LMFDB - Embedded newform 363.2.d.e.362.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,2,Mod(362,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("363.362");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	363.d (of order $2$, degree $1$, 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:	$2.89856959337$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.3588489216.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 10x^{6} - 8x^{5} + 8x^{4} + 4x^{3} + 16x^{2} + 32x + 22 $ x^8 - 4x^7 + 10x^6 - 8x^5 + 8x^4 + 4x^3 + 16x^2 + 32*x + 22
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			362.1
Root			$-0.697085 - 0.346269i$ of defining polynomial
Character	$\chi$	$=$	363.362
Dual form			363.2.d.e.362.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.39417 q^{2} +(0.366025 - 1.69293i) q^{3} +3.73205 q^{4} -1.23931i q^{5} +(-0.876327 + 4.05317i) q^{6} -2.82843i q^{7} -4.14682 q^{8} +(-2.73205 - 1.23931i) q^{9} +O(q^{10})$	\(q-2.39417 q^{2} +(0.366025 - 1.69293i) q^{3} +3.73205 q^{4} -1.23931i q^{5} +(-0.876327 + 4.05317i) q^{6} -2.82843i q^{7} -4.14682 q^{8} +(-2.73205 - 1.23931i) q^{9} +2.96713i q^{10} +(1.36603 - 6.31812i) q^{12} -3.34607i q^{13} +6.77174i q^{14} +(-2.09808 - 0.453620i) q^{15} +2.46410 q^{16} +4.14682 q^{17} +(6.54099 + 2.96713i) q^{18} +2.44949i q^{19} -4.62518i q^{20} +(-4.78834 - 1.03528i) q^{21} +(-1.51784 + 7.02030i) q^{24} +3.46410 q^{25} +8.01105i q^{26} +(-3.09808 + 4.17156i) q^{27} -10.5558i q^{28} -5.42986 q^{29} +(5.02315 + 1.08604i) q^{30} +0.196152 q^{31} +2.39417 q^{32} -9.92820 q^{34} -3.50531 q^{35} +(-10.1962 - 4.62518i) q^{36} -10.4641 q^{37} -5.86450i q^{38} +(-5.66467 - 1.22474i) q^{39} +5.13922i q^{40} -7.18251 q^{41} +(11.4641 + 2.47863i) q^{42} -4.24264i q^{43} +(-1.53590 + 3.38587i) q^{45} -3.38587i q^{47} +(0.901924 - 4.17156i) q^{48} -1.00000 q^{49} -8.29365 q^{50} +(1.51784 - 7.02030i) q^{51} -12.4877i q^{52} +7.10381i q^{53} +(7.41732 - 9.98743i) q^{54} +11.7290i q^{56} +(4.14682 + 0.896575i) q^{57} +13.0000 q^{58} -12.6362i q^{59} +(-7.83013 - 1.69293i) q^{60} +4.52004i q^{61} -0.469622 q^{62} +(-3.50531 + 7.72741i) q^{63} -10.6603 q^{64} -4.14682 q^{65} +2.00000 q^{67} +15.4762 q^{68} +8.39230 q^{70} +8.34312i q^{71} +(11.3293 + 5.13922i) q^{72} +8.10634i q^{73} +25.0528 q^{74} +(1.26795 - 5.86450i) q^{75} +9.14162i q^{76} +(13.5622 + 2.93225i) q^{78} -7.34847i q^{79} -3.05379i q^{80} +(5.92820 + 6.77174i) q^{81} +17.1962 q^{82} +14.8346 q^{83} +(-17.8703 - 3.86370i) q^{84} -5.13922i q^{85} +10.1576i q^{86} +(-1.98747 + 9.19239i) q^{87} -9.58244i q^{89} +(3.67720 - 8.10634i) q^{90} -9.46410 q^{91} +(0.0717968 - 0.332073i) q^{93} +8.10634i q^{94} +3.03569 q^{95} +(0.876327 - 4.05317i) q^{96} +2.26795 q^{97} +2.39417 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} + 16 q^{4} - 8 q^{9}+O(q^{10}) $ 8 * q - 4 * q^3 + 16 * q^4 - 8 * q^9	$ 8 q - 4 q^{3} + 16 q^{4} - 8 q^{9} + 4 q^{12} + 4 q^{15} - 8 q^{16} - 4 q^{27} - 40 q^{31} - 24 q^{34} - 40 q^{36} - 56 q^{37} + 64 q^{42} - 40 q^{45} + 28 q^{48} - 8 q^{49} + 104 q^{58} - 28 q^{60} - 16 q^{64} + 16 q^{67} - 16 q^{70} + 24 q^{75} + 60 q^{78} - 8 q^{81} + 96 q^{82} - 48 q^{91} + 56 q^{93} + 32 q^{97}+O(q^{100}) $ 8 * q - 4 * q^3 + 16 * q^4 - 8 * q^9 + 4 * q^12 + 4 * q^15 - 8 * q^16 - 4 * q^27 - 40 * q^31 - 24 * q^34 - 40 * q^36 - 56 * q^37 + 64 * q^42 - 40 * q^45 + 28 * q^48 - 8 * q^49 + 104 * q^58 - 28 * q^60 - 16 * q^64 + 16 * q^67 - 16 * q^70 + 24 * q^75 + 60 * q^78 - 8 * q^81 + 96 * q^82 - 48 * q^91 + 56 * q^93 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−2.39417			−1.69293			−0.846467	−	0.532441i	$-0.821275\pi$
$2$	−2.39417			−1.69293			−0.846467	+	0.532441i	$0.821275\pi$
$3$	0.366025	−	1.69293i	0.211325	−	0.977416i
$3$	0.366025	−	1.69293i	0.211325	−	0.977416i
$4$	3.73205			1.86603
$5$		−	1.23931i		−	0.554238i	−0.960836	−	0.277119i	$-0.910620\pi$
$5$		−	1.23931i		−	0.554238i	0.960836	−	0.277119i	$-0.0893796\pi$
$6$	−0.876327	+	4.05317i	−0.357759	+	1.65470i
$7$		−	2.82843i		−	1.06904i	−0.845154	−	0.534522i	$-0.820491\pi$
$7$		−	2.82843i		−	1.06904i	0.845154	−	0.534522i	$-0.179509\pi$
$8$	−4.14682			−1.46612
$9$	−2.73205	−	1.23931i	−0.910684	−	0.413105i
$10$			2.96713i			0.938288i
$11$		0			0
$11$		0			0
$12$	1.36603	−	6.31812i	0.394338	−	1.82388i
$13$		−	3.34607i		−	0.928032i	−0.885827	−	0.464016i	$-0.846408\pi$
$13$		−	3.34607i		−	0.928032i	0.885827	−	0.464016i	$-0.153592\pi$
$14$			6.77174i			1.80982i
$15$	−2.09808	−	0.453620i	−0.541721	−	0.117124i
$16$	2.46410			0.616025
$17$	4.14682			1.00575			0.502876	−	0.864358i	$-0.332275\pi$
$17$	4.14682			1.00575			0.502876	+	0.864358i	$0.332275\pi$
$18$	6.54099	+	2.96713i	1.54173	+	0.699359i
$19$			2.44949i			0.561951i	0.959715	+	0.280976i	$0.0906580\pi$
$19$			2.44949i			0.561951i	−0.959715	+	0.280976i	$0.909342\pi$
$20$		−	4.62518i		−	1.03422i
$21$	−4.78834	−	1.03528i	−1.04490	−	0.225916i
$22$		0			0
$23$		0			0		1.00000			$0$
$23$		0			0		−1.00000			$\pi$
$24$	−1.51784	+	7.02030i	−0.309828	+	1.43301i
$25$	3.46410			0.692820
$26$			8.01105i			1.57110i
$27$	−3.09808	+	4.17156i	−0.596225	+	0.802817i
$28$		−	10.5558i		−	1.99487i
$29$	−5.42986			−1.00830			−0.504150	−	0.863616i	$-0.668194\pi$
$29$	−5.42986			−1.00830			−0.504150	+	0.863616i	$0.668194\pi$
$30$	5.02315	+	1.08604i	0.917098	+	0.198284i
$31$	0.196152			0.0352300			0.0176150	−	0.999845i	$-0.494393\pi$
$31$	0.196152			0.0352300			0.0176150	+	0.999845i	$0.494393\pi$
$32$	2.39417			0.423233
$33$		0			0
$34$	−9.92820			−1.70267
$35$	−3.50531			−0.592505
$36$	−10.1962	−	4.62518i	−1.69936	−	0.770864i
$37$	−10.4641			−1.72029			−0.860144	−	0.510052i	$-0.829626\pi$
$37$	−10.4641			−1.72029			−0.860144	+	0.510052i	$0.829626\pi$
$38$		−	5.86450i		−	0.951347i
$39$	−5.66467	−	1.22474i	−0.907073	−	0.196116i
$40$			5.13922i			0.812581i
$41$	−7.18251			−1.12172			−0.560860	−	0.827911i	$-0.689529\pi$
$41$	−7.18251			−1.12172			−0.560860	+	0.827911i	$0.689529\pi$
$42$	11.4641	+	2.47863i	1.76895	+	0.382461i
$43$		−	4.24264i		−	0.646997i	−0.946229	−	0.323498i	$-0.895141\pi$
$43$		−	4.24264i		−	0.646997i	0.946229	−	0.323498i	$-0.104859\pi$
$44$		0			0
$45$	−1.53590	+	3.38587i	−0.228958	+	0.504735i
$46$		0			0
$47$		−	3.38587i		−	0.493880i	−0.969031	−	0.246940i	$-0.920575\pi$
$47$		−	3.38587i		−	0.493880i	0.969031	−	0.246940i	$-0.0794250\pi$
$48$	0.901924	−	4.17156i	0.130181	−	0.602113i
$49$	−1.00000			−0.142857
$50$	−8.29365			−1.17290
$51$	1.51784	−	7.02030i	0.212541	−	0.983039i
$52$		−	12.4877i		−	1.73173i
$53$			7.10381i			0.975783i	0.872904	+	0.487892i	$0.162234\pi$
$53$			7.10381i			0.975783i	−0.872904	+	0.487892i	$0.837766\pi$
$54$	7.41732	−	9.98743i	1.00937	−	1.35912i
$55$		0			0
$56$			11.7290i			1.56735i
$57$	4.14682	+	0.896575i	0.549260	+	0.118754i
$58$	13.0000			1.70698
$59$		−	12.6362i		−	1.64510i	−0.568695	−	0.822549i	$-0.692551\pi$
$59$		−	12.6362i		−	1.64510i	0.568695	−	0.822549i	$-0.307449\pi$
$60$	−7.83013	−	1.69293i	−1.01087	−	0.218557i
$61$			4.52004i			0.578732i	0.957219	+	0.289366i	$0.0934445\pi$
$61$			4.52004i			0.578732i	−0.957219	+	0.289366i	$0.906556\pi$
