LMFDB - Embedded newform 546.2.p.b.239.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("546.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.p (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.45474709504.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 38x^{6} + 481x^{4} + 2112x^{2} + 1024 $ x^8 + 38x^6 + 481x^4 + 2112*x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			239.1
Root			$0.742317i$ of defining polynomial
Character	$\chi$	$=$	546.239
Dual form			546.2.p.b.281.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-1.41421 - 1.00000i) q^{3} +1.00000i q^{4} +(-0.524897 - 0.524897i) q^{5} +(0.292893 + 1.70711i) q^{6} +(0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.00000 + 2.82843i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.41421 - 1.00000i) q^{3} +1.00000i q^{4} +(-0.524897 - 0.524897i) q^{5} +(0.292893 + 1.70711i) q^{6} +(0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.00000 + 2.82843i) q^{9} +0.742317i q^{10} +(3.26721 - 3.26721i) q^{11} +(1.00000 - 1.41421i) q^{12} +(1.23200 + 3.38853i) q^{13} -1.00000i q^{14} +(0.217420 + 1.26721i) q^{15} -1.00000 q^{16} -1.25768 q^{17} +(1.29289 - 2.70711i) q^{18} +(-1.47510 + 1.47510i) q^{19} +(0.524897 - 0.524897i) q^{20} +(-0.292893 - 1.70711i) q^{21} -4.62054 q^{22} +8.25612 q^{23} +(-1.70711 + 0.292893i) q^{24} -4.44897i q^{25} +(1.52490 - 3.26721i) q^{26} +(1.41421 - 5.00000i) q^{27} +(-0.707107 + 0.707107i) q^{28} -5.20632i q^{29} +(0.742317 - 1.04979i) q^{30} +(3.41421 - 3.41421i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-7.88775 + 1.35332i) q^{33} +(0.889316 + 0.889316i) q^{34} -0.742317i q^{35} +(-2.82843 + 1.00000i) q^{36} +(-6.68143 - 6.68143i) q^{37} +2.08611 q^{38} +(1.64622 - 6.02412i) q^{39} -0.742317 q^{40} +(-2.20632 - 2.20632i) q^{41} +(-1.00000 + 1.41421i) q^{42} +6.84191i q^{43} +(3.26721 + 3.26721i) q^{44} +(0.959736 - 2.00953i) q^{45} +(-5.83796 - 5.83796i) q^{46} +(-4.24264 + 4.24264i) q^{47} +(1.41421 + 1.00000i) q^{48} +1.00000i q^{49} +(-3.14589 + 3.14589i) q^{50} +(1.77863 + 1.25768i) q^{51} +(-3.38853 + 1.23200i) q^{52} -10.4339i q^{53} +(-4.53553 + 2.53553i) q^{54} -3.42990 q^{55} +1.00000 q^{56} +(3.56121 - 0.611008i) q^{57} +(-3.68143 + 3.68143i) q^{58} +(5.31306 - 5.31306i) q^{59} +(-1.26721 + 0.217420i) q^{60} +9.59991 q^{61} -4.82843 q^{62} +(-1.29289 + 2.70711i) q^{63} -1.00000i q^{64} +(1.13196 - 2.42531i) q^{65} +(6.53443 + 4.62054i) q^{66} +(6.12021 - 6.12021i) q^{67} -1.25768i q^{68} +(-11.6759 - 8.25612i) q^{69} +(-0.524897 + 0.524897i) q^{70} +(-6.15653 - 6.15653i) q^{71} +(2.70711 + 1.29289i) q^{72} +(9.28849 + 9.28849i) q^{73} +9.44897i q^{74} +(-4.44897 + 6.29179i) q^{75} +(-1.47510 - 1.47510i) q^{76} +4.62054 q^{77} +(-5.42374 + 3.09564i) q^{78} +7.87822 q^{79} +(0.524897 + 0.524897i) q^{80} +(-7.00000 + 5.65685i) q^{81} +3.12021i q^{82} +(2.25768 + 2.25768i) q^{83} +(1.70711 - 0.292893i) q^{84} +(0.660154 + 0.660154i) q^{85} +(4.83796 - 4.83796i) q^{86} +(-5.20632 + 7.36286i) q^{87} -4.62054i q^{88} +(1.75801 - 1.75801i) q^{89} +(-2.09959 + 0.742317i) q^{90} +(-1.52490 + 3.26721i) q^{91} +8.25612i q^{92} +(-8.24264 + 1.41421i) q^{93} +6.00000 q^{94} +1.54855 q^{95} +(-0.292893 - 1.70711i) q^{96} +(2.58579 - 2.58579i) q^{97} +(0.707107 - 0.707107i) q^{98} +(12.5083 + 5.97386i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{5} + 8 q^{6} + 8 q^{9}+O(q^{10}) $ 8 * q + 4 * q^5 + 8 * q^6 + 8 * q^9	$ 8 q + 4 q^{5} + 8 q^{6} + 8 q^{9} + 8 q^{11} + 8 q^{12} - 4 q^{13} - 8 q^{16} - 20 q^{17} + 16 q^{18} - 20 q^{19} - 4 q^{20} - 8 q^{21} + 12 q^{22} + 12 q^{23} - 8 q^{24} + 4 q^{26} - 4 q^{30} + 16 q^{31} + 4 q^{33} + 4 q^{34} - 24 q^{37} + 4 q^{38} - 12 q^{39} + 4 q^{40} + 20 q^{41} - 8 q^{42} + 8 q^{44} - 4 q^{45} + 4 q^{46} - 24 q^{50} + 8 q^{51} + 8 q^{52} - 8 q^{54} - 12 q^{55} + 8 q^{56} + 24 q^{57} + 8 q^{60} + 20 q^{61} - 16 q^{62} - 16 q^{63} - 28 q^{65} + 16 q^{66} + 24 q^{67} + 8 q^{69} + 4 q^{70} - 28 q^{71} + 16 q^{72} + 16 q^{73} + 36 q^{75} - 20 q^{76} - 12 q^{77} - 4 q^{78} + 24 q^{79} - 4 q^{80} - 56 q^{81} + 28 q^{83} + 8 q^{84} + 16 q^{85} - 12 q^{86} - 4 q^{87} + 16 q^{90} - 4 q^{91} - 32 q^{93} + 48 q^{94} - 92 q^{95} - 8 q^{96} + 32 q^{97} - 16 q^{99}+O(q^{100}) $ 8 * q + 4 * q^5 + 8 * q^6 + 8 * q^9 + 8 * q^11 + 8 * q^12 - 4 * q^13 - 8 * q^16 - 20 * q^17 + 16 * q^18 - 20 * q^19 - 4 * q^20 - 8 * q^21 + 12 * q^22 + 12 * q^23 - 8 * q^24 + 4 * q^26 - 4 * q^30 + 16 * q^31 + 4 * q^33 + 4 * q^34 - 24 * q^37 + 4 * q^38 - 12 * q^39 + 4 * q^40 + 20 * q^41 - 8 * q^42 + 8 * q^44 - 4 * q^45 + 4 * q^46 - 24 * q^50 + 8 * q^51 + 8 * q^52 - 8 * q^54 - 12 * q^55 + 8 * q^56 + 24 * q^57 + 8 * q^60 + 20 * q^61 - 16 * q^62 - 16 * q^63 - 28 * q^65 + 16 * q^66 + 24 * q^67 + 8 * q^69 + 4 * q^70 - 28 * q^71 + 16 * q^72 + 16 * q^73 + 36 * q^75 - 20 * q^76 - 12 * q^77 - 4 * q^78 + 24 * q^79 - 4 * q^80 - 56 * q^81 + 28 * q^83 + 8 * q^84 + 16 * q^85 - 12 * q^86 - 4 * q^87 + 16 * q^90 - 4 * q^91 - 32 * q^93 + 48 * q^94 - 92 * q^95 - 8 * q^96 + 32 * q^97 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	−1.41421	−	1.00000i	−0.816497	−	0.577350i
$3$	−1.41421	−	1.00000i	−0.816497	−	0.577350i
$4$			1.00000i			0.500000i
$5$	−0.524897	−	0.524897i	−0.234741	−	0.234741i	0.579927	−	0.814668i	$-0.303081\pi$
$5$	−0.524897	−	0.524897i	−0.234741	−	0.234741i	−0.814668	+	0.579927i	$0.803081\pi$
$6$	0.292893	+	1.70711i	0.119573	+	0.696923i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	1.00000	+	2.82843i	0.333333	+	0.942809i
$10$			0.742317i			0.234741i
$11$	3.26721	−	3.26721i	0.985102	−	0.985102i	−0.0147885	−	0.999891i	$-0.504708\pi$
$11$	3.26721	−	3.26721i	0.985102	−	0.985102i	0.999891	+	0.0147885i	$0.00470750\pi$
$12$	1.00000	−	1.41421i	0.288675	−	0.408248i
$13$	1.23200	+	3.38853i	0.341696	+	0.939810i
$13$	1.23200	+	3.38853i	0.341696	+	0.939810i
$14$		−	1.00000i		−	0.267261i
$15$	0.217420	+	1.26721i	0.0561375	+	0.327193i
$16$	−1.00000			−0.250000
$17$	−1.25768			−0.305033			−0.152516	−	0.988301i	$-0.548738\pi$
$17$	−1.25768			−0.305033			−0.152516	+	0.988301i	$0.548738\pi$
$18$	1.29289	−	2.70711i	0.304738	−	0.638071i
$19$	−1.47510	+	1.47510i	−0.338412	+	0.338412i	−0.855769	−	0.517358i	$-0.826916\pi$
$19$	−1.47510	+	1.47510i	−0.338412	+	0.338412i	0.517358	+	0.855769i	$0.326916\pi$
$20$	0.524897	−	0.524897i	0.117371	−	0.117371i
$21$	−0.292893	−	1.70711i	−0.0639145	−	0.372521i
$22$	−4.62054			−0.985102
$23$	8.25612			1.72152			0.860760	−	0.509011i	$-0.169989\pi$
$23$	8.25612			1.72152			0.860760	+	0.509011i	$0.169989\pi$
$24$	−1.70711	+	0.292893i	−0.348462	+	0.0597866i
$25$		−	4.44897i		−	0.889793i
$26$	1.52490	−	3.26721i	0.299057	−	0.640753i
$27$	1.41421	−	5.00000i	0.272166	−	0.962250i
$28$	−0.707107	+	0.707107i	−0.133631	+	0.133631i
$29$		−	5.20632i		−	0.966790i	−0.875402	−	0.483395i	$-0.839403\pi$
$29$		−	5.20632i		−	0.966790i	0.875402	−	0.483395i	$-0.160597\pi$
$30$	0.742317	−	1.04979i	0.135528	−	0.191665i
$31$	3.41421	−	3.41421i	0.613211	−	0.613211i	−0.330570	−	0.943781i	$-0.607241\pi$
$31$	3.41421	−	3.41421i	0.613211	−	0.613211i	0.943781	+	0.330570i	$0.107241\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−7.88775	+	1.35332i	−1.37308	+	0.235584i
$34$	0.889316	+	0.889316i	0.152516	+	0.152516i
$35$		−	0.742317i		−	0.125474i
$36$	−2.82843	+	1.00000i	−0.471405	+	0.166667i
$37$	−6.68143	−	6.68143i	−1.09842	−	1.09842i	−0.994596	−	0.103824i	$-0.966892\pi$
$37$	−6.68143	−	6.68143i	−1.09842	−	1.09842i	−0.103824	−	0.994596i	$-0.533108\pi$
$38$	2.08611			0.338412
$39$	1.64622	−	6.02412i	0.263606	−	0.964630i
$40$	−0.742317			−0.117371
$41$	−2.20632	−	2.20632i	−0.344570	−	0.344570i	0.513512	−	0.858082i	$-0.328344\pi$
$41$	−2.20632	−	2.20632i	−0.344570	−	0.344570i	−0.858082	+	0.513512i	$0.828344\pi$
$42$	−1.00000	+	1.41421i	−0.154303	+	0.218218i
$43$			6.84191i			1.04338i	0.853135	+	0.521690i	$0.174698\pi$
$43$			6.84191i			1.04338i	−0.853135	+	0.521690i	$0.825302\pi$
$44$	3.26721	+	3.26721i	0.492551	+	0.492551i
$45$	0.959736	−	2.00953i	0.143069	−	0.299563i
$46$	−5.83796	−	5.83796i	−0.860760	−	0.860760i
$47$	−4.24264	+	4.24264i	−0.618853	+	0.618853i	−0.945237	−	0.326384i	$-0.894170\pi$
$47$	−4.24264	+	4.24264i	−0.618853	+	0.618853i	0.326384	+	0.945237i	$0.394170\pi$
$48$	1.41421	+	1.00000i	0.204124	+	0.144338i
$49$			1.00000i			0.142857i
$50$	−3.14589	+	3.14589i	−0.444897	+	0.444897i
$51$	1.77863	+	1.25768i	0.249058	+	0.176111i
$52$	−3.38853	+	1.23200i	−0.469905	+	0.170848i
$53$		−	10.4339i		−	1.43321i	−0.697479	−	0.716605i	$-0.745695\pi$
$53$		−	10.4339i		−	1.43321i	0.697479	−	0.716605i	$-0.254305\pi$
$54$	−4.53553	+	2.53553i	−0.617208	+	0.345042i
$55$	−3.42990			−0.462488
$56$	1.00000			0.133631
$57$	3.56121	−	0.611008i	0.471694	−	0.0809299i
$58$	−3.68143	+	3.68143i	−0.483395	+	0.483395i
