LMFDB - Embedded newform 1148.2.n.e.141.1

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:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			141.1
Character	$\chi$	$=$	1148.141
Dual form			1148.2.n.e.57.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.87361 q^{3} +(2.43977 - 1.77260i) q^{5} +(-0.309017 + 0.951057i) q^{7} +5.25763 q^{9} +O(q^{10})$	\(q-2.87361 q^{3} +(2.43977 - 1.77260i) q^{5} +(-0.309017 + 0.951057i) q^{7} +5.25763 q^{9} +(-0.220999 - 0.160565i) q^{11} +(0.746236 + 2.29668i) q^{13} +(-7.01094 + 5.09375i) q^{15} +(2.08179 + 1.51251i) q^{17} +(-0.484683 + 1.49170i) q^{19} +(0.887994 - 2.73296i) q^{21} +(-0.540140 - 1.66238i) q^{23} +(1.26529 - 3.89416i) q^{25} -6.48754 q^{27} +(-4.86762 + 3.53653i) q^{29} +(-1.36436 - 0.991266i) q^{31} +(0.635066 + 0.461402i) q^{33} +(0.931909 + 2.86812i) q^{35} +(6.90205 - 5.01463i) q^{37} +(-2.14439 - 6.59975i) q^{39} +(2.41386 + 5.93071i) q^{41} +(-0.500213 - 1.53950i) q^{43} +(12.8274 - 9.31964i) q^{45} +(1.47917 + 4.55243i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(-5.98226 - 4.34636i) q^{51} +(7.63405 - 5.54646i) q^{53} -0.823805 q^{55} +(1.39279 - 4.28656i) q^{57} +(2.15789 + 6.64131i) q^{59} +(-1.03142 + 3.17438i) q^{61} +(-1.62470 + 5.00030i) q^{63} +(5.89172 + 4.28059i) q^{65} +(6.99833 - 5.08458i) q^{67} +(1.55215 + 4.77703i) q^{69} +(10.3783 + 7.54028i) q^{71} +12.6539 q^{73} +(-3.63595 + 11.1903i) q^{75} +(0.220999 - 0.160565i) q^{77} +9.64773 q^{79} +2.86976 q^{81} +5.26220 q^{83} +7.76016 q^{85} +(13.9876 - 10.1626i) q^{87} +(-3.72574 + 11.4667i) q^{89} -2.41487 q^{91} +(3.92064 + 2.84851i) q^{93} +(1.46167 + 4.49855i) q^{95} +(-4.44801 + 3.23167i) q^{97} +(-1.16193 - 0.844193i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{3} + 17 q^{5} + 6 q^{7} + 16 q^{9}+O(q^{10}) $ 24 * q + 12 * q^3 + 17 * q^5 + 6 * q^7 + 16 * q^9	$ 24 q + 12 q^{3} + 17 q^{5} + 6 q^{7} + 16 q^{9} - 8 q^{11} + 10 q^{15} + 8 q^{17} - 28 q^{19} + 3 q^{21} - 23 q^{23} + 17 q^{25} + 12 q^{27} - 31 q^{29} + 2 q^{31} + 12 q^{33} + 13 q^{35} + 7 q^{37} - 16 q^{39} - q^{41} - 2 q^{43} + 71 q^{45} + 15 q^{47} - 6 q^{49} + 2 q^{51} + 28 q^{53} - 16 q^{55} - 15 q^{57} + 17 q^{59} + 35 q^{61} - q^{63} + 62 q^{65} - 10 q^{67} - 9 q^{69} - 25 q^{71} - 74 q^{73} + 17 q^{75} + 8 q^{77} + 64 q^{81} + 96 q^{83} - 94 q^{85} - q^{87} - 33 q^{89} - 15 q^{93} - 29 q^{95} - 34 q^{97} - 3 q^{99}+O(q^{100}) $ 24 * q + 12 * q^3 + 17 * q^5 + 6 * q^7 + 16 * q^9 - 8 * q^11 + 10 * q^15 + 8 * q^17 - 28 * q^19 + 3 * q^21 - 23 * q^23 + 17 * q^25 + 12 * q^27 - 31 * q^29 + 2 * q^31 + 12 * q^33 + 13 * q^35 + 7 * q^37 - 16 * q^39 - q^41 - 2 * q^43 + 71 * q^45 + 15 * q^47 - 6 * q^49 + 2 * q^51 + 28 * q^53 - 16 * q^55 - 15 * q^57 + 17 * q^59 + 35 * q^61 - q^63 + 62 * q^65 - 10 * q^67 - 9 * q^69 - 25 * q^71 - 74 * q^73 + 17 * q^75 + 8 * q^77 + 64 * q^81 + 96 * q^83 - 94 * q^85 - q^87 - 33 * q^89 - 15 * q^93 - 29 * q^95 - 34 * q^97 - 3 * q^99

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
$3$	−2.87361			−1.65908			−0.829539	−	0.558448i	$-0.811397\pi$
$3$	−2.87361			−1.65908			−0.829539	+	0.558448i	$0.811397\pi$
$4$		0			0
$5$	2.43977	−	1.77260i	1.09110	−	0.792729i	0.111513	−	0.993763i	$-0.464430\pi$
$5$	2.43977	−	1.77260i	1.09110	−	0.792729i	0.979584	+	0.201034i	$0.0644302\pi$
$6$		0			0
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$8$		0			0
$9$	5.25763			1.75254
$10$		0			0
$11$	−0.220999	−	0.160565i	−0.0666338	−	0.0484123i	0.553970	−	0.832537i	$-0.313112\pi$
$11$	−0.220999	−	0.160565i	−0.0666338	−	0.0484123i	−0.620604	+	0.784125i	$0.713112\pi$
$12$		0			0
$13$	0.746236	+	2.29668i	0.206969	+	0.636984i	0.999627	+	0.0273175i	$0.00869652\pi$
$13$	0.746236	+	2.29668i	0.206969	+	0.636984i	−0.792658	+	0.609666i	$0.791303\pi$
$14$		0			0
$15$	−7.01094	+	5.09375i	−1.81022	+	1.31520i
$16$		0			0
$17$	2.08179	+	1.51251i	0.504909	+	0.366838i	0.810889	−	0.585200i	$-0.198984\pi$
$17$	2.08179	+	1.51251i	0.504909	+	0.366838i	−0.305980	+	0.952038i	$0.598984\pi$
$18$		0			0
$19$	−0.484683	+	1.49170i	−0.111194	+	0.342219i	−0.991134	−	0.132865i	$-0.957582\pi$
$19$	−0.484683	+	1.49170i	−0.111194	+	0.342219i	0.879940	+	0.475084i	$0.157582\pi$
$20$		0			0
$21$	0.887994	−	2.73296i	0.193776	−	0.596382i
$22$		0			0
$23$	−0.540140	−	1.66238i	−0.112627	−	0.346630i	0.878818	−	0.477158i	$-0.158333\pi$
$23$	−0.540140	−	1.66238i	−0.112627	−	0.346630i	−0.991445	+	0.130527i	$0.958333\pi$
$24$		0			0
$25$	1.26529	−	3.89416i	0.253058	−	0.778832i
$26$		0			0
$27$	−6.48754			−1.24853
$28$		0			0
$29$	−4.86762	+	3.53653i	−0.903893	+	0.656717i	−0.939463	−	0.342650i	$-0.888675\pi$
$29$	−4.86762	+	3.53653i	−0.903893	+	0.656717i	0.0355696	+	0.999367i	$0.488675\pi$
$30$		0			0
$31$	−1.36436	−	0.991266i	−0.245046	−	0.178037i	0.458482	−	0.888704i	$-0.348393\pi$
$31$	−1.36436	−	0.991266i	−0.245046	−	0.178037i	−0.703529	+	0.710667i	$0.748393\pi$
$32$		0			0
$33$	0.635066	+	0.461402i	0.110551	+	0.0803198i
$34$		0			0
$35$	0.931909	+	2.86812i	0.157521	+	0.484801i
$36$		0			0
$37$	6.90205	−	5.01463i	1.13469	−	0.824400i	0.148319	−	0.988940i	$-0.452614\pi$
$37$	6.90205	−	5.01463i	1.13469	−	0.824400i	0.986371	+	0.164539i	$0.0526138\pi$
$38$		0			0
$39$	−2.14439	−	6.59975i	−0.343377	−	1.05681i
$40$		0			0
$41$	2.41386	+	5.93071i	0.376982	+	0.926221i
$41$	2.41386	+	5.93071i	0.376982	+	0.926221i
$42$		0			0
$43$	−0.500213	−	1.53950i	−0.0762818	−	0.234771i	0.905644	−	0.424040i	$-0.139388\pi$
$43$	−0.500213	−	1.53950i	−0.0762818	−	0.234771i	−0.981925	+	0.189269i	$0.939388\pi$
$44$		0			0
$45$	12.8274	−	9.31964i	1.91219	−	1.38929i
$46$		0			0
$47$	1.47917	+	4.55243i	0.215760	+	0.664040i	0.999099	+	0.0424454i	$0.0135149\pi$
$47$	1.47917	+	4.55243i	0.215760	+	0.664040i	−0.783339	+	0.621595i	$0.786485\pi$
$48$		0			0
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$		0			0
$51$	−5.98226	−	4.34636i	−0.837684	−	0.608613i
$52$		0			0
$53$	7.63405	−	5.54646i	1.04862	−	0.761865i	0.0766685	−	0.997057i	$-0.475572\pi$
$53$	7.63405	−	5.54646i	1.04862	−	0.761865i	0.971949	+	0.235191i	$0.0755717\pi$
$54$		0			0
$55$	−0.823805			−0.111082
$56$		0			0
$57$	1.39279	−	4.28656i	0.184479	−	0.567769i
$58$		0			0
$59$	2.15789	+	6.64131i	0.280934	+	0.864625i	0.987588	+	0.157066i	$0.0502035\pi$
$59$	2.15789	+	6.64131i	0.280934	+	0.864625i	−0.706655	+	0.707559i	$0.749797\pi$
$60$		0			0
$61$	−1.03142	+	3.17438i	−0.132060	+	0.406438i	−0.995121	−	0.0986610i	$-0.968544\pi$
$61$	−1.03142	+	3.17438i	−0.132060	+	0.406438i	0.863061	+	0.505099i	$0.168544\pi$
$62$		0			0
$63$	−1.62470	+	5.00030i	−0.204692	+	0.629979i
$64$		0			0
$65$	5.89172	+	4.28059i	0.730778	+	0.530941i
$66$		0			0
$67$	6.99833	−	5.08458i	0.854982	−	0.621181i	−0.0715332	−	0.997438i	$-0.522789\pi$
