LMFDB - Embedded newform 60.2.j.a.7.4

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			7.4
Root			$-0.394157 + 1.35818i$ of defining polynomial
Character	$\chi$	$=$	60.7
Dual form			60.2.j.a.43.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.394157 + 1.35818i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-1.68928 + 1.07067i) q^{4} +(-1.75233 - 1.38900i) q^{5} +(-0.681664 + 1.23909i) q^{6} +(2.47817 - 2.47817i) q^{7} +(-2.12000 - 1.87233i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(0.394157 + 1.35818i) 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} +(-2.12000 - 1.87233i) q^{8} +1.00000i q^{9} +(1.19582 - 2.92746i) q^{10} +3.02831i q^{11} +(-1.95158 - 0.437425i) 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} +(-1.35818 + 0.394157i) q^{18} -4.95634 q^{19} +(4.44734 + 0.470252i) q^{20} +3.50466 q^{21} +(-4.11297 + 1.19363i) 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} +(-1.53303 + 6.83963i) q^{28} +3.50466i q^{29} +(2.91560 - 1.22446i) q^{30} +3.85607i q^{31} +(5.58591 + 0.893077i) 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} +(-1.95358 - 6.73158i) q^{38} +0.513824 q^{39} +(1.11427 + 6.22563i) q^{40} +2.72666 q^{41} +(1.38139 + 4.75995i) 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} +(3.76510 - 1.35056i) q^{48} -5.28267i q^{49} +(-6.16172 + 3.46889i) q^{50} -3.34225i q^{51} +(-0.224760 + 1.00277i) 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} +(-4.75995 + 1.38139i) q^{58} +8.68516 q^{59} +(2.81223 + 3.47726i) q^{60} -15.2920 q^{61} +(-5.23723 + 1.51990i) 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} +(6.52267 + 1.46199i) q^{68} -1.27334i q^{69} +(-4.29131 - 10.2182i) q^{70} -4.25583i q^{71} +(1.87233 - 2.12000i) 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} +(0.202527 + 0.697863i) q^{78} +0.399759 q^{79} +(-8.01630 + 3.96724i) q^{80} -1.00000 q^{81} +(1.07473 + 3.70328i) 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} +(5.66999 - 6.42000i) q^{88} +4.28267i q^{89} +(2.92746 + 1.19582i) q^{90} -1.80078i q^{91} +(2.48503 + 0.556993i) 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} +(7.17480 - 2.08220i) 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 $

$2$	0.394157	+	1.35818i	0.278711	+	0.960375i
$2$	0.394157	+	1.35818i	0.278711	+	0.960375i
$3$	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	$-0.519572\pi$
$7$	2.47817	−	2.47817i	0.936661	−	0.936661i	0.998110	+	0.0614493i	$0.0195722\pi$
$8$	−2.12000	−	1.87233i	−0.749532	−	0.661968i
$9$			1.00000i			0.333333i
$10$	1.19582	−	2.92746i	0.378151	−	0.925744i
$11$			3.02831i			0.913069i	0.889706	+	0.456534i	$0.150909\pi$
$11$			3.02831i			0.913069i	−0.889706	+	0.456534i	$0.849091\pi$
$12$	−1.95158	−	0.437425i	−0.563372	−	0.126274i
$13$	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	$0.882836\pi$
$18$	−1.35818	+	0.394157i	−0.320125	+	0.0929036i
$19$	−4.95634			−1.13706			−0.568532	−	0.822661i	$-0.692488\pi$
$19$	−4.95634			−1.13706			−0.568532	+	0.822661i	$0.692488\pi$
$20$	4.44734	+	0.470252i	0.994456	+	0.105151i
$21$	3.50466			0.764780
$22$	−4.11297	+	1.19363i	−0.876888	+	0.254482i
$23$	−0.900390	−	0.900390i	−0.187744	−	0.187744i	0.606976	−	0.794720i	$-0.292382\pi$
$23$	−0.900390	−	0.900390i	−0.187744	−	0.187744i	−0.794720	+	0.606976i	$0.792382\pi$
$24$	−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
$28$	−1.53303	+	6.83963i	−0.289715	+	1.29257i
$29$			3.50466i			0.650800i	0.945576	+	0.325400i	$0.105499\pi$
$29$			3.50466i			0.650800i	−0.945576	+	0.325400i	$0.894501\pi$
$30$	2.91560	−	1.22446i	0.532313	−	0.223554i
$31$			3.85607i			0.692571i	0.938129	+	0.346286i	$0.112557\pi$
$31$			3.85607i			0.692571i	−0.938129	+	0.346286i	$0.887443\pi$
$32$	5.58591	+	0.893077i	0.987459	+	0.157875i
$33$	−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	$0.763448\pi$
$38$	−1.95358	−	6.73158i	−0.316912	−	1.09201i
$39$	0.513824			0.0822776
$40$	1.11427	+	6.22563i	0.176181	+	0.984358i
$41$	2.72666			0.425832			0.212916	−	0.977070i	$-0.431704\pi$
$41$	2.72666			0.425832			0.212916	+	0.977070i	$0.431704\pi$
$42$	1.38139	+	4.75995i	0.213153	+	0.734476i
$43$	3.92870	+	3.92870i	0.599121	+	0.599121i	0.940079	−	0.340958i	$-0.110751\pi$
$43$	3.92870	+	3.92870i	0.599121	+	0.599121i	−0.340958	+	0.940079i	$0.610751\pi$
$44$	−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	$-0.543542\pi$
$47$	5.85673	−	5.85673i	0.854292	−	0.854292i	0.990659	+	0.136366i	$0.0435423\pi$
$48$	3.76510	−	1.35056i	0.543446	−	0.194936i
$49$		−	5.28267i		−	0.754667i
$50$	−6.16172	+	3.46889i	−0.871399	+	0.490575i
$51$		−	3.34225i		−	0.468009i
$52$	−0.224760	+	1.00277i	−0.0311685	+	0.139059i
$53$	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
$58$	−4.75995	+	1.38139i	−0.625012	+	0.181385i
$59$	8.68516			1.13071			0.565356	−	0.824847i	$-0.308739\pi$
$59$	8.68516			1.13071			0.565356	+	0.824847i	$0.308739\pi$
$60$	2.81223	+	3.47726i	0.363057	+	0.448913i
$61$	−15.2920			−1.95794			−0.978970	−	0.204004i	$-0.934604\pi$
$61$	−15.2920			−1.95794			−0.978970	+	0.204004i	$0.934604\pi$
$62$	−5.23723	+	1.51990i	−0.665128	+	0.193027i
$63$	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	$-0.860220\pi$
$67$	−3.92870	+	3.92870i	−0.479967	+	0.479967i	0.425154	+	0.905121i	$0.360220\pi$
$68$	6.52267	+	1.46199i	0.790989	+	0.177292i
$69$		−	1.27334i		−	0.153293i
$70$	−4.29131	−	10.2182i	−0.512909	−	1.22131i
$71$		−	4.25583i		−	0.505075i	−0.967587	−	0.252537i	$-0.918735\pi$
$71$		−	4.25583i		−	0.505075i	0.967587	−	0.252537i	$-0.0812650\pi$
$72$	1.87233	−	2.12000i	0.220656	−	0.249844i
