LMFDB - Embedded newform 91.2.q.a.43.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,2,Mod(36,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("91.36");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	91.q (of order $6$, degree $2$, 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:	$0.726638658394$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			43.3
Root			$1.34408 - 0.439820i$ of defining polynomial
Character	$\chi$	$=$	91.43
Dual form			91.2.q.a.36.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.104235 - 0.0601799i) q^{2} +(0.291146 - 0.504280i) q^{3} +(-0.992757 - 1.71951i) q^{4} -1.68817i q^{5} +(-0.0606950 + 0.0350423i) q^{6} +(0.866025 - 0.500000i) q^{7} +0.479696i q^{8} +(1.33047 + 2.30444i) q^{9} +O(q^{10})$	\(q+(-0.104235 - 0.0601799i) q^{2} +(0.291146 - 0.504280i) q^{3} +(-0.992757 - 1.71951i) q^{4} -1.68817i q^{5} +(-0.0606950 + 0.0350423i) q^{6} +(0.866025 - 0.500000i) q^{7} +0.479696i q^{8} +(1.33047 + 2.30444i) q^{9} +(-0.101594 + 0.175965i) q^{10} +(-0.315769 - 0.182309i) q^{11} -1.15615 q^{12} +(1.80124 + 3.12338i) q^{13} -0.120360 q^{14} +(-0.851308 - 0.491503i) q^{15} +(-1.95665 + 3.38901i) q^{16} +(-1.59277 - 2.75877i) q^{17} -0.320270i q^{18} +(1.25046 - 0.721954i) q^{19} +(-2.90281 + 1.67594i) q^{20} -0.582292i q^{21} +(0.0219427 + 0.0380059i) q^{22} +(-2.54161 + 4.40219i) q^{23} +(0.241901 + 0.139662i) q^{24} +2.15010 q^{25} +(0.000212944 - 0.433964i) q^{26} +3.29632 q^{27} +(-1.71951 - 0.992757i) q^{28} +(-4.09831 + 7.09848i) q^{29} +(0.0591572 + 0.102463i) q^{30} -4.69775i q^{31} +(1.23876 - 0.715198i) q^{32} +(-0.183870 + 0.106157i) q^{33} +0.383412i q^{34} +(-0.844083 - 1.46199i) q^{35} +(2.64166 - 4.57549i) q^{36} +(5.46967 + 3.15792i) q^{37} -0.173789 q^{38} +(2.09948 + 0.00103020i) q^{39} +0.809806 q^{40} +(-5.04661 - 2.91366i) q^{41} +(-0.0350423 + 0.0606950i) q^{42} +(-0.386561 - 0.669543i) q^{43} +0.723954i q^{44} +(3.89027 - 2.24605i) q^{45} +(0.529847 - 0.305907i) q^{46} -12.7905i q^{47} +(1.13934 + 1.97339i) q^{48} +(0.500000 - 0.866025i) q^{49} +(-0.224115 - 0.129393i) q^{50} -1.85492 q^{51} +(3.58248 - 6.19801i) q^{52} +1.37110 q^{53} +(-0.343591 - 0.198372i) q^{54} +(-0.307768 + 0.533070i) q^{55} +(0.239848 + 0.415429i) q^{56} -0.840776i q^{57} +(0.854372 - 0.493272i) q^{58} +(-8.10770 + 4.68098i) q^{59} +1.95177i q^{60} +(4.51242 + 7.81574i) q^{61} +(-0.282711 + 0.489669i) q^{62} +(2.30444 + 1.33047i) q^{63} +7.65442 q^{64} +(5.27279 - 3.04080i) q^{65} +0.0255541 q^{66} +(-11.6705 - 6.73797i) q^{67} +(-3.16247 + 5.47757i) q^{68} +(1.47996 + 2.56336i) q^{69} +0.203187i q^{70} +(-6.13246 + 3.54058i) q^{71} +(-1.10543 + 0.638220i) q^{72} +2.16083i q^{73} +(-0.380087 - 0.658329i) q^{74} +(0.625992 - 1.08425i) q^{75} +(-2.48281 - 1.43345i) q^{76} -0.364618 q^{77} +(-0.218777 - 0.126454i) q^{78} -6.88781 q^{79} +(5.72121 + 3.30314i) q^{80} +(-3.03169 + 5.25105i) q^{81} +(0.350688 + 0.607409i) q^{82} +0.567380i q^{83} +(-1.00125 + 0.578074i) q^{84} +(-4.65725 + 2.68887i) q^{85} +0.0930528i q^{86} +(2.38641 + 4.13339i) q^{87} +(0.0874529 - 0.151473i) q^{88} +(-0.986346 - 0.569467i) q^{89} -0.540669 q^{90} +(3.12161 + 1.80431i) q^{91} +10.0928 q^{92} +(-2.36898 - 1.36773i) q^{93} +(-0.769734 + 1.33322i) q^{94} +(-1.21878 - 2.11098i) q^{95} -0.832908i q^{96} +(6.86572 - 3.96393i) q^{97} +(-0.104235 + 0.0601799i) q^{98} -0.970225i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4} - 18 q^{6} - 4 q^{9}+O(q^{10}) $ 12 * q + 4 * q^4 - 18 * q^6 - 4 * q^9	$ 12 q + 4 q^{4} - 18 q^{6} - 4 q^{9} + 12 q^{10} + 6 q^{11} - 4 q^{12} + 4 q^{13} - 8 q^{14} + 6 q^{15} - 8 q^{16} - 4 q^{17} - 12 q^{20} + 6 q^{22} - 12 q^{23} + 12 q^{24} - 20 q^{25} - 42 q^{26} + 12 q^{27} + 8 q^{29} + 8 q^{30} + 36 q^{32} - 30 q^{33} + 6 q^{35} - 10 q^{36} - 42 q^{37} + 4 q^{38} - 4 q^{39} + 92 q^{40} + 30 q^{41} + 4 q^{42} + 2 q^{43} + 12 q^{46} - 2 q^{48} + 6 q^{49} - 18 q^{50} + 52 q^{51} + 2 q^{52} - 44 q^{53} + 12 q^{54} - 6 q^{55} - 12 q^{56} - 12 q^{58} + 18 q^{59} + 14 q^{61} - 4 q^{62} + 12 q^{63} - 52 q^{64} + 60 q^{65} - 52 q^{66} - 24 q^{67} - 8 q^{68} + 4 q^{69} - 24 q^{71} + 60 q^{72} + 6 q^{74} + 46 q^{75} - 18 q^{76} + 8 q^{77} - 10 q^{78} - 56 q^{79} - 72 q^{80} + 2 q^{81} + 14 q^{82} + 18 q^{84} - 48 q^{85} - 2 q^{87} - 14 q^{88} - 12 q^{89} + 24 q^{90} + 14 q^{91} + 24 q^{92} - 18 q^{93} + 4 q^{94} - 22 q^{95} + 6 q^{97}+O(q^{100}) $ 12 * q + 4 * q^4 - 18 * q^6 - 4 * q^9 + 12 * q^10 + 6 * q^11 - 4 * q^12 + 4 * q^13 - 8 * q^14 + 6 * q^15 - 8 * q^16 - 4 * q^17 - 12 * q^20 + 6 * q^22 - 12 * q^23 + 12 * q^24 - 20 * q^25 - 42 * q^26 + 12 * q^27 + 8 * q^29 + 8 * q^30 + 36 * q^32 - 30 * q^33 + 6 * q^35 - 10 * q^36 - 42 * q^37 + 4 * q^38 - 4 * q^39 + 92 * q^40 + 30 * q^41 + 4 * q^42 + 2 * q^43 + 12 * q^46 - 2 * q^48 + 6 * q^49 - 18 * q^50 + 52 * q^51 + 2 * q^52 - 44 * q^53 + 12 * q^54 - 6 * q^55 - 12 * q^56 - 12 * q^58 + 18 * q^59 + 14 * q^61 - 4 * q^62 + 12 * q^63 - 52 * q^64 + 60 * q^65 - 52 * q^66 - 24 * q^67 - 8 * q^68 + 4 * q^69 - 24 * q^71 + 60 * q^72 + 6 * q^74 + 46 * q^75 - 18 * q^76 + 8 * q^77 - 10 * q^78 - 56 * q^79 - 72 * q^80 + 2 * q^81 + 14 * q^82 + 18 * q^84 - 48 * q^85 - 2 * q^87 - 14 * q^88 - 12 * q^89 + 24 * q^90 + 14 * q^91 + 24 * q^92 - 18 * q^93 + 4 * q^94 - 22 * q^95 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	−0.104235	−	0.0601799i	−0.0737051	−	0.0425536i	0.462695	−	0.886518i	$-0.346883\pi$
$2$	−0.104235	−	0.0601799i	−0.0737051	−	0.0425536i	−0.536400	+	0.843964i	$0.680216\pi$
$3$	0.291146	−	0.504280i	0.168093	−	0.291146i	−0.769656	−	0.638459i	$-0.779572\pi$
$3$	0.291146	−	0.504280i	0.168093	−	0.291146i	0.937749	+	0.347313i	$0.112906\pi$
$4$	−0.992757	−	1.71951i	−0.496378	−	0.859753i
$5$		−	1.68817i		−	0.754971i	−0.926016	−	0.377485i	$-0.876789\pi$
$5$		−	1.68817i		−	0.754971i	0.926016	−	0.377485i	$-0.123211\pi$
$6$	−0.0606950	+	0.0350423i	−0.0247786	+	0.0143060i
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$8$			0.479696i			0.169598i
$9$	1.33047	+	2.30444i	0.443489	+	0.768146i
$10$	−0.101594	+	0.175965i	−0.0321267	+	0.0556452i
$11$	−0.315769	−	0.182309i	−0.0952078	−	0.0549682i	0.451640	−	0.892200i	$-0.350839\pi$
$11$	−0.315769	−	0.182309i	−0.0952078	−	0.0549682i	−0.546848	+	0.837232i	$0.684172\pi$
$12$	−1.15615			−0.333751
$13$	1.80124	+	3.12338i	0.499575	+	0.866271i
$13$	1.80124	+	3.12338i	0.499575	+	0.866271i
$14$	−0.120360			−0.0321675
$15$	−0.851308	−	0.491503i	−0.219807	−	0.126905i
$16$	−1.95665	+	3.38901i	−0.489161	+	0.847252i
$17$	−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	$0.959582\pi$
$18$		−	0.320270i		−	0.0754884i
$19$	1.25046	−	0.721954i	0.286875	−	0.165628i	−0.349657	−	0.936878i	$-0.613702\pi$
$19$	1.25046	−	0.721954i	0.286875	−	0.165628i	0.636532	+	0.771250i	$0.280368\pi$
$20$	−2.90281	+	1.67594i	−0.649088	+	0.374751i
$21$		−	0.582292i		−	0.127067i
$22$	0.0219427	+	0.0380059i	0.00467820	+	0.00810288i
$23$	−2.54161	+	4.40219i	−0.529962	+	0.917920i	0.469428	+	0.882971i	$0.344460\pi$
$23$	−2.54161	+	4.40219i	−0.529962	+	0.917920i	−0.999389	+	0.0349493i	$0.988873\pi$
$24$	0.241901	+	0.139662i	0.0493778	+	0.0285083i
$25$	2.15010			0.430020
$26$	0.000212944	−	0.433964i	4.17617e−5	−	0.0851073i
$27$	3.29632			0.634377
$28$	−1.71951	−	0.992757i	−0.324956	−	0.187613i
$29$	−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	$0.891357\pi$
$30$	0.0591572	+	0.102463i	0.0108006	+	0.0187071i
$31$		−	4.69775i		−	0.843742i	−0.906656	−	0.421871i	$-0.861374\pi$
$31$		−	4.69775i		−	0.843742i	0.906656	−	0.421871i	$-0.138626\pi$
$32$	1.23876	−	0.715198i	0.218984	−	0.126430i
$33$	−0.183870	+	0.106157i	−0.0320076	+	0.0184796i
$34$			0.383412i			0.0657546i
$35$	−0.844083	−	1.46199i	−0.142676	−	0.247122i
$36$	2.64166	−	4.57549i	0.440277	−	0.762582i
$37$	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	$0.492912\pi$
$38$	−0.173789			−0.0281922
$39$	2.09948	+	0.00103020i	0.336186	+	0.000164965i
$40$	0.809806			0.128042
$41$	−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	$0.817041\pi$
$42$	−0.0350423	+	0.0606950i	−0.00540714	+	0.00936545i
$43$	−0.386561	−	0.669543i	−0.0589500	−	0.102104i	0.835044	−	0.550183i	$-0.185442\pi$
$43$	−0.386561	−	0.669543i	−0.0589500	−	0.102104i	−0.893994	+	0.448078i	$0.852109\pi$
$44$			0.723954i			0.109140i
$45$	3.89027	−	2.24605i	0.579928	−	0.334821i
$46$	0.529847	−	0.305907i	0.0781217	−	0.0451036i
$47$		−	12.7905i		−	1.86569i	−0.360275	−	0.932846i	$-0.617317\pi$
$47$		−	12.7905i		−	1.86569i	0.360275	−	0.932846i	$-0.382683\pi$
$48$	1.13934	+	1.97339i	0.164449	+	0.284835i