$59$	5.31306	−	5.31306i	0.691702	−	0.691702i	−0.270905	−	0.962606i	$-0.587323\pi$
$59$	5.31306	−	5.31306i	0.691702	−	0.691702i	0.962606	+	0.270905i	$0.0873228\pi$
$60$	−1.26721	+	0.217420i	−0.163597	+	0.0280687i
$61$	9.59991			1.22914			0.614571	−	0.788861i	$-0.289329\pi$
$61$	9.59991			1.22914			0.614571	+	0.788861i	$0.289329\pi$
$62$	−4.82843			−0.613211
$63$	−1.29289	+	2.70711i	−0.162889	+	0.341063i
$64$		−	1.00000i		−	0.125000i
$65$	1.13196	−	2.42531i	0.140402	−	0.300822i
$66$	6.53443	+	4.62054i	0.804333	+	0.568749i
$67$	6.12021	−	6.12021i	0.747703	−	0.747703i	−0.226344	−	0.974047i	$-0.572677\pi$
$67$	6.12021	−	6.12021i	0.747703	−	0.747703i	0.974047	+	0.226344i	$0.0726774\pi$
$68$		−	1.25768i		−	0.152516i
$69$	−11.6759	−	8.25612i	−1.40562	−	0.993920i
$70$	−0.524897	+	0.524897i	−0.0627372	+	0.0627372i
$71$	−6.15653	−	6.15653i	−0.730646	−	0.730646i	0.240102	−	0.970748i	$-0.422819\pi$
$71$	−6.15653	−	6.15653i	−0.730646	−	0.730646i	−0.970748	+	0.240102i	$0.922819\pi$
$72$	2.70711	+	1.29289i	0.319036	+	0.152369i
$73$	9.28849	+	9.28849i	1.08714	+	1.08714i	0.995822	+	0.0913130i	$0.0291064\pi$
$73$	9.28849	+	9.28849i	1.08714	+	1.08714i	0.0913130	+	0.995822i	$0.470894\pi$
$74$			9.44897i			1.09842i
$75$	−4.44897	+	6.29179i	−0.513722	+	0.726513i
$76$	−1.47510	−	1.47510i	−0.169206	−	0.169206i
$77$	4.62054			0.526559
$78$	−5.42374	+	3.09564i	−0.614118	+	0.350512i
$79$	7.87822			0.886369			0.443185	−	0.896430i	$-0.353849\pi$
$79$	7.87822			0.886369			0.443185	+	0.896430i	$0.353849\pi$
$80$	0.524897	+	0.524897i	0.0586853	+	0.0586853i
$81$	−7.00000	+	5.65685i	−0.777778	+	0.628539i
$82$			3.12021i			0.344570i
$83$	2.25768	+	2.25768i	0.247813	+	0.247813i	0.820073	−	0.572260i	$-0.193933\pi$
$83$	2.25768	+	2.25768i	0.247813	+	0.247813i	−0.572260	+	0.820073i	$0.693933\pi$
$84$	1.70711	−	0.292893i	0.186261	−	0.0319573i
$85$	0.660154	+	0.660154i	0.0716038	+	0.0716038i
$86$	4.83796	−	4.83796i	0.521690	−	0.521690i
$87$	−5.20632	+	7.36286i	−0.558177	+	0.789381i
$88$		−	4.62054i		−	0.492551i
$89$	1.75801	−	1.75801i	0.186348	−	0.186348i	−0.607767	−	0.794115i	$-0.707935\pi$
$89$	1.75801	−	1.75801i	0.186348	−	0.186348i	0.794115	+	0.607767i	$0.207935\pi$
$90$	−2.09959	+	0.742317i	−0.221316	+	0.0782471i
$91$	−1.52490	+	3.26721i	−0.159853	+	0.342497i
$92$			8.25612i			0.860760i
$93$	−8.24264	+	1.41421i	−0.854722	+	0.146647i
$94$	6.00000			0.618853
$95$	1.54855			0.158878
$96$	−0.292893	−	1.70711i	−0.0298933	−	0.174231i
$97$	2.58579	−	2.58579i	0.262547	−	0.262547i	−0.563541	−	0.826088i	$-0.690561\pi$
$97$	2.58579	−	2.58579i	0.262547	−	0.262547i	0.826088	+	0.563541i	$0.190561\pi$
$98$	0.707107	−	0.707107i	0.0714286	−	0.0714286i
$99$	12.5083	+	5.97386i	1.25713	+	0.600396i
$100$	4.44897			0.444897
$101$	−13.0197			−1.29551			−0.647755	−	0.761849i	$-0.724292\pi$
$101$	−13.0197			−1.29551			−0.647755	+	0.761849i	$0.724292\pi$
$102$	−0.368367	−	2.14700i	−0.0364738	−	0.212585i
$103$			9.96212i			0.981597i	0.871273	+	0.490798i	$0.163295\pi$
$103$			9.96212i			0.981597i	−0.871273	+	0.490798i	$0.836705\pi$
$104$	3.26721	+	1.52490i	0.320377	+	0.149528i
$105$	−0.742317	+	1.04979i	−0.0724427	+	0.102449i
$106$	−7.37790	+	7.37790i	−0.716605	+	0.716605i
$107$			4.82843i			0.466782i	0.972383	+	0.233391i	$0.0749821\pi$
$107$			4.82843i			0.466782i	−0.972383	+	0.233391i	$0.925018\pi$
$108$	5.00000	+	1.41421i	0.481125	+	0.136083i
$109$	13.0941	−	13.0941i	1.25419	−	1.25419i	0.300359	−	0.953826i	$-0.402894\pi$
$109$	13.0941	−	13.0941i	1.25419	−	1.25419i	0.953826	−	0.300359i	$-0.0971065\pi$
$110$	2.42531	+	2.42531i	0.231244	+	0.231244i
$111$	2.76754	+	16.1304i	0.262683	+	1.53103i
$112$	−0.707107	−	0.707107i	−0.0668153	−	0.0668153i
$113$			12.4853i			1.17452i	0.809400	+	0.587258i	$0.199793\pi$
$113$			12.4853i			1.17452i	−0.809400	+	0.587258i	$0.800207\pi$
$114$	−2.95021	−	2.08611i	−0.276312	−	0.195382i
$115$	−4.33361	−	4.33361i	−0.404112	−	0.404112i
$116$	5.20632			0.483395
$117$	−8.35222	+	6.87317i	−0.772163	+	0.635425i
$118$	−7.51380			−0.691702
$119$	−0.889316	−	0.889316i	−0.0815235	−	0.0815235i
$120$	1.04979	+	0.742317i	0.0958327	+	0.0677639i
$121$		−	10.3494i		−	0.940852i
$122$	−6.78816	−	6.78816i	−0.614571	−	0.614571i
$123$	0.913890	+	5.32654i	0.0824027	+	0.480278i
$124$	3.41421	+	3.41421i	0.306605	+	0.306605i
$125$	−4.95974	+	4.95974i	−0.443612	+	0.443612i
$126$	2.82843	−	1.00000i	0.251976	−	0.0890871i
$127$			15.7485i			1.39746i	0.715387	+	0.698729i	$0.246251\pi$
$127$			15.7485i			1.39746i	−0.715387	+	0.698729i	$0.753749\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	6.84191	−	9.67592i	0.602396	−	0.851917i
$130$	−2.51537	+	0.914537i	−0.220612	+	0.0802102i
$131$		−	3.96433i		−	0.346365i	−0.984890	−	0.173183i	$-0.944595\pi$
$131$		−	3.96433i		−	0.346365i	0.984890	−	0.173183i	$-0.0554051\pi$
$132$	−1.35332	−	7.88775i	−0.117792	−	0.686541i
$133$	−2.08611			−0.180889
$134$	−8.65529			−0.747703
$135$	−3.36680	+	1.88217i	−0.289768	+	0.161991i
$136$	−0.889316	+	0.889316i	−0.0762582	+	0.0762582i
$137$	3.83952	−	3.83952i	0.328032	−	0.328032i	−0.523805	−	0.851838i	$-0.675488\pi$
$137$	3.83952	−	3.83952i	0.328032	−	0.328032i	0.851838	+	0.523805i	$0.175488\pi$
$138$	2.41816	+	14.0941i	0.205848	+	1.19977i
$139$	16.3131			1.38366			0.691828	−	0.722062i	$-0.256806\pi$
$139$	16.3131			1.38366			0.691828	+	0.722062i	$0.256806\pi$
$140$	0.742317			0.0627372
$141$	10.2426	−	1.75736i	0.862586	−	0.147996i
$142$			8.70665i			0.730646i
$143$	15.0963	+	7.04585i	1.26242	+	0.589203i
$144$	−1.00000	−	2.82843i	−0.0833333	−	0.235702i
$145$	−2.73279	+	2.73279i	−0.226946	+	0.226946i
$146$		−	13.1359i		−	1.08714i
$147$	1.00000	−	1.41421i	0.0824786	−	0.116642i
$148$	6.68143	−	6.68143i	0.549210	−	0.549210i
$149$	8.72013	+	8.72013i	0.714381	+	0.714381i	0.967449	−	0.253068i	$-0.0814396\pi$
$149$	8.72013	+	8.72013i	0.714381	+	0.714381i	−0.253068	+	0.967449i	$0.581440\pi$
$150$	7.59486	−	1.30307i	0.620118	−	0.106395i
$151$	5.13196	+	5.13196i	0.417633	+	0.417633i	0.884387	−	0.466754i	$-0.154577\pi$
$151$	5.13196	+	5.13196i	0.417633	+	0.417633i	−0.466754	+	0.884387i	$0.654577\pi$
$152$			2.08611i			0.169206i
$153$	−1.25768	−	3.55727i	−0.101678	−	0.287588i
$154$	−3.26721	−	3.26721i	−0.263280	−	0.263280i
$155$	−3.58422			−0.287892
$156$	6.02412	+	1.64622i	0.482315	+	0.131803i
$157$	−22.9818			−1.83415			−0.917075	−	0.398715i	$-0.869456\pi$
$157$	−22.9818			−1.83415			−0.917075	+	0.398715i	$0.869456\pi$
$158$	−5.57074	−	5.57074i	−0.443185	−	0.443185i
$159$	−10.4339	+	14.7558i	−0.827464	+	1.17021i
$160$		−	0.742317i		−	0.0586853i
$161$	5.83796	+	5.83796i	0.460096	+	0.460096i
$162$	8.94975	+	0.949747i	0.703159	+	0.0746192i
$163$	−3.68538	−	3.68538i	−0.288661	−	0.288661i	0.547890	−	0.836551i	$-0.315431\pi$
$163$	−3.68538	−	3.68538i	−0.288661	−	0.288661i	−0.836551	+	0.547890i	$0.815431\pi$
$164$	2.20632	−	2.20632i	0.172285	−	0.172285i
$165$	4.85062	+	3.42990i	0.377620	+	0.267018i
$166$		−	3.19285i		−	0.247813i
$167$	6.46006	−	6.46006i	0.499894	−	0.499894i	−0.411511	−	0.911405i	$-0.634999\pi$
$167$	6.46006	−	6.46006i	0.499894	−	0.499894i	0.911405	+	0.411511i	$0.134999\pi$
$168$	−1.41421	−	1.00000i	−0.109109	−	0.0771517i
$169$	−9.96433	+	8.34938i	−0.766487	+	0.642260i
$170$		−	0.933599i		−	0.0716038i
$171$	−5.64732	−	2.69712i	−0.431862	−	0.206254i
$172$	−6.84191			−0.521690
$173$	−25.0702			−1.90605			−0.953024	−	0.302894i	$-0.902047\pi$
$173$	−25.0702			−1.90605			−0.953024	+	0.302894i	$0.902047\pi$
$174$	8.88775	−	1.52490i	0.673779	−	0.115602i
$175$	3.14589	−	3.14589i	0.237807	−	0.237807i
$176$	−3.26721	+	3.26721i	−0.246276	+	0.246276i
$177$	−12.8269	+	2.20074i	−0.964126	+	0.165418i
$178$	−2.48620			−0.186348
$179$	15.3629			1.14827			0.574137	−	0.818759i	$-0.305338\pi$
$179$	15.3629			1.14827			0.574137	+	0.818759i	$0.305338\pi$
$180$	2.00953	+	0.959736i	0.149782	+	0.0715345i
$181$			1.22293i			0.0908997i	0.998967	+	0.0454499i	$0.0144721\pi$
$181$			1.22293i			0.0908997i	−0.998967	+	0.0454499i	$0.985528\pi$
$182$	3.38853	−	1.23200i	0.251175	−	0.0913222i
$183$	−13.5763	−	9.59991i	−1.00359	−	0.709646i
$184$	5.83796	−	5.83796i	0.430380	−	0.430380i
$185$			7.01413i			0.515689i
$186$	6.82843	+	4.82843i	0.500685	+	0.354037i
$187$	−4.10912	+	4.10912i	−0.300489	+	0.300489i
$188$	−4.24264	−	4.24264i	−0.309426	−	0.309426i
$189$	4.53553	−	2.53553i	0.329912	−	0.184433i
$190$	−1.09499	−	1.09499i	−0.0794392	−	0.0794392i
$191$			2.88537i			0.208778i	0.994537	+	0.104389i	$0.0332887\pi$
$191$			2.88537i			0.208778i	−0.994537	+	0.104389i	$0.966711\pi$
$192$	−1.00000	+	1.41421i	−0.0721688	+	0.102062i
$193$	−2.47115	−	2.47115i	−0.177878	−	0.177878i	0.612552	−	0.790430i	$-0.290143\pi$
$193$	−2.47115	−	2.47115i	−0.177878	−	0.177878i	−0.790430	+	0.612552i	$0.790143\pi$
