LMFDB - Embedded newform 1456.2.cc.c.225.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1456,2,Mod(225,1456)]

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, 0, 1]))

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

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

chi := DirichletCharacter("1456.225");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1456 = 2^{4} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1456.cc (of order $6$, 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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.58891012706304.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 $ x^12 - 5x^10 - 2x^9 + 15x^8 + 2x^7 - 30x^6 + 4x^5 + 60x^4 - 16x^3 - 80*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			225.3
Root			$1.34408 - 0.439820i$ of defining polynomial
Character	$\chi$	$=$	1456.225
Dual form			1456.2.cc.c.673.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.291146 + 0.504280i) q^{3} -1.68817i q^{5} +(-0.866025 + 0.500000i) q^{7} +(1.33047 + 2.30444i) q^{9} +O(q^{10})$	\(q+(-0.291146 + 0.504280i) q^{3} -1.68817i q^{5} +(-0.866025 + 0.500000i) q^{7} +(1.33047 + 2.30444i) q^{9} +(0.315769 + 0.182309i) q^{11} +(1.80124 + 3.12338i) q^{13} +(0.851308 + 0.491503i) q^{15} +(-1.59277 - 2.75877i) q^{17} +(-1.25046 + 0.721954i) q^{19} -0.582292i q^{21} +(2.54161 - 4.40219i) q^{23} +2.15010 q^{25} -3.29632 q^{27} +(-4.09831 + 7.09848i) q^{29} +4.69775i q^{31} +(-0.183870 + 0.106157i) q^{33} +(0.844083 + 1.46199i) q^{35} +(5.46967 + 3.15792i) q^{37} +(-2.09948 - 0.00103020i) q^{39} +(-5.04661 - 2.91366i) q^{41} +(0.386561 + 0.669543i) q^{43} +(3.89027 - 2.24605i) q^{45} +12.7905i q^{47} +(0.500000 - 0.866025i) q^{49} +1.85492 q^{51} +1.37110 q^{53} +(0.307768 - 0.533070i) q^{55} -0.840776i q^{57} +(8.10770 - 4.68098i) q^{59} +(4.51242 + 7.81574i) q^{61} +(-2.30444 - 1.33047i) q^{63} +(5.27279 - 3.04080i) q^{65} +(11.6705 + 6.73797i) q^{67} +(1.47996 + 2.56336i) q^{69} +(6.13246 - 3.54058i) q^{71} +2.16083i q^{73} +(-0.625992 + 1.08425i) q^{75} -0.364618 q^{77} +6.88781 q^{79} +(-3.03169 + 5.25105i) q^{81} -0.567380i q^{83} +(-4.65725 + 2.68887i) q^{85} +(-2.38641 - 4.13339i) q^{87} +(-0.986346 - 0.569467i) q^{89} +(-3.12161 - 1.80431i) q^{91} +(-2.36898 - 1.36773i) q^{93} +(1.21878 + 2.11098i) q^{95} +(6.86572 - 3.96393i) q^{97} +0.970225i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{9}+O(q^{10}) $ 12 * q - 4 * q^9	$ 12 q - 4 q^{9} - 6 q^{11} + 4 q^{13} - 6 q^{15} - 4 q^{17} + 12 q^{23} - 20 q^{25} - 12 q^{27} + 8 q^{29} - 30 q^{33} - 6 q^{35} - 42 q^{37} + 4 q^{39} + 30 q^{41} - 2 q^{43} + 6 q^{49} - 52 q^{51} - 44 q^{53} + 6 q^{55} - 18 q^{59} + 14 q^{61} - 12 q^{63} + 60 q^{65} + 24 q^{67} + 4 q^{69} + 24 q^{71} - 46 q^{75} + 8 q^{77} + 56 q^{79} + 2 q^{81} - 48 q^{85} + 2 q^{87} - 12 q^{89} - 14 q^{91} - 18 q^{93} + 22 q^{95} + 6 q^{97}+O(q^{100}) $ 12 * q - 4 * q^9 - 6 * q^11 + 4 * q^13 - 6 * q^15 - 4 * q^17 + 12 * q^23 - 20 * q^25 - 12 * q^27 + 8 * q^29 - 30 * q^33 - 6 * q^35 - 42 * q^37 + 4 * q^39 + 30 * q^41 - 2 * q^43 + 6 * q^49 - 52 * q^51 - 44 * q^53 + 6 * q^55 - 18 * q^59 + 14 * q^61 - 12 * q^63 + 60 * q^65 + 24 * q^67 + 4 * q^69 + 24 * q^71 - 46 * q^75 + 8 * q^77 + 56 * q^79 + 2 * q^81 - 48 * q^85 + 2 * q^87 - 12 * q^89 - 14 * q^91 - 18 * q^93 + 22 * q^95 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$561$	$911$	$1093$	$1249$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$	$1$

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
$3$	−0.291146	+	0.504280i	−0.168093	+	0.291146i	−0.937749	−	0.347313i	$-0.887094\pi$
$3$	−0.291146	+	0.504280i	−0.168093	+	0.291146i	0.769656	+	0.638459i	$0.220428\pi$
$4$		0			0
$5$		−	1.68817i		−	0.754971i	−0.926016	−	0.377485i	$-0.876789\pi$
$5$		−	1.68817i		−	0.754971i	0.926016	−	0.377485i	$-0.123211\pi$
$6$		0			0
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$8$		0			0
$9$	1.33047	+	2.30444i	0.443489	+	0.768146i
$10$		0			0
$11$	0.315769	+	0.182309i	0.0952078	+	0.0549682i	0.546848	−	0.837232i	$-0.315828\pi$
$11$	0.315769	+	0.182309i	0.0952078	+	0.0549682i	−0.451640	+	0.892200i	$0.649161\pi$
$12$		0			0
$13$	1.80124	+	3.12338i	0.499575	+	0.866271i
$13$	1.80124	+	3.12338i	0.499575	+	0.866271i
$14$		0			0
$15$	0.851308	+	0.491503i	0.219807	+	0.126905i
$16$		0			0
$17$	−1.59277	−	2.75877i	−0.386304	−	0.669099i	0.605645	−	0.795735i	$-0.292915\pi$
$17$	−1.59277	−	2.75877i	−0.386304	−	0.669099i	−0.991949	+	0.126636i	$0.959582\pi$
$18$		0			0
$19$	−1.25046	+	0.721954i	−0.286875	+	0.165628i	−0.636532	−	0.771250i	$-0.719632\pi$
$19$	−1.25046	+	0.721954i	−0.286875	+	0.165628i	0.349657	+	0.936878i	$0.386298\pi$
$20$		0			0
$21$		−	0.582292i		−	0.127067i
$22$		0			0
$23$	2.54161	−	4.40219i	0.529962	−	0.917920i	−0.469428	−	0.882971i	$-0.655540\pi$
$23$	2.54161	−	4.40219i	0.529962	−	0.917920i	0.999389	−	0.0349493i	$-0.0111270\pi$
$24$		0			0
$25$	2.15010			0.430020
$26$		0			0
$27$	−3.29632			−0.634377
$28$		0			0
$29$	−4.09831	+	7.09848i	−0.761037	+	1.31815i	0.181280	+	0.983432i	$0.441976\pi$
$29$	−4.09831	+	7.09848i	−0.761037	+	1.31815i	−0.942317	+	0.334723i	$0.891357\pi$
$30$		0			0
$31$			4.69775i			0.843742i	0.906656	+	0.421871i	$0.138626\pi$
$31$			4.69775i			0.843742i	−0.906656	+	0.421871i	$0.861374\pi$
$32$		0			0
$33$	−0.183870	+	0.106157i	−0.0320076	+	0.0184796i
$34$		0			0
$35$	0.844083	+	1.46199i	0.142676	+	0.247122i
$36$		0			0
$37$	5.46967	+	3.15792i	0.899209	+	0.519159i	0.876943	−	0.480594i	$-0.159579\pi$
$37$	5.46967	+	3.15792i	0.899209	+	0.519159i	0.0222655	+	0.999752i	$0.492912\pi$
$38$		0			0
$39$	−2.09948	−	0.00103020i	−0.336186	−	0.000164965i
$40$		0			0
$41$	−5.04661	−	2.91366i	−0.788148	−	0.455037i	0.0511624	−	0.998690i	$-0.483707\pi$
$41$	−5.04661	−	2.91366i	−0.788148	−	0.455037i	−0.839310	+	0.543653i	$0.817041\pi$
$42$		0			0
$43$	0.386561	+	0.669543i	0.0589500	+	0.102104i	0.893994	−	0.448078i	$-0.147891\pi$
$43$	0.386561	+	0.669543i	0.0589500	+	0.102104i	−0.835044	+	0.550183i	$0.814558\pi$
$44$		0			0
$45$	3.89027	−	2.24605i	0.579928	−	0.334821i
$46$		0			0
$47$			12.7905i			1.86569i	0.360275	+	0.932846i	$0.382683\pi$
$47$			12.7905i			1.86569i	−0.360275	+	0.932846i	$0.617317\pi$
$48$		0			0
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$		0			0
$51$	1.85492			0.259741
$52$		0			0
$53$	1.37110			0.188334			0.0941672	−	0.995556i	$-0.469981\pi$
$53$	1.37110			0.188334			0.0941672	+	0.995556i	$0.469981\pi$
$54$		0			0
$55$	0.307768	−	0.533070i	0.0414994	−	0.0718791i
$56$		0			0
$57$		−	0.840776i		−	0.111363i
$58$		0			0
$59$	8.10770	−	4.68098i	1.05553	−	0.609412i	0.131340	−	0.991337i	$-0.458072\pi$
$59$	8.10770	−	4.68098i	1.05553	−	0.609412i	0.924193	+	0.381925i	$0.124739\pi$
$60$		0			0
$61$	4.51242	+	7.81574i	0.577756	+	1.00070i	0.995736	+	0.0922469i	$0.0294049\pi$
