LMFDB - Embedded newform 1148.2.n.b.141.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(57,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("1148.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.n (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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.64000000.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 2x^{6} + 4x^{4} + 8x^{2} + 16 $ x^8 + 2x^6 + 4x^4 + 8*x^2 + 16
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			141.2
Root			$0.437016 + 1.34500i$ of defining polynomial
Character	$\chi$	$=$	1148.141
Dual form			1148.2.n.b.57.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.41421 q^{3} +(-1.95314 + 1.41904i) q^{5} +(0.309017 - 0.951057i) q^{7} +2.82843 q^{9} +O(q^{10})$	\(q+2.41421 q^{3} +(-1.95314 + 1.41904i) q^{5} +(0.309017 - 0.951057i) q^{7} +2.82843 q^{9} +(-1.50000 - 1.08981i) q^{11} +(1.66818 + 5.13413i) q^{13} +(-4.71530 + 3.42586i) q^{15} +(4.49535 + 3.26606i) q^{17} +(-2.03022 + 6.24836i) q^{19} +(0.746033 - 2.29605i) q^{21} +(0.195886 + 0.602877i) q^{23} +(0.255998 - 0.787881i) q^{25} -0.414214 q^{27} +(4.01148 - 2.91451i) q^{29} +(8.73674 + 6.34761i) q^{31} +(-3.62132 - 2.63104i) q^{33} +(0.746033 + 2.29605i) q^{35} +(9.41776 - 6.84240i) q^{37} +(4.02734 + 12.3949i) q^{39} +(-6.11213 - 1.90836i) q^{41} +(-2.64287 - 8.13391i) q^{43} +(-5.52431 + 4.01365i) q^{45} +(-0.265029 - 0.815676i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(10.8527 + 7.88498i) q^{51} +(2.43989 - 1.77268i) q^{53} +4.47620 q^{55} +(-4.90138 + 15.0849i) q^{57} +(1.74729 + 5.37760i) q^{59} +(-1.82263 + 5.60948i) q^{61} +(0.874032 - 2.68999i) q^{63} +(-10.5437 - 7.66046i) q^{65} +(-4.02567 + 2.92482i) q^{67} +(0.472912 + 1.45547i) q^{69} +(1.46639 + 1.06540i) q^{71} -4.10029 q^{73} +(0.618034 - 1.90211i) q^{75} +(-1.50000 + 1.08981i) q^{77} -7.64099 q^{79} -9.48528 q^{81} +1.94208 q^{83} -13.4147 q^{85} +(9.68456 - 7.03624i) q^{87} +(3.46765 - 10.6723i) q^{89} +5.39835 q^{91} +(21.0924 + 15.3245i) q^{93} +(-4.90138 - 15.0849i) q^{95} +(-6.05260 + 4.39747i) q^{97} +(-4.24264 - 3.08246i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{3} - 2 q^{5} - 2 q^{7}+O(q^{10}) $ 8 * q + 8 * q^3 - 2 * q^5 - 2 * q^7	$ 8 q + 8 q^{3} - 2 q^{5} - 2 q^{7} - 12 q^{11} + 10 q^{13} - 6 q^{15} + 12 q^{17} - 2 q^{19} - 2 q^{21} - 12 q^{23} + 4 q^{25} + 8 q^{27} - 2 q^{29} + 14 q^{31} - 12 q^{33} - 2 q^{35} + 14 q^{37} + 30 q^{39} - 18 q^{41} - 14 q^{43} - 8 q^{45} + 28 q^{47} - 2 q^{49} + 28 q^{51} + 4 q^{53} - 12 q^{55} - 30 q^{57} + 4 q^{59} - 4 q^{61} - 30 q^{65} - 28 q^{67} - 36 q^{69} - 44 q^{73} - 4 q^{75} - 12 q^{77} + 16 q^{79} - 8 q^{81} + 40 q^{83} - 12 q^{85} + 22 q^{87} + 14 q^{89} + 42 q^{93} - 30 q^{95} - 38 q^{97}+O(q^{100}) $ 8 * q + 8 * q^3 - 2 * q^5 - 2 * q^7 - 12 * q^11 + 10 * q^13 - 6 * q^15 + 12 * q^17 - 2 * q^19 - 2 * q^21 - 12 * q^23 + 4 * q^25 + 8 * q^27 - 2 * q^29 + 14 * q^31 - 12 * q^33 - 2 * q^35 + 14 * q^37 + 30 * q^39 - 18 * q^41 - 14 * q^43 - 8 * q^45 + 28 * q^47 - 2 * q^49 + 28 * q^51 + 4 * q^53 - 12 * q^55 - 30 * q^57 + 4 * q^59 - 4 * q^61 - 30 * q^65 - 28 * q^67 - 36 * q^69 - 44 * q^73 - 4 * q^75 - 12 * q^77 + 16 * q^79 - 8 * q^81 + 40 * q^83 - 12 * q^85 + 22 * q^87 + 14 * q^89 + 42 * q^93 - 30 * q^95 - 38 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.41421			1.39385			0.696923	−	0.717146i	$-0.254552\pi$
$3$	2.41421			1.39385			0.696923	+	0.717146i	$0.254552\pi$
$4$		0			0
$5$	−1.95314	+	1.41904i	−0.873471	+	0.634614i	−0.931516	−	0.363700i	$-0.881513\pi$
$5$	−1.95314	+	1.41904i	−0.873471	+	0.634614i	0.0580453	+	0.998314i	$0.481513\pi$
$6$		0			0
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$8$		0			0
$9$	2.82843			0.942809
$10$		0			0
$11$	−1.50000	−	1.08981i	−0.452267	−	0.328591i	0.338223	−	0.941066i	$-0.390174\pi$
$11$	−1.50000	−	1.08981i	−0.452267	−	0.328591i	−0.790490	+	0.612475i	$0.790174\pi$
$12$		0			0
$13$	1.66818	+	5.13413i	0.462670	+	1.42395i	0.861889	+	0.507096i	$0.169281\pi$
$13$	1.66818	+	5.13413i	0.462670	+	1.42395i	−0.399219	+	0.916855i	$0.630719\pi$
$14$		0			0
$15$	−4.71530	+	3.42586i	−1.21748	+	0.884554i
$16$		0			0
$17$	4.49535	+	3.26606i	1.09028	+	0.792137i	0.979447	−	0.201702i	$-0.0646471\pi$
$17$	4.49535	+	3.26606i	1.09028	+	0.792137i	0.110836	+	0.993839i	$0.464647\pi$
$18$		0			0
$19$	−2.03022	+	6.24836i	−0.465764	+	1.43347i	0.392256	+	0.919856i	$0.371695\pi$
$19$	−2.03022	+	6.24836i	−0.465764	+	1.43347i	−0.858020	+	0.513617i	$0.828305\pi$
$20$		0			0
$21$	0.746033	−	2.29605i	0.162798	−	0.501040i
$22$		0			0
$23$	0.195886	+	0.602877i	0.0408452	+	0.125708i	0.969400	−	0.245487i	$-0.0789479\pi$
$23$	0.195886	+	0.602877i	0.0408452	+	0.125708i	−0.928555	+	0.371196i	$0.878948\pi$
$24$		0			0
$25$	0.255998	−	0.787881i	0.0511996	−	0.157576i
$26$		0			0
$27$	−0.414214			−0.0797154
$28$		0			0
$29$	4.01148	−	2.91451i	0.744912	−	0.541211i	−0.149333	−	0.988787i	$-0.547713\pi$
$29$	4.01148	−	2.91451i	0.744912	−	0.541211i	0.894246	+	0.447576i	$0.147713\pi$
$30$		0			0
$31$	8.73674	+	6.34761i	1.56916	+	1.14006i	0.927951	+	0.372702i	$0.121569\pi$
$31$	8.73674	+	6.34761i	1.56916	+	1.14006i	0.641213	+	0.767363i	$0.278431\pi$
$32$		0			0
$33$	−3.62132	−	2.63104i	−0.630391	−	0.458006i
$34$		0			0
$35$	0.746033	+	2.29605i	0.126103	+	0.388104i
$36$		0			0
$37$	9.41776	−	6.84240i	1.54827	−	1.12488i	0.603399	−	0.797439i	$-0.293813\pi$
$37$	9.41776	−	6.84240i	1.54827	−	1.12488i	0.944871	−	0.327444i	$-0.106187\pi$
$38$		0			0
$39$	4.02734	+	12.3949i	0.644891	+	1.98477i
$40$		0			0
$41$	−6.11213	−	1.90836i	−0.954555	−	0.298036i
$41$	−6.11213	−	1.90836i	−0.954555	−	0.298036i
$42$		0			0
$43$	−2.64287	−	8.13391i	−0.403034	−	1.24041i	−0.922526	−	0.385935i	$-0.873879\pi$
$43$	−2.64287	−	8.13391i	−0.403034	−	1.24041i	0.519493	−	0.854475i	$-0.326121\pi$
$44$		0			0
$45$	−5.52431	+	4.01365i	−0.823516	+	0.598319i
$46$		0			0
$47$	−0.265029	−	0.815676i	−0.0386585	−	0.118979i	0.929865	−	0.367901i	$-0.119924\pi$
$47$	−0.265029	−	0.815676i	−0.0386585	−	0.118979i	−0.968523	+	0.248923i	$0.919924\pi$
$48$		0			0
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$		0			0
$51$	10.8527	+	7.88498i	1.51969	+	1.10412i
$52$		0			0
$53$	2.43989	−	1.77268i	0.335144	−	0.243497i	−0.407466	−	0.913220i	$-0.633587\pi$
$53$	2.43989	−	1.77268i	0.335144	−	0.243497i	0.742610	+	0.669724i	$0.233587\pi$
$54$		0			0
$55$	4.47620			0.603570
$56$		0			0
$57$	−4.90138	+	15.0849i	−0.649203	+	1.99804i
$58$		0			0
$59$	1.74729	+	5.37760i	0.227478	+	0.700104i	0.998031	+	0.0627281i	$0.0199801\pi$
$59$	1.74729	+	5.37760i	0.227478	+	0.700104i	−0.770553	+	0.637376i	$0.780020\pi$
$60$		0			0
$61$	−1.82263	+	5.60948i	−0.233364	+	0.718220i	0.763970	+	0.645251i	$0.223247\pi$
