LMFDB - Embedded newform 170.2.n.a.59.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,2,Mod(9,170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(170, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 1]))

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

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

chi := DirichletCharacter("170.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	170.n (of order $8$, degree $4$, 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:	$1.35745683436$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{8})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 16 x^{15} + 52 x^{14} + 992 x^{13} + 6181 x^{12} + 8952 x^{11} + 6244 x^{10} - 11448 x^{9} + \cdots + 2048 $ x^20 - 16x^15 + 52x^14 + 992x^13 + 6181x^12 + 8952x^11 + 6244x^10 - 11448x^9 - 14520x^8 + 27936x^7 + 27880x^6 - 121104x^5 + 187460x^4 - 142208x^3 + 73856x^2 - 19456*x + 2048
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			59.1
Root			$-0.969032 - 2.33945i$ of defining polynomial
Character	$\chi$	$=$	170.59
Dual form			170.2.n.a.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-2.33945 - 0.969032i) q^{3} +1.00000i q^{4} +(-0.309710 - 2.21452i) q^{5} +(-0.969032 - 2.33945i) q^{6} +(-1.26758 - 3.06021i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.41268 + 2.41268i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-2.33945 - 0.969032i) q^{3} +1.00000i q^{4} +(-0.309710 - 2.21452i) q^{5} +(-0.969032 - 2.33945i) q^{6} +(-1.26758 - 3.06021i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.41268 + 2.41268i) q^{9} +(1.34690 - 1.78490i) q^{10} +(-0.949504 - 2.29231i) q^{11} +(0.969032 - 2.33945i) q^{12} -0.777809 q^{13} +(1.26758 - 3.06021i) q^{14} +(-1.42139 + 5.48087i) q^{15} -1.00000 q^{16} +(4.04502 + 0.798615i) q^{17} +3.41205i q^{18} +(4.13806 - 4.13806i) q^{19} +(2.21452 - 0.309710i) q^{20} +8.38752i q^{21} +(0.949504 - 2.29231i) q^{22} +(-7.45510 + 3.08800i) q^{23} +(2.33945 - 0.969032i) q^{24} +(-4.80816 + 1.37171i) q^{25} +(-0.549994 - 0.549994i) q^{26} +(-0.399286 - 0.963960i) q^{27} +(3.06021 - 1.26758i) q^{28} +(0.319339 + 0.132275i) q^{29} +(-4.88063 + 2.87049i) q^{30} +(-0.719461 + 1.73693i) q^{31} +(-0.707107 - 0.707107i) q^{32} +6.28283i q^{33} +(2.29556 + 3.42497i) q^{34} +(-6.38429 + 3.75485i) q^{35} +(-2.41268 + 2.41268i) q^{36} +(4.26699 + 1.76745i) q^{37} +5.85211 q^{38} +(1.81964 + 0.753721i) q^{39} +(1.78490 + 1.34690i) q^{40} +(2.17392 - 0.900466i) q^{41} +(-5.93087 + 5.93087i) q^{42} +(8.03592 - 8.03592i) q^{43} +(2.29231 - 0.949504i) q^{44} +(4.59569 - 6.09015i) q^{45} +(-7.45510 - 3.08800i) q^{46} +9.25971 q^{47} +(2.33945 + 0.969032i) q^{48} +(-2.80835 + 2.80835i) q^{49} +(-4.36983 - 2.42993i) q^{50} +(-8.68924 - 5.78807i) q^{51} -0.777809i q^{52} +(-2.98917 - 2.98917i) q^{53} +(0.399286 - 0.963960i) q^{54} +(-4.78228 + 2.81264i) q^{55} +(3.06021 + 1.26758i) q^{56} +(-13.6907 + 5.67088i) q^{57} +(0.132275 + 0.319339i) q^{58} +(-9.06612 - 9.06612i) q^{59} +(-5.48087 - 1.42139i) q^{60} +(12.7953 - 5.29999i) q^{61} +(-1.73693 + 0.719461i) q^{62} +(4.32504 - 10.4416i) q^{63} -1.00000i q^{64} +(0.240895 + 1.72247i) q^{65} +(-4.44263 + 4.44263i) q^{66} +0.862303i q^{67} +(-0.798615 + 4.04502i) q^{68} +20.4332 q^{69} +(-7.16945 - 1.85930i) q^{70} +(-3.13819 + 7.57626i) q^{71} -3.41205 q^{72} +(3.75104 - 9.05580i) q^{73} +(1.76745 + 4.26699i) q^{74} +(12.5777 + 1.45021i) q^{75} +(4.13806 + 4.13806i) q^{76} +(-5.81136 + 5.81136i) q^{77} +(0.753721 + 1.81964i) q^{78} +(3.33195 + 8.04403i) q^{79} +(0.309710 + 2.21452i) q^{80} -7.59408i q^{81} +(2.17392 + 0.900466i) q^{82} +(-2.56072 - 2.56072i) q^{83} -8.38752 q^{84} +(0.515763 - 9.20511i) q^{85} +11.3645 q^{86} +(-0.618900 - 0.618900i) q^{87} +(2.29231 + 0.949504i) q^{88} +3.67668i q^{89} +(7.55603 - 1.05674i) q^{90} +(0.985934 + 2.38025i) q^{91} +(-3.08800 - 7.45510i) q^{92} +(3.36628 - 3.36628i) q^{93} +(6.54760 + 6.54760i) q^{94} +(-10.4454 - 7.88221i) q^{95} +(0.969032 + 2.33945i) q^{96} +(-1.05015 + 2.53530i) q^{97} -3.97161 q^{98} +(3.23975 - 7.82145i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{5}+O(q^{10}) $ 20 * q - 4 * q^5	$ 20 q - 4 q^{5} + 4 q^{10} - 8 q^{11} - 24 q^{13} + 8 q^{15} - 20 q^{16} + 8 q^{20} + 8 q^{22} + 16 q^{23} - 12 q^{25} - 12 q^{26} + 24 q^{27} - 12 q^{29} - 8 q^{30} + 8 q^{31} + 8 q^{34} - 8 q^{35} - 8 q^{37} - 8 q^{38} + 4 q^{40} + 4 q^{41} + 8 q^{42} + 16 q^{43} - 8 q^{44} - 12 q^{45} + 16 q^{46} + 40 q^{47} - 56 q^{49} + 8 q^{50} - 8 q^{51} + 44 q^{53} - 24 q^{54} - 72 q^{57} + 16 q^{59} + 16 q^{60} + 8 q^{61} - 8 q^{62} - 24 q^{63} - 8 q^{65} - 8 q^{66} + 20 q^{68} - 16 q^{69} - 16 q^{70} + 8 q^{71} - 28 q^{72} - 60 q^{73} + 28 q^{74} + 64 q^{75} + 8 q^{78} + 56 q^{79} + 4 q^{80} + 4 q^{82} + 16 q^{84} - 16 q^{85} + 48 q^{86} - 72 q^{87} - 8 q^{88} + 32 q^{90} - 24 q^{91} - 8 q^{92} + 72 q^{93} + 32 q^{94} + 8 q^{95} + 48 q^{97} - 36 q^{98} + 72 q^{99}+O(q^{100}) $ 20 * q - 4 * q^5 + 4 * q^10 - 8 * q^11 - 24 * q^13 + 8 * q^15 - 20 * q^16 + 8 * q^20 + 8 * q^22 + 16 * q^23 - 12 * q^25 - 12 * q^26 + 24 * q^27 - 12 * q^29 - 8 * q^30 + 8 * q^31 + 8 * q^34 - 8 * q^35 - 8 * q^37 - 8 * q^38 + 4 * q^40 + 4 * q^41 + 8 * q^42 + 16 * q^43 - 8 * q^44 - 12 * q^45 + 16 * q^46 + 40 * q^47 - 56 * q^49 + 8 * q^50 - 8 * q^51 + 44 * q^53 - 24 * q^54 - 72 * q^57 + 16 * q^59 + 16 * q^60 + 8 * q^61 - 8 * q^62 - 24 * q^63 - 8 * q^65 - 8 * q^66 + 20 * q^68 - 16 * q^69 - 16 * q^70 + 8 * q^71 - 28 * q^72 - 60 * q^73 + 28 * q^74 + 64 * q^75 + 8 * q^78 + 56 * q^79 + 4 * q^80 + 4 * q^82 + 16 * q^84 - 16 * q^85 + 48 * q^86 - 72 * q^87 - 8 * q^88 + 32 * q^90 - 24 * q^91 - 8 * q^92 + 72 * q^93 + 32 * q^94 + 8 * q^95 + 48 * q^97 - 36 * q^98 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/170\mathbb{Z}\right)^\times$.

$n$	$71$	$137$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$-1$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	−2.33945	−	0.969032i	−1.35068	−	0.559471i	−0.414200	−	0.910186i	$-0.635938\pi$
$3$	−2.33945	−	0.969032i	−1.35068	−	0.559471i	−0.936482	+	0.350715i	$0.885938\pi$
$4$			1.00000i			0.500000i
$5$	−0.309710	−	2.21452i	−0.138506	−	0.990362i
$5$	−0.309710	−	2.21452i	−0.138506	−	0.990362i
$6$	−0.969032	−	2.33945i	−0.395606	−	0.955076i
$7$	−1.26758	−	3.06021i	−0.479100	−	1.15665i	−0.960032	−	0.279891i	$-0.909702\pi$
$7$	−1.26758	−	3.06021i	−0.479100	−	1.15665i	0.480932	−	0.876758i	$-0.340298\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	2.41268	+	2.41268i	0.804227	+	0.804227i
$10$	1.34690	−	1.78490i	0.425928	−	0.564434i
$11$	−0.949504	−	2.29231i	−0.286286	−	0.691156i	0.713670	−	0.700482i	$-0.247032\pi$
$11$	−0.949504	−	2.29231i	−0.286286	−	0.691156i	−0.999957	+	0.00932562i	$0.997032\pi$
$12$	0.969032	−	2.33945i	0.279735	−	0.675341i
$13$	−0.777809			−0.215725			−0.107863	−	0.994166i	$-0.534401\pi$
$13$	−0.777809			−0.215725			−0.107863	+	0.994166i	$0.534401\pi$
$14$	1.26758	−	3.06021i	0.338775	−	0.817874i
$15$	−1.42139	+	5.48087i	−0.367000	+	1.41515i
$16$	−1.00000			−0.250000
$17$	4.04502	+	0.798615i	0.981062	+	0.193693i
$17$	4.04502	+	0.798615i	0.981062	+	0.193693i
$18$			3.41205i			0.804227i
$19$	4.13806	−	4.13806i	0.949337	−	0.949337i	−0.0494400	−	0.998777i	$-0.515744\pi$
$19$	4.13806	−	4.13806i	0.949337	−	0.949337i	0.998777	+	0.0494400i	$0.0157437\pi$
$20$	2.21452	−	0.309710i	0.495181	−	0.0692532i
$21$			8.38752i			1.83031i
$22$	0.949504	−	2.29231i	0.202435	−	0.488721i
$23$	−7.45510	+	3.08800i	−1.55450	+	0.643893i	−0.984122	−	0.177493i	$-0.943201\pi$
$23$	−7.45510	+	3.08800i	−1.55450	+	0.643893i	−0.570373	+	0.821386i	$0.693201\pi$
$24$	2.33945	−	0.969032i	0.477538	−	0.197803i
$25$	−4.80816	+	1.37171i	−0.961632	+	0.274343i
$26$	−0.549994	−	0.549994i	−0.107863	−	0.107863i
$27$	−0.399286	−	0.963960i	−0.0768425	−	0.185514i
$28$	3.06021	−	1.26758i	0.578324	−	0.239550i
$29$	0.319339	+	0.132275i	0.0592998	+	0.0245628i	0.412136	−	0.911122i	$-0.364783\pi$
$29$	0.319339	+	0.132275i	0.0592998	+	0.0245628i	−0.352836	+	0.935685i	$0.614783\pi$
$30$	−4.88063	+	2.87049i	−0.891077	+	0.524077i
$31$	−0.719461	+	1.73693i	−0.129219	+	0.311962i	−0.975226	−	0.221209i	$-0.929000\pi$
$31$	−0.719461	+	1.73693i	−0.129219	+	0.311962i	0.846008	+	0.533171i	$0.179000\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$			6.28283i			1.09370i
$34$	2.29556	+	3.42497i	0.393685	+	0.587377i
$35$	−6.38429	+	3.75485i	−1.07914	+	0.634685i
$36$	−2.41268	+	2.41268i	−0.402113	+	0.402113i
$37$	4.26699	+	1.76745i	0.701489	+	0.290566i	0.704778	−	0.709428i	$-0.251047\pi$
$37$	4.26699	+	1.76745i	0.701489	+	0.290566i	−0.00328857	+	0.999995i	$0.501047\pi$
$38$	5.85211			0.949337
$39$	1.81964	+	0.753721i	0.291376	+	0.120692i
$40$	1.78490	+	1.34690i	0.282217	+	0.212964i
$41$	2.17392	−	0.900466i	0.339509	−	0.140629i	−0.206414	−	0.978465i	$-0.566179\pi$
$41$	2.17392	−	0.900466i	0.339509	−	0.140629i	0.545923	+	0.837836i	$0.316179\pi$
$42$	−5.93087	+	5.93087i	−0.915153	+	0.915153i
$43$	8.03592	−	8.03592i	1.22547	−	1.22547i	0.259805	−	0.965661i	$-0.416342\pi$
$43$	8.03592	−	8.03592i	1.22547	−	1.22547i	0.965661	−	0.259805i	$-0.0836581\pi$
$44$	2.29231	−	0.949504i	0.345578	−	0.143143i
$45$	4.59569	−	6.09015i	0.685085	−	0.907866i
$46$	−7.45510	−	3.08800i	−1.09919	−	0.455301i
$47$	9.25971			1.35067			0.675334	−	0.737512i	$-0.264000\pi$
