LMFDB - Embedded newform 750.2.g.f.601.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(151,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("750.151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.g (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 24 x^{14} + 94 x^{13} + 262 x^{12} - 936 x^{11} - 1584 x^{10} + 4642 x^{9} + \cdots + 11105 $ x^16 - 4x^15 - 24x^14 + 94x^13 + 262x^12 - 936x^11 - 1584x^10 + 4642x^9 + 6259x^8 - 11958x^7 - 15752x^6 + 14670x^5 + 18271x^4 - 10440x^3 + 1135x^2 + 21080*x + 11105
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 5^{6} $
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			601.2
Root			$-0.705457 - 0.309017i$ of defining polynomial
Character	$\chi$	$=$	750.601
Dual form			750.2.g.f.151.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.809017 + 0.587785i) q^{6} -0.329315 q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.809017 + 0.587785i) q^{6} -0.329315 q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-1.55540 + 4.78704i) q^{11} +(0.309017 + 0.951057i) q^{12} +(-0.148993 - 0.458554i) q^{13} +(-0.101764 + 0.313197i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-5.49007 + 3.98877i) q^{17} +1.00000 q^{18} +(-4.40115 + 3.19762i) q^{19} +(0.266421 + 0.193566i) q^{21} +(4.07210 + 2.95855i) q^{22} +(2.00878 - 6.18239i) q^{23} +1.00000 q^{24} -0.482152 q^{26} +(0.309017 - 0.951057i) q^{27} +(0.266421 + 0.193566i) q^{28} +(4.87203 + 3.53974i) q^{29} +(-1.06685 + 0.775108i) q^{31} +1.00000 q^{32} +(4.07210 - 2.95855i) q^{33} +(2.09702 + 6.45396i) q^{34} +(0.309017 - 0.951057i) q^{36} +(0.241076 + 0.741956i) q^{37} +(1.68109 + 5.17386i) q^{38} +(-0.148993 + 0.458554i) q^{39} +(3.86905 + 11.9077i) q^{41} +(0.266421 - 0.193566i) q^{42} -2.47582 q^{43} +(4.07210 - 2.95855i) q^{44} +(-5.25906 - 3.82093i) q^{46} +(3.54381 + 2.57473i) q^{47} +(0.309017 - 0.951057i) q^{48} -6.89155 q^{49} +6.78610 q^{51} +(-0.148993 + 0.458554i) q^{52} +(1.36393 + 0.990953i) q^{53} +(-0.809017 - 0.587785i) q^{54} +(0.266421 - 0.193566i) q^{56} +5.44012 q^{57} +(4.87203 - 3.53974i) q^{58} +(0.313909 + 0.966113i) q^{59} +(1.29419 - 3.98310i) q^{61} +(0.407499 + 1.25415i) q^{62} +(-0.101764 - 0.313197i) q^{63} +(0.309017 - 0.951057i) q^{64} +(-1.55540 - 4.78704i) q^{66} +(-2.54381 + 1.84819i) q^{67} +6.78610 q^{68} +(-5.25906 + 3.82093i) q^{69} +(-4.62101 - 3.35736i) q^{71} +(-0.809017 - 0.587785i) q^{72} +(0.909340 - 2.79866i) q^{73} +0.780139 q^{74} +5.44012 q^{76} +(0.512218 - 1.57644i) q^{77} +(0.390069 + 0.283402i) q^{78} +(-6.86459 - 4.98742i) q^{79} +(-0.809017 + 0.587785i) q^{81} +12.5205 q^{82} +(-13.9114 + 10.1073i) q^{83} +(-0.101764 - 0.313197i) q^{84} +(-0.765070 + 2.35464i) q^{86} +(-1.86095 - 5.72742i) q^{87} +(-1.55540 - 4.78704i) q^{88} +(1.06683 - 3.28336i) q^{89} +(0.0490657 + 0.151009i) q^{91} +(-5.25906 + 3.82093i) q^{92} +1.31869 q^{93} +(3.54381 - 2.57473i) q^{94} +(-0.809017 - 0.587785i) q^{96} +(7.69378 + 5.58986i) q^{97} +(-2.12961 + 6.55426i) q^{98} -5.03339 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{6} + 8 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^6 + 8 * q^7 - 4 * q^8 - 4 * q^9	$ 16 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{6} + 8 q^{7} - 4 q^{8} - 4 q^{9} + 2 q^{11} - 4 q^{12} + 4 q^{13} - 2 q^{14} - 4 q^{16} - 2 q^{17} + 16 q^{18} - 2 q^{21} - 8 q^{22} - 6 q^{23} + 16 q^{24} + 4 q^{26} - 4 q^{27} - 2 q^{28} + 10 q^{29} - 18 q^{31} + 16 q^{32} - 8 q^{33} - 12 q^{34} - 4 q^{36} - 2 q^{37} - 10 q^{38} + 4 q^{39} + 22 q^{41} - 2 q^{42} + 4 q^{43} - 8 q^{44} - 6 q^{46} - 2 q^{47} - 4 q^{48} + 52 q^{49} + 28 q^{51} + 4 q^{52} - 16 q^{53} - 4 q^{54} - 2 q^{56} + 20 q^{57} + 10 q^{58} - 20 q^{59} + 12 q^{61} + 2 q^{62} - 2 q^{63} - 4 q^{64} + 2 q^{66} + 18 q^{67} + 28 q^{68} - 6 q^{69} - 28 q^{71} - 4 q^{72} + 24 q^{73} - 12 q^{74} + 20 q^{76} - 14 q^{77} - 6 q^{78} + 20 q^{79} - 4 q^{81} + 12 q^{82} - 36 q^{83} - 2 q^{84} - 6 q^{86} - 20 q^{87} + 2 q^{88} - 70 q^{89} + 12 q^{91} - 6 q^{92} + 32 q^{93} - 2 q^{94} - 4 q^{96} + 28 q^{97} - 38 q^{98} + 12 q^{99}+O(q^{100}) $ 16 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^6 + 8 * q^7 - 4 * q^8 - 4 * q^9 + 2 * q^11 - 4 * q^12 + 4 * q^13 - 2 * q^14 - 4 * q^16 - 2 * q^17 + 16 * q^18 - 2 * q^21 - 8 * q^22 - 6 * q^23 + 16 * q^24 + 4 * q^26 - 4 * q^27 - 2 * q^28 + 10 * q^29 - 18 * q^31 + 16 * q^32 - 8 * q^33 - 12 * q^34 - 4 * q^36 - 2 * q^37 - 10 * q^38 + 4 * q^39 + 22 * q^41 - 2 * q^42 + 4 * q^43 - 8 * q^44 - 6 * q^46 - 2 * q^47 - 4 * q^48 + 52 * q^49 + 28 * q^51 + 4 * q^52 - 16 * q^53 - 4 * q^54 - 2 * q^56 + 20 * q^57 + 10 * q^58 - 20 * q^59 + 12 * q^61 + 2 * q^62 - 2 * q^63 - 4 * q^64 + 2 * q^66 + 18 * q^67 + 28 * q^68 - 6 * q^69 - 28 * q^71 - 4 * q^72 + 24 * q^73 - 12 * q^74 + 20 * q^76 - 14 * q^77 - 6 * q^78 + 20 * q^79 - 4 * q^81 + 12 * q^82 - 36 * q^83 - 2 * q^84 - 6 * q^86 - 20 * q^87 + 2 * q^88 - 70 * q^89 + 12 * q^91 - 6 * q^92 + 32 * q^93 - 2 * q^94 - 4 * q^96 + 28 * q^97 - 38 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$		0			0
$5$		0			0
$6$	−0.809017	+	0.587785i	−0.330280	+	0.239962i
$7$	−0.329315			−0.124469			−0.0622347	−	0.998062i	$-0.519823\pi$
$7$	−0.329315			−0.124469			−0.0622347	+	0.998062i	$0.519823\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$		0			0
$11$	−1.55540	+	4.78704i	−0.468972	+	1.44335i	0.384946	+	0.922939i	$0.374220\pi$
$11$	−1.55540	+	4.78704i	−0.468972	+	1.44335i	−0.853918	+	0.520408i	$0.825780\pi$
$12$	0.309017	+	0.951057i	0.0892055	+	0.274546i
$13$	−0.148993	−	0.458554i	−0.0413233	−	0.127180i	0.928267	−	0.371915i	$-0.121299\pi$
$13$	−0.148993	−	0.458554i	−0.0413233	−	0.127180i	−0.969590	+	0.244735i	$0.921299\pi$
$14$	−0.101764	+	0.313197i	−0.0271975	+	0.0837054i
$15$		0			0
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−5.49007	+	3.98877i	−1.33154	+	0.967418i	−0.331827	+	0.943340i	$0.607665\pi$
$17$	−5.49007	+	3.98877i	−1.33154	+	0.967418i	−0.999710	+	0.0240779i	$0.992335\pi$
$18$	1.00000			0.235702
$19$	−4.40115	+	3.19762i	−1.00969	+	0.733585i	−0.964145	−	0.265377i	$-0.914504\pi$
$19$	−4.40115	+	3.19762i	−1.00969	+	0.733585i	−0.0455487	+	0.998962i	$0.514504\pi$
$20$		0			0
$21$	0.266421	+	0.193566i	0.0581379	+	0.0422397i
$22$	4.07210	+	2.95855i	0.868175	+	0.630766i
$23$	2.00878	−	6.18239i	0.418860	−	1.28912i	−0.489893	−	0.871783i	$-0.662964\pi$
$23$	2.00878	−	6.18239i	0.418860	−	1.28912i	0.908753	−	0.417335i	$-0.137036\pi$
$24$	1.00000			0.204124
$25$		0			0
$26$	−0.482152			−0.0945578
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	0.266421	+	0.193566i	0.0503489	+	0.0365806i
$29$	4.87203	+	3.53974i	0.904714	+	0.657313i	0.939672	−	0.342076i	$-0.111130\pi$
$29$	4.87203	+	3.53974i	0.904714	+	0.657313i	−0.0349585	+	0.999389i	$0.511130\pi$
$30$		0			0
$31$	−1.06685	+	0.775108i	−0.191611	+	0.139214i	−0.679455	−	0.733717i	$-0.737784\pi$
$31$	−1.06685	+	0.775108i	−0.191611	+	0.139214i	0.487844	+	0.872931i	$0.337784\pi$
$32$	1.00000			0.176777
$33$	4.07210	−	2.95855i	0.708862	−	0.515018i
$34$	2.09702	+	6.45396i	0.359636	+	1.10685i
$35$		0			0
$36$	0.309017	−	0.951057i	0.0515028	−	0.158509i
$37$	0.241076	+	0.741956i	0.0396327	+	0.121977i	0.968915	−	0.247393i	$-0.0795737\pi$
$37$	0.241076	+	0.741956i	0.0396327	+	0.121977i	−0.929283	+	0.369369i	$0.879574\pi$
$38$	1.68109	+	5.17386i	0.272709	+	0.839312i
$39$	−0.148993	+	0.458554i	−0.0238580	+	0.0734274i
$40$		0			0
$41$	3.86905	+	11.9077i	0.604245	+	1.85967i	0.501901	+	0.864925i	$0.332634\pi$
$41$	3.86905	+	11.9077i	0.604245	+	1.85967i	0.102344	+	0.994749i	$0.467366\pi$
$42$	0.266421	−	0.193566i	0.0411097	−	0.0298680i
$43$	−2.47582			−0.377559			−0.188779	−	0.982020i	$-0.560453\pi$
$43$	−2.47582			−0.377559			−0.188779	+	0.982020i	$0.560453\pi$
$44$	4.07210	−	2.95855i	0.613892	−	0.446019i
$45$		0			0
$46$	−5.25906	−	3.82093i	−0.775405	−	0.563365i
$47$	3.54381	+	2.57473i	0.516918	+	0.375563i	0.815442	−	0.578839i	$-0.196494\pi$
$47$	3.54381	+	2.57473i	0.516918	+	0.375563i	−0.298523	+	0.954402i	$0.596494\pi$
$48$	0.309017	−	0.951057i	0.0446028	−	0.137273i
$49$	−6.89155			−0.984507
$50$		0			0
$51$	6.78610			0.950244
$52$	−0.148993	+	0.458554i	−0.0206616	+	0.0635900i
$53$	1.36393	+	0.990953i	0.187350	+	0.136118i	0.677507	−	0.735516i	$-0.263060\pi$
$53$	1.36393	+	0.990953i	0.187350	+	0.136118i	−0.490157	+	0.871634i	$0.663060\pi$
$54$	−0.809017	−	0.587785i	−0.110093	−	0.0799874i
$55$		0			0
$56$	0.266421	−	0.193566i	0.0356021	−	0.0258664i
