LMFDB - Embedded newform 650.2.w.h.357.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,2,Mod(193,650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(650, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 7]))

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

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

chi := DirichletCharacter("650.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.w (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 28x^{14} + 294x^{12} + 1516x^{10} + 4147x^{8} + 6012x^{6} + 4338x^{4} + 1296x^{2} + 81 $ x^16 + 28x^14 + 294x^12 + 1516x^10 + 4147x^8 + 6012x^6 + 4338x^4 + 1296*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			357.4
Root			$2.38585i$ of defining polynomial
Character	$\chi$	$=$	650.357
Dual form			650.2.w.h.193.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.617503 + 2.30455i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.30455 + 0.617503i) q^{6} +(2.54433 - 1.46897i) q^{7} -1.00000 q^{8} +(-2.33157 + 1.34613i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.617503 + 2.30455i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.30455 + 0.617503i) q^{6} +(2.54433 - 1.46897i) q^{7} -1.00000 q^{8} +(-2.33157 + 1.34613i) q^{9} +(1.03948 - 0.278528i) q^{11} +(1.68705 - 1.68705i) q^{12} +(2.75817 - 2.32218i) q^{13} -2.93793i q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.41276 + 0.378548i) q^{17} +2.69227i q^{18} +(-0.564216 + 2.10568i) q^{19} +(4.95644 + 4.95644i) q^{21} +(0.278528 - 1.03948i) q^{22} +(1.19468 - 0.320113i) q^{23} +(-0.617503 - 2.30455i) q^{24} +(-0.631979 - 3.54973i) q^{26} +(0.519158 + 0.519158i) q^{27} +(-2.54433 - 1.46897i) q^{28} +(6.21027 + 3.58550i) q^{29} +(-5.92810 + 5.92810i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.28376 + 2.22354i) q^{33} +(1.03421 - 1.03421i) q^{34} +(2.33157 + 1.34613i) q^{36} +(-9.51761 - 5.49500i) q^{37} +(1.54147 + 1.54147i) q^{38} +(7.05475 + 4.92239i) q^{39} +(1.01470 + 3.78693i) q^{41} +(6.77062 - 1.81418i) q^{42} +(-1.88476 + 7.03403i) q^{43} +(-0.760952 - 0.760952i) q^{44} +(0.320113 - 1.19468i) q^{46} -13.0183i q^{47} +(-2.30455 - 0.617503i) q^{48} +(0.815727 - 1.41288i) q^{49} +3.48953i q^{51} +(-3.39015 - 1.22756i) q^{52} +(8.91376 - 8.91376i) q^{53} +(0.709183 - 0.190025i) q^{54} +(-2.54433 + 1.46897i) q^{56} -5.20106 q^{57} +(6.21027 - 3.58550i) q^{58} +(2.01875 + 0.540922i) q^{59} +(0.289104 + 0.500743i) q^{61} +(2.16984 + 8.09794i) q^{62} +(-3.95485 + 6.85001i) q^{63} +1.00000 q^{64} +2.56753 q^{66} +(-4.47153 + 7.74492i) q^{67} +(-0.378548 - 1.41276i) q^{68} +(1.47543 + 2.55553i) q^{69} +(-12.6595 - 3.39210i) q^{71} +(2.33157 - 1.34613i) q^{72} +5.77429 q^{73} +(-9.51761 + 5.49500i) q^{74} +(2.10568 - 0.564216i) q^{76} +(2.23563 - 2.23563i) q^{77} +(7.79029 - 3.64840i) q^{78} -6.64203i q^{79} +(-4.91425 + 8.51173i) q^{81} +(3.78693 + 1.01470i) q^{82} -0.332435i q^{83} +(1.81418 - 6.77062i) q^{84} +(5.14927 + 5.14927i) q^{86} +(-4.42812 + 16.5260i) q^{87} +(-1.03948 + 0.278528i) q^{88} +(-1.94317 - 7.25199i) q^{89} +(3.60648 - 9.96003i) q^{91} +(-0.874565 - 0.874565i) q^{92} +(-17.3222 - 10.0010i) q^{93} +(-11.2742 - 6.50916i) q^{94} +(-1.68705 + 1.68705i) q^{96} +(-5.95297 - 10.3109i) q^{97} +(-0.815727 - 1.41288i) q^{98} +(-2.04869 + 2.04869i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{2} - 8 q^{4} + 12 q^{7} - 16 q^{8} - 24 q^{9}+O(q^{10}) $ 16 * q + 8 * q^2 - 8 * q^4 + 12 * q^7 - 16 * q^8 - 24 * q^9	$ 16 q + 8 q^{2} - 8 q^{4} + 12 q^{7} - 16 q^{8} - 24 q^{9} - 4 q^{11} + 8 q^{13} - 8 q^{16} - 8 q^{17} + 16 q^{19} - 4 q^{21} + 4 q^{22} - 4 q^{23} + 4 q^{26} + 36 q^{27} - 12 q^{28} + 36 q^{29} - 8 q^{31} + 8 q^{32} - 16 q^{34} + 24 q^{36} - 36 q^{37} - 4 q^{38} + 32 q^{41} - 8 q^{42} - 36 q^{43} + 8 q^{44} + 4 q^{46} + 16 q^{49} - 4 q^{52} + 44 q^{53} + 36 q^{54} - 12 q^{56} - 48 q^{57} + 36 q^{58} - 24 q^{59} - 20 q^{61} + 8 q^{62} - 36 q^{63} + 16 q^{64} - 12 q^{67} - 8 q^{68} + 24 q^{69} + 16 q^{71} + 24 q^{72} - 36 q^{74} - 20 q^{76} + 16 q^{77} + 60 q^{78} + 16 q^{81} + 16 q^{82} - 4 q^{84} - 36 q^{86} + 12 q^{87} + 4 q^{88} - 28 q^{89} - 44 q^{91} + 8 q^{92} - 24 q^{93} + 24 q^{94} - 8 q^{97} - 16 q^{98} - 36 q^{99}+O(q^{100}) $ 16 * q + 8 * q^2 - 8 * q^4 + 12 * q^7 - 16 * q^8 - 24 * q^9 - 4 * q^11 + 8 * q^13 - 8 * q^16 - 8 * q^17 + 16 * q^19 - 4 * q^21 + 4 * q^22 - 4 * q^23 + 4 * q^26 + 36 * q^27 - 12 * q^28 + 36 * q^29 - 8 * q^31 + 8 * q^32 - 16 * q^34 + 24 * q^36 - 36 * q^37 - 4 * q^38 + 32 * q^41 - 8 * q^42 - 36 * q^43 + 8 * q^44 + 4 * q^46 + 16 * q^49 - 4 * q^52 + 44 * q^53 + 36 * q^54 - 12 * q^56 - 48 * q^57 + 36 * q^58 - 24 * q^59 - 20 * q^61 + 8 * q^62 - 36 * q^63 + 16 * q^64 - 12 * q^67 - 8 * q^68 + 24 * q^69 + 16 * q^71 + 24 * q^72 - 36 * q^74 - 20 * q^76 + 16 * q^77 + 60 * q^78 + 16 * q^81 + 16 * q^82 - 4 * q^84 - 36 * q^86 + 12 * q^87 + 4 * q^88 - 28 * q^89 - 44 * q^91 + 8 * q^92 - 24 * q^93 + 24 * q^94 - 8 * q^97 - 16 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{12}\right)$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	0.617503	+	2.30455i	0.356515	+	1.33053i	0.878567	+	0.477620i	$0.158500\pi$
$3$	0.617503	+	2.30455i	0.356515	+	1.33053i	−0.522051	+	0.852914i	$0.674833\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	2.30455	+	0.617503i	0.940829	+	0.252094i
$7$	2.54433	−	1.46897i	0.961665	−	0.555217i	0.0649796	−	0.997887i	$-0.479302\pi$
$7$	2.54433	−	1.46897i	0.961665	−	0.555217i	0.896685	+	0.442669i	$0.145968\pi$
$8$	−1.00000			−0.353553
$9$	−2.33157	+	1.34613i	−0.777191	+	0.448711i
$10$		0			0
$11$	1.03948	−	0.278528i	0.313415	−	0.0839793i	−0.0986828	−	0.995119i	$-0.531463\pi$
$11$	1.03948	−	0.278528i	0.313415	−	0.0839793i	0.412098	+	0.911140i	$0.364796\pi$
$12$	1.68705	−	1.68705i	0.487009	−	0.487009i
$13$	2.75817	−	2.32218i	0.764979	−	0.644056i
$13$	2.75817	−	2.32218i	0.764979	−	0.644056i
$14$		−	2.93793i		−	0.785196i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.41276	+	0.378548i	0.342645	+	0.0918114i	0.426038	−	0.904705i	$-0.359909\pi$
$17$	1.41276	+	0.378548i	0.342645	+	0.0918114i	−0.0833931	+	0.996517i	$0.526576\pi$
$18$			2.69227i			0.634574i
$19$	−0.564216	+	2.10568i	−0.129440	+	0.483077i	−0.999959	−	0.00905797i	$-0.997117\pi$
$19$	−0.564216	+	2.10568i	−0.129440	+	0.483077i	0.870519	+	0.492135i	$0.163783\pi$
$20$		0			0
$21$	4.95644	+	4.95644i	1.08158	+	1.08158i
$22$	0.278528	−	1.03948i	0.0593823	−	0.221618i
$23$	1.19468	−	0.320113i	0.249108	−	0.0667482i	−0.132104	−	0.991236i	$-0.542173\pi$
$23$	1.19468	−	0.320113i	0.249108	−	0.0667482i	0.381212	+	0.924488i	$0.375507\pi$
$24$	−0.617503	−	2.30455i	−0.126047	−	0.470415i
$25$		0			0
$26$	−0.631979	−	3.54973i	−0.123941	−	0.696160i
$27$	0.519158	+	0.519158i	0.0999120	+	0.0999120i
$28$	−2.54433	−	1.46897i	−0.480832	−	0.277609i
$29$	6.21027	+	3.58550i	1.15322	+	0.665811i	0.949670	−	0.313253i	$-0.101419\pi$
$29$	6.21027	+	3.58550i	1.15322	+	0.665811i	0.203549	+	0.979065i	$0.434752\pi$
$30$		0			0
$31$	−5.92810	+	5.92810i	−1.06472	+	1.06472i	−0.0669631	+	0.997755i	$0.521331\pi$
$31$	−5.92810	+	5.92810i	−1.06472	+	1.06472i	−0.997755	+	0.0669631i	$0.978669\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	1.28376	+	2.22354i	0.223474	+	0.387069i
$34$	1.03421	−	1.03421i	0.177366	−	0.177366i
$35$		0			0
$36$	2.33157	+	1.34613i	0.388595	+	0.224356i
$37$	−9.51761	−	5.49500i	−1.56469	−	0.903372i	−0.996772	−	0.0802840i	$-0.974417\pi$
$37$	−9.51761	−	5.49500i	−1.56469	−	0.903372i	−0.567914	−	0.823088i	$-0.692249\pi$
$38$	1.54147	+	1.54147i	0.250059	+	0.250059i
$39$	7.05475	+	4.92239i	1.12966	+	0.788214i
$40$		0			0
$41$	1.01470	+	3.78693i	0.158470	+	0.591419i	0.998783	+	0.0493172i	$0.0157045\pi$
$41$	1.01470	+	3.78693i	0.158470	+	0.591419i	−0.840313	+	0.542102i	$0.817629\pi$
$42$	6.77062	−	1.81418i	1.04473	−	0.279934i
$43$	−1.88476	+	7.03403i	−0.287424	+	1.07268i	0.659627	+	0.751593i	$0.270714\pi$
$43$	−1.88476	+	7.03403i	−0.287424	+	1.07268i	−0.947050	+	0.321086i	$0.895952\pi$
$44$	−0.760952	−	0.760952i	−0.114718	−	0.114718i
$45$		0			0
$46$	0.320113	−	1.19468i	0.0471981	−	0.176146i
$47$		−	13.0183i		−	1.89892i	−0.313894	−	0.949458i	$-0.601634\pi$
$47$		−	13.0183i		−	1.89892i	0.313894	−	0.949458i	$-0.398366\pi$
$48$	−2.30455	−	0.617503i	−0.332633	−	0.0891288i
$49$	0.815727	−	1.41288i	0.116532	−	0.201840i
$50$		0			0
$51$			3.48953i			0.488632i
$52$	−3.39015	−	1.22756i	−0.470129	−	0.170231i
$53$	8.91376	−	8.91376i	1.22440	−	1.22440i	0.258347	−	0.966052i	$-0.416822\pi$
