LMFDB - Embedded newform 60.2.j.a.43.6

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			43.6
Root			$-1.35818 - 0.394157i$ of defining polynomial
Character	$\chi$	$=$	60.43
Dual form			60.2.j.a.7.6

$q$-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 $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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	0.0614493	−	0.998110i	$-0.480428\pi$
$7$	−2.47817	−	2.47817i	−0.936661	−	0.936661i	−0.998110	+	0.0614493i	$0.980428\pi$
$8$	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	$0.150909\pi$
$11$			3.02831i			0.913069i	−0.889706	+	0.456534i	$0.849091\pi$
$12$	−0.437425	+	1.95158i	−0.126274	+	0.563372i
$13$	0.363328	+	0.363328i	0.100769	+	0.100769i	0.755694	−	0.654925i	$-0.227300\pi$
$13$	0.363328	+	0.363328i	0.100769	+	0.100769i	−0.654925	+	0.755694i	$0.727300\pi$
$14$	−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	−0.933019	−	0.359828i	$-0.882836\pi$
$17$	−2.36333	+	2.36333i	−0.573191	+	0.573191i	0.359828	+	0.933019i	$0.382836\pi$
$18$	−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	−0.606976	−	0.794720i	$-0.707618\pi$
$23$	0.900390	−	0.900390i	0.187744	−	0.187744i	0.794720	+	0.606976i	$0.207618\pi$
$24$	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	$-0.894501\pi$
$29$		−	3.50466i		−	0.650800i	0.945576	−	0.325400i	$-0.105499\pi$
$30$	−0.526593	−	3.11812i	−0.0961423	−	0.569289i
$31$			3.85607i			0.692571i	0.938129	+	0.346286i	$0.112557\pi$
$31$			3.85607i			0.692571i	−0.938129	+	0.346286i	$0.887443\pi$
$32$	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	−0.736341	−	0.676610i	$-0.763448\pi$
$37$	−0.363328	+	0.363328i	−0.0597308	+	0.0597308i	0.676610	+	0.736341i	$0.263448\pi$
$38$	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	−0.940079	−	0.340958i	$-0.889249\pi$
$43$	−3.92870	+	3.92870i	−0.599121	+	0.599121i	0.340958	+	0.940079i	$0.389249\pi$
$44$	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	0.136366	−	0.990659i	$-0.456458\pi$
$47$	−5.85673	−	5.85673i	−0.854292	−	0.854292i	−0.990659	+	0.136366i	$0.956458\pi$
$48$	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	0.889137	−	0.457641i	$-0.151306\pi$
$53$	3.14134	+	3.14134i	0.431496	+	0.431496i	−0.457641	+	0.889137i	$0.651306\pi$
$54$	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	0.905121	−	0.425154i	$-0.139780\pi$
$67$	3.92870	+	3.92870i	0.479967	+	0.479967i	−0.425154	+	0.905121i	$0.639780\pi$
$68$	−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	$-0.918735\pi$
$71$		−	4.25583i		−	0.505075i	0.967587	−	0.252537i	$-0.0812650\pi$
$72$	−2.12000	−	1.87233i	−0.249844	−	0.220656i
$73$	9.28267	+	9.28267i	1.08645	+	1.08645i	0.995891	+	0.0905640i	$0.0288670\pi$
$73$	9.28267	+	9.28267i	1.08645	+	1.08645i	0.0905640	+	0.995891i	$0.471133\pi$
$74$	−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	−0.696052	−	0.717991i	$-0.745062\pi$
$83$	0.199879	−	0.199879i	0.0219396	−	0.0219396i	0.717991	+	0.696052i	$0.245062\pi$
$84$	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	$-0.927114\pi$
$89$		−	4.28267i		−	0.453962i	0.973899	−	0.226981i	$-0.0728856\pi$
$90$	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	−0.276949	−	0.960885i	$-0.589323\pi$
$97$	6.73599	−	6.73599i	0.683936	−	0.683936i	0.960885	+	0.276949i	$0.0893233\pi$
$98$	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	0.355104	−	0.934827i	$-0.384445\pi$