$61$	4.51242	+	7.81574i	0.577756	+	1.00070i	−0.417980	+	0.908456i	$0.637262\pi$
$62$		0			0
$63$	−2.30444	−	1.33047i	−0.290332	−	0.167623i
$64$		0			0
$65$	5.27279	−	3.04080i	0.654009	−	0.377164i
$66$		0			0
$67$	11.6705	+	6.73797i	1.42578	+	0.823174i	0.996784	−	0.0801330i	$-0.0255345\pi$
$67$	11.6705	+	6.73797i	1.42578	+	0.823174i	0.428995	+	0.903307i	$0.358868\pi$
$68$		0			0
$69$	1.47996	+	2.56336i	0.178166	+	0.308592i
$70$		0			0
$71$	6.13246	−	3.54058i	0.727789	−	0.420189i	−0.0898239	−	0.995958i	$-0.528630\pi$
$71$	6.13246	−	3.54058i	0.727789	−	0.420189i	0.817613	+	0.575769i	$0.195297\pi$
$72$		0			0
$73$			2.16083i			0.252906i	0.991973	+	0.126453i	$0.0403592\pi$
$73$			2.16083i			0.252906i	−0.991973	+	0.126453i	$0.959641\pi$
$74$		0			0
$75$	−0.625992	+	1.08425i	−0.0722834	+	0.125198i
$76$		0			0
$77$	−0.364618			−0.0415521
$78$		0			0
$79$	6.88781			0.774940			0.387470	−	0.921882i	$-0.373349\pi$
$79$	6.88781			0.774940			0.387470	+	0.921882i	$0.373349\pi$
$80$		0			0
$81$	−3.03169	+	5.25105i	−0.336855	+	0.583450i
$82$		0			0
$83$		−	0.567380i		−	0.0622780i	−0.999515	−	0.0311390i	$-0.990087\pi$
$83$		−	0.567380i		−	0.0622780i	0.999515	−	0.0311390i	$-0.00991345\pi$
$84$		0			0
$85$	−4.65725	+	2.68887i	−0.505150	+	0.291648i
$86$		0			0
$87$	−2.38641	−	4.13339i	−0.255850	−	0.443146i
$88$		0			0
$89$	−0.986346	−	0.569467i	−0.104553	−	0.0603634i	0.446812	−	0.894628i	$-0.352559\pi$
$89$	−0.986346	−	0.569467i	−0.104553	−	0.0603634i	−0.551364	+	0.834264i	$0.685893\pi$
$90$		0			0
$91$	−3.12161	−	1.80431i	−0.327234	−	0.189143i
$92$		0			0
$93$	−2.36898	−	1.36773i	−0.245652	−	0.141827i
$94$		0			0
$95$	1.21878	+	2.11098i	0.125044	+	0.216582i
$96$		0			0
$97$	6.86572	−	3.96393i	0.697109	−	0.402476i	−0.109161	−	0.994024i	$-0.534816\pi$
$97$	6.86572	−	3.96393i	0.697109	−	0.402476i	0.806270	+	0.591548i	$0.201483\pi$
$98$		0			0
$99$			0.970225i			0.0975113i
$100$		0			0
$101$	−7.77322	+	13.4636i	−0.773465	+	1.33968i	0.162189	+	0.986760i	$0.448145\pi$
$101$	−7.77322	+	13.4636i	−0.773465	+	1.33968i	−0.935653	+	0.352920i	$0.885189\pi$
$102$		0			0
$103$	10.2982			1.01471			0.507354	−	0.861738i	$-0.330624\pi$
$103$	10.2982			1.01471			0.507354	+	0.861738i	$0.330624\pi$
$104$		0			0
$105$	−0.983005			−0.0959315
$106$		0			0
$107$	−6.56220	+	11.3661i	−0.634391	+	1.09880i	0.352252	+	0.935905i	$0.385416\pi$
$107$	−6.56220	+	11.3661i	−0.634391	+	1.09880i	−0.986644	+	0.162893i	$0.947917\pi$
$108$		0			0
$109$			10.4459i			1.00054i	0.865871	+	0.500268i	$0.166765\pi$
$109$			10.4459i			1.00054i	−0.865871	+	0.500268i	$0.833235\pi$
$110$		0			0
$111$	−3.18495	+	1.83883i	−0.302302	+	0.174534i
$112$		0			0
$113$	−2.47631	−	4.28909i	−0.232952	−	0.403484i	0.725724	−	0.687986i	$-0.241505\pi$
$113$	−2.47631	−	4.28909i	−0.232952	−	0.403484i	−0.958675	+	0.284502i	$0.908172\pi$
$114$		0			0
$115$	−7.43163	−	4.29065i	−0.693003	−	0.400105i
$116$		0			0
$117$	−4.80115	+	8.30642i	−0.443866	+	0.767928i
$118$		0			0
$119$	2.75877	+	1.59277i	0.252896	+	0.146009i
$120$		0			0
$121$	−5.43353	−	9.41114i	−0.493957	−	0.855559i
$122$		0			0
$123$	2.93860	−	1.69660i	0.264965	−	0.152977i
$124$		0			0
$125$		−	12.0705i		−	1.07962i
$126$		0			0
$127$	−4.03366	+	6.98650i	−0.357929	+	0.619951i	−0.987615	−	0.156899i	$-0.949850\pi$
$127$	−4.03366	+	6.98650i	−0.357929	+	0.619951i	0.629686	+	0.776850i	$0.283184\pi$
$128$		0			0
$129$	−0.450183			−0.0396364
$130$		0			0
$131$	−18.9039			−1.65164			−0.825820	−	0.563934i	$-0.809287\pi$
$131$	−18.9039			−1.65164			−0.825820	+	0.563934i	$0.809287\pi$
$132$		0			0
$133$	0.721954	−	1.25046i	0.0626013	−	0.108429i
$134$		0			0
$135$			5.56473i			0.478936i
$136$		0			0
$137$	15.7837	−	9.11274i	1.34850	−	0.778554i	0.360459	−	0.932775i	$-0.382620\pi$
$137$	15.7837	−	9.11274i	1.34850	−	0.778554i	0.988036	+	0.154221i	$0.0492867\pi$
$138$		0			0
$139$	2.62542	+	4.54737i	0.222686	+	0.385703i	0.955623	−	0.294594i	$-0.0951843\pi$
$139$	2.62542	+	4.54737i	0.222686	+	0.385703i	−0.732937	+	0.680297i	$0.761851\pi$
$140$		0			0
$141$	−6.45001	−	3.72392i	−0.543189	−	0.313610i
$142$		0			0
$143$	−0.000645091		1.31465i	−5.39452e−5		0.109936i
$144$		0			0
$145$	11.9834	+	6.91862i	0.995167	+	0.574560i
$146$		0			0
$147$	0.291146	+	0.504280i	0.0240133	+	0.0415923i
$148$		0			0
$149$	8.03073	−	4.63654i	0.657903	−	0.379841i	−0.133574	−	0.991039i	$-0.542646\pi$
$149$	8.03073	−	4.63654i	0.657903	−	0.379841i	0.791478	+	0.611198i	$0.209312\pi$
$150$		0			0
$151$		−	14.0132i		−	1.14038i	−0.821513	−	0.570189i	$-0.806870\pi$
$151$		−	14.0132i		−	1.14038i	0.821513	−	0.570189i	$-0.193130\pi$
$152$		0			0
$153$	4.23827	−	7.34090i	0.342644	−	0.593476i
$154$		0			0
$155$	7.93059			0.637000
$156$		0			0
$157$	−17.1825			−1.37131			−0.685656	−	0.727925i	$-0.740485\pi$
$157$	−17.1825			−1.37131			−0.685656	+	0.727925i	$0.740485\pi$
$158$		0			0
$159$	−0.399189	+	0.691415i	−0.0316577	+	0.0548328i
$160$		0			0
$161$			5.08321i			0.400613i
$162$		0			0
$163$	−10.2128	+	5.89637i	−0.799930	+	0.461840i	−0.843447	−	0.537213i	$-0.819477\pi$
$163$	−10.2128	+	5.89637i	−0.799930	+	0.461840i	0.0435169	+	0.999053i	$0.486144\pi$
$164$		0			0
$165$	0.179211	+	0.310402i	0.0139515	+	0.0241648i
$166$		0			0
$167$	−3.73852	−	2.15843i	−0.289295	−	0.167025i	0.348329	−	0.937372i	$-0.386749\pi$
$167$	−3.73852	−	2.15843i	−0.289295	−	0.167025i	−0.637624	+	0.770348i	$0.720083\pi$
$168$		0			0
$169$	−6.51105	+	11.2519i	−0.500850	+	0.865534i
$170$		0			0
$171$	−3.32739	−	1.92107i	−0.254452	−	0.146908i
$172$		0			0
$173$	6.25985	+	10.8424i	0.475928	+	0.824331i	0.999620	−	0.0275769i	$-0.00877910\pi$
$173$	6.25985	+	10.8424i	0.475928	+	0.824331i	−0.523692	+	0.851908i	$0.675446\pi$
$174$		0			0
$175$	−1.86204	+	1.07505i	−0.140757	+	0.0812660i
$176$		0			0
$177$			5.45140i			0.409752i
$178$		0			0
$179$	3.29767	−	5.71173i	0.246479	−	0.426915i	−0.716067	−	0.698031i	$-0.754060\pi$
$179$	3.29767	−	5.71173i	0.246479	−	0.426915i	0.962547	+	0.271117i	$0.0873929\pi$
$180$		0			0
$181$	−11.0157			−0.818791			−0.409395	−	0.912357i	$-0.634260\pi$
$181$	−11.0157			−0.818791			−0.409395	+	0.912357i	$0.634260\pi$
$182$		0			0
$183$	−5.25509			−0.388468
$184$		0			0
$185$	5.33109	−	9.23371i	0.391949	−	0.678876i
$186$		0			0
$187$		−	1.16151i		−	0.0849379i
$188$		0			0
$189$	2.85470	−	1.64816i	0.207649	−	0.119886i
$190$		0			0
$191$	2.96606	+	5.13737i	0.214617	+	0.371727i	0.953154	−	0.302486i	$-0.0978164\pi$
$191$	2.96606	+	5.13737i	0.214617	+	0.371727i	−0.738537	+	0.674213i	$0.764483\pi$
$192$		0			0
$193$	3.63380	+	2.09798i	0.261567	+	0.151016i	0.625049	−	0.780586i	$-0.285079\pi$
$193$	3.63380	+	2.09798i	0.261567	+	0.151016i	−0.363482	+	0.931601i	$0.618412\pi$
$194$		0			0
$195$	−0.00173916	+	3.54428i	−0.000124544	+	0.253811i
$196$		0			0
