LMFDB - Embedded newform 585.2.bs.b.289.10

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			289.10
Character	$\chi$	$=$	585.289
Dual form			585.2.bs.b.334.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.52669 - 0.881436i) q^{2} +(0.553860 - 0.959313i) q^{4} +(-1.52636 + 1.63408i) q^{5} +(1.92736 + 1.11276i) q^{7} +1.57298i q^{8} +O(q^{10})$	\(q+(1.52669 - 0.881436i) q^{2} +(0.553860 - 0.959313i) q^{4} +(-1.52636 + 1.63408i) q^{5} +(1.92736 + 1.11276i) q^{7} +1.57298i q^{8} +(-0.889946 + 3.84013i) q^{10} +(0.646605 + 1.11995i) q^{11} +(2.90148 + 2.14043i) q^{13} +3.92332 q^{14} +(2.49420 + 4.32008i) q^{16} +(-5.27558 - 3.04586i) q^{17} +(-2.01912 + 3.49721i) q^{19} +(0.722206 + 2.36931i) q^{20} +(1.97434 + 1.13988i) q^{22} +(3.29833 - 1.90429i) q^{23} +(-0.340442 - 4.98840i) q^{25} +(6.31631 + 0.710304i) q^{26} +(2.13497 - 1.23263i) q^{28} +(1.38868 + 2.40527i) q^{29} +10.4777 q^{31} +(4.89127 + 2.82398i) q^{32} -10.7389 q^{34} +(-4.76019 + 1.45099i) q^{35} +(6.77724 - 3.91284i) q^{37} +7.11889i q^{38} +(-2.57037 - 2.40093i) q^{40} +(-2.01836 - 3.49590i) q^{41} +(-9.27663 - 5.35587i) q^{43} +1.43252 q^{44} +(3.35702 - 5.81454i) q^{46} -1.00701i q^{47} +(-1.02352 - 1.77279i) q^{49} +(-4.91670 - 7.31567i) q^{50} +(3.66035 - 1.59793i) q^{52} -2.34409i q^{53} +(-2.81705 - 0.652848i) q^{55} +(-1.75035 + 3.03169i) q^{56} +(4.24018 + 2.44807i) q^{58} +(-5.29490 + 9.17104i) q^{59} +(-2.84828 + 4.93336i) q^{61} +(15.9962 - 9.23541i) q^{62} -0.0201689 q^{64} +(-7.92633 + 1.47419i) q^{65} +(-1.84572 + 1.06562i) q^{67} +(-5.84386 + 3.37395i) q^{68} +(-5.98840 + 6.41101i) q^{70} +(3.02430 - 5.23824i) q^{71} -3.10052i q^{73} +(6.89784 - 11.9474i) q^{74} +(2.23662 + 3.87393i) q^{76} +2.87807i q^{77} -8.02561 q^{79} +(-10.8664 - 2.51828i) q^{80} +(-6.16282 - 3.55811i) q^{82} -10.9481i q^{83} +(13.0296 - 3.97164i) q^{85} -18.8834 q^{86} +(-1.76166 + 1.01709i) q^{88} +(0.387332 + 0.670879i) q^{89} +(3.21041 + 7.35403i) q^{91} -4.21884i q^{92} +(-0.887616 - 1.53740i) q^{94} +(-2.63283 - 8.63741i) q^{95} +(-7.94767 - 4.58859i) q^{97} +(-3.12521 - 1.80434i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

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

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	$-0.452471\pi$
$2$	1.52669	−	0.881436i	1.07953	−	0.623270i	0.930771	+	0.365603i	$0.119137\pi$
$3$		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	$-0.195158\pi$
$7$	1.92736	+	1.11276i	0.728474	+	0.420584i	−0.0893898	+	0.995997i	$0.528492\pi$
$8$			1.57298i			0.556131i
$9$		0			0
$10$	−0.889946	+	3.84013i	−0.281426	+	1.21436i
$11$	0.646605	+	1.11995i	0.194959	+	0.337679i	0.946887	−	0.321566i	$-0.104209\pi$
$11$	0.646605	+	1.11995i	0.194959	+	0.337679i	−0.751928	+	0.659245i	$0.770876\pi$
$12$		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	$-0.597907\pi$
$17$	−5.27558	−	3.04586i	−1.27952	−	0.738728i	−0.976759	+	0.214340i	$0.931240\pi$
$18$		0			0
$19$	−2.01912	+	3.49721i	−0.463217	+	0.802316i	−0.999119	−	0.0419646i	$-0.986638\pi$
$19$	−2.01912	+	3.49721i	−0.463217	+	0.802316i	0.535902	+	0.844280i	$0.319972\pi$
$20$	0.722206	+	2.36931i	0.161490	+	0.529794i
$21$		0			0
$22$	1.97434	+	1.13988i	0.420930	+	0.243024i
$23$	3.29833	−	1.90429i	0.687750	−	0.397072i	−0.115019	−	0.993363i	$-0.536693\pi$
$23$	3.29833	−	1.90429i	0.687750	−	0.397072i	0.802768	+	0.596291i	$0.203360\pi$
$24$		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	0.965672	−	0.259766i	$-0.0836455\pi$
$29$	1.38868	+	2.40527i	0.257872	+	0.446647i	−0.707800	+	0.706413i	$0.750312\pi$
$30$		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
$35$	−4.76019	+	1.45099i	−0.804619	+	0.245261i
$36$		0			0
$37$	6.77724	−	3.91284i	1.11417	−	0.643267i	0.174264	−	0.984699i	$-0.444245\pi$
$37$	6.77724	−	3.91284i	1.11417	−	0.643267i	0.939906	+	0.341432i	$0.110912\pi$
$38$			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	0.664269	−	0.747494i	$-0.268743\pi$
$41$	−2.01836	−	3.49590i	−0.315214	−	0.545967i	−0.979483	+	0.201527i	$0.935410\pi$
$42$		0			0
$43$	−9.27663	−	5.35587i	−1.41467	−	0.816762i	−0.418849	−	0.908056i	$-0.637566\pi$
$43$	−9.27663	−	5.35587i	−1.41467	−	0.816762i	−0.995824	+	0.0912941i	$0.970900\pi$
$44$	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
$50$	−4.91670	−	7.31567i	−0.695327	−	1.03459i
$51$		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
$55$	−2.81705	−	0.652848i	−0.379851	−	0.0880300i
