LMFDB - Embedded newform 875.2.h.d.351.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [875,2,Mod(176,875)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(875, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 0]))

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

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

chi := DirichletCharacter("875.176");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.h (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			351.11
Character	$\chi$	$=$	875.351
Dual form			875.2.h.d.526.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.591863 - 1.82157i) q^{2} +(2.32470 + 1.68900i) q^{3} +(-1.34977 - 0.980668i) q^{4} +(4.45253 - 3.23495i) q^{6} -1.00000 q^{7} +(0.513801 - 0.373298i) q^{8} +(1.62449 + 4.99966i) q^{9} +O(q^{10})$	\(q+(0.591863 - 1.82157i) q^{2} +(2.32470 + 1.68900i) q^{3} +(-1.34977 - 0.980668i) q^{4} +(4.45253 - 3.23495i) q^{6} -1.00000 q^{7} +(0.513801 - 0.373298i) q^{8} +(1.62449 + 4.99966i) q^{9} +(-0.946113 + 2.91184i) q^{11} +(-1.48148 - 4.55953i) q^{12} +(1.86536 + 5.74099i) q^{13} +(-0.591863 + 1.82157i) q^{14} +(-1.40702 - 4.33037i) q^{16} +(1.11712 - 0.811636i) q^{17} +10.0687 q^{18} +(5.21871 - 3.79161i) q^{19} +(-2.32470 - 1.68900i) q^{21} +(4.74414 + 3.44682i) q^{22} +(0.613350 - 1.88770i) q^{23} +1.82493 q^{24} +11.5616 q^{26} +(-2.00408 + 6.16793i) q^{27} +(1.34977 + 0.980668i) q^{28} +(-1.48069 - 1.07578i) q^{29} +(-0.823057 + 0.597986i) q^{31} -7.45065 q^{32} +(-7.11751 + 5.17117i) q^{33} +(-0.817268 - 2.51529i) q^{34} +(2.71032 - 8.34150i) q^{36} +(-3.09806 - 9.53485i) q^{37} +(-3.81792 - 11.7503i) q^{38} +(-5.36009 + 16.4967i) q^{39} +(2.44609 + 7.52829i) q^{41} +(-4.45253 + 3.23495i) q^{42} -4.42793 q^{43} +(4.13258 - 3.00250i) q^{44} +(-3.07555 - 2.23452i) q^{46} +(-1.46218 - 1.06234i) q^{47} +(4.04307 - 12.4433i) q^{48} +1.00000 q^{49} +3.96783 q^{51} +(3.11219 - 9.57833i) q^{52} +(-6.89187 - 5.00723i) q^{53} +(10.0492 + 7.30114i) q^{54} +(-0.513801 + 0.373298i) q^{56} +18.5360 q^{57} +(-2.83598 + 2.06046i) q^{58} +(-1.23870 - 3.81234i) q^{59} +(-0.853734 + 2.62752i) q^{61} +(0.602135 + 1.85318i) q^{62} +(-1.62449 - 4.99966i) q^{63} +(-1.59572 + 4.91112i) q^{64} +(5.20705 + 16.0257i) q^{66} +(-6.22159 + 4.52025i) q^{67} -2.30381 q^{68} +(4.61417 - 3.35239i) q^{69} +(7.00021 + 5.08595i) q^{71} +(2.70103 + 1.96241i) q^{72} +(5.06928 - 15.6016i) q^{73} -19.2020 q^{74} -10.7624 q^{76} +(0.946113 - 2.91184i) q^{77} +(26.8774 + 19.5276i) q^{78} +(-0.563983 - 0.409757i) q^{79} +(-2.31760 + 1.68383i) q^{81} +15.1610 q^{82} +(-5.22011 + 3.79263i) q^{83} +(1.48148 + 4.55953i) q^{84} +(-2.62073 + 8.06578i) q^{86} +(-1.62517 - 5.00176i) q^{87} +(0.600869 + 1.84928i) q^{88} +(-1.35657 + 4.17510i) q^{89} +(-1.86536 - 5.74099i) q^{91} +(-2.67909 + 1.94647i) q^{92} -2.92336 q^{93} +(-2.80053 + 2.03470i) q^{94} +(-17.3206 - 12.5841i) q^{96} +(-7.94614 - 5.77321i) q^{97} +(0.591863 - 1.82157i) q^{98} -16.0951 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 4 q^{2} - 4 q^{3} - 12 q^{4} - 56 q^{7} - 12 q^{8} - 6 q^{9}+O(q^{10}) $ 56 * q - 4 * q^2 - 4 * q^3 - 12 * q^4 - 56 * q^7 - 12 * q^8 - 6 * q^9	$ 56 q - 4 q^{2} - 4 q^{3} - 12 q^{4} - 56 q^{7} - 12 q^{8} - 6 q^{9} + 8 q^{11} - 12 q^{12} - 8 q^{13} + 4 q^{14} - 32 q^{16} - 20 q^{17} + 48 q^{18} - 12 q^{19} + 4 q^{21} - 8 q^{22} - 16 q^{23} + 28 q^{24} + 12 q^{26} - 16 q^{27} + 12 q^{28} + 2 q^{29} + 12 q^{31} + 112 q^{32} - 14 q^{33} - 14 q^{36} - 16 q^{37} - 20 q^{38} + 4 q^{39} + 4 q^{41} + 32 q^{43} - 22 q^{44} - 4 q^{46} - 18 q^{47} - 48 q^{48} + 56 q^{49} - 44 q^{51} + 16 q^{52} - 20 q^{53} - 54 q^{54} + 12 q^{56} + 152 q^{57} + 32 q^{58} + 6 q^{59} - 4 q^{61} + 18 q^{62} + 6 q^{63} - 24 q^{64} - 74 q^{66} - 32 q^{67} + 124 q^{68} + 78 q^{69} - 8 q^{71} - 100 q^{72} - 48 q^{73} - 60 q^{74} + 52 q^{76} - 8 q^{77} + 124 q^{78} - 72 q^{81} + 44 q^{82} + 10 q^{83} + 12 q^{84} - 20 q^{86} + 26 q^{87} - 88 q^{88} - 38 q^{89} + 8 q^{91} - 96 q^{92} + 96 q^{93} - 88 q^{94} - 28 q^{96} - 90 q^{97} - 4 q^{98} - 60 q^{99}+O(q^{100}) $ 56 * q - 4 * q^2 - 4 * q^3 - 12 * q^4 - 56 * q^7 - 12 * q^8 - 6 * q^9 + 8 * q^11 - 12 * q^12 - 8 * q^13 + 4 * q^14 - 32 * q^16 - 20 * q^17 + 48 * q^18 - 12 * q^19 + 4 * q^21 - 8 * q^22 - 16 * q^23 + 28 * q^24 + 12 * q^26 - 16 * q^27 + 12 * q^28 + 2 * q^29 + 12 * q^31 + 112 * q^32 - 14 * q^33 - 14 * q^36 - 16 * q^37 - 20 * q^38 + 4 * q^39 + 4 * q^41 + 32 * q^43 - 22 * q^44 - 4 * q^46 - 18 * q^47 - 48 * q^48 + 56 * q^49 - 44 * q^51 + 16 * q^52 - 20 * q^53 - 54 * q^54 + 12 * q^56 + 152 * q^57 + 32 * q^58 + 6 * q^59 - 4 * q^61 + 18 * q^62 + 6 * q^63 - 24 * q^64 - 74 * q^66 - 32 * q^67 + 124 * q^68 + 78 * q^69 - 8 * q^71 - 100 * q^72 - 48 * q^73 - 60 * q^74 + 52 * q^76 - 8 * q^77 + 124 * q^78 - 72 * q^81 + 44 * q^82 + 10 * q^83 + 12 * q^84 - 20 * q^86 + 26 * q^87 - 88 * q^88 - 38 * q^89 + 8 * q^91 - 96 * q^92 + 96 * q^93 - 88 * q^94 - 28 * q^96 - 90 * q^97 - 4 * q^98 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.591863	−	1.82157i	0.418511	−	1.28804i	−0.490562	−	0.871406i	$-0.663209\pi$
$2$	0.591863	−	1.82157i	0.418511	−	1.28804i	0.909073	−	0.416637i	$-0.136791\pi$
$3$	2.32470	+	1.68900i	1.34217	+	0.975142i	0.999361	+	0.0357365i	$0.0113777\pi$
$3$	2.32470	+	1.68900i	1.34217	+	0.975142i	0.342807	+	0.939406i	$0.388622\pi$
$4$	−1.34977	−	0.980668i	−0.674887	−	0.490334i
$5$		0			0
$5$		0			0
$6$	4.45253	−	3.23495i	1.81774	−	1.32066i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	0.513801	−	0.373298i	0.181656	−	0.131981i
$9$	1.62449	+	4.99966i	0.541496	+	1.66655i
$10$		0			0
$11$	−0.946113	+	2.91184i	−0.285264	+	0.877951i	0.701056	+	0.713106i	$0.252712\pi$
$11$	−0.946113	+	2.91184i	−0.285264	+	0.877951i	−0.986319	+	0.164845i	$0.947288\pi$
$12$	−1.48148	−	4.55953i	−0.427666	−	1.31622i
$13$	1.86536	+	5.74099i	0.517358	+	1.59226i	0.778951	+	0.627085i	$0.215752\pi$
$13$	1.86536	+	5.74099i	0.517358	+	1.59226i	−0.261594	+	0.965178i	$0.584248\pi$
$14$	−0.591863	+	1.82157i	−0.158182	+	0.486835i
$15$		0			0
$16$	−1.40702	−	4.33037i	−0.351756	−	1.08259i
$17$	1.11712	−	0.811636i	0.270942	−	0.196851i	−0.444015	−	0.896019i	$-0.646446\pi$
$17$	1.11712	−	0.811636i	0.270942	−	0.196851i	0.714957	+	0.699169i	$0.246446\pi$
$18$	10.0687			2.37322
$19$	5.21871	−	3.79161i	1.19725	−	0.869855i	0.203241	−	0.979129i	$-0.434852\pi$
$19$	5.21871	−	3.79161i	1.19725	−	0.869855i	0.994012	+	0.109273i	$0.0348524\pi$
$20$		0			0
$21$	−2.32470	−	1.68900i	−0.507292	−	0.368569i
$22$	4.74414	+	3.44682i	1.01145	+	0.734864i
$23$	0.613350	−	1.88770i	0.127892	−	0.393612i	−0.866525	−	0.499134i	$-0.833651\pi$
$23$	0.613350	−	1.88770i	0.127892	−	0.393612i	0.994417	+	0.105522i	$0.0336514\pi$
$24$	1.82493			0.372513
$25$		0			0
$26$	11.5616			2.26742
$27$	−2.00408	+	6.16793i	−0.385686	+	1.18702i
$28$	1.34977	+	0.980668i	0.255083	+	0.185329i
$29$	−1.48069	−	1.07578i	−0.274957	−	0.199768i	0.441758	−	0.897134i	$-0.354355\pi$
$29$	−1.48069	−	1.07578i	−0.274957	−	0.199768i	−0.716715	+	0.697366i	$0.754355\pi$
$30$		0			0
$31$	−0.823057	+	0.597986i	−0.147825	+	0.107401i	−0.659240	−	0.751933i	$-0.729122\pi$
$31$	−0.823057	+	0.597986i	−0.147825	+	0.107401i	0.511414	+	0.859334i	$0.329122\pi$
$32$	−7.45065			−1.31710
$33$	−7.11751	+	5.17117i	−1.23900	+	0.900186i
$34$	−0.817268	−	2.51529i	−0.140160	−	0.431369i
$35$		0			0
$36$	2.71032	−	8.34150i	0.451720	−	1.39025i
$37$	−3.09806	−	9.53485i	−0.509318	−	1.56752i	−0.793388	−	0.608716i	$-0.791685\pi$
$37$	−3.09806	−	9.53485i	−0.509318	−	1.56752i	0.284070	−	0.958804i	$-0.408315\pi$
$38$	−3.81792	−	11.7503i	−0.619348	−	1.90616i
$39$	−5.36009	+	16.4967i	−0.858302	+	2.64158i
$40$		0			0
$41$	2.44609	+	7.52829i	0.382015	+	1.17572i	0.938623	+	0.344946i	$0.112103\pi$
$41$	2.44609	+	7.52829i	0.382015	+	1.17572i	−0.556608	+	0.830775i	$0.687897\pi$
$42$	−4.45253	+	3.23495i	−0.687040	+	0.499164i
$43$	−4.42793			−0.675253			−0.337627	−	0.941280i	$-0.609624\pi$
$43$	−4.42793			−0.675253			−0.337627	+	0.941280i	$0.609624\pi$
$44$	4.13258	−	3.00250i	0.623010	−	0.452644i
$45$		0			0
$46$	−3.07555	−	2.23452i	−0.453465	−	0.329462i
$47$	−1.46218	−	1.06234i	−0.213281	−	0.154958i	0.476016	−	0.879437i	$-0.342080\pi$
$47$	−1.46218	−	1.06234i	−0.213281	−	0.154958i	−0.689297	+	0.724479i	$0.742080\pi$
$48$	4.04307	−	12.4433i	0.583567	−	1.79603i
$49$	1.00000			0.142857
$50$		0			0
$51$	3.96783			0.555607