$197$	5.00990	+	2.89247i	0.356941	+	0.206080i	0.667738	−	0.744396i	$-0.267263\pi$
$197$	5.00990	+	2.89247i	0.356941	+	0.206080i	−0.310797	+	0.950476i	$0.600596\pi$
$198$		0			0
$199$	−5.97988	−	10.3575i	−0.423903	−	0.734221i	0.572415	−	0.819964i	$-0.306007\pi$
$199$	−5.97988	−	10.3575i	−0.423903	−	0.734221i	−0.996317	+	0.0857435i	$0.972673\pi$
$200$		0			0
$201$	−6.79564	+	3.92347i	−0.479328	+	0.276740i
$202$		0			0
$203$		−	8.19662i		−	0.575290i
$204$		0			0
$205$	−4.91874	+	8.51951i	−0.343540	+	0.595028i
$206$		0			0
$207$	13.5261			0.940129
$208$		0			0
$209$	−0.526475			−0.0364170
$210$		0			0
$211$	−4.11795	+	7.13251i	−0.283492	+	0.491022i	−0.972242	−	0.233976i	$-0.924826\pi$
$211$	−4.11795	+	7.13251i	−0.283492	+	0.491022i	0.688751	+	0.724998i	$0.258160\pi$
$212$		0			0
$213$			4.12330i			0.282524i
$214$		0			0
$215$	1.13030	−	0.652579i	0.0770858	−	0.0445055i
$216$		0			0
$217$	−2.34888	−	4.06838i	−0.159452	−	0.276179i
$218$		0			0
$219$	−1.08966	−	0.629116i	−0.0736325	−	0.0425117i
$220$		0			0
$221$	5.74771	−	9.94405i	0.386633	−	0.668909i
$222$		0			0
$223$	−13.2515	−	7.65073i	−0.887383	−	0.512331i	−0.0142977	−	0.999898i	$-0.504551\pi$
$223$	−13.2515	−	7.65073i	−0.887383	−	0.512331i	−0.873086	+	0.487567i	$0.837885\pi$
$224$		0			0
$225$	2.86064	+	4.95477i	0.190709	+	0.330318i
$226$		0			0
$227$	6.02292	−	3.47733i	0.399755	−	0.230799i	−0.286623	−	0.958043i	$-0.592533\pi$
$227$	6.02292	−	3.47733i	0.399755	−	0.230799i	0.686378	+	0.727245i	$0.259199\pi$
$228$		0			0
$229$		−	27.4219i		−	1.81209i	−0.423180	−	0.906045i	$-0.639086\pi$
$229$		−	27.4219i		−	1.81209i	0.423180	−	0.906045i	$-0.360914\pi$
$230$		0			0
$231$	0.106157	−	0.183870i	0.00698463	−	0.0120977i
$232$		0			0
$233$	6.85333			0.448976			0.224488	−	0.974477i	$-0.427929\pi$
$233$	6.85333			0.448976			0.224488	+	0.974477i	$0.427929\pi$
$234$		0			0
$235$	21.5926			1.40854
$236$		0			0
$237$	−2.00536	+	3.47338i	−0.130262	+	0.225621i
$238$		0			0
$239$		−	22.0754i		−	1.42794i	−0.700177	−	0.713970i	$-0.746895\pi$
$239$		−	22.0754i		−	1.42794i	0.700177	−	0.713970i	$-0.253105\pi$
$240$		0			0
$241$	13.6807	−	7.89855i	0.881251	−	0.508790i	0.0101802	−	0.999948i	$-0.496759\pi$
$241$	13.6807	−	7.89855i	0.881251	−	0.508790i	0.871071	+	0.491158i	$0.163426\pi$
$242$		0			0
$243$	−6.70981	−	11.6217i	−0.430434	−	0.745534i
$244$		0			0
$245$	−1.46199	−	0.844083i	−0.0934034	−	0.0539265i
$246$		0			0
$247$	−4.50732	−	2.60525i	−0.286794	−	0.165768i
$248$		0			0
$249$	0.286118	+	0.165190i	0.0181320	+	0.0104685i
$250$		0			0
$251$	−11.2783	−	19.5346i	−0.711882	−	1.23302i	−0.964150	−	0.265359i	$-0.914510\pi$
$251$	−11.2783	−	19.5346i	−0.711882	−	1.23302i	0.252268	−	0.967658i	$-0.418824\pi$
$252$		0			0
$253$	1.60512	−	0.926716i	0.100913	−	0.0582621i
$254$		0			0
$255$		−	3.13141i		−	0.196097i
$256$		0			0
$257$	10.2064	−	17.6781i	0.636660	−	1.10273i	−0.349501	−	0.936936i	$-0.613649\pi$
$257$	10.2064	−	17.6781i	0.636660	−	1.10273i	0.986161	−	0.165791i	$-0.0530179\pi$
$258$		0			0
$259$	−6.31584			−0.392447
$260$		0			0
$261$	−21.8107			−1.35005
$262$		0			0
$263$	−14.7701	+	25.5826i	−0.910764	+	1.57749i	−0.0977768	+	0.995208i	$0.531173\pi$
$263$	−14.7701	+	25.5826i	−0.910764	+	1.57749i	−0.812987	+	0.582281i	$0.802160\pi$
$264$		0			0
$265$		−	2.31464i		−	0.142187i
$266$		0			0
$267$	0.574342	−	0.331596i	0.0351491	−	0.0202934i
$268$		0			0
$269$	−13.9581	−	24.1762i	−0.851043	−	1.47405i	−0.880268	−	0.474477i	$-0.842637\pi$
$269$	−13.9581	−	24.1762i	−0.851043	−	1.47405i	0.0292252	−	0.999573i	$-0.490696\pi$
$270$		0			0
$271$	25.5036	+	14.7245i	1.54924	+	0.894451i	0.998200	+	0.0599690i	$0.0191002\pi$
$271$	25.5036	+	14.7245i	1.54924	+	0.894451i	0.551035	+	0.834482i	$0.314233\pi$
$272$		0			0
$273$	1.81872	−	1.04885i	0.110074	−	0.0634793i
$274$		0			0
$275$	0.678933	+	0.391982i	0.0409412	+	0.0236374i
$276$		0			0
$277$	3.42927	+	5.93967i	0.206045	+	0.356880i	0.950465	−	0.310831i	$-0.100607\pi$
$277$	3.42927	+	5.93967i	0.206045	+	0.356880i	−0.744420	+	0.667711i	$0.767274\pi$
$278$		0			0
$279$	−10.8257	+	6.25021i	−0.648117	+	0.374190i
$280$		0			0
$281$		−	29.0940i		−	1.73561i	−0.496909	−	0.867803i	$-0.665532\pi$
$281$		−	29.0940i		−	1.73561i	0.496909	−	0.867803i	$-0.334468\pi$
$282$		0			0
$283$	−5.80511	+	10.0547i	−0.345078	+	0.597692i	−0.985368	−	0.170441i	$-0.945481\pi$
$283$	−5.80511	+	10.0547i	−0.345078	+	0.597692i	0.640290	+	0.768133i	$0.278814\pi$
$284$		0			0
$285$	−1.41937			−0.0840761
$286$		0			0
$287$	5.82732			0.343976
$288$		0			0
$289$	3.42614	−	5.93425i	0.201538	−	0.349074i
$290$		0			0
$291$			4.61633i			0.270614i
$292$		0			0
$293$	−15.4054	+	8.89430i	−0.899992	+	0.519610i	−0.877197	−	0.480130i	$-0.840590\pi$
$293$	−15.4054	+	8.89430i	−0.899992	+	0.519610i	−0.0227942	+	0.999740i	$0.507256\pi$
$294$		0			0
$295$	−7.90228	−	13.6871i	−0.460088	−	0.796896i
$296$		0			0
$297$	−1.04087	−	0.600949i	−0.0603976	−	0.0348706i
$298$		0			0
$299$	18.3278	+	0.00899334i	1.05992	+	0.000520098i
$300$		0			0
$301$	−0.669543	−	0.386561i	−0.0385918	−	0.0222810i
$302$		0			0
$303$	−4.52629	−	7.83976i	−0.260028	−	0.450382i
$304$		0			0
$305$	13.1943	−	7.61771i	0.755501	−	0.436189i
$306$		0			0
$307$		−	9.07966i		−	0.518204i	−0.965850	−	0.259102i	$-0.916573\pi$
$307$		−	9.07966i		−	0.518204i	0.965850	−	0.259102i	$-0.0834265\pi$
$308$		0			0
$309$	−2.99827	+	5.19315i	−0.170566	+	0.295428i
$310$		0			0
$311$	1.57073			0.0890677			0.0445338	−	0.999008i	$-0.485820\pi$
$311$	1.57073			0.0890677			0.0445338	+	0.999008i	$0.485820\pi$
$312$		0			0
$313$	20.6232			1.16569			0.582846	−	0.812582i	$-0.301939\pi$
$313$	20.6232			1.16569			0.582846	+	0.812582i	$0.301939\pi$
$314$		0			0
$315$	−2.24605	+	3.89027i	−0.126551	+	0.219192i
$316$		0			0
$317$			30.5435i			1.71549i	0.514072	+	0.857747i	$0.328137\pi$
$317$			30.5435i			1.71549i	−0.514072	+	0.857747i	$0.671863\pi$
$318$		0			0
$319$	−2.58823	+	1.49432i	−0.144913	+	0.0836657i
$320$		0			0
$321$	−3.82111	−	6.61836i	−0.213274	−	0.369401i
$322$		0			0
$323$	3.98340	+	2.29982i	0.221642	+	0.127965i
$324$		0			0
$325$	3.87285	+	6.71558i	0.214827	+	0.372513i
$326$		0			0
$327$	−5.26765	−	3.04128i	−0.291302	−	0.168183i
$328$		0			0
$329$	−6.39527	−	11.0769i	−0.352583	−	0.610691i
$330$		0			0
$331$	22.3894	−	12.9265i	1.23063	−	0.710507i	0.263472	−	0.964667i	$-0.415132\pi$
$331$	22.3894	−	12.9265i	1.23063	−	0.710507i	0.967162	+	0.254161i	$0.0817992\pi$
$332$		0			0
$333$			16.8060i			0.920965i
$334$		0			0
$335$	11.3748	−	19.7017i	0.621472	−	1.07642i
$336$		0			0
$337$	−21.3954			−1.16548			−0.582742	−	0.812657i	$-0.698020\pi$
$337$	−21.3954			−1.16548			−0.582742	+	0.812657i	$0.698020\pi$
$338$		0			0
$339$	2.88387			0.156630
$340$		0			0
$341$	−0.856443	+	1.48340i	−0.0463790	+	0.0803308i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$		0			0
