LMFDB - Embedded newform 1148.2.n.e.57.4

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

Embedding invariants

Embedding label			57.4
Character	$\chi$	$=$	1148.57
Dual form			1148.2.n.e.141.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.18943 q^{3} +(-3.21254 - 2.33405i) q^{5} +(-0.309017 - 0.951057i) q^{7} -1.58525 q^{9} +O(q^{10})$	\(q+1.18943 q^{3} +(-3.21254 - 2.33405i) q^{5} +(-0.309017 - 0.951057i) q^{7} -1.58525 q^{9} +(-0.270405 + 0.196461i) q^{11} +(-1.61070 + 4.95723i) q^{13} +(-3.82110 - 2.77620i) q^{15} +(5.15310 - 3.74395i) q^{17} +(0.614274 + 1.89054i) q^{19} +(-0.367555 - 1.13122i) q^{21} +(-2.09627 + 6.45165i) q^{23} +(3.32756 + 10.2412i) q^{25} -5.45385 q^{27} +(-6.25392 - 4.54374i) q^{29} +(-3.48736 + 2.53372i) q^{31} +(-0.321629 + 0.233677i) q^{33} +(-1.22708 + 3.77657i) q^{35} +(4.94511 + 3.59284i) q^{37} +(-1.91582 + 5.89629i) q^{39} +(-5.78715 + 2.74023i) q^{41} +(-1.60534 + 4.94074i) q^{43} +(5.09268 + 3.70005i) q^{45} +(0.456641 - 1.40540i) q^{47} +(-0.809017 + 0.587785i) q^{49} +(6.12927 - 4.45317i) q^{51} +(-2.67830 - 1.94590i) q^{53} +1.32724 q^{55} +(0.730638 + 2.24867i) q^{57} +(-3.13879 + 9.66021i) q^{59} +(-0.474786 - 1.46124i) q^{61} +(0.489869 + 1.50766i) q^{63} +(16.7449 - 12.1658i) q^{65} +(-10.3062 - 7.48790i) q^{67} +(-2.49337 + 7.67380i) q^{69} +(-10.8913 + 7.91299i) q^{71} +10.0451 q^{73} +(3.95791 + 12.1812i) q^{75} +(0.270405 + 0.196461i) q^{77} +4.71169 q^{79} -1.73124 q^{81} +14.4964 q^{83} -25.2931 q^{85} +(-7.43862 - 5.40448i) q^{87} +(-0.890171 - 2.73966i) q^{89} +5.21234 q^{91} +(-4.14798 + 3.01369i) q^{93} +(2.43923 - 7.50719i) q^{95} +(-9.58928 - 6.96702i) q^{97} +(0.428660 - 0.311440i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{3} + 17 q^{5} + 6 q^{7} + 16 q^{9}+O(q^{10}) $ 24 * q + 12 * q^3 + 17 * q^5 + 6 * q^7 + 16 * q^9	$ 24 q + 12 q^{3} + 17 q^{5} + 6 q^{7} + 16 q^{9} - 8 q^{11} + 10 q^{15} + 8 q^{17} - 28 q^{19} + 3 q^{21} - 23 q^{23} + 17 q^{25} + 12 q^{27} - 31 q^{29} + 2 q^{31} + 12 q^{33} + 13 q^{35} + 7 q^{37} - 16 q^{39} - q^{41} - 2 q^{43} + 71 q^{45} + 15 q^{47} - 6 q^{49} + 2 q^{51} + 28 q^{53} - 16 q^{55} - 15 q^{57} + 17 q^{59} + 35 q^{61} - q^{63} + 62 q^{65} - 10 q^{67} - 9 q^{69} - 25 q^{71} - 74 q^{73} + 17 q^{75} + 8 q^{77} + 64 q^{81} + 96 q^{83} - 94 q^{85} - q^{87} - 33 q^{89} - 15 q^{93} - 29 q^{95} - 34 q^{97} - 3 q^{99}+O(q^{100}) $ 24 * q + 12 * q^3 + 17 * q^5 + 6 * q^7 + 16 * q^9 - 8 * q^11 + 10 * q^15 + 8 * q^17 - 28 * q^19 + 3 * q^21 - 23 * q^23 + 17 * q^25 + 12 * q^27 - 31 * q^29 + 2 * q^31 + 12 * q^33 + 13 * q^35 + 7 * q^37 - 16 * q^39 - q^41 - 2 * q^43 + 71 * q^45 + 15 * q^47 - 6 * q^49 + 2 * q^51 + 28 * q^53 - 16 * q^55 - 15 * q^57 + 17 * q^59 + 35 * q^61 - q^63 + 62 * q^65 - 10 * q^67 - 9 * q^69 - 25 * q^71 - 74 * q^73 + 17 * q^75 + 8 * q^77 + 64 * q^81 + 96 * q^83 - 94 * q^85 - q^87 - 33 * q^89 - 15 * q^93 - 29 * q^95 - 34 * q^97 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

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
$3$	1.18943			0.686719			0.343360	−	0.939204i	$-0.388435\pi$
$3$	1.18943			0.686719			0.343360	+	0.939204i	$0.388435\pi$
$4$		0			0
$5$	−3.21254	−	2.33405i	−1.43669	−	1.04382i	−0.988721	−	0.149771i	$-0.952146\pi$
$5$	−3.21254	−	2.33405i	−1.43669	−	1.04382i	−0.447972	−	0.894047i	$-0.647854\pi$
$6$		0			0
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$8$		0			0
$9$	−1.58525			−0.528416
$10$		0			0
$11$	−0.270405	+	0.196461i	−0.0815302	+	0.0592352i	−0.627804	−	0.778372i	$-0.716046\pi$
$11$	−0.270405	+	0.196461i	−0.0815302	+	0.0592352i	0.546273	+	0.837607i	$0.316046\pi$
$12$		0			0
$13$	−1.61070	+	4.95723i	−0.446728	+	1.37489i	0.433850	+	0.900985i	$0.357155\pi$
$13$	−1.61070	+	4.95723i	−0.446728	+	1.37489i	−0.880578	+	0.473902i	$0.842845\pi$
$14$		0			0
$15$	−3.82110	−	2.77620i	−0.986605	−	0.716810i
$16$		0			0
$17$	5.15310	−	3.74395i	1.24981	−	0.908040i	0.251600	−	0.967831i	$-0.419043\pi$
$17$	5.15310	−	3.74395i	1.24981	−	0.908040i	0.998211	+	0.0597909i	$0.0190434\pi$
$18$		0			0
$19$	0.614274	+	1.89054i	0.140924	+	0.433720i	0.996464	−	0.0840164i	$-0.0267748\pi$
$19$	0.614274	+	1.89054i	0.140924	+	0.433720i	−0.855540	+	0.517736i	$0.826775\pi$
$20$		0			0
$21$	−0.367555	−	1.13122i	−0.0802071	−	0.246852i
$22$		0			0
$23$	−2.09627	+	6.45165i	−0.437102	+	1.34526i	0.453815	+	0.891096i	$0.350063\pi$
$23$	−2.09627	+	6.45165i	−0.437102	+	1.34526i	−0.890917	+	0.454166i	$0.849937\pi$
$24$		0			0
$25$	3.32756	+	10.2412i	0.665513	+	2.04824i
$26$		0			0
$27$	−5.45385			−1.04959
$28$		0			0
$29$	−6.25392	−	4.54374i	−1.16132	−	0.843752i	−0.171380	−	0.985205i	$-0.554822\pi$
$29$	−6.25392	−	4.54374i	−1.16132	−	0.843752i	−0.989945	+	0.141453i	$0.954822\pi$
$30$		0			0
$31$	−3.48736	+	2.53372i	−0.626349	+	0.455069i	−0.855133	−	0.518408i	$-0.826525\pi$
$31$	−3.48736	+	2.53372i	−0.626349	+	0.455069i	0.228785	+	0.973477i	$0.426525\pi$
$32$		0			0
$33$	−0.321629	+	0.233677i	−0.0559884	+	0.0406780i
$34$		0			0
$35$	−1.22708	+	3.77657i	−0.207415	+	0.638357i
$36$		0			0
$37$	4.94511	+	3.59284i	0.812972	+	0.590658i	0.914691	−	0.404155i	$-0.132434\pi$
$37$	4.94511	+	3.59284i	0.812972	+	0.590658i	−0.101719	+	0.994813i	$0.532434\pi$
$38$		0			0
$39$	−1.91582	+	5.89629i	−0.306777	+	0.944162i
$40$		0			0
$41$	−5.78715	+	2.74023i	−0.903801	+	0.427952i
$41$	−5.78715	+	2.74023i	−0.903801	+	0.427952i
$42$		0			0
$43$	−1.60534	+	4.94074i	−0.244812	+	0.753455i	0.750855	+	0.660467i	$0.229642\pi$
$43$	−1.60534	+	4.94074i	−0.244812	+	0.753455i	−0.995667	+	0.0929880i	$0.970358\pi$
$44$		0			0
$45$	5.09268	+	3.70005i	0.759172	+	0.551571i
$46$		0			0
$47$	0.456641	−	1.40540i	0.0666079	−	0.204998i	−0.912213	−	0.409716i	$-0.865628\pi$
$47$	0.456641	−	1.40540i	0.0666079	−	0.204998i	0.978821	+	0.204718i	$0.0656277\pi$
$48$		0			0
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$		0			0
$51$	6.12927	−	4.45317i	0.858269	−	0.623569i
$52$		0			0
$53$	−2.67830	−	1.94590i	−0.367893	−	0.267290i	0.388443	−	0.921473i	$-0.373013\pi$
$53$	−2.67830	−	1.94590i	−0.367893	−	0.267290i	−0.756337	+	0.654182i	$0.773013\pi$
$54$		0			0
$55$	1.32724			0.178965
$56$		0			0
$57$	0.730638	+	2.24867i	0.0967753	+	0.297844i
$58$		0			0
$59$	−3.13879	+	9.66021i	−0.408636	+	1.25765i	0.509185	+	0.860657i	$0.329947\pi$
$59$	−3.13879	+	9.66021i	−0.408636	+	1.25765i	−0.917821	+	0.396995i	$0.870053\pi$
$60$		0			0
$61$	−0.474786	−	1.46124i	−0.0607901	−	0.187093i	0.916050	−	0.401065i	$-0.131360\pi$
$61$	−0.474786	−	1.46124i	−0.0607901	−	0.187093i	−0.976840	+	0.213972i	$0.931360\pi$
$62$		0			0
$63$	0.489869	+	1.50766i	0.0617177	+	0.189948i
$64$		0			0
$65$	16.7449	−	12.1658i	2.07694	−	1.50899i
$66$		0			0
