LMFDB - Embedded newform 546.2.p.c.239.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(239,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("546.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.p (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:	$4.35983195036$
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} - 20 x^{17} + 56 x^{16} - 140 x^{15} + 288 x^{14} - 532 x^{13} + \cdots + 59049 $ x^20 - 4x^19 + 8x^18 - 20x^17 + 56x^16 - 140x^15 + 288x^14 - 532x^13 + 1065x^12 - 2080x^11 + 3712x^10 - 6240x^9 + 9585x^8 - 14364x^7 + 23328x^6 - 34020x^5 + 40824x^4 - 43740x^3 + 52488x^2 - 78732*x + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			239.4
Root			$1.72939 + 0.0958811i$ of defining polynomial
Character	$\chi$	$=$	546.239
Dual form			546.2.p.c.281.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(1.15507 + 1.29067i) q^{3} +1.00000i q^{4} +(0.616653 + 0.616653i) q^{5} +(0.0958811 - 1.72939i) q^{6} +(0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.331633 + 2.98161i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(1.15507 + 1.29067i) q^{3} +1.00000i q^{4} +(0.616653 + 0.616653i) q^{5} +(0.0958811 - 1.72939i) q^{6} +(0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.331633 + 2.98161i) q^{9} -0.872079i q^{10} +(-2.63014 + 2.63014i) q^{11} +(-1.29067 + 1.15507i) q^{12} +(1.08413 + 3.43870i) q^{13} -1.00000i q^{14} +(-0.0836158 + 1.50817i) q^{15} -1.00000 q^{16} -5.36595 q^{17} +(2.34282 - 1.87382i) q^{18} +(3.60391 - 3.60391i) q^{19} +(-0.616653 + 0.616653i) q^{20} +(-0.0958811 + 1.72939i) q^{21} +3.71958 q^{22} +2.67136 q^{23} +(1.72939 + 0.0958811i) q^{24} -4.23948i q^{25} +(1.66493 - 3.19813i) q^{26} +(-4.23132 + 3.01594i) q^{27} +(-0.707107 + 0.707107i) q^{28} -3.00014i q^{29} +(1.12556 - 1.00731i) q^{30} +(-6.60062 + 6.60062i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-6.43263 - 0.356638i) q^{33} +(3.79430 + 3.79430i) q^{34} +0.872079i q^{35} +(-2.98161 - 0.331633i) q^{36} +(4.44970 + 4.44970i) q^{37} -5.09669 q^{38} +(-3.18596 + 5.37119i) q^{39} +0.872079 q^{40} +(8.43789 + 8.43789i) q^{41} +(1.29067 - 1.15507i) q^{42} +0.610209i q^{43} +(-2.63014 - 2.63014i) q^{44} +(-2.04312 + 1.63412i) q^{45} +(-1.88894 - 1.88894i) q^{46} +(3.46010 - 3.46010i) q^{47} +(-1.15507 - 1.29067i) q^{48} +1.00000i q^{49} +(-2.99776 + 2.99776i) q^{50} +(-6.19805 - 6.92565i) q^{51} +(-3.43870 + 1.08413i) q^{52} -0.464507i q^{53} +(5.12459 + 0.859404i) q^{54} -3.24377 q^{55} +1.00000 q^{56} +(8.81419 + 0.488676i) q^{57} +(-2.12142 + 2.12142i) q^{58} +(8.93448 - 8.93448i) q^{59} +(-1.50817 - 0.0836158i) q^{60} -8.37831 q^{61} +9.33468 q^{62} +(-2.34282 + 1.87382i) q^{63} -1.00000i q^{64} +(-1.45195 + 2.78902i) q^{65} +(4.29637 + 4.80074i) q^{66} +(1.77932 - 1.77932i) q^{67} -5.36595i q^{68} +(3.08561 + 3.44784i) q^{69} +(0.616653 - 0.616653i) q^{70} +(-0.00980127 - 0.00980127i) q^{71} +(1.87382 + 2.34282i) q^{72} +(11.1380 + 11.1380i) q^{73} -6.29283i q^{74} +(5.47175 - 4.89689i) q^{75} +(3.60391 + 3.60391i) q^{76} -3.71958 q^{77} +(6.05082 - 1.54519i) q^{78} +6.11811 q^{79} +(-0.616653 - 0.616653i) q^{80} +(-8.78004 - 1.97760i) q^{81} -11.9330i q^{82} +(-3.29926 - 3.29926i) q^{83} +(-1.72939 - 0.0958811i) q^{84} +(-3.30893 - 3.30893i) q^{85} +(0.431483 - 0.431483i) q^{86} +(3.87217 - 3.46536i) q^{87} +3.71958i q^{88} +(8.90085 - 8.90085i) q^{89} +(2.60020 + 0.289210i) q^{90} +(-1.66493 + 3.19813i) q^{91} +2.67136i q^{92} +(-16.1433 - 0.895019i) q^{93} -4.89332 q^{94} +4.44472 q^{95} +(-0.0958811 + 1.72939i) q^{96} +(-5.41720 + 5.41720i) q^{97} +(0.707107 - 0.707107i) q^{98} +(-6.96983 - 8.71431i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{5} - 4 q^{6} - 8 q^{9}+O(q^{10}) $ 20 * q - 4 * q^5 - 4 * q^6 - 8 * q^9	$ 20 q - 4 q^{5} - 4 q^{6} - 8 q^{9} - 16 q^{11} - 8 q^{12} + 4 q^{13} - 4 q^{15} - 20 q^{16} + 12 q^{17} - 8 q^{18} + 12 q^{19} + 4 q^{20} + 4 q^{21} - 12 q^{22} - 4 q^{23} + 4 q^{24} + 24 q^{27} + 12 q^{30} - 8 q^{31} - 48 q^{33} - 4 q^{34} + 32 q^{37} - 4 q^{38} - 16 q^{39} - 4 q^{40} + 8 q^{41} + 8 q^{42} - 16 q^{44} + 16 q^{45} - 8 q^{46} + 32 q^{50} - 8 q^{51} - 8 q^{52} + 28 q^{54} + 28 q^{55} + 20 q^{56} + 36 q^{57} - 4 q^{58} + 20 q^{59} - 4 q^{60} - 4 q^{61} + 48 q^{62} + 8 q^{63} + 52 q^{65} - 36 q^{67} + 68 q^{69} - 4 q^{70} - 28 q^{71} - 16 q^{72} - 24 q^{73} - 76 q^{75} + 12 q^{76} + 12 q^{77} + 40 q^{78} - 64 q^{79} + 4 q^{80} + 32 q^{81} - 24 q^{83} - 4 q^{84} + 24 q^{85} + 4 q^{86} + 4 q^{87} - 4 q^{89} - 8 q^{90} - 32 q^{93} - 40 q^{94} - 76 q^{95} + 4 q^{96} + 32 q^{97} - 4 q^{99}+O(q^{100}) $ 20 * q - 4 * q^5 - 4 * q^6 - 8 * q^9 - 16 * q^11 - 8 * q^12 + 4 * q^13 - 4 * q^15 - 20 * q^16 + 12 * q^17 - 8 * q^18 + 12 * q^19 + 4 * q^20 + 4 * q^21 - 12 * q^22 - 4 * q^23 + 4 * q^24 + 24 * q^27 + 12 * q^30 - 8 * q^31 - 48 * q^33 - 4 * q^34 + 32 * q^37 - 4 * q^38 - 16 * q^39 - 4 * q^40 + 8 * q^41 + 8 * q^42 - 16 * q^44 + 16 * q^45 - 8 * q^46 + 32 * q^50 - 8 * q^51 - 8 * q^52 + 28 * q^54 + 28 * q^55 + 20 * q^56 + 36 * q^57 - 4 * q^58 + 20 * q^59 - 4 * q^60 - 4 * q^61 + 48 * q^62 + 8 * q^63 + 52 * q^65 - 36 * q^67 + 68 * q^69 - 4 * q^70 - 28 * q^71 - 16 * q^72 - 24 * q^73 - 76 * q^75 + 12 * q^76 + 12 * q^77 + 40 * q^78 - 64 * q^79 + 4 * q^80 + 32 * q^81 - 24 * q^83 - 4 * q^84 + 24 * q^85 + 4 * q^86 + 4 * q^87 - 4 * q^89 - 8 * q^90 - 32 * q^93 - 40 * q^94 - 76 * q^95 + 4 * q^96 + 32 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	1.15507	+	1.29067i	0.666879	+	0.745166i
$3$	1.15507	+	1.29067i	0.666879	+	0.745166i
$4$			1.00000i			0.500000i
$5$	0.616653	+	0.616653i	0.275775	+	0.275775i	0.831420	−	0.555645i	$-0.187528\pi$
$5$	0.616653	+	0.616653i	0.275775	+	0.275775i	−0.555645	+	0.831420i	$0.687528\pi$
$6$	0.0958811	−	1.72939i	0.0391433	−	0.706023i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−0.331633	+	2.98161i	−0.110544	+	0.993871i
$10$		−	0.872079i		−	0.275775i
$11$	−2.63014	+	2.63014i	−0.793018	+	0.793018i	−0.981984	−	0.188966i	$-0.939486\pi$
$11$	−2.63014	+	2.63014i	−0.793018	+	0.793018i	0.188966	+	0.981984i	$0.439486\pi$
$12$	−1.29067	+	1.15507i	−0.372583	+	0.333440i
$13$	1.08413	+	3.43870i	0.300684	+	0.953724i
$13$	1.08413	+	3.43870i	0.300684	+	0.953724i
$14$		−	1.00000i		−	0.267261i
$15$	−0.0836158	+	1.50817i	−0.0215895	+	0.389407i
$16$	−1.00000			−0.250000
$17$	−5.36595			−1.30144			−0.650718	−	0.759320i	$-0.725532\pi$
$17$	−5.36595			−1.30144			−0.650718	+	0.759320i	$0.725532\pi$
$18$	2.34282	−	1.87382i	0.552208	−	0.441664i
$19$	3.60391	−	3.60391i	0.826793	−	0.826793i	−0.160279	−	0.987072i	$-0.551239\pi$
$19$	3.60391	−	3.60391i	0.826793	−	0.826793i	0.987072	+	0.160279i	$0.0512394\pi$
$20$	−0.616653	+	0.616653i	−0.137888	+	0.137888i
$21$	−0.0958811	+	1.72939i	−0.0209230	+	0.377385i
$22$	3.71958			0.793018
$23$	2.67136			0.557018			0.278509	−	0.960434i	$-0.410160\pi$
$23$	2.67136			0.557018			0.278509	+	0.960434i	$0.410160\pi$
$24$	1.72939	+	0.0958811i	0.353011	+	0.0195716i
$25$		−	4.23948i		−	0.847896i
$26$	1.66493	−	3.19813i	0.326520	−	0.627204i
$27$	−4.23132	+	3.01594i	−0.814318	+	0.580418i
$28$	−0.707107	+	0.707107i	−0.133631	+	0.133631i
$29$		−	3.00014i		−	0.557111i	−0.960420	−	0.278556i	$-0.910144\pi$
$29$		−	3.00014i		−	0.557111i	0.960420	−	0.278556i	$-0.0898556\pi$
$30$	1.12556	−	1.00731i	0.205498	−	0.183909i
$31$	−6.60062	+	6.60062i	−1.18551	+	1.18551i	−0.207209	+	0.978297i	$0.566438\pi$
$31$	−6.60062	+	6.60062i	−1.18551	+	1.18551i	−0.978297	+	0.207209i	$0.933562\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−6.43263	−	0.356638i	−1.11978	−	0.0620827i
$34$	3.79430	+	3.79430i	0.650718	+	0.650718i
$35$			0.872079i			0.147408i
$36$	−2.98161	−	0.331633i	−0.496936	−	0.0552721i
$37$	4.44970	+	4.44970i	0.731527	+	0.731527i	0.970922	−	0.239395i	$-0.0769492\pi$
$37$	4.44970	+	4.44970i	0.731527	+	0.731527i	−0.239395	+	0.970922i	$0.576949\pi$
$38$	−5.09669			−0.826793
$39$	−3.18596	+	5.37119i	−0.510162	+	0.860078i
$40$	0.872079			0.137888
$41$	8.43789	+	8.43789i	1.31778	+	1.31778i	0.915532	+	0.402245i	$0.131770\pi$
$41$	8.43789	+	8.43789i	1.31778	+	1.31778i	0.402245	+	0.915532i	$0.368230\pi$
$42$	1.29067	−	1.15507i	0.199154	−	0.178231i
$43$			0.610209i			0.0930560i	0.998917	+	0.0465280i	$0.0148157\pi$
$43$			0.610209i			0.0930560i	−0.998917	+	0.0465280i	$0.985184\pi$
$44$	−2.63014	−	2.63014i	−0.396509	−	0.396509i
$45$	−2.04312	+	1.63412i	−0.304571	+	0.243600i
$46$	−1.88894	−	1.88894i	−0.278509	−	0.278509i
$47$	3.46010	−	3.46010i	0.504707	−	0.504707i	−0.408190	−	0.912897i	$-0.633840\pi$
$47$	3.46010	−	3.46010i	0.504707	−	0.504707i	0.912897	+	0.408190i	$0.133840\pi$
$48$	−1.15507	−	1.29067i	−0.166720	−	0.186291i
$49$			1.00000i			0.142857i
$50$	−2.99776	+	2.99776i	−0.423948	+	0.423948i
$51$	−6.19805	−	6.92565i	−0.867900	−	0.969785i
$52$	−3.43870	+	1.08413i	−0.476862	+	0.150342i
$53$		−	0.464507i		−	0.0638049i	−0.999491	−	0.0319024i	$-0.989843\pi$