$52$	3.11219	−	9.57833i	0.431583	−	1.32828i
$53$	−6.89187	−	5.00723i	−0.946671	−	0.687796i	0.00334646	−	0.999994i	$-0.498935\pi$
$53$	−6.89187	−	5.00723i	−0.946671	−	0.687796i	−0.950017	+	0.312198i	$0.898935\pi$
$54$	10.0492	+	7.30114i	1.36752	+	0.993559i
$55$		0			0
$56$	−0.513801	+	0.373298i	−0.0686595	+	0.0498840i
$57$	18.5360			2.45515
$58$	−2.83598	+	2.06046i	−0.372382	+	0.270552i
$59$	−1.23870	−	3.81234i	−0.161266	−	0.496324i	0.837476	−	0.546474i	$-0.184030\pi$
$59$	−1.23870	−	3.81234i	−0.161266	−	0.496324i	−0.998742	+	0.0501495i	$0.984030\pi$
$60$		0			0
$61$	−0.853734	+	2.62752i	−0.109309	+	0.336420i	−0.990718	−	0.135935i	$-0.956596\pi$
$61$	−0.853734	+	2.62752i	−0.109309	+	0.336420i	0.881408	+	0.472355i	$0.156596\pi$
$62$	0.602135	+	1.85318i	0.0764712	+	0.235354i
$63$	−1.62449	−	4.99966i	−0.204666	−	0.629898i
$64$	−1.59572	+	4.91112i	−0.199465	+	0.613890i
$65$		0			0
$66$	5.20705	+	16.0257i	0.640944	+	1.97262i
$67$	−6.22159	+	4.52025i	−0.760089	+	0.552237i	−0.898938	−	0.438077i	$-0.855660\pi$
$67$	−6.22159	+	4.52025i	−0.760089	+	0.552237i	0.138849	+	0.990314i	$0.455660\pi$
$68$	−2.30381			−0.279378
$69$	4.61417	−	3.35239i	0.555481	−	0.403581i
$70$		0			0
$71$	7.00021	+	5.08595i	0.830772	+	0.603591i	0.919778	−	0.392440i	$-0.128369\pi$
$71$	7.00021	+	5.08595i	0.830772	+	0.603591i	−0.0890056	+	0.996031i	$0.528369\pi$
$72$	2.70103	+	1.96241i	0.318319	+	0.231272i
$73$	5.06928	−	15.6016i	0.593314	−	1.82603i	0.0303702	−	0.999539i	$-0.490331\pi$
$73$	5.06928	−	15.6016i	0.593314	−	1.82603i	0.562944	−	0.826495i	$-0.309669\pi$
$74$	−19.2020			−2.23219
$75$		0			0
$76$	−10.7624			−1.23453
$77$	0.946113	−	2.91184i	0.107820	−	0.331834i
$78$	26.8774	+	19.5276i	3.04326	+	2.21106i
$79$	−0.563983	−	0.409757i	−0.0634530	−	0.0461013i	0.555607	−	0.831445i	$-0.312486\pi$
$79$	−0.563983	−	0.409757i	−0.0634530	−	0.0461013i	−0.619060	+	0.785344i	$0.712486\pi$
$80$		0			0
$81$	−2.31760	+	1.68383i	−0.257511	+	0.187093i
$82$	15.1610			1.67426
$83$	−5.22011	+	3.79263i	−0.572981	+	0.416295i	−0.836187	−	0.548444i	$-0.815220\pi$
$83$	−5.22011	+	3.79263i	−0.572981	+	0.416295i	0.263206	+	0.964740i	$0.415220\pi$
$84$	1.48148	+	4.55953i	0.161643	+	0.497485i
$85$		0			0
$86$	−2.62073	+	8.06578i	−0.282601	+	0.869755i
$87$	−1.62517	−	5.00176i	−0.174236	−	0.536244i
$88$	0.600869	+	1.84928i	0.0640528	+	0.197134i
$89$	−1.35657	+	4.17510i	−0.143796	+	0.442560i	−0.996854	−	0.0792567i	$-0.974745\pi$
$89$	−1.35657	+	4.17510i	−0.143796	+	0.442560i	0.853058	+	0.521816i	$0.174745\pi$
$90$		0			0
$91$	−1.86536	−	5.74099i	−0.195543	−	0.601819i
$92$	−2.67909	+	1.94647i	−0.279314	+	0.202934i
$93$	−2.92336			−0.303138
$94$	−2.80053	+	2.03470i	−0.288853	+	0.209864i
$95$		0			0
$96$	−17.3206	−	12.5841i	−1.76777	−	1.28436i
$97$	−7.94614	−	5.77321i	−0.806808	−	0.586180i	0.106095	−	0.994356i	$-0.466165\pi$
$97$	−7.94614	−	5.77321i	−0.806808	−	0.586180i	−0.912903	+	0.408176i	$0.866165\pi$
$98$	0.591863	−	1.82157i	0.0597872	−	0.184006i
$99$	−16.0951			−1.61762
$100$		0			0
$101$	0.995054			0.0990115			0.0495058	−	0.998774i	$-0.484235\pi$
$101$	0.995054			0.0990115			0.0495058	+	0.998774i	$0.484235\pi$
$102$	2.34841	−	7.22767i	0.232527	−	0.715646i
$103$	−10.9719	−	7.97152i	−1.08109	−	0.785458i	−0.103217	−	0.994659i	$-0.532914\pi$
$103$	−10.9719	−	7.97152i	−1.08109	−	0.785458i	−0.977873	+	0.209201i	$0.932914\pi$
$104$	3.10152	+	2.25339i	0.304129	+	0.220963i
$105$		0			0
$106$	−13.2001	+	9.59041i	−1.28210	+	0.931503i
$107$	0.180414			0.0174413			0.00872066	−	0.999962i	$-0.497224\pi$
$107$	0.180414			0.0174413			0.00872066	+	0.999962i	$0.497224\pi$
$108$	8.75375	−	6.35997i	0.842330	−	0.611988i
$109$	2.44560	+	7.52677i	0.234246	+	0.720934i	0.997221	+	0.0745060i	$0.0237380\pi$
$109$	2.44560	+	7.52677i	0.234246	+	0.720934i	−0.762975	+	0.646428i	$0.776262\pi$
$110$		0			0
$111$	8.90225	−	27.3983i	0.844964	−	2.60053i
$112$	1.40702	+	4.33037i	0.132951	+	0.409182i
$113$	1.65798	+	5.10272i	0.155969	+	0.480024i	0.998258	−	0.0590029i	$-0.0187921\pi$
$113$	1.65798	+	5.10272i	0.155969	+	0.480024i	−0.842289	+	0.539027i	$0.818792\pi$
$114$	10.9708	−	33.7645i	1.02751	−	3.16234i
$115$		0			0
$116$	0.943609	+	2.90413i	0.0876119	+	0.269642i
$117$	−25.6727	+	18.6523i	−2.37344	+	1.72441i
$118$	−7.67758			−0.706778
$119$	−1.11712	+	0.811636i	−0.102406	+	0.0744026i
$120$		0			0
$121$	1.31553	+	0.955789i	0.119594	+	0.0868899i
$122$	4.28092	+	3.11027i	0.387576	+	0.281591i
$123$	−7.02882	+	21.6325i	−0.633767	+	1.95053i
$124$	1.69737			0.152428
$125$		0			0
$126$	−10.0687			−0.896991
$127$	0.660970	−	2.03426i	0.0586516	−	0.180511i	−0.917438	−	0.397878i	$-0.869747\pi$
$127$	0.660970	−	2.03426i	0.0586516	−	0.180511i	0.976090	+	0.217367i	$0.0697468\pi$
$128$	−4.05391	−	2.94534i	−0.358319	−	0.260334i
$129$	−10.2936	−	7.47876i	−0.906304	−	0.658468i
$130$		0			0
$131$	−10.5901	+	7.69414i	−0.925259	+	0.672240i	−0.944827	−	0.327569i	$-0.893771\pi$
$131$	−10.5901	+	7.69414i	−0.925259	+	0.672240i	0.0195687	+	0.999809i	$0.493771\pi$
$132$	14.6782			1.27758
$133$	−5.21871	+	3.79161i	−0.452519	+	0.328774i
$134$	4.55161	+	14.0084i	0.393200	+	1.21014i
$135$		0			0
$136$	0.270996	−	0.834038i	0.0232377	−	0.0715182i
$137$	2.59499	+	7.98654i	0.221705	+	0.682336i	0.998609	+	0.0527184i	$0.0167886\pi$
$137$	2.59499	+	7.98654i	0.221705	+	0.682336i	−0.776905	+	0.629618i	$0.783211\pi$
$138$	−3.37565	−	10.3892i	−0.287355	−	0.884386i
$139$	7.19021	−	22.1292i	0.609866	−	1.87697i	0.150822	−	0.988561i	$-0.451808\pi$
$139$	7.19021	−	22.1292i	0.609866	−	1.87697i	0.459044	−	0.888414i	$-0.348192\pi$
$140$		0			0
$141$	−1.60486	−	4.93924i	−0.135153	−	0.415959i
$142$	13.4076	−	9.74117i	1.12514	−	0.817461i
$143$	−18.4816			−1.54551
$144$	19.3647	−	14.0693i	1.61373	−	1.17244i
$145$		0			0
$146$	−25.4191	−	18.4681i	−2.10370	−	1.52843i
$147$	2.32470	+	1.68900i	0.191738	+	0.139306i
$148$	−5.16884	+	15.9081i	−0.424876	+	1.30763i
$149$	−14.6482			−1.20002			−0.600012	−	0.799991i	$-0.704838\pi$
$149$	−14.6482			−1.20002			−0.600012	+	0.799991i	$0.704838\pi$
$150$		0			0
$151$	4.82167			0.392382			0.196191	−	0.980566i	$-0.437143\pi$
$151$	4.82167			0.392382			0.196191	+	0.980566i	$0.437143\pi$
$152$	1.26597	−	3.89626i	0.102684	−	0.316029i
$153$	5.87266	+	4.26674i	0.474776	+	0.344945i
$154$	−4.74414	−	3.44682i	−0.382293	−	0.277752i
$155$		0			0
$156$	23.4127	−	17.0103i	1.87451	−	1.36191i
$157$	−2.79319			−0.222921			−0.111461	−	0.993769i	$-0.535553\pi$
$157$	−2.79319			−0.222921			−0.111461	+	0.993769i	$0.535553\pi$
$158$	−1.08020	+	0.784813i	−0.0859363	+	0.0624363i
$159$	−7.56435	−	23.2807i	−0.599892	−	1.84628i
$160$		0			0
$161$	−0.613350	+	1.88770i	−0.0483388	+	0.148771i
$162$	1.69552	+	5.21826i	0.133212	+	0.409986i
$163$	−0.171468	−	0.527726i	−0.0134304	−	0.0413347i	0.944117	−	0.329611i	$-0.106918\pi$
$163$	−0.171468	−	0.527726i	−0.0134304	−	0.0413347i	−0.957547	+	0.288277i	$0.906918\pi$
$164$	4.08109	−	12.5603i	0.318679	−	0.980794i
$165$		0			0
$166$	3.81894	+	11.7535i	0.296408	+	0.912249i
$167$	−13.1165	+	9.52971i	−1.01499	+	0.737431i	−0.965249	−	0.261331i	$-0.915839\pi$
$167$	−13.1165	+	9.52971i	−1.01499	+	0.737431i	−0.0497380	+	0.998762i	$0.515839\pi$
$168$	−1.82493			−0.140797
$169$	−18.9621	+	13.7768i	−1.45862	+	1.05975i
$170$		0			0
$171$	27.4345	+	19.9323i	2.09797	+	1.52426i
$172$	5.97671	+	4.34233i	0.455720	+	0.331100i
$173$	5.75941	−	17.7256i	0.437880	−	1.34766i	−0.452226	−	0.891903i	$-0.649370\pi$
$173$	5.75941	−	17.7256i	0.437880	−	1.34766i	0.890106	−	0.455753i	$-0.150630\pi$
$174$	−10.0729			−0.763626
$175$		0			0
$176$	13.9405			1.05081
$177$	3.55941	−	10.9547i	0.267541	−	0.823408i
$178$	6.80232	+	4.94218i	0.509855	+	0.370432i
$179$	18.1270	+	13.1700i	1.35487	+	0.984374i	0.998753	+	0.0499340i	$0.0159011\pi$
$179$	18.1270	+	13.1700i	1.35487	+	0.984374i	0.356122	+	0.934440i	$0.384099\pi$
$180$		0			0
$181$	−1.85130	+	1.34505i	−0.137606	+	0.0999769i	−0.654459	−	0.756098i	$-0.727104\pi$
$181$	−1.85130	+	1.34505i	−0.137606	+	0.0999769i	0.516853	+	0.856074i	$0.327104\pi$
$182$	−11.5616			−0.857005
$183$	−6.42255	+	4.66626i	−0.474769	+	0.344940i
$184$	−0.389534	−	1.19886i	−0.0287168	−	0.0883813i
$185$		0			0
$186$	−1.73023	+	5.32510i	−0.126867	+	0.390455i
$187$	1.30643	+	4.02077i	0.0955355	+	0.294028i
$188$	0.931815	+	2.86783i	0.0679596	+	0.209158i
$189$	2.00408	−	6.16793i	0.145775	−	0.448651i
$190$		0			0
$191$	−3.92233	−	12.0717i	−0.283810	−	0.873477i	−0.986753	−	0.162231i	$-0.948131\pi$
