LMFDB - Embedded newform 800.2.v.b.707.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [800,2,Mod(43,800)] 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("800.43"); 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, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 800 = 2^{5} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	800.v (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			707.7
Character	$\chi$	$=$	800.707
Dual form			800.2.v.b.43.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

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

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/800\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$577$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.816290	+	1.15485i	−0.577204	+	0.816600i
$2$	−0.816290	+	1.15485i	−0.577204	+	0.816600i
$3$	−1.28377	−	3.09930i	−0.741185	−	1.78938i	−0.600991	−	0.799256i	$-0.705227\pi$
$3$	−1.28377	−	3.09930i	−0.741185	−	1.78938i	−0.140194	−	0.990124i	$-0.544773\pi$
$4$	−0.667342	−	1.88538i	−0.333671	−	0.942690i
$5$		0			0
$5$		0			0
$6$	4.62714	+	1.04737i	1.88902	+	0.427585i
$7$		−	0.906290i		−	0.342545i	−0.985224	−	0.171273i	$-0.945212\pi$
$7$		−	0.906290i		−	0.342545i	0.985224	−	0.171273i	$-0.0547879\pi$
$8$	2.72207	+	0.768338i	0.962397	+	0.271648i
$9$	−5.83625	+	5.83625i	−1.94542	+	1.94542i
$10$		0			0
$11$	0.392432	+	0.947415i	0.118323	+	0.285656i	0.971934	−	0.235255i	$-0.0755924\pi$
$11$	0.392432	+	0.947415i	0.118323	+	0.285656i	−0.853611	+	0.520911i	$0.825592\pi$
$12$	−4.98663	+	4.48869i	−1.43952	+	1.29577i
$13$	1.59755	+	3.85684i	0.443082	+	1.06969i	0.974862	+	0.222811i	$0.0715234\pi$
$13$	1.59755	+	3.85684i	0.443082	+	1.06969i	−0.531780	+	0.846883i	$0.678477\pi$
$14$	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	−0.903624	−	0.428327i	$-0.859103\pi$
$17$	−1.95970	+	1.95970i	−0.475297	+	0.475297i	0.428327	+	0.903624i	$0.359103\pi$
$18$	−1.97590	−	11.5040i	−0.465725	−	2.71153i
$19$	−0.671071	+	1.62011i	−0.153954	+	0.371678i	−0.981973	−	0.189022i	$-0.939468\pi$
$19$	−0.671071	+	1.62011i	−0.153954	+	0.371678i	0.828019	+	0.560701i	$0.189468\pi$
$20$		0			0
$21$	−2.80886	+	1.16347i	−0.612944	+	0.253890i
$22$	−1.41446	−	0.320166i	−0.301563	−	0.0682596i
$23$			1.58299i			0.330076i	0.986287	+	0.165038i	$0.0527747\pi$
$23$			1.58299i			0.330076i	−0.986287	+	0.165038i	$0.947225\pi$
$24$	−1.11321	−	9.42287i	−0.227232	−	1.92343i
$25$		0			0
$26$	−5.75812	−	1.30337i	−1.12926	−	0.255611i
$27$	16.2828	+	6.74455i	3.13362	+	1.29799i
$28$	−1.70870	+	0.604805i	−0.322914	+	0.114297i
$29$	−2.34560	+	5.66278i	−0.435567	+	1.05155i	0.541896	+	0.840446i	$0.317707\pi$
$29$	−2.34560	+	5.66278i	−0.435567	+	1.05155i	−0.977463	+	0.211107i	$0.932293\pi$
$30$		0			0
$31$		−	4.17491i		−	0.749836i	−0.927058	−	0.374918i	$-0.877671\pi$
$31$		−	4.17491i		−	0.749836i	0.927058	−	0.374918i	$-0.122329\pi$
$32$	−0.367943	−	5.64488i	−0.0650438	−	0.997882i
$33$	2.43253	−	2.43253i	0.423448	−	0.423448i
$34$	−0.663470	−	3.86284i	−0.113784	−	0.662471i
$35$		0			0
$36$	14.8983	+	7.10877i	2.48305	+	1.18479i
$37$	1.45950	−	3.52354i	0.239940	−	0.579267i	−0.757336	−	0.653025i	$-0.773499\pi$
$37$	1.45950	−	3.52354i	0.239940	−	0.579267i	0.997276	+	0.0737587i	$0.0234995\pi$
$38$	−1.32319	−	2.09746i	−0.214649	−	0.340253i
$39$	9.90259	−	9.90259i	1.58568	−	1.58568i
$40$		0			0
$41$	0.655358	+	0.655358i	0.102350	+	0.102350i	0.756427	−	0.654078i	$-0.226943\pi$
$41$	0.655358	+	0.655358i	0.102350	+	0.102350i	−0.654078	+	0.756427i	$0.726943\pi$
$42$	0.949216	−	4.19353i	0.146467	−	0.647076i
$43$	6.17029	+	2.55582i	0.940961	+	0.389759i	0.799826	−	0.600232i	$-0.204925\pi$
$43$	6.17029	+	2.55582i	0.940961	+	0.389759i	0.141134	+	0.989990i	$0.454925\pi$
$44$	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	$0.865354\pi$
$48$	11.7907	+	6.40621i	1.70184	+	0.924656i
$49$	6.17864			0.882663
$50$		0			0
$51$	8.58950	+	3.55789i	1.20277	+	0.498204i
$52$	6.20548	−	5.58582i	0.860546	−	0.774615i
$53$	−2.52411	+	6.09374i	−0.346713	+	0.837040i	0.650290	+	0.759686i	$0.274647\pi$
$53$	−2.52411	+	6.09374i	−0.346713	+	0.837040i	−0.997004	+	0.0773541i	$0.975353\pi$
$54$	−21.0804	+	13.2986i	−2.86868	+	1.80971i
$55$		0			0
$56$	0.696336	−	2.46698i	0.0930519	−	0.329664i
$57$	5.88270			0.779182
$58$	−4.62496	−	7.33128i	−0.607287	−	0.962645i
$59$	4.29438	+	10.3675i	0.559080	+	1.34974i	0.910495	+	0.413519i	$0.135701\pi$
$59$	4.29438	+	10.3675i	0.559080	+	1.34974i	−0.351415	+	0.936220i	$0.614299\pi$
$60$		0			0
$61$	−1.24308	−	0.514899i	−0.159160	−	0.0659261i	0.301681	−	0.953409i	$-0.402452\pi$
$61$	−1.24308	−	0.514899i	−0.159160	−	0.0659261i	−0.460841	+	0.887483i	$0.652452\pi$
$62$	4.82138	+	3.40793i	0.612316	+	0.432808i
$63$	5.28933	+	5.28933i	0.666393	+	0.666393i
$64$	6.81931	+	4.18294i	0.852414	+	0.522867i
$65$		0			0
$66$	0.823549	+	4.79484i	0.101372	+	0.590204i
$67$	−10.2511	+	4.24615i	−1.25237	+	0.518750i	−0.907560	−	0.419922i	$-0.862057\pi$
$67$	−10.2511	+	4.24615i	−1.25237	+	0.518750i	−0.344812	+	0.938672i	$0.612057\pi$
$68$	5.00257	+	2.38699i	0.606650	+	0.289465i
$69$	4.90615	−	2.03219i	0.590631	−	0.244647i
$70$		0			0
$71$	5.43676	+	5.43676i	0.645224	+	0.645224i	0.951835	−	0.306611i	$-0.0991949\pi$
$71$	5.43676	+	5.43676i	0.645224	+	0.645224i	−0.306611	+	0.951835i	$0.599195\pi$
$72$	−20.3709	+	11.4025i	−2.40073	+	1.34379i
$73$	−5.21568			−0.610449			−0.305225	−	0.952280i	$-0.598732\pi$
$73$	−5.21568			−0.610449			−0.305225	+	0.952280i	$0.598732\pi$
$74$	2.87778	+	4.56173i	0.334535	+	0.530290i
$75$		0			0
$76$	3.50235	+	0.184056i	0.401747	+	0.0211127i
$77$	0.858632	−	0.355657i	0.0978502	−	0.0405309i
$78$	3.35259	+	19.5194i	0.379606	+	2.21013i
$79$		−	1.61999i		−	0.182263i	−0.995839	−	0.0911315i	$-0.970952\pi$
$79$		−	1.61999i		−	0.182263i	0.995839	−	0.0911315i	$-0.0290484\pi$
$80$		0			0
$81$		−	34.3625i		−	3.81806i
$82$	−1.29180	+	0.221876i	−0.142655	+	0.0245021i
$83$	7.18465	−	2.97598i	0.788618	−	0.326656i	0.0482299	−	0.998836i	$-0.484642\pi$
$83$	7.18465	−	2.97598i	0.788618	−	0.326656i	0.740388	+	0.672180i	$0.234642\pi$
$84$	4.06805	+	4.51933i	0.443861	+	0.493100i
$85$		0			0
$86$	−7.98832	+	5.03945i	−0.861403	+	0.543418i
$87$	20.5619			2.20446
$88$	0.340292	+	2.88045i	0.0362753	+	0.307057i
$89$	0.483064	+	0.483064i	0.0512046	+	0.0512046i	0.732245	−	0.681041i	$-0.238472\pi$
$89$	0.483064	+	0.483064i	0.0512046	+	0.0512046i	−0.681041	+	0.732245i	$0.738472\pi$
$90$		0			0
$91$	3.49541	−	1.44785i	0.366419	−	0.151776i
$92$	2.98453	−	1.05639i	0.311159	−	0.110137i
$93$	−12.9393	+	5.35962i	−1.34174	+	0.555767i
$94$	6.77507	−	1.16367i	0.698795	−	0.120023i
$95$		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	$0.810693\pi$
$98$	−5.04356	+	7.13538i	−0.509476	+	0.720782i
$99$	−7.81968	−	3.23902i	−0.785908	−	0.325534i
$100$		0			0
$101$	4.87445	+	11.7680i	0.485026	+	1.17096i	0.957194	+	0.289447i	$0.0934715\pi$
$101$	4.87445	+	11.7680i	0.485026	+	1.17096i	−0.472168	+	0.881509i	$0.656528\pi$
