LMFDB - Embedded newform 882.2.e.p.655.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(373,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("882.373");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.e (of order $3$, degree $2$, 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:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			655.1
Root			$0.500000 + 1.41036i$ of defining polynomial
Character	$\chi$	$=$	882.655
Dual form			882.2.e.p.373.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-1.09097 + 1.34528i) q^{3} +1.00000 q^{4} +(0.880438 - 1.52496i) q^{5} +(-1.09097 + 1.34528i) q^{6} +1.00000 q^{8} +(-0.619562 - 2.93533i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-1.09097 + 1.34528i) q^{3} +1.00000 q^{4} +(0.880438 - 1.52496i) q^{5} +(-1.09097 + 1.34528i) q^{6} +1.00000 q^{8} +(-0.619562 - 2.93533i) q^{9} +(0.880438 - 1.52496i) q^{10} +(-3.06238 - 5.30420i) q^{11} +(-1.09097 + 1.34528i) q^{12} +(0.380438 + 0.658939i) q^{13} +(1.09097 + 2.84813i) q^{15} +1.00000 q^{16} +(3.42107 - 5.92546i) q^{17} +(-0.619562 - 2.93533i) q^{18} +(-0.971410 - 1.68253i) q^{19} +(0.880438 - 1.52496i) q^{20} +(-3.06238 - 5.30420i) q^{22} +(0.210533 - 0.364654i) q^{23} +(-1.09097 + 1.34528i) q^{24} +(0.949657 + 1.64485i) q^{25} +(0.380438 + 0.658939i) q^{26} +(4.62476 + 2.36887i) q^{27} +(0.732287 - 1.26836i) q^{29} +(1.09097 + 2.84813i) q^{30} -7.70370 q^{31} +1.00000 q^{32} +(10.4766 + 1.66697i) q^{33} +(3.42107 - 5.92546i) q^{34} +(-0.619562 - 2.93533i) q^{36} +(1.44282 + 2.49904i) q^{37} +(-0.971410 - 1.68253i) q^{38} +(-1.30150 - 0.207087i) q^{39} +(0.880438 - 1.52496i) q^{40} +(3.47141 + 6.01266i) q^{41} +(4.33009 - 7.49994i) q^{43} +(-3.06238 - 5.30420i) q^{44} +(-5.02175 - 1.63957i) q^{45} +(0.210533 - 0.364654i) q^{46} -1.66019 q^{47} +(-1.09097 + 1.34528i) q^{48} +(0.949657 + 1.64485i) q^{50} +(4.23912 + 11.0668i) q^{51} +(0.380438 + 0.658939i) q^{52} +(-0.112725 + 0.195246i) q^{53} +(4.62476 + 2.36887i) q^{54} -10.7850 q^{55} +(3.32326 + 0.528775i) q^{57} +(0.732287 - 1.26836i) q^{58} -1.98633 q^{59} +(1.09097 + 2.84813i) q^{60} +10.3502 q^{61} -7.70370 q^{62} +1.00000 q^{64} +1.33981 q^{65} +(10.4766 + 1.66697i) q^{66} +6.78495 q^{67} +(3.42107 - 5.92546i) q^{68} +(0.260877 + 0.681054i) q^{69} +10.7850 q^{71} +(-0.619562 - 2.93533i) q^{72} +(-0.153353 + 0.265616i) q^{73} +(1.44282 + 2.49904i) q^{74} +(-3.24884 - 0.516934i) q^{75} +(-0.971410 - 1.68253i) q^{76} +(-1.30150 - 0.207087i) q^{78} -13.4451 q^{79} +(0.880438 - 1.52496i) q^{80} +(-8.23229 + 3.63723i) q^{81} +(3.47141 + 6.01266i) q^{82} +(1.56238 - 2.70612i) q^{83} +(-6.02408 - 10.4340i) q^{85} +(4.33009 - 7.49994i) q^{86} +(0.907394 + 2.36887i) q^{87} +(-3.06238 - 5.30420i) q^{88} +(-1.30150 - 2.25427i) q^{89} +(-5.02175 - 1.63957i) q^{90} +(0.210533 - 0.364654i) q^{92} +(8.40451 - 10.3636i) q^{93} -1.66019 q^{94} -3.42107 q^{95} +(-1.09097 + 1.34528i) q^{96} +(1.81806 - 3.14897i) q^{97} +(-13.6722 + 12.2754i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 2 q^{3} + 6 q^{4} + 5 q^{5} + 2 q^{6} + 6 q^{8} - 4 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + 2 * q^3 + 6 * q^4 + 5 * q^5 + 2 * q^6 + 6 * q^8 - 4 * q^9	$ 6 q + 6 q^{2} + 2 q^{3} + 6 q^{4} + 5 q^{5} + 2 q^{6} + 6 q^{8} - 4 q^{9} + 5 q^{10} - q^{11} + 2 q^{12} + 2 q^{13} - 2 q^{15} + 6 q^{16} + 4 q^{17} - 4 q^{18} + 3 q^{19} + 5 q^{20} - q^{22} - 7 q^{23} + 2 q^{24} - 2 q^{25} + 2 q^{26} - 7 q^{27} - 5 q^{29} - 2 q^{30} - 28 q^{31} + 6 q^{32} + 19 q^{33} + 4 q^{34} - 4 q^{36} - 9 q^{37} + 3 q^{38} + 9 q^{39} + 5 q^{40} + 12 q^{41} + 18 q^{43} - q^{44} - 29 q^{45} - 7 q^{46} + 6 q^{47} + 2 q^{48} - 2 q^{50} + 26 q^{51} + 2 q^{52} + 9 q^{53} - 7 q^{54} - 14 q^{55} + 2 q^{57} - 5 q^{58} + 8 q^{59} - 2 q^{60} + 8 q^{61} - 28 q^{62} + 6 q^{64} + 24 q^{65} + 19 q^{66} - 10 q^{67} + 4 q^{68} + q^{69} + 14 q^{71} - 4 q^{72} + 25 q^{73} - 9 q^{74} - 44 q^{75} + 3 q^{76} + 9 q^{78} - 14 q^{79} + 5 q^{80} - 40 q^{81} + 12 q^{82} - 8 q^{83} + 14 q^{85} + 18 q^{86} - 31 q^{87} - q^{88} + 9 q^{89} - 29 q^{90} - 7 q^{92} + 6 q^{94} - 4 q^{95} + 2 q^{96} + 28 q^{97} - 41 q^{99}+O(q^{100}) $ 6 * q + 6 * q^2 + 2 * q^3 + 6 * q^4 + 5 * q^5 + 2 * q^6 + 6 * q^8 - 4 * q^9 + 5 * q^10 - q^11 + 2 * q^12 + 2 * q^13 - 2 * q^15 + 6 * q^16 + 4 * q^17 - 4 * q^18 + 3 * q^19 + 5 * q^20 - q^22 - 7 * q^23 + 2 * q^24 - 2 * q^25 + 2 * q^26 - 7 * q^27 - 5 * q^29 - 2 * q^30 - 28 * q^31 + 6 * q^32 + 19 * q^33 + 4 * q^34 - 4 * q^36 - 9 * q^37 + 3 * q^38 + 9 * q^39 + 5 * q^40 + 12 * q^41 + 18 * q^43 - q^44 - 29 * q^45 - 7 * q^46 + 6 * q^47 + 2 * q^48 - 2 * q^50 + 26 * q^51 + 2 * q^52 + 9 * q^53 - 7 * q^54 - 14 * q^55 + 2 * q^57 - 5 * q^58 + 8 * q^59 - 2 * q^60 + 8 * q^61 - 28 * q^62 + 6 * q^64 + 24 * q^65 + 19 * q^66 - 10 * q^67 + 4 * q^68 + q^69 + 14 * q^71 - 4 * q^72 + 25 * q^73 - 9 * q^74 - 44 * q^75 + 3 * q^76 + 9 * q^78 - 14 * q^79 + 5 * q^80 - 40 * q^81 + 12 * q^82 - 8 * q^83 + 14 * q^85 + 18 * q^86 - 31 * q^87 - q^88 + 9 * q^89 - 29 * q^90 - 7 * q^92 + 6 * q^94 - 4 * q^95 + 2 * q^96 + 28 * q^97 - 41 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−1.09097	+	1.34528i	−0.629873	+	0.776698i
$3$	−1.09097	+	1.34528i	−0.629873	+	0.776698i
$4$	1.00000			0.500000
$5$	0.880438	−	1.52496i	0.393744	−	0.681985i	−0.599196	−	0.800602i	$-0.704513\pi$
$5$	0.880438	−	1.52496i	0.393744	−	0.681985i	0.992940	+	0.118618i	$0.0378463\pi$
$6$	−1.09097	+	1.34528i	−0.445387	+	0.549209i
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	−0.619562	−	2.93533i	−0.206521	−	0.978442i
$10$	0.880438	−	1.52496i	0.278419	−	0.482236i
$11$	−3.06238	−	5.30420i	−0.923343	−	1.59928i	−0.794205	−	0.607650i	$-0.792112\pi$
$11$	−3.06238	−	5.30420i	−0.923343	−	1.59928i	−0.129138	−	0.991627i	$-0.541221\pi$
$12$	−1.09097	+	1.34528i	−0.314936	+	0.388349i
$13$	0.380438	+	0.658939i	0.105515	+	0.182757i	0.913948	−	0.405831i	$-0.133018\pi$
$13$	0.380438	+	0.658939i	0.105515	+	0.182757i	−0.808434	+	0.588587i	$0.799684\pi$
$14$		0			0
$15$	1.09097	+	2.84813i	0.281688	+	0.735384i
$16$	1.00000			0.250000
$17$	3.42107	−	5.92546i	0.829731	−	1.43714i	−0.0685191	−	0.997650i	$-0.521827\pi$
$17$	3.42107	−	5.92546i	0.829731	−	1.43714i	0.898250	−	0.439486i	$-0.144839\pi$
$18$	−0.619562	−	2.93533i	−0.146032	−	0.691863i
$19$	−0.971410	−	1.68253i	−0.222857	−	0.385999i	0.732818	−	0.680425i	$-0.238205\pi$
$19$	−0.971410	−	1.68253i	−0.222857	−	0.385999i	−0.955674	+	0.294426i	$0.904872\pi$
$20$	0.880438	−	1.52496i	0.196872	−	0.340992i
$21$		0			0
$22$	−3.06238	−	5.30420i	−0.652902	−	1.13086i
$23$	0.210533	−	0.364654i	0.0438992	−	0.0760357i	−0.843241	−	0.537536i	$-0.819355\pi$
$23$	0.210533	−	0.364654i	0.0438992	−	0.0760357i	0.887140	+	0.461500i	$0.152689\pi$
$24$	−1.09097	+	1.34528i	−0.222694	+	0.274604i
$25$	0.949657	+	1.64485i	0.189931	+	0.328971i
$26$	0.380438	+	0.658939i	0.0746101	+	0.129228i
$27$	4.62476	+	2.36887i	0.890036	+	0.455890i
$28$		0			0
$29$	0.732287	−	1.26836i	0.135982	−	0.235528i	−0.789990	−	0.613120i	$-0.789914\pi$
$29$	0.732287	−	1.26836i	0.135982	−	0.235528i	0.925972	+	0.377592i	$0.123248\pi$
$30$	1.09097	+	2.84813i	0.199183	+	0.519995i
$31$	−7.70370			−1.38362			−0.691812	−	0.722077i	$-0.743187\pi$
$31$	−7.70370			−1.38362			−0.691812	+	0.722077i	$0.743187\pi$
$32$	1.00000			0.176777
$33$	10.4766	+	1.66697i	1.82374	+	0.290182i
$34$	3.42107	−	5.92546i	0.586708	−	1.01621i
$35$		0			0
$36$	−0.619562	−	2.93533i	−0.103260	−	0.489221i
$37$	1.44282	+	2.49904i	0.237198	+	0.410839i	0.959909	−	0.280311i	$-0.0904376\pi$
$37$	1.44282	+	2.49904i	0.237198	+	0.410839i	−0.722711	+	0.691150i	$0.757104\pi$
$38$	−0.971410	−	1.68253i	−0.157584	−	0.272943i
$39$	−1.30150	−	0.207087i	−0.208408	−	0.0331604i
$40$	0.880438	−	1.52496i	0.139210	−	0.241118i
$41$	3.47141	+	6.01266i	0.542143	+	0.939020i	0.998781	+	0.0493667i	$0.0157203\pi$
$41$	3.47141	+	6.01266i	0.542143	+	0.939020i	−0.456638	+	0.889653i	$0.650946\pi$
$42$		0			0
$43$	4.33009	−	7.49994i	0.660333	−	1.14373i	−0.320195	−	0.947352i	$-0.603748\pi$
$43$	4.33009	−	7.49994i	0.660333	−	1.14373i	0.980528	−	0.196379i	$-0.0629183\pi$
$44$	−3.06238	−	5.30420i	−0.461671	−	0.799638i
$45$	−5.02175	−	1.63957i	−0.748599	−	0.244412i
$46$	0.210533	−	0.364654i	0.0310414	−	0.0537654i
$47$	−1.66019			−0.242164			−0.121082	−	0.992643i	$-0.538636\pi$
$47$	−1.66019			−0.242164			−0.121082	+	0.992643i	$0.538636\pi$
$48$	−1.09097	+	1.34528i	−0.157468	+	0.194175i
$49$		0			0
$50$	0.949657	+	1.64485i	0.134302	+	0.232617i
$51$	4.23912	+	11.0668i	0.593596	+	1.54966i
$52$	0.380438	+	0.658939i	0.0527573	+	0.0913783i
$53$	−0.112725	+	0.195246i	−0.0154840	+	0.0268190i	−0.873664	−	0.486531i	$-0.838262\pi$
$53$	−0.112725	+	0.195246i	−0.0154840	+	0.0268190i	0.858180	+	0.513350i	$0.171596\pi$
$54$	4.62476	+	2.36887i	0.629351	+	0.322363i
$55$	−10.7850			−1.45424