$53$	8.91376	−	8.91376i	1.22440	−	1.22440i	0.966052	−	0.258347i	$-0.0831779\pi$
$54$	0.709183	−	0.190025i	0.0965076	−	0.0258591i
$55$		0			0
$56$	−2.54433	+	1.46897i	−0.340000	+	0.196299i
$57$	−5.20106			−0.688898
$58$	6.21027	−	3.58550i	0.815449	−	0.470800i
$59$	2.01875	+	0.540922i	0.262819	+	0.0704220i	0.387822	−	0.921734i	$-0.373228\pi$
$59$	2.01875	+	0.540922i	0.262819	+	0.0704220i	−0.125003	+	0.992156i	$0.539894\pi$
$60$		0			0
$61$	0.289104	+	0.500743i	0.0370160	+	0.0641136i	0.883940	−	0.467601i	$-0.154881\pi$
$61$	0.289104	+	0.500743i	0.0370160	+	0.0641136i	−0.846924	+	0.531714i	$0.821548\pi$
$62$	2.16984	+	8.09794i	0.275569	+	1.02844i
$63$	−3.95485	+	6.85001i	−0.498265	+	0.863020i
$64$	1.00000			0.125000
$65$		0			0
$66$	2.56753			0.316041
$67$	−4.47153	+	7.74492i	−0.546284	+	0.946192i	0.452241	+	0.891896i	$0.350625\pi$
$67$	−4.47153	+	7.74492i	−0.546284	+	0.946192i	−0.998525	+	0.0542961i	$0.982709\pi$
$68$	−0.378548	−	1.41276i	−0.0459057	−	0.171322i
$69$	1.47543	+	2.55553i	0.177621	+	0.307649i
$70$		0			0
$71$	−12.6595	−	3.39210i	−1.50240	−	0.402568i	−0.588500	−	0.808497i	$-0.700281\pi$
$71$	−12.6595	−	3.39210i	−1.50240	−	0.402568i	−0.913905	+	0.405929i	$0.866948\pi$
$72$	2.33157	−	1.34613i	0.274779	−	0.158643i
$73$	5.77429			0.675829			0.337915	−	0.941177i	$-0.390279\pi$
$73$	5.77429			0.675829			0.337915	+	0.941177i	$0.390279\pi$
$74$	−9.51761	+	5.49500i	−1.10640	+	0.638780i
$75$		0			0
$76$	2.10568	−	0.564216i	0.241539	−	0.0647201i
$77$	2.23563	−	2.23563i	0.254773	−	0.254773i
$78$	7.79029	−	3.64840i	0.882077	−	0.413100i
$79$		−	6.64203i		−	0.747287i	−0.927572	−	0.373643i	$-0.878108\pi$
$79$		−	6.64203i		−	0.747287i	0.927572	−	0.373643i	$-0.121892\pi$
$80$		0			0
$81$	−4.91425	+	8.51173i	−0.546028	+	0.945747i
$82$	3.78693	+	1.01470i	0.418196	+	0.112055i
$83$		−	0.332435i		−	0.0364894i	−0.999834	−	0.0182447i	$-0.994192\pi$
$83$		−	0.332435i		−	0.0364894i	0.999834	−	0.0182447i	$-0.00580780\pi$
$84$	1.81418	−	6.77062i	0.197944	−	0.738735i
$85$		0			0
$86$	5.14927	+	5.14927i	0.555260	+	0.555260i
$87$	−4.42812	+	16.5260i	−0.474744	+	1.77177i
$88$	−1.03948	+	0.278528i	−0.110809	+	0.0296912i
$89$	−1.94317	−	7.25199i	−0.205975	−	0.768710i	−0.989150	−	0.146908i	$-0.953068\pi$
$89$	−1.94317	−	7.25199i	−0.205975	−	0.768710i	0.783175	−	0.621801i	$-0.213599\pi$
$90$		0			0
$91$	3.60648	−	9.96003i	0.378062	−	1.04409i
$92$	−0.874565	−	0.874565i	−0.0911797	−	0.0911797i
$93$	−17.3222	−	10.0010i	−1.79623	−	1.03706i
$94$	−11.2742	−	6.50916i	−1.16284	−	0.671368i
$95$		0			0
$96$	−1.68705	+	1.68705i	−0.172184	+	0.172184i
$97$	−5.95297	−	10.3109i	−0.604433	−	1.04691i	−0.992141	−	0.125126i	$-0.960066\pi$
$97$	−5.95297	−	10.3109i	−0.604433	−	1.04691i	0.387708	−	0.921782i	$-0.373267\pi$
$98$	−0.815727	−	1.41288i	−0.0824009	−	0.142723i
$99$	−2.04869	+	2.04869i	−0.205901	+	0.205901i
$100$		0			0
$101$	−12.6778	−	7.31956i	−1.26149	−	0.728323i	−0.288130	−	0.957591i	$-0.593033\pi$
$101$	−12.6778	−	7.31956i	−1.26149	−	0.728323i	−0.973363	+	0.229268i	$0.926367\pi$
$102$	3.02203	+	1.74477i	0.299225	+	0.172758i
$103$	3.16004	+	3.16004i	0.311368	+	0.311368i	0.845439	−	0.534072i	$-0.179339\pi$
$103$	3.16004	+	3.16004i	0.311368	+	0.311368i	−0.534072	+	0.845439i	$0.679339\pi$
$104$	−2.75817	+	2.32218i	−0.270461	+	0.227708i
$105$		0			0
$106$	−3.26266	−	12.1764i	−0.316898	−	1.18268i
$107$	13.8345	−	3.70695i	1.33743	−	0.358364i	0.481952	−	0.876197i	$-0.339928\pi$
$107$	13.8345	−	3.70695i	1.33743	−	0.358364i	0.855482	+	0.517833i	$0.173261\pi$
$108$	0.190025	−	0.709183i	0.0182852	−	0.0682412i
$109$	−8.01500	−	8.01500i	−0.767698	−	0.767698i	0.210003	−	0.977701i	$-0.432653\pi$
$109$	−8.01500	−	8.01500i	−0.767698	−	0.767698i	−0.977701	+	0.210003i	$0.932653\pi$
$110$		0			0
$111$	6.78635	−	25.3270i	0.644132	−	2.40393i
$112$			2.93793i			0.277609i
$113$	−18.0045	−	4.82429i	−1.69372	−	0.453831i	−0.722376	−	0.691501i	$-0.756950\pi$
$113$	−18.0045	−	4.82429i	−1.69372	−	0.453831i	−0.971346	+	0.237669i	$0.923616\pi$
$114$	−2.60053	+	4.50425i	−0.243562	+	0.421862i
$115$		0			0
$116$		−	7.17101i		−	0.665811i
$117$	−3.30491	+	9.12719i	−0.305539	+	0.843809i
$118$	1.47783	−	1.47783i	0.136045	−	0.136045i
$119$	4.15060	−	1.11215i	0.380485	−	0.101951i
$120$		0			0
$121$	−8.52334	+	4.92095i	−0.774849	+	0.447359i
$122$	0.578208			0.0523485
$123$	−8.10059	+	4.67688i	−0.730406	+	0.421700i
$124$	8.09794	+	2.16984i	0.727216	+	0.194857i
$125$		0			0
$126$	3.95485	+	6.85001i	0.352326	+	0.610247i
$127$	4.41406	+	16.4735i	0.391684	+	1.46179i	0.827355	+	0.561679i	$0.189844\pi$
$127$	4.41406	+	16.4735i	0.391684	+	1.46179i	−0.435671	+	0.900106i	$0.643489\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−17.3741			−1.52971
$130$		0			0
$131$	−6.43837			−0.562523			−0.281262	−	0.959631i	$-0.590753\pi$
$131$	−6.43837			−0.562523			−0.281262	+	0.959631i	$0.590753\pi$
$132$	1.28376	−	2.22354i	0.111737	−	0.193535i
$133$	1.65763	+	6.18636i	0.143735	+	0.536425i
$134$	4.47153	+	7.74492i	0.386281	+	0.669059i
$135$		0			0
$136$	−1.41276	−	0.378548i	−0.121143	−	0.0324602i
$137$	−0.832387	+	0.480579i	−0.0711156	+	0.0410586i	−0.535136	−	0.844766i	$-0.679740\pi$
$137$	−0.832387	+	0.480579i	−0.0711156	+	0.0410586i	0.464021	+	0.885824i	$0.346406\pi$
$138$	2.95087			0.251195
$139$	−0.783638	+	0.452434i	−0.0664673	+	0.0383749i	−0.532865	−	0.846200i	$-0.678885\pi$
$139$	−0.783638	+	0.452434i	−0.0664673	+	0.0383749i	0.466398	+	0.884575i	$0.345551\pi$
$140$		0			0
$141$	30.0014	−	8.03884i	2.52657	−	0.676993i
$142$	−9.26739	+	9.26739i	−0.777702	+	0.777702i
$143$	2.22027	−	3.18208i	0.185668	−	0.266099i
$144$		−	2.69227i		−	0.224356i
$145$		0			0
$146$	2.88714	−	5.00068i	0.238942	−	0.413859i
$147$	3.75977	+	1.00743i	0.310101	+	0.0830912i
$148$			10.9900i			0.903372i
$149$	−2.52367	+	9.41848i	−0.206747	+	0.771592i	0.782162	+	0.623075i	$0.214117\pi$
$149$	−2.52367	+	9.41848i	−0.206747	+	0.771592i	−0.988910	+	0.148517i	$0.952550\pi$
$150$		0			0
$151$	8.00063	+	8.00063i	0.651082	+	0.651082i	0.953254	−	0.302172i	$-0.0977115\pi$
$151$	8.00063	+	8.00063i	0.651082	+	0.651082i	−0.302172	+	0.953254i	$0.597712\pi$
$152$	0.564216	−	2.10568i	0.0457640	−	0.170794i
$153$	−3.80353	+	1.01915i	−0.307497	+	0.0823936i
$154$	−0.818296	−	3.05392i	−0.0659402	−	0.246092i
$155$		0			0
$156$	0.735542	−	8.57079i	0.0588905	−	0.686213i
$157$	−6.24506	−	6.24506i	−0.498410	−	0.498410i	0.412533	−	0.910943i	$-0.364644\pi$
$157$	−6.24506	−	6.24506i	−0.498410	−	0.498410i	−0.910943	+	0.412533i	$0.864644\pi$
$158$	−5.75217	−	3.32102i	−0.457618	−	0.264206i
$159$	26.0465	+	15.0380i	2.06562	+	1.19259i
$160$		0			0
$161$	2.56941	−	2.56941i	0.202498	−	0.202498i
$162$	4.91425	+	8.51173i	0.386100	+	0.668744i
$163$	2.74434	+	4.75333i	0.214953	+	0.372309i	0.953258	−	0.302158i	$-0.0977069\pi$
$163$	2.74434	+	4.75333i	0.214953	+	0.372309i	−0.738305	+	0.674467i	$0.764374\pi$
$164$	2.77222	−	2.77222i	0.216474	−	0.216474i
$165$		0			0
$166$	−0.287897	−	0.166217i	−0.0223451	−	0.0129010i
$167$	−5.64013	−	3.25633i	−0.436447	−	0.251983i	0.265643	−	0.964072i	$-0.414416\pi$
$167$	−5.64013	−	3.25633i	−0.436447	−	0.251983i	−0.702089	+	0.712089i	$0.747749\pi$
$168$	−4.95644	−	4.95644i	−0.382397	−	0.382397i
$169$	2.21500	−	12.8099i	0.170384	−	0.985378i
$170$		0			0
$171$	−1.51902	−	5.66907i	−0.116163	−	0.433524i
$172$	7.03403	−	1.88476i	0.536340	−	0.143712i
$173$	4.65789	−	17.3835i	0.354133	−	1.32164i	−0.527439	−	0.849593i	$-0.676848\pi$
$173$	4.65789	−	17.3835i	0.354133	−	1.32164i	0.881572	−	0.472050i	$-0.156486\pi$
$174$	12.0978	+	12.0978i	0.917135	+	0.917135i
$175$		0			0
$176$	−0.278528	+	1.03948i	−0.0209948	+	0.0783537i
$177$			4.98633i			0.374795i
$178$	−7.25199	−	1.94317i	−0.543560	−	0.145646i
$179$	−7.49018	+	12.9734i	−0.559842	+	0.969675i	0.437667	+	0.899137i	$0.355805\pi$
$179$	−7.49018	+	12.9734i	−0.559842	+	0.969675i	−0.997509	+	0.0705377i	$0.977528\pi$
$180$		0			0
$181$			14.6328i			1.08764i	0.839200	+	0.543822i	$0.183024\pi$
$181$			14.6328i			1.08764i	−0.839200	+	0.543822i	$0.816976\pi$
$182$	−6.82240	−	8.10332i	−0.505710	−	0.600658i
$183$	−0.975466	+	0.975466i	−0.0721085	+	0.0721085i
$184$	−1.19468	+	0.320113i	−0.0880729	+	0.0235990i
$185$		0			0
$186$	−17.3222	+	10.0010i	−1.27013	+	0.733309i
$187$	1.57397			0.115100
$188$	−11.2742	+	6.50916i	−0.822255	+	0.474729i
$189$	2.08353	+	0.558281i	0.151555	+	0.0406090i
$190$		0			0
$191$	0.0540643	+	0.0936422i	0.00391196	+	0.00677571i	0.867975	−	0.496608i	$-0.165421\pi$