$103$	13.0914	−	13.0914i	1.28993	−	1.28993i	0.934827	−	0.355104i	$-0.115555\pi$
$104$	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	0.998242	−	0.0592694i	$-0.0188771\pi$
$107$	9.71281	+	9.71281i	0.938973	+	0.938973i	−0.0592694	+	0.998242i	$0.518877\pi$
$108$	1.95158	+	0.437425i	0.187791	+	0.0420913i
$109$			10.4626i			1.00214i	0.865407	+	0.501070i	$0.167060\pi$
$109$			10.4626i			1.00214i	−0.865407	+	0.501070i	$0.832940\pi$
$110$	−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	−0.999999	−	0.00149259i	$-0.999525\pi$
$113$	−10.6460	−	10.6460i	−1.00149	−	1.00149i	−0.00149259	−	0.999999i	$-0.500475\pi$
$114$	−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	0.781565	−	0.623823i	$-0.214422\pi$
$127$	1.77766	+	1.77766i	0.157742	+	0.157742i	−0.623823	+	0.781565i	$0.714422\pi$
$128$	−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	$-0.707477\pi$
$131$		−	18.1981i		−	1.58997i	0.606626	−	0.794987i	$-0.292523\pi$
$132$	−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	−0.913211	−	0.407487i	$-0.866405\pi$
$137$	−5.91934	+	5.91934i	−0.505724	+	0.505724i	0.407487	+	0.913211i	$0.366405\pi$
$138$	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	$0.0761833\pi$
$149$			5.78734i			0.474117i	−0.971495	+	0.237059i	$0.923817\pi$
$150$	5.25385	+	4.73255i	0.428975	+	0.386411i
$151$			18.0708i			1.47058i	0.677751	+	0.735292i	$0.262955\pi$
$151$			18.0708i			1.47058i	−0.677751	+	0.735292i	$0.737045\pi$
$152$	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	−0.845992	−	0.533195i	$-0.820991\pi$
$157$	−3.91934	+	3.91934i	−0.312798	+	0.312798i	0.533195	+	0.845992i	$0.320991\pi$
$158$	−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	−0.569287	−	0.822139i	$-0.692781\pi$
$163$	3.22819	−	3.22819i	0.252851	−	0.252851i	0.822139	+	0.569287i	$0.192781\pi$
$164$	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	0.923044	−	0.384695i	$-0.125693\pi$
$167$	6.95700	+	6.95700i	0.538349	+	0.538349i	−0.384695	+	0.923044i	$0.625693\pi$
$168$	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	0.730553	−	0.682857i	$-0.239263\pi$
$173$	0.627343	+	0.627343i	0.0476960	+	0.0476960i	−0.682857	+	0.730553i	$0.739263\pi$
$174$	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	$0.286008\pi$
$191$			21.6262i			1.56481i	−0.622768	+	0.782407i	$0.713992\pi$
$192$	6.31265	+	4.91431i	0.455576	+	0.354660i
$193$	11.5653	+	11.5653i	0.832492	+	0.832492i	0.987857	−	0.155365i	$-0.0496555\pi$
$193$	11.5653	+	11.5653i	0.832492	+	0.832492i	−0.155365	+	0.987857i	$0.549655\pi$
$194$	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	−0.958046	−	0.286614i	$-0.907470\pi$
$197$	−9.42401	+	9.42401i	−0.671433	+	0.671433i	0.286614	+	0.958046i	$0.407470\pi$
$198$	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	$-0.586584\pi$
$211$		−	27.9835i		−	1.92646i	0.268669	−	0.963232i	$-0.413416\pi$
$212$	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	−0.932556	−	0.361025i	$-0.882427\pi$
$223$	−8.53479	+	8.53479i	−0.571531	+	0.571531i	0.361025	+	0.932556i	$0.382427\pi$
$224$	−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	0.672180	−	0.740388i	$-0.265358\pi$
$227$	−1.02765	−	1.02765i	−0.0682074	−	0.0682074i	−0.740388	+	0.672180i	$0.765358\pi$
$228$	−2.16803	+	9.67269i	−0.143581	+	0.640590i
$229$		−	8.84802i		−	0.584693i	−0.956312	−	0.292347i	$-0.905564\pi$