$56$		0			0
$57$	3.32326	+	0.528775i	0.440176	+	0.0700379i
$58$	0.732287	−	1.26836i	0.0961540	−	0.166544i
$59$	−1.98633			−0.258598			−0.129299	−	0.991606i	$-0.541273\pi$
$59$	−1.98633			−0.258598			−0.129299	+	0.991606i	$0.541273\pi$
$60$	1.09097	+	2.84813i	0.140844	+	0.367692i
$61$	10.3502			1.32521			0.662605	−	0.748969i	$-0.269451\pi$
$61$	10.3502			1.32521			0.662605	+	0.748969i	$0.269451\pi$
$62$	−7.70370			−0.978370
$63$		0			0
$64$	1.00000			0.125000
$65$	1.33981			0.166183
$66$	10.4766	+	1.66697i	1.28958	+	0.205190i
$67$	6.78495			0.828914			0.414457	−	0.910069i	$-0.363972\pi$
$67$	6.78495			0.828914			0.414457	+	0.910069i	$0.363972\pi$
$68$	3.42107	−	5.92546i	0.414865	−	0.718568i
$69$	0.260877	+	0.681054i	0.0314059	+	0.0819893i
$70$		0			0
$71$	10.7850			1.27994			0.639969	−	0.768401i	$-0.278947\pi$
$71$	10.7850			1.27994			0.639969	+	0.768401i	$0.278947\pi$
$72$	−0.619562	−	2.93533i	−0.0730160	−	0.345932i
$73$	−0.153353	+	0.265616i	−0.0179487	+	0.0310880i	−0.874860	−	0.484375i	$-0.839047\pi$
$73$	−0.153353	+	0.265616i	−0.0179487	+	0.0310880i	0.856912	+	0.515463i	$0.172380\pi$
$74$	1.44282	+	2.49904i	0.167724	+	0.290507i
$75$	−3.24884	−	0.516934i	−0.375144	−	0.0596904i
$76$	−0.971410	−	1.68253i	−0.111428	−	0.193000i
$77$		0			0
$78$	−1.30150	−	0.207087i	−0.147366	−	0.0234480i
$79$	−13.4451			−1.51270			−0.756348	−	0.654169i	$-0.773018\pi$
$79$	−13.4451			−1.51270			−0.756348	+	0.654169i	$0.773018\pi$
$80$	0.880438	−	1.52496i	0.0984360	−	0.170496i
$81$	−8.23229	+	3.63723i	−0.914699	+	0.404137i
$82$	3.47141	+	6.01266i	0.383353	+	0.663987i
$83$	1.56238	−	2.70612i	0.171494	−	0.297036i	−0.767449	−	0.641110i	$-0.778474\pi$
$83$	1.56238	−	2.70612i	0.171494	−	0.297036i	0.938942	+	0.344075i	$0.111807\pi$
$84$		0			0
$85$	−6.02408	−	10.4340i	−0.653403	−	1.13173i
$86$	4.33009	−	7.49994i	0.466926	−	0.808740i
$87$	0.907394	+	2.36887i	0.0972828	+	0.253970i
$88$	−3.06238	−	5.30420i	−0.326451	−	0.565430i
$89$	−1.30150	−	2.25427i	−0.137959	−	0.238952i	0.788765	−	0.614695i	$-0.210721\pi$
$89$	−1.30150	−	2.25427i	−0.137959	−	0.238952i	−0.926724	+	0.375743i	$0.877388\pi$
$90$	−5.02175	−	1.63957i	−0.529339	−	0.172825i
$91$		0			0
$92$	0.210533	−	0.364654i	0.0219496	−	0.0380178i
$93$	8.40451	−	10.3636i	0.871508	−	1.07466i
$94$	−1.66019			−0.171236
$95$	−3.42107			−0.350994
$96$	−1.09097	+	1.34528i	−0.111347	+	0.137302i
$97$	1.81806	−	3.14897i	0.184596	−	0.319729i	−0.758845	−	0.651272i	$-0.774236\pi$
$97$	1.81806	−	3.14897i	0.184596	−	0.319729i	0.943440	+	0.331543i	$0.107569\pi$
$98$		0			0
$99$	−13.6722	+	12.2754i	−1.37411	+	1.23372i
$100$	0.949657	+	1.64485i	0.0949657	+	0.164485i
$101$	−4.00520	−	6.93721i	−0.398532	−	0.690278i	0.595013	−	0.803716i	$-0.297147\pi$
$101$	−4.00520	−	6.93721i	−0.398532	−	0.690278i	−0.993545	+	0.113438i	$0.963814\pi$
$102$	4.23912	+	11.0668i	0.419736	+	1.09578i
$103$	−3.41423	+	5.91362i	−0.336414	+	0.582686i	−0.983755	−	0.179514i	$-0.942548\pi$
$103$	−3.41423	+	5.91362i	−0.336414	+	0.582686i	0.647341	+	0.762200i	$0.275881\pi$
$104$	0.380438	+	0.658939i	0.0373051	+	0.0646142i
$105$		0			0
$106$	−0.112725	+	0.195246i	−0.0109488	+	0.0189639i
$107$	1.77292	+	3.07078i	0.171394	+	0.296863i	0.938908	−	0.344170i	$-0.111840\pi$
$107$	1.77292	+	3.07078i	0.171394	+	0.296863i	−0.767513	+	0.641033i	$0.778506\pi$
$108$	4.62476	+	2.36887i	0.445018	+	0.227945i
$109$	0.351848	−	0.609419i	0.0337010	−	0.0583718i	−0.848683	−	0.528902i	$-0.822604\pi$
$109$	0.351848	−	0.609419i	0.0337010	−	0.0583718i	0.882384	+	0.470530i	$0.155937\pi$
$110$	−10.7850			−1.02830
$111$	−4.93598	−	0.785381i	−0.468503	−	0.0745451i
$112$		0			0
$113$	4.25116	+	7.36323i	0.399916	+	0.692674i	0.993715	−	0.111939i	$-0.0357061\pi$
$113$	4.25116	+	7.36323i	0.399916	+	0.692674i	−0.593799	+	0.804613i	$0.702373\pi$
$114$	3.32326	+	0.528775i	0.311252	+	0.0495243i
$115$	−0.370723	−	0.642111i	−0.0345701	−	0.0598772i
$116$	0.732287	−	1.26836i	0.0679911	−	0.117764i
$117$	1.69850	−	1.52496i	0.157026	−	0.140983i
$118$	−1.98633			−0.182856
$119$		0			0
$120$	1.09097	+	2.84813i	0.0995916	+	0.259997i
$121$	−13.2564	+	22.9607i	−1.20512	+	2.08734i
$122$	10.3502			0.937064
$123$	−11.8759	−	1.88962i	−1.07082	−	0.170381i
$124$	−7.70370			−0.691812
$125$	12.1488			1.08663
$126$		0			0
$127$	−18.9532			−1.68183			−0.840913	−	0.541170i	$-0.817982\pi$
$127$	−18.9532			−1.68183			−0.840913	+	0.541170i	$0.817982\pi$
$128$	1.00000			0.0883883
$129$	5.36552	+	14.0074i	0.472408	+	1.23328i
$130$	1.33981			0.117509
$131$	−3.64652	+	6.31595i	−0.318598	+	0.551827i	−0.980196	−	0.198031i	$-0.936545\pi$
$131$	−3.64652	+	6.31595i	−0.318598	+	0.551827i	0.661598	+	0.749859i	$0.269879\pi$
$132$	10.4766	+	1.66697i	0.911872	+	0.145091i
$133$		0			0
$134$	6.78495			0.586131
$135$	7.68427	−	4.96695i	0.661356	−	0.427487i
$136$	3.42107	−	5.92546i	0.293354	−	0.508104i
$137$	4.09097	+	7.08577i	0.349515	+	0.605378i	0.986163	−	0.165776i	$-0.0530129\pi$
$137$	4.09097	+	7.08577i	0.349515	+	0.605378i	−0.636648	+	0.771154i	$0.719680\pi$
$138$	0.260877	+	0.681054i	0.0222073	+	0.0579752i
$139$	6.23229	+	10.7946i	0.528616	+	0.915589i	0.999443	+	0.0333640i	$0.0106220\pi$
$139$	6.23229	+	10.7946i	0.528616	+	0.915589i	−0.470828	+	0.882225i	$0.656045\pi$
$140$		0			0
$141$	1.81122	−	2.23342i	0.152532	−	0.188088i
$142$	10.7850			0.905053
$143$	2.33009	−	4.03584i	0.194852	−	0.337494i
$144$	−0.619562	−	2.93533i	−0.0516301	−	0.244611i
$145$	−1.28947	−	2.23342i	−0.107084	−	0.185476i
$146$	−0.153353	+	0.265616i	−0.0126916	+	0.0219825i
$147$		0			0
$148$	1.44282	+	2.49904i	0.118599	+	0.205420i
$149$	−4.41423	+	7.64567i	−0.361628	+	0.626358i	−0.988229	−	0.152982i	$-0.951112\pi$
$149$	−4.41423	+	7.64567i	−0.361628	+	0.626358i	0.626601	+	0.779340i	$0.284446\pi$
$150$	−3.24884	−	0.516934i	−0.265267	−	0.0422075i
$151$	7.49316	+	12.9785i	0.609785	+	1.05618i	0.991276	+	0.131806i	$0.0420775\pi$
$151$	7.49316	+	12.9785i	0.609785	+	1.05618i	−0.381491	+	0.924373i	$0.624589\pi$
$152$	−0.971410	−	1.68253i	−0.0787918	−	0.136471i
$153$	−19.5127	−	6.37076i	−1.57751	−	0.515045i
$154$		0			0
$155$	−6.78263	+	11.7479i	−0.544794	+	0.943611i
$156$	−1.30150	−	0.207087i	−0.104204	−	0.0165802i
$157$	−18.9806			−1.51481			−0.757407	−	0.652943i	$-0.773534\pi$
$157$	−18.9806			−1.51481			−0.757407	+	0.652943i	$0.773534\pi$
$158$	−13.4451			−1.06964
$159$	−0.139680	−	0.364654i	−0.0110774	−	0.0289190i
$160$	0.880438	−	1.52496i	0.0696048	−	0.120559i
$161$		0			0
$162$	−8.23229	+	3.63723i	−0.646790	+	0.285768i
$163$	−7.51887	−	13.0231i	−0.588924	−	1.02005i	−0.994374	−	0.105929i	$-0.966219\pi$
$163$	−7.51887	−	13.0231i	−0.588924	−	1.02005i	0.405450	−	0.914117i	$-0.367115\pi$
$164$	3.47141	+	6.01266i	0.271072	+	0.469510i
$165$	11.7661	−	14.5088i	0.915988	−	1.12951i
$166$	1.56238	−	2.70612i	0.121264	−	0.210036i
$167$	−0.572097	−	0.990901i	−0.0442702	−	0.0766782i	0.843041	−	0.537849i	$-0.180763\pi$
$167$	−0.572097	−	0.990901i	−0.0442702	−	0.0766782i	−0.887311	+	0.461171i	$0.847430\pi$
$168$		0			0
$169$	6.21053	−	10.7570i	0.477733	−	0.827458i
$170$	−6.02408	−	10.4340i	−0.462026	−	0.800252i
$171$	−4.33693	+	3.89384i	−0.331653	+	0.297769i
$172$	4.33009	−	7.49994i	0.330167	−	0.571865i
$173$	−0.497677			−0.0378377			−0.0189188	−	0.999821i	$-0.506022\pi$
$173$	−0.497677			−0.0378377			−0.0189188	+	0.999821i	$0.506022\pi$
$174$	0.907394	+	2.36887i	0.0687893	+	0.179584i
$175$		0			0
$176$	−3.06238	−	5.30420i	−0.230836	−	0.399819i
$177$	2.16703	−	2.67217i	0.162884	−	0.200852i
$178$	−1.30150	−	2.25427i	−0.0975519	−	0.168965i
$179$	4.41423	−	7.64567i	0.329935	−	0.571464i	−0.652564	−	0.757734i	$-0.726306\pi$
$179$	4.41423	−	7.64567i	0.329935	−	0.571464i	0.982499	+	0.186270i	$0.0596398\pi$
$180$	−5.02175	−	1.63957i	−0.374299	−	0.122206i
$181$	−1.32941			−0.0988140			−0.0494070	−	0.998779i	$-0.515733\pi$
$181$	−1.32941			−0.0988140			−0.0494070	+	0.998779i	$0.515733\pi$
$182$		0			0
$183$	−11.2918	+	13.9239i	−0.834713	+	1.02929i
$184$	0.210533	−	0.364654i	0.0155207	−	0.0268827i
$185$	5.08126			0.373581
$186$	8.40451	−	10.3636i	0.616249	−	0.759899i
$187$	−41.9064			−3.06450
$188$	−1.66019			−0.121082
$189$		0			0
$190$	−3.42107			−0.248190
$191$	−16.1683			−1.16989			−0.584947	−	0.811071i	$-0.698885\pi$
$191$	−16.1683			−1.16989			−0.584947	+	0.811071i	$0.698885\pi$
$192$	−1.09097	+	1.34528i	−0.0787341	+	0.0970873i
$193$	−14.1683			−1.01985			−0.509927	−	0.860218i	$-0.670328\pi$
$193$	−14.1683			−1.01985			−0.509927	+	0.860218i	$0.670328\pi$
$194$	1.81806	−	3.14897i	0.130529	−	0.226083i
$195$	−1.46169	+	1.80242i	−0.104674	+	0.129074i
$196$		0			0
$197$	15.8421			1.12871			0.564353	−	0.825534i	$-0.309126\pi$
$197$	15.8421			1.12871			0.564353	+	0.825534i	$0.309126\pi$
$198$	−13.6722	+	12.2754i	−0.971643	+	0.872373i
$199$	4.47141	−	7.74471i	0.316970	−	0.549008i	−0.662884	−	0.748722i	$-0.730668\pi$