$102$	−11.1203	+	7.01529i	−1.10108	+	0.694617i
$103$	−2.63961			−0.260089			−0.130044	−	0.991508i	$-0.541512\pi$
$103$	−2.63961			−0.260089			−0.130044	+	0.991508i	$0.541512\pi$
$104$	1.38530	+	11.7260i	0.135840	+	1.14983i
$105$		0			0
$106$	−4.97693	−	7.88922i	−0.483402	−	0.766269i
$107$	5.10959	−	12.3357i	0.493963	−	1.19253i	−0.458724	−	0.888579i	$-0.651693\pi$
$107$	5.10959	−	12.3357i	0.493963	−	1.19253i	0.952687	−	0.303953i	$-0.0983067\pi$
$108$	1.84985	−	35.2002i	0.178002	−	3.38714i
$109$	−14.7005	−	6.08914i	−1.40805	−	0.583233i	−0.456222	−	0.889866i	$-0.650798\pi$
$109$	−14.7005	−	6.08914i	−1.40805	−	0.583233i	−0.951828	+	0.306633i	$0.900798\pi$
$110$		0			0
$111$	−12.7942			−1.21437
$112$	2.28057	+	2.81793i	0.215494	+	0.266270i
$113$	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
$115$		0			0
$116$	12.2418	+	0.643334i	1.13662	+	0.0597321i
$117$	−31.8332	−	13.1857i	−2.94298	−	1.21902i
$118$	−15.4784	−	3.50357i	−1.42490	−	0.322530i
$119$	1.77606	+	1.77606i	0.162811	+	0.162811i
$120$		0			0
$121$	7.03458	−	7.03458i	0.639508	−	0.639508i
$122$	1.60934	−	1.01526i	0.145703	−	0.0919170i
$123$	1.18982	−	2.87248i	0.107282	−	0.259002i
$124$	−7.87128	+	2.78609i	−0.706862	+	0.250198i
$125$		0			0
$126$	−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	$0.332604\pi$
$128$	−10.3972	+	4.46078i	−0.918990	+	0.394281i
$129$		−	22.4046i		−	1.97262i
$130$		0			0
$131$	−6.23750	+	15.0586i	−0.544973	+	1.31568i	0.376205	+	0.926537i	$0.377229\pi$
$131$	−6.23750	+	15.0586i	−0.544973	+	1.31568i	−0.921177	+	0.389144i	$0.872771\pi$
$132$	−6.20956	−	2.96291i	−0.540473	−	0.257888i
$133$	1.46829	+	0.608184i	0.127317	+	0.0527363i
$134$	3.46422	−	15.3045i	0.299263	−	1.32211i
$135$		0			0
$136$	−6.84015	+	3.82873i	−0.586538	+	0.328311i
$137$			13.7858i			1.17780i	0.808205	+	0.588902i	$0.200439\pi$
$137$			13.7858i			1.17780i	−0.808205	+	0.588902i	$0.799561\pi$
$138$	−1.65797	+	7.32471i	−0.141136	+	0.623521i
$139$	5.66351	−	2.34590i	0.480373	−	0.198977i	−0.129339	−	0.991600i	$-0.541285\pi$
$139$	5.66351	−	2.34590i	0.480373	−	0.198977i	0.609711	+	0.792624i	$0.291285\pi$
$140$		0			0
$141$	−6.24021	+	15.0652i	−0.525521	+	1.26872i
$142$	−10.7166	+	1.84065i	−0.899316	+	0.154464i
$143$	−3.02709	+	3.02709i	−0.253138	+	0.253138i
$144$	3.46045	−	32.8330i	0.288371	−	2.73608i
$145$		0			0
$146$	4.25751	−	6.02331i	0.352354	−	0.498493i
$147$	−7.93196	−	19.1494i	−0.654217	−	1.57942i
$148$	−7.61720	−	0.400301i	−0.626130	−	0.0329045i
$149$	0.117762	+	0.284303i	0.00964745	+	0.0232910i	0.928630	−	0.371008i	$-0.120988\pi$
$149$	0.117762	+	0.284303i	0.00964745	+	0.0232910i	−0.918982	+	0.394299i	$0.870988\pi$
$150$		0			0
$151$	2.50445	−	2.50445i	0.203809	−	0.203809i	−0.597821	−	0.801630i	$-0.703967\pi$
$151$	2.50445	−	2.50445i	0.203809	−	0.203809i	0.801630	+	0.597821i	$0.203967\pi$
$152$	−3.07149	+	3.89444i	−0.249131	+	0.315880i
$153$		−	22.8746i		−	1.84930i
$154$	−0.290163	+	1.28191i	−0.0233820	+	0.103299i
$155$		0			0
$156$	−25.2785	−	12.0617i	−2.02390	−	0.965710i
$157$	8.87481	+	21.4257i	0.708287	+	1.70996i	0.704238	+	0.709964i	$0.251289\pi$
$157$	8.87481	+	21.4257i	0.708287	+	1.70996i	0.00404938	+	0.999992i	$0.498711\pi$
$158$	1.87084	+	1.32238i	0.148836	+	0.105203i
$159$	22.1267			1.75476
$160$		0			0
$161$	1.43465			0.113066
$162$	39.6835	+	28.0498i	3.11783	+	2.20380i
$163$	−0.447027	−	1.07922i	−0.0350138	−	0.0845309i	0.905405	−	0.424548i	$-0.139567\pi$
$163$	−0.447027	−	1.07922i	−0.0350138	−	0.0845309i	−0.940419	+	0.340017i	$0.889567\pi$
$164$	0.798250	−	1.67295i	0.0623328	−	0.130635i
$165$		0			0
$166$	−2.42795	+	10.7264i	−0.188446	+	0.832532i
$167$			1.33686i			0.103450i	0.998661	+	0.0517248i	$0.0164719\pi$
$167$			1.33686i			0.103450i	−0.998661	+	0.0517248i	$0.983528\pi$
$168$	−8.53985	+	1.00889i	−0.658863	+	0.0778373i
$169$	−3.13062	+	3.13062i	−0.240817	+	0.240817i
$170$		0			0
$171$	−5.53882	−	13.3719i	−0.423564	−	1.02257i
$172$	0.700991	−	13.3389i	0.0534501	−	1.01708i
$173$	6.30490	+	15.2214i	0.479352	+	1.15726i	0.959913	+	0.280298i	$0.0904332\pi$
$173$	6.30490	+	15.2214i	0.479352	+	1.15726i	−0.480561	+	0.876962i	$0.659567\pi$
$174$	−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
$178$	−0.952184	+	0.163545i	−0.0713692	+	0.0122582i
$179$	−3.18265	+	7.68360i	−0.237883	+	0.574299i	−0.997063	−	0.0765805i	$-0.975600\pi$
$179$	−3.18265	+	7.68360i	−0.237883	+	0.574299i	0.759181	+	0.650880i	$0.225600\pi$
$180$		0			0
$181$	4.55968	−	1.88868i	0.338919	−	0.140385i	−0.206732	−	0.978398i	$-0.566283\pi$
$181$	4.55968	−	1.88868i	0.338919	−	0.140385i	0.545650	+	0.838013i	$0.316283\pi$
$182$	−1.18123	+	5.21853i	−0.0875584	+	0.386823i
$183$			4.51368i			0.333661i
$184$	−1.21627	+	4.30900i	−0.0896646	+	0.317664i
$185$		0			0
$186$	4.37265	−	19.3179i	0.320619	−	1.41646i
$187$	−2.62570	−	1.08760i	−0.192010	−	0.0795331i
$188$	−4.18656	+	8.77406i	−0.305336	+	0.639914i
$189$	6.11252	−	14.7569i	0.444620	−	1.07341i
$190$		0			0
$191$		−	5.55963i		−	0.402281i	−0.979562	−	0.201140i	$-0.935535\pi$
$191$		−	5.55963i		−	0.402281i	0.979562	−	0.201140i	$-0.0644647\pi$
$192$	4.20972	−	26.5050i	0.303811	−	1.91283i
$193$	14.6069	−	14.6069i	1.05143	−	1.05143i	0.0528217	−	0.998604i	$-0.483178\pi$
$193$	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
$197$	−7.20550	+	17.3956i	−0.513371	+	1.23939i	0.428540	+	0.903523i	$0.359028\pi$
$197$	−7.20550	+	17.3956i	−0.513371	+	1.23939i	−0.941910	+	0.335864i	$0.890972\pi$
$198$	10.1237	−	6.38656i	0.719460	−	0.453873i
$199$	−12.1953	+	12.1953i	−0.864499	+	0.864499i	−0.991857	−	0.127358i	$-0.959350\pi$
$199$	−12.1953	+	12.1953i	−0.864499	+	0.864499i	0.127358	+	0.991857i	$0.459350\pi$
$200$		0			0
$201$	26.3201	+	26.3201i	1.85648	+	1.85648i
$202$	−17.5692	−	3.97682i	−1.23616	−	0.279808i
$203$	5.13212	+	2.12579i	0.360204	+	0.149202i
$204$	0.975831	−	18.5688i	0.0683218	−	1.30007i
$205$		0			0
$206$	2.15469	−	3.04835i	0.150124	−	0.212389i
$207$	−9.23872	−	9.23872i	−0.642135	−	0.642135i
$208$	−14.6726	−	7.97203i	−1.01736	−	0.552761i
$209$	−1.79826			−0.124388
$210$		0			0
$211$	−21.2722	−	8.81122i	−1.46444	−	0.606589i	−0.498854	−	0.866686i	$-0.666245\pi$
$211$	−21.2722	−	8.81122i	−1.46444	−	0.606589i	−0.965583	+	0.260097i	$0.916245\pi$
$212$	13.1735	+	0.692294i	0.904757	+	0.0475470i
$213$	9.87058	−	23.8297i	0.676321	−	1.63278i
$214$	10.0749	+	15.9703i	0.688704	+	1.09170i
$215$		0			0
$216$	39.1408	+	30.8698i	2.66319	+	2.10043i
$217$	−3.78368			−0.256853
$218$	19.0319	−	12.0063i	1.28900	−	0.813169i
$219$	6.69574	+	16.1649i	0.452456	+	1.09233i
$220$		0			0
$221$	−10.6890	−	4.42752i	−0.719018	−	0.297827i
$222$	10.4437	−	14.7753i	0.700938	−	0.991653i
$223$	15.9419	+	15.9419i	1.06755	+	1.06755i	0.997547	+	0.0700048i	$0.0223014\pi$
$223$	15.9419	+	15.9419i	1.06755	+	1.06755i	0.0700048	+	0.997547i	$0.477699\pi$
$224$	−5.11589	+	0.333463i	−0.341820	+	0.0222804i
$225$		0			0
$226$	−1.22128	+	0.209764i	−0.0812386	+	0.0139533i
$227$	18.9290	−	7.84063i	1.25636	−	0.520401i	0.347569	−	0.937654i	$-0.387007\pi$
