LMFDB - Embedded newform 800.2.bb.b.107.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [800,2,Mod(107,800)] 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("800.107"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(800, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([4, 5, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 800 = 2^{5} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	800.bb (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [88] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.38803216170$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 160)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			107.18
Character	$\chi$	$=$	800.107
Dual form			800.2.bb.b.643.18

$q$-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} +(4.62714 - 1.04737i) q^{6} -0.906290 q^{7} +(-0.768338 - 2.72207i) q^{8} +(5.83625 + 5.83625i) q^{9} +(0.392432 - 0.947415i) q^{11} +(4.48869 - 4.98663i) q^{12} +(-3.85684 - 1.59755i) q^{13} +(-1.04663 + 0.739795i) q^{14} +(-3.10931 - 2.51639i) q^{16} +(1.95970 - 1.95970i) q^{17} +(11.5040 + 1.97590i) q^{18} +(0.671071 + 1.62011i) q^{19} +(-2.80886 - 1.16347i) q^{21} +(-0.320166 - 1.41446i) q^{22} -1.58299 q^{23} +(1.11321 - 9.42287i) q^{24} +(-5.75812 + 1.30337i) q^{26} +(6.74455 + 16.2828i) q^{27} +(-0.604805 + 1.70870i) q^{28} +(2.34560 + 5.66278i) q^{29} +4.17491i q^{31} +(-5.64488 - 0.367943i) q^{32} +(2.43253 - 2.43253i) q^{33} +(0.663470 - 3.86284i) q^{34} +(14.8983 - 7.10877i) q^{36} +(-3.52354 + 1.45950i) q^{37} +(2.09746 + 1.32319i) q^{38} +(-9.90259 - 9.90259i) q^{39} +(0.655358 - 0.655358i) q^{41} +(-4.19353 + 0.949216i) q^{42} +(-2.55582 - 6.17029i) q^{43} +(-1.52435 - 1.37213i) q^{44} +(-1.82811 + 1.29218i) q^{46} +(-3.43714 - 3.43714i) q^{47} +(-6.40621 - 11.7907i) q^{48} -6.17864 q^{49} +(8.58950 - 3.55789i) q^{51} +(-5.58582 + 6.20548i) q^{52} +(-6.09374 + 2.52411i) q^{53} +(21.0804 + 13.2986i) q^{54} +(0.696336 + 2.46698i) q^{56} +5.88270i q^{57} +(7.33128 + 4.62496i) q^{58} +(-4.29438 + 10.3675i) q^{59} +(-1.24308 + 0.514899i) q^{61} +(3.40793 + 4.82138i) q^{62} +(-5.28933 - 5.28933i) q^{63} +(-6.81931 + 4.18294i) q^{64} +(0.823549 - 4.79484i) q^{66} +(4.24615 - 10.2511i) q^{67} +(-2.38699 - 5.00257i) q^{68} +(-4.90615 - 2.03219i) q^{69} +(5.43676 - 5.43676i) q^{71} +(11.4025 - 20.3709i) q^{72} +5.21568i q^{73} +(-2.87778 + 4.56173i) q^{74} +(3.50235 - 0.184056i) q^{76} +(-0.355657 + 0.858632i) q^{77} +(-19.5194 - 3.35259i) q^{78} -1.61999i q^{79} +34.3625i q^{81} +(0.221876 - 1.29180i) q^{82} +(2.97598 - 7.18465i) q^{83} +(-4.06805 + 4.51933i) q^{84} +(-7.98832 - 5.03945i) q^{86} +20.5619i q^{87} +(-2.88045 - 0.340292i) q^{88} +(-0.483064 + 0.483064i) q^{89} +(3.49541 + 1.44785i) q^{91} +(-1.05639 + 2.98453i) q^{92} +(-5.35962 + 12.9393i) q^{93} +(-6.77507 - 1.16367i) q^{94} +(-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} - 8 q^{6} + 8 q^{7} - 8 q^{8} - 8 q^{11} + 20 q^{12} + 4 q^{13} - 16 q^{14} - 8 q^{16} + 12 q^{18} - 16 q^{19} - 8 q^{21} + 20 q^{22} + 8 q^{23} + 32 q^{24} - 8 q^{26} - 8 q^{27}+ \cdots - 16 q^{98}+O(q^{100}) $ 88 * q + 4 * q^2 + 4 * q^3 - 8 * q^6 + 8 * q^7 - 8 * q^8 - 8 * q^11 + 20 * q^12 + 4 * q^13 - 16 * q^14 - 8 * q^16 + 12 * q^18 - 16 * q^19 - 8 * q^21 + 20 * q^22 + 8 * q^23 + 32 * q^24 - 8 * q^26 - 8 * q^27 + 20 * q^28 - 16 * q^32 + 8 * q^33 - 8 * q^34 - 8 * q^36 + 4 * q^37 + 4 * q^38 - 8 * q^41 + 68 * q^42 - 28 * q^43 - 16 * q^44 - 8 * q^46 + 8 * q^47 + 88 * q^48 + 40 * q^49 + 8 * q^51 - 48 * q^52 + 4 * q^53 + 56 * q^54 + 40 * q^56 + 36 * q^58 - 40 * q^61 + 32 * q^62 + 56 * q^63 - 48 * q^64 + 72 * q^66 + 28 * q^67 - 8 * q^68 - 24 * q^69 + 24 * q^71 - 88 * q^72 + 56 * q^76 + 32 * q^77 - 112 * q^78 - 68 * q^82 - 36 * q^83 - 56 * q^84 + 24 * q^86 + 24 * q^88 - 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 $\left(\mathbb{Z}/800\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$577$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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	$0.0447727\pi$
$3$	3.09930	+	1.28377i	1.78938	+	0.741185i	0.799256	+	0.600991i	$0.205227\pi$
$4$	0.667342	−	1.88538i	0.333671	−	0.942690i
$5$		0			0
$5$		0			0
$6$	4.62714	−	1.04737i	1.88902	−	0.427585i
$7$	−0.906290			−0.342545			−0.171273	−	0.985224i	$-0.554788\pi$
$7$	−0.906290			−0.342545			−0.171273	+	0.985224i	$0.554788\pi$
$8$	−0.768338	−	2.72207i	−0.271648	−	0.962397i
$9$	5.83625	+	5.83625i	1.94542	+	1.94542i
$10$		0			0
$11$	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	−0.222811	−	0.974862i	$-0.571523\pi$
$13$	−3.85684	−	1.59755i	−1.06969	−	0.443082i	−0.846883	+	0.531780i	$0.821523\pi$
$14$	−1.04663	+	0.739795i	−0.279722	+	0.197718i
$15$		0			0
$16$	−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	$0.140897\pi$
$18$	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			0
$21$	−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	$-0.552775\pi$
