LMFDB - Embedded newform 1456.2.r.p.625.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1456,2,Mod(417,1456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1456, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))

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

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

chi := DirichletCharacter("1456.417");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1456 = 2^{4} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1456.r (of order $3$, degree $2$, not 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:	$11.6262185343$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 8x^{8} + 7x^{7} + 41x^{6} + 18x^{5} + 58x^{4} + 28x^{3} + 64x^{2} + 16x + 4 $ x^10 - x^9 + 8x^8 + 7x^7 + 41x^6 + 18x^5 + 58x^4 + 28x^3 + 64x^2 + 16x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			625.1
Root			$-0.132804 + 0.230024i$ of defining polynomial
Character	$\chi$	$=$	1456.625
Dual form			1456.2.r.p.417.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31364 - 2.27529i) q^{3} +(1.45130 - 2.51373i) q^{5} +(1.29536 + 2.30696i) q^{7} +(-1.95130 + 3.37975i) q^{9} +O(q^{10})$	\(q+(-1.31364 - 2.27529i) q^{3} +(1.45130 - 2.51373i) q^{5} +(1.29536 + 2.30696i) q^{7} +(-1.95130 + 3.37975i) q^{9} +(1.01828 + 1.76372i) q^{11} +1.00000 q^{13} -7.62594 q^{15} +(-1.99933 - 3.46294i) q^{17} +(3.48105 - 6.02935i) q^{19} +(3.54736 - 5.97783i) q^{21} +(-0.313640 + 0.543240i) q^{23} +(-1.71254 - 2.96621i) q^{25} +2.37138 q^{27} +1.09606 q^{29} +(-5.21624 - 9.03479i) q^{31} +(2.67531 - 4.63378i) q^{33} +(7.67901 + 0.0919110i) q^{35} +(1.54268 - 2.67201i) q^{37} +(-1.31364 - 2.27529i) q^{39} -0.521150 q^{41} -0.329024 q^{43} +(5.66384 + 9.81006i) q^{45} +(5.27284 - 9.13283i) q^{47} +(-3.64409 + 5.97667i) q^{49} +(-5.25280 + 9.09812i) q^{51} +(-3.55950 - 6.16523i) q^{53} +5.91133 q^{55} -18.2914 q^{57} +(1.01828 + 1.76372i) q^{59} +(-1.20041 + 2.07917i) q^{61} +(-10.3246 - 0.123576i) q^{63} +(1.45130 - 2.51373i) q^{65} +(7.34709 + 12.7255i) q^{67} +1.64804 q^{69} -3.60141 q^{71} +(-1.48786 - 2.57706i) q^{73} +(-4.49933 + 7.79307i) q^{75} +(-2.74978 + 4.63378i) q^{77} +(-4.38075 + 7.58769i) q^{79} +(2.73876 + 4.74367i) q^{81} -12.8039 q^{83} -11.6065 q^{85} +(-1.43983 - 2.49386i) q^{87} +(1.34049 - 2.32180i) q^{89} +(1.29536 + 2.30696i) q^{91} +(-13.7045 + 23.7369i) q^{93} +(-10.1041 - 17.5008i) q^{95} -2.32902 q^{97} -7.94789 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{5} - q^{7} - 3 q^{9}+O(q^{10}) $ 10 * q - 2 * q^5 - q^7 - 3 * q^9	$ 10 q - 2 q^{5} - q^{7} - 3 q^{9} + 11 q^{11} + 10 q^{13} + 5 q^{17} + 9 q^{19} + 2 q^{21} + 10 q^{23} - 9 q^{25} - 6 q^{29} - 6 q^{31} - 8 q^{33} + 4 q^{35} - 4 q^{37} + 28 q^{41} - 4 q^{43} + 32 q^{45} + q^{47} - 11 q^{49} - 8 q^{51} - 17 q^{53} - 32 q^{57} + 11 q^{59} + 11 q^{61} - 5 q^{63} - 2 q^{65} + 13 q^{67} + 36 q^{69} - 30 q^{71} - 20 q^{75} - 46 q^{77} + 2 q^{79} + 19 q^{81} - 12 q^{83} - 44 q^{85} - 8 q^{87} + 4 q^{89} - q^{91} - 18 q^{93} - 12 q^{95} - 24 q^{97} - 22 q^{99}+O(q^{100}) $ 10 * q - 2 * q^5 - q^7 - 3 * q^9 + 11 * q^11 + 10 * q^13 + 5 * q^17 + 9 * q^19 + 2 * q^21 + 10 * q^23 - 9 * q^25 - 6 * q^29 - 6 * q^31 - 8 * q^33 + 4 * q^35 - 4 * q^37 + 28 * q^41 - 4 * q^43 + 32 * q^45 + q^47 - 11 * q^49 - 8 * q^51 - 17 * q^53 - 32 * q^57 + 11 * q^59 + 11 * q^61 - 5 * q^63 - 2 * q^65 + 13 * q^67 + 36 * q^69 - 30 * q^71 - 20 * q^75 - 46 * q^77 + 2 * q^79 + 19 * q^81 - 12 * q^83 - 44 * q^85 - 8 * q^87 + 4 * q^89 - q^91 - 18 * q^93 - 12 * q^95 - 24 * q^97 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times$.

$n$	$561$	$911$	$1093$	$1249$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	−1.31364	−	2.27529i	−0.758430	−	1.31364i	−0.943651	−	0.330943i	$-0.892633\pi$
$3$	−1.31364	−	2.27529i	−0.758430	−	1.31364i	0.185220	−	0.982697i	$-0.440700\pi$
$4$		0			0
$5$	1.45130	−	2.51373i	0.649041	−	1.12417i	−0.334311	−	0.942463i	$-0.608504\pi$
$5$	1.45130	−	2.51373i	0.649041	−	1.12417i	0.983352	−	0.181709i	$-0.0581630\pi$
$6$		0			0
$7$	1.29536	+	2.30696i	0.489599	+	0.871948i
$7$	1.29536	+	2.30696i	0.489599	+	0.871948i
$8$		0			0
$9$	−1.95130	+	3.37975i	−0.650433	+	1.12658i
$10$		0			0
$11$	1.01828	+	1.76372i	0.307024	+	0.531780i	0.977710	−	0.209961i	$-0.0673336\pi$
$11$	1.01828	+	1.76372i	0.307024	+	0.531780i	−0.670686	+	0.741741i	$0.734000\pi$
$12$		0			0
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$		0			0
$15$	−7.62594			−1.96901
$16$		0			0
$17$	−1.99933	−	3.46294i	−0.484909	−	0.839887i	0.514941	−	0.857226i	$-0.327814\pi$
$17$	−1.99933	−	3.46294i	−0.484909	−	0.839887i	−0.999850	+	0.0173386i	$0.994481\pi$
$18$		0			0
$19$	3.48105	−	6.02935i	0.798608	−	1.38323i	−0.121915	−	0.992540i	$-0.538904\pi$
$19$	3.48105	−	6.02935i	0.798608	−	1.38323i	0.920523	−	0.390688i	$-0.127763\pi$
$20$		0			0
$21$	3.54736	−	5.97783i	0.774098	−	1.30447i
$22$		0			0
$23$	−0.313640	+	0.543240i	−0.0653985	+	0.113273i	−0.896871	−	0.442293i	$-0.854165\pi$
$23$	−0.313640	+	0.543240i	−0.0653985	+	0.113273i	0.831472	+	0.555566i	$0.187499\pi$
$24$		0			0
$25$	−1.71254	−	2.96621i	−0.342509	−	0.593243i
$26$		0			0
$27$	2.37138			0.456373
$28$		0			0
$29$	1.09606			0.203534			0.101767	−	0.994808i	$-0.467550\pi$
$29$	1.09606			0.203534			0.101767	+	0.994808i	$0.467550\pi$
$30$		0			0
$31$	−5.21624	−	9.03479i	−0.936864	−	1.62270i	−0.771275	−	0.636502i	$-0.780381\pi$
$31$	−5.21624	−	9.03479i	−0.936864	−	1.62270i	−0.165589	−	0.986195i	$-0.552953\pi$
$32$		0			0
$33$	2.67531	−	4.63378i	0.465712	−	0.806637i
$34$		0			0
$35$	7.67901	+	0.0919110i	1.29799	+	0.0155358i
$36$		0			0
$37$	1.54268	−	2.67201i	0.253616	−	0.439275i	−0.710903	−	0.703290i	$-0.751713\pi$
$37$	1.54268	−	2.67201i	0.253616	−	0.439275i	0.964519	+	0.264015i	$0.0850468\pi$
$38$		0			0
$39$	−1.31364	−	2.27529i	−0.210351	−	0.364338i
$40$		0			0
$41$	−0.521150			−0.0813900			−0.0406950	−	0.999172i	$-0.512957\pi$
$41$	−0.521150			−0.0813900			−0.0406950	+	0.999172i	$0.512957\pi$
$42$		0			0
$43$	−0.329024			−0.0501757			−0.0250879	−	0.999685i	$-0.507987\pi$
$43$	−0.329024			−0.0501757			−0.0250879	+	0.999685i	$0.507987\pi$
$44$		0			0
$45$	5.66384	+	9.81006i	0.844316	+	1.46240i
$46$		0			0
$47$	5.27284	−	9.13283i	0.769123	−	1.33216i	−0.168916	−	0.985630i	$-0.554027\pi$
$47$	5.27284	−	9.13283i	0.769123	−	1.33216i	0.938039	−	0.346530i	$-0.112640\pi$
$48$		0			0
$49$	−3.64409	+	5.97667i	−0.520585	+	0.853810i
$50$		0			0
$51$	−5.25280	+	9.09812i	−0.735540	+	1.27399i
$52$		0			0
$53$	−3.55950	−	6.16523i	−0.488935	−	0.846860i	0.510984	−	0.859590i	$-0.329281\pi$
$53$	−3.55950	−	6.16523i	−0.488935	−	0.846860i	−0.999919	+	0.0127302i	$0.995948\pi$
$54$		0			0
$55$	5.91133			0.797084
$56$		0			0
$57$	−18.2914			−2.42275
$58$		0			0
