LMFDB - Embedded newform 1161.2.f.d.775.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1161,2,Mod(388,1161)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1161, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1161.388");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1161 = 3^{3} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1161.f (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.27063167467$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 387)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			775.20
Character	$\chi$	$=$	1161.775
Dual form			1161.2.f.d.388.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.31834 - 2.28344i) q^{2} +(-2.47606 - 4.28866i) q^{4} +(-1.39983 - 2.42457i) q^{5} +(1.99111 - 3.44870i) q^{7} -7.78382 q^{8} +O(q^{10})$	\(q+(1.31834 - 2.28344i) q^{2} +(-2.47606 - 4.28866i) q^{4} +(-1.39983 - 2.42457i) q^{5} +(1.99111 - 3.44870i) q^{7} -7.78382 q^{8} -7.38182 q^{10} +(2.07235 - 3.58941i) q^{11} +(1.53392 + 2.65683i) q^{13} +(-5.24992 - 9.09313i) q^{14} +(-5.30963 + 9.19655i) q^{16} +5.89483 q^{17} -0.423608 q^{19} +(-6.93212 + 12.0068i) q^{20} +(-5.46414 - 9.46416i) q^{22} +(-0.535334 - 0.927226i) q^{23} +(-1.41904 + 2.45784i) q^{25} +8.08895 q^{26} -19.7204 q^{28} +(-2.91479 + 5.04856i) q^{29} +(4.87493 + 8.44362i) q^{31} +(6.21601 + 10.7665i) q^{32} +(7.77142 - 13.4605i) q^{34} -11.1488 q^{35} +3.05211 q^{37} +(-0.558461 + 0.967284i) q^{38} +(10.8960 + 18.8724i) q^{40} +(5.02745 + 8.70780i) q^{41} +(0.500000 - 0.866025i) q^{43} -20.5250 q^{44} -2.82302 q^{46} +(-4.13133 + 7.15568i) q^{47} +(-4.42900 - 7.67126i) q^{49} +(3.74156 + 6.48057i) q^{50} +(7.59617 - 13.1570i) q^{52} +4.04613 q^{53} -11.6037 q^{55} +(-15.4984 + 26.8440i) q^{56} +(7.68539 + 13.3115i) q^{58} +(-1.40350 - 2.43093i) q^{59} +(6.49271 - 11.2457i) q^{61} +25.7073 q^{62} +11.5409 q^{64} +(4.29446 - 7.43822i) q^{65} +(-0.766282 - 1.32724i) q^{67} +(-14.5960 - 25.2810i) q^{68} +(-14.6980 + 25.4576i) q^{70} -3.85095 q^{71} +4.68286 q^{73} +(4.02373 - 6.96931i) q^{74} +(1.04888 + 1.81671i) q^{76} +(-8.25253 - 14.2938i) q^{77} +(-5.77387 + 10.0006i) q^{79} +29.7303 q^{80} +26.5116 q^{82} +(-0.655725 + 1.13575i) q^{83} +(-8.25175 - 14.2925i) q^{85} +(-1.31834 - 2.28344i) q^{86} +(-16.1308 + 27.9393i) q^{88} +0.630048 q^{89} +12.2168 q^{91} +(-2.65104 + 4.59173i) q^{92} +(10.8930 + 18.8673i) q^{94} +(0.592979 + 1.02707i) q^{95} +(-2.05730 + 3.56335i) q^{97} -23.3558 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 6 q^{2} - 22 q^{4} - 17 q^{5} - 3 q^{7} + 30 q^{8}+O(q^{10}) $ 40 * q - 6 * q^2 - 22 * q^4 - 17 * q^5 - 3 * q^7 + 30 * q^8	$ 40 q - 6 q^{2} - 22 q^{4} - 17 q^{5} - 3 q^{7} + 30 q^{8} - 4 q^{10} - 10 q^{11} + q^{13} - 10 q^{14} - 22 q^{16} + 40 q^{17} + 16 q^{19} - 30 q^{20} - 15 q^{22} - 19 q^{23} - 19 q^{25} + 50 q^{26} - 6 q^{28} - 25 q^{29} + 11 q^{31} - 36 q^{32} - 9 q^{34} + 18 q^{37} - 28 q^{38} - 12 q^{40} - 12 q^{41} + 20 q^{43} + 10 q^{44} + 8 q^{46} - 38 q^{47} - 37 q^{49} - 36 q^{50} + 8 q^{52} + 138 q^{53} - 18 q^{55} - 30 q^{56} + 27 q^{58} - 31 q^{59} - 19 q^{61} + 64 q^{62} + 22 q^{64} - 47 q^{65} - 9 q^{67} - 68 q^{68} + 6 q^{70} + 42 q^{71} - 4 q^{73} + 16 q^{74} - 37 q^{76} - 85 q^{77} + 4 q^{79} + 122 q^{80} + 2 q^{82} - 19 q^{83} + 6 q^{85} + 6 q^{86} - 60 q^{88} + 108 q^{89} - 6 q^{91} - 85 q^{92} + 19 q^{94} + 11 q^{95} - 2 q^{97} + 10 q^{98}+O(q^{100}) $ 40 * q - 6 * q^2 - 22 * q^4 - 17 * q^5 - 3 * q^7 + 30 * q^8 - 4 * q^10 - 10 * q^11 + q^13 - 10 * q^14 - 22 * q^16 + 40 * q^17 + 16 * q^19 - 30 * q^20 - 15 * q^22 - 19 * q^23 - 19 * q^25 + 50 * q^26 - 6 * q^28 - 25 * q^29 + 11 * q^31 - 36 * q^32 - 9 * q^34 + 18 * q^37 - 28 * q^38 - 12 * q^40 - 12 * q^41 + 20 * q^43 + 10 * q^44 + 8 * q^46 - 38 * q^47 - 37 * q^49 - 36 * q^50 + 8 * q^52 + 138 * q^53 - 18 * q^55 - 30 * q^56 + 27 * q^58 - 31 * q^59 - 19 * q^61 + 64 * q^62 + 22 * q^64 - 47 * q^65 - 9 * q^67 - 68 * q^68 + 6 * q^70 + 42 * q^71 - 4 * q^73 + 16 * q^74 - 37 * q^76 - 85 * q^77 + 4 * q^79 + 122 * q^80 + 2 * q^82 - 19 * q^83 + 6 * q^85 + 6 * q^86 - 60 * q^88 + 108 * q^89 - 6 * q^91 - 85 * q^92 + 19 * q^94 + 11 * q^95 - 2 * q^97 + 10 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1161\mathbb{Z}\right)^\times$.

$n$	$433$	$947$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.31834	−	2.28344i	0.932210	−	1.61463i	0.152674	−	0.988277i	$-0.451211\pi$
$2$	1.31834	−	2.28344i	0.932210	−	1.61463i	0.779535	−	0.626358i	$-0.215455\pi$
$3$		0			0
$3$		0			0
$4$	−2.47606	−	4.28866i	−1.23803	−	2.14433i
$5$	−1.39983	−	2.42457i	−0.626022	−	1.08430i	−0.988342	−	0.152248i	$-0.951349\pi$
$5$	−1.39983	−	2.42457i	−0.626022	−	1.08430i	0.362320	−	0.932054i	$-0.381985\pi$
$6$		0			0
$7$	1.99111	−	3.44870i	0.752567	−	1.30348i	−0.194008	−	0.981000i	$-0.562149\pi$
$7$	1.99111	−	3.44870i	0.752567	−	1.30348i	0.946575	−	0.322484i	$-0.104518\pi$
$8$	−7.78382			−2.75200
$9$		0			0
$10$	−7.38182			−2.33434
$11$	2.07235	−	3.58941i	0.624837	−	1.08225i	−0.363736	−	0.931502i	$-0.618499\pi$
$11$	2.07235	−	3.58941i	0.624837	−	1.08225i	0.988572	−	0.150747i	$-0.0481678\pi$
$12$		0			0
$13$	1.53392	+	2.65683i	0.425434	+	0.736873i	0.996461	−	0.0840584i	$-0.0267882\pi$
$13$	1.53392	+	2.65683i	0.425434	+	0.736873i	−0.571027	+	0.820931i	$0.693455\pi$
$14$	−5.24992	−	9.09313i	−1.40310	−	2.43024i
$15$		0			0
$16$	−5.30963	+	9.19655i	−1.32741	+	2.29914i
$17$	5.89483			1.42971			0.714854	−	0.699274i	$-0.246493\pi$
$17$	5.89483			1.42971			0.714854	+	0.699274i	$0.246493\pi$
$18$		0			0
$19$	−0.423608			−0.0971824			−0.0485912	−	0.998819i	$-0.515473\pi$
$19$	−0.423608			−0.0971824			−0.0485912	+	0.998819i	$0.515473\pi$
$20$	−6.93212	+	12.0068i	−1.55007	+	2.68480i
$21$		0			0
$22$	−5.46414	−	9.46416i	−1.16496	−	2.01777i
$23$	−0.535334	−	0.927226i	−0.111625	−	0.193340i	0.804801	−	0.593545i	$-0.202272\pi$
$23$	−0.535334	−	0.927226i	−0.111625	−	0.193340i	−0.916426	+	0.400205i	$0.868939\pi$
$24$		0			0
$25$	−1.41904	+	2.45784i	−0.283807	+	0.491569i
$26$	8.08895			1.58637
$27$		0			0
$28$	−19.7204			−3.72680
$29$	−2.91479	+	5.04856i	−0.541263	+	0.937495i	0.457569	+	0.889174i	$0.348720\pi$
$29$	−2.91479	+	5.04856i	−0.541263	+	0.937495i	−0.998832	+	0.0483207i	$0.984613\pi$
$30$		0			0
$31$	4.87493	+	8.44362i	0.875563	+	1.51652i	0.856162	+	0.516707i	$0.172843\pi$
$31$	4.87493	+	8.44362i	0.875563	+	1.51652i	0.0194008	+	0.999812i	$0.493824\pi$
$32$	6.21601	+	10.7665i	1.09885	+	1.90326i
$33$		0			0
$34$	7.77142	−	13.4605i	1.33279	−	2.30846i
$35$	−11.1488			−1.88449
$36$		0			0
$37$	3.05211			0.501764			0.250882	−	0.968018i	$-0.419279\pi$
$37$	3.05211			0.501764			0.250882	+	0.968018i	$0.419279\pi$
$38$	−0.558461	+	0.967284i	−0.0905944	+	0.156914i
$39$		0			0
$40$	10.8960	+	18.8724i	1.72281	+	2.98400i
$41$	5.02745	+	8.70780i	0.785156	+	1.35993i	0.928906	+	0.370316i	$0.120750\pi$
$41$	5.02745	+	8.70780i	0.785156	+	1.35993i	−0.143750	+	0.989614i	$0.545916\pi$
$42$		0			0
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i
$44$	−20.5250			−3.09427
$45$		0			0
$46$	−2.82302			−0.416231
$47$	−4.13133	+	7.15568i	−0.602617	+	1.04376i	0.389806	+	0.920897i	$0.372542\pi$
$47$	−4.13133	+	7.15568i	−0.602617	+	1.04376i	−0.992423	+	0.122866i	$0.960791\pi$
$48$		0			0
$49$	−4.42900	−	7.67126i	−0.632714	−	1.09589i
$50$	3.74156	+	6.48057i	0.529136	+	0.916491i
