LMFDB - Embedded newform 160.2.u.a.67.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [160,2,Mod(43,160)] 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("160.43"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(160, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([4, 5, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 160 = 2^{5} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	160.u (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.27760643234$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			67.16
Character	$\chi$	$=$	160.67
Dual form			160.2.u.a.43.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.816290 - 1.15485i) q^{2} +(1.28377 + 3.09930i) q^{3} +(-0.667342 - 1.88538i) q^{4} +(1.06380 - 1.96680i) q^{5} +(4.62714 + 1.04737i) q^{6} +0.906290i q^{7} +(-2.72207 - 0.768338i) q^{8} +(-5.83625 + 5.83625i) q^{9} +(-1.40298 - 2.83401i) q^{10} +(0.392432 + 0.947415i) q^{11} +(4.98663 - 4.48869i) q^{12} +(-1.59755 - 3.85684i) q^{13} +(1.04663 + 0.739795i) q^{14} +(7.46139 + 0.772121i) q^{15} +(-3.10931 + 2.51639i) q^{16} +(1.95970 - 1.95970i) q^{17} +(1.97590 + 11.5040i) q^{18} +(-0.671071 + 1.62011i) q^{19} +(-4.41809 - 0.693144i) q^{20} +(-2.80886 + 1.16347i) q^{21} +(1.41446 + 0.320166i) q^{22} -1.58299i q^{23} +(-1.11321 - 9.42287i) q^{24} +(-2.73664 - 4.18459i) q^{25} +(-5.75812 - 1.30337i) q^{26} +(-16.2828 - 6.74455i) q^{27} +(1.70870 - 0.604805i) q^{28} +(-2.34560 + 5.66278i) q^{29} +(6.98234 - 7.98649i) q^{30} -4.17491i q^{31} +(0.367943 + 5.64488i) q^{32} +(-2.43253 + 2.43253i) q^{33} +(-0.663470 - 3.86284i) q^{34} +(1.78249 + 0.964115i) q^{35} +(14.8983 + 7.10877i) q^{36} +(-1.45950 + 3.52354i) q^{37} +(1.32319 + 2.09746i) q^{38} +(9.90259 - 9.90259i) q^{39} +(-4.40692 + 4.53642i) q^{40} +(0.655358 + 0.655358i) q^{41} +(-0.949216 + 4.19353i) q^{42} +(-6.17029 - 2.55582i) q^{43} +(1.52435 - 1.37213i) q^{44} +(5.27013 + 17.6874i) q^{45} +(-1.82811 - 1.29218i) q^{46} +(3.43714 + 3.43714i) q^{47} +(-11.7907 - 6.40621i) q^{48} +6.17864 q^{49} +(-7.06645 - 0.255441i) q^{50} +(8.58950 + 3.55789i) q^{51} +(-6.20548 + 5.58582i) q^{52} +(2.52411 - 6.09374i) q^{53} +(-21.0804 + 13.2986i) q^{54} +(2.28085 + 0.236027i) q^{55} +(0.696336 - 2.46698i) q^{56} -5.88270 q^{57} +(4.62496 + 7.33128i) q^{58} +(4.29438 + 10.3675i) q^{59} +(-3.52356 - 14.5828i) q^{60} +(-1.24308 - 0.514899i) q^{61} +(-4.82138 - 3.40793i) q^{62} +(-5.28933 - 5.28933i) q^{63} +(6.81931 + 4.18294i) q^{64} +(-9.28513 - 0.960845i) q^{65} +(0.823549 + 4.79484i) q^{66} +(10.2511 - 4.24615i) q^{67} +(-5.00257 - 2.38699i) q^{68} +(4.90615 - 2.03219i) q^{69} +(2.56844 - 1.27151i) q^{70} +(5.43676 + 5.43676i) q^{71} +(20.3709 - 11.4025i) q^{72} +5.21568 q^{73} +(2.87778 + 4.56173i) q^{74} +(9.45607 - 13.8537i) q^{75} +(3.50235 + 0.184056i) q^{76} +(-0.858632 + 0.355657i) q^{77} +(-3.35259 - 19.5194i) q^{78} -1.61999i q^{79} +(1.64154 + 8.79235i) q^{80} -34.3625i q^{81} +(1.29180 - 0.221876i) q^{82} +(-7.18465 + 2.97598i) q^{83} +(4.06805 + 4.51933i) q^{84} +(-1.76961 - 5.93908i) q^{85} +(-7.98832 + 5.03945i) q^{86} -20.5619 q^{87} +(-0.340292 - 2.88045i) q^{88} +(0.483064 + 0.483064i) q^{89} +(24.7282 + 8.35184i) q^{90} +(3.49541 - 1.44785i) q^{91} +(-2.98453 + 1.05639i) q^{92} +(12.9393 - 5.35962i) q^{93} +(6.77507 - 1.16367i) q^{94} +(2.47255 + 3.04334i) q^{95} +(-17.0228 + 8.38709i) q^{96} +(2.63970 + 2.63970i) q^{97} +(5.04356 - 7.13538i) q^{98} +(-7.81968 - 3.23902i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} - 16 q^{8} - 16 q^{10} - 8 q^{11} - 20 q^{12} - 4 q^{13} + 16 q^{14} - 8 q^{15} - 8 q^{16} + 4 q^{18} + 16 q^{19} + 24 q^{20} - 8 q^{21} - 20 q^{22} - 32 q^{24}+ \cdots - 16 q^{98}+O(q^{100}) $ 88 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 - 8 * q^6 - 16 * q^8 - 16 * q^10 - 8 * q^11 - 20 * q^12 - 4 * q^13 + 16 * q^14 - 8 * q^15 - 8 * q^16 + 4 * q^18 + 16 * q^19 + 24 * q^20 - 8 * q^21 - 20 * q^22 - 32 * q^24 - 4 * q^25 - 8 * q^26 - 16 * q^27 + 12 * q^28 + 8 * q^30 - 24 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 8 * q^36 - 4 * q^37 - 60 * q^38 + 16 * q^40 - 8 * q^41 + 60 * q^42 - 36 * q^43 + 16 * q^44 - 4 * q^45 - 8 * q^46 - 8 * q^47 - 24 * q^48 - 40 * q^49 - 12 * q^50 + 8 * q^51 - 56 * q^52 - 4 * q^53 - 56 * q^54 - 36 * q^55 + 40 * q^56 - 8 * q^57 - 36 * q^58 + 12 * q^60 - 40 * q^61 + 40 * q^62 + 56 * q^63 + 48 * q^64 - 8 * q^65 + 72 * q^66 + 20 * q^67 + 8 * q^68 + 24 * q^69 + 60 * q^70 + 24 * q^71 + 24 * q^72 - 8 * q^73 + 8 * q^75 + 56 * q^76 + 24 * q^77 + 32 * q^78 - 8 * q^80 + 84 * q^82 - 44 * q^83 + 56 * q^84 - 4 * q^85 + 24 * q^86 - 120 * q^87 + 104 * q^88 + 148 * q^90 - 8 * q^91 + 124 * q^92 + 8 * q^93 - 32 * q^94 + 24 * q^96 - 8 * q^97 - 16 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/160\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$101$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{8}\right)$

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 $

$2$	0.816290	−	1.15485i	0.577204	−	0.816600i
$2$	0.816290	−	1.15485i	0.577204	−	0.816600i
$3$	1.28377	+	3.09930i	0.741185	+	1.78938i	0.600991	+	0.799256i	$0.294773\pi$
$3$	1.28377	+	3.09930i	0.741185	+	1.78938i	0.140194	+	0.990124i	$0.455227\pi$
$4$	−0.667342	−	1.88538i	−0.333671	−	0.942690i
$5$	1.06380	−	1.96680i	0.475748	−	0.879582i
$5$	1.06380	−	1.96680i	0.475748	−	0.879582i
$6$	4.62714	+	1.04737i	1.88902	+	0.427585i
$7$			0.906290i			0.342545i	0.985224	+	0.171273i	$0.0547879\pi$
$7$			0.906290i			0.342545i	−0.985224	+	0.171273i	$0.945212\pi$
$8$	−2.72207	−	0.768338i	−0.962397	−	0.271648i
$9$	−5.83625	+	5.83625i	−1.94542	+	1.94542i
$10$	−1.40298	−	2.83401i	−0.443663	−	0.896194i
$11$	0.392432	+	0.947415i	0.118323	+	0.285656i	0.971934	−	0.235255i	$-0.0755924\pi$
$11$	0.392432	+	0.947415i	0.118323	+	0.285656i	−0.853611	+	0.520911i	$0.825592\pi$
$12$	4.98663	−	4.48869i	1.43952	−	1.29577i
$13$	−1.59755	−	3.85684i	−0.443082	−	1.06969i	−0.974862	−	0.222811i	$-0.928477\pi$
$13$	−1.59755	−	3.85684i	−0.443082	−	1.06969i	0.531780	−	0.846883i	$-0.321523\pi$
$14$	1.04663	+	0.739795i	0.279722	+	0.197718i
$15$	7.46139	+	0.772121i	1.92652	+	0.199361i
$16$	−3.10931	+	2.51639i	−0.777327	+	0.629096i
$17$	1.95970	−	1.95970i	0.475297	−	0.475297i	−0.428327	−	0.903624i	$-0.640897\pi$
$17$	1.95970	−	1.95970i	0.475297	−	0.475297i	0.903624	+	0.428327i	$0.140897\pi$
$18$	1.97590	+	11.5040i	0.465725	+	2.71153i
$19$	−0.671071	+	1.62011i	−0.153954	+	0.371678i	−0.981973	−	0.189022i	$-0.939468\pi$
$19$	−0.671071	+	1.62011i	−0.153954	+	0.371678i	0.828019	+	0.560701i	$0.189468\pi$
$20$	−4.41809	−	0.693144i	−0.987916	−	0.154992i
$21$	−2.80886	+	1.16347i	−0.612944	+	0.253890i
$22$	1.41446	+	0.320166i	0.301563	+	0.0682596i
$23$		−	1.58299i		−	0.330076i	−0.986287	−	0.165038i	$-0.947225\pi$
$23$		−	1.58299i		−	0.330076i	0.986287	−	0.165038i	$-0.0527747\pi$
$24$	−1.11321	−	9.42287i	−0.227232	−	1.92343i
$25$	−2.73664	−	4.18459i	−0.547328	−	0.836918i
$26$	−5.75812	−	1.30337i	−1.12926	−	0.255611i
$27$	−16.2828	−	6.74455i	−3.13362	−	1.29799i
$28$	1.70870	−	0.604805i	0.322914	−	0.114297i
$29$	−2.34560	+	5.66278i	−0.435567	+	1.05155i	0.541896	+	0.840446i	$0.317707\pi$
$29$	−2.34560	+	5.66278i	−0.435567	+	1.05155i	−0.977463	+	0.211107i	$0.932293\pi$
$30$	6.98234	−	7.98649i	1.27479	−	1.45813i
$31$		−	4.17491i		−	0.749836i	−0.927058	−	0.374918i	$-0.877671\pi$
$31$		−	4.17491i		−	0.749836i	0.927058	−	0.374918i	$-0.122329\pi$
$32$	0.367943	+	5.64488i	0.0650438	+	0.997882i
$33$	−2.43253	+	2.43253i	−0.423448	+	0.423448i
$34$	−0.663470	−	3.86284i	−0.113784	−	0.662471i
$35$	1.78249	+	0.964115i	0.301297	+	0.162965i
$36$	14.8983	+	7.10877i	2.48305	+	1.18479i
$37$	−1.45950	+	3.52354i	−0.239940	+	0.579267i	−0.997276	−	0.0737587i	$-0.976501\pi$
$37$	−1.45950	+	3.52354i	−0.239940	+	0.579267i	0.757336	+	0.653025i	$0.226501\pi$
$38$	1.32319	+	2.09746i	0.214649	+	0.340253i
$39$	9.90259	−	9.90259i	1.58568	−	1.58568i
$40$	−4.40692	+	4.53642i	−0.696795	+	0.717270i
$41$	0.655358	+	0.655358i	0.102350	+	0.102350i	0.756427	−	0.654078i	$-0.226943\pi$
$41$	0.655358	+	0.655358i	0.102350	+	0.102350i	−0.654078	+	0.756427i	$0.726943\pi$
$42$	−0.949216	+	4.19353i	−0.146467	+	0.647076i
$43$	−6.17029	−	2.55582i	−0.940961	−	0.389759i	−0.141134	−	0.989990i	$-0.545075\pi$
$43$	−6.17029	−	2.55582i	−0.940961	−	0.389759i	−0.799826	+	0.600232i	$0.795075\pi$
$44$	1.52435	−	1.37213i	0.229804	−	0.206857i
$45$	5.27013	+	17.6874i	0.785625	+	2.63668i
$46$	−1.82811	−	1.29218i	−0.269540	−	0.190521i
$47$	3.43714	+	3.43714i	0.501358	+	0.501358i	0.911860	−	0.410502i	$-0.134646\pi$
$47$	3.43714	+	3.43714i	0.501358	+	0.501358i	−0.410502	+	0.911860i	$0.634646\pi$
$48$	−11.7907	−	6.40621i	−1.70184	−	0.924656i
$49$	6.17864			0.882663
$50$	−7.06645	−	0.255441i	−0.999347	−	0.0361248i
$51$	8.58950	+	3.55789i	1.20277	+	0.498204i
$52$	−6.20548	+	5.58582i	−0.860546	+	0.774615i
$53$	2.52411	−	6.09374i	0.346713	−	0.837040i	−0.650290	−	0.759686i	$-0.725353\pi$
$53$	2.52411	−	6.09374i	0.346713	−	0.837040i	0.997004	−	0.0773541i	$-0.0246472\pi$
$54$	−21.0804	+	13.2986i	−2.86868	+	1.80971i
$55$	2.28085	+	0.236027i	0.307550	+	0.0318259i
$56$	0.696336	−	2.46698i	0.0930519	−	0.329664i
$57$	−5.88270			−0.779182
$58$	4.62496	+	7.33128i	0.607287	+	0.962645i
$59$	4.29438	+	10.3675i	0.559080	+	1.34974i	0.910495	+	0.413519i	$0.135701\pi$
$59$	4.29438	+	10.3675i	0.559080	+	1.34974i	−0.351415	+	0.936220i	$0.614299\pi$
