LMFDB - Embedded newform 104.2.i.b.81.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [104,2,Mod(9,104)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(104, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("104.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 104 = 2^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	104.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.830444181021$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			81.2
Root			$-0.780776 - 1.35234i$ of defining polynomial
Character	$\chi$	$=$	104.81
Dual form			104.2.i.b.9.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.780776 + 1.35234i) q^{3} +0.561553 q^{5} +(-0.780776 + 1.35234i) q^{7} +(0.280776 - 0.486319i) q^{9} +O(q^{10})$	\(q+(0.780776 + 1.35234i) q^{3} +0.561553 q^{5} +(-0.780776 + 1.35234i) q^{7} +(0.280776 - 0.486319i) q^{9} +(0.780776 + 1.35234i) q^{11} +(-2.84233 - 2.21837i) q^{13} +(0.438447 + 0.759413i) q^{15} +(2.50000 - 4.33013i) q^{17} +(-0.780776 + 1.35234i) q^{19} -2.43845 q^{21} +(-4.34233 - 7.52113i) q^{23} -4.68466 q^{25} +5.56155 q^{27} +(2.50000 + 4.33013i) q^{29} -8.00000 q^{31} +(-1.21922 + 2.11176i) q^{33} +(-0.438447 + 0.759413i) q^{35} +(0.500000 + 0.866025i) q^{37} +(0.780776 - 5.57586i) q^{39} +(3.62311 + 6.27540i) q^{41} +(1.21922 - 2.11176i) q^{43} +(0.157671 - 0.273094i) q^{45} +4.00000 q^{47} +(2.28078 + 3.95042i) q^{49} +7.80776 q^{51} +8.56155 q^{53} +(0.438447 + 0.759413i) q^{55} -2.43845 q^{57} +(-0.780776 + 1.35234i) q^{59} +(-4.62311 + 8.00745i) q^{61} +(0.438447 + 0.759413i) q^{63} +(-1.59612 - 1.24573i) q^{65} +(6.78078 + 11.7446i) q^{67} +(6.78078 - 11.7446i) q^{69} +(2.34233 - 4.05703i) q^{71} -13.6847 q^{73} +(-3.65767 - 6.33527i) q^{75} -2.43845 q^{77} -4.00000 q^{79} +(3.50000 + 6.06218i) q^{81} -14.2462 q^{83} +(1.40388 - 2.43160i) q^{85} +(-3.90388 + 6.76172i) q^{87} +(-1.34233 - 2.32498i) q^{89} +(5.21922 - 2.11176i) q^{91} +(-6.24621 - 10.8188i) q^{93} +(-0.438447 + 0.759413i) q^{95} +(8.90388 - 15.4220i) q^{97} +0.876894 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/104\mathbb{Z}\right)^\times$.

$n$	$41$	$53$	$79$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	0.780776	+	1.35234i	0.450781	+	0.780776i	0.998435	−	0.0559290i	$-0.0178120\pi$
$3$	0.780776	+	1.35234i	0.450781	+	0.780776i	−0.547653	+	0.836705i	$0.684479\pi$
$4$		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	$-0.928688\pi$
$7$	−0.780776	+	1.35234i	−0.295106	+	0.511138i	0.679904	+	0.733301i	$0.262022\pi$
$8$		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	$-0.0910224\pi$
$11$	0.780776	+	1.35234i	0.235413	+	0.407747i	−0.723980	+	0.689821i	$0.757689\pi$
$12$		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	−0.385499	−	0.922708i	$-0.625971\pi$
$17$	2.50000	−	4.33013i	0.606339	−	1.05021i	0.991838	−	0.127502i	$-0.0406959\pi$
$18$		0			0
$19$	−0.780776	+	1.35234i	−0.179122	+	0.310249i	−0.941580	−	0.336789i	$-0.890659\pi$
$19$	−0.780776	+	1.35234i	−0.179122	+	0.310249i	0.762458	+	0.647038i	$0.223992\pi$
$20$		0			0
$21$	−2.43845			−0.532113
$22$		0			0
$23$	−4.34233	−	7.52113i	−0.905438	−	1.56827i	−0.820328	−	0.571893i	$-0.806209\pi$
$23$	−4.34233	−	7.52113i	−0.905438	−	1.56827i	−0.0851104	−	0.996372i	$-0.527124\pi$
$24$		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	0.999167	−	0.0408130i	$-0.0129948\pi$
$29$	2.50000	+	4.33013i	0.464238	+	0.804084i	−0.534928	+	0.844897i	$0.679661\pi$
$30$		0			0
$31$	−8.00000			−1.43684			−0.718421	−	0.695608i	$-0.755135\pi$
$31$	−8.00000			−1.43684			−0.718421	+	0.695608i	$0.755135\pi$
$32$		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	0.904194	−	0.427121i	$-0.140472\pi$
