LMFDB - Embedded newform 512.2.i.b.161.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [512,2,Mod(33,512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(512, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 15]))

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

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

chi := DirichletCharacter("512.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.i (of order $16$, degree $8$, 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:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 64)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			161.1
Character	$\chi$	$=$	512.161
Dual form			512.2.i.b.353.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.97142 - 0.392140i) q^{3} +(0.153107 - 0.229142i) q^{5} +(-0.843108 + 0.349227i) q^{7} +(0.961093 + 0.398098i) q^{9} +O(q^{10})$	\(q+(-1.97142 - 0.392140i) q^{3} +(0.153107 - 0.229142i) q^{5} +(-0.843108 + 0.349227i) q^{7} +(0.961093 + 0.398098i) q^{9} +(-0.575451 - 2.89299i) q^{11} +(3.63027 + 5.43308i) q^{13} +(-0.391695 + 0.391695i) q^{15} +(-3.22910 - 3.22910i) q^{17} +(-5.20741 + 3.47948i) q^{19} +(1.79907 - 0.357857i) q^{21} +(-2.33779 + 5.64392i) q^{23} +(1.88435 + 4.54923i) q^{25} +(3.27526 + 2.18846i) q^{27} +(-0.693313 + 3.48552i) q^{29} +3.92256i q^{31} +5.92895i q^{33} +(-0.0490638 + 0.246660i) q^{35} +(-4.35133 - 2.90747i) q^{37} +(-5.02627 - 12.1345i) q^{39} +(-0.653569 + 1.57786i) q^{41} +(3.96655 - 0.788996i) q^{43} +(0.238371 - 0.159275i) q^{45} +(3.42980 + 3.42980i) q^{47} +(-4.36088 + 4.36088i) q^{49} +(5.09966 + 7.63219i) q^{51} +(0.321835 + 1.61797i) q^{53} +(-0.751009 - 0.311078i) q^{55} +(11.6304 - 4.81749i) q^{57} +(-3.43310 + 5.13800i) q^{59} +(-11.5586 - 2.29915i) q^{61} -0.949332 q^{63} +1.80077 q^{65} +(-6.90108 - 1.37271i) q^{67} +(6.82198 - 10.2098i) q^{69} +(2.53894 - 1.05166i) q^{71} +(2.05602 + 0.851633i) q^{73} +(-1.93092 - 9.70739i) q^{75} +(1.49548 + 2.23814i) q^{77} +(4.21203 - 4.21203i) q^{79} +(-7.80551 - 7.80551i) q^{81} +(8.64283 - 5.77496i) q^{83} +(-1.23432 + 0.245522i) q^{85} +(2.73363 - 6.59956i) q^{87} +(-3.87335 - 9.35109i) q^{89} +(-4.95809 - 3.31289i) q^{91} +(1.53819 - 7.73303i) q^{93} +1.72597i q^{95} +1.83166i q^{97} +(0.598630 - 3.00951i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 8 q^{3} + 8 q^{5} - 8 q^{7} - 8 q^{9}+O(q^{10}) $ 56 * q + 8 * q^3 + 8 * q^5 - 8 * q^7 - 8 * q^9	$ 56 q + 8 q^{3} + 8 q^{5} - 8 q^{7} - 8 q^{9} + 8 q^{11} + 8 q^{13} - 8 q^{15} - 8 q^{17} + 8 q^{19} + 8 q^{21} - 8 q^{23} - 8 q^{25} + 8 q^{27} + 8 q^{29} + 8 q^{35} + 8 q^{37} - 8 q^{39} - 8 q^{41} + 8 q^{43} + 8 q^{45} - 8 q^{47} - 8 q^{49} - 24 q^{51} + 8 q^{53} + 56 q^{55} - 8 q^{57} - 56 q^{59} + 8 q^{61} + 64 q^{63} - 16 q^{65} - 72 q^{67} + 8 q^{69} + 56 q^{71} - 8 q^{73} - 56 q^{75} + 8 q^{77} + 24 q^{79} - 8 q^{81} + 8 q^{83} + 8 q^{85} - 8 q^{87} - 8 q^{89} + 8 q^{91} - 16 q^{93} - 16 q^{99}+O(q^{100}) $ 56 * q + 8 * q^3 + 8 * q^5 - 8 * q^7 - 8 * q^9 + 8 * q^11 + 8 * q^13 - 8 * q^15 - 8 * q^17 + 8 * q^19 + 8 * q^21 - 8 * q^23 - 8 * q^25 + 8 * q^27 + 8 * q^29 + 8 * q^35 + 8 * q^37 - 8 * q^39 - 8 * q^41 + 8 * q^43 + 8 * q^45 - 8 * q^47 - 8 * q^49 - 24 * q^51 + 8 * q^53 + 56 * q^55 - 8 * q^57 - 56 * q^59 + 8 * q^61 + 64 * q^63 - 16 * q^65 - 72 * q^67 + 8 * q^69 + 56 * q^71 - 8 * q^73 - 56 * q^75 + 8 * q^77 + 24 * q^79 - 8 * q^81 + 8 * q^83 + 8 * q^85 - 8 * q^87 - 8 * q^89 + 8 * q^91 - 16 * q^93 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{11}{16}\right)$	$1$

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
$3$	−1.97142	−	0.392140i	−1.13820	−	0.226402i	−0.410211	−	0.911990i	$-0.634545\pi$
$3$	−1.97142	−	0.392140i	−1.13820	−	0.226402i	−0.727990	+	0.685588i	$0.759545\pi$
$4$		0			0
$5$	0.153107	−	0.229142i	0.0684717	−	0.102475i	−0.795654	−	0.605752i	$-0.792872\pi$
$5$	0.153107	−	0.229142i	0.0684717	−	0.102475i	0.864125	+	0.503277i	$0.167872\pi$
$6$		0			0
$7$	−0.843108	+	0.349227i	−0.318665	+	0.131995i	−0.536282	−	0.844039i	$-0.680172\pi$
$7$	−0.843108	+	0.349227i	−0.318665	+	0.131995i	0.217617	+	0.976034i	$0.430172\pi$
$8$		0			0
$9$	0.961093	+	0.398098i	0.320364	+	0.132699i
$10$		0			0
$11$	−0.575451	−	2.89299i	−0.173505	−	0.872268i	−0.965232	−	0.261394i	$-0.915818\pi$
$11$	−0.575451	−	2.89299i	−0.173505	−	0.872268i	0.791727	−	0.610875i	$-0.209182\pi$
$12$		0			0
$13$	3.63027	+	5.43308i	1.00686	+	1.50687i	0.855110	+	0.518447i	$0.173490\pi$
$13$	3.63027	+	5.43308i	1.00686	+	1.50687i	0.151746	+	0.988419i	$0.451510\pi$
$14$		0			0
$15$	−0.391695	+	0.391695i	−0.101135	+	0.101135i
$16$		0			0
$17$	−3.22910	−	3.22910i	−0.783172	−	0.783172i	0.197192	−	0.980365i	$-0.436818\pi$
$17$	−3.22910	−	3.22910i	−0.783172	−	0.783172i	−0.980365	+	0.197192i	$0.936818\pi$
$18$		0			0
$19$	−5.20741	+	3.47948i	−1.19466	+	0.798247i	−0.983800	−	0.179269i	$-0.942627\pi$
$19$	−5.20741	+	3.47948i	−1.19466	+	0.798247i	−0.210861	+	0.977516i	$0.567627\pi$
$20$		0			0
$21$	1.79907	−	0.357857i	0.392589	−	0.0780908i
$22$		0			0
$23$	−2.33779	+	5.64392i	−0.487463	+	1.17684i	0.468530	+	0.883448i	$0.344784\pi$
$23$	−2.33779	+	5.64392i	−0.487463	+	1.17684i	−0.955992	+	0.293391i	$0.905216\pi$
$24$		0			0
$25$	1.88435	+	4.54923i	0.376871	+	0.909846i
$26$		0			0
$27$	3.27526	+	2.18846i	0.630325	+	0.421170i
$28$		0			0
$29$	−0.693313	+	3.48552i	−0.128745	+	0.647245i	0.861483	+	0.507787i	$0.169536\pi$
$29$	−0.693313	+	3.48552i	−0.128745	+	0.647245i	−0.990228	+	0.139458i	$0.955464\pi$
$30$		0			0
$31$			3.92256i			0.704513i	0.935904	+	0.352256i	$0.114586\pi$
$31$			3.92256i			0.704513i	−0.935904	+	0.352256i	$0.885414\pi$
$32$		0			0
$33$			5.92895i			1.03210i
$34$		0			0
$35$	−0.0490638	+	0.246660i	−0.00829330	+	0.0416932i
$36$		0			0
$37$	−4.35133	−	2.90747i	−0.715354	−	0.477984i	0.143862	−	0.989598i	$-0.454048\pi$
$37$	−4.35133	−	2.90747i	−0.715354	−	0.477984i	−0.859216	+	0.511614i	$0.829048\pi$
$38$		0			0
$39$	−5.02627	−	12.1345i	−0.804847	−	1.94307i
$40$		0			0
$41$	−0.653569	+	1.57786i	−0.102070	+	0.246420i	−0.966662	−	0.256055i	$-0.917577\pi$
$41$	−0.653569	+	1.57786i	−0.102070	+	0.246420i	0.864592	+	0.502475i	$0.167577\pi$
$42$		0			0
$43$	3.96655	−	0.788996i	0.604893	−	0.120321i	0.116864	−	0.993148i	$-0.462716\pi$
$43$	3.96655	−	0.788996i	0.604893	−	0.120321i	0.488029	+	0.872827i	$0.337716\pi$
$44$		0			0
$45$	0.238371	−	0.159275i	0.0355343	−	0.0237432i
$46$		0			0
$47$	3.42980	+	3.42980i	0.500288	+	0.500288i	0.911527	−	0.411240i	$-0.134904\pi$
$47$	3.42980	+	3.42980i	0.500288	+	0.500288i	−0.411240	+	0.911527i	$0.634904\pi$
$48$		0			0
$49$	−4.36088	+	4.36088i	−0.622982	+	0.622982i
$50$		0			0
$51$	5.09966	+	7.63219i	0.714096	+	1.06872i
$52$		0			0
$53$	0.321835	+	1.61797i	0.0442075	+	0.222246i	0.996574	−	0.0827111i	$-0.0263579\pi$
$53$	0.321835	+	1.61797i	0.0442075	+	0.222246i	−0.952366	+	0.304957i	$0.901358\pi$
$54$		0			0
$55$	−0.751009	−	0.311078i	−0.101266	−	0.0419458i
$56$		0			0
$57$	11.6304	−	4.81749i	1.54049	−	0.638092i
$58$		0			0
$59$	−3.43310	+	5.13800i	−0.446952	+	0.668910i	−0.984713	−	0.174187i	$-0.944270\pi$
