LMFDB - Embedded newform 585.2.bs.b.334.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(289,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("585.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bs (of order $6$, degree $2$, 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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			334.3
Character	$\chi$	$=$	585.334
Dual form			585.2.bs.b.289.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.52669 - 0.881436i) q^{2} +(0.553860 + 0.959313i) q^{4} +(-1.52636 + 1.63408i) q^{5} +(-1.92736 + 1.11276i) q^{7} +1.57298i q^{8} +O(q^{10})$	\(q+(-1.52669 - 0.881436i) q^{2} +(0.553860 + 0.959313i) q^{4} +(-1.52636 + 1.63408i) q^{5} +(-1.92736 + 1.11276i) q^{7} +1.57298i q^{8} +(3.77062 - 1.14935i) q^{10} +(0.646605 - 1.11995i) q^{11} +(-2.90148 + 2.14043i) q^{13} +3.92332 q^{14} +(2.49420 - 4.32008i) q^{16} +(5.27558 - 3.04586i) q^{17} +(-2.01912 - 3.49721i) q^{19} +(-2.41299 - 0.559207i) q^{20} +(-1.97434 + 1.13988i) q^{22} +(-3.29833 - 1.90429i) q^{23} +(-0.340442 - 4.98840i) q^{25} +(6.31631 - 0.710304i) q^{26} +(-2.13497 - 1.23263i) q^{28} +(1.38868 - 2.40527i) q^{29} +10.4777 q^{31} +(-4.89127 + 2.82398i) q^{32} -10.7389 q^{34} +(1.12350 - 4.84794i) q^{35} +(-6.77724 - 3.91284i) q^{37} +7.11889i q^{38} +(-2.57037 - 2.40093i) q^{40} +(-2.01836 + 3.49590i) q^{41} +(9.27663 - 5.35587i) q^{43} +1.43252 q^{44} +(3.35702 + 5.81454i) q^{46} -1.00701i q^{47} +(-1.02352 + 1.77279i) q^{49} +(-3.87720 + 7.91583i) q^{50} +(-3.66035 - 1.59793i) q^{52} -2.34409i q^{53} +(0.843141 + 2.76606i) q^{55} +(-1.75035 - 3.03169i) q^{56} +(-4.24018 + 2.44807i) q^{58} +(-5.29490 - 9.17104i) q^{59} +(-2.84828 - 4.93336i) q^{61} +(-15.9962 - 9.23541i) q^{62} -0.0201689 q^{64} +(0.931075 - 8.00831i) q^{65} +(1.84572 + 1.06562i) q^{67} +(5.84386 + 3.37395i) q^{68} +(-5.98840 + 6.41101i) q^{70} +(3.02430 + 5.23824i) q^{71} -3.10052i q^{73} +(6.89784 + 11.9474i) q^{74} +(2.23662 - 3.87393i) q^{76} +2.87807i q^{77} -8.02561 q^{79} +(3.25231 + 10.6697i) q^{80} +(6.16282 - 3.55811i) q^{82} -10.9481i q^{83} +(-3.07526 + 13.2698i) q^{85} -18.8834 q^{86} +(1.76166 + 1.01709i) q^{88} +(0.387332 - 0.670879i) q^{89} +(3.21041 - 7.35403i) q^{91} -4.21884i q^{92} +(-0.887616 + 1.53740i) q^{94} +(8.79663 + 2.03861i) q^{95} +(7.94767 - 4.58859i) q^{97} +(3.12521 - 1.80434i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{4} - 4 q^{5}+O(q^{10}) $ 24 * q + 8 * q^4 - 4 * q^5	$ 24 q + 8 q^{4} - 4 q^{5} - 4 q^{10} - 4 q^{11} - 24 q^{14} + 16 q^{16} - 16 q^{19} + 16 q^{20} - 16 q^{25} + 48 q^{26} + 12 q^{29} + 8 q^{31} - 32 q^{34} - 10 q^{35} - 48 q^{40} + 40 q^{41} - 40 q^{44} - 24 q^{46} - 16 q^{49} - 20 q^{50} + 20 q^{55} + 24 q^{56} - 12 q^{59} + 20 q^{61} + 48 q^{64} - 14 q^{65} - 56 q^{70} - 4 q^{71} + 12 q^{74} + 8 q^{76} + 136 q^{79} + 4 q^{80} - 4 q^{85} - 48 q^{86} + 64 q^{89} + 60 q^{91} - 48 q^{94} + 28 q^{95}+O(q^{100}) $ 24 * q + 8 * q^4 - 4 * q^5 - 4 * q^10 - 4 * q^11 - 24 * q^14 + 16 * q^16 - 16 * q^19 + 16 * q^20 - 16 * q^25 + 48 * q^26 + 12 * q^29 + 8 * q^31 - 32 * q^34 - 10 * q^35 - 48 * q^40 + 40 * q^41 - 40 * q^44 - 24 * q^46 - 16 * q^49 - 20 * q^50 + 20 * q^55 + 24 * q^56 - 12 * q^59 + 20 * q^61 + 48 * q^64 - 14 * q^65 - 56 * q^70 - 4 * q^71 + 12 * q^74 + 8 * q^76 + 136 * q^79 + 4 * q^80 - 4 * q^85 - 48 * q^86 + 64 * q^89 + 60 * q^91 - 48 * q^94 + 28 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.52669	−	0.881436i	−1.07953	−	0.623270i	−0.148764	−	0.988873i	$-0.547529\pi$
$2$	−1.52669	−	0.881436i	−1.07953	−	0.623270i	−0.930771	+	0.365603i	$0.880863\pi$
$3$		0			0
$3$		0			0
$4$	0.553860	+	0.959313i	0.276930	+	0.479657i
$5$	−1.52636	+	1.63408i	−0.682610	+	0.730783i
$5$	−1.52636	+	1.63408i	−0.682610	+	0.730783i
$6$		0			0
$7$	−1.92736	+	1.11276i	−0.728474	+	0.420584i	−0.817864	−	0.575412i	$-0.804842\pi$
$7$	−1.92736	+	1.11276i	−0.728474	+	0.420584i	0.0893898	+	0.995997i	$0.471508\pi$
$8$			1.57298i			0.556131i
$9$		0			0
$10$	3.77062	−	1.14935i	1.19238	−	0.363456i
$11$	0.646605	−	1.11995i	0.194959	−	0.337679i	−0.751928	−	0.659245i	$-0.770876\pi$
$11$	0.646605	−	1.11995i	0.194959	−	0.337679i	0.946887	+	0.321566i	$0.104209\pi$
$12$		0			0
$13$	−2.90148	+	2.14043i	−0.804725	+	0.593647i
$13$	−2.90148	+	2.14043i	−0.804725	+	0.593647i
$14$	3.92332			1.04855
$15$		0			0
$16$	2.49420	−	4.32008i	0.623550	−	1.08002i
$17$	5.27558	−	3.04586i	1.27952	−	0.738728i	0.302756	−	0.953068i	$-0.402093\pi$
$17$	5.27558	−	3.04586i	1.27952	−	0.738728i	0.976759	+	0.214340i	$0.0687599\pi$
$18$		0			0
$19$	−2.01912	−	3.49721i	−0.463217	−	0.802316i	0.535902	−	0.844280i	$-0.319972\pi$
$19$	−2.01912	−	3.49721i	−0.463217	−	0.802316i	−0.999119	+	0.0419646i	$0.986638\pi$
$20$	−2.41299	−	0.559207i	−0.539560	−	0.125042i
$21$		0			0
$22$	−1.97434	+	1.13988i	−0.420930	+	0.243024i
$23$	−3.29833	−	1.90429i	−0.687750	−	0.397072i	0.115019	−	0.993363i	$-0.463307\pi$
$23$	−3.29833	−	1.90429i	−0.687750	−	0.397072i	−0.802768	+	0.596291i	$0.796640\pi$
$24$		0			0
$25$	−0.340442	−	4.98840i	−0.0680884	−	0.997679i
$26$	6.31631	−	0.710304i	1.23873	−	0.139302i
$27$		0			0
$28$	−2.13497	−	1.23263i	−0.403472	−	0.232945i
$29$	1.38868	−	2.40527i	0.257872	−	0.446647i	−0.707800	−	0.706413i	$-0.750312\pi$
$29$	1.38868	−	2.40527i	0.257872	−	0.446647i	0.965672	+	0.259766i	$0.0836455\pi$
$30$		0			0
$31$	10.4777			1.88185			0.940923	−	0.338620i	$-0.109960\pi$
$31$	10.4777			1.88185			0.940923	+	0.338620i	$0.109960\pi$
$32$	−4.89127	+	2.82398i	−0.864663	+	0.499213i
$33$		0			0
$34$	−10.7389			−1.84171
$35$	1.12350	−	4.84794i	0.189907	−	0.819451i
$36$		0			0
$37$	−6.77724	−	3.91284i	−1.11417	−	0.643267i	−0.174264	−	0.984699i	$-0.555755\pi$
$37$	−6.77724	−	3.91284i	−1.11417	−	0.643267i	−0.939906	+	0.341432i	$0.889088\pi$
$38$			7.11889i			1.15484i
$39$		0			0
$40$	−2.57037	−	2.40093i	−0.406411	−	0.379620i
$41$	−2.01836	+	3.49590i	−0.315214	+	0.545967i	−0.979483	−	0.201527i	$-0.935410\pi$
$41$	−2.01836	+	3.49590i	−0.315214	+	0.545967i	0.664269	+	0.747494i	$0.268743\pi$
$42$		0			0
$43$	9.27663	−	5.35587i	1.41467	−	0.816762i	0.418849	−	0.908056i	$-0.362434\pi$
$43$	9.27663	−	5.35587i	1.41467	−	0.816762i	0.995824	+	0.0912941i	$0.0291003\pi$
$44$	1.43252			0.215960
$45$		0			0
$46$	3.35702	+	5.81454i	0.494966	+	0.857307i
$47$		−	1.00701i		−	0.146888i	−0.997299	−	0.0734438i	$-0.976601\pi$
$47$		−	1.00701i		−	0.146888i	0.997299	−	0.0734438i	$-0.0233990\pi$
$48$		0			0
$49$	−1.02352	+	1.77279i	−0.146217	+	0.253256i
$50$	−3.87720	+	7.91583i	−0.548319	+	1.11947i
$51$		0			0
$52$	−3.66035	−	1.59793i	−0.507599	−	0.221593i
$53$		−	2.34409i		−	0.321986i	−0.986956	−	0.160993i	$-0.948530\pi$
$53$		−	2.34409i		−	0.321986i	0.986956	−	0.160993i	$-0.0514696\pi$
$54$		0			0
$55$	0.843141	+	2.76606i	0.113689	+	0.372975i
$56$	−1.75035	−	3.03169i	−0.233900	−	0.405127i
$57$		0			0
$58$	−4.24018	+	2.44807i	−0.556763	+	0.321447i
$59$	−5.29490	−	9.17104i	−0.689337	−	1.19397i	−0.972053	−	0.234763i	$-0.924568\pi$
$59$	−5.29490	−	9.17104i	−0.689337	−	1.19397i	0.282715	−	0.959204i	$-0.408765\pi$
$60$		0			0
$61$	−2.84828	−	4.93336i	−0.364685	−	0.631653i	0.624041	−	0.781392i	$-0.285490\pi$
$61$	−2.84828	−	4.93336i	−0.364685	−	0.631653i	−0.988726	+	0.149739i	$0.952157\pi$
$62$	−15.9962	−	9.23541i	−2.03152	−	1.17290i
$63$		0			0
$64$	−0.0201689			−0.00252111
$65$	0.931075	−	8.00831i	0.115486	−	0.993309i
$66$		0			0
