LMFDB - Embedded newform 208.2.i.e.113.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [208,2,Mod(81,208)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(208, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("208.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 208 = 2^{4} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	208.i (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:	$1.66088836204$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 5x^{2} + 4x + 16 $ x^4 - x^3 + 5x^2 + 4x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			113.1
Root			$-0.780776 + 1.35234i$ of defining polynomial
Character	$\chi$	$=$	208.113
Dual form			208.2.i.e.81.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.780776 + 1.35234i) q^{3} +0.561553 q^{5} +(0.780776 + 1.35234i) q^{7} +(0.280776 + 0.486319i) q^{9} +O(q^{10})$	\(q+(-0.780776 + 1.35234i) q^{3} +0.561553 q^{5} +(0.780776 + 1.35234i) q^{7} +(0.280776 + 0.486319i) q^{9} +(-0.780776 + 1.35234i) q^{11} +(-2.84233 + 2.21837i) q^{13} +(-0.438447 + 0.759413i) q^{15} +(2.50000 + 4.33013i) q^{17} +(0.780776 + 1.35234i) q^{19} -2.43845 q^{21} +(4.34233 - 7.52113i) q^{23} -4.68466 q^{25} -5.56155 q^{27} +(2.50000 - 4.33013i) q^{29} +8.00000 q^{31} +(-1.21922 - 2.11176i) q^{33} +(0.438447 + 0.759413i) q^{35} +(0.500000 - 0.866025i) q^{37} +(-0.780776 - 5.57586i) q^{39} +(3.62311 - 6.27540i) q^{41} +(-1.21922 - 2.11176i) q^{43} +(0.157671 + 0.273094i) q^{45} -4.00000 q^{47} +(2.28078 - 3.95042i) q^{49} -7.80776 q^{51} +8.56155 q^{53} +(-0.438447 + 0.759413i) q^{55} -2.43845 q^{57} +(0.780776 + 1.35234i) q^{59} +(-4.62311 - 8.00745i) q^{61} +(-0.438447 + 0.759413i) q^{63} +(-1.59612 + 1.24573i) q^{65} +(-6.78078 + 11.7446i) q^{67} +(6.78078 + 11.7446i) q^{69} +(-2.34233 - 4.05703i) q^{71} -13.6847 q^{73} +(3.65767 - 6.33527i) q^{75} -2.43845 q^{77} +4.00000 q^{79} +(3.50000 - 6.06218i) q^{81} +14.2462 q^{83} +(1.40388 + 2.43160i) q^{85} +(3.90388 + 6.76172i) q^{87} +(-1.34233 + 2.32498i) q^{89} +(-5.21922 - 2.11176i) q^{91} +(-6.24621 + 10.8188i) q^{93} +(0.438447 + 0.759413i) q^{95} +(8.90388 + 15.4220i) q^{97} -0.876894 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{3} - 6 q^{5} - q^{7} - 3 q^{9}+O(q^{10}) $ 4 * q + q^3 - 6 * q^5 - q^7 - 3 * q^9	$ 4 q + q^{3} - 6 q^{5} - q^{7} - 3 q^{9} + q^{11} + q^{13} - 10 q^{15} + 10 q^{17} - q^{19} - 18 q^{21} + 5 q^{23} + 6 q^{25} - 14 q^{27} + 10 q^{29} + 32 q^{31} - 9 q^{33} + 10 q^{35} + 2 q^{37} + q^{39} - 2 q^{41} - 9 q^{43} + 13 q^{45} - 16 q^{47} + 5 q^{49} + 10 q^{51} + 26 q^{53} - 10 q^{55} - 18 q^{57} - q^{59} - 2 q^{61} - 10 q^{63} - 27 q^{65} - 23 q^{67} + 23 q^{69} + 3 q^{71} - 30 q^{73} + 27 q^{75} - 18 q^{77} + 16 q^{79} + 14 q^{81} + 24 q^{83} - 15 q^{85} - 5 q^{87} + 7 q^{89} - 25 q^{91} + 8 q^{93} + 10 q^{95} + 15 q^{97} - 20 q^{99}+O(q^{100}) $ 4 * q + q^3 - 6 * q^5 - q^7 - 3 * q^9 + q^11 + q^13 - 10 * q^15 + 10 * q^17 - q^19 - 18 * q^21 + 5 * q^23 + 6 * q^25 - 14 * q^27 + 10 * q^29 + 32 * q^31 - 9 * q^33 + 10 * q^35 + 2 * q^37 + q^39 - 2 * q^41 - 9 * q^43 + 13 * q^45 - 16 * q^47 + 5 * q^49 + 10 * q^51 + 26 * q^53 - 10 * q^55 - 18 * q^57 - q^59 - 2 * q^61 - 10 * q^63 - 27 * q^65 - 23 * q^67 + 23 * q^69 + 3 * q^71 - 30 * q^73 + 27 * q^75 - 18 * q^77 + 16 * q^79 + 14 * q^81 + 24 * q^83 - 15 * q^85 - 5 * q^87 + 7 * q^89 - 25 * q^91 + 8 * q^93 + 10 * q^95 + 15 * q^97 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/208\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.780776	+	1.35234i	−0.450781	+	0.780776i	−0.998435	−	0.0559290i	$-0.982188\pi$
$3$	−0.780776	+	1.35234i	−0.450781	+	0.780776i	0.547653	+	0.836705i	$0.315521\pi$
$4$		0			0
$5$	0.561553			0.251134			0.125567	−	0.992085i	$-0.459925\pi$
$5$	0.561553			0.251134			0.125567	+	0.992085i	$0.459925\pi$
$6$		0			0
$7$	0.780776	+	1.35234i	0.295106	+	0.511138i	0.975009	−	0.222163i	$-0.0713118\pi$
$7$	0.780776	+	1.35234i	0.295106	+	0.511138i	−0.679904	+	0.733301i	$0.737978\pi$
$8$		0			0
$9$	0.280776	+	0.486319i	0.0935921	+	0.162106i
$10$		0			0
$11$	−0.780776	+	1.35234i	−0.235413	+	0.407747i	−0.959393	−	0.282074i	$-0.908978\pi$
$11$	−0.780776	+	1.35234i	−0.235413	+	0.407747i	0.723980	+	0.689821i	$0.242311\pi$
$12$		0			0
$13$	−2.84233	+	2.21837i	−0.788320	+	0.615265i
$13$	−2.84233	+	2.21837i	−0.788320	+	0.615265i
$14$		0			0
$15$	−0.438447	+	0.759413i	−0.113207	+	0.196080i
$16$		0			0
$17$	2.50000	+	4.33013i	0.606339	+	1.05021i	0.991838	+	0.127502i	$0.0406959\pi$
$17$	2.50000	+	4.33013i	0.606339	+	1.05021i	−0.385499	+	0.922708i	$0.625971\pi$
$18$		0			0
$19$	0.780776	+	1.35234i	0.179122	+	0.310249i	0.941580	−	0.336789i	$-0.109341\pi$
$19$	0.780776	+	1.35234i	0.179122	+	0.310249i	−0.762458	+	0.647038i	$0.776008\pi$
$20$		0			0
$21$	−2.43845			−0.532113
$22$		0			0
$23$	4.34233	−	7.52113i	0.905438	−	1.56827i	0.0851104	−	0.996372i	$-0.472876\pi$
$23$	4.34233	−	7.52113i	0.905438	−	1.56827i	0.820328	−	0.571893i	$-0.193791\pi$
$24$		0			0
$25$	−4.68466			−0.936932
$26$		0			0
$27$	−5.56155			−1.07032
$28$		0			0
$29$	2.50000	−	4.33013i	0.464238	−	0.804084i	−0.534928	−	0.844897i	$-0.679661\pi$
$29$	2.50000	−	4.33013i	0.464238	−	0.804084i	0.999167	+	0.0408130i	$0.0129948\pi$
$30$		0			0
$31$	8.00000			1.43684			0.718421	−	0.695608i	$-0.244865\pi$
$31$	8.00000			1.43684			0.718421	+	0.695608i	$0.244865\pi$
$32$		0			0
$33$	−1.21922	−	2.11176i	−0.212240	−	0.367610i
$34$		0			0
$35$	0.438447	+	0.759413i	0.0741111	+	0.128364i
$36$		0			0
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	0.904194	+	0.427121i	$0.140472\pi$
$38$		0			0
$39$	−0.780776	−	5.57586i	−0.125024	−	0.892852i
$40$		0			0
$41$	3.62311	−	6.27540i	0.565834	−	0.980053i	−0.431138	−	0.902286i	$-0.641888\pi$
$41$	3.62311	−	6.27540i	0.565834	−	0.980053i	0.996972	−	0.0777671i	$-0.0247790\pi$
$42$		0			0
$43$	−1.21922	−	2.11176i	−0.185930	−	0.322040i	0.757960	−	0.652301i	$-0.226196\pi$
$43$	−1.21922	−	2.11176i	−0.185930	−	0.322040i	−0.943889	+	0.330262i	$0.892863\pi$
$44$		0			0
$45$	0.157671	+	0.273094i	0.0235042	+	0.0407104i
$46$		0			0
$47$	−4.00000			−0.583460			−0.291730	−	0.956501i	$-0.594231\pi$
$47$	−4.00000			−0.583460			−0.291730	+	0.956501i	$0.594231\pi$
$48$		0			0
$49$	2.28078	−	3.95042i	0.325825	−	0.564346i
$50$		0			0
$51$	−7.80776			−1.09331
$52$		0			0
$53$	8.56155			1.17602			0.588010	−	0.808854i	$-0.299912\pi$
$53$	8.56155			1.17602			0.588010	+	0.808854i	$0.299912\pi$
$54$		0			0
$55$	−0.438447	+	0.759413i	−0.0591202	+	0.102399i
$56$		0			0
$57$	−2.43845			−0.322980
$58$		0			0
$59$	0.780776	+	1.35234i	0.101648	+	0.176060i	0.912364	−	0.409380i	$-0.134255\pi$
$59$	0.780776	+	1.35234i	0.101648	+	0.176060i	−0.810716	+	0.585440i	$0.800922\pi$
$60$		0			0
$61$	−4.62311	−	8.00745i	−0.591928	−	1.02525i	−0.993973	−	0.109629i	$-0.965034\pi$
