LMFDB - Embedded newform 462.2.u.a.13.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(13,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 1]))

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

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

chi := DirichletCharacter("462.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.u (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			13.3
Character	$\chi$	$=$	462.13
Dual form			462.2.u.a.391.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 - 0.309017i) q^{2} +(0.587785 + 0.809017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(1.43844 - 0.467378i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(2.01686 + 1.71239i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.951057 - 0.309017i) q^{2} +(0.587785 + 0.809017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(1.43844 - 0.467378i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(2.01686 + 1.71239i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} -1.51247 q^{10} +(0.803473 + 3.21783i) q^{11} +1.00000i q^{12} +(-1.11452 + 3.43014i) q^{13} +(-1.38899 - 2.25182i) q^{14} +(1.22361 + 0.889005i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-2.43958 - 7.50825i) q^{17} +(0.587785 - 0.809017i) q^{18} +(1.13803 - 0.826829i) q^{19} +(1.43844 + 0.467378i) q^{20} +(-0.199875 + 2.63819i) q^{21} +(0.230216 - 3.30863i) q^{22} +4.44637 q^{23} +(0.309017 - 0.951057i) q^{24} +(-2.19441 + 1.59434i) q^{25} +(2.11995 - 2.91785i) q^{26} +(-0.951057 + 0.309017i) q^{27} +(0.625153 + 2.57083i) q^{28} +(-2.52662 + 3.47759i) q^{29} +(-0.889005 - 1.22361i) q^{30} +(-0.641816 - 0.208539i) q^{31} -1.00000i q^{32} +(-2.13101 + 2.54142i) q^{33} +7.89464i q^{34} +(3.70146 + 1.52054i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(9.55078 + 6.93905i) q^{37} +(-1.33784 + 0.434690i) q^{38} +(-3.43014 + 1.11452i) q^{39} +(-1.22361 - 0.889005i) q^{40} +(1.97733 - 1.43661i) q^{41} +(1.00534 - 2.44730i) q^{42} -0.927497i q^{43} +(-1.24137 + 3.07555i) q^{44} +1.51247i q^{45} +(-4.22875 - 1.37401i) q^{46} +(-1.75083 - 2.40981i) q^{47} +(-0.587785 + 0.809017i) q^{48} +(1.13543 + 6.90730i) q^{49} +(2.57969 - 0.838192i) q^{50} +(4.64035 - 6.38690i) q^{51} +(-2.91785 + 2.11995i) q^{52} +(0.341368 - 1.05062i) q^{53} +1.00000 q^{54} +(2.65969 + 4.25313i) q^{55} +(0.199875 - 2.63819i) q^{56} +(1.33784 + 0.434690i) q^{57} +(3.47759 - 2.52662i) q^{58} +(6.24961 - 8.60185i) q^{59} +(0.467378 + 1.43844i) q^{60} +(-0.413748 - 1.27338i) q^{61} +(0.545961 + 0.396664i) q^{62} +(-2.25182 + 1.38899i) q^{63} +(-0.309017 + 0.951057i) q^{64} +5.45496i q^{65} +(2.81205 - 1.75851i) q^{66} +6.63732 q^{67} +(2.43958 - 7.50825i) q^{68} +(2.61351 + 3.59719i) q^{69} +(-3.05043 - 2.58994i) q^{70} +(-1.38430 - 4.26045i) q^{71} +(0.951057 - 0.309017i) q^{72} +(-5.69522 - 4.13782i) q^{73} +(-6.93905 - 9.55078i) q^{74} +(-2.57969 - 0.838192i) q^{75} +1.40668 q^{76} +(-3.88970 + 7.86576i) q^{77} +3.60667 q^{78} +(-14.5456 - 4.72616i) q^{79} +(0.889005 + 1.22361i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-2.32449 + 0.755273i) q^{82} +(3.33747 + 10.2717i) q^{83} +(-1.71239 + 2.01686i) q^{84} +(-7.01838 - 9.65997i) q^{85} +(-0.286612 + 0.882102i) q^{86} -4.29854 q^{87} +(2.13101 - 2.54142i) q^{88} -8.35266i q^{89} +(0.467378 - 1.43844i) q^{90} +(-8.12158 + 5.00961i) q^{91} +(3.59719 + 2.61351i) q^{92} +(-0.208539 - 0.641816i) q^{93} +(0.920466 + 2.83290i) q^{94} +(1.25055 - 1.72124i) q^{95} +(0.809017 - 0.587785i) q^{96} +(7.04376 + 2.28866i) q^{97} +(1.05462 - 6.92010i) q^{98} +(-3.30863 - 0.230216i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{4} - 10 q^{5} + 8 q^{6} - 10 q^{7} + 8 q^{9}+O(q^{10}) $ 32 * q + 8 * q^4 - 10 * q^5 + 8 * q^6 - 10 * q^7 + 8 * q^9	$ 32 q + 8 q^{4} - 10 q^{5} + 8 q^{6} - 10 q^{7} + 8 q^{9} - 4 q^{10} + 8 q^{11} - 2 q^{14} + 6 q^{15} - 8 q^{16} + 12 q^{17} + 16 q^{19} - 10 q^{20} + 8 q^{21} - 4 q^{22} + 8 q^{23} - 8 q^{24} + 6 q^{25} + 20 q^{29} + 50 q^{31} + 16 q^{33} + 32 q^{35} - 8 q^{36} - 16 q^{37} - 6 q^{40} - 40 q^{41} - 10 q^{42} + 12 q^{44} - 28 q^{49} + 40 q^{51} + 32 q^{54} + 40 q^{55} - 8 q^{56} + 10 q^{58} - 60 q^{59} + 4 q^{60} + 4 q^{61} - 20 q^{62} - 10 q^{63} + 8 q^{64} - 8 q^{66} - 16 q^{67} - 12 q^{68} - 30 q^{69} - 18 q^{70} - 48 q^{71} + 74 q^{73} - 40 q^{74} + 24 q^{76} - 70 q^{77} - 60 q^{79} - 8 q^{81} - 20 q^{82} - 4 q^{83} + 2 q^{84} - 10 q^{85} - 36 q^{86} - 20 q^{87} - 16 q^{88} + 4 q^{90} - 60 q^{91} - 8 q^{92} - 10 q^{93} - 20 q^{95} + 8 q^{96} - 60 q^{97} + 40 q^{98} - 8 q^{99}+O(q^{100}) $ 32 * q + 8 * q^4 - 10 * q^5 + 8 * q^6 - 10 * q^7 + 8 * q^9 - 4 * q^10 + 8 * q^11 - 2 * q^14 + 6 * q^15 - 8 * q^16 + 12 * q^17 + 16 * q^19 - 10 * q^20 + 8 * q^21 - 4 * q^22 + 8 * q^23 - 8 * q^24 + 6 * q^25 + 20 * q^29 + 50 * q^31 + 16 * q^33 + 32 * q^35 - 8 * q^36 - 16 * q^37 - 6 * q^40 - 40 * q^41 - 10 * q^42 + 12 * q^44 - 28 * q^49 + 40 * q^51 + 32 * q^54 + 40 * q^55 - 8 * q^56 + 10 * q^58 - 60 * q^59 + 4 * q^60 + 4 * q^61 - 20 * q^62 - 10 * q^63 + 8 * q^64 - 8 * q^66 - 16 * q^67 - 12 * q^68 - 30 * q^69 - 18 * q^70 - 48 * q^71 + 74 * q^73 - 40 * q^74 + 24 * q^76 - 70 * q^77 - 60 * q^79 - 8 * q^81 - 20 * q^82 - 4 * q^83 + 2 * q^84 - 10 * q^85 - 36 * q^86 - 20 * q^87 - 16 * q^88 + 4 * q^90 - 60 * q^91 - 8 * q^92 - 10 * q^93 - 20 * q^95 + 8 * q^96 - 60 * q^97 + 40 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	1.43844	−	0.467378i	0.643290	−	0.209018i	0.0308370	−	0.999524i	$-0.490183\pi$
$5$	1.43844	−	0.467378i	0.643290	−	0.209018i	0.612453	+	0.790507i	$0.290183\pi$
$6$	−0.309017	−	0.951057i	−0.126156	−	0.388267i
$7$	2.01686	+	1.71239i	0.762300	+	0.647223i
$7$	2.01686	+	1.71239i	0.762300	+	0.647223i
$8$	−0.587785	−	0.809017i	−0.207813	−	0.286031i
$9$	−0.309017	+	0.951057i	−0.103006	+	0.317019i
$10$	−1.51247			−0.478284
$11$	0.803473	+	3.21783i	0.242256	+	0.970212i
$11$	0.803473	+	3.21783i	0.242256	+	0.970212i
$12$			1.00000i			0.288675i
$13$	−1.11452	+	3.43014i	−0.309113	+	0.951351i	0.668998	+	0.743264i	$0.266724\pi$
$13$	−1.11452	+	3.43014i	−0.309113	+	0.951351i	−0.978110	+	0.208086i	$0.933276\pi$
$14$	−1.38899	−	2.25182i	−0.371222	−	0.601826i
$15$	1.22361	+	0.889005i	0.315935	+	0.229540i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−2.43958	−	7.50825i	−0.591685	−	1.82102i	−0.570582	−	0.821241i	$-0.693282\pi$
$17$	−2.43958	−	7.50825i	−0.591685	−	1.82102i	−0.0211024	−	0.999777i	$-0.506718\pi$
$18$	0.587785	−	0.809017i	0.138542	−	0.190687i
$19$	1.13803	−	0.826829i	0.261082	−	0.189687i	−0.449542	−	0.893259i	$-0.648413\pi$
$19$	1.13803	−	0.826829i	0.261082	−	0.189687i	0.710624	+	0.703572i	$0.248413\pi$
$20$	1.43844	+	0.467378i	0.321645	+	0.104509i
$21$	−0.199875	+	2.63819i	−0.0436164	+	0.575700i
$22$	0.230216	−	3.30863i	0.0490822	−	0.705401i
$23$	4.44637			0.927133			0.463567	−	0.886062i	$-0.346570\pi$
$23$	4.44637			0.927133			0.463567	+	0.886062i	$0.346570\pi$
$24$	0.309017	−	0.951057i	0.0630778	−	0.194134i
$25$	−2.19441	+	1.59434i	−0.438883	+	0.318867i
$26$	2.11995	−	2.91785i	0.415755	−	0.572238i
$27$	−0.951057	+	0.309017i	−0.183031	+	0.0594703i
$28$	0.625153	+	2.57083i	0.118143	+	0.485842i
$29$	−2.52662	+	3.47759i	−0.469181	+	0.645772i	−0.976381	−	0.216056i	$-0.930681\pi$
$29$	−2.52662	+	3.47759i	−0.469181	+	0.645772i	0.507200	+	0.861828i	$0.330681\pi$
$30$	−0.889005	−	1.22361i	−0.162309	−	0.223400i
$31$	−0.641816	−	0.208539i	−0.115273	−	0.0374546i	0.250812	−	0.968036i	$-0.419302\pi$
$31$	−0.641816	−	0.208539i	−0.115273	−	0.0374546i	−0.366086	+	0.930581i	$0.619302\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−2.13101	+	2.54142i	−0.370961	+	0.442404i
$34$			7.89464i			1.35392i
$35$	3.70146	+	1.52054i	0.625662	+	0.257018i
$36$	−0.809017	+	0.587785i	−0.134836	+	0.0979642i
$37$	9.55078	+	6.93905i	1.57014	+	1.14077i	0.927024	+	0.375002i	$0.122358\pi$
$37$	9.55078	+	6.93905i	1.57014	+	1.14077i	0.643114	+	0.765770i	$0.277642\pi$
$38$	−1.33784	+	0.434690i	−0.217026	+	0.0705160i
$39$	−3.43014	+	1.11452i	−0.549263	+	0.178466i
$40$	−1.22361	−	0.889005i	−0.193470	−	0.140564i
$41$	1.97733	−	1.43661i	0.308807	−	0.224362i	−0.422577	−	0.906327i	$-0.638875\pi$
$41$	1.97733	−	1.43661i	0.308807	−	0.224362i	0.731385	+	0.681965i	$0.238875\pi$
$42$	1.00534	−	2.44730i	0.155127	−	0.377627i
$43$		−	0.927497i		−	0.141442i	−0.997496	−	0.0707210i	$-0.977470\pi$
$43$		−	0.927497i		−	0.141442i	0.997496	−	0.0707210i	$-0.0225300\pi$
$44$	−1.24137	+	3.07555i	−0.187144	+	0.463656i
$45$			1.51247i			0.225465i
$46$	−4.22875	−	1.37401i	−0.623496	−	0.202586i
$47$	−1.75083	−	2.40981i	−0.255385	−	0.351507i	0.662003	−	0.749501i	$-0.269706\pi$
$47$	−1.75083	−	2.40981i	−0.255385	−	0.351507i	−0.917388	+	0.397994i	$0.869706\pi$
$48$	−0.587785	+	0.809017i	−0.0848395	+	0.116772i
$49$	1.13543	+	6.90730i	0.162204	+	0.986757i
$50$	2.57969	−	0.838192i	0.364823	−	0.118538i
$51$	4.64035	−	6.38690i	0.649779	−	0.894345i
$52$	−2.91785	+	2.11995i	−0.404634	+	0.293984i
$53$	0.341368	−	1.05062i	0.0468905	−	0.144314i	−0.924870	−	0.380283i	$-0.875826\pi$
$53$	0.341368	−	1.05062i	0.0468905	−	0.144314i	0.971761	+	0.235969i	$0.0758265\pi$
$54$	1.00000			0.136083
$55$	2.65969	+	4.25313i	0.358633	+	0.573492i
$56$	0.199875	−	2.63819i	0.0267095	−	0.352543i
$57$	1.33784	+	0.434690i	0.177201	+	0.0575760i
$58$	3.47759	−	2.52662i	0.456630	−	0.331761i
$59$	6.24961	−	8.60185i	0.813630	−	1.11987i	−0.177123	−	0.984189i	$-0.556679\pi$