$57$	5.44012			0.720562
$58$	4.87203	−	3.53974i	0.639729	−	0.464791i
$59$	0.313909	+	0.966113i	0.0408675	+	0.125777i	0.969409	−	0.245452i	$-0.0789364\pi$
$59$	0.313909	+	0.966113i	0.0408675	+	0.125777i	−0.928541	+	0.371229i	$0.878936\pi$
$60$		0			0
$61$	1.29419	−	3.98310i	0.165704	−	0.509984i	−0.833384	−	0.552695i	$-0.813599\pi$
$61$	1.29419	−	3.98310i	0.165704	−	0.509984i	0.999087	+	0.0427111i	$0.0135995\pi$
$62$	0.407499	+	1.25415i	0.0517524	+	0.159277i
$63$	−0.101764	−	0.313197i	−0.0128210	−	0.0394591i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$		0			0
$66$	−1.55540	−	4.78704i	−0.191457	−	0.589244i
$67$	−2.54381	+	1.84819i	−0.310776	+	0.225792i	−0.732230	−	0.681058i	$-0.761520\pi$
$67$	−2.54381	+	1.84819i	−0.310776	+	0.225792i	0.421453	+	0.906850i	$0.361520\pi$
$68$	6.78610			0.822935
$69$	−5.25906	+	3.82093i	−0.633116	+	0.459986i
$70$		0			0
$71$	−4.62101	−	3.35736i	−0.548413	−	0.398446i	0.278787	−	0.960353i	$-0.410068\pi$
$71$	−4.62101	−	3.35736i	−0.548413	−	0.398446i	−0.827200	+	0.561907i	$0.810068\pi$
$72$	−0.809017	−	0.587785i	−0.0953436	−	0.0692712i
$73$	0.909340	−	2.79866i	0.106430	−	0.327558i	−0.883633	−	0.468180i	$-0.844910\pi$
$73$	0.909340	−	2.79866i	0.106430	−	0.327558i	0.990063	+	0.140621i	$0.0449100\pi$
$74$	0.780139			0.0906893
$75$		0			0
$76$	5.44012			0.624025
$77$	0.512218	−	1.57644i	0.0583726	−	0.179652i
$78$	0.390069	+	0.283402i	0.0441667	+	0.0320890i
$79$	−6.86459	−	4.98742i	−0.772327	−	0.561128i	0.130339	−	0.991469i	$-0.458393\pi$
$79$	−6.86459	−	4.98742i	−0.772327	−	0.561128i	−0.902666	+	0.430341i	$0.858393\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	12.5205			1.38266
$83$	−13.9114	+	10.1073i	−1.52698	+	1.10942i	−0.569092	+	0.822274i	$0.692705\pi$
$83$	−13.9114	+	10.1073i	−1.52698	+	1.10942i	−0.957888	+	0.287142i	$0.907295\pi$
$84$	−0.101764	−	0.313197i	−0.0111034	−	0.0341726i
$85$		0			0
$86$	−0.765070	+	2.35464i	−0.0824996	+	0.253908i
$87$	−1.86095	−	5.72742i	−0.199515	−	0.614044i
$88$	−1.55540	−	4.78704i	−0.165807	−	0.510300i
$89$	1.06683	−	3.28336i	0.113084	−	0.348036i	−0.878459	−	0.477818i	$-0.841428\pi$
$89$	1.06683	−	3.28336i	0.113084	−	0.348036i	0.991543	+	0.129782i	$0.0414279\pi$
$90$		0			0
$91$	0.0490657	+	0.151009i	0.00514348	+	0.0158300i
$92$	−5.25906	+	3.82093i	−0.548294	+	0.398359i
$93$	1.31869			0.136742
$94$	3.54381	−	2.57473i	0.365517	−	0.265563i
$95$		0			0
$96$	−0.809017	−	0.587785i	−0.0825700	−	0.0599906i
$97$	7.69378	+	5.58986i	0.781185	+	0.567564i	0.905334	−	0.424699i	$-0.139620\pi$
$97$	7.69378	+	5.58986i	0.781185	+	0.567564i	−0.124149	+	0.992264i	$0.539620\pi$
$98$	−2.12961	+	6.55426i	−0.215123	+	0.662080i
$99$	−5.03339			−0.505875
$100$		0			0
$101$	19.2435			1.91480			0.957400	−	0.288765i	$-0.0932447\pi$
$101$	19.2435			1.91480			0.957400	+	0.288765i	$0.0932447\pi$
$102$	2.09702	−	6.45396i	0.207636	−	0.639037i
$103$	−4.13156	−	3.00175i	−0.407095	−	0.295771i	0.365330	−	0.930878i	$-0.380956\pi$
$103$	−4.13156	−	3.00175i	−0.407095	−	0.295771i	−0.772424	+	0.635107i	$0.780956\pi$
$104$	0.390069	+	0.283402i	0.0382494	+	0.0277898i
$105$		0			0
$106$	1.36393	−	0.990953i	0.132477	−	0.0962499i
$107$	−15.3340			−1.48239			−0.741194	−	0.671290i	$-0.765740\pi$
$107$	−15.3340			−1.48239			−0.741194	+	0.671290i	$0.765740\pi$
$108$	−0.809017	+	0.587785i	−0.0778477	+	0.0565597i
$109$	−3.01609	−	9.28257i	−0.288889	−	0.889109i	−0.985206	−	0.171375i	$-0.945179\pi$
$109$	−3.01609	−	9.28257i	−0.288889	−	0.889109i	0.696317	−	0.717735i	$-0.254821\pi$
$110$		0			0
$111$	0.241076	−	0.741956i	0.0228819	−	0.0704233i
$112$	−0.101764	−	0.313197i	−0.00961579	−	0.0295943i
$113$	0.468364	+	1.44148i	0.0440599	+	0.135603i	0.970667	−	0.240429i	$-0.0772883\pi$
$113$	0.468364	+	1.44148i	0.0440599	+	0.135603i	−0.926607	+	0.376032i	$0.877288\pi$
$114$	1.68109	−	5.17386i	0.157449	−	0.484577i
$115$		0			0
$116$	−1.86095	−	5.72742i	−0.172785	−	0.531778i
$117$	0.390069	−	0.283402i	0.0360619	−	0.0262005i
$118$	1.01583			0.0935149
$119$	1.80796	−	1.31356i	0.165736	−	0.120414i
$120$		0			0
$121$	−11.5973	−	8.42593i	−1.05430	−	0.765993i
$122$	−3.38823	−	2.46169i	−0.306756	−	0.222871i
$123$	3.86905	−	11.9077i	0.348861	−	1.07368i
$124$	1.31869			0.118422
$125$		0			0
$126$	−0.329315			−0.0293377
$127$	3.89534	−	11.9886i	0.345656	−	1.06382i	−0.615576	−	0.788077i	$-0.711077\pi$
$127$	3.89534	−	11.9886i	0.345656	−	1.06382i	0.961232	−	0.275741i	$-0.0889233\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	2.00298	+	1.45525i	0.176352	+	0.128128i
$130$		0			0
$131$	−11.3715	+	8.26187i	−0.993532	+	0.721843i	−0.960692	−	0.277618i	$-0.910455\pi$
$131$	−11.3715	+	8.26187i	−0.993532	+	0.721843i	−0.0328399	+	0.999461i	$0.510455\pi$
$132$	−5.03339			−0.438101
$133$	1.44936	−	1.05303i	0.125676	−	0.0913089i
$134$	0.971651	+	2.99043i	0.0839378	+	0.258334i
$135$		0			0
$136$	2.09702	−	6.45396i	0.179818	−	0.553423i
$137$	−2.06690	−	6.36127i	−0.176587	−	0.543480i	0.823115	−	0.567874i	$-0.192234\pi$
$137$	−2.06690	−	6.36127i	−0.176587	−	0.543480i	−0.999702	+	0.0243949i	$0.992234\pi$
$138$	2.00878	+	6.18239i	0.170999	+	0.526280i
$139$	−0.951151	+	2.92734i	−0.0806755	+	0.248294i	−0.983257	−	0.182226i	$-0.941670\pi$
$139$	−0.951151	+	2.92734i	−0.0806755	+	0.248294i	0.902581	+	0.430520i	$0.141670\pi$
$140$		0			0
$141$	−1.35362	−	4.16600i	−0.113995	−	0.350841i
$142$	−4.62101	+	3.35736i	−0.387787	+	0.281744i
$143$	2.42686			0.202944
$144$	−0.809017	+	0.587785i	−0.0674181	+	0.0489821i
$145$		0			0
$146$	−2.38068	−	1.72967i	−0.197027	−	0.143148i
$147$	5.57538	+	4.05075i	0.459850	+	0.334100i
$148$	0.241076	−	0.741956i	0.0198163	−	0.0609884i
$149$	5.06465			0.414912			0.207456	−	0.978244i	$-0.433482\pi$
$149$	5.06465			0.414912			0.207456	+	0.978244i	$0.433482\pi$
$150$		0			0
$151$	−16.9581			−1.38003			−0.690015	−	0.723795i	$-0.742396\pi$
$151$	−16.9581			−1.38003			−0.690015	+	0.723795i	$0.742396\pi$
$152$	1.68109	−	5.17386i	0.136354	−	0.419656i
$153$	−5.49007	−	3.98877i	−0.443846	−	0.322473i
$154$	−1.34100	−	0.974296i	−0.108061	−	0.0785110i
$155$		0			0
$156$	0.390069	−	0.283402i	0.0312305	−	0.0226903i
$157$	−22.8284			−1.82190			−0.910952	−	0.412513i	$-0.864651\pi$
$157$	−22.8284			−1.82190			−0.910952	+	0.412513i	$0.864651\pi$
$158$	−6.86459	+	4.98742i	−0.546118	+	0.396778i
$159$	−0.520975	−	1.60340i	−0.0413160	−	0.127158i
$160$		0			0
$161$	−0.661521	+	2.03595i	−0.0521352	+	0.160456i
$162$	0.309017	+	0.951057i	0.0242787	+	0.0747221i
$163$	2.45923	+	7.56873i	0.192622	+	0.592829i	0.999996	+	0.00278919i	$0.000887829\pi$
$163$	2.45923	+	7.56873i	0.192622	+	0.592829i	−0.807374	+	0.590039i	$0.799112\pi$
$164$	3.86905	−	11.9077i	0.302122	−	0.929837i
$165$		0			0
$166$	5.31370	+	16.3539i	0.412423	+	1.26931i
$167$	−11.2860	+	8.19979i	−0.873340	+	0.634519i	−0.931481	−	0.363790i	$-0.881483\pi$
$167$	−11.2860	+	8.19979i	−0.873340	+	0.634519i	0.0581411	+	0.998308i	$0.481483\pi$
$168$	−0.329315			−0.0254072
$169$	10.3291	−	7.50457i	0.794550	−	0.577274i
$170$		0			0
$171$	−4.40115	−	3.19762i	−0.336564	−	0.244528i
$172$	2.00298	+	1.45525i	0.152726	+	0.110962i
$173$	−6.02610	+	18.5464i	−0.458156	+	1.41006i	0.409234	+	0.912430i	$0.365796\pi$
$173$	−6.02610	+	18.5464i	−0.458156	+	1.41006i	−0.867390	+	0.497629i	$0.834204\pi$
$174$	−6.02216			−0.456539
$175$		0			0
$176$	−5.03339			−0.379406
$177$	0.313909	−	0.966113i	0.0235949	−	0.0726175i
$178$	−2.79299	−	2.02923i	−0.209344	−	0.152097i
$179$	15.3641	+	11.1627i	1.14837	+	0.834338i	0.988263	−	0.152761i	$-0.0488166\pi$
$179$	15.3641	+	11.1627i	1.14837	+	0.834338i	0.160105	+	0.987100i	$0.448817\pi$
$180$		0			0
$181$	15.3296	−	11.1376i	1.13944	−	0.827850i	0.152397	−	0.988319i	$-0.451301\pi$
$181$	15.3296	−	11.1376i	1.13944	−	0.827850i	0.987041	+	0.160470i	$0.0513008\pi$
$182$	0.158780			0.0117695
$183$	−3.38823	+	2.46169i	−0.250465	+	0.181973i
$184$	2.00878	+	6.18239i	0.148089	+	0.455772i
$185$		0			0
$186$	0.407499	−	1.25415i	0.0298793	−	0.0919589i
$187$	−10.5551	−	32.4853i	−0.771867	−	2.37556i
$188$	−1.35362	−	4.16600i	−0.0987226	−	0.303837i
$189$	−0.101764	+	0.313197i	−0.00740223	+	0.0227817i
$190$		0			0
$191$	−3.73703	−	11.5014i	−0.270402	−	0.832212i	−0.990399	−	0.138235i	$-0.955857\pi$
$191$	−3.73703	−	11.5014i	−0.270402	−	0.832212i	0.719997	−	0.693977i	$-0.244143\pi$
$192$	−0.809017	+	0.587785i	−0.0583858	+	0.0424197i
$193$	−11.0357			−0.794368			−0.397184	−	0.917739i	$-0.630013\pi$