$67$	−10.3062	−	7.48790i	−1.25910	−	0.914792i	−0.260390	−	0.965503i	$-0.583851\pi$
$67$	−10.3062	−	7.48790i	−1.25910	−	0.914792i	−0.998713	+	0.0507112i	$0.983851\pi$
$68$		0			0
$69$	−2.49337	+	7.67380i	−0.300166	+	0.923817i
$70$		0			0
$71$	−10.8913	+	7.91299i	−1.29256	+	0.939100i	−0.999854	−	0.0171028i	$-0.994556\pi$
$71$	−10.8913	+	7.91299i	−1.29256	+	0.939100i	−0.292706	+	0.956202i	$0.594556\pi$
$72$		0			0
$73$	10.0451			1.17569			0.587845	−	0.808973i	$-0.299976\pi$
$73$	10.0451			1.17569			0.587845	+	0.808973i	$0.299976\pi$
$74$		0			0
$75$	3.95791	+	12.1812i	0.457020	+	1.40656i
$76$		0			0
$77$	0.270405	+	0.196461i	0.0308155	+	0.0223888i
$78$		0			0
$79$	4.71169			0.530107			0.265053	−	0.964234i	$-0.414610\pi$
$79$	4.71169			0.530107			0.265053	+	0.964234i	$0.414610\pi$
$80$		0			0
$81$	−1.73124			−0.192360
$82$		0			0
$83$	14.4964			1.59118			0.795592	−	0.605833i	$-0.207160\pi$
$83$	14.4964			1.59118			0.795592	+	0.605833i	$0.207160\pi$
$84$		0			0
$85$	−25.2931			−2.74342
$86$		0			0
$87$	−7.43862	−	5.40448i	−0.797504	−	0.579421i
$88$		0			0
$89$	−0.890171	−	2.73966i	−0.0943579	−	0.290404i	0.892728	−	0.450596i	$-0.148789\pi$
$89$	−0.890171	−	2.73966i	−0.0943579	−	0.290404i	−0.987086	+	0.160192i	$0.948789\pi$
$90$		0			0
$91$	5.21234			0.546401
$92$		0			0
$93$	−4.14798	+	3.01369i	−0.430126	+	0.312505i
$94$		0			0
$95$	2.43923	−	7.50719i	0.250260	−	0.770222i
$96$		0			0
$97$	−9.58928	−	6.96702i	−0.973644	−	0.707394i	−0.0173646	−	0.999849i	$-0.505528\pi$
$97$	−9.58928	−	6.96702i	−0.973644	−	0.707394i	−0.956279	+	0.292456i	$0.905528\pi$
$98$		0			0
$99$	0.428660	−	0.311440i	0.0430819	−	0.0313008i
$100$		0			0
$101$	−5.13052	−	15.7901i	−0.510506	−	1.57118i	−0.791312	−	0.611412i	$-0.790602\pi$
$101$	−5.13052	−	15.7901i	−0.510506	−	1.57118i	0.280806	−	0.959764i	$-0.409398\pi$
$102$		0			0
$103$	0.0864586	+	0.266092i	0.00851902	+	0.0262188i	0.955226	−	0.295878i	$-0.0956123\pi$
$103$	0.0864586	+	0.266092i	0.00851902	+	0.0262188i	−0.946707	+	0.322097i	$0.895612\pi$
$104$		0			0
$105$	−1.45953	+	4.49198i	−0.142436	+	0.438372i
$106$		0			0
$107$	−2.75943	−	8.49264i	−0.266764	−	0.821015i	−0.991282	−	0.131759i	$-0.957938\pi$
$107$	−2.75943	−	8.49264i	−0.266764	−	0.821015i	0.724518	−	0.689256i	$-0.242062\pi$
$108$		0			0
$109$	−12.3355			−1.18153			−0.590763	−	0.806845i	$-0.701173\pi$
$109$	−12.3355			−1.18153			−0.590763	+	0.806845i	$0.701173\pi$
$110$		0			0
$111$	5.88188	+	4.27344i	0.558283	+	0.405617i
$112$		0			0
$113$	−4.32785	+	3.14437i	−0.407130	+	0.295797i	−0.772439	−	0.635089i	$-0.780963\pi$
$113$	−4.32785	+	3.14437i	−0.407130	+	0.295797i	0.365309	+	0.930886i	$0.380963\pi$
$114$		0			0
$115$	21.7928	−	15.8334i	2.03219	−	1.47647i
$116$		0			0
$117$	2.55336	−	7.85844i	0.236058	−	0.726513i
$118$		0			0
$119$	−5.15310	−	3.74395i	−0.472384	−	0.343207i
$120$		0			0
$121$	−3.36466	+	10.3554i	−0.305879	+	0.941398i
$122$		0			0
$123$	−6.88343	+	3.25932i	−0.620658	+	0.293883i
$124$		0			0
$125$	7.07808	−	21.7841i	0.633083	−	1.94843i
$126$		0			0
$127$	−10.2516	−	7.44824i	−0.909684	−	0.660924i	0.0312508	−	0.999512i	$-0.490051\pi$
$127$	−10.2516	−	7.44824i	−0.909684	−	0.660924i	−0.940935	+	0.338587i	$0.890051\pi$
$128$		0			0
$129$	−1.90945	+	5.87668i	−0.168117	+	0.517412i
$130$		0			0
$131$	15.8729	−	11.5323i	1.38682	−	1.00759i	0.390618	−	0.920553i	$-0.372261\pi$
$131$	15.8729	−	11.5323i	1.38682	−	1.00759i	0.996205	−	0.0870331i	$-0.0277386\pi$
$132$		0			0
$133$	1.60819	−	1.16842i	0.139448	−	0.101315i
$134$		0			0
$135$	17.5207	+	12.7295i	1.50794	+	1.09558i
$136$		0			0
$137$	21.4527			1.83283			0.916413	−	0.400233i	$-0.131071\pi$
$137$	21.4527			1.83283			0.916413	+	0.400233i	$0.131071\pi$
$138$		0			0
$139$	0.622468	+	1.91576i	0.0527971	+	0.162493i	0.973978	−	0.226641i	$-0.0727744\pi$
$139$	0.622468	+	1.91576i	0.0527971	+	0.162493i	−0.921181	+	0.389134i	$0.872774\pi$
$140$		0			0
$141$	0.543144	−	1.67162i	0.0457410	−	0.140776i
$142$		0			0
$143$	−0.538359	−	1.65690i	−0.0450199	−	0.138557i
$144$		0			0
$145$	9.48568	+	29.1939i	0.787743	+	2.42442i
$146$		0			0
$147$	−0.962271	+	0.699131i	−0.0793668	+	0.0576634i
$148$		0			0
$149$	−2.85706	−	2.07577i	−0.234059	−	0.170054i	0.464573	−	0.885535i	$-0.346208\pi$
$149$	−2.85706	−	2.07577i	−0.234059	−	0.170054i	−0.698632	+	0.715481i	$0.746208\pi$
$150$		0			0
$151$	0.482195	−	1.48404i	0.0392405	−	0.120770i	−0.929517	−	0.368778i	$-0.879776\pi$
$151$	0.482195	−	1.48404i	0.0392405	−	0.120770i	0.968758	+	0.248009i	$0.0797761\pi$
$152$		0			0
$153$	−8.16895	+	5.93509i	−0.660420	+	0.479824i
$154$		0			0
$155$	17.1171			1.37488
$156$		0			0
$157$	4.19870	+	12.9223i	0.335093	+	1.03131i	0.966676	+	0.256001i	$0.0824051\pi$
$157$	4.19870	+	12.9223i	0.335093	+	1.03131i	−0.631584	+	0.775308i	$0.717595\pi$
$158$		0			0
$159$	−3.18566	−	2.31452i	−0.252640	−	0.183553i
$160$		0			0
$161$	6.78366			0.534628
$162$		0			0
$163$	−21.9432			−1.71872			−0.859360	−	0.511371i	$-0.829138\pi$
$163$	−21.9432			−1.71872			−0.859360	+	0.511371i	$0.829138\pi$
$164$		0			0
$165$	1.57866			0.122899
$166$		0			0
$167$	16.2909			1.26062			0.630312	−	0.776342i	$-0.282927\pi$
$167$	16.2909			1.26062			0.630312	+	0.776342i	$0.282927\pi$
$168$		0			0
$169$	−11.4625	−	8.32800i	−0.881732	−	0.640616i
$170$		0			0
$171$	−0.973777	−	2.99698i	−0.0744666	−	0.229185i
$172$		0			0
$173$	−18.2978			−1.39116			−0.695580	−	0.718449i	$-0.744852\pi$
$173$	−18.2978			−1.39116			−0.695580	+	0.718449i	$0.744852\pi$
$174$		0			0
$175$	8.71167	−	6.32940i	0.658540	−	0.478458i
$176$		0			0
$177$	−3.73338	+	11.4902i	−0.280618	+	0.863654i
$178$		0			0
$179$	−10.3560	−	7.52408i	−0.774044	−	0.562376i	0.129141	−	0.991626i	$-0.458778\pi$
$179$	−10.3560	−	7.52408i	−0.774044	−	0.562376i	−0.903186	+	0.429250i	$0.858778\pi$
$180$		0			0
$181$	−11.9333	+	8.67007i	−0.886997	+	0.644441i	−0.935093	−	0.354402i	$-0.884685\pi$
$181$	−11.9333	+	8.67007i	−0.886997	+	0.644441i	0.0480963	+	0.998843i	$0.484685\pi$
$182$		0			0
$183$	−0.564726	−	1.73805i	−0.0417458	−	0.128480i
$184$		0			0
$185$	−7.50054	−	23.0843i	−0.551450	−	1.69719i
$186$		0			0
$187$	−0.657886	+	2.02477i	−0.0481094	+	0.148066i
$188$		0			0
$189$	1.68533	+	5.18692i	0.122590	+	0.377293i
$190$		0			0
$191$	2.02844			0.146773			0.0733865	−	0.997304i	$-0.476619\pi$
$191$	2.02844			0.146773			0.0733865	+	0.997304i	$0.476619\pi$
$192$		0			0
$193$	−5.37938	−	3.90835i	−0.387216	−	0.281329i	0.377098	−	0.926174i	$-0.376922\pi$
$193$	−5.37938	−	3.90835i	−0.387216	−	0.281329i	−0.764314	+	0.644844i	$0.776922\pi$
$194$		0			0
$195$	19.9169	−	14.4705i	1.42628	−	1.03625i
$196$		0			0
$197$	−21.5341	+	15.6455i	−1.53424	+	1.11469i	−0.580423	+	0.814315i	$0.697113\pi$
$197$	−21.5341	+	15.6455i	−1.53424	+	1.11469i	−0.953820	+	0.300378i	$0.902887\pi$
