LMFDB - Embedded newform 133.2.f.c.58.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [133,2,Mod(39,133)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("133.39"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(133, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 133 = 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	133.f (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$1.06201034688$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			58.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	133.58
Dual form			133.2.f.c.39.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.207107 + 0.358719i) q^{2} +(0.707107 + 1.22474i) q^{3} +(0.914214 + 1.58346i) q^{4} +(-0.500000 + 0.866025i) q^{5} -0.585786 q^{6} +(-2.62132 - 0.358719i) q^{7} -1.58579 q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.207107 - 0.358719i) q^{10} +(-1.20711 - 2.09077i) q^{11} +(-1.29289 + 2.23936i) q^{12} +6.24264 q^{13} +(0.671573 - 0.866025i) q^{14} -1.41421 q^{15} +(-1.50000 + 2.59808i) q^{16} +(2.00000 + 3.46410i) q^{17} +(0.207107 + 0.358719i) q^{18} +(0.500000 - 0.866025i) q^{19} -1.82843 q^{20} +(-1.41421 - 3.46410i) q^{21} +1.00000 q^{22} +(4.20711 - 7.28692i) q^{23} +(-1.12132 - 1.94218i) q^{24} +(2.00000 + 3.46410i) q^{25} +(-1.29289 + 2.23936i) q^{26} +5.65685 q^{27} +(-1.82843 - 4.47871i) q^{28} -9.41421 q^{29} +(0.292893 - 0.507306i) q^{30} +(-1.12132 - 1.94218i) q^{31} +(-2.20711 - 3.82282i) q^{32} +(1.70711 - 2.95680i) q^{33} -1.65685 q^{34} +(1.62132 - 2.09077i) q^{35} +1.82843 q^{36} +(2.53553 - 4.39167i) q^{37} +(0.207107 + 0.358719i) q^{38} +(4.41421 + 7.64564i) q^{39} +(0.792893 - 1.37333i) q^{40} -8.82843 q^{41} +(1.53553 + 0.210133i) q^{42} -6.07107 q^{43} +(2.20711 - 3.82282i) q^{44} +(0.500000 + 0.866025i) q^{45} +(1.74264 + 3.01834i) q^{46} +(0.792893 - 1.37333i) q^{47} -4.24264 q^{48} +(6.74264 + 1.88064i) q^{49} -1.65685 q^{50} +(-2.82843 + 4.89898i) q^{51} +(5.70711 + 9.88500i) q^{52} +(-2.12132 - 3.67423i) q^{53} +(-1.17157 + 2.02922i) q^{54} +2.41421 q^{55} +(4.15685 + 0.568852i) q^{56} +1.41421 q^{57} +(1.94975 - 3.37706i) q^{58} +(-0.585786 - 1.01461i) q^{59} +(-1.29289 - 2.23936i) q^{60} +(-3.08579 + 5.34474i) q^{61} +0.928932 q^{62} +(-1.62132 + 2.09077i) q^{63} -4.17157 q^{64} +(-3.12132 + 5.40629i) q^{65} +(0.707107 + 1.22474i) q^{66} +(-3.41421 - 5.91359i) q^{67} +(-3.65685 + 6.33386i) q^{68} +11.8995 q^{69} +(0.414214 + 1.01461i) q^{70} -5.75736 q^{71} +(-0.792893 + 1.37333i) q^{72} +(6.57107 + 11.3814i) q^{73} +(1.05025 + 1.81909i) q^{74} +(-2.82843 + 4.89898i) q^{75} +1.82843 q^{76} +(2.41421 + 5.91359i) q^{77} -3.65685 q^{78} +(0.707107 - 1.22474i) q^{79} +(-1.50000 - 2.59808i) q^{80} +(2.50000 + 4.33013i) q^{81} +(1.82843 - 3.16693i) q^{82} +0.757359 q^{83} +(4.19239 - 5.40629i) q^{84} -4.00000 q^{85} +(1.25736 - 2.17781i) q^{86} +(-6.65685 - 11.5300i) q^{87} +(1.91421 + 3.31552i) q^{88} +(4.29289 - 7.43551i) q^{89} -0.414214 q^{90} +(-16.3640 - 2.23936i) q^{91} +15.3848 q^{92} +(1.58579 - 2.74666i) q^{93} +(0.328427 + 0.568852i) q^{94} +(0.500000 + 0.866025i) q^{95} +(3.12132 - 5.40629i) q^{96} -8.82843 q^{97} +(-2.07107 + 2.02922i) q^{98} -2.41421 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 8 q^{6} - 2 q^{7} - 12 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{11} - 8 q^{12} + 8 q^{13} + 14 q^{14} - 6 q^{16} + 8 q^{17} - 2 q^{18} + 2 q^{19} + 4 q^{20} + 4 q^{22} + 14 q^{23}+ \cdots - 4 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 - 8 * q^6 - 2 * q^7 - 12 * q^8 + 2 * q^9 + 2 * q^10 - 2 * q^11 - 8 * q^12 + 8 * q^13 + 14 * q^14 - 6 * q^16 + 8 * q^17 - 2 * q^18 + 2 * q^19 + 4 * q^20 + 4 * q^22 + 14 * q^23 + 4 * q^24 + 8 * q^25 - 8 * q^26 + 4 * q^28 - 32 * q^29 + 4 * q^30 + 4 * q^31 - 6 * q^32 + 4 * q^33 + 16 * q^34 - 2 * q^35 - 4 * q^36 - 4 * q^37 - 2 * q^38 + 12 * q^39 + 6 * q^40 - 24 * q^41 - 8 * q^42 + 4 * q^43 + 6 * q^44 + 2 * q^45 - 10 * q^46 + 6 * q^47 + 10 * q^49 + 16 * q^50 + 20 * q^52 - 16 * q^54 + 4 * q^55 - 6 * q^56 - 12 * q^58 - 8 * q^59 - 8 * q^60 - 18 * q^61 + 32 * q^62 + 2 * q^63 - 28 * q^64 - 4 * q^65 - 8 * q^67 + 8 * q^68 + 8 * q^69 - 4 * q^70 - 40 * q^71 - 6 * q^72 - 2 * q^73 + 24 * q^74 - 4 * q^76 + 4 * q^77 + 8 * q^78 - 6 * q^80 + 10 * q^81 - 4 * q^82 + 20 * q^83 - 20 * q^84 - 16 * q^85 + 22 * q^86 - 4 * q^87 + 2 * q^88 + 20 * q^89 + 4 * q^90 - 40 * q^91 - 12 * q^92 + 12 * q^93 - 10 * q^94 + 2 * q^95 + 4 * q^96 - 24 * q^97 + 20 * q^98 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/133\mathbb{Z}\right)^\times$.

$n$	$78$	$115$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.207107	+	0.358719i	−0.146447	+	0.253653i	−0.929912	−	0.367783i	$-0.880117\pi$
$2$	−0.207107	+	0.358719i	−0.146447	+	0.253653i	0.783465	+	0.621436i	$0.213450\pi$
$3$	0.707107	+	1.22474i	0.408248	+	0.707107i	0.994694	−	0.102882i	$-0.0328064\pi$
$3$	0.707107	+	1.22474i	0.408248	+	0.707107i	−0.586445	+	0.809989i	$0.699473\pi$
$4$	0.914214	+	1.58346i	0.457107	+	0.791732i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	−0.955901	−	0.293691i	$-0.905116\pi$
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	0.732294	+	0.680989i	$0.238450\pi$
$6$	−0.585786			−0.239146
$7$	−2.62132	−	0.358719i	−0.990766	−	0.135583i
$7$	−2.62132	−	0.358719i	−0.990766	−	0.135583i
$8$	−1.58579			−0.560660
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−0.207107	−	0.358719i	−0.0654929	−	0.113437i
$11$	−1.20711	−	2.09077i	−0.363956	−	0.630391i	0.624652	−	0.780903i	$-0.285241\pi$
$11$	−1.20711	−	2.09077i	−0.363956	−	0.630391i	−0.988608	+	0.150513i	$0.951908\pi$
$12$	−1.29289	+	2.23936i	−0.373226	+	0.646447i
$13$	6.24264			1.73140			0.865699	−	0.500566i	$-0.166875\pi$
$13$	6.24264			1.73140			0.865699	+	0.500566i	$0.166875\pi$
$14$	0.671573	−	0.866025i	0.179485	−	0.231455i
$15$	−1.41421			−0.365148
$16$	−1.50000	+	2.59808i	−0.375000	+	0.649519i
$17$	2.00000	+	3.46410i	0.485071	+	0.840168i	0.999853	−	0.0171533i	$-0.00546033\pi$
$17$	2.00000	+	3.46410i	0.485071	+	0.840168i	−0.514782	+	0.857321i	$0.672127\pi$
$18$	0.207107	+	0.358719i	0.0488155	+	0.0845510i
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i
$20$	−1.82843			−0.408849
$21$	−1.41421	−	3.46410i	−0.308607	−	0.755929i
$22$	1.00000			0.213201
$23$	4.20711	−	7.28692i	0.877242	−	1.51943i	0.0228877	−	0.999738i	$-0.492714\pi$
$23$	4.20711	−	7.28692i	0.877242	−	1.51943i	0.854355	−	0.519690i	$-0.173953\pi$
$24$	−1.12132	−	1.94218i	−0.228889	−	0.396447i
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$	−1.29289	+	2.23936i	−0.253557	+	0.439174i
$27$	5.65685			1.08866
$28$	−1.82843	−	4.47871i	−0.345540	−	0.846397i
$29$	−9.41421			−1.74818			−0.874088	−	0.485768i	$-0.838540\pi$
$29$	−9.41421			−1.74818			−0.874088	+	0.485768i	$0.838540\pi$
$30$	0.292893	−	0.507306i	0.0534747	−	0.0926210i
$31$	−1.12132	−	1.94218i	−0.201395	−	0.348827i	0.747583	−	0.664168i	$-0.231214\pi$
$31$	−1.12132	−	1.94218i	−0.201395	−	0.348827i	−0.948978	+	0.315342i	$0.897881\pi$
$32$	−2.20711	−	3.82282i	−0.390165	−	0.675786i
$33$	1.70711	−	2.95680i	0.297169	−	0.514712i
$34$	−1.65685			−0.284148
$35$	1.62132	−	2.09077i	0.274053	−	0.353405i
$36$	1.82843			0.304738
$37$	2.53553	−	4.39167i	0.416839	−	0.721987i	−0.578780	−	0.815483i	$-0.696471\pi$
$37$	2.53553	−	4.39167i	0.416839	−	0.721987i	0.995620	+	0.0934968i	$0.0298045\pi$
$38$	0.207107	+	0.358719i	0.0335972	+	0.0581920i
$39$	4.41421	+	7.64564i	0.706840	+	1.22428i
$40$	0.792893	−	1.37333i	0.125367	−	0.217143i
$41$	−8.82843			−1.37877			−0.689384	−	0.724396i	$-0.742119\pi$
$41$	−8.82843			−1.37877			−0.689384	+	0.724396i	$0.742119\pi$
$42$	1.53553	+	0.210133i	0.236938	+	0.0324242i
$43$	−6.07107			−0.925829			−0.462915	−	0.886403i	$-0.653196\pi$
$43$	−6.07107			−0.925829			−0.462915	+	0.886403i	$0.653196\pi$
$44$	2.20711	−	3.82282i	0.332734	−	0.576312i
$45$	0.500000	+	0.866025i	0.0745356	+	0.129099i
$46$	1.74264	+	3.01834i	0.256938	+	0.445030i
$47$	0.792893	−	1.37333i	0.115655	−	0.200321i	−0.802386	−	0.596805i	$-0.796437\pi$
$47$	0.792893	−	1.37333i	0.115655	−	0.200321i	0.918042	+	0.396484i	$0.129770\pi$
$48$	−4.24264			−0.612372
$49$	6.74264	+	1.88064i	0.963234	+	0.268662i
$50$	−1.65685			−0.234315
$51$	−2.82843	+	4.89898i	−0.396059	+	0.685994i
$52$	5.70711	+	9.88500i	0.791433	+	1.37080i
$53$	−2.12132	−	3.67423i	−0.291386	−	0.504695i	0.682752	−	0.730650i	$-0.260783\pi$
$53$	−2.12132	−	3.67423i	−0.291386	−	0.504695i	−0.974138	+	0.225955i	$0.927450\pi$
$54$	−1.17157	+	2.02922i	−0.159431	+	0.276142i
$55$	2.41421			0.325532
$56$	4.15685	+	0.568852i	0.555483	+	0.0760161i
$57$	1.41421			0.187317
$58$	1.94975	−	3.37706i	0.256014	−	0.443430i
$59$	−0.585786	−	1.01461i	−0.0762629	−	0.132091i	0.825372	−	0.564589i	$-0.190965\pi$
$59$	−0.585786	−	1.01461i	−0.0762629	−	0.132091i	−0.901635	+	0.432498i	$0.857632\pi$
