LMFDB - Embedded newform 572.2.n.b.157.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(53,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6, 0]))

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

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

chi := DirichletCharacter("572.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.n (of order $5$, degree $4$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			157.3
Character	$\chi$	$=$	572.157
Dual form			572.2.n.b.521.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.344293 - 1.05962i) q^{3} +(-0.665019 - 0.483164i) q^{5} +(0.816463 - 2.51281i) q^{7} +(1.42278 - 1.03371i) q^{9} +O(q^{10})$	\(q+(-0.344293 - 1.05962i) q^{3} +(-0.665019 - 0.483164i) q^{5} +(0.816463 - 2.51281i) q^{7} +(1.42278 - 1.03371i) q^{9} +(-3.22808 + 0.761259i) q^{11} +(0.809017 - 0.587785i) q^{13} +(-0.283012 + 0.871020i) q^{15} +(-4.38847 - 3.18841i) q^{17} +(1.81880 + 5.59770i) q^{19} -2.94374 q^{21} -2.27004 q^{23} +(-1.33628 - 4.11266i) q^{25} +(-4.28931 - 3.11637i) q^{27} +(2.34871 - 7.22859i) q^{29} +(-0.936910 + 0.680705i) q^{31} +(1.91805 + 3.15845i) q^{33} +(-1.75706 + 1.27658i) q^{35} +(0.433715 - 1.33484i) q^{37} +(-0.901370 - 0.654884i) q^{39} +(-1.26655 - 3.89804i) q^{41} -2.44419 q^{43} -1.44563 q^{45} +(-1.84411 - 5.67559i) q^{47} +(0.0154974 + 0.0112595i) q^{49} +(-1.86760 + 5.74788i) q^{51} +(-7.23696 + 5.25796i) q^{53} +(2.51454 + 1.05344i) q^{55} +(5.30526 - 3.85449i) q^{57} +(1.80514 - 5.55566i) q^{59} +(8.67192 + 6.30052i) q^{61} +(-1.43588 - 4.41918i) q^{63} -0.822008 q^{65} +3.00745 q^{67} +(0.781557 + 2.40539i) q^{69} +(7.89179 + 5.73372i) q^{71} +(1.32545 - 4.07931i) q^{73} +(-3.89780 + 2.83192i) q^{75} +(-0.722703 + 8.73310i) q^{77} +(-11.2040 + 8.14017i) q^{79} +(-0.195035 + 0.600256i) q^{81} +(3.92464 + 2.85142i) q^{83} +(1.37789 + 4.24071i) q^{85} -8.46824 q^{87} +14.1357 q^{89} +(-0.816463 - 2.51281i) q^{91} +(1.04386 + 0.758411i) q^{93} +(1.49507 - 4.60135i) q^{95} +(2.15987 - 1.56924i) q^{97} +(-3.80593 + 4.42001i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9}+O(q^{10}) $ 28 * q + q^3 - 7 * q^5 + 11 * q^7 - 22 * q^9	$ 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9} + q^{11} + 7 q^{13} - 24 q^{15} + 7 q^{17} - 7 q^{19} - 12 q^{21} + 34 q^{23} - 26 q^{25} - 11 q^{27} + 8 q^{29} - 17 q^{31} - 2 q^{33} - 6 q^{35} - 15 q^{37} + 4 q^{39} + 29 q^{41} - 8 q^{43} + 62 q^{45} - 27 q^{47} - 4 q^{49} + 69 q^{51} - 32 q^{53} + 19 q^{55} + 9 q^{57} - 37 q^{59} - 19 q^{61} + 46 q^{63} - 18 q^{65} + 10 q^{67} - 32 q^{69} - 27 q^{71} - 79 q^{75} + 13 q^{77} + 21 q^{79} - 18 q^{81} + 27 q^{83} + 7 q^{85} + 56 q^{87} + 82 q^{89} - 11 q^{91} - 53 q^{93} + 51 q^{95} - 88 q^{97} + 86 q^{99}+O(q^{100}) $ 28 * q + q^3 - 7 * q^5 + 11 * q^7 - 22 * q^9 + q^11 + 7 * q^13 - 24 * q^15 + 7 * q^17 - 7 * q^19 - 12 * q^21 + 34 * q^23 - 26 * q^25 - 11 * q^27 + 8 * q^29 - 17 * q^31 - 2 * q^33 - 6 * q^35 - 15 * q^37 + 4 * q^39 + 29 * q^41 - 8 * q^43 + 62 * q^45 - 27 * q^47 - 4 * q^49 + 69 * q^51 - 32 * q^53 + 19 * q^55 + 9 * q^57 - 37 * q^59 - 19 * q^61 + 46 * q^63 - 18 * q^65 + 10 * q^67 - 32 * q^69 - 27 * q^71 - 79 * q^75 + 13 * q^77 + 21 * q^79 - 18 * q^81 + 27 * q^83 + 7 * q^85 + 56 * q^87 + 82 * q^89 - 11 * q^91 - 53 * q^93 + 51 * q^95 - 88 * q^97 + 86 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	−0.344293	−	1.05962i	−0.198778	−	0.611775i	−0.999912	−	0.0132896i	$-0.995770\pi$
$3$	−0.344293	−	1.05962i	−0.198778	−	0.611775i	0.801134	−	0.598485i	$-0.204230\pi$
$4$		0			0
$5$	−0.665019	−	0.483164i	−0.297405	−	0.216078i	0.429068	−	0.903272i	$-0.358842\pi$
$5$	−0.665019	−	0.483164i	−0.297405	−	0.216078i	−0.726473	+	0.687195i	$0.758842\pi$
$6$		0			0
$7$	0.816463	−	2.51281i	0.308594	−	0.949754i	−0.669718	−	0.742616i	$-0.733585\pi$
$7$	0.816463	−	2.51281i	0.308594	−	0.949754i	0.978312	−	0.207139i	$-0.0664151\pi$
$8$		0			0
$9$	1.42278	−	1.03371i	0.474261	−	0.344571i
$10$		0			0
$11$	−3.22808	+	0.761259i	−0.973302	+	0.229528i
$11$	−3.22808	+	0.761259i	−0.973302	+	0.229528i
$12$		0			0
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i
$14$		0			0
$15$	−0.283012	+	0.871020i	−0.0730733	+	0.224896i
$16$		0			0
$17$	−4.38847	−	3.18841i	−1.06436	−	0.773304i	−0.0894707	−	0.995989i	$-0.528518\pi$
$17$	−4.38847	−	3.18841i	−1.06436	−	0.773304i	−0.974890	+	0.222686i	$0.928518\pi$
$18$		0			0
$19$	1.81880	+	5.59770i	0.417262	+	1.28420i	0.910212	+	0.414142i	$0.135918\pi$
$19$	1.81880	+	5.59770i	0.417262	+	1.28420i	−0.492950	+	0.870057i	$0.664082\pi$
$20$		0			0
$21$	−2.94374			−0.642377
$22$		0			0
$23$	−2.27004			−0.473335			−0.236668	−	0.971591i	$-0.576055\pi$
$23$	−2.27004			−0.473335			−0.236668	+	0.971591i	$0.576055\pi$
$24$		0			0
$25$	−1.33628	−	4.11266i	−0.267257	−	0.822531i
$26$		0			0
$27$	−4.28931	−	3.11637i	−0.825479	−	0.599746i
$28$		0			0
$29$	2.34871	−	7.22859i	0.436145	−	1.34232i	−0.455764	−	0.890101i	$-0.650634\pi$
$29$	2.34871	−	7.22859i	0.436145	−	1.34232i	0.891909	−	0.452215i	$-0.149366\pi$
$30$		0			0
$31$	−0.936910	+	0.680705i	−0.168274	+	0.122258i	−0.668735	−	0.743501i	$-0.733164\pi$
$31$	−0.936910	+	0.680705i	−0.168274	+	0.122258i	0.500461	+	0.865759i	$0.333164\pi$
$32$		0			0
$33$	1.91805	+	3.15845i	0.333890	+	0.549816i
$34$		0			0
$35$	−1.75706	+	1.27658i	−0.296998	+	0.215782i
$36$		0			0
$37$	0.433715	−	1.33484i	0.0713024	−	0.219446i	−0.909055	−	0.416677i	$-0.863195\pi$
$37$	0.433715	−	1.33484i	0.0713024	−	0.219446i	0.980357	+	0.197230i	$0.0631947\pi$
$38$		0			0
$39$	−0.901370	−	0.654884i	−0.144335	−	0.104865i
$40$		0			0
$41$	−1.26655	−	3.89804i	−0.197802	−	0.608772i	−0.999932	−	0.0116229i	$-0.996300\pi$
$41$	−1.26655	−	3.89804i	−0.197802	−	0.608772i	0.802131	−	0.597149i	$-0.203700\pi$
$42$		0			0
$43$	−2.44419			−0.372736			−0.186368	−	0.982480i	$-0.559672\pi$
$43$	−2.44419			−0.372736			−0.186368	+	0.982480i	$0.559672\pi$
$44$		0			0
$45$	−1.44563			−0.215502
$46$		0			0
$47$	−1.84411	−	5.67559i	−0.268991	−	0.827870i	−0.990747	−	0.135722i	$-0.956665\pi$
$47$	−1.84411	−	5.67559i	−0.268991	−	0.827870i	0.721756	−	0.692148i	$-0.243335\pi$
$48$		0			0
$49$	0.0154974	+	0.0112595i	0.00221391	+	0.00160850i
$50$		0			0
$51$	−1.86760	+	5.74788i	−0.261516	+	0.804864i
$52$		0			0
$53$	−7.23696	+	5.25796i	−0.994073	+	0.722237i	−0.960809	−	0.277210i	$-0.910590\pi$
$53$	−7.23696	+	5.25796i	−0.994073	+	0.722237i	−0.0332640	+	0.999447i	$0.510590\pi$
$54$		0			0
$55$	2.51454	+	1.05344i	0.339061	+	0.142046i
$56$		0			0
$57$	5.30526	−	3.85449i	0.702698	−	0.510540i
$58$		0			0
$59$	1.80514	−	5.55566i	0.235010	−	0.723285i	−0.762111	−	0.647447i	$-0.775837\pi$
$59$	1.80514	−	5.55566i	0.235010	−	0.723285i	0.997120	−	0.0758381i	$-0.0241632\pi$
$60$		0			0
$61$	8.67192	+	6.30052i	1.11033	+	0.806699i	0.982715	−	0.185126i	$-0.0592692\pi$