$61$	−4.62311	−	8.00745i	−0.591928	−	1.02525i	0.402045	−	0.915620i	$-0.368300\pi$
$62$		0			0
$63$	−0.438447	+	0.759413i	−0.0552392	+	0.0956770i
$64$		0			0
$65$	−1.59612	+	1.24573i	−0.197974	+	0.154514i
$66$		0			0
$67$	−6.78078	+	11.7446i	−0.828404	+	1.43484i	0.0708863	+	0.997484i	$0.477417\pi$
$67$	−6.78078	+	11.7446i	−0.828404	+	1.43484i	−0.899290	+	0.437353i	$0.855916\pi$
$68$		0			0
$69$	6.78078	+	11.7446i	0.816310	+	1.41389i
$70$		0			0
$71$	−2.34233	−	4.05703i	−0.277983	−	0.481481i	0.692900	−	0.721034i	$-0.256333\pi$
$71$	−2.34233	−	4.05703i	−0.277983	−	0.481481i	−0.970883	+	0.239552i	$0.922999\pi$
$72$		0			0
$73$	−13.6847			−1.60167			−0.800834	−	0.598886i	$-0.795610\pi$
$73$	−13.6847			−1.60167			−0.800834	+	0.598886i	$0.795610\pi$
$74$		0			0
$75$	3.65767	−	6.33527i	0.422351	−	0.731534i
$76$		0			0
$77$	−2.43845			−0.277887
$78$		0			0
$79$	4.00000			0.450035			0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000			0.450035			0.225018	+	0.974355i	$0.427756\pi$
$80$		0			0
$81$	3.50000	−	6.06218i	0.388889	−	0.673575i
$82$		0			0
$83$	14.2462			1.56372			0.781862	−	0.623451i	$-0.214270\pi$
$83$	14.2462			1.56372			0.781862	+	0.623451i	$0.214270\pi$
$84$		0			0
$85$	1.40388	+	2.43160i	0.152272	+	0.263744i
$86$		0			0
$87$	3.90388	+	6.76172i	0.418540	+	0.724933i
$88$		0			0
$89$	−1.34233	+	2.32498i	−0.142287	+	0.246448i	−0.928357	−	0.371689i	$-0.878779\pi$
$89$	−1.34233	+	2.32498i	−0.142287	+	0.246448i	0.786071	+	0.618137i	$0.212112\pi$
$90$		0			0
$91$	−5.21922	−	2.11176i	−0.547123	−	0.221372i
$92$		0			0
$93$	−6.24621	+	10.8188i	−0.647702	+	1.12185i
$94$		0			0
$95$	0.438447	+	0.759413i	0.0449837	+	0.0779141i
$96$		0			0
$97$	8.90388	+	15.4220i	0.904052	+	1.56586i	0.822184	+	0.569221i	$0.192755\pi$
$97$	8.90388	+	15.4220i	0.904052	+	1.56586i	0.0818678	+	0.996643i	$0.473911\pi$
$98$		0			0
$99$	−0.876894			−0.0881312
$100$		0			0
$101$	5.62311	−	9.73950i	0.559520	−	0.969117i	−0.438017	−	0.898967i	$-0.644319\pi$
$101$	5.62311	−	9.73950i	0.559520	−	0.969117i	0.997536	−	0.0701500i	$-0.0223478\pi$
$102$		0			0
$103$	2.24621			0.221326			0.110663	−	0.993858i	$-0.464703\pi$
$103$	2.24621			0.221326			0.110663	+	0.993858i	$0.464703\pi$
$104$		0			0
$105$	−1.36932			−0.133632
$106$		0			0
$107$	4.34233	−	7.52113i	0.419789	−	0.727096i	−0.576129	−	0.817359i	$-0.695437\pi$
$107$	4.34233	−	7.52113i	0.419789	−	0.727096i	0.995918	+	0.0902631i	$0.0287708\pi$
$108$		0			0
$109$	−8.24621			−0.789844			−0.394922	−	0.918715i	$-0.629228\pi$
$109$	−8.24621			−0.789844			−0.394922	+	0.918715i	$0.629228\pi$
$110$		0			0
$111$	0.780776	+	1.35234i	0.0741080	+	0.128359i
$112$		0			0
$113$	3.62311	+	6.27540i	0.340833	+	0.590340i	0.984588	−	0.174892i	$-0.0559576\pi$
$113$	3.62311	+	6.27540i	0.340833	+	0.590340i	−0.643755	+	0.765232i	$0.722624\pi$
$114$		0			0
$115$	2.43845	−	4.22351i	0.227386	−	0.393845i
$116$		0			0
$117$	−1.87689	−	0.759413i	−0.173519	−	0.0702077i
$118$		0			0
$119$	−3.90388	+	6.76172i	−0.357868	+	0.619846i
$120$		0			0
$121$	4.28078	+	7.41452i	0.389161	+	0.674047i
$122$		0			0
$123$	5.65767	+	9.79937i	0.510135	+	0.883580i
$124$		0			0
$125$	−5.43845			−0.486430
$126$		0			0
$127$	−3.90388	+	6.76172i	−0.346414	+	0.600006i	−0.985610	−	0.169038i	$-0.945934\pi$
$127$	−3.90388	+	6.76172i	−0.346414	+	0.600006i	0.639196	+	0.769044i	$0.279267\pi$
$128$		0			0
$129$	3.80776			0.335255
$130$		0			0
$131$	−1.75379			−0.153229			−0.0766146	−	0.997061i	$-0.524411\pi$
$131$	−1.75379			−0.153229			−0.0766146	+	0.997061i	$0.524411\pi$
$132$		0			0
$133$	−1.21922	+	2.11176i	−0.105720	+	0.183113i
$134$		0			0
$135$	−3.12311			−0.268794
$136$		0			0
$137$	−5.74621	−	9.95273i	−0.490932	−	0.850319i	0.509014	−	0.860759i	$-0.330010\pi$
$137$	−5.74621	−	9.95273i	−0.490932	−	0.850319i	−0.999946	+	0.0104394i	$0.996677\pi$
$138$		0			0
$139$	3.65767	+	6.33527i	0.310240	+	0.537351i	0.978414	−	0.206654i	$-0.0662574\pi$
$139$	3.65767	+	6.33527i	0.310240	+	0.537351i	−0.668175	+	0.744005i	$0.732924\pi$
$140$		0			0
$141$	3.12311	−	5.40938i	0.263013	−	0.455552i
$142$		0			0
$143$	−0.780776	−	5.57586i	−0.0652918	−	0.466277i
$144$		0			0
$145$	1.40388	−	2.43160i	0.116586	−	0.201933i
$146$		0			0
$147$	3.56155	+	6.16879i	0.293752	+	0.508793i
$148$		0			0
$149$	1.62311	+	2.81130i	0.132970	+	0.230311i	0.924820	−	0.380405i	$-0.124215\pi$
$149$	1.62311	+	2.81130i	0.132970	+	0.230311i	−0.791850	+	0.610715i	$0.790882\pi$
$150$		0			0
$151$	−20.4924			−1.66765			−0.833825	−	0.552029i	$-0.813854\pi$
$151$	−20.4924			−1.66765			−0.833825	+	0.552029i	$0.813854\pi$
$152$		0			0
$153$	−1.40388	+	2.43160i	−0.113497	+	0.196583i
$154$		0			0
$155$	4.49242			0.360840
$156$		0			0
$157$	2.80776			0.224084			0.112042	−	0.993703i	$-0.464261\pi$
$157$	2.80776			0.224084			0.112042	+	0.993703i	$0.464261\pi$
$158$		0			0
$159$	−6.68466	+	11.5782i	−0.530128	+	0.918208i
$160$		0			0
$161$	13.5616			1.06880
$162$		0			0
$163$	−11.4654	−	19.8587i	−0.898042	−	1.55545i	−0.829994	−	0.557773i	$-0.811656\pi$
$163$	−11.4654	−	19.8587i	−0.898042	−	1.55545i	−0.0680484	−	0.997682i	$-0.521677\pi$
$164$		0			0
$165$	−0.684658	−	1.18586i	−0.0533006	−	0.0923193i
$166$		0			0
$167$	−4.78078	+	8.28055i	−0.369948	+	0.640768i	−0.989557	−	0.144142i	$-0.953958\pi$
$167$	−4.78078	+	8.28055i	−0.369948	+	0.640768i	0.619609	+	0.784910i	$0.287291\pi$
$168$		0			0
$169$	3.15767	−	12.6107i	0.242898	−	0.970052i
$170$		0			0
$171$	−0.438447	+	0.759413i	−0.0335289	+	0.0580737i
$172$		0			0
$173$	−6.46543	−	11.1985i	−0.491558	−	0.851403i	0.508395	−	0.861124i	$-0.330239\pi$
$173$	−6.46543	−	11.1985i	−0.491558	−	0.851403i	−0.999953	+	0.00972081i	$0.996906\pi$
$174$		0			0
$175$	−3.65767	−	6.33527i	−0.276494	−	0.478902i
$176$		0			0
$177$	−2.43845			−0.183285
$178$		0			0
$179$	8.34233	−	14.4493i	0.623535	−	1.07999i	−0.365287	−	0.930895i	$-0.619029\pi$
$179$	8.34233	−	14.4493i	0.623535	−	1.07999i	0.988822	−	0.149099i	$-0.0476374\pi$
$180$		0			0
$181$	10.8078			0.803335			0.401667	−	0.915786i	$-0.368431\pi$
$181$	10.8078			0.803335			0.401667	+	0.915786i	$0.368431\pi$
$182$		0			0
$183$	14.4384			1.06732
$184$		0			0
$185$	0.280776	−	0.486319i	0.0206431	−	0.0357549i
$186$		0			0
$187$	−7.80776			−0.570960
$188$		0			0
$189$	−4.34233	−	7.52113i	−0.315858	−	0.547082i
$190$		0			0
$191$	−8.34233	−	14.4493i	−0.603630	−	1.04552i	−0.992266	−	0.124126i	$-0.960387\pi$
$191$	−8.34233	−	14.4493i	−0.603630	−	1.04552i	0.388637	−	0.921391i	$-0.372946\pi$
$192$		0			0
$193$	−1.50000	+	2.59808i	−0.107972	+	0.187014i	−0.914949	−	0.403570i	$-0.867769\pi$
$193$	−1.50000	+	2.59808i	−0.107972	+	0.187014i	0.806976	+	0.590584i	$0.201102\pi$
$194$		0			0
$195$	−0.438447	−	3.13114i	−0.0313979	−	0.224226i
$196$		0			0
$197$	−7.34233	+	12.7173i	−0.523119	+	0.906069i	0.476519	+	0.879164i	$0.341898\pi$
