LMFDB - Embedded newform 650.2.t.h.557.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,2,Mod(7,650)]

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([3, 11]))

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

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

chi := DirichletCharacter("650.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.t (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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			557.4
Root			$2.38585i$ of defining polynomial
Character	$\chi$	$=$	650.557
Dual form			650.2.t.h.643.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(2.30455 + 0.617503i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.30455 - 0.617503i) q^{6} +(1.46897 - 2.54433i) q^{7} -1.00000i q^{8} +(2.33157 + 1.34613i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(2.30455 + 0.617503i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.30455 - 0.617503i) q^{6} +(1.46897 - 2.54433i) q^{7} -1.00000i q^{8} +(2.33157 + 1.34613i) q^{9} +(1.03948 + 0.278528i) q^{11} +(1.68705 - 1.68705i) q^{12} +(-2.32218 + 2.75817i) q^{13} -2.93793i q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.378548 - 1.41276i) q^{17} +2.69227 q^{18} +(0.564216 + 2.10568i) q^{19} +(4.95644 - 4.95644i) q^{21} +(1.03948 - 0.278528i) q^{22} +(-0.320113 + 1.19468i) q^{23} +(0.617503 - 2.30455i) q^{24} +(-0.631979 + 3.54973i) q^{26} +(-0.519158 - 0.519158i) q^{27} +(-1.46897 - 2.54433i) q^{28} +(-6.21027 + 3.58550i) q^{29} +(-5.92810 - 5.92810i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(2.22354 + 1.28376i) q^{33} +(-1.03421 - 1.03421i) q^{34} +(2.33157 - 1.34613i) q^{36} +(5.49500 + 9.51761i) q^{37} +(1.54147 + 1.54147i) q^{38} +(-7.05475 + 4.92239i) q^{39} +(1.01470 - 3.78693i) q^{41} +(1.81418 - 6.77062i) q^{42} +(7.03403 - 1.88476i) q^{43} +(0.760952 - 0.760952i) q^{44} +(0.320113 + 1.19468i) q^{46} +13.0183 q^{47} +(-0.617503 - 2.30455i) q^{48} +(-0.815727 - 1.41288i) q^{49} -3.48953i q^{51} +(1.22756 + 3.39015i) q^{52} +(-8.91376 + 8.91376i) q^{53} +(-0.709183 - 0.190025i) q^{54} +(-2.54433 - 1.46897i) q^{56} +5.20106i q^{57} +(-3.58550 + 6.21027i) q^{58} +(-2.01875 + 0.540922i) q^{59} +(0.289104 - 0.500743i) q^{61} +(-8.09794 - 2.16984i) q^{62} +(6.85001 - 3.95485i) q^{63} -1.00000 q^{64} +2.56753 q^{66} +(-7.74492 + 4.47153i) q^{67} +(-1.41276 - 0.378548i) q^{68} +(-1.47543 + 2.55553i) q^{69} +(-12.6595 + 3.39210i) q^{71} +(1.34613 - 2.33157i) q^{72} +5.77429i q^{73} +(9.51761 + 5.49500i) q^{74} +(2.10568 + 0.564216i) q^{76} +(2.23563 - 2.23563i) q^{77} +(-3.64840 + 7.79029i) q^{78} -6.64203i q^{79} +(-4.91425 - 8.51173i) q^{81} +(-1.01470 - 3.78693i) q^{82} -0.332435 q^{83} +(-1.81418 - 6.77062i) q^{84} +(5.14927 - 5.14927i) q^{86} +(-16.5260 + 4.42812i) q^{87} +(0.278528 - 1.03948i) q^{88} +(1.94317 - 7.25199i) q^{89} +(3.60648 + 9.96003i) q^{91} +(0.874565 + 0.874565i) q^{92} +(-10.0010 - 17.3222i) q^{93} +(11.2742 - 6.50916i) q^{94} +(-1.68705 - 1.68705i) q^{96} +(10.3109 + 5.95297i) q^{97} +(-1.41288 - 0.815727i) q^{98} +(2.04869 + 2.04869i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 4 q^{7} + 24 q^{9}+O(q^{10}) $ 16 * q + 8 * q^4 + 4 * q^7 + 24 * q^9	$ 16 q + 8 q^{4} + 4 q^{7} + 24 q^{9} - 4 q^{11} - 12 q^{13} - 8 q^{16} - 8 q^{17} + 8 q^{18} - 16 q^{19} - 4 q^{21} - 4 q^{22} - 4 q^{23} + 4 q^{26} - 36 q^{27} - 4 q^{28} - 36 q^{29} - 8 q^{31} + 48 q^{33} + 16 q^{34} + 24 q^{36} - 20 q^{37} - 4 q^{38} + 32 q^{41} - 4 q^{42} - 8 q^{44} + 4 q^{46} + 32 q^{47} - 16 q^{49} - 12 q^{52} - 44 q^{53} - 36 q^{54} - 12 q^{56} - 12 q^{58} + 24 q^{59} - 20 q^{61} - 16 q^{62} + 108 q^{63} - 16 q^{64} + 8 q^{68} - 24 q^{69} + 16 q^{71} + 4 q^{72} + 36 q^{74} - 20 q^{76} + 16 q^{77} + 4 q^{78} + 16 q^{81} - 32 q^{82} - 80 q^{83} + 4 q^{84} - 36 q^{86} + 12 q^{87} + 4 q^{88} + 28 q^{89} - 44 q^{91} - 8 q^{92} - 24 q^{94} + 96 q^{97} + 12 q^{98} + 36 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 4 * q^7 + 24 * q^9 - 4 * q^11 - 12 * q^13 - 8 * q^16 - 8 * q^17 + 8 * q^18 - 16 * q^19 - 4 * q^21 - 4 * q^22 - 4 * q^23 + 4 * q^26 - 36 * q^27 - 4 * q^28 - 36 * q^29 - 8 * q^31 + 48 * q^33 + 16 * q^34 + 24 * q^36 - 20 * q^37 - 4 * q^38 + 32 * q^41 - 4 * q^42 - 8 * q^44 + 4 * q^46 + 32 * q^47 - 16 * q^49 - 12 * q^52 - 44 * q^53 - 36 * q^54 - 12 * q^56 - 12 * q^58 + 24 * q^59 - 20 * q^61 - 16 * q^62 + 108 * q^63 - 16 * q^64 + 8 * q^68 - 24 * q^69 + 16 * q^71 + 4 * q^72 + 36 * q^74 - 20 * q^76 + 16 * q^77 + 4 * q^78 + 16 * q^81 - 32 * q^82 - 80 * q^83 + 4 * q^84 - 36 * q^86 + 12 * q^87 + 4 * q^88 + 28 * q^89 - 44 * q^91 - 8 * q^92 - 24 * q^94 + 96 * q^97 + 12 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{12}\right)$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	2.30455	+	0.617503i	1.33053	+	0.356515i	0.852914	−	0.522051i	$-0.174833\pi$
$3$	2.30455	+	0.617503i	1.33053	+	0.356515i	0.477620	+	0.878567i	$0.341500\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	2.30455	−	0.617503i	0.940829	−	0.252094i
$7$	1.46897	−	2.54433i	0.555217	−	0.961665i	−0.442669	−	0.896685i	$-0.645968\pi$
$7$	1.46897	−	2.54433i	0.555217	−	0.961665i	0.997887	−	0.0649796i	$-0.0206982\pi$
$8$		−	1.00000i		−	0.353553i
$9$	2.33157	+	1.34613i	0.777191	+	0.448711i
$10$		0			0
$11$	1.03948	+	0.278528i	0.313415	+	0.0839793i	0.412098	−	0.911140i	$-0.364796\pi$
$11$	1.03948	+	0.278528i	0.313415	+	0.0839793i	−0.0986828	+	0.995119i	$0.531463\pi$
$12$	1.68705	−	1.68705i	0.487009	−	0.487009i
$13$	−2.32218	+	2.75817i	−0.644056	+	0.764979i
$13$	−2.32218	+	2.75817i	−0.644056	+	0.764979i
$14$		−	2.93793i		−	0.785196i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.378548	−	1.41276i	−0.0918114	−	0.342645i	0.904705	−	0.426038i	$-0.140091\pi$
$17$	−0.378548	−	1.41276i	−0.0918114	−	0.342645i	−0.996517	+	0.0833931i	$0.973424\pi$
$18$	2.69227			0.634574
$19$	0.564216	+	2.10568i	0.129440	+	0.483077i	0.999959	−	0.00905797i	$-0.00288328\pi$
$19$	0.564216	+	2.10568i	0.129440	+	0.483077i	−0.870519	+	0.492135i	$0.836217\pi$
$20$		0			0
$21$	4.95644	−	4.95644i	1.08158	−	1.08158i
$22$	1.03948	−	0.278528i	0.221618	−	0.0593823i
$23$	−0.320113	+	1.19468i	−0.0667482	+	0.249108i	−0.991236	−	0.132104i	$-0.957827\pi$
$23$	−0.320113	+	1.19468i	−0.0667482	+	0.249108i	0.924488	+	0.381212i	$0.124493\pi$
$24$	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
$28$	−1.46897	−	2.54433i	−0.277609	−	0.480832i
$29$	−6.21027	+	3.58550i	−1.15322	+	0.665811i	−0.949670	−	0.313253i	$-0.898581\pi$
$29$	−6.21027	+	3.58550i	−1.15322	+	0.665811i	−0.203549	+	0.979065i	$0.565248\pi$
$30$		0			0
$31$	−5.92810	−	5.92810i	−1.06472	−	1.06472i	−0.997755	−	0.0669631i	$-0.978669\pi$
$31$	−5.92810	−	5.92810i	−1.06472	−	1.06472i	−0.0669631	−	0.997755i	$-0.521331\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	2.22354	+	1.28376i	0.387069	+	0.223474i
$34$	−1.03421	−	1.03421i	−0.177366	−	0.177366i
$35$		0			0
$36$	2.33157	−	1.34613i	0.388595	−	0.224356i
$37$	5.49500	+	9.51761i	0.903372	+	1.56469i	0.823088	+	0.567914i	$0.192249\pi$
$37$	5.49500	+	9.51761i	0.903372	+	1.56469i	0.0802840	+	0.996772i	$0.474417\pi$
$38$	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	−0.840313	−	0.542102i	$-0.817629\pi$
$41$	1.01470	−	3.78693i	0.158470	−	0.591419i	0.998783	−	0.0493172i	$-0.0157045\pi$
$42$	1.81418	−	6.77062i	0.279934	−	1.04473i
$43$	7.03403	−	1.88476i	1.07268	−	0.287424i	0.321086	−	0.947050i	$-0.395952\pi$
$43$	7.03403	−	1.88476i	1.07268	−	0.287424i	0.751593	+	0.659627i	$0.229286\pi$
$44$	0.760952	−	0.760952i	0.114718	−	0.114718i
$45$		0			0
$46$	0.320113	+	1.19468i	0.0471981	+	0.176146i
$47$	13.0183			1.89892			0.949458	−	0.313894i	$-0.101634\pi$
$47$	13.0183			1.89892			0.949458	+	0.313894i	$0.101634\pi$
