LMFDB - Embedded newform 512.2.k.a.17.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [512,2,Mod(17,512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(512, base_ring=CyclotomicField(32))

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("512.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.k (of order $32$, degree $16$, 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:	$240$
Relative dimension:	$15$ over $\Q(\zeta_{32})$
Twist minimal:	no (minimal twist has level 128)
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			17.14
Character	$\chi$	$=$	512.17
Dual form			512.2.k.a.241.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.32215 - 2.47358i) q^{3} +(-2.12126 - 1.74087i) q^{5} +(3.19792 + 2.13678i) q^{7} +(-2.70377 - 4.04648i) q^{9} +O(q^{10})$	\(q+(1.32215 - 2.47358i) q^{3} +(-2.12126 - 1.74087i) q^{5} +(3.19792 + 2.13678i) q^{7} +(-2.70377 - 4.04648i) q^{9} +(1.25334 - 4.13171i) q^{11} +(-0.501092 - 0.610582i) q^{13} +(-7.11080 + 2.94539i) q^{15} +(0.240856 + 0.0997657i) q^{17} +(-4.44596 - 0.437888i) q^{19} +(9.51362 - 5.08513i) q^{21} +(4.69761 + 0.934412i) q^{23} +(0.493646 + 2.48173i) q^{25} +(-5.21033 + 0.513173i) q^{27} +(-8.51360 + 2.58257i) q^{29} +(-0.255806 + 0.255806i) q^{31} +(-8.56299 - 8.56299i) q^{33} +(-3.06374 - 10.0998i) q^{35} +(0.310120 + 3.14870i) q^{37} +(-2.17284 + 0.432205i) q^{39} +(0.805921 - 4.05164i) q^{41} +(4.76859 + 8.92140i) q^{43} +(-1.30900 + 13.2905i) q^{45} +(-0.436499 + 1.05380i) q^{47} +(2.98205 + 7.19932i) q^{49} +(0.565227 - 0.463869i) q^{51} +(3.17417 + 0.962875i) q^{53} +(-9.85142 + 6.58251i) q^{55} +(-6.96139 + 10.4185i) q^{57} +(6.23409 - 7.59626i) q^{59} +(3.61925 + 1.93453i) q^{61} -18.7177i q^{63} +2.16754i q^{65} +(9.15028 + 4.89093i) q^{67} +(8.52230 - 10.3845i) q^{69} +(6.29550 - 9.42188i) q^{71} +(2.44476 - 1.63354i) q^{73} +(6.79142 + 2.06015i) q^{75} +(12.8366 - 10.5347i) q^{77} +(-2.04705 - 4.94201i) q^{79} +(-0.0323130 + 0.0780105i) q^{81} +(-0.764603 + 7.76314i) q^{83} +(-0.337238 - 0.630927i) q^{85} +(-4.86810 + 24.4736i) q^{87} +(6.00085 - 1.19364i) q^{89} +(-0.297770 - 3.02331i) q^{91} +(0.294540 + 0.970969i) q^{93} +(8.66870 + 8.66870i) q^{95} +(-1.83234 + 1.83234i) q^{97} +(-20.1077 + 6.09959i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9}+O(q^{10}) $ 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9	$ 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9} + 16 q^{11} - 16 q^{13} + 16 q^{15} - 16 q^{17} + 16 q^{19} - 16 q^{21} + 16 q^{23} - 16 q^{25} + 16 q^{27} - 16 q^{29} + 16 q^{31} - 16 q^{33} + 16 q^{35} - 16 q^{37} + 16 q^{39} - 16 q^{41} + 16 q^{43} - 16 q^{45} + 16 q^{47} - 16 q^{49} + 16 q^{51} - 16 q^{53} + 16 q^{55} - 16 q^{57} + 16 q^{59} - 16 q^{61} + 16 q^{67} - 16 q^{69} + 16 q^{71} - 16 q^{73} + 16 q^{75} - 16 q^{77} + 16 q^{79} - 16 q^{81} + 16 q^{83} - 16 q^{85} + 16 q^{87} - 16 q^{89} + 16 q^{91} - 16 q^{93} + 16 q^{95} - 16 q^{97} + 16 q^{99}+O(q^{100}) $ 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9 + 16 * q^11 - 16 * q^13 + 16 * q^15 - 16 * q^17 + 16 * q^19 - 16 * q^21 + 16 * q^23 - 16 * q^25 + 16 * q^27 - 16 * q^29 + 16 * q^31 - 16 * q^33 + 16 * q^35 - 16 * q^37 + 16 * q^39 - 16 * q^41 + 16 * q^43 - 16 * q^45 + 16 * q^47 - 16 * q^49 + 16 * q^51 - 16 * q^53 + 16 * q^55 - 16 * q^57 + 16 * q^59 - 16 * q^61 + 16 * q^67 - 16 * q^69 + 16 * q^71 - 16 * q^73 + 16 * q^75 - 16 * q^77 + 16 * q^79 - 16 * q^81 + 16 * q^83 - 16 * q^85 + 16 * q^87 - 16 * q^89 + 16 * q^91 - 16 * q^93 + 16 * q^95 - 16 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{7}{32}\right)$	$1$

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
$3$	1.32215	−	2.47358i	0.763346	−	1.42812i	−0.135921	−	0.990720i	$-0.543399\pi$
$3$	1.32215	−	2.47358i	0.763346	−	1.42812i	0.899267	−	0.437400i	$-0.144101\pi$
$4$		0			0
$5$	−2.12126	−	1.74087i	−0.948654	−	0.778540i	0.0265957	−	0.999646i	$-0.491533\pi$
$5$	−2.12126	−	1.74087i	−0.948654	−	0.778540i	−0.975250	+	0.221106i	$0.929033\pi$
$6$		0			0
$7$	3.19792	+	2.13678i	1.20870	+	0.807626i	0.985916	−	0.167242i	$-0.0534861\pi$
$7$	3.19792	+	2.13678i	1.20870	+	0.807626i	0.222782	+	0.974868i	$0.428486\pi$
$8$		0			0
$9$	−2.70377	−	4.04648i	−0.901258	−	1.34883i
$10$		0			0
$11$	1.25334	−	4.13171i	0.377896	−	1.24576i	−0.537521	−	0.843251i	$-0.680639\pi$
$11$	1.25334	−	4.13171i	0.377896	−	1.24576i	0.915417	−	0.402507i	$-0.131861\pi$
$12$		0			0
$13$	−0.501092	−	0.610582i	−0.138978	−	0.169345i	0.698870	−	0.715249i	$-0.253687\pi$
$13$	−0.501092	−	0.610582i	−0.138978	−	0.169345i	−0.837848	+	0.545903i	$0.816187\pi$
$14$		0			0
$15$	−7.11080	+	2.94539i	−1.83600	+	0.760496i
$16$		0			0
$17$	0.240856	+	0.0997657i	0.0584161	+	0.0241967i	0.411700	−	0.911319i	$-0.364935\pi$
$17$	0.240856	+	0.0997657i	0.0584161	+	0.0241967i	−0.353284	+	0.935516i	$0.614935\pi$
$18$		0			0
$19$	−4.44596	−	0.437888i	−1.01997	−	0.100458i	−0.425817	−	0.904809i	$-0.640013\pi$
$19$	−4.44596	−	0.437888i	−1.01997	−	0.100458i	−0.594155	+	0.804351i	$0.702513\pi$
$20$		0			0
$21$	9.51362	−	5.08513i	2.07604	−	1.10967i
$22$		0			0
$23$	4.69761	+	0.934412i	0.979519	+	0.194838i	0.658785	−	0.752331i	$-0.271071\pi$
$23$	4.69761	+	0.934412i	0.979519	+	0.194838i	0.320734	+	0.947169i	$0.396071\pi$
$24$		0			0
$25$	0.493646	+	2.48173i	0.0987293	+	0.496346i
$26$		0			0
$27$	−5.21033	+	0.513173i	−1.00273	+	0.0987602i
$28$		0			0
$29$	−8.51360	+	2.58257i	−1.58094	+	0.479572i	−0.954077	−	0.299561i	$-0.903160\pi$
$29$	−8.51360	+	2.58257i	−1.58094	+	0.479572i	−0.626859	+	0.779133i	$0.715660\pi$
$30$		0			0
$31$	−0.255806	+	0.255806i	−0.0459440	+	0.0459440i	−0.729706	−	0.683762i	$-0.760343\pi$
$31$	−0.255806	+	0.255806i	−0.0459440	+	0.0459440i	0.683762	+	0.729706i	$0.260343\pi$
$32$		0			0
$33$	−8.56299	−	8.56299i	−1.49062	−	1.49062i
$34$		0			0
$35$	−3.06374	−	10.0998i	−0.517867	−	1.70718i
$36$		0			0
$37$	0.310120	+	3.14870i	0.0509834	+	0.517643i	0.986431	+	0.164177i	$0.0524969\pi$
$37$	0.310120	+	3.14870i	0.0509834	+	0.517643i	−0.935448	+	0.353466i	$0.885003\pi$
$38$		0			0
$39$	−2.17284	+	0.432205i	−0.347933	+	0.0692082i
$40$		0			0
$41$	0.805921	−	4.05164i	0.125864	−	0.632760i	−0.865423	−	0.501041i	$-0.832950\pi$
$41$	0.805921	−	4.05164i	0.125864	−	0.632760i	0.991287	−	0.131719i	$-0.0420495\pi$
$42$		0			0
$43$	4.76859	+	8.92140i	0.727203	+	1.36050i	0.924890	+	0.380236i	$0.124157\pi$
$43$	4.76859	+	8.92140i	0.727203	+	1.36050i	−0.197686	+	0.980265i	$0.563343\pi$
$44$		0			0
$45$	−1.30900	+	13.2905i	−0.195135	+	1.98124i
$46$		0			0
$47$	−0.436499	+	1.05380i	−0.0636699	+	0.153713i	−0.952512	−	0.304501i	$-0.901510\pi$
$47$	−0.436499	+	1.05380i	−0.0636699	+	0.153713i	0.888842	+	0.458213i	$0.151510\pi$
$48$		0			0
$49$	2.98205	+	7.19932i	0.426008	+	1.02847i
$50$		0			0
$51$	0.565227	−	0.463869i	0.0791475	−	0.0649547i
$52$		0			0
$53$	3.17417	+	0.962875i	0.436006	+	0.132261i	0.500655	−	0.865647i	$-0.333093\pi$
$53$	3.17417	+	0.962875i	0.436006	+	0.132261i	−0.0646484	+	0.997908i	$0.520593\pi$
$54$		0			0
$55$	−9.85142	+	6.58251i	−1.32837	+	0.887585i
$56$		0			0
$57$	−6.96139	+	10.4185i	−0.922058	+	1.37996i
$58$		0			0