$51$		0			0
$52$	7.59617	−	13.1570i	1.05340	−	1.82454i
$53$	4.04613			0.555778			0.277889	−	0.960613i	$-0.410365\pi$
$53$	4.04613			0.555778			0.277889	+	0.960613i	$0.410365\pi$
$54$		0			0
$55$	−11.6037			−1.56465
$56$	−15.4984	+	26.8440i	−2.07106	+	3.58718i
$57$		0			0
$58$	7.68539	+	13.3115i	1.00914	+	1.74788i
$59$	−1.40350	−	2.43093i	−0.182720	−	0.316481i	0.760086	−	0.649823i	$-0.225157\pi$
$59$	−1.40350	−	2.43093i	−0.182720	−	0.316481i	−0.942806	+	0.333342i	$0.891824\pi$
$60$		0			0
$61$	6.49271	−	11.2457i	0.831307	−	1.43987i	−0.0656957	−	0.997840i	$-0.520927\pi$
$61$	6.49271	−	11.2457i	0.831307	−	1.43987i	0.897002	−	0.442026i	$-0.145740\pi$
$62$	25.7073			3.26483
$63$		0			0
$64$	11.5409			1.44261
$65$	4.29446	−	7.43822i	0.532662	−	0.922597i
$66$		0			0
$67$	−0.766282	−	1.32724i	−0.0936162	−	0.162148i	0.815414	−	0.578878i	$-0.196509\pi$
$67$	−0.766282	−	1.32724i	−0.0936162	−	0.162148i	−0.909030	+	0.416730i	$0.863176\pi$
$68$	−14.5960	−	25.2810i	−1.77002	−	3.06577i
$69$		0			0
$70$	−14.6980	+	25.4576i	−1.75674	+	3.04277i
$71$	−3.85095			−0.457024			−0.228512	−	0.973541i	$-0.573386\pi$
$71$	−3.85095			−0.457024			−0.228512	+	0.973541i	$0.573386\pi$
$72$		0			0
$73$	4.68286			0.548087			0.274043	−	0.961717i	$-0.411639\pi$
$73$	4.68286			0.548087			0.274043	+	0.961717i	$0.411639\pi$
$74$	4.02373	−	6.96931i	0.467749	−	0.810165i
$75$		0			0
$76$	1.04888	+	1.81671i	0.120315	+	0.208391i
$77$	−8.25253	−	14.2938i	−0.940463	−	1.62893i
$78$		0			0
$79$	−5.77387	+	10.0006i	−0.649611	+	1.12516i	0.333605	+	0.942713i	$0.391735\pi$
$79$	−5.77387	+	10.0006i	−0.649611	+	1.12516i	−0.983216	+	0.182446i	$0.941599\pi$
$80$	29.7303			3.32395
$81$		0			0
$82$	26.5116			2.92772
$83$	−0.655725	+	1.13575i	−0.0719752	+	0.124665i	−0.899767	−	0.436371i	$-0.856264\pi$
$83$	−0.655725	+	1.13575i	−0.0719752	+	0.124665i	0.827792	+	0.561036i	$0.189597\pi$
$84$		0			0
$85$	−8.25175	−	14.2925i	−0.895028	−	1.55023i
$86$	−1.31834	−	2.28344i	−0.142161	−	0.246229i
$87$		0			0
$88$	−16.1308	+	27.9393i	−1.71955	+	2.97834i
$89$	0.630048			0.0667850			0.0333925	−	0.999442i	$-0.489369\pi$
$89$	0.630048			0.0667850			0.0333925	+	0.999442i	$0.489369\pi$
$90$		0			0
$91$	12.2168			1.28067
$92$	−2.65104	+	4.59173i	−0.276390	+	0.478721i
$93$		0			0
$94$	10.8930	+	18.8673i	1.12353	+	1.94601i
$95$	0.592979	+	1.02707i	0.0608384	+	0.105375i
$96$		0			0
$97$	−2.05730	+	3.56335i	−0.208887	+	0.361803i	−0.951364	−	0.308068i	$-0.900317\pi$
$97$	−2.05730	+	3.56335i	−0.208887	+	0.361803i	0.742477	+	0.669871i	$0.233651\pi$
$98$	−23.3558			−2.35929
$99$		0			0
$100$	14.0545			1.40545
$101$	−2.28610	+	3.95965i	−0.227476	+	0.394000i	−0.957059	−	0.289892i	$-0.906381\pi$
$101$	−2.28610	+	3.95965i	−0.227476	+	0.394000i	0.729583	+	0.683892i	$0.239714\pi$
$102$		0			0
$103$	−0.111247	−	0.192685i	−0.0109615	−	0.0189858i	0.860493	−	0.509463i	$-0.170156\pi$
$103$	−0.111247	−	0.192685i	−0.0109615	−	0.0189858i	−0.871454	+	0.490477i	$0.836823\pi$
$104$	−11.9398	−	20.6803i	−1.17079	−	2.02787i
$105$		0			0
$106$	5.33419	−	9.23908i	0.518102	−	0.897379i
$107$	−2.94239			−0.284452			−0.142226	−	0.989834i	$-0.545426\pi$
$107$	−2.94239			−0.284452			−0.142226	+	0.989834i	$0.545426\pi$
$108$		0			0
$109$	7.54440			0.722622			0.361311	−	0.932445i	$-0.382329\pi$
$109$	7.54440			0.722622			0.361311	+	0.932445i	$0.382329\pi$
$110$	−15.2977	+	26.4964i	−1.45858	+	2.52633i
$111$		0			0
$112$	21.1441	+	36.6226i	1.99793	+	3.46051i
$113$	−4.88746	−	8.46533i	−0.459773	−	0.796351i	0.539175	−	0.842194i	$-0.318736\pi$
$113$	−4.88746	−	8.46533i	−0.459773	−	0.796351i	−0.998949	+	0.0458427i	$0.985403\pi$
$114$		0			0
$115$	−1.49875	+	2.59591i	−0.139759	+	0.242070i
$116$	28.8688			2.68040
$117$		0			0
$118$	−7.40118			−0.681334
$119$	11.7372	−	20.3295i	1.07595	−	1.86360i
$120$		0			0
$121$	−3.08926	−	5.35076i	−0.280842	−	0.486432i
$122$	−17.1193	−	29.6514i	−1.54990	−	2.68451i
$123$		0			0
$124$	24.1412	−	41.8138i	2.16795	−	3.75499i
$125$	−6.05265			−0.541365
$126$		0			0
$127$	−3.17610			−0.281833			−0.140916	−	0.990021i	$-0.545005\pi$
$127$	−3.17610			−0.281833			−0.140916	+	0.990021i	$0.545005\pi$
$128$	2.78278	−	4.81992i	0.245966	−	0.426025i
$129$		0			0
$130$	−11.3231	−	19.6123i	−0.993105	−	1.72011i
$131$	2.33983	+	4.05271i	0.204432	+	0.354087i	0.949952	−	0.312397i	$-0.101132\pi$
$131$	2.33983	+	4.05271i	0.204432	+	0.354087i	−0.745520	+	0.666484i	$0.767799\pi$
$132$		0			0
$133$	−0.843449	+	1.46090i	−0.0731363	+	0.126676i
$134$	−4.04089			−0.349080
$135$		0			0
$136$	−45.8843			−3.93455
$137$	−9.95621	+	17.2447i	−0.850617	+	1.47331i	0.0300362	+	0.999549i	$0.490438\pi$
$137$	−9.95621	+	17.2447i	−0.850617	+	1.47331i	−0.880653	+	0.473762i	$0.842896\pi$
$138$		0			0
$139$	−1.81702	−	3.14717i	−0.154118	−	0.266940i	0.778620	−	0.627496i	$-0.215920\pi$
$139$	−1.81702	−	3.14717i	−0.154118	−	0.266940i	−0.932737	+	0.360556i	$0.882587\pi$
$140$	27.6052	+	47.8135i	2.33306	+	4.04098i
$141$		0			0
$142$	−5.07688	+	8.79342i	−0.426042	+	0.737927i
$143$	12.7153			1.06331
$144$		0			0
$145$	16.3208			1.35537
$146$	6.17361	−	10.6930i	0.510932	−	0.884960i
$147$		0			0
$148$	−7.55721	−	13.0895i	−0.621199	−	1.07595i
$149$	3.53945	+	6.13050i	0.289963	+	0.502230i	0.973801	−	0.227404i	$-0.0730238\pi$
$149$	3.53945	+	6.13050i	0.289963	+	0.502230i	−0.683838	+	0.729634i	$0.739690\pi$
$150$		0			0
$151$	3.99720	−	6.92336i	0.325288	−	0.563415i	−0.656283	−	0.754515i	$-0.727872\pi$
$151$	3.99720	−	6.92336i	0.325288	−	0.563415i	0.981571	+	0.191100i	$0.0612055\pi$
$152$	3.29729			0.267446
$153$		0			0
$154$	−43.5187			−3.50684
$155$	13.6481	−	23.6392i	1.09624	−	1.89875i
$156$		0			0
$157$	−7.54081	−	13.0611i	−0.601822	−	1.04239i	−0.992545	−	0.121878i	$-0.961108\pi$
$157$	−7.54081	−	13.0611i	−0.601822	−	1.04239i	0.390723	−	0.920508i	$-0.372225\pi$
$158$	15.2239	+	26.3685i	1.21115	+	2.09777i
$159$		0			0
$160$	17.4027	−	30.1424i	1.37580	−	2.38296i
$161$	−4.26363			−0.336021
$162$		0			0
$163$	−4.92573			−0.385813			−0.192906	−	0.981217i	$-0.561791\pi$
$163$	−4.92573			−0.385813			−0.192906	+	0.981217i	$0.561791\pi$
$164$	24.8965	−	43.1221i	1.94409	−	3.36727i
$165$		0			0
$166$	1.72894	+	2.99462i	0.134192	+	0.232427i
$167$	−9.20065	−	15.9360i	−0.711968	−	1.23316i	−0.964117	−	0.265476i	$-0.914471\pi$
$167$	−9.20065	−	15.9360i	−0.711968	−	1.23316i	0.252150	−	0.967688i	$-0.418862\pi$
$168$		0			0
$169$	1.79416	−	3.10758i	0.138012	−	0.239044i
$170$	−43.5146			−3.33742
$171$		0			0
$172$	−4.95212			−0.377596
$173$	2.50951	−	4.34660i	0.190795	−	0.330466i	−0.754719	−	0.656048i	$-0.772227\pi$
$173$	2.50951	−	4.34660i	0.190795	−	0.330466i	0.945514	+	0.325582i	$0.105560\pi$
$174$		0			0
$175$	5.65090	+	9.78765i	0.427168	+	0.739877i
$176$	22.0068	+	38.1169i	1.65883	+	2.87317i
$177$		0			0
$178$	0.830620	−	1.43868i	0.0622576	−	0.107833i
$179$	12.5210			0.935862			0.467931	−	0.883765i	$-0.345000\pi$
$179$	12.5210			0.935862			0.467931	+	0.883765i	$0.345000\pi$
$180$		0			0
$181$	18.7634			1.39467			0.697337	−	0.716744i	$-0.254368\pi$
$181$	18.7634			1.39467			0.697337	+	0.716744i	$0.254368\pi$
$182$	16.1060	−	27.8963i	1.19385	−	2.06781i
$183$		0			0
$184$	4.16694	+	7.21736i	0.307191	+	0.532071i
$185$	−4.27243	−	7.40006i	−0.314115	−	0.544064i
$186$		0			0
$187$	12.2162	−	21.1590i	0.893334	−	1.54730i
$188$	40.9177			2.98423
$189$		0			0