$227$	18.9290	−	7.84063i	1.25636	−	0.520401i	0.908790	+	0.417253i	$0.137007\pi$
$228$	−3.92577	−	11.0911i	−0.259990	−	0.734527i
$229$	−23.0497	+	9.54752i	−1.52317	+	0.630918i	−0.978224	−	0.207553i	$-0.933450\pi$
$229$	−23.0497	+	9.54752i	−1.52317	+	0.630918i	−0.544946	+	0.838471i	$0.683450\pi$
$230$		0			0
$231$	−2.20457	−	2.20457i	−0.145050	−	0.145050i
$232$	−10.7358	+	13.6123i	−0.704841	+	0.893689i
$233$	−13.5423			−0.887185			−0.443593	−	0.896229i	$-0.646296\pi$
$233$	−13.5423			−0.887185			−0.443593	+	0.896229i	$0.646296\pi$
$234$	41.2126	−	25.9991i	2.69415	−	1.69961i
$235$		0			0
$236$	16.6809	−	15.0152i	1.08584	−	0.977408i
$237$	−5.02083	+	2.07969i	−0.326138	+	0.135091i
$238$	−3.50085	+	0.601296i	−0.226926	+	0.0389762i
$239$		−	18.1767i		−	1.17575i	−0.808950	−	0.587877i	$-0.799964\pi$
$239$		−	18.1767i		−	1.17575i	0.808950	−	0.587877i	$-0.200036\pi$
$240$		0			0
$241$			3.95583i			0.254818i	0.991850	+	0.127409i	$0.0406660\pi$
$241$			3.95583i			0.254818i	−0.991850	+	0.127409i	$0.959334\pi$
$242$	2.38161	+	13.8661i	0.153096	+	0.891348i
$243$	−57.6513	+	23.8800i	−3.69833	+	1.53190i
$244$	−0.141223	+	2.68729i	−0.00904086	+	0.172036i
$245$		0			0
$246$	2.34603	+	3.71883i	0.149578	+	0.237104i
$247$	−7.32056			−0.465796
$248$	3.20774	−	11.3644i	0.203692	−	0.721639i
$249$	−18.4469	−	18.4469i	−1.16902	−	1.16902i
$250$		0			0
$251$	9.99284	−	4.13917i	0.630743	−	0.261262i	−0.0443259	−	0.999017i	$-0.514114\pi$
$251$	9.99284	−	4.13917i	0.630743	−	0.261262i	0.675069	+	0.737755i	$0.264114\pi$
$252$	6.44260	−	13.5022i	0.405846	−	0.850558i
$253$	−1.49975	+	0.621215i	−0.0942882	+	0.0390555i
$254$	−1.38456	−	8.06116i	−0.0868753	−	0.505802i
$255$		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	$0.653124\pi$
$258$	25.8739	+	18.2887i	1.61084	+	1.13860i
$259$	−3.19335	−	1.32273i	−0.198425	−	0.0821903i
$260$		0			0
$261$	−19.3599	−	46.7390i	−1.19835	−	2.89307i
$262$	−12.2988	−	19.4956i	−0.759824	−	1.20444i
$263$	−23.6751			−1.45987			−0.729934	−	0.683517i	$-0.760449\pi$
$263$	−23.6751			−1.45987			−0.729934	+	0.683517i	$0.760449\pi$
$264$	8.49050	−	4.75250i	0.522554	−	0.292496i
$265$		0			0
$266$	−1.90091	+	1.19919i	−0.116552	+	0.0735272i
$267$	0.877014	−	2.11730i	0.0536724	−	0.129577i
$268$	14.8466	+	16.4936i	0.906900	+	1.00751i
$269$	18.3200	+	7.58841i	1.11699	+	0.462674i	0.863341	−	0.504622i	$-0.168368\pi$
$269$	18.3200	+	7.58841i	1.11699	+	0.462674i	0.253653	+	0.967295i	$0.418368\pi$
$270$		0			0
$271$	−5.20237			−0.316021			−0.158011	−	0.987437i	$-0.550508\pi$
$271$	−5.20237			−0.316021			−0.158011	+	0.987437i	$0.550508\pi$
$272$	1.16195	−	11.0247i	0.0704536	−	0.668469i
$273$	−8.97461	−	8.97461i	−0.543168	−	0.543168i
$274$	−15.9205	−	11.2532i	−0.961794	−	0.679833i
$275$		0			0
$276$	−7.10554	−	7.89378i	−0.427703	−	0.475150i
$277$	7.66078	+	3.17320i	0.460292	+	0.190659i	0.600765	−	0.799425i	$-0.294863\pi$
$277$	7.66078	+	3.17320i	0.460292	+	0.190659i	−0.140474	+	0.990084i	$0.544863\pi$
$278$	−1.91391	+	8.45542i	−0.114788	+	0.507122i
$279$	24.3658	+	24.3658i	1.45874	+	1.45874i
$280$		0			0
$281$	5.30131	−	5.30131i	0.316250	−	0.316250i	−0.531075	−	0.847325i	$-0.678212\pi$
$281$	5.30131	−	5.30131i	0.316250	−	0.316250i	0.847325	+	0.531075i	$0.178212\pi$
$282$	−12.3042	−	19.5041i	−0.732704	−	1.16145i
$283$	−3.50116	+	8.45255i	−0.208122	+	0.502452i	−0.993128	−	0.117037i	$-0.962660\pi$
$283$	−3.50116	+	8.45255i	−0.208122	+	0.502452i	0.785005	+	0.619489i	$0.212660\pi$
$284$	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
$288$	35.0923	+	30.7975i	2.06783	+	1.81476i
$289$			9.31915i			0.548185i
$290$		0			0
$291$	−4.79244	+	11.5700i	−0.280938	+	0.678244i
$292$	3.48064	+	9.83354i	0.203689	+	0.575464i
$293$	−0.973169	−	0.403100i	−0.0568532	−	0.0235493i	0.354076	−	0.935217i	$-0.384796\pi$
$293$	−0.973169	−	0.403100i	−0.0568532	−	0.0235493i	−0.410929	+	0.911667i	$0.634796\pi$
$294$	28.5894	+	6.47129i	1.66737	+	0.377414i
$295$		0			0
$296$	6.68013	−	8.46993i	0.388274	−	0.492305i
$297$			18.0733i			1.04872i
$298$	−0.424455	−	0.0960764i	−0.0245880	−	0.00556556i
$299$	−6.10533	+	2.52891i	−0.353080	+	0.146251i
$300$		0			0
$301$	2.31631	−	5.59207i	0.133510	−	0.322322i
$302$	0.847898	+	4.93660i	0.0487910	+	0.284070i
$303$	30.2147	−	30.2147i	1.73579	−	1.73579i
$304$	−1.99025	−	6.72609i	−0.114149	−	0.385768i
$305$		0			0
$306$	26.4167	+	18.6723i	1.51014	+	1.06742i
$307$	3.83681	+	9.26288i	0.218978	+	0.528661i	0.994748	−	0.102356i	$-0.0326380\pi$
$307$	3.83681	+	9.26288i	0.218978	+	0.528661i	−0.775769	+	0.631017i	$0.782638\pi$
$308$	−1.24355	−	1.38150i	−0.0708578	−	0.0787184i
$309$	3.38866	+	8.18095i	0.192774	+	0.465398i
$310$		0			0
$311$	−16.6804	+	16.6804i	−0.945856	+	0.945856i	−0.998608	−	0.0527517i	$-0.983201\pi$
$311$	−16.6804	+	16.6804i	−0.945856	+	0.945856i	0.0527517	+	0.998608i	$0.483201\pi$
$312$	34.5641	−	19.3470i	1.95680	−	1.09531i
$313$		−	18.8189i		−	1.06371i	−0.846836	−	0.531854i	$-0.821496\pi$
$313$		−	18.8189i		−	1.06371i	0.846836	−	0.531854i	$-0.178504\pi$
$314$	−31.9878	−	7.24052i	−1.80518	−	0.408606i
$315$		0			0
$316$	−3.05429	+	1.08109i	−0.171817	+	0.0608159i
$317$	−3.54343	−	8.55459i	−0.199019	−	0.480474i	0.792589	−	0.609756i	$-0.208733\pi$
$317$	−3.54343	−	8.55459i	−0.199019	−	0.480474i	−0.991608	+	0.129282i	$0.958733\pi$
$318$	−18.0618	+	25.5529i	−1.01285	+	1.43294i
$319$	−6.28549			−0.351920
$320$		0			0
$321$	−44.7914			−2.50001
$322$	−1.17109	+	1.65680i	−0.0652621	+	0.0923296i
$323$	−1.85983	−	4.49002i	−0.103484	−	0.249832i
$324$	−64.7864	+	22.9316i	−3.59925	+	1.27398i
$325$		0			0
$326$	1.61123	+	0.364707i	0.0892380	+	0.0201993i
$327$			53.3782i			2.95182i
$328$	1.28039	+	2.28746i	0.0706978	+	0.126304i
$329$	−3.11504	+	3.11504i	−0.171738	+	0.171738i
$330$		0			0
$331$	2.48736	+	6.00502i	0.136718	+	0.330066i	0.977379	−	0.211496i	$-0.0678334\pi$
$331$	2.48736	+	6.00502i	0.136718	+	0.330066i	−0.840661	+	0.541561i	$0.817833\pi$
$332$	−10.4055	−	11.5598i	−0.571074	−	0.634426i
$333$	12.0463	+	29.0823i	0.660132	+	1.59370i
$334$	−1.54387	−	1.09127i	−0.0844769	−	0.0597115i
$335$		0			0
$336$	5.80588	−	10.6858i	0.316737	−	0.582956i
$337$	−18.5988	+	18.5988i	−1.01314	+	1.01314i	−0.0132301	+	0.999912i	$0.504211\pi$
$337$	−18.5988	+	18.5988i	−1.01314	+	1.01314i	−0.999912	+	0.0132301i	$0.995789\pi$
$338$	−1.05989	−	6.17088i	−0.0576506	−	0.335652i
$339$	1.12487	−	2.71568i	0.0610946	−	0.147495i
$340$		0			0
$341$	3.95537	−	1.63837i	0.214195	−	0.0887226i
$342$	19.9638	+	4.51885i	1.07952	+	0.244351i
$343$		−	11.9437i		−	0.644897i
$344$	14.8322	+	11.6980i	0.799700	+	0.630713i
$345$		0			0
$346$	−22.7250	−	5.14386i	−1.22170	−	0.276535i
$347$	−7.77311	−	3.21973i	−0.417283	−	0.172844i	0.164156	−	0.986434i	$-0.447510\pi$
$347$	−7.77311	−	3.21973i	−0.417283	−	0.172844i	−0.581439	+	0.813590i	$0.697510\pi$
$348$	−13.7218	−	38.7669i	−0.735566	−	2.07812i
$349$	−6.91854	+	16.7028i	−0.370341	+	0.894082i	0.623352	+	0.781942i	$0.285771\pi$