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	−0.821995	+	0.569495i	$0.807139\pi$
$38$		0			0
$39$	0.780776	−	5.57586i	0.125024	−	0.892852i
$40$		0			0
$41$	3.62311	+	6.27540i	0.565834	+	0.980053i	0.996972	+	0.0777671i	$0.0247790\pi$
$41$	3.62311	+	6.27540i	0.565834	+	0.980053i	−0.431138	+	0.902286i	$0.641888\pi$
$42$		0			0
$43$	1.21922	−	2.11176i	0.185930	−	0.322040i	−0.757960	−	0.652301i	$-0.773804\pi$
$43$	1.21922	−	2.11176i	0.185930	−	0.322040i	0.943889	+	0.330262i	$0.107137\pi$
$44$		0			0
$45$	0.157671	−	0.273094i	0.0235042	−	0.0407104i
$46$		0			0
$47$	4.00000			0.583460			0.291730	−	0.956501i	$-0.405769\pi$
$47$	4.00000			0.583460			0.291730	+	0.956501i	$0.405769\pi$
$48$		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	$-0.865745\pi$
$59$	−0.780776	+	1.35234i	−0.101648	+	0.176060i	0.810716	+	0.585440i	$0.199078\pi$
$60$		0			0
$61$	−4.62311	+	8.00745i	−0.591928	+	1.02525i	0.402045	+	0.915620i	$0.368300\pi$
$61$	−4.62311	+	8.00745i	−0.591928	+	1.02525i	−0.993973	+	0.109629i	$0.965034\pi$
$62$		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	0.899290	+	0.437353i	$0.144084\pi$
$67$	6.78078	+	11.7446i	0.828404	+	1.43484i	−0.0708863	+	0.997484i	$0.522583\pi$
$68$		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	$-0.743667\pi$
$71$	2.34233	−	4.05703i	0.277983	−	0.481481i	0.970883	+	0.239552i	$0.0770007\pi$
$72$		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	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$		0			0
$81$	3.50000	+	6.06218i	0.388889	+	0.673575i
$82$		0			0
$83$	−14.2462			−1.56372			−0.781862	−	0.623451i	$-0.785730\pi$
$83$	−14.2462			−1.56372			−0.781862	+	0.623451i	$0.785730\pi$
$84$		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	0.786071	−	0.618137i	$-0.212112\pi$
$89$	−1.34233	−	2.32498i	−0.142287	−	0.246448i	−0.928357	+	0.371689i	$0.878779\pi$
$90$		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	0.0818678	−	0.996643i	$-0.473911\pi$
$97$	8.90388	−	15.4220i	0.904052	−	1.56586i	0.822184	−	0.569221i	$-0.192755\pi$
$98$		0			0
$99$	0.876894			0.0881312
$100$		0			0
$101$	5.62311	+	9.73950i	0.559520	+	0.969117i	0.997536	+	0.0701500i	$0.0223478\pi$
$101$	5.62311	+	9.73950i	0.559520	+	0.969117i	−0.438017	+	0.898967i	$0.644319\pi$
$102$		0			0
$103$	−2.24621			−0.221326			−0.110663	−	0.993858i	$-0.535297\pi$
$103$	−2.24621			−0.221326			−0.110663	+	0.993858i	$0.535297\pi$
$104$		0			0
$105$	−1.36932			−0.133632
$106$		0			0
$107$	−4.34233	−	7.52113i	−0.419789	−	0.727096i	0.576129	−	0.817359i	$-0.304563\pi$
$107$	−4.34233	−	7.52113i	−0.419789	−	0.727096i	−0.995918	+	0.0902631i	$0.971229\pi$
$108$		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	−0.643755	−	0.765232i	$-0.722624\pi$
$113$	3.62311	−	6.27540i	0.340833	−	0.590340i	0.984588	+	0.174892i	$0.0559576\pi$
$114$		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	$-0.0540661\pi$
$127$	3.90388	+	6.76172i	0.346414	+	0.600006i	−0.639196	+	0.769044i	$0.720733\pi$
$128$		0			0
$129$	3.80776			0.335255
$130$		0			0
$131$	1.75379			0.153229			0.0766146	−	0.997061i	$-0.475589\pi$
$131$	1.75379			0.153229			0.0766146	+	0.997061i	$0.475589\pi$
$132$		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	−0.999946	−	0.0104394i	$-0.996677\pi$
$137$	−5.74621	+	9.95273i	−0.490932	+	0.850319i	0.509014	+	0.860759i	$0.330010\pi$
$138$		0			0
$139$	−3.65767	+	6.33527i	−0.310240	+	0.537351i	−0.978414	−	0.206654i	$-0.933743\pi$
$139$	−3.65767	+	6.33527i	−0.310240	+	0.537351i	0.668175	+	0.744005i	$0.267076\pi$
$140$		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	−0.791850	−	0.610715i	$-0.790882\pi$
$149$	1.62311	−	2.81130i	0.132970	−	0.230311i	0.924820	+	0.380405i	$0.124215\pi$