$60$	−1.29289	−	2.23936i	−0.166912	−	0.289100i
$61$	−3.08579	+	5.34474i	−0.395094	+	0.684324i	−0.993113	−	0.117158i	$-0.962621\pi$
$61$	−3.08579	+	5.34474i	−0.395094	+	0.684324i	0.598019	+	0.801482i	$0.295955\pi$
$62$	0.928932			0.117975
$63$	−1.62132	+	2.09077i	−0.204267	+	0.263412i
$64$	−4.17157			−0.521447
$65$	−3.12132	+	5.40629i	−0.387152	+	0.670567i
$66$	0.707107	+	1.22474i	0.0870388	+	0.150756i
$67$	−3.41421	−	5.91359i	−0.417113	−	0.722460i	0.578535	−	0.815657i	$-0.303625\pi$
$67$	−3.41421	−	5.91359i	−0.417113	−	0.722460i	−0.995648	+	0.0931973i	$0.970291\pi$
$68$	−3.65685	+	6.33386i	−0.443459	+	0.768093i
$69$	11.8995			1.43253
$70$	0.414214	+	1.01461i	0.0495080	+	0.121269i
$71$	−5.75736			−0.683273			−0.341636	−	0.939832i	$-0.610981\pi$
$71$	−5.75736			−0.683273			−0.341636	+	0.939832i	$0.610981\pi$
$72$	−0.792893	+	1.37333i	−0.0934434	+	0.161849i
$73$	6.57107	+	11.3814i	0.769085	+	1.33209i	0.938059	+	0.346474i	$0.112621\pi$
$73$	6.57107	+	11.3814i	0.769085	+	1.33209i	−0.168974	+	0.985620i	$0.554045\pi$
$74$	1.05025	+	1.81909i	0.122089	+	0.211465i
$75$	−2.82843	+	4.89898i	−0.326599	+	0.565685i
$76$	1.82843			0.209735
$77$	2.41421	+	5.91359i	0.275125	+	0.673916i
$78$	−3.65685			−0.414057
$79$	0.707107	−	1.22474i	0.0795557	−	0.137795i	−0.823503	−	0.567312i	$-0.807983\pi$
$79$	0.707107	−	1.22474i	0.0795557	−	0.137795i	0.903058	+	0.429518i	$0.141317\pi$
$80$	−1.50000	−	2.59808i	−0.167705	−	0.290474i
$81$	2.50000	+	4.33013i	0.277778	+	0.481125i
$82$	1.82843	−	3.16693i	0.201916	−	0.349729i
$83$	0.757359			0.0831310			0.0415655	−	0.999136i	$-0.486765\pi$
$83$	0.757359			0.0831310			0.0415655	+	0.999136i	$0.486765\pi$
$84$	4.19239	−	5.40629i	0.457427	−	0.589874i
$85$	−4.00000			−0.433861
$86$	1.25736	−	2.17781i	0.135585	−	0.234839i
$87$	−6.65685	−	11.5300i	−0.713690	−	1.23615i
$88$	1.91421	+	3.31552i	0.204056	+	0.353435i
$89$	4.29289	−	7.43551i	0.455046	−	0.788162i	−0.543645	−	0.839315i	$-0.682956\pi$
$89$	4.29289	−	7.43551i	0.455046	−	0.788162i	0.998691	+	0.0511528i	$0.0162896\pi$
$90$	−0.414214			−0.0436619
$91$	−16.3640	−	2.23936i	−1.71541	−	0.234748i
$92$	15.3848			1.60397
$93$	1.58579	−	2.74666i	0.164438	−	0.284816i
$94$	0.328427	+	0.568852i	0.0338747	+	0.0586727i
$95$	0.500000	+	0.866025i	0.0512989	+	0.0888523i
$96$	3.12132	−	5.40629i	0.318568	−	0.551777i
$97$	−8.82843			−0.896391			−0.448195	−	0.893936i	$-0.647933\pi$
$97$	−8.82843			−0.896391			−0.448195	+	0.893936i	$0.647933\pi$
$98$	−2.07107	+	2.02922i	−0.209209	+	0.204983i
$99$	−2.41421			−0.242638
$100$	−3.65685	+	6.33386i	−0.365685	+	0.633386i
$101$	2.15685	+	3.73578i	0.214615	+	0.371724i	0.953153	−	0.302487i	$-0.0978170\pi$
$101$	2.15685	+	3.73578i	0.214615	+	0.371724i	−0.738538	+	0.674211i	$0.764484\pi$
$102$	−1.17157	−	2.02922i	−0.116003	−	0.200923i
$103$	3.00000	−	5.19615i	0.295599	−	0.511992i	−0.679525	−	0.733652i	$-0.737814\pi$
$103$	3.00000	−	5.19615i	0.295599	−	0.511992i	0.975124	+	0.221660i	$0.0711475\pi$
$104$	−9.89949			−0.970725
$105$	3.70711	+	0.507306i	0.361777	+	0.0495080i
$106$	1.75736			0.170690
$107$	−2.94975	+	5.10911i	−0.285163	+	0.493917i	−0.972649	−	0.232281i	$-0.925381\pi$
$107$	−2.94975	+	5.10911i	−0.285163	+	0.493917i	0.687486	+	0.726198i	$0.258714\pi$
$108$	5.17157	+	8.95743i	0.497635	+	0.861929i
$109$	−0.828427	−	1.43488i	−0.0793489	−	0.137436i	0.823620	−	0.567142i	$-0.191951\pi$
$109$	−0.828427	−	1.43488i	−0.0793489	−	0.137436i	−0.902969	+	0.429705i	$0.858617\pi$
$110$	−0.500000	+	0.866025i	−0.0476731	+	0.0825723i
$111$	7.17157			0.680696
$112$	4.86396	−	6.27231i	0.459601	−	0.592678i
$113$	8.24264			0.775402			0.387701	−	0.921785i	$-0.373269\pi$
$113$	8.24264			0.775402			0.387701	+	0.921785i	$0.373269\pi$
$114$	−0.292893	+	0.507306i	−0.0274320	+	0.0475136i
$115$	4.20711	+	7.28692i	0.392315	+	0.679509i
$116$	−8.60660	−	14.9071i	−0.799103	−	1.38409i
$117$	3.12132	−	5.40629i	0.288566	−	0.499811i
$118$	0.485281			0.0446738
$119$	−4.00000	−	9.79796i	−0.366679	−	0.898177i
$120$	2.24264			0.204724
$121$	2.58579	−	4.47871i	0.235071	−	0.407156i
$122$	−1.27817	−	2.21386i	−0.115720	−	0.200434i
$123$	−6.24264	−	10.8126i	−0.562880	−	0.974937i
$124$	2.05025	−	3.55114i	0.184118	−	0.318902i
$125$	−9.00000			−0.804984
$126$	−0.414214	−	1.01461i	−0.0369011	−	0.0903888i
$127$	−4.24264			−0.376473			−0.188237	−	0.982124i	$-0.560277\pi$
$127$	−4.24264			−0.376473			−0.188237	+	0.982124i	$0.560277\pi$
$128$	5.27817	−	9.14207i	0.466529	−	0.808052i
$129$	−4.29289	−	7.43551i	−0.377968	−	0.654660i
$130$	−1.29289	−	2.23936i	−0.113394	−	0.196405i
$131$	−10.2426	+	17.7408i	−0.894904	+	1.55002i	−0.0609799	+	0.998139i	$0.519423\pi$
$131$	−10.2426	+	17.7408i	−0.894904	+	1.55002i	−0.833924	+	0.551880i	$0.813911\pi$
$132$	6.24264			0.543352
$133$	−1.62132	+	2.09077i	−0.140586	+	0.181293i
$134$	2.82843			0.244339
$135$	−2.82843	+	4.89898i	−0.243432	+	0.421637i
$136$	−3.17157	−	5.49333i	−0.271960	−	0.471049i
$137$	7.08579	+	12.2729i	0.605380	+	1.04855i	0.991991	+	0.126306i	$0.0403120\pi$
$137$	7.08579	+	12.2729i	0.605380	+	1.04855i	−0.386612	+	0.922243i	$0.626355\pi$
$138$	−2.46447	+	4.26858i	−0.209789	+	0.363366i
$139$	8.07107			0.684579			0.342290	−	0.939595i	$-0.388798\pi$
$139$	8.07107			0.684579			0.342290	+	0.939595i	$0.388798\pi$
$140$	4.79289	+	0.655892i	0.405073	+	0.0554330i
$141$	2.24264			0.188864
$142$	1.19239	−	2.06528i	0.100063	−	0.173314i
$143$	−7.53553	−	13.0519i	−0.630153	−	1.09146i
$144$	1.50000	+	2.59808i	0.125000	+	0.216506i
$145$	4.70711	−	8.15295i	0.390904	−	0.677065i
$146$	−5.44365			−0.450520
$147$	2.46447	+	9.58783i	0.203266	+	0.790791i
$148$	9.27208			0.762160
$149$	2.91421	−	5.04757i	0.238742	−	0.413513i	−0.721612	−	0.692298i	$-0.756598\pi$
$149$	2.91421	−	5.04757i	0.238742	−	0.413513i	0.960353	+	0.278785i	$0.0899317\pi$
$150$	−1.17157	−	2.02922i	−0.0956585	−	0.165685i
$151$	−2.65685	−	4.60181i	−0.216212	−	0.374490i	0.737435	−	0.675418i	$-0.236037\pi$
$151$	−2.65685	−	4.60181i	−0.216212	−	0.374490i	−0.953647	+	0.300928i	$0.902703\pi$
$152$	−0.792893	+	1.37333i	−0.0643121	+	0.111392i
$153$	4.00000			0.323381
$154$	−2.62132	−	0.358719i	−0.211232	−	0.0289064i
$155$	2.24264			0.180133
$156$	−8.07107	+	13.9795i	−0.646203	+	1.11926i
$157$	−5.91421	−	10.2437i	−0.472006	−	0.817538i	0.527481	−	0.849567i	$-0.323136\pi$
$157$	−5.91421	−	10.2437i	−0.472006	−	0.817538i	−0.999487	+	0.0320289i	$0.989803\pi$
$158$	0.292893	+	0.507306i	0.0233013	+	0.0403591i
$159$	3.00000	−	5.19615i	0.237915	−	0.412082i
$160$	4.41421			0.348974
$161$	−13.6421	+	17.5922i	−1.07515	+	1.38646i
$162$	−2.07107			−0.162718
$163$	−9.03553	+	15.6500i	−0.707718	+	1.22580i	0.257984	+	0.966149i	$0.416942\pi$
$163$	−9.03553	+	15.6500i	−0.707718	+	1.22580i	−0.965702	+	0.259654i	$0.916392\pi$
$164$	−8.07107	−	13.9795i	−0.630245	−	1.09162i
$165$	1.70711	+	2.95680i	0.132898	+	0.230186i
$166$	−0.156854	+	0.271680i	−0.0121743	+	0.0210864i
$167$	−1.07107			−0.0828817			−0.0414409	−	0.999141i	$-0.513195\pi$
$167$	−1.07107			−0.0828817			−0.0414409	+	0.999141i	$0.513195\pi$
$168$	2.24264	+	5.49333i	0.173023	+	0.423819i
$169$	25.9706			1.99774
$170$	0.828427	−	1.43488i	0.0635375	−	0.110050i
$171$	−0.500000	−	0.866025i	−0.0382360	−	0.0662266i
$172$	−5.55025	−	9.61332i	−0.423203	−	0.733009i
$173$	−7.65685	+	13.2621i	−0.582140	+	1.00830i	0.413086	+	0.910692i	$0.364451\pi$
$173$	−7.65685	+	13.2621i	−0.582140	+	1.00830i	−0.995225	+	0.0976036i	$0.968882\pi$
$174$	5.51472			0.418070
$175$	−4.00000	−	9.79796i	−0.302372	−	0.740656i
$176$	7.24264			0.545935
$177$	0.828427	−	1.43488i	0.0622684	−	0.107852i
$178$	1.77817	+	3.07989i	0.133280	+	0.230847i
$179$	10.8995	+	18.8785i	0.814667	+	1.41104i	0.909567	+	0.415557i	$0.136413\pi$
$179$	10.8995	+	18.8785i	0.814667	+	1.41104i	−0.0949006	+	0.995487i	$0.530253\pi$
$180$	−0.914214	+	1.58346i	−0.0681415	+	0.118024i
$181$	−9.89949			−0.735824			−0.367912	−	0.929861i	$-0.619927\pi$
$181$	−9.89949			−0.735824			−0.367912	+	0.929861i	$0.619927\pi$
$182$	4.19239	−	5.40629i	0.310760	−	0.400741i
$183$	−8.72792			−0.645187
$184$	−6.67157	+	11.5555i	−0.491835	+	0.851883i
$185$	2.53553	+	4.39167i	0.186416	+	0.322882i
$186$	0.656854	+	1.13770i	0.0481629	+	0.0834206i
$187$	4.82843	−	8.36308i	0.353090	−	0.611569i
$188$	2.89949			0.211467
$189$	−14.8284	−	2.02922i	−1.07861	−	0.147604i
$190$	−0.414214			−0.0300502
$191$	−2.79289	+	4.83743i	−0.202087	+	0.350024i	−0.949201	−	0.314672i	$-0.898106\pi$
$191$	−2.79289	+	4.83743i	−0.202087	+	0.350024i	0.747114	+	0.664696i	$0.231439\pi$
$192$	−2.94975	−	5.10911i	−0.212880	−	0.368718i
$193$	5.94975	+	10.3053i	0.428272	+	0.741789i	0.996720	−	0.0809303i	$-0.0257891\pi$
$193$	5.94975	+	10.3053i	0.428272	+	0.741789i	−0.568448	+	0.822719i	$0.692456\pi$
$194$	1.82843	−	3.16693i	0.131273	−	0.227372i
$195$	−8.82843			−0.632217