$198$		0			0
$199$	−2.28195	+	7.02313i	−0.161763	+	0.497857i	−0.998783	−	0.0493159i	$-0.984296\pi$
$199$	−2.28195	+	7.02313i	−0.161763	+	0.497857i	0.837020	+	0.547173i	$0.184296\pi$
$200$		0			0
$201$	−12.2585	−	8.90635i	−0.864651	−	0.628206i
$202$		0			0
$203$	−2.38879	+	7.35193i	−0.167660	+	0.516004i
$204$		0			0
$205$	24.9873	+	4.70438i	1.74519	+	0.328568i
$206$		0			0
$207$	3.32311	−	10.2275i	0.230972	−	0.710858i
$208$		0			0
$209$	−0.537520	−	0.390531i	−0.0371811	−	0.0270136i
$210$		0			0
$211$	2.46695	−	7.59248i	0.169832	−	0.522688i	−0.829528	−	0.558465i	$-0.811391\pi$
$211$	2.46695	−	7.59248i	0.169832	−	0.522688i	0.999360	+	0.0357769i	$0.0113906\pi$
$212$		0			0
$213$	−12.9545	+	9.41198i	−0.887626	+	0.644898i
$214$		0			0
$215$	16.6892	−	12.1254i	1.13819	−	0.826944i
$216$		0			0
$217$	3.48736	+	2.53372i	0.236738	+	0.172000i
$218$		0			0
$219$	11.9480			0.807370
$220$		0			0
$221$	10.2595	+	31.5755i	0.690128	+	2.12400i
$222$		0			0
$223$	−2.04290	+	6.28739i	−0.136803	+	0.421035i	−0.995866	−	0.0908340i	$-0.971047\pi$
$223$	−2.04290	+	6.28739i	−0.136803	+	0.421035i	0.859063	+	0.511869i	$0.171047\pi$
$224$		0			0
$225$	−5.27502	−	16.2348i	−0.351668	−	1.08232i
$226$		0			0
$227$	4.23020	+	13.0192i	0.280768	+	0.864115i	0.987635	+	0.156769i	$0.0501077\pi$
$227$	4.23020	+	13.0192i	0.280768	+	0.864115i	−0.706867	+	0.707346i	$0.749892\pi$
$228$		0			0
$229$	−6.64192	+	4.82564i	−0.438910	+	0.318887i	−0.785202	−	0.619240i	$-0.787441\pi$
$229$	−6.64192	+	4.82564i	−0.438910	+	0.318887i	0.346291	+	0.938127i	$0.387441\pi$
$230$		0			0
$231$	0.321629	+	0.233677i	0.0211616	+	0.0153748i
$232$		0			0
$233$	0.569769	−	1.75357i	0.0373268	−	0.114880i	−0.930657	−	0.365893i	$-0.880764\pi$
$233$	0.569769	−	1.75357i	0.0373268	−	0.114880i	0.967984	+	0.251013i	$0.0807636\pi$
$234$		0			0
$235$	−4.74724	+	3.44907i	−0.309676	+	0.224993i
$236$		0			0
$237$	5.60424			0.364034
$238$		0			0
$239$	−5.33357	−	16.4150i	−0.345000	−	1.06180i	−0.961584	−	0.274511i	$-0.911484\pi$
$239$	−5.33357	−	16.4150i	−0.345000	−	1.06180i	0.616584	−	0.787289i	$-0.288516\pi$
$240$		0			0
$241$	−2.39129	−	1.73737i	−0.154036	−	0.111914i	0.508097	−	0.861300i	$-0.330349\pi$
$241$	−2.39129	−	1.73737i	−0.154036	−	0.111914i	−0.662134	+	0.749386i	$0.730349\pi$
$242$		0			0
$243$	14.3023			0.917496
$244$		0			0
$245$	3.97092			0.253693
$246$		0			0
$247$	−10.3613			−0.659271
$248$		0			0
$249$	17.2425			1.09270
$250$		0			0
$251$	8.03746	+	5.83955i	0.507320	+	0.368589i	0.811806	−	0.583927i	$-0.198485\pi$
$251$	8.03746	+	5.83955i	0.507320	+	0.368589i	−0.304486	+	0.952517i	$0.598485\pi$
$252$		0			0
$253$	−0.700655	−	2.15639i	−0.0440498	−	0.135571i
$254$		0			0
$255$	−30.0845			−1.88396
$256$		0			0
$257$	7.23631	−	5.25749i	0.451389	−	0.327953i	−0.338755	−	0.940875i	$-0.610006\pi$
$257$	7.23631	−	5.25749i	0.451389	−	0.327953i	0.790144	+	0.612921i	$0.210006\pi$
$258$		0			0
$259$	1.88887	−	5.81333i	0.117368	−	0.361223i
$260$		0			0
$261$	9.91403	+	7.20296i	0.613663	+	0.445852i
$262$		0			0
$263$	21.2611	−	15.4471i	1.31101	−	0.952508i	0.311017	−	0.950404i	$-0.399330\pi$
$263$	21.2611	−	15.4471i	1.31101	−	0.952508i	0.999998	−	0.00210386i	$-0.000669680\pi$
$264$		0			0
$265$	4.06234	+	12.5026i	0.249547	+	0.768028i
$266$		0			0
$267$	−1.05880	−	3.25865i	−0.0647974	−	0.199426i
$268$		0			0
$269$	−0.277859	+	0.855163i	−0.0169414	+	0.0521402i	−0.959170	−	0.282831i	$-0.908727\pi$
$269$	−0.277859	+	0.855163i	−0.0169414	+	0.0521402i	0.942228	+	0.334971i	$0.108727\pi$
$270$		0			0
$271$	4.98540	+	15.3435i	0.302841	+	0.932050i	0.980474	+	0.196649i	$0.0630060\pi$
$271$	4.98540	+	15.3435i	0.302841	+	0.932050i	−0.677633	+	0.735401i	$0.736994\pi$
$272$		0			0
$273$	6.19972			0.375224
$274$		0			0
$275$	−2.91178	−	2.11553i	−0.175587	−	0.127572i
$276$		0			0
$277$	−5.14272	+	3.73641i	−0.308996	+	0.224499i	−0.731466	−	0.681878i	$-0.761163\pi$
$277$	−5.14272	+	3.73641i	−0.308996	+	0.224499i	0.422469	+	0.906377i	$0.361163\pi$
$278$		0			0
$279$	5.52834	−	4.01657i	0.330973	−	0.240466i
$280$		0			0
$281$	0.731101	−	2.25010i	0.0436138	−	0.134230i	−0.926879	−	0.375361i	$-0.877519\pi$
$281$	0.731101	−	2.25010i	0.0436138	−	0.134230i	0.970492	+	0.241132i	$0.0775186\pi$
$282$		0			0
$283$	10.7276	+	7.79403i	0.637687	+	0.463307i	0.859055	−	0.511883i	$-0.171052\pi$
$283$	10.7276	+	7.79403i	0.637687	+	0.463307i	−0.221368	+	0.975190i	$0.571052\pi$
$284$		0			0
$285$	2.90131	−	8.92930i	0.171859	−	0.528926i
$286$		0			0
$287$	4.39444	+	4.65713i	0.259396	+	0.274902i
$288$		0			0
$289$	7.28402	−	22.4179i	0.428472	−	1.31870i
$290$		0			0
$291$	−11.4058	−	8.28680i	−0.668620	−	0.485781i
$292$		0			0
$293$	8.88691	−	27.3511i	0.519179	−	1.59787i	−0.256369	−	0.966579i	$-0.582526\pi$
$293$	8.88691	−	27.3511i	0.519179	−	1.59787i	0.775548	−	0.631289i	$-0.217474\pi$
$294$		0			0
$295$	32.6309	−	23.7077i	1.89984	−	1.38032i
$296$		0			0
$297$	1.47475	−	1.07147i	0.0855736	−	0.0621729i
$298$		0			0
$299$	−28.6058	−	20.7833i	−1.65432	−	1.20193i
$300$		0			0
$301$	5.19500			0.299435
$302$		0			0
$303$	−6.10241	−	18.7813i	−0.350575	−	1.07896i
$304$		0			0
$305$	−1.88534	+	5.80247i	−0.107954	+	0.332249i
$306$		0			0
$307$	−0.421081	−	1.29595i	−0.0240324	−	0.0739640i	0.938321	−	0.345765i	$-0.112381\pi$
$307$	−0.421081	−	1.29595i	−0.0240324	−	0.0739640i	−0.962353	+	0.271801i	$0.912381\pi$
$308$		0			0
$309$	0.102837	+	0.316499i	0.00585017	+	0.0180050i
$310$		0			0
$311$	1.56469	−	1.13681i	0.0887254	−	0.0644628i	−0.542538	−	0.840031i	$-0.682537\pi$
$311$	1.56469	−	1.13681i	0.0887254	−	0.0644628i	0.631264	+	0.775568i	$0.282537\pi$
$312$		0			0
$313$	−8.51774	−	6.18850i	−0.481451	−	0.349795i	0.320436	−	0.947270i	$-0.396171\pi$
$313$	−8.51774	−	6.18850i	−0.481451	−	0.349795i	−0.801887	+	0.597475i	$0.796171\pi$
$314$		0			0
$315$	1.94523	−	5.98681i	0.109601	−	0.337318i
$316$		0			0
$317$	−26.4711	+	19.2324i	−1.48677	+	1.08020i	−0.511468	+	0.859302i	$0.670898\pi$
$317$	−26.4711	+	19.2324i	−1.48677	+	1.08020i	−0.975297	+	0.220896i	$0.929102\pi$
$318$		0			0
$319$	2.58376			0.144663
$320$		0			0
$321$	−3.28215	−	10.1014i	−0.183192	−	0.563807i
$322$		0			0
$323$	10.2435	+	7.44234i	0.569964	+	0.414103i
$324$		0			0
$325$	−56.1276			−3.11340
$326$		0			0
$327$	−14.6723			−0.811377
$328$		0			0
$329$	−1.47772			−0.0814694
$330$		0			0
$331$	21.8035			1.19843			0.599215	−	0.800588i	$-0.295480\pi$
$331$	21.8035			1.19843			0.599215	+	0.800588i	$0.295480\pi$
$332$		0			0
$333$	−7.83924	−	5.69554i	−0.429588	−	0.312114i
$334$		0			0
$335$	15.6320	+	48.1104i	0.854068	+	2.62855i
$336$		0			0
$337$	0.276196			0.0150454			0.00752269	−	0.999972i	$-0.497605\pi$
$337$	0.276196			0.0150454			0.00752269	+	0.999972i	$0.497605\pi$
$338$		0			0