$73$	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
$78$	0.202527	+	0.697863i	0.0229317	+	0.0790174i
$79$	0.399759			0.0449764			0.0224882	−	0.999747i	$-0.492841\pi$
$79$	0.399759			0.0449764			0.0224882	+	0.999747i	$0.492841\pi$
$80$	−8.01630	+	3.96724i	−0.896249	+	0.443551i
$81$	−1.00000			−0.111111
$82$	1.07473	+	3.70328i	0.118684	+	0.408959i
$83$	−0.199879	−	0.199879i	−0.0219396	−	0.0219396i	0.696052	−	0.717991i	$-0.254938\pi$
$83$	−0.199879	−	0.199879i	−0.0219396	−	0.0219396i	−0.717991	+	0.696052i	$0.754938\pi$
$84$	−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
$88$	5.66999	−	6.42000i	0.604422	−	0.684374i
$89$			4.28267i			0.453962i	0.973899	+	0.226981i	$0.0728856\pi$
$89$			4.28267i			0.453962i	−0.973899	+	0.226981i	$0.927114\pi$
$90$	2.92746	+	1.19582i	0.308581	+	0.126050i
$91$		−	1.80078i		−	0.188773i
$92$	2.48503	+	0.556993i	0.259082	+	0.0580705i
$93$	−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	$0.589323\pi$
$98$	7.17480	−	2.08220i	0.724764	−	0.210334i
$99$	−3.02831			−0.304356
$100$	−7.14004	−	7.00141i	−0.714004	−	0.700141i
$101$	5.78734			0.575862			0.287931	−	0.957651i	$-0.407033\pi$
$101$	5.78734			0.575862			0.287931	+	0.957651i	$0.407033\pi$
$102$	4.53936	−	1.31737i	0.449464	−	0.130439i
$103$	−13.0914	−	13.0914i	−1.28993	−	1.28993i	−0.934827	−	0.355104i	$-0.884445\pi$
$103$	−13.0914	−	13.0914i	−1.28993	−	1.28993i	−0.355104	−	0.934827i	$-0.615555\pi$
$104$	−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	$-0.981123\pi$
$107$	−9.71281	+	9.71281i	−0.938973	+	0.938973i	0.0592694	+	0.998242i	$0.481123\pi$
$108$	0.437425	−	1.95158i	0.0420913	−	0.187791i
$109$		−	10.4626i		−	1.00214i	−0.865407	−	0.501070i	$-0.832940\pi$
$109$		−	10.4626i		−	1.00214i	0.865407	−	0.501070i	$-0.167060\pi$
$110$	8.86525	+	3.62130i	0.845268	+	0.345278i
$111$		−	0.513824i		−	0.0487700i
$112$	−4.73325	−	13.1954i	−0.447251	−	1.24685i
$113$	−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
$118$	3.42331	+	11.7960i	0.315142	+	1.08591i
$119$	−11.7135			−1.07377
$120$	−3.61428	+	5.19009i	−0.329937	+	0.473788i
$121$	1.82936			0.166305
$122$	−6.02745	−	20.7692i	−0.545699	−	1.88036i
$123$	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	$-0.785578\pi$
$127$	−1.77766	+	1.77766i	−0.157742	+	0.157742i	0.623823	+	0.781565i	$0.285578\pi$
$128$	−10.3924	+	4.47200i	−0.918564	+	0.395273i
$129$			5.55602i			0.489180i
$130$	−0.629155	−	1.49810i	−0.0551805	−	0.131392i
$131$		−	18.1981i		−	1.58997i	−0.606626	−	0.794987i	$-0.707477\pi$
$131$		−	18.1981i		−	1.58997i	0.606626	−	0.794987i	$-0.292523\pi$
$132$	1.32466	−	5.90998i	0.115297	−	0.514398i
$133$	−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	$0.866405\pi$
$138$	1.72942	−	0.501897i	0.147218	−	0.0427243i
$139$	12.4140			1.05294			0.526470	−	0.850194i	$-0.323515\pi$
$139$	12.4140			1.05294			0.526470	+	0.850194i	$0.323515\pi$
$140$	12.1866	−	9.85592i	1.02996	−	0.832977i
$141$	8.28267			0.697527
$142$	5.78017	−	1.67747i	0.485061	−	0.140770i
$143$	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
$148$	1.00277	+	0.224760i	0.0824270	+	0.0184751i
$149$		−	5.78734i		−	0.474117i	−0.971495	−	0.237059i	$-0.923817\pi$
$149$		−	5.78734i		−	0.474117i	0.971495	−	0.237059i	$-0.0761833\pi$
$150$	−6.80987	−	1.90412i	−0.556023	−	0.155471i
$151$			18.0708i			1.47058i	0.677751	+	0.735292i	$0.262955\pi$
$151$			18.0708i			1.47058i	−0.677751	+	0.735292i	$0.737045\pi$
$152$	10.5074	+	9.27990i	0.852265	+	0.752700i
$153$	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	$0.820991\pi$
$158$	0.157568	+	0.542943i	0.0125354	+	0.0431942i
$159$	4.44252			0.352315
$160$	−8.54789	−	9.32382i	−0.675770	−	0.737113i
$161$	−4.46264			−0.351705
$162$	−0.394157	−	1.35818i	−0.0309679	−	0.106708i
$163$	−3.22819	−	3.22819i	−0.252851	−	0.252851i	0.569287	−	0.822139i	$-0.307219\pi$
$163$	−3.22819	−	3.22819i	−0.252851	−	0.252851i	−0.822139	+	0.569287i	$0.807219\pi$
$164$	−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	$-0.874307\pi$
$167$	−6.95700	+	6.95700i	−0.538349	+	0.538349i	0.384695	+	0.923044i	$0.374307\pi$
$168$	−7.42988	−	6.56188i	−0.573227	−	0.506260i
$169$			12.7360i			0.979691i
$170$	−9.74466	+	4.09244i	−0.747381	+	0.313876i
$171$		−	4.95634i		−	0.379021i
$172$	−10.8430	−	2.43034i	−0.826771	−	0.185312i
$173$	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
$178$	−5.81662	+	1.68804i	−0.435974	+	0.126524i
$179$	8.93968			0.668183			0.334091	−	0.942541i	$-0.391571\pi$
$179$	8.93968			0.668183			0.334091	+	0.942541i	$0.391571\pi$
$180$	−0.470252	+	4.44734i	−0.0350505	+	0.331485i
$181$	−1.00933			−0.0750228			−0.0375114	−	0.999296i	$-0.511943\pi$
$181$	−1.00933			−0.0750228			−0.0375114	+	0.999296i	$0.511943\pi$
$182$	2.44577	−	0.709789i	0.181293	−	0.0526131i
$183$	−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
$188$	−3.62305	+	16.1643i	−0.264238	+	1.17890i
$189$			3.50466i			0.254927i
$190$	−5.92688	+	14.5095i	−0.429981	+	1.05263i
$191$			21.6262i			1.56481i	0.622768	+	0.782407i	$0.286008\pi$
$191$			21.6262i			1.56481i	−0.622768	+	0.782407i	$0.713992\pi$
$192$	−4.91431	+	6.31265i	−0.354660	+	0.455576i
$193$	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	$0.907470\pi$
$198$	−1.19363	−	4.11297i	−0.0848274	−	0.292296i
$199$	−11.0130			−0.780688			−0.390344	−	0.920669i	$-0.627644\pi$
$199$	−11.0130			−0.780688			−0.390344	+	0.920669i	$0.627644\pi$
$200$	6.69485	−	12.4571i	0.473398	−	0.880849i
$201$	−5.55602			−0.391891
$202$	2.28112	+	7.86022i	0.160499	+	0.553043i
$203$	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
