LMFDB - Embedded newform 483.2.i.f.415.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(277,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("483.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.i (of order $3$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 8 x^{10} - 3 x^{9} + 42 x^{8} - 15 x^{7} + 101 x^{6} + 6 x^{5} + 150 x^{4} - 28 x^{3} + \cdots + 4 $ x^12 - x^11 + 8x^10 - 3x^9 + 42x^8 - 15x^7 + 101x^6 + 6x^5 + 150x^4 - 28x^3 + 40x^2 + 8x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			415.1
Root			$-1.02170 - 1.76964i$ of defining polynomial
Character	$\chi$	$=$	483.415
Dual form			483.2.i.f.277.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.02170 + 1.76964i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.08774 - 1.88403i) q^{4} +(-0.971745 + 1.68311i) q^{5} -2.04340 q^{6} +(-1.16166 - 2.37709i) q^{7} +0.358585 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.02170 + 1.76964i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.08774 - 1.88403i) q^{4} +(-0.971745 + 1.68311i) q^{5} -2.04340 q^{6} +(-1.16166 - 2.37709i) q^{7} +0.358585 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.98566 - 3.43927i) q^{10} +(2.83264 + 4.90628i) q^{11} +(1.08774 - 1.88403i) q^{12} -6.17812 q^{13} +(5.39345 + 0.372961i) q^{14} -1.94349 q^{15} +(1.80912 - 3.13348i) q^{16} +(-3.61732 - 6.26537i) q^{17} +(-1.02170 - 1.76964i) q^{18} +(-0.395110 + 0.684350i) q^{19} +4.22803 q^{20} +(1.47779 - 2.19457i) q^{21} -11.5765 q^{22} +(0.500000 - 0.866025i) q^{23} +(0.179293 + 0.310544i) q^{24} +(0.611424 + 1.05902i) q^{25} +(6.31219 - 10.9330i) q^{26} -1.00000 q^{27} +(-3.21491 + 4.77425i) q^{28} -5.34085 q^{29} +(1.98566 - 3.43927i) q^{30} +(-0.455658 - 0.789223i) q^{31} +(4.05534 + 7.02405i) q^{32} +(-2.83264 + 4.90628i) q^{33} +14.7832 q^{34} +(5.12974 + 0.354726i) q^{35} +2.17548 q^{36} +(0.486660 - 0.842920i) q^{37} +(-0.807367 - 1.39840i) q^{38} +(-3.08906 - 5.35041i) q^{39} +(-0.348454 + 0.603539i) q^{40} -1.51843 q^{41} +(2.37373 + 4.85734i) q^{42} -2.70342 q^{43} +(6.16237 - 10.6735i) q^{44} +(-0.971745 - 1.68311i) q^{45} +(1.02170 + 1.76964i) q^{46} +(0.764197 - 1.32363i) q^{47} +3.61824 q^{48} +(-4.30111 + 5.52273i) q^{49} -2.49877 q^{50} +(3.61732 - 6.26537i) q^{51} +(6.72020 + 11.6397i) q^{52} +(4.47902 + 7.75789i) q^{53} +(1.02170 - 1.76964i) q^{54} -11.0104 q^{55} +(-0.416553 - 0.852390i) q^{56} -0.790220 q^{57} +(5.45674 - 9.45136i) q^{58} +(5.44656 + 9.43371i) q^{59} +(2.11402 + 3.66158i) q^{60} +(3.15887 - 5.47133i) q^{61} +1.86218 q^{62} +(2.63945 + 0.182520i) q^{63} -9.33688 q^{64} +(6.00356 - 10.3985i) q^{65} +(-5.78823 - 10.0255i) q^{66} +(-3.65917 - 6.33786i) q^{67} +(-7.86941 + 13.6302i) q^{68} +1.00000 q^{69} +(-5.86879 + 8.71535i) q^{70} -8.75692 q^{71} +(-0.179293 + 0.310544i) q^{72} +(0.437625 + 0.757990i) q^{73} +(0.994442 + 1.72242i) q^{74} +(-0.611424 + 1.05902i) q^{75} +1.71911 q^{76} +(8.37211 - 12.4329i) q^{77} +12.6244 q^{78} +(-2.98327 + 5.16718i) q^{79} +(3.51600 + 6.08989i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.55138 - 2.68708i) q^{82} -0.273554 q^{83} +(-5.74208 - 0.397069i) q^{84} +14.0604 q^{85} +(2.76208 - 4.78407i) q^{86} +(-2.67042 - 4.62531i) q^{87} +(1.01575 + 1.75932i) q^{88} +(-8.81350 + 15.2654i) q^{89} +3.97133 q^{90} +(7.17686 + 14.6859i) q^{91} -2.17548 q^{92} +(0.455658 - 0.789223i) q^{93} +(1.56156 + 2.70470i) q^{94} +(-0.767892 - 1.33003i) q^{95} +(-4.05534 + 7.02405i) q^{96} +3.09620 q^{97} +(-5.37878 - 13.2540i) q^{98} -5.66529 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + q^{2} + 6 q^{3} - 3 q^{4} - 3 q^{5} + 2 q^{6} - 2 q^{7} - 6 q^{8} - 6 q^{9}+O(q^{10}) $ 12 * q + q^2 + 6 * q^3 - 3 * q^4 - 3 * q^5 + 2 * q^6 - 2 * q^7 - 6 * q^8 - 6 * q^9	\( 12 q + q^{2} + 6 q^{3} - 3 q^{4} - 3 q^{5} + 2 q^{6} - 2 q^{7} - 6 q^{8} - 6 q^{9} + 3 q^{10} + 14 q^{11} + 3 q^{12} - q^{14} - 6 q^{15} + 7 q^{16} - 15 q^{17} + q^{18} + q^{19} + 34 q^{20} - 4 q^{21} - 12 q^{22} + 6 q^{23} - 3 q^{24} - 9 q^{25} + 15 q^{26} - 12 q^{27} - 2 q^{28} - 12 q^{29} - 3 q^{30} + 11 q^{31} - 3 q^{32} - 14 q^{33} + 30 q^{34} - q^{35} + 6 q^{36} + 5 q^{37} - 14 q^{38} + 17 q^{40} + 36 q^{41} - 17 q^{42} - 74 q^{43} + 10 q^{44} - 3 q^{45} - q^{46} - 3 q^{47} + 14 q^{48} - 6 q^{49} - 60 q^{50} + 15 q^{51} + 7 q^{52} + 15 q^{53} - q^{54} - 4 q^{55} - 21 q^{56} + 2 q^{57} - 4 q^{58} + 2 q^{59} + 17 q^{60} + 12 q^{61} + 72 q^{62} - 2 q^{63} - 46 q^{64} + 17 q^{65} - 6 q^{66} + 10 q^{67} + q^{68} + 12 q^{69} - 56 q^{70} - 42 q^{71} + 3 q^{72} + 8 q^{73} + 16 q^{74} + 9 q^{75} + 36 q^{76} - 40 q^{77} + 30 q^{78} + 17 q^{79} - 3 q^{80} - 6 q^{81} + 48 q^{82} + 24 q^{83} - 25 q^{84} - 26 q^{85} - 22 q^{86} - 6 q^{87} + 2 q^{88} - 18 q^{89} - 6 q^{90} + 22 q^{91} - 6 q^{92} - 11 q^{93} - 3 q^{94} + 16 q^{95} + 3 q^{96} - 4 q^{97} - 62 q^{98} - 28 q^{99}+O(q^{100}) \) 12 * q + q^2 + 6 * q^3 - 3 * q^4 - 3 * q^5 + 2 * q^6 - 2 * q^7 - 6 * q^8 - 6 * q^9 + 3 * q^10 + 14 * q^11 + 3 * q^12 - q^14 - 6 * q^15 + 7 * q^16 - 15 * q^17 + q^18 + q^19 + 34 * q^20 - 4 * q^21 - 12 * q^22 + 6 * q^23 - 3 * q^24 - 9 * q^25 + 15 * q^26 - 12 * q^27 - 2 * q^28 - 12 * q^29 - 3 * q^30 + 11 * q^31 - 3 * q^32 - 14 * q^33 + 30 * q^34 - q^35 + 6 * q^36 + 5 * q^37 - 14 * q^38 + 17 * q^40 + 36 * q^41 - 17 * q^42 - 74 * q^43 + 10 * q^44 - 3 * q^45 - q^46 - 3 * q^47 + 14 * q^48 - 6 * q^49 - 60 * q^50 + 15 * q^51 + 7 * q^52 + 15 * q^53 - q^54 - 4 * q^55 - 21 * q^56 + 2 * q^57 - 4 * q^58 + 2 * q^59 + 17 * q^60 + 12 * q^61 + 72 * q^62 - 2 * q^63 - 46 * q^64 + 17 * q^65 - 6 * q^66 + 10 * q^67 + q^68 + 12 * q^69 - 56 * q^70 - 42 * q^71 + 3 * q^72 + 8 * q^73 + 16 * q^74 + 9 * q^75 + 36 * q^76 - 40 * q^77 + 30 * q^78 + 17 * q^79 - 3 * q^80 - 6 * q^81 + 48 * q^82 + 24 * q^83 - 25 * q^84 - 26 * q^85 - 22 * q^86 - 6 * q^87 + 2 * q^88 - 18 * q^89 - 6 * q^90 + 22 * q^91 - 6 * q^92 - 11 * q^93 - 3 * q^94 + 16 * q^95 + 3 * q^96 - 4 * q^97 - 62 * q^98 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−1.02170	+	1.76964i	−0.722451	+	1.25132i	0.237563	+	0.971372i	$0.423651\pi$
$2$	−1.02170	+	1.76964i	−0.722451	+	1.25132i	−0.960015	+	0.279950i	$0.909682\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−1.08774	−	1.88403i	−0.543871	−	0.942013i
$5$	−0.971745	+	1.68311i	−0.434577	+	0.752710i	−0.997261	−	0.0739621i	$-0.976436\pi$
$5$	−0.971745	+	1.68311i	−0.434577	+	0.752710i	0.562684	+	0.826672i	$0.309769\pi$
$6$	−2.04340			−0.834215
$7$	−1.16166	−	2.37709i	−0.439065	−	0.898455i
$7$	−1.16166	−	2.37709i	−0.439065	−	0.898455i
$8$	0.358585			0.126779
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.98566	−	3.43927i	−0.627922	−	1.08759i
$11$	2.83264	+	4.90628i	0.854074	+	1.47930i	0.877501	+	0.479575i	$0.159209\pi$
$11$	2.83264	+	4.90628i	0.854074	+	1.47930i	−0.0234266	+	0.999726i	$0.507458\pi$
$12$	1.08774	−	1.88403i	0.314004	−	0.543871i
$13$	−6.17812			−1.71350			−0.856751	−	0.515730i	$-0.827521\pi$
$13$	−6.17812			−1.71350			−0.856751	+	0.515730i	$0.827521\pi$
$14$	5.39345	+	0.372961i	1.44146	+	0.0996781i
$15$	−1.94349			−0.501807
$16$	1.80912	−	3.13348i	0.452279	−	0.783371i
$17$	−3.61732	−	6.26537i	−0.877328	−	1.51958i	−0.854262	−	0.519842i	$-0.825991\pi$
$17$	−3.61732	−	6.26537i	−0.877328	−	1.51958i	−0.0230655	−	0.999734i	$-0.507343\pi$
$18$	−1.02170	−	1.76964i	−0.240817	−	0.417107i
$19$	−0.395110	+	0.684350i	−0.0906444	+	0.157001i	−0.907782	−	0.419441i	$-0.862226\pi$
$19$	−0.395110	+	0.684350i	−0.0906444	+	0.157001i	0.817138	+	0.576442i	$0.195559\pi$
$20$	4.22803			0.945417
$21$	1.47779	−	2.19457i	0.322480	−	0.478894i
$22$	−11.5765			−2.46811
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$24$	0.179293	+	0.310544i	0.0365980	+	0.0633896i
$25$	0.611424	+	1.05902i	0.122285	+	0.211804i
$26$	6.31219	−	10.9330i	1.23792	−	2.14414i
$27$	−1.00000			−0.192450
$28$	−3.21491	+	4.77425i	−0.607561	+	0.902249i
$29$	−5.34085			−0.991770			−0.495885	−	0.868388i	$-0.665156\pi$
$29$	−5.34085			−0.991770			−0.495885	+	0.868388i	$0.665156\pi$
$30$	1.98566	−	3.43927i	0.362531	−	0.627922i
$31$	−0.455658	−	0.789223i	−0.0818386	−	0.141749i	0.822201	−	0.569197i	$-0.192746\pi$
$31$	−0.455658	−	0.789223i	−0.0818386	−	0.141749i	−0.904040	+	0.427449i	$0.859413\pi$
$32$	4.05534	+	7.02405i	0.716889	+	1.24169i
$33$	−2.83264	+	4.90628i	−0.493100	+	0.854074i
$34$	14.7832			2.53531
$35$	5.12974	+	0.354726i	0.867084	+	0.0599596i
$36$	2.17548			0.362581
$37$	0.486660	−	0.842920i	0.0800064	−	0.138575i	−0.823246	−	0.567685i	$-0.807839\pi$
$37$	0.486660	−	0.842920i	0.0800064	−	0.138575i	0.903252	+	0.429110i	$0.141173\pi$
$38$	−0.807367	−	1.39840i	−0.130972	−	0.226851i
$39$	−3.08906	−	5.35041i	−0.494645	−	0.856751i
$40$	−0.348454	+	0.603539i	−0.0550953	+	0.0954279i
$41$	−1.51843			−0.237140			−0.118570	−	0.992946i	$-0.537831\pi$
$41$	−1.51843			−0.237140			−0.118570	+	0.992946i	$0.537831\pi$
$42$	2.37373	+	4.85734i	0.366275	+	0.749505i
$43$	−2.70342			−0.412268			−0.206134	−	0.978524i	$-0.566088\pi$
$43$	−2.70342			−0.412268			−0.206134	+	0.978524i	$0.566088\pi$
$44$	6.16237	−	10.6735i	0.929013	−	1.60910i