$53$		−	0.464507i		−	0.0638049i	0.999491	−	0.0319024i	$-0.0101566\pi$
$54$	5.12459	+	0.859404i	0.697368	+	0.116950i
$55$	−3.24377			−0.437390
$56$	1.00000			0.133631
$57$	8.81419	+	0.488676i	1.16747	+	0.0647268i
$58$	−2.12142	+	2.12142i	−0.278556	+	0.278556i
$59$	8.93448	−	8.93448i	1.16317	−	1.16317i	0.179393	−	0.983778i	$-0.442587\pi$
$59$	8.93448	−	8.93448i	1.16317	−	1.16317i	0.983778	−	0.179393i	$-0.0574133\pi$
$60$	−1.50817	−	0.0836158i	−0.194704	−	0.0107948i
$61$	−8.37831			−1.07273			−0.536367	−	0.843985i	$-0.680204\pi$
$61$	−8.37831			−1.07273			−0.536367	+	0.843985i	$0.680204\pi$
$62$	9.33468			1.18551
$63$	−2.34282	+	1.87382i	−0.295167	+	0.236079i
$64$		−	1.00000i		−	0.125000i
$65$	−1.45195	+	2.78902i	−0.180092	+	0.345935i
$66$	4.29637	+	4.80074i	0.528847	+	0.590930i
$67$	1.77932	−	1.77932i	0.217379	−	0.217379i	−0.590014	−	0.807393i	$-0.700878\pi$
$67$	1.77932	−	1.77932i	0.217379	−	0.217379i	0.807393	+	0.590014i	$0.200878\pi$
$68$		−	5.36595i		−	0.650718i
$69$	3.08561	+	3.44784i	0.371464	+	0.415071i
$70$	0.616653	−	0.616653i	0.0737041	−	0.0737041i
$71$	−0.00980127	−	0.00980127i	−0.00116320	−	0.00116320i	0.706525	−	0.707688i	$-0.250262\pi$
$71$	−0.00980127	−	0.00980127i	−0.00116320	−	0.00116320i	−0.707688	+	0.706525i	$0.750262\pi$
$72$	1.87382	+	2.34282i	0.220832	+	0.276104i
$73$	11.1380	+	11.1380i	1.30360	+	1.30360i	0.925948	+	0.377650i	$0.123268\pi$
$73$	11.1380	+	11.1380i	1.30360	+	1.30360i	0.377650	+	0.925948i	$0.376732\pi$
$74$		−	6.29283i		−	0.731527i
$75$	5.47175	−	4.89689i	0.631823	−	0.565444i
$76$	3.60391	+	3.60391i	0.413396	+	0.413396i
$77$	−3.71958			−0.423886
$78$	6.05082	−	1.54519i	0.685120	−	0.174958i
$79$	6.11811			0.688341			0.344170	−	0.938907i	$-0.388160\pi$
$79$	6.11811			0.688341			0.344170	+	0.938907i	$0.388160\pi$
$80$	−0.616653	−	0.616653i	−0.0689439	−	0.0689439i
$81$	−8.78004	−	1.97760i	−0.975560	−	0.219733i
$82$		−	11.9330i		−	1.31778i
$83$	−3.29926	−	3.29926i	−0.362141	−	0.362141i	0.502460	−	0.864601i	$-0.332428\pi$
$83$	−3.29926	−	3.29926i	−0.362141	−	0.362141i	−0.864601	+	0.502460i	$0.832428\pi$
$84$	−1.72939	−	0.0958811i	−0.188692	−	0.0104615i
$85$	−3.30893	−	3.30893i	−0.358904	−	0.358904i
$86$	0.431483	−	0.431483i	0.0465280	−	0.0465280i
$87$	3.87217	−	3.46536i	0.415140	−	0.371526i
$88$			3.71958i			0.396509i
$89$	8.90085	−	8.90085i	0.943489	−	0.943489i	−0.0549979	−	0.998486i	$-0.517515\pi$
$89$	8.90085	−	8.90085i	0.943489	−	0.943489i	0.998486	+	0.0549979i	$0.0175152\pi$
$90$	2.60020	+	0.289210i	0.274085	+	0.0304854i
$91$	−1.66493	+	3.19813i	−0.174532	+	0.335255i
$92$			2.67136i			0.278509i
$93$	−16.1433	−	0.895019i	−1.67399	−	0.0928092i
$94$	−4.89332			−0.504707
$95$	4.44472			0.456018
$96$	−0.0958811	+	1.72939i	−0.00978582	+	0.176506i
$97$	−5.41720	+	5.41720i	−0.550033	+	0.550033i	−0.926450	−	0.376417i	$-0.877156\pi$
$97$	−5.41720	+	5.41720i	−0.550033	+	0.550033i	0.376417	+	0.926450i	$0.377156\pi$
$98$	0.707107	−	0.707107i	0.0714286	−	0.0714286i
$99$	−6.96983	−	8.71431i	−0.700494	−	0.875821i
$100$	4.23948			0.423948
$101$	9.74113			0.969278			0.484639	−	0.874714i	$-0.338951\pi$
$101$	9.74113			0.969278			0.484639	+	0.874714i	$0.338951\pi$
$102$	−0.514494	+	9.27985i	−0.0509424	+	0.918842i
$103$		−	13.8659i		−	1.36625i	−0.730302	−	0.683124i	$-0.760621\pi$
$103$		−	13.8659i		−	1.36625i	0.730302	−	0.683124i	$-0.239379\pi$
$104$	3.19813	+	1.66493i	0.313602	+	0.163260i
$105$	−1.12556	+	1.00731i	−0.109844	+	0.0983035i
$106$	−0.328456	+	0.328456i	−0.0319024	+	0.0319024i
$107$			2.77130i			0.267911i	0.990987	+	0.133956i	$0.0427680\pi$
$107$			2.77130i			0.267911i	−0.990987	+	0.133956i	$0.957232\pi$
$108$	−3.01594	−	4.23132i	−0.290209	−	0.407159i
$109$	2.22915	−	2.22915i	0.213513	−	0.213513i	−0.592245	−	0.805758i	$-0.701758\pi$
$109$	2.22915	−	2.22915i	0.213513	−	0.213513i	0.805758	+	0.592245i	$0.201758\pi$
$110$	2.29369	+	2.29369i	0.218695	+	0.218695i
$111$	−0.603364	+	10.8828i	−0.0572687	+	1.03295i
$112$	−0.707107	−	0.707107i	−0.0668153	−	0.0668153i
$113$		−	13.7999i		−	1.29818i	−0.760710	−	0.649091i	$-0.775149\pi$
$113$		−	13.7999i		−	1.29818i	0.760710	−	0.649091i	$-0.224851\pi$
$114$	−5.88703	−	6.57812i	−0.551371	−	0.616098i
$115$	1.64730	+	1.64730i	0.153612	+	0.153612i
$116$	3.00014			0.278556
$117$	−10.6124	+	2.09208i	−0.981117	+	0.193413i
$118$	−12.6353			−1.16317
$119$	−3.79430	−	3.79430i	−0.347823	−	0.347823i
$120$	1.00731	+	1.12556i	0.0919545	+	0.102749i
$121$		−	2.83530i		−	0.257754i
$122$	5.92436	+	5.92436i	0.536367	+	0.536367i
$123$	−1.14415	+	20.6368i	−0.103164	+	1.86076i
$124$	−6.60062	−	6.60062i	−0.592753	−	0.592753i
$125$	5.69755	−	5.69755i	0.509604	−	0.509604i
$126$	2.98161	+	0.331633i	0.265623	+	0.0295442i
$127$		−	21.3350i		−	1.89317i	−0.322453	−	0.946585i	$-0.604508\pi$
$127$		−	21.3350i		−	1.89317i	0.322453	−	0.946585i	$-0.395492\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	−0.787575	+	0.704833i	−0.0693421	+	0.0620571i
$130$	2.99882	−	0.945448i	0.263014	−	0.0829213i
$131$			8.16389i			0.713282i	0.934242	+	0.356641i	$0.116078\pi$
$131$			8.16389i			0.713282i	−0.934242	+	0.356641i	$0.883922\pi$
$132$	0.356638	−	6.43263i	0.0310413	−	0.559888i
$133$	5.09669			0.441939
$134$	−2.51634			−0.217379
$135$	−4.46905	−	0.749468i	−0.384634	−	0.0645039i
$136$	−3.79430	+	3.79430i	−0.325359	+	0.325359i
$137$	−9.21910	+	9.21910i	−0.787641	+	0.787641i	−0.981107	−	0.193466i	$-0.938027\pi$
$137$	−9.21910	+	9.21910i	−0.787641	+	0.787641i	0.193466	+	0.981107i	$0.438027\pi$
$138$	0.256133	−	4.61984i	0.0218035	−	0.393267i
$139$	−2.49440			−0.211572			−0.105786	−	0.994389i	$-0.533736\pi$
$139$	−2.49440			−0.211572			−0.105786	+	0.994389i	$0.533736\pi$
$140$	−0.872079			−0.0737041
$141$	8.46248	+	0.469177i	0.712670	+	0.0395118i
$142$			0.0138611i			0.00116320i
$143$	−11.8957	−	6.19285i	−0.994768	−	0.517872i
$144$	0.331633	−	2.98161i	0.0276360	−	0.248468i
$145$	1.85004	−	1.85004i	0.153638	−	0.153638i
$146$		−	15.7514i		−	1.30360i
$147$	−1.29067	+	1.15507i	−0.106452	+	0.0952685i
$148$	−4.44970	+	4.44970i	−0.365763	+	0.365763i
$149$	−12.3117	−	12.3117i	−1.00862	−	1.00862i	−0.999963	−	0.00865511i	$-0.997245\pi$
$149$	−12.3117	−	12.3117i	−1.00862	−	1.00862i	−0.00865511	−	0.999963i	$-0.502755\pi$
$150$	−7.33173	−	0.406486i	−0.598634	−	0.0331894i
$151$	−3.48920	−	3.48920i	−0.283947	−	0.283947i	0.550734	−	0.834681i	$-0.314348\pi$
$151$	−3.48920	−	3.48920i	−0.283947	−	0.283947i	−0.834681	+	0.550734i	$0.814348\pi$
$152$		−	5.09669i		−	0.413396i
$153$	1.77952	−	15.9992i	0.143866	−	1.29346i
$154$	2.63014	+	2.63014i	0.211943	+	0.211943i
$155$	−8.14057			−0.653867
$156$	−5.37119	−	3.18596i	−0.430039	−	0.255081i
$157$	0.911415			0.0727388			0.0363694	−	0.999338i	$-0.488421\pi$
$157$	0.911415			0.0727388			0.0363694	+	0.999338i	$0.488421\pi$
$158$	−4.32615	−	4.32615i	−0.344170	−	0.344170i
$159$	0.599522	−	0.536537i	0.0475452	−	0.0425502i
$160$			0.872079i			0.0689439i
$161$	1.88894	+	1.88894i	0.148869	+	0.148869i
$162$	4.81005	+	7.60680i	0.377913	+	0.597647i
$163$	−13.4803	−	13.4803i	−1.05586	−	1.05586i	−0.998345	−	0.0575128i	$-0.981683\pi$
$163$	−13.4803	−	13.4803i	−1.05586	−	1.05586i	−0.0575128	−	0.998345i	$-0.518317\pi$
$164$	−8.43789	+	8.43789i	−0.658888	+	0.658888i
$165$	−3.74678	−	4.18662i	−0.291686	−	0.325928i
$166$			4.66586i			0.362141i
$167$	4.56615	−	4.56615i	0.353339	−	0.353339i	−0.508011	−	0.861350i	$-0.669619\pi$
$167$	4.56615	−	4.56615i	0.353339	−	0.353339i	0.861350	+	0.508011i	$0.169619\pi$
$168$	1.15507	+	1.29067i	0.0891155	+	0.0995770i
$169$	−10.6493	+	7.45601i	−0.819178	+	0.573539i
$170$			4.67953i			0.358904i
$171$	9.55028	+	11.9406i	0.730328	+	0.913122i
$172$	−0.610209			−0.0465280
$173$	20.5507			1.56244			0.781221	−	0.624255i	$-0.214597\pi$
$173$	20.5507			1.56244			0.781221	+	0.624255i	$0.214597\pi$
$174$	−5.18842	−	0.287656i	−0.393333	−	0.0218072i
$175$	2.99776	−	2.99776i	0.226610	−	0.226610i
$176$	2.63014	−	2.63014i	0.198254	−	0.198254i
$177$	21.8514	+	1.21148i	1.64245	+	0.0910606i
$178$	−12.5877			−0.943489
$179$	−12.5336			−0.936809			−0.468404	−	0.883514i	$-0.655171\pi$
$179$	−12.5336			−0.936809			−0.468404	+	0.883514i	$0.655171\pi$
$180$	−1.63412	−	2.04312i	−0.121800	−	0.152285i
$181$		−	13.2739i		−	0.986643i	−0.869847	−	0.493321i	$-0.835783\pi$
$181$		−	13.2739i		−	0.986643i	0.869847	−	0.493321i	$-0.164217\pi$
$182$	3.43870	−	1.08413i	0.254893	−	0.0803612i
$183$	−9.67753	−	10.8136i	−0.715383	−	0.799364i
$184$	1.88894	−	1.88894i	0.139254	−	0.139254i
$185$			5.48784i			0.403474i
$186$	10.7822	+	12.0479i	0.790589	+	0.883398i
$187$	14.1132	−	14.1132i	1.03206	−	1.03206i
$188$	3.46010	+	3.46010i	0.252354	+	0.252354i
$189$	−5.12459	−	0.859404i	−0.372759	−	0.0625124i
$190$	−3.14289	−	3.14289i	−0.228009	−	0.228009i
$191$			3.21043i			0.232299i	0.993232	+	0.116149i	$0.0370552\pi$
$191$			3.21043i			0.232299i	−0.993232	+	0.116149i	$0.962945\pi$