$48$	−0.617503	−	2.30455i	−0.0891288	−	0.332633i
$49$	−0.815727	−	1.41288i	−0.116532	−	0.201840i
$50$		0			0
$51$		−	3.48953i		−	0.488632i
$52$	1.22756	+	3.39015i	0.170231	+	0.470129i
$53$	−8.91376	+	8.91376i	−1.22440	+	1.22440i	−0.258347	+	0.966052i	$0.583178\pi$
$53$	−8.91376	+	8.91376i	−1.22440	+	1.22440i	−0.966052	+	0.258347i	$0.916822\pi$
$54$	−0.709183	−	0.190025i	−0.0965076	−	0.0258591i
$55$		0			0
$56$	−2.54433	−	1.46897i	−0.340000	−	0.196299i
$57$			5.20106i			0.688898i
$58$	−3.58550	+	6.21027i	−0.470800	+	0.815449i
$59$	−2.01875	+	0.540922i	−0.262819	+	0.0704220i	−0.387822	−	0.921734i	$-0.626772\pi$
$59$	−2.01875	+	0.540922i	−0.262819	+	0.0704220i	0.125003	+	0.992156i	$0.460106\pi$
$60$		0			0
$61$	0.289104	−	0.500743i	0.0370160	−	0.0641136i	−0.846924	−	0.531714i	$-0.821548\pi$
$61$	0.289104	−	0.500743i	0.0370160	−	0.0641136i	0.883940	+	0.467601i	$0.154881\pi$
$62$	−8.09794	−	2.16984i	−1.02844	−	0.275569i
$63$	6.85001	−	3.95485i	0.863020	−	0.498265i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	2.56753			0.316041
$67$	−7.74492	+	4.47153i	−0.946192	+	0.546284i	−0.891896	−	0.452241i	$-0.850625\pi$
$67$	−7.74492	+	4.47153i	−0.946192	+	0.546284i	−0.0542961	+	0.998525i	$0.517291\pi$
$68$	−1.41276	−	0.378548i	−0.171322	−	0.0459057i
$69$	−1.47543	+	2.55553i	−0.177621	+	0.307649i
$70$		0			0
$71$	−12.6595	+	3.39210i	−1.50240	+	0.402568i	−0.913905	−	0.405929i	$-0.866948\pi$
$71$	−12.6595	+	3.39210i	−1.50240	+	0.402568i	−0.588500	+	0.808497i	$0.700281\pi$
$72$	1.34613	−	2.33157i	0.158643	−	0.274779i
$73$			5.77429i			0.675829i	0.941177	+	0.337915i	$0.109721\pi$
$73$			5.77429i			0.675829i	−0.941177	+	0.337915i	$0.890279\pi$
$74$	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
$78$	−3.64840	+	7.79029i	−0.413100	+	0.882077i
$79$		−	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
$82$	−1.01470	−	3.78693i	−0.112055	−	0.418196i
$83$	−0.332435			−0.0364894			−0.0182447	−	0.999834i	$-0.505808\pi$
$83$	−0.332435			−0.0364894			−0.0182447	+	0.999834i	$0.505808\pi$
$84$	−1.81418	−	6.77062i	−0.197944	−	0.738735i
$85$		0			0
$86$	5.14927	−	5.14927i	0.555260	−	0.555260i
$87$	−16.5260	+	4.42812i	−1.77177	+	0.474744i
$88$	0.278528	−	1.03948i	0.0296912	−	0.110809i
$89$	1.94317	−	7.25199i	0.205975	−	0.768710i	−0.783175	−	0.621801i	$-0.786401\pi$
$89$	1.94317	−	7.25199i	0.205975	−	0.768710i	0.989150	−	0.146908i	$-0.0469322\pi$
$90$		0			0
$91$	3.60648	+	9.96003i	0.378062	+	1.04409i
$92$	0.874565	+	0.874565i	0.0911797	+	0.0911797i
$93$	−10.0010	−	17.3222i	−1.03706	−	1.79623i
$94$	11.2742	−	6.50916i	1.16284	−	0.671368i
$95$		0			0
$96$	−1.68705	−	1.68705i	−0.172184	−	0.172184i
$97$	10.3109	+	5.95297i	1.04691	+	0.604433i	0.921782	−	0.387708i	$-0.126733\pi$
$97$	10.3109	+	5.95297i	1.04691	+	0.604433i	0.125126	+	0.992141i	$0.460066\pi$
$98$	−1.41288	−	0.815727i	−0.142723	−	0.0824009i
$99$	2.04869	+	2.04869i	0.205901	+	0.205901i
$100$		0			0
$101$	−12.6778	+	7.31956i	−1.26149	+	0.728323i	−0.973363	−	0.229268i	$-0.926367\pi$
$101$	−12.6778	+	7.31956i	−1.26149	+	0.728323i	−0.288130	+	0.957591i	$0.593033\pi$
$102$	−1.74477	−	3.02203i	−0.172758	−	0.299225i
$103$	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
$107$	3.70695	−	13.8345i	0.358364	−	1.33743i	−0.517833	−	0.855482i	$-0.673261\pi$
$107$	3.70695	−	13.8345i	0.358364	−	1.33743i	0.876197	−	0.481952i	$-0.160072\pi$
$108$	−0.709183	+	0.190025i	−0.0682412	+	0.0182852i
$109$	8.01500	−	8.01500i	0.767698	−	0.767698i	−0.210003	−	0.977701i	$-0.567347\pi$
$109$	8.01500	−	8.01500i	0.767698	−	0.767698i	0.977701	+	0.210003i	$0.0673474\pi$
$110$		0			0
$111$	6.78635	+	25.3270i	0.644132	+	2.40393i
$112$	−2.93793			−0.277609
$113$	−4.82429	−	18.0045i	−0.453831	−	1.69372i	−0.691501	−	0.722376i	$-0.743050\pi$
$113$	−4.82429	−	18.0045i	−0.453831	−	1.69372i	0.237669	−	0.971346i	$-0.423616\pi$
$114$	2.60053	+	4.50425i	0.243562	+	0.421862i
$115$		0			0
$116$			7.17101i			0.665811i
$117$	−9.12719	+	3.30491i	−0.843809	+	0.305539i
$118$	−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
$122$		−	0.578208i		−	0.0523485i
$123$	4.67688	−	8.10059i	0.421700	−	0.730406i
$124$	−8.09794	+	2.16984i	−0.727216	+	0.194857i
$125$		0			0
$126$	3.95485	−	6.85001i	0.352326	−	0.610247i
$127$	−16.4735	−	4.41406i	−1.46179	−	0.391684i	−0.561679	−	0.827355i	$-0.689844\pi$
$127$	−16.4735	−	4.41406i	−1.46179	−	0.391684i	−0.900106	+	0.435671i	$0.856511\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	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	$0.590753\pi$
$132$	2.22354	−	1.28376i	0.193535	−	0.111737i
$133$	6.18636	+	1.65763i	0.536425	+	0.143735i
$134$	−4.47153	+	7.74492i	−0.386281	+	0.669059i
$135$		0			0
$136$	−1.41276	+	0.378548i	−0.121143	+	0.0324602i
$137$	−0.480579	+	0.832387i	−0.0410586	+	0.0711156i	−0.885824	−	0.464021i	$-0.846406\pi$
$137$	−0.480579	+	0.832387i	−0.0410586	+	0.0711156i	0.844766	+	0.535136i	$0.179740\pi$
$138$			2.95087i			0.251195i
$139$	0.783638	+	0.452434i	0.0664673	+	0.0383749i	0.532865	−	0.846200i	$-0.321115\pi$
$139$	0.783638	+	0.452434i	0.0664673	+	0.0383749i	−0.466398	+	0.884575i	$0.654449\pi$
$140$		0			0
$141$	30.0014	+	8.03884i	2.52657	+	0.676993i
$142$	−9.26739	+	9.26739i	−0.777702	+	0.777702i
$143$	−3.18208	+	2.22027i	−0.266099	+	0.185668i
$144$		−	2.69227i		−	0.224356i
$145$		0			0
$146$	2.88714	+	5.00068i	0.238942	+	0.413859i
$147$	−1.00743	−	3.75977i	−0.0830912	−	0.310101i
$148$	10.9900			0.903372
$149$	2.52367	+	9.41848i	0.206747	+	0.771592i	0.988910	+	0.148517i	$0.0474500\pi$
$149$	2.52367	+	9.41848i	0.206747	+	0.771592i	−0.782162	+	0.623075i	$0.785883\pi$
$150$		0			0
$151$	8.00063	−	8.00063i	0.651082	−	0.651082i	−0.302172	−	0.953254i	$-0.597712\pi$
$151$	8.00063	−	8.00063i	0.651082	−	0.651082i	0.953254	+	0.302172i	$0.0977115\pi$
$152$	2.10568	−	0.564216i	0.170794	−	0.0457640i
$153$	1.01915	−	3.80353i	0.0823936	−	0.307497i
$154$	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	0.910943	−	0.412533i	$-0.135356\pi$
$157$	6.24506	+	6.24506i	0.498410	+	0.498410i	−0.412533	+	0.910943i	$0.635356\pi$
$158$	−3.32102	−	5.75217i	−0.264206	−	0.457618i
$159$	−26.0465	+	15.0380i	−2.06562	+	1.19259i
$160$		0			0
$161$	2.56941	+	2.56941i	0.202498	+	0.202498i
$162$	−8.51173	−	4.91425i	−0.668744	−	0.386100i
$163$	4.75333	+	2.74434i	0.372309	+	0.214953i	0.674467	−	0.738305i	$-0.264374\pi$
$163$	4.75333	+	2.74434i	0.372309	+	0.214953i	−0.302158	+	0.953258i	$0.597707\pi$
$164$	−2.77222	−	2.77222i	−0.216474	−	0.216474i
$165$		0			0
$166$	−0.287897	+	0.166217i	−0.0223451	+	0.0129010i
$167$	3.25633	+	5.64013i	0.251983	+	0.436447i	0.964072	−	0.265643i	$-0.0855841\pi$
$167$	3.25633	+	5.64013i	0.251983	+	0.436447i	−0.712089	+	0.702089i	$0.752251\pi$
$168$	−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
$172$	1.88476	−	7.03403i	0.143712	−	0.536340i
$173$	−17.3835	+	4.65789i	−1.32164	+	0.354133i	−0.849593	−	0.527439i	$-0.823152\pi$
$173$	−17.3835	+	4.65789i	−1.32164	+	0.354133i	−0.472050	+	0.881572i	$0.656486\pi$
$174$	−12.0978	+	12.0978i	−0.917135	+	0.917135i
$175$		0			0
$176$	−0.278528	−	1.03948i	−0.0209948	−	0.0783537i
$177$	−4.98633			−0.374795
$178$	−1.94317	−	7.25199i	−0.145646	−	0.543560i
$179$	7.49018	+	12.9734i	0.559842	+	0.969675i	0.997509	+	0.0705377i	$0.0224715\pi$
$179$	7.49018	+	12.9734i	0.559842	+	0.969675i	−0.437667	+	0.899137i	$0.644195\pi$
$180$		0			0
$181$		−	14.6328i		−	1.08764i	−0.839200	−	0.543822i	$-0.816976\pi$
$181$		−	14.6328i		−	1.08764i	0.839200	−	0.543822i	$-0.183024\pi$
$182$	8.10332	+	6.82240i	0.600658	+	0.505710i
$183$	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
$187$		−	1.57397i		−	0.115100i
$188$	6.50916	−	11.2742i	0.474729	−	0.822255i
$189$	−2.08353	+	0.558281i	−0.151555	+	0.0406090i
$190$		0			0
