LMFDB - Embedded newform 160.2.ba.a.107.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [160,2,Mod(3,160)] 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("160.3"); 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, 3, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 160 = 2^{5} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	160.ba (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			107.5
Character	$\chi$	$=$	160.107
Dual form			160.2.ba.a.3.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.15485 + 0.816290i) q^{2} +(-3.09930 - 1.28377i) q^{3} +(0.667342 - 1.88538i) q^{4} +(-2.14296 + 0.638517i) q^{5} +(4.62714 - 1.04737i) q^{6} +0.906290 q^{7} +(0.768338 + 2.72207i) q^{8} +(5.83625 + 5.83625i) q^{9} +(1.95358 - 2.48667i) q^{10} +(0.392432 - 0.947415i) q^{11} +(-4.48869 + 4.98663i) q^{12} +(3.85684 + 1.59755i) 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} +(-11.5040 - 1.97590i) q^{18} +(0.671071 + 1.62011i) q^{19} +(-0.226244 + 4.46641i) q^{20} +(-2.80886 - 1.16347i) q^{21} +(0.320166 + 1.41446i) q^{22} +1.58299 q^{23} +(1.11321 - 9.42287i) q^{24} +(4.18459 - 2.73664i) q^{25} +(-5.75812 + 1.30337i) q^{26} +(-6.74455 - 16.2828i) q^{27} +(0.604805 - 1.70870i) q^{28} +(2.34560 + 5.66278i) q^{29} +(-9.24704 + 5.19898i) q^{30} +4.17491i q^{31} +(5.64488 + 0.367943i) q^{32} +(-2.43253 + 2.43253i) q^{33} +(0.663470 - 3.86284i) q^{34} +(-1.94215 + 0.578681i) q^{35} +(14.8983 - 7.10877i) q^{36} +(3.52354 - 1.45950i) q^{37} +(-2.09746 - 1.32319i) q^{38} +(-9.90259 - 9.90259i) q^{39} +(-3.38461 - 5.34270i) q^{40} +(0.655358 - 0.655358i) q^{41} +(4.19353 - 0.949216i) q^{42} +(2.55582 + 6.17029i) q^{43} +(-1.52435 - 1.37213i) q^{44} +(-16.2334 - 8.78033i) q^{45} +(-1.82811 + 1.29218i) q^{46} +(3.43714 + 3.43714i) q^{47} +(6.40621 + 11.7907i) q^{48} -6.17864 q^{49} +(-2.59867 + 6.57624i) q^{50} +(8.58950 - 3.55789i) q^{51} +(5.58582 - 6.20548i) q^{52} +(6.09374 - 2.52411i) q^{53} +(21.0804 + 13.2986i) q^{54} +(-0.236027 + 2.28085i) q^{55} +(0.696336 + 2.46698i) q^{56} -5.88270i q^{57} +(-7.33128 - 4.62496i) q^{58} +(-4.29438 + 10.3675i) q^{59} +(6.43504 - 13.5523i) q^{60} +(-1.24308 + 0.514899i) q^{61} +(-3.40793 - 4.82138i) 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} +(-4.24615 + 10.2511i) q^{67} +(2.38699 + 5.00257i) q^{68} +(-4.90615 - 2.03219i) q^{69} +(1.77051 - 2.25364i) q^{70} +(5.43676 - 5.43676i) q^{71} +(-11.4025 + 20.3709i) q^{72} -5.21568i q^{73} +(-2.87778 + 4.56173i) q^{74} +(-16.4825 + 3.10960i) q^{75} +(3.50235 - 0.184056i) q^{76} +(0.355657 - 0.858632i) q^{77} +(19.5194 + 3.35259i) q^{78} -1.61999i q^{79} +(8.26989 + 3.40718i) q^{80} +34.3625i q^{81} +(-0.221876 + 1.29180i) q^{82} +(-2.97598 + 7.18465i) q^{83} +(-4.06805 + 4.51933i) q^{84} +(2.94827 - 5.45087i) q^{85} +(-7.98832 - 5.03945i) q^{86} -20.5619i q^{87} +(2.88045 + 0.340292i) q^{88} +(-0.483064 + 0.483064i) q^{89} +(25.9144 - 3.11124i) q^{90} +(3.49541 + 1.44785i) q^{91} +(1.05639 - 2.98453i) q^{92} +(5.35962 - 12.9393i) 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} +(7.13538 - 5.04356i) 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} - 8 q^{7} + 8 q^{8} + 8 q^{10} - 8 q^{11} - 20 q^{12} - 4 q^{13} - 16 q^{14} - 8 q^{15} - 8 q^{16} - 12 q^{18} - 16 q^{19} - 32 q^{20} - 8 q^{21} - 20 q^{22}+ \cdots + 16 q^{98}+O(q^{100}) $ 88 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 - 8 * q^6 - 8 * q^7 + 8 * q^8 + 8 * q^10 - 8 * q^11 - 20 * q^12 - 4 * q^13 - 16 * q^14 - 8 * q^15 - 8 * q^16 - 12 * q^18 - 16 * q^19 - 32 * q^20 - 8 * q^21 - 20 * q^22 - 8 * q^23 + 32 * q^24 - 4 * q^25 - 8 * q^26 + 8 * q^27 - 20 * q^28 + 64 * q^30 + 16 * q^32 - 8 * q^33 - 8 * q^34 - 48 * q^35 - 8 * q^36 - 4 * q^37 - 4 * q^38 + 16 * q^40 - 8 * q^41 - 68 * q^42 + 28 * q^43 - 16 * q^44 - 4 * q^45 - 8 * q^46 - 8 * q^47 - 88 * q^48 + 40 * q^49 + 4 * q^50 + 8 * q^51 + 48 * q^52 - 4 * q^53 + 56 * q^54 + 28 * q^55 + 40 * q^56 - 36 * q^58 + 12 * q^60 - 40 * q^61 - 32 * q^62 - 56 * q^63 - 48 * q^64 - 8 * q^65 + 72 * q^66 - 28 * q^67 + 8 * q^68 - 24 * q^69 + 4 * q^70 + 24 * q^71 + 88 * q^72 - 16 * q^75 + 56 * q^76 - 32 * q^77 + 112 * q^78 + 80 * q^80 + 68 * q^82 + 36 * q^83 - 56 * q^84 - 4 * q^85 + 24 * q^86 - 24 * q^88 - 84 * q^90 - 8 * q^91 + 92 * 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 $\left(\mathbb{Z}/160\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$101$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{8}\right)$

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 $

$2$	−1.15485	+	0.816290i	−0.816600	+	0.577204i
$2$	−1.15485	+	0.816290i	−0.816600	+	0.577204i
$3$	−3.09930	−	1.28377i	−1.78938	−	0.741185i	−0.990124	−	0.140194i	$-0.955227\pi$
$3$	−3.09930	−	1.28377i	−1.78938	−	0.741185i	−0.799256	−	0.600991i	$-0.794773\pi$
$4$	0.667342	−	1.88538i	0.333671	−	0.942690i
$5$	−2.14296	+	0.638517i	−0.958363	+	0.285554i
$5$	−2.14296	+	0.638517i	−0.958363	+	0.285554i
$6$	4.62714	−	1.04737i	1.88902	−	0.427585i
$7$	0.906290			0.342545			0.171273	−	0.985224i	$-0.445212\pi$
$7$	0.906290			0.342545			0.171273	+	0.985224i	$0.445212\pi$
$8$	0.768338	+	2.72207i	0.271648	+	0.962397i
$9$	5.83625	+	5.83625i	1.94542	+	1.94542i
$10$	1.95358	−	2.48667i	0.617776	−	0.786354i
$11$	0.392432	−	0.947415i	0.118323	−	0.285656i	−0.853611	−	0.520911i	$-0.825592\pi$
$11$	0.392432	−	0.947415i	0.118323	−	0.285656i	0.971934	+	0.235255i	$0.0755924\pi$
$12$	−4.48869	+	4.98663i	−1.29577	+	1.43952i
$13$	3.85684	+	1.59755i	1.06969	+	0.443082i	0.846883	−	0.531780i	$-0.178477\pi$
$13$	3.85684	+	1.59755i	1.06969	+	0.443082i	0.222811	+	0.974862i	$0.428477\pi$
$14$	−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	−0.903624	−	0.428327i	$-0.859103\pi$
$17$	−1.95970	+	1.95970i	−0.475297	+	0.475297i	0.428327	+	0.903624i	$0.359103\pi$
$18$	−11.5040	−	1.97590i	−2.71153	−	0.465725i
$19$	0.671071	+	1.62011i	0.153954	+	0.371678i	0.981973	−	0.189022i	$-0.0605319\pi$
$19$	0.671071	+	1.62011i	0.153954	+	0.371678i	−0.828019	+	0.560701i	$0.810532\pi$
$20$	−0.226244	+	4.46641i	−0.0505896	+	0.998720i
$21$	−2.80886	−	1.16347i	−0.612944	−	0.253890i
$22$	0.320166	+	1.41446i	0.0682596	+	0.301563i
$23$	1.58299			0.330076			0.165038	−	0.986287i	$-0.447225\pi$
$23$	1.58299			0.330076			0.165038	+	0.986287i	$0.447225\pi$
$24$	1.11321	−	9.42287i	0.227232	−	1.92343i
$25$	4.18459	−	2.73664i	0.836918	−	0.547328i
$26$	−5.75812	+	1.30337i	−1.12926	+	0.255611i
$27$	−6.74455	−	16.2828i	−1.29799	−	3.13362i
$28$	0.604805	−	1.70870i	0.114297	−	0.322914i
$29$	2.34560	+	5.66278i	0.435567	+	1.05155i	0.977463	+	0.211107i	$0.0677068\pi$
$29$	2.34560	+	5.66278i	0.435567	+	1.05155i	−0.541896	+	0.840446i	$0.682293\pi$
$30$	−9.24704	+	5.19898i	−1.68827	+	0.949199i
$31$			4.17491i			0.749836i	0.927058	+	0.374918i	$0.122329\pi$
$31$			4.17491i			0.749836i	−0.927058	+	0.374918i	$0.877671\pi$
$32$	5.64488	+	0.367943i	0.997882	+	0.0650438i
$33$	−2.43253	+	2.43253i	−0.423448	+	0.423448i
$34$	0.663470	−	3.86284i	0.113784	−	0.662471i
$35$	−1.94215	+	0.578681i	−0.328283	+	0.0978150i
$36$	14.8983	−	7.10877i	2.48305	−	1.18479i
$37$	3.52354	−	1.45950i	0.579267	−	0.239940i	−0.0737587	−	0.997276i	$-0.523499\pi$
$37$	3.52354	−	1.45950i	0.579267	−	0.239940i	0.653025	+	0.757336i	$0.273499\pi$
$38$	−2.09746	−	1.32319i	−0.340253	−	0.214649i
$39$	−9.90259	−	9.90259i	−1.58568	−	1.58568i
$40$	−3.38461	−	5.34270i	−0.535153	−	0.844755i
$41$	0.655358	−	0.655358i	0.102350	−	0.102350i	−0.654078	−	0.756427i	$-0.726943\pi$
$41$	0.655358	−	0.655358i	0.102350	−	0.102350i	0.756427	+	0.654078i	$0.226943\pi$
$42$	4.19353	−	0.949216i	0.647076	−	0.146467i
$43$	2.55582	+	6.17029i	0.389759	+	0.940961i	0.989990	+	0.141134i	$0.0450750\pi$
$43$	2.55582	+	6.17029i	0.389759	+	0.940961i	−0.600232	+	0.799826i	$0.704925\pi$
$44$	−1.52435	−	1.37213i	−0.229804	−	0.206857i
$45$	−16.2334	−	8.78033i	−2.41994	−	1.30889i
$46$	−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	$0.634646\pi$
$48$	6.40621	+	11.7907i	0.924656	+	1.70184i
$49$	−6.17864			−0.882663
$50$	−2.59867	+	6.57624i	−0.367508	+	0.930020i
$51$	8.58950	−	3.55789i	1.20277	−	0.498204i
$52$	5.58582	−	6.20548i	0.774615	−	0.860546i
$53$	6.09374	−	2.52411i	0.837040	−	0.346713i	0.0773541	−	0.997004i	$-0.475353\pi$
$53$	6.09374	−	2.52411i	0.837040	−	0.346713i	0.759686	+	0.650290i	$0.225353\pi$
$54$	21.0804	+	13.2986i	2.86868	+	1.80971i
$55$	−0.236027	+	2.28085i	−0.0318259	+	0.307550i
$56$	0.696336	+	2.46698i	0.0930519	+	0.329664i
$57$		−	5.88270i		−	0.779182i
$58$	−7.33128	−	4.62496i	−0.962645	−	0.607287i
$59$	−4.29438	+	10.3675i	−0.559080	+	1.34974i	0.351415	+	0.936220i	$0.385701\pi$
$59$	−4.29438	+	10.3675i	−0.559080	+	1.34974i	−0.910495	+	0.413519i	$0.864299\pi$
$60$	6.43504	−	13.5523i	0.830760	−	1.74959i