$199$	4.47141	−	7.74471i	0.316970	−	0.549008i	0.979854	+	0.199714i	$0.0640013\pi$
$200$	0.949657	+	1.64485i	0.0671509	+	0.116309i
$201$	−7.40219	+	9.12767i	−0.522110	+	0.643816i
$202$	−4.00520	−	6.93721i	−0.281805	−	0.488101i
$203$		0			0
$204$	4.23912	+	11.0668i	0.296798	+	0.774831i
$205$	12.2255			0.853862
$206$	−3.41423	+	5.91362i	−0.237881	+	0.412021i
$207$	−1.20082	−	0.392058i	−0.0834626	−	0.0272499i
$208$	0.380438	+	0.658939i	0.0263787	+	0.0456892i
$209$	−5.94966	+	10.3051i	−0.411546	+	0.712819i
$210$		0			0
$211$	11.3856	+	19.7205i	0.783820	+	1.35762i	0.929702	+	0.368314i	$0.120065\pi$
$211$	11.3856	+	19.7205i	0.783820	+	1.35762i	−0.145882	+	0.989302i	$0.546602\pi$
$212$	−0.112725	+	0.195246i	−0.00774199	+	0.0134095i
$213$	−11.7661	+	14.5088i	−0.806198	+	0.994126i
$214$	1.77292	+	3.07078i	0.121194	+	0.209914i
$215$	−7.62476	−	13.2065i	−0.520005	−	0.900674i
$216$	4.62476	+	2.36887i	0.314675	+	0.161181i
$217$		0			0
$218$	0.351848	−	0.609419i	0.0238302	−	0.0412751i
$219$	−0.190024	−	0.496083i	−0.0128406	−	0.0335222i
$220$	−10.7850			−0.727121
$221$	5.20602			0.350195
$222$	−4.93598	−	0.785381i	−0.331282	−	0.0527113i
$223$	6.44282	−	11.1593i	0.431443	−	0.747281i	−0.565555	−	0.824711i	$-0.691338\pi$
$223$	6.44282	−	11.1593i	0.431443	−	0.747281i	0.996998	+	0.0774293i	$0.0246712\pi$
$224$		0			0
$225$	4.23981	−	3.80664i	0.282654	−	0.253776i
$226$	4.25116	+	7.36323i	0.282783	+	0.489795i
$227$	10.9984	+	19.0497i	0.729987	+	1.26437i	0.956888	+	0.290457i	$0.0938073\pi$
$227$	10.9984	+	19.0497i	0.729987	+	1.26437i	−0.226901	+	0.973918i	$0.572859\pi$
$228$	3.32326	+	0.528775i	0.220088	+	0.0350190i
$229$	−1.89931	+	3.28971i	−0.125510	+	0.217390i	−0.921932	−	0.387351i	$-0.873390\pi$
$229$	−1.89931	+	3.28971i	−0.125510	+	0.217390i	0.796422	+	0.604741i	$0.206723\pi$
$230$	−0.370723	−	0.642111i	−0.0244448	−	0.0423396i
$231$		0			0
$232$	0.732287	−	1.26836i	0.0480770	−	0.0832718i
$233$	−3.33530	−	5.77690i	−0.218503	−	0.378458i	0.735848	−	0.677147i	$-0.236784\pi$
$233$	−3.33530	−	5.77690i	−0.218503	−	0.378458i	−0.954350	+	0.298689i	$0.903451\pi$
$234$	1.69850	−	1.52496i	0.111034	−	0.0996900i
$235$	−1.46169	+	2.53173i	−0.0953505	+	0.165152i
$236$	−1.98633			−0.129299
$237$	14.6683	−	18.0875i	0.952807	−	1.17491i
$238$		0			0
$239$	−7.82038	−	13.5453i	−0.505858	−	0.876172i	−0.999977	−	0.00677786i	$-0.997843\pi$
$239$	−7.82038	−	13.5453i	−0.505858	−	0.876172i	0.494119	−	0.869394i	$-0.335491\pi$
$240$	1.09097	+	2.84813i	0.0704219	+	0.183846i
$241$	10.7060	+	18.5434i	0.689635	+	1.19448i	0.971956	+	0.235163i	$0.0755625\pi$
$241$	10.7060	+	18.5434i	0.689635	+	1.19448i	−0.282320	+	0.959320i	$0.591104\pi$
$242$	−13.2564	+	22.9607i	−0.852151	+	1.47597i
$243$	4.08809	−	15.0429i	0.262251	−	0.965000i
$244$	10.3502			0.662605
$245$		0			0
$246$	−11.8759	−	1.88962i	−0.757181	−	0.120478i
$247$	0.739123	−	1.28020i	0.0470293	−	0.0814571i
$248$	−7.70370			−0.489185
$249$	1.93598	+	5.05415i	0.122688	+	0.320294i
$250$	12.1488			0.768360
$251$	23.6030			1.48981			0.744904	−	0.667171i	$-0.232495\pi$
$251$	23.6030			1.48981			0.744904	+	0.667171i	$0.232495\pi$
$252$		0			0
$253$	−2.57893			−0.162136
$254$	−18.9532			−1.18923
$255$	20.6088	+	3.27913i	1.29057	+	0.205347i
$256$	1.00000			0.0625000
$257$	10.1300	−	17.5456i	0.631890	−	1.09447i	−0.355275	−	0.934762i	$-0.615613\pi$
$257$	10.1300	−	17.5456i	0.631890	−	1.09447i	0.987165	−	0.159704i	$-0.0510538\pi$
$258$	5.36552	+	14.0074i	0.334043	+	0.872064i
$259$		0			0
$260$	1.33981			0.0830915
$261$	−4.17674	−	1.36368i	−0.258534	−	0.0844094i
$262$	−3.64652	+	6.31595i	−0.225283	+	0.390201i
$263$	11.2443	+	19.4757i	0.693355	+	1.20093i	0.970732	+	0.240165i	$0.0772014\pi$
$263$	11.2443	+	19.4757i	0.693355	+	1.20093i	−0.277377	+	0.960761i	$0.589465\pi$
$264$	10.4766	+	1.66697i	0.644791	+	0.102595i
$265$	0.198495	+	0.343803i	0.0121935	+	0.0211197i
$266$		0			0
$267$	4.45254	+	0.708458i	0.272491	+	0.0433569i
$268$	6.78495			0.414457
$269$	12.6706	−	21.9461i	0.772540	−	1.33808i	−0.163627	−	0.986522i	$-0.552319\pi$
$269$	12.6706	−	21.9461i	0.772540	−	1.33808i	0.936167	−	0.351556i	$-0.114347\pi$
$270$	7.68427	−	4.96695i	0.467650	−	0.302279i
$271$	6.87880	+	11.9144i	0.417858	+	0.723751i	0.995724	−	0.0923810i	$-0.0294478\pi$
$271$	6.87880	+	11.9144i	0.417858	+	0.723751i	−0.577866	+	0.816132i	$0.696114\pi$
$272$	3.42107	−	5.92546i	0.207433	−	0.359284i
$273$		0			0
$274$	4.09097	+	7.08577i	0.247145	+	0.428067i
$275$	5.81642	−	10.0743i	0.350743	−	0.607505i
$276$	0.260877	+	0.681054i	0.0157029	+	0.0409946i
$277$	1.64132	+	2.84284i	0.0986171	+	0.170810i	0.911112	−	0.412158i	$-0.135225\pi$
$277$	1.64132	+	2.84284i	0.0986171	+	0.170810i	−0.812495	+	0.582968i	$0.801891\pi$
$278$	6.23229	+	10.7946i	0.373788	+	0.647419i
$279$	4.77292	+	22.6129i	0.285747	+	1.35380i
$280$		0			0
$281$	0.634479	−	1.09895i	0.0378498	−	0.0655578i	−0.846480	−	0.532421i	$-0.821282\pi$
$281$	0.634479	−	1.09895i	0.0378498	−	0.0655578i	0.884330	+	0.466863i	$0.154616\pi$
$282$	1.81122	−	2.23342i	0.107857	−	0.132998i
$283$	8.19235			0.486984			0.243492	−	0.969903i	$-0.421707\pi$
$283$	8.19235			0.486984			0.243492	+	0.969903i	$0.421707\pi$
$284$	10.7850			0.639969
$285$	3.73229	−	4.60230i	0.221082	−	0.272616i
$286$	2.33009	−	4.03584i	0.137781	−	0.238644i
$287$		0			0
$288$	−0.619562	−	2.93533i	−0.0365080	−	0.172966i
$289$	−14.9074	−	25.8204i	−0.876906	−	1.51884i
$290$	−1.28947	−	2.23342i	−0.0757201	−	0.131151i
$291$	2.25280	+	5.88123i	0.132061	+	0.344764i
$292$	−0.153353	+	0.265616i	−0.00897433	+	0.0155440i
$293$	−7.72545	−	13.3809i	−0.451326	−	0.781719i	0.547143	−	0.837039i	$-0.315715\pi$
$293$	−7.72545	−	13.3809i	−0.451326	−	0.781719i	−0.998469	+	0.0553202i	$0.982382\pi$
$294$		0			0
$295$	−1.74884	+	3.02908i	−0.101821	+	0.176360i
$296$	1.44282	+	2.49904i	0.0838622	+	0.145254i
$297$	−1.59781	−	31.7851i	−0.0927142	−	1.84436i
$298$	−4.41423	+	7.64567i	−0.255709	+	0.442902i
$299$	0.320380			0.0185280
$300$	−3.24884	−	0.516934i	−0.187572	−	0.0298452i
$301$		0			0
$302$	7.49316	+	12.9785i	0.431183	+	0.746831i
$303$	13.7021	+	2.18018i	0.787163	+	0.125248i
$304$	−0.971410	−	1.68253i	−0.0557142	−	0.0964998i
$305$	9.11273	−	15.7837i	0.521793	−	0.903772i
$306$	−19.5127	−	6.37076i	−1.11547	−	0.364192i
$307$	−4.89931			−0.279619			−0.139809	−	0.990178i	$-0.544649\pi$
$307$	−4.89931			−0.279619			−0.139809	+	0.990178i	$0.544649\pi$
$308$		0			0
$309$	−4.23065	−	11.0447i	−0.240673	−	0.628310i
$310$	−6.78263	+	11.7479i	−0.385228	+	0.667234i
$311$	7.69002			0.436061			0.218031	−	0.975942i	$-0.430037\pi$
$311$	7.69002			0.436061			0.218031	+	0.975942i	$0.430037\pi$
$312$	−1.30150	−	0.207087i	−0.0736832	−	0.0117240i
$313$	1.72313			0.0973969			0.0486985	−	0.998814i	$-0.484493\pi$
$313$	1.72313			0.0973969			0.0486985	+	0.998814i	$0.484493\pi$
$314$	−18.9806			−1.07114
$315$		0			0
$316$	−13.4451			−0.756348
$317$	33.2028			1.86485			0.932426	−	0.361361i	$-0.117688\pi$
$317$	33.2028			1.86485			0.932426	+	0.361361i	$0.117688\pi$
$318$	−0.139680	−	0.364654i	−0.00783288	−	0.0204488i
$319$	−8.97017			−0.502233
$320$	0.880438	−	1.52496i	0.0492180	−	0.0852481i
$321$	−6.06526	−	0.965064i	−0.338530	−	0.0538646i
$322$		0			0
$323$	−13.2930			−0.739644
$324$	−8.23229	+	3.63723i	−0.457349	+	0.202068i
$325$	−0.722572	+	1.25153i	−0.0400811	+	0.0694224i
$326$	−7.51887	−	13.0231i	−0.416432	−	0.721281i
$327$	0.435984	+	1.13819i	0.0241099	+	0.0629423i
$328$	3.47141	+	6.01266i	0.191677	+	0.331994i
$329$		0			0
$330$	11.7661	−	14.5088i	0.647701	−	0.798683i
$331$	2.88891			0.158789			0.0793944	−	0.996843i	$-0.474701\pi$
$331$	2.88891			0.158789			0.0793944	+	0.996843i	$0.474701\pi$
$332$	1.56238	−	2.70612i	0.0857468	−	0.148518i
$333$	6.44158	−	5.78346i	0.352996	−	0.316931i
$334$	−0.572097	−	0.990901i	−0.0313037	−	0.0542197i
$335$	5.97373	−	10.3468i	0.326380	−	0.565307i
$336$		0			0
$337$	−4.36156	−	7.55445i	−0.237590	−	0.411517i	0.722433	−	0.691441i	$-0.243024\pi$
$337$	−4.36156	−	7.55445i	−0.237590	−	0.411517i	−0.960022	+	0.279924i	$0.909691\pi$
$338$	6.21053	−	10.7570i	0.337808	−	0.585101i
$339$	−14.5435	−	2.31407i	−0.789895	−	0.125683i
$340$	−6.02408	−	10.4340i	−0.326701	−	0.565863i
$341$	23.5917	+	40.8620i	1.27756	+	2.21280i
$342$	−4.33693	+	3.89384i	−0.234514	+	0.210555i
$343$		0			0
$344$	4.33009	−	7.49994i	0.233463	−	0.404370i
$345$	1.26827	+	0.201799i	0.0682813	+	0.0108645i
$346$	−0.497677			−0.0267553
$347$	9.69467			0.520437			0.260219	−	0.965550i	$-0.416205\pi$
$347$	9.69467			0.520437			0.260219	+	0.965550i	$0.416205\pi$
$348$	0.907394	+	2.36887i	0.0486414	+	0.126985i
$349$	−14.1992	+	24.5937i	−0.760065	+	1.31647i	0.182752	+	0.983159i	$0.441500\pi$
$349$	−14.1992	+	24.5937i	−0.760065	+	1.31647i	−0.942817	+	0.333312i	$0.891834\pi$
$350$		0			0
$351$	0.198495	+	3.94865i	0.0105949	+	0.210763i