$192$	1.29067	−	1.15507i	0.0931457	−	0.0833599i
$193$	16.2407	+	16.2407i	1.16903	+	1.16903i	0.982437	+	0.186594i	$0.0597450\pi$
$193$	16.2407	+	16.2407i	1.16903	+	1.16903i	0.186594	+	0.982437i	$0.440255\pi$
$194$	7.66107			0.550033
$195$	−5.27679	+	1.34752i	−0.377879	+	0.0964982i
$196$	−1.00000			−0.0714286
$197$	14.8966	+	14.8966i	1.06134	+	1.06134i	0.997992	+	0.0633475i	$0.0201777\pi$
$197$	14.8966	+	14.8966i	1.06134	+	1.06134i	0.0633475	+	0.997992i	$0.479822\pi$
$198$	−1.23353	+	11.0904i	−0.0876635	+	0.788158i
$199$		−	15.1640i		−	1.07495i	−0.843281	−	0.537473i	$-0.819379\pi$
$199$		−	15.1640i		−	1.07495i	0.843281	−	0.537473i	$-0.180621\pi$
$200$	−2.99776	−	2.99776i	−0.211974	−	0.211974i
$201$	4.35175	+	0.241270i	0.306949	+	0.0170178i
$202$	−6.88802	−	6.88802i	−0.484639	−	0.484639i
$203$	2.12142	−	2.12142i	0.148894	−	0.148894i
$204$	6.92565	−	6.19805i	0.484892	−	0.433950i
$205$			10.4065i			0.726821i
$206$	−9.80468	+	9.80468i	−0.683124	+	0.683124i
$207$	−0.885911	+	7.96498i	−0.0615751	+	0.553604i
$208$	−1.08413	−	3.43870i	−0.0751710	−	0.238431i
$209$			18.9576i			1.31132i
$210$	1.50817	+	0.0836158i	0.104073	+	0.00577004i
$211$	2.49834			0.171993			0.0859965	−	0.996295i	$-0.472593\pi$
$211$	2.49834			0.171993			0.0859965	+	0.996295i	$0.472593\pi$
$212$	0.464507			0.0319024
$213$	0.00132902	−	0.0239713i	9.10627e−5	−	0.00164249i
$214$	1.95960	−	1.95960i	0.133956	−	0.133956i
$215$	−0.376287	+	0.376287i	−0.0256626	+	0.0256626i
$216$	−0.859404	+	5.12459i	−0.0584750	+	0.348684i
$217$	−9.33468			−0.633679
$218$	−3.15249			−0.213513
$219$	−1.51027	+	27.2405i	−0.102054	+	1.84074i
$220$		−	3.24377i		−	0.218695i
$221$	−5.81740	−	18.4519i	−0.391321	−	1.24121i
$222$	8.12194	−	7.26865i	0.545109	−	0.487840i
$223$	6.63646	−	6.63646i	0.444410	−	0.444410i	−0.449081	−	0.893491i	$-0.648249\pi$
$223$	6.63646	−	6.63646i	0.444410	−	0.444410i	0.893491	+	0.449081i	$0.148249\pi$
$224$			1.00000i			0.0668153i
$225$	12.6405	+	1.40595i	0.842699	+	0.0937299i
$226$	−9.75798	+	9.75798i	−0.649091	+	0.649091i
$227$	−8.75850	−	8.75850i	−0.581322	−	0.581322i	0.353944	−	0.935266i	$-0.384840\pi$
$227$	−8.75850	−	8.75850i	−0.581322	−	0.581322i	−0.935266	+	0.353944i	$0.884840\pi$
$228$	−0.488676	+	8.81419i	−0.0323634	+	0.583734i
$229$	4.24481	+	4.24481i	0.280505	+	0.280505i	0.833310	−	0.552805i	$-0.186443\pi$
$229$	4.24481	+	4.24481i	0.280505	+	0.280505i	−0.552805	+	0.833310i	$0.686443\pi$
$230$		−	2.32964i		−	0.153612i
$231$	−4.29637	−	4.80074i	−0.282681	−	0.315865i
$232$	−2.12142	−	2.12142i	−0.139278	−	0.139278i
$233$	5.81776			0.381134			0.190567	−	0.981674i	$-0.438967\pi$
$233$	5.81776			0.381134			0.190567	+	0.981674i	$0.438967\pi$
$234$	8.98343	+	6.02478i	0.587265	+	0.393852i
$235$	4.26736			0.278372
$236$	8.93448	+	8.93448i	0.581585	+	0.581585i
$237$	7.06683	+	7.89643i	0.459040	+	0.512928i
$238$			5.36595i			0.347823i
$239$	−6.19473	−	6.19473i	−0.400704	−	0.400704i	0.477777	−	0.878481i	$-0.341443\pi$
$239$	−6.19473	−	6.19473i	−0.400704	−	0.400704i	−0.878481	+	0.477777i	$0.841443\pi$
$240$	0.0836158	−	1.50817i	0.00539738	−	0.0973518i
$241$	19.2493	+	19.2493i	1.23996	+	1.23996i	0.960018	+	0.279940i	$0.0903144\pi$
$241$	19.2493	+	19.2493i	1.23996	+	1.23996i	0.279940	+	0.960018i	$0.409686\pi$
$242$	−2.00486	+	2.00486i	−0.128877	+	0.128877i
$243$	−7.58913	−	13.6164i	−0.486843	−	0.873490i
$244$		−	8.37831i		−	0.536367i
$245$	−0.616653	+	0.616653i	−0.0393965	+	0.0393965i
$246$	15.4015	−	13.7834i	0.981962	−	0.878798i
$247$	16.2999	+	8.48564i	1.03714	+	0.539928i
$248$			9.33468i			0.592753i
$249$	0.447367	−	8.06911i	0.0283508	−	0.511359i
$250$	−8.05755			−0.509604
$251$	−21.2530			−1.34148			−0.670738	−	0.741694i	$-0.734023\pi$
$251$	−21.2530			−1.34148			−0.670738	+	0.741694i	$0.734023\pi$
$252$	−1.87382	−	2.34282i	−0.118040	−	0.147584i
$253$	−7.02607	+	7.02607i	−0.441725	+	0.441725i
$254$	−15.0861	+	15.0861i	−0.946585	+	0.946585i
$255$	0.448679	−	8.09276i	0.0280974	−	0.506788i
$256$	1.00000			0.0625000
$257$	13.2098			0.824005			0.412002	−	0.911183i	$-0.364830\pi$
$257$	13.2098			0.824005			0.412002	+	0.911183i	$0.364830\pi$
$258$	1.05529	+	0.0585075i	0.0656996	+	0.00364252i
$259$			6.29283i			0.391018i
$260$	−2.78902	−	1.45195i	−0.172967	−	0.0900461i
$261$	8.94524	+	0.994943i	0.553697	+	0.0615854i
$262$	5.77274	−	5.77274i	0.356641	−	0.356641i
$263$			15.8036i			0.974493i	0.873264	+	0.487247i	$0.161999\pi$
$263$			15.8036i			0.974493i	−0.873264	+	0.487247i	$0.838001\pi$
$264$	−4.80074	+	4.29637i	−0.295465	+	0.264424i
$265$	0.286439	−	0.286439i	0.0175958	−	0.0175958i
$266$	−3.60391	−	3.60391i	−0.220970	−	0.220970i
$267$	21.7691	+	1.20692i	1.33225	+	0.0738625i
$268$	1.77932	+	1.77932i	0.108689	+	0.108689i
$269$		−	7.86513i		−	0.479545i	−0.970829	−	0.239773i	$-0.922927\pi$
$269$		−	7.86513i		−	0.479545i	0.970829	−	0.239773i	$-0.0770729\pi$
$270$	2.63014	+	3.69005i	0.160065	+	0.224569i
$271$	7.27480	+	7.27480i	0.441913	+	0.441913i	0.892654	−	0.450742i	$-0.148840\pi$
$271$	7.27480	+	7.27480i	0.441913	+	0.441913i	−0.450742	+	0.892654i	$0.648840\pi$
$272$	5.36595			0.325359
$273$	−6.05082	+	1.54519i	−0.366212	+	0.0935189i
$274$	13.0378			0.787641
$275$	11.1504	+	11.1504i	0.672396	+	0.672396i
$276$	−3.44784	+	3.08561i	−0.207535	+	0.185732i
$277$			15.2302i			0.915091i	0.889186	+	0.457546i	$0.151271\pi$
$277$			15.2302i			0.915091i	−0.889186	+	0.457546i	$0.848729\pi$
$278$	1.76381	+	1.76381i	0.105786	+	0.105786i
$279$	−17.4915	−	21.8695i	−1.04719	−	1.30929i
$280$	0.616653	+	0.616653i	0.0368520	+	0.0368520i
$281$	−19.8714	+	19.8714i	−1.18543	+	1.18543i	−0.207110	+	0.978318i	$0.566406\pi$
$281$	−19.8714	+	19.8714i	−1.18543	+	1.18543i	−0.978318	+	0.207110i	$0.933594\pi$
$282$	−5.65212	−	6.31564i	−0.336579	−	0.376091i
$283$			11.9364i			0.709548i	0.934952	+	0.354774i	$0.115442\pi$
$283$			11.9364i			0.709548i	−0.934952	+	0.354774i	$0.884558\pi$
$284$	0.00980127	−	0.00980127i	0.000581598	−	0.000581598i
$285$	5.13395	+	5.73664i	0.304109	+	0.339809i
$286$	4.03252	+	12.7905i	0.238448	+	0.756320i
$287$			11.9330i			0.704381i
$288$	−2.34282	+	1.87382i	−0.138052	+	0.110416i
$289$	11.7935			0.693733
$290$	−2.61635			−0.153638
$291$	−13.2490	−	0.734552i	−0.776672	−	0.0430602i
$292$	−11.1380	+	11.1380i	−0.651799	+	0.651799i
$293$	12.0322	−	12.0322i	0.702931	−	0.702931i	−0.262108	−	0.965039i	$-0.584418\pi$
$293$	12.0322	−	12.0322i	0.702931	−	0.702931i	0.965039	+	0.262108i	$0.0844175\pi$
$294$	1.72939	+	0.0958811i	0.100860	+	0.00559190i
$295$	11.0189			0.641548
$296$	6.29283			0.365763
$297$	3.19662	−	19.0613i	0.185487	−	1.10605i
$298$			17.4114i			1.00862i
$299$	2.89611	+	9.18602i	0.167486	+	0.531241i
$300$	4.89689	+	5.47175i	0.282722	+	0.315911i
$301$	−0.431483	+	0.431483i	−0.0248703	+	0.0248703i
$302$			4.93447i			0.283947i
$303$	11.2517	+	12.5725i	0.646392	+	0.722273i
$304$	−3.60391	+	3.60391i	−0.206698	+	0.206698i
$305$	−5.16651	−	5.16651i	−0.295833	−	0.295833i
$306$	−12.5715	+	10.0548i	−0.718662	+	0.574796i
$307$	−8.97229	−	8.97229i	−0.512076	−	0.512076i	0.403086	−	0.915162i	$-0.367937\pi$
$307$	−8.97229	−	8.97229i	−0.512076	−	0.512076i	−0.915162	+	0.403086i	$0.867937\pi$
$308$		−	3.71958i		−	0.211943i
$309$	17.8962	−	16.0161i	1.01808	−	0.911123i
$310$	5.75626	+	5.75626i	0.326933	+	0.326933i
$311$	−27.6299			−1.56675			−0.783373	−	0.621551i	$-0.786503\pi$
$311$	−27.6299			−1.56675			−0.783373	+	0.621551i	$0.786503\pi$
$312$	1.54519	+	6.05082i	0.0874790	+	0.342560i
$313$	14.2907			0.807757			0.403878	−	0.914813i	$-0.367662\pi$
$313$	14.2907			0.807757			0.403878	+	0.914813i	$0.367662\pi$
$314$	−0.644468	−	0.644468i	−0.0363694	−	0.0363694i
$315$	−2.60020	−	0.289210i	−0.146505	−	0.0162951i
$316$			6.11811i			0.344170i
$317$	2.71639	+	2.71639i	0.152568	+	0.152568i	0.779264	−	0.626696i	$-0.215593\pi$
$317$	2.71639	+	2.71639i	0.152568	+	0.152568i	−0.626696	+	0.779264i	$0.715593\pi$
$318$	−0.803315	−	0.0445374i	−0.0450477	−	0.00249753i
$319$	7.89078	+	7.89078i	0.441799	+	0.441799i
$320$	0.616653	−	0.616653i	0.0344719	−	0.0344719i
$321$	−3.57682	+	3.20104i	−0.199638	+	0.178665i
$322$		−	2.67136i		−	0.148869i
$323$	−19.3384	+	19.3384i	−1.07602	+	1.07602i
$324$	1.97760	−	8.78004i	0.109867	−	0.487780i
$325$	14.5783	−	4.59616i	0.808658	−	0.254949i
$326$			19.0640i			1.05586i
$327$	5.45190	+	0.302264i	0.301491	+	0.0167152i
$328$	11.9330			0.658888
$329$	4.89332			0.269777
$330$	−0.311016	+	5.60976i	−0.0171209	+	0.308807i
$331$	−10.6402	+	10.6402i	−0.584837	+	0.584837i	−0.936229	−	0.351392i	$-0.885709\pi$
$331$	−10.6402	+	10.6402i	−0.584837	+	0.584837i	0.351392	+	0.936229i	$0.385709\pi$
$332$	3.29926	−	3.29926i	0.181070	−	0.181070i
$333$	−14.7430	+	11.7916i	−0.807910	+	0.646178i
$334$	−6.45750			−0.353339
$335$	2.19445			0.119895
$336$	0.0958811	−	1.72939i	0.00523074	−	0.0943462i
$337$		−	26.4051i		−	1.43838i	−0.694816	−	0.719188i	$-0.744514\pi$