$208$	−0.693949	−	1.93460i	−0.0481167	−	0.134140i
$209$		−	15.0093i		−	1.03822i
$210$	4.19094	−	10.2598i	0.289202	−	0.707991i
$211$		−	27.9835i		−	1.92646i	−0.268669	−	0.963232i	$-0.586584\pi$
$211$		−	27.9835i		−	1.92646i	0.268669	−	0.963232i	$-0.413416\pi$
$212$	−1.94327	+	8.66993i	−0.133464	+	0.595453i
$213$	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
$218$	14.2101	−	4.12392i	0.962430	−	0.279307i
$219$	13.1277			0.887086
$220$	−1.42407	+	13.4679i	−0.0960105	+	0.908007i
$221$	−1.71733			−0.115520
$222$	0.697863	−	0.202527i	0.0468375	−	0.0135927i
$223$	8.53479	+	8.53479i	0.571531	+	0.571531i	0.932556	−	0.361025i	$-0.117573\pi$
$223$	8.53479	+	8.53479i	0.571531	+	0.571531i	−0.361025	+	0.932556i	$0.617573\pi$
$224$	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	$-0.734642\pi$
$227$	1.02765	−	1.02765i	0.0682074	−	0.0682074i	0.740388	+	0.672180i	$0.234642\pi$
$228$	9.67269	+	2.16803i	0.640590	+	0.143581i
$229$			8.84802i			0.584693i	0.956312	+	0.292347i	$0.0944361\pi$
$229$			8.84802i			0.584693i	−0.956312	+	0.292347i	$0.905564\pi$
$230$	−3.71256	+	1.55915i	−0.244799	+	0.102808i
$231$			10.6132i			0.698297i
$232$	6.56188	−	7.42988i	0.430809	−	0.487795i
$233$	−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
$238$	−4.61694	−	15.9089i	−0.299272	−	1.03122i
$239$	−19.0259			−1.23068			−0.615340	−	0.788262i	$-0.710981\pi$
$239$	−19.0259			−1.23068			−0.615340	+	0.788262i	$0.710981\pi$
$240$	−8.47364	−	2.86311i	−0.546971	−	0.184813i
$241$	2.90663			0.187232			0.0936161	−	0.995608i	$-0.470157\pi$
$241$	2.90663			0.187232			0.0936161	+	0.995608i	$0.470157\pi$
$242$	0.721054	+	2.48459i	0.0463511	+	0.159716i
$243$	−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
$248$	7.21984	−	8.17486i	0.458460	−	0.519104i
$249$		−	0.282672i		−	0.0179136i
$250$	15.6157	+	2.48001i	0.987622	+	0.156850i
$251$		−	2.77379i		−	0.175080i	−0.996161	−	0.0875401i	$-0.972099\pi$
$251$		−	2.77379i		−	0.175080i	0.996161	−	0.0875401i	$-0.0279006\pi$
$252$	−6.83963	−	1.53303i	−0.430856	−	0.0965717i
$253$	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	$0.779254\pi$
$258$	−7.54604	+	2.18994i	−0.469796	+	0.136340i
$259$	−1.80078			−0.111895
$260$	1.78670	−	1.44499i	0.110807	−	0.0896145i
$261$	−3.50466			−0.216933
$262$	24.7162	−	7.17290i	1.52697	−	0.443143i
$263$	−4.75646	−	4.75646i	−0.293296	−	0.293296i	0.545085	−	0.838381i	$-0.316497\pi$
$263$	−4.75646	−	4.75646i	−0.293296	−	0.293296i	−0.838381	+	0.545085i	$0.816497\pi$
$264$	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
$268$	2.43034	−	10.8430i	0.148457	−	0.662342i
$269$			21.6846i			1.32214i	0.750326	+	0.661068i	$0.229896\pi$
$269$			21.6846i			1.32214i	−0.750326	+	0.661068i	$0.770104\pi$
$270$	1.22446	+	2.91560i	0.0745180	+	0.177438i
$271$		−	3.15556i		−	0.191687i	−0.995396	−	0.0958434i	$-0.969445\pi$
$271$		−	3.15556i		−	0.191687i	0.995396	−	0.0958434i	$-0.0305548\pi$
$272$	−12.5839	+	4.51391i	−0.763012	+	0.273696i
$273$	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	$0.797974\pi$
$278$	4.89305	+	16.8604i	0.293466	+	1.01122i
$279$	−3.85607			−0.230857
$280$	18.1895	+	12.6668i	1.08703	+	0.756988i
$281$	0.179969			0.0107361			0.00536804	−	0.999986i	$-0.498291\pi$
$281$	0.179969			0.0107361			0.00536804	+	0.999986i	$0.498291\pi$
$282$	3.26467	+	11.2493i	0.194408	+	0.669887i
$283$	9.84007	+	9.84007i	0.584931	+	0.584931i	0.936254	−	0.351323i	$-0.114268\pi$
$283$	9.84007	+	9.84007i	0.584931	+	0.584931i	−0.351323	+	0.936254i	$0.614268\pi$
$284$	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
$288$	−0.893077	+	5.58591i	−0.0526250	+	0.329153i
$289$		−	5.82936i		−	0.342903i
$290$	10.2598	+	4.19094i	0.602474	+	0.246100i
$291$			9.52612i			0.558431i
$292$	−5.74238	+	25.6197i	−0.336047	+	1.49928i
$293$	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
$298$	7.86022	−	2.28112i	0.455330	−	0.132142i
$299$	−0.654274			−0.0378376
$300$	−0.0980239	−	9.99952i	−0.00565941	−	0.577323i
$301$	19.4720			1.12235
$302$	−24.5434	+	7.12274i	−1.41231	+	0.409868i
$303$	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	$-0.648275\pi$
$307$	7.78477	−	7.78477i	0.444300	−	0.444300i	0.893454	+	0.449154i	$0.148275\pi$
$308$	−20.7125	−	4.64248i	−1.18020	−	0.264530i
$309$		−	18.5140i		−	1.05322i
$310$	11.2885	+	4.61116i	0.641144	+	0.261896i
$311$			7.05788i			0.400215i	0.979774	+	0.200108i	$0.0641292\pi$
$311$			7.05788i			0.400215i	−0.979774	+	0.200108i	$0.935871\pi$
$312$	−1.08930	−	0.962047i	−0.0616697	−	0.0544652i
$313$	−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	$0.468522\pi$
$318$	1.75105	+	6.03372i	0.0981940	+	0.338354i
$319$	−10.6132			−0.594225
$320$	9.29418	−	15.2846i	0.519560	−	0.854434i
$321$	−13.7360			−0.766668
$322$	−1.75898	−	6.06105i	−0.0980241	−	0.337769i
$323$	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
$328$	−5.78050	−	5.10520i	−0.319175	−	0.281887i
$329$		−	29.0280i		−	1.60036i
$330$	3.70803	+	8.82932i	0.204120	+	0.486038i
$331$			15.0143i			0.825259i	0.910899	+	0.412630i	$0.135390\pi$
$331$			15.0143i			0.825259i	−0.910899	+	0.412630i	$0.864610\pi$
$332$	0.551657	+	0.123648i	0.0302761	+	0.00678607i
$333$	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	$-0.562451\pi$
$338$	−17.2977	+	5.01997i	−0.940871	+	0.273051i
$339$	−15.0557			−0.817714
$340$	−9.39917	−	11.6219i	−0.509742	−	0.630286i
$341$	−11.6774			−0.632365
$342$	6.73158	−	1.95358i	0.364002	−	0.105637i
$343$	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	$-0.526776\pi$
$347$	16.9969	−	16.9969i	0.912444	−	0.912444i	0.996464	+	0.0840201i	$0.0267760\pi$