$352$	−3.06238	−	5.30420i	−0.163225	−	0.282715i
$353$	−2.19686	−	3.80507i	−0.116927	−	0.202524i	0.801621	−	0.597832i	$-0.203971\pi$
$353$	−2.19686	−	3.80507i	−0.116927	−	0.202524i	−0.918548	+	0.395308i	$0.870638\pi$
$354$	2.16703	−	2.67217i	0.115176	−	0.142024i
$355$	9.49549	−	16.4467i	0.503968	−	0.872898i
$356$	−1.30150	−	2.25427i	−0.0689796	−	0.119476i
$357$		0			0
$358$	4.41423	−	7.64567i	0.233299	−	0.404086i
$359$	16.0796	+	27.8507i	0.848650	+	1.46990i	0.882413	+	0.470475i	$0.155917\pi$
$359$	16.0796	+	27.8507i	0.848650	+	1.46990i	−0.0337633	+	0.999430i	$0.510749\pi$
$360$	−5.02175	−	1.63957i	−0.264670	−	0.0864127i
$361$	7.61273	−	13.1856i	0.400670	−	0.693980i
$362$	−1.32941			−0.0698721
$363$	−16.4263	−	42.8830i	−0.862155	−	2.25077i
$364$		0			0
$365$	0.270036	+	0.467717i	0.0141343	+	0.0244814i
$366$	−11.2918	+	13.9239i	−0.590231	+	0.727816i
$367$	17.3015	+	29.9671i	0.903131	+	1.56427i	0.823406	+	0.567452i	$0.192071\pi$
$367$	17.3015	+	29.9671i	0.903131	+	1.56427i	0.0797249	+	0.996817i	$0.474596\pi$
$368$	0.210533	−	0.364654i	0.0109748	−	0.0190089i
$369$	15.4984	−	13.9149i	0.806813	−	0.724383i
$370$	5.08126			0.264162
$371$		0			0
$372$	8.40451	−	10.3636i	0.435754	−	0.537330i
$373$	−5.48796	+	9.50543i	−0.284156	+	0.492172i	−0.972404	−	0.233303i	$-0.925047\pi$
$373$	−5.48796	+	9.50543i	−0.284156	+	0.492172i	0.688248	+	0.725475i	$0.258380\pi$
$374$	−41.9064			−2.16693
$375$	−13.2540	+	16.3436i	−0.684436	+	0.843980i
$376$	−1.66019			−0.0856178
$377$	1.11436			0.0573925
$378$		0			0
$379$	33.9877			1.74583			0.872916	−	0.487871i	$-0.162226\pi$
$379$	33.9877			1.74583			0.872916	+	0.487871i	$0.162226\pi$
$380$	−3.42107			−0.175497
$381$	20.6774	−	25.4974i	1.05934	−	1.30627i
$382$	−16.1683			−0.827241
$383$	−10.5120	+	18.2074i	−0.537140	+	0.930354i	0.461916	+	0.886923i	$0.347162\pi$
$383$	−10.5120	+	18.2074i	−0.537140	+	0.930354i	−0.999056	+	0.0434304i	$0.986171\pi$
$384$	−1.09097	+	1.34528i	−0.0556734	+	0.0686511i
$385$		0			0
$386$	−14.1683			−0.721146
$387$	−24.6975	−	8.06357i	−1.25545	−	0.409894i
$388$	1.81806	−	3.14897i	0.0922978	−	0.159865i
$389$	−6.86909	−	11.8976i	−0.348277	−	0.603233i	0.637667	−	0.770312i	$-0.279900\pi$
$389$	−6.86909	−	11.8976i	−0.348277	−	0.603233i	−0.985943	+	0.167080i	$0.946566\pi$
$390$	−1.46169	+	1.80242i	−0.0740158	+	0.0912691i
$391$	−1.44050	−	2.49501i	−0.0728491	−	0.126178i
$392$		0			0
$393$	−4.51848	−	11.7961i	−0.227927	−	0.595035i
$394$	15.8421			0.798115
$395$	−11.8376	+	20.5034i	−0.595615	+	1.03164i
$396$	−13.6722	+	12.2754i	−0.687055	+	0.616861i
$397$	3.57893	+	6.19889i	0.179622	+	0.311114i	0.941751	−	0.336311i	$-0.109179\pi$
$397$	3.57893	+	6.19889i	0.179622	+	0.311114i	−0.762129	+	0.647425i	$0.775846\pi$
$398$	4.47141	−	7.74471i	0.224132	−	0.388207i
$399$		0			0
$400$	0.949657	+	1.64485i	0.0474828	+	0.0822427i
$401$	4.63968	−	8.03616i	0.231695	−	0.401307i	−0.726612	−	0.687048i	$-0.758906\pi$
$401$	4.63968	−	8.03616i	0.231695	−	0.401307i	0.958307	+	0.285741i	$0.0922397\pi$
$402$	−7.40219	+	9.12767i	−0.369188	+	0.455247i
$403$	−2.93078	−	5.07626i	−0.145993	−	0.252867i
$404$	−4.00520	−	6.93721i	−0.199266	−	0.345139i
$405$	−1.70137	+	15.7563i	−0.0845419	+	0.782937i
$406$		0			0
$407$	8.83693	−	15.3060i	0.438030	−	0.758691i
$408$	4.23912	+	11.0668i	0.209868	+	0.547889i
$409$	−15.1683			−0.750023			−0.375011	−	0.927020i	$-0.622361\pi$
$409$	−15.1683			−0.750023			−0.375011	+	0.927020i	$0.622361\pi$
$410$	12.2255			0.603772
$411$	−13.9955	−	2.22687i	−0.690346	−	0.109843i
$412$	−3.41423	+	5.91362i	−0.168207	+	0.291343i
$413$		0			0
$414$	−1.20082	−	0.392058i	−0.0590170	−	0.0192686i
$415$	−2.75116	−	4.76515i	−0.135049	−	0.233912i
$416$	0.380438	+	0.658939i	0.0186525	+	0.0323071i
$417$	−21.3211	−	3.39247i	−1.04410	−	0.166130i
$418$	−5.94966	+	10.3051i	−0.291007	+	0.504039i
$419$	4.16827	+	7.21966i	0.203633	+	0.352703i	0.949696	−	0.313172i	$-0.101392\pi$
$419$	4.16827	+	7.21966i	0.203633	+	0.352703i	−0.746063	+	0.665875i	$0.768058\pi$
$420$		0			0
$421$	−3.50232	+	6.06620i	−0.170693	+	0.295649i	−0.938662	−	0.344838i	$-0.887934\pi$
$421$	−3.50232	+	6.06620i	−0.170693	+	0.295649i	0.767969	+	0.640486i	$0.221267\pi$
$422$	11.3856	+	19.7205i	0.554244	+	0.959979i
$423$	1.02859	+	4.87320i	0.0500118	+	0.236943i
$424$	−0.112725	+	0.195246i	−0.00547442	+	0.00948197i
$425$	12.9954			0.630367
$426$	−11.7661	+	14.5088i	−0.570068	+	0.702953i
$427$		0			0
$428$	1.77292	+	3.07078i	0.0856971	+	0.148432i
$429$	2.88727	+	7.53762i	0.139399	+	0.363920i
$430$	−7.62476	−	13.2065i	−0.367699	−	0.636873i
$431$	−1.72545	+	2.98857i	−0.0831120	+	0.143954i	−0.904585	−	0.426293i	$-0.859819\pi$
$431$	−1.72545	+	2.98857i	−0.0831120	+	0.143954i	0.821473	+	0.570247i	$0.193153\pi$
$432$	4.62476	+	2.36887i	0.222509	+	0.113972i
$433$	−28.2599			−1.35809			−0.679043	−	0.734099i	$-0.737605\pi$
$433$	−28.2599			−1.35809			−0.679043	+	0.734099i	$0.737605\pi$
$434$		0			0
$435$	4.41135	+	0.701905i	0.211508	+	0.0336538i
$436$	0.351848	−	0.609419i	0.0168505	−	0.0291859i
$437$	−0.818057			−0.0391330
$438$	−0.190024	−	0.496083i	−0.00907968	−	0.0237037i
$439$	28.8960			1.37913			0.689566	−	0.724222i	$-0.257801\pi$
$439$	28.8960			1.37913			0.689566	+	0.724222i	$0.257801\pi$
$440$	−10.7850			−0.514152
$441$		0			0
$442$	5.20602			0.247625
$443$	−13.7609			−0.653799			−0.326899	−	0.945059i	$-0.606004\pi$
$443$	−13.7609			−0.653799			−0.326899	+	0.945059i	$0.606004\pi$
$444$	−4.93598	−	0.785381i	−0.234251	−	0.0372725i
$445$	−4.58358			−0.217283
$446$	6.44282	−	11.1593i	0.305076	−	0.528408i
$447$	−5.46978	−	14.2796i	−0.258711	−	0.675401i
$448$		0			0
$449$	−20.2003			−0.953309			−0.476655	−	0.879091i	$-0.658151\pi$
$449$	−20.2003			−0.953309			−0.476655	+	0.879091i	$0.658151\pi$
$450$	4.23981	−	3.80664i	0.199867	−	0.179447i
$451$	21.2616	−	36.8261i	1.00117	−	1.73407i
$452$	4.25116	+	7.36323i	0.199958	+	0.346337i
$453$	−25.6346	−	4.07881i	−1.20442	−	0.191639i
$454$	10.9984	+	19.0497i	0.516179	+	0.894048i
$455$		0			0
$456$	3.32326	+	0.528775i	0.155626	+	0.0247621i
$457$	20.0298			0.936956			0.468478	−	0.883475i	$-0.344803\pi$
$457$	20.0298			0.936956			0.468478	+	0.883475i	$0.344803\pi$
$458$	−1.89931	+	3.28971i	−0.0887491	+	0.153718i
$459$	29.8583	−	19.2998i	1.39367	−	0.900837i
$460$	−0.370723	−	0.642111i	−0.0172851	−	0.0299386i
$461$	−5.97661	+	10.3518i	−0.278359	+	0.482131i	−0.970977	−	0.239173i	$-0.923124\pi$
$461$	−5.97661	+	10.3518i	−0.278359	+	0.482131i	0.692618	+	0.721304i	$0.256457\pi$
$462$		0			0
$463$	6.64527	+	11.5100i	0.308832	+	0.534913i	0.978107	−	0.208102i	$-0.0667286\pi$
$463$	6.64527	+	11.5100i	0.308832	+	0.534913i	−0.669275	+	0.743015i	$0.733395\pi$
$464$	0.732287	−	1.26836i	0.0339956	−	0.0588820i
$465$	−8.40451	−	21.9411i	−0.389750	−	1.01750i
$466$	−3.33530	−	5.77690i	−0.154505	−	0.267610i
$467$	5.61505	+	9.72555i	0.259833	+	0.450045i	0.966197	−	0.257804i	$-0.0829990\pi$
$467$	5.61505	+	9.72555i	0.259833	+	0.450045i	−0.706364	+	0.707849i	$0.749666\pi$
$468$	1.69850	−	1.52496i	0.0785130	−	0.0704915i
$469$		0			0
$470$	−1.46169	+	2.53173i	−0.0674230	+	0.116780i
$471$	20.7073	−	25.5342i	0.954140	−	1.17655i
$472$	−1.98633			−0.0914281
$473$	−53.0416			−2.43886
$474$	14.6683	−	18.0875i	0.673736	−	0.830786i
$475$	1.84501	−	3.19565i	0.0846550	−	0.146627i
$476$		0			0
$477$	0.642950	+	0.209918i	0.0294387	+	0.00961150i
$478$	−7.82038	−	13.5453i	−0.357696	−	0.619547i
$479$	−16.3135	−	28.2559i	−0.745385	−	1.29104i	−0.950015	−	0.312205i	$-0.898932\pi$
$479$	−16.3135	−	28.2559i	−0.745385	−	1.29104i	0.204630	−	0.978839i	$-0.434401\pi$
$480$	1.09097	+	2.84813i	0.0497958	+	0.129999i
$481$	−1.09781	+	1.90146i	−0.0500557	+	0.0866991i
$482$	10.7060	+	18.5434i	0.487646	+	0.844627i
$483$		0			0
$484$	−13.2564	+	22.9607i	−0.602562	+	1.04367i
$485$	−3.20137	−	5.54494i	−0.145367	−	0.251783i
$486$	4.08809	−	15.0429i	0.185440	−	0.682358i
$487$	1.84897	−	3.20251i	0.0837848	−	0.145120i	−0.821088	−	0.570802i	$-0.806632\pi$
$487$	1.84897	−	3.20251i	0.0837848	−	0.145120i	0.904873	+	0.425682i	$0.139966\pi$
$488$	10.3502			0.468532
$489$	25.7226	+	4.09280i	1.16321	+	0.185083i
$490$		0			0
$491$	−18.7804	−	32.5287i	−0.847549	−	1.46800i	−0.883389	−	0.468641i	$-0.844744\pi$
$491$	−18.7804	−	32.5287i	−0.847549	−	1.46800i	0.0358393	−	0.999358i	$-0.488590\pi$
$492$	−11.8759	−	1.88962i	−0.535408	−	0.0851906i
$493$	−5.01040	−	8.67827i	−0.225657	−	0.390850i
$494$	0.739123	−	1.28020i	0.0332547	−	0.0575989i
$495$	6.68194	+	31.6574i	0.300331	+	1.42289i
$496$	−7.70370			−0.345906
$497$		0			0
$498$	1.93598	+	5.05415i	0.0867535	+	0.226482i
$499$	15.8977	−	27.5356i	0.711678	−	1.23266i	−0.252549	−	0.967584i	$-0.581269\pi$
$499$	15.8977	−	27.5356i	0.711678	−	1.23266i	0.964227	−	0.265078i	$-0.0853977\pi$
$500$	12.1488			0.543313
$501$	1.95718	+	0.311414i	0.0874404	+	0.0139129i
$502$	23.6030			1.05345
