LMFDB - Embedded newform 60.2.j.a.7.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,2,Mod(7,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1]))

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

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

chi := DirichletCharacter("60.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	60.j (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:	$0.479102412128$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.426337261060096.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{9} - 3x^{8} + 4x^{7} + 8x^{6} + 8x^{5} - 12x^{4} - 32x^{3} + 64 $ x^12 - 4x^9 - 3x^8 + 4x^7 + 8x^6 + 8x^5 - 12x^4 - 32*x^3 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.6
Root			$-1.35818 + 0.394157i$ of defining polynomial
Character	$\chi$	$=$	60.7
Dual form			60.2.j.a.43.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.35818 + 0.394157i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(1.68928 + 1.07067i) q^{4} +(-1.75233 - 1.38900i) q^{5} +(-0.681664 - 1.23909i) q^{6} +(-2.47817 + 2.47817i) q^{7} +(1.87233 + 2.12000i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(1.35818 + 0.394157i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(1.68928 + 1.07067i) q^{4} +(-1.75233 - 1.38900i) q^{5} +(-0.681664 - 1.23909i) q^{6} +(-2.47817 + 2.47817i) q^{7} +(1.87233 + 2.12000i) q^{8} +1.00000i q^{9} +(-1.83249 - 2.57720i) q^{10} -3.02831i q^{11} +(-0.437425 - 1.95158i) q^{12} +(0.363328 - 0.363328i) q^{13} +(-4.34258 + 2.38900i) q^{14} +(0.256912 + 2.22126i) q^{15} +(1.70734 + 3.61732i) q^{16} +(-2.36333 - 2.36333i) q^{17} +(-0.394157 + 1.35818i) q^{18} +4.95634 q^{19} +(-1.47302 - 4.22258i) q^{20} +3.50466 q^{21} +(1.19363 - 4.11297i) q^{22} +(0.900390 + 0.900390i) q^{23} +(0.175128 - 2.82300i) q^{24} +(1.14134 + 4.86799i) q^{25} +(0.636672 - 0.350255i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-6.83963 + 1.53303i) q^{28} +3.50466i q^{29} +(-0.526593 + 3.11812i) q^{30} -3.85607i q^{31} +(0.893077 + 5.58591i) q^{32} +(-2.14134 + 2.14134i) q^{33} +(-2.27829 - 4.14134i) q^{34} +(7.78477 - 0.900390i) q^{35} +(-1.07067 + 1.68928i) q^{36} +(-0.363328 - 0.363328i) q^{37} +(6.73158 + 1.95358i) q^{38} -0.513824 q^{39} +(-0.336258 - 6.31561i) q^{40} +2.72666 q^{41} +(4.75995 + 1.38139i) q^{42} +(-3.92870 - 3.92870i) q^{43} +(3.24231 - 5.11566i) q^{44} +(1.38900 - 1.75233i) q^{45} +(0.867993 + 1.57778i) q^{46} +(-5.85673 + 5.85673i) q^{47} +(1.35056 - 3.76510i) q^{48} -5.28267i q^{49} +(-0.368618 + 7.06145i) q^{50} +3.34225i q^{51} +(1.00277 - 0.224760i) q^{52} +(3.14134 - 3.14134i) q^{53} +(1.23909 - 0.681664i) q^{54} +(-4.20633 + 5.30660i) q^{55} +(-9.89367 - 0.613763i) q^{56} +(-3.50466 - 3.50466i) q^{57} +(-1.38139 + 4.75995i) q^{58} -8.68516 q^{59} +(-1.94424 + 4.02740i) q^{60} -15.2920 q^{61} +(1.51990 - 5.23723i) q^{62} +(-2.47817 - 2.47817i) q^{63} +(-0.988770 + 7.93866i) q^{64} +(-1.14134 + 0.132007i) q^{65} +(-3.75233 + 2.06429i) q^{66} +(3.92870 - 3.92870i) q^{67} +(-1.46199 - 6.52267i) q^{68} -1.27334i q^{69} +(10.9280 + 1.84553i) q^{70} +4.25583i q^{71} +(-2.12000 + 1.87233i) q^{72} +(9.28267 - 9.28267i) q^{73} +(-0.350255 - 0.636672i) q^{74} +(2.63514 - 4.24924i) q^{75} +(8.37266 + 5.30660i) q^{76} +(7.50466 + 7.50466i) q^{77} +(-0.697863 - 0.202527i) q^{78} -0.399759 q^{79} +(2.03264 - 8.71024i) q^{80} -1.00000 q^{81} +(3.70328 + 1.07473i) q^{82} +(0.199879 + 0.199879i) q^{83} +(5.92036 + 3.75233i) q^{84} +(0.858664 + 7.42401i) q^{85} +(-3.78734 - 6.88438i) q^{86} +(2.47817 - 2.47817i) q^{87} +(6.42000 - 5.66999i) q^{88} +4.28267i q^{89} +(2.57720 - 1.83249i) q^{90} +1.80078i q^{91} +(0.556993 + 2.48503i) q^{92} +(-2.72666 + 2.72666i) q^{93} +(-10.2629 + 5.64600i) q^{94} +(-8.68516 - 6.88438i) q^{95} +(3.31834 - 4.58134i) q^{96} +(6.73599 + 6.73599i) q^{97} +(2.08220 - 7.17480i) q^{98} +3.02831 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{6} - 12 q^{8}+O(q^{10}) $ 12 * q - 4 * q^6 - 12 * q^8	$ 12 q - 4 q^{6} - 12 q^{8} - 8 q^{10} - 8 q^{12} - 4 q^{13} + 12 q^{16} - 20 q^{17} + 20 q^{20} + 12 q^{22} - 20 q^{25} + 16 q^{26} - 4 q^{28} + 8 q^{30} + 20 q^{32} + 8 q^{33} + 4 q^{36} + 4 q^{37} + 16 q^{38} - 8 q^{40} + 16 q^{41} + 20 q^{42} + 4 q^{45} - 40 q^{46} + 16 q^{48} - 16 q^{50} - 8 q^{52} + 4 q^{53} - 64 q^{56} - 20 q^{58} - 20 q^{60} - 32 q^{61} - 56 q^{62} + 20 q^{65} - 24 q^{66} - 16 q^{68} + 44 q^{70} - 12 q^{72} + 44 q^{73} + 8 q^{76} + 48 q^{77} - 24 q^{78} + 4 q^{80} - 12 q^{81} + 16 q^{82} + 44 q^{85} + 64 q^{86} + 60 q^{88} + 12 q^{90} + 56 q^{92} - 16 q^{93} + 44 q^{96} - 20 q^{97} + 24 q^{98}+O(q^{100}) $ 12 * q - 4 * q^6 - 12 * q^8 - 8 * q^10 - 8 * q^12 - 4 * q^13 + 12 * q^16 - 20 * q^17 + 20 * q^20 + 12 * q^22 - 20 * q^25 + 16 * q^26 - 4 * q^28 + 8 * q^30 + 20 * q^32 + 8 * q^33 + 4 * q^36 + 4 * q^37 + 16 * q^38 - 8 * q^40 + 16 * q^41 + 20 * q^42 + 4 * q^45 - 40 * q^46 + 16 * q^48 - 16 * q^50 - 8 * q^52 + 4 * q^53 - 64 * q^56 - 20 * q^58 - 20 * q^60 - 32 * q^61 - 56 * q^62 + 20 * q^65 - 24 * q^66 - 16 * q^68 + 44 * q^70 - 12 * q^72 + 44 * q^73 + 8 * q^76 + 48 * q^77 - 24 * q^78 + 4 * q^80 - 12 * q^81 + 16 * q^82 + 44 * q^85 + 64 * q^86 + 60 * q^88 + 12 * q^90 + 56 * q^92 - 16 * q^93 + 44 * q^96 - 20 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	1.35818	+	0.394157i	0.960375	+	0.278711i
$2$	1.35818	+	0.394157i	0.960375	+	0.278711i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	1.68928	+	1.07067i	0.844640	+	0.535334i
$5$	−1.75233	−	1.38900i	−0.783667	−	0.621181i
$5$	−1.75233	−	1.38900i	−0.783667	−	0.621181i
$6$	−0.681664	−	1.23909i	−0.278288	−	0.505855i
$7$	−2.47817	+	2.47817i	−0.936661	+	0.936661i	−0.998110	−	0.0614493i	$-0.980428\pi$
$7$	−2.47817	+	2.47817i	−0.936661	+	0.936661i	0.0614493	+	0.998110i	$0.480428\pi$
$8$	1.87233	+	2.12000i	0.661968	+	0.749532i
$9$			1.00000i			0.333333i
$10$	−1.83249	−	2.57720i	−0.579484	−	0.814984i
$11$		−	3.02831i		−	0.913069i	−0.889706	−	0.456534i	$-0.849091\pi$
$11$		−	3.02831i		−	0.913069i	0.889706	−	0.456534i	$-0.150909\pi$
$12$	−0.437425	−	1.95158i	−0.126274	−	0.563372i
$13$	0.363328	−	0.363328i	0.100769	−	0.100769i	−0.654925	−	0.755694i	$-0.727300\pi$
$13$	0.363328	−	0.363328i	0.100769	−	0.100769i	0.755694	+	0.654925i	$0.227300\pi$
$14$	−4.34258	+	2.38900i	−1.16060	+	0.638488i
$15$	0.256912	+	2.22126i	0.0663344	+	0.573527i
$16$	1.70734	+	3.61732i	0.426835	+	0.904330i
$17$	−2.36333	−	2.36333i	−0.573191	−	0.573191i	0.359828	−	0.933019i	$-0.382836\pi$
$17$	−2.36333	−	2.36333i	−0.573191	−	0.573191i	−0.933019	+	0.359828i	$0.882836\pi$
$18$	−0.394157	+	1.35818i	−0.0929036	+	0.320125i
$19$	4.95634			1.13706			0.568532	−	0.822661i	$-0.307512\pi$
$19$	4.95634			1.13706			0.568532	+	0.822661i	$0.307512\pi$
$20$	−1.47302	−	4.22258i	−0.329377	−	0.944198i
$21$	3.50466			0.764780
$22$	1.19363	−	4.11297i	0.254482	−	0.876888i
$23$	0.900390	+	0.900390i	0.187744	+	0.187744i	0.794720	−	0.606976i	$-0.207618\pi$
$23$	0.900390	+	0.900390i	0.187744	+	0.187744i	−0.606976	+	0.794720i	$0.707618\pi$
$24$	0.175128	−	2.82300i	0.0357478	−	0.576243i
$25$	1.14134	+	4.86799i	0.228267	+	0.973599i
$26$	0.636672	−	0.350255i	0.124862	−	0.0686907i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−6.83963	+	1.53303i	−1.29257	+	0.289715i
$29$			3.50466i			0.650800i	0.945576	+	0.325400i	$0.105499\pi$
$29$			3.50466i			0.650800i	−0.945576	+	0.325400i	$0.894501\pi$
$30$	−0.526593	+	3.11812i	−0.0961423	+	0.569289i
$31$		−	3.85607i		−	0.692571i	−0.938129	−	0.346286i	$-0.887443\pi$
$31$		−	3.85607i		−	0.692571i	0.938129	−	0.346286i	$-0.112557\pi$
$32$	0.893077	+	5.58591i	0.157875	+	0.987459i
$33$	−2.14134	+	2.14134i	−0.372759	+	0.372759i
$34$	−2.27829	−	4.14134i	−0.390724	−	0.710233i
$35$	7.78477	−	0.900390i	1.31587	−	0.152194i
$36$	−1.07067	+	1.68928i	−0.178445	+	0.281547i
$37$	−0.363328	−	0.363328i	−0.0597308	−	0.0597308i	0.676610	−	0.736341i	$-0.263448\pi$
$37$	−0.363328	−	0.363328i	−0.0597308	−	0.0597308i	−0.736341	+	0.676610i	$0.763448\pi$
$38$	6.73158	+	1.95358i	1.09201	+	0.316912i
$39$	−0.513824			−0.0822776
$40$	−0.336258	−	6.31561i	−0.0531671	−	0.998586i
$41$	2.72666			0.425832			0.212916	−	0.977070i	$-0.431704\pi$
$41$	2.72666			0.425832			0.212916	+	0.977070i	$0.431704\pi$
$42$	4.75995	+	1.38139i	0.734476	+	0.213153i
$43$	−3.92870	−	3.92870i	−0.599121	−	0.599121i	0.340958	−	0.940079i	$-0.389249\pi$
$43$	−3.92870	−	3.92870i	−0.599121	−	0.599121i	−0.940079	+	0.340958i	$0.889249\pi$
$44$	3.24231	−	5.11566i	0.488797	−	0.771215i
$45$	1.38900	−	1.75233i	0.207060	−	0.261222i
$46$	0.867993	+	1.57778i	0.127979	+	0.232631i
$47$	−5.85673	+	5.85673i	−0.854292	+	0.854292i	−0.990659	−	0.136366i	$-0.956458\pi$
$47$	−5.85673	+	5.85673i	−0.854292	+	0.854292i	0.136366	+	0.990659i	$0.456458\pi$
$48$	1.35056	−	3.76510i	0.194936	−	0.543446i
$49$		−	5.28267i		−	0.754667i
$50$	−0.368618	+	7.06145i	−0.0521304	+	0.998640i
$51$			3.34225i			0.468009i
$52$	1.00277	−	0.224760i	0.139059	−	0.0311685i
$53$	3.14134	−	3.14134i	0.431496	−	0.431496i	−0.457641	−	0.889137i	$-0.651306\pi$
$53$	3.14134	−	3.14134i	0.431496	−	0.431496i	0.889137	+	0.457641i	$0.151306\pi$
$54$	1.23909	−	0.681664i	0.168618	−	0.0927627i
$55$	−4.20633	+	5.30660i	−0.567181	+	0.715542i