$59$	6.24961	−	8.60185i	0.813630	−	1.11987i	0.990753	−	0.135677i	$-0.0433209\pi$
$60$	0.467378	+	1.43844i	0.0603382	+	0.185702i
$61$	−0.413748	−	1.27338i	−0.0529750	−	0.163040i	0.921069	−	0.389400i	$-0.127318\pi$
$61$	−0.413748	−	1.27338i	−0.0529750	−	0.163040i	−0.974044	+	0.226360i	$0.927318\pi$
$62$	0.545961	+	0.396664i	0.0693371	+	0.0503764i
$63$	−2.25182	+	1.38899i	−0.283703	+	0.174996i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$			5.45496i			0.676605i
$66$	2.81205	−	1.75851i	0.346140	−	0.216458i
$67$	6.63732			0.810878			0.405439	−	0.914122i	$-0.367119\pi$
$67$	6.63732			0.810878			0.405439	+	0.914122i	$0.367119\pi$
$68$	2.43958	−	7.50825i	0.295842	−	0.910509i
$69$	2.61351	+	3.59719i	0.314630	+	0.433051i
$70$	−3.05043	−	2.58994i	−0.364596	−	0.309557i
$71$	−1.38430	−	4.26045i	−0.164287	−	0.505622i	0.834696	−	0.550710i	$-0.185643\pi$
$71$	−1.38430	−	4.26045i	−0.164287	−	0.505622i	−0.998983	+	0.0450881i	$0.985643\pi$
$72$	0.951057	−	0.309017i	0.112083	−	0.0364180i
$73$	−5.69522	−	4.13782i	−0.666575	−	0.484295i	0.202302	−	0.979323i	$-0.435158\pi$
$73$	−5.69522	−	4.13782i	−0.666575	−	0.484295i	−0.868877	+	0.495028i	$0.835158\pi$
$74$	−6.93905	−	9.55078i	−0.806648	−	1.11026i
$75$	−2.57969	−	0.838192i	−0.297877	−	0.0967860i
$76$	1.40668			0.161358
$77$	−3.88970	+	7.86576i	−0.443272	+	0.896387i
$78$	3.60667			0.408375
$79$	−14.5456	−	4.72616i	−1.63651	−	0.531734i	−0.660756	−	0.750601i	$-0.729764\pi$
$79$	−14.5456	−	4.72616i	−1.63651	−	0.531734i	−0.975755	+	0.218867i	$0.929764\pi$
$80$	0.889005	+	1.22361i	0.0993938	+	0.136804i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−2.32449	+	0.755273i	−0.256697	+	0.0834060i
$83$	3.33747	+	10.2717i	0.366335	+	1.12746i	0.949141	+	0.314851i	$0.101955\pi$
$83$	3.33747	+	10.2717i	0.366335	+	1.12746i	−0.582806	+	0.812611i	$0.698045\pi$
$84$	−1.71239	+	2.01686i	−0.186837	+	0.220057i
$85$	−7.01838	−	9.65997i	−0.761250	−	1.04777i
$86$	−0.286612	+	0.882102i	−0.0309062	+	0.0951195i
$87$	−4.29854			−0.460852
$88$	2.13101	−	2.54142i	0.227166	−	0.270916i
$89$		−	8.35266i		−	0.885381i	−0.896675	−	0.442690i	$-0.854024\pi$
$89$		−	8.35266i		−	0.885381i	0.896675	−	0.442690i	$-0.145976\pi$
$90$	0.467378	−	1.43844i	0.0492659	−	0.151625i
$91$	−8.12158	+	5.00961i	−0.851373	+	0.525150i
$92$	3.59719	+	2.61351i	0.375033	+	0.272478i
$93$	−0.208539	−	0.641816i	−0.0216244	−	0.0665532i
$94$	0.920466	+	2.83290i	0.0949388	+	0.292191i
$95$	1.25055	−	1.72124i	0.128304	−	0.176595i
$96$	0.809017	−	0.587785i	0.0825700	−	0.0599906i
$97$	7.04376	+	2.28866i	0.715185	+	0.232378i	0.643934	−	0.765081i	$-0.277301\pi$
$97$	7.04376	+	2.28866i	0.715185	+	0.232378i	0.0712508	+	0.997458i	$0.477301\pi$
$98$	1.05462	−	6.92010i	0.106533	−	0.699036i
$99$	−3.30863	−	0.230216i	−0.332529	−	0.0231376i
$100$	−2.71245			−0.271245
$101$	2.65883	−	8.18303i	0.264563	−	0.814242i	−0.727230	−	0.686393i	$-0.759193\pi$
$101$	2.65883	−	8.18303i	0.264563	−	0.814242i	0.991794	−	0.127849i	$-0.0408072\pi$
$102$	−6.38690	+	4.64035i	−0.632397	+	0.459463i
$103$	7.09278	−	9.76237i	0.698872	−	0.961915i	−0.301093	−	0.953595i	$-0.597352\pi$
$103$	7.09278	−	9.76237i	0.698872	−	0.961915i	0.999965	−	0.00832038i	$-0.00264849\pi$
$104$	3.43014	−	1.11452i	0.336353	−	0.109288i
$105$	0.945523	+	3.88830i	0.0922736	+	0.379459i
$106$	−0.649320	+	0.893712i	−0.0630675	+	0.0868050i
$107$	−11.0922	−	15.2671i	−1.07232	−	1.47592i	−0.867703	−	0.497083i	$-0.834404\pi$
$107$	−11.0922	−	15.2671i	−1.07232	−	1.47592i	−0.204619	−	0.978842i	$-0.565596\pi$
$108$	−0.951057	−	0.309017i	−0.0915155	−	0.0297352i
$109$		−	9.51191i		−	0.911075i	−0.890217	−	0.455538i	$-0.849447\pi$
$109$		−	9.51191i		−	0.911075i	0.890217	−	0.455538i	$-0.150553\pi$
$110$	−1.21523	−	4.86686i	−0.115867	−	0.464037i
$111$			11.8054i			1.12052i
$112$	−1.00534	+	2.44730i	−0.0949956	+	0.231248i
$113$	−14.5581	+	10.5771i	−1.36951	+	0.995008i	−0.371736	+	0.928338i	$0.621237\pi$
$113$	−14.5581	+	10.5771i	−1.36951	+	0.995008i	−0.997775	+	0.0666699i	$0.978763\pi$
$114$	−1.13803	−	0.826829i	−0.106586	−	0.0774396i
$115$	6.39585	−	2.07814i	0.596416	−	0.193787i
$116$	−4.08815	+	1.32832i	−0.379575	+	0.123332i
$117$	−2.91785	−	2.11995i	−0.269756	−	0.195989i
$118$	−8.60185	+	6.24961i	−0.791865	+	0.575323i
$119$	7.93679	−	19.3206i	0.727564	−	1.77111i
$120$		−	1.51247i		−	0.138069i
$121$	−9.70886	+	5.17088i	−0.882624	+	0.470080i
$122$			1.33892i			0.121220i
$123$	2.32449	+	0.755273i	0.209592	+	0.0681007i
$124$	−0.396664	−	0.545961i	−0.0356215	−	0.0490287i
$125$	−6.85641	+	9.43703i	−0.613256	+	0.844074i
$126$	2.57083	−	0.625153i	0.229028	−	0.0556931i
$127$	14.4799	−	4.70481i	1.28488	−	0.417484i	0.414586	−	0.910010i	$-0.363926\pi$
$127$	14.4799	−	4.70481i	1.28488	−	0.417484i	0.870298	+	0.492526i	$0.163926\pi$
$128$	0.587785	−	0.809017i	0.0519534	−	0.0715077i
$129$	0.750361	−	0.545169i	0.0660656	−	0.0479995i
$130$	1.68568	−	5.18798i	0.147844	−	0.455016i
$131$	−14.4783			−1.26497			−0.632486	−	0.774572i	$-0.717965\pi$
$131$	−14.4783			−1.26497			−0.632486	+	0.774572i	$0.717965\pi$
$132$	−3.21783	+	0.803473i	−0.280076	+	0.0699333i
$133$	3.71110	+	0.281162i	0.321793	+	0.0243798i
$134$	−6.31247	−	2.05105i	−0.545314	−	0.177183i
$135$	−1.22361	+	0.889005i	−0.105312	+	0.0765134i
$136$	−4.64035	+	6.38690i	−0.397907	+	0.547672i
$137$	−0.141564	−	0.435688i	−0.0120946	−	0.0372233i	0.944827	−	0.327569i	$-0.106230\pi$
$137$	−0.141564	−	0.435688i	−0.0120946	−	0.0372233i	−0.956922	+	0.290346i	$0.906230\pi$
$138$	−1.37401	−	4.22875i	−0.116963	−	0.359975i
$139$	−5.94959	−	4.32263i	−0.504638	−	0.366641i	0.306148	−	0.951984i	$-0.400960\pi$
$139$	−5.94959	−	4.32263i	−0.504638	−	0.366641i	−0.810786	+	0.585343i	$0.800960\pi$
$140$	2.10080	+	3.40581i	0.177550	+	0.287843i
$141$	0.920466	−	2.83290i	0.0775172	−	0.238573i
$142$			4.47970i			0.375928i
$143$	−11.9331	−	0.830313i	−0.997897	−	0.0694342i
$144$	−1.00000			−0.0833333
$145$	−2.00904	+	6.18319i	−0.166842	+	0.513486i
$146$	4.13782	+	5.69522i	0.342448	+	0.471339i
$147$	−4.92074	+	4.97859i	−0.405856	+	0.410627i
$148$	3.64807	+	11.2276i	0.299870	+	0.922904i
$149$	−10.8197	+	3.51552i	−0.886381	+	0.288003i	−0.716604	−	0.697480i	$-0.754305\pi$
$149$	−10.8197	+	3.51552i	−0.886381	+	0.288003i	−0.169777	+	0.985483i	$0.554305\pi$
$150$	2.19441	+	1.59434i	0.179173	+	0.130177i
$151$	−5.26708	−	7.24952i	−0.428629	−	0.589957i	0.539009	−	0.842300i	$-0.318799\pi$
$151$	−5.26708	−	7.24952i	−0.428629	−	0.589957i	−0.967638	+	0.252343i	$0.918799\pi$
$152$	−1.33784	−	0.434690i	−0.108513	−	0.0352580i
$153$	7.89464			0.638244
$154$	6.12998	−	6.27880i	0.493968	−	0.505960i
$155$	−1.02068			−0.0819830
$156$	−3.43014	−	1.11452i	−0.274631	−	0.0892331i
$157$	−10.4758	−	14.4187i	−0.836057	−	1.15073i	−0.986765	−	0.162155i	$-0.948155\pi$
$157$	−10.4758	−	14.4187i	−0.836057	−	1.15073i	0.150708	−	0.988578i	$-0.451845\pi$
$158$	12.3732	+	8.98969i	0.984363	+	0.715181i
$159$	1.05062	−	0.341368i	0.0833197	−	0.0270722i
$160$	−0.467378	−	1.43844i	−0.0369495	−	0.113719i
$161$	8.96770	+	7.61394i	0.706754	+	0.600062i
$162$	0.587785	+	0.809017i	0.0461808	+	0.0635624i
$163$	3.80531	−	11.7116i	0.298055	−	0.917320i	−0.684123	−	0.729367i	$-0.739815\pi$
$163$	3.80531	−	11.7116i	0.298055	−	0.917320i	0.982178	−	0.187953i	$-0.0601852\pi$
$164$	2.44412			0.190853
$165$	−1.87753	+	4.65166i	−0.146166	+	0.362132i
$166$		−	10.8003i		−	0.838264i
$167$	−0.678089	+	2.08694i	−0.0524721	+	0.161492i	−0.973859	−	0.227155i	$-0.927058\pi$
$167$	−0.678089	+	2.08694i	−0.0524721	+	0.161492i	0.921387	+	0.388647i	$0.127058\pi$
$168$	2.25182	−	1.38899i	0.173732	−	0.107163i
$169$	−0.00650609	−	0.00472695i	−0.000500469	−	0.000363612i
$170$	3.68978	+	11.3560i	0.282993	+	0.870963i
$171$	0.434690	+	1.33784i	0.0332415	+	0.102307i
$172$	0.545169	−	0.750361i	0.0415688	−	0.0572145i
$173$	6.84496	−	4.97315i	0.520413	−	0.378102i	−0.296347	−	0.955080i	$-0.595768\pi$
$173$	6.84496	−	4.97315i	0.520413	−	0.378102i	0.816759	+	0.576979i	$0.195768\pi$
$174$	4.08815	+	1.32832i	0.309922	+	0.100700i
$175$	−7.15595	−	0.542151i	−0.540939	−	0.0409828i
$176$	−2.81205	+	1.75851i	−0.211966	+	0.132553i
$177$	10.6325			0.799186
$178$	−2.58112	+	7.94386i	−0.193463	+	0.595417i
$179$	−3.53515	+	2.56844i	−0.264230	+	0.191974i	−0.712010	−	0.702170i	$-0.752215\pi$
$179$	−3.53515	+	2.56844i	−0.264230	+	0.191974i	0.447780	+	0.894144i	$0.352215\pi$
$180$	−0.889005	+	1.22361i	−0.0662626	+	0.0912026i
$181$	6.97833	−	2.26740i	0.518695	−	0.168534i	−0.0379580	−	0.999279i	$-0.512085\pi$
$181$	6.97833	−	2.26740i	0.518695	−	0.168534i	0.556653	+	0.830745i	$0.312085\pi$
$182$	9.27214	−	2.25472i	0.687297	−	0.167131i
$183$	0.786995	−	1.08321i	0.0581764	−	0.0800729i
$184$	−2.61351	−	3.59719i	−0.192671	−	0.265189i
$185$	16.9814	+	5.51759i	1.24850	+	0.405661i
$186$			0.674845i			0.0494820i
$187$	22.2001	−	13.8828i	1.62343	−	1.01521i
$188$		−	2.97869i		−	0.217243i
$189$	−2.44730	−	1.00534i	−0.178015	−	0.0731276i
$190$	−1.72124	+	1.25055i	−0.124872	+	0.0907245i
$191$	20.5006	+	14.8946i	1.48337	+	1.07773i	0.976451	+	0.215741i	$0.0692167\pi$
$191$	20.5006	+	14.8946i	1.48337	+	1.07773i	0.506922	+	0.861992i	$0.330783\pi$
$192$	−0.951057	+	0.309017i	−0.0686366	+	0.0223014i
$193$	−4.84903	+	1.57554i	−0.349040	+	0.113410i	−0.478290	−	0.878202i	$-0.658743\pi$
$193$	−4.84903	+	1.57554i	−0.349040	+	0.113410i	0.129249	+	0.991612i	$0.458743\pi$
$194$	−5.99178	−	4.35328i	−0.430185	−	0.312547i