$47$	9.25971			1.35067			0.675334	+	0.737512i	$0.264000\pi$
$48$	2.33945	+	0.969032i	0.337670	+	0.139868i
$49$	−2.80835	+	2.80835i	−0.401193	+	0.401193i
$50$	−4.36983	−	2.42993i	−0.617987	−	0.343645i
$51$	−8.68924	−	5.78807i	−1.21674	−	0.810493i
$52$		−	0.777809i		−	0.107863i
$53$	−2.98917	−	2.98917i	−0.410594	−	0.410594i	0.471352	−	0.881945i	$-0.343766\pi$
$53$	−2.98917	−	2.98917i	−0.410594	−	0.410594i	−0.881945	+	0.471352i	$0.843766\pi$
$54$	0.399286	−	0.963960i	0.0543359	−	0.131178i
$55$	−4.78228	+	2.81264i	−0.644842	+	0.379256i
$56$	3.06021	+	1.26758i	0.408937	+	0.169387i
$57$	−13.6907	+	5.67088i	−1.81338	+	0.751126i
$58$	0.132275	+	0.319339i	0.0173685	+	0.0419313i
$59$	−9.06612	−	9.06612i	−1.18031	−	1.18031i	−0.979664	−	0.200644i	$-0.935697\pi$
$59$	−9.06612	−	9.06612i	−1.18031	−	1.18031i	−0.200644	−	0.979664i	$-0.564303\pi$
$60$	−5.48087	−	1.42139i	−0.707577	−	0.183500i
$61$	12.7953	−	5.29999i	1.63827	−	0.678595i	0.642151	−	0.766579i	$-0.278042\pi$
$61$	12.7953	−	5.29999i	1.63827	−	0.678595i	0.996122	+	0.0879839i	$0.0280424\pi$
$62$	−1.73693	+	0.719461i	−0.220590	+	0.0913716i
$63$	4.32504	−	10.4416i	0.544903	−	1.31551i
$64$		−	1.00000i		−	0.125000i
$65$	0.240895	+	1.72247i	0.0298793	+	0.213646i
$66$	−4.44263	+	4.44263i	−0.546850	+	0.546850i
$67$			0.862303i			0.105347i	0.998612	+	0.0526736i	$0.0167743\pi$
$67$			0.862303i			0.105347i	−0.998612	+	0.0526736i	$0.983226\pi$
$68$	−0.798615	+	4.04502i	−0.0968463	+	0.490531i
$69$	20.4332			2.45987
$70$	−7.16945	−	1.85930i	−0.856914	−	0.222229i
$71$	−3.13819	+	7.57626i	−0.372435	+	0.899137i	0.620902	+	0.783888i	$0.286767\pi$
$71$	−3.13819	+	7.57626i	−0.372435	+	0.899137i	−0.993337	+	0.115249i	$0.963233\pi$
$72$	−3.41205			−0.402113
$73$	3.75104	−	9.05580i	0.439026	−	1.05990i	−0.537260	−	0.843417i	$-0.680541\pi$
$73$	3.75104	−	9.05580i	0.439026	−	1.05990i	0.976286	−	0.216485i	$-0.0694593\pi$
$74$	1.76745	+	4.26699i	0.205461	+	0.496028i
$75$	12.5777	+	1.45021i	1.45235	+	0.167455i
$76$	4.13806	+	4.13806i	0.474669	+	0.474669i
$77$	−5.81136	+	5.81136i	−0.662265	+	0.662265i
$78$	0.753721	+	1.81964i	0.0853421	+	0.206034i
$79$	3.33195	+	8.04403i	0.374873	+	0.905024i	0.992909	+	0.118874i	$0.0379286\pi$
$79$	3.33195	+	8.04403i	0.374873	+	0.905024i	−0.618036	+	0.786150i	$0.712071\pi$
$80$	0.309710	+	2.21452i	0.0346266	+	0.247590i
$81$		−	7.59408i		−	0.843787i
$82$	2.17392	+	0.900466i	0.240069	+	0.0994399i
$83$	−2.56072	−	2.56072i	−0.281075	−	0.281075i	0.552462	−	0.833538i	$-0.313688\pi$
$83$	−2.56072	−	2.56072i	−0.281075	−	0.281075i	−0.833538	+	0.552462i	$0.813688\pi$
$84$	−8.38752			−0.915153
$85$	0.515763	−	9.20511i	0.0559423	−	0.998434i
$86$	11.3645			1.22547
$87$	−0.618900	−	0.618900i	−0.0663530	−	0.0663530i
$88$	2.29231	+	0.949504i	0.244361	+	0.101217i
$89$			3.67668i			0.389728i	0.980830	+	0.194864i	$0.0624265\pi$
$89$			3.67668i			0.389728i	−0.980830	+	0.194864i	$0.937574\pi$
$90$	7.55603	−	1.05674i	0.796475	−	0.111391i
$91$	0.985934	+	2.38025i	0.103354	+	0.249519i
$92$	−3.08800	−	7.45510i	−0.321947	−	0.777248i
$93$	3.36628	−	3.36628i	0.349067	−	0.349067i
$94$	6.54760	+	6.54760i	0.675334	+	0.675334i
$95$	−10.4454	−	7.88221i	−1.07168	−	0.808698i
$96$	0.969032	+	2.33945i	0.0989014	+	0.238769i
$97$	−1.05015	+	2.53530i	−0.106627	+	0.257420i	−0.968183	−	0.250241i	$-0.919490\pi$
$97$	−1.05015	+	2.53530i	−0.106627	+	0.257420i	0.861556	+	0.507662i	$0.169490\pi$
$98$	−3.97161			−0.401193
$99$	3.23975	−	7.82145i	0.325607	−	0.786086i
$100$	−1.37171	−	4.80816i	−0.137171	−	0.480816i
$101$	−9.51804			−0.947080			−0.473540	−	0.880772i	$-0.657024\pi$
$101$	−9.51804			−0.947080			−0.473540	+	0.880772i	$0.657024\pi$
$102$	−2.05144	−	10.2370i	−0.203123	−	1.01362i
$103$			12.8896i			1.27005i	0.772490	+	0.635027i	$0.219011\pi$
$103$			12.8896i			1.27005i	−0.772490	+	0.635027i	$0.780989\pi$
$104$	0.549994	−	0.549994i	0.0539313	−	0.0539313i
$105$	18.5743	−	2.59769i	1.81267	−	0.253509i
$106$		−	4.22732i		−	0.410594i
$107$	−1.95011	+	4.70799i	−0.188525	+	0.455139i	−0.989676	−	0.143323i	$-0.954221\pi$
$107$	−1.95011	+	4.70799i	−0.188525	+	0.455139i	0.801151	+	0.598462i	$0.204221\pi$
$108$	0.963960	−	0.399286i	0.0927571	−	0.0384213i
$109$	0.169155	−	0.0700661i	0.0162021	−	0.00671112i	−0.374568	−	0.927200i	$-0.622209\pi$
$109$	0.169155	−	0.0700661i	0.0162021	−	0.00671112i	0.390770	+	0.920488i	$0.372209\pi$
$110$	−5.37042	−	1.39274i	−0.512049	−	0.132793i
$111$	−8.26970	−	8.26970i	−0.784925	−	0.784925i
$112$	1.26758	+	3.06021i	0.119775	+	0.289162i
$113$	−11.1347	+	4.61213i	−1.04746	+	0.433873i	−0.838985	−	0.544154i	$-0.816851\pi$
$113$	−11.1347	+	4.61213i	−1.04746	+	0.433873i	−0.208477	+	0.978027i	$0.566851\pi$
$114$	−13.6907	−	5.67088i	−1.28225	−	0.531126i
$115$	9.14734	+	15.5530i	0.852994	+	1.45033i
$116$	−0.132275	+	0.319339i	−0.0122814	+	0.0296499i
$117$	−1.87660	−	1.87660i	−0.173492	−	0.173492i
$118$		−	12.8214i		−	1.18031i
$119$	−2.68346	−	13.3909i	−0.245992	−	1.22754i
$120$	−2.87049	−	4.88063i	−0.262038	−	0.445538i
$121$	3.42507	−	3.42507i	0.311370	−	0.311370i
$122$	12.7953	+	5.29999i	1.15843	+	0.479839i
$123$	−5.95835			−0.537246
$124$	−1.73693	−	0.719461i	−0.155981	−	0.0646095i
$125$	4.52681	+	10.2229i	0.404891	+	0.914365i
$126$	10.4416	−	4.32504i	0.930208	−	0.385305i
$127$	13.6948	−	13.6948i	1.21522	−	1.21522i	0.245934	−	0.969286i	$-0.420905\pi$
$127$	13.6948	−	13.6948i	1.21522	−	1.21522i	0.969286	−	0.245934i	$-0.0790948\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−26.5867	+	11.0126i	−2.34083	+	0.969602i
$130$	−1.04763	+	1.38831i	−0.0918834	+	0.121763i
$131$	6.17744	+	2.55878i	0.539725	+	0.223561i	0.635857	−	0.771807i	$-0.280647\pi$
$131$	6.17744	+	2.55878i	0.539725	+	0.223561i	−0.0961315	+	0.995369i	$0.530647\pi$
$132$	−6.28283			−0.546850
$133$	−17.9086	−	7.41801i	−1.55288	−	0.643223i
$134$	−0.609741	+	0.609741i	−0.0526736	+	0.0526736i
$135$	−2.01104	+	1.18277i	−0.173083	+	0.101797i
$136$	−3.42497	+	2.29556i	−0.293689	+	0.196842i
$137$		−	2.17815i		−	0.186092i	−0.995662	−	0.0930461i	$-0.970340\pi$
$137$		−	2.17815i		−	0.186092i	0.995662	−	0.0930461i	$-0.0296604\pi$
$138$	14.4485	+	14.4485i	1.22993	+	1.22993i
$139$	3.84818	−	9.29033i	0.326398	−	0.787995i	−0.672456	−	0.740137i	$-0.734761\pi$
$139$	3.84818	−	9.29033i	0.326398	−	0.787995i	0.998854	−	0.0478580i	$-0.0152395\pi$
$140$	−3.75485	−	6.38429i	−0.317343	−	0.539571i
$141$	−21.6626	−	8.97295i	−1.82432	−	0.755659i
$142$	−7.57626	+	3.13819i	−0.635786	+	0.263351i
$143$	0.738533	+	1.78298i	0.0617592	+	0.149100i
$144$	−2.41268	−	2.41268i	−0.201057	−	0.201057i
$145$	0.194022	−	0.748149i	0.0161126	−	0.0621304i
$146$	9.05580	−	3.75104i	0.749464	−	0.310438i
$147$	9.29139	−	3.84862i	0.766341	−	0.317429i
$148$	−1.76745	+	4.26699i	−0.145283	+	0.350745i
$149$			12.2117i			1.00043i	0.865903	+	0.500213i	$0.166745\pi$
$149$			12.2117i			1.00043i	−0.865903	+	0.500213i	$0.833255\pi$
$150$	7.86831	+	9.91921i	0.642445	+	0.809900i
$151$	−8.45256	+	8.45256i	−0.687860	+	0.687860i	−0.961759	−	0.273899i	$-0.911687\pi$
$151$	−8.45256	+	8.45256i	−0.687860	+	0.687860i	0.273899	+	0.961759i	$0.411687\pi$
$152$			5.85211i			0.474669i
$153$	7.83255	+	11.6862i	0.633224	+	0.944769i
$154$	−8.21850			−0.662265
$155$	4.06929	+	1.05531i	0.326853	+	0.0847647i
$156$	−0.753721	+	1.81964i	−0.0603460	+	0.145688i
$157$	−8.98017			−0.716696			−0.358348	−	0.933588i	$-0.616660\pi$
$157$	−8.98017			−0.716696			−0.358348	+	0.933588i	$0.616660\pi$
$158$	−3.33195	+	8.04403i	−0.265075	+	0.639949i
$159$	4.09641	+	9.88961i	0.324866	+	0.784297i
$160$	−1.34690	+	1.78490i	−0.106482	+	0.141108i
$161$	18.8998	+	18.8998i	1.48952	+	1.48952i
$162$	5.36983	−	5.36983i	0.421893	−	0.421893i
$163$	4.06748	+	9.81976i	0.318589	+	0.769143i	0.999329	+	0.0366176i	$0.0116584\pi$
$163$	4.06748	+	9.81976i	0.318589	+	0.769143i	−0.680740	+	0.732525i	$0.738342\pi$
$164$	0.900466	+	2.17392i	0.0703146	+	0.169754i
$165$	13.9134	−	1.94585i	1.08316	−	0.151484i
$166$		−	3.62140i		−	0.281075i
$167$	4.96753	+	2.05762i	0.384399	+	0.159223i	0.566510	−	0.824055i	$-0.308293\pi$
$167$	4.96753	+	2.05762i	0.384399	+	0.159223i	−0.182111	+	0.983278i	$0.558293\pi$
$168$	−5.93087	−	5.93087i	−0.457577	−	0.457577i
$169$	−12.3950			−0.953463
$170$	6.87369	−	6.14429i	0.527188	−	0.471246i
$171$	19.9677			1.52696
$172$	8.03592	+	8.03592i	0.612733	+	0.612733i
$173$	−3.90622	−	1.61801i	−0.296985	−	0.123015i	0.229216	−	0.973376i	$-0.426384\pi$
$173$	−3.90622	−	1.61801i	−0.296985	−	0.123015i	−0.526201	+	0.850361i	$0.676384\pi$
$174$		−	0.875257i		−	0.0663530i
$175$	10.2924	+	12.9752i	0.778036	+	0.980833i
$176$	0.949504	+	2.29231i	0.0715716	+	0.172789i
$177$	12.4244	+	29.9951i	0.933873	+	2.25457i
$178$	−2.59981	+	2.59981i	−0.194864	+	0.194864i
$179$	3.76205	+	3.76205i	0.281189	+	0.281189i	0.833583	−	0.552394i	$-0.186286\pi$
$179$	3.76205	+	3.76205i	0.281189	+	0.281189i	−0.552394	+	0.833583i	$0.686286\pi$
$180$	6.09015	+	4.59569i	0.453933	+	0.342542i
$181$	−6.05136	−	14.6093i	−0.449794	−	1.08590i	−0.972399	−	0.233324i	$-0.925040\pi$
$181$	−6.05136	−	14.6093i	−0.449794	−	1.08590i	0.522605	−	0.852575i	$-0.324960\pi$
$182$	−0.985934	+	2.38025i	−0.0730823	+	0.176436i
$183$	−35.0699			−2.59244
$184$	3.08800	−	7.45510i	0.227651	−	0.549597i
$185$	2.59251	−	9.99671i	0.190605	−	0.734973i
$186$	4.76064			0.349067
$187$	−2.01010	−	10.0307i	−0.146993	−	0.733519i
$188$			9.25971i			0.675334i
$189$	−2.44379	+	2.44379i	−0.177760	+	0.177760i