$61$	8.67192	+	6.30052i	1.11033	+	0.806699i	0.127611	+	0.991824i	$0.459269\pi$
$62$		0			0
$63$	−1.43588	−	4.41918i	−0.180904	−	0.556764i
$64$		0			0
$65$	−0.822008			−0.101958
$66$		0			0
$67$	3.00745			0.367419			0.183709	−	0.982981i	$-0.441189\pi$
$67$	3.00745			0.367419			0.183709	+	0.982981i	$0.441189\pi$
$68$		0			0
$69$	0.781557	+	2.40539i	0.0940884	+	0.289574i
$70$		0			0
$71$	7.89179	+	5.73372i	0.936583	+	0.680468i	0.947596	−	0.319472i	$-0.103505\pi$
$71$	7.89179	+	5.73372i	0.936583	+	0.680468i	−0.0110125	+	0.999939i	$0.503505\pi$
$72$		0			0
$73$	1.32545	−	4.07931i	0.155132	−	0.477447i	−0.843042	−	0.537847i	$-0.819238\pi$
$73$	1.32545	−	4.07931i	0.155132	−	0.477447i	0.998174	+	0.0604005i	$0.0192378\pi$
$74$		0			0
$75$	−3.89780	+	2.83192i	−0.450079	+	0.327002i
$76$		0			0
$77$	−0.722703	+	8.73310i	−0.0823597	+	0.995229i
$78$		0			0
$79$	−11.2040	+	8.14017i	−1.26055	+	0.915840i	−0.998784	−	0.0492920i	$-0.984303\pi$
$79$	−11.2040	+	8.14017i	−1.26055	+	0.915840i	−0.261762	+	0.965132i	$0.584303\pi$
$80$		0			0
$81$	−0.195035	+	0.600256i	−0.0216706	+	0.0666951i
$82$		0			0
$83$	3.92464	+	2.85142i	0.430785	+	0.312984i	0.781963	−	0.623325i	$-0.214219\pi$
$83$	3.92464	+	2.85142i	0.430785	+	0.312984i	−0.351178	+	0.936309i	$0.614219\pi$
$84$		0			0
$85$	1.37789	+	4.24071i	0.149453	+	0.459969i
$86$		0			0
$87$	−8.46824			−0.907891
$88$		0			0
$89$	14.1357			1.49838			0.749191	−	0.662354i	$-0.230442\pi$
$89$	14.1357			1.49838			0.749191	+	0.662354i	$0.230442\pi$
$90$		0			0
$91$	−0.816463	−	2.51281i	−0.0855885	−	0.263414i
$92$		0			0
$93$	1.04386	+	0.758411i	0.108244	+	0.0786435i
$94$		0			0
$95$	1.49507	−	4.60135i	0.153391	−	0.472089i
$96$		0			0
$97$	2.15987	−	1.56924i	0.219302	−	0.159332i	−0.472710	−	0.881218i	$-0.656724\pi$
$97$	2.15987	−	1.56924i	0.219302	−	0.159332i	0.692012	+	0.721886i	$0.256724\pi$
$98$		0			0
$99$	−3.80593	+	4.42001i	−0.382511	+	0.444228i
$100$		0			0
$101$	10.9506	−	7.95606i	1.08962	−	0.791657i	0.110287	−	0.993900i	$-0.464823\pi$
$101$	10.9506	−	7.95606i	1.08962	−	0.791657i	0.979335	+	0.202243i	$0.0648229\pi$
$102$		0			0
$103$	3.69001	−	11.3567i	0.363588	−	1.11901i	−0.587273	−	0.809389i	$-0.699798\pi$
$103$	3.69001	−	11.3567i	0.363588	−	1.11901i	0.950861	−	0.309619i	$-0.100202\pi$
$104$		0			0
$105$	1.95764	+	1.42231i	0.191046	+	0.138803i
$106$		0			0
$107$	4.84602	+	14.9145i	0.468483	+	1.44184i	0.854549	+	0.519371i	$0.173834\pi$
$107$	4.84602	+	14.9145i	0.468483	+	1.44184i	−0.386066	+	0.922471i	$0.626166\pi$
$108$		0			0
$109$	17.0144			1.62968			0.814840	−	0.579686i	$-0.196825\pi$
$109$	17.0144			1.62968			0.814840	+	0.579686i	$0.196825\pi$
$110$		0			0
$111$	−1.56375			−0.148425
$112$		0			0
$113$	−4.37523	−	13.4656i	−0.411587	−	1.26674i	−0.915268	−	0.402845i	$-0.868021\pi$
$113$	−4.37523	−	13.4656i	−0.411587	−	1.26674i	0.503681	−	0.863890i	$-0.331979\pi$
$114$		0			0
$115$	1.50962	+	1.09680i	0.140772	+	0.102277i
$116$		0			0
$117$	0.543455	−	1.67258i	0.0502425	−	0.154630i
$118$		0			0
$119$	−11.5949	+	8.42420i	−1.06290	+	0.772245i
$120$		0			0
$121$	9.84097	−	4.91481i	0.894634	−	0.446801i
$122$		0			0
$123$	−3.69439	+	2.68413i	−0.333112	+	0.242020i
$124$		0			0
$125$	−2.36851	+	7.28952i	−0.211846	+	0.651994i
$126$		0			0
$127$	6.59879	+	4.79430i	0.585548	+	0.425425i	0.840720	−	0.541470i	$-0.182132\pi$
$127$	6.59879	+	4.79430i	0.585548	+	0.425425i	−0.255172	+	0.966896i	$0.582132\pi$
$128$		0			0
$129$	0.841518	+	2.58993i	0.0740915	+	0.228030i
$130$		0			0
$131$	−9.45929			−0.826462			−0.413231	−	0.910626i	$-0.635600\pi$
$131$	−9.45929			−0.826462			−0.413231	+	0.910626i	$0.635600\pi$
$132$		0			0
$133$	15.5510			1.34844
$134$		0			0
$135$	1.34676	+	4.14489i	0.115910	+	0.356735i
$136$		0			0
$137$	−7.01045	−	5.09339i	−0.598943	−	0.435157i	0.246561	−	0.969127i	$-0.420700\pi$
$137$	−7.01045	−	5.09339i	−0.598943	−	0.435157i	−0.845503	+	0.533970i	$0.820700\pi$
$138$		0			0
$139$	2.20072	−	6.77312i	0.186663	−	0.574488i	−0.813311	−	0.581830i	$-0.802337\pi$
$139$	2.20072	−	6.77312i	0.186663	−	0.574488i	0.999973	+	0.00734172i	$0.00233696\pi$
$140$		0			0
$141$	−5.37908	+	3.90813i	−0.453001	+	0.329124i
$142$		0			0
$143$	−2.16411	+	2.51329i	−0.180972	+	0.210172i
$144$		0			0
$145$	−5.05453	+	3.67233i	−0.419756	+	0.304971i
$146$		0			0
$147$	0.00659522	−	0.0202980i	0.000543964	−	0.00167415i
$148$		0			0
$149$	14.3630	+	10.4353i	1.17666	+	0.854893i	0.991791	−	0.127870i	$-0.0408142\pi$
$149$	14.3630	+	10.4353i	1.17666	+	0.854893i	0.184868	+	0.982763i	$0.440814\pi$
$150$		0			0
$151$	1.79787	+	5.53328i	0.146309	+	0.450292i	0.997177	−	0.0750872i	$-0.0239235\pi$
$151$	1.79787	+	5.53328i	0.146309	+	0.450292i	−0.850868	+	0.525379i	$0.823924\pi$
$152$		0			0
$153$	−9.53975			−0.771243
$154$		0			0
$155$	0.951955			0.0764628
$156$		0			0
$157$	4.93734	+	15.1956i	0.394043	+	1.21274i	0.929705	+	0.368306i	$0.120062\pi$
$157$	4.93734	+	15.1956i	0.394043	+	1.21274i	−0.535662	+	0.844433i	$0.679938\pi$
$158$		0			0
$159$	8.06310	+	5.85819i	0.639445	+	0.464584i
$160$		0			0
$161$	−1.85340	+	5.70418i	−0.146068	+	0.449552i
$162$		0			0
$163$	16.9815	−	12.3378i	1.33010	−	0.966371i	0.330349	−	0.943859i	$-0.392834\pi$
$163$	16.9815	−	12.3378i	1.33010	−	0.966371i	0.999747	−	0.0225123i	$-0.00716649\pi$
$164$		0			0
$165$	0.250512	−	3.02717i	0.0195023	−	0.235664i
$166$		0			0
$167$	−10.5747	+	7.68298i	−0.818296	+	0.594527i	−0.916224	−	0.400666i	$-0.868779\pi$
$167$	−10.5747	+	7.68298i	−0.818296	+	0.594527i	0.0979277	+	0.995194i	$0.468779\pi$
$168$		0			0
$169$	0.309017	−	0.951057i	0.0237705	−	0.0731582i
$170$		0			0
$171$	8.37418	+	6.08420i	0.640389	+	0.465270i
$172$		0			0
$173$	1.70048	+	5.23354i	0.129285	+	0.397898i	0.994657	−	0.103231i	$-0.0329181\pi$
$173$	1.70048	+	5.23354i	0.129285	+	0.397898i	−0.865372	+	0.501129i	$0.832918\pi$
$174$		0			0
$175$	−11.4254			−0.863676
$176$		0			0
$177$	−6.50841			−0.489202
$178$		0			0
$179$	0.945782	+	2.91082i	0.0706911	+	0.217565i	0.980160	−	0.198207i	$-0.0635117\pi$
$179$	0.945782	+	2.91082i	0.0706911	+	0.217565i	−0.909469	+	0.415771i	$0.863512\pi$
$180$		0			0
$181$	−19.7198	−	14.3273i	−1.46576	−	1.06494i	−0.981814	−	0.189844i	$-0.939202\pi$
$181$	−19.7198	−	14.3273i	−1.46576	−	1.06494i	−0.483950	−	0.875096i	$-0.660798\pi$
$182$		0			0
$183$	3.69050	−	11.3582i	0.272810	−	0.839623i
$184$		0			0
$185$	−0.933375	+	0.678137i	−0.0686231	+	0.0498576i
$186$		0			0
$187$	16.5935	+	6.95168i	1.21344	+	0.508357i
$188$		0			0
$189$	−11.3329	+	8.23385i	−0.824349	+	0.598924i
$190$		0			0
$191$	0.885513	−	2.72533i	0.0640735	−	0.197198i	−0.913895	−	0.405951i	$-0.866940\pi$
$191$	0.885513	−	2.72533i	0.0640735	−	0.197198i	0.977968	+	0.208753i	$0.0669404\pi$
$192$		0			0
$193$	17.0948	+	12.4201i	1.23051	+	0.894020i	0.996929	−	0.0783169i	$-0.0249546\pi$
$193$	17.0948	+	12.4201i	1.23051	+	0.894020i	0.233584	+	0.972337i	$0.424955\pi$