$67$	6.99833	−	5.08458i	0.854982	−	0.621181i	0.926515	+	0.376257i	$0.122789\pi$
$68$		0			0
$69$	1.55215	+	4.77703i	0.186857	+	0.575087i
$70$		0			0
$71$	10.3783	+	7.54028i	1.23168	+	0.894867i	0.997015	−	0.0772100i	$-0.0246012\pi$
$71$	10.3783	+	7.54028i	1.23168	+	0.894867i	0.234663	+	0.972077i	$0.424601\pi$
$72$		0			0
$73$	12.6539			1.48102			0.740511	−	0.672044i	$-0.234583\pi$
$73$	12.6539			1.48102			0.740511	+	0.672044i	$0.234583\pi$
$74$		0			0
$75$	−3.63595	+	11.1903i	−0.419843	+	1.29214i
$76$		0			0
$77$	0.220999	−	0.160565i	0.0251852	−	0.0182981i
$78$		0			0
$79$	9.64773			1.08545			0.542727	−	0.839909i	$-0.317392\pi$
$79$	9.64773			1.08545			0.542727	+	0.839909i	$0.317392\pi$
$80$		0			0
$81$	2.86976			0.318862
$82$		0			0
$83$	5.26220			0.577601			0.288801	−	0.957389i	$-0.406744\pi$
$83$	5.26220			0.577601			0.288801	+	0.957389i	$0.406744\pi$
$84$		0			0
$85$	7.76016			0.841708
$86$		0			0
$87$	13.9876	−	10.1626i	1.49963	−	1.08955i
$88$		0			0
$89$	−3.72574	+	11.4667i	−0.394928	+	1.21546i	0.534090	+	0.845428i	$0.320654\pi$
$89$	−3.72574	+	11.4667i	−0.394928	+	1.21546i	−0.929018	+	0.370035i	$0.879346\pi$
$90$		0			0
$91$	−2.41487			−0.253147
$92$		0			0
$93$	3.92064	+	2.84851i	0.406551	+	0.295377i
$94$		0			0
$95$	1.46167	+	4.49855i	0.149964	+	0.461541i
$96$		0			0
$97$	−4.44801	+	3.23167i	−0.451627	+	0.328127i	−0.790238	−	0.612800i	$-0.790043\pi$
$97$	−4.44801	+	3.23167i	−0.451627	+	0.328127i	0.338611	+	0.940927i	$0.390043\pi$
$98$		0			0
$99$	−1.16193	−	0.844193i	−0.116779	−	0.0848446i
$100$		0			0
$101$	6.04634	−	18.6087i	0.601633	−	1.85164i	0.0831711	−	0.996535i	$-0.473495\pi$
$101$	6.04634	−	18.6087i	0.601633	−	1.85164i	0.518462	−	0.855101i	$-0.326505\pi$
$102$		0			0
$103$	−0.512876	+	1.57847i	−0.0505352	+	0.155531i	−0.973139	−	0.230217i	$-0.926057\pi$
$103$	−0.512876	+	1.57847i	−0.0505352	+	0.155531i	0.922604	+	0.385748i	$0.126057\pi$
$104$		0			0
$105$	−2.67794	−	8.24185i	−0.261340	−	0.804323i
$106$		0			0
$107$	3.39974	−	10.4633i	0.328665	−	1.01153i	−0.641093	−	0.767463i	$-0.721519\pi$
$107$	3.39974	−	10.4633i	0.328665	−	1.01153i	0.969759	−	0.244065i	$-0.0784811\pi$
$108$		0			0
$109$	−0.620648			−0.0594473			−0.0297236	−	0.999558i	$-0.509463\pi$
$109$	−0.620648			−0.0594473			−0.0297236	+	0.999558i	$0.509463\pi$
$110$		0			0
$111$	−19.8338	+	14.4101i	−1.88254	+	1.36774i
$112$		0			0
$113$	1.20554	+	0.875874i	0.113407	+	0.0823953i	0.643043	−	0.765830i	$-0.277671\pi$
$113$	1.20554	+	0.875874i	0.113407	+	0.0823953i	−0.529636	+	0.848225i	$0.677671\pi$
$114$		0			0
$115$	−4.26455	−	3.09837i	−0.397671	−	0.288925i
$116$		0			0
$117$	3.92343	+	12.0751i	0.362721	+	1.11634i
$118$		0			0
$119$	−2.08179	+	1.51251i	−0.190838	+	0.138652i
$120$		0			0
$121$	−3.37613	−	10.3907i	−0.306921	−	0.944605i
$122$		0			0
$123$	−6.93649	−	17.0425i	−0.625442	−	1.53667i
$124$		0			0
$125$	0.843784	+	2.59690i	0.0754704	+	0.232274i
$126$		0			0
$127$	4.41477	−	3.20752i	0.391748	−	0.284622i	−0.374423	−	0.927258i	$-0.622159\pi$
$127$	4.41477	−	3.20752i	0.391748	−	0.284622i	0.766171	+	0.642636i	$0.222159\pi$
$128$		0			0
$129$	1.43742	+	4.42391i	0.126558	+	0.389504i
$130$		0			0
$131$	0.531398	+	0.386083i	0.0464285	+	0.0337323i	0.610757	−	0.791818i	$-0.290865\pi$
$131$	0.531398	+	0.386083i	0.0464285	+	0.0337323i	−0.564329	+	0.825550i	$0.690865\pi$
$132$		0			0
$133$	−1.26892	−	0.921921i	−0.110029	−	0.0799407i
$134$		0			0
$135$	−15.8281	+	11.4998i	−1.36226	+	0.989743i
$136$		0			0
$137$	8.28568			0.707893			0.353947	−	0.935266i	$-0.384839\pi$
$137$	8.28568			0.707893			0.353947	+	0.935266i	$0.384839\pi$
$138$		0			0
$139$	−2.04200	+	6.28462i	−0.173200	+	0.533055i	−0.999547	−	0.0301071i	$-0.990415\pi$
$139$	−2.04200	+	6.28462i	−0.173200	+	0.533055i	0.826347	+	0.563162i	$0.190415\pi$
$140$		0			0
$141$	−4.25057	−	13.0819i	−0.357962	−	1.10169i
$142$		0			0
$143$	0.203849	−	0.627384i	0.0170467	−	0.0524645i
$144$		0			0
$145$	−5.60702	+	17.2566i	−0.465637	+	1.43308i
$146$		0			0
$147$	2.32480	+	1.68906i	0.191746	+	0.139312i
$148$		0			0
$149$	−7.71915	+	5.60829i	−0.632377	+	0.459449i	−0.857223	−	0.514945i	$-0.827812\pi$
$149$	−7.71915	+	5.60829i	−0.632377	+	0.459449i	0.224846	+	0.974394i	$0.427812\pi$
$150$		0			0
$151$	1.81315	+	5.58031i	0.147552	+	0.454119i	0.997330	−	0.0730213i	$-0.0232641\pi$
$151$	1.81315	+	5.58031i	0.147552	+	0.454119i	−0.849778	+	0.527141i	$0.823264\pi$
$152$		0			0
$153$	10.9453	+	7.95222i	0.884874	+	0.642899i
$154$		0			0
$155$	−5.08583			−0.408504
$156$		0			0
$157$	2.93884	−	9.04482i	0.234545	−	0.721855i	−0.762636	−	0.646827i	$-0.776095\pi$
$157$	2.93884	−	9.04482i	0.234545	−	0.721855i	0.997181	−	0.0750278i	$-0.0239046\pi$
$158$		0			0
$159$	−21.9373	+	15.9384i	−1.73974	+	1.26399i
$160$		0			0
$161$	1.74793			0.137756
$162$		0			0
$163$	21.5406			1.68719			0.843594	−	0.536981i	$-0.180435\pi$
$163$	21.5406			1.68719			0.843594	+	0.536981i	$0.180435\pi$
$164$		0			0
$165$	2.36729			0.184293
$166$		0			0
$167$	−0.754749			−0.0584042			−0.0292021	−	0.999574i	$-0.509297\pi$
$167$	−0.754749			−0.0584042			−0.0292021	+	0.999574i	$0.509297\pi$
$168$		0			0
$169$	5.79936	−	4.21348i	0.446105	−	0.324114i
$170$		0			0
$171$	−2.54828	+	7.84280i	−0.194872	+	0.599754i
$172$		0			0
$173$	−25.7360			−1.95668			−0.978338	−	0.207016i	$-0.933625\pi$
$173$	−25.7360			−1.95668			−0.978338	+	0.207016i	$0.933625\pi$
$174$		0			0
$175$	3.31257	+	2.40672i	0.250407	+	0.181931i
$176$		0			0
$177$	−6.20094	−	19.0845i	−0.466091	−	1.43448i
$178$		0			0
$179$	−8.96668	+	6.51468i	−0.670201	+	0.486930i	−0.870093	−	0.492888i	$-0.835941\pi$
$179$	−8.96668	+	6.51468i	−0.670201	+	0.486930i	0.199891	+	0.979818i	$0.435941\pi$
$180$		0			0
$181$	3.00771	+	2.18523i	0.223561	+	0.162427i	0.693928	−	0.720044i	$-0.255878\pi$
$181$	3.00771	+	2.18523i	0.223561	+	0.162427i	−0.470367	+	0.882471i	$0.655878\pi$
$182$		0			0
$183$	2.96390	−	9.12193i	0.219097	−	0.674313i
$184$		0			0
$185$	7.95048	−	24.4691i	0.584531	−	1.79900i
$186$		0			0
$187$	−0.217218	−	0.668528i	−0.0158845	−	0.0488876i
$188$		0			0
$189$	2.00476	−	6.17001i	0.145825	−	0.448802i
$190$		0			0
$191$	−3.84706			−0.278363			−0.139182	−	0.990267i	$-0.544447\pi$
$191$	−3.84706			−0.278363			−0.139182	+	0.990267i	$0.544447\pi$
$192$		0			0
$193$	−15.8139	+	11.4894i	−1.13831	+	0.827028i	−0.986882	−	0.161441i	$-0.948386\pi$
$193$	−15.8139	+	11.4894i	−1.13831	+	0.827028i	−0.151424	+	0.988469i	$0.548386\pi$
$194$		0			0
$195$	−16.9305	−	12.3007i	−1.21242	−	0.880874i
$196$		0			0
$197$	−14.0770	−	10.2276i	−1.00295	−	0.728684i	−0.0402295	−	0.999190i	$-0.512809\pi$
$197$	−14.0770	−	10.2276i	−1.00295	−	0.728684i	−0.962718	+	0.270506i	$0.912809\pi$
$198$		0			0