$45$	−0.971745	−	1.68311i	−0.144859	−	0.250903i
$46$	1.02170	+	1.76964i	0.150641	+	0.260919i
$47$	0.764197	−	1.32363i	0.111470	−	0.193071i	−0.804893	−	0.593419i	$-0.797778\pi$
$47$	0.764197	−	1.32363i	0.111470	−	0.193071i	0.916363	+	0.400348i	$0.131111\pi$
$48$	3.61824			0.522247
$49$	−4.30111	+	5.52273i	−0.614444	+	0.788961i
$50$	−2.49877			−0.353379
$51$	3.61732	−	6.26537i	0.506525	−	0.877328i
$52$	6.72020	+	11.6397i	0.931924	+	1.61414i
$53$	4.47902	+	7.75789i	0.615240	+	1.06563i	0.990342	+	0.138644i	$0.0442744\pi$
$53$	4.47902	+	7.75789i	0.615240	+	1.06563i	−0.375102	+	0.926984i	$0.622392\pi$
$54$	1.02170	−	1.76964i	0.139036	−	0.240817i
$55$	−11.0104			−1.48465
$56$	−0.416553	−	0.852390i	−0.0556643	−	0.113905i
$57$	−0.790220			−0.104667
$58$	5.45674	−	9.45136i	0.716506	−	1.24102i
$59$	5.44656	+	9.43371i	0.709081	+	1.22817i	0.965198	+	0.261519i	$0.0842235\pi$
$59$	5.44656	+	9.43371i	0.709081	+	1.22817i	−0.256117	+	0.966646i	$0.582443\pi$
$60$	2.11402	+	3.66158i	0.272918	+	0.472708i
$61$	3.15887	−	5.47133i	0.404452	−	0.700532i	−0.589805	−	0.807546i	$-0.700795\pi$
$61$	3.15887	−	5.47133i	0.404452	−	0.700532i	0.994258	+	0.107014i	$0.0341288\pi$
$62$	1.86218			0.236497
$63$	2.63945	+	0.182520i	0.332539	+	0.0229954i
$64$	−9.33688			−1.16711
$65$	6.00356	−	10.3985i	0.744649	−	1.28977i
$66$	−5.78823	−	10.0255i	−0.712481	−	1.23405i
$67$	−3.65917	−	6.33786i	−0.447038	−	0.774293i	0.551153	−	0.834404i	$-0.314188\pi$
$67$	−3.65917	−	6.33786i	−0.447038	−	0.774293i	−0.998192	+	0.0601108i	$0.980855\pi$
$68$	−7.86941	+	13.6302i	−0.954307	+	1.65291i
$69$	1.00000			0.120386
$70$	−5.86879	+	8.71535i	−0.701455	+	1.04168i
$71$	−8.75692			−1.03926			−0.519628	−	0.854393i	$-0.673929\pi$
$71$	−8.75692			−1.03926			−0.519628	+	0.854393i	$0.673929\pi$
$72$	−0.179293	+	0.310544i	−0.0211299	+	0.0365980i
$73$	0.437625	+	0.757990i	0.0512202	+	0.0887160i	0.890499	−	0.454986i	$-0.150356\pi$
$73$	0.437625	+	0.757990i	0.0512202	+	0.0887160i	−0.839279	+	0.543702i	$0.817022\pi$
$74$	0.994442	+	1.72242i	0.115601	+	0.200228i
$75$	−0.611424	+	1.05902i	−0.0706012	+	0.122285i
$76$	1.71911			0.197196
$77$	8.37211	−	12.4329i	0.954091	−	1.41686i
$78$	12.6244			1.42943
$79$	−2.98327	+	5.16718i	−0.335644	+	0.581353i	−0.983608	−	0.180318i	$-0.942287\pi$
$79$	−2.98327	+	5.16718i	−0.335644	+	0.581353i	0.647964	+	0.761671i	$0.275621\pi$
$80$	3.51600	+	6.08989i	0.393101	+	0.680871i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.55138	−	2.68708i	0.171322	−	0.296738i
$83$	−0.273554			−0.0300265			−0.0150132	−	0.999887i	$-0.504779\pi$
$83$	−0.273554			−0.0300265			−0.0150132	+	0.999887i	$0.504779\pi$
$84$	−5.74208	−	0.397069i	−0.626512	−	0.0433238i
$85$	14.0604			1.52507
$86$	2.76208	−	4.78407i	0.297843	−	0.515879i
$87$	−2.67042	−	4.62531i	−0.286299	−	0.495885i
$88$	1.01575	+	1.75932i	0.108279	+	0.187544i
$89$	−8.81350	+	15.2654i	−0.934229	+	1.61813i	−0.158227	+	0.987403i	$0.550578\pi$
$89$	−8.81350	+	15.2654i	−0.934229	+	1.61813i	−0.776002	+	0.630730i	$0.782755\pi$
$90$	3.97133			0.418615
$91$	7.17686	+	14.6859i	0.752339	+	1.53950i
$92$	−2.17548			−0.226810
$93$	0.455658	−	0.789223i	0.0472495	−	0.0818386i
$94$	1.56156	+	2.70470i	0.161063	+	0.278969i
$95$	−0.767892	−	1.33003i	−0.0787840	−	0.136458i
$96$	−4.05534	+	7.02405i	−0.413896	+	0.716889i
$97$	3.09620			0.314372			0.157186	−	0.987569i	$-0.449758\pi$
$97$	3.09620			0.314372			0.157186	+	0.987569i	$0.449758\pi$
$98$	−5.37878	−	13.2540i	−0.543338	−	1.33885i
$99$	−5.66529			−0.569383
$100$	1.33014	−	2.30388i	0.133014	−	0.230388i
$101$	−6.71382	−	11.6287i	−0.668050	−	1.15710i	−0.978449	−	0.206491i	$-0.933796\pi$
$101$	−6.71382	−	11.6287i	−0.668050	−	1.15710i	0.310398	−	0.950607i	$-0.399538\pi$
$102$	7.39162	+	12.8027i	0.731880	+	1.26765i
$103$	−3.16827	+	5.48760i	−0.312178	+	0.540709i	−0.978834	−	0.204657i	$-0.934392\pi$
$103$	−3.16827	+	5.48760i	−0.312178	+	0.540709i	0.666655	+	0.745366i	$0.267725\pi$
$104$	−2.21538			−0.217236
$105$	2.25767	+	4.61985i	0.220326	+	0.450851i
$106$	−18.3049			−1.77792
$107$	−7.98043	+	13.8225i	−0.771497	+	1.33627i	0.165245	+	0.986253i	$0.447159\pi$
$107$	−7.98043	+	13.8225i	−0.771497	+	1.33627i	−0.936742	+	0.350020i	$0.886175\pi$
$108$	1.08774	+	1.88403i	0.104668	+	0.181290i
$109$	0.0235357	+	0.0407651i	0.00225431	+	0.00390459i	0.867150	−	0.498046i	$-0.165949\pi$
$109$	0.0235357	+	0.0407651i	0.00225431	+	0.00390459i	−0.864896	+	0.501951i	$0.832616\pi$
$110$	11.2494	−	19.4845i	1.07258	−	1.85777i
$111$	0.973320			0.0923835
$112$	−9.55015	−	0.660400i	−0.902404	−	0.0624020i
$113$	−6.27141			−0.589965			−0.294982	−	0.955503i	$-0.595314\pi$
$113$	−6.27141			−0.589965			−0.294982	+	0.955503i	$0.595314\pi$
$114$	0.807367	−	1.39840i	0.0756169	−	0.130972i
$115$	0.971745	+	1.68311i	0.0906157	+	0.156951i
$116$	5.80947	+	10.0623i	0.539395	+	0.934260i
$117$	3.08906	−	5.35041i	0.285584	−	0.494645i
$118$	−22.2590			−2.04911
$119$	−10.6913	+	15.8769i	−0.980067	+	1.45543i
$120$	−0.696907			−0.0636186
$121$	−10.5477	+	18.2692i	−0.958886	+	1.66084i
$122$	6.45484	+	11.1801i	0.584394	+	1.01220i
$123$	−0.759217	−	1.31500i	−0.0684563	−	0.118570i
$124$	−0.991277	+	1.71694i	−0.0890193	+	0.154186i
$125$	−12.0940			−1.08172
$126$	−3.01972	+	4.48438i	−0.269018	+	0.399501i
$127$	−12.4325			−1.10320			−0.551601	−	0.834108i	$-0.685983\pi$
$127$	−12.4325			−1.10320			−0.551601	+	0.834108i	$0.685983\pi$
$128$	1.42882	−	2.47479i	0.126291	−	0.218743i
$129$	−1.35171	−	2.34123i	−0.119011	−	0.206134i
$130$	12.2677	+	21.2482i	1.07595	+	1.86359i
$131$	1.65549	−	2.86739i	0.144641	−	0.250525i	−0.784598	−	0.620005i	$-0.787131\pi$
$131$	1.65549	−	2.86739i	0.144641	−	0.250525i	0.929239	+	0.369480i	$0.120464\pi$
$132$	12.3247			1.07273
$133$	2.08574	+	0.144231i	0.180857	+	0.0125064i
$134$	14.9543			1.29185
$135$	0.971745	−	1.68311i	0.0836345	−	0.144859i
$136$	−1.29712	−	2.24667i	−0.111227	−	0.192651i
$137$	6.52210	+	11.2966i	0.557220	+	0.965134i	0.997727	+	0.0673847i	$0.0214655\pi$
$137$	6.52210	+	11.2966i	0.557220	+	0.965134i	−0.440507	+	0.897749i	$0.645201\pi$
$138$	−1.02170	+	1.76964i	−0.0869729	+	0.150641i
$139$	−11.3674			−0.964169			−0.482084	−	0.876125i	$-0.660120\pi$
$139$	−11.3674			−0.964169			−0.482084	+	0.876125i	$0.660120\pi$
$140$	−4.91152	−	10.0504i	−0.415099	−	0.849415i
$141$	1.52839			0.128714
$142$	8.94694	−	15.4966i	0.750811	−	1.30044i
$143$	−17.5004	−	30.3116i	−1.46346	−	2.53478i
$144$	1.80912	+	3.13348i	0.150760	+	0.261124i
$145$	5.18994	−	8.98924i	0.431001	−	0.746516i
$146$	−1.78849			−0.148016
$147$	−6.93337	−	0.963504i	−0.571855	−	0.0794685i
$148$	−2.11744			−0.174053
$149$	−8.10300	+	14.0348i	−0.663824	+	1.14978i	0.315779	+	0.948833i	$0.397734\pi$
$149$	−8.10300	+	14.0348i	−0.663824	+	1.14978i	−0.979603	+	0.200944i	$0.935599\pi$
$150$	−1.24938	−	2.16400i	−0.102012	−	0.176690i
$151$	6.46687	+	11.2009i	0.526266	+	0.911520i	0.999532	+	0.0305999i	$0.00974177\pi$
$151$	6.46687	+	11.2009i	0.526266	+	0.911520i	−0.473266	+	0.880920i	$0.656925\pi$
$152$	−0.141681	+	0.245398i	−0.0114918	+	0.0199044i
$153$	7.23463			0.584885
$154$	13.4479	+	27.5183i	1.08366	+	2.21748i
$155$	1.77113			0.142261
$156$	−6.72020	+	11.6397i	−0.538047	+	0.931924i
$157$	4.86721	+	8.43026i	0.388446	+	0.672808i	0.992241	−	0.124332i	$-0.0396787\pi$
$157$	4.86721	+	8.43026i	0.388446	+	0.672808i	−0.603795	+	0.797140i	$0.706345\pi$
$158$	−6.09602	−	10.5586i	−0.484973	−	0.839999i
$159$	−4.47902	+	7.75789i	−0.355209	+	0.615240i
$160$	−15.7630			−1.24618
$161$	−2.63945	−	0.182520i	−0.208018	−	0.0143846i
$162$	2.04340			0.160545
$163$	12.0461	−	20.8645i	0.943525	−	1.63423i	0.184848	−	0.982767i	$-0.440821\pi$
$163$	12.0461	−	20.8645i	0.943525	−	1.63423i	0.758677	−	0.651467i	$-0.225846\pi$
$164$	1.65167	+	2.86077i	0.128973	+	0.223389i
$165$	−5.50521	−	9.53531i	−0.428580	−	0.742323i
$166$	0.279490	−	0.484091i	0.0216927	−	0.0375728i
$167$	−12.2582			−0.948566			−0.474283	−	0.880373i	$-0.657293\pi$
$167$	−12.2582			−0.948566			−0.474283	+	0.880373i	$0.657293\pi$
$168$	0.529914	−	0.786941i	0.0408838	−	0.0607138i
$169$	25.1692			1.93609
$170$	−14.3655	+	24.8818i	−1.10179	+	1.90835i
$171$	−0.395110	−	0.684350i	−0.0302148	−	0.0523336i
$172$	2.94062	+	5.09331i	0.224220	+	0.388361i
$173$	2.94398	−	5.09912i	0.223826	−	0.387679i	−0.732140	−	0.681154i	$-0.761478\pi$
$173$	2.94398	−	5.09912i	0.223826	−	0.387679i	0.955967	+	0.293475i	$0.0948118\pi$
$174$	10.9135			0.827349
$175$	1.80711	−	2.68363i	0.136605	−	0.202863i
$176$	20.4984			1.54512
$177$	−5.44656	+	9.43371i	−0.409388	+	0.709081i
$178$	−18.0095	−	31.1934i	−1.34987	−	2.33804i
$179$	8.48661	+	14.6992i	0.634319	+	1.09867i	0.986659	+	0.162801i	$0.0520528\pi$
$179$	8.48661	+	14.6992i	0.634319	+	1.09867i	−0.352340	+	0.935872i	$0.614614\pi$
$180$	−2.11402	+	3.66158i	−0.157569	+	0.272918i
$181$	19.1241			1.42149			0.710743	−	0.703452i	$-0.248359\pi$
$181$	19.1241			1.42149			0.710743	+	0.703452i	$0.248359\pi$
$182$	−33.3214	−	2.30420i	−2.46994	−	0.170799i
$183$	6.31775			0.467021
$184$	0.179293	−	0.310544i	0.0132176	−	0.0228936i