$229$		−	8.84802i		−	0.584693i	0.956312	−	0.292347i	$-0.0944361\pi$
$230$	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	0.527740	−	0.849406i	$-0.323040\pi$
$233$	−4.91002	−	4.91002i	−0.321666	−	0.321666i	−0.849406	+	0.527740i	$0.823040\pi$
$234$	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	$-0.972099\pi$
$251$		−	2.77379i		−	0.175080i	0.996161	−	0.0875401i	$-0.0279006\pi$
$252$	−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	−0.769017	−	0.639229i	$-0.779254\pi$
$257$	−2.08066	+	2.08066i	−0.129788	+	0.129788i	0.639229	+	0.769017i	$0.279254\pi$
$258$	−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	−0.545085	−	0.838381i	$-0.683503\pi$
$263$	4.75646	−	4.75646i	0.293296	−	0.293296i	0.838381	+	0.545085i	$0.183503\pi$
$264$	−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	$-0.770104\pi$
$269$		−	21.6846i		−	1.32214i	0.750326	−	0.661068i	$-0.229896\pi$
$270$	−3.11812	+	0.526593i	−0.189763	+	0.0320474i
$271$		−	3.15556i		−	0.191687i	−0.995396	−	0.0958434i	$-0.969445\pi$
$271$		−	3.15556i		−	0.191687i	0.995396	−	0.0958434i	$-0.0305548\pi$
$272$	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	−0.805259	−	0.592923i	$-0.797974\pi$
$277$	−3.53397	+	3.53397i	−0.212336	+	0.212336i	0.592923	+	0.805259i	$0.297974\pi$
$278$	−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	−0.936254	−	0.351323i	$-0.885732\pi$
$283$	−9.84007	+	9.84007i	−0.584931	+	0.584931i	0.351323	+	0.936254i	$0.385732\pi$
$284$	−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	0.997512	−	0.0704942i	$-0.0224576\pi$
$293$	15.8680	+	15.8680i	0.927018	+	0.927018i	−0.0704942	+	0.997512i	$0.522458\pi$
$294$	−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	0.449154	−	0.893454i	$-0.351725\pi$
$307$	−7.78477	−	7.78477i	−0.444300	−	0.444300i	−0.893454	+	0.449154i	$0.851725\pi$
$308$	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	$0.0641292\pi$
$311$			7.05788i			0.400215i	−0.979774	+	0.200108i	$0.935871\pi$
$312$	−0.962047	+	1.08930i	−0.0544652	+	0.0616697i
$313$	−11.3013	−	11.3013i	−0.638789	−	0.638789i	0.311468	−	0.950257i	$-0.399179\pi$
$313$	−11.3013	−	11.3013i	−0.638789	−	0.638789i	−0.950257	+	0.311468i	$0.899179\pi$
$314$	−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	0.0987310	−	0.995114i	$-0.468522\pi$
$317$	19.4754	−	19.4754i	1.09385	−	1.09385i	0.995114	−	0.0987310i	$-0.0314783\pi$
$318$	−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	$0.135390\pi$
$331$			15.0143i			0.825259i	−0.910899	+	0.412630i	$0.864610\pi$
$332$	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	−0.194940	+	0.980815i	$0.562451\pi$
$337$	−21.5840	+	21.5840i	−1.17576	+	1.17576i	−0.980815	+	0.194940i	$0.937549\pi$
$338$	−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	0.0840201	−	0.996464i	$-0.473224\pi$
$347$	−16.9969	−	16.9969i	−0.912444	−	0.912444i	−0.996464	+	0.0840201i	$0.973224\pi$
$348$	6.83963	+	1.53303i	0.366643	+	0.0821790i
$349$			4.38538i			0.234744i	0.993088	+	0.117372i	$0.0374469\pi$
$349$			4.38538i			0.234744i	−0.993088	+	0.117372i	$0.962553\pi$
$350$	−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	0.633722	−	0.773561i	$-0.281526\pi$
$353$	−2.62734	−	2.62734i	−0.139839	−	0.139839i	−0.773561	+	0.633722i	$0.781526\pi$
$354$	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	0.398516	−	0.917161i	$-0.369525\pi$