$349$	−6.91854	+	16.7028i	−0.370341	+	0.894082i	−0.993692	+	0.112140i	$0.964229\pi$
$350$		0			0
$351$			73.5749i			3.92714i
$352$	5.20364	−	2.56382i	0.277355	−	0.136652i
$353$	−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
$357$	3.22447	−	7.78457i	0.170657	−	0.412003i
$358$	−6.27542	−	9.94752i	−0.331666	−	0.525743i
$359$	−4.49159	+	4.49159i	−0.237057	+	0.237057i	−0.815630	−	0.578573i	$-0.803610\pi$
$359$	−4.49159	+	4.49159i	−0.237057	+	0.237057i	0.578573	+	0.815630i	$0.303610\pi$
$360$		0			0
$361$	11.2606	+	11.2606i	0.592664	+	0.592664i
$362$	−1.54088	+	6.80745i	−0.0809871	+	0.357792i
$363$	−30.8331	−	12.7715i	−1.61832	−	0.670328i
$364$	−5.06237	−	5.62397i	−0.265341	−	0.294776i
$365$		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	$0.801068\pi$
$368$	−3.98341	−	4.92200i	−0.207650	−	0.256577i
$369$	−7.64966			−0.398226
$370$		0			0
$371$	5.52269	+	2.28757i	0.286724	+	0.118765i
$372$	18.7398	+	20.8187i	0.971616	+	1.07940i
$373$	−0.872108	+	2.10545i	−0.0451560	+	0.109016i	−0.944848	−	0.327509i	$-0.893791\pi$
$373$	−0.872108	+	2.10545i	−0.0451560	+	0.109016i	0.899692	+	0.436525i	$0.143791\pi$
$374$	3.39934	−	2.14448i	0.175776	−	0.110889i
$375$		0			0
$376$	−6.71524	−	11.9970i	−0.346312	−	0.618699i
$377$	−25.5877			−1.31783
$378$	12.0524	+	19.1049i	0.619909	+	0.982652i
$379$	−12.3034	−	29.7030i	−0.631982	−	1.52574i	−0.837128	−	0.547008i	$-0.815767\pi$
$379$	−12.3034	−	29.7030i	−0.631982	−	1.52574i	0.205146	−	0.978731i	$-0.434233\pi$
$380$		0			0
$381$	17.9250	+	7.42478i	0.918326	+	0.380383i
$382$	6.42052	+	4.53827i	0.328502	+	0.232198i
$383$	16.7729	+	16.7729i	0.857057	+	0.857057i	0.990990	−	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			0
$386$	4.94526	+	28.7921i	0.251707	+	1.46548i
$387$	−50.9278	+	21.0950i	−2.58880	+	1.07232i
$388$	−3.21525	+	6.73841i	−0.163230	+	0.342091i
$389$	22.8738	−	9.47462i	1.15975	−	0.480382i	0.281955	−	0.959428i	$-0.409017\pi$
$389$	22.8738	−	9.47462i	1.15975	−	0.480382i	0.877790	+	0.479045i	$0.159017\pi$
$390$		0			0
$391$	−3.10218	−	3.10218i	−0.156884	−	0.156884i
$392$	16.8187	+	4.74728i	0.849472	+	0.239774i
$393$	54.6787			2.75818
$394$	−14.2075	−	22.5211i	−0.715764	−	1.13460i
$395$		0			0
$396$	−0.888374	+	16.9046i	−0.0446425	+	0.849488i
$397$	15.3133	−	6.34300i	0.768555	−	0.318346i	0.0362680	−	0.999342i	$-0.488453\pi$
$397$	15.3133	−	6.34300i	0.768555	−	0.318346i	0.732287	+	0.680996i	$0.238453\pi$
$398$	−4.12879	−	24.0385i	−0.206957	−	1.20494i
$399$		−	5.33142i		−	0.266905i
$400$		0			0
$401$			12.2631i			0.612389i	0.951969	+	0.306195i	$0.0990558\pi$
$401$			12.2631i			0.612389i	−0.951969	+	0.306195i	$0.900944\pi$
$402$	−51.8806	+	8.91087i	−2.58757	+	0.444434i
$403$	16.1019	−	6.66964i	0.802095	−	0.332238i
$404$	18.9341	−	17.0434i	0.942009	−	0.847943i
$405$		0			0
$406$	−6.64427	+	4.19155i	−0.329749	+	0.208023i
$407$	3.91101			0.193861
$408$	20.6475	+	16.2844i	1.02221	+	0.806200i
$409$	−15.5820	−	15.5820i	−0.770479	−	0.770479i	0.207711	−	0.978190i	$-0.433399\pi$
$409$	−15.5820	−	15.5820i	−0.770479	−	0.770479i	−0.978190	+	0.207711i	$0.933399\pi$
$410$		0			0
$411$	42.7264	−	17.6978i	2.10754	−	0.872970i
$412$	1.76153	+	4.97667i	0.0867842	+	0.245183i
$413$	9.39600	−	3.89195i	0.462347	−	0.191510i
$414$	18.2108	−	3.12783i	0.895011	−	0.153725i
$415$		0			0
$416$	21.1836	−	10.4371i	1.03861	−	0.511720i
$417$	−14.5413	−	14.5413i	−0.712090	−	0.712090i
$418$	1.46790	−	2.07672i	0.0717975	−	0.101576i
$419$	27.6906	+	11.4698i	1.35278	+	0.560338i	0.937064	−	0.349158i	$-0.113532\pi$
$419$	27.6906	+	11.4698i	1.35278	+	0.560338i	0.415712	+	0.909496i	$0.363532\pi$
$420$		0			0
$421$	10.5101	+	25.3736i	0.512231	+	1.23663i	0.942582	+	0.333973i	$0.108390\pi$
$421$	10.5101	+	25.3736i	0.512231	+	1.23663i	−0.430352	+	0.902661i	$0.641610\pi$
$422$	27.5399	−	17.3736i	1.34062	−	0.845733i
$423$	40.1200			1.95070
$424$	−11.5529	+	14.6482i	−0.561056	+	0.711380i
$425$		0			0
$426$	19.4624	+	30.8509i	0.942955	+	1.49473i
$427$	−0.466648	+	1.12659i	−0.0225827	+	0.0545194i
$428$	−26.6672	−	1.40142i	−1.28901	−	0.0677403i
$429$	13.2679	+	5.49576i	0.640583	+	0.265338i
$430$		0			0
$431$	11.3673			0.547542			0.273771	−	0.961795i	$-0.411729\pi$
$431$	11.3673			0.547542			0.273771	+	0.961795i	$0.411729\pi$
$432$	−67.6001	+	20.0029i	−3.25241	+	0.962390i
$433$	−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
$435$		0			0
$436$	−1.67008	+	31.7795i	−0.0799825	+	1.52196i
$437$	−2.56461	−	1.06230i	−0.122682	−	0.0508165i
$438$	−24.1337	−	5.46272i	−1.15315	−	0.261019i
$439$	−24.2793	−	24.2793i	−1.15879	−	1.15879i	−0.984737	−	0.174052i	$-0.944314\pi$
$439$	−24.2793	−	24.2793i	−1.15879	−	1.15879i	−0.174052	−	0.984737i	$-0.555686\pi$
$440$		0			0
$441$	−36.0601	+	36.0601i	−1.71715	+	1.71715i
$442$	13.8384	−	8.72999i	0.658225	−	0.415243i
$443$	−8.53951	+	20.6162i	−0.405724	+	0.979505i	0.580525	+	0.814242i	$0.302847\pi$
$443$	−8.53951	+	20.6162i	−0.405724	+	0.979505i	−0.986250	+	0.165263i	$0.947153\pi$
$444$	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
$448$	3.79095	−	6.18027i	0.179106	−	0.291990i
$449$		−	1.60758i		−	0.0758663i	−0.999280	−	0.0379332i	$-0.987923\pi$
$449$		−	1.60758i		−	0.0758663i	0.999280	−	0.0379332i	$-0.0120774\pi$
$450$		0			0
$451$	−0.363712	+	0.878079i	−0.0171265	+	0.0413471i
$452$	0.754676	−	1.58162i	0.0354970	−	0.0743933i
$453$	−10.9772	−	4.54689i	−0.515752	−	0.213631i
$454$	−6.39679	+	28.2603i	−0.300216	+	1.32632i
$455$		0			0
$456$	16.0131	+	4.51990i	0.749882	+	0.211664i
$457$			4.76573i			0.222932i	0.993768	+	0.111466i	$0.0355545\pi$
$457$			4.76573i			0.222932i	−0.993768	+	0.111466i	$0.964445\pi$
$458$	7.78935	−	34.4125i	0.363973	−	1.60799i
$459$	−45.1267	+	18.6921i	−2.10633	+	0.872472i
$460$		0			0
$461$	1.89178	−	4.56715i	0.0881088	−	0.212714i	−0.873683	−	0.486496i	$-0.838275\pi$
$461$	1.89178	−	4.56715i	0.0881088	−	0.212714i	0.961792	+	0.273782i	$0.0882748\pi$
$462$	4.34551	−	0.746374i	0.202172	−	0.0347244i
$463$	12.2119	−	12.2119i	0.567536	−	0.567536i	−0.363901	−	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
$467$	−6.11934	−	14.7734i	−0.283169	−	0.683631i	0.716737	−	0.697344i	$-0.245635\pi$
$467$	−6.11934	−	14.7734i	−0.283169	−	0.683631i	−0.999906	+	0.0137126i	$0.995635\pi$
$468$	−3.61649	+	68.8170i	−0.167172	+	3.18107i
$469$	3.84824	+	9.29047i	0.177695	+	0.428994i
$470$		0			0
$471$	55.0113	−	55.0113i	2.53479	−	2.53479i
$472$	3.72382	+	31.5207i	0.171402	+	1.45086i
$473$			6.84881i			0.314909i
$474$	1.69672	−	7.49592i	0.0779330	−	0.344299i
$475$		0			0
$476$	2.16330	−	4.53377i	0.0991548	−	0.207805i
$477$	−20.8333	−	50.2960i	−0.953890	−	2.30289i
$478$	20.9913	+	14.8375i	0.960121	+	0.678650i
$479$	−28.6370			−1.30846			−0.654229	−	0.756297i	$-0.727007\pi$
$479$	−28.6370			−1.30846			−0.654229	+	0.756297i	$0.727007\pi$
$480$		0			0
$481$	15.9214			0.725951
$482$	−4.56838	−	3.22910i	−0.208084	−	0.147082i
$483$	−1.84176	−	4.44639i	−0.0838028	−	0.202318i
$484$	−17.9573	−	8.56838i	−0.816242	−	0.389472i
$485$		0			0
$486$	19.4825	−	86.0714i	0.883744	−	3.90428i