$191$	0.0540643	−	0.0936422i	0.00391196	−	0.00677571i	−0.864063	−	0.503384i	$-0.832088\pi$
$191$	0.0540643	−	0.0936422i	0.00391196	−	0.00677571i	0.867975	+	0.496608i	$0.165421\pi$
$192$	−2.30455	−	0.617503i	−0.166317	−	0.0445644i
$193$	22.1287	−	12.7760i	1.59286	−	0.919637i	0.600045	−	0.799966i	$-0.295149\pi$
$193$	22.1287	−	12.7760i	1.59286	−	0.919637i	0.992814	−	0.119671i	$-0.0381841\pi$
$194$	11.9059			0.854797
$195$		0			0
$196$	−1.63145			−0.116532
$197$	−4.58472	+	2.64699i	−0.326648	+	0.188590i	−0.654352	−	0.756190i	$-0.727058\pi$
$197$	−4.58472	+	2.64699i	−0.326648	+	0.188590i	0.327704	+	0.944780i	$0.393725\pi$
$198$	2.79856	+	0.749871i	0.198885	+	0.0532910i
$199$	5.17091	−	8.95629i	0.366556	−	0.634894i	−0.622468	−	0.782645i	$-0.713870\pi$
$199$	5.17091	−	8.95629i	0.366556	−	0.634894i	0.989025	+	0.147751i	$0.0472033\pi$
$200$		0			0
$201$	−20.6097	+	5.52236i	−1.45370	+	0.389517i
$202$	−7.31956	+	12.6778i	−0.515002	+	0.892010i
$203$			21.0679i			1.47868i
$204$	−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
$208$	3.54973	+	0.631979i	0.246130	+	0.0438199i
$209$			2.34597i			0.162274i
$210$		0			0
$211$	3.81808	+	6.61311i	0.262848	+	0.455265i	0.966997	−	0.254786i	$-0.0820050\pi$
$211$	3.81808	+	6.61311i	0.262848	+	0.455265i	−0.704150	+	0.710051i	$0.748672\pi$
$212$	3.26266	+	12.1764i	0.224081	+	0.836280i
$213$	−31.2691			−2.14252
$214$	−3.70695	−	13.8345i	−0.253402	−	0.945709i
$215$		0			0
$216$	−0.519158	+	0.519158i	−0.0353242	+	0.0353242i
$217$	−23.7912	+	6.37483i	−1.61505	+	0.432752i
$218$	2.93369	−	10.9487i	0.198695	−	0.741539i
$219$	−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
$223$	6.94953	+	12.0369i	0.465375	+	0.806054i	0.999218	−	0.0395300i	$-0.0125861\pi$
$223$	6.94953	+	12.0369i	0.465375	+	0.806054i	−0.533843	+	0.845584i	$0.679253\pi$
$224$	−2.54433	+	1.46897i	−0.170000	+	0.0981495i
$225$		0			0
$226$	−13.1802	−	13.1802i	−0.876735	−	0.876735i
$227$	6.13084	+	3.53964i	0.406918	+	0.234934i	0.689465	−	0.724319i	$-0.257846\pi$
$227$	6.13084	+	3.53964i	0.406918	+	0.234934i	−0.282547	+	0.959254i	$0.591179\pi$
$228$	4.50425	+	2.60053i	0.298301	+	0.172224i
$229$	0.613107	+	0.613107i	0.0405153	+	0.0405153i	0.727074	−	0.686559i	$-0.240880\pi$
$229$	0.613107	+	0.613107i	0.0405153	+	0.0405153i	−0.686559	+	0.727074i	$0.740880\pi$
$230$		0			0
$231$	6.53262	−	3.77161i	0.429815	−	0.248154i
$232$	3.58550	+	6.21027i	0.235400	+	0.407724i
$233$	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
$237$	4.10147	−	15.3069i	0.266419	−	0.994290i
$238$	−4.15060	+	1.11215i	−0.269043	+	0.0720899i
$239$	0.891326	−	0.891326i	0.0576551	−	0.0576551i	−0.677691	−	0.735346i	$-0.737019\pi$
$239$	0.891326	−	0.891326i	0.0576551	−	0.0576551i	0.735346	+	0.677691i	$0.237019\pi$
$240$		0			0
$241$	−2.92478	−	10.9154i	−0.188401	−	0.703123i	−0.993877	−	0.110494i	$-0.964757\pi$
$241$	−2.92478	−	10.9154i	−0.188401	−	0.703123i	0.805475	−	0.592629i	$-0.201910\pi$
$242$	−9.84190			−0.632662
$243$	−5.49905	−	20.5227i	−0.352764	−	1.31653i
$244$	−0.289104	−	0.500743i	−0.0185080	−	0.0320568i
$245$		0			0
$246$		−	9.35375i		−	0.596374i
$247$	−7.11804	−	3.33357i	−0.452910	−	0.212110i
$248$	−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	0.640979	−	0.767559i	$-0.278529\pi$
$251$	4.70128	+	2.71429i	0.296742	+	0.171324i	−0.344236	+	0.938883i	$0.611862\pi$
$252$		−	7.90971i		−	0.498265i
$253$	−0.665502	+	1.15268i	−0.0418398	+	0.0724686i
$254$	−16.4735	+	4.41406i	−1.03364	+	0.276962i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.87115	+	1.30522i	0.303854	+	0.0814175i	0.407525	−	0.913194i	$-0.366392\pi$
$257$	4.87115	+	1.30522i	0.303854	+	0.0814175i	−0.103670	+	0.994612i	$0.533059\pi$
$258$	15.0464	−	8.68706i	0.936750	−	0.540833i
$259$	32.2879			2.00627
$260$		0			0
$261$	−19.3063			−1.19503
$262$	−5.57580	+	3.21919i	−0.344474	+	0.198882i
$263$	26.2343	+	7.02946i	1.61768	+	0.433455i	0.950318	−	0.311282i	$-0.100758\pi$
$263$	26.2343	+	7.02946i	1.61768	+	0.433455i	0.667358	+	0.744737i	$0.267425\pi$
$264$	1.28376	−	2.22354i	0.0790102	−	0.136850i
$265$		0			0
$266$	6.18636	−	1.65763i	0.379310	−	0.101636i
$267$	8.95625	−	15.5127i	0.548114	−	0.949361i
$268$			8.94306i			0.546284i
$269$	−5.54757	−	3.20289i	−0.338241	−	0.195284i	0.321253	−	0.946993i	$-0.395896\pi$
$269$	−5.54757	−	3.20289i	−0.338241	−	0.195284i	−0.659494	+	0.751710i	$0.729229\pi$
$270$		0			0
$271$	19.7676	+	5.29672i	1.20080	+	0.321753i	0.803145	−	0.595784i	$-0.203158\pi$
$271$	19.7676	+	5.29672i	1.20080	+	0.321753i	0.397652	+	0.917536i	$0.369825\pi$
$272$	−1.03421	+	1.03421i	−0.0627083	+	0.0627083i
$273$	2.16097	+	25.1804i	0.130788	+	1.52399i
$274$			0.961158i			0.0580657i
$275$		0			0
$276$	1.47543	+	2.55553i	0.0888107	+	0.153825i
$277$	−4.36008	−	16.2720i	−0.261972	−	0.977693i	−0.964078	−	0.265620i	$-0.914423\pi$
$277$	−4.36008	−	16.2720i	−0.261972	−	0.977693i	0.702106	−	0.712073i	$-0.252243\pi$
$278$	0.904867			0.0542703
$279$	−5.84178	−	21.8018i	−0.349738	−	1.30524i
$280$		0			0
$281$	−10.2071	+	10.2071i	−0.608907	+	0.608907i	−0.942660	−	0.333753i	$-0.891685\pi$
$281$	−10.2071	+	10.2071i	−0.608907	+	0.608907i	0.333753	+	0.942660i	$0.391685\pi$
$282$	30.0014	−	8.03884i	1.78656	−	0.478706i
$283$	−3.48740	+	13.0152i	−0.207304	+	0.773671i	0.781430	+	0.623992i	$0.214490\pi$
$283$	−3.48740	+	13.0152i	−0.207304	+	0.773671i	−0.988735	+	0.149678i	$0.952176\pi$
$284$	−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
$288$	−1.34613	−	2.33157i	−0.0793217	−	0.137389i
$289$	12.8698	−	7.43040i	0.757049	−	0.437083i
$290$		0			0
$291$	20.0859	+	20.0859i	1.17746	+	1.17746i
$292$	5.00068	+	2.88714i	0.292643	+	0.168957i
$293$	−16.0996	−	9.29509i	−0.940547	−	0.543025i	−0.0504153	−	0.998728i	$-0.516054\pi$
$293$	−16.0996	−	9.29509i	−0.940547	−	0.543025i	−0.890132	+	0.455703i	$0.849388\pi$
$294$	−2.75234	−	2.75234i	−0.160520	−	0.160520i
$295$		0			0
$296$	9.51761	−	5.49500i	0.553200	−	0.319390i
$297$	−0.395054	−	0.684254i	−0.0229234	−	0.0397045i
$298$	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
$302$	2.92843	−	10.9291i	0.168512	−	0.628897i
$303$	−33.7366	+	9.03969i	−1.93812	+	0.519317i
$304$	1.54147	−	1.54147i	0.0884092	−	0.0884092i
$305$		0			0
$306$	−1.01915	−	3.80353i	−0.0582611	−	0.217433i
$307$	33.5791			1.91646			0.958230	−	0.285998i	$-0.0923250\pi$
$307$	33.5791			1.91646			0.958230	+	0.285998i	$0.0923250\pi$
$308$	−0.818296	−	3.05392i	−0.0466267	−	0.174013i
$309$	5.33113	+	9.23380i	0.303278	+	0.525292i
$310$		0			0
$311$		−	22.0875i		−	1.25247i	−0.779635	−	0.626234i	$-0.784596\pi$
$311$		−	22.0875i		−	1.25247i	0.779635	−	0.626234i	$-0.215404\pi$
$312$	4.92239	+	7.05475i	0.278676	+	0.399397i
$313$	12.3966	−	12.3966i	0.700700	−	0.700700i	−0.263861	−	0.964561i	$-0.584996\pi$
$313$	12.3966	−	12.3966i	0.700700	−	0.700700i	0.964561	+	0.263861i	$0.0849960\pi$
$314$	8.53091	+	2.28585i	0.481427	+	0.128998i
$315$		0			0
$316$	−5.75217	−	3.32102i	−0.323585	−	0.186822i
$317$		−	17.8338i		−	1.00164i	−0.865550	−	0.500822i	$-0.833031\pi$
$317$		−	17.8338i		−	1.00164i	0.865550	−	0.500822i	$-0.166969\pi$
$318$	−15.0380	+	26.0465i	−0.843287	+	1.46062i
$319$	−7.45411	+	1.99732i	−0.417350	+	0.111829i
$320$		0			0
$321$	17.0857	−	29.5933i	0.953632	−	1.65174i
$322$	3.50989	+	0.940471i	0.195598	+	0.0524104i
$323$	2.76124	−	1.59421i	0.153640	−	0.0887039i
$324$	−9.82850			−0.546028
$325$		0			0
$326$	5.48867			0.303989
$327$	23.4203	−	13.5217i	1.29514	−	0.747751i
$328$	−3.78693	−	1.01470i	−0.209098	−	0.0560277i
$329$	19.1235	−	33.1228i	1.05431	−	1.82612i
$330$		0			0
$331$	−15.6854	+	4.20288i	−0.862145	+	0.231011i	−0.662688	−	0.748896i	$-0.730584\pi$
$331$	−15.6854	+	4.20288i	−0.862145	+	0.231011i	−0.199457	+	0.979907i	$0.563918\pi$
$332$	−0.166217	+	0.287897i	−0.00912236	+	0.0158004i
