LMFDB - Embedded newform 1148.2.n.c.365.4

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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 12 x^{14} - 19 x^{13} + 49 x^{12} - 91 x^{11} + 269 x^{10} - 367 x^{9} + 1058 x^{8} + \cdots + 1 $ x^16 - 3x^15 + 12x^14 - 19x^13 + 49x^12 - 91x^11 + 269x^10 - 367x^9 + 1058x^8 - 1675x^7 + 2755x^6 - 2800x^5 + 4032x^4 - 2186x^3 + 2189x^2 + 76*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			365.4
Root			$0.842594 - 2.59324i$ of defining polynomial
Character	$\chi$	$=$	1148.365
Dual form			1148.2.n.c.953.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.72669 q^{3} +(-0.323246 + 0.994850i) q^{5} +(0.809017 + 0.587785i) q^{7} +4.43484 q^{9} +O(q^{10})$	\(q+2.72669 q^{3} +(-0.323246 + 0.994850i) q^{5} +(0.809017 + 0.587785i) q^{7} +4.43484 q^{9} +(-1.27722 - 3.93087i) q^{11} +(1.98131 - 1.43950i) q^{13} +(-0.881393 + 2.71265i) q^{15} +(1.62894 + 5.01335i) q^{17} +(0.543573 + 0.394929i) q^{19} +(2.20594 + 1.60271i) q^{21} +(5.08786 - 3.69655i) q^{23} +(3.15985 + 2.29576i) q^{25} +3.91236 q^{27} +(0.554766 - 1.70739i) q^{29} +(-0.299218 - 0.920897i) q^{31} +(-3.48257 - 10.7183i) q^{33} +(-0.846270 + 0.614851i) q^{35} +(-0.475999 + 1.46498i) q^{37} +(5.40241 - 3.92508i) q^{39} +(3.09655 + 5.60459i) q^{41} +(1.58860 - 1.15418i) q^{43} +(-1.43355 + 4.41200i) q^{45} +(-7.27123 + 5.28286i) q^{47} +(0.309017 + 0.951057i) q^{49} +(4.44161 + 13.6699i) q^{51} +(0.322574 - 0.992781i) q^{53} +4.32348 q^{55} +(1.48215 + 1.07685i) q^{57} +(-9.41756 + 6.84226i) q^{59} +(-7.91258 - 5.74882i) q^{61} +(3.58786 + 2.60673i) q^{63} +(0.791640 + 2.43642i) q^{65} +(-2.76822 + 8.51972i) q^{67} +(13.8730 - 10.0793i) q^{69} +(-3.81811 - 11.7509i) q^{71} +13.0364 q^{73} +(8.61592 + 6.25983i) q^{75} +(1.27722 - 3.93087i) q^{77} +5.61764 q^{79} -2.63672 q^{81} -15.9564 q^{83} -5.51408 q^{85} +(1.51268 - 4.65554i) q^{87} +(-0.0547737 - 0.0397954i) q^{89} +2.44903 q^{91} +(-0.815874 - 2.51100i) q^{93} +(-0.568603 + 0.413114i) q^{95} +(-0.922681 + 2.83972i) q^{97} +(-5.66425 - 17.4328i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{3} - 13 q^{5} + 4 q^{7} + 2 q^{9}+O(q^{10}) $ 16 * q - 2 * q^3 - 13 * q^5 + 4 * q^7 + 2 * q^9	$ 16 q - 2 q^{3} - 13 q^{5} + 4 q^{7} + 2 q^{9} - q^{11} - 6 q^{13} - q^{17} + 15 q^{19} + 2 q^{21} + 27 q^{23} - 3 q^{25} + 28 q^{27} - q^{29} - 14 q^{31} - 13 q^{33} - 12 q^{35} - 16 q^{37} + 10 q^{39} + 26 q^{41} + 5 q^{43} - 9 q^{45} - 14 q^{47} - 4 q^{49} + 4 q^{51} - 20 q^{53} + 10 q^{55} - 13 q^{57} - 47 q^{61} + 3 q^{63} - 29 q^{65} - 27 q^{67} + 15 q^{69} - 11 q^{71} + 70 q^{73} + 14 q^{75} + q^{77} + 30 q^{79} - 72 q^{81} - 78 q^{83} + 72 q^{85} + 21 q^{87} + 17 q^{89} - 24 q^{91} - 7 q^{93} + 27 q^{95} - 17 q^{97} + 13 q^{99}+O(q^{100}) $ 16 * q - 2 * q^3 - 13 * q^5 + 4 * q^7 + 2 * q^9 - q^11 - 6 * q^13 - q^17 + 15 * q^19 + 2 * q^21 + 27 * q^23 - 3 * q^25 + 28 * q^27 - q^29 - 14 * q^31 - 13 * q^33 - 12 * q^35 - 16 * q^37 + 10 * q^39 + 26 * q^41 + 5 * q^43 - 9 * q^45 - 14 * q^47 - 4 * q^49 + 4 * q^51 - 20 * q^53 + 10 * q^55 - 13 * q^57 - 47 * q^61 + 3 * q^63 - 29 * q^65 - 27 * q^67 + 15 * q^69 - 11 * q^71 + 70 * q^73 + 14 * q^75 + q^77 + 30 * q^79 - 72 * q^81 - 78 * q^83 + 72 * q^85 + 21 * q^87 + 17 * q^89 - 24 * q^91 - 7 * q^93 + 27 * q^95 - 17 * q^97 + 13 * 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
$3$	2.72669			1.57426			0.787128	−	0.616790i	$-0.211567\pi$
$3$	2.72669			1.57426			0.787128	+	0.616790i	$0.211567\pi$
$4$		0			0
$5$	−0.323246	+	0.994850i	−0.144560	+	0.444910i	−0.996954	−	0.0779896i	$-0.975150\pi$
$5$	−0.323246	+	0.994850i	−0.144560	+	0.444910i	0.852394	+	0.522900i	$0.175150\pi$
$6$		0			0
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$8$		0			0
$9$	4.43484			1.47828
$10$		0			0
$11$	−1.27722	−	3.93087i	−0.385095	−	1.18520i	−0.936411	−	0.350905i	$-0.885874\pi$
$11$	−1.27722	−	3.93087i	−0.385095	−	1.18520i	0.551316	−	0.834297i	$-0.314126\pi$
$12$		0			0
$13$	1.98131	−	1.43950i	0.549516	−	0.399246i	−0.278091	−	0.960555i	$-0.589702\pi$
$13$	1.98131	−	1.43950i	0.549516	−	0.399246i	0.827607	+	0.561308i	$0.189702\pi$
$14$		0			0
$15$	−0.881393	+	2.71265i	−0.227575	+	0.700403i
$16$		0			0
$17$	1.62894	+	5.01335i	0.395075	+	1.21592i	0.928903	+	0.370324i	$0.120753\pi$
$17$	1.62894	+	5.01335i	0.395075	+	1.21592i	−0.533827	+	0.845593i	$0.679247\pi$
$18$		0			0
$19$	0.543573	+	0.394929i	0.124704	+	0.0906029i	0.648389	−	0.761309i	$-0.275443\pi$
$19$	0.543573	+	0.394929i	0.124704	+	0.0906029i	−0.523685	+	0.851912i	$0.675443\pi$
$20$		0			0
$21$	2.20594	+	1.60271i	0.481375	+	0.349740i
$22$		0			0
$23$	5.08786	−	3.69655i	1.06089	−	0.770783i	0.0866389	−	0.996240i	$-0.472387\pi$
$23$	5.08786	−	3.69655i	1.06089	−	0.770783i	0.974253	+	0.225457i	$0.0723874\pi$
$24$		0			0
$25$	3.15985	+	2.29576i	0.631969	+	0.459153i
$26$		0			0
$27$	3.91236			0.752934
$28$		0			0
$29$	0.554766	−	1.70739i	0.103017	−	0.317055i	−0.886243	−	0.463221i	$-0.846693\pi$
$29$	0.554766	−	1.70739i	0.103017	−	0.317055i	0.989260	+	0.146166i	$0.0466934\pi$
$30$		0			0
$31$	−0.299218	−	0.920897i	−0.0537411	−	0.165398i	0.920584	−	0.390546i	$-0.127714\pi$
$31$	−0.299218	−	0.920897i	−0.0537411	−	0.165398i	−0.974325	+	0.225148i	$0.927714\pi$
$32$		0			0
$33$	−3.48257	−	10.7183i	−0.606238	−	1.86581i
$34$		0			0
$35$	−0.846270	+	0.614851i	−0.143046	+	0.103929i
$36$		0			0
$37$	−0.475999	+	1.46498i	−0.0782538	+	0.240840i	−0.982529	−	0.186110i	$-0.940412\pi$
$37$	−0.475999	+	1.46498i	−0.0782538	+	0.240840i	0.904275	+	0.426950i	$0.140412\pi$
$38$		0			0
$39$	5.40241	−	3.92508i	0.865078	−	0.628516i
$40$		0			0
$41$	3.09655	+	5.60459i	0.483599	+	0.875290i
$41$	3.09655	+	5.60459i	0.483599	+	0.875290i
$42$		0			0
$43$	1.58860	−	1.15418i	0.242259	−	0.176011i	−0.460030	−	0.887903i	$-0.652161\pi$
$43$	1.58860	−	1.15418i	0.242259	−	0.176011i	0.702289	+	0.711892i	$0.252161\pi$
$44$		0			0
$45$	−1.43355	+	4.41200i	−0.213700	+	0.657702i
$46$		0			0
$47$	−7.27123	+	5.28286i	−1.06062	+	0.770584i	−0.974202	−	0.225676i	$-0.927541\pi$
$47$	−7.27123	+	5.28286i	−1.06062	+	0.770584i	−0.0864148	+	0.996259i	$0.527541\pi$
$48$		0			0
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$		0			0
$51$	4.44161	+	13.6699i	0.621949	+	1.91416i
$52$		0			0
$53$	0.322574	−	0.992781i	0.0443090	−	0.136369i	−0.926455	−	0.376406i	$-0.877160\pi$
$53$	0.322574	−	0.992781i	0.0443090	−	0.136369i	0.970764	+	0.240037i	$0.0771597\pi$
$54$		0			0
$55$	4.32348			0.582978
$56$		0			0
$57$	1.48215	+	1.07685i	0.196316	+	0.142632i
$58$		0			0
$59$	−9.41756	+	6.84226i	−1.22606	+	0.890786i	−0.996589	−	0.0825293i	$-0.973700\pi$
$59$	−9.41756	+	6.84226i	−1.22606	+	0.890786i	−0.229473	+	0.973315i	$0.573700\pi$
$60$		0			0
$61$	−7.91258	−	5.74882i	−1.01310	−	0.736061i	−0.0482441	−	0.998836i	$-0.515363\pi$