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	−0.224115	−	0.129393i	−0.0316946	−	0.0182989i
$51$	−1.85492			−0.259741
$52$	3.58248	−	6.19801i	0.496800	−	0.859509i
$53$	1.37110			0.188334			0.0941672	−	0.995556i	$-0.469981\pi$
$53$	1.37110			0.188334			0.0941672	+	0.995556i	$0.469981\pi$
$54$	−0.343591	−	0.198372i	−0.0467568	−	0.0269950i
$55$	−0.307768	+	0.533070i	−0.0414994	+	0.0718791i
$56$	0.239848	+	0.415429i	0.0320510	+	0.0555140i
$57$		−	0.840776i		−	0.111363i
$58$	0.854372	−	0.493272i	0.112185	−	0.0647698i
$59$	−8.10770	+	4.68098i	−1.05553	+	0.609412i	−0.924193	−	0.381925i	$-0.875261\pi$
$59$	−8.10770	+	4.68098i	−1.05553	+	0.609412i	−0.131340	+	0.991337i	$0.541928\pi$
$60$			1.95177i			0.251972i
$61$	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	$0.637262\pi$
$62$	−0.282711	+	0.489669i	−0.0359043	+	0.0621880i
$63$	2.30444	+	1.33047i	0.290332	+	0.167623i
$64$	7.65442			0.956802
$65$	5.27279	−	3.04080i	0.654009	−	0.377164i
$66$	0.0255541			0.00314549
$67$	−11.6705	−	6.73797i	−1.42578	−	0.823174i	−0.428995	−	0.903307i	$-0.641132\pi$
$67$	−11.6705	−	6.73797i	−1.42578	−	0.823174i	−0.996784	+	0.0801330i	$0.974466\pi$
$68$	−3.16247	+	5.47757i	−0.383506	+	0.664252i
$69$	1.47996	+	2.56336i	0.178166	+	0.308592i
$70$			0.203187i			0.0242855i
$71$	−6.13246	+	3.54058i	−0.727789	+	0.420189i	−0.817613	−	0.575769i	$-0.804703\pi$
$71$	−6.13246	+	3.54058i	−0.727789	+	0.420189i	0.0898239	+	0.995958i	$0.471370\pi$
$72$	−1.10543	+	0.638220i	−0.130276	+	0.0752150i
$73$			2.16083i			0.252906i	0.991973	+	0.126453i	$0.0403592\pi$
$73$			2.16083i			0.252906i	−0.991973	+	0.126453i	$0.959641\pi$
$74$	−0.380087	−	0.658329i	−0.0441842	−	0.0765292i
$75$	0.625992	−	1.08425i	0.0722834	−	0.125198i
$76$	−2.48281	−	1.43345i	−0.284797	−	0.164428i
$77$	−0.364618			−0.0415521
$78$	−0.218777	−	0.126454i	−0.0247716	−	0.0143181i
$79$	−6.88781			−0.774940			−0.387470	−	0.921882i	$-0.626651\pi$
$79$	−6.88781			−0.774940			−0.387470	+	0.921882i	$0.626651\pi$
$80$	5.72121	+	3.30314i	0.639651	+	0.369302i
$81$	−3.03169	+	5.25105i	−0.336855	+	0.583450i
$82$	0.350688	+	0.607409i	0.0387270	+	0.0670771i
$83$			0.567380i			0.0622780i	0.999515	+	0.0311390i	$0.00991345\pi$
$83$			0.567380i			0.0622780i	−0.999515	+	0.0311390i	$0.990087\pi$
$84$	−1.00125	+	0.578074i	−0.109246	+	0.0630731i
$85$	−4.65725	+	2.68887i	−0.505150	+	0.291648i
$86$			0.0930528i			0.0100341i
$87$	2.38641	+	4.13339i	0.255850	+	0.443146i
$88$	0.0874529	−	0.151473i	0.00932251	−	0.0161471i
$89$	−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	$0.685893\pi$
$90$	−0.540669			−0.0569915
$91$	3.12161	+	1.80431i	0.327234	+	0.189143i
$92$	10.0928			1.05225
$93$	−2.36898	−	1.36773i	−0.245652	−	0.141827i
$94$	−0.769734	+	1.33322i	−0.0793920	+	0.137511i
$95$	−1.21878	−	2.11098i	−0.125044	−	0.216582i
$96$		−	0.832908i		−	0.0850083i
$97$	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	$0.201483\pi$
$98$	−0.104235	+	0.0601799i	−0.0105293	+	0.00607909i
$99$		−	0.970225i		−	0.0975113i
$100$	−2.13452	−	3.69710i	−0.213452	−	0.369710i
$101$	−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	$0.885189\pi$
$102$	0.193347	+	0.111629i	0.0191442	+	0.0110529i
$103$	−10.2982			−1.01471			−0.507354	−	0.861738i	$-0.669376\pi$
$103$	−10.2982			−1.01471			−0.507354	+	0.861738i	$0.669376\pi$
$104$	−1.49827	+	0.864049i	−0.146918	+	0.0847270i
$105$	−0.983005			−0.0959315
$106$	−0.142916	−	0.0825124i	−0.0138812	−	0.00801432i
$107$	6.56220	−	11.3661i	0.634391	−	1.09880i	−0.352252	−	0.935905i	$-0.614584\pi$
$107$	6.56220	−	11.3661i	0.634391	−	1.09880i	0.986644	−	0.162893i	$-0.0520826\pi$
$108$	−3.27244	−	5.66804i	−0.314891	−	0.545407i
$109$			10.4459i			1.00054i	0.865871	+	0.500268i	$0.166765\pi$
$109$			10.4459i			1.00054i	−0.865871	+	0.500268i	$0.833235\pi$
$110$	0.0641602	−	0.0370429i	0.00611743	−	0.00353190i
$111$	3.18495	−	1.83883i	0.302302	−	0.174534i
$112$			3.91329i			0.369771i
$113$	−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	$0.908172\pi$
$114$	−0.0505978	+	0.0876380i	−0.00473892	+	0.00820805i
$115$	7.43163	+	4.29065i	0.693003	+	0.400105i
$116$	16.2745			1.51105
$117$	−4.80115	+	8.30642i	−0.443866	+	0.767928i
$118$	1.12681			0.103731
$119$	−2.75877	−	1.59277i	−0.252896	−	0.146009i
$120$	0.235772	−	0.408369i	0.0215229	−	0.0372788i
$121$	−5.43353	−	9.41114i	−0.493957	−	0.855559i
$122$		−	1.08623i		−	0.0983425i
$123$	−2.93860	+	1.69660i	−0.264965	+	0.152977i
$124$	−8.07781	+	4.66373i	−0.725409	+	0.418815i
$125$		−	12.0705i		−	1.07962i
$126$	−0.160135	−	0.277362i	−0.0142660	−	0.0247094i
$127$	4.03366	−	6.98650i	0.357929	−	0.619951i	−0.629686	−	0.776850i	$-0.716816\pi$
$127$	4.03366	−	6.98650i	0.357929	−	0.619951i	0.987615	+	0.156899i	$0.0501496\pi$
$128$	−3.27537	−	1.89104i	−0.289505	−	0.167146i
$129$	−0.450183			−0.0396364
$130$	−0.732603		0.000359484i	−0.0642535		3.15288e-5i
$131$	18.9039			1.65164			0.825820	−	0.563934i	$-0.190713\pi$
$131$	18.9039			1.65164			0.825820	+	0.563934i	$0.190713\pi$
$132$	0.365075	+	0.210776i	0.0317757	+	0.0183457i
$133$	0.721954	−	1.25046i	0.0626013	−	0.108429i
$134$	0.810981	+	1.40466i	0.0700581	+	0.121344i
$135$		−	5.56473i		−	0.478936i
$136$	1.32337	−	0.764047i	0.113478	−	0.0655165i
$137$	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	$0.0492867\pi$
$138$		−	0.356255i		−	0.0303264i
$139$	−2.62542	−	4.54737i	−0.222686	−	0.385703i	0.732937	−	0.680297i	$-0.238149\pi$
$139$	−2.62542	−	4.54737i	−0.222686	−	0.385703i	−0.955623	+	0.294594i	$0.904816\pi$
$140$	−1.67594	+	2.90281i	−0.141643	+	0.245332i
$141$	−6.45001	−	3.72392i	−0.543189	−	0.313610i
$142$	0.852287			0.0715223
$143$	0.000645091	−	1.31465i	5.39452e−5	−	0.109936i
$144$	−10.4130			−0.867751
$145$	11.9834	+	6.91862i	0.995167	+	0.574560i
$146$	0.130038	−	0.225233i	0.0107621	−	0.0186404i
$147$	−0.291146	−	0.504280i	−0.0240133	−	0.0415923i
$148$		−	12.5402i		−	1.03080i
$149$	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	$0.209312\pi$
$150$	−0.130500	+	0.0753444i	−0.0106553	+	0.00615184i
$151$			14.0132i			1.14038i	0.821513	+	0.570189i	$0.193130\pi$
$151$			14.0132i			1.14038i	−0.821513	+	0.570189i	$0.806870\pi$
$152$	0.346318	+	0.599841i	0.0280901	+	0.0486535i
$153$	4.23827	−	7.34090i	0.342644	−	0.593476i
$154$	0.0380059	+	0.0219427i	0.00306260	+	0.00176819i
$155$	−7.93059			−0.637000
$156$	−2.08250	−	3.61110i	−0.166734	−	0.289119i
$157$	−17.1825			−1.37131			−0.685656	−	0.727925i	$-0.740485\pi$
$157$	−17.1825			−1.37131			−0.685656	+	0.727925i	$0.740485\pi$
$158$	0.717949	+	0.414508i	0.0571170	+	0.0329765i
$159$	0.399189	−	0.691415i	0.0316577	−	0.0548328i
$160$	−1.20737	−	2.09123i	−0.0954511	−	0.165326i
$161$			5.08321i			0.400613i
$162$	0.632016	−	0.364894i	0.0496558	−	0.0286688i
$163$	10.2128	−	5.89637i	0.799930	−	0.461840i	−0.0435169	−	0.999053i	$-0.513856\pi$
$163$	10.2128	−	5.89637i	0.799930	−	0.461840i	0.843447	+	0.537213i	$0.180523\pi$
$164$			11.5702i			0.903482i
$165$	0.179211	+	0.310402i	0.0139515	+	0.0241648i
$166$	0.0341449	−	0.0591407i	0.00265016	−	0.00459021i
$167$	3.73852	+	2.15843i	0.289295	+	0.167025i	0.637624	−	0.770348i	$-0.279917\pi$
$167$	3.73852	+	2.15843i	0.289295	+	0.167025i	−0.348329	+	0.937372i	$0.613251\pi$
$168$	0.279323			0.0215502
$169$	−6.51105	+	11.2519i	−0.500850	+	0.865534i
$170$	0.647263			0.0496428
$171$	3.32739	+	1.92107i	0.254452	+	0.146908i
$172$	−0.767522	+	1.32939i	−0.0585230	+	0.101365i
$173$	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	$0.675446\pi$
$174$		−	0.574457i		−	0.0435494i
$175$	1.86204	−	1.07505i	0.140757	−	0.0812660i
$176$	1.23569	−	0.713428i	0.0931440	−	0.0537767i
$177$			5.45140i			0.409752i
$178$	0.0685410	+	0.118717i	0.00513737	+	0.00889818i
$179$	−3.29767	+	5.71173i	−0.246479	+	0.426915i	−0.962547	−	0.271117i	$-0.912607\pi$
$179$	−3.29767	+	5.71173i	−0.246479	+	0.426915i	0.716067	+	0.698031i	$0.245940\pi$
$180$	−7.72419	−	4.45956i	−0.575727	−	0.332396i
$181$	−11.0157			−0.818791			−0.409395	−	0.912357i	$-0.634260\pi$
$181$	−11.0157			−0.818791			−0.409395	+	0.912357i	$0.634260\pi$
$182$	−0.216797	−	0.375930i	−0.0160701	−	0.0278658i
$183$	5.25509			0.388468
$184$	−2.11171	−	1.21920i	−0.155678	−	0.0898805i
$185$	5.33109	−	9.23371i	0.391949	−	0.678876i
$186$	0.164620	+	0.285130i	0.0120705	+	0.0209068i
$187$			1.16151i			0.0849379i
$188$	−21.9934	+	12.6979i	−1.60403	+	0.926089i
$189$	2.85470	−	1.64816i	0.207649	−	0.119886i
$190$			0.293384i			0.0212843i
$191$	−2.96606	−	5.13737i	−0.214617	−	0.371727i	0.738537	−	0.674213i	$-0.235517\pi$
$191$	−2.96606	−	5.13737i	−0.214617	−	0.371727i	−0.953154	+	0.302486i	$0.902184\pi$
$192$	2.22855	−	3.85997i	0.160832	−	0.278569i