$56$	−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	0.282715	+	0.959204i	$0.408765\pi$
$59$	−5.29490	+	9.17104i	−0.689337	+	1.19397i	−0.972053	+	0.234763i	$0.924568\pi$
$60$		0			0
$61$	−2.84828	+	4.93336i	−0.364685	+	0.631653i	−0.988726	−	0.149739i	$-0.952157\pi$
$61$	−2.84828	+	4.93336i	−0.364685	+	0.631653i	0.624041	+	0.781392i	$0.285490\pi$
$62$	15.9962	−	9.23541i	2.03152	−	1.17290i
$63$		0			0
$64$	−0.0201689			−0.00252111
$65$	−7.92633	+	1.47419i	−0.983141	+	0.182850i
$66$		0			0
$67$	−1.84572	+	1.06562i	−0.225490	+	0.130187i	−0.608490	−	0.793562i	$-0.708224\pi$
$67$	−1.84572	+	1.06562i	−0.225490	+	0.130187i	0.383000	+	0.923748i	$0.374891\pi$
$68$	−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	−0.628862	−	0.777517i	$-0.716479\pi$
$71$	3.02430	−	5.23824i	0.358918	−	0.621665i	0.987780	+	0.155852i	$0.0498123\pi$
$72$		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	$0.649102\pi$
$80$	−10.8664	−	2.51828i	−1.21490	−	0.281552i
$81$		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
$85$	13.0296	−	3.97164i	1.41326	−	0.430785i
$86$	−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	0.885824	−	0.464022i	$-0.153594\pi$
$89$	0.387332	+	0.670879i	0.0410571	+	0.0711130i	−0.844767	+	0.535135i	$0.820261\pi$
$90$		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
$95$	−2.63283	−	8.63741i	−0.270122	−	0.886180i
$96$		0			0
$97$	−7.94767	−	4.58859i	−0.806963	−	0.465900i	0.0389369	−	0.999242i	$-0.487603\pi$
$97$	−7.94767	−	4.58859i	−0.806963	−	0.465900i	−0.845900	+	0.533341i	$0.820936\pi$
$98$	−3.12521	−	1.80434i	−0.315693	−	0.182266i
$99$		0			0
$100$	−4.97399	−	2.43628i	−0.497399	−	0.243628i
$101$	7.09306	+	12.2855i	0.705786	+	1.22246i	0.966407	+	0.257016i	$0.0827393\pi$
$101$	7.09306	+	12.2855i	0.705786	+	1.22246i	−0.260621	+	0.965441i	$0.583927\pi$
$102$		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	$-0.490339\pi$
$107$	9.42495	−	5.44150i	0.911144	−	0.526049i	0.880799	+	0.473490i	$0.157006\pi$
$108$		0			0
$109$	4.09384			0.392119			0.196059	−	0.980592i	$-0.437185\pi$
$109$	4.09384			0.392119			0.196059	+	0.980592i	$0.437185\pi$
$110$	−4.87621	+	1.48635i	−0.464928	+	0.141718i
$111$		0			0
$112$			11.1018i			1.04902i
$113$	−1.11573	−	0.644166i	−0.104959	−	0.0605980i	0.446602	−	0.894733i	$-0.352634\pi$
$113$	−1.11573	−	0.644166i	−0.104959	−	0.0605980i	−0.551561	+	0.834135i	$0.685967\pi$
$114$		0			0
$115$	−1.92268	+	8.29638i	−0.179291	+	0.773641i
$116$	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	$-0.572683\pi$
$127$	5.67987	−	3.27927i	0.504007	−	0.290989i	0.730367	+	0.683055i	$0.239349\pi$
$128$	−9.81334	+	5.66573i	−0.867385	+	0.500785i
$129$		0			0
$130$	−10.8017	+	9.23719i	−0.947369	+	0.810155i
$131$	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	0.994507	+	0.104672i	$0.0333793\pi$
$137$	18.5216	+	10.6935i	1.58241	+	0.913604i	0.587902	+	0.808932i	$0.299954\pi$
$138$		0			0
$139$	5.74807	−	9.95595i	0.487545	−	0.844453i	−0.512352	−	0.858775i	$-0.671226\pi$
$139$	5.74807	−	9.95595i	0.487545	−	0.844453i	0.999897	+	0.0143224i	$0.00455911\pi$
$140$	−1.24453	+	5.37016i	−0.105182	+	0.453861i
$141$		0			0
$142$		−	10.6629i		−	0.894811i
$143$	−0.521066	+	4.63353i	−0.0435737	+	0.387475i
$144$		0			0
$145$	−6.05003	−	1.40209i	−0.502428	−	0.116437i
$146$	−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	−0.401295	−	0.915949i	$-0.631440\pi$
$149$	7.23346	−	12.5287i	0.592588	−	1.02639i	0.993882	−	0.110443i	$-0.0352270\pi$
$150$		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
$160$	−12.0805	+	3.68233i	−0.955044	+	0.291113i
$161$	8.47610			0.668010
$162$		0			0
$163$	−15.0970	−	8.71628i	−1.18249	−	0.682712i	−0.225902	−	0.974150i	$-0.572533\pi$
$163$	−15.0970	−	8.71628i	−1.18249	−	0.682712i	−0.956590	+	0.291439i	$0.905866\pi$
$164$	−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	$-0.664299\pi$
$167$	0.166478	−	0.0961162i	0.0128825	−	0.00743769i	0.506427	+	0.862283i	$0.330966\pi$
$168$		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	$-0.406418\pi$
$173$	−5.18483	−	2.99346i	−0.394195	−	0.227589i	−0.683976	+	0.729504i	$0.739751\pi$
$174$		0			0
$175$	4.89474	−	9.99327i	0.370008	−	0.755420i
$176$	−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	0.992285	−	0.123981i	$-0.0395662\pi$
$179$	5.20141	+	9.00910i	0.388771	+	0.673372i	−0.603513	+	0.797353i	$0.706233\pi$
$180$		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
$185$	−3.95062	+	17.0470i	−0.290455	+	1.25332i