$23$	−1.58299			−0.330076			−0.165038	+	0.986287i	$0.552775\pi$
$24$	1.11321	−	9.42287i	0.227232	−	1.92343i
$25$		0			0
$26$	−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	$0.682293\pi$
$30$		0			0
$31$			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
$35$		0			0
$36$	14.8983	−	7.10877i	2.48305	−	1.18479i
$37$	−3.52354	+	1.45950i	−0.579267	+	0.239940i	−0.653025	−	0.757336i	$-0.726501\pi$
$37$	−3.52354	+	1.45950i	−0.579267	+	0.239940i	0.0737587	+	0.997276i	$0.476501\pi$
$38$	2.09746	+	1.32319i	0.340253	+	0.214649i
$39$	−9.90259	−	9.90259i	−1.58568	−	1.58568i
$40$		0			0
$41$	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	$-0.954925\pi$
$43$	−2.55582	−	6.17029i	−0.389759	−	0.940961i	0.600232	−	0.799826i	$-0.295075\pi$
$44$	−1.52435	−	1.37213i	−0.229804	−	0.206857i
$45$		0			0
$46$	−1.82811	+	1.29218i	−0.269540	+	0.190521i
$47$	−3.43714	−	3.43714i	−0.501358	−	0.501358i	0.410502	−	0.911860i	$-0.365354\pi$
$47$	−3.43714	−	3.43714i	−0.501358	−	0.501358i	−0.911860	+	0.410502i	$0.865354\pi$
$48$	−6.40621	−	11.7907i	−0.924656	−	1.70184i
$49$	−6.17864			−0.882663
$50$		0			0
$51$	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	−0.759686	−	0.650290i	$-0.774647\pi$
$53$	−6.09374	+	2.52411i	−0.837040	+	0.346713i	−0.0773541	+	0.997004i	$0.524647\pi$
$54$	21.0804	+	13.2986i	2.86868	+	1.80971i
$55$		0			0
$56$	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	$0.864299\pi$
$60$		0			0
$61$	−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
$65$		0			0
$66$	0.823549	−	4.79484i	0.101372	−	0.590204i
$67$	4.24615	−	10.2511i	0.518750	−	1.25237i	−0.419922	−	0.907560i	$-0.637943\pi$
$67$	4.24615	−	10.2511i	0.518750	−	1.25237i	0.938672	−	0.344812i	$-0.112057\pi$
$68$	−2.38699	−	5.00257i	−0.289465	−	0.606650i
$69$	−4.90615	−	2.03219i	−0.590631	−	0.244647i
$70$		0			0
$71$	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	$0.0987315\pi$
$73$			5.21568i			0.610449i	−0.952280	+	0.305225i	$0.901268\pi$
$74$	−2.87778	+	4.56173i	−0.334535	+	0.530290i
$75$		0			0
$76$	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	$-0.0290484\pi$
$80$		0			0
$81$			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	$-0.734642\pi$
$83$	2.97598	−	7.18465i	0.326656	−	0.788618i	0.998836	−	0.0482299i	$-0.0153580\pi$
$84$	−4.06805	+	4.51933i	−0.443861	+	0.493100i
$85$		0			0
$86$	−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	$0.261528\pi$
$90$		0			0
$91$	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
$95$		0			0
$96$	−17.0228	−	8.38709i	−1.73738	−	0.856004i
$97$	−2.63970	−	2.63970i	−0.268021	−	0.268021i	0.560282	−	0.828302i	$-0.310693\pi$
$97$	−2.63970	−	2.63970i	−0.268021	−	0.268021i	−0.828302	+	0.560282i	$0.810693\pi$
$98$	−7.13538	+	5.04356i	−0.720782	+	0.509476i
$99$	7.81968	−	3.23902i	0.785908	−	0.325534i
$100$		0			0
$101$	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	$0.0415120\pi$
$103$			2.63961i			0.260089i	−0.991508	+	0.130044i	$0.958488\pi$
$104$	−1.38530	+	11.7260i	−0.135840	+	1.14983i
$105$		0			0
$106$	−4.97693	+	7.88922i	−0.483402	+	0.766269i
$107$	−12.3357	+	5.10959i	−1.19253	+	0.493963i	−0.888579	−	0.458724i	$-0.848307\pi$
$107$	−12.3357	+	5.10959i	−1.19253	+	0.493963i	−0.303953	+	0.952687i	$0.598307\pi$
$108$	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	$0.0992023\pi$
$110$		0			0
$111$	−12.7942			−1.21437
$112$	2.81793	+	2.28057i	0.266270	+	0.215494i
$113$	−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
$115$		0			0
$116$	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
$120$		0			0
$121$	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
$125$		0			0
$126$	−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	$0.167396\pi$
$128$	−4.46078	+	10.3972i	−0.394281	+	0.918990i
$129$		−	22.4046i		−	1.97262i
$130$		0			0
$131$	−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
$135$		0			0
$136$	−6.84015	−	3.82873i	−0.586538	−	0.328311i
$137$	13.7858			1.17780			0.588902	−	0.808205i	$-0.299561\pi$
$137$	13.7858			1.17780			0.588902	+	0.808205i	$0.299561\pi$
$138$	−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			0
$141$	−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
$145$		0			0
$146$	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	$0.129012\pi$
$150$		0			0
$151$	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
$155$		0			0
$156$	−25.2785	+	12.0617i	−2.02390	+	0.965710i
$157$	21.4257	+	8.87481i	1.70996	+	0.708287i	0.999992	+	0.00404938i	$0.00128896\pi$
$157$	21.4257	+	8.87481i	1.70996	+	0.708287i	0.709964	+	0.704238i	$0.248711\pi$
$158$	−1.32238	−	1.87084i	−0.105203	−	0.148836i
$159$	−22.1267			−1.75476
$160$		0			0
$161$	1.43465			0.113066
$162$	28.0498	+	39.6835i	2.20380	+	3.11783i
$163$	1.07922	+	0.447027i	0.0845309	+	0.0350138i	0.424548	−	0.905405i	$-0.360433\pi$
$163$	1.07922	+	0.447027i	0.0845309	+	0.0350138i	−0.340017	+	0.940419i	$0.610433\pi$
$164$	−0.798250	−	1.67295i	−0.0623328	−	0.130635i
$165$		0			0