$194$	−3.65685			−0.262547
$195$	−4.02614	+	2.29795i	−0.288318	+	0.164559i
$196$	−1.00000			−0.0714286
$197$	−7.05538	−	7.05538i	−0.502675	−	0.502675i	0.409593	−	0.912268i	$-0.365671\pi$
$197$	−7.05538	−	7.05538i	−0.502675	−	0.502675i	−0.912268	+	0.409593i	$0.865671\pi$
$198$	−4.62054	−	13.0689i	−0.328367	−	0.928763i
$199$		−	26.2752i		−	1.86260i	−0.364255	−	0.931299i	$-0.618676\pi$
$199$		−	26.2752i		−	1.86260i	0.364255	−	0.931299i	$-0.381324\pi$
$200$	−3.14589	−	3.14589i	−0.222448	−	0.222448i
$201$	−14.7755	+	2.53508i	−1.04218	+	0.178810i
$202$	9.20632	+	9.20632i	0.647755	+	0.647755i
$203$	3.68143	−	3.68143i	0.258386	−	0.258386i
$204$	−1.25768	+	1.77863i	−0.0880554	+	0.124529i
$205$			2.31619i			0.161770i
$206$	7.04428	−	7.04428i	0.490798	−	0.490798i
$207$	8.25612	+	23.3518i	0.573840	+	1.62306i
$208$	−1.23200	−	3.38853i	−0.0854241	−	0.234953i
$209$			9.63895i			0.666740i
$210$	1.26721	−	0.217420i	0.0874461	−	0.0150034i
$211$	5.32719			0.366739			0.183369	−	0.983044i	$-0.441300\pi$
$211$	5.32719			0.366739			0.183369	+	0.983044i	$0.441300\pi$
$212$	10.4339			0.716605
$213$	2.55012	+	14.8632i	0.174731	+	1.01841i
$214$	3.41421	−	3.41421i	0.233391	−	0.233391i
$215$	3.59130	−	3.59130i	0.244924	−	0.244924i
$216$	−2.53553	−	4.53553i	−0.172521	−	0.308604i
$217$	4.82843			0.327775
$218$	−18.5178			−1.25419
$219$	−3.84742	−	22.4244i	−0.259984	−	1.51530i
$220$		−	3.42990i		−	0.231244i
$221$	−1.54947	−	4.26170i	−0.104229	−	0.286673i
$222$	9.44897	−	13.3629i	0.634173	−	0.896856i
$223$	−8.76138	+	8.76138i	−0.586705	+	0.586705i	−0.936738	−	0.350032i	$-0.886171\pi$
$223$	−8.76138	+	8.76138i	−0.586705	+	0.586705i	0.350032	+	0.936738i	$0.386171\pi$
$224$			1.00000i			0.0668153i
$225$	12.5836	−	4.44897i	0.838905	−	0.296598i
$226$	8.82843	−	8.82843i	0.587258	−	0.587258i
$227$	−9.09959	−	9.09959i	−0.603961	−	0.603961i	0.337400	−	0.941361i	$-0.390452\pi$
$227$	−9.09959	−	9.09959i	−0.603961	−	0.603961i	−0.941361	+	0.337400i	$0.890452\pi$
$228$	0.611008	+	3.56121i	0.0404650	+	0.235847i
$229$	−6.70665	−	6.70665i	−0.443188	−	0.443188i	0.449894	−	0.893082i	$-0.351462\pi$
$229$	−6.70665	−	6.70665i	−0.443188	−	0.443188i	−0.893082	+	0.449894i	$0.851462\pi$
$230$			6.12866i			0.404112i
$231$	−6.53443	−	4.62054i	−0.429934	−	0.304009i
$232$	−3.68143	−	3.68143i	−0.241698	−	0.241698i
$233$	−6.63714			−0.434814			−0.217407	−	0.976081i	$-0.569760\pi$
$233$	−6.63714			−0.434814			−0.217407	+	0.976081i	$0.569760\pi$
$234$	10.7660	+	1.04585i	0.703794	+	0.0683691i
$235$	4.45390			0.290540
$236$	5.31306	+	5.31306i	0.345851	+	0.345851i
$237$	−11.1415	−	7.87822i	−0.723717	−	0.511745i
$238$			1.25768i			0.0815235i
$239$	0.313061	+	0.313061i	0.0202502	+	0.0202502i	0.717159	−	0.696909i	$-0.245442\pi$
$239$	0.313061	+	0.313061i	0.0202502	+	0.0202502i	−0.696909	+	0.717159i	$0.745442\pi$
$240$	−0.217420	−	1.26721i	−0.0140344	−	0.0817983i
$241$	−8.94929	−	8.94929i	−0.576474	−	0.576474i	0.357456	−	0.933930i	$-0.383644\pi$
$241$	−8.94929	−	8.94929i	−0.576474	−	0.576474i	−0.933930	+	0.357456i	$0.883644\pi$
$242$	−7.31811	+	7.31811i	−0.470426	+	0.470426i
$243$	15.5563	−	1.00000i	0.997940	−	0.0641500i
$244$			9.59991i			0.614571i
$245$	0.524897	−	0.524897i	0.0335345	−	0.0335345i
$246$	3.12021	−	4.41265i	0.198938	−	0.281340i
$247$	−6.81577	−	3.18110i	−0.433677	−	0.202409i
$248$		−	4.82843i		−	0.306605i
$249$	−0.935163	−	5.45053i	−0.0592635	−	0.345413i
$250$	7.01413			0.443612
$251$	0.478403			0.0301965			0.0150983	−	0.999886i	$-0.495194\pi$
$251$	0.478403			0.0301965			0.0150983	+	0.999886i	$0.495194\pi$
$252$	−2.70711	−	1.29289i	−0.170532	−	0.0814446i
$253$	26.9745	−	26.9745i	1.69587	−	1.69587i
$254$	11.1359	−	11.1359i	0.698729	−	0.698729i
$255$	−0.273445	−	1.59375i	−0.0171238	−	0.0998047i
$256$	1.00000			0.0625000
$257$	−12.0695			−0.752875			−0.376437	−	0.926442i	$-0.622851\pi$
$257$	−12.0695			−0.752875			−0.376437	+	0.926442i	$0.622851\pi$
$258$	−11.6799	+	2.00395i	−0.727157	+	0.124760i
$259$		−	9.44897i		−	0.587130i
$260$	2.42531	+	1.13196i	0.150411	+	0.0702010i
$261$	14.7257	−	5.20632i	0.911499	−	0.322263i
$262$	−2.80321	+	2.80321i	−0.173183	+	0.173183i
$263$			26.3613i			1.62551i	0.582608	+	0.812753i	$0.302032\pi$
$263$			26.3613i			1.62551i	−0.582608	+	0.812753i	$0.697968\pi$
$264$	−4.62054	+	6.53443i	−0.284374	+	0.402166i
$265$	−5.47674	+	5.47674i	−0.336433	+	0.336433i
$266$	1.47510	+	1.47510i	0.0904444	+	0.0904444i
$267$	−4.24420	+	0.728190i	−0.259741	+	0.0445645i
$268$	6.12021	+	6.12021i	0.373852	+	0.373852i
$269$			7.36286i			0.448921i	0.974483	+	0.224461i	$0.0720620\pi$
$269$			7.36286i			0.448921i	−0.974483	+	0.224461i	$0.927938\pi$
$270$	3.71158	+	1.04979i	0.225880	+	0.0638885i
$271$	−4.74232	−	4.74232i	−0.288075	−	0.288075i	0.548244	−	0.836319i	$-0.315297\pi$
$271$	−4.74232	−	4.74232i	−0.288075	−	0.288075i	−0.836319	+	0.548244i	$0.815297\pi$
$272$	1.25768			0.0762582
$273$	5.42374	−	3.09564i	0.328260	−	0.187357i
$274$	−5.42990			−0.328032
$275$	−14.5357	−	14.5357i	−0.876537	−	0.876537i
$276$	8.25612	−	11.6759i	0.496960	−	0.702808i
$277$			25.1605i			1.51175i	0.654715	+	0.755875i	$0.272788\pi$
$277$			25.1605i			1.51175i	−0.654715	+	0.755875i	$0.727212\pi$
$278$	−11.5351	−	11.5351i	−0.691828	−	0.691828i
$279$	13.0711	+	6.24264i	0.782544	+	0.373737i
$280$	−0.524897	−	0.524897i	−0.0313686	−	0.0313686i
$281$	−13.7051	+	13.7051i	−0.817577	+	0.817577i	−0.985756	−	0.168180i	$-0.946211\pi$
$281$	−13.7051	+	13.7051i	−0.817577	+	0.817577i	0.168180	+	0.985756i	$0.446211\pi$
$282$	−8.48528	−	6.00000i	−0.505291	−	0.357295i
$283$			14.2527i			0.847238i	0.905840	+	0.423619i	$0.139240\pi$
$283$			14.2527i			0.847238i	−0.905840	+	0.423619i	$0.860760\pi$
$284$	6.15653	−	6.15653i	0.365323	−	0.365323i
$285$	−2.18999	−	1.54855i	−0.129724	−	0.0917285i
$286$	−5.69252	−	15.6569i	−0.336606	−	0.925809i
$287$		−	3.12021i		−	0.184180i
$288$	−1.29289	+	2.70711i	−0.0761845	+	0.159518i
$289$	−15.4182			−0.906955
$290$	3.86474			0.226946
$291$	−6.24264	+	1.07107i	−0.365950	+	0.0627871i
$292$	−9.28849	+	9.28849i	−0.543568	+	0.543568i
$293$	19.7755	−	19.7755i	1.15530	−	1.15530i	0.169823	−	0.985475i	$-0.445680\pi$
$293$	19.7755	−	19.7755i	1.15530	−	1.15530i	0.985475	−	0.169823i	$-0.0543195\pi$
$294$	−1.70711	+	0.292893i	−0.0995605	+	0.0170819i
$295$	−5.57762			−0.324742
$296$	−9.44897			−0.549210
$297$	−11.7155	−	20.9566i	−0.679804	−	1.21603i
$298$		−	12.3321i		−	0.714381i
$299$	10.1716	+	27.9761i	0.588237	+	1.61790i
$300$	−6.29179	−	4.44897i	−0.363257	−	0.256861i
$301$	−4.83796	+	4.83796i	−0.278855	+	0.278855i
$302$		−	7.25768i		−	0.417633i
$303$	18.4126	+	13.0197i	1.05778	+	0.747963i
$304$	1.47510	−	1.47510i	0.0846029	−	0.0846029i
$305$	−5.03897	−	5.03897i	−0.288530	−	0.288530i
$306$	−1.62605	+	3.40468i	−0.0929551	+	0.194633i
$307$	−11.9477	−	11.9477i	−0.681893	−	0.681893i	0.278534	−	0.960426i	$-0.410152\pi$
$307$	−11.9477	−	11.9477i	−0.681893	−	0.681893i	−0.960426	+	0.278534i	$0.910152\pi$
$308$			4.62054i			0.263280i
$309$	9.96212	−	14.0886i	0.566725	−	0.801471i
$310$	2.53443	+	2.53443i	0.143946	+	0.143946i
$311$	−7.77551			−0.440908			−0.220454	−	0.975397i	$-0.570754\pi$
$311$	−7.77551			−0.440908			−0.220454	+	0.975397i	$0.570754\pi$
$312$	−3.09564	−	5.42374i	−0.175256	−	0.307059i
$313$	22.2182			1.25585			0.627925	−	0.778274i	$-0.283905\pi$
$313$	22.2182			1.25585			0.627925	+	0.778274i	$0.283905\pi$
$314$	16.2506	+	16.2506i	0.917075	+	0.917075i
$315$	2.09959	−	0.742317i	0.118298	−	0.0418248i
$316$			7.87822i			0.443185i
$317$	20.5557	+	20.5557i	1.15452	+	1.15452i	0.985635	+	0.168888i	$0.0540176\pi$
$317$	20.5557	+	20.5557i	1.15452	+	1.15452i	0.168888	+	0.985635i	$0.445982\pi$
$318$	17.8118	−	3.05603i	0.998837	−	0.171373i
$319$	−17.0102	−	17.0102i	−0.952387	−	0.952387i
$320$	−0.524897	+	0.524897i	−0.0293427	+	0.0293427i
$321$	4.82843	−	6.82843i	0.269497	−	0.381126i
$322$		−	8.25612i		−	0.460096i
$323$	1.85521	−	1.85521i	0.103227	−	0.103227i
$324$	−5.65685	−	7.00000i	−0.314270	−	0.388889i
$325$	15.0755	−	5.48114i	0.836237	−	0.304039i
$326$			5.21191i			0.288661i
$327$	−31.6119	+	5.42374i	−1.74814	+	0.299934i
$328$	−3.12021			−0.172285
$329$	−6.00000			−0.330791
$330$	−1.00460	−	5.85521i	−0.0553012	−	0.322319i
$331$	5.99844	−	5.99844i	0.329704	−	0.329704i	−0.522770	−	0.852474i	$-0.675101\pi$
$331$	5.99844	−	5.99844i	0.329704	−	0.329704i	0.852474	+	0.522770i	$0.175101\pi$
$332$	−2.25768	+	2.25768i	−0.123906	+	0.123906i
$333$	12.2165	−	25.5794i	0.669460	−	1.40174i
$334$	−9.13590			−0.499894
$335$	−6.42497			−0.351034
$336$	0.292893	+	1.70711i	0.0159786	+	0.0931303i
$337$			24.9336i			1.35822i	0.734037	+	0.679110i	$0.237634\pi$
$337$			24.9336i			1.35822i	−0.734037	+	0.679110i	$0.762366\pi$
$338$	12.9497	+	1.14195i	0.704373	+	0.0621137i
$339$	12.4853	−	17.6569i	0.678107	−	0.958989i