$186$		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	−0.256467	−	0.966553i	$-0.582558\pi$
$191$	9.79617	−	16.9675i	0.708826	−	1.22772i	0.965293	−	0.261170i	$-0.0841082\pi$
$192$		0			0
$193$	17.8654	−	10.3146i	1.28598	−	0.742462i	0.308047	−	0.951371i	$-0.400325\pi$
$193$	17.8654	−	10.3146i	1.28598	−	0.742462i	0.977935	+	0.208909i	$0.0669914\pi$
$194$	−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	$-0.688339\pi$
$197$	−1.65391	+	0.954884i	−0.117836	+	0.0680327i	0.439924	+	0.898035i	$0.355006\pi$
$198$		0			0
$199$	−3.07298	+	5.32255i	−0.217838	+	0.377306i	−0.954147	−	0.299340i	$-0.903234\pi$
$199$	−3.07298	+	5.32255i	−0.217838	+	0.377306i	0.736309	+	0.676645i	$0.236567\pi$
$200$	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
$205$	8.79332	+	2.03784i	0.614152	+	0.142329i
$206$	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	0.988374	+	0.152044i	$0.0485857\pi$
$211$	9.09116	+	15.7463i	0.625861	+	1.08402i	−0.362513	+	0.931979i	$0.618081\pi$
$212$	−2.24872	−	1.29830i	−0.154443	−	0.0891675i
$213$		0			0
$214$	9.59267	−	16.6150i	0.655741	−	1.13578i
$215$	22.9114	−	6.98378i	1.56255	−	0.476290i
$216$		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	$-0.667203\pi$
$223$	−0.0435655	+	0.0251526i	−0.00291736	+	0.00168434i	0.498541	+	0.866866i	$0.333869\pi$
$224$	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	$-0.492263\pi$
$227$	−12.4948	−	7.21390i	−0.829312	−	0.478804i	−0.853617	+	0.520901i	$0.825596\pi$
$228$		0			0
$229$	−16.7880			−1.10938			−0.554691	−	0.832057i	$-0.687163\pi$
$229$	−16.7880			−1.10938			−0.554691	+	0.832057i	$0.687163\pi$
$230$	4.37739	+	14.3607i	0.288637	+	0.946919i
$231$		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	0.438246	+	0.898855i	$0.355600\pi$
$241$	−8.68280	+	15.0390i	−0.559308	+	0.968750i	−0.997554	+	0.0698951i	$0.977734\pi$
$242$		−	16.4434i		−	1.05702i
$243$		0			0
$244$	3.15510	+	5.46479i	0.201984	+	0.349847i
$245$	4.45915	+	1.03340i	0.284885	+	0.0660217i
$246$		0			0
$247$	−13.3439	+	5.82532i	−0.849055	+	0.370656i
$248$			16.4811i			1.04655i
$249$		0			0
$250$	19.4591	+	3.13206i	1.23070	+	0.198089i
$251$	2.80444	−	4.85744i	0.177015	−	0.306599i	−0.763842	−	0.645403i	$-0.776689\pi$
$251$	2.80444	−	4.85744i	0.177015	−	0.306599i	0.940857	+	0.338805i	$0.110023\pi$
$252$		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	$-0.568163\pi$
$257$	8.45618	−	4.88218i	0.527482	−	0.304542i	0.739991	+	0.672617i	$0.234830\pi$
$258$		0			0
$259$	17.4162			1.08219
$260$	−2.97587	+	8.42033i	−0.184556	+	0.522207i
$261$		0			0
$262$	20.6292	−	11.9103i	1.27448	−	0.735820i
$263$	−0.610495	+	0.352470i	−0.0376447	+	0.0217342i	−0.518704	−	0.854954i	$-0.673585\pi$
$263$	−0.610495	+	0.352470i	−0.0376447	+	0.0217342i	0.481060	+	0.876688i	$0.340252\pi$
$264$		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	−0.137973	+	0.990436i	$0.544059\pi$
$269$	−15.1995	+	26.3263i	−0.926729	+	1.60514i	−0.788756	+	0.614706i	$0.789275\pi$
$270$		0			0
$271$	−9.52279	−	16.4940i	−0.578468	−	1.00194i	−0.995655	−	0.0931159i	$-0.970317\pi$
$271$	−9.52279	−	16.4940i	−0.578468	−	1.00194i	0.417187	−	0.908821i	$-0.363016\pi$
$272$		−	30.3879i		−	1.84254i
$273$		0			0
$274$	37.7024			2.27769
$275$	5.36664	−	3.60680i	0.323621	−	0.217498i
$276$		0			0
$277$	10.1366	+	5.85235i	0.609047	+	0.351634i	0.772593	−	0.634902i	$-0.218960\pi$
$277$	10.1366	+	5.85235i	0.609047	+	0.351634i	−0.163545	+	0.986536i	$0.552293\pi$
$278$		−	20.2662i		−	1.21549i
$279$		0			0
$280$	−2.28237	−	7.48767i	−0.136398	−	0.447474i
$281$	−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	$-0.486800\pi$
$283$	15.6024	−	9.00803i	0.927465	−	0.535472i	0.886009	+	0.463668i	$0.153467\pi$
$284$	−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
$290$	−10.4724	+	3.19216i	−0.614960	+	0.187450i
$291$		0			0
$292$	−2.97437	−	1.71725i	−0.174062	−	0.100495i
$293$	17.5440	+	10.1291i	1.02493	+	0.591746i	0.915529	−	0.402251i	$-0.131772\pi$
$293$	17.5440	+	10.1291i	1.02493	+	0.591746i	0.109405	+	0.993997i	$0.465106\pi$
$294$		0			0
$295$	−6.90429	−	22.6506i	−0.401983	−	1.31877i
$296$	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
$305$	−3.71401	−	12.1844i	−0.212664	−	0.697678i
$306$		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
$310$	−9.32457	+	40.2356i	−0.529600	+	2.28523i
$311$	−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
$325$	9.68951	−	15.2024i	0.537477	−	0.843278i