$199$	2.94118	+	9.05201i	0.208495	+	0.641680i	0.999552	+	0.0299381i	$0.00953101\pi$
$199$	2.94118	+	9.05201i	0.208495	+	0.641680i	−0.791057	+	0.611742i	$0.790469\pi$
$200$		0			0
$201$	−20.1105	+	14.6111i	−1.41848	+	1.03059i
$202$		0			0
$203$	−1.85926	−	5.72222i	−0.130495	−	0.401621i
$204$		0			0
$205$	16.4020	+	10.1908i	1.14557	+	0.711753i
$206$		0			0
$207$	−2.83986	−	8.74018i	−0.197384	−	0.607484i
$208$		0			0
$209$	0.346630	−	0.251841i	0.0239769	−	0.0174202i
$210$		0			0
$211$	−5.12707	−	15.7795i	−0.352962	−	1.08631i	−0.957182	−	0.289488i	$-0.906515\pi$
$211$	−5.12707	−	15.7795i	−0.352962	−	1.08631i	0.604219	−	0.796818i	$-0.293485\pi$
$212$		0			0
$213$	−29.8232	−	21.6678i	−2.04345	−	1.48465i
$214$		0			0
$215$	−3.94931	−	2.86934i	−0.269341	−	0.195688i
$216$		0			0
$217$	1.36436	−	0.991266i	0.0926188	−	0.0672915i
$218$		0			0
$219$	−36.3623			−2.45713
$220$		0			0
$221$	−1.92024	+	5.90990i	−0.129169	+	0.397543i
$222$		0			0
$223$	−1.09907	−	3.38260i	−0.0735994	−	0.226516i	0.907489	−	0.420076i	$-0.137997\pi$
$223$	−1.09907	−	3.38260i	−0.0735994	−	0.226516i	−0.981088	+	0.193560i	$0.937997\pi$
$224$		0			0
$225$	6.65242	−	20.4740i	0.443495	−	1.36494i
$226$		0			0
$227$	0.271170	−	0.834575i	0.0179982	−	0.0553927i	−0.941654	−	0.336582i	$-0.890729\pi$
$227$	0.271170	−	0.834575i	0.0179982	−	0.0553927i	0.959652	+	0.281190i	$0.0907290\pi$
$228$		0			0
$229$	−7.54286	−	5.48021i	−0.498446	−	0.362143i	0.309977	−	0.950744i	$-0.399679\pi$
$229$	−7.54286	−	5.48021i	−0.498446	−	0.362143i	−0.808423	+	0.588602i	$0.799679\pi$
$230$		0			0
$231$	−0.635066	+	0.461402i	−0.0417843	+	0.0303580i
$232$		0			0
$233$	−2.59966	−	8.00094i	−0.170310	−	0.524159i	0.829079	−	0.559132i	$-0.188866\pi$
$233$	−2.59966	−	8.00094i	−0.170310	−	0.524159i	−0.999388	+	0.0349728i	$0.988866\pi$
$234$		0			0
$235$	11.6785	+	8.48489i	0.761818	+	0.553494i
$236$		0			0
$237$	−27.7238			−1.80086
$238$		0			0
$239$	−7.60865	+	23.4170i	−0.492163	+	1.51472i	0.329170	+	0.944271i	$0.393231\pi$
$239$	−7.60865	+	23.4170i	−0.492163	+	1.51472i	−0.821332	+	0.570450i	$0.806769\pi$
$240$		0			0
$241$	−5.22375	+	3.79528i	−0.336491	+	0.244475i	−0.743180	−	0.669092i	$-0.766683\pi$
$241$	−5.22375	+	3.79528i	−0.336491	+	0.244475i	0.406689	+	0.913567i	$0.366683\pi$
$242$		0			0
$243$	11.2160			0.719510
$244$		0			0
$245$	−3.01572			−0.192667
$246$		0			0
$247$	−3.78764			−0.241002
$248$		0			0
$249$	−15.1215			−0.958286
$250$		0			0
$251$	23.3634	−	16.9745i	1.47468	−	1.07142i	0.495463	−	0.868629i	$-0.334998\pi$
$251$	23.3634	−	16.9745i	1.47468	−	1.07142i	0.979222	−	0.202792i	$-0.0650016\pi$
$252$		0			0
$253$	−0.147550	+	0.454113i	−0.00927640	+	0.0285498i
$254$		0			0
$255$	−22.2997			−1.39646
$256$		0			0
$257$	11.3323	+	8.23339i	0.706889	+	0.513585i	0.882169	−	0.470934i	$-0.156083\pi$
$257$	11.3323	+	8.23339i	0.706889	+	0.513585i	−0.175279	+	0.984519i	$0.556083\pi$
$258$		0			0
$259$	2.63635	+	8.11384i	0.163815	+	0.504170i
$260$		0			0
$261$	−25.5921	+	18.5938i	−1.58411	+	1.15092i
$262$		0			0
$263$	−18.0995	−	13.1500i	−1.11606	−	0.810866i	−0.132454	−	0.991189i	$-0.542286\pi$
$263$	−18.0995	−	13.1500i	−1.11606	−	0.810866i	−0.983607	+	0.180323i	$0.942286\pi$
$264$		0			0
$265$	8.79368	−	27.0642i	0.540192	−	1.66254i
$266$		0			0
$267$	10.7063	−	32.9507i	0.655216	−	2.01655i
$268$		0			0
$269$	0.383077	+	1.17899i	0.0233566	+	0.0718842i	0.962055	−	0.272854i	$-0.0879676\pi$
$269$	0.383077	+	1.17899i	0.0233566	+	0.0718842i	−0.938699	+	0.344738i	$0.887968\pi$
$270$		0			0
$271$	−3.47488	+	10.6946i	−0.211084	+	0.649650i	0.788324	+	0.615260i	$0.210949\pi$
$271$	−3.47488	+	10.6946i	−0.211084	+	0.649650i	−0.999408	+	0.0343904i	$0.989051\pi$
$272$		0			0
$273$	6.93939			0.419991
$274$		0			0
$275$	−0.904896	+	0.657445i	−0.0545673	+	0.0396454i
$276$		0			0
$277$	−1.91945	−	1.39456i	−0.115329	−	0.0837912i	0.528626	−	0.848855i	$-0.322707\pi$
$277$	−1.91945	−	1.39456i	−0.115329	−	0.0837912i	−0.643955	+	0.765064i	$0.722707\pi$
$278$		0			0
$279$	−7.17330	−	5.21170i	−0.429454	−	0.312017i
$280$		0			0
$281$	3.00576	+	9.25078i	0.179309	+	0.551855i	0.999804	−	0.0197979i	$-0.00630229\pi$
$281$	3.00576	+	9.25078i	0.179309	+	0.551855i	−0.820495	+	0.571653i	$0.806302\pi$
$282$		0			0
$283$	−7.90299	+	5.74186i	−0.469784	+	0.341318i	−0.797357	−	0.603508i	$-0.793769\pi$
$283$	−7.90299	+	5.74186i	−0.469784	+	0.341318i	0.327573	+	0.944826i	$0.393769\pi$
$284$		0			0
$285$	−4.20026	−	12.9271i	−0.248802	−	0.765733i
$286$		0			0
$287$	−6.38636	+	0.463028i	−0.376975	+	0.0273317i
$288$		0			0
$289$	−3.20712	−	9.87049i	−0.188654	−	0.580617i
$290$		0			0
$291$	12.7819	−	9.28656i	0.749285	−	0.544388i
$292$		0			0
$293$	9.47886	+	29.1729i	0.553761	+	1.70430i	0.699193	+	0.714933i	$0.253543\pi$
$293$	9.47886	+	29.1729i	0.553761	+	1.70430i	−0.145432	+	0.989368i	$0.546457\pi$
$294$		0			0
$295$	17.0371	+	12.3782i	0.991939	+	0.720686i
$296$		0			0
$297$	1.43374	+	1.04167i	0.0831941	+	0.0604441i
$298$		0			0
$299$	3.41488	−	2.48106i	0.197488	−	0.143483i
$300$		0			0
$301$	1.61872			0.0933017
$302$		0			0
$303$	−17.3748	+	53.4742i	−0.998157	+	3.07201i
$304$		0			0
$305$	3.11047	+	9.57305i	0.178105	+	0.548151i
$306$		0			0
$307$	4.93497	−	15.1883i	0.281653	−	0.866840i	−0.705728	−	0.708483i	$-0.749380\pi$
$307$	4.93497	−	15.1883i	0.281653	−	0.866840i	0.987382	−	0.158358i	$-0.0506199\pi$
$308$		0			0
$309$	1.47380	−	4.53591i	0.0838418	−	0.258039i
$310$		0			0
$311$	−12.7763	−	9.28254i	−0.724479	−	0.526365i	0.163333	−	0.986571i	$-0.447775\pi$
$311$	−12.7763	−	9.28254i	−0.724479	−	0.526365i	−0.887812	+	0.460206i	$0.847775\pi$
$312$		0			0
$313$	6.05452	−	4.39887i	0.342222	−	0.248639i	−0.403377	−	0.915034i	$-0.632164\pi$
$313$	6.05452	−	4.39887i	0.342222	−	0.248639i	0.745599	+	0.666395i	$0.232164\pi$
$314$		0			0
$315$	4.89963	+	15.0795i	0.276063	+	0.849634i
$316$		0			0
$317$	8.12076	+	5.90008i	0.456107	+	0.331381i	0.792002	−	0.610518i	$-0.209039\pi$
$317$	8.12076	+	5.90008i	0.456107	+	0.331381i	−0.335895	+	0.941899i	$0.609039\pi$
$318$		0			0
$319$	1.64358			0.0920230
$320$		0			0
$321$	−9.76953	+	30.0675i	−0.545282	+	1.67821i
$322$		0			0
$323$	−3.26522	+	2.37232i	−0.181682	+	0.132000i
$324$		0			0
$325$	9.88784			0.548479
$326$		0			0
$327$	1.78350			0.0986277
$328$		0			0
$329$	−4.78671			−0.263900
$330$		0			0
$331$	24.9160			1.36951			0.684754	−	0.728774i	$-0.259910\pi$
$331$	24.9160			1.36951			0.684754	+	0.728774i	$0.259910\pi$
$332$		0			0
$333$	36.2884	−	26.3651i	1.98859	−	1.44480i
$334$		0			0
$335$	8.06139	−	24.8104i	0.440441	−	1.35554i
$336$		0			0
$337$	−9.73747			−0.530434			−0.265217	−	0.964189i	$-0.585444\pi$
$337$	−9.73747			−0.530434			−0.265217	+	0.964189i	$0.585444\pi$
$338$		0			0
$339$	−3.46424	−	2.51692i	−0.188152	−	0.136700i