$61$	−1.24308	+	0.514899i	−0.159160	+	0.0659261i	−0.460841	−	0.887483i	$-0.652452\pi$
$61$	−1.24308	+	0.514899i	−0.159160	+	0.0659261i	0.301681	+	0.953409i	$0.402452\pi$
$62$	−3.40793	−	4.82138i	−0.432808	−	0.612316i
$63$	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
$67$	−4.24615	+	10.2511i	−0.518750	+	1.25237i	0.419922	+	0.907560i	$0.362057\pi$
$67$	−4.24615	+	10.2511i	−0.518750	+	1.25237i	−0.938672	+	0.344812i	$0.887943\pi$
$68$	2.38699	+	5.00257i	0.289465	+	0.606650i
$69$	−4.90615	−	2.03219i	−0.590631	−	0.244647i
$70$	1.77051	−	2.25364i	0.211616	−	0.269362i
$71$	5.43676	−	5.43676i	0.645224	−	0.645224i	−0.306611	−	0.951835i	$-0.599195\pi$
$71$	5.43676	−	5.43676i	0.645224	−	0.645224i	0.951835	+	0.306611i	$0.0991949\pi$
$72$	−11.4025	+	20.3709i	−1.34379	+	2.40073i
$73$		−	5.21568i		−	0.610449i	−0.952280	−	0.305225i	$-0.901268\pi$
$73$		−	5.21568i		−	0.610449i	0.952280	−	0.305225i	$-0.0987315\pi$
$74$	−2.87778	+	4.56173i	−0.334535	+	0.530290i
$75$	−16.4825	+	3.10960i	−1.90324	+	0.359066i
$76$	3.50235	−	0.184056i	0.401747	−	0.0211127i
$77$	0.355657	−	0.858632i	0.0405309	−	0.0978502i
$78$	19.5194	+	3.35259i	2.21013	+	0.379606i
$79$		−	1.61999i		−	0.182263i	−0.995839	−	0.0911315i	$-0.970952\pi$
$79$		−	1.61999i		−	0.182263i	0.995839	−	0.0911315i	$-0.0290484\pi$
$80$	8.26989	+	3.40718i	0.924602	+	0.380934i
$81$			34.3625i			3.81806i
$82$	−0.221876	+	1.29180i	−0.0245021	+	0.142655i
$83$	−2.97598	+	7.18465i	−0.326656	+	0.788618i	0.672180	+	0.740388i	$0.265358\pi$
$83$	−2.97598	+	7.18465i	−0.326656	+	0.788618i	−0.998836	+	0.0482299i	$0.984642\pi$
$84$	−4.06805	+	4.51933i	−0.443861	+	0.493100i
$85$	2.94827	−	5.45087i	0.319784	−	0.591230i
$86$	−7.98832	−	5.03945i	−0.861403	−	0.543418i
$87$		−	20.5619i		−	2.20446i
$88$	2.88045	+	0.340292i	0.307057	+	0.0362753i
$89$	−0.483064	+	0.483064i	−0.0512046	+	0.0512046i	−0.732245	−	0.681041i	$-0.761528\pi$
$89$	−0.483064	+	0.483064i	−0.0512046	+	0.0512046i	0.681041	+	0.732245i	$0.261528\pi$
$90$	25.9144	−	3.11124i	2.73162	−	0.327953i
$91$	3.49541	+	1.44785i	0.366419	+	0.151776i
$92$	1.05639	−	2.98453i	0.110137	−	0.311159i
$93$	5.35962	−	12.9393i	0.555767	−	1.34174i
$94$	−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	$0.689307\pi$
$98$	7.13538	−	5.04356i	0.720782	−	0.509476i
$99$	7.81968	−	3.23902i	0.785908	−	0.325534i
$100$	−2.36705	−	9.71582i	−0.236705	−	0.971582i
$101$	4.87445	−	11.7680i	0.485026	−	1.17096i	−0.472168	−	0.881509i	$-0.656528\pi$
$101$	4.87445	−	11.7680i	0.485026	−	1.17096i	0.957194	−	0.289447i	$-0.0934715\pi$
$102$	−7.01529	+	11.1203i	−0.694617	+	1.10108i
$103$		−	2.63961i		−	0.260089i	−0.991508	−	0.130044i	$-0.958488\pi$
$103$		−	2.63961i		−	0.260089i	0.991508	−	0.130044i	$-0.0415120\pi$
$104$	−1.38530	+	11.7260i	−0.135840	+	1.14983i
$105$	6.76218	+	0.699765i	0.659921	+	0.0682901i
$106$	−4.97693	+	7.88922i	−0.483402	+	0.766269i
$107$	12.3357	−	5.10959i	1.19253	−	0.493963i	0.303953	−	0.952687i	$-0.401693\pi$
$107$	12.3357	−	5.10959i	1.19253	−	0.493963i	0.888579	+	0.458724i	$0.151693\pi$
$108$	−35.2002	+	1.84985i	−3.38714	+	0.178002i
$109$	14.7005	−	6.08914i	1.40805	−	0.583233i	0.456222	−	0.889866i	$-0.349202\pi$
$109$	14.7005	−	6.08914i	1.40805	−	0.583233i	0.951828	+	0.306633i	$0.0992023\pi$
$110$	−1.58926	−	2.82670i	−0.151530	−	0.269515i
$111$	−12.7942			−1.21437
$112$	−2.81793	−	2.28057i	−0.266270	−	0.215494i
$113$	0.619584	+	0.619584i	0.0582855	+	0.0582855i	0.735649	−	0.677363i	$-0.236877\pi$
$113$	0.619584	+	0.619584i	0.0582855	+	0.0582855i	−0.677363	+	0.735649i	$0.736877\pi$
$114$	4.80198	+	6.79361i	0.449747	+	0.636280i
$115$	−3.39229	+	1.01077i	−0.316332	+	0.0942543i
$116$	12.2418	−	0.643334i	1.13662	−	0.0597321i
$117$	13.1857	+	31.8332i	1.21902	+	2.94298i
$118$	−3.50357	−	15.4784i	−0.322530	−	1.42490i
$119$	−1.77606	+	1.77606i	−0.162811	+	0.162811i
$120$	3.63110	+	20.9037i	0.331473	+	1.90824i
$121$	7.03458	+	7.03458i	0.639508	+	0.639508i
$122$	1.01526	−	1.60934i	0.0919170	−	0.145703i
$123$	−2.87248	+	1.18982i	−0.259002	+	0.107282i
$124$	7.87128	+	2.78609i	0.706862	+	0.250198i
$125$	−7.22004	+	8.53645i	−0.645780	+	0.763524i
$126$	−10.4260	−	1.79074i	−0.928822	−	0.159532i
$127$	−4.08960	+	4.08960i	−0.362894	+	0.362894i	−0.864877	−	0.501984i	$-0.832604\pi$
$127$	−4.08960	+	4.08960i	−0.362894	+	0.362894i	0.501984	+	0.864877i	$0.332604\pi$
$128$	4.46078	−	10.3972i	0.394281	−	0.918990i
$129$		−	22.4046i		−	1.97262i
$130$	11.5072	−	6.46973i	1.00925	−	0.567433i
$131$	−6.23750	−	15.0586i	−0.544973	−	1.31568i	−0.921177	−	0.389144i	$-0.872771\pi$
$131$	−6.23750	−	15.0586i	−0.544973	−	1.31568i	0.376205	−	0.926537i	$-0.377229\pi$
$132$	2.96291	+	6.20956i	0.257888	+	0.540473i
$133$	0.608184	+	1.46829i	0.0527363	+	0.127317i
$134$	−3.46422	−	15.3045i	−0.299263	−	1.32211i
$135$	24.8502	+	30.5869i	2.13876	+	2.63250i
$136$	−6.84015	−	3.82873i	−0.586538	−	0.328311i
$137$	−13.7858			−1.17780			−0.588902	−	0.808205i	$-0.700439\pi$
$137$	−13.7858			−1.17780			−0.588902	+	0.808205i	$0.700439\pi$
$138$	7.32471	−	1.65797i	0.623521	−	0.141136i
$139$	−5.66351	−	2.34590i	−0.480373	−	0.198977i	0.129339	−	0.991600i	$-0.458715\pi$
$139$	−5.66351	−	2.34590i	−0.480373	−	0.198977i	−0.609711	+	0.792624i	$0.708715\pi$
$140$	−0.205042	+	4.04786i	−0.0173292	+	0.342107i
$141$	−6.24021	−	15.0652i	−0.525521	−	1.26872i
$142$	−1.84065	+	10.7166i	−0.154464	+	0.899316i
$143$	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
$147$	19.1494	+	7.93196i	1.57942	+	0.654217i
$148$	−0.400301	−	7.61720i	−0.0329045	−	0.626130i
$149$	−0.117762	+	0.284303i	−0.00964745	+	0.0232910i	−0.928630	−	0.371008i	$-0.879012\pi$
$149$	−0.117762	+	0.284303i	−0.00964745	+	0.0232910i	0.918982	+	0.394299i	$0.129012\pi$
$150$	16.4964	−	17.0456i	1.34693	−	1.39177i
$151$	2.50445	+	2.50445i	0.203809	+	0.203809i	0.801630	−	0.597821i	$-0.203967\pi$
$151$	2.50445	+	2.50445i	0.203809	+	0.203809i	−0.597821	+	0.801630i	$0.703967\pi$
$152$	−3.89444	+	3.07149i	−0.315880	+	0.249131i
$153$	−22.8746			−1.84930
$154$	0.290163	+	1.28191i	0.0233820	+	0.103299i
$155$	−2.66575	−	8.94668i	−0.214118	−	0.718615i
$156$	−25.2785	+	12.0617i	−2.02390	+	0.965710i
$157$	−21.4257	−	8.87481i	−1.70996	−	0.708287i	−0.999992	−	0.00404938i	$-0.998711\pi$
$157$	−21.4257	−	8.87481i	−1.70996	−	0.708287i	−0.709964	−	0.704238i	$-0.751289\pi$
$158$	1.32238	+	1.87084i	0.105203	+	0.148836i
$159$	−22.1267			−1.75476
$160$	−12.3317	+	2.81586i	−0.974907	+	0.222613i
$161$	1.43465			0.113066
$162$	−28.0498	−	39.6835i	−2.20380	−	3.11783i
$163$	−1.07922	−	0.447027i	−0.0845309	−	0.0350138i	0.340017	−	0.940419i	$-0.389567\pi$
$163$	−1.07922	−	0.447027i	−0.0845309	−	0.0350138i	−0.424548	+	0.905405i	$0.639567\pi$
$164$	−0.798250	−	1.67295i	−0.0623328	−	0.130635i
$165$	3.65961	−	6.76603i	0.284900	−	0.526734i
$166$	−2.42795	−	10.7264i	−0.188446	−	0.832532i
$167$	−1.33686			−0.103450			−0.0517248	−	0.998661i	$-0.516472\pi$
$167$	−1.33686			−0.103450			−0.0517248	+	0.998661i	$0.516472\pi$
$168$	1.00889	−	8.53985i	0.0778373	−	0.658863i
$169$	3.13062	+	3.13062i	0.240817	+	0.240817i
$170$	1.04469	+	8.70156i	0.0801244	+	0.667379i
$171$	−5.53882	+	13.3719i	−0.423564	+	1.02257i
$172$	13.3389	−	0.700991i	1.01708	−	0.0534501i
$173$	15.2214	+	6.30490i	1.15726	+	0.479352i	0.876962	−	0.480561i	$-0.159567\pi$
$173$	15.2214	+	6.30490i	1.15726	+	0.479352i	0.280298	+	0.959913i	$0.409567\pi$
$174$	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
$178$	0.163545	−	0.952184i	0.0122582	−	0.0713692i
$179$	3.18265	+	7.68360i	0.237883	+	0.574299i	0.997063	−	0.0765805i	$-0.0244002\pi$
$179$	3.18265	+	7.68360i	0.237883	+	0.574299i	−0.759181	+	0.650880i	$0.774400\pi$
$180$	−27.3875	+	24.7467i	−2.04134	+	1.84451i
$181$	4.55968	+	1.88868i	0.338919	+	0.140385i	0.545650	−	0.838013i	$-0.316283\pi$
$181$	4.55968	+	1.88868i	0.338919	+	0.140385i	−0.206732	+	0.978398i	$0.566283\pi$
$182$	−5.21853	+	1.18123i	−0.386823	+	0.0875584i
$183$	4.51368			0.333661
$184$	1.21627	+	4.30900i	0.0896646	+	0.317664i
$185$	−6.61891	+	5.37750i	−0.486632	+	0.395361i
$186$	4.37265	+	19.3179i	0.320619	+	1.41646i
$187$	1.08760	+	2.62570i	0.0795331	+	0.192010i
$188$	8.77406	−	4.18656i	0.639914	−	0.305336i
$189$	−6.11252	−	14.7569i	−0.444620	−	1.07341i
$190$	5.33966	+	1.49628i	0.387380	+	0.108552i
$191$			5.55963i			0.402281i	0.979562	+	0.201140i	$0.0644647\pi$
$191$			5.55963i			0.402281i	−0.979562	+	0.201140i	$0.935535\pi$
$192$	26.5050	−	4.20972i	1.91283	−	0.303811i
$193$	−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
$195$	27.5439	+	14.8979i	1.97246	+	1.06686i
$196$	−4.12327	+	11.6491i	−0.294519	+	0.832077i
$197$	−17.3956	+	7.20550i	−1.23939	+	0.513371i	−0.903523	−	0.428540i	$-0.859028\pi$
$197$	−17.3956	+	7.20550i	−1.23939	+	0.513371i	−0.335864	+	0.941910i	$0.609028\pi$
$198$	−6.38656	+	10.1237i	−0.453873	+	0.719460i