$193$	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	$0.618412\pi$
$194$	−0.954196			−0.0685073
$195$	0.00173916	−	3.54428i	0.000124544	−	0.253811i
$196$	−1.98551			−0.141822
$197$	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	$0.600596\pi$
$198$	−0.0583881	+	0.101131i	−0.00414946	+	0.00718708i
$199$	5.97988	+	10.3575i	0.423903	+	0.734221i	0.996317	−	0.0857435i	$-0.0273266\pi$
$199$	5.97988	+	10.3575i	0.423903	+	0.734221i	−0.572415	+	0.819964i	$0.693993\pi$
$200$			1.03139i			0.0729305i
$201$	−6.79564	+	3.92347i	−0.479328	+	0.276740i
$202$	1.62048	−	0.935584i	0.114017	−	0.0658275i
$203$			8.19662i			0.575290i
$204$	1.84148	+	3.18954i	0.128930	+	0.223313i
$205$	−4.91874	+	8.51951i	−0.343540	+	0.595028i
$206$	1.07343	+	0.619743i	0.0747891	+	0.0431795i
$207$	−13.5261			−0.940129
$208$	−14.1096	−	0.00692349i	−0.978323	−	0.000480057i
$209$	−0.526475			−0.0364170
$210$	0.102463	+	0.0591572i	0.00707064	+	0.00408223i
$211$	4.11795	−	7.13251i	0.283492	−	0.491022i	−0.688751	−	0.724998i	$-0.741840\pi$
$211$	4.11795	−	7.13251i	0.283492	−	0.491022i	0.972242	+	0.233976i	$0.0751738\pi$
$212$	−1.36116	−	2.35761i	−0.0934851	−	0.161921i
$213$			4.12330i			0.282524i
$214$	−1.36802	+	0.789825i	−0.0935157	+	0.0539913i
$215$	−1.13030	+	0.652579i	−0.0770858	+	0.0445055i
$216$			1.58123i			0.107589i
$217$	−2.34888	−	4.06838i	−0.159452	−	0.276179i
$218$	0.628633	−	1.08882i	0.0425764	−	0.0737445i
$219$	1.08966	+	0.629116i	0.0736325	+	0.0425117i
$220$	1.22215			0.0823976
$221$	5.74771	−	9.94405i	0.386633	−	0.668909i
$222$	−0.442643			−0.0297082
$223$	13.2515	+	7.65073i	0.887383	+	0.512331i	0.873086	−	0.487567i	$-0.162115\pi$
$223$	13.2515	+	7.65073i	0.887383	+	0.512331i	0.0142977	+	0.999898i	$0.495449\pi$
$224$	0.715198	−	1.23876i	0.0477861	−	0.0827680i
$225$	2.86064	+	4.95477i	0.190709	+	0.330318i
$226$			0.596097i			0.0396518i
$227$	−6.02292	+	3.47733i	−0.399755	+	0.230799i	−0.686378	−	0.727245i	$-0.740801\pi$
$227$	−6.02292	+	3.47733i	−0.399755	+	0.230799i	0.286623	+	0.958043i	$0.407467\pi$
$228$	−1.44572	+	0.834686i	−0.0957450	+	0.0552784i
$229$		−	27.4219i		−	1.81209i	−0.423180	−	0.906045i	$-0.639086\pi$
$229$		−	27.4219i		−	1.81209i	0.423180	−	0.906045i	$-0.360914\pi$
$230$	−0.516422	−	0.894470i	−0.0340519	−	0.0589796i
$231$	−0.106157	+	0.183870i	−0.00698463	+	0.0120977i
$232$	−3.40511	−	1.96594i	−0.223556	−	0.129070i
$233$	6.85333			0.448976			0.224488	−	0.974477i	$-0.427929\pi$
$233$	6.85333			0.448976			0.224488	+	0.974477i	$0.427929\pi$
$234$	1.00033	−	0.576884i	0.0653933	−	0.0377121i
$235$	−21.5926			−1.40854
$236$	16.0980	+	9.29416i	1.04789	+	0.604998i
$237$	−2.00536	+	3.47338i	−0.130262	+	0.225621i
$238$	0.191706	+	0.332045i	0.0124265	+	0.0215233i
$239$			22.0754i			1.42794i	0.700177	+	0.713970i	$0.253105\pi$
$239$			22.0754i			1.42794i	−0.700177	+	0.713970i	$0.746895\pi$
$240$	3.33141	−	1.92339i	0.215042	−	0.124154i
$241$	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	$0.163426\pi$
$242$			1.30796i			0.0840787i
$243$	6.70981	+	11.6217i	0.430434	+	0.745534i
$244$	8.95947	−	15.5183i	0.573571	−	0.993455i
$245$	−1.46199	−	0.844083i	−0.0934034	−	0.0539265i
$246$	0.408405			0.0260390
$247$	4.50732	+	2.60525i	0.286794	+	0.165768i
$248$	2.25349			0.143097
$249$	0.286118	+	0.165190i	0.0181320	+	0.0104685i
$250$	−0.726405	+	1.25817i	−0.0459419	+	0.0795737i
$251$	11.2783	+	19.5346i	0.711882	+	1.23302i	0.964150	+	0.265359i	$0.0854903\pi$
$251$	11.2783	+	19.5346i	0.711882	+	1.23302i	−0.252268	+	0.967658i	$0.581176\pi$
$252$		−	5.28332i		−	0.332818i
$253$	1.60512	−	0.926716i	0.100913	−	0.0582621i
$254$	−0.840894	+	0.485490i	−0.0527624	+	0.0304624i
$255$			3.13141i			0.196097i
$256$	−7.42681	−	12.8636i	−0.464176	−	0.803976i
$257$	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	$-0.0530179\pi$
$258$	0.0469247	+	0.0270920i	0.00292140	+	0.00168667i
$259$	6.31584			0.392447
$260$	−10.4633	−	6.04781i	−0.648904	−	0.375069i
$261$	−21.8107			−1.35005
$262$	−1.97044	−	1.13763i	−0.121734	−	0.0702833i
$263$	14.7701	−	25.5826i	0.910764	−	1.57749i	0.0977768	−	0.995208i	$-0.468827\pi$
$263$	14.7701	−	25.5826i	0.910764	−	1.57749i	0.812987	−	0.582281i	$-0.197840\pi$
$264$	−0.0509231	−	0.0882015i	−0.00313410	−	0.00542842i
$265$		−	2.31464i		−	0.142187i
$266$	−0.150505	+	0.0868943i	−0.00922807	+	0.00532783i
$267$	−0.574342	+	0.331596i	−0.0351491	+	0.0202934i
$268$			26.7567i			1.63442i
$269$	−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	$-0.490696\pi$
$270$	−0.334885	+	0.580038i	−0.0203805	+	0.0353000i
$271$	−25.5036	−	14.7245i	−1.54924	−	0.894451i	−0.998200	−	0.0599690i	$-0.980900\pi$
$271$	−25.5036	−	14.7245i	−1.54924	−	0.894451i	−0.551035	−	0.834482i	$-0.685767\pi$
$272$	12.4660			0.755861
$273$	1.81872	−	1.04885i	0.110074	−	0.0634793i
$274$	−2.19362			−0.132521
$275$	−0.678933	−	0.391982i	−0.0409412	−	0.0236374i
$276$	2.93847	−	5.08959i	0.176875	−	0.306357i
$277$	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	$0.767274\pi$
$278$			0.631992i			0.0379043i
$279$	10.8257	−	6.25021i	0.648117	−	0.374190i
$280$	0.701313	−	0.404903i	0.0419114	−	0.0241976i
$281$		−	29.0940i		−	1.73561i	−0.496909	−	0.867803i	$-0.665532\pi$
$281$		−	29.0940i		−	1.73561i	0.496909	−	0.867803i	$-0.334468\pi$
$282$	0.448210	+	0.776323i	0.0266905	+	0.0462293i
$283$	5.80511	−	10.0547i	0.345078	−	0.597692i	−0.640290	−	0.768133i	$-0.721186\pi$
$283$	5.80511	−	10.0547i	0.345078	−	0.597692i	0.985368	+	0.170441i	$0.0545192\pi$
$284$	12.1761	+	7.02986i	0.722517	+	0.417146i
$285$	−1.41937			−0.0840761
$286$	−0.0791828	+	0.136993i	−0.00468217	+	0.00810058i
$287$	−5.82732			−0.343976
$288$	3.29626	+	1.90310i	0.194234	+	0.112141i
$289$	3.42614	−	5.93425i	0.201538	−	0.349074i
$290$	−0.832724	−	1.44232i	−0.0488993	−	0.0846960i
$291$		−	4.61633i		−	0.270614i
$292$	3.71555	−	2.14517i	0.217436	−	0.125537i
$293$	−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	$0.507256\pi$
$294$			0.0700846i			0.00408742i
$295$	7.90228	+	13.6871i	0.460088	+	0.796896i
$296$	−1.51484	+	2.62378i	−0.0880483	+	0.152504i
$297$	−1.04087	−	0.600949i	−0.0603976	−	0.0348706i
$298$	−1.11611			−0.0646544
$299$	−18.3278	−	0.00899334i	−1.05992	−	0.000520098i
$300$	−2.48583			−0.143520
$301$	−0.669543	−	0.386561i	−0.0385918	−	0.0222810i
$302$	0.843314	−	1.46066i	0.0485273	−	0.0840517i
$303$	4.52629	+	7.83976i	0.260028	+	0.450382i
$304$			5.65043i			0.324074i
$305$	13.1943	−	7.61771i	0.755501	−	0.436189i
$306$	−0.883550	+	0.510118i	−0.0505092	+	0.0291615i
$307$			9.07966i			0.518204i	0.965850	+	0.259102i	$0.0834265\pi$
$307$			9.07966i			0.518204i	−0.965850	+	0.259102i	$0.916573\pi$
$308$	0.361977	+	0.626963i	0.0206256	+	0.0357245i
$309$	−2.99827	+	5.19315i	−0.170566	+	0.295428i
$310$	0.826643	+	0.477262i	0.0469501	+	0.0271067i
$311$	−1.57073			−0.0890677			−0.0445338	−	0.999008i	$-0.514180\pi$
$311$	−1.57073			−0.0890677			−0.0445338	+	0.999008i	$0.514180\pi$
$312$	−0.000494185		1.00711i	−2.79777e−5		0.0570166i
$313$	20.6232			1.16569			0.582846	−	0.812582i	$-0.301939\pi$
$313$	20.6232			1.16569			0.582846	+	0.812582i	$0.301939\pi$
$314$	1.79101	+	1.03404i	0.101073	+	0.0583544i
$315$	2.24605	−	3.89027i	0.126551	−	0.219192i
$316$	6.83792	+	11.8436i	0.384663	+	0.666256i
$317$			30.5435i			1.71549i	0.514072	+	0.857747i	$0.328137\pi$
$317$			30.5435i			1.71549i	−0.514072	+	0.857747i	$0.671863\pi$
$318$	−0.0832187	+	0.0480463i	−0.00466667	+	0.00269430i
$319$	2.58823	−	1.49432i	0.144913	−	0.0836657i
$320$		−	12.9219i		−	0.722358i
$321$	−3.82111	−	6.61836i	−0.213274	−	0.369401i
$322$	0.305907	−	0.529847i	0.0170476	−	0.0295272i
$323$	−3.98340	−	2.29982i	−0.221642	−	0.127965i
$324$	12.0389			0.668830
$325$	3.87285	+	6.71558i	0.214827	+	0.372513i
$326$	−1.41937			−0.0786118
$327$	5.26765	+	3.04128i	0.291302	+	0.168183i
$328$	1.39767	−	2.42084i	0.0771735	−	0.133668i
$329$	−6.39527	−	11.0769i	−0.352583	−	0.610691i
$330$		−	0.0431396i		−	0.00237476i
$331$	−22.3894	+	12.9265i	−1.23063	+	0.710507i	−0.967162	−	0.254161i	$-0.918201\pi$
$331$	−22.3894	+	12.9265i	−1.23063	+	0.710507i	−0.263472	+	0.964667i	$0.584868\pi$
$332$	0.975612	−	0.563270i	0.0535437	−	0.0309135i
$333$			16.8060i			0.920965i
$334$	−0.259789	−	0.449967i	−0.0142150	−	0.0246211i
$335$	−11.3748	+	19.7017i	−0.621472	+	1.07642i
$336$	1.97339	+	1.13934i	0.107657	+	0.0621560i
$337$	−21.3954			−1.16548			−0.582742	−	0.812657i	$-0.698020\pi$
$337$	−21.3954			−1.16548			−0.582742	+	0.812657i	$0.698020\pi$
$338$	1.35582	−	0.781009i	0.0737468	−	0.0424813i
$339$	−2.88387			−0.156630
$340$	9.24704	+	5.33878i	0.501491	+	0.289536i
$341$	−0.856443	+	1.48340i	−0.0463790	+	0.0803308i