$190$	3.12700			0.226856
$191$	−4.45605	+	7.71810i	−0.322428	+	0.558462i	−0.980988	−	0.194066i	$-0.937832\pi$
$191$	−4.45605	+	7.71810i	−0.322428	+	0.558462i	0.658560	+	0.752528i	$0.271166\pi$
$192$		0			0
$193$	2.75595	+	4.77344i	0.198378	+	0.343600i	0.948003	−	0.318263i	$-0.103099\pi$
$193$	2.75595	+	4.77344i	0.198378	+	0.343600i	−0.749625	+	0.661863i	$0.769766\pi$
$194$	5.42445	+	9.39543i	0.389453	+	0.674553i
$195$		0			0
$196$	−21.9329	+	37.9890i	−1.56664	+	2.71350i
$197$	5.01927			0.357608			0.178804	−	0.983885i	$-0.442777\pi$
$197$	5.01927			0.357608			0.178804	+	0.983885i	$0.442777\pi$
$198$		0			0
$199$	0.286051			0.0202776			0.0101388	−	0.999949i	$-0.496773\pi$
$199$	0.286051			0.0202776			0.0101388	+	0.999949i	$0.496773\pi$
$200$	11.0455	−	19.1314i	0.781037	−	1.35280i
$201$		0			0
$202$	6.02774	+	10.4404i	0.424111	+	0.734581i
$203$	11.6073	+	20.1044i	0.814673	+	1.41106i
$204$		0			0
$205$	14.0751	−	24.3788i	0.983050	−	1.70269i
$206$	−0.586646			−0.0408735
$207$		0			0
$208$	−32.5782			−2.25890
$209$	−0.877864	+	1.52051i	−0.0607232	+	0.105176i
$210$		0			0
$211$	−8.78760	−	15.2206i	−0.604963	−	1.04783i	−0.992057	−	0.125787i	$-0.959854\pi$
$211$	−8.78760	−	15.2206i	−0.604963	−	1.04783i	0.387094	−	0.922040i	$-0.373479\pi$
$212$	−10.0185	−	17.3525i	−0.688070	−	1.19177i
$213$		0			0
$214$	−3.87908	+	6.71877i	−0.265169	+	0.459285i
$215$	−2.79966			−0.190935
$216$		0			0
$217$	38.8260			2.63568
$218$	9.94611	−	17.2272i	0.673635	−	1.16677i
$219$		0			0
$220$	28.7315	+	49.7645i	1.93708	+	3.35512i
$221$	9.04222	+	15.6616i	0.608246	+	1.05351i
$222$		0			0
$223$	−5.44391	+	9.42913i	−0.364551	+	0.631421i	−0.988704	−	0.149881i	$-0.952111\pi$
$223$	−5.44391	+	9.42913i	−0.364551	+	0.631421i	0.624153	+	0.781302i	$0.285444\pi$
$224$	49.5070			3.30782
$225$		0			0
$226$	−25.7734			−1.71442
$227$	−5.22224	+	9.04519i	−0.346612	+	0.600350i	−0.985645	−	0.168829i	$-0.946001\pi$
$227$	−5.22224	+	9.04519i	−0.346612	+	0.600350i	0.639033	+	0.769179i	$0.279335\pi$
$228$		0			0
$229$	−7.64089	−	13.2344i	−0.504925	−	0.874555i	−0.999984	−	0.00569574i	$-0.998187\pi$
$229$	−7.64089	−	13.2344i	−0.504925	−	0.874555i	0.495059	−	0.868859i	$-0.335146\pi$
$230$	3.95174	+	6.84461i	0.260570	+	0.451320i
$231$		0			0
$232$	22.6882	−	39.2971i	1.48955	−	2.57998i
$233$	−21.3798			−1.40064			−0.700319	−	0.713830i	$-0.746959\pi$
$233$	−21.3798			−1.40064			−0.700319	+	0.713830i	$0.746959\pi$
$234$		0			0
$235$	23.1326			1.50901
$236$	−6.95030	+	12.0383i	−0.452426	+	0.783625i
$237$		0			0
$238$	−30.9474	−	53.6025i	−2.00602	−	3.47453i
$239$	−0.604130	−	1.04638i	−0.0390779	−	0.0676850i	0.845825	−	0.533461i	$-0.179109\pi$
$239$	−0.604130	−	1.04638i	−0.0390779	−	0.0676850i	−0.884903	+	0.465776i	$0.845775\pi$
$240$		0			0
$241$	−14.1265	+	24.4678i	−0.909968	+	1.57611i	−0.0958618	+	0.995395i	$0.530561\pi$
$241$	−14.1265	+	24.4678i	−0.909968	+	1.57611i	−0.814106	+	0.580716i	$0.802773\pi$
$242$	−16.2908			−1.04721
$243$		0			0
$244$	−64.3054			−4.11673
$245$	−12.3997	+	21.4769i	−0.792187	+	1.37211i
$246$		0			0
$247$	−0.649783	−	1.12546i	−0.0413447	−	0.0716111i
$248$	−37.9456	−	65.7236i	−2.40955	−	4.17345i
$249$		0			0
$250$	−7.97947	+	13.8208i	−0.504666	+	0.874107i
$251$	−15.9212			−1.00494			−0.502469	−	0.864595i	$-0.667575\pi$
$251$	−15.9212			−1.00494			−0.502469	+	0.864595i	$0.667575\pi$
$252$		0			0
$253$	−4.43760			−0.278989
$254$	−4.18719	+	7.25242i	−0.262727	+	0.455057i
$255$		0			0
$256$	4.20352	+	7.28071i	0.262720	+	0.455045i
$257$	−9.27207	−	16.0597i	−0.578376	−	1.00178i	−0.995666	−	0.0930031i	$-0.970353\pi$
$257$	−9.27207	−	16.0597i	−0.578376	−	1.00178i	0.417290	−	0.908773i	$-0.362980\pi$
$258$		0			0
$259$	6.07707	−	10.5258i	0.377611	−	0.654041i
$260$	−42.5333			−2.63781
$261$		0			0
$262$	12.3388			0.762294
$263$	0.781763	−	1.35405i	0.0482056	−	0.0834945i	−0.840916	−	0.541166i	$-0.817983\pi$
$263$	0.781763	−	1.35405i	0.0482056	−	0.0834945i	0.889121	+	0.457671i	$0.151316\pi$
$264$		0			0
$265$	−5.66388	−	9.81013i	−0.347930	−	0.602632i
$266$	2.22391	+	3.85193i	0.136357	+	0.236177i
$267$		0			0
$268$	−3.79472	+	6.57265i	−0.231799	+	0.401488i
$269$	16.6610			1.01584			0.507919	−	0.861405i	$-0.330415\pi$
$269$	16.6610			1.01584			0.507919	+	0.861405i	$0.330415\pi$
$270$		0			0
$271$	−23.5537			−1.43078			−0.715392	−	0.698724i	$-0.753752\pi$
$271$	−23.5537			−1.43078			−0.715392	+	0.698724i	$0.753752\pi$
$272$	−31.2994	+	54.2121i	−1.89780	+	3.28709i
$273$		0			0
$274$	26.2514	+	45.4688i	1.58591	+	2.74687i
$275$	5.88148	+	10.1870i	0.354667	+	0.614301i
$276$		0			0
$277$	−10.7167	+	18.5619i	−0.643904	+	1.11528i	0.340649	+	0.940191i	$0.389353\pi$
$277$	−10.7167	+	18.5619i	−0.643904	+	1.11528i	−0.984553	+	0.175085i	$0.943980\pi$
$278$	−9.58183			−0.574680
$279$		0			0
$280$	86.7804			5.18612
$281$	−1.04696	+	1.81339i	−0.0624566	+	0.108178i	−0.895563	−	0.444935i	$-0.853227\pi$
$281$	−1.04696	+	1.81339i	−0.0624566	+	0.108178i	0.833106	+	0.553113i	$0.186560\pi$
$282$		0			0
$283$	5.02403	+	8.70187i	0.298647	+	0.517272i	0.975827	−	0.218546i	$-0.0701312\pi$
$283$	5.02403	+	8.70187i	0.298647	+	0.517272i	−0.677179	+	0.735818i	$0.736798\pi$
$284$	9.53519	+	16.5154i	0.565810	+	0.980011i
$285$		0			0
$286$	16.7631	−	29.0346i	0.991225	−	1.71685i
$287$	40.0407			2.36353
$288$		0			0
$289$	17.7491			1.04406
$290$	21.5165	−	37.2676i	1.26349	−	2.18843i
$291$		0			0
$292$	−11.5950	−	20.0832i	−0.678548	−	1.17528i
$293$	13.4087	+	23.2246i	0.783346	+	1.35679i	0.929982	+	0.367604i	$0.119822\pi$
$293$	13.4087	+	23.2246i	0.783346	+	1.35679i	−0.146637	+	0.989190i	$0.546845\pi$
$294$		0			0
$295$	−3.92932	+	6.80578i	−0.228774	+	0.396248i
$296$	−23.7571			−1.38085
$297$		0			0
$298$	18.6648			1.08122
$299$	1.64232	−	2.84459i	0.0949779	−	0.164507i
$300$		0			0
$301$	−1.99111	−	3.44870i	−0.114765	−	0.198780i
$302$	−10.5394	−	18.2547i	−0.606473	−	1.05044i
$303$		0			0
$304$	2.24920	−	3.89574i	0.129001	−	0.223436i
$305$	−36.3547			−2.08167
$306$		0			0
$307$	−1.57624			−0.0899608			−0.0449804	−	0.998988i	$-0.514323\pi$
$307$	−1.57624			−0.0899608			−0.0449804	+	0.998988i	$0.514323\pi$
$308$	−40.8675	+	70.7846i	−2.32864	+	4.03333i
$309$		0			0
$310$	−35.9858	−	62.3293i	−2.04386	−	3.54007i
$311$	15.6121	+	27.0410i	0.885281	+	1.53335i	0.845391	+	0.534148i	$0.179368\pi$
$311$	15.6121	+	27.0410i	0.885281	+	1.53335i	0.0398905	+	0.999204i	$0.487299\pi$
$312$		0			0
$313$	−13.2903	+	23.0195i	−0.751213	+	1.30114i	0.196023	+	0.980599i	$0.437197\pi$
$313$	−13.2903	+	23.0195i	−0.751213	+	1.30114i	−0.947235	+	0.320539i	$0.896136\pi$
$314$	−39.7655			−2.24410
$315$		0			0
$316$	57.1858			3.21695
$317$	−14.6177	+	25.3186i	−0.821013	+	1.42204i	0.0839155	+	0.996473i	$0.473257\pi$
$317$	−14.6177	+	25.3186i	−0.821013	+	1.42204i	−0.904929	+	0.425563i	$0.860076\pi$
$318$		0			0
$319$	12.0809	+	20.9248i	0.676402	+	1.17156i
$320$	−16.1552	−	27.9816i	−0.903104	−	1.56422i
$321$		0			0
$322$	−5.62092	+	9.73573i	−0.313242	+	0.542551i
$323$	−2.49710			−0.138942
$324$		0			0
$325$	−8.70677			−0.482965
$326$	−6.49380	+	11.2476i	−0.359659	+	0.622947i
$327$		0			0
$328$	−39.1328	−	67.7799i	−2.16075	−	3.74252i
$329$	16.4518	+	28.4954i	0.907019	+	1.57100i
$330$		0			0
$331$	−0.816193	+	1.41369i	−0.0448620	+	0.0777033i	−0.887584	−	0.460645i	$-0.847618\pi$
$331$	−0.816193	+	1.41369i	−0.0448620	+	0.0777033i	0.842722	+	0.538348i	$0.180951\pi$