$185$	0.945819	+	1.63821i	0.0695380	+	0.120443i
$186$	0.931092	+	1.61270i	0.0682709	+	0.118249i
$187$	20.4931	−	35.4952i	1.49861	−	2.59566i
$188$	−3.32500			−0.242500
$189$	1.16166	+	2.37709i	0.0844981	+	0.172908i
$190$	3.13822			0.227670
$191$	10.3435	−	17.9155i	0.748432	−	1.29632i	−0.200142	−	0.979767i	$-0.564140\pi$
$191$	10.3435	−	17.9155i	0.748432	−	1.29632i	0.948574	−	0.316555i	$-0.102526\pi$
$192$	−4.66844	−	8.08598i	−0.336916	−	0.583555i
$193$	−1.11450	−	1.93038i	−0.0802237	−	0.138952i	0.823122	−	0.567864i	$-0.192230\pi$
$193$	−1.11450	−	1.93038i	−0.0802237	−	0.138952i	−0.903346	+	0.428913i	$0.858897\pi$
$194$	−3.16339	+	5.47916i	−0.227118	+	0.393380i
$195$	12.0071			0.859847
$196$	15.0834	+	2.09609i	1.07739	+	0.149721i
$197$	19.3710			1.38013			0.690064	−	0.723748i	$-0.257582\pi$
$197$	19.3710			1.38013			0.690064	+	0.723748i	$0.257582\pi$
$198$	5.78823	−	10.0255i	0.411351	−	0.712481i
$199$	−12.3420	−	21.3770i	−0.874902	−	1.51538i	−0.856867	−	0.515538i	$-0.827592\pi$
$199$	−12.3420	−	21.3770i	−0.874902	−	1.51538i	−0.0180354	−	0.999837i	$-0.505741\pi$
$200$	0.219248	+	0.379748i	0.0155032	+	0.0268523i
$201$	3.65917	−	6.33786i	0.258098	−	0.447038i
$202$	27.4381			1.93054
$203$	6.20423	+	12.6957i	0.435452	+	0.891061i
$204$	−15.7388			−1.10194
$205$	1.47553	−	2.55569i	0.103056	−	0.178497i
$206$	−6.47403	−	11.2134i	−0.451067	−	0.781272i
$207$	0.500000	+	0.866025i	0.0347524	+	0.0601929i
$208$	−11.1769	+	19.3590i	−0.774982	+	1.34231i
$209$	−4.47682			−0.309668
$210$	−10.4821	−	0.724846i	−0.723334	−	0.0500192i
$211$	9.90378			0.681804			0.340902	−	0.940099i	$-0.389267\pi$
$211$	9.90378			0.681804			0.340902	+	0.940099i	$0.389267\pi$
$212$	9.74403	−	16.8772i	0.669223	−	1.15913i
$213$	−4.37846	−	7.58371i	−0.300007	−	0.519628i
$214$	−16.3072	−	28.2449i	−1.11474	−	1.93078i
$215$	2.62703	−	4.55016i	0.179162	−	0.310318i
$216$	−0.358585			−0.0243987
$217$	−1.34673	+	1.99995i	−0.0914223	+	0.135765i
$218$	−0.0961859			−0.00651453
$219$	−0.437625	+	0.757990i	−0.0295720	+	0.0512202i
$220$	11.9765	+	20.7439i	0.807456	+	1.39856i
$221$	22.3482	+	38.7082i	1.50330	+	2.60380i
$222$	−0.994442	+	1.72242i	−0.0667425	+	0.115601i
$223$	2.21461			0.148301			0.0741507	−	0.997247i	$-0.476375\pi$
$223$	2.21461			0.148301			0.0741507	+	0.997247i	$0.476375\pi$
$224$	11.9859	−	17.7994i	0.800840	−	1.18927i
$225$	−1.22285			−0.0815232
$226$	6.40750	−	11.0981i	0.426221	−	0.738236i
$227$	2.79017	+	4.83271i	0.185190	+	0.320758i	0.943640	−	0.330972i	$-0.107377\pi$
$227$	2.79017	+	4.83271i	0.185190	+	0.320758i	−0.758451	+	0.651730i	$0.774043\pi$
$228$	0.859555	+	1.48879i	0.0569254	+	0.0985978i
$229$	−3.48930	+	6.04364i	−0.230579	+	0.399375i	−0.957979	−	0.286839i	$-0.907395\pi$
$229$	−3.48930	+	6.04364i	−0.230579	+	0.399375i	0.727400	+	0.686214i	$0.240729\pi$
$230$	−3.97133			−0.261862
$231$	14.9532	+	1.03403i	0.983851	+	0.0680341i
$232$	−1.91515			−0.125736
$233$	−12.2021	+	21.1347i	−0.799388	+	1.38458i	0.120628	+	0.992698i	$0.461509\pi$
$233$	−12.2021	+	21.1347i	−0.799388	+	1.38458i	−0.920015	+	0.391882i	$0.871824\pi$
$234$	6.31219	+	10.9330i	0.412640	+	0.714714i
$235$	1.48521	+	2.57246i	0.0968843	+	0.167809i
$236$	11.8489	−	20.5229i	0.771298	−	1.33593i
$237$	−5.96655			−0.387569
$238$	−17.1731	−	35.1411i	−1.11316	−	2.27786i
$239$	0.424159			0.0274365			0.0137183	−	0.999906i	$-0.495633\pi$
$239$	0.424159			0.0274365			0.0137183	+	0.999906i	$0.495633\pi$
$240$	−3.51600	+	6.08989i	−0.226957	+	0.393101i
$241$	8.15623	+	14.1270i	0.525389	+	0.910000i	0.999563	+	0.0295691i	$0.00941352\pi$
$241$	8.15623	+	14.1270i	0.525389	+	0.910000i	−0.474174	+	0.880431i	$0.657253\pi$
$242$	−21.5533	−	37.3314i	−1.38550	−	2.39975i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−13.7442			−0.879880
$245$	−5.11578	−	12.6059i	−0.326835	−	0.805363i
$246$	3.10277			0.197825
$247$	2.44104	−	4.22800i	0.155319	−	0.269021i
$248$	−0.163392	−	0.283004i	−0.0103754	−	0.0179708i
$249$	−0.136777	−	0.236905i	−0.00866790	−	0.0150132i
$250$	12.3565	−	21.4021i	0.781493	−	1.35358i
$251$	−15.9242			−1.00513			−0.502564	−	0.864540i	$-0.667610\pi$
$251$	−15.9242			−1.00513			−0.502564	+	0.864540i	$0.667610\pi$
$252$	−2.52717	−	5.17132i	−0.159197	−	0.325763i
$253$	5.66529			0.356174
$254$	12.7022	−	22.0009i	0.797010	−	1.38046i
$255$	7.03021	+	12.1767i	0.440249	+	0.762534i
$256$	−6.41723	−	11.1150i	−0.401077	−	0.694686i
$257$	15.0785	−	26.1167i	0.940569	−	1.62911i	0.176181	−	0.984358i	$-0.443626\pi$
$257$	15.0785	−	26.1167i	0.940569	−	1.62911i	0.764389	−	0.644756i	$-0.223041\pi$
$258$	5.52417			0.343920
$259$	−2.56903	−	0.177650i	−0.159632	−	0.0110387i
$260$	−26.1213			−1.61997
$261$	2.67042	−	4.62531i	0.165295	−	0.286299i
$262$	3.38283	+	5.85923i	0.208992	+	0.361984i
$263$	−7.58281	−	13.1338i	−0.467576	−	0.809866i	0.531737	−	0.846909i	$-0.321539\pi$
$263$	−7.58281	−	13.1338i	−0.467576	−	0.809866i	−0.999314	+	0.0370435i	$0.988206\pi$
$264$	−1.01575	+	1.75932i	−0.0625148	+	0.108279i
$265$	−17.4098			−1.06948
$266$	−2.38624	+	3.54365i	−0.146310	+	0.217275i
$267$	−17.6270			−1.07876
$268$	−7.96046	+	13.7879i	−0.486263	+	0.842231i
$269$	−0.235417	−	0.407754i	−0.0143536	−	0.0248612i	0.858759	−	0.512379i	$-0.171236\pi$
$269$	−0.235417	−	0.407754i	−0.0143536	−	0.0248612i	−0.873113	+	0.487518i	$0.837902\pi$
$270$	1.98566	+	3.43927i	0.120844	+	0.209307i
$271$	3.64368	−	6.31104i	0.221338	−	0.383368i	−0.733877	−	0.679283i	$-0.762291\pi$
$271$	3.64368	−	6.31104i	0.221338	−	0.383368i	0.955214	+	0.295914i	$0.0956243\pi$
$272$	−26.1766			−1.58719
$273$	−9.12997	+	13.5583i	−0.552571	+	0.820586i
$274$	−26.6545			−1.61026
$275$	−3.46389	+	5.99964i	−0.208881	+	0.361792i
$276$	−1.08774	−	1.88403i	−0.0654744	−	0.113405i
$277$	−1.48011	−	2.56362i	−0.0889310	−	0.154033i	0.818129	−	0.575035i	$-0.195012\pi$
$277$	−1.48011	−	2.56362i	−0.0889310	−	0.154033i	−0.907060	+	0.421002i	$0.861678\pi$
$278$	11.6141	−	20.1161i	0.696565	−	1.20649i
$279$	0.911316			0.0545591
$280$	1.83945	+	0.127199i	0.109928	+	0.00760162i
$281$	7.16141			0.427214			0.213607	−	0.976920i	$-0.431479\pi$
$281$	7.16141			0.427214			0.213607	+	0.976920i	$0.431479\pi$
$282$	−1.56156	+	2.70470i	−0.0929895	+	0.161063i
$283$	10.0053	+	17.3297i	0.594753	+	1.03014i	0.993582	+	0.113117i	$0.0360835\pi$
$283$	10.0053	+	17.3297i	0.594753	+	1.03014i	−0.398828	+	0.917026i	$0.630583\pi$
$284$	9.52527	+	16.4983i	0.565221	+	0.978991i
$285$	0.767892	−	1.33003i	0.0454860	−	0.0787840i
$286$	71.5207			4.22911
$287$	1.76390	+	3.60945i	0.104120	+	0.213059i
$288$	−8.11067			−0.477926
$289$	−17.6699	+	30.6052i	−1.03941	+	1.80031i
$290$	10.6051	+	18.3686i	0.622754	+	1.07864i
$291$	1.54810	+	2.68139i	0.0907514	+	0.157186i
$292$	0.952047	−	1.64899i	0.0557144	−	0.0965001i
$293$	6.27910			0.366829			0.183414	−	0.983036i	$-0.441285\pi$
$293$	6.27910			0.366829			0.183414	+	0.983036i	$0.441285\pi$
$294$	8.78888	−	11.2851i	0.512578	−	0.658163i
$295$	−21.1707			−1.23260
$296$	0.174509	−	0.302259i	0.0101431	−	0.0175684i
$297$	−2.83264	−	4.90628i	−0.164367	−	0.284691i
$298$	−16.5577	−	28.6787i	−0.959161	−	1.66132i
$299$	−3.08906	+	5.35041i	−0.178645	+	0.309422i
$300$	2.66029			0.153592
$301$	3.14045	+	6.42627i	0.181012	+	0.370404i
$302$	−26.4288			−1.52081
$303$	6.71382	−	11.6287i	0.385699	−	0.668050i
$304$	1.42960	+	2.47614i	0.0819932	+	0.142016i
$305$	6.13924	+	10.6335i	0.351532	+	0.608871i
$306$	−7.39162	+	12.8027i	−0.422551	+	0.731880i
$307$	25.1923			1.43780			0.718900	−	0.695114i	$-0.244646\pi$
$307$	25.1923			1.43780			0.718900	+	0.695114i	$0.244646\pi$
$308$	−32.5305	−	2.24951i	−1.85360	−	0.128178i
$309$	−6.33653			−0.360473
$310$	−1.80957	+	3.13426i	−0.102776	+	0.178014i
$311$	−5.96103	−	10.3248i	−0.338019	−	0.585466i	0.646041	−	0.763303i	$-0.276423\pi$
$311$	−5.96103	−	10.3248i	−0.338019	−	0.585466i	−0.984060	+	0.177837i	$0.943090\pi$
$312$	−1.10769	−	1.91858i	−0.0627107	−	0.108618i
$313$	−5.02115	+	8.69689i	−0.283812	+	0.491578i	−0.972320	−	0.233651i	$-0.924933\pi$
$313$	−5.02115	+	8.69689i	−0.283812	+	0.491578i	0.688508	+	0.725229i	$0.258266\pi$
$314$	−19.8913			−1.12253
$315$	−2.87207	+	4.26512i	−0.161823	+	0.240312i
$316$	12.9801			0.730189
$317$	4.43105	−	7.67480i	0.248872	−	0.431060i	−0.714341	−	0.699798i	$-0.753273\pi$
$317$	4.43105	−	7.67480i	0.248872	−	0.431060i	0.963213	+	0.268738i	$0.0866067\pi$
$318$	−9.15243	−	15.8525i	−0.513243	−	0.888962i
$319$	−15.1287	−	26.2037i	−0.847046	−	1.46713i
$320$	9.07307	−	15.7150i	0.507200	−	0.878496i
$321$	−15.9609			−0.890849
$322$	3.01972	−	4.48438i	0.168282	−	0.249905i
$323$	5.71695			0.318099
$324$	−1.08774	+	1.88403i	−0.0604301	+	0.104668i
$325$	−3.77745	−	6.54274i	−0.209535	−	0.362926i
$326$	24.6151	+	42.6345i	1.36330	+	2.36131i
$327$	−0.0235357	+	0.0407651i	−0.00130153	+	0.00225431i
$328$	−0.544489			−0.0300644
$329$	−4.03412	−	0.278962i	−0.222408	−	0.0153797i
$330$	22.4987			1.23851
$331$	11.4496	−	19.8313i	0.629327	−	1.09003i	−0.358360	−	0.933584i	$-0.616664\pi$
$331$	11.4496	−	19.8313i	0.629327	−	1.09003i	0.987687	−	0.156443i	$-0.0500028\pi$
$332$	0.297556	+	0.515383i	0.0163305	+	0.0282853i