$367$	−9.93581	−	9.93581i	−0.518645	−	0.518645i	−0.917161	+	0.398516i	$0.869525\pi$
$368$	−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	0.499315	−	0.866421i	$-0.333585\pi$
$373$	−7.08998	−	7.08998i	−0.367105	−	0.367105i	−0.866421	+	0.499315i	$0.833585\pi$
$374$	−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	−0.333874	−	0.942618i	$-0.608356\pi$
$383$	11.9133	−	11.9133i	0.608744	−	0.608744i	0.942618	+	0.333874i	$0.108356\pi$
$384$	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	$-0.864102\pi$
$389$		−	16.3340i		−	0.828168i	0.910239	−	0.414084i	$-0.135898\pi$
$390$	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	−0.999348	−	0.0360950i	$-0.988508\pi$
$397$	−19.1927	+	19.1927i	−0.963253	+	0.963253i	0.0360950	+	0.999348i	$0.488508\pi$
$398$	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	$-0.783938\pi$
$409$		−	25.3947i		−	1.25569i	0.778339	−	0.627844i	$-0.216062\pi$
$410$	−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	$0.124458\pi$
$431$			15.8241i			0.762218i	−0.924530	+	0.381109i	$0.875542\pi$
$432$	3.76510	−	1.35056i	0.181149	−	0.0649788i
$433$	−21.1214	−	21.1214i	−1.01503	−	1.01503i	−0.999885	−	0.0151424i	$-0.995180\pi$
$433$	−21.1214	−	21.1214i	−1.01503	−	1.01503i	−0.0151424	−	0.999885i	$-0.504820\pi$
$434$	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	−0.271525	−	0.962431i	$-0.587528\pi$
$443$	14.5419	−	14.5419i	0.690906	−	0.690906i	0.962431	+	0.271525i	$0.0875280\pi$
$444$	−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	$-0.708453\pi$
$449$		−	33.6120i		−	1.58625i	0.609060	−	0.793124i	$-0.291547\pi$
$450$	−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	−0.242128	−	0.970244i	$-0.577845\pi$
$457$	15.5653	−	15.5653i	0.728116	−	0.728116i	0.970244	+	0.242128i	$0.0778454\pi$
$458$	−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	−0.559953	−	0.828525i	$-0.689181\pi$
$463$	5.77898	−	5.77898i	0.268572	−	0.268572i	0.828525	+	0.559953i	$0.189181\pi$
$464$	−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	0.757357	−	0.653000i	$-0.226490\pi$
$467$	2.25517	+	2.25517i	0.104357	+	0.104357i	−0.653000	+	0.757357i	$0.726490\pi$
$468$	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	0.728921	−	0.684597i	$-0.240022\pi$
$487$	0.978144	+	0.978144i	0.0443239	+	0.0443239i	−0.684597	+	0.728921i	$0.740022\pi$
$488$	−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	$0.303201\pi$
$491$			36.1134i			1.62978i	−0.579619	+	0.814888i	$0.696799\pi$
$492$	−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	−0.211735	−	0.977327i	$-0.567911\pi$
$503$	17.1704	−	17.1704i	0.765592	−	0.765592i	0.977327	+	0.211735i	$0.0679114\pi$
$504$	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	$0.137369\pi$
$509$			18.8739i			0.836572i	−0.908315	+	0.418286i	$0.862631\pi$
$510$	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	−0.619532	−	0.784971i	$-0.712678\pi$
$523$	3.78345	−	3.78345i	0.165439	−	0.165439i	0.784971	+	0.619532i	$0.212678\pi$
$524$	−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	0.722476	−	0.691396i	$-0.243004\pi$
$547$	0.726896	+	0.726896i	0.0310798	+	0.0310798i	−0.691396	+	0.722476i	$0.743004\pi$
$548$	−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	−0.906674	−	0.421832i	$-0.861387\pi$
$557$	−11.4427	+	11.4427i	−0.484841	+	0.484841i	0.421832	+	0.906674i	$0.361387\pi$
$558$	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	−0.840452	−	0.541886i	$-0.817710\pi$
