LMFDB - Embedded newform 336.2.w.a.253.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(85,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("336.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.w (of order $4$, 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:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 8 x^{18} - 16 x^{17} + 35 x^{16} - 56 x^{15} + 64 x^{14} - 84 x^{13} + 125 x^{12} + \cdots + 1024 $ x^20 - 4x^19 + 8x^18 - 16x^17 + 35x^16 - 56x^15 + 64x^14 - 84x^13 + 125x^12 - 120x^11 + 100x^10 - 240x^9 + 500x^8 - 672x^7 + 1024x^6 - 1792x^5 + 2240x^4 - 2048x^3 + 2048x^2 - 2048*x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			253.6
Root			$1.35964 + 0.389081i$ of defining polynomial
Character	$\chi$	$=$	336.253
Dual form			336.2.w.a.85.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.196445 + 1.40050i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-1.92282 + 0.550244i) q^{4} +(-1.69093 + 1.69093i) q^{5} +(-0.851398 + 1.12921i) q^{6} -1.00000i q^{7} +(-1.14835 - 2.58482i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(0.196445 + 1.40050i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-1.92282 + 0.550244i) q^{4} +(-1.69093 + 1.69093i) q^{5} +(-0.851398 + 1.12921i) q^{6} -1.00000i q^{7} +(-1.14835 - 2.58482i) q^{8} +1.00000i q^{9} +(-2.70032 - 2.03597i) q^{10} +(-3.89817 + 3.89817i) q^{11} +(-1.74872 - 0.970557i) q^{12} +(0.555931 + 0.555931i) q^{13} +(1.40050 - 0.196445i) q^{14} -2.39133 q^{15} +(3.39446 - 2.11604i) q^{16} -3.10154 q^{17} +(-1.40050 + 0.196445i) q^{18} +(2.57604 + 2.57604i) q^{19} +(2.32092 - 4.18177i) q^{20} +(0.707107 - 0.707107i) q^{21} +(-6.22518 - 4.69363i) q^{22} -5.08612i q^{23} +(1.01574 - 2.63975i) q^{24} -0.718471i q^{25} +(-0.669373 + 0.887793i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(0.550244 + 1.92282i) q^{28} +(4.60420 + 4.60420i) q^{29} +(-0.469766 - 3.34907i) q^{30} -0.822587 q^{31} +(3.63035 + 4.33827i) q^{32} -5.51285 q^{33} +(-0.609281 - 4.34371i) q^{34} +(1.69093 + 1.69093i) q^{35} +(-0.550244 - 1.92282i) q^{36} +(3.07113 - 3.07113i) q^{37} +(-3.10170 + 4.11380i) q^{38} +0.786205i q^{39} +(6.31252 + 2.42897i) q^{40} +11.4508i q^{41} +(1.12921 + 0.851398i) q^{42} +(0.0897468 - 0.0897468i) q^{43} +(5.35054 - 9.64043i) q^{44} +(-1.69093 - 1.69093i) q^{45} +(7.12313 - 0.999144i) q^{46} +10.0997 q^{47} +(3.89651 + 0.903982i) q^{48} -1.00000 q^{49} +(1.00622 - 0.141140i) q^{50} +(-2.19312 - 2.19312i) q^{51} +(-1.37485 - 0.763056i) q^{52} +(-7.36105 + 7.36105i) q^{53} +(-1.12921 - 0.851398i) q^{54} -13.1831i q^{55} +(-2.58482 + 1.14835i) q^{56} +3.64307i q^{57} +(-5.54372 + 7.35267i) q^{58} +(0.651584 - 0.651584i) q^{59} +(4.59810 - 1.31582i) q^{60} +(5.54741 + 5.54741i) q^{61} +(-0.161593 - 1.15204i) q^{62} +1.00000 q^{63} +(-5.36260 + 5.93654i) q^{64} -1.88008 q^{65} +(-1.08297 - 7.72077i) q^{66} +(-7.37998 - 7.37998i) q^{67} +(5.96369 - 1.70660i) q^{68} +(3.59643 - 3.59643i) q^{69} +(-2.03597 + 2.70032i) q^{70} -14.2192i q^{71} +(2.58482 - 1.14835i) q^{72} +4.93461i q^{73} +(4.90444 + 3.69782i) q^{74} +(0.508035 - 0.508035i) q^{75} +(-6.37070 - 3.53580i) q^{76} +(3.89817 + 3.89817i) q^{77} +(-1.10108 + 0.154446i) q^{78} -2.22554 q^{79} +(-2.16172 + 9.31786i) q^{80} -1.00000 q^{81} +(-16.0369 + 2.24945i) q^{82} +(10.5724 + 10.5724i) q^{83} +(-0.970557 + 1.74872i) q^{84} +(5.24447 - 5.24447i) q^{85} +(0.143321 + 0.108060i) q^{86} +6.51132i q^{87} +(14.5525 + 5.59963i) q^{88} +10.3158i q^{89} +(2.03597 - 2.70032i) q^{90} +(0.555931 - 0.555931i) q^{91} +(2.79861 + 9.77969i) q^{92} +(-0.581657 - 0.581657i) q^{93} +(1.98403 + 14.1446i) q^{94} -8.71179 q^{95} +(-0.500579 + 5.63466i) q^{96} +11.6494 q^{97} +(-0.196445 - 1.40050i) q^{98} +(-3.89817 - 3.89817i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{4}+O(q^{10}) $ 20 * q + 4 * q^4	$ 20 q + 4 q^{4} - 4 q^{10} + 12 q^{11} - 8 q^{12} + 4 q^{14} + 8 q^{15} - 4 q^{18} + 8 q^{19} + 28 q^{20} - 12 q^{22} + 8 q^{24} - 20 q^{26} - 4 q^{28} + 12 q^{29} + 8 q^{30} - 24 q^{33} - 44 q^{34} + 4 q^{36} + 12 q^{37} - 4 q^{38} + 16 q^{40} + 4 q^{42} + 4 q^{43} - 4 q^{44} + 20 q^{46} - 16 q^{48} - 20 q^{49} + 48 q^{50} - 8 q^{51} + 16 q^{52} - 36 q^{53} - 4 q^{54} - 16 q^{56} + 16 q^{58} - 12 q^{60} + 8 q^{61} + 12 q^{62} + 20 q^{63} - 32 q^{64} + 16 q^{65} - 24 q^{66} - 12 q^{67} + 4 q^{68} - 16 q^{69} - 20 q^{70} + 16 q^{72} - 16 q^{74} - 16 q^{75} - 32 q^{76} - 12 q^{77} + 12 q^{78} + 24 q^{79} - 8 q^{80} - 20 q^{81} - 76 q^{82} + 40 q^{83} - 16 q^{85} - 84 q^{86} + 16 q^{88} + 20 q^{90} - 4 q^{92} - 32 q^{94} - 72 q^{97} + 12 q^{99}+O(q^{100}) $ 20 * q + 4 * q^4 - 4 * q^10 + 12 * q^11 - 8 * q^12 + 4 * q^14 + 8 * q^15 - 4 * q^18 + 8 * q^19 + 28 * q^20 - 12 * q^22 + 8 * q^24 - 20 * q^26 - 4 * q^28 + 12 * q^29 + 8 * q^30 - 24 * q^33 - 44 * q^34 + 4 * q^36 + 12 * q^37 - 4 * q^38 + 16 * q^40 + 4 * q^42 + 4 * q^43 - 4 * q^44 + 20 * q^46 - 16 * q^48 - 20 * q^49 + 48 * q^50 - 8 * q^51 + 16 * q^52 - 36 * q^53 - 4 * q^54 - 16 * q^56 + 16 * q^58 - 12 * q^60 + 8 * q^61 + 12 * q^62 + 20 * q^63 - 32 * q^64 + 16 * q^65 - 24 * q^66 - 12 * q^67 + 4 * q^68 - 16 * q^69 - 20 * q^70 + 16 * q^72 - 16 * q^74 - 16 * q^75 - 32 * q^76 - 12 * q^77 + 12 * q^78 + 24 * q^79 - 8 * q^80 - 20 * q^81 - 76 * q^82 + 40 * q^83 - 16 * q^85 - 84 * q^86 + 16 * q^88 + 20 * q^90 - 4 * q^92 - 32 * q^94 - 72 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$	0.196445	+	1.40050i	0.138908	+	0.990305i
$2$	0.196445	+	1.40050i	0.138908	+	0.990305i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$	−1.92282	+	0.550244i	−0.961409	+	0.275122i
$5$	−1.69093	+	1.69093i	−0.756206	+	0.756206i	−0.975630	−	0.219424i	$-0.929582\pi$
$5$	−1.69093	+	1.69093i	−0.756206	+	0.756206i	0.219424	+	0.975630i	$0.429582\pi$
$6$	−0.851398	+	1.12921i	−0.347582	+	0.460999i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−1.14835	−	2.58482i	−0.406002	−	0.913872i
$9$			1.00000i			0.333333i
$10$	−2.70032	−	2.03597i	−0.853917	−	0.643832i
$11$	−3.89817	+	3.89817i	−1.17534	+	1.17534i	−0.194427	+	0.980917i	$0.562285\pi$
$11$	−3.89817	+	3.89817i	−1.17534	+	1.17534i	−0.980917	+	0.194427i	$0.937715\pi$
$12$	−1.74872	−	0.970557i	−0.504812	−	0.280176i
$13$	0.555931	+	0.555931i	0.154187	+	0.154187i	0.779985	−	0.625798i	$-0.215227\pi$
$13$	0.555931	+	0.555931i	0.154187	+	0.154187i	−0.625798	+	0.779985i	$0.715227\pi$
$14$	1.40050	−	0.196445i	0.374300	−	0.0525022i
$15$	−2.39133			−0.617439
$16$	3.39446	−	2.11604i	0.848616	−	0.529010i
$17$	−3.10154			−0.752233			−0.376116	−	0.926572i	$-0.622741\pi$
$17$	−3.10154			−0.752233			−0.376116	+	0.926572i	$0.622741\pi$
$18$	−1.40050	+	0.196445i	−0.330102	+	0.0463026i
$19$	2.57604	+	2.57604i	0.590984	+	0.590984i	0.937897	−	0.346913i	$-0.112770\pi$
$19$	2.57604	+	2.57604i	0.590984	+	0.590984i	−0.346913	+	0.937897i	$0.612770\pi$
$20$	2.32092	−	4.18177i	0.518974	−	0.935072i
$21$	0.707107	−	0.707107i	0.154303	−	0.154303i
$22$	−6.22518	−	4.69363i	−1.32721	−	1.00068i
$23$		−	5.08612i		−	1.06053i	−0.847832	−	0.530265i	$-0.822093\pi$
$23$		−	5.08612i		−	1.06053i	0.847832	−	0.530265i	$-0.177907\pi$
$24$	1.01574	−	2.63975i	0.207337	−	0.538836i
$25$		−	0.718471i		−	0.143694i
$26$	−0.669373	+	0.887793i	−0.131275	+	0.174110i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	0.550244	+	1.92282i	0.103986	+	0.363379i
$29$	4.60420	+	4.60420i	0.854978	+	0.854978i	0.990741	−	0.135763i	$-0.0433487\pi$
$29$	4.60420	+	4.60420i	0.854978	+	0.854978i	−0.135763	+	0.990741i	$0.543349\pi$
$30$	−0.469766	−	3.34907i	−0.0857671	−	0.611454i
$31$	−0.822587			−0.147741			−0.0738705	−	0.997268i	$-0.523535\pi$
$31$	−0.822587			−0.147741			−0.0738705	+	0.997268i	$0.523535\pi$
$32$	3.63035	+	4.33827i	0.641760	+	0.766905i
$33$	−5.51285			−0.959664
$34$	−0.609281	−	4.34371i	−0.104491	−	0.744940i
$35$	1.69093	+	1.69093i	0.285819	+	0.285819i
$36$	−0.550244	−	1.92282i	−0.0917073	−	0.320470i
$37$	3.07113	−	3.07113i	0.504891	−	0.504891i	−0.408063	−	0.912954i	$-0.633796\pi$
$37$	3.07113	−	3.07113i	0.504891	−	0.504891i	0.912954	+	0.408063i	$0.133796\pi$
$38$	−3.10170	+	4.11380i	−0.503162	+	0.667347i
$39$			0.786205i			0.125894i
$40$	6.31252	+	2.42897i	0.998096	+	0.384054i
$41$			11.4508i			1.78831i	0.447757	+	0.894156i	$0.352223\pi$
$41$			11.4508i			1.78831i	−0.447757	+	0.894156i	$0.647777\pi$
$42$	1.12921	+	0.851398i	0.174241	+	0.131374i
$43$	0.0897468	−	0.0897468i	0.0136863	−	0.0136863i	−0.700231	−	0.713917i	$-0.746919\pi$
$43$	0.0897468	−	0.0897468i	0.0136863	−	0.0136863i	0.713917	+	0.700231i	$0.246919\pi$
$44$	5.35054	−	9.64043i	0.806624	−	1.45335i
$45$	−1.69093	−	1.69093i	−0.252069	−	0.252069i
$46$	7.12313	−	0.999144i	1.05025	−	0.147316i
$47$	10.0997			1.47319			0.736595	−	0.676334i	$-0.236432\pi$
$47$	10.0997			1.47319			0.736595	+	0.676334i	$0.236432\pi$
$48$	3.89651	+	0.903982i	0.562413	+	0.130479i
$49$	−1.00000			−0.142857
$50$	1.00622	−	0.141140i	0.142301	−	0.0199602i
$51$	−2.19312	−	2.19312i	−0.307098	−	0.307098i
$52$	−1.37485	−	0.763056i	−0.190658	−	0.105817i