$199$	12.1953	+	12.1953i	0.864499	+	0.864499i	0.991857	−	0.127358i	$-0.0406498\pi$
$199$	12.1953	+	12.1953i	0.864499	+	0.864499i	−0.127358	+	0.991857i	$0.540650\pi$
$200$	10.6645	+	9.28808i	0.754094	+	0.656767i
$201$	26.3201	−	26.3201i	1.85648	−	1.85648i
$202$	3.97682	+	17.5692i	0.279808	+	1.23616i
$203$	2.12579	+	5.13212i	0.149202	+	0.360204i
$204$	−0.975831	−	18.5688i	−0.0683218	−	1.30007i
$205$	−0.985951	+	1.82286i	−0.0688618	+	0.127314i
$206$	2.15469	+	3.04835i	0.150124	+	0.212389i
$207$	9.23872	+	9.23872i	0.642135	+	0.642135i
$208$	−7.97203	−	14.6726i	−0.552761	−	1.01736i
$209$	1.79826			0.124388
$210$	−8.38049	+	4.71178i	−0.578309	+	0.325144i
$211$	−21.2722	+	8.81122i	−1.46444	+	0.606589i	−0.965583	−	0.260097i	$-0.916245\pi$
$211$	−21.2722	+	8.81122i	−1.46444	+	0.606589i	−0.498854	+	0.866686i	$0.666245\pi$
$212$	−0.692294	−	13.1735i	−0.0475470	−	0.904757i
$213$	−23.8297	+	9.87058i	−1.63278	+	0.676321i
$214$	−10.0749	+	15.9703i	−0.688704	+	1.09170i
$215$	−9.41686	−	11.5908i	−0.642225	−	0.790485i
$216$	39.1408	−	30.8698i	2.66319	−	2.10043i
$217$			3.78368i			0.256853i
$218$	−12.0063	+	19.0319i	−0.813169	+	1.28900i
$219$	−6.69574	+	16.1649i	−0.452456	+	1.09233i
$220$	4.14276	+	1.96711i	0.279305	+	0.132622i
$221$	−10.6890	+	4.42752i	−0.719018	+	0.297827i
$222$	14.7753	−	10.4437i	0.991653	−	0.700938i
$223$	15.9419	+	15.9419i	1.06755	+	1.06755i	0.997547	+	0.0700048i	$0.0223014\pi$
$223$	15.9419	+	15.9419i	1.06755	+	1.06755i	0.0700048	+	0.997547i	$0.477699\pi$
$224$	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
$227$	7.84063	−	18.9290i	0.520401	−	1.25636i	−0.417253	−	0.908790i	$-0.637007\pi$
$227$	7.84063	−	18.9290i	0.520401	−	1.25636i	0.937654	−	0.347569i	$-0.112993\pi$
$228$	−11.0911	−	3.92577i	−0.734527	−	0.259990i
$229$	23.0497	+	9.54752i	1.52317	+	0.630918i	0.978224	−	0.207553i	$-0.0665500\pi$
$229$	23.0497	+	9.54752i	1.52317	+	0.630918i	0.544946	+	0.838471i	$0.316550\pi$
$230$	3.09249	−	3.93637i	0.203913	−	0.259556i
$231$	−2.20457	+	2.20457i	−0.145050	+	0.145050i
$232$	−13.6123	+	10.7358i	−0.893689	+	0.704841i
$233$		−	13.5423i		−	0.887185i	−0.896229	−	0.443593i	$-0.853704\pi$
$233$		−	13.5423i		−	0.887185i	0.896229	−	0.443593i	$-0.146296\pi$
$234$	−41.2126	−	25.9991i	−2.69415	−	1.69961i
$235$	−9.56034	−	5.17099i	−0.623648	−	0.337318i
$236$	16.6809	+	15.0152i	1.08584	+	0.977408i
$237$	−2.07969	+	5.02083i	−0.135091	+	0.326138i
$238$	0.601296	−	3.50085i	0.0389762	−	0.226926i
$239$		−	18.1767i		−	1.17575i	−0.808950	−	0.587877i	$-0.799964\pi$
$239$		−	18.1767i		−	1.17575i	0.808950	−	0.587877i	$-0.200036\pi$
$240$	−21.2568	−	21.1765i	−1.37212	−	1.36694i
$241$		−	3.95583i		−	0.254818i	−0.991850	−	0.127409i	$-0.959334\pi$
$241$		−	3.95583i		−	0.254818i	0.991850	−	0.127409i	$-0.0406660\pi$
$242$	−13.8661	−	2.38161i	−0.891348	−	0.153096i
$243$	23.8800	−	57.6513i	1.53190	−	3.69833i
$244$	0.141223	+	2.68729i	0.00904086	+	0.172036i
$245$	13.2406	−	3.94517i	0.845911	−	0.252047i
$246$	2.34603	−	3.71883i	0.149578	−	0.237104i
$247$			7.32056i			0.465796i
$248$	−11.3644	+	3.20774i	−0.721639	+	0.203692i
$249$	18.4469	−	18.4469i	1.16902	−	1.16902i
$250$	1.36982	−	15.7519i	0.0866351	−	0.996240i
$251$	9.99284	+	4.13917i	0.630743	+	0.261262i	0.675069	−	0.737755i	$-0.264114\pi$
$251$	9.99284	+	4.13917i	0.630743	+	0.261262i	−0.0443259	+	0.999017i	$0.514114\pi$
$252$	13.5022	−	6.44260i	0.850558	−	0.405846i
$253$	0.621215	−	1.49975i	0.0390555	−	0.0942882i
$254$	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	$0.846876\pi$
$258$	18.2887	+	25.8739i	1.13860	+	1.61084i
$259$	3.19335	−	1.32273i	0.198425	−	0.0821903i
$260$	−8.00791	+	16.8648i	−0.496630	+	1.04591i
$261$	−19.3599	+	46.7390i	−1.19835	+	2.89307i
$262$	19.4956	+	12.2988i	1.20444	+	0.759824i
$263$		−	23.6751i		−	1.45987i	−0.683517	−	0.729934i	$-0.739551\pi$
$263$		−	23.6751i		−	1.45987i	0.683517	−	0.729934i	$-0.260449\pi$
$264$	−8.49050	−	4.75250i	−0.522554	−	0.292496i
$265$	−11.4470	+	9.30004i	−0.703183	+	0.571297i
$266$	−1.90091	−	1.19919i	−0.116552	−	0.0735272i
$267$	2.11730	−	0.877014i	0.129577	−	0.0536724i
$268$	16.4936	+	14.8466i	1.00751	+	0.906900i
$269$	−18.3200	+	7.58841i	−1.11699	+	0.462674i	−0.863341	−	0.504622i	$-0.831632\pi$
$269$	−18.3200	+	7.58841i	−1.11699	+	0.462674i	−0.253653	+	0.967295i	$0.581632\pi$
$270$	−53.6659	−	15.0383i	−3.26601	−	0.915200i
$271$	−5.20237			−0.316021			−0.158011	−	0.987437i	$-0.550508\pi$
$271$	−5.20237			−0.316021			−0.158011	+	0.987437i	$0.550508\pi$
$272$	11.0247	−	1.16195i	0.668469	−	0.0704536i
$273$	−8.97461	−	8.97461i	−0.543168	−	0.543168i
$274$	15.9205	−	11.2532i	0.961794	−	0.679833i
$275$	−0.950564	−	5.03849i	−0.0573212	−	0.303832i
$276$	−7.10554	+	7.89378i	−0.427703	+	0.475150i
$277$	−3.17320	−	7.66078i	−0.190659	−	0.460292i	0.799425	−	0.600765i	$-0.205137\pi$
$277$	−3.17320	−	7.66078i	−0.190659	−	0.460292i	−0.990084	+	0.140474i	$0.955137\pi$
$278$	8.45542	−	1.91391i	0.507122	−	0.114788i
$279$	−24.3658	+	24.3658i	−1.45874	+	1.45874i
$280$	−3.06743	−	4.84203i	−0.183314	−	0.289367i
$281$	5.30131	+	5.30131i	0.316250	+	0.316250i	0.847325	−	0.531075i	$-0.178212\pi$
$281$	5.30131	+	5.30131i	0.316250	+	0.316250i	−0.531075	+	0.847325i	$0.678212\pi$
$282$	19.5041	+	12.3042i	1.16145	+	0.732704i
$283$	8.45255	−	3.50116i	0.502452	−	0.208122i	−0.117037	−	0.993128i	$-0.537340\pi$
$283$	8.45255	−	3.50116i	0.502452	−	0.208122i	0.619489	+	0.785005i	$0.287340\pi$
$284$	−6.62217	−	13.8785i	−0.392954	−	0.823539i
$285$	3.75620	+	12.6064i	0.222498	+	0.746739i
$286$	−1.02484	+	5.96681i	−0.0606003	+	0.352825i
$287$	0.593944	−	0.593944i	0.0350594	−	0.0350594i
$288$	30.7975	+	35.0923i	1.81476	+	2.06783i
$289$			9.31915i			0.548185i
$290$	18.6638	+	5.22997i	1.09598	+	0.307114i
$291$	−4.79244	−	11.5700i	−0.280938	−	0.678244i
$292$	−9.83354	−	3.48064i	−0.575464	−	0.203689i
$293$	−0.403100	−	0.973169i	−0.0235493	−	0.0568532i	0.911667	−	0.410929i	$-0.134796\pi$
$293$	−0.403100	−	0.973169i	−0.0235493	−	0.0568532i	−0.935217	+	0.354076i	$0.884796\pi$
$294$	−28.5894	+	6.47129i	−1.66737	+	0.377414i
$295$	2.58284	−	24.9593i	0.150379	−	1.45319i
$296$	6.68013	+	8.46993i	0.388274	+	0.492305i
$297$	−18.0733			−1.04872
$298$	−0.0960764	−	0.424455i	−0.00556556	−	0.0245880i
$299$	6.10533	+	2.52891i	0.353080	+	0.146251i
$300$	−5.13670	+	33.1509i	−0.296567	+	1.91397i
$301$	2.31631	+	5.59207i	0.133510	+	0.322322i
$302$	−4.93660	−	0.847898i	−0.284070	−	0.0487910i
$303$	−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
$307$	−9.26288	−	3.83681i	−0.528661	−	0.218978i	0.102356	−	0.994748i	$-0.467362\pi$
$307$	−9.26288	−	3.83681i	−0.528661	−	0.218978i	−0.631017	+	0.775769i	$0.717362\pi$
$308$	−1.38150	−	1.24355i	−0.0787184	−	0.0708578i
$309$	−3.38866	+	8.18095i	−0.192774	+	0.465398i
$310$	10.3816	+	8.15602i	0.589636	+	0.463231i
$311$	−16.6804	−	16.6804i	−0.945856	−	0.945856i	0.0527517	−	0.998608i	$-0.483201\pi$
$311$	−16.6804	−	16.6804i	−0.945856	−	0.945856i	−0.998608	+	0.0527517i	$0.983201\pi$
$312$	19.3470	−	34.5641i	1.09531	−	1.95680i
$313$	−18.8189			−1.06371			−0.531854	−	0.846836i	$-0.678504\pi$
$313$	−18.8189			−1.06371			−0.531854	+	0.846836i	$0.678504\pi$
$314$	31.9878	−	7.24052i	1.80518	−	0.408606i
$315$	−14.7122	−	7.95752i	−0.828938	−	0.448356i
$316$	−3.05429	−	1.08109i	−0.171817	−	0.0608159i
$317$	8.55459	+	3.54343i	0.480474	+	0.199019i	0.609756	−	0.792589i	$-0.291267\pi$
$317$	8.55459	+	3.54343i	0.480474	+	0.199019i	−0.129282	+	0.991608i	$0.541267\pi$
$318$	25.5529	−	18.0618i	1.43294	−	1.01285i
$319$	6.28549			0.351920
$320$	11.9427	−	13.3181i	0.667616	−	0.744506i
$321$	−44.7914			−2.50001
$322$	−1.65680	+	1.17109i	−0.0923296	+	0.0652621i
$323$	−4.49002	−	1.85983i	−0.249832	−	0.103484i
$324$	64.7864	+	22.9316i	3.59925	+	1.27398i
$325$	20.5112	−	3.86966i	1.13776	−	0.214650i
$326$	1.61123	−	0.364707i	0.0892380	−	0.0201993i
$327$	−53.3782			−2.95182
$328$	2.28746	+	1.28039i	0.126304	+	0.0706978i
$329$	3.11504	+	3.11504i	0.171738	+	0.171738i
$330$	1.29675	+	10.8010i	0.0713839	+	0.594577i
$331$	2.48736	−	6.00502i	0.136718	−	0.330066i	−0.840661	−	0.541561i	$-0.817833\pi$
$331$	2.48736	−	6.00502i	0.136718	−	0.330066i	0.977379	+	0.211496i	$0.0678334\pi$
$332$	11.5598	+	10.4055i	0.634426	+	0.571074i
$333$	29.0823	+	12.0463i	1.59370	+	0.660132i
$334$	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	$0.504211\pi$
$337$	−18.5988	+	18.5988i	−1.01314	+	1.01314i	−0.999912	+	0.0132301i	$0.995789\pi$
$338$	−6.17088	−	1.05989i	−0.335652	−	0.0576506i
$339$	−1.12487	−	2.71568i	−0.0610946	−	0.147495i
$340$	−8.30945	−	9.19619i	−0.450643	−	0.498734i
$341$	3.95537	+	1.63837i	0.214195	+	0.0887226i
$342$	−4.51885	−	19.9638i	−0.244351	−	1.07952i
$343$	−11.9437			−0.644897
$344$	−14.8322	+	11.6980i	−0.799700	+	0.630713i