$195$	−4.41316	+	3.20635i	−0.316033	+	0.229611i
$196$	−3.14143	+	6.25551i	−0.224388	+	0.446822i
$197$			10.3826i			0.739731i	0.929085	+	0.369865i	$0.120596\pi$
$197$			10.3826i			0.739731i	−0.929085	+	0.369865i	$0.879404\pi$
$198$	3.07555	+	1.24137i	0.218570	+	0.0882203i
$199$		−	13.6319i		−	0.966343i	−0.875526	−	0.483171i	$-0.839485\pi$
$199$		−	13.6319i		−	0.966343i	0.875526	−	0.483171i	$-0.160515\pi$
$200$	2.57969	+	0.838192i	0.182412	+	0.0592691i
$201$	3.90132	+	5.36971i	0.275178	+	0.378750i
$202$	−5.05739	+	6.96090i	−0.355837	+	0.489767i
$203$	−11.0508	+	2.68724i	−0.775616	+	0.188608i
$204$	7.50825	−	2.43958i	0.525683	−	0.170805i
$205$	2.17283	−	2.99065i	0.151757	−	0.208876i
$206$	−9.76237	+	7.09278i	−0.680177	+	0.494177i
$207$	−1.37401	+	4.22875i	−0.0955000	+	0.293919i
$208$	−3.60667			−0.250077
$209$	3.57497	+	2.99766i	0.247286	+	0.207352i
$210$	0.302305	−	3.99017i	0.0208610	−	0.275348i
$211$	14.8791	+	4.83451i	1.02432	+	0.332821i	0.772541	−	0.634964i	$-0.218985\pi$
$211$	14.8791	+	4.83451i	1.02432	+	0.332821i	0.251776	+	0.967785i	$0.418985\pi$
$212$	0.893712	−	0.649320i	0.0613804	−	0.0445955i
$213$	2.63310	−	3.62415i	0.180417	−	0.248323i
$214$	5.83151	+	17.9475i	0.398634	+	1.22687i
$215$	−0.433492	−	1.33415i	−0.0295639	−	0.0909883i
$216$	0.809017	+	0.587785i	0.0550466	+	0.0399937i
$217$	−0.937351	−	1.51963i	−0.0636315	−	0.103159i
$218$	−2.93934	+	9.04636i	−0.199077	+	0.612697i
$219$		−	7.03967i		−	0.475697i
$220$	−0.348194	+	5.00418i	−0.0234752	+	0.337382i
$221$	28.4733			1.91532
$222$	3.64807	−	11.2276i	0.244843	−	0.753548i
$223$	1.15986	+	1.59641i	0.0776700	+	0.106904i	0.846084	−	0.533049i	$-0.178954\pi$
$223$	1.15986	+	1.59641i	0.0776700	+	0.106904i	−0.768414	+	0.639953i	$0.778954\pi$
$224$	1.71239	−	2.01686i	0.114414	−	0.134757i
$225$	−0.838192	−	2.57969i	−0.0558794	−	0.171979i
$226$	17.1141	−	5.56070i	1.13841	−	0.369892i
$227$	18.1690	+	13.2006i	1.20592	+	0.876154i	0.994854	−	0.101318i	$-0.0323058\pi$
$227$	18.1690	+	13.2006i	1.20592	+	0.876154i	0.211068	+	0.977471i	$0.432306\pi$
$228$	0.826829	+	1.13803i	0.0547581	+	0.0753680i
$229$	−17.5181	−	5.69199i	−1.15763	−	0.376137i	−0.333618	−	0.942708i	$-0.608270\pi$
$229$	−17.5181	−	5.69199i	−1.15763	−	0.376137i	−0.824013	+	0.566571i	$0.808270\pi$
$230$	−6.72499			−0.443433
$231$	−8.64984	+	1.47655i	−0.569118	+	0.0971498i
$232$	4.29854			0.282213
$233$	10.2609	+	3.33397i	0.672214	+	0.218416i	0.625183	−	0.780478i	$-0.285024\pi$
$233$	10.2609	+	3.33397i	0.672214	+	0.218416i	0.0470305	+	0.998893i	$0.485024\pi$
$234$	2.11995	+	2.91785i	0.138585	+	0.190746i
$235$	−3.64476	−	2.64807i	−0.237758	−	0.172741i
$236$	10.1121	−	3.28562i	0.658241	−	0.213875i
$237$	−4.72616	−	14.5456i	−0.306997	−	0.944840i
$238$	−13.5187	+	15.9224i	−0.876288	+	1.03209i
$239$	−4.82258	−	6.63771i	−0.311947	−	0.429358i	0.624040	−	0.781392i	$-0.285490\pi$
$239$	−4.82258	−	6.63771i	−0.311947	−	0.429358i	−0.935987	+	0.352034i	$0.885490\pi$
$240$	−0.467378	+	1.43844i	−0.0301691	+	0.0928510i
$241$	14.9887			0.965507			0.482753	−	0.875756i	$-0.339637\pi$
$241$	14.9887			0.965507			0.482753	+	0.875756i	$0.339637\pi$
$242$	10.8316	−	1.91759i	0.696279	−	0.123268i
$243$		−	1.00000i		−	0.0641500i
$244$	0.413748	−	1.27338i	0.0264875	−	0.0815201i
$245$	4.86156	+	9.40507i	0.310594	+	0.600868i
$246$	−1.97733	−	1.43661i	−0.126070	−	0.0915952i
$247$	1.56778	+	4.82513i	0.0997555	+	0.307016i
$248$	0.208539	+	0.641816i	0.0132422	+	0.0407553i
$249$	−6.34824	+	8.73761i	−0.402303	+	0.553723i
$250$	9.43703	−	6.85641i	0.596850	−	0.433637i
$251$	−27.0254	−	8.78108i	−1.70583	−	0.554257i	−0.716197	−	0.697898i	$-0.754119\pi$
$251$	−27.0254	−	8.78108i	−1.70583	−	0.554257i	−0.989630	+	0.143642i	$0.954119\pi$
$252$	−2.63819	−	0.199875i	−0.166190	−	0.0125910i
$253$	3.57254	+	14.3077i	0.224604	+	0.899516i
$254$	−15.2251			−0.955306
$255$	3.68978	−	11.3560i	0.231063	−	0.711139i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−9.63509	+	13.2616i	−0.601020	+	0.827234i	−0.995801	−	0.0915417i	$-0.970821\pi$
$257$	−9.63509	+	13.2616i	−0.601020	+	0.827234i	0.394781	+	0.918775i	$0.370821\pi$
$258$	−0.882102	+	0.286612i	−0.0549173	+	0.0178437i
$259$	7.38019	+	30.3497i	0.458583	+	1.88584i
$260$	−3.20635	+	4.41316i	−0.198849	+	0.273692i
$261$	−2.52662	−	3.47759i	−0.156394	−	0.215257i
$262$	13.7696	+	4.47403i	0.850692	+	0.276406i
$263$		−	2.18656i		−	0.134829i	−0.997725	−	0.0674147i	$-0.978525\pi$
$263$		−	2.18656i		−	0.134829i	0.997725	−	0.0674147i	$-0.0214750\pi$
$264$	3.30863	+	0.230216i	0.203632	+	0.0141688i
$265$		−	1.67081i		−	0.102637i
$266$	−3.44258	−	1.41419i	−0.211078	−	0.0867098i
$267$	6.75745	−	4.90957i	0.413549	−	0.300461i
$268$	5.36971	+	3.90132i	0.328007	+	0.238311i
$269$	−23.5313	+	7.64578i	−1.43473	+	0.466171i	−0.920250	−	0.391332i	$-0.872014\pi$
$269$	−23.5313	+	7.64578i	−1.43473	+	0.466171i	−0.514478	+	0.857503i	$0.672014\pi$
$270$	1.43844	−	0.467378i	0.0875407	−	0.0284437i
$271$	−16.0197	−	11.6390i	−0.973128	−	0.707019i	−0.0169656	−	0.999856i	$-0.505401\pi$
$271$	−16.0197	−	11.6390i	−0.973128	−	0.707019i	−0.956162	+	0.292837i	$0.905401\pi$
$272$	6.38690	−	4.64035i	0.387263	−	0.281363i
$273$	−8.82661	−	3.62592i	−0.534211	−	0.219451i
$274$			0.458109i			0.0276754i
$275$	−6.89345	−	5.78025i	−0.415691	−	0.348562i
$276$			4.44637i			0.267640i
$277$	24.2351	+	7.87447i	1.45615	+	0.473131i	0.926891	−	0.375331i	$-0.122471\pi$
$277$	24.2351	+	7.87447i	1.45615	+	0.473131i	0.529257	+	0.848462i	$0.322471\pi$
$278$	4.32263	+	5.94959i	0.259254	+	0.356833i
$279$	0.396664	−	0.545961i	0.0237476	−	0.0326858i
$280$	−0.945523	−	3.88830i	−0.0565058	−	0.232370i
$281$	−5.91718	+	1.92261i	−0.352989	+	0.114693i	−0.480144	−	0.877190i	$-0.659416\pi$
$281$	−5.91718	+	1.92261i	−0.352989	+	0.114693i	0.127155	+	0.991883i	$0.459416\pi$
$282$	−1.75083	+	2.40981i	−0.104260	+	0.143502i
$283$	8.90438	−	6.46941i	0.529310	−	0.384567i	−0.290789	−	0.956787i	$-0.593918\pi$
$283$	8.90438	−	6.46941i	0.529310	−	0.384567i	0.820100	+	0.572221i	$0.193918\pi$
$284$	1.38430	−	4.26045i	0.0821433	−	0.252811i
$285$	2.12756			0.126026
$286$	11.0925	+	4.47721i	0.655912	+	0.264743i
$287$	6.44804	+	0.488518i	0.380616	+	0.0288363i
$288$	0.951057	+	0.309017i	0.0560415	+	0.0182090i
$289$	−36.6690	+	26.6416i	−2.15700	+	1.56715i
$290$	3.82142	−	5.25974i	0.224402	−	0.308862i
$291$	2.28866	+	7.04376i	0.134163	+	0.412912i
$292$	−2.17538	−	6.69513i	−0.127304	−	0.391803i
$293$	5.63311	+	4.09269i	0.329090	+	0.239098i	0.740044	−	0.672558i	$-0.234805\pi$
$293$	5.63311	+	4.09269i	0.329090	+	0.239098i	−0.410955	+	0.911656i	$0.634805\pi$
$294$	6.21837	−	3.21433i	0.362663	−	0.187463i
$295$	4.96938	−	15.2942i	0.289329	−	0.890462i
$296$		−	11.8054i		−	0.686176i
$297$	−1.75851	−	2.81205i	−0.102039	−	0.163172i
$298$	11.3765			0.659021
$299$	−4.95558	+	15.2517i	−0.286588	+	0.882029i
$300$	−1.59434	−	2.19441i	−0.0920490	−	0.126695i
$301$	1.58824	−	1.87063i	0.0915446	−	0.107821i
$302$	2.76907	+	8.52232i	0.159342	+	0.490404i
$303$	8.18303	−	2.65883i	0.470103	−	0.152746i
$304$	1.13803	+	0.826829i	0.0652706	+	0.0474219i
$305$	−1.19030	−	1.63831i	−0.0681566	−	0.0938095i
$306$	−7.50825	−	2.43958i	−0.429218	−	0.139461i
$307$	21.0529			1.20155			0.600777	−	0.799417i	$-0.294858\pi$
$307$	21.0529			1.20155			0.600777	+	0.799417i	$0.294858\pi$
$308$	−7.77021	+	4.07723i	−0.442749	+	0.232322i
$309$	12.0670			0.686465
$310$	0.970725	+	0.315408i	0.0551334	+	0.0179139i
$311$	9.22633	+	12.6990i	0.523177	+	0.720092i	0.986072	−	0.166322i	$-0.0531890\pi$
$311$	9.22633	+	12.6990i	0.523177	+	0.720092i	−0.462894	+	0.886414i	$0.653189\pi$
$312$	2.91785	+	2.11995i	0.165191	+	0.120018i
$313$	−14.0629	+	4.56932i	−0.794884	+	0.258273i	−0.678182	−	0.734894i	$-0.737232\pi$
$313$	−14.0629	+	4.56932i	−0.794884	+	0.258273i	−0.116701	+	0.993167i	$0.537232\pi$
$314$	5.50744	+	16.9501i	0.310803	+	0.956552i
$315$	−2.58994	+	3.05043i	−0.145926	+	0.171872i
$316$	−8.98969	−	12.3732i	−0.505709	−	0.696049i
$317$	6.47364	−	19.9238i	0.363596	−	1.11903i	−0.587260	−	0.809399i	$-0.699793\pi$
$317$	6.47364	−	19.9238i	0.363596	−	1.11903i	0.950856	−	0.309635i	$-0.100207\pi$
$318$	−1.10469			−0.0619479
$319$	−13.2204	−	5.33608i	−0.740198	−	0.298763i
$320$			1.51247i			0.0845494i
$321$	5.83151	−	17.9475i	0.325483	−	1.00173i
$322$	−6.17596	−	10.0125i	−0.344173	−	0.557972i
$323$	−8.98435	−	6.52751i	−0.499903	−	0.363201i
$324$	−0.309017	−	0.951057i	−0.0171676	−	0.0528365i
$325$	−3.02308	−	9.30408i	−0.167690	−	0.516097i
$326$	−7.23814	+	9.96244i	−0.400883	+	0.551769i
$327$	7.69529	−	5.59096i	0.425551	−	0.309181i
$328$	−2.32449	−	0.755273i	−0.128349	−	0.0417030i
$329$	0.595366	−	7.85835i	0.0328236	−	0.433245i
$330$	3.22308	−	3.84381i	0.177425	−	0.211595i
$331$	5.27071			0.289704			0.144852	−	0.989453i	$-0.453729\pi$
$331$	5.27071			0.289704			0.144852	+	0.989453i	$0.453729\pi$
$332$	−3.33747	+	10.2717i	−0.183167	+	0.563731i
$333$	−9.55078	+	6.93905i	−0.523379	+	0.380257i
$334$	1.28980	−	1.77526i	0.0705748	−	0.0971379i
$335$	9.54740	−	3.10214i	0.521630	−	0.169488i
$336$	−2.57083	+	0.625153i	−0.140250	+	0.0341049i
$337$	2.45514	−	3.37922i	0.133740	−	0.184078i	−0.736894	−	0.676008i	$-0.763709\pi$
$337$	2.45514	−	3.37922i	0.133740	−	0.184078i	0.870635	+	0.491930i	$0.163709\pi$
$338$	0.00472695	+	0.00650609i	0.000257112	+	0.000353885i
$339$	−17.1141	−	5.56070i	−0.929509	−	0.302016i
$340$		−	11.9404i		−	0.647558i