$62$	−0.469622			−0.0596421
$63$	−3.50531	+	7.72741i	−0.441627	+	0.973562i
$64$	−10.6603			−1.33253
$65$	−4.14682			−0.514350
$66$		0			0
$67$	2.00000			0.244339			0.122169	−	0.992509i	$-0.461015\pi$
$67$	2.00000			0.244339			0.122169	+	0.992509i	$0.461015\pi$
$68$	15.4762			1.87676
$69$		0			0
$70$	8.39230			1.00307
$71$			8.34312i			0.990146i	0.868851	+	0.495073i	$0.164859\pi$
$71$			8.34312i			0.990146i	−0.868851	+	0.495073i	$0.835141\pi$
$72$	11.3293	+	5.13922i	1.33517	+	0.605662i
$73$			8.10634i			0.948776i	0.880316	+	0.474388i	$0.157331\pi$
$73$			8.10634i			0.948776i	−0.880316	+	0.474388i	$0.842669\pi$
$74$	25.0528			2.91233
$75$	1.26795	−	5.86450i	0.146410	−	0.677174i
$76$			9.14162i			1.04862i
$77$		0			0
$78$	13.5622	+	2.93225i	1.53561	+	0.332012i
$79$		−	7.34847i		−	0.826767i	−0.910557	−	0.413384i	$-0.864347\pi$
$79$		−	7.34847i		−	0.826767i	0.910557	−	0.413384i	$-0.135653\pi$
$80$		−	3.05379i		−	0.341425i
$81$	5.92820	+	6.77174i	0.658689	+	0.752415i
$82$	17.1962			1.89900
$83$	14.8346			1.62831			0.814157	−	0.580645i	$-0.197200\pi$
$83$	14.8346			1.62831			0.814157	+	0.580645i	$0.197200\pi$
$84$	−17.8703	−	3.86370i	−1.94981	−	0.421565i
$85$		−	5.13922i		−	0.557426i
$86$			10.1576i			1.09532i
$87$	−1.98747	+	9.19239i	−0.213079	+	0.985527i
$88$		0			0
$89$		−	9.58244i		−	1.01574i	−0.861435	−	0.507868i	$-0.830434\pi$
$89$		−	9.58244i		−	1.01574i	0.861435	−	0.507868i	$-0.169566\pi$
$90$	3.67720	−	8.10634i	0.387611	−	0.854484i
$91$	−9.46410			−0.992107
$92$		0			0
$93$	0.0717968	−	0.332073i	0.00744498	−	0.0344344i
$94$			8.10634i			0.836106i
$95$	3.03569			0.311455
$96$	0.876327	−	4.05317i	0.0894398	−	0.413675i
$97$	2.26795			0.230275			0.115138	−	0.993350i	$-0.463269\pi$
$97$	2.26795			0.230275			0.115138	+	0.993350i	$0.463269\pi$
$98$	2.39417			0.241848
$99$		0			0
$100$	12.9282			1.29282
$101$	0.469622			0.0467292			0.0233646	−	0.999727i	$-0.492562\pi$
$101$	0.469622			0.0467292			0.0233646	+	0.999727i	$0.492562\pi$
$102$	−3.63397	+	16.8078i	−0.359817	+	1.66422i
$103$	12.7321			1.25453			0.627263	−	0.778807i	$-0.284175\pi$
$103$	12.7321			1.25453			0.627263	+	0.778807i	$0.284175\pi$
$104$			13.8755i			1.36061i
$105$	−1.28303	+	5.93426i	−0.125211	+	0.579124i
$106$		−	17.0077i		−	1.65194i
$107$	3.50531			0.338871			0.169435	−	0.985541i	$-0.445806\pi$
$107$	3.50531			0.338871			0.169435	+	0.985541i	$0.445806\pi$
$108$	−11.5622	+	15.5685i	−1.11257	+	1.49808i
$109$			10.6945i			1.02435i	0.858881	+	0.512175i	$0.171160\pi$
$109$			10.6945i			1.02435i	−0.858881	+	0.512175i	$0.828840\pi$
$110$		0			0
$111$	−3.83013	+	17.7150i	−0.363540	+	1.68144i
$112$		−	6.96953i		−	0.658559i
$113$		−	12.9683i		−	1.21996i	−0.792419	−	0.609978i	$-0.791178\pi$
$113$		−	12.9683i		−	1.21996i	0.792419	−	0.609978i	$-0.208822\pi$
$114$	−9.92820	−	2.14655i	−0.929861	−	0.201043i
$115$		0			0
$116$	−20.2645			−1.88151
$117$	−4.14682	+	9.14162i	−0.383374	+	0.845143i
$118$			30.2533i			2.78504i
$119$		−	11.7290i		−	1.07519i
$120$	8.70035	+	1.88108i	0.794230	+	0.171719i
$121$		0			0
$122$		−	10.8217i		−	0.979755i
$123$	−2.62898	+	12.1595i	−0.237047	+	1.09639i
$124$	0.732051			0.0657401
$125$		−	10.4897i		−	0.938225i
$126$	8.39230	−	18.5007i	0.747646	−	1.64818i
$127$		−	14.4195i		−	1.27953i	−0.768572	−	0.639764i	$-0.779032\pi$
$127$		−	14.4195i		−	1.27953i	0.768572	−	0.639764i	$-0.220968\pi$
$128$	20.7341			1.83265
$129$	−7.18251	−	1.55291i	−0.632385	−	0.136726i
$130$	9.92820			0.870761
$131$	13.5516			1.18401			0.592005	−	0.805934i	$-0.298337\pi$
$131$	13.5516			1.18401			0.592005	+	0.805934i	$0.298337\pi$
$132$		0			0
$133$	6.92820			0.600751
$134$	−4.78834			−0.413650
$135$	5.16987	+	3.83949i	0.444952	+	0.330451i
$136$	−17.1962			−1.47456
$137$		−	17.8366i		−	1.52388i	−0.647647	−	0.761941i	$-0.724247\pi$
$137$		−	17.8366i		−	1.52388i	0.647647	−	0.761941i	$-0.275753\pi$
$138$		0			0
$139$			5.17638i			0.439055i	0.975606	+	0.219527i	$0.0704516\pi$
$139$			5.17638i			0.439055i	−0.975606	+	0.219527i	$0.929548\pi$
$140$	−13.0820			−1.10563
$141$	−5.73205	−	1.23931i	−0.482726	−	0.104369i
$142$		−	19.9749i		−	1.67625i
$143$		0			0
$144$	−6.73205	−	3.05379i	−0.561004	−	0.254483i
$145$			6.72930i			0.558838i
$146$		−	19.4080i		−	1.60621i
$147$	−0.366025	+	1.69293i	−0.0301893	+	0.139631i
$148$	−39.0526			−3.21010
$149$	−9.40479			−0.770470			−0.385235	−	0.922818i	$-0.625880\pi$
$149$	−9.40479			−0.770470			−0.385235	+	0.922818i	$0.625880\pi$
$150$	−3.03569	+	14.0406i	−0.247863	+	1.14641i
$151$		−	16.4901i		−	1.34194i	−0.741482	−	0.670972i	$-0.765877\pi$
$151$		−	16.4901i		−	1.34194i	0.741482	−	0.670972i	$-0.234123\pi$
$152$		−	10.1576i		−	0.823890i
$153$	−11.3293	−	5.13922i	−0.915922	−	0.415481i
$154$		0			0
$155$		−	0.243094i		−	0.0195258i
$156$	−21.1408	−	4.57081i	−1.69262	−	0.365958i
$157$	−11.4641			−0.914935			−0.457467	−	0.889226i	$-0.651243\pi$
$157$	−11.4641			−0.914935			−0.457467	+	0.889226i	$0.651243\pi$
$158$			17.5935i			1.39966i
$159$	12.0263	+	2.60017i	0.953746	+	0.206207i
$160$		−	2.96713i		−	0.234572i
$161$		0			0
$162$	−14.1931	−	16.2127i	−1.11512	−	1.27379i
$163$	12.3923			0.970640			0.485320	−	0.874337i	$-0.338703\pi$
$163$	12.3923			0.970640			0.485320	+	0.874337i	$0.338703\pi$
$164$	−26.8055			−2.09316
$165$		0			0
$166$	−35.5167			−2.75663
$167$	−5.25796			−0.406873			−0.203437	−	0.979088i	$-0.565211\pi$
$167$	−5.25796			−0.406873			−0.203437	+	0.979088i	$0.565211\pi$
$168$	19.8564	+	4.29311i	1.53196	+	0.331221i
$169$	1.80385			0.138758
$170$			12.3042i			0.943686i
$171$	3.03569	−	6.69213i	0.232145	−	0.511760i
$172$		−	15.8338i		−	1.20731i
$173$	11.3293			0.861353			0.430677	−	0.902506i	$-0.358275\pi$
$173$	11.3293			0.861353			0.430677	+	0.902506i	$0.358275\pi$
$174$	4.75833	−	22.0081i	0.360728	−	1.66843i
$175$		−	9.79796i		−	0.740656i
$176$		0			0
$177$	−21.3923	−	4.62518i	−1.60794	−	0.347650i
$178$			22.9420i			1.71957i
$179$			22.7938i			1.70369i	0.523793	+	0.851846i	$0.324517\pi$
$179$			22.7938i			1.70369i	−0.523793	+	0.851846i	$0.675483\pi$
$180$	−5.73205	+	12.6362i	−0.427242	+	0.941849i
$181$	12.8564			0.955609			0.477805	−	0.878466i	$-0.341433\pi$
$181$	12.8564			0.955609			0.477805	+	0.878466i	$0.341433\pi$
$182$	22.6587			1.67957
$183$	7.65213	+	1.65445i	0.565662	+	0.122300i
$184$		0			0
$185$			12.9683i			0.953449i
$186$	−0.171894	+	0.795040i	−0.0126039	+	0.0582951i
$187$		0			0
$188$		−	12.6362i		−	0.921592i
$189$	11.7990	+	8.76268i	0.858248	+	0.637391i
$190$	−7.26795			−0.527272
$191$			2.47863i			0.179347i	0.995971	+	0.0896736i	$0.0285824\pi$
$191$			2.47863i			0.179347i	−0.995971	+	0.0896736i	$0.971418\pi$
$192$	−3.90192	+	18.0471i	−0.281597	+	1.30244i
$193$		−	2.86559i		−	0.206270i	−0.994667	−	0.103135i	$-0.967113\pi$
$193$		−	2.86559i		−	0.206270i	0.994667	−	0.103135i	$-0.0328873\pi$
$194$	−5.42986			−0.389841
$195$	−1.51784	+	7.02030i	−0.108695	+	0.502734i
$196$	−3.73205			−0.266575
$197$	−10.6878			−0.761476			−0.380738	−	0.924683i	$-0.624330\pi$
$197$	−10.6878			−0.761476			−0.380738	+	0.924683i	$0.624330\pi$
$198$		0			0
$199$	7.66025			0.543021			0.271511	−	0.962435i	$-0.412477\pi$