$563$	−7.08426	+	7.08426i	−0.298566	+	0.298566i	0.541886	+	0.840452i	$0.317710\pi$
$564$	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	$0.420920\pi$
$569$			46.2427i			1.93860i	−0.245890	+	0.969298i	$0.579080\pi$
$570$	−2.60998	−	15.4545i	−0.109320	−	0.647318i
$571$		−	31.2381i		−	1.30727i	−0.756808	−	0.653637i	$-0.773242\pi$
$571$		−	31.2381i		−	1.30727i	0.756808	−	0.653637i	$-0.226758\pi$
$572$	−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	−0.682520	−	0.730866i	$-0.739116\pi$
$577$	1.16131	−	1.16131i	0.0483461	−	0.0483461i	0.730866	+	0.682520i	$0.239116\pi$
$578$	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	0.999699	−	0.0245164i	$-0.00780461\pi$
$587$	23.6268	+	23.6268i	0.975183	+	0.975183i	−0.0245164	+	0.999699i	$0.507805\pi$
$588$	−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	0.701735	−	0.712438i	$-0.252409\pi$
$593$	−0.260625	−	0.260625i	−0.0107026	−	0.0107026i	−0.712438	+	0.701735i	$0.752409\pi$
$594$	−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	0.609092	−	0.793100i	$-0.291534\pi$
$607$	−4.53347	−	4.53347i	−0.184008	−	0.184008i	−0.793100	+	0.609092i	$0.791534\pi$
$608$	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	0.166901	−	0.985974i	$-0.446624\pi$
$613$	−20.2793	−	20.2793i	−0.819073	−	0.819073i	−0.985974	+	0.166901i	$0.946624\pi$
$614$	−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	−0.273192	−	0.961960i	$-0.588079\pi$
$617$	17.1086	−	17.1086i	0.688768	−	0.688768i	0.961960	+	0.273192i	$0.0880793\pi$
$618$	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	$0.0333693\pi$
$631$			5.25710i			0.209282i	−0.994510	+	0.104641i	$0.966631\pi$
$632$	−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	−0.866073	−	0.499917i	$-0.833364\pi$
$643$	−9.28480	+	9.28480i	−0.366157	+	0.366157i	0.499917	+	0.866073i	$0.333364\pi$
$644$	−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	0.990204	+	0.139630i	$0.0445912\pi$
$647$	28.7387	+	28.7387i	1.12983	+	1.12983i	0.139630	+	0.990204i	$0.455409\pi$
$648$	−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	0.433826	−	0.900996i	$-0.357163\pi$
$653$	−11.9380	−	11.9380i	−0.467170	−	0.467170i	−0.900996	+	0.433826i	$0.857163\pi$
$654$	−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	0.846988	+	0.531611i	$0.178413\pi$
$673$	35.7640	+	35.7640i	1.37860	+	1.37860i	0.531611	+	0.846988i	$0.321587\pi$
$674$	−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	−0.323525	−	0.946219i	$-0.604868\pi$
$677$	16.2020	−	16.2020i	0.622694	−	0.622694i	0.946219	+	0.323525i	$0.104868\pi$
$678$	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	0.335897	−	0.941899i	$-0.390961\pi$
$683$	33.3943	−	33.3943i	1.27780	−	1.27780i	0.941899	−	0.335897i	$-0.109039\pi$
$684$	−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	$0.155244\pi$
$691$			24.6365i			0.937216i	−0.883406	+	0.468608i	$0.844756\pi$
$692$	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	$0.250674\pi$
$709$			37.7360i			1.41720i	−0.705608	+	0.708602i	$0.749326\pi$
$710$	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	0.860838	−	0.508880i	$-0.169940\pi$
$727$	9.48981	+	9.48981i	0.351958	+	0.351958i	−0.508880	+	0.860838i	$0.669940\pi$
$728$	−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	0.763922	−	0.645308i	$-0.223271\pi$
$733$	3.21134	+	3.21134i	0.118614	+	0.118614i	−0.645308	+	0.763922i	$0.723271\pi$