$59$	1.01828	+	1.76372i	0.132569	+	0.229616i	0.924666	−	0.380779i	$-0.124344\pi$
$59$	1.01828	+	1.76372i	0.132569	+	0.229616i	−0.792097	+	0.610395i	$0.791011\pi$
$60$		0			0
$61$	−1.20041	+	2.07917i	−0.153696	+	0.266210i	−0.932584	−	0.360954i	$-0.882451\pi$
$61$	−1.20041	+	2.07917i	−0.153696	+	0.266210i	0.778887	+	0.627164i	$0.215784\pi$
$62$		0			0
$63$	−10.3246	−	0.123576i	−1.30077	−	0.0155691i
$64$		0			0
$65$	1.45130	−	2.51373i	0.180012	−	0.311789i
$66$		0			0
$67$	7.34709	+	12.7255i	0.897589	+	1.55467i	0.830567	+	0.556919i	$0.188017\pi$
$67$	7.34709	+	12.7255i	0.897589	+	1.55467i	0.0670226	+	0.997751i	$0.478650\pi$
$68$		0			0
$69$	1.64804			0.198401
$70$		0			0
$71$	−3.60141			−0.427409			−0.213704	−	0.976898i	$-0.568553\pi$
$71$	−3.60141			−0.427409			−0.213704	+	0.976898i	$0.568553\pi$
$72$		0			0
$73$	−1.48786	−	2.57706i	−0.174141	−	0.301622i	0.765722	−	0.643171i	$-0.222382\pi$
$73$	−1.48786	−	2.57706i	−0.174141	−	0.301622i	−0.939864	+	0.341550i	$0.889048\pi$
$74$		0			0
$75$	−4.49933	+	7.79307i	−0.519538	+	0.899866i
$76$		0			0
$77$	−2.74978	+	4.63378i	−0.313366	+	0.528068i
$78$		0			0
$79$	−4.38075	+	7.58769i	−0.492873	+	0.853681i	−0.999966	−	0.00820995i	$-0.997387\pi$
$79$	−4.38075	+	7.58769i	−0.492873	+	0.853681i	0.507093	+	0.861891i	$0.330720\pi$
$80$		0			0
$81$	2.73876	+	4.74367i	0.304306	+	0.527074i
$82$		0			0
$83$	−12.8039			−1.40541			−0.702703	−	0.711483i	$-0.748024\pi$
$83$	−12.8039			−1.40541			−0.702703	+	0.711483i	$0.748024\pi$
$84$		0			0
$85$	−11.6065			−1.25890
$86$		0			0
$87$	−1.43983	−	2.49386i	−0.154366	−	0.267370i
$88$		0			0
$89$	1.34049	−	2.32180i	0.142092	−	0.246110i	−0.786192	−	0.617982i	$-0.787950\pi$
$89$	1.34049	−	2.32180i	0.142092	−	0.246110i	0.928284	+	0.371872i	$0.121284\pi$
$90$		0			0
$91$	1.29536	+	2.30696i	0.135790	+	0.241835i
$92$		0			0
$93$	−13.7045	+	23.7369i	−1.42109	+	2.46141i
$94$		0			0
$95$	−10.1041	−	17.5008i	−1.03666	−	1.79554i
$96$		0			0
$97$	−2.32902			−0.236477			−0.118238	−	0.992985i	$-0.537725\pi$
$97$	−2.32902			−0.236477			−0.118238	+	0.992985i	$0.537725\pi$
$98$		0			0
$99$	−7.94789			−0.798793
$100$		0			0
$101$	−0.726620	−	1.25854i	−0.0723014	−	0.125230i	0.827608	−	0.561306i	$-0.189701\pi$
$101$	−0.726620	−	1.25854i	−0.0723014	−	0.125230i	−0.899910	+	0.436077i	$0.856368\pi$
$102$		0			0
$103$	−5.81765	+	10.0765i	−0.573230	+	0.992864i	0.423001	+	0.906129i	$0.360977\pi$
$103$	−5.81765	+	10.0765i	−0.573230	+	0.992864i	−0.996231	+	0.0867346i	$0.972357\pi$
$104$		0			0
$105$	−9.87833	−	17.5927i	−0.964026	−	1.71687i
$106$		0			0
$107$	9.81297	−	16.9966i	0.948656	−	1.64312i	0.200395	−	0.979715i	$-0.435777\pi$
$107$	9.81297	−	16.9966i	0.948656	−	1.64312i	0.748261	−	0.663405i	$-0.230889\pi$
$108$		0			0
$109$	0.553378	+	0.958479i	0.0530040	+	0.0918057i	0.891310	−	0.453394i	$-0.149787\pi$
$109$	0.553378	+	0.958479i	0.0530040	+	0.0918057i	−0.838306	+	0.545200i	$0.816454\pi$
$110$		0			0
$111$	−8.10613			−0.769400
$112$		0			0
$113$	−1.09606			−0.103109			−0.0515545	−	0.998670i	$-0.516418\pi$
$113$	−1.09606			−0.103109			−0.0515545	+	0.998670i	$0.516418\pi$
$114$		0			0
$115$	0.910371	+	1.57681i	0.0848926	+	0.147038i
$116$		0			0
$117$	−1.95130	+	3.37975i	−0.180398	+	0.312458i
$118$		0			0
$119$	5.39901	−	9.09812i	0.494926	−	0.834024i
$120$		0			0
$121$	3.42620	−	5.93436i	0.311473	−	0.539487i
$122$		0			0
$123$	0.684604	+	1.18577i	0.0617286	+	0.106917i
$124$		0			0
$125$	4.57134			0.408873
$126$		0			0
$127$	−5.18143			−0.459778			−0.229889	−	0.973217i	$-0.573836\pi$
$127$	−5.18143			−0.459778			−0.229889	+	0.973217i	$0.573836\pi$
$128$		0			0
$129$	0.432219	+	0.748626i	0.0380548	+	0.0659128i
$130$		0			0
$131$	5.28335	−	9.15103i	0.461609	−	0.799530i	−0.537433	−	0.843307i	$-0.680606\pi$
$131$	5.28335	−	9.15103i	0.461609	−	0.799530i	0.999041	+	0.0437770i	$0.0139391\pi$
$132$		0			0
$133$	18.4187	+	0.220455i	1.59710	+	0.0191159i
$134$		0			0
$135$	3.44159	−	5.96101i	0.296205	−	0.513042i
$136$		0			0
$137$	2.93589	+	5.08510i	0.250830	+	0.434450i	0.963754	−	0.266791i	$-0.0859632\pi$
$137$	2.93589	+	5.08510i	0.250830	+	0.434450i	−0.712925	+	0.701241i	$0.752630\pi$
$138$		0			0
$139$	4.00000			0.339276			0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000			0.339276			0.169638	+	0.985506i	$0.445740\pi$
$140$		0			0
$141$	−27.7065			−2.33331
$142$		0			0
$143$	1.01828	+	1.76372i	0.0851530	+	0.147489i
$144$		0			0
$145$	1.59072	−	2.75520i	0.132102	−	0.228807i
$146$		0			0
$147$	18.3857	+	0.440185i	1.51643	+	0.0363058i
$148$		0			0
$149$	5.05271	−	8.75155i	0.413934	−	0.716955i	−0.581382	−	0.813631i	$-0.697488\pi$
$149$	5.05271	−	8.75155i	0.413934	−	0.716955i	0.995316	+	0.0966760i	$0.0308211\pi$
$150$		0			0
$151$	−0.0938631	−	0.162576i	−0.00763847	−	0.0132302i	0.862181	−	0.506601i	$-0.169098\pi$
$151$	−0.0938631	−	0.162576i	−0.00763847	−	0.0132302i	−0.869819	+	0.493370i	$0.835765\pi$
$152$		0			0
$153$	15.6052			1.26160
$154$		0			0
$155$	−30.2813			−2.43225
$156$		0			0
$157$	6.03590	+	10.4545i	0.481717	+	0.834358i	0.999780	−	0.0209844i	$-0.00668003\pi$
$157$	6.03590	+	10.4545i	0.481717	+	0.834358i	−0.518063	+	0.855343i	$0.673347\pi$
$158$		0			0
$159$	−9.35180	+	16.1978i	−0.741646	+	1.28457i
$160$		0			0
$161$	−1.65951	−	0.0198629i	−0.130788	−	0.00156541i
$162$		0			0
$163$	7.45678	−	12.9155i	0.584060	−	1.01162i	−0.410932	−	0.911666i	$-0.634797\pi$
$163$	7.45678	−	12.9155i	0.584060	−	1.01162i	0.994992	−	0.0999554i	$-0.0318700\pi$
$164$		0			0
$165$	−7.76536	−	13.4500i	−0.604532	−	1.04708i
$166$		0			0
$167$	−5.05664			−0.391294			−0.195647	−	0.980674i	$-0.562681\pi$
$167$	−5.05664			−0.391294			−0.195647	+	0.980674i	$0.562681\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$		0			0
$171$	13.5851	+	23.5302i	1.03888	+	1.79940i
$172$		0			0
$173$	0.297807	−	0.515817i	0.0226419	−	0.0392169i	−0.854482	−	0.519480i	$-0.826126\pi$
$173$	0.297807	−	0.515817i	0.0226419	−	0.0392169i	0.877124	+	0.480263i	$0.159459\pi$
$174$		0			0
$175$	4.62457	−	7.79307i	0.349584	−	0.589101i
$176$		0			0
$177$	2.67531	−	4.63378i	0.201089	−	0.348296i
$178$		0			0
$179$	4.03832	+	6.99458i	0.301838	+	0.522799i	0.976552	−	0.215280i	$-0.0690664\pi$
$179$	4.03832	+	6.99458i	0.301838	+	0.522799i	−0.674714	+	0.738079i	$0.735733\pi$
$180$		0			0
$181$	1.89324			0.140724			0.0703618	−	0.997522i	$-0.477585\pi$
$181$	1.89324			0.140724			0.0703618	+	0.997522i	$0.477585\pi$
$182$		0			0
$183$	6.30761			0.466272
$184$		0			0
$185$	−4.47780	−	7.75577i	−0.329214	−	0.570216i
$186$		0			0
$187$	4.07177	−	7.05251i	0.297757	−	0.515730i
$188$		0			0
$189$	3.07179	+	5.47068i	0.223440	+	0.397933i
$190$		0			0
$191$	1.85087	−	3.20580i	0.133924	−	0.231964i	−0.791262	−	0.611478i	$-0.790575\pi$