$60$	−3.52356	−	14.5828i	−0.454890	−	1.88263i
$61$	−1.24308	−	0.514899i	−0.159160	−	0.0659261i	0.301681	−	0.953409i	$-0.402452\pi$
$61$	−1.24308	−	0.514899i	−0.159160	−	0.0659261i	−0.460841	+	0.887483i	$0.652452\pi$
$62$	−4.82138	−	3.40793i	−0.612316	−	0.432808i
$63$	−5.28933	−	5.28933i	−0.666393	−	0.666393i
$64$	6.81931	+	4.18294i	0.852414	+	0.522867i
$65$	−9.28513	−	0.960845i	−1.15168	−	0.119178i
$66$	0.823549	+	4.79484i	0.101372	+	0.590204i
$67$	10.2511	−	4.24615i	1.25237	−	0.518750i	0.344812	−	0.938672i	$-0.387943\pi$
$67$	10.2511	−	4.24615i	1.25237	−	0.518750i	0.907560	+	0.419922i	$0.137943\pi$
$68$	−5.00257	−	2.38699i	−0.606650	−	0.289465i
$69$	4.90615	−	2.03219i	0.590631	−	0.244647i
$70$	2.56844	−	1.27151i	0.306987	−	0.151975i
$71$	5.43676	+	5.43676i	0.645224	+	0.645224i	0.951835	−	0.306611i	$-0.0991949\pi$
$71$	5.43676	+	5.43676i	0.645224	+	0.645224i	−0.306611	+	0.951835i	$0.599195\pi$
$72$	20.3709	−	11.4025i	2.40073	−	1.34379i
$73$	5.21568			0.610449			0.305225	−	0.952280i	$-0.401268\pi$
$73$	5.21568			0.610449			0.305225	+	0.952280i	$0.401268\pi$
$74$	2.87778	+	4.56173i	0.334535	+	0.530290i
$75$	9.45607	−	13.8537i	1.09189	−	1.59969i
$76$	3.50235	+	0.184056i	0.401747	+	0.0211127i
$77$	−0.858632	+	0.355657i	−0.0978502	+	0.0405309i
$78$	−3.35259	−	19.5194i	−0.379606	−	2.21013i
$79$		−	1.61999i		−	0.182263i	−0.995839	−	0.0911315i	$-0.970952\pi$
$79$		−	1.61999i		−	0.182263i	0.995839	−	0.0911315i	$-0.0290484\pi$
$80$	1.64154	+	8.79235i	0.183530	+	0.983014i
$81$		−	34.3625i		−	3.81806i
$82$	1.29180	−	0.221876i	0.142655	−	0.0245021i
$83$	−7.18465	+	2.97598i	−0.788618	+	0.326656i	−0.740388	−	0.672180i	$-0.765358\pi$
$83$	−7.18465	+	2.97598i	−0.788618	+	0.326656i	−0.0482299	+	0.998836i	$0.515358\pi$
$84$	4.06805	+	4.51933i	0.443861	+	0.493100i
$85$	−1.76961	−	5.93908i	−0.191941	−	0.644184i
$86$	−7.98832	+	5.03945i	−0.861403	+	0.543418i
$87$	−20.5619			−2.20446
$88$	−0.340292	−	2.88045i	−0.0362753	−	0.307057i
$89$	0.483064	+	0.483064i	0.0512046	+	0.0512046i	0.732245	−	0.681041i	$-0.238472\pi$
$89$	0.483064	+	0.483064i	0.0512046	+	0.0512046i	−0.681041	+	0.732245i	$0.738472\pi$
$90$	24.7282	+	8.35184i	2.60658	+	0.880362i
$91$	3.49541	−	1.44785i	0.366419	−	0.151776i
$92$	−2.98453	+	1.05639i	−0.311159	+	0.110137i
$93$	12.9393	−	5.35962i	1.34174	−	0.555767i
$94$	6.77507	−	1.16367i	0.698795	−	0.120023i
$95$	2.47255	+	3.04334i	0.253678	+	0.312240i
$96$	−17.0228	+	8.38709i	−1.73738	+	0.856004i
$97$	2.63970	+	2.63970i	0.268021	+	0.268021i	0.828302	−	0.560282i	$-0.189307\pi$
$97$	2.63970	+	2.63970i	0.268021	+	0.268021i	−0.560282	+	0.828302i	$0.689307\pi$
$98$	5.04356	−	7.13538i	0.509476	−	0.720782i
$99$	−7.81968	−	3.23902i	−0.785908	−	0.325534i
$100$	−6.06327	+	7.95216i	−0.606327	+	0.795216i
$101$	4.87445	+	11.7680i	0.485026	+	1.17096i	0.957194	+	0.289447i	$0.0934715\pi$
$101$	4.87445	+	11.7680i	0.485026	+	1.17096i	−0.472168	+	0.881509i	$0.656528\pi$
$102$	11.1203	−	7.01529i	1.10108	−	0.694617i
$103$	2.63961			0.260089			0.130044	−	0.991508i	$-0.458488\pi$
$103$	2.63961			0.260089			0.130044	+	0.991508i	$0.458488\pi$
$104$	1.38530	+	11.7260i	0.135840	+	1.14983i
$105$	−0.699765	+	6.76218i	−0.0682901	+	0.659921i
$106$	−4.97693	−	7.88922i	−0.483402	−	0.766269i
$107$	−5.10959	+	12.3357i	−0.493963	+	1.19253i	0.458724	+	0.888579i	$0.348307\pi$
$107$	−5.10959	+	12.3357i	−0.493963	+	1.19253i	−0.952687	+	0.303953i	$0.901693\pi$
$108$	−1.84985	+	35.2002i	−0.178002	+	3.38714i
$109$	−14.7005	−	6.08914i	−1.40805	−	0.583233i	−0.456222	−	0.889866i	$-0.650798\pi$
$109$	−14.7005	−	6.08914i	−1.40805	−	0.583233i	−0.951828	+	0.306633i	$0.900798\pi$
$110$	2.13441	−	2.44137i	0.203508	−	0.232775i
$111$	−12.7942			−1.21437
$112$	−2.28057	−	2.81793i	−0.215494	−	0.266270i
$113$	−0.619584	−	0.619584i	−0.0582855	−	0.0582855i	0.677363	−	0.735649i	$-0.263123\pi$
$113$	−0.619584	−	0.619584i	−0.0582855	−	0.0582855i	−0.735649	+	0.677363i	$0.763123\pi$
$114$	−4.80198	+	6.79361i	−0.449747	+	0.636280i
$115$	−3.11343	−	1.68399i	−0.290329	−	0.157033i
$116$	12.2418	+	0.643334i	1.13662	+	0.0597321i
$117$	31.8332	+	13.1857i	2.94298	+	1.21902i
$118$	15.4784	+	3.50357i	1.42490	+	0.322530i
$119$	1.77606	+	1.77606i	0.162811	+	0.162811i
$120$	−19.7172	−	7.83463i	−1.79992	−	0.715201i
$121$	7.03458	−	7.03458i	0.639508	−	0.639508i
$122$	−1.60934	+	1.01526i	−0.145703	+	0.0919170i
$123$	−1.18982	+	2.87248i	−0.107282	+	0.259002i
$124$	−7.87128	+	2.78609i	−0.706862	+	0.250198i
$125$	−11.1415	+	0.930844i	−0.996528	+	0.0832573i
$126$	−10.4260	+	1.79074i	−0.928822	+	0.159532i
$127$	4.08960	−	4.08960i	0.362894	−	0.362894i	−0.501984	−	0.864877i	$-0.667396\pi$
$127$	4.08960	−	4.08960i	0.362894	−	0.362894i	0.864877	+	0.501984i	$0.167396\pi$
$128$	10.3972	−	4.46078i	0.918990	−	0.394281i
$129$		−	22.4046i		−	1.97262i
$130$	−8.68898	+	9.93857i	−0.762074	+	0.871671i
$131$	−6.23750	+	15.0586i	−0.544973	+	1.31568i	0.376205	+	0.926537i	$0.377229\pi$
$131$	−6.23750	+	15.0586i	−0.544973	+	1.31568i	−0.921177	+	0.389144i	$0.872771\pi$
$132$	6.20956	+	2.96291i	0.540473	+	0.257888i
$133$	−1.46829	−	0.608184i	−0.127317	−	0.0527363i
$134$	3.46422	−	15.3045i	0.299263	−	1.32211i
$135$	−30.5869	+	24.8502i	−2.63250	+	2.13876i
$136$	−6.84015	+	3.82873i	−0.586538	+	0.328311i
$137$		−	13.7858i		−	1.17780i	−0.808205	−	0.588902i	$-0.799561\pi$
$137$		−	13.7858i		−	1.17780i	0.808205	−	0.588902i	$-0.200439\pi$
$138$	1.65797	−	7.32471i	0.141136	−	0.623521i
$139$	5.66351	−	2.34590i	0.480373	−	0.198977i	−0.129339	−	0.991600i	$-0.541285\pi$
$139$	5.66351	−	2.34590i	0.480373	−	0.198977i	0.609711	+	0.792624i	$0.291285\pi$
$140$	0.628189	−	4.00407i	0.0530917	−	0.338406i
$141$	−6.24021	+	15.0652i	−0.525521	+	1.26872i
$142$	10.7166	−	1.84065i	0.899316	−	0.154464i
$143$	3.02709	−	3.02709i	0.253138	−	0.253138i
$144$	3.46045	−	32.8330i	0.288371	−	2.73608i
$145$	8.64233	+	10.6374i	0.717706	+	0.883391i
$146$	4.25751	−	6.02331i	0.352354	−	0.498493i
$147$	7.93196	+	19.1494i	0.654217	+	1.57942i
$148$	7.61720	+	0.400301i	0.626130	+	0.0329045i
$149$	0.117762	+	0.284303i	0.00964745	+	0.0232910i	0.928630	−	0.371008i	$-0.120988\pi$
$149$	0.117762	+	0.284303i	0.00964745	+	0.0232910i	−0.918982	+	0.394299i	$0.870988\pi$
$150$	−8.28002	−	22.2290i	−0.676061	−	1.81499i
$151$	2.50445	−	2.50445i	0.203809	−	0.203809i	−0.597821	−	0.801630i	$-0.703967\pi$
$151$	2.50445	−	2.50445i	0.203809	−	0.203809i	0.801630	+	0.597821i	$0.203967\pi$
$152$	3.07149	−	3.89444i	0.249131	−	0.315880i
$153$			22.8746i			1.84930i
$154$	−0.290163	+	1.28191i	−0.0233820	+	0.103299i
$155$	−8.21123	−	4.44129i	−0.659542	−	0.356733i
$156$	−25.2785	−	12.0617i	−2.02390	−	0.965710i
$157$	−8.87481	−	21.4257i	−0.708287	−	1.70996i	−0.704238	−	0.709964i	$-0.748711\pi$
$157$	−8.87481	−	21.4257i	−0.708287	−	1.70996i	−0.00404938	−	0.999992i	$-0.501289\pi$
$158$	−1.87084	−	1.32238i	−0.148836	−	0.105203i
$159$	22.1267			1.75476
$160$	11.4938	+	5.28137i	0.908664	+	0.417529i
$161$	1.43465			0.113066
$162$	−39.6835	−	28.0498i	−3.11783	−	2.20380i
$163$	0.447027	+	1.07922i	0.0350138	+	0.0845309i	0.940419	−	0.340017i	$-0.110433\pi$
$163$	0.447027	+	1.07922i	0.0350138	+	0.0845309i	−0.905405	+	0.424548i	$0.860433\pi$
$164$	0.798250	−	1.67295i	0.0623328	−	0.130635i
$165$	2.19657	+	7.37204i	0.171003	+	0.573912i
$166$	−2.42795	+	10.7264i	−0.188446	+	0.832532i
$167$		−	1.33686i		−	0.103450i	−0.998661	−	0.0517248i	$-0.983528\pi$
$167$		−	1.33686i		−	0.103450i	0.998661	−	0.0517248i	$-0.0164719\pi$
$168$	8.53985	−	1.00889i	0.658863	−	0.0778373i
$169$	−3.13062	+	3.13062i	−0.240817	+	0.240817i
$170$	−8.30325	−	2.80439i	−0.636830	−	0.215087i
$171$	−5.53882	−	13.3719i	−0.423564	−	1.02257i
$172$	−0.700991	+	13.3389i	−0.0534501	+	1.01708i
$173$	−6.30490	−	15.2214i	−0.479352	−	1.15726i	−0.959913	−	0.280298i	$-0.909567\pi$
$173$	−6.30490	−	15.2214i	−0.479352	−	1.15726i	0.480561	−	0.876962i	$-0.340433\pi$
$174$	−16.7844	+	23.7458i	−1.27242	+	1.80016i
$175$	3.79245	−	2.48019i	0.286682	−	0.187485i
$176$	−3.60425	−	1.95829i	−0.271681	−	0.147612i
$177$	−26.6191	+	26.6191i	−2.00081	+	2.00081i
$178$	0.952184	−	0.163545i	0.0713692	−	0.0122582i
$179$	−3.18265	+	7.68360i	−0.237883	+	0.574299i	−0.997063	−	0.0765805i	$-0.975600\pi$
$179$	−3.18265	+	7.68360i	−0.237883	+	0.574299i	0.759181	+	0.650880i	$0.225600\pi$
$180$	29.8305	−	21.7397i	2.22343	−	1.62038i
$181$	4.55968	−	1.88868i	0.338919	−	0.140385i	−0.206732	−	0.978398i	$-0.566283\pi$
$181$	4.55968	−	1.88868i	0.338919	−	0.140385i	0.545650	+	0.838013i	$0.316283\pi$
$182$	1.18123	−	5.21853i	0.0875584	−	0.386823i
$183$		−	4.51368i		−	0.333661i
$184$	−1.21627	+	4.30900i	−0.0896646	+	0.317664i
$185$	5.37750	+	6.61891i	0.395361	+	0.486632i
$186$	4.37265	−	19.3179i	0.320619	−	1.41646i
$187$	2.62570	+	1.08760i	0.192010	+	0.0795331i
$188$	4.18656	−	8.77406i	0.305336	−	0.639914i
$189$	6.11252	−	14.7569i	0.444620	−	1.07341i
$190$	5.53291	−	0.371163i	0.401399	−	0.0269270i
$191$		−	5.55963i		−	0.402281i	−0.979562	−	0.201140i	$-0.935535\pi$
$191$		−	5.55963i		−	0.402281i	0.979562	−	0.201140i	$-0.0644647\pi$
$192$	−4.20972	+	26.5050i	−0.303811	+	1.91283i
$193$	−14.6069	+	14.6069i	−1.05143	+	1.05143i	−0.0528217	+	0.998604i	$0.516822\pi$
$193$	−14.6069	+	14.6069i	−1.05143	+	1.05143i	−0.998604	+	0.0528217i	$0.983178\pi$
$194$	5.20320	−	0.893688i	0.373568	−	0.0641631i
$195$	−8.94203	−	30.0109i	−0.640352	−	2.14912i
