LMFDB - Embedded newform 1148.2.n.d.365.6

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			365.6
Character	$\chi$	$=$	1148.365
Dual form			1148.2.n.d.953.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.85770 q^{3} +(-1.27648 + 3.92860i) q^{5} +(-0.809017 - 0.587785i) q^{7} +0.451065 q^{9} +O(q^{10})$	\(q+1.85770 q^{3} +(-1.27648 + 3.92860i) q^{5} +(-0.809017 - 0.587785i) q^{7} +0.451065 q^{9} +(1.01446 + 3.12220i) q^{11} +(1.36768 - 0.993681i) q^{13} +(-2.37132 + 7.29817i) q^{15} +(1.46860 + 4.51989i) q^{17} +(-4.77393 - 3.46846i) q^{19} +(-1.50291 - 1.09193i) q^{21} +(3.94310 - 2.86483i) q^{23} +(-9.75940 - 7.09062i) q^{25} -4.73517 q^{27} +(-1.01826 + 3.13387i) q^{29} +(1.76389 + 5.42869i) q^{31} +(1.88457 + 5.80012i) q^{33} +(3.34186 - 2.42801i) q^{35} +(-1.62259 + 4.99382i) q^{37} +(2.54075 - 1.84596i) q^{39} +(-3.90619 + 5.07362i) q^{41} +(-4.26764 + 3.10062i) q^{43} +(-0.575774 + 1.77205i) q^{45} +(0.898680 - 0.652929i) q^{47} +(0.309017 + 0.951057i) q^{49} +(2.72822 + 8.39661i) q^{51} +(-2.77745 + 8.54810i) q^{53} -13.5608 q^{55} +(-8.86855 - 6.44338i) q^{57} +(6.58307 - 4.78288i) q^{59} +(0.303906 + 0.220801i) q^{61} +(-0.364919 - 0.265129i) q^{63} +(2.15795 + 6.64149i) q^{65} +(2.46767 - 7.59469i) q^{67} +(7.32511 - 5.32200i) q^{69} +(-3.70326 - 11.3975i) q^{71} -2.91522 q^{73} +(-18.1301 - 13.1723i) q^{75} +(1.01446 - 3.12220i) q^{77} +6.54825 q^{79} -10.1497 q^{81} +7.52545 q^{83} -19.6315 q^{85} +(-1.89162 + 5.82181i) q^{87} +(12.9488 + 9.40782i) q^{89} -1.69055 q^{91} +(3.27678 + 10.0849i) q^{93} +(19.7200 - 14.3274i) q^{95} +(0.870418 - 2.67887i) q^{97} +(0.457588 + 1.40831i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 10 q^{3} + 4 q^{5} - 6 q^{7} + 38 q^{9}+O(q^{10}) $ 24 * q - 10 * q^3 + 4 * q^5 - 6 * q^7 + 38 * q^9	$ 24 q - 10 q^{3} + 4 q^{5} - 6 q^{7} + 38 q^{9} + 11 q^{11} - 4 q^{13} + 10 q^{15} + 9 q^{17} - 23 q^{19} + 5 q^{21} + 28 q^{23} - 10 q^{25} - 76 q^{27} + 28 q^{29} - 18 q^{31} - 27 q^{33} - q^{35} - 29 q^{37} - 6 q^{39} + 65 q^{41} - 15 q^{43} - 20 q^{45} - 11 q^{47} - 6 q^{49} - 18 q^{51} + 8 q^{53} - 50 q^{55} + 8 q^{57} + 55 q^{59} - 10 q^{61} - 2 q^{63} - 11 q^{65} + 65 q^{67} - 2 q^{69} - 14 q^{71} + 48 q^{73} - 77 q^{75} + 11 q^{77} + 22 q^{79} + 80 q^{81} - 22 q^{83} - 78 q^{85} - 4 q^{87} + 16 q^{89} - 4 q^{91} - 60 q^{93} + 56 q^{95} + 15 q^{97} + 80 q^{99}+O(q^{100}) $ 24 * q - 10 * q^3 + 4 * q^5 - 6 * q^7 + 38 * q^9 + 11 * q^11 - 4 * q^13 + 10 * q^15 + 9 * q^17 - 23 * q^19 + 5 * q^21 + 28 * q^23 - 10 * q^25 - 76 * q^27 + 28 * q^29 - 18 * q^31 - 27 * q^33 - q^35 - 29 * q^37 - 6 * q^39 + 65 * q^41 - 15 * q^43 - 20 * q^45 - 11 * q^47 - 6 * q^49 - 18 * q^51 + 8 * q^53 - 50 * q^55 + 8 * q^57 + 55 * q^59 - 10 * q^61 - 2 * q^63 - 11 * q^65 + 65 * q^67 - 2 * q^69 - 14 * q^71 + 48 * q^73 - 77 * q^75 + 11 * q^77 + 22 * q^79 + 80 * q^81 - 22 * q^83 - 78 * q^85 - 4 * q^87 + 16 * q^89 - 4 * q^91 - 60 * q^93 + 56 * q^95 + 15 * q^97 + 80 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

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
$3$	1.85770			1.07255			0.536273	−	0.844045i	$-0.319832\pi$
$3$	1.85770			1.07255			0.536273	+	0.844045i	$0.319832\pi$
$4$		0			0
$5$	−1.27648	+	3.92860i	−0.570859	+	1.75692i	0.0790079	+	0.996874i	$0.474825\pi$
$5$	−1.27648	+	3.92860i	−0.570859	+	1.75692i	−0.649867	+	0.760048i	$0.725175\pi$
$6$		0			0
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$8$		0			0
$9$	0.451065			0.150355
$10$		0			0
$11$	1.01446	+	3.12220i	0.305872	+	0.941377i	0.979350	+	0.202170i	$0.0647995\pi$
$11$	1.01446	+	3.12220i	0.305872	+	0.941377i	−0.673478	+	0.739207i	$0.735201\pi$
$12$		0			0
$13$	1.36768	−	0.993681i	0.379327	−	0.275597i	−0.381741	−	0.924269i	$-0.624675\pi$
$13$	1.36768	−	0.993681i	0.379327	−	0.275597i	0.761068	+	0.648672i	$0.224675\pi$
$14$		0			0
$15$	−2.37132	+	7.29817i	−0.612272	+	1.88438i
$16$		0			0
$17$	1.46860	+	4.51989i	0.356188	+	1.09623i	0.955318	+	0.295582i	$0.0955134\pi$
$17$	1.46860	+	4.51989i	0.356188	+	1.09623i	−0.599130	+	0.800652i	$0.704487\pi$
$18$		0			0
$19$	−4.77393	−	3.46846i	−1.09522	−	0.795720i	−0.114943	−	0.993372i	$-0.536669\pi$
$19$	−4.77393	−	3.46846i	−1.09522	−	0.795720i	−0.980272	+	0.197652i	$0.936669\pi$
$20$		0			0
$21$	−1.50291	−	1.09193i	−0.327963	−	0.238279i
$22$		0			0
$23$	3.94310	−	2.86483i	0.822193	−	0.597358i	−0.0951469	−	0.995463i	$-0.530332\pi$
$23$	3.94310	−	2.86483i	0.822193	−	0.597358i	0.917340	+	0.398105i	$0.130332\pi$
$24$		0			0
$25$	−9.75940	−	7.09062i	−1.95188	−	1.41812i
$26$		0			0
$27$	−4.73517			−0.911283
$28$		0			0
$29$	−1.01826	+	3.13387i	−0.189086	+	0.581946i	−0.999995	−	0.00322634i	$-0.998973\pi$
$29$	−1.01826	+	3.13387i	−0.189086	+	0.581946i	0.810909	+	0.585172i	$0.198973\pi$
$30$		0			0
$31$	1.76389	+	5.42869i	0.316804	+	0.975021i	0.975006	+	0.222180i	$0.0713172\pi$
$31$	1.76389	+	5.42869i	0.316804	+	0.975021i	−0.658202	+	0.752841i	$0.728683\pi$
$32$		0			0
$33$	1.88457	+	5.80012i	0.328062	+	1.00967i
$34$		0			0
$35$	3.34186	−	2.42801i	0.564878	−	0.410408i
$36$		0			0
$37$	−1.62259	+	4.99382i	−0.266752	+	0.820979i	0.724532	+	0.689241i	$0.242056\pi$
$37$	−1.62259	+	4.99382i	−0.266752	+	0.820979i	−0.991285	+	0.131738i	$0.957944\pi$
$38$		0			0
$39$	2.54075	−	1.84596i	0.406846	−	0.295591i
$40$		0			0
$41$	−3.90619	+	5.07362i	−0.610045	+	0.792367i
$41$	−3.90619	+	5.07362i	−0.610045	+	0.792367i
$42$		0			0
$43$	−4.26764	+	3.10062i	−0.650809	+	0.472841i	−0.863547	−	0.504269i	$-0.831762\pi$
$43$	−4.26764	+	3.10062i	−0.650809	+	0.472841i	0.212737	+	0.977109i	$0.431762\pi$
$44$		0			0
$45$	−0.575774	+	1.77205i	−0.0858314	+	0.264162i
$46$		0			0
$47$	0.898680	−	0.652929i	0.131086	−	0.0952395i	−0.520310	−	0.853977i	$-0.674184\pi$
$47$	0.898680	−	0.652929i	0.131086	−	0.0952395i	0.651396	+	0.758738i	$0.274184\pi$
$48$		0			0
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$		0			0
$51$	2.72822	+	8.39661i	0.382028	+	1.17576i
$52$		0			0
$53$	−2.77745	+	8.54810i	−0.381512	+	1.17417i	0.557468	+	0.830199i	$0.311773\pi$
$53$	−2.77745	+	8.54810i	−0.381512	+	1.17417i	−0.938979	+	0.343974i	$0.888227\pi$
$54$		0			0
$55$	−13.5608			−1.82854
$56$		0			0
$57$	−8.86855	−	6.44338i	−1.17467	−	0.853447i
$58$		0			0
$59$	6.58307	−	4.78288i	0.857043	−	0.622678i	−0.0700358	−	0.997544i	$-0.522311\pi$
$59$	6.58307	−	4.78288i	0.857043	−	0.622678i	0.927079	+	0.374866i	$0.122311\pi$
$60$		0			0
$61$	0.303906	+	0.220801i	0.0389112	+	0.0282707i	0.607071	−	0.794648i	$-0.292344\pi$
$61$	0.303906	+	0.220801i	0.0389112	+	0.0282707i	−0.568160	+	0.822918i	$0.692344\pi$
$62$		0			0
$63$	−0.364919	−	0.265129i	−0.0459755	−	0.0334031i
$64$		0			0
$65$	2.15795	+	6.64149i	0.267661	+	0.823776i
$66$		0			0