$53$	−7.36105	+	7.36105i	−1.01112	+	1.01112i	−0.0111802	+	0.999937i	$0.503559\pi$
$53$	−7.36105	+	7.36105i	−1.01112	+	1.01112i	−0.999937	+	0.0111802i	$0.996441\pi$
$54$	−1.12921	−	0.851398i	−0.153666	−	0.115861i
$55$		−	13.1831i		−	1.77760i
$56$	−2.58482	+	1.14835i	−0.345411	+	0.153454i
$57$			3.64307i			0.482536i
$58$	−5.54372	+	7.35267i	−0.727926	+	0.965452i
$59$	0.651584	−	0.651584i	0.0848291	−	0.0848291i	−0.663419	−	0.748248i	$-0.730895\pi$
$59$	0.651584	−	0.651584i	0.0848291	−	0.0848291i	0.748248	+	0.663419i	$0.230895\pi$
$60$	4.59810	−	1.31582i	0.593612	−	0.169871i
$61$	5.54741	+	5.54741i	0.710273	+	0.710273i	0.966592	−	0.256319i	$-0.0825097\pi$
$61$	5.54741	+	5.54741i	0.710273	+	0.710273i	−0.256319	+	0.966592i	$0.582510\pi$
$62$	−0.161593	−	1.15204i	−0.0205224	−	0.146309i
$63$	1.00000			0.125988
$64$	−5.36260	+	5.93654i	−0.670325	+	0.742068i
$65$	−1.88008			−0.233195
$66$	−1.08297	−	7.72077i	−0.133305	−	0.950361i
$67$	−7.37998	−	7.37998i	−0.901609	−	0.901609i	0.0939667	−	0.995575i	$-0.470045\pi$
$67$	−7.37998	−	7.37998i	−0.901609	−	0.901609i	−0.995575	+	0.0939667i	$0.970045\pi$
$68$	5.96369	−	1.70660i	0.723204	−	0.206956i
$69$	3.59643	−	3.59643i	0.432959	−	0.432959i
$70$	−2.03597	+	2.70032i	−0.243346	+	0.322750i
$71$		−	14.2192i		−	1.68751i	−0.536726	−	0.843757i	$-0.680339\pi$
$71$		−	14.2192i		−	1.68751i	0.536726	−	0.843757i	$-0.319661\pi$
$72$	2.58482	−	1.14835i	0.304624	−	0.135334i
$73$			4.93461i			0.577552i	0.957397	+	0.288776i	$0.0932483\pi$
$73$			4.93461i			0.577552i	−0.957397	+	0.288776i	$0.906752\pi$
$74$	4.90444	+	3.69782i	0.570129	+	0.429863i
$75$	0.508035	−	0.508035i	0.0586629	−	0.0586629i
$76$	−6.37070	−	3.53580i	−0.730770	−	0.405585i
$77$	3.89817	+	3.89817i	0.444238	+	0.444238i
$78$	−1.10108	+	0.154446i	−0.124673	+	0.0174876i
$79$	−2.22554			−0.250393			−0.125196	−	0.992132i	$-0.539956\pi$
$79$	−2.22554			−0.250393			−0.125196	+	0.992132i	$0.539956\pi$
$80$	−2.16172	+	9.31786i	−0.241688	+	1.04177i
$81$	−1.00000			−0.111111
$82$	−16.0369	+	2.24945i	−1.77097	+	0.248410i
$83$	10.5724	+	10.5724i	1.16047	+	1.16047i	0.984372	+	0.176101i	$0.0563484\pi$
$83$	10.5724	+	10.5724i	1.16047	+	1.16047i	0.176101	+	0.984372i	$0.443652\pi$
$84$	−0.970557	+	1.74872i	−0.105896	+	0.190801i
$85$	5.24447	−	5.24447i	0.568843	−	0.568843i
$86$	0.143321	+	0.108060i	0.0154547	+	0.0116525i
$87$			6.51132i			0.698087i
$88$	14.5525	+	5.59963i	1.55131	+	0.596922i
$89$			10.3158i			1.09347i	0.837306	+	0.546734i	$0.184129\pi$
$89$			10.3158i			1.09347i	−0.837306	+	0.546734i	$0.815871\pi$
$90$	2.03597	−	2.70032i	0.214611	−	0.284639i
$91$	0.555931	−	0.555931i	0.0582774	−	0.0582774i
$92$	2.79861	+	9.77969i	0.291775	+	1.01960i
$93$	−0.581657	−	0.581657i	−0.0603150	−	0.0603150i
$94$	1.98403	+	14.1446i	0.204637	+	1.45891i
$95$	−8.71179			−0.893811
$96$	−0.500579	+	5.63466i	−0.0510901	+	0.575085i
$97$	11.6494			1.18282			0.591409	−	0.806371i	$-0.298572\pi$
$97$	11.6494			1.18282			0.591409	+	0.806371i	$0.298572\pi$
$98$	−0.196445	−	1.40050i	−0.0198440	−	0.141472i
$99$	−3.89817	−	3.89817i	−0.391781	−	0.391781i
$100$	0.395334	+	1.38149i	0.0395334	+	0.138149i
$101$	6.81224	−	6.81224i	0.677844	−	0.677844i	−0.281668	−	0.959512i	$-0.590888\pi$
$101$	6.81224	−	6.81224i	0.677844	−	0.677844i	0.959512	+	0.281668i	$0.0908877\pi$
$102$	2.64064	−	3.50229i	0.261462	−	0.346779i
$103$			3.43951i			0.338905i	0.985538	+	0.169453i	$0.0541999\pi$
$103$			3.43951i			0.338905i	−0.985538	+	0.169453i	$0.945800\pi$
$104$	0.798580	−	2.07538i	0.0783072	−	0.203508i
$105$			2.39133i			0.233370i
$106$	−11.7552	−	8.86313i	−1.14177	−	0.860863i
$107$	8.90089	−	8.90089i	0.860482	−	0.860482i	−0.130912	−	0.991394i	$-0.541791\pi$
$107$	8.90089	−	8.90089i	0.860482	−	0.860482i	0.991394	+	0.130912i	$0.0417907\pi$
$108$	0.970557	−	1.74872i	0.0933919	−	0.168271i
$109$	2.84417	+	2.84417i	0.272422	+	0.272422i	0.830075	−	0.557652i	$-0.188298\pi$
$109$	2.84417	+	2.84417i	0.272422	+	0.272422i	−0.557652	+	0.830075i	$0.688298\pi$
$110$	18.4629	−	2.58975i	1.76037	−	0.246923i
$111$	4.34323			0.412242
$112$	−2.11604	−	3.39446i	−0.199947	−	0.320747i
$113$	−1.61788			−0.152197			−0.0760985	−	0.997100i	$-0.524246\pi$
$113$	−1.61788			−0.152197			−0.0760985	+	0.997100i	$0.524246\pi$
$114$	−5.10213	+	0.715663i	−0.477858	+	0.0670280i
$115$	8.60026	+	8.60026i	0.801978	+	0.801978i
$116$	−11.3865	−	6.31960i	−1.05721	−	0.586761i
$117$	−0.555931	+	0.555931i	−0.0513958	+	0.0513958i
$118$	1.04055	+	0.784546i	0.0957901	+	0.0722233i
$119$			3.10154i			0.284317i
$120$	2.74608	+	6.18117i	0.250682	+	0.564261i
$121$		−	19.3915i		−	1.76287i
$122$	−6.67941	+	8.85893i	−0.604725	+	0.802050i
$123$	−8.09692	+	8.09692i	−0.730075	+	0.730075i
$124$	1.58169	−	0.452624i	0.142040	−	0.0406468i
$125$	−7.23976	−	7.23976i	−0.647543	−	0.647543i
$126$	0.196445	+	1.40050i	0.0175007	+	0.124767i
$127$	−17.0480			−1.51277			−0.756384	−	0.654128i	$-0.773036\pi$
$127$	−17.0480			−1.51277			−0.756384	+	0.654128i	$0.773036\pi$
$128$	−9.36760	−	6.34413i	−0.827987	−	0.560747i
$129$	0.126921			0.0111748
$130$	−0.369332	−	2.63305i	−0.0323926	−	0.230934i
$131$	−10.3871	−	10.3871i	−0.907527	−	0.907527i	0.0885449	−	0.996072i	$-0.471778\pi$
$131$	−10.3871	−	10.3871i	−0.907527	−	0.907527i	−0.996072	+	0.0885449i	$0.971778\pi$
$132$	10.6002	−	3.03341i	0.922630	−	0.264025i
$133$	2.57604	−	2.57604i	0.223371	−	0.223371i
$134$	8.88593	−	11.7855i	0.767627	−	1.01811i
$135$		−	2.39133i		−	0.205813i
$136$	3.56164	+	8.01691i	0.305408	+	0.687445i
$137$		−	4.46101i		−	0.381130i	−0.981675	−	0.190565i	$-0.938968\pi$
$137$		−	4.46101i		−	0.381130i	0.981675	−	0.190565i	$-0.0610320\pi$
$138$	5.74331	+	4.33031i	0.488903	+	0.368621i
$139$	0.890644	−	0.890644i	0.0755434	−	0.0755434i	−0.668326	−	0.743869i	$-0.732989\pi$
$139$	0.890644	−	0.890644i	0.0755434	−	0.0755434i	0.743869	+	0.668326i	$0.232989\pi$
$140$	−4.18177	−	2.32092i	−0.353424	−	0.196154i
$141$	7.14155	+	7.14155i	0.601427	+	0.601427i
$142$	19.9141	−	2.79330i	1.67115	−	0.234409i
$143$	−4.33423			−0.362447
$144$	2.11604	+	3.39446i	0.176337	+	0.282872i
$145$	−15.5707			−1.29308
$146$	−6.91094	+	0.969380i	−0.571953	+	0.0802265i
$147$	−0.707107	−	0.707107i	−0.0583212	−	0.0583212i
$148$	−4.21536	+	7.59510i	−0.346500	+	0.624313i
$149$	−5.22193	+	5.22193i	−0.427797	+	0.427797i	−0.887877	−	0.460080i	$-0.847821\pi$
$149$	−5.22193	+	5.22193i	−0.427797	+	0.427797i	0.460080	+	0.887877i	$0.347821\pi$
$150$	0.811306	+	0.611704i	0.0662429	+	0.0499454i
$151$		−	15.6463i		−	1.27328i	−0.771163	−	0.636638i	$-0.780325\pi$
$151$		−	15.6463i		−	1.27328i	0.771163	−	0.636638i	$-0.219675\pi$
$152$	3.70041	−	9.61678i	0.300143	−	0.780024i
$153$		−	3.10154i		−	0.250744i
$154$	−4.69363	+	6.22518i	−0.378223	+	0.501640i
$155$	1.39093	−	1.39093i	0.111723	−	0.111723i
$156$	−0.432604	−	1.51173i	−0.0346361	−	0.121035i
$157$	4.03816	+	4.03816i	0.322280	+	0.322280i	0.849641	−	0.527361i	$-0.176818\pi$
$157$	4.03816	+	4.03816i	0.322280	+	0.322280i	−0.527361	+	0.849641i	$0.676818\pi$
$158$	−0.437196	−	3.11687i	−0.0347815	−	0.247965i
$159$	−10.4101			−0.825574
$160$	−13.4744	−	1.19705i	−1.06524	−	0.0946352i
$161$	−5.08612			−0.400842
$162$	−0.196445	−	1.40050i	−0.0154342	−	0.110034i
$163$	14.7587	+	14.7587i	1.15599	+	1.15599i	0.985331	+	0.170656i	$0.0545887\pi$
$163$	14.7587	+	14.7587i	1.15599	+	1.15599i	0.170656	+	0.985331i	$0.445411\pi$
$164$	−6.30072	−	22.0178i	−0.492004	−	1.71930i
$165$	9.32183	−	9.32183i	0.725704	−	0.725704i
$166$	−12.7298	+	16.8836i	−0.988024	+	1.31042i
$167$		−	18.5376i		−	1.43448i	−0.696825	−	0.717242i	$-0.745404\pi$
$167$		−	18.5376i		−	1.43448i	0.696825	−	0.717242i	$-0.254596\pi$
$168$	−2.63975	−	1.01574i	−0.203661	−	0.0783661i
$169$		−	12.3819i		−	0.952452i
$170$	8.37515	+	6.31465i	0.642345	+	0.484311i
$171$	−2.57604	+	2.57604i	−0.196995	+	0.196995i
$172$	−0.123184	+	0.221950i	−0.00939271	+	0.0169235i
$173$	−9.85404	−	9.85404i	−0.749189	−	0.749189i	0.225138	−	0.974327i	$-0.427717\pi$
$173$	−9.85404	−	9.85404i	−0.749189	−	0.749189i	−0.974327	+	0.225138i	$0.927717\pi$
$174$	−9.11912	+	1.27912i	−0.691319	+	0.0969696i
$175$	−0.718471			−0.0543113
$176$	−4.98352	+	21.4809i	−0.375647	+	1.61918i
$177$	0.921480			0.0692626
$178$	−14.4473	+	2.02648i	−1.08287	+	0.151891i
$179$	−2.90579	−	2.90579i	−0.217189	−	0.217189i	0.590124	−	0.807313i	$-0.299079\pi$
$179$	−2.90579	−	2.90579i	−0.217189	−	0.217189i	−0.807313	+	0.590124i	$0.799079\pi$
$180$	4.18177	+	2.32092i	0.311691	+	0.172991i
$181$	−6.04724	+	6.04724i	−0.449488	+	0.449488i	−0.895184	−	0.445696i	$-0.852956\pi$
$181$	−6.04724	+	6.04724i	−0.449488	+	0.449488i	0.445696	+	0.895184i	$0.352956\pi$
$182$	0.887793	+	0.669373i	0.0658076	+	0.0496172i
$183$			7.84523i			0.579936i
$184$	−13.1467	+	5.84063i	−0.969188	+	0.430577i
$185$			10.3861i			0.763603i
$186$	0.700349	−	0.928876i	0.0513520	−	0.0681085i
$187$	12.0903	−	12.0903i	0.884132	−	0.884132i
$188$	−19.4199	+	5.55729i	−1.41634	+	0.405307i
$189$	0.707107	+	0.707107i	0.0514344	+	0.0514344i
$190$	−1.71139	−	12.2009i	−0.124157	−	0.885145i
$191$	−4.21313			−0.304851			−0.152426	−	0.988315i	$-0.548708\pi$