$199$	7.66025			0.543021			0.271511	+	0.962435i	$0.412477\pi$
$200$	−14.3650			−1.01576
$201$	0.732051	−	3.38587i	0.0516349	−	0.238821i
$202$	−1.12436			−0.0791094
$203$			15.3580i			1.07792i
$204$	5.66467	−	26.2001i	0.396606	−	1.83438i
$205$			8.90138i			0.621700i
$206$	−30.4827			−2.12383
$207$		0			0
$208$		−	8.24504i		−	0.571691i
$209$		0			0
$210$	3.07180	−	14.2076i	0.211974	−	0.980419i
$211$			1.89469i			0.130436i	0.997871	+	0.0652178i	$0.0207742\pi$
$211$			1.89469i			0.130436i	−0.997871	+	0.0652178i	$0.979226\pi$
$212$			26.5118i			1.82084i
$213$	14.1244	+	3.05379i	0.967785	+	0.209243i
$214$	−8.39230			−0.573686
$215$	−5.25796			−0.358590
$216$	12.8472	−	17.2987i	0.874140	−	1.17703i
$217$		−	0.554803i		−	0.0376625i
$218$		−	25.6045i		−	1.73416i
$219$	13.7235	+	2.96713i	0.927349	+	0.200500i
$220$		0			0
$221$		−	13.8755i		−	0.933370i
$222$	9.16998	−	42.4128i	0.615448	−	2.84656i
$223$	12.9282			0.865737			0.432868	−	0.901457i	$-0.357502\pi$
$223$	12.9282			0.865737			0.432868	+	0.901457i	$0.357502\pi$
$224$		−	6.77174i		−	0.452456i
$225$	−9.46410	−	4.29311i	−0.630940	−	0.286207i
$226$			31.0483i			2.06530i
$227$	5.25796			0.348983			0.174492	−	0.984659i	$-0.444172\pi$
$227$	5.25796			0.348983			0.174492	+	0.984659i	$0.444172\pi$
$228$	15.4762	+	3.34607i	1.02493	+	0.221599i
$229$	5.53590			0.365822			0.182911	−	0.983129i	$-0.441448\pi$
$229$	5.53590			0.365822			0.182911	+	0.983129i	$0.441448\pi$
$230$		0			0
$231$		0			0
$232$	22.5167			1.47829
$233$	5.42986			0.355722			0.177861	−	0.984056i	$-0.443082\pi$
$233$	5.42986			0.355722			0.177861	+	0.984056i	$0.443082\pi$
$234$	9.92820	−	21.8866i	0.649027	−	1.43077i
$235$	−4.19615			−0.273727
$236$		−	47.1591i		−	3.06979i
$237$	−12.4405	−	2.68973i	−0.808096	−	0.174717i
$238$			28.0812i			1.82023i
$239$	−10.0463			−0.649841			−0.324921	−	0.945741i	$-0.605338\pi$
$239$	−10.0463			−0.649841			−0.324921	+	0.945741i	$0.605338\pi$
$240$	−5.16987	−	1.11777i	−0.333714	−	0.0721515i
$241$			3.76217i			0.242343i	0.992632	+	0.121171i	$0.0386650\pi$
$241$			3.76217i			0.242343i	−0.992632	+	0.121171i	$0.961335\pi$
$242$		0			0
$243$	13.6340	−	7.55743i	0.874620	−	0.484809i
$244$			16.8690i			1.07993i
$245$			1.23931i			0.0791768i
$246$	6.29423	−	29.1120i	0.401305	−	1.85611i
$247$	8.19615			0.521509
$248$	−0.813410			−0.0516516
$249$	5.42986	−	25.1141i	0.344103	−	1.59154i
$250$			25.1141i			1.58835i
$251$			8.58622i			0.541957i	0.962585	+	0.270979i	$0.0873473\pi$
$251$			8.58622i			0.541957i	−0.962585	+	0.270979i	$0.912653\pi$
$252$	−13.0820	+	28.8391i	−0.824088	+	1.81669i
$253$		0			0
$254$			34.5228i			2.16615i
$255$	−8.70035	−	1.88108i	−0.544837	−	0.117798i
$256$	−28.3205			−1.77003
$257$			23.1259i			1.44255i	0.692646	+	0.721277i	$0.256445\pi$
$257$			23.1259i			1.44255i	−0.692646	+	0.721277i	$0.743555\pi$
$258$	17.1962	+	3.71794i	1.07059	+	0.231469i
$259$			29.5969i			1.83906i
$260$	−15.4762			−0.959791
$261$	14.8346	+	6.72930i	0.918241	+	0.416533i
$262$	−32.4449			−2.00445
$263$	23.4721			1.44735			0.723675	−	0.690141i	$-0.242451\pi$
$263$	23.4721			1.44735			0.723675	+	0.690141i	$0.242451\pi$
$264$		0			0
$265$	8.80385			0.540816
$266$	−16.5873			−1.01703
$267$	−16.2224	−	3.50742i	−0.992797	−	0.214650i
$268$	7.46410			0.455943
$269$		−	16.3542i		−	0.997131i	−0.866852	−	0.498566i	$-0.833860\pi$
$269$		−	16.3542i		−	0.997131i	0.866852	−	0.498566i	$-0.166140\pi$
$270$	−12.3776	−	9.19239i	−0.753274	−	0.559431i
$271$		−	9.14162i		−	0.555314i	−0.960680	−	0.277657i	$-0.910442\pi$
$271$		−	9.14162i		−	0.555314i	0.960680	−	0.277657i	$-0.0895579\pi$
$272$	10.2182			0.619569
$273$	−3.46410	+	16.0221i	−0.209657	+	0.969702i
$274$			42.7038i			2.57983i
$275$		0			0
$276$		0			0
$277$		−	6.27603i		−	0.377090i	−0.982065	−	0.188545i	$-0.939623\pi$
$277$		−	6.27603i		−	0.377090i	0.982065	−	0.188545i	$-0.0603771\pi$
$278$		−	12.3931i		−	0.743291i
$279$	−0.535898	−	0.243094i	−0.0320834	−	0.0145537i
$280$	14.5359			0.868686
$281$	−0.813410			−0.0485240			−0.0242620	−	0.999706i	$-0.507724\pi$
$281$	−0.813410			−0.0485240			−0.0242620	+	0.999706i	$0.507724\pi$
$282$	13.7235	+	2.96713i	0.817223	+	0.176690i
$283$		−	6.79367i		−	0.403842i	−0.979402	−	0.201921i	$-0.935282\pi$
$283$		−	6.79367i		−	0.403842i	0.979402	−	0.201921i	$-0.0647184\pi$
$284$			31.1370i			1.84764i
$285$	1.11114	−	5.13922i	0.0658181	−	0.304421i
$286$		0			0
$287$			20.3152i			1.19917i
$288$	−6.54099	−	2.96713i	−0.385432	−	0.174840i
$289$	0.196152			0.0115384
$290$		−	16.1111i		−	0.946075i
$291$	0.830127	−	3.83949i	0.0486629	−	0.225075i
$292$			30.2533i			1.77044i
$293$	−32.5331			−1.90060			−0.950301	−	0.311331i	$-0.899225\pi$
$293$	−32.5331			−1.90060			−0.950301	+	0.311331i	$0.899225\pi$
$294$	0.876327	−	4.05317i	0.0511084	−	0.236386i
$295$	−15.6603			−0.911775
$296$	43.3928			2.52215
$297$		0			0
$298$	22.5167			1.30436
$299$		0			0
$300$	4.73205	−	21.8866i	0.273205	−	1.26362i
$301$	−12.0000			−0.691669
$302$			39.4801i			2.27182i
$303$	0.171894	−	0.795040i	0.00987503	−	0.0456738i
$304$			6.03579i			0.346176i
$305$	5.60175			0.320755
$306$	27.1244	+	12.3042i	1.55060	+	0.703382i
$307$		−	31.1870i		−	1.77994i	−0.456021	−	0.889969i	$-0.650726\pi$
$307$		−	31.1870i		−	1.77994i	0.456021	−	0.889969i	$-0.349274\pi$
$308$		0			0
$309$	4.66025	−	21.5545i	0.265113	−	1.22619i
$310$			0.582009i			0.0330559i
$311$			0.664146i			0.0376603i	0.999823	+	0.0188301i	$0.00599417\pi$
$311$			0.664146i			0.0376603i	−0.999823	+	0.0188301i	$0.994006\pi$
$312$	23.4904	+	5.07880i	1.32988	+	0.287531i
$313$	−7.39230			−0.417838			−0.208919	−	0.977933i	$-0.566994\pi$
$313$	−7.39230			−0.417838			−0.208919	+	0.977933i	$0.566994\pi$
$314$	27.4470			1.54892
$315$	9.57668	+	4.34418i	0.539585	+	0.244767i
$316$		−	27.4249i		−	1.54277i
$317$		−	24.6083i		−	1.38214i	−0.722787	−	0.691070i	$-0.757139\pi$
$317$		−	24.6083i		−	1.38214i	0.722787	−	0.691070i	$-0.242861\pi$
$318$	−28.7930	−	6.22526i	−1.61463	−	0.349095i
$319$		0			0
$320$			13.2114i			0.738540i
$321$	1.28303	−	5.93426i	0.0716119	−	0.331218i
$322$		0			0
$323$			10.1576i			0.565184i
$324$	22.1244	+	25.2725i	1.22913	+	1.40403i
$325$		−	11.5911i		−	0.642959i
$326$	−29.6693			−1.64323
$327$	18.1051	+	3.91447i	1.00122	+	0.216471i
$328$	29.7846			1.64458
$329$	−9.57668			−0.527979
$330$		0			0
$331$	−0.392305			−0.0215630			−0.0107815	−	0.999942i	$-0.503432\pi$
$331$	−0.392305			−0.0215630			−0.0107815	+	0.999942i	$0.503432\pi$
$332$	55.3636			3.03847
$333$	28.5885	+	12.9683i	1.56664	+	0.710659i
$334$	12.5885			0.688810
$335$		−	2.47863i		−	0.135422i
$336$	−11.7990	−	2.55103i	−0.643686	−	0.139170i
$337$		−	8.52245i		−	0.464247i	−0.972686	−	0.232124i	$-0.925433\pi$
$337$		−	8.52245i		−	0.464247i	0.972686	−	0.232124i	$-0.0745674\pi$
$338$	−4.31872			−0.234907
$339$	−21.9545	−	4.74673i	−1.19240	−	0.257807i
$340$		−	19.1798i		−	1.04017i
$341$		0			0
$342$	−7.26795	+	16.0221i	−0.393006	+	0.866376i
$343$		−	16.9706i		−	0.916324i
$344$			17.5935i			0.948577i
$345$		0			0
$346$	−27.1244			−1.45821
$347$	1.28303			0.0688768			0.0344384	−	0.999407i	$-0.489036\pi$