$166$	−2.42795	−	10.7264i	−0.188446	−	0.832532i
$167$	1.33686			0.103450			0.0517248	−	0.998661i	$-0.483528\pi$
$167$	1.33686			0.103450			0.0517248	+	0.998661i	$0.483528\pi$
$168$	−1.00889	+	8.53985i	−0.0778373	+	0.658863i
$169$	3.13062	+	3.13062i	0.240817	+	0.240817i
$170$		0			0
$171$	−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	−0.280298	−	0.959913i	$-0.590433\pi$
$173$	−15.2214	−	6.30490i	−1.15726	−	0.479352i	−0.876962	+	0.480561i	$0.840433\pi$
$174$	16.7844	+	23.7458i	1.27242	+	1.80016i
$175$		0			0
$176$	−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	$0.774400\pi$
$180$		0			0
$181$	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
$185$		0			0
$186$	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
$190$		0			0
$191$			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	$-0.483178\pi$
$193$	14.6069	−	14.6069i	1.05143	−	1.05143i	0.998604	−	0.0528217i	$-0.0168215\pi$
$194$	−5.20320	−	0.893688i	−0.373568	−	0.0641631i
$195$		0			0
$196$	−4.12327	+	11.6491i	−0.294519	+	0.832077i
$197$	17.3956	−	7.20550i	1.23939	−	0.513371i	0.335864	−	0.941910i	$-0.390972\pi$
$197$	17.3956	−	7.20550i	1.23939	−	0.513371i	0.903523	+	0.428540i	$0.140972\pi$
$198$	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	$0.540650\pi$
$200$		0			0
$201$	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			0
$206$	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
$210$		0			0
$211$	−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
$215$		0			0
$216$	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
$220$		0			0
$221$	−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	$-0.977699\pi$
$223$	−15.9419	−	15.9419i	−1.06755	−	1.06755i	−0.0700048	−	0.997547i	$-0.522301\pi$
$224$	5.11589	+	0.333463i	0.341820	+	0.0222804i
$225$		0			0
$226$	−1.22128	−	0.209764i	−0.0812386	−	0.0139533i
$227$	−7.84063	+	18.9290i	−0.520401	+	1.25636i	0.417253	+	0.908790i	$0.362993\pi$
$227$	−7.84063	+	18.9290i	−0.520401	+	1.25636i	−0.937654	+	0.347569i	$0.887007\pi$
$228$	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	$0.316550\pi$
$230$		0			0
$231$	−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	$0.146296\pi$
$233$			13.5423i			0.887185i	−0.896229	+	0.443593i	$0.853704\pi$
$234$	−41.2126	−	25.9991i	−2.69415	−	1.69961i
$235$		0			0
$236$	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	$-0.200036\pi$
$240$		0			0
$241$		−	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
$245$		0			0
$246$	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
$250$		0			0
$251$	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
$255$		0			0
$256$	3.33560	+	15.6484i	0.208475	+	0.978028i
$257$	6.79396	+	6.79396i	0.423795	+	0.423795i	0.886508	−	0.462713i	$-0.153124\pi$
$257$	6.79396	+	6.79396i	0.423795	+	0.423795i	−0.462713	+	0.886508i	$0.653124\pi$
$258$	−18.2887	−	25.8739i	−1.13860	−	1.61084i
$259$	3.19335	−	1.32273i	0.198425	−	0.0821903i
$260$		0			0
$261$	−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	$0.260449\pi$
$263$			23.6751i			1.45987i	−0.683517	+	0.729934i	$0.739551\pi$
$264$	−8.49050	−	4.75250i	−0.522554	−	0.292496i
$265$		0			0
$266$	−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	$0.581632\pi$
$270$		0			0
$271$	−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			0
$276$	−7.10554	+	7.89378i	−0.427703	+	0.475150i
$277$	3.17320	+	7.66078i	0.190659	+	0.460292i	0.990084	−	0.140474i	$-0.0448626\pi$
$277$	3.17320	+	7.66078i	0.190659	+	0.460292i	−0.799425	+	0.600765i	$0.794863\pi$
$278$	−8.45542	+	1.91391i	−0.507122	+	0.114788i
$279$	−24.3658	+	24.3658i	−1.45874	+	1.45874i
$280$		0			0
$281$	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	−0.619489	−	0.785005i	$-0.712660\pi$
$283$	−8.45255	+	3.50116i	−0.502452	+	0.208122i	0.117037	+	0.993128i	$0.462660\pi$
$284$	−6.62217	−	13.8785i	−0.392954	−	0.823539i
$285$		0			0
$286$	−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
$290$		0			0
$291$	−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	0.935217	−	0.354076i	$-0.115204\pi$
$293$	0.403100	+	0.973169i	0.0235493	+	0.0568532i	−0.911667	+	0.410929i	$0.865204\pi$
$294$	−28.5894	+	6.47129i	−1.66737	+	0.377414i
$295$		0			0
$296$	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
$300$		0			0
$301$	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
$305$		0			0
$306$	26.4167	−	18.6723i	1.51014	−	1.06742i
$307$	9.26288	+	3.83681i	0.528661	+	0.218978i	0.631017	−	0.775769i	$-0.282638\pi$
$307$	9.26288	+	3.83681i	0.528661	+	0.218978i	−0.102356	+	0.994748i	$0.532638\pi$
$308$	1.38150	+	1.24355i	0.0787184	+	0.0708578i
$309$	−3.38866	+	8.18095i	−0.192774	+	0.465398i
$310$		0			0
$311$	−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	$-0.321496\pi$
$313$	18.8189			1.06371			0.531854	+	0.846836i	$0.321496\pi$
$314$	31.9878	−	7.24052i	1.80518	−	0.408606i
$315$		0			0
$316$	−3.05429	−	1.08109i	−0.171817	−	0.0608159i