$191$	−4.21313			−0.304851			−0.152426	+	0.988315i	$0.548708\pi$
$192$	−7.98970	+	0.405839i	−0.576607	+	0.0292889i
$193$	−13.4325			−0.966892			−0.483446	−	0.875374i	$-0.660615\pi$
$193$	−13.4325			−0.966892			−0.483446	+	0.875374i	$0.660615\pi$
$194$	2.28847	+	16.3150i	0.164303	+	1.17135i
$195$	−1.32942	−	1.32942i	−0.0952014	−	0.0952014i
$196$	1.92282	−	0.550244i	0.137344	−	0.0393031i
$197$	16.2767	−	16.2767i	1.15967	−	1.15967i	0.175119	−	0.984547i	$-0.443969\pi$
$197$	16.2767	−	16.2767i	1.15967	−	1.15967i	0.984547	−	0.175119i	$-0.0560309\pi$
$198$	4.69363	−	6.22518i	0.333562	−	0.442404i
$199$			5.27884i			0.374207i	0.982340	+	0.187104i	$0.0599100\pi$
$199$			5.27884i			0.374207i	−0.982340	+	0.187104i	$0.940090\pi$
$200$	−1.85712	+	0.825053i	−0.131318	+	0.0583401i
$201$		−	10.4369i		−	0.736160i
$202$	10.8788	+	8.20234i	0.765430	+	0.577115i
$203$	4.60420	−	4.60420i	0.323151	−	0.323151i
$204$	5.42371	+	3.01022i	0.379736	+	0.210757i
$205$	−19.3624	−	19.3624i	−1.35233	−	1.35233i
$206$	−4.81705	+	0.675675i	−0.335619	+	0.0470765i
$207$	5.08612			0.353510
$208$	3.06346	+	0.710715i	0.212413	+	0.0492792i
$209$	−20.0837			−1.38922
$210$	−3.34907	+	0.469766i	−0.231108	+	0.0324169i
$211$	12.3567	+	12.3567i	0.850671	+	0.850671i	0.990216	−	0.139545i	$-0.0445641\pi$
$211$	12.3567	+	12.3567i	0.850671	+	0.850671i	−0.139545	+	0.990216i	$0.544564\pi$
$212$	10.1036	−	18.2043i	0.693917	−	1.25028i
$213$	10.0545	−	10.0545i	0.688925	−	0.688925i
$214$	14.2143	+	10.7172i	0.971667	+	0.732612i
$215$			0.303511i			0.0206993i
$216$	2.63975	+	1.01574i	0.179612	+	0.0691124i
$217$			0.822587i			0.0558408i
$218$	−3.42455	+	4.54199i	−0.231940	+	0.307623i
$219$	−3.48930	+	3.48930i	−0.235785	+	0.235785i
$220$	7.25390	+	25.3486i	0.489058	+	1.70900i
$221$	−1.72424	−	1.72424i	−0.115985	−	0.115985i
$222$	0.853207	+	6.08271i	0.0572635	+	0.408245i
$223$	22.7559			1.52385			0.761923	−	0.647668i	$-0.224255\pi$
$223$	22.7559			1.52385			0.761923	+	0.647668i	$0.224255\pi$
$224$	4.33827	−	3.63035i	0.289863	−	0.242563i
$225$	0.718471			0.0478980
$226$	−0.317824	−	2.26584i	−0.0211413	−	0.150722i
$227$	−8.18208	−	8.18208i	−0.543064	−	0.543064i	0.381362	−	0.924426i	$-0.375455\pi$
$227$	−8.18208	−	8.18208i	−0.543064	−	0.543064i	−0.924426	+	0.381362i	$0.875455\pi$
$228$	−2.00458	−	7.00496i	−0.132756	−	0.463915i
$229$	−9.08817	+	9.08817i	−0.600563	+	0.600563i	−0.940462	−	0.339899i	$-0.889607\pi$
$229$	−9.08817	+	9.08817i	−0.600563	+	0.600563i	0.339899	+	0.940462i	$0.389607\pi$
$230$	−10.3552	+	13.7342i	−0.682803	+	0.905604i
$231$			5.51285i			0.362719i
$232$	6.61381	−	17.1882i	0.434218	−	1.12846i
$233$			1.72597i			0.113072i	0.998401	+	0.0565359i	$0.0180055\pi$
$233$			1.72597i			0.113072i	−0.998401	+	0.0565359i	$0.981994\pi$
$234$	−0.887793	−	0.669373i	−0.0580368	−	0.0437583i
$235$	−17.0778	+	17.0778i	−1.11403	+	1.11403i
$236$	−0.894348	+	1.61141i	−0.0582171	+	0.104894i
$237$	−1.57369	−	1.57369i	−0.102222	−	0.102222i
$238$	−4.34371	+	0.609281i	−0.281561	+	0.0394938i
$239$	11.8222			0.764714			0.382357	−	0.924015i	$-0.375113\pi$
$239$	11.8222			0.764714			0.382357	+	0.924015i	$0.375113\pi$
$240$	−8.11729	+	5.06015i	−0.523969	+	0.326631i
$241$	25.4267			1.63788			0.818938	−	0.573881i	$-0.194563\pi$
$241$	25.4267			1.63788			0.818938	+	0.573881i	$0.194563\pi$
$242$	27.1579	−	3.80937i	1.74578	−	0.244876i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	−13.7191	−	7.61424i	−0.878275	−	0.487452i
$245$	1.69093	−	1.69093i	0.108029	−	0.108029i
$246$	−12.9304	−	9.74917i	−0.824410	−	0.621584i
$247$			2.86420i			0.182245i
$248$	0.944615	+	2.12624i	0.0599831	+	0.135016i
$249$			14.9516i			0.947522i
$250$	8.71709	−	11.5615i	0.551317	−	0.731214i
$251$	−15.7985	+	15.7985i	−0.997195	+	0.997195i	−0.999996	−	0.00280085i	$-0.999108\pi$
$251$	−15.7985	+	15.7985i	−0.997195	+	0.997195i	0.00280085	+	0.999996i	$0.499108\pi$
$252$	−1.92282	+	0.550244i	−0.121126	+	0.0346621i
$253$	19.8266	+	19.8266i	1.24649	+	1.24649i
$254$	−3.34900	−	23.8758i	−0.210135	−	1.49810i
$255$	7.41680			0.464458
$256$	7.04476	−	14.3656i	0.440297	−	0.897852i
$257$	−26.4972			−1.65285			−0.826425	−	0.563047i	$-0.809629\pi$
$257$	−26.4972			−1.65285			−0.826425	+	0.563047i	$0.809629\pi$
$258$	0.0249330	+	0.177754i	0.00155226	+	0.0110665i
$259$	−3.07113	−	3.07113i	−0.190831	−	0.190831i
$260$	3.61505	−	1.03450i	0.224196	−	0.0641570i
$261$	−4.60420	+	4.60420i	−0.284993	+	0.284993i
$262$	12.5067	−	16.5877i	0.772667	−	1.02479i
$263$			26.9273i			1.66041i	0.557457	+	0.830206i	$0.311777\pi$
$263$			26.9273i			1.66041i	−0.557457	+	0.830206i	$0.688223\pi$
$264$	6.33067	+	14.2497i	0.389626	+	0.877010i
$265$		−	24.8940i		−	1.52923i
$266$	4.11380	+	3.10170i	0.252233	+	0.190177i
$267$	−7.29434	+	7.29434i	−0.446407	+	0.446407i
$268$	18.2512	+	10.1296i	1.11487	+	0.618763i
$269$	13.3764	+	13.3764i	0.815573	+	0.815573i	0.985463	−	0.169890i	$-0.0543411\pi$
$269$	13.3764	+	13.3764i	0.815573	+	0.815573i	−0.169890	+	0.985463i	$0.554341\pi$
$270$	3.34907	−	0.469766i	0.203818	−	0.0285890i
$271$	−9.85067			−0.598386			−0.299193	−	0.954193i	$-0.596717\pi$
$271$	−9.85067			−0.598386			−0.299193	+	0.954193i	$0.596717\pi$
$272$	−10.5280	+	6.56297i	−0.638357	+	0.397938i
$273$	0.786205			0.0475833
$274$	6.24766	−	0.876344i	0.377435	−	0.0529419i
$275$	2.80072	+	2.80072i	0.168890	+	0.168890i
$276$	−4.93637	+	8.89420i	−0.297134	+	0.535368i
$277$	9.16193	−	9.16193i	0.550487	−	0.550487i	−0.376094	−	0.926581i	$-0.622733\pi$
$277$	9.16193	−	9.16193i	0.550487	−	0.550487i	0.926581	+	0.376094i	$0.122733\pi$
$278$	1.42231	+	1.07239i	0.0853046	+	0.0643175i
$279$		−	0.822587i		−	0.0492470i
$280$	2.42897	−	6.31252i	0.145159	−	0.377245i
$281$		−	3.97687i		−	0.237240i	−0.992940	−	0.118620i	$-0.962153\pi$
$281$		−	3.97687i		−	0.237240i	0.992940	−	0.118620i	$-0.0378470\pi$
$282$	−8.59885	+	11.4047i	−0.512054	+	0.679140i
$283$	7.50679	−	7.50679i	0.446233	−	0.446233i	−0.447867	−	0.894100i	$-0.647816\pi$
$283$	7.50679	−	7.50679i	0.446233	−	0.446233i	0.894100	+	0.447867i	$0.147816\pi$
$284$	7.82405	+	27.3410i	0.464272	+	1.62239i
$285$	−6.16016	−	6.16016i	−0.364897	−	0.364897i
$286$	−0.851438	−	6.07010i	−0.0503466	−	0.358933i
$287$	11.4508			0.675918
$288$	−4.33827	+	3.63035i	−0.255635	+	0.213920i
$289$	−7.38048			−0.434146
$290$	−3.05879	−	21.8069i	−0.179619	−	1.28054i
$291$	8.23738	+	8.23738i	0.482884	+	0.482884i
$292$	−2.71524	−	9.48836i	−0.158897	−	0.555264i
$293$	−4.34807	+	4.34807i	−0.254017	+	0.254017i	−0.822615	−	0.568598i	$-0.807486\pi$
$293$	−4.34807	+	4.34807i	−0.254017	+	0.254017i	0.568598	+	0.822615i	$0.307486\pi$
$294$	0.851398	−	1.12921i	0.0496545	−	0.0658570i
$295$			2.20356i			0.128296i
$296$	−11.4650	−	4.41160i	−0.666392	−	0.256419i
$297$		−	5.51285i		−	0.319888i
$298$	−8.33915	−	6.28751i	−0.483074	−	0.364225i
$299$	2.82753	−	2.82753i	0.163520	−	0.163520i
$300$	−0.697317	+	1.25640i	−0.0402596	+	0.0725385i
$301$	−0.0897468	−	0.0897468i	−0.00517292	−	0.00517292i
$302$	21.9126	−	3.07363i	1.26093	−	0.176868i
$303$	9.63397			0.553457
$304$	14.1953	+	3.29327i	0.814154	+	0.188882i
$305$	−18.7605			−1.07423
$306$	4.34371	−	0.609281i	0.248313	−	0.0348303i
$307$	17.7732	+	17.7732i	1.01437	+	1.01437i	0.999895	+	0.0144747i	$0.00460760\pi$
$307$	17.7732	+	17.7732i	1.01437	+	1.01437i	0.0144747	+	0.999895i	$0.495392\pi$
$308$	−9.64043	−	5.35054i	−0.549314	−	0.304875i
$309$	−2.43210	+	2.43210i	−0.138357	+	0.138357i
$310$	2.22125	+	1.67477i	0.126159	+	0.0951203i
$311$			12.7168i			0.721103i	0.932739	+	0.360552i	$0.117412\pi$
$311$			12.7168i			0.721103i	−0.932739	+	0.360552i	$0.882588\pi$
$312$	2.03220	−	0.902836i	0.115051	−	0.0511130i
$313$			11.8925i			0.672205i	0.941825	+	0.336103i	$0.109109\pi$
$313$			11.8925i			0.672205i	−0.941825	+	0.336103i	$0.890891\pi$
$314$	−4.86218	+	6.44873i	−0.274389	+	0.363923i
$315$	−1.69093	+	1.69093i	−0.0952730	+	0.0952730i
$316$	4.27931	−	1.22459i	0.240730	−	0.0688885i
$317$	11.1563	+	11.1563i	0.626601	+	0.626601i	0.947211	−	0.320610i	$-0.103888\pi$
$317$	11.1563	+	11.1563i	0.626601	+	0.626601i	−0.320610	+	0.947211i	$0.603888\pi$
$318$	−2.04501	−	14.5794i	−0.114679	−	0.817571i
$319$	−35.8959			−2.00979
$320$	−0.970497	−	19.1060i	−0.0542524	−	1.06806i
$321$	12.5878			0.702580
$322$	−0.999144	−	7.12313i	−0.0556801	−	0.396956i
$323$	−7.98967	−	7.98967i	−0.444557	−	0.444557i
$324$	1.92282	−	0.550244i	0.106823	−	0.0305691i
$325$	0.399420	−	0.399420i	0.0221558	−	0.0221558i
$326$	−17.7703	+	23.5688i	−0.984204	+	1.30536i
$327$			4.02227i			0.222432i
$328$	29.5982	−	13.1495i	1.63429	−	0.726058i
$329$		−	10.0997i		−	0.556814i
$330$	14.8865	+	11.2240i	0.819474	+	0.617862i
$331$	−19.0605	+	19.0605i	−1.04766	+	1.04766i	−0.0488511	+	0.998806i	$0.515556\pi$
$331$	−19.0605	+	19.0605i	−1.04766	+	1.04766i	−0.998806	+	0.0488511i	$0.984444\pi$
$332$	−26.1462	−	14.5114i	−1.43496	−	0.796418i
$333$	3.07113	+	3.07113i	0.168297	+	0.168297i
$334$	25.9620	−	3.64162i	1.42058	−	0.199261i
$335$	24.9580			1.36360
$336$	0.903982	−	3.89651i	0.0493163	−	0.212572i
$337$	31.5228			1.71716			0.858578	−	0.512683i	$-0.171348\pi$