$59$	−3.43310	+	5.13800i	−0.446952	+	0.668910i	0.537761	+	0.843097i	$0.319270\pi$
$60$		0			0
$61$	−11.5586	−	2.29915i	−1.47993	−	0.294376i	−0.611917	−	0.790922i	$-0.709601\pi$
$61$	−11.5586	−	2.29915i	−1.47993	−	0.294376i	−0.868010	+	0.496546i	$0.834601\pi$
$62$		0			0
$63$	−0.949332			−0.119605
$64$		0			0
$65$	1.80077			0.223358
$66$		0			0
$67$	−6.90108	−	1.37271i	−0.843101	−	0.167703i	−0.245400	−	0.969422i	$-0.578919\pi$
$67$	−6.90108	−	1.37271i	−0.843101	−	0.167703i	−0.597701	+	0.801719i	$0.703919\pi$
$68$		0			0
$69$	6.82198	−	10.2098i	0.821270	−	1.22912i
$70$		0			0
$71$	2.53894	−	1.05166i	0.301317	−	0.124809i	−0.226903	−	0.973917i	$-0.572860\pi$
$71$	2.53894	−	1.05166i	0.301317	−	0.124809i	0.528219	+	0.849108i	$0.322860\pi$
$72$		0			0
$73$	2.05602	+	0.851633i	0.240640	+	0.0996762i	0.499744	−	0.866173i	$-0.333427\pi$
$73$	2.05602	+	0.851633i	0.240640	+	0.0996762i	−0.259105	+	0.965849i	$0.583427\pi$
$74$		0			0
$75$	−1.93092	−	9.70739i	−0.222963	−	1.12091i
$76$		0			0
$77$	1.49548	+	2.23814i	0.170425	+	0.255059i
$78$		0			0
$79$	4.21203	−	4.21203i	0.473890	−	0.473890i	−0.429281	−	0.903171i	$-0.641233\pi$
$79$	4.21203	−	4.21203i	0.473890	−	0.473890i	0.903171	+	0.429281i	$0.141233\pi$
$80$		0			0
$81$	−7.80551	−	7.80551i	−0.867279	−	0.867279i
$82$		0			0
$83$	8.64283	−	5.77496i	0.948674	−	0.633884i	0.0180410	−	0.999837i	$-0.494257\pi$
$83$	8.64283	−	5.77496i	0.948674	−	0.633884i	0.930633	+	0.365953i	$0.119257\pi$
$84$		0			0
$85$	−1.23432	+	0.245522i	−0.133881	+	0.0266306i
$86$		0			0
$87$	2.73363	−	6.59956i	0.293076	−	0.707547i
$88$		0			0
$89$	−3.87335	−	9.35109i	−0.410574	−	0.991214i	−0.984984	−	0.172646i	$-0.944768\pi$
$89$	−3.87335	−	9.35109i	−0.410574	−	0.991214i	0.574410	−	0.818568i	$-0.305232\pi$
$90$		0			0
$91$	−4.95809	−	3.31289i	−0.519749	−	0.347285i
$92$		0			0
$93$	1.53819	−	7.73303i	0.159503	−	0.801877i
$94$		0			0
$95$			1.72597i			0.177081i
$96$		0			0
$97$			1.83166i			0.185977i	0.995667	+	0.0929884i	$0.0296419\pi$
$97$			1.83166i			0.185977i	−0.995667	+	0.0929884i	$0.970358\pi$
$98$		0			0
$99$	0.598630	−	3.00951i	0.0601645	−	0.302468i
$100$		0			0
$101$	−0.569062	−	0.380235i	−0.0566238	−	0.0378348i	0.526936	−	0.849905i	$-0.323341\pi$
$101$	−0.569062	−	0.380235i	−0.0566238	−	0.0378348i	−0.583560	+	0.812070i	$0.698341\pi$
$102$		0			0
$103$	−1.03003	−	2.48672i	−0.101492	−	0.245024i	0.864975	−	0.501816i	$-0.167334\pi$
$103$	−1.03003	−	2.48672i	−0.101492	−	0.245024i	−0.966467	+	0.256792i	$0.917334\pi$
$104$		0			0
$105$	0.193451	−	0.467032i	0.0188789	−	0.0455776i
$106$		0			0
$107$	12.3947	−	2.46545i	1.19824	−	0.238344i	0.444658	−	0.895701i	$-0.353325\pi$
$107$	12.3947	−	2.46545i	1.19824	−	0.238344i	0.753580	+	0.657356i	$0.228325\pi$
$108$		0			0
$109$	5.11373	−	3.41688i	0.489806	−	0.327278i	−0.286021	−	0.958223i	$-0.592333\pi$
$109$	5.11373	−	3.41688i	0.489806	−	0.327278i	0.775827	+	0.630945i	$0.217333\pi$
$110$		0			0
$111$	7.43817	+	7.43817i	0.706000	+	0.706000i
$112$		0			0
$113$	6.83631	−	6.83631i	0.643106	−	0.643106i	−0.308212	−	0.951318i	$-0.599730\pi$
$113$	6.83631	−	6.83631i	0.643106	−	0.643106i	0.951318	+	0.308212i	$0.0997305\pi$
$114$		0			0
$115$	0.935324	+	1.39981i	0.0872194	+	0.130533i
$116$		0			0
$117$	1.32613	+	6.66690i	0.122601	+	0.616355i
$118$		0			0
$119$	3.85017	+	1.59479i	0.352945	+	0.146194i
$120$		0			0
$121$	2.12445	−	0.879976i	0.193132	−	0.0799978i
$122$		0			0
$123$	1.90720	−	2.85433i	0.171967	−	0.257366i
$124$		0			0
$125$	2.68238	+	0.533559i	0.239919	+	0.0477229i
$126$		0			0
$127$	−11.4576			−1.01669			−0.508347	−	0.861152i	$-0.669743\pi$
$127$	−11.4576			−1.01669			−0.508347	+	0.861152i	$0.669743\pi$
$128$		0			0
$129$	−8.12914			−0.715731
$130$		0			0
$131$	−2.37921	−	0.473254i	−0.207872	−	0.0413484i	0.0900556	−	0.995937i	$-0.471296\pi$
$131$	−2.37921	−	0.473254i	−0.207872	−	0.0413484i	−0.297928	+	0.954588i	$0.596296\pi$
$132$		0			0
$133$	3.17528	−	4.75215i	0.275332	−	0.412063i
$134$		0			0
$135$	1.00293	−	0.415429i	0.0863189	−	0.0357544i
$136$		0			0
$137$	−21.2383	−	8.79718i	−1.81451	−	0.751594i	−0.979526	−	0.201319i	$-0.935477\pi$
$137$	−21.2383	−	8.79718i	−1.81451	−	0.751594i	−0.834983	−	0.550276i	$-0.814523\pi$
$138$		0			0
$139$	1.92573	+	9.68131i	0.163338	+	0.821158i	0.972379	+	0.233406i	$0.0749870\pi$
$139$	1.92573	+	9.68131i	0.163338	+	0.821158i	−0.809041	+	0.587752i	$0.800013\pi$
$140$		0			0
$141$	−5.41662	−	8.10654i	−0.456162	−	0.682694i
$142$		0			0
$143$	13.6288	−	13.6288i	1.13970	−	1.13970i
$144$		0			0
$145$	0.692526	+	0.692526i	0.0575112	+	0.0575112i
$146$		0			0
$147$	10.3072	−	6.88705i	0.850124	−	0.568034i
$148$		0			0
$149$	−15.3683	+	3.05694i	−1.25902	+	0.250434i	−0.779111	−	0.626886i	$-0.784329\pi$
$149$	−15.3683	+	3.05694i	−1.25902	+	0.250434i	−0.479906	+	0.877320i	$0.659329\pi$
$150$		0			0
$151$	−4.19983	+	10.1393i	−0.341777	+	0.825123i	0.655759	+	0.754970i	$0.272349\pi$
$151$	−4.19983	+	10.1393i	−0.341777	+	0.825123i	−0.997536	+	0.0701526i	$0.977651\pi$
$152$		0			0
$153$	−1.81797	−	4.38897i	−0.146974	−	0.354827i
$154$		0			0
$155$	0.898822	+	0.600574i	0.0721951	+	0.0482392i
$156$		0			0
$157$	−4.25698	+	21.4013i	−0.339744	+	1.70801i	0.312430	+	0.949941i	$0.398857\pi$
$157$	−4.25698	+	21.4013i	−0.339744	+	1.70801i	−0.652174	+	0.758069i	$0.726143\pi$
$158$		0			0
$159$		−	3.31592i		−	0.262969i
$160$		0			0
$161$		−	5.57486i		−	0.439360i
$162$		0			0
$163$	0.0534145	−	0.268533i	0.00418374	−	0.0210331i	−0.978637	−	0.205596i	$-0.934087\pi$
$163$	0.0534145	−	0.268533i	0.00418374	−	0.0210331i	0.982821	+	0.184563i	$0.0590868\pi$
$164$		0			0
$165$	1.35857	+	0.907767i	0.105765	+	0.0706696i
$166$		0			0
$167$	8.36818	+	20.2026i	0.647549	+	1.56332i	0.816278	+	0.577659i	$0.196034\pi$
$167$	8.36818	+	20.2026i	0.647549	+	1.56332i	−0.168729	+	0.985662i	$0.553966\pi$
$168$		0			0
$169$	−11.3647	+	27.4367i	−0.874204	+	2.11052i
$170$		0			0
$171$	−6.38998	+	1.27105i	−0.488654	+	0.0971993i
$172$		0			0
$173$	11.3220	−	7.56510i	0.860793	−	0.575164i	−0.0449505	−	0.998989i	$-0.514313\pi$
$173$	11.3220	−	7.56510i	0.860793	−	0.575164i	0.905744	+	0.423825i	$0.139313\pi$
$174$		0			0
$175$	−3.17743	−	3.17743i	−0.240191	−	0.240191i
$176$		0			0
$177$	8.78291	−	8.78291i	0.660164	−	0.660164i
$178$		0			0
$179$	−3.53996	−	5.29793i	−0.264589	−	0.395986i	0.675258	−	0.737582i	$-0.264032\pi$
$179$	−3.53996	−	5.29793i	−0.264589	−	0.395986i	−0.939847	+	0.341596i	$0.889032\pi$
$180$		0			0
$181$	1.23356	+	6.20153i	0.0916898	+	0.460956i	0.999165	+	0.0408508i	$0.0130068\pi$
$181$	1.23356	+	6.20153i	0.0916898	+	0.460956i	−0.907475	+	0.420105i	$0.861993\pi$
$182$		0			0
$183$	21.8853	+	9.06518i	1.61781	+	0.670118i
$184$		0			0
$185$	−1.33244	+	0.551916i	−0.0979631	+	0.0405776i
$186$		0			0
$187$	−7.48356	+	11.1999i	−0.547252	+	0.819021i
$188$		0			0
$189$	−3.52567	−	0.701300i	−0.256455	−	0.0510120i
$190$		0			0
$191$	−12.7011			−0.919021			−0.459511	−	0.888172i	$-0.651975\pi$
$191$	−12.7011			−0.919021			−0.459511	+	0.888172i	$0.651975\pi$
$192$		0			0