$56$	−9.89367	−	0.613763i	−1.32210	−	0.0820176i
$57$	−3.50466	−	3.50466i	−0.464204	−	0.464204i
$58$	−1.38139	+	4.75995i	−0.181385	+	0.625012i
$59$	−8.68516			−1.13071			−0.565356	−	0.824847i	$-0.691261\pi$
$59$	−8.68516			−1.13071			−0.565356	+	0.824847i	$0.691261\pi$
$60$	−1.94424	+	4.02740i	−0.251000	+	0.519935i
$61$	−15.2920			−1.95794			−0.978970	−	0.204004i	$-0.934604\pi$
$61$	−15.2920			−1.95794			−0.978970	+	0.204004i	$0.934604\pi$
$62$	1.51990	−	5.23723i	0.193027	−	0.665128i
$63$	−2.47817	−	2.47817i	−0.312220	−	0.312220i
$64$	−0.988770	+	7.93866i	−0.123596	+	0.992333i
$65$	−1.14134	+	0.132007i	−0.141565	+	0.0163735i
$66$	−3.75233	+	2.06429i	−0.461880	+	0.254096i
$67$	3.92870	−	3.92870i	0.479967	−	0.479967i	−0.425154	−	0.905121i	$-0.639780\pi$
$67$	3.92870	−	3.92870i	0.479967	−	0.479967i	0.905121	+	0.425154i	$0.139780\pi$
$68$	−1.46199	−	6.52267i	−0.177292	−	0.790989i
$69$		−	1.27334i		−	0.153293i
$70$	10.9280	+	1.84553i	1.30614	+	0.220583i
$71$			4.25583i			0.505075i	0.967587	+	0.252537i	$0.0812650\pi$
$71$			4.25583i			0.505075i	−0.967587	+	0.252537i	$0.918735\pi$
$72$	−2.12000	+	1.87233i	−0.249844	+	0.220656i
$73$	9.28267	−	9.28267i	1.08645	−	1.08645i	0.0905640	−	0.995891i	$-0.471133\pi$
$73$	9.28267	−	9.28267i	1.08645	−	1.08645i	0.995891	−	0.0905640i	$-0.0288670\pi$
$74$	−0.350255	−	0.636672i	−0.0407163	−	0.0740116i
$75$	2.63514	−	4.24924i	0.304280	−	0.490660i
$76$	8.37266	+	5.30660i	0.960410	+	0.608709i
$77$	7.50466	+	7.50466i	0.855236	+	0.855236i
$78$	−0.697863	−	0.202527i	−0.0790174	−	0.0229317i
$79$	−0.399759			−0.0449764			−0.0224882	−	0.999747i	$-0.507159\pi$
$79$	−0.399759			−0.0449764			−0.0224882	+	0.999747i	$0.507159\pi$
$80$	2.03264	−	8.71024i	0.227256	−	0.973835i
$81$	−1.00000			−0.111111
$82$	3.70328	+	1.07473i	0.408959	+	0.118684i
$83$	0.199879	+	0.199879i	0.0219396	+	0.0219396i	0.717991	−	0.696052i	$-0.245062\pi$
$83$	0.199879	+	0.199879i	0.0219396	+	0.0219396i	−0.696052	+	0.717991i	$0.745062\pi$
$84$	5.92036	+	3.75233i	0.645965	+	0.409413i
$85$	0.858664	+	7.42401i	0.0931352	+	0.805247i
$86$	−3.78734	−	6.88438i	−0.408399	−	0.742362i
$87$	2.47817	−	2.47817i	0.265688	−	0.265688i
$88$	6.42000	−	5.66999i	0.684374	−	0.604422i
$89$			4.28267i			0.453962i	0.973899	+	0.226981i	$0.0728856\pi$
$89$			4.28267i			0.453962i	−0.973899	+	0.226981i	$0.927114\pi$
$90$	2.57720	−	1.83249i	0.271661	−	0.193161i
$91$			1.80078i			0.188773i
$92$	0.556993	+	2.48503i	0.0580705	+	0.259082i
$93$	−2.72666	+	2.72666i	−0.282741	+	0.282741i
$94$	−10.2629	+	5.64600i	−1.05854	+	0.582340i
$95$	−8.68516	−	6.88438i	−0.891079	−	0.706323i
$96$	3.31834	−	4.58134i	0.338676	−	0.467581i
$97$	6.73599	+	6.73599i	0.683936	+	0.683936i	0.960885	−	0.276949i	$-0.0893233\pi$
$97$	6.73599	+	6.73599i	0.683936	+	0.683936i	−0.276949	+	0.960885i	$0.589323\pi$
$98$	2.08220	−	7.17480i	0.210334	−	0.724764i
$99$	3.02831			0.304356
$100$	−3.28397	+	9.44540i	−0.328397	+	0.944540i
$101$	5.78734			0.575862			0.287931	−	0.957651i	$-0.407033\pi$
$101$	5.78734			0.575862			0.287931	+	0.957651i	$0.407033\pi$
$102$	−1.31737	+	4.53936i	−0.130439	+	0.449464i
$103$	13.0914	+	13.0914i	1.28993	+	1.28993i	0.934827	+	0.355104i	$0.115555\pi$
$103$	13.0914	+	13.0914i	1.28993	+	1.28993i	0.355104	+	0.934827i	$0.384445\pi$
$104$	1.45052	+	0.0899847i	0.142236	+	0.00882373i
$105$	−6.14134	−	4.86799i	−0.599333	−	0.475067i
$106$	5.50466	−	3.02831i	0.534660	−	0.294135i
$107$	9.71281	−	9.71281i	0.938973	−	0.938973i	−0.0592694	−	0.998242i	$-0.518877\pi$
$107$	9.71281	−	9.71281i	0.938973	−	0.938973i	0.998242	+	0.0592694i	$0.0188771\pi$
$108$	1.95158	−	0.437425i	0.187791	−	0.0420913i
$109$		−	10.4626i		−	1.00214i	−0.865407	−	0.501070i	$-0.832940\pi$
$109$		−	10.4626i		−	1.00214i	0.865407	−	0.501070i	$-0.167060\pi$
$110$	−7.80457	+	5.54934i	−0.744136	+	0.529109i
$111$			0.513824i			0.0487700i
$112$	−13.1954	−	4.73325i	−1.24685	−	0.447251i
$113$	−10.6460	+	10.6460i	−1.00149	+	1.00149i	−0.00149259	+	0.999999i	$0.500475\pi$
$113$	−10.6460	+	10.6460i	−1.00149	+	1.00149i	−0.999999	+	0.00149259i	$0.999525\pi$
$114$	−3.37856	−	6.14134i	−0.316431	−	0.575189i
$115$	−0.327137	−	2.82843i	−0.0305057	−	0.263752i
$116$	−3.75233	+	5.92036i	−0.348395	+	0.549692i
$117$	0.363328	+	0.363328i	0.0335897	+	0.0335897i
$118$	−11.7960	−	3.42331i	−1.08591	−	0.315142i
$119$	11.7135			1.07377
$120$	−4.22804	+	4.70358i	−0.385965	+	0.429376i
$121$	1.82936			0.166305
$122$	−20.7692	−	6.02745i	−1.88036	−	0.545699i
$123$	−1.92804	−	1.92804i	−0.173845	−	0.173845i
$124$	4.12858	−	6.51399i	0.370757	−	0.584974i
$125$	4.76166	−	10.1157i	0.425896	−	0.904772i
$126$	−2.38900	−	4.34258i	−0.212829	−	0.386868i
$127$	1.77766	−	1.77766i	0.157742	−	0.157742i	−0.623823	−	0.781565i	$-0.714422\pi$
$127$	1.77766	−	1.77766i	0.157742	−	0.157742i	0.781565	+	0.623823i	$0.214422\pi$
$128$	−4.47200	+	10.3924i	−0.395273	+	0.918564i
$129$			5.55602i			0.489180i
$130$	−1.60217	−	0.270576i	−0.140519	−	0.0237311i
$131$			18.1981i			1.58997i	0.606626	+	0.794987i	$0.292523\pi$
$131$			18.1981i			1.58997i	−0.606626	+	0.794987i	$0.707477\pi$
$132$	−5.90998	+	1.32466i	−0.514398	+	0.115297i
$133$	−12.2827	+	12.2827i	−1.06504	+	1.06504i
$134$	6.88438	−	3.78734i	0.594720	−	0.327176i
$135$	−2.22126	+	0.256912i	−0.191176	+	0.0221115i
$136$	0.585320	−	9.43517i	0.0501908	−	0.809060i
$137$	−5.91934	−	5.91934i	−0.505724	−	0.505724i	0.407487	−	0.913211i	$-0.366405\pi$
$137$	−5.91934	−	5.91934i	−0.505724	−	0.505724i	−0.913211	+	0.407487i	$0.866405\pi$
$138$	0.501897	−	1.72942i	0.0427243	−	0.147218i
$139$	−12.4140			−1.05294			−0.526470	−	0.850194i	$-0.676485\pi$
$139$	−12.4140			−1.05294			−0.526470	+	0.850194i	$0.676485\pi$
$140$	14.1147	+	6.81389i	1.19291	+	0.575879i
$141$	8.28267			0.697527
$142$	−1.67747	+	5.78017i	−0.140770	+	0.485061i
$143$	−1.10027	−	1.10027i	−0.0920091	−	0.0920091i
$144$	−3.61732	+	1.70734i	−0.301443	+	0.142278i
$145$	4.86799	−	6.14134i	0.404265	−	0.510010i
$146$	16.2663	−	8.94867i	1.34621	−	0.740597i
$147$	−3.73541	+	3.73541i	−0.308092	+	0.308092i
$148$	−0.224760	−	1.00277i	−0.0184751	−	0.0824270i
$149$		−	5.78734i		−	0.474117i	−0.971495	−	0.237059i	$-0.923817\pi$
$149$		−	5.78734i		−	0.474117i	0.971495	−	0.237059i	$-0.0761833\pi$
$150$	5.25385	−	4.73255i	0.428975	−	0.386411i
$151$		−	18.0708i		−	1.47058i	−0.677751	−	0.735292i	$-0.737045\pi$
$151$		−	18.0708i		−	1.47058i	0.677751	−	0.735292i	$-0.262955\pi$
$152$	9.27990	+	10.5074i	0.752700	+	0.852265i
$153$	2.36333	−	2.36333i	0.191064	−	0.191064i
$154$	7.23464	+	13.1507i	0.582984	+	1.05971i
$155$	−5.35610	+	6.75712i	−0.430213	+	0.542745i
$156$	−0.867993	−	0.550135i	−0.0694950	−	0.0440460i
$157$	−3.91934	−	3.91934i	−0.312798	−	0.312798i	0.533195	−	0.845992i	$-0.320991\pi$
$157$	−3.91934	−	3.91934i	−0.312798	−	0.312798i	−0.845992	+	0.533195i	$0.820991\pi$
$158$	−0.542943	−	0.157568i	−0.0431942	−	0.0125354i
$159$	−4.44252			−0.352315
$160$	6.19389	−	11.0289i	0.489670	−	0.871908i
$161$	−4.46264			−0.351705
$162$	−1.35818	−	0.394157i	−0.106708	−	0.0309679i
$163$	3.22819	+	3.22819i	0.252851	+	0.252851i	0.822139	−	0.569287i	$-0.192781\pi$
$163$	3.22819	+	3.22819i	0.252851	+	0.252851i	−0.569287	+	0.822139i	$0.692781\pi$
$164$	4.60609	+	2.91934i	0.359675	+	0.227962i
$165$	6.72666	−	0.778008i	0.523669	−	0.0605678i
$166$	0.192688	+	0.350255i	0.0149555	+	0.0271851i
$167$	6.95700	−	6.95700i	0.538349	−	0.538349i	−0.384695	−	0.923044i	$-0.625693\pi$
$167$	6.95700	−	6.95700i	0.538349	−	0.538349i	0.923044	+	0.384695i	$0.125693\pi$
$168$	6.56188	+	7.42988i	0.506260	+	0.573227i
$169$			12.7360i			0.979691i
$170$	−1.76001	+	10.4216i	−0.134986	+	0.799297i
$171$			4.95634i			0.379021i
$172$	−2.43034	−	10.8430i	−0.185312	−	0.826771i
$173$	0.627343	−	0.627343i	0.0476960	−	0.0476960i	−0.682857	−	0.730553i	$-0.739263\pi$
$173$	0.627343	−	0.627343i	0.0476960	−	0.0476960i	0.730553	+	0.682857i	$0.239263\pi$
$174$	4.34258	−	2.38900i	0.329210	−	0.181110i
$175$	−14.8921	−	9.23530i	−1.12574	−	0.698123i
$176$	10.9543	−	5.17035i	0.825715	−	0.389730i
$177$	6.14134	+	6.14134i	0.461611	+	0.461611i
$178$	−1.68804	+	5.81662i	−0.126524	+	0.435974i
$179$	−8.93968			−0.668183			−0.334091	−	0.942541i	$-0.608429\pi$
$179$	−8.93968			−0.668183			−0.334091	+	0.942541i	$0.608429\pi$
$180$	4.22258	−	1.47302i	0.314733	−	0.109792i
$181$	−1.00933			−0.0750228			−0.0375114	−	0.999296i	$-0.511943\pi$
$181$	−1.00933			−0.0750228			−0.0375114	+	0.999296i	$0.511943\pi$
$182$	−0.709789	+	2.44577i	−0.0526131	+	0.181293i
$183$	10.8131	+	10.8131i	0.799326	+	0.799326i
$184$	−0.222998	+	3.59465i	−0.0164396	+	0.265001i
$185$	0.132007	+	1.14134i	0.00970538	+	0.0839127i
$186$	−4.77801	+	2.62855i	−0.350341	+	0.192734i
$187$	−7.15688	+	7.15688i	−0.523363	+	0.523363i
$188$	−16.1643	+	3.62305i	−1.17890	+	0.264238i
$189$			3.50466i			0.254927i
$190$	−9.08245	−	12.7735i	−0.658910	−	0.926688i
$191$		−	21.6262i		−	1.56481i	−0.622768	−	0.782407i	$-0.713992\pi$
$191$		−	21.6262i		−	1.56481i	0.622768	−	0.782407i	$-0.286008\pi$
$192$	6.31265	−	4.91431i	0.455576	−	0.354660i
$193$	11.5653	−	11.5653i	0.832492	−	0.832492i	−0.155365	−	0.987857i	$-0.549655\pi$
$193$	11.5653	−	11.5653i	0.832492	−	0.832492i	0.987857	+	0.155365i	$0.0496555\pi$
$194$	6.49362	+	11.8037i	0.466214	+	0.847455i
$195$	0.900390	+	0.713703i	0.0644783	+	0.0511093i