$345$	4.32738	−	2.49841i	0.232978	−	0.134510i
$346$		0			0
$347$	1.10442	+	1.91291i	0.0592882	+	0.102690i	0.894146	−	0.447775i	$-0.147784\pi$
$347$	1.10442	+	1.91291i	0.0592882	+	0.102690i	−0.834858	+	0.550466i	$0.814450\pi$
$348$		0			0
$349$	−9.77843	−	5.64558i	−0.523427	−	0.302201i	0.214908	−	0.976634i	$-0.431055\pi$
$349$	−9.77843	−	5.64558i	−0.523427	−	0.302201i	−0.738336	+	0.674433i	$0.764388\pi$
$350$		0			0
$351$	−5.93747	−	10.2957i	−0.316919	−	0.549542i
$352$		0			0
$353$	−30.8680	−	17.8217i	−1.64294	−	0.948552i	−0.979781	−	0.200072i	$-0.935882\pi$
$353$	−30.8680	−	17.8217i	−1.64294	−	0.948552i	−0.663158	−	0.748479i	$-0.730784\pi$
$354$		0			0
$355$	−5.97708	−	10.3526i	−0.317230	−	0.549459i
$356$		0			0
$357$	−1.60641	+	0.927459i	−0.0850201	+	0.0490864i
$358$		0			0
$359$		−	19.3218i		−	1.01976i	−0.860244	−	0.509882i	$-0.829689\pi$
$359$		−	19.3218i		−	1.01976i	0.860244	−	0.509882i	$-0.170311\pi$
$360$		0			0
$361$	−8.45757	+	14.6489i	−0.445135	+	0.770997i
$362$		0			0
$363$	6.32780			0.332123
$364$		0			0
$365$	3.64783			0.190936
$366$		0			0
$367$	−1.86032	+	3.22218i	−0.0971082	+	0.168196i	−0.910487	−	0.413539i	$-0.864293\pi$
$367$	−1.86032	+	3.22218i	−0.0971082	+	0.168196i	0.813378	+	0.581735i	$0.197626\pi$
$368$		0			0
$369$		−	15.5061i		−	0.807217i
$370$		0			0
$371$	−1.18740	+	0.685548i	−0.0616469	+	0.0355919i
$372$		0			0
$373$	1.75638	+	3.04214i	0.0909420	+	0.157516i	0.907908	−	0.419170i	$-0.137679\pi$
$373$	1.75638	+	3.04214i	0.0909420	+	0.157516i	−0.816966	+	0.576686i	$0.804346\pi$
$374$		0			0
$375$	6.08693	+	3.51429i	0.314328	+	0.181477i
$376$		0			0
$377$	−29.5533	−	0.0145016i	−1.52207	−	0.000746873i
$378$		0			0
$379$	−21.6647	−	12.5081i	−1.11284	−	0.642500i	−0.173279	−	0.984873i	$-0.555436\pi$
$379$	−21.6647	−	12.5081i	−1.11284	−	0.642500i	−0.939564	+	0.342373i	$0.888770\pi$
$380$		0			0
$381$	−2.34877	−	4.06818i	−0.120331	−	0.208419i
$382$		0			0
$383$	19.4556	−	11.2327i	0.994134	−	0.573964i	0.0876266	−	0.996153i	$-0.472072\pi$
$383$	19.4556	−	11.2327i	0.994134	−	0.573964i	0.906507	+	0.422190i	$0.138738\pi$
$384$		0			0
$385$			0.615536i			0.0313706i
$386$		0			0
$387$	−1.02861	+	1.78161i	−0.0522874	+	0.0905644i
$388$		0			0
$389$	13.3364			0.676184			0.338092	−	0.941113i	$-0.390219\pi$
$389$	13.3364			0.676184			0.338092	+	0.941113i	$0.390219\pi$
$390$		0			0
$391$	−16.1928			−0.818906
$392$		0			0
$393$	5.50379	−	9.53284i	0.277629	−	0.480868i
$394$		0			0
$395$		−	11.6278i		−	0.585057i
$396$		0			0
$397$	−22.3723	+	12.9166i	−1.12283	+	0.648268i	−0.942123	−	0.335268i	$-0.891173\pi$
$397$	−22.3723	+	12.9166i	−1.12283	+	0.648268i	−0.180710	+	0.983536i	$0.557840\pi$
$398$		0			0
$399$	0.420388	+	0.728133i	0.0210457	+	0.0364522i
$400$		0			0
$401$	15.2078	+	8.78025i	0.759443	+	0.438465i	0.829096	−	0.559106i	$-0.188856\pi$
$401$	15.2078	+	8.78025i	0.759443	+	0.438465i	−0.0696524	+	0.997571i	$0.522189\pi$
$402$		0			0
$403$	−14.6729	+	8.46180i	−0.730909	+	0.421512i
$404$		0			0
$405$	8.86464	+	5.11800i	0.440487	+	0.254316i
$406$		0			0
$407$	1.15143	+	1.99434i	0.0570745	+	0.0988559i
$408$		0			0
$409$	12.5818	−	7.26410i	0.622129	−	0.359186i	−0.155568	−	0.987825i	$-0.549721\pi$
$409$	12.5818	−	7.26410i	0.622129	−	0.359186i	0.777698	+	0.628639i	$0.216388\pi$
$410$		0			0
$411$			10.6126i			0.523479i
$412$		0			0
$413$	−4.68098	+	8.10770i	−0.230336	+	0.398954i
$414$		0			0
$415$	−0.957831			−0.0470181
$416$		0			0
$417$	−3.05753			−0.149728
$418$		0			0
$419$	−2.30096	+	3.98538i	−0.112409	+	0.194699i	−0.916741	−	0.399482i	$-0.869190\pi$
$419$	−2.30096	+	3.98538i	−0.112409	+	0.194699i	0.804332	+	0.594180i	$0.202523\pi$
$420$		0			0
$421$		−	19.2645i		−	0.938895i	−0.882960	−	0.469447i	$-0.844453\pi$
$421$		−	19.2645i		−	0.938895i	0.882960	−	0.469447i	$-0.155547\pi$
$422$		0			0
$423$	−29.4750	+	17.0174i	−1.43312	+	0.827415i
$424$		0			0
$425$	−3.42462	−	5.93161i	−0.166118	−	0.287726i
$426$		0			0
$427$	−7.81574	−	4.51242i	−0.378230	−	0.218371i
$428$		0			0
$429$	−0.662763	−	0.383080i	−0.0319985	−	0.0184953i
$430$		0			0
$431$	24.5649	+	14.1825i	1.18325	+	0.683149i	0.956764	−	0.290865i	$-0.0939432\pi$
$431$	24.5649	+	14.1825i	1.18325	+	0.683149i	0.226485	+	0.974015i	$0.427277\pi$
$432$		0			0
$433$	−6.26014	−	10.8429i	−0.300843	−	0.521076i	0.675484	−	0.737375i	$-0.263935\pi$
$433$	−6.26014	−	10.8429i	−0.300843	−	0.521076i	−0.976327	+	0.216299i	$0.930601\pi$
$434$		0			0
$435$	−6.97784	+	4.02866i	−0.334562	+	0.193159i
$436$		0			0
$437$			7.33969i			0.351105i
$438$		0			0
$439$	−15.8637	+	27.4767i	−0.757132	+	1.31139i	0.187176	+	0.982326i	$0.440067\pi$
$439$	−15.8637	+	27.4767i	−0.757132	+	1.31139i	−0.944307	+	0.329064i	$0.893267\pi$
$440$		0			0
$441$	2.66094			0.126711
$442$		0			0
$443$	−1.73048			−0.0822177			−0.0411088	−	0.999155i	$-0.513089\pi$
$443$	−1.73048			−0.0822177			−0.0411088	+	0.999155i	$0.513089\pi$
$444$		0			0
$445$	−0.961355	+	1.66512i	−0.0455726	+	0.0789341i
$446$		0			0
$447$			5.39965i			0.255394i
$448$		0			0
$449$	−9.14208	+	5.27818i	−0.431442	+	0.249093i	−0.699961	−	0.714181i	$-0.746799\pi$
$449$	−9.14208	+	5.27818i	−0.431442	+	0.249093i	0.268519	+	0.963274i	$0.413466\pi$
$450$		0			0
$451$	−1.06237	−	1.84008i	−0.0500252	−	0.0866462i
$452$		0			0
$453$	7.06658	+	4.07989i	0.332017	+	0.191690i
$454$		0			0
$455$	−3.04597	+	5.26980i	−0.142797	+	0.247052i
$456$		0			0
$457$	−6.88399	−	3.97447i	−0.322019	−	0.185918i	0.330273	−	0.943885i	$-0.392859\pi$
$457$	−6.88399	−	3.97447i	−0.322019	−	0.185918i	−0.652292	+	0.757968i	$0.726193\pi$
$458$		0			0
$459$	5.25029	+	9.09377i	0.245062	+	0.424461i
$460$		0			0
$461$	9.43262	−	5.44592i	0.439321	−	0.253642i	−0.263989	−	0.964526i	$-0.585038\pi$
$461$	9.43262	−	5.44592i	0.439321	−	0.253642i	0.703309	+	0.710884i	$0.251705\pi$
$462$		0			0
$463$			35.8227i			1.66482i	0.554158	+	0.832411i	$0.313040\pi$
$463$			35.8227i			1.66482i	−0.554158	+	0.832411i	$0.686960\pi$
$464$		0			0
$465$	−2.30896	+	3.99923i	−0.107075	+	0.185460i
$466$		0			0
$467$	19.8983			0.920785			0.460393	−	0.887715i	$-0.347709\pi$
$467$	19.8983			0.920785			0.460393	+	0.887715i	$0.347709\pi$
$468$		0			0
$469$	−13.4759			−0.622261
$470$		0			0
$471$	5.00262	−	8.66479i	0.230508	−	0.399252i
$472$		0			0
$473$			0.281894i			0.0129615i
$474$		0			0
$475$	−2.68861	+	1.55227i	−0.123362	+	0.0712231i
$476$		0			0
$477$	1.82420	+	3.15960i	0.0835243	+	0.144668i
$478$		0			0
$479$	−22.7680	−	13.1451i	−1.04030	−	0.600615i	−0.120379	−	0.992728i	$-0.538411\pi$
$479$	−22.7680	−	13.1451i	−1.04030	−	0.600615i	−0.919917	+	0.392113i	$0.871744\pi$
$480$		0			0
$481$	−0.0111741	+	22.7721i	−0.000509496	+	1.03832i
$482$		0			0
$483$	−2.56336	−	1.47996i	−0.116637	−	0.0673404i
$484$		0			0
$485$	−6.69177	−	11.5905i	−0.303857	−	0.526296i