$190$	−1.81245	−	12.9596i	−0.131489	−	0.940187i
$191$			26.3384i			1.90578i	0.303318	+	0.952890i	$0.401906\pi$
$191$			26.3384i			1.90578i	−0.303318	+	0.952890i	$0.598094\pi$
$192$	−0.969032	+	2.33945i	−0.0699338	+	0.168835i
$193$	12.6427	−	5.23679i	0.910044	−	0.376953i	0.121971	−	0.992534i	$-0.461079\pi$
$193$	12.6427	−	5.23679i	0.910044	−	0.376953i	0.788074	+	0.615581i	$0.211079\pi$
$194$	−2.53530	+	1.05015i	−0.182024	+	0.0753967i
$195$	1.10557	−	4.26307i	0.0791713	−	0.305285i
$196$	−2.80835	−	2.80835i	−0.200597	−	0.200597i
$197$	2.48851	+	6.00780i	0.177299	+	0.428038i	0.987398	−	0.158255i	$-0.0505867\pi$
$197$	2.48851	+	6.00780i	0.177299	+	0.428038i	−0.810099	+	0.586293i	$0.800587\pi$
$198$	7.82145	−	3.23975i	0.555846	−	0.230239i
$199$	−10.2616	−	4.25049i	−0.727424	−	0.301309i	−0.0119313	−	0.999929i	$-0.503798\pi$
$199$	−10.2616	−	4.25049i	−0.727424	−	0.301309i	−0.715493	+	0.698620i	$0.753798\pi$
$200$	2.42993	−	4.36983i	0.171822	−	0.308994i
$201$	0.835599	−	2.01732i	0.0589386	−	0.142290i
$202$	−6.73027	−	6.73027i	−0.473540	−	0.473540i
$203$		−	1.14491i		−	0.0803571i
$204$	5.78807	−	8.68924i	0.405246	−	0.608369i
$205$	−2.66738	−	4.53529i	−0.186298	−	0.316759i
$206$	−9.11435	+	9.11435i	−0.635027	+	0.635027i
$207$	−25.4371	−	10.5364i	−1.76800	−	0.732331i
$208$	0.777809			0.0539313
$209$	−13.4148	−	5.55660i	−0.927922	−	0.384358i
$210$	14.9709	+	11.2972i	1.03309	+	0.779578i
$211$	−4.39176	+	1.81913i	−0.302342	+	0.125234i	−0.528697	−	0.848811i	$-0.677319\pi$
$211$	−4.39176	+	1.81913i	−0.302342	+	0.125234i	0.226355	+	0.974045i	$0.427319\pi$
$212$	2.98917	−	2.98917i	0.205297	−	0.205297i
$213$	14.6833	−	14.6833i	1.00608	−	1.00608i
$214$	−4.70799	+	1.95011i	−0.321832	+	0.133307i
$215$	−20.2845	−	15.3069i	−1.38339	−	1.04392i
$216$	0.963960	+	0.399286i	0.0655892	+	0.0271679i
$217$	6.22734			0.422739
$218$	0.169155	+	0.0700661i	0.0114566	+	0.00474548i
$219$	−17.5507	+	17.5507i	−1.18597	+	1.18597i
$220$	−2.81264	−	4.78228i	−0.189628	−	0.322421i
$221$	−3.14626	−	0.621170i	−0.211640	−	0.0417844i
$222$		−	11.6951i		−	0.784925i
$223$	13.4824	+	13.4824i	0.902845	+	0.902845i	0.995681	−	0.0928360i	$-0.0295932\pi$
$223$	13.4824	+	13.4824i	0.902845	+	0.902845i	−0.0928360	+	0.995681i	$0.529593\pi$
$224$	−1.26758	+	3.06021i	−0.0846937	+	0.204469i
$225$	−14.9101	−	8.29105i	−0.994004	−	0.552737i
$226$	−11.1347	−	4.61213i	−0.740667	−	0.306794i
$227$	16.6070	−	6.87885i	1.10225	−	0.456565i	0.243985	−	0.969779i	$-0.421545\pi$
$227$	16.6070	−	6.87885i	1.10225	−	0.456565i	0.858261	+	0.513214i	$0.171545\pi$
$228$	−5.67088	−	13.6907i	−0.375563	−	0.906689i
$229$	0.797989	+	0.797989i	0.0527326	+	0.0527326i	0.732981	−	0.680249i	$-0.238128\pi$
$229$	0.797989	+	0.797989i	0.0527326	+	0.0527326i	−0.680249	+	0.732981i	$0.738128\pi$
$230$	−4.52952	+	17.4658i	−0.298667	+	1.15166i
$231$	19.2268	−	7.96398i	1.26503	−	0.523992i
$232$	−0.319339	+	0.132275i	−0.0209657	+	0.00868426i
$233$	8.55988	−	20.6654i	0.560776	−	1.35383i	−0.348370	−	0.937357i	$-0.613265\pi$
$233$	8.55988	−	20.6654i	0.560776	−	1.35383i	0.909146	−	0.416477i	$-0.136735\pi$
$234$		−	2.65392i		−	0.173492i
$235$	−2.86782	−	20.5058i	−0.187076	−	1.33765i
$236$	9.06612	−	9.06612i	0.590154	−	0.590154i
$237$		−	22.0474i		−	1.43213i
$238$	7.57131	−	11.3663i	0.490775	−	0.736768i
$239$	−11.2657			−0.728714			−0.364357	−	0.931259i	$-0.618711\pi$
$239$	−11.2657			−0.728714			−0.364357	+	0.931259i	$0.618711\pi$
$240$	1.42139	−	5.48087i	0.0917501	−	0.353788i
$241$	−0.166358	+	0.401624i	−0.0107161	+	0.0258709i	−0.929147	−	0.369710i	$-0.879457\pi$
$241$	−0.166358	+	0.401624i	−0.0107161	+	0.0258709i	0.918431	+	0.395581i	$0.129457\pi$
$242$	4.84378			0.311370
$243$	−8.55676	+	20.6578i	−0.548916	+	1.32520i
$244$	5.29999	+	12.7953i	0.339297	+	0.819136i
$245$	7.08892	+	5.34937i	0.452894	+	0.341759i
$246$	−4.21319	−	4.21319i	−0.268623	−	0.268623i
$247$	−3.21862	+	3.21862i	−0.204796	+	0.204796i
$248$	−0.719461	−	1.73693i	−0.0456858	−	0.110295i
$249$	3.50926	+	8.47209i	0.222390	+	0.536897i
$250$	−4.02775	+	10.4296i	−0.254737	+	0.659628i
$251$		−	23.8942i		−	1.50819i	−0.656767	−	0.754094i	$-0.728077\pi$
$251$		−	23.8942i		−	1.50819i	0.656767	−	0.754094i	$-0.271923\pi$
$252$	10.4416	+	4.32504i	0.657757	+	0.272452i
$253$	14.1573	+	14.1573i	0.890061	+	0.890061i
$254$	19.3674			1.21522
$255$	−10.1266	+	21.0351i	−0.634155	+	1.31727i
$256$	1.00000			0.0625000
$257$	−20.7578	−	20.7578i	−1.29483	−	1.29483i	−0.931761	−	0.363073i	$-0.881727\pi$
$257$	−20.7578	−	20.7578i	−1.29483	−	1.29483i	−0.363073	−	0.931761i	$-0.618273\pi$
$258$	−26.5867	−	11.0126i	−1.65521	−	0.685612i
$259$		−	15.2982i		−	0.950587i
$260$	−1.72247	+	0.240895i	−0.106823	+	0.0149397i
$261$	0.451327	+	1.08960i	0.0279365	+	0.0674446i
$262$	2.55878	+	6.17744i	0.158082	+	0.381643i
$263$	14.2208	−	14.2208i	0.876892	−	0.876892i	−0.116320	−	0.993212i	$-0.537110\pi$
$263$	14.2208	−	14.2208i	0.876892	−	0.876892i	0.993212	+	0.116320i	$0.0371098\pi$
$264$	−4.44263	−	4.44263i	−0.273425	−	0.273425i
$265$	−5.69379	+	7.54534i	−0.349767	+	0.463506i
$266$	−7.41801	−	17.9086i	−0.454827	−	1.09805i
$267$	3.56282	−	8.60141i	0.218041	−	0.526398i
$268$	−0.862303			−0.0526736
$269$	1.10168	−	2.65969i	0.0671707	−	0.162164i	−0.886729	−	0.462289i	$-0.847028\pi$
$269$	1.10168	−	2.65969i	0.0671707	−	0.162164i	0.953900	+	0.300125i	$0.0970283\pi$
$270$	−2.25837	−	0.585676i	−0.137440	−	0.0356431i
$271$	18.7793			1.14076			0.570380	−	0.821381i	$-0.306796\pi$
$271$	18.7793			1.14076			0.570380	+	0.821381i	$0.306796\pi$
$272$	−4.04502	−	0.798615i	−0.245266	−	0.0484231i
$273$		−	6.52389i		−	0.394844i
$274$	1.54019	−	1.54019i	0.0930461	−	0.0930461i
$275$	7.70975	+	9.71933i	0.464916	+	0.586097i
$276$			20.4332i			1.22993i
$277$	−3.35394	+	8.09712i	−0.201519	+	0.486509i	−0.992040	−	0.125926i	$-0.959810\pi$
$277$	−3.35394	+	8.09712i	−0.201519	+	0.486509i	0.790521	+	0.612435i	$0.209810\pi$
$278$	9.29033	−	3.84818i	0.557197	−	0.230798i
$279$	−5.92649	+	2.45483i	−0.354810	+	0.146967i
$280$	1.85930	−	7.16945i	0.111114	−	0.428457i
$281$	21.5263	+	21.5263i	1.28415	+	1.28415i	0.938284	+	0.345866i	$0.112415\pi$
$281$	21.5263	+	21.5263i	1.28415	+	1.28415i	0.345866	+	0.938284i	$0.387585\pi$
$282$	−8.97295	−	21.6626i	−0.534332	−	1.28999i
$283$	−8.83075	+	3.65782i	−0.524934	+	0.217435i	−0.629383	−	0.777096i	$-0.716692\pi$
$283$	−8.83075	+	3.65782i	−0.524934	+	0.217435i	0.104449	+	0.994530i	$0.466692\pi$
$284$	−7.57626	−	3.13819i	−0.449569	−	0.186217i
$285$	16.7984	+	28.5620i	0.995051	+	1.69186i
$286$	−0.738533	+	1.78298i	−0.0436704	+	0.105430i
$287$	−5.51122	−	5.51122i	−0.325317	−	0.325317i
$288$		−	3.41205i		−	0.201057i
$289$	15.7244	+	6.46083i	0.924966	+	0.380049i
$290$	0.666215	−	0.391827i	0.0391215	−	0.0230089i
$291$	4.91357	−	4.91357i	0.288038	−	0.288038i
$292$	9.05580	+	3.75104i	0.529951	+	0.219513i
$293$	5.34949			0.312521			0.156260	−	0.987716i	$-0.450056\pi$
$293$	5.34949			0.312521			0.156260	+	0.987716i	$0.450056\pi$
$294$	9.29139	+	3.84862i	0.541885	+	0.224456i
$295$	−17.2692	+	22.8849i	−1.00545	+	1.33241i
$296$	−4.26699	+	1.76745i	−0.248014	+	0.102731i
$297$	−1.83057	+	1.83057i	−0.106220	+	0.106220i
$298$	−8.63501	+	8.63501i	−0.500213	+	0.500213i
$299$	5.79864	−	2.40188i	0.335344	−	0.138904i
$300$	−1.45021	+	12.5777i	−0.0837277	+	0.726173i
$301$	−34.7777	−	14.4054i	−2.00455	−	0.830313i
$302$	−11.9537			−0.687860
$303$	22.2670	+	9.22328i	1.27920	+	0.529864i
$304$	−4.13806	+	4.13806i	−0.237334	+	0.237334i
$305$	−15.6998	−	26.6940i	−0.898965	−	1.52849i
$306$	−2.72491	+	13.8018i	−0.155773	+	0.788997i
$307$			19.6367i			1.12073i	0.828247	+	0.560363i	$0.189338\pi$
$307$			19.6367i			1.12073i	−0.828247	+	0.560363i	$0.810662\pi$
$308$	−5.81136	−	5.81136i	−0.331133	−	0.331133i
$309$	12.4905	−	30.1547i	0.710558	−	1.71544i
$310$	2.13120	+	3.62364i	0.121044	+	0.205809i
$311$	12.6908	+	5.25670i	0.719629	+	0.298080i	0.712283	−	0.701893i	$-0.247661\pi$
$311$	12.6908	+	5.25670i	0.719629	+	0.298080i	0.00734657	+	0.999973i	$0.497661\pi$
$312$	−1.81964	+	0.753721i	−0.103017	+	0.0426711i
$313$	−2.35732	−	5.69107i	−0.133244	−	0.321678i	0.843150	−	0.537679i	$-0.180699\pi$
$313$	−2.35732	−	5.69107i	−0.133244	−	0.321678i	−0.976393	+	0.216001i	$0.930699\pi$
$314$	−6.34994	−	6.34994i	−0.358348	−	0.358348i
$315$	−24.4625	−	6.34401i	−1.37831	−	0.357444i
$316$	−8.04403	+	3.33195i	−0.452512	+	0.187437i
$317$	−4.69756	+	1.94579i	−0.263841	+	0.109287i	−0.510683	−	0.859769i	$-0.670607\pi$
$317$	−4.69756	+	1.94579i	−0.263841	+	0.109287i	0.246842	+	0.969056i	$0.420607\pi$
$318$	−4.09641	+	9.88961i	−0.229715	+	0.554582i
$319$		−	0.857619i		−	0.0480174i
$320$	−2.21452	+	0.309710i	−0.123795	+	0.0173133i
$321$	9.12439	−	9.12439i	0.509274	−	0.509274i
$322$			26.7284i			1.48952i
$323$	20.0433	−	13.4338i	1.11524	−	0.747479i
$324$	7.59408			0.421893
$325$	3.73983	−	1.06693i	0.207448	−	0.0591827i
$326$	−4.06748	+	9.81976i	−0.225277	+	0.543866i
$327$	−0.463625			−0.0256385
$328$	−0.900466	+	2.17392i	−0.0497199	+	0.120035i
$329$	−11.7374	−	28.3366i	−0.647104	−	1.56225i
$330$	11.2142	+	8.46236i	0.617322	+	0.465837i
$331$	2.30132	+	2.30132i	0.126492	+	0.126492i	0.767519	−	0.641027i	$-0.221491\pi$
$331$	2.30132	+	2.30132i	0.126492	+	0.126492i	−0.641027	+	0.767519i	$0.721491\pi$
$332$	2.56072	−	2.56072i	0.140538	−	0.140538i
$333$	6.03061	+	14.5592i	0.330475	+	0.797838i
