LMFDB - Embedded newform 308.2.j.b.113.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [308,2,Mod(113,308)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(308, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("308.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 308 = 2^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	308.j (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.45939238226$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 13x^{6} - 25x^{5} + 126x^{4} + 135x^{3} + 717x^{2} + 1068x + 7921 $ x^8 - x^7 + 13x^6 - 25x^5 + 126x^4 + 135x^3 + 717x^2 + 1068x + 7921
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			113.2
Root			$-1.97240 + 1.43303i$ of defining polynomial
Character	$\chi$	$=$	308.113
Dual form			308.2.j.b.169.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.118034 + 0.363271i) q^{3} +(1.97240 + 1.43303i) q^{5} +(-0.309017 + 0.951057i) q^{7} +(2.30902 - 1.67760i) q^{9} +O(q^{10})$	\(q+(0.118034 + 0.363271i) q^{3} +(1.97240 + 1.43303i) q^{5} +(-0.309017 + 0.951057i) q^{7} +(2.30902 - 1.67760i) q^{9} +(-2.37142 + 2.31870i) q^{11} +(-0.163383 + 0.118705i) q^{13} +(-0.287769 + 0.885663i) q^{15} +(1.57338 + 1.14313i) q^{17} +(0.774638 + 2.38409i) q^{19} -0.381966 q^{21} +2.38197 q^{23} +(0.291695 + 0.897745i) q^{25} +(1.80902 + 1.31433i) q^{27} +(0.0385696 - 0.118705i) q^{29} +(3.38239 - 2.45745i) q^{31} +(-1.12222 - 0.587785i) q^{33} +(-1.97240 + 1.43303i) q^{35} +(1.59679 - 4.91440i) q^{37} +(-0.0624068 - 0.0453412i) q^{39} +(-0.118034 - 0.363271i) q^{41} -11.6535 q^{43} +6.95836 q^{45} +(-1.06660 - 3.28265i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(-0.229553 + 0.706490i) q^{51} +(-2.63509 + 1.91451i) q^{53} +(-8.00016 + 1.17507i) q^{55} +(-0.774638 + 0.562807i) q^{57} +(2.96143 - 9.11435i) q^{59} +(-5.60071 - 4.06916i) q^{61} +(0.881966 + 2.71441i) q^{63} -0.492365 q^{65} -6.43888 q^{67} +(0.281153 + 0.865300i) q^{69} +(-7.20890 - 5.23757i) q^{71} +(2.59043 - 7.97254i) q^{73} +(-0.291695 + 0.211929i) q^{75} +(-1.47240 - 2.97187i) q^{77} +(-0.0166300 + 0.0120824i) q^{79} +(2.38197 - 7.33094i) q^{81} +(-2.61846 - 1.90242i) q^{83} +(1.46519 + 4.50940i) q^{85} +0.0476746 q^{87} +11.6394 q^{89} +(-0.0624068 - 0.192069i) q^{91} +(1.29196 + 0.938663i) q^{93} +(-1.88858 + 5.81246i) q^{95} +(-14.3379 + 10.4171i) q^{97} +(-1.58582 + 9.33221i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{3} - q^{5} + 2 q^{7} + 14 q^{9}+O(q^{10}) $ 8 * q - 8 * q^3 - q^5 + 2 * q^7 + 14 * q^9	$ 8 q - 8 q^{3} - q^{5} + 2 q^{7} + 14 q^{9} - 5 q^{11} + 11 q^{13} - 4 q^{15} - 7 q^{17} - 5 q^{19} - 12 q^{21} + 28 q^{23} - 15 q^{25} + 10 q^{27} + 7 q^{29} + 3 q^{31} + q^{35} + 10 q^{37} + 9 q^{39} + 8 q^{41} - 44 q^{43} + 2 q^{45} + q^{47} - 2 q^{49} - 13 q^{51} - 6 q^{53} - 12 q^{55} + 5 q^{57} + 17 q^{59} - 23 q^{61} + 16 q^{63} - 80 q^{65} + 38 q^{67} - 38 q^{69} + 10 q^{71} - 5 q^{73} + 15 q^{75} + 5 q^{77} - 27 q^{79} + 28 q^{81} + 21 q^{83} + 38 q^{85} - 32 q^{87} + 26 q^{89} + 9 q^{91} + 12 q^{93} - 66 q^{95} - 28 q^{97} - 20 q^{99}+O(q^{100}) $ 8 * q - 8 * q^3 - q^5 + 2 * q^7 + 14 * q^9 - 5 * q^11 + 11 * q^13 - 4 * q^15 - 7 * q^17 - 5 * q^19 - 12 * q^21 + 28 * q^23 - 15 * q^25 + 10 * q^27 + 7 * q^29 + 3 * q^31 + q^35 + 10 * q^37 + 9 * q^39 + 8 * q^41 - 44 * q^43 + 2 * q^45 + q^47 - 2 * q^49 - 13 * q^51 - 6 * q^53 - 12 * q^55 + 5 * q^57 + 17 * q^59 - 23 * q^61 + 16 * q^63 - 80 * q^65 + 38 * q^67 - 38 * q^69 + 10 * q^71 - 5 * q^73 + 15 * q^75 + 5 * q^77 - 27 * q^79 + 28 * q^81 + 21 * q^83 + 38 * q^85 - 32 * q^87 + 26 * q^89 + 9 * q^91 + 12 * q^93 - 66 * q^95 - 28 * q^97 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/308\mathbb{Z}\right)^\times$.

$n$	$45$	$57$	$155$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$	$1$

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
$3$	0.118034	+	0.363271i	0.0681470	+	0.209735i	0.979331	−	0.202265i	$-0.0648303\pi$
$3$	0.118034	+	0.363271i	0.0681470	+	0.209735i	−0.911184	+	0.412000i	$0.864830\pi$
$4$		0			0
$5$	1.97240	+	1.43303i	0.882084	+	0.640872i	0.933802	−	0.357790i	$-0.116470\pi$
$5$	1.97240	+	1.43303i	0.882084	+	0.640872i	−0.0517179	+	0.998662i	$0.516470\pi$
$6$		0			0
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$8$		0			0
$9$	2.30902	−	1.67760i	0.769672	−	0.559200i
$10$		0			0
$11$	−2.37142	+	2.31870i	−0.715011	+	0.699113i
$11$	−2.37142	+	2.31870i	−0.715011	+	0.699113i
$12$		0			0
$13$	−0.163383	+	0.118705i	−0.0453144	+	0.0329228i	−0.610212	−	0.792238i	$-0.708916\pi$
$13$	−0.163383	+	0.118705i	−0.0453144	+	0.0329228i	0.564898	+	0.825161i	$0.308916\pi$
$14$		0			0
$15$	−0.287769	+	0.885663i	−0.0743017	+	0.228677i
$16$		0			0
$17$	1.57338	+	1.14313i	0.381600	+	0.277249i	0.762005	−	0.647572i	$-0.224215\pi$
$17$	1.57338	+	1.14313i	0.381600	+	0.277249i	−0.380405	+	0.924820i	$0.624215\pi$
$18$		0			0
$19$	0.774638	+	2.38409i	0.177714	+	0.546948i	0.999747	−	0.0224923i	$-0.00716013\pi$
$19$	0.774638	+	2.38409i	0.177714	+	0.546948i	−0.822033	+	0.569440i	$0.807160\pi$
$20$		0			0
$21$	−0.381966			−0.0833518
$22$		0			0
$23$	2.38197			0.496674			0.248337	−	0.968674i	$-0.420116\pi$
$23$	2.38197			0.496674			0.248337	+	0.968674i	$0.420116\pi$
$24$		0			0
$25$	0.291695	+	0.897745i	0.0583390	+	0.179549i
$26$		0			0
$27$	1.80902	+	1.31433i	0.348145	+	0.252942i
$28$		0			0
$29$	0.0385696	−	0.118705i	0.00716219	−	0.0220429i	−0.947412	−	0.320018i	$-0.896311\pi$
$29$	0.0385696	−	0.118705i	0.00716219	−	0.0220429i	0.954574	+	0.297975i	$0.0963111\pi$
$30$		0			0
$31$	3.38239	−	2.45745i	0.607496	−	0.441372i	−0.241036	−	0.970516i	$-0.577487\pi$
$31$	3.38239	−	2.45745i	0.607496	−	0.441372i	0.848532	+	0.529145i	$0.177487\pi$
$32$		0			0
$33$	−1.12222	−	0.587785i	−0.195354	−	0.102320i
$34$		0			0
$35$	−1.97240	+	1.43303i	−0.333396	+	0.242227i
$36$		0			0
$37$	1.59679	−	4.91440i	0.262510	−	0.807923i	−0.729747	−	0.683718i	$-0.760362\pi$
$37$	1.59679	−	4.91440i	0.262510	−	0.807923i	0.992257	−	0.124205i	$-0.0396381\pi$
$38$		0			0
$39$	−0.0624068	−	0.0453412i	−0.00999309	−	0.00726041i
$40$		0			0
$41$	−0.118034	−	0.363271i	−0.0184338	−	0.0567334i	0.941416	−	0.337246i	$-0.109495\pi$
$41$	−0.118034	−	0.363271i	−0.0184338	−	0.0567334i	−0.959850	+	0.280513i	$0.909495\pi$
$42$		0			0
$43$	−11.6535			−1.77715			−0.888574	−	0.458734i	$-0.848303\pi$
$43$	−11.6535			−1.77715			−0.888574	+	0.458734i	$0.848303\pi$
$44$		0			0
$45$	6.95836			1.03729
$46$		0			0
$47$	−1.06660	−	3.28265i	−0.155579	−	0.478823i	0.842640	−	0.538477i	$-0.181000\pi$
$47$	−1.06660	−	3.28265i	−0.155579	−	0.478823i	−0.998219	+	0.0596540i	$0.981000\pi$
$48$		0			0
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$		0			0
$51$	−0.229553	+	0.706490i	−0.0321438	+	0.0989284i
$52$		0			0
$53$	−2.63509	+	1.91451i	−0.361958	+	0.262978i	−0.753868	−	0.657026i	$-0.771814\pi$
$53$	−2.63509	+	1.91451i	−0.361958	+	0.262978i	0.391911	+	0.920003i	$0.371814\pi$
$54$		0			0
$55$	−8.00016	+	1.17507i	−1.07874	+	0.158446i