$332$	6.49446			0.356430
$333$		0			0
$334$	−48.5185			−2.65481
$335$	−2.14533	+	3.71581i	−0.117212	+	0.203017i
$336$		0			0
$337$	−10.5307	−	18.2397i	−0.573644	−	0.993580i	−0.996188	−	0.0872375i	$-0.972196\pi$
$337$	−10.5307	−	18.2397i	−0.573644	−	0.993580i	0.422544	−	0.906342i	$-0.361137\pi$
$338$	−4.73064	−	8.19371i	−0.257313	−	0.445679i
$339$		0			0
$340$	−40.8637	+	70.7780i	−2.21614	+	3.83848i
$341$	40.4102			2.18834
$342$		0			0
$343$	−7.39896			−0.399506
$344$	−3.89191	+	6.74099i	−0.209838	+	0.363450i
$345$		0			0
$346$	−6.61680	−	11.4606i	−0.355721	−	0.616127i
$347$	−1.11639	−	1.93365i	−0.0599312	−	0.103804i	0.834503	−	0.551003i	$-0.185755\pi$
$347$	−1.11639	−	1.93365i	−0.0599312	−	0.103804i	−0.894434	+	0.447199i	$0.852421\pi$
$348$		0			0
$349$	16.2649	−	28.1717i	0.870642	−	1.50800i	0.00930889	−	0.999957i	$-0.497037\pi$
$349$	16.2649	−	28.1717i	0.870642	−	1.50800i	0.861333	−	0.508040i	$-0.169630\pi$
$350$	29.7993			1.59284
$351$		0			0
$352$	51.5270			2.74640
$353$	12.0631	−	20.8939i	0.642054	−	1.11207i	−0.342919	−	0.939365i	$-0.611416\pi$
$353$	12.0631	−	20.8939i	0.642054	−	1.11207i	0.984973	−	0.172706i	$-0.0552510\pi$
$354$		0			0
$355$	5.39067	+	9.33692i	0.286107	+	0.495552i
$356$	−1.56004	−	2.70206i	−0.0826818	−	0.143209i
$357$		0			0
$358$	16.5070	−	28.5909i	0.872420	−	1.51108i
$359$	11.7399			0.619610			0.309805	−	0.950800i	$-0.399736\pi$
$359$	11.7399			0.619610			0.309805	+	0.950800i	$0.399736\pi$
$360$		0			0
$361$	−18.8206			−0.990556
$362$	24.7366	−	42.8451i	1.30013	−	2.25189i
$363$		0			0
$364$	−30.2496	−	52.3938i	−1.58551	−	2.74618i
$365$	−6.55519	−	11.3539i	−0.343114	−	0.594292i
$366$		0			0
$367$	−11.7190	+	20.2978i	−0.611725	+	1.05954i	0.379225	+	0.925304i	$0.376191\pi$
$367$	−11.7190	+	20.2978i	−0.611725	+	1.05954i	−0.990950	+	0.134234i	$0.957143\pi$
$368$	11.3697			0.592687
$369$		0			0
$370$	−22.5301			−1.17129
$371$	8.05627	−	13.9539i	0.418261	−	0.724448i
$372$		0			0
$373$	14.8316	+	25.6890i	0.767950	+	1.33013i	0.938673	+	0.344809i	$0.112056\pi$
$373$	14.8316	+	25.6890i	0.767950	+	1.33013i	−0.170723	+	0.985319i	$0.554610\pi$
$374$	−32.2102	−	55.7897i	−1.66555	−	2.88482i
$375$		0			0
$376$	32.1576	−	55.6985i	1.65840	−	2.87243i
$377$	−17.8843			−0.921086
$378$		0			0
$379$	6.39478			0.328478			0.164239	−	0.986421i	$-0.447483\pi$
$379$	6.39478			0.328478			0.164239	+	0.986421i	$0.447483\pi$
$380$	2.93650	−	5.08617i	0.150639	−	0.260915i
$381$		0			0
$382$	11.7492	+	20.3502i	0.601141	+	1.04121i
$383$	−18.2711	−	31.6465i	−0.933610	−	1.61706i	−0.777093	−	0.629385i	$-0.783307\pi$
$383$	−18.2711	−	31.6465i	−0.933610	−	1.61706i	−0.156517	−	0.987675i	$-0.550027\pi$
$384$		0			0
$385$	−23.1042	+	40.0177i	−1.17750	+	2.03949i
$386$	14.5332			0.739718
$387$		0			0
$388$	20.3760			1.03443
$389$	−10.6761	+	18.4916i	−0.541300	+	0.937559i	0.457530	+	0.889194i	$0.348734\pi$
$389$	−10.6761	+	18.4916i	−0.541300	+	0.937559i	−0.998830	+	0.0483649i	$0.984599\pi$
$390$		0			0
$391$	−3.15571	−	5.46584i	−0.159591	−	0.276420i
$392$	34.4745	+	59.7117i	1.74123	+	3.01589i
$393$		0			0
$394$	6.61713	−	11.4612i	0.333366	−	0.577407i
$395$	32.3297			1.62668
$396$		0			0
$397$	1.77261			0.0889646			0.0444823	−	0.999010i	$-0.485836\pi$
$397$	1.77261			0.0889646			0.0444823	+	0.999010i	$0.485836\pi$
$398$	0.377114	−	0.653181i	0.0189030	−	0.0327410i
$399$		0			0
$400$	−15.0691	−	26.1005i	−0.753456	−	1.30502i
$401$	4.64888	+	8.05210i	0.232154	+	0.402103i	0.958442	−	0.285288i	$-0.0920893\pi$
$401$	4.64888	+	8.05210i	0.232154	+	0.402103i	−0.726288	+	0.687391i	$0.758756\pi$
$402$		0			0
$403$	−14.9555	+	25.9037i	−0.744988	+	1.29036i
$404$	22.6421			1.12649
$405$		0			0
$406$	61.2097			3.03779
$407$	6.32504	−	10.9553i	0.313520	−	0.543033i
$408$		0			0
$409$	−10.3979	−	18.0097i	−0.514144	−	0.890523i	−0.999865	−	0.0164093i	$-0.994777\pi$
$409$	−10.3979	−	18.0097i	−0.514144	−	0.890523i	0.485722	−	0.874113i	$-0.338557\pi$
$410$	−37.1117	−	64.2794i	−1.83282	−	3.17453i
$411$		0			0
$412$	−0.550907	+	0.954199i	−0.0271412	+	0.0470100i
$413$	−11.1781			−0.550037
$414$		0			0
$415$	3.67161			0.180232
$416$	−19.0698	+	33.0298i	−0.934972	+	1.61942i
$417$		0			0
$418$	2.31465	+	4.00910i	0.113213	+	0.196091i
$419$	−17.0187	−	29.4772i	−0.831417	−	1.44006i	−0.896915	−	0.442203i	$-0.854197\pi$
$419$	−17.0187	−	29.4772i	−0.831417	−	1.44006i	0.0654984	−	0.997853i	$-0.479136\pi$
$420$		0			0
$421$	−11.1239	+	19.2671i	−0.542145	+	0.939022i	0.456636	+	0.889654i	$0.349054\pi$
$421$	−11.1239	+	19.2671i	−0.542145	+	0.939022i	−0.998781	+	0.0493685i	$0.984279\pi$
$422$	−46.3403			−2.25581
$423$		0			0
$424$	−31.4943			−1.52950
$425$	−8.36499	+	14.4886i	−0.405762	+	0.702800i
$426$		0			0
$427$	−25.8554	−	44.7828i	−1.25123	−	2.16719i
$428$	7.28554	+	12.6189i	0.352160	+	0.609958i
$429$		0			0
$430$	−3.69091	+	6.39284i	−0.177991	+	0.308290i
$431$	−13.1389			−0.632879			−0.316439	−	0.948613i	$-0.602487\pi$
$431$	−13.1389			−0.632879			−0.316439	+	0.948613i	$0.602487\pi$
$432$		0			0
$433$	4.43558			0.213160			0.106580	−	0.994304i	$-0.466010\pi$
$433$	4.43558			0.213160			0.106580	+	0.994304i	$0.466010\pi$
$434$	51.1860	−	88.6567i	2.45701	−	4.25566i
$435$		0			0
$436$	−18.6804	−	32.3554i	−0.894628	−	1.54954i
$437$	0.226772	+	0.392781i	0.0108480	+	0.0187892i
$438$		0			0
$439$	−5.27411	+	9.13503i	−0.251720	+	0.435991i	−0.963999	−	0.265905i	$-0.914329\pi$
$439$	−5.27411	+	9.13503i	−0.251720	+	0.435991i	0.712280	+	0.701896i	$0.247663\pi$
$440$	90.3213			4.30590
$441$		0			0
$442$	47.6830			2.26805
$443$	14.0548	−	24.3437i	0.667766	−	1.15660i	−0.310762	−	0.950488i	$-0.600584\pi$
$443$	14.0548	−	24.3437i	0.667766	−	1.15660i	0.978527	−	0.206116i	$-0.0660825\pi$
$444$		0			0
$445$	−0.881959	−	1.52760i	−0.0418089	−	0.0724151i
$446$	14.3539	+	24.8617i	0.679677	+	1.17723i
$447$		0			0
$448$	22.9791	−	39.8009i	1.08566	−	1.88042i
$449$	29.5048			1.39242			0.696208	−	0.717840i	$-0.254869\pi$
$449$	29.5048			1.39242			0.696208	+	0.717840i	$0.254869\pi$
$450$		0			0
$451$	41.6745			1.96238
$452$	−24.2033	+	41.9213i	−1.13843	+	1.97181i
$453$		0			0
$454$	13.7694	+	23.8493i	0.646231	+	1.11930i
$455$	−17.1014	−	29.6205i	−0.801727	−	1.38863i
$456$		0			0
$457$	18.2519	−	31.6132i	0.853789	−	1.47881i	−0.0239758	−	0.999713i	$-0.507632\pi$
$457$	18.2519	−	31.6132i	0.853789	−	1.47881i	0.877764	−	0.479093i	$-0.159034\pi$
$458$	−40.2933			−1.88278
$459$		0			0
$460$	14.8440			0.692105
$461$	−10.1261	+	17.5389i	−0.471619	+	0.816869i	−0.999473	−	0.0324669i	$-0.989664\pi$
$461$	−10.1261	+	17.5389i	−0.471619	+	0.816869i	0.527854	+	0.849335i	$0.322997\pi$
$462$		0			0
$463$	10.9574	+	18.9788i	0.509233	+	0.882017i	0.999943	+	0.0106943i	$0.00340417\pi$
$463$	10.9574	+	18.9788i	0.509233	+	0.882017i	−0.490710	+	0.871323i	$0.663262\pi$
$464$	−30.9529	−	53.6120i	−1.43695	−	2.48888i
$465$		0			0
$466$	−28.1859	+	48.8195i	−1.30569	+	2.26152i
$467$	1.61995			0.0749623			0.0374812	−	0.999297i	$-0.488067\pi$
$467$	1.61995			0.0749623			0.0374812	+	0.999297i	$0.488067\pi$
$468$		0			0
$469$	−6.10299			−0.281810
$470$	30.4968	−	52.8219i	1.40671	−	2.43649i
$471$		0			0
$472$	10.9246	+	18.9219i	0.502845	+	0.870953i
$473$	−2.07235	−	3.58941i	−0.0952867	−	0.165041i
$474$		0			0
$475$	0.601116	−	1.04116i	0.0275811	−	0.0477719i
$476$	−116.248			−5.32824
$477$		0			0