$734$	−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	−0.227285	+	0.973828i	$0.572985\pi$
$743$	−32.7400	+	32.7400i	−1.20111	+	1.20111i	−0.973828	+	0.227285i	$0.927015\pi$
$744$	−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	$0.147387\pi$
$751$			24.4810i			0.893323i	−0.894703	+	0.446662i	$0.852613\pi$
$752$	−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	−0.154031	−	0.988066i	$-0.549226\pi$
$757$	22.9473	−	22.9473i	0.834035	−	0.834035i	0.988066	+	0.154031i	$0.0492256\pi$
$758$	−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	$-0.961892\pi$
$769$		−	6.62395i		−	0.238866i	0.992842	−	0.119433i	$-0.0381077\pi$
$770$	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	0.936233	−	0.351379i	$-0.114287\pi$
$773$	16.2606	+	16.2606i	0.584854	+	0.584854i	−0.351379	+	0.936233i	$0.614287\pi$
$774$	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	−0.992801	−	0.119776i	$-0.961782\pi$
$787$	−31.2117	−	31.2117i	−1.11258	−	1.11258i	−0.119776	−	0.992801i	$-0.538218\pi$
$788$	−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	−0.329460	−	0.944170i	$-0.606867\pi$
$797$	17.3540	−	17.3540i	0.614710	−	0.614710i	0.944170	+	0.329460i	$0.106867\pi$
$798$	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	$-0.839827\pi$
$809$		−	27.4320i		−	0.964458i	0.876045	−	0.482229i	$-0.160173\pi$
$810$	1.83249	−	2.57720i	0.0643871	−	0.0905537i
$811$			27.1840i			0.954559i	0.878751	+	0.477280i	$0.158377\pi$
$811$			27.1840i			0.954559i	−0.878751	+	0.477280i	$0.841623\pi$
$812$	−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	−0.131709	−	0.991288i	$-0.542046\pi$
$823$	24.6596	−	24.6596i	0.859579	−	0.859579i	0.991288	+	0.131709i	$0.0420465\pi$
$824$	−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	0.431337	−	0.902191i	$-0.358042\pi$
$827$	−13.5406	−	13.5406i	−0.470854	−	0.470854i	−0.902191	+	0.431337i	$0.858042\pi$
$828$	−2.48503	−	0.556993i	−0.0863608	−	0.0193568i
$829$			9.00933i			0.312907i	0.987685	+	0.156453i	$0.0500061\pi$
$829$			9.00933i			0.312907i	−0.987685	+	0.156453i	$0.949994\pi$
$830$	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	0.936488	−	0.350699i	$-0.114056\pi$
$853$	17.1086	+	17.1086i	0.585789	+	0.585789i	−0.350699	+	0.936488i	$0.614056\pi$
$854$	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	−0.996611	−	0.0822556i	$-0.973788\pi$
$857$	−26.7674	+	26.7674i	−0.914356	+	0.914356i	0.0822556	+	0.996611i	$0.473788\pi$
$858$	−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	−0.923050	−	0.384679i	$-0.874312\pi$
$863$	−15.8157	+	15.8157i	−0.538371	+	0.538371i	0.384679	+	0.923050i	$0.374312\pi$
$864$	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	−0.936718	−	0.350085i	$-0.886153\pi$
$877$	−17.3727	+	17.3727i	−0.586633	+	0.586633i	0.350085	+	0.936718i	$0.386153\pi$
$878$	−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	−0.914953	−	0.403561i	$-0.867772\pi$
$883$	−15.1962	+	15.1962i	−0.511392	+	0.511392i	0.403561	+	0.914953i	$0.367772\pi$
$884$	−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	0.496451	−	0.868065i	$-0.334636\pi$
$887$	−11.0676	−	11.0676i	−0.371613	−	0.371613i	−0.868065	+	0.496451i	$0.834636\pi$
$888$	−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	0.0628084	−	0.998026i	$-0.479994\pi$
$907$	−28.1654	−	28.1654i	−0.935217	−	0.935217i	−0.998026	+	0.0628084i	$0.979994\pi$