$342$	−0.231220	−	0.400485i	−0.0125029	−	0.0216557i
$343$		−	1.00000i		−	0.0539949i
$344$	0.321177	−	0.185432i	0.0173167	−	0.00999781i
$345$	4.32738	−	2.49841i	0.232978	−	0.134510i
$346$		−	1.50687i		−	0.0810098i
$347$	−1.10442	−	1.91291i	−0.0592882	−	0.102690i	0.834858	−	0.550466i	$-0.185550\pi$
$347$	−1.10442	−	1.91291i	−0.0592882	−	0.102690i	−0.894146	+	0.447775i	$0.852216\pi$
$348$	4.73825	−	8.20689i	0.253997	−	0.439936i
$349$	−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	$0.764388\pi$
$350$	−0.258786			−0.0138327
$351$	5.93747	+	10.2957i	0.316919	+	0.549542i
$352$	−0.521548			−0.0277986
$353$	−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	$-0.730784\pi$
$354$	0.328065	−	0.568225i	0.0174365	−	0.0302008i
$355$	5.97708	+	10.3526i	0.317230	+	0.549459i
$356$			2.26137i			0.119852i
$357$	−1.60641	+	0.927459i	−0.0850201	+	0.0490864i
$358$	0.687464	−	0.396907i	0.0363336	−	0.0209772i
$359$			19.3218i			1.01976i	0.860244	+	0.509882i	$0.170311\pi$
$359$			19.3218i			1.01976i	−0.860244	+	0.509882i	$0.829689\pi$
$360$	1.07742	+	1.86615i	0.0567851	+	0.0983546i
$361$	−8.45757	+	14.6489i	−0.445135	+	0.770997i
$362$	1.14822	+	0.662924i	0.0603490	+	0.0348425i
$363$	−6.32780			−0.332123
$364$	0.00351282	−	7.15887i	0.000184122	−	0.375227i
$365$	3.64783			0.190936
$366$	−0.547763	−	0.316251i	−0.0286320	−	0.0165307i
$367$	1.86032	−	3.22218i	0.0971082	−	0.168196i	−0.813378	−	0.581735i	$-0.802374\pi$
$367$	1.86032	−	3.22218i	0.0971082	−	0.168196i	0.910487	+	0.413539i	$0.135707\pi$
$368$	−9.94604	−	17.2271i	−0.518473	−	0.898022i
$369$		−	15.5061i		−	0.807217i
$370$	−1.11137	+	0.641649i	−0.0577773	+	0.0333578i
$371$	1.18740	−	0.685548i	0.0616469	−	0.0355919i
$372$			5.43130i			0.281600i
$373$	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	$0.804346\pi$
$374$	0.0698995	−	0.121070i	0.00361442	−	0.00626035i
$375$	−6.08693	−	3.51429i	−0.314328	−	0.181477i
$376$	6.13557			0.316418
$377$	−29.5533	−	0.0145016i	−1.52207	−	0.000746873i
$378$	−0.396744			−0.0204063
$379$	21.6647	+	12.5081i	1.11284	+	0.642500i	0.939564	−	0.342373i	$-0.111230\pi$
$379$	21.6647	+	12.5081i	1.11284	+	0.642500i	0.173279	+	0.984873i	$0.444564\pi$
$380$	−2.41990	+	4.19139i	−0.124138	+	0.215014i
$381$	−2.34877	−	4.06818i	−0.120331	−	0.208419i
$382$			0.713990i			0.0365309i
$383$	−19.4556	+	11.2327i	−0.994134	+	0.573964i	−0.906507	−	0.422190i	$-0.861262\pi$
$383$	−19.4556	+	11.2327i	−0.994134	+	0.573964i	−0.0876266	+	0.996153i	$0.527928\pi$
$384$	−1.90722	+	1.10114i	−0.0973276	+	0.0561921i
$385$			0.615536i			0.0313706i
$386$	−0.252512	−	0.437364i	−0.0128525	−	0.0222612i
$387$	1.02861	−	1.78161i	0.0522874	−	0.0905644i
$388$	−13.6320	−	7.87043i	−0.692059	−	0.399561i
$389$	13.3364			0.676184			0.338092	−	0.941113i	$-0.390219\pi$
$389$	13.3364			0.676184			0.338092	+	0.941113i	$0.390219\pi$
$390$	−0.213476	+	0.369332i	−0.0108098	+	0.0187018i
$391$	16.1928			0.818906
$392$	0.415429	+	0.239848i	0.0209823	+	0.0121142i
$393$	5.50379	−	9.53284i	0.277629	−	0.480868i
$394$	−0.348137	−	0.602991i	−0.0175389	−	0.0303783i
$395$			11.6278i			0.585057i
$396$	−1.66831	+	0.963198i	−0.0838356	+	0.0484025i
$397$	−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	$0.557840\pi$
$398$		−	1.43948i		−	0.0721544i
$399$	−0.420388	−	0.728133i	−0.0210457	−	0.0364522i
$400$	−4.20698	+	7.28670i	−0.210349	+	0.364335i
$401$	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	$0.522189\pi$
$402$	0.944456			0.0471052
$403$	14.6729	−	8.46180i	0.730909	−	0.421512i
$404$	30.8677			1.53572
$405$	8.86464	+	5.11800i	0.440487	+	0.254316i
$406$	0.493272	−	0.854372i	0.0244807	−	0.0424018i
$407$	−1.15143	−	1.99434i	−0.0570745	−	0.0988559i
$408$		−	0.889797i		−	0.0440515i
$409$	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	$0.216388\pi$
$410$	1.02541	−	0.592019i	0.0506412	−	0.0292377i
$411$		−	10.6126i		−	0.523479i
$412$	10.2236	+	17.7077i	0.503679	+	0.872398i
$413$	−4.68098	+	8.10770i	−0.230336	+	0.398954i
$414$	1.40989	+	0.814000i	0.0692923	+	0.0400059i
$415$	0.957831			0.0470181
$416$	4.46514	+	2.58087i	0.218922	+	0.126538i
$417$	−3.05753			−0.149728
$418$	0.0548769	+	0.0316832i	0.00268412	+	0.00154968i
$419$	2.30096	−	3.98538i	0.112409	−	0.194699i	−0.804332	−	0.594180i	$-0.797477\pi$
$419$	2.30096	−	3.98538i	0.112409	−	0.194699i	0.916741	+	0.399482i	$0.130810\pi$
$420$	0.975885	+	1.69028i	0.0476183	+	0.0824773i
$421$		−	19.2645i		−	0.938895i	−0.882960	−	0.469447i	$-0.844453\pi$
$421$		−	19.2645i		−	0.938895i	0.882960	−	0.469447i	$-0.155547\pi$
$422$	−0.858468	+	0.495637i	−0.0417896	+	0.0241272i
$423$	29.4750	−	17.0174i	1.43312	−	0.827415i
$424$			0.657709i			0.0319412i
$425$	−3.42462	−	5.93161i	−0.166118	−	0.287726i
$426$	0.248140	−	0.429791i	0.0120224	−	0.0208234i
$427$	7.81574	+	4.51242i	0.378230	+	0.218371i
$428$	−26.0587			−1.25959
$429$	−0.662763	−	0.383080i	−0.0319985	−	0.0184953i
$430$	0.157089			0.00757548
$431$	−24.5649	−	14.1825i	−1.18325	−	0.683149i	−0.226485	−	0.974015i	$-0.572723\pi$
$431$	−24.5649	−	14.1825i	−1.18325	−	0.683149i	−0.956764	+	0.290865i	$0.906057\pi$
$432$	−6.44973	+	11.1713i	−0.310313	+	0.537477i
$433$	−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	$0.930601\pi$
$434$			0.565421i			0.0271411i
$435$	6.97784	−	4.02866i	0.334562	−	0.193159i
$436$	17.9618	−	10.3702i	0.860213	−	0.496644i
$437$			7.33969i			0.351105i
$438$	−0.0757203	−	0.131151i	−0.00361806	−	0.00626666i
$439$	15.8637	−	27.4767i	0.757132	−	1.31139i	−0.187176	−	0.982326i	$-0.559933\pi$
$439$	15.8637	−	27.4767i	0.757132	−	1.31139i	0.944307	−	0.329064i	$-0.106733\pi$
$440$	−0.255711	−	0.147635i	−0.0121906	−	0.00703822i
$441$	2.66094			0.126711
$442$	−1.19754	+	0.690619i	−0.0569613	+	0.0328494i
$443$	1.73048			0.0822177			0.0411088	−	0.999155i	$-0.486911\pi$
$443$	1.73048			0.0822177			0.0411088	+	0.999155i	$0.486911\pi$
$444$	−6.32376	−	3.65102i	−0.300112	−	0.173270i
$445$	−0.961355	+	1.66512i	−0.0455726	+	0.0789341i
$446$	−0.920842	−	1.59494i	−0.0436031	−	0.0755228i
$447$		−	5.39965i		−	0.255394i
$448$	6.62892	−	3.82721i	0.313187	−	0.180819i
$449$	−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	$0.413466\pi$
$450$		−	0.688612i		−	0.0324615i
$451$	1.06237	+	1.84008i	0.0500252	+	0.0866462i
$452$	−4.91675	+	8.51605i	−0.231264	+	0.400561i
$453$	7.06658	+	4.07989i	0.332017	+	0.191690i
$454$	0.837063			0.0392853
$455$	3.04597	−	5.26980i	0.142797	−	0.247052i
$456$	0.403317			0.0188870
$457$	−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	$0.726193\pi$
$458$	−1.65025	+	2.85832i	−0.0771111	+	0.133560i
$459$	−5.25029	−	9.09377i	−0.245062	−	0.424461i
$460$		−	17.0383i		−	0.794415i
$461$	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	$0.251705\pi$
$462$	0.0221305	−	0.0127771i	0.00102960	−	0.000594443i
$463$		−	35.8227i		−	1.66482i	−0.554158	−	0.832411i	$-0.686960\pi$
$463$		−	35.8227i		−	1.66482i	0.554158	−	0.832411i	$-0.313040\pi$
$464$	−16.0379	−	27.7784i	−0.744539	−	1.28958i
$465$	−2.30896	+	3.99923i	−0.107075	+	0.185460i
$466$	−0.714355	−	0.412433i	−0.0330918	−	0.0191056i
$467$	−19.8983			−0.920785			−0.460393	−	0.887715i	$-0.652291\pi$
$467$	−19.8983			−0.920785			−0.460393	+	0.887715i	$0.652291\pi$
$468$	19.0493	+	0.00934738i	0.880554	+	0.000432083i
$469$	−13.4759			−0.622261
$470$	2.25069	+	1.29944i	0.103817	+	0.0599386i
$471$	−5.00262	+	8.66479i	−0.230508	+	0.399252i
$472$	−2.24545	−	3.88923i	−0.103355	−	0.179016i
$473$			0.281894i			0.0129615i
$474$	0.418056	−	0.241365i	0.0192020	−	0.0110863i
$475$	2.68861	−	1.55227i	0.123362	−	0.0712231i
$476$			6.32495i			0.289904i
$477$	1.82420	+	3.15960i	0.0835243	+	0.144668i
$478$	1.32850	−	2.30102i	0.0607640	−	0.105246i
$479$	22.7680	+	13.1451i	1.04030	+	0.600615i	0.919917	−	0.392113i	$-0.128256\pi$
$479$	22.7680	+	13.1451i	1.04030	+	0.600615i	0.120379	+	0.992728i	$0.461589\pi$
$480$	−1.40609			−0.0641788
$481$	−0.0111741	+	22.7721i	−0.000509496	+	1.03832i
$482$	−1.90134			−0.0866035
$483$	2.56336	+	1.47996i	0.116637	+	0.0673404i
$484$	−10.7883	+	18.6860i	−0.490379	+	0.849362i
$485$	−6.69177	−	11.5905i	−0.303857	−	0.526296i
$486$		−	1.61518i		−	0.0732662i
$487$	5.52491	−	3.18981i	0.250358	−	0.144544i	−0.369570	−	0.929203i	$-0.620495\pi$
$487$	5.52491	−	3.18981i	0.250358	−	0.144544i	0.619928	+	0.784659i	$0.287162\pi$
$488$	−3.74918	+	2.16459i	−0.169717	+	0.0979864i
$489$		−	6.86682i		−	0.310528i
$490$	0.101594	+	0.175965i	0.00458954	+	0.00794931i
$491$	−1.48384	+	2.57008i	−0.0669647	+	0.115986i	−0.897564	−	0.440885i	$-0.854665\pi$
$491$	−1.48384	+	2.57008i	−0.0669647	+	0.115986i	0.830599	+	0.556871i	$0.187998\pi$
$492$	5.83463	+	3.36862i	0.263045	+	0.151869i