$340$	−0.660154	+	0.660154i	−0.0358019	+	0.0358019i
$341$		−	22.3099i		−	1.20815i
$342$	2.08611	+	5.90041i	0.112804	+	0.319058i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	4.83796	+	4.83796i	0.260845	+	0.260845i
$345$	1.79504	+	10.4623i	0.0966418	+	0.563270i
$346$	17.7273	+	17.7273i	0.953024	+	0.953024i
$347$		−	5.14149i		−	0.276010i	−0.990432	−	0.138005i	$-0.955931\pi$
$347$		−	5.14149i		−	0.276010i	0.990432	−	0.138005i	$-0.0440689\pi$
$348$	−7.36286	−	5.20632i	−0.394690	−	0.279088i
$349$	−3.98652	−	3.98652i	−0.213394	−	0.213394i	0.592314	−	0.805707i	$-0.298215\pi$
$349$	−3.98652	−	3.98652i	−0.213394	−	0.213394i	−0.805707	+	0.592314i	$0.798215\pi$
$350$	−4.44897			−0.237807
$351$	18.6850	−	1.36791i	0.997331	−	0.0730136i
$352$	4.62054			0.246276
$353$	0.341582	+	0.341582i	0.0181806	+	0.0181806i	0.716139	−	0.697958i	$-0.245908\pi$
$353$	0.341582	+	0.341582i	0.0181806	+	0.0181806i	−0.697958	+	0.716139i	$0.745908\pi$
$354$	10.6261	+	7.51380i	0.564772	+	0.399354i
$355$			6.46309i			0.343025i
$356$	1.75801	+	1.75801i	0.0931742	+	0.0931742i
$357$	0.368367	+	2.14700i	0.0194960	+	0.113631i
$358$	−10.8632	−	10.8632i	−0.574137	−	0.574137i
$359$	−4.22916	+	4.22916i	−0.223207	+	0.223207i	−0.809847	−	0.586641i	$-0.800450\pi$
$359$	−4.22916	+	4.22916i	−0.223207	+	0.223207i	0.586641	+	0.809847i	$0.300450\pi$
$360$	−0.742317	−	2.09959i	−0.0391235	−	0.110658i
$361$			14.6481i			0.770955i
$362$	0.864743	−	0.864743i	0.0454499	−	0.0454499i
$363$	−10.3494	+	14.6362i	−0.543201	+	0.768203i
$364$	−3.26721	−	1.52490i	−0.171249	−	0.0799263i
$365$		−	9.75100i		−	0.510391i
$366$	2.81175	+	16.3881i	0.146972	+	0.856618i
$367$	−5.83476			−0.304572			−0.152286	−	0.988336i	$-0.548663\pi$
$367$	−5.83476			−0.304572			−0.152286	+	0.988336i	$0.548663\pi$
$368$	−8.25612			−0.430380
$369$	4.03410	−	8.44675i	0.210007	−	0.439720i
$370$	4.95974	−	4.95974i	0.257844	−	0.257844i
$371$	7.37790	−	7.37790i	0.383041	−	0.383041i
$372$	−1.41421	−	8.24264i	−0.0733236	−	0.427361i
$373$	−8.70665			−0.450813			−0.225407	−	0.974265i	$-0.572371\pi$
$373$	−8.70665			−0.450813			−0.225407	+	0.974265i	$0.572371\pi$
$374$	5.81117			0.300489
$375$	11.9739	−	2.05439i	0.618328	−	0.106088i
$376$			6.00000i			0.309426i
$377$	17.6418	−	6.41421i	0.908600	−	0.330349i
$378$	−5.00000	−	1.41421i	−0.257172	−	0.0727393i
$379$	19.2070	−	19.2070i	0.986596	−	0.986596i	−0.0133154	−	0.999911i	$-0.504239\pi$
$379$	19.2070	−	19.2070i	0.986596	−	0.986596i	0.999911	+	0.0133154i	$0.00423856\pi$
$380$			1.54855i			0.0794392i
$381$	15.7485	−	22.2718i	0.806823	−	1.14102i
$382$	2.04026	−	2.04026i	0.104389	−	0.104389i
$383$	9.09408	+	9.09408i	0.464686	+	0.464686i	0.900188	−	0.435502i	$-0.143429\pi$
$383$	9.09408	+	9.09408i	0.464686	+	0.464686i	−0.435502	+	0.900188i	$0.643429\pi$
$384$	1.70711	−	0.292893i	0.0871154	−	0.0149466i
$385$	−2.42531	−	2.42531i	−0.123605	−	0.123605i
$386$			3.49474i			0.177878i
$387$	−19.3518	+	6.84191i	−0.983709	+	0.347794i
$388$	2.58579	+	2.58579i	0.131273	+	0.131273i
$389$	−17.9800			−0.911623			−0.455812	−	0.890076i	$-0.650651\pi$
$389$	−17.9800			−0.911623			−0.455812	+	0.890076i	$0.650651\pi$
$390$	4.47180	+	1.22202i	0.226439	+	0.0618791i
$391$	−10.3836			−0.525120
$392$	0.707107	+	0.707107i	0.0357143	+	0.0357143i
$393$	−3.96433	+	5.60641i	−0.199974	+	0.282806i
$394$			9.97781i			0.502675i
$395$	−4.13526	−	4.13526i	−0.208067	−	0.208067i
$396$	−5.97386	+	12.5083i	−0.300198	+	0.628565i
$397$	2.34781	+	2.34781i	0.117833	+	0.117833i	0.763565	−	0.645731i	$-0.223447\pi$
$397$	2.34781	+	2.34781i	0.117833	+	0.117833i	−0.645731	+	0.763565i	$0.723447\pi$
$398$	−18.5794	+	18.5794i	−0.931299	+	0.931299i
$399$	2.95021	+	2.08611i	0.147695	+	0.104436i
$400$			4.44897i			0.222448i
$401$	21.5138	−	21.5138i	1.07435	−	1.07435i	0.0773435	−	0.997005i	$-0.475356\pi$
$401$	21.5138	−	21.5138i	1.07435	−	1.07435i	0.997005	−	0.0773435i	$-0.0246438\pi$
$402$	12.2404	+	8.65529i	0.610497	+	0.431687i
$403$	15.7755	+	7.36286i	0.785834	+	0.366770i
$404$		−	13.0197i		−	0.647755i
$405$	6.64355	+	0.705014i	0.330121	+	0.0350324i
$406$	−5.20632			−0.258386
$407$	−43.6593			−2.16411
$408$	2.14700	−	0.368367i	0.106292	−	0.0182369i
$409$	−12.7306	+	12.7306i	−0.629486	+	0.629486i	−0.947939	−	0.318452i	$-0.896837\pi$
$409$	−12.7306	+	12.7306i	−0.629486	+	0.629486i	0.318452	+	0.947939i	$0.396837\pi$
$410$	1.63779	−	1.63779i	0.0808848	−	0.0808848i
$411$	−9.26943	+	1.59038i	−0.457227	+	0.0784478i
$412$	−9.96212			−0.490798
$413$	7.51380			0.369730
$414$	10.6743	−	22.3502i	0.524612	−	1.09845i
$415$		−	2.37010i		−	0.116344i
$416$	−1.52490	+	3.26721i	−0.0747642	+	0.160188i
$417$	−23.0702	−	16.3131i	−1.12975	−	0.798854i
$418$	6.81577	−	6.81577i	0.333370	−	0.333370i
$419$			13.1058i			0.640261i	0.947373	+	0.320131i	$0.103727\pi$
$419$			13.1058i			0.640261i	−0.947373	+	0.320131i	$0.896273\pi$
$420$	−1.04979	−	0.742317i	−0.0512247	−	0.0362214i
$421$	−14.9762	+	14.9762i	−0.729898	+	0.729898i	−0.970599	−	0.240702i	$-0.922623\pi$
$421$	−14.9762	+	14.9762i	−0.729898	+	0.729898i	0.240702	+	0.970599i	$0.422623\pi$
$422$	−3.76689	−	3.76689i	−0.183369	−	0.183369i
$423$	−16.2426	−	7.75736i	−0.789744	−	0.377176i
$424$	−7.37790	−	7.37790i	−0.358302	−	0.358302i
$425$			5.59539i			0.271416i
$426$	8.70665	−	12.3131i	0.421839	−	0.596570i
$427$	6.78816	+	6.78816i	0.328502	+	0.328502i
$428$	−4.82843			−0.233391
$429$	−14.3035	−	25.0606i	−0.690581	−	1.20994i
$430$	−5.07886			−0.244924
$431$	−7.55635	−	7.55635i	−0.363977	−	0.363977i	0.501298	−	0.865275i	$-0.332856\pi$
$431$	−7.55635	−	7.55635i	−0.363977	−	0.363977i	−0.865275	+	0.501298i	$0.832856\pi$
$432$	−1.41421	+	5.00000i	−0.0680414	+	0.240563i
$433$			14.0000i			0.672797i	0.941720	+	0.336399i	$0.109209\pi$
$433$			14.0000i			0.672797i	−0.941720	+	0.336399i	$0.890791\pi$
$434$	−3.41421	−	3.41421i	−0.163887	−	0.163887i
$435$	6.59753	−	1.13196i	0.316327	−	0.0542732i
$436$	13.0941	+	13.0941i	0.627093	+	0.627093i
$437$	−12.1786	+	12.1786i	−0.582583	+	0.582583i
$438$	−13.1359	+	18.5770i	−0.627658	+	0.887642i
$439$			26.6640i			1.27260i	0.771440	+	0.636302i	$0.219537\pi$
$439$			26.6640i			1.27260i	−0.771440	+	0.636302i	$0.780463\pi$
$440$	−2.42531	+	2.42531i	−0.115622	+	0.115622i
$441$	−2.82843	+	1.00000i	−0.134687	+	0.0476190i
$442$	−1.91784	+	4.10912i	−0.0912222	+	0.195451i
$443$			14.6845i			0.697680i	0.937182	+	0.348840i	$0.113424\pi$
$443$			14.6845i			0.697680i	−0.937182	+	0.348840i	$0.886576\pi$
$444$	−16.1304	+	2.76754i	−0.765515	+	0.131342i
$445$	−1.84555			−0.0874873
$446$	12.3905			0.586705
$447$	−3.61200	−	21.0523i	−0.170842	−	0.995737i
$448$	0.707107	−	0.707107i	0.0334077	−	0.0334077i
$449$	−22.2712	+	22.2712i	−1.05104	+	1.05104i	−0.0524193	+	0.998625i	$0.516693\pi$
$449$	−22.2712	+	22.2712i	−1.05104	+	1.05104i	−0.998625	+	0.0524193i	$0.983307\pi$
$450$	−12.0438	−	5.75204i	−0.567751	−	0.271154i
$451$	−14.4171			−0.678873
$452$	−12.4853			−0.587258
$453$	−2.12573	−	12.3896i	−0.0998753	−	0.582116i
$454$			12.8688i			0.603961i
$455$	2.51537	−	0.914537i	0.117922	−	0.0428742i
$456$	2.08611	−	2.95021i	0.0976911	−	0.138156i
$457$	7.17780	−	7.17780i	0.335763	−	0.335763i	−0.519007	−	0.854770i	$-0.673698\pi$
$457$	7.17780	−	7.17780i	0.335763	−	0.335763i	0.854770	+	0.519007i	$0.173698\pi$
$458$			9.48463i			0.443188i
$459$	−1.77863	+	6.28842i	−0.0830195	+	0.293518i
$460$	4.33361	−	4.33361i	0.202056	−	0.202056i
$461$	24.2734	+	24.2734i	1.13053	+	1.13053i	0.990090	+	0.140437i	$0.0448509\pi$
$461$	24.2734	+	24.2734i	1.13053	+	1.13053i	0.140437	+	0.990090i	$0.455149\pi$
$462$	1.35332	+	7.88775i	0.0629623	+	0.366971i
$463$	−3.47510	−	3.47510i	−0.161502	−	0.161502i	0.621730	−	0.783232i	$-0.286430\pi$
$463$	−3.47510	−	3.47510i	−0.161502	−	0.161502i	−0.783232	+	0.621730i	$0.786430\pi$
$464$			5.20632i			0.241698i
$465$	5.06886	+	3.58422i	0.235063	+	0.166214i
$466$	4.69317	+	4.69317i	0.217407	+	0.217407i
$467$	24.0751			1.11406			0.557031	−	0.830492i	$-0.311940\pi$
$467$	24.0751			1.11406			0.557031	+	0.830492i	$0.311940\pi$
$468$	−6.87317	−	8.35222i	−0.317712	−	0.386081i
$469$	8.65529			0.399664
$470$	−3.14938	−	3.14938i	−0.145270	−	0.145270i
$471$	32.5012	+	22.9818i	1.49758	+	1.05895i
$472$		−	7.51380i		−	0.345851i
$473$	22.3540	+	22.3540i	1.02784	+	1.02784i
$474$	2.30748	+	13.4490i	0.105986	+	0.617731i
$475$	6.56268	+	6.56268i	0.301116	+	0.301116i
$476$	0.889316	−	0.889316i	0.0407617	−	0.0407617i
$477$	29.5116	−	10.4339i	1.35124	−	0.477737i
$478$		−	0.442735i		−	0.0202502i
$479$	−24.0712	+	24.0712i	−1.09984	+	1.09984i	−0.105415	+	0.994428i	$0.533617\pi$
$479$	−24.0712	+	24.0712i	−1.09984	+	1.09984i	−0.994428	+	0.105415i	$0.966383\pi$
$480$	−0.742317	+	1.04979i	−0.0338820	+	0.0479163i
$481$	14.4087	−	30.8718i	0.656980	−	1.40763i
$482$			12.6562i			0.576474i