$61$	−7.91258	−	5.74882i	−1.01310	−	0.736061i	−0.964857	+	0.262774i	$0.915363\pi$
$62$		0			0
$63$	3.58786	+	2.60673i	0.452028	+	0.328417i
$64$		0			0
$65$	0.791640	+	2.43642i	0.0981908	+	0.302200i
$66$		0			0
$67$	−2.76822	+	8.51972i	−0.338192	+	1.04085i	0.626936	+	0.779071i	$0.284309\pi$
$67$	−2.76822	+	8.51972i	−0.338192	+	1.04085i	−0.965128	+	0.261778i	$0.915691\pi$
$68$		0			0
$69$	13.8730	−	10.0793i	1.67011	−	1.21341i
$70$		0			0
$71$	−3.81811	−	11.7509i	−0.453126	−	1.39458i	−0.873321	−	0.487145i	$-0.838038\pi$
$71$	−3.81811	−	11.7509i	−0.453126	−	1.39458i	0.420194	−	0.907434i	$-0.361962\pi$
$72$		0			0
$73$	13.0364			1.52579			0.762895	−	0.646522i	$-0.223777\pi$
$73$	13.0364			1.52579			0.762895	+	0.646522i	$0.223777\pi$
$74$		0			0
$75$	8.61592	+	6.25983i	0.994881	+	0.722823i
$76$		0			0
$77$	1.27722	−	3.93087i	0.145552	−	0.447964i
$78$		0			0
$79$	5.61764			0.632034			0.316017	−	0.948754i	$-0.397654\pi$
$79$	5.61764			0.632034			0.316017	+	0.948754i	$0.397654\pi$
$80$		0			0
$81$	−2.63672			−0.292969
$82$		0			0
$83$	−15.9564			−1.75145			−0.875723	−	0.482814i	$-0.839615\pi$
$83$	−15.9564			−1.75145			−0.875723	+	0.482814i	$0.839615\pi$
$84$		0			0
$85$	−5.51408			−0.598086
$86$		0			0
$87$	1.51268	−	4.65554i	0.162176	−	0.499126i
$88$		0			0
$89$	−0.0547737	−	0.0397954i	−0.00580600	−	0.00421830i	0.584878	−	0.811121i	$-0.301142\pi$
$89$	−0.0547737	−	0.0397954i	−0.00580600	−	0.00421830i	−0.590684	+	0.806903i	$0.701142\pi$
$90$		0			0
$91$	2.44903			0.256728
$92$		0			0
$93$	−0.815874	−	2.51100i	−0.0846022	−	0.260379i
$94$		0			0
$95$	−0.568603	+	0.413114i	−0.0583374	+	0.0423846i
$96$		0			0
$97$	−0.922681	+	2.83972i	−0.0936841	+	0.288330i	−0.986909	−	0.161281i	$-0.948437\pi$
$97$	−0.922681	+	2.83972i	−0.0936841	+	0.288330i	0.893224	+	0.449611i	$0.148437\pi$
$98$		0			0
$99$	−5.66425	−	17.4328i	−0.569278	−	1.75206i
$100$		0			0
$101$	−7.40004	−	5.37645i	−0.736332	−	0.534976i	0.155228	−	0.987879i	$-0.450389\pi$
$101$	−7.40004	−	5.37645i	−0.736332	−	0.534976i	−0.891560	+	0.452902i	$0.850389\pi$
$102$		0			0
$103$	−5.37902	−	3.90809i	−0.530011	−	0.385075i	0.290351	−	0.956920i	$-0.406228\pi$
$103$	−5.37902	−	3.90809i	−0.530011	−	0.385075i	−0.820362	+	0.571845i	$0.806228\pi$
$104$		0			0
$105$	−2.30752	+	1.67651i	−0.225190	+	0.163610i
$106$		0			0
$107$	−0.210920	−	0.153243i	−0.0203905	−	0.0148145i	0.577543	−	0.816360i	$-0.304011\pi$
$107$	−0.210920	−	0.153243i	−0.0203905	−	0.0148145i	−0.597934	+	0.801545i	$0.704011\pi$
$108$		0			0
$109$	−11.1828			−1.07112			−0.535561	−	0.844496i	$-0.679900\pi$
$109$	−11.1828			−1.07112			−0.535561	+	0.844496i	$0.679900\pi$
$110$		0			0
$111$	−1.29790	+	3.99453i	−0.123191	+	0.379144i
$112$		0			0
$113$	−5.93635	−	18.2702i	−0.558445	−	1.71872i	−0.686668	−	0.726971i	$-0.740927\pi$
$113$	−5.93635	−	18.2702i	−0.558445	−	1.71872i	0.128223	−	0.991745i	$-0.459073\pi$
$114$		0			0
$115$	2.03288	+	6.25655i	0.189567	+	0.583427i
$116$		0			0
$117$	8.78678	−	6.38397i	0.812338	−	0.590198i
$118$		0			0
$119$	−1.62894	+	5.01335i	−0.149324	+	0.459573i
$120$		0			0
$121$	−4.92126	+	3.57550i	−0.447387	+	0.325046i
$122$		0			0
$123$	8.44332	+	15.2820i	0.761309	+	1.37793i
$124$		0			0
$125$	−7.53670	+	5.47573i	−0.674103	+	0.489764i
$126$		0			0
$127$	3.75184	−	11.5470i	0.332922	−	1.02463i	−0.634814	−	0.772665i	$-0.718923\pi$
$127$	3.75184	−	11.5470i	0.332922	−	1.02463i	0.967736	−	0.251965i	$-0.0810767\pi$
$128$		0			0
$129$	4.33161	−	3.14710i	0.381377	−	0.277086i
$130$		0			0
$131$	−3.45567	−	10.6355i	−0.301924	−	0.929226i	−0.980807	−	0.194980i	$-0.937536\pi$
$131$	−3.45567	−	10.6355i	−0.301924	−	0.929226i	0.678884	−	0.734246i	$-0.262464\pi$
$132$		0			0
$133$	0.207626	+	0.639008i	0.0180035	+	0.0554090i
$134$		0			0
$135$	−1.26466	+	3.89221i	−0.108844	+	0.334988i
$136$		0			0
$137$	20.6995			1.76847			0.884237	−	0.467038i	$-0.154679\pi$
$137$	20.6995			1.76847			0.884237	+	0.467038i	$0.154679\pi$
$138$		0			0
$139$	−8.66184	−	6.29319i	−0.734687	−	0.533782i	0.156355	−	0.987701i	$-0.450025\pi$
$139$	−8.66184	−	6.29319i	−0.734687	−	0.533782i	−0.891043	+	0.453919i	$0.850025\pi$
$140$		0			0
$141$	−19.8264	+	14.4047i	−1.66968	+	1.21310i
$142$		0			0
$143$	−8.18906	−	5.94970i	−0.684803	−	0.497539i
$144$		0			0
$145$	1.51928	+	1.10382i	0.126169	+	0.0916671i
$146$		0			0
$147$	0.842594	+	2.59324i	0.0694959	+	0.213887i
$148$		0			0
$149$	−3.96755	+	12.2109i	−0.325034	+	1.00035i	0.646391	+	0.763006i	$0.276277\pi$
$149$	−3.96755	+	12.2109i	−0.325034	+	1.00035i	−0.971425	+	0.237346i	$0.923723\pi$
$150$		0			0
$151$	−2.78585	+	2.02404i	−0.226709	+	0.164714i	−0.695342	−	0.718679i	$-0.744747\pi$
$151$	−2.78585	+	2.02404i	−0.226709	+	0.164714i	0.468632	+	0.883393i	$0.344747\pi$
$152$		0			0
$153$	7.22407	+	22.2334i	0.584032	+	1.79747i
$154$		0			0
$155$	1.01288			0.0813561
$156$		0			0
$157$	4.68426	+	3.40331i	0.373844	+	0.271614i	0.758803	−	0.651320i	$-0.225784\pi$
$157$	4.68426	+	3.40331i	0.373844	+	0.271614i	−0.384959	+	0.922934i	$0.625784\pi$
$158$		0			0
$159$	0.879559	−	2.70701i	0.0697536	−	0.214680i
$160$		0			0
$161$	6.28894			0.495638
$162$		0			0
$163$	19.6328			1.53776			0.768879	−	0.639395i	$-0.220815\pi$
$163$	19.6328			1.53776			0.768879	+	0.639395i	$0.220815\pi$
$164$		0			0
$165$	11.7888			0.917756
$166$		0			0
$167$	−1.44663			−0.111944			−0.0559719	−	0.998432i	$-0.517826\pi$
$167$	−1.44663			−0.111944			−0.0559719	+	0.998432i	$0.517826\pi$
$168$		0			0
$169$	−2.16382	+	6.65954i	−0.166447	+	0.512272i
$170$		0			0
$171$	2.41066	+	1.75145i	0.184348	+	0.133936i
$172$		0			0
$173$	−2.41833			−0.183862			−0.0919312	−	0.995765i	$-0.529304\pi$
$173$	−2.41833			−0.183862			−0.0919312	+	0.995765i	$0.529304\pi$
$174$		0			0
$175$	1.20695	+	3.71462i	0.0912371	+	0.280799i
$176$		0			0
$177$	−25.6788	+	18.6567i	−1.93013	+	1.40232i
$178$		0			0
$179$	0.119055	−	0.366412i	0.00889855	−	0.0273869i	−0.946509	−	0.322678i	$-0.895417\pi$
$179$	0.119055	−	0.366412i	0.00889855	−	0.0273869i	0.955407	+	0.295291i	$0.0954168\pi$
$180$		0			0
$181$	−5.66312	−	17.4293i	−0.420936	−	1.29551i	−0.906832	−	0.421492i	$-0.861507\pi$
$181$	−5.66312	−	17.4293i	−0.420936	−	1.29551i	0.485896	−	0.874016i	$-0.338493\pi$
$182$		0			0
$183$	−21.5751	−	15.6753i	−1.59488	−	1.15875i
$184$		0			0
$185$	−1.30357	−	0.947096i	−0.0958401	−	0.0696319i
$186$		0			0
$187$	17.6263	−	12.8063i	1.28896	−	0.936488i
$188$		0			0
$189$	3.16517	+	2.29963i	0.230232	+	0.167273i
$190$		0			0
$191$	5.30277			0.383695			0.191848	−	0.981425i	$-0.438552\pi$
$191$	5.30277			0.383695			0.191848	+	0.981425i	$0.438552\pi$
$192$		0			0
$193$	−0.417895	+	1.28615i	−0.0300807	+	0.0925789i	−0.964970	−	0.262361i	$-0.915499\pi$
$193$	−0.417895	+	1.28615i	−0.0300807	+	0.0925789i	0.934889	+	0.354940i	$0.115499\pi$