$193$	−11.0357			−0.794368			−0.397184	+	0.917739i	$0.630013\pi$
$194$	7.69378	−	5.58986i	0.552381	−	0.401329i
$195$		0			0
$196$	5.57538	+	4.05075i	0.398242	+	0.289339i
$197$	16.6829	+	12.1208i	1.18861	+	0.863573i	0.993116	−	0.117133i	$-0.0373704\pi$
$197$	16.6829	+	12.1208i	1.18861	+	0.863573i	0.195490	+	0.980706i	$0.437370\pi$
$198$	−1.55540	+	4.78704i	−0.110538	+	0.340200i
$199$	18.5313			1.31365			0.656826	−	0.754042i	$-0.271899\pi$
$199$	18.5313			1.31365			0.656826	+	0.754042i	$0.271899\pi$
$200$		0			0
$201$	3.14433			0.221784
$202$	5.94657	−	18.3017i	0.418399	−	1.28770i
$203$	−1.60443	−	1.16569i	−0.112609	−	0.0818153i
$204$	−5.49007	−	3.98877i	−0.384382	−	0.279270i
$205$		0			0
$206$	−4.13156	+	3.00175i	−0.287859	+	0.209142i
$207$	6.50055			0.451819
$208$	0.390069	−	0.283402i	0.0270464	−	0.0196504i
$209$	−8.46159	−	26.0421i	−0.585300	−	1.80137i
$210$		0			0
$211$	4.87129	−	14.9923i	0.335353	−	1.03211i	−0.631194	−	0.775625i	$-0.717435\pi$
$211$	4.87129	−	14.9923i	0.335353	−	1.03211i	0.966548	−	0.256487i	$-0.0825650\pi$
$212$	−0.520975	−	1.60340i	−0.0357807	−	0.110122i
$213$	1.76507	+	5.43233i	0.120941	+	0.372217i
$214$	−4.73845	+	14.5835i	−0.323914	+	0.996904i
$215$		0			0
$216$	0.309017	+	0.951057i	0.0210259	+	0.0647112i
$217$	0.351328	−	0.255255i	0.0238497	−	0.0173278i
$218$	−9.76027			−0.661049
$219$	−2.38068	+	1.72967i	−0.160872	+	0.116880i
$220$		0			0
$221$	2.64705	+	1.92319i	0.178060	+	0.129368i
$222$	−0.631145	−	0.458554i	−0.0423597	−	0.0307761i
$223$	−6.85345	+	21.0928i	−0.458941	+	1.41248i	0.407504	+	0.913203i	$0.366399\pi$
$223$	−6.85345	+	21.0928i	−0.458941	+	1.41248i	−0.866445	+	0.499272i	$0.833601\pi$
$224$	−0.329315			−0.0220033
$225$		0			0
$226$	1.51566			0.100820
$227$	3.42913	−	10.5538i	0.227600	−	0.700480i	−0.770418	−	0.637539i	$-0.779952\pi$
$227$	3.42913	−	10.5538i	0.227600	−	0.700480i	0.998017	−	0.0629401i	$-0.0200477\pi$
$228$	−4.40115	−	3.19762i	−0.291473	−	0.211768i
$229$	−1.45525	−	1.05730i	−0.0961658	−	0.0698685i	0.538663	−	0.842521i	$-0.318929\pi$
$229$	−1.45525	−	1.05730i	−0.0961658	−	0.0698685i	−0.634829	+	0.772653i	$0.718929\pi$
$230$		0			0
$231$	−1.34100	+	0.974296i	−0.0882315	+	0.0641040i
$232$	−6.02216			−0.395374
$233$	−2.99805	+	2.17821i	−0.196409	+	0.142699i	−0.681643	−	0.731685i	$-0.738734\pi$
$233$	−2.99805	+	2.17821i	−0.196409	+	0.142699i	0.485234	+	0.874384i	$0.338734\pi$
$234$	−0.148993	−	0.458554i	−0.00973999	−	0.0299766i
$235$		0			0
$236$	0.313909	−	0.966113i	0.0204338	−	0.0628886i
$237$	2.62204	+	8.06981i	0.170320	+	0.524191i
$238$	−0.690580	−	2.12539i	−0.0447636	−	0.137768i
$239$	−5.21415	+	16.0475i	−0.337275	+	1.03803i	0.628315	+	0.777959i	$0.283745\pi$
$239$	−5.21415	+	16.0475i	−0.337275	+	1.03803i	−0.965590	+	0.260068i	$0.916255\pi$
$240$		0			0
$241$	6.37366	+	19.6161i	0.410564	+	1.26359i	0.916159	+	0.400815i	$0.131273\pi$
$241$	6.37366	+	19.6161i	0.410564	+	1.26359i	−0.505595	+	0.862771i	$0.668727\pi$
$242$	−11.5973	+	8.42593i	−0.745502	+	0.541639i
$243$	1.00000			0.0641500
$244$	−3.38823	+	2.46169i	−0.216909	+	0.157594i
$245$		0			0
$246$	−10.1293	−	7.35938i	−0.645822	−	0.469217i
$247$	2.12202	+	1.54174i	0.135021	+	0.0980986i
$248$	0.407499	−	1.25415i	0.0258762	−	0.0796387i
$249$	17.1955			1.08972
$250$		0			0
$251$	8.69615			0.548896			0.274448	−	0.961602i	$-0.411505\pi$
$251$	8.69615			0.548896			0.274448	+	0.961602i	$0.411505\pi$
$252$	−0.101764	+	0.313197i	−0.00641052	+	0.0197296i
$253$	26.4709	+	19.2322i	1.66421	+	1.20912i
$254$	−10.1981	−	7.40938i	−0.639888	−	0.464906i
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	7.10714			0.443331			0.221666	−	0.975123i	$-0.428851\pi$
$257$	7.10714			0.443331			0.221666	+	0.975123i	$0.428851\pi$
$258$	2.00298	−	1.45525i	0.124700	−	0.0905999i
$259$	−0.0793900	−	0.244337i	−0.00493305	−	0.0151824i
$260$		0			0
$261$	−1.86095	+	5.72742i	−0.115190	+	0.354518i
$262$	4.34352	+	13.3680i	0.268344	+	0.825877i
$263$	−4.90130	−	15.0847i	−0.302227	−	0.930160i	−0.980697	−	0.195532i	$-0.937357\pi$
$263$	−4.90130	−	15.0847i	−0.302227	−	0.930160i	0.678470	−	0.734628i	$-0.262643\pi$
$264$	−1.55540	+	4.78704i	−0.0957285	+	0.294622i
$265$		0			0
$266$	−0.553608	−	1.70383i	−0.0339439	−	0.104469i
$267$	−2.79299	+	2.02923i	−0.170928	+	0.124187i
$268$	3.14433			0.192070
$269$	−3.65623	+	2.65641i	−0.222925	+	0.161964i	−0.693642	−	0.720320i	$-0.743995\pi$
$269$	−3.65623	+	2.65641i	−0.222925	+	0.161964i	0.470718	+	0.882284i	$0.343995\pi$
$270$		0			0
$271$	−9.00551	−	6.54289i	−0.547046	−	0.397452i	0.279649	−	0.960102i	$-0.409782\pi$
$271$	−9.00551	−	6.54289i	−0.547046	−	0.397452i	−0.826695	+	0.562650i	$0.809782\pi$
$272$	−5.49007	−	3.98877i	−0.332884	−	0.241855i
$273$	0.0490657	−	0.151009i	0.00296959	−	0.00913946i
$274$	−6.68863			−0.404075
$275$		0			0
$276$	6.50055			0.391287
$277$	−7.05603	+	21.7162i	−0.423956	+	1.30480i	0.480035	+	0.877249i	$0.340624\pi$
$277$	−7.05603	+	21.7162i	−0.423956	+	1.30480i	−0.903991	+	0.427552i	$0.859376\pi$
$278$	2.49014	+	1.80920i	0.149349	+	0.108508i
$279$	−1.06685	−	0.775108i	−0.0638704	−	0.0464045i
$280$		0			0
$281$	−23.2631	+	16.9016i	−1.38776	+	1.00827i	−0.391653	+	0.920113i	$0.628097\pi$
$281$	−23.2631	+	16.9016i	−1.38776	+	1.00827i	−0.996107	+	0.0881540i	$0.971903\pi$
$282$	−4.38040			−0.260849
$283$	15.6522	−	11.3720i	0.930424	−	0.675992i	−0.0156727	−	0.999877i	$-0.504989\pi$
$283$	15.6522	−	11.3720i	0.930424	−	0.675992i	0.946097	+	0.323885i	$0.104989\pi$
$284$	1.76507	+	5.43233i	0.104738	+	0.322349i
$285$		0			0
$286$	0.749941	−	2.30808i	0.0443450	−	0.136480i
$287$	−1.27414	−	3.92139i	−0.0752100	−	0.231472i
$288$	0.309017	+	0.951057i	0.0182090	+	0.0560415i
$289$	8.97729	−	27.6292i	0.528076	−	1.62525i
$290$		0			0
$291$	−2.93876	−	9.04458i	−0.172273	−	0.530203i
$292$	−2.38068	+	1.72967i	−0.139319	+	0.101221i
$293$	15.0301			0.878069			0.439035	−	0.898470i	$-0.355321\pi$
$293$	15.0301			0.878069			0.439035	+	0.898470i	$0.355321\pi$
$294$	5.57538	−	4.05075i	0.325163	−	0.236245i
$295$		0			0
$296$	−0.631145	−	0.458554i	−0.0366846	−	0.0266529i
$297$	4.07210	+	2.95855i	0.236287	+	0.171673i
$298$	1.56506	−	4.81677i	0.0906617	−	0.279028i
$299$	−3.13425			−0.181259
$300$		0			0
$301$	0.815324			0.0469945
$302$	−5.24034	+	16.1281i	−0.301548	+	0.928069i
$303$	−15.5683	−	11.3110i	−0.894377	−	0.649803i
$304$	−4.40115	−	3.19762i	−0.252423	−	0.183396i
$305$		0			0
$306$	−5.49007	+	3.98877i	−0.313846	+	0.228023i
$307$	19.7061			1.12468			0.562342	−	0.826905i	$-0.309900\pi$
$307$	19.7061			1.12468			0.562342	+	0.826905i	$0.309900\pi$
$308$	−1.34100	+	0.974296i	−0.0764108	+	0.0555157i
$309$	1.57811	+	4.85694i	0.0897758	+	0.276302i
$310$		0			0
$311$	8.72642	−	26.8572i	0.494830	−	1.52293i	−0.322392	−	0.946606i	$-0.604487\pi$
$311$	8.72642	−	26.8572i	0.494830	−	1.52293i	0.817222	−	0.576323i	$-0.195513\pi$
$312$	−0.148993	−	0.458554i	−0.00843508	−	0.0259605i
$313$	−3.47577	−	10.6973i	−0.196462	−	0.604648i	−0.999956	−	0.00933550i	$-0.997028\pi$
$313$	−3.47577	−	10.6973i	−0.196462	−	0.604648i	0.803494	−	0.595312i	$-0.202972\pi$
$314$	−7.05436	+	21.7111i	−0.398101	+	1.22523i
$315$		0			0
$316$	2.62204	+	8.06981i	0.147501	+	0.453962i
$317$	18.8433	−	13.6905i	1.05835	−	0.768935i	0.0845658	−	0.996418i	$-0.473050\pi$
$317$	18.8433	−	13.6905i	1.05835	−	0.768935i	0.973782	+	0.227483i	$0.0730497\pi$
$318$	−1.68591			−0.0945412
$319$	−24.5229	+	17.8169i	−1.37302	+	0.997555i
$320$		0			0
$321$	12.4054	+	9.01307i	0.692403	+	0.503060i
$322$	1.73189	+	1.25829i	0.0965142	+	0.0701217i
$323$	11.4080	−	35.1103i	0.634760	−	1.95359i
$324$	1.00000			0.0555556
$325$		0			0
$326$	7.95823			0.440766
$327$	−3.01609	+	9.28257i	−0.166790	+	0.513327i
$328$	−10.1293	−	7.35938i	−0.559298	−	0.406354i
$329$	−1.16703	−	0.847898i	−0.0643405	−	0.0467461i
$330$		0			0
$331$	−0.104633	+	0.0760205i	−0.00575116	+	0.00417847i	−0.590657	−	0.806923i	$-0.701131\pi$
$331$	−0.104633	+	0.0760205i	−0.00575116	+	0.00417847i	0.584906	+	0.811101i	$0.301131\pi$
$332$	17.1955			0.943725
$333$	−0.631145	+	0.458554i	−0.0345866	+	0.0251286i
$334$	4.31088	+	13.2675i	0.235881	+	0.725967i
$335$		0			0
$336$	−0.101764	+	0.313197i	−0.00555168	+	0.0170863i
$337$	0.166272	+	0.511734i	0.00905743	+	0.0278759i	0.955483	−	0.295046i	$-0.0953349\pi$
$337$	0.166272	+	0.511734i	0.00905743	+	0.0278759i	−0.946426	+	0.322922i	$0.895335\pi$
$338$	−3.94538	−	12.1426i	−0.214601	−	0.660473i
$339$	0.468364	−	1.44148i	0.0254380	−	0.0782902i
$340$		0			0