$326$	−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	−0.675809	−	0.737076i	$-0.736206\pi$
$331$	5.46570	−	9.46687i	0.300422	−	0.520346i	0.976232	+	0.216730i	$0.0695391\pi$
$332$	−10.5027	−	6.06371i	−0.576408	−	0.332789i
$333$		0			0
$334$	0.169441	−	0.293480i	0.00927138	−	0.0160585i
$335$	1.07591	−	4.64258i	0.0587834	−	0.253651i
$336$		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
$340$	3.40653	−	14.6992i	0.184745	−	0.797177i
$341$	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	$-0.371203\pi$
$347$	−3.82951	−	2.21097i	−0.205579	−	0.118691i	−0.599255	+	0.800558i	$0.704536\pi$
$348$		0			0
$349$	12.5520	+	21.7407i	0.671893	+	1.16375i	0.977367	+	0.211552i	$0.0678518\pi$
$349$	12.5520	+	21.7407i	0.671893	+	1.16375i	−0.305474	+	0.952200i	$0.598815\pi$
$350$	−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	$-0.656823\pi$
$353$	1.00623	−	0.580945i	0.0535561	−	0.0309206i	0.526539	+	0.850151i	$0.323489\pi$
$354$		0			0
$355$	3.94354	+	12.9374i	0.209301	+	0.686646i
$356$	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	−0.577014	+	0.816734i	$0.695782\pi$
$367$	−30.1312	+	17.3962i	−1.57283	+	0.908076i	−0.995820	+	0.0913414i	$0.970885\pi$
$368$	16.4534	+	9.49937i	0.857692	+	0.495189i
$369$		0			0
$370$	8.99444	+	29.5077i	0.467598	+	1.53403i
$371$	2.60842	−	4.51791i	0.135422	−	0.234558i
$372$		0			0
$373$	−9.47953	−	5.47301i	−0.490831	−	0.283382i	0.234088	−	0.972215i	$-0.424790\pi$
$373$	−9.47953	−	5.47301i	−0.490831	−	0.283382i	−0.724919	+	0.688834i	$0.758123\pi$
$374$	−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	−0.999057	−	0.0434141i	$-0.986177\pi$
$379$	−10.4567	−	18.1116i	−0.537126	−	0.930330i	0.461931	−	0.886916i	$-0.347157\pi$
$380$	−9.74420	−	2.25821i	−0.499867	−	0.115844i
$381$		0			0
$382$		−	34.5388i		−	1.76716i
$383$	−25.6423	−	14.8046i	−1.31026	−	0.756479i	−0.328122	−	0.944636i	$-0.606416\pi$
$383$	−25.6423	−	14.8046i	−1.31026	−	0.756479i	−0.982139	+	0.188156i	$0.939749\pi$
$384$		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	$-0.230725\pi$
$397$	10.9330	+	6.31218i	0.548712	+	0.316799i	−0.199890	+	0.979818i	$0.564059\pi$
$398$			10.8345i			0.543086i
$399$		0			0
$400$	20.7011	−	13.9128i	1.03506	−	0.695639i
$401$	5.05705	+	8.75906i	0.252537	+	0.437407i	0.964224	−	0.265090i	$-0.0854017\pi$
$401$	5.05705	+	8.75906i	0.252537	+	0.437407i	−0.711687	+	0.702497i	$0.752068\pi$
$402$		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	−0.999998	−	0.00185917i	$-0.999408\pi$
$409$	−10.0793	+	17.4579i	−0.498389	+	0.863235i	0.501609	+	0.865094i	$0.332742\pi$
$410$	15.2209	−	4.63959i	0.751708	−	0.229133i
$411$		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	0.999625	−	0.0273900i	$-0.00871961\pi$
$419$	9.74536	+	16.8795i	0.476092	+	0.824615i	−0.523533	+	0.852005i	$0.675386\pi$
$420$		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
$425$	−13.3979	+	27.3536i	−0.649894	+	1.32684i
$426$		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	0.974702	−	0.223509i	$-0.0717511\pi$
$431$	6.09917	+	10.5641i	0.293787	+	0.508854i	−0.680915	+	0.732362i	$0.738418\pi$
$432$		0			0
$433$	16.3475	+	9.43824i	0.785611	+	0.453573i	0.838415	−	0.545032i	$-0.183483\pi$
$433$	16.3475	+	9.43824i	0.785611	+	0.453573i	−0.0528040	+	0.998605i	$0.516816\pi$
$434$	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	−0.974769	−	0.223218i	$-0.928344\pi$
$439$	−14.2622	−	24.7028i	−0.680697	−	1.17900i	0.294072	−	0.955783i	$-0.404990\pi$
$440$	1.02691	−	4.43115i	0.0489562	−	0.211247i
$441$		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
$445$	−1.68748	−	0.391071i	−0.0799942	−	0.0185386i
$446$	−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	−0.969344	−	0.245708i	$-0.920980\pi$
$449$	−5.76109	+	9.97850i	−0.271883	+	0.470914i	0.697461	+	0.716622i	$0.254313\pi$
$450$		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
$455$	−16.9173	−	5.97883i	−0.793096	−	0.280292i
$456$		0			0
$457$	−21.7263	+	12.5437i	−1.01631	+	0.586768i	−0.913034	−	0.407884i	$-0.866267\pi$
$457$	−21.7263	+	12.5437i	−1.01631	+	0.586768i	−0.103279	+	0.994652i	$0.532933\pi$
$458$	−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	−0.990750	−	0.135698i	$-0.956672\pi$
$461$	−8.11294	+	14.0520i	−0.377857	+	0.654468i	0.612893	+	0.790166i	$0.290006\pi$
$462$		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
$470$	3.86705	+	0.896185i	0.178374	+	0.0413379i
$471$		0			0
$472$	−14.4258	−	8.32875i	−0.664002	−	0.383362i
$473$		−	13.8525i		−	0.636940i