$337$	31.5228			1.71716			0.858578	+	0.512683i	$0.171348\pi$
$338$	17.3409	−	2.43236i	0.943219	−	0.132303i
$339$	−1.14401	−	1.14401i	−0.0621342	−	0.0621342i
$340$	−7.19843	+	12.9699i	−0.390390	+	0.703392i
$341$	3.20659	−	3.20659i	0.173646	−	0.173646i
$342$	−4.11380	−	3.10170i	−0.222449	−	0.167721i
$343$			1.00000i			0.0539949i
$344$	−0.335040	−	0.128919i	−0.0180641	−	0.00695085i
$345$			12.1626i			0.654813i
$346$	11.8648	−	15.7364i	0.637857	−	0.845993i
$347$	12.1013	−	12.1013i	0.649630	−	0.649630i	−0.303274	−	0.952903i	$-0.598080\pi$
$347$	12.1013	−	12.1013i	0.649630	−	0.649630i	0.952903	+	0.303274i	$0.0980796\pi$
$348$	−3.58281	−	12.5201i	−0.192059	−	0.671147i
$349$	−5.09850	−	5.09850i	−0.272917	−	0.272917i	0.557357	−	0.830273i	$-0.311816\pi$
$349$	−5.09850	−	5.09850i	−0.272917	−	0.272917i	−0.830273	+	0.557357i	$0.811816\pi$
$350$	−0.141140	−	1.00622i	−0.00754425	−	0.0537847i
$351$	−0.786205			−0.0419645
$352$	−31.0631	−	2.75962i	−1.65567	−	0.147088i
$353$	16.6270			0.884968			0.442484	−	0.896776i	$-0.354097\pi$
$353$	16.6270			0.884968			0.442484	+	0.896776i	$0.354097\pi$
$354$	0.181020	+	1.29054i	0.00962111	+	0.0685912i
$355$	24.0437	+	24.0437i	1.27611	+	1.27611i
$356$	−5.67619	−	19.8353i	−0.300837	−	1.05127i
$357$	−2.19312	+	2.19312i	−0.116072	+	0.116072i
$358$	3.49874	−	4.64039i	0.184914	−	0.245252i
$359$		−	13.8869i		−	0.732924i	−0.930433	−	0.366462i	$-0.880569\pi$
$359$		−	13.8869i		−	0.732924i	0.930433	−	0.366462i	$-0.119431\pi$
$360$	−2.42897	+	6.31252i	−0.128018	+	0.332699i
$361$		−	5.72805i		−	0.301476i
$362$	−9.65713	−	7.28123i	−0.507568	−	0.382693i
$363$	13.7119	−	13.7119i	0.719687	−	0.719687i
$364$	−0.763056	+	1.37485i	−0.0399950	+	0.0720618i
$365$	−8.34407	−	8.34407i	−0.436748	−	0.436748i
$366$	−10.9873	+	1.54116i	−0.574314	+	0.0805575i
$367$	−7.40914			−0.386754			−0.193377	−	0.981125i	$-0.561944\pi$
$367$	−7.40914			−0.386754			−0.193377	+	0.981125i	$0.561944\pi$
$368$	−10.7624	−	17.2646i	−0.561030	−	0.899982i
$369$	−11.4508			−0.596104
$370$	−14.5458	+	2.04030i	−0.756200	+	0.106070i
$371$	7.36105	+	7.36105i	0.382167	+	0.382167i
$372$	1.43847	+	0.798367i	0.0745814	+	0.0413934i
$373$	−22.9931	+	22.9931i	−1.19054	+	1.19054i	−0.213619	+	0.976917i	$0.568525\pi$
$373$	−22.9931	+	22.9931i	−1.19054	+	1.19054i	−0.976917	+	0.213619i	$0.931475\pi$
$374$	19.3076	+	14.5575i	0.998373	+	0.752748i
$375$		−	10.2386i		−	0.528717i
$376$	−11.5979	−	26.1059i	−0.598118	−	1.34631i
$377$			5.11923i			0.263654i
$378$	−0.851398	+	1.12921i	−0.0437912	+	0.0580805i
$379$	−18.5189	+	18.5189i	−0.951253	+	0.951253i	−0.998866	−	0.0476128i	$-0.984839\pi$
$379$	−18.5189	+	18.5189i	−0.951253	+	0.951253i	0.0476128	+	0.998866i	$0.484839\pi$
$380$	16.7512	−	4.79361i	0.859318	−	0.245907i
$381$	−12.0548	−	12.0548i	−0.617585	−	0.617585i
$382$	−0.827648	−	5.90050i	−0.0423462	−	0.301896i
$383$	15.1962			0.776487			0.388244	−	0.921557i	$-0.373082\pi$
$383$	15.1962			0.776487			0.388244	+	0.921557i	$0.373082\pi$
$384$	−2.13792	−	11.1099i	−0.109100	−	0.566948i
$385$	−13.1831			−0.671871
$386$	−2.63875	−	18.8122i	−0.134309	−	0.957518i
$387$	0.0897468	+	0.0897468i	0.00456209	+	0.00456209i
$388$	−22.3997	+	6.41002i	−1.13717	+	0.325419i
$389$	3.28467	−	3.28467i	0.166539	−	0.166539i	−0.618917	−	0.785456i	$-0.712428\pi$
$389$	3.28467	−	3.28467i	0.166539	−	0.166539i	0.785456	+	0.618917i	$0.212428\pi$
$390$	1.60069	−	2.12301i	0.0810542	−	0.107503i
$391$			15.7748i			0.797765i
$392$	1.14835	+	2.58482i	0.0580003	+	0.130553i
$393$		−	14.6896i		−	0.740993i
$394$	25.9930	+	19.5981i	1.30951	+	0.987337i
$395$	3.76322	−	3.76322i	0.189348	−	0.189348i
$396$	9.64043	+	5.35054i	0.484450	+	0.268875i
$397$	10.9111	+	10.9111i	0.547611	+	0.547611i	0.925749	−	0.378138i	$-0.123436\pi$
$397$	10.9111	+	10.9111i	0.547611	+	0.547611i	−0.378138	+	0.925749i	$0.623436\pi$
$398$	−7.39304	+	1.03700i	−0.370579	+	0.0519803i
$399$	3.64307			0.182382
$400$	−1.52031	−	2.43882i	−0.0760156	−	0.121941i
$401$	36.8743			1.84141			0.920707	−	0.390256i	$-0.127613\pi$
$401$	36.8743			1.84141			0.920707	+	0.390256i	$0.127613\pi$
$402$	14.6169	−	2.05027i	0.729024	−	0.102258i
$403$	−0.457301	−	0.457301i	−0.0227798	−	0.0227798i
$404$	−9.35031	+	16.8471i	−0.465195	+	0.838175i
$405$	1.69093	−	1.69093i	0.0840229	−	0.0840229i
$406$	7.35267	+	5.54372i	0.364907	+	0.275130i
$407$			23.9436i			1.18684i
$408$	−3.15035	+	8.18727i	−0.155966	+	0.405330i
$409$		−	18.1369i		−	0.896810i	−0.893831	−	0.448405i	$-0.851992\pi$
$409$		−	18.1369i		−	0.896810i	0.893831	−	0.448405i	$-0.148008\pi$
$410$	23.3135	−	30.9208i	1.15137	−	1.52707i
$411$	3.15441	−	3.15441i	0.155596	−	0.155596i
$412$	−1.89257	−	6.61355i	−0.0932402	−	0.325826i
$413$	−0.651584	−	0.651584i	−0.0320624	−	0.0320624i
$414$	0.999144	+	7.12313i	0.0491052	+	0.350083i
$415$	−35.7544			−1.75511
$416$	−0.393558	+	4.43000i	−0.0192958	+	0.217199i
$417$	1.25956			0.0616809
$418$	−3.94534	−	28.1273i	−0.192973	−	1.37575i
$419$	0.628000	+	0.628000i	0.0306798	+	0.0306798i	0.722280	−	0.691600i	$-0.243094\pi$
$419$	0.628000	+	0.628000i	0.0306798	+	0.0306798i	−0.691600	+	0.722280i	$0.743094\pi$
$420$	−1.31582	−	4.59810i	−0.0642053	−	0.224364i
$421$	−8.72877	+	8.72877i	−0.425414	+	0.425414i	−0.887063	−	0.461649i	$-0.847258\pi$
$421$	−8.72877	+	8.72877i	−0.425414	+	0.425414i	0.461649	+	0.887063i	$0.347258\pi$
$422$	−14.8782	+	19.7330i	−0.724259	+	0.960588i
$423$			10.0997i			0.491063i
$424$	27.4800	+	10.5740i	1.33455	+	0.513517i
$425$			2.22836i			0.108091i
$426$	16.0566	+	12.1062i	0.777943	+	0.586549i
$427$	5.54741	−	5.54741i	0.268458	−	0.268458i
$428$	−12.2171	+	22.0125i	−0.590538	+	1.06401i
$429$	−3.06476	−	3.06476i	−0.147968	−	0.147968i
$430$	−0.425068	+	0.0596232i	−0.0204986	+	0.00287529i
$431$	23.7077			1.14196			0.570979	−	0.820965i	$-0.306564\pi$
$431$	23.7077			1.14196			0.570979	+	0.820965i	$0.306564\pi$
$432$	−0.903982	+	3.89651i	−0.0434929	+	0.187471i
$433$	33.8823			1.62828			0.814141	−	0.580668i	$-0.197208\pi$
$433$	33.8823			1.62828			0.814141	+	0.580668i	$0.197208\pi$
$434$	−1.15204	+	0.161593i	−0.0552995	+	0.00775672i
$435$	−11.0102	−	11.0102i	−0.527897	−	0.527897i
$436$	−7.03381	−	3.90384i	−0.336859	−	0.186960i
$437$	13.1020	−	13.1020i	0.626756	−	0.626756i
$438$	−5.57223	−	4.20131i	−0.266251	−	0.200747i
$439$			13.7271i			0.655158i	0.944824	+	0.327579i	$0.106233\pi$
$439$			13.7271i			0.655158i	−0.944824	+	0.327579i	$0.893767\pi$
$440$	−34.0758	+	15.1387i	−1.62450	+	0.721710i
$441$		−	1.00000i		−	0.0476190i
$442$	2.07608	−	2.75352i	0.0987492	−	0.130972i
$443$	5.70746	−	5.70746i	0.271170	−	0.271170i	−0.558401	−	0.829571i	$-0.688585\pi$
$443$	5.70746	−	5.70746i	0.271170	−	0.271170i	0.829571	+	0.558401i	$0.188585\pi$
$444$	−8.35125	+	2.38984i	−0.396333	+	0.113417i
$445$	−17.4432	−	17.4432i	−0.826887	−	0.826887i
$446$	4.47028	+	31.8697i	0.211674	+	1.50907i
$447$	−7.38492			−0.349295
$448$	5.93654	+	5.36260i	0.280475	+	0.253359i
$449$	19.8635			0.937419			0.468709	−	0.883352i	$-0.344719\pi$
$449$	19.8635			0.937419			0.468709	+	0.883352i	$0.344719\pi$
$450$	0.141140	+	1.00622i	0.00665341	+	0.0474337i
$451$	−44.6371	−	44.6371i	−2.10188	−	2.10188i
$452$	3.11088	−	0.890227i	0.146324	−	0.0418728i
$453$	11.0636	−	11.0636i	0.519812	−	0.519812i
$454$	9.85170	−	13.0664i	0.462363	−	0.613235i
$455$			1.88008i			0.0881394i
$456$	9.41668	−	4.18351i	0.440976	−	0.195911i
$457$			16.6647i			0.779540i	0.920912	+	0.389770i	$0.127445\pi$
$457$			16.6647i			0.779540i	−0.920912	+	0.389770i	$0.872555\pi$
$458$	−14.5133	−	10.9427i	−0.678164	−	0.511318i
$459$	2.19312	−	2.19312i	0.102366	−	0.102366i
$460$	−21.2690	−	11.8045i	−0.991671	−	0.550388i
$461$	2.99747	+	2.99747i	0.139606	+	0.139606i	0.773456	−	0.633850i	$-0.218526\pi$
$461$	2.99747	+	2.99747i	0.139606	+	0.139606i	−0.633850	+	0.773456i	$0.718526\pi$
$462$	−7.72077	+	1.08297i	−0.359203	+	0.0503844i
$463$	−15.5468			−0.722523			−0.361262	−	0.932465i	$-0.617654\pi$
$463$	−15.5468			−0.722523			−0.361262	+	0.932465i	$0.617654\pi$
$464$	25.3714	+	5.88612i	1.17784	+	0.273256i
$465$	1.96708			0.0912211
$466$	−2.41722	+	0.339058i	−0.111976	+	0.0157065i
$467$	−22.1148	−	22.1148i	−1.02335	−	1.02335i	−0.999721	−	0.0236312i	$-0.992477\pi$
$467$	−22.1148	−	22.1148i	−1.02335	−	1.02335i	−0.0236312	−	0.999721i	$-0.507523\pi$
$468$	0.763056	−	1.37485i	0.0352723	−	0.0635525i
$469$	−7.37998	+	7.37998i	−0.340776	+	0.340776i
$470$	−27.2724	−	20.5627i	−1.25798	−	0.948487i
$471$			5.71082i			0.263141i
$472$	−2.43247	−	0.935984i	−0.111964	−	0.0430822i
$473$			0.699698i			0.0321721i
$474$	1.89482	−	2.51311i	0.0870319	−	0.115431i
$475$	1.85081	−	1.85081i	0.0849209	−	0.0849209i
$476$	−1.70660	−	5.96369i	−0.0782219	−	0.273345i
$477$	−7.36105	−	7.36105i	−0.337039	−	0.337039i
$478$	2.32241	+	16.5570i	0.106225	+	0.757300i
$479$	−19.2208			−0.878219			−0.439109	−	0.898434i	$-0.644706\pi$
$479$	−19.2208			−0.878219			−0.439109	+	0.898434i	$0.644706\pi$
$480$	−8.68136	−	10.3742i	−0.396248	−	0.473517i
$481$	3.41467			0.155696
$482$	4.99495	+	35.6102i	0.227514	+	1.62200i
$483$	−3.59643	−	3.59643i	−0.163643	−	0.163643i