$317$	−8.55459	−	3.54343i	−0.480474	−	0.199019i	0.129282	−	0.991608i	$-0.458733\pi$
$317$	−8.55459	−	3.54343i	−0.480474	−	0.199019i	−0.609756	+	0.792589i	$0.708733\pi$
$318$	−25.5529	+	18.0618i	−1.43294	+	1.01285i
$319$	6.28549			0.351920
$320$		0			0
$321$	−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
$325$		0			0
$326$	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
$330$		0			0
$331$	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
$335$		0			0
$336$	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	$-0.00421140\pi$
$338$	6.17088	+	1.05989i	0.335652	+	0.0576506i
$339$	−1.12487	−	2.71568i	−0.0610946	−	0.147495i
$340$		0			0
$341$	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
$345$		0			0
$346$	−22.7250	+	5.14386i	−1.22170	+	0.276535i
$347$	−3.21973	−	7.77311i	−0.172844	−	0.417283i	0.813590	−	0.581439i	$-0.197510\pi$
$347$	−3.21973	−	7.77311i	−0.172844	−	0.417283i	−0.986434	+	0.164156i	$0.947510\pi$
$348$	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	$0.714229\pi$
$350$		0			0
$351$		−	73.5749i		−	3.92714i
$352$	−2.56382	+	5.20364i	−0.136652	+	0.277355i
$353$	−16.1883	+	16.1883i	−0.861617	+	0.861617i	−0.991526	−	0.129909i	$-0.958532\pi$
$353$	−16.1883	+	16.1883i	−0.861617	+	0.861617i	0.129909	+	0.991526i	$0.458532\pi$
$354$	−9.01208	+	52.4699i	−0.478987	+	2.78874i
$355$		0			0
$356$	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	$0.696390\pi$
$360$		0			0
$361$	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
$365$		0			0
$366$	−5.21260	+	3.68447i	−0.272467	+	0.192590i
$367$	−4.32797	−	4.32797i	−0.225918	−	0.225918i	0.585067	−	0.810985i	$-0.301068\pi$
$367$	−4.32797	−	4.32797i	−0.225918	−	0.225918i	−0.810985	+	0.585067i	$0.801068\pi$
$368$	4.92200	+	3.98341i	0.256577	+	0.207650i
$369$	7.64966			0.398226
$370$		0			0
$371$	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	−0.436525	−	0.899692i	$-0.643791\pi$
$373$	−2.10545	+	0.872108i	−0.109016	+	0.0451560i	0.327509	+	0.944848i	$0.393791\pi$
$374$	−3.39934	−	2.14448i	−0.175776	−	0.110889i
$375$		0			0
$376$	−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	$-0.184233\pi$
$380$		0			0
$381$	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	0.133933	−	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			0
$386$	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	$0.840983\pi$
$390$		0			0
$391$	−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
$395$		0			0
$396$	−0.888374	−	16.9046i	−0.0446425	−	0.849488i
$397$	−6.34300	+	15.3133i	−0.318346	+	0.768555i	0.680996	+	0.732287i	$0.261547\pi$
$397$	−6.34300	+	15.3133i	−0.318346	+	0.768555i	−0.999342	+	0.0362680i	$0.988453\pi$
$398$	24.0385	+	4.12879i	1.20494	+	0.206957i
$399$		−	5.33142i		−	0.266905i
$400$		0			0
$401$		−	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
$405$		0			0
$406$	−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			0
$411$	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
$415$		0			0
$416$	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	$0.636468\pi$
$420$		0			0
$421$	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
$425$		0			0
$426$	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
$430$		0			0
$431$	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	0.980014	−	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
$435$		0			0
$436$	−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	$-0.0556860\pi$
$440$		0			0
$441$	−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	−0.814242	−	0.580525i	$-0.802847\pi$
$443$	−20.6162	+	8.53951i	−0.979505	+	0.405724i	−0.165263	+	0.986250i	$0.552847\pi$
$444$	−8.53808	+	24.1218i	−0.405200	+	1.14477i
$445$		0			0
$446$	−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	$-0.0120774\pi$
$450$		0			0
$451$	−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
$455$		0			0
$456$	16.0131	−	4.51990i	0.749882	−	0.211664i
$457$	4.76573			0.222932			0.111466	−	0.993768i	$-0.464445\pi$
$457$	4.76573			0.222932			0.111466	+	0.993768i	$0.464445\pi$
$458$	34.4125	−	7.78935i	1.60799	−	0.363973i
$459$	45.1267	+	18.6921i	2.10633	+	0.872472i
$460$		0			0
$461$	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	−0.363901	−	0.931437i	$-0.618555\pi$
$463$	12.2119	−	12.2119i	0.567536	−	0.567536i	0.931437	+	0.363901i	$0.118555\pi$
$464$	6.95655	−	23.5098i	0.322950	−	1.09141i
$465$		0			0
$466$	11.0544	+	15.6393i	0.512087	+	0.724475i
$467$	−14.7734	−	6.11934i	−0.683631	−	0.283169i	0.0137126	−	0.999906i	$-0.495635\pi$
$467$	−14.7734	−	6.11934i	−0.683631	−	0.283169i	−0.697344	+	0.716737i	$0.745635\pi$
$468$	−68.8170	+	3.61649i	−3.18107	+	0.167172i
$469$	−3.84824	+	9.29047i	−0.177695	+	0.428994i
$470$		0			0
$471$	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
$475$		0			0
$476$	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	$0.272993\pi$
$480$		0			0
$481$	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
$485$		0			0
$486$	19.4825	+	86.0714i	0.883744	+	3.90428i