$340$		0			0
$341$	0.142360	+	0.438138i	0.00770921	+	0.0237265i
$342$		0			0
$343$	0.809017	−	0.587785i	0.0436828	−	0.0317374i
$344$		0			0
$345$	12.2546	+	8.90351i	0.659767	+	0.479349i
$346$		0			0
$347$	5.35809	−	16.4905i	0.287637	−	0.885256i	−0.697959	−	0.716138i	$-0.745908\pi$
$347$	5.35809	−	16.4905i	0.287637	−	0.885256i	0.985596	−	0.169118i	$-0.0540919\pi$
$348$		0			0
$349$	−10.3138	+	31.7426i	−0.552084	+	1.69914i	0.151437	+	0.988467i	$0.451610\pi$
$349$	−10.3138	+	31.7426i	−0.552084	+	1.69914i	−0.703522	+	0.710674i	$0.748390\pi$
$350$		0			0
$351$	−4.84123	−	14.8998i	−0.258406	−	0.795291i
$352$		0			0
$353$	−8.05991	+	24.8059i	−0.428986	+	1.32028i	0.470140	+	0.882592i	$0.344203\pi$
$353$	−8.05991	+	24.8059i	−0.428986	+	1.32028i	−0.899126	+	0.437691i	$0.855797\pi$
$354$		0			0
$355$	38.6865			2.05327
$356$		0			0
$357$	5.98226	−	4.34636i	0.316615	−	0.230034i
$358$		0			0
$359$	8.59440	+	6.24419i	0.453595	+	0.329556i	0.791013	−	0.611799i	$-0.209554\pi$
$359$	8.59440	+	6.24419i	0.453595	+	0.329556i	−0.337419	+	0.941355i	$0.609554\pi$
$360$		0			0
$361$	13.3811	+	9.72192i	0.704267	+	0.511680i
$362$		0			0
$363$	9.70167	+	29.8587i	0.509206	+	1.56717i
$364$		0			0
$365$	30.8725	−	22.4302i	1.61594	−	1.17405i
$366$		0			0
$367$	7.44409	+	22.9105i	0.388578	+	1.19592i	0.933851	+	0.357662i	$0.116426\pi$
$367$	7.44409	+	22.9105i	0.388578	+	1.19592i	−0.545273	+	0.838259i	$0.683574\pi$
$368$		0			0
$369$	12.6912	+	31.1814i	0.660676	+	1.62324i
$370$		0			0
$371$	2.91595	+	8.97437i	0.151388	+	0.465926i
$372$		0			0
$373$	17.0758	−	12.4063i	0.884153	−	0.642375i	−0.0501940	−	0.998739i	$-0.515984\pi$
$373$	17.0758	−	12.4063i	0.884153	−	0.642375i	0.934347	+	0.356365i	$0.115984\pi$
$374$		0			0
$375$	−2.42471	−	7.46248i	−0.125211	−	0.385361i
$376$		0			0
$377$	−11.7547	−	8.54026i	−0.605396	−	0.439846i
$378$		0			0
$379$	13.0017	+	9.44629i	0.667852	+	0.485223i	0.869306	−	0.494275i	$-0.164566\pi$
$379$	13.0017	+	9.44629i	0.667852	+	0.485223i	−0.201453	+	0.979498i	$0.564566\pi$
$380$		0			0
$381$	−12.6863	+	9.21716i	−0.649941	+	0.472209i
$382$		0			0
$383$	−20.5966			−1.05244			−0.526219	−	0.850349i	$-0.676391\pi$
$383$	−20.5966			−1.05244			−0.526219	+	0.850349i	$0.676391\pi$
$384$		0			0
$385$	0.254570	−	0.783485i	0.0129741	−	0.0399301i
$386$		0			0
$387$	−2.62993	−	8.09411i	−0.133687	−	0.411447i
$388$		0			0
$389$	2.95981	−	9.10936i	0.150068	−	0.461863i	−0.847560	−	0.530700i	$-0.821929\pi$
$389$	2.95981	−	9.10936i	0.150068	−	0.461863i	0.997628	+	0.0688374i	$0.0219290\pi$
$390$		0			0
$391$	1.38991	−	4.27770i	0.0702907	−	0.216333i
$392$		0			0
$393$	−1.52703	−	1.10945i	−0.0770285	−	0.0559645i
$394$		0			0
$395$	23.5382	−	17.1015i	1.18434	−	0.860471i
$396$		0			0
$397$	−7.50215	−	23.0892i	−0.376522	−	1.15882i	−0.942446	−	0.334359i	$-0.891480\pi$
$397$	−7.50215	−	23.0892i	−0.376522	−	1.15882i	0.565924	−	0.824458i	$-0.308520\pi$
$398$		0			0
$399$	3.64637	+	2.64924i	0.182547	+	0.132628i
$400$		0			0
$401$	−31.3650			−1.56629			−0.783147	−	0.621837i	$-0.786387\pi$
$401$	−31.3650			−1.56629			−0.783147	+	0.621837i	$0.786387\pi$
$402$		0			0
$403$	1.25848	−	3.87321i	0.0626895	−	0.192938i
$404$		0			0
$405$	7.00154	−	5.08692i	0.347910	−	0.252771i
$406$		0			0
$407$	−2.33052			−0.115520
$408$		0			0
$409$	−8.32846			−0.411816			−0.205908	−	0.978571i	$-0.566015\pi$
$409$	−8.32846			−0.411816			−0.205908	+	0.978571i	$0.566015\pi$
$410$		0			0
$411$	−23.8098			−1.17445
$412$		0			0
$413$	−6.98308			−0.343615
$414$		0			0
$415$	12.8385	−	9.32775i	0.630219	−	0.457881i
$416$		0			0
$417$	5.86790	−	18.0595i	0.287352	−	0.884379i
$418$		0			0
$419$	−15.0231			−0.733927			−0.366964	−	0.930235i	$-0.619603\pi$
$419$	−15.0231			−0.733927			−0.366964	+	0.930235i	$0.619603\pi$
$420$		0			0
$421$	28.8508	+	20.9613i	1.40610	+	1.02159i	0.993875	+	0.110513i	$0.0352494\pi$
$421$	28.8508	+	20.9613i	1.40610	+	1.02159i	0.412228	+	0.911081i	$0.364751\pi$
$422$		0			0
$423$	7.77694	+	23.9350i	0.378128	+	1.16376i
$424$		0			0
$425$	8.52403	−	6.19307i	0.413476	−	0.300408i
$426$		0			0
$427$	−2.70029	−	1.96188i	−0.130676	−	0.0949418i
$428$		0			0
$429$	−0.585783	+	1.80286i	−0.0282819	+	0.0870427i
$430$		0			0
$431$	−5.41376	+	16.6618i	−0.260772	+	0.802572i	0.731866	+	0.681449i	$0.238650\pi$
$431$	−5.41376	+	16.6618i	−0.260772	+	0.802572i	−0.992637	+	0.121124i	$0.961350\pi$
$432$		0			0
$433$	12.2768	+	37.7840i	0.589983	+	1.81578i	0.578263	+	0.815851i	$0.303731\pi$
$433$	12.2768	+	37.7840i	0.589983	+	1.81578i	0.0117209	+	0.999931i	$0.496269\pi$
$434$		0			0
$435$	16.1124	−	49.5888i	0.772529	−	2.37760i
$436$		0			0
$437$	2.74157			0.131147
$438$		0			0
$439$	8.32033	−	6.04507i	0.397108	−	0.288516i	−0.371254	−	0.928531i	$-0.621072\pi$
$439$	8.32033	−	6.04507i	0.397108	−	0.288516i	0.768362	+	0.640016i	$0.221072\pi$
$440$		0			0
$441$	−4.25351	−	3.09036i	−0.202548	−	0.147160i
$442$		0			0
$443$	−24.0536	−	17.4759i	−1.14282	−	0.830306i	−0.155309	−	0.987866i	$-0.549637\pi$
$443$	−24.0536	−	17.4759i	−1.14282	−	0.830306i	−0.987509	+	0.157559i	$0.949637\pi$
$444$		0			0
$445$	11.2358	+	34.5802i	0.532628	+	1.63926i
$446$		0			0
$447$	22.1818	−	16.1160i	1.04916	−	0.762262i
$448$		0			0
$449$	−5.55811	−	17.1061i	−0.262303	−	0.807286i	−0.992302	−	0.123838i	$-0.960480\pi$
$449$	−5.55811	−	17.1061i	−0.262303	−	0.807286i	0.729999	−	0.683448i	$-0.239520\pi$
$450$		0			0
$451$	0.418805	−	1.69826i	0.0197208	−	0.0799682i
$452$		0			0
$453$	−5.21029	−	16.0356i	−0.244801	−	0.753420i
$454$		0			0
$455$	−5.89172	+	4.28059i	−0.276208	+	0.200677i
$456$		0			0
$457$	2.21915	+	6.82984i	0.103807	+	0.319486i	0.989449	−	0.144884i	$-0.0462808\pi$
$457$	2.21915	+	6.82984i	0.103807	+	0.319486i	−0.885641	+	0.464370i	$0.846281\pi$
$458$		0			0
$459$	−13.5057	−	9.81247i	−0.630392	−	0.458007i
$460$		0			0
$461$	14.3715	+	10.4415i	0.669349	+	0.486310i	0.869807	−	0.493392i	$-0.164243\pi$
$461$	14.3715	+	10.4415i	0.669349	+	0.486310i	−0.200458	+	0.979702i	$0.564243\pi$
$462$		0			0
$463$	−4.63579	+	3.36810i	−0.215444	+	0.156529i	−0.690273	−	0.723549i	$-0.742510\pi$
$463$	−4.63579	+	3.36810i	−0.215444	+	0.156529i	0.474830	+	0.880078i	$0.342510\pi$
$464$		0			0
$465$	14.6147			0.677740
$466$		0			0
$467$	0.0825781	−	0.254149i	0.00382126	−	0.0117606i	−0.949128	−	0.314891i	$-0.898032\pi$
$467$	0.0825781	−	0.254149i	0.00382126	−	0.0117606i	0.952949	+	0.303131i	$0.0980319\pi$
$468$		0			0
$469$	2.67312	+	8.22703i	0.123433	+	0.379889i
$470$		0			0
$471$	−8.44508	+	25.9913i	−0.389129	+	1.19761i
$472$		0			0
$473$	−0.136643	+	0.420545i	−0.00628287	+	0.0193367i
$474$		0			0
$475$	5.19566	+	3.77486i	0.238393	+	0.173203i
$476$		0			0
$477$	40.1370	−	29.1612i	1.83775	−	1.33520i
$478$		0			0