$67$	1.84572	+	1.06562i	0.225490	+	0.130187i	0.608490	−	0.793562i	$-0.291776\pi$
$67$	1.84572	+	1.06562i	0.225490	+	0.130187i	−0.383000	+	0.923748i	$0.625109\pi$
$68$	5.84386	+	3.37395i	0.708672	+	0.409152i
$69$		0			0
$70$	−5.98840	+	6.41101i	−0.715750	+	0.766263i
$71$	3.02430	+	5.23824i	0.358918	+	0.621665i	0.987780	−	0.155852i	$-0.0498123\pi$
$71$	3.02430	+	5.23824i	0.358918	+	0.621665i	−0.628862	+	0.777517i	$0.716479\pi$
$72$		0			0
$73$		−	3.10052i		−	0.362889i	−0.983401	−	0.181444i	$-0.941923\pi$
$73$		−	3.10052i		−	0.362889i	0.983401	−	0.181444i	$-0.0580772\pi$
$74$	6.89784	+	11.9474i	0.801857	+	1.38886i
$75$		0			0
$76$	2.23662	−	3.87393i	0.256557	−	0.444370i
$77$			2.87807i			0.327987i
$78$		0			0
$79$	−8.02561			−0.902951			−0.451476	−	0.892283i	$-0.649102\pi$
$79$	−8.02561			−0.902951			−0.451476	+	0.892283i	$0.649102\pi$
$80$	3.25231	+	10.6697i	0.363619	+	1.19291i
$81$		0			0
$82$	6.16282	−	3.55811i	0.680570	−	0.392927i
$83$		−	10.9481i		−	1.20171i	−0.799358	−	0.600855i	$-0.794827\pi$
$83$		−	10.9481i		−	1.20171i	0.799358	−	0.600855i	$-0.205173\pi$
$84$		0			0
$85$	−3.07526	+	13.2698i	−0.333559	+	1.43931i
$86$	−18.8834			−2.03625
$87$		0			0
$88$	1.76166	+	1.01709i	0.187794	+	0.108423i
$89$	0.387332	−	0.670879i	0.0410571	−	0.0711130i	−0.844767	−	0.535135i	$-0.820261\pi$
$89$	0.387332	−	0.670879i	0.0410571	−	0.0711130i	0.885824	+	0.464022i	$0.153594\pi$
$90$		0			0
$91$	3.21041	−	7.35403i	0.336542	−	0.770911i
$92$		−	4.21884i		−	0.439845i
$93$		0			0
$94$	−0.887616	+	1.53740i	−0.0915506	+	0.158570i
$95$	8.79663	+	2.03861i	0.902515	+	0.209157i
$96$		0			0
$97$	7.94767	−	4.58859i	0.806963	−	0.465900i	−0.0389369	−	0.999242i	$-0.512397\pi$
$97$	7.94767	−	4.58859i	0.806963	−	0.465900i	0.845900	+	0.533341i	$0.179064\pi$
$98$	3.12521	−	1.80434i	0.315693	−	0.182266i
$99$		0			0
$100$	4.59688	−	3.08946i	0.459688	−	0.308946i
$101$	7.09306	−	12.2855i	0.705786	−	1.22246i	−0.260621	−	0.965441i	$-0.583927\pi$
$101$	7.09306	−	12.2855i	0.705786	−	1.22246i	0.966407	−	0.257016i	$-0.0827393\pi$
$102$		0			0
$103$			2.14122i			0.210980i	0.994420	+	0.105490i	$0.0336412\pi$
$103$			2.14122i			0.210980i	−0.994420	+	0.105490i	$0.966359\pi$
$104$	−3.36684	−	4.56396i	−0.330146	−	0.447533i
$105$		0			0
$106$	−2.06617	+	3.57871i	−0.200684	+	0.347595i
$107$	−9.42495	−	5.44150i	−0.911144	−	0.526049i	−0.0303452	−	0.999539i	$-0.509661\pi$
$107$	−9.42495	−	5.44150i	−0.911144	−	0.526049i	−0.880799	+	0.473490i	$0.842994\pi$
$108$		0			0
$109$	4.09384			0.392119			0.196059	−	0.980592i	$-0.437185\pi$
$109$	4.09384			0.392119			0.196059	+	0.980592i	$0.437185\pi$
$110$	1.15089	−	4.96610i	0.109733	−	0.473499i
$111$		0			0
$112$			11.1018i			1.04902i
$113$	1.11573	−	0.644166i	0.104959	−	0.0605980i	−0.446602	−	0.894733i	$-0.647366\pi$
$113$	1.11573	−	0.644166i	0.104959	−	0.0605980i	0.551561	+	0.834135i	$0.314033\pi$
$114$		0			0
$115$	8.14621	−	2.48310i	0.759638	−	0.231550i
$116$	3.07654			0.285649
$117$		0			0
$118$			18.6685i			1.71857i
$119$	−6.77862	+	11.7409i	−0.621395	+	1.07629i
$120$		0			0
$121$	4.66380	+	8.07794i	0.423982	+	0.734359i
$122$			10.0423i			0.909188i
$123$		0			0
$124$	5.80316	+	10.0514i	0.521140	+	0.902640i
$125$	8.67108	+	7.05779i	0.775565	+	0.631268i
$126$		0			0
$127$	−5.67987	−	3.27927i	−0.504007	−	0.290989i	0.226360	−	0.974044i	$-0.427317\pi$
$127$	−5.67987	−	3.27927i	−0.504007	−	0.290989i	−0.730367	+	0.683055i	$0.760651\pi$
$128$	9.81334	+	5.66573i	0.867385	+	0.500785i
$129$		0			0
$130$	−8.48028	+	11.4055i	−0.743770	+	1.00033i
$131$	13.5124			1.18058			0.590290	−	0.807191i	$-0.299013\pi$
$131$	13.5124			1.18058			0.590290	+	0.807191i	$0.299013\pi$
$132$		0			0
$133$	7.78313	+	4.49359i	0.674883	+	0.389644i
$134$	−1.87856	−	3.25376i	−0.162283	−	0.281082i
$135$		0			0
$136$	4.79106	+	8.29836i	0.410830	+	0.711578i
$137$	−18.5216	+	10.6935i	−1.58241	+	0.913604i	−0.587902	+	0.808932i	$0.700046\pi$
$137$	−18.5216	+	10.6935i	−1.58241	+	0.913604i	−0.994507	+	0.104672i	$0.966621\pi$
$138$		0			0
$139$	5.74807	+	9.95595i	0.487545	+	0.844453i	0.999897	−	0.0143224i	$-0.00455911\pi$
$139$	5.74807	+	9.95595i	0.487545	+	0.844453i	−0.512352	+	0.858775i	$0.671226\pi$
$140$	5.27296	−	1.60729i	0.445646	−	0.135840i
$141$		0			0
$142$		−	10.6629i		−	0.894811i
$143$	0.521066	+	4.63353i	0.0435737	+	0.387475i
$144$		0			0
$145$	1.81077	+	5.94052i	0.150376	+	0.493334i
$146$	−2.73291	+	4.73354i	−0.226177	+	0.391751i
$147$		0			0
$148$		−	8.66866i		−	0.712559i
$149$	7.23346	+	12.5287i	0.592588	+	1.02639i	0.993882	+	0.110443i	$0.0352270\pi$
$149$	7.23346	+	12.5287i	0.592588	+	1.02639i	−0.401295	+	0.915949i	$0.631440\pi$
$150$		0			0
$151$	5.73707			0.466876			0.233438	−	0.972372i	$-0.425002\pi$
$151$	5.73707			0.466876			0.233438	+	0.972372i	$0.425002\pi$
$152$	5.50103	−	3.17602i	0.446193	−	0.257609i
$153$		0			0
$154$	2.53684	−	4.39393i	0.204424	−	0.354073i
$155$	−15.9927	+	17.1214i	−1.28457	+	1.37522i
$156$		0			0
$157$		−	5.55155i		−	0.443062i	−0.975153	−	0.221531i	$-0.928895\pi$
$157$		−	5.55155i		−	0.443062i	0.975153	−	0.221531i	$-0.0711054\pi$
$158$	12.2526	+	7.07406i	0.974767	+	0.562782i
$159$		0			0
$160$	2.85124	−	12.3031i	0.225410	−	0.972649i
$161$	8.47610			0.668010
$162$		0			0
$163$	15.0970	−	8.71628i	1.18249	−	0.682712i	0.225902	−	0.974150i	$-0.427467\pi$
$163$	15.0970	−	8.71628i	1.18249	−	0.682712i	0.956590	+	0.291439i	$0.0941339\pi$
$164$	−4.47155			−0.349169
$165$		0			0
$166$	−9.65005	+	16.7144i	−0.748989	+	1.29729i
$167$	−0.166478	−	0.0961162i	−0.0128825	−	0.00743769i	0.493545	−	0.869720i	$-0.335701\pi$
$167$	−0.166478	−	0.0961162i	−0.0128825	−	0.00743769i	−0.506427	+	0.862283i	$0.669034\pi$
$168$		0			0
$169$	3.83715	−	12.4208i	0.295166	−	0.955446i
$170$	16.3915	−	17.5483i	1.25717	−	1.34589i
$171$		0			0
$172$	10.2759	+	5.93280i	0.783531	+	0.452372i
$173$	5.18483	−	2.99346i	0.394195	−	0.227589i	−0.289781	−	0.957093i	$-0.593582\pi$
$173$	5.18483	−	2.99346i	0.394195	−	0.227589i	0.683976	+	0.729504i	$0.260249\pi$
$174$		0			0
$175$	6.20705	+	9.23561i	0.469209	+	0.698146i
$176$	−3.22552	−	5.58677i	−0.243133	−	0.421119i
$177$		0			0
$178$	−1.18267	+	0.682817i	−0.0886451	+	0.0511793i
$179$	5.20141	−	9.00910i	0.388771	−	0.673372i	−0.603513	−	0.797353i	$-0.706233\pi$
$179$	5.20141	−	9.00910i	0.388771	−	0.673372i	0.992285	+	0.123981i	$0.0395662\pi$
$180$		0			0
$181$	−25.5027			−1.89560			−0.947800	−	0.318866i	$-0.896698\pi$
$181$	−25.5027			−1.89560			−0.947800	+	0.318866i	$0.896698\pi$
$182$	−11.3834	+	8.39757i	−0.843795	+	0.622469i
$183$		0			0
$184$	2.99541	−	5.18820i	0.220824	−	0.382479i
$185$	16.7384	−	5.10215i	1.23063	−	0.375117i
$186$		0			0
$187$		−	7.87787i		−	0.576087i
$188$	0.966039	−	0.557743i	0.0704556	−	0.0406776i
$189$		0			0
$190$	−11.6328	−	10.8660i	−0.843935	−	0.788302i
$191$	9.79617	+	16.9675i	0.708826	+	1.22772i	0.965293	+	0.261170i	$0.0841082\pi$
$191$	9.79617	+	16.9675i	0.708826	+	1.22772i	−0.256467	+	0.966553i	$0.582558\pi$
$192$		0			0
$193$	−17.8654	−	10.3146i	−1.28598	−	0.742462i	−0.308047	−	0.951371i	$-0.599675\pi$
$193$	−17.8654	−	10.3146i	−1.28598	−	0.742462i	−0.977935	+	0.208909i	$0.933009\pi$
$194$	−16.1782			−1.16153
$195$		0			0
$196$	−2.26755			−0.161968
$197$	1.65391	+	0.954884i	0.117836	+	0.0680327i	0.557760	−	0.830003i	$-0.311661\pi$
$197$	1.65391	+	0.954884i	0.117836	+	0.0680327i	−0.439924	+	0.898035i	$0.644994\pi$
$198$		0			0
$199$	−3.07298	−	5.32255i	−0.217838	−	0.377306i	0.736309	−	0.676645i	$-0.236567\pi$
