$619$	−0.0931149	−	0.224799i	−0.00374260	−	0.00903545i	0.921997	−	0.387197i	$-0.126557\pi$
$619$	−0.0931149	−	0.224799i	−0.00374260	−	0.00903545i	−0.925740	+	0.378161i	$0.876557\pi$
$620$		0			0
$621$	−5.53304	−	2.29186i	−0.222033	−	0.0919691i
$622$		0			0
$623$		−	23.1917i		−	0.929157i
$624$		0			0
$625$			14.5563i			0.582254i
$626$		0			0
$627$	−0.394316	−	0.163331i	−0.0157475	−	0.00652282i
$628$		0			0
$629$	−11.1618	−	26.9469i	−0.445048	−	1.07444i
$630$		0			0
$631$	−1.15481	−	1.15481i	−0.0459722	−	0.0459722i	0.683747	−	0.729719i	$-0.260349\pi$
$631$	−1.15481	−	1.15481i	−0.0459722	−	0.0459722i	−0.729719	+	0.683747i	$0.760349\pi$
$632$		0			0
$633$	−13.3404	+	13.3404i	−0.530233	+	0.530233i
$634$		0			0
$635$	−26.2931	+	10.8910i	−1.04341	+	0.432195i
$636$		0			0
$637$	−9.58199	+	23.1330i	−0.379652	+	0.916562i
$638$		0			0
$639$	5.22690			0.206773
$640$		0			0
$641$	−14.1953			−0.560679			−0.280339	−	0.959901i	$-0.590447\pi$
$641$	−14.1953			−0.560679			−0.280339	+	0.959901i	$0.590447\pi$
$642$		0			0
$643$	14.0557	−	33.9334i	0.554302	−	1.33820i	−0.359917	−	0.932984i	$-0.617195\pi$
$643$	14.0557	−	33.9334i	0.554302	−	1.33820i	0.914219	−	0.405219i	$-0.132805\pi$
$644$		0			0
$645$	−15.6202	+	6.47010i	−0.615045	+	0.254760i
$646$		0			0
$647$	−8.73969	+	8.73969i	−0.343593	+	0.343593i	−0.857716	−	0.514123i	$-0.828117\pi$
$647$	−8.73969	+	8.73969i	−0.343593	+	0.343593i	0.514123	+	0.857716i	$0.328117\pi$
$648$		0			0
$649$	−0.389231	−	0.389231i	−0.0152786	−	0.0152786i
$650$		0			0
$651$	−2.41275	−	5.82490i	−0.0945632	−	0.228296i
$652$		0			0
$653$	−38.9127	−	16.1182i	−1.52277	−	0.630753i	−0.544627	−	0.838679i	$-0.683329\pi$
$653$	−38.9127	−	16.1182i	−1.52277	−	0.630753i	−0.978145	+	0.207926i	$0.933329\pi$
$654$		0			0
$655$			5.92763i			0.231612i
$656$		0			0
$657$			0.678143i			0.0264569i
$658$		0			0
$659$	21.5821	+	8.93958i	0.840718	+	0.348237i	0.761136	−	0.648592i	$-0.224642\pi$
$659$	21.5821	+	8.93958i	0.840718	+	0.348237i	0.0795812	+	0.996828i	$0.474642\pi$
$660$		0			0
$661$	−9.11633	−	22.0088i	−0.354584	−	0.856042i	−0.996042	−	0.0888835i	$-0.971670\pi$
$661$	−9.11633	−	22.0088i	−0.354584	−	0.856042i	0.641458	−	0.767158i	$-0.278330\pi$
$662$		0			0
$663$	−19.4647	−	19.4647i	−0.755947	−	0.755947i
$664$		0			0
$665$	−10.6881	+	10.6881i	−0.414468	+	0.414468i
$666$		0			0
$667$	−4.58107	+	1.89754i	−0.177380	+	0.0734732i
$668$		0			0
$669$	−0.508825	+	1.22841i	−0.0196723	+	0.0474931i
$670$		0			0
$671$	−0.550028			−0.0212336
$672$		0			0
$673$	45.0980			1.73840			0.869200	−	0.494460i	$-0.164634\pi$
$673$	45.0980			1.73840			0.869200	+	0.494460i	$0.164634\pi$
$674$		0			0
$675$	−3.43058	+	8.28216i	−0.132043	+	0.318780i
$676$		0			0