$493$	26.1107			1.17597
$494$	−0.313035	−	0.542808i	−0.0140841	−	0.0244221i
$495$	−1.63790			−0.0736182
$496$	15.9207	+	9.19184i	0.714862	+	0.412726i
$497$	−3.54058	+	6.13246i	−0.158817	+	0.275078i
$498$	−0.0198823	−	0.0344371i	−0.000890947	−	0.00154316i
$499$		−	28.1331i		−	1.25941i	−0.776835	−	0.629704i	$-0.783176\pi$
$499$		−	28.1331i		−	1.25941i	0.776835	−	0.629704i	$-0.216824\pi$
$500$	−20.7554	+	11.9831i	−0.928208	+	0.535901i
$501$	2.17691	−	1.25684i	0.0972571	−	0.0561514i
$502$		−	2.71492i		−	0.121173i
$503$	15.7688	+	27.3124i	0.703097	+	1.21780i	0.967374	+	0.253353i	$0.0815334\pi$
$503$	15.7688	+	27.3124i	0.703097	+	1.21780i	−0.264277	+	0.964447i	$0.585133\pi$
$504$	−0.638220	+	1.10543i	−0.0284286	+	0.0492398i
$505$	22.7288	+	13.1225i	1.01142	+	0.583943i
$506$	−0.223079			−0.00991706
$507$	3.77846	+	6.55935i	0.167807	+	0.291311i
$508$	−16.0178			−0.710673
$509$	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	$0.569253\pi$
$510$	0.188448	−	0.326402i	0.00834462	−	0.0144533i
$511$	1.08041	+	1.87133i	0.0477947	+	0.0827828i
$512$			9.35193i			0.413301i
$513$	4.12191	−	2.37979i	0.181987	−	0.105070i
$514$	−2.12773	+	1.22845i	−0.0938502	+	0.0541844i
$515$			17.3850i			0.766074i
$516$	0.446922	+	0.774091i	0.0196746	+	0.0340775i
$517$	−2.33183	+	4.03885i	−0.102554	+	0.177628i
$518$	−0.658329	−	0.380087i	−0.0289253	−	0.0167000i
$519$	7.29012			0.320001
$520$	1.45866	+	2.52933i	0.0639664	+	0.110919i
$521$	8.78344			0.384810			0.192405	−	0.981316i	$-0.438371\pi$
$521$	8.78344			0.384810			0.192405	+	0.981316i	$0.438371\pi$
$522$	2.27343	+	1.31256i	0.0995053	+	0.0574494i
$523$	−16.2849	+	28.2063i	−0.712088	+	1.23337i	0.251983	+	0.967732i	$0.418917\pi$
$523$	−16.2849	+	28.2063i	−0.712088	+	1.23337i	−0.964072	+	0.265642i	$0.914416\pi$
$524$	−18.7670	−	32.5053i	−0.819838	−	1.42000i
$525$		−	1.25198i		−	0.0546411i
$526$	−3.07912	+	1.77773i	−0.134256	+	0.0775127i
$527$	−12.9600	+	7.48246i	−0.564547	+	0.325941i
$528$		−	0.830847i		−	0.0361580i
$529$	−1.41953	−	2.45869i	−0.0617185	−	0.106900i
$530$	−0.139295	+	0.241265i	−0.00605057	+	0.0104799i
$531$	−21.5741	−	12.4558i	−0.936235	−	0.540536i
$532$	−2.86690			−0.124296
$533$	0.0103098	−	21.0107i	0.000446568	−	0.910074i
$534$	0.0798218			0.00345423
$535$	−19.1878	−	11.0781i	−0.829560	−	0.478947i
$536$	3.23218	−	5.59829i	0.139609	−	0.241809i
$537$	1.92021	+	3.32590i	0.0828631	+	0.143523i
$538$			3.36000i			0.144860i
$539$	−0.315769	+	0.182309i	−0.0136011	+	0.00785261i
$540$	−9.56858	+	5.52442i	−0.411766	+	0.237733i
$541$		−	6.94870i		−	0.298748i	−0.988781	−	0.149374i	$-0.952274\pi$
$541$		−	6.94870i		−	0.298748i	0.988781	−	0.149374i	$-0.0477258\pi$
$542$	1.77224	+	3.06961i	0.0761243	+	0.131851i
$543$	−3.20718	+	5.55500i	−0.137633	+	0.238388i
$544$	−3.94612	−	2.27830i	−0.169189	−	0.0976811i
$545$	17.6344			0.755375
$546$	−0.252694		0.000123995i	−0.0108143		5.30651e-6i
$547$	10.9095			0.466457			0.233229	−	0.972422i	$-0.425071\pi$
$547$	10.9095			0.466457			0.233229	+	0.972422i	$0.425071\pi$
$548$	−31.3388	−	18.0935i	−1.33873	−	0.772915i
$549$	−12.0073	+	20.7972i	−0.512457	+	0.887602i
$550$	0.0471789	+	0.0817163i	0.00201172	+	0.00348440i
$551$			11.8352i			0.504194i
$552$	−1.22963	+	0.709929i	−0.0523367	+	0.0302166i
$553$	−5.96502	+	3.44391i	−0.253659	+	0.146450i
$554$		−	0.825493i		−	0.0350718i
$555$	−3.10425	−	5.37672i	−0.131768	−	0.228229i
$556$	−5.21282	+	9.02886i	−0.221073	+	0.382909i
$557$	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	$0.404482\pi$
$558$	−1.50455			−0.0636927
$559$	1.39495	−	2.41339i	0.0590001	−	0.102075i
$560$	6.60628			0.279166
$561$	0.585725	+	0.338169i	0.0247293	+	0.0142775i
$562$	−1.75088	+	3.03261i	−0.0738563	+	0.127923i
$563$	4.56839	+	7.91269i	0.192535	+	0.333480i	0.946090	−	0.323905i	$-0.104996\pi$
$563$	4.56839	+	7.91269i	0.192535	+	0.333480i	−0.753555	+	0.657385i	$0.771662\pi$
$564$			14.7878i			0.622677i
$565$	−7.24070	+	4.18042i	−0.304618	+	0.175872i
$566$	−1.21019	+	0.698702i	−0.0508680	+	0.0293686i
$567$			6.06339i			0.254638i
$568$	−1.69840	−	2.94172i	−0.0712633	−	0.123432i
$569$	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	$0.0413549\pi$
$570$	0.147947	+	0.0854175i	0.00619684	+	0.00357775i
$571$	−10.1791			−0.425981			−0.212990	−	0.977054i	$-0.568320\pi$
$571$	−10.1791			−0.425981			−0.212990	+	0.977054i	$0.568320\pi$
$572$	−2.26119	+	1.30402i	−0.0945450	+	0.0545237i
$573$	−3.45423			−0.144303
$574$	0.607409	+	0.350688i	0.0253528	+	0.0146374i
$575$	−5.46470	+	9.46514i	−0.227894	+	0.394724i
$576$	10.1840	+	17.6391i	0.424332	+	0.734964i
$577$			19.5165i			0.812482i	0.913766	+	0.406241i	$0.133161\pi$
$577$			19.5165i			0.812482i	−0.913766	+	0.406241i	$0.866839\pi$
$578$	−0.714246	+	0.412370i	−0.0297087	+	0.0171523i
$579$	2.11593	−	1.22163i	0.0879352	−	0.0507694i
$580$		−	27.4740i		−	1.14080i
$581$	0.283690	+	0.491365i	0.0117694	+	0.0203853i
$582$	−0.277810	+	0.481182i	−0.0115156	+	0.0199456i
$583$	−0.432949	−	0.249963i	−0.0179309	−	0.0103524i
$584$	−1.03654			−0.0428923
$585$	14.0226	+	8.10513i	0.579763	+	0.335106i
$586$	2.14103			0.0884453
$587$	−30.6486	−	17.6950i	−1.26501	−	0.730351i	−0.290967	−	0.956733i	$-0.593977\pi$
$587$	−30.6486	−	17.6950i	−1.26501	−	0.730351i	−0.974039	+	0.226382i	$0.927310\pi$
$588$	−0.578074	+	1.00125i	−0.0238394	+	0.0412910i
$589$	−3.39156	−	5.87436i	−0.139747	−	0.242049i
$590$		−	1.90223i		−	0.0783137i
$591$	2.91723	−	1.68426i	0.119999	−	0.0692812i
$592$	−21.4044	+	12.3579i	−0.879716	+	0.507905i
$593$		−	18.0881i		−	0.742790i	−0.928475	−	0.371395i	$-0.878880\pi$
$593$		−	18.0881i		−	0.742790i	0.928475	−	0.371395i	$-0.121120\pi$
$594$	0.0723301	+	0.125279i	0.00296774	+	0.00514028i
$595$	−2.68887	+	4.65725i	−0.110233	+	0.190929i
$596$	−15.9451	−	9.20592i	−0.653138	−	0.377089i
$597$	6.96407			0.285021
$598$	1.90985	+	1.10390i	0.0780996	+	0.0451419i
$599$	9.05992			0.370178			0.185089	−	0.982722i	$-0.440743\pi$
$599$	9.05992			0.370178			0.185089	+	0.982722i	$0.440743\pi$
$600$	0.520111	+	0.300286i	0.0212334	+	0.0122591i
$601$	−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	$0.962890\pi$
$602$	0.0465264	+	0.0805861i	0.00189628	+	0.00328444i
$603$		−	35.8586i		−	1.46028i
$604$	24.0958	−	13.9117i	0.980444	−	0.566059i
$605$	−15.8876	+	9.17269i	−0.645922	+	0.372923i
$606$		−	1.08957i		−	0.0442606i
$607$	19.6825	+	34.0911i	0.798887	+	1.38371i	0.920341	+	0.391116i	$0.127911\pi$
$607$	19.6825	+	34.0911i	0.798887	+	1.38371i	−0.121454	+	0.992597i	$0.538756\pi$
$608$	1.03268	−	1.78865i	0.0418807	−	0.0725394i
$609$	4.13339	+	2.38641i	0.167493	+	0.0967023i
$610$	−1.83373			−0.0742457
$611$	39.9498	−	23.0389i	1.61619	−	0.932053i
$612$	−16.8303			−0.680324
$613$	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	$0.631024\pi$
$614$	0.546413	−	0.946416i	0.0220514	−	0.0381942i
$615$	2.86414	+	4.96084i	0.115493	+	0.200040i
$616$		−	0.174906i		−	0.00704716i
$617$	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	$0.251832\pi$
$618$	0.625047	−	0.360871i	0.0251431	−	0.0145164i
$619$			22.3955i			0.900149i	0.892991	+	0.450075i	$0.148603\pi$
$619$			22.3955i			0.900149i	−0.892991	+	0.450075i	$0.851397\pi$
$620$	7.87314	+	13.6367i	0.316193	+	0.547662i
$621$	−8.37794	+	14.5110i	−0.336195	+	0.582307i
$622$	0.163724	+	0.0945262i	0.00656474	+	0.00379015i
$623$	−1.13893			−0.0456305
$624$	−4.11144	+	7.11315i	−0.164589	+	0.284754i
$625$	−9.62659			−0.385064
$626$	−2.14965	−	1.24110i	−0.0859175	−	0.0496045i
$627$	−0.153281	+	0.265491i	−0.00612145	+	0.0106027i
$628$	17.0580	+	29.5454i	0.680690	+	1.17899i
$629$		−	20.1194i		−	0.802213i
$630$	−0.468233	+	0.270334i	−0.0186548	+	0.0107704i
$631$	1.68778	−	0.974439i	0.0671894	−	0.0387918i	−0.466029	−	0.884769i	$-0.654316\pi$
$631$	1.68778	−	0.974439i	0.0671894	−	0.0387918i	0.533218	+	0.845978i	$0.320982\pi$
$632$		−	3.30406i		−	0.131428i
$633$	−2.39785	−	4.15320i	−0.0953061	−	0.165075i
$634$	1.83811	−	3.18369i	0.0730005	−	0.126441i
$635$	−11.7944	−	6.80948i	−0.468045	−	0.270226i
$636$	−1.58519			−0.0628569
$637$	3.60555	+	0.00176922i	0.142857	+	7.00992e-5i
$638$	−0.359712			−0.0142411
$639$	−16.3181	−	9.42125i	−0.645533	−	0.372699i
$640$	−3.19238	+	5.52937i	−0.126190	+	0.218568i
$641$	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	$0.767353\pi$
$642$			0.919818i			0.0363023i
$643$	13.2247	−	7.63531i	0.521533	−	0.301107i	−0.216029	−	0.976387i	$-0.569310\pi$
$643$	13.2247	−	7.63531i	0.521533	−	0.301107i	0.737562	+	0.675280i	$0.235977\pi$
$644$	8.74061	−	5.04639i	0.344428	−	0.198856i
$645$			0.759983i			0.0299243i
$646$	0.276806	+	0.479442i	0.0108908	+	0.0188634i