$191$	−3.92233	−	12.0717i	−0.283810	−	0.873477i	0.702943	−	0.711246i	$-0.251869\pi$
$192$	−12.0044	+	8.72174i	−0.866346	+	0.629437i
$193$	23.4541			1.68826			0.844131	−	0.536137i	$-0.180117\pi$
$193$	23.4541			1.68826			0.844131	+	0.536137i	$0.180117\pi$
$194$	−15.2193	+	11.0575i	−1.09268	+	0.793881i
$195$		0			0
$196$	−1.34977	−	0.980668i	−0.0964124	−	0.0700477i
$197$	−1.24252	−	0.902743i	−0.0885258	−	0.0643178i	0.542642	−	0.839964i	$-0.317424\pi$
$197$	−1.24252	−	0.902743i	−0.0885258	−	0.0643178i	−0.631168	+	0.775646i	$0.717424\pi$
$198$	−9.52612	+	29.3184i	−0.676992	+	2.08357i
$199$	−0.533975			−0.0378525			−0.0189262	−	0.999821i	$-0.506025\pi$
$199$	−0.533975			−0.0378525			−0.0189262	+	0.999821i	$0.506025\pi$
$200$		0			0
$201$	−22.0981			−1.55868
$202$	0.588936	−	1.81256i	0.0414374	−	0.127531i
$203$	1.48069	+	1.07578i	0.103924	+	0.0755052i
$204$	−5.35567	−	3.89112i	−0.374972	−	0.272433i
$205$		0			0
$206$	−21.0145	+	15.2679i	−1.46415	+	1.06377i
$207$	10.4342			0.725229
$208$	22.2360	−	16.1554i	1.54179	−	1.12018i
$209$	6.10307	+	18.7833i	0.422158	+	1.29927i
$210$		0			0
$211$	0.338743	−	1.04254i	0.0233200	−	0.0717716i	−0.938719	−	0.344683i	$-0.887987\pi$
$211$	0.338743	−	1.04254i	0.0233200	−	0.0717716i	0.962039	+	0.272911i	$0.0879865\pi$
$212$	4.39203	+	13.5173i	0.301646	+	0.928370i
$213$	7.68326	+	23.6467i	0.526449	+	1.62024i
$214$	0.106781	−	0.328637i	0.00729938	−	0.0224652i
$215$		0			0
$216$	1.27278	+	3.91720i	0.0866015	+	0.266532i
$217$	0.823057	−	0.597986i	0.0558728	−	0.0405939i
$218$	15.1580			1.02663
$219$	38.1357	−	27.7072i	2.57697	−	1.87228i
$220$		0			0
$221$	6.74343	+	4.89939i	0.453612	+	0.329568i
$222$	−44.6390	−	32.4321i	−2.99597	−	2.17670i
$223$	−2.49033	+	7.66444i	−0.166765	+	0.513249i	−0.999162	−	0.0409303i	$-0.986968\pi$
$223$	−2.49033	+	7.66444i	−0.166765	+	0.513249i	0.832397	+	0.554179i	$0.186968\pi$
$224$	7.45065			0.497818
$225$		0			0
$226$	10.2763			0.683566
$227$	0.279751	−	0.860985i	0.0185677	−	0.0571456i	−0.941343	−	0.337450i	$-0.890436\pi$
$227$	0.279751	−	0.860985i	0.0185677	−	0.0571456i	0.959911	+	0.280305i	$0.0904355\pi$
$228$	−25.0194	−	18.1776i	−1.65695	−	1.20384i
$229$	6.10920	+	4.43859i	0.403707	+	0.293310i	0.771049	−	0.636775i	$-0.219732\pi$
$229$	6.10920	+	4.43859i	0.403707	+	0.293310i	−0.367342	+	0.930086i	$0.619732\pi$
$230$		0			0
$231$	7.11751	−	5.17117i	0.468298	−	0.340238i
$232$	−1.16237			−0.0763131
$233$	−9.43009	+	6.85136i	−0.617786	+	0.448848i	−0.852147	−	0.523302i	$-0.824700\pi$
$233$	−9.43009	+	6.85136i	−0.617786	+	0.448848i	0.234362	+	0.972150i	$0.424700\pi$
$234$	18.7817	+	57.8043i	1.22780	+	3.77878i
$235$		0			0
$236$	−2.06667	+	6.36056i	−0.134529	+	0.414037i
$237$	−0.619014	−	1.90513i	−0.0402093	−	0.123751i
$238$	0.817268	+	2.51529i	0.0529756	+	0.163042i
$239$	4.18625	−	12.8839i	0.270786	−	0.833393i	−0.719518	−	0.694474i	$-0.755637\pi$
$239$	4.18625	−	12.8839i	0.270786	−	0.833393i	0.990304	−	0.138919i	$-0.0443629\pi$
$240$		0			0
$241$	−4.08802	−	12.5816i	−0.263333	−	0.810454i	−0.992073	−	0.125664i	$-0.959894\pi$
$241$	−4.08802	−	12.5816i	−0.263333	−	0.810454i	0.728740	−	0.684790i	$-0.240106\pi$
$242$	2.51965	−	1.83063i	0.161969	−	0.117678i
$243$	11.2243			0.720039
$244$	3.72908	−	2.70933i	0.238730	−	0.173447i
$245$		0			0
$246$	35.2449	+	25.6069i	2.24713	+	1.63264i
$247$	31.5023	+	22.8878i	2.00445	+	1.45632i
$248$	−0.199660	+	0.614491i	−0.0126784	+	0.0390202i
$249$	−18.5409			−1.17498
$250$		0			0
$251$	25.6476			1.61887			0.809433	−	0.587213i	$-0.199775\pi$
$251$	25.6476			1.61887			0.809433	+	0.587213i	$0.199775\pi$
$252$	−2.71032	+	8.34150i	−0.170734	+	0.525465i
$253$	4.91637	+	3.57195i	0.309089	+	0.224567i
$254$	−3.31434	−	2.40801i	−0.207960	−	0.151092i
$255$		0			0
$256$	−16.1198	+	11.7117i	−1.00749	+	0.731982i
$257$	−6.16031			−0.384269			−0.192135	−	0.981369i	$-0.561541\pi$
$257$	−6.16031			−0.384269			−0.192135	+	0.981369i	$0.561541\pi$
$258$	−19.7155	+	14.3241i	−1.22743	+	0.891782i
$259$	3.09806	+	9.53485i	0.192504	+	0.592467i
$260$		0			0
$261$	2.97319	−	9.15054i	0.184036	−	0.566404i
$262$	7.74752	+	23.8444i	0.478643	+	1.47311i
$263$	0.447083	+	1.37598i	0.0275683	+	0.0848466i	0.963894	−	0.266286i	$-0.0857966\pi$
$263$	0.447083	+	1.37598i	0.0275683	+	0.0848466i	−0.936326	+	0.351133i	$0.885797\pi$
$264$	−1.72659	+	5.31390i	−0.106264	+	0.327048i
$265$		0			0
$266$	3.81792	+	11.7503i	0.234092	+	0.720460i
$267$	−10.2054	+	7.41462i	−0.624557	+	0.453767i
$268$	12.8306			0.783755
$269$	2.81792	−	2.04734i	0.171812	−	0.124829i	−0.498556	−	0.866857i	$-0.666136\pi$
$269$	2.81792	−	2.04734i	0.171812	−	0.124829i	0.670368	+	0.742029i	$0.266136\pi$
$270$		0			0
$271$	−18.7911	−	13.6525i	−1.14148	−	0.829332i	−0.154154	−	0.988047i	$-0.549265\pi$
$271$	−18.7911	−	13.6525i	−1.14148	−	0.829332i	−0.987325	+	0.158715i	$0.949265\pi$
$272$	−5.08651	−	3.69556i	−0.308415	−	0.224076i
$273$	5.36009	−	16.4967i	0.324408	−	0.998424i
$274$	16.0839			0.971665
$275$		0			0
$276$	−9.51568			−0.572776
$277$	−6.85737	+	21.1048i	−0.412019	+	1.26807i	0.502871	+	0.864362i	$0.332277\pi$
$277$	−6.85737	+	21.1048i	−0.412019	+	1.26807i	−0.914890	+	0.403703i	$0.867723\pi$
$278$	−36.0542	−	26.1949i	−2.16239	−	1.57107i
$279$	−4.32678	−	3.14359i	−0.259037	−	0.188202i
$280$		0			0
$281$	−14.0470	+	10.2058i	−0.837975	+	0.608824i	−0.921804	−	0.387656i	$-0.873285\pi$
$281$	−14.0470	+	10.2058i	−0.837975	+	0.608824i	0.0838293	+	0.996480i	$0.473285\pi$
$282$	−9.94701			−0.592336
$283$	13.1375	−	9.54494i	0.780943	−	0.567388i	−0.124319	−	0.992242i	$-0.539675\pi$
$283$	13.1375	−	9.54494i	0.780943	−	0.567388i	0.905262	+	0.424854i	$0.139675\pi$
$284$	−4.46107	−	13.7298i	−0.264716	−	0.814712i
$285$		0			0
$286$	−10.9386	+	33.6656i	−0.646813	+	1.99069i
$287$	−2.44609	−	7.52829i	−0.144388	−	0.444381i
$288$	−12.1035	−	37.2507i	−0.713205	−	2.19502i
$289$	−4.66408	+	14.3546i	−0.274358	+	0.844386i
$290$		0			0
$291$	−8.72149	−	26.8420i	−0.511263	−	1.57351i
$292$	−22.1424	+	16.0874i	−1.29579	+	0.941444i
$293$	−15.2633			−0.891693			−0.445846	−	0.895109i	$-0.647097\pi$
$293$	−15.2633			−0.891693			−0.445846	+	0.895109i	$0.647097\pi$
$294$	4.45253	−	3.23495i	0.259677	−	0.188666i
$295$		0			0
$296$	−5.15112	−	3.74251i	−0.299403	−	0.217529i
$297$	−16.0639	−	11.6711i	−0.932122	−	0.677226i
$298$	−8.66971	+	26.6826i	−0.502223	+	1.54568i
$299$	11.9814			0.692900
$300$		0			0
$301$	4.42793			0.255222
$302$	2.85377	−	8.78301i	0.164216	−	0.505405i
$303$	2.31320	+	1.68064i	0.132890	+	0.0965503i
$304$	−23.7619	−	17.2641i	−1.36284	−	0.990162i
$305$		0			0
$306$	11.2480	−	8.17212i	0.643003	−	0.467169i
$307$	0.729338			0.0416255			0.0208127	−	0.999783i	$-0.493375\pi$
$307$	0.729338			0.0416255			0.0208127	+	0.999783i	$0.493375\pi$
$308$	−4.13258	+	3.00250i	−0.235476	+	0.171083i
$309$	−12.0425	−	37.0629i	−0.685071	−	2.10843i
$310$		0			0
$311$	−3.66283	+	11.2730i	−0.207700	+	0.639236i	0.791891	+	0.610662i	$0.209097\pi$
$311$	−3.66283	+	11.2730i	−0.207700	+	0.639236i	−0.999592	+	0.0285737i	$0.990903\pi$
$312$	3.40415	+	10.4769i	0.192722	+	0.593138i
$313$	6.40551	+	19.7141i	0.362061	+	1.11431i	0.951801	+	0.306715i	$0.0992299\pi$
$313$	6.40551	+	19.7141i	0.362061	+	1.11431i	−0.589741	+	0.807593i	$0.700770\pi$
$314$	−1.65319	+	5.08799i	−0.0932949	+	0.287132i
$315$		0			0
$316$	0.359413	+	1.10616i	0.0202186	+	0.0622264i
$317$	−22.0232	+	16.0008i	−1.23695	+	0.898694i	−0.997391	−	0.0721893i	$-0.977001\pi$
$317$	−22.0232	+	16.0008i	−1.23695	+	0.898694i	−0.239555	+	0.970883i	$0.577001\pi$
$318$	−46.8844			−2.62915
$319$	4.53340	−	3.29371i	0.253822	−	0.184412i
$320$		0			0
$321$	0.419410	+	0.304719i	0.0234092	+	0.0170078i
$322$	3.07555	+	2.23452i	0.171394	+	0.124525i
$323$	2.75252	−	8.47138i	0.153154	−	0.471360i
$324$	4.77952			0.265529
$325$		0			0
$326$	−1.06277			−0.0588616
$327$	−7.02740	+	21.6281i	−0.388616	+	1.19604i
$328$	4.06710	+	2.95492i	0.224568	+	0.163158i
$329$	1.46218	+	1.06234i	0.0806127	+	0.0585685i
$330$		0			0
$331$	14.7484	−	10.7154i	0.810648	−	0.588970i	−0.103370	−	0.994643i	$-0.532963\pi$
$331$	14.7484	−	10.7154i	0.810648	−	0.588970i	0.914018	+	0.405673i	$0.132963\pi$
$332$	10.7653			0.590822
$333$	42.6383	−	30.9785i	2.33656	−	1.69761i
$334$	9.59583	+	29.5329i	0.525061	+	1.61597i
$335$		0			0
$336$	−4.04307	+	12.4433i	−0.220568	+	0.678837i
$337$	−5.80701	−	17.8721i	−0.316328	−	0.973557i	−0.975204	−	0.221306i	$-0.928968\pi$