$191$	0.0540643	+	0.0936422i	0.00391196	+	0.00677571i	−0.864063	+	0.503384i	$0.832088\pi$
$192$	0.617503	+	2.30455i	0.0445644	+	0.166317i
$193$	−12.7760	+	22.1287i	−0.919637	+	1.59286i	−0.119671	+	0.992814i	$0.538184\pi$
$193$	−12.7760	+	22.1287i	−0.919637	+	1.59286i	−0.799966	+	0.600045i	$0.795149\pi$
$194$	−11.9059			−0.854797
$195$		0			0
$196$	−1.63145			−0.116532
$197$	−2.64699	+	4.58472i	−0.188590	+	0.326648i	−0.944780	−	0.327704i	$-0.893725\pi$
$197$	−2.64699	+	4.58472i	−0.188590	+	0.326648i	0.756190	+	0.654352i	$0.227058\pi$
$198$	0.749871	+	2.79856i	0.0532910	+	0.198885i
$199$	−5.17091	−	8.95629i	−0.366556	−	0.634894i	0.622468	−	0.782645i	$-0.286130\pi$
$199$	−5.17091	−	8.95629i	−0.366556	−	0.634894i	−0.989025	+	0.147751i	$0.952797\pi$
$200$		0			0
$201$	−20.6097	−	5.52236i	−1.45370	−	0.389517i
$202$	−12.6778	+	7.31956i	−0.892010	+	0.515002i
$203$	21.0679			1.47868
$204$	3.02203	−	1.74477i	0.211584	−	0.122158i
$205$		0			0
$206$	4.31669	−	1.15665i	0.300758	−	0.0805879i
$207$	−2.35456	+	2.35456i	−0.163654	+	0.163654i
$208$	0.631979	+	3.54973i	0.0438199	+	0.246130i
$209$			2.34597i			0.162274i
$210$		0			0
$211$	3.81808	−	6.61311i	0.262848	−	0.455265i	−0.704150	−	0.710051i	$-0.748672\pi$
$211$	3.81808	−	6.61311i	0.262848	−	0.455265i	0.966997	+	0.254786i	$0.0820050\pi$
$212$	−12.1764	−	3.26266i	−0.836280	−	0.224081i
$213$		−	31.2691i		−	2.14252i
$214$	3.70695	−	13.8345i	0.253402	−	0.945709i
$215$		0			0
$216$	−0.519158	−	0.519158i	−0.0353242	−	0.0353242i
$217$	−6.37483	+	23.7912i	−0.432752	+	1.61505i
$218$	−10.9487	+	2.93369i	−0.741539	+	0.198695i
$219$	3.56564	+	13.3071i	0.240943	+	0.899213i
$220$		0			0
$221$	4.77569	−	2.23658i	0.321248	−	0.150449i
$222$	−18.5407	−	18.5407i	−1.24437	−	1.24437i
$223$	12.0369	+	6.94953i	0.806054	+	0.465375i	0.845584	−	0.533843i	$-0.179253\pi$
$223$	12.0369	+	6.94953i	0.806054	+	0.465375i	−0.0395300	+	0.999218i	$0.512586\pi$
$224$	2.54433	+	1.46897i	0.170000	+	0.0981495i
$225$		0			0
$226$	−13.1802	+	13.1802i	−0.876735	+	0.876735i
$227$	−3.53964	−	6.13084i	−0.234934	−	0.406918i	0.724319	−	0.689465i	$-0.242154\pi$
$227$	−3.53964	−	6.13084i	−0.234934	−	0.406918i	−0.959254	+	0.282547i	$0.908821\pi$
$228$	2.60053	+	4.50425i	0.172224	+	0.298301i
$229$	−0.613107	+	0.613107i	−0.0405153	+	0.0405153i	−0.727074	−	0.686559i	$-0.759120\pi$
$229$	−0.613107	+	0.613107i	−0.0405153	+	0.0405153i	0.686559	+	0.727074i	$0.259120\pi$
$230$		0			0
$231$	6.53262	+	3.77161i	0.429815	+	0.248154i
$232$	−6.21027	−	3.58550i	−0.407724	−	0.235400i
$233$	5.24088	+	5.24088i	0.343341	+	0.343341i	0.857622	−	0.514281i	$-0.171941\pi$
$233$	5.24088	+	5.24088i	0.343341	+	0.343341i	−0.514281	+	0.857622i	$0.671941\pi$
$234$	6.25192	+	7.42573i	0.408701	+	0.485435i
$235$		0			0
$236$	−0.540922	−	2.01875i	−0.0352110	−	0.131409i
$237$	15.3069	−	4.10147i	0.994290	−	0.266419i
$238$	1.11215	−	4.15060i	0.0720899	−	0.269043i
$239$	−0.891326	−	0.891326i	−0.0576551	−	0.0576551i	0.677691	−	0.735346i	$-0.262981\pi$
$239$	−0.891326	−	0.891326i	−0.0576551	−	0.0576551i	−0.735346	+	0.677691i	$0.762981\pi$
$240$		0			0
$241$	−2.92478	+	10.9154i	−0.188401	+	0.703123i	0.805475	+	0.592629i	$0.201910\pi$
$241$	−2.92478	+	10.9154i	−0.188401	+	0.703123i	−0.993877	+	0.110494i	$0.964757\pi$
$242$			9.84190i			0.632662i
$243$	−20.5227	−	5.49905i	−1.31653	−	0.352764i
$244$	0.289104	−	0.500743i	0.0185080	−	0.0320568i
$245$		0			0
$246$			9.35375i			0.596374i
$247$	3.33357	+	7.11804i	0.212110	+	0.452910i
$248$	5.92810	−	5.92810i	0.376435	−	0.376435i
$249$	0.766113	−	0.205279i	0.0485504	−	0.0130090i
$250$		0			0
$251$	4.70128	−	2.71429i	0.296742	−	0.171324i	−0.344236	−	0.938883i	$-0.611862\pi$
$251$	4.70128	−	2.71429i	0.296742	−	0.171324i	0.640979	+	0.767559i	$0.278529\pi$
$252$	7.90971			0.498265
$253$	1.15268	−	0.665502i	0.0724686	−	0.0418398i
$254$	16.4735	+	4.41406i	1.03364	+	0.276962i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−1.30522	−	4.87115i	−0.0814175	−	0.303854i	0.913194	−	0.407525i	$-0.133608\pi$
$257$	−1.30522	−	4.87115i	−0.0814175	−	0.303854i	−0.994612	+	0.103670i	$0.966941\pi$
$258$	−8.68706	+	15.0464i	−0.540833	+	0.936750i
$259$	−32.2879			−2.00627
$260$		0			0
$261$	−19.3063			−1.19503
$262$	−3.21919	+	5.57580i	−0.198882	+	0.344474i
$263$	7.02946	+	26.2343i	0.433455	+	1.61768i	0.744737	+	0.667358i	$0.232575\pi$
$263$	7.02946	+	26.2343i	0.433455	+	1.61768i	−0.311282	+	0.950318i	$0.600758\pi$
$264$	−1.28376	−	2.22354i	−0.0790102	−	0.136850i
$265$		0			0
$266$	6.18636	+	1.65763i	0.379310	+	0.101636i
$267$	15.5127	−	8.95625i	0.949361	−	0.548114i
$268$	8.94306			0.546284
$269$	5.54757	−	3.20289i	0.338241	−	0.195284i	−0.321253	−	0.946993i	$-0.604104\pi$
$269$	5.54757	−	3.20289i	0.338241	−	0.195284i	0.659494	+	0.751710i	$0.270771\pi$
$270$		0			0
$271$	19.7676	−	5.29672i	1.20080	−	0.321753i	0.397652	−	0.917536i	$-0.369825\pi$
$271$	19.7676	−	5.29672i	1.20080	−	0.321753i	0.803145	+	0.595784i	$0.203158\pi$
$272$	−1.03421	+	1.03421i	−0.0627083	+	0.0627083i
$273$	25.1804	+	2.16097i	1.52399	+	0.130788i
$274$			0.961158i			0.0580657i
$275$		0			0
$276$	1.47543	−	2.55553i	0.0888107	−	0.153825i
$277$	16.2720	+	4.36008i	0.977693	+	0.261972i	0.712073	−	0.702106i	$-0.247757\pi$
$277$	16.2720	+	4.36008i	0.977693	+	0.261972i	0.265620	+	0.964078i	$0.414423\pi$
$278$			0.904867i			0.0542703i
$279$	5.84178	−	21.8018i	0.349738	−	1.30524i
$280$		0			0
$281$	−10.2071	−	10.2071i	−0.608907	−	0.608907i	0.333753	−	0.942660i	$-0.391685\pi$
$281$	−10.2071	−	10.2071i	−0.608907	−	0.608907i	−0.942660	+	0.333753i	$0.891685\pi$
$282$	8.03884	−	30.0014i	0.478706	−	1.78656i
$283$	13.0152	−	3.48740i	0.773671	−	0.207304i	0.149678	−	0.988735i	$-0.452176\pi$
$283$	13.0152	−	3.48740i	0.773671	−	0.207304i	0.623992	+	0.781430i	$0.285510\pi$
$284$	3.39210	+	12.6595i	0.201284	+	0.751202i
$285$		0			0
$286$	−1.64563	−	3.51385i	−0.0973080	−	0.207778i
$287$	8.14461	+	8.14461i	0.480761	+	0.480761i
$288$	−2.33157	−	1.34613i	−0.137389	−	0.0793217i
$289$	−12.8698	−	7.43040i	−0.757049	−	0.437083i
$290$		0			0
$291$	20.0859	−	20.0859i	1.17746	−	1.17746i
$292$	−2.88714	−	5.00068i	−0.168957	−	0.292643i
$293$	−9.29509	−	16.0996i	−0.543025	−	0.940547i	−0.998728	−	0.0504153i	$-0.983946\pi$
$293$	−9.29509	−	16.0996i	−0.543025	−	0.940547i	0.455703	−	0.890132i	$-0.349388\pi$
$294$	2.75234	−	2.75234i	0.160520	−	0.160520i
$295$		0			0
$296$	9.51761	+	5.49500i	0.553200	+	0.319390i
$297$	0.684254	+	0.395054i	0.0397045	+	0.0229234i
$298$	6.89480	+	6.89480i	0.399405	+	0.399405i
$299$	2.55177	−	3.65718i	0.147572	−	0.211500i
$300$		0			0
$301$	5.53731	+	20.6655i	0.319165	+	1.19114i
$302$	10.9291	−	2.92843i	0.628897	−	0.168512i
$303$	9.03969	−	33.7366i	0.519317	−	1.93812i
$304$	−1.54147	−	1.54147i	−0.0884092	−	0.0884092i
$305$		0			0
$306$	−1.01915	+	3.80353i	−0.0582611	+	0.217433i
$307$		−	33.5791i		−	1.91646i	−0.285998	−	0.958230i	$-0.592325\pi$
$307$		−	33.5791i		−	1.91646i	0.285998	−	0.958230i	$-0.407675\pi$
$308$	−3.05392	−	0.818296i	−0.174013	−	0.0466267i
$309$	−5.33113	+	9.23380i	−0.303278	+	0.525292i
$310$		0			0
$311$			22.0875i			1.25247i	0.779635	+	0.626234i	$0.215404\pi$
$311$			22.0875i			1.25247i	−0.779635	+	0.626234i	$0.784596\pi$
$312$	−7.05475	−	4.92239i	−0.399397	−	0.278676i
$313$	−12.3966	+	12.3966i	−0.700700	+	0.700700i	−0.964561	−	0.263861i	$-0.915004\pi$
$313$	−12.3966	+	12.3966i	−0.700700	+	0.700700i	0.263861	+	0.964561i	$0.415004\pi$
$314$	−8.53091	+	2.28585i	−0.481427	+	0.128998i
$315$		0			0
$316$	−5.75217	+	3.32102i	−0.323585	+	0.186822i
$317$	17.8338			1.00164			0.500822	−	0.865550i	$-0.333031\pi$
$317$	17.8338			1.00164			0.500822	+	0.865550i	$0.333031\pi$
$318$	26.0465	−	15.0380i	1.46062	−	0.843287i
$319$	7.45411	+	1.99732i	0.417350	+	0.111829i
$320$		0			0
$321$	17.0857	+	29.5933i	0.953632	+	1.65174i
$322$	−0.940471	−	3.50989i	−0.0524104	−	0.195598i
$323$	−1.59421	+	2.76124i	−0.0887039	+	0.153640i
$324$	9.82850			0.546028
$325$		0			0
$326$	5.48867			0.303989
$327$	13.5217	−	23.4203i	0.747751	−	1.29514i
$328$	−1.01470	−	3.78693i	−0.0560277	−	0.209098i
$329$	−19.1235	−	33.1228i	−1.05431	−	1.82612i
$330$		0			0
$331$	−15.6854	−	4.20288i	−0.862145	−	0.231011i	−0.199457	−	0.979907i	$-0.563918\pi$
$331$	−15.6854	−	4.20288i	−0.862145	−	0.231011i	−0.662688	+	0.748896i	$0.730584\pi$
$332$	−0.287897	+	0.166217i	−0.0158004	+	0.00912236i
$333$	29.5880			1.62141
$334$	−5.64013	+	3.25633i	−0.308614	+	0.178179i
$335$		0			0
$336$	−6.77062	+	1.81418i	−0.369368	+	0.0989718i