$193$	13.2427			0.953228			0.476614	−	0.879113i	$-0.341864\pi$
$193$	13.2427			0.953228			0.476614	+	0.879113i	$0.341864\pi$
$194$		0			0
$195$	−3.55007	−	0.706153i	−0.254226	−	0.0505687i
$196$		0			0
$197$	−4.91763	+	7.35976i	−0.350367	+	0.524361i	−0.964235	−	0.265047i	$-0.914612\pi$
$197$	−4.91763	+	7.35976i	−0.350367	+	0.524361i	0.613869	+	0.789408i	$0.289612\pi$
$198$		0			0
$199$	1.07833	−	0.446660i	0.0764410	−	0.0316629i	−0.344135	−	0.938920i	$-0.611828\pi$
$199$	1.07833	−	0.446660i	0.0764410	−	0.0316629i	0.420576	+	0.907257i	$0.361828\pi$
$200$		0			0
$201$	13.0666	+	5.41238i	0.921650	+	0.381760i
$202$		0			0
$203$	−0.632700	−	3.18080i	−0.0444068	−	0.223248i
$204$		0			0
$205$	0.261486	+	0.391341i	0.0182630	+	0.0273325i
$206$		0			0
$207$	−4.49366	+	4.49366i	−0.312331	+	0.312331i
$208$		0			0
$209$	13.0627	+	13.0627i	0.903565	+	0.903565i
$210$		0			0
$211$	−9.00912	+	6.01970i	−0.620213	+	0.414413i	−0.825591	−	0.564270i	$-0.809158\pi$
$211$	−9.00912	+	6.01970i	−0.620213	+	0.414413i	0.205377	+	0.978683i	$0.434158\pi$
$212$		0			0
$213$	−5.41772	+	1.07765i	−0.371216	+	0.0738395i
$214$		0			0
$215$	0.426517	−	1.02970i	0.0290882	−	0.0702251i
$216$		0			0
$217$	−1.36986	−	3.30714i	−0.0929924	−	0.224504i
$218$		0			0
$219$	−3.71933	−	2.48518i	−0.251329	−	0.167933i
$220$		0			0
$221$	5.82147	−	29.2665i	0.391594	−	1.96868i
$222$		0			0
$223$		−	13.6571i		−	0.914545i	−0.889327	−	0.457273i	$-0.848826\pi$
$223$		−	13.6571i		−	0.914545i	0.889327	−	0.457273i	$-0.151174\pi$
$224$		0			0
$225$			5.12239i			0.341493i
$226$		0			0
$227$	0.0149278	−	0.0750473i	0.000990796	−	0.00498107i	−0.980287	−	0.197580i	$-0.936692\pi$
$227$	0.0149278	−	0.0750473i	0.000990796	−	0.00498107i	0.981278	+	0.192599i	$0.0616917\pi$
$228$		0			0
$229$	3.11926	+	2.08423i	0.206127	+	0.137730i	0.654349	−	0.756193i	$-0.272943\pi$
$229$	3.11926	+	2.08423i	0.206127	+	0.137730i	−0.448222	+	0.893922i	$0.647943\pi$
$230$		0			0
$231$	−2.07055	−	4.99875i	−0.136232	−	0.328894i
$232$		0			0
$233$	5.43841	−	13.1295i	0.356282	−	0.860141i	−0.639534	−	0.768763i	$-0.720873\pi$
$233$	5.43841	−	13.1295i	0.356282	−	0.860141i	0.995816	−	0.0913785i	$-0.0291273\pi$
$234$		0			0
$235$	1.31104	−	0.260782i	0.0855226	−	0.0170115i
$236$		0			0
$237$	−9.95539	+	6.65198i	−0.646672	+	0.432092i
$238$		0			0
$239$	−18.6031	−	18.6031i	−1.20333	−	1.20333i	−0.973147	−	0.230186i	$-0.926066\pi$
$239$	−18.6031	−	18.6031i	−1.20333	−	1.20333i	−0.230186	−	0.973147i	$-0.573934\pi$
$240$		0			0
$241$	−8.43324	+	8.43324i	−0.543233	+	0.543233i	−0.924475	−	0.381242i	$-0.875496\pi$
$241$	−8.43324	+	8.43324i	−0.543233	+	0.543233i	0.381242	+	0.924475i	$0.375496\pi$
$242$		0			0
$243$	5.76172	+	8.62302i	0.369614	+	0.553167i
$244$		0			0
$245$	0.331575	+	1.66694i	0.0211836	+	0.106497i
$246$		0			0
$247$	−37.8086	−	15.6608i	−2.40570	−	0.996475i
$248$		0			0
$249$	−19.3033	+	7.99567i	−1.22329	+	0.506705i
$250$		0			0
$251$	−3.56767	+	5.33939i	−0.225189	+	0.337019i	−0.926810	−	0.375532i	$-0.877460\pi$
$251$	−3.56767	+	5.33939i	−0.225189	+	0.337019i	0.701621	+	0.712551i	$0.252460\pi$
$252$		0			0
$253$	17.6731	+	3.51539i	1.11110	+	0.221011i
$254$		0			0
$255$	2.52965			0.158413
$256$		0			0
$257$	22.6435			1.41246			0.706230	−	0.707982i	$-0.250394\pi$
$257$	22.6435			1.41246			0.706230	+	0.707982i	$0.250394\pi$
$258$		0			0
$259$	4.68401	+	0.931707i	0.291050	+	0.0578934i
$260$		0			0
$261$	−2.05392	+	3.07390i	−0.127134	+	0.190270i
$262$		0			0
$263$	−4.08591	+	1.69244i	−0.251948	+	0.104360i	−0.505083	−	0.863071i	$-0.668538\pi$
$263$	−4.08591	+	1.69244i	−0.251948	+	0.104360i	0.253135	+	0.967431i	$0.418538\pi$
$264$		0			0
$265$	0.420021	+	0.173978i	0.0258017	+	0.0106874i
$266$		0			0
$267$	3.96907	+	19.9538i	0.242903	+	1.22116i
$268$		0			0
$269$	−0.00106182	−	0.00158913i	−6.47403e−5	−	9.68908e-5i	0.831437	−	0.555619i	$-0.187519\pi$
$269$	−0.00106182	−	0.00158913i	−6.47403e−5	−	9.68908e-5i	−0.831502	+	0.555522i	$0.812519\pi$
$270$		0			0
$271$	−19.1266	+	19.1266i	−1.16186	+	1.16186i	−0.177788	+	0.984069i	$0.556894\pi$
$271$	−19.1266	+	19.1266i	−1.16186	+	1.16186i	−0.984069	+	0.177788i	$0.943106\pi$
$272$		0			0
$273$	8.47537	+	8.47537i	0.512953	+	0.512953i
$274$		0			0
$275$	12.0765	−	8.06927i	0.728241	−	0.486595i
$276$		0			0
$277$	24.9785	−	4.96854i	1.50082	−	0.298531i	0.624789	−	0.780794i	$-0.285185\pi$
$277$	24.9785	−	4.96854i	1.50082	−	0.298531i	0.876026	+	0.482263i	$0.160185\pi$
$278$		0			0
$279$	−1.56156	+	3.76995i	−0.0934883	+	0.225701i
$280$		0			0
$281$	8.84989	+	21.3655i	0.527940	+	1.27456i	0.932870	+	0.360213i	$0.117296\pi$
$281$	8.84989	+	21.3655i	0.527940	+	1.27456i	−0.404930	+	0.914348i	$0.632704\pi$
$282$		0			0
$283$	−0.552579	−	0.369221i	−0.0328474	−	0.0219479i	0.539038	−	0.842281i	$-0.318788\pi$
$283$	−0.552579	−	0.369221i	−0.0328474	−	0.0219479i	−0.571886	+	0.820333i	$0.693788\pi$
$284$		0			0
$285$	0.676821	−	3.40261i	0.0400914	−	0.201553i
$286$		0			0
$287$		−	1.55855i		−	0.0919981i
$288$		0			0
$289$			3.85420i			0.226718i
$290$		0			0
$291$	0.718267	−	3.61097i	0.0421056	−	0.211679i
$292$		0			0
$293$	14.0919	+	9.41592i	0.823259	+	0.550084i	0.894341	−	0.447387i	$-0.147645\pi$
$293$	14.0919	+	9.41592i	0.823259	+	0.550084i	−0.0710819	+	0.997470i	$0.522645\pi$
$294$		0			0
$295$	0.651695	+	1.57333i	0.0379432	+	0.0916029i
$296$		0			0
$297$	4.44643	−	10.7346i	0.258008	−	0.622887i
$298$		0			0
$299$	−39.1507	+	7.78756i	−2.26414	+	0.450366i
$300$		0			0
$301$	−3.06869	+	2.05043i	−0.176876	+	0.118185i
$302$		0			0
$303$	0.972757	+	0.972757i	0.0558834	+	0.0558834i
$304$		0			0
$305$	−2.29654	+	2.29654i	−0.131499	+	0.131499i
$306$		0			0
$307$	−11.9514	−	17.8865i	−0.682100	−	1.02083i	−0.997416	−	0.0718479i	$-0.977110\pi$
$307$	−11.9514	−	17.8865i	−0.682100	−	1.02083i	0.315316	−	0.948987i	$-0.397890\pi$
$308$		0			0
$309$	1.05549	+	5.30629i	0.0600446	+	0.301864i
$310$		0			0
$311$	28.0762	+	11.6295i	1.59205	+	0.659450i	0.990264	−	0.139204i	$-0.0444545\pi$
$311$	28.0762	+	11.6295i	1.59205	+	0.659450i	0.601790	+	0.798655i	$0.294455\pi$
$312$		0			0
$313$	6.79018	−	2.81259i	0.383804	−	0.158977i	−0.182435	−	0.983218i	$-0.558398\pi$
$313$	6.79018	−	2.81259i	0.383804	−	0.158977i	0.566239	+	0.824241i	$0.308398\pi$
$314$		0			0
$315$	−0.145350	+	0.217531i	−0.00818953	+	0.0122565i
$316$		0			0
$317$	−19.5241	−	3.88359i	−1.09658	−	0.218124i	−0.386534	−	0.922275i	$-0.626328\pi$
$317$	−19.5241	−	3.88359i	−1.09658	−	0.218124i	−0.710051	+	0.704151i	$0.751328\pi$
$318$		0			0
$319$	10.4825			0.586909
$320$		0			0
$321$	−25.4019			−1.41780
$322$		0			0
$323$	28.0509	+	5.57966i	1.56079	+	0.310461i
$324$		0			0
$325$	−17.8756	+	26.7528i	−0.991562	+	1.48398i
$326$		0			0
$327$	−11.4212	+	4.73082i	−0.631594	+	0.261615i
$328$		0			0
$329$	−4.08947	−	1.69391i	−0.225460	−	0.0933885i
$330$		0			0
$331$	−2.07742	−	10.4439i	−0.114185	−	0.574049i	−0.994940	−	0.100475i	$-0.967964\pi$
$331$	−2.07742	−	10.4439i	−0.114185	−	0.574049i	0.880754	−	0.473574i	$-0.157036\pi$
$332$		0			0
$333$	−3.02458	−	4.52660i	−0.165746	−	0.248056i
$334$		0			0
$335$	−1.37115	+	1.37115i	−0.0749140	+	0.0749140i