$337$		−	26.4051i		−	1.43838i	0.694816	−	0.719188i	$-0.255486\pi$
$338$	12.8024	+	2.25801i	0.696359	+	0.122819i
$339$	17.8110	−	15.9398i	0.967361	−	0.865731i
$340$	3.30893	−	3.30893i	0.179452	−	0.179452i
$341$		−	34.7211i		−	1.88025i
$342$	1.69023	−	15.1964i	0.0913971	−	0.821725i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	0.431483	+	0.431483i	0.0232640	+	0.0232640i
$345$	−0.223368	+	4.02887i	−0.0120257	+	0.216907i
$346$	−14.5316	−	14.5316i	−0.781221	−	0.781221i
$347$			10.1701i			0.545960i	0.962020	+	0.272980i	$0.0880092\pi$
$347$			10.1701i			0.545960i	−0.962020	+	0.272980i	$0.911991\pi$
$348$	3.46536	+	3.87217i	0.185763	+	0.207570i
$349$	0.699211	+	0.699211i	0.0374279	+	0.0374279i	0.725573	−	0.688145i	$-0.241575\pi$
$349$	0.699211	+	0.699211i	0.0374279	+	0.0374279i	−0.688145	+	0.725573i	$0.741575\pi$
$350$	−4.23948			−0.226610
$351$	−14.9582	−	11.2806i	−0.798411	−	0.602112i
$352$	−3.71958			−0.198254
$353$	−1.42912	−	1.42912i	−0.0760646	−	0.0760646i	0.668051	−	0.744116i	$-0.267129\pi$
$353$	−1.42912	−	1.42912i	−0.0760646	−	0.0760646i	−0.744116	+	0.668051i	$0.767129\pi$
$354$	−14.5946	−	16.3079i	−0.775694	−	0.866755i
$355$		−	0.0120880i		−	0.000641562i
$356$	8.90085	+	8.90085i	0.471744	+	0.471744i
$357$	0.514494	−	9.27985i	0.0272299	−	0.491142i
$358$	8.86263	+	8.86263i	0.468404	+	0.468404i
$359$	9.15856	−	9.15856i	0.483370	−	0.483370i	−0.422836	−	0.906206i	$-0.638965\pi$
$359$	9.15856	−	9.15856i	0.483370	−	0.483370i	0.906206	+	0.422836i	$0.138965\pi$
$360$	−0.289210	+	2.60020i	−0.0152427	+	0.137043i
$361$		−	6.97627i		−	0.367172i
$362$	−9.38608	+	9.38608i	−0.493321	+	0.493321i
$363$	3.65942	−	3.27497i	0.192070	−	0.171891i
$364$	−3.19813	−	1.66493i	−0.167627	−	0.0872661i
$365$			13.7365i			0.719001i
$366$	−0.803322	+	14.4894i	−0.0419903	+	0.757374i
$367$	34.3663			1.79391			0.896953	−	0.442125i	$-0.145775\pi$
$367$	34.3663			1.79391			0.896953	+	0.442125i	$0.145775\pi$
$368$	−2.67136			−0.139254
$369$	−27.9568	+	22.3602i	−1.45537	+	1.16403i
$370$	3.88049	−	3.88049i	0.201737	−	0.201737i
$371$	0.328456	−	0.328456i	0.0170526	−	0.0170526i
$372$	0.895019	−	16.1433i	0.0464046	−	0.836994i
$373$	−27.8414			−1.44157			−0.720787	−	0.693157i	$-0.756219\pi$
$373$	−27.8414			−1.44157			−0.720787	+	0.693157i	$0.756219\pi$
$374$	−19.9591			−1.03206
$375$	13.9347	+	0.772567i	0.719584	+	0.0398952i
$376$		−	4.89332i		−	0.252354i
$377$	10.3166	−	3.25254i	0.531330	−	0.167515i
$378$	3.01594	+	4.23132i	0.155123	+	0.217636i
$379$	−0.998941	+	0.998941i	−0.0513121	+	0.0513121i	−0.732297	−	0.680985i	$-0.761552\pi$
$379$	−0.998941	+	0.998941i	−0.0513121	+	0.0513121i	0.680985	+	0.732297i	$0.261552\pi$
$380$			4.44472i			0.228009i
$381$	27.5363	−	24.6433i	1.41073	−	1.26252i
$382$	2.27012	−	2.27012i	0.116149	−	0.116149i
$383$	−10.4955	−	10.4955i	−0.536296	−	0.536296i	0.386143	−	0.922439i	$-0.373807\pi$
$383$	−10.4955	−	10.4955i	−0.536296	−	0.536296i	−0.922439	+	0.386143i	$0.873807\pi$
$384$	−1.72939	−	0.0958811i	−0.0882528	−	0.00489291i
$385$	−2.29369	−	2.29369i	−0.116897	−	0.116897i
$386$		−	22.9678i		−	1.16903i
$387$	−1.81941	−	0.202365i	−0.0924857	−	0.0102868i
$388$	−5.41720	−	5.41720i	−0.275017	−	0.275017i
$389$	−24.1159			−1.22273			−0.611363	−	0.791350i	$-0.709379\pi$
$389$	−24.1159			−1.22273			−0.611363	+	0.791350i	$0.709379\pi$
$390$	4.68410	+	2.77841i	0.237188	+	0.140690i
$391$	−14.3344			−0.724923
$392$	0.707107	+	0.707107i	0.0357143	+	0.0357143i
$393$	−10.5368	+	9.42985i	−0.531513	+	0.475673i
$394$		−	21.0670i		−	1.06134i
$395$	3.77275	+	3.77275i	0.189827	+	0.189827i
$396$	8.71431	−	6.96983i	0.437911	−	0.350247i
$397$	0.284448	+	0.284448i	0.0142760	+	0.0142760i	0.714209	−	0.699933i	$-0.246787\pi$
$397$	0.284448	+	0.284448i	0.0142760	+	0.0142760i	−0.699933	+	0.714209i	$0.746787\pi$
$398$	−10.7226	+	10.7226i	−0.537473	+	0.537473i
$399$	5.88703	+	6.57812i	0.294720	+	0.329318i
$400$			4.23948i			0.211974i
$401$	−4.67831	+	4.67831i	−0.233623	+	0.233623i	−0.814203	−	0.580580i	$-0.802826\pi$
$401$	−4.67831	+	4.67831i	−0.233623	+	0.233623i	0.580580	+	0.814203i	$0.302826\pi$
$402$	−2.90655	−	3.24775i	−0.144965	−	0.161983i
$403$	−29.8535	−	15.5416i	−1.48711	−	0.774182i
$404$			9.74113i			0.484639i
$405$	−4.19474	−	6.63373i	−0.208438	−	0.329633i
$406$	−3.00014			−0.148894
$407$	−23.4067			−1.16023
$408$	−9.27985	−	0.514494i	−0.459421	−	0.0254712i
$409$	−20.7469	+	20.7469i	−1.02587	+	1.02587i	−0.0262127	+	0.999656i	$0.508345\pi$
$409$	−20.7469	+	20.7469i	−1.02587	+	1.02587i	−0.999656	+	0.0262127i	$0.991655\pi$
$410$	7.35850	−	7.35850i	0.363411	−	0.363411i
$411$	−22.5475	−	1.25008i	−1.11218	−	0.0616617i
$412$	13.8659			0.683124
$413$	12.6353			0.621741
$414$	6.25852	−	5.00565i	0.307590	−	0.246014i
$415$		−	4.06899i		−	0.199739i
$416$	−1.66493	+	3.19813i	−0.0816299	+	0.156801i
$417$	−2.88120	−	3.21943i	−0.141093	−	0.157656i
$418$	13.4050	−	13.4050i	0.655661	−	0.655661i
$419$			19.4610i			0.950732i	0.879788	+	0.475366i	$0.157684\pi$
$419$			19.4610i			0.950732i	−0.879788	+	0.475366i	$0.842316\pi$
$420$	−1.00731	−	1.12556i	−0.0491517	−	0.0549218i
$421$	−12.3696	+	12.3696i	−0.602858	+	0.602858i	−0.941070	−	0.338212i	$-0.890178\pi$
$421$	−12.3696	+	12.3696i	−0.602858	+	0.602858i	0.338212	+	0.941070i	$0.390178\pi$
$422$	−1.76660	−	1.76660i	−0.0859965	−	0.0859965i
$423$	9.16920	+	11.4642i	0.445822	+	0.557407i
$424$	−0.328456	−	0.328456i	−0.0159512	−	0.0159512i
$425$			22.7488i			1.10348i
$426$	−0.0178900	+	0.0160105i	−0.000866774	+	0.000775711i
$427$	−5.92436	−	5.92436i	−0.286700	−	0.286700i
$428$	−2.77130			−0.133956
$429$	−5.74745	−	22.5065i	−0.277490	−	1.08663i
$430$	0.532150			0.0256626
$431$	8.30885	+	8.30885i	0.400223	+	0.400223i	0.878312	−	0.478088i	$-0.158670\pi$
$431$	8.30885	+	8.30885i	0.400223	+	0.400223i	−0.478088	+	0.878312i	$0.658670\pi$
$432$	4.23132	−	3.01594i	0.203580	−	0.145105i
$433$			9.90076i			0.475800i	0.971290	+	0.237900i	$0.0764591\pi$
$433$			9.90076i			0.475800i	−0.971290	+	0.237900i	$0.923541\pi$
$434$	6.60062	+	6.60062i	0.316840	+	0.316840i
$435$	4.52471	+	0.250859i	0.216943	+	0.0120278i
$436$	2.22915	+	2.22915i	0.106757	+	0.106757i
$437$	9.62734	−	9.62734i	0.460538	−	0.460538i
$438$	20.3298	−	18.1940i	0.971397	−	0.869343i
$439$		−	16.7403i		−	0.798972i	−0.916739	−	0.399486i	$-0.869189\pi$
$439$		−	16.7403i		−	0.798972i	0.916739	−	0.399486i	$-0.130811\pi$
$440$	−2.29369	+	2.29369i	−0.109347	+	0.109347i
$441$	−2.98161	−	0.331633i	−0.141982	−	0.0157920i
$442$	−8.93394	+	17.1610i	−0.424944	+	0.816265i
$443$		−	7.56632i		−	0.359487i	−0.983714	−	0.179743i	$-0.942473\pi$
$443$		−	7.56632i		−	0.359487i	0.983714	−	0.179743i	$-0.0575267\pi$
$444$	−10.8828	−	0.603364i	−0.516474	−	0.0286344i
$445$	10.9775			0.520382
$446$	−9.38537			−0.444410
$447$	1.66943	−	30.1113i	0.0789612	−	1.42421i
$448$	0.707107	−	0.707107i	0.0334077	−	0.0334077i
$449$	12.1480	−	12.1480i	0.573301	−	0.573301i	−0.359748	−	0.933049i	$-0.617137\pi$
$449$	12.1480	−	12.1480i	0.573301	−	0.573301i	0.933049	+	0.359748i	$0.117137\pi$
$450$	−7.94402	−	9.93233i	−0.374485	−	0.468215i
$451$	−44.3857			−2.09004
$452$	13.7999			0.649091
$453$	0.473122	−	8.53365i	0.0222292	−	0.400946i
$454$			12.3864i			0.581322i
$455$	−2.99882	+	0.945448i	−0.140587	+	0.0443233i
$456$	6.57812	−	5.88703i	0.308049	−	0.275685i
$457$	17.0229	−	17.0229i	0.796296	−	0.796296i	−0.186213	−	0.982509i	$-0.559621\pi$
$457$	17.0229	−	17.0229i	0.796296	−	0.796296i	0.982509	+	0.186213i	$0.0596215\pi$
$458$		−	6.00307i		−	0.280505i
$459$	22.7051	−	16.1834i	1.05978	−	0.755377i
$460$	−1.64730	+	1.64730i	−0.0768059	+	0.0768059i
$461$	−4.28202	−	4.28202i	−0.199434	−	0.199434i	0.600324	−	0.799757i	$-0.295038\pi$
$461$	−4.28202	−	4.28202i	−0.199434	−	0.199434i	−0.799757	+	0.600324i	$0.795038\pi$
$462$	−0.356638	+	6.43263i	−0.0165923	+	0.299273i
$463$	−14.6083	−	14.6083i	−0.678904	−	0.678904i	0.280848	−	0.959752i	$-0.409384\pi$
$463$	−14.6083	−	14.6083i	−0.678904	−	0.678904i	−0.959752	+	0.280848i	$0.909384\pi$
$464$			3.00014i			0.139278i
$465$	−9.40292	−	10.5068i	−0.436050	−	0.487239i
$466$	−4.11378	−	4.11378i	−0.190567	−	0.190567i
$467$	31.2477			1.44597			0.722985	−	0.690864i	$-0.242770\pi$
$467$	31.2477			1.44597			0.722985	+	0.690864i	$0.242770\pi$
$468$	−2.09208	−	10.6124i	−0.0967064	−	0.490559i
$469$	2.51634			0.116194
$470$	−3.01748	−	3.01748i	−0.139186	−	0.139186i
$471$	1.05275	+	1.17633i	0.0485080	+	0.0542025i
$472$		−	12.6353i		−	0.581585i
$473$	−1.60494	−	1.60494i	−0.0737951	−	0.0737951i
$474$	0.586611	−	10.5806i	0.0269439	−	0.485984i
$475$	−15.2787	−	15.2787i	−0.701034	−	0.701034i
$476$	3.79430	−	3.79430i	0.173912	−	0.173912i
$477$	1.38498	+	0.154046i	0.0634138	+	0.00705326i
$478$			8.76067i			0.400704i
$479$	−10.8416	+	10.8416i	−0.495365	+	0.495365i	−0.909992	−	0.414627i	$-0.863912\pi$
$479$	−10.8416	+	10.8416i	−0.495365	+	0.495365i	0.414627	+	0.909992i	$0.363912\pi$