$908$	−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	$-0.804101\pi$
$911$		−	34.8499i		−	1.15463i	0.816522	−	0.577315i	$-0.195899\pi$
$912$	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	$0.221416\pi$
$929$			39.0653i			1.28169i	−0.767670	+	0.640845i	$0.778584\pi$
$930$	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	−0.676594	−	0.736356i	$-0.736545\pi$
$937$	1.82936	−	1.82936i	0.0597626	−	0.0597626i	0.736356	+	0.676594i	$0.236545\pi$
$938$	−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	0.398913	−	0.916989i	$-0.369387\pi$
$947$	−15.9429	−	15.9429i	−0.518075	−	0.518075i	−0.916989	+	0.398913i	$0.869387\pi$
$948$	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	0.112221	−	0.993683i	$-0.464203\pi$
$953$	−27.2113	−	27.2113i	−0.881462	−	0.881462i	−0.993683	+	0.112221i	$0.964203\pi$
$954$	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	0.904780	−	0.425880i	$-0.140036\pi$
$967$	14.8921	+	14.8921i	0.478899	+	0.478899i	−0.425880	+	0.904780i	$0.640036\pi$
$968$	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	$0.232809\pi$
$971$			41.6250i			1.33581i	−0.744246	+	0.667905i	$0.767191\pi$
$972$	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	−0.873435	−	0.486941i	$-0.838113\pi$
$977$	−12.0807	+	12.0807i	−0.386494	+	0.386494i	0.486941	+	0.873435i	$0.338113\pi$
$978$	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	−0.966302	−	0.257410i	$-0.917131\pi$
$983$	−22.2258	+	22.2258i	−0.708893	+	0.708893i	0.257410	+	0.966302i	$0.417131\pi$
$984$	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	$0.00178732\pi$
$991$			0.353523i			0.0112300i	−0.999984	+	0.00561501i	$0.998213\pi$
$992$	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	−0.109213	−	0.994018i	$-0.534833\pi$
$997$	27.9380	−	27.9380i	0.884805	−	0.884805i	0.994018	+	0.109213i	$0.0348331\pi$
$998$	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.43.6	yes	12
3.2	odd	2		180.2.k.e.163.1		12
4.3	odd	2	inner	60.2.j.a.43.4	yes	12
5.2	odd	4	inner	60.2.j.a.7.4	✓	12
5.3	odd	4		300.2.j.d.7.3		12
5.4	even	2		300.2.j.d.43.1		12
8.3	odd	2		960.2.w.g.703.3		12
8.5	even	2		960.2.w.g.703.6		12
12.11	even	2		180.2.k.e.163.3		12
15.2	even	4		180.2.k.e.127.3		12
15.8	even	4		900.2.k.n.307.4		12
15.14	odd	2		900.2.k.n.343.6		12
20.3	even	4		300.2.j.d.7.1		12
20.7	even	4	inner	60.2.j.a.7.6	yes	12
20.19	odd	2		300.2.j.d.43.3		12
40.27	even	4		960.2.w.g.127.6		12
40.37	odd	4		960.2.w.g.127.3		12
60.23	odd	4		900.2.k.n.307.6		12
60.47	odd	4		180.2.k.e.127.1		12
60.59	even	2		900.2.k.n.343.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.2.j.a.7.4	✓	12	5.2	odd	4	inner
60.2.j.a.7.6	yes	12	20.7	even	4	inner
60.2.j.a.43.4	yes	12	4.3	odd	2	inner
60.2.j.a.43.6	yes	12	1.1	even	1	trivial
180.2.k.e.127.1		12	60.47	odd	4
180.2.k.e.127.3		12	15.2	even	4
180.2.k.e.163.1		12	3.2	odd	2
180.2.k.e.163.3		12	12.11	even	2
300.2.j.d.7.1		12	20.3	even	4
300.2.j.d.7.3		12	5.3	odd	4
300.2.j.d.43.1		12	5.4	even	2
300.2.j.d.43.3		12	20.19	odd	2
900.2.k.n.307.4		12	15.8	even	4
900.2.k.n.307.6		12	60.23	odd	4
900.2.k.n.343.4		12	60.59	even	2
900.2.k.n.343.6		12	15.14	odd	2
960.2.w.g.127.3		12	40.37	odd	4
960.2.w.g.127.6		12	40.27	even	4
960.2.w.g.703.3		12	8.3	odd	2
960.2.w.g.703.6		12	8.5	even	2

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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