$61$	−1.82263	+	5.60948i	−0.233364	+	0.718220i	−0.997334	+	0.0729688i	$0.976753\pi$
$62$		0			0
$63$	0.874032	−	2.68999i	0.110118	−	0.338907i
$64$		0			0
$65$	−10.5437	−	7.66046i	−1.30779	−	0.950164i
$66$		0			0
$67$	−4.02567	+	2.92482i	−0.491814	+	0.357324i	−0.805882	−	0.592077i	$-0.798308\pi$
$67$	−4.02567	+	2.92482i	−0.491814	+	0.357324i	0.314067	+	0.949401i	$0.398308\pi$
$68$		0			0
$69$	0.472912	+	1.45547i	0.0569319	+	0.175218i
$70$		0			0
$71$	1.46639	+	1.06540i	0.174029	+	0.126439i	0.671390	−	0.741104i	$-0.265698\pi$
$71$	1.46639	+	1.06540i	0.174029	+	0.126439i	−0.497361	+	0.867544i	$0.665698\pi$
$72$		0			0
$73$	−4.10029			−0.479903			−0.239952	−	0.970785i	$-0.577132\pi$
$73$	−4.10029			−0.479903			−0.239952	+	0.970785i	$0.577132\pi$
$74$		0			0
$75$	0.618034	−	1.90211i	0.0713644	−	0.219637i
$76$		0			0
$77$	−1.50000	+	1.08981i	−0.170941	+	0.124196i
$78$		0			0
$79$	−7.64099			−0.859678			−0.429839	−	0.902906i	$-0.641430\pi$
$79$	−7.64099			−0.859678			−0.429839	+	0.902906i	$0.641430\pi$
$80$		0			0
$81$	−9.48528			−1.05392
$82$		0			0
$83$	1.94208			0.213171			0.106585	−	0.994304i	$-0.466008\pi$
$83$	1.94208			0.213171			0.106585	+	0.994304i	$0.466008\pi$
$84$		0			0
$85$	−13.4147			−1.45503
$86$		0			0
$87$	9.68456	−	7.03624i	1.03829	−	0.754365i
$88$		0			0
$89$	3.46765	−	10.6723i	0.367570	−	1.13126i	−0.580786	−	0.814056i	$-0.697255\pi$
$89$	3.46765	−	10.6723i	0.367570	−	1.13126i	0.948356	−	0.317207i	$-0.102745\pi$
$90$		0			0
$91$	5.39835			0.565900
$92$		0			0
$93$	21.0924	+	15.3245i	2.18717	+	1.58908i
$94$		0			0
$95$	−4.90138	−	15.0849i	−0.502871	−	1.54768i
$96$		0			0
$97$	−6.05260	+	4.39747i	−0.614549	+	0.446496i	−0.851013	−	0.525144i	$-0.824011\pi$
$97$	−6.05260	+	4.39747i	−0.614549	+	0.446496i	0.236464	+	0.971640i	$0.424011\pi$
$98$		0			0
$99$	−4.24264	−	3.08246i	−0.426401	−	0.309799i
$100$		0			0
$101$	4.17611	−	12.8528i	0.415539	−	1.27890i	−0.496229	−	0.868192i	$-0.665282\pi$
$101$	4.17611	−	12.8528i	0.415539	−	1.27890i	0.911768	−	0.410706i	$-0.134718\pi$
$102$		0			0
$103$	−0.0823941	+	0.253583i	−0.00811853	+	0.0249863i	−0.955034	−	0.296497i	$-0.904181\pi$
$103$	−0.0823941	+	0.253583i	−0.00811853	+	0.0249863i	0.946915	+	0.321483i	$0.104181\pi$
$104$		0			0
$105$	1.80108	+	5.54316i	0.175768	+	0.540957i
$106$		0			0
$107$	−2.69537	+	8.29549i	−0.260571	+	0.801955i	0.732110	+	0.681187i	$0.238536\pi$
$107$	−2.69537	+	8.29549i	−0.260571	+	0.801955i	−0.992681	+	0.120768i	$0.961464\pi$
$108$		0			0
$109$	14.8436			1.42176			0.710881	−	0.703312i	$-0.248296\pi$
$109$	14.8436			1.42176			0.710881	+	0.703312i	$0.248296\pi$
$110$		0			0
$111$	22.7365	−	16.5190i	2.15805	−	1.56792i
$112$		0			0
$113$	−15.1224	−	10.9871i	−1.42260	−	1.03358i	−0.991336	−	0.131350i	$-0.958069\pi$
$113$	−15.1224	−	10.9871i	−1.42260	−	1.03358i	−0.431261	−	0.902227i	$-0.641931\pi$
$114$		0			0
$115$	−1.23810	−	0.899532i	−0.115453	−	0.0838818i
$116$		0			0
$117$	4.71833	+	14.5215i	0.436209	+	1.34251i
$118$		0			0
$119$	4.49535	−	3.26606i	0.412088	−	0.299400i
$120$		0			0
$121$	−2.33688	−	7.19218i	−0.212444	−	0.653835i
$122$		0			0
$123$	−14.7560	−	4.60720i	−1.33050	−	0.415417i
$124$		0			0
$125$	−3.11213	−	9.57815i	−0.278357	−	0.856696i
$126$		0			0
$127$	−13.9421	+	10.1295i	−1.23716	+	0.898848i	−0.997406	−	0.0719856i	$-0.977066\pi$
$127$	−13.9421	+	10.1295i	−1.23716	+	0.898848i	−0.239753	+	0.970834i	$0.577066\pi$
$128$		0			0
$129$	−6.38045	−	19.6370i	−0.561767	−	1.72894i
$130$		0			0
$131$	−14.7295	−	10.7016i	−1.28692	−	0.935002i	−0.287182	−	0.957876i	$-0.592718\pi$
$131$	−14.7295	−	10.7016i	−1.28692	−	0.935002i	−0.999738	+	0.0228739i	$0.992718\pi$
$132$		0			0
$133$	5.31518	+	3.86170i	0.460884	+	0.334852i
$134$		0			0
$135$	0.809017	−	0.587785i	0.0696291	−	0.0505885i
$136$		0			0
$137$	16.6974			1.42655			0.713276	−	0.700884i	$-0.247211\pi$
$137$	16.6974			1.42655			0.713276	+	0.700884i	$0.247211\pi$
$138$		0			0
$139$	−3.25725	+	10.0248i	−0.276277	+	0.850292i	0.712602	+	0.701568i	$0.247516\pi$
$139$	−3.25725	+	10.0248i	−0.276277	+	0.850292i	−0.988879	+	0.148724i	$0.952484\pi$
$140$		0			0
$141$	−0.639837	−	1.96922i	−0.0538840	−	0.165838i
$142$		0			0
$143$	3.09298	−	9.51920i	0.258648	−	0.796036i
$144$		0			0
$145$	−3.69917	+	11.3849i	−0.307200	+	0.945463i
$146$		0			0
$147$	−1.95314	−	1.41904i	−0.161092	−	0.117040i
$148$		0			0
$149$	15.2825	−	11.1034i	1.25199	−	0.909624i	0.253655	−	0.967295i	$-0.418367\pi$
$149$	15.2825	−	11.1034i	1.25199	−	0.909624i	0.998336	+	0.0576704i	$0.0183672\pi$
$150$		0			0
$151$	−1.76445	−	5.43042i	−0.143589	−	0.441922i	0.853238	−	0.521522i	$-0.174636\pi$
$151$	−1.76445	−	5.43042i	−0.143589	−	0.441922i	−0.996827	+	0.0796004i	$0.974636\pi$
$152$		0			0
$153$	12.7148	+	9.23783i	1.02793	+	0.746834i
$154$		0			0
$155$	−26.0716			−2.09412
$156$		0			0
$157$	−4.52306	+	13.9205i	−0.360979	+	1.11098i	0.591481	+	0.806319i	$0.298543\pi$
$157$	−4.52306	+	13.9205i	−0.360979	+	1.11098i	−0.952461	+	0.304662i	$0.901457\pi$
$158$		0			0
$159$	5.89041	−	4.27963i	0.467140	−	0.339397i
$160$		0			0
$161$	0.633902			0.0499585
$162$		0			0
$163$	14.4546			1.13217			0.566085	−	0.824347i	$-0.308457\pi$
$163$	14.4546			1.13217			0.566085	+	0.824347i	$0.308457\pi$
$164$		0			0
$165$	10.8065			0.841285
$166$		0			0
$167$	−13.8902			−1.07486			−0.537428	−	0.843310i	$-0.680604\pi$
$167$	−13.8902			−1.07486			−0.537428	+	0.843310i	$0.680604\pi$
$168$		0			0
$169$	−13.0593	+	9.48811i	−1.00456	+	0.729855i
$170$		0			0
$171$	−5.74232	+	17.6730i	−0.439126	+	1.35149i
$172$		0			0
$173$	16.0907			1.22335			0.611676	−	0.791108i	$-0.290496\pi$
$173$	16.0907			1.22335			0.611676	+	0.791108i	$0.290496\pi$
$174$		0			0
$175$	−0.670212	−	0.486937i	−0.0506632	−	0.0368090i
$176$		0			0
$177$	4.21833	+	12.9827i	0.317069	+	0.975838i
$178$		0			0
$179$	12.0836	−	8.77925i	0.903170	−	0.656192i	−0.0361079	−	0.999348i	$-0.511496\pi$
$179$	12.0836	−	8.77925i	0.903170	−	0.656192i	0.939278	+	0.343156i	$0.111496\pi$
$180$		0			0
$181$	−0.286215	−	0.207947i	−0.0212742	−	0.0154566i	0.577097	−	0.816675i	$-0.304185\pi$
$181$	−0.286215	−	0.207947i	−0.0212742	−	0.0154566i	−0.598372	+	0.801219i	$0.704185\pi$
$182$		0			0
$183$	−4.40022	+	13.5425i	−0.325274	+	1.00109i
$184$		0			0
$185$	−8.68456	+	26.7283i	−0.638502	+	1.96511i
$186$		0			0
$187$	−3.18363	−	9.79819i	−0.232810	−	0.716515i
$188$		0			0
$189$	−0.127999	+	0.393941i	−0.00931056	+	0.0286550i
$190$		0			0
$191$	2.36610			0.171205			0.0856024	−	0.996329i	$-0.472719\pi$
$191$	2.36610			0.171205			0.0856024	+	0.996329i	$0.472719\pi$
$192$		0			0
$193$	11.3784	−	8.26690i	0.819036	−	0.595065i	−0.0974000	−	0.995245i	$-0.531053\pi$
$193$	11.3784	−	8.26690i	0.819036	−	0.595065i	0.916436	+	0.400181i	$0.131053\pi$
$194$		0			0