$334$	2.05762	+	4.96753i	0.112588	+	0.271811i
$335$	1.90958	−	0.267064i	0.104332	−	0.0145912i
$336$		−	8.38752i		−	0.457577i
$337$	−5.37723	−	2.22732i	−0.292917	−	0.121330i	0.231386	−	0.972862i	$-0.425674\pi$
$337$	−5.37723	−	2.22732i	−0.292917	−	0.121330i	−0.524303	+	0.851532i	$0.675674\pi$
$338$	−8.76460	−	8.76460i	−0.476731	−	0.476731i
$339$	30.5183			1.65753
$340$	9.20511	+	0.515763i	0.499217	+	0.0279712i
$341$	4.66471			0.252608
$342$	14.1193	+	14.1193i	0.763482	+	0.763482i
$343$	−9.26749	−	3.83872i	−0.500397	−	0.207271i
$344$			11.3645i			0.612733i
$345$	−6.32836	−	45.2496i	−0.340707	−	2.43616i
$346$	−1.61801	−	3.90622i	−0.0869848	−	0.210000i
$347$	4.68855	+	11.3192i	0.251695	+	0.607645i	0.998341	−	0.0575764i	$-0.0183373\pi$
$347$	4.68855	+	11.3192i	0.251695	+	0.607645i	−0.746646	+	0.665221i	$0.768337\pi$
$348$	0.618900	−	0.618900i	0.0331765	−	0.0331765i
$349$	−4.08452	−	4.08452i	−0.218640	−	0.218640i	0.589285	−	0.807925i	$-0.299409\pi$
$349$	−4.08452	−	4.08452i	−0.218640	−	0.218640i	−0.807925	+	0.589285i	$0.799409\pi$
$350$	−1.89700	+	16.4527i	−0.101399	+	0.879434i
$351$	0.310568	+	0.749777i	0.0165769	+	0.0400201i
$352$	−0.949504	+	2.29231i	−0.0506087	+	0.122180i
$353$	12.5280			0.666797			0.333398	−	0.942786i	$-0.391805\pi$
$353$	12.5280			0.666797			0.333398	+	0.942786i	$0.391805\pi$
$354$	−12.4244	+	29.9951i	−0.660348	+	1.59422i
$355$	17.7497	+	4.60313i	0.942055	+	0.244309i
$356$	−3.67668			−0.194864
$357$	−6.69840	+	33.9277i	−0.354517	+	1.79564i
$358$			5.32034i			0.281189i
$359$	−4.29559	+	4.29559i	−0.226713	+	0.226713i	−0.811318	−	0.584605i	$-0.801249\pi$
$359$	−4.29559	+	4.29559i	−0.226713	+	0.226713i	0.584605	+	0.811318i	$0.301249\pi$
$360$	1.05674	+	7.55603i	0.0556953	+	0.398238i
$361$		−	15.2472i		−	0.802482i
$362$	6.05136	−	14.6093i	0.318052	−	0.767847i
$363$	−11.3318	+	4.69377i	−0.594764	+	0.246359i
$364$	−2.38025	+	0.985934i	−0.124759	+	0.0516770i
$365$	−21.2160	−	5.50206i	−1.11049	−	0.287991i
$366$	−24.7981	−	24.7981i	−1.29622	−	1.29622i
$367$	3.76510	+	9.08975i	0.196536	+	0.474481i	0.991168	−	0.132611i	$-0.0423360\pi$
$367$	3.76510	+	9.08975i	0.196536	+	0.474481i	−0.794632	+	0.607092i	$0.792336\pi$
$368$	7.45510	−	3.08800i	0.388624	−	0.160973i
$369$	7.41751	+	3.07243i	0.386140	+	0.159944i
$370$	8.90192	−	5.23556i	0.462789	−	0.272184i
$371$	−5.35846	+	12.9365i	−0.278198	+	0.671628i
$372$	3.36628	+	3.36628i	0.174534	+	0.174534i
$373$			10.2057i			0.528431i	0.964464	+	0.264215i	$0.0851130\pi$
$373$			10.2057i			0.528431i	−0.964464	+	0.264215i	$0.914887\pi$
$374$	5.67144	−	8.51414i	0.293263	−	0.440256i
$375$	−0.683924	−	28.3026i	−0.0353177	−	1.46154i
$376$	−6.54760	+	6.54760i	−0.337667	+	0.337667i
$377$	−0.248385	−	0.102884i	−0.0127925	−	0.00529882i
$378$	−3.45604			−0.177760
$379$	20.4751	+	8.48108i	1.05174	+	0.435644i	0.840512	−	0.541793i	$-0.182254\pi$
$379$	20.4751	+	8.48108i	1.05174	+	0.435644i	0.211226	+	0.977437i	$0.432254\pi$
$380$	7.88221	−	10.4454i	0.404349	−	0.535838i
$381$	−45.3091	+	18.7677i	−2.32126	+	0.961496i
$382$	−18.6241	+	18.6241i	−0.952890	+	0.952890i
$383$	−7.19636	+	7.19636i	−0.367717	+	0.367717i	−0.866644	−	0.498927i	$-0.833727\pi$
$383$	−7.19636	+	7.19636i	−0.367717	+	0.367717i	0.498927	+	0.866644i	$0.333727\pi$
$384$	−2.33945	+	0.969032i	−0.119385	+	0.0494507i
$385$	14.6692	+	11.0695i	0.747610	+	0.564154i
$386$	12.6427	+	5.23679i	0.643498	+	0.266546i
$387$	38.7762			1.97111
$388$	−2.53530	−	1.05015i	−0.128710	−	0.0533135i
$389$	−6.49707	+	6.49707i	−0.329414	+	0.329414i	−0.852364	−	0.522949i	$-0.824832\pi$
$389$	−6.49707	+	6.49707i	−0.329414	+	0.329414i	0.522949	+	0.852364i	$0.324832\pi$
$390$	3.79620	−	2.23269i	0.192228	−	0.113057i
$391$	−32.6222	+	6.53729i	−1.64977	+	0.330605i
$392$		−	3.97161i		−	0.200597i
$393$	−11.9723	−	11.9723i	−0.603921	−	0.603921i
$394$	−2.48851	+	6.00780i	−0.125370	+	0.302669i
$395$	16.7817	−	9.86996i	0.844379	−	0.496612i
$396$	7.82145	+	3.23975i	0.393043	+	0.162804i
$397$	23.5614	−	9.75944i	1.18251	−	0.489812i	0.297202	−	0.954815i	$-0.403947\pi$
$397$	23.5614	−	9.75944i	1.18251	−	0.489812i	0.885309	+	0.465003i	$0.153947\pi$
$398$	−4.25049	−	10.2616i	−0.213058	−	0.514367i
$399$	34.7081	+	34.7081i	1.73758	+	1.73758i
$400$	4.80816	−	1.37171i	0.240408	−	0.0685857i
$401$	33.7790	−	13.9917i	1.68684	−	0.698712i	0.687226	−	0.726444i	$-0.258828\pi$
$401$	33.7790	−	13.9917i	1.68684	−	0.698712i	0.999615	+	0.0277317i	$0.00882842\pi$
$402$	2.01732	−	0.835599i	0.100615	−	0.0416759i
$403$	0.559603	−	1.35100i	0.0278758	−	0.0672981i
$404$		−	9.51804i		−	0.473540i
$405$	−16.8172	+	2.35196i	−0.835654	+	0.116870i
$406$	0.809575	−	0.809575i	0.0401786	−	0.0401786i
$407$		−	11.4594i		−	0.568024i
$408$	10.2370	−	2.05144i	0.506808	−	0.101561i
$409$	−14.9024			−0.736875			−0.368438	−	0.929652i	$-0.620107\pi$
$409$	−14.9024			−0.736875			−0.368438	+	0.929652i	$0.620107\pi$
$410$	1.32081	−	5.09306i	0.0652303	−	0.251528i
$411$	−2.11070	+	5.09568i	−0.104113	+	0.251351i
$412$	−12.8896			−0.635027
$413$	−16.2522	+	39.2362i	−0.799717	+	1.93069i
$414$	−10.5364	−	25.4371i	−0.517836	−	1.25017i
$415$	−4.87767	+	6.46383i	−0.239436	+	0.317297i
$416$	0.549994	+	0.549994i	0.0269657	+	0.0269657i
$417$	−18.0052	+	18.0052i	−0.881720	+	0.881720i
$418$	−5.55660	−	13.4148i	−0.271782	−	0.656140i
$419$	0.678866	+	1.63893i	0.0331648	+	0.0800668i	0.939594	−	0.342291i	$-0.111203\pi$
$419$	0.678866	+	1.63893i	0.0331648	+	0.0800668i	−0.906429	+	0.422357i	$0.861203\pi$
$420$	2.59769	+	18.5743i	0.126755	+	0.906333i
$421$			25.1213i			1.22434i	0.790728	+	0.612168i	$0.209702\pi$
$421$			25.1213i			1.22434i	−0.790728	+	0.612168i	$0.790298\pi$
$422$	−4.39176	−	1.81913i	−0.213788	−	0.0885538i
$423$	22.3407	+	22.3407i	1.08624	+	1.08624i
$424$	4.22732			0.205297
$425$	−20.5446	+	1.70874i	−0.996559	+	0.0828863i
$426$	20.7653			1.00608
$427$	−32.4381	−	32.4381i	−1.56979	−	1.56979i
$428$	−4.70799	−	1.95011i	−0.227569	−	0.0942623i
$429$		−	4.88684i		−	0.235939i
$430$	−3.51969	−	25.1669i	−0.169735	−	1.21365i
$431$	−8.98389	−	21.6890i	−0.432739	−	1.04472i	−0.978400	−	0.206718i	$-0.933722\pi$
$431$	−8.98389	−	21.6890i	−0.432739	−	1.04472i	0.545662	−	0.838006i	$-0.316278\pi$
$432$	0.399286	+	0.963960i	0.0192106	+	0.0463786i
$433$	−20.4541	+	20.4541i	−0.982961	+	0.982961i	−0.999857	−	0.0168966i	$-0.994621\pi$
$433$	−20.4541	+	20.4541i	−0.982961	+	0.982961i	0.0168966	+	0.999857i	$0.494621\pi$
$434$	4.40339	+	4.40339i	0.211370	+	0.211370i
$435$	−1.17888	+	1.56224i	−0.0565232	+	0.0749038i
$436$	0.0700661	+	0.169155i	0.00335556	+	0.00810103i
$437$	−18.0713	+	43.6280i	−0.864468	+	2.08701i
$438$	−24.8205			−1.18597
$439$	−0.391020	+	0.944005i	−0.0186624	+	0.0450549i	−0.932936	−	0.360042i	$-0.882762\pi$
$439$	−0.391020	+	0.944005i	−0.0186624	+	0.0450549i	0.914274	+	0.405097i	$0.132762\pi$
$440$	1.39274	−	5.37042i	0.0663964	−	0.256025i
$441$	−13.5513			−0.645301
$442$	−1.78551	−	2.66397i	−0.0849278	−	0.126712i
$443$			23.1860i			1.10160i	0.834637	+	0.550801i	$0.185678\pi$
$443$			23.1860i			1.10160i	−0.834637	+	0.550801i	$0.814322\pi$
$444$	8.26970	−	8.26970i	0.392463	−	0.392463i
$445$	8.14207	−	1.13870i	0.385971	−	0.0539797i
$446$			19.0669i			0.902845i
$447$	11.8336	−	28.5688i	0.559709	−	1.35126i
$448$	−3.06021	+	1.26758i	−0.144581	+	0.0598875i
$449$	25.7449	−	10.6639i	1.21498	−	0.503259i	0.319166	−	0.947699i	$-0.396597\pi$
$449$	25.7449	−	10.6639i	1.21498	−	0.503259i	0.895809	+	0.444440i	$0.146597\pi$
$450$	−4.68035	−	16.4057i	−0.220634	−	0.773370i
$451$	−4.12829	−	4.12829i	−0.194393	−	0.194393i
$452$	−4.61213	−	11.1347i	−0.216936	−	0.523731i
$453$	27.9651	−	11.5835i	1.31392	−	0.544242i
$454$	16.6070	+	6.87885i	0.779405	+	0.322840i
$455$	4.96576	−	2.92055i	0.232798	−	0.136918i
$456$	5.67088	−	13.6907i	0.265563	−	0.641126i
$457$	−21.7244	−	21.7244i	−1.01623	−	1.01623i	−0.999866	−	0.0163596i	$-0.994792\pi$
$457$	−21.7244	−	21.7244i	−1.01623	−	1.01623i	−0.0163596	−	0.999866i	$-0.505208\pi$
$458$			1.12853i			0.0527326i
$459$	−0.845286	−	4.21812i	−0.0394546	−	0.196885i
$460$	−15.5530	+	9.14734i	−0.725165	+	0.426497i
$461$	2.37157	−	2.37157i	0.110455	−	0.110455i	−0.649719	−	0.760174i	$-0.725114\pi$
$461$	2.37157	−	2.37157i	0.110455	−	0.110455i	0.760174	+	0.649719i	$0.225114\pi$
$462$	19.2268	+	7.96398i	0.894510	+	0.370518i
$463$	25.7516			1.19678			0.598389	−	0.801206i	$-0.295808\pi$
$463$	25.7516			1.19678			0.598389	+	0.801206i	$0.295808\pi$
$464$	−0.319339	−	0.132275i	−0.0148250	−	0.00614070i
$465$	−8.49726	−	6.41212i	−0.394051	−	0.297355i
$466$	20.6654	−	8.55988i	0.957305	−	0.396529i
$467$	9.24427	−	9.24427i	0.427774	−	0.427774i	−0.460096	−	0.887869i	$-0.652185\pi$
$467$	9.24427	−	9.24427i	0.427774	−	0.427774i	0.887869	+	0.460096i	$0.152185\pi$
$468$	1.87660	−	1.87660i	0.0867461	−	0.0867461i
$469$	2.63883	−	1.09304i	0.121850	−	0.0504718i
$470$	12.4719	−	16.5276i	0.575287	−	0.762363i
$471$	21.0087	+	8.70207i	0.968028	+	0.400970i
$472$	12.8214			0.590154
$473$	−26.0509	−	10.7906i	−1.19782	−	0.496154i
$474$	15.5898	−	15.5898i	0.716065	−	0.716065i
$475$	−14.2202	+	25.5727i	−0.652469	+	1.17336i
$476$	13.3909	−	2.68346i	0.613771	−	0.122996i
$477$		−	14.4238i		−	0.660421i
$478$	−7.96602	−	7.96602i	−0.364357	−	0.364357i
$479$	−10.0693	+	24.3093i	−0.460076	+	1.11072i	0.508290	+	0.861186i	$0.330278\pi$
$479$	−10.0693	+	24.3093i	−0.460076	+	1.11072i	−0.968366	+	0.249535i	$0.919722\pi$