$484$	10.6701	+	37.2864i	0.485003	+	1.69484i
$485$	−19.6983	+	19.6983i	−0.894454	+	0.894454i
$486$	0.851398	−	1.12921i	0.0386202	−	0.0512221i
$487$		−	10.5693i		−	0.478939i	−0.970904	−	0.239470i	$-0.923026\pi$
$487$		−	10.5693i		−	0.478939i	0.970904	−	0.239470i	$-0.0769735\pi$
$488$	7.96871	−	20.7094i	0.360727	−	0.937471i
$489$			20.8719i			0.943859i
$490$	2.70032	+	2.03597i	0.121988	+	0.0919760i
$491$	−24.5989	+	24.5989i	−1.11013	+	1.11013i	−0.117003	+	0.993132i	$0.537329\pi$
$491$	−24.5989	+	24.5989i	−1.11013	+	1.11013i	−0.993132	+	0.117003i	$0.962671\pi$
$492$	11.1136	−	20.0242i	0.501041	−	0.902761i
$493$	−14.2801	−	14.2801i	−0.643142	−	0.643142i
$494$	−4.01132	+	0.562658i	−0.180478	+	0.0253152i
$495$	13.1831			0.592534
$496$	−2.79224	+	1.74063i	−0.125375	+	0.0781564i
$497$	−14.2192			−0.637820
$498$	−20.9398	+	2.93718i	−0.938336	+	0.131618i
$499$	14.1958	+	14.1958i	0.635489	+	0.635489i	0.949440	−	0.313950i	$-0.101652\pi$
$499$	14.1958	+	14.1958i	0.635489	+	0.635489i	−0.313950	+	0.949440i	$0.601652\pi$
$500$	17.9044	+	9.93710i	0.800708	+	0.444401i
$501$	13.1081	−	13.1081i	0.585625	−	0.585625i
$502$	−25.2295	−	19.0224i	−1.12605	−	0.849010i
$503$			4.33923i			0.193477i	0.995310	+	0.0967383i	$0.0308410\pi$
$503$			4.33923i			0.193477i	−0.995310	+	0.0967383i	$0.969159\pi$
$504$	−1.14835	−	2.58482i	−0.0511514	−	0.115137i
$505$			23.0380i			1.02518i
$506$	−23.8724	+	31.6620i	−1.06126	+	1.40755i
$507$	8.75531	−	8.75531i	0.388837	−	0.388837i
$508$	32.7803	−	9.38057i	1.45439	−	0.416196i
$509$	−19.1001	−	19.1001i	−0.846596	−	0.846596i	0.143111	−	0.989707i	$-0.454289\pi$
$509$	−19.1001	−	19.1001i	−0.846596	−	0.846596i	−0.989707	+	0.143111i	$0.954289\pi$
$510$	1.45699	+	10.3873i	0.0645168	+	0.459955i
$511$	4.93461			0.218294
$512$	21.5030	+	7.04415i	0.950308	+	0.311310i
$513$	−3.64307			−0.160845
$514$	−5.20525	−	37.1094i	−0.229594	−	1.63683i
$515$	−5.81596	−	5.81596i	−0.256282	−	0.256282i
$516$	−0.244046	+	0.0698376i	−0.0107435	+	0.00307443i
$517$	−39.3703	+	39.3703i	−1.73150	+	1.73150i
$518$	3.69782	−	4.90444i	0.162473	−	0.215489i
$519$		−	13.9357i		−	0.611710i
$520$	2.15898	+	4.85966i	0.0946776	+	0.213110i
$521$			14.2041i			0.622294i	0.950362	+	0.311147i	$0.100713\pi$
$521$			14.2041i			0.622294i	−0.950362	+	0.311147i	$0.899287\pi$
$522$	−7.35267	−	5.54372i	−0.321817	−	0.242642i
$523$	1.34524	−	1.34524i	0.0588231	−	0.0588231i	−0.677083	−	0.735906i	$-0.736756\pi$
$523$	1.34524	−	1.34524i	0.0588231	−	0.0588231i	0.735906	+	0.677083i	$0.236756\pi$
$524$	25.6880	+	14.2571i	1.12219	+	0.622824i
$525$	−0.508035	−	0.508035i	−0.0221725	−	0.0221725i
$526$	−37.7118	+	5.28975i	−1.64431	+	0.230644i
$527$	2.55128			0.111136
$528$	−18.7132	+	11.6654i	−0.814386	+	0.507672i
$529$	−2.86862			−0.124723
$530$	34.8641	−	4.89030i	1.51440	−	0.212421i
$531$	0.651584	+	0.651584i	0.0282764	+	0.0282764i
$532$	−3.53580	+	6.37070i	−0.153297	+	0.276205i
$533$	−6.36584	+	6.36584i	−0.275735	+	0.275735i
$534$	−11.6487	−	8.78281i	−0.504088	−	0.380070i
$535$			30.1015i			1.30140i
$536$	−10.6012	+	27.5507i	−0.457900	+	1.19001i
$537$		−	4.10940i		−	0.177334i
$538$	−16.1060	+	21.3614i	−0.694377	+	0.920956i
$539$	3.89817	−	3.89817i	0.167906	−	0.167906i
$540$	1.31582	+	4.59810i	0.0566237	+	0.197871i
$541$	−8.94718	−	8.94718i	−0.384669	−	0.384669i	0.488112	−	0.872781i	$-0.337686\pi$
$541$	−8.94718	−	8.94718i	−0.384669	−	0.384669i	−0.872781	+	0.488112i	$0.837686\pi$
$542$	−1.93512	−	13.7959i	−0.0831204	−	0.592585i
$543$	−8.55209			−0.367005
$544$	−11.2596	−	13.4553i	−0.482753	−	0.576891i
$545$	−9.61857			−0.412014
$546$	0.154446	+	1.10108i	0.00660968	+	0.0471220i
$547$	−10.6265	−	10.6265i	−0.454356	−	0.454356i	0.442441	−	0.896798i	$-0.354113\pi$
$547$	−10.6265	−	10.6265i	−0.454356	−	0.454356i	−0.896798	+	0.442441i	$0.854113\pi$
$548$	2.45464	+	8.57771i	0.104857	+	0.366422i
$549$	−5.54741	+	5.54741i	−0.236758	+	0.236758i
$550$	−3.37223	+	4.47261i	−0.143793	+	0.190713i
$551$			23.7212i			1.01056i
$552$	−13.4261	−	5.16618i	−0.571452	−	0.219887i
$553$			2.22554i			0.0946395i
$554$	14.6311	+	11.0315i	0.621617	+	0.468683i
$555$	−7.34409	+	7.34409i	−0.311739	+	0.311739i
$556$	−1.22247	+	2.20262i	−0.0518445	+	0.0934118i
$557$	−14.1160	−	14.1160i	−0.598113	−	0.598113i	0.341697	−	0.939810i	$-0.388998\pi$
$557$	−14.1160	−	14.1160i	−0.598113	−	0.598113i	−0.939810	+	0.341697i	$0.888998\pi$
$558$	1.15204	−	0.161593i	0.0487696	−	0.00684078i
$559$	0.0997861			0.00422050
$560$	9.31786	+	2.16172i	0.393751	+	0.0913494i
$561$	17.0983			0.721891
$562$	5.56962	−	0.781236i	0.234940	−	0.0329545i
$563$	−22.6360	−	22.6360i	−0.953993	−	0.953993i	0.0449940	−	0.998987i	$-0.485673\pi$
$563$	−22.6360	−	22.6360i	−0.953993	−	0.953993i	−0.998987	+	0.0449940i	$0.985673\pi$
$564$	−17.6615	−	9.80232i	−0.743684	−	0.412752i
$565$	2.73571	−	2.73571i	0.115092	−	0.115092i
$566$	11.9880	+	9.03862i	0.503892	+	0.379921i
$567$			1.00000i			0.0419961i
$568$	−36.7542	+	16.3286i	−1.54217	+	0.685134i
$569$			2.79971i			0.117370i	0.998277	+	0.0586849i	$0.0186907\pi$
$569$			2.79971i			0.117370i	−0.998277	+	0.0586849i	$0.981309\pi$
$570$	7.41720	−	9.83746i	0.310672	−	0.412046i
$571$	24.1243	−	24.1243i	1.00957	−	1.00957i	0.00961587	−	0.999954i	$-0.496939\pi$
$571$	24.1243	−	24.1243i	1.00957	−	1.00957i	0.999954	−	0.00961587i	$-0.00306087\pi$
$572$	8.33394	−	2.38488i	0.348459	−	0.0997170i
$573$	−2.97913	−	2.97913i	−0.124455	−	0.124455i
$574$	2.24945	+	16.0369i	0.0938902	+	0.669365i
$575$	−3.65423			−0.152392
$576$	−5.93654	−	5.36260i	−0.247356	−	0.223442i
$577$	−27.2095			−1.13275			−0.566373	−	0.824149i	$-0.691654\pi$
$577$	−27.2095			−1.13275			−0.566373	+	0.824149i	$0.691654\pi$
$578$	−1.44986	−	10.3364i	−0.0603062	−	0.429937i
$579$	−9.49821	−	9.49821i	−0.394732	−	0.394732i
$580$	29.9397	−	8.56770i	1.24318	−	0.355754i
$581$	10.5724	−	10.5724i	0.438617	−	0.438617i
$582$	−9.91828	+	13.1547i	−0.411126	+	0.545279i
$583$		−	57.3893i		−	2.37682i
$584$	12.7551	−	5.66664i	0.527809	−	0.234487i
$585$		−	1.88008i		−	0.0777316i
$586$	−6.94365	−	5.23533i	−0.286840	−	0.216270i
$587$	13.7509	−	13.7509i	0.567561	−	0.567561i	−0.363884	−	0.931444i	$-0.618549\pi$
$587$	13.7509	−	13.7509i	0.567561	−	0.567561i	0.931444	+	0.363884i	$0.118549\pi$
$588$	1.74872	+	0.970557i	0.0721160	+	0.0400251i
$589$	−2.11902	−	2.11902i	−0.0873125	−	0.0873125i
$590$	−3.08610	+	0.432879i	−0.127053	+	0.0178214i
$591$	23.0187			0.946863
$592$	3.92621	−	16.9235i	0.161366	−	0.695550i
$593$	31.5237			1.29452			0.647262	−	0.762268i	$-0.275914\pi$
$593$	31.5237			1.29452			0.647262	+	0.762268i	$0.275914\pi$
$594$	7.72077	−	1.08297i	0.316787	−	0.0444349i
$595$	−5.24447	−	5.24447i	−0.215002	−	0.215002i
$596$	7.16749	−	12.9142i	0.293592	−	0.528985i
$597$	−3.73271	+	3.73271i	−0.152769	+	0.152769i
$598$	4.51542	+	3.40451i	0.184649	+	0.139221i
$599$			25.4415i			1.03951i	0.854315	+	0.519756i	$0.173977\pi$
$599$			25.4415i			1.03951i	−0.854315	+	0.519756i	$0.826023\pi$
$600$	−1.89658	−	0.729780i	−0.0774276	−	0.0297931i
$601$		−	30.2510i		−	1.23396i	−0.786978	−	0.616981i	$-0.788355\pi$
$601$		−	30.2510i		−	1.23396i	0.786978	−	0.616981i	$-0.211645\pi$
$602$	0.108060	−	0.143321i	0.00440421	−	0.00584133i
$603$	7.37998	−	7.37998i	0.300536	−	0.300536i
$604$	8.60926	+	30.0849i	0.350306	+	1.22414i
$605$	32.7897	+	32.7897i	1.33309	+	1.33309i
$606$	1.89255	+	13.4924i	0.0768794	+	0.548091i
$607$	22.3111			0.905580			0.452790	−	0.891617i	$-0.350429\pi$
$607$	22.3111			0.905580			0.452790	+	0.891617i	$0.350429\pi$
$608$	−1.82364	+	20.5275i	−0.0739585	+	0.832498i
$609$	6.51132			0.263852
$610$	−3.68542	−	26.2742i	−0.149218	−	1.06381i
$611$	5.61472	+	5.61472i	0.227147	+	0.227147i
$612$	1.70660	+	5.96369i	0.0689853	+	0.241068i
$613$	−17.8201	+	17.8201i	−0.719747	+	0.719747i	−0.968553	−	0.248806i	$-0.919962\pi$
$613$	−17.8201	+	17.8201i	−0.719747	+	0.719747i	0.248806	+	0.968553i	$0.419962\pi$
$614$	−21.4000	+	28.3829i	−0.863632	+	1.14544i
$615$		−	27.3826i		−	1.10417i
$616$	5.59963	−	14.5525i	0.225615	−	0.586339i
$617$		−	8.73124i		−	0.351506i	−0.984434	−	0.175753i	$-0.943764\pi$
$617$		−	8.73124i		−	0.351506i	0.984434	−	0.175753i	$-0.0562361\pi$
$618$	−3.88394	−	2.92839i	−0.156235	−	0.117797i
$619$	10.3735	−	10.3735i	0.416944	−	0.416944i	−0.467205	−	0.884149i	$-0.654739\pi$
$619$	10.3735	−	10.3735i	0.416944	−	0.416944i	0.884149	+	0.467205i	$0.154739\pi$
$620$	−1.90916	+	3.43987i	−0.0766738	+	0.138148i
$621$	3.59643	+	3.59643i	0.144320	+	0.144320i
$622$	−17.8099	+	2.49815i	−0.714112	+	0.100167i
$623$	10.3158			0.413292
$624$	1.66364	+	2.66874i	0.0665989	+	0.106835i
$625$	28.0762			1.12305
$626$	−16.6555	+	2.33623i	−0.665689	+	0.0933745i
$627$	−14.2013	−	14.2013i	−0.567146	−	0.567146i
$628$	−9.98662	−	5.54267i	−0.398510	−	0.221177i
$629$	−9.52522	+	9.52522i	−0.379795	+	0.379795i
$630$	−2.70032	−	2.03597i	−0.107583	−	0.0811152i
$631$		−	17.8045i		−	0.708788i	−0.935096	−	0.354394i	$-0.884687\pi$
$631$		−	17.8045i		−	0.708788i	0.935096	−	0.354394i	$-0.115313\pi$
$632$	2.55569	+	5.75262i	0.101660	+	0.228827i
$633$			17.4750i			0.694570i