$333$			29.5880i			1.62141i
$334$	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	$0.111163\pi$
$338$	−8.32320	−	9.98621i	−0.452722	−	0.543178i
$339$		−	44.4713i		−	2.41535i
$340$		0			0
$341$	−4.51100	−	7.81328i	−0.244284	−	0.423113i
$342$	1.51902	+	5.66907i	0.0821393	+	0.306548i
$343$	15.7724			0.851631
$344$	−1.88476	−	7.03403i	−0.101620	−	0.379249i
$345$		0			0
$346$	−12.7256	+	12.7256i	−0.684133	+	0.684133i
$347$	22.6374	−	6.06567i	1.21524	−	0.325622i	0.406423	−	0.913685i	$-0.366776\pi$
$347$	22.6374	−	6.06567i	1.21524	−	0.325622i	0.808815	+	0.588063i	$0.200109\pi$
$348$	−4.42812	+	16.5260i	−0.237372	+	0.885884i
$349$	−3.17175	+	11.8371i	−0.169780	+	0.633626i	0.827602	+	0.561315i	$0.189704\pi$
$349$	−3.17175	+	11.8371i	−0.169780	+	0.633626i	−0.997382	+	0.0723116i	$0.976962\pi$
$350$		0			0
$351$	2.63750	−	0.226349i	0.140779	−	0.0120816i
$352$	−0.760952	−	0.760952i	−0.0405589	−	0.0405589i
$353$	−0.278269	−	0.481977i	−0.0148108	−	0.0256530i	0.858525	−	0.512772i	$-0.171381\pi$
$353$	−0.278269	−	0.481977i	−0.0148108	−	0.0256530i	−0.873336	+	0.487119i	$0.838048\pi$
$354$	−4.31829	+	2.49316i	−0.229514	+	0.132510i
$355$		0			0
$356$	−5.30883	−	5.30883i	−0.281367	−	0.281367i
$357$	−8.87851	−	5.12601i	−0.469901	−	0.271297i
$358$	12.9734	+	7.49018i	0.685664	+	0.395868i
$359$	−1.79211	−	1.79211i	−0.0945837	−	0.0945837i	0.658232	−	0.752815i	$-0.271305\pi$
$359$	−1.79211	−	1.79211i	−0.0945837	−	0.0945837i	−0.752815	+	0.658232i	$0.771305\pi$
$360$		0			0
$361$	12.3389	−	7.12388i	0.649417	−	0.374941i
$362$	−7.31638	−	12.6723i	−0.384541	−	0.666044i
$363$	−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
$367$	−9.26158	+	34.5647i	−0.483450	+	1.80426i	0.103489	+	0.994631i	$0.466999\pi$
$367$	−9.26158	+	34.5647i	−0.483450	+	1.80426i	−0.586939	+	0.809631i	$0.699667\pi$
$368$	1.19468	−	0.320113i	0.0622769	−	0.0166870i
$369$	7.46357	−	7.46357i	0.388538	−	0.388538i
$370$		0			0
$371$	9.58549	+	35.7735i	0.497654	+	1.85727i
$372$	−20.0020			−1.03706
$373$	−8.68674	−	32.4193i	−0.449782	−	1.67861i	−0.702991	−	0.711198i	$-0.748153\pi$
$373$	−8.68674	−	32.4193i	−0.449782	−	1.67861i	0.253209	−	0.967412i	$-0.418514\pi$
$374$	−0.786986	−	1.36310i	−0.0406941	−	0.0704842i
$375$		0			0
$376$		−	13.0183i		−	0.671368i
$377$	4.53192	−	25.4552i	0.233406	−	1.31101i
$378$	−1.52525	+	1.52525i	−0.0784505	+	0.0784505i
$379$	−14.5983	−	3.91160i	−0.749863	−	0.200925i	−0.136406	−	0.990653i	$-0.543555\pi$
$379$	−14.5983	−	3.91160i	−0.749863	−	0.200925i	−0.613458	+	0.789728i	$0.710222\pi$
$380$		0			0
$381$	−35.2383	−	20.3448i	−1.80531	−	1.04230i
$382$		−	0.108129i		−	0.00553234i
$383$	−10.9912	+	19.0373i	−0.561625	+	0.972763i	0.435730	+	0.900077i	$0.356490\pi$
$383$	−10.9912	+	19.0373i	−0.561625	+	0.972763i	−0.997355	+	0.0726852i	$0.976843\pi$
$384$	−2.30455	+	0.617503i	−0.117604	+	0.0315118i
$385$		0			0
$386$	12.7760	−	22.1287i	0.650282	−	1.12632i
$387$	18.9375	+	5.07429i	0.962647	+	0.257940i
$388$	10.3109	−	5.95297i	0.523454	−	0.302216i
$389$	−12.3782			−0.627599			−0.313800	−	0.949489i	$-0.601602\pi$
$389$	−12.3782			−0.627599			−0.313800	+	0.949489i	$0.601602\pi$
$390$		0			0
$391$	1.80897			0.0914837
$392$	−1.41288	+	0.815727i	−0.0713613	+	0.0412004i
$393$	−14.8376	−	3.97571i	−0.748456	−	0.200548i
$394$	−2.64699	+	4.58472i	−0.133353	+	0.230975i
$395$		0			0
$396$	2.79856	−	0.749871i	0.140633	−	0.0376825i
$397$	8.08858	−	14.0098i	0.405954	−	0.703134i	−0.588478	−	0.808513i	$-0.700273\pi$
$397$	8.08858	−	14.0098i	0.405954	−	0.703134i	0.994432	+	0.105380i	$0.0336059\pi$
$398$		−	10.3418i		−	0.518389i
$399$	13.2332	+	7.64019i	0.662488	+	0.382488i
$400$		0			0
$401$	9.83091	+	2.63419i	0.490932	+	0.131545i	0.495789	−	0.868443i	$-0.334879\pi$
$401$	9.83091	+	2.63419i	0.490932	+	0.131545i	−0.00485613	+	0.999988i	$0.501546\pi$
$402$	−15.0874	+	15.0874i	−0.752490	+	0.752490i
$403$	30.1168	−	2.58461i	1.50023	−	0.128749i
$404$			14.6391i			0.728323i
$405$		0			0
$406$	10.5340	+	18.2454i	0.522792	+	0.905503i
$407$	3.06102	+	11.4239i	0.151729	+	0.566260i
$408$	−3.48953			−0.172758
$409$	0.405425	+	1.51307i	0.0200470	+	0.0748164i	0.975225	−	0.221217i	$-0.0710028\pi$
$409$	0.405425	+	1.51307i	0.0200470	+	0.0748164i	−0.955178	+	0.296033i	$0.904336\pi$
$410$		0			0
$411$	−1.62152	+	1.62152i	−0.0799837	+	0.0799837i
$412$	4.31669	−	1.15665i	0.212668	−	0.0569842i
$413$	−1.58919	+	5.93095i	−0.0781990	+	0.291843i
$414$	−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
$418$	1.17298	+	2.03167i	0.0573725	+	0.0993720i
$419$	−28.2092	+	16.2866i	−1.37811	+	0.795652i	−0.991932	−	0.126772i	$-0.959538\pi$
$419$	−28.2092	+	16.2866i	−1.37811	+	0.795652i	−0.386178	+	0.922424i	$0.626205\pi$
$420$		0			0
$421$	16.3225	+	16.3225i	0.795511	+	0.795511i	0.982384	−	0.186873i	$-0.0598354\pi$
$421$	16.3225	+	16.3225i	0.795511	+	0.795511i	−0.186873	+	0.982384i	$0.559835\pi$
$422$	6.61311	+	3.81808i	0.321921	+	0.185861i
$423$	30.3531	+	17.5244i	1.47582	+	0.852065i
$424$	8.91376	+	8.91376i	0.432891	+	0.432891i
$425$		0			0
$426$	−27.0798	+	15.6345i	−1.31202	+	0.757496i
$427$	−0.849369	−	1.47115i	−0.0411039	−	0.0711940i
$428$	−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	−0.700098	−	0.714047i	$-0.746860\pi$
$431$	5.46475	−	20.3947i	0.263228	−	0.982380i	0.963326	−	0.268333i	$-0.0864729\pi$
$432$	−0.190025	+	0.709183i	−0.00914259	+	0.0341206i
$433$	8.70105	−	2.33144i	0.418146	−	0.112042i	−0.0436106	−	0.999049i	$-0.513886\pi$
$433$	8.70105	−	2.33144i	0.418146	−	0.112042i	0.461756	+	0.887007i	$0.347219\pi$
$434$	−17.4164	+	17.4164i	−0.836013	+	0.836013i
$435$		0			0
$436$	−2.93369	−	10.9487i	−0.140498	−	0.524347i
$437$	−2.69623			−0.128978
$438$	3.56564	+	13.3071i	0.170373	+	0.635840i
$439$	3.16344	+	5.47924i	0.150983	+	0.261510i	0.931589	−	0.363513i	$-0.118423\pi$
$439$	3.16344	+	5.47924i	0.150983	+	0.261510i	−0.780606	+	0.625023i	$0.785089\pi$
$440$		0			0
$441$		−	4.39231i		−	0.209158i
$442$	5.25416	−	0.450910i	0.249915	−	0.0214476i
$443$	−4.88192	+	4.88192i	−0.231947	+	0.231947i	−0.813505	−	0.581558i	$-0.802443\pi$
$443$	−4.88192	+	4.88192i	−0.231947	+	0.231947i	0.581558	+	0.813505i	$0.302443\pi$
$444$	25.3270	+	6.78635i	1.20197	+	0.322066i
$445$		0			0
$446$	12.0369	+	6.94953i	0.569966	+	0.329070i
$447$			23.2637i			1.10034i
$448$	−1.46897	+	2.54433i	−0.0694022	+	0.120208i
$449$	−19.0679	+	5.10922i	−0.899868	+	0.241119i	−0.678960	−	0.734176i	$-0.737569\pi$
$449$	−19.0679	+	5.10922i	−0.899868	+	0.241119i	−0.220909	+	0.975295i	$0.570902\pi$
$450$		0			0
$451$	2.10953	−	3.65381i	0.0993338	−	0.172051i
$452$	−18.0045	−	4.82429i	−0.846861	−	0.226916i
$453$	23.3783	−	13.4975i	1.09841	−	0.634166i
$454$	7.07929			0.332247
$455$		0			0
$456$	5.20106			0.243562
$457$	3.11852	−	1.80048i	0.145878	−	0.0842227i	−0.425284	−	0.905060i	$-0.639826\pi$
$457$	3.11852	−	1.80048i	0.145878	−	0.0842227i	0.571162	+	0.820837i	$0.306493\pi$
$458$	0.837520	+	0.224413i	0.0391347	+	0.0104861i
$459$	−0.536920	+	0.929972i	−0.0250613	+	0.0434074i
$460$		0			0
$461$	−2.73243	+	0.732151i	−0.127262	+	0.0340997i	−0.321888	−	0.946778i	$-0.604317\pi$
$461$	−2.73243	+	0.732151i	−0.127262	+	0.0340997i	0.194626	+	0.980878i	$0.437651\pi$
$462$	3.77161	−	6.53262i	0.175471	−	0.303925i
$463$		−	39.4042i		−	1.83127i	−0.402014	−	0.915634i	$-0.631690\pi$
$463$		−	39.4042i		−	1.83127i	0.402014	−	0.915634i	$-0.368310\pi$
$464$	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	$0.910820\pi$
$468$	−1.70146	+	9.55683i	−0.0786499	+	0.441765i
$469$			26.2741i			1.21323i
$470$		0			0
$471$	10.5357	+	18.2484i	0.485460	+	0.840842i
$472$	0.540922	+	2.01875i	0.0248979	+	0.0929204i
$473$	7.83669			0.360331
$474$	−4.10147	−	15.3069i	−0.188387	−	0.703070i
$475$		0			0
$476$	−3.03845	+	3.03845i	−0.139267	+	0.139267i