$150$		0			0
$151$	20.4924			1.66765			0.833825	−	0.552029i	$-0.186146\pi$
$151$	20.4924			1.66765			0.833825	+	0.552029i	$0.186146\pi$
$152$		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	0.0680484	−	0.997682i	$-0.478323\pi$
$163$	11.4654	−	19.8587i	0.898042	−	1.55545i	0.829994	−	0.557773i	$-0.188344\pi$
$164$		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	$-0.0460423\pi$
$167$	4.78078	+	8.28055i	0.369948	+	0.640768i	−0.619609	+	0.784910i	$0.712709\pi$
$168$		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	−0.999953	−	0.00972081i	$-0.996906\pi$
$173$	−6.46543	+	11.1985i	−0.491558	+	0.851403i	0.508395	+	0.861124i	$0.330239\pi$
$174$		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	−0.988822	−	0.149099i	$-0.952363\pi$
$179$	−8.34233	−	14.4493i	−0.623535	−	1.07999i	0.365287	−	0.930895i	$-0.380971\pi$
$180$		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	−0.388637	−	0.921391i	$-0.627054\pi$
$191$	8.34233	−	14.4493i	0.603630	−	1.04552i	0.992266	−	0.124126i	$-0.0396128\pi$
$192$		0			0
$193$	−1.50000	−	2.59808i	−0.107972	−	0.187014i	0.806976	−	0.590584i	$-0.201102\pi$
$193$	−1.50000	−	2.59808i	−0.107972	−	0.187014i	−0.914949	+	0.403570i	$0.867769\pi$
$194$		0			0
$195$	0.438447	−	3.13114i	0.0313979	−	0.224226i
$196$		0			0
$197$	−7.34233	−	12.7173i	−0.523119	−	0.906069i	−0.999638	−	0.0269049i	$-0.991435\pi$
$197$	−7.34233	−	12.7173i	−0.523119	−	0.906069i	0.476519	−	0.879164i	$-0.341898\pi$
$198$		0			0
$199$	−6.78078	+	11.7446i	−0.480676	+	0.832556i	−0.999754	−	0.0221709i	$-0.992942\pi$
$199$	−6.78078	+	11.7446i	−0.480676	+	0.832556i	0.519078	+	0.854727i	$0.326276\pi$
$200$		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	−0.881493	−	0.472197i	$-0.843461\pi$
$211$	−12.3423	−	21.3775i	−0.849681	−	1.47169i	0.0318122	−	0.999494i	$-0.489872\pi$
$212$		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	$-0.260583\pi$
$223$	−4.34233	−	7.52113i	−0.290784	−	0.503652i	−0.973995	+	0.226568i	$0.927249\pi$
$224$		0			0
$225$	−1.31534	+	2.27824i	−0.0876894	+	0.151883i
$226$		0			0
$227$	−15.0270	+	26.0275i	−0.997376	+	1.72751i	−0.435994	+	0.899950i	$0.643603\pi$
$227$	−15.0270	+	26.0275i	−0.997376	+	1.72751i	−0.561382	+	0.827557i	$0.689730\pi$
$228$		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	$-0.299079\pi$
$239$	18.2462			1.18025			0.590125	+	0.807312i	$0.299079\pi$
$240$		0			0
$241$	−3.74621	+	6.48863i	−0.241315	+	0.417969i	−0.961089	−	0.276239i	$-0.910912\pi$
$241$	−3.74621	+	6.48863i	−0.241315	+	0.417969i	0.719774	+	0.694208i	$0.244245\pi$
$242$		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	$-0.844076\pi$
$251$	−0.534565	+	0.925894i	−0.0337415	+	0.0584419i	0.848662	+	0.528936i	$0.177409\pi$
$252$		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	0.772541	−	0.634965i	$-0.218985\pi$
$257$	−2.62311	−	4.54335i	−0.163625	−	0.283407i	−0.936166	+	0.351558i	$0.885652\pi$
$258$		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	$-0.0480607\pi$
$263$	5.90388	+	10.2258i	0.364049	+	0.630551i	−0.624574	+	0.780966i	$0.714727\pi$
$264$		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	−0.763817	−	0.645433i	$-0.776677\pi$
$269$	2.90388	−	5.02967i	0.177053	−	0.306664i	0.940870	+	0.338768i	$0.110010\pi$
$270$		0			0
$271$	4.78078	+	8.28055i	0.290411	+	0.503007i	0.973907	−	0.226947i	$-0.0728745\pi$
$271$	4.78078	+	8.28055i	0.290411	+	0.503007i	−0.683496	+	0.729955i	$0.739541\pi$
$272$		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	−0.982603	−	0.185720i	$-0.940538\pi$
$277$	−5.50000	+	9.52628i	−0.330463	+	0.572379i	0.652140	+	0.758099i	$0.273872\pi$
$278$		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	0.942984	+	0.332838i	$0.108006\pi$