$347$	1.28303			0.0688768			0.0344384	+	0.999407i	$0.489036\pi$
$348$	−7.41732	+	34.3065i	−0.397610	+	1.83902i
$349$			20.3166i			1.08752i	0.839239	+	0.543762i	$0.183001\pi$
$349$			20.3166i			1.08752i	−0.839239	+	0.543762i	$0.816999\pi$
$350$			23.4580i			1.25388i
$351$	13.9583	+	10.3664i	0.745040	+	0.553316i
$352$		0			0
$353$			9.58244i			0.510022i	0.966938	+	0.255011i	$0.0820790\pi$
$353$			9.58244i			0.510022i	−0.966938	+	0.255011i	$0.917921\pi$
$354$	51.2168	+	11.0735i	2.72214	+	0.588548i
$355$	10.3397			0.548777
$356$		−	35.7621i		−	1.89539i
$357$	−19.8564	−	4.29311i	−1.05091	−	0.227215i
$358$		−	54.5723i		−	2.88424i
$359$	34.4576			1.81860			0.909302	−	0.416137i	$-0.136616\pi$
$359$	34.4576			1.81860			0.909302	+	0.416137i	$0.136616\pi$
$360$	6.36910	−	14.0406i	0.335681	−	0.740005i
$361$	13.0000			0.684211
$362$	−30.7804			−1.61778
$363$		0			0
$364$	−35.3205			−1.85130
$365$	10.0463			0.525848
$366$	−18.3205	−	3.96104i	−0.957628	−	0.207047i
$367$	−23.8564			−1.24529			−0.622647	−	0.782503i	$-0.713943\pi$
$367$	−23.8564			−1.24529			−0.622647	+	0.782503i	$0.713943\pi$
$368$		0			0
$369$	19.6230	+	8.90138i	1.02153	+	0.463388i
$370$		−	31.0483i		−	1.61413i
$371$	20.0926			1.04316
$372$	0.267949	−	1.23931i	0.0138925	−	0.0642554i
$373$			9.62209i			0.498213i	0.968476	+	0.249107i	$0.0801369\pi$
$373$			9.62209i			0.498213i	−0.968476	+	0.249107i	$0.919863\pi$
$374$		0			0
$375$	−17.7583	−	3.83949i	−0.917036	−	0.198270i
$376$			14.0406i			0.724089i
$377$			18.1687i			0.935733i
$378$	−28.2487	−	20.9794i	−1.45296	−	1.07906i
$379$	−30.5885			−1.57122			−0.785612	−	0.618720i	$-0.787652\pi$
$379$	−30.5885			−1.57122			−0.785612	+	0.618720i	$0.787652\pi$
$380$	11.3293			0.581183
$381$	−24.4113	−	5.27792i	−1.25063	−	0.270396i
$382$		−	5.93426i		−	0.303623i
$383$		−	9.49346i		−	0.485093i	−0.970140	−	0.242547i	$-0.922017\pi$
$383$		−	9.49346i		−	0.485093i	0.970140	−	0.242547i	$-0.0779827\pi$
$384$	7.58922	−	35.1015i	0.387286	−	1.79127i
$385$		0			0
$386$			6.86071i			0.349201i
$387$	−5.25796	+	11.5911i	−0.267277	+	0.589209i
$388$	8.46410			0.429700
$389$			19.0759i			0.967186i	0.875293	+	0.483593i	$0.160669\pi$
$389$			19.0759i			0.967186i	−0.875293	+	0.483593i	$0.839331\pi$
$390$	3.63397	−	16.8078i	0.184013	−	0.851096i
$391$		0			0
$392$	4.14682			0.209446
$393$	4.96023	−	22.9420i	0.250211	−	1.15727i
$394$	25.5885			1.28913
$395$	−9.10706			−0.458226
$396$		0			0
$397$	−21.1962			−1.06380			−0.531902	−	0.846806i	$-0.678523\pi$
$397$	−21.1962			−1.06380			−0.531902	+	0.846806i	$0.678523\pi$
$398$	−18.3400			−0.919299
$399$	2.53590	−	11.7290i	0.126954	−	0.587184i
$400$	8.53590			0.426795
$401$		−	1.23931i		−	0.0618884i	−0.999521	−	0.0309442i	$-0.990149\pi$
$401$		−	1.23931i		−	0.0618884i	0.999521	−	0.0309442i	$-0.00985141\pi$
$402$	−1.75265	+	8.10634i	−0.0874144	+	0.404308i
$403$		−	0.656339i		−	0.0326946i
$404$	1.75265			0.0871978
$405$	8.39230	−	7.34690i	0.417017	−	0.365071i
$406$		−	36.7696i		−	1.82484i
$407$		0			0
$408$	−6.29423	+	29.1120i	−0.311611	+	1.44126i
$409$		−	33.2204i		−	1.64264i	−0.570465	−	0.821322i	$-0.693237\pi$
$409$		−	33.2204i		−	1.64264i	0.570465	−	0.821322i	$-0.306763\pi$
$410$		−	21.3114i		−	1.05250i
$411$	−30.1962	−	6.52864i	−1.48947	−	0.322034i
$412$	47.5167			2.34098
$413$	−35.7407			−1.75868
$414$		0			0
$415$		−	18.3848i		−	0.902473i
$416$		−	8.01105i		−	0.392774i
$417$	8.76327	+	1.89469i	0.429139	+	0.0927832i
$418$		0			0
$419$			11.0648i			0.540553i	0.962783	+	0.270277i	$0.0871151\pi$
$419$			11.0648i			0.540553i	−0.962783	+	0.270277i	$0.912885\pi$
$420$	−4.78834	+	22.1469i	−0.233647	+	1.08066i
$421$	−19.1962			−0.935563			−0.467782	−	0.883844i	$-0.654947\pi$
$421$	−19.1962			−0.935563			−0.467782	+	0.883844i	$0.654947\pi$
$422$		−	4.53620i		−	0.220819i
$423$	−4.19615	+	9.25036i	−0.204024	+	0.449768i
$424$		−	29.4582i		−	1.43062i
$425$	14.3650			0.696806
$426$	−33.8161	−	7.31130i	−1.63840	−	0.354234i
$427$	12.7846			0.618691
$428$	13.0820			0.632342
$429$		0			0
$430$	12.5885			0.607069
$431$	−20.9060			−1.00701			−0.503504	−	0.863993i	$-0.667956\pi$
$431$	−20.9060			−1.00701			−0.503504	+	0.863993i	$0.667956\pi$
$432$	−7.63397	+	10.2792i	−0.367290	+	0.494556i
$433$	13.0526			0.627266			0.313633	−	0.949544i	$-0.398454\pi$
$433$	13.0526			0.627266			0.313633	+	0.949544i	$0.398454\pi$
$434$			1.32829i			0.0637601i
$435$	11.3923	+	2.46309i	0.546217	+	0.118096i
$436$			39.9125i			1.91146i
$437$		0			0
$438$	−32.8564	−	7.10381i	−1.56994	−	0.339433i
$439$			8.38375i			0.400134i	0.979782	+	0.200067i	$0.0641160\pi$
$439$			8.38375i			0.400134i	−0.979782	+	0.200067i	$0.935884\pi$
$440$		0			0
$441$	2.73205	+	1.23931i	0.130098	+	0.0590149i
$442$			33.2204i			1.58013i
$443$		−	25.5156i		−	1.21228i	−0.795358	−	0.606140i	$-0.792717\pi$
$443$		−	25.5156i		−	1.21228i	0.795358	−	0.606140i	$-0.207283\pi$
$444$	−14.2942	+	66.1134i	−0.678374	+	3.13760i
$445$	−11.8756			−0.562960
$446$	−30.9523			−1.46563
$447$	−3.44239	+	15.9217i	−0.162820	+	0.753070i
$448$			30.1518i			1.42454i
$449$			40.2983i			1.90180i	0.309504	+	0.950898i	$0.399837\pi$
$449$			40.2983i			1.90180i	−0.309504	+	0.950898i	$0.600163\pi$
$450$	22.6587	+	10.2784i	1.06814	+	0.484530i
$451$		0			0
$452$		−	48.3984i		−	2.27647i
$453$	−27.9166	−	6.03579i	−1.31164	−	0.283586i
$454$	−12.5885			−0.590806
$455$			11.7290i			0.549864i
$456$	−17.1962	−	3.71794i	−0.805284	−	0.174109i
$457$		−	18.4219i		−	0.861742i	−0.902414	−	0.430871i	$-0.858206\pi$
$457$		−	18.4219i		−	0.861742i	0.902414	−	0.430871i	$-0.141794\pi$
$458$	−13.2539			−0.619313
$459$	−12.8472	+	17.2987i	−0.599655	+	0.807436i
$460$		0			0
$461$	2.86379			0.133380			0.0666901	−	0.997774i	$-0.478756\pi$
$461$	2.86379			0.133380			0.0666901	+	0.997774i	$0.478756\pi$
$462$		0			0
$463$	−1.26795			−0.0589266			−0.0294633	−	0.999566i	$-0.509380\pi$
$463$	−1.26795			−0.0589266			−0.0294633	+	0.999566i	$0.509380\pi$
$464$	−13.3797			−0.621138
$465$	−0.411543	−	0.0889787i	−0.0190848	−	0.00412629i
$466$	−13.0000			−0.602213
$467$			19.4080i			0.898094i	0.893508	+	0.449047i	$0.148236\pi$
$467$			19.4080i			0.898094i	−0.893508	+	0.449047i	$0.851764\pi$
$468$	−15.4762	+	34.1170i	−0.715386	+	1.57706i
$469$		−	5.65685i		−	0.261209i
$470$	10.0463			0.463401
$471$	−4.19615	+	19.4080i	−0.193348	+	0.894272i
$472$			52.4002i			2.41192i
$473$		0			0
$474$	29.7846	+	6.43966i	1.36805	+	0.295784i
$475$			8.48528i			0.389331i
$476$		−	43.7732i		−	2.00634i
$477$	8.80385	−	19.4080i	0.403100	−	0.888630i
$478$	24.0526			1.10014
$479$	−6.54099			−0.298866			−0.149433	−	0.988772i	$-0.547745\pi$
$479$	−6.54099			−0.298866			−0.149433	+	0.988772i	$0.547745\pi$
$480$	−5.02315	−	1.08604i	−0.229274	−	0.0495709i
$481$			35.0136i			1.59648i
$482$		−	9.00727i		−	0.410270i
$483$		0			0
$484$		0			0
$485$		−	2.81070i		−	0.127627i
$486$	−32.6421	+	18.0938i	−1.48067	+	0.820750i
$487$	33.1769			1.50339			0.751695	−	0.659511i	$-0.229237\pi$
$487$	33.1769			1.50339			0.751695	+	0.659511i	$0.229237\pi$
$488$		−	18.7438i		−	0.848493i
$489$	4.53590	−	20.9794i	0.205120	−	0.948719i
$490$		−	2.96713i		−	0.134041i