$677$	−32.8474	+	13.6058i	−1.26243	+	0.522915i	−0.910654	−	0.413170i	$-0.864421\pi$
$677$	−32.8474	+	13.6058i	−1.26243	+	0.522915i	−0.351774	+	0.936085i	$0.614421\pi$
$678$		0			0
$679$	28.3892	−	28.3892i	1.08948	−	1.08948i
$680$		0			0
$681$	−15.0117	−	15.0117i	−0.575248	−	0.575248i
$682$		0			0
$683$	7.79305	+	18.8141i	0.298193	+	0.719901i	0.999972	+	0.00750651i	$0.00238942\pi$
$683$	7.79305	+	18.8141i	0.298193	+	0.719901i	−0.701779	+	0.712395i	$0.747611\pi$
$684$		0			0
$685$	−26.0148	−	10.7757i	−0.993974	−	0.411718i
$686$		0			0
$687$			6.52547i			0.248962i
$688$		0			0
$689$		−	5.50267i		−	0.209635i
$690$		0			0
$691$	−30.4967	−	12.6322i	−1.16015	−	0.480550i	−0.282226	−	0.959348i	$-0.591073\pi$
$691$	−30.4967	−	12.6322i	−1.16015	−	0.480550i	−0.877925	+	0.478798i	$0.841073\pi$
$692$		0			0
$693$	0.236351	+	0.570601i	0.00897822	+	0.0216753i
$694$		0			0
$695$	6.76521	+	6.76521i	0.256619	+	0.256619i
$696$		0			0
$697$	−16.1023	+	16.1023i	−0.609920	+	0.609920i
$698$		0			0
$699$	30.3684	−	12.5790i	1.14864	−	0.475782i
$700$		0			0
$701$	0.379146	−	0.915341i	0.0143202	−	0.0345719i	−0.916558	−	0.399902i	$-0.869044\pi$
$701$	0.379146	−	0.915341i	0.0143202	−	0.0345719i	0.930878	+	0.365330i	$0.119044\pi$
$702$		0			0
$703$	9.52138			0.359106
$704$		0			0
$705$	−6.82843			−0.257173
$706$		0			0
$707$	16.7858	−	40.5244i	0.631293	−	1.52408i
$708$		0			0
$709$	45.7920	−	18.9677i	1.71975	−	0.712346i	0.719922	−	0.694055i	$-0.244177\pi$
$709$	45.7920	−	18.9677i	1.71975	−	0.712346i	0.999833	−	0.0182911i	$-0.00582257\pi$
$710$		0			0
$711$	−5.42350	+	5.42350i	−0.203397	+	0.203397i
$712$		0			0
$713$	−0.877646	−	0.877646i	−0.0328681	−	0.0328681i
$714$		0			0
$715$	−0.319719	−	0.771869i	−0.0119568	−	0.0288663i
$716$		0			0
$717$	−20.2583	−	8.39128i	−0.756561	−	0.313378i
$718$		0			0
$719$			12.7931i			0.477102i	0.971130	+	0.238551i	$0.0766724\pi$
$719$			12.7931i			0.477102i	−0.971130	+	0.238551i	$0.923328\pi$
$720$		0			0
$721$			73.2004i			2.72612i
$722$		0			0
$723$	−0.400700	−	0.165975i	−0.0149022	−	0.00617269i
$724$		0			0
$725$	2.84035	+	6.85720i	0.105488	+	0.254670i
$726$		0			0
$727$	0.466154	+	0.466154i	0.0172887	+	0.0172887i	0.715698	−	0.698410i	$-0.246109\pi$
$727$	0.466154	+	0.466154i	0.0172887	+	0.0172887i	−0.698410	+	0.715698i	$0.746109\pi$
$728$		0			0
$729$	20.1043	−	20.1043i	0.744603	−	0.744603i
$730$		0			0
$731$	39.3642	−	16.3052i	1.45594	−	0.603069i
$732$		0			0
$733$	14.0945	−	34.0271i	0.520591	−	1.25682i	−0.416945	−	0.908932i	$-0.636899\pi$
$733$	14.0945	−	34.0271i	0.520591	−	1.25682i	0.937536	−	0.347887i	$-0.113101\pi$
$734$		0			0
$735$	−20.7561			−0.765599
$736$		0			0
$737$	−2.23322			−0.0822616
$738$		0			0
$739$	3.42068	−	8.25825i	0.125832	−	0.303785i	−0.848392	−	0.529368i	$-0.822429\pi$