$283$	12.7808	+	22.1370i	0.759738	+	1.31591i	−0.183246	+	0.983067i	$0.558660\pi$
$284$		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	−0.360192	−	0.932878i	$-0.617289\pi$
$293$	10.7462	−	18.6130i	0.627800	−	1.08738i	0.987992	−	0.154504i	$-0.0493779\pi$
$294$		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	$-0.589784\pi$
$307$	−9.75379			−0.556678			−0.278339	+	0.960483i	$0.589784\pi$
$308$		0			0
$309$	−1.75379	−	3.03765i	−0.0997696	−	0.172806i
$310$		0			0
$311$	2.24621			0.127371			0.0636855	−	0.997970i	$-0.479715\pi$
$311$	2.24621			0.127371			0.0636855	+	0.997970i	$0.479715\pi$
$312$		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	$-0.772330\pi$
$331$	3.46543	−	6.00231i	0.190478	−	0.329917i	0.945409	+	0.325887i	$0.105663\pi$
$332$		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	$-0.850891\pi$
$347$	−1.02699	+	1.77879i	−0.0551316	+	0.0954907i	0.837142	+	0.546985i	$0.184224\pi$
$348$		0			0
$349$	−8.21922	−	14.2361i	−0.439965	−	0.762042i	0.557721	−	0.830028i	$-0.311676\pi$
$349$	−8.21922	−	14.2361i	−0.439965	−	0.762042i	−0.997686	+	0.0679866i	$0.978342\pi$
$350$		0			0
$351$	−15.8078	−	12.3376i	−0.843756	−	0.658531i
$352$		0			0
$353$	4.50000	+	7.79423i	0.239511	+	0.414845i	0.960574	−	0.278024i	$-0.0896796\pi$
$353$	4.50000	+	7.79423i	0.239511	+	0.414845i	−0.721063	+	0.692869i	$0.756346\pi$
$354$		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	$-0.229144\pi$
$359$	28.4924			1.50377			0.751886	+	0.659293i	$0.229144\pi$
$360$		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	$-0.278421\pi$
$367$	−6.58854	−	11.4117i	−0.343919	−	0.595685i	−0.985157	+	0.171657i	$0.945088\pi$
$368$		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	−0.925910	−	0.377744i	$-0.876700\pi$
$373$	−2.62311	+	4.54335i	−0.135819	+	0.235246i	0.790091	+	0.612990i	$0.210033\pi$
$374$		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	$-0.190650\pi$
$379$	−1.46543	−	2.53821i	−0.0752743	−	0.130379i	−0.901206	+	0.433392i	$0.857317\pi$
$380$		0			0
$381$	−6.09612	+	10.5588i	−0.312314	+	0.540943i
$382$		0			0
$383$	14.5885	−	25.2681i	0.745440	−	1.29114i	−0.204550	−	0.978856i	$-0.565573\pi$
$383$	14.5885	−	25.2681i	0.745440	−	1.29114i	0.949989	−	0.312283i	$-0.101094\pi$
$384$		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	−0.725150	−	0.688591i	$-0.758230\pi$
$397$	4.65767	−	8.06732i	0.233762	−	0.404887i	0.958912	+	0.283703i	$0.0915631\pi$
$398$		0			0
$399$	1.90388	−	3.29762i	0.0953133	−	0.165088i
$400$		0			0
$401$	−11.7462	−	20.3450i	−0.586578	−	1.01598i	−0.994677	−	0.103045i	$-0.967141\pi$
$401$	−11.7462	−	20.3450i	−0.586578	−	1.01598i	0.408099	−	0.912938i	$-0.366192\pi$
$402$		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	−0.613677	−	0.789557i	$-0.710310\pi$
$409$	7.62311	−	13.2036i	0.376938	−	0.652876i	0.990615	+	0.136681i	$0.0436435\pi$
$410$		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	$-0.285499\pi$
$419$	−7.46543	−	12.9305i	−0.364710	−	0.631697i	−0.988730	+	0.149712i	$0.952165\pi$
$420$		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	−0.950221	−	0.311577i	$-0.899143\pi$
$431$	−15.4654	−	26.7869i	−0.744944	−	1.29028i	0.205277	−	0.978704i	$-0.434190\pi$
$432$		0			0
$433$	−15.7462	+	27.2732i	−0.756715	+	1.31067i	0.187803	+	0.982207i	$0.439863\pi$
$433$	−15.7462	+	27.2732i	−0.756715	+	1.31067i	−0.944517	+	0.328461i	$0.893470\pi$
$434$		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	$-0.0972276\pi$
$439$	4.53457	+	7.85410i	0.216423	+	0.374856i	−0.737289	+	0.675578i	$0.763894\pi$
$440$		0			0
$441$	2.56155			0.121979
$442$		0			0
$443$	38.2462			1.81713			0.908566	−	0.417741i	$-0.137178\pi$