$487$	−25.7000			−1.16458			−0.582289	−	0.812982i	$-0.697843\pi$
$487$	−25.7000			−1.16458			−0.582289	+	0.812982i	$0.697843\pi$
$488$	2.35669	+	2.98812i	0.106683	+	0.135266i
$489$	2.77094	+	2.77094i	0.125306	+	0.125306i
$490$		0			0
$491$	−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
$495$		0			0
$496$	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	$-0.340315\pi$
$500$		0			0
$501$	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	$-0.276985\pi$
$503$	28.9180			1.28939			0.644695	+	0.764440i	$0.276985\pi$
$504$	−10.3339	+	18.4619i	−0.460310	+	0.822359i
$505$		0			0
$506$	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	$0.593004\pi$
$510$		0			0
$511$		−	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
$515$		0			0
$516$	−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
$520$		0			0
$521$	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	0.989967	−	0.141301i	$-0.0451286\pi$
$523$	4.34605	+	10.4923i	0.190039	+	0.458796i	−0.799927	+	0.600097i	$0.795129\pi$
$524$	−32.5538	+	1.71077i	−1.42212	+	0.0747355i
$525$		0			0
$526$	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
$530$		0			0
$531$	−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
$535$		0			0
$536$	−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
$540$		0			0
$541$	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
$545$		0			0
$546$	17.6902	+	3.03842i	0.757070	+	0.130032i
$547$	−12.2962	+	29.6855i	−0.525746	+	1.26926i	0.408541	+	0.912740i	$0.366038\pi$
$547$	−12.2962	+	29.6855i	−0.525746	+	1.26926i	−0.934287	+	0.356522i	$0.883962\pi$
$548$	9.19987	−	25.9915i	0.392999	−	1.11030i
$549$	−10.2600	−	4.24983i	−0.437886	−	0.181378i
$550$		0			0
$551$	−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
$555$		0			0
$556$	−8.20241	+	9.11234i	−0.347860	+	0.386449i
$557$	12.4244	−	29.9952i	0.526440	−	1.27094i	−0.407400	−	0.913250i	$-0.633565\pi$
$557$	12.4244	−	29.9952i	0.526440	−	1.27094i	0.933841	−	0.357689i	$-0.116435\pi$
$558$	−8.24922	+	48.0283i	−0.349217	+	2.03320i
$559$			27.8809i			1.17923i
$560$		0			0
$561$		−	9.53404i		−	0.402528i
$562$	10.4496	+	1.79480i	0.440790	+	0.0757089i
$563$	0.242757	−	0.586068i	0.0102310	−	0.0246998i	−0.918681	−	0.394999i	$-0.870745\pi$
$563$	0.242757	−	0.586068i	0.0102310	−	0.0246998i	0.928912	+	0.370299i	$0.120745\pi$
$564$	−32.5680	+	1.71152i	−1.37136	+	0.0720680i
$565$		0			0
$566$	−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	$0.250487\pi$
$570$		0			0
$571$	−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
$575$		0			0
$576$	−64.2119	−	15.3866i	−2.67550	−	0.641107i
$577$	−0.380039	−	0.380039i	−0.0158212	−	0.0158212i	0.699152	−	0.714973i	$-0.253561\pi$
$577$	−0.380039	−	0.380039i	−0.0158212	−	0.0158212i	−0.714973	+	0.699152i	$0.753561\pi$
$578$	7.60713	+	10.7622i	0.316415	+	0.447648i
$579$	64.0229	−	26.5192i	2.66070	−	1.10210i
$580$		0			0
$581$	−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
$585$		0			0
$586$	1.25991	+	0.794815i	0.0520463	+	0.0328335i
$587$	−37.8003	+	15.6574i	−1.56019	+	0.646250i	−0.985122	−	0.171858i	$-0.945023\pi$
$587$	−37.8003	+	15.6574i	−1.56019	+	0.646250i	−0.575065	+	0.818108i	$0.695023\pi$
$588$	−27.7340	+	30.8106i	−1.14373	+	1.27061i
$589$	−6.76380	+	2.80166i	−0.278698	+	0.115440i
$590$		0			0
$591$	63.1644			2.59824
$592$	14.6284	+	4.32856i	0.601225	+	0.177903i
$593$	−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
$595$		0			0
$596$	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	$0.417857\pi$
$600$		0			0
$601$	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
$605$		0			0
$606$	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	$0.135003\pi$
$608$	−3.19200	−	9.39222i	−0.129453	−	0.380905i
$609$		−	18.6350i		−	0.755128i
$610$		0			0
$611$	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	0.971628	−	0.236515i	$-0.0760052\pi$
$613$	2.90525	+	7.01389i	0.117342	+	0.283288i	−0.854286	+	0.519803i	$0.826005\pi$
$614$	13.8292	−	3.13027i	0.558100	−	0.126327i
$615$		0			0
$616$	2.61052	+	0.308403i	0.105181	+	0.0124259i
$617$	−10.1074			−0.406909			−0.203455	−	0.979084i	$-0.565217\pi$
$617$	−10.1074			−0.406909			−0.203455	+	0.979084i	$0.565217\pi$
$618$	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	$-0.775654\pi$
$620$		0			0
$621$	−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
$625$		0			0
$626$	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
$630$		0			0
$631$	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
$635$		0			0
$636$	−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
$640$		0			0
$641$	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	0.582947	−	0.812510i	$-0.301900\pi$
$643$	10.6659	+	4.41795i	0.420621	+	0.174227i	−0.162326	+	0.986737i	$0.551900\pi$
$644$	0.957399	−	2.70485i	0.0377268	−	0.106586i
$645$		0			0
$646$	6.70345	−	1.51734i	0.263744	−	0.0596990i
$647$	−5.34896			−0.210289			−0.105145	−	0.994457i	$-0.533531\pi$