$341$	−2.05110	−	6.31264i	−0.111073	−	0.341849i
$342$	−4.40115	+	3.19762i	−0.237987	+	0.172908i
$343$	4.57470			0.247010
$344$	2.00298	−	1.45525i	0.107993	−	0.0784618i
$345$		0			0
$346$	15.7765	+	11.4623i	0.848152	+	0.616218i
$347$	18.3773	+	13.3519i	0.986546	+	0.716767i	0.959162	−	0.282858i	$-0.0912824\pi$
$347$	18.3773	+	13.3519i	0.986546	+	0.716767i	0.0273838	+	0.999625i	$0.491282\pi$
$348$	−1.86095	+	5.72742i	−0.0997575	+	0.307022i
$349$	6.84350			0.366324			0.183162	−	0.983083i	$-0.441367\pi$
$349$	6.84350			0.366324			0.183162	+	0.983083i	$0.441367\pi$
$350$		0			0
$351$	−0.482152			−0.0257354
$352$	−1.55540	+	4.78704i	−0.0829033	+	0.255150i
$353$	13.5744	+	9.86237i	0.722492	+	0.524921i	0.887179	−	0.461425i	$-0.152662\pi$
$353$	13.5744	+	9.86237i	0.722492	+	0.524921i	−0.164688	+	0.986346i	$0.552662\pi$
$354$	−0.821825	−	0.597091i	−0.0436795	−	0.0317350i
$355$		0			0
$356$	−2.79299	+	2.02923i	−0.148028	+	0.107549i
$357$	−2.23476			−0.118276
$358$	15.3641	−	11.1627i	0.812019	−	0.589966i
$359$	−2.30639	−	7.09834i	−0.121727	−	0.374636i	0.871564	−	0.490282i	$-0.163106\pi$
$359$	−2.30639	−	7.09834i	−0.121727	−	0.374636i	−0.993291	+	0.115646i	$0.963106\pi$
$360$		0			0
$361$	3.27401	−	10.0764i	0.172317	−	0.530336i
$362$	−5.85537	−	18.0210i	−0.307752	−	0.947162i
$363$	4.42977	+	13.6334i	0.232503	+	0.715570i
$364$	0.0490657	−	0.151009i	0.00257174	−	0.00791500i
$365$		0			0
$366$	1.29419	+	3.98310i	0.0676483	+	0.208200i
$367$	−4.97929	+	3.61766i	−0.259917	+	0.188841i	−0.710110	−	0.704090i	$-0.751355\pi$
$367$	−4.97929	+	3.61766i	−0.259917	+	0.188841i	0.450194	+	0.892931i	$0.351355\pi$
$368$	6.50055			0.338865
$369$	−10.1293	+	7.35938i	−0.527311	+	0.383114i
$370$		0			0
$371$	−0.449163	−	0.326336i	−0.0233194	−	0.0169425i
$372$	−1.06685	−	0.775108i	−0.0553134	−	0.0401875i
$373$	−2.83346	+	8.72051i	−0.146711	+	0.451531i	−0.997227	−	0.0744187i	$-0.976290\pi$
$373$	−2.83346	+	8.72051i	−0.146711	+	0.451531i	0.850516	+	0.525949i	$0.176290\pi$
$374$	−34.1571			−1.76622
$375$		0			0
$376$	−4.38040			−0.225902
$377$	0.897262	−	2.76149i	0.0462113	−	0.142224i
$378$	0.266421	+	0.193566i	0.0137032	+	0.00995598i
$379$	28.0179	+	20.3562i	1.43918	+	1.04563i	0.988212	+	0.153090i	$0.0489226\pi$
$379$	28.0179	+	20.3562i	1.43918	+	1.04563i	0.450972	+	0.892538i	$0.351077\pi$
$380$		0			0
$381$	−10.1981	+	7.40938i	−0.522466	+	0.379594i
$382$	−12.0933			−0.618746
$383$	7.70220	−	5.59597i	0.393564	−	0.285941i	−0.373350	−	0.927690i	$-0.621791\pi$
$383$	7.70220	−	5.59597i	0.393564	−	0.285941i	0.766914	+	0.641749i	$0.221791\pi$
$384$	0.309017	+	0.951057i	0.0157695	+	0.0485334i
$385$		0			0
$386$	−3.41022	+	10.4956i	−0.173576	+	0.534211i
$387$	−0.765070	−	2.35464i	−0.0388907	−	0.119693i
$388$	−2.93876	−	9.04458i	−0.149193	−	0.459169i
$389$	−5.39091	+	16.5915i	−0.273330	+	0.841224i	0.716326	+	0.697766i	$0.245822\pi$
$389$	−5.39091	+	16.5915i	−0.273330	+	0.841224i	−0.989656	+	0.143458i	$0.954178\pi$
$390$		0			0
$391$	13.6318	+	41.9543i	0.689389	+	2.12172i
$392$	5.57538	−	4.05075i	0.281599	−	0.204594i
$393$	14.0559			0.709028
$394$	16.6829	−	12.1208i	0.840471	−	0.610638i
$395$		0			0
$396$	4.07210	+	2.95855i	0.204631	+	0.148673i
$397$	10.9663	+	7.96751i	0.550385	+	0.399878i	0.827927	−	0.560835i	$-0.189520\pi$
$397$	10.9663	+	7.96751i	0.550385	+	0.399878i	−0.277542	+	0.960713i	$0.589520\pi$
$398$	5.72650	−	17.6244i	0.287044	−	0.883429i
$399$	−1.79151			−0.0896879
$400$		0			0
$401$	14.1105			0.704642			0.352321	−	0.935879i	$-0.385392\pi$
$401$	14.1105			0.704642			0.352321	+	0.935879i	$0.385392\pi$
$402$	0.971651	−	2.99043i	0.0484615	−	0.149149i
$403$	0.514382	+	0.373720i	0.0256232	+	0.0186163i
$404$	−15.5683	−	11.3110i	−0.774553	−	0.562746i
$405$		0			0
$406$	−1.60443	+	1.16569i	−0.0796267	+	0.0578522i
$407$	−3.92674			−0.194641
$408$	−5.49007	+	3.98877i	−0.271799	+	0.197473i
$409$	−5.11848	−	15.7531i	−0.253092	−	0.778938i	−0.994200	−	0.107552i	$-0.965699\pi$
$409$	−5.11848	−	15.7531i	−0.253092	−	0.778938i	0.741107	−	0.671387i	$-0.234301\pi$
$410$		0			0
$411$	−2.06690	+	6.36127i	−0.101953	+	0.313778i
$412$	1.57811	+	4.85694i	0.0777481	+	0.239284i
$413$	−0.103375	−	0.318156i	−0.00508675	−	0.0156554i
$414$	2.00878	−	6.18239i	0.0987262	−	0.303848i
$415$		0			0
$416$	−0.148993	−	0.458554i	−0.00730499	−	0.0224825i
$417$	2.49014	−	1.80920i	0.121943	−	0.0885967i
$418$	−27.3823			−1.33931
$419$	−13.7294	+	9.97500i	−0.670725	+	0.487310i	−0.870268	−	0.492579i	$-0.836054\pi$
$419$	−13.7294	+	9.97500i	−0.670725	+	0.487310i	0.199543	+	0.979889i	$0.436054\pi$
$420$		0			0
$421$	5.71360	+	4.15118i	0.278464	+	0.202316i	0.718247	−	0.695788i	$-0.244945\pi$
$421$	5.71360	+	4.15118i	0.278464	+	0.202316i	−0.439783	+	0.898104i	$0.644945\pi$
$422$	−12.7532	−	9.26574i	−0.620816	−	0.451049i
$423$	−1.35362	+	4.16600i	−0.0658151	+	0.202558i
$424$	−1.68591			−0.0818751
$425$		0			0
$426$	5.71189			0.276742
$427$	−0.426195	+	1.31169i	−0.0206250	+	0.0634773i
$428$	12.4054	+	9.01307i	0.599639	+	0.435663i
$429$	−1.96337	−	1.42647i	−0.0947925	−	0.0688708i
$430$		0			0
$431$	14.4476	−	10.4968i	0.695915	−	0.505612i	−0.182684	−	0.983172i	$-0.558479\pi$
$431$	14.4476	−	10.4968i	0.695915	−	0.505612i	0.878599	+	0.477560i	$0.158479\pi$
$432$	1.00000			0.0481125
$433$	19.5618	−	14.2125i	0.940078	−	0.683007i	−0.00836116	−	0.999965i	$-0.502661\pi$
$433$	19.5618	−	14.2125i	0.940078	−	0.683007i	0.948440	+	0.316958i	$0.102661\pi$
$434$	−0.134195	−	0.413011i	−0.00644158	−	0.0198252i
$435$		0			0
$436$	−3.01609	+	9.28257i	−0.144445	+	0.444555i
$437$	10.9280	+	33.6330i	0.522758	+	1.60888i
$438$	0.909340	+	2.79866i	0.0434499	+	0.133725i
$439$	−5.84359	+	17.9847i	−0.278899	+	0.858364i	0.709262	+	0.704945i	$0.249028\pi$
$439$	−5.84359	+	17.9847i	−0.278899	+	0.858364i	−0.988161	+	0.153419i	$0.950972\pi$
$440$		0			0
$441$	−2.12961	−	6.55426i	−0.101410	−	0.312107i
$442$	2.64705	−	1.92319i	0.125907	−	0.0914770i
$443$	4.05769			0.192787			0.0963933	−	0.995343i	$-0.469269\pi$
$443$	4.05769			0.192787			0.0963933	+	0.995343i	$0.469269\pi$
$444$	−0.631145	+	0.458554i	−0.0299528	+	0.0217620i
$445$		0			0
$446$	17.9426	+	13.0360i	0.849605	+	0.617274i
$447$	−4.09739	−	2.97693i	−0.193800	−	0.140804i
$448$	−0.101764	+	0.313197i	−0.00480789	+	0.0147972i
$449$	−6.26150			−0.295498			−0.147749	−	0.989025i	$-0.547203\pi$
$449$	−6.26150			−0.295498			−0.147749	+	0.989025i	$0.547203\pi$
$450$		0			0
$451$	−63.0207			−2.96753
$452$	0.468364	−	1.44148i	0.0220300	−	0.0678013i
$453$	13.7194	+	9.96772i	0.644593	+	0.468325i
$454$	−8.97759	−	6.52260i	−0.421339	−	0.306121i
$455$		0			0
$456$	−4.40115	+	3.19762i	−0.206103	+	0.149742i
$457$	1.94229			0.0908564			0.0454282	−	0.998968i	$-0.485535\pi$
$457$	1.94229			0.0908564			0.0454282	+	0.998968i	$0.485535\pi$
$458$	−1.45525	+	1.05730i	−0.0679995	+	0.0494045i
$459$	2.09702	+	6.45396i	0.0978805	+	0.301245i
$460$		0			0
$461$	0.965342	−	2.97102i	0.0449605	−	0.138374i	−0.926056	−	0.377385i	$-0.876823\pi$
$461$	0.965342	−	2.97102i	0.0449605	−	0.138374i	0.971017	+	0.239011i	$0.0768233\pi$
$462$	0.512218	+	1.57644i	0.0238305	+	0.0733428i
$463$	−2.55446	−	7.86182i	−0.118716	−	0.365370i	0.873988	−	0.485947i	$-0.161525\pi$
$463$	−2.55446	−	7.86182i	−0.118716	−	0.365370i	−0.992704	+	0.120578i	$0.961525\pi$
$464$	−1.86095	+	5.72742i	−0.0863925	+	0.265889i
$465$		0			0
$466$	1.14515	+	3.52442i	0.0530482	+	0.163265i
$467$	24.7715	−	17.9975i	1.14629	−	0.832827i	0.158305	−	0.987390i	$-0.449397\pi$
$467$	24.7715	−	17.9975i	1.14629	−	0.832827i	0.987983	+	0.154563i	$0.0493971\pi$
$468$	−0.482152			−0.0222875
$469$	0.837716	−	0.608636i	0.0386821	−	0.0281042i
$470$		0			0
$471$	18.4686	+	13.4182i	0.850986	+	0.618278i
$472$	−0.821825	−	0.597091i	−0.0378276	−	0.0274833i
$473$	3.85090	−	11.8518i	0.177064	−	0.544948i
$474$	8.48510			0.389734
$475$		0			0
$476$	−2.23476			−0.102430
$477$	−0.520975	+	1.60340i	−0.0238538	+	0.0734145i
$478$	13.6508	+	9.91790i	0.624374	+	0.453634i
$479$	0.948887	+	0.689407i	0.0433558	+	0.0314998i	0.609252	−	0.792977i	$-0.291470\pi$
$479$	0.948887	+	0.689407i	0.0433558	+	0.0314998i	−0.565896	+	0.824476i	$0.691470\pi$
$480$		0			0
$481$	0.304308	−	0.221093i	0.0138753	−	0.0100810i
$482$	20.6256			0.939471
$483$	1.73189	−	1.25829i	0.0788035	−	0.0572541i
$484$	4.42977	+	13.6334i	0.201353	+	0.619702i
$485$		0			0
$486$	0.309017	−	0.951057i	0.0140173	−	0.0431408i
$487$	3.63267	+	11.1802i	0.164612	+	0.506623i	0.999007	−	0.0445428i	$-0.0141831\pi$