$337$	−5.80701	−	17.8721i	−0.316328	−	0.973557i	0.658877	−	0.752251i	$-0.271032\pi$
$338$	13.8724	+	42.6948i	0.754558	+	2.32229i
$339$	−4.76418	+	14.6626i	−0.258755	+	0.796365i
$340$		0			0
$341$	−0.962532	−	2.96237i	−0.0521241	−	0.160421i
$342$	52.5456	−	38.1766i	2.84134	−	2.06435i
$343$	−1.00000			−0.0539949
$344$	−2.27507	+	1.65294i	−0.122664	+	0.0891204i
$345$		0			0
$346$	−28.8797	−	20.9823i	−1.55258	−	1.12802i
$347$	−7.98758	−	5.80332i	−0.428796	−	0.311538i	0.352371	−	0.935860i	$-0.385375\pi$
$347$	−7.98758	−	5.80332i	−0.428796	−	0.311538i	−0.781167	+	0.624322i	$0.785375\pi$
$348$	−2.71145	+	8.34499i	−0.145349	+	0.447339i
$349$	29.2500			1.56572			0.782859	−	0.622200i	$-0.213761\pi$
$349$	29.2500			1.56572			0.782859	+	0.622200i	$0.213761\pi$
$350$		0			0
$351$	−39.1483			−2.08958
$352$	7.04916	−	21.6951i	0.375721	−	1.15635i
$353$	7.54103	+	5.47888i	0.401369	+	0.291611i	0.770098	−	0.637925i	$-0.220207\pi$
$353$	7.54103	+	5.47888i	0.401369	+	0.291611i	−0.368730	+	0.929537i	$0.620207\pi$
$354$	−17.8481	−	12.9674i	−0.948616	−	0.689210i
$355$		0			0
$356$	5.92545	−	4.30509i	0.314048	−	0.228169i
$357$	−3.96783			−0.210000
$358$	34.7188	−	25.2247i	1.83494	−	1.33317i
$359$	0.500419	+	1.54013i	0.0264111	+	0.0812850i	0.963393	−	0.268092i	$-0.0863932\pi$
$359$	0.500419	+	1.54013i	0.0264111	+	0.0812850i	−0.936982	+	0.349377i	$0.886393\pi$
$360$		0			0
$361$	6.98725	−	21.5045i	0.367750	−	1.13182i
$362$	1.35438	+	4.16836i	0.0711848	+	0.219084i
$363$	1.44390	+	4.44385i	0.0757848	+	0.233242i
$364$	−3.11219	+	9.57833i	−0.163123	+	0.502041i
$365$		0			0
$366$	4.69863	+	14.4609i	0.245602	+	0.755884i
$367$	25.5042	−	18.5299i	1.33131	−	0.967251i	0.331591	−	0.943423i	$-0.392415\pi$
$367$	25.5042	−	18.5299i	1.33131	−	0.967251i	0.999716	−	0.0238277i	$-0.00758531\pi$
$368$	−9.03744			−0.471109
$369$	−33.6652	+	24.4592i	−1.75254	+	1.27330i
$370$		0			0
$371$	6.89187	+	5.00723i	0.357808	+	0.259963i
$372$	3.94588	+	2.86685i	0.204584	+	0.148639i
$373$	5.21416	−	16.0475i	0.269979	−	0.830909i	−0.720526	−	0.693428i	$-0.756099\pi$
$373$	5.21416	−	16.0475i	0.269979	−	0.830909i	0.990504	−	0.137481i	$-0.0439006\pi$
$374$	8.09734			0.418704
$375$		0			0
$376$	−1.14784			−0.0591952
$377$	3.41404	−	10.5073i	0.175832	−	0.541155i
$378$	−10.0492	−	7.30114i	−0.516873	−	0.375530i
$379$	8.12046	+	5.89986i	0.417120	+	0.303055i	0.776478	−	0.630144i	$-0.217004\pi$
$379$	8.12046	+	5.89986i	0.417120	+	0.303055i	−0.359358	+	0.933200i	$0.617004\pi$
$380$		0			0
$381$	4.97241	−	3.61267i	0.254744	−	0.185083i
$382$	−24.3109			−1.24385
$383$	−8.38809	+	6.09431i	−0.428611	+	0.311404i	−0.781093	−	0.624414i	$-0.785338\pi$
$383$	−8.38809	+	6.09431i	−0.428611	+	0.311404i	0.352482	+	0.935819i	$0.385338\pi$
$384$	−4.44948	−	13.6941i	−0.227061	−	0.698823i
$385$		0			0
$386$	13.8816	−	42.7232i	0.706556	−	2.17455i
$387$	−7.19312	−	22.1382i	−0.365647	−	1.12535i
$388$	5.06389	+	15.5851i	0.257080	+	0.791211i
$389$	−3.22016	+	9.91064i	−0.163269	+	0.502489i	−0.998905	−	0.0467945i	$-0.985099\pi$
$389$	−3.22016	+	9.91064i	−0.163269	+	0.502489i	0.835636	+	0.549284i	$0.185099\pi$
$390$		0			0
$391$	−0.846938	−	2.60661i	−0.0428315	−	0.131822i
$392$	0.513801	−	0.373298i	0.0259508	−	0.0188544i
$393$	−37.6141			−1.89738
$394$	−2.37981	+	1.72903i	−0.119893	+	0.0871074i
$395$		0			0
$396$	21.7248	+	15.7840i	1.09171	+	0.793176i
$397$	26.0464	+	18.9238i	1.30723	+	0.949760i	0.999998	−	0.00187340i	$-0.000596321\pi$
$397$	26.0464	+	18.9238i	1.30723	+	0.949760i	0.307235	+	0.951634i	$0.400596\pi$
$398$	−0.316040	+	0.972671i	−0.0158417	+	0.0487556i
$399$	−18.5360			−0.927959
$400$		0			0
$401$	−10.4221			−0.520453			−0.260226	−	0.965548i	$-0.583797\pi$
$401$	−10.4221			−0.520453			−0.260226	+	0.965548i	$0.583797\pi$
$402$	−13.0790	+	40.2531i	−0.652323	+	2.00764i
$403$	−4.96833	−	3.60970i	−0.247490	−	0.179812i
$404$	−1.34310	−	0.975818i	−0.0668216	−	0.0485487i
$405$		0			0
$406$	2.83598	−	2.06046i	0.140747	−	0.102259i
$407$	30.6950			1.52150
$408$	2.03867	−	1.48118i	0.100929	−	0.0733294i
$409$	9.59710	+	29.5368i	0.474546	+	1.46050i	0.846569	+	0.532279i	$0.178664\pi$
$409$	9.59710	+	29.5368i	0.474546	+	1.46050i	−0.372023	+	0.928223i	$0.621336\pi$
$410$		0			0
$411$	−7.45667	+	22.9493i	−0.367810	+	1.13200i
$412$	6.99212	+	21.5195i	0.344477	+	1.06019i
$413$	1.23870	+	3.81234i	0.0609526	+	0.187593i
$414$	6.17564	−	19.0067i	0.303516	−	0.934127i
$415$		0			0
$416$	−13.8981	−	42.7741i	−0.681412	−	2.09717i
$417$	54.0913	−	39.2996i	2.64886	−	1.92451i
$418$	37.8272			1.85019
$419$	−11.0249	+	8.01005i	−0.538601	+	0.391316i	−0.823565	−	0.567222i	$-0.808018\pi$
$419$	−11.0249	+	8.01005i	−0.538601	+	0.391316i	0.284964	+	0.958538i	$0.408018\pi$
$420$		0			0
$421$	16.6608	+	12.1048i	0.811997	+	0.589950i	0.914409	−	0.404792i	$-0.132656\pi$
$421$	16.6608	+	12.1048i	0.811997	+	0.589950i	−0.102412	+	0.994742i	$0.532656\pi$
$422$	−1.69857	−	1.23409i	−0.0826853	−	0.0600744i
$423$	2.93603	−	9.03617i	0.142755	−	0.439353i
$424$	−5.41023			−0.262744
$425$		0			0
$426$	47.6214			2.30727
$427$	0.853734	−	2.62752i	0.0413151	−	0.127155i
$428$	−0.243519	−	0.176927i	−0.0117709	−	0.00855208i
$429$	−42.9643	−	31.2154i	−2.07434	−	1.50709i
$430$		0			0
$431$	1.12535	−	0.817613i	0.0542061	−	0.0393830i	−0.560352	−	0.828254i	$-0.689334\pi$
$431$	1.12535	−	0.817613i	0.0542061	−	0.0393830i	0.614558	+	0.788871i	$0.289334\pi$
$432$	29.5292			1.42072
$433$	5.71617	−	4.15304i	0.274702	−	0.199582i	−0.441902	−	0.897064i	$-0.645696\pi$
$433$	5.71617	−	4.15304i	0.274702	−	0.199582i	0.716603	+	0.697481i	$0.245696\pi$
$434$	−0.602135	−	1.85318i	−0.0289034	−	0.0889555i
$435$		0			0
$436$	4.08027	−	12.5578i	0.195409	−	0.601408i
$437$	−3.95652	−	12.1769i	−0.189266	−	0.582501i
$438$	−27.8994	−	85.8656i	−1.33309	−	4.10282i
$439$	5.73054	−	17.6368i	0.273504	−	0.841758i	−0.716108	−	0.697990i	$-0.754078\pi$
$439$	5.73054	−	17.6368i	0.273504	−	0.841758i	0.989611	−	0.143768i	$-0.0459220\pi$
$440$		0			0
$441$	1.62449	+	4.99966i	0.0773566	+	0.238079i
$442$	12.9158	−	9.38384i	0.614340	−	0.446344i
$443$	29.7479			1.41337			0.706683	−	0.707530i	$-0.250191\pi$
$443$	29.7479			1.41337			0.706683	+	0.707530i	$0.250191\pi$
$444$	−38.8847	+	28.2514i	−1.84539	+	1.34075i
$445$		0			0
$446$	12.4874	+	9.07261i	0.591294	+	0.429600i
$447$	−34.0526	−	24.7407i	−1.61063	−	1.17019i
$448$	1.59572	−	4.91112i	0.0753907	−	0.232029i
$449$	−17.2909			−0.816006			−0.408003	−	0.912981i	$-0.633775\pi$
$449$	−17.2909			−0.816006			−0.408003	+	0.912981i	$0.633775\pi$
$450$		0			0
$451$	−24.2354			−1.14120
$452$	2.76619	−	8.51345i	0.130111	−	0.400439i
$453$	11.2090	+	8.14379i	0.526643	+	0.382629i
$454$	−1.40277	−	1.01917i	−0.0658352	−	0.0478321i
$455$		0			0
$456$	9.52379	−	6.91944i	0.445992	−	0.324032i
$457$	20.4059			0.954550			0.477275	−	0.878754i	$-0.341625\pi$
$457$	20.4059			0.954550			0.477275	+	0.878754i	$0.341625\pi$
$458$	11.7010	−	8.50128i	0.546752	−	0.397239i
$459$	2.76731	+	8.51691i	0.129167	+	0.397535i
$460$		0			0
$461$	−2.25553	+	6.94180i	−0.105050	+	0.323312i	−0.989742	−	0.142864i	$-0.954369\pi$
$461$	−2.25553	+	6.94180i	−0.105050	+	0.323312i	0.884692	+	0.466176i	$0.154369\pi$
$462$	−5.20705	−	16.0257i	−0.242254	−	0.745581i
$463$	−3.42376	−	10.5372i	−0.159116	−	0.489707i	0.839439	−	0.543454i	$-0.182884\pi$
$463$	−3.42376	−	10.5372i	−0.159116	−	0.489707i	−0.998555	+	0.0537464i	$0.982884\pi$
$464$	−2.57518	+	7.92559i	−0.119550	+	0.367936i
$465$		0			0
$466$	6.89890	+	21.2326i	0.319585	+	0.983582i
$467$	29.4575	−	21.4021i	1.36313	−	0.990373i	0.364893	−	0.931050i	$-0.381106\pi$
$467$	29.4575	−	21.4021i	1.36313	−	0.990373i	0.998239	−	0.0593237i	$-0.0188944\pi$
$468$	52.9441			2.44734
$469$	6.22159	−	4.52025i	0.287287	−	0.208726i
$470$		0			0
$471$	−6.49335	−	4.71769i	−0.299198	−	0.217380i
$472$	−2.05959	−	1.49638i	−0.0948001	−	0.0688763i
$473$	4.18932	−	12.8934i	0.192625	−	0.592840i
$474$	−3.83669			−0.176225
$475$		0			0
$476$	2.30381			0.105595
$477$	13.8387	−	42.5912i	0.633631	−	1.95012i
$478$	−20.9913	−	15.2511i	−0.960120	−	0.697568i
$479$	−9.22180	−	6.70003i	−0.421355	−	0.306132i	0.356828	−	0.934170i	$-0.383858\pi$
$479$	−9.22180	−	6.70003i	−0.421355	−	0.306132i	−0.778183	+	0.628038i	$0.783858\pi$
$480$		0			0
$481$	48.9604	−	35.5718i	2.23240	−	1.62194i
$482$	−25.3379			−1.15411
$483$	−4.61417	+	3.35239i	−0.209952	+	0.152539i
$484$	−0.838357	−	2.58020i	−0.0381072	−	0.117282i