$196$	3.18629	+	12.3960i	0.227592	+	0.885431i
$197$	21.4853			1.53076			0.765381	−	0.643577i	$-0.222550\pi$
$197$	21.4853			1.53076			0.765381	+	0.643577i	$0.222550\pi$
$198$	0.500000	−	0.866025i	0.0355335	−	0.0615457i
$199$	−0.964466	−	1.67050i	−0.0683692	−	0.118419i	0.829814	−	0.558039i	$-0.188446\pi$
$199$	−0.964466	−	1.67050i	−0.0683692	−	0.118419i	−0.898184	+	0.439621i	$0.855113\pi$
$200$	−3.17157	−	5.49333i	−0.224264	−	0.388437i
$201$	4.82843	−	8.36308i	0.340571	−	0.589886i
$202$	−1.78680			−0.125719
$203$	24.6777	+	3.37706i	1.73203	+	0.237023i
$204$	−10.3431			−0.724165
$205$	4.41421	−	7.64564i	0.308302	−	0.533995i
$206$	1.24264	+	2.15232i	0.0865789	+	0.149959i
$207$	−4.20711	−	7.28692i	−0.292414	−	0.506476i
$208$	−9.36396	+	16.2189i	−0.649274	+	1.12458i
$209$	−2.41421			−0.166995
$210$	−0.949747	+	1.22474i	−0.0655388	+	0.0845154i
$211$	−6.82843			−0.470088			−0.235044	−	0.971985i	$-0.575523\pi$
$211$	−6.82843			−0.470088			−0.235044	+	0.971985i	$0.575523\pi$
$212$	3.87868	−	6.71807i	0.266389	−	0.461399i
$213$	−4.07107	−	7.05130i	−0.278945	−	0.483147i
$214$	−1.22183	−	2.11626i	−0.0835223	−	0.144665i
$215$	3.03553	−	5.25770i	0.207022	−	0.358572i
$216$	−8.97056			−0.610369
$217$	2.24264	+	5.49333i	0.152240	+	0.372911i
$218$	0.686292			0.0464815
$219$	−9.29289	+	16.0958i	−0.627956	+	1.08765i
$220$	2.20711	+	3.82282i	0.148803	+	0.257735i
$221$	12.4853	+	21.6251i	0.839851	+	1.45466i
$222$	−1.48528	+	2.57258i	−0.0996856	+	0.172660i
$223$	−6.24264			−0.418038			−0.209019	−	0.977912i	$-0.567027\pi$
$223$	−6.24264			−0.418038			−0.209019	+	0.977912i	$0.567027\pi$
$224$	4.41421	+	10.8126i	0.294937	+	0.722445i
$225$	4.00000			0.266667
$226$	−1.70711	+	2.95680i	−0.113555	+	0.196683i
$227$	5.87868	+	10.1822i	0.390182	+	0.675814i	0.992473	−	0.122462i	$-0.0390789\pi$
$227$	5.87868	+	10.1822i	0.390182	+	0.675814i	−0.602292	+	0.798276i	$0.705746\pi$
$228$	1.29289	+	2.23936i	0.0856239	+	0.148305i
$229$	2.24264	−	3.88437i	0.148198	−	0.256686i	−0.782364	−	0.622822i	$-0.785986\pi$
$229$	2.24264	−	3.88437i	0.148198	−	0.256686i	0.930561	+	0.366136i	$0.119319\pi$
$230$	−3.48528			−0.229813
$231$	−5.53553	+	7.13834i	−0.364211	+	0.469668i
$232$	14.9289			0.980132
$233$	8.24264	−	14.2767i	0.539993	−	0.935296i	−0.458910	−	0.888483i	$-0.651760\pi$
$233$	8.24264	−	14.2767i	0.539993	−	0.935296i	0.998904	−	0.0468133i	$-0.0149066\pi$
$234$	1.29289	+	2.23936i	0.0845191	+	0.146391i
$235$	0.792893	+	1.37333i	0.0517227	+	0.0895863i
$236$	1.07107	−	1.85514i	0.0697206	−	0.120760i
$237$	2.00000			0.129914
$238$	4.34315	+	0.594346i	0.281524	+	0.0385257i
$239$	2.00000			0.129369			0.0646846	−	0.997906i	$-0.479396\pi$
$239$	2.00000			0.129369			0.0646846	+	0.997906i	$0.479396\pi$
$240$	2.12132	−	3.67423i	0.136931	−	0.237171i
$241$	−11.0208	−	19.0886i	−0.709913	−	1.22961i	−0.964889	−	0.262658i	$-0.915401\pi$
$241$	−11.0208	−	19.0886i	−0.709913	−	1.22961i	0.254976	−	0.966947i	$-0.417932\pi$
$242$	1.07107	+	1.85514i	0.0688508	+	0.119253i
$243$	4.94975	−	8.57321i	0.317526	−	0.549972i
$244$	−11.2843			−0.722401
$245$	−5.00000	+	4.89898i	−0.319438	+	0.312984i
$246$	5.17157			0.329727
$247$	3.12132	−	5.40629i	0.198605	−	0.343994i
$248$	1.77817	+	3.07989i	0.112914	+	0.195573i
$249$	0.535534	+	0.927572i	0.0339381	+	0.0587825i
$250$	1.86396	−	3.22848i	0.117887	−	0.204187i
$251$	11.7279			0.740260			0.370130	−	0.928980i	$-0.379313\pi$
$251$	11.7279			0.740260			0.370130	+	0.928980i	$0.379313\pi$
$252$	−4.79289	−	0.655892i	−0.301924	−	0.0413173i
$253$	−20.3137			−1.27711
$254$	0.878680	−	1.52192i	0.0551333	−	0.0954936i
$255$	−2.82843	−	4.89898i	−0.177123	−	0.306786i
$256$	−1.98528	−	3.43861i	−0.124080	−	0.214913i
$257$	6.65685	−	11.5300i	0.415243	−	0.719222i	−0.580211	−	0.814466i	$-0.697030\pi$
$257$	6.65685	−	11.5300i	0.415243	−	0.719222i	0.995454	+	0.0952441i	$0.0303632\pi$
$258$	3.55635			0.221409
$259$	−8.22183	+	10.6024i	−0.510879	+	0.658803i
$260$	−11.4142			−0.707879
$261$	−4.70711	+	8.15295i	−0.291363	+	0.504655i
$262$	−4.24264	−	7.34847i	−0.262111	−	0.453990i
$263$	0.242641	+	0.420266i	0.0149619	+	0.0259147i	0.873409	−	0.486987i	$-0.161904\pi$
$263$	0.242641	+	0.420266i	0.0149619	+	0.0259147i	−0.858448	+	0.512901i	$0.828571\pi$
$264$	−2.70711	+	4.68885i	−0.166611	+	0.288579i
$265$	4.24264			0.260623
$266$	−0.414214	−	1.01461i	−0.0253971	−	0.0622098i
$267$	12.1421			0.743087
$268$	6.24264	−	10.8126i	0.381330	−	0.660483i
$269$	2.00000	+	3.46410i	0.121942	+	0.211210i	0.920534	−	0.390664i	$-0.127754\pi$
$269$	2.00000	+	3.46410i	0.121942	+	0.211210i	−0.798591	+	0.601874i	$0.794421\pi$
$270$	−1.17157	−	2.02922i	−0.0712997	−	0.123495i
$271$	3.37868	−	5.85204i	0.205240	−	0.355486i	−0.744969	−	0.667099i	$-0.767536\pi$
$271$	3.37868	−	5.85204i	0.205240	−	0.355486i	0.950209	+	0.311613i	$0.100869\pi$
$272$	−12.0000			−0.727607
$273$	−8.82843	−	21.6251i	−0.534321	−	1.30881i
$274$	−5.87006			−0.354623
$275$	4.82843	−	8.36308i	0.291165	−	0.504313i
$276$	10.8787	+	18.8424i	0.654820	+	1.13418i
$277$	−14.2279	−	24.6435i	−0.854873	−	1.48068i	−0.876763	−	0.480923i	$-0.840302\pi$
$277$	−14.2279	−	24.6435i	−0.854873	−	1.48068i	0.0218898	−	0.999760i	$-0.493032\pi$
$278$	−1.67157	+	2.89525i	−0.100254	+	0.173646i
$279$	−2.24264			−0.134263
$280$	−2.57107	+	3.31552i	−0.153651	+	0.198140i
$281$	−19.7574			−1.17863			−0.589313	−	0.807905i	$-0.700601\pi$
$281$	−19.7574			−1.17863			−0.589313	+	0.807905i	$0.700601\pi$
$282$	−0.464466	+	0.804479i	−0.0276586	+	0.0479060i
$283$	−7.96447	−	13.7949i	−0.473438	−	0.820019i	0.526099	−	0.850423i	$-0.323654\pi$
$283$	−7.96447	−	13.7949i	−0.473438	−	0.820019i	−0.999538	+	0.0304038i	$0.990321\pi$
$284$	−5.26346	−	9.11657i	−0.312329	−	0.540969i
$285$	−0.707107	+	1.22474i	−0.0418854	+	0.0725476i
$286$	6.24264			0.369135
$287$	23.1421	+	3.16693i	1.36604	+	0.186938i
$288$	−4.41421			−0.260110
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$	1.94975	+	3.37706i	0.114493	+	0.198308i
$291$	−6.24264	−	10.8126i	−0.365950	−	0.633844i
$292$	−12.0147	+	20.8101i	−0.703108	+	1.21782i
$293$	8.82843			0.515762			0.257881	−	0.966177i	$-0.416976\pi$
$293$	8.82843			0.515762			0.257881	+	0.966177i	$0.416976\pi$
$294$	−3.94975	−	1.10165i	−0.230354	−	0.0642496i
$295$	1.17157			0.0682116
$296$	−4.02082	+	6.96426i	−0.233705	+	0.404789i
$297$	−6.82843	−	11.8272i	−0.396226	−	0.686283i
$298$	1.20711	+	2.09077i	0.0699258	+	0.121115i
$299$	26.2635	−	45.4896i	1.51885	−	2.63073i
$300$	−10.3431			−0.597162
$301$	15.9142	+	2.17781i	0.917280	+	0.125527i
$302$	2.20101			0.126654
$303$	−3.05025	+	5.28319i	−0.175232	+	0.303511i
$304$	1.50000	+	2.59808i	0.0860309	+	0.149010i
$305$	−3.08579	−	5.34474i	−0.176692	−	0.306039i
$306$	−0.828427	+	1.43488i	−0.0473580	+	0.0820265i
$307$	6.68629			0.381607			0.190803	−	0.981628i	$-0.438891\pi$
$307$	6.68629			0.381607			0.190803	+	0.981628i	$0.438891\pi$
$308$	−7.15685	+	9.22911i	−0.407800	+	0.525877i
$309$	8.48528			0.482711
$310$	−0.464466	+	0.804479i	−0.0263799	+	0.0456913i
$311$	−7.89949	−	13.6823i	−0.447939	−	0.775854i	0.550312	−	0.834959i	$-0.314509\pi$
$311$	−7.89949	−	13.6823i	−0.447939	−	0.775854i	−0.998252	+	0.0591052i	$0.981175\pi$
$312$	−7.00000	−	12.1244i	−0.396297	−	0.686406i
$313$	−2.32843	+	4.03295i	−0.131610	+	0.227956i	−0.924298	−	0.381673i	$-0.875348\pi$
$313$	−2.32843	+	4.03295i	−0.131610	+	0.227956i	0.792687	+	0.609629i	$0.208681\pi$
$314$	4.89949			0.276494
$315$	−1.00000	−	2.44949i	−0.0563436	−	0.138013i
$316$	2.58579			0.145462
$317$	5.87868	−	10.1822i	0.330180	−	0.571888i	−0.652367	−	0.757903i	$-0.726224\pi$
$317$	5.87868	−	10.1822i	0.330180	−	0.571888i	0.982547	+	0.186015i	$0.0595574\pi$
$318$	1.24264	+	2.15232i	0.0696838	+	0.120696i
$319$	11.3640	+	19.6830i	0.636260	+	1.10203i
$320$	2.08579	−	3.61269i	0.116599	−	0.201955i
$321$	−8.34315			−0.465669
$322$	−3.48528	−	8.53716i	−0.194227	−	0.475757i
$323$	4.00000			0.222566
$324$	−4.57107	+	7.91732i	−0.253948	+	0.439851i
$325$	12.4853	+	21.6251i	0.692559	+	1.19955i
$326$	−3.74264	−	6.48244i	−0.207286	−	0.359029i
$327$	1.17157	−	2.02922i	0.0647881	−	0.112216i
$328$	14.0000			0.773021
$329$	−2.57107	+	3.31552i	−0.141748	+	0.182790i
$330$	−1.41421			−0.0778499
$331$	−9.72792	+	16.8493i	−0.534695	+	0.926119i	0.464483	+	0.885582i	$0.346240\pi$
$331$	−9.72792	+	16.8493i	−0.534695	+	0.926119i	−0.999178	+	0.0405368i	$0.987093\pi$
$332$	0.692388	+	1.19925i	0.0379997	+	0.0658175i
$333$	−2.53553	−	4.39167i	−0.138946	−	0.240662i
$334$	0.221825	−	0.384213i	0.0121377	−	0.0210232i
$335$	6.82843			0.373077
$336$	11.1213	+	1.52192i	0.606718	+	0.0830274i
$337$	−11.5563			−0.629514			−0.314757	−	0.949172i	$-0.601923\pi$
$337$	−11.5563			−0.629514			−0.314757	+	0.949172i	$0.601923\pi$
$338$	−5.37868	+	9.31615i	−0.292562	+	0.506732i
$339$	5.82843	+	10.0951i	0.316557	+	0.548292i
$340$	−3.65685	−	6.33386i	−0.198321	−	0.343502i