$487$	3.63267	+	11.1802i	0.164612	+	0.506623i	−0.834396	+	0.551166i	$0.814183\pi$
$488$	1.29419	+	3.98310i	0.0585851	+	0.180307i
$489$	2.45923	−	7.56873i	0.111210	−	0.342270i
$490$		0			0
$491$	1.27640	+	3.92836i	0.0576031	+	0.177284i	0.975718	−	0.219030i	$-0.0702892\pi$
$491$	1.27640	+	3.92836i	0.0576031	+	0.177284i	−0.918115	+	0.396314i	$0.870289\pi$
$492$	−10.1293	+	7.35938i	−0.456665	+	0.331786i
$493$	−40.8670			−1.84056
$494$	2.12202	−	1.54174i	0.0954744	−	0.0693662i
$495$		0			0
$496$	−1.06685	−	0.775108i	−0.0479028	−	0.0348034i
$497$	1.52177	+	1.10563i	0.0682606	+	0.0495943i
$498$	5.31370	−	16.3539i	0.238113	−	0.732835i
$499$	9.59154			0.429376			0.214688	−	0.976683i	$-0.431127\pi$
$499$	9.59154			0.429376			0.214688	+	0.976683i	$0.431127\pi$
$500$		0			0
$501$	13.9503			0.623254
$502$	2.68726	−	8.27053i	0.119938	−	0.369132i
$503$	−13.7091	−	9.96021i	−0.611257	−	0.444104i	0.238600	−	0.971118i	$-0.423312\pi$
$503$	−13.7091	−	9.96021i	−0.611257	−	0.444104i	−0.849857	+	0.527014i	$0.823312\pi$
$504$	0.266421	+	0.193566i	0.0118674	+	0.00862213i
$505$		0			0
$506$	26.4709	−	19.2322i	1.17677	−	0.854977i
$507$	−12.7675			−0.567026
$508$	−10.1981	+	7.40938i	−0.452469	+	0.328738i
$509$	10.5993	+	32.6213i	0.469805	+	1.44591i	0.852837	+	0.522177i	$0.174880\pi$
$509$	10.5993	+	32.6213i	0.469805	+	1.44591i	−0.383032	+	0.923735i	$0.625120\pi$
$510$		0			0
$511$	−0.299459	+	0.921641i	−0.0132473	+	0.0407710i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	1.68109	+	5.17386i	0.0742220	+	0.228432i
$514$	2.19623	−	6.75929i	0.0968714	−	0.298140i
$515$		0			0
$516$	−0.765070	−	2.35464i	−0.0336803	−	0.103657i
$517$	−17.8374	+	12.9596i	−0.784488	+	0.569964i
$518$	−0.256911			−0.0112880
$519$	15.7765	−	11.4623i	0.692513	−	0.503140i
$520$		0			0
$521$	−17.2185	−	12.5100i	−0.754356	−	0.548072i	0.142818	−	0.989749i	$-0.454384\pi$
$521$	−17.2185	−	12.5100i	−0.754356	−	0.548072i	−0.897174	+	0.441677i	$0.854384\pi$
$522$	4.87203	+	3.53974i	0.213243	+	0.154930i
$523$	−12.7776	+	39.3254i	−0.558726	+	1.71958i	0.127170	+	0.991881i	$0.459411\pi$
$523$	−12.7776	+	39.3254i	−0.558726	+	1.71958i	−0.685896	+	0.727700i	$0.740589\pi$
$524$	14.0559			0.614036
$525$		0			0
$526$	−15.8609			−0.691570
$527$	2.76533	−	8.51080i	0.120459	−	0.370736i
$528$	4.07210	+	2.95855i	0.177215	+	0.128755i
$529$	−15.5794	−	11.3191i	−0.677364	−	0.492133i
$530$		0			0
$531$	−0.821825	+	0.597091i	−0.0356642	+	0.0259115i
$532$	−1.79151			−0.0776720
$533$	4.88387	−	3.54834i	0.211544	−	0.153696i
$534$	1.06683	+	3.28336i	0.0461662	+	0.142085i
$535$		0			0
$536$	0.971651	−	2.99043i	0.0419689	−	0.129167i
$537$	−5.86857	−	18.0616i	−0.253248	−	0.779416i
$538$	1.39656	+	4.29816i	0.0602099	+	0.185307i
$539$	10.7191	−	32.9901i	0.461706	−	1.42099i
$540$		0			0
$541$	−11.0695	−	34.0685i	−0.475916	−	1.46472i	−0.844719	−	0.535210i	$-0.820232\pi$
$541$	−11.0695	−	34.0685i	−0.475916	−	1.46472i	0.368803	−	0.929507i	$-0.379768\pi$
$542$	−9.00551	+	6.54289i	−0.386820	+	0.281041i
$543$	−18.9484			−0.813153
$544$	−5.49007	+	3.98877i	−0.235385	+	0.171017i
$545$		0			0
$546$	−0.128456	−	0.0933285i	−0.00549739	−	0.00399409i
$547$	−6.76543	−	4.91537i	−0.289269	−	0.210166i	0.433681	−	0.901066i	$-0.357214\pi$
$547$	−6.76543	−	4.91537i	−0.289269	−	0.210166i	−0.722950	+	0.690900i	$0.757214\pi$
$548$	−2.06690	+	6.36127i	−0.0882936	+	0.271740i
$549$	4.18808			0.178743
$550$		0			0
$551$	−32.7613			−1.39568
$552$	2.00878	−	6.18239i	0.0854994	−	0.263140i
$553$	2.26061	+	1.64243i	0.0961310	+	0.0698433i
$554$	18.4729	+	13.4214i	0.784840	+	0.570219i
$555$		0			0
$556$	2.49014	−	1.80920i	0.105606	−	0.0767270i
$557$	−28.1467			−1.19262			−0.596308	−	0.802756i	$-0.703366\pi$
$557$	−28.1467			−1.19262			−0.596308	+	0.802756i	$0.703366\pi$
$558$	−1.06685	+	0.775108i	−0.0451632	+	0.0328130i
$559$	0.368880	+	1.13530i	0.0156020	+	0.0480179i
$560$		0			0
$561$	−10.5551	+	32.4853i	−0.445638	+	1.37153i
$562$	8.88571	+	27.3474i	0.374821	+	1.15358i
$563$	−1.06633	−	3.28183i	−0.0449406	−	0.138313i	0.926069	−	0.377355i	$-0.123166\pi$
$563$	−1.06633	−	3.28183i	−0.0449406	−	0.138313i	−0.971009	+	0.239043i	$0.923166\pi$
$564$	−1.35362	+	4.16600i	−0.0569975	+	0.175420i
$565$		0			0
$566$	−5.97859	−	18.4002i	−0.251299	−	0.773418i
$567$	0.266421	−	0.193566i	0.0111886	−	0.00812903i
$568$	5.71189			0.239665
$569$	−14.0801	+	10.2298i	−0.590270	+	0.428856i	−0.842412	−	0.538834i	$-0.818865\pi$
$569$	−14.0801	+	10.2298i	−0.590270	+	0.428856i	0.252142	+	0.967690i	$0.418865\pi$
$570$		0			0
$571$	30.1126	+	21.8781i	1.26017	+	0.915570i	0.998766	−	0.0496580i	$-0.0158131\pi$
$571$	30.1126	+	21.8781i	1.26017	+	0.915570i	0.261408	+	0.965228i	$0.415813\pi$
$572$	−1.96337	−	1.42647i	−0.0820927	−	0.0596438i
$573$	−3.73703	+	11.5014i	−0.156117	+	0.480478i
$574$	−4.12320			−0.172099
$575$		0			0
$576$	1.00000			0.0416667
$577$	−6.21250	+	19.1201i	−0.258630	+	0.795980i	0.734463	+	0.678649i	$0.237434\pi$
$577$	−6.21250	+	19.1201i	−0.258630	+	0.795980i	−0.993093	+	0.117332i	$0.962566\pi$
$578$	−23.5028	−	17.0758i	−0.977589	−	0.710260i
$579$	8.92808	+	6.48663i	0.371038	+	0.269575i
$580$		0			0
$581$	4.58125	−	3.32847i	0.190062	−	0.138088i
$582$	−9.51004			−0.394204
$583$	−6.86520	+	4.98786i	−0.284327	+	0.206576i
$584$	0.909340	+	2.79866i	0.0376287	+	0.115809i
$585$		0			0
$586$	4.64456	−	14.2945i	0.191865	−	0.590500i
$587$	−1.89068	−	5.81892i	−0.0780368	−	0.240173i	0.904426	−	0.426630i	$-0.140299\pi$
$587$	−1.89068	−	5.81892i	−0.0780368	−	0.240173i	−0.982463	+	0.186457i	$0.940299\pi$
$588$	−2.12961	−	6.55426i	−0.0878235	−	0.270293i
$589$	2.21684	−	6.82274i	0.0913434	−	0.281126i
$590$		0			0
$591$	−6.37229	−	19.6119i	−0.262121	−	0.806726i
$592$	−0.631145	+	0.458554i	−0.0259399	+	0.0188465i
$593$	24.9458			1.02440			0.512201	−	0.858866i	$-0.328830\pi$
$593$	24.9458			1.02440			0.512201	+	0.858866i	$0.328830\pi$
$594$	4.07210	−	2.95855i	0.167080	−	0.121391i
$595$		0			0
$596$	−4.09739	−	2.97693i	−0.167836	−	0.121940i
$597$	−14.9922	−	10.8925i	−0.613589	−	0.445798i
$598$	−0.968538	+	2.98085i	−0.0396065	+	0.121896i
$599$	−0.941228			−0.0384575			−0.0192288	−	0.999815i	$-0.506121\pi$
$599$	−0.941228			−0.0384575			−0.0192288	+	0.999815i	$0.506121\pi$
$600$		0			0
$601$	10.2333			0.417426			0.208713	−	0.977977i	$-0.433073\pi$
$601$	10.2333			0.417426			0.208713	+	0.977977i	$0.433073\pi$
$602$	0.251949	−	0.775419i	0.0102687	−	0.0316037i
$603$	−2.54381	−	1.84819i	−0.103592	−	0.0752641i
$604$	13.7194	+	9.96772i	0.558234	+	0.405581i
$605$		0			0
$606$	−15.5683	+	11.3110i	−0.632420	+	0.459480i
$607$	6.80623			0.276256			0.138128	−	0.990414i	$-0.455891\pi$
$607$	6.80623			0.276256			0.138128	+	0.990414i	$0.455891\pi$
$608$	−4.40115	+	3.19762i	−0.178490	+	0.129681i
$609$	0.612839	+	1.88612i	0.0248335	+	0.0764296i
$610$		0			0
$611$	0.652649	−	2.00865i	0.0264034	−	0.0812612i
$612$	2.09702	+	6.45396i	0.0847670	+	0.260886i
$613$	−0.352106	−	1.08367i	−0.0142214	−	0.0437690i	0.943694	−	0.330820i	$-0.107325\pi$
$613$	−0.352106	−	1.08367i	−0.0142214	−	0.0437690i	−0.957915	+	0.287051i	$0.907325\pi$
$614$	6.08951	−	18.7416i	0.245753	−	0.756349i
$615$		0			0
$616$	0.512218	+	1.57644i	0.0206378	+	0.0635167i
$617$	11.6156	−	8.43925i	0.467628	−	0.339752i	−0.328888	−	0.944369i	$-0.606674\pi$
$617$	11.6156	−	8.43925i	0.467628	−	0.339752i	0.796516	+	0.604617i	$0.206674\pi$
$618$	5.10689			0.205429
$619$	−0.385511	+	0.280090i	−0.0154950	+	0.0112578i	−0.595506	−	0.803351i	$-0.703048\pi$
$619$	−0.385511	+	0.280090i	−0.0154950	+	0.0112578i	0.580011	+	0.814609i	$0.303048\pi$
$620$		0			0
$621$	−5.25906	−	3.82093i	−0.211039	−	0.153329i
$622$	−22.8461	−	16.5986i	−0.916044	−	0.665545i
$623$	−0.351323	+	1.08126i	−0.0140754	+	0.0433198i
$624$	−0.482152			−0.0193015
$625$		0			0
$626$	−11.2478			−0.449553
$627$	−8.46159	+	26.0421i	−0.337923	+	1.04002i
$628$	18.4686	+	13.4182i	0.736976	+	0.535444i
$629$	−4.28301	−	3.11179i	−0.170775	−	0.124075i
$630$		0			0
$631$	13.7958	−	10.0232i	0.549201	−	0.399018i	−0.278290	−	0.960497i	$-0.589768\pi$
$631$	13.7958	−	10.0232i	0.549201	−	0.399018i	0.827491	+	0.561479i	$0.189768\pi$
$632$	8.48510			0.337519
$633$	−12.7532	+	9.26574i	−0.506894	+	0.368280i
$634$	−7.19752	−	22.1517i	−0.285850	−	0.879756i
$635$		0			0
$636$	−0.520975	+	1.60340i	−0.0206580	+	0.0635788i
$637$	1.02679	+	3.16015i	0.0406831	+	0.125210i
$638$	9.36690	+	28.8283i	0.370839	+	1.14133i
$639$	1.76507	−	5.43233i	0.0698251	−	0.214900i
$640$		0			0