$487$		−	25.7000i		−	1.16458i	−0.812982	−	0.582289i	$-0.802157\pi$
$487$		−	25.7000i		−	1.16458i	0.812982	−	0.582289i	$-0.197843\pi$
$488$	−2.98812	−	2.35669i	−0.135266	−	0.106683i
$489$	−2.77094	+	2.77094i	−0.125306	+	0.125306i
$490$		0			0
$491$	−1.37835	−	3.32764i	−0.0622042	−	0.150174i	0.889721	−	0.456505i	$-0.150899\pi$
$491$	−1.37835	−	3.32764i	−0.0622042	−	0.150174i	−0.951925	+	0.306330i	$0.900899\pi$
$492$	−6.20972	−	0.326335i	−0.279956	−	0.0147123i
$493$	−6.50068	−	15.6940i	−0.292776	−	0.706824i
$494$	5.97570	−	8.45413i	0.268859	−	0.380369i
$495$		0			0
$496$	10.5057	+	12.9811i	0.471719	+	0.582868i
$497$	4.92728	−	4.92728i	0.221019	−	0.221019i
$498$	36.3613	−	6.24532i	1.62939	−	0.279860i
$499$	10.7030	−	25.8393i	0.479131	−	1.15673i	−0.480885	−	0.876783i	$-0.659685\pi$
$499$	10.7030	−	25.8393i	0.479131	−	1.15673i	0.960017	−	0.279942i	$-0.0903153\pi$
$500$		0			0
$501$	4.14333	−	1.71623i	0.185111	−	0.0766753i
$502$	−3.37695	+	14.9190i	−0.150721	+	0.665866i
$503$		−	28.9180i		−	1.28939i	−0.764440	−	0.644695i	$-0.776985\pi$
$503$		−	28.9180i		−	1.28939i	0.764440	−	0.644695i	$-0.223015\pi$
$504$	10.3339	+	18.4619i	0.460310	+	0.822359i
$505$		0			0
$506$	0.506819	−	2.23907i	0.0225309	−	0.0995387i
$507$	13.7217	+	5.68372i	0.609403	+	0.252423i
$508$	10.4396	+	4.98129i	0.463183	+	0.221009i
$509$	−13.3736	+	32.2866i	−0.592772	+	1.43108i	0.288042	+	0.957618i	$0.406996\pi$
$509$	−13.3736	+	32.2866i	−0.592772	+	1.43108i	−0.880815	+	0.473461i	$0.843004\pi$
$510$		0			0
$511$			4.72692i			0.209106i
$512$	15.3487	+	16.6258i	0.678325	+	0.734762i
$513$	−21.8538	+	21.8538i	−0.964869	+	0.964869i
$514$	−13.3918	+	2.30014i	−0.590688	+	0.101455i
$515$		0			0
$516$	−42.2413	+	14.9516i	−1.85957	+	0.658206i
$517$	1.90755	−	4.60524i	0.0838940	−	0.202538i
$518$	4.13425	−	2.60810i	0.181648	−	0.114593i
$519$	39.0815	−	39.0815i	1.71549	−	1.71549i
$520$		0			0
$521$	7.57884	+	7.57884i	0.332035	+	0.332035i	0.853359	−	0.521324i	$-0.174562\pi$
$521$	7.57884	+	7.57884i	0.332035	+	0.332035i	−0.521324	+	0.853359i	$0.674562\pi$
$522$	69.7796	+	15.7948i	3.05417	+	0.691320i
$523$	−10.4923	−	4.34605i	−0.458796	−	0.190039i	0.141301	−	0.989967i	$-0.454871\pi$
$523$	−10.4923	−	4.34605i	−0.458796	−	0.190039i	−0.600097	+	0.799927i	$0.704871\pi$
$524$	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
$528$	−1.44230	+	13.6846i	−0.0627681	+	0.595548i
$529$	20.4941			0.891050
$530$		0			0
$531$	−85.5707	−	35.4445i	−3.71345	−	1.53816i
$532$	0.166808	−	3.17414i	0.00723206	−	0.137617i
$533$	−1.48064	+	3.57458i	−0.0641336	+	0.154832i
$534$	1.72926	+	2.74115i	0.0748324	+	0.118621i
$535$		0			0
$536$	−31.1667	+	3.68199i	−1.34620	+	0.159038i
$537$	27.8996			1.20395
$538$	−23.7179	+	14.9625i	−1.02255	+	0.645079i
$539$	2.42470	+	5.85373i	0.104439	+	0.252138i
$540$		0			0
$541$	11.7217	+	4.85528i	0.503955	+	0.208745i	0.620153	−	0.784481i	$-0.287071\pi$
$541$	11.7217	+	4.85528i	0.503955	+	0.208745i	−0.116198	+	0.993226i	$0.537071\pi$
$542$	4.24664	−	6.00793i	0.182409	−	0.258063i
$543$	−11.7072	−	11.7072i	−0.502403	−	0.502403i
$544$	11.7833	+	10.3412i	0.505206	+	0.443375i
$545$		0			0
$546$	17.6902	−	3.03842i	0.757070	−	0.130032i
$547$	29.6855	−	12.2962i	1.26926	−	0.525746i	0.356522	−	0.934287i	$-0.383962\pi$
$547$	29.6855	−	12.2962i	1.26926	−	0.525746i	0.912740	+	0.408541i	$0.133962\pi$
$548$	25.9915	−	9.19987i	1.11030	−	0.392999i
$549$	10.2600	−	4.24983i	0.437886	−	0.181378i
$550$		0			0
$551$	−7.60026	−	7.60026i	−0.323782	−	0.323782i
$552$	14.9163	−	1.76219i	0.634879	−	0.0750038i
$553$	−1.46818			−0.0624333
$554$	−9.91798	+	6.25678i	−0.421374	+	0.265825i
$555$		0			0
$556$	−8.20241	−	9.11234i	−0.347860	−	0.386449i
$557$	−29.9952	+	12.4244i	−1.27094	+	0.526440i	−0.913250	−	0.407400i	$-0.866435\pi$
$557$	−29.9952	+	12.4244i	−1.27094	+	0.526440i	−0.357689	+	0.933841i	$0.616435\pi$
$558$	−48.0283	+	8.24922i	−2.03320	+	0.349217i
$559$			27.8809i			1.17923i
$560$		0			0
$561$			9.53404i			0.402528i
$562$	1.79480	+	10.4496i	0.0757089	+	0.440790i
$563$	0.586068	−	0.242757i	0.0246998	−	0.0102310i	−0.370299	−	0.928912i	$-0.620745\pi$
$563$	0.586068	−	0.242757i	0.0246998	−	0.0102310i	0.394999	+	0.918681i	$0.370745\pi$
$564$	32.5680	+	1.71152i	1.37136	+	0.0720680i
$565$		0			0
$566$	−6.90344	−	10.9430i	−0.290173	−	0.459970i
$567$	−31.1424			−1.30786
$568$	10.6220	+	18.9765i	0.445688	+	0.796236i
$569$	0.0516248	+	0.0516248i	0.00216422	+	0.00216422i	0.708188	−	0.706024i	$-0.249513\pi$
$569$	0.0516248	+	0.0516248i	0.00216422	+	0.00216422i	−0.706024	+	0.708188i	$0.749513\pi$
$570$		0			0
$571$	−23.4324	+	9.70604i	−0.980617	+	0.406185i	−0.814654	−	0.579947i	$-0.803073\pi$
$571$	−23.4324	+	9.70604i	−0.980617	+	0.406185i	−0.165963	+	0.986132i	$0.553073\pi$
$572$	7.72732	+	3.68711i	0.323096	+	0.154166i
$573$	−17.2309	+	7.13729i	−0.719833	+	0.298164i
$574$	0.201084	+	1.17074i	0.00839308	+	0.0488659i
$575$		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	$0.753561\pi$
$578$	−10.7622	−	7.60713i	−0.447648	−	0.316415i
$579$	−64.0229	−	26.5192i	−2.66070	−	1.10210i
$580$		0			0
$581$	−2.69710	−	6.51137i	−0.111894	−	0.270137i
$582$	−9.44952	−	14.9790i	−0.391695	−	0.620899i
$583$	−6.76384			−0.280130
$584$	−14.1974	−	4.00740i	−0.587494	−	0.165828i
$585$		0			0
$586$	1.25991	−	0.794815i	0.0520463	−	0.0328335i
$587$	15.6574	−	37.8003i	0.646250	−	1.56019i	−0.171858	−	0.985122i	$-0.554977\pi$
$587$	15.6574	−	37.8003i	0.646250	−	1.56019i	0.818108	−	0.575065i	$-0.195023\pi$
$588$	−30.8106	+	27.7340i	−1.27061	+	1.14373i
$589$	6.76380	+	2.80166i	0.278698	+	0.115440i
$590$		0			0
$591$	63.1644			2.59824
$592$	4.32856	+	14.6284i	0.177903	+	0.601225i
$593$	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
$595$		0			0
$596$	0.457431	−	0.411754i	0.0187371	−	0.0168661i
$597$	53.4526	+	22.1408i	2.18767	+	0.906162i
$598$	2.06321	−	9.11504i	0.0843710	−	0.372742i
$599$	17.4180	+	17.4180i	0.711682	+	0.711682i	0.966887	−	0.255205i	$-0.0821430\pi$
$599$	17.4180	+	17.4180i	0.711682	+	0.711682i	−0.255205	+	0.966887i	$0.582143\pi$
$600$		0			0
$601$	24.9826	−	24.9826i	1.01906	−	1.01906i	0.0192475	−	0.999815i	$-0.493873\pi$
$601$	24.9826	−	24.9826i	1.01906	−	1.01906i	0.999815	−	0.0192475i	$-0.00612705\pi$
$602$	4.56720	+	7.23973i	0.186145	+	0.295070i
$603$	35.0465	−	84.6096i	1.42720	−	3.44557i
$604$	−6.39315	−	3.05051i	−0.260134	−	0.124123i
$605$		0			0
$606$	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	$0.364997\pi$
$608$	9.39222	+	3.19200i	0.380905	+	0.129453i
$609$		−	18.6350i		−	0.755128i
$610$		0			0
$611$	7.76547	−	18.7475i	0.314157	−	0.758443i
$612$	−43.1273	+	15.2652i	−1.74332	+	0.617059i
$613$	−7.01389	−	2.90525i	−0.283288	−	0.117342i	0.236515	−	0.971628i	$-0.423995\pi$
$613$	−7.01389	−	2.90525i	−0.283288	−	0.117342i	−0.519803	+	0.854286i	$0.673995\pi$
$614$	−13.8292	−	3.13027i	−0.558100	−	0.126327i
$615$		0			0
$616$	2.61052	−	0.308403i	0.105181	−	0.0124259i
$617$		−	10.1074i		−	0.406909i	−0.979084	−	0.203455i	$-0.934783\pi$