$196$	−4.12327	−	11.6491i	−0.294519	−	0.832077i
$197$	7.20550	−	17.3956i	0.513371	−	1.23939i	−0.428540	−	0.903523i	$-0.640972\pi$
$197$	7.20550	−	17.3956i	0.513371	−	1.23939i	0.941910	−	0.335864i	$-0.109028\pi$
$198$	−10.1237	+	6.38656i	−0.719460	+	0.453873i
$199$	−12.1953	+	12.1953i	−0.864499	+	0.864499i	−0.991857	−	0.127358i	$-0.959350\pi$
$199$	−12.1953	+	12.1953i	−0.864499	+	0.864499i	0.127358	+	0.991857i	$0.459350\pi$
$200$	4.23414	+	13.4934i	0.299399	+	0.954128i
$201$	26.3201	+	26.3201i	1.85648	+	1.85648i
$202$	17.5692	+	3.97682i	1.23616	+	0.279808i
$203$	−5.13212	−	2.12579i	−0.360204	−	0.149202i
$204$	0.975831	−	18.5688i	0.0683218	−	1.30007i
$205$	1.98613	−	0.591788i	0.138718	−	0.0413322i
$206$	2.15469	−	3.04835i	0.150124	−	0.212389i
$207$	9.23872	+	9.23872i	0.642135	+	0.642135i
$208$	14.6726	+	7.97203i	1.01736	+	0.552761i
$209$	−1.79826			−0.124388
$210$	7.23807	+	6.32802i	0.499474	+	0.436675i
$211$	−21.2722	−	8.81122i	−1.46444	−	0.606589i	−0.498854	−	0.866686i	$-0.666245\pi$
$211$	−21.2722	−	8.81122i	−1.46444	−	0.606589i	−0.965583	+	0.260097i	$0.916245\pi$
$212$	−13.1735	−	0.692294i	−0.904757	−	0.0475470i
$213$	−9.87058	+	23.8297i	−0.676321	+	1.63278i
$214$	10.0749	+	15.9703i	0.688704	+	1.09170i
$215$	−11.5908	+	9.41686i	−0.790485	+	0.642225i
$216$	39.1408	+	30.8698i	2.66319	+	2.10043i
$217$	3.78368			0.256853
$218$	−19.0319	+	12.0063i	−1.28900	+	0.813169i
$219$	6.69574	+	16.1649i	0.452456	+	1.09233i
$220$	−1.07711	−	4.45778i	−0.0726185	−	0.300543i
$221$	−10.6890	−	4.42752i	−0.719018	−	0.297827i
$222$	−10.4437	+	14.7753i	−0.700938	+	0.991653i
$223$	−15.9419	−	15.9419i	−1.06755	−	1.06755i	−0.997547	−	0.0700048i	$-0.977699\pi$
$223$	−15.9419	−	15.9419i	−1.06755	−	1.06755i	−0.0700048	−	0.997547i	$-0.522301\pi$
$224$	−5.11589	+	0.333463i	−0.341820	+	0.0222804i
$225$	40.3940	+	8.45062i	2.69294	+	0.563374i
$226$	−1.22128	+	0.209764i	−0.0812386	+	0.0139533i
$227$	−18.9290	+	7.84063i	−1.25636	+	0.520401i	−0.908790	−	0.417253i	$-0.862993\pi$
$227$	−18.9290	+	7.84063i	−1.25636	+	0.520401i	−0.347569	+	0.937654i	$0.612993\pi$
$228$	3.92577	+	11.0911i	0.259990	+	0.734527i
$229$	−23.0497	+	9.54752i	−1.52317	+	0.630918i	−0.978224	−	0.207553i	$-0.933450\pi$
$229$	−23.0497	+	9.54752i	−1.52317	+	0.630918i	−0.544946	+	0.838471i	$0.683450\pi$
$230$	−4.48621	+	2.22091i	−0.295812	+	0.146442i
$231$	−2.20457	−	2.20457i	−0.145050	−	0.145050i
$232$	10.7358	−	13.6123i	0.704841	−	0.893689i
$233$	13.5423			0.887185			0.443593	−	0.896229i	$-0.353704\pi$
$233$	13.5423			0.887185			0.443593	+	0.896229i	$0.353704\pi$
$234$	41.2126	−	25.9991i	2.69415	−	1.69961i
$235$	10.4166	−	3.10373i	0.679506	−	0.202465i
$236$	16.6809	−	15.0152i	1.08584	−	0.977408i
$237$	5.02083	−	2.07969i	0.326138	−	0.135091i
$238$	3.50085	−	0.601296i	0.226926	−	0.0389762i
$239$		−	18.1767i		−	1.17575i	−0.808950	−	0.587877i	$-0.799964\pi$
$239$		−	18.1767i		−	1.17575i	0.808950	−	0.587877i	$-0.200036\pi$
$240$	−25.1427	+	16.3750i	−1.62296	+	1.05700i
$241$			3.95583i			0.254818i	0.991850	+	0.127409i	$0.0406660\pi$
$241$			3.95583i			0.254818i	−0.991850	+	0.127409i	$0.959334\pi$
$242$	−2.38161	−	13.8661i	−0.153096	−	0.891348i
$243$	57.6513	−	23.8800i	3.69833	−	1.53190i
$244$	−0.141223	+	2.68729i	−0.00904086	+	0.172036i
$245$	6.57287	−	12.1522i	0.419925	−	0.776374i
$246$	2.34603	+	3.71883i	0.149578	+	0.237104i
$247$	7.32056			0.465796
$248$	−3.20774	+	11.3644i	−0.203692	+	0.721639i
$249$	−18.4469	−	18.4469i	−1.16902	−	1.16902i
$250$	−8.01973	+	13.6266i	−0.507212	+	0.861821i
$251$	9.99284	−	4.13917i	0.630743	−	0.261262i	−0.0443259	−	0.999017i	$-0.514114\pi$
$251$	9.99284	−	4.13917i	0.630743	−	0.261262i	0.675069	+	0.737755i	$0.264114\pi$
$252$	−6.44260	+	13.5022i	−0.405846	+	0.850558i
$253$	1.49975	−	0.621215i	0.0942882	−	0.0390555i
$254$	−1.38456	−	8.06116i	−0.0868753	−	0.505802i
$255$	16.1352	−	13.1090i	1.01043	−	0.820915i
$256$	3.33560	−	15.6484i	0.208475	−	0.978028i
$257$	−6.79396	−	6.79396i	−0.423795	−	0.423795i	0.462713	−	0.886508i	$-0.346876\pi$
$257$	−6.79396	−	6.79396i	−0.423795	−	0.423795i	−0.886508	+	0.462713i	$0.846876\pi$
$258$	−25.8739	−	18.2887i	−1.61084	−	1.13860i
$259$	−3.19335	−	1.32273i	−0.198425	−	0.0821903i
$260$	4.38480	+	18.1472i	0.271934	+	1.12544i
$261$	−19.3599	−	46.7390i	−1.19835	−	2.89307i
$262$	12.2988	+	19.4956i	0.759824	+	1.20444i
$263$	23.6751			1.45987			0.729934	−	0.683517i	$-0.239551\pi$
$263$	23.6751			1.45987			0.729934	+	0.683517i	$0.239551\pi$
$264$	8.49050	−	4.75250i	0.522554	−	0.292496i
$265$	−9.30004	−	11.4470i	−0.571297	−	0.703183i
$266$	−1.90091	+	1.19919i	−0.116552	+	0.0735272i
$267$	−0.877014	+	2.11730i	−0.0536724	+	0.129577i
$268$	−14.8466	−	16.4936i	−0.906900	−	1.00751i
$269$	18.3200	+	7.58841i	1.11699	+	0.462674i	0.863341	−	0.504622i	$-0.168368\pi$
$269$	18.3200	+	7.58841i	1.11699	+	0.462674i	0.253653	+	0.967295i	$0.418368\pi$
$270$	3.73035	+	55.6082i	0.227022	+	3.38421i
$271$	−5.20237			−0.316021			−0.158011	−	0.987437i	$-0.550508\pi$
$271$	−5.20237			−0.316021			−0.158011	+	0.987437i	$0.550508\pi$
$272$	−1.16195	+	11.0247i	−0.0704536	+	0.668469i
$273$	8.97461	+	8.97461i	0.543168	+	0.543168i
$274$	−15.9205	−	11.2532i	−0.961794	−	0.679833i
$275$	2.89060	−	4.23490i	0.174310	−	0.255374i
$276$	−7.10554	−	7.89378i	−0.427703	−	0.475150i
$277$	−7.66078	−	3.17320i	−0.460292	−	0.190659i	0.140474	−	0.990084i	$-0.455137\pi$
$277$	−7.66078	−	3.17320i	−0.460292	−	0.190659i	−0.600765	+	0.799425i	$0.705137\pi$
$278$	1.91391	−	8.45542i	0.114788	−	0.507122i
$279$	24.3658	+	24.3658i	1.45874	+	1.45874i
$280$	−4.11131	−	3.99394i	−0.245697	−	0.238684i
$281$	5.30131	−	5.30131i	0.316250	−	0.316250i	−0.531075	−	0.847325i	$-0.678212\pi$
$281$	5.30131	−	5.30131i	0.316250	−	0.316250i	0.847325	+	0.531075i	$0.178212\pi$
$282$	12.3042	+	19.5041i	0.732704	+	1.16145i
$283$	3.50116	−	8.45255i	0.208122	−	0.502452i	−0.785005	−	0.619489i	$-0.787340\pi$
$283$	3.50116	−	8.45255i	0.208122	−	0.502452i	0.993128	+	0.117037i	$0.0373397\pi$
$284$	6.62217	−	13.8785i	0.392954	−	0.823539i
$285$	−6.25804	+	11.5701i	−0.370694	+	0.685354i
$286$	−1.02484	−	5.96681i	−0.0606003	−	0.352825i
$287$	−0.593944	+	0.593944i	−0.0350594	+	0.0350594i
$288$	−35.0923	−	30.7975i	−2.06783	−	1.81476i
$289$			9.31915i			0.548185i
$290$	19.3393	−	1.29733i	1.13564	−	0.0761819i
$291$	−4.79244	+	11.5700i	−0.280938	+	0.678244i
$292$	−3.48064	−	9.83354i	−0.203689	−	0.575464i
$293$	0.973169	+	0.403100i	0.0568532	+	0.0235493i	0.410929	−	0.911667i	$-0.365204\pi$
$293$	0.973169	+	0.403100i	0.0568532	+	0.0235493i	−0.354076	+	0.935217i	$0.615204\pi$
$294$	28.5894	+	6.47129i	1.66737	+	0.377414i
$295$	24.9593	+	2.58284i	1.45319	+	0.150379i
$296$	6.68013	−	8.46993i	0.388274	−	0.492305i
$297$		−	18.0733i		−	1.04872i
$298$	0.424455	+	0.0960764i	0.0245880	+	0.00556556i
$299$	−6.10533	+	2.52891i	−0.353080	+	0.146251i
$300$	−32.4299	−	8.58312i	−1.87234	−	0.495547i
$301$	2.31631	−	5.59207i	0.133510	−	0.322322i
$302$	−0.847898	−	4.93660i	−0.0487910	−	0.284070i
$303$	−30.2147	+	30.2147i	−1.73579	+	1.73579i
$304$	−1.99025	−	6.72609i	−0.114149	−	0.385768i
$305$	−2.33510	+	1.89714i	−0.133707	+	0.108630i
$306$	26.4167	+	18.6723i	1.51014	+	1.06742i
$307$	−3.83681	−	9.26288i	−0.218978	−	0.528661i	0.775769	−	0.631017i	$-0.217362\pi$
$307$	−3.83681	−	9.26288i	−0.218978	−	0.528661i	−0.994748	+	0.102356i	$0.967362\pi$
$308$	1.24355	+	1.38150i	0.0708578	+	0.0787184i
$309$	3.38866	+	8.18095i	0.192774	+	0.465398i
$310$	−11.8317	+	5.85733i	−0.671998	+	0.332674i
$311$	−16.6804	+	16.6804i	−0.945856	+	0.945856i	−0.998608	−	0.0527517i	$-0.983201\pi$
$311$	−16.6804	+	16.6804i	−0.945856	+	0.945856i	0.0527517	+	0.998608i	$0.483201\pi$
$312$	−34.5641	+	19.3470i	−1.95680	+	1.09531i
$313$			18.8189i			1.06371i	0.846836	+	0.531854i	$0.178504\pi$
$313$			18.8189i			1.06371i	−0.846836	+	0.531854i	$0.821496\pi$
$314$	−31.9878	−	7.24052i	−1.80518	−	0.408606i
$315$	−16.0299	+	4.77627i	−0.903183	+	0.269112i
$316$	−3.05429	+	1.08109i	−0.171817	+	0.0608159i
$317$	3.54343	+	8.55459i	0.199019	+	0.480474i	0.991608	−	0.129282i	$-0.0412674\pi$
$317$	3.54343	+	8.55459i	0.199019	+	0.480474i	−0.792589	+	0.609756i	$0.791267\pi$
$318$	18.0618	−	25.5529i	1.01285	−	1.43294i
$319$	−6.28549			−0.351920
$320$	15.4814	−	8.96243i	0.865439	−	0.501015i
$321$	−44.7914			−2.50001
$322$	1.17109	−	1.65680i	0.0652621	−	0.0923296i
$323$	1.85983	+	4.49002i	0.103484	+	0.249832i
$324$	−64.7864	+	22.9316i	−3.59925	+	1.27398i
$325$	−11.7674	+	17.2399i	−0.652736	+	0.956296i
$326$	1.61123	+	0.364707i	0.0892380	+	0.0201993i
$327$		−	53.3782i		−	2.95182i
$328$	−1.28039	−	2.28746i	−0.0706978	−	0.126304i
$329$	−3.11504	+	3.11504i	−0.171738	+	0.171738i
$330$	10.3066	+	3.48102i	0.567360	+	0.191624i
$331$	2.48736	+	6.00502i	0.136718	+	0.330066i	0.977379	−	0.211496i	$-0.0678334\pi$
$331$	2.48736	+	6.00502i	0.136718	+	0.330066i	−0.840661	+	0.541561i	$0.817833\pi$
$332$	10.4055	+	11.5598i	0.571074	+	0.634426i
$333$	−12.0463	−	29.0823i	−0.660132	−	1.59370i
$334$	−1.54387	−	1.09127i	−0.0844769	−	0.0597115i
$335$	2.55384	−	24.6790i	0.139531	−	1.34836i
$336$	5.80588	−	10.6858i	0.316737	−	0.582956i
$337$	18.5988	−	18.5988i	1.01314	−	1.01314i	0.0132301	−	0.999912i	$-0.495789\pi$
$337$	18.5988	−	18.5988i	1.01314	−	1.01314i	0.999912	−	0.0132301i	$-0.00421140\pi$
$338$	1.05989	+	6.17088i	0.0576506	+	0.335652i
$339$	1.12487	−	2.71568i	0.0610946	−	0.147495i