$345$	11.8113	+	1.22226i	0.635899	+	0.0658042i
$346$	−22.7250	+	5.14386i	−1.22170	+	0.276535i
$347$	3.21973	+	7.77311i	0.172844	+	0.417283i	0.986434	−	0.164156i	$-0.0524900\pi$
$347$	3.21973	+	7.77311i	0.172844	+	0.417283i	−0.813590	+	0.581439i	$0.802490\pi$
$348$	−38.7669	−	13.7218i	−2.07812	−	0.735566i
$349$	6.91854	+	16.7028i	0.370341	+	0.894082i	0.993692	+	0.112140i	$0.0357706\pi$
$349$	6.91854	+	16.7028i	0.370341	+	0.894082i	−0.623352	+	0.781942i	$0.714229\pi$
$350$	−2.35515	+	5.95998i	−0.125888	+	0.318574i
$351$		−	73.5749i		−	3.92714i
$352$	2.56382	−	5.20364i	0.136652	−	0.277355i
$353$	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
$355$	−8.17932	+	15.1222i	−0.434113	+	0.802605i
$356$	0.588389	+	1.23313i	0.0311846	+	0.0653556i
$357$	7.78457	−	3.22447i	0.412003	−	0.170657i
$358$	−9.94752	−	6.27542i	−0.525743	−	0.331666i
$359$	4.49159	+	4.49159i	0.237057	+	0.237057i	0.815630	−	0.578573i	$-0.196390\pi$
$359$	4.49159	+	4.49159i	0.237057	+	0.237057i	−0.578573	+	0.815630i	$0.696390\pi$
$360$	11.4279	−	50.9348i	0.602304	−	2.68450i
$361$	11.2606	−	11.2606i	0.592664	−	0.592664i
$362$	−6.80745	+	1.54088i	−0.357792	+	0.0809871i
$363$	−12.7715	−	30.8331i	−0.670328	−	1.61832i
$364$	5.06237	−	5.62397i	0.265341	−	0.294776i
$365$	3.33030	+	11.1770i	0.174316	+	0.585032i
$366$	−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	$0.698932\pi$
$368$	−4.92200	−	3.98341i	−0.256577	−	0.207650i
$369$	7.64966			0.398226
$370$	3.25423	−	11.6131i	0.169179	−	0.603738i
$371$	5.52269	−	2.28757i	0.286724	−	0.118765i
$372$	−20.8187	−	18.7398i	−1.07940	−	0.971616i
$373$	2.10545	−	0.872108i	0.109016	−	0.0451560i	−0.327509	−	0.944848i	$-0.606209\pi$
$373$	2.10545	−	0.872108i	0.109016	−	0.0451560i	0.436525	+	0.899692i	$0.356209\pi$
$374$	−3.39934	−	2.14448i	−0.175776	−	0.110889i
$375$	33.3359	−	17.1881i	1.72146	−	0.887591i
$376$	−6.71524	+	11.9970i	−0.346312	+	0.618699i
$377$			25.5877i			1.31783i
$378$	19.1049	+	12.0524i	0.982652	+	0.619909i
$379$	12.3034	−	29.7030i	0.631982	−	1.52574i	−0.205146	−	0.978731i	$-0.565767\pi$
$379$	12.3034	−	29.7030i	0.631982	−	1.52574i	0.837128	−	0.547008i	$-0.184233\pi$
$380$	−7.38789	+	2.63074i	−0.378991	+	0.134954i
$381$	17.9250	−	7.42478i	0.918326	−	0.380383i
$382$	−4.53827	−	6.42052i	−0.232198	−	0.328502i
$383$	16.7729	+	16.7729i	0.857057	+	0.857057i	0.990990	−	0.133933i	$-0.0427608\pi$
$383$	16.7729	+	16.7729i	0.857057	+	0.857057i	−0.133933	+	0.990990i	$0.542761\pi$
$384$	−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
$387$	−21.0950	+	50.9278i	−1.07232	+	2.58880i
$388$	6.73841	−	3.21525i	0.342091	−	0.163230i
$389$	−22.8738	−	9.47462i	−1.15975	−	0.480382i	−0.281955	−	0.959428i	$-0.590983\pi$
$389$	−22.8738	−	9.47462i	−1.15975	−	0.480382i	−0.877790	+	0.479045i	$0.840983\pi$
$390$	−43.9700	+	5.27896i	−2.22651	+	0.267310i
$391$	−3.10218	+	3.10218i	−0.156884	+	0.156884i
$392$	−4.74728	−	16.8187i	−0.239774	−	0.849472i
$393$			54.6787i			2.75818i
$394$	14.2075	−	22.5211i	0.715764	−	1.13460i
$395$	1.03439	+	3.47158i	0.0520458	+	0.174674i
$396$	−0.888374	−	16.9046i	−0.0446425	−	0.849488i
$397$	6.34300	−	15.3133i	0.318346	−	0.768555i	−0.680996	−	0.732287i	$-0.738453\pi$
$397$	6.34300	−	15.3133i	0.318346	−	0.768555i	0.999342	−	0.0362680i	$-0.0115470\pi$
$398$	−24.0385	−	4.12879i	−1.20494	−	0.206957i
$399$		−	5.33142i		−	0.266905i
$400$	−19.8976	−	2.02099i	−0.994881	−	0.101050i
$401$		−	12.2631i		−	0.612389i	−0.951969	−	0.306195i	$-0.900944\pi$
$401$		−	12.2631i		−	0.612389i	0.951969	−	0.306195i	$-0.0990558\pi$
$402$	−8.91087	+	51.8806i	−0.444434	+	2.58757i
$403$	−6.66964	+	16.1019i	−0.332238	+	0.802095i
$404$	−18.9341	−	17.0434i	−0.942009	−	0.847943i
$405$	−21.9411	−	73.6377i	−1.09026	−	3.65909i
$406$	−6.64427	−	4.19155i	−0.329749	−	0.208023i
$407$		−	3.91101i		−	0.193861i
$408$	16.2844	+	20.6475i	0.806200	+	1.02221i
$409$	15.5820	−	15.5820i	0.770479	−	0.770479i	−0.207711	−	0.978190i	$-0.566601\pi$
$409$	15.5820	−	15.5820i	0.770479	−	0.770479i	0.978190	+	0.207711i	$0.0666014\pi$
$410$	−0.349364	−	2.90995i	−0.0172538	−	0.143712i
$411$	42.7264	+	17.6978i	2.10754	+	0.872970i
$412$	−4.97667	−	1.76153i	−0.245183	−	0.0867842i
$413$	−3.89195	+	9.39600i	−0.191510	+	0.462347i
$414$	−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
$418$	−2.07672	+	1.46790i	−0.101576	+	0.0717975i
$419$	−27.6906	+	11.4698i	−1.35278	+	0.560338i	−0.937064	−	0.349158i	$-0.886468\pi$
$419$	−27.6906	+	11.4698i	−1.35278	+	0.560338i	−0.415712	+	0.909496i	$0.636468\pi$
$420$	5.83201	−	12.2823i	0.284573	−	0.599314i
$421$	10.5101	−	25.3736i	0.512231	−	1.23663i	−0.430352	−	0.902661i	$-0.641610\pi$
$421$	10.5101	−	25.3736i	0.512231	−	1.23663i	0.942582	−	0.333973i	$-0.108390\pi$
$422$	17.3736	−	27.5399i	0.845733	−	1.34062i
$423$			40.1200i			1.95070i
$424$	11.5529	+	14.6482i	0.561056	+	0.711380i
$425$	−2.83755	+	13.5635i	−0.137642	+	0.657928i
$426$	19.4624	−	30.8509i	0.942955	−	1.49473i
$427$	−1.12659	+	0.466648i	−0.0545194	+	0.0225827i
$428$	−1.40142	−	26.6672i	−0.0677403	−	1.28901i
$429$	−13.2679	+	5.49576i	−0.640583	+	0.265338i
$430$	20.3365	+	5.69869i	0.980712	+	0.274815i
$431$	11.3673			0.547542			0.273771	−	0.961795i	$-0.411729\pi$
$431$	11.3673			0.547542			0.273771	+	0.961795i	$0.411729\pi$
$432$	−20.0029	+	67.6001i	−0.962390	+	3.25241i
$433$	−16.2533	−	16.2533i	−0.781085	−	0.781085i	0.198929	−	0.980014i	$-0.436254\pi$
$433$	−16.2533	−	16.2533i	−0.781085	−	0.781085i	−0.980014	+	0.198929i	$0.936254\pi$
$434$	−3.08858	−	4.36957i	−0.148256	−	0.209746i
$435$	13.1291	+	44.0633i	0.629492	+	2.11268i
$436$	−1.67008	−	31.7795i	−0.0799825	−	1.52196i
$437$	1.06230	+	2.56461i	0.0508165	+	0.122682i
$438$	−5.46272	−	24.1337i	−0.261019	−	1.15315i
$439$	24.2793	−	24.2793i	1.15879	−	1.15879i	0.174052	−	0.984737i	$-0.444314\pi$
$439$	24.2793	−	24.2793i	1.15879	−	1.15879i	0.984737	−	0.174052i	$-0.0556860\pi$
$440$	−6.38998	+	1.10998i	−0.304630	+	0.0529163i
$441$	−36.0601	−	36.0601i	−1.71715	−	1.71715i
$442$	8.72999	−	13.8384i	0.415243	−	0.658225i
$443$	20.6162	−	8.53951i	0.979505	−	0.405724i	0.165263	−	0.986250i	$-0.447153\pi$
$443$	20.6162	−	8.53951i	0.979505	−	0.405724i	0.814242	+	0.580525i	$0.197153\pi$
$444$	−8.53808	+	24.1218i	−0.405200	+	1.14477i
$445$	0.726744	−	1.34363i	0.0344510	−	0.0636943i
$446$	−31.4237	−	5.39726i	−1.48796	−	0.255568i
$447$	0.729960	−	0.729960i	0.0345259	−	0.0345259i
$448$	−6.18027	+	3.79095i	−0.291990	+	0.179106i
$449$		−	1.60758i		−	0.0758663i	−0.999280	−	0.0379332i	$-0.987923\pi$
$449$		−	1.60758i		−	0.0758663i	0.999280	−	0.0379332i	$-0.0120774\pi$
$450$	−53.5471	+	23.2141i	−2.52423	+	1.09432i
$451$	−0.363712	−	0.878079i	−0.0171265	−	0.0413471i
$452$	1.58162	−	0.754676i	0.0743933	−	0.0354970i
$453$	−4.54689	−	10.9772i	−0.213631	−	0.515752i
$454$	6.39679	+	28.2603i	0.300216	+	1.32632i
$455$	−8.41501	−	0.870804i	−0.394502	−	0.0408239i
$456$	16.0131	−	4.51990i	0.749882	−	0.211664i
$457$	−4.76573			−0.222932			−0.111466	−	0.993768i	$-0.535555\pi$
$457$	−4.76573			−0.222932			−0.111466	+	0.993768i	$0.535555\pi$
$458$	−34.4125	+	7.78935i	−1.60799	+	0.363973i
$459$	45.1267	+	18.6921i	2.10633	+	0.872472i
$460$	−0.358141	+	7.07027i	−0.0166984	+	0.329653i
$461$	1.89178	+	4.56715i	0.0881088	+	0.212714i	0.961792	−	0.273782i	$-0.0882748\pi$
$461$	1.89178	+	4.56715i	0.0881088	+	0.212714i	−0.873683	+	0.486496i	$0.838275\pi$
$462$	0.746374	−	4.34551i	0.0347244	−	0.202172i
$463$	−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
$467$	14.7734	+	6.11934i	0.683631	+	0.283169i	0.697344	−	0.716737i	$-0.254365\pi$
$467$	14.7734	+	6.11934i	0.683631	+	0.283169i	−0.0137126	+	0.999906i	$0.504365\pi$
$468$	68.8170	−	3.61649i	3.18107	−	0.167172i
$469$	−3.84824	+	9.29047i	−0.177695	+	0.428994i
$470$	15.2618	−	1.83230i	0.703972	−	0.0845177i
$471$	55.0113	+	55.0113i	2.53479	+	2.53479i
$472$	−31.5207	−	3.72382i	−1.45086	−	0.171402i
$473$	6.84881			0.314909
$474$	−1.69672	−	7.49592i	−0.0779330	−	0.344299i
$475$	7.24181	+	4.94301i	0.332277	+	0.226801i
$476$	2.16330	+	4.53377i	0.0991548	+	0.207805i
$477$	50.2960	+	20.8333i	2.30289	+	0.953890i
$478$	14.8375	+	20.9913i	0.678650	+	0.960121i
$479$	28.6370			1.30846			0.654229	−	0.756297i	$-0.272993\pi$
$479$	28.6370			1.30846			0.654229	+	0.756297i	$0.272993\pi$
$480$	41.8345	+	7.10389i	1.90948	+	0.324247i
$481$	15.9214			0.725951
$482$	3.22910	+	4.56838i	0.147082	+	0.208084i
$483$	−4.44639	−	1.84176i	−0.202318	−	0.0838028i
$484$	17.9573	−	8.56838i	0.816242	−	0.389472i
$485$	−7.34227	−	3.97128i	−0.333395	−	0.180327i
$486$	19.4825	+	86.0714i	0.883744	+	3.90428i
$487$	25.7000			1.16458			0.582289	−	0.812982i	$-0.302157\pi$
$487$	25.7000			1.16458			0.582289	+	0.812982i	$0.302157\pi$
$488$	−2.35669	−	2.98812i	−0.106683	−	0.135266i
$489$	2.77094	+	2.77094i	0.125306	+	0.125306i