$199$	−3.07298	−	5.32255i	−0.217838	−	0.377306i	−0.954147	+	0.299340i	$0.903234\pi$
$200$	7.84663	−	0.535507i	0.554841	−	0.0378661i
$201$		0			0
$202$	−21.6578	+	12.5042i	−1.52384	+	0.879790i
$203$			6.18109i			0.433827i
$204$		0			0
$205$	−2.63184	−	8.63416i	−0.183815	−	0.603036i
$206$	1.88735	−	3.26898i	0.131498	−	0.227761i
$207$		0			0
$208$	2.00995	+	17.8733i	0.139365	+	1.23929i
$209$	−5.22229			−0.361233
$210$		0			0
$211$	9.09116	−	15.7463i	0.625861	−	1.08402i	−0.362513	−	0.931979i	$-0.618081\pi$
$211$	9.09116	−	15.7463i	0.625861	−	1.08402i	0.988374	−	0.152044i	$-0.0485857\pi$
$212$	2.24872	−	1.29830i	0.154443	−	0.0891675i
$213$		0			0
$214$	9.59267	+	16.6150i	0.655741	+	1.13578i
$215$	−5.40757	+	23.3338i	−0.368793	+	1.59135i
$216$		0			0
$217$	−20.1943	+	11.6592i	−1.37088	+	0.791475i
$218$	−6.25004	−	3.60846i	−0.423306	−	0.244396i
$219$		0			0
$220$	−2.18654	+	2.34085i	−0.147416	+	0.157820i
$221$	−8.78754	+	20.1295i	−0.591114	+	1.35405i
$222$		0			0
$223$	0.0435655	+	0.0251526i	0.00291736	+	0.00168434i	0.501458	−	0.865182i	$-0.332797\pi$
$223$	0.0435655	+	0.0251526i	0.00291736	+	0.00168434i	−0.498541	+	0.866866i	$0.666131\pi$
$224$	6.28483	−	10.8856i	0.419923	−	0.727328i
$225$		0			0
$226$	−2.27116			−0.151076
$227$	12.4948	−	7.21390i	0.829312	−	0.478804i	−0.0243048	−	0.999705i	$-0.507737\pi$
$227$	12.4948	−	7.21390i	0.829312	−	0.478804i	0.853617	+	0.520901i	$0.174404\pi$
$228$		0			0
$229$	−16.7880			−1.10938			−0.554691	−	0.832057i	$-0.687163\pi$
$229$	−16.7880			−1.10938			−0.554691	+	0.832057i	$0.687163\pi$
$230$	−14.6255	−	3.38943i	−0.964374	−	0.223493i
$231$		0			0
$232$	3.78343	+	2.18436i	0.248394	+	0.143410i
$233$		−	19.1033i		−	1.25150i	−0.780025	−	0.625748i	$-0.784794\pi$
$233$		−	19.1033i		−	1.25150i	0.780025	−	0.625748i	$-0.215206\pi$
$234$		0			0
$235$	1.64554	+	1.53706i	0.107343	+	0.100267i
$236$	5.86527	−	10.1589i	0.381796	−	0.661291i
$237$		0			0
$238$	20.6977	−	11.9499i	1.34164	−	0.774594i
$239$	−20.5189			−1.32725			−0.663627	−	0.748063i	$-0.730984\pi$
$239$	−20.5189			−1.32725			−0.663627	+	0.748063i	$0.730984\pi$
$240$		0			0
$241$	−8.68280	−	15.0390i	−0.559308	−	0.968750i	−0.997554	−	0.0698951i	$-0.977734\pi$
$241$	−8.68280	−	15.0390i	−0.559308	−	0.968750i	0.438246	−	0.898855i	$-0.355600\pi$
$242$		−	16.4434i		−	1.05702i
$243$		0			0
$244$	3.15510	−	5.46479i	0.201984	−	0.349847i
$245$	−1.33462	−	4.37844i	−0.0852658	−	0.279728i
$246$		0			0
$247$	13.3439	+	5.82532i	0.849055	+	0.370656i
$248$			16.4811i			1.04655i
$249$		0			0
$250$	−7.01709	−	18.4181i	−0.443800	−	1.16486i
$251$	2.80444	+	4.85744i	0.177015	+	0.306599i	0.940857	−	0.338805i	$-0.110023\pi$
$251$	2.80444	+	4.85744i	0.177015	+	0.306599i	−0.763842	+	0.645403i	$0.776689\pi$
$252$		0			0
$253$	−4.26544	+	2.46265i	−0.268166	+	0.154826i
$254$	5.78094	+	10.0129i	0.362729	+	0.628264i
$255$		0			0
$256$	−9.96779	−	17.2647i	−0.622987	−	1.07905i
$257$	−8.45618	−	4.88218i	−0.527482	−	0.304542i	0.212508	−	0.977159i	$-0.431837\pi$
$257$	−8.45618	−	4.88218i	−0.527482	−	0.304542i	−0.739991	+	0.672617i	$0.765170\pi$
$258$		0			0
$259$	17.4162			1.08219
$260$	8.19817	−	3.54229i	0.508429	−	0.219684i
$261$		0			0
$262$	−20.6292	−	11.9103i	−1.27448	−	0.735820i
$263$	0.610495	+	0.352470i	0.0376447	+	0.0217342i	0.518704	−	0.854954i	$-0.326415\pi$
$263$	0.610495	+	0.352470i	0.0376447	+	0.0217342i	−0.481060	+	0.876688i	$0.659748\pi$
$264$		0			0
$265$	3.83044	+	3.57793i	0.235302	+	0.219791i
$266$	−7.92163	−	13.7207i	−0.485706	−	0.841268i
$267$		0			0
$268$			2.36083i			0.144210i
$269$	−15.1995	−	26.3263i	−0.926729	−	1.60514i	−0.788756	−	0.614706i	$-0.789275\pi$
$269$	−15.1995	−	26.3263i	−0.926729	−	1.60514i	−0.137973	−	0.990436i	$-0.544059\pi$
$270$		0			0
$271$	−9.52279	+	16.4940i	−0.578468	+	1.00194i	0.417187	+	0.908821i	$0.363016\pi$
$271$	−9.52279	+	16.4940i	−0.578468	+	1.00194i	−0.995655	+	0.0931159i	$0.970317\pi$
$272$		−	30.3879i		−	1.84254i
$273$		0			0
$274$	37.7024			2.27769
$275$	−5.80690	−	2.84424i	−0.350169	−	0.171514i
$276$		0			0
$277$	−10.1366	+	5.85235i	−0.609047	+	0.351634i	−0.772593	−	0.634902i	$-0.781040\pi$
$277$	−10.1366	+	5.85235i	−0.609047	+	0.351634i	0.163545	+	0.986536i	$0.447707\pi$
$278$		−	20.2662i		−	1.21549i
$279$		0			0
$280$	7.62569	+	1.76725i	0.455722	+	0.105613i
$281$	−29.4311			−1.75571			−0.877855	−	0.478926i	$-0.841026\pi$
$281$	−29.4311			−1.75571			−0.877855	+	0.478926i	$0.841026\pi$
$282$		0			0
$283$	−15.6024	−	9.00803i	−0.927465	−	0.535472i	−0.0414558	−	0.999140i	$-0.513200\pi$
$283$	−15.6024	−	9.00803i	−0.927465	−	0.535472i	−0.886009	+	0.463668i	$0.846533\pi$
$284$	−3.35008	+	5.80250i	−0.198790	+	0.344315i
$285$		0			0
$286$	3.28866	−	7.53326i	0.194462	−	0.445451i
$287$		−	8.98380i		−	0.530297i
$288$		0			0
$289$	10.0545	−	17.4149i	0.591440	−	1.02440i
$290$	2.47170	−	10.6654i	0.145143	−	0.626296i
$291$		0			0
$292$	2.97437	−	1.71725i	0.174062	−	0.100495i
$293$	−17.5440	+	10.1291i	−1.02493	+	0.591746i	−0.915529	−	0.402251i	$-0.868228\pi$
$293$	−17.5440	+	10.1291i	−1.02493	+	0.591746i	−0.109405	+	0.993997i	$0.534894\pi$
$294$		0			0
$295$	23.0682	+	5.34602i	1.34308	+	0.311257i
$296$	6.15480	−	10.6604i	0.357741	−	0.619625i
$297$		0			0
$298$		−	25.5033i		−	1.47737i
$299$	13.6460	−	1.53457i	0.789170	−	0.0887465i
$300$		0			0
$301$	−11.9196	+	20.6454i	−0.687035	+	1.18998i
$302$	−8.75874	−	5.05686i	−0.504009	−	0.290989i
$303$		0			0
$304$	−20.1443			−1.15536
$305$	12.4090	+	2.87578i	0.710538	+	0.164667i
$306$		0			0
$307$		−	19.0505i		−	1.08727i	−0.839321	−	0.543636i	$-0.817047\pi$
$307$		−	19.0505i		−	1.08727i	0.839321	−	0.543636i	$-0.182953\pi$
$308$	−2.76097	+	1.59405i	−0.157321	+	0.0908293i
$309$		0			0
$310$	39.5074	−	12.0425i	2.24387	−	0.683968i
$311$	−7.41122			−0.420252			−0.210126	−	0.977674i	$-0.567387\pi$
$311$	−7.41122			−0.420252			−0.210126	+	0.977674i	$0.567387\pi$
$312$		0			0
$313$			27.0945i			1.53147i	0.643156	+	0.765735i	$0.277625\pi$
$313$			27.0945i			1.53147i	−0.643156	+	0.765735i	$0.722375\pi$
$314$	−4.89334	+	8.47551i	−0.276147	+	0.478301i
$315$		0			0
$316$	−4.44506	−	7.69907i	−0.250054	−	0.433107i
$317$			16.8955i			0.948946i	0.880270	+	0.474473i	$0.157361\pi$
$317$			16.8955i			0.948946i	−0.880270	+	0.474473i	$0.842639\pi$
$318$		0			0
$319$	−1.79586	−	3.11052i	−0.100549	−	0.174155i
$320$	0.0307850	−	0.0329576i	0.00172093	−	0.00184238i
$321$		0			0
$322$	−12.9404	−	7.47114i	−0.721140	−	0.416350i
$323$	−21.3040	−	12.2999i	−1.18539	−	0.684383i
$324$		0			0
$325$	11.6651	+	13.7450i	0.647062	+	0.762437i
$326$	−30.7314			−1.70205
$327$		0			0
$328$	−5.49896	−	3.17483i	−0.303629	−	0.175301i
$329$	1.12056	+	1.94087i	0.0617786	+	0.107004i
$330$		0			0
$331$	5.46570	+	9.46687i	0.300422	+	0.520346i	0.976232	−	0.216730i	$-0.0695391\pi$
$331$	5.46570	+	9.46687i	0.300422	+	0.520346i	−0.675809	+	0.737076i	$0.736206\pi$
$332$	10.5027	−	6.06371i	0.576408	−	0.332789i
$333$		0			0
$334$	0.169441	+	0.293480i	0.00927138	+	0.0160585i
$335$	−4.55855	+	1.38952i	−0.249060	+	0.0759177i
$336$		0			0
$337$			18.2778i			0.995656i	0.867276	+	0.497828i	$0.165869\pi$
$337$			18.2778i			0.995656i	−0.867276	+	0.497828i	$0.834131\pi$
$338$	−16.8063	+	15.5805i	−0.914142	+	0.847469i
$339$		0			0
$340$	−14.4332	+	4.39947i	−0.782748	+	0.238595i
$341$	6.77492	−	11.7345i	0.366883	−	0.635459i
$342$		0			0
$343$		−	20.1344i		−	1.08716i
$344$	8.42465	+	14.5919i	0.454227	+	0.786744i
$345$		0			0
$346$	−10.5542			−0.567397