$340$	−10.0165	+	7.29978i	−0.543221	+	0.395886i
$341$	3.95537	−	1.63837i	0.214195	−	0.0887226i
$342$	−19.9638	−	4.51885i	−1.07952	−	0.244351i
$343$			11.9437i			0.644897i
$344$	14.8322	+	11.6980i	0.799700	+	0.630713i
$345$	1.22226	−	11.8113i	0.0658042	−	0.635899i
$346$	−22.7250	−	5.14386i	−1.22170	−	0.276535i
$347$	7.77311	+	3.21973i	0.417283	+	0.172844i	0.581439	−	0.813590i	$-0.302490\pi$
$347$	7.77311	+	3.21973i	0.417283	+	0.172844i	−0.164156	+	0.986434i	$0.552490\pi$
$348$	13.7218	+	38.7669i	0.735566	+	2.07812i
$349$	−6.91854	+	16.7028i	−0.370341	+	0.894082i	0.623352	+	0.781942i	$0.285771\pi$
$349$	−6.91854	+	16.7028i	−0.370341	+	0.894082i	−0.993692	+	0.112140i	$0.964229\pi$
$350$	0.231503	−	6.40425i	0.0123744	−	0.342322i
$351$			73.5749i			3.92714i
$352$	−5.20364	+	2.56382i	−0.277355	+	0.136652i
$353$	16.1883	−	16.1883i	0.861617	−	0.861617i	−0.129909	−	0.991526i	$-0.541468\pi$
$353$	16.1883	−	16.1883i	0.861617	−	0.861617i	0.991526	+	0.129909i	$0.0414684\pi$
$354$	9.01208	+	52.4699i	0.478987	+	2.78874i
$355$	16.4767	−	4.90939i	0.874492	−	0.260563i
$356$	0.588389	−	1.23313i	0.0311846	−	0.0653556i
$357$	−3.22447	+	7.78457i	−0.170657	+	0.412003i
$358$	6.27542	+	9.94752i	0.331666	+	0.525743i
$359$	−4.49159	+	4.49159i	−0.237057	+	0.237057i	−0.815630	−	0.578573i	$-0.803610\pi$
$359$	−4.49159	+	4.49159i	−0.237057	+	0.237057i	0.578573	+	0.815630i	$0.303610\pi$
$360$	−0.755769	−	52.1955i	−0.0398325	−	2.75095i
$361$	11.2606	+	11.2606i	0.592664	+	0.592664i
$362$	1.54088	−	6.80745i	0.0809871	−	0.357792i
$363$	30.8331	+	12.7715i	1.61832	+	0.670328i
$364$	−5.06237	−	5.62397i	−0.265341	−	0.294776i
$365$	5.54847	−	10.2582i	0.290420	−	0.536940i
$366$	−5.21260	−	3.68447i	−0.272467	−	0.192590i
$367$	4.32797	+	4.32797i	0.225918	+	0.225918i	0.810985	−	0.585067i	$-0.198932\pi$
$367$	4.32797	+	4.32797i	0.225918	+	0.225918i	−0.585067	+	0.810985i	$0.698932\pi$
$368$	3.98341	+	4.92200i	0.207650	+	0.256577i
$369$	−7.64966			−0.398226
$370$	12.0334	−	0.807236i	0.625588	−	0.0419662i
$371$	5.52269	+	2.28757i	0.286724	+	0.118765i
$372$	−18.7398	−	20.8187i	−0.971616	−	1.07940i
$373$	0.872108	−	2.10545i	0.0451560	−	0.109016i	−0.899692	−	0.436525i	$-0.856209\pi$
$373$	0.872108	−	2.10545i	0.0451560	−	0.109016i	0.944848	+	0.327509i	$0.106209\pi$
$374$	3.39934	−	2.14448i	0.175776	−	0.110889i
$375$	−17.1881	−	33.3359i	−0.887591	−	1.72146i
$376$	−6.71524	−	11.9970i	−0.346312	−	0.618699i
$377$	25.5877			1.31783
$378$	−12.0524	−	19.1049i	−0.619909	−	0.982652i
$379$	−12.3034	−	29.7030i	−0.631982	−	1.52574i	−0.837128	−	0.547008i	$-0.815767\pi$
$379$	−12.3034	−	29.7030i	−0.631982	−	1.52574i	0.205146	−	0.978731i	$-0.434233\pi$
$380$	4.08782	−	6.69264i	0.209701	−	0.343325i
$381$	17.9250	+	7.42478i	0.918326	+	0.380383i
$382$	−6.42052	−	4.53827i	−0.328502	−	0.232198i
$383$	−16.7729	−	16.7729i	−0.857057	−	0.857057i	0.133933	−	0.990990i	$-0.457239\pi$
$383$	−16.7729	−	16.7729i	−0.857057	−	0.857057i	−0.990990	+	0.133933i	$0.957239\pi$
$384$	27.1729	+	26.4973i	1.38666	+	1.35219i
$385$	−0.213909	+	2.06711i	−0.0109018	+	0.105350i
$386$	4.94526	+	28.7921i	0.251707	+	1.46548i
$387$	50.9278	−	21.0950i	2.58880	−	1.07232i
$388$	3.21525	−	6.73841i	0.163230	−	0.342091i
$389$	22.8738	−	9.47462i	1.15975	−	0.480382i	0.281955	−	0.959428i	$-0.409017\pi$
$389$	22.8738	−	9.47462i	1.15975	−	0.480382i	0.877790	+	0.479045i	$0.159017\pi$
$390$	−41.9572	−	14.1709i	−2.12459	−	0.717571i
$391$	−3.10218	−	3.10218i	−0.156884	−	0.156884i
$392$	−16.8187	−	4.74728i	−0.849472	−	0.239774i
$393$	−54.6787			−2.75818
$394$	−14.2075	−	22.5211i	−0.715764	−	1.13460i
$395$	−3.18620	−	1.72335i	−0.160315	−	0.0867113i
$396$	−0.888374	+	16.9046i	−0.0446425	+	0.849488i
$397$	−15.3133	+	6.34300i	−0.768555	+	0.318346i	−0.732287	−	0.680996i	$-0.761547\pi$
$397$	−15.3133	+	6.34300i	−0.768555	+	0.318346i	−0.0362680	+	0.999342i	$0.511547\pi$
$398$	4.12879	+	24.0385i	0.206957	+	1.20494i
$399$		−	5.33142i		−	0.266905i
$400$	19.0391	+	6.12475i	0.951955	+	0.306237i
$401$			12.2631i			0.612389i	0.951969	+	0.306195i	$0.0990558\pi$
$401$			12.2631i			0.612389i	−0.951969	+	0.306195i	$0.900944\pi$
$402$	51.8806	−	8.91087i	2.58757	−	0.444434i
$403$	−16.1019	+	6.66964i	−0.802095	+	0.332238i
$404$	18.9341	−	17.0434i	0.942009	−	0.847943i
$405$	−67.5844	−	36.5550i	−3.35830	−	1.81643i
$406$	−6.64427	+	4.19155i	−0.329749	+	0.208023i
$407$	−3.91101			−0.193861
$408$	−20.6475	−	16.2844i	−1.02221	−	0.806200i
$409$	−15.5820	−	15.5820i	−0.770479	−	0.770479i	0.207711	−	0.978190i	$-0.433399\pi$
$409$	−15.5820	−	15.5820i	−0.770479	−	0.770479i	−0.978190	+	0.207711i	$0.933399\pi$
$410$	0.937836	−	2.77675i	0.0463164	−	0.137134i
$411$	42.7264	−	17.6978i	2.10754	−	0.872970i
$412$	−1.76153	−	4.97667i	−0.0867842	−	0.245183i
$413$	−9.39600	+	3.89195i	−0.462347	+	0.191510i
$414$	18.2108	−	3.12783i	0.895011	−	0.153725i
$415$	−1.78989	+	17.2967i	−0.0878625	+	0.849059i
$416$	21.1836	−	10.4371i	1.03861	−	0.511720i
$417$	14.5413	+	14.5413i	0.712090	+	0.712090i
$418$	−1.46790	+	2.07672i	−0.0717975	+	0.101576i
$419$	27.6906	+	11.4698i	1.35278	+	0.560338i	0.937064	−	0.349158i	$-0.113532\pi$
$419$	27.6906	+	11.4698i	1.35278	+	0.560338i	0.415712	+	0.909496i	$0.363532\pi$
$420$	13.2163	−	3.19337i	0.644887	−	0.155820i
$421$	10.5101	+	25.3736i	0.512231	+	1.23663i	0.942582	+	0.333973i	$0.108390\pi$
$421$	10.5101	+	25.3736i	0.512231	+	1.23663i	−0.430352	+	0.902661i	$0.641610\pi$
$422$	−27.5399	+	17.3736i	−1.34062	+	0.845733i
$423$	−40.1200			−1.95070
$424$	−11.5529	+	14.6482i	−0.561056	+	0.711380i
$425$	−13.5635	−	2.83755i	−0.657928	−	0.137642i
$426$	19.4624	+	30.8509i	0.942955	+	1.49473i
$427$	0.466648	−	1.12659i	0.0225827	−	0.0545194i
$428$	26.6672	+	1.40142i	1.28901	+	0.0677403i
$429$	13.2679	+	5.49576i	0.640583	+	0.265338i
$430$	1.41360	+	21.0725i	0.0681699	+	1.01620i
$431$	11.3673			0.547542			0.273771	−	0.961795i	$-0.411729\pi$
$431$	11.3673			0.547542			0.273771	+	0.961795i	$0.411729\pi$
$432$	67.6001	−	20.0029i	3.25241	−	0.962390i
$433$	16.2533	+	16.2533i	0.781085	+	0.781085i	0.980014	−	0.198929i	$-0.0637462\pi$
$433$	16.2533	+	16.2533i	0.781085	+	0.781085i	−0.198929	+	0.980014i	$0.563746\pi$
$434$	3.08858	−	4.36957i	0.148256	−	0.209746i
$435$	−21.8738	+	40.4412i	−1.04877	+	1.93901i
$436$	−1.67008	+	31.7795i	−0.0799825	+	1.52196i
$437$	2.56461	+	1.06230i	0.122682	+	0.0508165i
$438$	24.1337	+	5.46272i	1.15315	+	0.261019i
$439$	−24.2793	−	24.2793i	−1.15879	−	1.15879i	−0.984737	−	0.174052i	$-0.944314\pi$
$439$	−24.2793	−	24.2793i	−1.15879	−	1.15879i	−0.174052	−	0.984737i	$-0.555686\pi$
$440$	−6.02728	−	2.39495i	−0.287339	−	0.114175i
$441$	−36.0601	+	36.0601i	−1.71715	+	1.71715i
$442$	−13.8384	+	8.72999i	−0.658225	+	0.415243i
$443$	8.53951	−	20.6162i	0.405724	−	0.979505i	−0.580525	−	0.814242i	$-0.697153\pi$
$443$	8.53951	−	20.6162i	0.405724	−	0.979505i	0.986250	−	0.165263i	$-0.0528473\pi$
$444$	8.53808	+	24.1218i	0.405200	+	1.14477i
$445$	1.46398	−	0.436206i	0.0693992	−	0.0206782i
$446$	−31.4237	+	5.39726i	−1.48796	+	0.255568i
$447$	−0.729960	+	0.729960i	−0.0345259	+	0.0345259i
$448$	−3.79095	+	6.18027i	−0.179106	+	0.291990i
$449$		−	1.60758i		−	0.0758663i	−0.999280	−	0.0379332i	$-0.987923\pi$
$449$		−	1.60758i		−	0.0758663i	0.999280	−	0.0379332i	$-0.0120774\pi$
$450$	42.7324	−	39.7508i	2.01443	−	1.87387i
$451$	−0.363712	+	0.878079i	−0.0171265	+	0.0413471i
$452$	−0.754676	+	1.58162i	−0.0354970	+	0.0743933i
$453$	10.9772	+	4.54689i	0.515752	+	0.213631i
$454$	−6.39679	+	28.2603i	−0.300216	+	1.32632i
$455$	0.870804	−	8.41501i	0.0408239	−	0.394502i
$456$	16.0131	+	4.51990i	0.749882	+	0.211664i
$457$		−	4.76573i		−	0.222932i	−0.993768	−	0.111466i	$-0.964445\pi$
$457$		−	4.76573i		−	0.222932i	0.993768	−	0.111466i	$-0.0355545\pi$
$458$	−7.78935	+	34.4125i	−0.363973	+	1.60799i
$459$	−45.1267	+	18.6921i	−2.10633	+	0.872472i
$460$	−1.09724	+	6.99379i	−0.0511590	+	0.326087i
$461$	1.89178	−	4.56715i	0.0881088	−	0.212714i	−0.873683	−	0.486496i	$-0.838275\pi$
$461$	1.89178	−	4.56715i	0.0881088	−	0.212714i	0.961792	+	0.273782i	$0.0882748\pi$
$462$	−4.34551	+	0.746374i	−0.202172	+	0.0347244i
$463$	−12.2119	+	12.2119i	−0.567536	+	0.567536i	−0.931437	−	0.363901i	$-0.881445\pi$
$463$	−12.2119	+	12.2119i	−0.567536	+	0.567536i	0.363901	+	0.931437i	$0.381445\pi$
$464$	−6.95655	−	23.5098i	−0.322950	−	1.09141i
$465$	3.22353	−	31.1506i	0.149488	−	1.44458i
$466$	11.0544	−	15.6393i	0.512087	−	0.724475i
$467$	6.11934	+	14.7734i	0.283169	+	0.683631i	0.999906	−	0.0137126i	$-0.00436500\pi$
$467$	6.11934	+	14.7734i	0.283169	+	0.683631i	−0.716737	+	0.697344i	$0.754365\pi$
$468$	3.61649	−	68.8170i	0.167172	−	3.18107i
$469$	3.84824	+	9.29047i	0.177695	+	0.428994i
$470$	4.91864	−	14.5632i	0.226880	−	0.671748i
$471$	55.0113	−	55.0113i	2.53479	−	2.53479i
$472$	−3.72382	−	31.5207i	−0.171402	−	1.45086i
$473$		−	6.84881i		−	0.314909i
$474$	1.69672	−	7.49592i	0.0779330	−	0.344299i
$475$	8.61597	−	1.62549i	0.395328	−	0.0745827i
$476$	2.16330	−	4.53377i	0.0991548	−	0.207805i
$477$	20.8333	+	50.2960i	0.953890	+	2.30289i
$478$	−20.9913	−	14.8375i	−0.960121	−	0.678650i
$479$	−28.6370			−1.30846			−0.654229	−	0.756297i	$-0.727007\pi$
$479$	−28.6370			−1.30846			−0.654229	+	0.756297i	$0.727007\pi$
$480$	−1.61316	+	42.4027i	−0.0736302	+	1.93541i
$481$	15.9214			0.725951
$482$	4.56838	+	3.22910i	0.208084	+	0.147082i
$483$	1.84176	+	4.44639i	0.0838028	+	0.202318i
$484$	−17.9573	−	8.56838i	−0.816242	−	0.389472i