$197$	−7.34233	+	12.7173i	−0.523119	+	0.906069i	−0.999638	+	0.0269049i	$0.991435\pi$
$198$		0			0
$199$	6.78078	+	11.7446i	0.480676	+	0.832556i	0.999754	−	0.0221709i	$-0.00705781\pi$
$199$	6.78078	+	11.7446i	0.480676	+	0.832556i	−0.519078	+	0.854727i	$0.673724\pi$
$200$		0			0
$201$	−10.5885	−	18.3399i	−0.746858	−	1.29360i
$202$		0			0
$203$	7.80776			0.547998
$204$		0			0
$205$	2.03457	−	3.52397i	0.142100	−	0.246125i
$206$		0			0
$207$	4.87689			0.338968
$208$		0			0
$209$	−2.43845			−0.168671
$210$		0			0
$211$	12.3423	−	21.3775i	0.849681	−	1.47169i	−0.0318122	−	0.999494i	$-0.510128\pi$
$211$	12.3423	−	21.3775i	0.849681	−	1.47169i	0.881493	−	0.472197i	$-0.156539\pi$
$212$		0			0
$213$	7.31534			0.501239
$214$		0			0
$215$	−0.684658	−	1.18586i	−0.0466933	−	0.0808752i
$216$		0			0
$217$	6.24621	+	10.8188i	0.424020	+	0.734425i
$218$		0			0
$219$	10.6847	−	18.5064i	0.722002	−	1.25054i
$220$		0			0
$221$	−16.7116	−	6.76172i	−1.12415	−	0.454843i
$222$		0			0
$223$	4.34233	−	7.52113i	0.290784	−	0.503652i	−0.683211	−	0.730221i	$-0.739417\pi$
$223$	4.34233	−	7.52113i	0.290784	−	0.503652i	0.973995	+	0.226568i	$0.0727506\pi$
$224$		0			0
$225$	−1.31534	−	2.27824i	−0.0876894	−	0.151883i
$226$		0			0
$227$	15.0270	+	26.0275i	0.997376	+	1.72751i	0.561382	+	0.827557i	$0.310270\pi$
$227$	15.0270	+	26.0275i	0.997376	+	1.72751i	0.435994	+	0.899950i	$0.356397\pi$
$228$		0			0
$229$	12.2462			0.809252			0.404626	−	0.914482i	$-0.367402\pi$
$229$	12.2462			0.809252			0.404626	+	0.914482i	$0.367402\pi$
$230$		0			0
$231$	1.90388	−	3.29762i	0.125266	−	0.216967i
$232$		0			0
$233$	−12.2462			−0.802276			−0.401138	−	0.916018i	$-0.631385\pi$
$233$	−12.2462			−0.802276			−0.401138	+	0.916018i	$0.631385\pi$
$234$		0			0
$235$	−2.24621			−0.146527
$236$		0			0
$237$	−3.12311	+	5.40938i	−0.202868	+	0.351377i
$238$		0			0
$239$	−18.2462			−1.18025			−0.590125	−	0.807312i	$-0.700921\pi$
$239$	−18.2462			−1.18025			−0.590125	+	0.807312i	$0.700921\pi$
$240$		0			0
$241$	−3.74621	−	6.48863i	−0.241315	−	0.417969i	0.719774	−	0.694208i	$-0.244245\pi$
$241$	−3.74621	−	6.48863i	−0.241315	−	0.417969i	−0.961089	+	0.276239i	$0.910912\pi$
$242$		0			0
$243$	−2.87689	−	4.98293i	−0.184553	−	0.319655i
$244$		0			0
$245$	1.28078	−	2.21837i	0.0818258	−	0.141726i
$246$		0			0
$247$	−5.21922	−	2.11176i	−0.332091	−	0.134368i
$248$		0			0
$249$	−11.1231	+	19.2658i	−0.704898	+	1.22092i
$250$		0			0
$251$	0.534565	+	0.925894i	0.0337415	+	0.0584419i	0.882403	−	0.470494i	$-0.155924\pi$
$251$	0.534565	+	0.925894i	0.0337415	+	0.0584419i	−0.848662	+	0.528936i	$0.822591\pi$
$252$		0			0
$253$	6.78078	+	11.7446i	0.426304	+	0.738380i
$254$		0			0
$255$	−4.38447			−0.274566
$256$		0			0
$257$	−2.62311	+	4.54335i	−0.163625	+	0.283407i	−0.936166	−	0.351558i	$-0.885652\pi$
$257$	−2.62311	+	4.54335i	−0.163625	+	0.283407i	0.772541	+	0.634965i	$0.218985\pi$
$258$		0			0
$259$	1.56155			0.0970302
$260$		0			0
$261$	2.80776			0.173796
$262$		0			0
$263$	−5.90388	+	10.2258i	−0.364049	+	0.630551i	−0.988623	−	0.150414i	$-0.951939\pi$
$263$	−5.90388	+	10.2258i	−0.364049	+	0.630551i	0.624574	+	0.780966i	$0.285273\pi$
$264$		0			0
$265$	4.80776			0.295339
$266$		0			0
$267$	−2.09612	−	3.63058i	−0.128280	−	0.222188i
$268$		0			0
$269$	2.90388	+	5.02967i	0.177053	+	0.306664i	0.940870	−	0.338768i	$-0.110010\pi$
$269$	2.90388	+	5.02967i	0.177053	+	0.306664i	−0.763817	+	0.645433i	$0.776677\pi$
$270$		0			0
$271$	−4.78078	+	8.28055i	−0.290411	+	0.503007i	−0.973907	−	0.226947i	$-0.927126\pi$
$271$	−4.78078	+	8.28055i	−0.290411	+	0.503007i	0.683496	+	0.729955i	$0.260459\pi$
$272$		0			0
$273$	6.93087	−	5.40938i	0.419475	−	0.327390i
$274$		0			0
$275$	3.65767	−	6.33527i	0.220566	−	0.382031i
$276$		0			0
$277$	−5.50000	−	9.52628i	−0.330463	−	0.572379i	0.652140	−	0.758099i	$-0.273872\pi$
$277$	−5.50000	−	9.52628i	−0.330463	−	0.572379i	−0.982603	+	0.185720i	$0.940538\pi$
$278$		0			0
$279$	2.24621	+	3.89055i	0.134477	+	0.232921i
$280$		0			0
$281$	2.31534			0.138122			0.0690608	−	0.997612i	$-0.478000\pi$
$281$	2.31534			0.138122			0.0690608	+	0.997612i	$0.478000\pi$
$282$		0			0
$283$	−12.7808	+	22.1370i	−0.759738	+	1.31591i	0.183246	+	0.983067i	$0.441340\pi$
$283$	−12.7808	+	22.1370i	−0.759738	+	1.31591i	−0.942984	+	0.332838i	$0.891994\pi$
$284$		0			0
$285$	−1.36932			−0.0811113
$286$		0			0
$287$	11.3153			0.667923
$288$		0			0
$289$	−4.00000	+	6.92820i	−0.235294	+	0.407541i
$290$		0			0
$291$	−27.8078			−1.63012
$292$		0			0
$293$	10.7462	+	18.6130i	0.627800	+	1.08738i	0.987992	+	0.154504i	$0.0493779\pi$
$293$	10.7462	+	18.6130i	0.627800	+	1.08738i	−0.360192	+	0.932878i	$0.617289\pi$
$294$		0			0
$295$	0.438447	+	0.759413i	0.0255274	+	0.0442147i
$296$		0			0
$297$	4.34233	−	7.52113i	0.251967	−	0.436421i
$298$		0			0
$299$	4.34233	+	31.0104i	0.251123	+	1.79338i
$300$		0			0
$301$	1.90388	−	3.29762i	0.109738	−	0.190072i
$302$		0			0
$303$	8.78078	+	15.2088i	0.504442	+	0.873720i
$304$		0			0
$305$	−2.59612	−	4.49661i	−0.148653	−	0.257475i
$306$		0			0
$307$	9.75379			0.556678			0.278339	−	0.960483i	$-0.410216\pi$
$307$	9.75379			0.556678			0.278339	+	0.960483i	$0.410216\pi$
$308$		0			0
$309$	−1.75379	+	3.03765i	−0.0997696	+	0.172806i
$310$		0			0
$311$	−2.24621			−0.127371			−0.0636855	−	0.997970i	$-0.520285\pi$
$311$	−2.24621			−0.127371			−0.0636855	+	0.997970i	$0.520285\pi$
$312$		0			0
$313$	−15.7538			−0.890457			−0.445228	−	0.895417i	$-0.646878\pi$
$313$	−15.7538			−0.890457			−0.445228	+	0.895417i	$0.646878\pi$
$314$		0			0
$315$	−0.246211	+	0.426450i	−0.0138724	+	0.0240278i
$316$		0			0
$317$	20.5616			1.15485			0.577426	−	0.816443i	$-0.304057\pi$
$317$	20.5616			1.15485			0.577426	+	0.816443i	$0.304057\pi$
$318$		0			0
$319$	3.90388	+	6.76172i	0.218575	+	0.378584i
$320$		0			0
$321$	6.78078	+	11.7446i	0.378466	+	0.655522i
$322$		0			0
$323$	−3.90388	+	6.76172i	−0.217218	+	0.376232i
$324$		0			0
$325$	13.3153	−	10.3923i	0.738602	−	0.576461i
$326$		0			0
$327$	6.43845	−	11.1517i	0.356047	−	0.616691i
$328$		0			0
$329$	−3.12311	−	5.40938i	−0.172182	−	0.298229i
$330$		0			0
$331$	−3.46543	−	6.00231i	−0.190478	−	0.329917i	0.754931	−	0.655804i	$-0.227670\pi$
$331$	−3.46543	−	6.00231i	−0.190478	−	0.329917i	−0.945409	+	0.325887i	$0.894337\pi$
$332$		0			0
$333$	0.561553			0.0307729
$334$		0			0
$335$	−3.80776	+	6.59524i	−0.208040	+	0.360336i
$336$		0			0
$337$	20.5616			1.12006			0.560030	−	0.828473i	$-0.310790\pi$
$337$	20.5616			1.12006			0.560030	+	0.828473i	$0.310790\pi$
$338$		0			0
$339$	−11.3153			−0.614565
$340$		0			0
$341$	−6.24621	+	10.8188i	−0.338251	+	0.585868i
$342$		0			0
$343$	18.0540			0.974823
$344$		0			0
$345$	3.80776	+	6.59524i	0.205003	+	0.355076i
$346$		0			0
$347$	1.02699	+	1.77879i	0.0551316	+	0.0954907i	0.892274	−	0.451494i	$-0.149109\pi$