$483$	−2.41816	−	14.0941i	−0.110030	−	0.641303i
$484$	10.3494			0.470426
$485$	−2.71454			−0.123261
$486$	−11.7071	−	10.2929i	−0.531045	−	0.466895i
$487$	12.9502	−	12.9502i	0.586830	−	0.586830i	−0.349942	−	0.936771i	$-0.613799\pi$
$487$	12.9502	−	12.9502i	0.586830	−	0.586830i	0.936771	+	0.349942i	$0.113799\pi$
$488$	6.78816	−	6.78816i	0.307286	−	0.307286i
$489$	1.52653	+	8.89728i	0.0690322	+	0.402349i
$490$	−0.742317			−0.0335345
$491$	−14.8776			−0.671416			−0.335708	−	0.941966i	$-0.608975\pi$
$491$	−14.8776			−0.671416			−0.335708	+	0.941966i	$0.608975\pi$
$492$	−5.32654	+	0.913890i	−0.240139	+	0.0412013i
$493$			6.54791i			0.294903i
$494$	2.57010	+	7.06886i	0.115634	+	0.318043i
$495$	−3.42990	−	9.70123i	−0.154163	−	0.436038i
$496$	−3.41421	+	3.41421i	−0.153303	+	0.153303i
$497$		−	8.70665i		−	0.390547i
$498$	−3.19285	+	4.51537i	−0.143075	+	0.202338i
$499$	−0.738297	+	0.738297i	−0.0330507	+	0.0330507i	−0.723439	−	0.690388i	$-0.757440\pi$
$499$	−0.738297	+	0.738297i	−0.0330507	+	0.0330507i	0.690388	+	0.723439i	$0.257440\pi$
$500$	−4.95974	−	4.95974i	−0.221806	−	0.221806i
$501$	−15.5960	+	2.67584i	−0.696776	+	0.119548i
$502$	−0.338282	−	0.338282i	−0.0150983	−	0.0150983i
$503$		−	16.4853i		−	0.735042i	−0.930015	−	0.367521i	$-0.880207\pi$
$503$		−	16.4853i		−	0.735042i	0.930015	−	0.367521i	$-0.119793\pi$
$504$	1.00000	+	2.82843i	0.0445435	+	0.125988i
$505$	6.83401	+	6.83401i	0.304109	+	0.304109i
$506$	−38.1477			−1.69587
$507$	22.4411	−	1.84347i	0.996643	−	0.0818714i
$508$	−15.7485			−0.698729
$509$	6.21184	+	6.21184i	0.275335	+	0.275335i	0.831243	−	0.555909i	$-0.187630\pi$
$509$	6.21184	+	6.21184i	0.275335	+	0.275335i	−0.555909	+	0.831243i	$0.687630\pi$
$510$	−0.933599	+	1.32031i	−0.0413405	+	0.0584643i
$511$			13.1359i			0.581098i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	5.28940	+	9.46162i	0.233533	+	0.417741i
$514$	8.53443	+	8.53443i	0.376437	+	0.376437i
$515$	5.22909	−	5.22909i	0.230421	−	0.230421i
$516$	9.67592	+	6.84191i	0.425958	+	0.301198i
$517$			27.7232i			1.21927i
$518$	−6.68143	+	6.68143i	−0.293565	+	0.293565i
$519$	35.4545	+	25.0702i	1.55628	+	1.10046i
$520$	−0.914537	−	2.51537i	−0.0401051	−	0.110306i
$521$			24.2270i			1.06140i	0.847559	+	0.530701i	$0.178071\pi$
$521$			24.2270i			1.06140i	−0.847559	+	0.530701i	$0.821929\pi$
$522$	−14.0941	−	6.73122i	−0.616881	−	0.294618i
$523$	33.0401			1.44474			0.722371	−	0.691506i	$-0.243052\pi$
$523$	33.0401			1.44474			0.722371	+	0.691506i	$0.243052\pi$
$524$	3.96433			0.173183
$525$	−7.59486	+	1.30307i	−0.331467	+	0.0568707i
$526$	18.6402	−	18.6402i	0.812753	−	0.812753i
$527$	−4.29400	+	4.29400i	−0.187050	+	0.187050i
$528$	7.88775	−	1.35332i	0.343270	−	0.0588959i
$529$	45.1635			1.96363
$530$	7.74528			0.336433
$531$	20.3407	+	9.71454i	0.882710	+	0.421575i
$532$		−	2.08611i		−	0.0904444i
$533$	4.75801	−	10.1944i	0.206092	−	0.441569i
$534$	3.51601	+	2.48620i	0.152153	+	0.107588i
$535$	2.53443	−	2.53443i	0.109573	−	0.109573i
$536$		−	8.65529i		−	0.373852i
$537$	−21.7264	−	15.3629i	−0.937562	−	0.662956i
$538$	5.20632	−	5.20632i	0.224461	−	0.224461i
$539$	3.26721	+	3.26721i	0.140729	+	0.140729i
$540$	−1.88217	−	3.36680i	−0.0809957	−	0.144884i
$541$	3.22375	+	3.22375i	0.138600	+	0.138600i	0.773003	−	0.634403i	$-0.218754\pi$
$541$	3.22375	+	3.22375i	0.138600	+	0.138600i	−0.634403	+	0.773003i	$0.718754\pi$
$542$			6.70665i			0.288075i
$543$	1.22293	−	1.72949i	0.0524810	−	0.0742193i
$544$	−0.889316	−	0.889316i	−0.0381291	−	0.0381291i
$545$	−13.7461			−0.588818
$546$	−6.02412	−	1.64622i	−0.257808	−	0.0704516i
$547$	−1.48776			−0.0636121			−0.0318060	−	0.999494i	$-0.510126\pi$
$547$	−1.48776			−0.0636121			−0.0318060	+	0.999494i	$0.510126\pi$
$548$	3.83952	+	3.83952i	0.164016	+	0.164016i
$549$	9.59991	+	27.1527i	0.409714	+	1.15885i
$550$			20.5566i			0.876537i
$551$	7.67986	+	7.67986i	0.327173	+	0.327173i
$552$	−14.0941	+	2.41816i	−0.599884	+	0.102924i
$553$	5.57074	+	5.57074i	0.236892	+	0.236892i
$554$	17.7912	−	17.7912i	0.755875	−	0.755875i
$555$	7.01413	−	9.91947i	0.297733	−	0.421058i
$556$			16.3131i			0.691828i
$557$	−12.2371	+	12.2371i	−0.518501	+	0.518501i	−0.917118	−	0.398617i	$-0.869490\pi$
$557$	−12.2371	+	12.2371i	−0.518501	+	0.518501i	0.398617	+	0.917118i	$0.369490\pi$
$558$	−4.82843	−	13.6569i	−0.204404	−	0.578141i
$559$	−23.1840	+	8.42926i	−0.980580	+	0.356520i
$560$			0.742317i			0.0313686i
$561$	9.92029	−	1.70205i	0.418835	−	0.0718607i
$562$	19.3819			0.817577
$563$	−29.1772			−1.22967			−0.614835	−	0.788656i	$-0.710778\pi$
$563$	−29.1772			−1.22967			−0.614835	+	0.788656i	$0.710778\pi$
$564$	1.75736	+	10.2426i	0.0739982	+	0.431293i
$565$	6.55349	−	6.55349i	0.275707	−	0.275707i
$566$	10.0782	−	10.0782i	0.423619	−	0.423619i
$567$	−8.94975	−	0.949747i	−0.375854	−	0.0398856i
$568$	−8.70665			−0.365323
$569$	−12.4095			−0.520234			−0.260117	−	0.965577i	$-0.583761\pi$
$569$	−12.4095			−0.520234			−0.260117	+	0.965577i	$0.583761\pi$
$570$	0.453561	+	2.64355i	0.0189976	+	0.110726i
$571$		−	7.55414i		−	0.316131i	−0.987429	−	0.158065i	$-0.949474\pi$
$571$		−	7.55414i		−	0.316131i	0.987429	−	0.158065i	$-0.0505257\pi$
$572$	−7.04585	+	15.0963i	−0.294602	+	0.631208i
$573$	2.88537	−	4.08053i	0.120538	−	0.170466i
$574$	−2.20632	+	2.20632i	−0.0920902	+	0.0920902i
$575$		−	36.7312i		−	1.53180i
$576$	2.82843	−	1.00000i	0.117851	−	0.0416667i
$577$	−20.6362	+	20.6362i	−0.859097	+	0.859097i	−0.991232	−	0.132134i	$-0.957817\pi$
$577$	−20.6362	+	20.6362i	−0.859097	+	0.859097i	0.132134	+	0.991232i	$0.457817\pi$
$578$	10.9023	+	10.9023i	0.453477	+	0.453477i
$579$	1.02359	+	5.96590i	0.0425388	+	0.247934i
$580$	−2.73279	−	2.73279i	−0.113473	−	0.113473i
$581$			3.19285i			0.132462i
$582$	5.17157	+	3.65685i	0.214369	+	0.151581i
$583$	−34.0899	−	34.0899i	−1.41186	−	1.41186i
$584$	13.1359			0.543568
$585$	7.99176	+	0.776350i	0.330419	+	0.0320981i
$586$	−27.9668			−1.15530
$587$	−8.09894	−	8.09894i	−0.334279	−	0.334279i	0.519930	−	0.854209i	$-0.325958\pi$
$587$	−8.09894	−	8.09894i	−0.334279	−	0.334279i	−0.854209	+	0.519930i	$0.825958\pi$
$588$	1.41421	+	1.00000i	0.0583212	+	0.0412393i
$589$			10.0726i			0.415036i
$590$	3.94397	+	3.94397i	0.162371	+	0.162371i
$591$	2.92243	+	17.0332i	0.120213	+	0.700652i
$592$	6.68143	+	6.68143i	0.274605	+	0.274605i
$593$	11.1891	−	11.1891i	0.459480	−	0.459480i	−0.439005	−	0.898485i	$-0.644669\pi$
$593$	11.1891	−	11.1891i	0.459480	−	0.459480i	0.898485	+	0.439005i	$0.144669\pi$
$594$	−6.53443	+	23.1027i	−0.268111	+	0.947915i
$595$			0.933599i			0.0382738i
$596$	−8.72013	+	8.72013i	−0.357190	+	0.357190i
$597$	−26.2752	+	37.1587i	−1.07537	+	1.52081i
$598$	12.5897	−	26.9745i	0.514833	−	1.10307i
$599$			12.8822i			0.526354i	0.964748	+	0.263177i	$0.0847703\pi$
$599$			12.8822i			0.526354i	−0.964748	+	0.263177i	$0.915230\pi$
$600$	1.30307	+	7.59486i	0.0531977	+	0.310059i
$601$	20.7683			0.847155			0.423577	−	0.905860i	$-0.360774\pi$
$601$	20.7683			0.847155			0.423577	+	0.905860i	$0.360774\pi$
$602$	6.84191			0.278855
$603$	23.4308	+	11.1904i	0.954176	+	0.455707i
$604$	−5.13196	+	5.13196i	−0.208816	+	0.208816i
$605$	−5.43236	+	5.43236i	−0.220857	+	0.220857i
$606$	−3.81338	−	22.2260i	−0.154908	−	0.902871i
$607$	−25.6158			−1.03972			−0.519858	−	0.854253i	$-0.674015\pi$
$607$	−25.6158			−1.03972			−0.519858	+	0.854253i	$0.674015\pi$
$608$	−2.08611			−0.0846029
$609$	−8.88775	+	1.52490i	−0.360150	+	0.0617920i
$610$			7.12618i			0.288530i
$611$	−19.6033	−	9.14938i	−0.793064	−	0.370144i
$612$	3.55727	−	1.25768i	0.143794	−	0.0508388i
$613$	−19.3690	+	19.3690i	−0.782307	+	0.782307i	−0.980220	−	0.197913i	$-0.936584\pi$
$613$	−19.3690	+	19.3690i	−0.782307	+	0.782307i	0.197913	+	0.980220i	$0.436584\pi$
$614$			16.8966i			0.681893i
$615$	2.31619	−	3.27558i	0.0933977	−	0.132084i
$616$	3.26721	−	3.26721i	0.131640	−	0.131640i
$617$	−13.8855	−	13.8855i	−0.559011	−	0.559011i	0.370015	−	0.929026i	$-0.379353\pi$
$617$	−13.8855	−	13.8855i	−0.559011	−	0.559011i	−0.929026	+	0.370015i	$0.879353\pi$
$618$	−17.0064	+	2.91784i	−0.684098	+	0.117373i
$619$	19.2315	+	19.2315i	0.772981	+	0.772981i	0.978627	−	0.205645i	$-0.0659294\pi$
$619$	19.2315	+	19.2315i	0.772981	+	0.772981i	−0.205645	+	0.978627i	$0.565929\pi$
$620$		−	3.58422i		−	0.143946i
$621$	11.6759	−	41.2806i	0.468538	−	1.65653i
$622$	5.49811	+	5.49811i	0.220454	+	0.220454i
$623$	2.48620			0.0996074
$624$	−1.64622	+	6.02412i	−0.0659014	+	0.241158i
$625$	−17.0381			−0.681525
$626$	−15.7107	−	15.7107i	−0.627925	−	0.627925i
$627$	9.63895	−	13.6315i	0.384943	−	0.544391i
$628$		−	22.9818i		−	0.917075i
$629$	8.40312	+	8.40312i	0.335054	+	0.335054i
$630$	−2.00953	−	0.959736i	−0.0800616	−	0.0382368i
$631$	−31.7850	−	31.7850i	−1.26534	−	1.26534i	−0.948467	−	0.316875i	$-0.897366\pi$
$631$	−31.7850	−	31.7850i	−1.26534	−	1.26534i	−0.316875	−	0.948467i	$-0.602634\pi$