$336$		0			0
$337$	−9.26878	−	9.26878i	−0.504902	−	0.504902i	0.408055	−	0.912957i	$-0.366207\pi$
$337$	−9.26878	−	9.26878i	−0.504902	−	0.504902i	−0.912957	+	0.408055i	$0.866207\pi$
$338$		0			0
$339$	−16.1581	+	10.7965i	−0.877585	+	0.586384i
$340$		0			0
$341$	11.3479	−	2.25724i	0.614524	−	0.122236i
$342$		0			0
$343$	4.59834	−	11.1014i	0.248287	−	0.599418i
$344$		0			0
$345$	−1.29500	−	3.12640i	−0.0697202	−	0.168320i
$346$		0			0
$347$	−6.76125	−	4.51772i	−0.362963	−	0.242524i	0.360694	−	0.932684i	$-0.382540\pi$
$347$	−6.76125	−	4.51772i	−0.362963	−	0.242524i	−0.723656	+	0.690160i	$0.757540\pi$
$348$		0			0
$349$	−2.20654	+	11.0931i	−0.118114	+	0.593797i	0.875711	+	0.482836i	$0.160393\pi$
$349$	−2.20654	+	11.0931i	−0.118114	+	0.593797i	−0.993825	+	0.110962i	$0.964607\pi$
$350$		0			0
$351$			25.7395i			1.37387i
$352$		0			0
$353$			2.13438i			0.113602i	0.998386	+	0.0568008i	$0.0180900\pi$
$353$			2.13438i			0.113602i	−0.998386	+	0.0568008i	$0.981910\pi$
$354$		0			0
$355$	0.147751	−	0.742794i	0.00784180	−	0.0394234i
$356$		0			0
$357$	−6.96493	−	4.65382i	−0.368623	−	0.246306i
$358$		0			0
$359$	−1.13471	−	2.73943i	−0.0598876	−	0.144581i	0.891103	−	0.453801i	$-0.149932\pi$
$359$	−1.13471	−	2.73943i	−0.0598876	−	0.144581i	−0.950991	+	0.309219i	$0.899932\pi$
$360$		0			0
$361$	7.73934	−	18.6844i	0.407334	−	0.983391i
$362$		0			0
$363$	−4.53326	+	0.901722i	−0.237934	+	0.0473281i
$364$		0			0
$365$	0.509937	−	0.340729i	0.0266913	−	0.0178346i
$366$		0			0
$367$	8.53257	+	8.53257i	0.445396	+	0.445396i	0.893821	−	0.448424i	$-0.148015\pi$
$367$	8.53257	+	8.53257i	0.445396	+	0.445396i	−0.448424	+	0.893821i	$0.648015\pi$
$368$		0			0
$369$	−1.25628	+	1.25628i	−0.0653994	+	0.0653994i
$370$		0			0
$371$	−0.836382	−	1.25173i	−0.0434228	−	0.0649868i
$372$		0			0
$373$	−1.44487	−	7.26383i	−0.0748123	−	0.376107i	0.925182	−	0.379524i	$-0.123912\pi$
$373$	−1.44487	−	7.26383i	−0.0748123	−	0.376107i	−0.999994	+	0.00341725i	$0.998912\pi$
$374$		0			0
$375$	−5.07887	−	2.10374i	−0.262272	−	0.108637i
$376$		0			0
$377$	−21.4540	+	8.88656i	−1.10494	+	0.457681i
$378$		0			0
$379$	18.0363	−	26.9933i	0.926464	−	1.38655i	0.00420008	−	0.999991i	$-0.498663\pi$
$379$	18.0363	−	26.9933i	0.926464	−	1.38655i	0.922264	−	0.386560i	$-0.126337\pi$
$380$		0			0
$381$	22.5877	+	4.49297i	1.15720	+	0.230182i
$382$		0			0
$383$	34.5409			1.76496			0.882479	−	0.470351i	$-0.155873\pi$
$383$	34.5409			1.76496			0.882479	+	0.470351i	$0.155873\pi$
$384$		0			0
$385$	0.741819			0.0378066
$386$		0			0
$387$	4.12632	+	0.820776i	0.209753	+	0.0417224i
$388$		0			0
$389$	−7.37213	+	11.0332i	−0.373782	+	0.559404i	−0.969903	−	0.243490i	$-0.921708\pi$
$389$	−7.37213	+	11.0332i	−0.373782	+	0.559404i	0.596121	+	0.802894i	$0.296708\pi$
$390$		0			0
$391$	25.7738	−	10.6758i	1.30344	−	0.539900i
$392$		0			0
$393$	4.50484	+	1.86597i	0.227239	+	0.0941255i
$394$		0			0
$395$	−0.320257	−	1.61004i	−0.0161139	−	0.0810100i
$396$		0			0
$397$	2.85471	+	4.27237i	0.143274	+	0.214424i	0.896165	−	0.443720i	$-0.146342\pi$
$397$	2.85471	+	4.27237i	0.143274	+	0.214424i	−0.752892	+	0.658144i	$0.771342\pi$
$398$		0			0
$399$	−8.12333	+	8.12333i	−0.406675	+	0.406675i
$400$		0			0
$401$	4.16307	+	4.16307i	0.207894	+	0.207894i	0.803372	−	0.595478i	$-0.203037\pi$
$401$	4.16307	+	4.16307i	0.207894	+	0.207894i	−0.595478	+	0.803372i	$0.703037\pi$
$402$		0			0
$403$	−21.3116	+	14.2400i	−1.06161	+	0.709343i
$404$		0			0
$405$	−2.98365	+	0.593485i	−0.148259	+	0.0294905i
$406$		0			0
$407$	−5.90728	+	14.2614i	−0.292813	+	0.706913i
$408$		0			0
$409$	1.24674	+	3.00991i	0.0616475	+	0.148830i	0.951701	−	0.307025i	$-0.0993335\pi$
$409$	1.24674	+	3.00991i	0.0616475	+	0.148830i	−0.890054	+	0.455855i	$0.849333\pi$
$410$		0			0
$411$	38.4199	+	25.6714i	1.89511	+	1.26627i
$412$		0			0
$413$	1.10015	−	5.53082i	0.0541348	−	0.272154i
$414$		0			0
$415$		−	2.86462i		−	0.140619i
$416$		0			0
$417$		−	19.8411i		−	0.971623i
$418$		0			0
$419$	1.34847	−	6.77921i	0.0658771	−	0.331186i	−0.933767	−	0.357883i	$-0.883499\pi$
$419$	1.34847	−	6.77921i	0.0658771	−	0.331186i	0.999644	+	0.0266964i	$0.00849875\pi$
$420$		0			0
$421$	−4.37453	−	2.92296i	−0.213201	−	0.142457i	0.444385	−	0.895836i	$-0.353422\pi$
$421$	−4.37453	−	2.92296i	−0.213201	−	0.142457i	−0.657586	+	0.753380i	$0.728422\pi$
$422$		0			0
$423$	1.93096	+	4.66175i	0.0938865	+	0.226662i
$424$		0			0
$425$	8.60516	−	20.7747i	0.417412	−	1.00772i
$426$		0			0
$427$	10.5481	−	2.09814i	0.510457	−	0.101536i
$428$		0			0
$429$	−32.2125	+	21.5237i	−1.55523	+	1.03917i
$430$		0			0
$431$	−14.3235	−	14.3235i	−0.689941	−	0.689941i	0.272278	−	0.962219i	$-0.412223\pi$
$431$	−14.3235	−	14.3235i	−0.689941	−	0.689941i	−0.962219	+	0.272278i	$0.912223\pi$
$432$		0			0
$433$	−8.31597	+	8.31597i	−0.399640	+	0.399640i	−0.878106	−	0.478466i	$-0.841193\pi$
$433$	−8.31597	+	8.31597i	−0.399640	+	0.399640i	0.478466	+	0.878106i	$0.341193\pi$
$434$		0			0
$435$	−1.09369	−	1.63683i	−0.0524386	−	0.0784800i
$436$		0			0
$437$	−7.46409	−	37.5245i	−0.357056	−	1.79504i
$438$		0			0
$439$	−14.3157	−	5.92976i	−0.683251	−	0.283012i	0.0139342	−	0.999903i	$-0.495564\pi$
$439$	−14.3157	−	5.92976i	−0.683251	−	0.283012i	−0.697185	+	0.716891i	$0.745564\pi$
$440$		0			0
$441$	−5.92726	+	2.45515i	−0.282250	+	0.116912i
$442$		0			0
$443$	−3.72766	+	5.57883i	−0.177106	+	0.265058i	−0.909393	−	0.415938i	$-0.863453\pi$
$443$	−3.72766	+	5.57883i	−0.177106	+	0.265058i	0.732287	+	0.680997i	$0.238453\pi$
$444$		0			0
$445$	−2.73576	−	0.544177i	−0.129688	−	0.0257965i
$446$		0			0
$447$	31.4961			1.48971
$448$		0			0
$449$	−12.1738			−0.574519			−0.287259	−	0.957853i	$-0.592744\pi$
$449$	−12.1738			−0.574519			−0.287259	+	0.957853i	$0.592744\pi$
$450$		0			0
$451$	4.94081	+	0.982788i	0.232654	+	0.0462777i
$452$		0			0
$453$	12.2556	−	18.3419i	0.575821	−	0.861776i
$454$		0			0
$455$	−1.51824	+	0.628876i	−0.0711763	+	0.0294822i
$456$		0			0
$457$	21.6386	+	8.96300i	1.01221	+	0.419271i	0.826261	−	0.563288i	$-0.190464\pi$
$457$	21.6386	+	8.96300i	1.01221	+	0.419271i	0.185950	+	0.982559i	$0.440464\pi$
$458$		0			0
$459$	−3.50940	−	17.6429i	−0.163805	−	0.823501i
$460$		0			0
$461$	−3.40229	−	5.09189i	−0.158461	−	0.237153i	0.743741	−	0.668468i	$-0.233050\pi$
$461$	−3.40229	−	5.09189i	−0.158461	−	0.237153i	−0.902201	+	0.431315i	$0.858050\pi$
$462$		0			0
$463$	−8.70982	+	8.70982i	−0.404780	+	0.404780i	−0.879914	−	0.475134i	$-0.842400\pi$
$463$	−8.70982	+	8.70982i	−0.404780	+	0.404780i	0.475134	+	0.879914i	$0.342400\pi$
$464$		0			0
$465$	−1.53645	−	1.53645i	−0.0712511	−	0.0712511i
$466$		0			0
$467$	5.86536	−	3.91911i	0.271416	−	0.181355i	−0.412412	−	0.910997i	$-0.635314\pi$
$467$	5.86536	−	3.91911i	0.271416	−	0.181355i	0.683829	+	0.729643i	$0.260314\pi$
$468$		0			0
$469$	6.29775	−	1.25270i	0.290803	−	0.0578443i
$470$		0			0
$471$	16.7846	−	40.5217i	0.773395	−	1.86714i
$472$		0			0
$473$	−4.56511	−	11.0211i	−0.209904	−	0.506753i
$474$		0			0
$475$	−25.6416	−	17.1331i	−1.17652	−	0.786122i
$476$		0			0
$477$	−0.334799	+	1.68315i	−0.0153294	+	0.0770659i