$480$	−1.12556	+	1.00731i	−0.0513746	+	0.0459772i
$481$	−10.4771	+	20.1253i	−0.477716	+	0.917633i
$482$		−	27.2226i		−	1.23996i
$483$	−0.256133	+	4.61984i	−0.0116545	+	0.210210i
$484$	2.83530			0.128877
$485$	−6.68106			−0.303371
$486$	−4.26189	+	14.9945i	−0.193323	+	0.680166i
$487$	17.7146	−	17.7146i	0.802727	−	0.802727i	−0.180794	−	0.983521i	$-0.557867\pi$
$487$	17.7146	−	17.7146i	0.802727	−	0.802727i	0.983521	+	0.180794i	$0.0578669\pi$
$488$	−5.92436	+	5.92436i	−0.268183	+	0.268183i
$489$	1.82788	−	32.9692i	0.0826595	−	1.49092i
$490$	0.872079			0.0393965
$491$	−8.91977			−0.402543			−0.201272	−	0.979535i	$-0.564507\pi$
$491$	−8.91977			−0.402543			−0.201272	+	0.979535i	$0.564507\pi$
$492$	−20.6368	−	1.14415i	−0.930380	−	0.0515821i
$493$			16.0986i			0.725044i
$494$	−5.52549	−	17.5260i	−0.248603	−	0.788532i
$495$	1.07574	−	9.67166i	0.0483509	−	0.434709i
$496$	6.60062	−	6.60062i	0.296376	−	0.296376i
$497$		−	0.0138611i		−	0.000621755i
$498$	−6.02206	+	5.38938i	−0.269855	+	0.241504i
$499$	−20.1012	+	20.1012i	−0.899854	+	0.899854i	−0.995423	−	0.0955687i	$-0.969533\pi$
$499$	−20.1012	+	20.1012i	−0.899854	+	0.899854i	0.0955687	+	0.995423i	$0.469533\pi$
$500$	5.69755	+	5.69755i	0.254802	+	0.254802i
$501$	11.1676	+	0.619153i	0.498930	+	0.0276617i
$502$	15.0281	+	15.0281i	0.670738	+	0.670738i
$503$			1.38296i			0.0616631i	0.999525	+	0.0308316i	$0.00981554\pi$
$503$			1.38296i			0.0616631i	−0.999525	+	0.0308316i	$0.990184\pi$
$504$	−0.331633	+	2.98161i	−0.0147721	+	0.132812i
$505$	6.00689	+	6.00689i	0.267303	+	0.267303i
$506$	9.93636			0.441725
$507$	−21.9239	−	5.13249i	−0.973675	−	0.227942i
$508$	21.3350			0.946585
$509$	15.7238	+	15.7238i	0.696947	+	0.696947i	0.963751	−	0.266804i	$-0.0859676\pi$
$509$	15.7238	+	15.7238i	0.696947	+	0.696947i	−0.266804	+	0.963751i	$0.585968\pi$
$510$	−6.03971	+	5.40518i	−0.267443	+	0.239346i
$511$			15.7514i			0.696803i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−4.38012	+	26.1185i	−0.193387	+	1.15316i
$514$	−9.34074	−	9.34074i	−0.412002	−	0.412002i
$515$	8.55045	−	8.55045i	0.376778	−	0.376778i
$516$	−0.704833	−	0.787575i	−0.0310286	−	0.0346711i
$517$			18.2011i			0.800484i
$518$	4.44970	−	4.44970i	0.195509	−	0.195509i
$519$	23.7375	+	26.5241i	1.04196	+	1.16428i
$520$	0.945448	+	2.99882i	0.0414607	+	0.131507i
$521$			24.0452i			1.05344i	0.850039	+	0.526720i	$0.176578\pi$
$521$			24.0452i			1.05344i	−0.850039	+	0.526720i	$0.823422\pi$
$522$	−5.62171	−	7.02877i	−0.246056	−	0.307641i
$523$	−11.7120			−0.512132			−0.256066	−	0.966659i	$-0.582426\pi$
$523$	−11.7120			−0.512132			−0.256066	+	0.966659i	$0.582426\pi$
$524$	−8.16389			−0.356641
$525$	7.33173	+	0.406486i	0.319983	+	0.0177405i
$526$	11.1748	−	11.1748i	0.487247	−	0.487247i
$527$	35.4186	−	35.4186i	1.54286	−	1.54286i
$528$	6.43263	+	0.356638i	0.279944	+	0.0155207i
$529$	−15.8638			−0.689731
$530$	−0.405086			−0.0175958
$531$	23.6762	+	29.6021i	1.02746	+	1.28462i
$532$			5.09669i			0.220970i
$533$	−19.8676	+	38.1632i	−0.860561	+	1.65303i
$534$	−14.5397	−	16.2465i	−0.629193	−	0.703055i
$535$	−1.70893	+	1.70893i	−0.0738834	+	0.0738834i
$536$		−	2.51634i		−	0.108689i
$537$	−14.4772	−	16.1767i	−0.624738	−	0.698078i
$538$	−5.56149	+	5.56149i	−0.239773	+	0.239773i
$539$	−2.63014	−	2.63014i	−0.113288	−	0.113288i
$540$	0.749468	−	4.46905i	0.0322520	−	0.192317i
$541$	1.33026	+	1.33026i	0.0571925	+	0.0571925i	0.735125	−	0.677932i	$-0.237124\pi$
$541$	1.33026	+	1.33026i	0.0571925	+	0.0571925i	−0.677932	+	0.735125i	$0.737124\pi$
$542$		−	10.2881i		−	0.441913i
$543$	17.1322	−	15.3323i	0.735213	−	0.657972i
$544$	−3.79430	−	3.79430i	−0.162679	−	0.162679i
$545$	2.74922			0.117764
$546$	5.37119	+	3.18596i	0.229866	+	0.136347i
$547$	−13.7724			−0.588865			−0.294433	−	0.955672i	$-0.595131\pi$
$547$	−13.7724			−0.588865			−0.294433	+	0.955672i	$0.595131\pi$
$548$	−9.21910	−	9.21910i	−0.393821	−	0.393821i
$549$	2.77852	−	24.9809i	0.118584	−	1.06616i
$550$		−	15.7691i		−	0.672396i
$551$	−10.8122	−	10.8122i	−0.460615	−	0.460615i
$552$	4.61984	+	0.256133i	0.196634	+	0.0109018i
$553$	4.32615	+	4.32615i	0.183967	+	0.183967i
$554$	10.7693	−	10.7693i	0.457546	−	0.457546i
$555$	−7.08297	+	6.33884i	−0.300655	+	0.269069i
$556$		−	2.49440i		−	0.105786i
$557$	−17.7921	+	17.7921i	−0.753876	+	0.753876i	−0.975200	−	0.221324i	$-0.928962\pi$
$557$	−17.7921	+	17.7921i	−0.753876	+	0.753876i	0.221324	+	0.975200i	$0.428962\pi$
$558$	−3.09568	+	27.8324i	−0.131051	+	1.17824i
$559$	−2.09833	+	0.661547i	−0.0887497	+	0.0279805i
$560$		−	0.872079i		−	0.0368520i
$561$	34.5172	+	1.91370i	1.45732	+	0.0807965i
$562$	28.1024			1.18543
$563$	2.64079			0.111296			0.0556480	−	0.998450i	$-0.482278\pi$
$563$	2.64079			0.111296			0.0556480	+	0.998450i	$0.482278\pi$
$564$	−0.469177	+	8.46248i	−0.0197559	+	0.356335i
$565$	8.50973	−	8.50973i	0.358007	−	0.358007i
$566$	8.44034	−	8.44034i	0.354774	−	0.354774i
$567$	−4.81005	−	7.60680i	−0.202003	−	0.319456i
$568$	−0.0138611			−0.000581598
$569$	−1.57360			−0.0659689			−0.0329844	−	0.999456i	$-0.510501\pi$
$569$	−1.57360			−0.0659689			−0.0329844	+	0.999456i	$0.510501\pi$
$570$	0.426164	−	7.68667i	0.0178501	−	0.321959i
$571$		−	13.0500i		−	0.546126i	−0.961996	−	0.273063i	$-0.911963\pi$
$571$		−	13.0500i		−	0.546126i	0.961996	−	0.273063i	$-0.0880367\pi$
$572$	6.19285	−	11.8957i	0.258936	−	0.497384i
$573$	−4.14360	+	3.70827i	−0.173101	+	0.154915i
$574$	8.43789	−	8.43789i	0.352191	−	0.352191i
$575$		−	11.3252i		−	0.472293i
$576$	2.98161	+	0.331633i	0.124234	+	0.0138180i
$577$	30.4816	−	30.4816i	1.26896	−	1.26896i	0.322340	−	0.946624i	$-0.395531\pi$
$577$	30.4816	−	30.4816i	1.26896	−	1.26896i	0.946624	−	0.322340i	$-0.104469\pi$
$578$	−8.33924	−	8.33924i	−0.346867	−	0.346867i
$579$	−2.20218	+	39.7204i	−0.0915195	+	1.65072i
$580$	1.85004	+	1.85004i	0.0768188	+	0.0768188i
$581$		−	4.66586i		−	0.193572i
$582$	8.84907	+	9.88788i	0.366806	+	0.409866i
$583$	1.22172	+	1.22172i	0.0505984	+	0.0505984i
$584$	15.7514			0.651799
$585$	−7.83426	−	5.25408i	−0.323907	−	0.217230i
$586$	−17.0162			−0.702931
$587$	8.10578	+	8.10578i	0.334561	+	0.334561i	0.854316	−	0.519754i	$-0.173977\pi$
$587$	8.10578	+	8.10578i	0.334561	+	0.334561i	−0.519754	+	0.854316i	$0.673977\pi$
$588$	−1.15507	−	1.29067i	−0.0476342	−	0.0532261i
$589$			47.5760i			1.96033i
$590$	−7.79157	−	7.79157i	−0.320774	−	0.320774i
$591$	−2.01992	+	36.4331i	−0.0830886	+	1.49866i
$592$	−4.44970	−	4.44970i	−0.182882	−	0.182882i
$593$	17.6343	−	17.6343i	0.724154	−	0.724154i	−0.245295	−	0.969449i	$-0.578885\pi$
$593$	17.6343	−	17.6343i	0.724154	−	0.724154i	0.969449	+	0.245295i	$0.0788847\pi$
$594$	−15.7388	+	11.2180i	−0.645769	+	0.460282i
$595$		−	4.67953i		−	0.191842i
$596$	12.3117	−	12.3117i	0.504309	−	0.504309i
$597$	19.5716	−	17.5154i	0.801013	−	0.716859i
$598$	4.44764	−	8.54336i	0.181877	−	0.349364i
$599$			22.8023i			0.931675i	0.884870	+	0.465838i	$0.154247\pi$
$599$			22.8023i			0.931675i	−0.884870	+	0.465838i	$0.845753\pi$
$600$	0.406486	−	7.33173i	0.0165947	−	0.299317i
$601$	10.1241			0.412970			0.206485	−	0.978450i	$-0.433798\pi$
$601$	10.1241			0.412970			0.206485	+	0.978450i	$0.433798\pi$
$602$	0.610209			0.0248703
$603$	4.71517	+	5.89533i	0.192017	+	0.240076i
$604$	3.48920	−	3.48920i	0.141973	−	0.141973i
$605$	1.74839	−	1.74839i	0.0710824	−	0.0710824i
$606$	0.933990	−	16.8463i	0.0379407	−	0.684332i
$607$	−30.2863			−1.22928			−0.614642	−	0.788806i	$-0.710699\pi$
$607$	−30.2863			−1.22928			−0.614642	+	0.788806i	$0.710699\pi$
$608$	5.09669			0.206698
$609$	5.18842	+	0.287656i	0.210245	+	0.0116564i
$610$			7.30655i			0.295833i
$611$	15.6494	+	8.14704i	0.633109	+	0.329594i
$612$	15.9992	+	1.77952i	0.646729	+	0.0719330i
$613$	15.8557	−	15.8557i	0.640406	−	0.640406i	−0.310249	−	0.950655i	$-0.600412\pi$
$613$	15.8557	−	15.8557i	0.640406	−	0.640406i	0.950655	+	0.310249i	$0.100412\pi$
$614$			12.6887i			0.512076i
$615$	−13.4313	+	12.0202i	−0.541602	+	0.484702i
$616$	−2.63014	+	2.63014i	−0.105971	+	0.105971i
$617$	−9.52955	−	9.52955i	−0.383645	−	0.383645i	0.488768	−	0.872414i	$-0.337446\pi$
$617$	−9.52955	−	9.52955i	−0.383645	−	0.383645i	−0.872414	+	0.488768i	$0.837446\pi$
$618$	−23.9796	−	1.32948i	−0.964602	−	0.0534795i
$619$	8.43686	+	8.43686i	0.339106	+	0.339106i	0.856031	−	0.516925i	$-0.172923\pi$
$619$	8.43686	+	8.43686i	0.339106	+	0.339106i	−0.516925	+	0.856031i	$0.672923\pi$
$620$		−	8.14057i		−	0.326933i
$621$	−11.3034	+	8.05668i	−0.453590	+	0.323303i
$622$	19.5373	+	19.5373i	0.783373	+	0.783373i
$623$	12.5877			0.504316
$624$	3.18596	−	5.37119i	0.127541	−	0.215020i
$625$	−14.1706			−0.566823
$626$	−10.1050	−	10.1050i	−0.403878	−	0.403878i
$627$	−24.4679	+	21.8973i	−0.977153	+	0.874494i
$628$			0.911415i			0.0363694i
$629$	−23.8769	−	23.8769i	−0.952035	−	0.952035i
$630$	1.63412	+	2.04312i	0.0651048	+	0.0813999i
$631$	6.47280	+	6.47280i	0.257678	+	0.257678i	0.824109	−	0.566431i	$-0.191676\pi$