$347$	3.82951	−	2.21097i	0.205579	−	0.118691i	−0.393676	−	0.919249i	$-0.628797\pi$
$347$	3.82951	−	2.21097i	0.205579	−	0.118691i	0.599255	+	0.800558i	$0.295464\pi$
$348$		0			0
$349$	12.5520	−	21.7407i	0.671893	−	1.16375i	−0.305474	−	0.952200i	$-0.598815\pi$
$349$	12.5520	−	21.7407i	0.671893	−	1.16375i	0.977367	−	0.211552i	$-0.0678518\pi$
$350$	−1.33566	−	19.5711i	−0.0713941	−	1.04612i
$351$		0			0
$352$			7.30400i			0.389304i
$353$	−1.00623	−	0.580945i	−0.0535561	−	0.0309206i	0.472983	−	0.881072i	$-0.343177\pi$
$353$	−1.00623	−	0.580945i	−0.0535561	−	0.0309206i	−0.526539	+	0.850151i	$0.676511\pi$
$354$		0			0
$355$	−13.1759	−	3.05350i	−0.699303	−	0.162063i
$356$	0.858111			0.0454798
$357$		0			0
$358$	−15.8819	+	9.16942i	−0.839385	+	0.484619i
$359$	7.51441			0.396595			0.198298	−	0.980142i	$-0.436459\pi$
$359$	7.51441			0.396595			0.198298	+	0.980142i	$0.436459\pi$
$360$		0			0
$361$	1.34634	−	2.33192i	0.0708598	−	0.122733i
$362$	38.9348	+	22.4790i	2.04637	+	1.18147i
$363$		0			0
$364$	8.83293	−	0.993311i	0.462972	−	0.0520637i
$365$	5.06650	+	4.73252i	0.265193	+	0.247711i
$366$		0			0
$367$	30.1312	+	17.3962i	1.57283	+	0.908076i	0.995820	+	0.0913414i	$0.0291154\pi$
$367$	30.1312	+	17.3962i	1.57283	+	0.908076i	0.577014	+	0.816734i	$0.304218\pi$
$368$	−16.4534	+	9.49937i	−0.857692	+	0.495189i
$369$		0			0
$370$	−30.0516	−	6.96443i	−1.56231	−	0.362064i
$371$	2.60842	+	4.51791i	0.135422	+	0.234558i
$372$		0			0
$373$	9.47953	−	5.47301i	0.490831	−	0.283382i	−0.234088	−	0.972215i	$-0.575210\pi$
$373$	9.47953	−	5.47301i	0.490831	−	0.283382i	0.724919	+	0.688834i	$0.241877\pi$
$374$	−6.94384	+	12.0271i	−0.359057	+	0.621905i
$375$		0			0
$376$	1.58400			0.0816888
$377$	1.11907	+	9.95120i	0.0576348	+	0.512513i
$378$		0			0
$379$	−10.4567	+	18.1116i	−0.537126	+	0.930330i	0.461931	+	0.886916i	$0.347157\pi$
$379$	−10.4567	+	18.1116i	−0.537126	+	0.930330i	−0.999057	+	0.0434141i	$0.986177\pi$
$380$	2.91643	+	9.56783i	0.149610	+	0.490819i
$381$		0			0
$382$		−	34.5388i		−	1.76716i
$383$	25.6423	−	14.8046i	1.31026	−	0.756479i	0.328122	−	0.944636i	$-0.393584\pi$
$383$	25.6423	−	14.8046i	1.31026	−	0.756479i	0.982139	+	0.188156i	$0.0602511\pi$
$384$		0			0
$385$	−4.70300	−	4.39298i	−0.239687	−	0.223887i
$386$	18.1833	+	31.4945i	0.925508	+	1.60303i
$387$		0			0
$388$	8.80379	+	5.08287i	0.446945	+	0.258044i
$389$	21.0201			1.06576			0.532881	−	0.846190i	$-0.321109\pi$
$389$	21.0201			1.06576			0.532881	+	0.846190i	$0.321109\pi$
$390$		0			0
$391$	−23.2008			−1.17331
$392$	−2.78856	−	1.60998i	−0.140844	−	0.0813160i
$393$		0			0
$394$	−1.68334	−	2.91563i	−0.0848054	−	0.146887i
$395$	12.2500	−	13.1145i	0.616363	−	0.659862i
$396$		0			0
$397$	−10.9330	+	6.31218i	−0.548712	+	0.316799i	−0.748602	−	0.663019i	$-0.769275\pi$
$397$	−10.9330	+	6.31218i	−0.548712	+	0.316799i	0.199890	+	0.979818i	$0.435941\pi$
$398$			10.8345i			0.543086i
$399$		0			0
$400$	−22.3994	−	10.9713i	−1.11997	−	0.548566i
$401$	5.05705	−	8.75906i	0.252537	−	0.437407i	−0.711687	−	0.702497i	$-0.752068\pi$
$401$	5.05705	−	8.75906i	0.252537	−	0.437407i	0.964224	+	0.265090i	$0.0854017\pi$
$402$		0			0
$403$	−30.4008	+	22.4267i	−1.51437	+	1.11715i
$404$	15.7142			0.781813
$405$		0			0
$406$	5.44823	−	9.43662i	0.270391	−	0.468331i
$407$	−8.76440	+	5.06013i	−0.434435	+	0.250821i
$408$		0			0
$409$	−10.0793	−	17.4579i	−0.498389	−	0.863235i	0.501609	−	0.865094i	$-0.332742\pi$
$409$	−10.0793	−	17.4579i	−0.498389	−	0.863235i	−0.999998	+	0.00185917i	$0.999408\pi$
$410$	−3.59246	+	15.5015i	−0.177419	+	0.765565i
$411$		0			0
$412$	−2.05410	+	1.18593i	−0.101198	+	0.0584268i
$413$	20.4104	+	11.7839i	1.00433	+	0.579849i
$414$		0			0
$415$	17.8901	+	16.7107i	0.878189	+	0.820298i
$416$	8.14741	−	18.6631i	0.399459	−	0.915034i
$417$		0			0
$418$	7.97283	+	4.60311i	0.389964	+	0.225146i
$419$	9.74536	−	16.8795i	0.476092	−	0.824615i	−0.523533	−	0.852005i	$-0.675386\pi$
$419$	9.74536	−	16.8795i	0.476092	−	0.824615i	0.999625	+	0.0273900i	$0.00871961\pi$
$420$		0			0
$421$	−6.94471			−0.338464			−0.169232	−	0.985576i	$-0.554129\pi$
$421$	−6.94471			−0.338464			−0.169232	+	0.985576i	$0.554129\pi$
$422$	−27.7588	+	16.0266i	−1.35128	+	0.780160i
$423$		0			0
$424$	3.68720			0.179066
$425$	−16.9900	−	25.2797i	−0.824134	−	1.22625i
$426$		0			0
$427$	10.9793	+	6.33891i	0.531327	+	0.306762i
$428$		−	12.0553i		−	0.582715i
$429$		0			0
$430$	28.8229	−	30.8570i	1.38996	−	1.48806i
$431$	6.09917	−	10.5641i	0.293787	−	0.508854i	−0.680915	−	0.732362i	$-0.738418\pi$
$431$	6.09917	−	10.5641i	0.293787	−	0.508854i	0.974702	+	0.223509i	$0.0717511\pi$
$432$		0			0
$433$	−16.3475	+	9.43824i	−0.785611	+	0.453573i	−0.838415	−	0.545032i	$-0.816517\pi$
$433$	−16.3475	+	9.43824i	−0.785611	+	0.453573i	0.0528040	+	0.998605i	$0.483184\pi$
$434$	41.1072			1.97321
$435$		0			0
$436$	2.26741	+	3.92728i	0.108589	+	0.188082i
$437$			15.3800i			0.735723i
$438$		0			0
$439$	−14.2622	+	24.7028i	−0.680697	+	1.17900i	0.294072	+	0.955783i	$0.404990\pi$
$439$	−14.2622	+	24.7028i	−0.680697	+	1.17900i	−0.974769	+	0.223218i	$0.928344\pi$
$440$	−4.35095	+	1.32624i	−0.207423	+	0.0632261i
$441$		0			0
$442$	31.1587	−	22.9858i	1.48207	−	1.09333i
$443$			22.8334i			1.08485i	0.840105	+	0.542425i	$0.182494\pi$
$443$			22.8334i			1.08485i	−0.840105	+	0.542425i	$0.817506\pi$
$444$		0			0
$445$	0.505062	+	1.65694i	0.0239422	+	0.0785463i
$446$	−0.0443408	−	0.0768005i	−0.00209960	−	0.00363661i
$447$		0			0
$448$	0.0388727	−	0.0224431i	0.00183656	−	0.00106034i
$449$	−5.76109	−	9.97850i	−0.271883	−	0.470914i	0.697461	−	0.716622i	$-0.254313\pi$
$449$	−5.76109	−	9.97850i	−0.271883	−	0.470914i	−0.969344	+	0.245708i	$0.920980\pi$
$450$		0			0
$451$	2.61016	+	4.52093i	0.122908	+	0.212882i
$452$	1.23591	+	0.713555i	0.0581325	+	0.0335628i
$453$		0			0
$454$	−25.4344			−1.19370
$455$	7.11683	+	16.4710i	0.333642	+	0.772171i
$456$		0			0
$457$	21.7263	+	12.5437i	1.01631	+	0.586768i	0.913034	−	0.407884i	$-0.133733\pi$
$457$	21.7263	+	12.5437i	1.01631	+	0.586768i	0.103279	+	0.994652i	$0.467067\pi$
$458$	25.6301	+	14.7975i	1.19762	+	0.691444i
$459$		0			0
$460$	6.89393	+	6.43948i	0.321431	+	0.300242i
$461$	−8.11294	−	14.0520i	−0.377857	−	0.654468i	0.612893	−	0.790166i	$-0.290006\pi$
$461$	−8.11294	−	14.0520i	−0.377857	−	0.654468i	−0.990750	+	0.135698i	$0.956672\pi$
$462$		0			0
$463$		−	19.6809i		−	0.914649i	−0.889300	−	0.457325i	$-0.848808\pi$
$463$		−	19.6809i		−	0.914649i	0.889300	−	0.457325i	$-0.151192\pi$
$464$	−6.92729	−	11.9984i	−0.321591	−	0.557013i
$465$		0			0
$466$	−16.8383	+	29.1648i	−0.780020	+	1.35103i
$467$			28.7884i			1.33217i	0.745877	+	0.666084i	$0.232031\pi$
$467$			28.7884i			1.33217i	−0.745877	+	0.666084i	$0.767969\pi$
$468$		0			0
$469$	−4.74315			−0.219018
$470$	−1.15741	−	3.79706i	−0.0533872	−	0.175145i
$471$		0			0
$472$	14.4258	−	8.32875i	0.664002	−	0.383362i
$473$		−	13.8525i		−	0.636940i
$474$		0			0
$475$	−16.7581	+	11.2628i	−0.768914	+	0.516770i
$476$	−15.0176			−0.688332
$477$		0			0
$478$	31.3260	+	18.0861i	1.43282	+	0.827237i
$479$	9.41008	−	16.2987i	0.429957	−	0.744708i	−0.566912	−	0.823779i	$-0.691862\pi$
$479$	9.41008	−	16.2987i	0.429957	−	0.744708i	0.996869	+	0.0790705i	$0.0251952\pi$
$480$		0			0
$481$	28.0392	−	3.15316i	1.27848	−	0.143771i
$482$			30.6133i			1.39440i
$483$		0			0
$484$	−5.16619	+	8.94810i	−0.234827	+	0.406732i
$485$	−4.63289	+	19.9910i	−0.210369	+	0.907743i
$486$		0			0