$196$	5.65599	−	8.92392i	0.403999	−	0.637423i
$197$	−9.42401	−	9.42401i	−0.671433	−	0.671433i	0.286614	−	0.958046i	$-0.407470\pi$
$197$	−9.42401	−	9.42401i	−0.671433	−	0.671433i	−0.958046	+	0.286614i	$0.907470\pi$
$198$	4.11297	+	1.19363i	0.292296	+	0.0848274i
$199$	11.0130			0.780688			0.390344	−	0.920669i	$-0.372356\pi$
$199$	11.0130			0.780688			0.390344	+	0.920669i	$0.372356\pi$
$200$	−8.18317	+	11.5341i	−0.578638	+	0.815585i
$201$	−5.55602			−0.391891
$202$	7.86022	+	2.28112i	0.553043	+	0.160499i
$203$	−8.68516	−	8.68516i	−0.609579	−	0.609579i
$204$	−3.57844	+	5.64600i	−0.250541	+	0.395299i
$205$	−4.77801	−	3.78734i	−0.333711	−	0.264519i
$206$	12.6203	+	22.9404i	0.879300	+	1.59834i
$207$	−0.900390	+	0.900390i	−0.0625814	+	0.0625814i
$208$	1.93460	+	0.693949i	0.134140	+	0.0481167i
$209$		−	15.0093i		−	1.03822i
$210$	−6.42226	−	9.03224i	−0.443178	−	0.623284i
$211$			27.9835i			1.92646i	0.268669	+	0.963232i	$0.413416\pi$
$211$			27.9835i			1.92646i	−0.268669	+	0.963232i	$0.586584\pi$
$212$	8.66993	−	1.94327i	0.595453	−	0.133464i
$213$	3.00933	−	3.00933i	0.206196	−	0.206196i
$214$	17.0201	−	9.36333i	1.16347	−	0.640064i
$215$	1.42741	+	12.3414i	0.0973483	+	0.841673i
$216$	2.82300	+	0.175128i	0.192081	+	0.0119159i
$217$	9.55602	+	9.55602i	0.648705	+	0.648705i
$218$	4.12392	−	14.2101i	0.279307	−	0.962430i
$219$	−13.1277			−0.887086
$220$	−12.7873	+	4.46075i	−0.862118	+	0.300744i
$221$	−1.71733			−0.115520
$222$	−0.202527	+	0.697863i	−0.0135927	+	0.0468375i
$223$	−8.53479	−	8.53479i	−0.571531	−	0.571531i	0.361025	−	0.932556i	$-0.382427\pi$
$223$	−8.53479	−	8.53479i	−0.571531	−	0.571531i	−0.932556	+	0.361025i	$0.882427\pi$
$224$	−16.0560	−	11.6297i	−1.07279	−	0.777039i
$225$	−4.86799	+	1.14134i	−0.324533	+	0.0760891i
$226$	−18.6553	+	10.2629i	−1.24093	+	0.682681i
$227$	−1.02765	+	1.02765i	−0.0682074	+	0.0682074i	−0.740388	−	0.672180i	$-0.765358\pi$
$227$	−1.02765	+	1.02765i	−0.0682074	+	0.0682074i	0.672180	+	0.740388i	$0.265358\pi$
$228$	−2.16803	−	9.67269i	−0.143581	−	0.640590i
$229$			8.84802i			0.584693i	0.956312	+	0.292347i	$0.0944361\pi$
$229$			8.84802i			0.584693i	−0.956312	+	0.292347i	$0.905564\pi$
$230$	0.670534	−	3.97044i	0.0442137	−	0.261803i
$231$		−	10.6132i		−	0.698297i
$232$	−7.42988	+	6.56188i	−0.487795	+	0.430809i
$233$	−4.91002	+	4.91002i	−0.321666	+	0.321666i	−0.849406	−	0.527740i	$-0.823040\pi$
$233$	−4.91002	+	4.91002i	−0.321666	+	0.321666i	0.527740	+	0.849406i	$0.323040\pi$
$234$	0.350255	+	0.636672i	0.0228969	+	0.0416205i
$235$	18.3980	−	2.12792i	1.20015	−	0.138810i
$236$	−14.6717	−	9.29892i	−0.955045	−	0.605308i
$237$	0.282672	+	0.282672i	0.0183615	+	0.0183615i
$238$	15.9089	+	4.61694i	1.03122	+	0.299272i
$239$	19.0259			1.23068			0.615340	−	0.788262i	$-0.289019\pi$
$239$	19.0259			1.23068			0.615340	+	0.788262i	$0.289019\pi$
$240$	−7.59637	+	4.72178i	−0.490343	+	0.304789i
$241$	2.90663			0.187232			0.0936161	−	0.995608i	$-0.470157\pi$
$241$	2.90663			0.187232			0.0936161	+	0.995608i	$0.470157\pi$
$242$	2.48459	+	0.721054i	0.159716	+	0.0463511i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	−25.8325	−	16.3727i	−1.65376	−	1.04815i
$245$	−7.33765	+	9.25700i	−0.468785	+	0.591408i
$246$	−1.85866	−	3.37856i	−0.118504	−	0.215409i
$247$	1.80078	−	1.80078i	0.114581	−	0.114581i
$248$	8.17486	−	7.21984i	0.519104	−	0.458460i
$249$		−	0.282672i		−	0.0179136i
$250$	10.4543	−	11.8620i	0.661190	−	0.750219i
$251$			2.77379i			0.175080i	0.996161	+	0.0875401i	$0.0279006\pi$
$251$			2.77379i			0.175080i	−0.996161	+	0.0875401i	$0.972099\pi$
$252$	−1.53303	−	6.83963i	−0.0965717	−	0.430856i
$253$	2.72666	−	2.72666i	0.171423	−	0.171423i
$254$	3.11505	−	1.71370i	0.195456	−	0.107527i
$255$	4.64240	−	5.85673i	0.290718	−	0.366763i
$256$	−10.1700	+	12.3520i	−0.635624	+	0.771999i
$257$	−2.08066	−	2.08066i	−0.129788	−	0.129788i	0.639229	−	0.769017i	$-0.279254\pi$
$257$	−2.08066	−	2.08066i	−0.129788	−	0.129788i	−0.769017	+	0.639229i	$0.779254\pi$
$258$	−2.18994	+	7.54604i	−0.136340	+	0.469796i
$259$	1.80078			0.111895
$260$	−2.06937	−	0.998995i	−0.128337	−	0.0619550i
$261$	−3.50466			−0.216933
$262$	−7.17290	+	24.7162i	−0.443143	+	1.52697i
$263$	4.75646	+	4.75646i	0.293296	+	0.293296i	0.838381	−	0.545085i	$-0.183503\pi$
$263$	4.75646	+	4.75646i	0.293296	+	0.293296i	−0.545085	+	0.838381i	$0.683503\pi$
$264$	−8.54891	−	0.530340i	−0.526149	−	0.0326402i
$265$	−9.86799	+	1.14134i	−0.606186	+	0.0701117i
$266$	−21.5233	+	11.8407i	−1.31968	+	0.726001i
$267$	3.02831	−	3.02831i	0.185329	−	0.185329i
$268$	10.8430	−	2.43034i	0.662342	−	0.148457i
$269$			21.6846i			1.32214i	0.750326	+	0.661068i	$0.229896\pi$
$269$			21.6846i			1.32214i	−0.750326	+	0.661068i	$0.770104\pi$
$270$	−3.11812	−	0.526593i	−0.189763	−	0.0320474i
$271$			3.15556i			0.191687i	0.995396	+	0.0958434i	$0.0305548\pi$
$271$			3.15556i			0.191687i	−0.995396	+	0.0958434i	$0.969445\pi$
$272$	4.51391	−	12.5839i	0.273696	−	0.763012i
$273$	1.27334	−	1.27334i	0.0770663	−	0.0770663i
$274$	−5.70636	−	10.3727i	−0.344734	−	0.626635i
$275$	14.7418	−	3.45632i	0.888962	−	0.208424i
$276$	1.36333	−	2.15103i	0.0820627	−	0.129477i
$277$	−3.53397	−	3.53397i	−0.212336	−	0.212336i	0.592923	−	0.805259i	$-0.297974\pi$
$277$	−3.53397	−	3.53397i	−0.212336	−	0.212336i	−0.805259	+	0.592923i	$0.797974\pi$
$278$	−16.8604	−	4.89305i	−1.01122	−	0.293466i
$279$	3.85607			0.230857
$280$	16.4845	+	14.8179i	0.985136	+	0.885537i
$281$	0.179969			0.0107361			0.00536804	−	0.999986i	$-0.498291\pi$
$281$	0.179969			0.0107361			0.00536804	+	0.999986i	$0.498291\pi$
$282$	11.2493	+	3.26467i	0.669887	+	0.194408i
$283$	−9.84007	−	9.84007i	−0.584931	−	0.584931i	0.351323	−	0.936254i	$-0.385732\pi$
$283$	−9.84007	−	9.84007i	−0.584931	−	0.584931i	−0.936254	+	0.351323i	$0.885732\pi$
$284$	−4.55658	+	7.18930i	−0.270384	+	0.426606i
$285$	1.27334	+	11.0093i	0.0754264	+	0.652136i
$286$	−1.06068	−	1.92804i	−0.0627193	−	0.114007i
$287$	−6.75712	+	6.75712i	−0.398860	+	0.398860i
$288$	−5.58591	+	0.893077i	−0.329153	+	0.0526250i
$289$		−	5.82936i		−	0.342903i
$290$	9.03224	−	6.42226i	0.530391	−	0.377128i
$291$		−	9.52612i		−	0.558431i
$292$	25.6197	−	5.74238i	1.49928	−	0.336047i
$293$	15.8680	−	15.8680i	0.927018	−	0.927018i	−0.0704942	−	0.997512i	$-0.522458\pi$
$293$	15.8680	−	15.8680i	0.927018	−	0.927018i	0.997512	+	0.0704942i	$0.0224576\pi$
$294$	−6.54569	+	3.60101i	−0.381752	+	0.210015i
$295$	15.2193	+	12.0637i	0.886101	+	0.702377i
$296$	0.0899847	−	1.45052i	0.00523026	−	0.0843100i
$297$	−2.14134	−	2.14134i	−0.124253	−	0.124253i
$298$	2.28112	−	7.86022i	0.132142	−	0.455330i
$299$	0.654274			0.0378376
$300$	9.00102	−	4.35679i	0.519674	−	0.251539i
$301$	19.4720			1.12235
$302$	7.12274	−	24.5434i	0.409868	−	1.41231i
$303$	−4.09226	−	4.09226i	−0.235094	−	0.235094i
$304$	8.46216	+	17.9287i	0.485338	+	1.02828i
$305$	26.7967	+	21.2406i	1.53437	+	1.21624i
$306$	4.14134	−	2.27829i	0.236744	−	0.130241i
$307$	−7.78477	+	7.78477i	−0.444300	+	0.444300i	−0.893454	−	0.449154i	$-0.851725\pi$
$307$	−7.78477	+	7.78477i	−0.444300	+	0.444300i	0.449154	+	0.893454i	$0.351725\pi$
$308$	4.64248	+	20.7125i	0.264530	+	1.18020i
$309$		−	18.5140i		−	1.05322i
$310$	−9.93789	+	7.06621i	−0.564434	+	0.401334i
$311$		−	7.05788i		−	0.400215i	−0.979774	−	0.200108i	$-0.935871\pi$
$311$		−	7.05788i		−	0.400215i	0.979774	−	0.200108i	$-0.0641292\pi$
$312$	−0.962047	−	1.08930i	−0.0544652	−	0.0616697i
$313$	−11.3013	+	11.3013i	−0.638789	+	0.638789i	−0.950257	−	0.311468i	$-0.899179\pi$
$313$	−11.3013	+	11.3013i	−0.638789	+	0.638789i	0.311468	+	0.950257i	$0.399179\pi$
$314$	−3.77832	−	6.86799i	−0.213223	−	0.387583i
$315$	0.900390	+	7.78477i	0.0507312	+	0.438622i
$316$	−0.675305	−	0.428009i	−0.0379889	−	0.0240774i
$317$	19.4754	+	19.4754i	1.09385	+	1.09385i	0.995114	+	0.0987310i	$0.0314783\pi$
$317$	19.4754	+	19.4754i	1.09385	+	1.09385i	0.0987310	+	0.995114i	$0.468522\pi$
$318$	−6.03372	−	1.75105i	−0.338354	−	0.0981940i
$319$	10.6132			0.594225
$320$	12.7595	−	12.5378i	0.713277	−	0.700882i
$321$	−13.7360			−0.766668
$322$	−6.06105	−	1.75898i	−0.337769	−	0.0980241i
$323$	−11.7135	−	11.7135i	−0.651755	−	0.651755i
$324$	−1.68928	−	1.07067i	−0.0938489	−	0.0594816i
$325$	2.18336	+	1.35400i	0.121111	+	0.0751064i
$326$	3.11203	+	5.65685i	0.172359	+	0.313304i
$327$	−7.39820	+	7.39820i	−0.409122	+	0.409122i
$328$	5.10520	+	5.78050i	0.281887	+	0.319175i
$329$		−	29.0280i		−	1.60036i
$330$	9.44264	+	1.59469i	0.519800	+	0.0877846i
$331$		−	15.0143i		−	0.825259i	−0.910899	−	0.412630i	$-0.864610\pi$
$331$		−	15.0143i		−	0.825259i	0.910899	−	0.412630i	$-0.135390\pi$
$332$	0.123648	+	0.551657i	0.00678607	+	0.0302761i
$333$	0.363328	−	0.363328i	0.0199103	−	0.0199103i
$334$	12.1910	−	6.70668i	0.667061	−	0.366973i
$335$	−12.3414	+	1.42741i	−0.674280	+	0.0779875i
$336$	5.98365	+	12.6775i	0.326435	+	0.691614i
$337$	−21.5840	−	21.5840i	−1.17576	−	1.17576i	−0.980815	−	0.194940i	$-0.937549\pi$
$337$	−21.5840	−	21.5840i	−1.17576	−	1.17576i	−0.194940	−	0.980815i	$-0.562451\pi$
$338$	−5.01997	+	17.2977i	−0.273051	+	0.940871i
$339$	15.0557			0.817714
$340$	−6.49812	+	13.4606i	−0.352410	+	0.730002i
$341$	−11.6774			−0.632365
$342$	−1.95358	+	6.73158i	−0.105637	+	0.364002i
$343$	−4.25583	−	4.25583i	−0.229793	−	0.229793i