$341$	0.155360	−	2.23281i	0.00841322	−	0.120913i
$342$		−	1.40668i		−	0.0760648i
$343$	−9.53801	+	15.8753i	−0.515004	+	0.857188i
$344$	−0.750361	+	0.545169i	−0.0404567	+	0.0293935i
$345$	5.44063	+	3.95285i	0.292914	+	0.212814i
$346$	−8.04673	+	2.61454i	−0.432595	+	0.140559i
$347$	14.5241	−	4.71916i	0.779694	−	0.253338i	0.107985	−	0.994153i	$-0.465560\pi$
$347$	14.5241	−	4.71916i	0.779694	−	0.253338i	0.671710	+	0.740815i	$0.265560\pi$
$348$	−3.47759	−	2.52662i	−0.186418	−	0.135441i
$349$	−22.6754	+	16.4746i	−1.21378	+	0.881866i	−0.995569	−	0.0940344i	$-0.970024\pi$
$349$	−22.6754	+	16.4746i	−1.21378	+	0.881866i	−0.218216	+	0.975901i	$0.570024\pi$
$350$	6.63818	+	2.72693i	0.354825	+	0.145760i
$351$		−	3.60667i		−	0.192510i
$352$	3.21783	−	0.803473i	0.171511	−	0.0428252i
$353$		−	8.93399i		−	0.475508i	−0.971325	−	0.237754i	$-0.923589\pi$
$353$		−	8.93399i		−	0.475508i	0.971325	−	0.237754i	$-0.0764113\pi$
$354$	−10.1121	−	3.28562i	−0.537451	−	0.174628i
$355$	−3.98248	−	5.48141i	−0.211368	−	0.290923i
$356$	4.90957	−	6.75745i	0.260207	−	0.358144i
$357$	20.2958	−	4.93536i	1.07417	−	0.261207i
$358$	4.15582	−	1.35031i	0.219642	−	0.0713660i
$359$	−14.6315	+	20.1386i	−0.772222	+	1.06287i	0.223875	+	0.974618i	$0.428129\pi$
$359$	−14.6315	+	20.1386i	−0.772222	+	1.06287i	−0.996098	+	0.0882552i	$0.971871\pi$
$360$	1.22361	−	0.889005i	0.0644900	−	0.0468547i
$361$	−5.25985	+	16.1882i	−0.276834	+	0.852008i
$362$	−7.33745			−0.385648
$363$	−9.89005	−	4.81527i	−0.519093	−	0.252736i
$364$	−9.51507	−	0.720884i	−0.498725	−	0.0377846i
$365$	−10.1262	−	3.29019i	−0.530027	−	0.172216i
$366$	−1.08321	+	0.786995i	−0.0566201	+	0.0411369i
$367$	9.18468	−	12.6416i	0.479437	−	0.659888i	−0.498960	−	0.866625i	$-0.666285\pi$
$367$	9.18468	−	12.6416i	0.479437	−	0.659888i	0.978397	+	0.206737i	$0.0662845\pi$
$368$	1.37401	+	4.22875i	0.0716250	+	0.220439i
$369$	0.755273	+	2.32449i	0.0393179	+	0.121008i
$370$	−14.4452	−	10.4951i	−0.750972	−	0.545613i
$371$	2.48757	−	1.53440i	0.129148	−	0.0796620i
$372$	0.208539	−	0.641816i	0.0108122	−	0.0332766i
$373$		−	5.34373i		−	0.276688i	−0.990384	−	0.138344i	$-0.955822\pi$
$373$		−	5.34373i		−	0.276688i	0.990384	−	0.138344i	$-0.0441779\pi$
$374$	−25.4036	+	6.34313i	−1.31359	+	0.327995i
$375$	−11.6648			−0.602368
$376$	−0.920466	+	2.83290i	−0.0474694	+	0.146096i
$377$	−9.11266	−	12.5425i	−0.469326	−	0.645972i
$378$	2.01686	+	1.71239i	0.103736	+	0.0880759i
$379$	−9.77892	−	30.0964i	−0.502309	−	1.54595i	−0.805247	−	0.592939i	$-0.797968\pi$
$379$	−9.77892	−	30.0964i	−0.502309	−	1.54595i	0.302938	−	0.953010i	$-0.402032\pi$
$380$	2.02343	−	0.657453i	0.103800	−	0.0337266i
$381$	12.3173	+	8.94908i	0.631037	+	0.458475i
$382$	−14.8946	−	20.5006i	−0.762072	−	1.04890i
$383$	6.34849	+	2.06275i	0.324392	+	0.105402i	0.466686	−	0.884423i	$-0.345448\pi$
$383$	6.34849	+	2.06275i	0.324392	+	0.105402i	−0.142294	+	0.989824i	$0.545448\pi$
$384$	1.00000			0.0510310
$385$	−1.91882	+	13.1324i	−0.0977919	+	0.669289i
$386$	5.09857			0.259510
$387$	0.882102	+	0.286612i	0.0448398	+	0.0145693i
$388$	4.35328	+	5.99178i	0.221004	+	0.304186i
$389$	−24.2034	−	17.5848i	−1.22716	−	0.891586i	−0.230489	−	0.973075i	$-0.574032\pi$
$389$	−24.2034	−	17.5848i	−1.22716	−	0.891586i	−0.996674	+	0.0814889i	$0.974032\pi$
$390$	5.18798	−	1.68568i	0.262703	−	0.0853575i
$391$	−10.8473	−	33.3845i	−0.548570	−	1.68833i
$392$	4.92074	−	4.97859i	0.248535	−	0.251457i
$393$	−8.51011	−	11.7132i	−0.429278	−	0.590851i
$394$	3.20840	−	9.87445i	0.161637	−	0.497468i
$395$	−23.1319			−1.16389
$396$	−2.54142	−	2.13101i	−0.127711	−	0.107087i
$397$			23.3581i			1.17231i	0.810199	+	0.586155i	$0.199359\pi$
$397$			23.3581i			1.17231i	−0.810199	+	0.586155i	$0.800641\pi$
$398$	−4.21250	+	12.9647i	−0.211154	+	0.649864i
$399$	1.95387	+	3.16761i	0.0978157	+	0.158579i
$400$	−2.19441	−	1.59434i	−0.109721	−	0.0797168i
$401$	−2.73082	−	8.40459i	−0.136371	−	0.419705i	0.859430	−	0.511253i	$-0.170819\pi$
$401$	−2.73082	−	8.40459i	−0.136371	−	0.419705i	−0.995801	+	0.0915478i	$0.970819\pi$
$402$	−2.05105	−	6.31247i	−0.102297	−	0.314837i
$403$	1.43063	−	1.96910i	0.0712650	−	0.0980878i
$404$	6.96090	−	5.05739i	0.346318	−	0.251615i
$405$	−1.43844	−	0.467378i	−0.0714767	−	0.0232242i
$406$	11.3404	+	0.859172i	0.562813	+	0.0426400i
$407$	−14.6549	+	36.3081i	−0.726416	+	1.79973i
$408$	−7.89464			−0.390843
$409$	−9.69986	+	29.8531i	−0.479627	+	1.47614i	0.359987	+	0.932957i	$0.382781\pi$
$409$	−9.69986	+	29.8531i	−0.479627	+	1.47614i	−0.839614	+	0.543183i	$0.817219\pi$
$410$	−2.99065	+	2.17283i	−0.147697	+	0.107309i
$411$	0.269270	−	0.370618i	0.0132821	−	0.0182813i
$412$	11.4764	−	3.72889i	0.565400	−	0.183709i
$413$	27.3343	−	6.64692i	1.34503	−	0.327074i
$414$	2.61351	−	3.59719i	0.128447	−	0.176792i
$415$	9.60150	+	13.2153i	0.471319	+	0.648715i
$416$	3.43014	+	1.11452i	0.168177	+	0.0546439i
$417$		−	7.35410i		−	0.360132i
$418$	−2.47367	−	3.95567i	−0.120991	−	0.193478i
$419$			4.36485i			0.213237i	0.994300	+	0.106618i	$0.0340023\pi$
$419$			4.36485i			0.213237i	−0.994300	+	0.106618i	$0.965998\pi$
$420$	−1.52054	+	3.70146i	−0.0741948	+	0.180613i
$421$	26.3717	−	19.1602i	1.28528	−	0.933809i	0.285579	−	0.958355i	$-0.407814\pi$
$421$	26.3717	−	19.1602i	1.28528	−	0.933809i	0.999699	+	0.0245465i	$0.00781419\pi$
$422$	−12.6569	−	9.19578i	−0.616128	−	0.447643i
$423$	2.83290	−	0.920466i	0.137740	−	0.0447546i
$424$	−1.05062	+	0.341368i	−0.0510227	+	0.0165783i
$425$	17.3241	+	12.5867i	0.840343	+	0.610545i
$426$	−3.62415	+	2.63310i	−0.175591	+	0.127574i
$427$	1.34606	−	3.27673i	0.0651406	−	0.158572i
$428$		−	18.8712i		−	0.912172i
$429$	−6.34237	−	10.1421i	−0.306212	−	0.489667i
$430$			1.40281i			0.0676494i
$431$	7.38267	+	2.39877i	0.355610	+	0.115545i	0.481374	−	0.876515i	$-0.340138\pi$
$431$	7.38267	+	2.39877i	0.355610	+	0.115545i	−0.125763	+	0.992060i	$0.540138\pi$
$432$	−0.587785	−	0.809017i	−0.0282798	−	0.0389238i
$433$	6.99991	−	9.63455i	0.336394	−	0.463007i	−0.606990	−	0.794710i	$-0.707623\pi$
$433$	6.99991	−	9.63455i	0.336394	−	0.463007i	0.943384	+	0.331703i	$0.107623\pi$
$434$	0.421881	+	1.73491i	0.0202509	+	0.0832785i
$435$	−6.18319	+	2.00904i	−0.296461	+	0.0963261i
$436$	5.59096	−	7.69529i	0.267758	−	0.368538i
$437$	5.06012	−	3.67639i	0.242058	−	0.175866i
$438$	−2.17538	+	6.69513i	−0.103944	+	0.319906i
$439$	31.3879			1.49806			0.749031	−	0.662535i	$-0.230519\pi$
$439$	31.3879			1.49806			0.749031	+	0.662535i	$0.230519\pi$
$440$	1.87753	−	4.65166i	0.0895077	−	0.221759i
$441$	−6.92010	−	1.05462i	−0.329529	−	0.0502199i
$442$	−27.0797	−	8.79874i	−1.28805	−	0.418514i
$443$	5.49777	−	3.99437i	0.261207	−	0.189778i	−0.449472	−	0.893294i	$-0.648388\pi$
$443$	5.49777	−	3.99437i	0.261207	−	0.189778i	0.710679	+	0.703516i	$0.248388\pi$
$444$	−6.93905	+	9.55078i	−0.329313	+	0.453260i
$445$	−3.90385	−	12.0148i	−0.185060	−	0.569557i
$446$	−0.609775	−	1.87669i	−0.0288737	−	0.0888640i
$447$	−9.20375	−	6.68692i	−0.435323	−	0.316280i
$448$	−2.25182	+	1.38899i	−0.106389	+	0.0656235i
$449$	−11.7059	+	36.0270i	−0.552435	+	1.70022i	0.150187	+	0.988658i	$0.452012\pi$
$449$	−11.7059	+	36.0270i	−0.552435	+	1.70022i	−0.702622	+	0.711563i	$0.747988\pi$
$450$			2.71245i			0.127866i
$451$	6.21151	+	5.20843i	0.292489	+	0.245256i
$452$	−17.9948			−0.846405
$453$	2.76907	−	8.52232i	0.130102	−	0.400413i
$454$	−13.2006	−	18.1690i	−0.619534	−	0.852716i
$455$	−9.34103	+	11.0019i	−0.437914	+	0.515776i
$456$	−0.434690	−	1.33784i	−0.0203562	−	0.0626499i
$457$	−25.1501	+	8.17175i	−1.17647	+	0.382258i	−0.831054	−	0.556192i	$-0.812262\pi$
$457$	−25.1501	+	8.17175i	−1.17647	+	0.382258i	−0.345416	+	0.938450i	$0.612262\pi$
$458$	14.9018	+	10.8268i	0.696316	+	0.505903i
$459$	4.64035	+	6.38690i	0.216593	+	0.298115i
$460$	6.39585	+	2.07814i	0.298208	+	0.0968936i
$461$	16.9687			0.790310			0.395155	−	0.918614i	$-0.370691\pi$
$461$	16.9687			0.790310			0.395155	+	0.918614i	$0.370691\pi$
$462$	8.68277	+	1.26867i	0.403959	+	0.0590237i
$463$	22.4426			1.04300			0.521498	−	0.853253i	$-0.325373\pi$
$463$	22.4426			1.04300			0.521498	+	0.853253i	$0.325373\pi$
$464$	−4.08815	−	1.32832i	−0.189788	−	0.0616658i
$465$	−0.599941	−	0.825748i	−0.0278216	−	0.0382931i
$466$	−8.72844	−	6.34158i	−0.404337	−	0.293768i
$467$	11.2703	−	3.66193i	0.521526	−	0.169454i	−0.0364118	−	0.999337i	$-0.511593\pi$
$467$	11.2703	−	3.66193i	0.521526	−	0.169454i	0.557938	+	0.829883i	$0.311593\pi$
$468$	−1.11452	−	3.43014i	−0.0515188	−	0.158558i
$469$	13.3865	+	11.3657i	0.618133	+	0.524819i
$470$	2.64807	+	3.64476i	0.122146	+	0.168120i
$471$	5.50744	−	16.9501i	0.253769	−	0.781021i
$472$	−10.6325			−0.489399
$473$	2.98453	−	0.745219i	0.137229	−	0.0342652i
$474$			15.2942i			0.702485i
$475$	−1.17907	+	3.62881i	−0.0540995	+	0.166501i
$476$	17.7773	−	10.9656i	0.814823	−	0.502605i
$477$	0.893712	+	0.649320i	0.0409203	+	0.0297303i
$478$	2.53538	+	7.80310i	0.115966	+	0.356905i
$479$	−11.1271	−	34.2456i	−0.508409	−	1.56472i	−0.794964	−	0.606657i	$-0.792510\pi$
$479$	−11.1271	−	34.2456i	−0.508409	−	1.56472i	0.286555	−	0.958064i	$-0.407490\pi$
$480$	0.889005	−	1.22361i	0.0405774	−	0.0558499i
$481$	−34.4465	+	25.0268i	−1.57062	+	1.14113i
$482$	−14.2551	−	4.63176i	−0.649302	−	0.210971i
$483$	−0.888720	+	11.7304i	−0.0404382	+	0.533751i
$484$	−10.8940	−	1.52340i	−0.495182	−	0.0692454i
$485$	11.2017			0.508643
$486$	−0.309017	+	0.951057i	−0.0140173	+	0.0431408i