$486$		0			0
$487$	−5.52491	+	3.18981i	−0.250358	+	0.144544i	−0.619928	−	0.784659i	$-0.712838\pi$
$487$	−5.52491	+	3.18981i	−0.250358	+	0.144544i	0.369570	+	0.929203i	$0.379505\pi$
$488$		0			0
$489$		−	6.86682i		−	0.310528i
$490$		0			0
$491$	1.48384	−	2.57008i	0.0669647	−	0.115986i	−0.830599	−	0.556871i	$-0.812002\pi$
$491$	1.48384	−	2.57008i	0.0669647	−	0.115986i	0.897564	+	0.440885i	$0.145335\pi$
$492$		0			0
$493$	26.1107			1.17597
$494$		0			0
$495$	1.63790			0.0736182
$496$		0			0
$497$	−3.54058	+	6.13246i	−0.158817	+	0.275078i
$498$		0			0
$499$			28.1331i			1.25941i	0.776835	+	0.629704i	$0.216824\pi$
$499$			28.1331i			1.25941i	−0.776835	+	0.629704i	$0.783176\pi$
$500$		0			0
$501$	2.17691	−	1.25684i	0.0972571	−	0.0561514i
$502$		0			0
$503$	−15.7688	−	27.3124i	−0.703097	−	1.21780i	−0.967374	−	0.253353i	$-0.918467\pi$
$503$	−15.7688	−	27.3124i	−0.703097	−	1.21780i	0.264277	−	0.964447i	$-0.414867\pi$
$504$		0			0
$505$	22.7288	+	13.1225i	1.01142	+	0.583943i
$506$		0			0
$507$	−3.77846	−	6.55935i	−0.167807	−	0.291311i
$508$		0			0
$509$	11.7731	+	6.79719i	0.521832	+	0.301280i	0.737684	−	0.675146i	$-0.235919\pi$
$509$	11.7731	+	6.79719i	0.521832	+	0.301280i	−0.215852	+	0.976426i	$0.569253\pi$
$510$		0			0
$511$	−1.08041	−	1.87133i	−0.0477947	−	0.0827828i
$512$		0			0
$513$	4.12191	−	2.37979i	0.181987	−	0.105070i
$514$		0			0
$515$		−	17.3850i		−	0.766074i
$516$		0			0
$517$	−2.33183	+	4.03885i	−0.102554	+	0.177628i
$518$		0			0
$519$	−7.29012			−0.320001
$520$		0			0
$521$	8.78344			0.384810			0.192405	−	0.981316i	$-0.438371\pi$
$521$	8.78344			0.384810			0.192405	+	0.981316i	$0.438371\pi$
$522$		0			0
$523$	16.2849	−	28.2063i	0.712088	−	1.23337i	−0.251983	−	0.967732i	$-0.581083\pi$
$523$	16.2849	−	28.2063i	0.712088	−	1.23337i	0.964072	−	0.265642i	$-0.0855839\pi$
$524$		0			0
$525$		−	1.25198i		−	0.0546411i
$526$		0			0
$527$	12.9600	−	7.48246i	0.564547	−	0.325941i
$528$		0			0
$529$	−1.41953	−	2.45869i	−0.0617185	−	0.106900i
$530$		0			0
$531$	21.5741	+	12.4558i	0.936235	+	0.540536i
$532$		0			0
$533$	0.0103098	−	21.0107i	0.000446568	−	0.910074i
$534$		0			0
$535$	19.1878	+	11.0781i	0.829560	+	0.478947i
$536$		0			0
$537$	1.92021	+	3.32590i	0.0828631	+	0.143523i
$538$		0			0
$539$	0.315769	−	0.182309i	0.0136011	−	0.00785261i
$540$		0			0
$541$		−	6.94870i		−	0.298748i	−0.988781	−	0.149374i	$-0.952274\pi$
$541$		−	6.94870i		−	0.298748i	0.988781	−	0.149374i	$-0.0477258\pi$
$542$		0			0
$543$	3.20718	−	5.55500i	0.137633	−	0.238388i
$544$		0			0
$545$	17.6344			0.755375
$546$		0			0
$547$	−10.9095			−0.466457			−0.233229	−	0.972422i	$-0.574929\pi$
$547$	−10.9095			−0.466457			−0.233229	+	0.972422i	$0.574929\pi$
$548$		0			0
$549$	−12.0073	+	20.7972i	−0.512457	+	0.887602i
$550$		0			0
$551$		−	11.8352i		−	0.504194i
$552$		0			0
$553$	−5.96502	+	3.44391i	−0.253659	+	0.146450i
$554$		0			0
$555$	3.10425	+	5.37672i	0.131768	+	0.228229i
$556$		0			0
$557$	29.9901	+	17.3148i	1.27072	+	0.733650i	0.975123	−	0.221662i	$-0.0711483\pi$
$557$	29.9901	+	17.3148i	1.27072	+	0.733650i	0.295596	+	0.955313i	$0.404482\pi$
$558$		0			0
$559$	−1.39495	+	2.41339i	−0.0590001	+	0.102075i
$560$		0			0
$561$	0.585725	+	0.338169i	0.0247293	+	0.0142775i
$562$		0			0
$563$	−4.56839	−	7.91269i	−0.192535	−	0.333480i	0.753555	−	0.657385i	$-0.228338\pi$
$563$	−4.56839	−	7.91269i	−0.192535	−	0.333480i	−0.946090	+	0.323905i	$0.895004\pi$
$564$		0			0
$565$	−7.24070	+	4.18042i	−0.304618	+	0.175872i
$566$		0			0
$567$		−	6.06339i		−	0.254638i
$568$		0			0
$569$	9.15000	−	15.8483i	0.383588	−	0.664394i	−0.607984	−	0.793949i	$-0.708022\pi$
$569$	9.15000	−	15.8483i	0.383588	−	0.664394i	0.991572	+	0.129555i	$0.0413549\pi$
$570$		0			0
$571$	10.1791			0.425981			0.212990	−	0.977054i	$-0.431680\pi$
$571$	10.1791			0.425981			0.212990	+	0.977054i	$0.431680\pi$
$572$		0			0
$573$	−3.45423			−0.144303
$574$		0			0
$575$	5.46470	−	9.46514i	0.227894	−	0.394724i
$576$		0			0
$577$			19.5165i			0.812482i	0.913766	+	0.406241i	$0.133161\pi$
$577$			19.5165i			0.812482i	−0.913766	+	0.406241i	$0.866839\pi$
$578$		0			0
$579$	−2.11593	+	1.22163i	−0.0879352	+	0.0507694i
$580$		0			0
$581$	0.283690	+	0.491365i	0.0117694	+	0.0203853i
$582$		0			0
$583$	0.432949	+	0.249963i	0.0179309	+	0.0103524i
$584$		0			0
$585$	14.0226	+	8.10513i	0.579763	+	0.335106i
$586$		0			0
$587$	30.6486	+	17.6950i	1.26501	+	0.730351i	0.974039	−	0.226382i	$-0.0726898\pi$
$587$	30.6486	+	17.6950i	1.26501	+	0.730351i	0.290967	+	0.956733i	$0.406023\pi$
$588$		0			0
$589$	−3.39156	−	5.87436i	−0.139747	−	0.242049i
$590$		0			0
$591$	−2.91723	+	1.68426i	−0.119999	+	0.0692812i
$592$		0			0
$593$		−	18.0881i		−	0.742790i	−0.928475	−	0.371395i	$-0.878880\pi$
$593$		−	18.0881i		−	0.742790i	0.928475	−	0.371395i	$-0.121120\pi$
$594$		0			0
$595$	2.68887	−	4.65725i	0.110233	−	0.190929i
$596$		0			0
$597$	6.96407			0.285021
$598$		0			0
$599$	−9.05992			−0.370178			−0.185089	−	0.982722i	$-0.559257\pi$
$599$	−9.05992			−0.370178			−0.185089	+	0.982722i	$0.559257\pi$
$600$		0			0
$601$	−14.6440	+	25.3642i	−0.597343	+	1.03463i	0.395869	+	0.918307i	$0.370444\pi$
$601$	−14.6440	+	25.3642i	−0.597343	+	1.03463i	−0.993212	+	0.116321i	$0.962890\pi$
$602$		0			0
$603$			35.8586i			1.46028i
$604$		0			0
$605$	−15.8876	+	9.17269i	−0.645922	+	0.372923i
$606$		0			0
$607$	−19.6825	−	34.0911i	−0.798887	−	1.38371i	−0.920341	−	0.391116i	$-0.872089\pi$
$607$	−19.6825	−	34.0911i	−0.798887	−	1.38371i	0.121454	−	0.992597i	$-0.461244\pi$
$608$		0			0
$609$	4.13339	+	2.38641i	0.167493	+	0.0967023i
$610$		0			0
$611$	−39.9498	+	23.0389i	−1.61619	+	0.932053i
$612$		0			0
$613$	4.79186	+	2.76658i	0.193541	+	0.111741i	0.593639	−	0.804731i	$-0.297691\pi$
$613$	4.79186	+	2.76658i	0.193541	+	0.111741i	−0.400098	+	0.916472i	$0.631024\pi$
$614$		0			0
$615$	−2.86414	−	4.96084i	−0.115493	−	0.200040i
$616$		0			0
$617$	10.8959	−	6.29077i	0.438654	−	0.253257i	−0.264373	−	0.964421i	$-0.585165\pi$
$617$	10.8959	−	6.29077i	0.438654	−	0.253257i	0.703026	+	0.711164i	$0.251832\pi$
$618$		0			0
$619$		−	22.3955i		−	0.900149i	−0.892991	−	0.450075i	$-0.851397\pi$
$619$		−	22.3955i		−	0.900149i	0.892991	−	0.450075i	$-0.148603\pi$
$620$		0			0
$621$	−8.37794	+	14.5110i	−0.336195	+	0.582307i
$622$		0			0
$623$	1.13893			0.0456305
$624$		0			0
$625$	−9.62659			−0.385064
$626$		0			0
$627$	0.153281	−	0.265491i	0.00612145	−	0.0106027i
$628$		0			0
$629$		−	20.1194i		−	0.802213i
$630$		0			0
$631$	−1.68778	+	0.974439i	−0.0671894	+	0.0387918i	−0.533218	−	0.845978i	$-0.679018\pi$
$631$	−1.68778	+	0.974439i	−0.0671894	+	0.0387918i	0.466029	+	0.884769i	$0.345684\pi$
$632$		0			0
$633$	−2.39785	−	4.15320i	−0.0953061	−	0.165075i
$634$		0			0
$635$	11.7944	+	6.80948i	0.468045	+	0.270226i
$636$		0			0
$637$	3.60555	+	0.00176922i	0.142857	+	7.00992e-5i