$344$	0.973012	−	15.6846i	0.0524613	−	0.845659i
$345$	−1.76868	+	2.23132i	−0.0952225	+	0.120130i
$346$	1.09931	−	0.604770i	0.0590995	−	0.0325127i
$347$	−16.9969	+	16.9969i	−0.912444	+	0.912444i	−0.996464	−	0.0840201i	$-0.973224\pi$
$347$	−16.9969	+	16.9969i	−0.912444	+	0.912444i	0.0840201	+	0.996464i	$0.473224\pi$
$348$	6.83963	−	1.53303i	0.366643	−	0.0821790i
$349$		−	4.38538i		−	0.234744i	−0.993088	−	0.117372i	$-0.962553\pi$
$349$		−	4.38538i		−	0.234744i	0.993088	−	0.117372i	$-0.0374469\pi$
$350$	−16.5860	−	18.4130i	−0.886559	−	0.984216i
$351$		−	0.513824i		−	0.0274259i
$352$	16.9159	−	2.70451i	0.901618	−	0.144151i
$353$	−2.62734	+	2.62734i	−0.139839	+	0.139839i	−0.773561	−	0.633722i	$-0.781526\pi$
$353$	−2.62734	+	2.62734i	−0.139839	+	0.139839i	0.633722	+	0.773561i	$0.281526\pi$
$354$	5.92036	+	10.7617i	0.314664	+	0.571976i
$355$	5.91137	−	7.45763i	0.313743	−	0.395810i
$356$	−4.58532	+	7.23464i	−0.243021	+	0.383435i
$357$	−8.28267	−	8.28267i	−0.438366	−	0.438366i
$358$	−12.1416	−	3.52363i	−0.641706	−	0.186230i
$359$	−34.9952			−1.84697			−0.923487	−	0.383630i	$-0.874674\pi$
$359$	−34.9952			−1.84697			−0.923487	+	0.383630i	$0.874674\pi$
$360$	6.31561	−	0.336258i	0.332862	−	0.0177224i
$361$	5.56534			0.292913
$362$	−1.37085	−	0.397834i	−0.0720500	−	0.0209097i
$363$	−1.29355	−	1.29355i	−0.0678939	−	0.0678939i
$364$	−1.92804	+	3.04202i	−0.101057	+	0.159445i
$365$	−29.1600	+	3.37266i	−1.52630	+	0.176533i
$366$	10.4240	+	18.9481i	0.544872	+	0.990433i
$367$	−9.93581	+	9.93581i	−0.518645	+	0.518645i	−0.917161	−	0.398516i	$-0.869525\pi$
$367$	−9.93581	+	9.93581i	−0.518645	+	0.518645i	0.398516	+	0.917161i	$0.369525\pi$
$368$	−1.71973	+	4.79427i	−0.0896469	+	0.249918i
$369$			2.72666i			0.141944i
$370$	−0.270576	+	1.60217i	−0.0140666	+	0.0832927i
$371$			15.5695i			0.808330i
$372$	−7.52543	+	1.68674i	−0.390176	+	0.0874536i
$373$	−7.08998	+	7.08998i	−0.367105	+	0.367105i	−0.866421	−	0.499315i	$-0.833585\pi$
$373$	−7.08998	+	7.08998i	−0.367105	+	0.367105i	0.499315	+	0.866421i	$0.333585\pi$
$374$	−12.5412	+	6.89937i	−0.648492	+	0.356758i
$375$	−10.5199	+	3.78585i	−0.543243	+	0.195500i
$376$	−23.3820	−	1.45052i	−1.20583	−	0.0748051i
$377$	1.27334	+	1.27334i	0.0655805	+	0.0655805i
$378$	−1.38139	+	4.75995i	−0.0710509	+	0.244825i
$379$	−30.0388			−1.54299			−0.771495	−	0.636235i	$-0.780491\pi$
$379$	−30.0388			−1.54299			−0.771495	+	0.636235i	$0.780491\pi$
$380$	−7.30079	−	20.9286i	−0.374523	−	1.07361i
$381$	−2.51399			−0.128796
$382$	8.52410	−	29.3721i	0.436131	−	1.50281i
$383$	11.9133	+	11.9133i	0.608744	+	0.608744i	0.942618	−	0.333874i	$-0.108356\pi$
$383$	11.9133	+	11.9133i	0.608744	+	0.608744i	−0.333874	+	0.942618i	$0.608356\pi$
$384$	10.5107	−	4.18633i	0.536372	−	0.213633i
$385$	−2.72666	−	23.5747i	−0.138963	−	1.20148i
$386$	20.2663	−	11.1492i	1.03153	−	0.567480i
$387$	3.92870	−	3.92870i	0.199707	−	0.199707i
$388$	4.16697	+	18.5910i	0.211546	+	0.943814i
$389$			16.3340i			0.828168i	0.910239	+	0.414084i	$0.135898\pi$
$389$			16.3340i			0.828168i	−0.910239	+	0.414084i	$0.864102\pi$
$390$	0.941576	+	1.32423i	0.0476786	+	0.0670549i
$391$		−	4.25583i		−	0.215227i
$392$	11.1992	−	9.89090i	0.565647	−	0.499566i
$393$	12.8680	−	12.8680i	0.649104	−	0.649104i
$394$	−9.08492	−	16.5140i	−0.457692	−	0.831963i
$395$	0.700510	+	0.555267i	0.0352465	+	0.0279385i
$396$	5.11566	+	3.24231i	0.257072	+	0.162932i
$397$	−19.1927	−	19.1927i	−0.963253	−	0.963253i	0.0360950	−	0.999348i	$-0.488508\pi$
$397$	−19.1927	−	19.1927i	−0.963253	−	0.963253i	−0.999348	+	0.0360950i	$0.988508\pi$
$398$	14.9575	+	4.34083i	0.749753	+	0.217586i
$399$	17.3703			0.869604
$400$	−15.6604	+	12.4399i	−0.783021	+	0.621995i
$401$	26.5653			1.32661			0.663305	−	0.748349i	$-0.269153\pi$
$401$	26.5653			1.32661			0.663305	+	0.748349i	$0.269153\pi$
$402$	−7.54604	−	2.18994i	−0.376362	−	0.109224i
$403$	−1.40102	−	1.40102i	−0.0697898	−	0.0697898i
$404$	9.77644	+	6.19632i	0.486396	+	0.308278i
$405$	1.75233	+	1.38900i	0.0870741	+	0.0690202i
$406$	−8.37266	−	15.2193i	−0.415528	−	0.755321i
$407$	−1.10027	+	1.10027i	−0.0545383	+	0.0545383i
$408$	−7.08556	+	6.25779i	−0.350787	+	0.309807i
$409$			25.3947i			1.25569i	0.778339	+	0.627844i	$0.216062\pi$
$409$			25.3947i			1.25569i	−0.778339	+	0.627844i	$0.783938\pi$
$410$	−4.99657	−	7.02715i	−0.246763	−	0.347046i
$411$			8.37122i			0.412922i
$412$	8.09849	+	36.1315i	0.398984	+	1.78007i
$413$	21.5233	−	21.5233i	1.05909	−	1.05909i
$414$	−1.57778	+	0.867993i	−0.0775438	+	0.0426595i
$415$	−0.0726218	−	0.627889i	−0.00356487	−	0.0308218i
$416$	2.35400	+	1.70504i	0.115414	+	0.0835964i
$417$	8.77801	+	8.77801i	0.429861	+	0.429861i
$418$	5.91603	−	20.3853i	0.289362	−	0.997078i
$419$	40.0788			1.95798			0.978988	−	0.203919i	$-0.0653679\pi$
$419$	40.0788			1.95798			0.978988	+	0.203919i	$0.0653679\pi$
$420$	−5.16244	−	14.7987i	−0.251901	−	0.722105i
$421$	19.3947			0.945240			0.472620	−	0.881266i	$-0.343308\pi$
$421$	19.3947			0.945240			0.472620	+	0.881266i	$0.343308\pi$
$422$	−11.0299	+	38.0065i	−0.536927	+	1.85013i
$423$	−5.85673	−	5.85673i	−0.284764	−	0.284764i
$424$	12.5412	+	0.778008i	0.609056	+	0.0377834i
$425$	8.80731	−	14.2020i	0.427217	−	0.688899i
$426$	5.27334	−	2.90105i	0.255494	−	0.140556i
$427$	37.8962	−	37.8962i	1.83393	−	1.83393i
$428$	26.8069	−	6.00847i	1.29576	−	0.290430i
$429$			1.55602i			0.0751251i
$430$	−2.92576	+	17.3243i	−0.141093	+	0.835454i
$431$		−	15.8241i		−	0.762218i	−0.924530	−	0.381109i	$-0.875542\pi$
$431$		−	15.8241i		−	0.762218i	0.924530	−	0.381109i	$-0.124458\pi$
$432$	3.76510	+	1.35056i	0.181149	+	0.0649788i
$433$	−21.1214	+	21.1214i	−1.01503	+	1.01503i	−0.0151424	+	0.999885i	$0.504820\pi$
$433$	−21.1214	+	21.1214i	−1.01503	+	1.01503i	−0.999885	+	0.0151424i	$0.995180\pi$
$434$	9.21218	+	16.7453i	0.442199	+	0.803801i
$435$	−7.78477	+	0.900390i	−0.373251	+	0.0431704i
$436$	11.2020	−	17.6743i	0.536479	−	0.846447i
$437$	4.46264	+	4.46264i	0.213477	+	0.213477i
$438$	−17.8297	−	5.17436i	−0.851936	−	0.247241i
$439$	−6.61188			−0.315568			−0.157784	−	0.987474i	$-0.550435\pi$
$439$	−6.61188			−0.315568			−0.157784	+	0.987474i	$0.550435\pi$
$440$	−19.1256	+	1.01829i	−0.911777	+	0.0485452i
$441$	5.28267			0.251556
$442$	−2.33243	−	0.676896i	−0.110942	−	0.0321967i
$443$	14.5419	+	14.5419i	0.690906	+	0.690906i	0.962431	−	0.271525i	$-0.0875280\pi$
$443$	14.5419	+	14.5419i	0.690906	+	0.690906i	−0.271525	+	0.962431i	$0.587528\pi$
$444$	−0.550135	+	0.867993i	−0.0261082	+	0.0411931i
$445$	5.94865	−	7.50466i	0.281993	−	0.355755i
$446$	−8.22769	−	14.9558i	−0.389593	−	0.708177i
$447$	−4.09226	+	4.09226i	−0.193557	+	0.193557i
$448$	−17.2230	−	22.1237i	−0.813711	−	1.04525i
$449$			33.6120i			1.58625i	0.609060	+	0.793124i	$0.291547\pi$
$449$			33.6120i			1.58625i	−0.609060	+	0.793124i	$0.708453\pi$
$450$	−7.06145	−	0.368618i	−0.332880	−	0.0173768i
$451$		−	8.25715i		−	0.388814i
$452$	−29.3824	+	6.58575i	−1.38203	+	0.309768i
$453$	−12.7780	+	12.7780i	−0.600363	+	0.600363i
$454$	−1.80078	+	0.990671i	−0.0845148	+	0.0464945i
$455$	2.50129	−	3.15556i	0.117262	−	0.147935i
$456$	0.867993	−	13.9918i	0.0406475	−	0.655224i
$457$	15.5653	+	15.5653i	0.728116	+	0.728116i	0.970244	−	0.242128i	$-0.0778454\pi$
$457$	15.5653	+	15.5653i	0.728116	+	0.728116i	−0.242128	+	0.970244i	$0.577845\pi$
$458$	−3.48751	+	12.0172i	−0.162960	+	0.561525i
$459$	−3.34225			−0.156003
$460$	2.47568	−	5.12826i	0.115429	−	0.239106i
$461$	−26.1473			−1.21780			−0.608900	−	0.793247i	$-0.708389\pi$
$461$	−26.1473			−1.21780			−0.608900	+	0.793247i	$0.708389\pi$
$462$	4.18326	−	14.4146i	0.194623	−	0.670627i
$463$	5.77898	+	5.77898i	0.268572	+	0.268572i	0.828525	−	0.559953i	$-0.189181\pi$
$463$	5.77898	+	5.77898i	0.268572	+	0.268572i	−0.559953	+	0.828525i	$0.689181\pi$
$464$	−12.6775	+	5.98365i	−0.588538	+	0.277784i
$465$	8.56534	−	0.990671i	0.397208	−	0.0459413i
$466$	−8.60398	+	4.73335i	−0.398572	+	0.219268i
$467$	2.25517	−	2.25517i	0.104357	−	0.104357i	−0.653000	−	0.757357i	$-0.726490\pi$
$467$	2.25517	−	2.25517i	0.104357	−	0.104357i	0.757357	+	0.653000i	$0.226490\pi$
$468$	0.224760	+	1.00277i	0.0103895	+	0.0463529i
$469$			19.4720i			0.899132i
$470$	25.8264	+	4.36160i	1.19128	+	0.201186i
$471$			5.54279i			0.255398i
$472$	−16.2615	−	18.4125i	−0.748495	−	0.847505i
$473$	−11.8973	+	11.8973i	−0.547038	+	0.547038i
$474$	0.272501	+	0.495336i	0.0125164	+	0.0227515i
$475$	5.65685	+	24.1274i	0.259554	+	1.10704i
$476$	19.7873	+	12.5412i	0.906951	+	0.574827i
$477$	3.14134	+	3.14134i	0.143832	+	0.143832i
$478$	25.8405	+	7.49917i	1.18191	+	0.343004i
$479$	1.40102			0.0640143			0.0320071	−	0.999488i	$-0.489810\pi$
$479$	1.40102			0.0640143			0.0320071	+	0.999488i	$0.489810\pi$
$480$	−12.1783	+	3.41884i	−0.555862	+	0.156048i
$481$	−0.264015			−0.0120380
$482$	3.94771	+	1.14567i	0.179813	+	0.0521837i
$483$	3.15556	+	3.15556i	0.143583	+	0.143583i
$484$	3.09030	+	1.95864i	0.140468	+	0.0890289i
$485$	−2.44737	−	21.1600i	−0.111130	−	0.960826i
$486$	0.681664	+	1.23909i	0.0309209	+	0.0562061i
$487$	0.978144	−	0.978144i	0.0443239	−	0.0443239i	−0.684597	−	0.728921i	$-0.740022\pi$
$487$	0.978144	−	0.978144i	0.0443239	−	0.0443239i	0.728921	+	0.684597i	$0.240022\pi$
$488$	−28.6317	−	32.4190i	−1.29609	−	1.46754i
$489$		−	4.56534i		−	0.206452i