$480$	4.88063	−	2.87049i	0.222769	−	0.131019i
$481$	−3.31890	−	1.37473i	−0.151329	−	0.0626825i
$482$	−0.401624	+	0.166358i	−0.0182935	+	0.00757741i
$483$	−25.9007	−	62.5298i	−1.17852	−	2.84520i
$484$	3.42507	+	3.42507i	0.155685	+	0.155685i
$485$	5.93970	+	1.54038i	0.269708	+	0.0699450i
$486$	−20.6578	+	8.55676i	−0.937059	+	0.388143i
$487$	−19.0022	+	7.87096i	−0.861071	+	0.356667i	−0.769126	−	0.639097i	$-0.779308\pi$
$487$	−19.0022	+	7.87096i	−0.861071	+	0.356667i	−0.0919445	+	0.995764i	$0.529308\pi$
$488$	−5.29999	+	12.7953i	−0.239919	+	0.579217i
$489$		−	26.9143i		−	1.21711i
$490$	1.23005	+	8.79520i	0.0555678	+	0.397327i
$491$	2.44344	−	2.44344i	0.110271	−	0.110271i	−0.649818	−	0.760089i	$-0.725155\pi$
$491$	2.44344	−	2.44344i	0.110271	−	0.110271i	0.760089	+	0.649818i	$0.225155\pi$
$492$		−	5.95835i		−	0.268623i
$493$	1.18610	+	0.790083i	0.0534192	+	0.0355836i
$494$	−4.55182			−0.204796
$495$	−18.3241	−	4.75210i	−0.823608	−	0.213591i
$496$	0.719461	−	1.73693i	0.0323047	−	0.0779905i
$497$	27.1628			1.21842
$498$	−3.50926	+	8.47209i	−0.157253	+	0.379643i
$499$	2.11896	+	5.11563i	0.0948579	+	0.229007i	0.964185	−	0.265229i	$-0.0854477\pi$
$499$	2.11896	+	5.11563i	0.0948579	+	0.229007i	−0.869327	+	0.494237i	$0.835448\pi$
$500$	−10.2229	+	4.52681i	−0.457183	+	0.202445i
$501$	−9.62739	−	9.62739i	−0.430120	−	0.430120i
$502$	16.8957	−	16.8957i	0.754094	−	0.754094i
$503$	−6.60394	−	15.9433i	−0.294455	−	0.710878i	−0.999998	−	0.00221001i	$-0.999297\pi$
$503$	−6.60394	−	15.9433i	−0.294455	−	0.710878i	0.705542	−	0.708668i	$-0.250703\pi$
$504$	4.32504	+	10.4416i	0.192652	+	0.465104i
$505$	2.94783	+	21.0779i	0.131177	+	0.937952i
$506$			20.0214i			0.890061i
$507$	28.9975	+	12.0112i	1.28782	+	0.533434i
$508$	13.6948	+	13.6948i	0.607610	+	0.607610i
$509$	−11.3910			−0.504899			−0.252450	−	0.967610i	$-0.581236\pi$
$509$	−11.3910			−0.504899			−0.252450	+	0.967610i	$0.581236\pi$
$510$	−22.0347	+	7.71344i	−0.975712	+	0.341557i
$511$	−32.4674			−1.43627
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−5.64120	−	2.33666i	−0.249065	−	0.103166i
$514$		−	29.3559i		−	1.29483i
$515$	28.5443	−	3.99204i	1.25781	−	0.175910i
$516$	−11.0126	−	26.5867i	−0.484801	−	1.17041i
$517$	−8.79213	−	21.2261i	−0.386678	−	0.933522i
$518$	10.8175	−	10.8175i	0.475293	−	0.475293i
$519$	7.57051	+	7.57051i	0.332309	+	0.332309i
$520$	−1.38831	−	1.04763i	−0.0608814	−	0.0459417i
$521$	14.4478	+	34.8802i	0.632972	+	1.52813i	0.835869	+	0.548929i	$0.184964\pi$
$521$	14.4478	+	34.8802i	0.632972	+	1.52813i	−0.202897	+	0.979200i	$0.565036\pi$
$522$	−0.451327	+	1.08960i	−0.0197541	+	0.0476905i
$523$	−17.2841			−0.755782			−0.377891	−	0.925850i	$-0.623351\pi$
$523$	−17.2841			−0.755782			−0.377891	+	0.925850i	$0.623351\pi$
$524$	−2.55878	+	6.17744i	−0.111781	+	0.269863i
$525$	−11.5053	−	40.3285i	−0.502131	−	1.76008i
$526$	20.1112			0.876892
$527$	−4.29737	+	6.45136i	−0.187197	+	0.281025i
$528$		−	6.28283i		−	0.273425i
$529$	29.7793	−	29.7793i	1.29475	−	1.29475i
$530$	−9.36147	+	1.30924i	−0.406636	+	0.0568699i
$531$		−	43.7473i		−	1.89847i
$532$	7.41801	−	17.9086i	0.321611	−	0.776438i
$533$	−1.69089	+	0.700391i	−0.0732407	+	0.0303373i
$534$	8.60141	−	3.56282i	0.372220	−	0.154178i
$535$	11.0299	+	2.86045i	0.476864	+	0.123668i
$536$	−0.609741	−	0.609741i	−0.0263368	−	0.0263368i
$537$	−5.15558	−	12.4467i	−0.222480	−	0.537113i
$538$	2.65969	−	1.10168i	0.114668	−	0.0474969i
$539$	9.10415	+	3.77106i	0.392144	+	0.162431i
$540$	−1.18277	−	2.01104i	−0.0508984	−	0.0865415i
$541$	−1.67743	+	4.04967i	−0.0721182	+	0.174109i	−0.955828	−	0.293926i	$-0.905038\pi$
$541$	−1.67743	+	4.04967i	−0.0721182	+	0.174109i	0.883710	+	0.468035i	$0.155038\pi$
$542$	13.2789	+	13.2789i	0.570380	+	0.570380i
$543$			40.0416i			1.71835i
$544$	−2.29556	−	3.42497i	−0.0984212	−	0.146844i
$545$	−0.207551	−	0.352895i	−0.00889052	−	0.0151164i
$546$	4.61308	−	4.61308i	0.197422	−	0.197422i
$547$	−11.6639	−	4.83135i	−0.498713	−	0.206574i	0.119125	−	0.992879i	$-0.461991\pi$
$547$	−11.6639	−	4.83135i	−0.498713	−	0.206574i	−0.617838	+	0.786306i	$0.711991\pi$
$548$	2.17815			0.0930461
$549$	43.6582	+	18.0838i	1.86329	+	0.771799i
$550$	−1.42098	+	12.3242i	−0.0605909	+	0.525507i
$551$	1.86881	−	0.774086i	0.0796139	−	0.0329772i
$552$	−14.4485	+	14.4485i	−0.614967	+	0.614967i
$553$	20.3929	−	20.3929i	0.867194	−	0.867194i
$554$	−8.09712	+	3.35394i	−0.344014	+	0.142495i
$555$	−15.7522	+	20.8746i	−0.668643	+	0.886077i
$556$	9.29033	+	3.84818i	0.393998	+	0.163199i
$557$	−33.3916			−1.41485			−0.707423	−	0.706790i	$-0.750143\pi$
$557$	−33.3916			−1.41485			−0.707423	+	0.706790i	$0.750143\pi$
$558$	−5.92649	−	2.45483i	−0.250888	−	0.103921i
$559$	−6.25041	+	6.25041i	−0.264364	+	0.264364i
$560$	6.38429	−	3.75485i	0.269786	−	0.158671i
$561$	−5.01756	+	25.4142i	−0.211842	+	1.07299i
$562$			30.4428i			1.28415i
$563$	−3.53877	−	3.53877i	−0.149141	−	0.149141i	0.628593	−	0.777734i	$-0.283631\pi$
$563$	−3.53877	−	3.53877i	−0.149141	−	0.149141i	−0.777734	+	0.628593i	$0.783631\pi$
$564$	8.97295	−	21.6626i	0.377829	−	0.912161i
$565$	13.6622	+	23.2295i	0.574771	+	0.977272i
$566$	−8.83075	−	3.65782i	−0.371184	−	0.153749i
$567$	−23.2394	+	9.62609i	−0.975965	+	0.404258i
$568$	−3.13819	−	7.57626i	−0.131676	−	0.317893i
$569$	−0.875778	−	0.875778i	−0.0367145	−	0.0367145i	0.688511	−	0.725226i	$-0.258265\pi$
$569$	−0.875778	−	0.875778i	−0.0367145	−	0.0367145i	−0.725226	+	0.688511i	$0.758265\pi$
$570$	−8.31810	+	32.0746i	−0.348407	+	1.34346i
$571$	−21.1567	+	8.76339i	−0.885380	+	0.366736i	−0.778581	−	0.627544i	$-0.784060\pi$
$571$	−21.1567	+	8.76339i	−0.885380	+	0.366736i	−0.106799	+	0.994281i	$0.534060\pi$
$572$	−1.78298	+	0.738533i	−0.0745500	+	0.0308796i
$573$	25.5227	−	61.6173i	1.06623	−	2.57410i
$574$		−	7.79405i		−	0.325317i
$575$	31.6094	−	25.0739i	1.31821	−	1.04565i
$576$	2.41268	−	2.41268i	0.100528	−	0.100528i
$577$			8.94035i			0.372192i	0.982532	+	0.186096i	$0.0595835\pi$
$577$			8.94035i			0.372192i	−0.982532	+	0.186096i	$0.940416\pi$
$578$	6.55035	+	15.6873i	0.272459	+	0.652508i
$579$	−34.6517			−1.44007
$580$	0.748149	+	0.194022i	0.0310652	+	0.00805632i
$581$	−4.59041	+	11.0822i	−0.190442	+	0.459769i
$582$	6.94883			0.288038
$583$	−4.01386	+	9.69032i	−0.166237	+	0.401332i
$584$	3.75104	+	9.05580i	0.155219	+	0.374732i
$585$	−3.57457	+	4.73697i	−0.147790	+	0.195850i
$586$	3.78266	+	3.78266i	0.156260	+	0.156260i
$587$	−2.61621	+	2.61621i	−0.107983	+	0.107983i	−0.759034	−	0.651051i	$-0.774328\pi$
$587$	−2.61621	+	2.61621i	−0.107983	+	0.107983i	0.651051	+	0.759034i	$0.274328\pi$
$588$	3.84862	+	9.29139i	0.158714	+	0.383170i
$589$	4.21036	+	10.1647i	0.173485	+	0.418829i
$590$	−28.3933	+	3.97092i	−1.16893	+	0.163480i
$591$		−	16.4664i		−	0.677337i
$592$	−4.26699	−	1.76745i	−0.175372	−	0.0726416i
$593$	29.8060	+	29.8060i	1.22399	+	1.22399i	0.966202	+	0.257785i	$0.0829927\pi$
$593$	29.8060	+	29.8060i	1.22399	+	1.22399i	0.257785	+	0.966202i	$0.417007\pi$
$594$	−2.58882			−0.106220
$595$	−28.8233	+	10.0899i	−1.18164	+	0.413644i
$596$	−12.2117			−0.500213
$597$	19.8876	+	19.8876i	0.813945	+	0.813945i
$598$	5.79864	+	2.40188i	0.237124	+	0.0982200i
$599$		−	18.0176i		−	0.736178i	−0.929790	−	0.368089i	$-0.880012\pi$
$599$		−	18.0176i		−	0.736178i	0.929790	−	0.368089i	$-0.119988\pi$
$600$	−9.91921	+	7.86831i	−0.404950	+	0.321223i
$601$	3.49949	+	8.44852i	0.142747	+	0.344622i	0.979042	−	0.203657i	$-0.0652829\pi$
$601$	3.49949	+	8.44852i	0.142747	+	0.344622i	−0.836295	+	0.548280i	$0.815283\pi$
$602$	−14.4054	−	34.7777i	−0.587120	−	1.41743i
$603$	−2.08046	+	2.08046i	−0.0847230	+	0.0847230i
$604$	−8.45256	−	8.45256i	−0.343930	−	0.343930i
$605$	−8.64564	−	6.52409i	−0.351495	−	0.265242i
$606$	9.22328	+	22.2670i	0.374670	+	0.904534i
$607$	5.67532	−	13.7014i	0.230354	−	0.556124i	−0.765865	−	0.643001i	$-0.777689\pi$
$607$	5.67532	−	13.7014i	0.230354	−	0.556124i	0.996219	+	0.0868777i	$0.0276889\pi$
$608$	−5.85211			−0.237334
$609$	−1.10946	+	2.67847i	−0.0449574	+	0.108537i
$610$	7.77409	−	29.9769i	0.314764	−	1.21373i
$611$	−7.20228			−0.291373
$612$	−11.6862	+	7.83255i	−0.472385	+	0.316612i
$613$			21.3405i			0.861933i	0.902368	+	0.430967i	$0.141827\pi$
$613$			21.3405i			0.861933i	−0.902368	+	0.430967i	$0.858173\pi$
$614$	−13.8852	+	13.8852i	−0.560363	+	0.560363i
$615$	1.84536	+	13.1949i	0.0744120	+	0.532068i
$616$		−	8.21850i		−	0.331133i
$617$	−5.10375	+	12.3215i	−0.205469	+	0.496047i	−0.992700	−	0.120612i	$-0.961514\pi$
$617$	−5.10375	+	12.3215i	−0.205469	+	0.496047i	0.787230	+	0.616659i	$0.211514\pi$
$618$	30.1547	−	12.4905i	1.21300	−	0.502440i
$619$	−15.1303	+	6.26719i	−0.608139	+	0.251900i	−0.665433	−	0.746458i	$-0.731753\pi$
$619$	−15.1303	+	6.26719i	−0.608139	+	0.251900i	0.0572934	+	0.998357i	$0.481753\pi$
$620$	−1.05531	+	4.06929i	−0.0423824	+	0.163426i
$621$	5.95342	+	5.95342i	0.238903	+	0.238903i
$622$	5.25670	+	12.6908i	0.210774	+	0.508855i
$623$	11.2514	−	4.66048i	0.450778	−	0.186718i
$624$	−1.81964	−	0.753721i	−0.0728441	−	0.0301730i
$625$	21.2368	−	13.1908i	0.849472	−	0.527633i
$626$	2.35732	−	5.69107i	0.0942174	−	0.227461i
$627$	25.9988	+	25.9988i	1.03829	+	1.03829i
$628$		−	8.98017i		−	0.358348i
$629$	15.8486	+	10.5570i	0.631924	+	0.420937i
$630$	−12.8117	−	21.7835i	−0.510431	−	0.867875i
$631$	9.58945	−	9.58945i	0.381750	−	0.381750i	−0.489982	−	0.871732i	$-0.662997\pi$