$67$	2.46767	−	7.59469i	0.301473	−	0.927840i	−0.679496	−	0.733679i	$-0.737802\pi$
$67$	2.46767	−	7.59469i	0.301473	−	0.927840i	0.980970	−	0.194161i	$-0.0621983\pi$
$68$		0			0
$69$	7.32511	−	5.32200i	0.881840	−	0.640694i
$70$		0			0
$71$	−3.70326	−	11.3975i	−0.439496	−	1.35263i	−0.888409	−	0.459054i	$-0.848189\pi$
$71$	−3.70326	−	11.3975i	−0.439496	−	1.35263i	0.448913	−	0.893576i	$-0.351811\pi$
$72$		0			0
$73$	−2.91522			−0.341201			−0.170600	−	0.985340i	$-0.554571\pi$
$73$	−2.91522			−0.341201			−0.170600	+	0.985340i	$0.554571\pi$
$74$		0			0
$75$	−18.1301	−	13.1723i	−2.09348	−	1.52100i
$76$		0			0
$77$	1.01446	−	3.12220i	0.115609	−	0.355807i
$78$		0			0
$79$	6.54825			0.736736			0.368368	−	0.929680i	$-0.379917\pi$
$79$	6.54825			0.736736			0.368368	+	0.929680i	$0.379917\pi$
$80$		0			0
$81$	−10.1497			−1.12775
$82$		0			0
$83$	7.52545			0.826026			0.413013	−	0.910725i	$-0.364476\pi$
$83$	7.52545			0.826026			0.413013	+	0.910725i	$0.364476\pi$
$84$		0			0
$85$	−19.6315			−2.12933
$86$		0			0
$87$	−1.89162	+	5.82181i	−0.202803	+	0.624164i
$88$		0			0
$89$	12.9488	+	9.40782i	1.37257	+	0.997227i	0.997532	+	0.0702162i	$0.0223689\pi$
$89$	12.9488	+	9.40782i	1.37257	+	0.997227i	0.375034	+	0.927011i	$0.377631\pi$
$90$		0			0
$91$	−1.69055			−0.177218
$92$		0			0
$93$	3.27678	+	10.0849i	0.339786	+	1.04576i
$94$		0			0
$95$	19.7200	−	14.3274i	2.02323	−	1.46996i
$96$		0			0
$97$	0.870418	−	2.67887i	0.0883776	−	0.271998i	−0.897094	−	0.441840i	$-0.854326\pi$
$97$	0.870418	−	2.67887i	0.0883776	−	0.271998i	0.985471	+	0.169842i	$0.0543258\pi$
$98$		0			0
$99$	0.457588	+	1.40831i	0.0459894	+	0.141541i
$100$		0			0
$101$	4.79791	+	3.48588i	0.477410	+	0.346858i	0.800322	−	0.599571i	$-0.204662\pi$
$101$	4.79791	+	3.48588i	0.477410	+	0.346858i	−0.322912	+	0.946429i	$0.604662\pi$
$102$		0			0
$103$	12.4595	+	9.05236i	1.22767	+	0.891956i	0.996713	−	0.0810081i	$-0.0258140\pi$
$103$	12.4595	+	9.05236i	1.22767	+	0.891956i	0.230958	+	0.972964i	$0.425814\pi$
$104$		0			0
$105$	6.20820	−	4.51052i	0.605858	−	0.440182i
$106$		0			0
$107$	0.396569	+	0.288124i	0.0383378	+	0.0278540i	0.606789	−	0.794863i	$-0.292457\pi$
$107$	0.396569	+	0.288124i	0.0383378	+	0.0278540i	−0.568451	+	0.822717i	$0.692457\pi$
$108$		0			0
$109$	20.4999			1.96353			0.981766	−	0.190095i	$-0.0608797\pi$
$109$	20.4999			1.96353			0.981766	+	0.190095i	$0.0608797\pi$
$110$		0			0
$111$	−3.01429	+	9.27704i	−0.286104	+	0.880537i
$112$		0			0
$113$	−5.93770	−	18.2744i	−0.558572	−	1.71911i	−0.686320	−	0.727300i	$-0.740775\pi$
$113$	−5.93770	−	18.2744i	−0.558572	−	1.71911i	0.127748	−	0.991807i	$-0.459225\pi$
$114$		0			0
$115$	6.22148	+	19.1477i	0.580156	+	1.78554i
$116$		0			0
$117$	0.616914	−	0.448214i	0.0570337	−	0.0414374i
$118$		0			0
$119$	1.46860	−	4.51989i	0.134626	−	0.414337i
$120$		0			0
$121$	0.180216	−	0.130934i	0.0163832	−	0.0119031i
$122$		0			0
$123$	−7.25655	+	9.42529i	−0.654301	+	0.849850i
$124$		0			0
$125$	23.6045	−	17.1497i	2.11125	−	1.53391i
$126$		0			0
$127$	−2.04023	+	6.27918i	−0.181041	+	0.557187i	−0.999858	−	0.0168681i	$-0.994630\pi$
$127$	−2.04023	+	6.27918i	−0.181041	+	0.557187i	0.818817	+	0.574055i	$0.194630\pi$
$128$		0			0
$129$	−7.92802	+	5.76004i	−0.698023	+	0.507143i
$130$		0			0
$131$	3.74113	+	11.5140i	0.326864	+	1.00598i	0.970592	+	0.240730i	$0.0773867\pi$
$131$	3.74113	+	11.5140i	0.326864	+	1.00598i	−0.643728	+	0.765254i	$0.722613\pi$
$132$		0			0
$133$	1.82348	+	5.61209i	0.158116	+	0.486630i
$134$		0			0
$135$	6.04434	−	18.6026i	0.520214	−	1.60105i
$136$		0			0
$137$	−13.4022			−1.14503			−0.572514	−	0.819895i	$-0.694032\pi$
$137$	−13.4022			−1.14503			−0.572514	+	0.819895i	$0.694032\pi$
$138$		0			0
$139$	−3.71358	−	2.69807i	−0.314982	−	0.228848i	0.419049	−	0.907963i	$-0.362363\pi$
$139$	−3.71358	−	2.69807i	−0.314982	−	0.228848i	−0.734031	+	0.679116i	$0.762363\pi$
$140$		0			0
$141$	1.66948	−	1.21295i	0.140596	−	0.102149i
$142$		0			0
$143$	4.48993	+	3.26212i	0.375467	+	0.272793i
$144$		0			0
$145$	−11.0119	−	8.00065i	−0.914492	−	0.664417i
$146$		0			0
$147$	0.574062	+	1.76678i	0.0473478	+	0.145722i
$148$		0			0
$149$	5.84241	−	17.9811i	0.478629	−	1.47307i	−0.362372	−	0.932033i	$-0.618033\pi$
$149$	5.84241	−	17.9811i	0.478629	−	1.47307i	0.841001	−	0.541034i	$-0.181967\pi$
$150$		0			0
$151$	9.34776	−	6.79154i	0.760710	−	0.552688i	−0.138418	−	0.990374i	$-0.544202\pi$
$151$	9.34776	−	6.79154i	0.760710	−	0.552688i	0.899128	+	0.437686i	$0.144202\pi$
$152$		0			0
$153$	0.662434	+	2.03876i	0.0535546	+	0.164824i
$154$		0			0
$155$	−23.5787			−1.89389
$156$		0			0
$157$	4.88764	+	3.55108i	0.390076	+	0.283407i	0.765487	−	0.643452i	$-0.222498\pi$
$157$	4.88764	+	3.55108i	0.390076	+	0.283407i	−0.375410	+	0.926859i	$0.622498\pi$
$158$		0			0
$159$	−5.15968	+	15.8798i	−0.409189	+	1.25935i
$160$		0			0
$161$	−4.87394			−0.384120
$162$		0			0
$163$	7.07247			0.553959			0.276979	−	0.960876i	$-0.410667\pi$
$163$	7.07247			0.553959			0.276979	+	0.960876i	$0.410667\pi$
$164$		0			0
$165$	−25.1919			−1.96119
$166$		0			0
$167$	−1.09817			−0.0849789			−0.0424894	−	0.999097i	$-0.513529\pi$
$167$	−1.09817			−0.0849789			−0.0424894	+	0.999097i	$0.513529\pi$
$168$		0			0
$169$	−3.13406	+	9.64565i	−0.241082	+	0.741973i
$170$		0			0
$171$	−2.15335	−	1.56450i	−0.164671	−	0.119640i
$172$		0			0
$173$	7.65539			0.582029			0.291014	−	0.956719i	$-0.406007\pi$
$173$	7.65539			0.582029			0.291014	+	0.956719i	$0.406007\pi$
$174$		0			0
$175$	3.72776	+	11.4729i	0.281792	+	0.867267i
$176$		0			0
$177$	12.2294	−	8.88518i	0.919218	−	0.667851i
$178$		0			0
$179$	−7.07845	+	21.7852i	−0.529068	+	1.62830i	0.227061	+	0.973881i	$0.427088\pi$
$179$	−7.07845	+	21.7852i	−0.529068	+	1.62830i	−0.756129	+	0.654423i	$0.772912\pi$
$180$		0			0
$181$	−0.0617168	−	0.189945i	−0.00458738	−	0.0141185i	0.948737	−	0.316068i	$-0.102363\pi$
$181$	−0.0617168	−	0.189945i	−0.00458738	−	0.0141185i	−0.953324	+	0.301949i	$0.902363\pi$
$182$		0			0
$183$	0.564568	+	0.410183i	0.0417341	+	0.0303216i
$184$		0			0
$185$	−17.5475	−	12.7490i	−1.29012	−	0.937326i
$186$		0			0
$187$	−12.6221	+	9.17052i	−0.923022	+	0.670615i
$188$		0			0
$189$	3.83083	+	2.78326i	0.278652	+	0.202453i
$190$		0			0
$191$	22.9200			1.65843			0.829217	−	0.558926i	$-0.188786\pi$
$191$	22.9200			1.65843			0.829217	+	0.558926i	$0.188786\pi$
$192$		0			0
$193$	5.61311	−	17.2754i	0.404041	−	1.24351i	−0.517653	−	0.855591i	$-0.673194\pi$
$193$	5.61311	−	17.2754i	0.404041	−	1.24351i	0.921694	−	0.387919i	$-0.126806\pi$
$194$		0			0
$195$	4.00884	+	12.3379i	0.287079	+	0.883537i
$196$		0			0
$197$	4.39997	+	13.5417i	0.313485	+	0.964807i	0.976374	+	0.216089i	$0.0693302\pi$
$197$	4.39997	+	13.5417i	0.313485	+	0.964807i	−0.662889	+	0.748718i	$0.730670\pi$
$198$		0			0