$191$	1.85087	−	3.20580i	0.133924	−	0.231964i	0.925186	+	0.379514i	$0.123909\pi$
$192$		0			0
$193$	−6.79373	−	11.7671i	−0.489024	−	0.847014i	0.510897	−	0.859642i	$-0.329313\pi$
$193$	−6.79373	−	11.7671i	−0.489024	−	0.847014i	−0.999920	+	0.0126285i	$0.995980\pi$
$194$		0			0
$195$	−7.62594			−0.546105
$196$		0			0
$197$	−9.70258			−0.691280			−0.345640	−	0.938367i	$-0.612338\pi$
$197$	−9.70258			−0.691280			−0.345640	+	0.938367i	$0.612338\pi$
$198$		0			0
$199$	13.1360	+	22.7522i	0.931185	+	1.61286i	0.781299	+	0.624156i	$0.214557\pi$
$199$	13.1360	+	22.7522i	0.931185	+	1.61286i	0.149885	+	0.988703i	$0.452109\pi$
$200$		0			0
$201$	19.3029	−	33.4335i	1.36152	−	2.35822i
$202$		0			0
$203$	1.41979	+	2.52857i	0.0996500	+	0.177471i
$204$		0			0
$205$	−0.756345	+	1.31003i	−0.0528255	+	0.0914964i
$206$		0			0
$207$	−1.22401	−	2.12005i	−0.0850747	−	0.147354i
$208$		0			0
$209$	14.1788			0.980765
$210$		0			0
$211$	−10.0338			−0.690758			−0.345379	−	0.938463i	$-0.612250\pi$
$211$	−10.0338			−0.690758			−0.345379	+	0.938463i	$0.612250\pi$
$212$		0			0
$213$	4.73096	+	8.19426i	0.324160	+	0.561461i
$214$		0			0
$215$	−0.477513	+	0.827077i	−0.0325661	+	0.0564062i
$216$		0			0
$217$	14.0860	−	23.7369i	0.956218	−	1.61137i
$218$		0			0
$219$	−3.90903	+	6.77065i	−0.264148	+	0.457518i
$220$		0			0
$221$	−1.99933	−	3.46294i	−0.134490	−	0.232943i
$222$		0			0
$223$	−17.4961			−1.17163			−0.585813	−	0.810446i	$-0.699225\pi$
$223$	−17.4961			−1.17163			−0.585813	+	0.810446i	$0.699225\pi$
$224$		0			0
$225$	13.3667			0.891116
$226$		0			0
$227$	−4.75815	−	8.24136i	−0.315810	−	0.546998i	0.663800	−	0.747910i	$-0.268943\pi$
$227$	−4.75815	−	8.24136i	−0.315810	−	0.546998i	−0.979609	+	0.200912i	$0.935609\pi$
$228$		0			0
$229$	−10.5585	+	18.2878i	−0.697725	+	1.20849i	0.271529	+	0.962430i	$0.412471\pi$
$229$	−10.5585	+	18.2878i	−0.697725	+	1.20849i	−0.969254	+	0.246064i	$0.920863\pi$
$230$		0			0
$231$	14.1554	+	0.169428i	0.931357	+	0.0111475i
$232$		0			0
$233$	−7.08938	+	12.2792i	−0.464441	+	0.804435i	−0.999176	−	0.0405847i	$-0.987078\pi$
$233$	−7.08938	+	12.2792i	−0.464441	+	0.804435i	0.534735	+	0.845020i	$0.320411\pi$
$234$		0			0
$235$	−15.3050	−	26.5090i	−0.998385	−	1.72925i
$236$		0			0
$237$	23.0189			1.49524
$238$		0			0
$239$	16.5275			1.06907			0.534536	−	0.845145i	$-0.320486\pi$
$239$	16.5275			1.06907			0.534536	+	0.845145i	$0.320486\pi$
$240$		0			0
$241$	6.84450	+	11.8550i	0.440893	+	0.763649i	0.997756	−	0.0669552i	$-0.0213284\pi$
$241$	6.84450	+	11.8550i	0.440893	+	0.763649i	−0.556863	+	0.830604i	$0.687995\pi$
$242$		0			0
$243$	10.7526	−	18.6240i	0.689777	−	1.19473i
$244$		0			0
$245$	9.73503	+	17.8342i	0.621948	+	1.13938i
$246$		0			0
$247$	3.48105	−	6.02935i	0.221494	−	0.383639i
$248$		0			0
$249$	16.8197	+	29.1325i	1.06590	+	1.84620i
$250$		0			0
$251$	14.6603			0.925349			0.462674	−	0.886528i	$-0.346890\pi$
$251$	14.6603			0.925349			0.462674	+	0.886528i	$0.346890\pi$
$252$		0			0
$253$	−1.27750			−0.0803155
$254$		0			0
$255$	15.2468	+	26.4082i	0.954791	+	1.65375i
$256$		0			0
$257$	0.876387	−	1.51795i	0.0546675	−	0.0946869i	−0.837397	−	0.546596i	$-0.815923\pi$
$257$	0.876387	−	1.51795i	0.0546675	−	0.0946869i	0.892064	+	0.451909i	$0.149257\pi$
$258$		0			0
$259$	8.16254	+	0.0976985i	0.507195	+	0.00607069i
$260$		0			0
$261$	−2.13875	+	3.70442i	−0.132385	+	0.229298i
$262$		0			0
$263$	13.4708	+	23.3321i	0.830645	+	1.43872i	0.897527	+	0.440959i	$0.145361\pi$
$263$	13.4708	+	23.3321i	0.830645	+	1.43872i	−0.0668823	+	0.997761i	$0.521305\pi$
$264$		0			0
$265$	−20.6636			−1.26936
$266$		0			0
$267$	−7.04370			−0.431067
$268$		0			0
$269$	11.0346	+	19.1124i	0.672789	+	1.16530i	0.977110	+	0.212735i	$0.0682371\pi$
$269$	11.0346	+	19.1124i	0.672789	+	1.16530i	−0.304321	+	0.952570i	$0.598430\pi$
$270$		0			0
$271$	−4.48105	+	7.76141i	−0.272204	+	0.471472i	−0.969426	−	0.245384i	$-0.921086\pi$
$271$	−4.48105	+	7.76141i	−0.272204	+	0.471472i	0.697222	+	0.716856i	$0.254419\pi$
$272$		0			0
$273$	3.54736	−	5.97783i	0.214696	−	0.361795i
$274$		0			0
$275$	3.48770	−	6.04088i	0.210316	−	0.364279i
$276$		0			0
$277$	3.76463	+	6.52052i	0.226194	+	0.391780i	0.956677	−	0.291151i	$-0.0940382\pi$
$277$	3.76463	+	6.52052i	0.226194	+	0.391780i	−0.730483	+	0.682931i	$0.760705\pi$
$278$		0			0
$279$	40.7138			2.43747
$280$		0			0
$281$	29.7762			1.77630			0.888151	−	0.459553i	$-0.151990\pi$
$281$	29.7762			1.77630			0.888151	+	0.459553i	$0.151990\pi$
$282$		0			0
$283$	0.150726	+	0.261064i	0.00895970	+	0.0155187i	0.870470	−	0.492221i	$-0.163815\pi$
$283$	0.150726	+	0.261064i	0.00895970	+	0.0155187i	−0.861511	+	0.507739i	$0.830481\pi$
$284$		0			0
$285$	−26.5463	+	45.9795i	−1.57247	+	2.72359i
$286$		0			0
$287$	−0.675076	−	1.20227i	−0.0398485	−	0.0709678i
$288$		0			0
$289$	0.505347	−	0.875286i	0.0297263	−	0.0514874i
$290$		0			0
$291$	3.05950	+	5.29921i	0.179351	+	0.310645i
$292$		0			0
$293$	−19.2471			−1.12443			−0.562214	−	0.826992i	$-0.690050\pi$
$293$	−19.2471			−1.12443			−0.562214	+	0.826992i	$0.690050\pi$
$294$		0			0
$295$	5.91133			0.344171
$296$		0			0
$297$	2.41474	+	4.18245i	0.140117	+	0.242690i
$298$		0			0
$299$	−0.313640	+	0.543240i	−0.0181383	+	0.0314164i
$300$		0			0
$301$	−0.426204	−	0.759044i	−0.0245660	−	0.0437506i
$302$		0			0
$303$	−1.90903	+	3.30654i	−0.109671	+	0.189956i
$304$		0			0
$305$	3.48430	+	6.03499i	0.199511	+	0.345562i
$306$		0			0
$307$	3.57779			0.204195			0.102098	−	0.994774i	$-0.467445\pi$
$307$	3.57779			0.204195			0.102098	+	0.994774i	$0.467445\pi$
$308$		0			0
$309$	30.5692			1.73902
$310$		0			0
$311$	−11.9153	−	20.6379i	−0.675655	−	1.17027i	−0.976277	−	0.216526i	$-0.930527\pi$
$311$	−11.9153	−	20.6379i	−0.675655	−	1.17027i	0.300622	−	0.953743i	$-0.402806\pi$
$312$		0			0
$313$	9.04068	−	15.6589i	0.511009	−	0.885094i	−0.488909	−	0.872335i	$-0.662605\pi$
$313$	9.04068	−	15.6589i	0.511009	−	0.885094i	0.999919	−	0.0127596i	$-0.00406161\pi$
$314$		0			0
$315$	−15.2947	+	25.7738i	−0.861758	+	1.45219i
$316$		0			0
$317$	13.7741	−	23.8574i	0.773630	−	1.33997i	−0.161931	−	0.986802i	$-0.551772\pi$
$317$	13.7741	−	23.8574i	0.773630	−	1.33997i	0.935561	−	0.353164i	$-0.114894\pi$
$318$		0			0
$319$	1.11610	+	1.93314i	0.0624897	+	0.108235i
$320$		0			0
$321$	−51.5628			−2.87796
$322$		0			0
$323$	−27.8391			−1.54901
$324$		0			0
$325$	−1.71254	−	2.96621i	−0.0949948	−	0.164536i
$326$		0			0
$327$	1.45388	−	2.51819i	0.0803997	−	0.139256i
$328$		0			0
$329$	27.8993	+	0.333930i	1.53814	+	0.0184101i
$330$		0			0
$331$	−9.09069	+	15.7455i	−0.499669	+	0.865453i	−1.00000		0.000381757i	$-0.999878\pi$
$331$	−9.09069	+	15.7455i	−0.499669	+	0.865453i	0.500331	+	0.865834i	$0.333212\pi$
$332$		0			0
$333$	6.02048	+	10.4278i	0.329920	+	0.571439i
$334$		0			0
$335$	42.6513			2.33029