$333$	0.486660	+	0.842920i	0.0266688	+	0.0461917i
$334$	12.5242	−	21.6925i	0.685292	−	1.18696i
$335$	14.2231			0.777091
$336$	−4.20315	−	8.60087i	−0.229301	−	0.469216i
$337$	12.2517			0.667392			0.333696	−	0.942681i	$-0.391704\pi$
$337$	12.2517			0.667392			0.333696	+	0.942681i	$0.391704\pi$
$338$	−25.7153	+	44.5403i	−1.39873	+	2.42267i
$339$	−3.13570	−	5.43120i	−0.170308	−	0.294982i
$340$	−15.2941	−	26.4902i	−0.829440	−	1.43663i
$341$	2.58143	−	4.47117i	0.139792	−	0.242128i
$342$	1.61473			0.0873149
$343$	18.1244	+	3.80860i	0.978627	+	0.205645i
$344$	−0.969407			−0.0522669
$345$	−0.971745	+	1.68311i	−0.0523170	+	0.0906157i
$346$	6.01572	+	10.4195i	0.323407	+	0.560158i
$347$	3.22916	+	5.59307i	0.173351	+	0.300252i	0.939589	−	0.342304i	$-0.111207\pi$
$347$	3.22916	+	5.59307i	0.173351	+	0.300252i	−0.766239	+	0.642556i	$0.777874\pi$
$348$	−5.80947	+	10.0623i	−0.311420	+	0.539395i
$349$	20.5047			1.09759			0.548795	−	0.835957i	$-0.315087\pi$
$349$	20.5047			1.09759			0.548795	+	0.835957i	$0.315087\pi$
$350$	2.90271	+	5.93980i	0.155156	+	0.317495i
$351$	6.17812			0.329764
$352$	−22.9747	+	39.7933i	−1.22455	+	2.12099i
$353$	−7.25563	−	12.5671i	−0.386178	−	0.668881i	0.605754	−	0.795652i	$-0.292872\pi$
$353$	−7.25563	−	12.5671i	−0.386178	−	0.668881i	−0.991932	+	0.126772i	$0.959538\pi$
$354$	−11.1295	−	19.2769i	−0.591526	−	1.02455i
$355$	8.50949	−	14.7389i	0.451637	−	0.782258i
$356$	38.3473			2.03240
$357$	−19.0954	−	1.32046i	−1.01064	−	0.0698864i
$358$	−34.6831			−1.83306
$359$	−2.33890	+	4.05109i	−0.123442	+	0.213808i	−0.921123	−	0.389272i	$-0.872727\pi$
$359$	−2.33890	+	4.05109i	−0.123442	+	0.213808i	0.797681	+	0.603080i	$0.206060\pi$
$360$	−0.348454	−	0.603539i	−0.0183651	−	0.0318093i
$361$	9.18778	+	15.9137i	0.483567	+	0.837563i
$362$	−19.5391	+	33.8428i	−1.02695	+	1.77874i
$363$	−21.0955			−1.10723
$364$	19.8621	−	29.4959i	1.04106	−	1.54601i
$365$	−1.70104			−0.0890366
$366$	−6.45484	+	11.1801i	−0.337400	+	0.584394i
$367$	14.0330	+	24.3058i	0.732515	+	1.26875i	0.955805	+	0.294002i	$0.0949872\pi$
$367$	14.0330	+	24.3058i	0.732515	+	1.26875i	−0.223289	+	0.974752i	$0.571679\pi$
$368$	−1.80912	−	3.13348i	−0.0943068	−	0.163344i
$369$	0.759217	−	1.31500i	0.0395233	−	0.0684563i
$370$	−3.86537			−0.200951
$371$	13.2381	−	19.6590i	0.687288	−	1.02065i
$372$	−1.98255			−0.102791
$373$	−7.31514	+	12.6702i	−0.378763	+	0.656037i	−0.990883	−	0.134728i	$-0.956984\pi$
$373$	−7.31514	+	12.6702i	−0.378763	+	0.656037i	0.612119	+	0.790765i	$0.290317\pi$
$374$	41.8757	+	72.5308i	2.16534	+	3.75048i
$375$	−6.04702	−	10.4737i	−0.312267	−	0.540862i
$376$	0.274030	−	0.474634i	0.0141320	−	0.0244774i
$377$	32.9964			1.69940
$378$	−5.39345	−	0.372961i	−0.277409	−	0.0191831i
$379$	−2.44369			−0.125524			−0.0627620	−	0.998029i	$-0.519991\pi$
$379$	−2.44369			−0.125524			−0.0627620	+	0.998029i	$0.519991\pi$
$380$	−1.67054	+	2.89345i	−0.0856967	+	0.148431i
$381$	−6.21623	−	10.7668i	−0.318467	−	0.551601i
$382$	21.1360	+	36.6086i	1.08141	+	1.87306i
$383$	−15.3896	+	26.6555i	−0.786371	+	1.36203i	0.141806	+	0.989894i	$0.454709\pi$
$383$	−15.3896	+	26.6555i	−0.786371	+	1.36203i	−0.928177	+	0.372140i	$0.878624\pi$
$384$	2.85764			0.145828
$385$	12.7903	+	26.1728i	0.651856	+	1.33389i
$386$	4.55475			0.231831
$387$	1.35171	−	2.34123i	0.0687113	−	0.119011i
$388$	−3.36787	−	5.83333i	−0.170978	−	0.296142i
$389$	−6.09275	−	10.5530i	−0.308915	−	0.535056i	0.669210	−	0.743073i	$-0.266632\pi$
$389$	−6.09275	−	10.5530i	−0.308915	−	0.535056i	−0.978125	+	0.208017i	$0.933299\pi$
$390$	−12.2677	+	21.2482i	−0.621197	+	1.07595i
$391$	−7.23463			−0.365871
$392$	−1.54231	+	1.98037i	−0.0778986	+	0.100024i
$393$	3.31098			0.167017
$394$	−19.7914	+	34.2797i	−0.997075	+	1.72698i
$395$	−5.79796	−	10.0424i	−0.291727	−	0.505286i
$396$	6.16237	+	10.6735i	0.309671	+	0.536366i
$397$	−10.6522	+	18.4501i	−0.534618	+	0.925986i	0.464563	+	0.885540i	$0.346211\pi$
$397$	−10.6522	+	18.4501i	−0.534618	+	0.925986i	−0.999182	+	0.0404462i	$0.987122\pi$
$398$	50.4394			2.52830
$399$	0.917964	+	1.87842i	0.0459557	+	0.0940387i
$400$	4.42455			0.221228
$401$	−3.70140	+	6.41101i	−0.184839	+	0.320151i	−0.943522	−	0.331309i	$-0.892510\pi$
$401$	−3.70140	+	6.41101i	−0.184839	+	0.320151i	0.758683	+	0.651460i	$0.225843\pi$
$402$	7.47714	+	12.9508i	0.372926	+	0.645927i
$403$	2.81511	+	4.87591i	0.140231	+	0.242886i
$404$	−14.6058	+	25.2980i	−0.726667	+	1.25862i
$405$	1.94349			0.0965728
$406$	−28.8056	−	1.99193i	−1.42960	−	0.0988578i
$407$	5.51414			0.273326
$408$	1.29712	−	2.24667i	0.0642168	−	0.111227i
$409$	−13.2337	−	22.9214i	−0.654364	−	1.13339i	−0.982053	−	0.188606i	$-0.939603\pi$
$409$	−13.2337	−	22.9214i	−0.654364	−	1.13339i	0.327689	−	0.944786i	$-0.393730\pi$
$410$	3.01510	+	5.22231i	0.148905	+	0.257911i
$411$	−6.52210	+	11.2966i	−0.321711	+	0.557220i
$412$	13.7850			0.679140
$413$	16.0977	−	23.9057i	0.792118	−	1.17632i
$414$	−2.04340			−0.100428
$415$	0.265825	−	0.460422i	0.0130488	−	0.0226012i
$416$	−25.0544	−	43.3954i	−1.22839	−	2.12764i
$417$	−5.68369	−	9.84444i	−0.278331	−	0.482084i
$418$	4.57397	−	7.92235i	0.223720	−	0.387495i
$419$	−30.7294			−1.50123			−0.750614	−	0.660741i	$-0.770242\pi$
$419$	−30.7294			−1.50123			−0.750614	+	0.660741i	$0.770242\pi$
$420$	6.24815	−	9.27871i	0.304878	−	0.452755i
$421$	2.65571			0.129432			0.0647158	−	0.997904i	$-0.479386\pi$
$421$	2.65571			0.129432			0.0647158	+	0.997904i	$0.479386\pi$
$422$	−10.1187	+	17.5261i	−0.492570	+	0.853157i
$423$	0.764197	+	1.32363i	0.0371565	+	0.0643570i
$424$	1.60611	+	2.78187i	0.0779996	+	0.135099i
$425$	4.42343	−	7.66160i	0.214568	−	0.371642i
$426$	17.8939			0.866962
$427$	−16.6754	−	1.15311i	−0.806978	−	0.0558031i
$428$	34.7226			1.67838
$429$	17.5004	−	30.3116i	0.844928	−	1.46346i
$430$	5.36808	+	9.29779i	0.258872	+	0.448379i
$431$	−10.6270	−	18.4066i	−0.511887	−	0.886613i	−0.999905	−	0.0137802i	$-0.995613\pi$
$431$	−10.6270	−	18.4066i	−0.511887	−	0.886613i	0.488019	−	0.872833i	$-0.337720\pi$
$432$	−1.80912	+	3.13348i	−0.0870412	+	0.150760i
$433$	−16.8730			−0.810864			−0.405432	−	0.914125i	$-0.632879\pi$
$433$	−16.8730			−0.810864			−0.405432	+	0.914125i	$0.632879\pi$
$434$	−2.16322	−	4.42658i	−0.103838	−	0.212482i
$435$	10.3799			0.497677
$436$	0.0512016	−	0.0886838i	0.00245211	−	0.00424719i
$437$	0.395110	+	0.684350i	0.0189007	+	0.0327369i
$438$	−0.894244	−	1.54888i	−0.0427286	−	0.0740082i
$439$	5.54524	−	9.60464i	0.264660	−	0.458405i	−0.702814	−	0.711373i	$-0.748074\pi$
$439$	5.54524	−	9.60464i	0.264660	−	0.458405i	0.967474	+	0.252969i	$0.0814069\pi$
$440$	−3.94818			−0.188222
$441$	−2.63227	−	6.48623i	−0.125346	−	0.308868i
$442$	−91.3327			−4.34425
$443$	6.38709	−	11.0628i	0.303460	−	0.525608i	−0.673457	−	0.739226i	$-0.735191\pi$
$443$	6.38709	−	11.0628i	0.303460	−	0.525608i	0.976917	+	0.213618i	$0.0685248\pi$
$444$	−1.05872	−	1.83376i	−0.0502447	−	0.0870264i
$445$	−17.1290	−	29.6682i	−0.811990	−	1.40641i
$446$	−2.26267	+	3.91906i	−0.107140	+	0.185573i
$447$	−16.2060			−0.766518
$448$	10.8463	+	22.1946i	0.512438	+	1.04860i
$449$	38.7094			1.82681			0.913405	−	0.407052i	$-0.133443\pi$
$449$	38.7094			1.82681			0.913405	+	0.407052i	$0.133443\pi$
$450$	1.24938	−	2.16400i	0.0588965	−	0.102012i
$451$	−4.30119	−	7.44987i	−0.202535	−	0.350801i
$452$	6.82168	+	11.8155i	0.320865	+	0.555754i
$453$	−6.46687	+	11.2009i	−0.303840	+	0.526266i
$454$	−11.4029			−0.535162
$455$	−31.6921	−	2.19154i	−1.48575	−	0.102741i
$456$	−0.283361			−0.0132696
$457$	18.1453	−	31.4287i	0.848803	−	1.47017i	−0.0334733	−	0.999440i	$-0.510657\pi$
$457$	18.1453	−	31.4287i	0.848803	−	1.47017i	0.882277	−	0.470731i	$-0.156010\pi$
$458$	−7.13003	−	12.3496i	−0.333164	−	0.577057i
$459$	3.61732	+	6.26537i	0.168842	+	0.292443i
$460$	2.11402	−	3.66158i	0.0985665	−	0.170722i
$461$	−3.70588			−0.172600			−0.0862999	−	0.996269i	$-0.527504\pi$
$461$	−3.70588			−0.172600			−0.0862999	+	0.996269i	$0.527504\pi$
$462$	−17.1076	+	25.4053i	−0.795917	+	1.18196i
$463$	−29.9926			−1.39387			−0.696937	−	0.717132i	$-0.745454\pi$
$463$	−29.9926			−1.39387			−0.696937	+	0.717132i	$0.745454\pi$
$464$	−9.66222	+	16.7355i	−0.448557	+	0.776924i
$465$	0.885566	+	1.53385i	0.0410672	+	0.0711304i
$466$	−24.9338	−	43.1866i	−1.15504	−	2.00058i
$467$	−14.0422	+	24.3219i	−0.649797	+	1.12548i	0.333374	+	0.942795i	$0.391813\pi$
$467$	−14.0422	+	24.3219i	−0.649797	+	1.12548i	−0.983171	+	0.182687i	$0.941521\pi$
$468$	−13.4404			−0.621283
$469$	−10.8150	+	16.0606i	−0.499389	+	0.741609i
$470$	−6.06975			−0.279977
$471$	−4.86721	+	8.43026i	−0.224269	+	0.388446i
$472$	1.95306	+	3.38279i	0.0898967	+	0.155706i
$473$	−7.65782	−	13.2637i	−0.352107	−	0.609867i
$474$	6.09602	−	10.5586i	0.280000	−	0.484973i
$475$	−0.966319			−0.0443377
$476$	41.5418	+	2.87265i	1.90407	+	0.131668i
$477$	−8.95803			−0.410160
$478$	−0.433363	+	0.750607i	−0.0198216	+	0.0343319i
$479$	6.40920	+	11.1011i	0.292844	+	0.507221i	0.974481	−	0.224470i	$-0.0720650\pi$
$479$	6.40920	+	11.1011i	0.292844	+	0.507221i	−0.681637	+	0.731690i	$0.738732\pi$
$480$	−7.88151	−	13.6512i	−0.359740	−	0.623088i