$485$	7.99989	−	2.38365i	0.363256	−	0.108236i
$486$	19.4825	−	86.0714i	0.883744	−	3.90428i
$487$			25.7000i			1.16458i	0.812982	+	0.582289i	$0.197843\pi$
$487$			25.7000i			1.16458i	−0.812982	+	0.582289i	$0.802157\pi$
$488$	2.98812	+	2.35669i	0.135266	+	0.106683i
$489$	−2.77094	+	2.77094i	−0.125306	+	0.125306i
$490$	−8.66854	−	17.5103i	−0.391605	−	0.791037i
$491$	−1.37835	−	3.32764i	−0.0622042	−	0.150174i	0.889721	−	0.456505i	$-0.150899\pi$
$491$	−1.37835	−	3.32764i	−0.0622042	−	0.150174i	−0.951925	+	0.306330i	$0.900899\pi$
$492$	6.20972	+	0.326335i	0.279956	+	0.0147123i
$493$	6.50068	+	15.6940i	0.292776	+	0.706824i
$494$	5.97570	−	8.45413i	0.268859	−	0.380369i
$495$	−14.6891	+	11.9341i	−0.660227	+	0.536398i
$496$	10.5057	+	12.9811i	0.471719	+	0.582868i
$497$	−4.92728	+	4.92728i	−0.221019	+	0.221019i
$498$	−36.3613	+	6.24532i	−1.62939	+	0.279860i
$499$	10.7030	−	25.8393i	0.479131	−	1.15673i	−0.480885	−	0.876783i	$-0.659685\pi$
$499$	10.7030	−	25.8393i	0.479131	−	1.15673i	0.960017	−	0.279942i	$-0.0903153\pi$
$500$	9.19020	+	20.3848i	0.410998	+	0.911636i
$501$	4.14333	−	1.71623i	0.185111	−	0.0766753i
$502$	3.37695	−	14.9190i	0.150721	−	0.665866i
$503$			28.9180i			1.28939i	0.764440	+	0.644695i	$0.223015\pi$
$503$			28.9180i			1.28939i	−0.764440	+	0.644695i	$0.776985\pi$
$504$	10.3339	+	18.4619i	0.460310	+	0.822359i
$505$	28.3307	+	2.93173i	1.26070	+	0.130460i
$506$	0.506819	−	2.23907i	0.0225309	−	0.0995387i
$507$	−13.7217	−	5.68372i	−0.609403	−	0.252423i
$508$	−10.4396	−	4.98129i	−0.463183	−	0.221009i
$509$	−13.3736	+	32.2866i	−0.592772	+	1.43108i	0.288042	+	0.957618i	$0.406996\pi$
$509$	−13.3736	+	32.2866i	−0.592772	+	1.43108i	−0.880815	+	0.473461i	$0.843004\pi$
$510$	−1.96784	−	29.3344i	−0.0871372	−	1.29895i
$511$			4.72692i			0.209106i
$512$	−15.3487	−	16.6258i	−0.678325	−	0.734762i
$513$	21.8538	−	21.8538i	0.964869	−	0.964869i
$514$	−13.3918	+	2.30014i	−0.590688	+	0.101455i
$515$	2.80803	−	5.19161i	0.123737	−	0.228769i
$516$	−42.2413	+	14.9516i	−1.85957	+	0.658206i
$517$	−1.90755	+	4.60524i	−0.0838940	+	0.202538i
$518$	−4.13425	+	2.60810i	−0.181648	+	0.114593i
$519$	39.0815	−	39.0815i	1.71549	−	1.71549i
$520$	24.5365	+	9.74960i	1.07600	+	0.427548i
$521$	7.57884	+	7.57884i	0.332035	+	0.332035i	0.853359	−	0.521324i	$-0.174562\pi$
$521$	7.57884	+	7.57884i	0.332035	+	0.332035i	−0.521324	+	0.853359i	$0.674562\pi$
$522$	−69.7796	−	15.7948i	−3.05417	−	0.691320i
$523$	10.4923	+	4.34605i	0.458796	+	0.190039i	0.600097	−	0.799927i	$-0.295129\pi$
$523$	10.4923	+	4.34605i	0.458796	+	0.190039i	−0.141301	+	0.989967i	$0.545129\pi$
$524$	32.5538	+	1.71077i	1.42212	+	0.0747355i
$525$	12.5555	+	8.56994i	0.547966	+	0.374023i
$526$	19.3257	−	27.3411i	0.842642	−	1.19213i
$527$	−8.18157	−	8.18157i	−0.356395	−	0.356395i
$528$	1.44230	−	13.6846i	0.0627681	−	0.595548i
$529$	20.4941			0.891050
$530$	−20.8110	+	1.39606i	−0.903974	+	0.0606411i
$531$	−85.5707	−	35.4445i	−3.71345	−	1.53816i
$532$	−0.166808	+	3.17414i	−0.00723206	+	0.137617i
$533$	1.48064	−	3.57458i	0.0641336	−	0.154832i
$534$	1.72926	+	2.74115i	0.0748324	+	0.118621i
$535$	18.8262	+	23.1723i	0.813928	+	1.00183i
$536$	−31.1667	+	3.68199i	−1.34620	+	0.159038i
$537$	−27.8996			−1.20395
$538$	23.7179	−	14.9625i	1.02255	−	0.645079i
$539$	2.42470	+	5.85373i	0.104439	+	0.252138i
$540$	67.2640	+	41.0844i	2.89458	+	1.76799i
$541$	11.7217	+	4.85528i	0.503955	+	0.208745i	0.620153	−	0.784481i	$-0.287071\pi$
$541$	11.7217	+	4.85528i	0.503955	+	0.208745i	−0.116198	+	0.993226i	$0.537071\pi$
$542$	−4.24664	+	6.00793i	−0.182409	+	0.258063i
$543$	11.7072	+	11.7072i	0.502403	+	0.502403i
$544$	11.7833	+	10.3412i	0.505206	+	0.443375i
$545$	−27.6146	+	22.4353i	−1.18288	+	0.961023i
$546$	17.6902	−	3.03842i	0.757070	−	0.130032i
$547$	−29.6855	+	12.2962i	−1.26926	+	0.525746i	−0.912740	−	0.408541i	$-0.866038\pi$
$547$	−29.6855	+	12.2962i	−1.26926	+	0.525746i	−0.356522	+	0.934287i	$0.616038\pi$
$548$	−25.9915	+	9.19987i	−1.11030	+	0.392999i
$549$	10.2600	−	4.24983i	0.437886	−	0.181378i
$550$	−2.53109	−	6.79510i	−0.107926	−	0.289744i
$551$	−7.60026	−	7.60026i	−0.323782	−	0.323782i
$552$	−14.9163	+	1.76219i	−0.634879	+	0.0750038i
$553$	1.46818			0.0624333
$554$	−9.91798	+	6.25678i	−0.421374	+	0.265825i
$555$	−13.6105	+	25.1636i	−0.577733	+	1.06814i
$556$	−8.20241	−	9.11234i	−0.347860	−	0.386449i
$557$	29.9952	−	12.4244i	1.27094	−	0.526440i	0.357689	−	0.933841i	$-0.383565\pi$
$557$	29.9952	−	12.4244i	1.27094	−	0.526440i	0.913250	+	0.407400i	$0.133565\pi$
$558$	48.0283	−	8.24922i	2.03320	−	0.349217i
$559$			27.8809i			1.17923i
$560$	−7.96841	+	1.48771i	−0.336727	+	0.0628673i
$561$			9.53404i			0.402528i
$562$	−1.79480	−	10.4496i	−0.0757089	−	0.440790i
$563$	−0.586068	+	0.242757i	−0.0246998	+	0.0102310i	−0.394999	−	0.918681i	$-0.629255\pi$
$563$	−0.586068	+	0.242757i	−0.0246998	+	0.0102310i	0.370299	+	0.928912i	$0.379255\pi$
$564$	32.5680	+	1.71152i	1.37136	+	0.0720680i
$565$	−1.87772	+	0.559484i	−0.0789961	+	0.0235377i
$566$	−6.90344	−	10.9430i	−0.290173	−	0.459970i
$567$	31.1424			1.30786
$568$	−10.6220	−	18.9765i	−0.445688	−	0.796236i
$569$	0.0516248	+	0.0516248i	0.00216422	+	0.00216422i	0.708188	−	0.706024i	$-0.249513\pi$
$569$	0.0516248	+	0.0516248i	0.00216422	+	0.00216422i	−0.706024	+	0.708188i	$0.749513\pi$
$570$	8.25333	+	16.6716i	0.345694	+	0.698298i
$571$	−23.4324	+	9.70604i	−0.980617	+	0.406185i	−0.814654	−	0.579947i	$-0.803073\pi$
$571$	−23.4324	+	9.70604i	−0.980617	+	0.406185i	−0.165963	+	0.986132i	$0.553073\pi$
$572$	−7.72732	−	3.68711i	−0.323096	−	0.154166i
$573$	17.2309	−	7.13729i	0.719833	−	0.298164i
$574$	0.201084	+	1.17074i	0.00839308	+	0.0488659i
$575$	−6.62416	+	4.33207i	−0.276247	+	0.180660i
$576$	−64.2119	+	15.3866i	−2.67550	+	0.641107i
$577$	0.380039	+	0.380039i	0.0158212	+	0.0158212i	0.714973	−	0.699152i	$-0.246439\pi$
$577$	0.380039	+	0.380039i	0.0158212	+	0.0158212i	−0.699152	+	0.714973i	$0.746439\pi$
$578$	10.7622	+	7.60713i	0.447648	+	0.316415i
$579$	−64.0229	−	26.5192i	−2.66070	−	1.10210i
$580$	14.2882	−	23.3929i	0.593286	−	0.971336i
$581$	−2.69710	−	6.51137i	−0.111894	−	0.270137i
$582$	9.44952	+	14.9790i	0.391695	+	0.620899i
$583$	6.76384			0.280130
$584$	−14.1974	−	4.00740i	−0.587494	−	0.165828i
$585$	59.7981	−	48.5826i	2.47235	−	2.00864i
$586$	1.25991	−	0.794815i	0.0520463	−	0.0328335i
$587$	−15.6574	+	37.8003i	−0.646250	+	1.56019i	0.171858	+	0.985122i	$0.445023\pi$
$587$	−15.6574	+	37.8003i	−0.646250	+	1.56019i	−0.818108	+	0.575065i	$0.804977\pi$
$588$	30.8106	−	27.7340i	1.27061	−	1.14373i
$589$	6.76380	+	2.80166i	0.278698	+	0.115440i
$590$	23.3568	−	26.7158i	0.961585	−	1.09987i
$591$	63.1644			2.59824
$592$	−4.32856	−	14.6284i	−0.177903	−	0.601225i
$593$	−22.6847	−	22.6847i	−0.931549	−	0.931549i	0.0662543	−	0.997803i	$-0.478895\pi$
$593$	−22.6847	−	22.6847i	−0.931549	−	0.931549i	−0.997803	+	0.0662543i	$0.978895\pi$
$594$	−20.8719	−	14.7531i	−0.856386	−	0.605326i
$595$	5.38253	−	1.60378i	0.220662	−	0.0657485i
$596$	0.457431	−	0.411754i	0.0187371	−	0.0168661i
$597$	−53.4526	−	22.1408i	−2.18767	−	0.906162i
$598$	−2.06321	+	9.11504i	−0.0843710	+	0.372742i
$599$	17.4180	+	17.4180i	0.711682	+	0.711682i	0.966887	−	0.255205i	$-0.0821430\pi$
$599$	17.4180	+	17.4180i	0.711682	+	0.711682i	−0.255205	+	0.966887i	$0.582143\pi$
$600$	−36.3844	+	30.4453i	−1.48539	+	1.24292i
$601$	24.9826	−	24.9826i	1.01906	−	1.01906i	0.0192475	−	0.999815i	$-0.493873\pi$
$601$	24.9826	−	24.9826i	1.01906	−	1.01906i	0.999815	−	0.0192475i	$-0.00612705\pi$
$602$	−4.56720	−	7.23973i	−0.186145	−	0.295070i
$603$	−35.0465	+	84.6096i	−1.42720	+	3.44557i
$604$	−6.39315	−	3.05051i	−0.260134	−	0.124123i
$605$	−6.35223	−	21.3191i	−0.258255	−	0.866744i
$606$	10.2294	+	59.5573i	0.415541	+	2.41935i
$607$	12.3157	−	12.3157i	0.499877	−	0.499877i	−0.411522	−	0.911400i	$-0.635003\pi$
$607$	12.3157	−	12.3157i	0.499877	−	0.499877i	0.911400	+	0.411522i	$0.135003\pi$
$608$	−9.39222	−	3.19200i	−0.380905	−	0.129453i
$609$		−	18.6350i		−	0.755128i
$610$	0.284786	+	4.24529i	0.0115307	+	0.171887i
$611$	7.76547	−	18.7475i	0.314157	−	0.758443i
$612$	43.1273	−	15.2652i	1.74332	−	0.617059i
$613$	7.01389	+	2.90525i	0.283288	+	0.117342i	0.519803	−	0.854286i	$-0.326005\pi$
$613$	7.01389	+	2.90525i	0.283288	+	0.117342i	−0.236515	+	0.971628i	$0.576005\pi$
$614$	−13.8292	−	3.13027i	−0.558100	−	0.126327i
$615$	4.38386	+	5.39589i	0.176774	+	0.217583i
$616$	2.61052	−	0.308403i	0.105181	−	0.0124259i
$617$			10.1074i			0.406909i	0.979084	+	0.203455i	$0.0652170\pi$
$617$			10.1074i			0.406909i	−0.979084	+	0.203455i	$0.934783\pi$
$618$	12.2139	+	2.76464i	0.491314	+	0.111210i
$619$	43.7508	−	18.1222i	1.75849	−	0.728392i	0.761739	−	0.647884i	$-0.224346\pi$
$619$	43.7508	−	18.1222i	1.75849	−	0.728392i	0.996754	−	0.0805075i	$-0.0256541\pi$
$620$	−2.89381	+	18.4451i	−0.116218	+	0.740774i
$621$	−10.6765	+	25.7755i	−0.428435	+	1.03433i
$622$	5.64725	+	32.8792i	0.226434	+	1.31834i
$623$	−0.437795	+	0.437795i	−0.0175399	+	0.0175399i
$624$	−5.87147	+	55.7089i	−0.235047	+	2.23014i
$625$	−10.0216	+	22.9034i	−0.400865	+	0.916137i
$626$	21.7330	+	15.3617i	0.868624	+	0.613976i
$627$	−2.30856	−	5.57335i	−0.0921949	−	0.222578i
$628$	−34.4730	+	31.0306i	−1.37562	+	1.23826i
$629$	4.04490	+	9.76526i	0.161281	+	0.389367i
$630$	−7.56919	+	22.4109i	−0.301564	+	0.892872i
$631$	11.1608	−	11.1608i	0.444306	−	0.444306i	−0.449150	−	0.893456i	$-0.648273\pi$