$477$	−32.7822	+	8.78397i	−1.50099	+	0.402190i
$478$	0.326248	−	1.21757i	0.0149222	−	0.0556905i
$479$	1.49589	−	5.58274i	0.0683490	−	0.255082i	−0.923294	−	0.384094i	$-0.874514\pi$
$479$	1.49589	−	5.58274i	0.0683490	−	0.255082i	0.991643	+	0.129012i	$0.0411806\pi$
$480$		0			0
$481$	−39.0115	−	6.94544i	−1.77877	−	0.316685i
$482$	−7.99064	−	7.99064i	−0.363963	−	0.363963i
$483$	4.33473	+	7.50797i	0.197237	+	0.341624i
$484$	−8.52334	+	4.92095i	−0.387425	+	0.223680i
$485$		0			0
$486$	−15.0237	−	15.0237i	−0.681488	−	0.681488i
$487$	11.0238	+	6.36460i	0.499537	+	0.288408i	0.728522	−	0.685022i	$-0.240207\pi$
$487$	11.0238	+	6.36460i	0.499537	+	0.288408i	−0.228985	+	0.973430i	$0.573541\pi$
$488$	−0.500743	−	0.289104i	−0.0226676	−	0.0130871i
$489$	9.25966	+	9.25966i	0.418736	+	0.418736i
$490$		0			0
$491$	33.2862	−	19.2178i	1.50219	−	0.867287i	0.502188	−	0.864758i	$-0.332528\pi$
$491$	33.2862	−	19.2178i	1.50219	−	0.867287i	0.999997	−	0.00252888i	$-0.000804969\pi$
$492$	−4.67688	−	8.10059i	−0.210850	−	0.365203i
$493$	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
$497$	−9.96576	+	37.1927i	−0.447026	+	1.66832i
$498$	−0.766113	+	0.205279i	−0.0343303	+	0.00919878i
$499$	5.89435	−	5.89435i	0.263867	−	0.263867i	−0.562756	−	0.826623i	$-0.690259\pi$
$499$	5.89435	−	5.89435i	0.263867	−	0.263867i	0.826623	+	0.562756i	$0.190259\pi$
$500$		0			0
$501$	4.02159	+	15.0088i	0.179671	+	0.670543i
$502$	5.42857			0.242289
$503$	−1.28446	−	4.79368i	−0.0572714	−	0.213740i	0.931360	−	0.364100i	$-0.118623\pi$
$503$	−1.28446	−	4.79368i	−0.0572714	−	0.213740i	−0.988631	+	0.150360i	$0.951957\pi$
$504$	−3.95485	−	6.85001i	−0.176163	−	0.305124i
$505$		0			0
$506$			1.33100i			0.0591703i
$507$	2.80558	−	30.8889i	0.124600	−	1.37182i
$508$	−12.0594	+	12.0594i	−0.535050	+	0.535050i
$509$	4.73409	+	1.26850i	0.209835	+	0.0562251i	0.362205	−	0.932098i	$-0.382024\pi$
$509$	4.73409	+	1.26850i	0.209835	+	0.0562251i	−0.152370	+	0.988323i	$0.548691\pi$
$510$		0			0
$511$	14.6917	+	8.48223i	0.649921	+	0.375232i
$512$			1.00000i			0.0441942i
$513$	0.800266	−	1.38610i	0.0353326	−	0.0611978i
$514$	4.87115	−	1.30522i	0.214857	−	0.0575708i
$515$		0			0
$516$	8.68706	−	15.0464i	0.382427	−	0.662382i
$517$	13.5323	+	3.62596i	0.595149	+	0.159470i
$518$	27.9621	−	16.1439i	1.22858	−	0.709324i
$519$	−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	$0.690667\pi$
$522$	−16.7197	+	9.65314i	−0.731802	+	0.422506i
$523$	8.61433	+	2.30820i	0.376678	+	0.100931i	0.442191	−	0.896921i	$-0.354202\pi$
$523$	8.61433	+	2.30820i	0.376678	+	0.100931i	−0.0655123	+	0.997852i	$0.520868\pi$
$524$	−3.21919	+	5.57580i	−0.140631	+	0.243580i
$525$		0			0
$526$	26.2343	−	7.02946i	1.14387	−	0.306499i
$527$	−6.13092	+	10.6191i	−0.267067	+	0.462573i
$528$		−	2.56753i		−	0.111737i
$529$	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
$533$	8.08867	+	11.5926i	0.350359	+	0.502133i
$534$		−	17.9125i		−	0.775150i
$535$		0			0
$536$	4.47153	+	7.74492i	0.193141	+	0.334529i
$537$	9.25041	+	34.5230i	0.399185	+	1.48978i
$538$	−6.40578			−0.276173
$539$	−0.454405	−	1.69586i	−0.0195726	−	0.0730460i
$540$		0			0
$541$	−17.9672	+	17.9672i	−0.772472	+	0.772472i	−0.978538	−	0.206066i	$-0.933934\pi$
$541$	−17.9672	+	17.9672i	−0.772472	+	0.772472i	0.206066	+	0.978538i	$0.433934\pi$
$542$	19.7676	−	5.29672i	0.849092	−	0.227513i
$543$	9.03577	−	33.7220i	0.387762	−	1.44715i
$544$	−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	0.0883402	−	0.996090i	$-0.471844\pi$
$547$	−21.2305	−	21.2305i	−0.907750	−	0.907750i	−0.996090	+	0.0883402i	$0.971844\pi$
$548$	0.480579	+	0.832387i	0.0205293	+	0.0355578i
$549$	1.34814	−	0.778346i	0.0575370	−	0.0332190i
$550$		0			0
$551$	−11.0539	−	11.0539i	−0.470911	−	0.470911i
$552$	2.55553	+	1.47543i	0.108770	+	0.0627987i
$553$	−16.8995	−	9.75692i	−0.718639	−	0.414907i
$554$	−11.9120	−	11.9120i	−0.506091	−	0.506091i
$555$		0			0
$556$	0.783638	−	0.452434i	0.0332336	−	0.0191875i
$557$	−12.3014	−	21.3067i	−0.521228	−	0.902793i	−0.999695	−	0.0246877i	$-0.992141\pi$
$557$	−12.3014	−	21.3067i	−0.521228	−	0.902793i	0.478467	−	0.878105i	$-0.341192\pi$
$558$	−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
$562$	−3.73607	+	13.9432i	−0.157597	+	0.588159i
$563$	−33.9104	+	9.08627i	−1.42915	+	0.382941i	−0.888722	−	0.458447i	$-0.848406\pi$
$563$	−33.9104	+	9.08627i	−1.42915	+	0.382941i	−0.540432	+	0.841387i	$0.681739\pi$
$564$	21.9625	−	21.9625i	0.924789	−	0.924789i
$565$		0			0
$566$	3.48740	+	13.0152i	0.146586	+	0.547068i
$567$	−28.8755			−1.21266
$568$	3.39210	+	12.6595i	0.142329	+	0.531180i
$569$	−9.34909	−	16.1931i	−0.391934	−	0.678850i	0.600771	−	0.799422i	$-0.294861\pi$
$569$	−9.34909	−	16.1931i	−0.391934	−	0.678850i	−0.992705	+	0.120572i	$0.961527\pi$
$570$		0			0
$571$		−	18.8705i		−	0.789707i	−0.918744	−	0.394854i	$-0.870795\pi$
$571$		−	18.8705i		−	0.789707i	0.918744	−	0.394854i	$-0.129205\pi$
$572$	0.331770	+	3.86590i	0.0138720	+	0.161641i
$573$	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
$577$			37.0325i			1.54168i	0.637028	+	0.770841i	$0.280164\pi$
$577$			37.0325i			1.54168i	−0.637028	+	0.770841i	$0.719836\pi$
$578$	7.43040	−	12.8698i	0.309064	−	0.535315i
$579$	58.8860	−	15.7784i	2.44722	−	0.655730i
$580$		0			0
$581$	−0.488335	+	0.845822i	−0.0202596	+	0.0350906i
$582$	27.4379	+	7.35195i	1.13734	+	0.304748i
$583$	−11.7484	+	6.78294i	−0.486569	+	0.280921i
$584$	5.77429			0.238942
$585$		0			0
$586$	−18.5902			−0.767953
$587$	20.5572	−	11.8687i	0.848486	−	0.489873i	−0.0116539	−	0.999932i	$-0.503710\pi$
$587$	20.5572	−	11.8687i	0.848486	−	0.489873i	0.860140	+	0.510059i	$0.170376\pi$
$588$	−3.75977	−	1.00743i	−0.155050	−	0.0415456i
$589$	9.13798	−	15.8274i	0.376524	−	0.652158i
$590$		0			0
$591$	−12.2003	+	3.26905i	−0.501851	+	0.134471i
$592$	5.49500	−	9.51761i	0.225843	−	0.391172i
$593$		−	25.3673i		−	1.04171i	−0.853645	−	0.520855i	$-0.825613\pi$
$593$		−	25.3673i		−	1.04171i	0.853645	−	0.520855i	$-0.174387\pi$
$594$	−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
$598$	−4.03848	−	1.89133i	−0.165146	−	0.0773421i
$599$			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	0.725702	+	0.688009i	$0.241515\pi$
$601$	23.5024	+	40.7074i	0.958684	+	1.66049i	0.232982	+	0.972481i	$0.425152\pi$
$602$	−5.53731	−	20.6655i	−0.225684	−	0.842263i
$603$	−24.0771			−0.980496
$604$	−2.92843	−	10.9291i	−0.119156	−	0.444697i
$605$		0			0
$606$	−24.6969	+	24.6969i	−1.00324	+	1.00324i
$607$	−34.3224	+	9.19667i	−1.39311	+	0.373281i	−0.875864	−	0.482558i	$-0.839708\pi$
$607$	−34.3224	+	9.19667i	−1.39311	+	0.373281i	−0.517241	+	0.855840i	$0.673041\pi$
$608$	0.564216	−	2.10568i	0.0228820	−	0.0853968i
$609$	−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
$613$	−7.51739	−	13.0205i	−0.303625	−	0.525893i	0.673330	−	0.739342i	$-0.264864\pi$
$613$	−7.51739	−	13.0205i	−0.303625	−	0.525893i	−0.976954	+	0.213449i	$0.931530\pi$
$614$	29.0804	−	16.7896i	1.17359	−	0.677571i
$615$		0			0
$616$	−2.23563	−	2.23563i	−0.0900759	−	0.0900759i
$617$	−29.0986	−	16.8001i	−1.17147	−	0.676346i	−0.217440	−	0.976074i	$-0.569771\pi$
$617$	−29.0986	−	16.8001i	−1.17147	−	0.676346i	−0.954025	+	0.299728i	$0.903104\pi$
$618$	9.23380	+	5.33113i	0.371438	+	0.214450i
$619$	21.1991	+	21.1991i	0.852063	+	0.852063i	0.990387	−	0.138324i	$-0.0441716\pi$
$619$	21.1991	+	21.1991i	0.852063	+	0.852063i	−0.138324	+	0.990387i	$0.544172\pi$
$620$		0			0
$621$	0.786416	−	0.454038i	0.0315578	−	0.0182199i
$622$	−11.0438	−	19.1283i	−0.442814	−	0.766977i
$623$	−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
$627$	−1.44864	+	5.40640i	−0.0578531	+	0.215911i
$628$	8.53091	−	2.28585i	0.340420	−	0.0912153i
$629$	11.3660	−	11.3660i	0.453192	−	0.453192i
$630$		0			0