$739$	3.42068	−	8.25825i	0.125832	−	0.303785i	0.974224	+	0.225584i	$0.0724289\pi$
$740$		0			0
$741$	8.30205	−	3.43882i	0.304984	−	0.126328i
$742$		0			0
$743$	32.4060	−	32.4060i	1.18886	−	1.18886i	0.211477	−	0.977383i	$-0.432173\pi$
$743$	32.4060	−	32.4060i	1.18886	−	1.18886i	0.977383	−	0.211477i	$-0.0678273\pi$
$744$		0			0
$745$	6.11529	+	6.11529i	0.224047	+	0.224047i
$746$		0			0
$747$	−3.25057	−	7.84757i	−0.118932	−	0.287127i
$748$		0			0
$749$	51.5165	+	21.3388i	1.88237	+	0.779704i
$750$		0			0
$751$		−	21.5108i		−	0.784939i	−0.919765	−	0.392470i	$-0.871621\pi$
$751$		−	21.5108i		−	0.784939i	0.919765	−	0.392470i	$-0.128379\pi$
$752$		0			0
$753$		−	12.8732i		−	0.469126i
$754$		0			0
$755$	−31.9507	−	13.2344i	−1.16280	−	0.481649i
$756$		0			0
$757$	−7.19276	−	17.3649i	−0.261425	−	0.631137i	0.737602	−	0.675236i	$-0.235958\pi$
$757$	−7.19276	−	17.3649i	−0.261425	−	0.631137i	−0.999027	+	0.0440993i	$0.985958\pi$
$758$		0			0
$759$	−0.151955	−	0.151955i	−0.00551563	−	0.00551563i
$760$		0			0
$761$	37.8574	−	37.8574i	1.37233	−	1.37233i	0.515354	−	0.856977i	$-0.327660\pi$
$761$	37.8574	−	37.8574i	1.37233	−	1.37233i	0.856977	−	0.515354i	$-0.172340\pi$
$762$		0			0
$763$	45.7585	−	18.9538i	1.65657	−	0.686174i
$764$		0			0
$765$	−4.94059	+	11.9276i	−0.178627	+	0.431245i
$766$		0			0
$767$	11.5894			0.418471
$768$		0			0
$769$	3.07370			0.110840			0.0554201	−	0.998463i	$-0.482350\pi$
$769$	3.07370			0.110840			0.0554201	+	0.998463i	$0.482350\pi$
$770$		0			0
$771$	10.0137	−	24.1753i	0.360635	−	0.870651i
$772$		0			0
$773$	15.8332	−	6.55831i	0.569479	−	0.235886i	−0.0793155	−	0.996850i	$-0.525273\pi$
$773$	15.8332	−	6.55831i	0.569479	−	0.235886i	0.648795	+	0.760964i	$0.275273\pi$
$774$		0			0
$775$	−1.31371	+	1.31371i	−0.0471898	+	0.0471898i
$776$		0			0
$777$	17.2197	+	17.2197i	0.617753	+	0.617753i
$778$		0			0
$779$	−2.84479	−	6.86794i	−0.101925	−	0.246070i
$780$		0			0
$781$	0.652818	+	0.270406i	0.0233597	+	0.00967589i
$782$		0			0
$783$		−	26.4588i		−	0.945561i
$784$		0			0
$785$			31.9058i			1.13877i
$786$		0			0
$787$	16.3613	+	6.77706i	0.583216	+	0.241576i	0.654729	−	0.755864i	$-0.272783\pi$
$787$	16.3613	+	6.77706i	0.583216	+	0.241576i	−0.0715129	+	0.997440i	$0.522783\pi$
$788$		0			0
$789$	−12.4627	−	30.0877i	−0.443685	−	1.07115i
$790$		0			0
$791$	16.1680	+	16.1680i	0.574869	+	0.574869i
$792$		0			0
$793$	8.18862	−	8.18862i	0.290786	−	0.290786i
$794$		0			0
$795$	4.21422	−	1.74559i	0.149463	−	0.0619096i
$796$		0			0
$797$	−13.4402	+	32.4476i	−0.476077	+	1.14935i	0.485356	+	0.874316i	$0.338690\pi$
$797$	−13.4402	+	32.4476i	−0.476077	+	1.14935i	−0.961434	+	0.275036i	$0.911310\pi$
$798$		0			0
$799$	17.2082			0.608783
$800$		0			0
$801$	6.46640			0.228479
$802$		0			0