$478$		0			0
$479$		−	26.1701i		−	1.19574i	−0.801592	−	0.597871i	$-0.796013\pi$
$479$		−	26.1701i		−	1.19574i	0.801592	−	0.597871i	$-0.203987\pi$
$480$		0			0
$481$		−	34.1960i		−	1.55920i
$482$		0			0
$483$	−2.18613	+	10.9904i	−0.0994721	+	0.500080i
$484$		0			0
$485$	0.419709	+	0.280441i	0.0190580	+	0.0127342i
$486$		0			0
$487$	11.8872	+	28.6983i	0.538662	+	1.30044i	0.925657	+	0.378363i	$0.123513\pi$
$487$	11.8872	+	28.6983i	0.538662	+	1.30044i	−0.386996	+	0.922082i	$0.626487\pi$
$488$		0			0
$489$	−0.210605	+	0.508445i	−0.00952389	+	0.0229927i
$490$		0			0
$491$	26.5981	−	5.29070i	1.20036	−	0.238766i	0.445880	−	0.895093i	$-0.352891\pi$
$491$	26.5981	−	5.29070i	1.20036	−	0.238766i	0.754476	+	0.656327i	$0.227891\pi$
$492$		0			0
$493$	13.4939	−	9.01633i	0.607734	−	0.406075i
$494$		0			0
$495$	−0.597950	−	0.597950i	−0.0268759	−	0.0268759i
$496$		0			0
$497$	−1.77333	+	1.77333i	−0.0795448	+	0.0795448i
$498$		0			0
$499$	−11.9390	−	17.8680i	−0.534462	−	0.799879i	0.461734	−	0.887019i	$-0.347228\pi$
$499$	−11.9390	−	17.8680i	−0.534462	−	0.799879i	−0.996196	+	0.0871391i	$0.972228\pi$
$500$		0			0
$501$	−8.57497	−	43.1093i	−0.383101	−	1.92598i
$502$		0			0
$503$	−28.1800	−	11.6725i	−1.25649	−	0.520453i	−0.347656	−	0.937622i	$-0.613022\pi$
$503$	−28.1800	−	11.6725i	−1.25649	−	0.520453i	−0.908829	+	0.417169i	$0.863022\pi$
$504$		0			0
$505$	−0.174255	+	0.0721790i	−0.00775427	+	0.00321192i
$506$		0			0
$507$	33.1636	−	49.6328i	1.47285	−	2.20427i
$508$		0			0
$509$	23.3694	+	4.64846i	1.03583	+	0.206039i	0.683587	−	0.729869i	$-0.260419\pi$
$509$	23.3694	+	4.64846i	1.03583	+	0.206039i	0.352243	+	0.935908i	$0.385419\pi$
$510$		0			0
$511$	−2.03087			−0.0898402
$512$		0			0
$513$	−24.6703			−1.08922
$514$		0			0
$515$	−0.727516	−	0.144712i	−0.0320582	−	0.00637677i
$516$		0			0
$517$	7.94868	−	11.8960i	0.349583	−	0.523187i
$518$		0			0
$519$	−25.2870	+	10.4742i	−1.10997	+	0.459766i
$520$		0			0
$521$	5.84704	+	2.42192i	0.256163	+	0.106106i	0.507070	−	0.861905i	$-0.330729\pi$
$521$	5.84704	+	2.42192i	0.256163	+	0.106106i	−0.250906	+	0.968011i	$0.580729\pi$
$522$		0			0
$523$	5.95365	+	29.9310i	0.260335	+	1.30879i	0.860719	+	0.509080i	$0.170014\pi$
$523$	5.95365	+	29.9310i	0.260335	+	1.30879i	−0.600384	+	0.799712i	$0.704986\pi$
$524$		0			0
$525$	5.01805	+	7.51005i	0.219006	+	0.327765i
$526$		0			0
$527$	12.6664	−	12.6664i	0.551755	−	0.551755i
$528$		0			0
$529$	−10.1251	−	10.1251i	−0.440223	−	0.440223i
$530$		0			0
$531$	−5.34495	+	3.57138i	−0.231951	+	0.154985i
$532$		0			0
$533$	−10.9453	+	2.17715i	−0.474092	+	0.0943027i
$534$		0			0
$535$	1.33278	−	3.21761i	0.0576210	−	0.139109i
$536$		0			0
$537$	4.90123	+	11.8326i	0.211504	+	0.510615i
$538$		0			0
$539$	15.1254	+	10.1065i	0.651498	+	0.435317i
$540$		0			0
$541$	−3.06081	+	15.3877i	−0.131594	+	0.661570i	0.857523	+	0.514445i	$0.172002\pi$
$541$	−3.06081	+	15.3877i	−0.131594	+	0.661570i	−0.989118	+	0.147125i	$0.952998\pi$
$542$		0			0
$543$		−	12.7096i		−	0.545419i
$544$		0			0
$545$		−	1.69492i		−	0.0726023i
$546$		0			0
$547$	−3.60776	+	18.1374i	−0.154257	+	0.775500i	0.823754	+	0.566947i	$0.191875\pi$
$547$	−3.60776	+	18.1374i	−0.154257	+	0.775500i	−0.978011	+	0.208553i	$0.933125\pi$
$548$		0			0
$549$	−10.1936	−	6.81115i	−0.435052	−	0.290693i
$550$		0			0
$551$	−8.51743	−	20.5629i	−0.362855	−	0.876009i
$552$		0			0
$553$	−2.08024	+	5.02215i	−0.0884609	+	0.213563i
$554$		0			0
$555$	2.84323	−	0.565554i	0.120689	−	0.0240064i
$556$		0			0
$557$	3.89299	−	2.60121i	0.164951	−	0.110217i	−0.470355	−	0.882477i	$-0.655874\pi$
$557$	3.89299	−	2.60121i	0.164951	−	0.110217i	0.635306	+	0.772261i	$0.280874\pi$
$558$		0			0
$559$	18.6863	+	18.6863i	0.790347	+	0.790347i
$560$		0			0
$561$	19.1452	−	19.1452i	0.808311	−	0.808311i
$562$		0			0
$563$	11.9617	+	17.9019i	0.504124	+	0.754475i	0.993030	−	0.117862i	$-0.0376039\pi$
$563$	11.9617	+	17.9019i	0.504124	+	0.754475i	−0.488906	+	0.872336i	$0.662604\pi$
$564$		0			0
$565$	−0.519793	−	2.61317i	−0.0218678	−	0.109937i
$566$		0			0
$567$	9.30678	+	3.85500i	0.390848	+	0.161895i
$568$		0			0
$569$	3.57864	−	1.48232i	0.150024	−	0.0621422i	−0.306408	−	0.951900i	$-0.599127\pi$
$569$	3.57864	−	1.48232i	0.150024	−	0.0621422i	0.456432	+	0.889758i	$0.349127\pi$
$570$		0			0
$571$	3.89635	−	5.83130i	0.163057	−	0.244032i	−0.740940	−	0.671572i	$-0.765619\pi$
$571$	3.89635	−	5.83130i	0.163057	−	0.244032i	0.903997	+	0.427539i	$0.140619\pi$
$572$		0			0
$573$	25.0393	+	4.98062i	1.04603	+	0.208068i
$574$		0			0
$575$	−30.0807			−1.25445
$576$		0			0
$577$	11.5627			0.481361			0.240680	−	0.970604i	$-0.422629\pi$
$577$	11.5627			0.481361			0.240680	+	0.970604i	$0.422629\pi$
$578$		0			0
$579$	−26.1069	−	5.19298i	−1.08496	−	0.215813i
$580$		0			0
$581$	−5.27007	+	7.88722i	−0.218640	+	0.327217i
$582$		0			0
$583$	4.49558	−	1.86213i	0.186188	−	0.0771215i
$584$		0			0
$585$	1.73070	+	0.716881i	0.0715558	+	0.0296394i
$586$		0			0
$587$	2.87452	+	14.4512i	0.118644	+	0.596464i	0.993665	+	0.112380i	$0.0358473\pi$
$587$	2.87452	+	14.4512i	0.118644	+	0.596464i	−0.875021	+	0.484084i	$0.839153\pi$
$588$		0			0
$589$	−13.6485	−	20.4264i	−0.562376	−	0.841655i
$590$		0			0
$591$	12.5808	−	12.5808i	0.517504	−	0.517504i
$592$		0			0
$593$	25.9026	+	25.9026i	1.06369	+	1.06369i	0.997829	+	0.0658644i	$0.0209805\pi$
$593$	25.9026	+	25.9026i	1.06369	+	1.06369i	0.0658644	+	0.997829i	$0.479020\pi$
$594$		0			0
$595$	0.954924	−	0.638060i	0.0391481	−	0.0261579i
$596$		0			0
$597$	−2.30100	+	0.457698i	−0.0941738	+	0.0187323i
$598$		0			0
$599$	15.4679	−	37.3427i	0.632000	−	1.52578i	−0.205105	−	0.978740i	$-0.565754\pi$
$599$	15.4679	−	37.3427i	0.632000	−	1.52578i	0.837105	−	0.547043i	$-0.184246\pi$
$600$		0			0
$601$	1.55993	+	3.76600i	0.0636308	+	0.153618i	0.952497	−	0.304549i	$-0.0985059\pi$
$601$	1.55993	+	3.76600i	0.0636308	+	0.153618i	−0.888866	+	0.458168i	$0.848506\pi$
$602$		0			0
$603$	−6.08611	−	4.06661i	−0.247845	−	0.165605i
$604$		0			0
$605$	0.123630	−	0.621530i	0.00502628	−	0.0252688i
$606$		0			0
$607$			23.7080i			0.962278i	0.876644	+	0.481139i	$0.159777\pi$
$607$			23.7080i			0.962278i	−0.876644	+	0.481139i	$0.840223\pi$
$608$		0			0
$609$			6.51880i			0.264155i
$610$		0			0
$611$	−6.18329	+	31.0855i	−0.250149	+	1.25758i
$612$		0			0
$613$	−20.1792	−	13.4833i	−0.815031	−	0.544587i	0.0767514	−	0.997050i	$-0.475545\pi$
$613$	−20.1792	−	13.4833i	−0.815031	−	0.544587i	−0.891783	+	0.452464i	$0.850545\pi$
$614$		0			0
$615$	−0.362038	−	0.874038i	−0.0145988	−	0.0352446i
$616$		0			0
$617$	−5.64022	+	13.6167i	−0.227067	+	0.548187i	−0.995818	−	0.0913607i	$-0.970878\pi$
$617$	−5.64022	+	13.6167i	−0.227067	+	0.548187i	0.768751	+	0.639548i	$0.220878\pi$
$618$		0			0
$619$	22.0029	−	4.37665i	0.884371	−	0.175912i	0.268048	−	0.963406i	$-0.413621\pi$
$619$	22.0029	−	4.37665i	0.884371	−	0.175912i	0.616323	+	0.787493i	$0.288621\pi$
$620$		0			0
$621$	−20.0084	+	13.3692i	−0.802908	+	0.536486i
$622$		0			0
$623$	6.53131	+	6.53131i	0.261671	+	0.261671i
$624$		0			0
$625$	−16.8762	+	16.8762i	−0.675048	+	0.675048i
$626$		0			0