$487$	−15.5056	+	11.2655i	−0.702628	+	0.510489i	−0.880787	−	0.473513i	$-0.842986\pi$
$487$	−15.5056	+	11.2655i	−0.702628	+	0.510489i	0.178159	+	0.984002i	$0.442986\pi$
$488$	−0.786995	+	1.08321i	−0.0356256	+	0.0490344i
$489$	11.7116	−	3.80531i	0.529615	−	0.172082i
$490$	−1.71729	−	10.4471i	−0.0775795	−	0.471950i
$491$	−9.91427	+	13.6458i	−0.447425	+	0.615827i	−0.971842	−	0.235634i	$-0.924283\pi$
$491$	−9.91427	+	13.6458i	−0.447425	+	0.615827i	0.524417	+	0.851462i	$0.324283\pi$
$492$	1.43661	+	1.97733i	0.0647676	+	0.0891450i
$493$	32.2745	+	10.4866i	1.45357	+	0.472293i
$494$		−	5.07344i		−	0.228265i
$495$	−4.86686	+	1.21523i	−0.218749	+	0.0546203i
$496$		−	0.674845i		−	0.0303014i
$497$	4.50362	−	10.9632i	0.202015	−	0.491766i
$498$	8.73761	−	6.34824i	0.391541	−	0.284472i
$499$	−6.22714	−	4.52428i	−0.278765	−	0.202535i	0.439613	−	0.898187i	$-0.355115\pi$
$499$	−6.22714	−	4.52428i	−0.278765	−	0.202535i	−0.718379	+	0.695652i	$0.755115\pi$
$500$	−11.0939	+	3.60463i	−0.496134	+	0.161204i
$501$	−2.08694	+	0.678089i	−0.0932377	+	0.0302948i
$502$	22.9892	+	16.7026i	1.02606	+	0.745474i
$503$	5.05833	−	3.67509i	0.225540	−	0.163864i	−0.469277	−	0.883051i	$-0.655485\pi$
$503$	5.05833	−	3.67509i	0.225540	−	0.163864i	0.694817	+	0.719187i	$0.255485\pi$
$504$	2.44730	+	1.00534i	0.109012	+	0.0447813i
$505$		−	13.0135i		−	0.579093i
$506$	1.02363	−	14.7114i	0.0455058	−	0.654001i
$507$		−	0.00804197i		−	0.000357157i
$508$	14.4799	+	4.70481i	0.642442	+	0.208742i
$509$	4.93163	+	6.78781i	0.218591	+	0.300864i	0.904203	−	0.427102i	$-0.140466\pi$
$509$	4.93163	+	6.78781i	0.218591	+	0.300864i	−0.685613	+	0.727967i	$0.740466\pi$
$510$	−7.01838	+	9.65997i	−0.310779	+	0.427751i
$511$	−4.40087	−	18.0978i	−0.194683	−	0.800601i
$512$	0.951057	−	0.309017i	0.0420312	−	0.0136568i
$513$	−0.826829	+	1.13803i	−0.0365054	+	0.0502453i
$514$	13.2616	−	9.63509i	0.584943	−	0.424986i
$515$	5.63983	−	17.3576i	0.248520	−	0.764867i
$516$	0.927497			0.0408308
$517$	6.34762	−	7.57009i	0.279168	−	0.332932i
$518$	2.35961	−	31.1449i	0.103675	−	1.36843i
$519$	8.04673	+	2.61454i	0.353212	+	0.114766i
$520$	4.41316	−	3.20635i	0.193530	−	0.140608i
$521$	12.0199	−	16.5439i	0.526599	−	0.724802i	−0.460008	−	0.887915i	$-0.652153\pi$
$521$	12.0199	−	16.5439i	0.526599	−	0.724802i	0.986607	+	0.163113i	$0.0521535\pi$
$522$	1.32832	+	4.08815i	0.0581390	+	0.178934i
$523$	10.2649	+	31.5921i	0.448852	+	1.38143i	0.878203	+	0.478287i	$0.158742\pi$
$523$	10.2649	+	31.5921i	0.448852	+	1.38143i	−0.429351	+	0.903138i	$0.641258\pi$
$524$	−11.7132	−	8.51011i	−0.511692	−	0.371766i
$525$	−3.76755	−	6.10795i	−0.164429	−	0.266573i
$526$	−0.675685	+	2.07955i	−0.0294613	+	0.0906725i
$527$			5.32766i			0.232076i
$528$	−3.07555	−	1.24137i	−0.133846	−	0.0540237i
$529$	−3.22976			−0.140424
$530$	−0.516307	+	1.58903i	−0.0224269	+	0.0690231i
$531$	6.24961	+	8.60185i	0.271210	+	0.373289i
$532$	2.83708	+	2.40880i	0.123003	+	0.104435i
$533$	2.72402	+	8.38367i	0.117990	+	0.363137i
$534$	−7.94386	+	2.58112i	−0.343764	+	0.111696i
$535$	−23.0910	−	16.7766i	−0.998309	−	0.725314i
$536$	−3.90132	−	5.36971i	−0.168511	−	0.231936i
$537$	−4.15582	−	1.35031i	−0.179337	−	0.0582701i
$538$	24.7423			1.06671
$539$	−21.3142	+	9.20344i	−0.918069	+	0.396420i
$540$	−1.51247			−0.0650862
$541$	29.3111	+	9.52374i	1.26018	+	0.409458i	0.861559	−	0.507657i	$-0.169488\pi$
$541$	29.3111	+	9.52374i	1.26018	+	0.409458i	0.398622	+	0.917115i	$0.369488\pi$
$542$	11.6390	+	16.0197i	0.499938	+	0.688105i
$543$	5.93612	+	4.31284i	0.254743	+	0.185082i
$544$	−7.50825	+	2.43958i	−0.321914	+	0.104596i
$545$	−4.44565	−	13.6823i	−0.190431	−	0.586086i
$546$	7.27413	+	6.17603i	0.311304	+	0.264310i
$547$	23.9357	+	32.9447i	1.02342	+	1.40861i	0.909781	+	0.415089i	$0.136250\pi$
$547$	23.9357	+	32.9447i	1.02342	+	1.40861i	0.113636	+	0.993522i	$0.463750\pi$
$548$	0.141564	−	0.435688i	0.00604730	−	0.0186117i
$549$	1.33892			0.0571435
$550$	4.76987	+	7.62754i	0.203388	+	0.325239i
$551$			6.04669i			0.257598i
$552$	1.37401	−	4.22875i	0.0584815	−	0.179988i
$553$	−21.2434	−	34.4398i	−0.903362	−	1.46453i
$554$	−20.6156	−	14.9781i	−0.875874	−	0.636360i
$555$	5.51759	+	16.9814i	0.234209	+	0.720820i
$556$	−2.27254	−	6.99416i	−0.0963772	−	0.296619i
$557$	25.1624	−	34.6331i	1.06617	−	1.46745i	0.192268	−	0.981342i	$-0.438416\pi$
$557$	25.1624	−	34.6331i	1.06617	−	1.46745i	0.873898	−	0.486109i	$-0.161584\pi$
$558$	−0.545961	+	0.396664i	−0.0231124	+	0.0167921i
$559$	3.18145	+	1.03372i	0.134561	+	0.0437215i
$560$	−0.302305	+	3.99017i	−0.0127747	+	0.168616i
$561$	24.2804	+	9.80017i	1.02512	+	0.413763i
$562$	6.22169			0.262446
$563$	4.32950	−	13.3248i	0.182467	−	0.561575i	−0.817429	−	0.576030i	$-0.804601\pi$
$563$	4.32950	−	13.3248i	0.182467	−	0.561575i	0.999896	+	0.0144549i	$0.00460129\pi$
$564$	2.40981	−	1.75083i	0.101471	−	0.0737232i
$565$	−15.9975	+	22.0186i	−0.673019	+	0.926331i
$566$	−10.4677	+	3.40117i	−0.439991	+	0.142962i
$567$	−0.625153	−	2.57083i	−0.0262540	−	0.107965i
$568$	−2.63310	+	3.62415i	−0.110483	+	0.152066i
$569$	−1.37917	−	1.89827i	−0.0578180	−	0.0795797i	0.779129	−	0.626864i	$-0.215662\pi$
$569$	−1.37917	−	1.89827i	−0.0578180	−	0.0795797i	−0.836947	+	0.547284i	$0.815662\pi$
$570$	−2.02343	−	0.657453i	−0.0847523	−	0.0275377i
$571$			36.0952i			1.51054i	0.655416	+	0.755268i	$0.272494\pi$
$571$			36.0952i			1.51054i	−0.655416	+	0.755268i	$0.727506\pi$
$572$	−9.16604	−	7.68584i	−0.383251	−	0.321361i
$573$			25.3402i			1.05860i
$574$	−5.98149	−	2.45716i	−0.249663	−	0.102560i
$575$	−9.75719	+	7.08901i	−0.406903	+	0.295632i
$576$	−0.809017	−	0.587785i	−0.0337090	−	0.0244911i
$577$	−34.9652	+	11.3609i	−1.45562	+	0.472960i	−0.926730	−	0.375729i	$-0.877393\pi$
$577$	−34.9652	+	11.3609i	−1.45562	+	0.472960i	−0.528892	+	0.848689i	$0.677393\pi$
$578$	43.1070	−	14.0063i	1.79301	−	0.582585i
$579$	−4.12483	−	2.99686i	−0.171422	−	0.124545i
$580$	−5.25974	+	3.82142i	−0.218399	+	0.158676i
$581$	−10.8579	+	26.4315i	−0.450463	+	1.09657i
$582$		−	7.40625i		−	0.306999i
$583$	3.65500	+	0.254317i	0.151375	+	0.0105327i
$584$			7.03967i			0.291304i
$585$	−5.18798	−	1.68568i	−0.214496	−	0.0696941i
$586$	−4.09269	−	5.63311i	−0.169068	−	0.232702i
$587$	−22.6572	+	31.1850i	−0.935164	+	1.28714i	0.0226471	+	0.999744i	$0.492791\pi$
$587$	−22.6572	+	31.1850i	−0.935164	+	1.28714i	−0.957811	+	0.287399i	$0.907209\pi$
$588$	−6.90730	+	1.13543i	−0.284852	+	0.0468242i
$589$	−0.902832	+	0.293348i	−0.0372006	+	0.0120872i
$590$	−9.45233	+	13.0100i	−0.389146	+	0.535614i
$591$	−8.39971	+	6.10275i	−0.345518	+	0.251033i
$592$	−3.64807	+	11.2276i	−0.149935	+	0.461452i
$593$	−26.6505			−1.09440			−0.547202	−	0.837000i	$-0.684307\pi$
$593$	−26.6505			−1.09440			−0.547202	+	0.837000i	$0.684307\pi$
$594$	0.803473	+	3.21783i	0.0329669	+	0.132029i
$595$	2.38659	−	31.5010i	0.0978405	−	1.29141i
$596$	−10.8197	−	3.51552i	−0.443191	−	0.144001i
$597$	11.0285	−	8.01265i	0.451365	−	0.327936i
$598$	9.42607	−	12.9739i	0.385461	−	0.530541i
$599$	−2.86334	−	8.81247i	−0.116993	−	0.360068i	0.875364	−	0.483464i	$-0.160621\pi$
$599$	−2.86334	−	8.81247i	−0.116993	−	0.360068i	−0.992358	+	0.123396i	$0.960621\pi$
$600$	0.838192	+	2.57969i	0.0342190	+	0.105315i
$601$	−24.2748	−	17.6367i	−0.990191	−	0.719416i	−0.0302285	−	0.999543i	$-0.509623\pi$
$601$	−24.2748	−	17.6367i	−0.990191	−	0.719416i	−0.959963	+	0.280127i	$0.909623\pi$
$602$	−2.08856	+	1.28828i	−0.0851234	+	0.0525064i
$603$	−2.05105	+	6.31247i	−0.0835250	+	0.257064i
$604$		−	8.96090i		−	0.364614i
$605$	−11.5489	+	11.9757i	−0.469528	+	0.486882i
$606$	−8.60415			−0.349520
$607$	−6.87027	+	21.1445i	−0.278856	+	0.858230i	0.709318	+	0.704889i	$0.249003\pi$
$607$	−6.87027	+	21.1445i	−0.278856	+	0.858230i	−0.988173	+	0.153341i	$0.950997\pi$
$608$	−0.826829	−	1.13803i	−0.0335323	−	0.0461533i
$609$	−8.66954	−	7.36078i	−0.351307	−	0.298274i
$610$	0.625780	+	1.92595i	0.0253371	+	0.0779795i
$611$	10.2173	−	3.31981i	0.413349	−	0.134305i
$612$	6.38690	+	4.64035i	0.258175	+	0.187575i
$613$	−6.16543	−	8.48599i	−0.249019	−	0.342746i	0.666148	−	0.745819i	$-0.267942\pi$
$613$	−6.16543	−	8.48599i	−0.249019	−	0.342746i	−0.915168	+	0.403074i	$0.867942\pi$
$614$	−20.0225	−	6.50571i	−0.808043	−	0.262549i
$615$	3.69664			0.149063
$616$	8.64984	−	1.47655i	0.348512	−	0.0594919i
$617$	−3.53597			−0.142353			−0.0711763	−	0.997464i	$-0.522675\pi$
$617$	−3.53597			−0.142353			−0.0711763	+	0.997464i	$0.522675\pi$
$618$	−11.4764	−	3.72889i	−0.461647	−	0.149998i
$619$	16.5933	+	22.8387i	0.666941	+	0.917966i	0.999686	−	0.0250511i	$-0.00797484\pi$
$619$	16.5933	+	22.8387i	0.666941	+	0.917966i	−0.332745	+	0.943017i	$0.607975\pi$
$620$	−0.825748	−	0.599941i	−0.0331628	−	0.0240942i
$621$	−4.22875	+	1.37401i	−0.169694	+	0.0551369i
$622$	−4.85057	−	14.9285i	−0.194490	−	0.598579i
$623$	14.3030	−	16.8461i	0.573039	−	0.674926i
$624$	−2.11995	−	2.91785i	−0.0848657	−	0.116808i
$625$	−1.26092	+	3.88070i	−0.0504367	+	0.155228i
$626$	14.7866			0.590993
$627$	−0.323842	+	4.65419i	−0.0129330	+	0.185871i
$628$		−	17.8224i		−	0.711193i
$629$	28.8002	−	88.6380i	1.14834	−	3.53423i
$630$	3.40581	−	2.10080i	0.135691	−	0.0836977i
$631$	8.85592	+	6.43420i	0.352548	+	0.256141i	0.749937	−	0.661509i	$-0.230084\pi$
$631$	8.85592	+	6.43420i	0.352548	+	0.256141i	−0.397389	+	0.917650i	$0.630084\pi$
$632$	4.72616	+	14.5456i	0.187997	+	0.578594i
$633$	4.83451	+	14.8791i	0.192154	+	0.591390i
$634$	−12.3136	+	16.9482i	−0.489036	+	0.673100i