$339$	−5.14769	+	3.74002i	−0.279584	+	0.203130i
$340$		0			0
$341$	0.445225	−	1.37026i	0.0241103	−	0.0742038i
$342$		0			0
$343$	0.809017	+	0.587785i	0.0436828	+	0.0317374i
$344$		0			0
$345$	25.9211	−	18.8328i	1.39554	−	1.01392i
$346$		0			0
$347$	1.44202	+	4.43809i	0.0774118	+	0.238249i	0.982272	−	0.187459i	$-0.0600251\pi$
$347$	1.44202	+	4.43809i	0.0774118	+	0.238249i	−0.904861	+	0.425708i	$0.860025\pi$
$348$		0			0
$349$	−1.84582	−	5.68084i	−0.0988043	−	0.304088i	0.889422	−	0.457087i	$-0.151107\pi$
$349$	−1.84582	−	5.68084i	−0.0988043	−	0.304088i	−0.988226	+	0.152998i	$0.951107\pi$
$350$		0			0
$351$	8.78451	−	27.0359i	0.468883	−	1.44307i
$352$		0			0
$353$	4.04408	+	12.4464i	0.215245	+	0.662455i	0.999136	+	0.0415571i	$0.0132319\pi$
$353$	4.04408	+	12.4464i	0.215245	+	0.662455i	−0.783891	+	0.620898i	$0.786768\pi$
$354$		0			0
$355$	53.4581			2.83726
$356$		0			0
$357$	−6.12927	−	4.45317i	−0.324395	−	0.235687i
$358$		0			0
$359$	4.65956	−	3.38537i	0.245922	−	0.178673i	−0.457995	−	0.888955i	$-0.651432\pi$
$359$	4.65956	−	3.38537i	0.245922	−	0.178673i	0.703918	+	0.710282i	$0.251432\pi$
$360$		0			0
$361$	12.1745	−	8.84530i	0.640764	−	0.465542i
$362$		0			0
$363$	−4.00204	+	12.3170i	−0.210053	+	0.646476i
$364$		0			0
$365$	−32.2703	−	23.4458i	−1.68911	−	1.22721i
$366$		0			0
$367$	5.45099	−	16.7764i	0.284539	−	0.875722i	−0.701997	−	0.712180i	$-0.747708\pi$
$367$	5.45099	−	16.7764i	0.284539	−	0.875722i	0.986536	−	0.163542i	$-0.0522919\pi$
$368$		0			0
$369$	9.17408	−	4.34395i	0.477583	−	0.226137i
$370$		0			0
$371$	−1.02302	+	3.14854i	−0.0531126	+	0.163464i
$372$		0			0
$373$	−3.87265	−	2.81365i	−0.200518	−	0.145685i	0.482995	−	0.875623i	$-0.339549\pi$
$373$	−3.87265	−	2.81365i	−0.200518	−	0.145685i	−0.683513	+	0.729938i	$0.739549\pi$
$374$		0			0
$375$	8.41890	−	25.9107i	0.434750	−	1.33802i
$376$		0			0
$377$	32.5975	−	23.6835i	1.67886	−	1.21976i
$378$		0			0
$379$	−20.9630	+	15.2305i	−1.07680	+	0.782339i	−0.977122	−	0.212681i	$-0.931780\pi$
$379$	−20.9630	+	15.2305i	−1.07680	+	0.782339i	−0.0996755	+	0.995020i	$0.531780\pi$
$380$		0			0
$381$	−12.1936	−	8.85918i	−0.624698	−	0.453870i
$382$		0			0
$383$	−20.4550			−1.04520			−0.522602	−	0.852577i	$-0.675039\pi$
$383$	−20.4550			−1.04520			−0.522602	+	0.852577i	$0.675039\pi$
$384$		0			0
$385$	−0.410139	−	1.26228i	−0.0209026	−	0.0643317i
$386$		0			0
$387$	2.54487	−	7.83230i	0.129363	−	0.398138i
$388$		0			0
$389$	−8.56755	−	26.3682i	−0.434392	−	1.33692i	−0.893708	−	0.448648i	$-0.851906\pi$
$389$	−8.56755	−	26.3682i	−0.434392	−	1.33692i	0.459316	−	0.888273i	$-0.348094\pi$
$390$		0			0
$391$	13.3523	+	41.0943i	0.675257	+	2.07823i
$392$		0			0
$393$	18.8798	−	13.7170i	0.952358	−	0.691929i
$394$		0			0
$395$	−15.1365	−	10.9973i	−0.761600	−	0.553335i
$396$		0			0
$397$	−5.42259	+	16.6890i	−0.272152	+	0.837598i	0.717807	+	0.696242i	$0.245146\pi$
$397$	−5.42259	+	16.6890i	−0.272152	+	0.837598i	−0.989959	+	0.141356i	$0.954854\pi$
$398$		0			0
$399$	1.91283	−	1.38976i	0.0957615	−	0.0695748i
$400$		0			0
$401$	−8.61276			−0.430101			−0.215050	−	0.976603i	$-0.568992\pi$
$401$	−8.61276			−0.430101			−0.215050	+	0.976603i	$0.568992\pi$
$402$		0			0
$403$	−6.94311	−	21.3687i	−0.345861	−	1.06445i
$404$		0			0
$405$	5.56167	+	4.04079i	0.276362	+	0.200789i
$406$		0			0
$407$	−2.04304			−0.101270
$408$		0			0
$409$	−19.2022			−0.949486			−0.474743	−	0.880124i	$-0.657459\pi$
$409$	−19.2022			−0.949486			−0.474743	+	0.880124i	$0.657459\pi$
$410$		0			0
$411$	25.5165			1.25864
$412$		0			0
$413$	10.1573			0.499810
$414$		0			0
$415$	−46.5702	−	33.8353i	−2.28604	−	1.66091i
$416$		0			0
$417$	0.740384	+	2.27867i	0.0362568	+	0.111587i
$418$		0			0
$419$	9.44471			0.461404			0.230702	−	0.973024i	$-0.425898\pi$
$419$	9.44471			0.461404			0.230702	+	0.973024i	$0.425898\pi$
$420$		0			0
$421$	8.02771	−	5.83247i	0.391247	−	0.284257i	−0.374720	−	0.927138i	$-0.622261\pi$
$421$	8.02771	−	5.83247i	0.391247	−	0.284257i	0.765966	+	0.642881i	$0.222261\pi$
$422$		0			0
$423$	−0.723890	+	2.22790i	−0.0351967	+	0.108324i
$424$		0			0
$425$	55.4897	+	40.3156i	2.69165	+	1.95560i
$426$		0			0
$427$	−1.24301	+	0.903097i	−0.0601533	+	0.0437039i
$428$		0			0
$429$	−0.640342	−	1.97077i	−0.0309160	−	0.0951497i
$430$		0			0
$431$	5.73174	+	17.6405i	0.276088	+	0.849713i	0.988929	+	0.148387i	$0.0474081\pi$
$431$	5.73174	+	17.6405i	0.276088	+	0.849713i	−0.712841	+	0.701326i	$0.752592\pi$
$432$		0			0
$433$	9.40813	−	28.9552i	0.452126	−	1.39150i	−0.422351	−	0.906432i	$-0.638795\pi$
$433$	9.40813	−	28.9552i	0.452126	−	1.39150i	0.874477	−	0.485068i	$-0.161205\pi$
$434$		0			0
$435$	11.2826	+	34.7242i	0.540958	+	1.66490i
$436$		0			0
$437$	−13.4848			−0.645065
$438$		0			0
$439$	28.7012	+	20.8526i	1.36983	+	0.995242i	0.997750	+	0.0670424i	$0.0213563\pi$
$439$	28.7012	+	20.8526i	1.36983	+	0.995242i	0.372083	+	0.928200i	$0.378644\pi$
$440$		0			0
$441$	1.28249	−	0.931786i	0.0610711	−	0.0443708i
$442$		0			0
$443$	−23.7795	+	17.2768i	−1.12980	+	0.820845i	−0.985665	−	0.168714i	$-0.946039\pi$
$443$	−23.7795	+	17.2768i	−1.12980	+	0.820845i	−0.144131	+	0.989559i	$0.546039\pi$
$444$		0			0
$445$	−3.53480	+	10.8790i	−0.167566	+	0.515714i
$446$		0			0
$447$	−3.39828	−	2.46899i	−0.160733	−	0.116779i
$448$		0			0
$449$	−4.15241	+	12.7798i	−0.195964	+	0.603116i	0.804000	+	0.594630i	$0.202701\pi$
$449$	−4.15241	+	12.7798i	−0.195964	+	0.603116i	−0.999964	+	0.00848631i	$0.997299\pi$
$450$		0			0
$451$	1.02653	−	1.87792i	0.0483373	−	0.0884279i
$452$		0			0
$453$	0.573539	−	1.76517i	0.0269472	−	0.0829350i
$454$		0			0
$455$	−16.7449	−	12.1658i	−0.785011	−	0.570344i
$456$		0			0
$457$	−10.3157	+	31.7485i	−0.482549	+	1.48513i	0.352951	+	0.935642i	$0.385178\pi$
$457$	−10.3157	+	31.7485i	−0.482549	+	1.48513i	−0.835500	+	0.549491i	$0.814822\pi$
$458$		0			0
$459$	−28.1042	+	20.4189i	−1.31179	+	0.953073i
$460$		0			0
$461$	−9.39940	+	6.82907i	−0.437774	+	0.318061i	−0.784750	−	0.619813i	$-0.787209\pi$
$461$	−9.39940	+	6.82907i	−0.437774	+	0.318061i	0.346976	+	0.937874i	$0.387209\pi$
$462$		0			0
$463$	−6.87852	−	4.99754i	−0.319672	−	0.232255i	0.416364	−	0.909198i	$-0.363304\pi$
$463$	−6.87852	−	4.99754i	−0.319672	−	0.232255i	−0.736035	+	0.676943i	$0.763304\pi$
$464$		0			0
$465$	20.3597			0.944157
$466$		0			0
$467$	7.59649	+	23.3796i	0.351524	+	1.08188i	0.957998	+	0.286776i	$0.0925834\pi$
$467$	7.59649	+	23.3796i	0.351524	+	1.08188i	−0.606474	+	0.795103i	$0.707417\pi$
$468$		0			0
$469$	−3.93662	+	12.1157i	−0.181776	+	0.559450i
$470$		0			0
$471$	4.99407	+	15.3702i	0.230115	+	0.708220i
$472$		0			0
$473$	−0.536569	−	1.65139i	−0.0246714	−	0.0759309i
$474$		0			0
$475$	−17.3173	+	12.5818i	−0.794574	+	0.577292i
$476$		0			0