$503$	−30.8252			−1.37443			−0.687214	−	0.726455i	$-0.741166\pi$
$503$	−30.8252			−1.37443			−0.687214	+	0.726455i	$0.741166\pi$
$504$		0			0
$505$	−14.1053			−0.627679
$506$	−2.57893			−0.114648
$507$	7.69562	+	20.0904i	0.341774	+	0.892248i
$508$	−18.9532			−0.840913
$509$	4.00808	−	6.94220i	0.177655	−	0.307708i	−0.763422	−	0.645900i	$-0.776482\pi$
$509$	4.00808	−	6.94220i	0.177655	−	0.307708i	0.941077	+	0.338193i	$0.109816\pi$
$510$	20.6088	+	3.27913i	0.912572	+	0.145202i
$511$		0			0
$512$	1.00000			0.0441942
$513$	−0.506837	−	10.0825i	−0.0223774	−	0.445151i
$514$	10.1300	−	17.5456i	0.446814	−	0.773904i
$515$	6.01204	+	10.4132i	0.264922	+	0.458858i
$516$	5.36552	+	14.0074i	0.236204	+	0.616642i
$517$	5.08414	+	8.80598i	0.223600	+	0.387287i
$518$		0			0
$519$	0.542951	−	0.669515i	0.0238329	−	0.0293885i
$520$	1.33981			0.0587546
$521$	−14.8646	+	25.7462i	−0.651229	+	1.12796i	0.331596	+	0.943421i	$0.392413\pi$
$521$	−14.8646	+	25.7462i	−0.651229	+	1.12796i	−0.982825	+	0.184540i	$0.940920\pi$
$522$	−4.17674	−	1.36368i	−0.182811	−	0.0596864i
$523$	−13.4698	−	23.3303i	−0.588992	−	1.02016i	−0.994365	−	0.106013i	$-0.966192\pi$
$523$	−13.4698	−	23.3303i	−0.588992	−	1.02016i	0.405373	−	0.914152i	$-0.367142\pi$
$524$	−3.64652	+	6.31595i	−0.159299	+	0.275914i
$525$		0			0
$526$	11.2443	+	19.4757i	0.490276	+	0.849183i
$527$	−26.3549	+	45.6480i	−1.14804	+	1.98846i
$528$	10.4766	+	1.66697i	0.455936	+	0.0725455i
$529$	11.4114	+	19.7650i	0.496146	+	0.859350i
$530$	0.198495	+	0.343803i	0.00862207	+	0.0149339i
$531$	1.23065	+	5.83052i	0.0534057	+	0.253023i
$532$		0			0
$533$	−2.64132	+	4.57489i	−0.114408	+	0.198161i
$534$	4.45254	+	0.708458i	0.192680	+	0.0306580i
$535$	6.24377			0.269942
$536$	6.78495			0.293065
$537$	5.46978	+	14.2796i	0.236038	+	0.616210i
$538$	12.6706	−	21.9461i	0.546268	−	0.946164i
$539$		0			0
$540$	7.68427	−	4.96695i	0.330678	−	0.213744i
$541$	7.15568	+	12.3940i	0.307647	+	0.532859i	0.977847	−	0.209321i	$-0.0671252\pi$
$541$	7.15568	+	12.3940i	0.307647	+	0.532859i	−0.670201	+	0.742180i	$0.733792\pi$
$542$	6.87880	+	11.9144i	0.295470	+	0.511769i
$543$	1.45034	−	1.78843i	0.0622403	−	0.0767487i
$544$	3.42107	−	5.92546i	0.146677	−	0.254052i
$545$	−0.619562	−	1.07311i	−0.0265391	−	0.0459671i
$546$		0			0
$547$	1.02463	−	1.77471i	0.0438101	−	0.0758813i	−0.843289	−	0.537461i	$-0.819384\pi$
$547$	1.02463	−	1.77471i	0.0438101	−	0.0758813i	0.887099	+	0.461579i	$0.152717\pi$
$548$	4.09097	+	7.08577i	0.174758	+	0.302689i
$549$	−6.41260	−	30.3813i	−0.273683	−	1.29664i
$550$	5.81642	−	10.0743i	0.248013	−	0.429571i
$551$	−2.84540			−0.121218
$552$	0.260877	+	0.681054i	0.0111037	+	0.0289876i
$553$		0			0
$554$	1.64132	+	2.84284i	0.0697328	+	0.120781i
$555$	−5.54351	+	6.83572i	−0.235309	+	0.290160i
$556$	6.23229	+	10.7946i	0.264308	+	0.457795i
$557$	8.84338	−	15.3172i	0.374706	−	0.649010i	−0.615577	−	0.788077i	$-0.711077\pi$
$557$	8.84338	−	15.3172i	0.374706	−	0.649010i	0.990283	+	0.139067i	$0.0444103\pi$
$558$	4.77292	+	22.6129i	0.202054	+	0.957279i
$559$	6.58934			0.278699
$560$		0			0
$561$	45.7187	−	56.3759i	1.93025	−	2.38019i
$562$	0.634479	−	1.09895i	0.0267639	−	0.0463564i
$563$	−0.937063			−0.0394925			−0.0197462	−	0.999805i	$-0.506286\pi$
$563$	−0.937063			−0.0394925			−0.0197462	+	0.999805i	$0.506286\pi$
$564$	1.81122	−	2.23342i	0.0762661	−	0.0940440i
$565$	14.9715			0.629858
$566$	8.19235			0.344350
$567$		0			0
$568$	10.7850			0.452527
$569$	23.5264			0.986278			0.493139	−	0.869951i	$-0.335849\pi$
$569$	23.5264			0.986278			0.493139	+	0.869951i	$0.335849\pi$
$570$	3.73229	−	4.60230i	0.156328	−	0.192769i
$571$	−0.484004			−0.0202549			−0.0101275	−	0.999949i	$-0.503224\pi$
$571$	−0.484004			−0.0202549			−0.0101275	+	0.999949i	$0.503224\pi$
$572$	2.33009	−	4.03584i	0.0974262	−	0.168747i
$573$	17.6391	−	21.7509i	0.736885	−	0.908655i
$574$		0			0
$575$	0.799737			0.0333514
$576$	−0.619562	−	2.93533i	−0.0258151	−	0.122305i
$577$	2.23065	−	3.86360i	0.0928633	−	0.160844i	−0.815852	−	0.578261i	$-0.803731\pi$
$577$	2.23065	−	3.86360i	0.0928633	−	0.160844i	0.908715	+	0.417417i	$0.137065\pi$
$578$	−14.9074	−	25.8204i	−0.620066	−	1.07399i
$579$	15.4572	−	19.0603i	0.642379	−	0.792119i
$580$	−1.28947	−	2.23342i	−0.0535422	−	0.0927378i
$581$		0			0
$582$	2.25280	+	5.88123i	0.0933814	+	0.243785i
$583$	1.38083			0.0571881
$584$	−0.153353	+	0.265616i	−0.00634581	+	0.0109913i
$585$	−0.830095	−	3.93278i	−0.0343202	−	0.162600i
$586$	−7.72545	−	13.3809i	−0.319135	−	0.552759i
$587$	−8.31518	+	14.4023i	−0.343204	+	0.594447i	−0.985026	−	0.172407i	$-0.944846\pi$
$587$	−8.31518	+	14.4023i	−0.343204	+	0.594447i	0.641822	+	0.766854i	$0.278179\pi$
$588$		0			0
$589$	7.48345	+	12.9617i	0.308350	+	0.534078i
$590$	−1.74884	+	3.02908i	−0.0719985	+	0.124705i
$591$	−17.2833	+	21.3121i	−0.710941	+	0.876663i
$592$	1.44282	+	2.49904i	0.0592995	+	0.102710i
$593$	−20.7632	−	35.9629i	−0.852642	−	1.47682i	−0.878815	−	0.477163i	$-0.841665\pi$
$593$	−20.7632	−	35.9629i	−0.852642	−	1.47682i	0.0261726	−	0.999657i	$-0.491668\pi$
$594$	−1.59781	−	31.7851i	−0.0655589	−	1.30416i
$595$		0			0
$596$	−4.41423	+	7.64567i	−0.180814	+	0.313179i
$597$	5.54063	+	14.4646i	0.226763	+	0.591995i
$598$	0.320380			0.0131013
$599$	15.0766			0.616014			0.308007	−	0.951384i	$-0.400338\pi$
$599$	15.0766			0.616014			0.308007	+	0.951384i	$0.400338\pi$
$600$	−3.24884	−	0.516934i	−0.132633	−	0.0211037i
$601$	8.05555	−	13.9526i	0.328593	−	0.569139i	−0.653640	−	0.756805i	$-0.726759\pi$
$601$	8.05555	−	13.9526i	0.328593	−	0.569139i	0.982233	+	0.187666i	$0.0600924\pi$
$602$		0			0
$603$	−4.20370	−	19.9161i	−0.171188	−	0.811044i
$604$	7.49316	+	12.9785i	0.304892	+	0.528089i
$605$	23.3428	+	40.4310i	0.949021	+	1.64375i
$606$	13.7021	+	2.18018i	0.556608	+	0.0885638i
$607$	9.78659	−	16.9509i	0.397225	−	0.688014i	−0.596157	−	0.802868i	$-0.703306\pi$
$607$	9.78659	−	16.9509i	0.397225	−	0.688014i	0.993382	+	0.114853i	$0.0366398\pi$
$608$	−0.971410	−	1.68253i	−0.0393959	−	0.0682357i
$609$		0			0
$610$	9.11273	−	15.7837i	0.368963	−	0.639063i
$611$	−0.631600	−	1.09396i	−0.0255518	−	0.0442570i
$612$	−19.5127	−	6.37076i	−0.788755	−	0.257523i
$613$	−2.77579	+	4.80782i	−0.112113	+	0.194186i	−0.916622	−	0.399755i	$-0.869095\pi$
$613$	−2.77579	+	4.80782i	−0.112113	+	0.194186i	0.804509	+	0.593941i	$0.202429\pi$
$614$	−4.89931			−0.197720
$615$	−13.3376	+	16.4467i	−0.537825	+	0.663194i
$616$		0			0
$617$	0.634479	+	1.09895i	0.0255431	+	0.0442420i	0.878514	−	0.477716i	$-0.158535\pi$
$617$	0.634479	+	1.09895i	0.0255431	+	0.0442420i	−0.852971	+	0.521958i	$0.825202\pi$
$618$	−4.23065	−	11.0447i	−0.170182	−	0.444283i
$619$	2.25116	+	3.89913i	0.0904818	+	0.156719i	0.907714	−	0.419589i	$-0.137826\pi$
$619$	2.25116	+	3.89913i	0.0904818	+	0.156719i	−0.817232	+	0.576309i	$0.804493\pi$
$620$	−6.78263	+	11.7479i	−0.272397	+	0.471805i
$621$	1.83749	−	1.18771i	0.0737358	−	0.0476613i
$622$	7.69002			0.308342
$623$		0			0
$624$	−1.30150	−	0.207087i	−0.0521019	−	0.00829011i
$625$	5.94802	−	10.3023i	0.237921	−	0.412091i
$626$	1.72313			0.0688700
$627$	−7.37236	−	19.2465i	−0.294424	−	0.768633i
$628$	−18.9806			−0.757407
$629$	19.7439			0.787242
$630$		0			0
$631$	−1.69905			−0.0676381			−0.0338191	−	0.999428i	$-0.510767\pi$
$631$	−1.69905			−0.0676381			−0.0338191	+	0.999428i	$0.510767\pi$
$632$	−13.4451			−0.534819
$633$	−38.9510	−	6.19763i	−1.54816	−	0.246334i
$634$	33.2028			1.31865
$635$	−16.6871	+	28.9030i	−0.662209	+	1.14698i
$636$	−0.139680	−	0.364654i	−0.00553868	−	0.0144595i
$637$		0			0
$638$	−8.97017			−0.355132
$639$	−6.68194	−	31.6574i	−0.264334	−	1.25235i
$640$	0.880438	−	1.52496i	0.0348024	−	0.0602795i
$641$	0.474289	+	0.821492i	0.0187333	+	0.0324470i	0.875240	−	0.483689i	$-0.160703\pi$
$641$	0.474289	+	0.821492i	0.0187333	+	0.0324470i	−0.856507	+	0.516136i	$0.827370\pi$
$642$	−6.06526	−	0.965064i	−0.239377	−	0.0380880i
$643$	9.84897	+	17.0589i	0.388405	+	0.672738i	0.992235	−	0.124375i	$-0.0396927\pi$
$643$	9.84897	+	17.0589i	0.388405	+	0.672738i	−0.603830	+	0.797113i	$0.706359\pi$
$644$		0			0
$645$	26.0848	+	4.15044i	1.02709	+	0.163424i
$646$	−13.2930			−0.523007
$647$	−11.7271	+	20.3119i	−0.461039	+	0.798543i	−0.999013	−	0.0444181i	$-0.985857\pi$
$647$	−11.7271	+	20.3119i	−0.461039	+	0.798543i	0.537974	+	0.842962i	$0.319190\pi$
$648$	−8.23229	+	3.63723i	−0.323395	+	0.142884i
$649$	6.08289	+	10.5359i	0.238774	+	0.413569i
$650$	−0.722572	+	1.25153i	−0.0283416	+	0.0490891i
$651$		0			0
$652$	−7.51887	−	13.0231i	−0.294462	−	0.510023i
$653$	−11.3954	+	19.7373i	−0.445935	+	0.772382i	−0.998117	−	0.0613420i	$-0.980462\pi$
$653$	−11.3954	+	19.7373i	−0.445935	+	0.772382i	0.552182	+	0.833724i	$0.313795\pi$
$654$	0.435984	+	1.13819i	0.0170483	+	0.0445069i
$655$	6.42107	+	11.1216i	0.250892	+	0.434557i
$656$	3.47141	+	6.01266i	0.135536	+	0.234755i