$59$	6.23409	−	7.59626i	0.811609	−	0.988949i	−0.188367	−	0.982099i	$-0.560319\pi$
$59$	6.23409	−	7.59626i	0.811609	−	0.988949i	0.999977	−	0.00685027i	$-0.00218053\pi$
$60$		0			0
$61$	3.61925	+	1.93453i	0.463397	+	0.247691i	0.686536	−	0.727096i	$-0.259130\pi$
$61$	3.61925	+	1.93453i	0.463397	+	0.247691i	−0.223139	+	0.974787i	$0.571630\pi$
$62$		0			0
$63$		−	18.7177i		−	2.35821i
$64$		0			0
$65$			2.16754i			0.268850i
$66$		0			0
$67$	9.15028	+	4.89093i	1.11788	+	0.597522i	0.923575	−	0.383418i	$-0.125253\pi$
$67$	9.15028	+	4.89093i	1.11788	+	0.597522i	0.194310	+	0.980940i	$0.437753\pi$
$68$		0			0
$69$	8.52230	−	10.3845i	1.02596	−	1.25014i
$70$		0			0
$71$	6.29550	−	9.42188i	0.747138	−	1.11817i	−0.241870	−	0.970309i	$-0.577761\pi$
$71$	6.29550	−	9.42188i	0.747138	−	1.11817i	0.989008	−	0.147863i	$-0.0472394\pi$
$72$		0			0
$73$	2.44476	−	1.63354i	0.286138	−	0.191191i	−0.404215	−	0.914664i	$-0.632455\pi$
$73$	2.44476	−	1.63354i	0.286138	−	0.191191i	0.690353	+	0.723473i	$0.257455\pi$
$74$		0			0
$75$	6.79142	+	2.06015i	0.784206	+	0.237886i
$76$		0			0
$77$	12.8366	−	10.5347i	1.46287	−	1.20055i
$78$		0			0
$79$	−2.04705	−	4.94201i	−0.230311	−	0.556020i	0.765903	−	0.642956i	$-0.222292\pi$
$79$	−2.04705	−	4.94201i	−0.230311	−	0.556020i	−0.996214	+	0.0869364i	$0.972292\pi$
$80$		0			0
$81$	−0.0323130	+	0.0780105i	−0.00359033	+	0.00866783i
$82$		0			0
$83$	−0.764603	+	7.76314i	−0.0839261	+	0.852116i	0.857407	+	0.514638i	$0.172074\pi$
$83$	−0.764603	+	7.76314i	−0.0839261	+	0.852116i	−0.941334	+	0.337478i	$0.890426\pi$
$84$		0			0
$85$	−0.337238	−	0.630927i	−0.0365785	−	0.0684336i
$86$		0			0
$87$	−4.86810	+	24.4736i	−0.521915	+	2.62384i
$88$		0			0
$89$	6.00085	−	1.19364i	0.636089	−	0.126526i	0.133496	−	0.991049i	$-0.457380\pi$
$89$	6.00085	−	1.19364i	0.636089	−	0.126526i	0.502593	+	0.864523i	$0.332380\pi$
$90$		0			0
$91$	−0.297770	−	3.02331i	−0.0312148	−	0.316929i
$92$		0			0
$93$	0.294540	+	0.970969i	0.0305424	+	0.100685i
$94$		0			0
$95$	8.66870	+	8.66870i	0.889390	+	0.889390i
$96$		0			0
$97$	−1.83234	+	1.83234i	−0.186046	+	0.186046i	−0.793984	−	0.607938i	$-0.791997\pi$
$97$	−1.83234	+	1.83234i	−0.186046	+	0.186046i	0.607938	+	0.793984i	$0.291997\pi$
$98$		0			0
$99$	−20.1077	+	6.09959i	−2.02089	+	0.613032i
$100$		0			0
$101$	−1.22184	+	0.120340i	−0.121577	+	0.0119743i	−0.158623	−	0.987339i	$-0.550705\pi$
$101$	−1.22184	+	0.120340i	−0.121577	+	0.0119743i	0.0370455	+	0.999314i	$0.488205\pi$
$102$		0			0
$103$	−0.827184	−	4.15854i	−0.0815049	−	0.409753i	−0.999901	−	0.0140900i	$-0.995515\pi$
$103$	−0.827184	−	4.15854i	−0.0815049	−	0.409753i	0.918396	−	0.395663i	$-0.129485\pi$
$104$		0			0
$105$	−29.0334	−	5.77510i	−2.83337	−	0.563592i
$106$		0			0
$107$	17.8813	−	9.55774i	1.72865	−	0.923981i	0.770625	−	0.637289i	$-0.219944\pi$
$107$	17.8813	−	9.55774i	1.72865	−	0.923981i	0.958023	−	0.286692i	$-0.0925557\pi$
$108$		0			0
$109$	12.7099	+	1.25182i	1.21739	+	0.119903i	0.686241	−	0.727374i	$-0.259260\pi$
$109$	12.7099	+	1.25182i	1.21739	+	0.119903i	0.531151	+	0.847277i	$0.321760\pi$
$110$		0			0
$111$	8.19857	+	3.39596i	0.778174	+	0.322330i
$112$		0			0
$113$	−7.12404	+	2.95087i	−0.670173	+	0.277595i	−0.691712	−	0.722173i	$-0.743143\pi$
$113$	−7.12404	+	2.95087i	−0.670173	+	0.277595i	0.0215392	+	0.999768i	$0.493143\pi$
$114$		0			0
$115$	−8.33814	−	10.1600i	−0.777535	−	0.947429i
$116$		0			0
$117$	−1.11587	+	3.67854i	−0.103162	+	0.340081i
$118$		0			0
$119$	0.557059	+	0.833698i	0.0510655	+	0.0764250i
$120$		0			0
$121$	−6.35400	−	4.24561i	−0.577636	−	0.385964i
$122$		0			0
$123$	−8.95649	−	7.35040i	−0.807579	−	0.662763i
$124$		0			0
$125$	−3.19470	+	5.97686i	−0.285742	+	0.534587i
$126$		0			0
$127$	−0.233514			−0.0207210			−0.0103605	−	0.999946i	$-0.503298\pi$
$127$	−0.233514			−0.0207210			−0.0103605	+	0.999946i	$0.503298\pi$
$128$		0			0
$129$	28.3726			2.49807
$130$		0			0
$131$	−10.3038	+	19.2771i	−0.900249	+	1.68425i	−0.188183	+	0.982134i	$0.560260\pi$
$131$	−10.3038	+	19.2771i	−0.900249	+	1.68425i	−0.712065	+	0.702113i	$0.752240\pi$
$132$		0			0
$133$	−13.2821	−	10.9004i	−1.15171	−	0.945180i
$134$		0			0
$135$	11.9458	+	7.98194i	1.02813	+	0.686976i
$136$		0			0
$137$	5.54635	+	8.30070i	0.473857	+	0.709177i	0.988998	−	0.147929i	$-0.0472606\pi$
$137$	5.54635	+	8.30070i	0.473857	+	0.709177i	−0.515141	+	0.857105i	$0.672261\pi$
$138$		0			0
$139$	−3.05162	+	10.0599i	−0.258835	+	0.853266i	0.727156	+	0.686472i	$0.240842\pi$
$139$	−3.05162	+	10.0599i	−0.258835	+	0.853266i	−0.985992	+	0.166794i	$0.946658\pi$
$140$		0			0
$141$	2.02954	+	2.47300i	0.170918	+	0.208264i
$142$		0			0
$143$	−3.15079	+	1.30510i	−0.263482	+	0.109138i
$144$		0			0
$145$	22.5554	+	9.34277i	1.87313	+	0.775875i
$146$		0			0
$147$	21.7508	+	2.14227i	1.79397	+	0.176691i
$148$		0			0
$149$	−6.47560	+	3.46128i	−0.530502	+	0.283559i	−0.714821	−	0.699307i	$-0.753492\pi$
$149$	−6.47560	+	3.46128i	−0.530502	+	0.283559i	0.184319	+	0.982866i	$0.440992\pi$
$150$		0			0
$151$	0.107021	+	0.0212878i	0.00870926	+	0.00173238i	0.199443	−	0.979909i	$-0.436087\pi$
$151$	0.107021	+	0.0212878i	0.00870926	+	0.00173238i	−0.190734	+	0.981642i	$0.561087\pi$
$152$		0			0
$153$	−0.247519	−	1.24436i	−0.0200107	−	0.100601i
$154$		0			0
$155$	0.987953	−	0.0973049i	0.0793543	−	0.00781572i
$156$		0			0
$157$	−19.1482	+	5.80853i	−1.52819	+	0.463572i	−0.938854	−	0.344316i	$-0.888111\pi$
$157$	−19.1482	+	5.80853i	−1.52819	+	0.463572i	−0.589337	+	0.807888i	$0.700611\pi$
$158$		0			0
$159$	6.57849	−	6.57849i	0.521708	−	0.521708i
$160$		0			0
$161$	13.0259	+	13.0259i	1.02659	+	1.02659i
$162$		0			0
$163$	2.15947	+	7.11881i	0.169142	+	0.557588i	0.999999	+	0.00110187i	$0.000350738\pi$
$163$	2.15947	+	7.11881i	0.169142	+	0.557588i	−0.830857	+	0.556486i	$0.812149\pi$
$164$		0			0
$165$	3.25724	+	33.0713i	0.253576	+	2.57460i
$166$		0			0
$167$	−7.95268	+	1.58189i	−0.615397	+	0.122410i	−0.492939	−	0.870064i	$-0.664078\pi$
$167$	−7.95268	+	1.58189i	−0.615397	+	0.122410i	−0.122458	+	0.992474i	$0.539078\pi$
$168$		0			0
$169$	2.41446	−	12.1383i	0.185727	−	0.933715i
$170$		0			0
$171$	10.2490	+	19.1744i	0.783757	+	1.46631i
$172$		0			0
$173$	1.03204	−	10.4785i	0.0784649	−	0.796668i	−0.872756	−	0.488157i	$-0.837669\pi$
$173$	1.03204	−	10.4785i	0.0784649	−	0.796668i	0.951221	−	0.308511i	$-0.0998306\pi$
$174$		0			0
$175$	−3.72426	+	8.99117i	−0.281528	+	0.679669i
$176$		0			0
$177$	−10.5475	−	25.4639i	−0.792799	−	1.91399i
$178$		0			0
$179$	−3.34418	+	2.74450i	−0.249956	+	0.205134i	−0.751025	−	0.660274i	$-0.770440\pi$
$179$	−3.34418	+	2.74450i	−0.249956	+	0.205134i	0.501069	+	0.865407i	$0.332940\pi$
$180$		0			0
$181$	−4.66741	−	1.41584i	−0.346926	−	0.105239i	0.112013	−	0.993707i	$-0.464270\pi$
$181$	−4.66741	−	1.41584i	−0.346926	−	0.105239i	−0.458939	+	0.888468i	$0.651770\pi$
$182$		0			0
$183$	9.57040	−	6.39474i	0.707465	−	0.472713i
$184$		0			0
$185$	4.82363	−	7.21907i	0.354640	−	0.530757i
$186$		0			0
$187$	0.714077	−	0.870106i	0.0522185	−	0.0636284i
$188$		0			0
$189$	−17.7587	−	9.49225i	−1.29176	−	0.690459i
$190$		0			0
$191$			3.79551i			0.274633i	0.990527	+	0.137317i	$0.0438478\pi$