$491$	20.9060			0.943475			0.471738	−	0.881739i	$-0.343627\pi$
$491$	20.9060			0.943475			0.471738	+	0.881739i	$0.343627\pi$
$492$	−9.81149	+	45.3799i	−0.442336	+	2.04589i
$493$	−22.5167			−1.01410
$494$	−19.6230			−0.882880
$495$		0			0
$496$	0.483340			0.0217026
$497$	23.5979			1.05851
$498$	−13.0000	+	60.1274i	−0.582544	+	2.69437i
$499$	25.8038			1.15514			0.577569	−	0.816342i	$-0.304001\pi$
$499$	25.8038			1.15514			0.577569	+	0.816342i	$0.304001\pi$
$500$		−	39.1480i		−	1.75075i
$501$	−1.92455	+	8.90138i	−0.0859825	+	0.397684i
$502$		−	20.5569i		−	0.917498i
$503$	3.50531			0.156294			0.0781470	−	0.996942i	$-0.475100\pi$
$503$	3.50531			0.156294			0.0781470	+	0.996942i	$0.475100\pi$
$504$	14.5359	−	32.0442i	0.647480	−	1.42736i
$505$		−	0.582009i		−	0.0258991i
$506$		0			0
$507$	0.660254	−	3.05379i	0.0293229	−	0.135624i
$508$		−	53.8144i		−	2.38763i
$509$			11.7290i			0.519878i	0.965625	+	0.259939i	$0.0837025\pi$
$509$			11.7290i			0.519878i	−0.965625	+	0.259939i	$0.916297\pi$
$510$	20.8301	+	4.50363i	0.922374	+	0.199424i
$511$	22.9282			1.01428
$512$	26.3359			1.16389
$513$	−10.2182	−	7.58871i	−0.451144	−	0.335050i
$514$		−	55.3674i		−	2.44215i
$515$		−	15.7790i		−	0.695306i
$516$	−26.8055	−	5.79555i	−1.18005	−	0.255135i
$517$		0			0
$518$		−	70.8601i		−	3.11342i
$519$	4.14682	−	19.1798i	0.182025	−	0.841900i
$520$	17.1962			0.754101
$521$			2.47863i			0.108591i	0.998525	+	0.0542953i	$0.0172912\pi$
$521$			2.47863i			0.108591i	−0.998525	+	0.0542953i	$0.982709\pi$
$522$	−35.5167	−	16.1111i	−1.55452	−	0.705163i
$523$			36.0860i			1.57793i	0.614438	+	0.788965i	$0.289383\pi$
$523$			36.0860i			1.57793i	−0.614438	+	0.788965i	$0.710617\pi$
$524$	50.5753			2.20939
$525$	−16.5873	−	3.58630i	−0.723929	−	0.156519i
$526$	−56.1962			−2.45027
$527$	0.813410			0.0354327
$528$		0			0
$529$	23.0000			1.00000
$530$	−21.0779			−0.915566
$531$	−15.6603	+	34.5228i	−0.679597	+	1.49816i
$532$	25.8564			1.12102
$533$			24.0331i			1.04099i
$534$	38.8393	+	8.39735i	1.68074	+	0.363389i
$535$		−	4.34418i		−	0.187815i
$536$	−8.29365			−0.358231
$537$	38.5885	+	8.34312i	1.66521	+	0.360032i
$538$			39.1547i			1.68808i
$539$		0			0
$540$	19.2942	+	14.3292i	0.830291	+	0.616629i
$541$			5.27792i			0.226915i	0.993543	+	0.113458i	$0.0361926\pi$
$541$			5.27792i			0.226915i	−0.993543	+	0.113458i	$0.963807\pi$
$542$			21.8866i			0.940110i
$543$	4.70577	−	21.7650i	0.201944	−	0.934028i
$544$	9.92820			0.425668
$545$	13.2539			0.567734
$546$	8.29365	−	38.3596i	0.354935	−	1.64164i
$547$		−	21.1117i		−	0.902670i	−0.892355	−	0.451335i	$-0.850948\pi$
$547$		−	21.1117i		−	0.902670i	0.892355	−	0.451335i	$-0.149052\pi$
$548$		−	66.5670i		−	2.84360i
$549$	5.60175	−	12.3490i	0.239077	−	0.527042i
$550$		0			0
$551$		−	13.3004i		−	0.566615i
$552$		0			0
$553$	−20.7846			−0.883852
$554$			15.0259i			0.638388i
$555$	21.9545	+	4.74673i	0.931916	+	0.201487i
$556$			19.3185i			0.819288i
$557$	−10.3901			−0.440242			−0.220121	−	0.975473i	$-0.570645\pi$
$557$	−10.3901			−0.440242			−0.220121	+	0.975473i	$0.570645\pi$
$558$	1.28303	+	0.582009i	0.0543151	+	0.0246384i
$559$	−14.1962			−0.600433
$560$	−8.63744			−0.364998
$561$		0			0
$562$	1.94744			0.0821478
$563$	35.3969			1.49180			0.745900	−	0.666058i	$-0.232020\pi$
$563$	35.3969			1.49180			0.745900	+	0.666058i	$0.232020\pi$
$564$	−21.3923	−	4.62518i	−0.900779	−	0.194755i
$565$	−16.0718			−0.676146
$566$			16.2652i			0.683677i
$567$	19.1534	−	16.7675i	0.804366	−	0.704168i
$568$		−	34.5975i		−	1.45168i
$569$	−31.4219			−1.31728			−0.658638	−	0.752460i	$-0.728867\pi$
$569$	−31.4219			−1.31728			−0.658638	+	0.752460i	$0.728867\pi$
$570$	−2.66025	+	12.3042i	−0.111426	+	0.515364i
$571$			27.3233i			1.14345i	0.820447	+	0.571723i	$0.193725\pi$
$571$			27.3233i			1.14345i	−0.820447	+	0.571723i	$0.806275\pi$
$572$		0			0
$573$	4.19615	+	0.907241i	0.175297	+	0.0379005i
$574$		−	48.6381i		−	2.03011i
$575$		0			0
$576$	29.1244	+	13.2114i	1.21351	+	0.550475i
$577$	4.80385			0.199987			0.0999934	−	0.994988i	$-0.468118\pi$
$577$	4.80385			0.199987			0.0999934	+	0.994988i	$0.468118\pi$
$578$	−0.469622			−0.0195337
$579$	−4.85126	−	1.04888i	−0.201611	−	0.0435899i
$580$			25.1141i			1.04281i
$581$		−	41.9587i		−	1.74074i
$582$	−1.98747	+	9.19239i	−0.0823831	+	0.381037i
$583$		0			0
$584$		−	33.6156i		−	1.39102i
$585$	11.3293	+	5.13922i	0.468410	+	0.212480i
$586$	77.8897			3.21759
$587$			6.52864i			0.269466i	0.990882	+	0.134733i	$0.0430177\pi$
$587$			6.52864i			0.269466i	−0.990882	+	0.134733i	$0.956982\pi$
$588$	−1.36603	+	6.31812i	−0.0563339	+	0.260555i
$589$			0.480473i			0.0197976i
$590$	37.4933			1.54358
$591$	−3.91201	+	18.0938i	−0.160919	+	0.744278i
$592$	−25.7846			−1.05974
$593$	−26.3359			−1.08148			−0.540742	−	0.841188i	$-0.681857\pi$
$593$	−26.3359			−1.08148			−0.540742	+	0.841188i	$0.681857\pi$
$594$		0			0
$595$	−14.5359			−0.595914
$596$	−35.0991			−1.43772
$597$	2.80385	−	12.9683i	0.114754	−	0.530757i
$598$		0			0
$599$		−	2.72172i		−	0.111207i	−0.998453	−	0.0556033i	$-0.982292\pi$
$599$		−	2.72172i		−	0.111207i	0.998453	−	0.0556033i	$-0.0177082\pi$
$600$	−5.25796	+	24.3190i	−0.214655	+	0.992820i
$601$			41.5298i			1.69404i	0.531563	+	0.847019i	$0.321605\pi$
$601$			41.5298i			1.69404i	−0.531563	+	0.847019i	$0.678395\pi$
$602$	28.7300			1.17095
$603$	−5.46410	−	2.47863i	−0.222515	−	0.100938i
$604$		−	61.5419i		−	2.50410i
$605$		0			0
$606$	−0.411543	+	1.90346i	−0.0167178	+	0.0773228i
$607$			44.3954i			1.80195i	0.433866	+	0.900977i	$0.357149\pi$
$607$			44.3954i			1.80195i	−0.433866	+	0.900977i	$0.642851\pi$
$608$			5.86450i			0.237837i
$609$	26.0000	+	5.62140i	1.05357	+	0.227791i
$610$	−13.4115			−0.543017
$611$	−11.3293			−0.458336
$612$	−42.2817	−	19.1798i	−1.70913	−	0.775298i
$613$		−	15.4176i		−	0.622713i	−0.950293	−	0.311356i	$-0.899217\pi$
$613$		−	15.4176i		−	0.622713i	0.950293	−	0.311356i	$-0.100783\pi$
$614$			74.6671i			3.01332i
$615$	15.0695	+	3.25813i	0.607659	+	0.131381i
$616$		0			0
$617$			13.6325i			0.548822i	0.961613	+	0.274411i	$0.0884828\pi$
$617$			13.6325i			0.548822i	−0.961613	+	0.274411i	$0.911517\pi$
$618$	−11.1574	+	51.6052i	−0.448818	+	2.07587i
$619$	−0.143594			−0.00577151			−0.00288576	−	0.999996i	$-0.500919\pi$
$619$	−0.143594			−0.00577151			−0.00288576	+	0.999996i	$0.500919\pi$
$620$		−	0.907241i		−	0.0364357i
$621$		0			0
$622$		−	1.59008i		−	0.0637564i
$623$	−27.1032			−1.08587
$624$	−13.9583	−	3.01790i	−0.558780	−	0.120813i
$625$	4.32051			0.172820
$626$	17.6984			0.707372
$627$		0			0
$628$	−42.7846			−1.70729
$629$	−43.3928			−1.73018
$630$	−22.9282	−	10.4007i	−0.913481	−	0.414374i
$631$	27.3205			1.08761			0.543806	−	0.839211i	$-0.316983\pi$
$631$	27.3205			1.08761			0.543806	+	0.839211i	$0.316983\pi$
$632$			30.4728i			1.21214i
$633$	3.20758	+	0.693504i	0.127490	+	0.0275643i
$634$			58.9165i			2.33987i
$635$	−17.8703			−0.709162
$636$	44.8827	+	9.70398i	1.77971	+	0.384788i
$637$			3.34607i			0.132576i
$638$		0			0
$639$	10.3397	−	22.7938i	0.409034	−	0.901710i
$640$		−	25.6961i		−	1.01573i
$641$		−	47.2480i		−	1.86619i	−0.359636	−	0.933093i	$-0.617099\pi$