$657$	0.874681	+	0.285577i	0.0341246	+	0.0111414i
$658$		0			0
$659$	−13.2398	+	22.9320i	−0.515750	+	0.893305i	0.484083	+	0.875022i	$0.339153\pi$
$659$	−13.2398	+	22.9320i	−0.515750	+	0.893305i	−0.999833	+	0.0182828i	$0.994180\pi$
$660$	11.7661	−	14.5088i	0.457994	−	0.564754i
$661$	26.7382			1.03999			0.519997	−	0.854168i	$-0.325933\pi$
$661$	26.7382			1.03999			0.519997	+	0.854168i	$0.325933\pi$
$662$	2.88891			0.112281
$663$	−5.67962	+	7.00356i	−0.220578	+	0.271996i
$664$	1.56238	−	2.70612i	0.0606322	−	0.105018i
$665$		0			0
$666$	6.44158	−	5.78346i	0.249606	−	0.224104i
$667$	−0.308342	−	0.534063i	−0.0119390	−	0.0206790i
$668$	−0.572097	−	0.990901i	−0.0221351	−	0.0383391i
$669$	7.98345	+	20.8419i	0.308658	+	0.805793i
$670$	5.97373	−	10.3468i	0.230785	−	0.399732i
$671$	−31.6963	−	54.8996i	−1.22362	−	2.11938i
$672$		0			0
$673$	−10.3856	+	17.9885i	−0.400337	+	0.693404i	−0.993766	−	0.111482i	$-0.964440\pi$
$673$	−10.3856	+	17.9885i	−0.400337	+	0.693404i	0.593429	+	0.804886i	$0.297774\pi$
$674$	−4.36156	−	7.55445i	−0.168001	−	0.290987i
$675$	0.495487	+	9.85667i	0.0190713	+	0.379384i
$676$	6.21053	−	10.7570i	0.238867	−	0.413729i
$677$	20.6979			0.795486			0.397743	−	0.917497i	$-0.369793\pi$
$677$	20.6979			0.795486			0.397743	+	0.917497i	$0.369793\pi$
$678$	−14.5435	−	2.31407i	−0.558540	−	0.0888712i
$679$		0			0
$680$	−6.02408	−	10.4340i	−0.231013	−	0.400126i
$681$	−37.6261	−	5.98682i	−1.44184	−	0.229416i
$682$	23.5917	+	40.8620i	0.903371	+	1.56469i
$683$	14.2918	−	24.7541i	0.546860	−	0.947190i	−0.451627	−	0.892207i	$-0.649156\pi$
$683$	14.2918	−	24.7541i	0.546860	−	0.947190i	0.998487	−	0.0549828i	$-0.0175104\pi$
$684$	−4.33693	+	3.89384i	−0.165827	+	0.148885i
$685$	14.4074			0.550478
$686$		0			0
$687$	−2.35348	−	6.14409i	−0.0897910	−	0.234412i
$688$	4.33009	−	7.49994i	0.165083	−	0.285933i
$689$	−0.171540			−0.00653515
$690$	1.26827	+	0.201799i	0.0482822	+	0.00768234i
$691$	6.69794			0.254802			0.127401	−	0.991851i	$-0.459337\pi$
$691$	6.69794			0.254802			0.127401	+	0.991851i	$0.459337\pi$
$692$	−0.497677			−0.0189188
$693$		0			0
$694$	9.69467			0.368005
$695$	21.9486			0.832557
$696$	0.907394	+	2.36887i	0.0343947	+	0.0897919i
$697$	47.5037			1.79933
$698$	−14.1992	+	24.5937i	−0.537447	+	0.930886i
$699$	11.4103	+	1.81553i	0.431576	+	0.0686695i
$700$		0			0
$701$	−25.1442			−0.949683			−0.474842	−	0.880071i	$-0.657495\pi$
$701$	−25.1442			−0.949683			−0.474842	+	0.880071i	$0.657495\pi$
$702$	0.198495	+	3.94865i	0.00749171	+	0.149032i
$703$	2.80314	−	4.85518i	0.105722	−	0.183117i
$704$	−3.06238	−	5.30420i	−0.115418	−	0.199910i
$705$	−1.81122	−	4.72844i	−0.0682145	−	0.178083i
$706$	−2.19686	−	3.80507i	−0.0826799	−	0.143206i
$707$		0			0
$708$	2.16703	−	2.67217i	0.0814418	−	0.100426i
$709$	8.86621			0.332977			0.166489	−	0.986043i	$-0.446757\pi$
$709$	8.86621			0.332977			0.166489	+	0.986043i	$0.446757\pi$
$710$	9.49549	−	16.4467i	0.356359	−	0.617232i
$711$	8.33009	+	39.4659i	0.312403	+	1.48009i
$712$	−1.30150	−	2.25427i	−0.0487760	−	0.0844824i
$713$	−1.62188	+	2.80919i	−0.0607401	+	0.105205i
$714$		0			0
$715$	−4.10301	−	7.10662i	−0.153444	−	0.265773i
$716$	4.41423	−	7.64567i	0.164968	−	0.285732i
$717$	26.7540	+	4.25693i	0.999148	+	0.158978i
$718$	16.0796	+	27.8507i	0.600086	+	1.03938i
$719$	−11.8015	−	20.4408i	−0.440122	−	0.762313i	0.557576	−	0.830126i	$-0.311731\pi$
$719$	−11.8015	−	20.4408i	−0.440122	−	0.762313i	−0.997698	+	0.0678123i	$0.978398\pi$
$720$	−5.02175	−	1.63957i	−0.187150	−	0.0611030i
$721$		0			0
$722$	7.61273	−	13.1856i	0.283316	−	0.490718i
$723$	−36.6260	−	5.82769i	−1.36214	−	0.216734i
$724$	−1.32941			−0.0494070
$725$	2.78168			0.103309
$726$	−16.4263	−	42.8830i	−0.609636	−	1.59154i
$727$	−3.25692	+	5.64115i	−0.120792	+	0.209219i	−0.920080	−	0.391730i	$-0.871877\pi$
$727$	−3.25692	+	5.64115i	−0.120792	+	0.209219i	0.799288	+	0.600948i	$0.205210\pi$
$728$		0			0
$729$	15.7769	+	21.9110i	0.584329	+	0.811517i
$730$	0.270036	+	0.467717i	0.00999449	+	0.0173110i
$731$	−29.6271	−	51.3156i	−1.09580	−	1.89798i
$732$	−11.2918	+	13.9239i	−0.417357	+	0.514644i
$733$	−11.5991	+	20.0901i	−0.428421	+	0.742047i	−0.996733	−	0.0807664i	$-0.974263\pi$
$733$	−11.5991	+	20.0901i	−0.428421	+	0.742047i	0.568312	+	0.822813i	$0.307597\pi$
$734$	17.3015	+	29.9671i	0.638610	+	1.10611i
$735$		0			0
$736$	0.210533	−	0.364654i	0.00776036	−	0.0134413i
$737$	−20.7781	−	35.9888i	−0.765372	−	1.32566i
$738$	15.4984	−	13.9149i	0.570503	−	0.512216i
$739$	−7.57838	+	13.1261i	−0.278775	+	0.482853i	−0.971081	−	0.238752i	$-0.923262\pi$
$739$	−7.57838	+	13.1261i	−0.278775	+	0.482853i	0.692305	+	0.721605i	$0.256595\pi$
$740$	5.08126			0.186791
$741$	0.915865	+	2.39099i	0.0336451	+	0.0878352i
$742$		0			0
$743$	−5.21737	−	9.03675i	−0.191407	−	0.331526i	0.754310	−	0.656518i	$-0.227972\pi$
$743$	−5.21737	−	9.03675i	−0.191407	−	0.331526i	−0.945717	+	0.324992i	$0.894638\pi$
$744$	8.40451	−	10.3636i	0.308124	−	0.379949i
$745$	7.77292	+	13.4631i	0.284778	+	0.493249i
$746$	−5.48796	+	9.50543i	−0.200929	+	0.348018i
$747$	−8.91135	−	2.90949i	−0.326049	−	0.106453i
$748$	−41.9064			−1.53225
$749$		0			0
$750$	−13.2540	+	16.3436i	−0.483969	+	0.596784i
$751$	−20.1059	+	34.8244i	−0.733674	+	1.27076i	0.221628	+	0.975131i	$0.428863\pi$
$751$	−20.1059	+	34.8244i	−0.733674	+	1.27076i	−0.955303	+	0.295630i	$0.904470\pi$
$752$	−1.66019			−0.0605409
$753$	−25.7502	+	31.7527i	−0.938390	+	1.15713i
$754$	1.11436			0.0405826
$755$	26.3891			0.960397
$756$		0			0
$757$	−21.5206			−0.782181			−0.391091	−	0.920352i	$-0.627902\pi$
$757$	−21.5206			−0.782181			−0.391091	+	0.920352i	$0.627902\pi$
$758$	33.9877			1.23449
$759$	2.81354	−	3.46939i	0.102125	−	0.125931i
$760$	−3.42107			−0.124095
$761$	−11.8313	+	20.4925i	−0.428886	+	0.742852i	−0.996774	−	0.0802535i	$-0.974427\pi$
$761$	−11.8313	+	20.4925i	−0.428886	+	0.742852i	0.567889	+	0.823105i	$0.307760\pi$
$762$	20.6774	−	25.4974i	0.749064	−	0.923674i
$763$		0			0
$764$	−16.1683			−0.584947
$765$	−26.8949	+	24.1471i	−0.972388	+	0.873042i
$766$	−10.5120	+	18.2074i	−0.379815	+	0.657860i
$767$	−0.755675	−	1.30887i	−0.0272858	−	0.0472605i
$768$	−1.09097	+	1.34528i	−0.0393670	+	0.0485436i
$769$	5.62764	+	9.74736i	0.202938	+	0.351499i	0.949474	−	0.313846i	$-0.101618\pi$
$769$	5.62764	+	9.74736i	0.202938	+	0.351499i	−0.746536	+	0.665345i	$0.768284\pi$
$770$		0			0
$771$	12.5523	+	32.7694i	0.452059	+	1.18016i
$772$	−14.1683			−0.509927
$773$	−0.138992	+	0.240741i	−0.00499919	+	0.00865886i	−0.868514	−	0.495664i	$-0.834925\pi$
$773$	−0.138992	+	0.240741i	−0.00499919	+	0.00865886i	0.863515	+	0.504323i	$0.168258\pi$
$774$	−24.6975	−	8.06357i	−0.887735	−	0.289839i
$775$	−7.31587	−	12.6715i	−0.262794	−	0.455172i
$776$	1.81806	−	3.14897i	0.0652644	−	0.113041i
$777$		0			0
$778$	−6.86909	−	11.8976i	−0.246269	−	0.426550i
$779$	6.74433	−	11.6815i	0.241641	−	0.418534i
$780$	−1.46169	+	1.80242i	−0.0523371	+	0.0645370i
$781$	−33.0276	−	57.2056i	−1.18182	−	2.04698i
$782$	−1.44050	−	2.49501i	−0.0515121	−	0.0892215i
$783$	6.39123	−	4.13116i	0.228404	−	0.147636i
$784$		0			0
$785$	−16.7112	+	28.9447i	−0.596449	+	1.03308i
$786$	−4.51848	−	11.7961i	−0.161169	−	0.420753i
$787$	29.3880			1.04757			0.523784	−	0.851851i	$-0.324520\pi$
$787$	29.3880			1.04757			0.523784	+	0.851851i	$0.324520\pi$
$788$	15.8421			0.564353
$789$	−38.4676	−	6.12071i	−1.36948	−	0.217903i
$790$	−11.8376	+	20.5034i	−0.421164	+	0.729477i
$791$		0			0
$792$	−13.6722	+	12.2754i	−0.485821	+	0.436186i
$793$	3.93762	+	6.82015i	0.139829	+	0.242191i
$794$	3.57893	+	6.19889i	0.127012	+	0.219991i
$795$	−0.679065	−	0.108048i	−0.0240839	−	0.00383208i
$796$	4.47141	−	7.74471i	0.158485	−	0.274504i
$797$	−0.433105	−	0.750160i	−0.0153414	−	0.0265720i	0.858253	−	0.513227i	$-0.171550\pi$
$797$	−0.433105	−	0.750160i	−0.0153414	−	0.0265720i	−0.873594	+	0.486655i	$0.838217\pi$
$798$		0			0
$799$	−5.67962	+	9.83739i	−0.200931	+	0.348022i
$800$	0.949657	+	1.64485i	0.0335754	+	0.0581544i
$801$	−5.81066	+	5.21700i	−0.205310	+	0.184334i
$802$	4.63968	−	8.03616i	0.163833	−	0.283767i
$803$	1.87851			0.0662910
$804$	−7.40219	+	9.12767i	−0.261055	+	0.321908i
$805$		0			0
$806$	−2.93078	−	5.07626i	−0.103232	−	0.178804i
$807$	15.7004	+	40.9881i	0.552681	+	1.44285i
$808$	−4.00520	−	6.93721i	−0.140903	−	0.244050i
$809$	9.66703	−	16.7438i	0.339875	−	0.588680i	−0.644534	−	0.764575i	$-0.722949\pi$
$809$	9.66703	−	16.7438i	0.339875	−	0.588680i	0.984409	+	0.175895i	$0.0562820\pi$
$810$	−1.70137	+	15.7563i	−0.0597802	+	0.553620i
$811$	47.0391			1.65177			0.825884	−	0.563841i	$-0.190677\pi$
$811$	47.0391			1.65177			0.825884	+	0.563841i	$0.190677\pi$
$812$		0			0
$813$	−23.5328	−	3.74439i	−0.825333	−	0.131321i
$814$	8.83693	−	15.3060i	0.309734	−	0.536476i
$815$	−26.4796			−0.927541
$816$	4.23912	+	11.0668i	0.148399	+	0.387416i
$817$	−16.8252			−0.588639