$631$	9.58945	−	9.58945i	0.381750	−	0.381750i	0.871732	+	0.489982i	$0.162997\pi$
$632$	−8.04403	−	3.33195i	−0.319974	−	0.132538i
$633$	12.0371			0.478432
$634$	−4.69756	−	1.94579i	−0.186564	−	0.0772773i
$635$	−34.5689	−	26.0860i	−1.37182	−	1.03519i
$636$	−9.88961	+	4.09641i	−0.392149	+	0.162433i
$637$	2.18436	−	2.18436i	0.0865476	−	0.0865476i
$638$	0.606428	−	0.606428i	0.0240087	−	0.0240087i
$639$	−25.8506	+	10.7077i	−1.02263	+	0.423588i
$640$	−1.78490	−	1.34690i	−0.0705542	−	0.0532410i
$641$	22.9560	+	9.50869i	0.906707	+	0.375571i	0.786795	−	0.617214i	$-0.211739\pi$
$641$	22.9560	+	9.50869i	0.906707	+	0.375571i	0.119912	+	0.992785i	$0.461739\pi$
$642$	12.9038			0.509274
$643$	−6.62075	−	2.74240i	−0.261097	−	0.108150i	0.248295	−	0.968684i	$-0.420130\pi$
$643$	−6.62075	−	2.74240i	−0.261097	−	0.108150i	−0.509392	+	0.860535i	$0.670130\pi$
$644$	−18.8998	+	18.8998i	−0.744758	+	0.744758i
$645$	32.6216	+	55.4659i	1.28448	+	2.18397i
$646$	23.6719	+	4.67358i	0.931359	+	0.183880i
$647$		−	32.6880i		−	1.28510i	−0.766244	−	0.642550i	$-0.777877\pi$
$647$		−	32.6880i		−	1.28510i	0.766244	−	0.642550i	$-0.222123\pi$
$648$	5.36983	+	5.36983i	0.210947	+	0.210947i
$649$	−12.1740	+	29.3906i	−0.477871	+	1.15368i
$650$	3.39889	+	1.89002i	0.133316	+	0.0741329i
$651$	−14.5685	−	6.03449i	−0.570986	−	0.236510i
$652$	−9.81976	+	4.06748i	−0.384571	+	0.159295i
$653$	3.25759	+	7.86453i	0.127480	+	0.307763i	0.974714	−	0.223456i	$-0.0717341\pi$
$653$	3.25759	+	7.86453i	0.127480	+	0.307763i	−0.847234	+	0.531219i	$0.821734\pi$
$654$	−0.327832	−	0.327832i	−0.0128193	−	0.0128193i
$655$	3.75324	−	14.4725i	0.146651	−	0.565488i
$656$	−2.17392	+	0.900466i	−0.0848772	+	0.0351573i
$657$	30.8988	−	12.7987i	1.20548	−	0.499325i
$658$	11.7374	−	28.3366i	0.457572	−	1.10468i
$659$		−	10.0536i		−	0.391632i	−0.980641	−	0.195816i	$-0.937264\pi$
$659$		−	10.0536i		−	0.391632i	0.980641	−	0.195816i	$-0.0627355\pi$
$660$	1.94585	+	13.9134i	0.0757422	+	0.541580i
$661$	19.9368	−	19.9368i	0.775451	−	0.775451i	−0.203603	−	0.979054i	$-0.565265\pi$
$661$	19.9368	−	19.9368i	0.775451	−	0.775451i	0.979054	+	0.203603i	$0.0652650\pi$
$662$			3.25455i			0.126492i
$663$	6.75857	+	4.50202i	0.262481	+	0.174844i
$664$	3.62140			0.140538
$665$	−10.8808	+	41.9564i	−0.421940	+	1.62700i
$666$	−6.03061	+	14.5592i	−0.233681	+	0.564156i
$667$	−2.78917			−0.107997
$668$	−2.05762	+	4.96753i	−0.0796116	+	0.192200i
$669$	−18.4765	−	44.6061i	−0.714341	−	1.72457i
$670$	1.53912	+	1.16144i	0.0594615	+	0.0448703i
$671$	−24.2984	−	24.2984i	−0.938030	−	0.938030i
$672$	5.93087	−	5.93087i	0.228788	−	0.228788i
$673$	−1.83418	−	4.42810i	−0.0707025	−	0.170691i	0.884578	−	0.466393i	$-0.154447\pi$
$673$	−1.83418	−	4.42810i	−0.0707025	−	0.170691i	−0.955280	+	0.295702i	$0.904447\pi$
$674$	−2.22732	−	5.37723i	−0.0857933	−	0.207123i
$675$	3.24211	+	4.08717i	0.124789	+	0.157315i
$676$		−	12.3950i		−	0.476731i
$677$	−11.5273	−	4.77476i	−0.443030	−	0.183509i	0.150006	−	0.988685i	$-0.452071\pi$
$677$	−11.5273	−	4.77476i	−0.443030	−	0.183509i	−0.593036	+	0.805176i	$0.702071\pi$
$678$	21.5797	+	21.5797i	0.828763	+	0.828763i
$679$	9.08968			0.348830
$680$	6.14429	+	6.87369i	0.235623	+	0.263594i
$681$	−45.5171			−1.74422
$682$	3.29845	+	3.29845i	0.126304	+	0.126304i
$683$	−10.4418	−	4.32512i	−0.399543	−	0.165496i	0.173858	−	0.984771i	$-0.444376\pi$
$683$	−10.4418	−	4.32512i	−0.399543	−	0.165496i	−0.573401	+	0.819275i	$0.694376\pi$
$684$			19.9677i			0.763482i
$685$	−4.82355	+	0.674595i	−0.184298	+	0.0257749i
$686$	−3.83872	−	9.26749i	−0.146563	−	0.353834i
$687$	−1.09358	−	2.64013i	−0.0417226	−	0.100727i
$688$	−8.03592	+	8.03592i	−0.306366	+	0.306366i
$689$	2.32500	+	2.32500i	0.0885755	+	0.0885755i
$690$	27.5215	−	36.4711i	1.04773	−	1.38843i
$691$	−9.79890	−	23.6566i	−0.372768	−	0.899941i	−0.993279	−	0.115744i	$-0.963075\pi$
$691$	−9.79890	−	23.6566i	−0.372768	−	0.899941i	0.620511	−	0.784197i	$-0.286925\pi$
$692$	1.61801	−	3.90622i	0.0615076	−	0.148492i
$693$	−28.0419			−1.06522
$694$	−4.68855	+	11.3192i	−0.177975	+	0.429670i
$695$	−21.7654	−	5.64455i	−0.825608	−	0.214110i
$696$	0.875257			0.0331765
$697$	9.51267	−	1.90628i	0.360318	−	0.0722056i
$698$		−	5.77639i		−	0.218640i
$699$	−40.0508	+	40.0508i	−1.51486	+	1.51486i
$700$	−12.9752	+	10.2924i	−0.490417	+	0.389018i
$701$		−	22.2922i		−	0.841966i	−0.907068	−	0.420983i	$-0.861685\pi$
$701$		−	22.2922i		−	0.841966i	0.907068	−	0.420983i	$-0.138315\pi$
$702$	−0.310568	+	0.749777i	−0.0117216	+	0.0282985i
$703$	24.9709	−	10.3433i	0.941795	−	0.390104i
$704$	−2.29231	+	0.949504i	−0.0863945	+	0.0357858i
$705$	−13.1616	+	50.7512i	−0.495695	+	1.91140i
$706$	8.85861	+	8.85861i	0.333398	+	0.333398i
$707$	12.0649	+	29.1272i	0.453746	+	1.09544i
$708$	−29.9951	+	12.4244i	−1.12728	+	0.466936i
$709$	−27.3200	−	11.3163i	−1.02602	−	0.424993i	−0.194748	−	0.980853i	$-0.562389\pi$
$709$	−27.3200	−	11.3163i	−1.02602	−	0.424993i	−0.831276	+	0.555860i	$0.812389\pi$
$710$	9.29602	+	15.8058i	0.348873	+	0.593182i
$711$	−11.3688	+	27.4466i	−0.426362	+	1.02933i
$712$	−2.59981	−	2.59981i	−0.0974319	−	0.0974319i
$713$		−	15.1707i		−	0.568147i
$714$	−28.7270	+	19.2540i	−1.07508	+	0.720564i
$715$	3.71970	−	2.18770i	0.139109	−	0.0818152i
$716$	−3.76205	+	3.76205i	−0.140594	+	0.140594i
$717$	26.3554	+	10.9168i	0.984261	+	0.407694i
$718$	−6.07488			−0.226713
$719$	−17.1054	−	7.08529i	−0.637924	−	0.264237i	0.0401916	−	0.999192i	$-0.487203\pi$
$719$	−17.1054	−	7.08529i	−0.637924	−	0.264237i	−0.678116	+	0.734955i	$0.737203\pi$
$720$	−4.59569	+	6.09015i	−0.171271	+	0.226966i
$721$	39.4449	−	16.3386i	1.46901	−	0.608482i
$722$	10.7814	−	10.7814i	0.401241	−	0.401241i
$723$	0.778374	−	0.778374i	0.0289480	−	0.0289480i
$724$	14.6093	−	6.05136i	0.542949	−	0.224897i
$725$	−1.71688	−	0.197956i	−0.0637632	−	0.00735190i
$726$	−11.3318	−	4.69377i	−0.420561	−	0.174202i
$727$	18.3747			0.681480			0.340740	−	0.940158i	$-0.389322\pi$
$727$	18.3747			0.681480			0.340740	+	0.940158i	$0.389322\pi$
$728$	−2.38025	−	0.985934i	−0.0882181	−	0.0365411i
$729$	23.9267	−	23.9267i	0.886176	−	0.886176i
$730$	−11.1114	−	18.8925i	−0.411251	−	0.699242i
$731$	38.9231	−	26.0879i	1.43962	−	0.964895i
$732$		−	35.0699i		−	1.29622i
$733$	0.587977	+	0.587977i	0.0217174	+	0.0217174i	0.717882	−	0.696165i	$-0.245112\pi$
$733$	0.587977	+	0.587977i	0.0217174	+	0.0217174i	−0.696165	+	0.717882i	$0.745112\pi$
$734$	−3.76510	+	9.08975i	−0.138972	+	0.335509i
$735$	−11.4005	−	19.3840i	−0.420512	−	0.714988i
$736$	7.45510	+	3.08800i	0.274799	+	0.113825i
$737$	1.97666	−	0.818761i	0.0728113	−	0.0301594i
$738$	3.07243	+	7.41751i	0.113098	+	0.273042i
$739$	−2.33228	−	2.33228i	−0.0857943	−	0.0857943i	0.662907	−	0.748702i	$-0.269322\pi$
$739$	−2.33228	−	2.33228i	−0.0857943	−	0.0857943i	−0.748702	+	0.662907i	$0.769322\pi$
$740$	9.99671	+	2.59251i	0.367487	+	0.0953025i
$741$	10.6488	−	4.41086i	0.391192	−	0.162037i
$742$	−12.9365	+	5.35846i	−0.474913	+	0.196715i
$743$	−7.05841	+	17.0405i	−0.258948	+	0.625156i	−0.998869	−	0.0475376i	$-0.984863\pi$
$743$	−7.05841	+	17.0405i	−0.258948	+	0.625156i	0.739922	+	0.672693i	$0.234863\pi$
$744$			4.76064i			0.174534i
$745$	27.0431	−	3.78209i	0.990783	−	0.138565i
$746$	−7.21651	+	7.21651i	−0.264215	+	0.264215i
$747$		−	12.3564i		−	0.452097i
$748$	10.0307	−	2.01010i	0.366759	−	0.0734964i
$749$	16.8793			0.616758
$750$	19.5294	−	20.4966i	0.713112	−	0.748429i
$751$	6.27632	−	15.1524i	0.229026	−	0.552918i	−0.767033	−	0.641607i	$-0.778268\pi$
$751$	6.27632	−	15.1524i	0.229026	−	0.552918i	0.996059	+	0.0886896i	$0.0282679\pi$
$752$	−9.25971			−0.337667
$753$	−23.1542	+	55.8992i	−0.843786	+	2.03708i
$754$	−0.102884	−	0.248385i	−0.00374683	−	0.00904565i
$755$	21.3362	+	16.1005i	0.776503	+	0.585957i
$756$	−2.44379	−	2.44379i	−0.0888798	−	0.0888798i
$757$	−1.27297	+	1.27297i	−0.0462668	+	0.0462668i	−0.729862	−	0.683595i	$-0.760416\pi$
$757$	−1.27297	+	1.27297i	−0.0462668	+	0.0462668i	0.683595	+	0.729862i	$0.260416\pi$
$758$	8.48108	+	20.4751i	0.308047	+	0.743691i
$759$	−19.4014	−	46.8391i	−0.704226	−	1.70015i
$760$	12.9596	−	1.81245i	0.470093	−	0.0657446i
$761$			9.64351i			0.349577i	0.984606	+	0.174788i	$0.0559241\pi$
$761$			9.64351i			0.349577i	−0.984606	+	0.174788i	$0.944076\pi$
$762$	−45.3091	−	18.7677i	−1.64138	−	0.679881i
$763$	−0.428833	−	0.428833i	−0.0155248	−	0.0155248i
$764$	−26.3384			−0.952890
$765$	23.4534	−	20.9646i	0.847958	−	0.757977i
$766$	−10.1772			−0.367717
$767$	7.05171	+	7.05171i	0.254622	+	0.254622i
$768$	−2.33945	−	0.969032i	−0.0844176	−	0.0349669i
$769$			33.9195i			1.22317i	0.791179	+	0.611585i	$0.209468\pi$
$769$			33.9195i			1.22317i	−0.791179	+	0.611585i	$0.790532\pi$
$770$	2.54535	+	18.2000i	0.0917279	+	0.655882i
$771$	28.4468	+	68.6767i	1.02449	+	2.47333i
$772$	5.23679	+	12.6427i	0.188476	+	0.455022i
$773$	16.9057	−	16.9057i	0.608055	−	0.608055i	−0.334382	−	0.942438i	$-0.608528\pi$
$773$	16.9057	−	16.9057i	0.608055	−	0.608055i	0.942438	+	0.334382i	$0.108528\pi$
$774$	27.4189	+	27.4189i	0.985553	+	0.985553i
$775$	1.07671	−	9.33834i	0.0386765	−	0.335443i
$776$	−1.05015	−	2.53530i	−0.0376983	−	0.0910119i
$777$	−14.8245	+	35.7895i	−0.531825	+	1.28394i
$778$	−9.18824			−0.329414
$779$	5.26962	−	12.7220i	0.188804	−	0.455813i
$780$	4.26307	+	1.10557i	0.152642	+	0.0395856i
$781$	20.3468			0.728067
$782$	−27.6899	−	18.4448i	−0.990189	−	0.659584i
$783$		−	0.360646i		−	0.0128884i
$784$	2.80835	−	2.80835i	0.100298	−	0.100298i