$490$	−13.6145	+	9.68044i	−0.615042	+	0.437318i
$491$		−	36.1134i		−	1.62978i	−0.579619	−	0.814888i	$-0.696799\pi$
$491$		−	36.1134i		−	1.62978i	0.579619	−	0.814888i	$-0.303201\pi$
$492$	−1.19271	−	5.32128i	−0.0537715	−	0.239902i
$493$	8.28267	−	8.28267i	0.373033	−	0.373033i
$494$	3.15556	−	1.73599i	0.141976	−	0.0781057i
$495$	−5.30660	−	4.20633i	−0.238514	−	0.189060i
$496$	13.9486	−	6.58363i	0.626313	−	0.295614i
$497$	−10.5467	−	10.5467i	−0.473084	−	0.473084i
$498$	0.111417	−	0.383918i	0.00499272	−	0.0172038i
$499$	6.35736			0.284595			0.142297	−	0.989824i	$-0.454551\pi$
$499$	6.35736			0.284595			0.142297	+	0.989824i	$0.454551\pi$
$500$	18.8743	−	11.9900i	0.844084	−	0.536211i
$501$	−9.83869			−0.439560
$502$	−1.09331	+	3.76730i	−0.0487968	+	0.168143i
$503$	17.1704	+	17.1704i	0.765592	+	0.765592i	0.977327	−	0.211735i	$-0.0679114\pi$
$503$	17.1704	+	17.1704i	0.765592	+	0.765592i	−0.211735	+	0.977327i	$0.567911\pi$
$504$	0.613763	−	9.89367i	0.0273392	−	0.440699i
$505$	−10.1413	−	8.03863i	−0.451284	−	0.357714i
$506$	4.77801	−	2.62855i	0.212408	−	0.116853i
$507$	9.00570	−	9.00570i	0.399957	−	0.399957i
$508$	4.90626	−	1.09968i	0.217680	−	0.0487906i
$509$		−	18.8739i		−	0.836572i	−0.908315	−	0.418286i	$-0.862631\pi$
$509$		−	18.8739i		−	0.836572i	0.908315	−	0.418286i	$-0.137369\pi$
$510$	8.61366	−	6.12464i	0.381419	−	0.271204i
$511$			46.0081i			2.03528i
$512$	−18.6812	+	12.7676i	−0.825602	+	0.564253i
$513$	3.50466	−	3.50466i	0.154735	−	0.154735i
$514$	−2.00579	−	3.64600i	−0.0884717	−	0.160818i
$515$	−4.75646	−	41.1244i	−0.209595	−	1.81216i
$516$	−5.94865	+	9.38567i	−0.261875	+	0.413181i
$517$	17.7360	+	17.7360i	0.780028	+	0.780028i
$518$	2.44577	+	0.709789i	0.107461	+	0.0311864i
$519$	−0.887197			−0.0389436
$520$	−2.41681	−	2.17247i	−0.105984	−	0.0952690i
$521$	−33.9346			−1.48670			−0.743351	−	0.668901i	$-0.766765\pi$
$521$	−33.9346			−1.48670			−0.743351	+	0.668901i	$0.766765\pi$
$522$	−4.75995	−	1.38139i	−0.208337	−	0.0604617i
$523$	3.78345	+	3.78345i	0.165439	+	0.165439i	0.784971	−	0.619532i	$-0.212678\pi$
$523$	3.78345	+	3.78345i	0.165439	+	0.165439i	−0.619532	+	0.784971i	$0.712678\pi$
$524$	−19.4841	+	30.7417i	−0.851167	+	1.34296i
$525$	4.00000	+	17.0607i	0.174574	+	0.744589i
$526$	4.58532	+	8.33491i	0.199929	+	0.363419i
$527$	−9.11317	+	9.11317i	−0.396976	+	0.396976i
$528$	−11.4019	−	4.08991i	−0.496203	−	0.177990i
$529$		−	21.3786i		−	0.929504i
$530$	−13.8523	−	2.33940i	−0.601707	−	0.101617i
$531$		−	8.68516i		−	0.376904i
$532$	−33.8995	+	7.59822i	−1.46973	+	0.329425i
$533$	0.990671	−	0.990671i	0.0429107	−	0.0429107i
$534$	5.30660	−	2.91934i	0.229639	−	0.126332i
$535$	−30.5112	+	3.52894i	−1.31911	+	0.152569i
$536$	15.6846	+	0.973012i	0.677473	+	0.0420277i
$537$	6.32131	+	6.32131i	0.272784	+	0.272784i
$538$	−8.54715	+	29.4515i	−0.368494	+	1.26975i
$539$	−15.9976			−0.689063
$540$	−4.02740	−	1.94424i	−0.173312	−	0.0836666i
$541$	28.4813			1.22451			0.612253	−	0.790662i	$-0.290263\pi$
$541$	28.4813			1.22451			0.612253	+	0.790662i	$0.290263\pi$
$542$	−1.24379	+	4.28581i	−0.0534252	+	0.184091i
$543$	0.713703	+	0.713703i	0.0306279	+	0.0306279i
$544$	11.0907	−	15.3120i	0.475510	−	0.656496i
$545$	−14.5327	+	18.3340i	−0.622510	+	0.785343i
$546$	2.23132	−	1.22753i	0.0954917	−	0.0525333i
$547$	0.726896	−	0.726896i	0.0310798	−	0.0310798i	−0.691396	−	0.722476i	$-0.743004\pi$
$547$	0.726896	−	0.726896i	0.0310798	−	0.0310798i	0.722476	+	0.691396i	$0.243004\pi$
$548$	−3.66178	−	16.3371i	−0.156424	−	0.697886i
$549$		−	15.2920i		−	0.652647i
$550$	21.3842	+	1.11629i	0.911827	+	0.0475986i
$551$			17.3703i			0.740001i
$552$	2.69948	−	2.38412i	0.114898	−	0.101475i
$553$	0.990671	−	0.990671i	0.0421276	−	0.0421276i
$554$	−3.40681	−	6.19269i	−0.144742	−	0.263102i
$555$	0.713703	−	0.900390i	0.0302950	−	0.0382194i
$556$	−20.9707	−	13.2912i	−0.889356	−	0.563675i
$557$	−11.4427	−	11.4427i	−0.484841	−	0.484841i	0.421832	−	0.906674i	$-0.361387\pi$
$557$	−11.4427	−	11.4427i	−0.484841	−	0.484841i	−0.906674	+	0.421832i	$0.861387\pi$
$558$	5.23723	+	1.51990i	0.221709	+	0.0643424i
$559$	−2.85481			−0.120746
$560$	16.5482	+	26.6227i	0.699291	+	1.12502i
$561$	10.1214			0.427324
$562$	0.244430	+	0.0709362i	0.0103107	+	0.00299226i
$563$	−7.08426	−	7.08426i	−0.298566	−	0.298566i	0.541886	−	0.840452i	$-0.317710\pi$
$563$	−7.08426	−	7.08426i	−0.298566	−	0.298566i	−0.840452	+	0.541886i	$0.817710\pi$
$564$	13.9918	+	8.86799i	0.589159	+	0.373410i
$565$	33.4427	−	3.86799i	1.40694	−	0.162728i
$566$	−9.48601	−	17.2431i	−0.398727	−	0.724780i
$567$	2.47817	−	2.47817i	0.104073	−	0.104073i
$568$	−9.02235	+	7.96832i	−0.378569	+	0.334343i
$569$		−	46.2427i		−	1.93860i	−0.245890	−	0.969298i	$-0.579080\pi$
$569$		−	46.2427i		−	1.93860i	0.245890	−	0.969298i	$-0.420920\pi$
$570$	−2.60998	+	15.4545i	−0.109320	+	0.647318i
$571$			31.2381i			1.30727i	0.756808	+	0.653637i	$0.226758\pi$
$571$			31.2381i			1.30727i	−0.756808	+	0.653637i	$0.773242\pi$
$572$	−0.680641	−	3.03669i	−0.0284590	−	0.126970i
$573$	−15.2920	+	15.2920i	−0.638833	+	0.638833i
$574$	−11.8407	+	6.51399i	−0.494222	+	0.271889i
$575$	−3.35544	+	5.41074i	−0.139932	+	0.225643i
$576$	−7.93866	−	0.988770i	−0.330778	−	0.0411988i
$577$	1.16131	+	1.16131i	0.0483461	+	0.0483461i	0.730866	−	0.682520i	$-0.239116\pi$
$577$	1.16131	+	1.16131i	0.0483461	+	0.0483461i	−0.682520	+	0.730866i	$0.739116\pi$
$578$	2.29768	−	7.91729i	0.0955709	−	0.329316i
$579$	−16.3559			−0.679727
$580$	14.7987	−	5.16244i	0.614484	−	0.214359i
$581$	−0.990671			−0.0411000
$582$	3.75479	−	12.9381i	0.155641	−	0.536303i
$583$	−9.51293	−	9.51293i	−0.393985	−	0.393985i
$584$	37.0594	+	2.29902i	1.53353	+	0.0951341i
$585$	−0.132007	−	1.14134i	−0.00545783	−	0.0471884i
$586$	27.8060	−	15.2970i	1.14866	−	0.631915i
$587$	23.6268	−	23.6268i	0.975183	−	0.975183i	−0.0245164	−	0.999699i	$-0.507805\pi$
$587$	23.6268	−	23.6268i	0.975183	−	0.975183i	0.999699	+	0.0245164i	$0.00780461\pi$
$588$	−10.3096	+	2.31077i	−0.425159	+	0.0952947i
$589$		−	19.1120i		−	0.787498i
$590$	15.9155	+	22.3834i	0.655229	+	0.921511i
$591$			13.3276i			0.548223i
$592$	0.693949	−	1.93460i	0.0285211	−	0.0795115i
$593$	−0.260625	+	0.260625i	−0.0107026	+	0.0107026i	−0.712438	−	0.701735i	$-0.752409\pi$
$593$	−0.260625	+	0.260625i	−0.0107026	+	0.0107026i	0.701735	+	0.712438i	$0.252409\pi$
$594$	−2.06429	−	3.75233i	−0.0846988	−	0.153960i
$595$	−20.5259	−	16.2701i	−0.841479	−	0.667007i
$596$	6.19632	−	9.77644i	0.253811	−	0.400458i
$597$	−7.78734	−	7.78734i	−0.318714	−	0.318714i
$598$	0.888619	+	0.257887i	0.0363383	+	0.0105458i
$599$	−33.0851			−1.35182			−0.675910	−	0.736984i	$-0.736249\pi$
$599$	−33.0851			−1.35182			−0.675910	+	0.736984i	$0.736249\pi$
$600$	13.9422	−	2.36947i	0.569189	−	0.0967333i
$601$	−24.3200			−0.992033			−0.496016	−	0.868313i	$-0.665204\pi$
$601$	−24.3200			−0.992033			−0.496016	+	0.868313i	$0.665204\pi$
$602$	26.4464	+	7.67501i	1.07787	+	0.312810i
$603$	3.92870	+	3.92870i	0.159989	+	0.159989i
$604$	19.3479	−	30.5267i	0.787253	−	1.24211i
$605$	−3.20565	−	2.54099i	−0.130328	−	0.103306i
$606$	−3.94502	−	7.17101i	−0.160255	−	0.291302i
$607$	−4.53347	+	4.53347i	−0.184008	+	0.184008i	−0.793100	−	0.609092i	$-0.791534\pi$
$607$	−4.53347	+	4.53347i	−0.184008	+	0.184008i	0.609092	+	0.793100i	$0.291534\pi$
$608$	4.42639	+	27.6857i	0.179514	+	1.12280i
$609$			12.2827i			0.497719i
$610$	28.0224	+	39.4106i	1.13459	+	1.59569i
$611$			4.25583i			0.172173i
$612$	6.52267	−	1.46199i	0.263663	−	0.0590972i
$613$	−20.2793	+	20.2793i	−0.819073	+	0.819073i	−0.985974	−	0.166901i	$-0.946624\pi$
$613$	−20.2793	+	20.2793i	−0.819073	+	0.819073i	0.166901	+	0.985974i	$0.446624\pi$
$614$	−13.6415	+	7.50466i	−0.550526	+	0.302864i
$615$	0.700510	+	6.05661i	0.0282473	+	0.244226i
$616$	−1.85866	+	29.9611i	−0.0748877	+	1.20717i
$617$	17.1086	+	17.1086i	0.688768	+	0.688768i	0.961960	−	0.273192i	$-0.0880793\pi$
$617$	17.1086	+	17.1086i	0.688768	+	0.688768i	−0.273192	+	0.961960i	$0.588079\pi$
$618$	7.29742	−	25.1453i	0.293545	−	1.01149i
$619$	29.4373			1.18319			0.591593	−	0.806237i	$-0.298499\pi$
$619$	29.4373			1.18319			0.591593	+	0.806237i	$0.298499\pi$
$620$	−16.2826	+	5.68007i	−0.653925	+	0.228117i
$621$	1.27334			0.0510975
$622$	2.78191	−	9.58583i	0.111544	−	0.384357i
$623$	−10.6132	−	10.6132i	−0.425209	−	0.425209i
$624$	−0.877272	−	1.85866i	−0.0351190	−	0.0744061i
$625$	−22.3947	+	11.1120i	−0.895788	+	0.444481i
$626$	−19.8037	+	10.8947i	−0.791514	+	0.435439i
$627$	−10.6132	+	10.6132i	−0.423850	+	0.423850i
$628$	−2.42456	−	10.8172i	−0.0967503	−	0.431653i
$629$			1.71733i			0.0684743i
$630$	−1.84553	+	10.9280i	−0.0735278	+	0.435381i
$631$		−	5.25710i		−	0.209282i	−0.994510	−	0.104641i	$-0.966631\pi$
$631$		−	5.25710i		−	0.209282i	0.994510	−	0.104641i	$-0.0333693\pi$
$632$	−0.748480	−	0.847487i	−0.0297729	−	0.0337112i
$633$	19.7873	−	19.7873i	0.786476	−	0.786476i
$634$	18.7746	+	34.1273i	0.745635	+	1.35537i
$635$	−5.58423	+	0.645875i	−0.221604	+	0.0256308i
$636$	−7.50466	−	4.75646i	−0.297579	−	0.188606i
$637$	−1.91934	−	1.91934i	−0.0760472	−	0.0760472i
$638$	14.4146	+	4.18326i	0.570679	+	0.165617i
$639$	−4.25583			−0.168358
$640$	22.2715	−	11.9992i	0.880357	−	0.474312i
$641$	20.0773			0.793004			0.396502	−	0.918034i	$-0.370224\pi$