$641$	−10.1127	−	31.1237i	−0.399428	−	1.22931i	−0.925459	−	0.378848i	$-0.876320\pi$
$641$	−10.1127	−	31.1237i	−0.399428	−	1.22931i	0.526031	−	0.850465i	$-0.323680\pi$
$642$	12.4054	−	9.01307i	0.489603	−	0.355717i
$643$	−12.5844			−0.496281			−0.248141	−	0.968724i	$-0.579820\pi$
$643$	−12.5844			−0.496281			−0.248141	+	0.968724i	$0.579820\pi$
$644$	1.73189	−	1.25829i	0.0682458	−	0.0495835i
$645$		0			0
$646$	−29.8666	−	21.6994i	−1.17509	−	0.853751i
$647$	−20.7430	−	15.0706i	−0.815490	−	0.592488i	0.0999273	−	0.994995i	$-0.468139\pi$
$647$	−20.7430	−	15.0706i	−0.815490	−	0.592488i	−0.915417	+	0.402507i	$0.868139\pi$
$648$	0.309017	−	0.951057i	0.0121393	−	0.0373610i
$649$	−5.11308			−0.200706
$650$		0			0
$651$	−0.434265			−0.0170202
$652$	2.45923	−	7.56873i	0.0963109	−	0.296414i
$653$	−24.3165	−	17.6669i	−0.951577	−	0.691361i	−0.000397632	−	1.00000i	$-0.500127\pi$
$653$	−24.3165	−	17.6669i	−0.951577	−	0.691361i	−0.951179	+	0.308639i	$0.900127\pi$
$654$	7.89623	+	5.73695i	0.308767	+	0.224332i
$655$		0			0
$656$	−10.1293	+	7.35938i	−0.395483	+	0.287335i
$657$	2.94269			0.114805
$658$	−1.16703	+	0.847898i	−0.0454956	+	0.0330545i
$659$	−2.48706	−	7.65438i	−0.0968821	−	0.298172i	0.890858	−	0.454283i	$-0.150104\pi$
$659$	−2.48706	−	7.65438i	−0.0968821	−	0.298172i	−0.987740	+	0.156110i	$0.950104\pi$
$660$		0			0
$661$	−0.225140	+	0.692909i	−0.00875692	+	0.0269510i	−0.955340	−	0.295510i	$-0.904510\pi$
$661$	−0.225140	+	0.692909i	−0.00875692	+	0.0269510i	0.946583	+	0.322461i	$0.104510\pi$
$662$	0.0399663	+	0.123004i	0.00155334	+	0.00478068i
$663$	−1.01108	−	3.11179i	−0.0392672	−	0.120852i
$664$	5.31370	−	16.3539i	0.206212	−	0.634654i
$665$		0			0
$666$	0.241076	+	0.741956i	0.00934151	+	0.0287502i
$667$	31.6709	−	23.0103i	1.22630	−	0.890961i
$668$	13.9503			0.539754
$669$	17.9426	−	13.0360i	0.693700	−	0.504002i
$670$		0			0
$671$	17.0543	+	12.3907i	0.658373	+	0.478336i
$672$	0.266421	+	0.193566i	0.0102774	+	0.00746699i
$673$	2.28926	−	7.04563i	0.0882446	−	0.271589i	−0.897190	−	0.441645i	$-0.854395\pi$
$673$	2.28926	−	7.04563i	0.0882446	−	0.271589i	0.985434	+	0.170056i	$0.0543950\pi$
$674$	0.538069			0.0207256
$675$		0			0
$676$	−12.7675			−0.491059
$677$	3.02683	−	9.31563i	0.116331	−	0.358029i	−0.875892	−	0.482508i	$-0.839726\pi$
$677$	3.02683	−	9.31563i	0.116331	−	0.358029i	0.992222	+	0.124479i	$0.0397260\pi$
$678$	−1.22619	−	0.890881i	−0.0470916	−	0.0342141i
$679$	−2.53368	−	1.84082i	−0.0972336	−	0.0706444i
$680$		0			0
$681$	−8.97759	+	6.52260i	−0.344022	+	0.249947i
$682$	−6.63750			−0.254163
$683$	−27.1706	+	19.7406i	−1.03966	+	0.755354i	−0.970218	−	0.242233i	$-0.922120\pi$
$683$	−27.1706	+	19.7406i	−1.03966	+	0.755354i	−0.0694369	+	0.997586i	$0.522120\pi$
$684$	1.68109	+	5.17386i	0.0642781	+	0.197828i
$685$		0			0
$686$	1.41366	−	4.35079i	0.0539737	−	0.166114i
$687$	0.555857	+	1.71075i	0.0212073	+	0.0652692i
$688$	−0.765070	−	2.35464i	−0.0291680	−	0.0897699i
$689$	0.251189	−	0.773081i	0.00956955	−	0.0294520i
$690$		0			0
$691$	8.06874	+	24.8330i	0.306950	+	0.944693i	0.978943	+	0.204136i	$0.0654385\pi$
$691$	8.06874	+	24.8330i	0.306950	+	0.944693i	−0.671993	+	0.740557i	$0.734562\pi$
$692$	15.7765	−	11.4623i	0.599734	−	0.435732i
$693$	1.65757			0.0629659
$694$	18.3773	−	13.3519i	0.697593	−	0.506831i
$695$		0			0
$696$	4.87203	+	3.53974i	0.184674	+	0.134173i
$697$	−68.7385	−	49.9415i	−2.60366	−	1.89167i
$698$	2.11476	−	6.50855i	0.0800447	−	0.246352i
$699$	3.70579			0.140166
$700$		0			0
$701$	41.8212			1.57956			0.789782	−	0.613388i	$-0.210194\pi$
$701$	41.8212			1.57956			0.789782	+	0.613388i	$0.210194\pi$
$702$	−0.148993	+	0.458554i	−0.00562339	+	0.0173070i
$703$	−3.43351	−	2.49459i	−0.129497	−	0.0940852i
$704$	4.07210	+	2.95855i	0.153473	+	0.111505i
$705$		0			0
$706$	13.5744	−	9.86237i	0.510879	−	0.371175i
$707$	−6.33717			−0.238334
$708$	−0.821825	+	0.597091i	−0.0308861	+	0.0224401i
$709$	−2.74068	−	8.43495i	−0.102928	−	0.316781i	0.886310	−	0.463092i	$-0.153260\pi$
$709$	−2.74068	−	8.43495i	−0.102928	−	0.316781i	−0.989239	+	0.146311i	$0.953260\pi$
$710$		0			0
$711$	2.62204	−	8.06981i	0.0983342	−	0.302642i
$712$	1.06683	+	3.28336i	0.0399811	+	0.123049i
$713$	2.64897	+	8.15268i	0.0992045	+	0.305320i
$714$	−0.690580	+	2.12539i	−0.0258443	+	0.0795406i
$715$		0			0
$716$	−5.86857	−	18.0616i	−0.219319	−	0.674994i
$717$	13.6508	−	9.91790i	0.509799	−	0.370391i
$718$	−7.46364			−0.278541
$719$	2.14802	−	1.56062i	0.0801074	−	0.0582015i	−0.547011	−	0.837126i	$-0.684234\pi$
$719$	2.14802	−	1.56062i	0.0801074	−	0.0582015i	0.627118	+	0.778924i	$0.284234\pi$
$720$		0			0
$721$	1.36058	+	0.988522i	0.0506708	+	0.0368145i
$722$	−8.57148	−	6.22755i	−0.318998	−	0.231765i
$723$	6.37366	−	19.6161i	0.237039	−	0.729531i
$724$	−18.9484			−0.704211
$725$		0			0
$726$	14.3350			0.532023
$727$	−2.17449	+	6.69240i	−0.0806475	+	0.248207i	−0.983248	−	0.182271i	$-0.941655\pi$
$727$	−2.17449	+	6.69240i	−0.0806475	+	0.248207i	0.902601	+	0.430479i	$0.141655\pi$
$728$	−0.128456	−	0.0933285i	−0.00476088	−	0.00345898i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$		0			0
$731$	13.5924	−	9.87546i	0.502733	−	0.365257i
$732$	4.18808			0.154796
$733$	−16.3908	+	11.9086i	−0.605407	+	0.439854i	−0.847794	−	0.530326i	$-0.822070\pi$
$733$	−16.3908	+	11.9086i	−0.605407	+	0.439854i	0.242387	+	0.970180i	$0.422070\pi$
$734$	1.90192	+	5.85350i	0.0702011	+	0.216057i
$735$		0			0
$736$	2.00878	−	6.18239i	0.0740446	−	0.227886i
$737$	−4.89070	−	15.0520i	−0.180151	−	0.554448i
$738$	3.86905	+	11.9077i	0.142422	+	0.438329i
$739$	5.30003	−	16.3118i	0.194965	−	0.600039i	−0.805012	−	0.593258i	$-0.797841\pi$
$739$	5.30003	−	16.3118i	0.194965	−	0.600039i	0.999977	−	0.00678134i	$-0.00215858\pi$
$740$		0			0
$741$	−0.810541	−	2.49459i	−0.0297760	−	0.0916410i
$742$	−0.449163	+	0.326336i	−0.0164893	+	0.0119802i
$743$	−9.94252			−0.364756			−0.182378	−	0.983229i	$-0.558379\pi$
$743$	−9.94252			−0.364756			−0.182378	+	0.983229i	$0.558379\pi$
$744$	−1.06685	+	0.775108i	−0.0391124	+	0.0284169i
$745$		0			0
$746$	7.41811	+	5.38957i	0.271596	+	0.197326i
$747$	−13.9114	−	10.1073i	−0.508993	−	0.369805i
$748$	−10.5551	+	32.4853i	−0.385933	+	1.18778i
$749$	5.04970			0.184512
$750$		0			0
$751$	−17.6941			−0.645667			−0.322833	−	0.946456i	$-0.604635\pi$
$751$	−17.6941			−0.645667			−0.322833	+	0.946456i	$0.604635\pi$
$752$	−1.35362	+	4.16600i	−0.0493613	+	0.151919i
$753$	−7.03533	−	5.11147i	−0.256382	−	0.186272i
$754$	−2.34906	−	1.70669i	−0.0855478	−	0.0621541i
$755$		0			0
$756$	0.266421	−	0.193566i	0.00968965	−	0.00703994i
$757$	37.1272			1.34941			0.674706	−	0.738087i	$-0.264271\pi$
$757$	37.1272			1.34941			0.674706	+	0.738087i	$0.264271\pi$
$758$	28.0179	−	20.3562i	1.01766	−	0.739371i
$759$	−10.1110	−	31.1184i	−0.367005	−	1.12953i
$760$		0			0
$761$	−15.3161	+	47.1381i	−0.555208	+	1.70876i	0.140184	+	0.990125i	$0.455230\pi$
$761$	−15.3161	+	47.1381i	−0.555208	+	1.70876i	−0.695393	+	0.718630i	$0.744770\pi$
$762$	3.89534	+	11.9886i	0.141113	+	0.434302i
$763$	0.993244	+	3.05689i	0.0359578	+	0.110667i
$764$	−3.73703	+	11.5014i	−0.135201	+	0.416106i
$765$		0			0
$766$	−2.94198	−	9.05448i	−0.106298	−	0.327152i
$767$	0.396245	−	0.287889i	0.0143076	−	0.0103951i
$768$	1.00000			0.0360844
$769$	−27.8015	+	20.1990i	−1.00255	+	0.728393i	−0.962633	−	0.270810i	$-0.912709\pi$
$769$	−27.8015	+	20.1990i	−1.00255	+	0.728393i	−0.0399144	+	0.999203i	$0.512709\pi$
$770$		0			0
$771$	−5.74980	−	4.17747i	−0.207074	−	0.150448i
$772$	8.92808	+	6.48663i	0.321329	+	0.233459i
$773$	−7.10509	+	21.8672i	−0.255552	+	0.786510i	0.738168	+	0.674617i	$0.235691\pi$
$773$	−7.10509	+	21.8672i	−0.255552	+	0.786510i	−0.993720	+	0.111893i	$0.964309\pi$
$774$	−2.47582			−0.0889915
$775$		0			0
$776$	−9.51004			−0.341390
$777$	−0.0793900	+	0.244337i	−0.00284810	+	0.00876555i
$778$	14.1136	+	10.2541i	0.505997	+	0.367628i
$779$	−55.1047	−	40.0359i	−1.97433	−	1.43444i
$780$		0			0
$781$	23.2594	−	16.8989i	0.832286	−	0.604691i
$782$	44.1134			1.57749
$783$	4.87203	−	3.53974i	0.174112	−	0.126500i
$784$	−2.12961	−	6.55426i	−0.0760574	−	0.234081i
$785$		0			0
$786$	4.34352	−	13.3680i	0.154928	−	0.476820i
$787$	−2.59940	−	8.00012i	−0.0926585	−	0.285174i	0.893978	−	0.448111i	$-0.147903\pi$
$787$	−2.59940	−	8.00012i	−0.0926585	−	0.285174i	−0.986636	+	0.162938i	$0.947903\pi$
$788$	−6.37229	−	19.6119i	−0.227004	−	0.698645i
$789$	−4.90130	+	15.0847i	−0.174491	+	0.537028i
$790$		0			0
$791$	−0.154239	−	0.474699i	−0.00548411	−	0.0168784i