$485$		0			0
$486$	6.64325	−	20.4458i	0.301344	−	0.927442i
$487$	−9.84756	−	30.3077i	−0.446235	−	1.37337i	−0.881123	−	0.472887i	$-0.843212\pi$
$487$	−9.84756	−	30.3077i	−0.446235	−	1.37337i	0.434888	−	0.900485i	$-0.356788\pi$
$488$	0.542200	+	1.66872i	0.0245442	+	0.0755394i
$489$	0.492713	−	1.51641i	0.0222813	−	0.0685747i
$490$		0			0
$491$	−0.747941	−	2.30193i	−0.0337541	−	0.103884i	0.932760	−	0.360498i	$-0.117393\pi$
$491$	−0.747941	−	2.30193i	−0.0337541	−	0.103884i	−0.966514	+	0.256614i	$0.917393\pi$
$492$	30.7016	−	22.3060i	1.38414	−	1.00563i
$493$	−2.52725			−0.113822
$494$	60.3368	−	43.8372i	2.71468	−	1.97233i
$495$		0			0
$496$	3.74757	+	2.72277i	0.168271	+	0.122256i
$497$	−7.00021	−	5.08595i	−0.314002	−	0.228136i
$498$	−10.9737	+	33.7736i	−0.491743	+	1.51343i
$499$	18.2352			0.816318			0.408159	−	0.912911i	$-0.366171\pi$
$499$	18.2352			0.816318			0.408159	+	0.912911i	$0.366171\pi$
$500$		0			0
$501$	−46.5877			−2.08138
$502$	15.1799	−	46.7189i	0.677512	−	2.08517i
$503$	−8.97682	−	6.52204i	−0.400257	−	0.290803i	0.369389	−	0.929275i	$-0.379567\pi$
$503$	−8.97682	−	6.52204i	−0.400257	−	0.290803i	−0.769646	+	0.638471i	$0.779567\pi$
$504$	−2.70103	−	1.96241i	−0.120313	−	0.0874127i
$505$		0			0
$506$	9.41637	−	6.84139i	0.418609	−	0.304137i
$507$	−67.3503			−2.99113
$508$	−2.88709	+	2.09760i	−0.128094	+	0.0930658i
$509$	−10.7784	−	33.1724i	−0.477743	−	1.47034i	−0.842222	−	0.539131i	$-0.818753\pi$
$509$	−10.7784	−	33.1724i	−0.477743	−	1.47034i	0.364479	−	0.931212i	$-0.381247\pi$
$510$		0			0
$511$	−5.06928	+	15.6016i	−0.224252	+	0.690176i
$512$	8.69606	+	26.7637i	0.384315	+	1.18280i
$513$	12.9277	+	39.7873i	0.570771	+	1.75665i
$514$	−3.64606	+	11.2214i	−0.160821	+	0.494956i
$515$		0			0
$516$	6.55989	+	20.1893i	0.288783	+	0.888783i
$517$	4.47674	−	3.25254i	0.196887	−	0.143047i
$518$	19.2020			0.843688
$519$	43.3275	−	31.4793i	1.90187	−	1.38179i
$520$		0			0
$521$	14.0879	+	10.2355i	0.617203	+	0.448424i	0.851943	−	0.523634i	$-0.175424\pi$
$521$	14.0879	+	10.2355i	0.617203	+	0.448424i	−0.234741	+	0.972058i	$0.575424\pi$
$522$	−14.9086	−	10.8317i	−0.652532	−	0.474092i
$523$	−12.5454	+	38.6107i	−0.548571	+	1.68833i	0.163775	+	0.986498i	$0.447633\pi$
$523$	−12.5454	+	38.6107i	−0.548571	+	1.68833i	−0.712345	+	0.701829i	$0.752367\pi$
$524$	21.8396			0.954067
$525$		0			0
$526$	2.77105			0.120824
$527$	−0.434108	+	1.33605i	−0.0189100	+	0.0581991i
$528$	32.4076	+	23.5455i	1.41036	+	1.02469i
$529$	15.4202	+	11.2034i	0.670443	+	0.487105i
$530$		0			0
$531$	17.0481	−	12.3862i	0.739826	−	0.537515i
$532$	10.7624			0.466609
$533$	−38.6570	+	28.0859i	−1.67442	+	1.21654i
$534$	7.46606	+	22.9782i	0.323088	+	0.994363i
$535$		0			0
$536$	−1.50926	+	4.64502i	−0.0651900	+	0.200634i
$537$	19.8957	+	61.2328i	0.858565	+	2.64239i
$538$	−2.06155	−	6.34479i	−0.0888796	−	0.273543i
$539$	−0.946113	+	2.91184i	−0.0407520	+	0.125422i
$540$		0			0
$541$	7.56376	+	23.2789i	0.325192	+	1.00084i	0.971354	+	0.237637i	$0.0763729\pi$
$541$	7.56376	+	23.2789i	0.325192	+	1.00084i	−0.646162	+	0.763200i	$0.723627\pi$
$542$	−35.9908	+	26.1488i	−1.54594	+	1.12319i
$543$	−6.57552			−0.282183
$544$	−8.32329	+	6.04722i	−0.356858	+	0.259272i
$545$		0			0
$546$	−26.8774	−	19.5276i	−1.15025	−	0.835702i
$547$	−20.5382	−	14.9219i	−0.878149	−	0.638013i	0.0546121	−	0.998508i	$-0.482608\pi$
$547$	−20.5382	−	14.9219i	−0.878149	−	0.638013i	−0.932761	+	0.360495i	$0.882608\pi$
$548$	4.32951	−	13.3249i	0.184947	−	0.569209i
$549$	−14.5236			−0.619852
$550$		0			0
$551$	−11.8062			−0.502962
$552$	1.11932	−	3.44492i	0.0476415	−	0.146626i
$553$	0.563983	+	0.409757i	0.0239830	+	0.0174247i
$554$	34.3852	+	24.9823i	1.46089	+	1.06140i
$555$		0			0
$556$	−31.4066	+	22.8182i	−1.33194	+	0.967708i
$557$	−25.6992			−1.08891			−0.544454	−	0.838790i	$-0.683263\pi$
$557$	−25.6992			−1.08891			−0.544454	+	0.838790i	$0.683263\pi$
$558$	−8.28712	+	6.02094i	−0.350822	+	0.254887i
$559$	−8.25968	−	25.4207i	−0.349347	−	1.07518i
$560$		0			0
$561$	−3.75401	+	11.5537i	−0.158495	+	0.487796i
$562$	10.2766	+	31.6280i	0.433491	+	1.33415i
$563$	−9.51747	−	29.2918i	−0.401114	−	1.23450i	−0.924097	−	0.382158i	$-0.875181\pi$
$563$	−9.51747	−	29.2918i	−0.401114	−	1.23450i	0.522983	−	0.852343i	$-0.324819\pi$
$564$	−2.67756	+	8.24069i	−0.112746	+	0.346995i
$565$		0			0
$566$	−9.61117	−	29.5801i	−0.403987	−	1.24335i
$567$	2.31760	−	1.68383i	0.0973300	−	0.0707144i
$568$	5.49529			0.230577
$569$	−23.4426	+	17.0321i	−0.982765	+	0.714021i	−0.958325	−	0.285680i	$-0.907780\pi$
$569$	−23.4426	+	17.0321i	−0.982765	+	0.714021i	−0.0244405	+	0.999701i	$0.507780\pi$
$570$		0			0
$571$	−2.85552	−	2.07466i	−0.119500	−	0.0868217i	0.526430	−	0.850218i	$-0.323530\pi$
$571$	−2.85552	−	2.07466i	−0.119500	−	0.0868217i	−0.645930	+	0.763397i	$0.723530\pi$
$572$	24.9460	+	18.1244i	1.04305	+	0.757818i
$573$	11.2708	−	34.6879i	0.470844	−	1.44911i
$574$	−15.1610			−0.632810
$575$		0			0
$576$	−27.1462			−1.13109
$577$	−12.5587	+	38.6516i	−0.522824	+	1.60909i	0.245756	+	0.969332i	$0.420964\pi$
$577$	−12.5587	+	38.6516i	−0.522824	+	1.60909i	−0.768580	+	0.639754i	$0.779036\pi$
$578$	23.3873	+	16.9919i	0.972784	+	0.706769i
$579$	54.5238	+	39.6139i	2.26593	+	1.64630i
$580$		0			0
$581$	5.22011	−	3.79263i	0.216567	−	0.157345i
$582$	−54.0565			−2.24071
$583$	21.1007	−	15.3306i	0.873903	−	0.634927i
$584$	−3.21946	−	9.90848i	−0.133222	−	0.410016i
$585$		0			0
$586$	−9.03380	+	27.8032i	−0.373183	+	1.14854i
$587$	7.37968	+	22.7123i	0.304592	+	0.937438i	0.979829	+	0.199837i	$0.0640412\pi$
$587$	7.37968	+	22.7123i	0.304592	+	0.937438i	−0.675237	+	0.737601i	$0.735959\pi$
$588$	−1.48148	−	4.55953i	−0.0610952	−	0.188032i
$589$	−2.02796	+	6.24143i	−0.0835608	+	0.257174i
$590$		0			0
$591$	−1.36376	−	4.19722i	−0.0560976	−	0.172651i
$592$	−36.9304	+	26.8315i	−1.51783	+	1.10277i
$593$	−3.07757			−0.126381			−0.0631903	−	0.998001i	$-0.520128\pi$
$593$	−3.07757			−0.126381			−0.0631903	+	0.998001i	$0.520128\pi$
$594$	−30.7673	+	22.3538i	−1.26240	+	0.917187i
$595$		0			0
$596$	19.7717	+	14.3650i	0.809881	+	0.588413i
$597$	−1.24133	−	0.901881i	−0.0508044	−	0.0369115i
$598$	7.09133	−	21.8249i	0.289986	−	0.892485i
$599$	−16.5930			−0.677972			−0.338986	−	0.940791i	$-0.610084\pi$
$599$	−16.5930			−0.677972			−0.338986	+	0.940791i	$0.610084\pi$
$600$		0			0
$601$	−6.06622			−0.247446			−0.123723	−	0.992317i	$-0.539483\pi$
$601$	−6.06622			−0.247446			−0.123723	+	0.992317i	$0.539483\pi$
$602$	2.62073	−	8.06578i	0.106813	−	0.328737i
$603$	−32.7066	−	23.7628i	−1.33192	−	0.967695i
$604$	−6.50817	−	4.72846i	−0.264814	−	0.192398i
$605$		0			0
$606$	4.43050	−	3.21895i	0.179977	−	0.130761i
$607$	−25.1099			−1.01918			−0.509590	−	0.860418i	$-0.670203\pi$
$607$	−25.1099			−1.01918			−0.509590	+	0.860418i	$0.670203\pi$
$608$	−38.8828	+	28.2500i	−1.57690	+	1.14569i
$609$	1.62517	+	5.00176i	0.0658552	+	0.202681i
$610$		0			0
$611$	3.37137	−	10.3760i	0.136391	−	0.419768i
$612$	−3.74251	−	11.5183i	−0.151282	−	0.465598i
$613$	1.59003	+	4.89361i	0.0642208	+	0.197651i	0.978018	−	0.208519i	$-0.0668642\pi$
$613$	1.59003	+	4.89361i	0.0642208	+	0.197651i	−0.913798	+	0.406170i	$0.866864\pi$
$614$	0.431668	−	1.32854i	0.0174207	−	0.0536154i
$615$		0			0
$616$	−0.600869	−	1.84928i	−0.0242097	−	0.0745098i
$617$	−24.2172	+	17.5948i	−0.974947	+	0.708340i	−0.956574	−	0.291491i	$-0.905849\pi$
$617$	−24.2172	+	17.5948i	−0.974947	+	0.708340i	−0.0183732	+	0.999831i	$0.505849\pi$
$618$	−74.6400			−3.00246
$619$	−1.73936	+	1.26372i	−0.0699107	+	0.0507931i	−0.622192	−	0.782865i	$-0.713758\pi$
$619$	−1.73936	+	1.26372i	−0.0699107	+	0.0507931i	0.552281	+	0.833658i	$0.313758\pi$
$620$		0			0
$621$	10.4140	+	7.56620i	0.417899	+	0.303621i
$622$	18.3667	+	13.3442i	0.736438	+	0.535054i
$623$	1.35657	−	4.17510i	0.0543499	−	0.167272i
$624$	78.9785			3.16167
$625$		0			0
$626$	39.7018			1.58680
$627$	−17.5371	+	53.9737i	−0.700365	+	2.15550i
$628$	3.77018	+	2.73920i	0.150447	+	0.109306i
$629$	−11.1997	−	8.13709i	−0.446563	−	0.324447i
$630$		0			0
$631$	−23.6097	+	17.1535i	−0.939889	+	0.682869i	−0.948394	−	0.317095i	$-0.897293\pi$
$631$	−23.6097	+	17.1535i	−0.939889	+	0.682869i	0.00850531	+	0.999964i	$0.497293\pi$
$632$	−0.442736			−0.0176111
$633$	2.54833	−	1.85147i	0.101287	−	0.0735892i
$634$	16.1118	+	49.5870i	0.639881	+	1.96935i
$635$		0			0
$636$	−12.6205	+	38.8418i	−0.500434	+	1.54018i
$637$	1.86536	+	5.74099i	0.0739082	+	0.227466i