$631$	11.1608	−	11.1608i	0.444306	−	0.444306i	0.893456	+	0.449150i	$0.148273\pi$
$632$	−1.24470	+	4.40972i	−0.0495115	+	0.175409i
$633$		−	77.2403i		−	3.07003i
$634$	12.7717	+	2.89091i	0.507229	+	0.114813i
$635$	−3.69291	−	12.3940i	−0.146549	−	0.491840i
$636$	−14.7661	−	41.7172i	−0.585513	−	1.65419i
$637$	−9.87071	−	23.8300i	−0.391092	−	0.944179i
$638$	−5.13078	+	7.25878i	−0.203130	+	0.287378i
$639$	−63.4606			−2.51046
$640$	2.28710	−	25.1946i	0.0904057	−	0.995905i
$641$	8.01643			0.316630			0.158315	−	0.987389i	$-0.449394\pi$
$641$	8.01643			0.316630			0.158315	+	0.987389i	$0.449394\pi$
$642$	−36.5627	+	51.7272i	−1.44302	+	2.04151i
$643$	4.41795	+	10.6659i	0.174227	+	0.420621i	0.986737	−	0.162326i	$-0.0518996\pi$
$643$	4.41795	+	10.6659i	0.174227	+	0.420621i	−0.812510	+	0.582947i	$0.801900\pi$
$644$	−0.957399	−	2.70485i	−0.0377268	−	0.106586i
$645$	−44.0656	−	23.8342i	−1.73508	−	0.938470i
$646$	6.70345	+	1.51734i	0.263744	+	0.0596990i
$647$			5.34896i			0.210289i	0.994457	+	0.105145i	$0.0335305\pi$
$647$			5.34896i			0.210289i	−0.994457	+	0.105145i	$0.966469\pi$
$648$	−26.4020	+	93.5372i	−1.03717	+	3.67449i
$649$	−8.13711	+	8.13711i	−0.319410	+	0.319410i
$650$	10.3038	+	27.6622i	0.404150	+	1.08500i
$651$	4.85737	+	11.7267i	0.190375	+	0.459607i
$652$	1.73642	−	1.56302i	0.0680033	−	0.0612127i
$653$	2.98939	+	7.21702i	0.116984	+	0.282424i	0.971516	−	0.236975i	$-0.0761559\pi$
$653$	2.98939	+	7.21702i	0.116984	+	0.282424i	−0.854532	+	0.519399i	$0.826156\pi$
$654$	−61.6436	−	43.5721i	−2.41046	−	1.70380i
$655$	22.9819	+	28.2874i	0.897979	+	1.10528i
$656$	−3.68684	−	0.388577i	−0.143947	−	0.0151714i
$657$	−30.4400	+	30.4400i	−1.18758	+	1.18758i
$658$	1.05462	+	6.14017i	0.0411134	+	0.239369i
$659$	15.6674	−	37.8244i	0.610314	−	1.47343i	−0.252343	−	0.967638i	$-0.581201\pi$
$659$	15.6674	−	37.8244i	0.610314	−	1.47343i	0.862657	−	0.505790i	$-0.168799\pi$
$660$	12.4332	−	9.06104i	0.483962	−	0.352700i
$661$	12.8189	−	5.30974i	0.498596	−	0.206525i	−0.119190	−	0.992871i	$-0.538030\pi$
$661$	12.8189	−	5.30974i	0.498596	−	0.206525i	0.617786	+	0.786346i	$0.288030\pi$
$662$	8.96529	+	2.02932i	0.348446	+	0.0788716i
$663$		−	38.8122i		−	1.50734i
$664$	21.8437	−	2.58058i	0.847698	−	0.100146i
$665$	−2.75815	+	2.24084i	−0.106956	+	0.0868962i
$666$	−43.4188	−	9.82796i	−1.68245	−	0.380826i
$667$	8.96412	+	3.71306i	0.347092	+	0.143770i
$668$	−2.52049	+	0.892145i	−0.0975208	+	0.0345181i
$669$	28.9430	−	69.8746i	1.11900	−	2.70151i
$670$	−26.4158	−	23.0945i	−1.02053	−	0.892218i
$671$		−	1.37977i		−	0.0532655i
$672$	−7.60113	−	15.4276i	−0.293220	−	0.595132i
$673$	−10.5543	+	10.5543i	−0.406839	+	0.406839i	−0.880635	−	0.473796i	$-0.842883\pi$
$673$	−10.5543	+	10.5543i	−0.406839	+	0.406839i	0.473796	+	0.880635i	$0.342883\pi$
$674$	−6.29676	−	36.6608i	−0.242542	−	1.41212i
$675$	16.3369	+	86.5942i	0.628808	+	3.33301i
$676$	7.99160	+	3.81321i	0.307369	+	0.146662i
$677$	−2.04241	+	4.93081i	−0.0784961	+	0.189506i	−0.958256	−	0.285912i	$-0.907703\pi$
$677$	−2.04241	+	4.93081i	−0.0784961	+	0.189506i	0.879760	+	0.475419i	$0.157703\pi$
$678$	−2.21797	−	3.51583i	−0.0851806	−	0.135025i
$679$	−2.39233	+	2.39233i	−0.0918092	+	0.0918092i
$680$	0.253773	+	17.5263i	0.00973174	+	0.672101i
$681$	−48.6009	−	48.6009i	−1.86239	−	1.86239i
$682$	1.33666	−	5.90523i	0.0511835	−	0.226123i
$683$	−45.2713	−	18.7520i	−1.73226	−	0.717525i	−0.999306	−	0.0372447i	$-0.988142\pi$
$683$	−45.2713	−	18.7520i	−1.73226	−	0.717525i	−0.732952	−	0.680280i	$-0.761858\pi$
$684$	−21.5148	+	19.3664i	−0.822639	+	0.740493i
$685$	−27.1140	−	14.6654i	−1.03597	−	0.560337i
$686$	13.7931	+	9.74949i	0.526623	+	0.372237i
$687$	−59.1812	−	59.1812i	−2.25790	−	2.25790i
$688$	25.6168	−	7.58001i	0.976630	−	0.288985i
$689$	−27.5350			−1.04900
$690$	−12.6425	−	11.0530i	−0.481292	−	0.420779i
$691$	−8.69376	−	3.60107i	−0.330726	−	0.136991i	0.211141	−	0.977456i	$-0.432282\pi$
$691$	−8.69376	−	3.60107i	−0.330726	−	0.136991i	−0.541867	+	0.840464i	$0.682282\pi$
$692$	−24.4905	+	22.0450i	−0.930990	+	0.838025i
$693$	2.93549	−	7.08690i	0.111510	−	0.269209i
$694$	10.0634	−	6.34852i	0.382002	−	0.240987i
$695$	1.41094	−	13.6346i	0.0535199	−	0.517190i
$696$	55.9708	+	15.7985i	2.12157	+	0.598839i
$697$	2.56861			0.0972930
$698$	13.6417	+	21.6242i	0.516345	+	0.818488i
$699$	17.3852	+	41.9716i	0.657569	+	1.58751i
$700$	−7.20696	−	5.49508i	−0.272397	−	0.207694i
$701$	−44.3758	−	18.3811i	−1.67605	−	0.694243i	−0.676926	−	0.736051i	$-0.736688\pi$
$701$	−44.3758	−	18.3811i	−1.67605	−	0.694243i	−0.999126	+	0.0418077i	$0.986688\pi$
$702$	84.9677	+	60.0584i	3.20690	+	2.26676i
$703$	−4.72909	−	4.72909i	−0.178361	−	0.178361i
$704$	−1.28686	+	8.10224i	−0.0485003	+	0.305364i
$705$	22.9919	+	28.2997i	0.865927	+	1.06583i
$706$	−5.48067	−	31.9094i	−0.206268	−	1.20093i
$707$	−10.6652	+	4.41766i	−0.401105	+	0.166143i
$708$	67.9511	+	32.4230i	2.55376	+	1.21853i
$709$	41.9278	−	17.3671i	1.57463	−	0.652234i	0.587081	−	0.809528i	$-0.300277\pi$
$709$	41.9278	−	17.3671i	1.57463	−	0.652234i	0.987552	+	0.157294i	$0.0502772\pi$
$710$	7.78016	−	23.0355i	0.291984	−	0.864508i
$711$	9.45466	+	9.45466i	0.354578	+	0.354578i
$712$	−0.943776	−	1.68609i	−0.0353695	−	0.0631888i
$713$	−6.60883			−0.247503
$714$	6.35788	+	10.0782i	0.237938	+	0.377169i
$715$	−2.73346	−	9.17393i	−0.102226	−	0.343086i
$716$	16.6104	+	0.872914i	0.620760	+	0.0326223i
$717$	56.3350	−	23.3347i	2.10387	−	0.871452i
$718$	1.52066	+	8.85354i	0.0567505	+	0.330411i
$719$		−	3.82423i		−	0.142620i	−0.997454	−	0.0713099i	$-0.977282\pi$
$719$		−	3.82423i		−	0.142620i	0.997454	−	0.0713099i	$-0.0227179\pi$
$720$	−60.8948	−	41.7339i	−2.26941	−	1.55533i
$721$			2.39225i			0.0890922i
$722$	22.1962	−	3.81236i	0.826057	−	0.141881i
$723$	−12.2603	+	5.07838i	−0.455965	+	0.188867i
$724$	−6.60375	−	7.33634i	−0.245427	−	0.272653i
$725$	30.1155	−	5.68161i	1.11846	−	0.211010i
$726$	39.9178	−	25.1822i	1.48149	−	0.934600i
$727$	−15.0951			−0.559846			−0.279923	−	0.960022i	$-0.590309\pi$
$727$	−15.0951			−0.559846			−0.279923	+	0.960022i	$0.590309\pi$
$728$	−10.6272	+	1.25548i	−0.393870	+	0.0465313i
$729$	75.1282	+	75.1282i	2.78253	+	2.78253i
$730$	−7.31752	−	14.7813i	−0.270834	−	0.547081i
$731$	−17.1006	+	7.08328i	−0.632487	+	0.261985i
$732$	−8.50999	+	3.01217i	−0.314538	+	0.111333i
$733$	43.3702	−	17.9645i	1.60191	−	0.663534i	0.610228	−	0.792226i	$-0.291078\pi$
$733$	43.3702	−	17.9645i	1.60191	−	0.663534i	0.991685	+	0.128691i	$0.0410777\pi$
$734$	8.53101	−	1.46526i	0.314885	−	0.0540839i
$735$	46.1012	+	4.77066i	1.70047	+	0.175968i
$736$	8.93577	−	0.582450i	0.329377	−	0.0214694i
$737$	8.04573	+	8.04573i	0.296368	+	0.296368i
$738$	−6.24434	+	8.83419i	−0.229857	+	0.325191i
$739$	−19.0295	−	7.88226i	−0.700010	−	0.289954i	0.00415371	−	0.999991i	$-0.498678\pi$
$739$	−19.0295	−	7.88226i	−0.700010	−	0.289954i	−0.704164	+	0.710038i	$0.748678\pi$
$740$	8.89052	−	14.5557i	0.326822	−	0.535078i
$741$	9.39792	+	22.6886i	0.345241	+	0.833486i
$742$	7.14992	−	4.51054i	0.262482	−	0.165587i
$743$	−17.8922			−0.656401			−0.328201	−	0.944608i	$-0.606442\pi$
$743$	−17.8922			−0.656401			−0.328201	+	0.944608i	$0.606442\pi$
$744$	−39.3396	+	4.64753i	−1.44226	+	0.170387i
$745$	0.684445	+	0.0708278i	0.0250761	+	0.00259493i
$746$	−1.71958	−	2.72581i	−0.0629585	−	0.0997991i
$747$	24.5629	−	59.3000i	0.898708	−	2.16967i
$748$	0.298299	−	5.67624i	0.0109069	−	0.207544i
$749$	−11.1797	−	4.63077i	−0.408496	−	0.169205i
$750$	−52.5283	−	7.36210i	−1.91806	−	0.268826i
$751$	−26.7884			−0.977522			−0.488761	−	0.872418i	$-0.662551\pi$
$751$	−26.7884			−0.977522			−0.488761	+	0.872418i	$0.662551\pi$
$752$	−19.3363	−	2.03796i	−0.705122	−	0.0743167i
$753$	25.6570	+	25.6570i	0.934994	+	0.934994i
$754$	20.8869	−	29.5498i	0.760658	−	1.07614i
$755$	−2.26151	−	7.59000i	−0.0823049	−	0.276228i
$756$	−31.9015	−	1.67650i	−1.16025	−	0.0609736i
$757$	−36.1520	−	14.9747i	−1.31397	−	0.544264i	−0.387929	−	0.921689i	$-0.626809\pi$
$757$	−36.1520	−	14.9747i	−1.31397	−	0.544264i	−0.926040	+	0.377426i	$0.876809\pi$
$758$	−44.3455	−	10.0377i	−1.61070	−	0.364586i
$759$	3.85066	+	3.85066i	0.139770	+	0.139770i
$760$	−4.39213	−	10.1839i	−0.159319	−	0.369410i
$761$	−7.36989	+	7.36989i	−0.267158	+	0.267158i	−0.827954	−	0.560796i	$-0.810495\pi$
$761$	−7.36989	+	7.36989i	−0.267158	+	0.267158i	0.560796	+	0.827954i	$0.310495\pi$
$762$	23.2065	−	14.6399i	0.840682	−	0.530346i
$763$	5.51852	−	13.3229i	0.199784	−	0.482321i
$764$	−10.4820	+	3.71017i	−0.379226	+	0.134229i
$765$	44.9899	+	24.3341i	1.62661	+	0.879802i
$766$	−33.0618	+	5.67860i	−1.19457	+	0.205176i
$767$	33.1254	−	33.1254i	1.19609	−	1.19609i
$768$	52.7813	−	9.75099i	1.90458	−	0.351858i
$769$		−	5.73423i		−	0.206782i	−0.994641	−	0.103391i	$-0.967031\pi$
$769$		−	5.73423i		−	0.206782i	0.994641	−	0.103391i	$-0.0329692\pi$
$770$	2.21258	+	1.93439i	0.0797360	+	0.0697107i
$771$	12.3346	−	29.7784i	0.444220	−	1.07244i
$772$	37.2873	+	17.7917i	1.34200	+	0.640338i
$773$	36.8844	+	15.2780i	1.32664	+	0.549513i	0.929695	−	0.368329i	$-0.120070\pi$
$773$	36.8844	+	15.2780i	1.32664	+	0.549513i	0.396946	+	0.917842i	$0.370070\pi$
$774$	17.2104	−	76.0334i	0.618613	−	2.73296i
$775$	−17.4703	+	11.4252i	−0.627551	+	0.410406i
$776$	−5.15726	−	9.21361i	−0.185135	−	0.330749i
$777$		−	11.5952i		−	0.415976i
$778$	7.72988	−	34.1497i	0.277130	−	1.22433i
$779$	−1.50154	+	0.621959i	−0.0537983	+	0.0222840i