$199$	4.80260	−	3.48929i	0.340447	−	0.247349i	−0.404403	−	0.914581i	$-0.632521\pi$
$199$	4.80260	−	3.48929i	0.340447	−	0.247349i	0.744850	+	0.667231i	$0.232521\pi$
$200$		0			0
$201$	4.58419	−	14.1087i	0.323344	−	0.995151i
$202$		0			0
$203$	2.66583	−	1.93684i	0.187105	−	0.135940i
$204$		0			0
$205$	−14.9460	−	21.8222i	−1.04388	−	1.52413i
$206$		0			0
$207$	1.77859	−	1.29222i	0.123621	−	0.0898157i
$208$		0			0
$209$	5.98625	−	18.4238i	0.414078	−	1.27440i
$210$		0			0
$211$	−22.1703	+	16.1077i	−1.52627	+	1.10890i	−0.567997	+	0.823031i	$0.692281\pi$
$211$	−22.1703	+	16.1077i	−1.52627	+	1.10890i	−0.958269	+	0.285866i	$0.907719\pi$
$212$		0			0
$213$	−6.87956	−	21.1731i	−0.471380	−	1.45076i
$214$		0			0
$215$	−6.73355	−	20.7237i	−0.459224	−	1.41335i
$216$		0			0
$217$	1.76389	−	5.42869i	0.119740	−	0.368523i
$218$		0			0
$219$	−5.41561			−0.365953
$220$		0			0
$221$	6.49990	+	4.72246i	0.437231	+	0.317667i
$222$		0			0
$223$	13.5975	−	9.87916i	0.910556	−	0.661557i	−0.0305997	−	0.999532i	$-0.509742\pi$
$223$	13.5975	−	9.87916i	0.910556	−	0.661557i	0.941155	+	0.337974i	$0.109742\pi$
$224$		0			0
$225$	−4.40212	−	3.19833i	−0.293475	−	0.213222i
$226$		0			0
$227$	6.80399	+	4.94339i	0.451596	+	0.328104i	0.790226	−	0.612816i	$-0.209963\pi$
$227$	6.80399	+	4.94339i	0.451596	+	0.328104i	−0.338629	+	0.940920i	$0.609963\pi$
$228$		0			0
$229$	3.46255	+	10.6566i	0.228812	+	0.704211i	0.997882	+	0.0650465i	$0.0207196\pi$
$229$	3.46255	+	10.6566i	0.228812	+	0.704211i	−0.769070	+	0.639164i	$0.779280\pi$
$230$		0			0
$231$	1.88457	−	5.80012i	0.123996	−	0.381620i
$232$		0			0
$233$	−18.3059	+	13.3000i	−1.19926	+	0.871312i	−0.994212	−	0.107441i	$-0.965734\pi$
$233$	−18.3059	+	13.3000i	−1.19926	+	0.871312i	−0.205046	+	0.978752i	$0.565734\pi$
$234$		0			0
$235$	1.41795	+	4.36400i	0.0924969	+	0.284676i
$236$		0			0
$237$	12.1647			0.790183
$238$		0			0
$239$	−12.7184	−	9.24045i	−0.822684	−	0.597715i	0.0947962	−	0.995497i	$-0.469780\pi$
$239$	−12.7184	−	9.24045i	−0.822684	−	0.597715i	−0.917480	+	0.397782i	$0.869780\pi$
$240$		0			0
$241$	3.12907	−	9.63027i	0.201561	−	0.620341i	−0.798276	−	0.602291i	$-0.794255\pi$
$241$	3.12907	−	9.63027i	0.201561	−	0.620341i	0.999837	−	0.0180490i	$-0.00574550\pi$
$242$		0			0
$243$	−4.64970			−0.298278
$244$		0			0
$245$	−4.13077			−0.263905
$246$		0			0
$247$	−9.97578			−0.634743
$248$		0			0
$249$	13.9801			0.885950
$250$		0			0
$251$	−8.77347	+	27.0020i	−0.553777	+	1.70435i	0.145376	+	0.989377i	$0.453561\pi$
$251$	−8.77347	+	27.0020i	−0.553777	+	1.70435i	−0.699152	+	0.714973i	$0.746439\pi$
$252$		0			0
$253$	12.9447	+	9.40486i	0.813825	+	0.591279i
$254$		0			0
$255$	−36.4694			−2.28380
$256$		0			0
$257$	−3.79063	−	11.6664i	−0.236453	−	0.727728i	−0.996925	−	0.0783576i	$-0.975032\pi$
$257$	−3.79063	−	11.6664i	−0.236453	−	0.727728i	0.760472	−	0.649371i	$-0.224968\pi$
$258$		0			0
$259$	4.24800	−	3.08635i	0.263958	−	0.191776i
$260$		0			0
$261$	−0.459300	+	1.41358i	−0.0284299	+	0.0874984i
$262$		0			0
$263$	0.245976	+	0.757036i	0.0151675	+	0.0466808i	0.958354	−	0.285583i	$-0.0921874\pi$
$263$	0.245976	+	0.757036i	0.0151675	+	0.0466808i	−0.943186	+	0.332264i	$0.892187\pi$
$264$		0			0
$265$	−30.0367	−	21.8229i	−1.84514	−	1.34057i
$266$		0			0
$267$	24.0550	+	17.4770i	1.47214	+	1.06957i
$268$		0			0
$269$	12.3690	−	8.98658i	0.754149	−	0.547922i	−0.142961	−	0.989728i	$-0.545662\pi$
$269$	12.3690	−	8.98658i	0.754149	−	0.547922i	0.897110	+	0.441807i	$0.145662\pi$
$270$		0			0
$271$	−6.37879	−	4.63446i	−0.387484	−	0.281523i	0.376940	−	0.926238i	$-0.376976\pi$
$271$	−6.37879	−	4.63446i	−0.387484	−	0.281523i	−0.764424	+	0.644714i	$0.776976\pi$
$272$		0			0
$273$	−3.14054			−0.190074
$274$		0			0
$275$	12.2377	−	37.6639i	0.737964	−	2.27122i
$276$		0			0
$277$	2.47423	+	7.61489i	0.148662	+	0.457534i	0.997464	−	0.0711768i	$-0.0226754\pi$
$277$	2.47423	+	7.61489i	0.148662	+	0.457534i	−0.848802	+	0.528711i	$0.822675\pi$
$278$		0			0
$279$	0.795627	+	2.44869i	0.0476330	+	0.146599i
$280$		0			0
$281$	−12.9374	+	9.39956i	−0.771779	+	0.560731i	−0.902501	−	0.430689i	$-0.858271\pi$
$281$	−12.9374	+	9.39956i	−0.771779	+	0.560731i	0.130721	+	0.991419i	$0.458271\pi$
$282$		0			0
$283$	4.91198	−	15.1175i	0.291987	−	0.898643i	−0.692230	−	0.721677i	$-0.743372\pi$
$283$	4.91198	−	15.1175i	0.291987	−	0.898643i	0.984217	−	0.176966i	$-0.0566283\pi$
$284$		0			0
$285$	36.6340	−	26.6161i	2.17001	−	1.57660i
$286$		0			0
$287$	6.14238	−	1.80864i	0.362573	−	0.106761i
$288$		0			0
$289$	−4.51930	+	3.28347i	−0.265841	+	0.193145i
$290$		0			0
$291$	1.61698	−	4.97655i	0.0947890	−	0.291731i
$292$		0			0
$293$	5.37748	−	3.90697i	0.314156	−	0.228248i	−0.419522	−	0.907745i	$-0.637802\pi$
$293$	5.37748	−	3.90697i	0.314156	−	0.228248i	0.733678	+	0.679498i	$0.237802\pi$
$294$		0			0
$295$	10.3869	+	31.9675i	0.604747	+	1.86122i
$296$		0			0
$297$	−4.80365	−	14.7841i	−0.278736	−	0.857862i
$298$		0			0
$299$	2.54619	−	7.83636i	0.147250	−	0.453188i
$300$		0			0
$301$	5.27510			0.304051
$302$		0			0
$303$	8.91309	+	6.47574i	0.512044	+	0.372022i
$304$		0			0
$305$	−1.25537	+	0.912078i	−0.0718822	+	0.0522255i
$306$		0			0
$307$	8.62612	+	6.26724i	0.492319	+	0.357690i	0.806075	−	0.591813i	$-0.201588\pi$
$307$	8.62612	+	6.26724i	0.492319	+	0.357690i	−0.313757	+	0.949503i	$0.601588\pi$
$308$		0			0
$309$	23.1461	+	16.8166i	1.31673	+	0.956663i
$310$		0			0
$311$	3.12345	+	9.61298i	0.177114	+	0.545102i	0.999724	−	0.0235049i	$-0.00748252\pi$
$311$	3.12345	+	9.61298i	0.177114	+	0.545102i	−0.822609	+	0.568607i	$0.807483\pi$
$312$		0			0
$313$	8.09834	−	24.9241i	0.457745	−	1.40879i	−0.410137	−	0.912024i	$-0.634519\pi$
$313$	8.09834	−	24.9241i	0.457745	−	1.40879i	0.867882	−	0.496770i	$-0.165481\pi$
$314$		0			0
$315$	1.50740	−	1.09519i	0.0849322	−	0.0617069i
$316$		0			0
$317$	−2.61934	−	8.06150i	−0.147117	−	0.452779i	0.850160	−	0.526524i	$-0.176505\pi$
$317$	−2.61934	−	8.06150i	−0.147117	−	0.452779i	−0.997277	+	0.0737449i	$0.976505\pi$
$318$		0			0
$319$	−10.8176			−0.605667
$320$		0			0
$321$	0.736708	+	0.535249i	0.0411190	+	0.0298747i
$322$		0			0
$323$	8.66607	−	26.6714i	0.482193	−	1.48404i
$324$		0			0
$325$	−20.3936			−1.13123
$326$		0			0
$327$	38.0827			2.10598
$328$		0			0
$329$	−1.11083			−0.0612420
$330$		0			0
$331$	20.9928			1.15387			0.576933	−	0.816791i	$-0.304249\pi$
$331$	20.9928			1.15387			0.576933	+	0.816791i	$0.304249\pi$
$332$		0			0
$333$	−0.731893	+	2.25253i	−0.0401075	+	0.123438i
$334$		0			0
$335$	26.6866	+	19.3889i	1.45804	+	1.05933i
$336$		0			0
$337$	−23.7168			−1.29194			−0.645969	−	0.763364i	$-0.723546\pi$
$337$	−23.7168			−1.29194			−0.645969	+	0.763364i	$0.723546\pi$
$338$		0			0
$339$	−11.0305	−	33.9483i	−0.599094	−	1.84382i
$340$		0			0