$641$		−	47.2480i		−	1.86619i	0.359636	−	0.933093i	$-0.382901\pi$
$642$	−3.07180	+	14.2076i	−0.121234	+	0.560730i
$643$	−3.80385			−0.150009			−0.0750046	−	0.997183i	$-0.523897\pi$
$643$	−3.80385			−0.150009			−0.0750046	+	0.997183i	$0.523897\pi$
$644$		0			0
$645$	−1.92455	+	8.90138i	−0.0757790	+	0.350492i
$646$		−	24.3190i		−	0.956820i
$647$			16.6862i			0.656004i	0.944677	+	0.328002i	$0.106375\pi$
$647$			16.6862i			0.656004i	−0.944677	+	0.328002i	$0.893625\pi$
$648$	−24.5832	−	28.0812i	−0.965720	−	1.10313i
$649$		0			0
$650$			27.7511i			1.08849i
$651$	−0.939245	−	0.203072i	−0.0368119	−	0.00795902i
$652$	46.2487			1.81124
$653$		−	38.8159i		−	1.51898i	−0.650516	−	0.759492i	$-0.725447\pi$
$653$		−	38.8159i		−	1.51898i	0.650516	−	0.759492i	$-0.274553\pi$
$654$	−43.3468	−	9.37191i	−1.69499	−	0.366471i
$655$		−	16.7947i		−	0.656223i
$656$	−17.6984			−0.691008
$657$	10.0463	−	22.1469i	0.391944	−	0.864035i
$658$	22.9282			0.893834
$659$	−13.5516			−0.527896			−0.263948	−	0.964537i	$-0.585025\pi$
$659$	−13.5516			−0.527896			−0.263948	+	0.964537i	$0.585025\pi$
$660$		0			0
$661$	3.19615			0.124316			0.0621580	−	0.998066i	$-0.480202\pi$
$661$	3.19615			0.124316			0.0621580	+	0.998066i	$0.480202\pi$
$662$	0.939245			0.0365048
$663$	−23.4904	−	5.07880i	−0.912291	−	0.197244i
$664$	−61.5167			−2.38731
$665$		−	8.58622i		−	0.332959i
$666$	−68.4456	−	31.0483i	−2.65221	−	1.20310i
$667$		0			0
$668$	−19.6230			−0.759236
$669$	4.73205	−	21.8866i	0.182952	−	0.846185i
$670$			5.93426i			0.229260i
$671$		0			0
$672$	−11.4641	−	2.47863i	−0.442237	−	0.0956151i
$673$			36.3906i			1.40276i	0.712790	+	0.701378i	$0.247431\pi$
$673$			36.3906i			1.40276i	−0.712790	+	0.701378i	$0.752569\pi$
$674$			20.4042i			0.785940i
$675$	−10.7321	+	14.4507i	−0.413077	+	0.556208i
$676$	6.73205			0.258925
$677$	−11.5012			−0.442028			−0.221014	−	0.975271i	$-0.570937\pi$
$677$	−11.5012			−0.442028			−0.221014	+	0.975271i	$0.570937\pi$
$678$	52.5628	+	11.3645i	2.01866	+	0.436450i
$679$		−	6.41473i		−	0.246175i
$680$			21.3114i			0.817256i
$681$	1.92455	−	8.90138i	0.0737488	−	0.341102i
$682$		0			0
$683$			41.2946i			1.58009i	0.613047	+	0.790046i	$0.289944\pi$
$683$			41.2946i			1.58009i	−0.613047	+	0.790046i	$0.710056\pi$
$684$	11.3293	−	24.9754i	0.433188	−	0.954957i
$685$	−22.1051			−0.844593
$686$			40.6304i			1.55128i
$687$	2.02628	−	9.37191i	0.0773074	−	0.357561i
$688$		−	10.4543i		−	0.398566i
$689$	23.7698			0.905558
$690$		0			0
$691$	2.58846			0.0984696			0.0492348	−	0.998787i	$-0.484322\pi$
$691$	2.58846			0.0984696			0.0492348	+	0.998787i	$0.484322\pi$
$692$	42.2817			1.60731
$693$		0			0
$694$	−3.07180			−0.116604
$695$	6.41516			0.243341
$696$	8.24167	−	38.1192i	0.312400	−	1.44491i
$697$	−29.7846			−1.12817
$698$		−	48.6415i		−	1.84111i
$699$	1.98747	−	9.19239i	0.0751728	−	0.347688i
$700$		−	36.5665i		−	1.38208i
$701$	19.9207			0.752395			0.376197	−	0.926540i	$-0.377231\pi$
$701$	19.9207			0.752395			0.376197	+	0.926540i	$0.377231\pi$
$702$	−33.4186	−	24.8188i	−1.26130	−	0.936727i
$703$		−	25.6317i		−	0.966718i
$704$		0			0
$705$	−1.53590	+	7.10381i	−0.0578453	+	0.267545i
$706$		−	22.9420i		−	0.863433i
$707$		−	1.32829i		−	0.0499556i
$708$	−79.8372	−	17.2614i	−3.00046	−	0.648724i
$709$	39.3205			1.47671			0.738356	−	0.674411i	$-0.235602\pi$
$709$	39.3205			1.47671			0.738356	+	0.674411i	$0.235602\pi$
$710$	−24.7551			−0.929043
$711$	−9.10706	+	20.0764i	−0.341541	+	0.752923i
$712$			39.7367i			1.48920i
$713$		0			0
$714$	47.5396	+	10.2784i	1.77913	+	0.384661i
$715$		0			0
$716$			85.0677i			3.17913i
$717$	−3.67720	+	17.0077i	−0.137328	+	0.635165i
$718$	−82.4974			−3.07878
$719$		−	35.8511i		−	1.33702i	−0.743703	−	0.668511i	$-0.766932\pi$
$719$		−	35.8511i		−	1.33702i	0.743703	−	0.668511i	$-0.233068\pi$
$720$	−3.78461	+	8.34312i	−0.141044	+	0.310930i
$721$		−	36.0117i		−	1.34114i
$722$	−31.1242			−1.15832
$723$	6.36910	+	1.37705i	0.236869	+	0.0512130i
$724$	47.9808			1.78319
$725$	−18.8096			−0.698570
$726$		0			0
$727$	−28.9282			−1.07289			−0.536444	−	0.843936i	$-0.680233\pi$
$727$	−28.9282			−1.07289			−0.536444	+	0.843936i	$0.680233\pi$
$728$	39.2460			1.45455
$729$	−7.80385	−	25.8476i	−0.289031	−	0.957320i
$730$	−24.0526			−0.890225
$731$		−	17.5935i		−	0.650719i
$732$	28.5581	+	6.17449i	1.05554	+	0.228216i
$733$		−	28.7004i		−	1.06007i	−0.847975	−	0.530036i	$-0.822178\pi$
$733$		−	28.7004i		−	1.06007i	0.847975	−	0.530036i	$-0.177822\pi$
$734$	57.1163			2.10820
$735$	2.09808	+	0.453620i	0.0773887	+	0.0167320i
$736$		0			0
$737$		0			0
$738$	−46.9808	−	21.3114i	−1.72939	−	0.784484i
$739$			22.5259i			0.828628i	0.910134	+	0.414314i	$0.135978\pi$
$739$			22.5259i			0.828628i	−0.910134	+	0.414314i	$0.864022\pi$
$740$			48.3984i			1.77916i
$741$	3.00000	−	13.8755i	0.110208	−	0.509731i
$742$	−48.1051			−1.76599
$743$	28.3863			1.04139			0.520695	−	0.853743i	$-0.325673\pi$
$743$	28.3863			1.04139			0.520695	+	0.853743i	$0.325673\pi$
$744$	−0.297729	+	1.37705i	−0.0109153	+	0.0504851i
$745$			11.6555i			0.427024i
$746$		−	23.0369i		−	0.843442i
$747$	−40.5290	−	18.3848i	−1.48288	−	0.672664i
$748$		0			0
$749$		−	9.91451i		−	0.362268i
$750$	42.5165	+	9.19239i	1.55248	+	0.335659i
$751$	4.87564			0.177915			0.0889574	−	0.996035i	$-0.471647\pi$
$751$	4.87564			0.177915			0.0889574	+	0.996035i	$0.471647\pi$
$752$		−	8.34312i		−	0.304242i
$753$	14.5359	+	3.14277i	0.529718	+	0.114529i
$754$		−	43.4988i		−	1.58413i
$755$	−20.4364			−0.743757
$756$	44.0343	+	32.7028i	1.60151	+	1.18939i
$757$	−6.66025			−0.242071			−0.121036	−	0.992648i	$-0.538621\pi$
$757$	−6.66025			−0.242071			−0.121036	+	0.992648i	$0.538621\pi$
$758$	73.2340			2.65998
$759$		0			0
$760$	−12.5885			−0.456631
$761$	28.9019			1.04769			0.523847	−	0.851812i	$-0.324496\pi$
$761$	28.9019			1.04769			0.523847	+	0.851812i	$0.324496\pi$
$762$	58.4449	+	12.6362i	2.11723	+	0.457762i
$763$	30.2487			1.09508
$764$			9.25036i			0.334666i
$765$	−6.36910	+	14.0406i	−0.230275	+	0.507639i
$766$			22.7290i			0.821230i
$767$	−42.2817			−1.52670
$768$	−10.3660	+	47.9447i	−0.374052	+	1.73006i
$769$			11.9329i			0.430311i	0.976580	+	0.215155i	$0.0690258\pi$
$769$			11.9329i			0.430311i	−0.976580	+	0.215155i	$0.930974\pi$
$770$		0			0
$771$	39.1506	+	8.46467i	1.40998	+	0.304848i
$772$		−	10.6945i		−	0.384905i
$773$			30.8939i			1.11118i	0.831458	+	0.555588i	$0.187507\pi$
$773$			30.8939i			1.11118i	−0.831458	+	0.555588i	$0.812493\pi$
$774$	12.5885	−	27.7511i	0.452483	−	0.997492i
$775$	0.679492			0.0244081
$776$	−9.40479			−0.337612
$777$	50.1057	+	10.8332i	1.79753	+	0.388640i
$778$		−	45.6709i		−	1.63738i
$779$		−	17.5935i		−	0.630352i
$780$	−5.66467	+	26.2001i	−0.202828	+	0.938115i
$781$		0			0
$782$		0			0
$783$	16.8221	−	22.6510i	0.601173	−	0.809480i
$784$	−2.46410			−0.0880036
$785$			14.2076i			0.507092i
$786$	−11.8756	+	54.9270i	−0.423590	+	1.95918i
$787$		−	45.5322i		−	1.62305i	−0.584318	−	0.811524i	$-0.698638\pi$
$787$		−	45.5322i		−	1.62305i	0.584318	−	0.811524i	$-0.301362\pi$
$788$	−39.8875			−1.42093
$789$	8.59138	−	39.7367i	0.305861	−	1.41466i
$790$	21.8038			0.775746
$791$	−36.6799			−1.30419
$792$		0			0