$785$	2.78124	+	19.8867i	0.0992669	+	0.709788i
$786$		−	16.9313i		−	0.603921i
$787$	13.9830	−	33.7579i	0.498439	−	1.20334i	−0.451885	−	0.892076i	$-0.649248\pi$
$787$	13.9830	−	33.7579i	0.498439	−	1.20334i	0.950324	−	0.311262i	$-0.100752\pi$
$788$	−6.00780	+	2.48851i	−0.214019	+	0.0886496i
$789$	−47.0492	+	19.4884i	−1.67500	+	0.693807i
$790$	18.8456	+	4.88734i	0.670495	+	0.173884i
$791$	28.2281	+	28.2281i	1.00368	+	1.00368i
$792$	3.23975	+	7.82145i	0.115120	+	0.277923i
$793$	−9.95231	+	4.12238i	−0.353417	+	0.146390i
$794$	23.5614	+	9.75944i	0.836162	+	0.346349i
$795$	20.6320	−	12.1345i	0.731742	−	0.430365i
$796$	4.25049	−	10.2616i	0.150655	−	0.363712i
$797$	10.0544	+	10.0544i	0.356147	+	0.356147i	0.862390	−	0.506244i	$-0.168966\pi$
$797$	10.0544	+	10.0544i	0.356147	+	0.356147i	−0.506244	+	0.862390i	$0.668966\pi$
$798$			49.0847i			1.73758i
$799$	37.4557	+	7.39494i	1.32509	+	0.261614i
$800$	4.36983	+	2.42993i	0.154497	+	0.0859112i
$801$	−8.87066	+	8.87066i	−0.313429	+	0.313429i
$802$	33.7790	+	13.9917i	1.19278	+	0.494064i
$803$	−24.3203			−0.858245
$804$	2.01732	+	0.835599i	0.0711452	+	0.0294693i
$805$	36.0005	−	47.7075i	1.26885	−	1.68147i
$806$	1.35100	−	0.559603i	0.0475870	−	0.0197112i
$807$	−5.15466	+	5.15466i	−0.181453	+	0.181453i
$808$	6.73027	−	6.73027i	0.236770	−	0.236770i
$809$	−4.32037	+	1.78955i	−0.151896	+	0.0629174i	−0.457336	−	0.889294i	$-0.651196\pi$
$809$	−4.32037	+	1.78955i	−0.151896	+	0.0629174i	0.305440	+	0.952211i	$0.401196\pi$
$810$	−13.5547	−	10.2285i	−0.476262	−	0.359392i
$811$	40.2894	+	16.6884i	1.41475	+	0.586009i	0.953536	−	0.301280i	$-0.0974137\pi$
$811$	40.2894	+	16.6884i	1.41475	+	0.586009i	0.461215	+	0.887288i	$0.347414\pi$
$812$	1.14491			0.0401786
$813$	−43.9332	−	18.1977i	−1.54080	−	0.638221i
$814$	8.10305	−	8.10305i	0.284012	−	0.284012i
$815$	20.4863	−	12.0488i	0.717603	−	0.422050i
$816$	8.68924	+	5.78807i	0.304184	+	0.202623i
$817$		−	66.5063i		−	2.32676i
$818$	−10.5376	−	10.5376i	−0.368438	−	0.368438i
$819$	−3.36405	+	8.12154i	−0.117549	+	0.283790i
$820$	4.53529	−	2.66738i	0.158379	−	0.0931489i
$821$	32.1854	+	13.3316i	1.12328	+	0.465277i	0.865490	−	0.500925i	$-0.167007\pi$
$821$	32.1854	+	13.3316i	1.12328	+	0.465277i	0.257786	+	0.966202i	$0.417007\pi$
$822$	−5.09568	+	2.11070i	−0.177732	+	0.0736191i
$823$	−11.8633	−	28.6405i	−0.413528	−	0.998344i	−0.984183	−	0.177154i	$-0.943311\pi$
$823$	−11.8633	−	28.6405i	−0.413528	−	0.998344i	0.570656	−	0.821190i	$-0.306689\pi$
$824$	−9.11435	−	9.11435i	−0.317513	−	0.317513i
$825$	−8.61825	−	30.2089i	−0.300049	−	1.05174i
$826$	−39.2362	+	16.2522i	−1.36520	+	0.565485i
$827$	−24.0440	+	9.95934i	−0.836091	+	0.346320i	−0.759311	−	0.650728i	$-0.774464\pi$
$827$	−24.0440	+	9.95934i	−0.836091	+	0.346320i	−0.0767796	+	0.997048i	$0.524464\pi$
$828$	10.5364	−	25.4371i	0.366165	−	0.884002i
$829$			31.3054i			1.08728i	0.839318	+	0.543641i	$0.182955\pi$
$829$			31.3054i			1.08728i	−0.839318	+	0.543641i	$0.817045\pi$
$830$	−8.01966	+	1.12158i	−0.278366	+	0.0389307i
$831$	15.6927	−	15.6927i	0.544375	−	0.544375i
$832$			0.777809i			0.0269657i
$833$	−13.6027	+	9.11707i	−0.471304	+	0.315888i
$834$	−25.4633			−0.881720
$835$	3.01814	−	11.6379i	0.104447	−	0.402747i
$836$	5.55660	−	13.4148i	0.192179	−	0.463961i
$837$	1.96160			0.0678029
$838$	−0.678866	+	1.63893i	−0.0234510	+	0.0566158i
$839$	−11.2215	−	27.0910i	−0.387408	−	0.935285i	−0.990487	−	0.137604i	$-0.956060\pi$
$839$	−11.2215	−	27.0910i	−0.387408	−	0.935285i	0.603080	−	0.797681i	$-0.293940\pi$
$840$	−11.2972	+	14.9709i	−0.389789	+	0.516544i
$841$	−20.4216	−	20.4216i	−0.704194	−	0.704194i
$842$	−17.7634	+	17.7634i	−0.612168	+	0.612168i
$843$	−29.5000	−	71.2193i	−1.01603	−	2.45292i
$844$	−1.81913	−	4.39176i	−0.0626170	−	0.151171i
$845$	3.83885	+	27.4490i	0.132061	+	0.944273i
$846$			31.5946i			1.08624i
$847$	−14.8229	−	6.13987i	−0.509323	−	0.210968i
$848$	2.98917	+	2.98917i	0.102648	+	0.102648i
$849$	24.2036			0.830666
$850$	−15.7355	−	13.3190i	−0.539723	−	0.456836i
$851$	−37.2687			−1.27755
$852$	14.6833	+	14.6833i	0.503041	+	0.503041i
$853$	−48.0043	−	19.8840i	−1.64364	−	0.680816i	−0.646978	−	0.762508i	$-0.723968\pi$
$853$	−48.0043	−	19.8840i	−1.64364	−	0.680816i	−0.996658	+	0.0816920i	$0.973968\pi$
$854$		−	45.8745i		−	1.56979i
$855$	−6.18417	−	44.2187i	−0.211494	−	1.51225i
$856$	−1.95011	−	4.70799i	−0.0666535	−	0.160916i
$857$	22.0112	+	53.1397i	0.751888	+	1.81522i	0.548567	+	0.836107i	$0.315174\pi$
$857$	22.0112	+	53.1397i	0.751888	+	1.81522i	0.203321	+	0.979112i	$0.434826\pi$
$858$	3.45552	−	3.45552i	0.117970	−	0.117970i
$859$	−34.5161	−	34.5161i	−1.17768	−	1.17768i	−0.980335	−	0.197341i	$-0.936769\pi$
$859$	−34.5161	−	34.5161i	−1.17768	−	1.17768i	−0.197341	−	0.980335i	$-0.563231\pi$
$860$	15.3069	−	20.2845i	0.521960	−	0.691694i
$861$	7.55268	+	18.2338i	0.257395	+	0.621405i
$862$	8.98389	−	21.6890i	0.305993	−	0.738731i
$863$	−19.9590			−0.679414			−0.339707	−	0.940531i	$-0.610328\pi$
$863$	−19.9590			−0.679414			−0.339707	+	0.940531i	$0.610328\pi$
$864$	−0.399286	+	0.963960i	−0.0135840	+	0.0327946i
$865$	−2.37332	+	9.15151i	−0.0806952	+	0.311161i
$866$	−28.9264			−0.982961
$867$	−30.5258	−	30.3523i	−1.03671	−	1.03082i
$868$			6.22734i			0.211370i
$869$	15.2757	−	15.2757i	0.518192	−	0.518192i
$870$	−1.93827	+	0.271075i	−0.0657135	+	0.00919031i
$871$		−	0.670707i		−	0.0227260i
$872$	−0.0700661	+	0.169155i	−0.00237274	+	0.00572830i
$873$	−8.65055	+	3.58317i	−0.292777	+	0.121272i
$874$	−43.6280	+	18.0713i	−1.47574	+	0.611271i
$875$	25.5461	−	26.8113i	0.863617	−	0.906388i
$876$	−17.5507	−	17.5507i	−0.592984	−	0.592984i
$877$	−5.21753	−	12.5962i	−0.176184	−	0.425345i	0.810977	−	0.585079i	$-0.198936\pi$
$877$	−5.21753	−	12.5962i	−0.176184	−	0.425345i	−0.987160	+	0.159734i	$0.948936\pi$
$878$	−0.944005	+	0.391020i	−0.0318586	+	0.0131963i
$879$	−12.5149	−	5.18383i	−0.422116	−	0.174846i
$880$	4.78228	−	2.81264i	0.161211	−	0.0948141i
$881$	6.20068	−	14.9698i	0.208906	−	0.504344i	−0.784345	−	0.620324i	$-0.787001\pi$
$881$	6.20068	−	14.9698i	0.208906	−	0.504344i	0.993251	+	0.115980i	$0.0370010\pi$
$882$	−9.58223	−	9.58223i	−0.322651	−	0.322651i
$883$		−	5.19724i		−	0.174901i	−0.996169	−	0.0874506i	$-0.972128\pi$
$883$		−	5.19724i		−	0.174901i	0.996169	−	0.0874506i	$-0.0278720\pi$
$884$	0.621170	−	3.14626i	0.0208922	−	0.105820i
$885$	62.5766	−	36.8037i	2.10349	−	1.23714i
$886$	−16.3950	+	16.3950i	−0.550801	+	0.550801i
$887$	−3.27376	−	1.35604i	−0.109922	−	0.0455312i	0.327045	−	0.945009i	$-0.393947\pi$
$887$	−3.27376	−	1.35604i	−0.109922	−	0.0455312i	−0.436967	+	0.899478i	$0.643947\pi$
$888$	11.6951			0.392463
$889$	−59.2683	−	24.5497i	−1.98780	−	0.823372i
$890$	6.56250	+	4.95213i	0.219975	+	0.165996i
$891$	−17.4080	+	7.21061i	−0.583188	+	0.241565i
$892$	−13.4824	+	13.4824i	−0.451423	+	0.451423i
$893$	38.3173	−	38.3173i	1.28224	−	1.28224i
$894$	28.5688	−	11.8336i	0.955482	−	0.395774i
$895$	7.16597	−	9.49626i	0.239532	−	0.317425i
$896$	−3.06021	−	1.26758i	−0.102234	−	0.0423468i
$897$	−15.8931			−0.530656
$898$	25.7449	+	10.6639i	0.859117	+	0.355858i
$899$	−0.459504	+	0.459504i	−0.0153253	+	0.0153253i
$900$	8.29105	−	14.9101i	0.276368	−	0.497002i
$901$	−9.70406	−	14.4785i	−0.323289	−	0.482347i
$902$		−	5.83828i		−	0.194393i
$903$	67.4014	+	67.4014i	2.24298	+	2.24298i
$904$	4.61213	−	11.1347i	0.153397	−	0.370334i
$905$	−30.4783	+	17.9255i	−1.01313	+	0.595863i
$906$	27.9651	+	11.5835i	0.929080	+	0.384837i
$907$	40.4620	−	16.7599i	1.34352	−	0.556504i	0.409038	−	0.912517i	$-0.365864\pi$
$907$	40.4620	−	16.7599i	1.34352	−	0.556504i	0.934481	+	0.356013i	$0.115864\pi$
$908$	6.87885	+	16.6070i	0.228283	+	0.551123i
$909$	−22.9640	−	22.9640i	−0.761668	−	0.761668i
$910$	5.57647	+	1.44618i	0.184858	+	0.0479404i
$911$	−21.0931	+	8.73705i	−0.698846	+	0.289471i	−0.703680	−	0.710517i	$-0.748461\pi$
$911$	−21.0931	+	8.73705i	−0.698846	+	0.289471i	0.00483423	+	0.999988i	$0.498461\pi$
$912$	13.6907	−	5.67088i	0.453345	−	0.187781i
$913$	−3.43854	+	8.30136i	−0.113799	+	0.274735i
$914$		−	30.7230i		−	1.01623i
$915$	10.8615	+	77.6628i	0.359069	+	2.56745i
$916$	−0.797989	+	0.797989i	−0.0263663	+	0.0263663i
$917$		−	22.1477i		−	0.731381i
$918$	2.38495	−	3.58037i	0.0787152	−	0.118170i
$919$	46.6106			1.53754			0.768771	−	0.639524i	$-0.220868\pi$
$919$	46.6106			1.53754			0.768771	+	0.639524i	$0.220868\pi$
$920$	−17.4658	−	4.52952i	−0.575831	−	0.149334i
$921$	19.0286	−	45.9391i	0.627013	−	1.51374i
$922$	3.35390			0.110455
$923$	2.44091	−	5.89289i	0.0803436	−	0.193967i
$924$	7.96398	+	19.2268i	0.261996	+	0.632514i
$925$	−22.9408	−	2.64507i	−0.754289	−	0.0869695i
$926$	18.2091	+	18.2091i	0.598389	+	0.598389i
$927$	−31.0986	+	31.0986i	−1.02141	+	1.02141i
$928$	−0.132275	−	0.319339i	−0.00434213	−	0.0104828i
$929$	2.87430	+	6.93918i	0.0943028	+	0.227667i	0.963991	−	0.265934i	$-0.0856803\pi$
$929$	2.87430	+	6.93918i	0.0943028	+	0.227667i	−0.869688	+	0.493601i	$0.835680\pi$
$930$	−1.47442	−	10.5425i	−0.0483480	−	0.345703i
$931$			23.2423i			0.761736i
$932$	20.6654	+	8.55988i	0.676917	+	0.280388i
$933$	−24.5956	−	24.5956i	−0.805223	−	0.805223i
$934$	13.0734			0.427774
$935$	−21.5906	+	7.55800i	−0.706089	+	0.247173i
$936$	2.65392			0.0867461
$937$	29.2503	+	29.2503i	0.955567	+	0.955567i	0.999054	−	0.0434874i	$-0.0138468\pi$
$937$	29.2503	+	29.2503i	0.955567	+	0.955567i	−0.0434874	+	0.999054i	$0.513847\pi$