$631$	−3.00634	−	11.2198i	−0.119680	−	0.446653i	0.879914	−	0.475133i	$-0.157600\pi$
$631$	−3.00634	−	11.2198i	−0.119680	−	0.446653i	−0.999594	+	0.0284797i	$0.990933\pi$
$632$	−6.64203			−0.264206
$633$	4.71535	+	17.5979i	0.187418	+	0.699455i
$634$	−8.91689	−	15.4445i	−0.354135	−	0.613380i
$635$		0			0
$636$			30.0759i			1.19259i
$637$	5.79123	+	1.03104i	0.229457	+	0.0408515i
$638$	−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	0.853424	−	0.521218i	$-0.174522\pi$
$641$	20.9822	+	12.1141i	0.828748	+	0.478478i	−0.0246761	+	0.999695i	$0.507855\pi$
$642$		−	34.1714i		−	1.34864i
$643$	−17.3483	+	30.0482i	−0.684151	+	1.18498i	0.289552	+	0.957162i	$0.406494\pi$
$643$	−17.3483	+	30.0482i	−0.684151	+	1.18498i	−0.973703	+	0.227821i	$0.926840\pi$
$644$	3.50989	−	0.940471i	0.138309	−	0.0370597i
$645$		0			0
$646$	1.59421	−	2.76124i	0.0627232	−	0.108640i
$647$	−18.0109	−	4.82600i	−0.708081	−	0.189730i	−0.113234	−	0.993568i	$-0.536121\pi$
$647$	−18.0109	−	4.82600i	−0.708081	−	0.189730i	−0.594848	+	0.803839i	$0.702788\pi$
$648$	−8.51173	+	4.91425i	−0.334372	+	0.193050i
$649$	−2.24911			−0.0882852
$650$		0			0
$651$	−58.7645			−2.30316
$652$	4.75333	−	2.74434i	0.186155	−	0.107476i
$653$	−28.4063	−	7.61144i	−1.11162	−	0.297859i	−0.344134	−	0.938921i	$-0.611827\pi$
$653$	−28.4063	−	7.61144i	−1.11162	−	0.297859i	−0.767489	+	0.641062i	$0.778494\pi$
$654$	13.5217	−	23.4203i	0.528740	−	0.915805i
$655$		0			0
$656$	−3.78693	+	1.01470i	−0.147855	+	0.0396175i
$657$	−7.77296	+	13.4632i	−0.303252	+	0.525248i
$658$		−	38.2469i		−	1.49102i
$659$	4.31737	+	2.49263i	0.168181	+	0.0970993i	0.581728	−	0.813384i	$-0.302377\pi$
$659$	4.31737	+	2.49263i	0.168181	+	0.0970993i	−0.413547	+	0.910483i	$0.635710\pi$
$660$		0			0
$661$	6.22456	+	1.66786i	0.242107	+	0.0648724i	0.377832	−	0.925874i	$-0.376670\pi$
$661$	6.22456	+	1.66786i	0.242107	+	0.0648724i	−0.135725	+	0.990747i	$0.543336\pi$
$662$	−11.4825	+	11.4825i	−0.446279	+	0.446279i
$663$	9.62473	+	8.10331i	0.373793	+	0.314707i
$664$			0.332435i			0.0129010i
$665$		0			0
$666$	14.7940	+	25.6240i	0.573256	+	0.992909i
$667$	−2.29553	−	8.56705i	−0.0888834	−	0.331717i
$668$	6.51267			0.251983
$669$	8.58271	+	32.0311i	0.331827	+	1.23839i
$670$		0			0
$671$	0.439989	−	0.439989i	0.0169856	−	0.0169856i
$672$	−6.77062	+	1.81418i	−0.261182	+	0.0699836i
$673$	−4.25240	+	15.8702i	−0.163918	+	0.611750i	0.834258	+	0.551375i	$0.185896\pi$
$673$	−4.25240	+	15.8702i	−0.163918	+	0.611750i	−0.998176	+	0.0603754i	$0.980770\pi$
$674$	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	0.466955	−	0.884281i	$-0.345351\pi$
$677$	−10.8585	−	10.8585i	−0.417326	−	0.417326i	−0.884281	+	0.466955i	$0.845351\pi$
$678$	−22.2357	−	38.5133i	−0.853956	−	1.47909i
$679$	30.2926	−	17.4894i	1.16252	−	0.671183i
$680$		0			0
$681$	11.9431	+	11.9431i	0.457661	+	0.457661i
$682$	−7.81328	−	4.51100i	−0.299186	−	0.172735i
$683$	32.0053	+	18.4783i	1.22465	+	0.707051i	0.965905	−	0.258895i	$-0.0833585\pi$
$683$	32.0053	+	18.4783i	1.22465	+	0.707051i	0.258743	+	0.965946i	$0.416692\pi$
$684$	4.15005	+	4.15005i	0.158681	+	0.158681i
$685$		0			0
$686$	13.6593	−	7.88622i	0.521515	−	0.301097i
$687$	1.03434	+	1.79153i	0.0394626	+	0.0683512i
$688$	−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	0.832766	+	0.553625i	$0.186756\pi$
$691$	−4.34372	+	16.2110i	−0.165243	+	0.616694i	−0.998009	+	0.0630698i	$0.979911\pi$
$692$	−4.65789	+	17.3835i	−0.177067	+	0.660821i
$693$	8.22198	−	2.20307i	0.312327	−	0.0836878i
$694$	16.5717	−	16.5717i	0.629053	−	0.629053i
$695$		0			0
$696$	4.42812	+	16.5260i	0.167847	+	0.626415i
$697$	−5.73414			−0.217196
$698$	3.17175	+	11.8371i	0.120052	+	0.448041i
$699$	8.84162	+	15.3141i	0.334421	+	0.579234i
$700$		0			0
$701$			35.3603i			1.33554i	0.744368	+	0.667770i	$0.232751\pi$
$701$			35.3603i			1.33554i	−0.744368	+	0.667770i	$0.767249\pi$
$702$	2.17097	−	1.51478i	0.0819380	−	0.0571715i
$703$	−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
$707$			43.0088i			1.61751i
$708$	−2.49316	+	4.31829i	−0.0936988	+	0.162291i
$709$	−50.1238	+	13.4306i	−1.88244	+	0.504398i	−0.883054	+	0.469271i	$0.844517\pi$
$709$	−50.1238	+	13.4306i	−1.88244	+	0.504398i	−0.999383	+	0.0351269i	$0.988816\pi$
$710$		0			0
$711$	8.94107	−	15.4864i	0.335316	−	0.580785i
$712$	−7.25199	−	1.94317i	−0.271780	−	0.0728232i
$713$	8.97984	−	5.18451i	0.336298	−	0.194161i
$714$	−10.2520			−0.383672
$715$		0			0
$716$	14.9804			0.559842
$717$	2.60450	−	1.50371i	0.0972669	−	0.0561571i
$718$	−2.44806	−	0.655956i	−0.0913609	−	0.0244801i
$719$	−14.5944	+	25.2783i	−0.544279	+	0.942720i	0.454372	+	0.890812i	$0.349864\pi$
$719$	−14.5944	+	25.2783i	−0.544279	+	0.942720i	−0.998652	+	0.0519079i	$0.983470\pi$
$720$		0			0
$721$	12.6821	−	3.39817i	0.472308	−	0.126554i
$722$	7.12388	−	12.3389i	0.265123	−	0.459207i
$723$		−	26.9612i		−	1.00270i
$724$	−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	$0.157729\pi$
$728$	9.96003	−	3.60648i	0.369143	−	0.133665i
$729$		−	21.2059i		−	0.785403i
$730$		0			0
$731$	−5.32543	−	9.22392i	−0.196968	−	0.341159i
$732$	−0.357045	−	1.33251i	−0.0131968	−	0.0492510i
$733$	−2.22697			−0.0822550			−0.0411275	−	0.999154i	$-0.513095\pi$
$733$	−2.22697			−0.0822550			−0.0411275	+	0.999154i	$0.513095\pi$
$734$	9.26158	+	34.5647i	0.341851	+	1.27581i
$735$		0			0
$736$	0.874565	−	0.874565i	0.0322369	−	0.0322369i
$737$	−9.29613	+	2.49089i	−0.342427	+	0.0917531i
$738$	2.73186	−	10.1954i	0.100561	−	0.375299i
$739$	3.70543	−	13.8288i	0.136306	−	0.508702i	−0.863683	−	0.504036i	$-0.831848\pi$
$739$	3.70543	−	13.8288i	0.136306	−	0.508702i	0.999989	−	0.00466650i	$-0.00148540\pi$
$740$		0			0
$741$	−14.3454	−	12.0778i	−0.526992	−	0.443689i
$742$	26.1880	+	26.1880i	0.961393	+	0.961393i
$743$	13.4756	+	23.3403i	0.494370	+	0.856274i	0.999979	−	0.00648861i	$-0.00206540\pi$
$743$	13.4756	+	23.3403i	0.494370	+	0.856274i	−0.505609	+	0.862763i	$0.668732\pi$
$744$	−17.3222	+	10.0010i	−0.635064	+	0.366654i
$745$		0			0
$746$	−23.7326	−	23.7326i	−0.868912	−	0.868912i
$747$	−0.775095	−	0.447502i	−0.0283593	−	0.0163732i
$748$	−1.36310	−	0.786986i	−0.0498399	−	0.0287751i
$749$	−29.7541	−	29.7541i	−1.08719	−	1.08719i
$750$		0			0
$751$	7.19473	−	4.15388i	0.262539	−	0.151577i	−0.362953	−	0.931807i	$-0.618231\pi$
$751$	7.19473	−	4.15388i	0.262539	−	0.151577i	0.625492	+	0.780230i	$0.284898\pi$
$752$	−6.50916	−	11.2742i	−0.237364	−	0.411127i
$753$	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
$757$	−1.81147	+	6.76049i	−0.0658389	+	0.245714i	−0.991000	−	0.133860i	$-0.957263\pi$
$757$	−1.81147	+	6.76049i	−0.0658389	+	0.245714i	0.925161	+	0.379574i	$0.123929\pi$
$758$	−14.5983	+	3.91160i	−0.530234	+	0.142076i
$759$	−2.24547	+	2.24547i	−0.0815054	+	0.0815054i
$760$		0			0
$761$	−3.17582	−	11.8523i	−0.115123	−	0.429647i	0.884173	−	0.467160i	$-0.154723\pi$
$761$	−3.17582	−	11.8523i	−0.115123	−	0.429647i	−0.999296	+	0.0375136i	$0.988056\pi$
$762$	−40.6897			−1.47403
$763$	−8.61900	−	32.1665i	−0.312029	−	1.16451i
$764$	−0.0540643	−	0.0936422i	−0.00195598	−	0.00338786i
$765$		0			0
$766$			21.9824i			0.794257i
$767$	3.19593	−	6.82416i	0.115398	−	0.246406i
$768$	−1.68705	+	1.68705i	−0.0608761	+	0.0608761i
$769$	21.4689	+	5.75258i	0.774189	+	0.207443i	0.624221	−	0.781248i	$-0.285416\pi$
$769$	21.4689	+	5.75258i	0.774189	+	0.207443i	0.149968	+	0.988691i	$0.452083\pi$
$770$		0			0
$771$	10.4198	+	6.01590i	0.375261	+	0.216657i
$772$		−	25.5520i		−	0.919637i
$773$	−1.31808	+	2.28298i	−0.0474080	+	0.0821131i	−0.888756	−	0.458381i	$-0.848429\pi$
$773$	−1.31808	+	2.28298i	−0.0474080	+	0.0821131i	0.841348	+	0.540494i	$0.181763\pi$
$774$	18.9375	−	5.07429i	0.680694	−	0.182391i
$775$		0			0
$776$	5.95297	−	10.3109i	0.213699	−	0.370138i
$777$	74.4091	+	19.9379i	2.66941	+	0.715266i