$632$	5.57074	−	5.57074i	0.221592	−	0.221592i
$633$	−7.53378	−	5.32719i	−0.299441	−	0.211737i
$634$		−	29.0702i		−	1.15452i
$635$	8.26637	−	8.26637i	0.328041	−	0.328041i
$636$	−14.7558	−	10.4339i	−0.585105	−	0.413732i
$637$	−3.38853	+	1.23200i	−0.134259	+	0.0488138i
$638$			24.0560i			0.952387i
$639$	11.2568	−	23.5698i	0.445311	−	0.932408i
$640$	0.742317			0.0293427
$641$	−38.9865			−1.53987			−0.769937	−	0.638120i	$-0.779712\pi$
$641$	−38.9865			−1.53987			−0.769937	+	0.638120i	$0.779712\pi$
$642$	−8.24264	+	1.41421i	−0.325311	+	0.0558146i
$643$	3.89088	−	3.89088i	0.153441	−	0.153441i	−0.626212	−	0.779653i	$-0.715395\pi$
$643$	3.89088	−	3.89088i	0.153441	−	0.153441i	0.779653	+	0.626212i	$0.215395\pi$
$644$	−5.83796	+	5.83796i	−0.230048	+	0.230048i
$645$	−8.67016	+	1.48756i	−0.341387	+	0.0585728i
$646$	−2.62367			−0.103227
$647$	−17.1906			−0.675834			−0.337917	−	0.941176i	$-0.609722\pi$
$647$	−17.1906			−0.675834			−0.337917	+	0.941176i	$0.609722\pi$
$648$	−0.949747	+	8.94975i	−0.0373096	+	0.351579i
$649$		−	34.7178i		−	1.36279i
$650$	−14.5357	−	6.78422i	−0.570138	−	0.266099i
$651$	−6.82843	−	4.82843i	−0.267627	−	0.189241i
$652$	3.68538	−	3.68538i	0.144330	−	0.144330i
$653$		−	41.7186i		−	1.63257i	−0.577647	−	0.816287i	$-0.696029\pi$
$653$		−	41.7186i		−	1.63257i	0.577647	−	0.816287i	$-0.303971\pi$
$654$	26.1882	+	18.5178i	1.02404	+	0.724104i
$655$	−2.08087	+	2.08087i	−0.0813062	+	0.0813062i
$656$	2.20632	+	2.20632i	0.0861425	+	0.0861425i
$657$	−16.9833	+	35.5603i	−0.662583	+	1.38734i
$658$	4.24264	+	4.24264i	0.165395	+	0.165395i
$659$			24.7571i			0.964399i	0.876061	+	0.482200i	$0.160162\pi$
$659$			24.7571i			0.964399i	−0.876061	+	0.482200i	$0.839838\pi$
$660$	−3.42990	+	4.85062i	−0.133509	+	0.188810i
$661$	23.7476	+	23.7476i	0.923676	+	0.923676i	0.997287	−	0.0736112i	$-0.0234524\pi$
$661$	23.7476	+	23.7476i	0.923676	+	0.923676i	−0.0736112	+	0.997287i	$0.523452\pi$
$662$	−8.48307			−0.329704
$663$	−2.07042	+	7.57643i	−0.0804085	+	0.294244i
$664$	3.19285			0.123906
$665$	1.09499	+	1.09499i	0.0424620	+	0.0424620i
$666$	−26.7257	+	9.44897i	−1.03560	+	0.366140i
$667$		−	42.9840i		−	1.66435i
$668$	6.46006	+	6.46006i	0.249947	+	0.249947i
$669$	21.1518	−	3.62908i	0.817777	−	0.140308i
$670$	4.54314	+	4.54314i	0.175517	+	0.175517i
$671$	31.3650	−	31.3650i	1.21083	−	1.21083i
$672$	1.00000	−	1.41421i	0.0385758	−	0.0545545i
$673$		−	28.6789i		−	1.10549i	−0.833351	−	0.552745i	$-0.813580\pi$
$673$		−	28.6789i		−	1.10549i	0.833351	−	0.552745i	$-0.186420\pi$
$674$	17.6307	−	17.6307i	0.679110	−	0.679110i
$675$	−22.2448	−	6.29179i	−0.856204	−	0.242171i
$676$	−8.34938	−	9.96433i	−0.321130	−	0.383244i
$677$		−	3.17947i		−	0.122197i	−0.998132	−	0.0610985i	$-0.980540\pi$
$677$		−	3.17947i		−	0.122197i	0.998132	−	0.0610985i	$-0.0194604\pi$
$678$	−21.3137	+	3.65685i	−0.818548	+	0.140441i
$679$	3.65685			0.140337
$680$	0.933599			0.0358019
$681$	3.76917	+	21.9684i	0.144435	+	0.841829i
$682$	−15.7755	+	15.7755i	−0.604075	+	0.604075i
$683$	21.6072	−	21.6072i	0.826778	−	0.826778i	−0.160292	−	0.987070i	$-0.551244\pi$
$683$	21.6072	−	21.6072i	0.826778	−	0.826778i	0.987070	+	0.160292i	$0.0512435\pi$
$684$	2.69712	−	5.64732i	0.103127	−	0.215931i
$685$	−4.03071			−0.154005
$686$	1.00000			0.0381802
$687$	2.77798	+	16.1913i	0.105987	+	0.617736i
$688$		−	6.84191i		−	0.260845i
$689$	35.3557	−	12.8546i	1.34695	−	0.489723i
$690$	6.12866	−	8.66723i	0.233314	−	0.329956i
$691$	9.18274	−	9.18274i	0.349328	−	0.349328i	−0.510531	−	0.859859i	$-0.670551\pi$
$691$	9.18274	−	9.18274i	0.349328	−	0.349328i	0.859859	+	0.510531i	$0.170551\pi$
$692$		−	25.0702i		−	0.953024i
$693$	4.62054	+	13.0689i	0.175520	+	0.496445i
$694$	−3.63558	+	3.63558i	−0.138005	+	0.138005i
$695$	−8.56268	−	8.56268i	−0.324801	−	0.324801i
$696$	1.52490	+	8.88775i	0.0578011	+	0.336889i
$697$	2.77486	+	2.77486i	0.105105	+	0.105105i
$698$			5.63779i			0.213394i
$699$	9.38634	+	6.63714i	0.355024	+	0.251040i
$700$	3.14589	+	3.14589i	0.118904	+	0.118904i
$701$	−19.9899			−0.755008			−0.377504	−	0.926008i	$-0.623218\pi$
$701$	−19.9899			−0.755008			−0.377504	+	0.926008i	$0.623218\pi$
$702$	−14.1795	−	12.2450i	−0.535172	−	0.462159i
$703$	19.7116			0.743436
$704$	−3.26721	−	3.26721i	−0.123138	−	0.123138i
$705$	−6.29877	−	4.45390i	−0.237225	−	0.167744i
$706$		−	0.483070i		−	0.0181806i
$707$	−9.20632	−	9.20632i	−0.346239	−	0.346239i
$708$	−2.20074	−	12.8269i	−0.0827089	−	0.482063i
$709$	4.13189	+	4.13189i	0.155176	+	0.155176i	0.780425	−	0.625249i	$-0.215003\pi$
$709$	4.13189	+	4.13189i	0.155176	+	0.155176i	−0.625249	+	0.780425i	$0.715003\pi$
$710$	4.57010	−	4.57010i	0.171513	−	0.171513i
$711$	7.87822	+	22.2830i	0.295456	+	0.835677i
$712$		−	2.48620i		−	0.0931742i
$713$	28.1882	−	28.1882i	1.05565	−	1.05565i
$714$	1.25768	−	1.77863i	0.0470676	−	0.0665637i
$715$	−4.22566	−	11.6223i	−0.158031	−	0.434651i
$716$			15.3629i			0.574137i
$717$	−0.129674	−	0.755796i	−0.00484277	−	0.0282257i
$718$	5.98094			0.223207
$719$	37.7122			1.40643			0.703214	−	0.710978i	$-0.251748\pi$
$719$	37.7122			1.40643			0.703214	+	0.710978i	$0.251748\pi$
$720$	−0.959736	+	2.00953i	−0.0357673	+	0.0748908i
$721$	−7.04428	+	7.04428i	−0.262343	+	0.262343i
$722$	10.3578	−	10.3578i	0.385477	−	0.385477i
$723$	3.70692	+	21.6055i	0.137862	+	0.803517i
$724$	−1.22293			−0.0454499
$725$	−23.1628			−0.860243
$726$	17.6675	−	3.03126i	0.655702	−	0.112501i
$727$		−	20.1375i		−	0.746857i	−0.927659	−	0.373429i	$-0.878182\pi$
$727$		−	20.1375i		−	0.746857i	0.927659	−	0.373429i	$-0.121818\pi$
$728$	1.23200	+	3.38853i	0.0456611	+	0.125587i
$729$	−23.0000	−	14.1421i	−0.851852	−	0.523783i
$730$	−6.89500	+	6.89500i	−0.255195	+	0.255195i
$731$		−	8.60495i		−	0.318266i
$732$	9.59991	−	13.5763i	0.354823	−	0.501795i
$733$	−19.6156	+	19.6156i	−0.724519	+	0.724519i	−0.969522	−	0.245003i	$-0.921211\pi$
$733$	−19.6156	+	19.6156i	−0.724519	+	0.724519i	0.245003	+	0.969522i	$0.421211\pi$
$734$	4.12580	+	4.12580i	0.152286	+	0.152286i
$735$	−1.26721	+	0.217420i	−0.0467419	+	0.00801964i
$736$	5.83796	+	5.83796i	0.215190	+	0.215190i
$737$		−	39.9921i		−	1.47313i
$738$	−8.82530	+	3.12021i	−0.324864	+	0.114857i
$739$	−18.5250	−	18.5250i	−0.681452	−	0.681452i	0.278875	−	0.960327i	$-0.410038\pi$
$739$	−18.5250	−	18.5250i	−0.681452	−	0.681452i	−0.960327	+	0.278875i	$0.910038\pi$
$740$	−7.01413			−0.257844
$741$	6.45785	+	11.3145i	0.237235	+	0.415650i
$742$	−10.4339			−0.383041
$743$	30.1556	+	30.1556i	1.10630	+	1.10630i	0.993632	+	0.112670i	$0.0359402\pi$
$743$	30.1556	+	30.1556i	1.10630	+	1.10630i	0.112670	+	0.993632i	$0.464060\pi$
$744$	−4.82843	+	6.82843i	−0.177019	+	0.250342i
$745$		−	9.15434i		−	0.335389i
$746$	6.15653	+	6.15653i	0.225407	+	0.225407i
$747$	−4.12801	+	8.64338i	−0.151036	+	0.316245i
$748$	−4.10912	−	4.10912i	−0.150244	−	0.150244i
$749$	−3.41421	+	3.41421i	−0.124753	+	0.124753i
$750$	−9.91947	−	7.01413i	−0.362208	−	0.256120i
$751$			29.4133i			1.07331i	0.843803	+	0.536653i	$0.180312\pi$
$751$			29.4133i			1.07331i	−0.843803	+	0.536653i	$0.819688\pi$
$752$	4.24264	−	4.24264i	0.154713	−	0.154713i
$753$	−0.676564	−	0.478403i	−0.0246554	−	0.0174340i
$754$	−17.0102	−	7.93911i	−0.619474	−	0.289125i
$755$		−	5.38750i		−	0.196071i
$756$	2.53553	+	4.53553i	0.0922165	+	0.164956i
$757$	−11.3863			−0.413844			−0.206922	−	0.978357i	$-0.566345\pi$
$757$	−11.3863			−0.413844			−0.206922	+	0.978357i	$0.566345\pi$
$758$	−27.1628			−0.986596
$759$	−65.1222	+	11.1732i	−2.36379	+	0.405562i
$760$	1.09499	−	1.09499i	0.0397196	−	0.0397196i
$761$	32.3619	−	32.3619i	1.17312	−	1.17312i	0.191658	−	0.981462i	$-0.438614\pi$
$761$	32.3619	−	32.3619i	1.17312	−	1.17312i	0.981462	−	0.191658i	$-0.0613863\pi$
$762$	−26.8845	+	4.61264i	−0.973921	+	0.167098i
$763$	18.5178			0.670390
$764$	−2.88537			−0.104389
$765$	−1.20704	+	2.52735i	−0.0436408	+	0.0913767i
$766$		−	12.8610i		−	0.464686i
$767$	24.5492	+	11.4578i	0.886420	+	0.413716i
$768$	−1.41421	−	1.00000i	−0.0510310	−	0.0360844i
$769$	18.4078	−	18.4078i	0.663802	−	0.663802i	−0.292472	−	0.956274i	$-0.594478\pi$
$769$	18.4078	−	18.4078i	0.663802	−	0.663802i	0.956274	+	0.292472i	$0.0944779\pi$
$770$			3.42990i			0.123605i
$771$	17.0689	+	12.0695i	0.614720	+	0.434673i
$772$	2.47115	−	2.47115i	0.0889388	−	0.0889388i
$773$	−16.7397	−	16.7397i	−0.602084	−	0.602084i	0.338781	−	0.940865i	$-0.389985\pi$
$773$	−16.7397	−	16.7397i	−0.602084	−	0.602084i	−0.940865	+	0.338781i	$0.889985\pi$
$774$	18.5218	+	8.84585i	0.665751	+	0.317958i
$775$	−15.1897	−	15.1897i	−0.545631	−	0.545631i
$776$		−	3.65685i		−	0.131273i
$777$	−9.44897	+	13.3629i	−0.338980	+	0.479390i
$778$	12.7138	+	12.7138i	0.455812	+	0.455812i
$779$	6.50911			0.233213
$780$	−2.29795	−	4.02614i	−0.0822797	−	0.144159i
$781$	−40.2294			−1.43952