$191$			3.79551i			0.274633i	−0.990527	+	0.137317i	$0.956152\pi$
$192$		0			0
$193$			16.5298i			1.18984i	0.803785	+	0.594920i	$0.202816\pi$
$193$			16.5298i			1.18984i	−0.803785	+	0.594920i	$0.797184\pi$
$194$		0			0
$195$	5.36156	+	2.86582i	0.383950	+	0.205225i
$196$		0			0
$197$	−4.61131	+	5.61889i	−0.328542	+	0.400329i	−0.910916	−	0.412591i	$-0.864624\pi$
$197$	−4.61131	+	5.61889i	−0.328542	+	0.400329i	0.582374	+	0.812921i	$0.302124\pi$
$198$		0			0
$199$	−14.7924	+	22.1384i	−1.04861	+	1.56935i	−0.249298	+	0.968427i	$0.580200\pi$
$199$	−14.7924	+	22.1384i	−1.04861	+	1.56935i	−0.799307	+	0.600922i	$0.794800\pi$
$200$		0			0
$201$	24.1962	−	16.1674i	1.70667	−	1.14036i
$202$		0			0
$203$	−32.7442	−	9.93283i	−2.29819	−	0.697148i
$204$		0			0
$205$	−8.76294	+	7.19156i	−0.612030	+	0.502280i
$206$		0			0
$207$	−8.92019	−	21.5352i	−0.619996	−	1.49680i
$208$		0			0
$209$	−7.38152	+	17.8206i	−0.510591	+	1.23267i
$210$		0			0
$211$	1.72753	−	17.5399i	0.118928	−	1.20750i	−0.731661	−	0.681669i	$-0.761254\pi$
$211$	1.72753	−	17.5399i	0.118928	−	1.20750i	0.850589	−	0.525831i	$-0.176246\pi$
$212$		0			0
$213$	−14.9821	−	28.0296i	−1.02656	−	1.92055i
$214$		0			0
$215$	5.41560	−	27.2261i	0.369341	−	1.85680i
$216$		0			0
$217$	−1.36464	+	0.271445i	−0.0926381	+	0.0184269i
$218$		0			0
$219$	−0.808328	−	8.20709i	−0.0546217	−	0.554584i
$220$		0			0
$221$	−0.0597757	−	0.197054i	−0.00402095	−	0.0132553i
$222$		0			0
$223$	−0.158525	−	0.158525i	−0.0106156	−	0.0106156i	0.701779	−	0.712395i	$-0.252389\pi$
$223$	−0.158525	−	0.158525i	−0.0106156	−	0.0106156i	−0.712395	+	0.701779i	$0.752389\pi$
$224$		0			0
$225$	8.70757	−	8.70757i	0.580504	−	0.580504i
$226$		0			0
$227$	1.08410	−	0.328859i	0.0719545	−	0.0218271i	−0.254102	−	0.967177i	$-0.581780\pi$
$227$	1.08410	−	0.328859i	0.0719545	−	0.0218271i	0.326057	+	0.945350i	$0.394280\pi$
$228$		0			0
$229$	−16.0292	+	1.57874i	−1.05924	+	0.104326i	−0.612604	−	0.790390i	$-0.709878\pi$
$229$	−16.0292	+	1.57874i	−1.05924	+	0.104326i	−0.446636	+	0.894716i	$0.647378\pi$
$230$		0			0
$231$	−9.08650	−	45.6809i	−0.597848	−	3.00558i
$232$		0			0
$233$	−5.46588	−	1.08723i	−0.358082	−	0.0712268i	0.0127714	−	0.999918i	$-0.495935\pi$
$233$	−5.46588	−	1.08723i	−0.358082	−	0.0712268i	−0.370853	+	0.928692i	$0.620935\pi$
$234$		0			0
$235$	2.76045	−	1.47549i	0.180072	−	0.0962506i
$236$		0			0
$237$	−14.9310	−	1.47057i	−0.969870	−	0.0955238i
$238$		0			0
$239$	−2.18280	−	0.904145i	−0.141194	−	0.0584843i	0.310968	−	0.950420i	$-0.399347\pi$
$239$	−2.18280	−	0.904145i	−0.141194	−	0.0584843i	−0.452161	+	0.891936i	$0.649347\pi$
$240$		0			0
$241$	−20.8481	+	8.63558i	−1.34295	+	0.556266i	−0.934320	−	0.356435i	$-0.883992\pi$
$241$	−20.8481	+	8.63558i	−1.34295	+	0.556266i	−0.408626	+	0.912702i	$0.633992\pi$
$242$		0			0
$243$	−9.81394	−	11.9583i	−0.629565	−	0.767127i
$244$		0			0
$245$	6.20737	−	20.4630i	0.396574	−	1.30733i
$246$		0			0
$247$	1.96047	+	2.93404i	0.124741	+	0.186689i
$248$		0			0
$249$	18.1918	+	12.1554i	1.15286	+	0.770315i
$250$		0			0
$251$	−2.18699	−	1.79482i	−0.138041	−	0.113288i	0.562839	−	0.826567i	$-0.309709\pi$
$251$	−2.18699	−	1.79482i	−0.138041	−	0.113288i	−0.700880	+	0.713279i	$0.747209\pi$
$252$		0			0
$253$	9.74842	−	18.2380i	0.612878	−	1.14661i
$254$		0			0
$255$	−2.00653			−0.125654
$256$		0			0
$257$	16.0445			1.00083			0.500415	−	0.865786i	$-0.333181\pi$
$257$	16.0445			1.00083			0.500415	+	0.865786i	$0.333181\pi$
$258$		0			0
$259$	−5.73633	+	10.7319i	−0.356438	+	0.666850i
$260$		0			0
$261$	33.4692	+	27.4675i	2.07169	+	1.70019i
$262$		0			0
$263$	2.18327	+	1.45881i	0.134626	+	0.0899541i	0.621060	−	0.783763i	$-0.286702\pi$
$263$	2.18327	+	1.45881i	0.134626	+	0.0899541i	−0.486434	+	0.873717i	$0.661702\pi$
$264$		0			0
$265$	−5.05699	−	7.56833i	−0.310649	−	0.464919i
$266$		0			0
$267$	4.98148	−	16.4217i	0.304862	−	1.00499i
$268$		0			0
$269$	−5.05055	−	6.15411i	−0.307937	−	0.375223i	0.595929	−	0.803037i	$-0.296784\pi$
$269$	−5.05055	−	6.15411i	−0.307937	−	0.375223i	−0.903867	+	0.427814i	$0.859284\pi$
$270$		0			0
$271$	16.4393	−	6.80937i	0.998615	−	0.413640i	0.177326	−	0.984152i	$-0.443255\pi$
$271$	16.4393	−	6.80937i	0.998615	−	0.413640i	0.821289	+	0.570512i	$0.193255\pi$
$272$		0			0
$273$	−7.87209	−	3.26073i	−0.476441	−	0.197348i
$274$		0			0
$275$	10.8725	+	1.07085i	0.655636	+	0.0645745i
$276$		0			0
$277$	19.9433	−	10.6599i	1.19828	−	0.640492i	0.253222	−	0.967408i	$-0.418510\pi$
$277$	19.9433	−	10.6599i	1.19828	−	0.640492i	0.945053	+	0.326917i	$0.106010\pi$
$278$		0			0
$279$	1.72675	+	0.343473i	0.103378	+	0.0205632i
$280$		0			0
$281$	5.52721	+	27.7872i	0.329726	+	1.65764i	0.689262	+	0.724512i	$0.257935\pi$
$281$	5.52721	+	27.7872i	0.329726	+	1.65764i	−0.359537	+	0.933131i	$0.617065\pi$
$282$		0			0
$283$	6.73623	−	0.663460i	0.400427	−	0.0394386i	0.104200	−	0.994556i	$-0.466772\pi$
$283$	6.73623	−	0.663460i	0.400427	−	0.0394386i	0.296227	+	0.955118i	$0.404272\pi$
$284$		0			0
$285$	32.9040	−	9.98133i	1.94907	−	0.591243i
$286$		0			0
$287$	11.2347	−	11.2347i	0.663165	−	0.663165i
$288$		0			0
$289$	−11.9728	−	11.9728i	−0.704280	−	0.704280i
$290$		0			0
$291$	2.10980	+	6.95507i	0.123678	+	0.407713i
$292$		0			0
$293$	−1.32420	−	13.4448i	−0.0773606	−	0.785455i	−0.953097	−	0.302665i	$-0.902124\pi$
$293$	−1.32420	−	13.4448i	−0.0773606	−	0.785455i	0.875736	−	0.482790i	$-0.160376\pi$
$294$		0			0
$295$	−26.4482	+	5.26087i	−1.53987	+	0.306300i
$296$		0			0
$297$	−4.41004	+	22.1708i	−0.255897	+	1.28648i
$298$		0			0
$299$	−1.78340	−	3.33650i	−0.103137	−	0.192955i
$300$		0			0
$301$	−3.81352	+	38.7193i	−0.219808	+	2.23174i
$302$		0			0
$303$	−1.31778	+	3.18141i	−0.0757047	+	0.182767i
$304$		0			0
$305$	−4.30959	−	10.4043i	−0.246766	−	0.595746i
$306$		0			0
$307$	10.6061	−	8.70416i	0.605319	−	0.496773i	−0.281086	−	0.959683i	$-0.590695\pi$
$307$	10.6061	−	8.70416i	0.605319	−	0.496773i	0.886405	+	0.462910i	$0.153195\pi$
$308$		0			0
$309$	−11.3801	−	3.45212i	−0.647392	−	0.196384i
$310$		0			0
$311$	9.25189	−	6.18192i	0.524627	−	0.350544i	−0.264885	−	0.964280i	$-0.585334\pi$
$311$	9.25189	−	6.18192i	0.524627	−	0.350544i	0.789512	+	0.613736i	$0.210334\pi$
$312$		0			0
$313$	13.1661	−	19.7045i	0.744192	−	1.11376i	−0.245339	−	0.969437i	$-0.578899\pi$
$313$	13.1661	−	19.7045i	0.744192	−	1.11376i	0.989530	−	0.144324i	$-0.0461009\pi$
$314$		0			0
$315$	−32.5850	+	39.7050i	−1.83596	+	2.23712i
$316$		0			0
$317$	−20.0842	−	10.7352i	−1.12804	−	0.602951i	−0.201630	−	0.979462i	$-0.564624\pi$
$317$	−20.0842	−	10.7352i	−1.12804	−	0.602951i	−0.926412	+	0.376510i	$0.877124\pi$
$318$		0			0
$319$			38.4126i			2.15069i
$320$		0			0
$321$		−	56.8675i		−	3.17403i
$322$		0			0
$323$	−1.02715	−	0.549022i	−0.0571520	−	0.0305484i
$324$		0			0
$325$	1.26794	−	1.54499i	0.0703325	−	0.0857004i
$326$		0			0
$327$	19.9010	−	29.7839i	1.10053	−	1.64705i
$328$		0			0
$329$	−3.64762	+	2.43726i	−0.201100	+	0.134371i
$330$		0			0
$331$	14.5487	+	4.41330i	0.799670	+	0.242577i	0.663566	−	0.748117i	$-0.269042\pi$
$331$	14.5487	+	4.41330i	0.799670	+	0.242577i	0.136103	+	0.990695i	$0.456542\pi$
$332$		0			0