$938$	2.63883	+	1.09304i	0.0861607	+	0.0356889i
$939$			15.5983i			0.509031i
$940$	20.5058	−	2.86782i	0.668825	−	0.0935380i
$941$	−7.76691	−	18.7510i	−0.253194	−	0.611264i	0.745264	−	0.666769i	$-0.232323\pi$
$941$	−7.76691	−	18.7510i	−0.253194	−	0.611264i	−0.998458	+	0.0555046i	$0.982323\pi$
$942$	8.70207	+	21.0087i	0.283529	+	0.684499i
$943$	−13.4261	+	13.4261i	−0.437215	+	0.437215i
$944$	9.06612	+	9.06612i	0.295077	+	0.295077i
$945$	6.16868	+	4.65495i	0.200667	+	0.151426i
$946$	−10.7906	−	26.0509i	−0.350834	−	0.846988i
$947$	−10.0051	+	24.1545i	−0.325123	+	0.784915i	0.673818	+	0.738897i	$0.264653\pi$
$947$	−10.0051	+	24.1545i	−0.325123	+	0.784915i	−0.998941	+	0.0460180i	$0.985347\pi$
$948$	22.0474			0.716065
$949$	−2.91759	+	7.04369i	−0.0947090	+	0.228648i
$950$	−28.1379	+	8.02741i	−0.912913	+	0.260444i
$951$	12.8752			0.417508
$952$	11.3663	+	7.57131i	0.368384	+	0.245388i
$953$			10.2410i			0.331738i	0.986148	+	0.165869i	$0.0530430\pi$
$953$			10.2410i			0.331738i	−0.986148	+	0.165869i	$0.946957\pi$
$954$	10.1992	−	10.1992i	0.330211	−	0.330211i
$955$	58.3268	−	8.15725i	1.88741	−	0.263962i
$956$		−	11.2657i		−	0.364357i
$957$	−0.831060	+	2.00636i	−0.0268643	+	0.0648563i
$958$	−24.3093	+	10.0693i	−0.785399	+	0.325323i
$959$	−6.66559	+	2.76098i	−0.215243	+	0.0891567i
$960$	5.48087	+	1.42139i	0.176894	+	0.0458750i
$961$	19.4210	+	19.4210i	0.626484	+	0.626484i
$962$	−1.37473	−	3.31890i	−0.0443232	−	0.107006i
$963$	−16.0639	+	6.65388i	−0.517651	+	0.214418i
$964$	−0.401624	−	0.166358i	−0.0129355	−	0.00535804i
$965$	−15.5125	−	26.3757i	−0.499366	−	0.849062i
$966$	25.9007	−	62.5298i	0.833341	−	2.01186i
$967$	−1.61879	−	1.61879i	−0.0520569	−	0.0520569i	0.680599	−	0.732656i	$-0.261720\pi$
$967$	−1.61879	−	1.61879i	−0.0520569	−	0.0520569i	−0.732656	+	0.680599i	$0.761720\pi$
$968$			4.84378i			0.155685i
$969$	−59.9081	+	12.0052i	−1.92452	+	0.385663i
$970$	3.11079	+	5.28921i	0.0998814	+	0.169826i
$971$	−9.60331	+	9.60331i	−0.308185	+	0.308185i	−0.844205	−	0.536020i	$-0.819927\pi$
$971$	−9.60331	+	9.60331i	−0.308185	+	0.308185i	0.536020	+	0.844205i	$0.319927\pi$
$972$	−20.6578	−	8.55676i	−0.662601	−	0.274458i
$973$	−33.3082			−1.06781
$974$	−19.0022	−	7.87096i	−0.608869	−	0.252202i
$975$	−9.78303	−	1.12798i	−0.313308	−	0.0361244i
$976$	−12.7953	+	5.29999i	−0.409568	+	0.169649i
$977$	−17.0701	+	17.0701i	−0.546120	+	0.546120i	−0.925316	−	0.379196i	$-0.876201\pi$
$977$	−17.0701	+	17.0701i	−0.546120	+	0.546120i	0.379196	+	0.925316i	$0.376201\pi$
$978$	19.0313	−	19.0313i	0.608554	−	0.608554i
$979$	8.42808	−	3.49103i	0.269363	−	0.111574i
$980$	−5.34937	+	7.08892i	−0.170879	+	0.226447i
$981$	0.577163	+	0.239069i	0.0184274	+	0.00763288i
$982$	3.45555			0.110271
$983$	51.6554	+	21.3964i	1.64755	+	0.682439i	0.997028	−	0.0770464i	$-0.0245490\pi$
$983$	51.6554	+	21.3964i	1.64755	+	0.682439i	0.650525	+	0.759485i	$0.274549\pi$
$984$	4.21319	−	4.21319i	0.134312	−	0.134312i
$985$	12.5337	−	7.37153i	0.399356	−	0.234876i
$986$	0.280025	+	1.39737i	0.00891781	+	0.0445014i
$987$			77.6660i			2.47214i
$988$	−3.21862	−	3.21862i	−0.102398	−	0.102398i
$989$	−35.0936	+	84.7235i	−1.11591	+	2.69405i
$990$	−9.59686	−	16.3173i	−0.305008	−	0.518599i
$991$	28.9890	+	12.0076i	0.920866	+	0.381435i	0.792206	−	0.610253i	$-0.208932\pi$
$991$	28.9890	+	12.0076i	0.920866	+	0.381435i	0.128660	+	0.991689i	$0.458932\pi$
$992$	1.73693	−	0.719461i	0.0551476	−	0.0228429i
$993$	−3.15376	−	7.61386i	−0.100082	−	0.241618i
$994$	19.2070	+	19.2070i	0.609210	+	0.609210i
$995$	−6.23466	+	24.0409i	−0.197652	+	0.762146i
$996$	−8.47209	+	3.50926i	−0.268448	+	0.111195i
$997$	−44.1910	+	18.3045i	−1.39954	+	0.579710i	−0.949633	−	0.313365i	$-0.898544\pi$
$997$	−44.1910	+	18.3045i	−1.39954	+	0.579710i	−0.449910	+	0.893074i	$0.648544\pi$
$998$	−2.11896	+	5.11563i	−0.0670746	+	0.161933i
$999$		−	4.81893i		−	0.152464i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.2.n.a.59.1	yes	20
5.2	odd	4		850.2.l.i.501.1		20
5.3	odd	4		850.2.l.h.501.5		20
5.4	even	2		170.2.n.b.59.5	yes	20
17.15	even	8		170.2.n.b.49.5	yes	20
85.32	odd	8		850.2.l.i.151.1		20
85.49	even	8	inner	170.2.n.a.49.1	✓	20
85.83	odd	8		850.2.l.h.151.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.n.a.49.1	✓	20	85.49	even	8	inner
170.2.n.a.59.1	yes	20	1.1	even	1	trivial
170.2.n.b.49.5	yes	20	17.15	even	8
170.2.n.b.59.5	yes	20	5.4	even	2
850.2.l.h.151.5		20	85.83	odd	8
850.2.l.h.501.5		20	5.3	odd	4
850.2.l.i.151.1		20	85.32	odd	8
850.2.l.i.501.1		20	5.2	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:	\( N \)	\(=\)	\( 170 = 2 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	170.n (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-2.33945 - 0.969032i) q^{3} +1.00000i q^{4} +(-0.309710 - 2.21452i) q^{5} +(-0.969032 - 2.33945i) q^{6} +(-1.26758 - 3.06021i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.41268 + 2.41268i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-2.33945 - 0.969032i) q^{3} +1.00000i q^{4} +(-0.309710 - 2.21452i) q^{5} +(-0.969032 - 2.33945i) q^{6} +(-1.26758 - 3.06021i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.41268 + 2.41268i) q^{9} +(1.34690 - 1.78490i) q^{10} +(-0.949504 - 2.29231i) q^{11} +(0.969032 - 2.33945i) q^{12} -0.777809 q^{13} +(1.26758 - 3.06021i) q^{14} +(-1.42139 + 5.48087i) q^{15} -1.00000 q^{16} +(4.04502 + 0.798615i) q^{17} +3.41205i q^{18} +(4.13806 - 4.13806i) q^{19} +(2.21452 - 0.309710i) q^{20} +8.38752i q^{21} +(0.949504 - 2.29231i) q^{22} +(-7.45510 + 3.08800i) q^{23} +(2.33945 - 0.969032i) q^{24} +(-4.80816 + 1.37171i) q^{25} +(-0.549994 - 0.549994i) q^{26} +(-0.399286 - 0.963960i) q^{27} +(3.06021 - 1.26758i) q^{28} +(0.319339 + 0.132275i) q^{29} +(-4.88063 + 2.87049i) q^{30} +(-0.719461 + 1.73693i) q^{31} +(-0.707107 - 0.707107i) q^{32} +6.28283i q^{33} +(2.29556 + 3.42497i) q^{34} +(-6.38429 + 3.75485i) q^{35} +(-2.41268 + 2.41268i) q^{36} +(4.26699 + 1.76745i) q^{37} +5.85211 q^{38} +(1.81964 + 0.753721i) q^{39} +(1.78490 + 1.34690i) q^{40} +(2.17392 - 0.900466i) q^{41} +(-5.93087 + 5.93087i) q^{42} +(8.03592 - 8.03592i) q^{43} +(2.29231 - 0.949504i) q^{44} +(4.59569 - 6.09015i) q^{45} +(-7.45510 - 3.08800i) q^{46} +9.25971 q^{47} +(2.33945 + 0.969032i) q^{48} +(-2.80835 + 2.80835i) q^{49} +(-4.36983 - 2.42993i) q^{50} +(-8.68924 - 5.78807i) q^{51} -0.777809i q^{52} +(-2.98917 - 2.98917i) q^{53} +(0.399286 - 0.963960i) q^{54} +(-4.78228 + 2.81264i) q^{55} +(3.06021 + 1.26758i) q^{56} +(-13.6907 + 5.67088i) q^{57} +(0.132275 + 0.319339i) q^{58} +(-9.06612 - 9.06612i) q^{59} +(-5.48087 - 1.42139i) q^{60} +(12.7953 - 5.29999i) q^{61} +(-1.73693 + 0.719461i) q^{62} +(4.32504 - 10.4416i) q^{63} -1.00000i q^{64} +(0.240895 + 1.72247i) q^{65} +(-4.44263 + 4.44263i) q^{66} +0.862303i q^{67} +(-0.798615 + 4.04502i) q^{68} +20.4332 q^{69} +(-7.16945 - 1.85930i) q^{70} +(-3.13819 + 7.57626i) q^{71} -3.41205 q^{72} +(3.75104 - 9.05580i) q^{73} +(1.76745 + 4.26699i) q^{74} +(12.5777 + 1.45021i) q^{75} +(4.13806 + 4.13806i) q^{76} +(-5.81136 + 5.81136i) q^{77} +(0.753721 + 1.81964i) q^{78} +(3.33195 + 8.04403i) q^{79} +(0.309710 + 2.21452i) q^{80} -7.59408i q^{81} +(2.17392 + 0.900466i) q^{82} +(-2.56072 - 2.56072i) q^{83} -8.38752 q^{84} +(0.515763 - 9.20511i) q^{85} +11.3645 q^{86} +(-0.618900 - 0.618900i) q^{87} +(2.29231 + 0.949504i) q^{88} +3.67668i q^{89} +(7.55603 - 1.05674i) q^{90} +(0.985934 + 2.38025i) q^{91} +(-3.08800 - 7.45510i) q^{92} +(3.36628 - 3.36628i) q^{93} +(6.54760 + 6.54760i) q^{94} +(-10.4454 - 7.88221i) q^{95} +(0.969032 + 2.33945i) q^{96} +(-1.05015 + 2.53530i) q^{97} -3.97161 q^{98} +(3.23975 - 7.82145i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{5}+O(q^{10}) \) 20 * q - 4 * q^5	\( 20 q - 4 q^{5} + 4 q^{10} - 8 q^{11} - 24 q^{13} + 8 q^{15} - 20 q^{16} + 8 q^{20} + 8 q^{22} + 16 q^{23} - 12 q^{25} - 12 q^{26} + 24 q^{27} - 12 q^{29} - 8 q^{30} + 8 q^{31} + 8 q^{34} - 8 q^{35} - 8 q^{37} - 8 q^{38} + 4 q^{40} + 4 q^{41} + 8 q^{42} + 16 q^{43} - 8 q^{44} - 12 q^{45} + 16 q^{46} + 40 q^{47} - 56 q^{49} + 8 q^{50} - 8 q^{51} + 44 q^{53} - 24 q^{54} - 72 q^{57} + 16 q^{59} + 16 q^{60} + 8 q^{61} - 8 q^{62} - 24 q^{63} - 8 q^{65} - 8 q^{66} + 20 q^{68} - 16 q^{69} - 16 q^{70} + 8 q^{71} - 28 q^{72} - 60 q^{73} + 28 q^{74} + 64 q^{75} + 8 q^{78} + 56 q^{79} + 4 q^{80} + 4 q^{82} + 16 q^{84} - 16 q^{85} + 48 q^{86} - 72 q^{87} - 8 q^{88} + 32 q^{90} - 24 q^{91} - 8 q^{92} + 72 q^{93} + 32 q^{94} + 8 q^{95} + 48 q^{97} - 36 q^{98} + 72 q^{99}+O(q^{100}) \) 20 * q - 4 * q^5 + 4 * q^10 - 8 * q^11 - 24 * q^13 + 8 * q^15 - 20 * q^16 + 8 * q^20 + 8 * q^22 + 16 * q^23 - 12 * q^25 - 12 * q^26 + 24 * q^27 - 12 * q^29 - 8 * q^30 + 8 * q^31 + 8 * q^34 - 8 * q^35 - 8 * q^37 - 8 * q^38 + 4 * q^40 + 4 * q^41 + 8 * q^42 + 16 * q^43 - 8 * q^44 - 12 * q^45 + 16 * q^46 + 40 * q^47 - 56 * q^49 + 8 * q^50 - 8 * q^51 + 44 * q^53 - 24 * q^54 - 72 * q^57 + 16 * q^59 + 16 * q^60 + 8 * q^61 - 8 * q^62 - 24 * q^63 - 8 * q^65 - 8 * q^66 + 20 * q^68 - 16 * q^69 - 16 * q^70 + 8 * q^71 - 28 * q^72 - 60 * q^73 + 28 * q^74 + 64 * q^75 + 8 * q^78 + 56 * q^79 + 4 * q^80 + 4 * q^82 + 16 * q^84 - 16 * q^85 + 48 * q^86 - 72 * q^87 - 8 * q^88 + 32 * q^90 - 24 * q^91 - 8 * q^92 + 72 * q^93 + 32 * q^94 + 8 * q^95 + 48 * q^97 - 36 * q^98 + 72 * q^99

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