$478$	−3.18580			−0.145715
$479$	−3.62256	+	6.27445i	−0.165519	+	0.286687i	−0.936839	−	0.349760i	$-0.886263\pi$
$479$	−3.62256	+	6.27445i	−0.165519	+	0.286687i	0.771321	+	0.636447i	$0.219597\pi$
$480$		0			0
$481$	4.68170	+	8.10894i	0.213467	+	0.369736i
$482$	37.2472	+	64.5140i	1.69656	+	2.93853i
$483$		0			0
$484$	−15.2984	+	26.4976i	−0.695381	+	1.20444i
$485$	11.5195			0.523072
$486$		0			0
$487$	−29.5624			−1.33960			−0.669800	−	0.742542i	$-0.733620\pi$
$487$	−29.5624			−1.33960			−0.669800	+	0.742542i	$0.733620\pi$
$488$	−50.5381	+	87.5346i	−2.28775	+	3.96250i
$489$		0			0
$490$	32.6941	+	56.6278i	1.47697	+	2.55818i
$491$	−5.75467	−	9.96738i	−0.259705	−	0.449822i	0.706458	−	0.707755i	$-0.250292\pi$
$491$	−5.75467	−	9.96738i	−0.259705	−	0.449822i	−0.966163	+	0.257933i	$0.916959\pi$
$492$		0			0
$493$	−17.1822	+	29.7605i	−0.773848	+	1.34034i
$494$	−3.42655			−0.154168
$495$		0			0
$496$	−103.536			−4.64891
$497$	−7.66765	+	13.2808i	−0.343941	+	0.595724i
$498$		0			0
$499$	−15.5985	−	27.0174i	−0.698286	−	1.20947i	−0.969060	−	0.246824i	$-0.920613\pi$
$499$	−15.5985	−	27.0174i	−0.698286	−	1.20947i	0.270775	−	0.962643i	$-0.412720\pi$
$500$	14.9867	+	25.9578i	0.670227	+	1.16087i
$501$		0			0
$502$	−20.9896	+	36.3551i	−0.936813	+	1.62261i
$503$	17.1085			0.762831			0.381416	−	0.924404i	$-0.375437\pi$
$503$	17.1085			0.762831			0.381416	+	0.924404i	$0.375437\pi$
$504$		0			0
$505$	12.8006			0.569620
$506$	−5.85028	+	10.1330i	−0.260076	+	0.450466i
$507$		0			0
$508$	7.86421	+	13.6212i	0.348918	+	0.604343i
$509$	14.5671	+	25.2309i	0.645674	+	1.11834i	0.984145	+	0.177363i	$0.0567567\pi$
$509$	14.5671	+	25.2309i	0.645674	+	1.11834i	−0.338472	+	0.940977i	$0.609910\pi$
$510$		0			0
$511$	9.32406	−	16.1497i	0.412472	−	0.714423i
$512$	33.2979			1.47157
$513$		0			0
$514$	−48.8951			−2.15667
$515$	−0.311453	+	0.539452i	−0.0137242	+	0.0237711i
$516$		0			0
$517$	17.1231	+	29.6581i	0.753074	+	1.30436i
$518$	−16.0233	−	27.7532i	−0.704025	−	1.21941i
$519$		0			0
$520$	−33.4273	+	57.8977i	−1.46588	+	2.53898i
$521$	32.9618			1.44408			0.722042	−	0.691850i	$-0.243204\pi$
$521$	32.9618			1.44408			0.722042	+	0.691850i	$0.243204\pi$
$522$		0			0
$523$	9.33844			0.408342			0.204171	−	0.978935i	$-0.434550\pi$
$523$	9.33844			0.408342			0.204171	+	0.978935i	$0.434550\pi$
$524$	11.5871	−	20.0695i	0.506186	−	0.876740i
$525$		0			0
$526$	−2.06126	−	3.57021i	−0.0898754	−	0.155669i
$527$	28.7369	+	49.7738i	1.25180	+	2.16818i
$528$		0			0
$529$	10.9268	−	18.9258i	0.475080	−	0.822862i
$530$	−29.8678			−1.29737
$531$		0			0
$532$	8.35372			0.362180
$533$	−15.4234	+	26.7142i	−0.668063	+	1.15712i
$534$		0			0
$535$	4.11884	+	7.13404i	0.178073	+	0.308431i
$536$	5.96460	+	10.3310i	0.257632	+	0.446231i
$537$		0			0
$538$	21.9649	−	38.0444i	0.946975	−	1.64021i
$539$	−36.7137			−1.58137
$540$		0			0
$541$	−13.4426			−0.577943			−0.288972	−	0.957338i	$-0.593313\pi$
$541$	−13.4426			−0.577943			−0.288972	+	0.957338i	$0.593313\pi$
$542$	−31.0518	+	53.7833i	−1.33379	+	2.31019i
$543$		0			0
$544$	36.6424	+	63.4665i	1.57103	+	2.72110i
$545$	−10.5609	−	18.2919i	−0.452377	−	0.783541i
$546$		0			0
$547$	15.0500	−	26.0674i	0.643493	−	1.11456i	−0.341154	−	0.940007i	$-0.610818\pi$
$547$	15.0500	−	26.0674i	0.643493	−	1.11456i	0.984647	−	0.174556i	$-0.0558489\pi$
$548$	98.6087			4.21236
$549$		0			0
$550$	31.0152			1.32249
$551$	1.23473	−	2.13861i	0.0526012	−	0.0911080i
$552$		0			0
$553$	22.9927	+	39.8246i	0.977751	+	1.69351i
$554$	28.2566	+	48.9419i	1.20051	+	2.07934i
$555$		0			0
$556$	−8.99811	+	15.5852i	−0.381605	+	0.660959i
$557$	24.0468			1.01890			0.509448	−	0.860502i	$-0.329850\pi$
$557$	24.0468			1.01890			0.509448	+	0.860502i	$0.329850\pi$
$558$		0			0
$559$	3.06785			0.129756
$560$	59.1961	−	102.531i	2.50149	−	4.33271i
$561$		0			0
$562$	2.76052	+	4.78135i	0.116445	+	0.201689i
$563$	−14.1990	−	24.5934i	−0.598418	−	1.03649i	−0.993055	−	0.117653i	$-0.962463\pi$
$563$	−14.1990	−	24.5934i	−0.598418	−	1.03649i	0.394637	−	0.918837i	$-0.370870\pi$
$564$		0			0
$565$	−13.6832	+	23.7000i	−0.575657	+	0.997067i
$566$	26.4936			1.11361
$567$		0			0
$568$	29.9751			1.25773
$569$	3.78124	−	6.54930i	0.158518	−	0.274561i	−0.775817	−	0.630958i	$-0.782662\pi$
$569$	3.78124	−	6.54930i	0.158518	−	0.274561i	0.934334	+	0.356398i	$0.115995\pi$
$570$		0			0
$571$	−0.371104	−	0.642771i	−0.0155302	−	0.0268991i	0.858156	−	0.513389i	$-0.171610\pi$
$571$	−0.371104	−	0.642771i	−0.0155302	−	0.0268991i	−0.873686	+	0.486490i	$0.838277\pi$
$572$	−31.4838	−	54.5316i	−1.31641	−	2.28008i
$573$		0			0
$574$	52.7874	−	91.4305i	2.20331	−	3.81624i
$575$	3.03864			0.126720
$576$		0			0
$577$	−35.8196			−1.49119			−0.745596	−	0.666399i	$-0.767835\pi$
$577$	−35.8196			−1.49119			−0.745596	+	0.666399i	$0.767835\pi$
$578$	23.3994	−	40.5289i	0.973286	−	1.68578i
$579$		0			0
$580$	−40.4113	−	69.9945i	−1.67799	−	2.90636i
$581$	2.61124	+	4.52279i	0.108332	+	0.187637i
$582$		0			0
$583$	8.38499	−	14.5232i	0.347271	−	0.601491i
$584$	−36.4505			−1.50833
$585$		0			0
$586$	70.7092			2.92097
$587$	14.5053	−	25.1240i	0.598699	−	1.03698i	−0.394314	−	0.918976i	$-0.629018\pi$
$587$	14.5053	−	25.1240i	0.598699	−	1.03698i	0.993013	−	0.118002i	$-0.0376489\pi$
$588$		0			0
$589$	−2.06506	−	3.57679i	−0.0850893	−	0.147379i
$590$	10.3604	+	17.9447i	0.426530	+	0.738772i
$591$		0			0
$592$	−16.2056	+	28.0689i	−0.666045	+	1.15362i
$593$	37.8607			1.55475			0.777376	−	0.629036i	$-0.216550\pi$
$593$	37.8607			1.55475			0.777376	+	0.629036i	$0.216550\pi$
$594$		0			0
$595$	−65.7205			−2.69428
$596$	17.5278	−	30.3590i	0.717965	−	1.24355i
$597$		0			0
$598$	−4.33029	−	7.50028i	−0.177079	−	0.306709i
$599$	12.6312	+	21.8779i	0.516098	+	0.893908i	0.999825	+	0.0186890i	$0.00594924\pi$
$599$	12.6312	+	21.8779i	0.516098	+	0.893908i	−0.483728	+	0.875219i	$0.660717\pi$
$600$		0			0
$601$	13.2093	−	22.8791i	0.538818	−	0.933260i	−0.460150	−	0.887841i	$-0.652204\pi$
$601$	13.2093	−	22.8791i	0.538818	−	0.933260i	0.998968	−	0.0454186i	$-0.0144622\pi$
$602$	−10.4998			−0.427942
$603$		0			0
$604$	−39.5893			−1.61086
$605$	−8.64887	+	14.9803i	−0.351626	+	0.609035i
$606$		0			0
$607$	−1.46630	−	2.53971i	−0.0595153	−	0.103084i	0.834733	−	0.550655i	$-0.185622\pi$
$607$	−1.46630	−	2.53971i	−0.0595153	−	0.103084i	−0.894248	+	0.447572i	$0.852289\pi$
$608$	−2.63316	−	4.56076i	−0.106789	−	0.184963i
$609$		0			0
$610$	−47.9280	+	83.0138i	−1.94055	+	3.36113i
$611$	−25.3486			−1.02549
$612$		0			0
$613$	−17.6161			−0.711506			−0.355753	−	0.934580i	$-0.615776\pi$
$613$	−17.6161			−0.711506			−0.355753	+	0.934580i	$0.615776\pi$
$614$	−2.07803	+	3.59925i	−0.0838624	+	0.145254i
$615$		0			0
$616$	64.2362	+	111.260i	2.58815	+	4.48281i
$617$	−3.48648	−	6.03877i	−0.140361	−	0.243112i	0.787272	−	0.616606i	$-0.211493\pi$
$617$	−3.48648	−	6.03877i	−0.140361	−	0.243112i	−0.927632	+	0.373494i	$0.878160\pi$
$618$		0			0
$619$	−17.8000	+	30.8305i	−0.715443	+	1.23918i	0.247345	+	0.968927i	$0.420442\pi$
$619$	−17.8000	+	30.8305i	−0.715443	+	1.23918i	−0.962788	+	0.270256i	$0.912892\pi$
$620$	−135.174			−5.42873
$621$		0			0
$622$	82.3285			3.30107
$623$	1.25449	−	2.17284i	0.0502602	−	0.0870532i
$624$		0			0
$625$	15.5679	+	26.9643i	0.622714	+	1.07857i
$626$	35.0424	+	60.6952i	1.40058	+	2.42587i
$627$		0			0
$628$	−37.3430	+	64.6800i	−1.49015	+	2.58101i
$629$	17.9917			0.717375