$194$		0			0
$195$	0.283012	+	0.871020i	0.0202669	+	0.0623750i
$196$		0			0
$197$	−5.55474			−0.395759			−0.197879	−	0.980226i	$-0.563405\pi$
$197$	−5.55474			−0.395759			−0.197879	+	0.980226i	$0.563405\pi$
$198$		0			0
$199$	−22.4583			−1.59202			−0.796012	−	0.605281i	$-0.793061\pi$
$199$	−22.4583			−1.59202			−0.796012	+	0.605281i	$0.793061\pi$
$200$		0			0
$201$	−1.03544	−	3.18677i	−0.0730346	−	0.224777i
$202$		0			0
$203$	−16.2465	−	11.8038i	−1.14028	−	0.828461i
$204$		0			0
$205$	−1.04111	+	3.20422i	−0.0727146	+	0.223792i
$206$		0			0
$207$	−3.22977	+	2.34657i	−0.224485	+	0.163098i
$208$		0			0
$209$	−10.1325	−	16.6852i	−0.700882	−	1.15414i
$210$		0			0
$211$	18.4177	−	13.3812i	1.26792	−	0.921200i	0.268806	−	0.963194i	$-0.413371\pi$
$211$	18.4177	−	13.3812i	1.26792	−	0.921200i	0.999118	+	0.0419942i	$0.0133711\pi$
$212$		0			0
$213$	3.35851	−	10.3364i	0.230121	−	0.708240i
$214$		0			0
$215$	1.62543	+	1.18095i	0.110854	+	0.0805399i
$216$		0			0
$217$	0.945532	+	2.91005i	0.0641869	+	0.197547i
$218$		0			0
$219$	−4.77887			−0.322926
$220$		0			0
$221$	−5.42445			−0.364888
$222$		0			0
$223$	−2.72527	−	8.38753i	−0.182498	−	0.561670i	0.817399	−	0.576073i	$-0.195415\pi$
$223$	−2.72527	−	8.38753i	−0.182498	−	0.561670i	−0.999896	+	0.0144022i	$0.995415\pi$
$224$		0			0
$225$	−6.15255	−	4.47009i	−0.410170	−	0.298006i
$226$		0			0
$227$	6.72445	−	20.6957i	0.446317	−	1.37362i	−0.434716	−	0.900568i	$-0.643151\pi$
$227$	6.72445	−	20.6957i	0.446317	−	1.37362i	0.881033	−	0.473055i	$-0.156849\pi$
$228$		0			0
$229$	−17.8670	+	12.9811i	−1.18069	+	0.857818i	−0.992249	−	0.124267i	$-0.960342\pi$
$229$	−17.8670	+	12.9811i	−1.18069	+	0.857818i	−0.188436	+	0.982085i	$0.560342\pi$
$230$		0			0
$231$	9.50263	−	2.24095i	0.625227	−	0.147444i
$232$		0			0
$233$	−5.17728	+	3.76151i	−0.339175	+	0.246425i	−0.744314	−	0.667830i	$-0.767223\pi$
$233$	−5.17728	+	3.76151i	−0.339175	+	0.246425i	0.405139	+	0.914255i	$0.367223\pi$
$234$		0			0
$235$	−1.51588	+	4.66538i	−0.0988848	+	0.304336i
$236$		0			0
$237$	12.4830	+	9.06941i	0.810856	+	0.589122i
$238$		0			0
$239$	2.03437	+	6.26114i	0.131592	+	0.404999i	0.995044	−	0.0994314i	$-0.0317024\pi$
$239$	2.03437	+	6.26114i	0.131592	+	0.404999i	−0.863452	+	0.504431i	$0.831702\pi$
$240$		0			0
$241$	12.0626			0.777023			0.388512	−	0.921444i	$-0.372989\pi$
$241$	12.0626			0.777023			0.388512	+	0.921444i	$0.372989\pi$
$242$		0			0
$243$	−15.2025			−0.975238
$244$		0			0
$245$	−0.00486586	−	0.0149756i	−0.000310868	−	0.000956754i
$246$		0			0
$247$	4.76169	+	3.45957i	0.302979	+	0.220127i
$248$		0			0
$249$	1.67021	−	5.14036i	0.105845	−	0.325757i
$250$		0			0
$251$	−13.6640	+	9.92746i	−0.862463	+	0.626616i	−0.928554	−	0.371198i	$-0.878947\pi$
$251$	−13.6640	+	9.92746i	−0.862463	+	0.626616i	0.0660912	+	0.997814i	$0.478947\pi$
$252$		0			0
$253$	7.32785	−	1.72808i	0.460698	−	0.108644i
$254$		0			0
$255$	4.01916	−	2.92009i	0.251690	−	0.182863i
$256$		0			0
$257$	7.94511	−	24.4525i	0.495602	−	1.52531i	−0.320413	−	0.947278i	$-0.603822\pi$
$257$	7.94511	−	24.4525i	0.495602	−	1.52531i	0.816016	−	0.578030i	$-0.196178\pi$
$258$		0			0
$259$	−3.00009	−	2.17969i	−0.186416	−	0.135439i
$260$		0			0
$261$	−4.13058	−	12.7126i	−0.255677	−	0.786892i
$262$		0			0
$263$	15.0580			0.928513			0.464257	−	0.885701i	$-0.346322\pi$
$263$	15.0580			0.928513			0.464257	+	0.885701i	$0.346322\pi$
$264$		0			0
$265$	7.35317			0.451702
$266$		0			0
$267$	−4.86683	−	14.9786i	−0.297845	−	0.916672i
$268$		0			0
$269$	−2.23212	−	1.62173i	−0.136094	−	0.0988784i	0.517655	−	0.855589i	$-0.326805\pi$
$269$	−2.23212	−	1.62173i	−0.136094	−	0.0988784i	−0.653750	+	0.756711i	$0.726805\pi$
$270$		0			0
$271$	0.481193	−	1.48096i	0.0292304	−	0.0899620i	−0.935377	−	0.353652i	$-0.884940\pi$
$271$	0.481193	−	1.48096i	0.0292304	−	0.0899620i	0.964607	+	0.263690i	$0.0849397\pi$
$272$		0			0
$273$	−2.38154	+	1.73029i	−0.144137	+	0.104722i
$274$		0			0
$275$	7.44442	+	12.2587i	0.448916	+	0.739228i
$276$		0			0
$277$	4.11306	−	2.98831i	0.247130	−	0.179550i	−0.457324	−	0.889300i	$-0.651192\pi$
$277$	4.11306	−	2.98831i	0.247130	−	0.179550i	0.704454	+	0.709750i	$0.251192\pi$
$278$		0			0
$279$	−0.629367	+	1.93699i	−0.0376792	+	0.115965i
$280$		0			0
$281$	−11.8487	−	8.60858i	−0.706833	−	0.513545i	0.175317	−	0.984512i	$-0.443905\pi$
$281$	−11.8487	−	8.60858i	−0.706833	−	0.513545i	−0.882151	+	0.470967i	$0.843905\pi$
$282$		0			0
$283$	−3.57418	−	11.0002i	−0.212463	−	0.653894i	−0.999324	−	0.0367634i	$-0.988295\pi$
$283$	−3.57418	−	11.0002i	−0.212463	−	0.653894i	0.786861	−	0.617130i	$-0.211705\pi$
$284$		0			0
$285$	−5.39045			−0.319303
$286$		0			0
$287$	−10.8291			−0.639224
$288$		0			0
$289$	3.83943	+	11.8166i	0.225849	+	0.695092i
$290$		0			0
$291$	−2.40643	−	1.74838i	−0.141068	−	0.102492i
$292$		0			0
$293$	2.02727	−	6.23929i	0.118434	−	0.364503i	−0.874214	−	0.485542i	$-0.838622\pi$
$293$	2.02727	−	6.23929i	0.118434	−	0.364503i	0.992648	+	0.121038i	$0.0386224\pi$
$294$		0			0
$295$	−3.88475	+	2.82243i	−0.226179	+	0.164329i
$296$		0			0
$297$	16.2186	+	6.79460i	0.941099	+	0.394263i
$298$		0			0
$299$	−1.83650	+	1.33429i	−0.106207	+	0.0771642i
$300$		0			0
$301$	−1.99559	+	6.14180i	−0.115024	+	0.354007i
$302$		0			0
$303$	−12.2006	−	8.86428i	−0.700908	−	0.509240i
$304$		0			0
$305$	−2.72280	−	8.37992i	−0.155907	−	0.479833i
$306$		0			0
$307$	−19.9475			−1.13846			−0.569231	−	0.822178i	$-0.692759\pi$
$307$	−19.9475			−1.13846			−0.569231	+	0.822178i	$0.692759\pi$
$308$		0			0
$309$	−13.3043			−0.756854
$310$		0			0
$311$	−3.89513	−	11.9880i	−0.220872	−	0.679775i	−0.998684	−	0.0512782i	$-0.983670\pi$
$311$	−3.89513	−	11.9880i	−0.220872	−	0.679775i	0.777812	−	0.628497i	$-0.216330\pi$
$312$		0			0
$313$	−21.8459	−	15.8720i	−1.23481	−	0.897139i	−0.237565	−	0.971372i	$-0.576349\pi$
$313$	−21.8459	−	15.8720i	−1.23481	−	0.897139i	−0.997241	+	0.0742325i	$0.976349\pi$
$314$		0			0
$315$	−1.18030	+	3.63260i	−0.0665026	+	0.204674i
$316$		0			0
$317$	−11.9749	+	8.70029i	−0.672579	+	0.488657i	−0.870887	−	0.491483i	$-0.836455\pi$
$317$	−11.9749	+	8.70029i	−0.672579	+	0.488657i	0.198309	+	0.980140i	$0.436455\pi$
$318$		0			0
$319$	−2.07899	+	25.1224i	−0.116401	+	1.40659i
$320$		0			0
$321$	14.1353	−	10.2699i	0.788958	−	0.573212i
$322$		0			0
$323$	9.86600	−	30.3644i	0.548959	−	1.68952i
$324$		0			0
$325$	−3.49843	−	2.54176i	−0.194058	−	0.140992i
$326$		0			0
$327$	−5.85792	−	18.0288i	−0.323944	−	0.996996i
$328$		0			0
$329$	−15.7674			−0.869283
$330$		0			0
$331$	35.4378			1.94784			0.973918	−	0.226901i	$-0.0728595\pi$
$331$	35.4378			1.94784			0.973918	+	0.226901i	$0.0728595\pi$
$332$		0			0
$333$	−0.762757	−	2.34753i	−0.0417988	−	0.128644i
$334$		0			0
$335$	−2.00001	−	1.45309i	−0.109272	−	0.0793910i
$336$		0			0
$337$	−0.0800136	+	0.246257i	−0.00435862	+	0.0134145i	−0.953212	−	0.302302i	$-0.902245\pi$