$194$		0			0
$195$	2.15856	+	6.64335i	0.154577	+	0.475740i
$196$		0			0
$197$	−2.28015	−	7.01757i	−0.162454	−	0.499981i	0.836386	−	0.548141i	$-0.184664\pi$
$197$	−2.28015	−	7.01757i	−0.162454	−	0.499981i	−0.998840	+	0.0481598i	$0.984664\pi$
$198$		0			0
$199$	12.0438	−	8.75035i	0.853764	−	0.620296i	−0.0724171	−	0.997374i	$-0.523071\pi$
$199$	12.0438	−	8.75035i	0.853764	−	0.620296i	0.926181	+	0.377078i	$0.123071\pi$
$200$		0			0
$201$	−7.54809	+	23.2306i	−0.532401	+	1.63856i
$202$		0			0
$203$	1.45240	−	1.05523i	0.101938	−	0.0740625i
$204$		0			0
$205$	−6.57667	+	1.26894i	−0.459335	+	0.0886264i
$206$		0			0
$207$	22.5638	−	16.3936i	1.56830	−	1.13943i
$208$		0			0
$209$	0.858153	−	2.64112i	0.0593597	−	0.182690i
$210$		0			0
$211$	1.20084	−	0.872464i	0.0826695	−	0.0600629i	−0.545683	−	0.837992i	$-0.683730\pi$
$211$	1.20084	−	0.872464i	0.0826695	−	0.0600629i	0.628352	+	0.777929i	$0.283730\pi$
$212$		0			0
$213$	−10.4108	−	32.0412i	−0.713337	−	2.19542i
$214$		0			0
$215$	0.634730	+	1.95350i	0.0432883	+	0.133228i
$216$		0			0
$217$	0.299218	−	0.920897i	0.0203122	−	0.0625146i
$218$		0			0
$219$	35.5461			2.40198
$220$		0			0
$221$	10.4442	+	7.58813i	0.702551	+	0.510433i
$222$		0			0
$223$	−3.13356	+	2.27666i	−0.209839	+	0.152457i	−0.687741	−	0.725956i	$-0.741397\pi$
$223$	−3.13356	+	2.27666i	−0.209839	+	0.152457i	0.477902	+	0.878413i	$0.341397\pi$
$224$		0			0
$225$	14.0134	+	10.1813i	0.934227	+	0.678756i
$226$		0			0
$227$	3.33708	+	2.42453i	0.221490	+	0.160922i	0.692997	−	0.720941i	$-0.256290\pi$
$227$	3.33708	+	2.42453i	0.221490	+	0.160922i	−0.471507	+	0.881862i	$0.656290\pi$
$228$		0			0
$229$	3.64782	+	11.2268i	0.241055	+	0.741891i	0.996260	+	0.0864026i	$0.0275372\pi$
$229$	3.64782	+	11.2268i	0.241055	+	0.741891i	−0.755205	+	0.655488i	$0.772463\pi$
$230$		0			0
$231$	3.48257	−	10.7183i	0.229137	−	0.705210i
$232$		0			0
$233$	−2.90518	+	2.11073i	−0.190324	+	0.138279i	−0.678867	−	0.734261i	$-0.737529\pi$
$233$	−2.90518	+	2.11073i	−0.190324	+	0.138279i	0.488543	+	0.872540i	$0.337529\pi$
$234$		0			0
$235$	−2.90525	−	8.94144i	−0.189518	−	0.583275i
$236$		0			0
$237$	15.3176			0.994983
$238$		0			0
$239$	−16.9319	−	12.3018i	−1.09524	−	0.795736i	−0.114961	−	0.993370i	$-0.536674\pi$
$239$	−16.9319	−	12.3018i	−1.09524	−	0.795736i	−0.980276	+	0.197634i	$0.936674\pi$
$240$		0			0
$241$	−5.18744	+	15.9653i	−0.334153	+	1.02842i	0.632985	+	0.774164i	$0.281829\pi$
$241$	−5.18744	+	15.9653i	−0.334153	+	1.02842i	−0.967138	+	0.254252i	$0.918171\pi$
$242$		0			0
$243$	−18.9266			−1.21414
$244$		0			0
$245$	−1.04605			−0.0668295
$246$		0			0
$247$	1.64549			0.104700
$248$		0			0
$249$	−43.5082			−2.75722
$250$		0			0
$251$	−1.04040	+	3.20201i	−0.0656693	+	0.202109i	−0.978507	−	0.206213i	$-0.933886\pi$
$251$	−1.04040	+	3.20201i	−0.0656693	+	0.202109i	0.912838	+	0.408322i	$0.133886\pi$
$252$		0			0
$253$	−21.0289	−	15.2784i	−1.32208	−	0.960546i
$254$		0			0
$255$	−15.0352			−0.941540
$256$		0			0
$257$	2.64443	+	8.13872i	0.164955	+	0.507679i	0.999033	−	0.0439672i	$-0.0139997\pi$
$257$	2.64443	+	8.13872i	0.164955	+	0.507679i	−0.834078	+	0.551647i	$0.814000\pi$
$258$		0			0
$259$	−1.24618	+	0.905405i	−0.0774340	+	0.0562591i
$260$		0			0
$261$	2.46030	−	7.57202i	0.152289	−	0.468696i
$262$		0			0
$263$	0.0925396	+	0.284808i	0.00570624	+	0.0175620i	0.953869	−	0.300223i	$-0.0970610\pi$
$263$	0.0925396	+	0.284808i	0.00570624	+	0.0175620i	−0.948163	+	0.317785i	$0.897061\pi$
$264$		0			0
$265$	0.883397	+	0.641826i	0.0542667	+	0.0394270i
$266$		0			0
$267$	−0.149351	−	0.108510i	−0.00914012	−	0.00664069i
$268$		0			0
$269$	−23.4802	+	17.0594i	−1.43161	+	1.04013i	−0.441899	+	0.897065i	$0.645695\pi$
$269$	−23.4802	+	17.0594i	−1.43161	+	1.04013i	−0.989714	+	0.143062i	$0.954305\pi$
$270$		0			0
$271$	1.72631	+	1.25424i	0.104866	+	0.0761897i	0.638983	−	0.769221i	$-0.279356\pi$
$271$	1.72631	+	1.25424i	0.104866	+	0.0761897i	−0.534116	+	0.845411i	$0.679356\pi$
$272$		0			0
$273$	6.67774			0.404156
$274$		0			0
$275$	4.98853	−	15.3531i	0.300820	−	0.925828i
$276$		0			0
$277$	9.36577	+	28.8249i	0.562735	+	1.73192i	0.674588	+	0.738194i	$0.264321\pi$
$277$	9.36577	+	28.8249i	0.562735	+	1.73192i	−0.111854	+	0.993725i	$0.535679\pi$
$278$		0			0
$279$	−1.32698	−	4.08403i	−0.0794443	−	0.244505i
$280$		0			0
$281$	−18.4906	+	13.4342i	−1.10306	+	0.801417i	−0.981556	−	0.191175i	$-0.938770\pi$
$281$	−18.4906	+	13.4342i	−1.10306	+	0.801417i	−0.121499	+	0.992592i	$0.538770\pi$
$282$		0			0
$283$	−5.81755	+	17.9046i	−0.345817	+	1.06432i	0.615328	+	0.788271i	$0.289024\pi$
$283$	−5.81755	+	17.9046i	−0.345817	+	1.06432i	−0.961145	+	0.276044i	$0.910976\pi$
$284$		0			0
$285$	−1.55040	+	1.12643i	−0.0918380	+	0.0667242i
$286$		0			0
$287$	−0.789135	+	6.35431i	−0.0465812	+	0.375083i
$288$		0			0
$289$	−8.72699	+	6.34053i	−0.513352	+	0.372972i
$290$		0			0
$291$	−2.51587	+	7.74304i	−0.147483	+	0.453905i
$292$		0			0
$293$	1.77976	−	1.29307i	0.103975	−	0.0755419i	−0.534583	−	0.845116i	$-0.679531\pi$
$293$	1.77976	−	1.29307i	0.103975	−	0.0755419i	0.638558	+	0.769574i	$0.279531\pi$
$294$		0			0
$295$	−3.76283	−	11.5808i	−0.219080	−	0.674260i
$296$		0			0
$297$	−4.99693	−	15.3790i	−0.289951	−	0.892379i
$298$		0			0
$299$	4.75942	−	14.6480i	0.275244	−	0.847115i
$300$		0			0
$301$	1.96361			0.113181
$302$		0			0
$303$	−20.1776	−	14.6599i	−1.15917	−	0.842189i
$304$		0			0
$305$	8.27693	−	6.01354i	0.473935	−	0.344334i
$306$		0			0
$307$	2.50582	+	1.82059i	0.143015	+	0.103906i	0.656992	−	0.753897i	$-0.271828\pi$
$307$	2.50582	+	1.82059i	0.143015	+	0.103906i	−0.513977	+	0.857804i	$0.671828\pi$
$308$		0			0
$309$	−14.6669	−	10.6561i	−0.834372	−	0.606207i
$310$		0			0
$311$	−7.74512	−	23.8370i	−0.439186	−	1.35167i	−0.888736	−	0.458420i	$-0.848416\pi$
$311$	−7.74512	−	23.8370i	−0.439186	−	1.35167i	0.449550	−	0.893255i	$-0.351584\pi$
$312$		0			0
$313$	−5.18696	+	15.9638i	−0.293184	+	0.902328i	0.690641	+	0.723198i	$0.257328\pi$
$313$	−5.18696	+	15.9638i	−0.293184	+	0.902328i	−0.983825	+	0.179131i	$0.942672\pi$
$314$		0			0
$315$	−3.75307	+	2.72677i	−0.211462	+	0.153636i
$316$		0			0
$317$	1.16318	+	3.57989i	0.0653306	+	0.201067i	0.978393	−	0.206752i	$-0.0662894\pi$
$317$	1.16318	+	3.57989i	0.0653306	+	0.201067i	−0.913063	+	0.407819i	$0.866289\pi$
$318$		0			0
$319$	−7.42010			−0.415446
$320$		0			0
$321$	−0.575115	−	0.417845i	−0.0320998	−	0.0233219i
$322$		0			0
$323$	−1.09447	+	3.36844i	−0.0608980	+	0.187425i
$324$		0			0
$325$	9.56538			0.530592
$326$		0			0
$327$	−30.4922			−1.68622
$328$		0			0
$329$	−8.98773			−0.495510
$330$		0			0
$331$	27.8159			1.52890			0.764450	−	0.644683i	$-0.223011\pi$
$331$	27.8159			1.52890			0.764450	+	0.644683i	$0.223011\pi$
$332$		0			0
$333$	−2.11098	+	6.49693i	−0.115681	+	0.356030i