$792$	4.07210	−	2.95855i	0.144696	−	0.105128i
$793$	−2.01929			−0.0717072
$794$	10.9663	−	7.96751i	0.389181	−	0.282757i
$795$		0			0
$796$	−14.9922	−	10.8925i	−0.531383	−	0.386073i
$797$	−30.9647	−	22.4972i	−1.09683	−	0.796890i	−0.116287	−	0.993216i	$-0.537099\pi$
$797$	−30.9647	−	22.4972i	−1.09683	−	0.796890i	−0.980539	+	0.196325i	$0.937099\pi$
$798$	−0.553608	+	1.70383i	−0.0195975	+	0.0603149i
$799$	−29.7258			−1.05162
$800$		0			0
$801$	3.45233			0.121982
$802$	4.36037	−	13.4198i	0.153970	−	0.473871i
$803$	11.9829	+	8.70609i	0.422868	+	0.307231i
$804$	−2.54381	−	1.84819i	−0.0897134	−	0.0651806i
$805$		0			0
$806$	0.514382	−	0.373720i	0.0181183	−	0.0131637i
$807$	4.51935			0.159089
$808$	−15.5683	+	11.3110i	−0.547692	+	0.397921i
$809$	−9.51817	−	29.2939i	−0.334641	−	1.02992i	−0.966899	−	0.255161i	$-0.917872\pi$
$809$	−9.51817	−	29.2939i	−0.334641	−	1.02992i	0.632258	−	0.774758i	$-0.282128\pi$
$810$		0			0
$811$	−0.243268	+	0.748703i	−0.00854230	+	0.0262905i	−0.955237	−	0.295842i	$-0.904400\pi$
$811$	−0.243268	+	0.748703i	−0.00854230	+	0.0262905i	0.946695	+	0.322133i	$0.104400\pi$
$812$	0.612839	+	1.88612i	0.0215064	+	0.0661900i
$813$	3.43980	+	10.5866i	0.120639	+	0.371289i
$814$	−1.21343	+	3.73456i	−0.0425307	+	0.130896i
$815$		0			0
$816$	2.09702	+	6.45396i	0.0734104	+	0.225934i
$817$	10.8965	−	7.91674i	0.381219	−	0.276972i
$818$	−16.5637			−0.579138
$819$	−0.128456	+	0.0933285i	−0.00448860	+	0.00326116i
$820$		0			0
$821$	−14.1344	−	10.2692i	−0.493293	−	0.358398i	0.313157	−	0.949702i	$-0.398614\pi$
$821$	−14.1344	−	10.2692i	−0.493293	−	0.358398i	−0.806449	+	0.591303i	$0.798614\pi$
$822$	5.41122	+	3.93148i	0.188738	+	0.137126i
$823$	11.5655	−	35.5950i	0.403149	−	1.24077i	−0.519282	−	0.854603i	$-0.673801\pi$
$823$	11.5655	−	35.5950i	0.403149	−	1.24077i	0.922431	−	0.386162i	$-0.126199\pi$
$824$	5.10689			0.177907
$825$		0			0
$826$	−0.334529			−0.0116397
$827$	−3.64386	+	11.2147i	−0.126710	+	0.389972i	−0.994209	−	0.107467i	$-0.965726\pi$
$827$	−3.64386	+	11.2147i	−0.126710	+	0.389972i	0.867499	+	0.497439i	$0.165726\pi$
$828$	−5.25906	−	3.82093i	−0.182765	−	0.132786i
$829$	28.3388	+	20.5893i	0.984247	+	0.715098i	0.958654	−	0.284575i	$-0.0918524\pi$
$829$	28.3388	+	20.5893i	0.984247	+	0.715098i	0.0255936	+	0.999672i	$0.491852\pi$
$830$		0			0
$831$	18.4729	−	13.4214i	0.640819	−	0.465582i
$832$	−0.482152			−0.0167156
$833$	37.8351	−	27.4888i	1.31091	−	0.952430i
$834$	−0.951151	−	2.92734i	−0.0329357	−	0.101366i
$835$		0			0
$836$	−8.46159	+	26.0421i	−0.292650	+	0.900684i
$837$	0.407499	+	1.25415i	0.0140852	+	0.0433498i
$838$	5.24417	+	16.1399i	0.181157	+	0.557543i
$839$	0.154094	−	0.474252i	0.00531991	−	0.0163730i	−0.948361	−	0.317192i	$-0.897260\pi$
$839$	0.154094	−	0.474252i	0.00531991	−	0.0163730i	0.953681	+	0.300819i	$0.0972600\pi$
$840$		0			0
$841$	2.24546	+	6.91082i	0.0774297	+	0.238304i
$842$	5.71360	−	4.15118i	0.196904	−	0.143059i
$843$	28.7548			0.990367
$844$	−12.7532	+	9.26574i	−0.438983	+	0.318940i
$845$		0			0
$846$	3.54381	+	2.57473i	0.121839	+	0.0885211i
$847$	3.81916	+	2.77478i	0.131228	+	0.0953427i
$848$	−0.520975	+	1.60340i	−0.0178904	+	0.0550609i
$849$	−19.3471			−0.663992
$850$		0			0
$851$	5.07133			0.173843
$852$	1.76507	−	5.43233i	0.0604703	−	0.186108i
$853$	−17.2793	−	12.5542i	−0.591633	−	0.429846i	0.251266	−	0.967918i	$-0.419153\pi$
$853$	−17.2793	−	12.5542i	−0.591633	−	0.429846i	−0.842899	+	0.538072i	$0.819153\pi$
$854$	1.11579	+	0.810672i	0.0381817	+	0.0277406i
$855$		0			0
$856$	12.4054	−	9.01307i	0.424009	−	0.308060i
$857$	−33.4831			−1.14376			−0.571880	−	0.820337i	$-0.693786\pi$
$857$	−33.4831			−1.14376			−0.571880	+	0.820337i	$0.693786\pi$
$858$	−1.96337	+	1.42647i	−0.0670284	+	0.0486990i
$859$	14.0563	+	43.2610i	0.479596	+	1.47605i	0.839657	+	0.543117i	$0.182756\pi$
$859$	14.0563	+	43.2610i	0.479596	+	1.47605i	−0.360061	+	0.932929i	$0.617244\pi$
$860$		0			0
$861$	−1.27414	+	3.92139i	−0.0434225	+	0.133641i
$862$	−5.51848	−	16.9841i	−0.187960	−	0.578482i
$863$	4.47115	+	13.7608i	0.152200	+	0.468423i	0.997866	−	0.0652888i	$-0.0207969\pi$
$863$	4.47115	+	13.7608i	0.152200	+	0.468423i	−0.845667	+	0.533711i	$0.820797\pi$
$864$	0.309017	−	0.951057i	0.0105130	−	0.0323556i
$865$		0			0
$866$	−7.47193	−	22.9962i	−0.253906	−	0.781444i
$867$	−23.5028	+	17.0758i	−0.798198	+	0.579925i
$868$	−0.434265			−0.0147399
$869$	34.5522	−	25.1036i	1.17210	−	0.851582i
$870$		0			0
$871$	1.22651	+	0.891108i	0.0415586	+	0.0301941i
$872$	7.89623	+	5.73695i	0.267400	+	0.194277i
$873$	−2.93876	+	9.04458i	−0.0994621	+	0.306113i
$874$	35.3638			1.19620
$875$		0			0
$876$	2.94269			0.0994241
$877$	−13.9673	+	42.9869i	−0.471641	+	1.45156i	0.378793	+	0.925482i	$0.376339\pi$
$877$	−13.9673	+	42.9869i	−0.471641	+	1.45156i	−0.850434	+	0.526082i	$0.823661\pi$
$878$	15.2987	+	11.1152i	0.516307	+	0.375119i
$879$	−12.1596	−	8.83449i	−0.410134	−	0.297980i
$880$		0			0
$881$	−11.3062	+	8.21440i	−0.380914	+	0.276750i	−0.761722	−	0.647904i	$-0.775646\pi$
$881$	−11.3062	+	8.21440i	−0.380914	+	0.276750i	0.380808	+	0.924654i	$0.375646\pi$
$882$	−6.89155			−0.232051
$883$	9.49373	−	6.89760i	0.319490	−	0.232123i	−0.416468	−	0.909150i	$-0.636732\pi$
$883$	9.49373	−	6.89760i	0.319490	−	0.232123i	0.735958	+	0.677028i	$0.236732\pi$
$884$	−1.01108	−	3.11179i	−0.0340064	−	0.104661i
$885$		0			0
$886$	1.25389	−	3.85909i	0.0421254	−	0.129649i
$887$	6.10346	+	18.7845i	0.204934	+	0.630722i	0.999716	+	0.0238271i	$0.00758513\pi$
$887$	6.10346	+	18.7845i	0.204934	+	0.630722i	−0.794782	+	0.606895i	$0.792415\pi$
$888$	0.241076	+	0.741956i	0.00808998	+	0.0248984i
$889$	−1.28279	+	3.94803i	−0.0430235	+	0.132413i
$890$		0			0
$891$	−1.55540	−	4.78704i	−0.0521080	−	0.160372i
$892$	17.9426	−	13.0360i	0.600762	−	0.436479i
$893$	−23.8299			−0.797437
$894$	−4.09739	+	2.97693i	−0.137037	+	0.0995634i
$895$		0			0
$896$	0.266421	+	0.193566i	0.00890051	+	0.00646660i
$897$	2.53566	+	1.84227i	0.0846634	+	0.0615116i
$898$	−1.93491	+	5.95504i	−0.0645688	+	0.198722i
$899$	−7.94139			−0.264860
$900$		0			0
$901$	−11.4408			−0.381147
$902$	−19.4745	+	59.9363i	−0.648429	+	1.99566i
$903$	−0.659611	−	0.479235i	−0.0219505	−	0.0159480i
$904$	−1.22619	−	0.890881i	−0.0407825	−	0.0296302i
$905$		0			0
$906$	13.7194	−	9.96772i	0.455796	−	0.331155i
$907$	−21.0111			−0.697661			−0.348831	−	0.937186i	$-0.613421\pi$
$907$	−21.0111			−0.697661			−0.348831	+	0.937186i	$0.613421\pi$
$908$	−8.97759	+	6.52260i	−0.297932	+	0.216460i
$909$	5.94657	+	18.3017i	0.197235	+	0.607028i
$910$		0			0
$911$	7.67252	−	23.6136i	0.254202	−	0.782353i	−0.739784	−	0.672844i	$-0.765072\pi$
$911$	7.67252	−	23.6136i	0.254202	−	0.782353i	0.993986	−	0.109508i	$-0.0349277\pi$
$912$	1.68109	+	5.17386i	0.0556665	+	0.171324i
$913$	−26.7459	−	82.3155i	−0.885161	−	2.72425i
$914$	0.600200	−	1.84723i	0.0198528	−	0.0611008i
$915$		0			0
$916$	0.555857	+	1.71075i	0.0183660	+	0.0565248i
$917$	3.74480	−	2.72076i	0.123664	−	0.0898473i
$918$	6.78610			0.223975
$919$	29.1482	−	21.1774i	0.961511	−	0.698579i	0.00801012	−	0.999968i	$-0.497450\pi$
$919$	29.1482	−	21.1774i	0.961511	−	0.698579i	0.953501	+	0.301389i	$0.0974503\pi$
$920$		0			0
$921$	−15.9425	−	11.5829i	−0.525325	−	0.381671i
$922$	−2.52730	−	1.83619i	−0.0832321	−	0.0604717i
$923$	−0.851032	+	2.61921i	−0.0280121	+	0.0862123i
$924$	1.65757			0.0545301
$925$		0			0
$926$	−8.26641			−0.271651
$927$	1.57811	−	4.85694i	0.0518321	−	0.159523i
$928$	4.87203	+	3.53974i	0.159932	+	0.116198i
$929$	46.0844	+	33.4822i	1.51198	+	1.09852i	0.965290	+	0.261181i	$0.0841119\pi$
$929$	46.0844	+	33.4822i	1.51198	+	1.09852i	0.546689	+	0.837336i	$0.315888\pi$
$930$		0			0
$931$	30.3308	−	22.0366i	0.994051	−	0.722220i
$932$	3.70579			0.121387
$933$	−22.8461	+	16.5986i	−0.747946	+	0.543415i
$934$	−9.46187	−	29.1206i	−0.309602	−	0.952856i
$935$		0			0
$936$	−0.148993	+	0.458554i	−0.00487000	+	0.0149883i
$937$	12.9036	+	39.7133i	0.421543	+	1.29738i	0.906266	+	0.422708i	$0.138920\pi$
$937$	12.9036	+	39.7133i	0.421543	+	1.29738i	−0.484723	+	0.874668i	$0.661080\pi$
$938$	−0.319979	−	0.984794i	−0.0104477	−	0.0321547i
$939$	−3.47577	+	10.6973i	−0.113427	+	0.349094i
$940$		0			0
$941$	−7.05275	−	21.7061i	−0.229913	−	0.707599i	−0.997756	−	0.0669608i	$-0.978670\pi$
$941$	−7.05275	−	21.7061i	−0.229913	−	0.707599i	0.767843	−	0.640638i	$-0.221330\pi$
$942$	18.4686	−	13.4182i	0.601738	−	0.437188i
$943$	81.3903			2.65043