$341$	−2.70711	+	4.68885i	−0.146598	+	0.253915i
$342$	0.414214			0.0223981
$343$	−17.0000	−	7.34847i	−0.917914	−	0.396780i
$344$	9.62742			0.519076
$345$	−5.94975	+	10.3053i	−0.320324	+	0.554817i
$346$	−3.17157	−	5.49333i	−0.170505	−	0.295323i
$347$	10.5208	+	18.2226i	0.564787	+	0.978240i	0.997069	+	0.0765015i	$0.0243750\pi$
$347$	10.5208	+	18.2226i	0.564787	+	0.978240i	−0.432283	+	0.901738i	$0.642292\pi$
$348$	12.1716	−	21.0818i	0.652465	−	1.13010i
$349$	−12.4853			−0.668322			−0.334161	−	0.942516i	$-0.608453\pi$
$349$	−12.4853			−0.668322			−0.334161	+	0.942516i	$0.608453\pi$
$350$	4.34315	+	0.594346i	0.232151	+	0.0317691i
$351$	35.3137			1.88491
$352$	−5.32843	+	9.22911i	−0.284006	+	0.491913i
$353$	8.24264	+	14.2767i	0.438711	+	0.759871i	0.997590	−	0.0693787i	$-0.0221017\pi$
$353$	8.24264	+	14.2767i	0.438711	+	0.759871i	−0.558879	+	0.829249i	$0.688768\pi$
$354$	0.343146	+	0.594346i	0.0182380	+	0.0315891i
$355$	2.87868	−	4.98602i	0.152784	−	0.264630i
$356$	15.6985			0.832018
$357$	9.17157	−	11.8272i	0.485411	−	0.625961i
$358$	−9.02944			−0.477221
$359$	1.62132	−	2.80821i	0.0855700	−	0.148212i	−0.820064	−	0.572272i	$-0.806062\pi$
$359$	1.62132	−	2.80821i	0.0855700	−	0.148212i	0.905634	+	0.424060i	$0.139396\pi$
$360$	−0.792893	−	1.37333i	−0.0417891	−	0.0723809i
$361$	−0.500000	−	0.866025i	−0.0263158	−	0.0455803i
$362$	2.05025	−	3.55114i	0.107759	−	0.186644i
$363$	7.31371			0.383870
$364$	−11.4142	−	27.9590i	−0.598267	−	1.46545i
$365$	−13.1421			−0.687891
$366$	1.80761	−	3.13088i	0.0944854	−	0.163653i
$367$	17.8284	+	30.8797i	0.930636	+	1.61191i	0.782236	+	0.622982i	$0.214079\pi$
$367$	17.8284	+	30.8797i	0.930636	+	1.61191i	0.148400	+	0.988927i	$0.452588\pi$
$368$	12.6213	+	21.8608i	0.657932	+	1.13957i
$369$	−4.41421	+	7.64564i	−0.229795	+	0.398016i
$370$	−2.10051			−0.109200
$371$	4.24264	+	10.3923i	0.220267	+	0.539542i
$372$	5.79899			0.300664
$373$	5.65685	−	9.79796i	0.292901	−	0.507319i	−0.681594	−	0.731731i	$-0.738713\pi$
$373$	5.65685	−	9.79796i	0.292901	−	0.507319i	0.974494	+	0.224412i	$0.0720461\pi$
$374$	2.00000	+	3.46410i	0.103418	+	0.179124i
$375$	−6.36396	−	11.0227i	−0.328634	−	0.569210i
$376$	−1.25736	+	2.17781i	−0.0648434	+	0.112312i
$377$	−58.7696			−3.02679
$378$	3.79899	−	4.89898i	0.195399	−	0.251976i
$379$	−4.24264			−0.217930			−0.108965	−	0.994046i	$-0.534754\pi$
$379$	−4.24264			−0.217930			−0.108965	+	0.994046i	$0.534754\pi$
$380$	−0.914214	+	1.58346i	−0.0468982	+	0.0812300i
$381$	−3.00000	−	5.19615i	−0.153695	−	0.266207i
$382$	−1.15685	−	2.00373i	−0.0591898	−	0.102520i
$383$	−14.1213	+	24.4588i	−0.721566	+	1.24979i	0.238806	+	0.971067i	$0.423244\pi$
$383$	−14.1213	+	24.4588i	−0.721566	+	1.24979i	−0.960372	+	0.278721i	$0.910089\pi$
$384$	14.9289			0.761839
$385$	−6.32843	−	0.866025i	−0.322527	−	0.0441367i
$386$	−4.92893			−0.250876
$387$	−3.03553	+	5.25770i	−0.154305	+	0.267264i
$388$	−8.07107	−	13.9795i	−0.409746	−	0.709702i
$389$	14.2426	+	24.6690i	0.722131	+	1.25077i	0.960144	+	0.279505i	$0.0901704\pi$
$389$	14.2426	+	24.6690i	0.722131	+	1.25077i	−0.238014	+	0.971262i	$0.576496\pi$
$390$	1.82843	−	3.16693i	0.0925860	−	0.160364i
$391$	33.6569			1.70210
$392$	−10.6924	−	2.98229i	−0.540047	−	0.150628i
$393$	−28.9706			−1.46137
$394$	−4.44975	+	7.70719i	−0.224175	+	0.388283i
$395$	0.707107	+	1.22474i	0.0355784	+	0.0616236i
$396$	−2.20711	−	3.82282i	−0.110911	−	0.192104i
$397$	−18.3137	+	31.7203i	−0.919139	+	1.59199i	−0.118412	+	0.992965i	$0.537780\pi$
$397$	−18.3137	+	31.7203i	−0.919139	+	1.59199i	−0.800726	+	0.599030i	$0.795553\pi$
$398$	0.798990			0.0400497
$399$	−3.70711	−	0.507306i	−0.185587	−	0.0253971i
$400$	−12.0000			−0.600000
$401$	8.24264	−	14.2767i	0.411618	−	0.712943i	−0.583449	−	0.812150i	$-0.698297\pi$
$401$	8.24264	−	14.2767i	0.411618	−	0.712943i	0.995067	+	0.0992068i	$0.0316305\pi$
$402$	2.00000	+	3.46410i	0.0997509	+	0.172774i
$403$	−7.00000	−	12.1244i	−0.348695	−	0.603957i
$404$	−3.94365	+	6.83060i	−0.196204	+	0.339835i
$405$	−5.00000			−0.248452
$406$	−6.32233	+	8.15295i	−0.313772	+	0.404624i
$407$	−12.2426			−0.606845
$408$	4.48528	−	7.76874i	0.222055	−	0.384610i
$409$	12.6569	+	21.9223i	0.625841	+	1.08399i	0.988378	+	0.152019i	$0.0485775\pi$
$409$	12.6569	+	21.9223i	0.625841	+	1.08399i	−0.362536	+	0.931970i	$0.618089\pi$
$410$	1.82843	+	3.16693i	0.0902996	+	0.156403i
$411$	−10.0208	+	17.3566i	−0.494290	+	0.856136i
$412$	10.9706			0.540481
$413$	1.17157	+	2.86976i	0.0576493	+	0.141211i
$414$	3.48528			0.171292
$415$	−0.378680	+	0.655892i	−0.0185887	+	0.0321965i
$416$	−13.7782	−	23.8645i	−0.675531	−	1.17005i
$417$	5.70711	+	9.88500i	0.279478	+	0.484070i
$418$	0.500000	−	0.866025i	0.0244558	−	0.0423587i
$419$	−8.07107			−0.394297			−0.197149	−	0.980374i	$-0.563168\pi$
$419$	−8.07107			−0.394297			−0.197149	+	0.980374i	$0.563168\pi$
$420$	2.58579	+	6.33386i	0.126173	+	0.309061i
$421$	5.21320			0.254076			0.127038	−	0.991898i	$-0.459453\pi$
$421$	5.21320			0.254076			0.127038	+	0.991898i	$0.459453\pi$
$422$	1.41421	−	2.44949i	0.0688428	−	0.119239i
$423$	−0.792893	−	1.37333i	−0.0385518	−	0.0667737i
$424$	3.36396	+	5.82655i	0.163368	+	0.282962i
$425$	−8.00000	+	13.8564i	−0.388057	+	0.672134i
$426$	3.37258			0.163402
$427$	10.0061	−	12.9033i	0.484229	−	0.624436i
$428$	−10.7868			−0.521399
$429$	10.6569	−	18.4582i	0.514518	−	0.891171i
$430$	1.25736	+	2.17781i	0.0606353	+	0.105023i
$431$	−19.0208	−	32.9450i	−0.916200	−	1.58691i	−0.805134	−	0.593093i	$-0.797907\pi$
$431$	−19.0208	−	32.9450i	−0.916200	−	1.58691i	−0.111066	−	0.993813i	$-0.535427\pi$
$432$	−8.48528	+	14.6969i	−0.408248	+	0.707107i
$433$	28.0000			1.34559			0.672797	−	0.739827i	$-0.265093\pi$
$433$	28.0000			1.34559			0.672797	+	0.739827i	$0.265093\pi$
$434$	−2.43503	−	0.333226i	−0.116885	−	0.0159954i
$435$	13.3137			0.638343
$436$	1.51472	−	2.62357i	0.0725419	−	0.125646i
$437$	−4.20711	−	7.28692i	−0.201253	−	0.348581i
$438$	−3.84924	−	6.66708i	−0.183924	−	0.318566i
$439$	3.75736	−	6.50794i	0.179329	−	0.310607i	−0.762322	−	0.647198i	$-0.775941\pi$
$439$	3.75736	−	6.50794i	0.179329	−	0.310607i	0.941651	+	0.336591i	$0.109274\pi$
$440$	−3.82843			−0.182513
$441$	5.00000	−	4.89898i	0.238095	−	0.233285i
$442$	−10.3431			−0.491973
$443$	−3.17157	+	5.49333i	−0.150686	+	0.260996i	−0.931480	−	0.363793i	$-0.881482\pi$
$443$	−3.17157	+	5.49333i	−0.150686	+	0.260996i	0.780794	+	0.624789i	$0.214815\pi$
$444$	6.55635	+	11.3559i	0.311151	+	0.538929i
$445$	4.29289	+	7.43551i	0.203503	+	0.352477i
$446$	1.29289	−	2.23936i	0.0612203	−	0.106037i
$447$	8.24264			0.389864
$448$	10.9350	+	1.49642i	0.516632	+	0.0706994i
$449$	−1.65685			−0.0781918			−0.0390959	−	0.999235i	$-0.512448\pi$
$449$	−1.65685			−0.0781918			−0.0390959	+	0.999235i	$0.512448\pi$
$450$	−0.828427	+	1.43488i	−0.0390524	+	0.0676408i
$451$	10.6569	+	18.4582i	0.501812	+	0.869163i
$452$	7.53553	+	13.0519i	0.354442	+	0.613911i
$453$	3.75736	−	6.50794i	0.176536	−	0.305770i
$454$	−4.87006			−0.228563
$455$	10.1213	−	13.0519i	0.474495	−	0.611884i
$456$	−2.24264			−0.105021
$457$	1.08579	−	1.88064i	0.0507909	−	0.0879725i	−0.839512	−	0.543341i	$-0.817159\pi$
$457$	1.08579	−	1.88064i	0.0507909	−	0.0879725i	0.890303	+	0.455368i	$0.150492\pi$
$458$	0.928932	+	1.60896i	0.0434062	+	0.0751817i
$459$	11.3137	+	19.5959i	0.528079	+	0.914659i
$460$	−7.69239	+	13.3236i	−0.358659	+	0.621216i
$461$	−3.97056			−0.184928			−0.0924638	−	0.995716i	$-0.529474\pi$
$461$	−3.97056			−0.184928			−0.0924638	+	0.995716i	$0.529474\pi$
$462$	−1.41421	−	3.46410i	−0.0657952	−	0.161165i
$463$	10.0711			0.468042			0.234021	−	0.972232i	$-0.424812\pi$
$463$	10.0711			0.468042			0.234021	+	0.972232i	$0.424812\pi$
$464$	14.1213	−	24.4588i	0.655566	−	1.13547i
$465$	1.58579	+	2.74666i	0.0735391	+	0.127373i
$466$	3.41421	+	5.91359i	0.158160	+	0.273942i
$467$	−19.4497	+	33.6880i	−0.900027	+	1.55889i	−0.0725700	+	0.997363i	$0.523120\pi$
$467$	−19.4497	+	33.6880i	−0.900027	+	1.55889i	−0.827457	+	0.561529i	$0.810213\pi$
$468$	11.4142			0.527622
$469$	6.82843	+	16.7262i	0.315307	+	0.772342i
$470$	−0.656854			−0.0302984
$471$	8.36396	−	14.4868i	0.385391	−	0.667517i
$472$	0.928932	+	1.60896i	0.0427576	+	0.0740583i
$473$	7.32843	+	12.6932i	0.336961	+	0.583634i
$474$	−0.414214	+	0.717439i	−0.0190255	+	0.0329531i
$475$	4.00000			0.183533
$476$	11.8579	−	15.2913i	0.543504	−	0.700875i
$477$	−4.24264			−0.194257
$478$	−0.414214	+	0.717439i	−0.0189457	+	0.0328149i
$479$	−5.69239	−	9.85951i	−0.260092	−	0.450492i	0.706174	−	0.708038i	$-0.250420\pi$
$479$	−5.69239	−	9.85951i	−0.260092	−	0.450492i	−0.966266	+	0.257546i	$0.917086\pi$
$480$	3.12132	+	5.40629i	0.142468	+	0.246762i
$481$	15.8284	−	27.4156i	0.721714	−	1.25005i
$482$	9.12994			0.415857
$483$	−31.1924	−	4.26858i	−1.41930	−	0.194227i
$484$	9.45584			0.429811