$337$	−0.0800136	+	0.246257i	−0.00435862	+	0.0134145i	0.948854	+	0.315717i	$0.102245\pi$
$338$		0			0
$339$	−12.7621	+	9.27221i	−0.693142	+	0.503597i
$340$		0			0
$341$	2.50622	−	2.91060i	0.135720	−	0.157618i
$342$		0			0
$343$	15.0036	−	10.9008i	0.810120	−	0.588587i
$344$		0			0
$345$	0.642446	−	1.97725i	0.0345881	−	0.106451i
$346$		0			0
$347$	9.27701	+	6.74014i	0.498016	+	0.361830i	0.808259	−	0.588827i	$-0.200410\pi$
$347$	9.27701	+	6.74014i	0.498016	+	0.361830i	−0.310243	+	0.950657i	$0.600410\pi$
$348$		0			0
$349$	4.93847	+	15.1990i	0.264350	+	0.813586i	0.991842	+	0.127470i	$0.0406857\pi$
$349$	4.93847	+	15.1990i	0.264350	+	0.813586i	−0.727492	+	0.686116i	$0.759314\pi$
$350$		0			0
$351$	−5.30188			−0.282994
$352$		0			0
$353$	10.7634			0.572877			0.286439	−	0.958099i	$-0.407529\pi$
$353$	10.7634			0.572877			0.286439	+	0.958099i	$0.407529\pi$
$354$		0			0
$355$	−2.47786	−	7.62606i	−0.131511	−	0.404749i
$356$		0			0
$357$	12.9185	+	9.38586i	0.683721	+	0.496752i
$358$		0			0
$359$	0.939144	−	2.89039i	0.0495661	−	0.152549i	−0.923210	−	0.384296i	$-0.874444\pi$
$359$	0.939144	−	2.89039i	0.0495661	−	0.152549i	0.972776	+	0.231747i	$0.0744442\pi$
$360$		0			0
$361$	−12.6549	+	9.19429i	−0.666045	+	0.483910i
$362$		0			0
$363$	−8.59602	−	8.73560i	−0.451174	−	0.458500i
$364$		0			0
$365$	−2.85242	+	2.07241i	−0.149303	+	0.108475i
$366$		0			0
$367$	−1.39053	+	4.27960i	−0.0725849	+	0.223393i	−0.980767	−	0.195182i	$-0.937470\pi$
$367$	−1.39053	+	4.27960i	−0.0725849	+	0.223393i	0.908182	+	0.418575i	$0.137470\pi$
$368$		0			0
$369$	−5.83148	−	4.23682i	−0.303575	−	0.220560i
$370$		0			0
$371$	7.30357	+	22.4781i	0.379182	+	1.16700i
$372$		0			0
$373$	6.79873			0.352025			0.176012	−	0.984388i	$-0.443680\pi$
$373$	6.79873			0.352025			0.176012	+	0.984388i	$0.443680\pi$
$374$		0			0
$375$	8.53961			0.440984
$376$		0			0
$377$	−2.34871	−	7.22859i	−0.120965	−	0.372291i
$378$		0			0
$379$	6.53318	+	4.74664i	0.335587	+	0.243818i	0.742798	−	0.669516i	$-0.233498\pi$
$379$	6.53318	+	4.74664i	0.335587	+	0.243818i	−0.407210	+	0.913334i	$0.633498\pi$
$380$		0			0
$381$	2.80824	−	8.64288i	0.143871	−	0.442788i
$382$		0			0
$383$	−10.0279	+	7.28572i	−0.512403	+	0.372283i	−0.813735	−	0.581237i	$-0.802569\pi$
$383$	−10.0279	+	7.28572i	−0.512403	+	0.372283i	0.301331	+	0.953520i	$0.402569\pi$
$384$		0			0
$385$	4.70013	−	5.45849i	0.239541	−	0.278190i
$386$		0			0
$387$	−3.47756	+	2.52659i	−0.176774	+	0.128434i
$388$		0			0
$389$	−4.22752	+	13.0110i	−0.214344	+	0.659682i	0.784856	+	0.619678i	$0.212737\pi$
$389$	−4.22752	+	13.0110i	−0.214344	+	0.659682i	−0.999200	+	0.0400034i	$0.987263\pi$
$390$		0			0
$391$	9.96199	+	7.23781i	0.503799	+	0.366032i
$392$		0			0
$393$	3.25677	+	10.0233i	0.164282	+	0.505609i
$394$		0			0
$395$	11.3839			0.572786
$396$		0			0
$397$	−17.7662			−0.891661			−0.445830	−	0.895117i	$-0.647092\pi$
$397$	−17.7662			−0.891661			−0.445830	+	0.895117i	$0.647092\pi$
$398$		0			0
$399$	−5.35408	−	16.4782i	−0.268039	−	0.824941i
$400$		0			0
$401$	−8.08438	−	5.87364i	−0.403714	−	0.293316i	0.367338	−	0.930088i	$-0.380269\pi$
$401$	−8.08438	−	5.87364i	−0.403714	−	0.293316i	−0.771052	+	0.636772i	$0.780269\pi$
$402$		0			0
$403$	−0.357868	+	1.10140i	−0.0178267	+	0.0548648i
$404$		0			0
$405$	0.419724	−	0.304948i	0.0208563	−	0.0151530i
$406$		0			0
$407$	−0.383909	+	4.63913i	−0.0190297	+	0.229953i
$408$		0			0
$409$	−7.93630	+	5.76606i	−0.392425	+	0.285113i	−0.766448	−	0.642306i	$-0.777978\pi$
$409$	−7.93630	+	5.76606i	−0.392425	+	0.285113i	0.374024	+	0.927419i	$0.377978\pi$
$410$		0			0
$411$	−2.98343	+	9.18206i	−0.147162	+	0.452918i
$412$		0			0
$413$	−12.4865	−	9.07197i	−0.614421	−	0.446403i
$414$		0			0
$415$	−1.23225	−	3.79249i	−0.0604890	−	0.186166i
$416$		0			0
$417$	−7.93465			−0.388562
$418$		0			0
$419$	−20.4247			−0.997813			−0.498906	−	0.866656i	$-0.666265\pi$
$419$	−20.4247			−0.997813			−0.498906	+	0.866656i	$0.666265\pi$
$420$		0			0
$421$	5.01182	+	15.4248i	0.244261	+	0.751758i	0.995757	+	0.0920204i	$0.0293325\pi$
$421$	5.01182	+	15.4248i	0.244261	+	0.751758i	−0.751496	+	0.659737i	$0.770668\pi$
$422$		0			0
$423$	−8.49071	−	6.16886i	−0.412832	−	0.299940i
$424$		0			0
$425$	−7.24860	+	22.3089i	−0.351609	+	1.08214i
$426$		0			0
$427$	22.9123	−	16.6468i	1.10881	−	0.805594i
$428$		0			0
$429$	3.40823	+	1.42784i	0.164551	+	0.0689368i
$430$		0			0
$431$	−6.69361	+	4.86319i	−0.322420	+	0.234252i	−0.737207	−	0.675667i	$-0.763856\pi$
$431$	−6.69361	+	4.86319i	−0.322420	+	0.234252i	0.414788	+	0.909918i	$0.363856\pi$
$432$		0			0
$433$	4.01399	−	12.3538i	0.192900	−	0.593686i	−0.807095	−	0.590422i	$-0.798961\pi$
$433$	4.01399	−	12.3538i	0.192900	−	0.593686i	0.999995	−	0.00326332i	$-0.00103875\pi$
$434$		0			0
$435$	5.63154	+	4.09155i	0.270011	+	0.196175i
$436$		0			0
$437$	−4.12875	−	12.7070i	−0.197505	−	0.607857i
$438$		0			0
$439$	8.63283			0.412023			0.206011	−	0.978550i	$-0.433952\pi$
$439$	8.63283			0.412023			0.206011	+	0.978550i	$0.433952\pi$
$440$		0			0
$441$	0.0336886			0.00160422
$442$		0			0
$443$	−1.18264	−	3.63980i	−0.0561890	−	0.172932i	0.919023	−	0.394203i	$-0.128979\pi$
$443$	−1.18264	−	3.63980i	−0.0561890	−	0.172932i	−0.975212	+	0.221271i	$0.928979\pi$
$444$		0			0
$445$	−9.40051	−	6.82987i	−0.445627	−	0.323767i
$446$		0			0
$447$	6.11243	−	18.8121i	0.289108	−	0.889784i
$448$		0			0
$449$	−20.5263	+	14.9133i	−0.968698	+	0.703800i	−0.955154	−	0.296108i	$-0.904311\pi$
$449$	−20.5263	+	14.9133i	−0.968698	+	0.703800i	−0.0135435	+	0.999908i	$0.504311\pi$
$450$		0			0
$451$	7.05594	+	11.6190i	0.332251	+	0.547117i
$452$		0			0
$453$	5.24420	−	3.81014i	0.246394	−	0.179016i
$454$		0			0
$455$	−0.671139	+	2.06555i	−0.0314635	+	0.0968346i
$456$		0			0
$457$	−18.8905	−	13.7247i	−0.883658	−	0.642015i	0.0505585	−	0.998721i	$-0.483900\pi$
$457$	−18.8905	−	13.7247i	−0.883658	−	0.642015i	−0.934217	+	0.356706i	$0.883900\pi$
$458$		0			0
$459$	8.88727	+	27.3522i	0.414822	+	1.27669i
$460$		0			0
$461$	25.4854			1.18697			0.593487	−	0.804844i	$-0.297751\pi$
$461$	25.4854			1.18697			0.593487	+	0.804844i	$0.297751\pi$
$462$		0			0
$463$	23.7754			1.10494			0.552469	−	0.833533i	$-0.313686\pi$
$463$	23.7754			1.10494			0.552469	+	0.833533i	$0.313686\pi$
$464$		0			0
$465$	−0.327751	−	1.00871i	−0.0151991	−	0.0467780i
$466$		0			0
$467$	4.82747	+	3.50736i	0.223388	+	0.162301i	0.693851	−	0.720119i	$-0.255913\pi$
$467$	4.82747	+	3.50736i	0.223388	+	0.162301i	−0.470462	+	0.882420i	$0.655913\pi$
$468$		0			0
$469$	2.45547	−	7.55717i	0.113383	−	0.348958i
$470$		0			0
$471$	14.4017	−	10.4635i	0.663596	−	0.482131i
$472$		0			0
$473$	7.89004	−	1.86066i	0.362785	−	0.0855534i
$474$		0			0
$475$	20.5910	−	14.9602i	0.944779	−	0.686422i
$476$		0			0
$477$	−4.86141	+	14.9619i	−0.222589	+	0.685058i
$478$		0			0