$337$	10.9679	−	10.9679i	0.597462	−	0.597462i	−0.342175	−	0.939636i	$-0.611163\pi$
$337$	10.9679	−	10.9679i	0.597462	−	0.597462i	0.939636	+	0.342175i	$0.111163\pi$
$338$	−9.98621	−	8.32320i	−0.543178	−	0.452722i
$339$		−	44.4713i		−	2.41535i
$340$		0			0
$341$	−4.51100	+	7.81328i	−0.244284	+	0.423113i
$342$	−5.66907	−	1.51902i	−0.306548	−	0.0821393i
$343$			15.7724i			0.851631i
$344$	1.88476	−	7.03403i	0.101620	−	0.379249i
$345$		0			0
$346$	−12.7256	−	12.7256i	−0.684133	−	0.684133i
$347$	6.06567	−	22.6374i	0.325622	−	1.21524i	−0.588063	−	0.808815i	$-0.700109\pi$
$347$	6.06567	−	22.6374i	0.325622	−	1.21524i	0.913685	−	0.406423i	$-0.133224\pi$
$348$	16.5260	−	4.42812i	0.885884	−	0.237372i
$349$	3.17175	+	11.8371i	0.169780	+	0.633626i	0.997382	+	0.0723116i	$0.0230376\pi$
$349$	3.17175	+	11.8371i	0.169780	+	0.633626i	−0.827602	+	0.561315i	$0.810296\pi$
$350$		0			0
$351$	2.63750	+	0.226349i	0.140779	+	0.0120816i
$352$	0.760952	+	0.760952i	0.0405589	+	0.0405589i
$353$	−0.481977	−	0.278269i	−0.0256530	−	0.0148108i	0.487119	−	0.873336i	$-0.338048\pi$
$353$	−0.481977	−	0.278269i	−0.0256530	−	0.0148108i	−0.512772	+	0.858525i	$0.671381\pi$
$354$	4.31829	+	2.49316i	0.229514	+	0.132510i
$355$		0			0
$356$	−5.30883	+	5.30883i	−0.281367	+	0.281367i
$357$	5.12601	+	8.87851i	0.271297	+	0.469901i
$358$	7.49018	+	12.9734i	0.395868	+	0.685664i
$359$	1.79211	−	1.79211i	0.0945837	−	0.0945837i	−0.658232	−	0.752815i	$-0.728695\pi$
$359$	1.79211	−	1.79211i	0.0945837	−	0.0945837i	0.752815	+	0.658232i	$0.228695\pi$
$360$		0			0
$361$	12.3389	+	7.12388i	0.649417	+	0.374941i
$362$	12.6723	+	7.31638i	0.666044	+	0.384541i
$363$	−16.6038	−	16.6038i	−0.871472	−	0.871472i
$364$	−10.4289	+	1.85671i	−0.546622	+	0.0973182i
$365$		0			0
$366$	0.357045	+	1.33251i	0.0186631	+	0.0696515i
$367$	−34.5647	+	9.26158i	−1.80426	+	0.483450i	−0.994631	−	0.103489i	$-0.966999\pi$
$367$	−34.5647	+	9.26158i	−1.80426	+	0.483450i	−0.809631	+	0.586939i	$0.800333\pi$
$368$	−0.320113	+	1.19468i	−0.0166870	+	0.0622769i
$369$	−7.46357	−	7.46357i	−0.388538	−	0.388538i
$370$		0			0
$371$	9.58549	−	35.7735i	0.497654	−	1.85727i
$372$			20.0020i			1.03706i
$373$	−32.4193	−	8.68674i	−1.67861	−	0.449782i	−0.711198	−	0.702991i	$-0.751847\pi$
$373$	−32.4193	−	8.68674i	−1.67861	−	0.449782i	−0.967412	+	0.253209i	$0.918514\pi$
$374$	0.786986	−	1.36310i	0.0406941	−	0.0704842i
$375$		0			0
$376$			13.0183i			0.671368i
$377$	25.4552	−	4.53192i	1.31101	−	0.233406i
$378$	1.52525	−	1.52525i	0.0784505	−	0.0784505i
$379$	14.5983	−	3.91160i	0.749863	−	0.200925i	0.136406	−	0.990653i	$-0.456445\pi$
$379$	14.5983	−	3.91160i	0.749863	−	0.200925i	0.613458	+	0.789728i	$0.289778\pi$
$380$		0			0
$381$	−35.2383	+	20.3448i	−1.80531	+	1.04230i
$382$	0.108129			0.00553234
$383$	19.0373	−	10.9912i	0.972763	−	0.561625i	0.0726852	−	0.997355i	$-0.476843\pi$
$383$	19.0373	−	10.9912i	0.972763	−	0.561625i	0.900077	+	0.435730i	$0.143510\pi$
$384$	2.30455	+	0.617503i	0.117604	+	0.0315118i
$385$		0			0
$386$	12.7760	+	22.1287i	0.650282	+	1.12632i
$387$	−5.07429	−	18.9375i	−0.257940	−	0.962647i
$388$	−5.95297	+	10.3109i	−0.302216	+	0.523454i
$389$	12.3782			0.627599			0.313800	−	0.949489i	$-0.398398\pi$
$389$	12.3782			0.627599			0.313800	+	0.949489i	$0.398398\pi$
$390$		0			0
$391$	1.80897			0.0914837
$392$	−0.815727	+	1.41288i	−0.0412004	+	0.0713613i
$393$	−3.97571	−	14.8376i	−0.200548	−	0.748456i
$394$	2.64699	+	4.58472i	0.133353	+	0.230975i
$395$		0			0
$396$	2.79856	+	0.749871i	0.140633	+	0.0376825i
$397$	14.0098	−	8.08858i	0.703134	−	0.405954i	−0.105380	−	0.994432i	$-0.533606\pi$
$397$	14.0098	−	8.08858i	0.703134	−	0.405954i	0.808513	+	0.588478i	$0.200273\pi$
$398$	−10.3418			−0.518389
$399$	−13.2332	+	7.64019i	−0.662488	+	0.382488i
$400$		0			0
$401$	9.83091	−	2.63419i	0.490932	−	0.131545i	−0.00485613	−	0.999988i	$-0.501546\pi$
$401$	9.83091	−	2.63419i	0.490932	−	0.131545i	0.495789	+	0.868443i	$0.334879\pi$
$402$	−15.0874	+	15.0874i	−0.752490	+	0.752490i
$403$	−2.58461	+	30.1168i	−0.128749	+	1.50023i
$404$			14.6391i			0.728323i
$405$		0			0
$406$	10.5340	−	18.2454i	0.522792	−	0.905503i
$407$	−11.4239	−	3.06102i	−0.566260	−	0.151729i
$408$		−	3.48953i		−	0.172758i
$409$	−0.405425	+	1.51307i	−0.0200470	+	0.0748164i	−0.975225	−	0.221217i	$-0.928997\pi$
$409$	−0.405425	+	1.51307i	−0.0200470	+	0.0748164i	0.955178	+	0.296033i	$0.0956639\pi$
$410$		0			0
$411$	−1.62152	−	1.62152i	−0.0799837	−	0.0799837i
$412$	1.15665	−	4.31669i	0.0569842	−	0.212668i
$413$	5.93095	−	1.58919i	0.291843	−	0.0781990i
$414$	0.861830	+	3.21639i	0.0423567	+	0.158077i
$415$		0			0
$416$	3.39015	+	1.22756i	0.166216	+	0.0601859i
$417$	−1.52656	−	1.52656i	−0.0747557	−	0.0747557i
$418$	2.03167	+	1.17298i	0.0993720	+	0.0573725i
$419$	28.2092	+	16.2866i	1.37811	+	0.795652i	0.991932	−	0.126772i	$-0.0404617\pi$
$419$	28.2092	+	16.2866i	1.37811	+	0.795652i	0.386178	+	0.922424i	$0.373795\pi$
$420$		0			0
$421$	16.3225	−	16.3225i	0.795511	−	0.795511i	−0.186873	−	0.982384i	$-0.559835\pi$
$421$	16.3225	−	16.3225i	0.795511	−	0.795511i	0.982384	+	0.186873i	$0.0598354\pi$
$422$	−3.81808	−	6.61311i	−0.185861	−	0.321921i
$423$	17.5244	+	30.3531i	0.852065	+	1.47582i
$424$	−8.91376	+	8.91376i	−0.432891	+	0.432891i
$425$		0			0
$426$	−27.0798	−	15.6345i	−1.31202	−	0.757496i
$427$	1.47115	+	0.849369i	0.0711940	+	0.0411039i
$428$	−10.1276	−	10.1276i	−0.489535	−	0.489535i
$429$	8.70429	+	3.15178i	0.420247	+	0.152170i
$430$		0			0
$431$	5.46475	+	20.3947i	0.263228	+	0.982380i	0.963326	+	0.268333i	$0.0864729\pi$
$431$	5.46475	+	20.3947i	0.263228	+	0.982380i	−0.700098	+	0.714047i	$0.746860\pi$
$432$	−0.709183	+	0.190025i	−0.0341206	+	0.00914259i
$433$	−2.33144	+	8.70105i	−0.112042	+	0.418146i	−0.999049	−	0.0436106i	$-0.986114\pi$
$433$	−2.33144	+	8.70105i	−0.112042	+	0.418146i	0.887007	+	0.461756i	$0.152781\pi$
$434$	17.4164	+	17.4164i	0.836013	+	0.836013i
$435$		0			0
$436$	−2.93369	+	10.9487i	−0.140498	+	0.524347i
$437$			2.69623i			0.128978i
$438$	13.3071	+	3.56564i	0.635840	+	0.170373i
$439$	−3.16344	+	5.47924i	−0.150983	+	0.261510i	−0.931589	−	0.363513i	$-0.881577\pi$
$439$	−3.16344	+	5.47924i	−0.150983	+	0.261510i	0.780606	+	0.625023i	$0.214911\pi$
$440$		0			0
$441$			4.39231i			0.209158i
$442$	0.450910	−	5.25416i	0.0214476	−	0.249915i
$443$	4.88192	−	4.88192i	0.231947	−	0.231947i	−0.581558	−	0.813505i	$-0.697557\pi$
$443$	4.88192	−	4.88192i	0.231947	−	0.231947i	0.813505	+	0.581558i	$0.197557\pi$
$444$	−25.3270	+	6.78635i	−1.20197	+	0.322066i
$445$		0			0
$446$	12.0369	−	6.94953i	0.569966	−	0.329070i
$447$	−23.2637			−1.10034
$448$	2.54433	−	1.46897i	0.120208	−	0.0694022i
$449$	19.0679	+	5.10922i	0.899868	+	0.241119i	0.678960	−	0.734176i	$-0.262431\pi$
$449$	19.0679	+	5.10922i	0.899868	+	0.241119i	0.220909	+	0.975295i	$0.429098\pi$
$450$		0			0
$451$	2.10953	+	3.65381i	0.0993338	+	0.172051i
$452$	4.82429	+	18.0045i	0.226916	+	0.846861i
$453$	−13.4975	+	23.3783i	−0.634166	+	1.09841i
$454$	−7.07929			−0.332247
$455$		0			0
$456$	5.20106			0.243562
$457$	1.80048	−	3.11852i	0.0842227	−	0.145878i	−0.820837	−	0.571162i	$-0.806493\pi$
$457$	1.80048	−	3.11852i	0.0842227	−	0.145878i	0.905060	+	0.425284i	$0.139826\pi$
$458$	0.224413	+	0.837520i	0.0104861	+	0.0391347i
$459$	0.536920	+	0.929972i	0.0250613	+	0.0434074i
$460$		0			0
$461$	−2.73243	−	0.732151i	−0.127262	−	0.0340997i	0.194626	−	0.980878i	$-0.437651\pi$
$461$	−2.73243	−	0.732151i	−0.127262	−	0.0340997i	−0.321888	+	0.946778i	$0.604317\pi$
$462$	6.53262	−	3.77161i	0.303925	−	0.175471i
$463$	−39.4042			−1.83127			−0.915634	−	0.402014i	$-0.868310\pi$
$463$	−39.4042			−1.83127			−0.915634	+	0.402014i	$0.868310\pi$
$464$	−6.21027	+	3.58550i	−0.288305	+	0.166453i
$465$		0			0
$466$	7.15918	−	1.91830i	0.331642	−	0.0888633i
$467$	−26.7431	+	26.7431i	−1.23753	+	1.23753i	−0.276516	+	0.961009i	$0.589180\pi$
$467$	−26.7431	+	26.7431i	−1.23753	+	1.23753i	−0.961009	+	0.276516i	$0.910820\pi$
$468$	9.55683	−	1.70146i	0.441765	−	0.0786499i
$469$			26.2741i			1.21323i
$470$		0			0
$471$	10.5357	−	18.2484i	0.485460	−	0.840842i
$472$	−2.01875	−	0.540922i	−0.0929204	−	0.0248979i
$473$			7.83669i			0.360331i
$474$	4.10147	−	15.3069i	0.188387	−	0.703070i
$475$		0			0
$476$	−3.03845	−	3.03845i	−0.139267	−	0.139267i
$477$	−8.78397	+	32.7822i	−0.402190	+	1.50099i
$478$	−1.21757	+	0.326248i	−0.0556905	+	0.0149222i
$479$	−1.49589	−	5.58274i	−0.0683490	−	0.255082i	0.923294	−	0.384094i	$-0.125486\pi$
$479$	−1.49589	−	5.58274i	−0.0683490	−	0.255082i	−0.991643	+	0.129012i	$0.958819\pi$