$617$		−	10.1074i		−	0.406909i	0.979084	−	0.203455i	$-0.0652170\pi$
$618$	−12.2139	−	2.76464i	−0.491314	−	0.111210i
$619$	43.7508	−	18.1222i	1.75849	−	0.728392i	0.761739	−	0.647884i	$-0.224346\pi$
$619$	43.7508	−	18.1222i	1.75849	−	0.728392i	0.996754	−	0.0805075i	$-0.0256541\pi$
$620$		0			0
$621$	−10.6765	+	25.7755i	−0.428435	+	1.03433i
$622$	−5.64725	−	32.8792i	−0.226434	−	1.31834i
$623$	0.437795	−	0.437795i	0.0175399	−	0.0175399i
$624$	−5.87147	+	55.7089i	−0.235047	+	2.23014i
$625$		0			0
$626$	21.7330	+	15.3617i	0.868624	+	0.613976i
$627$	2.30856	+	5.57335i	0.0921949	+	0.222578i
$628$	34.4730	−	31.0306i	1.37562	−	1.23826i
$629$	4.04490	+	9.76526i	0.161281	+	0.389367i
$630$		0			0
$631$	11.1608	−	11.1608i	0.444306	−	0.444306i	−0.449150	−	0.893456i	$-0.648273\pi$
$631$	11.1608	−	11.1608i	0.444306	−	0.444306i	0.893456	+	0.449150i	$0.148273\pi$
$632$	1.24470	−	4.40972i	0.0495115	−	0.175409i
$633$			77.2403i			3.07003i
$634$	12.7717	+	2.89091i	0.507229	+	0.114813i
$635$		0			0
$636$	−14.7661	−	41.7172i	−0.585513	−	1.65419i
$637$	9.87071	+	23.8300i	0.391092	+	0.944179i
$638$	5.13078	−	7.25878i	0.203130	−	0.287378i
$639$	−63.4606			−2.51046
$640$		0			0
$641$	8.01643			0.316630			0.158315	−	0.987389i	$-0.449394\pi$
$641$	8.01643			0.316630			0.158315	+	0.987389i	$0.449394\pi$
$642$	36.5627	−	51.7272i	1.44302	−	2.04151i
$643$	−4.41795	−	10.6659i	−0.174227	−	0.420621i	0.812510	−	0.582947i	$-0.198100\pi$
$643$	−4.41795	−	10.6659i	−0.174227	−	0.420621i	−0.986737	+	0.162326i	$0.948100\pi$
$644$	−0.957399	−	2.70485i	−0.0377268	−	0.106586i
$645$		0			0
$646$	6.70345	+	1.51734i	0.263744	+	0.0596990i
$647$		−	5.34896i		−	0.210289i	−0.994457	−	0.105145i	$-0.966469\pi$
$647$		−	5.34896i		−	0.210289i	0.994457	−	0.105145i	$-0.0335305\pi$
$648$	26.4020	−	93.5372i	1.03717	−	3.67449i
$649$	−8.13711	+	8.13711i	−0.319410	+	0.319410i
$650$		0			0
$651$	4.85737	+	11.7267i	0.190375	+	0.459607i
$652$	−1.73642	+	1.56302i	−0.0680033	+	0.0612127i
$653$	−2.98939	−	7.21702i	−0.116984	−	0.282424i	0.854532	−	0.519399i	$-0.173844\pi$
$653$	−2.98939	−	7.21702i	−0.116984	−	0.282424i	−0.971516	+	0.236975i	$0.923844\pi$
$654$	−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
$658$	−1.05462	−	6.14017i	−0.0411134	−	0.239369i
$659$	15.6674	−	37.8244i	0.610314	−	1.47343i	−0.252343	−	0.967638i	$-0.581201\pi$
$659$	15.6674	−	37.8244i	0.610314	−	1.47343i	0.862657	−	0.505790i	$-0.168799\pi$
$660$		0			0
$661$	12.8189	−	5.30974i	0.498596	−	0.206525i	−0.119190	−	0.992871i	$-0.538030\pi$
$661$	12.8189	−	5.30974i	0.498596	−	0.206525i	0.617786	+	0.786346i	$0.288030\pi$
$662$	−8.96529	−	2.02932i	−0.348446	−	0.0788716i
$663$			38.8122i			1.50734i
$664$	21.8437	−	2.58058i	0.847698	−	0.100146i
$665$		0			0
$666$	−43.4188	−	9.82796i	−1.68245	−	0.380826i
$667$	−8.96412	−	3.71306i	−0.347092	−	0.143770i
$668$	2.52049	−	0.892145i	0.0975208	−	0.0345181i
$669$	28.9430	−	69.8746i	1.11900	−	2.70151i
$670$		0			0
$671$		−	1.37977i		−	0.0532655i
$672$	7.60113	+	15.4276i	0.293220	+	0.595132i
$673$	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
$677$	2.04241	−	4.93081i	0.0784961	−	0.189506i	−0.879760	−	0.475419i	$-0.842297\pi$
$677$	2.04241	−	4.93081i	0.0784961	−	0.189506i	0.958256	+	0.285912i	$0.0922966\pi$
$678$	2.21797	+	3.51583i	0.0851806	+	0.135025i
$679$	−2.39233	+	2.39233i	−0.0918092	+	0.0918092i
$680$		0			0
$681$	−48.6009	−	48.6009i	−1.86239	−	1.86239i
$682$	−1.33666	+	5.90523i	−0.0511835	+	0.226123i
$683$	45.2713	+	18.7520i	1.73226	+	0.717525i	0.999306	+	0.0372447i	$0.0118581\pi$
$683$	45.2713	+	18.7520i	1.73226	+	0.717525i	0.732952	+	0.680280i	$0.238142\pi$
$684$	−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
$688$	−25.6168	+	7.58001i	−0.976630	+	0.288985i
$689$	−27.5350			−1.04900
$690$		0			0
$691$	−8.69376	−	3.60107i	−0.330726	−	0.136991i	0.211141	−	0.977456i	$-0.432282\pi$
$691$	−8.69376	−	3.60107i	−0.330726	−	0.136991i	−0.541867	+	0.840464i	$0.682282\pi$
$692$	24.4905	−	22.0450i	0.930990	−	0.838025i
$693$	−2.93549	+	7.08690i	−0.111510	+	0.269209i
$694$	10.0634	−	6.34852i	0.382002	−	0.240987i
$695$		0			0
$696$	55.9708	+	15.7985i	2.12157	+	0.598839i
$697$	−2.56861			−0.0972930
$698$	−13.6417	−	21.6242i	−0.516345	−	0.818488i
$699$	17.3852	+	41.9716i	0.657569	+	1.58751i
$700$		0			0
$701$	−44.3758	−	18.3811i	−1.67605	−	0.694243i	−0.676926	−	0.736051i	$-0.736688\pi$
$701$	−44.3758	−	18.3811i	−1.67605	−	0.694243i	−0.999126	+	0.0418077i	$0.986688\pi$
$702$	−84.9677	−	60.0584i	−3.20690	−	2.26676i
$703$	4.72909	+	4.72909i	0.178361	+	0.178361i
$704$	−1.28686	+	8.10224i	−0.0485003	+	0.305364i
$705$		0			0
$706$	−5.48067	−	31.9094i	−0.206268	−	1.20093i
$707$	10.6652	−	4.41766i	0.401105	−	0.166143i
$708$	−67.9511	−	32.4230i	−2.55376	−	1.21853i
$709$	41.9278	−	17.3671i	1.57463	−	0.652234i	0.587081	−	0.809528i	$-0.300277\pi$
$709$	41.9278	−	17.3671i	1.57463	−	0.652234i	0.987552	+	0.157294i	$0.0502772\pi$
$710$		0			0
$711$	9.45466	+	9.45466i	0.354578	+	0.354578i
$712$	0.943776	+	1.68609i	0.0353695	+	0.0631888i
$713$	6.60883			0.247503
$714$	6.35788	+	10.0782i	0.237938	+	0.377169i
$715$		0			0
$716$	16.6104	+	0.872914i	0.620760	+	0.0326223i
$717$	−56.3350	+	23.3347i	−2.10387	+	0.871452i
$718$	−1.52066	−	8.85354i	−0.0567505	−	0.330411i
$719$		−	3.82423i		−	0.142620i	−0.997454	−	0.0713099i	$-0.977282\pi$
$719$		−	3.82423i		−	0.142620i	0.997454	−	0.0713099i	$-0.0227179\pi$
$720$		0			0
$721$			2.39225i			0.0890922i
$722$	−22.1962	+	3.81236i	−0.826057	+	0.141881i
$723$	12.2603	−	5.07838i	0.455965	−	0.188867i
$724$	−6.60375	−	7.33634i	−0.245427	−	0.272653i
$725$		0			0
$726$	39.9178	−	25.1822i	1.48149	−	0.934600i
$727$	15.0951			0.559846			0.279923	−	0.960022i	$-0.409691\pi$
$727$	15.0951			0.559846			0.279923	+	0.960022i	$0.409691\pi$
$728$	10.6272	−	1.25548i	0.393870	−	0.0465313i
$729$	75.1282	+	75.1282i	2.78253	+	2.78253i
$730$		0			0
$731$	−17.1006	+	7.08328i	−0.632487	+	0.261985i
$732$	8.50999	−	3.01217i	0.314538	−	0.111333i
$733$	−43.3702	+	17.9645i	−1.60191	+	0.663534i	−0.991685	−	0.128691i	$-0.958922\pi$
$733$	−43.3702	+	17.9645i	−1.60191	+	0.663534i	−0.610228	+	0.792226i	$0.708922\pi$
$734$	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
$738$	6.24434	−	8.83419i	0.229857	−	0.325191i
$739$	−19.0295	−	7.88226i	−0.700010	−	0.289954i	0.00415371	−	0.999991i	$-0.498678\pi$
$739$	−19.0295	−	7.88226i	−0.700010	−	0.289954i	−0.704164	+	0.710038i	$0.748678\pi$
$740$		0			0
$741$	9.39792	+	22.6886i	0.345241	+	0.833486i
$742$	−7.14992	+	4.51054i	−0.262482	+	0.165587i
$743$	17.8922			0.656401			0.328201	−	0.944608i	$-0.393558\pi$
$743$	17.8922			0.656401			0.328201	+	0.944608i	$0.393558\pi$
$744$	−39.3396	+	4.64753i	−1.44226	+	0.170387i
$745$		0			0
$746$	−1.71958	−	2.72581i	−0.0629585	−	0.0997991i
$747$	−24.5629	+	59.3000i	−0.898708	+	2.16967i
$748$	−0.298299	+	5.67624i	−0.0109069	+	0.207544i
$749$	−11.1797	−	4.63077i	−0.408496	−	0.169205i
$750$		0			0