$477$	4.24578	+	3.08474i	0.194401	+	0.141241i
$478$		0			0
$479$	8.64063	−	26.5931i	0.394800	−	1.21507i	−0.534317	−	0.845284i	$-0.679431\pi$
$479$	8.64063	−	26.5931i	0.394800	−	1.21507i	0.929117	−	0.369786i	$-0.120569\pi$
$480$		0			0
$481$	−25.7756	+	18.7271i	−1.17527	+	0.853881i
$482$		0			0
$483$	8.06871			0.367139
$484$		0			0
$485$	14.5446	+	44.7637i	0.660436	+	2.03261i
$486$		0			0
$487$	33.2501	+	24.1576i	1.50671	+	1.09469i	0.967612	+	0.252443i	$0.0812340\pi$
$487$	33.2501	+	24.1576i	1.50671	+	1.09469i	0.539096	+	0.842244i	$0.318766\pi$
$488$		0			0
$489$	−26.0999			−1.18028
$490$		0			0
$491$	−26.6095			−1.20087			−0.600435	−	0.799674i	$-0.705006\pi$
$491$	−26.6095			−1.20087			−0.600435	+	0.799674i	$0.705006\pi$
$492$		0			0
$493$	−49.2386			−2.21760
$494$		0			0
$495$	−2.10400			−0.0945679
$496$		0			0
$497$	10.8913	+	7.91299i	0.488542	+	0.354946i
$498$		0			0
$499$	6.04671	+	18.6099i	0.270688	+	0.833092i	0.990328	+	0.138745i	$0.0443068\pi$
$499$	6.04671	+	18.6099i	0.270688	+	0.833092i	−0.719640	+	0.694347i	$0.755693\pi$
$500$		0			0
$501$	19.3769			0.865696
$502$		0			0
$503$	−3.73036	+	2.71027i	−0.166329	+	0.120845i	−0.667836	−	0.744309i	$-0.732779\pi$
$503$	−3.73036	+	2.71027i	−0.166329	+	0.120845i	0.501507	+	0.865154i	$0.332779\pi$
$504$		0			0
$505$	−20.3729	+	62.7014i	−0.906582	+	2.79017i
$506$		0			0
$507$	−13.6339	−	9.90560i	−0.605502	−	0.439923i
$508$		0			0
$509$	−16.4758	+	11.9704i	−0.730278	+	0.530578i	−0.889651	−	0.456641i	$-0.849053\pi$
$509$	−16.4758	+	11.9704i	−0.730278	+	0.530578i	0.159374	+	0.987218i	$0.449053\pi$
$510$		0			0
$511$	−3.10411	−	9.55346i	−0.137318	−	0.422620i
$512$		0			0
$513$	−3.35016	−	10.3107i	−0.147913	−	0.455229i
$514$		0			0
$515$	0.343320	−	1.05663i	0.0151285	−	0.0465607i
$516$		0			0
$517$	0.152627	+	0.469739i	0.00671254	+	0.0206591i
$518$		0			0
$519$	−21.7641			−0.955336
$520$		0			0
$521$	5.01539	+	3.64389i	0.219728	+	0.159642i	0.692204	−	0.721702i	$-0.256640\pi$
$521$	5.01539	+	3.64389i	0.219728	+	0.159642i	−0.472476	+	0.881343i	$0.656640\pi$
$522$		0			0
$523$	25.5007	−	18.5273i	1.11507	−	0.810144i	0.131614	−	0.991301i	$-0.457984\pi$
$523$	25.5007	−	18.5273i	1.11507	−	0.810144i	0.983454	+	0.181157i	$0.0579842\pi$
$524$		0			0
$525$	10.3619	−	7.52840i	0.452233	−	0.328566i
$526$		0			0
$527$	−8.48463	+	26.1130i	−0.369596	+	1.13750i
$528$		0			0
$529$	−18.6220	−	13.5297i	−0.809653	−	0.588247i
$530$		0			0
$531$	4.97577	−	15.3138i	0.215930	−	0.664564i
$532$		0			0
$533$	−4.26259	−	33.1019i	−0.184633	−	1.43380i
$534$		0			0
$535$	−10.9575	+	33.7236i	−0.473733	+	1.45800i
$536$		0			0
$537$	−12.3178	−	8.94939i	−0.531551	−	0.386195i
$538$		0			0
$539$	0.103286	−	0.317880i	0.00444883	−	0.0136921i
$540$		0			0
$541$	10.8686	−	7.89650i	0.467278	−	0.339497i	−0.329102	−	0.944294i	$-0.606746\pi$
$541$	10.8686	−	7.89650i	0.467278	−	0.339497i	0.796379	+	0.604797i	$0.206746\pi$
$542$		0			0
$543$	−14.1939	+	10.3125i	−0.609118	+	0.442550i
$544$		0			0
$545$	39.6283	+	28.7917i	1.69749	+	1.23330i
$546$		0			0
$547$	−11.8436			−0.506396			−0.253198	−	0.967414i	$-0.581482\pi$
$547$	−11.8436			−0.506396			−0.253198	+	0.967414i	$0.581482\pi$
$548$		0			0
$549$	0.752654	+	2.31643i	0.0321225	+	0.0988629i
$550$		0			0
$551$	4.74851	−	14.6144i	0.202293	−	0.622594i
$552$		0			0
$553$	−1.45599	−	4.48108i	−0.0619151	−	0.190555i
$554$		0			0
$555$	−8.92138	−	27.4572i	−0.378692	−	1.16549i
$556$		0			0
$557$	−16.1205	+	11.7123i	−0.683049	+	0.496264i	−0.874368	−	0.485264i	$-0.838724\pi$
$557$	−16.1205	+	11.7123i	−0.683049	+	0.496264i	0.191319	+	0.981528i	$0.438724\pi$
$558$		0			0
$559$	−21.9066	−	15.9161i	−0.926551	−	0.673179i
$560$		0			0
$561$	−0.782512	+	2.40832i	−0.0330377	+	0.101679i
$562$		0			0
$563$	−36.4207	+	26.4612i	−1.53495	+	1.11521i	−0.581546	+	0.813514i	$0.697552\pi$
$563$	−36.4207	+	26.4612i	−1.53495	+	1.11521i	−0.953405	+	0.301693i	$0.902448\pi$
$564$		0			0
$565$	21.2425			0.893680
$566$		0			0
$567$	0.534982	+	1.64650i	0.0224671	+	0.0691467i
$568$		0			0
$569$	13.7510	+	9.99067i	0.576471	+	0.418831i	0.837450	−	0.546514i	$-0.184045\pi$
$569$	13.7510	+	9.99067i	0.576471	+	0.418831i	−0.260979	+	0.965344i	$0.584045\pi$
$570$		0			0
$571$	−1.34579			−0.0563194			−0.0281597	−	0.999603i	$-0.508965\pi$
$571$	−1.34579			−0.0563194			−0.0281597	+	0.999603i	$0.508965\pi$
$572$		0			0
$573$	2.41270			0.100792
$574$		0			0
$575$	−73.0480			−3.04631
$576$		0			0
$577$	9.53499			0.396947			0.198473	−	0.980106i	$-0.436402\pi$
$577$	9.53499			0.396947			0.198473	+	0.980106i	$0.436402\pi$
$578$		0			0
$579$	−6.39841	−	4.64872i	−0.265909	−	0.193194i
$580$		0			0
$581$	−4.47963	−	13.7869i	−0.185846	−	0.571976i
$582$		0			0
$583$	1.10652			0.0458274
$584$		0			0
$585$	−26.5448	+	19.2859i	−1.09749	+	0.797374i
$586$		0			0
$587$	13.2334	−	40.7282i	0.546201	−	1.68103i	−0.171917	−	0.985111i	$-0.554996\pi$
$587$	13.2334	−	40.7282i	0.546201	−	1.68103i	0.718118	−	0.695922i	$-0.245004\pi$
$588$		0			0
$589$	−6.93229	−	5.03661i	−0.285640	−	0.207530i
$590$		0			0
$591$	−25.6134	+	18.6092i	−1.05359	+	0.765481i
$592$		0			0
$593$	2.00330	+	6.16551i	0.0822655	+	0.253187i	0.983726	−	0.179674i	$-0.0575041\pi$
$593$	2.00330	+	6.16551i	0.0822655	+	0.253187i	−0.901461	+	0.432861i	$0.857504\pi$
$594$		0			0
$595$	7.81600	+	24.0552i	0.320425	+	0.986166i
$596$		0			0
$597$	−2.71423	+	8.35355i	−0.111086	+	0.341888i
$598$		0			0
$599$	0.535823	+	1.64909i	0.0218931	+	0.0673801i	0.961406	−	0.275133i	$-0.0887219\pi$
$599$	0.535823	+	1.64909i	0.0218931	+	0.0673801i	−0.939513	+	0.342513i	$0.888722\pi$
$600$		0			0
$601$	6.59091			0.268849			0.134424	−	0.990924i	$-0.457081\pi$
$601$	6.59091			0.268849			0.134424	+	0.990924i	$0.457081\pi$
$602$		0			0
$603$	16.3379	+	11.8702i	0.665331	+	0.483391i
$604$		0			0
$605$	34.9791	−	25.4138i	1.42210	−	1.03322i
$606$		0			0
$607$	−8.06839	+	5.86203i	−0.327486	+	0.237932i	−0.739363	−	0.673307i	$-0.764873\pi$
$607$	−8.06839	+	5.86203i	−0.327486	+	0.237932i	0.411877	+	0.911239i	$0.364873\pi$
$608$		0			0
$609$	−2.84130	+	8.74463i	−0.115135	+	0.354350i
$610$		0			0
$611$	6.23135	+	4.52734i	0.252094	+	0.183157i
$612$		0			0
$613$	11.1383	−	34.2803i	0.449873	−	1.38457i	−0.427177	−	0.904168i	$-0.640492\pi$
$613$	11.1383	−	34.2803i	0.449873	−	1.38457i	0.877050	−	0.480399i	$-0.159508\pi$
$614$		0			0
$615$	29.7207	+	5.59554i	1.19846	+	0.225634i
$616$		0			0
$617$	4.43121	−	13.6379i	0.178394	−	0.549040i	−0.821378	−	0.570384i	$-0.806794\pi$
$617$	4.43121	−	13.6379i	0.178394	−	0.549040i	0.999772	+	0.0213439i	$0.00679448\pi$
$618$		0			0
$619$	−2.24611	−	1.63190i	−0.0902789	−	0.0655914i	0.541730	−	0.840552i	$-0.317769\pi$
$619$	−2.24611	−	1.63190i	−0.0902789	−	0.0655914i	−0.632009	+	0.774961i	$0.717769\pi$