$443$	38.2462			1.81713			0.908566	+	0.417741i	$0.137178\pi$
$444$		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	−0.429215	−	0.903202i	$-0.641210\pi$
$449$	12.0270	−	20.8314i	0.567589	−	0.983092i	0.996804	−	0.0798900i	$-0.0254569\pi$
$450$		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	0.951871	−	0.306497i	$-0.0991571\pi$
$457$	4.50000	+	7.79423i	0.210501	+	0.364599i	−0.741370	+	0.671096i	$0.765824\pi$
$458$		0			0
$459$	13.9039	−	24.0822i	0.648978	−	1.12406i
$460$		0			0
$461$	−11.7462	+	20.3450i	−0.547076	+	0.947563i	0.451398	+	0.892323i	$0.350926\pi$
$461$	−11.7462	+	20.3450i	−0.547076	+	0.947563i	−0.998473	+	0.0552398i	$0.982408\pi$
$462$		0			0
$463$	−32.9848			−1.53294			−0.766468	−	0.642283i	$-0.777988\pi$
$463$	−32.9848			−1.53294			−0.766468	+	0.642283i	$0.777988\pi$
$464$		0			0
$465$	−3.50758	−	6.07530i	−0.162660	−	0.281735i
$466$		0			0
$467$	26.2462			1.21453			0.607265	−	0.794499i	$-0.292267\pi$
$467$	26.2462			1.21453			0.607265	+	0.794499i	$0.292267\pi$
$468$		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	$-0.0131632\pi$
$479$	10.1501	+	17.5805i	0.463770	+	0.803273i	−0.535375	+	0.844614i	$0.679830\pi$
$480$		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	−0.151503	−	0.988457i	$-0.548411\pi$
$487$	17.2192	−	29.8246i	0.780278	−	1.35148i	0.931780	−	0.363023i	$-0.118256\pi$
$488$		0			0
$489$	35.8078			1.61928
$490$		0			0
$491$	1.02699	+	1.77879i	0.0463473	+	0.0802759i	0.888268	−	0.459325i	$-0.151909\pi$
$491$	1.02699	+	1.77879i	0.0463473	+	0.0802759i	−0.841921	+	0.539601i	$0.818575\pi$
$492$		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	$-0.620352\pi$
$499$	−16.4924			−0.738302			−0.369151	+	0.929369i	$0.620352\pi$
$500$		0			0
$501$	−7.46543	+	12.9305i	−0.333531	+	0.577693i
$502$		0			0
$503$	16.3423	−	28.3057i	0.728668	−	1.26209i	−0.228778	−	0.973479i	$-0.573473\pi$
$503$	16.3423	−	28.3057i	0.728668	−	1.26209i	0.957446	−	0.288612i	$-0.0931938\pi$
$504$		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	0.956306	+	0.292366i	$0.0944425\pi$
$509$	16.5000	+	28.5788i	0.731350	+	1.26673i	−0.224957	+	0.974369i	$0.572224\pi$
$510$		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	$-0.0799984\pi$
$523$	6.15009	+	10.6523i	0.268925	+	0.465791i	−0.699660	+	0.714476i	$0.746665\pi$
$524$		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	$-0.385304\pi$
$547$	16.4924			0.705165			0.352583	+	0.935781i	$0.385304\pi$
$548$		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	−0.978687	−	0.205358i	$-0.934164\pi$
$557$	−15.7462	−	27.2732i	−0.667188	−	1.15560i	0.311499	−	0.950247i	$-0.399169\pi$
$558$		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	$-0.874052\pi$
$563$	−3.02699	+	5.24290i	−0.127572	+	0.220962i	0.795163	+	0.606396i	$0.207385\pi$
$564$		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	0.601017	−	0.799237i	$-0.294763\pi$
$569$	−9.34233	−	16.1814i	−0.391651	−	0.678359i	−0.992667	+	0.120877i	$0.961429\pi$
$570$		0			0
$571$	−8.49242			−0.355397			−0.177698	−	0.984085i	$-0.556865\pi$
$571$	−8.49242			−0.355397			−0.177698	+	0.984085i	$0.556865\pi$
$572$		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	$-0.266370\pi$
$587$	−7.46543	−	12.9305i	−0.308131	−	0.533699i	−0.977954	+	0.208822i	$0.933037\pi$
$588$		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	$-0.316053\pi$
$599$	26.7386			1.09251			0.546255	+	0.837619i	$0.316053\pi$
$600$		0			0
$601$	−13.9924	−	24.2356i	−0.570763	−	0.988590i	−0.996488	−	0.0837376i	$-0.973314\pi$
$601$	−13.9924	−	24.2356i	−0.570763	−	0.988590i	0.425725	−	0.904853i	$-0.360019\pi$
$602$		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	$-0.961548\pi$
$607$	−9.65767	+	16.7276i	−0.391993	+	0.678951i	0.600720	+	0.799460i	$0.294881\pi$