$341$	−15.1600	+	11.0144i	−0.820962	+	0.596463i
$342$		0			0
$343$	0.309017	−	0.951057i	0.0166853	−	0.0513522i
$344$		0			0
$345$	11.5577	+	35.5708i	0.622244	+	1.91507i
$346$		0			0
$347$	10.7041	+	7.77698i	0.574626	+	0.417490i	0.836783	−	0.547535i	$-0.184434\pi$
$347$	10.7041	+	7.77698i	0.574626	+	0.417490i	−0.262157	+	0.965025i	$0.584434\pi$
$348$		0			0
$349$	−20.3930	−	14.8164i	−1.09161	−	0.793103i	−0.111942	−	0.993715i	$-0.535707\pi$
$349$	−20.3930	−	14.8164i	−1.09161	−	0.793103i	−0.979671	+	0.200612i	$0.935707\pi$
$350$		0			0
$351$	−6.47621	+	4.70524i	−0.345675	+	0.251147i
$352$		0			0
$353$	−0.707625	−	0.514120i	−0.0376631	−	0.0273638i	0.568794	−	0.822480i	$-0.307410\pi$
$353$	−0.707625	−	0.514120i	−0.0376631	−	0.0273638i	−0.606458	+	0.795116i	$0.707410\pi$
$354$		0			0
$355$	49.5032			2.62735
$356$		0			0
$357$	2.72822	−	8.39661i	0.144393	−	0.444396i
$358$		0			0
$359$	−7.30165	−	22.4722i	−0.385366	−	1.18604i	−0.936214	−	0.351430i	$-0.885695\pi$
$359$	−7.30165	−	22.4722i	−0.385366	−	1.18604i	0.550848	−	0.834606i	$-0.314305\pi$
$360$		0			0
$361$	4.88886	+	15.0464i	0.257308	+	0.791914i
$362$		0			0
$363$	0.334787	−	0.243237i	0.0175718	−	0.0127666i
$364$		0			0
$365$	3.72122	−	11.4527i	0.194777	−	0.599463i
$366$		0			0
$367$	4.34266	−	3.15513i	0.226685	−	0.164696i	−0.468646	−	0.883386i	$-0.655258\pi$
$367$	4.34266	−	3.15513i	0.226685	−	0.164696i	0.695331	+	0.718690i	$0.255258\pi$
$368$		0			0
$369$	−1.76195	+	2.28853i	−0.0917233	+	0.119136i
$370$		0			0
$371$	7.27145	−	5.28302i	0.377515	−	0.274281i
$372$		0			0
$373$	−3.82350	+	11.7675i	−0.197973	+	0.609299i	0.801956	+	0.597383i	$0.203793\pi$
$373$	−3.82350	+	11.7675i	−0.197973	+	0.609299i	−0.999929	+	0.0119156i	$0.996207\pi$
$374$		0			0
$375$	43.8502	−	31.8590i	2.26442	−	1.64519i
$376$		0			0
$377$	1.72142	+	5.29797i	0.0886574	+	0.272859i
$378$		0			0
$379$	1.59595	+	4.91181i	0.0819782	+	0.252303i	0.983642	−	0.180135i	$-0.0576535\pi$
$379$	1.59595	+	4.91181i	0.0819782	+	0.252303i	−0.901664	+	0.432438i	$0.857653\pi$
$380$		0			0
$381$	−3.79014	+	11.6649i	−0.194175	+	0.597609i
$382$		0			0
$383$	−3.11799			−0.159322			−0.0796608	−	0.996822i	$-0.525384\pi$
$383$	−3.11799			−0.159322			−0.0796608	+	0.996822i	$0.525384\pi$
$384$		0			0
$385$	10.9709	+	7.97083i	0.559129	+	0.406231i
$386$		0			0
$387$	−1.92498	+	1.39858i	−0.0978524	+	0.0710939i
$388$		0			0
$389$	8.83974	+	6.42245i	0.448193	+	0.325631i	0.788882	−	0.614545i	$-0.210660\pi$
$389$	8.83974	+	6.42245i	0.448193	+	0.325631i	−0.340689	+	0.940176i	$0.610660\pi$
$390$		0			0
$391$	18.7395	+	13.6151i	0.947699	+	0.688544i
$392$		0			0
$393$	6.94991	+	21.3896i	0.350577	+	1.07896i
$394$		0			0
$395$	−8.35871	+	25.7255i	−0.420572	+	1.29439i
$396$		0			0
$397$	−8.38270	+	6.09039i	−0.420716	+	0.305668i	−0.777926	−	0.628356i	$-0.783728\pi$
$397$	−8.38270	+	6.09039i	−0.420716	+	0.305668i	0.357210	+	0.934024i	$0.383728\pi$
$398$		0			0
$399$	3.38749	+	10.4256i	0.169586	+	0.521933i
$400$		0			0
$401$	−31.4231			−1.56919			−0.784597	−	0.620006i	$-0.787130\pi$
$401$	−31.4231			−1.56919			−0.784597	+	0.620006i	$0.787130\pi$
$402$		0			0
$403$	7.80682	+	5.67199i	0.388886	+	0.282542i
$404$		0			0
$405$	12.9559	−	39.8742i	0.643785	−	1.98137i
$406$		0			0
$407$	−17.2377			−0.854443
$408$		0			0
$409$	−9.53139			−0.471297			−0.235648	−	0.971838i	$-0.575721\pi$
$409$	−9.53139			−0.471297			−0.235648	+	0.971838i	$0.575721\pi$
$410$		0			0
$411$	−24.8973			−1.22809
$412$		0			0
$413$	−8.13713			−0.400402
$414$		0			0
$415$	−9.60608	+	29.5645i	−0.471544	+	1.45126i
$416$		0			0
$417$	−6.89874	−	5.01222i	−0.337833	−	0.245450i
$418$		0			0
$419$	33.8736			1.65483			0.827416	−	0.561590i	$-0.189810\pi$
$419$	33.8736			1.65483			0.827416	+	0.561590i	$0.189810\pi$
$420$		0			0
$421$	−5.69858	−	17.5384i	−0.277732	−	0.854771i	−0.988484	−	0.151328i	$-0.951645\pi$
$421$	−5.69858	−	17.5384i	−0.277732	−	0.854771i	0.710752	−	0.703443i	$-0.248355\pi$
$422$		0			0
$423$	0.405363	−	0.294513i	0.0197094	−	0.0143197i
$424$		0			0
$425$	17.7161	−	54.5247i	0.859359	−	2.64483i
$426$		0			0
$427$	−0.116082	−	0.357263i	−0.00561760	−	0.0172892i
$428$		0			0
$429$	8.34096	+	6.06006i	0.402705	+	0.292583i
$430$		0			0
$431$	−19.0945	−	13.8730i	−0.919749	−	0.668237i	0.0237123	−	0.999719i	$-0.492451\pi$
$431$	−19.0945	−	13.8730i	−0.919749	−	0.668237i	−0.943462	+	0.331482i	$0.892451\pi$
$432$		0			0
$433$	1.00892	−	0.733026i	0.0484858	−	0.0352270i	−0.563278	−	0.826267i	$-0.690460\pi$
$433$	1.00892	−	0.733026i	0.0484858	−	0.0352270i	0.611764	+	0.791040i	$0.290460\pi$
$434$		0			0
$435$	−20.4569	−	14.8628i	−0.980835	−	0.712618i
$436$		0			0
$437$	−28.7606			−1.37581
$438$		0			0
$439$	−11.1067	+	34.1828i	−0.530093	+	1.63146i	0.223928	+	0.974606i	$0.428112\pi$
$439$	−11.1067	+	34.1828i	−0.530093	+	1.63146i	−0.754020	+	0.656851i	$0.771888\pi$
$440$		0			0
$441$	0.139387	+	0.428988i	0.00663746	+	0.0204280i
$442$		0			0
$443$	−10.0008	−	30.7794i	−0.475154	−	1.46237i	−0.845750	−	0.533579i	$-0.820847\pi$
$443$	−10.0008	−	30.7794i	−0.475154	−	1.46237i	0.370596	−	0.928794i	$-0.379153\pi$
$444$		0			0
$445$	−53.4884	+	38.8616i	−2.53559	+	1.84222i
$446$		0			0
$447$	10.8535	−	33.4035i	0.513351	−	1.57993i
$448$		0			0
$449$	6.77627	−	4.92325i	0.319792	−	0.232343i	−0.416295	−	0.909230i	$-0.636672\pi$
$449$	6.77627	−	4.92325i	0.319792	−	0.232343i	0.736087	+	0.676887i	$0.236672\pi$
$450$		0			0
$451$	−19.8035	−	7.04890i	−0.932512	−	0.331920i
$452$		0			0
$453$	17.3654	−	12.6167i	0.815896	−	0.592783i
$454$		0			0
$455$	2.15795	−	6.64149i	0.101166	−	0.311358i
$456$		0			0
$457$	5.89350	−	4.28188i	0.275686	−	0.200298i	−0.441347	−	0.897336i	$-0.645499\pi$
$457$	5.89350	−	4.28188i	0.275686	−	0.200298i	0.717034	+	0.697039i	$0.245499\pi$
$458$		0			0
$459$	−6.95407	−	21.4024i	−0.324588	−	0.998980i
$460$		0			0
$461$	−7.16819	−	22.0614i	−0.333856	−	1.02750i	−0.967283	−	0.253701i	$-0.918352\pi$
$461$	−7.16819	−	22.0614i	−0.333856	−	1.02750i	0.633427	−	0.773803i	$-0.281648\pi$
$462$		0			0
$463$	1.75716	−	5.40799i	0.0816622	−	0.251330i	−0.901887	−	0.431973i	$-0.857818\pi$
$463$	1.75716	−	5.40799i	0.0816622	−	0.251330i	0.983549	+	0.180642i	$0.0578177\pi$
$464$		0			0
$465$	−43.8022			−2.03128
$466$		0			0
$467$	−20.1321	−	14.6268i	−0.931603	−	0.676849i	0.0147821	−	0.999891i	$-0.495295\pi$
$467$	−20.1321	−	14.6268i	−0.931603	−	0.676849i	−0.946385	+	0.323042i	$0.895295\pi$
$468$		0			0
$469$	−6.46043	+	4.69378i	−0.298315	+	0.216739i
$470$		0			0
$471$	9.07979	+	6.59686i	0.418375	+	0.303967i
$472$		0			0
$473$	−14.0101	−	10.1789i	−0.644186	−	0.468028i
$474$		0			0
$475$	21.9971	+	67.7002i	1.00930	+	3.10630i
$476$		0			0
$477$	−1.25281	+	3.85575i	−0.0573622	+	0.176543i
$478$		0			0