$474$		0			0
$475$	18.1329	+	8.88156i	0.831993	+	0.407514i
$476$	−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	0.996869	−	0.0790705i	$-0.0251952\pi$
$479$	9.41008	+	16.2987i	0.429957	+	0.744708i	−0.566912	+	0.823779i	$0.691862\pi$
$480$		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
$485$	19.6291	−	5.98329i	0.891313	−	0.271687i
$486$		0			0
$487$	3.02050	+	1.74388i	0.136872	+	0.0790229i	0.566872	−	0.823806i	$-0.308153\pi$
$487$	3.02050	+	1.74388i	0.136872	+	0.0790229i	−0.430001	+	0.902829i	$0.641487\pi$
$488$	−7.76007	−	4.48028i	−0.351282	−	0.202813i
$489$		0			0
$490$	7.71863	−	2.35277i	0.348692	−	0.106287i
$491$	−14.4283	−	24.9906i	−0.651142	−	1.12781i	−0.982846	−	0.184428i	$-0.940957\pi$
$491$	−14.4283	−	24.9906i	−0.651142	−	1.12781i	0.331704	−	0.943384i	$-0.392377\pi$
$492$		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	$0.512475\pi$
$500$	11.5732	−	4.40926i	0.517569	−	0.197188i
$501$		0			0
$502$		−	9.88775i		−	0.441312i
$503$	3.43700	+	1.98435i	0.153248	+	0.0884779i	0.574663	−	0.818390i	$-0.305133\pi$
$503$	3.43700	+	1.98435i	0.153248	+	0.0884779i	−0.421415	+	0.906868i	$0.638466\pi$
$504$		0			0
$505$	−30.9021	−	7.16154i	−1.37513	−	0.318684i
$506$	8.68268			0.385992
$507$		0			0
$508$		−	7.26503i		−	0.322334i
$509$	−6.93143	−	12.0056i	−0.307230	−	0.532139i	0.670525	−	0.741887i	$-0.266069\pi$
$509$	−6.93143	−	12.0056i	−0.307230	−	0.532139i	−0.977755	+	0.209748i	$0.932736\pi$
$510$		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
$520$	−2.31886	−	12.4679i	−0.101689	−	0.546755i
$521$	−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	$-0.730371\pi$
$523$	−7.87461	+	4.54641i	−0.344333	+	0.198801i	0.317854	+	0.948140i	$0.397038\pi$
$524$	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
$530$	9.00162	+	2.08612i	0.391005	+	0.0906151i
$531$		0			0
$532$			9.95528i			0.431616i
$533$	1.62649	−	14.4634i	0.0704511	−	0.626480i
$534$		0			0
$535$	−5.49403	+	23.7068i	−0.237528	+	1.02494i
$536$	−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
$550$	5.01404	−	10.2368i	0.213799	−	0.436500i
$551$	−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	$-0.706588\pi$
$557$	−5.11331	+	2.95217i	−0.216658	+	0.125088i	0.387744	+	0.921767i	$0.373255\pi$
$558$		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	$-0.526494\pi$
$563$	−23.4366	−	13.5311i	−0.987734	−	0.570269i	−0.904596	+	0.426270i	$0.859828\pi$
$564$		0			0
$565$	2.75562	−	0.839960i	0.115930	−	0.0353374i
$566$	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	−0.763221	−	0.646138i	$-0.776383\pi$
$569$	−22.4507	−	38.8857i	−0.941182	−	1.63018i	−0.177961	−	0.984037i	$-0.556950\pi$
$570$		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
$575$	−10.6223	−	15.8051i	−0.442979	−	0.659117i
$576$		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	$-0.548258\pi$
$587$	15.2529	−	8.80625i	0.629553	−	0.363473i	0.780579	+	0.625057i	$0.214924\pi$
$588$		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
$595$	29.5322	+	6.84407i	1.21070	+	0.280579i
$596$	−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	0.966756	−	0.255702i	$-0.0823066\pi$
$601$	6.42137	+	11.1221i	0.261933	+	0.453682i	−0.704822	+	0.709384i	$0.748973\pi$
$602$	−36.3951	−	21.0127i	−1.48336	−	0.856416i
$603$		0			0
$604$	3.17753	−	5.50364i	0.129292	−	0.223940i
$605$	6.08137	+	19.9509i	0.247243	+	0.811119i
$606$		0			0
$607$	−11.6146	−	6.70567i	−0.471421	−	0.272175i	0.245414	−	0.969418i	$-0.421076\pi$
$607$	−11.6146	−	6.70567i	−0.471421	−	0.272175i	−0.716834	+	0.697244i	$0.754410\pi$
$608$	−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	0.583490	−	0.812120i	$-0.301687\pi$
$613$	39.0831	−	22.5646i	1.57855	−	0.911377i	0.995062	−	0.0992571i	$-0.0316466\pi$
$614$	−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	$-0.369418\pi$
$617$	−4.86681	−	2.80985i	−0.195930	−	0.113120i	−0.594756	+	0.803906i	$0.702751\pi$
$618$		0			0
$619$	6.91332			0.277870			0.138935	−	0.990302i	$-0.455632\pi$
$619$	6.91332			0.277870			0.138935	+	0.990302i	$0.455632\pi$
$620$	7.56704	+	24.8249i	0.303900	+	0.996991i
$621$		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	−0.248498	−	0.968632i	$-0.579937\pi$
$631$	17.9508	−	31.0918i	0.714612	−	1.23774i	0.963109	−	0.269111i	$-0.0867298\pi$
$632$		−	12.6241i		−	0.502159i
$633$		0			0
$634$	14.8923	+	25.7942i	0.591449	+	1.02442i
$635$	−3.31093	+	14.2867i	−0.131390	+	0.566951i
$636$		0			0
$637$	0.824803	−	7.33449i	0.0326799	−	0.290603i