$334$		0			0
$335$	−7.58102	−	5.50793i	−0.414195	−	0.300931i
$336$		0			0
$337$	−13.1351			−0.715513			−0.357756	−	0.933815i	$-0.616458\pi$
$337$	−13.1351			−0.715513			−0.357756	+	0.933815i	$0.616458\pi$
$338$		0			0
$339$	−16.1866	−	49.8172i	−0.879135	−	2.70570i
$340$		0			0
$341$	−3.23776	+	2.35237i	−0.175335	+	0.127388i
$342$		0			0
$343$	−0.309017	+	0.951057i	−0.0166853	+	0.0513522i
$344$		0			0
$345$	5.54303	+	17.0597i	0.298426	+	0.918462i
$346$		0			0
$347$	−25.8175	−	18.7575i	−1.38596	−	1.00696i	−0.996295	−	0.0859972i	$-0.972592\pi$
$347$	−25.8175	−	18.7575i	−1.38596	−	1.00696i	−0.389660	−	0.920959i	$-0.627408\pi$
$348$		0			0
$349$	−6.54256	−	4.75345i	−0.350215	−	0.254446i	0.398744	−	0.917062i	$-0.369446\pi$
$349$	−6.54256	−	4.75345i	−0.350215	−	0.254446i	−0.748959	+	0.662616i	$0.769446\pi$
$350$		0			0
$351$	7.75159	−	5.63186i	0.413749	−	0.300606i
$352$		0			0
$353$	8.30445	+	6.03354i	0.442001	+	0.321133i	0.786430	−	0.617680i	$-0.211927\pi$
$353$	8.30445	+	6.03354i	0.442001	+	0.321133i	−0.344428	+	0.938813i	$0.611927\pi$
$354$		0			0
$355$	12.9246			0.685967
$356$		0			0
$357$	−4.44161	+	13.6699i	−0.235075	+	0.723486i
$358$		0			0
$359$	0.209175	+	0.643775i	0.0110399	+	0.0339772i	0.956425	−	0.291979i	$-0.0943138\pi$
$359$	0.209175	+	0.643775i	0.0110399	+	0.0339772i	−0.945385	+	0.325956i	$0.894314\pi$
$360$		0			0
$361$	−5.73182	−	17.6407i	−0.301675	−	0.928459i
$362$		0			0
$363$	−13.4187	+	9.74929i	−0.704301	+	0.511705i
$364$		0			0
$365$	−4.21395	+	12.9692i	−0.220568	+	0.678840i
$366$		0			0
$367$	−13.7959	+	10.0233i	−0.720139	+	0.523211i	−0.886429	−	0.462865i	$-0.846821\pi$
$367$	−13.7959	+	10.0233i	−0.720139	+	0.523211i	0.166290	+	0.986077i	$0.446821\pi$
$368$		0			0
$369$	13.7327	+	24.8554i	0.714895	+	1.29392i
$370$		0			0
$371$	0.844510	−	0.613572i	0.0438448	−	0.0318551i
$372$		0			0
$373$	2.01880	−	6.21322i	0.104529	−	0.321708i	−0.885090	−	0.465419i	$-0.845904\pi$
$373$	2.01880	−	6.21322i	0.104529	−	0.321708i	0.989620	+	0.143711i	$0.0459035\pi$
$374$		0			0
$375$	−20.5502	+	14.9306i	−1.06121	+	0.771014i
$376$		0			0
$377$	−1.35864	−	4.18146i	−0.0699735	−	0.215356i
$378$		0			0
$379$	4.77246	+	14.6881i	0.245145	+	0.754478i	0.995613	+	0.0935709i	$0.0298282\pi$
$379$	4.77246	+	14.6881i	0.245145	+	0.754478i	−0.750468	+	0.660907i	$0.770172\pi$
$380$		0			0
$381$	10.2301	−	31.4851i	0.524105	−	1.61303i
$382$		0			0
$383$	27.8670			1.42394			0.711968	−	0.702212i	$-0.247804\pi$
$383$	27.8670			1.42394			0.711968	+	0.702212i	$0.247804\pi$
$384$		0			0
$385$	3.49777	+	2.54128i	0.178263	+	0.129516i
$386$		0			0
$387$	7.04516	−	5.11861i	0.358126	−	0.260194i
$388$		0			0
$389$	−26.9330	−	19.5680i	−1.36556	−	0.992135i	−0.998070	−	0.0621067i	$-0.980218\pi$
$389$	−26.9330	−	19.5680i	−1.36556	−	0.992135i	−0.367487	−	0.930029i	$-0.619782\pi$
$390$		0			0
$391$	26.8199	+	19.4858i	1.35634	+	0.985439i
$392$		0			0
$393$	−9.42255	−	28.9996i	−0.475305	−	1.46284i
$394$		0			0
$395$	−1.81588	+	5.58871i	−0.0913669	+	0.281198i
$396$		0			0
$397$	−1.16779	+	0.848448i	−0.0586096	+	0.0425824i	−0.616704	−	0.787195i	$-0.711533\pi$
$397$	−1.16779	+	0.848448i	−0.0586096	+	0.0425824i	0.558095	+	0.829777i	$0.311533\pi$
$398$		0			0
$399$	0.566133	+	1.74238i	0.0283421	+	0.0872280i
$400$		0			0
$401$	−0.481725			−0.0240562			−0.0120281	−	0.999928i	$-0.503829\pi$
$401$	−0.481725			−0.0240562			−0.0120281	+	0.999928i	$0.503829\pi$
$402$		0			0
$403$	−1.91848	−	1.39385i	−0.0955661	−	0.0694329i
$404$		0			0
$405$	0.852311	−	2.62314i	0.0423517	−	0.130345i
$406$		0			0
$407$	6.36658			0.315580
$408$		0			0
$409$	23.1708			1.14572			0.572862	−	0.819652i	$-0.305833\pi$
$409$	23.1708			1.14572			0.572862	+	0.819652i	$0.305833\pi$
$410$		0			0
$411$	56.4410			2.78403
$412$		0			0
$413$	−11.6407			−0.572803
$414$		0			0
$415$	5.15786	−	15.8743i	0.253189	−	0.779236i
$416$		0			0
$417$	−23.6181	−	17.1596i	−1.15659	−	0.840309i
$418$		0			0
$419$	16.0917			0.786130			0.393065	−	0.919511i	$-0.371415\pi$
$419$	16.0917			0.786130			0.393065	+	0.919511i	$0.371415\pi$
$420$		0			0
$421$	6.80558	+	20.9454i	0.331683	+	1.02082i	0.968333	+	0.249663i	$0.0803199\pi$
$421$	6.80558	+	20.9454i	0.331683	+	1.02082i	−0.636649	+	0.771153i	$0.719680\pi$
$422$		0			0
$423$	−32.2467	+	23.4286i	−1.56789	+	1.13914i
$424$		0			0
$425$	−6.36228	+	19.5811i	−0.308616	+	0.949822i
$426$		0			0
$427$	−3.02233	−	9.30179i	−0.146261	−	0.450145i
$428$		0			0
$429$	−22.3290	−	16.2230i	−1.07806	−	0.783253i
$430$		0			0
$431$	−20.1887	−	14.6680i	−0.972456	−	0.706531i	−0.0164463	−	0.999865i	$-0.505235\pi$
$431$	−20.1887	−	14.6680i	−0.972456	−	0.706531i	−0.956010	+	0.293334i	$0.905235\pi$
$432$		0			0
$433$	28.3105	−	20.5688i	1.36052	−	0.988474i	0.362106	−	0.932137i	$-0.382058\pi$
$433$	28.3105	−	20.5688i	1.36052	−	0.988474i	0.998412	−	0.0563370i	$-0.0179421\pi$
$434$		0			0
$435$	4.14259	+	3.00977i	0.198622	+	0.144307i
$436$		0			0
$437$	4.22550			0.202133
$438$		0			0
$439$	0.835814	−	2.57237i	0.0398912	−	0.122773i	−0.929128	−	0.369759i	$-0.879440\pi$
$439$	0.835814	−	2.57237i	0.0398912	−	0.122773i	0.969019	+	0.246986i	$0.0794403\pi$
$440$		0			0
$441$	1.37044	+	4.21778i	0.0652591	+	0.200847i
$442$		0			0
$443$	1.35901	+	4.18259i	0.0645684	+	0.198721i	0.978136	−	0.207965i	$-0.0666842\pi$
$443$	1.35901	+	4.18259i	0.0645684	+	0.198721i	−0.913568	+	0.406686i	$0.866684\pi$
$444$		0			0
$445$	0.0572958	−	0.0416279i	0.00271608	−	0.00197335i
$446$		0			0
$447$	−10.8183	+	33.2952i	−0.511687	+	1.57481i
$448$		0			0
$449$	−1.36392	+	0.990944i	−0.0643672	+	0.0467655i	−0.619504	−	0.784994i	$-0.712666\pi$
$449$	−1.36392	+	0.990944i	−0.0643672	+	0.0467655i	0.555136	+	0.831759i	$0.312666\pi$
$450$		0			0
$451$	18.0759	−	19.3304i	0.851163	−	0.910232i
$452$		0			0
$453$	−7.59616	+	5.51893i	−0.356899	+	0.259302i
$454$		0			0
$455$	−0.791640	+	2.43642i	−0.0371127	+	0.114221i
$456$		0			0
$457$	−17.2942	+	12.5649i	−0.808987	+	0.587764i	−0.913537	−	0.406756i	$-0.866660\pi$
$457$	−17.2942	+	12.5649i	−0.808987	+	0.587764i	0.104550	+	0.994520i	$0.466660\pi$
$458$		0			0
$459$	6.37299	+	19.6140i	0.297466	+	0.915505i
$460$		0			0
$461$	7.11623	+	21.9015i	0.331436	+	1.02005i	0.968451	+	0.249204i	$0.0801688\pi$
$461$	7.11623	+	21.9015i	0.331436	+	1.02005i	−0.637015	+	0.770851i	$0.719831\pi$
$462$		0			0
$463$	7.59811	−	23.3846i	0.353114	−	1.08677i	−0.603981	−	0.796999i	$-0.706420\pi$
$463$	7.59811	−	23.3846i	0.353114	−	1.08677i	0.957095	−	0.289775i	$-0.0935803\pi$
$464$		0			0
$465$	2.76180			0.128075
$466$		0			0
$467$	9.70544	+	7.05142i	0.449114	+	0.326301i	0.789246	−	0.614077i	$-0.210472\pi$
$467$	9.70544	+	7.05142i	0.449114	+	0.326301i	−0.340132	+	0.940378i	$0.610472\pi$
$468$		0			0
$469$	−7.24730	+	5.26547i	−0.334649	+	0.243137i
$470$		0			0