$480$		0			0
$481$	−39.0115	+	6.94544i	−1.77877	+	0.316685i
$482$	7.99064	+	7.99064i	0.363963	+	0.363963i
$483$	7.50797	+	4.33473i	0.341624	+	0.197237i
$484$	8.52334	+	4.92095i	0.387425	+	0.223680i
$485$		0			0
$486$	−15.0237	+	15.0237i	−0.681488	+	0.681488i
$487$	−6.36460	−	11.0238i	−0.288408	−	0.499537i	0.685022	−	0.728522i	$-0.259793\pi$
$487$	−6.36460	−	11.0238i	−0.288408	−	0.499537i	−0.973430	+	0.228985i	$0.926459\pi$
$488$	−0.289104	−	0.500743i	−0.0130871	−	0.0226676i
$489$	−9.25966	+	9.25966i	−0.418736	+	0.418736i
$490$		0			0
$491$	33.2862	+	19.2178i	1.50219	+	0.867287i	0.999997	+	0.00252888i	$0.000804969\pi$
$491$	33.2862	+	19.2178i	1.50219	+	0.867287i	0.502188	+	0.864758i	$0.332528\pi$
$492$	8.10059	+	4.67688i	0.365203	+	0.210850i
$493$	7.41634	+	7.41634i	0.334015	+	0.334015i
$494$	7.83119	+	0.672069i	0.352342	+	0.0302378i
$495$		0			0
$496$	−2.16984	−	8.09794i	−0.0974285	−	0.363608i
$497$	−37.1927	+	9.96576i	−1.66832	+	0.447026i
$498$	0.205279	−	0.766113i	0.00919878	−	0.0343303i
$499$	−5.89435	−	5.89435i	−0.263867	−	0.263867i	0.562756	−	0.826623i	$-0.309741\pi$
$499$	−5.89435	−	5.89435i	−0.263867	−	0.263867i	−0.826623	+	0.562756i	$0.809741\pi$
$500$		0			0
$501$	4.02159	−	15.0088i	0.179671	−	0.670543i
$502$		−	5.42857i		−	0.242289i
$503$	−4.79368	−	1.28446i	−0.213740	−	0.0572714i	0.150360	−	0.988631i	$-0.451957\pi$
$503$	−4.79368	−	1.28446i	−0.213740	−	0.0572714i	−0.364100	+	0.931360i	$0.618623\pi$
$504$	3.95485	−	6.85001i	0.176163	−	0.305124i
$505$		0			0
$506$		−	1.33100i		−	0.0591703i
$507$	30.8889	−	2.80558i	1.37182	−	0.124600i
$508$	12.0594	−	12.0594i	0.535050	−	0.535050i
$509$	−4.73409	+	1.26850i	−0.209835	+	0.0562251i	−0.362205	−	0.932098i	$-0.617976\pi$
$509$	−4.73409	+	1.26850i	−0.209835	+	0.0562251i	0.152370	+	0.988323i	$0.451309\pi$
$510$		0			0
$511$	14.6917	−	8.48223i	0.649921	−	0.375232i
$512$	−1.00000			−0.0441942
$513$	−1.38610	+	0.800266i	−0.0611978	+	0.0353326i
$514$	−4.87115	−	1.30522i	−0.214857	−	0.0575708i
$515$		0			0
$516$	8.68706	+	15.0464i	0.382427	+	0.662382i
$517$	−3.62596	−	13.5323i	−0.159470	−	0.595149i
$518$	−16.1439	+	27.9621i	−0.709324	+	1.22858i
$519$	42.9374			1.88474
$520$		0			0
$521$	−25.7386			−1.12763			−0.563814	−	0.825902i	$-0.690667\pi$
$521$	−25.7386			−1.12763			−0.563814	+	0.825902i	$0.690667\pi$
$522$	−9.65314	+	16.7197i	−0.422506	+	0.731802i
$523$	2.30820	+	8.61433i	0.100931	+	0.376678i	0.997852	−	0.0655123i	$-0.0208682\pi$
$523$	2.30820	+	8.61433i	0.100931	+	0.376678i	−0.896921	+	0.442191i	$0.854202\pi$
$524$	3.21919	+	5.57580i	0.140631	+	0.243580i
$525$		0			0
$526$	26.2343	+	7.02946i	1.14387	+	0.306499i
$527$	−10.6191	+	6.13092i	−0.462573	+	0.267067i
$528$	−2.56753			−0.111737
$529$	−18.5938	+	10.7351i	−0.808426	+	0.466745i
$530$		0			0
$531$	−5.43501	+	1.45631i	−0.235859	+	0.0631983i
$532$	4.52873	−	4.52873i	0.196345	−	0.196345i
$533$	11.5926	+	8.08867i	0.502133	+	0.350359i
$534$		−	17.9125i		−	0.775150i
$535$		0			0
$536$	4.47153	−	7.74492i	0.193141	−	0.334529i
$537$	−34.5230	−	9.25041i	−1.48978	−	0.399185i
$538$		−	6.40578i		−	0.276173i
$539$	0.454405	−	1.69586i	0.0195726	−	0.0730460i
$540$		0			0
$541$	−17.9672	−	17.9672i	−0.772472	−	0.772472i	0.206066	−	0.978538i	$-0.433934\pi$
$541$	−17.9672	−	17.9672i	−0.772472	−	0.772472i	−0.978538	+	0.206066i	$0.933934\pi$
$542$	5.29672	−	19.7676i	0.227513	−	0.849092i
$543$	−33.7220	+	9.03577i	−1.44715	+	0.387762i
$544$	0.378548	+	1.41276i	0.0162301	+	0.0605716i
$545$		0			0
$546$	14.4617	−	20.7264i	0.618902	−	0.887008i
$547$	21.2305	+	21.2305i	0.907750	+	0.907750i	0.996090	−	0.0883402i	$-0.0281563\pi$
$547$	21.2305	+	21.2305i	0.907750	+	0.907750i	−0.0883402	+	0.996090i	$0.528156\pi$
$548$	0.832387	+	0.480579i	0.0355578	+	0.0205293i
$549$	−1.34814	−	0.778346i	−0.0575370	−	0.0332190i
$550$		0			0
$551$	−11.0539	+	11.0539i	−0.470911	+	0.470911i
$552$	−1.47543	−	2.55553i	−0.0627987	−	0.108770i
$553$	−9.75692	−	16.8995i	−0.414907	−	0.718639i
$554$	11.9120	−	11.9120i	0.506091	−	0.506091i
$555$		0			0
$556$	0.783638	+	0.452434i	0.0332336	+	0.0191875i
$557$	21.3067	+	12.3014i	0.902793	+	0.521228i	0.878105	−	0.478467i	$-0.158808\pi$
$557$	21.3067	+	12.3014i	0.902793	+	0.521228i	0.0246877	+	0.999695i	$0.492141\pi$
$558$	−15.9600	−	15.9600i	−0.675642	−	0.675642i
$559$	11.1358	+	23.7778i	0.470992	+	1.00569i
$560$		0			0
$561$	0.971932	+	3.62730i	0.0410350	+	0.153145i
$562$	−13.9432	+	3.73607i	−0.588159	+	0.157597i
$563$	9.08627	−	33.9104i	0.382941	−	1.42915i	−0.458447	−	0.888722i	$-0.651594\pi$
$563$	9.08627	−	33.9104i	0.382941	−	1.42915i	0.841387	−	0.540432i	$-0.181739\pi$
$564$	−21.9625	−	21.9625i	−0.924789	−	0.924789i
$565$		0			0
$566$	3.48740	−	13.0152i	0.146586	−	0.547068i
$567$			28.8755i			1.21266i
$568$	12.6595	+	3.39210i	0.531180	+	0.142329i
$569$	9.34909	−	16.1931i	0.391934	−	0.678850i	−0.600771	−	0.799422i	$-0.705139\pi$
$569$	9.34909	−	16.1931i	0.391934	−	0.678850i	0.992705	+	0.120572i	$0.0384728\pi$
$570$		0			0
$571$			18.8705i			0.789707i	0.918744	+	0.394854i	$0.129205\pi$
$571$			18.8705i			0.789707i	−0.918744	+	0.394854i	$0.870795\pi$
$572$	−3.86590	−	0.331770i	−0.161641	−	0.0138720i
$573$	−0.182418	+	0.182418i	−0.00762064	+	0.00762064i
$574$	11.1257	−	2.98113i	0.464380	−	0.124430i
$575$		0			0
$576$	−2.33157	+	1.34613i	−0.0971489	+	0.0560889i
$577$	−37.0325			−1.54168			−0.770841	−	0.637028i	$-0.780164\pi$
$577$	−37.0325			−1.54168			−0.770841	+	0.637028i	$0.780164\pi$
$578$	−12.8698	+	7.43040i	−0.535315	+	0.309064i
$579$	−58.8860	−	15.7784i	−2.44722	−	0.655730i
$580$		0			0
$581$	−0.488335	−	0.845822i	−0.0202596	−	0.0350906i
$582$	−7.35195	−	27.4379i	−0.304748	−	1.13734i
$583$	6.78294	−	11.7484i	0.280921	−	0.486569i
$584$	−5.77429			−0.238942
$585$		0			0
$586$	−18.5902			−0.767953
$587$	11.8687	−	20.5572i	0.489873	−	0.848486i	−0.510059	−	0.860140i	$-0.670376\pi$
$587$	11.8687	−	20.5572i	0.489873	−	0.848486i	0.999932	+	0.0116539i	$0.00370963\pi$
$588$	−1.00743	−	3.75977i	−0.0415456	−	0.155050i
$589$	−9.13798	−	15.8274i	−0.376524	−	0.652158i
$590$		0			0
$591$	−12.2003	−	3.26905i	−0.501851	−	0.134471i
$592$	9.51761	−	5.49500i	0.391172	−	0.225843i
$593$	−25.3673			−1.04171			−0.520855	−	0.853645i	$-0.674387\pi$
$593$	−25.3673			−1.04171			−0.520855	+	0.853645i	$0.674387\pi$
$594$	0.684254	−	0.395054i	0.0280753	−	0.0162093i
$595$		0			0
$596$	9.41848	−	2.52367i	0.385796	−	0.103374i
$597$	17.4472	−	17.4472i	0.714065	−	0.714065i
$598$	−1.89133	−	4.03848i	−0.0773421	−	0.165146i
$599$			28.5229i			1.16542i	0.812682	+	0.582708i	$0.198007\pi$
$599$			28.5229i			1.16542i	−0.812682	+	0.582708i	$0.801993\pi$
$600$		0			0
$601$	23.5024	−	40.7074i	0.958684	−	1.66049i	0.232982	−	0.972481i	$-0.425152\pi$
$601$	23.5024	−	40.7074i	0.958684	−	1.66049i	0.725702	−	0.688009i	$-0.241515\pi$
$602$	20.6655	+	5.53731i	0.842263	+	0.225684i
$603$		−	24.0771i		−	0.980496i
$604$	2.92843	−	10.9291i	0.119156	−	0.444697i
$605$		0			0
$606$	−24.6969	−	24.6969i	−1.00324	−	1.00324i
$607$	−9.19667	+	34.3224i	−0.373281	+	1.39311i	0.482558	+	0.875864i	$0.339708\pi$
$607$	−9.19667	+	34.3224i	−0.373281	+	1.39311i	−0.855840	+	0.517241i	$0.826959\pi$
$608$	−2.10568	+	0.564216i	−0.0853968	+	0.0228820i
$609$	13.0095	+	48.5522i	0.527172	+	1.96743i
$610$		0			0
$611$	−30.2308	−	35.9067i	−1.22301	−	1.45263i
$612$	2.78438	+	2.78438i	0.112552	+	0.112552i
$613$	−13.0205	−	7.51739i	−0.525893	−	0.303625i	0.213449	−	0.976954i	$-0.431530\pi$
$613$	−13.0205	−	7.51739i	−0.525893	−	0.303625i	−0.739342	+	0.673330i	$0.764864\pi$
$614$	−29.0804	−	16.7896i	−1.17359	−	0.677571i
$615$		0			0
$616$	−2.23563	+	2.23563i	−0.0900759	+	0.0900759i
$617$	16.8001	+	29.0986i	0.676346	+	1.17147i	0.976074	+	0.217440i	$0.0697708\pi$
$617$	16.8001	+	29.0986i	0.676346	+	1.17147i	−0.299728	+	0.954025i	$0.596896\pi$
$618$	5.33113	+	9.23380i	0.214450	+	0.371438i
$619$	−21.1991	+	21.1991i	−0.852063	+	0.852063i	−0.990387	−	0.138324i	$-0.955828\pi$
$619$	−21.1991	+	21.1991i	−0.852063	+	0.852063i	0.138324	+	0.990387i	$0.455828\pi$
$620$		0			0
$621$	0.786416	+	0.454038i	0.0315578	+	0.0182199i
$622$	19.1283	+	11.0438i	0.766977	+	0.442814i
$623$	−15.5970	−	15.5970i	−0.624880	−	0.624880i
$624$	−7.79029	+	3.64840i	−0.311861	+	0.146053i
$625$		0			0
$626$	4.53749	+	16.9341i	0.181354	+	0.676824i
$627$	−5.40640	+	1.44864i	−0.215911	+	0.0578531i
$628$	−2.28585	+	8.53091i	−0.0912153	+	0.340420i
$629$	−11.3660	−	11.3660i	−0.453192	−	0.453192i
$630$		0			0