$336$		0			0
$337$	−17.1381			−0.933572			−0.466786	−	0.884370i	$-0.654588\pi$
$337$	−17.1381			−0.933572			−0.466786	+	0.884370i	$0.654588\pi$
$338$		0			0
$339$	1.43983	+	2.49386i	0.0782010	+	0.135448i
$340$		0			0
$341$	10.6232	−	18.3999i	0.575279	−	0.996412i
$342$		0			0
$343$	−18.5083	−	0.664840i	−0.999355	−	0.0358980i
$344$		0			0
$345$	2.39180	−	4.14272i	0.128770	−	0.223037i
$346$		0			0
$347$	11.1344	+	19.2853i	0.597725	+	1.03529i	0.993156	+	0.116794i	$0.0372619\pi$
$347$	11.1344	+	19.2853i	0.597725	+	1.03529i	−0.395431	+	0.918496i	$0.629405\pi$
$348$		0			0
$349$	19.9368			1.06719			0.533595	−	0.845740i	$-0.320841\pi$
$349$	19.9368			1.06719			0.533595	+	0.845740i	$0.320841\pi$
$350$		0			0
$351$	2.37138			0.126575
$352$		0			0
$353$	−11.4576	−	19.8451i	−0.609825	−	1.05625i	−0.991269	−	0.131856i	$-0.957906\pi$
$353$	−11.4576	−	19.8451i	−0.609825	−	1.05625i	0.381444	−	0.924392i	$-0.375427\pi$
$354$		0			0
$355$	−5.22673	+	9.05296i	−0.277406	+	0.480481i
$356$		0			0
$357$	−27.7932	−	0.332661i	−1.47097	−	0.0176063i
$358$		0			0
$359$	13.6157	−	23.5831i	0.718610	−	1.24467i	−0.242940	−	0.970041i	$-0.578112\pi$
$359$	13.6157	−	23.5831i	0.718610	−	1.24467i	0.961551	−	0.274628i	$-0.0885547\pi$
$360$		0			0
$361$	−14.7354	−	25.5225i	−0.775548	−	1.34329i
$362$		0			0
$363$	−18.0032			−0.944923
$364$		0			0
$365$	−8.63735			−0.452099
$366$		0			0
$367$	−5.42822	−	9.40195i	−0.283351	−	0.490778i	0.688857	−	0.724897i	$-0.258113\pi$
$367$	−5.42822	−	9.40195i	−0.283351	−	0.490778i	−0.972208	+	0.234119i	$0.924779\pi$
$368$		0			0
$369$	1.01692	−	1.76136i	0.0529388	−	0.0916926i
$370$		0			0
$371$	9.61210	−	16.1978i	0.499035	−	0.840948i
$372$		0			0
$373$	1.18572	−	2.05373i	0.0613943	−	0.106338i	−0.833695	−	0.552226i	$-0.813779\pi$
$373$	1.18572	−	2.05373i	0.0613943	−	0.106338i	0.895089	+	0.445888i	$0.147112\pi$
$374$		0			0
$375$	−6.00510	−	10.4011i	−0.310102	−	0.537112i
$376$		0			0
$377$	1.09606			0.0564501
$378$		0			0
$379$	29.2197			1.50092			0.750458	−	0.660918i	$-0.229833\pi$
$379$	29.2197			1.50092			0.750458	+	0.660918i	$0.229833\pi$
$380$		0			0
$381$	6.80654	+	11.7893i	0.348709	+	0.603982i
$382$		0			0
$383$	−1.53297	+	2.65519i	−0.0783313	+	0.135674i	−0.902530	−	0.430627i	$-0.858293\pi$
$383$	−1.53297	+	2.65519i	−0.0783313	+	0.135674i	0.824199	+	0.566301i	$0.191626\pi$
$384$		0			0
$385$	7.65729	+	13.6372i	0.390252	+	0.695015i
$386$		0			0
$387$	0.642025	−	1.11202i	0.0326360	−	0.0565271i
$388$		0			0
$389$	−13.8705	−	24.0244i	−0.703261	−	1.21808i	−0.967315	−	0.253576i	$-0.918393\pi$
$389$	−13.8705	−	24.0244i	−0.703261	−	1.21808i	0.264054	−	0.964508i	$-0.414940\pi$
$390$		0			0
$391$	2.50828			0.126849
$392$		0			0
$393$	−27.7617			−1.40039
$394$		0			0
$395$	12.7156	+	22.0240i	0.639790	+	1.10815i
$396$		0			0
$397$	−8.61559	+	14.9226i	−0.432404	+	0.748946i	−0.997080	−	0.0763669i	$-0.975668\pi$
$397$	−8.61559	+	14.9226i	−0.432404	+	0.748946i	0.564676	+	0.825313i	$0.309001\pi$
$398$		0			0
$399$	−23.6939	−	42.1974i	−1.18618	−	2.11251i
$400$		0			0
$401$	−8.32201	+	14.4142i	−0.415582	+	0.719808i	−0.995489	−	0.0948737i	$-0.969755\pi$
$401$	−8.32201	+	14.4142i	−0.415582	+	0.719808i	0.579908	+	0.814682i	$0.303089\pi$
$402$		0			0
$403$	−5.21624	−	9.03479i	−0.259839	−	0.450055i
$404$		0			0
$405$	15.8990			0.790029
$406$		0			0
$407$	6.28355			0.311464
$408$		0			0
$409$	6.81689	+	11.8072i	0.337073	+	0.583828i	0.983881	−	0.178825i	$-0.0572296\pi$
$409$	6.81689	+	11.8072i	0.337073	+	0.583828i	−0.646807	+	0.762653i	$0.723896\pi$
$410$		0			0
$411$	7.71340	−	13.3600i	0.380474	−	0.659000i
$412$		0			0
$413$	−2.74978	+	4.63378i	−0.135308	+	0.228013i
$414$		0			0
$415$	−18.5822	+	32.1854i	−0.912167	+	1.57992i
$416$		0			0
$417$	−5.25456	−	9.10116i	−0.257317	−	0.445686i
$418$		0			0
$419$	10.8502			0.530066			0.265033	−	0.964239i	$-0.414617\pi$
$419$	10.8502			0.530066			0.265033	+	0.964239i	$0.414617\pi$
$420$		0			0
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$		0			0
$423$	20.5778	+	35.6418i	1.00053	+	1.73296i
$424$		0			0
$425$	−6.84788	+	11.8609i	−0.332171	+	0.575337i
$426$		0			0
$427$	−6.35150	−	0.0760220i	−0.307371	−	0.00367896i
$428$		0			0
$429$	2.67531	−	4.63378i	0.129165	−	0.223721i
$430$		0			0
$431$	0.604764	+	1.04748i	0.0291304	+	0.0504554i	0.880223	−	0.474560i	$-0.157393\pi$
$431$	0.604764	+	1.04748i	0.0291304	+	0.0504554i	−0.851093	+	0.525016i	$0.824060\pi$
$432$		0			0
$433$	−5.56422			−0.267399			−0.133700	−	0.991022i	$-0.542686\pi$
$433$	−5.56422			−0.267399			−0.133700	+	0.991022i	$0.542686\pi$
$434$		0			0
$435$	−8.35851			−0.400760
$436$		0			0
$437$	2.18359	+	3.78209i	0.104455	+	0.180922i
$438$		0			0
$439$	−9.85960	+	17.0773i	−0.470573	+	0.815057i	−0.999434	−	0.0336522i	$-0.989286\pi$
$439$	−9.85960	+	17.0773i	−0.470573	+	0.815057i	0.528860	+	0.848709i	$0.322619\pi$
$440$		0			0
$441$	−13.0889	−	23.9784i	−0.623282	−	1.14183i
$442$		0			0
$443$	11.1155	−	19.2526i	0.528113	−	0.914719i	−0.471350	−	0.881946i	$-0.656233\pi$
$443$	11.1155	−	19.2526i	0.528113	−	0.914719i	0.999463	−	0.0327726i	$-0.0104337\pi$
$444$		0			0
$445$	−3.89091	−	6.73926i	−0.184447	−	0.319471i
$446$		0			0
$447$	−26.5498			−1.25576
$448$		0			0
$449$	18.4579			0.871082			0.435541	−	0.900169i	$-0.356557\pi$
$449$	18.4579			0.871082			0.435541	+	0.900169i	$0.356557\pi$
$450$		0			0
$451$	−0.530678	−	0.919161i	−0.0249886	−	0.0432816i
$452$		0			0
$453$	−0.246605	+	0.427132i	−0.0115865	+	0.0200684i
$454$		0			0
$455$	7.67901	+	0.0919110i	0.359997	+	0.00430886i
$456$		0			0
$457$	14.9910	−	25.9651i	0.701248	−	1.21460i	−0.266781	−	0.963757i	$-0.585960\pi$
$457$	14.9910	−	25.9651i	0.701248	−	1.21460i	0.968029	−	0.250840i	$-0.0807067\pi$
$458$		0			0
$459$	−4.74118	−	8.21197i	−0.221299	−	0.383302i
$460$		0			0
$461$	29.1498			1.35764			0.678821	−	0.734304i	$-0.262491\pi$
$461$	29.1498			1.35764			0.678821	+	0.734304i	$0.262491\pi$
$462$		0			0
$463$	−1.55900			−0.0724530			−0.0362265	−	0.999344i	$-0.511534\pi$
$463$	−1.55900			−0.0724530			−0.0362265	+	0.999344i	$0.511534\pi$
$464$		0			0
$465$	39.7787	+	68.8988i	1.84470	+	3.19511i
$466$		0			0
$467$	6.21156	−	10.7587i	0.287437	−	0.497855i	−0.685760	−	0.727827i	$-0.740530\pi$
$467$	6.21156	−	10.7587i	0.287437	−	0.497855i	0.973197	+	0.229972i	$0.0738635\pi$
$468$		0			0
$469$	−19.8401	+	33.4335i	−0.916132	+	1.54382i
$470$		0			0
$471$	15.8580	−	27.4668i	0.730697	−	1.26561i
$472$		0			0
$473$	−0.335039	−	0.580305i	−0.0154051	−	0.0266825i
$474$		0			0
$475$	−23.8458			−1.09412
$476$		0			0
$477$	27.7826			1.27208
$478$		0			0
$479$	18.0279	+	31.2252i	0.823716	+	1.42672i	0.902897	+	0.429857i	$0.141436\pi$
$479$	18.0279	+	31.2252i	0.823716	+	1.42672i	−0.0791811	+	0.996860i	$0.525231\pi$
$480$		0			0