$348$	1.53303	−	6.83963i	0.0821790	−	0.366643i
$349$		−	4.38538i		−	0.234744i	−0.993088	−	0.117372i	$-0.962553\pi$
$349$		−	4.38538i		−	0.234744i	0.993088	−	0.117372i	$-0.0374469\pi$
$350$	−6.67331	+	23.8663i	−0.356703	+	1.27571i
$351$			0.513824i			0.0274259i
$352$	−2.70451	+	16.9159i	−0.144151	+	0.901618i
$353$	−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
$358$	3.52363	+	12.1416i	0.186230	+	0.641706i
$359$	34.9952			1.84697			0.923487	−	0.383630i	$-0.125326\pi$
$359$	34.9952			1.84697			0.923487	+	0.383630i	$0.125326\pi$
$360$	−6.22563	+	1.11427i	−0.328119	+	0.0587270i
$361$	5.56534			0.292913
$362$	−0.397834	−	1.37085i	−0.0209097	−	0.0720500i
$363$	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	$-0.630475\pi$
$367$	9.93581	−	9.93581i	0.518645	−	0.518645i	0.917161	+	0.398516i	$0.130475\pi$
$368$	−4.79427	+	1.71973i	−0.249918	+	0.0896469i
$369$			2.72666i			0.141944i
$370$	−1.49810	+	0.629155i	−0.0778827	+	0.0327082i
$371$		−	15.5695i		−	0.808330i
$372$	1.68674	−	7.52543i	0.0874536	−	0.390176i
$373$	−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
$378$	−4.75995	+	1.38139i	−0.244825	+	0.0710509i
$379$	30.0388			1.54299			0.771495	−	0.636235i	$-0.219509\pi$
$379$	30.0388			1.54299			0.771495	+	0.636235i	$0.219509\pi$
$380$	−22.0426	−	2.33073i	−1.13076	−	0.119564i
$381$	−2.51399			−0.128796
$382$	−29.3721	+	8.52410i	−1.50281	+	0.436131i
$383$	−11.9133	−	11.9133i	−0.608744	−	0.608744i	0.333874	−	0.942618i	$-0.391644\pi$
$383$	−11.9133	−	11.9133i	−0.608744	−	0.608744i	−0.942618	+	0.333874i	$0.891644\pi$
$384$	−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
$388$	−18.5910	−	4.16697i	−0.943814	−	0.211546i
$389$			16.3340i			0.828168i	0.910239	+	0.414084i	$0.135898\pi$
$389$			16.3340i			0.828168i	−0.910239	+	0.414084i	$0.864102\pi$
$390$	0.614439	−	1.50420i	0.0311133	−	0.0761680i
$391$			4.25583i			0.215227i
$392$	−9.89090	+	11.1992i	−0.499566	+	0.565647i
$393$	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	$0.988508\pi$
$398$	−4.34083	−	14.9575i	−0.217586	−	0.749753i
$399$	−17.3703			−0.869604
$400$	19.5577	+	4.18274i	0.977886	+	0.209137i
$401$	26.5653			1.32661			0.663305	−	0.748349i	$-0.269153\pi$
$401$	26.5653			1.32661			0.663305	+	0.748349i	$0.269153\pi$
$402$	−2.18994	−	7.54604i	−0.109224	−	0.376362i
$403$	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
$408$	−6.25779	+	7.08556i	−0.309807	+	0.350787i
$409$			25.3947i			1.25569i	0.778339	+	0.627844i	$0.216062\pi$
$409$			25.3947i			1.25569i	−0.778339	+	0.627844i	$0.783938\pi$
$410$	3.26058	−	7.98218i	0.161029	−	0.394212i
$411$		−	8.37122i		−	0.412922i
$412$	36.1315	+	8.09849i	1.78007	+	0.398984i
$413$	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
$418$	20.3853	−	5.91603i	0.997078	−	0.289362i
$419$	−40.0788			−1.95798			−0.978988	−	0.203919i	$-0.934632\pi$
$419$	−40.0788			−1.95798			−0.978988	+	0.203919i	$0.934632\pi$
$420$	15.5864	+	1.64807i	0.760541	+	0.0804178i
$421$	19.3947			0.945240			0.472620	−	0.881266i	$-0.343308\pi$
$421$	19.3947			0.945240			0.472620	+	0.881266i	$0.343308\pi$
$422$	38.0065	−	11.0299i	1.85013	−	0.536927i
$423$	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
$428$	6.00847	−	26.8069i	0.290430	−	1.29576i
$429$			1.55602i			0.0751251i
$430$	16.1991	−	6.80310i	0.781190	−	0.328074i
$431$			15.8241i			0.762218i	0.924530	+	0.381109i	$0.124458\pi$
$431$			15.8241i			0.762218i	−0.924530	+	0.381109i	$0.875542\pi$
$432$	1.35056	+	3.76510i	0.0649788	+	0.181149i
$433$	−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
$438$	5.17436	+	17.8297i	0.247241	+	0.851936i
$439$	6.61188			0.315568			0.157784	−	0.987474i	$-0.449565\pi$
$439$	6.61188			0.315568			0.157784	+	0.987474i	$0.449565\pi$
$440$	−18.8531	+	3.37434i	−0.898786	+	0.160865i
$441$	5.28267			0.251556
$442$	−0.676896	−	2.33243i	−0.0321967	−	0.110942i
$443$	−14.5419	−	14.5419i	−0.690906	−	0.690906i	0.271525	−	0.962431i	$-0.412472\pi$
$443$	−14.5419	−	14.5419i	−0.690906	−	0.690906i	−0.962431	+	0.271525i	$0.912472\pi$
$444$	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
$448$	22.1237	+	17.2230i	1.04525	+	0.813711i
$449$			33.6120i			1.58625i	0.609060	+	0.793124i	$0.291547\pi$
$449$			33.6120i			1.58625i	−0.609060	+	0.793124i	$0.708453\pi$
$450$	−3.46889	−	6.16172i	−0.163525	−	0.290466i
$451$			8.25715i			0.388814i
$452$	6.58575	−	29.3824i	0.309768	−	1.38203i
$453$	−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	$0.577845\pi$
$458$	−12.0172	+	3.48751i	−0.561525	+	0.162960i
$459$	3.34225			0.156003
$460$	−3.58093	−	4.42775i	−0.166962	−	0.206445i
$461$	−26.1473			−1.21780			−0.608900	−	0.793247i	$-0.708389\pi$
$461$	−26.1473			−1.21780			−0.608900	+	0.793247i	$0.708389\pi$
$462$	−14.4146	+	4.18326i	−0.670627	+	0.194623i
$463$	−5.77898	−	5.77898i	−0.268572	−	0.268572i	0.559953	−	0.828525i	$-0.310819\pi$
$463$	−5.77898	−	5.77898i	−0.268572	−	0.268572i	−0.828525	+	0.559953i	$0.810819\pi$
$464$	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	$-0.773510\pi$
$467$	−2.25517	+	2.25517i	−0.104357	+	0.104357i	0.653000	+	0.757357i	$0.273510\pi$
$468$	−1.00277	−	0.224760i	−0.0463529	−	0.0103895i
$469$			19.4720i			0.899132i
$470$	−10.1418	−	24.1489i	−0.467805	−	1.11391i
$471$		−	5.54279i		−	0.255398i
$472$	−18.4125	−	16.2615i	−0.847505	−	0.748495i
$473$	−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
$478$	−7.49917	−	25.8405i	−0.343004	−	1.18191i
$479$	−1.40102			−0.0640143			−0.0320071	−	0.999488i	$-0.510190\pi$
$479$	−1.40102			−0.0640143			−0.0320071	+	0.999488i	$0.510190\pi$
$480$	0.548668	−	12.6372i	0.0250432	−	0.576807i