$803$	−0.0350828	+	0.0846974i	−0.00123805	+	0.00298891i
$804$		0			0
$805$	−7.03127	+	2.91245i	−0.247820	+	0.102650i
$806$		0			0
$807$	12.8150	−	12.8150i	0.451109	−	0.451109i
$808$		0			0
$809$	−11.2704	−	11.2704i	−0.396246	−	0.396246i	0.480661	−	0.876907i	$-0.340397\pi$
$809$	−11.2704	−	11.2704i	−0.396246	−	0.396246i	−0.876907	+	0.480661i	$0.840397\pi$
$810$		0			0
$811$	−6.76529	−	16.3328i	−0.237561	−	0.573524i	0.759468	−	0.650545i	$-0.225459\pi$
$811$	−6.76529	−	16.3328i	−0.237561	−	0.573524i	−0.997029	+	0.0770206i	$0.975459\pi$
$812$		0			0
$813$	−36.0809	−	14.9452i	−1.26541	−	0.524150i
$814$		0			0
$815$		−	21.2976i		−	0.746023i
$816$		0			0
$817$			13.9089i			0.486611i
$818$		0			0
$819$	−12.0136	−	4.97620i	−0.419789	−	0.173882i
$820$		0			0
$821$	12.2244	+	29.5124i	0.426636	+	1.02999i	0.980347	+	0.197281i	$0.0632111\pi$
$821$	12.2244	+	29.5124i	0.426636	+	1.02999i	−0.553711	+	0.832709i	$0.686789\pi$
$822$		0			0
$823$	−1.00381	−	1.00381i	−0.0349906	−	0.0349906i	0.689395	−	0.724386i	$-0.257876\pi$
$823$	−1.00381	−	1.00381i	−0.0349906	−	0.0349906i	−0.724386	+	0.689395i	$0.757876\pi$
$824$		0			0
$825$	−0.227455	+	0.227455i	−0.00791898	+	0.00791898i
$826$		0			0
$827$	−37.9176	+	15.7060i	−1.31852	+	0.546151i	−0.927360	−	0.374170i	$-0.877928\pi$
$827$	−37.9176	+	15.7060i	−1.31852	+	0.546151i	−0.391165	+	0.920321i	$0.627928\pi$
$828$		0			0
$829$	13.2468	−	31.9806i	0.460081	−	1.11073i	−0.508283	−	0.861190i	$-0.669720\pi$
$829$	13.2468	−	31.9806i	0.460081	−	1.11073i	0.968364	−	0.249543i	$-0.0802804\pi$
$830$		0			0
$831$	−32.6984			−1.13430
$832$		0			0
$833$	52.3070			1.81233
$834$		0			0
$835$	2.98677	−	7.21069i	0.103361	−	0.249536i
$836$		0			0
$837$	6.11882	−	2.53450i	0.211498	−	0.0876051i
$838$		0			0
$839$	−3.42599	+	3.42599i	−0.118278	+	0.118278i	−0.763768	−	0.645490i	$-0.776653\pi$
$839$	−3.42599	+	3.42599i	−0.118278	+	0.118278i	0.645490	+	0.763768i	$0.276653\pi$
$840$		0			0
$841$	5.01582	+	5.01582i	0.172959	+	0.172959i
$842$		0			0
$843$	2.25234	+	5.43764i	0.0775749	+	0.187282i
$844$		0			0
$845$	−5.94123	−	2.46094i	−0.204384	−	0.0846588i
$846$		0			0
$847$		−	42.6827i		−	1.46660i
$848$		0			0
$849$			2.56638i			0.0880779i
$850$		0			0
$851$	4.42912	+	1.83460i	0.151828	+	0.0628893i
$852$		0			0
$853$	−13.8653	−	33.4739i	−0.474740	−	1.14612i	−0.962045	−	0.272892i	$-0.912020\pi$
$853$	−13.8653	−	33.4739i	−0.474740	−	1.14612i	0.487305	−	0.873232i	$-0.337980\pi$
$854$		0			0
$855$	−2.98010	−	2.98010i	−0.101917	−	0.101917i
$856$		0			0
$857$	−19.6667	+	19.6667i	−0.671800	+	0.671800i	−0.958131	−	0.286331i	$-0.907564\pi$
$857$	−19.6667	+	19.6667i	−0.671800	+	0.671800i	0.286331	+	0.958131i	$0.407564\pi$
$858$		0			0