$631$	6.47280	+	6.47280i	0.257678	+	0.257678i	−0.566431	+	0.824109i	$0.691676\pi$
$632$	4.32615	−	4.32615i	0.172085	−	0.172085i
$633$	2.88576	+	3.22452i	0.114699	+	0.128163i
$634$		−	3.84155i		−	0.152568i
$635$	13.1563	−	13.1563i	0.522090	−	0.522090i
$636$	0.536537	+	0.599522i	0.0212751	+	0.0237726i
$637$	−3.43870	+	1.08413i	−0.136246	+	0.0429549i
$638$		−	11.1593i		−	0.441799i
$639$	0.0324740	−	0.0259732i	0.00128465	−	0.00102748i
$640$	−0.872079			−0.0344719
$641$	−9.04638			−0.357311			−0.178655	−	0.983912i	$-0.557175\pi$
$641$	−9.04638			−0.357311			−0.178655	+	0.983912i	$0.557175\pi$
$642$	4.79267	+	0.265715i	0.189151	+	0.0104869i
$643$	21.3385	−	21.3385i	0.841508	−	0.841508i	−0.147547	−	0.989055i	$-0.547138\pi$
$643$	21.3385	−	21.3385i	0.841508	−	0.841508i	0.989055	+	0.147547i	$0.0471378\pi$
$644$	−1.88894	+	1.88894i	−0.0744347	+	0.0744347i
$645$	−0.920298	−	0.0510231i	−0.0362367	−	0.00200903i
$646$	27.3486			1.07602
$647$	23.9618			0.942037			0.471018	−	0.882123i	$-0.343887\pi$
$647$	23.9618			0.942037			0.471018	+	0.882123i	$0.343887\pi$
$648$	−7.60680	+	4.81005i	−0.298823	+	0.188957i
$649$			46.9979i			1.84483i
$650$	−13.5584	−	7.05844i	−0.531804	−	0.276855i
$651$	−10.7822	−	12.0479i	−0.422588	−	0.472196i
$652$	13.4803	−	13.4803i	0.527929	−	0.527929i
$653$		−	16.8655i		−	0.659997i	−0.943981	−	0.329998i	$-0.892952\pi$
$653$		−	16.8655i		−	0.659997i	0.943981	−	0.329998i	$-0.107048\pi$
$654$	−3.64134	−	4.06881i	−0.142388	−	0.159103i
$655$	−5.03428	+	5.03428i	−0.196706	+	0.196706i
$656$	−8.43789	−	8.43789i	−0.329444	−	0.329444i
$657$	−36.9028	+	29.5154i	−1.43971	+	1.15150i
$658$	−3.46010	−	3.46010i	−0.134889	−	0.134889i
$659$			23.3034i			0.907773i	0.891060	+	0.453886i	$0.149963\pi$
$659$			23.3034i			0.907773i	−0.891060	+	0.453886i	$0.850037\pi$
$660$	4.18662	−	3.74678i	0.162964	−	0.145843i
$661$	−33.0664	−	33.0664i	−1.28613	−	1.28613i	−0.937116	−	0.349019i	$-0.886515\pi$
$661$	−33.0664	−	33.0664i	−1.28613	−	1.28613i	−0.349019	−	0.937116i	$-0.613485\pi$
$662$	15.0475			0.584837
$663$	17.0957	−	28.8215i	0.663943	−	1.11934i
$664$	−4.66586			−0.181070
$665$	3.14289	+	3.14289i	0.121876	+	0.121876i
$666$	18.7628	+	2.08691i	0.727044	+	0.0808660i
$667$		−	8.01445i		−	0.310321i
$668$	4.56615	+	4.56615i	0.176669	+	0.176669i
$669$	16.2310	+	0.899879i	0.627527	+	0.0347913i
$670$	−1.55171	−	1.55171i	−0.0599477	−	0.0599477i
$671$	22.0362	−	22.0362i	0.850696	−	0.850696i
$672$	−1.29067	+	1.15507i	−0.0497885	+	0.0445577i
$673$			27.1641i			1.04710i	0.851996	+	0.523549i	$0.175392\pi$
$673$			27.1641i			1.04710i	−0.851996	+	0.523549i	$0.824608\pi$
$674$	−18.6712	+	18.6712i	−0.719188	+	0.719188i
$675$	12.7860	+	17.9386i	0.492134	+	0.690457i
$676$	−7.45601	−	10.6493i	−0.286770	−	0.409589i
$677$			21.1789i			0.813969i	0.913435	+	0.406985i	$0.133420\pi$
$677$			21.1789i			0.813969i	−0.913435	+	0.406985i	$0.866580\pi$
$678$	−23.8654	−	1.32315i	−0.916546	−	0.0508151i
$679$	−7.66107			−0.294005
$680$	−4.67953			−0.179452
$681$	1.18762	−	21.4210i	0.0455097	−	0.820853i
$682$	−24.5515	+	24.5515i	−0.940127	+	0.940127i
$683$	16.6542	−	16.6542i	0.637256	−	0.637256i	−0.312622	−	0.949878i	$-0.601207\pi$
$683$	16.6542	−	16.6542i	0.637256	−	0.637256i	0.949878	+	0.312622i	$0.101207\pi$
$684$	−11.9406	+	9.55028i	−0.456561	+	0.365164i
$685$	−11.3700			−0.434424
$686$	1.00000			0.0381802
$687$	−0.575581	+	10.3817i	−0.0219598	+	0.396086i
$688$		−	0.610209i		−	0.0232640i
$689$	1.59730	−	0.503587i	0.0608522	−	0.0191851i
$690$	3.00678	−	2.69089i	0.114466	−	0.102441i
$691$	−12.0327	+	12.0327i	−0.457746	+	0.457746i	−0.897915	−	0.440169i	$-0.854919\pi$
$691$	−12.0327	+	12.0327i	−0.457746	+	0.457746i	0.440169	+	0.897915i	$0.354919\pi$
$692$			20.5507i			0.781221i
$693$	1.23353	−	11.0904i	0.0468581	−	0.421288i
$694$	7.19135	−	7.19135i	0.272980	−	0.272980i
$695$	−1.53818	−	1.53818i	−0.0583464	−	0.0583464i
$696$	0.287656	−	5.18842i	0.0109036	−	0.196667i
$697$	−45.2773	−	45.2773i	−1.71500	−	1.71500i
$698$		−	0.988833i		−	0.0374279i
$699$	6.71991	+	7.50878i	0.254170	+	0.284008i
$700$	2.99776	+	2.99776i	0.113305	+	0.113305i
$701$	−46.7003			−1.76385			−0.881923	−	0.471393i	$-0.843751\pi$
$701$	−46.7003			−1.76385			−0.881923	+	0.471393i	$0.843751\pi$
$702$	2.60050	+	18.5536i	0.0981496	+	0.700262i
$703$	32.0726			1.20964
$704$	2.63014	+	2.63014i	0.0991272	+	0.0991272i
$705$	4.92909	+	5.50773i	0.185640	+	0.207433i
$706$			2.02109i			0.0760646i
$707$	6.88802	+	6.88802i	0.259051	+	0.259051i
$708$	−1.21148	+	21.8514i	−0.0455303	+	0.821224i
$709$	−23.8602	−	23.8602i	−0.896089	−	0.896089i	0.0989984	−	0.995088i	$-0.468436\pi$
$709$	−23.8602	−	23.8602i	−0.896089	−	0.896089i	−0.995088	+	0.0989984i	$0.968436\pi$
$710$	−0.00854747	+	0.00854747i	−0.000320781	+	0.000320781i
$711$	−2.02896	+	18.2418i	−0.0760921	+	0.684122i
$712$		−	12.5877i		−	0.471744i
$713$	−17.6326	+	17.6326i	−0.660348	+	0.660348i
$714$	−6.92565	+	6.19805i	−0.259186	+	0.231956i
$715$	−3.51667	−	11.1543i	−0.131516	−	0.417149i
$716$		−	12.5336i		−	0.468404i
$717$	0.839982	−	15.1507i	0.0313697	−	0.565812i
$718$	−12.9522			−0.483370
$719$	−18.8987			−0.704802			−0.352401	−	0.935849i	$-0.614635\pi$
$719$	−18.8987			−0.704802			−0.352401	+	0.935849i	$0.614635\pi$
$720$	2.04312	−	1.63412i	0.0761427	−	0.0609000i
$721$	9.80468	−	9.80468i	0.365145	−	0.365145i
$722$	−4.93297	+	4.93297i	−0.183586	+	0.183586i
$723$	−2.61014	+	47.0787i	−0.0970720	+	1.75088i
$724$	13.2739			0.493321
$725$	−12.7190			−0.472372
$726$	−4.90335	−	0.271852i	−0.181980	−	0.0100894i
$727$			9.73860i			0.361185i	0.983558	+	0.180592i	$0.0578015\pi$
$727$			9.73860i			0.361185i	−0.983558	+	0.180592i	$0.942199\pi$
$728$	1.08413	+	3.43870i	0.0401806	+	0.127447i
$729$	8.80819	−	25.5228i	0.326229	−	0.945291i
$730$	9.71317	−	9.71317i	0.359500	−	0.359500i
$731$		−	3.27435i		−	0.121106i
$732$	10.8136	−	9.67753i	0.399682	−	0.357692i
$733$	2.79274	−	2.79274i	0.103152	−	0.103152i	−0.653647	−	0.756799i	$-0.726762\pi$
$733$	2.79274	−	2.79274i	0.103152	−	0.103152i	0.756799	+	0.653647i	$0.226762\pi$
$734$	−24.3006	−	24.3006i	−0.896953	−	0.896953i
$735$	−1.50817	−	0.0836158i	−0.0556296	−	0.00308422i
$736$	1.88894	+	1.88894i	0.0696272	+	0.0696272i
$737$			9.35974i			0.344770i
$738$	35.5795	+	3.95736i	1.30970	+	0.145673i
$739$	−4.29662	−	4.29662i	−0.158054	−	0.158054i	0.623650	−	0.781704i	$-0.285649\pi$
$739$	−4.29662	−	4.29662i	−0.158054	−	0.158054i	−0.781704	+	0.623650i	$0.785649\pi$
$740$	−5.48784			−0.201737
$741$	7.87534	+	30.8392i	0.289308	+	1.13290i
$742$	−0.464507			−0.0170526
$743$	−26.3150	−	26.3150i	−0.965406	−	0.965406i	0.0340158	−	0.999421i	$-0.489170\pi$
$743$	−26.3150	−	26.3150i	−0.965406	−	0.965406i	−0.999421	+	0.0340158i	$0.989170\pi$
$744$	−12.0479	+	10.7822i	−0.441699	+	0.395295i
$745$		−	15.1841i		−	0.556304i
$746$	19.6868	+	19.6868i	0.720787	+	0.720787i
$747$	10.9313	−	8.74297i	0.399954	−	0.319889i
$748$	14.1132	+	14.1132i	0.516031	+	0.516031i
$749$	−1.95960	+	1.95960i	−0.0716023	+	0.0716023i
$750$	−9.30703	−	10.3996i	−0.339845	−	0.379740i
$751$		−	39.0092i		−	1.42347i	−0.702450	−	0.711733i	$-0.747910\pi$
$751$		−	39.0092i		−	1.42347i	0.702450	−	0.711733i	$-0.252090\pi$
$752$	−3.46010	+	3.46010i	−0.126177	+	0.126177i
$753$	−24.5487	−	27.4305i	−0.894603	−	0.999623i
$754$	−9.59481	−	4.99502i	−0.349422	−	0.181908i
$755$		−	4.30325i		−	0.156611i
$756$	0.859404	−	5.12459i	0.0312562	−	0.186380i
$757$	−25.7810			−0.937025			−0.468513	−	0.883457i	$-0.655210\pi$
$757$	−25.7810			−0.937025			−0.468513	+	0.883457i	$0.655210\pi$
$758$	1.41272			0.0513121
$759$	−17.1839	−	0.952709i	−0.623736	−	0.0345812i
$760$	3.14289	−	3.14289i	0.114005	−	0.114005i
$761$	−16.8635	+	16.8635i	−0.611300	+	0.611300i	−0.943285	−	0.331985i	$-0.892282\pi$
$761$	−16.8635	+	16.8635i	−0.611300	+	0.611300i	0.331985	+	0.943285i	$0.392282\pi$
$762$	−36.8966	−	2.04562i	−1.33662	−	0.0741049i
$763$	3.15249			0.114128
$764$	−3.21043			−0.116149
$765$	10.9633	−	8.76860i	0.396379	−	0.317029i
$766$			14.8429i			0.536296i
$767$	40.4092	+	21.0368i	1.45909	+	0.759596i
$768$	1.15507	+	1.29067i	0.0416800	+	0.0465729i
$769$	−29.5659	+	29.5659i	−1.06617	+	1.06617i	−0.0685256	+	0.997649i	$0.521829\pi$
$769$	−29.5659	+	29.5659i	−1.06617	+	1.06617i	−0.997649	+	0.0685256i	$0.978171\pi$
$770$			3.24377i			0.116897i
$771$	15.2582	+	17.0494i	0.549512	+	0.614020i
$772$	−16.2407	+	16.2407i	−0.584516	+	0.584516i
$773$	16.1450	+	16.1450i	0.580696	+	0.580696i	0.935095	−	0.354398i	$-0.115314\pi$
$773$	16.1450	+	16.1450i	0.580696	+	0.580696i	−0.354398	+	0.935095i	$0.615314\pi$
$774$	1.14342	+	1.42961i	0.0410994	+	0.0513862i
$775$	27.9832	+	27.9832i	1.00519	+	1.00519i
$776$			7.66107i			0.275017i
$777$	−8.12194	+	7.26865i	−0.291373	+	0.260762i
$778$	17.0525	+	17.0525i	0.611363	+	0.611363i
$779$	60.8187			2.17906
$780$	−1.34752	−	5.27679i	−0.0482491	−	0.188939i
$781$	0.0515575			0.00184487