$195$	−25.4548	−	18.4940i	−1.82286	−	1.32438i
$196$		0			0
$197$	−0.974325	−	0.707889i	−0.0694178	−	0.0504350i	0.552535	−	0.833490i	$-0.313661\pi$
$197$	−0.974325	−	0.707889i	−0.0694178	−	0.0504350i	−0.621953	+	0.783055i	$0.713661\pi$
$198$		0			0
$199$	−2.57195	−	7.91565i	−0.182321	−	0.561125i	0.817571	−	0.575827i	$-0.195320\pi$
$199$	−2.57195	−	7.91565i	−0.182321	−	0.561125i	−0.999892	+	0.0147021i	$0.995320\pi$
$200$		0			0
$201$	−9.71884	+	7.06115i	−0.685514	+	0.498055i
$202$		0			0
$203$	−1.53225	−	4.71577i	−0.107543	−	0.330982i
$204$		0			0
$205$	14.6459	−	4.94605i	1.02291	−	0.345447i
$206$		0			0
$207$	0.554051	+	1.70519i	0.0385092	+	0.118519i
$208$		0			0
$209$	9.85488	−	7.15999i	0.681676	−	0.495267i
$210$		0			0
$211$	2.51941	+	7.75395i	0.173443	+	0.533804i	0.999559	−	0.0296969i	$-0.00945422\pi$
$211$	2.51941	+	7.75395i	0.173443	+	0.533804i	−0.826116	+	0.563501i	$0.809454\pi$
$212$		0			0
$213$	3.54018	+	2.57209i	0.242569	+	0.176237i
$214$		0			0
$215$	16.7042	+	12.1363i	1.13922	+	0.827691i
$216$		0			0
$217$	8.73674	−	6.34761i	0.593088	−	0.430904i
$218$		0			0
$219$	−9.89898			−0.668911
$220$		0			0
$221$	−9.26935	+	28.5281i	−0.623524	+	1.91901i
$222$		0			0
$223$	0.721561	+	2.22074i	0.0483193	+	0.148712i	0.972305	−	0.233715i	$-0.0750884\pi$
$223$	0.721561	+	2.22074i	0.0483193	+	0.148712i	−0.923986	+	0.382427i	$0.875088\pi$
$224$		0			0
$225$	0.724072	−	2.22846i	0.0482715	−	0.148564i
$226$		0			0
$227$	−4.36861	+	13.4452i	−0.289955	+	0.892389i	0.694915	+	0.719092i	$0.255442\pi$
$227$	−4.36861	+	13.4452i	−0.289955	+	0.892389i	−0.984870	+	0.173297i	$0.944558\pi$
$228$		0			0
$229$	20.8538	+	15.1512i	1.37806	+	1.00122i	0.997058	+	0.0766453i	$0.0244209\pi$
$229$	20.8538	+	15.1512i	1.37806	+	1.00122i	0.381002	+	0.924574i	$0.375579\pi$
$230$		0			0
$231$	−3.62132	+	2.63104i	−0.238265	+	0.173110i
$232$		0			0
$233$	−3.42924	−	10.5541i	−0.224657	−	0.691423i	−0.998326	−	0.0578334i	$-0.981581\pi$
$233$	−3.42924	−	10.5541i	−0.224657	−	0.691423i	0.773669	−	0.633590i	$-0.218419\pi$
$234$		0			0
$235$	1.67512	+	1.21704i	0.109272	+	0.0793911i
$236$		0			0
$237$	−18.4470			−1.19826
$238$		0			0
$239$	3.20872	−	9.87544i	0.207555	−	0.638789i	−0.792044	−	0.610464i	$-0.790983\pi$
$239$	3.20872	−	9.87544i	0.207555	−	0.638789i	0.999599	−	0.0283245i	$-0.00901717\pi$
$240$		0			0
$241$	19.8710	−	14.4372i	1.28001	−	0.929979i	0.280453	−	0.959868i	$-0.409515\pi$
$241$	19.8710	−	14.4372i	1.28001	−	0.929979i	0.999553	+	0.0298885i	$0.00951521\pi$
$242$		0			0
$243$	−21.6569			−1.38929
$244$		0			0
$245$	2.41421			0.154238
$246$		0			0
$247$	−35.4667			−2.25669
$248$		0			0
$249$	4.68859			0.297127
$250$		0			0
$251$	19.1417	−	13.9072i	1.20821	−	0.877816i	0.213144	−	0.977021i	$-0.431630\pi$
$251$	19.1417	−	13.9072i	1.20821	−	0.877816i	0.995067	+	0.0992045i	$0.0316298\pi$
$252$		0			0
$253$	0.363193	−	1.11779i	0.0228338	−	0.0702751i
$254$		0			0
$255$	−32.3860			−2.02809
$256$		0			0
$257$	−24.1038	−	17.5125i	−1.50356	−	1.09240i	−0.968938	−	0.247303i	$-0.920456\pi$
$257$	−24.1038	−	17.5125i	−1.50356	−	1.09240i	−0.534617	−	0.845094i	$-0.679544\pi$
$258$		0			0
$259$	−3.59726	−	11.0712i	−0.223523	−	0.687933i
$260$		0			0
$261$	11.3462	−	8.24347i	0.702310	−	0.510258i
$262$		0			0
$263$	3.08964	+	2.24475i	0.190515	+	0.138417i	0.678954	−	0.734181i	$-0.262434\pi$
$263$	3.08964	+	2.24475i	0.190515	+	0.138417i	−0.488439	+	0.872598i	$0.662434\pi$
$264$		0			0
$265$	−2.24994	+	6.92459i	−0.138213	+	0.425374i
$266$		0			0
$267$	8.37164	−	25.7653i	0.512336	−	1.57681i
$268$		0			0
$269$	−4.22829	−	13.0133i	−0.257804	−	0.793438i	−0.993264	−	0.115870i	$-0.963034\pi$
$269$	−4.22829	−	13.0133i	−0.257804	−	0.793438i	0.735461	−	0.677567i	$-0.236966\pi$
$270$		0			0
$271$	−0.0929446	+	0.286054i	−0.00564598	+	0.0173765i	−0.953840	−	0.300316i	$-0.902908\pi$
$271$	−0.0929446	+	0.286054i	−0.00564598	+	0.0173765i	0.948194	+	0.317692i	$0.102908\pi$
$272$		0			0
$273$	13.0328			0.788778
$274$		0			0
$275$	−1.24264	+	0.902831i	−0.0749341	+	0.0544428i
$276$		0			0
$277$	−11.1839	−	8.12556i	−0.671974	−	0.488217i	0.198712	−	0.980058i	$-0.436324\pi$
$277$	−11.1839	−	8.12556i	−0.671974	−	0.488217i	−0.870685	+	0.491841i	$0.836324\pi$
$278$		0			0
$279$	24.7112	+	17.9538i	1.47942	+	1.07486i
$280$		0			0
$281$	4.16176	+	12.8086i	0.248270	+	0.764095i	0.995081	+	0.0990600i	$0.0315836\pi$
$281$	4.16176	+	12.8086i	0.248270	+	0.764095i	−0.746812	+	0.665035i	$0.768416\pi$
$282$		0			0
$283$	9.06121	−	6.58335i	0.538633	−	0.391340i	−0.284944	−	0.958544i	$-0.591975\pi$
$283$	9.06121	−	6.58335i	0.538633	−	0.391340i	0.823577	+	0.567204i	$0.191975\pi$
$284$		0			0
$285$	−11.8330	−	36.4181i	−0.700925	−	2.15722i
$286$		0			0
$287$	−3.70371	+	5.22327i	−0.218623	+	0.308320i
$288$		0			0
$289$	4.28773	+	13.1963i	0.252219	+	0.776251i
$290$		0			0
$291$	−14.6123	+	10.6164i	−0.856587	+	0.622347i
$292$		0			0
$293$	5.68408	+	17.4938i	0.332068	+	1.02200i	0.968149	+	0.250377i	$0.0805544\pi$
$293$	5.68408	+	17.4938i	0.332068	+	1.02200i	−0.636081	+	0.771622i	$0.719446\pi$
$294$		0			0
$295$	−11.0437	−	8.02373i	−0.642990	−	0.467160i
$296$		0			0
$297$	0.621320	+	0.451416i	0.0360527	+	0.0261938i
$298$		0			0
$299$	−2.76847	+	2.01141i	−0.160105	+	0.116323i
$300$		0			0
$301$	−8.55250			−0.492958
$302$		0			0
$303$	10.0820	−	31.0293i	0.579198	−	1.78259i
$304$		0			0
$305$	−4.40022	−	13.5425i	−0.251956	−	0.775440i
$306$		0			0
$307$	7.48632	−	23.0405i	0.427267	−	1.31499i	−0.473540	−	0.880772i	$-0.657024\pi$
$307$	7.48632	−	23.0405i	0.427267	−	1.31499i	0.900807	−	0.434220i	$-0.142976\pi$
$308$		0			0
$309$	−0.198917	+	0.612203i	−0.0113160	+	0.0348270i
$310$		0			0
$311$	−23.4263	−	17.0202i	−1.32838	−	0.965126i	−0.999787	−	0.0206549i	$-0.993425\pi$
$311$	−23.4263	−	17.0202i	−1.32838	−	0.965126i	−0.328595	−	0.944471i	$-0.606575\pi$
$312$		0			0
$313$	15.3434	−	11.1477i	0.867263	−	0.630103i	−0.0625883	−	0.998039i	$-0.519935\pi$
$313$	15.3434	−	11.1477i	0.867263	−	0.630103i	0.929851	+	0.367936i	$0.119935\pi$
$314$		0			0
$315$	2.11010	+	6.49422i	0.118891	+	0.365908i
$316$		0			0
$317$	−3.95625	−	2.87439i	−0.222205	−	0.161442i	0.471113	−	0.882073i	$-0.343852\pi$
$317$	−3.95625	−	2.87439i	−0.222205	−	0.161442i	−0.693319	+	0.720631i	$0.743852\pi$
$318$		0			0
$319$	−9.19349			−0.514736
$320$		0			0
$321$	−6.50719	+	20.0271i	−0.363196	+	1.11780i
$322$		0			0
$323$	−29.5341	+	21.4578i	−1.64332	+	1.19394i
$324$		0			0
$325$	4.47214			0.248069
$326$		0			0
$327$	35.8357			1.98172
$328$		0			0
$329$	−0.857652			−0.0472839
$330$		0			0
$331$	−19.0081			−1.04478			−0.522391	−	0.852706i	$-0.674960\pi$
$331$	−19.0081			−1.04478			−0.522391	+	0.852706i	$0.674960\pi$
$332$		0			0
$333$	26.6374	−	19.3532i	1.45972	−	1.06055i
$334$		0			0