$56$		0			0
$57$	−0.774638	+	0.562807i	−0.102603	+	0.0745456i
$58$		0			0
$59$	2.96143	−	9.11435i	0.385545	−	1.18659i	−0.550538	−	0.834810i	$-0.685578\pi$
$59$	2.96143	−	9.11435i	0.385545	−	1.18659i	0.936084	−	0.351777i	$-0.114422\pi$
$60$		0			0
$61$	−5.60071	−	4.06916i	−0.717098	−	0.521002i	0.168358	−	0.985726i	$-0.446154\pi$
$61$	−5.60071	−	4.06916i	−0.717098	−	0.521002i	−0.885456	+	0.464724i	$0.846154\pi$
$62$		0			0
$63$	0.881966	+	2.71441i	0.111117	+	0.341984i
$64$		0			0
$65$	−0.492365			−0.0610704
$66$		0			0
$67$	−6.43888			−0.786634			−0.393317	−	0.919403i	$-0.628672\pi$
$67$	−6.43888			−0.786634			−0.393317	+	0.919403i	$0.628672\pi$
$68$		0			0
$69$	0.281153	+	0.865300i	0.0338468	+	0.104170i
$70$		0			0
$71$	−7.20890	−	5.23757i	−0.855539	−	0.621585i	0.0711290	−	0.997467i	$-0.477340\pi$
$71$	−7.20890	−	5.23757i	−0.855539	−	0.621585i	−0.926668	+	0.375882i	$0.877340\pi$
$72$		0			0
$73$	2.59043	−	7.97254i	0.303187	−	0.933115i	−0.677160	−	0.735836i	$-0.736790\pi$
$73$	2.59043	−	7.97254i	0.303187	−	0.933115i	0.980347	−	0.197279i	$-0.0632105\pi$
$74$		0			0
$75$	−0.291695	+	0.211929i	−0.0336821	+	0.0244714i
$76$		0			0
$77$	−1.47240	−	2.97187i	−0.167796	−	0.338677i
$78$		0			0
$79$	−0.0166300	+	0.0120824i	−0.00187102	+	0.00135938i	−0.588720	−	0.808337i	$-0.700368\pi$
$79$	−0.0166300	+	0.0120824i	−0.00187102	+	0.00135938i	0.586849	+	0.809696i	$0.300368\pi$
$80$		0			0
$81$	2.38197	−	7.33094i	0.264663	−	0.814549i
$82$		0			0
$83$	−2.61846	−	1.90242i	−0.287413	−	0.208818i	0.434731	−	0.900560i	$-0.356843\pi$
$83$	−2.61846	−	1.90242i	−0.287413	−	0.208818i	−0.722145	+	0.691742i	$0.756843\pi$
$84$		0			0
$85$	1.46519	+	4.50940i	0.158922	+	0.489113i
$86$		0			0
$87$	0.0476746			0.00511125
$88$		0			0
$89$	11.6394			1.23378			0.616889	−	0.787050i	$-0.288393\pi$
$89$	11.6394			1.23378			0.616889	+	0.787050i	$0.288393\pi$
$90$		0			0
$91$	−0.0624068	−	0.192069i	−0.00654201	−	0.0201343i
$92$		0			0
$93$	1.29196	+	0.938663i	0.133970	+	0.0973349i
$94$		0			0
$95$	−1.88858	+	5.81246i	−0.193764	+	0.596346i
$96$		0			0
$97$	−14.3379	+	10.4171i	−1.45579	+	1.05770i	−0.471359	+	0.881941i	$0.656236\pi$
$97$	−14.3379	+	10.4171i	−1.45579	+	1.05770i	−0.984434	+	0.175754i	$0.943764\pi$
$98$		0			0
$99$	−1.58582	+	9.33221i	−0.159381	+	0.937922i
$100$		0			0
$101$	14.8269	−	10.7724i	1.47533	−	1.07189i	0.496311	−	0.868145i	$-0.334687\pi$
$101$	14.8269	−	10.7724i	1.47533	−	1.07189i	0.979023	−	0.203749i	$-0.0653126\pi$
$102$		0			0
$103$	3.21249	−	9.88704i	0.316537	−	0.974199i	−0.658581	−	0.752510i	$-0.728843\pi$
$103$	3.21249	−	9.88704i	0.316537	−	0.974199i	0.975117	−	0.221689i	$-0.0711571\pi$
$104$		0			0
$105$	−0.753390	−	0.547370i	−0.0735233	−	0.0534178i
$106$		0			0
$107$	4.53062	+	13.9438i	0.437991	+	1.34800i	0.889990	+	0.455980i	$0.150711\pi$
$107$	4.53062	+	13.9438i	0.437991	+	1.34800i	−0.451999	+	0.892019i	$0.649289\pi$
$108$		0			0
$109$	−16.3407			−1.56515			−0.782575	−	0.622556i	$-0.786094\pi$
$109$	−16.3407			−1.56515			−0.782575	+	0.622556i	$0.786094\pi$
$110$		0			0
$111$	1.97374			0.187339
$112$		0			0
$113$	4.68087	+	14.4062i	0.440339	+	1.35522i	0.887515	+	0.460778i	$0.152430\pi$
$113$	4.68087	+	14.4062i	0.440339	+	1.35522i	−0.447176	+	0.894446i	$0.647570\pi$
$114$		0			0
$115$	4.69819	+	3.41344i	0.438109	+	0.318304i
$116$		0			0
$117$	−0.178115	+	0.548183i	−0.0164668	+	0.0506795i
$118$		0			0
$119$	−1.57338	+	1.14313i	−0.144231	+	0.104790i
$120$		0			0
$121$	0.247302	−	10.9972i	0.0224820	−	0.999747i
$122$		0			0
$123$	0.118034	−	0.0857567i	0.0106428	−	0.00773242i
$124$		0			0
$125$	3.05579	−	9.40476i	0.273318	−	0.841187i
$126$		0			0
$127$	−10.5111	−	7.63679i	−0.932712	−	0.677655i	0.0139432	−	0.999903i	$-0.495562\pi$
$127$	−10.5111	−	7.63679i	−0.932712	−	0.677655i	−0.946655	+	0.322248i	$0.895562\pi$
$128$		0			0
$129$	−1.37551	−	4.23339i	−0.121107	−	0.372730i
$130$		0			0
$131$	13.3837			1.16934			0.584669	−	0.811272i	$-0.301225\pi$
$131$	13.3837			1.16934			0.584669	+	0.811272i	$0.301225\pi$
$132$		0			0
$133$	−2.50678			−0.217365
$134$		0			0
$135$	1.68463	+	5.18476i	0.144990	+	0.446233i
$136$		0			0
$137$	4.14537	+	3.01179i	0.354163	+	0.257314i	0.750613	−	0.660742i	$-0.229758\pi$
$137$	4.14537	+	3.01179i	0.354163	+	0.257314i	−0.396450	+	0.918056i	$0.629758\pi$
$138$		0			0
$139$	−3.56660	+	10.9769i	−0.302515	+	0.931045i	0.678078	+	0.734990i	$0.262813\pi$
$139$	−3.56660	+	10.9769i	−0.302515	+	0.931045i	−0.980593	+	0.196055i	$0.937187\pi$
$140$		0			0
$141$	1.06660	−	0.774928i	0.0898237	−	0.0652607i
$142$		0			0
$143$	0.112210	−	0.660336i	0.00938351	−	0.0552200i
$144$		0			0
$145$	0.246183	−	0.178862i	0.0204443	−	0.0148537i
$146$		0			0
$147$	0.118034	−	0.363271i	0.00973528	−	0.0299621i
$148$		0			0
$149$	−2.23633	−	1.62479i	−0.183207	−	0.133108i	0.492401	−	0.870368i	$-0.336119\pi$
$149$	−2.23633	−	1.62479i	−0.183207	−	0.133108i	−0.675609	+	0.737260i	$0.736119\pi$
$150$		0			0
$151$	0.916509	+	2.82072i	0.0745844	+	0.229547i	0.981398	−	0.191985i	$-0.0614925\pi$
$151$	0.916509	+	2.82072i	0.0745844	+	0.229547i	−0.906813	+	0.421532i	$0.861492\pi$
$152$		0			0
$153$	5.55066			0.448744
$154$		0			0
$155$	10.1930			0.818725
$156$		0			0
$157$	4.52426	+	13.9243i	0.361076	+	1.11128i	0.952402	+	0.304844i	$0.0986044\pi$
$157$	4.52426	+	13.9243i	0.361076	+	1.11128i	−0.591327	+	0.806432i	$0.701396\pi$
$158$		0			0
$159$	−1.00652	−	0.731276i	−0.0798219	−	0.0579940i
$160$		0			0
$161$	−0.736068	+	2.26538i	−0.0580103	+	0.178537i
$162$		0			0
$163$	4.13466	−	3.00401i	0.323852	−	0.235292i	−0.413965	−	0.910293i	$-0.635857\pi$
$163$	4.13466	−	3.00401i	0.323852	−	0.235292i	0.737817	+	0.675000i	$0.235857\pi$
$164$		0			0
$165$	−1.37116	−	2.76753i	−0.106745	−	0.215452i
$166$		0			0
$167$	7.25313	−	5.26970i	0.561264	−	0.407782i	−0.270658	−	0.962676i	$-0.587241\pi$
$167$	7.25313	−	5.26970i	0.561264	−	0.407782i	0.831921	+	0.554894i	$0.187241\pi$
$168$		0			0
$169$	−4.00462	+	12.3249i	−0.308048	+	0.948073i
$170$		0			0
$171$	5.78820	+	4.20537i	0.442634	+	0.321593i
$172$		0			0
$173$	6.21917	+	19.1406i	0.472835	+	1.45524i	0.848855	+	0.528625i	$0.177292\pi$
$173$	6.21917	+	19.1406i	0.472835	+	1.45524i	−0.376020	+	0.926611i	$0.622708\pi$
$174$		0			0
$175$	−0.943945			−0.0713556
$176$		0			0
$177$	3.66053			0.275142
$178$		0			0
$179$	7.29212	+	22.4428i	0.545039	+	1.67746i	0.720898	+	0.693042i	$0.243730\pi$
$179$	7.29212	+	22.4428i	0.545039	+	1.67746i	−0.175859	+	0.984415i	$0.556270\pi$
$180$		0			0
$181$	11.0834	+	8.05255i	0.823822	+	0.598542i	0.917805	−	0.397032i	$-0.129960\pi$
$181$	11.0834	+	8.05255i	0.823822	+	0.598542i	−0.0939828	+	0.995574i	$0.529960\pi$
$182$		0			0
$183$	0.817133	−	2.51488i	0.0604042	−	0.185905i
$184$		0			0
$185$	10.1920	−	7.40492i	0.749331	−	0.544421i
$186$		0			0
$187$	−6.38170	+	0.937347i	−0.466676	+	0.0685456i
$188$		0			0
$189$	−1.80902	+	1.31433i	−0.131587	+	0.0956033i
$190$		0			0