$793$	15.1244			0.537082
$794$	50.7472			1.80095
$795$	3.22243	−	14.9043i	0.114288	−	0.528602i
$796$	28.5885			1.01329
$797$			15.3580i			0.544007i	0.962296	+	0.272003i	$0.0876862\pi$
$797$			15.3580i			0.544007i	−0.962296	+	0.272003i	$0.912314\pi$
$798$	−6.07137	+	28.0812i	−0.214924	+	0.994064i
$799$		−	14.0406i		−	0.496721i
$800$	8.29365			0.293225
$801$	−11.8756	+	26.1797i	−0.419605	+	0.925014i
$802$			2.96713i			0.104773i
$803$		0			0
$804$	2.73205	−	12.6362i	0.0963520	−	0.445646i
$805$		0			0
$806$			1.57139i			0.0553497i
$807$	−27.6865	−	5.98604i	−0.974612	−	0.210719i
$808$	−1.94744			−0.0685107
$809$	51.8583			1.82324			0.911621	−	0.411032i	$-0.134832\pi$
$809$	51.8583			1.82324			0.911621	+	0.411032i	$0.134832\pi$
$810$	−20.0926	+	17.5897i	−0.705982	+	0.618040i
$811$			26.0106i			0.913357i	0.889632	+	0.456679i	$0.150961\pi$
$811$			26.0106i			0.913357i	−0.889632	+	0.456679i	$0.849039\pi$
$812$			57.3167i			2.01142i
$813$	−15.4762	−	3.34607i	−0.542773	−	0.117352i
$814$		0			0
$815$		−	15.3580i		−	0.537966i
$816$	3.74012	−	17.2987i	0.130930	−	0.605577i
$817$	10.3923			0.363581
$818$			79.5353i			2.78089i
$819$	25.8564	+	11.7290i	0.903496	+	0.409844i
$820$			33.2204i			1.16011i
$821$	−21.8453			−0.762405			−0.381202	−	0.924492i	$-0.624490\pi$
$821$	−21.8453			−0.762405			−0.381202	+	0.924492i	$0.624490\pi$
$822$	72.2947	+	15.6307i	2.52157	+	0.545183i
$823$	32.8756			1.14597			0.572986	−	0.819565i	$-0.305785\pi$
$823$	32.8756			1.14597			0.572986	+	0.819565i	$0.305785\pi$
$824$	−52.7976			−1.83929
$825$		0			0
$826$	85.5692			2.97733
$827$	−18.8096			−0.654073			−0.327036	−	0.945012i	$-0.606050\pi$
$827$	−18.8096			−0.654073			−0.327036	+	0.945012i	$0.606050\pi$
$828$		0			0
$829$	19.5885			0.680335			0.340168	−	0.940365i	$-0.389516\pi$
$829$	19.5885			0.680335			0.340168	+	0.940365i	$0.389516\pi$
$830$			44.0163i			1.52783i
$831$	−10.6249	−	2.29719i	−0.368574	−	0.0796885i
$832$			35.6699i			1.23663i
$833$	−4.14682			−0.143679
$834$	−20.9808	−	4.53620i	−0.726504	−	0.157076i
$835$			6.51626i			0.225505i
$836$		0			0
$837$	−0.607695	+	0.818262i	−0.0210050	+	0.0282833i
$838$		−	26.4911i		−	0.915121i
$839$			18.7438i			0.647109i	0.946210	+	0.323554i	$0.104878\pi$
$839$			18.7438i			0.647109i	−0.946210	+	0.323554i	$0.895122\pi$
$840$	5.32051	−	24.6083i	0.183575	−	0.849068i
$841$	0.483340			0.0166669
$842$	45.9589			1.58385
$843$	−0.297729	+	1.37705i	−0.0102543	+	0.0474281i
$844$			7.07107i			0.243396i
$845$		−	2.23553i		−	0.0769047i
$846$	10.0463	−	22.1469i	0.345399	−	0.761428i
$847$		0			0
$848$			17.5045i			0.601107i
$849$	−11.5012	−	2.48665i	−0.394721	−	0.0853418i
$850$	−34.3923			−1.17965
$851$		0			0
$852$	52.7128	+	11.3969i	1.80591	+	0.390452i
$853$			42.5651i			1.45740i	0.684832	+	0.728701i	$0.259875\pi$
$853$			42.5651i			1.45740i	−0.684832	+	0.728701i	$0.740125\pi$
$854$	−30.6085			−1.04740
$855$	−8.29365	−	3.76217i	−0.283637	−	0.128663i
$856$	−14.5359			−0.496827
$857$	56.3029			1.92327			0.961635	−	0.274332i	$-0.0884568\pi$
$857$	56.3029			1.92327			0.961635	+	0.274332i	$0.0884568\pi$
$858$		0			0
$859$	1.12436			0.0383625			0.0191813	−	0.999816i	$-0.493894\pi$
$859$	1.12436			0.0383625			0.0191813	+	0.999816i	$0.493894\pi$
$860$	−19.6230			−0.669138
$861$	34.3923	+	7.43588i	1.17209	+	0.253414i
$862$	50.0526			1.70480
$863$		−	28.9014i		−	0.983816i	−0.870647	−	0.491908i	$-0.836300\pi$
$863$		−	28.9014i		−	0.983816i	0.870647	−	0.491908i	$-0.163700\pi$
$864$	−7.41732	+	9.98743i	−0.252342	+	0.339779i
$865$		−	14.0406i		−	0.477395i
$866$	−31.2500			−1.06192
$867$	0.0717968	−	0.332073i	0.00243835	−	0.0112778i
$868$		−	2.07055i		−	0.0702791i
$869$		0			0
$870$	−27.2750	−	5.89706i	−0.924709	−	0.199929i
$871$		−	6.69213i		−	0.226754i
$872$		−	44.3484i		−	1.50182i
$873$	−6.19615	−	2.81070i	−0.209708	−	0.0951278i
$874$		0			0
$875$	−29.6693			−1.00300
$876$	51.2168	+	11.0735i	1.73046	+	0.374138i
$877$			28.7747i			0.971653i	0.874055	+	0.485826i	$0.161481\pi$
$877$			28.7747i			0.971653i	−0.874055	+	0.485826i	$0.838519\pi$
$878$		−	20.0721i		−	0.677401i
$879$	−11.9079	+	55.0764i	−0.401645	+	1.85768i
$880$		0			0
$881$			13.6325i			0.459289i	0.973275	+	0.229644i	$0.0737563\pi$
$881$			13.6325i			0.459289i	−0.973275	+	0.229644i	$0.926244\pi$
$882$	−6.54099	−	2.96713i	−0.220247	−	0.0999084i
$883$	−11.4641			−0.385798			−0.192899	−	0.981219i	$-0.561789\pi$
$883$	−11.4641			−0.385798			−0.192899	+	0.981219i	$0.561789\pi$
$884$		−	51.7842i		−	1.74169i
$885$	−5.73205	+	26.5118i	−0.192681	+	0.891184i
$886$			61.0886i			2.05231i
$887$	−45.3173			−1.52161			−0.760804	−	0.648982i	$-0.775195\pi$
$887$	−45.3173			−1.52161			−0.760804	+	0.648982i	$0.775195\pi$
$888$	15.8829	−	73.4611i	0.532994	−	2.46519i
$889$	−40.7846			−1.36787
$890$	28.4323			0.953053
$891$		0			0
$892$	48.2487			1.61549
$893$	8.29365			0.277536
$894$	8.24167	−	38.1192i	0.275643	−	1.27490i
$895$	28.2487			0.944250
$896$		−	58.6450i		−	1.95919i
$897$		0			0
$898$		−	96.4811i		−	3.21962i
$899$	−1.06508			−0.0355224
$900$	−35.3205	−	16.0221i	−1.17735	−	0.534070i
$901$			29.4582i			0.981397i
$902$		0			0
$903$	−4.39230	+	20.3152i	−0.146167	+	0.676048i
$904$			53.7773i			1.78861i
$905$		−	15.9331i		−	0.529635i
$906$	66.8372	+	14.4507i	2.22052	+	0.480093i
$907$	−26.4449			−0.878087			−0.439044	−	0.898466i	$-0.644683\pi$
$907$	−26.4449			−0.878087			−0.439044	+	0.898466i	$0.644683\pi$
$908$	19.6230			0.651212
$909$	−1.28303	−	0.582009i	−0.0425555	−	0.0193040i
$910$		−	28.0812i		−	0.930883i
$911$			31.8011i			1.05362i	0.849984	+	0.526809i	$0.176612\pi$
$911$			31.8011i			1.05362i	−0.849984	+	0.526809i	$0.823388\pi$
$912$	10.2182	+	2.20925i	0.338358	+	0.0731557i
$913$		0			0
$914$			44.1053i			1.45887i
$915$	2.05038	−	9.48339i	0.0677836	−	0.313511i
$916$	20.6603			0.682634
$917$		−	38.3297i		−	1.26576i
$918$	30.7583	−	41.4161i	1.01518	−	1.36694i
$919$			39.0160i			1.28702i	0.765438	+	0.643509i	$0.222522\pi$
$919$			39.0160i			1.28702i	−0.765438	+	0.643509i	$0.777478\pi$
$920$		0			0
$921$	−52.7976	−	11.4152i	−1.73974	−	0.376145i
$922$	−6.85641			−0.225804
$923$	27.9166			0.918887
$924$		0			0
$925$	−36.2487			−1.19185
$926$	3.03569			0.0997588
$927$	−34.7846	−	15.7790i	−1.14248	−	0.518251i
$928$	−13.0000			−0.426746
$929$			31.9552i			1.04842i	0.851590	+	0.524208i	$0.175639\pi$
$929$			31.9552i			1.04842i	−0.851590	+	0.524208i	$0.824361\pi$
$930$	0.985303	+	0.213030i	0.0323094	+	0.00698554i
$931$		−	2.44949i		−	0.0802788i
$932$	20.2645			0.663786
$933$	1.12436	+	0.243094i	0.0368098	+	0.00795855i
$934$		−	46.4660i		−	1.52041i
$935$		0			0
$936$	17.1962	−	37.9087i	0.562074	−	1.23908i
$937$		−	28.5988i		−	0.934283i	−0.884182	−	0.467142i	$-0.845284\pi$
$937$		−	28.5988i		−	0.934283i	0.884182	−	0.467142i	$-0.154716\pi$
$938$			13.5435i			0.442210i
$939$	−2.70577	+	12.5147i	−0.0882995	+	0.408401i
$940$	−15.6603			−0.510781
$941$	2.05038			0.0668406			0.0334203	−	0.999441i	$-0.489360\pi$
$941$	2.05038			0.0668406			0.0334203	+	0.999441i	$0.489360\pi$
$942$	10.0463	−	46.4660i	0.327326	−	1.51394i
$943$		0			0
$944$		−	31.1370i		−	1.01342i