$751$	−26.7884			−0.977522			−0.488761	−	0.872418i	$-0.662551\pi$
$751$	−26.7884			−0.977522			−0.488761	+	0.872418i	$0.662551\pi$
$752$	19.3363	+	2.03796i	0.705122	+	0.0743167i
$753$	−25.6570	−	25.6570i	−0.934994	−	0.934994i
$754$	20.8869	−	29.5498i	0.760658	−	1.07614i
$755$		0			0
$756$	−31.9015	−	1.67650i	−1.16025	−	0.0609736i
$757$	36.1520	+	14.9747i	1.31397	+	0.544264i	0.926040	−	0.377426i	$-0.123191\pi$
$757$	36.1520	+	14.9747i	1.31397	+	0.544264i	0.387929	+	0.921689i	$0.373191\pi$
$758$	44.3455	+	10.0377i	1.61070	+	0.364586i
$759$	3.85066	+	3.85066i	0.139770	+	0.139770i
$760$		0			0
$761$	−7.36989	+	7.36989i	−0.267158	+	0.267158i	−0.827954	−	0.560796i	$-0.810495\pi$
$761$	−7.36989	+	7.36989i	−0.267158	+	0.267158i	0.560796	+	0.827954i	$0.310495\pi$
$762$	−23.2065	+	14.6399i	−0.840682	+	0.530346i
$763$	−5.51852	+	13.3229i	−0.199784	+	0.482321i
$764$	−10.4820	+	3.71017i	−0.379226	+	0.134229i
$765$		0			0
$766$	−33.0618	+	5.67860i	−1.19457	+	0.205176i
$767$	−33.1254	+	33.1254i	−1.19609	+	1.19609i
$768$	−52.7813	+	9.75099i	−1.90458	+	0.351858i
$769$		−	5.73423i		−	0.206782i	−0.994641	−	0.103391i	$-0.967031\pi$
$769$		−	5.73423i		−	0.206782i	0.994641	−	0.103391i	$-0.0329692\pi$
$770$		0			0
$771$	12.3346	−	29.7784i	0.444220	−	1.07244i
$772$	−37.2873	−	17.7917i	−1.34200	−	0.640338i
$773$	−36.8844	−	15.2780i	−1.32664	−	0.549513i	−0.396946	−	0.917842i	$-0.629930\pi$
$773$	−36.8844	−	15.2780i	−1.32664	−	0.549513i	−0.929695	+	0.368329i	$0.879930\pi$
$774$	17.2104	−	76.0334i	0.618613	−	2.73296i
$775$		0			0
$776$	−5.15726	−	9.21361i	−0.185135	−	0.330749i
$777$			11.5952i			0.415976i
$778$	−7.72988	+	34.1497i	−0.277130	+	1.22433i
$779$	−1.50154	+	0.621959i	−0.0537983	+	0.0222840i
$780$		0			0
$781$	−3.01731	+	7.28442i	−0.107968	+	0.260657i
$782$	6.11482	−	1.05027i	0.218666	−	0.0375574i
$783$	−76.3859	+	76.3859i	−2.72981	+	2.72981i
$784$	−19.2113	+	15.5478i	−0.686118	+	0.555280i
$785$		0			0
$786$	−44.6337	+	63.1456i	−1.59203	+	2.25233i
$787$	1.55921	+	3.76428i	0.0555800	+	0.134182i	0.949230	−	0.314582i	$-0.101864\pi$
$787$	1.55921	+	3.76428i	0.0555800	+	0.134182i	−0.893650	+	0.448764i	$0.851864\pi$
$788$	37.6059	+	1.97627i	1.33965	+	0.0704018i
$789$	30.3934	+	73.3761i	1.08203	+	2.61226i
$790$		0			0
$791$	0.561522	−	0.561522i	0.0199654	−	0.0199654i
$792$	−18.7970	−	14.8250i	−0.667924	−	0.526783i
$793$		−	5.61692i		−	0.199463i
$794$	−5.17494	+	22.8623i	−0.183652	+	0.811353i
$795$		0			0
$796$	31.1311	+	14.8543i	1.10341	+	0.526496i
$797$	−10.2363	−	24.7126i	−0.362588	−	0.875365i	−0.994920	−	0.100667i	$-0.967902\pi$
$797$	−10.2363	−	24.7126i	−0.362588	−	0.875365i	0.632332	−	0.774697i	$-0.282098\pi$
$798$	6.15698	+	4.35199i	0.217955	+	0.154059i
$799$	13.4715			0.476588
$800$		0			0
$801$	−5.63856			−0.199229
$802$	−14.1620	−	10.0102i	−0.500077	−	0.353474i
$803$	−2.04680	−	4.94141i	−0.0722300	−	0.174379i
$804$	32.0589	−	67.1880i	1.13063	−	2.36954i
$805$		0			0
$806$	−5.44143	+	24.0396i	−0.191666	+	0.846760i
$807$		−	66.5210i		−	2.34165i
$808$	4.22682	+	35.7784i	0.148699	+	1.25868i
$809$	14.6573	−	14.6573i	0.515322	−	0.515322i	−0.400831	−	0.916152i	$-0.631278\pi$
$809$	14.6573	−	14.6573i	0.515322	−	0.515322i	0.916152	+	0.400831i	$0.131278\pi$
$810$		0			0
$811$	11.3438	+	27.3863i	0.398333	+	0.961661i	0.988062	+	0.154060i	$0.0492348\pi$
$811$	11.3438	+	27.3863i	0.398333	+	0.961661i	−0.589728	+	0.807602i	$0.700765\pi$
$812$	0.583047	−	11.0946i	0.0204609	−	0.389345i
$813$	6.67864	+	16.1237i	0.234230	+	0.565482i
$814$	−3.19252	+	4.51662i	−0.111898	+	0.158307i
$815$		0			0
$816$	−35.6604	+	10.5519i	−1.24836	+	0.369391i
$817$	−8.28140	+	8.28140i	−0.289730	+	0.289730i
$818$	30.7142	−	5.27539i	1.07390	−	0.184450i
$819$	−11.9501	+	28.8501i	−0.417570	+	1.00810i
$820$		0			0
$821$	−32.4192	+	13.4285i	−1.13144	+	0.468657i	−0.868269	−	0.496093i	$-0.834767\pi$
$821$	−32.4192	+	13.4285i	−1.13144	+	0.468657i	−0.263168	+	0.964750i	$0.584767\pi$
$822$	−14.4388	+	63.7890i	−0.503611	+	2.22490i
$823$		−	18.1415i		−	0.632373i	−0.948697	−	0.316187i	$-0.897597\pi$
$823$		−	18.1415i		−	0.632373i	0.948697	−	0.316187i	$-0.102403\pi$
$824$	−7.18521	−	2.02812i	−0.250309	−	0.0706527i
$825$		0			0
$826$	−3.17525	+	14.0279i	−0.110481	+	0.488093i
$827$	−33.7217	−	13.9680i	−1.17262	−	0.485714i	−0.290561	−	0.956857i	$-0.593842\pi$
$827$	−33.7217	−	13.9680i	−1.17262	−	0.485714i	−0.882057	+	0.471142i	$0.843842\pi$
$828$	−11.2531	+	23.5839i	−0.391072	+	0.819596i
$829$	−11.3256	+	27.3423i	−0.393353	+	0.949637i	0.595852	+	0.803094i	$0.296815\pi$
$829$	−11.3256	+	27.3423i	−0.393353	+	0.949637i	−0.989204	+	0.146543i	$0.953185\pi$
$830$		0			0
$831$		−	27.8167i		−	0.964950i
$832$	−5.23868	+	32.9834i	−0.181618	+	1.14350i
$833$	−12.1083	+	12.1083i	−0.419527	+	0.419527i
$834$	28.6629	−	4.92306i	0.992514	−	0.170472i
$835$		0			0
$836$	1.20006	+	3.39041i	0.0415048	+	0.117260i
$837$	28.1579	−	67.9792i	0.973279	−	2.34970i
$838$	−35.8495	+	22.6157i	−1.23840	+	0.781247i
$839$	−21.4869	+	21.4869i	−0.741811	+	0.741811i	−0.972926	−	0.231116i	$-0.925762\pi$
$839$	−21.4869	+	21.4869i	−0.741811	+	0.741811i	0.231116	+	0.972926i	$0.425762\pi$
$840$		0			0
$841$	−6.05918	−	6.05918i	−0.208937	−	0.208937i
$842$	−37.8819	−	8.57467i	−1.30550	−	0.295503i
$843$	−23.2360	−	9.62467i	−0.800291	−	0.331491i
$844$	−2.41668	+	45.9862i	−0.0831854	+	1.58291i
$845$		0			0
$846$	−32.7496	+	46.3325i	−1.12595	+	1.59294i
$847$	−6.37537	−	6.37537i	−0.219060	−	0.219060i
$848$	−7.48597	−	25.2990i	−0.257069	−	0.868770i
$849$	30.6916			1.05333
$850$		0			0
$851$	5.57772	+	2.31037i	0.191202	+	0.0791984i
$852$	−51.5150	−	2.70723i	−1.76488	−	0.0927481i
$853$	15.3415	−	37.0377i	0.525283	−	1.26815i	−0.409300	−	0.912400i	$-0.634227\pi$
$853$	15.3415	−	37.0377i	0.525283	−	1.26815i	0.934583	−	0.355746i	$-0.115773\pi$
$854$	−0.920116	−	1.45853i	−0.0314857	−	0.0499098i
$855$		0			0
$856$	23.3866	−	29.6526i	0.799338	−	1.01350i
$857$	47.3694			1.61811			0.809055	−	0.587733i	$-0.199980\pi$
$857$	47.3694			1.61811			0.809055	+	0.587733i	$0.199980\pi$
$858$	−17.1773	+	10.8363i	−0.586422	+	0.369946i
$859$	5.28829	+	12.7671i	0.180434	+	0.435607i	0.988056	−	0.154094i	$-0.0492458\pi$
$859$	5.28829	+	12.7671i	0.180434	+	0.435607i	−0.807622	+	0.589700i	$0.799246\pi$
$860$		0			0
$861$	−2.60330	−	1.07832i	−0.0887201	−	0.0367491i
$862$	−9.27898	+	13.1275i	−0.316043	+	0.447123i
$863$	−12.9803	−	12.9803i	−0.441853	−	0.441853i	0.450781	−	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
$865$		0			0
$866$	32.0375	−	5.50268i	1.08868	−	0.186989i
$867$	28.8828	−	11.9637i	0.980912	−	0.406307i
$868$	2.52501	+	7.13366i	0.0857043	+	0.242132i
$869$	1.53480	−	0.635736i	0.0520646	−	0.0215659i
$870$		0			0
$871$	−32.7534	−	32.7534i	−1.10981	−	1.10981i
$872$	−35.3372	−	27.8700i	−1.19667	−	0.943796i
$873$	30.8119			1.04282
$874$	3.32026	−	2.09459i	0.112309	−	0.0708506i
$875$		0			0
$876$	26.0087	−	23.4116i	0.878752	−	0.791003i
$877$	41.9560	−	17.3787i	1.41675	−	0.586838i	0.462710	−	0.886510i	$-0.346877\pi$