$481$	−0.264015			−0.0120380
$482$	1.14567	+	3.94771i	0.0521837	+	0.179813i
$483$	−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	$-0.759978\pi$
$487$	−0.978144	+	0.978144i	−0.0443239	+	0.0443239i	0.684597	+	0.728921i	$0.259978\pi$
$488$	32.4190	+	28.6317i	1.46754	+	1.29609i
$489$		−	4.56534i		−	0.206452i
$490$	−15.4648	−	6.31711i	−0.698629	−	0.285378i
$491$			36.1134i			1.62978i	0.579619	+	0.814888i	$0.303201\pi$
$491$			36.1134i			1.62978i	−0.579619	+	0.814888i	$0.696799\pi$
$492$	−5.32128	−	1.19271i	−0.239902	−	0.0537715i
$493$	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
$498$	0.383918	−	0.111417i	0.0172038	−	0.00499272i
$499$	−6.35736			−0.284595			−0.142297	−	0.989824i	$-0.545449\pi$
$499$	−6.35736			−0.284595			−0.142297	+	0.989824i	$0.545449\pi$
$500$	2.78673	+	22.1863i	0.124626	+	0.992204i
$501$	−9.83869			−0.439560
$502$	3.76730	−	1.09331i	0.168143	−	0.0487968i
$503$	−17.1704	−	17.1704i	−0.765592	−	0.765592i	0.211735	−	0.977327i	$-0.432089\pi$
$503$	−17.1704	−	17.1704i	−0.765592	−	0.765592i	−0.977327	+	0.211735i	$0.932089\pi$
$504$	−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
$508$	1.09968	−	4.90626i	0.0487906	−	0.217680i
$509$		−	18.8739i		−	0.836572i	−0.908315	−	0.418286i	$-0.862631\pi$
$509$		−	18.8739i		−	0.836572i	0.908315	−	0.418286i	$-0.137369\pi$
$510$	−9.78430	−	3.99672i	−0.433256	−	0.176978i
$511$		−	46.0081i		−	2.03528i
$512$	12.7676	−	18.6812i	0.564253	−	0.825602i
$513$	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
$518$	−0.709789	−	2.44577i	−0.0311864	−	0.107461i
$519$	0.887197			0.0389436
$520$	2.66679	+	1.85710i	0.116946	+	0.0814393i
$521$	−33.9346			−1.48670			−0.743351	−	0.668901i	$-0.766765\pi$
$521$	−33.9346			−1.48670			−0.743351	+	0.668901i	$0.766765\pi$
$522$	−1.38139	−	4.75995i	−0.0604617	−	0.208337i
$523$	−3.78345	−	3.78345i	−0.165439	−	0.165439i	0.619532	−	0.784971i	$-0.287322\pi$
$523$	−3.78345	−	3.78345i	−0.165439	−	0.165439i	−0.784971	+	0.619532i	$0.787322\pi$
$524$	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
$528$	4.08991	+	11.4019i	0.177990	+	0.496203i
$529$		−	21.3786i		−	0.929504i
$530$	−5.43967	−	12.9526i	−0.236284	−	0.562625i
$531$			8.68516i			0.376904i
$532$	7.59822	−	33.8995i	0.329425	−	1.46973i
$533$	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
$538$	−29.4515	+	8.54715i	−1.26975	+	0.368494i
$539$	15.9976			0.689063
$540$	−3.47726	+	2.81223i	−0.149638	+	0.121019i
$541$	28.4813			1.22451			0.612253	−	0.790662i	$-0.290263\pi$
$541$	28.4813			1.22451			0.612253	+	0.790662i	$0.290263\pi$
$542$	4.28581	−	1.24379i	0.184091	−	0.0534252i
$543$	−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	$-0.756996\pi$
$547$	−0.726896	+	0.726896i	−0.0310798	+	0.0310798i	0.691396	+	0.722476i	$0.256996\pi$
$548$	16.3371	+	3.66178i	0.697886	+	0.156424i
$549$		−	15.2920i		−	0.652647i
$550$	−10.5049	−	18.6596i	−0.447928	−	0.795647i
$551$		−	17.3703i		−	0.740001i
$552$	−2.38412	+	2.69948i	−0.101475	+	0.114898i
$553$	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	$0.861387\pi$
$558$	−1.51990	−	5.23723i	−0.0643424	−	0.221709i
$559$	2.85481			0.120746
$560$	−10.0343	+	29.6973i	−0.424025	+	1.25494i
$561$	10.1214			0.427324
$562$	0.0709362	+	0.244430i	0.00299226	+	0.0103107i
$563$	7.08426	+	7.08426i	0.298566	+	0.298566i	0.840452	−	0.541886i	$-0.182290\pi$
$563$	7.08426	+	7.08426i	0.298566	+	0.298566i	−0.541886	+	0.840452i	$0.682290\pi$
$564$	−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
$568$	−7.96832	+	9.02235i	−0.334343	+	0.378569i
$569$		−	46.2427i		−	1.93860i	−0.245890	−	0.969298i	$-0.579080\pi$
$569$		−	46.2427i		−	1.93860i	0.245890	−	0.969298i	$-0.420920\pi$
$570$	−14.4507	+	6.06883i	−0.605273	+	0.254195i
$571$		−	31.2381i		−	1.30727i	−0.756808	−	0.653637i	$-0.773242\pi$
$571$		−	31.2381i		−	1.30727i	0.756808	−	0.653637i	$-0.226758\pi$
$572$	−3.03669	−	0.680641i	−0.126970	−	0.0284590i
$573$	−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	$0.739116\pi$
$578$	7.91729	−	2.29768i	0.329316	−	0.0955709i
$579$	16.3559			0.679727
$580$	−1.64807	+	15.5864i	−0.0684326	+	0.647192i
$581$	−0.990671			−0.0411000
$582$	−12.9381	+	3.75479i	−0.536303	+	0.155641i
$583$	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	$-0.992195\pi$
$587$	−23.6268	+	23.6268i	−0.975183	+	0.975183i	0.0245164	+	0.999699i	$0.492195\pi$
$588$	−2.31077	+	10.3096i	−0.0952947	+	0.425159i
$589$		−	19.1120i		−	0.787498i
$590$	10.3859	−	25.4255i	0.427579	−	1.04675i
$591$		−	13.3276i		−	0.548223i
$592$	−1.93460	+	0.693949i	−0.0795115	+	0.0285211i
$593$	−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
$598$	−0.257887	−	0.888619i	−0.0105458	−	0.0363383i
$599$	33.0851			1.35182			0.675910	−	0.736984i	$-0.263751\pi$
$599$	33.0851			1.35182			0.675910	+	0.736984i	$0.263751\pi$
$600$	13.5425	−	4.07451i	0.552869	−	0.166341i
$601$	−24.3200			−0.992033			−0.496016	−	0.868313i	$-0.665204\pi$
$601$	−24.3200			−0.992033			−0.496016	+	0.868313i	$0.665204\pi$
$602$	7.67501	+	26.4464i	0.312810	+	1.07787i
$603$	−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	$-0.708466\pi$
$607$	4.53347	−	4.53347i	0.184008	−	0.184008i	0.793100	+	0.609092i	$0.208466\pi$
$608$	−27.6857	−	4.42639i	−1.12280	−	0.179514i
$609$			12.2827i			0.497719i
$610$	−18.2864	+	44.7667i	−0.740396	+	1.81255i
$611$		−	4.25583i		−	0.172173i
$612$	−1.46199	+	6.52267i	−0.0590972	+	0.263663i
$613$	−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	$0.588079\pi$
$618$	25.1453	−	7.29742i	1.01149	−	0.293545i
$619$	−29.4373			−1.18319			−0.591593	−	0.806237i	$-0.701501\pi$