$481$	1.54268	−	2.67201i	0.0703404	−	0.121833i
$482$		0			0
$483$	2.13480	+	3.80196i	0.0971369	+	0.172995i
$484$		0			0
$485$	−3.38011	+	5.85453i	−0.153483	+	0.265840i
$486$		0			0
$487$	3.65002	+	6.32202i	0.165398	+	0.286478i	0.936797	−	0.349874i	$-0.113776\pi$
$487$	3.65002	+	6.32202i	0.165398	+	0.286478i	−0.771398	+	0.636352i	$0.780442\pi$
$488$		0			0
$489$	−39.1821			−1.77188
$490$		0			0
$491$	−4.49178			−0.202711			−0.101356	−	0.994850i	$-0.532318\pi$
$491$	−4.49178			−0.202711			−0.101356	+	0.994850i	$0.532318\pi$
$492$		0			0
$493$	−2.19139	−	3.79560i	−0.0986954	−	0.170945i
$494$		0			0
$495$	−11.5348	+	19.9788i	−0.518450	+	0.897981i
$496$		0			0
$497$	−4.66512	−	8.30829i	−0.209259	−	0.372678i
$498$		0			0
$499$	5.68369	−	9.84443i	0.254437	−	0.440697i	−0.710306	−	0.703893i	$-0.751443\pi$
$499$	5.68369	−	9.84443i	0.254437	−	0.440697i	0.964742	+	0.263196i	$0.0847766\pi$
$500$		0			0
$501$	6.64260	+	11.5053i	0.296770	+	0.514020i
$502$		0			0
$503$	−17.1080			−0.762806			−0.381403	−	0.924409i	$-0.624559\pi$
$503$	−17.1080			−0.762806			−0.381403	+	0.924409i	$0.624559\pi$
$504$		0			0
$505$	−4.21818			−0.187706
$506$		0			0
$507$	−1.31364	−	2.27529i	−0.0583408	−	0.101049i
$508$		0			0
$509$	−1.64142	+	2.84303i	−0.0727547	+	0.126015i	−0.900108	−	0.435667i	$-0.856512\pi$
$509$	−1.64142	+	2.84303i	−0.0727547	+	0.126015i	0.827353	+	0.561682i	$0.189846\pi$
$510$		0			0
$511$	4.01784	−	6.77065i	0.177739	−	0.299516i
$512$		0			0
$513$	8.25490	−	14.2979i	0.364463	−	0.631268i
$514$		0			0
$515$	16.8863	+	29.2479i	0.744100	+	1.28882i
$516$		0			0
$517$	21.4770			0.944555
$518$		0			0
$519$	−1.56485			−0.0686891
$520$		0			0
$521$	2.38530	+	4.13147i	0.104502	+	0.181003i	0.913535	−	0.406761i	$-0.133342\pi$
$521$	2.38530	+	4.13147i	0.104502	+	0.181003i	−0.809033	+	0.587764i	$0.800008\pi$
$522$		0			0
$523$	12.7562	−	22.0944i	0.557789	−	0.966119i	−0.439892	−	0.898051i	$-0.644983\pi$
$523$	12.7562	−	22.0944i	0.557789	−	0.966119i	0.997681	−	0.0680682i	$-0.0216835\pi$
$524$		0			0
$525$	−23.8065	−	0.284943i	−1.03900	−	0.0124359i
$526$		0			0
$527$	−20.8580	+	36.1271i	−0.908588	+	1.57372i
$528$		0			0
$529$	11.3033	+	19.5778i	0.491446	+	0.851210i
$530$		0			0
$531$	−7.94789			−0.344909
$532$		0			0
$533$	−0.521150			−0.0225735
$534$		0			0
$535$	−28.4831	−	49.3342i	−1.23143	−	2.13290i
$536$		0			0
$537$	10.6098	−	18.3767i	0.457847	−	0.793013i
$538$		0			0
$539$	−14.2519	−	0.341214i	−0.613871	−	0.0146971i
$540$		0			0
$541$	8.25784	−	14.3030i	0.355032	−	0.614934i	−0.632091	−	0.774894i	$-0.717803\pi$
$541$	8.25784	−	14.3030i	0.355032	−	0.614934i	0.987123	+	0.159960i	$0.0511366\pi$
$542$		0			0
$543$	−2.48704	−	4.30768i	−0.106729	−	0.184860i
$544$		0			0
$545$	3.21247			0.137607
$546$		0			0
$547$	−23.3317			−0.997591			−0.498796	−	0.866720i	$-0.666224\pi$
$547$	−23.3317			−0.997591			−0.498796	+	0.866720i	$0.666224\pi$
$548$		0			0
$549$	−4.68471	−	8.11416i	−0.199939	−	0.346304i
$550$		0			0
$551$	3.81545	−	6.60855i	0.162544	−	0.281534i
$552$		0			0
$553$	−23.1791	−	0.277434i	−0.985676	−	0.0117977i
$554$		0			0
$555$	−11.7644	+	20.3766i	−0.499372	+	0.864938i
$556$		0			0
$557$	10.0235	+	17.3613i	0.424711	+	0.735621i	0.996393	−	0.0848540i	$-0.0270424\pi$
$557$	10.0235	+	17.3613i	0.424711	+	0.735621i	−0.571682	+	0.820475i	$0.693709\pi$
$558$		0			0
$559$	−0.329024			−0.0139162
$560$		0			0
$561$	−21.3953			−0.903312
$562$		0			0
$563$	−20.2642	−	35.0986i	−0.854034	−	1.47923i	−0.877539	−	0.479506i	$-0.840816\pi$
$563$	−20.2642	−	35.0986i	−0.854034	−	1.47923i	0.0235047	−	0.999724i	$-0.492518\pi$
$564$		0			0
$565$	−1.59072	+	2.75520i	−0.0669219	+	0.115912i
$566$		0			0
$567$	−7.39576	+	12.4629i	−0.310593	+	0.523394i
$568$		0			0
$569$	10.7252	−	18.5766i	0.449623	−	0.778770i	−0.548739	−	0.835994i	$-0.684892\pi$
$569$	10.7252	−	18.5766i	0.449623	−	0.778770i	0.998361	+	0.0572245i	$0.0182251\pi$
$570$		0			0
$571$	−5.47793	−	9.48806i	−0.229244	−	0.397063i	0.728340	−	0.685216i	$-0.240292\pi$
$571$	−5.47793	−	9.48806i	−0.229244	−	0.397063i	−0.957584	+	0.288153i	$0.906959\pi$
$572$		0			0
$573$	−9.72552			−0.406289
$574$		0			0
$575$	2.14849			0.0895982
$576$		0			0
$577$	−17.3708	−	30.0870i	−0.723154	−	1.25254i	−0.959729	−	0.280927i	$-0.909358\pi$
$577$	−17.3708	−	30.0870i	−0.723154	−	1.25254i	0.236575	−	0.971613i	$-0.423975\pi$
$578$		0			0
$579$	−17.8490	+	30.9154i	−0.741781	+	1.28480i
$580$		0			0
$581$	−16.5856	−	29.5380i	−0.688086	−	1.22544i
$582$		0			0
$583$	7.24915	−	12.5559i	0.300229	−	0.520012i
$584$		0			0
$585$	5.66384	+	9.81006i	0.234171	+	0.405596i
$586$		0			0
$587$	22.8463			0.942967			0.471483	−	0.881875i	$-0.343719\pi$
$587$	22.8463			0.942967			0.471483	+	0.881875i	$0.343719\pi$
$588$		0			0
$589$	−72.6320			−2.99275
$590$		0			0
$591$	12.7457	+	22.0762i	0.524288	+	0.908094i
$592$		0			0
$593$	−8.79676	+	15.2364i	−0.361240	+	0.625686i	−0.988165	−	0.153394i	$-0.950980\pi$
$593$	−8.79676	+	15.2364i	−0.361240	+	0.625686i	0.626925	+	0.779079i	$0.284313\pi$
$594$		0			0
$595$	−15.0346	−	26.7757i	−0.616359	−	1.09770i
$596$		0			0
$597$	34.5119	−	59.7764i	1.41248	−	2.44648i
$598$		0			0
$599$	15.5036	+	26.8531i	0.633461	+	1.09719i	0.986839	+	0.161706i	$0.0516997\pi$
$599$	15.5036	+	26.8531i	0.633461	+	1.09719i	−0.353378	+	0.935481i	$0.614967\pi$
$600$		0			0
$601$	−1.43754			−0.0586385			−0.0293193	−	0.999570i	$-0.509334\pi$
$601$	−1.43754			−0.0586385			−0.0293193	+	0.999570i	$0.509334\pi$
$602$		0			0
$603$	−57.3455			−2.33529
$604$		0			0
$605$	−9.94490	−	17.2251i	−0.404318	−	0.700299i
$606$		0			0
$607$	−16.5085	+	28.5936i	−0.670061	+	1.16058i	0.307826	+	0.951443i	$0.400399\pi$
$607$	−16.5085	+	28.5936i	−0.670061	+	1.16058i	−0.977887	+	0.209136i	$0.932935\pi$
$608$		0			0
$609$	3.88813	−	6.55208i	0.157555	−	0.265503i
$610$		0			0
$611$	5.27284	−	9.13283i	0.213316	−	0.369475i
$612$		0			0
$613$	21.5829	+	37.3826i	0.871723	+	1.50987i	0.860213	+	0.509935i	$0.170331\pi$
$613$	21.5829	+	37.3826i	0.871723	+	1.50987i	0.0115102	+	0.999934i	$0.496336\pi$
$614$		0			0
$615$	3.97426			0.160258
$616$		0			0
$617$	2.45772			0.0989441			0.0494721	−	0.998776i	$-0.484246\pi$
$617$	2.45772			0.0989441			0.0494721	+	0.998776i	$0.484246\pi$
$618$		0			0
$619$	18.8894	+	32.7175i	0.759231	+	1.31503i	0.943243	+	0.332102i	$0.107758\pi$
$619$	18.8894	+	32.7175i	0.759231	+	1.31503i	−0.184013	+	0.982924i	$0.558909\pi$
$620$		0			0
$621$	−0.743761	+	1.28823i	−0.0298461	+	0.0516949i
$622$		0			0
$623$	7.09271	+	0.0848936i	0.284163	+	0.00340119i
$624$		0			0
$625$	15.1971	−	26.3222i	0.607884	−	1.05289i
$626$		0			0
$627$	−18.6258	−	32.2608i	−0.743842	−	1.28837i
$628$		0			0
$629$	−12.3374			−0.491922
$630$		0			0
$631$	28.4828			1.13388			0.566942	−	0.823758i	$-0.308126\pi$