$335$	3.71227	−	11.4252i	0.202823	−	0.624224i
$336$		0			0
$337$	12.5656			0.684494			0.342247	−	0.939610i	$-0.388812\pi$
$337$	12.5656			0.684494			0.342247	+	0.939610i	$0.388812\pi$
$338$		0			0
$339$	−36.5087	−	26.5252i	−1.98288	−	1.44065i
$340$		0			0
$341$	−6.18739	−	19.0428i	−0.335066	−	1.03123i
$342$		0			0
$343$	−0.809017	+	0.587785i	−0.0436828	+	0.0317374i
$344$		0			0
$345$	−2.98904	−	2.17166i	−0.160924	−	0.116918i
$346$		0			0
$347$	4.60771	−	14.1811i	0.247355	−	0.761279i	−0.747886	−	0.663828i	$-0.768931\pi$
$347$	4.60771	−	14.1811i	0.247355	−	0.761279i	0.995240	−	0.0974518i	$-0.0310692\pi$
$348$		0			0
$349$	−7.55608	+	23.2552i	−0.404468	+	1.24482i	0.516871	+	0.856063i	$0.327097\pi$
$349$	−7.55608	+	23.2552i	−0.404468	+	1.24482i	−0.921339	+	0.388761i	$0.872903\pi$
$350$		0			0
$351$	−0.690983	−	2.12663i	−0.0368819	−	0.113511i
$352$		0			0
$353$	−8.36615	+	25.7484i	−0.445285	+	1.37045i	0.436885	+	0.899517i	$0.356082\pi$
$353$	−8.36615	+	25.7484i	−0.445285	+	1.37045i	−0.882171	+	0.470930i	$0.843918\pi$
$354$		0			0
$355$	−4.37591			−0.232249
$356$		0			0
$357$	10.8527	−	7.88498i	0.574388	−	0.417317i
$358$		0			0
$359$	−1.91691	−	1.39272i	−0.101171	−	0.0735049i	0.536050	−	0.844186i	$-0.319916\pi$
$359$	−1.91691	−	1.39272i	−0.101171	−	0.0735049i	−0.637221	+	0.770681i	$0.719916\pi$
$360$		0			0
$361$	−19.5489	−	14.2031i	−1.02889	−	0.747534i
$362$		0			0
$363$	−5.64173	−	17.3635i	−0.296114	−	0.911345i
$364$		0			0
$365$	8.00845	−	5.81848i	0.419181	−	0.304553i
$366$		0			0
$367$	−7.26599	−	22.3624i	−0.379281	−	1.16731i	−0.940544	−	0.339671i	$-0.889684\pi$
$367$	−7.26599	−	22.3624i	−0.379281	−	1.16731i	0.561263	−	0.827638i	$-0.310316\pi$
$368$		0			0
$369$	−17.2877	−	5.39767i	−0.899963	−	0.280991i
$370$		0			0
$371$	−0.931954	−	2.86826i	−0.0483847	−	0.148913i
$372$		0			0
$373$	27.5672	−	20.0287i	1.42737	−	1.03705i	0.436876	−	0.899522i	$-0.356085\pi$
$373$	27.5672	−	20.0287i	1.42737	−	1.03705i	0.990498	−	0.137526i	$-0.0439152\pi$
$374$		0			0
$375$	−7.51335	−	23.1237i	−0.387988	−	1.19410i
$376$		0			0
$377$	21.6553	+	15.7335i	1.11531	+	0.810318i
$378$		0			0
$379$	21.4448	+	15.5805i	1.10154	+	0.800318i	0.981311	−	0.192427i	$-0.0616360\pi$
$379$	21.4448	+	15.5805i	1.10154	+	0.800318i	0.120233	+	0.992746i	$0.461636\pi$
$380$		0			0
$381$	−33.6591	+	24.4548i	−1.72441	+	1.25286i
$382$		0			0
$383$	9.53225			0.487075			0.243538	−	0.969891i	$-0.421692\pi$
$383$	9.53225			0.487075			0.243538	+	0.969891i	$0.421692\pi$
$384$		0			0
$385$	1.38322	−	4.25712i	0.0704955	−	0.216963i
$386$		0			0
$387$	−7.47516	−	23.0062i	−0.379984	−	1.16947i
$388$		0			0
$389$	−6.70537	+	20.6370i	−0.339976	+	1.04634i	0.624243	+	0.781230i	$0.285408\pi$
$389$	−6.70537	+	20.6370i	−0.339976	+	1.04634i	−0.964219	+	0.265108i	$0.914592\pi$
$390$		0			0
$391$	−1.08846	+	3.34992i	−0.0550455	+	0.169413i
$392$		0			0
$393$	−35.5601	−	25.8359i	−1.79377	−	1.30325i
$394$		0			0
$395$	14.9239	−	10.8429i	0.750904	−	0.545563i
$396$		0			0
$397$	0.620329	+	1.90918i	0.0311334	+	0.0958188i	0.965416	−	0.260715i	$-0.0839584\pi$
$397$	0.620329	+	1.90918i	0.0311334	+	0.0958188i	−0.934282	+	0.356534i	$0.883958\pi$
$398$		0			0
$399$	12.8320	+	9.32297i	0.642402	+	0.466732i
$400$		0			0
$401$	−0.0678336			−0.00338745			−0.00169372	−	0.999999i	$-0.500539\pi$
$401$	−0.0678336			−0.00338745			−0.00169372	+	0.999999i	$0.500539\pi$
$402$		0			0
$403$	−18.0150	+	55.4445i	−0.897392	+	2.76189i
$404$		0			0
$405$	18.5261	−	13.4600i	0.920568	−	0.668832i
$406$		0			0
$407$	−21.5836			−1.06986
$408$		0			0
$409$	22.6828			1.12159			0.560797	−	0.827953i	$-0.310495\pi$
$409$	22.6828			1.12159			0.560797	+	0.827953i	$0.310495\pi$
$410$		0			0
$411$	40.3110			1.98839
$412$		0			0
$413$	5.65434			0.278232
$414$		0			0
$415$	−3.79315	+	2.75588i	−0.186198	+	0.135281i
$416$		0			0
$417$	−7.86371	+	24.2020i	−0.385087	+	1.18518i
$418$		0			0
$419$	18.1290			0.885659			0.442830	−	0.896606i	$-0.353975\pi$
$419$	18.1290			0.885659			0.442830	+	0.896606i	$0.353975\pi$
$420$		0			0
$421$	20.8825	+	15.1720i	1.01775	+	0.739438i	0.965820	−	0.259213i	$-0.0834632\pi$
$421$	20.8825	+	15.1720i	1.01775	+	0.739438i	0.0519285	+	0.998651i	$0.483463\pi$
$422$		0			0
$423$	−0.749616	−	2.30708i	−0.0364476	−	0.112174i
$424$		0			0
$425$	3.72407	−	2.70570i	0.180644	−	0.131246i
$426$		0			0
$427$	4.77171	+	3.46685i	0.230919	+	0.167773i
$428$		0			0
$429$	7.46711	−	22.9814i	0.360515	−	1.10955i
$430$		0			0
$431$	−3.53663	+	10.8846i	−0.170354	+	0.524294i	−0.999391	−	0.0348990i	$-0.988889\pi$
$431$	−3.53663	+	10.8846i	−0.170354	+	0.524294i	0.829037	+	0.559193i	$0.188889\pi$
$432$		0			0
$433$	−1.54627	−	4.75894i	−0.0743092	−	0.228700i	0.907002	−	0.421125i	$-0.138365\pi$
$433$	−1.54627	−	4.75894i	−0.0743092	−	0.228700i	−0.981312	+	0.192425i	$0.938365\pi$
$434$		0			0
$435$	−8.93059	+	27.4855i	−0.428189	+	1.31783i
$436$		0			0
$437$	−4.16468			−0.199224
$438$		0			0
$439$	5.67030	−	4.11971i	0.270628	−	0.196623i	−0.444191	−	0.895932i	$-0.646509\pi$
$439$	5.67030	−	4.11971i	0.270628	−	0.196623i	0.714819	+	0.699309i	$0.246509\pi$
$440$		0			0
$441$	−2.28825	−	1.66251i	−0.108964	−	0.0791670i
$442$		0			0
$443$	−14.3268	−	10.4090i	−0.680685	−	0.494546i	0.192900	−	0.981218i	$-0.438211\pi$
$443$	−14.3268	−	10.4090i	−0.680685	−	0.494546i	−0.873585	+	0.486672i	$0.838211\pi$
$444$		0			0
$445$	8.37164	+	25.7653i	0.396854	+	1.22139i
$446$		0			0
$447$	36.8952	−	26.8059i	1.74508	−	1.26788i
$448$		0			0
$449$	−4.62346	−	14.2295i	−0.218194	−	0.671533i	−0.998911	−	0.0466486i	$-0.985146\pi$
$449$	−4.62346	−	14.2295i	−0.218194	−	0.671533i	0.780717	−	0.624885i	$-0.214854\pi$
$450$		0			0
$451$	7.08844	+	9.52363i	0.333781	+	0.448450i
$452$		0			0
$453$	−4.25976	−	13.1102i	−0.200141	−	0.615971i
$454$		0			0
$455$	−10.5437	+	7.66046i	−0.494297	+	0.359128i
$456$		0			0
$457$	1.20581	+	3.71110i	0.0564055	+	0.173598i	0.975290	−	0.220928i	$-0.0709087\pi$
$457$	1.20581	+	3.71110i	0.0564055	+	0.173598i	−0.918885	+	0.394526i	$0.870909\pi$
$458$		0			0
$459$	−1.86204	−	1.35285i	−0.0869124	−	0.0631456i
$460$		0			0
$461$	−17.9257	−	13.0238i	−0.834882	−	0.606577i	0.0860541	−	0.996290i	$-0.472574\pi$
$461$	−17.9257	−	13.0238i	−0.834882	−	0.606577i	−0.920936	+	0.389713i	$0.872574\pi$
$462$		0			0
$463$	8.09674	−	5.88263i	0.376288	−	0.273389i	−0.383526	−	0.923530i	$-0.625290\pi$
$463$	8.09674	−	5.88263i	0.376288	−	0.273389i	0.759813	+	0.650141i	$0.225290\pi$
$464$		0			0
$465$	−62.9424			−2.91888
$466$		0			0
$467$	−5.87278	+	18.0745i	−0.271760	+	0.836390i	0.718299	+	0.695735i	$0.244921\pi$
$467$	−5.87278	+	18.0745i	−0.271760	+	0.836390i	−0.990059	+	0.140656i	$0.955079\pi$
$468$		0			0
$469$	1.53767	+	4.73246i	0.0710030	+	0.218525i
$470$		0			0