$479$	−8.47328	−	26.0781i	−0.387154	−	1.19154i	−0.934906	−	0.354896i	$-0.884516\pi$
$479$	−8.47328	−	26.0781i	−0.387154	−	1.19154i	0.547752	−	0.836641i	$-0.315484\pi$
$480$		0			0
$481$	16.6675	+	12.1097i	0.759975	+	0.552154i
$482$		0			0
$483$	−5.02287			−0.228548
$484$		0			0
$485$	−5.12368	+	15.7691i	−0.232654	+	0.716036i
$486$		0			0
$487$	3.00681	−	2.18457i	0.136251	−	0.0989925i	−0.517572	−	0.855640i	$-0.673164\pi$
$487$	3.00681	−	2.18457i	0.136251	−	0.0989925i	0.653823	+	0.756647i	$0.273164\pi$
$488$		0			0
$489$	−61.8992			−2.79918
$490$		0			0
$491$	−11.0665			−0.499423			−0.249712	−	0.968320i	$-0.580336\pi$
$491$	−11.0665			−0.499423			−0.249712	+	0.968320i	$0.580336\pi$
$492$		0			0
$493$	−15.4824			−0.697292
$494$		0			0
$495$	−4.33126			−0.194676
$496$		0			0
$497$	−10.3783	+	7.54028i	−0.465531	+	0.338228i
$498$		0			0
$499$	−2.58014	+	7.94085i	−0.115503	+	0.355481i	−0.992052	−	0.125832i	$-0.959840\pi$
$499$	−2.58014	+	7.94085i	−0.115503	+	0.355481i	0.876549	+	0.481313i	$0.159840\pi$
$500$		0			0
$501$	2.16885			0.0968972
$502$		0			0
$503$	−17.3754	−	12.6240i	−0.774732	−	0.562876i	0.128661	−	0.991689i	$-0.458932\pi$
$503$	−17.3754	−	12.6240i	−0.774732	−	0.562876i	−0.903393	+	0.428813i	$0.858932\pi$
$504$		0			0
$505$	−18.2341	−	56.1187i	−0.811405	−	2.49725i
$506$		0			0
$507$	−16.6651	+	12.1079i	−0.740123	+	0.537731i
$508$		0			0
$509$	−14.0340	−	10.1963i	−0.622044	−	0.451941i	0.231591	−	0.972813i	$-0.425607\pi$
$509$	−14.0340	−	10.1963i	−0.622044	−	0.451941i	−0.853635	+	0.520872i	$0.825607\pi$
$510$		0			0
$511$	−3.91026	+	12.0345i	−0.172980	+	0.532377i
$512$		0			0
$513$	3.14440	−	9.67745i	0.138828	−	0.427270i
$514$		0			0
$515$	1.54669	+	4.76022i	0.0681553	+	0.209760i
$516$		0			0
$517$	0.404066	−	1.24359i	0.0177708	−	0.0546929i
$518$		0			0
$519$	73.9553			3.24628
$520$		0			0
$521$	−21.2289	+	15.4237i	−0.930054	+	0.675724i	−0.946006	−	0.324149i	$-0.894922\pi$
$521$	−21.2289	+	15.4237i	−0.930054	+	0.675724i	0.0159521	+	0.999873i	$0.494922\pi$
$522$		0			0
$523$	−22.1366	−	16.0832i	−0.967964	−	0.703267i	−0.0129775	−	0.999916i	$-0.504131\pi$
$523$	−22.1366	−	16.0832i	−0.967964	−	0.703267i	−0.954987	+	0.296649i	$0.904131\pi$
$524$		0			0
$525$	−9.51903	−	6.91598i	−0.415445	−	0.301838i
$526$		0			0
$527$	−1.34101	−	4.12722i	−0.0584155	−	0.179784i
$528$		0			0
$529$	16.1356	−	11.7232i	0.701549	−	0.509705i
$530$		0			0
$531$	11.3454	+	34.9175i	0.492348	+	1.51529i
$532$		0			0
$533$	−11.8196	+	9.96956i	−0.511964	+	0.431830i
$534$		0			0
$535$	−10.2527	−	31.5545i	−0.443261	−	1.36422i
$536$		0			0
$537$	25.7667	−	18.7206i	1.11192	−	0.807855i
$538$		0			0
$539$	0.0844142	+	0.259800i	0.00363598	+	0.0111904i
$540$		0			0
$541$	−30.5035	−	22.1621i	−1.31145	−	0.952823i	−0.999997	−	0.00256100i	$-0.999185\pi$
$541$	−30.5035	−	22.1621i	−1.31145	−	0.952823i	−0.311452	−	0.950262i	$-0.600815\pi$
$542$		0			0
$543$	−8.64298	−	6.27949i	−0.370906	−	0.269479i
$544$		0			0
$545$	−1.51424	+	1.10016i	−0.0648628	+	0.0471256i
$546$		0			0
$547$	−0.106511			−0.00455408			−0.00227704	−	0.999997i	$-0.500725\pi$
$547$	−0.106511			−0.00455408			−0.00227704	+	0.999997i	$0.500725\pi$
$548$		0			0
$549$	−5.42282	+	16.6897i	−0.231440	+	0.712300i
$550$		0			0
$551$	−2.91619	−	8.97511i	−0.124234	−	0.382353i
$552$		0			0
$553$	−2.98131	+	9.17554i	−0.126778	+	0.390184i
$554$		0			0
$555$	−22.8466	+	70.3145i	−0.969783	+	2.98469i
$556$		0			0
$557$	−21.4701	−	15.5990i	−0.909718	−	0.660949i	0.0312252	−	0.999512i	$-0.490059\pi$
$557$	−21.4701	−	15.5990i	−0.909718	−	0.660949i	−0.940944	+	0.338563i	$0.890059\pi$
$558$		0			0
$559$	3.16245	−	2.29766i	0.133758	−	0.0971805i
$560$		0			0
$561$	0.624199	+	1.92109i	0.0263537	+	0.0811084i
$562$		0			0
$563$	−19.1223	−	13.8931i	−0.805907	−	0.585526i	0.106734	−	0.994288i	$-0.465961\pi$
$563$	−19.1223	−	13.8931i	−0.805907	−	0.585526i	−0.912641	+	0.408762i	$0.865961\pi$
$564$		0			0
$565$	4.49380			0.189056
$566$		0			0
$567$	−0.886804	+	2.72930i	−0.0372423	+	0.114620i
$568$		0			0
$569$	1.99185	−	1.44716i	0.0835027	−	0.0606682i	−0.545251	−	0.838273i	$-0.683566\pi$
$569$	1.99185	−	1.44716i	0.0835027	−	0.0606682i	0.628753	+	0.777605i	$0.283566\pi$
$570$		0			0
$571$	−41.2970			−1.72823			−0.864113	−	0.503299i	$-0.832120\pi$
$571$	−41.2970			−1.72823			−0.864113	+	0.503299i	$0.832120\pi$
$572$		0			0
$573$	11.0549			0.461827
$574$		0			0
$575$	−7.15701			−0.298468
$576$		0			0
$577$	30.0416			1.25065			0.625324	−	0.780365i	$-0.284967\pi$
$577$	30.0416			1.25065			0.625324	+	0.780365i	$0.284967\pi$
$578$		0			0
$579$	45.4428	−	33.0162i	1.88854	−	1.37210i
$580$		0			0
$581$	−1.62611	+	5.00465i	−0.0674624	+	0.207628i
$582$		0			0
$583$	−2.57769			−0.106757
$584$		0			0
$585$	30.9765	+	22.5057i	1.28072	+	0.930497i
$586$		0			0
$587$	1.39272	+	4.28635i	0.0574837	+	0.176917i	0.975676	−	0.219219i	$-0.0703510\pi$
$587$	1.39272	+	4.28635i	0.0574837	+	0.176917i	−0.918192	+	0.396136i	$0.870351\pi$
$588$		0			0
$589$	2.13995	−	1.55477i	0.0881752	−	0.0640630i
$590$		0			0
$591$	40.4519	+	29.3900i	1.66397	+	1.20894i
$592$		0			0
$593$	−6.14275	+	18.9055i	−0.252253	+	0.776354i	0.742106	+	0.670283i	$0.233827\pi$
$593$	−6.14275	+	18.9055i	−0.252253	+	0.776354i	−0.994359	+	0.106071i	$0.966173\pi$
$594$		0			0
$595$	−2.39802	+	7.38035i	−0.0983093	+	0.302565i
$596$		0			0
$597$	−8.45179	−	26.0119i	−0.345909	−	1.06460i
$598$		0			0
$599$	0.942036	−	2.89929i	0.0384906	−	0.118462i	−0.929965	−	0.367648i	$-0.880163\pi$
$599$	0.942036	−	2.89929i	0.0384906	−	0.118462i	0.968456	+	0.249186i	$0.0801631\pi$
$600$		0			0
$601$	−25.0139			−1.02034			−0.510169	−	0.860074i	$-0.670417\pi$
$601$	−25.0139			−1.02034			−0.510169	+	0.860074i	$0.670417\pi$
$602$		0			0
$603$	36.7946	−	26.7328i	1.49839	−	1.08865i
$604$		0			0
$605$	−26.6554	−	19.3663i	−1.08370	−	0.787351i
$606$		0			0
$607$	−14.1043	−	10.2474i	−0.572476	−	0.415928i	0.263528	−	0.964652i	$-0.415114\pi$
$607$	−14.1043	−	10.2474i	−0.572476	−	0.415928i	−0.836004	+	0.548724i	$0.815114\pi$
$608$		0			0
$609$	5.34280	+	16.4434i	0.216501	+	0.666322i
$610$		0			0
$611$	−9.35165	+	6.79437i	−0.378327	+	0.274871i
$612$		0			0
$613$	7.16706	+	22.0579i	0.289475	+	0.890912i	0.985022	+	0.172431i	$0.0551622\pi$
$613$	7.16706	+	22.0579i	0.289475	+	0.890912i	−0.695547	+	0.718481i	$0.744838\pi$
$614$		0			0
$615$	−47.1329	−	29.2842i	−1.90058	−	1.18085i
$616$		0			0
$617$	−11.5806	−	35.6414i	−0.466217	−	1.43487i	−0.857446	−	0.514574i	$-0.827950\pi$
$617$	−11.5806	−	35.6414i	−0.466217	−	1.43487i	0.391230	−	0.920293i	$-0.372050\pi$
$618$		0			0
$619$	35.7744	−	25.9916i	1.43790	−	1.04469i	0.449419	−	0.893321i	$-0.351631\pi$
$619$	35.7744	−	25.9916i	1.43790	−	1.04469i	0.988477	−	0.151371i	$-0.0483689\pi$