$630$		0			0
$631$	−31.8092			−1.26630			−0.633151	−	0.774028i	$-0.718239\pi$
$631$	−31.8092			−1.26630			−0.633151	+	0.774028i	$0.718239\pi$
$632$	44.9427	−	77.8431i	1.78773	−	3.09643i
$633$		0			0
$634$	38.5424	+	66.7573i	1.53071	+	2.65127i
$635$	4.44599	+	7.70068i	0.176434	+	0.305592i
$636$		0			0
$637$	13.5875	−	23.5342i	0.538356	−	0.932460i
$638$	63.7072			2.52219
$639$		0			0
$640$	−15.5817			−0.615920
$641$	−17.5758	+	30.4421i	−0.694201	+	1.20239i	0.276249	+	0.961086i	$0.410909\pi$
$641$	−17.5758	+	30.4421i	−0.694201	+	1.20239i	−0.970449	+	0.241305i	$0.922425\pi$
$642$		0			0
$643$	0.964272	+	1.67017i	0.0380272	+	0.0658650i	0.884413	−	0.466706i	$-0.154559\pi$
$643$	0.964272	+	1.67017i	0.0380272	+	0.0658650i	−0.846385	+	0.532571i	$0.821226\pi$
$644$	10.5570	+	18.2853i	0.416004	+	0.720540i
$645$		0			0
$646$	−3.29204	+	5.70198i	−0.129524	+	0.224341i
$647$	23.8139			0.936221			0.468111	−	0.883670i	$-0.344935\pi$
$647$	23.8139			0.936221			0.468111	+	0.883670i	$0.344935\pi$
$648$		0			0
$649$	−11.6342			−0.456681
$650$	−11.4785	+	19.8814i	−0.450225	+	0.779812i
$651$		0			0
$652$	12.1964	+	21.1248i	0.477648	+	0.827311i
$653$	0.767582	+	1.32949i	0.0300378	+	0.0520270i	0.880654	−	0.473761i	$-0.157104\pi$
$653$	0.767582	+	1.32949i	0.0300378	+	0.0520270i	−0.850616	+	0.525788i	$0.823771\pi$
$654$		0			0
$655$	6.55072	−	11.3462i	0.255958	−	0.443332i
$656$	−106.776			−4.16889
$657$		0			0
$658$	86.7567			3.38213
$659$	−4.91274	+	8.50911i	−0.191373	+	0.331468i	−0.945705	−	0.325025i	$-0.894627\pi$
$659$	−4.91274	+	8.50911i	−0.191373	+	0.331468i	0.754332	+	0.656493i	$0.227961\pi$
$660$		0			0
$661$	−1.49661	−	2.59220i	−0.0582113	−	0.100825i	0.835451	−	0.549565i	$-0.185206\pi$
$661$	−1.49661	−	2.59220i	−0.0582113	−	0.100825i	−0.893663	+	0.448740i	$0.851873\pi$
$662$	2.15204	+	3.72745i	0.0836416	+	0.144871i
$663$		0			0
$664$	5.10405	−	8.84047i	0.198075	−	0.343077i
$665$	4.72273			0.183140
$666$		0			0
$667$	6.24154			0.241674
$668$	−45.5627	+	78.9170i	−1.76288	+	3.05339i
$669$		0			0
$670$	5.65655	+	9.79744i	0.218532	+	0.378508i
$671$	−26.9103	−	46.6101i	−1.03886	−	1.79936i
$672$		0			0
$673$	−6.80885	+	11.7933i	−0.262462	+	0.454598i	−0.966896	−	0.255172i	$-0.917868\pi$
$673$	−6.80885	+	11.7933i	−0.262462	+	0.454598i	0.704434	+	0.709770i	$0.251201\pi$
$674$	−55.5323			−2.13903
$675$		0			0
$676$	−17.7698			−0.683454
$677$	−12.8430	+	22.2447i	−0.493595	+	0.854932i	−0.999973	−	0.00738021i	$-0.997651\pi$
$677$	−12.8430	+	22.2447i	−0.493595	+	0.854932i	0.506378	+	0.862312i	$0.330984\pi$
$678$		0			0
$679$	8.19260	+	14.1900i	0.314403	+	0.544562i
$680$	64.2302	+	111.250i	2.46311	+	4.26624i
$681$		0			0
$682$	53.2745	−	92.2742i	2.03999	−	3.53336i
$683$	19.3240			0.739413			0.369707	−	0.929149i	$-0.379458\pi$
$683$	19.3240			0.739413			0.369707	+	0.929149i	$0.379458\pi$
$684$		0			0
$685$	55.7479			2.13002
$686$	−9.75437	+	16.8951i	−0.372424	+	0.645057i
$687$		0			0
$688$	5.30963	+	9.19655i	0.202428	+	0.350615i
$689$	6.20645	+	10.7499i	0.236447	+	0.409538i
$690$		0			0
$691$	19.9695	−	34.5883i	0.759677	−	1.31580i	−0.183338	−	0.983050i	$-0.558690\pi$
$691$	19.9695	−	34.5883i	0.759677	−	1.31580i	0.943015	−	0.332750i	$-0.107976\pi$
$692$	−24.8548			−0.944838
$693$		0			0
$694$	−5.88716			−0.223474
$695$	−5.08703	+	8.81100i	−0.192962	+	0.334220i
$696$		0			0
$697$	29.6360	+	51.3310i	1.12254	+	1.94430i
$698$	−42.8856	−	74.2800i	−1.62324	−	2.81154i
$699$		0			0
$700$	27.9840	−	48.4696i	1.05769	−	1.83198i
$701$	1.68883			0.0637864			0.0318932	−	0.999491i	$-0.489846\pi$
$701$	1.68883			0.0637864			0.0318932	+	0.999491i	$0.489846\pi$
$702$		0			0
$703$	−1.29290			−0.0487626
$704$	23.9167	−	41.4249i	0.901394	−	1.56126i
$705$		0			0
$706$	−31.8066	−	55.0907i	−1.19706	−	2.07337i
$707$	9.10375	+	15.7682i	0.342382	+	0.593023i
$708$		0			0
$709$	−12.9666	+	22.4587i	−0.486969	+	0.843455i	−0.999888	−	0.0149821i	$-0.995231\pi$
$709$	−12.9666	+	22.4587i	−0.486969	+	0.843455i	0.512919	+	0.858437i	$0.328564\pi$
$710$	28.4270			1.06685
$711$		0			0
$712$	−4.90418			−0.183792
$713$	5.21943	−	9.04032i	0.195469	−	0.338562i
$714$		0			0
$715$	−17.7992	−	30.8292i	−0.665653	−	1.15295i
$716$	−31.0027	−	53.6983i	−1.15863	−	2.00680i
$717$		0			0
$718$	15.4773	−	26.8074i	0.577606	−	1.00044i
$719$	18.4698			0.688808			0.344404	−	0.938822i	$-0.388081\pi$
$719$	18.4698			0.688808			0.344404	+	0.938822i	$0.388081\pi$
$720$		0			0
$721$	−0.886016			−0.0329969
$722$	−24.8120	+	42.9756i	−0.923406	+	1.59939i
$723$		0			0
$724$	−46.4593	−	80.4699i	−1.72665	−	2.99064i
$725$	−8.27239	−	14.3282i	−0.307229	−	0.532136i
$726$		0			0
$727$	−0.496885	+	0.860630i	−0.0184284	+	0.0319190i	−0.875093	−	0.483956i	$-0.839200\pi$
$727$	−0.496885	+	0.860630i	−0.0184284	+	0.0319190i	0.856664	+	0.515875i	$0.172533\pi$
$728$	−95.0934			−3.52440
$729$		0			0
$730$	−34.5680			−1.27942
$731$	2.94742	−	5.10508i	0.109014	−	0.188818i
$732$		0			0
$733$	−13.3517	−	23.1259i	−0.493157	−	0.854173i	0.506812	−	0.862057i	$-0.330824\pi$
$733$	−13.3517	−	23.1259i	−0.493157	−	0.854173i	−0.999969	+	0.00788351i	$0.997491\pi$
$734$	30.8992	+	53.5190i	1.14051	+	1.97542i
$735$		0			0
$736$	6.65529	−	11.5273i	0.245317	−	0.424902i
$737$	−6.35201			−0.233979
$738$		0			0
$739$	9.66176			0.355413			0.177707	−	0.984083i	$-0.443132\pi$
$739$	9.66176			0.355413			0.177707	+	0.984083i	$0.443132\pi$
$740$	−21.1576	+	36.6460i	−0.777768	+	1.34713i
$741$		0			0
$742$	−21.2419	−	36.7920i	−0.779813	−	1.35068i
$743$	−10.7735	−	18.6602i	−0.395241	−	0.684578i	0.597891	−	0.801578i	$-0.296006\pi$
$743$	−10.7735	−	18.6602i	−0.395241	−	0.684578i	−0.993132	+	0.117000i	$0.962672\pi$
$744$		0			0
$745$	9.90923	−	17.1633i	0.363046	−	0.628814i
$746$	78.2124			2.86356
$747$		0			0
$748$	−120.992			−4.42390
$749$	−5.85861	+	10.1474i	−0.214069	+	0.370778i
$750$		0			0
$751$	1.77478	+	3.07401i	0.0647626	+	0.112172i	0.896589	−	0.442864i	$-0.146038\pi$
$751$	1.77478	+	3.07401i	0.0647626	+	0.112172i	−0.831826	+	0.555036i	$0.812704\pi$
$752$	−43.8717	−	75.9880i	−1.59984	−	2.77100i
$753$		0			0
$754$	−23.5776	+	40.8376i	−0.858645	+	1.48722i
$755$	−22.3816			−0.814550
$756$		0			0
$757$	21.5297			0.782509			0.391255	−	0.920282i	$-0.372041\pi$
$757$	21.5297			0.782509			0.391255	+	0.920282i	$0.372041\pi$
$758$	8.43051	−	14.6021i	0.306210	−	0.530371i
$759$		0			0
$760$	−4.61564	−	7.99453i	−0.167427	−	0.289992i
$761$	−7.00704	−	12.1366i	−0.254005	−	0.439950i	0.710620	−	0.703576i	$-0.248415\pi$
$761$	−7.00704	−	12.1366i	−0.254005	−	0.439950i	−0.964625	+	0.263627i	$0.915081\pi$
$762$		0			0
$763$	15.0217	−	26.0183i	0.543822	−	0.941927i
$764$	44.1338			1.59670
$765$		0			0
$766$	−96.3504			−3.48128
$767$	4.30572	−	7.45773i	0.155471	−	0.269283i
$768$		0			0
$769$	14.9750	+	25.9375i	0.540014	+	0.935332i	0.998903	+	0.0468377i	$0.0149144\pi$
$769$	14.9750	+	25.9375i	0.540014	+	0.935332i	−0.458889	+	0.888494i	$0.651752\pi$
$770$	60.9187	+	105.514i	2.19536	+	3.80247i
$771$		0			0
$772$	13.6478	−	23.6387i	0.491195	−	0.850775i
$773$	13.9807			0.502851			0.251425	−	0.967877i	$-0.419101\pi$
$773$	13.9807			0.502851			0.251425	+	0.967877i	$0.419101\pi$
$774$		0			0
$775$	−27.6708			−0.993965
$776$	16.0136	−	27.7364i	0.574856	−	0.995680i
$777$		0			0
$778$	28.1496	+	48.7565i	1.00921	+	1.74800i
$779$	−2.12967	−	3.68870i	−0.0763033	−	0.132161i
$780$		0			0