$487$	−3.02050	+	1.74388i	−0.136872	+	0.0790229i	−0.566872	−	0.823806i	$-0.691847\pi$
$487$	−3.02050	+	1.74388i	−0.136872	+	0.0790229i	0.430001	+	0.902829i	$0.358513\pi$
$488$	7.76007	−	4.48028i	0.351282	−	0.202813i
$489$		0			0
$490$	−1.82176	+	7.86091i	−0.0822986	+	0.355120i
$491$	−14.4283	+	24.9906i	−0.651142	+	1.12781i	0.331704	+	0.943384i	$0.392377\pi$
$491$	−14.4283	+	24.9906i	−0.651142	+	1.12781i	−0.982846	+	0.184428i	$0.940957\pi$
$492$		0			0
$493$		−	16.9189i		−	0.761988i
$494$	−15.2375	−	20.6553i	−0.685566	−	0.929326i
$495$		0			0
$496$	26.1334	−	45.2644i	1.17342	−	2.03243i
$497$	−11.6578	−	6.73065i	−0.522925	−	0.301911i
$498$		0			0
$499$	−1.75051			−0.0783638			−0.0391819	−	0.999232i	$-0.512475\pi$
$499$	−1.75051			−0.0783638			−0.0391819	+	0.999232i	$0.512475\pi$
$500$	−1.96806	+	12.2273i	−0.0880145	+	0.546822i
$501$		0			0
$502$		−	9.88775i		−	0.441312i
$503$	−3.43700	+	1.98435i	−0.153248	+	0.0884779i	−0.574663	−	0.818390i	$-0.694867\pi$
$503$	−3.43700	+	1.98435i	−0.153248	+	0.0884779i	0.421415	+	0.906868i	$0.361534\pi$
$504$		0			0
$505$	9.24900	+	30.3428i	0.411575	+	1.35024i
$506$	8.68268			0.385992
$507$		0			0
$508$		−	7.26503i		−	0.322334i
$509$	−6.93143	+	12.0056i	−0.307230	+	0.532139i	−0.977755	−	0.209748i	$-0.932736\pi$
$509$	−6.93143	+	12.0056i	−0.307230	+	0.532139i	0.670525	+	0.741887i	$0.266069\pi$
$510$		0			0
$511$	3.45014	+	5.97582i	0.152625	+	0.264355i
$512$			12.4810i			0.551586i
$513$		0			0
$514$	8.60666	+	14.9072i	0.379624	+	0.657527i
$515$	−3.49892	−	3.26827i	−0.154181	−	0.144017i
$516$		0			0
$517$	−1.12780	−	0.651138i	−0.0496008	−	0.0286370i
$518$	−26.5892	−	15.3513i	−1.16826	−	0.674498i
$519$		0			0
$520$	12.5969	+	1.46456i	0.552410	+	0.0642251i
$521$	−26.5396			−1.16272			−0.581361	−	0.813646i	$-0.697479\pi$
$521$	−26.5396			−1.16272			−0.581361	+	0.813646i	$0.697479\pi$
$522$		0			0
$523$	7.87461	+	4.54641i	0.344333	+	0.198801i	0.662186	−	0.749339i	$-0.269629\pi$
$523$	7.87461	+	4.54641i	0.344333	+	0.198801i	−0.317854	+	0.948140i	$0.602962\pi$
$524$	7.48396	+	12.9626i	0.326938	+	0.566273i
$525$		0			0
$526$	−0.621359	−	1.07623i	−0.0270925	−	0.0469256i
$527$	55.2758	−	31.9135i	2.40785	−	1.39017i
$528$		0			0
$529$	−4.24734	−	7.35661i	−0.184667	−	0.319853i
$530$	−2.69418	−	8.83869i	−0.117028	−	0.383928i
$531$		0			0
$532$			9.95528i			0.431616i
$533$	−1.62649	−	14.4634i	−0.0704511	−	0.626480i
$534$		0			0
$535$	23.2777	−	7.09544i	1.00638	−	0.306763i
$536$	−1.67620	+	2.90327i	−0.0724009	+	0.125402i
$537$		0			0
$538$			53.5895i			2.31041i
$539$	1.32363	+	2.29259i	0.0570127	+	0.0987490i
$540$		0			0
$541$	−10.1533			−0.436522			−0.218261	−	0.975890i	$-0.570038\pi$
$541$	−10.1533			−0.436522			−0.218261	+	0.975890i	$0.570038\pi$
$542$	29.0767	−	16.7875i	1.24895	−	0.721084i
$543$		0			0
$544$	−17.2029	+	29.7962i	−0.737566	+	1.27750i
$545$	−6.24868	+	6.68967i	−0.267664	+	0.286554i
$546$		0			0
$547$		−	27.4032i		−	1.17168i	−0.810428	−	0.585839i	$-0.800765\pi$
$547$		−	27.4032i		−	1.17168i	0.810428	−	0.585839i	$-0.199235\pi$
$548$	−20.5168	−	11.8454i	−0.876433	−	0.506009i
$549$		0			0
$550$	6.35833	+	9.46070i	0.271120	+	0.403406i
$551$	−11.2156			−0.477802
$552$		0			0
$553$	15.4682	−	8.93059i	0.657776	−	0.379767i
$554$	20.6339			0.876650
$555$		0			0
$556$	−6.36725	+	11.0284i	−0.270032	+	0.467709i
$557$	5.11331	+	2.95217i	0.216658	+	0.125088i	0.604402	−	0.796680i	$-0.293412\pi$
$557$	5.11331	+	2.95217i	0.216658	+	0.125088i	−0.387744	+	0.921767i	$0.626745\pi$
$558$		0			0
$559$	−15.4521	+	35.3959i	−0.653555	+	1.49709i
$560$	−18.1412	−	16.9454i	−0.766607	−	0.716072i
$561$		0			0
$562$	44.9322	+	25.9416i	1.89535	+	1.09428i
$563$	23.4366	−	13.5311i	0.987734	−	0.570269i	0.0831378	−	0.996538i	$-0.473506\pi$
$563$	23.4366	−	13.5311i	0.987734	−	0.570269i	0.904596	+	0.426270i	$0.140172\pi$
$564$		0			0
$565$	−0.650385	+	2.80642i	−0.0273619	+	0.118067i
$566$	15.8800	+	27.5050i	0.667487	+	1.15612i
$567$		0			0
$568$	−8.23963	+	4.75715i	−0.345727	+	0.199606i
$569$	−22.4507	+	38.8857i	−0.941182	+	1.63018i	−0.177961	+	0.984037i	$0.556950\pi$
$569$	−22.4507	+	38.8857i	−0.941182	+	1.63018i	−0.763221	+	0.646138i	$0.776383\pi$
$570$		0			0
$571$	−11.7379			−0.491217			−0.245608	−	0.969369i	$-0.578988\pi$
$571$	−11.7379			−0.491217			−0.245608	+	0.969369i	$0.578988\pi$
$572$	−4.15641	+	3.06619i	−0.173788	+	0.128204i
$573$		0			0
$574$	−7.91865	+	13.7155i	−0.330518	+	0.572474i
$575$	−8.37647	+	17.1017i	−0.349323	+	0.713190i
$576$		0			0
$577$			18.9907i			0.790592i	0.918554	+	0.395296i	$0.129358\pi$
$577$			18.9907i			0.790592i	−0.918554	+	0.395296i	$0.870642\pi$
$578$	−30.7002	+	17.7248i	−1.27696	+	0.737253i
$579$		0			0
$580$	−4.69591	+	5.02731i	−0.194987	+	0.208748i
$581$	12.1826	+	21.1009i	0.505420	+	0.875414i
$582$		0			0
$583$	−2.62527	−	1.51570i	−0.108728	−	0.0627740i
$584$	4.87705			0.201814
$585$		0			0
$586$	35.7125			1.47527
$587$	−15.2529	−	8.80625i	−0.629553	−	0.363473i	0.151026	−	0.988530i	$-0.451742\pi$
$587$	−15.2529	−	8.80625i	−0.629553	−	0.363473i	−0.780579	+	0.625057i	$0.785076\pi$
$588$		0			0
$589$	−21.1557	−	36.6427i	−0.871703	−	1.50983i
$590$	−30.5058	−	28.4948i	−1.25590	−	1.17311i
$591$		0			0
$592$	−33.8075	+	19.5188i	−1.38948	+	0.802218i
$593$		−	36.6410i		−	1.50467i	−0.658782	−	0.752334i	$-0.728928\pi$
$593$		−	36.6410i		−	1.50467i	0.658782	−	0.752334i	$-0.271072\pi$
$594$		0			0
$595$	−8.83899	−	28.9977i	−0.362363	−	1.18879i
$596$	−8.01264	+	13.8783i	−0.328211	+	0.568477i
$597$		0			0
$598$	−22.1859	−	9.68529i	−0.907250	−	0.396061i
$599$	10.2500			0.418805			0.209403	−	0.977830i	$-0.432848\pi$
$599$	10.2500			0.418805			0.209403	+	0.977830i	$0.432848\pi$
$600$		0			0
$601$	6.42137	−	11.1221i	0.261933	−	0.453682i	−0.704822	−	0.709384i	$-0.748973\pi$
$601$	6.42137	−	11.1221i	0.261933	−	0.453682i	0.966756	+	0.255702i	$0.0823066\pi$
$602$	36.3951	−	21.0127i	1.48336	−	0.856416i
$603$		0			0
$604$	3.17753	+	5.50364i	0.129292	+	0.223940i
$605$	−20.3187	−	4.70883i	−0.826071	−	0.191441i
$606$		0			0
$607$	11.6146	−	6.70567i	0.471421	−	0.272175i	−0.245414	−	0.969418i	$-0.578924\pi$
$607$	11.6146	−	6.70567i	0.471421	−	0.272175i	0.716834	+	0.697244i	$0.245590\pi$
$608$	19.7521	+	11.4039i	0.801053	+	0.462488i
$609$		0			0
$610$	−16.4099	−	15.3282i	−0.664419	−	0.620620i
$611$	2.15543	+	2.92182i	0.0871994	+	0.118204i
$612$		0			0
$613$	−39.0831	−	22.5646i	−1.57855	−	0.911377i	−0.995062	−	0.0992571i	$-0.968353\pi$
$613$	−39.0831	−	22.5646i	−1.57855	−	0.911377i	−0.583490	−	0.812120i	$-0.698313\pi$
$614$	−16.7918	+	29.0843i	−0.677663	+	1.17375i
$615$		0			0
$616$	−4.52714			−0.182404
$617$	4.86681	−	2.80985i	0.195930	−	0.113120i	−0.398825	−	0.917027i	$-0.630582\pi$
$617$	4.86681	−	2.80985i	0.195930	−	0.113120i	0.594756	+	0.803906i	$0.297249\pi$
$618$		0			0
$619$	6.91332			0.277870			0.138935	−	0.990302i	$-0.455632\pi$
$619$	6.91332			0.277870			0.138935	+	0.990302i	$0.455632\pi$
$620$	−25.2825	−	5.85919i	−1.01537	−	0.235311i
$621$		0			0
$622$	11.3147	+	6.53252i	0.453676	+	0.261930i
$623$			1.72403i			0.0690719i
$624$		0			0
$625$	−24.7682	+	3.39652i	−0.990728	+	0.135861i
$626$	23.8821	−	41.3649i	0.954519	−	1.65328i
$627$		0			0
$628$	5.32568	−	3.07478i	0.212518	−	0.122697i
$629$	−47.6718			−1.90080
$630$		0			0
$631$	17.9508	+	31.0918i	0.714612	+	1.23774i	0.963109	+	0.269111i	$0.0867298\pi$
$631$	17.9508	+	31.0918i	0.714612	+	1.23774i	−0.248498	+	0.968632i	$0.579937\pi$