$647$	−5.34896			−0.210289			−0.105145	+	0.994457i	$0.533531\pi$
$648$	93.5372	−	26.4020i	3.67449	−	1.03717i
$649$	8.13711	+	8.13711i	0.319410	+	0.319410i
$650$		0			0
$651$	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	0.519399	−	0.854532i	$-0.326156\pi$
$653$	7.21702	+	2.98939i	0.282424	+	0.116984i	−0.236975	+	0.971516i	$0.576156\pi$
$654$	61.6436	−	43.5721i	2.41046	−	1.70380i
$655$		0			0
$656$	−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	$-0.418799\pi$
$660$		0			0
$661$	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
$665$		0			0
$666$	−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
$670$		0			0
$671$			1.37977i			0.0532655i
$672$	15.4276	+	7.60113i	0.595132	+	0.293220i
$673$	10.5543	−	10.5543i	0.406839	−	0.406839i	−0.473796	−	0.880635i	$-0.657117\pi$
$673$	10.5543	−	10.5543i	0.406839	−	0.406839i	0.880635	+	0.473796i	$0.157117\pi$
$674$	6.29676	−	36.6608i	0.242542	−	1.41212i
$675$		0			0
$676$	7.99160	−	3.81321i	0.307369	−	0.146662i
$677$	−4.93081	+	2.04241i	−0.189506	+	0.0784961i	−0.475419	−	0.879760i	$-0.657703\pi$
$677$	−4.93081	+	2.04241i	−0.189506	+	0.0784961i	0.285912	+	0.958256i	$0.407703\pi$
$678$	−3.51583	−	2.21797i	−0.135025	−	0.0851806i
$679$	2.39233	+	2.39233i	0.0918092	+	0.0918092i
$680$		0			0
$681$	−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	$-0.738142\pi$
$683$	−18.7520	−	45.2713i	−0.717525	−	1.73226i	−0.0372447	−	0.999306i	$-0.511858\pi$
$684$	21.5148	+	19.3664i	0.822639	+	0.740493i
$685$		0			0
$686$	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
$690$		0			0
$691$	−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
$695$		0			0
$696$	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
$700$		0			0
$701$	−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
$705$		0			0
$706$	−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	$0.949723\pi$
$710$		0			0
$711$	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
$715$		0			0
$716$	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	$-0.0227179\pi$
$720$		0			0
$721$		−	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
$725$		0			0
$726$	39.9178	+	25.1822i	1.48149	+	0.934600i
$727$			15.0951i			0.559846i	0.960022	+	0.279923i	$0.0903090\pi$
$727$			15.0951i			0.559846i	−0.960022	+	0.279923i	$0.909691\pi$
$728$	1.25548	−	10.6272i	0.0465313	−	0.393870i
$729$	−75.1282	+	75.1282i	−2.78253	+	2.78253i
$730$		0			0
$731$	−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	$0.458922\pi$
$733$	−17.9645	+	43.3702i	−0.663534	+	1.60191i	−0.792226	+	0.610228i	$0.791078\pi$
$734$	−8.53101	−	1.46526i	−0.314885	−	0.0540839i
$735$		0			0
$736$	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	$0.251322\pi$
$740$		0			0
$741$	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	$-0.893558\pi$
$743$		−	17.8922i		−	0.656401i	0.944608	−	0.328201i	$-0.106442\pi$
$744$	39.3396	+	4.64753i	1.44226	+	0.170387i
$745$		0			0
$746$	−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
$750$		0			0
$751$	−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
$755$		0			0
$756$	−31.9015	+	1.67650i	−1.16025	+	0.0609736i
$757$	14.9747	+	36.1520i	0.544264	+	1.31397i	0.921689	+	0.387929i	$0.126809\pi$
$757$	14.9747	+	36.1520i	0.544264	+	1.31397i	−0.377426	+	0.926040i	$0.623191\pi$
$758$	−10.0377	−	44.3455i	−0.364586	−	1.61070i
$759$	−3.85066	+	3.85066i	−0.139770	+	0.139770i
$760$		0			0
$761$	−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
$765$		0			0
$766$	−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	$-0.0329692\pi$
$770$		0			0
$771$	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	$0.129930\pi$
$773$	15.2780	+	36.8844i	0.549513	+	1.32664i	−0.368329	+	0.929695i	$0.620070\pi$
$774$	−17.2104	−	76.0334i	−0.618613	−	2.73296i
$775$		0			0
$776$	−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
$780$		0			0
$781$	−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
$785$		0			0
$786$	−44.6337	−	63.1456i	−1.59203	−	2.25233i
$787$	3.76428	+	1.55921i	0.134182	+	0.0555800i	0.448764	−	0.893650i	$-0.351864\pi$
$787$	3.76428	+	1.55921i	0.134182	+	0.0555800i	−0.314582	+	0.949230i	$0.601864\pi$
$788$	−1.97627	−	37.6059i	−0.0704018	−	1.33965i
$789$	−30.3934	+	73.3761i	−1.08203	+	2.61226i
$790$		0			0
$791$	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
$795$		0			0
$796$	31.1311	−	14.8543i	1.10341	−	0.526496i
$797$	−24.7126	−	10.2363i	−0.875365	−	0.362588i	−0.100667	−	0.994920i	$-0.532098\pi$
$797$	−24.7126	−	10.2363i	−0.875365	−	0.362588i	−0.774697	+	0.632332i	$0.782098\pi$
$798$	−4.35199	−	6.15698i	−0.154059	−	0.217955i
$799$	−13.4715			−0.476588
$800$		0			0
$801$	−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
$805$		0			0
$806$	−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	$0.868722\pi$
$810$		0			0
$811$	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
$815$		0			0
$816$	−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
$820$		0			0