$638$		0			0
$639$	16.3181	+	9.42125i	0.645533	+	0.372699i
$640$		0			0
$641$	5.21051	+	9.02487i	0.205803	+	0.356461i	0.950388	−	0.311066i	$-0.100686\pi$
$641$	5.21051	+	9.02487i	0.205803	+	0.356461i	−0.744585	+	0.667527i	$0.767353\pi$
$642$		0			0
$643$	−13.2247	+	7.63531i	−0.521533	+	0.301107i	−0.737562	−	0.675280i	$-0.764023\pi$
$643$	−13.2247	+	7.63531i	−0.521533	+	0.301107i	0.216029	+	0.976387i	$0.430690\pi$
$644$		0			0
$645$			0.759983i			0.0299243i
$646$		0			0
$647$	−8.75328	+	15.1611i	−0.344127	+	0.596045i	−0.985195	−	0.171439i	$-0.945158\pi$
$647$	−8.75328	+	15.1611i	−0.344127	+	0.596045i	0.641068	+	0.767484i	$0.278492\pi$
$648$		0			0
$649$	3.41354			0.133993
$650$		0			0
$651$	2.73547			0.107211
$652$		0			0
$653$	5.09169	−	8.81906i	0.199253	−	0.345117i	−0.749033	−	0.662532i	$-0.769482\pi$
$653$	5.09169	−	8.81906i	0.199253	−	0.345117i	0.948287	+	0.317416i	$0.102815\pi$
$654$		0			0
$655$			31.9129i			1.24694i
$656$		0			0
$657$	−4.97949	+	2.87491i	−0.194268	+	0.112161i
$658$		0			0
$659$	−21.9294	−	37.9828i	−0.854247	−	1.47960i	−0.877342	−	0.479866i	$-0.840685\pi$
$659$	−21.9294	−	37.9828i	−0.854247	−	1.47960i	0.0230945	−	0.999733i	$-0.492648\pi$
$660$		0			0
$661$	−28.5156	−	16.4635i	−1.10913	−	0.640356i	−0.170526	−	0.985353i	$-0.554547\pi$
$661$	−28.5156	−	16.4635i	−1.10913	−	0.640356i	−0.938604	+	0.344997i	$0.887880\pi$
$662$		0			0
$663$	3.34116	+	5.79362i	0.129760	+	0.225006i
$664$		0			0
$665$	−2.11098	−	1.21878i	−0.0818604	−	0.0472621i
$666$		0			0
$667$	20.8326	+	36.0831i	0.806640	+	1.39714i
$668$		0			0
$669$	7.71622	−	4.45496i	0.298326	−	0.172239i
$670$		0			0
$671$			3.29062i			0.127033i
$672$		0			0
$673$	13.3423	−	23.1095i	0.514307	−	0.890806i	−0.485555	−	0.874206i	$-0.661383\pi$
$673$	13.3423	−	23.1095i	0.514307	−	0.890806i	0.999862	−	0.0165997i	$-0.00528409\pi$
$674$		0			0
$675$	−7.08740			−0.272794
$676$		0			0
$677$	29.5328			1.13504			0.567519	−	0.823361i	$-0.307904\pi$
$677$	29.5328			1.13504			0.567519	+	0.823361i	$0.307904\pi$
$678$		0			0
$679$	−3.96393	+	6.86572i	−0.152122	+	0.263482i
$680$		0			0
$681$			4.04965i			0.155183i
$682$		0			0
$683$	15.8379	−	9.14400i	0.606019	−	0.349885i	−0.165387	−	0.986229i	$-0.552887\pi$
$683$	15.8379	−	9.14400i	0.606019	−	0.349885i	0.771406	+	0.636343i	$0.219554\pi$
$684$		0			0
$685$	−15.3838	−	26.6456i	−0.587786	−	1.01807i
$686$		0			0
$687$	13.8283	+	7.98378i	0.527583	+	0.304600i
$688$		0			0
$689$	2.46968	+	4.28246i	0.0940872	+	0.163149i
$690$		0			0
$691$	8.95525	+	5.17031i	0.340674	+	0.196688i	0.660570	−	0.750765i	$-0.270315\pi$
$691$	8.95525	+	5.17031i	0.340674	+	0.196688i	−0.319896	+	0.947453i	$0.603648\pi$
$692$		0			0
$693$	−0.485113	−	0.840240i	−0.0184279	−	0.0319181i
$694$		0			0
$695$	7.67671	−	4.43215i	0.291194	−	0.168121i
$696$		0			0
$697$			18.5632i			0.703131i
$698$		0			0
$699$	−1.99532	+	3.45599i	−0.0754699	+	0.130718i
$700$		0			0
$701$	41.6959			1.57483			0.787415	−	0.616423i	$-0.211419\pi$
$701$	41.6959			1.57483			0.787415	+	0.616423i	$0.211419\pi$
$702$		0			0
$703$	−9.11948			−0.343948
$704$		0			0
$705$	−6.28659	+	10.8887i	−0.236766	+	0.410092i
$706$		0			0
$707$		−	15.5464i		−	0.584684i
$708$		0			0
$709$	0.00947974	−	0.00547313i	0.000356019	−	0.000205548i	−0.499822	−	0.866128i	$-0.666601\pi$
$709$	0.00947974	−	0.00547313i	0.000356019	−	0.000205548i	0.500178	+	0.865923i	$0.333268\pi$
$710$		0			0
$711$	9.16402	+	15.8725i	0.343677	+	0.595267i
$712$		0			0
$713$	20.6804	+	11.9398i	0.774488	+	0.447151i
$714$		0			0
$715$	2.21935	+	0.00108902i	0.0829988	+	4.07271e-5i
$716$		0			0
$717$	11.1322	+	6.42717i	0.415739	+	0.240027i
$718$		0			0
$719$	12.7330	+	22.0542i	0.474861	+	0.822484i	0.999586	−	0.0287885i	$-0.00916494\pi$
$719$	12.7330	+	22.0542i	0.474861	+	0.822484i	−0.524724	+	0.851272i	$0.675832\pi$
$720$		0			0
$721$	−8.91847	+	5.14908i	−0.332141	+	0.191762i
$722$		0			0
$723$			9.19853i			0.342097i
$724$		0			0
$725$	−8.81176	+	15.2624i	−0.327261	+	0.566832i
$726$		0			0
$727$	23.5565			0.873663			0.436831	−	0.899543i	$-0.356101\pi$
$727$	23.5565			0.873663			0.436831	+	0.899543i	$0.356101\pi$
$728$		0			0
$729$	−10.3760			−0.384297
$730$		0			0
$731$	1.23141	−	2.13286i	0.0455453	−	0.0788867i
$732$		0			0
$733$			6.23249i			0.230202i	0.993354	+	0.115101i	$0.0367192\pi$
$733$			6.23249i			0.230202i	−0.993354	+	0.115101i	$0.963281\pi$
$734$		0			0
$735$	0.851308	−	0.491503i	0.0314010	−	0.0181293i
$736$		0			0
$737$	2.45679	+	4.25528i	0.0904969	+	0.156745i
$738$		0			0
$739$	−1.12339	−	0.648588i	−0.0413244	−	0.0238587i	0.479195	−	0.877708i	$-0.340929\pi$
$739$	−1.12339	−	0.648588i	−0.0413244	−	0.0238587i	−0.520520	+	0.853850i	$0.674262\pi$
$740$		0			0
$741$	2.62606	−	1.51444i	0.0964709	−	0.0556344i
$742$		0			0
$743$	−5.25627	−	3.03471i	−0.192834	−	0.111333i	0.400475	−	0.916308i	$-0.368845\pi$
$743$	−5.25627	−	3.03471i	−0.192834	−	0.111333i	−0.593309	+	0.804975i	$0.702179\pi$
$744$		0			0
$745$	−7.82725	−	13.5572i	−0.286768	−	0.496697i
$746$		0			0
$747$	1.30749	−	0.754880i	0.0478386	−	0.0276196i
$748$		0			0
$749$		−	13.1244i		−	0.479555i
$750$		0			0
$751$	18.3023	−	31.7005i	0.667860	−	1.15677i	−0.310641	−	0.950527i	$-0.600544\pi$
$751$	18.3023	−	31.7005i	0.667860	−	1.15677i	0.978501	−	0.206241i	$-0.0661230\pi$
$752$		0			0
$753$	13.1346			0.478650
$754$		0			0
$755$	−23.6566			−0.860952
$756$		0			0
$757$	−5.83991	+	10.1150i	−0.212255	+	0.367636i	−0.952420	−	0.304789i	$-0.901414\pi$
$757$	−5.83991	+	10.1150i	−0.212255	+	0.367636i	0.740165	+	0.672425i	$0.234747\pi$
$758$		0			0
$759$			1.07924i			0.0391739i
$760$		0			0
$761$	−34.4408	+	19.8844i	−1.24848	+	0.720810i	−0.970806	−	0.239866i	$-0.922896\pi$
$761$	−34.4408	+	19.8844i	−1.24848	+	0.720810i	−0.277673	+	0.960676i	$0.589563\pi$
$762$		0			0
$763$	−5.22295	−	9.04641i	−0.189083	−	0.327502i
$764$		0			0
$765$	−12.3926	−	7.15490i	−0.448057	−	0.258686i
$766$		0			0
$767$	29.2245	+	16.8919i	1.05523	+	0.609930i
$768$		0			0
$769$	−8.62507	−	4.97969i	−0.311028	−	0.179572i	0.336358	−	0.941734i	$-0.390805\pi$
$769$	−8.62507	−	4.97969i	−0.311028	−	0.179572i	−0.647386	+	0.762162i	$0.724138\pi$
$770$		0			0
$771$	5.94313	+	10.2938i	0.214036	+	0.370722i
$772$		0			0
$773$	11.0433	−	6.37588i	0.397201	−	0.229324i	−0.288074	−	0.957608i	$-0.593015\pi$
$773$	11.0433	−	6.37588i	0.397201	−	0.229324i	0.685276	+	0.728284i	$0.259682\pi$
$774$		0			0
$775$			10.1006i			0.362825i
$776$		0			0
$777$	1.83883	−	3.18495i	0.0659677	−	0.114259i
$778$		0			0
$779$	8.41411			0.301467
$780$		0			0
$781$	2.58192			0.0923882
$782$		0			0
$783$	13.5093	−	23.3988i	0.482784	−	0.836206i
$784$		0			0
$785$			29.0069i			1.03530i
$786$		0			0
$787$	−7.52380	+	4.34387i	−0.268194	+	0.154842i	−0.628067	−	0.778159i	$-0.716154\pi$