$631$	−3.00634	+	11.2198i	−0.119680	+	0.446653i	−0.999594	−	0.0284797i	$-0.990933\pi$
$631$	−3.00634	+	11.2198i	−0.119680	+	0.446653i	0.879914	+	0.475133i	$0.157600\pi$
$632$			6.64203i			0.264206i
$633$	17.5979	+	4.71535i	0.699455	+	0.187418i
$634$	8.91689	−	15.4445i	0.354135	−	0.613380i
$635$		0			0
$636$		−	30.0759i		−	1.19259i
$637$	−1.03104	−	5.79123i	−0.0408515	−	0.229457i
$638$	5.45679	−	5.45679i	0.216036	−	0.216036i
$639$	34.0827	−	9.13244i	1.34829	−	0.361274i
$640$		0			0
$641$	20.9822	−	12.1141i	0.828748	−	0.478478i	−0.0246761	−	0.999695i	$-0.507855\pi$
$641$	20.9822	−	12.1141i	0.828748	−	0.478478i	0.853424	+	0.521218i	$0.174522\pi$
$642$	34.1714			1.34864
$643$	30.0482	−	17.3483i	1.18498	−	0.684151i	0.227821	−	0.973703i	$-0.426840\pi$
$643$	30.0482	−	17.3483i	1.18498	−	0.684151i	0.957162	+	0.289552i	$0.0935065\pi$
$644$	−3.50989	−	0.940471i	−0.138309	−	0.0370597i
$645$		0			0
$646$	1.59421	+	2.76124i	0.0627232	+	0.108640i
$647$	4.82600	+	18.0109i	0.189730	+	0.708081i	0.993568	+	0.113234i	$0.0361209\pi$
$647$	4.82600	+	18.0109i	0.189730	+	0.708081i	−0.803839	+	0.594848i	$0.797212\pi$
$648$	4.91425	−	8.51173i	0.193050	−	0.334372i
$649$	2.24911			0.0882852
$650$		0			0
$651$	−58.7645			−2.30316
$652$	2.74434	−	4.75333i	0.107476	−	0.186155i
$653$	−7.61144	−	28.4063i	−0.297859	−	1.11162i	−0.938921	−	0.344134i	$-0.888173\pi$
$653$	−7.61144	−	28.4063i	−0.297859	−	1.11162i	0.641062	−	0.767489i	$-0.278494\pi$
$654$	−13.5217	−	23.4203i	−0.528740	−	0.915805i
$655$		0			0
$656$	−3.78693	−	1.01470i	−0.147855	−	0.0396175i
$657$	−13.4632	+	7.77296i	−0.525248	+	0.303252i
$658$	−38.2469			−1.49102
$659$	−4.31737	+	2.49263i	−0.168181	+	0.0970993i	−0.581728	−	0.813384i	$-0.697623\pi$
$659$	−4.31737	+	2.49263i	−0.168181	+	0.0970993i	0.413547	+	0.910483i	$0.364290\pi$
$660$		0			0
$661$	6.22456	−	1.66786i	0.242107	−	0.0648724i	−0.135725	−	0.990747i	$-0.543336\pi$
$661$	6.22456	−	1.66786i	0.242107	−	0.0648724i	0.377832	+	0.925874i	$0.376670\pi$
$662$	−11.4825	+	11.4825i	−0.446279	+	0.446279i
$663$	8.10331	+	9.62473i	0.314707	+	0.373793i
$664$			0.332435i			0.0129010i
$665$		0			0
$666$	14.7940	−	25.6240i	0.573256	−	0.992909i
$667$	8.56705	+	2.29553i	0.331717	+	0.0888834i
$668$			6.51267i			0.251983i
$669$	−8.58271	+	32.0311i	−0.331827	+	1.23839i
$670$		0			0
$671$	0.439989	+	0.439989i	0.0169856	+	0.0169856i
$672$	−1.81418	+	6.77062i	−0.0699836	+	0.261182i
$673$	15.8702	−	4.25240i	0.611750	−	0.163918i	0.0603754	−	0.998176i	$-0.480770\pi$
$673$	15.8702	−	4.25240i	0.611750	−	0.163918i	0.551375	+	0.834258i	$0.314104\pi$
$674$	−4.01455	−	14.9825i	−0.154635	−	0.577104i
$675$		0			0
$676$	−12.2012	+	4.48671i	−0.469277	+	0.172566i
$677$	10.8585	+	10.8585i	0.417326	+	0.417326i	0.884281	−	0.466955i	$-0.154649\pi$
$677$	10.8585	+	10.8585i	0.417326	+	0.417326i	−0.466955	+	0.884281i	$0.654649\pi$
$678$	−38.5133	−	22.2357i	−1.47909	−	0.853956i
$679$	−30.2926	−	17.4894i	−1.16252	−	0.671183i
$680$		0			0
$681$	11.9431	−	11.9431i	0.457661	−	0.457661i
$682$	4.51100	+	7.81328i	0.172735	+	0.299186i
$683$	18.4783	+	32.0053i	0.707051	+	1.22465i	0.965946	+	0.258743i	$0.0833082\pi$
$683$	18.4783	+	32.0053i	0.707051	+	1.22465i	−0.258895	+	0.965905i	$0.583358\pi$
$684$	−4.15005	+	4.15005i	−0.158681	+	0.158681i
$685$		0			0
$686$	13.6593	+	7.88622i	0.521515	+	0.301097i
$687$	−1.79153	−	1.03434i	−0.0683512	−	0.0394626i
$688$	−5.14927	−	5.14927i	−0.196314	−	0.196314i
$689$	3.88634	−	45.2850i	0.148058	−	1.72522i
$690$		0			0
$691$	−4.34372	−	16.2110i	−0.165243	−	0.616694i	−0.998009	−	0.0630698i	$-0.979911\pi$
$691$	−4.34372	−	16.2110i	−0.165243	−	0.616694i	0.832766	−	0.553625i	$-0.186756\pi$
$692$	−17.3835	+	4.65789i	−0.660821	+	0.177067i
$693$	−2.20307	+	8.22198i	−0.0836878	+	0.312327i
$694$	−16.5717	−	16.5717i	−0.629053	−	0.629053i
$695$		0			0
$696$	4.42812	−	16.5260i	0.167847	−	0.626415i
$697$			5.73414i			0.217196i
$698$	11.8371	+	3.17175i	0.448041	+	0.120052i
$699$	−8.84162	+	15.3141i	−0.334421	+	0.579234i
$700$		0			0
$701$		−	35.3603i		−	1.33554i	−0.744368	−	0.667770i	$-0.767249\pi$
$701$		−	35.3603i		−	1.33554i	0.744368	−	0.667770i	$-0.232751\pi$
$702$	1.51478	−	2.17097i	0.0571715	−	0.0819380i
$703$	16.9407	−	16.9407i	0.638931	−	0.638931i
$704$	1.03948	−	0.278528i	0.0391769	−	0.0104974i
$705$		0			0
$706$	−0.481977	+	0.278269i	−0.0181394	+	0.0104728i
$707$	−43.0088			−1.61751
$708$	4.31829	−	2.49316i	0.162291	−	0.0936988i
$709$	50.1238	+	13.4306i	1.88244	+	0.504398i	0.999383	+	0.0351269i	$0.0111835\pi$
$709$	50.1238	+	13.4306i	1.88244	+	0.504398i	0.883054	+	0.469271i	$0.155483\pi$
$710$		0			0
$711$	8.94107	+	15.4864i	0.335316	+	0.580785i
$712$	1.94317	+	7.25199i	0.0728232	+	0.271780i
$713$	−5.18451	+	8.97984i	−0.194161	+	0.336298i
$714$	10.2520			0.383672
$715$		0			0
$716$	14.9804			0.559842
$717$	1.50371	−	2.60450i	0.0561571	−	0.0972669i
$718$	−0.655956	−	2.44806i	−0.0244801	−	0.0913609i
$719$	14.5944	+	25.2783i	0.544279	+	0.942720i	0.998652	+	0.0519079i	$0.0165302\pi$
$719$	14.5944	+	25.2783i	0.544279	+	0.942720i	−0.454372	+	0.890812i	$0.650136\pi$
$720$		0			0
$721$	12.6821	+	3.39817i	0.472308	+	0.126554i
$722$	12.3389	−	7.12388i	0.459207	−	0.265123i
$723$	−26.9612			−1.00270
$724$	12.6723	−	7.31638i	0.470964	−	0.271911i
$725$		0			0
$726$	−22.6812	+	6.07740i	−0.841777	+	0.225554i
$727$	10.8992	−	10.8992i	0.404230	−	0.404230i	−0.475491	−	0.879721i	$-0.657729\pi$
$727$	10.8992	−	10.8992i	0.404230	−	0.404230i	0.879721	+	0.475491i	$0.157729\pi$
$728$	−3.60648	+	9.96003i	−0.133665	+	0.369143i
$729$		−	21.2059i		−	0.785403i
$730$		0			0
$731$	−5.32543	+	9.22392i	−0.196968	+	0.341159i
$732$	1.33251	+	0.357045i	0.0492510	+	0.0131968i
$733$		−	2.22697i		−	0.0822550i	−0.999154	−	0.0411275i	$-0.986905\pi$
$733$		−	2.22697i		−	0.0822550i	0.999154	−	0.0411275i	$-0.0130950\pi$
$734$	−9.26158	+	34.5647i	−0.341851	+	1.27581i
$735$		0			0
$736$	0.874565	+	0.874565i	0.0322369	+	0.0322369i
$737$	−2.49089	+	9.29613i	−0.0917531	+	0.342427i
$738$	−10.1954	+	2.73186i	−0.375299	+	0.100561i
$739$	−3.70543	−	13.8288i	−0.136306	−	0.508702i	−0.999989	−	0.00466650i	$-0.998515\pi$
$739$	−3.70543	−	13.8288i	−0.136306	−	0.508702i	0.863683	−	0.504036i	$-0.168152\pi$
$740$		0			0
$741$	−14.3454	+	12.0778i	−0.526992	+	0.443689i
$742$	−26.1880	−	26.1880i	−0.961393	−	0.961393i
$743$	23.3403	+	13.4756i	0.856274	+	0.494370i	0.862763	−	0.505609i	$-0.168732\pi$
$743$	23.3403	+	13.4756i	0.856274	+	0.494370i	−0.00648861	+	0.999979i	$0.502065\pi$
$744$	17.3222	+	10.0010i	0.635064	+	0.366654i
$745$		0			0
$746$	−23.7326	+	23.7326i	−0.868912	+	0.868912i
$747$	0.447502	+	0.775095i	0.0163732	+	0.0283593i
$748$	−0.786986	−	1.36310i	−0.0287751	−	0.0498399i
$749$	29.7541	−	29.7541i	1.08719	−	1.08719i
$750$		0			0
$751$	7.19473	+	4.15388i	0.262539	+	0.151577i	0.625492	−	0.780230i	$-0.284898\pi$
$751$	7.19473	+	4.15388i	0.262539	+	0.151577i	−0.362953	+	0.931807i	$0.618231\pi$
$752$	11.2742	+	6.50916i	0.411127	+	0.237364i
$753$	9.15827	+	9.15827i	0.333746	+	0.333746i
$754$	8.80282	−	24.3108i	0.320580	−	0.885346i
$755$		0			0
$756$	−0.558281	−	2.08353i	−0.0203045	−	0.0757774i
$757$	−6.76049	+	1.81147i	−0.245714	+	0.0658389i	−0.379574	−	0.925161i	$-0.623929\pi$
$757$	−6.76049	+	1.81147i	−0.245714	+	0.0658389i	0.133860	+	0.991000i	$0.457263\pi$
$758$	3.91160	−	14.5983i	0.142076	−	0.530234i
$759$	2.24547	+	2.24547i	0.0815054	+	0.0815054i
$760$		0			0
$761$	−3.17582	+	11.8523i	−0.115123	+	0.429647i	−0.999296	−	0.0375136i	$-0.988056\pi$
$761$	−3.17582	+	11.8523i	−0.115123	+	0.429647i	0.884173	+	0.467160i	$0.154723\pi$
$762$			40.6897i			1.47403i
$763$	−32.1665	−	8.61900i	−1.16451	−	0.312029i
$764$	0.0540643	−	0.0936422i	0.00195598	−	0.00338786i
$765$		0			0
$766$		−	21.9824i		−	0.794257i
$767$	6.82416	−	3.19593i	0.246406	−	0.115398i
$768$	1.68705	−	1.68705i	0.0608761	−	0.0608761i
$769$	−21.4689	+	5.75258i	−0.774189	+	0.207443i	−0.624221	−	0.781248i	$-0.714584\pi$
$769$	−21.4689	+	5.75258i	−0.774189	+	0.207443i	−0.149968	+	0.988691i	$0.547917\pi$
$770$		0			0
$771$	10.4198	−	6.01590i	0.375261	−	0.216657i
$772$	25.5520			0.919637
$773$	2.28298	−	1.31808i	0.0821131	−	0.0474080i	−0.458381	−	0.888756i	$-0.651571\pi$
$773$	2.28298	−	1.31808i	0.0821131	−	0.0474080i	0.540494	+	0.841348i	$0.318237\pi$
$774$	−18.9375	−	5.07429i	−0.680694	−	0.182391i
$775$		0			0
$776$	5.95297	+	10.3109i	0.213699	+	0.370138i
$777$	−19.9379	−	74.4091i	−0.715266	−	2.66941i
$778$	6.18909	−	10.7198i	0.221890	−	0.384324i
$779$	−8.54659			−0.306213
$780$		0			0