$347$	1.02699	+	1.77879i	0.0551316	+	0.0954907i	−0.837142	+	0.546985i	$0.815776\pi$
$348$		0			0
$349$	−8.21922	+	14.2361i	−0.439965	+	0.762042i	−0.997686	−	0.0679866i	$-0.978342\pi$
$349$	−8.21922	+	14.2361i	−0.439965	+	0.762042i	0.557721	+	0.830028i	$0.311676\pi$
$350$		0			0
$351$	15.8078	−	12.3376i	0.843756	−	0.658531i
$352$		0			0
$353$	4.50000	−	7.79423i	0.239511	−	0.414845i	−0.721063	−	0.692869i	$-0.756346\pi$
$353$	4.50000	−	7.79423i	0.239511	−	0.414845i	0.960574	+	0.278024i	$0.0896796\pi$
$354$		0			0
$355$	−1.31534	−	2.27824i	−0.0698111	−	0.120916i
$356$		0			0
$357$	−6.09612	−	10.5588i	−0.322641	−	0.558830i
$358$		0			0
$359$	−28.4924			−1.50377			−0.751886	−	0.659293i	$-0.770856\pi$
$359$	−28.4924			−1.50377			−0.751886	+	0.659293i	$0.770856\pi$
$360$		0			0
$361$	8.28078	−	14.3427i	0.435830	−	0.754880i
$362$		0			0
$363$	−13.3693			−0.701707
$364$		0			0
$365$	−7.68466			−0.402233
$366$		0			0
$367$	6.58854	−	11.4117i	0.343919	−	0.595685i	−0.641238	−	0.767342i	$-0.721579\pi$
$367$	6.58854	−	11.4117i	0.343919	−	0.595685i	0.985157	+	0.171657i	$0.0549121\pi$
$368$		0			0
$369$	4.06913			0.211830
$370$		0			0
$371$	6.68466	+	11.5782i	0.347050	+	0.601109i
$372$		0			0
$373$	−2.62311	−	4.54335i	−0.135819	−	0.235246i	0.790091	−	0.612990i	$-0.210033\pi$
$373$	−2.62311	−	4.54335i	−0.135819	−	0.235246i	−0.925910	+	0.377744i	$0.876700\pi$
$374$		0			0
$375$	4.24621	−	7.35465i	0.219273	−	0.379793i
$376$		0			0
$377$	2.50000	+	17.8536i	0.128757	+	0.919506i
$378$		0			0
$379$	1.46543	−	2.53821i	0.0752743	−	0.130379i	−0.825931	−	0.563771i	$-0.809350\pi$
$379$	1.46543	−	2.53821i	0.0752743	−	0.130379i	0.901206	+	0.433392i	$0.142683\pi$
$380$		0			0
$381$	−6.09612	−	10.5588i	−0.312314	−	0.540943i
$382$		0			0
$383$	−14.5885	−	25.2681i	−0.745440	−	1.29114i	−0.949989	−	0.312283i	$-0.898906\pi$
$383$	−14.5885	−	25.2681i	−0.745440	−	1.29114i	0.204550	−	0.978856i	$-0.434427\pi$
$384$		0			0
$385$	−1.36932			−0.0697869
$386$		0			0
$387$	0.684658	−	1.18586i	0.0348031	−	0.0602808i
$388$		0			0
$389$	−29.6847			−1.50507			−0.752536	−	0.658551i	$-0.771170\pi$
$389$	−29.6847			−1.50507			−0.752536	+	0.658551i	$0.771170\pi$
$390$		0			0
$391$	43.4233			2.19601
$392$		0			0
$393$	1.36932	−	2.37173i	0.0690729	−	0.119638i
$394$		0			0
$395$	2.24621			0.113019
$396$		0			0
$397$	4.65767	+	8.06732i	0.233762	+	0.404887i	0.958912	−	0.283703i	$-0.0915631\pi$
$397$	4.65767	+	8.06732i	0.233762	+	0.404887i	−0.725150	+	0.688591i	$0.758230\pi$
$398$		0			0
$399$	−1.90388	−	3.29762i	−0.0953133	−	0.165088i
$400$		0			0
$401$	−11.7462	+	20.3450i	−0.586578	+	1.01598i	0.408099	+	0.912938i	$0.366192\pi$
$401$	−11.7462	+	20.3450i	−0.586578	+	1.01598i	−0.994677	+	0.103045i	$0.967141\pi$
$402$		0			0
$403$	−22.7386	+	17.7470i	−1.13269	+	0.884039i
$404$		0			0
$405$	1.96543	−	3.40423i	0.0976632	−	0.169158i
$406$		0			0
$407$	0.780776	+	1.35234i	0.0387016	+	0.0670332i
$408$		0			0
$409$	7.62311	+	13.2036i	0.376938	+	0.652876i	0.990615	−	0.136681i	$-0.0436435\pi$
$409$	7.62311	+	13.2036i	0.376938	+	0.652876i	−0.613677	+	0.789557i	$0.710310\pi$
$410$		0			0
$411$	17.9460			0.885212
$412$		0			0
$413$	−1.21922	+	2.11176i	−0.0599941	+	0.103913i
$414$		0			0
$415$	8.00000			0.392705
$416$		0			0
$417$	−11.4233			−0.559401
$418$		0			0
$419$	7.46543	−	12.9305i	0.364710	−	0.631697i	−0.624019	−	0.781409i	$-0.714501\pi$
$419$	7.46543	−	12.9305i	0.364710	−	0.631697i	0.988730	+	0.149712i	$0.0478347\pi$
$420$		0			0
$421$	−33.6847			−1.64169			−0.820845	−	0.571151i	$-0.806497\pi$
$421$	−33.6847			−1.64169			−0.820845	+	0.571151i	$0.806497\pi$
$422$		0			0
$423$	−1.12311	−	1.94528i	−0.0546073	−	0.0945826i
$424$		0			0
$425$	−11.7116	−	20.2852i	−0.568098	−	0.983975i
$426$		0			0
$427$	7.21922	−	12.5041i	0.349363	−	0.605114i
$428$		0			0
$429$	8.15009	+	3.29762i	0.393490	+	0.159211i
$430$		0			0
$431$	15.4654	−	26.7869i	0.744944	−	1.29028i	−0.205277	−	0.978704i	$-0.565810\pi$
$431$	15.4654	−	26.7869i	0.744944	−	1.29028i	0.950221	−	0.311577i	$-0.100857\pi$
$432$		0			0
$433$	−15.7462	−	27.2732i	−0.756715	−	1.31067i	−0.944517	−	0.328461i	$-0.893470\pi$
$433$	−15.7462	−	27.2732i	−0.756715	−	1.31067i	0.187803	−	0.982207i	$-0.439863\pi$
$434$		0			0
$435$	2.19224	+	3.79706i	0.105110	+	0.182055i
$436$		0			0
$437$	13.5616			0.648737
$438$		0			0
$439$	−4.53457	+	7.85410i	−0.216423	+	0.374856i	−0.953712	−	0.300722i	$-0.902772\pi$
$439$	−4.53457	+	7.85410i	−0.216423	+	0.374856i	0.737289	+	0.675578i	$0.236106\pi$
$440$		0			0
$441$	2.56155			0.121979
$442$		0			0
$443$	−38.2462			−1.81713			−0.908566	−	0.417741i	$-0.862822\pi$
$443$	−38.2462			−1.81713			−0.908566	+	0.417741i	$0.862822\pi$
$444$		0			0
$445$	−0.753789	+	1.30560i	−0.0357330	+	0.0618914i
$446$		0			0
$447$	−5.06913			−0.239762
$448$		0			0
$449$	12.0270	+	20.8314i	0.567589	+	0.983092i	0.996804	+	0.0798900i	$0.0254569\pi$
$449$	12.0270	+	20.8314i	0.567589	+	0.983092i	−0.429215	+	0.903202i	$0.641210\pi$
$450$		0			0
$451$	5.65767	+	9.79937i	0.266409	+	0.461434i
$452$		0			0
$453$	16.0000	−	27.7128i	0.751746	−	1.30206i
$454$		0			0
$455$	−2.93087	−	1.18586i	−0.137401	−	0.0555941i
$456$		0			0
$457$	4.50000	−	7.79423i	0.210501	−	0.364599i	−0.741370	−	0.671096i	$-0.765824\pi$
$457$	4.50000	−	7.79423i	0.210501	−	0.364599i	0.951871	+	0.306497i	$0.0991571\pi$
$458$		0			0
$459$	−13.9039	−	24.0822i	−0.648978	−	1.12406i
$460$		0			0
$461$	−11.7462	−	20.3450i	−0.547076	−	0.947563i	−0.998473	−	0.0552398i	$-0.982408\pi$
$461$	−11.7462	−	20.3450i	−0.547076	−	0.947563i	0.451398	−	0.892323i	$-0.350926\pi$
$462$		0			0
$463$	32.9848			1.53294			0.766468	−	0.642283i	$-0.222012\pi$
$463$	32.9848			1.53294			0.766468	+	0.642283i	$0.222012\pi$
$464$		0			0
$465$	−3.50758	+	6.07530i	−0.162660	+	0.281735i
$466$		0			0
$467$	−26.2462			−1.21453			−0.607265	−	0.794499i	$-0.707733\pi$
$467$	−26.2462			−1.21453			−0.607265	+	0.794499i	$0.707733\pi$
$468$		0			0
$469$	−21.1771			−0.977867
$470$		0			0
$471$	−2.19224	+	3.79706i	−0.101013	+	0.174959i
$472$		0			0
$473$	3.80776			0.175081
$474$		0			0
$475$	−3.65767	−	6.33527i	−0.167825	−	0.290682i
$476$		0			0
$477$	2.40388	+	4.16365i	0.110066	+	0.190640i
$478$		0			0
$479$	−10.1501	+	17.5805i	−0.463770	+	0.803273i	−0.999145	−	0.0413417i	$-0.986837\pi$
$479$	−10.1501	+	17.5805i	−0.463770	+	0.803273i	0.535375	+	0.844614i	$0.320170\pi$
$480$		0			0
$481$	0.500000	+	3.57071i	0.0227980	+	0.162811i
$482$		0			0
$483$	−10.5885	+	18.3399i	−0.481795	+	0.834494i
$484$		0			0
$485$	5.00000	+	8.66025i	0.227038	+	0.393242i
$486$		0			0
$487$	−17.2192	−	29.8246i	−0.780278	−	1.35148i	−0.931780	−	0.363023i	$-0.881744\pi$
$487$	−17.2192	−	29.8246i	−0.780278	−	1.35148i	0.151503	−	0.988457i	$-0.451589\pi$
$488$		0			0
$489$	35.8078			1.61928
$490$		0			0