$479$	−1.54062	−	1.11933i	−0.0703929	−	0.0511434i	0.552032	−	0.833823i	$-0.313853\pi$
$479$	−1.54062	−	1.11933i	−0.0703929	−	0.0511434i	−0.622425	+	0.782679i	$0.713853\pi$
$480$		0			0
$481$	−0.433715	−	1.33484i	−0.0197757	−	0.0608634i
$482$		0			0
$483$	6.68240			0.304060
$484$		0			0
$485$	−2.19456			−0.0996497
$486$		0			0
$487$	6.69229	+	20.5967i	0.303256	+	0.933327i	0.980322	+	0.197405i	$0.0632513\pi$
$487$	6.69229	+	20.5967i	0.303256	+	0.933327i	−0.677066	+	0.735923i	$0.736749\pi$
$488$		0			0
$489$	−18.9201	−	13.7462i	−0.855594	−	0.621626i
$490$		0			0
$491$	−10.7951	+	33.2238i	−0.487175	+	1.49937i	0.341631	+	0.939834i	$0.389021\pi$
$491$	−10.7951	+	33.2238i	−0.487175	+	1.49937i	−0.828806	+	0.559536i	$0.810979\pi$
$492$		0			0
$493$	−33.3550	+	24.2338i	−1.50223	+	1.09144i
$494$		0			0
$495$	4.66661	−	1.10050i	0.209749	−	0.0494638i
$496$		0			0
$497$	20.8511	−	15.1492i	0.935301	−	0.679536i
$498$		0			0
$499$	−6.43324	+	19.7995i	−0.287992	+	0.886347i	0.697495	+	0.716590i	$0.254298\pi$
$499$	−6.43324	+	19.7995i	−0.287992	+	0.886347i	−0.985486	+	0.169757i	$0.945702\pi$
$500$		0			0
$501$	11.7819	+	8.56004i	0.526375	+	0.382434i
$502$		0			0
$503$	11.2648	+	34.6694i	0.502272	+	1.54583i	0.805310	+	0.592855i	$0.201999\pi$
$503$	11.2648	+	34.6694i	0.502272	+	1.54583i	−0.303038	+	0.952978i	$0.598001\pi$
$504$		0			0
$505$	−11.1264			−0.495119
$506$		0			0
$507$	−1.11416			−0.0494814
$508$		0			0
$509$	7.35066	+	22.6230i	0.325812	+	1.00275i	0.971073	+	0.238785i	$0.0767490\pi$
$509$	7.35066	+	22.6230i	0.325812	+	1.00275i	−0.645260	+	0.763963i	$0.723251\pi$
$510$		0			0
$511$	−9.16836	−	6.66120i	−0.405584	−	0.294674i
$512$		0			0
$513$	9.64308	−	29.6783i	0.425752	−	1.31033i
$514$		0			0
$515$	−7.94107	+	5.76953i	−0.349926	+	0.254236i
$516$		0			0
$517$	10.2735	+	16.9174i	0.451829	+	0.744027i
$518$		0			0
$519$	4.96012	−	3.60374i	0.217725	−	0.158187i
$520$		0			0
$521$	10.9113	−	33.5814i	0.478032	−	1.47123i	−0.363794	−	0.931480i	$-0.618519\pi$
$521$	10.9113	−	33.5814i	0.478032	−	1.47123i	0.841825	−	0.539750i	$-0.181481\pi$
$522$		0			0
$523$	29.4519	+	21.3981i	1.28784	+	0.935672i	0.999759	−	0.0219341i	$-0.00698240\pi$
$523$	29.4519	+	21.3981i	1.28784	+	0.935672i	0.288082	+	0.957606i	$0.406982\pi$
$524$		0			0
$525$	3.93367	+	12.1066i	0.171680	+	0.528375i
$526$		0			0
$527$	6.28197			0.273647
$528$		0			0
$529$	−17.8469			−0.775954
$530$		0			0
$531$	−3.17463	−	9.77050i	−0.137767	−	0.424004i
$532$		0			0
$533$	−3.31587	−	2.40912i	−0.143626	−	0.104351i
$534$		0			0
$535$	3.98347	−	12.2599i	0.172220	−	0.530040i
$536$		0			0
$537$	2.75875	−	2.00435i	0.119049	−	0.0864940i
$538$		0			0
$539$	−0.0585982	−	0.0245491i	−0.00252400	−	0.00105740i
$540$		0			0
$541$	−10.8112	+	7.85482i	−0.464811	+	0.337705i	−0.795416	−	0.606064i	$-0.792747\pi$
$541$	−10.8112	+	7.85482i	−0.464811	+	0.337705i	0.330605	+	0.943769i	$0.392747\pi$
$542$		0			0
$543$	−8.39216	+	25.8284i	−0.360142	+	1.10840i
$544$		0			0
$545$	−11.3149	−	8.22073i	−0.484675	−	0.352137i
$546$		0			0
$547$	−4.90235	−	15.0879i	−0.209609	−	0.645111i	−0.999493	−	0.0318540i	$-0.989859\pi$
$547$	−4.90235	−	15.0879i	−0.209609	−	0.645111i	0.789883	−	0.613257i	$-0.210141\pi$
$548$		0			0
$549$	18.8512			0.804550
$550$		0			0
$551$	44.7353			1.90579
$552$		0			0
$553$	11.3071	+	34.7997i	0.480827	+	1.47983i
$554$		0			0
$555$	1.03992	+	0.755550i	0.0441424	+	0.0320713i
$556$		0			0
$557$	−12.7487	+	39.2363i	−0.540178	+	1.66250i	0.192008	+	0.981393i	$0.438500\pi$
$557$	−12.7487	+	39.2363i	−0.540178	+	1.66250i	−0.732187	+	0.681104i	$0.761500\pi$
$558$		0			0
$559$	−1.97739	+	1.43666i	−0.0836348	+	0.0607643i
$560$		0			0
$561$	1.65313	−	19.9763i	0.0697953	−	0.843401i
$562$		0			0
$563$	−16.1600	+	11.7410i	−0.681064	+	0.494822i	−0.873711	−	0.486446i	$-0.838293\pi$
$563$	−16.1600	+	11.7410i	−0.681064	+	0.494822i	0.192646	+	0.981268i	$0.438293\pi$
$564$		0			0
$565$	−3.59648	+	11.0688i	−0.151305	+	0.465669i
$566$		0			0
$567$	1.34909	+	0.980174i	0.0566566	+	0.0411634i
$568$		0			0
$569$	7.82436	+	24.0809i	0.328014	+	1.00952i	0.970062	+	0.242859i	$0.0780854\pi$
$569$	7.82436	+	24.0809i	0.328014	+	1.00952i	−0.642047	+	0.766665i	$0.721915\pi$
$570$		0			0
$571$	13.2793			0.555722			0.277861	−	0.960621i	$-0.410375\pi$
$571$	13.2793			0.555722			0.277861	+	0.960621i	$0.410375\pi$
$572$		0			0
$573$	−3.19270			−0.133377
$574$		0			0
$575$	3.03341	+	9.33587i	0.126502	+	0.389333i
$576$		0			0
$577$	25.1210	+	18.2514i	1.04580	+	0.759817i	0.971409	−	0.237412i	$-0.0762991\pi$
$577$	25.1210	+	18.2514i	1.04580	+	0.759817i	0.0743899	+	0.997229i	$0.476299\pi$
$578$		0			0
$579$	7.27504	−	22.3903i	0.302340	−	0.930507i
$580$		0			0
$581$	10.3694	−	7.53381i	0.430195	−	0.312555i
$582$		0			0
$583$	19.3588	−	22.4823i	0.801760	−	0.931122i
$584$		0			0
$585$	−1.16954	+	0.849721i	−0.0483545	+	0.0351316i
$586$		0			0
$587$	11.5908	−	35.6728i	0.478404	−	1.47238i	−0.362908	−	0.931825i	$-0.618216\pi$
$587$	11.5908	−	35.6728i	0.478404	−	1.47238i	0.841312	−	0.540550i	$-0.181784\pi$
$588$		0			0
$589$	−5.51443	−	4.00647i	−0.227218	−	0.165084i
$590$		0			0
$591$	1.91246	+	5.88594i	0.0786680	+	0.242115i
$592$		0			0
$593$	16.4148			0.674077			0.337038	−	0.941491i	$-0.390575\pi$
$593$	16.4148			0.674077			0.337038	+	0.941491i	$0.390575\pi$
$594$		0			0
$595$	11.7811			0.482978
$596$		0			0
$597$	7.73222	+	23.7973i	0.316459	+	0.973959i
$598$		0			0
$599$	10.3995	+	7.55566i	0.424911	+	0.308716i	0.779611	−	0.626264i	$-0.215417\pi$
$599$	10.3995	+	7.55566i	0.424911	+	0.308716i	−0.354700	+	0.934980i	$0.615417\pi$
$600$		0			0
$601$	12.2552	−	37.7177i	0.499902	−	1.53854i	−0.309275	−	0.950973i	$-0.600086\pi$
$601$	12.2552	−	37.7177i	0.499902	−	1.53854i	0.809176	−	0.587566i	$-0.199914\pi$
$602$		0			0
$603$	4.27896	−	3.10884i	0.174253	−	0.126602i
$604$		0			0
$605$	−8.91909	−	1.48637i	−0.362612	−	0.0604295i
$606$		0			0
$607$	−1.64201	+	1.19299i	−0.0666470	+	0.0484219i	−0.620610	−	0.784119i	$-0.713115\pi$
$607$	−1.64201	+	1.19299i	−0.0666470	+	0.0484219i	0.553963	+	0.832541i	$0.313115\pi$
$608$		0			0
$609$	−6.91400	+	21.2791i	−0.280169	+	0.862273i
$610$		0			0
$611$	−4.82795	−	3.50771i	−0.195318	−	0.141907i
$612$		0			0
$613$	−3.36101	−	10.3441i	−0.135750	−	0.417796i	0.859956	−	0.510368i	$-0.170491\pi$
$613$	−3.36101	−	10.3441i	−0.135750	−	0.417796i	−0.995706	+	0.0925727i	$0.970491\pi$
$614$		0			0
$615$	3.75372			0.151365
$616$		0			0
$617$	39.6255			1.59526			0.797630	−	0.603146i	$-0.206087\pi$
$617$	39.6255			1.59526			0.797630	+	0.603146i	$0.206087\pi$
$618$		0			0
$619$	−7.05183	−	21.7033i	−0.283437	−	0.872329i	−0.986863	−	0.161561i	$-0.948347\pi$
$619$	−7.05183	−	21.7033i	−0.283437	−	0.872329i	0.703426	−	0.710769i	$-0.251653\pi$
$620$		0			0
$621$	9.73689	+	7.07427i	0.390728	+	0.283881i
$622$		0			0
$623$	11.5413	−	35.5204i	0.462392	−	1.42310i