$631$	28.4828			1.13388			0.566942	+	0.823758i	$0.308126\pi$
$632$		0			0
$633$	13.1809	+	22.8299i	0.523892	+	0.907407i
$634$		0			0
$635$	−7.51981	+	13.0247i	−0.298415	+	0.516869i
$636$		0			0
$637$	−3.64409	+	5.97667i	−0.144384	+	0.236804i
$638$		0			0
$639$	7.02743	−	12.1719i	0.278001	−	0.481512i
$640$		0			0
$641$	13.5961	+	23.5492i	0.537014	+	0.930136i	0.999063	+	0.0432812i	$0.0137811\pi$
$641$	13.5961	+	23.5492i	0.537014	+	0.930136i	−0.462049	+	0.886854i	$0.652886\pi$
$642$		0			0
$643$	37.1664			1.46570			0.732849	−	0.680391i	$-0.238190\pi$
$643$	37.1664			1.46570			0.732849	+	0.680391i	$0.238190\pi$
$644$		0			0
$645$	2.50912			0.0987965
$646$		0			0
$647$	9.41593	+	16.3089i	0.370178	+	0.641168i	0.989593	−	0.143896i	$-0.0459632\pi$
$647$	9.41593	+	16.3089i	0.370178	+	0.641168i	−0.619414	+	0.785064i	$0.712630\pi$
$648$		0			0
$649$	−2.07380	+	3.59192i	−0.0814036	+	0.140995i
$650$		0			0
$651$	−72.5123	−	0.867909i	−2.84198	−	0.0340161i
$652$		0			0
$653$	13.0092	−	22.5326i	0.509090	−	0.881770i	−0.490854	−	0.871242i	$-0.663315\pi$
$653$	13.0092	−	22.5326i	0.509090	−	0.881770i	0.999945	−	0.0105286i	$-0.00335143\pi$
$654$		0			0
$655$	−15.3355	−	26.5618i	−0.599206	−	1.03786i
$656$		0			0
$657$	11.6131			0.453069
$658$		0			0
$659$	33.3339			1.29851			0.649253	−	0.760573i	$-0.275082\pi$
$659$	33.3339			1.29851			0.649253	+	0.760573i	$0.275082\pi$
$660$		0			0
$661$	−3.14920	−	5.45458i	−0.122490	−	0.212159i	0.798259	−	0.602314i	$-0.205755\pi$
$661$	−3.14920	−	5.45458i	−0.122490	−	0.212159i	−0.920749	+	0.390156i	$0.872421\pi$
$662$		0			0
$663$	−5.25280	+	9.09812i	−0.204002	+	0.353342i
$664$		0			0
$665$	27.2852	−	45.9795i	1.05807	−	1.78301i
$666$		0			0
$667$	−0.343769	+	0.595426i	−0.0133108	+	0.0230550i
$668$		0			0
$669$	22.9836	+	39.8088i	0.888597	+	1.53910i
$670$		0			0
$671$	−4.88941			−0.188754
$672$		0			0
$673$	18.3188			0.706137			0.353068	−	0.935598i	$-0.385138\pi$
$673$	18.3188			0.706137			0.353068	+	0.935598i	$0.385138\pi$
$674$		0			0
$675$	−4.06110	−	7.03403i	−0.156312	−	0.270740i
$676$		0			0
$677$	−12.1696	+	21.0783i	−0.467715	+	0.810106i	−0.999319	−	0.0368866i	$-0.988256\pi$
$677$	−12.1696	+	21.0783i	−0.467715	+	0.810106i	0.531604	+	0.846993i	$0.321589\pi$
$678$		0			0
$679$	−3.01692	−	5.37296i	−0.115779	−	0.206195i
$680$		0			0
$681$	−12.5010	+	21.6524i	−0.479039	+	0.829720i
$682$		0			0
$683$	5.88409	+	10.1916i	0.225149	+	0.389969i	0.956364	−	0.292178i	$-0.0943799\pi$
$683$	5.88409	+	10.1916i	0.225149	+	0.389969i	−0.731215	+	0.682147i	$0.761047\pi$
$684$		0			0
$685$	17.0434			0.651195
$686$		0			0
$687$	55.4802			2.11670
$688$		0			0
$689$	−3.55950	−	6.16523i	−0.135606	−	0.234877i
$690$		0			0
$691$	0.588923	−	1.02004i	0.0224037	−	0.0388043i	−0.854606	−	0.519277i	$-0.826201\pi$
$691$	0.588923	−	1.02004i	0.0224037	−	0.0388043i	0.877010	+	0.480472i	$0.159535\pi$
$692$		0			0
$693$	−10.2954	−	18.3354i	−0.391089	−	0.696506i
$694$		0			0
$695$	5.80520	−	10.0549i	0.220204	−	0.381404i
$696$		0			0
$697$	1.04195	+	1.80471i	0.0394668	+	0.0683584i
$698$		0			0
$699$	37.2516			1.40898
$700$		0			0
$701$	−31.2867			−1.18168			−0.590841	−	0.806788i	$-0.701204\pi$
$701$	−31.2867			−1.18168			−0.590841	+	0.806788i	$0.701204\pi$
$702$		0			0
$703$	−10.7403	−	18.6028i	−0.405079	−	0.701617i
$704$		0			0
$705$	−40.2104	+	69.6464i	−1.51441	+	2.62304i
$706$		0			0
$707$	1.96217	−	3.30654i	0.0737950	−	0.124355i
$708$		0			0
$709$	−7.68738	+	13.3149i	−0.288706	+	0.500053i	−0.973501	−	0.228682i	$-0.926558\pi$
$709$	−7.68738	+	13.3149i	−0.288706	+	0.500053i	0.684795	+	0.728735i	$0.259892\pi$
$710$		0			0
$711$	−17.0963	−	29.6117i	−0.641162	−	1.11053i
$712$		0			0
$713$	6.54409			0.245078
$714$		0			0
$715$	5.91133			0.221071
$716$		0			0
$717$	−21.7111	−	37.6048i	−0.810817	−	1.40438i
$718$		0			0
$719$	−5.57087	+	9.64904i	−0.207759	+	0.359848i	−0.951008	−	0.309166i	$-0.899950\pi$
$719$	−5.57087	+	9.64904i	−0.207759	+	0.359848i	0.743250	+	0.669014i	$0.233283\pi$
$720$		0			0
$721$	−30.7819	−	0.368433i	−1.14638	−	0.0137211i
$722$		0			0
$723$	17.9824	−	31.1465i	0.668773	−	1.15835i
$724$		0			0
$725$	−1.87706	−	3.25116i	−0.0697121	−	0.120745i
$726$		0			0
$727$	6.24735			0.231702			0.115851	−	0.993267i	$-0.463041\pi$
$727$	6.24735			0.231702			0.115851	+	0.993267i	$0.463041\pi$
$728$		0			0
$729$	−40.0674			−1.48398
$730$		0			0
$731$	0.657828	+	1.13939i	0.0243307	+	0.0421419i
$732$		0			0
$733$	−15.4834	+	26.8181i	−0.571894	+	0.990550i	0.424477	+	0.905439i	$0.360458\pi$
$733$	−15.4834	+	26.8181i	−0.571894	+	0.990550i	−0.996371	+	0.0851111i	$0.972875\pi$
$734$		0			0
$735$	27.7897	−	45.5777i	1.02504	−	1.68116i
$736$		0			0
$737$	−14.9628	+	25.9163i	−0.551162	+	0.954641i
$738$		0			0
$739$	1.16872	+	2.02429i	0.0429921	+	0.0744646i	0.886721	−	0.462305i	$-0.152978\pi$
$739$	1.16872	+	2.02429i	0.0429921	+	0.0744646i	−0.843729	+	0.536770i	$0.819644\pi$
$740$		0			0
$741$	−18.2914			−0.671951
$742$		0			0
$743$	−24.3612			−0.893726			−0.446863	−	0.894603i	$-0.647459\pi$
$743$	−24.3612			−0.893726			−0.446863	+	0.894603i	$0.647459\pi$
$744$		0			0
$745$	−14.6660	−	25.4022i	−0.537321	−	0.930666i
$746$		0			0
$747$	24.9842	−	43.2739i	0.914123	−	1.58331i
$748$		0			0
$749$	51.9216	+	0.621457i	1.89718	+	0.0227075i
$750$		0			0
$751$	−6.01266	+	10.4142i	−0.219405	+	0.380021i	−0.954626	−	0.297806i	$-0.903745\pi$
$751$	−6.01266	+	10.4142i	−0.219405	+	0.380021i	0.735221	+	0.677827i	$0.237078\pi$
$752$		0			0
$753$	−19.2583	−	33.3564i	−0.701813	−	1.21558i
$754$		0			0
$755$	−0.544894			−0.0198307
$756$		0			0
$757$	25.9905			0.944641			0.472321	−	0.881427i	$-0.343416\pi$
$757$	25.9905			0.944641			0.472321	+	0.881427i	$0.343416\pi$
$758$		0			0
$759$	1.67817	+	2.90667i	0.0609137	+	0.105506i
$760$		0			0
$761$	−6.66350	+	11.5415i	−0.241552	+	0.418380i	−0.961156	−	0.276004i	$-0.910990\pi$
$761$	−6.66350	+	11.5415i	−0.241552	+	0.418380i	0.719605	+	0.694384i	$0.244323\pi$
$762$		0			0
$763$	−1.49435	+	2.51819i	−0.0540990	+	0.0911647i
$764$		0			0
$765$	22.6478	−	39.2271i	0.818833	−	1.41826i
$766$		0			0
$767$	1.01828	+	1.76372i	0.0367680	+	0.0636841i
$768$		0			0
$769$	9.24486			0.333378			0.166689	−	0.986010i	$-0.446692\pi$
$769$	9.24486			0.333378			0.166689	+	0.986010i	$0.446692\pi$
$770$		0			0
$771$	−4.60503			−0.165846
$772$		0			0
$773$	5.07097	+	8.78317i	0.182390	+	0.315909i	0.942694	−	0.333659i	$-0.108283\pi$
$773$	5.07097	+	8.78317i	0.182390	+	0.315909i	−0.760304	+	0.649568i	$0.774950\pi$
$774$		0			0
$775$	−17.8661	+	30.9450i	−0.641768	+	1.11158i
$776$		0			0
$777$	−10.5003	−	18.7005i	−0.376698	−	0.670876i
$778$		0			0
$779$	−1.81415	+	3.14220i	−0.0649987	+	0.112581i
$780$		0			0
$781$	−3.66725	−	6.35186i	−0.131225	−	0.227288i
$782$		0			0
$783$	2.59919			0.0928873