$635$	18.6296	−	13.5352i	0.739292	−	0.537127i
$636$	1.05062	+	0.341368i	0.0416599	+	0.0135361i
$637$	−24.9585	−	3.80366i	−0.988891	−	0.150706i
$638$	10.9244	+	9.16023i	0.432500	+	0.362657i
$639$	4.47970			0.177214
$640$	0.467378	−	1.43844i	0.0184747	−	0.0568594i
$641$	4.99853	−	3.63164i	0.197430	−	0.143441i	−0.484678	−	0.874693i	$-0.661063\pi$
$641$	4.99853	−	3.63164i	0.197430	−	0.143441i	0.682108	+	0.731251i	$0.261063\pi$
$642$	−11.0922	+	15.2671i	−0.437774	+	0.602544i
$643$	−13.1372	+	4.26855i	−0.518082	+	0.168335i	−0.556375	−	0.830931i	$-0.687808\pi$
$643$	−13.1372	+	4.26855i	−0.518082	+	0.168335i	0.0382926	+	0.999267i	$0.487808\pi$
$644$	2.77966	+	11.4309i	0.109534	+	0.450440i
$645$	0.824550	−	1.13490i	0.0324666	−	0.0446865i
$646$	6.52751	+	8.98435i	0.256822	+	0.353485i
$647$	37.4603	+	12.1716i	1.47272	+	0.478515i	0.931928	−	0.362644i	$-0.118126\pi$
$647$	37.4603	+	12.1716i	1.47272	+	0.478515i	0.540789	+	0.841158i	$0.318126\pi$
$648$			1.00000i			0.0392837i
$649$	32.7007	+	13.1988i	1.28361	+	0.518100i
$650$			9.78289i			0.383716i
$651$	0.678447	−	1.65155i	0.0265905	−	0.0647294i
$652$	9.96244	−	7.23814i	0.390159	−	0.283467i
$653$	9.98815	+	7.25682i	0.390867	+	0.283981i	0.765811	−	0.643066i	$-0.222338\pi$
$653$	9.98815	+	7.25682i	0.390867	+	0.283981i	−0.374944	+	0.927048i	$0.622338\pi$
$654$	−9.04636	+	2.93934i	−0.353741	+	0.114937i
$655$	−20.8261	+	6.76682i	−0.813744	+	0.264401i
$656$	1.97733	+	1.43661i	0.0772018	+	0.0560904i
$657$	5.69522	−	4.13782i	0.222192	−	0.161432i
$658$	−2.99459	+	7.28976i	−0.116741	+	0.284184i
$659$			16.2854i			0.634388i	0.948361	+	0.317194i	$0.102741\pi$
$659$			16.2854i			0.634388i	−0.948361	+	0.317194i	$0.897259\pi$
$660$	−4.25313	+	2.65969i	−0.165553	+	0.103528i
$661$		−	5.92416i		−	0.230423i	−0.993341	−	0.115211i	$-0.963245\pi$
$661$		−	5.92416i		−	0.230423i	0.993341	−	0.115211i	$-0.0367546\pi$
$662$	−5.01274	−	1.62874i	−0.194826	−	0.0633028i
$663$	16.7362	+	23.0354i	0.649980	+	0.894621i
$664$	6.34824	−	8.73761i	0.246360	−	0.339085i
$665$	5.46961	−	1.33005i	0.212102	−	0.0515772i
$666$	11.2276	−	3.64807i	0.435061	−	0.141360i
$667$	−11.2343	+	15.4627i	−0.434993	+	0.598717i
$668$	−1.77526	+	1.28980i	−0.0686868	+	0.0499039i
$669$	−0.609775	+	1.87669i	−0.0235752	+	0.0725572i
$670$	−10.0387			−0.387830
$671$	3.76510	−	2.35450i	0.145350	−	0.0908945i
$672$	2.63819	+	0.199875i	0.101770	+	0.00771036i
$673$	−3.64048	−	1.18286i	−0.140330	−	0.0455960i	0.238010	−	0.971263i	$-0.423505\pi$
$673$	−3.64048	−	1.18286i	−0.140330	−	0.0455960i	−0.378340	+	0.925667i	$0.623505\pi$
$674$	−3.37922	+	2.45514i	−0.130163	+	0.0945686i
$675$	1.59434	−	2.19441i	0.0613660	−	0.0844630i
$676$	−0.00248511	−	0.00764837i	−9.55810e−5	−	0.000294168i
$677$	4.88503	+	15.0346i	0.187747	+	0.577825i	0.999985	−	0.00550075i	$-0.00175095\pi$
$677$	4.88503	+	15.0346i	0.187747	+	0.577825i	−0.812238	+	0.583326i	$0.801751\pi$
$678$	14.5581	+	10.5771i	0.559101	+	0.406210i
$679$	10.2872	+	16.6776i	0.394786	+	0.640026i
$680$	−3.68978	+	11.3560i	−0.141497	+	0.435482i
$681$			22.4582i			0.860599i
$682$	−0.837732	+	2.07552i	−0.0320784	+	0.0794757i
$683$	−16.5832			−0.634538			−0.317269	−	0.948336i	$-0.602766\pi$
$683$	−16.5832			−0.634538			−0.317269	+	0.948336i	$0.602766\pi$
$684$	−0.434690	+	1.33784i	−0.0166208	+	0.0511535i
$685$	−0.407262	−	0.560548i	−0.0155607	−	0.0214174i
$686$	13.9769	−	12.1509i	0.533642	−	0.463925i
$687$	−5.69199	−	17.5181i	−0.217163	−	0.668358i
$688$	0.882102	−	0.286612i	0.0336298	−	0.0109270i
$689$	3.22332	+	2.34188i	0.122799	+	0.0892185i
$690$	−3.95285	−	5.44063i	−0.150482	−	0.207121i
$691$	25.4723	+	8.27644i	0.969011	+	0.314851i	0.750417	−	0.660965i	$-0.229853\pi$
$691$	25.4723	+	8.27644i	0.969011	+	0.314851i	0.218594	+	0.975816i	$0.429853\pi$
$692$	8.46084			0.321633
$693$	−6.27880	−	6.12998i	−0.238512	−	0.232859i
$694$	−15.2715			−0.579699
$695$	−10.5784	−	3.43714i	−0.401263	−	0.130378i
$696$	2.52662	+	3.47759i	0.0957712	+	0.131818i
$697$	−15.6103	−	11.3416i	−0.591283	−	0.429592i
$698$	26.6565	−	8.66122i	1.00896	−	0.327832i
$699$	3.33397	+	10.2609i	0.126102	+	0.388103i
$700$	−5.47062	−	4.64477i	−0.206770	−	0.175556i
$701$	8.66447	+	11.9256i	0.327252	+	0.450424i	0.940664	−	0.339339i	$-0.110203\pi$
$701$	8.66447	+	11.9256i	0.327252	+	0.450424i	−0.613412	+	0.789763i	$0.710203\pi$
$702$	−1.11452	+	3.43014i	−0.0420649	+	0.129462i
$703$	16.6065			0.626326
$704$	−3.30863	−	0.230216i	−0.124699	−	0.00867660i
$705$		−	4.50517i		−	0.169674i
$706$	−2.76076	+	8.49673i	−0.103902	+	0.319779i
$707$	19.3750	−	11.9511i	0.728673	−	0.449466i
$708$	8.60185	+	6.24961i	0.323277	+	0.234875i
$709$	−10.0448	−	30.9146i	−0.377239	−	1.16102i	−0.941956	−	0.335737i	$-0.891015\pi$
$709$	−10.0448	−	30.9146i	−0.377239	−	1.16102i	0.564717	−	0.825285i	$-0.308985\pi$
$710$	2.09371	+	6.44379i	0.0785757	+	0.241831i
$711$	8.98969	−	12.3732i	0.337140	−	0.464033i
$712$	−6.75745	+	4.90957i	−0.253246	+	0.183994i
$713$	−2.85375	−	0.927240i	−0.106874	−	0.0347254i
$714$	−20.8276	−	1.57794i	−0.779452	−	0.0590531i
$715$	−17.5531	+	4.38291i	−0.656450	+	0.163912i
$716$	−4.36969			−0.163303
$717$	2.53538	−	7.80310i	0.0946855	−	0.291412i
$718$	20.1386	−	14.6315i	0.751565	−	0.546044i
$719$	1.16966	−	1.60990i	0.0436210	−	0.0600391i	−0.786649	−	0.617400i	$-0.788186\pi$
$719$	1.16966	−	1.60990i	0.0436210	−	0.0600391i	0.830270	+	0.557361i	$0.188186\pi$
$720$	−1.43844	+	0.467378i	−0.0536075	+	0.0174181i
$721$	31.0221	−	7.54369i	1.15532	−	0.280942i
$722$	10.0048	−	13.7705i	0.372341	−	0.512484i
$723$	8.81014	+	12.1261i	0.327652	+	0.450975i
$724$	6.97833	+	2.26740i	0.259348	+	0.0842671i
$725$		−	11.6595i		−	0.433025i
$726$	7.91800	+	7.63579i	0.293865	+	0.283391i
$727$			32.1874i			1.19376i	0.802329	+	0.596882i	$0.203594\pi$
$727$			32.1874i			1.19376i	−0.802329	+	0.596882i	$0.796406\pi$
$728$	8.82661	+	3.62592i	0.327136	+	0.134386i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$	8.61382	+	6.25831i	0.318812	+	0.231630i
$731$	−6.96388	+	2.26270i	−0.257568	+	0.0836890i
$732$	1.27338	−	0.413748i	0.0470657	−	0.0152926i
$733$	−37.7909	−	27.4567i	−1.39584	−	1.01414i	−0.995196	−	0.0979026i	$-0.968787\pi$
$733$	−37.7909	−	27.4567i	−1.39584	−	1.01414i	−0.400643	−	0.916234i	$-0.631213\pi$
$734$	−12.6416	+	9.18468i	−0.466611	+	0.339013i
$735$	−4.75131	+	9.46125i	−0.175255	+	0.348983i
$736$		−	4.44637i		−	0.163896i
$737$	5.33291	+	21.3578i	0.196440	+	0.786724i
$738$		−	2.44412i		−	0.0899691i
$739$	−5.07847	−	1.65010i	−0.186815	−	0.0606998i	0.214116	−	0.976808i	$-0.431313\pi$
$739$	−5.07847	−	1.65010i	−0.186815	−	0.0606998i	−0.400930	+	0.916109i	$0.631313\pi$
$740$	10.4951	+	14.4452i	0.385807	+	0.531017i
$741$	−2.98209	+	4.10450i	−0.109550	+	0.150783i
$742$	−2.83997	+	0.690600i	−0.104259	+	0.0253527i
$743$	−29.3866	+	9.54827i	−1.07809	+	0.350292i	−0.793633	−	0.608397i	$-0.791813\pi$
$743$	−29.3866	+	9.54827i	−1.07809	+	0.350292i	−0.284455	+	0.958689i	$0.591813\pi$
$744$	−0.396664	+	0.545961i	−0.0145424	+	0.0200159i
$745$	−13.9204	+	10.1137i	−0.510003	+	0.370539i
$746$	−1.65130	+	5.08219i	−0.0604585	+	0.186072i
$747$	−10.8003			−0.395161
$748$	26.1204	+	1.81747i	0.955057	+	0.0664534i
$749$	3.77188	−	49.7857i	0.137821	−	1.81913i
$750$	11.0939	+	3.60463i	0.405092	+	0.131622i
$751$	2.37005	−	1.72194i	0.0864843	−	0.0628345i	−0.543703	−	0.839278i	$-0.682978\pi$
$751$	2.37005	−	1.72194i	0.0864843	−	0.0628345i	0.630187	+	0.776443i	$0.282978\pi$
$752$	1.75083	−	2.40981i	0.0638462	−	0.0878767i
$753$	−8.78108	−	27.0254i	−0.320000	−	0.984859i
$754$	4.79081	+	14.7446i	0.174471	+	0.536967i
$755$	−10.9647	−	7.96629i	−0.399045	−	0.289923i
$756$	−1.38899	−	2.25182i	−0.0505170	−	0.0818981i
$757$	11.0625	−	34.0469i	0.402073	−	1.23745i	−0.521241	−	0.853409i	$-0.674531\pi$
$757$	11.0625	−	34.0469i	0.402073	−	1.23745i	0.923315	−	0.384045i	$-0.125469\pi$
$758$			31.6452i			1.14941i
$759$	−9.47527	+	11.3001i	−0.343930	+	0.410167i
$760$	−2.12756			−0.0771748
$761$	−11.8464	+	36.4594i	−0.429431	+	1.32165i	0.469255	+	0.883063i	$0.344522\pi$
$761$	−11.8464	+	36.4594i	−0.429431	+	1.32165i	−0.898687	+	0.438591i	$0.855478\pi$
$762$	−8.94908	−	12.3173i	−0.324191	−	0.446210i
$763$	16.2881	−	19.1842i	0.589669	−	0.694513i
$764$	7.83054	+	24.0999i	0.283299	+	0.871904i
$765$	11.3560	−	3.68978i	0.410576	−	0.133404i
$766$	−5.40034	−	3.92358i	−0.195122	−	0.141765i
$767$	22.5403	+	31.0240i	0.813882	+	1.12021i
$768$	−0.951057	−	0.309017i	−0.0343183	−	0.0111507i
$769$	19.9414			0.719105			0.359552	−	0.933125i	$-0.382929\pi$
$769$	19.9414			0.719105			0.359552	+	0.933125i	$0.382929\pi$
$770$	5.88304	−	11.8967i	0.212010	−	0.428727i
$771$	−16.3922			−0.590350
$772$	−4.84903	−	1.57554i	−0.174520	−	0.0567051i
$773$	−11.0852	−	15.2575i	−0.398708	−	0.548774i	0.561711	−	0.827333i	$-0.310143\pi$
$773$	−11.0852	−	15.2575i	−0.398708	−	0.548774i	−0.960419	+	0.278559i	$0.910143\pi$
$774$	−0.750361	−	0.545169i	−0.0269712	−	0.0195957i
$775$	1.74089	−	0.565649i	0.0625346	−	0.0203187i
$776$	−2.28866	−	7.04376i	−0.0821580	−	0.252856i
$777$	−20.2155	+	23.8098i	−0.725227	+	0.854173i
$778$	17.5848	+	24.2034i	0.630447	+	0.867735i
$779$	1.06243	−	3.26983i	0.0380656	−	0.117154i
$780$	−5.45496			−0.195319
$781$	12.5972	−	7.87761i	0.450762	−	0.281883i
$782$			35.1025i			1.25526i
$783$	1.32832	−	4.08815i	0.0474703	−	0.146099i
$784$	−6.21837	+	3.21433i	−0.222085	+	0.114797i
$785$	−21.8077	−	15.8442i	−0.778351	−	0.565505i