$485$	4.41421	−	7.64564i	0.200439	−	0.347171i
$486$	2.05025	+	3.55114i	0.0930013	+	0.161083i
$487$	−10.4142	−	18.0379i	−0.471913	−	0.817377i	0.527571	−	0.849511i	$-0.323103\pi$
$487$	−10.4142	−	18.0379i	−0.471913	−	0.817377i	−0.999484	+	0.0321338i	$0.989770\pi$
$488$	4.89340	−	8.47561i	0.221514	−	0.383673i
$489$	−25.5563			−1.15570
$490$	−0.721825	−	2.80821i	−0.0326087	−	0.126862i
$491$	−32.5563			−1.46925			−0.734624	−	0.678475i	$-0.762641\pi$
$491$	−32.5563			−1.46925			−0.734624	+	0.678475i	$0.762641\pi$
$492$	11.4142	−	19.7700i	0.514592	−	0.891300i
$493$	−18.8284	−	32.6118i	−0.847990	−	1.46876i
$494$	1.29289	+	2.23936i	0.0581700	+	0.100753i
$495$	1.20711	−	2.09077i	0.0542554	−	0.0939731i
$496$	6.72792			0.302093
$497$	15.0919	+	2.06528i	0.676963	+	0.0926403i
$498$	−0.443651			−0.0198805
$499$	−1.72183	+	2.98229i	−0.0770795	+	0.133506i	−0.901989	−	0.431760i	$-0.857893\pi$
$499$	−1.72183	+	2.98229i	−0.0770795	+	0.133506i	0.824909	+	0.565265i	$0.191226\pi$
$500$	−8.22792	−	14.2512i	−0.367964	−	0.637332i
$501$	−0.757359	−	1.31178i	−0.0338363	−	0.0586062i
$502$	−2.42893	+	4.20703i	−0.108409	+	0.187769i
$503$	19.0416			0.849024			0.424512	−	0.905422i	$-0.360446\pi$
$503$	19.0416			0.849024			0.424512	+	0.905422i	$0.360446\pi$
$504$	2.57107	−	3.31552i	0.114524	−	0.147685i
$505$	−4.31371			−0.191958
$506$	4.20711	−	7.28692i	0.187029	−	0.323943i
$507$	18.3640	+	31.8073i	0.815572	+	1.41261i
$508$	−3.87868	−	6.71807i	−0.172089	−	0.298066i
$509$	−9.48528	+	16.4290i	−0.420428	+	0.728202i	−0.995981	−	0.0895619i	$-0.971453\pi$
$509$	−9.48528	+	16.4290i	−0.420428	+	0.728202i	0.575554	+	0.817764i	$0.304787\pi$
$510$	2.34315			0.103756
$511$	−13.1421	−	32.1915i	−0.581374	−	1.42407i
$512$	22.7574			1.00574
$513$	2.82843	−	4.89898i	0.124878	−	0.216295i
$514$	2.75736	+	4.77589i	0.121622	+	0.210655i
$515$	3.00000	+	5.19615i	0.132196	+	0.228970i
$516$	7.84924	−	13.5953i	0.345544	−	0.598499i
$517$	−3.82843			−0.168374
$518$	−2.10051	−	5.14517i	−0.0922909	−	0.226066i
$519$	−21.6569			−0.950630
$520$	4.94975	−	8.57321i	0.217061	−	0.375960i
$521$	−5.22183	−	9.04447i	−0.228772	−	0.396245i	0.728672	−	0.684863i	$-0.240138\pi$
$521$	−5.22183	−	9.04447i	−0.228772	−	0.396245i	−0.957445	+	0.288617i	$0.906804\pi$
$522$	−1.94975	−	3.37706i	−0.0853381	−	0.147810i
$523$	11.8284	−	20.4874i	0.517221	−	0.895853i	−0.482579	−	0.875852i	$-0.660300\pi$
$523$	11.8284	−	20.4874i	0.517221	−	0.895853i	0.999800	−	0.0200006i	$-0.00636681\pi$
$524$	−37.4558			−1.63627
$525$	9.17157	−	11.8272i	0.400280	−	0.516181i
$526$	−0.201010			−0.00876446
$527$	4.48528	−	7.76874i	0.195382	−	0.338411i
$528$	5.12132	+	8.87039i	0.222877	+	0.386034i
$529$	−23.8995	−	41.3951i	−1.03911	−	1.79979i
$530$	−0.878680	+	1.52192i	−0.0381674	+	0.0661079i
$531$	−1.17157			−0.0508419
$532$	−4.79289	−	0.655892i	−0.207798	−	0.0284365i
$533$	−55.1127			−2.38720
$534$	−2.51472	+	4.35562i	−0.108823	+	0.188486i
$535$	−2.94975	−	5.10911i	−0.127529	−	0.220886i
$536$	5.41421	+	9.37769i	0.233858	+	0.405055i
$537$	−15.4142	+	26.6982i	−0.665172	+	1.15211i
$538$	−1.65685			−0.0714321
$539$	−4.20711	−	16.3674i	−0.181213	−	0.704996i
$540$	−10.3431			−0.445098
$541$	−2.57107	+	4.45322i	−0.110539	+	0.191459i	−0.915988	−	0.401206i	$-0.868591\pi$
$541$	−2.57107	+	4.45322i	−0.110539	+	0.191459i	0.805449	+	0.592665i	$0.201924\pi$
$542$	1.39949	+	2.42400i	0.0601135	+	0.104120i
$543$	−7.00000	−	12.1244i	−0.300399	−	0.520306i
$544$	8.82843	−	15.2913i	0.378516	−	0.655608i
$545$	1.65685			0.0709718
$546$	9.58579	+	1.31178i	0.410234	+	0.0561392i
$547$	29.5563			1.26374			0.631869	−	0.775075i	$-0.282288\pi$
$547$	29.5563			1.26374			0.631869	+	0.775075i	$0.282288\pi$
$548$	−12.9558	+	22.4402i	−0.553446	+	0.958597i
$549$	3.08579	+	5.34474i	0.131698	+	0.228108i
$550$	2.00000	+	3.46410i	0.0852803	+	0.147710i
$551$	−4.70711	+	8.15295i	−0.200529	+	0.347327i
$552$	−18.8701			−0.803163
$553$	−2.29289	+	2.95680i	−0.0975037	+	0.125736i
$554$	11.7868			0.500773
$555$	−3.58579	+	6.21076i	−0.152208	+	0.263632i
$556$	7.37868	+	12.7802i	0.312926	+	0.542003i
$557$	−5.08579	−	8.80884i	−0.215492	−	0.373243i	0.737933	−	0.674874i	$-0.235802\pi$
$557$	−5.08579	−	8.80884i	−0.215492	−	0.373243i	−0.953425	+	0.301632i	$0.902469\pi$
$558$	0.464466	−	0.804479i	0.0196624	−	0.0340563i
$559$	−37.8995			−1.60298
$560$	3.00000	+	7.34847i	0.126773	+	0.310530i
$561$	13.6569			0.576593
$562$	4.09188	−	7.08735i	0.172606	−	0.298962i
$563$	6.94975	+	12.0373i	0.292897	+	0.507312i	0.974493	−	0.224416i	$-0.0720474\pi$
$563$	6.94975	+	12.0373i	0.292897	+	0.507312i	−0.681597	+	0.731728i	$0.738714\pi$
$564$	2.05025	+	3.55114i	0.0863312	+	0.149530i
$565$	−4.12132	+	7.13834i	−0.173385	+	0.300312i
$566$	6.59798			0.277334
$567$	−5.00000	−	12.2474i	−0.209980	−	0.514344i
$568$	9.12994			0.383084
$569$	21.4853	−	37.2136i	0.900710	−	1.56008i	0.0741351	−	0.997248i	$-0.476380\pi$
$569$	21.4853	−	37.2136i	0.900710	−	1.56008i	0.826575	−	0.562827i	$-0.190286\pi$
$570$	−0.292893	−	0.507306i	−0.0122679	−	0.0212487i
$571$	9.44975	+	16.3674i	0.395460	+	0.684956i	0.993160	−	0.116764i	$-0.0372520\pi$
$571$	9.44975	+	16.3674i	0.395460	+	0.684956i	−0.597700	+	0.801720i	$0.703919\pi$
$572$	13.7782	−	23.8645i	0.576094	−	0.997825i
$573$	−7.89949			−0.330006
$574$	−5.92893	+	7.64564i	−0.247469	+	0.319123i
$575$	33.6569			1.40359
$576$	−2.08579	+	3.61269i	−0.0869078	+	0.150529i
$577$	−13.9853	−	24.2232i	−0.582215	−	1.00843i	−0.995216	−	0.0976954i	$-0.968853\pi$
$577$	−13.9853	−	24.2232i	−0.582215	−	1.00843i	0.413001	−	0.910730i	$-0.364480\pi$
$578$	0.207107	+	0.358719i	0.00861451	+	0.0149208i
$579$	−8.41421	+	14.5738i	−0.349683	+	0.605668i
$580$	17.2132			0.714739
$581$	−1.98528	−	0.271680i	−0.0823633	−	0.0112712i
$582$	5.17157			0.214369
$583$	−5.12132	+	8.87039i	−0.212103	+	0.367374i
$584$	−10.4203	−	18.0485i	−0.431196	−	0.746853i
$585$	3.12132	+	5.40629i	0.129051	+	0.223522i
$586$	−1.82843	+	3.16693i	−0.0755316	+	0.130825i
$587$	14.0000			0.577842			0.288921	−	0.957353i	$-0.406704\pi$
$587$	14.0000			0.577842			0.288921	+	0.957353i	$0.406704\pi$
$588$	−12.9289	+	12.6677i	−0.533180	+	0.522408i
$589$	−2.24264			−0.0924064
$590$	−0.242641	+	0.420266i	−0.00998936	+	0.0173021i
$591$	15.1924	+	26.3140i	0.624931	+	1.08241i
$592$	7.60660	+	13.1750i	0.312629	+	0.541490i
$593$	−3.08579	+	5.34474i	−0.126718	+	0.219482i	−0.922403	−	0.386228i	$-0.873778\pi$
$593$	−3.08579	+	5.34474i	−0.126718	+	0.219482i	0.795685	+	0.605710i	$0.207111\pi$
$594$	5.65685			0.232104
$595$	10.4853	+	1.43488i	0.429855	+	0.0588243i
$596$	10.6569			0.436522
$597$	1.36396	−	2.36245i	0.0558232	−	0.0966886i
$598$	10.8787	+	18.8424i	0.444862	+	0.770524i
$599$	15.8492	+	27.4517i	0.647582	+	1.12165i	0.983699	+	0.179825i	$0.0575532\pi$
$599$	15.8492	+	27.4517i	0.647582	+	1.12165i	−0.336116	+	0.941821i	$0.609113\pi$
$600$	4.48528	−	7.76874i	0.183111	−	0.317157i
$601$	−9.27208			−0.378216			−0.189108	−	0.981956i	$-0.560560\pi$
$601$	−9.27208			−0.378216			−0.189108	+	0.981956i	$0.560560\pi$
$602$	−4.07716	+	5.25770i	−0.166173	+	0.214288i
$603$	−6.82843			−0.278075
$604$	4.85786	−	8.41407i	0.197664	−	0.342364i
$605$	2.58579	+	4.47871i	0.105127	+	0.182086i
$606$	−1.26346	−	2.18837i	−0.0513244	−	0.0888965i
$607$	−16.2635	+	28.1691i	−0.660113	+	1.14335i	0.320472	+	0.947258i	$0.396158\pi$
$607$	−16.2635	+	28.1691i	−0.660113	+	1.14335i	−0.980586	+	0.196092i	$0.937175\pi$
$608$	−4.41421			−0.179020
$609$	13.3137	+	32.6118i	0.539499	+	1.32150i
$610$	2.55635			0.103504
$611$	4.94975	−	8.57321i	0.200245	−	0.346835i
$612$	3.65685	+	6.33386i	0.147820	+	0.256031i
$613$	4.34315	+	7.52255i	0.175418	+	0.303833i	0.940306	−	0.340331i	$-0.110539\pi$
$613$	4.34315	+	7.52255i	0.175418	+	0.303833i	−0.764888	+	0.644163i	$0.777206\pi$
$614$	−1.38478	+	2.39850i	−0.0558850	+	0.0967957i
$615$	12.4853			0.503455
$616$	−3.82843	−	9.37769i	−0.154252	−	0.377838i
$617$	−42.4558			−1.70921			−0.854604	−	0.519280i	$-0.826200\pi$
$617$	−42.4558			−1.70921			−0.854604	+	0.519280i	$0.826200\pi$
$618$	−1.75736	+	3.04384i	−0.0706914	+	0.122441i
$619$	−1.72183	−	2.98229i	−0.0692060	−	0.119868i	0.829346	−	0.558735i	$-0.188713\pi$
$619$	−1.72183	−	2.98229i	−0.0692060	−	0.119868i	−0.898552	+	0.438867i	$0.855380\pi$
$620$	2.05025	+	3.55114i	0.0823401	+	0.142617i
$621$	23.7990	−	41.2211i	0.955021	−	1.65414i
$622$	6.54416			0.262397
$623$	−13.9203	+	17.9509i	−0.557705	+	0.719188i
$624$	−26.4853			−1.06026
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$	−0.964466	−	1.67050i	−0.0385478	−	0.0667668i
$627$	−1.70711	−	2.95680i	−0.0681753	−	0.118083i
$628$	10.8137	−	18.7299i	0.431514	−	0.747404i
$629$	20.2843			0.808787
$630$	1.08579	+	0.148586i	0.0432588	+	0.00591983i
$631$	−5.44365			−0.216708			−0.108354	−	0.994112i	$-0.534558\pi$
$631$	−5.44365			−0.216708			−0.108354	+	0.994112i	$0.534558\pi$