$780$	−50.6145	+	36.8866i	−1.81229	+	1.32075i
$781$	−3.01731	+	7.28442i	−0.107968	+	0.260657i
$782$	−6.11482	+	1.05027i	−0.218666	+	0.0375574i
$783$	76.3859	−	76.3859i	2.72981	−	2.72981i
$784$	−19.2113	+	15.5478i	−0.686118	+	0.555280i
$785$	−51.5812	−	5.33773i	−1.84101	−	0.190512i
$786$	−44.6337	+	63.1456i	−1.59203	+	2.25233i
$787$	−1.55921	−	3.76428i	−0.0555800	−	0.134182i	0.893650	−	0.448764i	$-0.148136\pi$
$787$	−1.55921	−	3.76428i	−0.0555800	−	0.134182i	−0.949230	+	0.314582i	$0.898136\pi$
$788$	−37.6059	−	1.97627i	−1.33965	−	0.0704018i
$789$	30.3934	+	73.3761i	1.08203	+	2.61226i
$790$	−4.59107	+	2.27282i	−0.163343	+	0.0808633i
$791$	0.561522	−	0.561522i	0.0199654	−	0.0199654i
$792$	18.7970	+	14.8250i	0.667924	+	0.526783i
$793$			5.61692i			0.199463i
$794$	−5.17494	+	22.8623i	−0.183652	+	0.811353i
$795$	23.5385	−	43.5189i	0.834824	−	1.54346i
$796$	31.1311	+	14.8543i	1.10341	+	0.526496i
$797$	10.2363	+	24.7126i	0.362588	+	0.875365i	0.994920	+	0.100667i	$0.0320978\pi$
$797$	10.2363	+	24.7126i	0.362588	+	0.875365i	−0.632332	+	0.774697i	$0.717902\pi$
$798$	−6.15698	−	4.35199i	−0.217955	−	0.154059i
$799$	13.4715			0.476588
$800$	22.6146	−	16.9877i	0.799546	−	0.600605i
$801$	−5.63856			−0.199229
$802$	14.1620	+	10.0102i	0.500077	+	0.353474i
$803$	2.04680	+	4.94141i	0.0722300	+	0.174379i
$804$	32.0589	−	67.1880i	1.13063	−	2.36954i
$805$	1.52618	−	2.82167i	0.0537909	−	0.0994507i
$806$	−5.44143	+	24.0396i	−0.191666	+	0.846760i
$807$			66.5210i			2.34165i
$808$	−4.22682	−	35.7784i	−0.148699	−	1.25868i
$809$	14.6573	−	14.6573i	0.515322	−	0.515322i	−0.400831	−	0.916152i	$-0.631278\pi$
$809$	14.6573	−	14.6573i	0.515322	−	0.515322i	0.916152	+	0.400831i	$0.131278\pi$
$810$	−97.3839	+	48.2101i	−3.42172	+	1.69393i
$811$	11.3438	+	27.3863i	0.398333	+	0.961661i	0.988062	+	0.154060i	$0.0492348\pi$
$811$	11.3438	+	27.3863i	0.398333	+	0.961661i	−0.589728	+	0.807602i	$0.700765\pi$
$812$	−0.583047	+	11.0946i	−0.0204609	+	0.389345i
$813$	−6.67864	−	16.1237i	−0.234230	−	0.565482i
$814$	−3.19252	+	4.51662i	−0.111898	+	0.158307i
$815$	2.59816	+	0.268863i	0.0910096	+	0.00941787i
$816$	−35.6604	+	10.5519i	−1.24836	+	0.369391i
$817$	8.28140	−	8.28140i	0.289730	−	0.289730i
$818$	−30.7142	+	5.27539i	−1.07390	+	0.184450i
$819$	−11.9501	+	28.8501i	−0.417570	+	1.00810i
$820$	−2.44117	−	3.34969i	−0.0852495	−	0.116976i
$821$	−32.4192	+	13.4285i	−1.13144	+	0.468657i	−0.868269	−	0.496093i	$-0.834767\pi$
$821$	−32.4192	+	13.4285i	−1.13144	+	0.468657i	−0.263168	+	0.964750i	$0.584767\pi$
$822$	14.4388	−	63.7890i	0.503611	−	2.22490i
$823$			18.1415i			0.632373i	0.948697	+	0.316187i	$0.102403\pi$
$823$			18.1415i			0.632373i	−0.948697	+	0.316187i	$0.897597\pi$
$824$	−7.18521	−	2.02812i	−0.250309	−	0.0706527i
$825$	16.8361	+	3.52218i	0.586157	+	0.122627i
$826$	−3.17525	+	14.0279i	−0.110481	+	0.488093i
$827$	33.7217	+	13.9680i	1.17262	+	0.485714i	0.882057	−	0.471142i	$-0.156158\pi$
$827$	33.7217	+	13.9680i	1.17262	+	0.485714i	0.290561	+	0.956857i	$0.406158\pi$
$828$	11.2531	−	23.5839i	0.391072	−	0.819596i
$829$	−11.3256	+	27.3423i	−0.393353	+	0.949637i	0.595852	+	0.803094i	$0.296815\pi$
$829$	−11.3256	+	27.3423i	−0.393353	+	0.949637i	−0.989204	+	0.146543i	$0.953185\pi$
$830$	18.5139	+	16.1861i	0.642627	+	0.561829i
$831$		−	27.8167i		−	0.964950i
$832$	5.23868	−	32.9834i	0.181618	−	1.14350i
$833$	12.1083	−	12.1083i	0.419527	−	0.419527i
$834$	28.6629	−	4.92306i	0.992514	−	0.170472i
$835$	−2.62935	−	1.42216i	−0.0909923	−	0.0492159i
$836$	1.20006	+	3.39041i	0.0415048	+	0.117260i
$837$	−28.1579	+	67.9792i	−0.973279	+	2.34970i
$838$	35.8495	−	22.6157i	1.23840	−	0.781247i
$839$	−21.4869	+	21.4869i	−0.741811	+	0.741811i	−0.972926	−	0.231116i	$-0.925762\pi$
$839$	−21.4869	+	21.4869i	−0.741811	+	0.741811i	0.231116	+	0.972926i	$0.425762\pi$
$840$	7.10045	−	17.8695i	0.244989	−	0.616555i
$841$	−6.05918	−	6.05918i	−0.208937	−	0.208937i
$842$	37.8819	+	8.57467i	1.30550	+	0.295503i
$843$	23.2360	+	9.62467i	0.800291	+	0.331491i
$844$	−2.41668	+	45.9862i	−0.0831854	+	1.58291i
$845$	2.82695	+	9.48769i	0.0972500	+	0.326386i
$846$	−32.7496	+	46.3325i	−1.12595	+	1.59294i
$847$	6.37537	+	6.37537i	0.219060	+	0.219060i
$848$	7.48597	+	25.2990i	0.257069	+	0.868770i
$849$	30.6916			1.05333
$850$	−14.3487	+	13.3475i	−0.492157	+	0.457817i
$851$	5.57772	+	2.31037i	0.191202	+	0.0791984i
$852$	51.5150	+	2.70723i	1.76488	+	0.0927481i
$853$	−15.3415	+	37.0377i	−0.525283	+	1.26815i	0.409300	+	0.912400i	$0.365773\pi$
$853$	−15.3415	+	37.0377i	−0.525283	+	1.26815i	−0.934583	+	0.355746i	$0.884227\pi$
$854$	−0.920116	−	1.45853i	−0.0314857	−	0.0499098i
$855$	−32.1921	−	3.33131i	−1.10095	−	0.113928i
$856$	23.3866	−	29.6526i	0.799338	−	1.01350i
$857$	−47.3694			−1.61811			−0.809055	−	0.587733i	$-0.800020\pi$
$857$	−47.3694			−1.61811			−0.809055	+	0.587733i	$0.800020\pi$
$858$	17.1773	−	10.8363i	0.586422	−	0.369946i
$859$	5.28829	+	12.7671i	0.180434	+	0.435607i	0.988056	−	0.154094i	$-0.0492458\pi$
$859$	5.28829	+	12.7671i	0.180434	+	0.435607i	−0.807622	+	0.589700i	$0.799246\pi$
$860$	25.4894	+	15.5687i	0.869180	+	0.530890i
$861$	−2.60330	−	1.07832i	−0.0887201	−	0.0367491i
$862$	9.27898	−	13.1275i	0.316043	−	0.447123i
$863$	12.9803	+	12.9803i	0.441853	+	0.441853i	0.892634	−	0.450781i	$-0.148855\pi$
$863$	12.9803	+	12.9803i	0.441853	+	0.441853i	−0.450781	+	0.892634i	$0.648855\pi$
$864$	32.0810	−	94.3959i	1.09142	−	3.21142i
$865$	−36.6446	−	3.79207i	−1.24595	−	0.128934i
$866$	32.0375	−	5.50268i	1.08868	−	0.186989i
$867$	−28.8828	+	11.9637i	−0.980912	+	0.406307i
$868$	−2.52501	−	7.13366i	−0.0857043	−	0.242132i
$869$	1.53480	−	0.635736i	0.0520646	−	0.0215659i
$870$	28.8480	+	58.2726i	0.978038	+	1.97563i
$871$	−32.7534	−	32.7534i	−1.10981	−	1.10981i
$872$	35.3372	+	27.8700i	1.19667	+	0.943796i
$873$	−30.8119			−1.04282
$874$	3.32026	−	2.09459i	0.112309	−	0.0708506i
$875$	−0.843615	−	10.0974i	−0.0285194	−	0.341356i
$876$	26.0087	−	23.4116i	0.878752	−	0.791003i
$877$	−41.9560	+	17.3787i	−1.41675	+	0.586838i	−0.954042	−	0.299672i	$-0.903123\pi$
$877$	−41.9560	+	17.3787i	−1.41675	+	0.586838i	−0.462710	+	0.886510i	$0.653123\pi$
$878$	−47.8578	+	8.21993i	−1.61512	+	0.277409i
$879$			3.53363i			0.119186i
$880$	−7.68580	+	5.00562i	−0.259088	+	0.168739i
$881$		−	17.7034i		−	0.596441i	−0.954497	−	0.298221i	$-0.903607\pi$
$881$		−	17.7034i		−	0.596441i	0.954497	−	0.298221i	$-0.0963931\pi$
$882$	12.2084	+	71.0794i	0.411078	+	2.39337i
$883$	30.7304	−	12.7290i	1.03416	−	0.428363i	0.199948	−	0.979806i	$-0.435923\pi$
$883$	30.7304	−	12.7290i	1.03416	−	0.428363i	0.834213	+	0.551443i	$0.185923\pi$
$884$	−1.21435	+	23.1074i	−0.0408429	+	0.777187i
$885$	24.0370	+	80.6721i	0.807996	+	2.71176i
$886$	−16.8378	−	26.6906i	−0.565678	−	0.896689i
$887$	44.9270			1.50850			0.754250	−	0.656588i	$-0.228001\pi$
$887$	44.9270			1.50850			0.754250	+	0.656588i	$0.228001\pi$
$888$	34.8266	+	9.83024i	1.16870	+	0.329881i
$889$	3.70636	+	3.70636i	0.124307	+	0.124307i
$890$	0.691278	−	2.04674i	0.0231717	−	0.0686069i
$891$	32.5556	−	13.4850i	1.09065	−	0.451763i
$892$	−19.4179	+	40.6953i	−0.650159	+	1.36258i
$893$	−7.87510	+	3.26197i	−0.263530	+	0.109158i
$894$	0.247133	+	1.43885i	0.00826537	+	0.0481224i
$895$	11.7264	+	14.4335i	0.391971	+	0.482459i
$896$	4.04275	+	9.42286i	0.135059	+	0.314796i
$897$	−15.6757	−	15.6757i	−0.523396	−	0.523396i
$898$	−1.85651	−	1.31225i	−0.0619524	−	0.0437903i
$899$	23.6416	+	9.79267i	0.788492	+	0.326604i
$900$	−11.0240	−	81.7975i	−0.367468	−	2.72658i
$901$	−6.99541	−	16.8884i	−0.233051	−	0.562634i
$902$	0.717152	+	1.13680i	0.0238785	+	0.0378512i
$903$	20.3051			0.675711
$904$	1.21050	+	2.16260i	0.0402606	+	0.0719270i
$905$	1.13594	−	10.9772i	0.0377601	−	0.364894i
$906$	14.2115	−	8.96535i	0.472145	−	0.297854i
$907$	10.4809	−	25.3031i	0.348012	−	0.840176i	−0.648842	−	0.760923i	$-0.724746\pi$
$907$	10.4809	−	25.3031i	0.348012	−	0.840176i	0.996855	−	0.0792532i	$-0.0252536\pi$
$908$	27.4147	+	30.4559i	0.909787	+	1.01071i
$909$	−97.1293	−	40.2323i	−3.22158	−	1.33442i
$910$	−9.00722	−	7.87474i	−0.298587	−	0.261045i
$911$	−33.7228			−1.11729			−0.558643	−	0.829408i	$-0.688678\pi$
$911$	−33.7228			−1.11729			−0.558643	+	0.829408i	$0.688678\pi$
$912$	18.2911	−	14.8031i	0.605679	−	0.490181i
$913$	−5.63897	−	5.63897i	−0.186623	−	0.186623i
$914$	−5.50369	−	3.89022i	−0.182046	−	0.128677i
$915$	−8.87752	−	4.80167i	−0.293482	−	0.158738i
$916$	33.3828	+	37.0861i	1.10300	+	1.22536i
$917$	−13.6475	−	5.65298i	−0.450680	−	0.186678i
$918$	−15.2500	+	67.3726i	−0.503324	+	2.22363i
$919$	−33.1256	−	33.1256i	−1.09271	−	1.09271i	−0.995238	−	0.0974735i	$-0.968924\pi$
$919$	−33.1256	−	33.1256i	−1.09271	−	1.09271i	−0.0974735	−	0.995238i	$-0.531076\pi$
$920$	7.18109	+	6.97610i	0.236754	+	0.229995i
$921$	23.7828	−	23.7828i	0.783671	−	0.783671i
$922$	−3.73012	−	5.91283i	−0.122845	−	0.194729i
$923$	12.2832	−	29.6542i	0.404306	−	0.976080i
$924$	−2.68525	+	5.62766i	−0.0883383	+	0.185136i
$925$	18.7387	−	3.53525i	0.616125	−	0.116238i
$926$	4.13443	+	24.0714i	0.135866	+	0.791034i
$927$	−15.4055	+	15.4055i	−0.505981	+	0.505981i
$928$	−32.8288	−	11.1570i	−1.07766	−	0.366248i
$929$		−	32.2191i		−	1.05708i	−0.848910	−	0.528538i	$-0.822740\pi$
$929$		−	32.2191i		−	1.05708i	0.848910	−	0.528538i	$-0.177260\pi$
$930$	−33.3429	−	29.1506i	−1.09336	−	0.955886i
$931$	−4.14630	+	10.0101i	−0.135890	+	0.328067i