$638$			6.33174i			0.250676i
$639$		0			0
$640$	5.72043	−	24.6837i	0.226120	−	0.975711i
$641$	−4.14055	+	7.17165i	−0.163542	+	0.283263i	−0.936137	−	0.351637i	$-0.885625\pi$
$641$	−4.14055	+	7.17165i	−0.163542	+	0.283263i	0.772595	+	0.634900i	$0.218959\pi$
$642$		0			0
$643$	−27.4964	−	15.8750i	−1.08435	−	0.626051i	−0.152284	−	0.988337i	$-0.548663\pi$
$643$	−27.4964	−	15.8750i	−1.08435	−	0.626051i	−0.932067	+	0.362286i	$0.881996\pi$
$644$	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	$-0.856673\pi$
$647$	−24.7643	+	14.2977i	−0.973585	+	0.562099i	−0.0732574	+	0.997313i	$0.523339\pi$
$648$		0			0
$649$	−13.6948			−0.537570
$650$	1.39294	−	31.7501i	0.0546356	−	1.24534i
$651$		0			0
$652$	−16.7233	+	9.65519i	−0.654934	+	0.378127i
$653$	−10.5361	+	6.08300i	−0.412308	+	0.238046i	−0.691781	−	0.722107i	$-0.743174\pi$
$653$	−10.5361	+	6.08300i	−0.412308	+	0.238046i	0.279473	+	0.960154i	$0.409840\pi$
$654$		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	−0.821832	−	0.569729i	$-0.807048\pi$
$659$	2.11744	−	3.66752i	0.0824838	−	0.142866i	0.904316	+	0.426863i	$0.140381\pi$
$660$		0			0
$661$	3.38031	+	5.85487i	0.131479	+	0.227728i	0.924247	−	0.381796i	$-0.124694\pi$
$661$	3.38031	+	5.85487i	0.131479	+	0.227728i	−0.792768	+	0.609523i	$0.791361\pi$
$662$		−	19.2707i		−	0.748976i
$663$		0			0
$664$	17.2211			0.668308
$665$	4.53697	−	19.5771i	0.175936	−	0.759168i
$666$		0			0
$667$	9.16066	+	5.28891i	0.354702	+	0.204787i
$668$		−	0.212940i		−	0.00823888i
$669$		0			0
$670$	−2.44955	−	8.03614i	−0.0946343	−	0.310463i
$671$	−7.36685			−0.284394
$672$		0			0
$673$	−41.7070	+	24.0796i	−1.60769	+	0.928199i	−0.617803	+	0.786333i	$0.711977\pi$
$673$	−41.7070	+	24.0796i	−1.60769	+	0.928199i	−0.989886	+	0.141866i	$0.954690\pi$
$674$	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
$680$	6.24730	+	20.4953i	0.239573	+	0.785958i
$681$		0			0
$682$	20.6864	+	11.9433i	0.792125	+	0.457334i
$683$	−11.7725	−	6.79684i	−0.450461	−	0.260074i	0.257564	−	0.966261i	$-0.417080\pi$
$683$	−11.7725	−	6.79684i	−0.450461	−	0.260074i	−0.708025	+	0.706187i	$0.750414\pi$
$684$		0			0
$685$	−45.7447	+	13.9437i	−1.74781	+	0.532763i
$686$	−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	0.895817	−	0.444424i	$-0.146591\pi$
$691$	1.65676	+	2.86960i	0.0630263	+	0.109165i	−0.832790	+	0.553588i	$0.813258\pi$
$692$	−5.74334	+	3.31592i	−0.218329	+	0.126052i
$693$		0			0
$694$	−7.79531			−0.295906
$695$	7.49520	+	24.5892i	0.284309	+	0.932722i
$696$		0			0
$697$			24.5905i			0.931431i
$698$	38.3261	+	22.1276i	1.45066	+	0.837541i
$699$		0			0
$700$	−6.87567	−	10.2305i	−0.259876	−	0.386675i
$701$	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	−0.939983	−	0.341220i	$-0.889160\pi$
$709$	−4.64606	+	8.04722i	−0.174487	+	0.302220i	0.765497	+	0.643440i	$0.222493\pi$
$710$	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
$715$	−6.77623	−	7.92391i	−0.253417	−	0.296337i
$716$	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	0.337142	+	0.941454i	$0.390540\pi$
$719$	−17.3421	+	30.0374i	−0.646752	+	1.12021i	−0.983894	+	0.178754i	$0.942793\pi$
$720$		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
$725$	11.5257	−	7.74615i	0.428052	−	0.287685i
$726$		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
$730$	11.9064	+	2.75930i	0.440676	+	0.102126i
$731$	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	0.922756	−	0.385385i	$-0.125931\pi$
$739$	3.46941	+	6.00919i	0.127624	+	0.221052i	−0.795131	+	0.606437i	$0.792598\pi$
$740$	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	$-0.498668\pi$
$743$	23.7770	−	13.7277i	0.872294	−	0.503619i	0.868110	+	0.496372i	$0.165335\pi$
$744$		0			0
$745$	9.43206	+	30.9434i	0.345564	+	1.13368i
$746$	−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	0.995187	+	0.0979897i	$0.0312412\pi$
$751$	15.9618	+	27.6467i	0.582455	+	1.00884i	−0.412732	+	0.910852i	$0.635425\pi$
$752$	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	$-0.743086\pi$
$757$	−11.3313	+	6.54213i	−0.411843	+	0.237778i	0.279738	+	0.960076i	$0.409752\pi$
$758$	−31.9284	−	18.4339i	−1.15969	−	0.669549i
$759$		0			0
$760$	13.5864	−	4.14138i	0.492832	−	0.150223i
$761$	−16.9704	+	29.3936i	−0.615177	+	1.06552i	0.375176	+	0.926954i	$0.377582\pi$
$761$	−16.9704	+	29.3936i	−0.615177	+	1.06552i	−0.990353	+	0.138565i	$0.955751\pi$
$762$		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	0.699163	−	0.714962i	$-0.253556\pi$