$620$		0			0
$621$	3.50418	+	10.7848i	0.140618	+	0.432777i
$622$		0			0
$623$	−9.75412	−	7.08678i	−0.390790	−	0.283926i
$624$		0			0
$625$	23.2247	+	16.8738i	0.928990	+	0.674951i
$626$		0			0
$627$	−0.996079	+	0.723694i	−0.0397796	+	0.0289015i
$628$		0			0
$629$	21.9533			0.875336
$630$		0			0
$631$	−8.72904	+	26.8652i	−0.347498	+	1.06949i	0.612735	+	0.790288i	$0.290069\pi$
$631$	−8.72904	+	26.8652i	−0.347498	+	1.06949i	−0.960233	+	0.279200i	$0.909931\pi$
$632$		0			0
$633$	14.7332	+	45.3441i	0.585592	+	1.80227i
$634$		0			0
$635$	5.08539	−	15.6512i	0.201808	−	0.621100i
$636$		0			0
$637$	0.746236	−	2.29668i	0.0295669	−	0.0909977i
$638$		0			0
$639$	54.5653	+	39.6440i	2.15857	+	1.56829i
$640$		0			0
$641$	6.58143	−	4.78169i	0.259951	−	0.188865i	−0.450175	−	0.892941i	$-0.648638\pi$
$641$	6.58143	−	4.78169i	0.259951	−	0.188865i	0.710125	+	0.704075i	$0.248638\pi$
$642$		0			0
$643$	6.51145	+	20.0402i	0.256787	+	0.790308i	0.993472	+	0.114073i	$0.0363897\pi$
$643$	6.51145	+	20.0402i	0.256787	+	0.790308i	−0.736686	+	0.676235i	$0.763610\pi$
$644$		0			0
$645$	11.3488	+	8.24537i	0.446858	+	0.324661i
$646$		0			0
$647$	16.0147			0.629604			0.314802	−	0.949157i	$-0.398062\pi$
$647$	16.0147			0.629604			0.314802	+	0.949157i	$0.398062\pi$
$648$		0			0
$649$	0.589472	−	1.81421i	0.0231388	−	0.0712139i
$650$		0			0
$651$	−3.92064	+	2.84851i	−0.153662	+	0.111642i
$652$		0			0
$653$	−22.5776			−0.883529			−0.441765	−	0.897131i	$-0.645647\pi$
$653$	−22.5776			−0.883529			−0.441765	+	0.897131i	$0.645647\pi$
$654$		0			0
$655$	1.98086			0.0773985
$656$		0			0
$657$	66.5293			2.59555
$658$		0			0
$659$	−20.7103			−0.806760			−0.403380	−	0.915033i	$-0.632165\pi$
$659$	−20.7103			−0.806760			−0.403380	+	0.915033i	$0.632165\pi$
$660$		0			0
$661$	19.8505	−	14.4222i	0.772095	−	0.560960i	−0.130501	−	0.991448i	$-0.541659\pi$
$661$	19.8505	−	14.4222i	0.772095	−	0.560960i	0.902596	+	0.430488i	$0.141659\pi$
$662$		0			0
$663$	5.51802	−	16.9827i	0.214302	−	0.659555i
$664$		0			0
$665$	−4.73005			−0.183424
$666$		0			0
$667$	8.50825	+	6.18161i	0.329441	+	0.239353i
$668$		0			0
$669$	3.15831	+	9.72027i	0.122107	+	0.375807i
$670$		0			0
$671$	0.737639	−	0.535926i	0.0284762	−	0.0206892i
$672$		0			0
$673$	15.1606	+	11.0148i	0.584397	+	0.424590i	0.840307	−	0.542111i	$-0.182375\pi$
$673$	15.1606	+	11.0148i	0.584397	+	0.424590i	−0.255909	+	0.966701i	$0.582375\pi$
$674$		0			0
$675$	−8.20861	+	25.2635i	−0.315950	+	0.972393i
$676$		0			0
$677$	−5.89816	+	18.1527i	−0.226685	+	0.697664i	0.771431	+	0.636313i	$0.219541\pi$
$677$	−5.89816	+	18.1527i	−0.226685	+	0.697664i	−0.998116	+	0.0613518i	$0.980459\pi$
$678$		0			0
$679$	−1.69899	−	5.22895i	−0.0652013	−	0.200669i
$680$		0			0
$681$	−0.779236	+	2.39824i	−0.0298604	+	0.0919008i
$682$		0			0
$683$	40.6570			1.55570			0.777848	−	0.628453i	$-0.216311\pi$
$683$	40.6570			1.55570			0.777848	+	0.628453i	$0.216311\pi$
$684$		0			0
$685$	20.2151	−	14.6872i	0.772381	−	0.561168i
$686$		0			0
$687$	21.6752	+	15.7480i	0.826962	+	0.600823i
$688$		0			0
$689$	18.4352	+	13.3940i	0.702327	+	0.510270i
$690$		0			0
$691$	11.0326	+	33.9549i	0.419700	+	1.29170i	0.907979	+	0.419017i	$0.137625\pi$
$691$	11.0326	+	33.9549i	0.419700	+	1.29170i	−0.488278	+	0.872688i	$0.662375\pi$
$692$		0			0
$693$	1.16193	−	0.844193i	0.0441382	−	0.0320682i
$694$		0			0
$695$	6.15809	+	18.9527i	0.233590	+	0.718915i
$696$		0			0
$697$	−3.94510	+	15.9975i	−0.149431	+	0.605948i
$698$		0			0
$699$	7.47042	+	22.9916i	0.282557	+	0.869621i
$700$		0			0
$701$	−19.7397	+	14.3417i	−0.745558	+	0.541679i	−0.894447	−	0.447175i	$-0.852430\pi$
$701$	−19.7397	+	14.3417i	−0.745558	+	0.541679i	0.148889	+	0.988854i	$0.452430\pi$
$702$		0			0
$703$	4.13502	+	12.7263i	0.155955	+	0.479981i
$704$		0			0
$705$	−33.5593	−	24.3823i	−1.26392	−	0.918289i
$706$		0			0
$707$	15.8295	+	11.5008i	0.595330	+	0.432533i
$708$		0			0
$709$	1.42178	−	1.03298i	0.0533960	−	0.0387945i	−0.560767	−	0.827974i	$-0.689494\pi$
$709$	1.42178	−	1.03298i	0.0533960	−	0.0387945i	0.614163	+	0.789179i	$0.289494\pi$
$710$		0			0
$711$	50.7242			1.90231
$712$		0			0
$713$	−0.910915	+	2.80351i	−0.0341140	+	0.104992i
$714$		0			0
$715$	−0.614753	−	1.89201i	−0.0229904	−	0.0707573i
$716$		0			0
$717$	21.8643	−	67.2913i	0.816536	−	2.51304i
$718$		0			0
$719$	4.17997	−	12.8646i	0.155886	−	0.479769i	−0.842363	−	0.538910i	$-0.818836\pi$
$719$	4.17997	−	12.8646i	0.155886	−	0.479769i	0.998250	+	0.0591412i	$0.0188362\pi$
$720$		0			0
$721$	−1.34273	−	0.975548i	−0.0500058	−	0.0363313i
$722$		0			0
$723$	15.0110	−	10.9061i	0.558266	−	0.405604i
$724$		0			0
$725$	7.61287	+	23.4300i	0.282735	+	0.870169i
$726$		0			0
$727$	−25.0062	−	18.1680i	−0.927427	−	0.673815i	0.0179346	−	0.999839i	$-0.494291\pi$
$727$	−25.0062	−	18.1680i	−0.927427	−	0.673815i	−0.945361	+	0.326024i	$0.894291\pi$
$728$		0			0
$729$	−40.8398			−1.51259
$730$		0			0
$731$	1.28717	−	3.96149i	0.0476076	−	0.146521i
$732$		0			0
$733$	39.6390	−	28.7994i	1.46410	−	1.06373i	0.481830	−	0.876265i	$-0.339972\pi$
$733$	39.6390	−	28.7994i	1.46410	−	1.06373i	0.982271	−	0.187467i	$-0.0600277\pi$
$734$		0			0
$735$	8.66600			0.319650
$736$		0			0
$737$	−2.36303			−0.0870435
$738$		0			0
$739$	−44.3312			−1.63075			−0.815375	−	0.578933i	$-0.803469\pi$
$739$	−44.3312			−1.63075			−0.815375	+	0.578933i	$0.803469\pi$
$740$		0			0
$741$	10.8842			0.399841
$742$		0			0
$743$	−23.1410	+	16.8129i	−0.848960	+	0.616806i	−0.924859	−	0.380310i	$-0.875817\pi$
$743$	−23.1410	+	16.8129i	−0.848960	+	0.616806i	0.0758989	+	0.997116i	$0.475817\pi$
$744$		0			0
$745$	−8.89171	+	27.3659i	−0.325767	+	1.00261i
$746$		0			0
$747$	27.6667			1.01227
$748$		0			0
$749$	8.90064	+	6.46669i	0.325222	+	0.236288i
$750$		0			0
$751$	−16.1383	−	49.6686i	−0.588895	−	1.81243i	−0.583030	−	0.812451i	$-0.698133\pi$
$751$	−16.1383	−	49.6686i	−0.588895	−	1.81243i	−0.00586589	−	0.999983i	$-0.501867\pi$
$752$		0			0
$753$	−67.1373	+	48.7781i	−2.44662	+	1.77757i
$754$		0			0
$755$	14.3153	+	10.4007i	0.520987	+	0.378519i
$756$		0			0
$757$	4.37161	−	13.4544i	0.158889	−	0.489009i	−0.839645	−	0.543135i	$-0.817237\pi$
$757$	4.37161	−	13.4544i	0.158889	−	0.489009i	0.998534	+	0.0541258i	$0.0172372\pi$
$758$		0			0
$759$	0.424002	−	1.30494i	0.0153903	−	0.0473664i
$760$		0			0
$761$	−4.19461	−	12.9097i	−0.152055	−	0.467976i	0.845796	−	0.533507i	$-0.179126\pi$
$761$	−4.19461	−	12.9097i	−0.152055	−	0.467976i	−0.997851	+	0.0655305i	$0.979126\pi$
$762$		0			0
$763$	0.191791	−	0.590271i	0.00694329	−	0.0213693i
$764$		0			0
$765$	40.8000			1.47513
$766$		0			0
$767$	−13.6426	+	9.91196i	−0.492607	+	0.357900i
$768$		0			0
$769$	−34.6709	−	25.1899i	−1.25026	−	0.908370i	−0.252027	−	0.967720i	$-0.581097\pi$