$624$		0			0
$625$	−12.3950	+	9.00552i	−0.495801	+	0.360221i
$626$		0			0
$627$	−14.1915	+	16.4813i	−0.566754	+	0.658199i
$628$		0			0
$629$	−6.15937	+	4.47504i	−0.245590	+	0.178432i
$630$		0			0
$631$	5.86825	−	18.0606i	0.233611	−	0.718982i	−0.763691	−	0.645582i	$-0.776615\pi$
$631$	5.86825	−	18.0606i	0.233611	−	0.718982i	0.997303	−	0.0734000i	$-0.0233850\pi$
$632$		0			0
$633$	−20.5201	−	14.9087i	−0.815602	−	0.592569i
$634$		0			0
$635$	−2.07188	−	6.37660i	−0.0822201	−	0.253047i
$636$		0			0
$637$	0.0191558			0.000758982
$638$		0			0
$639$	17.1553			0.678655
$640$		0			0
$641$	6.17871	+	19.0161i	0.244044	+	0.751091i	0.995792	+	0.0916406i	$0.0292111\pi$
$641$	6.17871	+	19.0161i	0.244044	+	0.751091i	−0.751748	+	0.659451i	$0.770789\pi$
$642$		0			0
$643$	−24.9202	−	18.1056i	−0.982756	−	0.714014i	−0.0244332	−	0.999701i	$-0.507778\pi$
$643$	−24.9202	−	18.1056i	−0.982756	−	0.714014i	−0.958323	+	0.285687i	$0.907778\pi$
$644$		0			0
$645$	0.691735	−	2.12894i	0.0272370	−	0.0838269i
$646$		0			0
$647$	18.3869	−	13.3589i	0.722865	−	0.525193i	−0.164433	−	0.986388i	$-0.552579\pi$
$647$	18.3869	−	13.3589i	0.722865	−	0.525193i	0.887298	+	0.461196i	$0.152579\pi$
$648$		0			0
$649$	−1.59785	+	19.3083i	−0.0627210	+	0.757916i
$650$		0			0
$651$	2.75802	−	2.00382i	0.108095	−	0.0785359i
$652$		0			0
$653$	7.63273	−	23.4911i	0.298692	−	0.919278i	−0.683265	−	0.730171i	$-0.739440\pi$
$653$	7.63273	−	23.4911i	0.298692	−	0.919278i	0.981956	−	0.189108i	$-0.0605595\pi$
$654$		0			0
$655$	6.29060	+	4.57039i	0.245794	+	0.178580i
$656$		0			0
$657$	−2.33101	−	7.17410i	−0.0909413	−	0.279888i
$658$		0			0
$659$	−32.1917			−1.25401			−0.627006	−	0.779015i	$-0.715720\pi$
$659$	−32.1917			−1.25401			−0.627006	+	0.779015i	$0.715720\pi$
$660$		0			0
$661$	−49.8811			−1.94015			−0.970075	−	0.242804i	$-0.921933\pi$
$661$	−49.8811			−1.94015			−0.970075	+	0.242804i	$0.921933\pi$
$662$		0			0
$663$	1.86760	+	5.74788i	0.0725316	+	0.223229i
$664$		0			0
$665$	−10.3417	−	7.51367i	−0.401033	−	0.291367i
$666$		0			0
$667$	−5.33166	+	16.4092i	−0.206443	+	0.635365i
$668$		0			0
$669$	−7.94934	+	5.77553i	−0.307339	+	0.223295i
$670$		0			0
$671$	−32.7900	−	13.7370i	−1.26584	−	0.530311i
$672$		0			0
$673$	19.8253	−	14.4040i	0.764211	−	0.555232i	−0.135988	−	0.990710i	$-0.543421\pi$
$673$	19.8253	−	14.4040i	0.764211	−	0.555232i	0.900199	+	0.435479i	$0.143421\pi$
$674$		0			0
$675$	−7.08482	+	21.8048i	−0.272695	+	0.839268i
$676$		0			0
$677$	11.1592	+	8.10762i	0.428882	+	0.311601i	0.781202	−	0.624279i	$-0.214607\pi$
$677$	11.1592	+	8.10762i	0.428882	+	0.311601i	−0.352320	+	0.935880i	$0.614607\pi$
$678$		0			0
$679$	−2.17975	−	6.70859i	−0.0836512	−	0.257452i
$680$		0			0
$681$	−24.2449			−0.929065
$682$		0			0
$683$	−45.8094			−1.75285			−0.876425	−	0.481539i	$-0.840078\pi$
$683$	−45.8094			−1.75285			−0.876425	+	0.481539i	$0.840078\pi$
$684$		0			0
$685$	2.20113	+	6.77439i	0.0841010	+	0.258836i
$686$		0			0
$687$	19.9066	+	14.4630i	0.759485	+	0.551798i
$688$		0			0
$689$	−2.76427	+	8.50756i	−0.105310	+	0.324112i
$690$		0			0
$691$	−24.0663	+	17.4852i	−0.915524	+	0.665167i	−0.942406	−	0.334471i	$-0.891442\pi$
$691$	−24.0663	+	17.4852i	−0.915524	+	0.665167i	0.0268816	+	0.999639i	$0.491442\pi$
$692$		0			0
$693$	7.99927	+	13.1724i	0.303867	+	0.500377i
$694$		0			0
$695$	−4.73605	+	3.44094i	−0.179648	+	0.130522i
$696$		0			0
$697$	−6.87034	+	21.1447i	−0.260233	+	0.800914i
$698$		0			0
$699$	5.76829	+	4.19091i	0.218177	+	0.158515i
$700$		0			0
$701$	−2.48085	−	7.63527i	−0.0937004	−	0.288380i	0.893212	−	0.449635i	$-0.148446\pi$
$701$	−2.48085	−	7.63527i	−0.0937004	−	0.288380i	−0.986913	+	0.161255i	$0.948446\pi$
$702$		0			0
$703$	8.26087			0.311565
$704$		0			0
$705$	5.46546			0.205841
$706$		0			0
$707$	−11.0514	−	34.0126i	−0.415629	−	1.27917i
$708$		0			0
$709$	23.0407	+	16.7400i	0.865312	+	0.628686i	0.929325	−	0.369263i	$-0.120390\pi$
$709$	23.0407	+	16.7400i	0.865312	+	0.628686i	−0.0640132	+	0.997949i	$0.520390\pi$
$710$		0			0
$711$	−7.52625	+	23.1634i	−0.282256	+	0.868696i
$712$		0			0
$713$	2.12682	−	1.54522i	0.0796500	−	0.0578691i
$714$		0			0
$715$	2.65351	−	0.625761i	0.0992355	−	0.0234021i
$716$		0			0
$717$	5.93404	−	4.31133i	0.221611	−	0.161010i
$718$		0			0
$719$	−0.939725	+	2.89218i	−0.0350458	+	0.107860i	−0.967049	−	0.254590i	$-0.918060\pi$
$719$	−0.939725	+	2.89218i	−0.0350458	+	0.107860i	0.932003	+	0.362450i	$0.118060\pi$
$720$		0			0
$721$	−25.5245	−	18.5446i	−0.950582	−	0.690638i
$722$		0			0
$723$	−4.15308	−	12.7819i	−0.154455	−	0.475363i
$724$		0			0
$725$	−32.8673			−1.22066
$726$		0			0
$727$	9.54613			0.354046			0.177023	−	0.984207i	$-0.443353\pi$
$727$	9.54613			0.354046			0.177023	+	0.984207i	$0.443353\pi$
$728$		0			0
$729$	5.81920	+	17.9097i	0.215526	+	0.663321i
$730$		0			0
$731$	10.7263	+	7.79309i	0.396725	+	0.288238i
$732$		0			0
$733$	−10.1545	+	31.2525i	−0.375067	+	1.15434i	0.568367	+	0.822775i	$0.307575\pi$
$733$	−10.1545	+	31.2525i	−0.375067	+	1.15434i	−0.943434	+	0.331561i	$0.892425\pi$
$734$		0			0
$735$	−0.0141932	+	0.0103120i	−0.000523524	+	0.000380363i
$736$		0			0
$737$	−9.70829	+	2.28945i	−0.357609	+	0.0843330i
$738$		0			0
$739$	7.85562	−	5.70744i	0.288974	−	0.209952i	−0.433848	−	0.900986i	$-0.642845\pi$
$739$	7.85562	−	5.70744i	0.288974	−	0.209952i	0.722822	+	0.691034i	$0.242845\pi$
$740$		0			0
$741$	2.02643	−	6.23670i	0.0744427	−	0.229111i
$742$		0			0
$743$	36.1528	+	26.2666i	1.32632	+	0.963627i	0.999830	+	0.0184260i	$0.00586552\pi$
$743$	36.1528	+	26.2666i	1.32632	+	0.963627i	0.326489	+	0.945201i	$0.394134\pi$
$744$		0			0
$745$	−4.50967	−	13.8793i	−0.165221	−	0.508499i
$746$		0			0
$747$	8.53146			0.312150
$748$		0			0
$749$	41.4340			1.51397
$750$		0			0
$751$	−12.8081	−	39.4192i	−0.467373	−	1.43843i	−0.855973	−	0.517020i	$-0.827041\pi$
$751$	−12.8081	−	39.4192i	−0.467373	−	1.43843i	0.388600	−	0.921407i	$-0.372959\pi$
$752$		0			0
$753$	15.2238	+	11.0607i	0.554786	+	0.403075i
$754$		0			0
$755$	1.47786	−	4.54840i	0.0537850	−	0.165533i
$756$		0			0
$757$	−17.3520	+	12.6070i	−0.630669	+	0.458207i	−0.856632	−	0.515928i	$-0.827447\pi$
$757$	−17.3520	+	12.6070i	−0.630669	+	0.458207i	0.225963	+	0.974136i	$0.427447\pi$
$758$		0			0
$759$	−4.35405	−	7.16980i	−0.158042	−	0.260247i
$760$		0			0
$761$	−1.01622	+	0.738329i	−0.0368381	+	0.0267644i	−0.606052	−	0.795425i	$-0.707248\pi$
$761$	−1.01622	+	0.738329i	−0.0368381	+	0.0267644i	0.569214	+	0.822190i	$0.307248\pi$
$762$		0			0
$763$	13.8916	−	42.7539i	0.502909	−	1.54780i
$764$		0			0
$765$	6.34411	+	4.60927i	0.229372	+	0.166648i
$766$		0			0
$767$	−1.80514	−	5.55566i	−0.0651799	−	0.200603i
$768$		0			0
$769$	−24.1311			−0.870188			−0.435094	−	0.900385i	$-0.643285\pi$
$769$	−24.1311			−0.870188			−0.435094	+	0.900385i	$0.643285\pi$
$770$		0			0
$771$	−28.6460			−1.03166
$772$		0			0