$491$	−1.02699	+	1.77879i	−0.0463473	+	0.0802759i	−0.888268	−	0.459325i	$-0.848091\pi$
$491$	−1.02699	+	1.77879i	−0.0463473	+	0.0802759i	0.841921	+	0.539601i	$0.181425\pi$
$492$		0			0
$493$	25.0000			1.12594
$494$		0			0
$495$	−0.492423			−0.0221327
$496$		0			0
$497$	3.65767	−	6.33527i	0.164069	−	0.284176i
$498$		0			0
$499$	16.4924			0.738302			0.369151	−	0.929369i	$-0.379648\pi$
$499$	16.4924			0.738302			0.369151	+	0.929369i	$0.379648\pi$
$500$		0			0
$501$	−7.46543	−	12.9305i	−0.333531	−	0.577693i
$502$		0			0
$503$	−16.3423	−	28.3057i	−0.728668	−	1.26209i	−0.957446	−	0.288612i	$-0.906806\pi$
$503$	−16.3423	−	28.3057i	−0.728668	−	1.26209i	0.228778	−	0.973479i	$-0.426527\pi$
$504$		0			0
$505$	3.15767	−	5.46925i	0.140515	−	0.243378i
$506$		0			0
$507$	14.5885	+	14.1164i	0.647900	+	0.626930i
$508$		0			0
$509$	16.5000	−	28.5788i	0.731350	−	1.26673i	−0.224957	−	0.974369i	$-0.572224\pi$
$509$	16.5000	−	28.5788i	0.731350	−	1.26673i	0.956306	−	0.292366i	$-0.0944425\pi$
$510$		0			0
$511$	−10.6847	−	18.5064i	−0.472661	−	0.818674i
$512$		0			0
$513$	−4.34233	−	7.52113i	−0.191719	−	0.332066i
$514$		0			0
$515$	1.26137			0.0555824
$516$		0			0
$517$	3.12311	−	5.40938i	0.137354	−	0.237904i
$518$		0			0
$519$	20.1922			0.886341
$520$		0			0
$521$	9.05398			0.396662			0.198331	−	0.980135i	$-0.436448\pi$
$521$	9.05398			0.396662			0.198331	+	0.980135i	$0.436448\pi$
$522$		0			0
$523$	−6.15009	+	10.6523i	−0.268925	+	0.465791i	−0.968584	−	0.248685i	$-0.920002\pi$
$523$	−6.15009	+	10.6523i	−0.268925	+	0.465791i	0.699660	+	0.714476i	$0.253335\pi$
$524$		0			0
$525$	11.4233			0.498553
$526$		0			0
$527$	20.0000	+	34.6410i	0.871214	+	1.50899i
$528$		0			0
$529$	−26.2116	−	45.3999i	−1.13964	−	1.97391i
$530$		0			0
$531$	−0.438447	+	0.759413i	−0.0190270	+	0.0329557i
$532$		0			0
$533$	3.62311	+	25.8741i	0.156934	+	1.12073i
$534$		0			0
$535$	2.43845	−	4.22351i	0.105423	−	0.182598i
$536$		0			0
$537$	13.0270	+	22.5634i	0.562156	+	0.973683i
$538$		0			0
$539$	3.56155	+	6.16879i	0.153407	+	0.265709i
$540$		0			0
$541$	−5.68466			−0.244403			−0.122201	−	0.992505i	$-0.538995\pi$
$541$	−5.68466			−0.244403			−0.122201	+	0.992505i	$0.538995\pi$
$542$		0			0
$543$	−8.43845	+	14.6158i	−0.362128	+	0.627225i
$544$		0			0
$545$	−4.63068			−0.198357
$546$		0			0
$547$	−16.4924			−0.705165			−0.352583	−	0.935781i	$-0.614696\pi$
$547$	−16.4924			−0.705165			−0.352583	+	0.935781i	$0.614696\pi$
$548$		0			0
$549$	2.59612	−	4.49661i	0.110800	−	0.191911i
$550$		0			0
$551$	7.80776			0.332622
$552$		0			0
$553$	3.12311	+	5.40938i	0.132808	+	0.230030i
$554$		0			0
$555$	0.438447	+	0.759413i	0.0186110	+	0.0322353i
$556$		0			0
$557$	−15.7462	+	27.2732i	−0.667188	+	1.15560i	0.311499	+	0.950247i	$0.399169\pi$
$557$	−15.7462	+	27.2732i	−0.667188	+	1.15560i	−0.978687	+	0.205358i	$0.934164\pi$
$558$		0			0
$559$	8.15009	+	3.29762i	0.344712	+	0.139474i
$560$		0			0
$561$	6.09612	−	10.5588i	0.257378	−	0.445792i
$562$		0			0
$563$	3.02699	+	5.24290i	0.127572	+	0.220962i	0.922736	−	0.385434i	$-0.125948\pi$
$563$	3.02699	+	5.24290i	0.127572	+	0.220962i	−0.795163	+	0.606396i	$0.792615\pi$
$564$		0			0
$565$	2.03457	+	3.52397i	0.0855948	+	0.148255i
$566$		0			0
$567$	10.9309			0.459053
$568$		0			0
$569$	−9.34233	+	16.1814i	−0.391651	+	0.678359i	−0.992667	−	0.120877i	$-0.961429\pi$
$569$	−9.34233	+	16.1814i	−0.391651	+	0.678359i	0.601017	+	0.799237i	$0.294763\pi$
$570$		0			0
$571$	8.49242			0.355397			0.177698	−	0.984085i	$-0.443135\pi$
$571$	8.49242			0.355397			0.177698	+	0.984085i	$0.443135\pi$
$572$		0			0
$573$	26.0540			1.08842
$574$		0			0
$575$	−20.3423	+	35.2339i	−0.848334	+	1.46936i
$576$		0			0
$577$	−27.4384			−1.14228			−0.571139	−	0.820854i	$-0.693498\pi$
$577$	−27.4384			−1.14228			−0.571139	+	0.820854i	$0.693498\pi$
$578$		0			0
$579$	−2.34233	−	4.05703i	−0.0973439	−	0.168605i
$580$		0			0
$581$	11.1231	+	19.2658i	0.461464	+	0.799279i
$582$		0			0
$583$	−6.68466	+	11.5782i	−0.276850	+	0.479519i
$584$		0			0
$585$	−1.05398	−	0.426450i	−0.0435765	−	0.0176316i
$586$		0			0
$587$	7.46543	−	12.9305i	0.308131	−	0.533699i	−0.669822	−	0.742522i	$-0.733630\pi$
$587$	7.46543	−	12.9305i	0.308131	−	0.533699i	0.977954	+	0.208822i	$0.0669630\pi$
$588$		0			0
$589$	6.24621	+	10.8188i	0.257371	+	0.445779i
$590$		0			0
$591$	−11.4654	−	19.8587i	−0.471625	−	0.816878i
$592$		0			0
$593$	−19.4384			−0.798241			−0.399121	−	0.916898i	$-0.630685\pi$
$593$	−19.4384			−0.798241			−0.399121	+	0.916898i	$0.630685\pi$
$594$		0			0
$595$	−2.19224	+	3.79706i	−0.0898729	+	0.155664i
$596$		0			0
$597$	−21.1771			−0.866720
$598$		0			0
$599$	−26.7386			−1.09251			−0.546255	−	0.837619i	$-0.683947\pi$
$599$	−26.7386			−1.09251			−0.546255	+	0.837619i	$0.683947\pi$
$600$		0			0
$601$	−13.9924	+	24.2356i	−0.570763	+	0.988590i	0.425725	+	0.904853i	$0.360019\pi$
$601$	−13.9924	+	24.2356i	−0.570763	+	0.988590i	−0.996488	+	0.0837376i	$0.973314\pi$
$602$		0			0
$603$	−7.61553			−0.310128
$604$		0			0
$605$	2.40388	+	4.16365i	0.0977317	+	0.169276i
$606$		0			0
$607$	9.65767	+	16.7276i	0.391993	+	0.678951i	0.992712	−	0.120508i	$-0.0384525\pi$
$607$	9.65767	+	16.7276i	0.391993	+	0.678951i	−0.600720	+	0.799460i	$0.705119\pi$
$608$		0			0
$609$	−6.09612	+	10.5588i	−0.247027	+	0.427864i
$610$		0			0
$611$	11.3693	−	8.87348i	0.459953	−	0.358983i
$612$		0			0
$613$	4.50000	−	7.79423i	0.181753	−	0.314806i	−0.760724	−	0.649075i	$-0.775156\pi$
$613$	4.50000	−	7.79423i	0.181753	−	0.314806i	0.942478	+	0.334269i	$0.108489\pi$
$614$		0			0
$615$	3.17708	+	5.50287i	0.128112	+	0.221897i
$616$		0			0
$617$	−12.6231	−	21.8639i	−0.508187	−	0.880206i	−0.999955	−	0.00947959i	$-0.996983\pi$
$617$	−12.6231	−	21.8639i	−0.508187	−	0.880206i	0.491768	−	0.870726i	$-0.336351\pi$
$618$		0			0
$619$	28.9848			1.16500			0.582500	−	0.812831i	$-0.302075\pi$
$619$	28.9848			1.16500			0.582500	+	0.812831i	$0.302075\pi$
$620$		0			0
$621$	−24.1501	+	41.8292i	−0.969110	+	1.67855i
$622$		0			0
$623$	−4.19224			−0.167958
$624$		0			0
$625$	20.3693			0.814773
$626$		0			0
$627$	1.90388	−	3.29762i	0.0760337	−	0.131694i
$628$		0			0
$629$	5.00000			0.199363
$630$		0			0
$631$	5.02699	+	8.70700i	0.200121	+	0.346620i	0.948567	−	0.316576i	$-0.102533\pi$
$631$	5.02699	+	8.70700i	0.200121	+	0.346620i	−0.748446	+	0.663196i	$0.769200\pi$
$632$		0			0
$633$	19.2732	+	33.3822i	0.766041	+	1.32682i
$634$		0			0
$635$	−2.19224	+	3.79706i	−0.0869962	+	0.150682i
$636$		0			0
$637$	2.28078	+	16.2880i	0.0903677	+	0.645354i
$638$		0			0
$639$	1.31534	−	2.27824i	0.0520341	−	0.0901257i
$640$		0			0
$641$	0.746211	+	1.29248i	0.0294736	+	0.0510497i	0.880386	−	0.474258i	$-0.157284\pi$
$641$	0.746211	+	1.29248i	0.0294736	+	0.0510497i	−0.850912	+	0.525308i	$0.823950\pi$
$642$		0			0
$643$	10.1501	+	17.5805i	0.400281	+	0.693306i	0.993760	−	0.111543i	$-0.0355793\pi$