$191$	6.28142	−	19.3322i	0.454507	−	1.39883i	−0.417205	−	0.908812i	$-0.636990\pi$
$191$	6.28142	−	19.3322i	0.454507	−	1.39883i	0.871713	−	0.490018i	$-0.163010\pi$
$192$		0			0
$193$	−1.11195	−	0.807876i	−0.0800396	−	0.0581522i	0.547046	−	0.837103i	$-0.315752\pi$
$193$	−1.11195	−	0.807876i	−0.0800396	−	0.0581522i	−0.627085	+	0.778950i	$0.715752\pi$
$194$		0			0
$195$	−0.0581158	−	0.178862i	−0.00416176	−	0.0128086i
$196$		0			0
$197$	−17.5645			−1.25142			−0.625711	−	0.780055i	$-0.715191\pi$
$197$	−17.5645			−1.25142			−0.625711	+	0.780055i	$0.715191\pi$
$198$		0			0
$199$	4.50625			0.319440			0.159720	−	0.987162i	$-0.448941\pi$
$199$	4.50625			0.319440			0.159720	+	0.987162i	$0.448941\pi$
$200$		0			0
$201$	−0.760006	−	2.33906i	−0.0536067	−	0.164984i
$202$		0			0
$203$	0.100976	+	0.0733636i	0.00708715	+	0.00514912i
$204$		0			0
$205$	0.287769	−	0.885663i	0.0200987	−	0.0618574i
$206$		0			0
$207$	5.50000	−	3.99598i	0.382276	−	0.277740i
$208$		0			0
$209$	−7.36497	−	3.85754i	−0.509446	−	0.266831i
$210$		0			0
$211$	12.4739	−	9.06285i	0.858742	−	0.623913i	−0.0688005	−	0.997630i	$-0.521917\pi$
$211$	12.4739	−	9.06285i	0.858742	−	0.623913i	0.927542	+	0.373718i	$0.121917\pi$
$212$		0			0
$213$	1.05176	−	3.23700i	0.0720657	−	0.221795i
$214$		0			0
$215$	−22.9854	−	16.6999i	−1.56759	−	1.13892i
$216$		0			0
$217$	1.29196	+	3.97624i	0.0877039	+	0.269925i
$218$		0			0
$219$	3.20195			0.216368
$220$		0			0
$221$	−0.392758			−0.0264198
$222$		0			0
$223$	−2.93409	−	9.03022i	−0.196482	−	0.604708i	−0.999956	−	0.00936891i	$-0.997018\pi$
$223$	−2.93409	−	9.03022i	−0.196482	−	0.604708i	0.803475	−	0.595339i	$-0.202982\pi$
$224$		0			0
$225$	2.17959	+	1.58356i	0.145306	+	0.105571i
$226$		0			0
$227$	−5.75355	+	17.7076i	−0.381877	+	1.17530i	0.556844	+	0.830617i	$0.312012\pi$
$227$	−5.75355	+	17.7076i	−0.381877	+	1.17530i	−0.938721	+	0.344679i	$0.887988\pi$
$228$		0			0
$229$	−16.4737	+	11.9688i	−1.08861	+	0.790923i	−0.979164	−	0.203070i	$-0.934908\pi$
$229$	−16.4737	+	11.9688i	−1.08861	+	0.790923i	−0.109447	+	0.993993i	$0.534908\pi$
$230$		0			0
$231$	0.905803	−	0.885663i	0.0595975	−	0.0582723i
$232$		0			0
$233$	−0.556747	+	0.404500i	−0.0364737	+	0.0264997i	−0.605873	−	0.795562i	$-0.707176\pi$
$233$	−0.556747	+	0.404500i	−0.0364737	+	0.0264997i	0.569399	+	0.822061i	$0.307176\pi$
$234$		0			0
$235$	2.60039	−	8.00316i	0.169630	−	0.522069i
$236$		0			0
$237$	−0.00635209	−	0.00461506i	−0.000412613	−	0.000299781i
$238$		0			0
$239$	−3.50435	−	10.7853i	−0.226678	−	0.697642i	−0.998117	−	0.0613394i	$-0.980463\pi$
$239$	−3.50435	−	10.7853i	−0.226678	−	0.697642i	0.771439	−	0.636303i	$-0.219537\pi$
$240$		0			0
$241$	−26.9714			−1.73738			−0.868690	−	0.495356i	$-0.835038\pi$
$241$	−26.9714			−1.73738			−0.868690	+	0.495356i	$0.835038\pi$
$242$		0			0
$243$	9.65248			0.619207
$244$		0			0
$245$	−0.753390	−	2.31870i	−0.0481323	−	0.148136i
$246$		0			0
$247$	−0.409566	−	0.297567i	−0.0260600	−	0.0189337i
$248$		0			0
$249$	0.382028	−	1.17576i	0.0242101	−	0.0745109i
$250$		0			0
$251$	−2.79196	+	2.02848i	−0.176227	+	0.128036i	−0.672402	−	0.740186i	$-0.734737\pi$
$251$	−2.79196	+	2.02848i	−0.176227	+	0.128036i	0.496175	+	0.868222i	$0.334737\pi$
$252$		0			0
$253$	−5.64865	+	5.52305i	−0.355128	+	0.347231i
$254$		0			0
$255$	−1.46519	+	1.06452i	−0.0917539	+	0.0666631i
$256$		0			0
$257$	−6.07704	+	18.7032i	−0.379075	+	1.16667i	0.561613	+	0.827400i	$0.310181\pi$
$257$	−6.07704	+	18.7032i	−0.379075	+	1.16667i	−0.940688	+	0.339273i	$0.889819\pi$
$258$		0			0
$259$	4.18044	+	3.03727i	0.259760	+	0.188727i
$260$		0			0
$261$	−0.110081	−	0.338796i	−0.00681387	−	0.0209709i
$262$		0			0
$263$	−3.20895			−0.197872			−0.0989361	−	0.995094i	$-0.531544\pi$
$263$	−3.20895			−0.197872			−0.0989361	+	0.995094i	$0.531544\pi$
$264$		0			0
$265$	−7.94101			−0.487812
$266$		0			0
$267$	1.37385	+	4.22828i	0.0840783	+	0.258766i
$268$		0			0
$269$	−8.27130	−	6.00945i	−0.504310	−	0.366403i	0.306351	−	0.951919i	$-0.400892\pi$
$269$	−8.27130	−	6.00945i	−0.504310	−	0.366403i	−0.810661	+	0.585516i	$0.800892\pi$
$270$		0			0
$271$	9.15978	−	28.1909i	0.556417	−	1.71248i	−0.135754	−	0.990743i	$-0.543346\pi$
$271$	9.15978	−	28.1909i	0.556417	−	1.71248i	0.692171	−	0.721734i	$-0.256654\pi$
$272$		0			0
$273$	0.0624068	−	0.0453412i	0.00377703	−	0.00274418i
$274$		0			0
$275$	−2.77333	−	1.45258i	−0.167238	−	0.0875940i
$276$		0			0
$277$	−7.89267	+	5.73436i	−0.474225	+	0.344544i	−0.799085	−	0.601217i	$-0.794683\pi$
$277$	−7.89267	+	5.73436i	−0.474225	+	0.344544i	0.324861	+	0.945762i	$0.394683\pi$
$278$		0			0
$279$	3.68738	−	11.3486i	0.220758	−	0.679423i
$280$		0			0
$281$	−5.30790	−	3.85641i	−0.316643	−	0.230054i	0.418099	−	0.908402i	$-0.362697\pi$
$281$	−5.30790	−	3.85641i	−0.316643	−	0.230054i	−0.734742	+	0.678347i	$0.762697\pi$
$282$		0			0
$283$	0.857965	+	2.64055i	0.0510007	+	0.156964i	0.973313	−	0.229481i	$-0.0737029\pi$
$283$	0.857965	+	2.64055i	0.0510007	+	0.156964i	−0.922312	+	0.386445i	$0.873703\pi$
$284$		0			0
$285$	−2.33442			−0.138279
$286$		0			0
$287$	0.381966			0.0225467
$288$		0			0
$289$	−4.08451	−	12.5708i	−0.240265	−	0.739460i
$290$		0			0
$291$	−5.47659	−	3.97898i	−0.321043	−	0.233252i
$292$		0			0
$293$	5.30509	−	16.3274i	0.309927	−	0.953856i	−0.667866	−	0.744282i	$-0.732792\pi$
$293$	5.30509	−	16.3274i	0.309927	−	0.953856i	0.977793	−	0.209575i	$-0.0672080\pi$
$294$		0			0
$295$	18.9023	−	13.7333i	1.10053	−	0.799584i
$296$		0			0
$297$	−7.33747	+	1.07773i	−0.425763	+	0.0625363i
$298$		0			0
$299$	−0.389173	+	0.282751i	−0.0225065	+	0.0163519i
$300$		0			0
$301$	3.60114	−	11.0832i	0.207566	−	0.638823i
$302$		0			0
$303$	5.66338	+	4.11469i	0.325353	+	0.236383i
$304$		0			0
$305$	−5.21561	−	16.0520i	−0.298645	−	0.919135i
$306$		0			0
$307$	−1.35623			−0.0774042			−0.0387021	−	0.999251i	$-0.512322\pi$
$307$	−1.35623			−0.0774042			−0.0387021	+	0.999251i	$0.512322\pi$
$308$		0			0
$309$	3.97086			0.225894
$310$		0			0
$311$	−1.31337	−	4.04214i	−0.0744744	−	0.229209i	0.906889	−	0.421370i	$-0.138450\pi$
$311$	−1.31337	−	4.04214i	−0.0744744	−	0.229209i	−0.981363	+	0.192161i	$0.938450\pi$
$312$		0			0
$313$	20.2888	+	14.7407i	1.14679	+	0.833192i	0.988051	−	0.154129i	$-0.0492571\pi$
$313$	20.2888	+	14.7407i	1.14679	+	0.833192i	0.158739	+	0.987321i	$0.449257\pi$
$314$		0			0
$315$	−2.15025	+	6.61779i	−0.121153	+	0.372870i
$316$		0			0
$317$	−9.10071	+	6.61205i	−0.511147	+	0.371370i	−0.813258	−	0.581903i	$-0.802308\pi$
$317$	−9.10071	+	6.61205i	−0.511147	+	0.371370i	0.302112	+	0.953273i	$0.402308\pi$
$318$		0			0
$319$	0.183776	+	0.370931i	0.0102895	+	0.0207681i
$320$		0			0
$321$	−4.53062	+	3.29169i	−0.252874	+	0.183724i
$322$		0			0
$323$	−1.50652	+	4.63658i	−0.0838248	+	0.257986i
$324$		0			0
$325$	−0.154225	−	0.112051i	−0.00855485	−	0.00621547i
$326$		0			0
$327$	−1.92875	−	5.93609i	−0.106660	−	0.328266i
$328$		0			0
$329$	3.45158			0.190292
$330$		0			0
$331$	−5.00700			−0.275209			−0.137605	−	0.990487i	$-0.543940\pi$