$769$	−34.6709	−	25.1899i	−1.25026	−	0.908370i	−0.998237	+	0.0593496i	$0.981097\pi$
$770$		0			0
$771$	−32.5646	−	23.6596i	−1.17278	−	0.852078i
$772$		0			0
$773$	−7.95241	−	24.4750i	−0.286028	−	0.880305i	−0.986089	−	0.166221i	$-0.946844\pi$
$773$	−7.95241	−	24.4750i	−0.286028	−	0.880305i	0.700060	−	0.714084i	$-0.253156\pi$
$774$		0			0
$775$	−5.58646	+	4.05880i	−0.200671	+	0.145796i
$776$		0			0
$777$	−7.57583	−	23.3160i	−0.271781	−	0.836457i
$778$		0			0
$779$	−10.0168	+	0.726244i	−0.358889	+	0.0260204i
$780$		0			0
$781$	−1.08289	−	3.33279i	−0.0387489	−	0.119257i
$782$		0			0
$783$	31.5788	−	22.9434i	1.12854	−	0.819929i
$784$		0			0
$785$	−8.86272	−	27.2766i	−0.316324	−	0.973545i
$786$		0			0
$787$	−23.2716	−	16.9078i	−0.829544	−	0.602699i	0.0898862	−	0.995952i	$-0.471350\pi$
$787$	−23.2716	−	16.9078i	−0.829544	−	0.602699i	−0.919430	+	0.393253i	$0.871350\pi$
$788$		0			0
$789$	52.0108	+	37.7881i	1.85163	+	1.34529i
$790$		0			0
$791$	−1.20554	+	0.875874i	−0.0428639	+	0.0311425i
$792$		0			0
$793$	−8.06022			−0.286227
$794$		0			0
$795$	−25.2696	+	77.7718i	−0.896220	+	2.75828i
$796$		0			0
$797$	−8.07312	−	24.8465i	−0.285965	−	0.880108i	−0.986108	−	0.166106i	$-0.946881\pi$
$797$	−8.07312	−	24.8465i	−0.285965	−	0.880108i	0.700143	−	0.714002i	$-0.253119\pi$
$798$		0			0
$799$	−3.80627	+	11.7145i	−0.134656	+	0.414429i
$800$		0			0
$801$	−19.5886	+	60.2874i	−0.692128	+	2.13015i
$802$		0			0
$803$	−2.79650	−	2.03177i	−0.0986862	−	0.0716997i
$804$		0			0
$805$	4.26455	−	3.09837i	0.150305	−	0.109203i
$806$		0			0
$807$	−1.10081	−	3.38795i	−0.0387504	−	0.119262i
$808$		0			0
$809$	7.47988	+	5.43445i	0.262978	+	0.191065i	0.711459	−	0.702728i	$-0.248035\pi$
$809$	7.47988	+	5.43445i	0.262978	+	0.191065i	−0.448481	+	0.893793i	$0.648035\pi$
$810$		0			0
$811$	−6.59256			−0.231496			−0.115748	−	0.993279i	$-0.536927\pi$
$811$	−6.59256			−0.231496			−0.115748	+	0.993279i	$0.536927\pi$
$812$		0			0
$813$	9.98546	−	30.7321i	0.350205	−	1.07782i
$814$		0			0
$815$	52.5540	−	38.1827i	1.84089	−	1.33748i
$816$		0			0
$817$	2.53891			0.0888253
$818$		0			0
$819$	−12.6965			−0.443651
$820$		0			0
$821$	−23.4153			−0.817199			−0.408600	−	0.912714i	$-0.633983\pi$
$821$	−23.4153			−0.817199			−0.408600	+	0.912714i	$0.633983\pi$
$822$		0			0
$823$	−39.6248			−1.38123			−0.690616	−	0.723222i	$-0.742661\pi$
$823$	−39.6248			−1.38123			−0.690616	+	0.723222i	$0.742661\pi$
$824$		0			0
$825$	2.60032	−	1.88924i	0.0905314	−	0.0657749i
$826$		0			0
$827$	−14.2480	+	43.8508i	−0.495451	+	1.52484i	0.320803	+	0.947146i	$0.396047\pi$
$827$	−14.2480	+	43.8508i	−0.495451	+	1.52484i	−0.816253	+	0.577694i	$0.803953\pi$
$828$		0			0
$829$	43.9088			1.52502			0.762508	−	0.646979i	$-0.223968\pi$
$829$	43.9088			1.52502			0.762508	+	0.646979i	$0.223968\pi$
$830$		0			0
$831$	5.51576	+	4.00743i	0.191339	+	0.139016i
$832$		0			0
$833$	−0.795174	−	2.44729i	−0.0275511	−	0.0847937i
$834$		0			0
$835$	−1.84141	+	1.33786i	−0.0637247	+	0.0462987i
$836$		0			0
$837$	8.85133	+	6.43087i	0.305947	+	0.222283i
$838$		0			0
$839$	13.3969	−	41.2315i	0.462513	−	1.42347i	−0.399570	−	0.916703i	$-0.630841\pi$
$839$	13.3969	−	41.2315i	0.462513	−	1.42347i	0.862083	−	0.506766i	$-0.169159\pi$
$840$		0			0
$841$	2.22514	−	6.84829i	0.0767291	−	0.236148i
$842$		0			0
$843$	−8.63738	−	26.5831i	−0.297487	−	0.915571i
$844$		0			0
$845$	6.68030	−	20.5598i	0.229809	−	0.707280i
$846$		0			0
$847$	10.9254			0.375400
$848$		0			0
$849$	22.7101	−	16.4999i	0.779409	−	0.566274i
$850$		0			0
$851$	−12.0643	−	8.76523i	−0.413559	−	0.300468i
$852$		0			0
$853$	32.8044	+	23.8338i	1.12320	+	0.816054i	0.984691	−	0.174307i	$-0.0557685\pi$
$853$	32.8044	+	23.8338i	1.12320	+	0.816054i	0.138511	+	0.990361i	$0.455769\pi$
$854$		0			0
$855$	7.68490	+	23.6517i	0.262818	+	0.808871i
$856$		0			0
$857$	0.0876652	−	0.0636925i	0.00299459	−	0.00217569i	−0.586287	−	0.810103i	$-0.699411\pi$
$857$	0.0876652	−	0.0636925i	0.00299459	−	0.00217569i	0.589282	+	0.807928i	$0.299411\pi$
$858$		0			0
$859$	−2.23313	−	6.87287i	−0.0761934	−	0.234499i	0.905705	−	0.423909i	$-0.139342\pi$
$859$	−2.23313	−	6.87287i	−0.0761934	−	0.234499i	−0.981898	+	0.189410i	$0.939342\pi$
$860$		0			0
$861$	18.3519	−	1.33056i	0.625431	−	0.0453454i
$862$		0			0
$863$	14.7514	+	45.4002i	0.502145	+	1.54544i	0.805518	+	0.592571i	$0.201887\pi$
$863$	14.7514	+	45.4002i	0.502145	+	1.54544i	−0.303374	+	0.952872i	$0.598113\pi$
$864$		0			0
$865$	−62.7900	+	45.6196i	−2.13492	+	1.55111i
$866$		0			0
$867$	9.21600	+	28.3639i	0.312992	+	0.963290i
$868$		0			0
$869$	−2.13214	−	1.54909i	−0.0723280	−	0.0525494i
$870$		0			0
$871$	16.9001	+	12.2786i	0.572636	+	0.416045i
$872$		0			0
$873$	−23.3860	+	16.9909i	−0.791496	+	0.575056i
$874$		0			0
$875$	−2.73054			−0.0923092
$876$		0			0
$877$	14.0297	−	43.1791i	0.473750	−	1.45805i	−0.373885	−	0.927475i	$-0.621975\pi$
$877$	14.0297	−	43.1791i	0.473750	−	1.45805i	0.847636	−	0.530579i	$-0.178025\pi$
$878$		0			0
$879$	−27.2385	−	83.8316i	−0.918733	−	2.82757i
$880$		0			0
$881$	2.03494	−	6.26292i	0.0685590	−	0.211003i	−0.910907	−	0.412611i	$-0.864617\pi$
$881$	2.03494	−	6.26292i	0.0685590	−	0.211003i	0.979466	+	0.201608i	$0.0646168\pi$
$882$		0			0
$883$	1.52632	−	4.69754i	0.0513649	−	0.158085i	−0.922084	−	0.386990i	$-0.873515\pi$
$883$	1.52632	−	4.69754i	0.0513649	−	0.158085i	0.973449	+	0.228905i	$0.0735147\pi$
$884$		0			0
$885$	−48.9580	−	35.5700i	−1.64570	−	1.19567i
$886$		0			0
$887$	29.7264	−	21.5975i	0.998115	−	0.725173i	0.0364316	−	0.999336i	$-0.488401\pi$
$887$	29.7264	−	21.5975i	0.998115	−	0.725173i	0.961683	+	0.274163i	$0.0884009\pi$
$888$		0			0
$889$	1.68629	+	5.18988i	0.0565565	+	0.174063i
$890$		0			0
$891$	−0.634215	−	0.460784i	−0.0212470	−	0.0154368i
$892$		0			0
$893$	−7.50779			−0.251239
$894$		0			0
$895$	−10.3287	+	31.7886i	−0.345252	+	1.06258i
$896$		0			0
$897$	−9.81303	+	7.12958i	−0.327648	+	0.238050i
$898$		0			0
$899$	10.1468			0.338415
$900$		0			0
$901$	24.2816			0.808937
$902$		0			0
$903$	−4.65158			−0.154795
$904$		0			0
$905$	11.2116			0.372688
$906$		0			0
$907$	23.3614	−	16.9730i	0.775702	−	0.563581i	−0.127984	−	0.991776i	$-0.540851\pi$
$907$	23.3614	−	16.9730i	0.775702	−	0.563581i	0.903686	+	0.428196i	$0.140851\pi$
$908$		0			0
$909$	31.7894	−	97.8377i	1.05439	−	3.24507i
$910$		0			0
$911$	−34.2256			−1.13395			−0.566973	−	0.823736i	$-0.691886\pi$
$911$	−34.2256			−1.13395			−0.566973	+	0.823736i	$0.691886\pi$
$912$		0			0
$913$	−1.16294	−	0.844927i	−0.0384878	−	0.0279630i
$914$		0			0
$915$	−8.93828	−	27.5092i	−0.295490	−	0.909426i
$916$		0			0
$917$	−0.531398	+	0.386083i	−0.0175483	+	0.0127496i
$918$		0			0
$919$	5.24912	+	3.81371i	0.173152	+	0.125803i	0.670986	−	0.741470i	$-0.265871\pi$