$638$	−3.31656	−	10.2073i	−0.131304	−	0.404112i
$639$	−14.0563	+	43.2607i	−0.556057	+	1.71137i
$640$		0			0
$641$	13.5991	+	41.8537i	0.537132	+	1.65312i	0.738997	+	0.673708i	$0.235300\pi$
$641$	13.5991	+	41.8537i	0.537132	+	1.65312i	−0.201865	+	0.979413i	$0.564700\pi$
$642$	0.803301	−	0.583632i	0.0317037	−	0.0230341i
$643$	8.47935			0.334393			0.167196	−	0.985924i	$-0.446529\pi$
$643$	8.47935			0.334393			0.167196	+	0.985924i	$0.446529\pi$
$644$	2.67909	−	1.94647i	0.105571	−	0.0767018i
$645$		0			0
$646$	−13.8021	−	10.0278i	−0.543036	−	0.394539i
$647$	−5.37616	−	3.90601i	−0.211359	−	0.153561i	0.477070	−	0.878866i	$-0.341699\pi$
$647$	−5.37616	−	3.90601i	−0.211359	−	0.153561i	−0.688428	+	0.725305i	$0.741699\pi$
$648$	−0.562212	+	1.73031i	−0.0220858	+	0.0679730i
$649$	12.2729			0.481752
$650$		0			0
$651$	2.92336			0.114576
$652$	−0.286080	+	0.880464i	−0.0112038	+	0.0344816i
$653$	38.5258	+	27.9907i	1.50763	+	1.09536i	0.967214	+	0.253962i	$0.0817339\pi$
$653$	38.5258	+	27.9907i	1.50763	+	1.09536i	0.540418	+	0.841397i	$0.318266\pi$
$654$	35.2378	+	25.6018i	1.37791	+	1.00111i
$655$		0			0
$656$	29.1586	−	21.1850i	1.13845	−	0.827134i
$657$	86.2379			3.36446
$658$	2.80053	−	2.03470i	0.109176	−	0.0793210i
$659$	1.87292	+	5.76427i	0.0729587	+	0.224544i	0.980886	−	0.194584i	$-0.0623358\pi$
$659$	1.87292	+	5.76427i	0.0729587	+	0.224544i	−0.907927	+	0.419128i	$0.862336\pi$
$660$		0			0
$661$	−1.52692	+	4.69939i	−0.0593905	+	0.182785i	−0.976350	−	0.216194i	$-0.930636\pi$
$661$	−1.52692	+	4.69939i	−0.0593905	+	0.182785i	0.916960	+	0.398979i	$0.130636\pi$
$662$	−10.7897	−	33.2073i	−0.419354	−	1.29064i
$663$	7.40142	+	22.7792i	0.287447	+	0.884672i
$664$	−1.26631	+	3.89731i	−0.0491425	+	0.151245i
$665$		0			0
$666$	−31.1934	−	96.0035i	−1.20872	−	3.72006i
$667$	−2.93894	+	2.13526i	−0.113796	+	0.0826777i
$668$	27.0498			1.04659
$669$	−18.7345	+	13.6114i	−0.724317	+	0.526247i
$670$		0			0
$671$	−6.84319	−	4.97187i	−0.264178	−	0.191937i
$672$	17.3206	+	12.5841i	0.668155	+	0.485443i
$673$	0.404276	−	1.24423i	0.0155837	−	0.0479617i	−0.942962	−	0.332900i	$-0.891973\pi$
$673$	0.404276	−	1.24423i	0.0155837	−	0.0479617i	0.958546	+	0.284938i	$0.0919730\pi$
$674$	−35.9923			−1.38637
$675$		0			0
$676$	39.1051			1.50404
$677$	12.1869	−	37.5073i	0.468379	−	1.44152i	−0.386303	−	0.922372i	$-0.626248\pi$
$677$	12.1869	−	37.5073i	0.468379	−	1.44152i	0.854682	−	0.519151i	$-0.173752\pi$
$678$	23.8892	+	17.3566i	0.917461	+	0.666574i
$679$	7.94614	+	5.77321i	0.304945	+	0.221555i
$680$		0			0
$681$	2.10454	−	1.52904i	0.0806461	−	0.0585928i
$682$	−5.96585			−0.228444
$683$	−33.6472	+	24.4461i	−1.28747	+	0.935404i	−0.999751	−	0.0223098i	$-0.992898\pi$
$683$	−33.6472	+	24.4461i	−1.28747	+	0.935404i	−0.287722	+	0.957714i	$0.592898\pi$
$684$	−17.4834	−	53.8083i	−0.668494	−	2.05741i
$685$		0			0
$686$	−0.591863	+	1.82157i	−0.0225974	+	0.0695478i
$687$	6.70531	+	20.6368i	0.255824	+	0.787344i
$688$	6.23021	+	19.1746i	0.237524	+	0.731025i
$689$	15.8906	−	48.9064i	0.605386	−	1.86319i
$690$		0			0
$691$	−0.309788	−	0.953430i	−0.0117849	−	0.0362702i	0.944991	−	0.327096i	$-0.106070\pi$
$691$	−0.309788	−	0.953430i	−0.0117849	−	0.0362702i	−0.956776	+	0.290826i	$0.906070\pi$
$692$	−25.1569	+	18.2775i	−0.956321	+	0.694808i
$693$	16.0951			0.611404
$694$	−15.2987	+	11.1152i	−0.580730	+	0.421925i
$695$		0			0
$696$	−2.70216	−	1.96323i	−0.102425	−	0.0744161i
$697$	8.84281	+	6.42468i	0.334945	+	0.243352i
$698$	17.3120	−	53.2809i	0.655269	−	2.01671i
$699$	−33.4941			−1.26686
$700$		0			0
$701$	46.3396			1.75022			0.875111	−	0.483922i	$-0.160788\pi$
$701$	46.3396			1.75022			0.875111	+	0.483922i	$0.160788\pi$
$702$	−23.1704	+	71.3113i	−0.874512	+	2.69147i
$703$	−52.3203	−	38.0129i	−1.97330	−	1.43368i
$704$	−12.7906	−	9.29295i	−0.482066	−	0.350241i
$705$		0			0
$706$	14.4434	−	10.4938i	0.543585	−	0.394938i
$707$	−0.995054			−0.0374228
$708$	−15.5473	+	11.2958i	−0.584305	+	0.424523i
$709$	3.20623	+	9.86777i	0.120413	+	0.370592i	0.993037	−	0.117799i	$-0.0375839\pi$
$709$	3.20623	+	9.86777i	0.120413	+	0.370592i	−0.872625	+	0.488391i	$0.837584\pi$
$710$		0			0
$711$	1.13247	−	3.48537i	0.0424708	−	0.130712i
$712$	0.861548	+	2.65157i	0.0322879	+	0.0993719i
$713$	0.623995	+	1.92046i	0.0233688	+	0.0719218i
$714$	−2.34841	+	7.22767i	−0.0878871	+	0.270489i
$715$		0			0
$716$	−11.5519	−	35.5531i	−0.431715	−	1.32868i
$717$	31.4927	−	22.8808i	1.17612	−	0.854499i
$718$	3.10163			0.115752
$719$	−24.1273	+	17.5295i	−0.899797	+	0.653741i	−0.938414	−	0.345514i	$-0.887705\pi$
$719$	−24.1273	+	17.5295i	−0.899797	+	0.653741i	0.0386171	+	0.999254i	$0.487705\pi$
$720$		0			0
$721$	10.9719	+	7.97152i	0.408614	+	0.296875i
$722$	−35.0365	−	25.4555i	−1.30392	−	0.947355i
$723$	11.7469	−	36.1532i	0.436872	−	1.34455i
$724$	3.81789			0.141891
$725$		0			0
$726$	8.94937			0.332142
$727$	5.47948	−	16.8641i	0.203223	−	0.625455i	−0.796559	−	0.604561i	$-0.793349\pi$
$727$	5.47948	−	16.8641i	0.203223	−	0.625455i	0.999782	−	0.0208944i	$-0.00665137\pi$
$728$	−3.10152	−	2.25339i	−0.114950	−	0.0835161i
$729$	33.0460	+	24.0093i	1.22393	+	0.889234i
$730$		0			0
$731$	−4.94654	+	3.59387i	−0.182954	+	0.132924i
$732$	13.2451			0.489551
$733$	−17.2321	+	12.5199i	−0.636484	+	0.462433i	−0.858640	−	0.512578i	$-0.828690\pi$
$733$	−17.2321	+	12.5199i	−0.636484	+	0.462433i	0.222157	+	0.975011i	$0.428690\pi$
$734$	−18.6584	−	57.4247i	−0.688695	−	2.11959i
$735$		0			0
$736$	−4.56986	+	14.0646i	−0.168447	+	0.518427i
$737$	−7.27590	−	22.3929i	−0.268011	−	0.824854i
$738$	24.6289	+	75.8001i	0.906604	+	2.79024i
$739$	−2.81420	+	8.66123i	−0.103522	+	0.318608i	−0.989381	−	0.145347i	$-0.953570\pi$
$739$	−2.81420	+	8.66123i	−0.103522	+	0.318608i	0.885859	+	0.463955i	$0.153570\pi$
$740$		0			0
$741$	34.5762	+	106.415i	1.27019	+	3.90924i
$742$	13.2001	−	9.59041i	0.484589	−	0.352075i
$743$	−11.4642			−0.420580			−0.210290	−	0.977639i	$-0.567441\pi$
$743$	−11.4642			−0.420580			−0.210290	+	0.977639i	$0.567441\pi$
$744$	−1.50202	+	1.09128i	−0.0550669	+	0.0400084i
$745$		0			0
$746$	−26.1456	−	18.9959i	−0.957258	−	0.695489i
$747$	−27.4419	−	19.9377i	−1.00405	−	0.729482i
$748$	2.17966	−	6.70831i	0.0796963	−	0.245280i
$749$	−0.180414			−0.00659220
$750$		0			0
$751$	36.6511			1.33742			0.668709	−	0.743524i	$-0.266847\pi$
$751$	36.6511			1.33742			0.668709	+	0.743524i	$0.266847\pi$
$752$	−2.54299	+	7.82652i	−0.0927334	+	0.285404i
$753$	59.6232	+	43.3188i	2.17279	+	1.57862i
$754$	−17.1192	−	12.4378i	−0.623444	−	0.452958i
$755$		0			0
$756$	−8.75375	+	6.35997i	−0.318371	+	0.231310i
$757$	−22.2235			−0.807726			−0.403863	−	0.914820i	$-0.632333\pi$
$757$	−22.2235			−0.807726			−0.403863	+	0.914820i	$0.632333\pi$
$758$	15.5532	−	11.3001i	0.564917	−	0.410437i
$759$	5.39609	+	16.6075i	0.195866	+	0.602812i
$760$		0			0
$761$	3.30130	−	10.1604i	0.119672	−	0.368313i	−0.873221	−	0.487325i	$-0.837973\pi$
$761$	3.30130	−	10.1604i	0.119672	−	0.368313i	0.992893	+	0.119012i	$0.0379727\pi$
$762$	−3.63774	−	11.1958i	−0.131781	−	0.405581i
$763$	−2.44560	−	7.52677i	−0.0885366	−	0.272488i
$764$	−6.54407	+	20.1406i	−0.236756	+	0.728660i
$765$		0			0
$766$	6.13659	+	18.8865i	0.221724	+	0.682396i
$767$	19.5760	−	14.2228i	0.706847	−	0.513554i
$768$	−57.2548			−2.06600
$769$	20.7322	−	15.0628i	0.747621	−	0.543179i	−0.147467	−	0.989067i	$-0.547112\pi$
$769$	20.7322	−	15.0628i	0.747621	−	0.543179i	0.895089	+	0.445888i	$0.147112\pi$
$770$		0			0
$771$	−14.3209	−	10.4047i	−0.515754	−	0.374717i
$772$	−31.6577	−	23.0007i	−1.13939	−	0.827813i
$773$	−2.47094	+	7.60477i	−0.0888735	+	0.273525i	−0.985609	−	0.169043i	$-0.945932\pi$
$773$	−2.47094	+	7.60477i	−0.0888735	+	0.273525i	0.896735	+	0.442568i	$0.145932\pi$
$774$	−44.5835			−1.60252
$775$		0			0
$776$	−6.23786			−0.223926
$777$	−8.90225	+	27.3983i	−0.319366	+	0.982909i
$778$	16.1470	+	11.7315i	0.578898	+	0.420594i
$779$	41.3098	+	30.0133i	1.48008	+	1.07534i
$780$		0			0
$781$	−21.4324	+	15.5716i	−0.766913	+	0.557195i
$782$	−5.24938			−0.187718
$783$	9.60277	−	6.97682i	0.343175	−	0.249331i
$784$	−1.40702	−	4.33037i	−0.0502508	−	0.154656i
$785$		0			0
$786$	−22.2624	+	68.5167i	−0.794075	+	2.44391i
$787$	7.08165	+	21.7951i	0.252434	+	0.776911i	0.994324	+	0.106390i	$0.0339293\pi$
$787$	7.08165	+	21.7951i	0.252434	+	0.776911i	−0.741891	+	0.670521i	$0.766071\pi$
$788$	0.791829	+	2.43700i	0.0282077	+	0.0868145i
$789$	−1.28469	+	3.95387i	−0.0457362	+	0.140761i