$632$	−1.12132	+	1.94218i	−0.0446037	+	0.0772559i
$633$	−4.82843	−	8.36308i	−0.191913	−	0.332403i
$634$	2.43503	+	4.21759i	0.0967073	+	0.167502i
$635$	2.12132	−	3.67423i	0.0841820	−	0.145808i
$636$	10.9706			0.435011
$637$	42.0919	+	11.7401i	1.66774	+	0.465161i
$638$	−9.41421			−0.372712
$639$	−2.87868	+	4.98602i	−0.113879	+	0.197244i
$640$	5.27817	+	9.14207i	0.208638	+	0.361372i
$641$	−1.89949	−	3.29002i	−0.0750255	−	0.129948i	0.826072	−	0.563565i	$-0.190570\pi$
$641$	−1.89949	−	3.29002i	−0.0750255	−	0.129948i	−0.901097	+	0.433617i	$0.857237\pi$
$642$	1.72792	−	2.99285i	0.0681956	−	0.118118i
$643$	30.1421			1.18869			0.594345	−	0.804210i	$-0.297411\pi$
$643$	30.1421			1.18869			0.594345	+	0.804210i	$0.297411\pi$
$644$	−40.3284	−	5.51882i	−1.58916	−	0.217472i
$645$	8.58579			0.338065
$646$	−0.828427	+	1.43488i	−0.0325940	+	0.0564545i
$647$	−3.10660	−	5.38079i	−0.122133	−	0.211541i	0.798476	−	0.602027i	$-0.205640\pi$
$647$	−3.10660	−	5.38079i	−0.122133	−	0.211541i	−0.920609	+	0.390486i	$0.872307\pi$
$648$	−3.96447	−	6.86666i	−0.155739	−	0.269748i
$649$	−1.41421	+	2.44949i	−0.0555127	+	0.0961509i
$650$	−10.3431			−0.405692
$651$	−5.14214	+	6.63103i	−0.201536	+	0.259891i
$652$	−33.0416			−1.29401
$653$	0.928932	−	1.60896i	0.0363519	−	0.0629634i	−0.847277	−	0.531151i	$-0.821760\pi$
$653$	0.928932	−	1.60896i	0.0363519	−	0.0629634i	0.883629	+	0.468188i	$0.155093\pi$
$654$	0.485281	+	0.840532i	0.0189760	+	0.0328674i
$655$	−10.2426	−	17.7408i	−0.400213	−	0.693189i
$656$	13.2426	−	22.9369i	0.517038	−	0.895537i
$657$	13.1421			0.512724
$658$	−0.656854	−	1.60896i	−0.0256068	−	0.0627237i
$659$	−38.0416			−1.48189			−0.740946	−	0.671565i	$-0.765622\pi$
$659$	−38.0416			−1.48189			−0.740946	+	0.671565i	$0.765622\pi$
$660$	−3.12132	+	5.40629i	−0.121497	+	0.210439i
$661$	11.3640	+	19.6830i	0.442007	+	0.765578i	0.997838	−	0.0657167i	$-0.0209334\pi$
$661$	11.3640	+	19.6830i	0.442007	+	0.765578i	−0.555831	+	0.831295i	$0.687600\pi$
$662$	−4.02944	−	6.97919i	−0.156609	−	0.271254i
$663$	−17.6569	+	30.5826i	−0.685735	+	1.18773i
$664$	−1.20101			−0.0466082
$665$	−1.00000	−	2.44949i	−0.0387783	−	0.0949871i
$666$	2.10051			0.0813929
$667$	−39.6066	+	68.6006i	−1.53357	+	2.65623i
$668$	−0.979185	−	1.69600i	−0.0378858	−	0.0656201i
$669$	−4.41421	−	7.64564i	−0.170663	−	0.295598i
$670$	−1.41421	+	2.44949i	−0.0546358	+	0.0946320i
$671$	14.8995			0.575189
$672$	−10.1213	+	13.0519i	−0.390438	+	0.503489i
$673$	35.7990			1.37995			0.689975	−	0.723833i	$-0.257622\pi$
$673$	35.7990			1.37995			0.689975	+	0.723833i	$0.257622\pi$
$674$	2.39340	−	4.14549i	0.0921903	−	0.159678i
$675$	11.3137	+	19.5959i	0.435465	+	0.754247i
$676$	23.7426	+	41.1235i	0.913178	+	1.58167i
$677$	−0.343146	+	0.594346i	−0.0131882	+	0.0228426i	−0.872544	−	0.488535i	$-0.837531\pi$
$677$	−0.343146	+	0.594346i	−0.0131882	+	0.0228426i	0.859356	+	0.511378i	$0.170865\pi$
$678$	−4.82843			−0.185435
$679$	23.1421	+	3.16693i	0.888114	+	0.121536i
$680$	6.34315			0.243249
$681$	−8.31371	+	14.3998i	−0.318582	+	0.551800i
$682$	−1.12132	−	1.94218i	−0.0429376	−	0.0743701i
$683$	−5.24264	−	9.08052i	−0.200604	−	0.347456i	0.748119	−	0.663564i	$-0.230957\pi$
$683$	−5.24264	−	9.08052i	−0.200604	−	0.347456i	−0.948723	+	0.316108i	$0.897624\pi$
$684$	0.914214	−	1.58346i	0.0349558	−	0.0605453i
$685$	−14.1716			−0.541468
$686$	6.15685	−	4.57631i	0.235070	−	0.174724i
$687$	6.34315			0.242006
$688$	9.10660	−	15.7731i	0.347186	−	0.601344i
$689$	−13.2426	−	22.9369i	−0.504504	−	0.873827i
$690$	−2.46447	−	4.26858i	−0.0938206	−	0.162502i
$691$	1.48528	−	2.57258i	0.0565028	−	0.0978657i	−0.836390	−	0.548134i	$-0.815338\pi$
$691$	1.48528	−	2.57258i	0.0565028	−	0.0978657i	0.892893	+	0.450268i	$0.148672\pi$
$692$	−28.0000			−1.06440
$693$	6.32843	+	0.866025i	0.240397	+	0.0328976i
$694$	−8.71573			−0.330845
$695$	−4.03553	+	6.98975i	−0.153077	+	0.265136i
$696$	10.5563	+	18.2841i	0.400137	+	0.693058i
$697$	−17.6569	−	30.5826i	−0.668801	−	1.15840i
$698$	2.58579	−	4.47871i	0.0978735	−	0.169522i
$699$	23.3137			0.881805
$700$	11.8579	−	15.2913i	0.448185	−	0.577956i
$701$	3.82843			0.144598			0.0722988	−	0.997383i	$-0.476966\pi$
$701$	3.82843			0.144598			0.0722988	+	0.997383i	$0.476966\pi$
$702$	−7.31371	+	12.6677i	−0.276038	+	0.478112i
$703$	−2.53553	−	4.39167i	−0.0956295	−	0.165635i
$704$	5.03553	+	8.72180i	0.189784	+	0.328715i
$705$	−1.12132	+	1.94218i	−0.0422314	+	0.0731469i
$706$	−6.82843			−0.256991
$707$	−4.31371	−	10.5664i	−0.162234	−	0.397390i
$708$	3.02944			0.113853
$709$	−12.4706	+	21.5996i	−0.468342	+	0.811192i	−0.999345	−	0.0361778i	$-0.988482\pi$
$709$	−12.4706	+	21.5996i	−0.468342	+	0.811192i	0.531004	+	0.847370i	$0.321815\pi$
$710$	1.19239	+	2.06528i	0.0447495	+	0.0775085i
$711$	−0.707107	−	1.22474i	−0.0265186	−	0.0459315i
$712$	−6.80761	+	11.7911i	−0.255126	+	0.441891i
$713$	−18.8701			−0.706689
$714$	2.34315	+	5.73951i	0.0876900	+	0.214796i
$715$	15.0711			0.563626
$716$	−19.9289	+	34.5179i	−0.744779	+	1.29000i
$717$	1.41421	+	2.44949i	0.0528148	+	0.0914779i
$718$	0.671573	+	1.16320i	0.0250629	+	0.0434102i
$719$	22.0416	−	38.1772i	0.822014	−	1.42377i	−0.0821659	−	0.996619i	$-0.526184\pi$
$719$	22.0416	−	38.1772i	0.822014	−	1.42377i	0.904180	−	0.427152i	$-0.140483\pi$
$720$	−3.00000			−0.111803
$721$	−9.72792	+	12.5446i	−0.362287	+	0.467186i
$722$	0.414214			0.0154154
$723$	15.5858	−	26.9954i	0.579642	−	1.00397i
$724$	−9.05025	−	15.6755i	−0.336350	−	0.582575i
$725$	−18.8284	−	32.6118i	−0.699270	−	1.21117i
$726$	−1.51472	+	2.62357i	−0.0562165	+	0.0973698i
$727$	5.92893			0.219892			0.109946	−	0.993938i	$-0.464932\pi$
$727$	5.92893			0.219892			0.109946	+	0.993938i	$0.464932\pi$
$728$	25.9497	+	3.55114i	0.961762	+	0.131614i
$729$	29.0000			1.07407
$730$	2.72183	−	4.71434i	0.100739	−	0.174486i
$731$	−12.1421	−	21.0308i	−0.449093	−	0.777852i
$732$	−7.97918	−	13.8204i	−0.294919	−	0.510815i
$733$	14.7279	−	25.5095i	0.543988	−	0.942215i	−0.454682	−	0.890654i	$-0.650247\pi$
$733$	14.7279	−	25.5095i	0.543988	−	0.942215i	0.998670	−	0.0515612i	$-0.0164197\pi$
$734$	−14.7696			−0.545154
$735$	−9.53553	−	2.65962i	−0.351723	−	0.0981017i
$736$	−37.1421			−1.36908
$737$	−8.24264	+	14.2767i	−0.303622	+	0.525888i
$738$	−1.82843	−	3.16693i	−0.0673053	−	0.116576i
$739$	9.82843	+	17.0233i	0.361545	+	0.626214i	0.988215	−	0.153071i	$-0.0489162\pi$
$739$	9.82843	+	17.0233i	0.361545	+	0.626214i	−0.626671	+	0.779284i	$0.715583\pi$
$740$	−4.63604	+	8.02986i	−0.170424	+	0.295183i
$741$	8.82843			0.324320
$742$	−4.60660	−	0.630399i	−0.169114	−	0.0231427i
$743$	50.8701			1.86624			0.933121	−	0.359563i	$-0.117074\pi$
$743$	50.8701			1.86624			0.933121	+	0.359563i	$0.117074\pi$
$744$	−2.51472	+	4.35562i	−0.0921941	+	0.159685i
$745$	2.91421	+	5.04757i	0.106769	+	0.184929i
$746$	2.34315	+	4.05845i	0.0857887	+	0.148590i
$747$	0.378680	−	0.655892i	0.0138552	−	0.0239978i
$748$	17.6569			0.645599
$749$	9.56497	−	12.3345i	0.349496	−	0.450692i
$750$	5.27208			0.192509
$751$	20.7279	−	35.9018i	0.756373	−	1.31008i	−0.188316	−	0.982108i	$-0.560303\pi$
$751$	20.7279	−	35.9018i	0.756373	−	1.31008i	0.944689	−	0.327967i	$-0.106364\pi$
$752$	2.37868	+	4.11999i	0.0867415	+	0.150241i
$753$	8.29289	+	14.3637i	0.302210	+	0.523443i
$754$	12.1716	−	21.0818i	0.443263	−	0.767753i
$755$	5.31371			0.193386
$756$	−10.3431	−	25.3354i	−0.376177	−	0.921441i
$757$	−5.00000			−0.181728			−0.0908640	−	0.995863i	$-0.528963\pi$
$757$	−5.00000			−0.181728			−0.0908640	+	0.995863i	$0.528963\pi$
$758$	0.878680	−	1.52192i	0.0319151	−	0.0552785i
$759$	−14.3640	−	24.8791i	−0.521379	−	0.903054i
$760$	−0.792893	−	1.37333i	−0.0287613	−	0.0498160i
$761$	−14.0563	+	24.3463i	−0.509542	+	0.882553i	0.490397	+	0.871499i	$0.336852\pi$
$761$	−14.0563	+	24.3463i	−0.509542	+	0.882553i	−0.999939	+	0.0110537i	$0.996481\pi$
$762$	2.48528			0.0900322
$763$	1.65685	+	4.05845i	0.0599822	+	0.146926i
$764$	−10.2132			−0.369501
$765$	−2.00000	+	3.46410i	−0.0723102	+	0.125245i
$766$	−5.84924	−	10.1312i	−0.211342	−	0.366055i
$767$	−3.65685	−	6.33386i	−0.132041	−	0.228702i
$768$	2.80761	−	4.86293i	0.101311	−	0.175476i
$769$	41.4264			1.49387			0.746937	−	0.664895i	$-0.231524\pi$
$769$	41.4264			1.49387			0.746937	+	0.664895i	$0.231524\pi$
$770$	1.62132	−	2.09077i	0.0584283	−	0.0753461i
$771$	18.8284			0.678089
$772$	−10.8787	+	18.8424i	−0.391532	+	0.678154i
$773$	12.8787	+	22.3065i	0.463214	+	0.802310i	0.999119	−	0.0419682i	$-0.0133628\pi$
$773$	12.8787	+	22.3065i	0.463214	+	0.802310i	−0.535905	+	0.844278i	$0.680029\pi$
$774$	−1.25736	−	2.17781i	−0.0451948	−	0.0782798i
$775$	4.48528	−	7.76874i	0.161116	−	0.279061i
$776$	14.0000			0.502571
$777$	−18.7990	−	2.57258i	−0.674410	−	0.0922909i
$778$	−11.7990			−0.423014
$779$	−4.41421	+	7.64564i	−0.158156	+	0.273934i
$780$	−8.07107	−	13.9795i	−0.288991	−	0.500546i