$481$	−3.00664	+	5.20766i	−0.137091	+	0.237449i
$482$	−33.3329			−1.51827
$483$	−1.16166	−	2.37709i	−0.0528572	−	0.108161i
$484$	45.8929			2.08604
$485$	−3.00872	+	5.21126i	−0.136619	+	0.236631i
$486$	1.02170	+	1.76964i	0.0463453	+	0.0802723i
$487$	−4.66872	−	8.08646i	−0.211560	−	0.366433i	0.740643	−	0.671899i	$-0.234521\pi$
$487$	−4.66872	−	8.08646i	−0.211560	−	0.366433i	−0.952203	+	0.305466i	$0.901188\pi$
$488$	1.13273	−	1.96194i	0.0512761	−	0.0888128i
$489$	24.0922			1.08949
$490$	27.5347	+	3.82639i	1.24389	+	0.172859i
$491$	−1.98455			−0.0895616			−0.0447808	−	0.998997i	$-0.514259\pi$
$491$	−1.98455			−0.0895616			−0.0447808	+	0.998997i	$0.514259\pi$
$492$	−1.65167	+	2.86077i	−0.0744628	+	0.128973i
$493$	19.3195	+	33.4624i	0.870108	+	1.50707i
$494$	4.98801	+	8.63949i	0.224421	+	0.388709i
$495$	5.50521	−	9.53531i	0.247441	−	0.428580i
$496$	−3.29736			−0.148056
$497$	10.1725	+	20.8160i	0.456301	+	0.933724i
$498$	0.558981			0.0250485
$499$	20.4371	−	35.3981i	0.914890	−	1.58464i	0.107829	−	0.994169i	$-0.465610\pi$
$499$	20.4371	−	35.3981i	0.914890	−	1.58464i	0.807062	−	0.590467i	$-0.201057\pi$
$500$	13.1552	+	22.7855i	0.588318	+	1.01900i
$501$	−6.12909	−	10.6159i	−0.273827	−	0.474283i
$502$	16.2698	−	28.1801i	0.726156	−	1.25774i
$503$	−2.08575			−0.0929989			−0.0464994	−	0.998918i	$-0.514807\pi$
$503$	−2.08575			−0.0929989			−0.0464994	+	0.998918i	$0.514807\pi$
$504$	0.946468	+	0.0654490i	0.0421590	+	0.00291533i
$505$	26.0965			1.16128
$506$	−5.78823	+	10.0255i	−0.257318	+	0.445688i
$507$	12.5846	+	21.7971i	0.558901	+	0.968045i
$508$	13.5233	+	23.4231i	0.600000	+	1.03923i
$509$	8.70994	−	15.0861i	0.386062	−	0.668678i	−0.605854	−	0.795576i	$-0.707169\pi$
$509$	8.70994	−	15.0861i	0.386062	−	0.668678i	0.991916	+	0.126897i	$0.0405019\pi$
$510$	−28.7311			−1.27223
$511$	1.29344	−	1.92080i	0.0572183	−	0.0849711i
$512$	31.9412			1.41162
$513$	0.395110	−	0.684350i	0.0174445	−	0.0302148i
$514$	30.8114	+	53.3668i	1.35903	+	2.35391i
$515$	−6.15749	−	10.6651i	−0.271331	−	0.469960i
$516$	−2.94062	+	5.09331i	−0.129454	+	0.224220i
$517$	8.65879			0.380813
$518$	2.93915	−	4.36474i	0.129139	−	0.191776i
$519$	5.88796			0.258453
$520$	2.15279	−	3.72874i	0.0944060	−	0.163516i
$521$	6.62437	+	11.4737i	0.290219	+	0.502674i	0.973861	−	0.227143i	$-0.0729385\pi$
$521$	6.62437	+	11.4737i	0.290219	+	0.502674i	−0.683642	+	0.729817i	$0.739605\pi$
$522$	5.45674	+	9.45136i	0.238835	+	0.413675i
$523$	−3.24619	+	5.62257i	−0.141946	+	0.245858i	−0.928229	−	0.372008i	$-0.878669\pi$
$523$	−3.24619	+	5.62257i	−0.141946	+	0.245858i	0.786283	+	0.617866i	$0.212003\pi$
$524$	−7.20298			−0.314664
$525$	3.22764	+	0.223194i	0.140866	+	0.00974099i
$526$	30.9894			1.35120
$527$	−3.29652	+	5.70973i	−0.143599	+	0.248720i
$528$	10.2492	+	17.7521i	0.446038	+	0.772561i
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$	17.7876	−	30.8091i	0.772646	−	1.33826i
$531$	−10.8931			−0.472721
$532$	−1.99702	−	4.08648i	−0.0865817	−	0.177171i
$533$	9.38107			0.406339
$534$	18.0095	−	31.1934i	0.779348	−	1.34987i
$535$	−15.5099	−	26.8639i	−0.670551	−	1.16143i
$536$	−1.31212	−	2.27267i	−0.0566751	−	0.0981642i
$537$	−8.48661	+	14.6992i	−0.366224	+	0.634319i
$538$	0.962101			0.0414791
$539$	−39.2796	−	5.45853i	−1.69189	−	0.235115i
$540$	−4.22803			−0.181946
$541$	−8.51918	+	14.7556i	−0.366268	+	0.634395i	−0.988979	−	0.148057i	$-0.952698\pi$
$541$	−8.51918	+	14.7556i	−0.366268	+	0.634395i	0.622711	+	0.782452i	$0.286031\pi$
$542$	7.44550	+	12.8960i	0.319811	+	0.553930i
$543$	9.56206	+	16.5620i	0.410347	+	0.710743i
$544$	29.3389	−	50.8164i	1.25789	−	2.17874i
$545$	−0.0914829			−0.00391870
$546$	−14.6652	−	30.0093i	−0.627612	−	1.28428i
$547$	−29.4820			−1.26056			−0.630280	−	0.776368i	$-0.717060\pi$
$547$	−29.4820			−1.26056			−0.630280	+	0.776368i	$0.717060\pi$
$548$	14.1887	−	24.5756i	0.606112	−	1.04982i
$549$	3.15887	+	5.47133i	0.134817	+	0.233511i
$550$	−7.07812	−	12.2597i	−0.301812	−	0.522754i
$551$	2.11022	−	3.65501i	0.0898984	−	0.155709i
$552$	0.358585			0.0152624
$553$	15.7484	+	1.08901i	0.669690	+	0.0463096i
$554$	6.04890			0.256993
$555$	−0.945819	+	1.63821i	−0.0401478	+	0.0695380i
$556$	12.3648	+	21.4164i	0.524383	+	0.908259i
$557$	5.11579	+	8.86081i	0.216763	+	0.375445i	0.953817	−	0.300390i	$-0.0971167\pi$
$557$	5.11579	+	8.86081i	0.216763	+	0.375445i	−0.737053	+	0.675835i	$0.763783\pi$
$558$	−0.931092	+	1.61270i	−0.0394162	+	0.0682709i
$559$	16.7020			0.706421
$560$	10.3918	−	15.4322i	0.439135	−	0.652130i
$561$	40.9863			1.73044
$562$	−7.31681	+	12.6731i	−0.308641	+	0.534582i
$563$	−11.6300	−	20.1437i	−0.490144	−	0.848955i	0.509791	−	0.860298i	$-0.329723\pi$
$563$	−11.6300	−	20.1437i	−0.490144	−	0.848955i	−0.999936	+	0.0113434i	$0.996389\pi$
$564$	−1.66250	−	2.87953i	−0.0700038	−	0.121250i
$565$	6.09421	−	10.5555i	0.256385	−	0.444072i
$566$	−40.8897			−1.71872
$567$	−1.47779	+	2.19457i	−0.0620614	+	0.0921632i
$568$	−3.14010			−0.131756
$569$	−9.82012	+	17.0089i	−0.411681	+	0.713052i	−0.995074	−	0.0991379i	$-0.968392\pi$
$569$	−9.82012	+	17.0089i	−0.411681	+	0.713052i	0.583393	+	0.812190i	$0.301725\pi$
$570$	1.56911	+	2.71778i	0.0657228	+	0.113835i
$571$	20.7881	+	36.0060i	0.869953	+	1.50680i	0.862043	+	0.506835i	$0.169185\pi$
$571$	20.7881	+	36.0060i	0.869953	+	1.50680i	0.00791006	+	0.999969i	$0.497482\pi$
$572$	−38.0719	+	65.9424i	−1.59187	+	2.75719i
$573$	20.6871			0.864215
$574$	−8.18960	−	0.566317i	−0.341827	−	0.0236376i
$575$	1.22285			0.0509963
$576$	4.66844	−	8.08598i	0.194518	−	0.336916i
$577$	0.708839	+	1.22774i	0.0295093	+	0.0511117i	0.880403	−	0.474226i	$-0.157272\pi$
$577$	0.708839	+	1.22774i	0.0295093	+	0.0511117i	−0.850894	+	0.525338i	$0.823939\pi$
$578$	−36.1068	−	62.5387i	−1.50184	−	2.60127i
$579$	1.11450	−	1.93038i	0.0463172	−	0.0802237i
$580$	−22.5813			−0.937636
$581$	0.317776	+	0.650263i	0.0131836	+	0.0269774i
$582$	−6.32678			−0.262254
$583$	−25.3749	+	43.9507i	−1.05092	+	1.82025i
$584$	0.156926	+	0.271804i	0.00649365	+	0.0112473i
$585$	6.00356	+	10.3985i	0.248216	+	0.429924i
$586$	−6.41536	+	11.1117i	−0.265016	+	0.459021i
$587$	28.5127			1.17685			0.588423	−	0.808553i	$-0.299749\pi$
$587$	28.5127			1.17685			0.588423	+	0.808553i	$0.299749\pi$
$588$	5.72646	+	14.1107i	0.236155	+	0.581915i
$589$	0.720140			0.0296728
$590$	21.6301	−	37.4644i	0.890496	−	1.54238i
$591$	9.68551	+	16.7758i	0.398409	+	0.690064i
$592$	−1.76085	−	3.04988i	−0.0723705	−	0.125349i
$593$	4.12693	−	7.14806i	0.169473	−	0.293536i	−0.768762	−	0.639535i	$-0.779127\pi$
$593$	4.12693	−	7.14806i	0.169473	−	0.293536i	0.938235	+	0.346000i	$0.112460\pi$
$594$	11.5765			0.474988
$595$	−16.3334	−	33.4229i	−0.669604	−	1.37020i
$596$	35.2559			1.44414
$597$	12.3420	−	21.3770i	0.505125	−	0.874902i
$598$	−6.31219	−	10.9330i	−0.258124	−	0.447085i
$599$	−12.6215	−	21.8611i	−0.515700	−	0.893219i	−0.999834	−	0.0182252i	$-0.994198\pi$
$599$	−12.6215	−	21.8611i	−0.515700	−	0.893219i	0.484133	−	0.874994i	$-0.339135\pi$
$600$	−0.219248	+	0.379748i	−0.00895075	+	0.0155032i
$601$	19.9481			0.813702			0.406851	−	0.913495i	$-0.366627\pi$
$601$	19.9481			0.813702			0.406851	+	0.913495i	$0.366627\pi$
$602$	−14.5808	−	1.00827i	−0.594267	−	0.0410940i
$603$	7.31833			0.298026
$604$	14.0686	−	24.3675i	0.572442	−	0.991499i
$605$	−20.4994	−	35.5061i	−0.833421	−	1.44353i
$606$	13.7190	+	23.7621i	0.557297	+	0.965268i
$607$	−14.0308	+	24.3021i	−0.569493	+	0.986392i	0.427123	+	0.904194i	$0.359527\pi$
$607$	−14.0308	+	24.3021i	−0.569493	+	0.986392i	−0.996616	+	0.0821979i	$0.973806\pi$
$608$	−6.40921			−0.259928
$609$	−7.89266	+	11.7209i	−0.319827	+	0.474953i
$610$	−25.0898			−1.01586
$611$	−4.72130	+	8.17753i	−0.191003	+	0.330827i
$612$	−7.86941	−	13.6302i	−0.318102	−	0.550969i
$613$	17.4932	+	30.2992i	0.706545	+	1.22377i	0.966131	+	0.258053i	$0.0830808\pi$
$613$	17.4932	+	30.2992i	0.706545	+	1.22377i	−0.259585	+	0.965720i	$0.583586\pi$
$614$	−25.7390	+	44.5812i	−1.03874	+	1.79915i
$615$	2.95106			0.118998
$616$	3.00212	−	4.45825i	0.120959	−	0.179628i
$617$	−30.9952			−1.24782			−0.623911	−	0.781496i	$-0.714457\pi$
$617$	−30.9952			−1.24782			−0.623911	+	0.781496i	$0.714457\pi$
$618$	6.47403	−	11.2134i	0.260424	−	0.451067i
$619$	−15.6072	−	27.0324i	−0.627305	−	1.08652i	−0.988090	−	0.153875i	$-0.950825\pi$
$619$	−15.6072	−	27.0324i	−0.627305	−	1.08652i	0.360785	−	0.932649i	$-0.382509\pi$
$620$	−1.92654	−	3.33686i	−0.0773716	−	0.134011i
$621$	−0.500000	+	0.866025i	−0.0200643	+	0.0347524i
$622$	24.3615			0.976809
$623$	46.5256	+	3.21728i	1.86401	+	0.128898i
$624$	−22.3539			−0.894872
$625$	8.69520	−	15.0605i	0.347808	−	0.602421i
$626$	−10.2602	−	17.7712i	−0.410081	−	0.710281i
$627$	−2.23841	−	3.87704i	−0.0893935	−	0.154834i
$628$	10.5885	−	18.3399i	0.422529	−	0.731842i
$629$	−7.04161			−0.280767
$630$	−4.61332	−	9.44020i	−0.183799	−	0.376107i
$631$	19.1609			0.762782			0.381391	−	0.924414i	$-0.375445\pi$
$631$	19.1609			0.762782			0.381391	+	0.924414i	$0.375445\pi$
$632$	−1.06976	+	1.85288i	−0.0425527	+	0.0737035i
$633$	4.95189	+	8.57693i	0.196820	+	0.340902i
$634$	9.05441	+	15.6827i	0.359596	+	0.622839i