$490$	−12.0705	+	15.3642i	−0.545288	+	0.694085i
$491$	−1.37835	+	3.32764i	−0.0622042	+	0.150174i	−0.951925	−	0.306330i	$-0.900899\pi$
$491$	−1.37835	+	3.32764i	−0.0622042	+	0.150174i	0.889721	+	0.456505i	$0.150899\pi$
$492$	0.326335	+	6.20972i	0.0147123	+	0.279956i
$493$	−15.6940	−	6.50068i	−0.706824	−	0.292776i
$494$	−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
$498$	−6.24532	+	36.3613i	−0.279860	+	1.62939i
$499$	−10.7030	−	25.8393i	−0.479131	−	1.15673i	−0.960017	−	0.279942i	$-0.909685\pi$
$499$	−10.7030	−	25.8393i	−0.479131	−	1.15673i	0.480885	−	0.876783i	$-0.340315\pi$
$500$	11.2762	+	19.3092i	0.504288	+	0.863536i
$501$	4.14333	+	1.71623i	0.185111	+	0.0766753i
$502$	−14.9190	+	3.37695i	−0.665866	+	0.150721i
$503$	−28.9180			−1.28939			−0.644695	−	0.764440i	$-0.723015\pi$
$503$	−28.9180			−1.28939			−0.644695	+	0.764440i	$0.723015\pi$
$504$	−10.3339	+	18.4619i	−0.460310	+	0.822359i
$505$	−2.93173	+	28.3307i	−0.130460	+	1.26070i
$506$	0.506819	+	2.23907i	0.0225309	+	0.0995387i
$507$	−5.68372	−	13.7217i	−0.252423	−	0.609403i
$508$	4.98129	+	10.4396i	0.221009	+	0.463183i
$509$	13.3736	+	32.2866i	0.592772	+	1.43108i	0.880815	+	0.473461i	$0.156996\pi$
$509$	13.3736	+	32.2866i	0.592772	+	1.43108i	−0.288042	+	0.957618i	$0.593004\pi$
$510$	7.93299	−	28.3099i	0.351279	−	1.25358i
$511$		−	4.72692i		−	0.209106i
$512$	−16.6258	−	15.3487i	−0.734762	−	0.678325i
$513$	21.8538	−	21.8538i	0.964869	−	0.964869i
$514$	13.3918	+	2.30014i	0.590688	+	0.101455i
$515$	1.68544	+	5.65660i	0.0742693	+	0.249260i
$516$	−42.2413	−	14.9516i	−1.85957	−	0.658206i
$517$	4.60524	−	1.90755i	0.202538	−	0.0838940i
$518$	−2.60810	+	4.13425i	−0.114593	+	0.181648i
$519$	−39.0815	−	39.0815i	−1.71549	−	1.71549i
$520$	−4.51863	−	26.0130i	−0.198155	−	1.14075i
$521$	7.57884	−	7.57884i	0.332035	−	0.332035i	−0.521324	−	0.853359i	$-0.674562\pi$
$521$	7.57884	−	7.57884i	0.332035	−	0.332035i	0.853359	+	0.521324i	$0.174562\pi$
$522$	−15.7948	−	69.7796i	−0.691320	−	3.05417i
$523$	−4.34605	−	10.4923i	−0.190039	−	0.458796i	0.799927	−	0.600097i	$-0.204871\pi$
$523$	−4.34605	−	10.4923i	−0.190039	−	0.458796i	−0.989967	+	0.141301i	$0.954871\pi$
$524$	−32.5538	+	1.71077i	−1.42212	+	0.0747355i
$525$	−14.9379	+	2.81820i	−0.651944	+	0.122996i
$526$	19.3257	+	27.3411i	0.842642	+	1.19213i
$527$	−8.18157	−	8.18157i	−0.356395	−	0.356395i
$528$	13.6846	−	1.44230i	0.595548	−	0.0627681i
$529$	−20.4941			−0.891050
$530$	5.62799	−	20.0842i	0.244464	−	0.872401i
$531$	−85.5707	+	35.4445i	−3.71345	+	1.53816i
$532$	3.17414	−	0.166808i	0.137617	−	0.00723206i
$533$	3.57458	−	1.48064i	0.154832	−	0.0641336i
$534$	−1.72926	+	2.74115i	−0.0748324	+	0.118621i
$535$	−23.1723	+	18.8262i	−1.00183	+	0.813928i
$536$	−31.1667	−	3.68199i	−1.34620	−	0.159038i
$537$		−	27.8996i		−	1.20395i
$538$	14.9625	−	23.7179i	0.645079	−	1.02255i
$539$	−2.42470	+	5.85373i	−0.104439	+	0.252138i
$540$	74.2515	−	26.4401i	3.19528	−	1.13780i
$541$	11.7217	−	4.85528i	0.503955	−	0.208745i	−0.116198	−	0.993226i	$-0.537071\pi$
$541$	11.7217	−	4.85528i	0.503955	−	0.208745i	0.620153	+	0.784481i	$0.287071\pi$
$542$	6.00793	−	4.24664i	0.258063	−	0.182409i
$543$	−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
$547$	12.2962	−	29.6855i	0.525746	−	1.26926i	−0.408541	−	0.912740i	$-0.633962\pi$
$547$	12.2962	−	29.6855i	0.525746	−	1.26926i	0.934287	−	0.356522i	$-0.116038\pi$
$548$	−9.19987	+	25.9915i	−0.392999	+	1.11030i
$549$	−10.2600	−	4.24983i	−0.437886	−	0.181378i
$550$	5.21062	+	5.04275i	0.222182	+	0.215023i
$551$	−7.60026	+	7.60026i	−0.323782	+	0.323782i
$552$	1.76219	−	14.9163i	0.0750038	−	0.634879i
$553$		−	1.46818i		−	0.0624333i
$554$	9.91798	+	6.25678i	0.421374	+	0.265825i
$555$	27.4174	−	8.16929i	1.16381	−	0.346767i
$556$	−8.20241	+	9.11234i	−0.347860	+	0.386449i
$557$	−12.4244	+	29.9952i	−0.526440	+	1.27094i	0.407400	+	0.913250i	$0.366435\pi$
$557$	−12.4244	+	29.9952i	−0.526440	+	1.27094i	−0.933841	+	0.357689i	$0.883565\pi$
$558$	8.24922	−	48.0283i	0.349217	−	2.03320i
$559$			27.8809i			1.17923i
$560$	7.49492	+	3.08789i	0.316718	+	0.130487i
$561$		−	9.53404i		−	0.402528i
$562$	−10.4496	−	1.79480i	−0.440790	−	0.0757089i
$563$	−0.242757	+	0.586068i	−0.0102310	+	0.0246998i	−0.928912	−	0.370299i	$-0.879255\pi$
$563$	−0.242757	+	0.586068i	−0.0102310	+	0.0246998i	0.918681	+	0.394999i	$0.129255\pi$
$564$	−32.5680	+	1.71152i	−1.37136	+	0.0720680i
$565$	−1.72336	−	0.932131i	−0.0725023	−	0.0392150i
$566$	−6.90344	+	10.9430i	−0.290173	+	0.459970i
$567$			31.1424i			1.30786i
$568$	18.9765	+	10.6220i	0.796236	+	0.445688i
$569$	−0.0516248	+	0.0516248i	−0.00216422	+	0.00216422i	−0.708188	−	0.706024i	$-0.750487\pi$
$569$	−0.0516248	+	0.0516248i	−0.00216422	+	0.00216422i	0.706024	+	0.708188i	$0.250487\pi$
$570$	−14.6283	−	11.4923i	−0.612713	−	0.481360i
$571$	−23.4324	−	9.70604i	−0.980617	−	0.406185i	−0.165963	−	0.986132i	$-0.553073\pi$
$571$	−23.4324	−	9.70604i	−0.980617	−	0.406185i	−0.814654	+	0.579947i	$0.803073\pi$
$572$	−3.68711	−	7.72732i	−0.154166	−	0.323096i
$573$	7.13729	−	17.2309i	0.298164	−	0.719833i
$574$	−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	$0.746439\pi$
$578$	−7.60713	−	10.7622i	−0.316415	−	0.447648i
$579$	64.0229	−	26.5192i	2.66070	−	1.10210i
$580$	−25.8230	+	9.19525i	−1.07224	+	0.381812i
$581$	−2.69710	+	6.51137i	−0.111894	+	0.270137i
$582$	14.9790	+	9.44952i	0.620899	+	0.391695i
$583$		−	6.76384i		−	0.280130i
$584$	14.1974	−	4.00740i	0.587494	−	0.165828i
$585$	−48.5826	−	59.7981i	−2.00864	−	2.47235i
$586$	1.25991	+	0.794815i	0.0520463	+	0.0328335i
$587$	37.8003	−	15.6574i	1.56019	−	0.646250i	0.575065	−	0.818108i	$-0.304977\pi$
$587$	37.8003	−	15.6574i	1.56019	−	0.646250i	0.985122	+	0.171858i	$0.0549769\pi$
$588$	27.7340	−	30.8106i	1.14373	−	1.27061i
$589$	−6.76380	+	2.80166i	−0.278698	+	0.115440i
$590$	17.3912	+	30.9325i	0.715986	+	1.27347i
$591$	63.1644			2.59824
$592$	−14.6284	−	4.32856i	−0.601225	−	0.177903i
$593$	22.6847	+	22.6847i	0.931549	+	0.931549i	0.997803	−	0.0662543i	$-0.0211048\pi$
$593$	22.6847	+	22.6847i	0.931549	+	0.931549i	−0.0662543	+	0.997803i	$0.521105\pi$
$594$	20.8719	−	14.7531i	0.856386	−	0.605326i
$595$	2.67198	−	4.94007i	0.109541	−	0.202523i
$596$	0.457431	+	0.411754i	0.0187371	+	0.0168661i
$597$	−22.1408	−	53.4526i	−0.906162	−	2.18767i
$598$	−9.11504	+	2.06321i	−0.372742	+	0.0843710i
$599$	−17.4180	+	17.4180i	−0.711682	+	0.711682i	−0.966887	−	0.255205i	$-0.917857\pi$
$599$	−17.4180	+	17.4180i	−0.711682	+	0.711682i	0.255205	+	0.966887i	$0.417857\pi$
$600$	−21.1287	−	42.4773i	−0.862574	−	1.73413i
$601$	24.9826	+	24.9826i	1.01906	+	1.01906i	0.999815	+	0.0192475i	$0.00612705\pi$
$601$	24.9826	+	24.9826i	1.01906	+	1.01906i	0.0192475	+	0.999815i	$0.493873\pi$
$602$	−7.23973	−	4.56720i	−0.295070	−	0.186145i
$603$	−84.6096	+	35.0465i	−3.44557	+	1.42720i
$604$	6.39315	−	3.05051i	0.260134	−	0.124123i
$605$	−19.5666	−	10.5832i	−0.795494	−	0.430267i
$606$	10.2294	−	59.5573i	0.415541	−	2.41935i
$607$	−12.3157	+	12.3157i	−0.499877	+	0.499877i	−0.911400	−	0.411522i	$-0.864997\pi$
$607$	−12.3157	+	12.3157i	−0.499877	+	0.499877i	0.411522	+	0.911400i	$0.364997\pi$
$608$	3.19200	+	9.39222i	0.129453	+	0.380905i
$609$		−	18.6350i		−	0.755128i
$610$	−1.14807	+	4.09702i	−0.0464839	+	0.165883i
$611$	7.76547	+	18.7475i	0.314157	+	0.758443i
$612$	−15.2652	+	43.1273i	−0.617059	+	1.74332i
$613$	−2.90525	−	7.01389i	−0.117342	−	0.283288i	0.854286	−	0.519803i	$-0.173995\pi$
$613$	−2.90525	−	7.01389i	−0.117342	−	0.283288i	−0.971628	+	0.236515i	$0.923995\pi$
$614$	13.8292	−	3.13027i	0.558100	−	0.126327i
$615$	5.39589	−	4.38386i	0.217583	−	0.176774i
$616$	2.61052	+	0.308403i	0.105181	+	0.0124259i
$617$	10.1074			0.406909			0.203455	−	0.979084i	$-0.434783\pi$
$617$	10.1074			0.406909			0.203455	+	0.979084i	$0.434783\pi$
$618$	−2.76464	−	12.2139i	−0.111210	−	0.491314i
$619$	−43.7508	−	18.1222i	−1.75849	−	0.728392i	−0.996754	−	0.0805075i	$-0.974346\pi$
$619$	−43.7508	−	18.1222i	−1.75849	−	0.728392i	−0.761739	−	0.647884i	$-0.775654\pi$
$620$	−18.6468	−	0.944546i	−0.748875	−	0.0379339i
$621$	−10.6765	−	25.7755i	−0.428435	−	1.03433i
$622$	32.8792	+	5.64725i	1.31834	+	0.226434i
$623$	−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
$627$	−5.57335	−	2.30856i	−0.222578	−	0.0921949i
$628$	−31.0306	+	34.4730i	−1.23826	+	1.37562i
$629$	−4.04490	+	9.76526i	−0.161281	+	0.389367i
$630$	23.4860	−	2.81968i	0.935703	−	0.112339i
$631$	11.1608	+	11.1608i	0.444306	+	0.444306i	0.893456	−	0.449150i	$-0.148273\pi$
$631$	11.1608	+	11.1608i	0.444306	+	0.444306i	−0.449150	+	0.893456i	$0.648273\pi$
$632$	4.40972	−	1.24470i	0.175409	−	0.0495115i
$633$	77.2403			3.07003
$634$	−12.7717	+	2.89091i	−0.507229	+	0.114813i
$635$	6.15259	−	11.3752i	0.244158	−	0.451409i
$636$	−14.7661	+	41.7172i	−0.585513	+	1.65419i