$859$	−36.2424	+	15.0121i	−1.23658	+	0.512207i	−0.902643	−	0.430390i	$-0.858376\pi$
$859$	−36.2424	+	15.0121i	−1.23658	+	0.512207i	−0.333933	+	0.942597i	$0.608376\pi$
$860$		0			0
$861$	7.27598	−	17.5658i	0.247965	−	0.598640i
$862$		0			0
$863$	28.3727			0.965819			0.482909	−	0.875670i	$-0.339580\pi$
$863$	28.3727			0.965819			0.482909	+	0.875670i	$0.339580\pi$
$864$		0			0
$865$	−37.9058			−1.28883
$866$		0			0
$867$	−13.0013	+	31.3878i	−0.441546	+	1.06599i
$868$		0			0
$869$	−0.957951	+	0.396796i	−0.0324963	+	0.0134604i
$870$		0			0
$871$	33.2473	−	33.2473i	1.12654	−	1.12654i
$872$		0			0
$873$	7.91558	+	7.91558i	0.267902	+	0.267902i
$874$		0			0
$875$	18.1051	+	43.7096i	0.612064	+	1.47765i
$876$		0			0
$877$	24.4793	+	10.1396i	0.826606	+	0.342391i	0.755558	−	0.655082i	$-0.227366\pi$
$877$	24.4793	+	10.1396i	0.826606	+	0.342391i	0.0710476	+	0.997473i	$0.477366\pi$
$878$		0			0
$879$			38.0427i			1.28315i
$880$		0			0
$881$		−	9.35846i		−	0.315295i	−0.987495	−	0.157647i	$-0.949609\pi$
$881$		−	9.35846i		−	0.315295i	0.987495	−	0.157647i	$-0.0503909\pi$
$882$		0			0
$883$	−17.1218	−	7.09207i	−0.576193	−	0.238667i	0.0755050	−	0.997145i	$-0.475943\pi$
$883$	−17.1218	−	7.09207i	−0.576193	−	0.238667i	−0.651698	+	0.758478i	$0.725943\pi$
$884$		0			0
$885$	3.67647	+	8.87579i	0.123583	+	0.298356i
$886$		0			0
$887$	−30.8931	−	30.8931i	−1.03729	−	1.03729i	−0.999277	−	0.0380100i	$-0.987898\pi$
$887$	−30.8931	−	30.8931i	−1.03729	−	1.03729i	−0.0380100	−	0.999277i	$-0.512102\pi$
$888$		0			0
$889$	−42.3424	+	42.3424i	−1.42012	+	1.42012i
$890$		0			0
$891$	0.619115	−	0.256446i	0.0207411	−	0.00859126i
$892$		0			0
$893$	−2.14972	+	5.18989i	−0.0719378	+	0.173673i
$894$		0			0
$895$	46.3794			1.55029
$896$		0			0
$897$	4.52452			0.151069
$898$		0			0
$899$	2.09844	−	5.06608i	0.0699868	−	0.168963i
$900$		0			0
$901$	−10.6202	+	4.39903i	−0.353810	+	0.146553i
$902$		0			0
$903$	−25.1547	+	25.1547i	−0.837096	+	0.837096i
$904$		0			0
$905$	2.65685	+	2.65685i	0.0883168	+	0.0883168i
$906$		0			0
$907$	5.23891	+	12.6479i	0.173955	+	0.419965i	0.986678	−	0.162686i	$-0.0520156\pi$
$907$	5.23891	+	12.6479i	0.173955	+	0.419965i	−0.812723	+	0.582651i	$0.802016\pi$
$908$		0			0
$909$	11.2992	+	4.68027i	0.374770	+	0.155235i
$910$		0			0
$911$			35.3498i			1.17119i	0.810604	+	0.585595i	$0.199139\pi$
$911$			35.3498i			1.17119i	−0.810604	+	0.585595i	$0.800861\pi$
$912$		0			0
$913$		−	1.14829i		−	0.0380030i
$914$		0			0
$915$	8.86890	+	3.67362i	0.293197	+	0.121446i
$916$		0			0
$917$	4.77292	+	11.5228i	0.157616	+	0.380518i
$918$		0			0
$919$	30.0652	+	30.0652i	0.991759	+	0.991759i	0.999966	−	0.00820720i	$-0.00261246\pi$
$919$	30.0652	+	30.0652i	0.991759	+	0.991759i	−0.00820720	+	0.999966i	$0.502612\pi$
$920$		0			0