$635$	12.0812	−	20.9252i	0.479427	−	0.830392i
$636$	19.4881			0.772752
$637$	26.5727	−	34.1201i	1.05285	−	1.35189i
$638$	61.8281			2.44780
$639$	4.37846	−	7.58371i	0.173209	−	0.300007i
$640$	2.77690	+	4.80973i	0.109767	+	0.190121i
$641$	−8.07996	−	13.9949i	−0.319139	−	0.552765i	0.661169	−	0.750237i	$-0.270060\pi$
$641$	−8.07996	−	13.9949i	−0.319139	−	0.552765i	−0.980309	+	0.197471i	$0.936727\pi$
$642$	16.3072	−	28.2449i	0.643594	−	1.11474i
$643$	−44.7116			−1.76325			−0.881627	−	0.471947i	$-0.843551\pi$
$643$	−44.7116			−1.76325			−0.881627	+	0.471947i	$0.843551\pi$
$644$	2.52717	+	5.17132i	0.0995843	+	0.203779i
$645$	5.25407			0.206879
$646$	−5.84100	+	10.1169i	−0.229811	+	0.398045i
$647$	−3.97538	−	6.88557i	−0.156288	−	0.270700i	0.777239	−	0.629205i	$-0.216620\pi$
$647$	−3.97538	−	6.88557i	−0.156288	−	0.270700i	−0.933527	+	0.358506i	$0.883286\pi$
$648$	−0.179293	−	0.310544i	−0.00704328	−	0.0121993i
$649$	−30.8563	+	53.4447i	−1.21122	+	2.09789i
$650$	15.4377			0.605516
$651$	−2.40537	−	0.166333i	−0.0942739	−	0.00651912i
$652$	−52.4123			−2.05262
$653$	21.3512	−	36.9814i	0.835537	−	1.44719i	−0.0580551	−	0.998313i	$-0.518490\pi$
$653$	21.3512	−	36.9814i	0.835537	−	1.44719i	0.893592	−	0.448880i	$-0.148177\pi$
$654$	−0.0480929	−	0.0832994i	−0.00188058	−	0.00325726i
$655$	3.21742	+	5.57274i	0.125715	+	0.217745i
$656$	−2.74703	+	4.75799i	−0.107253	+	0.185768i
$657$	−0.875251			−0.0341468
$658$	4.61532	−	6.85390i	0.179924	−	0.267193i
$659$	−31.2099			−1.21577			−0.607883	−	0.794027i	$-0.707981\pi$
$659$	−31.2099			−1.21577			−0.607883	+	0.794027i	$0.707981\pi$
$660$	−11.9765	+	20.7439i	−0.466185	+	0.807456i
$661$	−2.94999	−	5.10953i	−0.114741	−	0.198738i	0.802935	−	0.596067i	$-0.203271\pi$
$661$	−2.94999	−	5.10953i	−0.114741	−	0.198738i	−0.917676	+	0.397329i	$0.869937\pi$
$662$	23.3961	+	40.5233i	0.909316	+	1.57498i
$663$	−22.3482	+	38.7082i	−0.867932	+	1.50330i
$664$	−0.0980926			−0.00380673
$665$	−2.26957	+	3.37038i	−0.0880100	+	0.130698i
$666$	−1.98888			−0.0770677
$667$	−2.67042	+	4.62531i	−0.103399	+	0.179093i
$668$	13.3337	+	23.0947i	0.515898	+	0.893561i
$669$	1.10731	+	1.91791i	0.0428109	+	0.0741507i
$670$	−14.5317	+	25.1697i	−0.561410	+	0.972391i
$671$	35.7919			1.38173
$672$	21.4077	+	1.48036i	0.825820	+	0.0571061i
$673$	−6.61159			−0.254858			−0.127429	−	0.991848i	$-0.540673\pi$
$673$	−6.61159			−0.254858			−0.127429	+	0.991848i	$0.540673\pi$
$674$	−12.5175	+	21.6810i	−0.482158	+	0.835122i
$675$	−0.611424	−	1.05902i	−0.0235337	−	0.0407616i
$676$	−27.3776	−	47.4193i	−1.05298	−	1.82382i
$677$	−1.85836	+	3.21878i	−0.0714227	+	0.123708i	−0.899525	−	0.436869i	$-0.856087\pi$
$677$	−1.85836	+	3.21878i	−0.0714227	+	0.123708i	0.828102	+	0.560577i	$0.189421\pi$
$678$	12.8150			0.492157
$679$	−3.59673	−	7.35995i	−0.138030	−	0.282449i
$680$	5.04187			0.193347
$681$	−2.79017	+	4.83271i	−0.106919	+	0.185190i
$682$	5.27490	+	9.13640i	0.201986	+	0.349851i
$683$	−14.7835	−	25.6057i	−0.565674	−	0.979775i	−0.996987	−	0.0775731i	$-0.975283\pi$
$683$	−14.7835	−	25.6057i	−0.565674	−	0.979775i	0.431313	−	0.902202i	$-0.358050\pi$
$684$	−0.859555	+	1.48879i	−0.0328659	+	0.0569254i
$685$	−25.3513			−0.968622
$686$	−25.2576	+	28.1824i	−0.964338	+	1.07601i
$687$	−6.97859			−0.266250
$688$	−4.89080	+	8.47112i	−0.186460	+	0.322958i
$689$	−27.6719	−	47.9291i	−1.05422	−	1.82596i
$690$	−1.98566	−	3.43927i	−0.0755929	−	0.130931i
$691$	−0.301946	+	0.522985i	−0.0114866	+	0.0198953i	−0.871712	−	0.490019i	$-0.836990\pi$
$691$	−0.301946	+	0.522985i	−0.0114866	+	0.0198953i	0.860225	+	0.509915i	$0.170323\pi$
$692$	−12.8092			−0.486931
$693$	6.58112	+	13.4669i	0.249996	+	0.511565i
$694$	−13.1969			−0.500949
$695$	11.0462	−	19.1326i	0.419006	−	0.725740i
$696$	−0.957575	−	1.65857i	−0.0362968	−	0.0628679i
$697$	5.49266	+	9.51356i	0.208049	+	0.360352i
$698$	−20.9496	+	36.2858i	−0.792955	+	1.37344i
$699$	−24.4042			−0.923053
$700$	−7.02169	−	0.485556i	−0.265395	−	0.0183523i
$701$	8.15835			0.308136			0.154068	−	0.988060i	$-0.450762\pi$
$701$	8.15835			0.308136			0.154068	+	0.988060i	$0.450762\pi$
$702$	−6.31219	+	10.9330i	−0.238238	+	0.412640i
$703$	0.384568	+	0.666092i	0.0145043	+	0.0251221i
$704$	−26.4481	−	45.8094i	−0.996799	−	1.72651i
$705$	−1.48521	+	2.57246i	−0.0559362	+	0.0968843i
$706$	29.6523			1.11598
$707$	−19.8433	+	29.4679i	−0.746282	+	1.10825i
$708$	23.6978			0.890618
$709$	12.1135	−	20.9812i	0.454932	−	0.787965i	−0.543753	−	0.839246i	$-0.682997\pi$
$709$	12.1135	−	20.9812i	0.454932	−	0.787965i	0.998684	+	0.0512807i	$0.0163303\pi$
$710$	17.3883	+	30.1174i	0.652571	+	1.13029i
$711$	−2.98327	−	5.16718i	−0.111881	−	0.193784i
$712$	−3.16039	+	5.47396i	−0.118441	+	0.205145i
$713$	−0.911316			−0.0341290
$714$	21.8465	−	32.4429i	0.817586	−	1.21414i
$715$	68.0238			2.54394
$716$	18.4625	−	31.9780i	0.689976	−	1.19507i
$717$	0.212079	+	0.367332i	0.00792025	+	0.0137183i
$718$	−4.77931	−	8.27800i	−0.178362	−	0.308932i
$719$	−1.29252	+	2.23871i	−0.0482029	+	0.0834899i	−0.889120	−	0.457674i	$-0.848683\pi$
$719$	−1.29252	+	2.23871i	−0.0482029	+	0.0834899i	0.840917	+	0.541164i	$0.182016\pi$
$720$	−7.03200			−0.262067
$721$	16.7249	+	1.15654i	0.622870	+	0.0430719i
$722$	−37.5486			−1.39741
$723$	−8.15623	+	14.1270i	−0.303333	+	0.525389i
$724$	−20.8021	−	36.0303i	−0.773105	−	1.33906i
$725$	−3.26552	−	5.65605i	−0.121278	−	0.210060i
$726$	21.5533	−	37.3314i	0.799917	−	1.38550i
$727$	−1.39574			−0.0517650			−0.0258825	−	0.999665i	$-0.508240\pi$
$727$	−1.39574			−0.0517650			−0.0258825	+	0.999665i	$0.508240\pi$
$728$	2.57352	+	5.26617i	0.0953809	+	0.195177i
$729$	1.00000			0.0370370
$730$	1.73795	−	3.01022i	0.0643246	−	0.111413i
$731$	9.77912	+	16.9379i	0.361694	+	0.626472i
$732$	−6.87208	−	11.9028i	−0.253999	−	0.439940i
$733$	−10.2450	+	17.7449i	−0.378408	+	0.655421i	−0.990831	−	0.135109i	$-0.956862\pi$
$733$	−10.2450	+	17.7449i	−0.378408	+	0.655421i	0.612423	+	0.790530i	$0.290195\pi$
$734$	−57.3500			−2.11683
$735$	8.35915	−	10.7334i	0.308332	−	0.395906i
$736$	8.11067			0.298963
$737$	20.7302	−	35.9058i	0.763608	−	1.32261i
$738$	1.55138	+	2.68708i	0.0571073	+	0.0989127i
$739$	23.7408	+	41.1203i	0.873320	+	1.51263i	0.858542	+	0.512743i	$0.171371\pi$
$739$	23.7408	+	41.1203i	0.873320	+	1.51263i	0.0147776	+	0.999891i	$0.495296\pi$
$740$	2.05761	−	3.56389i	0.0756394	−	0.131011i
$741$	4.88207			0.179347
$742$	21.2640	+	43.5123i	0.780625	+	1.59739i
$743$	−41.4450			−1.52047			−0.760235	−	0.649648i	$-0.774916\pi$
$743$	−41.4450			−1.52047			−0.760235	+	0.649648i	$0.774916\pi$
$744$	0.163392	−	0.283004i	0.00599025	−	0.0103754i
$745$	−15.7481	−	27.2765i	−0.576966	−	0.999334i
$746$	−14.9478	−	25.8903i	−0.547276	−	0.947910i
$747$	0.136777	−	0.236905i	0.00500441	−	0.00866790i
$748$	−89.1650			−3.26020
$749$	42.1279	+	2.91318i	1.53932	+	0.106445i
$750$	24.7130			0.902390
$751$	−5.79428	+	10.0360i	−0.211436	+	0.366218i	−0.952164	−	0.305587i	$-0.901147\pi$
$751$	−5.79428	+	10.0360i	−0.211436	+	0.366218i	0.740728	+	0.671805i	$0.234481\pi$
$752$	−2.76504	−	4.78920i	−0.100831	−	0.174644i
$753$	−7.96212	−	13.7908i	−0.290156	−	0.502564i
$754$	−33.7124	+	58.3916i	−1.22773	+	2.12650i
$755$	−25.1366			−0.914814
$756$	3.21491	−	4.77425i	0.116925	−	0.173638i
$757$	−11.3101			−0.411073			−0.205536	−	0.978649i	$-0.565894\pi$
$757$	−11.3101			−0.411073			−0.205536	+	0.978649i	$0.565894\pi$
$758$	2.49672	−	4.32445i	0.0906850	−	0.157071i
$759$	2.83264	+	4.90628i	0.102818	+	0.178087i
$760$	−0.275355	−	0.476929i	−0.00998817	−	0.0173000i
$761$	10.9129	−	18.9016i	0.395591	−	0.685184i	−0.597585	−	0.801805i	$-0.703873\pi$
$761$	10.9129	−	18.9016i	0.395591	−	0.685184i	0.993176	+	0.116621i	$0.0372063\pi$
$762$	25.4045			0.920308
$763$	0.0695618	−	0.103302i	0.00251831	−	0.00373977i
$764$	−45.0044			−1.62820
$765$	−7.03021	+	12.1767i	−0.254178	+	0.440249i
$766$	−31.4471	−	54.4679i	−1.13623	−	1.96801i
$767$	−33.6495	−	58.2826i	−1.21501	−	2.10446i
$768$	6.41723	−	11.1150i	0.231562	−	0.401077i
$769$	−24.1550			−0.871052			−0.435526	−	0.900176i	$-0.643438\pi$
$769$	−24.1550			−0.871052			−0.435526	+	0.900176i	$0.643438\pi$
$770$	−59.3842	−	4.10646i	−2.14006	−	0.147987i
$771$	30.1569			1.08608
$772$	−2.42459	+	4.19951i	−0.0872627	+	0.151144i
$773$	−7.36948	−	12.7643i	−0.265062	−	0.459101i	0.702518	−	0.711666i	$-0.252059\pi$
$773$	−7.36948	−	12.7643i	−0.265062	−	0.459101i	−0.967580	+	0.252565i	$0.918726\pi$
$774$	2.76208	+	4.78407i	0.0992810	+	0.171960i
$775$	0.557201	−	0.965100i	0.0200152	−	0.0346674i
$776$	1.11025			0.0398558
$777$	−1.13066	−	2.31367i	−0.0405624	−	0.0830024i
$778$	24.8999			0.892703
$779$	0.599948	−	1.03914i	0.0214954	−	0.0372311i
$780$	−13.0606	−	22.6217i	−0.467646	−	0.809987i
$781$	−24.8052	−	42.9639i	−0.887601	−	1.53737i
$782$	7.39162	−	12.8027i	0.264324	−	0.457822i
$783$	5.34085			0.190866
$784$	9.52416	+	23.4687i	0.340149	+	0.838168i
$785$	−18.9188			−0.675239
$786$	−3.38283	+	5.85923i	−0.120661	+	0.208992i
$787$	−11.9052	−	20.6203i	−0.424373	−	0.735036i	0.571989	−	0.820262i	$-0.306172\pi$