$471$	12.7725	+	9.27978i	0.588527	+	0.427590i
$472$		0			0
$473$	−6.56592	−	4.77042i	−0.301901	−	0.219344i
$474$		0			0
$475$	0.810944	+	2.49583i	0.0372087	+	0.114516i
$476$		0			0
$477$	1.43056	−	4.40282i	0.0655010	−	0.201591i
$478$		0			0
$479$	−15.7987	+	11.4784i	−0.721859	+	0.524461i	−0.886978	−	0.461812i	$-0.847199\pi$
$479$	−15.7987	+	11.4784i	−0.721859	+	0.524461i	0.165118	+	0.986274i	$0.447199\pi$
$480$		0			0
$481$	1.16574	+	3.58777i	0.0531530	+	0.163588i
$482$		0			0
$483$	17.1480			0.780261
$484$		0			0
$485$	−2.52684	−	1.83586i	−0.114738	−	0.0833620i
$486$		0			0
$487$	8.12166	−	24.9959i	0.368028	−	1.13267i	−0.580036	−	0.814591i	$-0.696961\pi$
$487$	8.12166	−	24.9959i	0.368028	−	1.13267i	0.948063	−	0.318082i	$-0.103039\pi$
$488$		0			0
$489$	53.5325			2.42082
$490$		0			0
$491$	9.81236			0.442825			0.221413	−	0.975180i	$-0.428933\pi$
$491$	9.81236			0.442825			0.221413	+	0.975180i	$0.428933\pi$
$492$		0			0
$493$	9.46345			0.426212
$494$		0			0
$495$	19.1739			0.861804
$496$		0			0
$497$	3.81811	−	11.7509i	0.171266	−	0.527102i
$498$		0			0
$499$	−32.4937	−	23.6081i	−1.45462	−	1.05684i	−0.984724	−	0.174120i	$-0.944292\pi$
$499$	−32.4937	−	23.6081i	−1.45462	−	1.05684i	−0.469895	−	0.882723i	$-0.655708\pi$
$500$		0			0
$501$	−3.94452			−0.176228
$502$		0			0
$503$	6.94743	+	21.3820i	0.309770	+	0.953376i	0.977854	+	0.209289i	$0.0671150\pi$
$503$	6.94743	+	21.3820i	0.309770	+	0.953376i	−0.668083	+	0.744086i	$0.732885\pi$
$504$		0			0
$505$	7.74079	−	5.62402i	0.344461	−	0.250265i
$506$		0			0
$507$	−5.90005	+	18.1585i	−0.262031	+	0.806447i
$508$		0			0
$509$	0.924888	+	2.84651i	0.0409949	+	0.126169i	0.969459	−	0.245252i	$-0.0788706\pi$
$509$	0.924888	+	2.84651i	0.0409949	+	0.126169i	−0.928464	+	0.371421i	$0.878871\pi$
$510$		0			0
$511$	10.5466	+	7.66258i	0.466556	+	0.338972i
$512$		0			0
$513$	2.12665	+	1.54510i	0.0938940	+	0.0682180i
$514$		0			0
$515$	5.62671	−	4.08804i	0.247942	−	0.180141i
$516$		0			0
$517$	30.0531	+	21.8349i	1.32174	+	0.960297i
$518$		0			0
$519$	−6.59404			−0.289446
$520$		0			0
$521$	−6.03650	+	18.5784i	−0.264464	+	0.813935i	0.727353	+	0.686264i	$0.240750\pi$
$521$	−6.03650	+	18.5784i	−0.264464	+	0.813935i	−0.991816	+	0.127672i	$0.959250\pi$
$522$		0			0
$523$	5.44378	+	16.7542i	0.238040	+	0.732611i	0.996704	+	0.0811289i	$0.0258526\pi$
$523$	5.44378	+	16.7542i	0.238040	+	0.732611i	−0.758664	+	0.651482i	$0.774147\pi$
$524$		0			0
$525$	3.29099	+	10.1286i	0.143631	+	0.442049i
$526$		0			0
$527$	4.12938	−	3.00017i	0.179878	−	0.130689i
$528$		0			0
$529$	5.11447	−	15.7407i	0.222368	−	0.684379i
$530$		0			0
$531$	−41.7653	+	30.3443i	−1.81246	+	1.31683i
$532$		0			0
$533$	14.2030	+	6.64692i	0.615202	+	0.287910i
$534$		0			0
$535$	0.220633	−	0.160299i	0.00953879	−	0.00693033i
$536$		0			0
$537$	0.324625	−	0.999093i	0.0140086	−	0.0431140i
$538$		0			0
$539$	3.34380	−	2.42941i	0.144028	−	0.104642i
$540$		0			0
$541$	12.1583	+	37.4193i	0.522725	+	1.60878i	0.768772	+	0.639523i	$0.220868\pi$
$541$	12.1583	+	37.4193i	0.522725	+	1.60878i	−0.246047	+	0.969258i	$0.579132\pi$
$542$		0			0
$543$	−15.4416	−	47.5242i	−0.662661	−	2.03946i
$544$		0			0
$545$	3.61482	−	11.1253i	0.154842	−	0.476554i
$546$		0			0
$547$	14.9602			0.639653			0.319827	−	0.947476i	$-0.396375\pi$
$547$	14.9602			0.639653			0.319827	+	0.947476i	$0.396375\pi$
$548$		0			0
$549$	−35.0910	−	25.4951i	−1.49765	−	1.08810i
$550$		0			0
$551$	0.975855	−	0.709000i	0.0415728	−	0.0302044i
$552$		0			0
$553$	4.54477	+	3.30197i	0.193263	+	0.140414i
$554$		0			0
$555$	−3.55442	−	2.58244i	−0.150877	−	0.109618i
$556$		0			0
$557$	−1.97547	−	6.07987i	−0.0837033	−	0.257612i	0.900442	−	0.434976i	$-0.143243\pi$
$557$	−1.97547	−	6.07987i	−0.0837033	−	0.257612i	−0.984145	+	0.177364i	$0.943243\pi$
$558$		0			0
$559$	1.48605	−	4.57358i	0.0628530	−	0.193442i
$560$		0			0
$561$	48.0615	−	34.9187i	2.02916	−	1.47427i
$562$		0			0
$563$	10.0780	+	31.0168i	0.424736	+	1.30720i	0.903247	+	0.429121i	$0.141177\pi$
$563$	10.0780	+	31.0168i	0.424736	+	1.30720i	−0.478511	+	0.878082i	$0.658823\pi$
$564$		0			0
$565$	20.0950			0.845404
$566$		0			0
$567$	−2.13315	−	1.54983i	−0.0895840	−	0.0650866i
$568$		0			0
$569$	1.63331	−	5.02681i	0.0684719	−	0.210735i	−0.910966	−	0.412482i	$-0.864662\pi$
$569$	1.63331	−	5.02681i	0.0684719	−	0.210735i	0.979438	+	0.201747i	$0.0646619\pi$
$570$		0			0
$571$	28.1348			1.17740			0.588702	−	0.808350i	$-0.299639\pi$
$571$	28.1348			1.17740			0.588702	+	0.808350i	$0.299639\pi$
$572$		0			0
$573$	14.4590			0.604034
$574$		0			0
$575$	24.5633			1.02436
$576$		0			0
$577$	37.1294			1.54572			0.772858	−	0.634579i	$-0.218827\pi$
$577$	37.1294			1.54572			0.772858	+	0.634579i	$0.218827\pi$
$578$		0			0
$579$	−1.13947	+	3.50693i	−0.0473547	+	0.145743i
$580$		0			0
$581$	−12.9090	−	9.37895i	−0.535556	−	0.389105i
$582$		0			0
$583$	−4.31449			−0.178688
$584$		0			0
$585$	3.51080	+	10.8051i	0.145154	+	0.446737i
$586$		0			0
$587$	−5.56260	+	4.04146i	−0.229593	+	0.166809i	−0.696634	−	0.717426i	$-0.745320\pi$
$587$	−5.56260	+	4.04146i	−0.229593	+	0.166809i	0.467041	+	0.884236i	$0.345320\pi$
$588$		0			0
$589$	0.201042	−	0.618744i	0.00828380	−	0.0254949i
$590$		0			0
$591$	−6.21725	−	19.1347i	−0.255744	−	0.787098i
$592$		0			0
$593$	26.9911	+	19.6101i	1.10839	+	0.805292i	0.982409	−	0.186740i	$-0.0597923\pi$
$593$	26.9911	+	19.6101i	1.10839	+	0.805292i	0.125980	+	0.992033i	$0.459792\pi$
$594$		0			0
$595$	−4.46099	−	3.24110i	−0.182883	−	0.132872i
$596$		0			0
$597$	32.8398	−	23.8595i	1.34404	−	0.976504i
$598$		0			0
$599$	19.0133	+	13.8140i	0.776864	+	0.564424i	0.904036	−	0.427456i	$-0.140590\pi$
$599$	19.0133	+	13.8140i	0.776864	+	0.564424i	−0.127172	+	0.991881i	$0.540590\pi$
$600$		0			0
$601$	8.84784			0.360911			0.180455	−	0.983583i	$-0.442243\pi$
$601$	8.84784			0.360911			0.180455	+	0.983583i	$0.442243\pi$
$602$		0			0
$603$	−12.2766	+	37.7836i	−0.499943	+	1.53867i
$604$		0			0
$605$	−1.96631	−	6.05168i	−0.0799419	−	0.246036i
$606$		0			0
$607$	10.4566	+	32.1820i	0.424419	+	1.30623i	0.903549	+	0.428484i	$0.140952\pi$
$607$	10.4566	+	32.1820i	0.424419	+	1.30623i	−0.479130	+	0.877744i	$0.659048\pi$
$608$		0			0
$609$	3.96024	−	2.87728i	0.160477	−	0.116593i
$610$		0			0
$611$	−6.80184	+	20.9339i	−0.275173	+	0.846895i
$612$		0			0
$613$	19.3302	−	14.0442i	0.780740	−	0.567241i	−0.124461	−	0.992225i	$-0.539720\pi$
$613$	19.3302	−	14.0442i	0.780740	−	0.567241i	0.905201	+	0.424984i	$0.139720\pi$
$614$		0			0
$615$	−17.9325	+	3.46000i	−0.723110	+	0.139521i
$616$		0			0
$617$	−22.3031	+	16.2041i	−0.897888	+	0.652354i	−0.937923	−	0.346845i	$-0.887253\pi$
$617$	−22.3031	+	16.2041i	−0.897888	+	0.652354i	0.0400348	+	0.999198i	$0.487253\pi$
$618$		0			0
$619$	7.85263	−	24.1679i	0.315624	−	0.971390i	−0.659873	−	0.751377i	$-0.729390\pi$