$632$		−	12.6241i		−	0.502159i
$633$		0			0
$634$	14.8923	−	25.7942i	0.591449	−	1.02442i
$635$	14.0281	−	4.27601i	0.556690	−	0.169688i
$636$		0			0
$637$	−0.824803	−	7.33449i	−0.0326799	−	0.290603i
$638$			6.33174i			0.250676i
$639$		0			0
$640$	−24.2370	+	7.38783i	−0.958050	+	0.292030i
$641$	−4.14055	−	7.17165i	−0.163542	−	0.283263i	0.772595	−	0.634900i	$-0.218959\pi$
$641$	−4.14055	−	7.17165i	−0.163542	−	0.283263i	−0.936137	+	0.351637i	$0.885625\pi$
$642$		0			0
$643$	27.4964	−	15.8750i	1.08435	−	0.626051i	0.152284	−	0.988337i	$-0.451337\pi$
$643$	27.4964	−	15.8750i	1.08435	−	0.626051i	0.932067	+	0.362286i	$0.118004\pi$
$644$	4.69457	+	8.13123i	0.184992	+	0.320415i
$645$		0			0
$646$	21.6831	+	37.5563i	0.853111	+	1.47763i
$647$	24.7643	+	14.2977i	0.973585	+	0.562099i	0.900327	−	0.435214i	$-0.143327\pi$
$647$	24.7643	+	14.2977i	0.973585	+	0.562099i	0.0732574	+	0.997313i	$0.476661\pi$
$648$		0			0
$649$	−13.6948			−0.537570
$650$	−5.69362	−	31.2665i	−0.223322	−	1.22637i
$651$		0			0
$652$	16.7233	+	9.65519i	0.654934	+	0.378127i
$653$	10.5361	+	6.08300i	0.412308	+	0.238046i	0.691781	−	0.722107i	$-0.256826\pi$
$653$	10.5361	+	6.08300i	0.412308	+	0.238046i	−0.279473	+	0.960154i	$0.590160\pi$
$654$		0			0
$655$	−20.6247	+	22.0803i	−0.805876	+	0.862749i
$656$	10.0684	+	17.4389i	0.393104	+	0.680875i
$657$		0			0
$658$		−	3.95082i		−	0.154019i
$659$	2.11744	+	3.66752i	0.0824838	+	0.142866i	0.904316	−	0.426863i	$-0.140381\pi$
$659$	2.11744	+	3.66752i	0.0824838	+	0.142866i	−0.821832	+	0.569729i	$0.807048\pi$
$660$		0			0
$661$	3.38031	−	5.85487i	0.131479	−	0.227728i	−0.792768	−	0.609523i	$-0.791361\pi$
$661$	3.38031	−	5.85487i	0.131479	−	0.227728i	0.924247	+	0.381796i	$0.124694\pi$
$662$		−	19.2707i		−	0.748976i
$663$		0			0
$664$	17.2211			0.668308
$665$	−19.2228	+	5.85942i	−0.745427	+	0.227219i
$666$		0			0
$667$	−9.16066	+	5.28891i	−0.354702	+	0.204787i
$668$		−	0.212940i		−	0.00823888i
$669$		0			0
$670$	8.18427	+	1.89670i	0.316186	+	0.0732758i
$671$	−7.36685			−0.284394
$672$		0			0
$673$	41.7070	+	24.0796i	1.60769	+	0.928199i	0.989886	+	0.141866i	$0.0453103\pi$
$673$	41.7070	+	24.0796i	1.60769	+	0.928199i	0.617803	+	0.786333i	$0.288023\pi$
$674$	16.1107	−	27.9046i	0.620562	−	1.07485i
$675$		0			0
$676$	14.0407	−	3.19835i	0.540026	−	0.123013i
$677$			12.3638i			0.475180i	0.971366	+	0.237590i	$0.0763574\pi$
$677$			12.3638i			0.475180i	−0.971366	+	0.237590i	$0.923643\pi$
$678$		0			0
$679$	−10.2120	+	17.6877i	−0.391901	+	0.678793i
$680$	−20.8731	−	4.83731i	−0.800446	−	0.185503i
$681$		0			0
$682$	−20.6864	+	11.9433i	−0.792125	+	0.457334i
$683$	11.7725	−	6.79684i	0.450461	−	0.260074i	−0.257564	−	0.966261i	$-0.582920\pi$
$683$	11.7725	−	6.79684i	0.450461	−	0.260074i	0.708025	+	0.706187i	$0.249586\pi$
$684$		0			0
$685$	10.7967	−	46.5879i	0.412521	−	1.78003i
$686$	−17.7472	+	30.7391i	−0.677591	+	1.17362i
$687$		0			0
$688$		−	53.4344i		−	2.03717i
$689$	5.01736	+	6.80133i	0.191146	+	0.259110i
$690$		0			0
$691$	1.65676	−	2.86960i	0.0630263	−	0.109165i	−0.832790	−	0.553588i	$-0.813258\pi$
$691$	1.65676	−	2.86960i	0.0630263	−	0.109165i	0.895817	+	0.444424i	$0.146591\pi$
$692$	5.74334	+	3.31592i	0.218329	+	0.126052i
$693$		0			0
$694$	−7.79531			−0.295906
$695$	−25.0425	−	5.80357i	−0.949915	−	0.220142i
$696$		0			0
$697$			24.5905i			0.931431i
$698$	−38.3261	+	22.1276i	−1.45066	+	0.837541i
$699$		0			0
$700$	−5.42200	+	11.0697i	−0.204932	+	0.418397i
$701$	19.3640			0.731367			0.365684	−	0.930739i	$-0.380835\pi$
$701$	19.3640			0.731367			0.365684	+	0.930739i	$0.380835\pi$
$702$		0			0
$703$			31.6019i			1.19189i
$704$	−0.0130413	+	0.0225882i	−0.000491512	+	0.000851324i
$705$		0			0
$706$	1.02413	+	1.77385i	0.0385437	+	0.0667597i
$707$			31.5715i			1.18737i
$708$		0			0
$709$	−4.64606	−	8.04722i	−0.174487	−	0.302220i	0.765497	−	0.643440i	$-0.222493\pi$
$709$	−4.64606	−	8.04722i	−0.174487	−	0.302220i	−0.939983	+	0.341220i	$0.889160\pi$
$710$	17.4241	+	16.2755i	0.653913	+	0.610807i
$711$		0			0
$712$	1.05528	+	0.609264i	0.0395482	+	0.0228331i
$713$	−34.5588	−	19.9526i	−1.29424	−	0.747229i
$714$		0			0
$715$	−8.36690	−	6.22098i	−0.312904	−	0.232651i
$716$	11.5234			0.430650
$717$		0			0
$718$	−11.4722	−	6.62347i	−0.428138	−	0.247186i
$719$	−17.3421	−	30.0374i	−0.646752	−	1.12021i	−0.983894	−	0.178754i	$-0.942793\pi$
$719$	−17.3421	−	30.0374i	−0.646752	−	1.12021i	0.337142	−	0.941454i	$-0.390540\pi$
$720$		0			0
$721$	−2.38266	−	4.12690i	−0.0887351	−	0.153694i
$722$	−4.11088	+	2.37342i	−0.152991	+	0.0883295i
$723$		0			0
$724$	−14.1249	−	24.4651i	−0.524948	−	0.909237i
$725$	−12.4712	−	6.10844i	−0.463168	−	0.226862i
$726$		0			0
$727$		−	10.6278i		−	0.394165i	−0.980387	−	0.197082i	$-0.936853\pi$
$727$		−	10.6278i		−	0.394165i	0.980387	−	0.197082i	$-0.0631467\pi$
$728$	11.5677	+	5.04990i	0.428728	+	0.187162i
$729$		0			0
$730$	−3.56358	−	11.6909i	−0.131894	−	0.432699i
$731$	32.6264	−	56.5106i	1.20673	−	2.09012i
$732$		0			0
$733$		−	37.3250i		−	1.37863i	−0.724462	−	0.689314i	$-0.757912\pi$
$733$		−	37.3250i		−	1.37863i	0.724462	−	0.689314i	$-0.242088\pi$
$734$	−30.6673	−	53.1174i	−1.13195	−	1.96060i
$735$		0			0
$736$	21.5107			0.792895
$737$	2.38690	−	1.37808i	0.0879226	−	0.0507621i
$738$		0			0
$739$	3.46941	−	6.00919i	0.127624	−	0.221052i	−0.795131	−	0.606437i	$-0.792598\pi$
$739$	3.46941	−	6.00919i	0.127624	−	0.221052i	0.922756	+	0.385385i	$0.125931\pi$
$740$	14.1653	+	13.2315i	0.520727	+	0.486400i
$741$		0			0
$742$		−	9.19661i		−	0.337618i
$743$	−23.7770	−	13.7277i	−0.872294	−	0.503619i	−0.00418384	−	0.999991i	$-0.501332\pi$
$743$	−23.7770	−	13.7277i	−0.872294	−	0.503619i	−0.868110	+	0.496372i	$0.834665\pi$
$744$		0			0
$745$	−31.5138	−	7.30329i	−1.15458	−	0.267572i
$746$	−19.2964			−0.706493
$747$		0			0
$748$	7.55734	−	4.36323i	0.276324	−	0.159536i
$749$	24.2204			0.884993
$750$		0			0
$751$	15.9618	−	27.6467i	0.582455	−	1.00884i	−0.412732	−	0.910852i	$-0.635425\pi$
$751$	15.9618	−	27.6467i	0.582455	−	1.00884i	0.995187	−	0.0979897i	$-0.0312412\pi$
$752$	−4.35036	−	2.51168i	−0.158641	−	0.0915917i
$753$		0			0
$754$	7.06288	−	16.1788i	0.257215	−	0.589197i
$755$	−8.75684	+	9.37483i	−0.318694	+	0.341185i
$756$		0			0
$757$	11.3313	+	6.54213i	0.411843	+	0.237778i	0.691581	−	0.722299i	$-0.256914\pi$
$757$	11.3313	+	6.54213i	0.411843	+	0.237778i	−0.279738	+	0.960076i	$0.590248\pi$
$758$	31.9284	−	18.4339i	1.15969	−	0.669549i
$759$		0			0
$760$	−3.20669	+	13.8369i	−0.116319	+	0.501917i
$761$	−16.9704	−	29.3936i	−0.615177	−	1.06552i	−0.990353	−	0.138565i	$-0.955751\pi$
$761$	−16.9704	−	29.3936i	−0.615177	−	1.06552i	0.375176	−	0.926954i	$-0.377582\pi$
$762$		0			0
$763$	−7.89031	+	4.55547i	−0.285648	+	0.164919i
$764$	−10.8514	+	18.7952i	−0.392590	+	0.679986i
$765$		0			0
$766$	−52.1972			−1.88596
$767$	34.9930	+	15.2762i	1.26352	+	0.551592i
$768$		0			0
$769$	−7.47606	+	12.9489i	−0.269594	+	0.466950i	−0.968757	−	0.248012i	$-0.920223\pi$
$769$	−7.47606	+	12.9489i	−0.269594	+	0.466950i	0.699163	+	0.714962i	$0.253556\pi$
$770$	3.30791	+	10.8521i	0.119209	+	0.391083i
$771$		0			0
$772$		−	22.8514i		−	0.822440i
$773$	−12.3714	+	7.14260i	−0.444967	+	0.256902i	−0.705702	−	0.708509i	$-0.749368\pi$
$773$	−12.3714	+	7.14260i	−0.444967	+	0.256902i	0.260735	+	0.965410i	$0.416035\pi$
$774$		0			0
$775$	−3.56704	−	52.2668i	−0.128132	−	1.87748i
$776$	7.21774	+	12.5015i	0.259102	+	0.448777i
$777$		0			0
$778$	−32.0913	−	18.5279i	−1.15053	−	0.664258i