$471$	−10.9196	+	33.6072i	−0.503150	+	1.54854i
$472$		0			0
$473$	−4.90015	+	15.0811i	−0.225309	+	0.693430i
$474$		0			0
$475$	4.40324	+	3.19914i	0.202034	+	0.146787i
$476$		0			0
$477$	6.90105	−	5.01390i	0.315977	−	0.229571i
$478$		0			0
$479$	−5.09674	−	15.6862i	−0.232876	−	0.716719i	−0.997396	−	0.0721189i	$-0.977024\pi$
$479$	−5.09674	−	15.6862i	−0.232876	−	0.716719i	0.764520	−	0.644600i	$-0.222976\pi$
$480$		0			0
$481$	50.8403	+	36.9376i	2.31812	+	1.68421i
$482$		0			0
$483$	1.53037			0.0696345
$484$		0			0
$485$	5.58139	−	17.1778i	0.253438	−	0.780002i
$486$		0			0
$487$	−17.7762	+	12.9152i	−0.805518	+	0.585243i	−0.912528	−	0.409015i	$-0.865872\pi$
$487$	−17.7762	+	12.9152i	−0.805518	+	0.585243i	0.107009	+	0.994258i	$0.465872\pi$
$488$		0			0
$489$	34.8965			1.57807
$490$		0			0
$491$	−15.5978			−0.703917			−0.351959	−	0.936016i	$-0.614484\pi$
$491$	−15.5978			−0.703917			−0.351959	+	0.936016i	$0.614484\pi$
$492$		0			0
$493$	27.5520			1.24088
$494$		0			0
$495$	12.6606			0.569052
$496$		0			0
$497$	1.46639	−	1.06540i	0.0657766	−	0.0477895i
$498$		0			0
$499$	−10.8034	+	33.2494i	−0.483626	+	1.48845i	0.350334	+	0.936625i	$0.386068\pi$
$499$	−10.8034	+	33.2494i	−0.483626	+	1.48845i	−0.833960	+	0.551824i	$0.813932\pi$
$500$		0			0
$501$	−33.5339			−1.49818
$502$		0			0
$503$	11.1535	+	8.10353i	0.497312	+	0.361318i	0.807989	−	0.589197i	$-0.200556\pi$
$503$	11.1535	+	8.10353i	0.497312	+	0.361318i	−0.310677	+	0.950515i	$0.600556\pi$
$504$		0			0
$505$	10.0820	+	31.0293i	0.448645	+	1.38079i
$506$		0			0
$507$	−31.5278	+	22.9063i	−1.40020	+	1.01731i
$508$		0			0
$509$	14.5306	+	10.5571i	0.644059	+	0.467936i	0.861242	−	0.508195i	$-0.169687\pi$
$509$	14.5306	+	10.5571i	0.644059	+	0.467936i	−0.217184	+	0.976131i	$0.569687\pi$
$510$		0			0
$511$	−1.26706	+	3.89961i	−0.0560514	+	0.172509i
$512$		0			0
$513$	0.840943	−	2.58816i	0.0371285	−	0.114270i
$514$		0			0
$515$	−0.198917	−	0.612203i	−0.00876533	−	0.0269769i
$516$		0			0
$517$	−0.491391	+	1.51235i	−0.0216114	+	0.0665129i
$518$		0			0
$519$	38.8463			1.70517
$520$		0			0
$521$	−31.7900	+	23.0968i	−1.39274	+	1.01189i	−0.397187	+	0.917738i	$0.630014\pi$
$521$	−31.7900	+	23.0968i	−1.39274	+	1.01189i	−0.995558	+	0.0941505i	$0.969986\pi$
$522$		0			0
$523$	11.6985	+	8.49944i	0.511539	+	0.371655i	0.813407	−	0.581695i	$-0.197610\pi$
$523$	11.6985	+	8.49944i	0.511539	+	0.371655i	−0.301868	+	0.953350i	$0.597610\pi$
$524$		0			0
$525$	−1.61803	−	1.17557i	−0.0706168	−	0.0513061i
$526$		0			0
$527$	18.5430	+	57.0695i	0.807746	+	2.48599i
$528$		0			0
$529$	18.2823	−	13.2829i	0.794883	−	0.577516i
$530$		0			0
$531$	4.94208	+	15.2102i	0.214468	+	0.660064i
$532$		0			0
$533$	−0.398346	−	34.5640i	−0.0172543	−	1.49713i
$534$		0			0
$535$	−6.50719	−	20.0271i	−0.281330	−	0.865846i
$536$		0			0
$537$	29.1724	−	21.1950i	1.25888	−	0.914631i
$538$		0			0
$539$	0.572949	+	1.76336i	0.0246787	+	0.0759531i
$540$		0			0
$541$	2.54290	+	1.84753i	0.109328	+	0.0794314i	0.641106	−	0.767452i	$-0.278476\pi$
$541$	2.54290	+	1.84753i	0.109328	+	0.0794314i	−0.531778	+	0.846884i	$0.678476\pi$
$542$		0			0
$543$	−0.690983	−	0.502029i	−0.0296529	−	0.0215441i
$544$		0			0
$545$	−28.9917	+	21.0637i	−1.24187	+	0.902270i
$546$		0			0
$547$	−19.6842			−0.841636			−0.420818	−	0.907145i	$-0.638257\pi$
$547$	−19.6842			−0.841636			−0.420818	+	0.907145i	$0.638257\pi$
$548$		0			0
$549$	−5.15518	+	15.8660i	−0.220018	+	0.677144i
$550$		0			0
$551$	10.0667	+	30.9822i	0.428858	+	1.31989i
$552$		0			0
$553$	−2.36119	+	7.26701i	−0.100408	+	0.309025i
$554$		0			0
$555$	−20.9664	+	64.5279i	−0.889973	+	2.73906i
$556$		0			0
$557$	−24.3847	−	17.7165i	−1.03321	−	0.750672i	−0.0642623	−	0.997933i	$-0.520469\pi$
$557$	−24.3847	−	17.7165i	−1.03321	−	0.750672i	−0.968949	+	0.247261i	$0.920469\pi$
$558$		0			0
$559$	37.3518	−	27.1377i	1.57981	−	1.14780i
$560$		0			0
$561$	−7.68595	−	23.6549i	−0.324501	−	0.998712i
$562$		0			0
$563$	24.7193	+	17.9596i	1.04179	+	0.756907i	0.970635	−	0.240558i	$-0.0773305\pi$
$563$	24.7193	+	17.9596i	1.04179	+	0.756907i	0.0711581	+	0.997465i	$0.477330\pi$
$564$		0			0
$565$	45.1273			1.89852
$566$		0			0
$567$	−2.93111	+	9.02104i	−0.123095	+	0.378848i
$568$		0			0
$569$	−27.3421	+	19.8652i	−1.14624	+	0.832792i	−0.987976	−	0.154604i	$-0.950590\pi$
$569$	−27.3421	+	19.8652i	−1.14624	+	0.832792i	−0.158264	+	0.987397i	$0.550590\pi$
$570$		0			0
$571$	−11.8825			−0.497267			−0.248634	−	0.968598i	$-0.579981\pi$
$571$	−11.8825			−0.497267			−0.248634	+	0.968598i	$0.579981\pi$
$572$		0			0
$573$	5.71227			0.238633
$574$		0			0
$575$	0.525142			0.0218999
$576$		0			0
$577$	20.2051			0.841151			0.420576	−	0.907258i	$-0.361828\pi$
$577$	20.2051			0.841151			0.420576	+	0.907258i	$0.361828\pi$
$578$		0			0
$579$	27.4699	−	19.9581i	1.14161	−	0.829429i
$580$		0			0
$581$	0.600135	−	1.84703i	0.0248978	−	0.0766275i
$582$		0			0
$583$	−5.59173			−0.231586
$584$		0			0
$585$	−29.8222	−	21.6671i	−1.23299	−	0.895823i
$586$		0			0
$587$	6.27839	+	19.3229i	0.259137	+	0.797541i	0.992986	+	0.118229i	$0.0377217\pi$
$587$	6.27839	+	19.3229i	0.259137	+	0.797541i	−0.733850	+	0.679312i	$0.762278\pi$
$588$		0			0
$589$	−57.3997	+	41.7033i	−2.36511	+	1.71835i
$590$		0			0
$591$	−2.35223	−	1.70899i	−0.0967578	−	0.0702986i
$592$		0			0
$593$	−2.58830	+	7.96596i	−0.106289	+	0.327123i	−0.990031	−	0.140851i	$-0.955016\pi$
$593$	−2.58830	+	7.96596i	−0.106289	+	0.327123i	0.883742	+	0.467974i	$0.155016\pi$
$594$		0			0
$595$	−4.14538	+	12.7582i	−0.169944	+	0.523034i
$596$		0			0
$597$	−6.20924	−	19.1101i	−0.254127	−	0.782123i
$598$		0			0
$599$	1.75851	−	5.41213i	0.0718507	−	0.221134i	−0.908682	−	0.417488i	$-0.862910\pi$
$599$	1.75851	−	5.41213i	0.0718507	−	0.221134i	0.980533	+	0.196355i	$0.0629104\pi$
$600$		0			0
$601$	−33.0530			−1.34826			−0.674130	−	0.738612i	$-0.735481\pi$
$601$	−33.0530			−1.34826			−0.674130	+	0.738612i	$0.735481\pi$
$602$		0			0
$603$	−11.3863	+	8.27265i	−0.463687	+	0.336888i
$604$		0			0
$605$	14.7702	+	10.7312i	0.600496	+	0.436286i
$606$		0			0
$607$	−11.0712	−	8.04366i	−0.449364	−	0.326482i	0.339980	−	0.940432i	$-0.389580\pi$
$607$	−11.0712	−	8.04366i	−0.449364	−	0.326482i	−0.789345	+	0.613950i	$0.789580\pi$
$608$		0			0
$609$	−3.69917	−	11.3849i	−0.149898	−	0.461339i
$610$		0			0
$611$	3.74567	−	2.72139i	0.151534	−	0.110096i
$612$		0			0
$613$	6.44802	+	19.8450i	0.260433	+	0.801531i	0.992710	+	0.120524i	$0.0384575\pi$
$613$	6.44802	+	19.8450i	0.260433	+	0.801531i	−0.732277	+	0.681007i	$0.761542\pi$
$614$		0			0
$615$	35.3583	−	11.9408i	1.42578	−	0.481501i
$616$		0			0
$617$	−0.562826	−	1.73220i	−0.0226585	−	0.0697357i	0.939088	−	0.343677i	$-0.111673\pi$
$617$	−0.562826	−	1.73220i	−0.0226585	−	0.0697357i	−0.961746	+	0.273941i	$0.911673\pi$
$618$		0			0