$787$	−11.9052	−	20.6203i	−0.424373	−	0.735036i	−0.996362	+	0.0852258i	$0.972839\pi$
$788$	−21.0707	−	36.4955i	−0.750612	−	1.30010i
$789$	7.58281	−	13.1338i	0.269955	−	0.467576i
$790$	23.6951			0.843034
$791$	7.28523	+	14.9077i	0.259033	+	0.530057i
$792$	−2.03149			−0.0721859
$793$	−19.5159	+	33.8025i	−0.693030	+	1.20036i
$794$	−21.7667	−	37.7010i	−0.772471	−	1.33796i
$795$	−8.70492	−	15.0774i	−0.308732	−	0.534739i
$796$	−26.8499	+	46.5053i	−0.951668	+	1.64834i
$797$	19.8938			0.704674			0.352337	−	0.935873i	$-0.385387\pi$
$797$	19.8938			0.704674			0.352337	+	0.935873i	$0.385387\pi$
$798$	−4.26201	−	0.294721i	−0.150873	−	0.0104330i
$799$	−11.0574			−0.391181
$800$	−4.95906	+	8.58935i	−0.175329	+	0.303679i
$801$	−8.81350	−	15.2654i	−0.311410	−	0.539378i
$802$	−7.56344	−	13.1003i	−0.267074	−	0.462586i
$803$	−2.47927	+	4.29423i	−0.0874917	+	0.151540i
$804$	−15.9209			−0.561488
$805$	2.87207	−	4.26512i	0.101227	−	0.150326i
$806$	−11.5048			−0.405239
$807$	0.235417	−	0.407754i	0.00828706	−	0.0143536i
$808$	−2.40748	−	4.16988i	−0.0846948	−	0.146696i
$809$	23.9563	+	41.4936i	0.842260	+	1.45884i	0.887980	+	0.459883i	$0.152109\pi$
$809$	23.9563	+	41.4936i	0.842260	+	1.45884i	−0.0457195	+	0.998954i	$0.514558\pi$
$810$	−1.98566	+	3.43927i	−0.0697691	+	0.120844i
$811$	−48.3843			−1.69900			−0.849500	−	0.527588i	$-0.823097\pi$
$811$	−48.3843			−1.69900			−0.849500	+	0.527588i	$0.823097\pi$
$812$	17.1704	−	25.4985i	0.602561	−	0.894824i
$813$	7.28736			0.255579
$814$	−5.63380	+	9.75803i	−0.197465	+	0.342019i
$815$	23.4115	+	40.5499i	0.820070	+	1.42040i
$816$	−13.0883	−	22.6696i	−0.458182	−	0.793595i
$817$	1.06815	−	1.85009i	0.0373697	−	0.0647263i
$818$	54.0835			1.89098
$819$	−16.3068	−	1.12763i	−0.569807	−	0.0394026i
$820$	−6.41999			−0.224196
$821$	4.08184	−	7.06995i	0.142457	−	0.246743i	−0.785964	−	0.618272i	$-0.787833\pi$
$821$	4.08184	−	7.06995i	0.142457	−	0.246743i	0.928421	+	0.371529i	$0.121166\pi$
$822$	−13.3273	−	23.0835i	−0.464841	−	0.805129i
$823$	16.6324	+	28.8082i	0.579769	+	1.00419i	0.995505	+	0.0947040i	$0.0301905\pi$
$823$	16.6324	+	28.8082i	0.579769	+	1.00419i	−0.415737	+	0.909485i	$0.636476\pi$
$824$	−1.13609	+	1.96777i	−0.0395777	+	0.0685506i
$825$	−6.92779			−0.241195
$826$	25.8573	+	52.9116i	0.899691	+	1.84103i
$827$	31.2711			1.08740			0.543701	−	0.839279i	$-0.317023\pi$
$827$	31.2711			1.08740			0.543701	+	0.839279i	$0.317023\pi$
$828$	1.08774	−	1.88403i	0.0378017	−	0.0654744i
$829$	8.90381	+	15.4219i	0.309242	+	0.535623i	0.978197	−	0.207680i	$-0.0665913\pi$
$829$	8.90381	+	15.4219i	0.309242	+	0.535623i	−0.668955	+	0.743303i	$0.733258\pi$
$830$	0.543187	+	0.940827i	0.0188543	+	0.0326566i
$831$	1.48011	−	2.56362i	0.0513443	−	0.0889310i
$832$	57.6844			1.99985
$833$	50.1604	+	6.97059i	1.73795	+	0.241517i
$834$	23.2281			0.804324
$835$	11.9118	−	20.6319i	0.412225	−	0.713995i
$836$	4.86963	+	8.43444i	0.168420	+	0.291711i
$837$	0.455658	+	0.789223i	0.0157498	+	0.0272795i
$838$	31.3962	−	54.3798i	1.08456	−	1.87852i
$839$	29.7947			1.02863			0.514313	−	0.857603i	$-0.328047\pi$
$839$	29.7947			1.02863			0.514313	+	0.857603i	$0.328047\pi$
$840$	0.809567	+	1.65661i	0.0279327	+	0.0571585i
$841$	−0.475352			−0.0163915
$842$	−2.71334	+	4.69965i	−0.0935080	+	0.161961i
$843$	3.58071	+	6.20196i	0.123326	+	0.213607i
$844$	−10.7728	−	18.6590i	−0.370814	−	0.642268i
$845$	−24.4580	+	42.3625i	−0.841381	+	1.45731i
$846$	−3.12312			−0.107375
$847$	55.6805	+	3.85035i	1.91320	+	0.132300i
$848$	32.4123			1.11304
$849$	−10.0053	+	17.3297i	−0.343381	+	0.594753i
$850$	9.03883	+	15.6557i	0.310029	+	0.536987i
$851$	−0.486660	−	0.842920i	−0.0166825	−	0.0288949i
$852$	−9.52527	+	16.4983i	−0.326330	+	0.565221i
$853$	−43.0902			−1.47538			−0.737690	−	0.675140i	$-0.764083\pi$
$853$	−43.0902			−1.47538			−0.737690	+	0.675140i	$0.764083\pi$
$854$	19.0778	−	28.3312i	0.652830	−	0.969474i
$855$	1.53578			0.0525227
$856$	−2.86167	+	4.95655i	−0.0978098	+	0.169411i
$857$	−24.0048	−	41.5775i	−0.819988	−	1.42026i	−0.905690	−	0.423940i	$-0.860647\pi$
$857$	−24.0048	−	41.5775i	−0.819988	−	1.42026i	0.0857023	−	0.996321i	$-0.472687\pi$
$858$	35.7604	+	61.9388i	1.22084	+	2.11455i
$859$	−5.87486	+	10.1756i	−0.200448	+	0.347186i	−0.948673	−	0.316259i	$-0.897573\pi$
$859$	−5.87486	+	10.1756i	−0.200448	+	0.347186i	0.748225	+	0.663445i	$0.230906\pi$
$860$	−11.4301			−0.389765
$861$	−2.24393	+	3.33231i	−0.0764729	+	0.113565i
$862$	43.4306			1.47925
$863$	2.80380	−	4.85632i	0.0954424	−	0.165311i	−0.814351	−	0.580373i	$-0.802907\pi$
$863$	2.80380	−	4.85632i	0.0954424	−	0.165311i	0.909793	+	0.415062i	$0.136240\pi$
$864$	−4.05534	−	7.02405i	−0.137965	−	0.238963i
$865$	5.72159	+	9.91008i	0.194540	+	0.336953i
$866$	17.2391	−	29.8590i	0.585809	−	1.01465i
$867$	−35.3399			−1.20021
$868$	5.23285	+	0.361856i	0.177614	+	0.0122822i
$869$	−33.8022			−1.14666
$870$	−10.6051	+	18.3686i	−0.359547	+	0.622754i
$871$	22.6068	+	39.1561i	0.766001	+	1.32675i
$872$	0.00843957	+	0.0146178i	0.000285800	+	0.000495020i
$873$	−1.54810	+	2.68139i	−0.0523953	+	0.0907514i
$874$	−1.61473			−0.0546192
$875$	14.0491	+	28.7486i	0.474947	+	0.971880i
$876$	1.90409			0.0643334
$877$	−8.38192	+	14.5179i	−0.283037	+	0.490235i	−0.972131	−	0.234437i	$-0.924675\pi$
$877$	−8.38192	+	14.5179i	−0.283037	+	0.490235i	0.689094	+	0.724672i	$0.258009\pi$
$878$	11.3312	+	19.6261i	0.382408	+	0.662350i
$879$	3.13955	+	5.43786i	0.105894	+	0.183414i
$880$	−19.9192	+	34.5010i	−0.671475	+	1.16303i
$881$	−39.4239			−1.32823			−0.664113	−	0.747632i	$-0.731191\pi$
$881$	−39.4239			−1.32823			−0.664113	+	0.747632i	$0.731191\pi$
$882$	14.1677	+	1.96882i	0.477050	+	0.0662938i
$883$	−17.4928			−0.588679			−0.294339	−	0.955701i	$-0.595100\pi$
$883$	−17.4928			−0.588679			−0.294339	+	0.955701i	$0.595100\pi$
$884$	48.6182	−	84.2092i	1.63521	−	2.83226i
$885$	−10.5853	−	18.3343i	−0.355822	−	0.616302i
$886$	13.0514	+	22.6057i	0.438470	+	0.759452i
$887$	−1.37606	+	2.38341i	−0.0462037	+	0.0800271i	−0.888202	−	0.459452i	$-0.848046\pi$
$887$	−1.37606	+	2.38341i	−0.0462037	+	0.0800271i	0.841999	+	0.539480i	$0.181379\pi$
$888$	0.349019			0.0117123
$889$	14.4423	+	29.5531i	0.484378	+	0.991178i
$890$	70.0026			2.34649
$891$	2.83264	−	4.90628i	0.0948972	−	0.164367i
$892$	−2.40893	−	4.17238i	−0.0806568	−	0.139702i
$893$	0.603883	+	1.04596i	0.0202082	+	0.0350016i
$894$	16.5577	−	28.6787i	0.553772	−	0.959161i
$895$	−32.9873			−1.10264
$896$	−7.54260	−	0.521577i	−0.251980	−	0.0174246i
$897$	−6.17812			−0.206281
$898$	−39.5494	+	68.5016i	−1.31978	+	2.28593i
$899$	2.43360	+	4.21512i	0.0811651	+	0.140582i
$900$	1.33014	+	2.30388i	0.0443381	+	0.0767959i
$901$	32.4040	−	56.1254i	1.07953	−	1.86981i
$902$	17.5781			0.585286
$903$	−3.99509	+	5.93284i	−0.132948	+	0.197433i
$904$	−2.24884			−0.0747952
$905$	−18.5838	+	32.1880i	−0.617745	+	1.06997i
$906$	−13.2144	−	22.8880i	−0.439019	−	0.760403i
$907$	14.5897	+	25.2701i	0.484443	+	0.839080i	0.999840	−	0.0178715i	$-0.00568896\pi$
$907$	14.5897	+	25.2701i	0.484443	+	0.839080i	−0.515397	+	0.856951i	$0.672356\pi$
$908$	6.06996	−	10.5135i	0.201439	−	0.348902i
$909$	13.4276			0.445367
$910$	36.2581	−	53.8445i	1.20194	−	1.78493i
$911$	−6.24020			−0.206747			−0.103374	−	0.994643i	$-0.532964\pi$
$911$	−6.24020			−0.206747			−0.103374	+	0.994643i	$0.532964\pi$
$912$	−1.42960	+	2.47614i	−0.0473388	+	0.0819932i
$913$	−0.774882	−	1.34213i	−0.0256448	−	0.0444182i
$914$	37.0782	+	64.2213i	1.22644	+	2.12425i
$915$	−6.13924	+	10.6335i	−0.202957	+	0.351532i
$916$	15.1818			0.501621
$917$	−8.73915	−	0.604319i	−0.288592	−	0.0199564i
$918$	−14.7832			−0.487920
$919$	18.2011	−	31.5252i	0.600398	−	1.03992i	−0.392362	−	0.919811i	$-0.628342\pi$
$919$	18.2011	−	31.5252i	0.600398	−	1.03992i	0.992761	−	0.120110i	$-0.0383246\pi$
$920$	0.348454	+	0.603539i	0.0114882	+	0.0198981i
$921$	12.5961	+	21.8172i	0.415057	+	0.718900i
$922$	3.78629	−	6.55806i	0.124695	−	0.215978i
$923$	54.1013			1.78077
$924$	−14.3171	−	29.2970i	−0.470999	−	0.963801i
$925$	1.19022			0.0391343
$926$	30.6435	−	53.0760i	1.00701	−	1.74419i
$927$	−3.16827	−	5.48760i	−0.104059	−	0.180236i
$928$	−21.6589	−	37.5144i	−0.710989	−	1.23147i
$929$	0.0256601	−	0.0444446i	0.000841881	−	0.00145818i	−0.865604	−	0.500729i	$-0.833065\pi$
$929$	0.0256601	−	0.0444446i	0.000841881	−	0.00145818i	0.866446	+	0.499271i	$0.166399\pi$
$930$	−3.61913			−0.118676
$931$	−2.08007	−	5.12554i	−0.0681715	−	0.167983i
$932$	53.0911			1.73906
$933$	5.96103	−	10.3248i	0.195155	−	0.338019i
$934$	−28.6939	−	49.6993i	−0.938893	−	1.62621i
$935$	39.8282	+	68.9845i	1.30252	+	2.25603i
$936$	1.10769	−	1.91858i	0.0362060	−	0.0627107i
$937$	−8.46139			−0.276421			−0.138211	−	0.990403i	$-0.544135\pi$
$937$	−8.46139			−0.276421			−0.138211	+	0.990403i	$0.544135\pi$
$938$	−17.3718	−	35.5477i	−0.567208	−	1.16067i
$939$	−10.0423			−0.327718
$940$	3.23105	−	5.59634i	0.105385	−	0.182532i
$941$	3.47072	+	6.01146i	0.113142	+	0.195968i	0.917036	−	0.398805i	$-0.130575\pi$
$941$	3.47072	+	6.01146i	0.113142	+	0.195968i	−0.803893	+	0.594773i	$0.797242\pi$
$942$	−9.94566	−	17.2264i	−0.324047	−	0.561266i