$608$		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	0.942478	−	0.334269i	$-0.108489\pi$
$613$	4.50000	+	7.79423i	0.181753	+	0.314806i	−0.760724	+	0.649075i	$0.775156\pi$
$614$		0			0
$615$	−3.17708	+	5.50287i	−0.128112	+	0.221897i
$616$		0			0
$617$	−12.6231	+	21.8639i	−0.508187	+	0.880206i	0.491768	+	0.870726i	$0.336351\pi$
$617$	−12.6231	+	21.8639i	−0.508187	+	0.880206i	−0.999955	+	0.00947959i	$0.996983\pi$
$618$		0			0
$619$	−28.9848			−1.16500			−0.582500	−	0.812831i	$-0.697925\pi$
$619$	−28.9848			−1.16500			−0.582500	+	0.812831i	$0.697925\pi$
$620$		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	$-0.897467\pi$
$631$	−5.02699	+	8.70700i	−0.200121	+	0.346620i	0.748446	+	0.663196i	$0.230800\pi$
$632$		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	−0.850912	−	0.525308i	$-0.823950\pi$
$641$	0.746211	−	1.29248i	0.0294736	−	0.0510497i	0.880386	+	0.474258i	$0.157284\pi$
$642$		0			0
$643$	−10.1501	+	17.5805i	−0.400281	+	0.693306i	−0.993760	−	0.111543i	$-0.964421\pi$
$643$	−10.1501	+	17.5805i	−0.400281	+	0.693306i	0.593479	+	0.804849i	$0.297754\pi$
$644$		0			0
$645$	2.13826			0.0841939
$646$		0			0
$647$	−11.4654	−	19.8587i	−0.450753	−	0.780727i	0.547680	−	0.836688i	$-0.315511\pi$
$647$	−11.4654	−	19.8587i	−0.450753	−	0.780727i	−0.998433	+	0.0559611i	$0.982178\pi$
$648$		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	0.999744	−	0.0226145i	$-0.00719904\pi$
$653$	12.2732	+	21.2578i	0.480287	+	0.831882i	−0.519457	+	0.854497i	$0.673866\pi$
$654$		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	$-0.971289\pi$
$659$	−10.7808	+	18.6729i	−0.419959	+	0.727391i	0.575975	+	0.817467i	$0.304622\pi$
$660$		0			0
$661$	−2.86932	−	4.96980i	−0.111603	−	0.193303i	0.804813	−	0.593528i	$-0.202265\pi$
$661$	−2.86932	−	4.96980i	−0.111603	−	0.193303i	−0.916417	+	0.400225i	$0.868932\pi$
$662$		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	0.650585	−	0.759434i	$-0.274524\pi$
$673$	−8.62311	−	14.9357i	−0.332396	−	0.575727i	−0.982981	+	0.183706i	$0.941190\pi$
$674$		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	$-0.878030\pi$
$683$	−3.65767	+	6.33527i	−0.139957	+	0.242412i	0.787523	+	0.616285i	$0.211363\pi$
$684$		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	$-0.00504799\pi$
$691$	12.7808	+	22.1370i	0.486204	+	0.842129i	−0.513671	+	0.857987i	$0.671715\pi$
$692$		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	0.353282	+	0.935517i	$0.385066\pi$
$709$	−16.8693	+	29.2185i	−0.633540	+	1.09732i	−0.986822	+	0.161807i	$0.948268\pi$
$710$		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	−0.118745	−	0.992925i	$-0.537887\pi$
$719$	21.4654	−	37.1792i	0.800526	−	1.38655i	0.919271	−	0.393626i	$-0.128780\pi$
$720$		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	$-0.460119\pi$
$727$	6.73863			0.249922			0.124961	+	0.992162i	$0.460119\pi$
$728$		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	−0.868833	−	0.495105i	$-0.835130\pi$
$739$	−23.4654	−	40.6433i	−0.863190	−	1.49509i	0.00564328	−	0.999984i	$-0.498204\pi$
$740$		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	$-0.113466\pi$
$743$	4.53457	+	7.85410i	0.166357	+	0.288139i	−0.770779	+	0.637102i	$0.780133\pi$
$744$		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	0.849953	+	0.526859i	$0.176630\pi$
$751$	24.1501	+	41.8292i	0.881249	+	1.52637i	0.0312965	+	0.999510i	$0.490036\pi$
$752$		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	0.976293	−	0.216451i	$-0.0694482\pi$
$757$	8.27320	+	14.3296i	0.300695	+	0.520818i	−0.675599	+	0.737269i	$0.736115\pi$
$758$		0			0
$759$	21.1771			0.768679
$760$		0			0