$818$	−15.1683			−0.530346
$819$		0			0
$820$	12.2255			0.426931
$821$	1.41066			0.0492325			0.0246162	−	0.999697i	$-0.492164\pi$
$821$	1.41066			0.0492325			0.0246162	+	0.999697i	$0.492164\pi$
$822$	−13.9955	−	2.22687i	−0.488149	−	0.0776710i
$823$	−35.0391			−1.22139			−0.610694	−	0.791867i	$-0.709109\pi$
$823$	−35.0391			−1.22139			−0.610694	+	0.791867i	$0.709109\pi$
$824$	−3.41423	+	5.91362i	−0.118940	+	0.206011i
$825$	7.20726	+	18.8155i	0.250925	+	0.655073i
$826$		0			0
$827$	−18.5997			−0.646776			−0.323388	−	0.946266i	$-0.604822\pi$
$827$	−18.5997			−0.646776			−0.323388	+	0.946266i	$0.604822\pi$
$828$	−1.20082	−	0.392058i	−0.0417313	−	0.0136250i
$829$	−19.0848	+	33.0559i	−0.662843	+	1.14808i	0.317022	+	0.948418i	$0.397317\pi$
$829$	−19.0848	+	33.0559i	−0.662843	+	1.14808i	−0.979865	+	0.199660i	$0.936016\pi$
$830$	−2.75116	−	4.76515i	−0.0954942	−	0.165401i
$831$	−5.61505	−	0.893429i	−0.194784	−	0.0309927i
$832$	0.380438	+	0.658939i	0.0131893	+	0.0228446i
$833$		0			0
$834$	−21.3211	−	3.39247i	−0.738288	−	0.117472i
$835$	−2.01478			−0.0697245
$836$	−5.94966	+	10.3051i	−0.205773	+	0.356410i
$837$	−35.6278	−	18.2491i	−1.23148	−	0.630781i
$838$	4.16827	+	7.21966i	0.143991	+	0.249399i
$839$	−17.3691	+	30.0841i	−0.599648	+	1.03862i	0.393225	+	0.919442i	$0.371359\pi$
$839$	−17.3691	+	30.0841i	−0.599648	+	1.03862i	−0.992873	+	0.119178i	$0.961974\pi$
$840$		0			0
$841$	13.4275	+	23.2571i	0.463018	+	0.801970i
$842$	−3.50232	+	6.06620i	−0.120698	+	0.209055i
$843$	0.786197	+	2.05247i	0.0270781	+	0.0706910i
$844$	11.3856	+	19.7205i	0.391910	+	0.678808i
$845$	−10.9360	−	18.9417i	−0.376209	−	0.651614i
$846$	1.02859	+	4.87320i	0.0353637	+	0.167544i
$847$		0			0
$848$	−0.112725	+	0.195246i	−0.00387100	+	0.00670476i
$849$	−8.93762	+	11.0210i	−0.306738	+	0.378240i
$850$	12.9954			0.445737
$851$	1.21505			0.0416513
$852$	−11.7661	+	14.5088i	−0.403099	+	0.497063i
$853$	21.1586	−	36.6477i	0.724455	−	1.25479i	−0.234743	−	0.972058i	$-0.575425\pi$
$853$	21.1586	−	36.6477i	0.724455	−	1.25479i	0.959198	−	0.282736i	$-0.0912419\pi$
$854$		0			0
$855$	2.11956	+	10.0419i	0.0724875	+	0.343427i
$856$	1.77292	+	3.07078i	0.0605970	+	0.104957i
$857$	7.46169	+	12.9240i	0.254887	+	0.441477i	0.964865	−	0.262747i	$-0.0846285\pi$
$857$	7.46169	+	12.9240i	0.254887	+	0.441477i	−0.709978	+	0.704224i	$0.751295\pi$
$858$	2.88727	+	7.53762i	0.0985699	+	0.257330i
$859$	9.70658	−	16.8123i	0.331184	−	0.573628i	−0.651560	−	0.758597i	$-0.725885\pi$
$859$	9.70658	−	16.8123i	0.331184	−	0.573628i	0.982744	+	0.184969i	$0.0592186\pi$
$860$	−7.62476	−	13.2065i	−0.260002	−	0.450337i
$861$		0			0
$862$	−1.72545	+	2.98857i	−0.0587691	+	0.101791i
$863$	−0.542263	−	0.939227i	−0.0184588	−	0.0319717i	0.856648	−	0.515901i	$-0.172543\pi$
$863$	−0.542263	−	0.939227i	−0.0184588	−	0.0319717i	−0.875107	+	0.483929i	$0.839209\pi$
$864$	4.62476	+	2.36887i	0.157338	+	0.0805907i
$865$	−0.438174	+	0.758939i	−0.0148984	+	0.0258047i
$866$	−28.2599			−0.960312
$867$	50.9992	+	8.11465i	1.73202	+	0.275588i
$868$		0			0
$869$	41.1742	+	71.3157i	1.39674	+	2.41922i
$870$	4.41135	+	0.701905i	0.149559	+	0.0237968i
$871$	2.58126	+	4.47087i	0.0874625	+	0.151490i
$872$	0.351848	−	0.609419i	0.0119151	−	0.0206375i
$873$	−10.3696	−	3.38561i	−0.350959	−	0.114586i
$874$	−0.818057			−0.0276712
$875$		0			0
$876$	−0.190024	−	0.496083i	−0.00642031	−	0.0167611i
$877$	14.2850	−	24.7423i	0.482369	−	0.835487i	−0.517427	−	0.855728i	$-0.673110\pi$
$877$	14.2850	−	24.7423i	0.482369	−	0.835487i	0.999795	+	0.0202407i	$0.00644326\pi$
$878$	28.8960			0.975194
$879$	26.4293	+	4.20525i	0.891437	+	0.141840i
$880$	−10.7850			−0.363561
$881$	−45.9967			−1.54967			−0.774835	−	0.632164i	$-0.782167\pi$
$881$	−45.9967			−1.54967			−0.774835	+	0.632164i	$0.782167\pi$
$882$		0			0
$883$	32.9384			1.10847			0.554233	−	0.832361i	$-0.313012\pi$
$883$	32.9384			1.10847			0.554233	+	0.832361i	$0.313012\pi$
$884$	5.20602			0.175097
$885$	−2.16703	−	5.65732i	−0.0728438	−	0.190169i
$886$	−13.7609			−0.462306
$887$	−14.1699	+	24.5430i	−0.475779	+	0.824073i	−0.999615	−	0.0277459i	$-0.991167\pi$
$887$	−14.1699	+	24.5430i	−0.475779	+	0.824073i	0.523836	+	0.851819i	$0.324500\pi$
$888$	−4.93598	−	0.785381i	−0.165641	−	0.0263557i
$889$		0			0
$890$	−4.58358			−0.153642
$891$	44.5030	+	32.5271i	1.49091	+	1.08970i
$892$	6.44282	−	11.1593i	0.215722	−	0.373641i
$893$	1.61273	+	2.79332i	0.0539678	+	0.0934750i
$894$	−5.46978	−	14.2796i	−0.182937	−	0.477581i
$895$	−7.77292	−	13.4631i	−0.259820	−	0.450021i
$896$		0			0
$897$	−0.349525	+	0.431001i	−0.0116703	+	0.0143907i
$898$	−20.2003			−0.674091
$899$	−5.64132	+	9.77104i	−0.188148	+	0.325883i
$900$	4.23981	−	3.80664i	0.141327	−	0.126888i
$901$	0.771280	+	1.33590i	0.0256951	+	0.0445052i
$902$	21.2616	−	36.8261i	0.707933	−	1.22618i
$903$		0			0
$904$	4.25116	+	7.36323i	0.141392	+	0.244897i
$905$	−1.17046	+	2.02730i	−0.0389074	+	0.0673896i
$906$	−25.6346	−	4.07881i	−0.851653	−	0.135509i
$907$	−3.97373	−	6.88271i	−0.131946	−	0.228537i	0.792481	−	0.609897i	$-0.208789\pi$
$907$	−3.97373	−	6.88271i	−0.131946	−	0.228537i	−0.924427	+	0.381360i	$0.875456\pi$
$908$	10.9984	+	19.0497i	0.364994	+	0.632187i
$909$	−17.8815	+	16.0546i	−0.593093	+	0.532498i
$910$		0			0
$911$	−4.00808	+	6.94220i	−0.132794	+	0.230005i	−0.924752	−	0.380569i	$-0.875728\pi$
$911$	−4.00808	+	6.94220i	−0.132794	+	0.230005i	0.791959	+	0.610575i	$0.209061\pi$
$912$	3.32326	+	0.528775i	0.110044	+	0.0175095i
$913$	−19.1384			−0.633390
$914$	20.0298			0.662528
$915$	11.2918	+	29.4787i	0.373295	+	0.974537i
$916$	−1.89931	+	3.28971i	−0.0627551	+	0.108695i
$917$		0			0
$918$	29.8583	−	19.2998i	0.985471	−	0.636988i
$919$	−12.0224	−	20.8235i	−0.396584	−	0.686903i	0.596718	−	0.802451i	$-0.296471\pi$
$919$	−12.0224	−	20.8235i	−0.396584	−	0.686903i	−0.993302	+	0.115548i	$0.963138\pi$
$920$	−0.370723	−	0.642111i	−0.0122224	−	0.0211698i
$921$	5.34501	−	6.59095i	0.176124	−	0.217179i
$922$	−5.97661	+	10.3518i	−0.196829	+	0.340918i
$923$	4.10301	+	7.10662i	0.135052	+	0.233917i
$924$		0			0
$925$	−2.74037	+	4.74646i	−0.0901027	+	0.156062i
$926$	6.64527	+	11.5100i	0.218377	+	0.378240i
$927$	19.4737	+	6.35803i	0.639601	+	0.208825i
$928$	0.732287	−	1.26836i	0.0240385	−	0.0416359i
$929$	−27.8662			−0.914261			−0.457130	−	0.889400i	$-0.651123\pi$
$929$	−27.8662			−0.914261			−0.457130	+	0.889400i	$0.651123\pi$
$930$	−8.40451	−	21.9411i	−0.275595	−	0.719478i
$931$		0			0
$932$	−3.33530	−	5.77690i	−0.109251	−	0.189229i
$933$	−8.38960	+	10.3452i	−0.274663	+	0.338688i
$934$	5.61505	+	9.72555i	0.183730	+	0.318230i
$935$	−36.8960	+	63.9058i	−1.20663	+	2.08994i
$936$	1.69850	−	1.52496i	0.0555170	−	0.0498450i
$937$	−53.2211			−1.73866			−0.869328	−	0.494235i	$-0.835448\pi$
$937$	−53.2211			−1.73866			−0.869328	+	0.494235i	$0.835448\pi$
$938$		0			0
$939$	−1.87988	+	2.31809i	−0.0613477	+	0.0756480i
$940$	−1.46169	+	2.53173i	−0.0476752	+	0.0825759i
$941$	30.0482			0.979542			0.489771	−	0.871851i	$-0.337080\pi$
$941$	30.0482			0.979542			0.489771	+	0.871851i	$0.337080\pi$
$942$	20.7073	−	25.5342i	0.674679	−	0.831949i
$943$	2.92339			0.0951987
$944$	−1.98633			−0.0646494
$945$		0			0
$946$	−53.0416			−1.72453
$947$	−39.6889			−1.28972			−0.644858	−	0.764302i	$-0.723084\pi$
$947$	−39.6889			−1.28972			−0.644858	+	0.764302i	$0.723084\pi$
$948$	14.6683	−	18.0875i	0.476403	−	0.587455i
$949$	−0.233366			−0.00757538
$950$	1.84501	−	3.19565i	0.0598601	−	0.103681i
$951$	−36.2233	+	44.6670i	−1.17462	+	1.44843i
$952$		0			0
$953$	23.0643			0.747126			0.373563	−	0.927605i	$-0.378136\pi$
$953$	23.0643			0.747126			0.373563	+	0.927605i	$0.378136\pi$
$954$	0.642950	+	0.209918i	0.0208163	+	0.00679636i
$955$	−14.2352	+	24.6560i	−0.460639	+	0.797850i
$956$	−7.82038	−	13.5453i	−0.252929	−	0.438086i
$957$	9.78620	−	12.0674i	0.316343	−	0.390083i
$958$	−16.3135	−	28.2559i	−0.527067	−	0.912906i
$959$		0			0
$960$	1.09097	+	2.84813i	0.0352110	+	0.0919230i
$961$	28.3469			0.914418
$962$	−1.09781	+	1.90146i	−0.0353948	+	0.0613055i
$963$	7.91531	−	7.10662i	0.255067	−	0.229008i
$964$	10.7060	+	18.5434i	0.344818	+	0.597242i
$965$	−12.4743	+	21.6061i	−0.401562	+	0.695525i
$966$		0			0
$967$	15.2902	+	26.4833i	0.491698	+	0.851646i	0.999954	−	0.00955967i	$-0.00304298\pi$
$967$	15.2902	+	26.4833i	0.491698	+	0.851646i	−0.508256	+	0.861206i	$0.669710\pi$
$968$	−13.2564	+	22.9607i	−0.426076	+	0.737985i
$969$	14.5023	−	17.8829i	0.465882	−	0.574480i
$970$	−3.20137	−	5.54494i	−0.102790	−	0.178037i
$971$	−13.1030	−	22.6951i	−0.420496	−	0.728320i	0.575492	−	0.817807i	$-0.304810\pi$
$971$	−13.1030	−	22.6951i	−0.420496	−	0.728320i	−0.995988	+	0.0894874i	$0.971477\pi$
$972$	4.08809	−	15.0429i	0.131126	−	0.482500i
$973$		0			0
$974$	1.84897	−	3.20251i	0.0592448	−	0.102615i
$975$	−0.895355	−	2.33745i	−0.0286743	−	0.0748582i
$976$	10.3502			0.331302