$786$	4.47403	+	13.7696i	0.159583	+	0.491147i
$787$	−3.93340	−	12.1058i	−0.140211	−	0.431524i	0.856153	−	0.516722i	$-0.172848\pi$
$787$	−3.93340	−	12.1058i	−0.140211	−	0.431524i	−0.996364	+	0.0851977i	$0.972848\pi$
$788$	−6.10275	+	8.39971i	−0.217401	+	0.299227i
$789$	1.76897	−	1.28523i	0.0629769	−	0.0457554i
$790$	21.9998	+	7.14816i	0.782716	+	0.254320i
$791$	−47.4737	−	3.59672i	−1.68797	−	0.127885i
$792$	1.75851	+	2.81205i	0.0624860	+	0.0999219i
$793$	4.82902			0.171484
$794$	7.21805	−	22.2149i	0.256159	−	0.788377i
$795$	1.35171	−	0.982075i	0.0479402	−	0.0348306i
$796$	8.01265	−	11.0285i	0.284001	−	0.390894i
$797$	31.4755	−	10.2270i	1.11492	−	0.362259i	0.307093	−	0.951680i	$-0.400644\pi$
$797$	31.4755	−	10.2270i	1.11492	−	0.362259i	0.807826	+	0.589420i	$0.200644\pi$
$798$	−0.879393	−	3.61635i	−0.0311302	−	0.128017i
$799$	−13.8222	+	19.0246i	−0.488993	+	0.673041i
$800$	1.59434	+	2.19441i	0.0563683	+	0.0775843i
$801$	7.94386	+	2.58112i	0.280682	+	0.0911992i
$802$			8.83711i			0.312049i
$803$	8.73884	−	21.6509i	0.308387	−	0.764042i
$804$			6.63732i			0.234080i
$805$	16.4581	+	6.76089i	0.580072	+	0.238290i
$806$	−1.96910	+	1.43063i	−0.0693586	+	0.0503919i
$807$	−20.0169	−	14.5431i	−0.704628	−	0.511943i
$808$	−8.18303	+	2.65883i	−0.287878	+	0.0935373i
$809$	−30.4969	+	9.90903i	−1.07221	+	0.348383i	−0.791349	−	0.611365i	$-0.790621\pi$
$809$	−30.4969	+	9.90903i	−1.07221	+	0.348383i	−0.280863	+	0.959748i	$0.590621\pi$
$810$	1.22361	+	0.889005i	0.0429933	+	0.0312365i
$811$	−13.6819	+	9.94050i	−0.480437	+	0.349058i	−0.801495	−	0.598002i	$-0.795962\pi$
$811$	−13.6819	+	9.94050i	−0.480437	+	0.349058i	0.321058	+	0.947060i	$0.395962\pi$
$812$	−10.5198	−	4.32149i	−0.369174	−	0.151654i
$813$		−	19.8014i		−	0.694467i
$814$	25.1574	−	30.0025i	0.881768	−	1.05159i
$815$		−	18.6249i		−	0.652402i
$816$	7.50825	+	2.43958i	0.262841	+	0.0854023i
$817$	−0.766881	−	1.05552i	−0.0268298	−	0.0369280i
$818$	18.4502	−	25.3946i	0.645097	−	0.887900i
$819$	−2.25472	−	9.27214i	−0.0787862	−	0.323995i
$820$	3.51572	−	1.14233i	0.122774	−	0.0398917i
$821$	24.4262	−	33.6198i	0.852480	−	1.17334i	−0.130831	−	0.991405i	$-0.541764\pi$
$821$	24.4262	−	33.6198i	0.852480	−	1.17334i	0.983311	−	0.181934i	$-0.0582356\pi$
$822$	−0.370618	+	0.269270i	−0.0129268	+	0.00939187i
$823$	−7.17078	+	22.0694i	−0.249958	+	0.769291i	0.744824	+	0.667261i	$0.232534\pi$
$823$	−7.17078	+	22.0694i	−0.249958	+	0.769291i	−0.994781	+	0.102029i	$0.967466\pi$
$824$	−12.0670			−0.420372
$825$	0.624449	−	8.97446i	0.0217405	−	0.312451i
$826$	−28.0505	−	2.12517i	−0.976001	−	0.0739441i
$827$	12.1264	+	3.94012i	0.421677	+	0.137011i	0.512166	−	0.858886i	$-0.328843\pi$
$827$	12.1264	+	3.94012i	0.421677	+	0.137011i	−0.0904893	+	0.995897i	$0.528843\pi$
$828$	−3.59719	+	2.61351i	−0.125011	+	0.0908259i
$829$	1.04135	−	1.43330i	0.0361676	−	0.0497805i	−0.790550	−	0.612397i	$-0.790205\pi$
$829$	1.04135	−	1.43330i	0.0361676	−	0.0497805i	0.826718	+	0.562617i	$0.190205\pi$
$830$	−5.04781	−	15.5356i	−0.175212	−	0.539247i
$831$	7.87447	+	24.2351i	0.273162	+	0.840707i
$832$	−2.91785	−	2.11995i	−0.101158	−	0.0734959i
$833$	49.0918	−	25.3760i	1.70093	−	0.879225i
$834$	−2.27254	+	6.99416i	−0.0786917	+	0.242188i
$835$			3.31887i			0.114854i
$836$	1.13023	+	4.52647i	0.0390899	+	0.156551i
$837$	0.674845			0.0233261
$838$	1.34881	−	4.15122i	0.0465939	−	0.143401i
$839$	3.06556	+	4.21939i	0.105835	+	0.145669i	0.858649	−	0.512564i	$-0.171304\pi$
$839$	3.06556	+	4.21939i	0.105835	+	0.145669i	−0.752814	+	0.658233i	$0.771304\pi$
$840$	2.58994	−	3.05043i	0.0893613	−	0.105250i
$841$	3.25165	+	10.0076i	0.112126	+	0.345088i
$842$	−31.0018	+	10.0731i	−1.06839	+	0.347142i
$843$	−5.03345	−	3.65702i	−0.173361	−	0.125954i
$844$	9.19578	+	12.6569i	0.316532	+	0.435668i
$845$	−0.0115679	−	0.00375864i	−0.000397948	−	0.000129301i
$846$	−2.97869			−0.102409
$847$	−28.4360	−	6.19646i	−0.977071	−	0.212913i
$848$	1.10469			0.0379352
$849$	10.4677	+	3.40117i	0.359251	+	0.116728i
$850$	−12.5867	−	17.3241i	−0.431720	−	0.594212i
$851$	42.4663	+	30.8536i	1.45573	+	1.05765i
$852$	4.26045	−	1.38430i	0.145961	−	0.0474255i
$853$	6.07372	+	18.6930i	0.207960	+	0.640036i	0.999579	+	0.0290203i	$0.00923875\pi$
$853$	6.07372	+	18.6930i	0.207960	+	0.640036i	−0.791619	+	0.611016i	$0.790761\pi$
$854$	−2.29275	+	2.70040i	−0.0784563	+	0.0924059i
$855$	1.25055	+	1.72124i	0.0427679	+	0.0588650i
$856$	−5.83151	+	17.9475i	−0.199317	+	0.613434i
$857$	−13.9751			−0.477380			−0.238690	−	0.971096i	$-0.576718\pi$
$857$	−13.9751			−0.477380			−0.238690	+	0.971096i	$0.576718\pi$
$858$	2.89786	+	11.6056i	0.0989313	+	0.396210i
$859$			14.4749i			0.493879i	0.969031	+	0.246939i	$0.0794249\pi$
$859$			14.4749i			0.493879i	−0.969031	+	0.246939i	$0.920575\pi$
$860$	0.433492	−	1.33415i	0.0147819	−	0.0454941i
$861$	3.39484	+	5.50372i	0.115696	+	0.187566i
$862$	−6.28007	−	4.56274i	−0.213900	−	0.155407i
$863$	−6.26530	−	19.2826i	−0.213273	−	0.656387i	−0.999272	−	0.0381590i	$-0.987851\pi$
$863$	−6.26530	−	19.2826i	−0.213273	−	0.656387i	0.785998	−	0.618228i	$-0.212149\pi$
$864$	0.309017	+	0.951057i	0.0105130	+	0.0323556i
$865$	7.52173	−	10.3528i	0.255746	−	0.352005i
$866$	−9.63455	+	6.99991i	−0.327395	+	0.237867i
$867$	−43.1070	−	14.0063i	−1.46399	−	0.475679i
$868$	0.134885	−	1.78037i	0.00457829	−	0.0604297i
$869$	3.52097	−	50.6027i	0.119441	−	1.71658i
$870$	6.50139			0.220418
$871$	−7.39744	+	22.7670i	−0.250653	+	0.771429i
$872$	−7.69529	+	5.59096i	−0.260596	+	0.189334i
$873$	−4.35328	+	5.99178i	−0.147336	+	0.202791i
$874$	−5.94852	+	1.93279i	−0.201212	+	0.0653777i
$875$	−29.9883	+	7.29229i	−1.01379	+	0.246525i
$876$	4.13782	−	5.69522i	0.139804	−	0.192423i
$877$	−10.9367	−	15.0531i	−0.369307	−	0.508307i	0.583405	−	0.812181i	$-0.301720\pi$
$877$	−10.9367	−	15.0531i	−0.369307	−	0.508307i	−0.952712	+	0.303874i	$0.901720\pi$
$878$	−29.8517	−	9.69939i	−1.00744	−	0.327339i
$879$			6.96291i			0.234853i
$880$	−3.22308	+	3.84381i	−0.108650	+	0.129575i
$881$			25.1979i			0.848939i	0.905442	+	0.424469i	$0.139539\pi$
$881$			25.1979i			0.848939i	−0.905442	+	0.424469i	$0.860461\pi$
$882$	6.25551	+	3.14143i	0.210634	+	0.105777i
$883$	40.1986	−	29.2060i	1.35279	−	0.982859i	0.353922	−	0.935275i	$-0.384848\pi$
$883$	40.1986	−	29.2060i	1.35279	−	0.982859i	0.998867	−	0.0475840i	$-0.0151522\pi$
$884$	23.0354	+	16.7362i	0.774765	+	0.562899i
$885$	15.2942	−	4.96938i	0.514108	−	0.167044i
$886$	−6.46302	+	2.09996i	−0.217129	+	0.0705496i
$887$	14.0947	+	10.2404i	0.473252	+	0.343838i	0.798707	−	0.601719i	$-0.205517\pi$
$887$	14.0947	+	10.2404i	0.473252	+	0.343838i	−0.325455	+	0.945558i	$0.605517\pi$
$888$	9.55078	−	6.93905i	0.320503	−	0.232859i
$889$	37.2604	+	15.3064i	1.24967	+	0.513359i
$890$			12.6331i			0.423463i
$891$	1.24137	−	3.07555i	0.0415875	−	0.103035i
$892$			1.97327i			0.0660700i
$893$	−3.98500	−	1.29480i	−0.133353	−	0.0433290i
$894$	6.68692	+	9.20375i	0.223644	+	0.307820i
$895$	−3.88468	+	5.34680i	−0.129850	+	0.178724i
$896$	2.57083	−	0.625153i	0.0858855	−	0.0208849i
$897$	−15.2517	+	4.95558i	−0.509239	+	0.165462i
$898$	22.2659	−	30.6464i	0.743024	−	1.02268i
$899$	2.34683	−	1.70507i	0.0782713	−	0.0568674i
$900$	0.838192	−	2.57969i	0.0279397	−	0.0859896i
$901$	−8.72112			−0.290543
$902$	−4.29801	−	6.87298i	−0.143108	−	0.228845i
$903$	2.44691	+	0.185384i	0.0814282	+	0.00616919i
$904$	17.1141	+	5.56070i	0.569206	+	0.184946i
$905$	8.97818	−	6.52303i	0.298445	−	0.216833i
$906$	−5.26708	+	7.24952i	−0.174987	+	0.240849i
$907$	5.95115	+	18.3158i	0.197605	+	0.608165i	0.999936	+	0.0112863i	$0.00359260\pi$
$907$	5.95115	+	18.3158i	0.197605	+	0.608165i	−0.802332	+	0.596879i	$0.796407\pi$
$908$	6.93996	+	21.3590i	0.230311	+	0.708823i
$909$	6.96090	+	5.05739i	0.230879	+	0.167743i
$910$	12.2836	−	7.57687i	0.407198	−	0.251171i
$911$	0.228037	−	0.701827i	0.00755521	−	0.0232526i	−0.947208	−	0.320620i	$-0.896109\pi$
$911$	0.228037	−	0.701827i	0.00755521	−	0.0232526i	0.954763	+	0.297368i	$0.0961087\pi$
$912$			1.40668i			0.0465800i
$913$	−30.3709	+	18.9924i	−1.00513	+	0.628557i
$914$	26.4443			0.874701
$915$	0.625780	−	1.92595i	0.0206876	−	0.0636700i
$916$	−10.8268	−	14.9018i	−0.357728	−	0.492370i
$917$	−29.2006	−	24.7925i	−0.964288	−	0.818719i
$918$	−2.43958	−	7.50825i	−0.0805181	−	0.247809i
$919$	10.5800	−	3.43764i	0.349001	−	0.113397i	−0.129270	−	0.991609i	$-0.541264\pi$
$919$	10.5800	−	3.43764i	0.349001	−	0.113397i	0.478271	+	0.878212i	$0.341264\pi$
$920$	−5.44063	−	3.95285i	−0.179372	−	0.130322i
$921$	12.3746	+	17.0322i	0.407757	+	0.561229i
$922$	−16.1382	−	5.24361i	−0.531482	−	0.172689i
$923$	16.1568			0.531807
$924$	−7.86576	−	3.88970i	−0.258765	−	0.127962i
$925$	−32.0215			−1.05286
$926$	−21.3442	−	6.93514i	−0.701413	−	0.227903i
$927$	7.09278	+	9.76237i	0.232957	+	0.320638i
$928$	3.47759	+	2.52662i	0.114157	+	0.0829403i
$929$	0.633328	−	0.205781i	0.0207788	−	0.00675145i	−0.298609	−	0.954375i	$-0.596523\pi$
$929$	0.633328	−	0.205781i	0.0207788	−	0.00675145i	0.319388	+	0.947624i	$0.396523\pi$
$930$	0.315408	+	0.970725i	0.0103426	+	0.0318313i
$931$	7.00331	+	6.92193i	0.229524	+	0.226857i
$932$	6.34158	+	8.72844i	0.207725	+	0.285910i
$933$	−4.85057	+	14.9285i	−0.158801	+	0.488738i
$934$	−11.8503			−0.387753
$935$	25.4451	−	30.3455i	0.832143	−	0.992403i
$936$			3.60667i			0.117888i
$937$	−2.76990	+	8.52486i	−0.0904885	+	0.278495i	−0.986052	−	0.166439i	$-0.946773\pi$