$479$	−0.617300	+	0.448494i	−0.0282051	+	0.0204922i	−0.601799	−	0.798648i	$-0.705549\pi$
$479$	−0.617300	+	0.448494i	−0.0282051	+	0.0204922i	0.573593	+	0.819140i	$0.305549\pi$
$480$		0			0
$481$	2.74307	+	8.44230i	0.125073	+	0.384936i
$482$		0			0
$483$	−9.05434			−0.411987
$484$		0			0
$485$	9.41314	+	6.83904i	0.427429	+	0.310545i
$486$		0			0
$487$	−8.68596	+	26.7326i	−0.393599	+	1.21137i	0.536449	+	0.843933i	$0.319765\pi$
$487$	−8.68596	+	26.7326i	−0.393599	+	1.21137i	−0.930048	+	0.367439i	$0.880235\pi$
$488$		0			0
$489$	13.1386			0.594146
$490$		0			0
$491$	9.42352			0.425278			0.212639	−	0.977131i	$-0.431794\pi$
$491$	9.42352			0.425278			0.212639	+	0.977131i	$0.431794\pi$
$492$		0			0
$493$	−15.6602			−0.705298
$494$		0			0
$495$	−6.11679			−0.274929
$496$		0			0
$497$	−3.70326	+	11.3975i	−0.166114	+	0.511246i
$498$		0			0
$499$	11.5054	+	8.35914i	0.515051	+	0.374207i	0.814736	−	0.579832i	$-0.196882\pi$
$499$	11.5054	+	8.35914i	0.515051	+	0.374207i	−0.299685	+	0.954038i	$0.596882\pi$
$500$		0			0
$501$	−2.04007			−0.0911438
$502$		0			0
$503$	−3.42001	−	10.5257i	−0.152491	−	0.469318i	0.845407	−	0.534122i	$-0.179358\pi$
$503$	−3.42001	−	10.5257i	−0.152491	−	0.469318i	−0.997898	+	0.0648041i	$0.979358\pi$
$504$		0			0
$505$	−19.8191	+	14.3994i	−0.881937	+	0.640764i
$506$		0			0
$507$	−5.82216	+	17.9188i	−0.258571	+	0.795800i
$508$		0			0
$509$	9.23494	+	28.4222i	0.409332	+	1.25979i	0.917224	+	0.398372i	$0.130425\pi$
$509$	9.23494	+	28.4222i	0.409332	+	1.25979i	−0.507892	+	0.861421i	$0.669575\pi$
$510$		0			0
$511$	2.35846	+	1.71352i	0.104332	+	0.0758018i
$512$		0			0
$513$	22.6054	+	16.4238i	0.998051	+	0.725127i
$514$		0			0
$515$	−51.4674	+	37.3932i	−2.26792	+	1.64774i
$516$		0			0
$517$	2.95025	+	2.14348i	0.129752	+	0.0942702i
$518$		0			0
$519$	14.2215			0.624253
$520$		0			0
$521$	11.1464	−	34.3052i	0.488334	−	1.50294i	−0.338760	−	0.940873i	$-0.610008\pi$
$521$	11.1464	−	34.3052i	0.488334	−	1.50294i	0.827094	−	0.562064i	$-0.189992\pi$
$522$		0			0
$523$	−8.09434	−	24.9118i	−0.353941	−	1.08932i	−0.956621	−	0.291335i	$-0.905901\pi$
$523$	−8.09434	−	24.9118i	−0.353941	−	1.08932i	0.602680	−	0.797983i	$-0.294099\pi$
$524$		0			0
$525$	6.92507	+	21.3132i	0.302235	+	0.930183i
$526$		0			0
$527$	−21.9466	+	15.9451i	−0.956009	+	0.694581i
$528$		0			0
$529$	0.233392	−	0.718308i	0.0101475	−	0.0312308i
$530$		0			0
$531$	2.96939	−	2.15739i	0.128861	−	0.0936227i
$532$		0			0
$533$	−0.300880	+	10.8206i	−0.0130325	+	0.468693i
$534$		0			0
$535$	−1.63814	+	1.19018i	−0.0708228	+	0.0514558i
$536$		0			0
$537$	−13.1497	+	40.4705i	−0.567450	+	1.74643i
$538$		0			0
$539$	−2.65590	+	1.92962i	−0.114398	+	0.0831148i
$540$		0			0
$541$	−12.7851	−	39.3485i	−0.549674	−	1.69172i	−0.709610	−	0.704595i	$-0.751129\pi$
$541$	−12.7851	−	39.3485i	−0.549674	−	1.69172i	0.159936	−	0.987127i	$-0.448871\pi$
$542$		0			0
$543$	−0.114652	−	0.352861i	−0.00492017	−	0.0151427i
$544$		0			0
$545$	−26.1676	+	80.5357i	−1.12090	+	3.44977i
$546$		0			0
$547$	−32.3192			−1.38187			−0.690934	−	0.722918i	$-0.742800\pi$
$547$	−32.3192			−1.38187			−0.690934	+	0.722918i	$0.742800\pi$
$548$		0			0
$549$	0.137081	+	0.0995955i	0.00585049	+	0.00425063i
$550$		0			0
$551$	15.7308	−	11.4291i	0.670156	−	0.486896i
$552$		0			0
$553$	−5.29765	−	3.84897i	−0.225279	−	0.163675i
$554$		0			0
$555$	−32.5981	−	23.6839i	−1.38371	−	1.00532i
$556$		0			0
$557$	12.1140	+	37.2832i	0.513289	+	1.57974i	0.786374	+	0.617750i	$0.211956\pi$
$557$	12.1140	+	37.2832i	0.513289	+	1.57974i	−0.273086	+	0.961990i	$0.588044\pi$
$558$		0			0
$559$	−2.75576	+	8.48135i	−0.116556	+	0.358723i
$560$		0			0
$561$	−23.4482	+	17.0361i	−0.989983	+	0.719265i
$562$		0			0
$563$	9.34178	+	28.7510i	0.393709	+	1.21171i	0.929962	+	0.367655i	$0.119839\pi$
$563$	9.34178	+	28.7510i	0.393709	+	1.21171i	−0.536253	+	0.844057i	$0.680161\pi$
$564$		0			0
$565$	79.3719			3.33920
$566$		0			0
$567$	8.21131	+	5.96586i	0.344843	+	0.250543i
$568$		0			0
$569$	1.96183	−	6.03790i	0.0822444	−	0.253122i	−0.901476	−	0.432830i	$-0.857515\pi$
$569$	1.96183	−	6.03790i	0.0822444	−	0.253122i	0.983720	+	0.179708i	$0.0575152\pi$
$570$		0			0
$571$	−42.7730			−1.78999			−0.894997	−	0.446071i	$-0.852823\pi$
$571$	−42.7730			−1.78999			−0.894997	+	0.446071i	$0.852823\pi$
$572$		0			0
$573$	42.5786			1.77875
$574$		0			0
$575$	−58.7957			−2.45195
$576$		0			0
$577$	30.2710			1.26020			0.630099	−	0.776515i	$-0.283014\pi$
$577$	30.2710			1.26020			0.630099	+	0.776515i	$0.283014\pi$
$578$		0			0
$579$	10.4275	−	32.0926i	0.433352	−	1.33372i
$580$		0			0
$581$	−6.08822	−	4.42335i	−0.252582	−	0.183511i
$582$		0			0
$583$	−29.5065			−1.22203
$584$		0			0
$585$	0.973376	+	2.99574i	0.0402441	+	0.123859i
$586$		0			0
$587$	28.6959	−	20.8488i	1.18441	−	0.860521i	0.191744	−	0.981445i	$-0.438586\pi$
$587$	28.6959	−	20.8488i	1.18441	−	0.860521i	0.992662	+	0.120924i	$0.0385856\pi$
$588$		0			0
$589$	10.4085	−	32.0342i	0.428876	−	1.31995i
$590$		0			0
$591$	8.17384	+	25.1565i	0.336227	+	1.03480i
$592$		0			0
$593$	32.5977	+	23.6836i	1.33863	+	0.972568i	0.999493	+	0.0318292i	$0.0101332\pi$
$593$	32.5977	+	23.6836i	1.33863	+	0.972568i	0.339132	+	0.940739i	$0.389867\pi$
$594$		0			0
$595$	15.8822	+	11.5391i	0.651106	+	0.473056i
$596$		0			0
$597$	8.92181	−	6.48207i	0.365145	−	0.265294i
$598$		0			0
$599$	22.5516	+	16.3847i	0.921433	+	0.669460i	0.943880	−	0.330288i	$-0.107146\pi$
$599$	22.5516	+	16.3847i	0.921433	+	0.669460i	−0.0224471	+	0.999748i	$0.507146\pi$
$600$		0			0
$601$	−26.1243			−1.06563			−0.532817	−	0.846230i	$-0.678867\pi$
$601$	−26.1243			−1.06563			−0.532817	+	0.846230i	$0.678867\pi$
$602$		0			0
$603$	1.11308	−	3.42570i	0.0453280	−	0.139505i
$604$		0			0
$605$	0.284347	+	0.875129i	0.0115603	+	0.0355791i
$606$		0			0
$607$	−1.42198	−	4.37642i	−0.0577165	−	0.177633i	0.918042	−	0.396483i	$-0.129769\pi$
$607$	−1.42198	−	4.37642i	−0.0577165	−	0.177633i	−0.975759	+	0.218850i	$0.929769\pi$
$608$		0			0
$609$	4.95233	−	3.59808i	0.200678	−	0.145801i
$610$		0			0
$611$	0.580307	−	1.78600i	0.0234767	−	0.0722539i
$612$		0			0
$613$	−1.96612	+	1.42847i	−0.0794110	+	0.0576955i	−0.626782	−	0.779194i	$-0.715629\pi$
$613$	−1.96612	+	1.42847i	−0.0794110	+	0.0576955i	0.547371	+	0.836890i	$0.315629\pi$
$614$		0			0
$615$	−27.7653	−	40.5393i	−1.11961	−	1.63470i
$616$		0			0
$617$	−6.24363	+	4.53627i	−0.251359	+	0.182623i	−0.706329	−	0.707884i	$-0.749650\pi$
$617$	−6.24363	+	4.53627i	−0.251359	+	0.182623i	0.454970	+	0.890507i	$0.349650\pi$
$618$		0			0
$619$	3.37499	−	10.3872i	0.135652	−	0.417495i	−0.860039	−	0.510229i	$-0.829561\pi$
$619$	3.37499	−	10.3872i	0.135652	−	0.417495i	0.995691	+	0.0927341i	$0.0295607\pi$
$620$		0			0
$621$	−18.6712	+	13.5654i	−0.749251	+	0.544363i