$779$	16.3012			0.584051
$780$		0			0
$781$	7.82211			0.279897
$782$	35.4205	+	20.4500i	1.26663	+	0.731291i
$783$		0			0
$784$	5.10573	+	8.84339i	0.182348	+	0.315835i
$785$	9.07168	+	8.47367i	0.323782	+	0.302438i
$786$		0			0
$787$	−24.9907	+	14.4284i	−0.890822	+	0.514316i	−0.874211	−	0.485546i	$-0.838621\pi$
$787$	−24.9907	+	14.4284i	−0.890822	+	0.514316i	−0.0166107	+	0.999862i	$0.505288\pi$
$788$			2.11549i			0.0753611i
$789$		0			0
$790$	−30.2615	+	9.22422i	−1.07666	+	0.328183i
$791$	−1.43361	+	2.48308i	−0.0509732	+	0.0882881i
$792$		0			0
$793$	18.8237	+	8.21752i	0.668450	+	0.291813i
$794$	22.2551			0.789805
$795$		0			0
$796$	3.40400	−	5.89590i	0.120651	−	0.208974i
$797$	−4.77532	+	2.75703i	−0.169150	+	0.0976590i	−0.582185	−	0.813056i	$-0.697802\pi$
$797$	−4.77532	+	2.75703i	−0.169150	+	0.0976590i	0.413035	+	0.910715i	$0.364469\pi$
$798$		0			0
$799$	−3.06721	−	5.31256i	−0.108510	−	0.187945i
$800$	15.7523	+	23.4382i	0.556928	+	0.828666i
$801$		0			0
$802$	−15.4411	+	8.91493i	−0.545245	+	0.314797i
$803$	−3.47244	−	2.00481i	−0.122540	−	0.0707483i
$804$		0			0
$805$	−12.9376	+	13.8506i	−0.455990	+	0.488171i
$806$	66.1803	−	7.44233i	2.33110	−	0.262145i
$807$		0			0
$808$	19.3249	+	11.1572i	0.679846	+	0.392510i
$809$	−21.2972	+	36.8878i	−0.748770	+	1.29691i	0.199643	+	0.979869i	$0.436022\pi$
$809$	−21.2972	+	36.8878i	−0.748770	+	1.29691i	−0.948413	+	0.317039i	$0.897311\pi$
$810$		0			0
$811$	30.9510			1.08684			0.543418	−	0.839462i	$-0.317130\pi$
$811$	30.9510			1.08684			0.543418	+	0.839462i	$0.317130\pi$
$812$	−5.92960	+	3.42346i	−0.208088	+	0.120140i
$813$		0			0
$814$	17.8407			0.625317
$815$	−8.80043	+	37.9740i	−0.308266	+	1.33017i
$816$		0			0
$817$	−37.4612	−	21.6282i	−1.31060	−	0.756676i
$818$			35.5370i			1.24252i
$819$		0			0
$820$	6.82520	−	7.30687i	0.238346	−	0.255167i
$821$	18.0072	−	31.1894i	0.628455	−	1.08852i	−0.359406	−	0.933181i	$-0.617021\pi$
$821$	18.0072	−	31.1894i	0.628455	−	1.08852i	0.987862	−	0.155336i	$-0.0496459\pi$
$822$		0			0
$823$	30.1737	−	17.4208i	1.05179	−	0.607250i	0.128639	−	0.991692i	$-0.458939\pi$
$823$	30.1737	−	17.4208i	1.05179	−	0.607250i	0.923149	+	0.384441i	$0.125606\pi$
$824$	−3.36808			−0.117333
$825$		0			0
$826$	−20.7736	−	35.9809i	−0.722805	−	1.25193i
$827$		−	52.8150i		−	1.83656i	−0.395934	−	0.918279i	$-0.629579\pi$
$827$		−	52.8150i		−	1.83656i	0.395934	−	0.918279i	$-0.370421\pi$
$828$		0			0
$829$	−0.566635	+	0.981440i	−0.0196800	+	0.0340868i	−0.875698	−	0.482860i	$-0.839598\pi$
$829$	−0.566635	+	0.981440i	−0.0196800	+	0.0340868i	0.856018	+	0.516947i	$0.172931\pi$
$830$	−12.5832	−	41.2811i	−0.436769	−	1.43289i
$831$		0			0
$832$	0.0585195	−	0.0431700i	0.00202880	−	0.00149665i
$833$			12.4700i			0.432060i
$834$		0			0
$835$	0.411167	−	0.125331i	0.0142290	−	0.00433725i
$836$	−2.89241	−	5.00981i	−0.100036	−	0.173268i
$837$		0			0
$838$	−29.7563	+	17.1798i	−1.02792	+	0.593467i
$839$	19.0071	+	32.9213i	0.656198	+	1.13657i	0.981592	+	0.190989i	$0.0611696\pi$
$839$	19.0071	+	32.9213i	0.656198	+	1.13657i	−0.325394	+	0.945578i	$0.605497\pi$
$840$		0			0
$841$	10.6431	+	18.4344i	0.367004	+	0.635670i
$842$	10.6024	+	6.12132i	0.365384	+	0.210955i
$843$		0			0
$844$	20.1409			0.693279
$845$	14.4397	+	25.2288i	0.496741	+	0.867899i
$846$		0			0
$847$	−17.9777	−	10.3794i	−0.617720	−	0.356641i
$848$	−10.1267	−	5.84663i	−0.347751	−	0.200774i
$849$		0			0
$850$	3.65598	+	53.5699i	0.125399	+	1.83743i
$851$	14.9024	+	25.8117i	0.510847	+	0.884813i
$852$		0			0
$853$			16.3247i			0.558946i	0.960154	+	0.279473i	$0.0901597\pi$
$853$			16.3247i			0.558946i	−0.960154	+	0.279473i	$0.909840\pi$
$854$	−11.1747	−	19.3551i	−0.382390	−	0.662319i
$855$		0			0
$856$	8.55935	−	14.8252i	0.292552	−	0.506716i
$857$			5.70196i			0.194775i	0.995247	+	0.0973876i	$0.0310486\pi$
$857$			5.70196i			0.194775i	−0.995247	+	0.0973876i	$0.968951\pi$
$858$		0			0
$859$	15.2817			0.521405			0.260702	−	0.965419i	$-0.416046\pi$
$859$	15.2817			0.521405			0.260702	+	0.965419i	$0.416046\pi$
$860$	−25.3794	+	7.73607i	−0.865431	+	0.263798i
$861$		0			0
$862$	−18.6231	+	10.7521i	−0.634306	+	0.366217i
$863$			31.6087i			1.07597i	0.842954	+	0.537986i	$0.180815\pi$
$863$			31.6087i			1.07597i	−0.842954	+	0.537986i	$0.819185\pi$
$864$		0			0
$865$	−3.02236	+	13.0415i	−0.102763	+	0.443426i
$866$	33.2768			1.13079
$867$		0			0
$868$	−22.3696	−	12.9151i	−0.759273	−	0.438366i
$869$	−5.18940	+	8.98830i	−0.176038	+	0.304907i
$870$		0			0
$871$	−7.63620	+	0.858732i	−0.258743	+	0.0290970i
$872$			6.43952i			0.218070i
$873$		0			0
$874$	13.5564	−	23.4805i	0.458554	−	0.794238i
$875$	−24.5659	−	3.95405i	−0.830480	−	0.133671i
$876$		0			0
$877$	17.8455	−	10.3031i	0.602600	−	0.347911i	−0.167464	−	0.985878i	$-0.553558\pi$
$877$	17.8455	−	10.3031i	0.602600	−	0.347911i	0.770064	+	0.637967i	$0.220224\pi$
$878$	43.5479	−	25.1424i	1.46967	−	0.848515i
$879$		0			0
$880$	14.0526	+	3.25666i	0.473711	+	0.109782i
$881$	−2.79747	+	4.84536i	−0.0942492	+	0.163244i	−0.909295	−	0.416152i	$-0.863378\pi$
$881$	−2.79747	+	4.84536i	−0.0942492	+	0.163244i	0.815046	+	0.579397i	$0.196712\pi$
$882$		0			0
$883$			35.6734i			1.20051i	0.799810	+	0.600253i	$0.204934\pi$
$883$			35.6734i			1.20051i	−0.799810	+	0.600253i	$0.795066\pi$
$884$	−24.1775	+	2.71890i	−0.813178	+	0.0914463i
$885$		0			0
$886$	20.1262	−	34.8596i	0.676153	−	1.17113i
$887$	−8.23896	−	4.75676i	−0.276637	−	0.159716i	0.355263	−	0.934766i	$-0.384391\pi$
$887$	−8.23896	−	4.75676i	−0.276637	−	0.159716i	−0.631900	+	0.775050i	$0.717725\pi$
$888$		0			0
$889$	14.5962			0.489541
$890$	0.689409	−	2.97481i	0.0231090	−	0.0997159i
$891$		0			0
$892$			0.0557240i			0.00186578i
$893$	−3.52173	+	2.03327i	−0.117850	+	0.0680408i
$894$		0			0
$895$	6.78238	+	22.2507i	0.226710	+	0.743758i
$896$	−25.2184			−0.842489
$897$		0			0
$898$			20.3121i			0.677825i
$899$	14.5502	−	25.2016i	0.485275	−	0.840521i
$900$		0			0
$901$	−7.13977	−	12.3664i	−0.237860	−	0.411986i
$902$		−	9.20276i		−	0.306418i
$903$		0			0
$904$	1.01326	+	1.75501i	0.0337004	+	0.0583709i
$905$	38.9263	−	41.6734i	1.29395	−	1.38527i
$906$		0			0
$907$	35.8337	+	20.6886i	1.18984	+	0.686953i	0.958270	−	0.285865i	$-0.0922810\pi$
$907$	35.8337	+	20.6886i	1.18984	+	0.686953i	0.231568	+	0.972819i	$0.425614\pi$
$908$	13.8408	+	7.99098i	0.459323	+	0.265190i
$909$		0			0
$910$	3.65290	−	31.4191i	0.121092	−	1.04153i
$911$	−50.4741			−1.67228			−0.836140	−	0.548516i	$-0.815193\pi$
$911$	−50.4741			−1.67228			−0.836140	+	0.548516i	$0.815193\pi$
$912$		0			0
$913$	−12.2614	−	7.07910i	−0.405792	−	0.234284i
$914$	−22.1129	−	38.3007i	−0.731430	−	1.26687i
$915$		0			0
$916$	−9.29819	−	16.1049i	−0.307221	−	0.532122i
$917$	−26.0432	+	15.0360i	−0.860022	+	0.496534i
$918$		0			0
$919$	2.74632	+	4.75677i	0.0905929	+	0.156911i	0.907761	−	0.419488i	$-0.137790\pi$
$919$	2.74632	+	4.75677i	0.0905929	+	0.156911i	−0.817168	+	0.576400i	$0.804457\pi$
$920$	3.90586	+	12.8138i	0.128772	+	0.422459i
$921$		0			0
$922$			28.6041i			0.942027i
$923$	−19.9870	−	8.72535i	−0.657880	−	0.287198i
$924$		0			0
$925$	−17.2115	+	35.1396i	−0.565912	+	1.15538i
$926$	−17.3475	+	30.0467i	−0.570073	+	0.987395i
$927$		0			0
$928$			15.6864i			0.514932i
$929$	16.2780	+	28.1943i	0.534063	+	0.925025i	0.999208	+	0.0397900i	$0.0126689\pi$
$929$	16.2780	+	28.1943i	0.534063	+	0.925025i	−0.465145	+	0.885235i	$0.653998\pi$
$930$		0			0
$931$	8.26644			0.270922
$932$	18.3260	−	10.5805i	0.600289	−	0.346577i