$641$	20.0773			0.793004			0.396502	+	0.918034i	$0.370224\pi$
$642$	−18.6559	−	5.41413i	−0.736289	−	0.213679i
$643$	−9.28480	−	9.28480i	−0.366157	−	0.366157i	0.499917	−	0.866073i	$-0.333364\pi$
$643$	−9.28480	−	9.28480i	−0.366157	−	0.366157i	−0.866073	+	0.499917i	$0.833364\pi$
$644$	−7.53866	−	4.77801i	−0.297065	−	0.188280i
$645$	7.71733	−	9.73599i	0.303869	−	0.383354i
$646$	−11.2920	−	20.5259i	−0.444278	−	0.807580i
$647$	28.7387	−	28.7387i	1.12983	−	1.12983i	0.139630	−	0.990204i	$-0.455409\pi$
$647$	28.7387	−	28.7387i	1.12983	−	1.12983i	0.990204	−	0.139630i	$-0.0445912\pi$
$648$	−1.87233	−	2.12000i	−0.0735520	−	0.0832813i
$649$			26.3013i			1.03242i
$650$	2.43170	+	2.69955i	0.0953790	+	0.105885i
$651$		−	13.5142i		−	0.529665i
$652$	1.99700	+	8.90963i	0.0782084	+	0.348928i
$653$	−11.9380	+	11.9380i	−0.467170	+	0.467170i	−0.900996	−	0.433826i	$-0.857163\pi$
$653$	−11.9380	+	11.9380i	−0.467170	+	0.467170i	0.433826	+	0.900996i	$0.357163\pi$
$654$	−12.9641	+	7.13201i	−0.506937	+	0.278884i
$655$	25.2772	−	31.8891i	0.987663	−	1.24601i
$656$	4.65533	+	9.86318i	0.181760	+	0.385093i
$657$	9.28267	+	9.28267i	0.362152	+	0.362152i
$658$	11.4416	−	39.4251i	0.446039	−	1.53695i
$659$	−17.9963			−0.701038			−0.350519	−	0.936556i	$-0.613995\pi$
$659$	−17.9963			−0.701038			−0.350519	+	0.936556i	$0.613995\pi$
$660$	12.1962	+	5.88774i	0.474736	+	0.229180i
$661$	−9.06794			−0.352702			−0.176351	−	0.984327i	$-0.556429\pi$
$661$	−9.06794			−0.352702			−0.176351	+	0.984327i	$0.556429\pi$
$662$	5.91798	−	20.3920i	0.230009	−	0.792558i
$663$	1.21433	+	1.21433i	0.0471608	+	0.0471608i
$664$	−0.0495037	+	0.797984i	−0.00192112	+	0.0309678i
$665$	38.5840	−	4.46264i	1.49622	−	0.173054i
$666$	0.636672	−	0.350255i	0.0246705	−	0.0135721i
$667$	−3.15556	+	3.15556i	−0.122184	+	0.122184i
$668$	19.2010	−	4.30369i	0.742908	−	0.166515i
$669$			12.0700i			0.466654i
$670$	−17.3243	−	2.92576i	−0.669298	−	0.113032i
$671$			46.3089i			1.78773i
$672$	3.12993	+	19.5767i	0.120740	+	0.755189i
$673$	35.7640	−	35.7640i	1.37860	−	1.37860i	0.531611	−	0.846988i	$-0.321587\pi$
$673$	35.7640	−	35.7640i	1.37860	−	1.37860i	0.846988	−	0.531611i	$-0.178413\pi$
$674$	−20.8074	−	37.8223i	−0.801470	−	1.45686i
$675$	4.24924	+	2.63514i	0.163553	+	0.101427i
$676$	−13.6360	+	21.5147i	−0.524462	+	0.827487i
$677$	16.2020	+	16.2020i	0.622694	+	0.622694i	0.946219	−	0.323525i	$-0.104868\pi$
$677$	16.2020	+	16.2020i	0.622694	+	0.622694i	−0.323525	+	0.946219i	$0.604868\pi$
$678$	20.4483	+	5.93431i	0.785312	+	0.227906i
$679$	−33.3859			−1.28123
$680$	−14.1312	+	15.7205i	−0.541906	+	0.602856i
$681$	1.45331			0.0556911
$682$	−15.8599	−	4.60272i	−0.607308	−	0.176247i
$683$	33.3943	+	33.3943i	1.27780	+	1.27780i	0.941899	+	0.335897i	$0.109039\pi$
$683$	33.3943	+	33.3943i	1.27780	+	1.27780i	0.335897	+	0.941899i	$0.390961\pi$
$684$	−5.30660	+	8.37266i	−0.202903	+	0.320137i
$685$	2.15066	+	18.5946i	0.0821727	+	0.710465i
$686$	−4.10270	−	7.45763i	−0.156642	−	0.284734i
$687$	6.25649	−	6.25649i	0.238700	−	0.238700i
$688$	7.50373	−	20.9190i	0.286077	−	0.797528i
$689$		−	2.28267i		−	0.0869629i
$690$	−3.28167	+	2.33339i	−0.124931	+	0.0888306i
$691$		−	24.6365i		−	0.937216i	−0.883406	−	0.468608i	$-0.844756\pi$
$691$		−	24.6365i		−	0.937216i	0.883406	−	0.468608i	$-0.155244\pi$
$692$	1.73143	−	0.388082i	0.0658193	−	0.0147527i
$693$	−7.50466	+	7.50466i	−0.285079	+	0.285079i
$694$	−29.7843	+	16.3854i	−1.13060	+	0.621980i
$695$	21.7534	+	17.2431i	0.825154	+	0.654067i
$696$	9.89367	+	0.613763i	0.375019	+	0.0232646i
$697$	−6.44398	−	6.44398i	−0.244083	−	0.244083i
$698$	1.72853	−	5.95611i	0.0654256	−	0.225442i
$699$	6.94381			0.262639
$700$	−15.2691	−	31.5456i	−0.577117	−	1.19231i
$701$	−23.0420			−0.870285			−0.435143	−	0.900362i	$-0.643302\pi$
$701$	−23.0420			−0.870285			−0.435143	+	0.900362i	$0.643302\pi$
$702$	0.202527	−	0.697863i	0.00764389	−	0.0263391i
$703$	−1.80078	−	1.80078i	−0.0679177	−	0.0679177i
$704$	24.0407	+	2.99430i	0.906068	+	0.112852i
$705$	−14.5140	−	11.5047i	−0.546629	−	0.433291i
$706$	−4.60398	+	2.53281i	−0.173273	+	0.0953235i
$707$	−14.3420	+	14.3420i	−0.539387	+	0.539387i
$708$	3.79911	+	16.9498i	0.142779	+	0.637012i
$709$		−	37.7360i		−	1.41720i	−0.705608	−	0.708602i	$-0.749326\pi$
$709$		−	37.7360i		−	1.41720i	0.705608	−	0.708602i	$-0.250674\pi$
$710$	10.9682	−	7.79877i	0.411627	−	0.292683i
$711$		−	0.399759i		−	0.0149921i
$712$	−9.07925	+	8.01857i	−0.340259	+	0.300509i
$713$	3.47197	−	3.47197i	0.130026	−	0.130026i
$714$	−7.98465	−	14.5140i	−0.298818	−	0.543173i
$715$	0.399759	+	3.45632i	0.0149501	+	0.129259i
$716$	−15.1016	−	9.57143i	−0.564374	−	0.357701i
$717$	−13.4533	−	13.4533i	−0.502423	−	0.502423i
$718$	−47.5296	−	13.7936i	−1.77379	−	0.514772i
$719$	41.3423			1.54181			0.770903	−	0.636953i	$-0.219805\pi$
$719$	41.3423			1.54181			0.770903	+	0.636953i	$0.219805\pi$
$720$	8.71024	+	2.03264i	0.324612	+	0.0757521i
$721$	−64.8853			−2.41646
$722$	7.55871	+	2.19362i	0.281306	+	0.0816380i
$723$	−2.05529	−	2.05529i	−0.0764372	−	0.0764372i
$724$	−1.70504	−	1.08066i	−0.0633673	−	0.0401623i
$725$	−17.0607	+	4.00000i	−0.633618	+	0.148556i
$726$	−1.24701	−	2.26673i	−0.0462808	−	0.0841264i
$727$	9.48981	−	9.48981i	0.351958	−	0.351958i	−0.508880	−	0.860838i	$-0.669940\pi$
$727$	9.48981	−	9.48981i	0.351958	−	0.351958i	0.860838	+	0.508880i	$0.169940\pi$
$728$	−3.81765	+	3.37165i	−0.141491	+	0.124962i
$729$		−	1.00000i		−	0.0370370i
$730$	−40.9337	−	6.91295i	−1.51503	−	0.255860i
$731$			18.5696i			0.686821i
$732$	6.68911	+	29.8435i	0.247237	+	1.10305i
$733$	3.21134	−	3.21134i	0.118614	−	0.118614i	−0.645308	−	0.763922i	$-0.723271\pi$
$733$	3.21134	−	3.21134i	0.118614	−	0.118614i	0.763922	+	0.645308i	$0.223271\pi$
$734$	−17.4108	+	9.57830i	−0.642646	+	0.353542i
$735$	11.7342	−	1.35718i	0.432822	−	0.0500604i
$736$	−4.22538	+	5.83362i	−0.155750	+	0.215030i
$737$	−11.8973	−	11.8973i	−0.438243	−	0.438243i
$738$	−1.07473	+	3.70328i	−0.0395614	+	0.136320i
$739$	25.3832			0.933737			0.466868	−	0.884327i	$-0.345382\pi$
$739$	25.3832			0.933737			0.466868	+	0.884327i	$0.345382\pi$
$740$	−0.998995	+	2.06937i	−0.0367238	+	0.0760717i
$741$	−2.54669			−0.0935549
$742$	−6.13684	+	21.1462i	−0.225290	+	0.776300i
$743$	−32.7400	−	32.7400i	−1.20111	−	1.20111i	−0.973828	−	0.227285i	$-0.927015\pi$
$743$	−32.7400	−	32.7400i	−1.20111	−	1.20111i	−0.227285	−	0.973828i	$-0.572985\pi$
$744$	−10.8857	−	0.675305i	−0.399089	−	0.0247579i
$745$	−8.03863	+	10.1413i	−0.294513	+	0.371550i
$746$	−12.4240	+	6.83488i	−0.454875	+	0.250243i
$747$	−0.199879	+	0.199879i	−0.00731321	+	0.00731321i
$748$	−19.7526	+	4.42734i	−0.722228	+	0.161880i
$749$			48.1400i			1.75900i
$750$	−15.7800	+	0.995376i	−0.576205	+	0.0363460i
$751$		−	24.4810i		−	0.893323i	−0.894703	−	0.446662i	$-0.852613\pi$
$751$		−	24.4810i		−	0.893323i	0.894703	−	0.446662i	$-0.147387\pi$
$752$	−31.1851	−	11.1862i	−1.13720	−	0.407920i
$753$	1.96137	−	1.96137i	0.0714762	−	0.0714762i
$754$	1.22753	+	2.23132i	0.0447039	+	0.0812599i
$755$	−25.1005	+	31.6661i	−0.913499	+	1.15245i
$756$	−3.75233	+	5.92036i	−0.136471	+	0.215322i
$757$	22.9473	+	22.9473i	0.834035	+	0.834035i	0.988066	−	0.154031i	$-0.0492256\pi$
$757$	22.9473	+	22.9473i	0.834035	+	0.834035i	−0.154031	+	0.988066i	$0.549226\pi$
$758$	−40.7980	−	11.8400i	−1.48185	−	0.430048i
$759$	−3.85607			−0.139967
$760$	−1.66661	−	31.3023i	−0.0604544	−	1.13546i
$761$	37.0466			1.34294			0.671470	−	0.741032i	$-0.265663\pi$
$761$	37.0466			1.34294			0.671470	+	0.741032i	$0.265663\pi$
$762$	−3.41444	−	0.990907i	−0.123692	−	0.0358968i
$763$	25.9282	+	25.9282i	0.938665	+	0.938665i
$764$	23.1544	−	36.5327i	0.837698	−	1.32170i
$765$	−7.42401	+	0.858664i	−0.268416	+	0.0310451i
$766$	11.4847	+	20.8761i	0.414959	+	0.754286i
$767$	−3.15556	+	3.15556i	−0.113941	+	0.113941i
$768$	15.9254	−	1.54291i	0.574660	−	0.0556749i
$769$			6.62395i			0.238866i	0.992842	+	0.119433i	$0.0381077\pi$
$769$			6.62395i			0.238866i	−0.992842	+	0.119433i	$0.961892\pi$
$770$	5.58884	−	33.0933i	0.201408	−	1.19260i
$771$			2.94249i			0.105971i
$772$	31.9198	−	7.15447i	1.14882	−	0.257495i
$773$	16.2606	−	16.2606i	0.584854	−	0.584854i	−0.351379	−	0.936233i	$-0.614287\pi$
$773$	16.2606	−	16.2606i	0.584854	−	0.584854i	0.936233	+	0.351379i	$0.114287\pi$
$774$	6.88438	−	3.78734i	0.247454	−	0.136133i
$775$	18.7713	−	4.40108i	0.674287	−	0.158091i
$776$	−1.66829	+	26.8922i	−0.0598880	+	0.965375i
$777$	−1.27334	−	1.27334i	−0.0456809	−	0.0456809i
$778$	−6.43817	+	22.1845i	−0.230819	+	0.795352i
$779$	13.5142			0.484198
$780$	0.756872	+	2.16966i	0.0271004	+	0.0776864i
$781$	12.8880			0.461168
$782$	1.67747	−	5.78017i	0.0599860	−	0.206698i
$783$	2.47817	+	2.47817i	0.0885626	+	0.0885626i
$784$	19.1091	−	9.01932i	0.682468	−	0.322118i
$785$	1.42401	+	12.3120i	0.0508250	+	0.439433i
$786$	22.5490	−	12.4050i	0.804296	−	0.442471i
$787$	−31.2117	+	31.2117i	−1.11258	+	1.11258i	−0.119776	+	0.992801i	$0.538218\pi$
$787$	−31.2117	+	31.2117i	−1.11258	+	1.11258i	−0.992801	+	0.119776i	$0.961782\pi$
$788$	−5.82981	−	26.0098i	−0.207678	−	0.926560i
$789$		−	6.72666i		−	0.239475i
$790$	0.732554	+	1.03026i	0.0260631	+	0.0366550i
$791$		−	52.7652i		−	1.87612i
$792$	5.66999	+	6.42000i	0.201474	+	0.228125i
$793$	−5.55602	+	5.55602i	−0.197300	+	0.197300i