$622$		0			0
$623$	−4.94599	−	15.2222i	−0.198157	−	0.609864i
$624$		0			0
$625$	18.6048	+	57.2596i	0.744190	+	2.29038i
$626$		0			0
$627$	11.1207	−	34.2259i	0.444117	−	1.36685i
$628$		0			0
$629$	−24.9544			−0.994998
$630$		0			0
$631$	23.3909	+	16.9945i	0.931177	+	0.676540i	0.946281	−	0.323346i	$-0.104808\pi$
$631$	23.3909	+	16.9945i	0.931177	+	0.676540i	−0.0151038	+	0.999886i	$0.504808\pi$
$632$		0			0
$633$	−41.1859	+	29.9233i	−1.63699	+	1.18934i
$634$		0			0
$635$	−22.0641	−	16.0305i	−0.875585	−	0.636150i
$636$		0			0
$637$	1.36768	+	0.993681i	0.0541896	+	0.0393711i
$638$		0			0
$639$	−1.67041	−	5.14099i	−0.0660804	−	0.203374i
$640$		0			0
$641$	−6.78266	+	20.8749i	−0.267899	+	0.824509i	0.723112	+	0.690731i	$0.242711\pi$
$641$	−6.78266	+	20.8749i	−0.267899	+	0.824509i	−0.991011	+	0.133778i	$0.957289\pi$
$642$		0			0
$643$	−18.7626	+	13.6318i	−0.739926	+	0.537587i	−0.892688	−	0.450676i	$-0.851183\pi$
$643$	−18.7626	+	13.6318i	−0.739926	+	0.537587i	0.152762	+	0.988263i	$0.451183\pi$
$644$		0			0
$645$	−12.5089	−	38.4986i	−0.492539	−	1.51588i
$646$		0			0
$647$	−13.0086			−0.511421			−0.255710	−	0.966753i	$-0.582309\pi$
$647$	−13.0086			−0.511421			−0.255710	+	0.966753i	$0.582309\pi$
$648$		0			0
$649$	21.6114	+	15.7016i	0.848321	+	0.616341i
$650$		0			0
$651$	3.27678	−	10.0849i	0.128427	−	0.395258i
$652$		0			0
$653$	−31.8563			−1.24663			−0.623317	−	0.781969i	$-0.714215\pi$
$653$	−31.8563			−1.24663			−0.623317	+	0.781969i	$0.714215\pi$
$654$		0			0
$655$	−50.0094			−1.95403
$656$		0			0
$657$	−1.31495			−0.0513012
$658$		0			0
$659$	6.49583			0.253042			0.126521	−	0.991964i	$-0.459619\pi$
$659$	6.49583			0.253042			0.126521	+	0.991964i	$0.459619\pi$
$660$		0			0
$661$	−4.95029	+	15.2354i	−0.192544	+	0.592589i	0.807453	+	0.589932i	$0.200846\pi$
$661$	−4.95029	+	15.2354i	−0.192544	+	0.592589i	−0.999996	+	0.00265652i	$0.999154\pi$
$662$		0			0
$663$	12.0749	+	8.77293i	0.468950	+	0.340712i
$664$		0			0
$665$	−24.3753			−0.945233
$666$		0			0
$667$	4.96292	+	15.2743i	0.192165	+	0.591423i
$668$		0			0
$669$	25.2601	−	18.3526i	0.976613	−	0.709551i
$670$		0			0
$671$	−0.381082	+	1.17285i	−0.0147115	+	0.0452774i
$672$		0			0
$673$	9.28160	+	28.5658i	0.357779	+	1.10113i	0.954380	+	0.298593i	$0.0965174\pi$
$673$	9.28160	+	28.5658i	0.357779	+	1.10113i	−0.596601	+	0.802538i	$0.703483\pi$
$674$		0			0
$675$	46.2124	+	33.5753i	1.77872	+	1.29231i
$676$		0			0
$677$	3.73443	+	2.71322i	0.143526	+	0.104277i	0.657231	−	0.753689i	$-0.271728\pi$
$677$	3.73443	+	2.71322i	0.143526	+	0.104277i	−0.513705	+	0.857967i	$0.671728\pi$
$678$		0			0
$679$	−2.27878	+	1.65563i	−0.0874517	+	0.0635374i
$680$		0			0
$681$	12.6398	+	9.18335i	0.484358	+	0.351907i
$682$		0			0
$683$	32.6869			1.25073			0.625365	−	0.780332i	$-0.284950\pi$
$683$	32.6869			1.25073			0.625365	+	0.780332i	$0.284950\pi$
$684$		0			0
$685$	17.1076	−	52.6519i	0.653649	−	2.01172i
$686$		0			0
$687$	6.43240	+	19.7969i	0.245411	+	0.755298i
$688$		0			0
$689$	4.69541	+	14.4510i	0.178881	+	0.550539i
$690$		0			0
$691$	−4.62290	+	3.35874i	−0.175864	+	0.127772i	−0.672235	−	0.740338i	$-0.734665\pi$
$691$	−4.62290	+	3.35874i	−0.175864	+	0.127772i	0.496371	+	0.868110i	$0.334665\pi$
$692$		0			0
$693$	0.457588	−	1.40831i	0.0173823	−	0.0534974i
$694$		0			0
$695$	15.3400	−	11.1451i	0.581878	−	0.422759i
$696$		0			0
$697$	−28.6688	−	10.2044i	−1.08591	−	0.386521i
$698$		0			0
$699$	−34.0069	+	24.7075i	−1.28626	+	0.934522i
$700$		0			0
$701$	0.106072	−	0.326455i	0.00400627	−	0.0123300i	−0.949033	−	0.315176i	$-0.897937\pi$
$701$	0.106072	−	0.326455i	0.00400627	−	0.0123300i	0.953040	+	0.302845i	$0.0979366\pi$
$702$		0			0
$703$	25.0670	−	18.2123i	0.945420	−	0.686888i
$704$		0			0
$705$	2.63413	+	8.10702i	0.0992071	+	0.305328i
$706$		0			0
$707$	−1.83264	−	5.64028i	−0.0689234	−	0.212124i
$708$		0			0
$709$	−9.26903	+	28.5272i	−0.348106	+	1.07136i	0.611794	+	0.791017i	$0.290448\pi$
$709$	−9.26903	+	28.5272i	−0.348106	+	1.07136i	−0.959900	+	0.280343i	$0.909552\pi$
$710$		0			0
$711$	2.95369			0.110772
$712$		0			0
$713$	22.5074	+	16.3526i	0.842910	+	0.612410i
$714$		0			0
$715$	−18.5469	+	13.4751i	−0.693614	+	0.503940i
$716$		0			0
$717$	−23.6270	−	17.1660i	−0.882366	−	0.641077i
$718$		0			0
$719$	19.8363	+	14.4119i	0.739768	+	0.537473i	0.892639	−	0.450773i	$-0.148852\pi$
$719$	19.8363	+	14.4119i	0.739768	+	0.537473i	−0.152870	+	0.988246i	$0.548852\pi$
$720$		0			0
$721$	−4.75911	−	14.6470i	−0.177238	−	0.545484i
$722$		0			0
$723$	5.81288	−	17.8902i	0.216183	−	0.665344i
$724$		0			0
$725$	32.1587	−	23.3646i	1.19434	−	0.867741i
$726$		0			0
$727$	8.64246	+	26.5987i	0.320531	+	0.986493i	0.973418	+	0.229037i	$0.0735578\pi$
$727$	8.64246	+	26.5987i	0.320531	+	0.986493i	−0.652887	+	0.757456i	$0.726442\pi$
$728$		0			0
$729$	21.8114			0.807831
$730$		0			0
$731$	−20.2819	−	14.7357i	−0.750154	−	0.545019i
$732$		0			0
$733$	−13.7359	+	42.2749i	−0.507348	+	1.56146i	0.289438	+	0.957197i	$0.406532\pi$
$733$	−13.7359	+	42.2749i	−0.507348	+	1.56146i	−0.796786	+	0.604261i	$0.793468\pi$
$734$		0			0
$735$	−7.67375			−0.283051
$736$		0			0
$737$	26.2155			0.965660
$738$		0			0
$739$	9.50843			0.349773			0.174887	−	0.984589i	$-0.444044\pi$
$739$	9.50843			0.349773			0.174887	+	0.984589i	$0.444044\pi$
$740$		0			0
$741$	−18.5320			−0.680792
$742$		0			0
$743$	5.85187	−	18.0102i	0.214684	−	0.660730i	−0.784492	−	0.620139i	$-0.787076\pi$
$743$	5.85187	−	18.0102i	0.214684	−	0.660730i	0.999176	−	0.0405905i	$-0.0129239\pi$
$744$		0			0
$745$	63.1827	+	45.9049i	2.31484	+	1.68183i
$746$		0			0
$747$	3.39447			0.124197
$748$		0			0
$749$	−0.151476	−	0.466195i	−0.00553481	−	0.0170344i
$750$		0			0
$751$	−35.6852	+	25.9269i	−1.30217	+	0.946084i	−0.999974	−	0.00716070i	$-0.997721\pi$
$751$	−35.6852	+	25.9269i	−1.30217	+	0.946084i	−0.302199	+	0.953245i	$0.597721\pi$
$752$		0			0
$753$	−16.2985	+	50.1617i	−0.593951	+	1.82799i
$754$		0			0
$755$	14.7490	+	45.3928i	0.536772	+	1.65201i
$756$		0			0
$757$	9.09140	+	6.60529i	0.330433	+	0.240073i	0.740614	−	0.671930i	$-0.234535\pi$
$757$	9.09140	+	6.60529i	0.330433	+	0.240073i	−0.410181	+	0.912004i	$0.634535\pi$
$758$		0			0
$759$	24.0474	+	17.4715i	0.872865	+	0.634174i
$760$		0			0
$761$	−4.29319	+	3.11918i	−0.155628	+	0.113070i	−0.662874	−	0.748731i	$-0.730664\pi$
$761$	−4.29319	+	3.11918i	−0.155628	+	0.113070i	0.507246	+	0.861801i	$0.330664\pi$
$762$		0			0
$763$	−16.5847	−	12.0495i	−0.600408	−	0.436222i
$764$		0			0
$765$	−8.85505			−0.320155
$766$		0			0
$767$	4.25091	−	13.0829i	0.153491	−	0.472398i
$768$		0			0
$769$	−14.2661	−	43.9064i	−0.514447	−	1.58331i	−0.784286	−	0.620400i	$-0.786970\pi$
$769$	−14.2661	−	43.9064i	−0.514447	−	1.58331i	0.269838	−	0.962906i	$-0.413030\pi$