$647$	8.75328	−	15.1611i	0.344127	−	0.596045i	−0.641068	−	0.767484i	$-0.721508\pi$
$647$	8.75328	−	15.1611i	0.344127	−	0.596045i	0.985195	+	0.171439i	$0.0548417\pi$
$648$	−2.51891	−	1.45429i	−0.0989520	−	0.0571300i
$649$	3.41354			0.133993
$650$	0.000457849	−	0.933064i	1.79583e−5	−	0.0365978i
$651$	−2.73547			−0.107211
$652$	−20.2777	−	11.7073i	−0.794136	−	0.458494i
$653$	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	$0.102815\pi$
$654$	−0.366048	−	0.634014i	−0.0143136	−	0.0247919i
$655$		−	31.9129i		−	1.24694i
$656$	19.7488	−	11.4020i	0.771063	−	0.445173i
$657$	−4.97949	+	2.87491i	−0.194268	+	0.112161i
$658$			1.53947i			0.0600147i
$659$	21.9294	+	37.9828i	0.854247	+	1.47960i	0.877342	+	0.479866i	$0.159315\pi$
$659$	21.9294	+	37.9828i	0.854247	+	1.47960i	−0.0230945	+	0.999733i	$0.507352\pi$
$660$	0.355825	−	0.616308i	0.0138505	−	0.0239897i
$661$	−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	$0.887880\pi$
$662$	3.11167			0.120939
$663$	−3.34116	−	5.79362i	−0.129760	−	0.225006i
$664$	−0.272170			−0.0105622
$665$	−2.11098	−	1.21878i	−0.0818604	−	0.0472621i
$666$	1.01139	−	1.75177i	0.0391904	−	0.0678798i
$667$	−20.8326	−	36.0831i	−0.806640	−	1.39714i
$668$		−	8.57120i		−	0.331630i
$669$	7.71622	−	4.45496i	0.298326	−	0.172239i
$670$	2.37130	−	1.36907i	0.0916113	−	0.0528918i
$671$		−	3.29062i		−	0.127033i
$672$	−0.416454	−	0.721319i	−0.0160651	−	0.0278255i
$673$	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	$-0.00528409\pi$
$674$	2.23015	+	1.28758i	0.0859021	+	0.0495956i
$675$	7.08740			0.272794
$676$	25.8117	+	0.0253313i	0.992756	+	0.000974280i
$677$	29.5328			1.13504			0.567519	−	0.823361i	$-0.307904\pi$
$677$	29.5328			1.13504			0.567519	+	0.823361i	$0.307904\pi$
$678$	0.300599	+	0.173551i	0.0115444	+	0.00666519i
$679$	3.96393	−	6.86572i	0.152122	−	0.263482i
$680$	−1.28984	−	2.23406i	−0.0494630	−	0.0856725i
$681$			4.04965i			0.155183i
$682$	0.178542	−	0.103081i	0.00683674	−	0.00394719i
$683$	−15.8379	+	9.14400i	−0.606019	+	0.349885i	−0.771406	−	0.636343i	$-0.780446\pi$
$683$	−15.8379	+	9.14400i	−0.606019	+	0.349885i	0.165387	+	0.986229i	$0.447113\pi$
$684$		−	7.62863i		−	0.291688i
$685$	−15.3838	−	26.6456i	−0.587786	−	1.01807i
$686$	−0.0601799	+	0.104235i	−0.00229768	+	0.00397970i
$687$	−13.8283	−	7.98378i	−0.527583	−	0.304600i
$688$	3.02545			0.115344
$689$	2.46968	+	4.28246i	0.0940872	+	0.163149i
$690$	−0.601417			−0.0228956
$691$	−8.95525	−	5.17031i	−0.340674	−	0.196688i	0.319896	−	0.947453i	$-0.396352\pi$
$691$	−8.95525	−	5.17031i	−0.340674	−	0.196688i	−0.660570	+	0.750765i	$0.729685\pi$
$692$	12.4290	−	21.5277i	0.472480	−	0.818360i
$693$	−0.485113	−	0.840240i	−0.0184279	−	0.0319181i
$694$			0.265855i			0.0100917i
$695$	−7.67671	+	4.43215i	−0.291194	+	0.168121i
$696$	−1.98277	+	1.14475i	−0.0751567	+	0.0433917i
$697$			18.5632i			0.703131i
$698$	0.679501	+	1.17693i	0.0257195	+	0.0445475i
$699$	1.99532	−	3.45599i	0.0754699	−	0.130718i
$700$	−3.69710	−	2.13452i	−0.139737	−	0.0806774i
$701$	41.6959			1.57483			0.787415	−	0.616423i	$-0.211419\pi$
$701$	41.6959			1.57483			0.787415	+	0.616423i	$0.211419\pi$
$702$	0.000701930	−	1.43048i	2.64926e−5	−	0.0539901i
$703$	9.11948			0.343948
$704$	−2.41702	−	1.39547i	−0.0910951	−	0.0525938i
$705$	−6.28659	+	10.8887i	−0.236766	+	0.410092i
$706$	2.14501	+	3.71527i	0.0807287	+	0.139826i
$707$			15.5464i			0.584684i
$708$	9.37371	−	5.41191i	0.352286	−	0.203392i
$709$	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	$0.333268\pi$
$710$		−	1.43880i		−	0.0539972i
$711$	−9.16402	−	15.8725i	−0.343677	−	0.595267i
$712$	0.273171	−	0.473146i	0.0102375	−	0.0177319i
$713$	20.6804	+	11.9398i	0.774488	+	0.447151i
$714$	0.223258			0.00835521
$715$	−2.21935	−	0.00108902i	−0.0829988	−	4.07271e-5i
$716$	13.0951			0.489388
$717$	11.1322	+	6.42717i	0.415739	+	0.240027i
$718$	1.16278	−	2.01400i	0.0433947	−	0.0751618i
$719$	−12.7330	−	22.0542i	−0.474861	−	0.822484i	0.524724	−	0.851272i	$-0.324168\pi$
$719$	−12.7330	−	22.0542i	−0.474861	−	0.822484i	−0.999586	+	0.0287885i	$0.990835\pi$
$720$			17.5789i			0.655127i
$721$	−8.91847	+	5.14908i	−0.332141	+	0.191762i
$722$	1.76314	−	1.01795i	0.0656174	−	0.0378842i
$723$		−	9.19853i		−	0.342097i
$724$	10.9359	+	18.9416i	0.406430	+	0.703957i
$725$	−8.81176	+	15.2624i	−0.327261	+	0.566832i
$726$	0.659576	+	0.380807i	0.0244792	+	0.0141331i
$727$	−23.5565			−0.873663			−0.436831	−	0.899543i	$-0.643899\pi$
$727$	−23.5565			−0.873663			−0.436831	+	0.899543i	$0.643899\pi$
$728$	−0.865519	+	1.49743i	−0.0320783	+	0.0554983i
$729$	−10.3760			−0.384297
$730$	−0.380231	−	0.219526i	−0.0140730	−	0.00812503i
$731$	−1.23141	+	2.13286i	−0.0455453	+	0.0788867i
$732$	−5.21703	−	9.03616i	−0.192827	−	0.333986i
$733$			6.23249i			0.230202i	0.993354	+	0.115101i	$0.0367192\pi$
$733$			6.23249i			0.230202i	−0.993354	+	0.115101i	$0.963281\pi$
$734$	−0.387821	+	0.223909i	−0.0143147	+	0.00826461i
$735$	−0.851308	+	0.491503i	−0.0314010	+	0.0181293i
$736$			7.27100i			0.268013i
$737$	2.45679	+	4.25528i	0.0904969	+	0.156745i
$738$	−0.933158	+	1.61628i	−0.0343500	+	0.0594960i
$739$	1.12339	+	0.648588i	0.0413244	+	0.0238587i	0.520520	−	0.853850i	$-0.325738\pi$
$739$	1.12339	+	0.648588i	0.0413244	+	0.0238587i	−0.479195	+	0.877708i	$0.659071\pi$
$740$	−21.1699			−0.778221
$741$	2.62606	−	1.51444i	0.0964709	−	0.0556344i
$742$	−0.165025			−0.00605825
$743$	5.25627	+	3.03471i	0.192834	+	0.111333i	0.593309	−	0.804975i	$-0.297821\pi$
$743$	5.25627	+	3.03471i	0.192834	+	0.111333i	−0.400475	+	0.916308i	$0.631155\pi$
$744$	0.656096	−	1.13639i	0.0240536	−	0.0416621i
$745$	−7.82725	−	13.5572i	−0.286768	−	0.496697i
$746$		−	0.422796i		−	0.0154797i
$747$	−1.30749	+	0.754880i	−0.0478386	+	0.0276196i
$748$	1.99722	−	1.15310i	0.0730256	−	0.0421613i
$749$		−	13.1244i		−	0.479555i
$750$	0.422980	+	0.732622i	0.0154450	+	0.0267516i
$751$	−18.3023	+	31.7005i	−0.667860	+	1.15677i	0.310641	+	0.950527i	$0.399456\pi$
$751$	−18.3023	+	31.7005i	−0.667860	+	1.15677i	−0.978501	+	0.206241i	$0.933877\pi$
$752$	43.3473	+	25.0266i	1.58071	+	0.912625i
$753$	13.1346			0.478650
$754$	3.07961	+	1.78003i	0.112153	+	0.0648248i
$755$	23.6566			0.860952
$756$	−5.66804	−	3.27244i	−0.206144	−	0.119018i
$757$	−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	$0.234747\pi$
$758$	−1.50548	−	2.60757i	−0.0546815	−	0.0947111i
$759$		−	1.07924i		−	0.0391739i
$760$	1.01263	−	0.584642i	0.0367320	−	0.0212072i
$761$	−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	$0.589563\pi$
$762$			0.565394i			0.0204821i
$763$	5.22295	+	9.04641i	0.189083	+	0.327502i
$764$	−5.88916	+	10.2003i	−0.213062	+	0.369035i
$765$	−12.3926	−	7.15490i	−0.448057	−	0.258686i
$766$	2.70393			0.0976970
$767$	−29.2245	−	16.8919i	−1.05523	−	0.609930i
$768$	−8.64915			−0.312099
$769$	−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	$0.724138\pi$
$770$	0.0370429	−	0.0641602i	0.00133493	−	0.00231217i
$771$	−5.94313	−	10.2938i	−0.214036	−	0.370722i
$772$		−	8.33112i		−	0.299843i
$773$	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	$0.259682\pi$
$774$	−0.214435	+	0.123804i	−0.00770769	+	0.00445004i
$775$		−	10.1006i		−	0.362825i
$776$	1.90148	+	3.29346i	0.0682592	+	0.118228i
$777$	1.83883	−	3.18495i	0.0659677	−	0.114259i
$778$	−1.39012	−	0.802586i	−0.0498382	−	0.0287741i
$779$	−8.41411			−0.301467
$780$	−6.09613	+	3.51561i	−0.218276	+	0.125879i
$781$	2.58192			0.0923882
$782$	−1.68785	−	0.974483i	−0.0603575	−	0.0348474i
$783$	−13.5093	+	23.3988i	−0.482784	+	0.836206i
$784$	1.95665	+	3.38901i	0.0698802	+	0.121036i
$785$			29.0069i			1.03530i
$786$	−1.14737	+	0.662435i	−0.0409254	+	0.0236283i
$787$	7.52380	−	4.34387i	0.268194	−	0.154842i	−0.359872	−	0.933002i	$-0.617180\pi$
$787$	7.52380	−	4.34387i	0.268194	−	0.154842i	0.628067	+	0.778159i	$0.283846\pi$
$788$		−	11.4861i		−	0.409174i
$789$	−8.60052	−	14.8965i	−0.306187	−	0.530331i
$790$	0.699759	−	1.21202i	0.0248963	−	0.0431216i
$791$	−4.28909	−	2.47631i	−0.152503	−	0.0880474i
$792$	0.465413			0.0165377
$793$	−16.2836	+	28.1721i	−0.578247	+	1.00042i
$794$	3.10929			0.110345
$795$	−1.16722	−	0.673897i	−0.0413972	−	0.0239007i
$796$	11.8731	−	20.5649i	0.420832	−	0.728903i
$797$	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	$0.592616\pi$
$798$			0.101196i			0.00358229i
$799$	−35.2861	+	20.3724i	−1.24833	+	0.720725i
$800$	2.66345	−	1.53774i	0.0941672	−	0.0543675i
$801$		−	3.03063i		−	0.107082i
$802$	−1.05679	−	1.83041i	−0.0373166	−	0.0646342i
$803$	0.393938	−	0.682321i	0.0139018	−	0.0240786i
$804$	13.4928	+	7.79009i	0.475856	+	0.274735i
$805$	8.58130			0.302451
$806$	−2.03866	−	0.00100036i	−0.0718086	−	3.52361e-5i
$807$	−16.2554			−0.572218