$627$	−20.6297	−	30.8745i	−0.823870	−	1.23301i
$628$		0			0
$629$	4.66238	+	23.4394i	0.185901	+	0.934590i
$630$		0			0
$631$	−4.18674	−	1.73421i	−0.166672	−	0.0690376i	0.297788	−	0.954632i	$-0.403751\pi$
$631$	−4.18674	−	1.73421i	−0.166672	−	0.0690376i	−0.464459	+	0.885595i	$0.653751\pi$
$632$		0			0
$633$	20.1213	−	8.33453i	0.799751	−	0.331268i
$634$		0			0
$635$	−1.75424	+	2.62540i	−0.0696148	+	0.104186i
$636$		0			0
$637$	−39.5242	−	7.86184i	−1.56600	−	0.311498i
$638$		0			0
$639$	2.85882			0.113093
$640$		0			0
$641$	−34.6244			−1.36758			−0.683791	−	0.729678i	$-0.739670\pi$
$641$	−34.6244			−1.36758			−0.683791	+	0.729678i	$0.739670\pi$
$642$		0			0
$643$	28.9603	+	5.76055i	1.14208	+	0.227174i	0.729654	−	0.683817i	$-0.239681\pi$
$643$	28.9603	+	5.76055i	1.14208	+	0.227174i	0.412427	+	0.910991i	$0.364681\pi$
$644$		0			0
$645$	−1.24463	+	1.86272i	−0.0490073	+	0.0733447i
$646$		0			0
$647$	−4.00964	+	1.66085i	−0.157635	+	0.0652946i	−0.460106	−	0.887864i	$-0.652189\pi$
$647$	−4.00964	+	1.66085i	−0.157635	+	0.0652946i	0.302471	+	0.953159i	$0.402189\pi$
$648$		0			0
$649$	16.8397	+	6.97525i	0.661018	+	0.273802i
$650$		0			0
$651$	1.40372	+	7.05696i	0.0550160	+	0.276584i
$652$		0			0
$653$	−17.9859	−	26.9178i	−0.703843	−	1.05338i	−0.995305	−	0.0967932i	$-0.969141\pi$
$653$	−17.9859	−	26.9178i	−0.703843	−	1.05338i	0.291461	−	0.956583i	$-0.405859\pi$
$654$		0			0
$655$	−0.472717	+	0.472717i	−0.0184706	+	0.0184706i
$656$		0			0
$657$	1.63700	+	1.63700i	0.0638654	+	0.0638654i
$658$		0			0
$659$	0.730386	−	0.488029i	0.0284518	−	0.0190109i	−0.541263	−	0.840853i	$-0.682054\pi$
$659$	0.730386	−	0.488029i	0.0284518	−	0.0190109i	0.569715	+	0.821842i	$0.307054\pi$
$660$		0			0
$661$	−0.894601	+	0.177947i	−0.0347959	+	0.00692134i	−0.212458	−	0.977170i	$-0.568147\pi$
$661$	−0.894601	+	0.177947i	−0.0347959	+	0.00692134i	0.177662	+	0.984092i	$0.443147\pi$
$662$		0			0
$663$	−22.9531	+	55.4138i	−0.891426	+	2.15209i
$664$		0			0
$665$	−0.602754	−	1.45518i	−0.0233738	−	0.0564294i
$666$		0			0
$667$	−18.0512	−	12.0614i	−0.698945	−	0.467020i
$668$		0			0
$669$	−5.35549	+	26.9239i	−0.207055	+	1.04094i
$670$		0			0
$671$			34.7619i			1.34197i
$672$		0			0
$673$			8.15010i			0.314163i	0.987586	+	0.157082i	$0.0502086\pi$
$673$			8.15010i			0.314163i	−0.987586	+	0.157082i	$0.949791\pi$
$674$		0			0
$675$	−3.78406	+	19.0238i	−0.145649	+	0.732225i
$676$		0			0
$677$	14.3667	+	9.59953i	0.552158	+	0.368940i	0.800130	−	0.599827i	$-0.204764\pi$
$677$	14.3667	+	9.59953i	0.552158	+	0.368940i	−0.247972	+	0.968767i	$0.579764\pi$
$678$		0			0
$679$	−0.639665	−	1.54429i	−0.0245481	−	0.0592643i
$680$		0			0
$681$	−0.0588582	+	0.142096i	−0.00225545	+	0.00544514i
$682$		0			0
$683$	−47.8740	+	9.52274i	−1.83185	+	0.364377i	−0.985692	−	0.168556i	$-0.946090\pi$
$683$	−47.8740	+	9.52274i	−1.83185	+	0.364377i	−0.846157	+	0.532933i	$0.821090\pi$
$684$		0			0
$685$	−5.26754	+	3.51966i	−0.201262	+	0.134479i
$686$		0			0
$687$	−5.33208	−	5.33208i	−0.203431	−	0.203431i
$688$		0			0
$689$	−7.62224	+	7.62224i	−0.290384	+	0.290384i
$690$		0			0
$691$	12.9075	+	19.3174i	0.491023	+	0.734868i	0.991390	−	0.130946i	$-0.0418014\pi$
$691$	12.9075	+	19.3174i	0.491023	+	0.734868i	−0.500366	+	0.865814i	$0.666801\pi$
$692$		0			0
$693$	0.546294	+	2.74640i	0.0207520	+	0.104327i
$694$		0			0
$695$	2.51323	+	1.04102i	0.0953324	+	0.0394880i
$696$		0			0
$697$	7.20550	−	2.98462i	0.272928	−	0.113050i
$698$		0			0
$699$	−15.8700	+	23.7511i	−0.600259	+	0.898351i
$700$		0			0
$701$	30.2742	+	6.02192i	1.14344	+	0.227445i	0.730237	−	0.683194i	$-0.239409\pi$
$701$	30.2742	+	6.02192i	1.14344	+	0.227445i	0.413204	+	0.910638i	$0.364409\pi$
$702$		0			0
$703$	32.7756			1.23616
$704$		0			0
$705$	−2.68687			−0.101193
$706$		0			0
$707$	0.612570	+	0.121848i	0.0230381	+	0.00458255i
$708$		0			0
$709$	21.3782	−	31.9948i	0.802876	−	1.20159i	−0.173355	−	0.984859i	$-0.555461\pi$
$709$	21.3782	−	31.9948i	0.802876	−	1.20159i	0.976232	−	0.216730i	$-0.0695391\pi$
$710$		0			0
$711$	5.72495	−	2.37135i	0.214702	−	0.0889326i
$712$		0			0
$713$	−22.1386	−	9.17012i	−0.829098	−	0.343424i
$714$		0			0
$715$	−1.03625	−	5.20959i	−0.0387537	−	0.194828i
$716$		0			0
$717$	29.3795	+	43.9695i	1.09720	+	1.64207i
$718$		0			0
$719$	−18.4708	+	18.4708i	−0.688844	+	0.688844i	−0.961976	−	0.273133i	$-0.911940\pi$
$719$	−18.4708	+	18.4708i	−0.688844	+	0.688844i	0.273133	+	0.961976i	$0.411940\pi$
$720$		0			0
$721$	1.73686	+	1.73686i	0.0646840	+	0.0646840i
$722$		0			0
$723$	19.9325	−	13.3185i	0.741297	−	0.495319i
$724$		0			0
$725$	−17.1629	+	3.41391i	−0.637414	+	0.126789i
$726$		0			0
$727$	13.4323	−	32.4285i	0.498177	−	1.20271i	−0.452287	−	0.891872i	$-0.649392\pi$
$727$	13.4323	−	32.4285i	0.498177	−	1.20271i	0.950464	−	0.310834i	$-0.100608\pi$
$728$		0			0
$729$	4.69559	+	11.3362i	0.173911	+	0.419858i
$730$		0			0
$731$	−15.3561	−	10.2606i	−0.567967	−	0.379504i
$732$		0			0
$733$	−4.74446	+	23.8520i	−0.175241	+	0.880995i	0.788680	+	0.614804i	$0.210765\pi$
$733$	−4.74446	+	23.8520i	−0.175241	+	0.880995i	−0.963920	+	0.266190i	$0.914235\pi$
$734$		0			0
$735$		−	3.41627i		−	0.126011i
$736$		0			0
$737$			20.7547i			0.764508i
$738$		0			0
$739$	8.14420	−	40.9437i	0.299589	−	1.50614i	−0.478558	−	0.878056i	$-0.658840\pi$
$739$	8.14420	−	40.9437i	0.299589	−	1.50614i	0.778148	−	0.628081i	$-0.216160\pi$
$740$		0			0
$741$	68.3955	+	45.7004i	2.51257	+	1.67885i
$742$		0			0
$743$	11.5706	+	27.9339i	0.424485	+	1.02480i	0.981008	+	0.193965i	$0.0621349\pi$
$743$	11.5706	+	27.9339i	0.424485	+	1.02480i	−0.556524	+	0.830832i	$0.687865\pi$
$744$		0			0
$745$	−1.65253	+	3.98955i	−0.0605438	+	0.146166i
$746$		0			0
$747$	10.6056	−	2.10958i	0.388037	−	0.0771854i
$748$		0			0
$749$	−9.58904	+	6.40719i	−0.350376	+	0.234114i
$750$		0			0
$751$	14.1774	+	14.1774i	0.517342	+	0.517342i	0.916766	−	0.399424i	$-0.130790\pi$
$751$	14.1774	+	14.1774i	0.517342	+	0.517342i	−0.399424	+	0.916766i	$0.630790\pi$
$752$		0			0
$753$	9.12717	−	9.12717i	0.332612	−	0.332612i
$754$		0			0
$755$	1.68030	+	2.51475i	0.0611525	+	0.0915213i
$756$		0			0
$757$	6.49319	+	32.6435i	0.235999	+	1.18645i	0.899041	+	0.437864i	$0.144265\pi$
$757$	6.49319	+	32.6435i	0.235999	+	1.18645i	−0.663042	+	0.748582i	$0.730735\pi$
$758$		0			0
$759$	−33.4626	−	13.8606i	−1.21461	−	0.503109i
$760$		0			0
$761$	20.5439	−	8.50957i	0.744717	−	0.308472i	0.0221328	−	0.999755i	$-0.492954\pi$
$761$	20.5439	−	8.50957i	0.744717	−	0.308472i	0.722584	+	0.691283i	$0.242954\pi$
$762$		0			0
$763$	−3.11816	+	4.66665i	−0.112885	+	0.168944i
$764$		0			0
$765$	−1.28404	−	0.255411i	−0.0464245	−	0.00923441i
$766$		0			0
$767$	−40.3783			−1.45797
$768$		0			0
$769$	−7.22636			−0.260589			−0.130295	−	0.991475i	$-0.541592\pi$
$769$	−7.22636			−0.260589			−0.130295	+	0.991475i	$0.541592\pi$
$770$		0			0
$771$	−44.6398	−	8.87941i	−1.60766	−	0.319784i
$772$		0			0
$773$	−12.0788	+	18.0772i	−0.434444	+	0.650192i	−0.982503	−	0.186248i	$-0.940367\pi$
$773$	−12.0788	+	18.0772i	−0.434444	+	0.650192i	0.548059	+	0.836440i	$0.315367\pi$
$774$		0			0