$794$	−18.5021	−	33.6320i	−0.656615	−	1.19355i
$795$	7.78477	+	6.17068i	0.276097	+	0.218851i
$796$	18.6040	+	11.7912i	0.659401	+	0.417929i
$797$	17.3540	+	17.3540i	0.614710	+	0.614710i	0.944170	−	0.329460i	$-0.106867\pi$
$797$	17.3540	+	17.3540i	0.614710	+	0.614710i	−0.329460	+	0.944170i	$0.606867\pi$
$798$	23.5919	+	6.84663i	0.835146	+	0.242368i
$799$	27.6828			0.979346
$800$	−26.1729	+	10.7229i	−0.925351	+	0.379112i
$801$	−4.28267			−0.151321
$802$	36.0804	+	10.4709i	1.27404	+	0.369741i
$803$	−28.1108	−	28.1108i	−0.992008	−	0.992008i
$804$	−9.38567	−	5.94865i	−0.331007	−	0.209793i
$805$	7.82003	+	6.19863i	0.275620	+	0.218473i
$806$	−1.35061	−	2.45505i	−0.0475732	−	0.0864756i
$807$	15.3334	−	15.3334i	0.539760	−	0.539760i
$808$	10.8358	+	12.2691i	0.381202	+	0.431627i
$809$			27.4320i			0.964458i	0.876045	+	0.482229i	$0.160173\pi$
$809$			27.4320i			0.964458i	−0.876045	+	0.482229i	$0.839827\pi$
$810$	1.83249	+	2.57720i	0.0643871	+	0.0905537i
$811$		−	27.1840i		−	0.954559i	−0.878751	−	0.477280i	$-0.841623\pi$
$811$		−	27.1840i		−	0.954559i	0.878751	−	0.477280i	$-0.158377\pi$
$812$	−5.37275	−	23.9706i	−0.188547	−	0.841203i
$813$	2.23132	−	2.23132i	0.0782558	−	0.0782558i
$814$	−1.92804	+	1.06068i	−0.0675777	+	0.0371768i
$815$	−1.17289	−	10.1408i	−0.0410846	−	0.355217i
$816$	−12.0900	+	5.70636i	−0.423234	+	0.199762i
$817$	−19.4720	−	19.4720i	−0.681238	−	0.681238i
$818$	−10.0095	+	34.4905i	−0.349974	+	1.20593i
$819$	−1.80078			−0.0629243
$820$	−4.01642	−	11.5135i	−0.140259	−	0.402070i
$821$	23.6074			0.823903			0.411951	−	0.911206i	$-0.364847\pi$
$821$	23.6074			0.823903			0.411951	+	0.911206i	$0.364847\pi$
$822$	−3.29957	+	11.3696i	−0.115086	+	0.396560i
$823$	24.6596	+	24.6596i	0.859579	+	0.859579i	0.991288	−	0.131709i	$-0.0420465\pi$
$823$	24.6596	+	24.6596i	0.859579	+	0.859579i	−0.131709	+	0.991288i	$0.542046\pi$
$824$	−3.24231	+	52.2650i	−0.112951	+	1.82074i
$825$	−12.8680	−	7.98002i	−0.448006	−	0.277829i
$826$	37.7160	−	20.7489i	1.31231	−	0.721946i
$827$	−13.5406	+	13.5406i	−0.470854	+	0.470854i	−0.902191	−	0.431337i	$-0.858042\pi$
$827$	−13.5406	+	13.5406i	−0.470854	+	0.470854i	0.431337	+	0.902191i	$0.358042\pi$
$828$	−2.48503	+	0.556993i	−0.0863608	+	0.0193568i
$829$		−	9.00933i		−	0.312907i	−0.987685	−	0.156453i	$-0.949994\pi$
$829$		−	9.00933i		−	0.312907i	0.987685	−	0.156453i	$-0.0500061\pi$
$830$	0.148853	−	0.881407i	0.00516677	−	0.0305941i
$831$			4.99779i			0.173371i
$832$	2.52509	+	3.24359i	0.0875418	+	0.112451i
$833$	−12.4847	+	12.4847i	−0.432569	+	0.432569i
$834$	8.46216	+	15.3820i	0.293021	+	0.532635i
$835$	−21.8543	+	2.52768i	−0.756299	+	0.0874738i
$836$	16.0700	−	25.3550i	0.555793	−	0.876920i
$837$	−2.72666	−	2.72666i	−0.0942470	−	0.0942470i
$838$	54.4340	+	15.7973i	1.88039	+	0.545709i
$839$	−10.2597			−0.354203			−0.177102	−	0.984193i	$-0.556672\pi$
$839$	−10.2597			−0.354203			−0.177102	+	0.984193i	$0.556672\pi$
$840$	−1.17847	−	22.1341i	−0.0406612	−	0.763699i
$841$	16.7173			0.576460
$842$	26.3414	+	7.64455i	0.907785	+	0.263449i
$843$	−0.127258	−	0.127258i	−0.00438298	−	0.00438298i
$844$	−29.9611	+	47.2720i	−1.03130	+	1.62717i
$845$	17.6903	−	22.3177i	0.608566	−	0.767751i
$846$	−5.64600	−	10.2629i	−0.194113	−	0.352847i
$847$	−4.53347	+	4.53347i	−0.155772	+	0.155772i
$848$	16.7265	+	5.99988i	0.574392	+	0.206037i
$849$			13.9160i			0.477594i
$850$	17.5597	−	15.8174i	0.602293	−	0.542531i
$851$		−	0.654274i		−	0.0224282i
$852$	8.30559	−	1.86161i	0.284545	−	0.0637777i
$853$	17.1086	−	17.1086i	0.585789	−	0.585789i	−0.350699	−	0.936488i	$-0.614056\pi$
$853$	17.1086	−	17.1086i	0.585789	−	0.585789i	0.936488	+	0.350699i	$0.114056\pi$
$854$	66.4067	−	36.5327i	2.27239	−	1.25012i
$855$	6.88438	−	8.68516i	0.235441	−	0.297026i
$856$	38.7767	+	2.40555i	1.32536	+	0.0822200i
$857$	−26.7674	−	26.7674i	−0.914356	−	0.914356i	0.0822556	−	0.996611i	$-0.473788\pi$
$857$	−26.7674	−	26.7674i	−0.914356	−	0.914356i	−0.996611	+	0.0822556i	$0.973788\pi$
$858$	−0.613314	+	2.11334i	−0.0209382	+	0.0721483i
$859$	−28.6378			−0.977109			−0.488554	−	0.872533i	$-0.662476\pi$
$859$	−28.6378			−0.977109			−0.488554	+	0.872533i	$0.662476\pi$
$860$	−10.8022	+	22.3763i	−0.368352	+	0.763025i
$861$	9.55602			0.325668
$862$	6.23716	−	21.4918i	0.212438	−	0.732015i
$863$	−15.8157	−	15.8157i	−0.538371	−	0.538371i	0.384679	−	0.923050i	$-0.374312\pi$
$863$	−15.8157	−	15.8157i	−0.538371	−	0.538371i	−0.923050	+	0.384679i	$0.874312\pi$
$864$	4.58134	+	3.31834i	0.155860	+	0.112892i
$865$	−1.97070	+	0.227931i	−0.0670057	+	0.00774990i
$866$	−37.0116	+	20.3614i	−1.25771	+	0.691908i
$867$	−4.12198	+	4.12198i	−0.139990	+	0.139990i
$868$	5.91147	+	26.3741i	0.200648	+	0.895196i
$869$			1.21059i			0.0410665i
$870$	−10.9280	−	1.84553i	−0.370493	−	0.0625694i
$871$		−	2.85481i		−	0.0967316i
$872$	22.1808	−	19.5895i	0.751135	−	0.663384i
$873$	−6.73599	+	6.73599i	−0.227979	+	0.227979i
$874$	4.30207	+	7.82003i	0.145520	+	0.264516i
$875$	13.2681	+	36.8686i	0.448545	+	1.24638i
$876$	−22.1763	−	14.0554i	−0.749269	−	0.474888i
$877$	−17.3727	−	17.3727i	−0.586633	−	0.586633i	0.350085	−	0.936718i	$-0.386153\pi$
$877$	−17.3727	−	17.3727i	−0.586633	−	0.586633i	−0.936718	+	0.350085i	$0.886153\pi$
$878$	−8.98009	−	2.60612i	−0.303063	−	0.0879522i
$879$	−22.4407			−0.756907
$880$	−26.3773	−	6.15547i	−0.889178	−	0.207501i
$881$	56.5254			1.90439			0.952194	−	0.305493i	$-0.0988211\pi$
$881$	56.5254			1.90439			0.952194	+	0.305493i	$0.0988211\pi$
$882$	7.17480	+	2.08220i	0.241588	+	0.0701114i
$883$	−15.1962	−	15.1962i	−0.511392	−	0.511392i	0.403561	−	0.914953i	$-0.367772\pi$
$883$	−15.1962	−	15.1962i	−0.511392	−	0.511392i	−0.914953	+	0.403561i	$0.867772\pi$
$884$	−2.90105	−	1.83869i	−0.0975728	−	0.0618418i
$885$	−2.23132	−	19.2920i	−0.0750050	−	0.648494i
$886$	14.0187	+	25.4822i	0.470966	+	0.856092i
$887$	−11.0676	+	11.0676i	−0.371613	+	0.371613i	−0.868065	−	0.496451i	$-0.834636\pi$
$887$	−11.0676	+	11.0676i	−0.371613	+	0.371613i	0.496451	+	0.868065i	$0.334636\pi$
$888$	−1.08930	+	0.962047i	−0.0365547	+	0.0322842i
$889$			8.81070i			0.295501i
$890$	11.0373	−	7.84795i	0.369972	−	0.263064i
$891$			3.02831i			0.101452i
$892$	−5.27973	−	23.5556i	−0.176778	−	0.788699i
$893$	−29.0280	+	29.0280i	−0.971385	+	0.971385i
$894$	−7.17101	+	3.94502i	−0.239834	+	0.131941i
$895$	15.6653	+	12.4172i	0.523633	+	0.415063i
$896$	−14.6717	−	36.8364i	−0.490146	−	1.23062i
$897$	−0.462642	−	0.462642i	−0.0154472	−	0.0154472i
$898$	−13.2484	+	45.6510i	−0.442105	+	1.52339i
$899$	13.5142			0.450725
$900$	−9.44540	−	3.28397i	−0.314847	−	0.109466i
$901$	−14.8480			−0.494659
$902$	3.25461	−	11.2147i	0.108367	−	0.373407i
$903$	−13.7688	−	13.7688i	−0.458196	−	0.458196i
$904$	−42.5023	−	2.63667i	−1.41361	−	0.0876944i
$905$	1.76868	+	1.40196i	0.0587929	+	0.0466028i
$906$	−22.3913	+	12.3182i	−0.743902	+	0.409246i
$907$	−28.1654	+	28.1654i	−0.935217	+	0.935217i	−0.998026	−	0.0628084i	$-0.979994\pi$
$907$	−28.1654	+	28.1654i	−0.935217	+	0.935217i	0.0628084	+	0.998026i	$0.479994\pi$
$908$	−2.83625	+	0.635716i	−0.0941244	+	0.0210970i
$909$			5.78734i			0.191954i
$910$	4.64098	−	3.29991i	0.153847	−	0.109391i
$911$			34.8499i			1.15463i	0.816522	+	0.577315i	$0.195899\pi$
$911$			34.8499i			1.15463i	−0.816522	+	0.577315i	$0.804101\pi$
$912$	6.69383	−	18.6611i	0.221655	−	0.617932i
$913$	0.605296	−	0.605296i	0.0200324	−	0.0200324i
$914$	15.0053	+	27.2757i	0.496331	+	0.902198i
$915$	−3.92870	−	33.9675i	−0.129879	−	1.12293i
$916$	−9.47329	+	14.9468i	−0.313006	+	0.493856i
$917$	−45.0980	−	45.0980i	−1.48927	−	1.48927i
$918$	−4.53936	−	1.31737i	−0.149821	−	0.0434797i
$919$	−21.1171			−0.696590			−0.348295	−	0.937385i	$-0.613239\pi$
$919$	−21.1171			−0.696590			−0.348295	+	0.937385i	$0.613239\pi$
$920$	5.38375	−	5.98927i	0.177497	−	0.197461i
$921$	11.0093			0.362770
$922$	−35.5126	−	10.3061i	−1.16954	−	0.339414i
$923$	1.54626	+	1.54626i	0.0508959	+	0.0508959i
$924$	11.3632	−	17.9287i	0.373822	−	0.589810i
$925$	1.35400	−	2.18336i	0.0445192	−	0.0717884i
$926$	5.57104	+	10.1267i	0.183076	+	0.332784i
$927$	−13.0914	+	13.0914i	−0.429977	+	0.429977i
$928$	−19.5767	+	3.12993i	−0.642638	+	0.102745i
$929$		−	39.0653i		−	1.28169i	−0.767670	−	0.640845i	$-0.778584\pi$
$929$		−	39.0653i		−	1.28169i	0.767670	−	0.640845i	$-0.221416\pi$
$930$	12.0237	+	2.03058i	0.394273	+	0.0665854i
$931$		−	26.1827i		−	0.858105i
$932$	−13.5514	+	3.03740i	−0.443891	+	0.0994933i
$933$	−4.99067	+	4.99067i	−0.163387	+	0.163387i
$934$	3.95181	−	2.17403i	0.129307	−	0.0711364i
$935$	22.4822	−	2.60030i	0.735246	−	0.0850388i
$936$	−0.0899847	+	1.45052i	−0.00294124	+	0.0474119i
$937$	1.82936	+	1.82936i	0.0597626	+	0.0597626i	0.736356	−	0.676594i	$-0.236545\pi$
$937$	1.82936	+	1.82936i	0.0597626	+	0.0597626i	−0.676594	+	0.736356i	$0.736545\pi$
$938$	−7.67501	+	26.4464i	−0.250598	+	0.863504i
$939$	15.9825			0.521569
$940$	33.3576	+	16.1035i	1.08801	+	0.525237i
$941$	1.58193			0.0515695			0.0257847	−	0.999668i	$-0.491792\pi$
$941$	1.58193			0.0515695			0.0257847	+	0.999668i	$0.491792\pi$
$942$	−2.18473	+	7.52808i	−0.0711823	+	0.245278i
$943$	2.45505	+	2.45505i	0.0799476	+	0.0799476i
$944$	−14.8285	−	31.4170i	−0.482627	−	1.02254i
$945$	4.86799	−	6.14134i	0.158356	−	0.199778i
$946$	−20.8480	+	11.4692i	−0.677827	+	0.372896i