$782$	10.1360	+	10.1360i	0.362461	+	0.362461i
$783$	9.04824	+	12.6945i	0.323358	+	0.453666i
$784$		−	1.00000i		−	0.0357143i
$785$	0.562026	+	0.562026i	0.0200596	+	0.0200596i
$786$	14.1186	+	0.782762i	0.503593	+	0.0279202i
$787$	11.6387	+	11.6387i	0.414876	+	0.414876i	0.883433	−	0.468557i	$-0.155226\pi$
$787$	11.6387	+	11.6387i	0.414876	+	0.414876i	−0.468557	+	0.883433i	$0.655226\pi$
$788$	−14.8966	+	14.8966i	−0.530670	+	0.530670i
$789$	−20.3972	+	18.2543i	−0.726159	+	0.649869i
$790$		−	5.33547i		−	0.189827i
$791$	9.75798	−	9.75798i	0.346954	−	0.346954i
$792$	−11.0904	−	1.23353i	−0.394079	−	0.0438318i
$793$	−9.08320	−	28.8105i	−0.322554	−	1.02309i
$794$		−	0.402270i		−	0.0142760i
$795$	0.700554	+	0.0388401i	0.0248461	+	0.00137752i
$796$	15.1640			0.537473
$797$	35.2474			1.24853			0.624264	−	0.781214i	$-0.285399\pi$
$797$	35.2474			1.24853			0.624264	+	0.781214i	$0.285399\pi$
$798$	0.488676	−	8.81419i	0.0172990	−	0.312019i
$799$	−18.5667	+	18.5667i	−0.656844	+	0.656844i
$800$	2.99776	−	2.99776i	0.105987	−	0.105987i
$801$	23.5871	+	29.4907i	0.833409	+	1.04200i
$802$	6.61612			0.233623
$803$	−58.5888			−2.06755
$804$	−0.241270	+	4.35175i	−0.00850892	+	0.153474i
$805$			2.32964i			0.0821090i
$806$	10.1200	+	32.0992i	0.356463	+	1.13064i
$807$	10.1512	−	9.08477i	0.357341	−	0.319799i
$808$	6.88802	−	6.88802i	0.242320	−	0.242320i
$809$		−	52.9887i		−	1.86298i	−0.363761	−	0.931492i	$-0.618508\pi$
$809$		−	52.9887i		−	1.86298i	0.363761	−	0.931492i	$-0.381492\pi$
$810$	−1.72462	+	7.65688i	−0.0605971	+	0.269035i
$811$	4.32230	−	4.32230i	0.151777	−	0.151777i	−0.627134	−	0.778911i	$-0.715772\pi$
$811$	4.32230	−	4.32230i	0.151777	−	0.151777i	0.778911	+	0.627134i	$0.215772\pi$
$812$	2.12142	+	2.12142i	0.0744471	+	0.0744471i
$813$	−0.986437	+	17.7922i	−0.0345958	+	0.624001i
$814$	16.5510	+	16.5510i	0.580114	+	0.580114i
$815$		−	16.6253i		−	0.582359i
$816$	6.19805	+	6.92565i	0.216975	+	0.242446i
$817$	2.19914	+	2.19914i	0.0769380	+	0.0769380i
$818$	29.3406			1.02587
$819$	−8.98343	−	6.02478i	−0.313906	−	0.210523i
$820$	−10.4065			−0.363411
$821$	−16.6689	−	16.6689i	−0.581747	−	0.581747i	0.353636	−	0.935383i	$-0.384945\pi$
$821$	−16.6689	−	16.6689i	−0.581747	−	0.581747i	−0.935383	+	0.353636i	$0.884945\pi$
$822$	15.0595	+	16.8274i	0.525261	+	0.586923i
$823$		−	2.89381i		−	0.100872i	−0.998727	−	0.0504359i	$-0.983939\pi$
$823$		−	2.89381i		−	0.100872i	0.998727	−	0.0504359i	$-0.0160611\pi$
$824$	−9.80468	−	9.80468i	−0.341562	−	0.341562i
$825$	−1.51196	+	27.2710i	−0.0526396	+	0.949454i
$826$	−8.93448	−	8.93448i	−0.310870	−	0.310870i
$827$	−22.3134	+	22.3134i	−0.775914	+	0.775914i	−0.979133	−	0.203219i	$-0.934860\pi$
$827$	−22.3134	+	22.3134i	−0.775914	+	0.775914i	0.203219	+	0.979133i	$0.434860\pi$
$828$	−7.96498	−	0.885911i	−0.276802	−	0.0307875i
$829$			41.7444i			1.44984i	0.688831	+	0.724922i	$0.258124\pi$
$829$			41.7444i			1.44984i	−0.688831	+	0.724922i	$0.741876\pi$
$830$	−2.87721	+	2.87721i	−0.0998695	+	0.0998695i
$831$	−19.6570	+	17.5919i	−0.681895	+	0.610255i
$832$	3.43870	−	1.08413i	0.119215	−	0.0375855i
$833$		−	5.36595i		−	0.185919i
$834$	−0.239166	+	4.31380i	−0.00828163	+	0.149375i
$835$	5.63145			0.194884
$836$	−18.9576			−0.655661
$837$	8.02226	−	47.8364i	0.277290	−	1.65347i
$838$	13.7610	−	13.7610i	0.475366	−	0.475366i
$839$	35.6454	−	35.6454i	1.23061	−	1.23061i	0.266887	−	0.963728i	$-0.414005\pi$
$839$	35.6454	−	35.6454i	1.23061	−	1.23061i	0.963728	−	0.266887i	$-0.0859951\pi$
$840$	−0.0836158	+	1.50817i	−0.00288502	+	0.0520367i
$841$	19.9992			0.689627
$842$	17.4933			0.602858
$843$	−48.6001	−	2.69449i	−1.67388	−	0.0928031i
$844$			2.49834i			0.0859965i
$845$	−11.1647	−	1.96916i	−0.384077	−	0.0677411i
$846$	1.62278	−	14.5900i	0.0557925	−	0.501614i
$847$	2.00486	−	2.00486i	0.0688878	−	0.0688878i
$848$			0.464507i			0.0159512i
$849$	−15.4060	+	13.7874i	−0.528731	+	0.473183i
$850$	16.0859	−	16.0859i	0.551741	−	0.551741i
$851$	11.8868	+	11.8868i	0.407474	+	0.407474i
$852$	0.0239713	+	0.00132902i	0.000821243	+	4.55313e-5i
$853$	5.75295	+	5.75295i	0.196977	+	0.196977i	0.798703	−	0.601726i	$-0.205520\pi$
$853$	5.75295	+	5.75295i	0.196977	+	0.196977i	−0.601726	+	0.798703i	$0.705520\pi$
$854$			8.37831i			0.286700i
$855$	−1.47401	+	13.2524i	−0.0504102	+	0.453223i
$856$	1.95960	+	1.95960i	0.0669778	+	0.0669778i
$857$	−23.4108			−0.799697			−0.399849	−	0.916581i	$-0.630937\pi$
$857$	−23.4108			−0.799697			−0.399849	+	0.916581i	$0.630937\pi$
$858$	−11.8505	+	19.9786i	−0.404568	+	0.682057i
$859$	56.2528			1.91932			0.959660	−	0.281162i	$-0.0907198\pi$
$859$	56.2528			1.91932			0.959660	+	0.281162i	$0.0907198\pi$
$860$	−0.376287	−	0.376287i	−0.0128313	−	0.0128313i
$861$	−15.4015	+	13.7834i	−0.524881	+	0.469737i
$862$		−	11.7505i		−	0.400223i
$863$	−11.3466	−	11.3466i	−0.386244	−	0.386244i	0.487101	−	0.873345i	$-0.338054\pi$
$863$	−11.3466	−	11.3466i	−0.386244	−	0.386244i	−0.873345	+	0.487101i	$0.838054\pi$
$864$	−5.12459	−	0.859404i	−0.174342	−	0.0292375i
$865$	12.6727	+	12.6727i	0.430883	+	0.430883i
$866$	7.00089	−	7.00089i	0.237900	−	0.237900i
$867$	13.6223	+	15.2214i	0.462636	+	0.516946i
$868$		−	9.33468i		−	0.316840i
$869$	−16.0915	+	16.0915i	−0.545866	+	0.545866i
$870$	−3.02207	−	3.37684i	−0.102458	−	0.114485i
$871$	8.04757	+	4.18953i	0.272682	+	0.141957i
$872$		−	3.15249i		−	0.106757i
$873$	−14.3555	−	17.9485i	−0.485859	−	0.607465i
$874$	−13.6151			−0.460538
$875$	8.05755			0.272395
$876$	−27.2405	−	1.51027i	−0.920370	−	0.0510271i
$877$	24.5954	−	24.5954i	0.830527	−	0.830527i	−0.157062	−	0.987589i	$-0.550202\pi$
$877$	24.5954	−	24.5954i	0.830527	−	0.830527i	0.987589	+	0.157062i	$0.0502022\pi$
$878$	−11.8372	+	11.8372i	−0.399486	+	0.399486i
$879$	29.4277	+	1.63153i	0.992570	+	0.0550301i
$880$	3.24377			0.109347
$881$	1.28707			0.0433624			0.0216812	−	0.999765i	$-0.493098\pi$
$881$	1.28707			0.0433624			0.0216812	+	0.999765i	$0.493098\pi$
$882$	1.87382	+	2.34282i	0.0630948	+	0.0788868i
$883$		−	31.8432i		−	1.07161i	−0.844342	−	0.535804i	$-0.820009\pi$
$883$		−	31.8432i		−	1.07161i	0.844342	−	0.535804i	$-0.179991\pi$
$884$	18.4519	−	5.81740i	0.620605	−	0.195660i
$885$	12.7276	+	14.2218i	0.427835	+	0.478059i
$886$	−5.35019	+	5.35019i	−0.179743	+	0.179743i
$887$		−	31.2740i		−	1.05008i	−0.851078	−	0.525039i	$-0.824051\pi$
$887$		−	31.2740i		−	1.05008i	0.851078	−	0.525039i	$-0.175949\pi$
$888$	7.26865	+	8.12194i	0.243920	+	0.272554i
$889$	15.0861	−	15.0861i	0.505971	−	0.505971i
$890$	−7.76224	−	7.76224i	−0.260191	−	0.260191i
$891$	28.2941	−	17.8914i	0.947889	−	0.599384i
$892$	6.63646	+	6.63646i	0.222205	+	0.222205i
$893$		−	24.9397i		−	0.834577i
$894$	−22.4723	+	20.1114i	−0.751587	+	0.672626i
$895$	−7.72891	−	7.72891i	−0.258349	−	0.258349i
$896$	−1.00000			−0.0334077
$897$	−8.51087	+	14.3484i	−0.284170	+	0.479079i
$898$	−17.1799			−0.573301
$899$	19.8027	+	19.8027i	0.660458	+	0.660458i
$900$	−1.40595	+	12.6405i	−0.0468650	+	0.421350i
$901$			2.49252i			0.0830379i
$902$	31.3854	+	31.3854i	1.04502	+	1.04502i
$903$	−1.05529	−	0.0585075i	−0.0351179	−	0.00194701i
$904$	−9.75798	−	9.75798i	−0.324546	−	0.324546i
$905$	8.18540	−	8.18540i	0.272092	−	0.272092i
$906$	−6.36875	+	5.69965i	−0.211587	+	0.189358i
$907$			31.7804i			1.05525i	0.849477	+	0.527626i	$0.176918\pi$
$907$			31.7804i			1.05525i	−0.849477	+	0.527626i	$0.823082\pi$
$908$	8.75850	−	8.75850i	0.290661	−	0.290661i
$909$	−3.23047	+	29.0443i	−0.107148	+	0.963338i
$910$	2.78902	+	1.45195i	0.0924550	+	0.0481317i
$911$		−	27.7211i		−	0.918441i	−0.888322	−	0.459220i	$-0.848129\pi$
$911$		−	27.7211i		−	0.918441i	0.888322	−	0.459220i	$-0.151871\pi$
$912$	−8.81419	−	0.488676i	−0.291867	−	0.0161817i
$913$	17.3550			0.574368
$914$	−24.0740			−0.796296
$915$	0.700560	−	12.6359i	0.0231598	−	0.417730i
$916$	−4.24481	+	4.24481i	−0.140252	+	0.140252i
$917$	−5.77274	+	5.77274i	−0.190633	+	0.190633i
$918$	−27.4983	−	4.61152i	−0.907580	−	0.152203i
$919$	−11.8757			−0.391742			−0.195871	−	0.980630i	$-0.562753\pi$
$919$	−11.8757			−0.391742			−0.195871	+	0.980630i	$0.562753\pi$
$920$	2.32964			0.0768059
$921$	1.21661	−	21.9438i	0.0400887	−	0.723074i
$922$			6.05569i			0.199434i
$923$	0.0230777	−	0.0443295i	0.000759613	−	0.00145912i
$924$	4.80074	−	4.29637i	0.157933	−	0.141340i
$925$	18.8644	−	18.8644i	0.620259	−	0.620259i
$926$			20.6592i			0.678904i
$927$	41.3428	+	4.59839i	1.35787	+	0.151031i
$928$	2.12142	−	2.12142i	0.0696389	−	0.0696389i
$929$	7.35645	+	7.35645i	0.241357	+	0.241357i	0.817411	−	0.576054i	$-0.195408\pi$
$929$	7.35645	+	7.35645i	0.241357	+	0.241357i	−0.576054	+	0.817411i	$0.695408\pi$
$930$	−0.780527	+	14.0783i	−0.0255945	+	0.461645i
$931$	3.60391	+	3.60391i	0.118113	+	0.118113i
$932$			5.81776i			0.190567i
$933$	−31.9144	−	35.6609i	−1.04483	−	1.16749i
$934$	−22.0954	−	22.0954i	−0.722985	−	0.722985i
$935$	17.4059			0.569234
$936$	−6.02478	+	8.98343i	−0.196926	+	0.293633i