$761$	11.5346	−	19.9785i	0.418128	−	0.724218i	−0.577623	−	0.816303i	$-0.696020\pi$
$761$	11.5346	−	19.9785i	0.418128	−	0.724218i	0.995751	+	0.0920850i	$0.0293531\pi$
$762$		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	0.857511	−	0.514465i	$-0.172009\pi$
$769$	−0.465435	−	0.806157i	−0.0167840	−	0.0290708i	−0.874295	+	0.485394i	$0.838676\pi$
$770$		0			0
$771$	4.09612	−	7.09468i	0.147518	−	0.255509i
$772$		0			0
$773$	−17.0961	+	29.6113i	−0.614905	+	1.06505i	0.375497	+	0.926824i	$0.377472\pi$
$773$	−17.0961	+	29.6113i	−0.614905	+	1.06505i	−0.990401	+	0.138222i	$0.955861\pi$
$774$		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	$-0.670780\pi$
$787$	13.7116	−	23.7493i	0.488767	−	0.846570i	0.999917	+	0.0129221i	$0.00411334\pi$
$788$		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	−0.957517	−	0.288376i	$-0.906885\pi$
$797$	−6.46543	+	11.1985i	−0.229017	+	0.396670i	0.728500	+	0.685046i	$0.240218\pi$
$798$		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	0.994738	−	0.102448i	$-0.0326675\pi$
$809$	11.6231	+	20.1318i	0.408647	+	0.707797i	−0.586092	+	0.810245i	$0.699334\pi$
$810$		0			0
$811$	8.00000			0.280918			0.140459	−	0.990086i	$-0.455142\pi$
$811$	8.00000			0.280918			0.140459	+	0.990086i	$0.455142\pi$
$812$		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	0.960984	−	0.276603i	$-0.0892086\pi$
$821$	6.90388	+	11.9579i	0.240947	+	0.417333i	−0.720037	+	0.693935i	$0.755875\pi$
$822$		0			0
$823$	0.588540	−	1.01938i	0.0205152	−	0.0355334i	−0.855586	−	0.517661i	$-0.826803\pi$
$823$	0.588540	−	1.01938i	0.0205152	−	0.0355334i	0.876101	+	0.482128i	$0.160136\pi$
$824$		0			0
$825$	5.71165	−	9.89286i	0.198854	−	0.344425i
$826$		0			0
$827$	−36.9848			−1.28609			−0.643045	−	0.765829i	$-0.722329\pi$
$827$	−36.9848			−1.28609			−0.643045	+	0.765829i	$0.722329\pi$
$828$		0			0
$829$	−3.25379	−	5.63573i	−0.113009	−	0.195737i	0.803973	−	0.594665i	$-0.202715\pi$
$829$	−3.25379	−	5.63573i	−0.113009	−	0.195737i	−0.916982	+	0.398929i	$0.869382\pi$
$830$		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	$-0.989626\pi$
$839$	−13.6577	+	23.6558i	−0.471515	+	0.816688i	0.527954	+	0.849273i	$0.322959\pi$
$840$		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	$-0.623909\pi$
$859$	−22.2462			−0.759031			−0.379515	+	0.925185i	$0.623909\pi$
$860$		0			0
$861$	−8.83475	−	15.3022i	−0.301088	−	0.521499i
$862$		0			0
$863$	−21.7538			−0.740508			−0.370254	−	0.928931i	$-0.620729\pi$
$863$	−21.7538			−0.740508			−0.370254	+	0.928931i	$0.620729\pi$
$864$		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	−0.306699	−	0.951807i	$-0.599224\pi$
$877$	19.8693	−	34.4147i	0.670939	−	1.16210i	0.977638	−	0.210294i	$-0.0674422\pi$
$878$		0			0
$879$	33.5616			1.13200
$880$		0			0
$881$	7.62311	+	13.2036i	0.256829	+	0.444841i	0.965391	−	0.260808i	$-0.0839890\pi$
$881$	7.62311	+	13.2036i	0.256829	+	0.444841i	−0.708562	+	0.705649i	$0.750656\pi$
$882$		0			0
$883$	20.0000			0.673054			0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000			0.673054			0.336527	+	0.941674i	$0.390748\pi$
$884$		0			0
$885$	−1.36932			−0.0460291
$886$		0			0
$887$	−10.3423	−	17.9134i	−0.347261	−	0.601474i	0.638501	−	0.769621i	$-0.279555\pi$
$887$	−10.3423	−	17.9134i	−0.347261	−	0.601474i	−0.985762	+	0.168147i	$0.946222\pi$
$888$		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	0.978164	+	0.207836i	$0.0666419\pi$
$907$	20.1501	+	34.9010i	0.669073	+	1.15887i	−0.309091	+	0.951033i	$0.600025\pi$
$908$		0			0
$909$	6.31534			0.209467
$910$		0			0
$911$	−30.7386			−1.01842			−0.509208	−	0.860643i	$-0.670062\pi$
$911$	−30.7386			−1.01842			−0.509208	+	0.860643i	$0.670062\pi$
$912$		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	−0.257731	+	0.966217i	$0.582975\pi$