$778$	−10.7198	+	6.18909i	−0.384324	+	0.221890i
$779$	8.54659			0.306213
$780$		0			0
$781$	−14.1041			−0.504683
$782$	1.56662	−	0.904486i	0.0560221	−	0.0323444i
$783$	5.08556	+	1.36267i	0.181743	+	0.0486979i
$784$	−0.815727	+	1.41288i	−0.0291331	+	0.0504600i
$785$		0			0
$786$	−14.8376	+	3.97571i	−0.529238	+	0.141809i
$787$	−1.71365	+	2.96813i	−0.0610849	+	0.105802i	−0.894951	−	0.446165i	$-0.852789\pi$
$787$	−1.71365	+	2.96813i	−0.0610849	+	0.105802i	0.833866	+	0.551967i	$0.186123\pi$
$788$			5.29398i			0.188590i
$789$	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
$793$	0.709784	+	1.96021i	0.0252052	+	0.0696092i
$794$		−	16.1772i		−	0.574106i
$795$		0			0
$796$	−5.17091	−	8.95629i	−0.183278	−	0.317447i
$797$	12.2492	+	45.7147i	0.433889	+	1.61930i	0.743710	+	0.668502i	$0.233064\pi$
$797$	12.2492	+	45.7147i	0.433889	+	1.61930i	−0.309821	+	0.950795i	$0.600269\pi$
$798$	15.2804			0.540920
$799$	−4.92806	−	18.3918i	−0.174342	−	0.650654i
$800$		0			0
$801$	14.2928	−	14.2928i	0.505011	−	0.505011i
$802$	9.83091	−	2.63419i	0.347142	−	0.0930163i
$803$	−1.60830	+	6.00225i	−0.0567556	+	0.211815i
$804$	−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
$808$	7.31956	+	12.6778i	0.257501	+	0.446005i
$809$	−9.86026	+	5.69282i	−0.346668	+	0.200149i	−0.663217	−	0.748427i	$-0.730809\pi$
$809$	−9.86026	+	5.69282i	−0.346668	+	0.200149i	0.316549	+	0.948576i	$0.397476\pi$
$810$		0			0
$811$	0.341638	+	0.341638i	0.0119965	+	0.0119965i	0.713080	−	0.701083i	$-0.247300\pi$
$811$	0.341638	+	0.341638i	0.0119965	+	0.0119965i	−0.701083	+	0.713080i	$0.747300\pi$
$812$	18.2454	+	10.5340i	0.640287	+	0.369670i
$813$	42.2848	+	24.4131i	1.48299	+	0.856205i
$814$	8.36286	+	8.36286i	0.293118	+	0.293118i
$815$		0			0
$816$	−3.02203	+	1.74477i	−0.105792	+	0.0610791i
$817$	7.93743	+	13.7480i	0.277695	+	0.480983i
$818$	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	−0.335845	−	0.941917i	$-0.609022\pi$
$821$	12.2052	−	45.5504i	0.425964	−	1.58972i	0.761809	−	0.647802i	$-0.224312\pi$
$822$	−0.593518	+	2.21504i	−0.0207013	+	0.0772583i
$823$	3.29216	−	0.882133i	0.114758	−	0.0307492i	−0.200983	−	0.979595i	$-0.564414\pi$
$823$	3.29216	−	0.882133i	0.114758	−	0.0307492i	0.315741	+	0.948845i	$0.397747\pi$
$824$	3.16004	−	3.16004i	0.110085	−	0.110085i
$825$		0			0
$826$	1.58919	+	5.93095i	0.0552951	+	0.206364i
$827$	12.0425			0.418758			0.209379	−	0.977835i	$-0.432856\pi$
$827$	12.0425			0.418758			0.209379	+	0.977835i	$0.432856\pi$
$828$	0.861830	+	3.21639i	0.0299507	+	0.111777i
$829$	−23.3013	−	40.3591i	−0.809289	−	1.40173i	−0.913357	−	0.407160i	$-0.866519\pi$
$829$	−23.3013	−	40.3591i	−0.809289	−	1.40173i	0.104068	−	0.994570i	$-0.466814\pi$
$830$		0			0
$831$		−	40.1921i		−	1.39425i
$832$	2.32218	−	2.75817i	0.0805070	−	0.0956223i
$833$	−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
$837$			6.15524i			0.212756i
$838$	−16.2866	+	28.2092i	−0.562611	+	0.974471i
$839$	−31.5488	+	8.45349i	−1.08919	+	0.291847i	−0.758354	−	0.651843i	$-0.773996\pi$
$839$	−31.5488	+	8.45349i	−1.08919	+	0.291847i	−0.330833	+	0.943689i	$0.607330\pi$
$840$		0			0
$841$	11.2117	−	19.4192i	0.386609	−	0.669627i
$842$	22.2970	+	5.97445i	0.768404	+	0.205893i
$843$	−29.8258	+	17.2200i	−1.02726	+	0.593087i
$844$	7.63616			0.262848
$845$		0			0
$846$	35.0488			1.20500
$847$	−25.0410	+	14.4574i	−0.860419	+	0.496763i
$848$	12.1764	+	3.26266i	0.418140	+	0.112040i
$849$	−16.0738	+	27.8406i	−0.551651	+	0.955488i
$850$		0			0
$851$	−13.1295	+	3.51804i	−0.450074	+	0.120597i
$852$	−15.6345	+	27.0798i	−0.535630	+	0.927739i
$853$			3.78389i			0.129558i	0.997900	+	0.0647789i	$0.0206342\pi$
$853$			3.78389i			0.129558i	−0.997900	+	0.0647789i	$0.979366\pi$
$854$	−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	$0.221509\pi$
$858$	−5.96225	+	7.08167i	−0.203548	+	0.241764i
$859$			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
$862$	−5.46475	−	20.3947i	−0.186130	−	0.694648i
$863$	−20.1783			−0.686877			−0.343438	−	0.939175i	$-0.611592\pi$
$863$	−20.1783			−0.686877			−0.343438	+	0.939175i	$0.611592\pi$
$864$	0.190025	+	0.709183i	0.00646478	+	0.0241269i
$865$		0			0
$866$	6.36961	−	6.36961i	0.216448	−	0.216448i
$867$	34.2475	−	9.17659i	1.16311	−	0.311653i
$868$	−6.37483	+	23.7912i	−0.216376	+	0.807526i
$869$	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
$873$	16.0270	+	27.7596i	0.542432	+	0.939519i
$874$	−2.33500	+	1.34811i	−0.0789826	+	0.0456006i
$875$		0			0
$876$	9.74150	+	9.74150i	0.329135	+	0.329135i
$877$	12.8186	+	7.40084i	0.432854	+	0.249909i	0.700562	−	0.713592i	$-0.252933\pi$
$877$	12.8186	+	7.40084i	0.432854	+	0.249909i	−0.267707	+	0.963500i	$0.586266\pi$
$878$	5.47924	+	3.16344i	0.184916	+	0.106761i
$879$	−31.3626	−	31.3626i	−1.05783	−	1.05783i
$880$		0			0
$881$	−41.4218	+	23.9149i	−1.39554	+	0.805713i	−0.993921	−	0.110095i	$-0.964884\pi$
$881$	−41.4218	+	23.9149i	−1.39554	+	0.805713i	−0.401615	+	0.915809i	$0.631551\pi$
$882$	−2.19616	−	3.80385i	−0.0739484	−	0.128082i
$883$	−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
$887$	0.378242	−	1.41162i	0.0127001	−	0.0473975i	−0.959285	−	0.282440i	$-0.908856\pi$
$887$	0.378242	−	1.41162i	0.0127001	−	0.0473975i	0.971985	+	0.235042i	$0.0755229\pi$
$888$	25.3270	−	6.78635i	0.849919	−	0.227735i
$889$	−35.4298	+	35.4298i	−1.18828	+	1.18828i
$890$		0			0
$891$	−2.73751	−	10.2165i	−0.0917100	−	0.342266i
$892$	13.8991			0.465375
$893$	7.34514	+	27.4125i	0.245796	+	0.917323i
$894$	11.6319	+	20.1470i	0.389028	+	0.673816i
$895$		0			0
$896$			2.93793i			0.0981495i
$897$	−3.62236	−	10.0039i	−0.120947	−	0.334020i
$898$	−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
$902$		−	4.21906i		−	0.140479i
$903$	25.5220	−	44.2054i	0.849319	−	1.47106i
$904$	−18.0045	+	4.82429i	−0.598821	+	0.160454i
$905$		0			0
$906$	13.4975	−	23.3783i	0.448423	−	0.776691i
$907$	−23.9556	−	6.41887i	−0.795431	−	0.213135i	−0.161854	−	0.986815i	$-0.551747\pi$
$907$	−23.9556	−	6.41887i	−0.795431	−	0.213135i	−0.633577	+	0.773680i	$0.718414\pi$
$908$	6.13084	−	3.53964i	0.203459	−	0.117467i
$909$	−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	$0.569756\pi$
$912$	4.50425	−	2.60053i	0.149151	−	0.0861122i
$913$	−0.345559	−	0.0925922i	−0.0114363	−	0.00306436i
$914$	1.80048	−	3.11852i	0.0595544	−	0.103151i
$915$		0			0
$916$	0.837520	−	0.224413i	0.0276724	−	0.00741481i
$917$	−9.45776	+	16.3813i	−0.312323	+	0.540959i
$918$			1.07384i			0.0354420i
$919$	−27.2540	−	15.7351i	−0.899025	−	0.519053i	−0.0221416	−	0.999755i	$-0.507048\pi$
$919$	−27.2540	−	15.7351i	−0.899025	−	0.519053i	−0.876884	+	0.480702i	$0.840382\pi$
$920$		0			0
$921$	77.3848	+	20.7352i	2.54992	+	0.683248i
$922$	−2.00027	+	2.00027i	−0.0658755	+	0.0658755i
$923$	20.0416	−	42.7941i	0.659676	−	1.40858i
$924$		−	7.54322i		−	0.248154i
$925$		0			0
$926$	−19.7021	−	34.1250i	−0.647451	−	1.12142i
$927$	3.11402	+	11.6217i	0.102278	+	0.381706i
$928$	7.17101			0.235400
$929$	−6.02497	−	22.4855i	−0.197673	−	0.737725i	−0.991559	−	0.129658i	$-0.958612\pi$
$929$	−6.02497	−	22.4855i	−0.197673	−	0.737725i	0.793886	−	0.608067i	$-0.208055\pi$
$930$		0			0
$931$	2.51483	−	2.51483i	0.0824204	−	0.0824204i
$932$	7.15918	−	1.91830i	0.234507	−	0.0628359i
$933$	13.6391	−	50.9018i	0.446524	−	1.66645i
$934$	−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	0.634679	−	0.772776i	$-0.281132\pi$
$937$	−4.22722	−	4.22722i	−0.138097	−	0.138097i	−0.772776	+	0.634679i	$0.781132\pi$
$938$	13.1371	+	22.7540i	0.428940	+	0.742946i
$939$	36.2237	−	20.9137i	1.18212	−	0.682494i
$940$		0			0
$941$	27.4996	+	27.4996i	0.896463	+	0.896463i	0.995121	−	0.0986587i	$-0.0314552\pi$
$941$	27.4996	+	27.4996i	0.896463	+	0.896463i	−0.0986587	+	0.995121i	$0.531455\pi$
$942$	18.2484	+	10.5357i	0.594565	+	0.343272i