$781$	6.94975	+	12.0373i	0.248682	+	0.430729i
$782$	−6.97056	+	12.0734i	−0.249267	+	0.431743i
$783$	−53.2548			−1.90317
$784$	−15.0000	+	14.6969i	−0.535714	+	0.524891i
$785$	11.8284			0.422175
$786$	6.00000	−	10.3923i	0.214013	−	0.370681i
$787$	20.5061	+	35.5176i	0.730963	+	1.26607i	0.956472	+	0.291825i	$0.0942623\pi$
$787$	20.5061	+	35.5176i	0.730963	+	1.26607i	−0.225508	+	0.974241i	$0.572404\pi$
$788$	19.6421	+	34.0212i	0.699722	+	1.21195i
$789$	−0.343146	+	0.594346i	−0.0122163	+	0.0211593i
$790$	−0.585786			−0.0208413
$791$	−21.6066	−	2.95680i	−0.768242	−	0.105132i
$792$	3.82843			0.136037
$793$	−19.2635	+	33.3653i	−0.684065	+	1.18484i
$794$	−7.58579	−	13.1390i	−0.269209	−	0.466285i
$795$	3.00000	+	5.19615i	0.106399	+	0.184289i
$796$	1.76346	−	3.05440i	0.0625040	−	0.108260i
$797$	−21.7574			−0.770685			−0.385343	−	0.922774i	$-0.625917\pi$
$797$	−21.7574			−0.770685			−0.385343	+	0.922774i	$0.625917\pi$
$798$	0.949747	−	1.22474i	0.0336207	−	0.0433555i
$799$	6.34315			0.224404
$800$	8.82843	−	15.2913i	0.312132	−	0.540629i
$801$	−4.29289	−	7.43551i	−0.151682	−	0.262721i
$802$	3.41421	+	5.91359i	0.120560	+	0.208816i
$803$	15.8640	−	27.4772i	0.559827	−	0.969649i
$804$	17.6569			0.622709
$805$	−8.41421	−	20.6105i	−0.296562	−	0.726426i
$806$	5.79899			0.204261
$807$	−2.82843	+	4.89898i	−0.0995654	+	0.172452i
$808$	−3.42031	−	5.92415i	−0.120326	−	0.208411i
$809$	−1.42893	−	2.47498i	−0.0502386	−	0.0870158i	0.839813	−	0.542877i	$-0.182665\pi$
$809$	−1.42893	−	2.47498i	−0.0502386	−	0.0870158i	−0.890051	+	0.455861i	$0.849332\pi$
$810$	1.03553	−	1.79360i	0.0363850	−	0.0630206i
$811$	−51.4558			−1.80686			−0.903430	−	0.428737i	$-0.858959\pi$
$811$	−51.4558			−1.80686			−0.903430	+	0.428737i	$0.858959\pi$
$812$	17.2132	+	42.1636i	0.604065	+	1.47965i
$813$	9.55635			0.335156
$814$	2.53553	−	4.39167i	0.0888704	−	0.153928i
$815$	−9.03553	−	15.6500i	−0.316501	−	0.548196i
$816$	−8.48528	−	14.6969i	−0.297044	−	0.514496i
$817$	−3.03553	+	5.25770i	−0.106200	+	0.183944i
$818$	−10.4853			−0.366609
$819$	−10.1213	+	13.0519i	−0.353668	+	0.456071i
$820$	16.1421			0.563708
$821$	26.0563	−	45.1309i	0.909373	−	1.57508i	0.0944355	−	0.995531i	$-0.469895\pi$
$821$	26.0563	−	45.1309i	0.909373	−	1.57508i	0.814937	−	0.579549i	$-0.196771\pi$
$822$	−4.15076	−	7.18932i	−0.144774	−	0.250756i
$823$	−18.1066	−	31.3616i	−0.631156	−	1.09320i	−0.987316	−	0.158770i	$-0.949247\pi$
$823$	−18.1066	−	31.3616i	−0.631156	−	1.09320i	0.356159	−	0.934425i	$-0.384086\pi$
$824$	−4.75736	+	8.23999i	−0.165730	+	0.287054i
$825$	13.6569			0.475471
$826$	−1.27208	−	0.174080i	−0.0442613	−	0.00605701i
$827$	−44.2843			−1.53991			−0.769957	−	0.638095i	$-0.779723\pi$
$827$	−44.2843			−1.53991			−0.769957	+	0.638095i	$0.779723\pi$
$828$	7.69239	−	13.3236i	0.267329	−	0.463027i
$829$	−14.1421	−	24.4949i	−0.491177	−	0.850743i	0.508772	−	0.860901i	$-0.330100\pi$
$829$	−14.1421	−	24.4949i	−0.491177	−	0.850743i	−0.999948	+	0.0101585i	$0.996766\pi$
$830$	−0.156854	−	0.271680i	−0.00544449	−	0.00943013i
$831$	20.1213	−	34.8511i	0.698001	−	1.20897i
$832$	−26.0416			−0.902831
$833$	6.97056	+	27.1185i	0.241516	+	0.939599i
$834$	−4.72792			−0.163715
$835$	0.535534	−	0.927572i	0.0185329	−	0.0321000i
$836$	−2.20711	−	3.82282i	−0.0763344	−	0.132215i
$837$	−6.34315	−	10.9867i	−0.219251	−	0.379754i
$838$	1.67157	−	2.89525i	0.0577435	−	0.100015i
$839$	19.7990			0.683537			0.341769	−	0.939784i	$-0.388974\pi$
$839$	19.7990			0.683537			0.341769	+	0.939784i	$0.388974\pi$
$840$	−5.87868	−	0.804479i	−0.202834	−	0.0277572i
$841$	59.6274			2.05612
$842$	−1.07969	+	1.87008i	−0.0372086	+	0.0644471i
$843$	−13.9706	−	24.1977i	−0.481172	−	0.833414i
$844$	−6.24264	−	10.8126i	−0.214881	−	0.372184i
$845$	−12.9853	+	22.4912i	−0.446707	+	0.773720i
$846$	0.656854			0.0225831
$847$	−8.38478	+	10.8126i	−0.288104	+	0.371524i
$848$	12.7279			0.437079
$849$	11.2635	−	19.5089i	0.386561	−	0.669543i
$850$	−3.31371	−	5.73951i	−0.113659	−	0.196864i
$851$	−21.3345	−	36.9525i	−0.731338	−	1.26671i
$852$	7.44365	−	12.8928i	0.255015	−	0.441699i
$853$	10.0294			0.343401			0.171701	−	0.985149i	$-0.445074\pi$
$853$	10.0294			0.343401			0.171701	+	0.985149i	$0.445074\pi$
$854$	2.55635	+	6.26175i	0.0874765	+	0.214273i
$855$	1.00000			0.0341993
$856$	4.67767	−	8.10196i	0.159879	−	0.276919i
$857$	−10.4853	−	18.1610i	−0.358170	−	0.620369i	0.629485	−	0.777013i	$-0.283266\pi$
$857$	−10.4853	−	18.1610i	−0.358170	−	0.620369i	−0.987655	+	0.156643i	$0.949933\pi$
$858$	4.41421	+	7.64564i	0.150699	+	0.261018i
$859$	−1.03553	+	1.79360i	−0.0353320	+	0.0611968i	−0.883151	−	0.469089i	$-0.844582\pi$
$859$	−1.03553	+	1.79360i	−0.0353320	+	0.0611968i	0.847819	+	0.530286i	$0.177916\pi$
$860$	11.1005			0.378524
$861$	12.4853	+	30.5826i	0.425497	+	1.04225i
$862$	15.7574			0.536698
$863$	−3.70711	+	6.42090i	−0.126191	+	0.218570i	−0.922198	−	0.386718i	$-0.873609\pi$
$863$	−3.70711	+	6.42090i	−0.126191	+	0.218570i	0.796007	+	0.605288i	$0.206942\pi$
$864$	−12.4853	−	21.6251i	−0.424758	−	0.735702i
$865$	−7.65685	−	13.2621i	−0.260341	−	0.450924i
$866$	−5.79899	+	10.0441i	−0.197058	+	0.341314i
$867$	1.41421			0.0480292
$868$	−6.64823	+	8.57321i	−0.225656	+	0.290994i
$869$	−3.41421			−0.115819
$870$	−2.75736	+	4.77589i	−0.0934832	+	0.161918i
$871$	−21.3137	−	36.9164i	−0.722187	−	1.25087i
$872$	1.31371	+	2.27541i	0.0444878	+	0.0770551i
$873$	−4.41421	+	7.64564i	−0.149398	+	0.258766i
$874$	3.48528			0.117891
$875$	23.5919	+	3.22848i	0.797551	+	0.109142i
$876$	−33.9828			−1.14817
$877$	4.05025	−	7.01524i	0.136767	−	0.236888i	−0.789504	−	0.613746i	$-0.789662\pi$
$877$	4.05025	−	7.01524i	0.136767	−	0.236888i	0.926271	+	0.376858i	$0.122995\pi$
$878$	1.55635	+	2.69568i	0.0525242	+	0.0909747i
$879$	6.24264	+	10.8126i	0.210559	+	0.364699i
$880$	−3.62132	+	6.27231i	−0.122075	+	0.211440i
$881$	4.28427			0.144341			0.0721704	−	0.997392i	$-0.477007\pi$
$881$	4.28427			0.144341			0.0721704	+	0.997392i	$0.477007\pi$
$882$	0.721825	+	2.80821i	0.0243051	+	0.0945573i
$883$	5.65685			0.190368			0.0951842	−	0.995460i	$-0.469656\pi$
$883$	5.65685			0.190368			0.0951842	+	0.995460i	$0.469656\pi$
$884$	−22.8284	+	39.5400i	−0.767803	+	1.32987i
$885$	0.828427	+	1.43488i	0.0278473	+	0.0482329i
$886$	−1.31371	−	2.27541i	−0.0441349	−	0.0764439i
$887$	−0.656854	+	1.13770i	−0.0220550	+	0.0382004i	−0.876842	−	0.480778i	$-0.840354\pi$
$887$	−0.656854	+	1.13770i	−0.0220550	+	0.0382004i	0.854787	+	0.518979i	$0.173688\pi$
$888$	−11.3726			−0.381639
$889$	11.1213	+	1.52192i	0.372997	+	0.0510435i
$890$	−3.55635			−0.119209
$891$	6.03553	−	10.4539i	0.202198	−	0.350217i
$892$	−5.70711	−	9.88500i	−0.191088	−	0.330974i
$893$	−0.792893	−	1.37333i	−0.0265332	−	0.0459568i
$894$	−1.70711	+	2.95680i	−0.0570942	+	0.0988900i
$895$	−21.7990			−0.728660
$896$	−17.1152	+	22.0709i	−0.571779	+	0.737337i
$897$	74.2843			2.48028
$898$	0.343146	−	0.594346i	0.0114509	−	0.0198336i
$899$	10.5563	+	18.2841i	0.352074	+	0.609810i
$900$	3.65685	+	6.33386i	0.121895	+	0.211129i
$901$	8.48528	−	14.6969i	0.282686	−	0.489626i
$902$	−8.82843			−0.293954
$903$	8.58579	+	21.0308i	0.285717	+	0.699861i
$904$	−13.0711			−0.434737
$905$	4.94975	−	8.57321i	0.164535	−	0.284983i
$906$	1.55635	+	2.69568i	0.0517062	+	0.0895578i
$907$	−14.2929	−	24.7560i	−0.474588	−	0.822010i	0.524989	−	0.851109i	$-0.324070\pi$
$907$	−14.2929	−	24.7560i	−0.474588	−	0.822010i	−0.999577	+	0.0290991i	$0.990736\pi$
$908$	−10.7487	+	18.6174i	−0.356709	+	0.617839i
$909$	4.31371			0.143077
$910$	2.58579	+	6.33386i	0.0857180	+	0.209965i
$911$	34.7279			1.15059			0.575294	−	0.817947i	$-0.304888\pi$
$911$	34.7279			1.15059			0.575294	+	0.817947i	$0.304888\pi$
$912$	−2.12132	+	3.67423i	−0.0702439	+	0.121666i
$913$	−0.914214	−	1.58346i	−0.0302561	−	0.0524050i
$914$	0.449747	+	0.778985i	0.0148763	+	0.0257665i
$915$	4.36396	−	7.55860i	0.144268	−	0.249880i
$916$	8.20101			0.270969
$917$	33.2132	−	42.8300i	1.09680	−	1.41437i
$918$	−9.37258			−0.309341
$919$	−14.5208	+	25.1508i	−0.478997	+	0.829648i	−0.999710	−	0.0240841i	$-0.992333\pi$
$919$	−14.5208	+	25.1508i	−0.478997	+	0.829648i	0.520712	+	0.853732i	$0.325666\pi$
$920$	−6.67157	−	11.5555i	−0.219955	−	0.380974i
$921$	4.72792	+	8.18900i	0.155790	+	0.269837i
$922$	0.822330	−	1.42432i	0.0270820	−	0.0469074i
$923$	−35.9411			−1.18302
$924$	−16.3640	−	2.23936i	−0.538335	−	0.0736694i
$925$	20.2843			0.666943
$926$	−2.08579	+	3.61269i	−0.0685432	+	0.118720i
$927$	−3.00000	−	5.19615i	−0.0985329	−	0.170664i
$928$	20.7782	+	35.9889i	0.682077	+	1.18139i
$929$	−7.50000	+	12.9904i	−0.246067	+	0.426201i	−0.962431	−	0.271526i	$-0.912472\pi$
$929$	−7.50000	+	12.9904i	−0.246067	+	0.426201i	0.716364	+	0.697727i	$0.245805\pi$
$930$	−1.31371			−0.0430782
$931$	5.00000	−	4.89898i	0.163868	−	0.160558i
$932$	30.1421			0.987338