$643$	10.1501	+	17.5805i	0.400281	+	0.693306i	−0.593479	+	0.804849i	$0.702246\pi$
$644$		0			0
$645$	2.13826			0.0841939
$646$		0			0
$647$	11.4654	−	19.8587i	0.450753	−	0.780727i	−0.547680	−	0.836688i	$-0.684489\pi$
$647$	11.4654	−	19.8587i	0.450753	−	0.780727i	0.998433	+	0.0559611i	$0.0178223\pi$
$648$		0			0
$649$	−2.43845			−0.0957174
$650$		0			0
$651$	−19.5076			−0.764562
$652$		0			0
$653$	12.2732	−	21.2578i	0.480287	−	0.831882i	−0.519457	−	0.854497i	$-0.673866\pi$
$653$	12.2732	−	21.2578i	0.480287	−	0.831882i	0.999744	+	0.0226145i	$0.00719904\pi$
$654$		0			0
$655$	−0.984845			−0.0384811
$656$		0			0
$657$	−3.84233	−	6.65511i	−0.149904	−	0.259641i
$658$		0			0
$659$	10.7808	+	18.6729i	0.419959	+	0.727391i	0.995935	−	0.0900759i	$-0.0287110\pi$
$659$	10.7808	+	18.6729i	0.419959	+	0.727391i	−0.575975	+	0.817467i	$0.695378\pi$
$660$		0			0
$661$	−2.86932	+	4.96980i	−0.111603	+	0.193303i	−0.916417	−	0.400225i	$-0.868932\pi$
$661$	−2.86932	+	4.96980i	−0.111603	+	0.193303i	0.804813	+	0.593528i	$0.202265\pi$
$662$		0			0
$663$	22.1922	−	17.3205i	0.861875	−	0.672673i
$664$		0			0
$665$	−0.684658	+	1.18586i	−0.0265499	+	0.0459858i
$666$		0			0
$667$	−21.7116	−	37.6057i	−0.840678	−	1.45610i
$668$		0			0
$669$	6.78078	+	11.7446i	0.262160	+	0.454074i
$670$		0			0
$671$	14.4384			0.557390
$672$		0			0
$673$	−8.62311	+	14.9357i	−0.332396	+	0.575727i	−0.982981	−	0.183706i	$-0.941190\pi$
$673$	−8.62311	+	14.9357i	−0.332396	+	0.575727i	0.650585	+	0.759434i	$0.274524\pi$
$674$		0			0
$675$	26.0540			1.00282
$676$		0			0
$677$	−28.7386			−1.10452			−0.552258	−	0.833673i	$-0.686234\pi$
$677$	−28.7386			−1.10452			−0.552258	+	0.833673i	$0.686234\pi$
$678$		0			0
$679$	−13.9039	+	24.0822i	−0.533582	+	0.924191i
$680$		0			0
$681$	−46.9309			−1.79839
$682$		0			0
$683$	3.65767	+	6.33527i	0.139957	+	0.242412i	0.927480	−	0.373873i	$-0.121970\pi$
$683$	3.65767	+	6.33527i	0.139957	+	0.242412i	−0.787523	+	0.616285i	$0.788637\pi$
$684$		0			0
$685$	−3.22680	−	5.58898i	−0.123290	−	0.213544i
$686$		0			0
$687$	−9.56155	+	16.5611i	−0.364796	+	0.631845i
$688$		0			0
$689$	−24.3348	+	18.9927i	−0.927080	+	0.723564i
$690$		0			0
$691$	−12.7808	+	22.1370i	−0.486204	+	0.842129i	−0.999874	−	0.0158581i	$-0.994952\pi$
$691$	−12.7808	+	22.1370i	−0.486204	+	0.842129i	0.513671	+	0.857987i	$0.328285\pi$
$692$		0			0
$693$	−0.684658	−	1.18586i	−0.0260080	−	0.0450472i
$694$		0			0
$695$	2.05398	+	3.55759i	0.0779117	+	0.134947i
$696$		0			0
$697$	36.2311			1.37235
$698$		0			0
$699$	9.56155	−	16.5611i	0.361651	−	0.626398i
$700$		0			0
$701$	32.7386			1.23652			0.618261	−	0.785973i	$-0.287838\pi$
$701$	32.7386			1.23652			0.618261	+	0.785973i	$0.287838\pi$
$702$		0			0
$703$	1.56155			0.0588951
$704$		0			0
$705$	1.75379	−	3.03765i	0.0660515	−	0.114405i
$706$		0			0
$707$	17.5616			0.660470
$708$		0			0
$709$	−16.8693	−	29.2185i	−0.633540	−	1.09732i	−0.986822	−	0.161807i	$-0.948268\pi$
$709$	−16.8693	−	29.2185i	−0.633540	−	1.09732i	0.353282	−	0.935517i	$-0.385066\pi$
$710$		0			0
$711$	1.12311	+	1.94528i	0.0421198	+	0.0729535i
$712$		0			0
$713$	34.7386	−	60.1691i	1.30097	−	2.25335i
$714$		0			0
$715$	−0.438447	−	3.13114i	−0.0163970	−	0.117098i
$716$		0			0
$717$	14.2462	−	24.6752i	0.532035	−	0.921511i
$718$		0			0
$719$	−21.4654	−	37.1792i	−0.800526	−	1.38655i	−0.919271	−	0.393626i	$-0.871220\pi$
$719$	−21.4654	−	37.1792i	−0.800526	−	1.38655i	0.118745	−	0.992925i	$-0.462113\pi$
$720$		0			0
$721$	1.75379	+	3.03765i	0.0653145	+	0.113128i
$722$		0			0
$723$	11.6998			0.435121
$724$		0			0
$725$	−11.7116	+	20.2852i	−0.434960	+	0.753372i
$726$		0			0
$727$	−6.73863			−0.249922			−0.124961	−	0.992162i	$-0.539881\pi$
$727$	−6.73863			−0.249922			−0.124961	+	0.992162i	$0.539881\pi$
$728$		0			0
$729$	29.9848			1.11055
$730$		0			0
$731$	6.09612	−	10.5588i	0.225473	−	0.390531i
$732$		0			0
$733$	−1.19224			−0.0440362			−0.0220181	−	0.999758i	$-0.507009\pi$
$733$	−1.19224			−0.0440362			−0.0220181	+	0.999758i	$0.507009\pi$
$734$		0			0
$735$	2.00000	+	3.46410i	0.0737711	+	0.127775i
$736$		0			0
$737$	−10.5885	−	18.3399i	−0.390034	−	0.675559i
$738$		0			0
$739$	23.4654	−	40.6433i	0.863190	−	1.49509i	−0.00564328	−	0.999984i	$-0.501796\pi$
$739$	23.4654	−	40.6433i	0.863190	−	1.49509i	0.868833	−	0.495105i	$-0.164870\pi$
$740$		0			0
$741$	6.93087	−	5.40938i	0.254612	−	0.198718i
$742$		0			0
$743$	−4.53457	+	7.85410i	−0.166357	+	0.288139i	−0.937136	−	0.348963i	$-0.886534\pi$
$743$	−4.53457	+	7.85410i	−0.166357	+	0.288139i	0.770779	+	0.637102i	$0.219867\pi$
$744$		0			0
$745$	0.911460	+	1.57869i	0.0333933	+	0.0578389i
$746$		0			0
$747$	4.00000	+	6.92820i	0.146352	+	0.253490i
$748$		0			0
$749$	13.5616			0.495528
$750$		0			0
$751$	−24.1501	+	41.8292i	−0.881249	+	1.52637i	−0.0312965	+	0.999510i	$0.509964\pi$
$751$	−24.1501	+	41.8292i	−0.881249	+	1.52637i	−0.849953	+	0.526859i	$0.823370\pi$
$752$		0			0
$753$	−1.66950			−0.0608401
$754$		0			0
$755$	−11.5076			−0.418804
$756$		0			0
$757$	8.27320	−	14.3296i	0.300695	−	0.520818i	−0.675599	−	0.737269i	$-0.736115\pi$
$757$	8.27320	−	14.3296i	0.300695	−	0.520818i	0.976293	+	0.216451i	$0.0694482\pi$
$758$		0			0
$759$	−21.1771			−0.768679
$760$		0			0
$761$	11.5346	+	19.9785i	0.418128	+	0.724218i	0.995751	−	0.0920850i	$-0.0293531\pi$
$761$	11.5346	+	19.9785i	0.418128	+	0.724218i	−0.577623	+	0.816303i	$0.696020\pi$
$762$		0			0
$763$	−6.43845	−	11.1517i	−0.233087	−	0.403719i
$764$		0			0
$765$	−0.788354	+	1.36547i	−0.0285030	+	0.0493686i
$766$		0			0
$767$	−5.21922	−	2.11176i	−0.188455	−	0.0762511i
$768$		0			0
$769$	−0.465435	+	0.806157i	−0.0167840	+	0.0290708i	−0.874295	−	0.485394i	$-0.838676\pi$
$769$	−0.465435	+	0.806157i	−0.0167840	+	0.0290708i	0.857511	+	0.514465i	$0.172009\pi$
$770$		0			0
$771$	−4.09612	−	7.09468i	−0.147518	−	0.255509i
$772$		0			0
$773$	−17.0961	−	29.6113i	−0.614905	−	1.06505i	−0.990401	−	0.138222i	$-0.955861\pi$
$773$	−17.0961	−	29.6113i	−0.614905	−	1.06505i	0.375497	−	0.926824i	$-0.377472\pi$
$774$		0			0
$775$	−37.4773			−1.34622
$776$		0			0
$777$	−1.21922	+	2.11176i	−0.0437394	+	0.0757589i
$778$		0			0
$779$	11.3153			0.405414
$780$		0			0
$781$	7.31534			0.261764
$782$		0			0
$783$	−13.9039	+	24.0822i	−0.496884	+	0.860629i
$784$		0			0
$785$	1.57671			0.0562751
$786$		0			0
$787$	−13.7116	−	23.7493i	−0.488767	−	0.846570i	0.511149	−	0.859492i	$-0.329220\pi$
$787$	−13.7116	−	23.7493i	−0.488767	−	0.846570i	−0.999917	+	0.0129221i	$0.995887\pi$
$788$		0			0
$789$	−9.21922	−	15.9682i	−0.328213	−	0.568482i
$790$		0			0
$791$	−5.65767	+	9.79937i	−0.201164	+	0.348426i
$792$		0			0
$793$	30.9039	+	12.5041i	1.09743	+	0.444032i
$794$		0			0
$795$	−3.75379	+	6.50175i	−0.133133	+	0.230593i
$796$		0			0
$797$	−6.46543	−	11.1985i	−0.229017	−	0.396670i	0.728500	−	0.685046i	$-0.240218\pi$