$620$		0			0
$621$	11.4327	−	35.1863i	0.458779	−	1.41198i
$622$		0			0
$623$	−2.33050	+	1.69321i	−0.0933694	+	0.0678368i
$624$		0			0
$625$	−30.0254	+	21.8147i	−1.20102	+	0.872589i
$626$		0			0
$627$	−0.639344	−	0.464511i	−0.0255330	−	0.0185508i
$628$		0			0
$629$	38.9341			1.55240
$630$		0			0
$631$	9.40744	+	28.9531i	0.374504	+	1.15261i	0.943812	+	0.330482i	$0.107211\pi$
$631$	9.40744	+	28.9531i	0.374504	+	1.15261i	−0.569308	+	0.822124i	$0.692789\pi$
$632$		0			0
$633$	2.93427	−	9.03075i	0.116627	−	0.358940i
$634$		0			0
$635$	15.5492	+	47.8556i	0.617052	+	1.89909i
$636$		0			0
$637$	−1.61070	−	4.95723i	−0.0638183	−	0.196412i
$638$		0			0
$639$	17.2654	−	12.5441i	0.683010	−	0.496236i
$640$		0			0
$641$	18.4237	+	13.3856i	0.727693	+	0.528700i	0.888833	−	0.458232i	$-0.151517\pi$
$641$	18.4237	+	13.3856i	0.727693	+	0.528700i	−0.161140	+	0.986932i	$0.551517\pi$
$642$		0			0
$643$	−13.3564	+	41.1068i	−0.526726	+	1.62110i	0.234151	+	0.972200i	$0.424769\pi$
$643$	−13.3564	+	41.1068i	−0.526726	+	1.62110i	−0.760877	+	0.648896i	$0.775231\pi$
$644$		0			0
$645$	19.8506	−	14.4223i	0.781618	−	0.567879i
$646$		0			0
$647$	21.8926			0.860685			0.430343	−	0.902666i	$-0.358393\pi$
$647$	21.8926			0.860685			0.430343	+	0.902666i	$0.358393\pi$
$648$		0			0
$649$	−1.04911	−	3.22882i	−0.0411811	−	0.126742i
$650$		0			0
$651$	4.14798	+	3.01369i	0.162572	+	0.118116i
$652$		0			0
$653$	−1.86747			−0.0730798			−0.0365399	−	0.999332i	$-0.511634\pi$
$653$	−1.86747			−0.0730798			−0.0365399	+	0.999332i	$0.511634\pi$
$654$		0			0
$655$	−77.9095			−3.04418
$656$		0			0
$657$	−15.9240			−0.621254
$658$		0			0
$659$	−8.06040			−0.313989			−0.156994	−	0.987599i	$-0.550180\pi$
$659$	−8.06040			−0.313989			−0.156994	+	0.987599i	$0.550180\pi$
$660$		0			0
$661$	34.8836	+	25.3444i	1.35681	+	0.985783i	0.998640	+	0.0521273i	$0.0166002\pi$
$661$	34.8836	+	25.3444i	1.35681	+	0.985783i	0.358173	+	0.933655i	$0.383400\pi$
$662$		0			0
$663$	12.2030	+	37.5569i	0.473924	+	1.45859i
$664$		0			0
$665$	−7.89353			−0.306098
$666$		0			0
$667$	42.4245	−	30.8232i	1.64268	−	1.19348i
$668$		0			0
$669$	−2.42989	+	7.47843i	−0.0939450	+	0.289133i
$670$		0			0
$671$	0.415461	+	0.301850i	0.0160387	+	0.0116528i
$672$		0			0
$673$	−12.5959	+	9.15147i	−0.485537	+	0.352763i	−0.803465	−	0.595351i	$-0.797013\pi$
$673$	−12.5959	+	9.15147i	−0.485537	+	0.352763i	0.317928	+	0.948115i	$0.397013\pi$
$674$		0			0
$675$	−18.1480	−	55.8538i	−0.698517	−	2.14982i
$676$		0			0
$677$	8.41286	+	25.8921i	0.323332	+	0.995115i	0.972188	+	0.234203i	$0.0752480\pi$
$677$	8.41286	+	25.8921i	0.323332	+	0.995115i	−0.648855	+	0.760912i	$0.724752\pi$
$678$		0			0
$679$	−3.66278	+	11.2729i	−0.140565	+	0.432613i
$680$		0			0
$681$	5.03153	+	15.4855i	0.192809	+	0.593404i
$682$		0			0
$683$	−20.8568			−0.798063			−0.399032	−	0.916937i	$-0.630654\pi$
$683$	−20.8568			−0.798063			−0.399032	+	0.916937i	$0.630654\pi$
$684$		0			0
$685$	−68.9177	−	50.0716i	−2.63321	−	1.91314i
$686$		0			0
$687$	−7.90012	+	5.73977i	−0.301408	+	0.218986i
$688$		0			0
$689$	13.9602	−	10.1427i	0.531842	−	0.386406i
$690$		0			0
$691$	4.50478	−	13.8643i	0.171370	−	0.527423i	−0.828079	−	0.560611i	$-0.810566\pi$
$691$	4.50478	−	13.8643i	0.171370	−	0.527423i	0.999449	+	0.0331887i	$0.0105662\pi$
$692$		0			0
$693$	−0.428660	−	0.311440i	−0.0162834	−	0.0118306i
$694$		0			0
$695$	2.47177	−	7.60733i	0.0937597	−	0.288563i
$696$		0			0
$697$	−19.5625	+	35.7875i	−0.740982	+	1.35555i
$698$		0			0
$699$	0.677702	−	2.08575i	0.0256330	−	0.0788904i
$700$		0			0
$701$	23.8876	+	17.3554i	0.902224	+	0.655504i	0.939036	−	0.343818i	$-0.111720\pi$
$701$	23.8876	+	17.3554i	0.902224	+	0.655504i	−0.0368122	+	0.999322i	$0.511720\pi$
$702$		0			0
$703$	−3.75475	+	11.5559i	−0.141613	+	0.435840i
$704$		0			0
$705$	−5.64653	+	4.10244i	−0.212660	+	0.154507i
$706$		0			0
$707$	−13.4319	+	9.75884i	−0.505158	+	0.367019i
$708$		0			0
$709$	−3.53378	−	2.56744i	−0.132714	−	0.0964222i	0.519448	−	0.854502i	$-0.326138\pi$
$709$	−3.53378	−	2.56744i	−0.132714	−	0.0964222i	−0.652162	+	0.758080i	$0.726138\pi$
$710$		0			0
$711$	−7.46920			−0.280117
$712$		0			0
$713$	−9.03620	−	27.8106i	−0.338409	−	1.04151i
$714$		0			0
$715$	−2.13778	+	6.57942i	−0.0799485	+	0.246056i
$716$		0			0
$717$	−6.34392	−	19.5246i	−0.236918	−	0.729159i
$718$		0			0
$719$	−10.2719	−	31.6138i	−0.383079	−	1.17900i	−0.937864	−	0.347002i	$-0.887200\pi$
$719$	−10.2719	−	31.6138i	−0.383079	−	1.17900i	0.554785	−	0.831994i	$-0.312800\pi$
$720$		0			0
$721$	0.226351	−	0.164454i	0.00842977	−	0.00612459i
$722$		0			0
$723$	−2.84428	−	2.06649i	−0.105780	−	0.0768535i
$724$		0			0
$725$	25.7230	−	79.1672i	0.955327	−	2.94019i
$726$		0			0
$727$	−3.89089	+	2.82690i	−0.144305	+	0.104844i	−0.657596	−	0.753371i	$-0.728426\pi$
$727$	−3.89089	+	2.82690i	−0.144305	+	0.104844i	0.513290	+	0.858215i	$0.328426\pi$
$728$		0			0
$729$	22.2054			0.822422
$730$		0			0
$731$	10.2254	+	31.4704i	0.378199	+	1.16398i
$732$		0			0
$733$	0.569190	+	0.413541i	0.0210235	+	0.0152745i	0.598247	−	0.801311i	$-0.295864\pi$
$733$	0.569190	+	0.413541i	0.0210235	+	0.0152745i	−0.577224	+	0.816586i	$0.695864\pi$
$734$		0			0
$735$	4.72315			0.174216
$736$		0			0
$737$	4.25793			0.156843
$738$		0			0
$739$	14.5602			0.535606			0.267803	−	0.963474i	$-0.413702\pi$
$739$	14.5602			0.535606			0.267803	+	0.963474i	$0.413702\pi$
$740$		0			0
$741$	−12.3240			−0.452734
$742$		0			0
$743$	−14.0544	−	10.2111i	−0.515607	−	0.374610i	0.299339	−	0.954147i	$-0.403234\pi$
$743$	−14.0544	−	10.2111i	−0.515607	−	0.374610i	−0.814946	+	0.579536i	$0.803234\pi$
$744$		0			0
$745$	4.33346	+	13.3370i	0.158766	+	0.488630i
$746$		0			0
$747$	−22.9804			−0.840808
$748$		0			0
$749$	−7.22427	+	5.24874i	−0.263969	+	0.191785i
$750$		0			0
$751$	5.16229	−	15.8879i	0.188375	−	0.579758i	−0.811615	−	0.584192i	$-0.801411\pi$
$751$	5.16229	−	15.8879i	0.188375	−	0.579758i	0.999990	+	0.00443434i	$0.00141150\pi$
$752$		0			0
$753$	9.56002	+	6.94576i	0.348386	+	0.253118i
$754$		0			0
$755$	−5.01291	+	3.64209i	−0.182438	+	0.132549i
$756$		0			0
$757$	−16.4725	−	50.6971i	−0.598702	−	1.84262i	−0.535359	−	0.844625i	$-0.679824\pi$
$757$	−16.4725	−	50.6971i	−0.598702	−	1.84262i	−0.0633437	−	0.997992i	$-0.520176\pi$
$758$		0			0
$759$	−0.833382	−	2.56489i	−0.0302498	−	0.0930995i
$760$		0			0
$761$	6.39226	−	19.6733i	0.231719	−	0.713158i	−0.765821	−	0.643054i	$-0.777667\pi$
$761$	6.39226	−	19.6733i	0.231719	−	0.713158i	0.997540	−	0.0701038i	$-0.0223331\pi$
$762$		0			0
$763$	3.81188	+	11.7318i	0.137999	+	0.424718i
$764$		0			0
$765$	40.0959			1.44967
$766$		0			0
$767$	−42.8322	−	31.1194i	−1.54658	−	1.12366i
$768$		0			0
$769$	−43.7395	+	31.7786i	−1.57729	+	1.14597i	−0.657566	+	0.753397i	$0.728414\pi$