$637$	−23.8300	−	9.87071i	−0.944179	−	0.391092i
$638$	−7.25878	+	5.13078i	−0.287378	+	0.203130i
$639$	63.4606			2.51046
$640$	−2.92050	+	25.1291i	−0.115443	+	0.993314i
$641$	8.01643			0.316630			0.158315	−	0.987389i	$-0.449394\pi$
$641$	8.01643			0.316630			0.158315	+	0.987389i	$0.449394\pi$
$642$	51.7272	−	36.5627i	2.04151	−	1.44302i
$643$	−10.6659	−	4.41795i	−0.420621	−	0.174227i	0.162326	−	0.986737i	$-0.448100\pi$
$643$	−10.6659	−	4.41795i	−0.420621	−	0.174227i	−0.582947	+	0.812510i	$0.698100\pi$
$644$	0.957399	−	2.70485i	0.0377268	−	0.106586i
$645$	14.3058	+	48.0124i	0.563288	+	1.89048i
$646$	6.70345	−	1.51734i	0.263744	−	0.0596990i
$647$	5.34896			0.210289			0.105145	−	0.994457i	$-0.466469\pi$
$647$	5.34896			0.210289			0.105145	+	0.994457i	$0.466469\pi$
$648$	−93.5372	+	26.4020i	−3.67449	+	1.03717i
$649$	8.13711	+	8.13711i	0.319410	+	0.319410i
$650$	−20.5285	+	21.2120i	−0.805196	+	0.832001i
$651$	4.85737	−	11.7267i	0.190375	−	0.459607i
$652$	−1.56302	+	1.73642i	−0.0612127	+	0.0680033i
$653$	−7.21702	−	2.98939i	−0.282424	−	0.116984i	0.236975	−	0.971516i	$-0.423844\pi$
$653$	−7.21702	−	2.98939i	−0.282424	−	0.116984i	−0.519399	+	0.854532i	$0.673844\pi$
$654$	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
$658$	−6.14017	−	1.05462i	−0.239369	−	0.0411134i
$659$	−15.6674	−	37.8244i	−0.610314	−	1.47343i	−0.862657	−	0.505790i	$-0.831201\pi$
$659$	−15.6674	−	37.8244i	−0.610314	−	1.47343i	0.252343	−	0.967638i	$-0.418799\pi$
$660$	−10.3143	−	11.4150i	−0.401484	−	0.444328i
$661$	12.8189	+	5.30974i	0.498596	+	0.206525i	0.617786	−	0.786346i	$-0.288030\pi$
$661$	12.8189	+	5.30974i	0.498596	+	0.206525i	−0.119190	+	0.992871i	$0.538030\pi$
$662$	2.02932	+	8.96529i	0.0788716	+	0.348446i
$663$	38.8122			1.50734
$664$	−21.8437	−	2.58058i	−0.847698	−	0.100146i
$665$	−2.24084	−	2.75815i	−0.0868962	−	0.106956i
$666$	−43.4188	+	9.82796i	−1.68245	+	0.380826i
$667$	3.71306	+	8.96412i	0.143770	+	0.347092i
$668$	−0.892145	+	2.52049i	−0.0345181	+	0.0975208i
$669$	−28.9430	−	69.8746i	−1.11900	−	2.70151i
$670$	17.1959	+	30.5851i	0.664337	+	1.18161i
$671$			1.37977i			0.0532655i
$672$	−15.4276	−	7.60113i	−0.595132	−	0.293220i
$673$	−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
$675$	−72.7833	−	49.6794i	−2.80143	−	1.91216i
$676$	7.99160	−	3.81321i	0.307369	−	0.146662i
$677$	4.93081	−	2.04241i	0.189506	−	0.0784961i	−0.285912	−	0.958256i	$-0.592297\pi$
$677$	4.93081	−	2.04241i	0.189506	−	0.0784961i	0.475419	+	0.879760i	$0.342297\pi$
$678$	3.51583	+	2.21797i	0.135025	+	0.0851806i
$679$	2.39233	+	2.39233i	0.0918092	+	0.0918092i
$680$	17.1029	+	3.83727i	0.655866	+	0.147153i
$681$	−48.6009	+	48.6009i	−1.86239	+	1.86239i
$682$	−5.90523	+	1.33666i	−0.226123	+	0.0511835i
$683$	18.7520	+	45.2713i	0.717525	+	1.73226i	0.680280	+	0.732952i	$0.261858\pi$
$683$	18.7520	+	45.2713i	0.717525	+	1.73226i	0.0372447	+	0.999306i	$0.488142\pi$
$684$	21.5148	+	19.3664i	0.822639	+	0.740493i
$685$	29.5425	−	8.80249i	1.12876	−	0.336326i
$686$	13.7931	−	9.74949i	0.526623	−	0.372237i
$687$	−59.1812	−	59.1812i	−2.25790	−	2.25790i
$688$	7.58001	−	25.6168i	0.288985	−	0.976630i
$689$	27.5350			1.04900
$690$	−14.6380	+	8.22992i	−0.557257	+	0.313308i
$691$	−8.69376	+	3.60107i	−0.330726	+	0.136991i	−0.541867	−	0.840464i	$-0.682282\pi$
$691$	−8.69376	+	3.60107i	−0.330726	+	0.136991i	0.211141	+	0.977456i	$0.432282\pi$
$692$	22.0450	−	24.4905i	0.838025	−	0.930990i
$693$	7.08690	−	2.93549i	0.269209	−	0.111510i
$694$	−10.0634	−	6.34852i	−0.382002	−	0.240987i
$695$	13.6346	+	1.41094i	0.517190	+	0.0535199i
$696$	55.9708	−	15.7985i	2.12157	−	0.598839i
$697$			2.56861i			0.0972930i
$698$	−21.6242	−	13.6417i	−0.818488	−	0.516345i
$699$	−17.3852	+	41.9716i	−0.657569	+	1.58751i
$700$	−2.14523	−	8.80534i	−0.0810821	−	0.332811i
$701$	−44.3758	+	18.3811i	−1.67605	+	0.694243i	−0.999126	−	0.0418077i	$-0.986688\pi$
$701$	−44.3758	+	18.3811i	−1.67605	+	0.694243i	−0.676926	+	0.736051i	$0.736688\pi$
$702$	60.0584	+	84.9677i	2.26676	+	3.20690i
$703$	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
$707$	4.41766	−	10.6652i	0.166143	−	0.401105i
$708$	−32.4230	−	67.9511i	−1.21853	−	2.55376i
$709$	−41.9278	−	17.3671i	−1.57463	−	0.652234i	−0.587081	−	0.809528i	$-0.699723\pi$
$709$	−41.9278	−	17.3671i	−1.57463	−	0.652234i	−0.987552	+	0.157294i	$0.949723\pi$
$710$	−2.89827	−	24.1406i	−0.108770	−	0.905979i
$711$	9.45466	−	9.45466i	0.354578	−	0.354578i
$712$	−1.68609	−	0.943776i	−0.0631888	−	0.0353695i
$713$			6.60883i			0.247503i
$714$	−6.35788	+	10.0782i	−0.237938	+	0.377169i
$715$	−4.55410	+	8.41980i	−0.170314	+	0.314883i
$716$	16.6104	−	0.872914i	0.620760	−	0.0326223i
$717$	−23.3347	+	56.3350i	−0.871452	+	2.10387i
$718$	−8.85354	−	1.52066i	−0.330411	−	0.0567505i
$719$		−	3.82423i		−	0.142620i	−0.997454	−	0.0713099i	$-0.977282\pi$
$719$		−	3.82423i		−	0.142620i	0.997454	−	0.0713099i	$-0.0227179\pi$
$720$	28.3800	+	68.1503i	1.05766	+	2.53981i
$721$		−	2.39225i		−	0.0890922i
$722$	−3.81236	+	22.1962i	−0.141881	+	0.826057i
$723$	−5.07838	+	12.2603i	−0.188867	+	0.455965i
$724$	6.60375	−	7.33634i	0.245427	−	0.272653i
$725$	25.3124	+	17.2774i	0.940078	+	0.641666i
$726$	39.9178	+	25.1822i	1.48149	+	0.934600i
$727$		−	15.0951i		−	0.559846i	−0.960022	−	0.279923i	$-0.909691\pi$
$727$		−	15.0951i		−	0.559846i	0.960022	−	0.279923i	$-0.0903090\pi$
$728$	−1.25548	+	10.6272i	−0.0465313	+	0.393870i
$729$	−75.1282	+	75.1282i	−2.78253	+	2.78253i
$730$	−12.9697	−	10.1893i	−0.480029	−	0.377121i
$731$	−17.1006	−	7.08328i	−0.632487	−	0.261985i
$732$	3.01217	−	8.50999i	0.111333	−	0.314538i
$733$	17.9645	−	43.3702i	0.663534	−	1.60191i	−0.128691	−	0.991685i	$-0.541078\pi$
$733$	17.9645	−	43.3702i	0.663534	−	1.60191i	0.792226	−	0.610228i	$-0.208922\pi$
$734$	−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
$738$	−8.83419	+	6.24434i	−0.325191	+	0.229857i
$739$	19.0295	−	7.88226i	0.700010	−	0.289954i	−0.00415371	−	0.999991i	$-0.501322\pi$
$739$	19.0295	−	7.88226i	0.700010	−	0.289954i	0.704164	+	0.710038i	$0.251322\pi$
$740$	5.72154	+	16.0678i	0.210328	+	0.590663i
$741$	9.39792	−	22.6886i	0.345241	−	0.833486i
$742$	−4.51054	+	7.14992i	−0.165587	+	0.262482i
$743$			17.8922i			0.656401i	0.944608	+	0.328201i	$0.106442\pi$
$743$			17.8922i			0.656401i	−0.944608	+	0.328201i	$0.893558\pi$
$744$	39.3396	+	4.64753i	1.44226	+	0.170387i
$745$	0.0708278	−	0.684445i	0.00259493	−	0.0250761i
$746$	−1.71958	+	2.72581i	−0.0629585	+	0.0997991i
$747$	−59.3000	+	24.5629i	−2.16967	+	0.898708i
$748$	5.67624	−	0.298299i	0.207544	−	0.0109069i
$749$	11.1797	−	4.63077i	0.408496	−	0.169205i
$750$	−24.4674	+	47.0614i	−0.893422	+	1.71844i
$751$	−26.7884			−0.977522			−0.488761	−	0.872418i	$-0.662551\pi$
$751$	−26.7884			−0.977522			−0.488761	+	0.872418i	$0.662551\pi$
$752$	−2.03796	−	19.3363i	−0.0743167	−	0.705122i
$753$	−25.6570	−	25.6570i	−0.934994	−	0.934994i
$754$	−20.8869	−	29.5498i	−0.760658	−	1.07614i
$755$	−6.96607	−	3.76781i	−0.253521	−	0.137125i
$756$	−31.9015	+	1.67650i	−1.16025	+	0.0609736i
$757$	−14.9747	−	36.1520i	−0.544264	−	1.31397i	−0.921689	−	0.387929i	$-0.873191\pi$
$757$	−14.9747	−	36.1520i	−0.544264	−	1.31397i	0.377426	−	0.926040i	$-0.376809\pi$
$758$	10.0377	+	44.3455i	0.364586	+	1.61070i
$759$	−3.85066	+	3.85066i	−0.139770	+	0.139770i
$760$	6.38444	−	9.06876i	0.231588	−	0.328958i
$761$	−7.36989	−	7.36989i	−0.267158	−	0.267158i	0.560796	−	0.827954i	$-0.310495\pi$
$761$	−7.36989	−	7.36989i	−0.267158	−	0.267158i	−0.827954	+	0.560796i	$0.810495\pi$
$762$	−14.6399	+	23.2065i	−0.530346	+	0.840682i
$763$	13.3229	−	5.51852i	0.482321	−	0.199784i
$764$	10.4820	+	3.71017i	0.379226	+	0.134229i
$765$	49.0195	−	14.6058i	1.77230	−	0.528075i
$766$	−33.0618	−	5.67860i	−1.19457	−	0.205176i
$767$	−33.1254	+	33.1254i	−1.19609	+	1.19609i
$768$	9.75099	−	52.7813i	0.351858	−	1.90458i
$769$		−	5.73423i		−	0.206782i	−0.994641	−	0.103391i	$-0.967031\pi$
$769$		−	5.73423i		−	0.206782i	0.994641	−	0.103391i	$-0.0329692\pi$
$770$	−1.44033	−	2.56181i	−0.0519059	−	0.0923211i
$771$	12.3346	+	29.7784i	0.444220	+	1.07244i
$772$	17.7917	+	37.2873i	0.640338	+	1.34200i
$773$	−15.2780	−	36.8844i	−0.549513	−	1.32664i	−0.917842	−	0.396946i	$-0.870070\pi$
$773$	−15.2780	−	36.8844i	−0.549513	−	1.32664i	0.368329	−	0.929695i	$-0.379930\pi$
$774$	−17.2104	−	76.0334i	−0.618613	−	2.73296i
$775$	11.4252	+	17.4703i	0.410406	+	0.627551i
$776$	−5.15726	+	9.21361i	−0.185135	+	0.330749i
$777$	−11.5952			−0.415976
$778$	34.1497	−	7.72988i	1.22433	−	0.277130i
$779$	1.50154	+	0.621959i	0.0537983	+	0.0222840i
$780$	46.4694	−	41.9886i	1.66387	−	1.50343i
$781$	−3.01731	−	7.28442i	−0.107968	−	0.260657i
$782$	1.05027	−	6.11482i	0.0375574	−	0.218666i
$783$	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