$619$	−29.4373			−1.18319			−0.591593	+	0.806237i	$0.701501\pi$
$620$	−1.81333	+	17.1493i	−0.0728249	+	0.688732i
$621$	1.27334			0.0510975
$622$	−9.58583	+	2.78191i	−0.384357	+	0.111544i
$623$	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
$628$	10.8172	+	2.42456i	0.431653	+	0.0967503i
$629$			1.71733i			0.0684743i
$630$	10.2182	−	4.29131i	0.407102	−	0.170970i
$631$			5.25710i			0.209282i	0.994510	+	0.104641i	$0.0333693\pi$
$631$			5.25710i			0.209282i	−0.994510	+	0.104641i	$0.966631\pi$
$632$	−0.847487	−	0.748480i	−0.0337112	−	0.0297729i
$633$	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
$638$	−4.18326	−	14.4146i	−0.165617	−	0.570679i
$639$	4.25583			0.168358
$640$	24.4225	+	6.59860i	0.965384	+	0.260833i
$641$	20.0773			0.793004			0.396502	−	0.918034i	$-0.370224\pi$
$641$	20.0773			0.793004			0.396502	+	0.918034i	$0.370224\pi$
$642$	−5.41413	−	18.6559i	−0.213679	−	0.736289i
$643$	9.28480	+	9.28480i	0.366157	+	0.366157i	0.866073	−	0.499917i	$-0.166636\pi$
$643$	9.28480	+	9.28480i	0.366157	+	0.366157i	−0.499917	+	0.866073i	$0.666636\pi$
$644$	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	$0.544591\pi$
$647$	−28.7387	+	28.7387i	−1.12983	+	1.12983i	−0.990204	+	0.139630i	$0.955409\pi$
$648$	2.12000	+	1.87233i	0.0832813	+	0.0735520i
$649$			26.3013i			1.03242i
$650$	−0.978383	+	3.49907i	−0.0383753	+	0.137245i
$651$			13.5142i			0.529665i
$652$	8.90963	+	1.99700i	0.348928	+	0.0782084i
$653$	−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
$658$	39.4251	−	11.4416i	1.53695	−	0.446039i
$659$	17.9963			0.701038			0.350519	−	0.936556i	$-0.386005\pi$
$659$	17.9963			0.701038			0.350519	+	0.936556i	$0.386005\pi$
$660$	−10.5302	+	8.51629i	−0.409888	+	0.331496i
$661$	−9.06794			−0.352702			−0.176351	−	0.984327i	$-0.556429\pi$
$661$	−9.06794			−0.352702			−0.176351	+	0.984327i	$0.556429\pi$
$662$	−20.3920	+	5.91798i	−0.792558	+	0.230009i
$663$	−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
$668$	4.30369	−	19.2010i	0.166515	−	0.742908i
$669$			12.0700i			0.466654i
$670$	6.80310	+	16.1991i	0.262827	+	0.625826i
$671$		−	46.3089i		−	1.78773i
$672$	19.5767	+	3.12993i	0.755189	+	0.120740i
$673$	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	$0.604868\pi$
$678$	−5.93431	−	20.4483i	−0.227906	−	0.785312i
$679$	33.3859			1.28123
$680$	12.0798	−	17.3466i	0.463240	−	0.665211i
$681$	1.45331			0.0556911
$682$	−4.60272	−	15.8599i	−0.176247	−	0.607308i
$683$	−33.3943	−	33.3943i	−1.27780	−	1.27780i	−0.941899	−	0.335897i	$-0.890961\pi$
$683$	−33.3943	−	33.3943i	−1.27780	−	1.27780i	−0.335897	−	0.941899i	$-0.609039\pi$
$684$	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
$688$	20.9190	−	7.50373i	0.797528	−	0.286077i
$689$		−	2.28267i		−	0.0869629i
$690$	−3.72766	−	1.52269i	−0.141910	−	0.0579677i
$691$			24.6365i			0.937216i	0.883406	+	0.468608i	$0.155244\pi$
$691$			24.6365i			0.937216i	−0.883406	+	0.468608i	$0.844756\pi$
$692$	−0.388082	+	1.73143i	−0.0147527	+	0.0658193i
$693$	−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
$698$	5.95611	−	1.72853i	0.225442	−	0.0654256i
$699$	−6.94381			−0.262639
$700$	−35.0450	+	0.343541i	−1.32457	+	0.0129846i
$701$	−23.0420			−0.870285			−0.435143	−	0.900362i	$-0.643302\pi$
$701$	−23.0420			−0.870285			−0.435143	+	0.900362i	$0.643302\pi$
$702$	−0.697863	+	0.202527i	−0.0263391	+	0.00764389i
$703$	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
$708$	−16.9498	−	3.79911i	−0.637012	−	0.142779i
$709$		−	37.7360i		−	1.41720i	−0.705608	−	0.708602i	$-0.749326\pi$
$709$		−	37.7360i		−	1.41720i	0.705608	−	0.708602i	$-0.250674\pi$
$710$	−12.4588	−	5.08920i	−0.467570	−	0.190994i
$711$			0.399759i			0.0149921i
$712$	8.01857	−	9.07925i	0.300509	−	0.340259i
$713$	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
$718$	13.7936	+	47.5296i	0.514772	+	1.77379i
$719$	−41.3423			−1.54181			−0.770903	−	0.636953i	$-0.780195\pi$
$719$	−41.3423			−1.54181			−0.770903	+	0.636953i	$0.780195\pi$
$720$	−3.96724	−	8.01630i	−0.147850	−	0.298750i
$721$	−64.8853			−2.41646
$722$	2.19362	+	7.55871i	0.0816380	+	0.281306i
$723$	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	$-0.830060\pi$
$727$	−9.48981	+	9.48981i	−0.351958	+	0.351958i	0.508880	+	0.860838i	$0.330060\pi$
$728$	−3.37165	+	3.81765i	−0.124962	+	0.141491i
$729$		−	1.00000i		−	0.0370370i
$730$	−16.0743	−	38.2750i	−0.594935	−	1.41662i
$731$		−	18.5696i		−	0.686821i
$732$	29.8435	+	6.68911i	1.10305	+	0.247237i
$733$	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
$738$	−3.70328	+	1.07473i	−0.136320	+	0.0395614i
$739$	−25.3832			−0.933737			−0.466868	−	0.884327i	$-0.654618\pi$
$739$	−25.3832			−0.933737			−0.466868	+	0.884327i	$0.654618\pi$
$740$	−1.44499	−	1.78670i	−0.0531189	−	0.0656804i
$741$	−2.54669			−0.0935549
$742$	21.1462	−	6.13684i	0.776300	−	0.225290i
$743$	32.7400	+	32.7400i	1.20111	+	1.20111i	0.973828	+	0.227285i	$0.0729850\pi$
$743$	32.7400	+	32.7400i	1.20111	+	1.20111i	0.227285	+	0.973828i	$0.427015\pi$
$744$	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
$748$	−4.42734	+	19.7526i	−0.161880	+	0.722228i
$749$			48.1400i			1.75900i
$750$	9.28832	+	12.7956i	0.339161	+	0.467229i
$751$			24.4810i			0.893323i	0.894703	+	0.446662i	$0.147387\pi$
$751$			24.4810i			0.893323i	−0.894703	+	0.446662i	$0.852613\pi$
$752$	−11.1862	−	31.1851i	−0.407920	−	1.13720i
$753$	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	$0.549226\pi$
$758$	11.8400	+	40.7980i	0.430048	+	1.48185i
$759$	3.85607			0.139967
$760$	−5.52269	−	30.8563i	−0.200329	−	1.11928i