$775$	−17.8446	+	7.39149i	−0.640998	+	0.265510i
$776$		0			0
$777$	−8.86879	−	3.67358i	−0.318166	−	0.131789i
$778$		0			0
$779$	−2.08671	−	10.4906i	−0.0747643	−	0.375865i
$780$		0			0
$781$	−4.50348	−	6.73993i	−0.161147	−	0.241174i
$782$		0			0
$783$	−9.89871	+	9.89871i	−0.353751	+	0.353751i
$784$		0			0
$785$	4.25215	+	4.25215i	0.151766	+	0.151766i
$786$		0			0
$787$	−16.3647	+	10.9345i	−0.583337	+	0.389773i	−0.811935	−	0.583748i	$-0.801586\pi$
$787$	−16.3647	+	10.9345i	−0.583337	+	0.389773i	0.228598	+	0.973521i	$0.426586\pi$
$788$		0			0
$789$	8.71872	−	1.73426i	0.310395	−	0.0617413i
$790$		0			0
$791$	−3.37633	+	8.15118i	−0.120048	+	0.289823i
$792$		0			0
$793$	−29.4694	−	71.1454i	−1.04649	−	2.52645i
$794$		0			0
$795$	−0.759814	−	0.507691i	−0.0269478	−	0.0180060i
$796$		0			0
$797$	9.67446	−	48.6368i	0.342687	−	1.72280i	−0.297620	−	0.954684i	$-0.596193\pi$
$797$	9.67446	−	48.6368i	0.342687	−	1.72280i	0.640307	−	0.768119i	$-0.278807\pi$
$798$		0			0
$799$		−	22.1503i		−	0.783623i
$800$		0			0
$801$		−	10.5292i		−	0.372032i
$802$		0			0
$803$	1.28062	−	6.43812i	0.0451922	−	0.227196i
$804$		0			0
$805$	−1.27743	−	0.853552i	−0.0450235	−	0.0300838i
$806$		0			0
$807$	0.00147014	+	0.00354922i	5.17512e−5	+	0.000124939i
$808$		0			0
$809$	−7.10619	+	17.1558i	−0.249840	+	0.603168i	−0.998190	−	0.0601366i	$-0.980846\pi$
$809$	−7.10619	+	17.1558i	−0.249840	+	0.603168i	0.748350	+	0.663304i	$0.230846\pi$
$810$		0			0
$811$	−8.30457	+	1.65188i	−0.291613	+	0.0580054i	−0.338729	−	0.940884i	$-0.609997\pi$
$811$	−8.30457	+	1.65188i	−0.291613	+	0.0580054i	0.0471161	+	0.998889i	$0.484997\pi$
$812$		0			0
$813$	45.2069	−	30.2063i	1.58547	−	1.05938i
$814$		0			0
$815$	−0.0533538	−	0.0533538i	−0.00186890	−	0.00186890i
$816$		0			0
$817$	−17.9101	+	17.9101i	−0.626597	+	0.626597i
$818$		0			0
$819$	−3.44633	−	5.15780i	−0.120425	−	0.180228i
$820$		0			0
$821$	6.55278	+	32.9430i	0.228694	+	1.14972i	0.909001	+	0.416793i	$0.136846\pi$
$821$	6.55278	+	32.9430i	0.228694	+	1.14972i	−0.680308	+	0.732927i	$0.738154\pi$
$822$		0			0
$823$	35.1942	+	14.5779i	1.22679	+	0.508155i	0.899563	−	0.436790i	$-0.143885\pi$
$823$	35.1942	+	14.5779i	1.22679	+	0.508155i	0.327230	+	0.944945i	$0.393885\pi$
$824$		0			0
$825$	−26.9722	+	11.1722i	−0.939051	+	0.388968i
$826$		0			0
$827$	−20.6833	+	30.9547i	−0.719229	+	1.07640i	0.274169	+	0.961681i	$0.411597\pi$
$827$	−20.6833	+	30.9547i	−0.719229	+	1.07640i	−0.993398	+	0.114720i	$0.963403\pi$
$828$		0			0
$829$	−14.0046	−	2.78569i	−0.486400	−	0.0967509i	−0.0542024	−	0.998530i	$-0.517262\pi$
$829$	−14.0046	−	2.78569i	−0.486400	−	0.0967509i	−0.432197	+	0.901779i	$0.642262\pi$
$830$		0			0
$831$	−51.1916			−1.77582
$832$		0			0
$833$	28.1634			0.975805
$834$		0			0
$835$	5.91048	+	1.17567i	0.204541	+	0.0406856i
$836$		0			0
$837$	−8.58437	+	12.8474i	−0.296719	+	0.444072i
$838$		0			0
$839$	1.76824	−	0.732431i	0.0610466	−	0.0252863i	−0.351951	−	0.936018i	$-0.614482\pi$
$839$	1.76824	−	0.732431i	0.0610466	−	0.0252863i	0.412998	+	0.910732i	$0.364482\pi$
$840$		0			0
$841$	15.1243	+	6.26470i	0.521529	+	0.216024i
$842$		0			0
$843$	−9.06859	−	45.5909i	−0.312339	−	1.57023i
$844$		0			0
$845$	4.54687	+	6.80488i	0.156417	+	0.234095i
$846$		0			0
$847$	−1.48383	+	1.48383i	−0.0509850	+	0.0509850i
$848$		0			0
$849$	0.944580	+	0.944580i	0.0324179	+	0.0324179i
$850$		0			0
$851$	26.5820	−	17.7615i	0.911219	−	0.608857i
$852$		0			0
$853$	6.56372	−	1.30561i	0.224738	−	0.0447031i	−0.0814369	−	0.996678i	$-0.525951\pi$
$853$	6.56372	−	1.30561i	0.224738	−	0.0447031i	0.306174	+	0.951975i	$0.400951\pi$
$854$		0			0
$855$	−0.687104	+	1.65882i	−0.0234985	+	0.0567303i
$856$		0			0
$857$	13.4560	+	32.4856i	0.459647	+	1.10969i	0.968540	+	0.248857i	$0.0800548\pi$
$857$	13.4560	+	32.4856i	0.459647	+	1.10969i	−0.508893	+	0.860830i	$0.669945\pi$
$858$		0			0
$859$	−2.78301	−	1.85955i	−0.0949550	−	0.0634469i	0.507186	−	0.861836i	$-0.330686\pi$
$859$	−2.78301	−	1.85955i	−0.0949550	−	0.0634469i	−0.602141	+	0.798390i	$0.705686\pi$
$860$		0			0
$861$	−0.611169	+	3.07255i	−0.0208286	+	0.104712i
$862$		0			0
$863$			10.8105i			0.367993i	0.982927	+	0.183997i	$0.0589036\pi$
$863$			10.8105i			0.367993i	−0.982927	+	0.183997i	$0.941096\pi$
$864$		0			0
$865$		−	3.75261i		−	0.127592i
$866$		0			0
$867$	1.51139	−	7.59826i	0.0513294	−	0.258051i
$868$		0			0
$869$	−14.6091	−	9.76152i	−0.495581	−	0.331137i
$870$		0			0
$871$	−17.5947	−	42.4775i	−0.596175	−	1.43929i
$872$		0			0
$873$	−0.729179	+	1.76039i	−0.0246790	+	0.0595803i
$874$		0			0
$875$	−2.44787	+	0.486912i	−0.0827531	+	0.0164606i
$876$		0			0
$877$	31.4200	−	20.9942i	1.06098	−	0.708924i	0.102687	−	0.994714i	$-0.467256\pi$
$877$	31.4200	−	20.9942i	1.06098	−	0.708924i	0.958292	+	0.285790i	$0.0922560\pi$
$878$		0			0
$879$	−24.0888	−	24.0888i	−0.812494	−	0.812494i
$880$		0			0
$881$	30.5938	−	30.5938i	1.03073	−	1.03073i	0.0312196	−	0.999513i	$-0.490061\pi$
$881$	30.5938	−	30.5938i	1.03073	−	1.03073i	0.999513	−	0.0312196i	$-0.00993912\pi$
$882$		0			0
$883$	24.8141	+	37.1370i	0.835062	+	1.24976i	0.966045	+	0.258374i	$0.0831865\pi$
$883$	24.8141	+	37.1370i	0.835062	+	1.24976i	−0.130983	+	0.991385i	$0.541813\pi$
$884$		0			0
$885$	−0.667800	−	3.35726i	−0.0224479	−	0.112853i
$886$		0			0
$887$	11.6990	+	4.84589i	0.392814	+	0.162709i	0.570343	−	0.821407i	$-0.306810\pi$
$887$	11.6990	+	4.84589i	0.392814	+	0.162709i	−0.177529	+	0.984116i	$0.556810\pi$
$888$		0			0
$889$	9.65997	−	4.00129i	0.323985	−	0.134199i
$890$		0			0
$891$	−18.0895	+	27.0729i	−0.606023	+	0.906977i
$892$		0			0
$893$	−29.7943	−	5.92645i	−0.997028	−	0.198321i
$894$		0			0
$895$	−1.75597			−0.0586956
$896$		0			0
$897$	80.2364			2.67902
$898$		0			0
$899$	−13.6722	−	2.71956i	−0.455993	−	0.0907026i
$900$		0			0
$901$	4.18537	−	6.26384i	0.139435	−	0.208679i
$902$		0			0
$903$	6.85375	−	2.83891i	0.228078	−	0.0944731i
$904$		0			0
$905$	1.60989	+	0.666840i	0.0535147	+	0.0221665i
$906$		0			0
$907$	10.1511	+	51.0331i	0.337062	+	1.69453i	0.662581	+	0.748990i	$0.269461\pi$
$907$	10.1511	+	51.0331i	0.337062	+	1.69453i	−0.325519	+	0.945536i	$0.605539\pi$
$908$		0			0
$909$	−0.395551	−	0.591984i	−0.0131196	−	0.0196349i
$910$		0			0
$911$	28.0572	−	28.0572i	0.929578	−	0.929578i	−0.0681006	−	0.997678i	$-0.521694\pi$
$911$	28.0572	−	28.0572i	0.929578	−	0.929578i	0.997678	+	0.0681006i	$0.0216939\pi$
$912$		0			0
$913$	−21.6804	−	21.6804i	−0.717516	−	0.717516i
$914$		0			0
$915$	5.42801	−	3.62688i	0.179445	−	0.119901i
$916$		0			0
$917$	2.17120	−	0.431879i	0.0716994	−	0.0142619i
$918$		0			0
$919$	−22.6448	+	54.6694i	−0.746984	+	1.80338i	−0.172219	+	0.985059i	$0.555094\pi$
$919$	−22.6448	+	54.6694i	−0.746984	+	1.80338i	−0.574764	+	0.818319i	$0.694906\pi$
$920$		0			0
$921$	16.5472	+	39.9484i	0.545248	+	1.31634i
$922$		0			0
$923$	14.9308	+	9.97645i	0.491454	+	0.328379i
$924$		0			0
$925$	5.02729	−	25.2739i	0.165296	−	0.831000i
$926$		0			0
$927$		−	2.80002i		−	0.0919648i
$928$		0			0
$929$			56.6874i			1.85985i	0.367744	+	0.929927i	$0.380130\pi$
$929$			56.6874i			1.85985i	−0.367744	+	0.929927i	$0.619870\pi$