$787$	−7.52380	+	4.34387i	−0.268194	+	0.154842i	0.359872	+	0.933002i	$0.382820\pi$
$788$		0			0
$789$	−8.60052	−	14.8965i	−0.306187	−	0.530331i
$790$		0			0
$791$	4.28909	+	2.47631i	0.152503	+	0.0880474i
$792$		0			0
$793$	−16.2836	+	28.1721i	−0.578247	+	1.00042i
$794$		0			0
$795$	1.16722	+	0.673897i	0.0413972	+	0.0239007i
$796$		0			0
$797$	19.3719	+	33.5531i	0.686187	+	1.18851i	0.973062	+	0.230543i	$0.0740503\pi$
$797$	19.3719	+	33.5531i	0.686187	+	1.18851i	−0.286875	+	0.957968i	$0.592616\pi$
$798$		0			0
$799$	35.2861	−	20.3724i	1.24833	−	0.720725i
$800$		0			0
$801$		−	3.03063i		−	0.107082i
$802$		0			0
$803$	−0.393938	+	0.682321i	−0.0139018	+	0.0240786i
$804$		0			0
$805$	8.58130			0.302451
$806$		0			0
$807$	16.2554			0.572218
$808$		0			0
$809$	−14.4275	+	24.9892i	−0.507244	+	0.878573i	0.492721	+	0.870188i	$0.336002\pi$
$809$	−14.4275	+	24.9892i	−0.507244	+	0.878573i	−0.999965	+	0.00838530i	$0.997331\pi$
$810$		0			0
$811$			12.3917i			0.435131i	0.976046	+	0.217566i	$0.0698116\pi$
$811$			12.3917i			0.435131i	−0.976046	+	0.217566i	$0.930188\pi$
$812$		0			0
$813$	−14.8506	+	8.57397i	−0.520832	+	0.300702i
$814$		0			0
$815$	9.95405	+	17.2409i	0.348675	+	0.603923i
$816$		0			0
$817$	−0.966758	−	0.558158i	−0.0338226	−	0.0195275i
$818$		0			0
$819$	0.00470779	−	9.59414i	0.000164504	−	0.335246i
$820$		0			0
$821$	35.5277	+	20.5119i	1.23992	+	0.715870i	0.969079	−	0.246753i	$-0.0793635\pi$
$821$	35.5277	+	20.5119i	1.23992	+	0.715870i	0.270845	+	0.962623i	$0.412697\pi$
$822$		0			0
$823$	1.06806	+	1.84994i	0.0372304	+	0.0644849i	0.884040	−	0.467411i	$-0.154813\pi$
$823$	1.06806	+	1.84994i	0.0372304	+	0.0644849i	−0.846810	+	0.531896i	$0.821480\pi$
$824$		0			0
$825$	−0.395337	+	0.228248i	−0.0137639	+	0.00794658i
$826$		0			0
$827$		−	8.54938i		−	0.297291i	−0.988891	−	0.148645i	$-0.952509\pi$
$827$		−	8.54938i		−	0.297291i	0.988891	−	0.148645i	$-0.0474913\pi$
$828$		0			0
$829$	−7.37844	+	12.7798i	−0.256264	+	0.443862i	−0.965238	−	0.261373i	$-0.915825\pi$
$829$	−7.37844	+	12.7798i	−0.256264	+	0.443862i	0.708974	+	0.705234i	$0.249158\pi$
$830$		0			0
$831$	−3.99367			−0.138539
$832$		0			0
$833$	−3.18555			−0.110373
$834$		0			0
$835$	−3.64379	+	6.31123i	−0.126099	+	0.218409i
$836$		0			0
$837$		−	15.4853i		−	0.535250i
$838$		0			0
$839$	−23.3581	+	13.4858i	−0.806411	+	0.465582i	−0.845708	−	0.533646i	$-0.820822\pi$
$839$	−23.3581	+	13.4858i	−0.806411	+	0.465582i	0.0392968	+	0.999228i	$0.487488\pi$
$840$		0			0
$841$	−19.0923	−	33.0687i	−0.658353	−	1.14030i
$842$		0			0
$843$	14.6715	+	8.47062i	0.505315	+	0.291743i
$844$		0			0
$845$	18.9951	+	10.9917i	0.653453	+	0.378127i
$846$		0			0
$847$	9.41114	+	5.43353i	0.323371	+	0.186698i
$848$		0			0
$849$	−3.38027	−	5.85479i	−0.116010	−	0.200936i
$850$		0			0
$851$	27.8035	−	16.0524i	0.953092	−	0.550268i
$852$		0			0
$853$			25.6332i			0.877665i	0.898569	+	0.438832i	$0.144608\pi$
$853$			25.6332i			0.877665i	−0.898569	+	0.438832i	$0.855392\pi$
$854$		0			0
$855$	−3.24309	+	5.61719i	−0.110911	+	0.192104i
$856$		0			0
$857$	−11.7653			−0.401894			−0.200947	−	0.979602i	$-0.564402\pi$
$857$	−11.7653			−0.401894			−0.200947	+	0.979602i	$0.564402\pi$
$858$		0			0
$859$	21.7761			0.742992			0.371496	−	0.928435i	$-0.378845\pi$
$859$	21.7761			0.742992			0.371496	+	0.928435i	$0.378845\pi$
$860$		0			0
$861$	−1.69660	+	2.93860i	−0.0578200	+	0.100147i
$862$		0			0
$863$		−	41.0575i		−	1.39761i	−0.715310	−	0.698807i	$-0.753715\pi$
$863$		−	41.0575i		−	1.39761i	0.715310	−	0.698807i	$-0.246285\pi$
$864$		0			0
$865$	18.3037	−	10.5677i	0.622345	−	0.359311i
$866$		0			0
$867$	1.99502	+	3.45547i	0.0677543	+	0.117354i
$868$		0			0
$869$	2.17496	+	1.25571i	0.0737803	+	0.0425971i
$870$		0			0
$871$	−0.0238420	+	48.5882i	−0.000807854	+	1.64635i
$872$		0			0
$873$	18.2693	+	10.5478i	0.618320	+	0.356987i
$874$		0			0
$875$	6.03527	+	10.4534i	0.204029	+	0.353389i
$876$		0			0
$877$	5.96788	−	3.44556i	0.201521	−	0.116348i	−0.395844	−	0.918318i	$-0.629548\pi$
$877$	5.96788	−	3.44556i	0.201521	−	0.116348i	0.597365	+	0.801970i	$0.296214\pi$
$878$		0			0
$879$		−	10.3582i		−	0.349372i
$880$		0			0
$881$	−5.32288	+	9.21950i	−0.179332	+	0.310613i	−0.941652	−	0.336588i	$-0.890727\pi$
$881$	−5.32288	+	9.21950i	−0.179332	+	0.310613i	0.762320	+	0.647201i	$0.224060\pi$
$882$		0			0
$883$	−21.3844			−0.719641			−0.359821	−	0.933022i	$-0.617162\pi$
$883$	−21.3844			−0.719641			−0.359821	+	0.933022i	$0.617162\pi$
$884$		0			0
$885$	9.20286			0.309351
$886$		0			0
$887$	−17.0575	+	29.5445i	−0.572735	+	0.992007i	0.423548	+	0.905874i	$0.360784\pi$
$887$	−17.0575	+	29.5445i	−0.572735	+	0.992007i	−0.996284	+	0.0861333i	$0.972549\pi$
$888$		0			0
$889$		−	8.06731i		−	0.270569i
$890$		0			0
$891$	−1.91463	+	1.10541i	−0.0641424	+	0.0370326i
$892$		0			0
$893$	−9.23418	−	15.9941i	−0.309010	−	0.535221i
$894$		0			0
$895$	−9.64235	−	5.56701i	−0.322308	−	0.186085i
$896$		0			0
$897$	−5.34060	+	9.23971i	−0.178317	+	0.308505i
$898$		0			0
$899$	−33.3469	−	19.2528i	−1.11218	−	0.642118i
$900$		0			0
$901$	−2.18384	−	3.78253i	−0.0727544	−	0.126014i
$902$		0			0
$903$	0.389870	−	0.225091i	0.0129740	−	0.00749057i
$904$		0			0
$905$			18.5963i			0.618163i
$906$		0			0
$907$	−21.0758	+	36.5043i	−0.699810	+	1.21211i	0.268723	+	0.963218i	$0.413399\pi$
$907$	−21.0758	+	36.5043i	−0.699810	+	1.21211i	−0.968532	+	0.248888i	$0.919935\pi$
$908$		0			0
$909$	−41.3681			−1.37209
$910$		0			0
$911$	−20.9947			−0.695584			−0.347792	−	0.937572i	$-0.613068\pi$
$911$	−20.9947			−0.695584			−0.347792	+	0.937572i	$0.613068\pi$
$912$		0			0
$913$	0.103438	−	0.179161i	0.00342331	−	0.00592935i
$914$		0			0
$915$			8.87147i			0.293282i
$916$		0			0
$917$	16.3712	−	9.45194i	0.540626	−	0.312131i
$918$		0			0
$919$	−7.14699	−	12.3789i	−0.235757	−	0.408344i	0.723735	−	0.690078i	$-0.242424\pi$
$919$	−7.14699	−	12.3789i	−0.235757	−	0.408344i	−0.959493	+	0.281734i	$0.909090\pi$
$920$		0			0
$921$	4.57869	+	2.64351i	0.150873	+	0.0871065i
$922$		0			0
$923$	22.1046	+	12.7766i	0.727583	+	0.420546i
$924$		0			0
$925$	11.7603	+	6.78983i	0.386677	+	0.223248i
$926$		0			0
$927$	13.7014	+	23.7315i	0.450012	+	0.779444i
$928$		0			0
$929$	5.89524	−	3.40362i	0.193416	−	0.111669i	−0.400164	−	0.916443i	$-0.631047\pi$
$929$	5.89524	−	3.40362i	0.193416	−	0.111669i	0.593581	+	0.804774i	$0.297714\pi$
$930$		0			0
$931$			1.44391i			0.0473221i
$932$		0			0
$933$	−0.457310	+	0.792085i	−0.0149717	+	0.0259317i
$934$		0			0
$935$	−1.96082			−0.0641256
$936$		0			0
$937$	−5.22890			−0.170821			−0.0854104	−	0.996346i	$-0.527220\pi$
$937$	−5.22890			−0.170821			−0.0854104	+	0.996346i	$0.527220\pi$
$938$		0			0
$939$	−6.00437	+	10.3999i	−0.195945	+	0.339387i
$940$		0			0
$941$		−	56.4403i		−	1.83990i	−0.392033	−	0.919951i	$-0.628228\pi$
$941$		−	56.4403i		−	1.83990i	0.392033	−	0.919951i	$-0.371772\pi$