$943$	4.19934	+	2.42449i	0.136749	+	0.0789523i
$944$	1.47783	+	1.47783i	0.0480991	+	0.0480991i
$945$		0			0
$946$	6.78677	−	3.91834i	0.220657	−	0.127396i
$947$	−10.1476	−	17.5762i	−0.329754	−	0.571150i	0.652709	−	0.757609i	$-0.273632\pi$
$947$	−10.1476	−	17.5762i	−0.329754	−	0.571150i	−0.982463	+	0.186458i	$0.940299\pi$
$948$	−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
$952$	−1.11215	+	4.15060i	−0.0360450	+	0.134522i
$953$	23.6540	−	6.33806i	0.766227	−	0.205310i	0.145523	−	0.989355i	$-0.453513\pi$
$953$	23.6540	−	6.33806i	0.766227	−	0.205310i	0.620704	+	0.784045i	$0.286847\pi$
$954$	−23.9982	+	23.9982i	−0.776972	+	0.776972i
$955$		0			0
$956$	−0.326248	−	1.21757i	−0.0105516	−	0.0393791i
$957$	−18.4117			−0.595167
$958$	−1.49589	−	5.58274i	−0.0483300	−	0.180370i
$959$	1.41191	+	2.44550i	0.0455929	+	0.0789693i
$960$		0			0
$961$			39.2848i			1.26725i
$962$	−37.2577	+	13.4908i	−1.20124	+	0.434962i
$963$	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
$967$		−	11.7605i		−	0.378191i	−0.981959	−	0.189096i	$-0.939444\pi$
$967$		−	11.7605i		−	0.378191i	0.981959	−	0.189096i	$-0.0605556\pi$
$968$	−4.92095	+	8.52334i	−0.158165	+	0.273951i
$969$	7.34786	−	1.96885i	0.236047	−	0.0632486i
$970$		0			0
$971$	−19.4868	+	33.7521i	−0.625361	+	1.08316i	0.363110	+	0.931746i	$0.381715\pi$
$971$	−19.4868	+	33.7521i	−0.625361	+	1.08316i	−0.988471	+	0.151411i	$0.951618\pi$
$972$	−20.5227	−	5.49905i	−0.658267	−	0.176382i
$973$	2.30228	−	1.32922i	0.0738076	−	0.0426128i
$974$	12.7292			0.407870
$975$		0			0
$976$	−0.578208			−0.0185080
$977$	48.5773	−	28.0461i	1.55412	−	0.897274i	0.556325	−	0.830965i	$-0.312211\pi$
$977$	48.5773	−	28.0461i	1.55412	−	0.897274i	0.997799	−	0.0663095i	$-0.0211225\pi$
$978$	12.6489	+	3.38927i	0.404468	+	0.108377i
$979$	4.03976	−	6.99707i	0.129111	−	0.223627i
$980$		0			0
$981$	29.4768	−	7.89829i	0.941122	−	0.252173i
$982$	19.2178	−	33.2862i	0.613265	−	1.06221i
$983$			3.26032i			0.103988i	0.998647	+	0.0519940i	$0.0165577\pi$
$983$			3.26032i			0.103988i	−0.998647	+	0.0519940i	$0.983442\pi$
$984$	−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
$988$	−6.44597	+	4.49762i	−0.205074	+	0.143088i
$989$			9.00674i			0.286398i
$990$		0			0
$991$	13.2861	+	23.0122i	0.422048	+	0.731008i	0.996140	−	0.0877829i	$-0.0279782\pi$
$991$	13.2861	+	23.0122i	0.422048	+	0.731008i	−0.574092	+	0.818791i	$0.694645\pi$
$992$	2.16984	+	8.09794i	0.0688924	+	0.257110i
$993$	−38.7430			−1.22947
$994$	9.96576	+	37.1927i	0.316095	+	1.17968i
$995$		0			0
$996$	−0.560833	+	0.560833i	−0.0177707	+	0.0177707i
$997$	41.5163	−	11.1243i	1.31483	−	0.352309i	0.467794	−	0.883838i	$-0.345049\pi$
$997$	41.5163	−	11.1243i	1.31483	−	0.352309i	0.847040	+	0.531529i	$0.178382\pi$
$998$	2.15748	−	8.05183i	0.0682938	−	0.254876i
$999$	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.t.h.557.4	yes	16
5.2	odd	4		650.2.w.h.193.4	yes	16
5.3	odd	4		650.2.w.f.193.1	yes	16
5.4	even	2		650.2.t.f.557.1	✓	16
13.6	odd	12		650.2.w.f.357.1	yes	16
65.19	odd	12		650.2.w.h.357.4	yes	16
65.32	even	12		650.2.t.f.643.1	yes	16
65.58	even	12	inner	650.2.t.h.643.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.t.f.557.1	✓	16	5.4	even	2
650.2.t.f.643.1	yes	16	65.32	even	12
650.2.t.h.557.4	yes	16	1.1	even	1	trivial
650.2.t.h.643.4	yes	16	65.58	even	12	inner
650.2.w.f.193.1	yes	16	5.3	odd	4
650.2.w.f.357.1	yes	16	13.6	odd	12
650.2.w.h.193.4	yes	16	5.2	odd	4
650.2.w.h.357.4	yes	16	65.19	odd	12

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.t (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(2.30455 + 0.617503i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.30455 - 0.617503i) q^{6} +(1.46897 - 2.54433i) q^{7} -1.00000i q^{8} +(2.33157 + 1.34613i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(2.30455 + 0.617503i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.30455 - 0.617503i) q^{6} +(1.46897 - 2.54433i) q^{7} -1.00000i q^{8} +(2.33157 + 1.34613i) q^{9} +(1.03948 + 0.278528i) q^{11} +(1.68705 - 1.68705i) q^{12} +(-2.32218 + 2.75817i) q^{13} -2.93793i q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.378548 - 1.41276i) q^{17} +2.69227 q^{18} +(0.564216 + 2.10568i) q^{19} +(4.95644 - 4.95644i) q^{21} +(1.03948 - 0.278528i) q^{22} +(-0.320113 + 1.19468i) q^{23} +(0.617503 - 2.30455i) q^{24} +(-0.631979 + 3.54973i) q^{26} +(-0.519158 - 0.519158i) q^{27} +(-1.46897 - 2.54433i) q^{28} +(-6.21027 + 3.58550i) q^{29} +(-5.92810 - 5.92810i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(2.22354 + 1.28376i) q^{33} +(-1.03421 - 1.03421i) q^{34} +(2.33157 - 1.34613i) q^{36} +(5.49500 + 9.51761i) q^{37} +(1.54147 + 1.54147i) q^{38} +(-7.05475 + 4.92239i) q^{39} +(1.01470 - 3.78693i) q^{41} +(1.81418 - 6.77062i) q^{42} +(7.03403 - 1.88476i) q^{43} +(0.760952 - 0.760952i) q^{44} +(0.320113 + 1.19468i) q^{46} +13.0183 q^{47} +(-0.617503 - 2.30455i) q^{48} +(-0.815727 - 1.41288i) q^{49} -3.48953i q^{51} +(1.22756 + 3.39015i) q^{52} +(-8.91376 + 8.91376i) q^{53} +(-0.709183 - 0.190025i) q^{54} +(-2.54433 - 1.46897i) q^{56} +5.20106i q^{57} +(-3.58550 + 6.21027i) q^{58} +(-2.01875 + 0.540922i) q^{59} +(0.289104 - 0.500743i) q^{61} +(-8.09794 - 2.16984i) q^{62} +(6.85001 - 3.95485i) q^{63} -1.00000 q^{64} +2.56753 q^{66} +(-7.74492 + 4.47153i) q^{67} +(-1.41276 - 0.378548i) q^{68} +(-1.47543 + 2.55553i) q^{69} +(-12.6595 + 3.39210i) q^{71} +(1.34613 - 2.33157i) q^{72} +5.77429i q^{73} +(9.51761 + 5.49500i) q^{74} +(2.10568 + 0.564216i) q^{76} +(2.23563 - 2.23563i) q^{77} +(-3.64840 + 7.79029i) q^{78} -6.64203i q^{79} +(-4.91425 - 8.51173i) q^{81} +(-1.01470 - 3.78693i) q^{82} -0.332435 q^{83} +(-1.81418 - 6.77062i) q^{84} +(5.14927 - 5.14927i) q^{86} +(-16.5260 + 4.42812i) q^{87} +(0.278528 - 1.03948i) q^{88} +(1.94317 - 7.25199i) q^{89} +(3.60648 + 9.96003i) q^{91} +(0.874565 + 0.874565i) q^{92} +(-10.0010 - 17.3222i) q^{93} +(11.2742 - 6.50916i) q^{94} +(-1.68705 - 1.68705i) q^{96} +(10.3109 + 5.95297i) q^{97} +(-1.41288 - 0.815727i) q^{98} +(2.04869 + 2.04869i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 4 q^{7} + 24 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 + 4 * q^7 + 24 * q^9	\( 16 q + 8 q^{4} + 4 q^{7} + 24 q^{9} - 4 q^{11} - 12 q^{13} - 8 q^{16} - 8 q^{17} + 8 q^{18} - 16 q^{19} - 4 q^{21} - 4 q^{22} - 4 q^{23} + 4 q^{26} - 36 q^{27} - 4 q^{28} - 36 q^{29} - 8 q^{31} + 48 q^{33} + 16 q^{34} + 24 q^{36} - 20 q^{37} - 4 q^{38} + 32 q^{41} - 4 q^{42} - 8 q^{44} + 4 q^{46} + 32 q^{47} - 16 q^{49} - 12 q^{52} - 44 q^{53} - 36 q^{54} - 12 q^{56} - 12 q^{58} + 24 q^{59} - 20 q^{61} - 16 q^{62} + 108 q^{63} - 16 q^{64} + 8 q^{68} - 24 q^{69} + 16 q^{71} + 4 q^{72} + 36 q^{74} - 20 q^{76} + 16 q^{77} + 4 q^{78} + 16 q^{81} - 32 q^{82} - 80 q^{83} + 4 q^{84} - 36 q^{86} + 12 q^{87} + 4 q^{88} + 28 q^{89} - 44 q^{91} - 8 q^{92} - 24 q^{94} + 96 q^{97} + 12 q^{98} + 36 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 4 * q^7 + 24 * q^9 - 4 * q^11 - 12 * q^13 - 8 * q^16 - 8 * q^17 + 8 * q^18 - 16 * q^19 - 4 * q^21 - 4 * q^22 - 4 * q^23 + 4 * q^26 - 36 * q^27 - 4 * q^28 - 36 * q^29 - 8 * q^31 + 48 * q^33 + 16 * q^34 + 24 * q^36 - 20 * q^37 - 4 * q^38 + 32 * q^41 - 4 * q^42 - 8 * q^44 + 4 * q^46 + 32 * q^47 - 16 * q^49 - 12 * q^52 - 44 * q^53 - 36 * q^54 - 12 * q^56 - 12 * q^58 + 24 * q^59 - 20 * q^61 - 16 * q^62 + 108 * q^63 - 16 * q^64 + 8 * q^68 - 24 * q^69 + 16 * q^71 + 4 * q^72 + 36 * q^74 - 20 * q^76 + 16 * q^77 + 4 * q^78 + 16 * q^81 - 32 * q^82 - 80 * q^83 + 4 * q^84 - 36 * q^86 + 12 * q^87 + 4 * q^88 + 28 * q^89 - 44 * q^91 - 8 * q^92 - 24 * q^94 + 96 * q^97 + 12 * q^98 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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