$932$	−9.03734	−	25.5324i	−0.296028	−	0.836340i
$933$	−73.1111	−	30.2836i	−2.39355	−	0.991441i
$934$	22.0562	+	4.99247i	0.721700	+	0.163359i
$935$	4.93232	−	4.00724i	0.161304	−	0.131051i
$936$	−76.5210	−	60.3511i	−2.50117	−	1.97264i
$937$			11.5426i			0.377080i	0.982066	+	0.188540i	$0.0603755\pi$
$937$			11.5426i			0.377080i	−0.982066	+	0.188540i	$0.939625\pi$
$938$	13.8704	+	3.13959i	0.452883	+	0.102511i
$939$	−58.3254	+	24.1592i	−1.90338	+	0.788405i
$940$	−12.8032	−	17.5680i	−0.417593	−	0.573006i
$941$	−19.3222	+	46.6478i	−0.629885	+	1.52068i	0.209881	+	0.977727i	$0.432692\pi$
$941$	−19.3222	+	46.6478i	−0.629885	+	1.52068i	−0.839765	+	0.542949i	$0.817308\pi$
$942$	−18.6245	−	108.435i	−0.606818	−	3.53300i
$943$	1.03742	−	1.03742i	0.0337831	−	0.0337831i
$944$	−39.4413	−	21.4296i	−1.28370	−	0.697474i
$945$	−22.5215	−	27.7206i	−0.732623	−	0.901752i
$946$	−7.90932	−	5.59061i	−0.257154	−	0.181766i
$947$	−1.03442	−	2.49731i	−0.0336141	−	0.0811516i	0.906181	−	0.422890i	$-0.138984\pi$
$947$	−1.03442	−	2.49731i	−0.0336141	−	0.0811516i	−0.939795	+	0.341738i	$0.888984\pi$
$948$	−7.27162	−	8.07829i	−0.236171	−	0.262371i
$949$	−8.33233	−	20.1160i	−0.270479	−	0.652994i
$950$	5.15593	−	11.2770i	0.167280	−	0.365874i
$951$	−21.9643	+	21.9643i	−0.712240	+	0.712240i
$952$	−3.46993	−	6.19916i	−0.112461	−	0.200916i
$953$			29.5188i			0.956208i	0.878303	+	0.478104i	$0.158676\pi$
$953$			29.5188i			0.956208i	−0.878303	+	0.478104i	$0.841324\pi$
$954$	75.0901	+	16.9968i	2.43113	+	0.550293i
$955$	−10.9347	−	5.91436i	−0.353839	−	0.191384i
$956$	−34.2700	+	12.1301i	−1.10837	+	0.392315i
$957$	−8.06913	−	19.4806i	−0.260838	−	0.629719i
$958$	−23.3761	+	33.0713i	−0.755247	+	1.06849i
$959$	12.4940			0.403451
$960$	47.6518	+	36.4759i	1.53796	+	1.17725i
$961$	13.5701			0.437747
$962$	12.9964	−	18.3867i	0.419022	−	0.592812i
$963$	−42.1731	−	101.815i	−1.35901	−	3.28094i
$964$	7.45824	−	2.63989i	0.240214	−	0.0850252i
$965$	13.1900	+	44.2677i	0.424601	+	1.42503i
$966$	6.63831	+	1.50260i	0.213584	+	0.0483453i
$967$			48.1906i			1.54971i	0.632141	+	0.774853i	$0.282176\pi$
$967$			48.1906i			1.54971i	−0.632141	+	0.774853i	$0.717824\pi$
$968$	−24.5536	+	13.7437i	−0.789181	+	0.441739i
$969$	−11.5283	+	11.5283i	−0.370343	+	0.370343i
$970$	3.77748	−	11.1844i	0.121288	−	0.359109i
$971$	−9.00286	−	21.7348i	−0.288916	−	0.697504i	0.711069	−	0.703123i	$-0.248212\pi$
$971$	−9.00286	−	21.7348i	−0.288916	−	0.697504i	−0.999984	+	0.00561859i	$0.998212\pi$
$972$	−83.4960	−	92.7585i	−2.67813	−	2.97523i
$973$	2.12607	+	5.13278i	0.0681586	+	0.164549i
$974$	29.6796	+	20.9787i	0.950995	+	0.672200i
$975$	−68.5381	−	14.3385i	−2.19498	−	0.459199i
$976$	5.16080	−	1.52708i	0.165193	−	0.0488806i
$977$	1.22028	−	1.22028i	0.0390403	−	0.0390403i	−0.687317	−	0.726357i	$-0.741212\pi$
$977$	1.22028	−	1.22028i	0.0390403	−	0.0390403i	0.726357	+	0.687317i	$0.241212\pi$
$978$	0.938120	+	5.46190i	0.0299978	+	0.174652i
$979$	−0.268092	+	0.647231i	−0.00856825	+	0.0206856i
$980$	−27.2978	−	4.28269i	−0.871996	−	0.136805i
$981$	121.333	−	50.2579i	3.87388	−	1.60461i
$982$	−4.96805	−	1.12453i	−0.158537	−	0.0358852i
$983$			28.8147i			0.919047i	0.888166	+	0.459524i	$0.151980\pi$
$983$			28.8147i			0.919047i	−0.888166	+	0.459524i	$0.848020\pi$
$984$	5.44580	−	6.90490i	0.173606	−	0.220120i
$985$	−26.5485	−	32.6774i	−0.845907	−	1.04119i
$986$	23.4306	+	5.30359i	0.746184	+	0.168901i
$987$	−13.6534	−	5.65544i	−0.434594	−	0.180015i
$988$	−4.88532	−	13.8020i	−0.155423	−	0.439101i
$989$	−4.04583	+	9.76750i	−0.128650	+	0.310588i
$990$	1.79147	+	26.7054i	0.0569367	+	0.848753i
$991$			13.7444i			0.436605i	0.975881	+	0.218303i	$0.0700520\pi$
$991$			13.7444i			0.436605i	−0.975881	+	0.218303i	$0.929948\pi$
$992$	23.5668	−	1.53613i	0.748248	−	0.0487722i
$993$	−15.4181	+	15.4181i	−0.489280	+	0.489280i
$994$	1.66816	+	9.71234i	0.0529110	+	0.308057i
$995$	11.0123	+	36.9590i	0.349114	+	1.17168i
$996$	−22.4690	+	47.0897i	−0.711957	+	1.49210i
$997$	7.72310	−	18.6452i	0.244593	−	0.590499i	−0.753135	−	0.657865i	$-0.771460\pi$
$997$	7.72310	−	18.6452i	0.244593	−	0.590499i	0.997728	+	0.0673660i	$0.0214595\pi$
$998$	−21.1037	−	33.4527i	−0.668025	−	1.05893i
$999$	47.5294	−	47.5294i	1.50376	−	1.50376i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.2.u.a.67.16	yes	88
4.3	odd	2		640.2.u.a.47.1		88
5.2	odd	4		800.2.bb.b.643.18		88
5.3	odd	4		160.2.ba.a.3.5	yes	88
5.4	even	2		800.2.v.b.707.7		88
20.3	even	4		640.2.ba.a.303.22		88
32.11	odd	8		160.2.ba.a.107.5	yes	88
32.21	even	8		640.2.ba.a.207.22		88
160.43	even	8	inner	160.2.u.a.43.16	✓	88
160.53	odd	8		640.2.u.a.463.1		88
160.107	even	8		800.2.v.b.43.7		88
160.139	odd	8		800.2.bb.b.107.18		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.2.u.a.43.16	✓	88	160.43	even	8	inner
160.2.u.a.67.16	yes	88	1.1	even	1	trivial
160.2.ba.a.3.5	yes	88	5.3	odd	4
160.2.ba.a.107.5	yes	88	32.11	odd	8
640.2.u.a.47.1		88	4.3	odd	2
640.2.u.a.463.1		88	160.53	odd	8
640.2.ba.a.207.22		88	32.21	even	8
640.2.ba.a.303.22		88	20.3	even	4
800.2.v.b.43.7		88	160.107	even	8
800.2.v.b.707.7		88	5.4	even	2
800.2.bb.b.107.18		88	160.139	odd	8
800.2.bb.b.643.18		88	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	160.u (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.816290 - 1.15485i) q^{2} +(1.28377 + 3.09930i) q^{3} +(-0.667342 - 1.88538i) q^{4} +(1.06380 - 1.96680i) q^{5} +(4.62714 + 1.04737i) q^{6} +0.906290i q^{7} +(-2.72207 - 0.768338i) q^{8} +(-5.83625 + 5.83625i) q^{9} +(-1.40298 - 2.83401i) q^{10} +(0.392432 + 0.947415i) q^{11} +(4.98663 - 4.48869i) q^{12} +(-1.59755 - 3.85684i) q^{13} +(1.04663 + 0.739795i) q^{14} +(7.46139 + 0.772121i) q^{15} +(-3.10931 + 2.51639i) q^{16} +(1.95970 - 1.95970i) q^{17} +(1.97590 + 11.5040i) q^{18} +(-0.671071 + 1.62011i) q^{19} +(-4.41809 - 0.693144i) q^{20} +(-2.80886 + 1.16347i) q^{21} +(1.41446 + 0.320166i) q^{22} -1.58299i q^{23} +(-1.11321 - 9.42287i) q^{24} +(-2.73664 - 4.18459i) q^{25} +(-5.75812 - 1.30337i) q^{26} +(-16.2828 - 6.74455i) q^{27} +(1.70870 - 0.604805i) q^{28} +(-2.34560 + 5.66278i) q^{29} +(6.98234 - 7.98649i) q^{30} -4.17491i q^{31} +(0.367943 + 5.64488i) q^{32} +(-2.43253 + 2.43253i) q^{33} +(-0.663470 - 3.86284i) q^{34} +(1.78249 + 0.964115i) q^{35} +(14.8983 + 7.10877i) q^{36} +(-1.45950 + 3.52354i) q^{37} +(1.32319 + 2.09746i) q^{38} +(9.90259 - 9.90259i) q^{39} +(-4.40692 + 4.53642i) q^{40} +(0.655358 + 0.655358i) q^{41} +(-0.949216 + 4.19353i) q^{42} +(-6.17029 - 2.55582i) q^{43} +(1.52435 - 1.37213i) q^{44} +(5.27013 + 17.6874i) q^{45} +(-1.82811 - 1.29218i) q^{46} +(3.43714 + 3.43714i) q^{47} +(-11.7907 - 6.40621i) q^{48} +6.17864 q^{49} +(-7.06645 - 0.255441i) q^{50} +(8.58950 + 3.55789i) q^{51} +(-6.20548 + 5.58582i) q^{52} +(2.52411 - 6.09374i) q^{53} +(-21.0804 + 13.2986i) q^{54} +(2.28085 + 0.236027i) q^{55} +(0.696336 - 2.46698i) q^{56} -5.88270 q^{57} +(4.62496 + 7.33128i) q^{58} +(4.29438 + 10.3675i) q^{59} +(-3.52356 - 14.5828i) q^{60} +(-1.24308 - 0.514899i) q^{61} +(-4.82138 - 3.40793i) q^{62} +(-5.28933 - 5.28933i) q^{63} +(6.81931 + 4.18294i) q^{64} +(-9.28513 - 0.960845i) q^{65} +(0.823549 + 4.79484i) q^{66} +(10.2511 - 4.24615i) q^{67} +(-5.00257 - 2.38699i) q^{68} +(4.90615 - 2.03219i) q^{69} +(2.56844 - 1.27151i) q^{70} +(5.43676 + 5.43676i) q^{71} +(20.3709 - 11.4025i) q^{72} +5.21568 q^{73} +(2.87778 + 4.56173i) q^{74} +(9.45607 - 13.8537i) q^{75} +(3.50235 + 0.184056i) q^{76} +(-0.858632 + 0.355657i) q^{77} +(-3.35259 - 19.5194i) q^{78} -1.61999i q^{79} +(1.64154 + 8.79235i) q^{80} -34.3625i q^{81} +(1.29180 - 0.221876i) q^{82} +(-7.18465 + 2.97598i) q^{83} +(4.06805 + 4.51933i) q^{84} +(-1.76961 - 5.93908i) q^{85} +(-7.98832 + 5.03945i) q^{86} -20.5619 q^{87} +(-0.340292 - 2.88045i) q^{88} +(0.483064 + 0.483064i) q^{89} +(24.7282 + 8.35184i) q^{90} +(3.49541 - 1.44785i) q^{91} +(-2.98453 + 1.05639i) q^{92} +(12.9393 - 5.35962i) q^{93} +(6.77507 - 1.16367i) q^{94} +(2.47255 + 3.04334i) q^{95} +(-17.0228 + 8.38709i) q^{96} +(2.63970 + 2.63970i) q^{97} +(5.04356 - 7.13538i) q^{98} +(-7.81968 - 3.23902i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} - 16 q^{8} - 16 q^{10} - 8 q^{11} - 20 q^{12} - 4 q^{13} + 16 q^{14} - 8 q^{15} - 8 q^{16} + 4 q^{18} + 16 q^{19} + 24 q^{20} - 8 q^{21} - 20 q^{22} - 32 q^{24}+ \cdots - 16 q^{98}+O(q^{100}) \) 88 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 - 8 * q^6 - 16 * q^8 - 16 * q^10 - 8 * q^11 - 20 * q^12 - 4 * q^13 + 16 * q^14 - 8 * q^15 - 8 * q^16 + 4 * q^18 + 16 * q^19 + 24 * q^20 - 8 * q^21 - 20 * q^22 - 32 * q^24 - 4 * q^25 - 8 * q^26 - 16 * q^27 + 12 * q^28 + 8 * q^30 - 24 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 8 * q^36 - 4 * q^37 - 60 * q^38 + 16 * q^40 - 8 * q^41 + 60 * q^42 - 36 * q^43 + 16 * q^44 - 4 * q^45 - 8 * q^46 - 8 * q^47 - 24 * q^48 - 40 * q^49 - 12 * q^50 + 8 * q^51 - 56 * q^52 - 4 * q^53 - 56 * q^54 - 36 * q^55 + 40 * q^56 - 8 * q^57 - 36 * q^58 + 12 * q^60 - 40 * q^61 + 40 * q^62 + 56 * q^63 + 48 * q^64 - 8 * q^65 + 72 * q^66 + 20 * q^67 + 8 * q^68 + 24 * q^69 + 60 * q^70 + 24 * q^71 + 24 * q^72 - 8 * q^73 + 8 * q^75 + 56 * q^76 + 24 * q^77 + 32 * q^78 - 8 * q^80 + 84 * q^82 - 44 * q^83 + 56 * q^84 - 4 * q^85 + 24 * q^86 - 120 * q^87 + 104 * q^88 + 148 * q^90 - 8 * q^91 + 124 * q^92 + 8 * q^93 - 32 * q^94 + 24 * q^96 - 8 * q^97 - 16 * q^98

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