$787$	−3.76428	−	1.55921i	−0.134182	−	0.0555800i	0.314582	−	0.949230i	$-0.398136\pi$
$787$	−3.76428	−	1.55921i	−0.134182	−	0.0555800i	−0.448764	+	0.893650i	$0.648136\pi$
$788$	1.97627	+	37.6059i	0.0704018	+	1.33965i
$789$	−30.3934	+	73.3761i	−1.08203	+	2.61226i
$790$	−4.02838	−	3.16478i	−0.143323	−	0.112598i
$791$	0.561522	+	0.561522i	0.0199654	+	0.0199654i
$792$	14.8250	+	18.7970i	0.526783	+	0.667924i
$793$	−5.61692			−0.199463
$794$	5.17494	+	22.8623i	0.183652	+	0.811353i
$795$	47.4167	−	14.1283i	1.68170	−	0.501078i
$796$	31.1311	−	14.8543i	1.10341	−	0.526496i
$797$	24.7126	+	10.2363i	0.875365	+	0.362588i	0.774697	−	0.632332i	$-0.217902\pi$
$797$	24.7126	+	10.2363i	0.875365	+	0.362588i	0.100667	+	0.994920i	$0.467902\pi$
$798$	4.35199	+	6.15698i	0.154059	+	0.217955i
$799$	−13.4715			−0.476588
$800$	24.6284	−	13.9083i	0.870746	−	0.491732i
$801$	−5.63856			−0.199229
$802$	10.0102	+	14.1620i	0.353474	+	0.500077i
$803$	−4.94141	−	2.04680i	−0.174379	−	0.0722300i
$804$	−32.0589	−	67.1880i	−1.13063	−	2.36954i
$805$	−3.07439	+	0.916046i	−0.108358	+	0.0322864i
$806$	−5.44143	−	24.0396i	−0.191666	−	0.846760i
$807$	66.5210			2.34165
$808$	35.7784	+	4.22682i	1.25868	+	0.148699i
$809$	−14.6573	−	14.6573i	−0.515322	−	0.515322i	0.400831	−	0.916152i	$-0.368722\pi$
$809$	−14.6573	−	14.6573i	−0.515322	−	0.515322i	−0.916152	+	0.400831i	$0.868722\pi$
$810$	85.4483	+	67.1300i	3.00235	+	2.35871i
$811$	11.3438	−	27.3863i	0.398333	−	0.961661i	−0.589728	−	0.807602i	$-0.700765\pi$
$811$	11.3438	−	27.3863i	0.398333	−	0.961661i	0.988062	−	0.154060i	$-0.0492348\pi$
$812$	11.0946	−	0.583047i	0.389345	−	0.0204609i
$813$	16.1237	+	6.67864i	0.565482	+	0.234230i
$814$	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
$818$	−5.27539	+	30.7142i	−0.184450	+	1.07390i
$819$	11.9501	+	28.8501i	0.417570	+	1.00810i
$820$	2.77882	+	3.07537i	0.0970408	+	0.107396i
$821$	−32.4192	−	13.4285i	−1.13144	−	0.468657i	−0.263168	−	0.964750i	$-0.584767\pi$
$821$	−32.4192	−	13.4285i	−1.13144	−	0.468657i	−0.868269	+	0.496093i	$0.834767\pi$
$822$	−63.7890	+	14.4388i	−2.22490	+	0.503611i
$823$	−18.1415			−0.632373			−0.316187	−	0.948697i	$-0.602403\pi$
$823$	−18.1415			−0.632373			−0.316187	+	0.948697i	$0.602403\pi$
$824$	7.18521	−	2.02812i	0.250309	−	0.0706527i
$825$	−3.52218	+	16.8361i	−0.122627	+	0.586157i
$826$	−3.17525	−	14.0279i	−0.110481	−	0.488093i
$827$	13.9680	+	33.7217i	0.485714	+	1.17262i	0.956857	+	0.290561i	$0.0938418\pi$
$827$	13.9680	+	33.7217i	0.485714	+	1.17262i	−0.471142	+	0.882057i	$0.656158\pi$
$828$	23.5839	−	11.2531i	0.819596	−	0.391072i
$829$	11.3256	+	27.3423i	0.393353	+	0.949637i	0.989204	+	0.146543i	$0.0468146\pi$
$829$	11.3256	+	27.3423i	0.393353	+	0.949637i	−0.595852	+	0.803094i	$0.703185\pi$
$830$	12.0520	+	21.4361i	0.418332	+	0.744057i
$831$			27.8167i			0.964950i
$832$	−32.9834	+	5.23868i	−1.14350	+	0.181618i
$833$	12.1083	−	12.1083i	0.419527	−	0.419527i
$834$	−28.6629	−	4.92306i	−0.992514	−	0.170472i
$835$	2.86485	−	0.853610i	0.0991422	−	0.0295404i
$836$	1.20006	−	3.39041i	0.0415048	−	0.117260i
$837$	67.9792	−	28.1579i	2.34970	−	0.973279i
$838$	22.6157	−	35.8495i	0.781247	−	1.23840i
$839$	21.4869	+	21.4869i	0.741811	+	0.741811i	0.972926	−	0.231116i	$-0.0742376\pi$
$839$	21.4869	+	21.4869i	0.741811	+	0.741811i	−0.231116	+	0.972926i	$0.574238\pi$
$840$	3.29083	+	18.9448i	0.113544	+	0.653657i
$841$	−6.05918	+	6.05918i	−0.208937	+	0.208937i
$842$	8.57467	+	37.8819i	0.295503	+	1.30550i
$843$	−9.62467	−	23.2360i	−0.331491	−	0.800291i
$844$	2.41668	+	45.9862i	0.0831854	+	1.58291i
$845$	−8.70777	−	4.70985i	−0.299556	−	0.162024i
$846$	−32.7496	−	46.3325i	−1.12595	−	1.59294i
$847$	6.37537	+	6.37537i	0.219060	+	0.219060i
$848$	−25.2990	−	7.48597i	−0.868770	−	0.257069i
$849$	−30.6916			−1.05333
$850$	−7.79484	−	17.9801i	−0.267361	−	0.616711i
$851$	5.57772	−	2.31037i	0.191202	−	0.0791984i
$852$	2.70723	+	51.5150i	0.0927481	+	1.76488i
$853$	−37.0377	+	15.3415i	−1.26815	+	0.525283i	−0.912400	−	0.409300i	$-0.865773\pi$
$853$	−37.0377	+	15.3415i	−1.26815	+	0.525283i	−0.355746	+	0.934583i	$0.615773\pi$
$854$	0.920116	−	1.45853i	0.0314857	−	0.0499098i
$855$	3.33131	−	32.1921i	0.113928	−	1.10095i
$856$	23.3866	+	29.6526i	0.799338	+	1.01350i
$857$		−	47.3694i		−	1.61811i	−0.587733	−	0.809055i	$-0.699980\pi$
$857$		−	47.3694i		−	1.61811i	0.587733	−	0.809055i	$-0.300020\pi$
$858$	10.8363	−	17.1773i	0.369946	−	0.586422i
$859$	−5.28829	+	12.7671i	−0.180434	+	0.435607i	−0.988056	−	0.154094i	$-0.950754\pi$
$859$	−5.28829	+	12.7671i	−0.180434	+	0.435607i	0.807622	+	0.589700i	$0.200754\pi$
$860$	−28.1373	+	10.0193i	−0.959473	+	0.341657i
$861$	−2.60330	+	1.07832i	−0.0887201	+	0.0367491i
$862$	−13.1275	+	9.27898i	−0.447123	+	0.316043i
$863$	−12.9803	−	12.9803i	−0.441853	−	0.441853i	0.450781	−	0.892634i	$-0.351145\pi$
$863$	−12.9803	−	12.9803i	−0.441853	−	0.441853i	−0.892634	+	0.450781i	$0.851145\pi$
$864$	−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
$867$	11.9637	−	28.8828i	0.406307	−	0.980912i
$868$	7.13366	+	2.52501i	0.242132	+	0.0857043i
$869$	−1.53480	−	0.635736i	−0.0520646	−	0.0215659i
$870$	−51.1305	−	40.1692i	−1.73349	−	1.36187i
$871$	−32.7534	+	32.7534i	−1.10981	+	1.10981i
$872$	27.8700	+	35.3372i	0.943796	+	1.19667i
$873$			30.8119i			1.04282i
$874$	−3.32026	−	2.09459i	−0.112309	−	0.0708506i
$875$	−6.54345	+	7.73650i	−0.221209	+	0.261541i
$876$	26.0087	+	23.4116i	0.878752	+	0.791003i
$877$	17.3787	−	41.9560i	0.586838	−	1.41675i	−0.299672	−	0.954042i	$-0.596877\pi$
$877$	17.3787	−	41.9560i	0.586838	−	1.41675i	0.886510	−	0.462710i	$-0.153123\pi$
$878$	−8.21993	+	47.8578i	−0.277409	+	1.61512i
$879$			3.53363i			0.119186i
$880$	6.47338	−	6.49793i	0.218218	−	0.219045i
$881$			17.7034i			0.596441i	0.954497	+	0.298221i	$0.0963931\pi$
$881$			17.7034i			0.596441i	−0.954497	+	0.298221i	$0.903607\pi$
$882$	71.0794	+	12.2084i	2.39337	+	0.411078i
$883$	12.7290	−	30.7304i	0.428363	−	1.03416i	−0.551443	−	0.834213i	$-0.685923\pi$
$883$	12.7290	−	30.7304i	0.428363	−	1.03416i	0.979806	−	0.199948i	$-0.0640774\pi$
$884$	1.21435	+	23.1074i	0.0408429	+	0.777187i
$885$	−40.0470	+	74.0405i	−1.34617	+	2.48885i
$886$	−16.8378	+	26.6906i	−0.565678	+	0.896689i
$887$			44.9270i			1.50850i	0.656588	+	0.754250i	$0.271999\pi$
$887$			44.9270i			1.50850i	−0.656588	+	0.754250i	$0.728001\pi$
$888$	−9.83024	−	34.8266i	−0.329881	−	1.16870i
$889$	−3.70636	+	3.70636i	−0.124307	+	0.124307i
$890$	0.257516	+	2.14492i	0.00863195	+	0.0718980i
$891$	32.5556	+	13.4850i	1.09065	+	0.451763i
$892$	40.6953	−	19.4179i	1.36258	−	0.650159i
$893$	−3.26197	+	7.87510i	−0.109158	+	0.263530i
$894$	−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
$898$	1.31225	+	1.85651i	0.0437903	+	0.0619524i
$899$	−23.6416	+	9.79267i	−0.788492	+	0.326604i
$900$	42.8893	−	70.5186i	1.42964	−	2.35062i
$901$	−6.99541	+	16.8884i	−0.233051	+	0.562634i
$902$	1.13680	+	0.717152i	0.0378512	+	0.0238785i
$903$		−	20.3051i		−	0.675711i
$904$	−1.21050	+	2.16260i	−0.0402606	+	0.0719270i
$905$	−10.9772	−	1.13594i	−0.364894	−	0.0377601i
$906$	14.2115	+	8.96535i	0.472145	+	0.297854i
$907$	−25.3031	+	10.4809i	−0.840176	+	0.348012i	−0.760923	−	0.648842i	$-0.775254\pi$
$907$	−25.3031	+	10.4809i	−0.840176	+	0.348012i	−0.0792532	+	0.996855i	$0.525254\pi$
$908$	−30.4559	−	27.4147i	−1.01071	−	0.909787i
$909$	97.1293	−	40.2323i	3.22158	−	1.33442i
$910$	10.4289	−	5.86345i	0.345714	−	0.194371i
$911$	−33.7228			−1.11729			−0.558643	−	0.829408i	$-0.688678\pi$
$911$	−33.7228			−1.11729			−0.558643	+	0.829408i	$0.688678\pi$
$912$	−14.8031	+	18.2911i	−0.490181	+	0.605679i
$913$	5.63897	+	5.63897i	0.186623	+	0.186623i
$914$	5.50369	−	3.89022i	0.182046	−	0.128677i
$915$	−9.67265	+	2.88206i	−0.319768	+	0.0952780i
$916$	33.3828	−	37.0861i	1.10300	−	1.22536i
$917$	−5.65298	−	13.6475i	−0.186678	−	0.450680i
$918$	−67.3726	+	15.2500i	−2.22363	+	0.503324i
$919$	33.1256	−	33.1256i	1.09271	−	1.09271i	0.0974735	−	0.995238i	$-0.468924\pi$
$919$	33.1256	−	33.1256i	1.09271	−	1.09271i	0.995238	−	0.0974735i	$-0.0310761\pi$
$920$	−5.35779	−	8.45743i	−0.176641	−	0.278833i
$921$	23.7828	+	23.7828i	0.783671	+	0.783671i
$922$	−5.91283	−	3.73012i	−0.194729	−	0.122845i
$923$	29.6542	−	12.2832i	0.976080	−	0.404306i
$924$	2.68525	+	5.62766i	0.0883383	+	0.185136i
$925$	10.7505	−	15.7501i	0.353473	−	0.517859i
$926$	4.13443	−	24.0714i	0.135866	−	0.791034i
$927$	15.4055	−	15.4055i	0.505981	−	0.505981i
$928$	11.1570	+	32.8288i	0.366248	+	1.07766i
$929$		−	32.2191i		−	1.05708i	−0.848910	−	0.528538i	$-0.822740\pi$
$929$		−	32.2191i		−	1.05708i	0.848910	−	0.528538i	$-0.177260\pi$
$930$	−21.7052	−	38.6055i	−0.711743	−	1.26593i
$931$	−4.14630	−	10.0101i	−0.135890	−	0.328067i
$932$	−25.5324	−	9.03734i	−0.836340	−	0.296028i
$933$	30.2836	+	73.1111i	0.991441	+	2.39355i