$773$	2.79525	+	8.60291i	0.100538	+	0.309425i	0.988657	−	0.150188i	$-0.0479880\pi$
$773$	2.79525	+	8.60291i	0.100538	+	0.309425i	−0.888119	+	0.459613i	$0.847988\pi$
$774$		0			0
$775$	4.05148	+	2.94357i	0.145534	+	0.105736i
$776$		0			0
$777$	−1.27675	+	3.92942i	−0.0458030	+	0.140967i
$778$		0			0
$779$	19.5164	−	14.1795i	0.699249	−	0.508034i
$780$		0			0
$781$	−29.8402	−	12.5012i	−1.06776	−	0.447328i
$782$		0			0
$783$	−32.6013	+	23.6862i	−1.16508	+	0.846478i
$784$		0			0
$785$	4.05853	−	12.4909i	0.144855	−	0.445819i
$786$		0			0
$787$	−25.3897	−	18.4467i	−0.905044	−	0.657553i	0.0347122	−	0.999397i	$-0.488949\pi$
$787$	−25.3897	−	18.4467i	−0.905044	−	0.657553i	−0.939757	+	0.341844i	$0.888949\pi$
$788$		0			0
$789$	−5.18435	−	15.9558i	−0.184568	−	0.568041i
$790$		0			0
$791$	−37.4087			−1.33010
$792$		0			0
$793$	10.7191			0.380646
$794$		0			0
$795$	−2.53165	−	7.79160i	−0.0897882	−	0.276340i
$796$		0			0
$797$	−19.2106	−	13.9573i	−0.680474	−	0.494394i	0.193041	−	0.981191i	$-0.438165\pi$
$797$	−19.2106	−	13.9573i	−0.680474	−	0.494394i	−0.873515	+	0.486797i	$0.838165\pi$
$798$		0			0
$799$	−10.0033	+	30.7870i	−0.353891	+	1.08916i
$800$		0			0
$801$	20.1121	−	14.6123i	0.710625	−	0.516299i
$802$		0			0
$803$	−1.17324	+	14.1773i	−0.0414026	+	0.500307i
$804$		0			0
$805$	3.98860	−	2.89789i	0.140580	−	0.102137i
$806$		0			0
$807$	−0.949920	+	2.92355i	−0.0334388	+	0.102914i
$808$		0			0
$809$	−6.21920	−	4.51851i	−0.218655	−	0.158862i	0.473066	−	0.881027i	$-0.343147\pi$
$809$	−6.21920	−	4.51851i	−0.218655	−	0.158862i	−0.691721	+	0.722165i	$0.743147\pi$
$810$		0			0
$811$	−9.14157	−	28.1349i	−0.321004	−	0.987949i	−0.973212	−	0.229909i	$-0.926157\pi$
$811$	−9.14157	−	28.1349i	−0.321004	−	0.987949i	0.652208	−	0.758040i	$-0.273843\pi$
$812$		0			0
$813$	−1.73493			−0.0608468
$814$		0			0
$815$	−17.2542			−0.604389
$816$		0			0
$817$	−4.44550	−	13.6818i	−0.155528	−	0.478667i
$818$		0			0
$819$	−3.75918	−	2.73120i	−0.131356	−	0.0954360i
$820$		0			0
$821$	−5.83369	+	17.9542i	−0.203597	+	0.626607i	0.796171	+	0.605072i	$0.206856\pi$
$821$	−5.83369	+	17.9542i	−0.203597	+	0.626607i	−0.999768	+	0.0215357i	$0.993144\pi$
$822$		0			0
$823$	39.8429	−	28.9475i	1.38883	−	1.00905i	0.392843	−	0.919606i	$-0.371492\pi$
$823$	39.8429	−	28.9475i	1.38883	−	1.00905i	0.995992	−	0.0894419i	$-0.0285083\pi$
$824$		0			0
$825$	10.4266	−	12.1089i	0.363007	−	0.421577i
$826$		0			0
$827$	−10.9975	+	7.99018i	−0.382422	+	0.277846i	−0.762343	−	0.647173i	$-0.775951\pi$
$827$	−10.9975	+	7.99018i	−0.382422	+	0.277846i	0.379921	+	0.925019i	$0.375951\pi$
$828$		0			0
$829$	6.31341	−	19.4307i	0.219274	−	0.674855i	−0.779549	−	0.626341i	$-0.784552\pi$
$829$	6.31341	−	19.4307i	0.219274	−	0.674855i	0.998823	−	0.0485136i	$-0.0154484\pi$
$830$		0			0
$831$	−4.58259	−	3.32945i	−0.158968	−	0.115497i
$832$		0			0
$833$	−0.0321099	−	0.0988241i	−0.00111254	−	0.00342405i
$834$		0			0
$835$	10.7445			0.371830
$836$		0			0
$837$	6.14003			0.212230
$838$		0			0
$839$	4.68558	+	14.4207i	0.161764	+	0.497858i	0.998783	−	0.0493150i	$-0.0157038\pi$
$839$	4.68558	+	14.4207i	0.161764	+	0.497858i	−0.837019	+	0.547173i	$0.815704\pi$
$840$		0			0
$841$	−23.2746	−	16.9100i	−0.802573	−	0.583103i
$842$		0			0
$843$	−5.04244	+	15.5190i	−0.173671	+	0.534504i
$844$		0			0
$845$	−0.665019	+	0.483164i	−0.0228773	+	0.0166214i
$846$		0			0
$847$	−4.31521	−	28.7413i	−0.148272	−	0.987562i
$848$		0			0
$849$	−10.4255	+	7.57458i	−0.357803	+	0.259959i
$850$		0			0
$851$	−0.984549	+	3.03013i	−0.0337499	+	0.103872i
$852$		0			0
$853$	−7.29120	−	5.29736i	−0.249646	−	0.181378i	0.455924	−	0.890019i	$-0.349309\pi$
$853$	−7.29120	−	5.29736i	−0.249646	−	0.181378i	−0.705570	+	0.708640i	$0.749309\pi$
$854$		0			0
$855$	−2.62932	−	8.09221i	−0.0899208	−	0.276748i
$856$		0			0
$857$	−4.43413			−0.151467			−0.0757335	−	0.997128i	$-0.524130\pi$
$857$	−4.43413			−0.151467			−0.0757335	+	0.997128i	$0.524130\pi$
$858$		0			0
$859$	−43.4756			−1.48337			−0.741684	−	0.670750i	$-0.765972\pi$
$859$	−43.4756			−1.48337			−0.741684	+	0.670750i	$0.765972\pi$
$860$		0			0
$861$	3.72840	+	11.4748i	0.127063	+	0.391061i
$862$		0			0
$863$	2.62597	+	1.90788i	0.0893889	+	0.0649448i	0.631582	−	0.775309i	$-0.282406\pi$
$863$	2.62597	+	1.90788i	0.0893889	+	0.0649448i	−0.542193	+	0.840254i	$0.682406\pi$
$864$		0			0
$865$	1.39781	−	4.30201i	0.0475269	−	0.146273i
$866$		0			0
$867$	11.1992	−	8.13671i	0.380346	−	0.276337i
$868$		0			0
$869$	29.9705	−	34.8062i	1.01668	−	1.18072i
$870$		0			0
$871$	2.43308	−	1.76774i	0.0824418	−	0.0598974i
$872$		0			0
$873$	1.45089	−	4.46538i	0.0491052	−	0.151130i
$874$		0			0
$875$	16.3834	+	11.9032i	0.553860	+	0.402403i
$876$		0			0
$877$	−13.7926	−	42.4493i	−0.465744	−	1.43341i	−0.858045	−	0.513575i	$-0.828321\pi$
$877$	−13.7926	−	42.4493i	−0.465744	−	1.43341i	0.392301	−	0.919837i	$-0.371679\pi$
$878$		0			0
$879$	−7.30928			−0.246536
$880$		0			0
$881$	−10.4661			−0.352613			−0.176307	−	0.984335i	$-0.556415\pi$
$881$	−10.4661			−0.352613			−0.176307	+	0.984335i	$0.556415\pi$
$882$		0			0
$883$	−14.5062	−	44.6455i	−0.488172	−	1.50244i	−0.827333	−	0.561712i	$-0.810143\pi$
$883$	−14.5062	−	44.6455i	−0.488172	−	1.50244i	0.339161	−	0.940729i	$-0.389857\pi$
$884$		0			0
$885$	4.32821	+	3.14463i	0.145491	+	0.105706i
$886$		0			0
$887$	−6.63065	+	20.4071i	−0.222636	+	0.685202i	0.775887	+	0.630871i	$0.217302\pi$
$887$	−6.63065	+	20.4071i	−0.222636	+	0.685202i	−0.998523	+	0.0543305i	$0.982698\pi$
$888$		0			0
$889$	17.4348	−	12.6672i	0.584746	−	0.424843i
$890$		0			0
$891$	0.172638	−	2.08615i	0.00578359	−	0.0698885i
$892$		0			0
$893$	28.4162	−	20.6456i	0.950911	−	0.690877i
$894$		0			0
$895$	0.777441	−	2.39272i	0.0259870	−	0.0799797i
$896$		0			0
$897$	2.04614	+	1.48661i	0.0683187	+	0.0496365i
$898$		0			0
$899$	2.72001	+	8.37132i	0.0907173	+	0.279199i
$900$		0			0
$901$	48.5238			1.61656
$902$		0			0
$903$	7.19507			0.239437
$904$		0			0
$905$	6.19162	+	19.0558i	0.205816	+	0.633438i
$906$		0			0
$907$	−1.24261	−	0.902812i	−0.0412603	−	0.0299774i	0.566964	−	0.823743i	$-0.308118\pi$
$907$	−1.24261	−	0.902812i	−0.0412603	−	0.0299774i	−0.608224	+	0.793765i	$0.708118\pi$
$908$		0			0
$909$	7.35602	−	22.6395i	0.243984	−	0.750905i
$910$		0			0
$911$	42.6206	−	30.9657i	1.41208	−	1.02594i	0.419067	−	0.907955i	$-0.362357\pi$
$911$	42.6206	−	30.9657i	1.41208	−	1.02594i	0.993016	−	0.117983i	$-0.0376427\pi$
$912$		0			0
$913$	−14.8397	−	6.21693i	−0.491122	−	0.205750i
$914$		0			0
$915$	−7.94213	+	5.77030i	−0.262559	+	0.190760i
$916$		0			0
$917$	−7.72316	+	23.7694i	−0.255041	+	0.784936i
$918$		0			0
$919$	21.6067	+	15.6982i	0.712739	+	0.517835i	0.884056	−	0.467381i	$-0.154802\pi$
$919$	21.6067	+	15.6982i	0.712739	+	0.517835i	−0.171317	+	0.985216i	$0.554802\pi$
$920$		0			0
$921$	6.86777	+	21.1368i	0.226301	+	0.696482i