$797$	−6.46543	−	11.1985i	−0.229017	−	0.396670i	−0.957517	+	0.288376i	$0.906885\pi$
$798$		0			0
$799$	−10.0000	−	17.3205i	−0.353775	−	0.612756i
$800$		0			0
$801$	−1.50758			−0.0532676
$802$		0			0
$803$	10.6847	−	18.5064i	0.377053	−	0.653076i
$804$		0			0
$805$	7.61553			0.268412
$806$		0			0
$807$	−9.06913			−0.319249
$808$		0			0
$809$	11.6231	−	20.1318i	0.408647	−	0.707797i	−0.586092	−	0.810245i	$-0.699334\pi$
$809$	11.6231	−	20.1318i	0.408647	−	0.707797i	0.994738	+	0.102448i	$0.0326675\pi$
$810$		0			0
$811$	−8.00000			−0.280918			−0.140459	−	0.990086i	$-0.544858\pi$
$811$	−8.00000			−0.280918			−0.140459	+	0.990086i	$0.544858\pi$
$812$		0			0
$813$	−7.46543	−	12.9305i	−0.261824	−	0.453493i
$814$		0			0
$815$	−6.43845	−	11.1517i	−0.225529	−	0.390628i
$816$		0			0
$817$	1.90388	−	3.29762i	0.0666084	−	0.115369i
$818$		0			0
$819$	−0.438447	−	3.13114i	−0.0153206	−	0.109411i
$820$		0			0
$821$	6.90388	−	11.9579i	0.240947	−	0.417333i	−0.720037	−	0.693935i	$-0.755875\pi$
$821$	6.90388	−	11.9579i	0.240947	−	0.417333i	0.960984	+	0.276603i	$0.0892086\pi$
$822$		0			0
$823$	−0.588540	−	1.01938i	−0.0205152	−	0.0355334i	0.855586	−	0.517661i	$-0.173197\pi$
$823$	−0.588540	−	1.01938i	−0.0205152	−	0.0355334i	−0.876101	+	0.482128i	$0.839864\pi$
$824$		0			0
$825$	5.71165	+	9.89286i	0.198854	+	0.344425i
$826$		0			0
$827$	36.9848			1.28609			0.643045	−	0.765829i	$-0.277671\pi$
$827$	36.9848			1.28609			0.643045	+	0.765829i	$0.277671\pi$
$828$		0			0
$829$	−3.25379	+	5.63573i	−0.113009	+	0.195737i	−0.916982	−	0.398929i	$-0.869382\pi$
$829$	−3.25379	+	5.63573i	−0.113009	+	0.195737i	0.803973	+	0.594665i	$0.202715\pi$
$830$		0			0
$831$	17.1771			0.595866
$832$		0			0
$833$	22.8078			0.790242
$834$		0			0
$835$	−2.68466	+	4.64996i	−0.0929064	+	0.160919i
$836$		0			0
$837$	−44.4924			−1.53788
$838$		0			0
$839$	13.6577	+	23.6558i	0.471515	+	0.816688i	0.999469	−	0.0325849i	$-0.0103739\pi$
$839$	13.6577	+	23.6558i	0.471515	+	0.816688i	−0.527954	+	0.849273i	$0.677041\pi$
$840$		0			0
$841$	2.00000	+	3.46410i	0.0689655	+	0.119452i
$842$		0			0
$843$	−1.80776	+	3.13114i	−0.0622627	+	0.107842i
$844$		0			0
$845$	1.77320	−	7.08156i	0.0609999	−	0.243613i
$846$		0			0
$847$	−6.68466	+	11.5782i	−0.229688	+	0.397831i
$848$		0			0
$849$	−19.9579	−	34.5680i	−0.684952	−	1.18637i
$850$		0			0
$851$	−4.34233	−	7.52113i	−0.148853	−	0.257821i
$852$		0			0
$853$	−48.4233			−1.65798			−0.828991	−	0.559262i	$-0.811085\pi$
$853$	−48.4233			−1.65798			−0.828991	+	0.559262i	$0.811085\pi$
$854$		0			0
$855$	−0.246211	+	0.426450i	−0.00842025	+	0.0145843i
$856$		0			0
$857$	−14.9460			−0.510546			−0.255273	−	0.966869i	$-0.582165\pi$
$857$	−14.9460			−0.510546			−0.255273	+	0.966869i	$0.582165\pi$
$858$		0			0
$859$	22.2462			0.759031			0.379515	−	0.925185i	$-0.376091\pi$
$859$	22.2462			0.759031			0.379515	+	0.925185i	$0.376091\pi$
$860$		0			0
$861$	−8.83475	+	15.3022i	−0.301088	+	0.521499i
$862$		0			0
$863$	21.7538			0.740508			0.370254	−	0.928931i	$-0.379271\pi$
$863$	21.7538			0.740508			0.370254	+	0.928931i	$0.379271\pi$
$864$		0			0
$865$	−3.63068	−	6.28853i	−0.123447	−	0.213816i
$866$		0			0
$867$	−6.24621	−	10.8188i	−0.212132	−	0.367424i
$868$		0			0
$869$	−3.12311	+	5.40938i	−0.105944	+	0.183501i
$870$		0			0
$871$	−6.78078	−	48.4244i	−0.229758	−	1.64080i
$872$		0			0
$873$	−5.00000	+	8.66025i	−0.169224	+	0.293105i
$874$		0			0
$875$	−4.24621	−	7.35465i	−0.143548	−	0.248633i
$876$		0			0
$877$	19.8693	+	34.4147i	0.670939	+	1.16210i	0.977638	+	0.210294i	$0.0674422\pi$
$877$	19.8693	+	34.4147i	0.670939	+	1.16210i	−0.306699	+	0.951807i	$0.599224\pi$
$878$		0			0
$879$	−33.5616			−1.13200
$880$		0			0
$881$	7.62311	−	13.2036i	0.256829	−	0.444841i	−0.708562	−	0.705649i	$-0.750656\pi$
$881$	7.62311	−	13.2036i	0.256829	−	0.444841i	0.965391	+	0.260808i	$0.0839890\pi$
$882$		0			0
$883$	−20.0000			−0.673054			−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000			−0.673054			−0.336527	+	0.941674i	$0.609252\pi$
$884$		0			0
$885$	−1.36932			−0.0460291
$886$		0			0
$887$	10.3423	−	17.9134i	0.347261	−	0.601474i	−0.638501	−	0.769621i	$-0.720445\pi$
$887$	10.3423	−	17.9134i	0.347261	−	0.601474i	0.985762	+	0.168147i	$0.0537783\pi$
$888$		0			0
$889$	−12.1922			−0.408914
$890$		0			0
$891$	5.46543	+	9.46641i	0.183099	+	0.317137i
$892$		0			0
$893$	−3.12311	−	5.40938i	−0.104511	−	0.181018i
$894$		0			0
$895$	4.68466	−	8.11407i	0.156591	−	0.271223i
$896$		0			0
$897$	−45.3272	−	18.3399i	−1.51343	−	0.612351i
$898$		0			0
$899$	20.0000	−	34.6410i	0.667037	−	1.15534i
$900$		0			0
$901$	21.4039	+	37.0726i	0.713067	+	1.23507i
$902$		0			0
$903$	2.97301	+	5.14941i	0.0989357	+	0.171362i
$904$		0			0
$905$	6.06913			0.201745
$906$		0			0
$907$	−20.1501	+	34.9010i	−0.669073	+	1.15887i	0.309091	+	0.951033i	$0.399975\pi$
$907$	−20.1501	+	34.9010i	−0.669073	+	1.15887i	−0.978164	+	0.207836i	$0.933358\pi$
$908$		0			0
$909$	6.31534			0.209467
$910$		0			0
$911$	30.7386			1.01842			0.509208	−	0.860643i	$-0.329938\pi$
$911$	30.7386			1.01842			0.509208	+	0.860643i	$0.329938\pi$
$912$		0			0
$913$	−11.1231	+	19.2658i	−0.368121	+	0.637604i
$914$		0			0
$915$	8.10795			0.268041
$916$		0			0
$917$	−1.36932	−	2.37173i	−0.0452188	−	0.0783213i
$918$		0			0
$919$	29.2732	+	50.7027i	0.965634	+	1.67253i	0.707903	+	0.706310i	$0.249642\pi$
$919$	29.2732	+	50.7027i	0.965634	+	1.67253i	0.257731	+	0.966217i	$0.417025\pi$
$920$		0			0
$921$	−7.61553	+	13.1905i	−0.250940	+	0.434641i
$922$		0			0
$923$	15.6577	+	6.33527i	0.515379	+	0.208528i
$924$		0			0
$925$	−2.34233	+	4.05703i	−0.0770153	+	0.133394i
$926$		0			0
$927$	0.630683	+	1.09238i	0.0207144	+	0.0358783i
$928$		0			0
$929$	18.9924	+	32.8958i	0.623121	+	1.07928i	0.988901	+	0.148576i	$0.0474690\pi$
$929$	18.9924	+	32.8958i	0.623121	+	1.07928i	−0.365780	+	0.930701i	$0.619198\pi$
$930$		0			0
$931$	7.12311			0.233450
$932$		0			0
$933$	1.75379	−	3.03765i	0.0574165	−	0.0994482i
$934$		0			0
$935$	−4.38447			−0.143388
$936$		0			0
$937$	−13.6847			−0.447058			−0.223529	−	0.974697i	$-0.571758\pi$
$937$	−13.6847			−0.447058			−0.223529	+	0.974697i	$0.571758\pi$
$938$		0			0
$939$	12.3002	−	21.3045i	0.401401	−	0.695248i
$940$		0			0
$941$	14.0000			0.456387			0.228193	−	0.973616i	$-0.426718\pi$
$941$	14.0000			0.456387			0.228193	+	0.973616i	$0.426718\pi$
$942$		0			0
$943$	−31.4654	−	54.4997i	−1.02466	−	1.77476i
$944$		0			0
$945$	−2.43845	−	4.22351i	−0.0793227	−	0.137391i
$946$		0			0
$947$	7.71165	−	13.3570i	0.250595	−	0.434043i	−0.713095	−	0.701068i	$-0.752707\pi$
$947$	7.71165	−	13.3570i	0.250595	−	0.434043i	0.963690	+	0.267025i	$0.0860405\pi$
$948$		0			0
$949$	38.8963	−	30.3576i	1.26263	−	0.985450i
$950$		0			0
$951$	−16.0540	+	27.8063i	−0.520586	+	0.901681i
$952$		0			0