$921$	−14.8386	+	14.8386i	−0.488949	+	0.488949i
$922$		0			0
$923$	−13.7446	+	5.69321i	−0.452410	+	0.187394i
$924$		0			0
$925$	2.74613	−	6.62975i	0.0902923	−	0.217985i
$926$		0			0
$927$	−20.4100			−0.670352
$928$		0			0
$929$	7.62858			0.250286			0.125143	−	0.992139i	$-0.460061\pi$
$929$	7.62858			0.250286			0.125143	+	0.992139i	$0.460061\pi$
$930$		0			0
$931$	−6.53442	+	15.7755i	−0.214157	+	0.517020i
$932$		0			0
$933$	−12.9397	+	5.35979i	−0.423626	+	0.175472i
$934$		0			0
$935$	−1.23412	+	1.23412i	−0.0403600	+	0.0403600i
$936$		0			0
$937$	21.2074	+	21.2074i	0.692817	+	0.692817i	0.962851	−	0.270034i	$-0.0870349\pi$
$937$	21.2074	+	21.2074i	0.692817	+	0.692817i	−0.270034	+	0.962851i	$0.587035\pi$
$938$		0			0
$939$	−8.87793	−	21.4332i	−0.289720	−	0.699446i
$940$		0			0
$941$	−31.4448	−	13.0249i	−1.02507	−	0.424599i	−0.194141	−	0.980974i	$-0.562192\pi$
$941$	−31.4448	−	13.0249i	−1.02507	−	0.424599i	−0.830931	+	0.556375i	$0.812192\pi$
$942$		0			0
$943$		−	3.74294i		−	0.121887i
$944$		0			0
$945$		−	40.6104i		−	1.32106i
$946$		0			0
$947$	44.9596	+	18.6229i	1.46099	+	0.605162i	0.964784	−	0.263043i	$-0.0847260\pi$
$947$	44.9596	+	18.6229i	1.46099	+	0.605162i	0.496206	+	0.868205i	$0.334726\pi$
$948$		0			0
$949$	−0.738644	−	1.78324i	−0.0239774	−	0.0578866i
$950$		0			0
$951$	−20.0628	−	20.0628i	−0.650582	−	0.650582i
$952$		0			0
$953$	33.7784	−	33.7784i	1.09419	−	1.09419i	0.0991142	−	0.995076i	$-0.468399\pi$
$953$	33.7784	−	33.7784i	1.09419	−	1.09419i	0.995076	−	0.0991142i	$-0.0316009\pi$
$954$		0			0
$955$	15.4647	−	6.40569i	0.500426	−	0.207283i
$956$		0			0
$957$	0.363323	−	0.877140i	0.0117446	−	0.0283539i
$958$		0			0
$959$	−59.2472			−1.91319
$960$		0			0
$961$	−29.6274			−0.955723
$962$		0			0
$963$	−5.94977	+	14.3640i	−0.191729	+	0.462874i
$964$		0			0
$965$	10.6644	−	4.41735i	0.343300	−	0.142199i
$966$		0			0
$967$	−19.3234	+	19.3234i	−0.621399	+	0.621399i	−0.945889	−	0.324490i	$-0.894807\pi$
$967$	−19.3234	+	19.3234i	−0.621399	+	0.621399i	0.324490	+	0.945889i	$0.394807\pi$
$968$		0			0
$969$	−13.2739	−	13.2739i	−0.426420	−	0.426420i
$970$		0			0
$971$	−21.9185	−	52.9160i	−0.703399	−	1.69816i	−0.715869	−	0.698234i	$-0.753969\pi$
$971$	−21.9185	−	52.9160i	−0.703399	−	1.69816i	0.0124699	−	0.999922i	$-0.496031\pi$
$972$		0			0
$973$	18.5983	+	7.70369i	0.596236	+	0.246969i
$974$		0			0
$975$		−	6.77254i		−	0.216895i
$976$		0			0
$977$		−	12.2792i		−	0.392848i	−0.980519	−	0.196424i	$-0.937067\pi$
$977$		−	12.2792i		−	0.392848i	0.980519	−	0.196424i	$-0.0629329\pi$
$978$		0			0
$979$	0.807628	+	0.334530i	0.0258119	+	0.0106916i
$980$		0			0
$981$	5.28477	+	12.7586i	0.168730	+	0.407349i
$982$		0			0
$983$	14.1052	+	14.1052i	0.449887	+	0.449887i	0.895317	−	0.445430i	$-0.146949\pi$