$937$	−2.76990	+	8.52486i	−0.0904885	+	0.278495i	0.895563	+	0.444934i	$0.146773\pi$
$938$	−9.21915	−	14.9461i	−0.301016	−	0.488007i
$939$	−11.9626	−	8.69137i	−0.390386	−	0.283632i
$940$	−1.39217	−	4.28467i	−0.0454077	−	0.139750i
$941$	6.97044	+	21.4528i	0.227230	+	0.699342i	0.998058	+	0.0622981i	$0.0198430\pi$
$941$	6.97044	+	21.4528i	0.227230	+	0.699342i	−0.770828	+	0.637044i	$0.780157\pi$
$942$	−10.4758	+	14.4187i	−0.341319	+	0.469785i
$943$	8.79195	−	6.38773i	0.286305	−	0.208013i
$944$	10.1121	+	3.28562i	0.329120	+	0.106938i
$945$	−3.99017	−	0.302305i	−0.129800	−	0.00983397i
$946$	−3.06874	−	0.213525i	−0.0997733	−	0.00694229i
$947$	−32.2656			−1.04849			−0.524246	−	0.851567i	$-0.675653\pi$
$947$	−32.2656			−1.04849			−0.524246	+	0.851567i	$0.675653\pi$
$948$	4.72616	−	14.5456i	0.153499	−	0.472420i
$949$	20.5407	−	14.9237i	0.666781	−	0.484445i
$950$	2.24273	−	3.08685i	0.0727637	−	0.100151i
$951$	19.9238	−	6.47364i	0.646074	−	0.209922i
$952$	−20.2958	+	4.93536i	−0.657791	+	0.159956i
$953$	16.2095	−	22.3104i	0.525077	−	0.722706i	−0.461294	−	0.887248i	$-0.652615\pi$
$953$	16.2095	−	22.3104i	0.525077	−	0.722706i	0.986370	+	0.164542i	$0.0526145\pi$
$954$	−0.649320	−	0.893712i	−0.0210225	−	0.0289350i
$955$	36.4503	+	11.8434i	1.17950	+	0.383244i
$956$		−	8.20466i		−	0.265358i
$957$	−3.45376	−	13.8320i	−0.111644	−	0.447124i
$958$			36.0079i			1.16336i
$959$	0.460555	−	1.12113i	0.0148721	−	0.0362033i
$960$	−1.22361	+	0.889005i	−0.0394919	+	0.0286925i
$961$	−24.7111	−	17.9537i	−0.797132	−	0.579150i
$962$	40.4943	−	13.1574i	1.30559	−	0.424211i
$963$	17.9475	−	5.83151i	0.578351	−	0.187918i
$964$	12.1261	+	8.81014i	0.390556	+	0.283755i
$965$	−6.23866	+	4.53265i	−0.200830	+	0.145911i
$966$	4.47011	−	10.8816i	0.143823	−	0.350111i
$967$			7.86662i			0.252973i	0.991968	+	0.126487i	$0.0403701\pi$
$967$			7.86662i			0.252973i	−0.991968	+	0.126487i	$0.959630\pi$
$968$	9.89005	+	4.81527i	0.317878	+	0.154769i
$969$		−	11.1053i		−	0.356753i
$970$	−10.6534	−	3.46152i	−0.342062	−	0.111143i
$971$	−23.3467	−	32.1339i	−0.749230	−	1.03123i	−0.998034	−	0.0626727i	$-0.980038\pi$
$971$	−23.3467	−	32.1339i	−0.749230	−	1.03123i	0.248804	−	0.968554i	$-0.419962\pi$
$972$	0.587785	−	0.809017i	0.0188532	−	0.0259492i
$973$	−4.59744	−	18.9062i	−0.147387	−	0.606104i
$974$	18.2280	−	5.92263i	0.584062	−	0.189773i
$975$	5.75024	−	7.91452i	0.184155	−	0.253468i
$976$	1.08321	−	0.786995i	0.0346726	−	0.0251911i
$977$	1.56375	−	4.81272i	0.0500288	−	0.153973i	−0.922921	−	0.384989i	$-0.874205\pi$
$977$	1.56375	−	4.81272i	0.0500288	−	0.153973i	0.972950	+	0.231017i	$0.0742052\pi$
$978$	−12.3143			−0.393766
$979$	26.8775	−	6.71114i	0.859007	−	0.214489i
$980$	−1.59507	+	10.4664i	−0.0509528	+	0.334337i
$981$	9.04636	+	2.93934i	0.288828	+	0.0938459i
$982$	13.6458	−	9.91427i	0.435456	−	0.316377i
$983$	−11.6189	+	15.9920i	−0.370585	+	0.510066i	−0.953060	−	0.302783i	$-0.902084\pi$
$983$	−11.6189	+	15.9920i	−0.370585	+	0.510066i	0.582475	+	0.812849i	$0.302084\pi$
$984$	−0.755273	−	2.32449i	−0.0240772	−	0.0741021i
$985$	4.85260	+	14.9348i	0.154617	+	0.475862i
$986$	−27.4543	−	19.9467i	−0.874324	−	0.635233i
$987$	6.70749	−	4.13736i	0.213502	−	0.131694i
$988$	−1.56778	+	4.82513i	−0.0498777	+	0.153508i
$989$		−	4.12400i		−	0.131136i
$990$	5.00418	+	0.348194i	0.159043	+	0.0110663i
$991$	−20.1725			−0.640801			−0.320401	−	0.947282i	$-0.603818\pi$
$991$	−20.1725			−0.640801			−0.320401	+	0.947282i	$0.603818\pi$
$992$	−0.208539	+	0.641816i	−0.00662110	+	0.0203777i
$993$	3.09805	+	4.26409i	0.0983135	+	0.135317i
$994$	−7.67101	+	9.03492i	−0.243310	+	0.286570i
$995$	−6.37127	−	19.6087i	−0.201983	−	0.621639i
$996$	−10.2717	+	3.33747i	−0.325470	+	0.105752i
$997$	5.73332	+	4.16550i	0.181576	+	0.131923i	0.674860	−	0.737945i	$-0.264204\pi$
$997$	5.73332	+	4.16550i	0.181576	+	0.131923i	−0.493284	+	0.869868i	$0.664204\pi$
$998$	4.52428	+	6.22714i	0.143214	+	0.197117i
$999$	−11.2276	−	3.64807i	−0.355226	−	0.115420i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.u.a.13.3	✓	32
7.6	odd	2		462.2.u.b.13.2	yes	32
11.6	odd	10		462.2.u.b.391.2	yes	32
77.6	even	10	inner	462.2.u.a.391.3	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.u.a.13.3	✓	32	1.1	even	1	trivial
462.2.u.a.391.3	yes	32	77.6	even	10	inner
462.2.u.b.13.2	yes	32	7.6	odd	2
462.2.u.b.391.2	yes	32	11.6	odd	10

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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.u (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 - 0.309017i) q^{2} +(0.587785 + 0.809017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(1.43844 - 0.467378i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(2.01686 + 1.71239i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.951057 - 0.309017i) q^{2} +(0.587785 + 0.809017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(1.43844 - 0.467378i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(2.01686 + 1.71239i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} -1.51247 q^{10} +(0.803473 + 3.21783i) q^{11} +1.00000i q^{12} +(-1.11452 + 3.43014i) q^{13} +(-1.38899 - 2.25182i) q^{14} +(1.22361 + 0.889005i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-2.43958 - 7.50825i) q^{17} +(0.587785 - 0.809017i) q^{18} +(1.13803 - 0.826829i) q^{19} +(1.43844 + 0.467378i) q^{20} +(-0.199875 + 2.63819i) q^{21} +(0.230216 - 3.30863i) q^{22} +4.44637 q^{23} +(0.309017 - 0.951057i) q^{24} +(-2.19441 + 1.59434i) q^{25} +(2.11995 - 2.91785i) q^{26} +(-0.951057 + 0.309017i) q^{27} +(0.625153 + 2.57083i) q^{28} +(-2.52662 + 3.47759i) q^{29} +(-0.889005 - 1.22361i) q^{30} +(-0.641816 - 0.208539i) q^{31} -1.00000i q^{32} +(-2.13101 + 2.54142i) q^{33} +7.89464i q^{34} +(3.70146 + 1.52054i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(9.55078 + 6.93905i) q^{37} +(-1.33784 + 0.434690i) q^{38} +(-3.43014 + 1.11452i) q^{39} +(-1.22361 - 0.889005i) q^{40} +(1.97733 - 1.43661i) q^{41} +(1.00534 - 2.44730i) q^{42} -0.927497i q^{43} +(-1.24137 + 3.07555i) q^{44} +1.51247i q^{45} +(-4.22875 - 1.37401i) q^{46} +(-1.75083 - 2.40981i) q^{47} +(-0.587785 + 0.809017i) q^{48} +(1.13543 + 6.90730i) q^{49} +(2.57969 - 0.838192i) q^{50} +(4.64035 - 6.38690i) q^{51} +(-2.91785 + 2.11995i) q^{52} +(0.341368 - 1.05062i) q^{53} +1.00000 q^{54} +(2.65969 + 4.25313i) q^{55} +(0.199875 - 2.63819i) q^{56} +(1.33784 + 0.434690i) q^{57} +(3.47759 - 2.52662i) q^{58} +(6.24961 - 8.60185i) q^{59} +(0.467378 + 1.43844i) q^{60} +(-0.413748 - 1.27338i) q^{61} +(0.545961 + 0.396664i) q^{62} +(-2.25182 + 1.38899i) q^{63} +(-0.309017 + 0.951057i) q^{64} +5.45496i q^{65} +(2.81205 - 1.75851i) q^{66} +6.63732 q^{67} +(2.43958 - 7.50825i) q^{68} +(2.61351 + 3.59719i) q^{69} +(-3.05043 - 2.58994i) q^{70} +(-1.38430 - 4.26045i) q^{71} +(0.951057 - 0.309017i) q^{72} +(-5.69522 - 4.13782i) q^{73} +(-6.93905 - 9.55078i) q^{74} +(-2.57969 - 0.838192i) q^{75} +1.40668 q^{76} +(-3.88970 + 7.86576i) q^{77} +3.60667 q^{78} +(-14.5456 - 4.72616i) q^{79} +(0.889005 + 1.22361i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-2.32449 + 0.755273i) q^{82} +(3.33747 + 10.2717i) q^{83} +(-1.71239 + 2.01686i) q^{84} +(-7.01838 - 9.65997i) q^{85} +(-0.286612 + 0.882102i) q^{86} -4.29854 q^{87} +(2.13101 - 2.54142i) q^{88} -8.35266i q^{89} +(0.467378 - 1.43844i) q^{90} +(-8.12158 + 5.00961i) q^{91} +(3.59719 + 2.61351i) q^{92} +(-0.208539 - 0.641816i) q^{93} +(0.920466 + 2.83290i) q^{94} +(1.25055 - 1.72124i) q^{95} +(0.809017 - 0.587785i) q^{96} +(7.04376 + 2.28866i) q^{97} +(1.05462 - 6.92010i) q^{98} +(-3.30863 - 0.230216i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{4} - 10 q^{5} + 8 q^{6} - 10 q^{7} + 8 q^{9}+O(q^{10}) \) 32 * q + 8 * q^4 - 10 * q^5 + 8 * q^6 - 10 * q^7 + 8 * q^9	\( 32 q + 8 q^{4} - 10 q^{5} + 8 q^{6} - 10 q^{7} + 8 q^{9} - 4 q^{10} + 8 q^{11} - 2 q^{14} + 6 q^{15} - 8 q^{16} + 12 q^{17} + 16 q^{19} - 10 q^{20} + 8 q^{21} - 4 q^{22} + 8 q^{23} - 8 q^{24} + 6 q^{25} + 20 q^{29} + 50 q^{31} + 16 q^{33} + 32 q^{35} - 8 q^{36} - 16 q^{37} - 6 q^{40} - 40 q^{41} - 10 q^{42} + 12 q^{44} - 28 q^{49} + 40 q^{51} + 32 q^{54} + 40 q^{55} - 8 q^{56} + 10 q^{58} - 60 q^{59} + 4 q^{60} + 4 q^{61} - 20 q^{62} - 10 q^{63} + 8 q^{64} - 8 q^{66} - 16 q^{67} - 12 q^{68} - 30 q^{69} - 18 q^{70} - 48 q^{71} + 74 q^{73} - 40 q^{74} + 24 q^{76} - 70 q^{77} - 60 q^{79} - 8 q^{81} - 20 q^{82} - 4 q^{83} + 2 q^{84} - 10 q^{85} - 36 q^{86} - 20 q^{87} - 16 q^{88} + 4 q^{90} - 60 q^{91} - 8 q^{92} - 10 q^{93} - 20 q^{95} + 8 q^{96} - 60 q^{97} + 40 q^{98} - 8 q^{99}+O(q^{100}) \) 32 * q + 8 * q^4 - 10 * q^5 + 8 * q^6 - 10 * q^7 + 8 * q^9 - 4 * q^10 + 8 * q^11 - 2 * q^14 + 6 * q^15 - 8 * q^16 + 12 * q^17 + 16 * q^19 - 10 * q^20 + 8 * q^21 - 4 * q^22 + 8 * q^23 - 8 * q^24 + 6 * q^25 + 20 * q^29 + 50 * q^31 + 16 * q^33 + 32 * q^35 - 8 * q^36 - 16 * q^37 - 6 * q^40 - 40 * q^41 - 10 * q^42 + 12 * q^44 - 28 * q^49 + 40 * q^51 + 32 * q^54 + 40 * q^55 - 8 * q^56 + 10 * q^58 - 60 * q^59 + 4 * q^60 + 4 * q^61 - 20 * q^62 - 10 * q^63 + 8 * q^64 - 8 * q^66 - 16 * q^67 - 12 * q^68 - 30 * q^69 - 18 * q^70 - 48 * q^71 + 74 * q^73 - 40 * q^74 + 24 * q^76 - 70 * q^77 - 60 * q^79 - 8 * q^81 - 20 * q^82 - 4 * q^83 + 2 * q^84 - 10 * q^85 - 36 * q^86 - 20 * q^87 - 16 * q^88 + 4 * q^90 - 60 * q^91 - 8 * q^92 - 10 * q^93 - 20 * q^95 + 8 * q^96 - 60 * q^97 + 40 * q^98 - 8 * q^99

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