$619$	7.85263	−	24.1679i	0.315624	−	0.971390i	0.975497	−	0.220013i	$-0.0706100\pi$
$620$		0			0
$621$	19.9055	−	14.4622i	0.798782	−	0.580349i
$622$		0			0
$623$	−0.0209217	−	0.0643903i	−0.000838209	−	0.00257974i
$624$		0			0
$625$	3.02345	+	9.30522i	0.120938	+	0.372209i
$626$		0			0
$627$	2.33992	−	7.20152i	0.0934473	−	0.287601i
$628$		0			0
$629$	−8.11981			−0.323758
$630$		0			0
$631$	−7.79338	−	5.66222i	−0.310250	−	0.225410i	0.421754	−	0.906710i	$-0.361415\pi$
$631$	−7.79338	−	5.66222i	−0.310250	−	0.225410i	−0.732004	+	0.681301i	$0.761415\pi$
$632$		0			0
$633$	3.27433	−	2.37894i	0.130143	−	0.0945544i
$634$		0			0
$635$	10.2748	+	7.46504i	0.407741	+	0.296241i
$636$		0			0
$637$	1.98131	+	1.43950i	0.0785022	+	0.0570352i
$638$		0			0
$639$	−16.9327	−	52.1135i	−0.669847	−	2.06158i
$640$		0			0
$641$	−0.498643	+	1.53467i	−0.0196952	+	0.0606156i	−0.960421	−	0.278552i	$-0.910145\pi$
$641$	−0.498643	+	1.53467i	−0.0196952	+	0.0606156i	0.940726	+	0.339168i	$0.110145\pi$
$642$		0			0
$643$	15.5733	−	11.3147i	0.614153	−	0.446208i	−0.236721	−	0.971578i	$-0.576073\pi$
$643$	15.5733	−	11.3147i	0.614153	−	0.446208i	0.850874	+	0.525369i	$0.176073\pi$
$644$		0			0
$645$	1.73071	+	5.32659i	0.0681468	+	0.209734i
$646$		0			0
$647$	46.2762			1.81931			0.909653	−	0.415368i	$-0.136347\pi$
$647$	46.2762			1.81931			0.909653	+	0.415368i	$0.136347\pi$
$648$		0			0
$649$	38.9243	+	28.2801i	1.52791	+	1.11009i
$650$		0			0
$651$	0.815874	−	2.51100i	0.0319766	−	0.0984139i
$652$		0			0
$653$	−10.5586			−0.413192			−0.206596	−	0.978426i	$-0.566239\pi$
$653$	−10.5586			−0.413192			−0.206596	+	0.978426i	$0.566239\pi$
$654$		0			0
$655$	11.6977			0.457068
$656$		0			0
$657$	57.8141			2.25554
$658$		0			0
$659$	−36.3337			−1.41536			−0.707679	−	0.706534i	$-0.750258\pi$
$659$	−36.3337			−1.41536			−0.707679	+	0.706534i	$0.750258\pi$
$660$		0			0
$661$	0.831646	−	2.55954i	0.0323473	−	0.0995547i	−0.933579	−	0.358371i	$-0.883332\pi$
$661$	0.831646	−	2.55954i	0.0323473	−	0.0995547i	0.965927	+	0.258816i	$0.0833324\pi$
$662$		0			0
$663$	28.4780	+	20.6905i	1.10599	+	0.803552i
$664$		0			0
$665$	−0.702832			−0.0272546
$666$		0			0
$667$	−3.48889	−	10.7377i	−0.135090	−	0.415766i
$668$		0			0
$669$	−8.54425	+	6.20776i	−0.330340	+	0.240006i
$670$		0			0
$671$	−12.4918	+	38.4458i	−0.482240	+	1.48418i
$672$		0			0
$673$	−11.6336	−	35.8044i	−0.448441	−	1.38016i	−0.878666	−	0.477438i	$-0.841566\pi$
$673$	−11.6336	−	35.8044i	−0.448441	−	1.38016i	0.430225	−	0.902722i	$-0.358434\pi$
$674$		0			0
$675$	12.3625	+	8.98185i	0.475831	+	0.345712i
$676$		0			0
$677$	−15.0690	−	10.9483i	−0.579150	−	0.420777i	0.259268	−	0.965805i	$-0.416519\pi$
$677$	−15.0690	−	10.9483i	−0.579150	−	0.420777i	−0.838417	+	0.545029i	$0.816519\pi$
$678$		0			0
$679$	−2.41561	+	1.75504i	−0.0927026	+	0.0673524i
$680$		0			0
$681$	9.09917	+	6.61094i	0.348681	+	0.253332i
$682$		0			0
$683$	−12.7145			−0.486505			−0.243253	−	0.969963i	$-0.578214\pi$
$683$	−12.7145			−0.486505			−0.243253	+	0.969963i	$0.578214\pi$
$684$		0			0
$685$	−6.69103	+	20.5929i	−0.255651	+	0.786813i
$686$		0			0
$687$	9.94649	+	30.6121i	0.379482	+	1.16793i
$688$		0			0
$689$	−0.789993	−	2.43135i	−0.0300964	−	0.0926270i
$690$		0			0
$691$	28.6945	−	20.8477i	1.09159	−	0.793086i	0.111922	−	0.993717i	$-0.464299\pi$
$691$	28.6945	−	20.8477i	1.09159	−	0.793086i	0.979667	+	0.200631i	$0.0642994\pi$
$692$		0			0
$693$	5.66425	−	17.4328i	0.215167	−	0.662216i
$694$		0			0
$695$	9.06069	−	6.58298i	0.343692	−	0.249707i
$696$		0			0
$697$	−23.0537	+	24.6536i	−0.873221	+	0.933822i
$698$		0			0
$699$	−7.92152	+	5.75532i	−0.299619	+	0.217686i
$700$		0			0
$701$	4.37975	−	13.4795i	0.165421	−	0.509113i	−0.833646	−	0.552299i	$-0.813751\pi$
$701$	4.37975	−	13.4795i	0.165421	−	0.509113i	0.999067	+	0.0431859i	$0.0137508\pi$
$702$		0			0
$703$	−0.837301	+	0.608335i	−0.0315794	+	0.0229438i
$704$		0			0
$705$	−7.92172	−	24.3805i	−0.298349	−	0.918224i
$706$		0			0
$707$	−2.82656	−	8.69927i	−0.106304	−	0.327170i
$708$		0			0
$709$	13.3451	−	41.0721i	0.501187	−	1.54249i	−0.305901	−	0.952063i	$-0.598958\pi$
$709$	13.3451	−	41.0721i	0.501187	−	1.54249i	0.807088	−	0.590431i	$-0.201042\pi$
$710$		0			0
$711$	24.9133			0.934323
$712$		0			0
$713$	−4.92652	−	3.57932i	−0.184499	−	0.134047i
$714$		0			0
$715$	8.56614	−	6.22366i	0.320355	−	0.232752i
$716$		0			0
$717$	−46.1682	−	33.5431i	−1.72418	−	1.25269i
$718$		0			0
$719$	11.3202	+	8.22459i	0.422172	+	0.306726i	0.778511	−	0.627631i	$-0.215975\pi$
$719$	11.3202	+	8.22459i	0.422172	+	0.306726i	−0.356339	+	0.934357i	$0.615975\pi$
$720$		0			0
$721$	−2.05460	−	6.32342i	−0.0765174	−	0.235496i
$722$		0			0
$723$	−14.1446	+	43.5325i	−0.526042	+	1.61899i
$724$		0			0
$725$	5.67275	−	4.12149i	0.210681	−	0.153068i
$726$		0			0
$727$	−8.05217	−	24.7820i	−0.298638	−	0.919114i	−0.981975	−	0.189011i	$-0.939472\pi$
$727$	−8.05217	−	24.7820i	−0.298638	−	0.919114i	0.683337	−	0.730103i	$-0.260528\pi$
$728$		0			0
$729$	−43.6968			−1.61840
$730$		0			0
$731$	8.37405	+	6.08410i	0.309725	+	0.225029i
$732$		0			0
$733$	−16.5338	+	50.8858i	−0.610690	+	1.87951i	−0.159165	+	0.987252i	$0.550880\pi$
$733$	−16.5338	+	50.8858i	−0.610690	+	1.87951i	−0.451525	+	0.892258i	$0.649120\pi$
$734$		0			0
$735$	−2.85225			−0.105207
$736$		0			0
$737$	37.0255			1.36385
$738$		0			0
$739$	11.4930			0.422776			0.211388	−	0.977402i	$-0.432202\pi$
$739$	11.4930			0.422776			0.211388	+	0.977402i	$0.432202\pi$
$740$		0			0
$741$	4.48673			0.164824
$742$		0			0
$743$	−1.58756	+	4.88601i	−0.0582420	+	0.179250i	−0.975945	−	0.218017i	$-0.930041\pi$
$743$	−1.58756	+	4.88601i	−0.0582420	+	0.179250i	0.917703	+	0.397267i	$0.130041\pi$
$744$		0			0
$745$	−10.8655	−	7.89423i	−0.398080	−	0.289222i
$746$		0			0
$747$	−70.7642			−2.58913
$748$		0			0
$749$	−0.0805645	−	0.247952i	−0.00294376	−	0.00905997i
$750$		0			0
$751$	−3.07929	+	2.23724i	−0.112365	+	0.0816379i	−0.642549	−	0.766245i	$-0.722123\pi$
$751$	−3.07929	+	2.23724i	−0.112365	+	0.0816379i	0.530184	+	0.847883i	$0.322123\pi$
$752$		0			0
$753$	−2.83684	+	8.73089i	−0.103380	+	0.318171i
$754$		0			0
$755$	−1.11310	−	3.42577i	−0.0405099	−	0.124677i
$756$		0			0
$757$	20.7824	+	15.0993i	0.755350	+	0.548794i	0.897481	−	0.441054i	$-0.145395\pi$
$757$	20.7824	+	15.0993i	0.755350	+	0.548794i	−0.142131	+	0.989848i	$0.545395\pi$
$758$		0			0
$759$	−57.3394	−	41.6595i	−2.08129	−	1.51214i
$760$		0			0
$761$	−3.07780	+	2.23615i	−0.111570	+	0.0810605i	−0.642171	−	0.766561i	$-0.721966\pi$
$761$	−3.07780	+	2.23615i	−0.111570	+	0.0810605i	0.530601	+	0.847622i	$0.321966\pi$
$762$		0			0
$763$	−9.04712	−	6.57311i	−0.327528	−	0.237963i
$764$		0			0
$765$	−24.4541			−0.884139
$766$		0			0
$767$	−8.80962	+	27.1132i	−0.318097	+	0.979001i
$768$		0			0