$808$	−6.45844	−	3.72878i	−0.227207	−	0.131178i
$809$	−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	$0.997331\pi$
$810$	−0.616002	−	1.06695i	−0.0216441	−	0.0374887i
$811$		−	12.3917i		−	0.435131i	−0.976046	−	0.217566i	$-0.930188\pi$
$811$		−	12.3917i		−	0.435131i	0.976046	−	0.217566i	$-0.0698116\pi$
$812$	14.0941	−	8.13725i	0.494607	−	0.285561i
$813$	−14.8506	+	8.57397i	−0.520832	+	0.300702i
$814$			0.277173i			0.00971491i
$815$	−9.95405	−	17.2409i	−0.348675	−	0.603923i
$816$	3.62942	−	6.28634i	0.127055	−	0.220066i
$817$	−0.966758	−	0.558158i	−0.0338226	−	0.0195275i
$818$	−1.74861			−0.0611388
$819$	−0.00470779	+	9.59414i	−0.000164504	+	0.335246i
$820$	19.5324			0.682103
$821$	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	$0.412697\pi$
$822$	−0.638663	+	1.10620i	−0.0222759	+	0.0385830i
$823$	−1.06806	−	1.84994i	−0.0372304	−	0.0644849i	0.846810	−	0.531896i	$-0.178520\pi$
$823$	−1.06806	−	1.84994i	−0.0372304	−	0.0644849i	−0.884040	+	0.467411i	$0.845187\pi$
$824$		−	4.93999i		−	0.172093i
$825$	−0.395337	+	0.228248i	−0.0137639	+	0.00794658i
$826$	0.975842	−	0.563403i	0.0339539	−	0.0196033i
$827$			8.54938i			0.297291i	0.988891	+	0.148645i	$0.0474913\pi$
$827$			8.54938i			0.297291i	−0.988891	+	0.148645i	$0.952509\pi$
$828$	13.4281	+	23.2582i	0.466660	+	0.808278i
$829$	−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	$0.249158\pi$
$830$	−0.0998392	−	0.0576422i	−0.00346547	−	0.00200079i
$831$	3.99367			0.138539
$832$	13.7875	+	23.9077i	0.477995	+	0.828850i
$833$	−3.18555			−0.110373
$834$	0.318701	+	0.184002i	0.0110357	+	0.00637146i
$835$	3.64379	−	6.31123i	0.126099	−	0.218409i
$836$	0.522661	+	0.905276i	0.0180766	+	0.0313096i
$837$		−	15.4853i		−	0.535250i
$838$	−0.479680	+	0.276943i	−0.0165703	+	0.00956685i
$839$	23.3581	−	13.4858i	0.806411	−	0.465582i	−0.0392968	−	0.999228i	$-0.512512\pi$
$839$	23.3581	−	13.4858i	0.806411	−	0.465582i	0.845708	+	0.533646i	$0.179178\pi$
$840$		−	0.471544i		−	0.0162698i
$841$	−19.0923	−	33.0687i	−0.658353	−	1.14030i
$842$	−1.15934	+	2.00803i	−0.0399534	+	0.0692013i
$843$	−14.6715	−	8.47062i	−0.505315	−	0.291743i
$844$	−16.3525			−0.562877
$845$	18.9951	+	10.9917i	0.653453	+	0.378127i
$846$	−4.09643			−0.140838
$847$	−9.41114	−	5.43353i	−0.323371	−	0.186698i
$848$	−2.68275	+	4.64665i	−0.0921259	+	0.159567i
$849$	−3.38027	−	5.85479i	−0.116010	−	0.200936i
$850$			0.824374i			0.0282758i
$851$	−27.8035	+	16.0524i	−0.953092	+	0.550268i
$852$	7.09003	−	4.09343i	0.242901	−	0.140239i
$853$			25.6332i			0.877665i	0.898569	+	0.438832i	$0.144608\pi$
$853$			25.6332i			0.877665i	−0.898569	+	0.438832i	$0.855392\pi$
$854$	−0.543114	−	0.940702i	−0.0185850	−	0.0321902i
$855$	3.24309	−	5.61719i	0.110911	−	0.192104i
$856$	5.45225	+	3.14786i	0.186354	+	0.107592i
$857$	−11.7653			−0.401894			−0.200947	−	0.979602i	$-0.564402\pi$
$857$	−11.7653			−0.401894			−0.200947	+	0.979602i	$0.564402\pi$
$858$	0.0460292	+	0.0798153i	0.00157141	+	0.00272485i
$859$	−21.7761			−0.742992			−0.371496	−	0.928435i	$-0.621155\pi$
$859$	−21.7761			−0.742992			−0.371496	+	0.928435i	$0.621155\pi$
$860$	2.24422	+	1.29570i	0.0765274	+	0.0441831i
$861$	−1.69660	+	2.93860i	−0.0578200	+	0.100147i
$862$	1.70701	+	2.95663i	0.0581410	+	0.100703i
$863$			41.0575i			1.39761i	0.715310	+	0.698807i	$0.246285\pi$
$863$			41.0575i			1.39761i	−0.715310	+	0.698807i	$0.753715\pi$
$864$	4.08334	−	2.35752i	0.138918	−	0.0802044i
$865$	18.3037	−	10.5677i	0.622345	−	0.359311i
$866$			1.50694i			0.0512079i
$867$	−1.99502	−	3.45547i	−0.0677543	−	0.117354i
$868$	−4.66373	+	8.07781i	−0.158297	+	0.274179i
$869$	2.17496	+	1.25571i	0.0737803	+	0.0425971i
$870$	−0.969778			−0.0328785
$871$	0.0238420	−	48.5882i	0.000807854	−	1.64635i
$872$	−5.01085			−0.169689
$873$	18.2693	+	10.5478i	0.618320	+	0.356987i
$874$	0.441702	−	0.765050i	0.0149408	−	0.0258782i
$875$	−6.03527	−	10.4534i	−0.204029	−	0.353389i
$876$		−	2.49824i		−	0.0844076i
$877$	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	$0.296214\pi$
$878$	−3.30709	+	1.90935i	−0.111609	+	0.0644374i
$879$			10.3582i			0.349372i
$880$	−1.20439	−	2.08606i	−0.0405998	−	0.0703209i
$881$	−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	$0.224060\pi$
$882$	−0.277362	−	0.160135i	−0.00933926	−	0.00539203i
$883$	21.3844			0.719641			0.359821	−	0.933022i	$-0.382838\pi$
$883$	21.3844			0.719641			0.359821	+	0.933022i	$0.382838\pi$
$884$	−22.8049	−	0.0111902i	−0.767012	−	0.000376369i
$885$	9.20286			0.309351
$886$	−0.180376	−	0.104140i	−0.00605986	−	0.00349866i
$887$	17.0575	−	29.5445i	0.572735	−	0.992007i	−0.423548	−	0.905874i	$-0.639216\pi$
$887$	17.0575	−	29.5445i	0.572735	−	0.992007i	0.996284	−	0.0861333i	$-0.0274511\pi$
$888$	0.882080	+	1.52781i	0.0296007	+	0.0512698i
$889$		−	8.06731i		−	0.270569i
$890$	0.200413	−	0.115709i	0.00671786	−	0.00387856i
$891$	1.91463	−	1.10541i	0.0641424	−	0.0370326i
$892$		−	30.3813i		−	1.01724i
$893$	−9.23418	−	15.9941i	−0.309010	−	0.535221i
$894$	−0.324950	+	0.562831i	−0.0108680	+	0.0188239i
$895$	9.64235	+	5.56701i	0.322308	+	0.186085i
$896$	−3.78208			−0.126350
$897$	−5.34060	+	9.23971i	−0.178317	+	0.308505i
$898$	1.27056			0.0423992
$899$	33.3469	+	19.2528i	1.11218	+	0.642118i
$900$	5.67983	−	9.83776i	0.189328	−	0.327925i
$901$	−2.18384	−	3.78253i	−0.0727544	−	0.126014i
$902$		−	0.255734i		−	0.00851502i
$903$	−0.389870	+	0.225091i	−0.0129740	+	0.00749057i
$904$	2.05746	−	1.18788i	0.0684301	−	0.0395081i
$905$			18.5963i			0.618163i
$906$	−0.491055	−	0.850532i	−0.0163142	−	0.0282570i
$907$	21.0758	−	36.5043i	0.699810	−	1.21211i	−0.268723	−	0.963218i	$-0.586601\pi$
$907$	21.0758	−	36.5043i	0.699810	−	1.21211i	0.968532	−	0.248888i	$-0.0800652\pi$
$908$	11.9586	+	6.90429i	0.396860	+	0.229127i
$909$	−41.3681			−1.37209
$910$	−0.634632	+	0.365990i	−0.0210379	+	0.0121324i
$911$	20.9947			0.695584			0.347792	−	0.937572i	$-0.386932\pi$
$911$	20.9947			0.695584			0.347792	+	0.937572i	$0.386932\pi$
$912$	2.84940	+	1.64510i	0.0943529	+	0.0544747i
$913$	0.103438	−	0.179161i	0.00342331	−	0.00592935i
$914$	0.478367	+	0.828556i	0.0158230	+	0.0274062i
$915$		−	8.87147i		−	0.293282i
$916$	−47.1521	+	27.2233i	−1.55795	+	0.899483i
$917$	16.3712	−	9.45194i	0.540626	−	0.312131i
$918$			1.26385i			0.0417132i
$919$	7.14699	+	12.3789i	0.235757	+	0.408344i	0.959493	−	0.281734i	$-0.0909096\pi$
$919$	7.14699	+	12.3789i	0.235757	+	0.408344i	−0.723735	+	0.690078i	$0.757576\pi$
$920$	−2.05821	+	3.56492i	−0.0678571	+	0.117532i
$921$	4.57869	+	2.64351i	0.150873	+	0.0871065i
$922$	−1.31094			−0.0431736
$923$	−22.1046	−	12.7766i	−0.727583	−	0.420546i
$924$	0.421553			0.0138681
$925$	11.7603	+	6.78983i	0.386677	+	0.223248i
$926$	−2.15581	+	3.73397i	−0.0708443	+	0.122706i
$927$	−13.7014	−	23.7315i	−0.450012	−	0.779444i
$928$			11.7244i			0.384872i
$929$	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	$0.297714\pi$
$930$	0.481347	−	0.277906i	0.0157840	−	0.00911290i
$931$		−	1.44391i		−	0.0473221i
$932$	−6.80369	−	11.7843i	−0.222862	−	0.386009i
$933$	−0.457310	+	0.792085i	−0.0149717	+	0.0259317i
$934$	2.07410	+	1.19748i	0.0678666	+	0.0391828i
$935$	1.96082			0.0641256
$936$	−3.98455	−	2.30309i	−0.130239	−	0.0752789i
$937$	−5.22890			−0.170821			−0.0854104	−	0.996346i	$-0.527220\pi$
$937$	−5.22890			−0.170821			−0.0854104	+	0.996346i	$0.527220\pi$
$938$	1.40466	+	0.810981i	0.0458638	+	0.0264795i
$939$	6.00437	−	10.3999i	0.195945	−	0.339387i
$940$	21.4362	+	37.1285i	0.699170	+	1.21100i
$941$		−	56.4403i		−	1.83990i	−0.392033	−	0.919951i	$-0.628228\pi$
$941$		−	56.4403i		−	1.83990i	0.392033	−	0.919951i	$-0.371772\pi$
$942$	1.04289	−	0.602114i	0.0339793	−	0.0196179i
$943$	25.6530	−	14.8108i	0.835376	−	0.482304i
$944$		−	36.6361i		−	1.19240i
$945$	−2.78236	−	4.81920i	−0.0905103	−	0.156769i
$946$	0.0169644	−	0.0293832i	0.000551559	−	0.000955329i
$947$	−5.06648	−	2.92513i	−0.164639	−	0.0950541i	0.415417	−	0.909631i	$-0.363636\pi$
$947$	−5.06648	−	2.92513i	−0.164639	−	0.0950541i	−0.580055	+	0.814577i	$0.696969\pi$
$948$	7.96334			0.258637
$949$	−6.74909	+	3.89217i	−0.219085	+	0.126345i
$950$	−0.373662			−0.0121232
$951$	15.4025	+	8.89262i	0.499459	+	0.288363i
$952$	0.764047	−	1.32337i	0.0247629	−	0.0428906i
$953$	−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	$0.947916\pi$
$954$		−	0.439121i		−	0.0142171i
$955$	−8.67273	+	5.00720i	−0.280643	+	0.162029i
$956$	37.9588	−	21.9155i	1.22767	−	0.708798i
$957$		−	1.74026i		−	0.0562546i
$958$	−1.58214	−	2.74035i	−0.0511167	−	0.0885368i
$959$	9.11274	−	15.7837i	0.294266	−	0.509683i
$960$	−6.51626	−	3.76217i	−0.210312	−	0.121423i
$961$	8.93110			0.288100