$944$	−0.821825	+	0.597091i	−0.0267481	+	0.0194337i
$945$		0			0
$946$	−10.0818	−	7.32484i	−0.327787	−	0.238151i
$947$	6.85030	+	4.97703i	0.222605	+	0.161732i	0.693498	−	0.720458i	$-0.256068\pi$
$947$	6.85030	+	4.97703i	0.222605	+	0.161732i	−0.470894	+	0.882190i	$0.656068\pi$
$948$	2.62204	−	8.06981i	0.0851599	−	0.262095i
$949$	−1.41882			−0.0460569
$950$		0			0
$951$	−23.2917			−0.755284
$952$	−0.690580	+	2.12539i	−0.0223818	+	0.0688841i
$953$	−20.1346	−	14.6287i	−0.652225	−	0.473869i	0.211803	−	0.977312i	$-0.432066\pi$
$953$	−20.1346	−	14.6287i	−0.652225	−	0.473869i	−0.864028	+	0.503443i	$0.832066\pi$
$954$	1.36393	+	0.990953i	0.0441589	+	0.0320833i
$955$		0			0
$956$	13.6508	−	9.91790i	0.441499	−	0.320768i
$957$	30.3119			0.979845
$958$	0.948887	−	0.689407i	0.0306571	−	0.0222737i
$959$	0.680661	+	2.09486i	0.0219797	+	0.0676465i
$960$		0			0
$961$	−9.04216	+	27.8289i	−0.291683	+	0.897707i
$962$	−0.116235	−	0.357736i	−0.00374758	−	0.0115339i
$963$	−4.73845	−	14.5835i	−0.152694	−	0.469945i
$964$	6.37366	−	19.6161i	0.205282	−	0.631793i
$965$		0			0
$966$	−0.661521	−	2.03595i	−0.0212841	−	0.0655057i
$967$	17.8993	−	13.0046i	0.575602	−	0.418199i	−0.261534	−	0.965194i	$-0.584228\pi$
$967$	17.8993	−	13.0046i	0.575602	−	0.418199i	0.837136	+	0.546995i	$0.184228\pi$
$968$	14.3350			0.460746
$969$	−29.8666	+	21.6994i	−0.959455	+	0.697085i
$970$		0			0
$971$	13.7573	+	9.99529i	0.441494	+	0.320764i	0.786228	−	0.617936i	$-0.212031\pi$
$971$	13.7573	+	9.99529i	0.441494	+	0.320764i	−0.344734	+	0.938700i	$0.612031\pi$
$972$	−0.809017	−	0.587785i	−0.0259492	−	0.0188532i
$973$	0.313228	−	0.964017i	0.0100416	−	0.0309050i
$974$	11.7556			0.376672
$975$		0			0
$976$	4.18808			0.134057
$977$	12.7633	−	39.2815i	0.408335	−	1.25673i	−0.509742	−	0.860327i	$-0.670259\pi$
$977$	12.7633	−	39.2815i	0.408335	−	1.25673i	0.918078	−	0.396400i	$-0.129741\pi$
$978$	−6.43835	−	4.67773i	−0.205876	−	0.149577i
$979$	14.0582	+	10.2139i	0.449303	+	0.326438i
$980$		0			0
$981$	7.89623	−	5.73695i	0.252107	−	0.183167i
$982$	4.13052			0.131810
$983$	−50.0911	+	36.3933i	−1.59766	+	1.16077i	−0.705842	+	0.708369i	$0.749431\pi$
$983$	−50.0911	+	36.3933i	−1.59766	+	1.16077i	−0.891816	+	0.452398i	$0.850569\pi$
$984$	3.86905	+	11.9077i	0.123341	+	0.379604i
$985$		0			0
$986$	−12.6286	+	38.8668i	−0.402176	+	1.23777i
$987$	0.445766	+	1.37193i	0.0141889	+	0.0436689i
$988$	−0.810541	−	2.49459i	−0.0257868	−	0.0793635i
$989$	−4.97338	+	15.3065i	−0.158144	+	0.486718i
$990$		0			0
$991$	1.52376	+	4.68964i	0.0484037	+	0.148971i	0.972337	−	0.233582i	$-0.0750448\pi$
$991$	1.52376	+	4.68964i	0.0484037	+	0.148971i	−0.923933	+	0.382553i	$0.875045\pi$
$992$	−1.06685	+	0.775108i	−0.0338724	+	0.0246097i
$993$	0.129334			0.00410428
$994$	1.52177	−	1.10563i	0.0482676	−	0.0350684i
$995$		0			0
$996$	−13.9114	−	10.1073i	−0.440801	−	0.320261i
$997$	40.0946	+	29.1304i	1.26981	+	0.922569i	0.999195	−	0.0401195i	$-0.0127739\pi$
$997$	40.0946	+	29.1304i	1.26981	+	0.922569i	0.270612	+	0.962688i	$0.412774\pi$
$998$	2.96395	−	9.12209i	0.0938221	−	0.288755i
$999$	0.780139			0.0246825

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.g.f.601.2		16
5.2	odd	4		150.2.h.b.79.4	yes	16
5.3	odd	4		750.2.h.d.649.2		16
5.4	even	2		750.2.g.g.601.3		16
15.2	even	4		450.2.l.c.379.1		16
25.6	even	5	inner	750.2.g.f.151.2		16
25.8	odd	20		150.2.h.b.19.4	✓	16
25.9	even	10		3750.2.a.u.1.5		8
25.12	odd	20		3750.2.c.k.1249.12		16
25.13	odd	20		3750.2.c.k.1249.5		16
25.16	even	5		3750.2.a.v.1.4		8
25.17	odd	20		750.2.h.d.349.1		16
25.19	even	10		750.2.g.g.151.3		16
75.8	even	20		450.2.l.c.19.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.h.b.19.4	✓	16	25.8	odd	20
150.2.h.b.79.4	yes	16	5.2	odd	4
450.2.l.c.19.1		16	75.8	even	20
450.2.l.c.379.1		16	15.2	even	4
750.2.g.f.151.2		16	25.6	even	5	inner
750.2.g.f.601.2		16	1.1	even	1	trivial
750.2.g.g.151.3		16	25.19	even	10
750.2.g.g.601.3		16	5.4	even	2
750.2.h.d.349.1		16	25.17	odd	20
750.2.h.d.649.2		16	5.3	odd	4
3750.2.a.u.1.5		8	25.9	even	10
3750.2.a.v.1.4		8	25.16	even	5
3750.2.c.k.1249.5		16	25.13	odd	20
3750.2.c.k.1249.12		16	25.12	odd	20

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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.809017 + 0.587785i) q^{6} -0.329315 q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.809017 + 0.587785i) q^{6} -0.329315 q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-1.55540 + 4.78704i) q^{11} +(0.309017 + 0.951057i) q^{12} +(-0.148993 - 0.458554i) q^{13} +(-0.101764 + 0.313197i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-5.49007 + 3.98877i) q^{17} +1.00000 q^{18} +(-4.40115 + 3.19762i) q^{19} +(0.266421 + 0.193566i) q^{21} +(4.07210 + 2.95855i) q^{22} +(2.00878 - 6.18239i) q^{23} +1.00000 q^{24} -0.482152 q^{26} +(0.309017 - 0.951057i) q^{27} +(0.266421 + 0.193566i) q^{28} +(4.87203 + 3.53974i) q^{29} +(-1.06685 + 0.775108i) q^{31} +1.00000 q^{32} +(4.07210 - 2.95855i) q^{33} +(2.09702 + 6.45396i) q^{34} +(0.309017 - 0.951057i) q^{36} +(0.241076 + 0.741956i) q^{37} +(1.68109 + 5.17386i) q^{38} +(-0.148993 + 0.458554i) q^{39} +(3.86905 + 11.9077i) q^{41} +(0.266421 - 0.193566i) q^{42} -2.47582 q^{43} +(4.07210 - 2.95855i) q^{44} +(-5.25906 - 3.82093i) q^{46} +(3.54381 + 2.57473i) q^{47} +(0.309017 - 0.951057i) q^{48} -6.89155 q^{49} +6.78610 q^{51} +(-0.148993 + 0.458554i) q^{52} +(1.36393 + 0.990953i) q^{53} +(-0.809017 - 0.587785i) q^{54} +(0.266421 - 0.193566i) q^{56} +5.44012 q^{57} +(4.87203 - 3.53974i) q^{58} +(0.313909 + 0.966113i) q^{59} +(1.29419 - 3.98310i) q^{61} +(0.407499 + 1.25415i) q^{62} +(-0.101764 - 0.313197i) q^{63} +(0.309017 - 0.951057i) q^{64} +(-1.55540 - 4.78704i) q^{66} +(-2.54381 + 1.84819i) q^{67} +6.78610 q^{68} +(-5.25906 + 3.82093i) q^{69} +(-4.62101 - 3.35736i) q^{71} +(-0.809017 - 0.587785i) q^{72} +(0.909340 - 2.79866i) q^{73} +0.780139 q^{74} +5.44012 q^{76} +(0.512218 - 1.57644i) q^{77} +(0.390069 + 0.283402i) q^{78} +(-6.86459 - 4.98742i) q^{79} +(-0.809017 + 0.587785i) q^{81} +12.5205 q^{82} +(-13.9114 + 10.1073i) q^{83} +(-0.101764 - 0.313197i) q^{84} +(-0.765070 + 2.35464i) q^{86} +(-1.86095 - 5.72742i) q^{87} +(-1.55540 - 4.78704i) q^{88} +(1.06683 - 3.28336i) q^{89} +(0.0490657 + 0.151009i) q^{91} +(-5.25906 + 3.82093i) q^{92} +1.31869 q^{93} +(3.54381 - 2.57473i) q^{94} +(-0.809017 - 0.587785i) q^{96} +(7.69378 + 5.58986i) q^{97} +(-2.12961 + 6.55426i) q^{98} -5.03339 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{6} + 8 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^6 + 8 * q^7 - 4 * q^8 - 4 * q^9	\( 16 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{6} + 8 q^{7} - 4 q^{8} - 4 q^{9} + 2 q^{11} - 4 q^{12} + 4 q^{13} - 2 q^{14} - 4 q^{16} - 2 q^{17} + 16 q^{18} - 2 q^{21} - 8 q^{22} - 6 q^{23} + 16 q^{24} + 4 q^{26} - 4 q^{27} - 2 q^{28} + 10 q^{29} - 18 q^{31} + 16 q^{32} - 8 q^{33} - 12 q^{34} - 4 q^{36} - 2 q^{37} - 10 q^{38} + 4 q^{39} + 22 q^{41} - 2 q^{42} + 4 q^{43} - 8 q^{44} - 6 q^{46} - 2 q^{47} - 4 q^{48} + 52 q^{49} + 28 q^{51} + 4 q^{52} - 16 q^{53} - 4 q^{54} - 2 q^{56} + 20 q^{57} + 10 q^{58} - 20 q^{59} + 12 q^{61} + 2 q^{62} - 2 q^{63} - 4 q^{64} + 2 q^{66} + 18 q^{67} + 28 q^{68} - 6 q^{69} - 28 q^{71} - 4 q^{72} + 24 q^{73} - 12 q^{74} + 20 q^{76} - 14 q^{77} - 6 q^{78} + 20 q^{79} - 4 q^{81} + 12 q^{82} - 36 q^{83} - 2 q^{84} - 6 q^{86} - 20 q^{87} + 2 q^{88} - 70 q^{89} + 12 q^{91} - 6 q^{92} + 32 q^{93} - 2 q^{94} - 4 q^{96} + 28 q^{97} - 38 q^{98} + 12 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^6 + 8 * q^7 - 4 * q^8 - 4 * q^9 + 2 * q^11 - 4 * q^12 + 4 * q^13 - 2 * q^14 - 4 * q^16 - 2 * q^17 + 16 * q^18 - 2 * q^21 - 8 * q^22 - 6 * q^23 + 16 * q^24 + 4 * q^26 - 4 * q^27 - 2 * q^28 + 10 * q^29 - 18 * q^31 + 16 * q^32 - 8 * q^33 - 12 * q^34 - 4 * q^36 - 2 * q^37 - 10 * q^38 + 4 * q^39 + 22 * q^41 - 2 * q^42 + 4 * q^43 - 8 * q^44 - 6 * q^46 - 2 * q^47 - 4 * q^48 + 52 * q^49 + 28 * q^51 + 4 * q^52 - 16 * q^53 - 4 * q^54 - 2 * q^56 + 20 * q^57 + 10 * q^58 - 20 * q^59 + 12 * q^61 + 2 * q^62 - 2 * q^63 - 4 * q^64 + 2 * q^66 + 18 * q^67 + 28 * q^68 - 6 * q^69 - 28 * q^71 - 4 * q^72 + 24 * q^73 - 12 * q^74 + 20 * q^76 - 14 * q^77 - 6 * q^78 + 20 * q^79 - 4 * q^81 + 12 * q^82 - 36 * q^83 - 2 * q^84 - 6 * q^86 - 20 * q^87 + 2 * q^88 - 70 * q^89 + 12 * q^91 - 6 * q^92 + 32 * q^93 - 2 * q^94 - 4 * q^96 + 28 * q^97 - 38 * q^98 + 12 * q^99

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