$333$	11.9027	−	9.76826i	0.652262	−	0.535298i
$334$		0			0
$335$	−10.8956	−	26.3043i	−0.595291	−	1.43716i
$336$		0			0
$337$	1.66026	−	4.00821i	0.0904399	−	0.218341i	−0.872187	−	0.489173i	$-0.837299\pi$
$337$	1.66026	−	4.00821i	0.0904399	−	0.218341i	0.962627	+	0.270832i	$0.0872987\pi$
$338$		0			0
$339$	−2.11987	+	21.5234i	−0.115135	+	1.16899i
$340$		0			0
$341$	0.736303	+	1.37753i	0.0398730	+	0.0745972i
$342$		0			0
$343$	−0.594630	+	2.98941i	−0.0321070	+	0.161413i
$344$		0			0
$345$	−36.1559	+	7.19186i	−1.94657	+	0.387197i
$346$		0			0
$347$	0.574858	+	5.83663i	0.0308600	+	0.313327i	0.998206	+	0.0598684i	$0.0190681\pi$
$347$	0.574858	+	5.83663i	0.0308600	+	0.313327i	−0.967346	+	0.253458i	$0.918432\pi$
$348$		0			0
$349$	6.23604	+	20.5575i	0.333808	+	1.10042i	0.949851	+	0.312704i	$0.101235\pi$
$349$	6.23604	+	20.5575i	0.333808	+	1.10042i	−0.616043	+	0.787713i	$0.711265\pi$
$350$		0			0
$351$	2.92419	+	2.92419i	0.156082	+	0.156082i
$352$		0			0
$353$	−9.30249	+	9.30249i	−0.495122	+	0.495122i	−0.909915	−	0.414794i	$-0.863854\pi$
$353$	−9.30249	+	9.30249i	−0.495122	+	0.495122i	0.414794	+	0.909915i	$0.363854\pi$
$354$		0			0
$355$	−29.7566	+	9.02657i	−1.57932	+	0.479081i
$356$		0			0
$357$	2.79873	−	0.275651i	0.148125	−	0.0145890i
$358$		0			0
$359$	3.27378	+	16.4584i	0.172784	+	0.868642i	0.965770	+	0.259402i	$0.0835254\pi$
$359$	3.27378	+	16.4584i	0.172784	+	0.868642i	−0.792986	+	0.609240i	$0.791475\pi$
$360$		0			0
$361$	0.939852	+	0.186948i	0.0494659	+	0.00983937i
$362$		0			0
$363$	−18.9028	+	10.1038i	−0.992139	+	0.530309i
$364$		0			0
$365$	−8.02974	−	0.790860i	−0.420296	−	0.0413955i
$366$		0			0
$367$	−23.8555	−	9.88127i	−1.24525	−	0.515798i	−0.339896	−	0.940463i	$-0.610392\pi$
$367$	−23.8555	−	9.88127i	−1.24525	−	0.515798i	−0.905351	+	0.424665i	$0.860392\pi$
$368$		0			0
$369$	−18.5739	+	7.69357i	−0.966920	+	0.400511i
$370$		0			0
$371$	8.09329	+	9.86170i	0.420183	+	0.511994i
$372$		0			0
$373$	−4.79211	+	15.7975i	−0.248126	+	0.817962i	0.741078	+	0.671419i	$0.234315\pi$
$373$	−4.79211	+	15.7975i	−0.248126	+	0.817962i	−0.989204	+	0.146543i	$0.953185\pi$
$374$		0			0
$375$	10.5603	+	15.8047i	0.545333	+	0.816149i
$376$		0			0
$377$	5.84297	+	3.90415i	0.300928	+	0.201074i
$378$		0			0
$379$	12.9832	+	10.6550i	0.666900	+	0.547311i	0.905785	−	0.423737i	$-0.139282\pi$
$379$	12.9832	+	10.6550i	0.666900	+	0.547311i	−0.238885	+	0.971048i	$0.576782\pi$
$380$		0			0
$381$	−0.308742	+	0.577615i	−0.0158173	+	0.0295921i
$382$		0			0
$383$	−9.84170			−0.502887			−0.251444	−	0.967872i	$-0.580905\pi$
$383$	−9.84170			−0.502887			−0.251444	+	0.967872i	$0.580905\pi$
$384$		0			0
$385$	−45.5694			−2.32243
$386$		0			0
$387$	23.2071	−	43.4175i	1.17968	−	2.20703i
$388$		0			0
$389$	−23.8326	−	19.5589i	−1.20836	−	0.991675i	−0.999907	−	0.0136431i	$-0.995657\pi$
$389$	−23.8326	−	19.5589i	−1.20836	−	0.991675i	−0.208453	−	0.978032i	$-0.566843\pi$
$390$		0			0
$391$	1.03822	+	0.693719i	0.0525052	+	0.0350829i
$392$		0			0
$393$	34.0601	+	50.9745i	1.71810	+	2.57133i
$394$		0			0
$395$	−4.26108	+	14.0469i	−0.214398	+	0.706777i
$396$		0			0
$397$	−6.30194	−	7.67894i	−0.316285	−	0.385395i	0.590465	−	0.807064i	$-0.298945\pi$
$397$	−6.30194	−	7.67894i	−0.316285	−	0.385395i	−0.906750	+	0.421669i	$0.861445\pi$
$398$		0			0
$399$	−44.5238	+	18.4424i	−2.22898	+	0.923274i
$400$		0			0
$401$	−18.5214	−	7.67180i	−0.924913	−	0.383112i	−0.131167	−	0.991360i	$-0.541872\pi$
$401$	−18.5214	−	7.67180i	−0.924913	−	0.383112i	−0.793747	+	0.608249i	$0.791872\pi$
$402$		0			0
$403$	0.284373	+	0.0280082i	0.0141656	+	0.00139519i
$404$		0			0
$405$	0.204350	−	0.109227i	0.0101542	−	0.00542755i
$406$		0			0
$407$	13.3982	+	2.66507i	0.664124	+	0.132102i
$408$		0			0
$409$	−1.19470	−	6.00614i	−0.0590739	−	0.296985i	0.939942	−	0.341334i	$-0.110879\pi$
$409$	−1.19470	−	6.00614i	−0.0590739	−	0.296985i	−0.999016	+	0.0443491i	$0.985879\pi$
$410$		0			0
$411$	27.8655	−	2.74452i	1.37451	−	0.135377i
$412$		0			0
$413$	36.1676	−	10.9713i	1.77969	−	0.539864i
$414$		0			0
$415$	15.1365	−	15.1365i	0.743023	−	0.743023i
$416$		0			0
$417$	20.8491	+	20.8491i	1.02098	+	1.02098i
$418$		0			0
$419$	−4.07432	−	13.4312i	−0.199043	−	0.656158i	−0.998465	−	0.0553875i	$-0.982361\pi$
$419$	−4.07432	−	13.4312i	−0.199043	−	0.656158i	0.799422	−	0.600770i	$-0.205139\pi$
$420$		0			0
$421$	3.36325	+	34.1476i	0.163915	+	1.66425i	0.627812	+	0.778365i	$0.283951\pi$
$421$	3.36325	+	34.1476i	0.163915	+	1.66425i	−0.463897	+	0.885889i	$0.653549\pi$
$422$		0			0
$423$	5.44438	−	1.08295i	0.264715	−	0.0526551i
$424$		0			0
$425$	−0.128694	+	0.646988i	−0.00624257	+	0.0313835i
$426$		0			0
$427$	7.44039	+	13.9200i	0.360066	+	0.673635i
$428$		0			0
$429$	−0.937565	+	9.51925i	−0.0452660	+	0.459594i
$430$		0			0
$431$	−5.07344	+	12.2484i	−0.244379	+	0.589984i	−0.997708	−	0.0676600i	$-0.978447\pi$
$431$	−5.07344	+	12.2484i	−0.244379	+	0.589984i	0.753329	+	0.657644i	$0.228447\pi$
$432$		0			0
$433$	3.37790	+	8.15498i	0.162332	+	0.391903i	0.984026	−	0.178025i	$-0.0569709\pi$
$433$	3.37790	+	8.15498i	0.162332	+	0.391903i	−0.821694	+	0.569929i	$0.806971\pi$
$434$		0			0
$435$	52.9318	−	43.4400i	2.53789	−	2.08279i
$436$		0			0
$437$	−20.4762	−	6.21138i	−0.979509	−	0.297131i
$438$		0			0
$439$	17.7594	−	11.8664i	0.847609	−	0.566354i	−0.0541798	−	0.998531i	$-0.517254\pi$
$439$	17.7594	−	11.8664i	0.847609	−	0.566354i	0.901789	+	0.432177i	$0.142254\pi$
$440$		0			0
$441$	21.0691	−	31.5322i	1.00329	−	1.50153i
$442$		0			0
$443$	−15.0097	+	18.2894i	−0.713132	+	0.868953i	−0.995921	−	0.0902286i	$-0.971240\pi$
$443$	−15.0097	+	18.2894i	−0.713132	+	0.868953i	0.282789	+	0.959182i	$0.408740\pi$
$444$		0			0
$445$	−14.8073	−	7.91467i	−0.701934	−	0.375192i
$446$		0			0
$447$			20.5942i			0.974073i
$448$		0			0
$449$		−	5.16847i		−	0.243915i	−0.992535	−	0.121958i	$-0.961083\pi$
$449$		−	5.16847i		−	0.243915i	0.992535	−	0.121958i	$-0.0389172\pi$
$450$		0			0
$451$	−15.7301	−	8.40792i	−0.740702	−	0.395913i
$452$		0			0
$453$	0.194156	−	0.236579i	0.00912222	−	0.0111155i
$454$		0			0
$455$	−4.63155	+	6.93160i	−0.217130	+	0.324958i
$456$		0			0
$457$	−32.3857	+	21.6395i	−1.51494	+	1.01225i	−0.528352	+	0.849026i	$0.677190\pi$
$457$	−32.3857	+	21.6395i	−1.51494	+	1.01225i	−0.986589	+	0.163225i	$0.947810\pi$
$458$		0			0
$459$	−1.30614	−	0.396212i	−0.0609652	−	0.0184936i
$460$		0			0
$461$	29.1398	−	23.9144i	1.35718	−	1.11380i	0.374755	−	0.927124i	$-0.377727\pi$
$461$	29.1398	−	23.9144i	1.35718	−	1.11380i	0.982421	−	0.186681i	$-0.0597730\pi$
$462$		0			0
$463$	12.5883	+	30.3909i	0.585029	+	1.41239i	0.888204	+	0.459450i	$0.151953\pi$
$463$	12.5883	+	30.3909i	0.585029	+	1.41239i	−0.303175	+	0.952935i	$0.598047\pi$
$464$		0			0
$465$	1.06553	−	2.57243i	0.0494130	−	0.119294i
$466$		0			0
$467$	−0.0654120	+	0.664139i	−0.00302691	+	0.0307327i	−0.996580	−	0.0826391i	$-0.973665\pi$
$467$	−0.0654120	+	0.664139i	−0.00302691	+	0.0307327i	0.993553	+	0.113372i	$0.0361651\pi$
$468$		0			0
$469$	18.8110	+	35.1929i	0.868611	+	1.62506i
$470$		0			0
$471$	−10.9490	+	55.0442i	−0.504502	+	2.53630i
$472$		0			0
$473$	42.8373	−	8.52087i	1.96966	−	0.391790i
$474$		0			0