$784$		0			0
$785$	35.0396			1.25062
$786$		0			0
$787$	22.6411	+	39.2156i	0.807070	+	1.39789i	0.914885	+	0.403715i	$0.132281\pi$
$787$	22.6411	+	39.2156i	0.807070	+	1.39789i	−0.107815	+	0.994171i	$0.534386\pi$
$788$		0			0
$789$	35.3916	−	61.3000i	1.25997	−	2.18234i
$790$		0			0
$791$	−1.41979	−	2.52857i	−0.0504821	−	0.0899056i
$792$		0			0
$793$	−1.20041	+	2.07917i	−0.0426277	+	0.0738334i
$794$		0			0
$795$	27.1445	+	47.0157i	0.962718	+	1.66748i
$796$		0			0
$797$	27.0784			0.959165			0.479583	−	0.877497i	$-0.340788\pi$
$797$	27.0784			0.959165			0.479583	+	0.877497i	$0.340788\pi$
$798$		0			0
$799$	−42.1686			−1.49182
$800$		0			0
$801$	5.23140	+	9.06106i	0.184843	+	0.320157i
$802$		0			0
$803$	3.03013	−	5.24834i	0.106931	−	0.185210i
$804$		0			0
$805$	−2.45837	+	4.14272i	−0.0866463	+	0.146012i
$806$		0			0
$807$	28.9909	−	50.2137i	1.02053	−	1.76760i
$808$		0			0
$809$	12.8899	+	22.3260i	0.453185	+	0.784939i	0.998582	−	0.0532388i	$-0.0169544\pi$
$809$	12.8899	+	22.3260i	0.453185	+	0.784939i	−0.545397	+	0.838178i	$0.683621\pi$
$810$		0			0
$811$	25.7829			0.905362			0.452681	−	0.891673i	$-0.350468\pi$
$811$	25.7829			0.905362			0.452681	+	0.891673i	$0.350468\pi$
$812$		0			0
$813$	23.5459			0.825792
$814$		0			0
$815$	−21.6440	−	37.4886i	−0.758158	−	1.31317i
$816$		0			0
$817$	−1.14535	+	1.98380i	−0.0400707	+	0.0694045i
$818$		0			0
$819$	−10.3246	−	0.123576i	−0.360770	−	0.00431810i
$820$		0			0
$821$	0.855366	−	1.48154i	0.0298525	−	0.0517060i	−0.850713	−	0.525630i	$-0.823830\pi$
$821$	0.855366	−	1.48154i	0.0298525	−	0.0517060i	0.880566	+	0.473924i	$0.157163\pi$
$822$		0			0
$823$	−20.1887	−	34.9678i	−0.703733	−	1.21890i	−0.967147	−	0.254218i	$-0.918182\pi$
$823$	−20.1887	−	34.9678i	−0.703733	−	1.21890i	0.263414	−	0.964683i	$-0.415151\pi$
$824$		0			0
$825$	−18.3264			−0.638042
$826$		0			0
$827$	−19.5698			−0.680509			−0.340254	−	0.940333i	$-0.610513\pi$
$827$	−19.5698			−0.680509			−0.340254	+	0.940333i	$0.610513\pi$
$828$		0			0
$829$	−20.7871	−	36.0043i	−0.721966	−	1.25048i	−0.960211	−	0.279277i	$-0.909905\pi$
$829$	−20.7871	−	36.0043i	−0.721966	−	1.25048i	0.238244	−	0.971205i	$-0.423428\pi$
$830$		0			0
$831$	9.89073	−	17.1312i	0.343106	−	0.594276i
$832$		0			0
$833$	27.9826	+	0.669951i	0.969540	+	0.0232124i
$834$		0			0
$835$	−7.33870	+	12.7110i	−0.253966	+	0.439882i
$836$		0			0
$837$	−12.3697	−	21.4250i	−0.427560	−	0.740555i
$838$		0			0
$839$	−45.8480			−1.58285			−0.791425	−	0.611266i	$-0.790660\pi$
$839$	−45.8480			−1.58285			−0.791425	+	0.611266i	$0.790660\pi$
$840$		0			0
$841$	−27.7986			−0.958574
$842$		0			0
$843$	−39.1152	−	67.7496i	−1.34720	−	2.33342i
$844$		0			0
$845$	1.45130	−	2.51373i	0.0499262	−	0.0864748i
$846$		0			0
$847$	18.1285	+	0.216982i	0.622902	+	0.00745559i
$848$		0			0
$849$	0.395998	−	0.685889i	0.0135906	−	0.0235397i
$850$		0			0
$851$	0.967695	+	1.67610i	0.0331722	+	0.0574559i
$852$		0			0
$853$	40.0236			1.37038			0.685191	−	0.728364i	$-0.259719\pi$
$853$	40.0236			1.37038			0.685191	+	0.728364i	$0.259719\pi$
$854$		0			0
$855$	78.8645			2.69711
$856$		0			0
$857$	−16.4351	−	28.4664i	−0.561412	−	0.972395i	−0.997374	−	0.0724294i	$-0.976925\pi$
$857$	−16.4351	−	28.4664i	−0.561412	−	0.972395i	0.435961	−	0.899966i	$-0.356409\pi$
$858$		0			0
$859$	−17.0252	+	29.4885i	−0.580891	+	1.00613i	0.414483	+	0.910057i	$0.363963\pi$
$859$	−17.0252	+	29.4885i	−0.580891	+	1.00613i	−0.995374	+	0.0960762i	$0.969371\pi$
$860$		0			0
$861$	−1.84871	+	3.11535i	−0.0630038	+	0.106171i
$862$		0			0
$863$	−7.03208	+	12.1799i	−0.239375	+	0.414609i	−0.960535	−	0.278159i	$-0.910276\pi$
$863$	−7.03208	+	12.1799i	−0.239375	+	0.414609i	0.721160	+	0.692768i	$0.243609\pi$
$864$		0			0
$865$	−0.864415	−	1.49721i	−0.0293910	−	0.0509067i
$866$		0			0
$867$	−2.65537			−0.0901813
$868$		0			0
$869$	−17.8434			−0.605295
$870$		0			0
$871$	7.34709	+	12.7255i	0.248947	+	0.431188i
$872$		0			0
$873$	4.54463	−	7.87152i	0.153812	−	0.266411i
$874$		0			0
$875$	5.92153	+	10.5459i	0.200184	+	0.356516i
$876$		0			0
$877$	−25.5335	+	44.2252i	−0.862204	+	1.49338i	0.00759373	+	0.999971i	$0.497583\pi$
$877$	−25.5335	+	44.2252i	−0.862204	+	1.49338i	−0.869797	+	0.493409i	$0.835751\pi$
$878$		0			0
$879$	25.2838	+	43.7927i	0.852800	+	1.47709i
$880$		0			0
$881$	−18.4203			−0.620597			−0.310298	−	0.950639i	$-0.600429\pi$
$881$	−18.4203			−0.620597			−0.310298	+	0.950639i	$0.600429\pi$
$882$		0			0
$883$	−0.126678			−0.00426305			−0.00213153	−	0.999998i	$-0.500678\pi$
$883$	−0.126678			−0.00426305			−0.00213153	+	0.999998i	$0.500678\pi$
$884$		0			0
$885$	−7.76536	−	13.4500i	−0.261030	−	0.452117i
$886$		0			0
$887$	1.93735	−	3.35559i	0.0650498	−	0.112670i	−0.831666	−	0.555276i	$-0.812613\pi$
$887$	1.93735	−	3.35559i	0.0650498	−	0.112670i	0.896716	+	0.442606i	$0.145946\pi$
$888$		0			0
$889$	−6.71181	−	11.9533i	−0.225107	−	0.400902i
$890$		0			0
$891$	−5.57765	+	9.66078i	−0.186858	+	0.323648i
$892$		0			0
$893$	−36.7100	−	63.5837i	−1.22845	−	2.12775i
$894$		0			0
$895$	23.4433			0.783622
$896$		0			0
$897$	1.64804			0.0550265
$898$		0			0
$899$	−5.71733	−	9.90270i	−0.190684	−	0.330274i
$900$		0			0
$901$	−14.2332	+	24.6527i	−0.474178	+	0.821300i
$902$		0			0
$903$	−1.16717	+	1.96685i	−0.0388409	+	0.0654527i
$904$		0			0
$905$	2.74766	−	4.75909i	0.0913355	−	0.158198i
$906$		0			0
$907$	−23.3871	−	40.5076i	−0.776555	−	1.34503i	−0.933916	−	0.357491i	$-0.883632\pi$
$907$	−23.3871	−	40.5076i	−0.776555	−	1.34503i	0.157362	−	0.987541i	$-0.449701\pi$
$908$		0			0
$909$	5.67142			0.188109
$910$		0			0
$911$	−5.93675			−0.196693			−0.0983467	−	0.995152i	$-0.531355\pi$
$911$	−5.93675			−0.196693			−0.0983467	+	0.995152i	$0.531355\pi$
$912$		0			0
$913$	−13.0379	−	22.5824i	−0.431493	−	0.747368i
$914$		0			0
$915$	9.15424	−	15.8556i	0.302630	−	0.524170i
$916$		0			0
$917$	27.9549	+	0.334595i	0.923151	+	0.0110493i
$918$		0			0
$919$	−4.29351	+	7.43657i	−0.141630	+	0.245310i	−0.928110	−	0.372305i	$-0.878568\pi$
$919$	−4.29351	+	7.43657i	−0.141630	+	0.245310i	0.786481	+	0.617615i	$0.211901\pi$
$920$		0			0
$921$	−4.69993	−	8.14051i	−0.154868	−	0.268239i
$922$		0			0
$923$	−3.60141			−0.118542
$924$		0			0
$925$	−10.5677			−0.347463
$926$		0			0
$927$	−22.7040	−	39.3244i	−0.745696	−	1.29158i
$928$		0			0
$929$	4.22972	−	7.32610i	0.138773	−	0.240361i	−0.788260	−	0.615343i	$-0.789018\pi$
$929$	4.22972	−	7.32610i	0.138773	−	0.240361i	0.927032	+	0.374981i	$0.122351\pi$
$930$		0			0
$931$	23.3502	+	42.7766i	0.765271	+	1.40195i
$932$		0			0
$933$	−31.3049	+	54.2216i	−1.02487	+	1.77514i
$934$		0			0
$935$	−11.8187	−	20.4706i	−0.386513	−	0.669460i
$936$		0			0
$937$	−33.3596			−1.08981			−0.544905	−	0.838498i	$-0.683434\pi$
$937$	−33.3596			−1.08981			−0.544905	+	0.838498i	$0.683434\pi$