$331$	−5.00700			−0.275209			−0.137605	+	0.990487i	$0.543940\pi$
$332$		0			0
$333$	−4.55739	−	14.0262i	−0.249743	−	0.768631i
$334$		0			0
$335$	−12.7000	−	9.22712i	−0.693877	−	0.504131i
$336$		0			0
$337$	5.62641	−	17.3163i	0.306490	−	0.943280i	−0.672627	−	0.739982i	$-0.734834\pi$
$337$	5.62641	−	17.3163i	0.306490	−	0.943280i	0.979117	−	0.203298i	$-0.0651661\pi$
$338$		0			0
$339$	−4.68087	+	3.40085i	−0.254230	+	0.184709i
$340$		0			0
$341$	−2.32300	+	13.6704i	−0.125798	+	0.740294i
$342$		0			0
$343$	0.809017	−	0.587785i	0.0436828	−	0.0317374i
$344$		0			0
$345$	−0.685457	+	2.10962i	−0.0369037	+	0.113578i
$346$		0			0
$347$	21.8902	+	15.9042i	1.17513	+	0.853780i	0.991614	−	0.129237i	$-0.0412529\pi$
$347$	21.8902	+	15.9042i	1.17513	+	0.853780i	0.183513	+	0.983017i	$0.441253\pi$
$348$		0			0
$349$	10.0657	+	30.9790i	0.538804	+	1.65827i	0.735283	+	0.677760i	$0.237049\pi$
$349$	10.0657	+	30.9790i	0.538804	+	1.65827i	−0.196479	+	0.980508i	$0.562951\pi$
$350$		0			0
$351$	−0.451580			−0.0241036
$352$		0			0
$353$	−27.9937			−1.48995			−0.744976	−	0.667091i	$-0.767539\pi$
$353$	−27.9937			−1.48995			−0.744976	+	0.667091i	$0.767539\pi$
$354$		0			0
$355$	−6.71322	−	20.6612i	−0.356301	−	1.09658i
$356$		0			0
$357$	−0.600976	−	0.436635i	−0.0318070	−	0.0231092i
$358$		0			0
$359$	−7.71885	+	23.7562i	−0.407385	+	1.25380i	0.511502	+	0.859282i	$0.329089\pi$
$359$	−7.71885	+	23.7562i	−0.407385	+	1.25380i	−0.918887	+	0.394521i	$0.870911\pi$
$360$		0			0
$361$	10.2875	−	7.47431i	0.541448	−	0.393385i
$362$		0			0
$363$	4.02416	−	1.20821i	0.211214	−	0.0634145i
$364$		0			0
$365$	16.5343	−	12.0129i	0.865444	−	0.628782i
$366$		0			0
$367$	−2.30133	+	7.08276i	−0.120128	+	0.369717i	−0.992982	−	0.118265i	$-0.962267\pi$
$367$	−2.30133	+	7.08276i	−0.120128	+	0.369717i	0.872854	+	0.487982i	$0.162267\pi$
$368$		0			0
$369$	−0.881966	−	0.640786i	−0.0459133	−	0.0333580i
$370$		0			0
$371$	−1.00652	−	3.09774i	−0.0522557	−	0.160826i
$372$		0			0
$373$	−25.8550			−1.33872			−0.669359	−	0.742939i	$-0.733431\pi$
$373$	−25.8550			−1.33872			−0.669359	+	0.742939i	$0.733431\pi$
$374$		0			0
$375$	3.77716			0.195052
$376$		0			0
$377$	0.00778923	+	0.0239728i	0.000401166	+	0.00123466i
$378$		0			0
$379$	3.19253	+	2.31951i	0.163989	+	0.119145i	0.666753	−	0.745279i	$-0.267684\pi$
$379$	3.19253	+	2.31951i	0.163989	+	0.119145i	−0.502764	+	0.864424i	$0.667684\pi$
$380$		0			0
$381$	1.53355	−	4.71979i	0.0785663	−	0.241802i
$382$		0			0
$383$	−17.3437	+	12.6010i	−0.886223	+	0.643879i	−0.934890	−	0.354936i	$-0.884503\pi$
$383$	−17.3437	+	12.6010i	−0.886223	+	0.643879i	0.0486676	+	0.998815i	$0.484503\pi$
$384$		0			0
$385$	1.35463	−	7.97172i	0.0690384	−	0.406277i
$386$		0			0
$387$	−26.9082	+	19.5500i	−1.36782	+	0.993780i
$388$		0			0
$389$	7.69301	−	23.6767i	0.390051	−	1.20045i	−0.542698	−	0.839928i	$-0.682597\pi$
$389$	7.69301	−	23.6767i	0.390051	−	1.20045i	0.932749	−	0.360526i	$-0.117403\pi$
$390$		0			0
$391$	3.74773	+	2.72288i	0.189531	+	0.137702i
$392$		0			0
$393$	1.57973	+	4.86191i	0.0796868	+	0.245251i
$394$		0			0
$395$	−0.0501155			−0.00252158
$396$		0			0
$397$	13.2355			0.664273			0.332136	−	0.943231i	$-0.392231\pi$
$397$	13.2355			0.664273			0.332136	+	0.943231i	$0.392231\pi$
$398$		0			0
$399$	−0.295885	−	0.910641i	−0.0148128	−	0.0455891i
$400$		0			0
$401$	5.55186	+	4.03367i	0.277247	+	0.201432i	0.717716	−	0.696336i	$-0.245188\pi$
$401$	5.55186	+	4.03367i	0.277247	+	0.201432i	−0.440469	+	0.897768i	$0.645188\pi$
$402$		0			0
$403$	−0.260915	+	0.803013i	−0.0129971	+	0.0400009i
$404$		0			0
$405$	15.2037	−	11.0461i	0.755476	−	0.548886i
$406$		0			0
$407$	7.60835	+	15.3566i	0.377132	+	0.761198i
$408$		0			0
$409$	−16.7650	+	12.1804i	−0.828973	+	0.602284i	−0.919269	−	0.393631i	$-0.871219\pi$
$409$	−16.7650	+	12.1804i	−0.828973	+	0.602284i	0.0902953	+	0.995915i	$0.471219\pi$
$410$		0			0
$411$	−0.604801	+	1.86139i	−0.0298326	+	0.0918154i
$412$		0			0
$413$	7.75313	+	5.63298i	0.381506	+	0.277181i
$414$		0			0
$415$	−2.43842	−	7.50468i	−0.119697	−	0.368390i
$416$		0			0
$417$	−4.40856			−0.215888
$418$		0			0
$419$	30.7108			1.50032			0.750160	−	0.661257i	$-0.229977\pi$
$419$	30.7108			1.50032			0.750160	+	0.661257i	$0.229977\pi$
$420$		0			0
$421$	−5.84975	−	18.0037i	−0.285099	−	0.877445i	−0.986369	−	0.164549i	$-0.947383\pi$
$421$	−5.84975	−	18.0037i	−0.285099	−	0.877445i	0.701270	−	0.712896i	$-0.252617\pi$
$422$		0			0
$423$	−7.96976	−	5.79037i	−0.387503	−	0.281537i
$424$		0			0
$425$	−0.567289	+	1.74594i	−0.0275175	+	0.0846903i
$426$		0			0
$427$	5.60071	−	4.06916i	0.271037	−	0.196920i
$428$		0			0
$429$	0.253126	−	0.0371792i	0.0122210	−	0.00179503i
$430$		0			0
$431$	2.08365	−	1.51386i	0.100366	−	0.0729202i	−0.536470	−	0.843919i	$-0.680243\pi$
$431$	2.08365	−	1.51386i	0.100366	−	0.0729202i	0.636836	+	0.770999i	$0.280243\pi$
$432$		0			0
$433$	−10.6955	+	32.9174i	−0.513993	+	1.58191i	0.271114	+	0.962547i	$0.412608\pi$
$433$	−10.6955	+	32.9174i	−0.513993	+	1.58191i	−0.785107	+	0.619360i	$0.787392\pi$
$434$		0			0
$435$	0.0940334	+	0.0683192i	0.00450855	+	0.00327566i
$436$		0			0
$437$	1.84516	+	5.67882i	0.0882660	+	0.271655i
$438$		0			0
$439$	37.1760			1.77431			0.887157	−	0.461467i	$-0.152677\pi$
$439$	37.1760			1.77431			0.887157	+	0.461467i	$0.152677\pi$
$440$		0			0
$441$	−2.85410			−0.135910
$442$		0			0
$443$	7.51319	+	23.1232i	0.356963	+	1.09862i	0.954863	+	0.297047i	$0.0960019\pi$
$443$	7.51319	+	23.1232i	0.356963	+	1.09862i	−0.597900	+	0.801571i	$0.703998\pi$
$444$		0			0
$445$	22.9576	+	16.6797i	1.08830	+	0.790694i
$446$		0			0
$447$	0.326276	−	1.00418i	0.0154323	−	0.0474959i
$448$		0			0
$449$	−8.01706	+	5.82473i	−0.378348	+	0.274886i	−0.760664	−	0.649146i	$-0.775127\pi$
$449$	−8.01706	+	5.82473i	−0.378348	+	0.274886i	0.382316	+	0.924032i	$0.375127\pi$
$450$		0			0
$451$	1.12222	+	0.587785i	0.0528435	+	0.0276777i
$452$		0			0
$453$	−0.916509	+	0.665883i	−0.0430613	+	0.0312859i
$454$		0			0
$455$	0.152149	−	0.468267i	0.00713286	−	0.0219527i
$456$		0			0
$457$	30.2829	+	22.0018i	1.41657	+	1.02920i	0.992325	+	0.123654i	$0.0394612\pi$
$457$	30.2829	+	22.0018i	1.41657	+	1.02920i	0.424247	+	0.905546i	$0.360539\pi$
$458$		0			0
$459$	1.34382	+	4.13587i	0.0627243	+	0.193046i
$460$		0			0
$461$	26.0362			1.21262			0.606312	−	0.795227i	$-0.292648\pi$
$461$	26.0362			1.21262			0.606312	+	0.795227i	$0.292648\pi$
$462$		0			0
$463$	20.9462			0.973452			0.486726	−	0.873555i	$-0.338191\pi$
$463$	20.9462			0.973452			0.486726	+	0.873555i	$0.338191\pi$
$464$		0			0
$465$	1.20313	+	3.70284i	0.0557936	+	0.171715i
$466$		0			0
$467$	−19.0262	−	13.8234i	−0.880429	−	0.639669i	0.0529357	−	0.998598i	$-0.483142\pi$
$467$	−19.0262	−	13.8234i	−0.880429	−	0.639669i	−0.933365	+	0.358929i	$0.883142\pi$
$468$		0			0
$469$	1.98972	−	6.12373i	0.0918768	−	0.282768i
$470$		0			0
$471$	−4.52426	+	3.28707i	−0.208467	+	0.151460i
$472$		0			0
$473$	27.6355	−	27.0210i	1.27068	−	1.24243i