$977$	21.0539			0.673574			0.336787	−	0.941581i	$-0.390660\pi$
$977$	21.0539			0.673574			0.336787	+	0.941581i	$0.390660\pi$
$978$	25.7226	+	4.09280i	0.822517	+	0.130873i
$979$	−7.97141	+	13.8069i	−0.254767	+	0.441270i
$980$		0			0
$981$	−2.00684	−	0.655217i	−0.0640734	−	0.0209195i
$982$	−18.7804	−	32.5287i	−0.599308	−	1.03803i
$983$	−9.76483	−	16.9132i	−0.311450	−	0.539447i	0.667227	−	0.744855i	$-0.267481\pi$
$983$	−9.76483	−	16.9132i	−0.311450	−	0.539447i	−0.978676	+	0.205408i	$0.934148\pi$
$984$	−11.8759	−	1.88962i	−0.378591	−	0.0602388i
$985$	13.9480	−	24.1587i	0.444421	−	0.769760i
$986$	−5.01040	−	8.67827i	−0.159564	−	0.276373i
$987$		0			0
$988$	0.739123	−	1.28020i	0.0235146	−	0.0407286i
$989$	−1.82326	−	3.15798i	−0.0579762	−	0.100418i
$990$	6.68194	+	31.6574i	0.212366	+	1.00614i
$991$	−7.49837	+	12.9875i	−0.238193	+	0.412563i	−0.960196	−	0.279327i	$-0.909889\pi$
$991$	−7.49837	+	12.9875i	−0.238193	+	0.412563i	0.722003	+	0.691890i	$0.243222\pi$
$992$	−7.70370			−0.244593
$993$	−3.15172	+	3.88640i	−0.100017	+	0.123331i
$994$		0			0
$995$	−7.87360	−	13.6375i	−0.249610	−	0.432337i
$996$	1.93598	+	5.05415i	0.0613440	+	0.160147i
$997$	−29.2821	−	50.7180i	−0.927373	−	1.60626i	−0.787700	−	0.616059i	$-0.788728\pi$
$997$	−29.2821	−	50.7180i	−0.927373	−	1.60626i	−0.139672	−	0.990198i	$-0.544605\pi$
$998$	15.8977	−	27.5356i	0.503232	−	0.871624i
$999$	0.752796	+	14.9753i	0.0238174	+	0.473798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.e.p.655.1		6
3.2	odd	2		2646.2.e.o.2125.2		6
7.2	even	3		882.2.h.o.79.2		6
7.3	odd	6		882.2.f.l.295.1		6
7.4	even	3		882.2.f.m.295.3		6
7.5	odd	6		126.2.h.c.79.2	yes	6
7.6	odd	2		126.2.e.d.25.3	✓	6
9.4	even	3		882.2.h.o.67.2		6
9.5	odd	6		2646.2.h.p.361.2		6
21.2	odd	6		2646.2.h.p.667.2		6
21.5	even	6		378.2.h.d.289.2		6
21.11	odd	6		2646.2.f.n.883.2		6
21.17	even	6		2646.2.f.o.883.2		6
21.20	even	2		378.2.e.c.235.2		6
28.19	even	6		1008.2.t.g.961.2		6
28.27	even	2		1008.2.q.h.529.1		6
63.4	even	3		882.2.f.m.589.3		6
63.5	even	6		378.2.e.c.37.2		6
63.11	odd	6		7938.2.a.bx.1.2		3
63.13	odd	6		126.2.h.c.67.2	yes	6
63.20	even	6		1134.2.g.n.487.2		6
63.23	odd	6		2646.2.e.o.1549.2		6
63.25	even	3		7938.2.a.by.1.2		3
63.31	odd	6		882.2.f.l.589.1		6
63.32	odd	6		2646.2.f.n.1765.2		6
63.34	odd	6		1134.2.g.k.487.2		6
63.38	even	6		7938.2.a.bu.1.2		3
63.40	odd	6		126.2.e.d.121.3	yes	6
63.41	even	6		378.2.h.d.361.2		6
63.47	even	6		1134.2.g.n.163.2		6
63.52	odd	6		7938.2.a.cb.1.2		3
63.58	even	3	inner	882.2.e.p.373.1		6
63.59	even	6		2646.2.f.o.1765.2		6
63.61	odd	6		1134.2.g.k.163.2		6
84.47	odd	6		3024.2.t.g.289.2		6
84.83	odd	2		3024.2.q.h.2881.2		6
252.103	even	6		1008.2.q.h.625.1		6
252.131	odd	6		3024.2.q.h.2305.2		6
252.139	even	6		1008.2.t.g.193.2		6
252.167	odd	6		3024.2.t.g.1873.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.d.25.3	✓	6	7.6	odd	2
126.2.e.d.121.3	yes	6	63.40	odd	6
126.2.h.c.67.2	yes	6	63.13	odd	6
126.2.h.c.79.2	yes	6	7.5	odd	6
378.2.e.c.37.2		6	63.5	even	6
378.2.e.c.235.2		6	21.20	even	2
378.2.h.d.289.2		6	21.5	even	6
378.2.h.d.361.2		6	63.41	even	6
882.2.e.p.373.1		6	63.58	even	3	inner
882.2.e.p.655.1		6	1.1	even	1	trivial
882.2.f.l.295.1		6	7.3	odd	6
882.2.f.l.589.1		6	63.31	odd	6
882.2.f.m.295.3		6	7.4	even	3
882.2.f.m.589.3		6	63.4	even	3
882.2.h.o.67.2		6	9.4	even	3
882.2.h.o.79.2		6	7.2	even	3
1008.2.q.h.529.1		6	28.27	even	2
1008.2.q.h.625.1		6	252.103	even	6
1008.2.t.g.193.2		6	252.139	even	6
1008.2.t.g.961.2		6	28.19	even	6
1134.2.g.k.163.2		6	63.61	odd	6
1134.2.g.k.487.2		6	63.34	odd	6
1134.2.g.n.163.2		6	63.47	even	6
1134.2.g.n.487.2		6	63.20	even	6
2646.2.e.o.1549.2		6	63.23	odd	6
2646.2.e.o.2125.2		6	3.2	odd	2
2646.2.f.n.883.2		6	21.11	odd	6
2646.2.f.n.1765.2		6	63.32	odd	6
2646.2.f.o.883.2		6	21.17	even	6
2646.2.f.o.1765.2		6	63.59	even	6
2646.2.h.p.361.2		6	9.5	odd	6
2646.2.h.p.667.2		6	21.2	odd	6
3024.2.q.h.2305.2		6	252.131	odd	6
3024.2.q.h.2881.2		6	84.83	odd	2
3024.2.t.g.289.2		6	84.47	odd	6
3024.2.t.g.1873.2		6	252.167	odd	6
7938.2.a.bu.1.2		3	63.38	even	6
7938.2.a.bx.1.2		3	63.11	odd	6
7938.2.a.by.1.2		3	63.25	even	3
7938.2.a.cb.1.2		3	63.52	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-1.09097 + 1.34528i) q^{3} +1.00000 q^{4} +(0.880438 - 1.52496i) q^{5} +(-1.09097 + 1.34528i) q^{6} +1.00000 q^{8} +(-0.619562 - 2.93533i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-1.09097 + 1.34528i) q^{3} +1.00000 q^{4} +(0.880438 - 1.52496i) q^{5} +(-1.09097 + 1.34528i) q^{6} +1.00000 q^{8} +(-0.619562 - 2.93533i) q^{9} +(0.880438 - 1.52496i) q^{10} +(-3.06238 - 5.30420i) q^{11} +(-1.09097 + 1.34528i) q^{12} +(0.380438 + 0.658939i) q^{13} +(1.09097 + 2.84813i) q^{15} +1.00000 q^{16} +(3.42107 - 5.92546i) q^{17} +(-0.619562 - 2.93533i) q^{18} +(-0.971410 - 1.68253i) q^{19} +(0.880438 - 1.52496i) q^{20} +(-3.06238 - 5.30420i) q^{22} +(0.210533 - 0.364654i) q^{23} +(-1.09097 + 1.34528i) q^{24} +(0.949657 + 1.64485i) q^{25} +(0.380438 + 0.658939i) q^{26} +(4.62476 + 2.36887i) q^{27} +(0.732287 - 1.26836i) q^{29} +(1.09097 + 2.84813i) q^{30} -7.70370 q^{31} +1.00000 q^{32} +(10.4766 + 1.66697i) q^{33} +(3.42107 - 5.92546i) q^{34} +(-0.619562 - 2.93533i) q^{36} +(1.44282 + 2.49904i) q^{37} +(-0.971410 - 1.68253i) q^{38} +(-1.30150 - 0.207087i) q^{39} +(0.880438 - 1.52496i) q^{40} +(3.47141 + 6.01266i) q^{41} +(4.33009 - 7.49994i) q^{43} +(-3.06238 - 5.30420i) q^{44} +(-5.02175 - 1.63957i) q^{45} +(0.210533 - 0.364654i) q^{46} -1.66019 q^{47} +(-1.09097 + 1.34528i) q^{48} +(0.949657 + 1.64485i) q^{50} +(4.23912 + 11.0668i) q^{51} +(0.380438 + 0.658939i) q^{52} +(-0.112725 + 0.195246i) q^{53} +(4.62476 + 2.36887i) q^{54} -10.7850 q^{55} +(3.32326 + 0.528775i) q^{57} +(0.732287 - 1.26836i) q^{58} -1.98633 q^{59} +(1.09097 + 2.84813i) q^{60} +10.3502 q^{61} -7.70370 q^{62} +1.00000 q^{64} +1.33981 q^{65} +(10.4766 + 1.66697i) q^{66} +6.78495 q^{67} +(3.42107 - 5.92546i) q^{68} +(0.260877 + 0.681054i) q^{69} +10.7850 q^{71} +(-0.619562 - 2.93533i) q^{72} +(-0.153353 + 0.265616i) q^{73} +(1.44282 + 2.49904i) q^{74} +(-3.24884 - 0.516934i) q^{75} +(-0.971410 - 1.68253i) q^{76} +(-1.30150 - 0.207087i) q^{78} -13.4451 q^{79} +(0.880438 - 1.52496i) q^{80} +(-8.23229 + 3.63723i) q^{81} +(3.47141 + 6.01266i) q^{82} +(1.56238 - 2.70612i) q^{83} +(-6.02408 - 10.4340i) q^{85} +(4.33009 - 7.49994i) q^{86} +(0.907394 + 2.36887i) q^{87} +(-3.06238 - 5.30420i) q^{88} +(-1.30150 - 2.25427i) q^{89} +(-5.02175 - 1.63957i) q^{90} +(0.210533 - 0.364654i) q^{92} +(8.40451 - 10.3636i) q^{93} -1.66019 q^{94} -3.42107 q^{95} +(-1.09097 + 1.34528i) q^{96} +(1.81806 - 3.14897i) q^{97} +(-13.6722 + 12.2754i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 2 q^{3} + 6 q^{4} + 5 q^{5} + 2 q^{6} + 6 q^{8} - 4 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + 2 * q^3 + 6 * q^4 + 5 * q^5 + 2 * q^6 + 6 * q^8 - 4 * q^9	\( 6 q + 6 q^{2} + 2 q^{3} + 6 q^{4} + 5 q^{5} + 2 q^{6} + 6 q^{8} - 4 q^{9} + 5 q^{10} - q^{11} + 2 q^{12} + 2 q^{13} - 2 q^{15} + 6 q^{16} + 4 q^{17} - 4 q^{18} + 3 q^{19} + 5 q^{20} - q^{22} - 7 q^{23} + 2 q^{24} - 2 q^{25} + 2 q^{26} - 7 q^{27} - 5 q^{29} - 2 q^{30} - 28 q^{31} + 6 q^{32} + 19 q^{33} + 4 q^{34} - 4 q^{36} - 9 q^{37} + 3 q^{38} + 9 q^{39} + 5 q^{40} + 12 q^{41} + 18 q^{43} - q^{44} - 29 q^{45} - 7 q^{46} + 6 q^{47} + 2 q^{48} - 2 q^{50} + 26 q^{51} + 2 q^{52} + 9 q^{53} - 7 q^{54} - 14 q^{55} + 2 q^{57} - 5 q^{58} + 8 q^{59} - 2 q^{60} + 8 q^{61} - 28 q^{62} + 6 q^{64} + 24 q^{65} + 19 q^{66} - 10 q^{67} + 4 q^{68} + q^{69} + 14 q^{71} - 4 q^{72} + 25 q^{73} - 9 q^{74} - 44 q^{75} + 3 q^{76} + 9 q^{78} - 14 q^{79} + 5 q^{80} - 40 q^{81} + 12 q^{82} - 8 q^{83} + 14 q^{85} + 18 q^{86} - 31 q^{87} - q^{88} + 9 q^{89} - 29 q^{90} - 7 q^{92} + 6 q^{94} - 4 q^{95} + 2 q^{96} + 28 q^{97} - 41 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 2 * q^3 + 6 * q^4 + 5 * q^5 + 2 * q^6 + 6 * q^8 - 4 * q^9 + 5 * q^10 - q^11 + 2 * q^12 + 2 * q^13 - 2 * q^15 + 6 * q^16 + 4 * q^17 - 4 * q^18 + 3 * q^19 + 5 * q^20 - q^22 - 7 * q^23 + 2 * q^24 - 2 * q^25 + 2 * q^26 - 7 * q^27 - 5 * q^29 - 2 * q^30 - 28 * q^31 + 6 * q^32 + 19 * q^33 + 4 * q^34 - 4 * q^36 - 9 * q^37 + 3 * q^38 + 9 * q^39 + 5 * q^40 + 12 * q^41 + 18 * q^43 - q^44 - 29 * q^45 - 7 * q^46 + 6 * q^47 + 2 * q^48 - 2 * q^50 + 26 * q^51 + 2 * q^52 + 9 * q^53 - 7 * q^54 - 14 * q^55 + 2 * q^57 - 5 * q^58 + 8 * q^59 - 2 * q^60 + 8 * q^61 - 28 * q^62 + 6 * q^64 + 24 * q^65 + 19 * q^66 - 10 * q^67 + 4 * q^68 + q^69 + 14 * q^71 - 4 * q^72 + 25 * q^73 - 9 * q^74 - 44 * q^75 + 3 * q^76 + 9 * q^78 - 14 * q^79 + 5 * q^80 - 40 * q^81 + 12 * q^82 - 8 * q^83 + 14 * q^85 + 18 * q^86 - 31 * q^87 - q^88 + 9 * q^89 - 29 * q^90 - 7 * q^92 + 6 * q^94 - 4 * q^95 + 2 * q^96 + 28 * q^97 - 41 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more