$634$	−13.4328	+	17.8161i	−0.533486	+	0.707566i
$635$	28.8270	−	28.8270i	1.14396	−	1.14396i
$636$	20.0167	−	5.72809i	0.793715	−	0.227134i
$637$	−0.555931	−	0.555931i	−0.0220268	−	0.0220268i
$638$	−7.05158	−	50.2724i	−0.279175	−	1.99030i
$639$	14.2192			0.562505
$640$	26.5674	−	5.11247i	1.05017	−	0.202088i
$641$	22.8423			0.902215			0.451107	−	0.892470i	$-0.351029\pi$
$641$	22.8423			0.902215			0.451107	+	0.892470i	$0.351029\pi$
$642$	2.47280	+	17.6292i	0.0975938	+	0.695769i
$643$	−8.91572	−	8.91572i	−0.351602	−	0.351602i	0.509103	−	0.860705i	$-0.329977\pi$
$643$	−8.91572	−	8.91572i	−0.351602	−	0.351602i	−0.860705	+	0.509103i	$0.829977\pi$
$644$	9.77969	−	2.79861i	0.385374	−	0.110281i
$645$	−0.214615	+	0.214615i	−0.00845044	+	0.00845044i
$646$	9.62003	−	12.7591i	0.378495	−	0.502000i
$647$		−	30.6010i		−	1.20305i	−0.798854	−	0.601524i	$-0.794560\pi$
$647$		−	30.6010i		−	1.20305i	0.798854	−	0.601524i	$-0.205440\pi$
$648$	1.14835	+	2.58482i	0.0451113	+	0.101541i
$649$			5.07998i			0.199407i
$650$	0.637853	+	0.480925i	0.0250186	+	0.0188634i
$651$	−0.581657	+	0.581657i	−0.0227969	+	0.0227969i
$652$	−36.4991	−	20.2573i	−1.42941	−	0.793339i
$653$	−24.7037	−	24.7037i	−0.966730	−	0.966730i	0.0327337	−	0.999464i	$-0.489579\pi$
$653$	−24.7037	−	24.7037i	−0.966730	−	0.966730i	−0.999464	+	0.0327337i	$0.989579\pi$
$654$	−5.63320	+	0.790154i	−0.220275	+	0.0308975i
$655$	35.1277			1.37255
$656$	24.2303	+	38.8692i	0.946034	+	1.51759i
$657$	−4.93461			−0.192517
$658$	14.1446	−	1.98403i	0.551415	−	0.0773457i
$659$	19.2669	+	19.2669i	0.750534	+	0.750534i	0.974579	−	0.224045i	$-0.0719263\pi$
$659$	19.2669	+	19.2669i	0.750534	+	0.750534i	−0.224045	+	0.974579i	$0.571926\pi$
$660$	−12.7949	+	23.0535i	−0.498041	+	0.897355i
$661$	−0.865297	+	0.865297i	−0.0336562	+	0.0336562i	−0.723735	−	0.690078i	$-0.757576\pi$
$661$	−0.865297	+	0.865297i	−0.0336562	+	0.0336562i	0.690078	+	0.723735i	$0.257576\pi$
$662$	−30.4386	−	22.9499i	−1.18303	−	0.891973i
$663$		−	2.43844i		−	0.0947012i
$664$	15.1870	−	39.4686i	0.589370	−	1.53168i
$665$			8.71179i			0.337829i
$666$	−3.69782	+	4.90444i	−0.143288	+	0.190043i
$667$	23.4175	−	23.4175i	0.906729	−	0.906729i
$668$	10.2002	+	35.6445i	0.394658	+	1.37913i
$669$	16.0908	+	16.0908i	0.622107	+	0.622107i
$670$	4.90288	+	34.9538i	0.189415	+	1.35038i
$671$	−43.2496			−1.66963
$672$	5.63466	+	0.500579i	0.217362	+	0.0193103i
$673$	14.0444			0.541372			0.270686	−	0.962668i	$-0.412750\pi$
$673$	14.0444			0.541372			0.270686	+	0.962668i	$0.412750\pi$
$674$	6.19250	+	44.1478i	0.238526	+	1.70051i
$675$	0.508035	+	0.508035i	0.0195543	+	0.0195543i
$676$	6.81306	+	23.8081i	0.262041	+	0.915697i
$677$	18.5528	−	18.5528i	0.713041	−	0.713041i	−0.254129	−	0.967170i	$-0.581789\pi$
$677$	18.5528	−	18.5528i	0.713041	−	0.713041i	0.967170	+	0.254129i	$0.0817889\pi$
$678$	1.37746	−	1.82693i	0.0529009	−	0.0701627i
$679$		−	11.6494i		−	0.447063i
$680$	−19.5785	−	7.53355i	−0.750801	−	0.288898i
$681$		−	11.5712i		−	0.443410i
$682$	5.12075	+	3.86092i	0.196084	+	0.147842i
$683$	−4.60339	+	4.60339i	−0.176144	+	0.176144i	−0.789673	−	0.613529i	$-0.789750\pi$
$683$	−4.60339	+	4.60339i	−0.176144	+	0.176144i	0.613529	+	0.789673i	$0.289750\pi$
$684$	3.53580	−	6.37070i	0.135195	−	0.243590i
$685$	7.54324	+	7.54324i	0.288213	+	0.288213i
$686$	−1.40050	+	0.196445i	−0.0534715	+	0.00750031i
$687$	−12.8526			−0.490358
$688$	0.114735	−	0.494550i	0.00437421	−	0.0188545i
$689$	−8.18447			−0.311803
$690$	−17.0338	+	2.38928i	−0.648464	+	0.0909585i
$691$	1.28822	+	1.28822i	0.0490063	+	0.0490063i	0.731185	−	0.682179i	$-0.238967\pi$
$691$	1.28822	+	1.28822i	0.0490063	+	0.0490063i	−0.682179	+	0.731185i	$0.738967\pi$
$692$	24.3696	+	13.5254i	0.926395	+	0.514159i
$693$	−3.89817	+	3.89817i	−0.148079	+	0.148079i
$694$	19.3251	+	14.5706i	0.733570	+	0.553093i
$695$			3.01203i			0.114253i
$696$	16.8306	−	7.47725i	0.637962	−	0.283425i
$697$		−	35.5150i		−	1.34523i
$698$	6.13889	−	8.14204i	0.232361	−	0.308181i
$699$	−1.22044	+	1.22044i	−0.0461614	+	0.0461614i
$700$	1.38149	−	0.395334i	0.0522154	−	0.0149422i
$701$	−2.18588	−	2.18588i	−0.0825596	−	0.0825596i	0.664621	−	0.747181i	$-0.268593\pi$
$701$	−2.18588	−	2.18588i	−0.0825596	−	0.0825596i	−0.747181	+	0.664621i	$0.768593\pi$
$702$	−0.154446	−	1.10108i	−0.00582919	−	0.0415577i
$703$	15.8227			0.596765
$704$	−2.23733	−	44.0460i	−0.0843226	−	1.66005i
$705$	−24.1517			−0.909606
$706$	3.26630	+	23.2862i	0.122929	+	0.876389i
$707$	−6.81224	−	6.81224i	−0.256201	−	0.256201i
$708$	−1.77184	+	0.507039i	−0.0665898	+	0.0190557i
$709$	−24.4924	+	24.4924i	−0.919833	+	0.919833i	−0.997017	−	0.0771840i	$-0.975407\pi$
$709$	−24.4924	+	24.4924i	−0.919833	+	0.919833i	0.0771840	+	0.997017i	$0.475407\pi$
$710$	−28.9500	+	38.3966i	−1.08647	+	1.44100i
$711$		−	2.22554i		−	0.0834642i
$712$	26.6644	−	11.8461i	0.999290	−	0.443950i
$713$			4.18378i			0.156684i
$714$	−3.50229	−	2.64064i	−0.131070	−	0.0988235i
$715$	7.32887	−	7.32887i	0.274084	−	0.274084i
$716$	7.18619	+	3.98841i	0.268561	+	0.149054i
$717$	8.35955	+	8.35955i	0.312193	+	0.312193i
$718$	19.4487	−	2.72802i	0.725818	−	0.101809i
$719$	−6.42412			−0.239579			−0.119790	−	0.992799i	$-0.538222\pi$
$719$	−6.42412			−0.239579			−0.119790	+	0.992799i	$0.538222\pi$
$720$	−9.31786	−	2.16172i	−0.347256	−	0.0805626i
$721$	3.43951			0.128094
$722$	8.02215	−	1.12525i	0.298554	−	0.0418774i
$723$	17.9794	+	17.9794i	0.668660	+	0.668660i
$724$	8.30029	−	14.9552i	0.308478	−	0.555806i
$725$	3.30798	−	3.30798i	0.122855	−	0.122855i
$726$	21.8972	+	16.5099i	0.812680	+	0.612740i
$727$			45.0050i			1.66914i	0.550900	+	0.834571i	$0.314285\pi$
$727$			45.0050i			1.66914i	−0.550900	+	0.834571i	$0.685715\pi$
$728$	−2.07538	−	0.798580i	−0.0769188	−	0.0295973i
$729$		−	1.00000i		−	0.0370370i
$730$	10.0467	−	13.3250i	0.371847	−	0.493182i
$731$	−0.278353	+	0.278353i	−0.0102953	+	0.0102953i
$732$	−4.31679	−	15.0849i	−0.159553	−	0.557556i
$733$	19.5933	+	19.5933i	0.723694	+	0.723694i	0.969356	−	0.245662i	$-0.0790052\pi$
$733$	19.5933	+	19.5933i	0.723694	+	0.723694i	−0.245662	+	0.969356i	$0.579005\pi$
$734$	−1.45549	−	10.3765i	−0.0537231	−	0.383005i
$735$	2.39133			0.0882056
$736$	22.0650	−	18.4644i	0.813325	−	0.680606i
$737$	57.5369			2.11940
$738$	−2.24945	−	16.0369i	−0.0828034	−	0.590325i
$739$	−24.5165	−	24.5165i	−0.901853	−	0.901853i	0.0937436	−	0.995596i	$-0.470117\pi$
$739$	−24.5165	−	24.5165i	−0.901853	−	0.901853i	−0.995596	+	0.0937436i	$0.970117\pi$
$740$	−5.71490	−	19.9706i	−0.210084	−	0.734135i
$741$	−2.02529	+	2.02529i	−0.0744010	+	0.0744010i
$742$	−8.86313	+	11.7552i	−0.325376	+	0.431547i
$743$		−	18.9047i		−	0.693546i	−0.937949	−	0.346773i	$-0.887277\pi$
$743$		−	18.9047i		−	0.693546i	0.937949	−	0.346773i	$-0.112723\pi$
$744$	−0.835535	+	2.17142i	−0.0306322	+	0.0796082i
$745$		−	17.6598i		−	0.647005i
$746$	−36.7187	−	27.6850i	−1.34437	−	1.01362i
$747$	−10.5724	+	10.5724i	−0.386824	+	0.386824i
$748$	−16.5949	+	29.9001i	−0.606769	+	1.09326i
$749$	−8.90089	−	8.90089i	−0.325231	−	0.325231i
$750$	14.3391	−	2.01132i	0.523591	−	0.0734428i
$751$	19.9268			0.727138			0.363569	−	0.931567i	$-0.381558\pi$
$751$	19.9268			0.727138			0.363569	+	0.931567i	$0.381558\pi$
$752$	34.2830	−	21.3713i	1.25017	−	0.779332i
$753$	−22.3425			−0.814206
$754$	−7.16950	+	1.00565i	−0.261098	+	0.0366235i
$755$	26.4567	+	26.4567i	0.962858	+	0.962858i
$756$	−1.74872	−	0.970557i	−0.0636003	−	0.0352988i
$757$	10.3666	−	10.3666i	0.376780	−	0.376780i	−0.493159	−	0.869939i	$-0.664158\pi$
$757$	10.3666	−	10.3666i	0.376780	−	0.376780i	0.869939	+	0.493159i	$0.164158\pi$
$758$	−29.5738	−	22.2979i	−1.07417	−	0.809895i
$759$			28.0390i			1.01775i
$760$	10.0042	+	22.5184i	0.362889	+	0.816829i
$761$		−	45.2454i		−	1.64014i	−0.572261	−	0.820071i	$-0.693934\pi$
$761$		−	45.2454i		−	1.64014i	0.572261	−	0.820071i	$-0.306066\pi$
$762$	14.5146	−	19.2508i	0.525810	−	0.697385i
$763$	2.84417	−	2.84417i	0.102966	−	0.102966i
$764$	8.10108	−	2.31825i	0.293087	−	0.0838712i
$765$	5.24447	+	5.24447i	0.189614	+	0.189614i
$766$	2.98521	+	21.2823i	0.107860	+	0.768960i
$767$	0.724472			0.0261592
$768$	15.1394	−	5.17664i	0.546297	−	0.186796i
$769$	−17.8184			−0.642546			−0.321273	−	0.946987i	$-0.604111\pi$
$769$	−17.8184			−0.642546			−0.321273	+	0.946987i	$0.604111\pi$
$770$	−2.58975	−	18.4629i	−0.0933280	−	0.665357i
$771$	−18.7364	−	18.7364i	−0.674773	−	0.674773i
$772$	25.8282	−	7.39115i	0.929579	−	0.266013i
$773$	21.1543	−	21.1543i	0.760867	−	0.760867i	−0.215612	−	0.976479i	$-0.569175\pi$
$773$	21.1543	−	21.1543i	0.760867	−	0.760867i	0.976479	+	0.215612i	$0.0691746\pi$
$774$	−0.108060	+	0.143321i	−0.00388415	+	0.00515157i
$775$			0.591004i			0.0212295i
$776$	−13.3776	−	30.1116i	−0.480227	−	1.08095i
$777$		−	4.34323i		−	0.155813i
$778$	5.24545	+	3.95493i	0.188058	+	0.141791i
$779$	−29.4976	+	29.4976i	−1.05686	+	1.05686i
$780$	3.28773	+	1.82472i	0.117720	+	0.0653355i
$781$	55.4291	+	55.4291i	1.98341	+	1.98341i
$782$	−22.0926	+	3.09888i	−0.790031	+	0.110816i
$783$	−6.51132			−0.232696
$784$	−3.39446	+	2.11604i	−0.121231	+	0.0755728i