$474$		0			0
$475$	−1.91435	+	1.39085i	−0.0878363	+	0.0638168i
$476$		0			0
$477$	−2.87270	+	8.84125i	−0.131532	+	0.404813i
$478$		0			0
$479$	4.25243	+	3.08957i	0.194299	+	0.141166i	0.680681	−	0.732580i	$-0.261684\pi$
$479$	4.25243	+	3.08957i	0.194299	+	0.141166i	−0.486383	+	0.873746i	$0.661684\pi$
$480$		0			0
$481$	0.322475	+	0.992477i	0.0147036	+	0.0452531i
$482$		0			0
$483$	−0.909830			−0.0413987
$484$		0			0
$485$	−43.2081			−1.96198
$486$		0			0
$487$	6.87631	+	21.1631i	0.311595	+	0.958991i	0.977133	+	0.212627i	$0.0682021\pi$
$487$	6.87631	+	21.1631i	0.311595	+	0.958991i	−0.665538	+	0.746364i	$0.731798\pi$
$488$		0			0
$489$	1.57930	+	1.14743i	0.0714185	+	0.0518886i
$490$		0			0
$491$	1.90607	−	5.86627i	0.0860196	−	0.264741i	−0.898790	−	0.438380i	$-0.855552\pi$
$491$	1.90607	−	5.86627i	0.0860196	−	0.264741i	0.984809	+	0.173639i	$0.0555525\pi$
$492$		0			0
$493$	0.196379	−	0.142678i	0.00884446	−	0.00642588i
$494$		0			0
$495$	−16.5012	+	16.1343i	−0.741675	+	0.725184i
$496$		0			0
$497$	7.20890	−	5.23757i	0.323363	−	0.234937i
$498$		0			0
$499$	0.0683313	−	0.210302i	0.00305893	−	0.00941442i	−0.949515	−	0.313720i	$-0.898425\pi$
$499$	0.0683313	−	0.210302i	0.00305893	−	0.00941442i	0.952574	+	0.304306i	$0.0984245\pi$
$500$		0			0
$501$	2.77045	+	2.01285i	0.123774	+	0.0899274i
$502$		0			0
$503$	−2.48580	−	7.65049i	−0.110836	−	0.341119i	0.880220	−	0.474566i	$-0.157395\pi$
$503$	−2.48580	−	7.65049i	−0.110836	−	0.341119i	−0.991056	+	0.133448i	$0.957395\pi$
$504$		0			0
$505$	44.6818			1.98832
$506$		0			0
$507$	−4.94998			−0.219836
$508$		0			0
$509$	0.384719	+	1.18404i	0.0170524	+	0.0524818i	0.959221	−	0.282658i	$-0.0912163\pi$
$509$	0.384719	+	1.18404i	0.0170524	+	0.0524818i	−0.942168	+	0.335140i	$0.891216\pi$
$510$		0			0
$511$	6.78184	+	4.92730i	0.300011	+	0.217971i
$512$		0			0
$513$	−1.73214	+	5.33099i	−0.0764759	+	0.235369i
$514$		0			0
$515$	20.5048	−	14.8976i	0.903549	−	0.656466i
$516$		0			0
$517$	10.1408	+	5.31144i	0.445992	+	0.233597i
$518$		0			0
$519$	−6.21917	+	4.51849i	−0.272991	+	0.198340i
$520$		0			0
$521$	−5.55186	+	17.0869i	−0.243232	+	0.748590i	0.752691	+	0.658374i	$0.228756\pi$
$521$	−5.55186	+	17.0869i	−0.243232	+	0.748590i	−0.995922	+	0.0902156i	$0.971244\pi$
$522$		0			0
$523$	−27.3329	−	19.8585i	−1.19518	−	0.868353i	−0.201382	−	0.979513i	$-0.564543\pi$
$523$	−27.3329	−	19.8585i	−1.19518	−	0.868353i	−0.993803	+	0.111160i	$0.964543\pi$
$524$		0			0
$525$	−0.111418	−	0.342908i	−0.00486266	−	0.0149657i
$526$		0			0
$527$	8.13095			0.354190
$528$		0			0
$529$	−17.3262			−0.753315
$530$		0			0
$531$	−8.45222	−	26.0133i	−0.366795	−	1.12888i
$532$		0			0
$533$	0.0624068	+	0.0453412i	0.00270314	+	0.00196395i
$534$		0			0
$535$	−11.0457	+	33.9953i	−0.477549	+	1.46974i
$536$		0			0
$537$	−7.29212	+	5.29804i	−0.314678	+	0.228627i
$538$		0			0
$539$	3.28142	−	0.481976i	0.141341	−	0.0207602i
$540$		0			0
$541$	26.3013	−	19.1090i	1.13078	−	0.821561i	0.144973	−	0.989436i	$-0.453690\pi$
$541$	26.3013	−	19.1090i	1.13078	−	0.821561i	0.985808	+	0.167875i	$0.0536904\pi$
$542$		0			0
$543$	−1.61704	+	4.97675i	−0.0693940	+	0.213573i
$544$		0			0
$545$	−32.2303	−	23.4167i	−1.38059	−	1.00306i
$546$		0			0
$547$	−10.6075	−	32.6465i	−0.453544	−	1.39586i	−0.872837	−	0.488013i	$-0.837722\pi$
$547$	−10.6075	−	32.6465i	−0.453544	−	1.39586i	0.419293	−	0.907851i	$-0.362278\pi$
$548$		0			0
$549$	−19.7586			−0.843274
$550$		0			0
$551$	0.312880			0.0133292
$552$		0			0
$553$	−0.00635209	−	0.0195497i	−0.000270118	−	0.000831339i
$554$		0			0
$555$	3.89300	+	2.82843i	0.165249	+	0.120060i
$556$		0			0
$557$	−2.73692	+	8.42338i	−0.115967	+	0.356910i	−0.992148	−	0.125073i	$-0.960083\pi$
$557$	−2.73692	+	8.42338i	−0.115967	+	0.356910i	0.876180	+	0.481983i	$0.160083\pi$
$558$		0			0
$559$	1.90399	−	1.38333i	0.0805303	−	0.0585087i
$560$		0			0
$561$	−1.09377	−	2.20765i	−0.0461790	−	0.0932071i
$562$		0			0
$563$	−22.3713	+	16.2537i	−0.942839	+	0.685013i	−0.949102	−	0.314968i	$-0.898006\pi$
$563$	−22.3713	+	16.2537i	−0.942839	+	0.685013i	0.00626349	+	0.999980i	$0.498006\pi$
$564$		0			0
$565$	−11.4121	+	35.1227i	−0.480109	+	1.47762i
$566$		0			0
$567$	6.23607	+	4.53077i	0.261890	+	0.190274i
$568$		0			0
$569$	−8.15837	−	25.1089i	−0.342017	−	1.05262i	−0.963162	−	0.268923i	$-0.913332\pi$
$569$	−8.15837	−	25.1089i	−0.342017	−	1.05262i	0.621145	−	0.783696i	$-0.286668\pi$
$570$		0			0
$571$	10.6669			0.446395			0.223198	−	0.974773i	$-0.428350\pi$
$571$	10.6669			0.446395			0.223198	+	0.974773i	$0.428350\pi$
$572$		0			0
$573$	7.76426			0.324357
$574$		0			0
$575$	0.694808	+	2.13840i	0.0289755	+	0.0891774i
$576$		0			0
$577$	−1.11221	−	0.808068i	−0.0463019	−	0.0336403i	0.564394	−	0.825506i	$-0.309110\pi$
$577$	−1.11221	−	0.808068i	−0.0463019	−	0.0336403i	−0.610696	+	0.791866i	$0.709110\pi$
$578$		0			0
$579$	0.162231	−	0.499295i	0.00674208	−	0.0207500i
$580$		0			0
$581$	2.61846	−	1.90242i	0.108632	−	0.0789258i
$582$		0			0
$583$	1.80976	−	10.6501i	0.0749527	−	0.441081i
$584$		0			0
$585$	−1.13688	+	0.825991i	−0.0470042	+	0.0341505i
$586$		0			0
$587$	−5.49565	+	16.9139i	−0.226830	+	0.698110i	0.771271	+	0.636507i	$0.219621\pi$
$587$	−5.49565	+	16.9139i	−0.226830	+	0.698110i	−0.998101	+	0.0616030i	$0.980379\pi$
$588$		0			0
$589$	8.47892	+	6.16029i	0.349368	+	0.253830i
$590$		0			0
$591$	−2.07321	−	6.38069i	−0.0852806	−	0.262467i
$592$		0			0
$593$	23.7073			0.973544			0.486772	−	0.873529i	$-0.338174\pi$
$593$	23.7073			0.973544			0.486772	+	0.873529i	$0.338174\pi$
$594$		0			0
$595$	−4.74146			−0.194381
$596$		0			0
$597$	0.531891	+	1.63699i	0.0217688	+	0.0669976i
$598$		0			0
$599$	−32.6437	−	23.7171i	−1.33379	−	0.969053i	−0.999648	−	0.0265294i	$-0.991554\pi$
$599$	−32.6437	−	23.7171i	−1.33379	−	0.969053i	−0.334139	−	0.942524i	$-0.608446\pi$
$600$		0			0
$601$	1.73358	−	5.33541i	0.0707142	−	0.217636i	−0.909454	−	0.415806i	$-0.863500\pi$
$601$	1.73358	−	5.33541i	0.0707142	−	0.217636i	0.980168	+	0.198170i	$0.0634997\pi$
$602$		0			0
$603$	−14.8675	+	10.8019i	−0.605450	+	0.439885i
$604$		0			0
$605$	16.2472	−	21.3365i	0.660541	−	0.867453i
$606$		0			0
$607$	−2.05424	+	1.49250i	−0.0833792	+	0.0605785i	−0.628694	−	0.777653i	$-0.716410\pi$
$607$	−2.05424	+	1.49250i	−0.0833792	+	0.0605785i	0.545315	+	0.838231i	$0.316410\pi$
$608$		0			0
$609$	−0.0147323	+	0.0453412i	−0.000596981	+	0.00183732i
$610$		0			0
$611$	0.563930	+	0.409719i	0.0228142	+	0.0165755i
$612$		0			0
$613$	1.67249	+	5.14739i	0.0675512	+	0.207901i	0.979134	−	0.203215i	$-0.0651391\pi$
$613$	1.67249	+	5.14739i	0.0675512	+	0.207901i	−0.911583	+	0.411116i	$0.865139\pi$
$614$		0			0
$615$	0.355702			0.0143433
$616$		0			0
$617$	−6.36926			−0.256417			−0.128208	−	0.991747i	$-0.540923\pi$
$617$	−6.36926			−0.256417			−0.128208	+	0.991747i	$0.540923\pi$
$618$		0			0
$619$	−0.767694	−	2.36272i	−0.0308562	−	0.0949658i	0.934442	−	0.356115i	$-0.115899\pi$
$619$	−0.767694	−	2.36272i	−0.0308562	−	0.0949658i	−0.965299	+	0.261149i	$0.915899\pi$