$933$		0			0
$934$	25.3751	−	43.9510i	0.830299	−	1.43812i
$935$	12.8731	+	12.0245i	0.420994	+	0.393242i
$936$		0			0
$937$		−	29.8356i		−	0.974686i	−0.873211	−	0.487343i	$-0.837966\pi$
$937$		−	29.8356i		−	0.974686i	0.873211	−	0.487343i	$-0.162034\pi$
$938$	7.24132	+	4.18078i	0.236438	+	0.136507i
$939$		0			0
$940$	−0.563127	+	2.42990i	−0.0183672	+	0.0792547i
$941$	58.7375			1.91479			0.957394	−	0.288784i	$-0.0932510\pi$
$941$	58.7375			1.91479			0.957394	+	0.288784i	$0.0932510\pi$
$942$		0			0
$943$	13.3144	−	7.68708i	0.433577	−	0.250326i
$944$	−52.8261			−1.71934
$945$		0			0
$946$	−12.2101	+	21.1485i	−0.396985	+	0.687599i
$947$	29.1327	+	16.8198i	0.946686	+	0.546569i	0.892050	−	0.451937i	$-0.149267\pi$
$947$	29.1327	+	16.8198i	0.946686	+	0.546569i	0.0546360	+	0.998506i	$0.482600\pi$
$948$		0			0
$949$	6.63644	+	8.99610i	0.215428	+	0.292026i
$950$	35.5118	−	2.42357i	1.15216	−	0.0786310i
$951$		0			0
$952$	−18.4682	−	10.6626i	−0.598558	−	0.345577i
$953$	−9.66930	+	5.58257i	−0.313219	+	0.180837i	−0.648366	−	0.761329i	$-0.724547\pi$
$953$	−9.66930	+	5.58257i	−0.313219	+	0.180837i	0.335147	+	0.942166i	$0.391214\pi$
$954$		0			0
$955$	−42.6787	−	9.89075i	−1.38105	−	0.320057i
$956$	−11.3646	−	19.6840i	−0.367556	−	0.636626i
$957$		0			0
$958$	−28.7326	+	16.5888i	−0.928308	+	0.535959i
$959$	23.7986	−	41.2203i	0.768496	−	1.33107i
$960$		0			0
$961$	78.7817			2.54135
$962$	−45.5865	−	19.9008i	−1.46977	−	0.641628i
$963$		0			0
$964$	9.61811	−	16.6590i	0.309778	−	0.536552i
$965$	44.1240	−	13.4497i	1.42040	−	0.432962i
$966$		0			0
$967$			13.7378i			0.441777i	0.975299	+	0.220889i	$0.0708957\pi$
$967$			13.7378i			0.441777i	−0.975299	+	0.220889i	$0.929104\pi$
$968$	−12.7064	+	7.33605i	−0.408400	+	0.235790i
$969$		0			0
$970$	24.6938	−	26.4365i	0.792869	−	0.848824i
$971$	−16.7671	−	29.0415i	−0.538082	−	0.931985i	−0.999007	−	0.0445460i	$-0.985816\pi$
$971$	−16.7671	−	29.0415i	−0.538082	−	0.931985i	0.460926	−	0.887439i	$-0.347517\pi$
$972$		0			0
$973$	−22.1572	−	12.7925i	−0.710328	−	0.410108i
$974$	6.14849			0.197010
$975$		0			0
$976$	−28.4167			−0.909596
$977$	−8.43350	−	4.86908i	−0.269811	−	0.155776i	0.358990	−	0.933341i	$-0.383121\pi$
$977$	−8.43350	−	4.86908i	−0.269811	−	0.155776i	−0.628802	+	0.777565i	$0.716454\pi$
$978$		0			0
$979$	−0.500902	−	0.867587i	−0.0160089	−	0.0277282i
$980$	3.46110	−	3.70536i	0.110561	−	0.118363i
$981$		0			0
$982$	44.0553	−	25.4353i	1.40586	−	0.811674i
$983$		−	5.18190i		−	0.165277i	−0.996580	−	0.0826384i	$-0.973665\pi$
$983$		−	5.18190i		−	0.165277i	0.996580	−	0.0826384i	$-0.0263347\pi$
$984$		0			0
$985$	−4.08482	+	1.24512i	−0.130153	+	0.0396729i
$986$	−14.9129	+	25.8299i	−0.474924	+	0.822593i
$987$		0			0
$988$	1.80237	+	16.0274i	0.0573411	+	0.509901i
$989$	−40.7965			−1.29725
$990$		0			0
$991$	−13.7084	+	23.7437i	−0.435463	+	0.754244i	−0.997333	−	0.0729816i	$-0.976749\pi$
$991$	−13.7084	+	23.7437i	−0.435463	+	0.754244i	0.561871	+	0.827225i	$0.310082\pi$
$992$	−51.2492	+	29.5887i	−1.62716	+	0.939443i
$993$		0			0
$994$	11.8653	+	20.5513i	0.376344	+	0.651847i
$995$	13.3880	+	3.10264i	0.424427	+	0.0983604i
$996$		0			0
$997$	23.1116	−	13.3435i	0.731951	−	0.422592i	−0.0871844	−	0.996192i	$-0.527787\pi$
$997$	23.1116	−	13.3435i	0.731951	−	0.422592i	0.819136	+	0.573600i	$0.194454\pi$
$998$	2.67250	+	1.54297i	0.0845964	+	0.0488417i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bs.b.334.3		24
3.2	odd	2		195.2.ba.a.139.10	yes	24
5.4	even	2	inner	585.2.bs.b.334.10		24
13.3	even	3	inner	585.2.bs.b.289.10		24
15.2	even	4		975.2.i.q.451.2		12
15.8	even	4		975.2.i.o.451.5		12
15.14	odd	2		195.2.ba.a.139.3	yes	24
39.29	odd	6		195.2.ba.a.94.3	✓	24
65.29	even	6	inner	585.2.bs.b.289.3		24
195.29	odd	6		195.2.ba.a.94.10	yes	24
195.68	even	12		975.2.i.o.601.5		12
195.107	even	12		975.2.i.q.601.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.ba.a.94.3	✓	24	39.29	odd	6
195.2.ba.a.94.10	yes	24	195.29	odd	6
195.2.ba.a.139.3	yes	24	15.14	odd	2
195.2.ba.a.139.10	yes	24	3.2	odd	2
585.2.bs.b.289.3		24	65.29	even	6	inner
585.2.bs.b.289.10		24	13.3	even	3	inner
585.2.bs.b.334.3		24	1.1	even	1	trivial
585.2.bs.b.334.10		24	5.4	even	2	inner
975.2.i.o.451.5		12	15.8	even	4
975.2.i.o.601.5		12	195.68	even	12
975.2.i.q.451.2		12	15.2	even	4
975.2.i.q.601.2		12	195.107	even	12

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.bs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.52669 - 0.881436i) q^{2} +(0.553860 + 0.959313i) q^{4} +(-1.52636 + 1.63408i) q^{5} +(-1.92736 + 1.11276i) q^{7} +1.57298i q^{8} +O(q^{10})\)	\(q+(-1.52669 - 0.881436i) q^{2} +(0.553860 + 0.959313i) q^{4} +(-1.52636 + 1.63408i) q^{5} +(-1.92736 + 1.11276i) q^{7} +1.57298i q^{8} +(3.77062 - 1.14935i) q^{10} +(0.646605 - 1.11995i) q^{11} +(-2.90148 + 2.14043i) q^{13} +3.92332 q^{14} +(2.49420 - 4.32008i) q^{16} +(5.27558 - 3.04586i) q^{17} +(-2.01912 - 3.49721i) q^{19} +(-2.41299 - 0.559207i) q^{20} +(-1.97434 + 1.13988i) q^{22} +(-3.29833 - 1.90429i) q^{23} +(-0.340442 - 4.98840i) q^{25} +(6.31631 - 0.710304i) q^{26} +(-2.13497 - 1.23263i) q^{28} +(1.38868 - 2.40527i) q^{29} +10.4777 q^{31} +(-4.89127 + 2.82398i) q^{32} -10.7389 q^{34} +(1.12350 - 4.84794i) q^{35} +(-6.77724 - 3.91284i) q^{37} +7.11889i q^{38} +(-2.57037 - 2.40093i) q^{40} +(-2.01836 + 3.49590i) q^{41} +(9.27663 - 5.35587i) q^{43} +1.43252 q^{44} +(3.35702 + 5.81454i) q^{46} -1.00701i q^{47} +(-1.02352 + 1.77279i) q^{49} +(-3.87720 + 7.91583i) q^{50} +(-3.66035 - 1.59793i) q^{52} -2.34409i q^{53} +(0.843141 + 2.76606i) q^{55} +(-1.75035 - 3.03169i) q^{56} +(-4.24018 + 2.44807i) q^{58} +(-5.29490 - 9.17104i) q^{59} +(-2.84828 - 4.93336i) q^{61} +(-15.9962 - 9.23541i) q^{62} -0.0201689 q^{64} +(0.931075 - 8.00831i) q^{65} +(1.84572 + 1.06562i) q^{67} +(5.84386 + 3.37395i) q^{68} +(-5.98840 + 6.41101i) q^{70} +(3.02430 + 5.23824i) q^{71} -3.10052i q^{73} +(6.89784 + 11.9474i) q^{74} +(2.23662 - 3.87393i) q^{76} +2.87807i q^{77} -8.02561 q^{79} +(3.25231 + 10.6697i) q^{80} +(6.16282 - 3.55811i) q^{82} -10.9481i q^{83} +(-3.07526 + 13.2698i) q^{85} -18.8834 q^{86} +(1.76166 + 1.01709i) q^{88} +(0.387332 - 0.670879i) q^{89} +(3.21041 - 7.35403i) q^{91} -4.21884i q^{92} +(-0.887616 + 1.53740i) q^{94} +(8.79663 + 2.03861i) q^{95} +(7.94767 - 4.58859i) q^{97} +(3.12521 - 1.80434i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{4} - 4 q^{5}+O(q^{10}) \) 24 * q + 8 * q^4 - 4 * q^5	\( 24 q + 8 q^{4} - 4 q^{5} - 4 q^{10} - 4 q^{11} - 24 q^{14} + 16 q^{16} - 16 q^{19} + 16 q^{20} - 16 q^{25} + 48 q^{26} + 12 q^{29} + 8 q^{31} - 32 q^{34} - 10 q^{35} - 48 q^{40} + 40 q^{41} - 40 q^{44} - 24 q^{46} - 16 q^{49} - 20 q^{50} + 20 q^{55} + 24 q^{56} - 12 q^{59} + 20 q^{61} + 48 q^{64} - 14 q^{65} - 56 q^{70} - 4 q^{71} + 12 q^{74} + 8 q^{76} + 136 q^{79} + 4 q^{80} - 4 q^{85} - 48 q^{86} + 64 q^{89} + 60 q^{91} - 48 q^{94} + 28 q^{95}+O(q^{100}) \) 24 * q + 8 * q^4 - 4 * q^5 - 4 * q^10 - 4 * q^11 - 24 * q^14 + 16 * q^16 - 16 * q^19 + 16 * q^20 - 16 * q^25 + 48 * q^26 + 12 * q^29 + 8 * q^31 - 32 * q^34 - 10 * q^35 - 48 * q^40 + 40 * q^41 - 40 * q^44 - 24 * q^46 - 16 * q^49 - 20 * q^50 + 20 * q^55 + 24 * q^56 - 12 * q^59 + 20 * q^61 + 48 * q^64 - 14 * q^65 - 56 * q^70 - 4 * q^71 + 12 * q^74 + 8 * q^76 + 136 * q^79 + 4 * q^80 - 4 * q^85 - 48 * q^86 + 64 * q^89 + 60 * q^91 - 48 * q^94 + 28 * q^95

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