$781$	−14.1041			−0.504683
$782$	0.904486	−	1.56662i	0.0323444	−	0.0560221i
$783$	1.36267	+	5.08556i	0.0486979	+	0.181743i
$784$	0.815727	+	1.41288i	0.0291331	+	0.0504600i
$785$		0			0
$786$	−14.8376	−	3.97571i	−0.529238	−	0.141809i
$787$	−2.96813	+	1.71365i	−0.105802	+	0.0610849i	−0.551967	−	0.833866i	$-0.686123\pi$
$787$	−2.96813	+	1.71365i	−0.105802	+	0.0610849i	0.446165	+	0.894951i	$0.352789\pi$
$788$	5.29398			0.188590
$789$	−56.1176	+	32.3995i	−1.99784	+	1.15345i
$790$		0			0
$791$	−52.8961	+	14.1735i	−1.88077	+	0.503950i
$792$	2.04869	−	2.04869i	0.0727969	−	0.0727969i
$793$	1.96021	+	0.709784i	0.0696092	+	0.0252052i
$794$		−	16.1772i		−	0.574106i
$795$		0			0
$796$	−5.17091	+	8.95629i	−0.183278	+	0.317447i
$797$	−45.7147	−	12.2492i	−1.61930	−	0.433889i	−0.668502	−	0.743710i	$-0.733064\pi$
$797$	−45.7147	−	12.2492i	−1.61930	−	0.433889i	−0.950795	+	0.309821i	$0.899731\pi$
$798$			15.2804i			0.540920i
$799$	4.92806	−	18.3918i	0.174342	−	0.650654i
$800$		0			0
$801$	14.2928	+	14.2928i	0.505011	+	0.505011i
$802$	2.63419	−	9.83091i	0.0930163	−	0.347142i
$803$	6.00225	−	1.60830i	0.211815	−	0.0567556i
$804$	5.52236	+	20.6097i	0.194759	+	0.726850i
$805$		0			0
$806$	24.7896	+	17.2967i	0.873177	+	0.609252i
$807$	10.8069	+	10.8069i	0.380420	+	0.380420i
$808$	12.6778	+	7.31956i	0.446005	+	0.257501i
$809$	9.86026	+	5.69282i	0.346668	+	0.200149i	0.663217	−	0.748427i	$-0.269191\pi$
$809$	9.86026	+	5.69282i	0.346668	+	0.200149i	−0.316549	+	0.948576i	$0.602524\pi$
$810$		0			0
$811$	0.341638	−	0.341638i	0.0119965	−	0.0119965i	−0.701083	−	0.713080i	$-0.747300\pi$
$811$	0.341638	−	0.341638i	0.0119965	−	0.0119965i	0.713080	+	0.701083i	$0.247300\pi$
$812$	−10.5340	−	18.2454i	−0.369670	−	0.640287i
$813$	24.4131	+	42.2848i	0.856205	+	1.48299i
$814$	−8.36286	+	8.36286i	−0.293118	+	0.293118i
$815$		0			0
$816$	−3.02203	−	1.74477i	−0.105792	−	0.0610791i
$817$	−13.7480	−	7.93743i	−0.480983	−	0.277695i
$818$	1.10764	+	1.10764i	0.0387278	+	0.0387278i
$819$	4.99877	+	28.0773i	0.174671	+	0.981102i
$820$		0			0
$821$	12.2052	+	45.5504i	0.425964	+	1.58972i	0.761809	+	0.647802i	$0.224312\pi$
$821$	12.2052	+	45.5504i	0.425964	+	1.58972i	−0.335845	+	0.941917i	$0.609022\pi$
$822$	−2.21504	+	0.593518i	−0.0772583	+	0.0207013i
$823$	−0.882133	+	3.29216i	−0.0307492	+	0.114758i	−0.979595	−	0.200983i	$-0.935586\pi$
$823$	−0.882133	+	3.29216i	−0.0307492	+	0.114758i	0.948845	+	0.315741i	$0.102253\pi$
$824$	−3.16004	−	3.16004i	−0.110085	−	0.110085i
$825$		0			0
$826$	1.58919	−	5.93095i	0.0552951	−	0.206364i
$827$		−	12.0425i		−	0.418758i	−0.977835	−	0.209379i	$-0.932856\pi$
$827$		−	12.0425i		−	0.418758i	0.977835	−	0.209379i	$-0.0671443\pi$
$828$	3.21639	+	0.861830i	0.111777	+	0.0299507i
$829$	23.3013	−	40.3591i	0.809289	−	1.40173i	−0.104068	−	0.994570i	$-0.533186\pi$
$829$	23.3013	−	40.3591i	0.809289	−	1.40173i	0.913357	−	0.407160i	$-0.133481\pi$
$830$		0			0
$831$			40.1921i			1.39425i
$832$	2.75817	−	2.32218i	0.0956223	−	0.0805070i
$833$	1.68727	−	1.68727i	0.0584605	−	0.0584605i
$834$	−2.08531	+	0.558758i	−0.0722085	+	0.0193482i
$835$		0			0
$836$	2.03167	−	1.17298i	0.0702666	−	0.0405685i
$837$	−6.15524			−0.212756
$838$	28.2092	−	16.2866i	0.974471	−	0.562611i
$839$	31.5488	+	8.45349i	1.08919	+	0.291847i	0.758354	−	0.651843i	$-0.226004\pi$
$839$	31.5488	+	8.45349i	1.08919	+	0.291847i	0.330833	+	0.943689i	$0.392670\pi$
$840$		0			0
$841$	11.2117	+	19.4192i	0.386609	+	0.669627i
$842$	−5.97445	−	22.2970i	−0.205893	−	0.768404i
$843$	17.2200	−	29.8258i	0.593087	−	1.02726i
$844$	−7.63616			−0.262848
$845$		0			0
$846$	35.0488			1.20500
$847$	−14.4574	+	25.0410i	−0.496763	+	0.860419i
$848$	3.26266	+	12.1764i	0.112040	+	0.418140i
$849$	16.0738	+	27.8406i	0.551651	+	0.955488i
$850$		0			0
$851$	−13.1295	−	3.51804i	−0.450074	−	0.120597i
$852$	−27.0798	+	15.6345i	−0.927739	+	0.535630i
$853$	3.78389			0.129558			0.0647789	−	0.997900i	$-0.479366\pi$
$853$	3.78389			0.129558			0.0647789	+	0.997900i	$0.479366\pi$
$854$	1.47115	−	0.849369i	0.0503417	−	0.0290648i
$855$		0			0
$856$	−13.8345	+	3.70695i	−0.472854	+	0.126701i
$857$	3.70075	−	3.70075i	0.126415	−	0.126415i	−0.641068	−	0.767484i	$-0.721509\pi$
$857$	3.70075	−	3.70075i	0.126415	−	0.126415i	0.767484	+	0.641068i	$0.221509\pi$
$858$	7.08167	−	5.96225i	0.241764	−	0.203548i
$859$			45.3288i			1.54660i	0.634041	+	0.773299i	$0.281395\pi$
$859$			45.3288i			1.54660i	−0.634041	+	0.773299i	$0.718605\pi$
$860$		0			0
$861$	−13.7404	+	23.7990i	−0.468270	+	0.811068i
$862$	20.3947	+	5.46475i	0.694648	+	0.186130i
$863$		−	20.1783i		−	0.686877i	−0.939175	−	0.343438i	$-0.888408\pi$
$863$		−	20.1783i		−	0.686877i	0.939175	−	0.343438i	$-0.111592\pi$
$864$	−0.190025	+	0.709183i	−0.00646478	+	0.0241269i
$865$		0			0
$866$	6.36961	+	6.36961i	0.216448	+	0.216448i
$867$	9.17659	−	34.2475i	0.311653	−	1.16311i
$868$	23.7912	−	6.37483i	0.807526	−	0.216376i
$869$	−1.84999	−	6.90426i	−0.0627566	−	0.234211i
$870$		0			0
$871$	5.65182	+	31.7455i	0.191505	+	1.07565i
$872$	8.01500	+	8.01500i	0.271422	+	0.271422i
$873$	27.7596	+	16.0270i	0.939519	+	0.542432i
$874$	2.33500	+	1.34811i	0.0789826	+	0.0456006i
$875$		0			0
$876$	9.74150	−	9.74150i	0.329135	−	0.329135i
$877$	−7.40084	−	12.8186i	−0.249909	−	0.432854i	0.713592	−	0.700562i	$-0.247067\pi$
$877$	−7.40084	−	12.8186i	−0.249909	−	0.432854i	−0.963500	+	0.267707i	$0.913734\pi$
$878$	3.16344	+	5.47924i	0.106761	+	0.184916i
$879$	31.3626	−	31.3626i	1.05783	−	1.05783i
$880$		0			0
$881$	−41.4218	−	23.9149i	−1.39554	−	0.805713i	−0.401615	−	0.915809i	$-0.631551\pi$
$881$	−41.4218	−	23.9149i	−1.39554	−	0.805713i	−0.993921	+	0.110095i	$0.964884\pi$
$882$	3.80385	+	2.19616i	0.128082	+	0.0739484i
$883$	−22.7158	−	22.7158i	−0.764449	−	0.764449i	0.212674	−	0.977123i	$-0.431783\pi$
$883$	−22.7158	−	22.7158i	−0.764449	−	0.764449i	−0.977123	+	0.212674i	$0.931783\pi$
$884$	−4.32478	−	3.01758i	−0.145458	−	0.101492i
$885$		0			0
$886$	−1.78691	−	6.66883i	−0.0600323	−	0.224044i
$887$	1.41162	−	0.378242i	0.0473975	−	0.0127001i	−0.235042	−	0.971985i	$-0.575523\pi$
$887$	1.41162	−	0.378242i	0.0473975	−	0.0127001i	0.282440	+	0.959285i	$0.408856\pi$
$888$	−6.78635	+	25.3270i	−0.227735	+	0.849919i
$889$	35.4298	+	35.4298i	1.18828	+	1.18828i
$890$		0			0
$891$	−2.73751	+	10.2165i	−0.0917100	+	0.342266i
$892$		−	13.8991i		−	0.465375i
$893$	27.4125	+	7.34514i	0.917323	+	0.245796i
$894$	−11.6319	+	20.1470i	−0.389028	+	0.673816i
$895$		0			0
$896$		−	2.93793i		−	0.0981495i
$897$	10.0039	+	3.62236i	0.334020	+	0.120947i
$898$	13.9586	−	13.9586i	0.465806	−	0.465806i
$899$	−58.0704	+	15.5599i	−1.93676	+	0.518952i
$900$		0			0
$901$	15.9673	−	9.21872i	0.531948	−	0.307120i
$902$	4.21906			0.140479
$903$	−44.2054	+	25.5220i	−1.47106	+	0.849319i
$904$	18.0045	+	4.82429i	0.598821	+	0.160454i
$905$		0			0
$906$	13.4975	+	23.3783i	0.448423	+	0.776691i
$907$	6.41887	+	23.9556i	0.213135	+	0.795431i	0.986815	+	0.161854i	$0.0517474\pi$
$907$	6.41887	+	23.9556i	0.213135	+	0.795431i	−0.773680	+	0.633577i	$0.781586\pi$
$908$	−3.53964	+	6.13084i	−0.117467	+	0.203459i
$909$	39.4124			1.30723
$910$		0			0
$911$	−13.1232			−0.434791			−0.217396	−	0.976084i	$-0.569756\pi$
$911$	−13.1232			−0.434791			−0.217396	+	0.976084i	$0.569756\pi$
$912$	2.60053	−	4.50425i	0.0861122	−	0.149151i
$913$	−0.0925922	−	0.345559i	−0.00306436	−	0.0114363i
$914$	−1.80048	−	3.11852i	−0.0595544	−	0.103151i
$915$		0			0
$916$	0.837520	+	0.224413i	0.0276724	+	0.00741481i
$917$	−16.3813	+	9.45776i	−0.540959	+	0.312323i
$918$	1.07384			0.0354420
$919$	27.2540	−	15.7351i	0.899025	−	0.519053i	0.0221416	−	0.999755i	$-0.492952\pi$
$919$	27.2540	−	15.7351i	0.899025	−	0.519053i	0.876884	+	0.480702i	$0.159618\pi$
$920$		0			0
$921$	77.3848	−	20.7352i	2.54992	−	0.683248i
$922$	−2.00027	+	2.00027i	−0.0658755	+	0.0658755i
$923$	−42.7941	+	20.0416i	−1.40858	+	0.659676i
$924$		−	7.54322i		−	0.248154i
$925$		0			0
$926$	−19.7021	+	34.1250i	−0.647451	+	1.12142i
$927$	−11.6217	−	3.11402i	−0.381706	−	0.102278i
$928$			7.17101i			0.235400i
$929$	6.02497	−	22.4855i	0.197673	−	0.737725i	−0.793886	−	0.608067i	$-0.791945\pi$
$929$	6.02497	−	22.4855i	0.197673	−	0.737725i	0.991559	−	0.129658i	$-0.0413880\pi$
$930$		0			0
$931$	2.51483	+	2.51483i	0.0824204	+	0.0824204i
$932$	1.91830	−	7.15918i	0.0628359	−	0.234507i
$933$	−50.9018	+	13.6391i	−1.66645	+	0.446524i
$934$	9.78867	+	36.5318i	0.320295	+	1.19536i
$935$		0			0
$936$	3.30491	−	9.12719i	0.108024	−	0.298332i
$937$	4.22722	+	4.22722i	0.138097	+	0.138097i	0.772776	−	0.634679i	$-0.218868\pi$