$934$	−22.0562	+	4.99247i	−0.721700	+	0.163359i
$935$	−4.00724	−	4.93232i	−0.131051	−	0.161304i
$936$	−76.5210	+	60.3511i	−2.50117	+	1.97264i
$937$	11.5426			0.377080			0.188540	−	0.982066i	$-0.439625\pi$
$937$	11.5426			0.377080			0.188540	+	0.982066i	$0.439625\pi$
$938$	−3.13959	−	13.8704i	−0.102511	−	0.452883i
$939$	58.3254	+	24.1592i	1.90338	+	0.788405i
$940$	−16.1293	+	14.5740i	−0.526080	+	0.475353i
$941$	−19.3222	−	46.6478i	−0.629885	−	1.52068i	−0.839765	−	0.542949i	$-0.817308\pi$
$941$	−19.3222	−	46.6478i	−0.629885	−	1.52068i	0.209881	−	0.977727i	$-0.432692\pi$
$942$	−108.435	−	18.6245i	−3.53300	−	0.606818i
$943$	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
$947$	−2.49731	−	1.03442i	−0.0811516	−	0.0336141i	0.341738	−	0.939795i	$-0.388984\pi$
$947$	−2.49731	−	1.03442i	−0.0811516	−	0.0336141i	−0.422890	+	0.906181i	$0.638984\pi$
$948$	8.07829	+	7.27162i	0.262371	+	0.236171i
$949$	8.33233	−	20.1160i	0.270479	−	0.652994i
$950$	−12.3981	+	0.202991i	−0.402248	+	0.00658590i
$951$	−21.9643	−	21.9643i	−0.712240	−	0.712240i
$952$	−6.19916	−	3.46993i	−0.200916	−	0.112461i
$953$	−29.5188			−0.956208			−0.478104	−	0.878303i	$-0.658676\pi$
$953$	−29.5188			−0.956208			−0.478104	+	0.878303i	$0.658676\pi$
$954$	−75.0901	+	16.9968i	−2.43113	+	0.550293i
$955$	−3.54992	−	11.9141i	−0.114873	−	0.385531i
$956$	−34.2700	−	12.1301i	−1.10837	−	0.392315i
$957$	−19.4806	−	8.06913i	−0.629719	−	0.260838i
$958$	−33.0713	+	23.3761i	−1.06849	+	0.755247i
$959$	−12.4940			−0.403451
$960$	−54.1113	+	25.9452i	−1.74643	+	0.837377i
$961$	13.5701			0.437747
$962$	−18.3867	+	12.9964i	−0.592812	+	0.419022i
$963$	101.815	+	42.1731i	3.28094	+	1.35901i
$964$	−7.45824	−	2.63989i	−0.240214	−	0.0850252i
$965$	21.9753	−	40.6287i	0.707409	−	1.30789i
$966$	6.63831	−	1.50260i	0.213584	−	0.0483453i
$967$	48.1906			1.54971			0.774853	−	0.632141i	$-0.217824\pi$
$967$	48.1906			1.54971			0.774853	+	0.632141i	$0.217824\pi$
$968$	−13.7437	+	24.5536i	−0.441739	+	0.789181i
$969$	11.5283	+	11.5283i	0.370343	+	0.370343i
$970$	11.7209	−	1.40719i	0.376336	−	0.0451822i
$971$	−9.00286	+	21.7348i	−0.288916	+	0.697504i	−0.999984	−	0.00561859i	$-0.998212\pi$
$971$	−9.00286	+	21.7348i	−0.288916	+	0.697504i	0.711069	+	0.703123i	$0.248212\pi$
$972$	−92.7585	−	83.4960i	−2.97523	−	2.67813i
$973$	−5.13278	−	2.12607i	−0.164549	−	0.0681586i
$974$	−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	−0.726357	−	0.687317i	$-0.758788\pi$
$977$	−1.22028	+	1.22028i	−0.0390403	+	0.0390403i	0.687317	+	0.726357i	$0.258788\pi$
$978$	−5.46190	−	0.938120i	−0.174652	−	0.0299978i
$979$	0.268092	+	0.647231i	0.00856825	+	0.0206856i
$980$	1.39788	−	27.5963i	0.0446536	−	0.881533i
$981$	121.333	+	50.2579i	3.87388	+	1.60461i
$982$	−1.12453	−	4.96805i	−0.0358852	−	0.158537i
$983$	−28.8147			−0.919047			−0.459524	−	0.888166i	$-0.651980\pi$
$983$	−28.8147			−0.919047			−0.459524	+	0.888166i	$0.651980\pi$
$984$	−5.44580	−	6.90490i	−0.173606	−	0.220120i
$985$	32.6774	−	26.5485i	1.04119	−	0.845907i
$986$	23.4306	−	5.30359i	0.746184	−	0.168901i
$987$	−5.65544	−	13.6534i	−0.180015	−	0.434594i
$988$	13.8020	+	4.88532i	0.439101	+	0.155423i
$989$	4.04583	+	9.76750i	0.128650	+	0.310588i
$990$	7.22201	−	25.7726i	0.229531	−	0.819108i
$991$		−	13.7444i		−	0.436605i	−0.975881	−	0.218303i	$-0.929948\pi$
$991$		−	13.7444i		−	0.436605i	0.975881	−	0.218303i	$-0.0700520\pi$
$992$	−1.53613	+	23.5668i	−0.0487722	+	0.748248i
$993$	−15.4181	+	15.4181i	−0.489280	+	0.489280i
$994$	−1.66816	+	9.71234i	−0.0529110	+	0.308057i
$995$	−33.9209	−	18.3471i	−1.07536	−	0.581643i
$996$	−22.4690	−	47.0897i	−0.711957	−	1.49210i
$997$	−18.6452	+	7.72310i	−0.590499	+	0.244593i	−0.657865	−	0.753135i	$-0.728540\pi$
$997$	−18.6452	+	7.72310i	−0.590499	+	0.244593i	0.0673660	+	0.997728i	$0.478540\pi$
$998$	33.4527	+	21.1037i	1.05893	+	0.668025i
$999$	−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.ba.a.107.5	yes	88
4.3	odd	2		640.2.ba.a.207.22		88
5.2	odd	4		800.2.v.b.43.7		88
5.3	odd	4		160.2.u.a.43.16	✓	88
5.4	even	2		800.2.bb.b.107.18		88
20.3	even	4		640.2.u.a.463.1		88
32.3	odd	8		160.2.u.a.67.16	yes	88
32.29	even	8		640.2.u.a.47.1		88
160.3	even	8	inner	160.2.ba.a.3.5	yes	88
160.67	even	8		800.2.bb.b.643.18		88
160.93	odd	8		640.2.ba.a.303.22		88
160.99	odd	8		800.2.v.b.707.7		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.2.u.a.43.16	✓	88	5.3	odd	4
160.2.u.a.67.16	yes	88	32.3	odd	8
160.2.ba.a.3.5	yes	88	160.3	even	8	inner
160.2.ba.a.107.5	yes	88	1.1	even	1	trivial
640.2.u.a.47.1		88	32.29	even	8
640.2.u.a.463.1		88	20.3	even	4
640.2.ba.a.207.22		88	4.3	odd	2
640.2.ba.a.303.22		88	160.93	odd	8
800.2.v.b.43.7		88	5.2	odd	4
800.2.v.b.707.7		88	160.99	odd	8
800.2.bb.b.107.18		88	5.4	even	2
800.2.bb.b.643.18		88	160.67	even	8

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.ba (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.15485 + 0.816290i) q^{2} +(-3.09930 - 1.28377i) q^{3} +(0.667342 - 1.88538i) q^{4} +(-2.14296 + 0.638517i) q^{5} +(4.62714 - 1.04737i) q^{6} +0.906290 q^{7} +(0.768338 + 2.72207i) q^{8} +(5.83625 + 5.83625i) q^{9} +(1.95358 - 2.48667i) q^{10} +(0.392432 - 0.947415i) q^{11} +(-4.48869 + 4.98663i) q^{12} +(3.85684 + 1.59755i) 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} +(-11.5040 - 1.97590i) q^{18} +(0.671071 + 1.62011i) q^{19} +(-0.226244 + 4.46641i) q^{20} +(-2.80886 - 1.16347i) q^{21} +(0.320166 + 1.41446i) q^{22} +1.58299 q^{23} +(1.11321 - 9.42287i) q^{24} +(4.18459 - 2.73664i) q^{25} +(-5.75812 + 1.30337i) q^{26} +(-6.74455 - 16.2828i) q^{27} +(0.604805 - 1.70870i) q^{28} +(2.34560 + 5.66278i) q^{29} +(-9.24704 + 5.19898i) q^{30} +4.17491i q^{31} +(5.64488 + 0.367943i) q^{32} +(-2.43253 + 2.43253i) q^{33} +(0.663470 - 3.86284i) q^{34} +(-1.94215 + 0.578681i) q^{35} +(14.8983 - 7.10877i) q^{36} +(3.52354 - 1.45950i) q^{37} +(-2.09746 - 1.32319i) q^{38} +(-9.90259 - 9.90259i) q^{39} +(-3.38461 - 5.34270i) q^{40} +(0.655358 - 0.655358i) q^{41} +(4.19353 - 0.949216i) q^{42} +(2.55582 + 6.17029i) q^{43} +(-1.52435 - 1.37213i) q^{44} +(-16.2334 - 8.78033i) q^{45} +(-1.82811 + 1.29218i) q^{46} +(3.43714 + 3.43714i) q^{47} +(6.40621 + 11.7907i) q^{48} -6.17864 q^{49} +(-2.59867 + 6.57624i) q^{50} +(8.58950 - 3.55789i) q^{51} +(5.58582 - 6.20548i) q^{52} +(6.09374 - 2.52411i) q^{53} +(21.0804 + 13.2986i) q^{54} +(-0.236027 + 2.28085i) q^{55} +(0.696336 + 2.46698i) q^{56} -5.88270i q^{57} +(-7.33128 - 4.62496i) q^{58} +(-4.29438 + 10.3675i) q^{59} +(6.43504 - 13.5523i) q^{60} +(-1.24308 + 0.514899i) q^{61} +(-3.40793 - 4.82138i) 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} +(-4.24615 + 10.2511i) q^{67} +(2.38699 + 5.00257i) q^{68} +(-4.90615 - 2.03219i) q^{69} +(1.77051 - 2.25364i) q^{70} +(5.43676 - 5.43676i) q^{71} +(-11.4025 + 20.3709i) q^{72} -5.21568i q^{73} +(-2.87778 + 4.56173i) q^{74} +(-16.4825 + 3.10960i) q^{75} +(3.50235 - 0.184056i) q^{76} +(0.355657 - 0.858632i) q^{77} +(19.5194 + 3.35259i) q^{78} -1.61999i q^{79} +(8.26989 + 3.40718i) q^{80} +34.3625i q^{81} +(-0.221876 + 1.29180i) q^{82} +(-2.97598 + 7.18465i) q^{83} +(-4.06805 + 4.51933i) q^{84} +(2.94827 - 5.45087i) q^{85} +(-7.98832 - 5.03945i) q^{86} -20.5619i q^{87} +(2.88045 + 0.340292i) q^{88} +(-0.483064 + 0.483064i) q^{89} +(25.9144 - 3.11124i) q^{90} +(3.49541 + 1.44785i) q^{91} +(1.05639 - 2.98453i) q^{92} +(5.35962 - 12.9393i) 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} +(7.13538 - 5.04356i) q^{98} +(7.81968 - 3.23902i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} - 8 q^{7} + 8 q^{8} + 8 q^{10} - 8 q^{11} - 20 q^{12} - 4 q^{13} - 16 q^{14} - 8 q^{15} - 8 q^{16} - 12 q^{18} - 16 q^{19} - 32 q^{20} - 8 q^{21} - 20 q^{22}+ \cdots + 16 q^{98}+O(q^{100}) \) 88 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 - 8 * q^6 - 8 * q^7 + 8 * q^8 + 8 * q^10 - 8 * q^11 - 20 * q^12 - 4 * q^13 - 16 * q^14 - 8 * q^15 - 8 * q^16 - 12 * q^18 - 16 * q^19 - 32 * q^20 - 8 * q^21 - 20 * q^22 - 8 * q^23 + 32 * q^24 - 4 * q^25 - 8 * q^26 + 8 * q^27 - 20 * q^28 + 64 * q^30 + 16 * q^32 - 8 * q^33 - 8 * q^34 - 48 * q^35 - 8 * q^36 - 4 * q^37 - 4 * q^38 + 16 * q^40 - 8 * q^41 - 68 * q^42 + 28 * q^43 - 16 * q^44 - 4 * q^45 - 8 * q^46 - 8 * q^47 - 88 * q^48 + 40 * q^49 + 4 * q^50 + 8 * q^51 + 48 * q^52 - 4 * q^53 + 56 * q^54 + 28 * q^55 + 40 * q^56 - 36 * q^58 + 12 * q^60 - 40 * q^61 - 32 * q^62 - 56 * q^63 - 48 * q^64 - 8 * q^65 + 72 * q^66 - 28 * q^67 + 8 * q^68 - 24 * q^69 + 4 * q^70 + 24 * q^71 + 88 * q^72 - 16 * q^75 + 56 * q^76 - 32 * q^77 + 112 * q^78 + 80 * q^80 + 68 * q^82 + 36 * q^83 - 56 * q^84 - 4 * q^85 + 24 * q^86 - 24 * q^88 - 84 * q^90 - 8 * q^91 + 92 * q^92 + 8 * q^93 + 32 * q^94 + 24 * q^96 - 8 * q^97 + 16 * q^98

Introduction

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