$785$	−13.6565			−0.487420
$786$	20.5728	−	2.88570i	0.733809	−	0.102930i
$787$	0.156502	+	0.156502i	0.00557870	+	0.00557870i	0.709891	−	0.704312i	$-0.248744\pi$
$787$	0.156502	+	0.156502i	0.00557870	+	0.00557870i	−0.704312	+	0.709891i	$0.748744\pi$
$788$	−22.3410	+	40.2533i	−0.795864	+	1.43396i
$789$	−19.0405	+	19.0405i	−0.677860	+	0.677860i
$790$	6.00968	+	4.53114i	0.213815	+	0.161211i
$791$			1.61788i			0.0575251i
$792$	−5.59963	+	14.5525i	−0.198974	+	0.517102i
$793$			6.16795i			0.219030i
$794$	−13.1376	+	17.4244i	−0.466235	+	0.618370i
$795$	17.6027	−	17.6027i	0.624304	−	0.624304i
$796$	−2.90465	−	10.1503i	−0.102953	−	0.359766i
$797$	−23.4351	−	23.4351i	−0.830114	−	0.830114i	0.157418	−	0.987532i	$-0.449683\pi$
$797$	−23.4351	−	23.4351i	−0.830114	−	0.830114i	−0.987532	+	0.157418i	$0.949683\pi$
$798$	0.715663	+	5.10213i	0.0253342	+	0.180613i
$799$	−31.3245			−1.10818
$800$	3.11692	−	2.60830i	0.110200	−	0.0922172i
$801$	−10.3158			−0.364489
$802$	7.24377	+	51.6425i	0.255786	+	1.82356i
$803$	−19.2360	−	19.2360i	−0.678823	−	0.678823i
$804$	5.74283	+	20.0682i	0.202534	+	0.707751i
$805$	8.60026	−	8.60026i	0.303119	−	0.303119i
$806$	0.550617	−	0.730287i	0.0193947	−	0.0257232i
$807$			18.9171i			0.665913i
$808$	−25.4313	−	9.78561i	−0.894668	−	0.344257i
$809$			23.3118i			0.819599i	0.912176	+	0.409800i	$0.134401\pi$
$809$			23.3118i			0.819599i	−0.912176	+	0.409800i	$0.865599\pi$
$810$	2.70032	+	2.03597i	0.0948797	+	0.0715369i
$811$	−1.01997	+	1.01997i	−0.0358160	+	0.0358160i	−0.724788	−	0.688972i	$-0.758062\pi$
$811$	−1.01997	+	1.01997i	−0.0358160	+	0.0358160i	0.688972	+	0.724788i	$0.258062\pi$
$812$	−6.31960	+	11.3865i	−0.221775	+	0.399587i
$813$	−6.96548	−	6.96548i	−0.244290	−	0.244290i
$814$	−33.5331	+	4.70360i	−1.17533	+	0.164861i
$815$	−49.9116			−1.74833
$816$	−12.0852	−	2.80373i	−0.423066	−	0.0981503i
$817$	0.462383			0.0161767
$818$	25.4007	−	3.56290i	0.888115	−	0.124574i
$819$	0.555931	+	0.555931i	0.0194258	+	0.0194258i
$820$	47.8845	+	26.5764i	1.67220	+	0.928088i
$821$	−28.2435	+	28.2435i	−0.985705	+	0.985705i	−0.999899	−	0.0141943i	$-0.995482\pi$
$821$	−28.2435	+	28.2435i	−0.985705	+	0.985705i	0.0141943	+	0.999899i	$0.495482\pi$
$822$	5.03743	+	3.79809i	0.175701	+	0.132474i
$823$			16.7459i			0.583725i	0.956460	+	0.291863i	$0.0942750\pi$
$823$			16.7459i			0.583725i	−0.956460	+	0.291863i	$0.905725\pi$
$824$	8.89052	−	3.94975i	0.309716	−	0.137596i
$825$			3.96082i			0.137898i
$826$	0.784546	−	1.04055i	0.0272978	−	0.0362053i
$827$	−22.2093	+	22.2093i	−0.772294	+	0.772294i	−0.978507	−	0.206213i	$-0.933886\pi$
$827$	−22.2093	+	22.2093i	−0.772294	+	0.772294i	0.206213	+	0.978507i	$0.433886\pi$
$828$	−9.77969	+	2.79861i	−0.339868	+	0.0972583i
$829$	−8.98428	−	8.98428i	−0.312037	−	0.312037i	0.533661	−	0.845698i	$-0.320816\pi$
$829$	−8.98428	−	8.98428i	−0.312037	−	0.312037i	−0.845698	+	0.533661i	$0.820816\pi$
$830$	−7.02377	−	50.0741i	−0.243799	−	1.73810i
$831$	12.9569			0.449471
$832$	−6.28154	+	0.319073i	−0.217773	+	0.0110619i
$833$	3.10154			0.107462
$834$	0.247434	+	1.76402i	0.00856795	+	0.0610830i
$835$	31.3457	+	31.3457i	1.08476	+	1.08476i
$836$	38.6173	−	11.0509i	1.33561	−	0.382205i
$837$	0.581657	−	0.581657i	0.0201050	−	0.0201050i
$838$	−0.756148	+	1.00288i	−0.0261207	+	0.0346440i
$839$		−	15.1682i		−	0.523664i	−0.965113	−	0.261832i	$-0.915673\pi$
$839$		−	15.1682i		−	0.523664i	0.965113	−	0.261832i	$-0.0843267\pi$
$840$	6.18117	−	2.74608i	0.213270	−	0.0947487i
$841$			13.3973i			0.461975i
$842$	−13.9394	−	10.5100i	−0.480383	−	0.362197i
$843$	2.81207	−	2.81207i	0.0968528	−	0.0968528i
$844$	−30.5589	−	16.9605i	−1.05188	−	0.583804i
$845$	20.9369	+	20.9369i	0.720250	+	0.720250i
$846$	−14.1446	+	1.98403i	−0.486303	+	0.0682125i
$847$	−19.3915			−0.666301
$848$	−9.41054	+	40.5631i	−0.323159	+	1.39294i
$849$	10.6162			0.364347
$850$	−3.12083	+	0.437751i	−0.107044	+	0.0150147i
$851$	−15.6201	−	15.6201i	−0.535452	−	0.535452i
$852$	−13.8006	+	24.8655i	−0.472800	+	0.851877i
$853$	4.91244	−	4.91244i	0.168199	−	0.168199i	−0.617988	−	0.786187i	$-0.712052\pi$
$853$	4.91244	−	4.91244i	0.168199	−	0.168199i	0.786187	+	0.617988i	$0.212052\pi$
$854$	8.85893	+	6.67941i	0.303146	+	0.228565i
$855$		−	8.71179i		−	0.297937i
$856$	−33.2285	−	12.7859i	−1.13573	−	0.437013i
$857$			34.2760i			1.17085i	0.810728	+	0.585423i	$0.199071\pi$
$857$			34.2760i			1.17085i	−0.810728	+	0.585423i	$0.800929\pi$
$858$	3.69015	−	4.89427i	0.125980	−	0.167088i
$859$	6.57462	−	6.57462i	0.224323	−	0.224323i	−0.585993	−	0.810316i	$-0.699295\pi$
$859$	6.57462	−	6.57462i	0.224323	−	0.224323i	0.810316	+	0.585993i	$0.199295\pi$
$860$	−0.167005	−	0.583596i	−0.00569482	−	0.0199005i
$861$	8.09692	+	8.09692i	0.275942	+	0.275942i
$862$	4.65725	+	33.2026i	0.158627	+	1.13089i
$863$	46.6838			1.58914			0.794568	−	0.607175i	$-0.207697\pi$
$863$	46.6838			1.58914			0.794568	+	0.607175i	$0.207697\pi$
$864$	−5.63466	−	0.500579i	−0.191695	−	0.0170300i
$865$	33.3249			1.13308
$866$	6.65602	+	47.4523i	0.226181	+	1.61250i
$867$	−5.21879	−	5.21879i	−0.177239	−	0.177239i
$868$	−0.452624	−	1.58169i	−0.0153630	−	0.0536859i
$869$	8.67554	−	8.67554i	0.294297	−	0.294297i
$870$	13.2569	−	17.5827i	0.449450	−	0.596108i
$871$		−	8.20552i		−	0.278033i
$872$	4.08558	−	10.6178i	0.138355	−	0.359563i
$873$			11.6494i			0.394273i
$874$	20.9233	+	15.7756i	0.707741	+	0.533618i
$875$	−7.23976	+	7.23976i	−0.244748	+	0.244748i
$876$	4.78932	−	8.62925i	0.161816	−	0.291555i
$877$	−23.7282	−	23.7282i	−0.801245	−	0.801245i	0.182045	−	0.983290i	$-0.441728\pi$
$877$	−23.7282	−	23.7282i	−0.801245	−	0.801245i	−0.983290	+	0.182045i	$0.941728\pi$
$878$	−19.2248	+	2.69662i	−0.648806	+	0.0910064i
$879$	−6.14911			−0.207404
$880$	−27.8959	−	44.7494i	−0.940369	−	1.50850i
$881$	−34.6115			−1.16609			−0.583045	−	0.812440i	$-0.698139\pi$
$881$	−34.6115			−1.16609			−0.583045	+	0.812440i	$0.698139\pi$
$882$	1.40050	−	0.196445i	0.0471574	−	0.00661465i
$883$	6.58783	+	6.58783i	0.221698	+	0.221698i	0.809213	−	0.587515i	$-0.199894\pi$
$883$	6.58783	+	6.58783i	0.221698	+	0.221698i	−0.587515	+	0.809213i	$0.699894\pi$
$884$	4.26415	+	2.36665i	0.143419	+	0.0795989i
$885$	−1.55815	+	1.55815i	−0.0523768	+	0.0523768i
$886$	9.11452	+	6.87211i	0.306208	+	0.230873i
$887$		−	1.40051i		−	0.0470244i	−0.999724	−	0.0235122i	$-0.992515\pi$
$887$		−	1.40051i		−	0.0470244i	0.999724	−	0.0235122i	$-0.00748486\pi$
$888$	−4.98754	−	11.2265i	−0.167371	−	0.376736i
$889$			17.0480i			0.571772i
$890$	21.0026	−	27.8559i	0.704010	−	0.933732i
$891$	3.89817	−	3.89817i	0.130594	−	0.130594i
$892$	−43.7554	+	12.5213i	−1.46504	+	0.419244i
$893$	26.0172	+	26.0172i	0.870631	+	0.870631i
$894$	−1.45073	−	10.3426i	−0.0485197	−	0.345909i
$895$	9.82695			0.328479
$896$	−6.34413	+	9.36760i	−0.211943	+	0.312950i
$897$	3.99873			0.133514
$898$	3.90210	+	27.8190i	0.130215	+	0.928331i
$899$	−3.78735	−	3.78735i	−0.126315	−	0.126315i
$900$	−1.38149	+	0.395334i	−0.0460496	+	0.0131778i
$901$	22.8305	−	22.8305i	0.760596	−	0.760596i
$902$	53.7457	−	71.2832i	1.78954	−	2.37347i
$903$		−	0.126921i		−	0.00422367i
$904$	1.85788	+	4.18192i	0.0617923	+	0.139089i
$905$		−	20.4509i		−	0.679811i
$906$	17.6680	+	13.3212i	0.586979	+	0.442567i
$907$	−0.706289	+	0.706289i	−0.0234519	+	0.0234519i	−0.718736	−	0.695284i	$-0.755279\pi$
$907$	−0.706289	+	0.706289i	−0.0234519	+	0.0234519i	0.695284	+	0.718736i	$0.255279\pi$
$908$	20.2348	+	11.2305i	0.671516	+	0.372698i
$909$	6.81224	+	6.81224i	0.225948	+	0.225948i
$910$	−2.63305	+	0.369332i	−0.0872849	+	0.0122432i
$911$	−20.3463			−0.674103			−0.337052	−	0.941486i	$-0.609430\pi$
$911$	−20.3463			−0.674103			−0.337052	+	0.941486i	$0.609430\pi$
$912$	7.70888	+	12.3663i	0.255266	+	0.409488i
$913$	−82.4262			−2.72791
$914$	−23.3389	+	3.27369i	−0.771982	+	0.108284i
$915$	−13.2657	−	13.2657i	−0.438551	−	0.438551i
$916$	12.4742	−	22.4756i	0.412159	−	0.742615i
$917$	−10.3871	+	10.3871i	−0.343013	+	0.343013i
$918$	3.50229	+	2.64064i	0.115593	+	0.0871541i
$919$		−	43.4615i		−	1.43366i	−0.697247	−	0.716831i	$-0.745592\pi$
$919$		−	43.4615i		−	1.43366i	0.697247	−	0.716831i	$-0.254408\pi$
$920$	12.3541	−	32.1062i	0.407301	−	1.05851i
$921$			25.1351i			0.828230i
$922$	−3.60913	+	4.78681i	−0.118860	+	0.157645i
$923$	7.90491	−	7.90491i	0.260193	−	0.260193i
$924$	−3.03341	−	10.6002i	−0.0997920	−	0.348721i
$925$	−2.20652	−	2.20652i	−0.0725498	−	0.0725498i
$926$	−3.05410	−	21.7734i	−0.100364	−	0.715518i
$927$	−3.43951			−0.112968
$928$	−3.25943	+	36.6891i	−0.106996	+	1.20438i
$929$	1.49003			0.0488864			0.0244432	−	0.999701i	$-0.492219\pi$
$929$	1.49003			0.0488864			0.0244432	+	0.999701i	$0.492219\pi$
$930$	0.386423	+	2.75490i	0.0126713	+	0.0903367i
$931$	−2.57604	−	2.57604i	−0.0844263	−	0.0844263i
$932$	−0.949703	−	3.31872i	−0.0311085	−	0.108708i
$933$	−8.99213	+	8.99213i	−0.294389	+	0.294389i
$934$	26.6275	−	35.3162i	0.871279	−	1.15558i
$935$			40.8877i			1.33717i
$936$	2.07538	+	0.798580i	0.0678360	+	0.0261024i
$937$			45.7959i			1.49609i	0.663650	+	0.748044i	$0.269007\pi$