$983$	14.1052	+	14.1052i	0.449887	+	0.449887i	−0.445430	+	0.895317i	$0.646949\pi$
$984$		0			0
$985$	6.18989	−	6.18989i	0.197226	−	0.197226i
$986$		0			0
$987$	−13.2739	+	5.49824i	−0.422513	+	0.175011i
$988$		0			0
$989$	−2.68000	+	6.47010i	−0.0852191	+	0.205737i
$990$		0			0
$991$	39.8015			1.26434			0.632169	−	0.774831i	$-0.282165\pi$
$991$	39.8015			1.26434			0.632169	+	0.774831i	$0.282165\pi$
$992$		0			0
$993$	14.8491			0.471222
$994$		0			0
$995$	−6.14186	+	14.8278i	−0.194710	+	0.470071i
$996$		0			0
$997$	−6.20720	+	2.57111i	−0.196584	+	0.0814278i	−0.478803	−	0.877922i	$-0.658929\pi$
$997$	−6.20720	+	2.57111i	−0.196584	+	0.0814278i	0.282219	+	0.959350i	$0.408929\pi$
$998$		0			0
$999$	−18.0886	+	18.0886i	−0.572299	+	0.572299i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.g.h.65.2		8
4.3	odd	2		512.2.g.f.65.1		8
8.3	odd	2		512.2.g.g.65.2		8
8.5	even	2		512.2.g.e.65.1		8
16.3	odd	4		128.2.g.b.81.1		8
16.5	even	4		256.2.g.d.161.1		8
16.11	odd	4		256.2.g.c.161.2		8
16.13	even	4		32.2.g.b.29.1	yes	8
32.3	odd	8		128.2.g.b.49.1		8
32.5	even	8	inner	512.2.g.h.449.2		8
32.11	odd	8		512.2.g.g.449.2		8
32.13	even	8		256.2.g.d.97.1		8
32.19	odd	8		256.2.g.c.97.2		8
32.21	even	8		512.2.g.e.449.1		8
32.27	odd	8		512.2.g.f.449.1		8
32.29	even	8		32.2.g.b.21.1	✓	8
48.29	odd	4		288.2.v.b.253.2		8
48.35	even	4		1152.2.v.b.721.2		8
64.5	even	16		4096.2.a.k.1.6		8
64.27	odd	16		4096.2.a.q.1.6		8
64.37	even	16		4096.2.a.k.1.3		8
64.59	odd	16		4096.2.a.q.1.3		8
80.13	odd	4		800.2.ba.c.349.1		8
80.29	even	4		800.2.y.b.701.2		8
80.77	odd	4		800.2.ba.d.349.2		8
96.29	odd	8		288.2.v.b.181.2		8
96.35	even	8		1152.2.v.b.433.2		8
160.29	even	8		800.2.y.b.501.2		8
160.93	odd	8		800.2.ba.d.149.2		8
160.157	odd	8		800.2.ba.c.149.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.2.g.b.21.1	✓	8	32.29	even	8
32.2.g.b.29.1	yes	8	16.13	even	4
128.2.g.b.49.1		8	32.3	odd	8
128.2.g.b.81.1		8	16.3	odd	4
256.2.g.c.97.2		8	32.19	odd	8
256.2.g.c.161.2		8	16.11	odd	4
256.2.g.d.97.1		8	32.13	even	8
256.2.g.d.161.1		8	16.5	even	4
288.2.v.b.181.2		8	96.29	odd	8
288.2.v.b.253.2		8	48.29	odd	4
512.2.g.e.65.1		8	8.5	even	2
512.2.g.e.449.1		8	32.21	even	8
512.2.g.f.65.1		8	4.3	odd	2
512.2.g.f.449.1		8	32.27	odd	8
512.2.g.g.65.2		8	8.3	odd	2
512.2.g.g.449.2		8	32.11	odd	8
512.2.g.h.65.2		8	1.1	even	1	trivial
512.2.g.h.449.2		8	32.5	even	8	inner
800.2.y.b.501.2		8	160.29	even	8
800.2.y.b.701.2		8	80.29	even	4
800.2.ba.c.149.1		8	160.157	odd	8
800.2.ba.c.349.1		8	80.13	odd	4
800.2.ba.d.149.2		8	160.93	odd	8
800.2.ba.d.349.2		8	80.77	odd	4
1152.2.v.b.433.2		8	96.35	even	8
1152.2.v.b.721.2		8	48.35	even	4
4096.2.a.k.1.3		8	64.37	even	16
4096.2.a.k.1.6		8	64.5	even	16
4096.2.a.q.1.3		8	64.59	odd	16