$953$	12.9039	+	22.3502i	0.417998	+	0.723993i	0.995738	−	0.0922274i	$-0.0293987\pi$
$953$	12.9039	+	22.3502i	0.417998	+	0.723993i	−0.577740	+	0.816221i	$0.696065\pi$
$954$		0			0
$955$	−4.68466	−	8.11407i	−0.151592	−	0.262565i
$956$		0			0
$957$	−12.1922			−0.394119
$958$		0			0
$959$	8.97301	−	15.5417i	0.289754	−	0.501868i
$960$		0			0
$961$	33.0000			1.06452
$962$		0			0
$963$	4.87689			0.157156
$964$		0			0
$965$	−0.842329	+	1.45896i	−0.0271155	+	0.0469655i
$966$		0			0
$967$	−5.75379			−0.185029			−0.0925147	−	0.995711i	$-0.529491\pi$
$967$	−5.75379			−0.185029			−0.0925147	+	0.995711i	$0.529491\pi$
$968$		0			0
$969$	−6.09612	−	10.5588i	−0.195836	−	0.339197i
$970$		0			0
$971$	9.65767	+	16.7276i	0.309929	+	0.536813i	0.978347	−	0.206973i	$-0.0663612\pi$
$971$	9.65767	+	16.7276i	0.309929	+	0.536813i	−0.668417	+	0.743787i	$0.733028\pi$
$972$		0			0
$973$	−5.71165	+	9.89286i	−0.183107	+	0.317151i
$974$		0			0
$975$	3.65767	+	26.1210i	0.117139	+	0.836541i
$976$		0			0
$977$	−0.623106	+	1.07925i	−0.0199349	+	0.0345283i	−0.875821	−	0.482636i	$-0.839679\pi$
$977$	−0.623106	+	1.07925i	−0.0199349	+	0.0345283i	0.855886	+	0.517165i	$0.173013\pi$
$978$		0			0
$979$	−2.09612	−	3.63058i	−0.0669922	−	0.116034i
$980$		0			0
$981$	−2.31534	−	4.01029i	−0.0739232	−	0.128039i
$982$		0			0
$983$	24.9848			0.796893			0.398446	−	0.917192i	$-0.369549\pi$
$983$	24.9848			0.796893			0.398446	+	0.917192i	$0.369549\pi$
$984$		0			0
$985$	−4.12311	+	7.14143i	−0.131373	+	0.227545i
$986$		0			0
$987$	9.75379			0.310467
$988$		0			0
$989$	−21.1771			−0.673392
$990$		0			0
$991$	1.84991	−	3.20413i	0.0587642	−	0.101783i	−0.835147	−	0.550027i	$-0.814617\pi$
$991$	1.84991	−	3.20413i	0.0587642	−	0.101783i	0.893911	+	0.448245i	$0.147951\pi$
$992$		0			0
$993$	10.8229			0.343455
$994$		0			0
$995$	3.80776	+	6.59524i	0.120714	+	0.209083i
$996$		0			0
$997$	21.6231	+	37.4523i	0.684811	+	1.18613i	0.973496	+	0.228703i	$0.0734484\pi$
$997$	21.6231	+	37.4523i	0.684811	+	1.18613i	−0.288686	+	0.957424i	$0.593218\pi$
$998$		0			0
$999$	−2.78078	+	4.81645i	−0.0879799	+	0.152386i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	208.2.i.e.113.1		4
3.2	odd	2		1872.2.t.s.1153.1		4
4.3	odd	2		104.2.i.b.9.2	✓	4
8.3	odd	2		832.2.i.o.321.1		4
8.5	even	2		832.2.i.l.321.2		4
12.11	even	2		936.2.t.f.217.1		4
13.3	even	3	inner	208.2.i.e.81.1		4
13.4	even	6		2704.2.a.r.1.2		2
13.6	odd	12		2704.2.f.l.337.3		4
13.7	odd	12		2704.2.f.l.337.4		4
13.9	even	3		2704.2.a.q.1.2		2
39.29	odd	6		1872.2.t.s.289.1		4
52.3	odd	6		104.2.i.b.81.2	yes	4
52.7	even	12		1352.2.f.d.337.2		4
52.11	even	12		1352.2.o.c.361.4		8
52.15	even	12		1352.2.o.c.361.3		8
52.19	even	12		1352.2.f.d.337.1		4
52.23	odd	6		1352.2.i.e.1329.2		4
52.31	even	4		1352.2.o.c.1161.3		8
52.35	odd	6		1352.2.a.f.1.1		2
52.43	odd	6		1352.2.a.h.1.1		2
52.47	even	4		1352.2.o.c.1161.4		8
52.51	odd	2		1352.2.i.e.529.2		4
104.3	odd	6		832.2.i.o.705.1		4
104.29	even	6		832.2.i.l.705.2		4
156.107	even	6		936.2.t.f.289.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.i.b.9.2	✓	4	4.3	odd	2
104.2.i.b.81.2	yes	4	52.3	odd	6
208.2.i.e.81.1		4	13.3	even	3	inner
208.2.i.e.113.1		4	1.1	even	1	trivial
832.2.i.l.321.2		4	8.5	even	2
832.2.i.l.705.2		4	104.29	even	6
832.2.i.o.321.1		4	8.3	odd	2
832.2.i.o.705.1		4	104.3	odd	6
936.2.t.f.217.1		4	12.11	even	2
936.2.t.f.289.1		4	156.107	even	6
1352.2.a.f.1.1		2	52.35	odd	6
1352.2.a.h.1.1		2	52.43	odd	6
1352.2.f.d.337.1		4	52.19	even	12
1352.2.f.d.337.2		4	52.7	even	12
1352.2.i.e.529.2		4	52.51	odd	2
1352.2.i.e.1329.2		4	52.23	odd	6
1352.2.o.c.361.3		8	52.15	even	12
1352.2.o.c.361.4		8	52.11	even	12
1352.2.o.c.1161.3		8	52.31	even	4
1352.2.o.c.1161.4		8	52.47	even	4
1872.2.t.s.289.1		4	39.29	odd	6
1872.2.t.s.1153.1		4	3.2	odd	2
2704.2.a.q.1.2		2	13.9	even	3
2704.2.a.r.1.2		2	13.4	even	6
2704.2.f.l.337.3		4	13.6	odd	12
2704.2.f.l.337.4		4	13.7	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	208.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.780776 + 1.35234i) q^{3} +0.561553 q^{5} +(0.780776 + 1.35234i) q^{7} +(0.280776 + 0.486319i) q^{9} +O(q^{10})\)	\(q+(-0.780776 + 1.35234i) q^{3} +0.561553 q^{5} +(0.780776 + 1.35234i) q^{7} +(0.280776 + 0.486319i) q^{9} +(-0.780776 + 1.35234i) q^{11} +(-2.84233 + 2.21837i) q^{13} +(-0.438447 + 0.759413i) q^{15} +(2.50000 + 4.33013i) q^{17} +(0.780776 + 1.35234i) q^{19} -2.43845 q^{21} +(4.34233 - 7.52113i) q^{23} -4.68466 q^{25} -5.56155 q^{27} +(2.50000 - 4.33013i) q^{29} +8.00000 q^{31} +(-1.21922 - 2.11176i) q^{33} +(0.438447 + 0.759413i) q^{35} +(0.500000 - 0.866025i) q^{37} +(-0.780776 - 5.57586i) q^{39} +(3.62311 - 6.27540i) q^{41} +(-1.21922 - 2.11176i) q^{43} +(0.157671 + 0.273094i) q^{45} -4.00000 q^{47} +(2.28078 - 3.95042i) q^{49} -7.80776 q^{51} +8.56155 q^{53} +(-0.438447 + 0.759413i) q^{55} -2.43845 q^{57} +(0.780776 + 1.35234i) q^{59} +(-4.62311 - 8.00745i) q^{61} +(-0.438447 + 0.759413i) q^{63} +(-1.59612 + 1.24573i) q^{65} +(-6.78078 + 11.7446i) q^{67} +(6.78078 + 11.7446i) q^{69} +(-2.34233 - 4.05703i) q^{71} -13.6847 q^{73} +(3.65767 - 6.33527i) q^{75} -2.43845 q^{77} +4.00000 q^{79} +(3.50000 - 6.06218i) q^{81} +14.2462 q^{83} +(1.40388 + 2.43160i) q^{85} +(3.90388 + 6.76172i) q^{87} +(-1.34233 + 2.32498i) q^{89} +(-5.21922 - 2.11176i) q^{91} +(-6.24621 + 10.8188i) q^{93} +(0.438447 + 0.759413i) q^{95} +(8.90388 + 15.4220i) q^{97} -0.876894 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{3} - 6 q^{5} - q^{7} - 3 q^{9}+O(q^{10}) \) 4 * q + q^3 - 6 * q^5 - q^7 - 3 * q^9	\( 4 q + q^{3} - 6 q^{5} - q^{7} - 3 q^{9} + q^{11} + q^{13} - 10 q^{15} + 10 q^{17} - q^{19} - 18 q^{21} + 5 q^{23} + 6 q^{25} - 14 q^{27} + 10 q^{29} + 32 q^{31} - 9 q^{33} + 10 q^{35} + 2 q^{37} + q^{39} - 2 q^{41} - 9 q^{43} + 13 q^{45} - 16 q^{47} + 5 q^{49} + 10 q^{51} + 26 q^{53} - 10 q^{55} - 18 q^{57} - q^{59} - 2 q^{61} - 10 q^{63} - 27 q^{65} - 23 q^{67} + 23 q^{69} + 3 q^{71} - 30 q^{73} + 27 q^{75} - 18 q^{77} + 16 q^{79} + 14 q^{81} + 24 q^{83} - 15 q^{85} - 5 q^{87} + 7 q^{89} - 25 q^{91} + 8 q^{93} + 10 q^{95} + 15 q^{97} - 20 q^{99}+O(q^{100}) \) 4 * q + q^3 - 6 * q^5 - q^7 - 3 * q^9 + q^11 + q^13 - 10 * q^15 + 10 * q^17 - q^19 - 18 * q^21 + 5 * q^23 + 6 * q^25 - 14 * q^27 + 10 * q^29 + 32 * q^31 - 9 * q^33 + 10 * q^35 + 2 * q^37 + q^39 - 2 * q^41 - 9 * q^43 + 13 * q^45 - 16 * q^47 + 5 * q^49 + 10 * q^51 + 26 * q^53 - 10 * q^55 - 18 * q^57 - q^59 - 2 * q^61 - 10 * q^63 - 27 * q^65 - 23 * q^67 + 23 * q^69 + 3 * q^71 - 30 * q^73 + 27 * q^75 - 18 * q^77 + 16 * q^79 + 14 * q^81 + 24 * q^83 - 15 * q^85 - 5 * q^87 + 7 * q^89 - 25 * q^91 + 8 * q^93 + 10 * q^95 + 15 * q^97 - 20 * q^99

Introduction

L-functions

Modular forms

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Database

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