$475$	−1.10801	−	11.2498i	−0.0508390	−	0.516177i
$476$		0			0
$477$	−4.68599	−	15.4476i	−0.214557	−	0.707299i
$478$		0			0
$479$	16.3247	+	16.3247i	0.745893	+	0.745893i	0.973705	−	0.227812i	$-0.0731572\pi$
$479$	16.3247	+	16.3247i	0.745893	+	0.745893i	−0.227812	+	0.973705i	$0.573157\pi$
$480$		0			0
$481$	1.76714	−	1.76714i	0.0805747	−	0.0805747i
$482$		0			0
$483$	49.4429	−	14.9983i	2.24973	−	0.682448i
$484$		0			0
$485$	7.07673	−	0.696997i	0.321338	−	0.0316490i
$486$		0			0
$487$	0.195952	+	0.985119i	0.00887945	+	0.0446400i	0.984971	−	0.172720i	$-0.0552555\pi$
$487$	0.195952	+	0.985119i	0.00887945	+	0.0446400i	−0.976092	+	0.217360i	$0.930256\pi$
$488$		0			0
$489$	20.4641	+	4.07055i	0.925416	+	0.184077i
$490$		0			0
$491$	−31.4673	+	16.8196i	−1.42010	+	0.759058i	−0.989642	−	0.143554i	$-0.954147\pi$
$491$	−31.4673	+	16.8196i	−1.42010	+	0.759058i	−0.430455	+	0.902612i	$0.641647\pi$
$492$		0			0
$493$	−2.30820	−	0.227338i	−0.103956	−	0.0102388i
$494$		0			0
$495$	53.2720	+	22.0660i	2.39440	+	0.991793i
$496$		0			0
$497$	40.2649	−	16.6783i	1.80613	−	0.748123i
$498$		0			0
$499$	−15.1199	−	18.4237i	−0.676861	−	0.824757i	0.315396	−	0.948960i	$-0.397863\pi$
$499$	−15.1199	−	18.4237i	−0.676861	−	0.824757i	−0.992257	+	0.124203i	$0.960363\pi$
$500$		0			0
$501$	−6.60175	+	21.7631i	−0.294944	+	0.972302i
$502$		0			0
$503$	−20.8213	−	31.1612i	−0.928374	−	1.38941i	−0.921053	−	0.389437i	$-0.872670\pi$
$503$	−20.8213	−	31.1612i	−0.928374	−	1.38941i	−0.00732085	−	0.999973i	$-0.502330\pi$
$504$		0			0
$505$	2.80132	+	1.87178i	0.124657	+	0.0832933i
$506$		0			0
$507$	−26.8327	−	22.0210i	−1.19168	−	0.977988i
$508$		0			0
$509$	−8.13694	+	15.2231i	−0.360663	+	0.674754i	−0.995170	−	0.0981635i	$-0.968703\pi$
$509$	−8.13694	+	15.2231i	−0.360663	+	0.674754i	0.634507	+	0.772917i	$0.281203\pi$
$510$		0			0
$511$	11.3086			0.500265
$512$		0			0
$513$	23.3896			1.03268
$514$		0			0
$515$	−5.48480	+	10.2613i	−0.241689	+	0.452169i
$516$		0			0
$517$	3.80692	+	3.12426i	0.167428	+	0.137405i
$518$		0			0
$519$	−24.5549	−	16.4071i	−1.07784	−	0.720190i
$520$		0			0
$521$	−21.0397	−	31.4881i	−0.921765	−	1.37952i	−0.925182	−	0.379524i	$-0.876088\pi$
$521$	−21.0397	−	31.4881i	−0.921765	−	1.37952i	0.00341737	−	0.999994i	$-0.498912\pi$
$522$		0			0
$523$	12.1261	−	39.9742i	0.530235	−	1.74795i	−0.124627	−	0.992204i	$-0.539774\pi$
$523$	12.1261	−	39.9742i	0.530235	−	1.74795i	0.654863	−	0.755748i	$-0.272726\pi$
$524$		0			0
$525$	17.3163	+	21.1000i	0.755745	+	0.920878i
$526$		0			0
$527$	−0.0871329	+	0.0360916i	−0.00379557	+	0.00157218i
$528$		0			0
$529$	−0.0548312	−	0.0227118i	−0.00238396	−	0.000987470i
$530$		0			0
$531$	−47.5937	−	4.68757i	−2.06539	−	0.203423i
$532$		0			0
$533$	−2.87770	+	1.53816i	−0.124647	+	0.0666252i
$534$		0			0
$535$	−54.5695	−	10.8545i	−2.35925	−	0.469283i
$536$		0			0
$537$	2.36721	+	11.9007i	0.102152	+	0.513555i
$538$		0			0
$539$	33.4830	−	3.29779i	1.44222	−	0.142046i
$540$		0			0
$541$	11.3859	−	3.45387i	0.489517	−	0.148493i	−0.0358704	−	0.999356i	$-0.511420\pi$
$541$	11.3859	−	3.45387i	0.489517	−	0.148493i	0.525388	+	0.850863i	$0.323920\pi$
$542$		0			0
$543$	−9.67323	+	9.67323i	−0.415118	+	0.415118i
$544$		0			0
$545$	−24.7818	−	24.7818i	−1.06154	−	1.06154i
$546$		0			0
$547$	9.95645	+	32.8220i	0.425707	+	1.40337i	0.863525	+	0.504305i	$0.168251\pi$
$547$	9.95645	+	32.8220i	0.425707	+	1.40337i	−0.437818	+	0.899064i	$0.644249\pi$
$548$		0			0
$549$	−1.95759	−	19.8758i	−0.0835480	−	0.848277i
$550$		0			0
$551$	38.9820	−	7.75399i	1.66069	−	0.330331i
$552$		0			0
$553$	4.01370	−	20.1782i	0.170680	−	0.858065i
$554$		0			0
$555$	−11.4793	−	21.4763i	−0.487271	−	0.911619i
$556$		0			0
$557$	2.81471	−	28.5782i	0.119263	−	1.21090i	−0.730195	−	0.683239i	$-0.760571\pi$
$557$	2.81471	−	28.5782i	0.119263	−	1.21090i	0.849457	−	0.527657i	$-0.176929\pi$
$558$		0			0
$559$	3.05775	−	7.38206i	0.129329	−	0.312228i
$560$		0			0
$561$	−1.20815	−	2.91674i	−0.0510082	−	0.123145i
$562$		0			0
$563$	−25.1415	+	20.6331i	−1.05959	+	0.869582i	−0.991759	−	0.128115i	$-0.959107\pi$
$563$	−25.1415	+	20.6331i	−1.05959	+	0.869582i	−0.0678297	+	0.997697i	$0.521607\pi$
$564$		0			0
$565$	20.2490	+	6.14246i	0.851881	+	0.258415i
$566$		0			0
$567$	−0.270025	+	0.180425i	−0.0113400	+	0.00757714i
$568$		0			0
$569$	−12.8540	+	19.2373i	−0.538867	+	0.806471i	−0.996580	−	0.0826284i	$-0.973669\pi$
$569$	−12.8540	+	19.2373i	−0.538867	+	0.806471i	0.457713	+	0.889100i	$0.348669\pi$
$570$		0			0
$571$	14.2502	−	17.3639i	0.596352	−	0.726657i	−0.384127	−	0.923280i	$-0.625498\pi$
$571$	14.2502	−	17.3639i	0.596352	−	0.726657i	0.980479	+	0.196623i	$0.0629975\pi$
$572$		0			0
$573$	9.38847	+	5.01824i	0.392209	+	0.209640i
$574$		0			0
$575$			12.1195i			0.505416i
$576$		0			0
$577$			10.3297i			0.430032i	0.976610	+	0.215016i	$0.0689804\pi$
$577$			10.3297i			0.430032i	−0.976610	+	0.215016i	$0.931020\pi$
$578$		0			0
$579$	40.8876	+	21.8549i	1.69923	+	0.908259i
$580$		0			0
$581$	−19.0333	+	23.1921i	−0.789632	+	0.962170i
$582$		0			0
$583$	7.95664	−	11.9080i	0.329530	−	0.493177i
$584$		0			0
$585$	8.77090	−	5.86053i	0.362632	−	0.242303i
$586$		0			0
$587$	−37.4521	−	11.3610i	−1.54581	−	0.468917i	−0.601750	−	0.798685i	$-0.705529\pi$
$587$	−37.4521	−	11.3610i	−1.54581	−	0.468917i	−0.944062	+	0.329768i	$0.893029\pi$
$588$		0			0
$589$	1.24931	−	1.02529i	0.0514771	−	0.0422462i
$590$		0			0
$591$	7.80190	+	18.8355i	0.320927	+	0.774787i
$592$		0			0
$593$	−12.1904	+	29.4303i	−0.500601	+	1.20856i	0.448556	+	0.893755i	$0.351938\pi$
$593$	−12.1904	+	29.4303i	−0.500601	+	1.20856i	−0.949157	+	0.314803i	$0.898062\pi$
$594$		0			0
$595$	0.269694	−	2.73825i	0.0110564	−	0.112257i
$596$		0			0
$597$	35.2032	+	65.8605i	1.44077	+	2.69549i
$598$		0			0
$599$	−1.71218	+	8.60769i	−0.0699576	+	0.351700i	−0.999871	−	0.0160787i	$-0.994882\pi$
$599$	−1.71218	+	8.60769i	−0.0699576	+	0.351700i	0.929913	+	0.367779i	$0.119882\pi$
$600$		0			0
$601$	−11.2236	+	2.23252i	−0.457821	+	0.0910662i	−0.418613	−	0.908165i	$-0.637484\pi$
$601$	−11.2236	+	2.23252i	−0.457821	+	0.0910662i	−0.0392081	+	0.999231i	$0.512484\pi$
$602$		0			0
$603$	−4.94924	−	50.2504i	−0.201548	−	2.04636i
$604$		0			0
$605$	6.08741	+	20.0675i	0.247488	+	0.815860i
$606$		0			0
$607$	−12.1300	−	12.1300i	−0.492340	−	0.492340i	0.416703	−	0.909043i	$-0.363186\pi$
$607$	−12.1300	−	12.1300i	−0.492340	−	0.492340i	−0.909043	+	0.416703i	$0.863186\pi$
$608$		0			0
$609$	−67.8624	+	67.8624i	−2.74992	+	2.74992i
$610$		0			0
$611$	0.862158	−	0.261533i	0.0348792	−	0.0105805i
$612$		0			0
$613$	43.6290	−	4.29708i	1.76216	−	0.173557i	0.835507	−	0.549479i	$-0.185174\pi$
$613$	43.6290	−	4.29708i	1.76216	−	0.173557i	0.926651	+	0.375922i	$0.122674\pi$
$614$		0			0
$615$	6.20291	+	31.1841i	0.250126	+	1.25747i
$616$		0			0
$617$	−5.04961	−	1.00443i	−0.203289	−	0.0404368i	0.0923951	−	0.995722i	$-0.470548\pi$
$617$	−5.04961	−	1.00443i	−0.203289	−	0.0404368i	−0.295685	+	0.955286i	$0.595548\pi$
$618$		0			0
$619$	17.7923	−	9.51016i	0.715131	−	0.382245i	−0.0733487	−	0.997306i	$-0.523369\pi$
$619$	17.7923	−	9.51016i	0.715131	−	0.382245i	0.788480	+	0.615061i	$0.210869\pi$