$919$	−29.2732	+	50.7027i	−0.965634	+	1.67253i	−0.707903	+	0.706310i	$0.750358\pi$
$920$		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	−0.365780	−	0.930701i	$-0.619198\pi$
$929$	18.9924	−	32.8958i	0.623121	−	1.07928i	0.988901	−	0.148576i	$-0.0474690\pi$
$930$		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	$-0.247293\pi$
$947$	−7.71165	−	13.3570i	−0.250595	−	0.434043i	−0.963690	+	0.267025i	$0.913960\pi$
$948$		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	−0.577740	−	0.816221i	$-0.696065\pi$
$953$	12.9039	−	22.3502i	0.417998	−	0.723993i	0.995738	+	0.0922274i	$0.0293987\pi$
$954$		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	$-0.470509\pi$
$967$	5.75379			0.185029			0.0925147	+	0.995711i	$0.470509\pi$
$968$		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	$-0.933639\pi$
$971$	−9.65767	+	16.7276i	−0.309929	+	0.536813i	0.668417	+	0.743787i	$0.266972\pi$
$972$		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	0.855886	−	0.517165i	$-0.173013\pi$
$977$	−0.623106	−	1.07925i	−0.0199349	−	0.0345283i	−0.875821	+	0.482636i	$0.839679\pi$
$978$		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	$-0.630451\pi$
$983$	−24.9848			−0.796893			−0.398446	+	0.917192i	$0.630451\pi$
$984$		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	$-0.185383\pi$
$991$	−1.84991	−	3.20413i	−0.0587642	−	0.101783i	−0.893911	+	0.448245i	$0.852049\pi$
$992$		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	−0.288686	−	0.957424i	$-0.593218\pi$
$997$	21.6231	−	37.4523i	0.684811	−	1.18613i	0.973496	−	0.228703i	$-0.0734484\pi$
$998$		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	104.2.i.b.81.2	yes	4
3.2	odd	2		936.2.t.f.289.1		4
4.3	odd	2		208.2.i.e.81.1		4
8.3	odd	2		832.2.i.l.705.2		4
8.5	even	2		832.2.i.o.705.1		4
12.11	even	2		1872.2.t.s.289.1		4
13.2	odd	12		1352.2.f.d.337.1		4
13.3	even	3		1352.2.a.f.1.1		2
13.4	even	6		1352.2.i.e.529.2		4
13.5	odd	4		1352.2.o.c.361.3		8
13.6	odd	12		1352.2.o.c.1161.3		8
13.7	odd	12		1352.2.o.c.1161.4		8
13.8	odd	4		1352.2.o.c.361.4		8
13.9	even	3	inner	104.2.i.b.9.2	✓	4
13.10	even	6		1352.2.a.h.1.1		2
13.11	odd	12		1352.2.f.d.337.2		4
13.12	even	2		1352.2.i.e.1329.2		4
39.35	odd	6		936.2.t.f.217.1		4
52.3	odd	6		2704.2.a.q.1.2		2
52.11	even	12		2704.2.f.l.337.4		4
52.15	even	12		2704.2.f.l.337.3		4
52.23	odd	6		2704.2.a.r.1.2		2
52.35	odd	6		208.2.i.e.113.1		4
104.35	odd	6		832.2.i.l.321.2		4
104.61	even	6		832.2.i.o.321.1		4
156.35	even	6		1872.2.t.s.1153.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.i.b.9.2	✓	4	13.9	even	3	inner
104.2.i.b.81.2	yes	4	1.1	even	1	trivial
208.2.i.e.81.1		4	4.3	odd	2
208.2.i.e.113.1		4	52.35	odd	6
832.2.i.l.321.2		4	104.35	odd	6
832.2.i.l.705.2		4	8.3	odd	2
832.2.i.o.321.1		4	104.61	even	6
832.2.i.o.705.1		4	8.5	even	2
936.2.t.f.217.1		4	39.35	odd	6
936.2.t.f.289.1		4	3.2	odd	2
1352.2.a.f.1.1		2	13.3	even	3
1352.2.a.h.1.1		2	13.10	even	6
1352.2.f.d.337.1		4	13.2	odd	12
1352.2.f.d.337.2		4	13.11	odd	12
1352.2.i.e.529.2		4	13.4	even	6
1352.2.i.e.1329.2		4	13.12	even	2
1352.2.o.c.361.3		8	13.5	odd	4
1352.2.o.c.361.4		8	13.8	odd	4
1352.2.o.c.1161.3		8	13.6	odd	12
1352.2.o.c.1161.4		8	13.7	odd	12
1872.2.t.s.289.1		4	12.11	even	2
1872.2.t.s.1153.1		4	156.35	even	6
2704.2.a.q.1.2		2	52.3	odd	6
2704.2.a.r.1.2		2	52.23	odd	6
2704.2.f.l.337.3		4	52.15	even	12
2704.2.f.l.337.4		4	52.11	even	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:	\( N \)	\(=\)	\( 104 = 2^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	104.i (of order \(3\), degree \(2\), 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

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