$769$	−7.47606	−	12.9489i	−0.269594	−	0.466950i	−0.968757	+	0.248012i	$0.920223\pi$
$770$	−11.0522	−	2.56133i	−0.398292	−	0.0923039i
$771$		0			0
$772$		−	22.8514i		−	0.822440i
$773$	12.3714	+	7.14260i	0.444967	+	0.256902i	0.705702	−	0.708509i	$-0.250632\pi$
$773$	12.3714	+	7.14260i	0.444967	+	0.256902i	−0.260735	+	0.965410i	$0.583965\pi$
$774$		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	$-0.161379\pi$
$787$	24.9907	+	14.4284i	0.890822	+	0.514316i	0.0166107	+	0.999862i	$0.494712\pi$
$788$			2.11549i			0.0753611i
$789$		0			0
$790$	7.14236	−	30.8194i	0.254114	−	1.09650i
$791$	−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	$-0.302198\pi$
$797$	4.77532	+	2.75703i	0.169150	+	0.0976590i	−0.413035	+	0.910715i	$0.635531\pi$
$798$		0			0
$799$	−3.06721	+	5.31256i	−0.108510	+	0.187945i
$800$	12.4219	−	25.3610i	0.439181	−	0.896647i
$801$		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	−0.948413	−	0.317039i	$-0.897311\pi$
$809$	−21.2972	−	36.8878i	−0.748770	−	1.29691i	0.199643	−	0.979869i	$-0.436022\pi$
$810$		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
$815$	37.2866	−	11.3656i	1.30609	−	0.398119i
$816$		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	0.987862	+	0.155336i	$0.0496459\pi$
$821$	18.0072	+	31.1894i	0.628455	+	1.08852i	−0.359406	+	0.933181i	$0.617021\pi$
$822$		0			0
$823$	−30.1737	−	17.4208i	−1.05179	−	0.607250i	−0.128639	−	0.991692i	$-0.541061\pi$
$823$	−30.1737	−	17.4208i	−1.05179	−	0.607250i	−0.923149	+	0.384441i	$0.874394\pi$
$824$	−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	0.856018	−	0.516947i	$-0.172931\pi$
$829$	−0.566635	−	0.981440i	−0.0196800	−	0.0340868i	−0.875698	+	0.482860i	$0.839598\pi$
$830$	42.0421	+	9.74321i	1.45930	+	0.338192i
$831$		0			0
$832$	−0.0585195	−	0.0431700i	−0.00202880	−	0.00149665i
$833$			12.4700i			0.432060i
$834$		0			0
$835$	−0.0970441	+	0.418747i	−0.00335835	+	0.0144913i
$836$	−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	−0.325394	−	0.945578i	$-0.605497\pi$
$839$	19.0071	−	32.9213i	0.656198	−	1.13657i	0.981592	−	0.190989i	$-0.0611696\pi$
$840$		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
$845$	−26.1535	−	12.6884i	−0.899707	−	0.436495i
$846$		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	$0.416046\pi$
$860$	5.99008	−	25.8473i	0.204260	−	0.881384i
$861$		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
$865$	12.8055	−	3.90333i	0.435400	−	0.132717i
$866$	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
$875$	8.85866	+	23.2517i	0.299477	+	0.786052i
$876$		0			0
$877$	−17.8455	−	10.3031i	−0.602600	−	0.347911i	0.167464	−	0.985878i	$-0.446442\pi$
$877$	−17.8455	−	10.3031i	−0.602600	−	0.347911i	−0.770064	+	0.637967i	$0.779776\pi$
$878$	−43.5479	−	25.1424i	−1.46967	−	0.848515i
$879$		0			0
$880$	−4.20592	−	13.7982i	−0.141782	−	0.465137i
$881$	−2.79747	−	4.84536i	−0.0942492	−	0.163244i	0.815046	−	0.579397i	$-0.196712\pi$
$881$	−2.79747	−	4.84536i	−0.0942492	−	0.163244i	−0.909295	+	0.416152i	$0.863378\pi$
$882$		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	$-0.615609\pi$
$887$	8.23896	−	4.75676i	0.276637	−	0.159716i	0.631900	+	0.775050i	$0.282275\pi$
$888$		0			0
$889$	14.5962			0.489541
$890$	−2.92097	+	0.890359i	−0.0979110	+	0.0298449i
$891$		0			0
$892$			0.0557240i			0.00186578i
$893$	3.52173	+	2.03327i	0.117850	+	0.0680408i
$894$		0			0
$895$	−22.6608	−	5.25162i	−0.757468	−	0.175542i
$896$	−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	$-0.907719\pi$
$907$	−35.8337	+	20.6886i	−1.18984	+	0.686953i	−0.231568	+	0.972819i	$0.574386\pi$
$908$	−13.8408	+	7.99098i	−0.459323	+	0.265190i
$909$		0			0
$910$	−31.0975	+	5.78370i	−1.03087	+	0.191728i
$911$	−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	−0.817168	−	0.576400i	$-0.804457\pi$
$919$	2.74632	−	4.75677i	0.0905929	−	0.156911i	0.907761	+	0.419488i	$0.137790\pi$
$920$	−13.0500	−	3.02433i	−0.430246	−	0.0997091i
$921$		0			0
$922$			28.6041i			0.942027i
$923$	19.9870	−	8.72535i	0.657880	−	0.287198i
$924$		0			0
$925$	−21.8261	−	32.4755i	−0.717636	−	1.06779i
$926$	−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	−0.465145	−	0.885235i	$-0.653998\pi$
$929$	16.2780	−	28.1943i	0.534063	−	0.925025i	0.999208	−	0.0397900i	$-0.0126689\pi$
$930$		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
$940$	2.38592	−	0.727269i	0.0778202	−	0.0237209i
$941$	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	$-0.850733\pi$