$945$	10.8597	−	14.6226i	0.353266	−	0.475674i
$946$		0			0
$947$		−	30.2297i		−	0.982334i	−0.871065	−	0.491167i	$-0.836571\pi$
$947$		−	30.2297i		−	0.982334i	0.871065	−	0.491167i	$-0.163429\pi$
$948$	−46.4285	−	10.0382i	−1.50793	−	0.326025i
$949$	27.1244			0.880494
$950$		−	20.3152i		−	0.659112i
$951$	−41.6603	−	9.00727i	−1.35093	−	0.292081i
$952$			48.6381i			1.57637i
$953$	55.0659			1.78376			0.891880	−	0.452272i	$-0.149386\pi$
$953$	55.0659			1.78376			0.891880	+	0.452272i	$0.149386\pi$
$954$	−21.0779	+	46.4660i	−0.682423	+	1.50439i
$955$	3.07180			0.0994010
$956$	−37.4933			−1.21262
$957$		0			0
$958$	15.6603			0.505960
$959$	−50.4495			−1.62910
$960$	22.3660	+	4.83571i	0.721860	+	0.156072i
$961$	−30.9615			−0.998759
$962$		−	83.8284i		−	2.70274i
$963$	−9.57668	−	4.34418i	−0.308604	−	0.139989i
$964$			14.0406i			0.452217i
$965$	−3.55137			−0.114323
$966$		0			0
$967$		−	45.0518i		−	1.44877i	−0.689397	−	0.724383i	$-0.742125\pi$
$967$		−	45.0518i		−	1.44877i	0.689397	−	0.724383i	$-0.257875\pi$
$968$		0			0
$969$	17.1962	+	3.71794i	0.552420	+	0.119437i
$970$			6.72930i			0.216065i
$971$		−	7.43588i		−	0.238629i	−0.992857	−	0.119314i	$-0.961930\pi$
$971$		−	7.43588i		−	0.238629i	0.992857	−	0.119314i	$-0.0380696\pi$
$972$	50.8827	−	28.2047i	1.63206	−	0.904666i
$973$	14.6410			0.469369
$974$	−79.4312			−2.54514
$975$	−19.6230	−	4.24264i	−0.628438	−	0.135873i
$976$			11.1378i			0.356514i
$977$			11.1538i			0.356842i	0.983954	+	0.178421i	$0.0570990\pi$
$977$			11.1538i			0.356842i	−0.983954	+	0.178421i	$0.942901\pi$
$978$	−10.8597	+	50.2281i	−0.347255	+	1.60612i
$979$		0			0
$980$			4.62518i			0.147746i
$981$	13.2539	−	29.2180i	0.423164	−	0.932859i
$982$	−50.0526			−1.59724
$983$		−	0.486189i		−	0.0155070i	−0.999970	−	0.00775351i	$-0.997532\pi$
$983$		−	0.486189i		−	0.0155070i	0.999970	−	0.00775351i	$-0.00246804\pi$
$984$	10.9019	−	50.4234i	0.347541	−	1.60744i
$985$			13.2456i			0.422039i
$986$	53.9087			1.71680
$987$	−3.50531	+	16.2127i	−0.111575	+	0.516056i
$988$	30.5885			0.973148
$989$		0			0
$990$		0			0
$991$	19.8564			0.630760			0.315380	−	0.948966i	$-0.397868\pi$
$991$	19.8564			0.630760			0.315380	+	0.948966i	$0.397868\pi$
$992$	0.469622			0.0149105
$993$	−0.143594	+	0.664146i	−0.00455680	+	0.0210760i
$994$	−56.4974			−1.79199
$995$		−	9.49346i		−	0.300963i
$996$	20.2645	−	93.7270i	0.642105	−	2.96985i
$997$			60.4694i			1.91509i	0.288291	+	0.957543i	$0.406913\pi$
$997$			60.4694i			1.91509i	−0.288291	+	0.957543i	$0.593087\pi$
$998$	−61.7788			−1.95557
$999$	32.4186	−	43.6516i	1.02568	−	1.38108i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.2.d.e.362.1	✓	8
3.2	odd	2	inner	363.2.d.e.362.8	yes	8
11.2	odd	10		363.2.f.i.161.1		32
11.3	even	5		363.2.f.i.233.2		32
11.4	even	5		363.2.f.i.215.1		32
11.5	even	5		363.2.f.i.239.8		32
11.6	odd	10		363.2.f.i.239.2		32
11.7	odd	10		363.2.f.i.215.7		32
11.8	odd	10		363.2.f.i.233.8		32
11.9	even	5		363.2.f.i.161.7		32
11.10	odd	2	inner	363.2.d.e.362.7	yes	8
33.2	even	10		363.2.f.i.161.8		32
33.5	odd	10		363.2.f.i.239.1		32
33.8	even	10		363.2.f.i.233.1		32
33.14	odd	10		363.2.f.i.233.7		32
33.17	even	10		363.2.f.i.239.7		32
33.20	odd	10		363.2.f.i.161.2		32
33.26	odd	10		363.2.f.i.215.8		32
33.29	even	10		363.2.f.i.215.2		32
33.32	even	2	inner	363.2.d.e.362.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
363.2.d.e.362.1	✓	8	1.1	even	1	trivial
363.2.d.e.362.2	yes	8	33.32	even	2	inner
363.2.d.e.362.7	yes	8	11.10	odd	2	inner
363.2.d.e.362.8	yes	8	3.2	odd	2	inner
363.2.f.i.161.1		32	11.2	odd	10
363.2.f.i.161.2		32	33.20	odd	10
363.2.f.i.161.7		32	11.9	even	5
363.2.f.i.161.8		32	33.2	even	10
363.2.f.i.215.1		32	11.4	even	5
363.2.f.i.215.2		32	33.29	even	10
363.2.f.i.215.7		32	11.7	odd	10
363.2.f.i.215.8		32	33.26	odd	10
363.2.f.i.233.1		32	33.8	even	10
363.2.f.i.233.2		32	11.3	even	5
363.2.f.i.233.7		32	33.14	odd	10
363.2.f.i.233.8		32	11.8	odd	10
363.2.f.i.239.1		32	33.5	odd	10
363.2.f.i.239.2		32	11.6	odd	10
363.2.f.i.239.7		32	33.17	even	10
363.2.f.i.239.8		32	11.5	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:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	363.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.39417 q^{2} +(0.366025 - 1.69293i) q^{3} +3.73205 q^{4} -1.23931i q^{5} +(-0.876327 + 4.05317i) q^{6} -2.82843i q^{7} -4.14682 q^{8} +(-2.73205 - 1.23931i) q^{9} +O(q^{10})\)	\(q-2.39417 q^{2} +(0.366025 - 1.69293i) q^{3} +3.73205 q^{4} -1.23931i q^{5} +(-0.876327 + 4.05317i) q^{6} -2.82843i q^{7} -4.14682 q^{8} +(-2.73205 - 1.23931i) q^{9} +2.96713i q^{10} +(1.36603 - 6.31812i) q^{12} -3.34607i q^{13} +6.77174i q^{14} +(-2.09808 - 0.453620i) q^{15} +2.46410 q^{16} +4.14682 q^{17} +(6.54099 + 2.96713i) q^{18} +2.44949i q^{19} -4.62518i q^{20} +(-4.78834 - 1.03528i) q^{21} +(-1.51784 + 7.02030i) q^{24} +3.46410 q^{25} +8.01105i q^{26} +(-3.09808 + 4.17156i) q^{27} -10.5558i q^{28} -5.42986 q^{29} +(5.02315 + 1.08604i) q^{30} +0.196152 q^{31} +2.39417 q^{32} -9.92820 q^{34} -3.50531 q^{35} +(-10.1962 - 4.62518i) q^{36} -10.4641 q^{37} -5.86450i q^{38} +(-5.66467 - 1.22474i) q^{39} +5.13922i q^{40} -7.18251 q^{41} +(11.4641 + 2.47863i) q^{42} -4.24264i q^{43} +(-1.53590 + 3.38587i) q^{45} -3.38587i q^{47} +(0.901924 - 4.17156i) q^{48} -1.00000 q^{49} -8.29365 q^{50} +(1.51784 - 7.02030i) q^{51} -12.4877i q^{52} +7.10381i q^{53} +(7.41732 - 9.98743i) q^{54} +11.7290i q^{56} +(4.14682 + 0.896575i) q^{57} +13.0000 q^{58} -12.6362i q^{59} +(-7.83013 - 1.69293i) q^{60} +4.52004i q^{61} -0.469622 q^{62} +(-3.50531 + 7.72741i) q^{63} -10.6603 q^{64} -4.14682 q^{65} +2.00000 q^{67} +15.4762 q^{68} +8.39230 q^{70} +8.34312i q^{71} +(11.3293 + 5.13922i) q^{72} +8.10634i q^{73} +25.0528 q^{74} +(1.26795 - 5.86450i) q^{75} +9.14162i q^{76} +(13.5622 + 2.93225i) q^{78} -7.34847i q^{79} -3.05379i q^{80} +(5.92820 + 6.77174i) q^{81} +17.1962 q^{82} +14.8346 q^{83} +(-17.8703 - 3.86370i) q^{84} -5.13922i q^{85} +10.1576i q^{86} +(-1.98747 + 9.19239i) q^{87} -9.58244i q^{89} +(3.67720 - 8.10634i) q^{90} -9.46410 q^{91} +(0.0717968 - 0.332073i) q^{93} +8.10634i q^{94} +3.03569 q^{95} +(0.876327 - 4.05317i) q^{96} +2.26795 q^{97} +2.39417 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} + 16 q^{4} - 8 q^{9}+O(q^{10}) \) 8 * q - 4 * q^3 + 16 * q^4 - 8 * q^9	\( 8 q - 4 q^{3} + 16 q^{4} - 8 q^{9} + 4 q^{12} + 4 q^{15} - 8 q^{16} - 4 q^{27} - 40 q^{31} - 24 q^{34} - 40 q^{36} - 56 q^{37} + 64 q^{42} - 40 q^{45} + 28 q^{48} - 8 q^{49} + 104 q^{58} - 28 q^{60} - 16 q^{64} + 16 q^{67} - 16 q^{70} + 24 q^{75} + 60 q^{78} - 8 q^{81} + 96 q^{82} - 48 q^{91} + 56 q^{93} + 32 q^{97}+O(q^{100}) \) 8 * q - 4 * q^3 + 16 * q^4 - 8 * q^9 + 4 * q^12 + 4 * q^15 - 8 * q^16 - 4 * q^27 - 40 * q^31 - 24 * q^34 - 40 * q^36 - 56 * q^37 + 64 * q^42 - 40 * q^45 + 28 * q^48 - 8 * q^49 + 104 * q^58 - 28 * q^60 - 16 * q^64 + 16 * q^67 - 16 * q^70 + 24 * q^75 + 60 * q^78 - 8 * q^81 + 96 * q^82 - 48 * q^91 + 56 * q^93 + 32 * q^97

Introduction

L-functions

Modular forms

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Database

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