$821$	−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	$-0.397597\pi$
$823$	18.1415			0.632373			0.316187	+	0.948697i	$0.397597\pi$
$824$	7.18521	−	2.02812i	0.250309	−	0.0706527i
$825$		0			0
$826$	−3.17525	−	14.0279i	−0.110481	−	0.488093i
$827$	−13.9680	−	33.7217i	−0.485714	−	1.17262i	−0.956857	−	0.290561i	$-0.906158\pi$
$827$	−13.9680	−	33.7217i	−0.485714	−	1.17262i	0.471142	−	0.882057i	$-0.343842\pi$
$828$	−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	$0.703185\pi$
$830$		0			0
$831$			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
$835$		0			0
$836$	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	$0.574238\pi$
$840$		0			0
$841$	−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
$845$		0			0
$846$	−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
$850$		0			0
$851$	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	0.355746	−	0.934583i	$-0.384227\pi$
$853$	37.0377	−	15.3415i	1.26815	−	0.525283i	0.912400	+	0.409300i	$0.134227\pi$
$854$	0.920116	−	1.45853i	0.0314857	−	0.0499098i
$855$		0			0
$856$	23.3866	+	29.6526i	0.799338	+	1.01350i
$857$			47.3694i			1.61811i	0.587733	+	0.809055i	$0.300020\pi$
$857$			47.3694i			1.61811i	−0.587733	+	0.809055i	$0.699980\pi$
$858$	−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	$0.200754\pi$
$860$		0			0
$861$	−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	0.892634	−	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
$865$		0			0
$866$	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
$870$		0			0
$871$	−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
$875$		0			0
$876$	26.0087	+	23.4116i	0.878752	+	0.791003i
$877$	−17.3787	+	41.9560i	−0.586838	+	1.41675i	0.299672	+	0.954042i	$0.403123\pi$
$877$	−17.3787	+	41.9560i	−0.586838	+	1.41675i	−0.886510	+	0.462710i	$0.846877\pi$
$878$	8.21993	−	47.8578i	0.277409	−	1.61512i
$879$			3.53363i			0.119186i
$880$		0			0
$881$			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	$0.314077\pi$
$883$	−12.7290	+	30.7304i	−0.428363	+	1.03416i	−0.979806	+	0.199948i	$0.935923\pi$
$884$	1.21435	+	23.1074i	0.0408429	+	0.777187i
$885$		0			0
$886$	−16.8378	+	26.6906i	−0.565678	+	0.896689i
$887$		−	44.9270i		−	1.50850i	−0.656588	−	0.754250i	$-0.728001\pi$
$887$		−	44.9270i		−	1.50850i	0.656588	−	0.754250i	$-0.271999\pi$
$888$	9.83024	+	34.8266i	0.329881	+	1.16870i
$889$	−3.70636	+	3.70636i	−0.124307	+	0.124307i
$890$		0			0
$891$	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
$895$		0			0
$896$	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
$900$		0			0
$901$	−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
$905$		0			0
$906$	14.2115	+	8.96535i	0.472145	+	0.297854i
$907$	25.3031	−	10.4809i	0.840176	−	0.348012i	0.0792532	−	0.996855i	$-0.474746\pi$
$907$	25.3031	−	10.4809i	0.840176	−	0.348012i	0.760923	+	0.648842i	$0.224746\pi$
$908$	30.4559	+	27.4147i	1.01071	+	0.909787i
$909$	97.1293	−	40.2323i	3.22158	−	1.33442i
$910$		0			0
$911$	−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
$915$		0			0
$916$	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	$-0.0310761\pi$
$920$		0			0
$921$	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
$925$		0			0
$926$	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	$-0.177260\pi$
$930$		0			0
$931$	−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
$935$		0			0
$936$	−76.5210	+	60.3511i	−2.50117	+	1.97264i
$937$	−11.5426			−0.377080			−0.188540	−	0.982066i	$-0.560375\pi$
$937$	−11.5426			−0.377080			−0.188540	+	0.982066i	$0.560375\pi$
$938$	3.13959	+	13.8704i	0.102511	+	0.452883i
$939$	58.3254	+	24.1592i	1.90338	+	0.788405i
$940$		0			0
$941$	−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
$945$		0			0
$946$	−7.90932	+	5.59061i	−0.257154	+	0.181766i
$947$	2.49731	+	1.03442i	0.0811516	+	0.0336141i	0.422890	−	0.906181i	$-0.361016\pi$
$947$	2.49731	+	1.03442i	0.0811516	+	0.0336141i	−0.341738	+	0.939795i	$0.611016\pi$
$948$	−8.07829	−	7.27162i	−0.262371	−	0.236171i
$949$	8.33233	−	20.1160i	0.270479	−	0.652994i
$950$		0			0
$951$	−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	$-0.341324\pi$
$953$	29.5188			0.956208			0.478104	+	0.878303i	$0.341324\pi$
$954$	−75.0901	+	16.9968i	−2.43113	+	0.550293i
$955$		0			0
$956$	−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
$960$		0			0
$961$	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
$965$		0			0
$966$	6.63831	−	1.50260i	0.213584	−	0.0483453i
$967$	−48.1906			−1.54971			−0.774853	−	0.632141i	$-0.782176\pi$
$967$	−48.1906			−1.54971			−0.774853	+	0.632141i	$0.782176\pi$
$968$	13.7437	−	24.5536i	0.441739	−	0.789181i
$969$	11.5283	+	11.5283i	0.370343	+	0.370343i
$970$		0			0
$971$	−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
$975$		0			0
$976$	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	$0.241212\pi$
$978$	5.46190	+	0.938120i	0.174652	+	0.0299978i
$979$	0.268092	+	0.647231i	0.00856825	+	0.0206856i
$980$		0			0