$619$	10.9015	−	7.92042i	0.438169	−	0.318349i	−0.346738	−	0.937962i	$-0.612711\pi$
$619$	10.9015	−	7.92042i	0.438169	−	0.318349i	0.784907	+	0.619613i	$0.212711\pi$
$620$		0			0
$621$	−0.0811388	−	0.249720i	−0.00325599	−	0.0100209i
$622$		0			0
$623$	−9.07842	−	6.59586i	−0.363719	−	0.264257i
$624$		0			0
$625$	23.0213	+	16.7259i	0.920850	+	0.669037i
$626$		0			0
$627$	23.7918	−	17.2857i	0.950152	−	0.690326i
$628$		0			0
$629$	64.6839			2.57911
$630$		0			0
$631$	1.74213	−	5.36172i	0.0693531	−	0.213447i	−0.910373	−	0.413789i	$-0.864205\pi$
$631$	1.74213	−	5.36172i	0.0693531	−	0.213447i	0.979726	+	0.200342i	$0.0642053\pi$
$632$		0			0
$633$	6.08239	+	18.7197i	0.241753	+	0.744041i
$634$		0			0
$635$	12.8566	−	39.5687i	0.510200	−	1.57024i
$636$		0			0
$637$	1.66818	−	5.13413i	0.0660957	−	0.203422i
$638$		0			0
$639$	4.14758	+	3.01339i	0.164076	+	0.119208i
$640$		0			0
$641$	8.16919	−	5.93527i	0.322664	−	0.234429i	−0.414648	−	0.909982i	$-0.636095\pi$
$641$	8.16919	−	5.93527i	0.322664	−	0.234429i	0.737311	+	0.675553i	$0.236095\pi$
$642$		0			0
$643$	−2.91860	−	8.98252i	−0.115098	−	0.354236i	0.876869	−	0.480729i	$-0.159628\pi$
$643$	−2.91860	−	8.98252i	−0.115098	−	0.354236i	−0.991968	+	0.126493i	$0.959628\pi$
$644$		0			0
$645$	40.3276	+	29.2997i	1.58790	+	1.15367i
$646$		0			0
$647$	34.3338			1.34980			0.674901	−	0.737909i	$-0.264186\pi$
$647$	34.3338			1.34980			0.674901	+	0.737909i	$0.264186\pi$
$648$		0			0
$649$	3.23965	−	9.97062i	0.127167	−	0.391381i
$650$		0			0
$651$	21.0924	−	15.3245i	0.826674	−	0.600614i
$652$		0			0
$653$	26.0682			1.02013			0.510064	−	0.860136i	$-0.329622\pi$
$653$	26.0682			1.02013			0.510064	+	0.860136i	$0.329622\pi$
$654$		0			0
$655$	43.9547			1.71745
$656$		0			0
$657$	−11.5974			−0.452457
$658$		0			0
$659$	32.6285			1.27103			0.635513	−	0.772090i	$-0.280789\pi$
$659$	32.6285			1.27103			0.635513	+	0.772090i	$0.280789\pi$
$660$		0			0
$661$	8.63658	−	6.27484i	0.335924	−	0.244063i	−0.407016	−	0.913421i	$-0.633431\pi$
$661$	8.63658	−	6.27484i	0.335924	−	0.244063i	0.742940	+	0.669358i	$0.233431\pi$
$662$		0			0
$663$	−22.3782	+	68.8730i	−0.869097	+	2.67480i
$664$		0			0
$665$	−15.8612			−0.615070
$666$		0			0
$667$	2.54288	+	1.84751i	0.0984608	+	0.0715360i
$668$		0			0
$669$	1.74200	+	5.36133i	0.0673497	+	0.207281i
$670$		0			0
$671$	8.84723	−	6.42789i	0.341544	−	0.248146i
$672$		0			0
$673$	−12.1055	−	8.79517i	−0.466633	−	0.339029i	0.329494	−	0.944158i	$-0.393122\pi$
$673$	−12.1055	−	8.79517i	−0.466633	−	0.339029i	−0.796128	+	0.605129i	$0.793122\pi$
$674$		0			0
$675$	−0.106038	+	0.326351i	−0.00408140	+	0.0125613i
$676$		0			0
$677$	8.31427	−	25.5887i	0.319543	−	0.983453i	−0.654300	−	0.756235i	$-0.727037\pi$
$677$	8.31427	−	25.5887i	0.319543	−	0.983453i	0.973844	−	0.227219i	$-0.0729632\pi$
$678$		0			0
$679$	2.31189	+	7.11526i	0.0887222	+	0.273059i
$680$		0			0
$681$	−10.5468	+	32.4596i	−0.404152	+	1.24385i
$682$		0			0
$683$	−42.3627			−1.62096			−0.810482	−	0.585763i	$-0.800795\pi$
$683$	−42.3627			−1.62096			−0.810482	+	0.585763i	$0.800795\pi$
$684$		0			0
$685$	−32.6123	+	23.6942i	−1.24605	+	0.905309i
$686$		0			0
$687$	50.3456	+	36.5782i	1.92081	+	1.39555i
$688$		0			0
$689$	13.1714	+	9.56955i	0.501789	+	0.364571i
$690$		0			0
$691$	−5.96468	−	18.3574i	−0.226907	−	0.698348i	−0.998092	−	0.0617377i	$-0.980336\pi$
$691$	−5.96468	−	18.3574i	−0.226907	−	0.698348i	0.771185	−	0.636611i	$-0.219664\pi$
$692$		0			0
$693$	−4.24264	+	3.08246i	−0.161165	+	0.117093i
$694$		0			0
$695$	−7.86371	−	24.2020i	−0.298287	−	0.918034i
$696$		0			0
$697$	−21.2433	−	28.5414i	−0.804649	−	1.08108i
$698$		0			0
$699$	−8.27892	−	25.4799i	−0.313137	−	0.963738i
$700$		0			0
$701$	−24.6568	+	17.9142i	−0.931276	+	0.676612i	−0.946305	−	0.323275i	$-0.895216\pi$
$701$	−24.6568	+	17.9142i	−0.931276	+	0.676612i	0.0150287	+	0.999887i	$0.495216\pi$
$702$		0			0
$703$	23.6337	+	72.7371i	0.891363	+	2.74333i
$704$		0			0
$705$	4.04409	+	2.93820i	0.152309	+	0.110659i
$706$		0			0
$707$	−10.9332	−	7.94344i	−0.411186	−	0.298744i
$708$		0			0
$709$	−0.636603	+	0.462519i	−0.0239081	+	0.0173703i	−0.599675	−	0.800244i	$-0.704704\pi$
$709$	−0.636603	+	0.462519i	−0.0239081	+	0.0173703i	0.575767	+	0.817614i	$0.304704\pi$
$710$		0			0
$711$	−21.6120			−0.810512
$712$		0			0
$713$	−2.11542	+	6.51059i	−0.0792230	+	0.243823i
$714$		0			0
$715$	7.46711	+	22.9814i	0.279254	+	0.859455i
$716$		0			0
$717$	7.74654	−	23.8414i	0.289300	−	0.890374i
$718$		0			0
$719$	−12.4368	+	38.2766i	−0.463815	+	1.42748i	0.396652	+	0.917969i	$0.370172\pi$
$719$	−12.4368	+	38.2766i	−0.463815	+	1.42748i	−0.860467	+	0.509507i	$0.829828\pi$
$720$		0			0
$721$	0.215711	+	0.156723i	0.00803348	+	0.00583667i
$722$		0			0
$723$	47.9729	−	34.8544i	1.78413	−	1.29625i
$724$		0			0
$725$	−1.26936	−	3.90667i	−0.0471427	−	0.145090i
$726$		0			0
$727$	−24.3395	−	17.6837i	−0.902701	−	0.655851i	0.0364574	−	0.999335i	$-0.488393\pi$
$727$	−24.3395	−	17.6837i	−0.902701	−	0.655851i	−0.939158	+	0.343485i	$0.888393\pi$
$728$		0			0
$729$	−23.8284			−0.882534
$730$		0			0
$731$	14.6853	−	45.1966i	0.543154	−	1.67166i
$732$		0			0
$733$	−26.3638	+	19.1544i	−0.973769	+	0.707485i	−0.956307	−	0.292363i	$-0.905559\pi$
$733$	−26.3638	+	19.1544i	−0.973769	+	0.707485i	−0.0174618	+	0.999848i	$0.505559\pi$
$734$		0			0
$735$	5.82843			0.214985
$736$		0			0
$737$	9.22603			0.339845
$738$		0			0
$739$	0.829451			0.0305118			0.0152559	−	0.999884i	$-0.495144\pi$
$739$	0.829451			0.0305118			0.0152559	+	0.999884i	$0.495144\pi$
$740$		0			0
$741$	−85.6242			−3.14548
$742$		0			0
$743$	5.34834	−	3.88579i	0.196211	−	0.142556i	−0.485342	−	0.874325i	$-0.661305\pi$
$743$	5.34834	−	3.88579i	0.196211	−	0.142556i	0.681553	+	0.731769i	$0.261305\pi$
$744$		0			0
$745$	−14.0927	+	43.3729i	−0.516317	+	1.58906i
$746$		0			0
$747$	5.49302			0.200979
$748$		0			0
$749$	7.05656	+	5.12689i	0.257841	+	0.187333i
$750$		0			0
$751$	−2.67667	−	8.23796i	−0.0976733	−	0.300607i	0.890268	−	0.455437i	$-0.150517\pi$
$751$	−2.67667	−	8.23796i	−0.0976733	−	0.300607i	−0.987941	+	0.154830i	$0.950517\pi$
$752$		0			0
$753$	46.2120	−	33.5750i	1.68406	−	1.22354i
$754$		0			0
$755$	11.1522	+	8.10255i	0.405870	+	0.294882i
$756$		0			0
$757$	3.94291	−	12.1350i	0.143308	−	0.441055i	−0.853482	−	0.521122i	$-0.825513\pi$
$757$	3.94291	−	12.1350i	0.143308	−	0.441055i	0.996789	+	0.0800672i	$0.0255135\pi$
$758$		0			0
$759$	0.876827	−	2.69859i	0.0318268	−	0.0979528i
$760$		0			0
$761$	−8.71897	−	26.8342i	−0.316062	−	0.972740i	−0.975315	−	0.220818i	$-0.929127\pi$
$761$	−8.71897	−	26.8342i	−0.316062	−	0.972740i	0.659253	−	0.751922i	$-0.270873\pi$
$762$		0			0
$763$	4.58694	−	14.1171i	0.166058	−	0.511075i
$764$		0			0
$765$	−37.9426			−1.37182
$766$		0			0