$770$		0			0
$771$	−7.04188	−	21.6727i	−0.253607	−	0.780522i
$772$		0			0
$773$	38.5042	−	27.9749i	1.38490	−	1.00619i	0.388495	−	0.921451i	$-0.372995\pi$
$773$	38.5042	−	27.9749i	1.38490	−	1.00619i	0.996403	−	0.0847368i	$-0.0270049\pi$
$774$		0			0
$775$	21.2783	−	65.4878i	0.764338	−	2.35239i
$776$		0			0
$777$	7.89152	−	5.73352i	0.283107	−	0.205689i
$778$		0			0
$779$	36.2456	−	10.6726i	1.29863	−	0.382387i
$780$		0			0
$781$	31.8283	−	23.1246i	1.13891	−	0.827463i
$782$		0			0
$783$	4.82162	−	14.8394i	0.172311	−	0.530317i
$784$		0			0
$785$	−20.1897	+	14.6687i	−0.720603	+	0.523548i
$786$		0			0
$787$	−12.4288	−	38.2518i	−0.443038	−	1.36353i	−0.884621	−	0.466311i	$-0.845583\pi$
$787$	−12.4288	−	38.2518i	−0.443038	−	1.36353i	0.441583	−	0.897220i	$-0.354417\pi$
$788$		0			0
$789$	0.456951	+	1.40635i	0.0162679	+	0.0500674i
$790$		0			0
$791$	−5.93770	+	18.2744i	−0.211120	+	0.649761i
$792$		0			0
$793$	0.635054			0.0225514
$794$		0			0
$795$	−55.7993	−	40.5406i	−1.97900	−	1.43783i
$796$		0			0
$797$	28.5062	−	20.7109i	1.00974	−	0.733619i	0.0455857	−	0.998960i	$-0.485485\pi$
$797$	28.5062	−	20.7109i	1.00974	−	0.733619i	0.964155	+	0.265341i	$0.0854846\pi$
$798$		0			0
$799$	4.27097	+	3.10304i	0.151096	+	0.109778i
$800$		0			0
$801$	5.84073	+	4.24354i	0.206372	+	0.149938i
$802$		0			0
$803$	−2.95738	−	9.10188i	−0.104364	−	0.321199i
$804$		0			0
$805$	6.22148	−	19.1477i	0.219278	−	0.674869i
$806$		0			0
$807$	22.9779	−	16.6944i	0.808860	−	0.587671i
$808$		0			0
$809$	−12.5307	−	38.5655i	−0.440555	−	1.35589i	−0.887285	−	0.461221i	$-0.847412\pi$
$809$	−12.5307	−	38.5655i	−0.440555	−	1.35589i	0.446730	−	0.894669i	$-0.352588\pi$
$810$		0			0
$811$	−7.30373			−0.256469			−0.128234	−	0.991744i	$-0.540931\pi$
$811$	−7.30373			−0.256469			−0.128234	+	0.991744i	$0.540931\pi$
$812$		0			0
$813$	−11.8499	−	8.60946i	−0.415594	−	0.301947i
$814$		0			0
$815$	−9.02786	+	27.7849i	−0.316232	+	0.973262i
$816$		0			0
$817$	31.1278			1.08903
$818$		0			0
$819$	−0.762547			−0.0266456
$820$		0			0
$821$	12.0762			0.421461			0.210731	−	0.977544i	$-0.432416\pi$
$821$	12.0762			0.421461			0.210731	+	0.977544i	$0.432416\pi$
$822$		0			0
$823$	−2.81210			−0.0980237			−0.0490119	−	0.998798i	$-0.515607\pi$
$823$	−2.81210			−0.0980237			−0.0490119	+	0.998798i	$0.515607\pi$
$824$		0			0
$825$	22.7341	−	69.9684i	0.791500	−	2.43599i
$826$		0			0
$827$	24.6072	+	17.8782i	0.855676	+	0.621685i	0.926705	−	0.375789i	$-0.122628\pi$
$827$	24.6072	+	17.8782i	0.855676	+	0.621685i	−0.0710293	+	0.997474i	$0.522628\pi$
$828$		0			0
$829$	−5.68354			−0.197398			−0.0986988	−	0.995117i	$-0.531468\pi$
$829$	−5.68354			−0.197398			−0.0986988	+	0.995117i	$0.531468\pi$
$830$		0			0
$831$	4.59638	+	14.1462i	0.159447	+	0.490727i
$832$		0			0
$833$	−3.84485	+	2.79344i	−0.133216	+	0.0967871i
$834$		0			0
$835$	1.40179	−	4.31427i	0.0485109	−	0.149301i
$836$		0			0
$837$	−8.35230	−	25.7057i	−0.288698	−	0.888521i
$838$		0			0
$839$	−27.8691	−	20.2481i	−0.962147	−	0.699041i	−0.00849867	−	0.999964i	$-0.502705\pi$
$839$	−27.8691	−	20.2481i	−0.962147	−	0.699041i	−0.953648	+	0.300923i	$0.902705\pi$
$840$		0			0
$841$	14.6772	+	10.6636i	0.506110	+	0.367710i
$842$		0			0
$843$	−24.0338	+	17.4616i	−0.827769	+	0.601409i
$844$		0			0
$845$	−33.8933	−	24.6249i	−1.16597	−	0.847124i
$846$		0			0
$847$	−0.222759			−0.00765408
$848$		0			0
$849$	9.12500	−	28.0839i	0.313169	−	0.963836i
$850$		0			0
$851$	7.90840	+	24.3396i	0.271097	+	0.834349i
$852$		0			0
$853$	−1.20389	−	3.70519i	−0.0412204	−	0.126863i	0.928329	−	0.371761i	$-0.121246\pi$
$853$	−1.20389	−	3.70519i	−0.0412204	−	0.126863i	−0.969549	+	0.244897i	$0.921246\pi$
$854$		0			0
$855$	8.89501	−	6.46260i	0.304203	−	0.221016i
$856$		0			0
$857$	−12.6066	+	38.7992i	−0.430634	+	1.32536i	0.466861	+	0.884331i	$0.345385\pi$
$857$	−12.6066	+	38.7992i	−0.430634	+	1.32536i	−0.897495	+	0.441025i	$0.854615\pi$
$858$		0			0
$859$	34.5408	−	25.0954i	1.17852	−	0.856243i	0.186513	−	0.982452i	$-0.440281\pi$
$859$	34.5408	−	25.0954i	1.17852	−	0.856243i	0.992004	+	0.126210i	$0.0402813\pi$
$860$		0			0
$861$	11.4107	−	3.35992i	0.388876	−	0.114506i
$862$		0			0
$863$	−20.4415	+	14.8516i	−0.695835	+	0.505554i	−0.878573	−	0.477608i	$-0.841504\pi$
$863$	−20.4415	+	14.8516i	−0.695835	+	0.505554i	0.182738	+	0.983162i	$0.441504\pi$
$864$		0			0
$865$	−9.77195	+	30.0750i	−0.332256	+	1.02258i
$866$		0			0
$867$	−8.39553	+	6.09971i	−0.285127	+	0.207157i
$868$		0			0
$869$	6.64296	+	20.4449i	0.225347	+	0.693547i
$870$		0			0
$871$	−4.17171	−	12.8392i	−0.141353	−	0.435040i
$872$		0			0
$873$	0.392615	−	1.20834i	0.0132880	−	0.0408962i
$874$		0			0
$875$	−29.1768			−0.986355
$876$		0			0
$877$	−37.4550	−	27.2127i	−1.26477	−	0.918906i	−0.265784	−	0.964032i	$-0.585631\pi$
$877$	−37.4550	−	27.2127i	−1.26477	−	0.918906i	−0.998981	+	0.0451264i	$0.985631\pi$
$878$		0			0
$879$	9.98977	−	7.25799i	0.336947	−	0.244806i
$880$		0			0
$881$	−25.2167	−	18.3210i	−0.849571	−	0.617250i	0.0754564	−	0.997149i	$-0.475959\pi$
$881$	−25.2167	−	18.3210i	−0.849571	−	0.617250i	−0.925028	+	0.379899i	$0.875959\pi$
$882$		0			0
$883$	−30.5188	−	22.1732i	−1.02704	−	0.746189i	−0.0593267	−	0.998239i	$-0.518895\pi$
$883$	−30.5188	−	22.1732i	−1.02704	−	0.746189i	−0.967714	+	0.252050i	$0.918895\pi$
$884$		0			0
$885$	19.2957	+	59.3861i	0.648619	+	1.99624i
$886$		0			0
$887$	−5.69858	+	17.5384i	−0.191340	+	0.588883i	0.808660	+	0.588276i	$0.200193\pi$
$887$	−5.69858	+	17.5384i	−0.191340	+	0.588883i	−1.00000		0.000606715i	$0.999807\pi$
$888$		0			0
$889$	5.34139	−	3.88075i	0.179144	−	0.130156i
$890$		0			0
$891$	−10.2965	−	31.6895i	−0.344947	−	1.06164i
$892$		0			0
$893$	−6.55490			−0.219351
$894$		0			0
$895$	−76.5499	−	55.6167i	−2.55878	−	1.85906i
$896$		0			0
$897$	4.73006	−	14.5576i	0.157932	−	0.486065i
$898$		0			0
$899$	−18.8089			−0.627312
$900$		0			0
$901$	−42.7154			−1.42306
$902$		0			0
$903$	9.79957			0.326109
$904$		0			0
$905$	0.824997			0.0274238
$906$		0			0
$907$	−2.79282	+	8.59541i	−0.0927340	+	0.285406i	−0.986657	−	0.162816i	$-0.947942\pi$
$907$	−2.79282	+	8.59541i	−0.0927340	+	0.285406i	0.893922	+	0.448222i	$0.147942\pi$
$908$		0			0
$909$	2.16417	+	1.57236i	0.0717809	+	0.0521518i
$910$		0			0
$911$	−4.53640			−0.150298			−0.0751488	−	0.997172i	$-0.523943\pi$
$911$	−4.53640			−0.150298			−0.0751488	+	0.997172i	$0.523943\pi$
$912$		0			0
$913$	7.63429	+	23.4959i	0.252658	+	0.777602i
$914$		0			0
$915$	−2.33210	+	1.69437i	−0.0770969	+	0.0560142i
$916$		0			0
$917$	3.74113	−	11.5140i	0.123543	−	0.380226i
$918$		0			0
$919$	8.28988	+	25.5136i	0.273458	+	0.841617i	0.989623	+	0.143686i	$0.0458956\pi$
$919$	8.28988	+	25.5136i	0.273458	+	0.841617i	−0.716165	+	0.697931i	$0.754104\pi$
$920$		0			0