$781$	−7.98052	+	13.8227i	−0.285565	+	0.494614i
$782$	−16.6412			−0.595089
$783$		0			0
$784$	94.0654			3.35948
$785$	−21.1117	+	36.5665i	−0.753508	+	1.30511i
$786$		0			0
$787$	3.83330	+	6.63948i	0.136643	+	0.236672i	0.926224	−	0.376974i	$-0.123036\pi$
$787$	3.83330	+	6.63948i	0.136643	+	0.236672i	−0.789581	+	0.613646i	$0.789702\pi$
$788$	−12.4280	−	21.5260i	−0.442730	−	0.766831i
$789$		0			0
$790$	42.6216	−	73.8228i	1.51641	−	2.62650i
$791$	−38.9258			−1.38404
$792$		0			0
$793$	39.8373			1.41466
$794$	2.33690	−	4.04764i	0.0829336	−	0.143645i
$795$		0			0
$796$	−0.708280	−	1.22678i	−0.0251043	−	0.0434820i
$797$	−5.90468	−	10.2272i	−0.209154	−	0.362266i	0.742294	−	0.670074i	$-0.233738\pi$
$797$	−5.90468	−	10.2272i	−0.209154	−	0.362266i	−0.951448	+	0.307808i	$0.900404\pi$
$798$		0			0
$799$	−24.3535	+	42.1816i	−0.861566	+	1.49228i
$800$	−35.2830			−1.24744
$801$		0			0
$802$	24.5153			0.865665
$803$	9.70451	−	16.8087i	0.342465	−	0.593166i
$804$		0			0
$805$	5.96834	+	10.3375i	0.210356	+	0.364348i
$806$	39.4330	+	68.3000i	1.38897	+	2.40577i
$807$		0			0
$808$	17.7946	−	30.8212i	0.626013	−	1.08429i
$809$	−29.3361			−1.03140			−0.515701	−	0.856769i	$-0.672468\pi$
$809$	−29.3361			−1.03140			−0.515701	+	0.856769i	$0.672468\pi$
$810$		0			0
$811$	−20.2768			−0.712016			−0.356008	−	0.934483i	$-0.615862\pi$
$811$	−20.2768			−0.712016			−0.356008	+	0.934483i	$0.615862\pi$
$812$	57.4808	−	99.5597i	2.01718	−	3.49386i
$813$		0			0
$814$	−16.6771	−	28.8857i	−0.584534	−	1.01244i
$815$	6.89517	+	11.9428i	0.241527	+	0.418338i
$816$		0			0
$817$	−0.211804	+	0.366856i	−0.00741009	+	0.0128347i
$818$	−54.8321			−1.91716
$819$		0			0
$820$	−139.403			−4.86818
$821$	8.16015	−	14.1338i	0.284791	−	0.493273i	−0.687767	−	0.725931i	$-0.741409\pi$
$821$	8.16015	−	14.1338i	0.284791	−	0.493273i	0.972559	+	0.232658i	$0.0747424\pi$
$822$		0			0
$823$	−9.24734	−	16.0169i	−0.322342	−	0.558312i	0.658629	−	0.752468i	$-0.271137\pi$
$823$	−9.24734	−	16.0169i	−0.322342	−	0.558312i	−0.980971	+	0.194155i	$0.937803\pi$
$824$	0.865924	+	1.49983i	0.0301659	+	0.0522489i
$825$		0			0
$826$	−14.7365	+	25.5244i	−0.512750	+	0.888108i
$827$	−12.6473			−0.439789			−0.219894	−	0.975524i	$-0.570571\pi$
$827$	−12.6473			−0.439789			−0.219894	+	0.975524i	$0.570571\pi$
$828$		0			0
$829$	36.0863			1.25333			0.626665	−	0.779289i	$-0.284419\pi$
$829$	36.0863			1.25333			0.626665	+	0.779289i	$0.284419\pi$
$830$	4.84044	−	8.38389i	0.168014	−	0.291009i
$831$		0			0
$832$	17.7028	+	30.6621i	0.613733	+	1.06302i
$833$	−26.1082	−	45.2208i	−0.904597	−	1.56681i
$834$		0			0
$835$	−25.7587	+	44.6153i	−0.891415	+	1.54398i
$836$	8.69458			0.300708
$837$		0			0
$838$	−89.7458			−3.10022
$839$	22.3275	−	38.6723i	0.770830	−	1.33512i	−0.166279	−	0.986079i	$-0.553175\pi$
$839$	22.3275	−	38.6723i	0.770830	−	1.33512i	0.937109	−	0.349038i	$-0.113492\pi$
$840$		0			0
$841$	−2.49200	−	4.31627i	−0.0859311	−	0.148837i
$842$	29.3302	+	50.8014i	1.01079	+	1.75073i
$843$		0			0
$844$	−43.5173	+	75.3741i	−1.49793	+	2.59448i
$845$	−10.0461			−0.345595
$846$		0			0
$847$	−24.6042			−0.845409
$848$	−21.4834	+	37.2104i	−0.737744	+	1.27781i
$849$		0			0
$850$	22.0559	+	38.2019i	0.756510	+	1.31031i
$851$	−1.63390	−	2.82999i	−0.0560093	−	0.0970110i
$852$		0			0
$853$	23.5820	−	40.8451i	0.807431	−	1.39851i	−0.107207	−	0.994237i	$-0.534191\pi$
$853$	23.5820	−	40.8451i	0.807431	−	1.39851i	0.914638	−	0.404275i	$-0.132476\pi$
$854$	−136.345			−4.66563
$855$		0			0
$856$	22.9030			0.782810
$857$	18.7348	−	32.4497i	0.639969	−	1.10846i	−0.345470	−	0.938430i	$-0.612280\pi$
$857$	18.7348	−	32.4497i	0.639969	−	1.10846i	0.985439	−	0.170030i	$-0.0543863\pi$
$858$		0			0
$859$	−15.2219	−	26.3652i	−0.519366	−	0.899568i	−0.999747	−	0.0225082i	$-0.992835\pi$
$859$	−15.2219	−	26.3652i	−0.519366	−	0.899568i	0.480381	−	0.877060i	$-0.340499\pi$
$860$	6.93212	+	12.0068i	0.236383	+	0.409428i
$861$		0			0
$862$	−17.3216	+	30.0019i	−0.589976	+	1.02187i
$863$	18.3473			0.624549			0.312275	−	0.949992i	$-0.398909\pi$
$863$	18.3473			0.624549			0.312275	+	0.949992i	$0.398909\pi$
$864$		0			0
$865$	−14.0515			−0.477767
$866$	5.84761	−	10.1284i	0.198710	−	0.344176i
$867$		0			0
$868$	−96.1355	−	166.512i	−3.26305	−	5.65177i
$869$	23.9309	+	41.4496i	0.811801	+	1.40608i
$870$		0			0
$871$	2.35084	−	4.07177i	0.0796550	−	0.137967i
$872$	−58.7242			−1.98865
$873$		0			0
$874$	1.19585			0.0404504
$875$	−12.0515	+	20.8737i	−0.407414	+	0.705661i
$876$		0			0
$877$	6.23156	+	10.7934i	0.210425	+	0.364466i	0.951848	−	0.306572i	$-0.0991820\pi$
$877$	6.23156	+	10.7934i	0.210425	+	0.364466i	−0.741423	+	0.671038i	$0.765849\pi$
$878$	13.9062	+	24.0862i	0.469311	+	0.812870i
$879$		0			0
$880$	61.6115	−	106.714i	2.07692	−	3.59734i
$881$	−31.5694			−1.06360			−0.531800	−	0.846870i	$-0.678484\pi$
$881$	−31.5694			−1.06360			−0.531800	+	0.846870i	$0.678484\pi$
$882$		0			0
$883$	−3.34872			−0.112693			−0.0563466	−	0.998411i	$-0.517945\pi$
$883$	−3.34872			−0.112693			−0.0563466	+	0.998411i	$0.517945\pi$
$884$	44.7782	−	77.5581i	1.50605	−	2.60856i
$885$		0			0
$886$	−37.0582	−	64.1867i	−1.24500	−	2.15640i
$887$	−22.4045	−	38.8057i	−0.752270	−	1.30297i	−0.946720	−	0.322057i	$-0.895626\pi$
$887$	−22.4045	−	38.8057i	−0.752270	−	1.30297i	0.194451	−	0.980912i	$-0.437708\pi$
$888$		0			0
$889$	−6.32394	+	10.9534i	−0.212098	+	0.367365i
$890$	−4.65090			−0.155899
$891$		0			0
$892$	53.9178			1.80530
$893$	1.75007	−	3.03121i	0.0585638	−	0.101435i
$894$		0			0
$895$	−17.5272	−	30.3580i	−0.585870	−	1.01476i
$896$	−11.0816	−	19.1939i	−0.370211	−	0.641225i
$897$		0			0
$898$	38.8975	−	67.3724i	1.29802	−	2.24824i
$899$	−56.8376			−1.89564
$900$		0			0
$901$	23.8513			0.794600
$902$	54.9413	−	95.1612i	1.82935	−	3.16852i
$903$		0			0
$904$	38.0431	+	65.8926i	1.26529	+	2.19155i
$905$	−26.2656	−	45.4933i	−0.873096	−	1.51225i
$906$		0			0
$907$	15.4188	−	26.7062i	0.511974	−	0.886765i	−0.487930	−	0.872883i	$-0.662248\pi$
$907$	15.4188	−	26.7062i	0.511974	−	0.886765i	0.999904	−	0.0138819i	$-0.00441889\pi$
$908$	51.7223			1.71647
$909$		0			0
$910$	−90.1823			−2.98951
$911$	−20.3087	+	35.1756i	−0.672856	+	1.16542i	0.304234	+	0.952597i	$0.401599\pi$
$911$	−20.3087	+	35.1756i	−0.672856	+	1.16542i	−0.977091	+	0.212824i	$0.931734\pi$
$912$		0			0
$913$	2.71778	+	4.70734i	0.0899455	+	0.155790i
$914$	−48.1246	−	83.3542i	−1.59182	−	2.75711i
$915$		0			0
$916$	−37.8386	+	65.5384i	−1.25022	+	2.16545i
$917$	18.6354			0.615395
$918$		0			0
$919$	15.3680			0.506944			0.253472	−	0.967343i	$-0.418427\pi$
$919$	15.3680			0.506944			0.253472	+	0.967343i	$0.418427\pi$
$920$	11.6660	−	20.2061i	0.384617	−	0.666176i
$921$		0			0
$922$	26.6993	+	46.2446i	0.879296	+	1.52299i
$923$	−5.90707	−	10.2313i	−0.194433	−	0.336769i
$924$		0			0
$925$	−4.33106	+	7.50161i	−0.142404	+	0.246651i
$926$	57.7824			1.89885
$927$		0			0
$928$	−72.4735			−2.37906
$929$	−22.6444	+	39.2212i	−0.742937	+	1.28680i	0.208215	+	0.978083i	$0.433235\pi$
$929$	−22.6444	+	39.2212i	−0.742937	+	1.28680i	−0.951152	+	0.308722i	$0.900099\pi$
$930$		0			0
$931$	1.87616	+	3.24961i	0.0614887	+	0.106502i
$932$	52.9377	+	91.6908i	1.73403	+	3.00343i
$933$		0			0
$934$	2.13565	−	3.69905i	0.0698806	−	0.121037i
$935$	−68.4021			−2.23699
$936$		0			0
$937$	2.74160			0.0895642			0.0447821	−	0.998997i	$-0.485741\pi$