$620$		0			0
$621$	−24.9556	−	2.45791i	−1.00143	−	0.0986327i
$622$		0			0
$623$	21.7408	+	9.00532i	0.871025	+	0.360791i
$624$		0			0
$625$	28.8704	−	11.9585i	1.15482	−	0.478340i
$626$		0			0
$627$	34.3210	+	41.8203i	1.37065	+	1.67014i
$628$		0			0
$629$	−0.239438	+	0.789322i	−0.00954702	+	0.0314723i
$630$		0			0
$631$	−8.38964	−	12.5560i	−0.333986	−	0.499846i	0.626027	−	0.779802i	$-0.284680\pi$
$631$	−8.38964	−	12.5560i	−0.333986	−	0.499846i	−0.960013	+	0.279956i	$0.909680\pi$
$632$		0			0
$633$	−41.1023	−	27.4637i	−1.63367	−	1.09158i
$634$		0			0
$635$	0.495343	+	0.406518i	0.0196571	+	0.0161322i
$636$		0			0
$637$	2.90149	−	5.42831i	0.114961	−	0.215077i
$638$		0			0
$639$	−55.1471			−2.18159
$640$		0			0
$641$	−13.0109			−0.513898			−0.256949	−	0.966425i	$-0.582717\pi$
$641$	−13.0109			−0.513898			−0.256949	+	0.966425i	$0.582717\pi$
$642$		0			0
$643$	18.0356	−	33.7421i	0.711253	−	1.33066i	−0.223270	−	0.974757i	$-0.571673\pi$
$643$	18.0356	−	33.7421i	0.711253	−	1.33066i	0.934523	−	0.355904i	$-0.115827\pi$
$644$		0			0
$645$	−60.1855	−	49.3929i	−2.36980	−	1.94484i
$646$		0			0
$647$	−5.34855	−	3.57379i	−0.210273	−	0.140500i	0.445974	−	0.895046i	$-0.352857\pi$
$647$	−5.34855	−	3.57379i	−0.210273	−	0.140500i	−0.656247	+	0.754546i	$0.727857\pi$
$648$		0			0
$649$	−23.5721	−	35.2782i	−0.925286	−	1.38479i
$650$		0			0
$651$	−1.13283	+	3.73444i	−0.0443991	+	0.146364i
$652$		0			0
$653$	8.59082	+	10.4679i	0.336185	+	0.409642i	0.913474	−	0.406898i	$-0.133389\pi$
$653$	8.59082	+	10.4679i	0.336185	+	0.409642i	−0.577289	+	0.816540i	$0.695889\pi$
$654$		0			0
$655$	55.4159	−	22.9540i	2.16528	−	0.896888i
$656$		0			0
$657$	−13.2202	−	5.47597i	−0.515768	−	0.213638i
$658$		0			0
$659$	−15.1531	−	1.49245i	−0.590282	−	0.0581377i	−0.201534	−	0.979482i	$-0.564593\pi$
$659$	−15.1531	−	1.49245i	−0.590282	−	0.0581377i	−0.388749	+	0.921344i	$0.627093\pi$
$660$		0			0
$661$	26.0024	−	13.8985i	1.01137	−	0.540591i	0.119481	−	0.992837i	$-0.461877\pi$
$661$	26.0024	−	13.8985i	1.01137	−	0.540591i	0.891893	+	0.452246i	$0.149377\pi$
$662$		0			0
$663$	−0.566461	−	0.112676i	−0.0219995	−	0.00437598i
$664$		0			0
$665$	9.19867	+	46.2449i	0.356709	+	1.79330i
$666$		0			0
$667$	−42.4067	+	4.17670i	−1.64200	+	0.161722i
$668$		0			0
$669$	−0.601717	+	0.182529i	−0.0232637	+	0.00705698i
$670$		0			0
$671$	12.5291	−	12.5291i	0.483679	−	0.483679i
$672$		0			0
$673$	24.3608	+	24.3608i	0.939039	+	0.939039i	0.998246	−	0.0592065i	$-0.0188570\pi$
$673$	24.3608	+	24.3608i	0.939039	+	0.939039i	−0.0592065	+	0.998246i	$0.518857\pi$
$674$		0			0
$675$	−3.84562	−	12.6773i	−0.148018	−	0.487950i
$676$		0			0
$677$	−0.607770	−	6.17079i	−0.0233585	−	0.237163i	−0.999774	−	0.0212626i	$-0.993231\pi$
$677$	−0.607770	−	6.17079i	−0.0233585	−	0.237163i	0.976415	−	0.215900i	$-0.0692686\pi$
$678$		0			0
$679$	−9.77497	+	1.94436i	−0.375129	+	0.0746178i
$680$		0			0
$681$	0.619893	−	3.11641i	0.0237544	−	0.119421i
$682$		0			0
$683$	−1.51589	−	2.83603i	−0.0580039	−	0.108518i	0.851249	−	0.524763i	$-0.175846\pi$
$683$	−1.51589	−	2.83603i	−0.0580039	−	0.108518i	−0.909253	+	0.416245i	$0.863346\pi$
$684$		0			0
$685$	2.68521	−	27.2634i	0.102597	−	1.04168i
$686$		0			0
$687$	−17.2880	+	41.7368i	−0.659577	+	1.59236i
$688$		0			0
$689$	−1.00264	−	2.42058i	−0.0381975	−	0.0922169i
$690$		0			0
$691$	−13.6663	+	11.2156i	−0.519889	+	0.426662i	−0.857393	−	0.514662i	$-0.827917\pi$
$691$	−13.6663	+	11.2156i	−0.519889	+	0.426662i	0.337504	+	0.941324i	$0.390417\pi$
$692$		0			0
$693$	−77.3360	−	23.4596i	−2.93775	−	0.891158i
$694$		0			0
$695$	23.9862	−	16.0270i	0.909847	−	0.607941i
$696$		0			0
$697$	0.598326	−	0.895458i	0.0226632	−	0.0339179i
$698$		0			0
$699$	−9.91608	+	12.0828i	−0.375060	+	0.457012i
$700$		0			0
$701$	−9.35421	−	4.99993i	−0.353303	−	0.188845i	0.285192	−	0.958471i	$-0.407943\pi$
$701$	−9.35421	−	4.99993i	−0.353303	−	0.188845i	−0.638495	+	0.769626i	$0.720443\pi$
$702$		0			0
$703$		−	14.1348i		−	0.533103i
$704$		0			0
$705$		−	8.77902i		−	0.330637i
$706$		0			0
$707$	−4.16447	−	2.22596i	−0.156621	−	0.0837157i
$708$		0			0
$709$	3.87133	−	4.71724i	0.145391	−	0.177159i	−0.695223	−	0.718794i	$-0.744694\pi$
$709$	3.87133	−	4.71724i	0.145391	−	0.177159i	0.840614	+	0.541635i	$0.182194\pi$
$710$		0			0
$711$	−14.4630	+	21.6454i	−0.542406	+	0.811767i
$712$		0			0
$713$	−1.44070	+	0.962647i	−0.0539547	+	0.0360514i
$714$		0			0
$715$	8.95563	+	2.71666i	0.334922	+	0.101597i
$716$		0			0
$717$	−5.12247	+	4.20390i	−0.191302	+	0.156998i
$718$		0			0
$719$	9.32590	+	22.5147i	0.347797	+	0.839657i	0.996879	+	0.0789388i	$0.0251532\pi$
$719$	9.32590	+	22.5147i	0.347797	+	0.839657i	−0.649082	+	0.760718i	$0.724847\pi$
$720$		0			0
$721$	6.24061	−	15.0662i	0.232412	−	0.561093i
$722$		0			0
$723$	−6.20368	+	62.9870i	−0.230717	+	2.34251i
$724$		0			0
$725$	−10.6120	−	19.8536i	−0.394118	−	0.737343i
$726$		0			0
$727$	−2.00077	+	10.0586i	−0.0742046	+	0.373052i	−0.999987	−	0.00500400i	$-0.998407\pi$
$727$	−2.00077	+	10.0586i	−0.0742046	+	0.373052i	0.925783	+	0.378056i	$0.123407\pi$
$728$		0			0
$729$	−42.8038	+	8.51420i	−1.58533	+	0.315341i
$730$		0			0
$731$	0.258492	+	2.62451i	0.00956067	+	0.0970712i
$732$		0			0
$733$	8.39035	+	27.6593i	0.309904	+	1.02162i	0.964155	+	0.265340i	$0.0854842\pi$
$733$	8.39035	+	27.6593i	0.309904	+	1.02162i	−0.654250	+	0.756278i	$0.727016\pi$
$734$		0			0
$735$	−42.4096	−	42.4096i	−1.56430	−	1.56430i
$736$		0			0
$737$	31.6763	−	31.6763i	1.16681	−	1.16681i
$738$		0			0
$739$	−37.2893	+	11.3116i	−1.37171	+	0.416104i	−0.888289	−	0.459285i	$-0.848106\pi$
$739$	−37.2893	+	11.3116i	−1.37171	+	0.416104i	−0.483421	+	0.875388i	$0.660606\pi$
$740$		0			0
$741$	9.84962	−	0.970103i	0.361835	−	0.0356376i
$742$		0			0
$743$	7.13311	+	35.8606i	0.261689	+	1.31560i	0.858334	+	0.513092i	$0.171500\pi$
$743$	7.13311	+	35.8606i	0.261689	+	1.31560i	−0.596645	+	0.802505i	$0.703500\pi$
$744$		0			0
$745$	19.7620	+	3.93091i	0.724025	+	0.144017i
$746$		0			0
$747$	33.4808	−	17.8958i	1.22500	−	0.654774i
$748$		0			0
$749$	77.6055	+	7.64348i	2.83565	+	0.279287i
$750$		0			0
$751$	−35.2218	−	14.5893i	−1.28526	−	0.532373i	−0.367691	−	0.929948i	$-0.619852\pi$
$751$	−35.2218	−	14.5893i	−1.28526	−	0.532373i	−0.917570	+	0.397575i	$0.869852\pi$
$752$		0			0
$753$	−7.33115	+	3.03666i	−0.267162	+	0.110662i
$754$		0			0
$755$	−0.189960	−	0.231467i	−0.00691335	−	0.00842394i
$756$		0			0
$757$	8.44873	−	27.8517i	0.307074	−	1.01229i	−0.658591	−	0.752501i	$-0.728847\pi$
$757$	8.44873	−	27.8517i	0.307074	−	1.01229i	0.965666	−	0.259788i	$-0.0836526\pi$
$758$		0			0
$759$	−32.2242	−	48.2269i	−1.16966	−	1.75053i
$760$		0			0
$761$	−39.7361	−	26.5508i	−1.44043	−	0.962466i	−0.997837	−	0.0657443i	$-0.979058\pi$
$761$	−39.7361	−	26.5508i	−1.44043	−	0.962466i	−0.442595	−	0.896721i	$-0.645942\pi$
$762$		0			0
$763$	37.9705	+	31.1616i	1.37462	+	1.12812i
$764$		0			0
$765$	−1.64122	+	3.07051i	−0.0593385	+	0.111015i
$766$		0			0
$767$	−7.76200			−0.280269
$768$		0			0
$769$	−3.25225			−0.117279			−0.0586395	−	0.998279i	$-0.518676\pi$
$769$	−3.25225			−0.117279			−0.0586395	+	0.998279i	$0.518676\pi$