$942$		0			0
$943$	−25.6530	+	14.8108i	−0.835376	+	0.482304i
$944$		0			0
$945$	−2.78236	−	4.81920i	−0.0905103	−	0.156769i
$946$		0			0
$947$	5.06648	+	2.92513i	0.164639	+	0.0950541i	0.580055	−	0.814577i	$-0.303031\pi$
$947$	5.06648	+	2.92513i	0.164639	+	0.0950541i	−0.415417	+	0.909631i	$0.636364\pi$
$948$		0			0
$949$	−6.74909	+	3.89217i	−0.219085	+	0.126345i
$950$		0			0
$951$	−15.4025	−	8.89262i	−0.499459	−	0.288363i
$952$		0			0
$953$	−10.8742	−	18.8346i	−0.352249	−	0.610114i	0.634394	−	0.773010i	$-0.281250\pi$
$953$	−10.8742	−	18.8346i	−0.352249	−	0.610114i	−0.986643	+	0.162896i	$0.947916\pi$
$954$		0			0
$955$	8.67273	−	5.00720i	0.280643	−	0.162029i
$956$		0			0
$957$		−	1.74026i		−	0.0562546i
$958$		0			0
$959$	−9.11274	+	15.7837i	−0.294266	+	0.509683i
$960$		0			0
$961$	8.93110			0.288100
$962$		0			0
$963$	−34.9232			−1.12538
$964$		0			0
$965$	3.54173	−	6.13446i	0.114012	−	0.197475i
$966$		0			0
$967$		−	13.3251i		−	0.428507i	−0.976778	−	0.214253i	$-0.931268\pi$
$967$		−	13.3251i		−	0.428507i	0.976778	−	0.214253i	$-0.0687318\pi$
$968$		0			0
$969$	−2.31950	+	1.33917i	−0.0745132	+	0.0430202i
$970$		0			0
$971$	3.73092	+	6.46215i	0.119731	+	0.207380i	0.919661	−	0.392713i	$-0.128463\pi$
$971$	3.73092	+	6.46215i	0.119731	+	0.207380i	−0.799930	+	0.600093i	$0.795130\pi$
$972$		0			0
$973$	−4.54737	−	2.62542i	−0.145782	−	0.0841673i
$974$		0			0
$975$	−4.51409	−	0.00221504i	−0.144567	−	7.09381e-5i
$976$		0			0
$977$	−9.49204	−	5.48023i	−0.303677	−	0.175328i	0.340416	−	0.940275i	$-0.389432\pi$
$977$	−9.49204	−	5.48023i	−0.303677	−	0.175328i	−0.644094	+	0.764947i	$0.722765\pi$
$978$		0			0
$979$	−0.207638	−	0.359640i	−0.00663614	−	0.0114941i
$980$		0			0
$981$	−24.0719	+	13.8979i	−0.768557	+	0.443727i
$982$		0			0
$983$		−	16.1441i		−	0.514918i	−0.966289	−	0.257459i	$-0.917115\pi$
$983$		−	16.1441i		−	0.514918i	0.966289	−	0.257459i	$-0.0828852\pi$
$984$		0			0
$985$	4.88296	−	8.45754i	0.155584	−	0.269480i
$986$		0			0
$987$	7.44783			0.237067
$988$		0			0
$989$	3.92994			0.124965
$990$		0			0
$991$	3.35748	−	5.81533i	0.106654	−	0.184730i	−0.807759	−	0.589513i	$-0.799320\pi$
$991$	3.35748	−	5.81533i	0.106654	−	0.184730i	0.914413	+	0.404783i	$0.132653\pi$
$992$		0			0
$993$			15.0540i			0.477725i
$994$		0			0
$995$	−17.4851	+	10.0950i	−0.554315	+	0.320034i
$996$		0			0
$997$	9.22057	+	15.9705i	0.292018	+	0.505791i	0.974287	−	0.225311i	$-0.0723399\pi$
$997$	9.22057	+	15.9705i	0.292018	+	0.505791i	−0.682269	+	0.731102i	$0.739007\pi$
$998$		0			0
$999$	−18.0298	−	10.4095i	−0.570437	−	0.329342i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1456.2.cc.c.225.3		12
4.3	odd	2		91.2.q.a.43.3	yes	12
12.11	even	2		819.2.ct.a.316.4		12
13.10	even	6	inner	1456.2.cc.c.673.3		12
28.3	even	6		637.2.u.i.30.4		12
28.11	odd	6		637.2.u.h.30.4		12
28.19	even	6		637.2.k.g.459.4		12
28.23	odd	6		637.2.k.h.459.4		12
28.27	even	2		637.2.q.h.589.3		12
52.7	even	12		1183.2.a.m.1.4		6
52.19	even	12		1183.2.a.p.1.3		6
52.23	odd	6		91.2.q.a.36.3	✓	12
52.35	odd	6		1183.2.c.i.337.7		12
52.43	odd	6		1183.2.c.i.337.6		12
156.23	even	6		819.2.ct.a.127.4		12
364.23	odd	6		637.2.u.h.361.4		12
364.75	even	6		637.2.u.i.361.4		12
364.111	odd	12		8281.2.a.by.1.4		6
364.179	odd	6		637.2.k.h.569.3		12
364.279	odd	12		8281.2.a.ch.1.3		6
364.283	even	6		637.2.k.g.569.3		12
364.335	even	6		637.2.q.h.491.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.q.a.36.3	✓	12	52.23	odd	6
91.2.q.a.43.3	yes	12	4.3	odd	2
637.2.k.g.459.4		12	28.19	even	6
637.2.k.g.569.3		12	364.283	even	6
637.2.k.h.459.4		12	28.23	odd	6
637.2.k.h.569.3		12	364.179	odd	6
637.2.q.h.491.3		12	364.335	even	6
637.2.q.h.589.3		12	28.27	even	2
637.2.u.h.30.4		12	28.11	odd	6
637.2.u.h.361.4		12	364.23	odd	6
637.2.u.i.30.4		12	28.3	even	6
637.2.u.i.361.4		12	364.75	even	6
819.2.ct.a.127.4		12	156.23	even	6
819.2.ct.a.316.4		12	12.11	even	2
1183.2.a.m.1.4		6	52.7	even	12
1183.2.a.p.1.3		6	52.19	even	12
1183.2.c.i.337.6		12	52.43	odd	6
1183.2.c.i.337.7		12	52.35	odd	6
1456.2.cc.c.225.3		12	1.1	even	1	trivial
1456.2.cc.c.673.3		12	13.10	even	6	inner
8281.2.a.by.1.4		6	364.111	odd	12
8281.2.a.ch.1.3		6	364.279	odd	12

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.cc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.291146 + 0.504280i) q^{3} -1.68817i q^{5} +(-0.866025 + 0.500000i) q^{7} +(1.33047 + 2.30444i) q^{9} +O(q^{10})\)	\(q+(-0.291146 + 0.504280i) q^{3} -1.68817i q^{5} +(-0.866025 + 0.500000i) q^{7} +(1.33047 + 2.30444i) q^{9} +(0.315769 + 0.182309i) q^{11} +(1.80124 + 3.12338i) q^{13} +(0.851308 + 0.491503i) q^{15} +(-1.59277 - 2.75877i) q^{17} +(-1.25046 + 0.721954i) q^{19} -0.582292i q^{21} +(2.54161 - 4.40219i) q^{23} +2.15010 q^{25} -3.29632 q^{27} +(-4.09831 + 7.09848i) q^{29} +4.69775i q^{31} +(-0.183870 + 0.106157i) q^{33} +(0.844083 + 1.46199i) q^{35} +(5.46967 + 3.15792i) q^{37} +(-2.09948 - 0.00103020i) q^{39} +(-5.04661 - 2.91366i) q^{41} +(0.386561 + 0.669543i) q^{43} +(3.89027 - 2.24605i) q^{45} +12.7905i q^{47} +(0.500000 - 0.866025i) q^{49} +1.85492 q^{51} +1.37110 q^{53} +(0.307768 - 0.533070i) q^{55} -0.840776i q^{57} +(8.10770 - 4.68098i) q^{59} +(4.51242 + 7.81574i) q^{61} +(-2.30444 - 1.33047i) q^{63} +(5.27279 - 3.04080i) q^{65} +(11.6705 + 6.73797i) q^{67} +(1.47996 + 2.56336i) q^{69} +(6.13246 - 3.54058i) q^{71} +2.16083i q^{73} +(-0.625992 + 1.08425i) q^{75} -0.364618 q^{77} +6.88781 q^{79} +(-3.03169 + 5.25105i) q^{81} -0.567380i q^{83} +(-4.65725 + 2.68887i) q^{85} +(-2.38641 - 4.13339i) q^{87} +(-0.986346 - 0.569467i) q^{89} +(-3.12161 - 1.80431i) q^{91} +(-2.36898 - 1.36773i) q^{93} +(1.21878 + 2.11098i) q^{95} +(6.86572 - 3.96393i) q^{97} +0.970225i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{9}+O(q^{10}) \) 12 * q - 4 * q^9	\( 12 q - 4 q^{9} - 6 q^{11} + 4 q^{13} - 6 q^{15} - 4 q^{17} + 12 q^{23} - 20 q^{25} - 12 q^{27} + 8 q^{29} - 30 q^{33} - 6 q^{35} - 42 q^{37} + 4 q^{39} + 30 q^{41} - 2 q^{43} + 6 q^{49} - 52 q^{51} - 44 q^{53} + 6 q^{55} - 18 q^{59} + 14 q^{61} - 12 q^{63} + 60 q^{65} + 24 q^{67} + 4 q^{69} + 24 q^{71} - 46 q^{75} + 8 q^{77} + 56 q^{79} + 2 q^{81} - 48 q^{85} + 2 q^{87} - 12 q^{89} - 14 q^{91} - 18 q^{93} + 22 q^{95} + 6 q^{97}+O(q^{100}) \) 12 * q - 4 * q^9 - 6 * q^11 + 4 * q^13 - 6 * q^15 - 4 * q^17 + 12 * q^23 - 20 * q^25 - 12 * q^27 + 8 * q^29 - 30 * q^33 - 6 * q^35 - 42 * q^37 + 4 * q^39 + 30 * q^41 - 2 * q^43 + 6 * q^49 - 52 * q^51 - 44 * q^53 + 6 * q^55 - 18 * q^59 + 14 * q^61 - 12 * q^63 + 60 * q^65 + 24 * q^67 + 4 * q^69 + 24 * q^71 - 46 * q^75 + 8 * q^77 + 56 * q^79 + 2 * q^81 - 48 * q^85 + 2 * q^87 - 12 * q^89 - 14 * q^91 - 18 * q^93 + 22 * q^95 + 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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