$981$	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	$-0.348020\pi$
$983$	28.8147			0.919047			0.459524	+	0.888166i	$0.348020\pi$
$984$	−5.44580	−	6.90490i	−0.173606	−	0.220120i
$985$		0			0
$986$	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
$990$		0			0
$991$		−	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
$995$		0			0
$996$	−22.4690	−	47.0897i	−0.711957	−	1.49210i
$997$	18.6452	−	7.72310i	0.590499	−	0.244593i	−0.0673660	−	0.997728i	$-0.521460\pi$
$997$	18.6452	−	7.72310i	0.590499	−	0.244593i	0.657865	+	0.753135i	$0.271460\pi$
$998$	−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	800.2.bb.b.107.18		88
5.2	odd	4		160.2.u.a.43.16	✓	88
5.3	odd	4		800.2.v.b.43.7		88
5.4	even	2		160.2.ba.a.107.5	yes	88
20.7	even	4		640.2.u.a.463.1		88
20.19	odd	2		640.2.ba.a.207.22		88
32.3	odd	8		800.2.v.b.707.7		88
160.3	even	8	inner	800.2.bb.b.643.18		88
160.29	even	8		640.2.u.a.47.1		88
160.67	even	8		160.2.ba.a.3.5	yes	88
160.99	odd	8		160.2.u.a.67.16	yes	88
160.157	odd	8		640.2.ba.a.303.22		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.2.u.a.43.16	✓	88	5.2	odd	4
160.2.u.a.67.16	yes	88	160.99	odd	8
160.2.ba.a.3.5	yes	88	160.67	even	8
160.2.ba.a.107.5	yes	88	5.4	even	2
640.2.u.a.47.1		88	160.29	even	8
640.2.u.a.463.1		88	20.7	even	4
640.2.ba.a.207.22		88	20.19	odd	2
640.2.ba.a.303.22		88	160.157	odd	8
800.2.v.b.43.7		88	5.3	odd	4
800.2.v.b.707.7		88	32.3	odd	8
800.2.bb.b.107.18		88	1.1	even	1	trivial
800.2.bb.b.643.18		88	160.3	even	8	inner

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:	\( N \)	\(=\)	\( 800 = 2^{5} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	800.bb (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} +(4.62714 - 1.04737i) q^{6} -0.906290 q^{7} +(-0.768338 - 2.72207i) q^{8} +(5.83625 + 5.83625i) q^{9} +(0.392432 - 0.947415i) q^{11} +(4.48869 - 4.98663i) q^{12} +(-3.85684 - 1.59755i) q^{13} +(-1.04663 + 0.739795i) q^{14} +(-3.10931 - 2.51639i) q^{16} +(1.95970 - 1.95970i) q^{17} +(11.5040 + 1.97590i) q^{18} +(0.671071 + 1.62011i) q^{19} +(-2.80886 - 1.16347i) q^{21} +(-0.320166 - 1.41446i) q^{22} -1.58299 q^{23} +(1.11321 - 9.42287i) q^{24} +(-5.75812 + 1.30337i) q^{26} +(6.74455 + 16.2828i) q^{27} +(-0.604805 + 1.70870i) q^{28} +(2.34560 + 5.66278i) q^{29} +4.17491i q^{31} +(-5.64488 - 0.367943i) q^{32} +(2.43253 - 2.43253i) q^{33} +(0.663470 - 3.86284i) q^{34} +(14.8983 - 7.10877i) q^{36} +(-3.52354 + 1.45950i) q^{37} +(2.09746 + 1.32319i) q^{38} +(-9.90259 - 9.90259i) q^{39} +(0.655358 - 0.655358i) q^{41} +(-4.19353 + 0.949216i) q^{42} +(-2.55582 - 6.17029i) q^{43} +(-1.52435 - 1.37213i) q^{44} +(-1.82811 + 1.29218i) q^{46} +(-3.43714 - 3.43714i) q^{47} +(-6.40621 - 11.7907i) q^{48} -6.17864 q^{49} +(8.58950 - 3.55789i) q^{51} +(-5.58582 + 6.20548i) q^{52} +(-6.09374 + 2.52411i) q^{53} +(21.0804 + 13.2986i) q^{54} +(0.696336 + 2.46698i) q^{56} +5.88270i q^{57} +(7.33128 + 4.62496i) q^{58} +(-4.29438 + 10.3675i) q^{59} +(-1.24308 + 0.514899i) q^{61} +(3.40793 + 4.82138i) q^{62} +(-5.28933 - 5.28933i) q^{63} +(-6.81931 + 4.18294i) q^{64} +(0.823549 - 4.79484i) q^{66} +(4.24615 - 10.2511i) q^{67} +(-2.38699 - 5.00257i) q^{68} +(-4.90615 - 2.03219i) q^{69} +(5.43676 - 5.43676i) q^{71} +(11.4025 - 20.3709i) q^{72} +5.21568i q^{73} +(-2.87778 + 4.56173i) q^{74} +(3.50235 - 0.184056i) q^{76} +(-0.355657 + 0.858632i) q^{77} +(-19.5194 - 3.35259i) q^{78} -1.61999i q^{79} +34.3625i q^{81} +(0.221876 - 1.29180i) q^{82} +(2.97598 - 7.18465i) q^{83} +(-4.06805 + 4.51933i) q^{84} +(-7.98832 - 5.03945i) q^{86} +20.5619i q^{87} +(-2.88045 - 0.340292i) q^{88} +(-0.483064 + 0.483064i) q^{89} +(3.49541 + 1.44785i) q^{91} +(-1.05639 + 2.98453i) q^{92} +(-5.35962 + 12.9393i) q^{93} +(-6.77507 - 1.16367i) q^{94} +(-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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 4 q^{2} + 4 q^{3} - 8 q^{6} + 8 q^{7} - 8 q^{8} - 8 q^{11} + 20 q^{12} + 4 q^{13} - 16 q^{14} - 8 q^{16} + 12 q^{18} - 16 q^{19} - 8 q^{21} + 20 q^{22} + 8 q^{23} + 32 q^{24} - 8 q^{26} - 8 q^{27}+ \cdots - 16 q^{98}+O(q^{100}) \) 88 * q + 4 * q^2 + 4 * q^3 - 8 * q^6 + 8 * q^7 - 8 * q^8 - 8 * q^11 + 20 * q^12 + 4 * q^13 - 16 * q^14 - 8 * q^16 + 12 * q^18 - 16 * q^19 - 8 * q^21 + 20 * q^22 + 8 * q^23 + 32 * q^24 - 8 * q^26 - 8 * q^27 + 20 * q^28 - 16 * q^32 + 8 * q^33 - 8 * q^34 - 8 * q^36 + 4 * q^37 + 4 * q^38 - 8 * q^41 + 68 * q^42 - 28 * q^43 - 16 * q^44 - 8 * q^46 + 8 * q^47 + 88 * q^48 + 40 * q^49 + 8 * q^51 - 48 * q^52 + 4 * q^53 + 56 * q^54 + 40 * q^56 + 36 * q^58 - 40 * q^61 + 32 * q^62 + 56 * q^63 - 48 * q^64 + 72 * q^66 + 28 * q^67 - 8 * q^68 - 24 * q^69 + 24 * q^71 - 88 * q^72 + 56 * q^76 + 32 * q^77 - 112 * q^78 - 68 * q^82 - 36 * q^83 - 56 * q^84 + 24 * q^86 + 24 * q^88 - 8 * q^91 - 92 * q^92 - 8 * q^93 + 32 * q^94 + 24 * q^96 + 8 * q^97 - 16 * q^98

Introduction

L-functions

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