$770$		0			0
$771$	21.2133	−	39.6873i	0.763979	−	1.42930i
$772$		0			0
$773$	32.5431	+	26.7074i	1.17049	+	0.960600i	0.999695	−	0.0247056i	$-0.00786484\pi$
$773$	32.5431	+	26.7074i	1.17049	+	0.960600i	0.170800	+	0.985306i	$0.445365\pi$
$774$		0			0
$775$	−0.761118	−	0.508563i	−0.0273402	−	0.0182681i
$776$		0			0
$777$	18.9619	+	28.3785i	0.680255	+	1.01807i
$778$		0			0
$779$	−5.35726	+	17.6605i	−0.191944	+	0.632753i
$780$		0			0
$781$	−31.0381	−	37.8200i	−1.11063	−	1.35331i
$782$		0			0
$783$	43.0334	−	17.8250i	1.53789	−	0.637014i
$784$		0			0
$785$	50.7301	+	21.0131i	1.81063	+	0.749989i
$786$		0			0
$787$	25.9035	+	2.55127i	0.923361	+	0.0909431i	0.548512	−	0.836143i	$-0.315195\pi$
$787$	25.9035	+	2.55127i	0.923361	+	0.0909431i	0.374849	+	0.927086i	$0.377695\pi$
$788$		0			0
$789$	6.49509	−	3.47170i	0.231231	−	0.123596i
$790$		0			0
$791$	−29.0874	−	5.78585i	−1.03423	−	0.205721i
$792$		0			0
$793$	−0.632387	−	3.17923i	−0.0224567	−	0.112898i
$794$		0			0
$795$	−25.4069	+	2.50237i	−0.901092	+	0.0887498i
$796$		0			0
$797$	−28.1281	+	8.53255i	−0.996347	+	0.302239i	−0.746020	−	0.665923i	$-0.768038\pi$
$797$	−28.1281	+	8.53255i	−0.996347	+	0.302239i	−0.250326	+	0.968162i	$0.580538\pi$
$798$		0			0
$799$	−0.210266	+	0.210266i	−0.00743869	+	0.00743869i
$800$		0			0
$801$	−21.0550	−	21.0550i	−0.743942	−	0.743942i
$802$		0			0
$803$	−3.68518	−	12.1484i	−0.130047	−	0.428708i
$804$		0			0
$805$	−4.95488	−	50.3077i	−0.174637	−	1.77311i
$806$		0			0
$807$	−21.9003	+	4.35623i	−0.770925	+	0.153347i
$808$		0			0
$809$	1.44105	−	7.24464i	0.0506646	−	0.254708i	−0.947149	−	0.320793i	$-0.896051\pi$
$809$	1.44105	−	7.24464i	0.0506646	−	0.254708i	0.997814	+	0.0660847i	$0.0210507\pi$
$810$		0			0
$811$	8.81137	+	16.4849i	0.309409	+	0.578863i	0.987780	−	0.155856i	$-0.0498137\pi$
$811$	8.81137	+	16.4849i	0.309409	+	0.578863i	−0.678371	+	0.734720i	$0.737314\pi$
$812$		0			0
$813$	4.89176	−	49.6668i	0.171561	−	1.74189i
$814$		0			0
$815$	7.81213	−	18.8602i	0.273647	−	0.660642i
$816$		0			0
$817$	−17.2944	−	41.7523i	−0.605053	−	1.46073i
$818$		0			0
$819$	−11.4287	+	9.37928i	−0.399351	+	0.327739i
$820$		0			0
$821$	28.0481	+	8.50831i	0.978887	+	0.296942i	0.738886	−	0.673831i	$-0.235352\pi$
$821$	28.0481	+	8.50831i	0.978887	+	0.296942i	0.240001	+	0.970773i	$0.422852\pi$
$822$		0			0
$823$	28.2177	−	18.8545i	0.983607	−	0.657225i	0.0438394	−	0.999039i	$-0.486041\pi$
$823$	28.2177	−	18.8545i	0.983607	−	0.657225i	0.939768	+	0.341813i	$0.111041\pi$
$824$		0			0
$825$	17.0239	−	25.4781i	0.592697	−	0.887034i
$826$		0			0
$827$	5.56282	−	6.77831i	0.193438	−	0.235705i	−0.667255	−	0.744830i	$-0.732531\pi$
$827$	5.56282	−	6.77831i	0.193438	−	0.235705i	0.860693	+	0.509125i	$0.170031\pi$
$828$		0			0
$829$	−12.7966	−	6.83995i	−0.444446	−	0.237561i	0.233963	−	0.972245i	$-0.424830\pi$
$829$	−12.7966	−	6.83995i	−0.444446	−	0.237561i	−0.678409	+	0.734684i	$0.737330\pi$
$830$		0			0
$831$		−	63.4252i		−	2.20020i
$832$		0			0
$833$			2.03150i			0.0703875i
$834$		0			0
$835$	19.6235	+	10.4890i	0.679100	+	0.362987i
$836$		0			0
$837$	1.20156	−	1.46411i	0.0415320	−	0.0506069i
$838$		0			0
$839$	12.8008	−	19.1578i	0.441934	−	0.661400i	−0.541909	−	0.840437i	$-0.682298\pi$
$839$	12.8008	−	19.1578i	0.441934	−	0.661400i	0.983842	+	0.179037i	$0.0572982\pi$
$840$		0			0
$841$	41.6991	−	27.8624i	1.43790	−	0.960774i
$842$		0			0
$843$	76.0415	+	23.0669i	2.61901	+	0.794467i
$844$		0			0
$845$	−26.2529	+	21.5452i	−0.903126	+	0.741176i
$846$		0			0
$847$	−11.2476	−	27.1542i	−0.386473	−	0.933029i
$848$		0			0
$849$	7.26521	−	17.5398i	0.249341	−	0.601963i
$850$		0			0
$851$	−1.48536	+	15.0811i	−0.0509175	+	0.516975i
$852$		0			0
$853$	14.3262	+	26.8025i	0.490521	+	0.917700i	0.998415	+	0.0562807i	$0.0179242\pi$
$853$	14.3262	+	26.8025i	0.490521	+	0.917700i	−0.507894	+	0.861420i	$0.669576\pi$
$854$		0			0
$855$	11.6395	−	58.5160i	0.398064	−	2.00120i
$856$		0			0
$857$	−7.22989	+	1.43811i	−0.246968	+	0.0491250i	−0.317022	−	0.948418i	$-0.602683\pi$
$857$	−7.22989	+	1.43811i	−0.246968	+	0.0491250i	0.0700538	+	0.997543i	$0.477683\pi$
$858$		0			0
$859$	3.81310	+	38.7151i	0.130101	+	1.32094i	0.809477	+	0.587151i	$0.199751\pi$
$859$	3.81310	+	38.7151i	0.130101	+	1.32094i	−0.679376	+	0.733791i	$0.737749\pi$
$860$		0			0
$861$	−12.9359	−	42.6440i	−0.440855	−	1.45330i
$862$		0			0
$863$	13.0444	+	13.0444i	0.444036	+	0.444036i	0.893366	−	0.449330i	$-0.148337\pi$
$863$	13.0444	+	13.0444i	0.444036	+	0.444036i	−0.449330	+	0.893366i	$0.648337\pi$
$864$		0			0
$865$	−20.4310	+	20.4310i	−0.694674	+	0.694674i
$866$		0			0
$867$	−45.4453	+	13.7857i	−1.54340	+	0.468187i
$868$		0			0
$869$	−22.9846	+	2.26379i	−0.779699	+	0.0767937i
$870$		0			0
$871$	−1.59882	−	8.03780i	−0.0541739	−	0.272351i
$872$		0			0
$873$	12.3688	+	2.46030i	0.418620	+	0.0832686i
$874$		0			0
$875$	−22.9876	+	12.2871i	−0.777123	+	0.415381i
$876$		0			0
$877$	−39.7492	−	3.91496i	−1.34224	−	0.132199i	−0.598742	−	0.800942i	$-0.704333\pi$
$877$	−39.7492	−	3.91496i	−1.34224	−	0.132199i	−0.743494	+	0.668743i	$0.766833\pi$
$878$		0			0
$879$	−35.0076	−	14.5006i	−1.18078	−	0.489094i
$880$		0			0
$881$	24.4633	−	10.1330i	0.824189	−	0.341390i	0.0695895	−	0.997576i	$-0.477831\pi$
$881$	24.4633	−	10.1330i	0.824189	−	0.341390i	0.754600	+	0.656185i	$0.227831\pi$
$882$		0			0
$883$	−18.7052	−	22.7923i	−0.629479	−	0.767022i	0.356427	−	0.934323i	$-0.383995\pi$
$883$	−18.7052	−	22.7923i	−0.629479	−	0.767022i	−0.985906	+	0.167301i	$0.946495\pi$
$884$		0			0
$885$	−21.9554	+	72.3773i	−0.738023	+	2.43294i
$886$		0			0
$887$	−4.86030	−	7.27396i	−0.163193	−	0.244236i	0.740857	−	0.671663i	$-0.234420\pi$
$887$	−4.86030	−	7.27396i	−0.163193	−	0.244236i	−0.904050	+	0.427428i	$0.859420\pi$
$888$		0			0
$889$	−0.746759	−	0.498968i	−0.0250455	−	0.0167349i
$890$		0			0
$891$	0.281817	+	0.231282i	0.00944124	+	0.00774822i
$892$		0			0
$893$	2.40210	−	4.49401i	0.0803832	−	0.150386i
$894$		0			0
$895$	11.8717			0.396827
$896$		0			0
$897$	−10.6110			−0.354292
$898$		0			0
$899$	1.51719	−	2.83846i	0.0506011	−	0.0946680i
$900$		0			0
$901$	0.668456	+	0.548588i	0.0222695	+	0.0182761i
$902$		0			0
$903$	90.7331	+	60.6259i	3.01941	+	2.01750i
$904$		0			0
$905$	7.43597	+	11.1287i	0.247180	+	0.369931i
$906$		0			0
$907$	−2.21282	+	7.29470i	−0.0734756	+	0.242217i	−0.985984	−	0.166842i	$-0.946643\pi$
$907$	−2.21282	+	7.29470i	−0.0734756	+	0.242217i	0.912508	+	0.409059i	$0.134143\pi$
$908$		0			0
$909$	3.79052	+	4.61877i	0.125724	+	0.153195i
$910$		0			0
$911$	36.0774	−	14.9438i	1.19530	−	0.495109i	0.305822	−	0.952089i	$-0.401069\pi$
$911$	36.0774	−	14.9438i	1.19530	−	0.495109i	0.889477	+	0.456980i	$0.151069\pi$
$912$		0			0
$913$	31.1168	+	12.8890i	1.02981	+	0.426563i
$914$		0			0
$915$	−31.4337	−	3.09595i	−1.03917	−	0.102349i
$916$		0			0
$917$	−74.1416	+	39.6295i	−2.44837	+	1.30868i
$918$		0			0
$919$	16.6420	+	3.31030i	0.548970	+	0.109197i	0.461779	−	0.886995i	$-0.347211\pi$
$919$	16.6420	+	3.31030i	0.548970	+	0.109197i	0.0871903	+	0.996192i	$0.472211\pi$
$920$		0			0
$921$	−7.50757	−	37.7431i	−0.247383	−	1.24368i
$922$		0			0
$923$	−8.90746	+	0.877308i	−0.293193	+	0.0288769i