$767$	−24.6945	+	17.9416i	−0.891667	+	0.647834i
$768$		0			0
$769$	−42.5777	−	30.9345i	−1.53539	−	1.11553i	−0.953144	−	0.302517i	$-0.902173\pi$
$769$	−42.5777	−	30.9345i	−1.53539	−	1.11553i	−0.582248	−	0.813011i	$-0.697827\pi$
$770$		0			0
$771$	−58.1918	−	42.2788i	−2.09573	−	1.52263i
$772$		0			0
$773$	−14.7753	−	45.4738i	−0.531432	−	1.63558i	−0.751234	−	0.660036i	$-0.770541\pi$
$773$	−14.7753	−	45.4738i	−0.531432	−	1.63558i	0.219802	−	0.975544i	$-0.429459\pi$
$774$		0			0
$775$	7.23775	−	5.25853i	0.259988	−	0.188892i
$776$		0			0
$777$	−8.68456	−	26.7283i	−0.311557	−	0.958873i
$778$		0			0
$779$	24.3331	−	34.3164i	0.871824	−	1.22951i
$780$		0			0
$781$	−1.03850	−	3.19619i	−0.0371606	−	0.114369i
$782$		0			0
$783$	−1.66161	+	1.20723i	−0.0593810	+	0.0431428i
$784$		0			0
$785$	−10.9196	−	33.6072i	−0.389738	−	1.19949i
$786$		0			0
$787$	−25.2405	−	18.3383i	−0.899727	−	0.653690i	0.0386687	−	0.999252i	$-0.487688\pi$
$787$	−25.2405	−	18.3383i	−0.899727	−	0.653690i	−0.938396	+	0.345562i	$0.887688\pi$
$788$		0			0
$789$	7.45904	+	5.41931i	0.265549	+	0.192933i
$790$		0			0
$791$	−15.1224	+	10.9871i	−0.537691	+	0.390656i
$792$		0			0
$793$	−31.8403			−1.13068
$794$		0			0
$795$	−5.43183	+	16.7174i	−0.192647	+	0.592907i
$796$		0			0
$797$	12.1361	+	37.3511i	0.429884	+	1.32305i	0.898240	+	0.439506i	$0.144846\pi$
$797$	12.1361	+	37.3511i	0.429884	+	1.32305i	−0.468356	+	0.883540i	$0.655154\pi$
$798$		0			0
$799$	1.47265	−	4.53235i	0.0520986	−	0.160343i
$800$		0			0
$801$	9.80799	−	30.1859i	0.346548	−	1.06657i
$802$		0			0
$803$	6.15044	+	4.46856i	0.217044	+	0.157692i
$804$		0			0
$805$	−1.23810	+	0.899532i	−0.0436373	+	0.0317043i
$806$		0			0
$807$	−10.2080	−	31.4170i	−0.359339	−	1.10593i
$808$		0			0
$809$	25.3060	+	18.3859i	0.889710	+	0.646412i	0.935802	−	0.352525i	$-0.114677\pi$
$809$	25.3060	+	18.3859i	0.889710	+	0.646412i	−0.0460921	+	0.998937i	$0.514677\pi$
$810$		0			0
$811$	−15.1560			−0.532200			−0.266100	−	0.963945i	$-0.585735\pi$
$811$	−15.1560			−0.532200			−0.266100	+	0.963945i	$0.585735\pi$
$812$		0			0
$813$	−0.224388	+	0.690596i	−0.00786963	+	0.0242202i
$814$		0			0
$815$	−28.2318	+	20.5116i	−0.988918	+	0.718491i
$816$		0			0
$817$	56.1892			1.96581
$818$		0			0
$819$	15.2688			0.533536
$820$		0			0
$821$	−32.7409			−1.14267			−0.571333	−	0.820718i	$-0.693574\pi$
$821$	−32.7409			−1.14267			−0.571333	+	0.820718i	$0.693574\pi$
$822$		0			0
$823$	5.97599			0.208310			0.104155	−	0.994561i	$-0.466786\pi$
$823$	5.97599			0.208310			0.104155	+	0.994561i	$0.466786\pi$
$824$		0			0
$825$	−3.00000	+	2.17963i	−0.104447	+	0.0758849i
$826$		0			0
$827$	−9.54082	+	29.3636i	−0.331767	+	1.02107i	0.636526	+	0.771255i	$0.280371\pi$
$827$	−9.54082	+	29.3636i	−0.331767	+	1.02107i	−0.968293	+	0.249818i	$0.919629\pi$
$828$		0			0
$829$	7.84083			0.272323			0.136162	−	0.990687i	$-0.456523\pi$
$829$	7.84083			0.272323			0.136162	+	0.990687i	$0.456523\pi$
$830$		0			0
$831$	−27.0002	−	19.6168i	−0.936628	−	0.680500i
$832$		0			0
$833$	−1.71707	−	5.28460i	−0.0594930	−	0.183101i
$834$		0			0
$835$	27.1295	−	19.7107i	0.938855	−	0.682118i
$836$		0			0
$837$	−3.61888	−	2.62927i	−0.125087	−	0.0908808i
$838$		0			0
$839$	17.1885	−	52.9008i	0.593413	−	1.82634i	0.0309436	−	0.999521i	$-0.490149\pi$
$839$	17.1885	−	52.9008i	0.593413	−	1.82634i	0.562470	−	0.826818i	$-0.309851\pi$
$840$		0			0
$841$	−1.36391	+	4.19768i	−0.0470313	+	0.144748i
$842$		0			0
$843$	10.0474	+	30.9226i	0.346050	+	1.06503i
$844$		0			0
$845$	12.0426	−	37.0632i	0.414277	−	1.27501i
$846$		0			0
$847$	−7.56231			−0.259844
$848$		0			0
$849$	21.8757	−	15.8936i	0.750772	−	0.545468i
$850$		0			0
$851$	5.96993	+	4.33741i	0.204647	+	0.148685i
$852$		0			0
$853$	21.8669	+	15.8873i	0.748709	+	0.543969i	0.895427	−	0.445209i	$-0.146871\pi$
$853$	21.8669	+	15.8873i	0.748709	+	0.543969i	−0.146717	+	0.989178i	$0.546871\pi$
$854$		0			0
$855$	−13.8632	−	42.6665i	−0.474111	−	1.45916i
$856$		0			0
$857$	1.04098	−	0.756315i	0.0355592	−	0.0258352i	−0.569864	−	0.821739i	$-0.693004\pi$
$857$	1.04098	−	0.756315i	0.0355592	−	0.0258352i	0.605423	+	0.795904i	$0.293004\pi$
$858$		0			0
$859$	8.62819	+	26.5548i	0.294390	+	0.906039i	0.983426	+	0.181312i	$0.0580343\pi$
$859$	8.62819	+	26.5548i	0.294390	+	0.906039i	−0.689036	+	0.724727i	$0.741966\pi$
$860$		0			0
$861$	−8.94156	+	12.6101i	−0.304727	+	0.429750i
$862$		0			0
$863$	−0.668140	−	2.05632i	−0.0227438	−	0.0699981i	0.939040	−	0.343807i	$-0.111717\pi$
$863$	−0.668140	−	2.05632i	−0.0227438	−	0.0699981i	−0.961784	+	0.273809i	$0.911717\pi$
$864$		0			0
$865$	−31.4274	+	22.8333i	−1.06856	+	0.776356i
$866$		0			0
$867$	10.3515	+	31.8586i	0.351555	+	1.08197i
$868$		0			0
$869$	11.4615	+	8.32725i	0.388804	+	0.282483i
$870$		0			0
$871$	−21.7320	−	15.7892i	−0.736360	−	0.534997i
$872$		0			0
$873$	−17.1194	+	12.4379i	−0.579402	+	0.420960i
$874$		0			0
$875$	−10.0711			−0.340464
$876$		0			0
$877$	−9.75341	+	30.0179i	−0.329349	+	1.01363i	0.640090	+	0.768300i	$0.278897\pi$
$877$	−9.75341	+	30.0179i	−0.329349	+	1.01363i	−0.969439	+	0.245332i	$0.921103\pi$
$878$		0			0
$879$	13.7226	+	42.2338i	0.462851	+	1.42451i
$880$		0			0
$881$	−1.56011	+	4.80153i	−0.0525615	+	0.161768i	−0.973892	−	0.227014i	$-0.927104\pi$
$881$	−1.56011	+	4.80153i	−0.0525615	+	0.161768i	0.921330	+	0.388781i	$0.127104\pi$
$882$		0			0
$883$	8.45929	−	26.0350i	0.284678	−	0.876148i	−0.701817	−	0.712357i	$-0.747628\pi$
$883$	8.45929	−	26.0350i	0.284678	−	0.876148i	0.986495	−	0.163791i	$-0.0523723\pi$
$884$		0			0
$885$	−26.6619	−	19.3710i	−0.896230	−	0.651149i
$886$		0			0
$887$	−18.7488	+	13.6218i	−0.629523	+	0.457375i	−0.856235	−	0.516587i	$-0.827202\pi$
$887$	−18.7488	+	13.6218i	−0.629523	+	0.457375i	0.226712	+	0.973962i	$0.427202\pi$
$888$		0			0
$889$	5.32540	+	16.3899i	0.178608	+	0.549699i
$890$		0			0
$891$	14.2279	+	10.3372i	0.476653	+	0.346309i
$892$		0			0
$893$	5.63471			0.188558
$894$		0			0
$895$	−11.1429	+	34.2942i	−0.372465	+	1.14633i
$896$		0			0
$897$	−6.68369	+	4.85598i	−0.223162	+	0.162137i
$898$		0			0
$899$	53.5474			1.78591
$900$		0			0
$901$	16.7579			0.558285
$902$		0			0
$903$	−20.6476			−0.687108
$904$		0			0
$905$	0.854102			0.0283913
$906$		0			0
$907$	8.11857	−	5.89848i	0.269573	−	0.195856i	−0.444784	−	0.895638i	$-0.646720\pi$
$907$	8.11857	−	5.89848i	0.269573	−	0.195856i	0.714356	+	0.699782i	$0.246720\pi$
$908$		0			0
$909$	11.8118	−	36.3531i	0.391774	−	1.20576i
$910$		0			0
$911$	−14.7197			−0.487684			−0.243842	−	0.969815i	$-0.578408\pi$
$911$	−14.7197			−0.487684			−0.243842	+	0.969815i	$0.578408\pi$
$912$		0			0
$913$	−2.91312	−	2.11650i	−0.0964101	−	0.0700460i
$914$		0			0
$915$	−10.6231	−	32.6944i	−0.351188	−	1.08084i
$916$		0			0
$917$	−14.7295	+	10.7016i	−0.486410	+	0.353398i