$769$	−43.7395	+	31.7786i	−1.57729	+	1.14597i	−0.919722	+	0.392570i	$0.871586\pi$
$770$		0			0
$771$	8.60711	−	6.25343i	0.309977	−	0.225212i
$772$		0			0
$773$	−1.03290	+	3.17893i	−0.0371507	+	0.114338i	−0.967912	−	0.251289i	$-0.919145\pi$
$773$	−1.03290	+	3.17893i	−0.0371507	+	0.114338i	0.930761	+	0.365627i	$0.119145\pi$
$774$		0			0
$775$	−37.5527	−	27.2836i	−1.34893	−	0.980056i
$776$		0			0
$777$	2.24668	−	6.91457i	0.0805991	−	0.248059i
$778$		0			0
$779$	−8.73542	−	9.25759i	−0.312979	−	0.331688i
$780$		0			0
$781$	1.39047	−	4.27943i	0.0497550	−	0.153130i
$782$		0			0
$783$	34.1079	+	24.7809i	1.21892	+	0.885596i
$784$		0			0
$785$	16.6727	−	51.3133i	0.595074	−	1.83145i
$786$		0			0
$787$	−3.13420	+	2.27713i	−0.111722	+	0.0811709i	−0.642243	−	0.766501i	$-0.721996\pi$
$787$	−3.13420	+	2.27713i	−0.111722	+	0.0811709i	0.530521	+	0.847672i	$0.321996\pi$
$788$		0			0
$789$	25.2886	−	18.3733i	0.900299	−	0.654106i
$790$		0			0
$791$	4.32785	+	3.14437i	0.153881	+	0.111801i
$792$		0			0
$793$	8.00844			0.284388
$794$		0			0
$795$	4.83188	+	14.8710i	0.171369	+	0.527420i
$796$		0			0
$797$	−0.344789	+	1.06115i	−0.0122131	+	0.0375880i	−0.956977	−	0.290163i	$-0.906291\pi$
$797$	−0.344789	+	1.06115i	−0.0122131	+	0.0375880i	0.944764	+	0.327751i	$0.106291\pi$
$798$		0			0
$799$	−2.90861	−	8.95179i	−0.102899	−	0.316691i
$800$		0			0
$801$	1.41114	+	4.34305i	0.0498603	+	0.153454i
$802$		0			0
$803$	−2.71625	+	1.97347i	−0.0958544	+	0.0696423i
$804$		0			0
$805$	−21.7928	−	15.8334i	−0.768096	−	0.558054i
$806$		0			0
$807$	−0.330495	+	1.01716i	−0.0116340	+	0.0358057i
$808$		0			0
$809$	−39.8522	+	28.9543i	−1.40113	+	1.01798i	−0.406590	+	0.913611i	$0.633282\pi$
$809$	−39.8522	+	28.9543i	−1.40113	+	1.01798i	−0.994539	+	0.104369i	$0.966718\pi$
$810$		0			0
$811$	18.0367			0.633354			0.316677	−	0.948533i	$-0.397433\pi$
$811$	18.0367			0.633354			0.316677	+	0.948533i	$0.397433\pi$
$812$		0			0
$813$	5.92980	+	18.2500i	0.207967	+	0.640057i
$814$		0			0
$815$	70.4933	+	51.2164i	2.46927	+	1.79403i
$816$		0			0
$817$	−10.3268			−0.361289
$818$		0			0
$819$	−8.26285			−0.288727
$820$		0			0
$821$	−33.4682			−1.16805			−0.584023	−	0.811737i	$-0.698522\pi$
$821$	−33.4682			−1.16805			−0.584023	+	0.811737i	$0.698522\pi$
$822$		0			0
$823$	33.5528			1.16958			0.584789	−	0.811185i	$-0.301177\pi$
$823$	33.5528			1.16958			0.584789	+	0.811185i	$0.301177\pi$
$824$		0			0
$825$	−3.46337	−	2.51629i	−0.120579	−	0.0876058i
$826$		0			0
$827$	5.71437	+	17.5870i	0.198708	+	0.611561i	0.999913	+	0.0131712i	$0.00419263\pi$
$827$	5.71437	+	17.5870i	0.198708	+	0.611561i	−0.801205	+	0.598390i	$0.795807\pi$
$828$		0			0
$829$	41.4242			1.43872			0.719361	−	0.694636i	$-0.244435\pi$
$829$	41.4242			1.43872			0.719361	+	0.694636i	$0.244435\pi$
$830$		0			0
$831$	−6.11692	+	4.44421i	−0.212194	+	0.154168i
$832$		0			0
$833$	−1.96831	+	6.05783i	−0.0681979	+	0.209891i
$834$		0			0
$835$	−52.3351	−	38.0237i	−1.81113	−	1.31586i
$836$		0			0
$837$	19.0195	−	13.8185i	0.657411	−	0.477637i
$838$		0			0
$839$	8.89158	+	27.3655i	0.306971	+	0.944761i	0.978934	+	0.204176i	$0.0654515\pi$
$839$	8.89158	+	27.3655i	0.306971	+	0.944761i	−0.671963	+	0.740585i	$0.734549\pi$
$840$		0			0
$841$	9.50448	+	29.2518i	0.327741	+	1.00868i
$842$		0			0
$843$	0.869596	−	2.67634i	0.0299505	−	0.0921780i
$844$		0			0
$845$	17.3858	+	53.5081i	0.598091	+	1.84074i
$846$		0			0
$847$	10.8883			0.374126
$848$		0			0
$849$	12.7597	+	9.27048i	0.437912	+	0.318162i
$850$		0			0
$851$	−33.5460	+	24.3726i	−1.14994	+	0.835481i
$852$		0			0
$853$	−24.4908	+	17.7936i	−0.838550	+	0.609242i	−0.921965	−	0.387273i	$-0.873417\pi$
$853$	−24.4908	+	17.7936i	−0.838550	+	0.609242i	0.0834153	+	0.996515i	$0.473417\pi$
$854$		0			0
$855$	−3.86679	+	11.9008i	−0.132242	+	0.406998i
$856$		0			0
$857$	−35.6097	−	25.8719i	−1.21640	−	0.883768i	−0.220607	−	0.975363i	$-0.570804\pi$
$857$	−35.6097	−	25.8719i	−1.21640	−	0.883768i	−0.995796	+	0.0915944i	$0.970804\pi$
$858$		0			0
$859$	11.9960	−	36.9199i	0.409298	−	1.25969i	−0.507955	−	0.861384i	$-0.669598\pi$
$859$	11.9960	−	36.9199i	0.409298	−	1.25969i	0.917253	−	0.398306i	$-0.130402\pi$
$860$		0			0
$861$	5.22690	+	5.53934i	0.178132	+	0.188780i
$862$		0			0
$863$	2.23145	−	6.86769i	0.0759594	−	0.233779i	−0.905866	−	0.423564i	$-0.860779\pi$
$863$	2.23145	−	6.86769i	0.0759594	−	0.233779i	0.981826	+	0.189785i	$0.0607790\pi$
$864$		0			0
$865$	58.7826	+	42.7081i	1.99867	+	1.45212i
$866$		0			0
$867$	8.66385	−	26.6646i	0.294240	−	0.905577i
$868$		0			0
$869$	−1.27407	+	0.925663i	−0.0432197	+	0.0314010i
$870$		0			0
$871$	53.7194	−	39.0294i	1.82021	−	1.32246i
$872$		0			0
$873$	15.2014	+	11.0445i	0.514489	+	0.373798i
$874$		0			0
$875$	−22.9051			−0.774335
$876$		0			0
$877$	−7.19352	−	22.1394i	−0.242908	−	0.747594i	−0.995973	−	0.0896484i	$-0.971426\pi$
$877$	−7.19352	−	22.1394i	−0.242908	−	0.747594i	0.753065	−	0.657946i	$-0.228574\pi$
$878$		0			0
$879$	10.5704	−	32.5323i	0.356530	−	1.09729i
$880$		0			0
$881$	12.4711	+	38.3821i	0.420162	+	1.29313i	0.907551	+	0.419941i	$0.137949\pi$
$881$	12.4711	+	38.3821i	0.420162	+	1.29313i	−0.487390	+	0.873185i	$0.662051\pi$
$882$		0			0
$883$	0.849570	+	2.61471i	0.0285903	+	0.0879920i	0.964334	−	0.264690i	$-0.0852697\pi$
$883$	0.849570	+	2.61471i	0.0285903	+	0.0879920i	−0.935743	+	0.352682i	$0.885270\pi$
$884$		0			0
$885$	38.8123	−	28.1988i	1.30466	−	0.947891i
$886$		0			0
$887$	−20.3374	−	14.7760i	−0.682862	−	0.496128i	0.191444	−	0.981504i	$-0.438683\pi$
$887$	−20.3374	−	14.7760i	−0.682862	−	0.496128i	−0.874306	+	0.485375i	$0.838683\pi$
$888$		0			0
$889$	−3.91577	+	12.0515i	−0.131331	+	0.404194i
$890$		0			0
$891$	0.468136	−	0.340120i	0.0156831	−	0.0113945i
$892$		0			0
$893$	2.93746			0.0982984
$894$		0			0
$895$	15.7075	+	48.3429i	0.525045	+	1.61592i
$896$		0			0
$897$	−34.0247	−	24.7204i	−1.13605	−	0.825390i
$898$		0			0
$899$	33.3223			1.11136
$900$		0			0
$901$	−21.0869			−0.702507
$902$		0			0
$903$	6.17910			0.205628
$904$		0			0
$905$	58.5727			1.94702
$906$		0			0
$907$	−31.9302	−	23.1987i	−1.06023	−	0.770299i	−0.0860957	−	0.996287i	$-0.527439\pi$
$907$	−31.9302	−	23.1987i	−1.06023	−	0.770299i	−0.974130	+	0.225988i	$0.927439\pi$
$908$		0			0
$909$	8.13316	+	25.0313i	0.269760	+	0.830235i
$910$		0			0
$911$	29.7133			0.984447			0.492223	−	0.870469i	$-0.336184\pi$
$911$	29.7133			0.984447			0.492223	+	0.870469i	$0.336184\pi$
$912$		0			0
$913$	−3.91990	+	2.84797i	−0.129730	+	0.0942541i
$914$		0			0
$915$	−2.24248	+	6.90165i	−0.0741342	+	0.228162i
$916$		0			0
$917$	−15.8729	−	11.5323i	−0.524170	−	0.380832i
$918$		0			0
$919$	8.47809	−	6.15969i	0.279666	−	0.203189i	−0.439106	−	0.898435i	$-0.644705\pi$