$933$	11.1716	−	19.3497i	0.365741	−	0.633482i
$934$	−8.05635	−	13.9540i	−0.263612	−	0.456589i
$935$	4.82843	+	8.36308i	0.157906	+	0.273502i
$936$	−4.94975	+	8.57321i	−0.161788	+	0.280224i
$937$	−56.3137			−1.83969			−0.919844	−	0.392284i	$-0.871685\pi$
$937$	−56.3137			−1.83969			−0.919844	+	0.392284i	$0.871685\pi$
$938$	−7.41421	−	1.01461i	−0.242083	−	0.0331283i
$939$	−6.58579			−0.214919
$940$	−1.44975	+	2.51104i	−0.0472855	+	0.0819010i
$941$	22.0208	+	38.1412i	0.717858	+	1.24337i	0.961847	+	0.273589i	$0.0882107\pi$
$941$	22.0208	+	38.1412i	0.717858	+	1.24337i	−0.243989	+	0.969778i	$0.578456\pi$
$942$	3.46447	+	6.00063i	0.112878	+	0.195511i
$943$	−37.1421	+	64.3321i	−1.20951	+	2.09494i
$944$	3.51472			0.114394
$945$	9.17157	−	11.8272i	0.298351	−	0.384738i
$946$	−6.07107			−0.197387
$947$	3.82843	−	6.63103i	0.124407	−	0.215480i	−0.797094	−	0.603855i	$-0.793630\pi$
$947$	3.82843	−	6.63103i	0.124407	−	0.215480i	0.921501	+	0.388376i	$0.126964\pi$
$948$	1.82843	+	3.16693i	0.0593846	+	0.102857i
$949$	41.0208	+	71.0501i	1.33159	+	2.30639i
$950$	−0.828427	+	1.43488i	−0.0268777	+	0.0465536i
$951$	16.6274			0.539181
$952$	6.34315	+	15.5375i	0.205583	+	0.503572i
$953$	−0.585786			−0.0189755			−0.00948774	−	0.999955i	$-0.503020\pi$
$953$	−0.585786			−0.0189755			−0.00948774	+	0.999955i	$0.503020\pi$
$954$	0.878680	−	1.52192i	0.0284483	−	0.0492739i
$955$	−2.79289	−	4.83743i	−0.0903759	−	0.156536i
$956$	1.82843	+	3.16693i	0.0591356	+	0.102426i
$957$	−16.0711	+	27.8359i	−0.519504	+	0.899807i
$958$	4.71573			0.152358
$959$	−14.1716	−	34.7131i	−0.457624	−	1.12095i
$960$	5.89949			0.190405
$961$	12.9853	−	22.4912i	0.418880	−	0.725522i
$962$	6.55635	+	11.3559i	0.211385	+	0.366130i
$963$	2.94975	+	5.10911i	0.0950543	+	0.164639i
$964$	20.1508	−	34.9021i	0.649012	−	1.12412i
$965$	−11.8995			−0.383058
$966$	7.99138	−	10.3053i	0.257118	−	0.331566i
$967$	20.2843			0.652298			0.326149	−	0.945318i	$-0.394249\pi$
$967$	20.2843			0.652298			0.326149	+	0.945318i	$0.394249\pi$
$968$	−4.10051	+	7.10228i	−0.131795	+	0.228276i
$969$	2.82843	+	4.89898i	0.0908622	+	0.157378i
$970$	1.82843	+	3.16693i	0.0587073	+	0.101684i
$971$	13.4350	−	23.2702i	0.431151	−	0.746775i	−0.565822	−	0.824527i	$-0.691441\pi$
$971$	13.4350	−	23.2702i	0.431151	−	0.746775i	0.996973	+	0.0777526i	$0.0247744\pi$
$972$	18.1005			0.580574
$973$	−21.1569	−	2.89525i	−0.678258	−	0.0928174i
$974$	8.62742			0.276440
$975$	−17.6569	+	30.5826i	−0.565472	+	0.979426i
$976$	−9.25736	−	16.0342i	−0.296321	−	0.513243i
$977$	−14.3848	−	24.9152i	−0.460210	−	0.797107i	0.538761	−	0.842458i	$-0.318892\pi$
$977$	−14.3848	−	24.9152i	−0.460210	−	0.797107i	−0.998971	+	0.0453518i	$0.985559\pi$
$978$	5.29289	−	9.16756i	0.169248	−	0.293146i
$979$	−20.7279			−0.662467
$980$	−12.3284	−	3.43861i	−0.393817	−	0.109842i
$981$	−1.65685			−0.0528993
$982$	6.74264	−	11.6786i	0.215166	−	0.372679i
$983$	23.0000	+	39.8372i	0.733586	+	1.27061i	0.955341	+	0.295506i	$0.0954882\pi$
$983$	23.0000	+	39.8372i	0.733586	+	1.27061i	−0.221755	+	0.975102i	$0.571178\pi$
$984$	9.89949	+	17.1464i	0.315584	+	0.546608i
$985$	−10.7426	+	18.6068i	−0.342289	+	0.592862i
$986$	15.5980			0.496741
$987$	−5.87868	−	0.804479i	−0.187120	−	0.0256068i
$988$	11.4142			0.363135
$989$	−25.5416	+	44.2394i	−0.812177	+	1.40673i
$990$	0.500000	+	0.866025i	0.0158910	+	0.0275241i
$991$	17.8995	+	31.0028i	0.568596	+	0.984837i	0.996705	+	0.0811104i	$0.0258466\pi$
$991$	17.8995	+	31.0028i	0.568596	+	0.984837i	−0.428109	+	0.903727i	$0.640820\pi$
$992$	−4.94975	+	8.57321i	−0.157155	+	0.272200i
$993$	−27.5147			−0.873153
$994$	−3.86649	+	4.98602i	−0.122638	+	0.158147i
$995$	1.92893			0.0611513
$996$	−0.979185	+	1.69600i	−0.0310267	+	0.0537397i
$997$	−14.1421	−	24.4949i	−0.447886	−	0.775761i	0.550362	−	0.834926i	$-0.314490\pi$
$997$	−14.1421	−	24.4949i	−0.447886	−	0.775761i	−0.998248	+	0.0591648i	$0.981156\pi$
$998$	−0.713203	−	1.23530i	−0.0225761	−	0.0391029i
$999$	14.3431	−	24.8431i	0.453797	−	0.786000i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	133.2.f.c.58.1	yes	4
3.2	odd	2		1197.2.j.e.856.2		4
7.2	even	3		931.2.a.f.1.2		2
7.3	odd	6		931.2.f.i.704.1		4
7.4	even	3	inner	133.2.f.c.39.1	✓	4
7.5	odd	6		931.2.a.e.1.2		2
7.6	odd	2		931.2.f.i.324.1		4
21.2	odd	6		8379.2.a.bi.1.1		2
21.5	even	6		8379.2.a.bl.1.1		2
21.11	odd	6		1197.2.j.e.172.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.2.f.c.39.1	✓	4	7.4	even	3	inner
133.2.f.c.58.1	yes	4	1.1	even	1	trivial
931.2.a.e.1.2		2	7.5	odd	6
931.2.a.f.1.2		2	7.2	even	3
931.2.f.i.324.1		4	7.6	odd	2
931.2.f.i.704.1		4	7.3	odd	6
1197.2.j.e.172.2		4	21.11	odd	6
1197.2.j.e.856.2		4	3.2	odd	2
8379.2.a.bi.1.1		2	21.2	odd	6
8379.2.a.bl.1.1		2	21.5	even	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 133 = 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	133.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.207107 + 0.358719i) q^{2} +(0.707107 + 1.22474i) q^{3} +(0.914214 + 1.58346i) q^{4} +(-0.500000 + 0.866025i) q^{5} -0.585786 q^{6} +(-2.62132 - 0.358719i) q^{7} -1.58579 q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.207107 - 0.358719i) q^{10} +(-1.20711 - 2.09077i) q^{11} +(-1.29289 + 2.23936i) q^{12} +6.24264 q^{13} +(0.671573 - 0.866025i) q^{14} -1.41421 q^{15} +(-1.50000 + 2.59808i) q^{16} +(2.00000 + 3.46410i) q^{17} +(0.207107 + 0.358719i) q^{18} +(0.500000 - 0.866025i) q^{19} -1.82843 q^{20} +(-1.41421 - 3.46410i) q^{21} +1.00000 q^{22} +(4.20711 - 7.28692i) q^{23} +(-1.12132 - 1.94218i) q^{24} +(2.00000 + 3.46410i) q^{25} +(-1.29289 + 2.23936i) q^{26} +5.65685 q^{27} +(-1.82843 - 4.47871i) q^{28} -9.41421 q^{29} +(0.292893 - 0.507306i) q^{30} +(-1.12132 - 1.94218i) q^{31} +(-2.20711 - 3.82282i) q^{32} +(1.70711 - 2.95680i) q^{33} -1.65685 q^{34} +(1.62132 - 2.09077i) q^{35} +1.82843 q^{36} +(2.53553 - 4.39167i) q^{37} +(0.207107 + 0.358719i) q^{38} +(4.41421 + 7.64564i) q^{39} +(0.792893 - 1.37333i) q^{40} -8.82843 q^{41} +(1.53553 + 0.210133i) q^{42} -6.07107 q^{43} +(2.20711 - 3.82282i) q^{44} +(0.500000 + 0.866025i) q^{45} +(1.74264 + 3.01834i) q^{46} +(0.792893 - 1.37333i) q^{47} -4.24264 q^{48} +(6.74264 + 1.88064i) q^{49} -1.65685 q^{50} +(-2.82843 + 4.89898i) q^{51} +(5.70711 + 9.88500i) q^{52} +(-2.12132 - 3.67423i) q^{53} +(-1.17157 + 2.02922i) q^{54} +2.41421 q^{55} +(4.15685 + 0.568852i) q^{56} +1.41421 q^{57} +(1.94975 - 3.37706i) q^{58} +(-0.585786 - 1.01461i) q^{59} +(-1.29289 - 2.23936i) q^{60} +(-3.08579 + 5.34474i) q^{61} +0.928932 q^{62} +(-1.62132 + 2.09077i) q^{63} -4.17157 q^{64} +(-3.12132 + 5.40629i) q^{65} +(0.707107 + 1.22474i) q^{66} +(-3.41421 - 5.91359i) q^{67} +(-3.65685 + 6.33386i) q^{68} +11.8995 q^{69} +(0.414214 + 1.01461i) q^{70} -5.75736 q^{71} +(-0.792893 + 1.37333i) q^{72} +(6.57107 + 11.3814i) q^{73} +(1.05025 + 1.81909i) q^{74} +(-2.82843 + 4.89898i) q^{75} +1.82843 q^{76} +(2.41421 + 5.91359i) q^{77} -3.65685 q^{78} +(0.707107 - 1.22474i) q^{79} +(-1.50000 - 2.59808i) q^{80} +(2.50000 + 4.33013i) q^{81} +(1.82843 - 3.16693i) q^{82} +0.757359 q^{83} +(4.19239 - 5.40629i) q^{84} -4.00000 q^{85} +(1.25736 - 2.17781i) q^{86} +(-6.65685 - 11.5300i) q^{87} +(1.91421 + 3.31552i) q^{88} +(4.29289 - 7.43551i) q^{89} -0.414214 q^{90} +(-16.3640 - 2.23936i) q^{91} +15.3848 q^{92} +(1.58579 - 2.74666i) q^{93} +(0.328427 + 0.568852i) q^{94} +(0.500000 + 0.866025i) q^{95} +(3.12132 - 5.40629i) q^{96} -8.82843 q^{97} +(-2.07107 + 2.02922i) q^{98} -2.41421 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 8 q^{6} - 2 q^{7} - 12 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{11} - 8 q^{12} + 8 q^{13} + 14 q^{14} - 6 q^{16} + 8 q^{17} - 2 q^{18} + 2 q^{19} + 4 q^{20} + 4 q^{22} + 14 q^{23}+ \cdots - 4 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 - 8 * q^6 - 2 * q^7 - 12 * q^8 + 2 * q^9 + 2 * q^10 - 2 * q^11 - 8 * q^12 + 8 * q^13 + 14 * q^14 - 6 * q^16 + 8 * q^17 - 2 * q^18 + 2 * q^19 + 4 * q^20 + 4 * q^22 + 14 * q^23 + 4 * q^24 + 8 * q^25 - 8 * q^26 + 4 * q^28 - 32 * q^29 + 4 * q^30 + 4 * q^31 - 6 * q^32 + 4 * q^33 + 16 * q^34 - 2 * q^35 - 4 * q^36 - 4 * q^37 - 2 * q^38 + 12 * q^39 + 6 * q^40 - 24 * q^41 - 8 * q^42 + 4 * q^43 + 6 * q^44 + 2 * q^45 - 10 * q^46 + 6 * q^47 + 10 * q^49 + 16 * q^50 + 20 * q^52 - 16 * q^54 + 4 * q^55 - 6 * q^56 - 12 * q^58 - 8 * q^59 - 8 * q^60 - 18 * q^61 + 32 * q^62 + 2 * q^63 - 28 * q^64 - 4 * q^65 - 8 * q^67 + 8 * q^68 + 8 * q^69 - 4 * q^70 - 40 * q^71 - 6 * q^72 - 2 * q^73 + 24 * q^74 - 4 * q^76 + 4 * q^77 + 8 * q^78 - 6 * q^80 + 10 * q^81 - 4 * q^82 + 20 * q^83 - 20 * q^84 - 16 * q^85 + 22 * q^86 - 4 * q^87 + 2 * q^88 + 20 * q^89 + 4 * q^90 - 40 * q^91 - 12 * q^92 + 12 * q^93 - 10 * q^94 + 2 * q^95 + 4 * q^96 - 24 * q^97 + 20 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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