$937$	2.74160			0.0895642			0.0447821	+	0.998997i	$0.485741\pi$
$938$	−8.04584	+	13.9358i	−0.262706	+	0.455020i
$939$		0			0
$940$	−57.2778	−	99.2080i	−1.86820	−	3.23581i
$941$	−22.2355	−	38.5130i	−0.724857	−	1.25549i	−0.959033	−	0.283295i	$-0.908573\pi$
$941$	−22.2355	−	38.5130i	−0.724857	−	1.25549i	0.234176	−	0.972194i	$-0.424761\pi$
$942$		0			0
$943$	5.38273	−	9.32316i	0.175286	−	0.303604i
$944$	29.8083			0.970176
$945$		0			0
$946$	−10.9283			−0.355309
$947$	16.9679	−	29.3893i	0.551383	−	0.955024i	−0.446792	−	0.894638i	$-0.647433\pi$
$947$	16.9679	−	29.3893i	0.551383	−	0.955024i	0.998175	−	0.0603861i	$-0.0192332\pi$
$948$		0			0
$949$	7.18314	+	12.4416i	0.233175	+	0.403870i
$950$	−1.58496	−	2.74522i	−0.0514227	−	0.0890668i
$951$		0			0
$952$	−91.3605	+	158.241i	−2.96101	+	5.12862i
$953$	−7.93119			−0.256916			−0.128458	−	0.991715i	$-0.541003\pi$
$953$	−7.93119			−0.256916			−0.128458	+	0.991715i	$0.541003\pi$
$954$		0			0
$955$	24.9508			0.807389
$956$	−2.99173	+	5.18182i	−0.0967593	+	0.167592i
$957$		0			0
$958$	9.55155	+	16.5438i	0.308597	+	0.534505i
$959$	39.6477	+	68.6719i	1.28029	+	2.21753i
$960$		0			0
$961$	−32.0298	+	55.4773i	−1.03322	+	1.78959i
$962$	24.6884			0.795985
$963$		0			0
$964$	139.912			4.50627
$965$	7.71571	−	13.3640i	0.248378	−	0.430202i
$966$		0			0
$967$	−23.5991	−	40.8749i	−0.758897	−	1.31445i	−0.943413	−	0.331619i	$-0.892405\pi$
$967$	−23.5991	−	40.8749i	−0.758897	−	1.31445i	0.184516	−	0.982829i	$-0.440928\pi$
$968$	24.0462	+	41.6493i	0.772876	+	1.33866i
$969$		0			0
$970$	15.1866	−	26.3040i	0.487613	−	0.844570i
$971$	−36.8198			−1.18160			−0.590801	−	0.806817i	$-0.701188\pi$
$971$	−36.8198			−1.18160			−0.590801	+	0.806817i	$0.701188\pi$
$972$		0			0
$973$	−14.4715			−0.463936
$974$	−38.9734	+	67.5039i	−1.24879	+	2.16296i
$975$		0			0
$976$	68.9478	+	119.421i	2.20697	+	3.82258i
$977$	2.41808	+	4.18824i	0.0773613	+	0.133994i	0.902111	−	0.431505i	$-0.142017\pi$
$977$	2.41808	+	4.18824i	0.0773613	+	0.133994i	−0.824749	+	0.565498i	$0.808684\pi$
$978$		0			0
$979$	1.30568	−	2.26150i	0.0417297	−	0.0722780i
$980$	122.809			3.92300
$981$		0			0
$982$	−30.3465			−0.968397
$983$	14.9629	−	25.9165i	0.477242	−	0.826607i	−0.522418	−	0.852689i	$-0.674970\pi$
$983$	14.9629	−	25.9165i	0.477242	−	0.826607i	0.999660	+	0.0260827i	$0.00830332\pi$
$984$		0			0
$985$	−7.02612	−	12.1696i	−0.223871	−	0.387756i
$986$	45.3041	+	78.4690i	1.44278	+	2.49896i
$987$		0			0
$988$	−3.21780	+	5.57340i	−0.102372	+	0.177313i
$989$	−1.07067			−0.0340453
$990$		0			0
$991$	−45.3361			−1.44015			−0.720074	−	0.693897i	$-0.755892\pi$
$991$	−45.3361			−1.44015			−0.720074	+	0.693897i	$0.755892\pi$
$992$	−60.6052	+	104.971i	−1.92422	+	3.33284i
$993$		0			0
$994$	20.2172	+	35.0172i	0.641251	+	1.11068i
$995$	−0.400423	−	0.693552i	−0.0126943	−	0.0219871i
$996$		0			0
$997$	19.9559	−	34.5647i	0.632011	−	1.09468i	−0.355129	−	0.934817i	$-0.615563\pi$
$997$	19.9559	−	34.5647i	0.632011	−	1.09468i	0.987140	−	0.159858i	$-0.0511037\pi$
$998$	−82.2569			−2.60380
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1161.2.f.d.775.20		40
3.2	odd	2		387.2.f.d.259.1	yes	40
9.2	odd	6		3483.2.a.t.1.20		20
9.4	even	3	inner	1161.2.f.d.388.20		40
9.5	odd	6		387.2.f.d.130.1	✓	40
9.7	even	3		3483.2.a.u.1.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
387.2.f.d.130.1	✓	40	9.5	odd	6
387.2.f.d.259.1	yes	40	3.2	odd	2
1161.2.f.d.388.20		40	9.4	even	3	inner
1161.2.f.d.775.20		40	1.1	even	1	trivial
3483.2.a.t.1.20		20	9.2	odd	6
3483.2.a.u.1.1		20	9.7	even	3

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:	\( N \)	\(=\)	\( 1161 = 3^{3} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1161.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.31834 - 2.28344i) q^{2} +(-2.47606 - 4.28866i) q^{4} +(-1.39983 - 2.42457i) q^{5} +(1.99111 - 3.44870i) q^{7} -7.78382 q^{8} +O(q^{10})\)	\(q+(1.31834 - 2.28344i) q^{2} +(-2.47606 - 4.28866i) q^{4} +(-1.39983 - 2.42457i) q^{5} +(1.99111 - 3.44870i) q^{7} -7.78382 q^{8} -7.38182 q^{10} +(2.07235 - 3.58941i) q^{11} +(1.53392 + 2.65683i) q^{13} +(-5.24992 - 9.09313i) q^{14} +(-5.30963 + 9.19655i) q^{16} +5.89483 q^{17} -0.423608 q^{19} +(-6.93212 + 12.0068i) q^{20} +(-5.46414 - 9.46416i) q^{22} +(-0.535334 - 0.927226i) q^{23} +(-1.41904 + 2.45784i) q^{25} +8.08895 q^{26} -19.7204 q^{28} +(-2.91479 + 5.04856i) q^{29} +(4.87493 + 8.44362i) q^{31} +(6.21601 + 10.7665i) q^{32} +(7.77142 - 13.4605i) q^{34} -11.1488 q^{35} +3.05211 q^{37} +(-0.558461 + 0.967284i) q^{38} +(10.8960 + 18.8724i) q^{40} +(5.02745 + 8.70780i) q^{41} +(0.500000 - 0.866025i) q^{43} -20.5250 q^{44} -2.82302 q^{46} +(-4.13133 + 7.15568i) q^{47} +(-4.42900 - 7.67126i) q^{49} +(3.74156 + 6.48057i) q^{50} +(7.59617 - 13.1570i) q^{52} +4.04613 q^{53} -11.6037 q^{55} +(-15.4984 + 26.8440i) q^{56} +(7.68539 + 13.3115i) q^{58} +(-1.40350 - 2.43093i) q^{59} +(6.49271 - 11.2457i) q^{61} +25.7073 q^{62} +11.5409 q^{64} +(4.29446 - 7.43822i) q^{65} +(-0.766282 - 1.32724i) q^{67} +(-14.5960 - 25.2810i) q^{68} +(-14.6980 + 25.4576i) q^{70} -3.85095 q^{71} +4.68286 q^{73} +(4.02373 - 6.96931i) q^{74} +(1.04888 + 1.81671i) q^{76} +(-8.25253 - 14.2938i) q^{77} +(-5.77387 + 10.0006i) q^{79} +29.7303 q^{80} +26.5116 q^{82} +(-0.655725 + 1.13575i) q^{83} +(-8.25175 - 14.2925i) q^{85} +(-1.31834 - 2.28344i) q^{86} +(-16.1308 + 27.9393i) q^{88} +0.630048 q^{89} +12.2168 q^{91} +(-2.65104 + 4.59173i) q^{92} +(10.8930 + 18.8673i) q^{94} +(0.592979 + 1.02707i) q^{95} +(-2.05730 + 3.56335i) q^{97} -23.3558 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 6 q^{2} - 22 q^{4} - 17 q^{5} - 3 q^{7} + 30 q^{8}+O(q^{10}) \) 40 * q - 6 * q^2 - 22 * q^4 - 17 * q^5 - 3 * q^7 + 30 * q^8	\( 40 q - 6 q^{2} - 22 q^{4} - 17 q^{5} - 3 q^{7} + 30 q^{8} - 4 q^{10} - 10 q^{11} + q^{13} - 10 q^{14} - 22 q^{16} + 40 q^{17} + 16 q^{19} - 30 q^{20} - 15 q^{22} - 19 q^{23} - 19 q^{25} + 50 q^{26} - 6 q^{28} - 25 q^{29} + 11 q^{31} - 36 q^{32} - 9 q^{34} + 18 q^{37} - 28 q^{38} - 12 q^{40} - 12 q^{41} + 20 q^{43} + 10 q^{44} + 8 q^{46} - 38 q^{47} - 37 q^{49} - 36 q^{50} + 8 q^{52} + 138 q^{53} - 18 q^{55} - 30 q^{56} + 27 q^{58} - 31 q^{59} - 19 q^{61} + 64 q^{62} + 22 q^{64} - 47 q^{65} - 9 q^{67} - 68 q^{68} + 6 q^{70} + 42 q^{71} - 4 q^{73} + 16 q^{74} - 37 q^{76} - 85 q^{77} + 4 q^{79} + 122 q^{80} + 2 q^{82} - 19 q^{83} + 6 q^{85} + 6 q^{86} - 60 q^{88} + 108 q^{89} - 6 q^{91} - 85 q^{92} + 19 q^{94} + 11 q^{95} - 2 q^{97} + 10 q^{98}+O(q^{100}) \) 40 * q - 6 * q^2 - 22 * q^4 - 17 * q^5 - 3 * q^7 + 30 * q^8 - 4 * q^10 - 10 * q^11 + q^13 - 10 * q^14 - 22 * q^16 + 40 * q^17 + 16 * q^19 - 30 * q^20 - 15 * q^22 - 19 * q^23 - 19 * q^25 + 50 * q^26 - 6 * q^28 - 25 * q^29 + 11 * q^31 - 36 * q^32 - 9 * q^34 + 18 * q^37 - 28 * q^38 - 12 * q^40 - 12 * q^41 + 20 * q^43 + 10 * q^44 + 8 * q^46 - 38 * q^47 - 37 * q^49 - 36 * q^50 + 8 * q^52 + 138 * q^53 - 18 * q^55 - 30 * q^56 + 27 * q^58 - 31 * q^59 - 19 * q^61 + 64 * q^62 + 22 * q^64 - 47 * q^65 - 9 * q^67 - 68 * q^68 + 6 * q^70 + 42 * q^71 - 4 * q^73 + 16 * q^74 - 37 * q^76 - 85 * q^77 + 4 * q^79 + 122 * q^80 + 2 * q^82 - 19 * q^83 + 6 * q^85 + 6 * q^86 - 60 * q^88 + 108 * q^89 - 6 * q^91 - 85 * q^92 + 19 * q^94 + 11 * q^95 - 2 * q^97 + 10 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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