$919$	5.24912	+	3.81371i	0.173152	+	0.125803i	−0.497834	+	0.867273i	$0.665871\pi$
$920$		0			0
$921$	−14.1812	+	43.6451i	−0.467285	+	1.43816i
$922$		0			0
$923$	−9.57293	+	29.4625i	−0.315097	+	0.969768i
$924$		0			0
$925$	−10.7947	−	33.2226i	−0.354927	−	1.09235i
$926$		0			0
$927$	−2.69651	+	8.29901i	−0.0885650	+	0.272575i
$928$		0			0
$929$	42.4963			1.39426			0.697129	−	0.716946i	$-0.254461\pi$
$929$	42.4963			1.39426			0.697129	+	0.716946i	$0.254461\pi$
$930$		0			0
$931$	1.26892	−	0.921921i	0.0415870	−	0.0302147i
$932$		0			0
$933$	36.7142	+	26.6744i	1.20197	+	0.873280i
$934$		0			0
$935$	−1.71499	−	1.24601i	−0.0560862	−	0.0407490i
$936$		0			0
$937$	−3.42291	−	10.5346i	−0.111822	−	0.344152i	0.879449	−	0.475993i	$-0.157911\pi$
$937$	−3.42291	−	10.5346i	−0.111822	−	0.344152i	−0.991271	+	0.131841i	$0.957911\pi$
$938$		0			0
$939$	−17.3983	+	12.6406i	−0.567773	+	0.412511i
$940$		0			0
$941$	0.594556	+	1.82985i	0.0193820	+	0.0596516i	0.960280	−	0.279039i	$-0.0900159\pi$
$941$	0.594556	+	1.82985i	0.0193820	+	0.0596516i	−0.940898	+	0.338691i	$0.890016\pi$
$942$		0			0
$943$	8.55527	−	7.21617i	0.278598	−	0.234991i
$944$		0			0
$945$	−6.04579	−	18.6070i	−0.196670	−	0.605287i
$946$		0			0
$947$	6.94810	−	5.04809i	0.225783	−	0.164041i	−0.469143	−	0.883122i	$-0.655437\pi$
$947$	6.94810	−	5.04809i	0.225783	−	0.164041i	0.694926	+	0.719081i	$0.255437\pi$
$948$		0			0
$949$	9.44277	+	29.0618i	0.306525	+	0.943387i
$950$		0			0
$951$	−23.3359	−	16.9545i	−0.756718	−	0.549788i
$952$		0			0
$953$	37.8247	+	27.4813i	1.22526	+	0.890206i	0.996526	−	0.0832818i	$-0.0265402\pi$
$953$	37.8247	+	27.4813i	1.22526	+	0.890206i	0.228738	+	0.973488i	$0.426540\pi$
$954$		0			0
$955$	−9.38593	+	6.81928i	−0.303722	+	0.220667i
$956$		0			0
$957$	−4.72302			−0.152673
$958$		0			0
$959$	−2.56042	+	7.88015i	−0.0826801	+	0.254463i
$960$		0			0
$961$	−8.70066	−	26.7779i	−0.280666	−	0.863802i
$962$		0			0
$963$	17.8746	−	55.0123i	0.576000	−	1.77275i
$964$		0			0
$965$	−18.2160	+	56.0632i	−0.586395	+	1.80474i
$966$		0			0
$967$	40.5598	+	29.4684i	1.30432	+	0.947640i	0.999988	−	0.00492704i	$-0.00156833\pi$
$967$	40.5598	+	29.4684i	1.30432	+	0.947640i	0.304327	+	0.952568i	$0.401568\pi$
$968$		0			0
$969$	9.38297	−	6.81712i	0.301424	−	0.218998i
$970$		0			0
$971$	6.77004	+	20.8360i	0.217261	+	0.668660i	0.998985	+	0.0450363i	$0.0143403\pi$
$971$	6.77004	+	20.8360i	0.217261	+	0.668660i	−0.781724	+	0.623624i	$0.785660\pi$
$972$		0			0
$973$	−5.34602	−	3.88411i	−0.171385	−	0.124519i
$974$		0			0
$975$	−28.4138			−0.909969
$976$		0			0
$977$	−12.7349	+	39.1939i	−0.407424	+	1.25392i	0.511430	+	0.859325i	$0.329116\pi$
$977$	−12.7349	+	39.1939i	−0.407424	+	1.25392i	−0.918854	+	0.394598i	$0.870884\pi$
$978$		0			0
$979$	2.66453	−	1.93590i	0.0851589	−	0.0618716i
$980$		0			0
$981$	−3.26313			−0.104184
$982$		0			0
$983$	37.1120			1.18369			0.591845	−	0.806052i	$-0.298400\pi$
$983$	37.1120			1.18369			0.591845	+	0.806052i	$0.298400\pi$
$984$		0			0
$985$	−52.4741			−1.67196
$986$		0			0
$987$	13.7551			0.437830
$988$		0			0
$989$	−2.28905	+	1.66309i	−0.0727875	+	0.0528832i
$990$		0			0
$991$	12.7727	−	39.3104i	0.405739	−	1.24874i	−0.514537	−	0.857468i	$-0.672036\pi$
$991$	12.7727	−	39.3104i	0.405739	−	1.24874i	0.920276	−	0.391269i	$-0.127964\pi$
$992$		0			0
$993$	−71.5989			−2.27212
$994$		0			0
$995$	23.2213	+	16.8713i	0.736166	+	0.534856i
$996$		0			0
$997$	−16.4313	−	50.5702i	−0.520383	−	1.60158i	−0.773268	−	0.634079i	$-0.781379\pi$
$997$	−16.4313	−	50.5702i	−0.520383	−	1.60158i	0.252885	−	0.967496i	$-0.418621\pi$
$998$		0			0
$999$	−44.7773	+	32.5326i	−1.41669	+	1.02929i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.n.e.141.1	yes	24
41.16	even	5	inner	1148.2.n.e.57.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.n.e.57.1	✓	24	41.16	even	5	inner
1148.2.n.e.141.1	yes	24	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)

\(f(q)\)	\(=\)	\(q-2.87361 q^{3} +(2.43977 - 1.77260i) q^{5} +(-0.309017 + 0.951057i) q^{7} +5.25763 q^{9} +O(q^{10})\)	\(q-2.87361 q^{3} +(2.43977 - 1.77260i) q^{5} +(-0.309017 + 0.951057i) q^{7} +5.25763 q^{9} +(-0.220999 - 0.160565i) q^{11} +(0.746236 + 2.29668i) q^{13} +(-7.01094 + 5.09375i) q^{15} +(2.08179 + 1.51251i) q^{17} +(-0.484683 + 1.49170i) q^{19} +(0.887994 - 2.73296i) q^{21} +(-0.540140 - 1.66238i) q^{23} +(1.26529 - 3.89416i) q^{25} -6.48754 q^{27} +(-4.86762 + 3.53653i) q^{29} +(-1.36436 - 0.991266i) q^{31} +(0.635066 + 0.461402i) q^{33} +(0.931909 + 2.86812i) q^{35} +(6.90205 - 5.01463i) q^{37} +(-2.14439 - 6.59975i) q^{39} +(2.41386 + 5.93071i) q^{41} +(-0.500213 - 1.53950i) q^{43} +(12.8274 - 9.31964i) q^{45} +(1.47917 + 4.55243i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(-5.98226 - 4.34636i) q^{51} +(7.63405 - 5.54646i) q^{53} -0.823805 q^{55} +(1.39279 - 4.28656i) q^{57} +(2.15789 + 6.64131i) q^{59} +(-1.03142 + 3.17438i) q^{61} +(-1.62470 + 5.00030i) q^{63} +(5.89172 + 4.28059i) q^{65} +(6.99833 - 5.08458i) q^{67} +(1.55215 + 4.77703i) q^{69} +(10.3783 + 7.54028i) q^{71} +12.6539 q^{73} +(-3.63595 + 11.1903i) q^{75} +(0.220999 - 0.160565i) q^{77} +9.64773 q^{79} +2.86976 q^{81} +5.26220 q^{83} +7.76016 q^{85} +(13.9876 - 10.1626i) q^{87} +(-3.72574 + 11.4667i) q^{89} -2.41487 q^{91} +(3.92064 + 2.84851i) q^{93} +(1.46167 + 4.49855i) q^{95} +(-4.44801 + 3.23167i) q^{97} +(-1.16193 - 0.844193i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{3} + 17 q^{5} + 6 q^{7} + 16 q^{9}+O(q^{10}) \) 24 * q + 12 * q^3 + 17 * q^5 + 6 * q^7 + 16 * q^9	\( 24 q + 12 q^{3} + 17 q^{5} + 6 q^{7} + 16 q^{9} - 8 q^{11} + 10 q^{15} + 8 q^{17} - 28 q^{19} + 3 q^{21} - 23 q^{23} + 17 q^{25} + 12 q^{27} - 31 q^{29} + 2 q^{31} + 12 q^{33} + 13 q^{35} + 7 q^{37} - 16 q^{39} - q^{41} - 2 q^{43} + 71 q^{45} + 15 q^{47} - 6 q^{49} + 2 q^{51} + 28 q^{53} - 16 q^{55} - 15 q^{57} + 17 q^{59} + 35 q^{61} - q^{63} + 62 q^{65} - 10 q^{67} - 9 q^{69} - 25 q^{71} - 74 q^{73} + 17 q^{75} + 8 q^{77} + 64 q^{81} + 96 q^{83} - 94 q^{85} - q^{87} - 33 q^{89} - 15 q^{93} - 29 q^{95} - 34 q^{97} - 3 q^{99}+O(q^{100}) \) 24 * q + 12 * q^3 + 17 * q^5 + 6 * q^7 + 16 * q^9 - 8 * q^11 + 10 * q^15 + 8 * q^17 - 28 * q^19 + 3 * q^21 - 23 * q^23 + 17 * q^25 + 12 * q^27 - 31 * q^29 + 2 * q^31 + 12 * q^33 + 13 * q^35 + 7 * q^37 - 16 * q^39 - q^41 - 2 * q^43 + 71 * q^45 + 15 * q^47 - 6 * q^49 + 2 * q^51 + 28 * q^53 - 16 * q^55 - 15 * q^57 + 17 * q^59 + 35 * q^61 - q^63 + 62 * q^65 - 10 * q^67 - 9 * q^69 - 25 * q^71 - 74 * q^73 + 17 * q^75 + 8 * q^77 + 64 * q^81 + 96 * q^83 - 94 * q^85 - q^87 - 33 * q^89 - 15 * q^93 - 29 * q^95 - 34 * q^97 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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