$924$		0			0
$925$	−7.66112	+	2.32398i	−0.251896	+	0.0764119i
$926$		0			0
$927$	−14.5909	+	14.5909i	−0.479229	+	0.479229i
$928$		0			0
$929$	−11.3602	−	11.3602i	−0.372716	−	0.372716i	0.495750	−	0.868465i	$-0.334893\pi$
$929$	−11.3602	−	11.3602i	−0.372716	−	0.372716i	−0.868465	+	0.495750i	$0.834893\pi$
$930$		0			0
$931$	−10.1056	−	33.3136i	−0.331197	−	1.09181i
$932$		0			0
$933$	−3.05901	−	31.0587i	−0.100148	−	1.01682i
$934$		0			0
$935$	−3.02948	+	0.602601i	−0.0990746	+	0.0197072i
$936$		0			0
$937$	−2.85933	+	14.3748i	−0.0934101	+	0.469604i	0.905559	+	0.424219i	$0.139451\pi$
$937$	−2.85933	+	14.3748i	−0.0934101	+	0.469604i	−0.998970	+	0.0453850i	$0.985549\pi$
$938$		0			0
$939$	−31.3329	−	58.6197i	−1.02251	−	1.91298i
$940$		0			0
$941$	−4.35248	+	44.1915i	−0.141887	+	1.44060i	0.615759	+	0.787935i	$0.288850\pi$
$941$	−4.35248	+	44.1915i	−0.141887	+	1.44060i	−0.757646	+	0.652666i	$0.773650\pi$
$942$		0			0
$943$	7.57181	−	18.2800i	0.246572	−	0.595277i
$944$		0			0
$945$	21.1461	+	51.0511i	0.687882	+	1.66069i
$946$		0			0
$947$	10.6075	−	8.70532i	0.344696	−	0.282885i	−0.446076	−	0.894995i	$-0.647179\pi$
$947$	10.6075	−	8.70532i	0.344696	−	0.282885i	0.790773	+	0.612110i	$0.209679\pi$
$948$		0			0
$949$	−2.22246	−	0.674176i	−0.0721441	−	0.0218847i
$950$		0			0
$951$	−53.1089	+	35.4862i	−1.72217	+	1.15072i
$952$		0			0
$953$	−15.2571	+	22.8338i	−0.494225	+	0.739659i	−0.991805	−	0.127758i	$-0.959222\pi$
$953$	−15.2571	+	22.8338i	−0.494225	+	0.739659i	0.497581	+	0.867418i	$0.334222\pi$
$954$		0			0
$955$	6.60748	−	8.05123i	0.213813	−	0.260532i
$956$		0			0
$957$	95.0164	+	50.7873i	3.07144	+	1.64172i
$958$		0			0
$959$			38.3963i			1.23988i
$960$		0			0
$961$			30.8691i			0.995778i
$962$		0			0
$963$	−87.0222	−	46.5143i	−2.80425	−	1.49890i
$964$		0			0
$965$	28.7762	−	35.0639i	0.926338	−	1.12875i
$966$		0			0
$967$	−12.8386	+	19.2143i	−0.412862	+	0.617892i	−0.978373	−	0.206849i	$-0.933679\pi$
$967$	−12.8386	+	19.2143i	−0.412862	+	0.617892i	0.565511	+	0.824741i	$0.308679\pi$
$968$		0			0
$969$	−2.71609	+	1.81484i	−0.0872535	+	0.0583009i
$970$		0			0
$971$	10.7168	+	3.25090i	0.343918	+	0.104326i	0.457519	−	0.889200i	$-0.348738\pi$
$971$	10.7168	+	3.25090i	0.343918	+	0.104326i	−0.113600	+	0.993527i	$0.536238\pi$
$972$		0			0
$973$	−31.2545	+	25.6499i	−1.00197	+	0.822299i
$974$		0			0
$975$	−2.14523	−	5.17905i	−0.0687024	−	0.165862i
$976$		0			0
$977$	−8.05317	+	19.4421i	−0.257644	+	0.622007i	−0.998782	−	0.0493457i	$-0.984286\pi$
$977$	−8.05317	+	19.4421i	−0.257644	+	0.622007i	0.741138	+	0.671353i	$0.234286\pi$
$978$		0			0
$979$	2.58932	−	26.2898i	0.0827551	−	0.840226i
$980$		0			0
$981$	−29.2994	−	54.8152i	−0.935457	−	1.75012i
$982$		0			0
$983$	−2.94304	+	14.7956i	−0.0938683	+	0.471908i	0.905046	+	0.425314i	$0.139836\pi$
$983$	−2.94304	+	14.7956i	−0.0938683	+	0.471908i	−0.998914	+	0.0465932i	$0.985164\pi$
$984$		0			0
$985$	19.5635	−	3.89142i	0.623345	−	0.123991i
$986$		0			0
$987$	1.20604	+	12.2451i	0.0383886	+	0.389766i
$988$		0			0
$989$	14.0647	+	46.3651i	0.447231	+	1.47432i
$990$		0			0
$991$	−0.356604	−	0.356604i	−0.0113279	−	0.0113279i	0.701420	−	0.712748i	$-0.252550\pi$
$991$	−0.356604	−	0.356604i	−0.0113279	−	0.0113279i	−0.712748	+	0.701420i	$0.752550\pi$
$992$		0			0
$993$	30.1523	−	30.1523i	0.956854	−	0.956854i
$994$		0			0
$995$	69.9185	−	21.2095i	2.21657	−	0.672388i
$996$		0			0
$997$	−26.4664	+	2.60671i	−0.838199	+	0.0825554i	−0.508001	−	0.861356i	$-0.669615\pi$
$997$	−26.4664	+	2.60671i	−0.838199	+	0.0825554i	−0.330198	+	0.943912i	$0.607115\pi$
$998$		0			0
$999$	−3.23165	−	16.2466i	−0.102245	−	0.514020i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.k.a.17.14		240
4.3	odd	2		128.2.k.a.45.8	yes	240
128.37	even	32	inner	512.2.k.a.241.14		240
128.91	odd	32		128.2.k.a.37.8	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.2.k.a.37.8	✓	240	128.91	odd	32
128.2.k.a.45.8	yes	240	4.3	odd	2
512.2.k.a.17.14		240	1.1	even	1	trivial
512.2.k.a.241.14		240	128.37	even	32	inner

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.k (of order \(32\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.32215 - 2.47358i) q^{3} +(-2.12126 - 1.74087i) q^{5} +(3.19792 + 2.13678i) q^{7} +(-2.70377 - 4.04648i) q^{9} +O(q^{10})\)	\(q+(1.32215 - 2.47358i) q^{3} +(-2.12126 - 1.74087i) q^{5} +(3.19792 + 2.13678i) q^{7} +(-2.70377 - 4.04648i) q^{9} +(1.25334 - 4.13171i) q^{11} +(-0.501092 - 0.610582i) q^{13} +(-7.11080 + 2.94539i) q^{15} +(0.240856 + 0.0997657i) q^{17} +(-4.44596 - 0.437888i) q^{19} +(9.51362 - 5.08513i) q^{21} +(4.69761 + 0.934412i) q^{23} +(0.493646 + 2.48173i) q^{25} +(-5.21033 + 0.513173i) q^{27} +(-8.51360 + 2.58257i) q^{29} +(-0.255806 + 0.255806i) q^{31} +(-8.56299 - 8.56299i) q^{33} +(-3.06374 - 10.0998i) q^{35} +(0.310120 + 3.14870i) q^{37} +(-2.17284 + 0.432205i) q^{39} +(0.805921 - 4.05164i) q^{41} +(4.76859 + 8.92140i) q^{43} +(-1.30900 + 13.2905i) q^{45} +(-0.436499 + 1.05380i) q^{47} +(2.98205 + 7.19932i) q^{49} +(0.565227 - 0.463869i) q^{51} +(3.17417 + 0.962875i) q^{53} +(-9.85142 + 6.58251i) q^{55} +(-6.96139 + 10.4185i) q^{57} +(6.23409 - 7.59626i) q^{59} +(3.61925 + 1.93453i) q^{61} -18.7177i q^{63} +2.16754i q^{65} +(9.15028 + 4.89093i) q^{67} +(8.52230 - 10.3845i) q^{69} +(6.29550 - 9.42188i) q^{71} +(2.44476 - 1.63354i) q^{73} +(6.79142 + 2.06015i) q^{75} +(12.8366 - 10.5347i) q^{77} +(-2.04705 - 4.94201i) q^{79} +(-0.0323130 + 0.0780105i) q^{81} +(-0.764603 + 7.76314i) q^{83} +(-0.337238 - 0.630927i) q^{85} +(-4.86810 + 24.4736i) q^{87} +(6.00085 - 1.19364i) q^{89} +(-0.297770 - 3.02331i) q^{91} +(0.294540 + 0.970969i) q^{93} +(8.66870 + 8.66870i) q^{95} +(-1.83234 + 1.83234i) q^{97} +(-20.1077 + 6.09959i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9}+O(q^{10}) \) 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9	\( 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9} + 16 q^{11} - 16 q^{13} + 16 q^{15} - 16 q^{17} + 16 q^{19} - 16 q^{21} + 16 q^{23} - 16 q^{25} + 16 q^{27} - 16 q^{29} + 16 q^{31} - 16 q^{33} + 16 q^{35} - 16 q^{37} + 16 q^{39} - 16 q^{41} + 16 q^{43} - 16 q^{45} + 16 q^{47} - 16 q^{49} + 16 q^{51} - 16 q^{53} + 16 q^{55} - 16 q^{57} + 16 q^{59} - 16 q^{61} + 16 q^{67} - 16 q^{69} + 16 q^{71} - 16 q^{73} + 16 q^{75} - 16 q^{77} + 16 q^{79} - 16 q^{81} + 16 q^{83} - 16 q^{85} + 16 q^{87} - 16 q^{89} + 16 q^{91} - 16 q^{93} + 16 q^{95} - 16 q^{97} + 16 q^{99}+O(q^{100}) \) 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9 + 16 * q^11 - 16 * q^13 + 16 * q^15 - 16 * q^17 + 16 * q^19 - 16 * q^21 + 16 * q^23 - 16 * q^25 + 16 * q^27 - 16 * q^29 + 16 * q^31 - 16 * q^33 + 16 * q^35 - 16 * q^37 + 16 * q^39 - 16 * q^41 + 16 * q^43 - 16 * q^45 + 16 * q^47 - 16 * q^49 + 16 * q^51 - 16 * q^53 + 16 * q^55 - 16 * q^57 + 16 * q^59 - 16 * q^61 + 16 * q^67 - 16 * q^69 + 16 * q^71 - 16 * q^73 + 16 * q^75 - 16 * q^77 + 16 * q^79 - 16 * q^81 + 16 * q^83 - 16 * q^85 + 16 * q^87 - 16 * q^89 + 16 * q^91 - 16 * q^93 + 16 * q^95 - 16 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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