$937$			45.7959i			1.49609i	−0.663650	+	0.748044i	$0.730993\pi$
$938$	−11.7855	−	8.88593i	−0.384809	−	0.290136i
$939$	−8.40929	+	8.40929i	−0.274427	+	0.274427i
$940$	23.4406	−	42.2345i	0.764548	−	1.37754i
$941$	14.6036	+	14.6036i	0.476063	+	0.476063i	0.903870	−	0.427807i	$-0.140714\pi$
$941$	14.6036	+	14.6036i	0.476063	+	0.476063i	−0.427807	+	0.903870i	$0.640714\pi$
$942$	−7.99802	+	1.12186i	−0.260590	+	0.0365523i
$943$	58.2400			1.89656
$944$	0.833001	−	3.59056i	0.0271119	−	0.116863i
$945$	−2.39133			−0.0777900
$946$	−0.979929	+	0.137452i	−0.0318602	+	0.00446896i
$947$	−0.157576	−	0.157576i	−0.00512053	−	0.00512053i	0.704542	−	0.709662i	$-0.251153\pi$
$947$	−0.157576	−	0.157576i	−0.00512053	−	0.00512053i	−0.709662	+	0.704542i	$0.751153\pi$
$948$	3.89184	+	2.16001i	0.126401	+	0.0701539i
$949$	−2.74330	+	2.74330i	−0.0890513	+	0.0890513i
$950$	2.95564	+	2.22848i	0.0958938	+	0.0723014i
$951$			15.7774i			0.511617i
$952$	8.01691	−	3.56164i	0.259830	−	0.115433i
$953$		−	39.1591i		−	1.26849i	−0.773133	−	0.634244i	$-0.781312\pi$
$953$		−	39.1591i		−	1.26849i	0.773133	−	0.634244i	$-0.218688\pi$
$954$	8.86313	−	11.7552i	0.286954	−	0.380589i
$955$	7.12409	−	7.12409i	0.230530	−	0.230530i
$956$	−22.7319	+	6.50509i	−0.735203	+	0.210390i
$957$	−25.3823	−	25.3823i	−0.820492	−	0.820492i
$958$	−3.77582	−	26.9187i	−0.121991	−	0.869705i
$959$	−4.46101			−0.144054
$960$	12.8238	−	14.1962i	0.413885	−	0.458182i
$961$	−30.3234			−0.978173
$962$	0.670796	+	4.78226i	0.0216273	+	0.154186i
$963$	8.90089	+	8.90089i	0.286827	+	0.286827i
$964$	−48.8909	+	13.9909i	−1.57467	+	0.450616i
$965$	22.7134	−	22.7134i	0.731169	−	0.731169i
$966$	4.33031	−	5.74331i	0.139325	−	0.184788i
$967$		−	6.60089i		−	0.212270i	−0.994352	−	0.106135i	$-0.966152\pi$
$967$		−	6.60089i		−	0.212270i	0.994352	−	0.106135i	$-0.0338476\pi$
$968$	−50.1236	+	22.2682i	−1.61103	+	0.715727i
$969$		−	11.2991i		−	0.362980i
$970$	−31.4572	−	23.7179i	−1.01003	−	0.761536i
$971$	−19.0184	+	19.0184i	−0.610330	+	0.610330i	−0.943032	−	0.332702i	$-0.892040\pi$
$971$	−19.0184	+	19.0184i	−0.610330	+	0.610330i	0.332702	+	0.943032i	$0.392040\pi$
$972$	1.74872	+	0.970557i	0.0560902	+	0.0311306i
$973$	−0.890644	−	0.890644i	−0.0285527	−	0.0285527i
$974$	14.8023	−	2.07628i	0.474296	−	0.0665283i
$975$	0.564865			0.0180902
$976$	30.5690	+	7.09195i	0.978491	+	0.227008i
$977$	0.118023			0.00377590			0.00188795	−	0.999998i	$-0.499399\pi$
$977$	0.118023			0.00377590			0.00188795	+	0.999998i	$0.499399\pi$
$978$	−29.2311	+	4.10018i	−0.934709	+	0.131109i
$979$	−40.2126	−	40.2126i	−1.28520	−	1.28520i
$980$	−2.32092	+	4.18177i	−0.0741392	+	0.133582i
$981$	−2.84417	+	2.84417i	−0.0908074	+	0.0908074i
$982$	−39.2832	−	29.6186i	−1.25358	−	0.945166i
$983$			29.5383i			0.942125i	0.882100	+	0.471062i	$0.156129\pi$
$983$			29.5383i			0.942125i	−0.882100	+	0.471062i	$0.843871\pi$
$984$	30.2272	+	11.6310i	0.963607	+	0.370783i
$985$			55.0454i			1.75389i
$986$	17.1940	−	22.8046i	0.547570	−	0.726245i
$987$	7.14155	−	7.14155i	0.227318	−	0.227318i
$988$	−1.57601	−	5.50733i	−0.0501395	−	0.175212i
$989$	−0.456463	−	0.456463i	−0.0145147	−	0.0145147i
$990$	2.58975	+	18.4629i	0.0823076	+	0.586790i
$991$	8.08478			0.256821			0.128411	−	0.991721i	$-0.459012\pi$
$991$	8.08478			0.256821			0.128411	+	0.991721i	$0.459012\pi$
$992$	−2.98627	−	3.56860i	−0.0948143	−	0.113303i
$993$	−26.9555			−0.855409
$994$	−2.79330	−	19.9141i	−0.0885981	−	0.631637i
$995$	−8.92614	−	8.92614i	−0.282978	−	0.282978i
$996$	−8.22705	−	28.7493i	−0.260684	−	0.910957i
$997$	6.99094	−	6.99094i	0.221405	−	0.221405i	−0.587685	−	0.809090i	$-0.699960\pi$
$997$	6.99094	−	6.99094i	0.221405	−	0.221405i	0.809090	+	0.587685i	$0.199960\pi$
$998$	−17.0925	+	22.6699i	−0.541054	+	0.717603i
$999$			4.34323i			0.137414i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.w.a.253.6	yes	20
4.3	odd	2		1344.2.w.a.337.1		20
8.3	odd	2		2688.2.w.b.673.10		20
8.5	even	2		2688.2.w.a.673.5		20
16.3	odd	4		2688.2.w.b.2017.10		20
16.5	even	4	inner	336.2.w.a.85.6	✓	20
16.11	odd	4		1344.2.w.a.1009.1		20
16.13	even	4		2688.2.w.a.2017.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.w.a.85.6	✓	20	16.5	even	4	inner
336.2.w.a.253.6	yes	20	1.1	even	1	trivial
1344.2.w.a.337.1		20	4.3	odd	2
1344.2.w.a.1009.1		20	16.11	odd	4
2688.2.w.a.673.5		20	8.5	even	2
2688.2.w.a.2017.5		20	16.13	even	4
2688.2.w.b.673.10		20	8.3	odd	2
2688.2.w.b.2017.10		20	16.3	odd	4

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.196445 + 1.40050i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-1.92282 + 0.550244i) q^{4} +(-1.69093 + 1.69093i) q^{5} +(-0.851398 + 1.12921i) q^{6} -1.00000i q^{7} +(-1.14835 - 2.58482i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(0.196445 + 1.40050i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-1.92282 + 0.550244i) q^{4} +(-1.69093 + 1.69093i) q^{5} +(-0.851398 + 1.12921i) q^{6} -1.00000i q^{7} +(-1.14835 - 2.58482i) q^{8} +1.00000i q^{9} +(-2.70032 - 2.03597i) q^{10} +(-3.89817 + 3.89817i) q^{11} +(-1.74872 - 0.970557i) q^{12} +(0.555931 + 0.555931i) q^{13} +(1.40050 - 0.196445i) q^{14} -2.39133 q^{15} +(3.39446 - 2.11604i) q^{16} -3.10154 q^{17} +(-1.40050 + 0.196445i) q^{18} +(2.57604 + 2.57604i) q^{19} +(2.32092 - 4.18177i) q^{20} +(0.707107 - 0.707107i) q^{21} +(-6.22518 - 4.69363i) q^{22} -5.08612i q^{23} +(1.01574 - 2.63975i) q^{24} -0.718471i q^{25} +(-0.669373 + 0.887793i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(0.550244 + 1.92282i) q^{28} +(4.60420 + 4.60420i) q^{29} +(-0.469766 - 3.34907i) q^{30} -0.822587 q^{31} +(3.63035 + 4.33827i) q^{32} -5.51285 q^{33} +(-0.609281 - 4.34371i) q^{34} +(1.69093 + 1.69093i) q^{35} +(-0.550244 - 1.92282i) q^{36} +(3.07113 - 3.07113i) q^{37} +(-3.10170 + 4.11380i) q^{38} +0.786205i q^{39} +(6.31252 + 2.42897i) q^{40} +11.4508i q^{41} +(1.12921 + 0.851398i) q^{42} +(0.0897468 - 0.0897468i) q^{43} +(5.35054 - 9.64043i) q^{44} +(-1.69093 - 1.69093i) q^{45} +(7.12313 - 0.999144i) q^{46} +10.0997 q^{47} +(3.89651 + 0.903982i) q^{48} -1.00000 q^{49} +(1.00622 - 0.141140i) q^{50} +(-2.19312 - 2.19312i) q^{51} +(-1.37485 - 0.763056i) q^{52} +(-7.36105 + 7.36105i) q^{53} +(-1.12921 - 0.851398i) q^{54} -13.1831i q^{55} +(-2.58482 + 1.14835i) q^{56} +3.64307i q^{57} +(-5.54372 + 7.35267i) q^{58} +(0.651584 - 0.651584i) q^{59} +(4.59810 - 1.31582i) q^{60} +(5.54741 + 5.54741i) q^{61} +(-0.161593 - 1.15204i) q^{62} +1.00000 q^{63} +(-5.36260 + 5.93654i) q^{64} -1.88008 q^{65} +(-1.08297 - 7.72077i) q^{66} +(-7.37998 - 7.37998i) q^{67} +(5.96369 - 1.70660i) q^{68} +(3.59643 - 3.59643i) q^{69} +(-2.03597 + 2.70032i) q^{70} -14.2192i q^{71} +(2.58482 - 1.14835i) q^{72} +4.93461i q^{73} +(4.90444 + 3.69782i) q^{74} +(0.508035 - 0.508035i) q^{75} +(-6.37070 - 3.53580i) q^{76} +(3.89817 + 3.89817i) q^{77} +(-1.10108 + 0.154446i) q^{78} -2.22554 q^{79} +(-2.16172 + 9.31786i) q^{80} -1.00000 q^{81} +(-16.0369 + 2.24945i) q^{82} +(10.5724 + 10.5724i) q^{83} +(-0.970557 + 1.74872i) q^{84} +(5.24447 - 5.24447i) q^{85} +(0.143321 + 0.108060i) q^{86} +6.51132i q^{87} +(14.5525 + 5.59963i) q^{88} +10.3158i q^{89} +(2.03597 - 2.70032i) q^{90} +(0.555931 - 0.555931i) q^{91} +(2.79861 + 9.77969i) q^{92} +(-0.581657 - 0.581657i) q^{93} +(1.98403 + 14.1446i) q^{94} -8.71179 q^{95} +(-0.500579 + 5.63466i) q^{96} +11.6494 q^{97} +(-0.196445 - 1.40050i) q^{98} +(-3.89817 - 3.89817i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{4}+O(q^{10}) \) 20 * q + 4 * q^4	\( 20 q + 4 q^{4} - 4 q^{10} + 12 q^{11} - 8 q^{12} + 4 q^{14} + 8 q^{15} - 4 q^{18} + 8 q^{19} + 28 q^{20} - 12 q^{22} + 8 q^{24} - 20 q^{26} - 4 q^{28} + 12 q^{29} + 8 q^{30} - 24 q^{33} - 44 q^{34} + 4 q^{36} + 12 q^{37} - 4 q^{38} + 16 q^{40} + 4 q^{42} + 4 q^{43} - 4 q^{44} + 20 q^{46} - 16 q^{48} - 20 q^{49} + 48 q^{50} - 8 q^{51} + 16 q^{52} - 36 q^{53} - 4 q^{54} - 16 q^{56} + 16 q^{58} - 12 q^{60} + 8 q^{61} + 12 q^{62} + 20 q^{63} - 32 q^{64} + 16 q^{65} - 24 q^{66} - 12 q^{67} + 4 q^{68} - 16 q^{69} - 20 q^{70} + 16 q^{72} - 16 q^{74} - 16 q^{75} - 32 q^{76} - 12 q^{77} + 12 q^{78} + 24 q^{79} - 8 q^{80} - 20 q^{81} - 76 q^{82} + 40 q^{83} - 16 q^{85} - 84 q^{86} + 16 q^{88} + 20 q^{90} - 4 q^{92} - 32 q^{94} - 72 q^{97} + 12 q^{99}+O(q^{100}) \) 20 * q + 4 * q^4 - 4 * q^10 + 12 * q^11 - 8 * q^12 + 4 * q^14 + 8 * q^15 - 4 * q^18 + 8 * q^19 + 28 * q^20 - 12 * q^22 + 8 * q^24 - 20 * q^26 - 4 * q^28 + 12 * q^29 + 8 * q^30 - 24 * q^33 - 44 * q^34 + 4 * q^36 + 12 * q^37 - 4 * q^38 + 16 * q^40 + 4 * q^42 + 4 * q^43 - 4 * q^44 + 20 * q^46 - 16 * q^48 - 20 * q^49 + 48 * q^50 - 8 * q^51 + 16 * q^52 - 36 * q^53 - 4 * q^54 - 16 * q^56 + 16 * q^58 - 12 * q^60 + 8 * q^61 + 12 * q^62 + 20 * q^63 - 32 * q^64 + 16 * q^65 - 24 * q^66 - 12 * q^67 + 4 * q^68 - 16 * q^69 - 20 * q^70 + 16 * q^72 - 16 * q^74 - 16 * q^75 - 32 * q^76 - 12 * q^77 + 12 * q^78 + 24 * q^79 - 8 * q^80 - 20 * q^81 - 76 * q^82 + 40 * q^83 - 16 * q^85 - 84 * q^86 + 16 * q^88 + 20 * q^90 - 4 * q^92 - 32 * q^94 - 72 * q^97 + 12 * q^99

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