$922$		0			0
$923$	9.75479			0.321083
$924$		0			0
$925$	−6.06930			−0.199557
$926$		0			0
$927$	−6.48947	−	19.9725i	−0.213142	−	0.655984i
$928$		0			0
$929$	−6.02094	−	4.37447i	−0.197541	−	0.143522i	0.484618	−	0.874726i	$-0.338959\pi$
$929$	−6.02094	−	4.37447i	−0.197541	−	0.143522i	−0.682159	+	0.731204i	$0.738959\pi$
$930$		0			0
$931$	−0.0348407	+	0.107229i	−0.00114186	+	0.00351427i
$932$		0			0
$933$	−11.3617	+	8.25474i	−0.371965	+	0.270248i
$934$		0			0
$935$	−7.67621	−	12.6404i	−0.251039	−	0.413385i
$936$		0			0
$937$	−33.9404	+	24.6591i	−1.10878	+	0.805578i	−0.982472	−	0.186412i	$-0.940314\pi$
$937$	−33.9404	+	24.6591i	−1.10878	+	0.805578i	−0.126312	+	0.991991i	$0.540314\pi$
$938$		0			0
$939$	−9.29697	+	28.6131i	−0.303395	+	0.933754i
$940$		0			0
$941$	−20.1060	−	14.6079i	−0.655437	−	0.476203i	0.209682	−	0.977770i	$-0.432757\pi$
$941$	−20.1060	−	14.6079i	−0.655437	−	0.476203i	−0.865119	+	0.501567i	$0.832757\pi$
$942$		0			0
$943$	2.87511	+	8.84869i	0.0936266	+	0.288153i
$944$		0			0
$945$	11.5149			0.374580
$946$		0			0
$947$	52.8734			1.71815			0.859077	−	0.511847i	$-0.171038\pi$
$947$	52.8734			1.71815			0.859077	+	0.511847i	$0.171038\pi$
$948$		0			0
$949$	−1.32545	−	4.07931i	−0.0430258	−	0.132420i
$950$		0			0
$951$	13.3419	+	9.69347i	0.432641	+	0.314332i
$952$		0			0
$953$	7.23368	−	22.2630i	0.234322	−	0.721168i	−0.762889	−	0.646530i	$-0.776220\pi$
$953$	7.23368	−	22.2630i	0.234322	−	0.721168i	0.997211	−	0.0746387i	$-0.0237804\pi$
$954$		0			0
$955$	−1.90566	+	1.38455i	−0.0616658	+	0.0448028i
$956$		0			0
$957$	27.3361	−	6.44652i	0.883652	−	0.208386i
$958$		0			0
$959$	−18.5225	+	13.4574i	−0.598123	+	0.434562i
$960$		0			0
$961$	−9.16509	+	28.2072i	−0.295648	+	0.909911i
$962$		0			0
$963$	22.3122	+	16.2108i	0.719000	+	0.522384i
$964$		0			0
$965$	−5.36742	−	16.5192i	−0.172783	−	0.531772i
$966$		0			0
$967$	−53.0924			−1.70734			−0.853668	−	0.520817i	$-0.825627\pi$
$967$	−53.0924			−1.70734			−0.853668	+	0.520817i	$0.825627\pi$
$968$		0			0
$969$	−35.5717			−1.14273
$970$		0			0
$971$	9.31778	+	28.6772i	0.299022	+	0.920295i	0.981841	+	0.189707i	$0.0607538\pi$
$971$	9.31778	+	28.6772i	0.299022	+	0.920295i	−0.682819	+	0.730588i	$0.739246\pi$
$972$		0			0
$973$	−15.2228	−	11.0600i	−0.488020	−	0.354567i
$974$		0			0
$975$	−1.48883	+	4.58214i	−0.0476806	+	0.146746i
$976$		0			0
$977$	12.6223	−	9.17061i	0.403822	−	0.293394i	−0.367274	−	0.930113i	$-0.619709\pi$
$977$	12.6223	−	9.17061i	0.403822	−	0.293394i	0.771096	+	0.636719i	$0.219709\pi$
$978$		0			0
$979$	−45.6312	+	10.7609i	−1.45838	+	0.343921i
$980$		0			0
$981$	24.2078	−	17.5880i	0.772894	−	0.561540i
$982$		0			0
$983$	4.10783	−	12.6426i	0.131019	−	0.403236i	−0.863930	−	0.503612i	$-0.832004\pi$
$983$	4.10783	−	12.6426i	0.131019	−	0.403236i	0.994950	+	0.100375i	$0.0320043\pi$
$984$		0			0
$985$	3.69400	+	2.68385i	0.117701	+	0.0855146i
$986$		0			0
$987$	5.42859	+	16.7075i	0.172794	+	0.531805i
$988$		0			0
$989$	5.54840			0.176429
$990$		0			0
$991$	−49.3932			−1.56903			−0.784513	−	0.620113i	$-0.787087\pi$
$991$	−49.3932			−1.56903			−0.784513	+	0.620113i	$0.787087\pi$
$992$		0			0
$993$	−12.2010	−	37.5507i	−0.387186	−	1.19164i
$994$		0			0
$995$	14.9352	+	10.8510i	0.473476	+	0.344001i
$996$		0			0
$997$	−10.1676	+	31.2927i	−0.322012	+	0.991050i	0.650760	+	0.759283i	$0.274450\pi$
$997$	−10.1676	+	31.2927i	−0.322012	+	0.991050i	−0.972772	+	0.231766i	$0.925550\pi$
$998$		0			0
$999$	−6.02019	+	4.37393i	−0.190470	+	0.138385i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.n.b.157.3	✓	28
11.2	odd	10		6292.2.a.y.1.5		14
11.4	even	5	inner	572.2.n.b.521.3	yes	28
11.9	even	5		6292.2.a.z.1.5		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.n.b.157.3	✓	28	1.1	even	1	trivial
572.2.n.b.521.3	yes	28	11.4	even	5	inner
6292.2.a.y.1.5		14	11.2	odd	10
6292.2.a.z.1.5		14	11.9	even	5

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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.344293 - 1.05962i) q^{3} +(-0.665019 - 0.483164i) q^{5} +(0.816463 - 2.51281i) q^{7} +(1.42278 - 1.03371i) q^{9} +O(q^{10})\)	\(q+(-0.344293 - 1.05962i) q^{3} +(-0.665019 - 0.483164i) q^{5} +(0.816463 - 2.51281i) q^{7} +(1.42278 - 1.03371i) q^{9} +(-3.22808 + 0.761259i) q^{11} +(0.809017 - 0.587785i) q^{13} +(-0.283012 + 0.871020i) q^{15} +(-4.38847 - 3.18841i) q^{17} +(1.81880 + 5.59770i) q^{19} -2.94374 q^{21} -2.27004 q^{23} +(-1.33628 - 4.11266i) q^{25} +(-4.28931 - 3.11637i) q^{27} +(2.34871 - 7.22859i) q^{29} +(-0.936910 + 0.680705i) q^{31} +(1.91805 + 3.15845i) q^{33} +(-1.75706 + 1.27658i) q^{35} +(0.433715 - 1.33484i) q^{37} +(-0.901370 - 0.654884i) q^{39} +(-1.26655 - 3.89804i) q^{41} -2.44419 q^{43} -1.44563 q^{45} +(-1.84411 - 5.67559i) q^{47} +(0.0154974 + 0.0112595i) q^{49} +(-1.86760 + 5.74788i) q^{51} +(-7.23696 + 5.25796i) q^{53} +(2.51454 + 1.05344i) q^{55} +(5.30526 - 3.85449i) q^{57} +(1.80514 - 5.55566i) q^{59} +(8.67192 + 6.30052i) q^{61} +(-1.43588 - 4.41918i) q^{63} -0.822008 q^{65} +3.00745 q^{67} +(0.781557 + 2.40539i) q^{69} +(7.89179 + 5.73372i) q^{71} +(1.32545 - 4.07931i) q^{73} +(-3.89780 + 2.83192i) q^{75} +(-0.722703 + 8.73310i) q^{77} +(-11.2040 + 8.14017i) q^{79} +(-0.195035 + 0.600256i) q^{81} +(3.92464 + 2.85142i) q^{83} +(1.37789 + 4.24071i) q^{85} -8.46824 q^{87} +14.1357 q^{89} +(-0.816463 - 2.51281i) q^{91} +(1.04386 + 0.758411i) q^{93} +(1.49507 - 4.60135i) q^{95} +(2.15987 - 1.56924i) q^{97} +(-3.80593 + 4.42001i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9}+O(q^{10}) \) 28 * q + q^3 - 7 * q^5 + 11 * q^7 - 22 * q^9	\( 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9} + q^{11} + 7 q^{13} - 24 q^{15} + 7 q^{17} - 7 q^{19} - 12 q^{21} + 34 q^{23} - 26 q^{25} - 11 q^{27} + 8 q^{29} - 17 q^{31} - 2 q^{33} - 6 q^{35} - 15 q^{37} + 4 q^{39} + 29 q^{41} - 8 q^{43} + 62 q^{45} - 27 q^{47} - 4 q^{49} + 69 q^{51} - 32 q^{53} + 19 q^{55} + 9 q^{57} - 37 q^{59} - 19 q^{61} + 46 q^{63} - 18 q^{65} + 10 q^{67} - 32 q^{69} - 27 q^{71} - 79 q^{75} + 13 q^{77} + 21 q^{79} - 18 q^{81} + 27 q^{83} + 7 q^{85} + 56 q^{87} + 82 q^{89} - 11 q^{91} - 53 q^{93} + 51 q^{95} - 88 q^{97} + 86 q^{99}+O(q^{100}) \) 28 * q + q^3 - 7 * q^5 + 11 * q^7 - 22 * q^9 + q^11 + 7 * q^13 - 24 * q^15 + 7 * q^17 - 7 * q^19 - 12 * q^21 + 34 * q^23 - 26 * q^25 - 11 * q^27 + 8 * q^29 - 17 * q^31 - 2 * q^33 - 6 * q^35 - 15 * q^37 + 4 * q^39 + 29 * q^41 - 8 * q^43 + 62 * q^45 - 27 * q^47 - 4 * q^49 + 69 * q^51 - 32 * q^53 + 19 * q^55 + 9 * q^57 - 37 * q^59 - 19 * q^61 + 46 * q^63 - 18 * q^65 + 10 * q^67 - 32 * q^69 - 27 * q^71 - 79 * q^75 + 13 * q^77 + 21 * q^79 - 18 * q^81 + 27 * q^83 + 7 * q^85 + 56 * q^87 + 82 * q^89 - 11 * q^91 - 53 * q^93 + 51 * q^95 - 88 * q^97 + 86 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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