$877$	41.9560	−	17.3787i	1.41675	−	0.586838i	0.954042	+	0.299672i	$0.0968773\pi$
$878$	47.8578	−	8.21993i	1.61512	−	0.277409i
$879$			3.53363i			0.119186i
$880$		0			0
$881$		−	17.7034i		−	0.596441i	−0.954497	−	0.298221i	$-0.903607\pi$
$881$		−	17.7034i		−	0.596441i	0.954497	−	0.298221i	$-0.0963931\pi$
$882$	−12.2084	−	71.0794i	−0.411078	−	2.39337i
$883$	−30.7304	+	12.7290i	−1.03416	+	0.428363i	−0.834213	−	0.551443i	$-0.814077\pi$
$883$	−30.7304	+	12.7290i	−1.03416	+	0.428363i	−0.199948	+	0.979806i	$0.564077\pi$
$884$	−1.21435	+	23.1074i	−0.0408429	+	0.777187i
$885$		0			0
$886$	−16.8378	−	26.6906i	−0.565678	−	0.896689i
$887$	−44.9270			−1.50850			−0.754250	−	0.656588i	$-0.771999\pi$
$887$	−44.9270			−1.50850			−0.754250	+	0.656588i	$0.771999\pi$
$888$	−34.8266	−	9.83024i	−1.16870	−	0.329881i
$889$	3.70636	+	3.70636i	0.124307	+	0.124307i
$890$		0			0
$891$	32.5556	−	13.4850i	1.09065	−	0.451763i
$892$	19.4179	−	40.6953i	0.650159	−	1.36258i
$893$	7.87510	−	3.26197i	0.263530	−	0.109158i
$894$	0.247133	+	1.43885i	0.00826537	+	0.0481224i
$895$		0			0
$896$	4.04275	+	9.42286i	0.135059	+	0.314796i
$897$	15.6757	+	15.6757i	0.523396	+	0.523396i
$898$	1.85651	+	1.31225i	0.0619524	+	0.0437903i
$899$	23.6416	+	9.79267i	0.788492	+	0.326604i
$900$		0			0
$901$	−6.99541	−	16.8884i	−0.233051	−	0.562634i
$902$	−0.717152	−	1.13680i	−0.0238785	−	0.0378512i
$903$	−20.3051			−0.675711
$904$	1.21050	+	2.16260i	0.0402606	+	0.0719270i
$905$		0			0
$906$	14.2115	−	8.96535i	0.472145	−	0.297854i
$907$	−10.4809	+	25.3031i	−0.348012	+	0.840176i	0.648842	+	0.760923i	$0.275254\pi$
$907$	−10.4809	+	25.3031i	−0.348012	+	0.840176i	−0.996855	+	0.0792532i	$0.974746\pi$
$908$	−27.4147	−	30.4559i	−0.909787	−	1.01071i
$909$	−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	$0.688678\pi$
$912$	−18.2911	+	14.8031i	−0.605679	+	0.490181i
$913$	5.63897	+	5.63897i	0.186623	+	0.186623i
$914$	−5.50369	−	3.89022i	−0.182046	−	0.128677i
$915$		0			0
$916$	33.3828	+	37.0861i	1.10300	+	1.22536i
$917$	13.6475	+	5.65298i	0.450680	+	0.186678i
$918$	15.2500	−	67.3726i	0.503324	−	2.22363i
$919$	−33.1256	−	33.1256i	−1.09271	−	1.09271i	−0.995238	−	0.0974735i	$-0.968924\pi$
$919$	−33.1256	−	33.1256i	−1.09271	−	1.09271i	−0.0974735	−	0.995238i	$-0.531076\pi$
$920$		0			0
$921$	23.7828	−	23.7828i	0.783671	−	0.783671i
$922$	3.73012	+	5.91283i	0.122845	+	0.194729i
$923$	−12.2832	+	29.6542i	−0.404306	+	0.976080i
$924$	−2.68525	+	5.62766i	−0.0883383	+	0.185136i
$925$		0			0
$926$	4.13443	+	24.0714i	0.135866	+	0.791034i
$927$	15.4055	−	15.4055i	0.505981	−	0.505981i
$928$	32.8288	+	11.1570i	1.07766	+	0.366248i
$929$		−	32.2191i		−	1.05708i	−0.848910	−	0.528538i	$-0.822740\pi$
$929$		−	32.2191i		−	1.05708i	0.848910	−	0.528538i	$-0.177260\pi$
$930$		0			0
$931$	−4.14630	+	10.0101i	−0.135890	+	0.328067i
$932$	9.03734	+	25.5324i	0.296028	+	0.836340i
$933$	73.1111	+	30.2836i	2.39355	+	0.991441i
$934$	22.0562	+	4.99247i	0.721700	+	0.163359i
$935$		0			0
$936$	−76.5210	−	60.3511i	−2.50117	−	1.97264i
$937$		−	11.5426i		−	0.377080i	−0.982066	−	0.188540i	$-0.939625\pi$
$937$		−	11.5426i		−	0.377080i	0.982066	−	0.188540i	$-0.0603755\pi$
$938$	−13.8704	−	3.13959i	−0.452883	−	0.102511i
$939$	−58.3254	+	24.1592i	−1.90338	+	0.788405i
$940$		0			0
$941$	−19.3222	+	46.6478i	−0.629885	+	1.52068i	0.209881	+	0.977727i	$0.432692\pi$
$941$	−19.3222	+	46.6478i	−0.629885	+	1.52068i	−0.839765	+	0.542949i	$0.817308\pi$
$942$	18.6245	+	108.435i	0.606818	+	3.53300i
$943$	−1.03742	+	1.03742i	−0.0337831	+	0.0337831i
$944$	−39.4413	−	21.4296i	−1.28370	−	0.697474i
$945$		0			0
$946$	−7.90932	−	5.59061i	−0.257154	−	0.181766i
$947$	1.03442	+	2.49731i	0.0336141	+	0.0811516i	0.939795	−	0.341738i	$-0.111016\pi$
$947$	1.03442	+	2.49731i	0.0336141	+	0.0811516i	−0.906181	+	0.422890i	$0.861016\pi$
$948$	7.27162	+	8.07829i	0.236171	+	0.262371i
$949$	−8.33233	−	20.1160i	−0.270479	−	0.652994i
$950$		0			0
$951$	−21.9643	+	21.9643i	−0.712240	+	0.712240i
$952$	3.46993	+	6.19916i	0.112461	+	0.200916i
$953$		−	29.5188i		−	0.956208i	−0.878303	−	0.478104i	$-0.841324\pi$
$953$		−	29.5188i		−	0.956208i	0.878303	−	0.478104i	$-0.158676\pi$
$954$	75.0901	+	16.9968i	2.43113	+	0.550293i
$955$		0			0
$956$	−34.2700	+	12.1301i	−1.10837	+	0.392315i
$957$	8.06913	+	19.4806i	0.260838	+	0.629719i
$958$	23.3761	−	33.0713i	0.755247	−	1.06849i
$959$	12.4940			0.403451
$960$		0			0
$961$	13.5701			0.437747
$962$	−12.9964	+	18.3867i	−0.419022	+	0.592812i
$963$	42.1731	+	101.815i	1.35901	+	3.28094i
$964$	7.45824	−	2.63989i	0.240214	−	0.0850252i
$965$		0			0
$966$	6.63831	+	1.50260i	0.213584	+	0.0483453i
$967$		−	48.1906i		−	1.54971i	−0.632141	−	0.774853i	$-0.717824\pi$
$967$		−	48.1906i		−	1.54971i	0.632141	−	0.774853i	$-0.282176\pi$
$968$	24.5536	−	13.7437i	0.789181	−	0.441739i
$969$	−11.5283	+	11.5283i	−0.370343	+	0.370343i
$970$		0			0
$971$	−9.00286	−	21.7348i	−0.288916	−	0.697504i	0.711069	−	0.703123i	$-0.248212\pi$
$971$	−9.00286	−	21.7348i	−0.288916	−	0.697504i	−0.999984	+	0.00561859i	$0.998212\pi$
$972$	83.4960	+	92.7585i	2.67813	+	2.97523i
$973$	−2.12607	−	5.13278i	−0.0681586	−	0.164549i
$974$	29.6796	+	20.9787i	0.950995	+	0.672200i
$975$		0			0
$976$	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	$0.258788\pi$
$978$	−0.938120	−	5.46190i	−0.0299978	−	0.174652i
$979$	−0.268092	+	0.647231i	−0.00856825	+	0.0206856i
$980$		0			0
$981$	121.333	−	50.2579i	3.87388	−	1.60461i
$982$	4.96805	+	1.12453i	0.158537	+	0.0358852i
$983$		−	28.8147i		−	0.919047i	−0.888166	−	0.459524i	$-0.848020\pi$
$983$		−	28.8147i		−	0.919047i	0.888166	−	0.459524i	$-0.151980\pi$
$984$	5.44580	−	6.90490i	0.173606	−	0.220120i
$985$		0			0
$986$	23.4306	+	5.30359i	0.746184	+	0.168901i
$987$	13.6534	+	5.65544i	0.434594	+	0.180015i
$988$	4.88532	+	13.8020i	0.155423	+	0.439101i
$989$	−4.04583	+	9.76750i	−0.128650	+	0.310588i
$990$		0			0
$991$			13.7444i			0.436605i	0.975881	+	0.218303i	$0.0700520\pi$
$991$			13.7444i			0.436605i	−0.975881	+	0.218303i	$0.929948\pi$
$992$	−23.5668	+	1.53613i	−0.748248	+	0.0487722i
$993$	15.4181	−	15.4181i	0.489280	−	0.489280i
$994$	1.66816	+	9.71234i	0.0529110	+	0.308057i
$995$		0			0
$996$	−22.4690	+	47.0897i	−0.711957	+	1.49210i
$997$	−7.72310	+	18.6452i	−0.244593	+	0.590499i	−0.997728	−	0.0673660i	$-0.978540\pi$
$997$	−7.72310	+	18.6452i	−0.244593	+	0.590499i	0.753135	+	0.657865i	$0.228540\pi$
$998$	21.1037	+	33.4527i	0.668025	+	1.05893i
$999$	47.5294	−	47.5294i	1.50376	−	1.50376i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.2.u.a.43.16	✓	88	160.107	even	8
160.2.u.a.67.16	yes	88	5.4	even	2
160.2.ba.a.3.5	yes	88	5.2	odd	4
160.2.ba.a.107.5	yes	88	160.139	odd	8
640.2.u.a.47.1		88	20.19	odd	2
640.2.u.a.463.1		88	160.117	odd	8
640.2.ba.a.207.22		88	160.149	even	8
640.2.ba.a.303.22		88	20.7	even	4
800.2.v.b.43.7		88	160.43	even	8	inner
800.2.v.b.707.7		88	1.1	even	1	trivial
800.2.bb.b.107.18		88	32.11	odd	8
800.2.bb.b.643.18		88	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more