$930$		0			0
$931$	7.53528	−	37.8824i	0.246959	−	1.24155i
$932$		0			0
$933$	−50.7896	−	33.9365i	−1.66278	−	1.11103i
$934$		0			0
$935$	1.42058	+	3.42959i	0.0464580	+	0.112160i
$936$		0			0
$937$	3.54560	−	8.55984i	0.115830	−	0.279638i	−0.855323	−	0.518095i	$-0.826642\pi$
$937$	3.54560	−	8.55984i	0.115830	−	0.279638i	0.971153	+	0.238457i	$0.0766415\pi$
$938$		0			0
$939$	−14.4892	+	2.88209i	−0.472839	+	0.0940535i
$940$		0			0
$941$	−25.5011	+	17.0393i	−0.831312	+	0.555465i	−0.896824	−	0.442387i	$-0.854132\pi$
$941$	−25.5011	+	17.0393i	−0.831312	+	0.555465i	0.0655122	+	0.997852i	$0.479132\pi$
$942$		0			0
$943$	−7.37739	−	7.37739i	−0.240241	−	0.240241i
$944$		0			0
$945$	−0.700504	+	0.700504i	−0.0227874	+	0.0227874i
$946$		0			0
$947$	−13.9505	−	20.8784i	−0.453331	−	0.678458i	0.532456	−	0.846458i	$-0.321269\pi$
$947$	−13.9505	−	20.8784i	−0.453331	−	0.678458i	−0.985787	+	0.168000i	$0.946269\pi$
$948$		0			0
$949$	2.83693	+	14.2622i	0.0920907	+	0.462971i
$950$		0			0
$951$	36.9674	+	15.3124i	1.19875	+	0.496539i
$952$		0			0
$953$	−20.3987	+	8.44942i	−0.660779	+	0.273704i	−0.687766	−	0.725932i	$-0.741409\pi$
$953$	−20.3987	+	8.44942i	−0.660779	+	0.273704i	0.0269874	+	0.999636i	$0.491409\pi$
$954$		0			0
$955$	−1.94464	+	2.91035i	−0.0629270	+	0.0941769i
$956$		0			0
$957$	−20.6655	−	4.11062i	−0.668021	−	0.132878i
$958$		0			0
$959$	20.9784			0.677427
$960$		0			0
$961$	15.6135			0.503661
$962$		0			0
$963$	12.8939	+	2.56476i	0.415501	+	0.0826482i
$964$		0			0
$965$	2.02755	−	3.03444i	0.0652692	−	0.0976822i
$966$		0			0
$967$	38.1280	−	15.7931i	1.22611	−	0.507873i	0.326766	−	0.945105i	$-0.394041\pi$
$967$	38.1280	−	15.7931i	1.22611	−	0.507873i	0.899349	+	0.437232i	$0.144041\pi$
$968$		0			0
$969$	−53.1121	−	21.9997i	−1.70621	−	0.706733i
$970$		0			0
$971$	−5.64453	−	28.3769i	−0.181141	−	0.910660i	−0.959256	−	0.282537i	$-0.908824\pi$
$971$	−5.64453	−	28.3769i	−0.181141	−	0.910660i	0.778115	−	0.628122i	$-0.216176\pi$
$972$		0			0
$973$	−5.00457	−	7.48987i	−0.160439	−	0.240114i
$974$		0			0
$975$	45.7313	−	45.7313i	1.46457	−	1.46457i
$976$		0			0
$977$	−33.6554	−	33.6554i	−1.07673	−	1.07673i	−0.996800	−	0.0799325i	$-0.974530\pi$
$977$	−33.6554	−	33.6554i	−1.07673	−	1.07673i	−0.0799325	−	0.996800i	$-0.525470\pi$
$978$		0			0
$979$	−24.8237	+	16.5866i	−0.793368	+	0.530111i
$980$		0			0
$981$	6.27502	−	1.24818i	0.200346	−	0.0398513i
$982$		0			0
$983$	−19.1346	+	46.1950i	−0.610299	+	1.47339i	0.252374	+	0.967630i	$0.418789\pi$
$983$	−19.1346	+	46.1950i	−0.610299	+	1.47339i	−0.862673	+	0.505762i	$0.831211\pi$
$984$		0			0
$985$	0.933500	+	2.25367i	0.0297438	+	0.0718078i
$986$		0			0
$987$	7.39782	+	4.94307i	0.235475	+	0.157340i
$988$		0			0
$989$	−4.81992	+	24.2314i	−0.153265	+	0.770514i
$990$		0			0
$991$		−	49.7101i		−	1.57909i	−0.613691	−	0.789547i	$-0.710316\pi$
$991$		−	49.7101i		−	1.57909i	0.613691	−	0.789547i	$-0.289684\pi$
$992$		0			0
$993$			21.4040i			0.679235i
$994$		0			0
$995$	0.0627525	−	0.315478i	0.00198939	−	0.0100013i
$996$		0			0
$997$	−42.0865	−	28.1213i	−1.33289	−	0.890611i	−0.334240	−	0.942488i	$-0.608479\pi$
$997$	−42.0865	−	28.1213i	−1.33289	−	0.890611i	−0.998653	+	0.0518774i	$0.983479\pi$
$998$		0			0
$999$	−7.88887	−	19.0454i	−0.249593	−	0.602571i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.i.b.161.1		56
4.3	odd	2		512.2.i.a.161.7		56
8.3	odd	2		256.2.i.a.209.1		56
8.5	even	2		64.2.i.a.29.3	✓	56
24.5	odd	2		576.2.bd.a.541.5		56
64.11	odd	16		512.2.i.a.353.7		56
64.21	even	16		64.2.i.a.53.3	yes	56
64.43	odd	16		256.2.i.a.49.1		56
64.53	even	16	inner	512.2.i.b.353.1		56
192.149	odd	16		576.2.bd.a.181.5		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.29.3	✓	56	8.5	even	2
64.2.i.a.53.3	yes	56	64.21	even	16
256.2.i.a.49.1		56	64.43	odd	16
256.2.i.a.209.1		56	8.3	odd	2
512.2.i.a.161.7		56	4.3	odd	2
512.2.i.a.353.7		56	64.11	odd	16
512.2.i.b.161.1		56	1.1	even	1	trivial
512.2.i.b.353.1		56	64.53	even	16	inner
576.2.bd.a.181.5		56	192.149	odd	16
576.2.bd.a.541.5		56	24.5	odd	2

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.i (of order \(16\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.97142 - 0.392140i) q^{3} +(0.153107 - 0.229142i) q^{5} +(-0.843108 + 0.349227i) q^{7} +(0.961093 + 0.398098i) q^{9} +O(q^{10})\)	\(q+(-1.97142 - 0.392140i) q^{3} +(0.153107 - 0.229142i) q^{5} +(-0.843108 + 0.349227i) q^{7} +(0.961093 + 0.398098i) q^{9} +(-0.575451 - 2.89299i) q^{11} +(3.63027 + 5.43308i) q^{13} +(-0.391695 + 0.391695i) q^{15} +(-3.22910 - 3.22910i) q^{17} +(-5.20741 + 3.47948i) q^{19} +(1.79907 - 0.357857i) q^{21} +(-2.33779 + 5.64392i) q^{23} +(1.88435 + 4.54923i) q^{25} +(3.27526 + 2.18846i) q^{27} +(-0.693313 + 3.48552i) q^{29} +3.92256i q^{31} +5.92895i q^{33} +(-0.0490638 + 0.246660i) q^{35} +(-4.35133 - 2.90747i) q^{37} +(-5.02627 - 12.1345i) q^{39} +(-0.653569 + 1.57786i) q^{41} +(3.96655 - 0.788996i) q^{43} +(0.238371 - 0.159275i) q^{45} +(3.42980 + 3.42980i) q^{47} +(-4.36088 + 4.36088i) q^{49} +(5.09966 + 7.63219i) q^{51} +(0.321835 + 1.61797i) q^{53} +(-0.751009 - 0.311078i) q^{55} +(11.6304 - 4.81749i) q^{57} +(-3.43310 + 5.13800i) q^{59} +(-11.5586 - 2.29915i) q^{61} -0.949332 q^{63} +1.80077 q^{65} +(-6.90108 - 1.37271i) q^{67} +(6.82198 - 10.2098i) q^{69} +(2.53894 - 1.05166i) q^{71} +(2.05602 + 0.851633i) q^{73} +(-1.93092 - 9.70739i) q^{75} +(1.49548 + 2.23814i) q^{77} +(4.21203 - 4.21203i) q^{79} +(-7.80551 - 7.80551i) q^{81} +(8.64283 - 5.77496i) q^{83} +(-1.23432 + 0.245522i) q^{85} +(2.73363 - 6.59956i) q^{87} +(-3.87335 - 9.35109i) q^{89} +(-4.95809 - 3.31289i) q^{91} +(1.53819 - 7.73303i) q^{93} +1.72597i q^{95} +1.83166i q^{97} +(0.598630 - 3.00951i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 8 q^{3} + 8 q^{5} - 8 q^{7} - 8 q^{9}+O(q^{10}) \) 56 * q + 8 * q^3 + 8 * q^5 - 8 * q^7 - 8 * q^9	\( 56 q + 8 q^{3} + 8 q^{5} - 8 q^{7} - 8 q^{9} + 8 q^{11} + 8 q^{13} - 8 q^{15} - 8 q^{17} + 8 q^{19} + 8 q^{21} - 8 q^{23} - 8 q^{25} + 8 q^{27} + 8 q^{29} + 8 q^{35} + 8 q^{37} - 8 q^{39} - 8 q^{41} + 8 q^{43} + 8 q^{45} - 8 q^{47} - 8 q^{49} - 24 q^{51} + 8 q^{53} + 56 q^{55} - 8 q^{57} - 56 q^{59} + 8 q^{61} + 64 q^{63} - 16 q^{65} - 72 q^{67} + 8 q^{69} + 56 q^{71} - 8 q^{73} - 56 q^{75} + 8 q^{77} + 24 q^{79} - 8 q^{81} + 8 q^{83} + 8 q^{85} - 8 q^{87} - 8 q^{89} + 8 q^{91} - 16 q^{93} - 16 q^{99}+O(q^{100}) \) 56 * q + 8 * q^3 + 8 * q^5 - 8 * q^7 - 8 * q^9 + 8 * q^11 + 8 * q^13 - 8 * q^15 - 8 * q^17 + 8 * q^19 + 8 * q^21 - 8 * q^23 - 8 * q^25 + 8 * q^27 + 8 * q^29 + 8 * q^35 + 8 * q^37 - 8 * q^39 - 8 * q^41 + 8 * q^43 + 8 * q^45 - 8 * q^47 - 8 * q^49 - 24 * q^51 + 8 * q^53 + 56 * q^55 - 8 * q^57 - 56 * q^59 + 8 * q^61 + 64 * q^63 - 16 * q^65 - 72 * q^67 + 8 * q^69 + 56 * q^71 - 8 * q^73 - 56 * q^75 + 8 * q^77 + 24 * q^79 - 8 * q^81 + 8 * q^83 + 8 * q^85 - 8 * q^87 - 8 * q^89 + 8 * q^91 - 16 * q^93 - 16 * q^99

Introduction

L-functions

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Groups

Database

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