$943$	−0.759217	+	1.31500i	−0.0247235	+	0.0428224i
$944$	39.4139			1.28281
$945$	−5.12974	−	0.354726i	−0.166870	−	0.0115392i
$946$	31.2960			1.01752
$947$	−3.02670	+	5.24241i	−0.0983547	+	0.170355i	−0.911004	−	0.412398i	$-0.864691\pi$
$947$	−3.02670	+	5.24241i	−0.0983547	+	0.170355i	0.812649	+	0.582753i	$0.198025\pi$
$948$	6.49007	+	11.2411i	0.210788	+	0.365095i
$949$	−2.70370	−	4.68295i	−0.0877659	−	0.152015i
$950$	0.987288	−	1.71003i	0.0320318	−	0.0554808i
$951$	8.86210			0.287373
$952$	−3.83373	+	5.69322i	−0.124252	+	0.184518i
$953$	−52.7135			−1.70756			−0.853778	−	0.520637i	$-0.825695\pi$
$953$	−52.7135			−1.70756			−0.853778	+	0.520637i	$0.825695\pi$
$954$	9.15243	−	15.8525i	0.296321	−	0.513243i
$955$	20.1026	+	34.8186i	0.650503	+	1.12670i
$956$	−0.461375	−	0.799125i	−0.0149219	−	0.0258456i
$957$	15.1287	−	26.2037i	0.489042	−	0.847046i
$958$	−26.1931			−0.846262
$959$	19.2766	−	28.6264i	0.622474	−	0.924394i
$960$	18.1461			0.585664
$961$	15.0848	−	26.1276i	0.486605	−	0.842824i
$962$	−6.14378	−	10.6413i	−0.198083	−	0.343090i
$963$	−7.98043	−	13.8225i	−0.257166	−	0.445424i
$964$	17.7438	−	30.7331i	0.571488	−	0.989846i
$965$	4.33205			0.139454
$966$	5.39345	+	0.372961i	0.173531	+	0.0119998i
$967$	−16.9757			−0.545900			−0.272950	−	0.962028i	$-0.587999\pi$
$967$	−16.9757			−0.545900			−0.272950	+	0.962028i	$0.587999\pi$
$968$	−3.78227	+	6.55108i	−0.121567	+	0.210560i
$969$	2.85847	+	4.95102i	0.0918274	+	0.159050i
$970$	−6.14802	−	10.6487i	−0.197401	−	0.341909i
$971$	14.5062	−	25.1254i	0.465525	−	0.806314i	−0.533700	−	0.845674i	$-0.679199\pi$
$971$	14.5062	−	25.1254i	0.465525	−	0.806314i	0.999225	+	0.0393603i	$0.0125320\pi$
$972$	−2.17548			−0.0697787
$973$	13.2050	+	27.0213i	0.423333	+	0.866262i
$974$	19.0801			0.611367
$975$	3.77745	−	6.54274i	0.120975	−	0.209535i
$976$	−11.4295	−	19.7966i	−0.365851	−	0.633672i
$977$	16.0933	+	27.8744i	0.514871	+	0.891783i	0.999851	+	0.0172574i	$0.00549349\pi$
$977$	16.0933	+	27.8744i	0.514871	+	0.891783i	−0.484980	+	0.874525i	$0.661173\pi$
$978$	−24.6151	+	42.6345i	−0.787103	+	1.36330i
$979$	−99.8621			−3.19161
$980$	−18.1852	+	23.3503i	−0.580905	+	0.745897i
$981$	−0.0470715			−0.00150288
$982$	2.02762	−	3.51194i	0.0647038	−	0.112070i
$983$	−3.01931	−	5.22959i	−0.0963009	−	0.166798i	0.813850	−	0.581075i	$-0.197368\pi$
$983$	−3.01931	−	5.22959i	−0.0963009	−	0.166798i	−0.910151	+	0.414277i	$0.864034\pi$
$984$	−0.272244	−	0.471541i	−0.00867883	−	0.0150322i
$985$	−18.8237	+	32.6036i	−0.599773	+	1.03884i
$986$	−78.9551			−2.51444
$987$	−1.77547	−	3.63313i	−0.0565138	−	0.115644i
$988$	−10.6209			−0.337895
$989$	−1.35171	+	2.34123i	−0.0429819	+	0.0744468i
$990$	11.2494	+	19.4845i	0.357528	+	0.619257i
$991$	−10.4054	−	18.0226i	−0.330538	−	0.572508i	0.652080	−	0.758150i	$-0.273897\pi$
$991$	−10.4054	−	18.0226i	−0.330538	−	0.572508i	−0.982617	+	0.185642i	$0.940563\pi$
$992$	3.69569	−	6.40113i	0.117338	−	0.203236i
$993$	22.8992			0.726684
$994$	−47.2300	−	3.26599i	−1.49804	−	0.103591i
$995$	47.9732			1.52085
$996$	−0.297556	+	0.515383i	−0.00942844	+	0.0163305i
$997$	26.5797	+	46.0374i	0.841788	+	1.45802i	0.888382	+	0.459105i	$0.151830\pi$
$997$	26.5797	+	46.0374i	0.841788	+	1.45802i	−0.0465944	+	0.998914i	$0.514837\pi$
$998$	41.7612	+	72.3325i	1.32193	+	2.28965i
$999$	−0.486660	+	0.842920i	−0.0153972	+	0.0266688i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.i.f.415.1	yes	12
7.2	even	3		3381.2.a.bc.1.6		6
7.4	even	3	inner	483.2.i.f.277.1	✓	12
7.5	odd	6		3381.2.a.bd.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.i.f.277.1	✓	12	7.4	even	3	inner
483.2.i.f.415.1	yes	12	1.1	even	1	trivial
3381.2.a.bc.1.6		6	7.2	even	3
3381.2.a.bd.1.6		6	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.02170 + 1.76964i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.08774 - 1.88403i) q^{4} +(-0.971745 + 1.68311i) q^{5} -2.04340 q^{6} +(-1.16166 - 2.37709i) q^{7} +0.358585 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.02170 + 1.76964i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.08774 - 1.88403i) q^{4} +(-0.971745 + 1.68311i) q^{5} -2.04340 q^{6} +(-1.16166 - 2.37709i) q^{7} +0.358585 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.98566 - 3.43927i) q^{10} +(2.83264 + 4.90628i) q^{11} +(1.08774 - 1.88403i) q^{12} -6.17812 q^{13} +(5.39345 + 0.372961i) q^{14} -1.94349 q^{15} +(1.80912 - 3.13348i) q^{16} +(-3.61732 - 6.26537i) q^{17} +(-1.02170 - 1.76964i) q^{18} +(-0.395110 + 0.684350i) q^{19} +4.22803 q^{20} +(1.47779 - 2.19457i) q^{21} -11.5765 q^{22} +(0.500000 - 0.866025i) q^{23} +(0.179293 + 0.310544i) q^{24} +(0.611424 + 1.05902i) q^{25} +(6.31219 - 10.9330i) q^{26} -1.00000 q^{27} +(-3.21491 + 4.77425i) q^{28} -5.34085 q^{29} +(1.98566 - 3.43927i) q^{30} +(-0.455658 - 0.789223i) q^{31} +(4.05534 + 7.02405i) q^{32} +(-2.83264 + 4.90628i) q^{33} +14.7832 q^{34} +(5.12974 + 0.354726i) q^{35} +2.17548 q^{36} +(0.486660 - 0.842920i) q^{37} +(-0.807367 - 1.39840i) q^{38} +(-3.08906 - 5.35041i) q^{39} +(-0.348454 + 0.603539i) q^{40} -1.51843 q^{41} +(2.37373 + 4.85734i) q^{42} -2.70342 q^{43} +(6.16237 - 10.6735i) q^{44} +(-0.971745 - 1.68311i) q^{45} +(1.02170 + 1.76964i) q^{46} +(0.764197 - 1.32363i) q^{47} +3.61824 q^{48} +(-4.30111 + 5.52273i) q^{49} -2.49877 q^{50} +(3.61732 - 6.26537i) q^{51} +(6.72020 + 11.6397i) q^{52} +(4.47902 + 7.75789i) q^{53} +(1.02170 - 1.76964i) q^{54} -11.0104 q^{55} +(-0.416553 - 0.852390i) q^{56} -0.790220 q^{57} +(5.45674 - 9.45136i) q^{58} +(5.44656 + 9.43371i) q^{59} +(2.11402 + 3.66158i) q^{60} +(3.15887 - 5.47133i) q^{61} +1.86218 q^{62} +(2.63945 + 0.182520i) q^{63} -9.33688 q^{64} +(6.00356 - 10.3985i) q^{65} +(-5.78823 - 10.0255i) q^{66} +(-3.65917 - 6.33786i) q^{67} +(-7.86941 + 13.6302i) q^{68} +1.00000 q^{69} +(-5.86879 + 8.71535i) q^{70} -8.75692 q^{71} +(-0.179293 + 0.310544i) q^{72} +(0.437625 + 0.757990i) q^{73} +(0.994442 + 1.72242i) q^{74} +(-0.611424 + 1.05902i) q^{75} +1.71911 q^{76} +(8.37211 - 12.4329i) q^{77} +12.6244 q^{78} +(-2.98327 + 5.16718i) q^{79} +(3.51600 + 6.08989i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.55138 - 2.68708i) q^{82} -0.273554 q^{83} +(-5.74208 - 0.397069i) q^{84} +14.0604 q^{85} +(2.76208 - 4.78407i) q^{86} +(-2.67042 - 4.62531i) q^{87} +(1.01575 + 1.75932i) q^{88} +(-8.81350 + 15.2654i) q^{89} +3.97133 q^{90} +(7.17686 + 14.6859i) q^{91} -2.17548 q^{92} +(0.455658 - 0.789223i) q^{93} +(1.56156 + 2.70470i) q^{94} +(-0.767892 - 1.33003i) q^{95} +(-4.05534 + 7.02405i) q^{96} +3.09620 q^{97} +(-5.37878 - 13.2540i) q^{98} -5.66529 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + q^{2} + 6 q^{3} - 3 q^{4} - 3 q^{5} + 2 q^{6} - 2 q^{7} - 6 q^{8} - 6 q^{9}+O(q^{10}) \) 12 * q + q^2 + 6 * q^3 - 3 * q^4 - 3 * q^5 + 2 * q^6 - 2 * q^7 - 6 * q^8 - 6 * q^9	\( 12 q + q^{2} + 6 q^{3} - 3 q^{4} - 3 q^{5} + 2 q^{6} - 2 q^{7} - 6 q^{8} - 6 q^{9} + 3 q^{10} + 14 q^{11} + 3 q^{12} - q^{14} - 6 q^{15} + 7 q^{16} - 15 q^{17} + q^{18} + q^{19} + 34 q^{20} - 4 q^{21} - 12 q^{22} + 6 q^{23} - 3 q^{24} - 9 q^{25} + 15 q^{26} - 12 q^{27} - 2 q^{28} - 12 q^{29} - 3 q^{30} + 11 q^{31} - 3 q^{32} - 14 q^{33} + 30 q^{34} - q^{35} + 6 q^{36} + 5 q^{37} - 14 q^{38} + 17 q^{40} + 36 q^{41} - 17 q^{42} - 74 q^{43} + 10 q^{44} - 3 q^{45} - q^{46} - 3 q^{47} + 14 q^{48} - 6 q^{49} - 60 q^{50} + 15 q^{51} + 7 q^{52} + 15 q^{53} - q^{54} - 4 q^{55} - 21 q^{56} + 2 q^{57} - 4 q^{58} + 2 q^{59} + 17 q^{60} + 12 q^{61} + 72 q^{62} - 2 q^{63} - 46 q^{64} + 17 q^{65} - 6 q^{66} + 10 q^{67} + q^{68} + 12 q^{69} - 56 q^{70} - 42 q^{71} + 3 q^{72} + 8 q^{73} + 16 q^{74} + 9 q^{75} + 36 q^{76} - 40 q^{77} + 30 q^{78} + 17 q^{79} - 3 q^{80} - 6 q^{81} + 48 q^{82} + 24 q^{83} - 25 q^{84} - 26 q^{85} - 22 q^{86} - 6 q^{87} + 2 q^{88} - 18 q^{89} - 6 q^{90} + 22 q^{91} - 6 q^{92} - 11 q^{93} - 3 q^{94} + 16 q^{95} + 3 q^{96} - 4 q^{97} - 62 q^{98} - 28 q^{99}+O(q^{100}) \) 12 * q + q^2 + 6 * q^3 - 3 * q^4 - 3 * q^5 + 2 * q^6 - 2 * q^7 - 6 * q^8 - 6 * q^9 + 3 * q^10 + 14 * q^11 + 3 * q^12 - q^14 - 6 * q^15 + 7 * q^16 - 15 * q^17 + q^18 + q^19 + 34 * q^20 - 4 * q^21 - 12 * q^22 + 6 * q^23 - 3 * q^24 - 9 * q^25 + 15 * q^26 - 12 * q^27 - 2 * q^28 - 12 * q^29 - 3 * q^30 + 11 * q^31 - 3 * q^32 - 14 * q^33 + 30 * q^34 - q^35 + 6 * q^36 + 5 * q^37 - 14 * q^38 + 17 * q^40 + 36 * q^41 - 17 * q^42 - 74 * q^43 + 10 * q^44 - 3 * q^45 - q^46 - 3 * q^47 + 14 * q^48 - 6 * q^49 - 60 * q^50 + 15 * q^51 + 7 * q^52 + 15 * q^53 - q^54 - 4 * q^55 - 21 * q^56 + 2 * q^57 - 4 * q^58 + 2 * q^59 + 17 * q^60 + 12 * q^61 + 72 * q^62 - 2 * q^63 - 46 * q^64 + 17 * q^65 - 6 * q^66 + 10 * q^67 + q^68 + 12 * q^69 - 56 * q^70 - 42 * q^71 + 3 * q^72 + 8 * q^73 + 16 * q^74 + 9 * q^75 + 36 * q^76 - 40 * q^77 + 30 * q^78 + 17 * q^79 - 3 * q^80 - 6 * q^81 + 48 * q^82 + 24 * q^83 - 25 * q^84 - 26 * q^85 - 22 * q^86 - 6 * q^87 + 2 * q^88 - 18 * q^89 - 6 * q^90 + 22 * q^91 - 6 * q^92 - 11 * q^93 - 3 * q^94 + 16 * q^95 + 3 * q^96 - 4 * q^97 - 62 * q^98 - 28 * q^99

Introduction

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