$937$	11.7655			0.384363			0.192182	−	0.981359i	$-0.438444\pi$
$937$	11.7655			0.384363			0.192182	+	0.981359i	$0.438444\pi$
$938$	−1.77932	−	1.77932i	−0.0580969	−	0.0580969i
$939$	16.5067	+	18.4445i	0.538676	+	0.601913i
$940$			4.26736i			0.139186i
$941$	−6.67209	−	6.67209i	−0.217504	−	0.217504i	0.589942	−	0.807446i	$-0.299151\pi$
$941$	−6.67209	−	6.67209i	−0.217504	−	0.217504i	−0.807446	+	0.589942i	$0.799151\pi$
$942$	0.0873875	−	1.57620i	0.00284724	−	0.0513553i
$943$	22.5407	+	22.5407i	0.734025	+	0.734025i
$944$	−8.93448	+	8.93448i	−0.290793	+	0.290793i
$945$	−2.63014	−	3.69005i	−0.0855584	−	0.120037i
$946$			2.26972i			0.0737951i
$947$	−36.4072	+	36.4072i	−1.18308	+	1.18308i	−0.204133	+	0.978943i	$0.565438\pi$
$947$	−36.4072	+	36.4072i	−1.18308	+	1.18308i	−0.978943	+	0.204133i	$0.934562\pi$
$948$	−7.89643	+	7.06683i	−0.256464	+	0.229520i
$949$	−26.2251	+	50.3751i	−0.851301	+	1.63524i
$950$			21.6073i			0.701034i
$951$	−0.368332	+	6.64356i	−0.0119440	+	0.215432i
$952$	−5.36595			−0.173912
$953$	8.94193			0.289657			0.144829	−	0.989457i	$-0.453737\pi$
$953$	8.94193			0.289657			0.144829	+	0.989457i	$0.453737\pi$
$954$	−0.870402	−	1.08825i	−0.0281803	−	0.0352336i
$955$	−1.97972	+	1.97972i	−0.0640623	+	0.0640623i
$956$	6.19473	−	6.19473i	0.200352	−	0.200352i
$957$	−1.06996	+	19.2988i	−0.0345869	+	0.623840i
$958$	15.3323			0.495365
$959$	−13.0378			−0.421012
$960$	1.50817	+	0.0836158i	0.0486759	+	0.00269869i
$961$		−	56.1363i		−	1.81085i
$962$	21.6392	−	6.82226i	0.697675	−	0.219959i
$963$	−8.26294	−	0.919052i	−0.266269	−	0.0296160i
$964$	−19.2493	+	19.2493i	−0.619979	+	0.619979i
$965$			20.0297i			0.644780i
$966$	3.44784	−	3.08561i	0.110932	−	0.0992778i
$967$	27.9937	−	27.9937i	0.900216	−	0.900216i	−0.0952382	−	0.995455i	$-0.530361\pi$
$967$	27.9937	−	27.9937i	0.900216	−	0.900216i	0.995455	+	0.0952382i	$0.0303613\pi$
$968$	−2.00486	−	2.00486i	−0.0644386	−	0.0644386i
$969$	−47.2966	−	2.62221i	−1.51938	−	0.0842377i
$970$	4.72422	+	4.72422i	0.151686	+	0.151686i
$971$		−	1.42350i		−	0.0456822i	−0.999739	−	0.0228411i	$-0.992729\pi$
$971$		−	1.42350i		−	0.0456822i	0.999739	−	0.0228411i	$-0.00727119\pi$
$972$	13.6164	−	7.58913i	0.436745	−	0.243421i
$973$	−1.76381	−	1.76381i	−0.0565451	−	0.0565451i
$974$	−25.0523			−0.802727
$975$	22.7710	+	13.5068i	0.729257	+	0.432564i
$976$	8.37831			0.268183
$977$	−12.1408	−	12.1408i	−0.388418	−	0.388418i	0.485705	−	0.874123i	$-0.338563\pi$
$977$	−12.1408	−	12.1408i	−0.388418	−	0.388418i	−0.874123	+	0.485705i	$0.838563\pi$
$978$	−24.6052	+	22.0202i	−0.786789	+	0.704129i
$979$			46.8210i			1.49641i
$980$	−0.616653	−	0.616653i	−0.0196982	−	0.0196982i
$981$	5.90720	+	7.38571i	0.188602	+	0.235808i
$982$	6.30723	+	6.30723i	0.201272	+	0.201272i
$983$	−12.3019	+	12.3019i	−0.392371	+	0.392371i	−0.875532	−	0.483161i	$-0.839489\pi$
$983$	−12.3019	+	12.3019i	−0.392371	+	0.392371i	0.483161	+	0.875532i	$0.339489\pi$
$984$	13.7834	+	15.4015i	0.439399	+	0.490981i
$985$			18.3721i			0.585382i
$986$	11.3834	−	11.3834i	0.362522	−	0.362522i
$987$	5.65212	+	6.31564i	0.179909	+	0.201029i
$988$	−8.48564	+	16.2999i	−0.269964	+	0.518568i
$989$			1.63009i			0.0518339i
$990$	−7.59956	+	6.07824i	−0.241530	+	0.193179i
$991$	−1.40127			−0.0445127			−0.0222564	−	0.999752i	$-0.507085\pi$
$991$	−1.40127			−0.0445127			−0.0222564	+	0.999752i	$0.507085\pi$
$992$	−9.33468			−0.296376
$993$	−26.0230	−	1.44277i	−0.825816	−	0.0457849i
$994$	−0.00980127	+	0.00980127i	−0.000310877	+	0.000310877i
$995$	9.35091	−	9.35091i	0.296444	−	0.296444i
$996$	8.06911	+	0.447367i	0.255679	+	0.0141754i
$997$	−36.0164			−1.14065			−0.570325	−	0.821419i	$-0.693183\pi$
$997$	−36.0164			−1.14065			−0.570325	+	0.821419i	$0.693183\pi$
$998$	28.4274			0.899854
$999$	−32.2482	−	5.40809i	−1.02029	−	0.171104i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.p.c.239.4	✓	20
3.2	odd	2		546.2.p.d.239.9	yes	20
13.8	odd	4		546.2.p.d.281.9	yes	20
39.8	even	4	inner	546.2.p.c.281.4	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.p.c.239.4	✓	20	1.1	even	1	trivial
546.2.p.c.281.4	yes	20	39.8	even	4	inner
546.2.p.d.239.9	yes	20	3.2	odd	2
546.2.p.d.281.9	yes	20	13.8	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(1.15507 + 1.29067i) q^{3} +1.00000i q^{4} +(0.616653 + 0.616653i) q^{5} +(0.0958811 - 1.72939i) q^{6} +(0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.331633 + 2.98161i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(1.15507 + 1.29067i) q^{3} +1.00000i q^{4} +(0.616653 + 0.616653i) q^{5} +(0.0958811 - 1.72939i) q^{6} +(0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.331633 + 2.98161i) q^{9} -0.872079i q^{10} +(-2.63014 + 2.63014i) q^{11} +(-1.29067 + 1.15507i) q^{12} +(1.08413 + 3.43870i) q^{13} -1.00000i q^{14} +(-0.0836158 + 1.50817i) q^{15} -1.00000 q^{16} -5.36595 q^{17} +(2.34282 - 1.87382i) q^{18} +(3.60391 - 3.60391i) q^{19} +(-0.616653 + 0.616653i) q^{20} +(-0.0958811 + 1.72939i) q^{21} +3.71958 q^{22} +2.67136 q^{23} +(1.72939 + 0.0958811i) q^{24} -4.23948i q^{25} +(1.66493 - 3.19813i) q^{26} +(-4.23132 + 3.01594i) q^{27} +(-0.707107 + 0.707107i) q^{28} -3.00014i q^{29} +(1.12556 - 1.00731i) q^{30} +(-6.60062 + 6.60062i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-6.43263 - 0.356638i) q^{33} +(3.79430 + 3.79430i) q^{34} +0.872079i q^{35} +(-2.98161 - 0.331633i) q^{36} +(4.44970 + 4.44970i) q^{37} -5.09669 q^{38} +(-3.18596 + 5.37119i) q^{39} +0.872079 q^{40} +(8.43789 + 8.43789i) q^{41} +(1.29067 - 1.15507i) q^{42} +0.610209i q^{43} +(-2.63014 - 2.63014i) q^{44} +(-2.04312 + 1.63412i) q^{45} +(-1.88894 - 1.88894i) q^{46} +(3.46010 - 3.46010i) q^{47} +(-1.15507 - 1.29067i) q^{48} +1.00000i q^{49} +(-2.99776 + 2.99776i) q^{50} +(-6.19805 - 6.92565i) q^{51} +(-3.43870 + 1.08413i) q^{52} -0.464507i q^{53} +(5.12459 + 0.859404i) q^{54} -3.24377 q^{55} +1.00000 q^{56} +(8.81419 + 0.488676i) q^{57} +(-2.12142 + 2.12142i) q^{58} +(8.93448 - 8.93448i) q^{59} +(-1.50817 - 0.0836158i) q^{60} -8.37831 q^{61} +9.33468 q^{62} +(-2.34282 + 1.87382i) q^{63} -1.00000i q^{64} +(-1.45195 + 2.78902i) q^{65} +(4.29637 + 4.80074i) q^{66} +(1.77932 - 1.77932i) q^{67} -5.36595i q^{68} +(3.08561 + 3.44784i) q^{69} +(0.616653 - 0.616653i) q^{70} +(-0.00980127 - 0.00980127i) q^{71} +(1.87382 + 2.34282i) q^{72} +(11.1380 + 11.1380i) q^{73} -6.29283i q^{74} +(5.47175 - 4.89689i) q^{75} +(3.60391 + 3.60391i) q^{76} -3.71958 q^{77} +(6.05082 - 1.54519i) q^{78} +6.11811 q^{79} +(-0.616653 - 0.616653i) q^{80} +(-8.78004 - 1.97760i) q^{81} -11.9330i q^{82} +(-3.29926 - 3.29926i) q^{83} +(-1.72939 - 0.0958811i) q^{84} +(-3.30893 - 3.30893i) q^{85} +(0.431483 - 0.431483i) q^{86} +(3.87217 - 3.46536i) q^{87} +3.71958i q^{88} +(8.90085 - 8.90085i) q^{89} +(2.60020 + 0.289210i) q^{90} +(-1.66493 + 3.19813i) q^{91} +2.67136i q^{92} +(-16.1433 - 0.895019i) q^{93} -4.89332 q^{94} +4.44472 q^{95} +(-0.0958811 + 1.72939i) q^{96} +(-5.41720 + 5.41720i) q^{97} +(0.707107 - 0.707107i) q^{98} +(-6.96983 - 8.71431i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{5} - 4 q^{6} - 8 q^{9}+O(q^{10}) \) 20 * q - 4 * q^5 - 4 * q^6 - 8 * q^9	\( 20 q - 4 q^{5} - 4 q^{6} - 8 q^{9} - 16 q^{11} - 8 q^{12} + 4 q^{13} - 4 q^{15} - 20 q^{16} + 12 q^{17} - 8 q^{18} + 12 q^{19} + 4 q^{20} + 4 q^{21} - 12 q^{22} - 4 q^{23} + 4 q^{24} + 24 q^{27} + 12 q^{30} - 8 q^{31} - 48 q^{33} - 4 q^{34} + 32 q^{37} - 4 q^{38} - 16 q^{39} - 4 q^{40} + 8 q^{41} + 8 q^{42} - 16 q^{44} + 16 q^{45} - 8 q^{46} + 32 q^{50} - 8 q^{51} - 8 q^{52} + 28 q^{54} + 28 q^{55} + 20 q^{56} + 36 q^{57} - 4 q^{58} + 20 q^{59} - 4 q^{60} - 4 q^{61} + 48 q^{62} + 8 q^{63} + 52 q^{65} - 36 q^{67} + 68 q^{69} - 4 q^{70} - 28 q^{71} - 16 q^{72} - 24 q^{73} - 76 q^{75} + 12 q^{76} + 12 q^{77} + 40 q^{78} - 64 q^{79} + 4 q^{80} + 32 q^{81} - 24 q^{83} - 4 q^{84} + 24 q^{85} + 4 q^{86} + 4 q^{87} - 4 q^{89} - 8 q^{90} - 32 q^{93} - 40 q^{94} - 76 q^{95} + 4 q^{96} + 32 q^{97} - 4 q^{99}+O(q^{100}) \) 20 * q - 4 * q^5 - 4 * q^6 - 8 * q^9 - 16 * q^11 - 8 * q^12 + 4 * q^13 - 4 * q^15 - 20 * q^16 + 12 * q^17 - 8 * q^18 + 12 * q^19 + 4 * q^20 + 4 * q^21 - 12 * q^22 - 4 * q^23 + 4 * q^24 + 24 * q^27 + 12 * q^30 - 8 * q^31 - 48 * q^33 - 4 * q^34 + 32 * q^37 - 4 * q^38 - 16 * q^39 - 4 * q^40 + 8 * q^41 + 8 * q^42 - 16 * q^44 + 16 * q^45 - 8 * q^46 + 32 * q^50 - 8 * q^51 - 8 * q^52 + 28 * q^54 + 28 * q^55 + 20 * q^56 + 36 * q^57 - 4 * q^58 + 20 * q^59 - 4 * q^60 - 4 * q^61 + 48 * q^62 + 8 * q^63 + 52 * q^65 - 36 * q^67 + 68 * q^69 - 4 * q^70 - 28 * q^71 - 16 * q^72 - 24 * q^73 - 76 * q^75 + 12 * q^76 + 12 * q^77 + 40 * q^78 - 64 * q^79 + 4 * q^80 + 32 * q^81 - 24 * q^83 - 4 * q^84 + 24 * q^85 + 4 * q^86 + 4 * q^87 - 4 * q^89 - 8 * q^90 - 32 * q^93 - 40 * q^94 - 76 * q^95 + 4 * q^96 + 32 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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