$918$		0			0
$919$	−10.6604	−	7.74523i	−0.351654	−	0.255492i	0.397909	−	0.917425i	$-0.369736\pi$
$919$	−10.6604	−	7.74523i	−0.351654	−	0.255492i	−0.749563	+	0.661933i	$0.769736\pi$
$920$		0			0
$921$	18.0736	−	55.6248i	0.595545	−	1.83290i
$922$		0			0
$923$	−3.02368	+	9.30592i	−0.0995255	+	0.306308i
$924$		0			0
$925$	−2.98007	−	9.17171i	−0.0979841	−	0.301564i
$926$		0			0
$927$	−0.233046	+	0.717241i	−0.00765423	+	0.0235573i
$928$		0			0
$929$	−2.28826			−0.0750754			−0.0375377	−	0.999295i	$-0.511951\pi$
$929$	−2.28826			−0.0750754			−0.0375377	+	0.999295i	$0.511951\pi$
$930$		0			0
$931$	5.31518	−	3.86170i	0.174198	−	0.126562i
$932$		0			0
$933$	−56.5560	−	41.0903i	−1.85156	−	1.34524i
$934$		0			0
$935$	20.1221	+	14.6196i	0.658063	+	0.478110i
$936$		0			0
$937$	11.6474	+	35.8470i	0.380504	+	1.17107i	0.939690	+	0.342028i	$0.111114\pi$
$937$	11.6474	+	35.8470i	0.380504	+	1.17107i	−0.559186	+	0.829042i	$0.688886\pi$
$938$		0			0
$939$	37.0424	−	26.9128i	1.20883	−	0.878268i
$940$		0			0
$941$	5.23673	+	16.1170i	0.170713	+	0.525399i	0.999412	−	0.0342949i	$-0.0109186\pi$
$941$	5.23673	+	16.1170i	0.170713	+	0.525399i	−0.828699	+	0.559694i	$0.810919\pi$
$942$		0			0
$943$	−0.0467758	−	4.05868i	−0.00152323	−	0.132169i
$944$		0			0
$945$	−0.309017	−	0.951057i	−0.0100523	−	0.0309379i
$946$		0			0
$947$	42.0358	−	30.5408i	1.36598	−	0.992442i	0.367939	−	0.929850i	$-0.380063\pi$
$947$	42.0358	−	30.5408i	1.36598	−	0.992442i	0.998039	−	0.0625918i	$-0.0199366\pi$
$948$		0			0
$949$	−6.84003	−	21.0514i	−0.222037	−	0.683359i
$950$		0			0
$951$	−9.55124	−	6.93938i	−0.309720	−	0.225025i
$952$		0			0
$953$	9.18795	+	6.67544i	0.297627	+	0.216239i	0.726569	−	0.687093i	$-0.241114\pi$
$953$	9.18795	+	6.67544i	0.297627	+	0.216239i	−0.428942	+	0.903332i	$0.641114\pi$
$954$		0			0
$955$	−4.62132	+	3.35759i	−0.149542	+	0.108649i
$956$		0			0
$957$	−22.1950			−0.717464
$958$		0			0
$959$	5.15977	−	15.8801i	0.166618	−	0.512796i
$960$		0			0
$961$	26.4589	+	81.4321i	0.853513	+	2.62684i
$962$		0			0
$963$	−7.62365	+	23.4632i	−0.245669	+	0.756090i
$964$		0			0
$965$	−10.4926	+	32.2928i	−0.337768	+	1.03954i
$966$		0			0
$967$	14.5675	+	10.5839i	0.468460	+	0.340356i	0.796841	−	0.604189i	$-0.206503\pi$
$967$	14.5675	+	10.5839i	0.468460	+	0.340356i	−0.328381	+	0.944545i	$0.606503\pi$
$968$		0			0
$969$	−71.3016	+	51.8037i	−2.29054	+	1.66417i
$970$		0			0
$971$	3.77582	+	11.6208i	0.121172	+	0.372929i	0.993184	−	0.116555i	$-0.0371852\pi$
$971$	3.77582	+	11.6208i	0.121172	+	0.372929i	−0.872012	+	0.489484i	$0.837185\pi$
$972$		0			0
$973$	8.52760	+	6.19566i	0.273382	+	0.198624i
$974$		0			0
$975$	10.7967			0.345771
$976$		0			0
$977$	1.66435	−	5.12234i	0.0532472	−	0.163878i	−0.920897	−	0.389807i	$-0.872542\pi$
$977$	1.66435	−	5.12234i	0.0532472	−	0.163878i	0.974144	+	0.225929i	$0.0725417\pi$
$978$		0			0
$979$	−16.8323	+	12.2294i	−0.537963	+	0.390853i
$980$		0			0
$981$	41.9841			1.34045
$982$		0			0
$983$	16.6072			0.529686			0.264843	−	0.964292i	$-0.414680\pi$
$983$	16.6072			0.529686			0.264843	+	0.964292i	$0.414680\pi$
$984$		0			0
$985$	2.90751			0.0926411
$986$		0			0
$987$	−2.07056			−0.0659065
$988$		0			0
$989$	4.38604	−	3.18665i	0.139468	−	0.101329i
$990$		0			0
$991$	10.5498	−	32.4689i	0.335125	−	1.03141i	−0.631536	−	0.775347i	$-0.717575\pi$
$991$	10.5498	−	32.4689i	0.335125	−	1.03141i	0.966660	−	0.256062i	$-0.0824250\pi$
$992$		0			0
$993$	−45.8897			−1.45626
$994$		0			0
$995$	16.2560	+	11.8107i	0.515350	+	0.374423i
$996$		0			0
$997$	−4.49806	−	13.8436i	−0.142455	−	0.438431i	0.854220	−	0.519912i	$-0.174035\pi$
$997$	−4.49806	−	13.8436i	−0.142455	−	0.438431i	−0.996675	+	0.0814805i	$0.974035\pi$
$998$		0			0
$999$	−3.90096	+	2.83421i	−0.123421	+	0.0896706i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.n.b.141.2	yes	8
41.16	even	5	inner	1148.2.n.b.57.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.n.b.57.2	✓	8	41.16	even	5	inner
1148.2.n.b.141.2	yes	8	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+2.41421 q^{3} +(-1.95314 + 1.41904i) q^{5} +(0.309017 - 0.951057i) q^{7} +2.82843 q^{9} +O(q^{10})\)	\(q+2.41421 q^{3} +(-1.95314 + 1.41904i) q^{5} +(0.309017 - 0.951057i) q^{7} +2.82843 q^{9} +(-1.50000 - 1.08981i) q^{11} +(1.66818 + 5.13413i) q^{13} +(-4.71530 + 3.42586i) q^{15} +(4.49535 + 3.26606i) q^{17} +(-2.03022 + 6.24836i) q^{19} +(0.746033 - 2.29605i) q^{21} +(0.195886 + 0.602877i) q^{23} +(0.255998 - 0.787881i) q^{25} -0.414214 q^{27} +(4.01148 - 2.91451i) q^{29} +(8.73674 + 6.34761i) q^{31} +(-3.62132 - 2.63104i) q^{33} +(0.746033 + 2.29605i) q^{35} +(9.41776 - 6.84240i) q^{37} +(4.02734 + 12.3949i) q^{39} +(-6.11213 - 1.90836i) q^{41} +(-2.64287 - 8.13391i) q^{43} +(-5.52431 + 4.01365i) q^{45} +(-0.265029 - 0.815676i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(10.8527 + 7.88498i) q^{51} +(2.43989 - 1.77268i) q^{53} +4.47620 q^{55} +(-4.90138 + 15.0849i) q^{57} +(1.74729 + 5.37760i) q^{59} +(-1.82263 + 5.60948i) q^{61} +(0.874032 - 2.68999i) q^{63} +(-10.5437 - 7.66046i) q^{65} +(-4.02567 + 2.92482i) q^{67} +(0.472912 + 1.45547i) q^{69} +(1.46639 + 1.06540i) q^{71} -4.10029 q^{73} +(0.618034 - 1.90211i) q^{75} +(-1.50000 + 1.08981i) q^{77} -7.64099 q^{79} -9.48528 q^{81} +1.94208 q^{83} -13.4147 q^{85} +(9.68456 - 7.03624i) q^{87} +(3.46765 - 10.6723i) q^{89} +5.39835 q^{91} +(21.0924 + 15.3245i) q^{93} +(-4.90138 - 15.0849i) q^{95} +(-6.05260 + 4.39747i) q^{97} +(-4.24264 - 3.08246i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{3} - 2 q^{5} - 2 q^{7}+O(q^{10}) \) 8 * q + 8 * q^3 - 2 * q^5 - 2 * q^7	\( 8 q + 8 q^{3} - 2 q^{5} - 2 q^{7} - 12 q^{11} + 10 q^{13} - 6 q^{15} + 12 q^{17} - 2 q^{19} - 2 q^{21} - 12 q^{23} + 4 q^{25} + 8 q^{27} - 2 q^{29} + 14 q^{31} - 12 q^{33} - 2 q^{35} + 14 q^{37} + 30 q^{39} - 18 q^{41} - 14 q^{43} - 8 q^{45} + 28 q^{47} - 2 q^{49} + 28 q^{51} + 4 q^{53} - 12 q^{55} - 30 q^{57} + 4 q^{59} - 4 q^{61} - 30 q^{65} - 28 q^{67} - 36 q^{69} - 44 q^{73} - 4 q^{75} - 12 q^{77} + 16 q^{79} - 8 q^{81} + 40 q^{83} - 12 q^{85} + 22 q^{87} + 14 q^{89} + 42 q^{93} - 30 q^{95} - 38 q^{97}+O(q^{100}) \) 8 * q + 8 * q^3 - 2 * q^5 - 2 * q^7 - 12 * q^11 + 10 * q^13 - 6 * q^15 + 12 * q^17 - 2 * q^19 - 2 * q^21 - 12 * q^23 + 4 * q^25 + 8 * q^27 - 2 * q^29 + 14 * q^31 - 12 * q^33 - 2 * q^35 + 14 * q^37 + 30 * q^39 - 18 * q^41 - 14 * q^43 - 8 * q^45 + 28 * q^47 - 2 * q^49 + 28 * q^51 + 4 * q^53 - 12 * q^55 - 30 * q^57 + 4 * q^59 - 4 * q^61 - 30 * q^65 - 28 * q^67 - 36 * q^69 - 44 * q^73 - 4 * q^75 - 12 * q^77 + 16 * q^79 - 8 * q^81 + 40 * q^83 - 12 * q^85 + 22 * q^87 + 14 * q^89 + 42 * q^93 - 30 * q^95 - 38 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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