$937$	4.22722	+	4.22722i	0.138097	+	0.138097i	−0.634679	+	0.772776i	$0.718868\pi$
$938$	22.7540	+	13.1371i	0.742946	+	0.428940i
$939$	−36.2237	−	20.9137i	−1.18212	−	0.682494i
$940$		0			0
$941$	27.4996	−	27.4996i	0.896463	−	0.896463i	−0.0986587	−	0.995121i	$-0.531455\pi$
$941$	27.4996	−	27.4996i	0.896463	−	0.896463i	0.995121	+	0.0986587i	$0.0314552\pi$
$942$	−10.5357	−	18.2484i	−0.343272	−	0.594565i
$943$	2.42449	+	4.19934i	0.0789523	+	0.136749i
$944$	−1.47783	+	1.47783i	−0.0480991	+	0.0480991i
$945$		0			0
$946$	6.78677	+	3.91834i	0.220657	+	0.127396i
$947$	17.5762	+	10.1476i	0.571150	+	0.329754i	0.757609	−	0.652709i	$-0.226368\pi$
$947$	17.5762	+	10.1476i	0.571150	+	0.329754i	−0.186458	+	0.982463i	$0.559701\pi$
$948$	−11.2054	−	11.2054i	−0.363936	−	0.363936i
$949$	15.9265	−	13.4089i	0.516995	−	0.435272i
$950$		0			0
$951$	11.0124	+	41.0989i	0.357102	+	1.33272i
$952$	−4.15060	+	1.11215i	−0.134522	+	0.0360450i
$953$	−6.33806	+	23.6540i	−0.205310	+	0.766227i	0.784045	+	0.620704i	$0.213153\pi$
$953$	−6.33806	+	23.6540i	−0.205310	+	0.766227i	−0.989355	+	0.145523i	$0.953513\pi$
$954$	23.9982	+	23.9982i	0.776972	+	0.776972i
$955$		0			0
$956$	−0.326248	+	1.21757i	−0.0105516	+	0.0393791i
$957$			18.4117i			0.595167i
$958$	−5.58274	−	1.49589i	−0.180370	−	0.0483300i
$959$	−1.41191	+	2.44550i	−0.0455929	+	0.0789693i
$960$		0			0
$961$		−	39.2848i		−	1.26725i
$962$	−13.4908	+	37.2577i	−0.434962	+	1.20124i
$963$	−27.2662	+	27.2662i	−0.878640	+	0.878640i
$964$	10.9154	−	2.92478i	0.351562	−	0.0942007i
$965$		0			0
$966$	7.50797	−	4.33473i	0.241565	−	0.139468i
$967$	11.7605			0.378191			0.189096	−	0.981959i	$-0.439444\pi$
$967$	11.7605			0.378191			0.189096	+	0.981959i	$0.439444\pi$
$968$	8.52334	−	4.92095i	0.273951	−	0.158165i
$969$	−7.34786	−	1.96885i	−0.236047	−	0.0632486i
$970$		0			0
$971$	−19.4868	−	33.7521i	−0.625361	−	1.08316i	−0.988471	−	0.151411i	$-0.951618\pi$
$971$	−19.4868	−	33.7521i	−0.625361	−	1.08316i	0.363110	−	0.931746i	$-0.381715\pi$
$972$	5.49905	+	20.5227i	0.176382	+	0.658267i
$973$	−1.32922	+	2.30228i	−0.0426128	+	0.0738076i
$974$	−12.7292			−0.407870
$975$		0			0
$976$	−0.578208			−0.0185080
$977$	28.0461	−	48.5773i	0.897274	−	1.55412i	0.0663095	−	0.997799i	$-0.478878\pi$
$977$	28.0461	−	48.5773i	0.897274	−	1.55412i	0.830965	−	0.556325i	$-0.187789\pi$
$978$	3.38927	+	12.6489i	0.108377	+	0.404468i
$979$	−4.03976	−	6.99707i	−0.129111	−	0.223627i
$980$		0			0
$981$	29.4768	+	7.89829i	0.941122	+	0.252173i
$982$	33.2862	−	19.2178i	1.06221	−	0.613265i
$983$	3.26032			0.103988			0.0519940	−	0.998647i	$-0.483442\pi$
$983$	3.26032			0.103988			0.0519940	+	0.998647i	$0.483442\pi$
$984$	8.10059	−	4.67688i	0.258237	−	0.149093i
$985$		0			0
$986$	10.1309	−	2.71457i	0.322634	−	0.0864495i
$987$	64.5245	−	64.5245i	2.05384	−	2.05384i
$988$	4.49762	−	6.44597i	0.143088	−	0.205074i
$989$			9.00674i			0.286398i
$990$		0			0
$991$	13.2861	−	23.0122i	0.422048	−	0.731008i	−0.574092	−	0.818791i	$-0.694645\pi$
$991$	13.2861	−	23.0122i	0.422048	−	0.731008i	0.996140	+	0.0877829i	$0.0279782\pi$
$992$	−8.09794	−	2.16984i	−0.257110	−	0.0688924i
$993$		−	38.7430i		−	1.22947i
$994$	−9.96576	+	37.1927i	−0.316095	+	1.17968i
$995$		0			0
$996$	−0.560833	−	0.560833i	−0.0177707	−	0.0177707i
$997$	11.1243	−	41.5163i	0.352309	−	1.31483i	−0.531529	−	0.847040i	$-0.678382\pi$
$997$	11.1243	−	41.5163i	0.352309	−	1.31483i	0.883838	−	0.467794i	$-0.154951\pi$
$998$	−8.05183	+	2.15748i	−0.254876	+	0.0682938i
$999$	−2.08837	−	7.79392i	−0.0660732	−	0.246589i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.w.h.357.4	yes	16
5.2	odd	4		650.2.t.h.643.4	yes	16
5.3	odd	4		650.2.t.f.643.1	yes	16
5.4	even	2		650.2.w.f.357.1	yes	16
13.11	odd	12		650.2.t.f.557.1	✓	16
65.24	odd	12		650.2.t.h.557.4	yes	16
65.37	even	12		650.2.w.f.193.1	yes	16
65.63	even	12	inner	650.2.w.h.193.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.t.f.557.1	✓	16	13.11	odd	12
650.2.t.f.643.1	yes	16	5.3	odd	4
650.2.t.h.557.4	yes	16	65.24	odd	12
650.2.t.h.643.4	yes	16	5.2	odd	4
650.2.w.f.193.1	yes	16	65.37	even	12
650.2.w.f.357.1	yes	16	5.4	even	2
650.2.w.h.193.4	yes	16	65.63	even	12	inner
650.2.w.h.357.4	yes	16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.617503 + 2.30455i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.30455 + 0.617503i) q^{6} +(2.54433 - 1.46897i) q^{7} -1.00000 q^{8} +(-2.33157 + 1.34613i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.617503 + 2.30455i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.30455 + 0.617503i) q^{6} +(2.54433 - 1.46897i) q^{7} -1.00000 q^{8} +(-2.33157 + 1.34613i) q^{9} +(1.03948 - 0.278528i) q^{11} +(1.68705 - 1.68705i) q^{12} +(2.75817 - 2.32218i) q^{13} -2.93793i q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.41276 + 0.378548i) q^{17} +2.69227i q^{18} +(-0.564216 + 2.10568i) q^{19} +(4.95644 + 4.95644i) q^{21} +(0.278528 - 1.03948i) q^{22} +(1.19468 - 0.320113i) q^{23} +(-0.617503 - 2.30455i) q^{24} +(-0.631979 - 3.54973i) q^{26} +(0.519158 + 0.519158i) q^{27} +(-2.54433 - 1.46897i) q^{28} +(6.21027 + 3.58550i) q^{29} +(-5.92810 + 5.92810i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.28376 + 2.22354i) q^{33} +(1.03421 - 1.03421i) q^{34} +(2.33157 + 1.34613i) q^{36} +(-9.51761 - 5.49500i) q^{37} +(1.54147 + 1.54147i) q^{38} +(7.05475 + 4.92239i) q^{39} +(1.01470 + 3.78693i) q^{41} +(6.77062 - 1.81418i) q^{42} +(-1.88476 + 7.03403i) q^{43} +(-0.760952 - 0.760952i) q^{44} +(0.320113 - 1.19468i) q^{46} -13.0183i q^{47} +(-2.30455 - 0.617503i) q^{48} +(0.815727 - 1.41288i) q^{49} +3.48953i q^{51} +(-3.39015 - 1.22756i) q^{52} +(8.91376 - 8.91376i) q^{53} +(0.709183 - 0.190025i) q^{54} +(-2.54433 + 1.46897i) q^{56} -5.20106 q^{57} +(6.21027 - 3.58550i) q^{58} +(2.01875 + 0.540922i) q^{59} +(0.289104 + 0.500743i) q^{61} +(2.16984 + 8.09794i) q^{62} +(-3.95485 + 6.85001i) q^{63} +1.00000 q^{64} +2.56753 q^{66} +(-4.47153 + 7.74492i) q^{67} +(-0.378548 - 1.41276i) q^{68} +(1.47543 + 2.55553i) q^{69} +(-12.6595 - 3.39210i) q^{71} +(2.33157 - 1.34613i) q^{72} +5.77429 q^{73} +(-9.51761 + 5.49500i) q^{74} +(2.10568 - 0.564216i) q^{76} +(2.23563 - 2.23563i) q^{77} +(7.79029 - 3.64840i) q^{78} -6.64203i q^{79} +(-4.91425 + 8.51173i) q^{81} +(3.78693 + 1.01470i) q^{82} -0.332435i q^{83} +(1.81418 - 6.77062i) q^{84} +(5.14927 + 5.14927i) q^{86} +(-4.42812 + 16.5260i) q^{87} +(-1.03948 + 0.278528i) q^{88} +(-1.94317 - 7.25199i) q^{89} +(3.60648 - 9.96003i) q^{91} +(-0.874565 - 0.874565i) q^{92} +(-17.3222 - 10.0010i) q^{93} +(-11.2742 - 6.50916i) q^{94} +(-1.68705 + 1.68705i) q^{96} +(-5.95297 - 10.3109i) q^{97} +(-0.815727 - 1.41288i) q^{98} +(-2.04869 + 2.04869i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{2} - 8 q^{4} + 12 q^{7} - 16 q^{8} - 24 q^{9}+O(q^{10}) \) 16 * q + 8 * q^2 - 8 * q^4 + 12 * q^7 - 16 * q^8 - 24 * q^9	\( 16 q + 8 q^{2} - 8 q^{4} + 12 q^{7} - 16 q^{8} - 24 q^{9} - 4 q^{11} + 8 q^{13} - 8 q^{16} - 8 q^{17} + 16 q^{19} - 4 q^{21} + 4 q^{22} - 4 q^{23} + 4 q^{26} + 36 q^{27} - 12 q^{28} + 36 q^{29} - 8 q^{31} + 8 q^{32} - 16 q^{34} + 24 q^{36} - 36 q^{37} - 4 q^{38} + 32 q^{41} - 8 q^{42} - 36 q^{43} + 8 q^{44} + 4 q^{46} + 16 q^{49} - 4 q^{52} + 44 q^{53} + 36 q^{54} - 12 q^{56} - 48 q^{57} + 36 q^{58} - 24 q^{59} - 20 q^{61} + 8 q^{62} - 36 q^{63} + 16 q^{64} - 12 q^{67} - 8 q^{68} + 24 q^{69} + 16 q^{71} + 24 q^{72} - 36 q^{74} - 20 q^{76} + 16 q^{77} + 60 q^{78} + 16 q^{81} + 16 q^{82} - 4 q^{84} - 36 q^{86} + 12 q^{87} + 4 q^{88} - 28 q^{89} - 44 q^{91} + 8 q^{92} - 24 q^{93} + 24 q^{94} - 8 q^{97} - 16 q^{98} - 36 q^{99}+O(q^{100}) \) 16 * q + 8 * q^2 - 8 * q^4 + 12 * q^7 - 16 * q^8 - 24 * q^9 - 4 * q^11 + 8 * q^13 - 8 * q^16 - 8 * q^17 + 16 * q^19 - 4 * q^21 + 4 * q^22 - 4 * q^23 + 4 * q^26 + 36 * q^27 - 12 * q^28 + 36 * q^29 - 8 * q^31 + 8 * q^32 - 16 * q^34 + 24 * q^36 - 36 * q^37 - 4 * q^38 + 32 * q^41 - 8 * q^42 - 36 * q^43 + 8 * q^44 + 4 * q^46 + 16 * q^49 - 4 * q^52 + 44 * q^53 + 36 * q^54 - 12 * q^56 - 48 * q^57 + 36 * q^58 - 24 * q^59 - 20 * q^61 + 8 * q^62 - 36 * q^63 + 16 * q^64 - 12 * q^67 - 8 * q^68 + 24 * q^69 + 16 * q^71 + 24 * q^72 - 36 * q^74 - 20 * q^76 + 16 * q^77 + 60 * q^78 + 16 * q^81 + 16 * q^82 - 4 * q^84 - 36 * q^86 + 12 * q^87 + 4 * q^88 - 28 * q^89 - 44 * q^91 + 8 * q^92 - 24 * q^93 + 24 * q^94 - 8 * q^97 - 16 * q^98 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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