$790$		0			0
$791$	−1.65798	−	5.10272i	−0.0589508	−	0.181432i
$792$	−8.26969	+	6.00828i	−0.293851	+	0.213495i
$793$	−16.6771			−0.592221
$794$	49.8870	−	36.2450i	1.77042	−	1.28629i
$795$		0			0
$796$	0.720745	+	0.523652i	0.0255461	+	0.0185604i
$797$	26.7854	+	19.4607i	0.948788	+	0.689335i	0.950520	−	0.310664i	$-0.100551\pi$
$797$	26.7854	+	19.4607i	0.948788	+	0.689335i	−0.00173186	+	0.999999i	$0.500551\pi$
$798$	−10.9708	+	33.7645i	−0.388361	+	1.19525i
$799$	−2.49567			−0.0882903
$800$		0			0
$801$	−23.0778			−0.815414
$802$	−6.16844	+	18.9845i	−0.217815	+	0.670366i
$803$	40.6333	+	29.5218i	1.43392	+	1.04180i
$804$	29.8274	+	21.6709i	1.05193	+	0.764272i
$805$		0			0
$806$	−9.51589	+	6.91370i	−0.335183	+	0.243525i
$807$	10.0088			0.352326
$808$	0.511259	−	0.371451i	0.0179860	−	0.0130676i
$809$	−7.74035	−	23.8224i	−0.272136	−	0.837550i	−0.989963	−	0.141328i	$-0.954863\pi$
$809$	−7.74035	−	23.8224i	−0.272136	−	0.837550i	0.717826	−	0.696222i	$-0.245137\pi$
$810$		0			0
$811$	9.18232	−	28.2603i	0.322435	−	0.992352i	−0.650151	−	0.759805i	$-0.725294\pi$
$811$	9.18232	−	28.2603i	0.322435	−	0.992352i	0.972585	−	0.232547i	$-0.0747058\pi$
$812$	−0.943609	−	2.90413i	−0.0331142	−	0.101915i
$813$	−20.6247	−	63.4762i	−0.723339	−	2.22621i
$814$	18.1673	−	55.9131i	0.636762	−	1.95975i
$815$		0			0
$816$	−5.58283	−	17.1822i	−0.195438	−	0.601497i
$817$	−23.1081	+	16.7890i	−0.808449	+	0.587373i
$818$	59.4835			2.07979
$819$	25.6727	−	18.6523i	0.897078	−	0.651765i
$820$		0			0
$821$	8.31326	+	6.03994i	0.290135	+	0.210795i	0.723326	−	0.690507i	$-0.242612\pi$
$821$	8.31326	+	6.03994i	0.290135	+	0.210795i	−0.433191	+	0.901302i	$0.642612\pi$
$822$	37.3903	+	27.1657i	1.30414	+	0.947511i
$823$	3.29329	−	10.1357i	0.114797	−	0.353308i	−0.877108	−	0.480293i	$-0.840530\pi$
$823$	3.29329	−	10.1357i	0.114797	−	0.353308i	0.991905	+	0.126985i	$0.0405302\pi$
$824$	−8.61310			−0.300052
$825$		0			0
$826$	7.67758			0.267137
$827$	3.29939	−	10.1545i	0.114731	−	0.353106i	−0.877160	−	0.480199i	$-0.840565\pi$
$827$	3.29939	−	10.1545i	0.114731	−	0.353106i	0.991891	+	0.127093i	$0.0405645\pi$
$828$	−14.0839	−	10.2325i	−0.489448	−	0.355605i
$829$	−6.62372	−	4.81241i	−0.230051	−	0.167142i	0.466788	−	0.884369i	$-0.345411\pi$
$829$	−6.62372	−	4.81241i	−0.230051	−	0.167142i	−0.696839	+	0.717227i	$0.745411\pi$
$830$		0			0
$831$	−51.5873	+	37.4804i	−1.78954	+	1.30018i
$832$	−31.1713			−1.08067
$833$	1.11712	−	0.811636i	0.0387060	−	0.0281215i
$834$	−39.5723	−	121.791i	−1.37028	−	4.21727i
$835$		0			0
$836$	10.1824	−	31.3383i	0.352167	−	1.08386i
$837$	−2.03886	−	6.27497i	−0.0704734	−	0.216895i
$838$	8.06562	+	24.8234i	0.278622	+	0.857511i
$839$	0.388324	−	1.19514i	0.0134064	−	0.0412607i	−0.944130	−	0.329575i	$-0.893095\pi$
$839$	0.388324	−	1.19514i	0.0134064	−	0.0412607i	0.957536	+	0.288314i	$0.0930947\pi$
$840$		0			0
$841$	−7.92636	−	24.3948i	−0.273323	−	0.841201i
$842$	31.9106	−	23.1844i	1.09971	−	0.798986i
$843$	−49.8926			−1.71839
$844$	−1.47961	+	1.07500i	−0.0509304	+	0.0370031i
$845$		0			0
$846$	−14.7223	−	10.6964i	−0.506162	−	0.367748i
$847$	−1.31553	−	0.955789i	−0.0452022	−	0.0328413i
$848$	−11.9862	+	36.8897i	−0.411607	+	1.26680i
$849$	46.6621			1.60144
$850$		0			0
$851$	−19.8991			−0.682133
$852$	12.8189	−	39.4524i	0.439167	−	1.35162i
$853$	−39.5210	−	28.7137i	−1.35317	−	0.983138i	−0.998847	−	0.0480160i	$-0.984710\pi$
$853$	−39.5210	−	28.7137i	−1.35317	−	0.983138i	−0.354326	−	0.935122i	$-0.615290\pi$
$854$	−4.28092	−	3.11027i	−0.146490	−	0.106431i
$855$		0			0
$856$	0.0926971	−	0.0673483i	0.00316832	−	0.00230192i
$857$	54.3699			1.85724			0.928620	−	0.371033i	$-0.120996\pi$
$857$	54.3699			1.85724			0.928620	+	0.371033i	$0.120996\pi$
$858$	−82.2900	+	59.7872i	−2.80934	+	2.04110i
$859$	−5.30256	−	16.3196i	−0.180921	−	0.556818i	0.818933	−	0.573889i	$-0.194566\pi$
$859$	−5.30256	−	16.3196i	−0.180921	−	0.556818i	−0.999854	+	0.0170711i	$0.994566\pi$
$860$		0			0
$861$	7.02882	−	21.6325i	0.239541	−	0.737233i
$862$	−0.823286	−	2.53381i	−0.0280412	−	0.0863020i
$863$	−1.05329	−	3.24169i	−0.0358544	−	0.110348i	0.931528	−	0.363671i	$-0.118477\pi$
$863$	−1.05329	−	3.24169i	−0.0358544	−	0.110348i	−0.967382	+	0.253322i	$0.918477\pi$
$864$	14.9317	−	45.9551i	0.507987	−	1.56342i
$865$		0			0
$866$	−4.18185	−	12.8704i	−0.142105	−	0.437355i
$867$	−35.0874	+	25.4925i	−1.19163	+	0.865771i
$868$	−1.69737			−0.0576124
$869$	1.72674	−	1.25455i	0.0585756	−	0.0425576i
$870$		0			0
$871$	−37.5562	−	27.2862i	−1.27254	−	0.924557i
$872$	4.06628	+	2.95432i	0.137702	+	0.100046i
$873$	15.9557	−	49.1065i	0.540018	−	1.66200i
$874$	−24.5228			−0.829497
$875$		0			0
$876$	−78.6461			−2.65721
$877$	−2.05073	+	6.31149i	−0.0692481	+	0.213124i	−0.979692	−	0.200509i	$-0.935740\pi$
$877$	−2.05073	+	6.31149i	−0.0692481	+	0.213124i	0.910444	+	0.413633i	$0.135740\pi$
$878$	−28.7349	−	20.8771i	−0.969757	−	0.704569i
$879$	−35.4827	−	25.7797i	−1.19680	−	0.869527i
$880$		0			0
$881$	−12.9336	+	9.39681i	−0.435744	+	0.316586i	−0.783942	−	0.620835i	$-0.786794\pi$
$881$	−12.9336	+	9.39681i	−0.435744	+	0.316586i	0.348198	+	0.937421i	$0.386794\pi$
$882$	10.0687			0.339031
$883$	31.7427	−	23.0624i	1.06823	−	0.776113i	0.0926347	−	0.995700i	$-0.470471\pi$
$883$	31.7427	−	23.0624i	1.06823	−	0.776113i	0.975593	+	0.219587i	$0.0704711\pi$
$884$	−4.29743	−	13.2261i	−0.144538	−	0.444843i
$885$		0			0
$886$	17.6067	−	54.1878i	0.591509	−	1.82048i
$887$	4.43760	+	13.6575i	0.149000	+	0.458575i	0.997504	−	0.0706148i	$-0.0224961\pi$
$887$	4.43760	+	13.6575i	0.149000	+	0.458575i	−0.848504	+	0.529189i	$0.822496\pi$
$888$	−5.65375	−	17.4005i	−0.189727	−	0.583921i
$889$	−0.660970	+	2.03426i	−0.0221682	+	0.0682268i
$890$		0			0
$891$	−2.71034	−	8.34156i	−0.0907998	−	0.279453i
$892$	10.8777	−	7.90308i	0.364211	−	0.264615i
$893$	−11.6587			−0.390142
$894$	−65.2214	+	47.3861i	−2.18133	+	1.58483i
$895$		0			0
$896$	4.05391	+	2.94534i	0.135432	+	0.0983969i
$897$	27.8531	+	20.2365i	0.929989	+	0.675676i
$898$	−10.2338	+	31.4965i	−0.341507	+	1.05105i
$899$	1.86200			0.0621010
$900$		0			0
$901$	−11.7631			−0.391886
$902$	−14.3441	+	44.1465i	−0.477605	+	1.46992i
$903$	10.2936	+	7.47876i	0.342551	+	0.248878i
$904$	2.75671	+	2.00286i	0.0916867	+	0.0666143i
$905$		0			0
$906$	21.4686	−	15.5979i	0.713248	−	0.518205i
$907$	−3.73711			−0.124089			−0.0620443	−	0.998073i	$-0.519762\pi$
$907$	−3.73711			−0.124089			−0.0620443	+	0.998073i	$0.519762\pi$
$908$	−1.22194	+	0.887793i	−0.0405516	+	0.0294624i
$909$	1.61645	+	4.97493i	0.0536144	+	0.165008i
$910$		0			0
$911$	6.83592	−	21.0388i	0.226484	−	0.697047i	−0.771653	−	0.636043i	$-0.780570\pi$
$911$	6.83592	−	21.0388i	0.226484	−	0.697047i	0.998138	−	0.0610034i	$-0.0194301\pi$
$912$	−26.0805	−	80.2676i	−0.863613	−	2.65793i
$913$	−6.10471	−	18.7884i	−0.202036	−	0.621804i
$914$	12.0775	−	37.1708i	0.399489	−	1.22950i
$915$		0			0
$916$	−3.89325	−	11.9822i	−0.128637	−	0.395903i
$917$	10.5901	−	7.69414i	0.349715	−	0.254083i
$918$	17.1520			0.566100
$919$	24.4618	−	17.7726i	0.806921	−	0.586262i	−0.106015	−	0.994364i	$-0.533809\pi$
$919$	24.4618	−	17.7726i	0.806921	−	0.586262i	0.912936	+	0.408102i	$0.133809\pi$
$920$		0			0
$921$	1.69549	+	1.23185i	0.0558684	+	0.0405908i
$922$	11.3100	+	8.21719i	0.372475	+	0.270619i
$923$	−16.1405	+	49.6752i	−0.531270	+	1.63508i
$924$	−14.6782			−0.482879
$925$		0			0
$926$	−21.2207			−0.697356
$927$	22.0313	−	67.8052i	0.723601	−	2.22702i
$928$	11.0321	+	8.01529i	0.362146	+	0.263115i
$929$	9.97863	+	7.24990i	0.327388	+	0.237861i	0.739322	−	0.673353i	$-0.235146\pi$
$929$	9.97863	+	7.24990i	0.327388	+	0.237861i	−0.411933	+	0.911214i	$0.635146\pi$
$930$		0			0
$931$	5.21871	−	3.79161i	0.171036	−	0.124265i
$932$	19.4474			0.637021
$933$	−27.5551	+	20.0200i	−0.902114	+	0.655424i
$934$	−21.5506	−	66.3260i	−0.705158	−	2.17025i
$935$		0			0
$936$	−6.22778	+	19.1672i	−0.203562	+	0.626498i
$937$	5.99415	+	18.4481i	0.195820	+	0.602673i	0.999966	+	0.00824088i	$0.00262318\pi$
$937$	5.99415	+	18.4481i	0.195820	+	0.602673i	−0.804146	+	0.594432i	$0.797377\pi$
$938$	−4.55161	−	14.0084i	−0.148615	−	0.457391i
$939$	−18.4062	+	56.6484i	−0.600663	+	1.84865i
$940$		0			0
$941$	10.3659	+	31.9030i	0.337919	+	1.04001i	0.965266	+	0.261268i	$0.0841407\pi$
$941$	10.3659	+	31.9030i	0.337919	+	1.04001i	−0.627347	+	0.778740i	$0.715859\pi$
$942$	−12.4368	+	9.03585i	−0.405212	+	0.294404i
$943$	15.7114			0.511635