4096.2.a.q.1.6		8	64.27	odd	16

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:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.g (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.529706 - 1.27882i) q^{3} +(1.70711 - 0.707107i) q^{5} +(2.74912 - 2.74912i) q^{7} +(0.766519 + 0.766519i) q^{9} +O(q^{10})\)	\(q+(0.529706 - 1.27882i) q^{3} +(1.70711 - 0.707107i) q^{5} +(2.74912 - 2.74912i) q^{7} +(0.766519 + 0.766519i) q^{9} +(0.0560803 + 0.135390i) q^{11} +(-2.85054 - 1.18073i) q^{13} -2.55765i q^{15} +6.44549i q^{17} +(-1.94392 - 0.805198i) q^{19} +(-2.05941 - 4.97186i) q^{21} +(-0.749118 - 0.749118i) q^{23} +(-1.12132 + 1.12132i) q^{25} +(5.22274 - 2.16333i) q^{27} +(1.79113 - 4.32417i) q^{29} +1.17157 q^{31} +0.202846 q^{33} +(2.74912 - 6.63696i) q^{35} +(-4.18073 + 1.73172i) q^{37} +(-3.01990 + 3.01990i) q^{39} +(2.49824 + 2.49824i) q^{41} +(-2.52971 - 6.10725i) q^{43} +(1.85054 + 0.766519i) q^{45} -2.66981i q^{47} -8.11529i q^{49} +(8.24264 + 3.41421i) q^{51} +(0.682497 + 1.64769i) q^{53} +(0.191470 + 0.191470i) q^{55} +(-2.05941 + 2.05941i) q^{57} +(-3.47029 + 1.43744i) q^{59} +(-1.43633 + 3.46760i) q^{61} +4.21450 q^{63} -5.70108 q^{65} +(-5.83176 + 14.0791i) q^{67} +(-1.35480 + 0.561177i) q^{69} +(3.40950 - 3.40950i) q^{71} +(0.442353 + 0.442353i) q^{73} +(0.840001 + 2.02794i) q^{75} +(0.526374 + 0.218031i) q^{77} +7.07550i q^{79} -4.57283i q^{81} +(-7.23931 - 2.99862i) q^{83} +(4.55765 + 11.0031i) q^{85} +(-4.58107 - 4.58107i) q^{87} +(4.21803 - 4.21803i) q^{89} +(-11.0824 + 4.59050i) q^{91} +(0.620589 - 1.49824i) q^{93} -3.88784 q^{95} +10.3267 q^{97} +(-0.0607923 + 0.146766i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} + 8 q^{5} + 8 q^{7}+O(q^{10}) \) 8 * q + 4 * q^3 + 8 * q^5 + 8 * q^7	\( 8 q + 4 q^{3} + 8 q^{5} + 8 q^{7} + 12 q^{11} - 4 q^{19} - 16 q^{21} + 8 q^{23} + 8 q^{25} + 16 q^{27} - 8 q^{29} + 32 q^{31} - 16 q^{33} + 8 q^{35} - 16 q^{37} - 16 q^{39} - 8 q^{41} - 20 q^{43} - 8 q^{45} + 32 q^{51} + 16 q^{53} + 16 q^{55} - 16 q^{57} - 28 q^{59} - 40 q^{63} - 12 q^{67} + 24 q^{71} + 32 q^{73} + 20 q^{75} + 16 q^{77} - 36 q^{83} + 8 q^{85} - 56 q^{87} + 16 q^{89} + 32 q^{93} - 8 q^{95} + 32 q^{97} - 4 q^{99}+O(q^{100}) \) 8 * q + 4 * q^3 + 8 * q^5 + 8 * q^7 + 12 * q^11 - 4 * q^19 - 16 * q^21 + 8 * q^23 + 8 * q^25 + 16 * q^27 - 8 * q^29 + 32 * q^31 - 16 * q^33 + 8 * q^35 - 16 * q^37 - 16 * q^39 - 8 * q^41 - 20 * q^43 - 8 * q^45 + 32 * q^51 + 16 * q^53 + 16 * q^55 - 16 * q^57 - 28 * q^59 - 40 * q^63 - 12 * q^67 + 24 * q^71 + 32 * q^73 + 20 * q^75 + 16 * q^77 - 36 * q^83 + 8 * q^85 - 56 * q^87 + 16 * q^89 + 32 * q^93 - 8 * q^95 + 32 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

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