$761$	37.0466			1.34294			0.671470	−	0.741032i	$-0.265663\pi$
$761$	37.0466			1.34294			0.671470	+	0.741032i	$0.265663\pi$
$762$	−0.990907	−	3.41444i	−0.0358968	−	0.123692i
$763$	−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
$768$	1.54291	−	15.9254i	0.0556749	−	0.574660i
$769$			6.62395i			0.238866i	0.992842	+	0.119433i	$0.0381077\pi$
$769$			6.62395i			0.238866i	−0.992842	+	0.119433i	$0.961892\pi$
$770$	30.9438	−	12.9954i	1.11514	−	0.468322i
$771$		−	2.94249i		−	0.105971i
$772$	−7.15447	+	31.9198i	−0.257495	+	1.14882i
$773$	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
$778$	−22.1845	+	6.43817i	−0.795352	+	0.230819i
$779$	−13.5142			−0.484198
$780$	2.28515	+	0.241626i	0.0818215	+	0.00865162i
$781$	12.8880			0.461168
$782$	−5.78017	+	1.67747i	−0.206698	+	0.0599860i
$783$	−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	$-0.461782\pi$
$787$	31.2117	−	31.2117i	1.11258	−	1.11258i	0.992801	−	0.119776i	$-0.0382177\pi$
$788$	26.0098	+	5.82981i	0.926560	+	0.207678i
$789$		−	6.72666i		−	0.239475i
$790$	0.478039	−	1.17028i	0.0170079	−	0.0416366i
$791$			52.7652i			1.87612i
$792$	6.42000	+	5.66999i	0.228125	+	0.201474i
$793$	−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	$0.606867\pi$
$798$	−6.84663	−	23.5919i	−0.242368	−	0.835146i
$799$	−27.6828			−0.979346
$800$	2.02791	+	28.2115i	0.0716976	+	0.997426i
$801$	−4.28267			−0.151321
$802$	10.4709	+	36.0804i	0.369741	+	1.27404i
$803$	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
$808$	−12.2691	−	10.8358i	−0.431627	−	0.381202i
$809$			27.4320i			0.964458i	0.876045	+	0.482229i	$0.160173\pi$
$809$			27.4320i			0.964458i	−0.876045	+	0.482229i	$0.839827\pi$
$810$	−1.19582	+	2.92746i	−0.0420167	+	0.102860i
$811$			27.1840i			0.954559i	0.878751	+	0.477280i	$0.158377\pi$
$811$			27.1840i			0.954559i	−0.878751	+	0.477280i	$0.841623\pi$
$812$	−23.9706	−	5.37275i	−0.841203	−	0.188547i
$813$	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
$818$	−34.4905	+	10.0095i	−1.20593	+	0.349974i
$819$	1.80078			0.0629243
$820$	12.1264	+	1.28221i	0.423471	+	0.0447769i
$821$	23.6074			0.823903			0.411951	−	0.911206i	$-0.364847\pi$
$821$	23.6074			0.823903			0.411951	+	0.911206i	$0.364847\pi$
$822$	11.3696	−	3.29957i	0.396560	−	0.115086i
$823$	−24.6596	−	24.6596i	−0.859579	−	0.859579i	0.131709	−	0.991288i	$-0.457954\pi$
$823$	−24.6596	−	24.6596i	−0.859579	−	0.859579i	−0.991288	+	0.131709i	$0.957954\pi$
$824$	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	$-0.641958\pi$
$827$	13.5406	−	13.5406i	0.470854	−	0.470854i	0.902191	+	0.431337i	$0.141958\pi$
$828$	−0.556993	+	2.48503i	−0.0193568	+	0.0863608i
$829$		−	9.00933i		−	0.312907i	−0.987685	−	0.156453i	$-0.949994\pi$
$829$		−	9.00933i		−	0.312907i	0.987685	−	0.156453i	$-0.0500061\pi$
$830$	−0.824158	+	0.346120i	−0.0286070	+	0.0120140i
$831$		−	4.99779i		−	0.173371i
$832$	3.24359	+	2.52509i	0.112451	+	0.0875418i
$833$	−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
$838$	−15.7973	−	54.4340i	−0.545709	−	1.88039i
$839$	10.2597			0.354203			0.177102	−	0.984193i	$-0.443328\pi$
$839$	10.2597			0.354203			0.177102	+	0.984193i	$0.443328\pi$
$840$	3.90513	+	21.8187i	0.134740	+	0.752818i
$841$	16.7173			0.576460
$842$	7.64455	+	26.3414i	0.263449	+	0.907785i
$843$	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
$848$	−5.99988	−	16.7265i	−0.206037	−	0.574392i
$849$			13.9160i			0.477594i
$850$	22.7603	+	6.36405i	0.780672	+	0.218285i
$851$			0.654274i			0.0224282i
$852$	−1.86161	+	8.30559i	−0.0637777	+	0.284545i
$853$	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	$0.973788\pi$
$858$	−2.11334	+	0.613314i	−0.0721483	+	0.0209382i
$859$	28.6378			0.977109			0.488554	−	0.872533i	$-0.337524\pi$
$859$	28.6378			0.977109			0.488554	+	0.872533i	$0.337524\pi$
$860$	15.6248	+	19.3197i	0.532801	+	0.658798i
$861$	9.55602			0.325668
$862$	−21.4918	+	6.23716i	−0.732015	+	0.212438i
$863$	15.8157	+	15.8157i	0.538371	+	0.538371i	0.923050	−	0.384679i	$-0.125688\pi$
$863$	15.8157	+	15.8157i	0.538371	+	0.538371i	−0.384679	+	0.923050i	$0.625688\pi$
$864$	−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
$868$	−26.3741	−	5.91147i	−0.895196	−	0.200648i
$869$			1.21059i			0.0410665i
$870$	4.29131	+	10.2182i	0.145489	+	0.346429i
$871$			2.85481i			0.0967316i
$872$	−19.5895	+	22.1808i	−0.663384	+	0.751135i
$873$	−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	$0.886153\pi$
$878$	2.60612	+	8.98009i	0.0879522	+	0.303063i
$879$	22.4407			0.756907
$880$	−12.0140	−	24.2758i	−0.404993	−	0.818337i
$881$	56.5254			1.90439			0.952194	−	0.305493i	$-0.0988211\pi$
$881$	56.5254			1.90439			0.952194	+	0.305493i	$0.0988211\pi$
$882$	2.08220	+	7.17480i	0.0701114	+	0.241588i
$883$	15.1962	+	15.1962i	0.511392	+	0.511392i	0.914953	−	0.403561i	$-0.132228\pi$
$883$	15.1962	+	15.1962i	0.511392	+	0.511392i	−0.403561	+	0.914953i	$0.632228\pi$
$884$	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	$-0.665364\pi$
$887$	11.0676	−	11.0676i	0.371613	−	0.371613i	0.868065	+	0.496451i	$0.165364\pi$
$888$	−0.962047	+	1.08930i	−0.0322842	+	0.0365547i
$889$			8.81070i			0.295501i
$890$	12.5374	+	5.12129i	0.420253	+	0.171666i
$891$		−	3.02831i		−	0.101452i
$892$	−23.5556	−	5.27973i	−0.788699	−	0.176778i
$893$	−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
$898$	−45.6510	+	13.2484i	−1.52339	+	0.442105i
$899$	−13.5142			−0.450725
$900$	7.00141	−	7.14004i	0.233380	−	0.238001i
$901$	−14.8480			−0.494659
$902$	−11.2147	+	3.25461i	−0.373407	+	0.108367i
$903$	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	$-0.520006\pi$