$944$	−14.7660	+	10.7281i	−0.480591	+	0.349170i
$945$		0			0
$946$	−21.0067	−	15.2623i	−0.682987	−	0.496219i
$947$	38.4416	+	27.9294i	1.24918	+	0.907584i	0.998174	−	0.0604004i	$-0.0192377\pi$
$947$	38.4416	+	27.9294i	1.24918	+	0.907584i	0.251009	+	0.967985i	$0.419238\pi$
$948$	−1.03277	+	3.17854i	−0.0335428	+	0.103234i
$949$	99.0248			3.21448
$950$		0			0
$951$	−78.2227			−2.53654
$952$	−0.270996	+	0.834038i	−0.00878302	+	0.0270313i
$953$	32.4747	+	23.5943i	1.05196	+	0.764293i	0.972584	−	0.232552i	$-0.0747075\pi$
$953$	32.4747	+	23.5943i	1.05196	+	0.764293i	0.0793752	+	0.996845i	$0.474707\pi$
$954$	−69.3921	−	50.4163i	−2.24665	−	1.63229i
$955$		0			0
$956$	−18.2854	+	13.2851i	−0.591391	+	0.429671i
$957$	16.1019			0.520500
$958$	−17.6626	+	12.8326i	−0.570653	+	0.414604i
$959$	−2.59499	−	7.98654i	−0.0837964	−	0.257899i
$960$		0			0
$961$	−9.25969	+	28.4984i	−0.298700	+	0.919303i
$962$	−35.8186	−	110.238i	−1.15484	−	3.55423i
$963$	0.293081	+	0.902011i	0.00944441	+	0.0290669i
$964$	−6.82051	+	20.9914i	−0.219674	+	0.676086i
$965$		0			0
$966$	3.37565	+	10.3892i	0.108610	+	0.334267i
$967$	−23.7914	+	17.2854i	−0.765078	+	0.555862i	−0.900464	−	0.434931i	$-0.856773\pi$
$967$	−23.7914	+	17.2854i	−0.765078	+	0.555862i	0.135385	+	0.990793i	$0.456773\pi$
$968$	1.03271			0.0331927
$969$	20.7069	−	15.0445i	0.665202	−	0.483298i
$970$		0			0
$971$	30.3483	+	22.0493i	0.973922	+	0.707596i	0.956342	−	0.292249i	$-0.0944038\pi$
$971$	30.3483	+	22.0493i	0.973922	+	0.707596i	0.0175802	+	0.999845i	$0.494404\pi$
$972$	−15.1503	−	11.0073i	−0.485945	−	0.353060i
$973$	−7.19021	+	22.1292i	−0.230508	+	0.709430i
$974$	−61.0359			−1.95572
$975$		0			0
$976$	12.5794			0.402656
$977$	4.11853	−	12.6755i	0.131764	−	0.405527i	−0.863309	−	0.504676i	$-0.831612\pi$
$977$	4.11853	−	12.6755i	0.131764	−	0.405527i	0.995073	+	0.0991491i	$0.0316121\pi$
$978$	−2.47063	−	1.79502i	−0.0790022	−	0.0573984i
$979$	−10.8737	−	7.90023i	−0.347526	−	0.252492i
$980$		0			0
$981$	−33.6585	+	24.4543i	−1.07463	+	0.780766i
$982$	−4.63579			−0.147934
$983$	12.0737	−	8.77208i	0.385092	−	0.279786i	−0.378349	−	0.925663i	$-0.623508\pi$
$983$	12.0737	−	8.77208i	0.385092	−	0.279786i	0.763441	+	0.645877i	$0.223508\pi$
$984$	4.46395	+	13.7386i	0.142305	+	0.437971i
$985$		0			0
$986$	−1.49579	+	4.60357i	−0.0476356	+	0.146607i
$987$	1.60486	+	4.93924i	0.0510831	+	0.157218i
$988$	−20.0757	−	61.7867i	−0.638694	−	1.96570i
$989$	−2.71587	+	8.35860i	−0.0863597	+	0.265788i
$990$		0			0
$991$	5.95058	+	18.3140i	0.189027	+	0.581764i	0.999994	−	0.00332680i	$-0.00105896\pi$
$991$	5.95058	+	18.3140i	0.189027	+	0.581764i	−0.810968	+	0.585091i	$0.801059\pi$
$992$	6.13231	−	4.45539i	0.194701	−	0.141459i
$993$	52.3840			1.66236
$994$	−13.4076	+	9.74117i	−0.425262	+	0.308971i
$995$		0			0
$996$	25.0261	+	18.1825i	0.792982	+	0.576135i
$997$	24.5837	+	17.8611i	0.778573	+	0.565667i	0.904550	−	0.426367i	$-0.140207\pi$
$997$	24.5837	+	17.8611i	0.778573	+	0.565667i	−0.125977	+	0.992033i	$0.540207\pi$
$998$	10.7927	−	33.2166i	0.341638	−	1.05145i
$999$	65.0190			2.05711

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.h.d.351.11		56
5.2	odd	4		875.2.n.c.274.12		56
5.3	odd	4		175.2.n.a.29.3	✓	56
5.4	even	2		875.2.h.e.351.4		56
25.6	even	5	inner	875.2.h.d.526.11		56
25.8	odd	20		875.2.n.c.99.12		56
25.9	even	10		4375.2.a.o.1.7		28
25.16	even	5		4375.2.a.p.1.22		28
25.17	odd	20		175.2.n.a.169.3	yes	56
25.19	even	10		875.2.h.e.526.4		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.n.a.29.3	✓	56	5.3	odd	4
175.2.n.a.169.3	yes	56	25.17	odd	20
875.2.h.d.351.11		56	1.1	even	1	trivial
875.2.h.d.526.11		56	25.6	even	5	inner
875.2.h.e.351.4		56	5.4	even	2
875.2.h.e.526.4		56	25.19	even	10
875.2.n.c.99.12		56	25.8	odd	20
875.2.n.c.274.12		56	5.2	odd	4
4375.2.a.o.1.7		28	25.9	even	10
4375.2.a.p.1.22		28	25.16	even	5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.h (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.591863 - 1.82157i) q^{2} +(2.32470 + 1.68900i) q^{3} +(-1.34977 - 0.980668i) q^{4} +(4.45253 - 3.23495i) q^{6} -1.00000 q^{7} +(0.513801 - 0.373298i) q^{8} +(1.62449 + 4.99966i) q^{9} +O(q^{10})\)	\(q+(0.591863 - 1.82157i) q^{2} +(2.32470 + 1.68900i) q^{3} +(-1.34977 - 0.980668i) q^{4} +(4.45253 - 3.23495i) q^{6} -1.00000 q^{7} +(0.513801 - 0.373298i) q^{8} +(1.62449 + 4.99966i) q^{9} +(-0.946113 + 2.91184i) q^{11} +(-1.48148 - 4.55953i) q^{12} +(1.86536 + 5.74099i) q^{13} +(-0.591863 + 1.82157i) q^{14} +(-1.40702 - 4.33037i) q^{16} +(1.11712 - 0.811636i) q^{17} +10.0687 q^{18} +(5.21871 - 3.79161i) q^{19} +(-2.32470 - 1.68900i) q^{21} +(4.74414 + 3.44682i) q^{22} +(0.613350 - 1.88770i) q^{23} +1.82493 q^{24} +11.5616 q^{26} +(-2.00408 + 6.16793i) q^{27} +(1.34977 + 0.980668i) q^{28} +(-1.48069 - 1.07578i) q^{29} +(-0.823057 + 0.597986i) q^{31} -7.45065 q^{32} +(-7.11751 + 5.17117i) q^{33} +(-0.817268 - 2.51529i) q^{34} +(2.71032 - 8.34150i) q^{36} +(-3.09806 - 9.53485i) q^{37} +(-3.81792 - 11.7503i) q^{38} +(-5.36009 + 16.4967i) q^{39} +(2.44609 + 7.52829i) q^{41} +(-4.45253 + 3.23495i) q^{42} -4.42793 q^{43} +(4.13258 - 3.00250i) q^{44} +(-3.07555 - 2.23452i) q^{46} +(-1.46218 - 1.06234i) q^{47} +(4.04307 - 12.4433i) q^{48} +1.00000 q^{49} +3.96783 q^{51} +(3.11219 - 9.57833i) q^{52} +(-6.89187 - 5.00723i) q^{53} +(10.0492 + 7.30114i) q^{54} +(-0.513801 + 0.373298i) q^{56} +18.5360 q^{57} +(-2.83598 + 2.06046i) q^{58} +(-1.23870 - 3.81234i) q^{59} +(-0.853734 + 2.62752i) q^{61} +(0.602135 + 1.85318i) q^{62} +(-1.62449 - 4.99966i) q^{63} +(-1.59572 + 4.91112i) q^{64} +(5.20705 + 16.0257i) q^{66} +(-6.22159 + 4.52025i) q^{67} -2.30381 q^{68} +(4.61417 - 3.35239i) q^{69} +(7.00021 + 5.08595i) q^{71} +(2.70103 + 1.96241i) q^{72} +(5.06928 - 15.6016i) q^{73} -19.2020 q^{74} -10.7624 q^{76} +(0.946113 - 2.91184i) q^{77} +(26.8774 + 19.5276i) q^{78} +(-0.563983 - 0.409757i) q^{79} +(-2.31760 + 1.68383i) q^{81} +15.1610 q^{82} +(-5.22011 + 3.79263i) q^{83} +(1.48148 + 4.55953i) q^{84} +(-2.62073 + 8.06578i) q^{86} +(-1.62517 - 5.00176i) q^{87} +(0.600869 + 1.84928i) q^{88} +(-1.35657 + 4.17510i) q^{89} +(-1.86536 - 5.74099i) q^{91} +(-2.67909 + 1.94647i) q^{92} -2.92336 q^{93} +(-2.80053 + 2.03470i) q^{94} +(-17.3206 - 12.5841i) q^{96} +(-7.94614 - 5.77321i) q^{97} +(0.591863 - 1.82157i) q^{98} -16.0951 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 4 q^{2} - 4 q^{3} - 12 q^{4} - 56 q^{7} - 12 q^{8} - 6 q^{9}+O(q^{10}) \) 56 * q - 4 * q^2 - 4 * q^3 - 12 * q^4 - 56 * q^7 - 12 * q^8 - 6 * q^9	\( 56 q - 4 q^{2} - 4 q^{3} - 12 q^{4} - 56 q^{7} - 12 q^{8} - 6 q^{9} + 8 q^{11} - 12 q^{12} - 8 q^{13} + 4 q^{14} - 32 q^{16} - 20 q^{17} + 48 q^{18} - 12 q^{19} + 4 q^{21} - 8 q^{22} - 16 q^{23} + 28 q^{24} + 12 q^{26} - 16 q^{27} + 12 q^{28} + 2 q^{29} + 12 q^{31} + 112 q^{32} - 14 q^{33} - 14 q^{36} - 16 q^{37} - 20 q^{38} + 4 q^{39} + 4 q^{41} + 32 q^{43} - 22 q^{44} - 4 q^{46} - 18 q^{47} - 48 q^{48} + 56 q^{49} - 44 q^{51} + 16 q^{52} - 20 q^{53} - 54 q^{54} + 12 q^{56} + 152 q^{57} + 32 q^{58} + 6 q^{59} - 4 q^{61} + 18 q^{62} + 6 q^{63} - 24 q^{64} - 74 q^{66} - 32 q^{67} + 124 q^{68} + 78 q^{69} - 8 q^{71} - 100 q^{72} - 48 q^{73} - 60 q^{74} + 52 q^{76} - 8 q^{77} + 124 q^{78} - 72 q^{81} + 44 q^{82} + 10 q^{83} + 12 q^{84} - 20 q^{86} + 26 q^{87} - 88 q^{88} - 38 q^{89} + 8 q^{91} - 96 q^{92} + 96 q^{93} - 88 q^{94} - 28 q^{96} - 90 q^{97} - 4 q^{98} - 60 q^{99}+O(q^{100}) \) 56 * q - 4 * q^2 - 4 * q^3 - 12 * q^4 - 56 * q^7 - 12 * q^8 - 6 * q^9 + 8 * q^11 - 12 * q^12 - 8 * q^13 + 4 * q^14 - 32 * q^16 - 20 * q^17 + 48 * q^18 - 12 * q^19 + 4 * q^21 - 8 * q^22 - 16 * q^23 + 28 * q^24 + 12 * q^26 - 16 * q^27 + 12 * q^28 + 2 * q^29 + 12 * q^31 + 112 * q^32 - 14 * q^33 - 14 * q^36 - 16 * q^37 - 20 * q^38 + 4 * q^39 + 4 * q^41 + 32 * q^43 - 22 * q^44 - 4 * q^46 - 18 * q^47 - 48 * q^48 + 56 * q^49 - 44 * q^51 + 16 * q^52 - 20 * q^53 - 54 * q^54 + 12 * q^56 + 152 * q^57 + 32 * q^58 + 6 * q^59 - 4 * q^61 + 18 * q^62 + 6 * q^63 - 24 * q^64 - 74 * q^66 - 32 * q^67 + 124 * q^68 + 78 * q^69 - 8 * q^71 - 100 * q^72 - 48 * q^73 - 60 * q^74 + 52 * q^76 - 8 * q^77 + 124 * q^78 - 72 * q^81 + 44 * q^82 + 10 * q^83 + 12 * q^84 - 20 * q^86 + 26 * q^87 - 88 * q^88 - 38 * q^89 + 8 * q^91 - 96 * q^92 + 96 * q^93 - 88 * q^94 - 28 * q^96 - 90 * q^97 - 4 * q^98 - 60 * q^99

Introduction

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