$620$		0			0
$621$	4.30902	+	3.13068i	0.172915	+	0.125630i
$622$		0			0
$623$	−3.59679	+	11.0698i	−0.144102	+	0.443501i
$624$		0			0
$625$	23.3229	−	16.9451i	0.932916	−	0.677803i
$626$		0			0
$627$	0.532016	−	3.13080i	0.0212467	−	0.125032i
$628$		0			0
$629$	8.13012	−	5.90688i	0.324169	−	0.235523i
$630$		0			0
$631$	2.99391	−	9.21431i	0.119186	−	0.366816i	−0.873611	−	0.486624i	$-0.838228\pi$
$631$	2.99391	−	9.21431i	0.119186	−	0.366816i	0.992797	+	0.119808i	$0.0382280\pi$
$632$		0			0
$633$	4.76462	+	3.46170i	0.189377	+	0.137590i
$634$		0			0
$635$	−9.78840	−	30.1256i	−0.388441	−	1.19550i
$636$		0			0
$637$	0.201953			0.00800166
$638$		0			0
$639$	−25.4320			−1.00607
$640$		0			0
$641$	−5.20932	−	16.0326i	−0.205756	−	0.633252i	−0.999682	−	0.0252366i	$-0.991966\pi$
$641$	−5.20932	−	16.0326i	−0.205756	−	0.633252i	0.793926	−	0.608015i	$-0.208034\pi$
$642$		0			0
$643$	−24.3860	−	17.7175i	−0.961690	−	0.698709i	−0.00814740	−	0.999967i	$-0.502593\pi$
$643$	−24.3860	−	17.7175i	−0.961690	−	0.698709i	−0.953543	+	0.301258i	$0.902593\pi$
$644$		0			0
$645$	3.35353	−	10.3211i	0.132045	−	0.406393i
$646$		0			0
$647$	−30.8952	+	22.4467i	−1.21462	+	0.882471i	−0.995642	−	0.0932594i	$-0.970271\pi$
$647$	−30.8952	+	22.4467i	−1.21462	+	0.882471i	−0.218975	+	0.975730i	$0.570271\pi$
$648$		0			0
$649$	14.1106	+	28.4806i	0.553889	+	1.11796i
$650$		0			0
$651$	−1.29196	+	0.938663i	−0.0506359	+	0.0367891i
$652$		0			0
$653$	2.67668	−	8.23797i	0.104747	−	0.322377i	−0.884924	−	0.465735i	$-0.845790\pi$
$653$	2.67668	−	8.23797i	0.104747	−	0.322377i	0.989671	+	0.143358i	$0.0457901\pi$
$654$		0			0
$655$	26.3980	+	19.1792i	1.03145	+	0.749395i
$656$		0			0
$657$	−7.39336	−	22.7544i	−0.288443	−	0.887735i
$658$		0			0
$659$	27.9373			1.08828			0.544141	−	0.838994i	$-0.316856\pi$
$659$	27.9373			1.08828			0.544141	+	0.838994i	$0.316856\pi$
$660$		0			0
$661$	−31.1601			−1.21199			−0.605994	−	0.795469i	$-0.707224\pi$
$661$	−31.1601			−1.21199			−0.605994	+	0.795469i	$0.707224\pi$
$662$		0			0
$663$	−0.0463588	−	0.142678i	−0.00180043	−	0.00554114i
$664$		0			0
$665$	−4.94437	−	3.59230i	−0.191735	−	0.139303i
$666$		0			0
$667$	0.0918714	−	0.282751i	0.00355727	−	0.0109482i
$668$		0			0
$669$	2.93409	−	2.13174i	0.113439	−	0.0824180i
$670$		0			0
$671$	22.7168	−	3.33665i	0.876972	−	0.128810i
$672$		0			0
$673$	16.8304	−	12.2280i	0.648765	−	0.471356i	−0.214085	−	0.976815i	$-0.568677\pi$
$673$	16.8304	−	12.2280i	0.648765	−	0.471356i	0.862850	+	0.505459i	$0.168677\pi$
$674$		0			0
$675$	−0.652250	+	2.00742i	−0.0251051	+	0.0772656i
$676$		0			0
$677$	−33.6129	−	24.4212i	−1.29185	−	0.938582i	−0.292006	−	0.956416i	$-0.594323\pi$
$677$	−33.6129	−	24.4212i	−1.29185	−	0.938582i	−0.999841	+	0.0178344i	$0.994323\pi$
$678$		0			0
$679$	−5.47659	−	16.8552i	−0.210172	−	0.646844i
$680$		0			0
$681$	−7.11178			−0.272524
$682$		0			0
$683$	−36.9041			−1.41210			−0.706049	−	0.708163i	$-0.749524\pi$
$683$	−36.9041			−1.41210			−0.706049	+	0.708163i	$0.749524\pi$
$684$		0			0
$685$	3.86034	+	11.8809i	0.147496	+	0.453946i
$686$		0			0
$687$	−6.29239	−	4.57169i	−0.240070	−	0.174421i
$688$		0			0
$689$	0.203269	−	0.625596i	0.00774392	−	0.0238333i
$690$		0			0
$691$	5.84983	−	4.25015i	0.222538	−	0.161683i	−0.470930	−	0.882170i	$-0.656082\pi$
$691$	5.84983	−	4.25015i	0.222538	−	0.161683i	0.693468	+	0.720487i	$0.256082\pi$
$692$		0			0
$693$	−8.38541	−	4.39201i	−0.318535	−	0.166839i
$694$		0			0
$695$	−22.7650	+	16.5397i	−0.863524	+	0.627387i
$696$		0			0
$697$	0.229553	−	0.706490i	0.00869492	−	0.0267602i
$698$		0			0
$699$	−0.212658	−	0.154505i	−0.00804348	−	0.00584393i
$700$		0			0
$701$	5.18765	+	15.9659i	0.195935	+	0.603025i	0.999964	+	0.00843600i	$0.00268529\pi$
$701$	5.18765	+	15.9659i	0.195935	+	0.603025i	−0.804030	+	0.594589i	$0.797315\pi$
$702$		0			0
$703$	12.9533			0.488543
$704$		0			0
$705$	3.21425			0.121056
$706$		0			0
$707$	5.66338	+	17.4301i	0.212993	+	0.655526i
$708$		0			0
$709$	−25.7177	−	18.6850i	−0.965847	−	0.701729i	−0.0113454	−	0.999936i	$-0.503611\pi$
$709$	−25.7177	−	18.6850i	−0.965847	−	0.701729i	−0.954501	+	0.298207i	$0.903611\pi$
$710$		0			0
$711$	−0.0181295	+	0.0557969i	−0.000679910	+	0.00209255i
$712$		0			0
$713$	8.05675	−	5.85357i	0.301728	−	0.219218i
$714$		0			0
$715$	1.16761	−	1.14164i	0.0436660	−	0.0426951i
$716$		0			0
$717$	3.50435	−	2.54606i	0.130872	−	0.0950844i
$718$		0			0
$719$	−15.3122	+	47.1261i	−0.571049	+	1.75751i	0.0782076	+	0.996937i	$0.475080\pi$
$719$	−15.3122	+	47.1261i	−0.571049	+	1.75751i	−0.649256	+	0.760570i	$0.724920\pi$
$720$		0			0
$721$	8.41042	+	6.11053i	0.313220	+	0.227568i
$722$		0			0
$723$	−3.18354	−	9.79793i	−0.118397	−	0.364389i
$724$		0			0
$725$	0.117817			0.00437562
$726$		0			0
$727$	15.8541			0.587996			0.293998	−	0.955806i	$-0.405014\pi$
$727$	15.8541			0.587996			0.293998	+	0.955806i	$0.405014\pi$
$728$		0			0
$729$	−6.00658	−	18.4863i	−0.222466	−	0.684679i
$730$		0			0
$731$	−18.3354	−	13.3214i	−0.678159	−	0.492711i
$732$		0			0
$733$	12.1247	−	37.3160i	0.447836	−	1.37830i	−0.431506	−	0.902110i	$-0.642018\pi$
$733$	12.1247	−	37.3160i	0.447836	−	1.37830i	0.879343	−	0.476189i	$-0.157982\pi$
$734$		0			0
$735$	0.753390	−	0.547370i	0.0277892	−	0.0201900i
$736$		0			0
$737$	15.2693	−	14.9298i	0.562452	−	0.549946i
$738$		0			0
$739$	−31.8623	+	23.1493i	−1.17207	+	0.851562i	−0.991256	−	0.131954i	$-0.957875\pi$
$739$	−31.8623	+	23.1493i	−1.17207	+	0.851562i	−0.180819	+	0.983516i	$0.557875\pi$
$740$		0			0
$741$	0.0597548	−	0.183906i	0.00219515	−	0.00675597i
$742$		0			0
$743$	−14.2286	−	10.3377i	−0.521997	−	0.379253i	0.295359	−	0.955386i	$-0.404561\pi$
$743$	−14.2286	−	10.3377i	−0.521997	−	0.379253i	−0.817356	+	0.576134i	$0.804561\pi$
$744$		0			0
$745$	−2.08256	−	6.40947i	−0.0762993	−	0.234825i
$746$		0			0
$747$	−9.23758			−0.337985
$748$		0			0
$749$	−14.6614			−0.535715
$750$		0			0
$751$	−3.85610	−	11.8679i	−0.140711	−	0.433064i	0.855723	−	0.517433i	$-0.173112\pi$
$751$	−3.85610	−	11.8679i	−0.140711	−	0.433064i	−0.996435	+	0.0843692i	$0.973112\pi$
$752$		0			0
$753$	−1.06643	−	0.774809i	−0.0388630	−	0.0282356i
$754$		0			0
$755$	−2.23447	+	6.87698i	−0.0813206	+	0.250279i
$756$		0			0
$757$	−32.8166	+	23.8426i	−1.19274	+	0.866575i	−0.993551	−	0.113387i	$-0.963830\pi$
$757$	−32.8166	+	23.8426i	−1.19274	+	0.866575i	−0.199187	+	0.979962i	$0.563830\pi$
$758$		0			0
$759$	−2.67310	−	1.40008i	−0.0970274	−	0.0508198i
$760$		0			0
$761$	36.2560	−	26.3416i	1.31428	−	0.954881i	0.314296	−	0.949325i	$-0.398232\pi$
$761$	36.2560	−	26.3416i	1.31428	−	0.954881i	0.999985	−	0.00555561i	$-0.00176841\pi$
$762$		0			0
$763$	5.04954	−	15.5409i	0.182806	−	0.562618i
$764$		0			0
$765$	10.9481	+	7.95428i	0.395830	+	0.287587i
$766$		0			0
$767$	0.598069	+	1.84067i	0.0215950	+	0.0664627i
$768$		0			0
$769$	−13.1658			−0.474769			−0.237385	−	0.971416i	$-0.576290\pi$
$769$	−13.1658			−0.474769			−0.237385	+	0.971416i	$0.576290\pi$