$947$	−15.9429	+	15.9429i	−0.518075	+	0.518075i	−0.916989	−	0.398913i	$-0.869387\pi$
$947$	−15.9429	+	15.9429i	−0.518075	+	0.518075i	0.398913	+	0.916989i	$0.369387\pi$
$948$	0.174865	+	0.780161i	0.00567934	+	0.0253384i
$949$		−	6.74531i		−	0.218962i
$950$	−1.82700	+	34.9990i	−0.0592756	+	1.13552i
$951$		−	27.5423i		−	0.893121i
$952$	21.9315	+	24.8325i	0.710803	+	0.804826i
$953$	−27.2113	+	27.2113i	−0.881462	+	0.881462i	−0.993683	−	0.112221i	$-0.964203\pi$
$953$	−27.2113	+	27.2113i	−0.881462	+	0.881462i	0.112221	+	0.993683i	$0.464203\pi$
$954$	3.02831	+	5.50466i	0.0980450	+	0.178220i
$955$	−30.0388	+	37.8962i	−0.972033	+	1.22629i
$956$	32.1400	+	20.3704i	1.03948	+	0.658825i
$957$	−7.50466	−	7.50466i	−0.242591	−	0.242591i
$958$	1.90283	+	0.552222i	0.0614777	+	0.0178415i
$959$	29.3383			0.947383
$960$	−17.8879	−	0.156780i	−0.577328	−	0.00506006i
$961$	16.1307			0.520345
$962$	−0.358578	−	0.104063i	−0.0115610	−	0.00335513i
$963$	9.71281	+	9.71281i	0.312991	+	0.312991i
$964$	4.91011	+	3.11203i	0.158144	+	0.100232i
$965$	−36.3306	+	4.20202i	−1.16952	+	0.135268i
$966$	3.04202	+	5.52960i	0.0978755	+	0.177912i
$967$	14.8921	−	14.8921i	0.478899	−	0.478899i	−0.425880	−	0.904780i	$-0.640036\pi$
$967$	14.8921	−	14.8921i	0.478899	−	0.478899i	0.904780	+	0.425880i	$0.140036\pi$
$968$	3.42516	+	3.87824i	0.110089	+	0.124651i
$969$			16.5653i			0.532156i
$970$	5.01639	−	29.7036i	0.161067	−	0.953726i
$971$		−	41.6250i		−	1.33581i	−0.744246	−	0.667905i	$-0.767191\pi$
$971$		−	41.6250i		−	1.33581i	0.744246	−	0.667905i	$-0.232809\pi$
$972$	0.437425	+	1.95158i	0.0140304	+	0.0625969i
$973$	30.7640	−	30.7640i	0.986248	−	0.986248i
$974$	1.71403	−	0.942949i	0.0549212	−	0.0302140i
$975$	−0.586446	−	2.50129i	−0.0187813	−	0.0801054i
$976$	−26.1086	−	55.3160i	−0.835717	−	1.77062i
$977$	−12.0807	−	12.0807i	−0.386494	−	0.386494i	0.486941	−	0.873435i	$-0.338113\pi$
$977$	−12.0807	−	12.0807i	−0.386494	−	0.386494i	−0.873435	+	0.486941i	$0.838113\pi$
$978$	1.79946	−	6.20054i	0.0575404	−	0.198271i
$979$	12.9692			0.414499
$980$	−22.3065	+	7.78148i	−0.712556	+	0.248570i
$981$	10.4626			0.334046
$982$	14.2343	−	49.0484i	0.454236	−	1.56520i
$983$	−22.2258	−	22.2258i	−0.708893	−	0.708893i	0.257410	−	0.966302i	$-0.417131\pi$
$983$	−22.2258	−	22.2258i	−0.708893	−	0.708893i	−0.966302	+	0.257410i	$0.917131\pi$
$984$	0.477513	−	7.69735i	0.0152226	−	0.245383i
$985$	3.42401	+	29.6040i	0.109098	+	0.943261i
$986$	14.5140	−	7.98465i	0.462220	−	0.254283i
$987$	−20.5259	+	20.5259i	−0.653346	+	0.653346i
$988$	4.97006	−	1.11399i	0.158119	−	0.0354406i
$989$		−	7.07472i		−	0.224963i
$990$	−5.54934	−	7.80457i	−0.176370	−	0.248045i
$991$		−	0.353523i		−	0.0112300i	−0.999984	−	0.00561501i	$-0.998213\pi$
$991$		−	0.353523i		−	0.0112300i	0.999984	−	0.00561501i	$-0.00178732\pi$
$992$	21.5397	−	3.44377i	0.683886	−	0.109340i
$993$	−10.6167	+	10.6167i	−0.336911	+	0.336911i
$994$	−10.1672	−	18.4813i	−0.322484	−	0.586191i
$995$	−19.2984	−	15.2970i	−0.611799	−	0.484949i
$996$	0.302648	−	0.477513i	0.00958977	−	0.0151306i
$997$	27.9380	+	27.9380i	0.884805	+	0.884805i	0.994018	−	0.109213i	$-0.0348331\pi$
$997$	27.9380	+	27.9380i	0.884805	+	0.884805i	−0.109213	+	0.994018i	$0.534833\pi$
$998$	8.63442	+	2.50580i	0.273318	+	0.0793197i
$999$	−0.513824			−0.0162567

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.2.j.a.7.6	yes	12
3.2	odd	2		180.2.k.e.127.1		12
4.3	odd	2	inner	60.2.j.a.7.4	✓	12
5.2	odd	4		300.2.j.d.43.3		12
5.3	odd	4	inner	60.2.j.a.43.4	yes	12
5.4	even	2		300.2.j.d.7.1		12
8.3	odd	2		960.2.w.g.127.3		12
8.5	even	2		960.2.w.g.127.6		12
12.11	even	2		180.2.k.e.127.3		12
15.2	even	4		900.2.k.n.343.4		12
15.8	even	4		180.2.k.e.163.3		12
15.14	odd	2		900.2.k.n.307.6		12
20.3	even	4	inner	60.2.j.a.43.6	yes	12
20.7	even	4		300.2.j.d.43.1		12
20.19	odd	2		300.2.j.d.7.3		12
40.3	even	4		960.2.w.g.703.6		12
40.13	odd	4		960.2.w.g.703.3		12
60.23	odd	4		180.2.k.e.163.1		12
60.47	odd	4		900.2.k.n.343.6		12
60.59	even	2		900.2.k.n.307.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.2.j.a.7.4	✓	12	4.3	odd	2	inner
60.2.j.a.7.6	yes	12	1.1	even	1	trivial
60.2.j.a.43.4	yes	12	5.3	odd	4	inner
60.2.j.a.43.6	yes	12	20.3	even	4	inner
180.2.k.e.127.1		12	3.2	odd	2
180.2.k.e.127.3		12	12.11	even	2
180.2.k.e.163.1		12	60.23	odd	4
180.2.k.e.163.3		12	15.8	even	4
300.2.j.d.7.1		12	5.4	even	2
300.2.j.d.7.3		12	20.19	odd	2
300.2.j.d.43.1		12	20.7	even	4
300.2.j.d.43.3		12	5.2	odd	4
900.2.k.n.307.4		12	60.59	even	2
900.2.k.n.307.6		12	15.14	odd	2
900.2.k.n.343.4		12	15.2	even	4
900.2.k.n.343.6		12	60.47	odd	4
960.2.w.g.127.3		12	8.3	odd	2
960.2.w.g.127.6		12	8.5	even	2
960.2.w.g.703.3		12	40.13	odd	4
960.2.w.g.703.6		12	40.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	60.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.35818 + 0.394157i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(1.68928 + 1.07067i) q^{4} +(-1.75233 - 1.38900i) q^{5} +(-0.681664 - 1.23909i) q^{6} +(-2.47817 + 2.47817i) q^{7} +(1.87233 + 2.12000i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(1.35818 + 0.394157i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(1.68928 + 1.07067i) q^{4} +(-1.75233 - 1.38900i) q^{5} +(-0.681664 - 1.23909i) q^{6} +(-2.47817 + 2.47817i) q^{7} +(1.87233 + 2.12000i) q^{8} +1.00000i q^{9} +(-1.83249 - 2.57720i) q^{10} -3.02831i q^{11} +(-0.437425 - 1.95158i) q^{12} +(0.363328 - 0.363328i) q^{13} +(-4.34258 + 2.38900i) q^{14} +(0.256912 + 2.22126i) q^{15} +(1.70734 + 3.61732i) q^{16} +(-2.36333 - 2.36333i) q^{17} +(-0.394157 + 1.35818i) q^{18} +4.95634 q^{19} +(-1.47302 - 4.22258i) q^{20} +3.50466 q^{21} +(1.19363 - 4.11297i) q^{22} +(0.900390 + 0.900390i) q^{23} +(0.175128 - 2.82300i) q^{24} +(1.14134 + 4.86799i) q^{25} +(0.636672 - 0.350255i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-6.83963 + 1.53303i) q^{28} +3.50466i q^{29} +(-0.526593 + 3.11812i) q^{30} -3.85607i q^{31} +(0.893077 + 5.58591i) q^{32} +(-2.14134 + 2.14134i) q^{33} +(-2.27829 - 4.14134i) q^{34} +(7.78477 - 0.900390i) q^{35} +(-1.07067 + 1.68928i) q^{36} +(-0.363328 - 0.363328i) q^{37} +(6.73158 + 1.95358i) q^{38} -0.513824 q^{39} +(-0.336258 - 6.31561i) q^{40} +2.72666 q^{41} +(4.75995 + 1.38139i) q^{42} +(-3.92870 - 3.92870i) q^{43} +(3.24231 - 5.11566i) q^{44} +(1.38900 - 1.75233i) q^{45} +(0.867993 + 1.57778i) q^{46} +(-5.85673 + 5.85673i) q^{47} +(1.35056 - 3.76510i) q^{48} -5.28267i q^{49} +(-0.368618 + 7.06145i) q^{50} +3.34225i q^{51} +(1.00277 - 0.224760i) q^{52} +(3.14134 - 3.14134i) q^{53} +(1.23909 - 0.681664i) q^{54} +(-4.20633 + 5.30660i) q^{55} +(-9.89367 - 0.613763i) q^{56} +(-3.50466 - 3.50466i) q^{57} +(-1.38139 + 4.75995i) q^{58} -8.68516 q^{59} +(-1.94424 + 4.02740i) q^{60} -15.2920 q^{61} +(1.51990 - 5.23723i) q^{62} +(-2.47817 - 2.47817i) q^{63} +(-0.988770 + 7.93866i) q^{64} +(-1.14134 + 0.132007i) q^{65} +(-3.75233 + 2.06429i) q^{66} +(3.92870 - 3.92870i) q^{67} +(-1.46199 - 6.52267i) q^{68} -1.27334i q^{69} +(10.9280 + 1.84553i) q^{70} +4.25583i q^{71} +(-2.12000 + 1.87233i) q^{72} +(9.28267 - 9.28267i) q^{73} +(-0.350255 - 0.636672i) q^{74} +(2.63514 - 4.24924i) q^{75} +(8.37266 + 5.30660i) q^{76} +(7.50466 + 7.50466i) q^{77} +(-0.697863 - 0.202527i) q^{78} -0.399759 q^{79} +(2.03264 - 8.71024i) q^{80} -1.00000 q^{81} +(3.70328 + 1.07473i) q^{82} +(0.199879 + 0.199879i) q^{83} +(5.92036 + 3.75233i) q^{84} +(0.858664 + 7.42401i) q^{85} +(-3.78734 - 6.88438i) q^{86} +(2.47817 - 2.47817i) q^{87} +(6.42000 - 5.66999i) q^{88} +4.28267i q^{89} +(2.57720 - 1.83249i) q^{90} +1.80078i q^{91} +(0.556993 + 2.48503i) q^{92} +(-2.72666 + 2.72666i) q^{93} +(-10.2629 + 5.64600i) q^{94} +(-8.68516 - 6.88438i) q^{95} +(3.31834 - 4.58134i) q^{96} +(6.73599 + 6.73599i) q^{97} +(2.08220 - 7.17480i) q^{98} +3.02831 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{6} - 12 q^{8}+O(q^{10}) \) 12 * q - 4 * q^6 - 12 * q^8	\( 12 q - 4 q^{6} - 12 q^{8} - 8 q^{10} - 8 q^{12} - 4 q^{13} + 12 q^{16} - 20 q^{17} + 20 q^{20} + 12 q^{22} - 20 q^{25} + 16 q^{26} - 4 q^{28} + 8 q^{30} + 20 q^{32} + 8 q^{33} + 4 q^{36} + 4 q^{37} + 16 q^{38} - 8 q^{40} + 16 q^{41} + 20 q^{42} + 4 q^{45} - 40 q^{46} + 16 q^{48} - 16 q^{50} - 8 q^{52} + 4 q^{53} - 64 q^{56} - 20 q^{58} - 20 q^{60} - 32 q^{61} - 56 q^{62} + 20 q^{65} - 24 q^{66} - 16 q^{68} + 44 q^{70} - 12 q^{72} + 44 q^{73} + 8 q^{76} + 48 q^{77} - 24 q^{78} + 4 q^{80} - 12 q^{81} + 16 q^{82} + 44 q^{85} + 64 q^{86} + 60 q^{88} + 12 q^{90} + 56 q^{92} - 16 q^{93} + 44 q^{96} - 20 q^{97} + 24 q^{98}+O(q^{100}) \) 12 * q - 4 * q^6 - 12 * q^8 - 8 * q^10 - 8 * q^12 - 4 * q^13 + 12 * q^16 - 20 * q^17 + 20 * q^20 + 12 * q^22 - 20 * q^25 + 16 * q^26 - 4 * q^28 + 8 * q^30 + 20 * q^32 + 8 * q^33 + 4 * q^36 + 4 * q^37 + 16 * q^38 - 8 * q^40 + 16 * q^41 + 20 * q^42 + 4 * q^45 - 40 * q^46 + 16 * q^48 - 16 * q^50 - 8 * q^52 + 4 * q^53 - 64 * q^56 - 20 * q^58 - 20 * q^60 - 32 * q^61 - 56 * q^62 + 20 * q^65 - 24 * q^66 - 16 * q^68 + 44 * q^70 - 12 * q^72 + 44 * q^73 + 8 * q^76 + 48 * q^77 - 24 * q^78 + 4 * q^80 - 12 * q^81 + 16 * q^82 + 44 * q^85 + 64 * q^86 + 60 * q^88 + 12 * q^90 + 56 * q^92 - 16 * q^93 + 44 * q^96 - 20 * q^97 + 24 * q^98

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