$782$	7.34230	+	7.34230i	0.262560	+	0.262560i
$783$	−26.0316	−	7.36286i	−0.930294	−	0.263127i
$784$		−	1.00000i		−	0.0357143i
$785$	12.0631	+	12.0631i	0.430551	+	0.430551i
$786$	6.76754	−	1.16113i	0.241390	−	0.0414160i
$787$	−25.0483	−	25.0483i	−0.892876	−	0.892876i	0.101917	−	0.994793i	$-0.467502\pi$
$787$	−25.0483	−	25.0483i	−0.892876	−	0.892876i	−0.994793	+	0.101917i	$0.967502\pi$
$788$	7.05538	−	7.05538i	0.251337	−	0.251337i
$789$	26.3613	−	37.2805i	0.938487	−	1.32722i
$790$			5.84814i			0.208067i
$791$	−8.82843	+	8.82843i	−0.313903	+	0.313903i
$792$	13.0689	−	4.62054i	0.464382	−	0.164184i
$793$	11.8271	+	32.5296i	0.419994	+	1.15516i
$794$		−	3.32031i		−	0.117833i
$795$	13.2220	−	2.26854i	0.468937	−	0.0804568i
$796$	26.2752			0.931299
$797$	−2.60706			−0.0923468			−0.0461734	−	0.998933i	$-0.514703\pi$
$797$	−2.60706			−0.0923468			−0.0461734	+	0.998933i	$0.514703\pi$
$798$	−0.611008	−	3.56121i	−0.0216294	−	0.126066i
$799$	5.33590	−	5.33590i	0.188770	−	0.188770i
$800$	3.14589	−	3.14589i	0.111224	−	0.111224i
$801$	6.73040	+	3.21439i	0.237807	+	0.113575i
$802$	−30.4251			−1.07435
$803$	60.6950			2.14188
$804$	−2.53508	−	14.7755i	−0.0894052	−	0.521092i
$805$		−	6.12866i		−	0.216007i
$806$	−5.94864	−	16.3613i	−0.209532	−	0.576302i
$807$	7.36286	−	10.4126i	0.259185	−	0.366543i
$808$	−9.20632	+	9.20632i	−0.323877	+	0.323877i
$809$			12.7904i			0.449688i	0.974395	+	0.224844i	$0.0721873\pi$
$809$			12.7904i			0.449688i	−0.974395	+	0.224844i	$0.927813\pi$
$810$	−4.19918	−	5.19622i	−0.147544	−	0.182576i
$811$	10.6848	−	10.6848i	0.375194	−	0.375194i	−0.494171	−	0.869365i	$-0.664528\pi$
$811$	10.6848	−	10.6848i	0.375194	−	0.375194i	0.869365	+	0.494171i	$0.164528\pi$
$812$	3.68143	+	3.68143i	0.129193	+	0.129193i
$813$	1.96433	+	11.4490i	0.0688921	+	0.401533i
$814$	30.8718	+	30.8718i	1.08206	+	1.08206i
$815$			3.86889i			0.135521i
$816$	−1.77863	−	1.25768i	−0.0622646	−	0.0440277i
$817$	−10.0925	−	10.0925i	−0.353092	−	0.353092i
$818$	18.0038			0.629486
$819$	−10.7660	−	1.04585i	−0.376194	−	0.0365448i
$820$	−2.31619			−0.0808848
$821$	22.6048	+	22.6048i	0.788915	+	0.788915i	0.981316	−	0.192402i	$-0.0616276\pi$
$821$	22.6048	+	22.6048i	0.788915	+	0.788915i	−0.192402	+	0.981316i	$0.561628\pi$
$822$	7.67904	+	5.42990i	0.267837	+	0.189390i
$823$		−	5.39771i		−	0.188152i	−0.995565	−	0.0940762i	$-0.970010\pi$
$823$		−	5.39771i		−	0.188152i	0.995565	−	0.0940762i	$-0.0299897\pi$
$824$	7.04428	+	7.04428i	0.245399	+	0.245399i
$825$	6.02089	+	35.0923i	0.209621	+	1.22176i
$826$	−5.31306	−	5.31306i	−0.184865	−	0.184865i
$827$	20.8135	−	20.8135i	0.723755	−	0.723755i	−0.245613	−	0.969368i	$-0.578989\pi$
$827$	20.8135	−	20.8135i	0.723755	−	0.723755i	0.969368	+	0.245613i	$0.0789893\pi$
$828$	−23.3518	+	8.25612i	−0.811532	+	0.286920i
$829$			1.76954i			0.0614588i	0.999528	+	0.0307294i	$0.00978301\pi$
$829$			1.76954i			0.0614588i	−0.999528	+	0.0307294i	$0.990217\pi$
$830$	−1.67592	+	1.67592i	−0.0581719	+	0.0581719i
$831$	25.1605	−	35.5824i	0.872810	−	1.23434i
$832$	3.38853	−	1.23200i	0.117476	−	0.0427121i
$833$		−	1.25768i		−	0.0435761i
$834$	4.77798	+	27.8481i	0.165448	+	0.964302i
$835$	−6.78174			−0.234692
$836$	−9.63895			−0.333370
$837$	−12.2426	−	21.8995i	−0.423168	−	0.756957i
$838$	9.26721	−	9.26721i	0.320131	−	0.320131i
$839$	−21.3319	+	21.3319i	−0.736457	+	0.736457i	−0.971891	−	0.235433i	$-0.924349\pi$
$839$	−21.3319	+	21.3319i	−0.736457	+	0.736457i	0.235433	+	0.971891i	$0.424349\pi$
$840$	0.217420	+	1.26721i	0.00750169	+	0.0437230i
$841$	1.89418			0.0653166
$842$	21.1796			0.729898
$843$	33.0870	−	5.67683i	1.13958	−	0.195520i
$844$			5.32719i			0.183369i
$845$	9.61282	+	0.847686i	0.330691	+	0.0291613i
$846$	6.00000	+	16.9706i	0.206284	+	0.583460i
$847$	7.31811	−	7.31811i	0.251453	−	0.251453i
$848$			10.4339i			0.358302i
$849$	14.2527	−	20.1564i	0.489153	−	0.691767i
$850$	3.95654	−	3.95654i	0.135708	−	0.135708i
$851$	−55.1627	−	55.1627i	−1.89095	−	1.89095i
$852$	−14.8632	+	2.55012i	−0.509204	+	0.0873656i
$853$	−31.2893	−	31.2893i	−1.07133	−	1.07133i	−0.997253	−	0.0740727i	$-0.976400\pi$
$853$	−31.2893	−	31.2893i	−1.07133	−	1.07133i	−0.0740727	−	0.997253i	$-0.523600\pi$
$854$		−	9.59991i		−	0.328502i
$855$	1.54855	+	4.37997i	0.0529595	+	0.149792i
$856$	3.41421	+	3.41421i	0.116695	+	0.116695i
$857$	40.4664			1.38230			0.691152	−	0.722709i	$-0.257103\pi$
$857$	40.4664			1.38230			0.691152	+	0.722709i	$0.257103\pi$
$858$	−7.60641	+	27.8347i	−0.259679	+	0.950260i
$859$	−34.9883			−1.19379			−0.596893	−	0.802321i	$-0.703598\pi$
$859$	−34.9883			−1.19379			−0.596893	+	0.802321i	$0.703598\pi$
$860$	3.59130	+	3.59130i	0.122462	+	0.122462i
$861$	−3.12021	+	4.41265i	−0.106337	+	0.150383i
$862$			10.6863i			0.363977i
$863$	19.0767	+	19.0767i	0.649377	+	0.649377i	0.952842	−	0.303466i	$-0.0981438\pi$
$863$	19.0767	+	19.0767i	0.649377	+	0.649377i	−0.303466	+	0.952842i	$0.598144\pi$
$864$	4.53553	−	2.53553i	0.154302	−	0.0862606i
$865$	13.1593	+	13.1593i	0.447428	+	0.447428i
$866$	9.89949	−	9.89949i	0.336399	−	0.336399i
$867$	21.8047	+	15.4182i	0.740526	+	0.523631i
$868$			4.82843i			0.163887i
$869$	25.7398	−	25.7398i	0.873164	−	0.873164i
$870$	−5.46557	−	3.86474i	−0.185300	−	0.131027i
$871$	28.2787	+	13.1984i	0.958187	+	0.447212i
$872$		−	18.5178i		−	0.627093i
$873$	9.89949	+	4.72792i	0.335047	+	0.160016i
$874$	17.2232			0.582583
$875$	−7.01413			−0.237121
$876$	22.4244	−	3.84742i	0.757650	−	0.129992i
$877$	−32.1891	+	32.1891i	−1.08695	+	1.08695i	−0.0911066	+	0.995841i	$0.529040\pi$
$877$	−32.1891	+	32.1891i	−1.08695	+	1.08695i	−0.995841	+	0.0911066i	$0.970960\pi$
$878$	18.8543	−	18.8543i	0.636302	−	0.636302i
$879$	−47.7423	+	8.19128i	−1.61031	+	0.276285i
$880$	3.42990			0.115622
$881$	−21.9990			−0.741165			−0.370582	−	0.928800i	$-0.620842\pi$
$881$	−21.9990			−0.741165			−0.370582	+	0.928800i	$0.620842\pi$
$882$	2.70711	+	1.29289i	0.0911530	+	0.0435340i
$883$			26.7849i			0.901382i	0.892680	+	0.450691i	$0.148822\pi$
$883$			26.7849i			0.901382i	−0.892680	+	0.450691i	$0.851178\pi$
$884$	4.26170	−	1.54947i	0.143337	−	0.0521143i
$885$	7.88795	+	5.57762i	0.265151	+	0.187490i
$886$	10.3835	−	10.3835i	0.348840	−	0.348840i
$887$		−	15.7911i		−	0.530213i	−0.964219	−	0.265107i	$-0.914593\pi$
$887$		−	15.7911i		−	0.530213i	0.964219	−	0.265107i	$-0.0854071\pi$
$888$	13.3629	+	9.44897i	0.448428	+	0.317087i
$889$	−11.1359	+	11.1359i	−0.373486	+	0.373486i
$890$	1.30500	+	1.30500i	0.0437436	+	0.0437436i
$891$	−4.38834	+	41.3527i	−0.147015	+	1.38537i
$892$	−8.76138	−	8.76138i	−0.293353	−	0.293353i
$893$		−	12.5167i		−	0.418854i
$894$	−12.3321	+	17.4403i	−0.412448	+	0.583289i
$895$	−8.06392	−	8.06392i	−0.269547	−	0.269547i
$896$	−1.00000			−0.0334077
$897$	13.5914	−	49.7358i	0.453803	−	1.66063i
$898$	31.4963			1.05104
$899$	−17.7755	−	17.7755i	−0.592846	−	0.592846i
$900$	4.44897	+	12.5836i	0.148299	+	0.419453i
$901$			13.1226i			0.437176i
$902$	10.1944	+	10.1944i	0.339437	+	0.339437i
$903$	11.6799	−	2.00395i	0.388682	−	0.0666872i
$904$	8.82843	+	8.82843i	0.293629	+	0.293629i
$905$	0.641913	−	0.641913i	0.0213379	−	0.0213379i
$906$	−7.25768	+	10.2639i	−0.241120	+	0.340996i
$907$			2.87097i			0.0953291i	0.998863	+	0.0476646i	$0.0151779\pi$
$907$			2.87097i			0.0953291i	−0.998863	+	0.0476646i	$0.984822\pi$
$908$	9.09959	−	9.09959i	0.301980	−	0.301980i
$909$	−13.0197	−	36.8253i	−0.431837	−	1.22142i
$910$	−2.42531	−	1.13196i	−0.0803982	−	0.0375240i
$911$			26.7383i			0.885879i	0.896552	+	0.442939i	$0.146064\pi$
$911$			26.7383i			0.885879i	−0.896552	+	0.442939i	$0.853936\pi$
$912$	−3.56121	+	0.611008i	−0.117924	+	0.0202325i
$913$	14.7527			0.488242
$914$	−10.1509			−0.335763
$915$	2.08721	+	12.1651i	0.0690010	+	0.402167i
$916$	6.70665	−	6.70665i	0.221594	−	0.221594i
$917$	2.80321	−	2.80321i	0.0925700	−	0.0925700i
$918$	5.70426	−	3.18890i	0.188269	−	0.105249i
$919$	−16.7939			−0.553980			−0.276990	−	0.960873i	$-0.589337\pi$
$919$	−16.7939			−0.553980			−0.276990	+	0.960873i	$0.589337\pi$
$920$	−6.12866			−0.202056
$921$	4.94891	+	28.8444i	0.163072	+	0.950454i
$922$		−	34.3278i		−	1.13053i
$923$	13.2767	−	28.4465i	0.437009	−	0.936327i
$924$	4.62054	−	6.53443i	0.152005	−	0.214967i
$925$	−29.7254	+	29.7254i	−0.977367	+	0.977367i
$926$			4.91454i			0.161502i
$927$	−28.1771	+	9.96212i	−0.925458	+	0.327199i
$928$	3.68143	−	3.68143i	0.120849	−	0.120849i
$929$	−16.4254	−	16.4254i	−0.538899	−	0.538899i	0.384306	−	0.923206i	$-0.374441\pi$
$929$	−16.4254	−	16.4254i	−0.538899	−	0.538899i	−0.923206	+	0.384306i	$0.874441\pi$
$930$	−1.04979	−	6.11865i	−0.0344241	−	0.200638i
$931$	−1.47510	−	1.47510i	−0.0483445	−	0.0483445i
$932$		−	6.63714i		−	0.217407i
$933$	10.9962	+	7.77551i	0.360000	+	0.254559i
$934$	−17.0237	−	17.0237i	−0.557031	−	0.557031i
$935$	4.31373			0.141074