$947$	−29.1327	+	16.8198i	−0.946686	+	0.546569i	−0.0546360	+	0.998506i	$0.517400\pi$
$948$		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	$-0.275453\pi$
$953$	9.66930	+	5.58257i	0.313219	+	0.180837i	−0.335147	+	0.942166i	$0.608786\pi$
$954$		0			0
$955$	12.7737	+	41.9062i	0.413348	+	1.35605i
$956$	−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
$965$	−10.4142	+	44.9374i	−0.335245	+	1.44659i
$966$		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	0.460926	+	0.887439i	$0.347517\pi$
$971$	−16.7671	+	29.0415i	−0.538082	+	0.931985i	−0.999007	+	0.0445460i	$0.985816\pi$
$972$		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	$-0.616879\pi$
$977$	8.43350	−	4.86908i	0.269811	−	0.155776i	0.628802	+	0.777565i	$0.283546\pi$
$978$		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
$985$	0.964103	−	4.16012i	0.0307189	−	0.132552i
$986$	−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	0.561871	−	0.827225i	$-0.310082\pi$
$991$	−13.7084	−	23.7437i	−0.435463	−	0.754244i	−0.997333	+	0.0729816i	$0.976749\pi$
$992$	51.2492	+	29.5887i	1.62716	+	0.939443i
$993$		0			0
$994$	11.8653	−	20.5513i	0.376344	−	0.651847i
$995$	−4.00701	−	13.1456i	−0.127031	−	0.416744i
$996$		0			0
$997$	−23.1116	−	13.3435i	−0.731951	−	0.422592i	0.0871844	−	0.996192i	$-0.472213\pi$
$997$	−23.1116	−	13.3435i	−0.731951	−	0.422592i	−0.819136	+	0.573600i	$0.805546\pi$
$998$	−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.289.10		24
3.2	odd	2		195.2.ba.a.94.3	✓	24
5.4	even	2	inner	585.2.bs.b.289.3		24
13.9	even	3	inner	585.2.bs.b.334.3		24
15.2	even	4		975.2.i.q.601.2		12
15.8	even	4		975.2.i.o.601.5		12
15.14	odd	2		195.2.ba.a.94.10	yes	24
39.35	odd	6		195.2.ba.a.139.10	yes	24
65.9	even	6	inner	585.2.bs.b.334.10		24
195.74	odd	6		195.2.ba.a.139.3	yes	24
195.113	even	12		975.2.i.o.451.5		12
195.152	even	12		975.2.i.q.451.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.ba.a.94.3	✓	24	3.2	odd	2
195.2.ba.a.94.10	yes	24	15.14	odd	2
195.2.ba.a.139.3	yes	24	195.74	odd	6
195.2.ba.a.139.10	yes	24	39.35	odd	6
585.2.bs.b.289.3		24	5.4	even	2	inner
585.2.bs.b.289.10		24	1.1	even	1	trivial
585.2.bs.b.334.3		24	13.9	even	3	inner
585.2.bs.b.334.10		24	65.9	even	6	inner
975.2.i.o.451.5		12	195.113	even	12
975.2.i.o.601.5		12	15.8	even	4
975.2.i.q.451.2		12	195.152	even	12
975.2.i.q.601.2		12	15.2	even	4

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)

\(f(q)\)	\(=\)	\(q+(1.52669 - 0.881436i) q^{2} +(0.553860 - 0.959313i) q^{4} +(-1.52636 + 1.63408i) q^{5} +(1.92736 + 1.11276i) q^{7} +1.57298i q^{8} +O(q^{10})\)	\(q+(1.52669 - 0.881436i) q^{2} +(0.553860 - 0.959313i) q^{4} +(-1.52636 + 1.63408i) q^{5} +(1.92736 + 1.11276i) q^{7} +1.57298i q^{8} +(-0.889946 + 3.84013i) q^{10} +(0.646605 + 1.11995i) q^{11} +(2.90148 + 2.14043i) q^{13} +3.92332 q^{14} +(2.49420 + 4.32008i) q^{16} +(-5.27558 - 3.04586i) q^{17} +(-2.01912 + 3.49721i) q^{19} +(0.722206 + 2.36931i) q^{20} +(1.97434 + 1.13988i) q^{22} +(3.29833 - 1.90429i) q^{23} +(-0.340442 - 4.98840i) q^{25} +(6.31631 + 0.710304i) q^{26} +(2.13497 - 1.23263i) q^{28} +(1.38868 + 2.40527i) q^{29} +10.4777 q^{31} +(4.89127 + 2.82398i) q^{32} -10.7389 q^{34} +(-4.76019 + 1.45099i) q^{35} +(6.77724 - 3.91284i) q^{37} +7.11889i q^{38} +(-2.57037 - 2.40093i) q^{40} +(-2.01836 - 3.49590i) q^{41} +(-9.27663 - 5.35587i) q^{43} +1.43252 q^{44} +(3.35702 - 5.81454i) q^{46} -1.00701i q^{47} +(-1.02352 - 1.77279i) q^{49} +(-4.91670 - 7.31567i) q^{50} +(3.66035 - 1.59793i) q^{52} -2.34409i q^{53} +(-2.81705 - 0.652848i) q^{55} +(-1.75035 + 3.03169i) q^{56} +(4.24018 + 2.44807i) q^{58} +(-5.29490 + 9.17104i) q^{59} +(-2.84828 + 4.93336i) q^{61} +(15.9962 - 9.23541i) q^{62} -0.0201689 q^{64} +(-7.92633 + 1.47419i) q^{65} +(-1.84572 + 1.06562i) q^{67} +(-5.84386 + 3.37395i) q^{68} +(-5.98840 + 6.41101i) q^{70} +(3.02430 - 5.23824i) q^{71} -3.10052i q^{73} +(6.89784 - 11.9474i) q^{74} +(2.23662 + 3.87393i) q^{76} +2.87807i q^{77} -8.02561 q^{79} +(-10.8664 - 2.51828i) q^{80} +(-6.16282 - 3.55811i) q^{82} -10.9481i q^{83} +(13.0296 - 3.97164i) q^{85} -18.8834 q^{86} +(-1.76166 + 1.01709i) q^{88} +(0.387332 + 0.670879i) q^{89} +(3.21041 + 7.35403i) q^{91} -4.21884i q^{92} +(-0.887616 - 1.53740i) q^{94} +(-2.63283 - 8.63741i) q^{95} +(-7.94767 - 4.58859i) q^{97} +(-3.12521 - 1.80434i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{4} - 4 q^{5}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more