$919$	8.47809	−	6.15969i	0.279666	−	0.203189i	0.718772	+	0.695246i	$0.244705\pi$
$920$		0			0
$921$	−0.500848	−	1.54145i	−0.0165035	−	0.0507925i
$922$		0			0
$923$	−21.6839	−	66.7361i	−0.713733	−	2.19665i
$924$		0			0
$925$	−20.3397	+	62.5992i	−0.668766	+	2.05825i
$926$		0			0
$927$	−0.137058	−	0.421822i	−0.00450159	−	0.0138545i
$928$		0			0
$929$	−11.3162			−0.371274			−0.185637	−	0.982618i	$-0.559435\pi$
$929$	−11.3162			−0.371274			−0.185637	+	0.982618i	$0.559435\pi$
$930$		0			0
$931$	−1.60819	−	1.16842i	−0.0527063	−	0.0382934i
$932$		0			0
$933$	1.86109	−	1.35216i	0.0609295	−	0.0442679i
$934$		0			0
$935$	6.83939	−	4.96911i	0.223672	−	0.162507i
$936$		0			0
$937$	−3.30729	+	10.1788i	−0.108044	+	0.332526i	−0.990433	−	0.137995i	$-0.955934\pi$
$937$	−3.30729	+	10.1788i	−0.108044	+	0.332526i	0.882389	+	0.470522i	$0.155934\pi$
$938$		0			0
$939$	−10.1313	−	7.36081i	−0.330622	−	0.240211i
$940$		0			0
$941$	1.50491	−	4.63163i	0.0490585	−	0.150987i	−0.923526	−	0.383535i	$-0.874706\pi$
$941$	1.50491	−	4.63163i	0.0490585	−	0.150987i	0.972585	+	0.232549i	$0.0747065\pi$
$942$		0			0
$943$	−5.54760	−	43.0809i	−0.180655	−	1.40291i
$944$		0			0
$945$	6.69232	−	20.5968i	0.217701	−	0.670015i
$946$		0			0
$947$	20.0043	+	14.5340i	0.650053	+	0.472291i	0.863289	−	0.504710i	$-0.168400\pi$
$947$	20.0043	+	14.5340i	0.650053	+	0.472291i	−0.213236	+	0.977001i	$0.568400\pi$
$948$		0			0
$949$	−16.1797	+	49.7959i	−0.525214	+	1.61644i
$950$		0			0
$951$	−31.4856	+	22.8756i	−1.02099	+	0.741793i
$952$		0			0
$953$	−2.98761	+	2.17063i	−0.0967782	+	0.0703135i	−0.635122	−	0.772412i	$-0.719050\pi$
$953$	−2.98761	+	2.17063i	−0.0967782	+	0.0703135i	0.538344	+	0.842725i	$0.319050\pi$
$954$		0			0
$955$	−6.51646	−	4.73449i	−0.210868	−	0.153204i
$956$		0			0
$957$	3.07321			0.0993428
$958$		0			0
$959$	−6.62924	−	20.4027i	−0.214069	−	0.658838i
$960$		0			0
$961$	−3.83755	+	11.8108i	−0.123792	+	0.380993i
$962$		0			0
$963$	4.37438	+	13.4630i	0.140962	+	0.433838i
$964$		0			0
$965$	8.15921	+	25.1115i	0.262654	+	0.808367i
$966$		0			0
$967$	−3.41045	+	2.47784i	−0.109673	+	0.0796818i	−0.641270	−	0.767316i	$-0.721592\pi$
$967$	−3.41045	+	2.47784i	−0.109673	+	0.0796818i	0.531597	+	0.846997i	$0.321592\pi$
$968$		0			0
$969$	12.1840	+	8.85216i	0.391405	+	0.284372i
$970$		0			0
$971$	2.70135	−	8.31389i	0.0866903	−	0.266805i	−0.898309	−	0.439365i	$-0.855204\pi$
$971$	2.70135	−	8.31389i	0.0866903	−	0.266805i	0.984999	+	0.172559i	$0.0552036\pi$
$972$		0			0
$973$	1.62964	−	1.18401i	0.0522440	−	0.0379575i
$974$		0			0
$975$	−66.7600			−2.13803
$976$		0			0
$977$	−5.37644	−	16.5470i	−0.172007	−	0.529384i	0.827477	−	0.561500i	$-0.189776\pi$
$977$	−5.37644	−	16.5470i	−0.172007	−	0.529384i	−0.999484	+	0.0321156i	$0.989776\pi$
$978$		0			0
$979$	0.778944	+	0.565936i	0.0248951	+	0.0180874i
$980$		0			0
$981$	19.5548			0.624338
$982$		0			0
$983$	40.9075			1.30475			0.652374	−	0.757897i	$-0.273773\pi$
$983$	40.9075			1.30475			0.652374	+	0.757897i	$0.273773\pi$
$984$		0			0
$985$	105.697			3.36777
$986$		0			0
$987$	−1.75765			−0.0559466
$988$		0			0
$989$	−28.5107	−	20.7142i	−0.906586	−	0.658674i
$990$		0			0
$991$	−4.30109	−	13.2374i	−0.136629	−	0.420500i	0.859211	−	0.511621i	$-0.170955\pi$
$991$	−4.30109	−	13.2374i	−0.136629	−	0.420500i	−0.995840	+	0.0911214i	$0.970955\pi$
$992$		0			0
$993$	25.9338			0.822985
$994$		0			0
$995$	23.7232	−	17.2359i	0.752076	−	0.546416i
$996$		0			0
$997$	4.46379	−	13.7381i	0.141370	−	0.435091i	−0.855157	−	0.518370i	$-0.826539\pi$
$997$	4.46379	−	13.7381i	0.141370	−	0.435091i	0.996526	+	0.0832784i	$0.0265391\pi$
$998$		0			0
$999$	−26.9699	−	19.5948i	−0.853290	−	0.619951i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.n.e.57.4	✓	24
41.18	even	5	inner	1148.2.n.e.141.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.n.e.57.4	✓	24	1.1	even	1	trivial
1148.2.n.e.141.4	yes	24	41.18	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)

\(f(q)\)	\(=\)	\(q+1.18943 q^{3} +(-3.21254 - 2.33405i) q^{5} +(-0.309017 - 0.951057i) q^{7} -1.58525 q^{9} +O(q^{10})\)	\(q+1.18943 q^{3} +(-3.21254 - 2.33405i) q^{5} +(-0.309017 - 0.951057i) q^{7} -1.58525 q^{9} +(-0.270405 + 0.196461i) q^{11} +(-1.61070 + 4.95723i) q^{13} +(-3.82110 - 2.77620i) q^{15} +(5.15310 - 3.74395i) q^{17} +(0.614274 + 1.89054i) q^{19} +(-0.367555 - 1.13122i) q^{21} +(-2.09627 + 6.45165i) q^{23} +(3.32756 + 10.2412i) q^{25} -5.45385 q^{27} +(-6.25392 - 4.54374i) q^{29} +(-3.48736 + 2.53372i) q^{31} +(-0.321629 + 0.233677i) q^{33} +(-1.22708 + 3.77657i) q^{35} +(4.94511 + 3.59284i) q^{37} +(-1.91582 + 5.89629i) q^{39} +(-5.78715 + 2.74023i) q^{41} +(-1.60534 + 4.94074i) q^{43} +(5.09268 + 3.70005i) q^{45} +(0.456641 - 1.40540i) q^{47} +(-0.809017 + 0.587785i) q^{49} +(6.12927 - 4.45317i) q^{51} +(-2.67830 - 1.94590i) q^{53} +1.32724 q^{55} +(0.730638 + 2.24867i) q^{57} +(-3.13879 + 9.66021i) q^{59} +(-0.474786 - 1.46124i) q^{61} +(0.489869 + 1.50766i) q^{63} +(16.7449 - 12.1658i) q^{65} +(-10.3062 - 7.48790i) q^{67} +(-2.49337 + 7.67380i) q^{69} +(-10.8913 + 7.91299i) q^{71} +10.0451 q^{73} +(3.95791 + 12.1812i) q^{75} +(0.270405 + 0.196461i) q^{77} +4.71169 q^{79} -1.73124 q^{81} +14.4964 q^{83} -25.2931 q^{85} +(-7.43862 - 5.40448i) q^{87} +(-0.890171 - 2.73966i) q^{89} +5.21234 q^{91} +(-4.14798 + 3.01369i) q^{93} +(2.43923 - 7.50719i) q^{95} +(-9.58928 - 6.96702i) q^{97} +(0.428660 - 0.311440i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{3} + 17 q^{5} + 6 q^{7} + 16 q^{9}+O(q^{10}) \) 24 * q + 12 * q^3 + 17 * q^5 + 6 * q^7 + 16 * q^9	\( 24 q + 12 q^{3} + 17 q^{5} + 6 q^{7} + 16 q^{9} - 8 q^{11} + 10 q^{15} + 8 q^{17} - 28 q^{19} + 3 q^{21} - 23 q^{23} + 17 q^{25} + 12 q^{27} - 31 q^{29} + 2 q^{31} + 12 q^{33} + 13 q^{35} + 7 q^{37} - 16 q^{39} - q^{41} - 2 q^{43} + 71 q^{45} + 15 q^{47} - 6 q^{49} + 2 q^{51} + 28 q^{53} - 16 q^{55} - 15 q^{57} + 17 q^{59} + 35 q^{61} - q^{63} + 62 q^{65} - 10 q^{67} - 9 q^{69} - 25 q^{71} - 74 q^{73} + 17 q^{75} + 8 q^{77} + 64 q^{81} + 96 q^{83} - 94 q^{85} - q^{87} - 33 q^{89} - 15 q^{93} - 29 q^{95} - 34 q^{97} - 3 q^{99}+O(q^{100}) \) 24 * q + 12 * q^3 + 17 * q^5 + 6 * q^7 + 16 * q^9 - 8 * q^11 + 10 * q^15 + 8 * q^17 - 28 * q^19 + 3 * q^21 - 23 * q^23 + 17 * q^25 + 12 * q^27 - 31 * q^29 + 2 * q^31 + 12 * q^33 + 13 * q^35 + 7 * q^37 - 16 * q^39 - q^41 - 2 * q^43 + 71 * q^45 + 15 * q^47 - 6 * q^49 + 2 * q^51 + 28 * q^53 - 16 * q^55 - 15 * q^57 + 17 * q^59 + 35 * q^61 - q^63 + 62 * q^65 - 10 * q^67 - 9 * q^69 - 25 * q^71 - 74 * q^73 + 17 * q^75 + 8 * q^77 + 64 * q^81 + 96 * q^83 - 94 * q^85 - q^87 - 33 * q^89 - 15 * q^93 - 29 * q^95 - 34 * q^97 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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