$936$	−1.04585	+	10.7660i	−0.0341846	+	0.351897i
$937$	50.0128			1.63385			0.816924	−	0.576746i	$-0.195678\pi$
$937$	50.0128			1.63385			0.816924	+	0.576746i	$0.195678\pi$
$938$	−6.12021	−	6.12021i	−0.199832	−	0.199832i
$939$	−31.4213	−	22.2182i	−1.02540	−	0.725065i
$940$			4.45390i			0.145270i
$941$	−21.0197	−	21.0197i	−0.685223	−	0.685223i	0.275949	−	0.961172i	$-0.411008\pi$
$941$	−21.0197	−	21.0197i	−0.685223	−	0.685223i	−0.961172	+	0.275949i	$0.911008\pi$
$942$	−6.73122	−	39.2324i	−0.219315	−	1.27826i
$943$	−18.2157	−	18.2157i	−0.593184	−	0.593184i
$944$	−5.31306	+	5.31306i	−0.172925	+	0.172925i
$945$	−3.71158	−	1.04979i	−0.120738	−	0.0341498i
$946$		−	31.6133i		−	1.02784i
$947$	−20.3060	+	20.3060i	−0.659856	+	0.659856i	−0.955346	−	0.295490i	$-0.904517\pi$
$947$	−20.3060	+	20.3060i	−0.659856	+	0.659856i	0.295490	+	0.955346i	$0.404517\pi$
$948$	7.87822	−	11.1415i	0.255873	−	0.361859i
$949$	−20.0309	+	42.9178i	−0.650231	+	1.39317i
$950$		−	9.28103i		−	0.301116i
$951$	−8.51445	−	49.6259i	−0.276100	−	1.60923i
$952$	−1.25768			−0.0407617
$953$	40.6120			1.31555			0.657775	−	0.753214i	$-0.271498\pi$
$953$	40.6120			1.31555			0.657775	+	0.753214i	$0.271498\pi$
$954$	−28.2457	−	13.4899i	−0.914490	−	0.436753i
$955$	1.51452	−	1.51452i	0.0490088	−	0.0490088i
$956$	−0.313061	+	0.313061i	−0.0101251	+	0.0101251i
$957$	7.04585	+	41.0662i	0.227760	+	1.32748i
$958$	34.0419			1.09984
$959$	5.42990			0.175341
$960$	1.26721	−	0.217420i	0.0408992	−	0.00701719i
$961$			7.68629i			0.247945i
$962$	−32.0181	+	11.6412i	−1.03231	+	0.375326i
$963$	−13.6569	+	4.82843i	−0.440086	+	0.155594i
$964$	8.94929	−	8.94929i	0.288237	−	0.288237i
$965$			2.59420i			0.0835104i
$966$	−8.25612	+	11.6759i	−0.265636	+	0.375666i
$967$	16.3730	−	16.3730i	0.526521	−	0.526521i	−0.393012	−	0.919533i	$-0.628567\pi$
$967$	16.3730	−	16.3730i	0.526521	−	0.526521i	0.919533	+	0.393012i	$0.128567\pi$
$968$	−7.31811	−	7.31811i	−0.235213	−	0.235213i
$969$	−4.47888	+	0.768454i	−0.143882	+	0.0246863i
$970$	1.91947	+	1.91947i	0.0616306	+	0.0616306i
$971$			3.30254i			0.105984i	0.998595	+	0.0529918i	$0.0168757\pi$
$971$			3.30254i			0.105984i	−0.998595	+	0.0529918i	$0.983124\pi$
$972$	1.00000	+	15.5563i	0.0320750	+	0.498970i
$973$	11.5351	+	11.5351i	0.369798	+	0.369798i
$974$	−18.3144			−0.586830
$975$	−26.8011	−	7.32397i	−0.858322	−	0.234555i
$976$	−9.59991			−0.307286
$977$	24.9792	+	24.9792i	0.799155	+	0.799155i	0.982962	−	0.183808i	$-0.0588423\pi$
$977$	24.9792	+	24.9792i	0.799155	+	0.799155i	−0.183808	+	0.982962i	$0.558842\pi$
$978$	5.21191	−	7.37075i	0.166658	−	0.235691i
$979$		−	11.4876i		−	0.367144i
$980$	0.524897	+	0.524897i	0.0167672	+	0.0167672i
$981$	50.1297	+	23.9416i	1.60052	+	0.764395i
$982$	10.5200	+	10.5200i	0.335708	+	0.335708i
$983$	−35.8420	+	35.8420i	−1.14318	+	1.14318i	−0.155317	+	0.987865i	$0.549640\pi$
$983$	−35.8420	+	35.8420i	−1.14318	+	1.14318i	−0.987865	+	0.155317i	$0.950360\pi$
$984$	4.41265	+	3.12021i	0.140670	+	0.0994688i
$985$			7.40670i			0.235997i
$986$	4.63007	−	4.63007i	0.147451	−	0.147451i
$987$	8.48528	+	6.00000i	0.270089	+	0.190982i
$988$	3.18110	−	6.81577i	0.101204	−	0.216838i
$989$			56.4876i			1.79620i
$990$	−4.43450	+	9.28512i	−0.140938	+	0.295100i
$991$	15.9765			0.507511			0.253755	−	0.967268i	$-0.418334\pi$
$991$	15.9765			0.507511			0.253755	+	0.967268i	$0.418334\pi$
$992$	4.82843			0.153303
$993$	−14.4815	+	2.48463i	−0.459557	+	0.0788475i
$994$	−6.15653	+	6.15653i	−0.195273	+	0.195273i
$995$	−13.7918	+	13.7918i	−0.437229	+	0.437229i
$996$	5.45053	−	0.935163i	0.172707	−	0.0296318i
$997$	−41.2167			−1.30535			−0.652673	−	0.757640i	$-0.726352\pi$
$997$	−41.2167			−1.30535			−0.652673	+	0.757640i	$0.726352\pi$
$998$	1.04411			0.0330507
$999$	−42.8561	+	23.9582i	−1.35591	+	0.758003i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.p.b.239.1	yes	8
3.2	odd	2		546.2.p.a.239.4	✓	8
13.8	odd	4		546.2.p.a.281.4	yes	8
39.8	even	4	inner	546.2.p.b.281.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.p.a.239.4	✓	8	3.2	odd	2
546.2.p.a.281.4	yes	8	13.8	odd	4
546.2.p.b.239.1	yes	8	1.1	even	1	trivial
546.2.p.b.281.1	yes	8	39.8	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.41421 - 1.00000i) q^{3} +1.00000i q^{4} +(-0.524897 - 0.524897i) q^{5} +(0.292893 + 1.70711i) q^{6} +(0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.00000 + 2.82843i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.41421 - 1.00000i) q^{3} +1.00000i q^{4} +(-0.524897 - 0.524897i) q^{5} +(0.292893 + 1.70711i) q^{6} +(0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.00000 + 2.82843i) q^{9} +0.742317i q^{10} +(3.26721 - 3.26721i) q^{11} +(1.00000 - 1.41421i) q^{12} +(1.23200 + 3.38853i) q^{13} -1.00000i q^{14} +(0.217420 + 1.26721i) q^{15} -1.00000 q^{16} -1.25768 q^{17} +(1.29289 - 2.70711i) q^{18} +(-1.47510 + 1.47510i) q^{19} +(0.524897 - 0.524897i) q^{20} +(-0.292893 - 1.70711i) q^{21} -4.62054 q^{22} +8.25612 q^{23} +(-1.70711 + 0.292893i) q^{24} -4.44897i q^{25} +(1.52490 - 3.26721i) q^{26} +(1.41421 - 5.00000i) q^{27} +(-0.707107 + 0.707107i) q^{28} -5.20632i q^{29} +(0.742317 - 1.04979i) q^{30} +(3.41421 - 3.41421i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-7.88775 + 1.35332i) q^{33} +(0.889316 + 0.889316i) q^{34} -0.742317i q^{35} +(-2.82843 + 1.00000i) q^{36} +(-6.68143 - 6.68143i) q^{37} +2.08611 q^{38} +(1.64622 - 6.02412i) q^{39} -0.742317 q^{40} +(-2.20632 - 2.20632i) q^{41} +(-1.00000 + 1.41421i) q^{42} +6.84191i q^{43} +(3.26721 + 3.26721i) q^{44} +(0.959736 - 2.00953i) q^{45} +(-5.83796 - 5.83796i) q^{46} +(-4.24264 + 4.24264i) q^{47} +(1.41421 + 1.00000i) q^{48} +1.00000i q^{49} +(-3.14589 + 3.14589i) q^{50} +(1.77863 + 1.25768i) q^{51} +(-3.38853 + 1.23200i) q^{52} -10.4339i q^{53} +(-4.53553 + 2.53553i) q^{54} -3.42990 q^{55} +1.00000 q^{56} +(3.56121 - 0.611008i) q^{57} +(-3.68143 + 3.68143i) q^{58} +(5.31306 - 5.31306i) q^{59} +(-1.26721 + 0.217420i) q^{60} +9.59991 q^{61} -4.82843 q^{62} +(-1.29289 + 2.70711i) q^{63} -1.00000i q^{64} +(1.13196 - 2.42531i) q^{65} +(6.53443 + 4.62054i) q^{66} +(6.12021 - 6.12021i) q^{67} -1.25768i q^{68} +(-11.6759 - 8.25612i) q^{69} +(-0.524897 + 0.524897i) q^{70} +(-6.15653 - 6.15653i) q^{71} +(2.70711 + 1.29289i) q^{72} +(9.28849 + 9.28849i) q^{73} +9.44897i q^{74} +(-4.44897 + 6.29179i) q^{75} +(-1.47510 - 1.47510i) q^{76} +4.62054 q^{77} +(-5.42374 + 3.09564i) q^{78} +7.87822 q^{79} +(0.524897 + 0.524897i) q^{80} +(-7.00000 + 5.65685i) q^{81} +3.12021i q^{82} +(2.25768 + 2.25768i) q^{83} +(1.70711 - 0.292893i) q^{84} +(0.660154 + 0.660154i) q^{85} +(4.83796 - 4.83796i) q^{86} +(-5.20632 + 7.36286i) q^{87} -4.62054i q^{88} +(1.75801 - 1.75801i) q^{89} +(-2.09959 + 0.742317i) q^{90} +(-1.52490 + 3.26721i) q^{91} +8.25612i q^{92} +(-8.24264 + 1.41421i) q^{93} +6.00000 q^{94} +1.54855 q^{95} +(-0.292893 - 1.70711i) q^{96} +(2.58579 - 2.58579i) q^{97} +(0.707107 - 0.707107i) q^{98} +(12.5083 + 5.97386i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{5} + 8 q^{6} + 8 q^{9}+O(q^{10}) \) 8 * q + 4 * q^5 + 8 * q^6 + 8 * q^9	\( 8 q + 4 q^{5} + 8 q^{6} + 8 q^{9} + 8 q^{11} + 8 q^{12} - 4 q^{13} - 8 q^{16} - 20 q^{17} + 16 q^{18} - 20 q^{19} - 4 q^{20} - 8 q^{21} + 12 q^{22} + 12 q^{23} - 8 q^{24} + 4 q^{26} - 4 q^{30} + 16 q^{31} + 4 q^{33} + 4 q^{34} - 24 q^{37} + 4 q^{38} - 12 q^{39} + 4 q^{40} + 20 q^{41} - 8 q^{42} + 8 q^{44} - 4 q^{45} + 4 q^{46} - 24 q^{50} + 8 q^{51} + 8 q^{52} - 8 q^{54} - 12 q^{55} + 8 q^{56} + 24 q^{57} + 8 q^{60} + 20 q^{61} - 16 q^{62} - 16 q^{63} - 28 q^{65} + 16 q^{66} + 24 q^{67} + 8 q^{69} + 4 q^{70} - 28 q^{71} + 16 q^{72} + 16 q^{73} + 36 q^{75} - 20 q^{76} - 12 q^{77} - 4 q^{78} + 24 q^{79} - 4 q^{80} - 56 q^{81} + 28 q^{83} + 8 q^{84} + 16 q^{85} - 12 q^{86} - 4 q^{87} + 16 q^{90} - 4 q^{91} - 32 q^{93} + 48 q^{94} - 92 q^{95} - 8 q^{96} + 32 q^{97} - 16 q^{99}+O(q^{100}) \) 8 * q + 4 * q^5 + 8 * q^6 + 8 * q^9 + 8 * q^11 + 8 * q^12 - 4 * q^13 - 8 * q^16 - 20 * q^17 + 16 * q^18 - 20 * q^19 - 4 * q^20 - 8 * q^21 + 12 * q^22 + 12 * q^23 - 8 * q^24 + 4 * q^26 - 4 * q^30 + 16 * q^31 + 4 * q^33 + 4 * q^34 - 24 * q^37 + 4 * q^38 - 12 * q^39 + 4 * q^40 + 20 * q^41 - 8 * q^42 + 8 * q^44 - 4 * q^45 + 4 * q^46 - 24 * q^50 + 8 * q^51 + 8 * q^52 - 8 * q^54 - 12 * q^55 + 8 * q^56 + 24 * q^57 + 8 * q^60 + 20 * q^61 - 16 * q^62 - 16 * q^63 - 28 * q^65 + 16 * q^66 + 24 * q^67 + 8 * q^69 + 4 * q^70 - 28 * q^71 + 16 * q^72 + 16 * q^73 + 36 * q^75 - 20 * q^76 - 12 * q^77 - 4 * q^78 + 24 * q^79 - 4 * q^80 - 56 * q^81 + 28 * q^83 + 8 * q^84 + 16 * q^85 - 12 * q^86 - 4 * q^87 + 16 * q^90 - 4 * q^91 - 32 * q^93 + 48 * q^94 - 92 * q^95 - 8 * q^96 + 32 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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