$907$	28.1654	−	28.1654i	0.935217	−	0.935217i	0.998026	+	0.0628084i	$0.0200057\pi$
$908$	−0.635716	+	2.83625i	−0.0210970	+	0.0941244i
$909$			5.78734i			0.191954i
$910$	−5.27171	−	2.15340i	−0.174755	−	0.0713846i
$911$		−	34.8499i		−	1.15463i	−0.816522	−	0.577315i	$-0.804101\pi$
$911$		−	34.8499i		−	1.15463i	0.816522	−	0.577315i	$-0.195899\pi$
$912$	−18.6611	+	6.69383i	−0.617932	+	0.221655i
$913$	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
$918$	1.31737	+	4.53936i	0.0434797	+	0.149821i
$919$	21.1171			0.696590			0.348295	−	0.937385i	$-0.386761\pi$
$919$	21.1171			0.696590			0.348295	+	0.937385i	$0.386761\pi$
$920$	4.60222	−	6.60876i	0.151731	−	0.217884i
$921$	11.0093			0.362770
$922$	−10.3061	−	35.5126i	−0.339414	−	1.16954i
$923$	−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
$928$	−3.12993	+	19.5767i	−0.102745	+	0.642638i
$929$		−	39.0653i		−	1.28169i	−0.767670	−	0.640845i	$-0.778584\pi$
$929$		−	39.0653i		−	1.28169i	0.767670	−	0.640845i	$-0.221416\pi$
$930$	4.72159	+	11.2428i	0.154827	+	0.368665i
$931$			26.1827i			0.858105i
$932$	3.03740	−	13.5514i	0.0994933	−	0.443891i
$933$	−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	$0.736545\pi$
$938$	−26.4464	+	7.67501i	−0.863504	+	0.250598i
$939$	−15.9825			−0.521569
$940$	28.8010	−	23.2928i	0.939387	−	0.759726i
$941$	1.58193			0.0515695			0.0257847	−	0.999668i	$-0.491792\pi$
$941$	1.58193			0.0515695			0.0257847	+	0.999668i	$0.491792\pi$
$942$	7.52808	−	2.18473i	0.245278	−	0.0711823i
$943$	−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	$-0.630613\pi$
$947$	15.9429	−	15.9429i	0.518075	−	0.518075i	0.916989	+	0.398913i	$0.130613\pi$
$948$	−0.780161	−	0.174865i	−0.0253384	−	0.00567934i
$949$		−	6.74531i		−	0.218962i
$950$	30.5396	−	17.1930i	0.990836	−	0.557814i
$951$			27.5423i			0.893121i
$952$	24.8325	+	21.9315i	0.804826	+	0.710803i
$953$	−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
$958$	−0.552222	−	1.90283i	−0.0178415	−	0.0614777i
$959$	−29.3383			−0.947383
$960$	17.3798	−	4.23585i	0.560931	−	0.136712i
$961$	16.1307			0.520345
$962$	−0.104063	−	0.358578i	−0.00335513	−	0.0115610i
$963$	−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	$-0.859964\pi$
$967$	−14.8921	+	14.8921i	−0.478899	+	0.478899i	0.425880	+	0.904780i	$0.359964\pi$
$968$	−3.87824	−	3.42516i	−0.124651	−	0.110089i
$969$			16.5653i			0.532156i
$970$	27.7743	−	11.6643i	0.891780	−	0.374519i
$971$			41.6250i			1.33581i	0.744246	+	0.667905i	$0.232809\pi$
$971$			41.6250i			1.33581i	−0.744246	+	0.667905i	$0.767191\pi$
$972$	1.95158	+	0.437425i	0.0625969	+	0.0140304i
$973$	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	$0.838113\pi$
$978$	6.20054	−	1.79946i	0.198271	−	0.0575404i
$979$	−12.9692			−0.414499
$980$	2.48419	−	23.4939i	0.0793544	−	0.750484i
$981$	10.4626			0.334046
$982$	−49.0484	+	14.2343i	−1.56520	+	0.454236i
$983$	22.2258	+	22.2258i	0.708893	+	0.708893i	0.966302	−	0.257410i	$-0.0828690\pi$
$983$	22.2258	+	22.2258i	0.708893	+	0.708893i	−0.257410	+	0.966302i	$0.582869\pi$
$984$	−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
$988$	1.11399	−	4.97006i	0.0354406	−	0.158119i
$989$		−	7.07472i		−	0.224963i
$990$	−3.62130	+	8.86525i	−0.115093	+	0.281756i
$991$			0.353523i			0.0112300i	0.999984	+	0.00561501i	$0.00178732\pi$
$991$			0.353523i			0.0112300i	−0.999984	+	0.00561501i	$0.998213\pi$
$992$	−3.44377	+	21.5397i	−0.109340	+	0.683886i
$993$	−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	$0.534833\pi$
$998$	−2.50580	−	8.63442i	−0.0793197	−	0.273318i
$999$	0.513824			0.0162567

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.394157 + 1.35818i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-1.68928 + 1.07067i) q^{4} +(-1.75233 - 1.38900i) q^{5} +(-0.681664 + 1.23909i) q^{6} +(2.47817 - 2.47817i) q^{7} +(-2.12000 - 1.87233i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(0.394157 + 1.35818i) 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} +(-2.12000 - 1.87233i) q^{8} +1.00000i q^{9} +(1.19582 - 2.92746i) q^{10} +3.02831i q^{11} +(-1.95158 - 0.437425i) 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} +(-1.35818 + 0.394157i) q^{18} -4.95634 q^{19} +(4.44734 + 0.470252i) q^{20} +3.50466 q^{21} +(-4.11297 + 1.19363i) 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} +(-1.53303 + 6.83963i) q^{28} +3.50466i q^{29} +(2.91560 - 1.22446i) q^{30} +3.85607i q^{31} +(5.58591 + 0.893077i) 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} +(-1.95358 - 6.73158i) q^{38} +0.513824 q^{39} +(1.11427 + 6.22563i) q^{40} +2.72666 q^{41} +(1.38139 + 4.75995i) 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} +(3.76510 - 1.35056i) q^{48} -5.28267i q^{49} +(-6.16172 + 3.46889i) q^{50} -3.34225i q^{51} +(-0.224760 + 1.00277i) 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} +(-4.75995 + 1.38139i) q^{58} +8.68516 q^{59} +(2.81223 + 3.47726i) q^{60} -15.2920 q^{61} +(-5.23723 + 1.51990i) 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} +(6.52267 + 1.46199i) q^{68} -1.27334i q^{69} +(-4.29131 - 10.2182i) q^{70} -4.25583i q^{71} +(1.87233 - 2.12000i) 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} +(0.202527 + 0.697863i) q^{78} +0.399759 q^{79} +(-8.01630 + 3.96724i) q^{80} -1.00000 q^{81} +(1.07473 + 3.70328i) 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} +(5.66999 - 6.42000i) q^{88} +4.28267i q^{89} +(2.92746 + 1.19582i) q^{90} -1.80078i q^{91} +(2.48503 + 0.556993i) 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} +(7.17480 - 2.08220i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more