$769$	−9.01067	−	27.7320i	−0.324933	−	1.00004i	−0.971471	−	0.237159i	$-0.923784\pi$
$769$	−9.01067	−	27.7320i	−0.324933	−	1.00004i	0.646538	−	0.762882i	$-0.276216\pi$
$770$		0			0
$771$	7.21054	+	22.1918i	0.259681	+	0.799217i
$772$		0			0
$773$	42.4091	−	30.8120i	1.52535	−	1.10823i	0.566593	−	0.823998i	$-0.308261\pi$
$773$	42.4091	−	30.8120i	1.52535	−	1.10823i	0.958755	−	0.284232i	$-0.0917388\pi$
$774$		0			0
$775$	1.16868	−	3.59683i	0.0419802	−	0.129202i
$776$		0			0
$777$	−3.39795	+	2.46876i	−0.121901	+	0.0885662i
$778$		0			0
$779$	−0.530215	+	4.26942i	−0.0189969	+	0.152968i
$780$		0			0
$781$	−41.3148	+	30.0170i	−1.47836	+	1.07409i
$782$		0			0
$783$	2.17045	−	6.67994i	0.0775654	−	0.238722i
$784$		0			0
$785$	−4.89995	+	3.56002i	−0.174887	+	0.127063i
$786$		0			0
$787$	11.1905	+	34.4409i	0.398899	+	1.22768i	0.925883	+	0.377810i	$0.123323\pi$
$787$	11.1905	+	34.4409i	0.398899	+	1.22768i	−0.526984	+	0.849875i	$0.676677\pi$
$788$		0			0
$789$	0.252327	+	0.776582i	0.00898307	+	0.0276471i
$790$		0			0
$791$	5.93635	−	18.2702i	0.211072	−	0.649614i
$792$		0			0
$793$	−23.9527			−0.850585
$794$		0			0
$795$	2.40875	+	1.75006i	0.0854296	+	0.0620682i
$796$		0			0
$797$	11.8315	−	8.59612i	0.419095	−	0.304490i	−0.358179	−	0.933653i	$-0.616602\pi$
$797$	11.8315	−	8.59612i	0.419095	−	0.304490i	0.777274	+	0.629163i	$0.216602\pi$
$798$		0			0
$799$	−38.3292	−	27.8478i	−1.35599	−	0.985184i
$800$		0			0
$801$	−0.242912	−	0.176486i	−0.00858289	−	0.00623583i
$802$		0			0
$803$	−16.6502	−	51.2442i	−0.587574	−	1.80837i
$804$		0			0
$805$	−2.03288	+	6.25655i	−0.0716495	+	0.220515i
$806$		0			0
$807$	−64.0232	+	46.5156i	−2.25372	+	1.63743i
$808$		0			0
$809$	−14.1415	−	43.5230i	−0.497188	−	1.53019i	−0.813520	−	0.581538i	$-0.802451\pi$
$809$	−14.1415	−	43.5230i	−0.497188	−	1.53019i	0.316332	−	0.948649i	$-0.397549\pi$
$810$		0			0
$811$	−32.4679			−1.14010			−0.570051	−	0.821609i	$-0.693077\pi$
$811$	−32.4679			−1.14010			−0.570051	+	0.821609i	$0.693077\pi$
$812$		0			0
$813$	4.70712	+	3.41993i	0.165086	+	0.119942i
$814$		0			0
$815$	−6.34622	+	19.5317i	−0.222298	+	0.684164i
$816$		0			0
$817$	1.31934			0.0461578
$818$		0			0
$819$	10.8611			0.379516
$820$		0			0
$821$	10.6063			0.370164			0.185082	−	0.982723i	$-0.440745\pi$
$821$	10.6063			0.370164			0.185082	+	0.982723i	$0.440745\pi$
$822$		0			0
$823$	44.5004			1.55119			0.775594	−	0.631232i	$-0.217451\pi$
$823$	44.5004			1.55119			0.775594	+	0.631232i	$0.217451\pi$
$824$		0			0
$825$	13.6022	−	41.8632i	0.473567	−	1.45749i
$826$		0			0
$827$	−14.7264	−	10.6994i	−0.512087	−	0.372053i	0.301528	−	0.953457i	$-0.402503\pi$
$827$	−14.7264	−	10.6994i	−0.512087	−	0.372053i	−0.813615	+	0.581404i	$0.802503\pi$
$828$		0			0
$829$	−21.2541			−0.738186			−0.369093	−	0.929392i	$-0.620332\pi$
$829$	−21.2541			−0.738186			−0.369093	+	0.929392i	$0.620332\pi$
$830$		0			0
$831$	25.5376	+	78.5965i	0.885888	+	2.72648i
$832$		0			0
$833$	−4.26461	+	3.09842i	−0.147760	+	0.107354i
$834$		0			0
$835$	0.467619	−	1.43918i	0.0161826	−	0.0498050i
$836$		0			0
$837$	−1.17065	−	3.60288i	−0.0404635	−	0.124534i
$838$		0			0
$839$	−45.0278	−	32.7146i	−1.55453	−	1.12943i	−0.940320	−	0.340292i	$-0.889474\pi$
$839$	−45.0278	−	32.7146i	−1.55453	−	1.12943i	−0.614212	−	0.789141i	$-0.710526\pi$
$840$		0			0
$841$	20.8541	+	15.1514i	0.719106	+	0.522461i
$842$		0			0
$843$	−50.4181	+	36.6309i	−1.73649	+	1.26163i
$844$		0			0
$845$	−5.92580	−	4.30534i	−0.203854	−	0.148108i
$846$		0			0
$847$	−6.08301			−0.209015
$848$		0			0
$849$	−15.8626	+	48.8202i	−0.544405	+	1.67550i
$850$		0			0
$851$	2.99353	+	9.21314i	0.102617	+	0.315822i
$852$		0			0
$853$	−11.1542	−	34.3291i	−0.381912	−	1.17540i	−0.938696	−	0.344747i	$-0.887965\pi$
$853$	−11.1542	−	34.3291i	−0.381912	−	1.17540i	0.556783	−	0.830658i	$-0.312035\pi$
$854$		0			0
$855$	−2.52166	+	1.83209i	−0.0862390	+	0.0626563i
$856$		0			0
$857$	10.6067	−	32.6440i	0.362317	−	1.11510i	−0.589327	−	0.807895i	$-0.700607\pi$
$857$	10.6067	−	32.6440i	0.362317	−	1.11510i	0.951644	−	0.307203i	$-0.0993931\pi$
$858$		0			0
$859$	−3.29173	+	2.39158i	−0.112313	+	0.0815998i	−0.642524	−	0.766266i	$-0.722113\pi$
$859$	−3.29173	+	2.39158i	−0.112313	+	0.0815998i	0.530211	+	0.847866i	$0.322113\pi$
$860$		0			0
$861$	−2.15173	+	17.3262i	−0.0733307	+	0.590477i
$862$		0			0
$863$	17.2048	−	12.5000i	0.585658	−	0.425505i	−0.255101	−	0.966914i	$-0.582109\pi$
$863$	17.2048	−	12.5000i	0.585658	−	0.425505i	0.840759	+	0.541409i	$0.182109\pi$
$864$		0			0
$865$	0.781717	−	2.40588i	0.0265792	−	0.0818023i
$866$		0			0
$867$	−23.7958	+	17.2887i	−0.808148	+	0.587154i
$868$		0			0
$869$	−7.17494	−	22.0822i	−0.243393	−	0.749087i
$870$		0			0
$871$	6.77946	+	20.8650i	0.229713	+	0.706985i
$872$		0			0
$873$	−4.09194	+	12.5937i	−0.138491	+	0.426232i
$874$		0			0
$875$	−9.31587			−0.314934
$876$		0			0
$877$	−1.00294	−	0.728677i	−0.0338668	−	0.0246057i	0.570723	−	0.821143i	$-0.306663\pi$
$877$	−1.00294	−	0.728677i	−0.0338668	−	0.0246057i	−0.604590	+	0.796537i	$0.706663\pi$
$878$		0			0
$879$	4.85285	−	3.52580i	0.163683	−	0.118922i
$880$		0			0
$881$	26.4640	+	19.2272i	0.891594	+	0.647781i	0.936293	−	0.351220i	$-0.114233\pi$
$881$	26.4640	+	19.2272i	0.891594	+	0.647781i	−0.0446991	+	0.999000i	$0.514233\pi$
$882$		0			0
$883$	−7.87102	−	5.71863i	−0.264881	−	0.192447i	0.447415	−	0.894326i	$-0.352345\pi$
$883$	−7.87102	−	5.71863i	−0.264881	−	0.192447i	−0.712296	+	0.701879i	$0.752345\pi$
$884$		0			0
$885$	−10.2601	−	31.5772i	−0.344888	−	1.06146i
$886$		0			0
$887$	7.91077	−	24.3469i	0.265618	−	0.817487i	−0.725933	−	0.687766i	$-0.758592\pi$
$887$	7.91077	−	24.3469i	0.265618	−	0.817487i	0.991550	−	0.129722i	$-0.0414084\pi$
$888$		0			0
$889$	9.82246	−	7.13643i	0.329435	−	0.239348i
$890$		0			0
$891$	3.36766	+	10.3646i	0.112821	+	0.347227i
$892$		0			0
$893$	−6.03879			−0.202080
$894$		0			0
$895$	0.326041	+	0.236883i	0.0108984	+	0.00791812i
$896$		0			0
$897$	12.9775	−	39.9405i	0.433305	−	1.33357i
$898$		0			0
$899$	−1.73833			−0.0579766
$900$		0			0
$901$	5.50261			0.183319
$902$		0			0
$903$	5.35416			0.178175
$904$		0			0
$905$	19.1701			0.637236
$906$		0			0
$907$	9.79658	−	30.1508i	0.325290	−	1.00114i	−0.646019	−	0.763321i	$-0.723568\pi$
$907$	9.79658	−	30.1508i	0.325290	−	1.00114i	0.971310	−	0.237819i	$-0.0764325\pi$
$908$		0			0
$909$	−32.8180	−	23.8437i	−1.08850	−	0.790845i
$910$		0			0
$911$	52.3995			1.73607			0.868036	−	0.496501i	$-0.165382\pi$
$911$	52.3995			1.73607			0.868036	+	0.496501i	$0.165382\pi$
$912$		0			0
$913$	20.3798	+	62.7226i	0.674473	+	2.07582i
$914$		0			0
$915$	22.5686	−	16.3971i	0.746095	−	0.542070i
$916$		0			0
$917$	3.45567	−	10.6355i	0.114116	−	0.351214i
$918$		0			0
$919$	17.0581	+	52.4994i	0.562694	+	1.73179i	0.674706	+	0.738087i	$0.264271\pi$