$962$	1.37159	−	2.37297i	0.0442217	−	0.0765075i
$963$	34.9232			1.12538
$964$	−27.1632	−	15.6827i	−0.874868	−	0.505105i
$965$	3.54173	−	6.13446i	0.114012	−	0.197475i
$966$	−0.178127	−	0.308526i	−0.00573116	−	0.00992666i
$967$			13.3251i			0.428507i	0.976778	+	0.214253i	$0.0687318\pi$
$967$			13.3251i			0.428507i	−0.976778	+	0.214253i	$0.931268\pi$
$968$	4.51449	−	2.60644i	0.145101	−	0.0837742i
$969$	−2.31950	+	1.33917i	−0.0745132	+	0.0430202i
$970$			1.61084i			0.0517210i
$971$	−3.73092	−	6.46215i	−0.119731	−	0.207380i	0.799930	−	0.600093i	$-0.204870\pi$
$971$	−3.73092	−	6.46215i	−0.119731	−	0.207380i	−0.919661	+	0.392713i	$0.871537\pi$
$972$	13.3224	−	23.0751i	0.427317	−	0.740134i
$973$	−4.54737	−	2.62542i	−0.145782	−	0.0841673i
$974$	−0.767850			−0.0246035
$975$	4.51409	+	0.00221504i	0.144567	+	7.09381e-5i
$976$	−35.3168			−1.13046
$977$	−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	$0.722765\pi$
$978$	−0.413245	+	0.715761i	−0.0132141	+	0.0228875i
$979$	0.207638	+	0.359640i	0.00663614	+	0.0114941i
$980$			3.35188i			0.107072i
$981$	−24.0719	+	13.8979i	−0.768557	+	0.443727i
$982$	0.309335	−	0.178595i	0.00987127	−	0.00569918i
$983$			16.1441i			0.514918i	0.966289	+	0.257459i	$0.0828852\pi$
$983$			16.1441i			0.514918i	−0.966289	+	0.257459i	$0.917115\pi$
$984$	−0.813853	−	1.40963i	−0.0259447	−	0.0449375i
$985$	4.88296	−	8.45754i	0.155584	−	0.269480i
$986$	−2.72164	−	1.57134i	−0.0866747	−	0.0500417i
$987$	−7.44783			−0.237067
$988$	0.00507218	−	10.3367i	0.000161368	−	0.328856i
$989$	3.92994			0.124965
$990$	0.170726	+	0.0985688i	0.00542603	+	0.00313272i
$991$	−3.35748	+	5.81533i	−0.106654	+	0.184730i	−0.914413	−	0.404783i	$-0.867347\pi$
$991$	−3.35748	+	5.81533i	−0.106654	+	0.184730i	0.807759	+	0.589513i	$0.200680\pi$
$992$	−3.35982	−	5.81938i	−0.106674	−	0.184766i
$993$			15.0540i			0.477725i
$994$	0.738102	−	0.426143i	0.0234112	−	0.0135164i
$995$	17.4851	−	10.0950i	0.554315	−	0.320034i
$996$		−	0.655975i		−	0.0207854i
$997$	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	$0.739007\pi$
$998$	−1.69305	+	2.93244i	−0.0535924	+	0.0928248i
$999$	18.0298	+	10.4095i	0.570437	+	0.329342i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.2.q.a.43.3	yes	12
3.2	odd	2		819.2.ct.a.316.4		12
4.3	odd	2		1456.2.cc.c.225.3		12
7.2	even	3		637.2.k.h.459.4		12
7.3	odd	6		637.2.u.i.30.4		12
7.4	even	3		637.2.u.h.30.4		12
7.5	odd	6		637.2.k.g.459.4		12
7.6	odd	2		637.2.q.h.589.3		12
13.4	even	6		1183.2.c.i.337.6		12
13.6	odd	12		1183.2.a.p.1.3		6
13.7	odd	12		1183.2.a.m.1.4		6
13.9	even	3		1183.2.c.i.337.7		12
13.10	even	6	inner	91.2.q.a.36.3	✓	12
39.23	odd	6		819.2.ct.a.127.4		12
52.23	odd	6		1456.2.cc.c.673.3		12
91.6	even	12		8281.2.a.ch.1.3		6
91.10	odd	6		637.2.k.g.569.3		12
91.20	even	12		8281.2.a.by.1.4		6
91.23	even	6		637.2.u.h.361.4		12
91.62	odd	6		637.2.q.h.491.3		12
91.75	odd	6		637.2.u.i.361.4		12
91.88	even	6		637.2.k.h.569.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.q.a.36.3	✓	12	13.10	even	6	inner
91.2.q.a.43.3	yes	12	1.1	even	1	trivial
637.2.k.g.459.4		12	7.5	odd	6
637.2.k.g.569.3		12	91.10	odd	6
637.2.k.h.459.4		12	7.2	even	3
637.2.k.h.569.3		12	91.88	even	6
637.2.q.h.491.3		12	91.62	odd	6
637.2.q.h.589.3		12	7.6	odd	2
637.2.u.h.30.4		12	7.4	even	3
637.2.u.h.361.4		12	91.23	even	6
637.2.u.i.30.4		12	7.3	odd	6
637.2.u.i.361.4		12	91.75	odd	6
819.2.ct.a.127.4		12	39.23	odd	6
819.2.ct.a.316.4		12	3.2	odd	2
1183.2.a.m.1.4		6	13.7	odd	12
1183.2.a.p.1.3		6	13.6	odd	12
1183.2.c.i.337.6		12	13.4	even	6
1183.2.c.i.337.7		12	13.9	even	3
1456.2.cc.c.225.3		12	4.3	odd	2
1456.2.cc.c.673.3		12	52.23	odd	6
8281.2.a.by.1.4		6	91.20	even	12
8281.2.a.ch.1.3		6	91.6	even	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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.104235 - 0.0601799i) q^{2} +(0.291146 - 0.504280i) q^{3} +(-0.992757 - 1.71951i) q^{4} -1.68817i q^{5} +(-0.0606950 + 0.0350423i) q^{6} +(0.866025 - 0.500000i) q^{7} +0.479696i q^{8} +(1.33047 + 2.30444i) q^{9} +O(q^{10})\)	\(q+(-0.104235 - 0.0601799i) q^{2} +(0.291146 - 0.504280i) q^{3} +(-0.992757 - 1.71951i) q^{4} -1.68817i q^{5} +(-0.0606950 + 0.0350423i) q^{6} +(0.866025 - 0.500000i) q^{7} +0.479696i q^{8} +(1.33047 + 2.30444i) q^{9} +(-0.101594 + 0.175965i) q^{10} +(-0.315769 - 0.182309i) q^{11} -1.15615 q^{12} +(1.80124 + 3.12338i) q^{13} -0.120360 q^{14} +(-0.851308 - 0.491503i) q^{15} +(-1.95665 + 3.38901i) q^{16} +(-1.59277 - 2.75877i) q^{17} -0.320270i q^{18} +(1.25046 - 0.721954i) q^{19} +(-2.90281 + 1.67594i) q^{20} -0.582292i q^{21} +(0.0219427 + 0.0380059i) q^{22} +(-2.54161 + 4.40219i) q^{23} +(0.241901 + 0.139662i) q^{24} +2.15010 q^{25} +(0.000212944 - 0.433964i) q^{26} +3.29632 q^{27} +(-1.71951 - 0.992757i) q^{28} +(-4.09831 + 7.09848i) q^{29} +(0.0591572 + 0.102463i) q^{30} -4.69775i q^{31} +(1.23876 - 0.715198i) q^{32} +(-0.183870 + 0.106157i) q^{33} +0.383412i q^{34} +(-0.844083 - 1.46199i) q^{35} +(2.64166 - 4.57549i) q^{36} +(5.46967 + 3.15792i) q^{37} -0.173789 q^{38} +(2.09948 + 0.00103020i) q^{39} +0.809806 q^{40} +(-5.04661 - 2.91366i) q^{41} +(-0.0350423 + 0.0606950i) q^{42} +(-0.386561 - 0.669543i) q^{43} +0.723954i q^{44} +(3.89027 - 2.24605i) q^{45} +(0.529847 - 0.305907i) q^{46} -12.7905i q^{47} +(1.13934 + 1.97339i) q^{48} +(0.500000 - 0.866025i) q^{49} +(-0.224115 - 0.129393i) q^{50} -1.85492 q^{51} +(3.58248 - 6.19801i) q^{52} +1.37110 q^{53} +(-0.343591 - 0.198372i) q^{54} +(-0.307768 + 0.533070i) q^{55} +(0.239848 + 0.415429i) q^{56} -0.840776i q^{57} +(0.854372 - 0.493272i) q^{58} +(-8.10770 + 4.68098i) q^{59} +1.95177i q^{60} +(4.51242 + 7.81574i) q^{61} +(-0.282711 + 0.489669i) q^{62} +(2.30444 + 1.33047i) q^{63} +7.65442 q^{64} +(5.27279 - 3.04080i) q^{65} +0.0255541 q^{66} +(-11.6705 - 6.73797i) q^{67} +(-3.16247 + 5.47757i) q^{68} +(1.47996 + 2.56336i) q^{69} +0.203187i q^{70} +(-6.13246 + 3.54058i) q^{71} +(-1.10543 + 0.638220i) q^{72} +2.16083i q^{73} +(-0.380087 - 0.658329i) q^{74} +(0.625992 - 1.08425i) q^{75} +(-2.48281 - 1.43345i) q^{76} -0.364618 q^{77} +(-0.218777 - 0.126454i) q^{78} -6.88781 q^{79} +(5.72121 + 3.30314i) q^{80} +(-3.03169 + 5.25105i) q^{81} +(0.350688 + 0.607409i) q^{82} +0.567380i q^{83} +(-1.00125 + 0.578074i) q^{84} +(-4.65725 + 2.68887i) q^{85} +0.0930528i q^{86} +(2.38641 + 4.13339i) q^{87} +(0.0874529 - 0.151473i) q^{88} +(-0.986346 - 0.569467i) q^{89} -0.540669 q^{90} +(3.12161 + 1.80431i) q^{91} +10.0928 q^{92} +(-2.36898 - 1.36773i) q^{93} +(-0.769734 + 1.33322i) q^{94} +(-1.21878 - 2.11098i) q^{95} -0.832908i q^{96} +(6.86572 - 3.96393i) q^{97} +(-0.104235 + 0.0601799i) q^{98} -0.970225i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} - 18 q^{6} - 4 q^{9}+O(q^{10}) \) 12 * q + 4 * q^4 - 18 * q^6 - 4 * q^9	\( 12 q + 4 q^{4} - 18 q^{6} - 4 q^{9} + 12 q^{10} + 6 q^{11} - 4 q^{12} + 4 q^{13} - 8 q^{14} + 6 q^{15} - 8 q^{16} - 4 q^{17} - 12 q^{20} + 6 q^{22} - 12 q^{23} + 12 q^{24} - 20 q^{25} - 42 q^{26} + 12 q^{27} + 8 q^{29} + 8 q^{30} + 36 q^{32} - 30 q^{33} + 6 q^{35} - 10 q^{36} - 42 q^{37} + 4 q^{38} - 4 q^{39} + 92 q^{40} + 30 q^{41} + 4 q^{42} + 2 q^{43} + 12 q^{46} - 2 q^{48} + 6 q^{49} - 18 q^{50} + 52 q^{51} + 2 q^{52} - 44 q^{53} + 12 q^{54} - 6 q^{55} - 12 q^{56} - 12 q^{58} + 18 q^{59} + 14 q^{61} - 4 q^{62} + 12 q^{63} - 52 q^{64} + 60 q^{65} - 52 q^{66} - 24 q^{67} - 8 q^{68} + 4 q^{69} - 24 q^{71} + 60 q^{72} + 6 q^{74} + 46 q^{75} - 18 q^{76} + 8 q^{77} - 10 q^{78} - 56 q^{79} - 72 q^{80} + 2 q^{81} + 14 q^{82} + 18 q^{84} - 48 q^{85} - 2 q^{87} - 14 q^{88} - 12 q^{89} + 24 q^{90} + 14 q^{91} + 24 q^{92} - 18 q^{93} + 4 q^{94} - 22 q^{95} + 6 q^{97}+O(q^{100}) \) 12 * q + 4 * q^4 - 18 * q^6 - 4 * q^9 + 12 * q^10 + 6 * q^11 - 4 * q^12 + 4 * q^13 - 8 * q^14 + 6 * q^15 - 8 * q^16 - 4 * q^17 - 12 * q^20 + 6 * q^22 - 12 * q^23 + 12 * q^24 - 20 * q^25 - 42 * q^26 + 12 * q^27 + 8 * q^29 + 8 * q^30 + 36 * q^32 - 30 * q^33 + 6 * q^35 - 10 * q^36 - 42 * q^37 + 4 * q^38 - 4 * q^39 + 92 * q^40 + 30 * q^41 + 4 * q^42 + 2 * q^43 + 12 * q^46 - 2 * q^48 + 6 * q^49 - 18 * q^50 + 52 * q^51 + 2 * q^52 - 44 * q^53 + 12 * q^54 - 6 * q^55 - 12 * q^56 - 12 * q^58 + 18 * q^59 + 14 * q^61 - 4 * q^62 + 12 * q^63 - 52 * q^64 + 60 * q^65 - 52 * q^66 - 24 * q^67 - 8 * q^68 + 4 * q^69 - 24 * q^71 + 60 * q^72 + 6 * q^74 + 46 * q^75 - 18 * q^76 + 8 * q^77 - 10 * q^78 - 56 * q^79 - 72 * q^80 + 2 * q^81 + 14 * q^82 + 18 * q^84 - 48 * q^85 - 2 * q^87 - 14 * q^88 - 12 * q^89 + 24 * q^90 + 14 * q^91 + 24 * q^92 - 18 * q^93 + 4 * q^94 - 22 * q^95 + 6 * q^97

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