$921$	16.0248	+	11.6427i	0.528034	+	0.383639i
$922$		0			0
$923$	−16.3903	−	11.9083i	−0.539494	−	0.391965i
$924$		0			0
$925$	51.2447	−	37.2315i	1.68492	−	1.22416i
$926$		0			0
$927$	5.62004	+	4.08320i	0.184586	+	0.134110i
$928$		0			0
$929$	−4.79563			−0.157340			−0.0786698	−	0.996901i	$-0.525067\pi$
$929$	−4.79563			−0.157340			−0.0786698	+	0.996901i	$0.525067\pi$
$930$		0			0
$931$	1.82348	−	5.61209i	0.0597621	−	0.183929i
$932$		0			0
$933$	5.80244	+	17.8581i	0.189963	+	0.584647i
$934$		0			0
$935$	−19.9154	−	61.2932i	−0.651303	−	2.00450i
$936$		0			0
$937$	−18.2195	+	13.2373i	−0.595206	+	0.432442i	−0.844174	−	0.536069i	$-0.819909\pi$
$937$	−18.2195	+	13.2373i	−0.595206	+	0.432442i	0.248968	+	0.968512i	$0.419909\pi$
$938$		0			0
$939$	15.0443	−	46.3016i	0.490953	−	1.51100i
$940$		0			0
$941$	24.7106	−	17.9533i	0.805544	−	0.585262i	−0.106992	−	0.994260i	$-0.534122\pi$
$941$	24.7106	−	17.9533i	0.805544	−	0.585262i	0.912535	+	0.408998i	$0.134122\pi$
$942$		0			0
$943$	−0.867451	+	31.1964i	−0.0282481	+	1.01589i
$944$		0			0
$945$	−15.8243	+	11.4970i	−0.514764	+	0.373998i
$946$		0			0
$947$	11.0178	−	33.9092i	0.358029	−	1.10190i	−0.596203	−	0.802833i	$-0.703325\pi$
$947$	11.0178	−	33.9092i	0.358029	−	1.10190i	0.954232	−	0.299066i	$-0.0966751\pi$
$948$		0			0
$949$	−3.98710	+	2.89680i	−0.129427	+	0.0940340i
$950$		0			0
$951$	−4.86596	−	14.9759i	−0.157790	−	0.485626i
$952$		0			0
$953$	−14.6098	−	44.9643i	−0.473257	−	1.45654i	−0.848293	−	0.529526i	$-0.822370\pi$
$953$	−14.6098	−	44.9643i	−0.473257	−	1.45654i	0.375036	−	0.927010i	$-0.377630\pi$
$954$		0			0
$955$	−29.2569	+	90.0436i	−0.946732	+	2.91374i
$956$		0			0
$957$	−20.0958			−0.649605
$958$		0			0
$959$	10.8426	+	7.87762i	0.350126	+	0.254381i
$960$		0			0
$961$	−1.27983	+	0.929848i	−0.0412847	+	0.0299951i
$962$		0			0
$963$	0.178878	+	0.129963i	0.00576427	+	0.00418799i
$964$		0			0
$965$	60.7030	+	44.1033i	1.95410	+	1.41974i
$966$		0			0
$967$	1.34242	+	4.13156i	0.0431695	+	0.132862i	0.970318	−	0.241831i	$-0.0777480\pi$
$967$	1.34242	+	4.13156i	0.0431695	+	0.132862i	−0.927149	+	0.374693i	$0.877748\pi$
$968$		0			0
$969$	16.0990	−	49.5476i	0.517174	−	1.59170i
$970$		0			0
$971$	−7.66816	+	5.57124i	−0.246083	+	0.178790i	−0.703989	−	0.710211i	$-0.748600\pi$
$971$	−7.66816	+	5.57124i	−0.246083	+	0.178790i	0.457906	+	0.889001i	$0.348600\pi$
$972$		0			0
$973$	1.41846	+	4.36558i	0.0454738	+	0.139954i
$974$		0			0
$975$	−37.8852			−1.21330
$976$		0			0
$977$	22.0038	+	15.9867i	0.703964	+	0.511460i	0.881221	−	0.472705i	$-0.156722\pi$
$977$	22.0038	+	15.9867i	0.703964	+	0.511460i	−0.177257	+	0.984165i	$0.556722\pi$
$978$		0			0
$979$	−16.2370	+	49.9724i	−0.518938	+	1.59713i
$980$		0			0
$981$	9.24677			0.295226
$982$		0			0
$983$	15.1950			0.484644			0.242322	−	0.970196i	$-0.422091\pi$
$983$	15.1950			0.484644			0.242322	+	0.970196i	$0.422091\pi$
$984$		0			0
$985$	−58.8164			−1.87405
$986$		0			0
$987$	−2.06359			−0.0656849
$988$		0			0
$989$	−7.94498	+	24.4521i	−0.252636	+	0.777533i
$990$		0			0
$991$	−39.4466	−	28.6596i	−1.25306	−	0.910403i	−0.254666	−	0.967029i	$-0.581966\pi$
$991$	−39.4466	−	28.6596i	−1.25306	−	0.910403i	−0.998395	+	0.0566264i	$0.981966\pi$
$992$		0			0
$993$	38.9983			1.23757
$994$		0			0
$995$	7.57761	+	23.3215i	0.240226	+	0.739341i
$996$		0			0
$997$	47.3614	−	34.4101i	1.49995	−	1.08978i	0.529549	−	0.848279i	$-0.322361\pi$
$997$	47.3614	−	34.4101i	1.49995	−	1.08978i	0.970401	−	0.241498i	$-0.0776388\pi$
$998$		0			0
$999$	7.68324	−	23.6466i	0.243087	−	0.748144i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.n.d.365.6	✓	24
41.10	even	5	inner	1148.2.n.d.953.6	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.n.d.365.6	✓	24	1.1	even	1	trivial
1148.2.n.d.953.6	yes	24	41.10	even	5	inner

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)

\(f(q)\)	\(=\)	\(q+1.85770 q^{3} +(-1.27648 + 3.92860i) q^{5} +(-0.809017 - 0.587785i) q^{7} +0.451065 q^{9} +O(q^{10})\)	\(q+1.85770 q^{3} +(-1.27648 + 3.92860i) q^{5} +(-0.809017 - 0.587785i) q^{7} +0.451065 q^{9} +(1.01446 + 3.12220i) q^{11} +(1.36768 - 0.993681i) q^{13} +(-2.37132 + 7.29817i) q^{15} +(1.46860 + 4.51989i) q^{17} +(-4.77393 - 3.46846i) q^{19} +(-1.50291 - 1.09193i) q^{21} +(3.94310 - 2.86483i) q^{23} +(-9.75940 - 7.09062i) q^{25} -4.73517 q^{27} +(-1.01826 + 3.13387i) q^{29} +(1.76389 + 5.42869i) q^{31} +(1.88457 + 5.80012i) q^{33} +(3.34186 - 2.42801i) q^{35} +(-1.62259 + 4.99382i) q^{37} +(2.54075 - 1.84596i) q^{39} +(-3.90619 + 5.07362i) q^{41} +(-4.26764 + 3.10062i) q^{43} +(-0.575774 + 1.77205i) q^{45} +(0.898680 - 0.652929i) q^{47} +(0.309017 + 0.951057i) q^{49} +(2.72822 + 8.39661i) q^{51} +(-2.77745 + 8.54810i) q^{53} -13.5608 q^{55} +(-8.86855 - 6.44338i) q^{57} +(6.58307 - 4.78288i) q^{59} +(0.303906 + 0.220801i) q^{61} +(-0.364919 - 0.265129i) q^{63} +(2.15795 + 6.64149i) q^{65} +(2.46767 - 7.59469i) q^{67} +(7.32511 - 5.32200i) q^{69} +(-3.70326 - 11.3975i) q^{71} -2.91522 q^{73} +(-18.1301 - 13.1723i) q^{75} +(1.01446 - 3.12220i) q^{77} +6.54825 q^{79} -10.1497 q^{81} +7.52545 q^{83} -19.6315 q^{85} +(-1.89162 + 5.82181i) q^{87} +(12.9488 + 9.40782i) q^{89} -1.69055 q^{91} +(3.27678 + 10.0849i) q^{93} +(19.7200 - 14.3274i) q^{95} +(0.870418 - 2.67887i) q^{97} +(0.457588 + 1.40831i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 10 q^{3} + 4 q^{5} - 6 q^{7} + 38 q^{9}+O(q^{10}) \) 24 * q - 10 * q^3 + 4 * q^5 - 6 * q^7 + 38 * q^9	\( 24 q - 10 q^{3} + 4 q^{5} - 6 q^{7} + 38 q^{9} + 11 q^{11} - 4 q^{13} + 10 q^{15} + 9 q^{17} - 23 q^{19} + 5 q^{21} + 28 q^{23} - 10 q^{25} - 76 q^{27} + 28 q^{29} - 18 q^{31} - 27 q^{33} - q^{35} - 29 q^{37} - 6 q^{39} + 65 q^{41} - 15 q^{43} - 20 q^{45} - 11 q^{47} - 6 q^{49} - 18 q^{51} + 8 q^{53} - 50 q^{55} + 8 q^{57} + 55 q^{59} - 10 q^{61} - 2 q^{63} - 11 q^{65} + 65 q^{67} - 2 q^{69} - 14 q^{71} + 48 q^{73} - 77 q^{75} + 11 q^{77} + 22 q^{79} + 80 q^{81} - 22 q^{83} - 78 q^{85} - 4 q^{87} + 16 q^{89} - 4 q^{91} - 60 q^{93} + 56 q^{95} + 15 q^{97} + 80 q^{99}+O(q^{100}) \) 24 * q - 10 * q^3 + 4 * q^5 - 6 * q^7 + 38 * q^9 + 11 * q^11 - 4 * q^13 + 10 * q^15 + 9 * q^17 - 23 * q^19 + 5 * q^21 + 28 * q^23 - 10 * q^25 - 76 * q^27 + 28 * q^29 - 18 * q^31 - 27 * q^33 - q^35 - 29 * q^37 - 6 * q^39 + 65 * q^41 - 15 * q^43 - 20 * q^45 - 11 * q^47 - 6 * q^49 - 18 * q^51 + 8 * q^53 - 50 * q^55 + 8 * q^57 + 55 * q^59 - 10 * q^61 - 2 * q^63 - 11 * q^65 + 65 * q^67 - 2 * q^69 - 14 * q^71 + 48 * q^73 - 77 * q^75 + 11 * q^77 + 22 * q^79 + 80 * q^81 - 22 * q^83 - 78 * q^85 - 4 * q^87 + 16 * q^89 - 4 * q^91 - 60 * q^93 + 56 * q^95 + 15 * q^97 + 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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