$770$		0			0
$771$	−7.51163			−0.270525
$772$		0			0
$773$	1.85135	+	5.69787i	0.0665884	+	0.204938i	0.978814	−	0.204749i	$-0.0656379\pi$
$773$	1.85135	+	5.69787i	0.0665884	+	0.204938i	−0.912226	+	0.409687i	$0.865638\pi$
$774$		0			0
$775$	3.19279	+	2.31970i	0.114689	+	0.0833261i
$776$		0			0
$777$	−0.609918	+	1.87713i	−0.0218807	+	0.0673418i
$778$		0			0
$779$	0.774638	−	0.562807i	0.0277543	−	0.0201647i
$780$		0			0
$781$	29.2397	−	4.29474i	1.04628	−	0.153678i
$782$		0			0
$783$	0.225790	−	0.164046i	0.00806908	−	0.00586253i
$784$		0			0
$785$	−11.0303	+	33.9476i	−0.393687	+	1.21164i
$786$		0			0
$787$	28.5103	+	20.7140i	1.01628	+	0.738373i	0.965518	−	0.260337i	$-0.0838337\pi$
$787$	28.5103	+	20.7140i	1.01628	+	0.738373i	0.0507661	+	0.998711i	$0.483834\pi$
$788$		0			0
$789$	−0.378765	−	1.16572i	−0.0134844	−	0.0415007i
$790$		0			0
$791$	−15.1476			−0.538587
$792$		0			0
$793$	1.39809			0.0496477
$794$		0			0
$795$	−0.937308	−	2.88474i	−0.0332429	−	0.102311i
$796$		0			0
$797$	9.92860	+	7.21355i	0.351689	+	0.255517i	0.749577	−	0.661917i	$-0.230257\pi$
$797$	9.92860	+	7.21355i	0.351689	+	0.255517i	−0.397888	+	0.917434i	$0.630257\pi$
$798$		0			0
$799$	2.07432	−	6.38409i	0.0733841	−	0.225853i
$800$		0			0
$801$	26.8757	−	19.5263i	0.949605	−	0.689929i
$802$		0			0
$803$	12.3429	+	24.9127i	0.435570	+	0.879150i
$804$		0			0
$805$	−4.69819	+	3.41344i	−0.165589	+	0.120308i
$806$		0			0
$807$	1.20677	−	3.71405i	0.0424802	−	0.130741i
$808$		0			0
$809$	−8.11539	−	5.89618i	−0.285322	−	0.207299i	0.435913	−	0.899989i	$-0.356425\pi$
$809$	−8.11539	−	5.89618i	−0.285322	−	0.207299i	−0.721235	+	0.692690i	$0.756425\pi$
$810$		0			0
$811$	−0.0736409	−	0.226643i	−0.00258588	−	0.00795853i	0.949755	−	0.312994i	$-0.101332\pi$
$811$	−0.0736409	−	0.226643i	−0.00258588	−	0.00795853i	−0.952341	+	0.305035i	$0.901332\pi$
$812$		0			0
$813$	11.3221			0.397084
$814$		0			0
$815$	12.4601			0.436457
$816$		0			0
$817$	−9.02726	−	27.7831i	−0.315824	−	0.972006i
$818$		0			0
$819$	−0.466312	−	0.338796i	−0.0162943	−	0.0118385i
$820$		0			0
$821$	−6.28793	+	19.3523i	−0.219450	+	0.675399i	0.779357	+	0.626580i	$0.215546\pi$
$821$	−6.28793	+	19.3523i	−0.219450	+	0.675399i	−0.998808	+	0.0488190i	$0.984454\pi$
$822$		0			0
$823$	10.3092	−	7.49006i	0.359355	−	0.261087i	−0.393428	−	0.919356i	$-0.628711\pi$
$823$	10.3092	−	7.49006i	0.359355	−	0.261087i	0.752783	+	0.658269i	$0.228711\pi$
$824$		0			0
$825$	0.200334	−	1.17893i	0.00697474	−	0.0410449i
$826$		0			0
$827$	−16.4003	+	11.9155i	−0.570295	+	0.414343i	−0.835212	−	0.549928i	$-0.814655\pi$
$827$	−16.4003	+	11.9155i	−0.570295	+	0.414343i	0.264918	+	0.964271i	$0.414655\pi$
$828$		0			0
$829$	5.79105	−	17.8230i	0.201132	−	0.619019i	−0.798719	−	0.601705i	$-0.794488\pi$
$829$	5.79105	−	17.8230i	0.201132	−	0.619019i	0.999850	−	0.0173144i	$-0.00551161\pi$
$830$		0			0
$831$	−3.01473	−	2.19033i	−0.104580	−	0.0759817i
$832$		0			0
$833$	−0.600976	−	1.84962i	−0.0208226	−	0.0640854i
$834$		0			0
$835$	21.8577			0.756418
$836$		0			0
$837$	9.34871			0.323139
$838$		0			0
$839$	5.38213	+	16.5645i	0.185812	+	0.571870i	0.999961	−	0.00878534i	$-0.00279650\pi$
$839$	5.38213	+	16.5645i	0.185812	+	0.571870i	−0.814150	+	0.580655i	$0.802796\pi$
$840$		0			0
$841$	23.4489	+	17.0366i	0.808582	+	0.587470i
$842$		0			0
$843$	0.774412	−	2.38339i	0.0266722	−	0.0820885i
$844$		0			0
$845$	−25.5608	+	18.5710i	−0.879317	+	0.638861i
$846$		0			0
$847$	10.3826	+	3.63353i	0.356749	+	0.124849i
$848$		0			0
$849$	−0.857965	+	0.623348i	−0.0294453	+	0.0213933i
$850$		0			0
$851$	3.80349	−	11.7059i	0.130382	−	0.401274i
$852$		0			0
$853$	26.1585	+	19.0052i	0.895649	+	0.650727i	0.937345	−	0.348403i	$-0.113276\pi$
$853$	26.1585	+	19.0052i	0.895649	+	0.650727i	−0.0416956	+	0.999130i	$0.513276\pi$
$854$		0			0
$855$	5.39021	+	16.5894i	0.184341	+	0.567344i
$856$		0			0
$857$	44.1363			1.50767			0.753833	−	0.657066i	$-0.228203\pi$
$857$	44.1363			1.50767			0.753833	+	0.657066i	$0.228203\pi$
$858$		0			0
$859$	40.4717			1.38088			0.690439	−	0.723391i	$-0.257417\pi$
$859$	40.4717			1.38088			0.690439	+	0.723391i	$0.257417\pi$
$860$		0			0
$861$	0.0450850	+	0.138757i	0.00153649	+	0.00472884i
$862$		0			0
$863$	0.704115	+	0.511569i	0.0239683	+	0.0174140i	0.599705	−	0.800221i	$-0.295285\pi$
$863$	0.704115	+	0.511569i	0.0239683	+	0.0174140i	−0.575737	+	0.817635i	$0.695285\pi$
$864$		0			0
$865$	−15.1625	+	46.6653i	−0.515540	+	1.58667i
$866$		0			0
$867$	4.08451	−	2.96757i	0.138717	−	0.100784i
$868$		0			0
$869$	0.0114214	−	0.0672124i	0.000387443	−	0.00228002i
$870$		0			0
$871$	1.05200	−	0.764326i	0.0356458	−	0.0258982i
$872$		0			0
$873$	−15.6307	+	48.1065i	−0.529021	+	1.62816i
$874$		0			0
$875$	8.00016	+	5.81246i	0.270455	+	0.196497i
$876$		0			0
$877$	−2.80984	−	8.64781i	−0.0948816	−	0.292016i	0.892341	−	0.451362i	$-0.149062\pi$
$877$	−2.80984	−	8.64781i	−0.0948816	−	0.292016i	−0.987223	+	0.159346i	$0.949062\pi$
$878$		0			0
$879$	6.55745			0.221177
$880$		0			0
$881$	−50.9937			−1.71802			−0.859010	−	0.511959i	$-0.828920\pi$
$881$	−50.9937			−1.71802			−0.859010	+	0.511959i	$0.828920\pi$
$882$		0			0
$883$	−17.5119	−	53.8962i	−0.589323	−	1.81375i	−0.581168	−	0.813784i	$-0.697404\pi$
$883$	−17.5119	−	53.8962i	−0.589323	−	1.81375i	−0.00815530	−	0.999967i	$-0.502596\pi$
$884$		0			0
$885$	7.22003	+	5.24566i	0.242699	+	0.176331i
$886$		0			0
$887$	15.5843	−	47.9637i	0.523271	−	1.61046i	−0.244438	−	0.969665i	$-0.578604\pi$
$887$	15.5843	−	47.9637i	0.523271	−	1.61046i	0.767709	−	0.640798i	$-0.221396\pi$
$888$		0			0
$889$	10.5111	−	7.63679i	0.352532	−	0.256130i
$890$		0			0
$891$	11.3496	+	22.9078i	0.380225	+	0.767441i
$892$		0			0
$893$	6.99990	−	5.08572i	0.234243	−	0.170187i
$894$		0			0
$895$	−17.7783	+	54.7161i	−0.594265	+	1.82896i
$896$		0			0
$897$	−0.148651	−	0.108001i	−0.00496331	−	0.00360606i
$898$		0			0
$899$	−0.161254	−	0.496289i	−0.00537813	−	0.0165522i
$900$		0			0
$901$	−6.33451			−0.211033
$902$		0			0
$903$	4.45125			0.148128
$904$		0			0
$905$	10.3213	+	31.7657i	0.343092	+	1.05593i
$906$		0			0
$907$	−3.86491	−	2.80802i	−0.128332	−	0.0932388i	0.521767	−	0.853088i	$-0.325273\pi$
$907$	−3.86491	−	2.80802i	−0.128332	−	0.0932388i	−0.650100	+	0.759849i	$0.725273\pi$
$908$		0			0
$909$	16.1639	−	49.7473i	0.536122	−	1.65001i
$910$		0			0
$911$	−30.3622	+	22.0595i	−1.00595	+	0.730863i	−0.963355	−	0.268230i	$-0.913561\pi$
$911$	−30.3622	+	22.0595i	−1.00595	+	0.730863i	−0.0425911	+	0.999093i	$0.513561\pi$
$912$		0			0
$913$	10.6206	−	1.55996i	0.351491	−	0.0516272i
$914$		0			0
$915$	5.21561	−	3.78936i	0.172423	−	0.125273i
$916$		0			0
$917$	−4.13578	+	12.7286i	−0.136576	+	0.420336i
$918$		0			0
$919$	47.7644	+	34.7029i	1.57560	+	1.14474i	0.921527	+	0.388315i	$0.126943\pi$
$919$	47.7644	+	34.7029i	1.57560	+	1.14474i	0.654077	+	0.756428i	$0.273057\pi$
$920$		0			0
$921$	−0.160081	−	0.492680i	−0.00527486	−	0.0162343i
$922$		0			0
$923$	1.79954			0.0592325