$919$	17.0581	+	52.4994i	0.562694	+	1.73179i	−0.112012	+	0.993707i	$0.535729\pi$
$920$		0			0
$921$	6.83261	+	4.96418i	0.225142	+	0.163575i
$922$		0			0
$923$	−24.4804	−	17.7860i	−0.805781	−	0.585434i
$924$		0			0
$925$	−4.86732	+	3.53632i	−0.160037	+	0.116273i
$926$		0			0
$927$	−23.8551	−	17.3317i	−0.783504	−	0.569249i
$928$		0			0
$929$	−43.7122			−1.43415			−0.717076	−	0.696995i	$-0.754520\pi$
$929$	−43.7122			−1.43415			−0.717076	+	0.696995i	$0.754520\pi$
$930$		0			0
$931$	−0.207626	+	0.639008i	−0.00680468	+	0.0209426i
$932$		0			0
$933$	−21.1186	−	64.9962i	−0.691390	−	2.12788i
$934$		0			0
$935$	7.04268	+	21.6751i	0.230320	+	0.708853i
$936$		0			0
$937$	−39.5531	+	28.7370i	−1.29214	+	0.938797i	−0.999846	−	0.0175303i	$-0.994420\pi$
$937$	−39.5531	+	28.7370i	−1.29214	+	0.938797i	−0.292297	+	0.956328i	$0.594420\pi$
$938$		0			0
$939$	−14.1432	+	43.5284i	−0.461547	+	1.42050i
$940$		0			0
$941$	15.3078	−	11.1218i	0.499020	−	0.362559i	−0.309623	−	0.950859i	$-0.600203\pi$
$941$	15.3078	−	11.1218i	0.499020	−	0.362559i	0.808642	+	0.588300i	$0.200203\pi$
$942$		0			0
$943$	36.4724	+	17.0688i	1.18771	+	0.555838i
$944$		0			0
$945$	−3.31091	+	2.40552i	−0.107704	+	0.0782515i
$946$		0			0
$947$	−13.8538	+	42.6376i	−0.450188	+	1.38554i	0.426505	+	0.904485i	$0.359744\pi$
$947$	−13.8538	+	42.6376i	−0.450188	+	1.38554i	−0.876693	+	0.481050i	$0.840256\pi$
$948$		0			0
$949$	25.8290	−	18.7659i	0.838445	−	0.609166i
$950$		0			0
$951$	3.17163	+	9.76126i	0.102847	+	0.316531i
$952$		0			0
$953$	−2.25934	−	6.95354i	−0.0731872	−	0.225247i	0.907771	−	0.419466i	$-0.137783\pi$
$953$	−2.25934	−	6.95354i	−0.0731872	−	0.225247i	−0.980958	+	0.194219i	$0.937783\pi$
$954$		0			0
$955$	−1.71410	+	5.27546i	−0.0554670	+	0.170710i
$956$		0			0
$957$	−20.2323			−0.654018
$958$		0			0
$959$	16.7462	+	12.1668i	0.540764	+	0.392888i
$960$		0			0
$961$	24.3210	−	17.6702i	0.784549	−	0.570008i
$962$		0			0
$963$	−0.935398	−	0.679607i	−0.0301428	−	0.0219000i
$964$		0			0
$965$	−1.14444	−	0.831485i	−0.0368409	−	0.0267665i
$966$		0			0
$967$	9.09213	+	27.9827i	0.292383	+	0.899863i	0.984088	+	0.177682i	$0.0568600\pi$
$967$	9.09213	+	27.9827i	0.292383	+	0.899863i	−0.691705	+	0.722180i	$0.743140\pi$
$968$		0			0
$969$	−2.98428	+	9.18468i	−0.0958690	+	0.295055i
$970$		0			0
$971$	24.0718	−	17.4892i	0.772502	−	0.561255i	−0.130218	−	0.991485i	$-0.541568\pi$
$971$	24.0718	−	17.4892i	0.772502	−	0.561255i	0.902719	+	0.430230i	$0.141568\pi$
$972$		0			0
$973$	−3.30853	−	10.1826i	−0.106067	−	0.326439i
$974$		0			0
$975$	26.0818			0.835287
$976$		0			0
$977$	0.844853	+	0.613822i	0.0270292	+	0.0196379i	0.601218	−	0.799085i	$-0.294682\pi$
$977$	0.844853	+	0.613822i	0.0270292	+	0.0196379i	−0.574189	+	0.818723i	$0.694682\pi$
$978$		0			0
$979$	−0.0864726	+	0.266135i	−0.00276368	+	0.00850572i
$980$		0			0
$981$	−49.5941			−1.58342
$982$		0			0
$983$	−38.1628			−1.21720			−0.608602	−	0.793476i	$-0.708269\pi$
$983$	−38.1628			−1.21720			−0.608602	+	0.793476i	$0.708269\pi$
$984$		0			0
$985$	7.71848			0.245931
$986$		0			0
$987$	−24.5068			−0.780059
$988$		0			0
$989$	3.81606	−	11.7446i	0.121344	−	0.373458i
$990$		0			0
$991$	7.54172	+	5.47938i	0.239571	+	0.174058i	0.701092	−	0.713071i	$-0.252696\pi$
$991$	7.54172	+	5.47938i	0.239571	+	0.174058i	−0.461521	+	0.887129i	$0.652696\pi$
$992$		0			0
$993$	75.8453			2.40688
$994$		0			0
$995$	4.81216	+	14.8103i	0.152556	+	0.469519i
$996$		0			0
$997$	−25.6538	+	18.6386i	−0.812463	+	0.590289i	−0.914544	−	0.404487i	$-0.867450\pi$
$997$	−25.6538	+	18.6386i	−0.812463	+	0.590289i	0.102080	+	0.994776i	$0.467450\pi$
$998$		0			0
$999$	−1.86228	+	5.73151i	−0.0589200	+	0.181337i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.n.c.365.4	✓	16
41.10	even	5	inner	1148.2.n.c.953.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.n.c.365.4	✓	16	1.1	even	1	trivial
1148.2.n.c.953.4	yes	16	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)

\(f(q)\)	\(=\)	\(q+2.72669 q^{3} +(-0.323246 + 0.994850i) q^{5} +(0.809017 + 0.587785i) q^{7} +4.43484 q^{9} +O(q^{10})\)	\(q+2.72669 q^{3} +(-0.323246 + 0.994850i) q^{5} +(0.809017 + 0.587785i) q^{7} +4.43484 q^{9} +(-1.27722 - 3.93087i) q^{11} +(1.98131 - 1.43950i) q^{13} +(-0.881393 + 2.71265i) q^{15} +(1.62894 + 5.01335i) q^{17} +(0.543573 + 0.394929i) q^{19} +(2.20594 + 1.60271i) q^{21} +(5.08786 - 3.69655i) q^{23} +(3.15985 + 2.29576i) q^{25} +3.91236 q^{27} +(0.554766 - 1.70739i) q^{29} +(-0.299218 - 0.920897i) q^{31} +(-3.48257 - 10.7183i) q^{33} +(-0.846270 + 0.614851i) q^{35} +(-0.475999 + 1.46498i) q^{37} +(5.40241 - 3.92508i) q^{39} +(3.09655 + 5.60459i) q^{41} +(1.58860 - 1.15418i) q^{43} +(-1.43355 + 4.41200i) q^{45} +(-7.27123 + 5.28286i) q^{47} +(0.309017 + 0.951057i) q^{49} +(4.44161 + 13.6699i) q^{51} +(0.322574 - 0.992781i) q^{53} +4.32348 q^{55} +(1.48215 + 1.07685i) q^{57} +(-9.41756 + 6.84226i) q^{59} +(-7.91258 - 5.74882i) q^{61} +(3.58786 + 2.60673i) q^{63} +(0.791640 + 2.43642i) q^{65} +(-2.76822 + 8.51972i) q^{67} +(13.8730 - 10.0793i) q^{69} +(-3.81811 - 11.7509i) q^{71} +13.0364 q^{73} +(8.61592 + 6.25983i) q^{75} +(1.27722 - 3.93087i) q^{77} +5.61764 q^{79} -2.63672 q^{81} -15.9564 q^{83} -5.51408 q^{85} +(1.51268 - 4.65554i) q^{87} +(-0.0547737 - 0.0397954i) q^{89} +2.44903 q^{91} +(-0.815874 - 2.51100i) q^{93} +(-0.568603 + 0.413114i) q^{95} +(-0.922681 + 2.83972i) q^{97} +(-5.66425 - 17.4328i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{3} - 13 q^{5} + 4 q^{7} + 2 q^{9}+O(q^{10}) \) 16 * q - 2 * q^3 - 13 * q^5 + 4 * q^7 + 2 * q^9	\( 16 q - 2 q^{3} - 13 q^{5} + 4 q^{7} + 2 q^{9} - q^{11} - 6 q^{13} - q^{17} + 15 q^{19} + 2 q^{21} + 27 q^{23} - 3 q^{25} + 28 q^{27} - q^{29} - 14 q^{31} - 13 q^{33} - 12 q^{35} - 16 q^{37} + 10 q^{39} + 26 q^{41} + 5 q^{43} - 9 q^{45} - 14 q^{47} - 4 q^{49} + 4 q^{51} - 20 q^{53} + 10 q^{55} - 13 q^{57} - 47 q^{61} + 3 q^{63} - 29 q^{65} - 27 q^{67} + 15 q^{69} - 11 q^{71} + 70 q^{73} + 14 q^{75} + q^{77} + 30 q^{79} - 72 q^{81} - 78 q^{83} + 72 q^{85} + 21 q^{87} + 17 q^{89} - 24 q^{91} - 7 q^{93} + 27 q^{95} - 17 q^{97} + 13 q^{99}+O(q^{100}) \) 16 * q - 2 * q^3 - 13 * q^5 + 4 * q^7 + 2 * q^9 - q^11 - 6 * q^13 - q^17 + 15 * q^19 + 2 * q^21 + 27 * q^23 - 3 * q^25 + 28 * q^27 - q^29 - 14 * q^31 - 13 * q^33 - 12 * q^35 - 16 * q^37 + 10 * q^39 + 26 * q^41 + 5 * q^43 - 9 * q^45 - 14 * q^47 - 4 * q^49 + 4 * q^51 - 20 * q^53 + 10 * q^55 - 13 * q^57 - 47 * q^61 + 3 * q^63 - 29 * q^65 - 27 * q^67 + 15 * q^69 - 11 * q^71 + 70 * q^73 + 14 * q^75 + q^77 + 30 * q^79 - 72 * q^81 - 78 * q^83 + 72 * q^85 + 21 * q^87 + 17 * q^89 - 24 * q^91 - 7 * q^93 + 27 * q^95 - 17 * q^97 + 13 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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