$938$		0			0
$939$	−47.5048			−1.55026
$940$		0			0
$941$	6.70187	+	11.6080i	0.218475	+	0.378409i	0.954342	−	0.298717i	$-0.0965586\pi$
$941$	6.70187	+	11.6080i	0.218475	+	0.378409i	−0.735867	+	0.677126i	$0.763225\pi$
$942$		0			0
$943$	0.163454	−	0.283110i	0.00532278	−	0.00921933i
$944$		0			0
$945$	18.2099	+	0.217956i	0.592367	+	0.00709012i
$946$		0			0
$947$	21.5397	−	37.3078i	0.699946	−	1.21234i	−0.268539	−	0.963269i	$-0.586541\pi$
$947$	21.5397	−	37.3078i	0.699946	−	1.21234i	0.968485	−	0.249073i	$-0.0801259\pi$
$948$		0			0
$949$	−1.48786	−	2.57706i	−0.0482981	−	0.0836548i
$950$		0			0
$951$	−72.3768			−2.34698
$952$		0			0
$953$	16.7332			0.542040			0.271020	−	0.962574i	$-0.412639\pi$
$953$	16.7332			0.542040			0.271020	+	0.962574i	$0.412639\pi$
$954$		0			0
$955$	−5.37234	−	9.30517i	−0.173845	−	0.301108i
$956$		0			0
$957$	2.93231	−	5.07891i	0.0947881	−	0.164178i
$958$		0			0
$959$	−7.92809	+	13.3600i	−0.256011	+	0.431417i
$960$		0			0
$961$	−38.9183	+	67.4085i	−1.25543	+	2.17447i
$962$		0			0
$963$	38.2961	+	66.3308i	1.23407	+	2.13748i
$964$		0			0
$965$	−39.4390			−1.26959
$966$		0			0
$967$	−44.7594			−1.43937			−0.719683	−	0.694303i	$-0.755713\pi$
$967$	−44.7594			−1.43937			−0.719683	+	0.694303i	$0.755713\pi$
$968$		0			0
$969$	36.5705	+	63.3420i	1.17482	+	2.03484i
$970$		0			0
$971$	−2.10129	+	3.63955i	−0.0674337	+	0.116799i	−0.897771	−	0.440463i	$-0.854814\pi$
$971$	−2.10129	+	3.63955i	−0.0674337	+	0.116799i	0.830337	+	0.557261i	$0.188148\pi$
$972$		0			0
$973$	5.18143	+	9.22783i	0.166109	+	0.295830i
$974$		0			0
$975$	−4.49933	+	7.79307i	−0.144094	+	0.249578i
$976$		0			0
$977$	12.8449	+	22.2481i	0.410946	+	0.711779i	0.994993	−	0.0999403i	$-0.0318652\pi$
$977$	12.8449	+	22.2481i	0.410946	+	0.711779i	−0.584048	+	0.811719i	$0.698532\pi$
$978$		0			0
$979$	5.45999			0.174502
$980$		0			0
$981$	−4.31923			−0.137902
$982$		0			0
$983$	−15.9122	−	27.5607i	−0.507520	−	0.879051i	−0.999962	−	0.00870538i	$-0.997229\pi$
$983$	−15.9122	−	27.5607i	−0.507520	−	0.879051i	0.492442	−	0.870345i	$-0.336104\pi$
$984$		0			0
$985$	−14.0814	+	24.3896i	−0.448669	+	0.777118i
$986$		0			0
$987$	−35.8898	−	63.9176i	−1.14238	−	2.03452i
$988$		0			0
$989$	0.103195	−	0.178739i	0.00328141	−	0.00568358i
$990$		0			0
$991$	4.73739	+	8.20540i	0.150488	+	0.260653i	0.931407	−	0.363979i	$-0.118582\pi$
$991$	4.73739	+	8.20540i	0.150488	+	0.260653i	−0.780919	+	0.624632i	$0.785249\pi$
$992$		0			0
$993$	47.7676			1.51586
$994$		0			0
$995$	76.2570			2.41751
$996$		0			0
$997$	−10.9755	−	19.0102i	−0.347599	−	0.602059i	0.638224	−	0.769851i	$-0.279670\pi$
$997$	−10.9755	−	19.0102i	−0.347599	−	0.602059i	−0.985822	+	0.167792i	$0.946336\pi$
$998$		0			0
$999$	3.65830	−	6.33636i	0.115743	−	0.200473i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1456.2.r.p.625.1		10
4.3	odd	2		91.2.e.c.79.3	yes	10
7.4	even	3	inner	1456.2.r.p.417.1		10
12.11	even	2		819.2.j.h.352.3		10
28.3	even	6		637.2.e.m.508.3		10
28.11	odd	6		91.2.e.c.53.3	✓	10
28.19	even	6		637.2.a.k.1.3		5
28.23	odd	6		637.2.a.l.1.3		5
28.27	even	2		637.2.e.m.79.3		10
52.51	odd	2		1183.2.e.f.170.3		10
84.11	even	6		819.2.j.h.235.3		10
84.23	even	6		5733.2.a.bl.1.3		5
84.47	odd	6		5733.2.a.bm.1.3		5
364.51	odd	6		8281.2.a.bw.1.3		5
364.103	even	6		8281.2.a.bx.1.3		5
364.207	odd	6		1183.2.e.f.508.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.e.c.53.3	✓	10	28.11	odd	6
91.2.e.c.79.3	yes	10	4.3	odd	2
637.2.a.k.1.3		5	28.19	even	6
637.2.a.l.1.3		5	28.23	odd	6
637.2.e.m.79.3		10	28.27	even	2
637.2.e.m.508.3		10	28.3	even	6
819.2.j.h.235.3		10	84.11	even	6
819.2.j.h.352.3		10	12.11	even	2
1183.2.e.f.170.3		10	52.51	odd	2
1183.2.e.f.508.3		10	364.207	odd	6
1456.2.r.p.417.1		10	7.4	even	3	inner
1456.2.r.p.625.1		10	1.1	even	1	trivial
5733.2.a.bl.1.3		5	84.23	even	6
5733.2.a.bm.1.3		5	84.47	odd	6
8281.2.a.bw.1.3		5	364.51	odd	6
8281.2.a.bx.1.3		5	364.103	even	6

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:	\( N \)	\(=\)	\( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1456.r (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.31364 - 2.27529i) q^{3} +(1.45130 - 2.51373i) q^{5} +(1.29536 + 2.30696i) q^{7} +(-1.95130 + 3.37975i) q^{9} +O(q^{10})\)	\(q+(-1.31364 - 2.27529i) q^{3} +(1.45130 - 2.51373i) q^{5} +(1.29536 + 2.30696i) q^{7} +(-1.95130 + 3.37975i) q^{9} +(1.01828 + 1.76372i) q^{11} +1.00000 q^{13} -7.62594 q^{15} +(-1.99933 - 3.46294i) q^{17} +(3.48105 - 6.02935i) q^{19} +(3.54736 - 5.97783i) q^{21} +(-0.313640 + 0.543240i) q^{23} +(-1.71254 - 2.96621i) q^{25} +2.37138 q^{27} +1.09606 q^{29} +(-5.21624 - 9.03479i) q^{31} +(2.67531 - 4.63378i) q^{33} +(7.67901 + 0.0919110i) q^{35} +(1.54268 - 2.67201i) q^{37} +(-1.31364 - 2.27529i) q^{39} -0.521150 q^{41} -0.329024 q^{43} +(5.66384 + 9.81006i) q^{45} +(5.27284 - 9.13283i) q^{47} +(-3.64409 + 5.97667i) q^{49} +(-5.25280 + 9.09812i) q^{51} +(-3.55950 - 6.16523i) q^{53} +5.91133 q^{55} -18.2914 q^{57} +(1.01828 + 1.76372i) q^{59} +(-1.20041 + 2.07917i) q^{61} +(-10.3246 - 0.123576i) q^{63} +(1.45130 - 2.51373i) q^{65} +(7.34709 + 12.7255i) q^{67} +1.64804 q^{69} -3.60141 q^{71} +(-1.48786 - 2.57706i) q^{73} +(-4.49933 + 7.79307i) q^{75} +(-2.74978 + 4.63378i) q^{77} +(-4.38075 + 7.58769i) q^{79} +(2.73876 + 4.74367i) q^{81} -12.8039 q^{83} -11.6065 q^{85} +(-1.43983 - 2.49386i) q^{87} +(1.34049 - 2.32180i) q^{89} +(1.29536 + 2.30696i) q^{91} +(-13.7045 + 23.7369i) q^{93} +(-10.1041 - 17.5008i) q^{95} -2.32902 q^{97} -7.94789 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{5} - q^{7} - 3 q^{9}+O(q^{10}) \) 10 * q - 2 * q^5 - q^7 - 3 * q^9	\( 10 q - 2 q^{5} - q^{7} - 3 q^{9} + 11 q^{11} + 10 q^{13} + 5 q^{17} + 9 q^{19} + 2 q^{21} + 10 q^{23} - 9 q^{25} - 6 q^{29} - 6 q^{31} - 8 q^{33} + 4 q^{35} - 4 q^{37} + 28 q^{41} - 4 q^{43} + 32 q^{45} + q^{47} - 11 q^{49} - 8 q^{51} - 17 q^{53} - 32 q^{57} + 11 q^{59} + 11 q^{61} - 5 q^{63} - 2 q^{65} + 13 q^{67} + 36 q^{69} - 30 q^{71} - 20 q^{75} - 46 q^{77} + 2 q^{79} + 19 q^{81} - 12 q^{83} - 44 q^{85} - 8 q^{87} + 4 q^{89} - q^{91} - 18 q^{93} - 12 q^{95} - 24 q^{97} - 22 q^{99}+O(q^{100}) \) 10 * q - 2 * q^5 - q^7 - 3 * q^9 + 11 * q^11 + 10 * q^13 + 5 * q^17 + 9 * q^19 + 2 * q^21 + 10 * q^23 - 9 * q^25 - 6 * q^29 - 6 * q^31 - 8 * q^33 + 4 * q^35 - 4 * q^37 + 28 * q^41 - 4 * q^43 + 32 * q^45 + q^47 - 11 * q^49 - 8 * q^51 - 17 * q^53 - 32 * q^57 + 11 * q^59 + 11 * q^61 - 5 * q^63 - 2 * q^65 + 13 * q^67 + 36 * q^69 - 30 * q^71 - 20 * q^75 - 46 * q^77 + 2 * q^79 + 19 * q^81 - 12 * q^83 - 44 * q^85 - 8 * q^87 + 4 * q^89 - q^91 - 18 * q^93 - 12 * q^95 - 24 * q^97 - 22 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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