$924$		0			0
$925$	4.87766			0.160376
$926$		0			0
$927$	−9.16879	−	28.2186i	−0.301143	−	0.926821i
$928$		0			0
$929$	10.1354	+	7.36377i	0.332530	+	0.241597i	0.741503	−	0.670949i	$-0.234113\pi$
$929$	10.1354	+	7.36377i	0.332530	+	0.241597i	−0.408973	+	0.912546i	$0.634113\pi$
$930$		0			0
$931$	0.774638	−	2.38409i	0.0253877	−	0.0781354i
$932$		0			0
$933$	1.31337	−	0.954219i	0.0429978	−	0.0312397i
$934$		0			0
$935$	−13.9305	−	7.29636i	−0.455577	−	0.238617i
$936$		0			0
$937$	−38.2198	+	27.7683i	−1.24859	+	0.907150i	−0.998139	−	0.0609802i	$-0.980577\pi$
$937$	−38.2198	+	27.7683i	−1.24859	+	0.907150i	−0.250446	+	0.968130i	$0.580577\pi$
$938$		0			0
$939$	−2.96009	+	9.11023i	−0.0965990	+	0.297301i
$940$		0			0
$941$	30.2334	+	21.9659i	0.985581	+	0.716066i	0.958949	−	0.283579i	$-0.0915218\pi$
$941$	30.2334	+	21.9659i	0.985581	+	0.716066i	0.0266318	+	0.999645i	$0.491522\pi$
$942$		0			0
$943$	−0.281153	−	0.865300i	−0.00915560	−	0.0281780i
$944$		0			0
$945$	−5.45158			−0.177340
$946$		0			0
$947$	−0.784814			−0.0255030			−0.0127515	−	0.999919i	$-0.504059\pi$
$947$	−0.784814			−0.0255030			−0.0127515	+	0.999919i	$0.504059\pi$
$948$		0			0
$949$	0.523145	+	1.61008i	0.0169820	+	0.0522653i
$950$		0			0
$951$	−3.47616	−	2.52558i	−0.112722	−	0.0818975i
$952$		0			0
$953$	−5.67216	+	17.4571i	−0.183739	+	0.565492i	−0.999924	−	0.0122991i	$-0.996085\pi$
$953$	−5.67216	+	17.4571i	−0.183739	+	0.565492i	0.816185	+	0.577791i	$0.196085\pi$
$954$		0			0
$955$	40.0932	−	29.1294i	1.29738	−	0.942605i
$956$		0			0
$957$	−0.113057	+	0.110543i	−0.00365460	+	0.00357334i
$958$		0			0
$959$	−4.14537	+	3.01179i	−0.133861	+	0.0972557i
$960$		0			0
$961$	−4.17801	+	12.8586i	−0.134775	+	0.414794i
$962$		0			0
$963$	33.8534	+	24.5959i	1.09091	+	0.792593i
$964$		0			0
$965$	−1.03549	−	3.18691i	−0.0333336	−	0.102590i
$966$		0			0
$967$	33.6774			1.08299			0.541496	−	0.840703i	$-0.317858\pi$
$967$	33.6774			1.08299			0.541496	+	0.840703i	$0.317858\pi$
$968$		0			0
$969$	−1.86216			−0.0598211
$970$		0			0
$971$	−1.71213	−	5.26939i	−0.0549449	−	0.169103i	0.919818	−	0.392345i	$-0.128336\pi$
$971$	−1.71213	−	5.26939i	−0.0549449	−	0.169103i	−0.974763	+	0.223242i	$0.928336\pi$
$972$		0			0
$973$	−9.33747	−	6.78407i	−0.299346	−	0.217487i
$974$		0			0
$975$	0.0225011	−	0.0692513i	0.000720612	−	0.00221782i
$976$		0			0
$977$	−3.07433	+	2.23363i	−0.0983566	+	0.0714603i	−0.635877	−	0.771791i	$-0.719361\pi$
$977$	−3.07433	+	2.23363i	−0.0983566	+	0.0714603i	0.537520	+	0.843251i	$0.319361\pi$
$978$		0			0
$979$	−27.6021	+	26.9883i	−0.882166	+	0.862551i
$980$		0			0
$981$	−37.7308	+	27.4131i	−1.20465	+	0.875232i
$982$		0			0
$983$	12.4986	−	38.4668i	0.398644	−	1.22690i	−0.527443	−	0.849591i	$-0.676849\pi$
$983$	12.4986	−	38.4668i	0.398644	−	1.22690i	0.926087	−	0.377310i	$-0.123151\pi$
$984$		0			0
$985$	−34.6443	−	25.1706i	−1.10386	−	0.802001i
$986$		0			0
$987$	0.407404	+	1.25386i	0.0129678	+	0.0399108i
$988$		0			0
$989$	−27.7583			−0.882663
$990$		0			0
$991$	−41.1904			−1.30846			−0.654229	−	0.756297i	$-0.727007\pi$
$991$	−41.1904			−1.30846			−0.654229	+	0.756297i	$0.727007\pi$
$992$		0			0
$993$	−0.590996	−	1.81890i	−0.0187547	−	0.0577210i
$994$		0			0
$995$	8.88813	+	6.45761i	0.281773	+	0.204720i
$996$		0			0
$997$	8.97096	−	27.6098i	0.284113	−	0.874411i	−0.702550	−	0.711635i	$-0.747955\pi$
$997$	8.97096	−	27.6098i	0.284113	−	0.874411i	0.986663	−	0.162776i	$-0.0520448\pi$
$998$		0			0
$999$	9.34775	−	6.79154i	0.295750	−	0.214875i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	308.2.j.b.113.2	✓	8
11.2	odd	10		3388.2.a.s.1.1		4
11.4	even	5	inner	308.2.j.b.169.2	yes	8
11.9	even	5		3388.2.a.r.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
308.2.j.b.113.2	✓	8	1.1	even	1	trivial
308.2.j.b.169.2	yes	8	11.4	even	5	inner
3388.2.a.r.1.1		4	11.9	even	5
3388.2.a.s.1.1		4	11.2	odd	10

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:	\( N \)	\(=\)	\( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	308.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.118034 + 0.363271i) q^{3} +(1.97240 + 1.43303i) q^{5} +(-0.309017 + 0.951057i) q^{7} +(2.30902 - 1.67760i) q^{9} +O(q^{10})\)	\(q+(0.118034 + 0.363271i) q^{3} +(1.97240 + 1.43303i) q^{5} +(-0.309017 + 0.951057i) q^{7} +(2.30902 - 1.67760i) q^{9} +(-2.37142 + 2.31870i) q^{11} +(-0.163383 + 0.118705i) q^{13} +(-0.287769 + 0.885663i) q^{15} +(1.57338 + 1.14313i) q^{17} +(0.774638 + 2.38409i) q^{19} -0.381966 q^{21} +2.38197 q^{23} +(0.291695 + 0.897745i) q^{25} +(1.80902 + 1.31433i) q^{27} +(0.0385696 - 0.118705i) q^{29} +(3.38239 - 2.45745i) q^{31} +(-1.12222 - 0.587785i) q^{33} +(-1.97240 + 1.43303i) q^{35} +(1.59679 - 4.91440i) q^{37} +(-0.0624068 - 0.0453412i) q^{39} +(-0.118034 - 0.363271i) q^{41} -11.6535 q^{43} +6.95836 q^{45} +(-1.06660 - 3.28265i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(-0.229553 + 0.706490i) q^{51} +(-2.63509 + 1.91451i) q^{53} +(-8.00016 + 1.17507i) q^{55} +(-0.774638 + 0.562807i) q^{57} +(2.96143 - 9.11435i) q^{59} +(-5.60071 - 4.06916i) q^{61} +(0.881966 + 2.71441i) q^{63} -0.492365 q^{65} -6.43888 q^{67} +(0.281153 + 0.865300i) q^{69} +(-7.20890 - 5.23757i) q^{71} +(2.59043 - 7.97254i) q^{73} +(-0.291695 + 0.211929i) q^{75} +(-1.47240 - 2.97187i) q^{77} +(-0.0166300 + 0.0120824i) q^{79} +(2.38197 - 7.33094i) q^{81} +(-2.61846 - 1.90242i) q^{83} +(1.46519 + 4.50940i) q^{85} +0.0476746 q^{87} +11.6394 q^{89} +(-0.0624068 - 0.192069i) q^{91} +(1.29196 + 0.938663i) q^{93} +(-1.88858 + 5.81246i) q^{95} +(-14.3379 + 10.4171i) q^{97} +(-1.58582 + 9.33221i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{3} - q^{5} + 2 q^{7} + 14 q^{9}+O(q^{10}) \) 8 * q - 8 * q^3 - q^5 + 2 * q^7 + 14 * q^9	\( 8 q - 8 q^{3} - q^{5} + 2 q^{7} + 14 q^{9} - 5 q^{11} + 11 q^{13} - 4 q^{15} - 7 q^{17} - 5 q^{19} - 12 q^{21} + 28 q^{23} - 15 q^{25} + 10 q^{27} + 7 q^{29} + 3 q^{31} + q^{35} + 10 q^{37} + 9 q^{39} + 8 q^{41} - 44 q^{43} + 2 q^{45} + q^{47} - 2 q^{49} - 13 q^{51} - 6 q^{53} - 12 q^{55} + 5 q^{57} + 17 q^{59} - 23 q^{61} + 16 q^{63} - 80 q^{65} + 38 q^{67} - 38 q^{69} + 10 q^{71} - 5 q^{73} + 15 q^{75} + 5 q^{77} - 27 q^{79} + 28 q^{81} + 21 q^{83} + 38 q^{85} - 32 q^{87} + 26 q^{89} + 9 q^{91} + 12 q^{93} - 66 q^{95} - 28 q^{97} - 20 q^{99}+O(q^{100}) \) 8 * q - 8 * q^3 - q^5 + 2 * q^7 + 14 * q^9 - 5 * q^11 + 11 * q^13 - 4 * q^15 - 7 * q^17 - 5 * q^19 - 12 * q^21 + 28 * q^23 - 15 * q^25 + 10 * q^27 + 7 * q^29 + 3 * q^31 + q^35 + 10 * q^37 + 9 * q^39 + 8 * q^41 - 44 * q^43 + 2 * q^45 + q^47 - 2 * q^49 - 13 * q^51 - 6 * q^53 - 12 * q^55 + 5 * q^57 + 17 * q^59 - 23 * q^61 + 16 * q^63 - 80 * q^65 + 38 * q^67 - 38 * q^69 + 10 * q^71 - 5 * q^73 + 15 * q^75 + 5 * q^77 - 27 * q^79 + 28 * q^81 + 21 * q^83 + 38 * q^85 - 32 * q^87 + 26 * q^89 + 9 * q^91 + 12 * q^93 - 66 * q^95 - 28 * q^97 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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