LMFDB - Embedded newform 775.2.bl.b.351.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [775,2,Mod(51,775)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(775, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([0, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("775.51"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.bl (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,-2,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$6.18840615665$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 155)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			351.1
Character	$\chi$	$=$	775.351
Dual form			775.2.bl.b.276.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.03762 - 1.48042i) q^{2} +(0.203052 + 1.93191i) q^{3} +(1.34222 + 4.13093i) q^{4} +(2.44628 - 4.23709i) q^{6} +(-0.816826 - 0.173622i) q^{7} +(1.82396 - 5.61358i) q^{8} +(-0.756592 + 0.160819i) q^{9} +(-3.03538 + 3.37113i) q^{11} +(-7.70804 + 3.43184i) q^{12} +(5.75194 + 2.56093i) q^{13} +(1.40735 + 1.56302i) q^{14} +(-4.99902 + 3.63200i) q^{16} +(-0.865839 - 0.961611i) q^{17} +(1.77972 + 0.792384i) q^{18} +(0.526383 - 0.234361i) q^{19} +(0.169563 - 1.61329i) q^{21} +(11.1756 - 2.37545i) q^{22} +(-0.729749 + 2.24594i) q^{23} +(11.2153 + 2.38388i) q^{24} +(-7.92902 - 13.7335i) q^{26} +(1.33653 + 4.11341i) q^{27} +(-0.379142 - 3.60729i) q^{28} +(-0.640127 - 0.465079i) q^{29} +(4.56993 - 3.18053i) q^{31} +3.75801 q^{32} +(-7.12905 - 5.17955i) q^{33} +(0.340664 + 3.24120i) q^{34} +(-1.67985 - 2.90958i) q^{36} +(5.64427 - 9.77616i) q^{37} +(-1.41952 - 0.301728i) q^{38} +(-3.77954 + 11.6322i) q^{39} +(-1.17622 + 11.1910i) q^{41} +(-2.73384 + 3.03624i) q^{42} +(-10.2075 + 4.54466i) q^{43} +(-18.0001 - 8.01414i) q^{44} +(4.81187 - 3.49603i) q^{46} +(-6.73909 + 4.89623i) q^{47} +(-8.03174 - 8.92015i) q^{48} +(-5.75776 - 2.56352i) q^{49} +(1.68193 - 1.86798i) q^{51} +(-2.85865 + 27.1982i) q^{52} +(-5.22161 + 1.10989i) q^{53} +(3.36622 - 10.3602i) q^{54} +(-2.46450 + 4.26864i) q^{56} +(0.559646 + 0.969336i) q^{57} +(0.615823 + 1.89531i) q^{58} +(0.557834 + 5.30744i) q^{59} -4.18717 q^{61} +(-14.0203 - 0.284685i) q^{62} +0.645926 q^{63} +(2.34063 + 1.70057i) q^{64} +(6.85838 + 21.1079i) q^{66} +(3.52238 + 6.10094i) q^{67} +(2.81020 - 4.86742i) q^{68} +(-4.48712 - 0.953766i) q^{69} +(2.94921 - 0.626874i) q^{71} +(-0.477228 + 4.54052i) q^{72} +(-6.92763 + 7.69391i) q^{73} +(-25.9736 + 11.5642i) q^{74} +(1.67465 + 1.85989i) q^{76} +(3.06468 - 2.22662i) q^{77} +(24.9218 - 18.1067i) q^{78} +(0.856267 + 0.950981i) q^{79} +(-9.79521 + 4.36111i) q^{81} +(18.9640 - 21.0616i) q^{82} +(1.37104 - 13.0446i) q^{83} +(6.89197 - 1.46493i) q^{84} +(27.5269 + 5.85103i) q^{86} +(0.768511 - 1.33110i) q^{87} +(13.3877 + 23.1882i) q^{88} +(1.14268 + 3.51681i) q^{89} +(-4.25370 - 3.09050i) q^{91} -10.2573 q^{92} +(7.07242 + 8.18286i) q^{93} +20.9802 q^{94} +(0.763071 + 7.26013i) q^{96} +(1.67517 + 5.15563i) q^{97} +(7.93704 + 13.7473i) q^{98} +(1.75440 - 3.03871i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 2 q^{2} - 3 q^{3} - 2 q^{4} - 12 q^{6} + 2 q^{7} + 31 q^{8} + 6 q^{9} + 16 q^{11} + q^{12} - 2 q^{13} - 10 q^{14} - 16 q^{16} - 4 q^{17} - 37 q^{18} - 9 q^{19} - 24 q^{21} + 2 q^{22} + 4 q^{23}+ \cdots + 17 q^{99}+O(q^{100}) $ 40 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 - 12 * q^6 + 2 * q^7 + 31 * q^8 + 6 * q^9 + 16 * q^11 + q^12 - 2 * q^13 - 10 * q^14 - 16 * q^16 - 4 * q^17 - 37 * q^18 - 9 * q^19 - 24 * q^21 + 2 * q^22 + 4 * q^23 + 110 * q^24 - 4 * q^26 + 9 * q^27 - 38 * q^28 - 22 * q^29 - 6 * q^31 + 60 * q^32 - 9 * q^33 - 16 * q^34 - q^36 + 38 * q^37 + 32 * q^38 - 55 * q^39 - 24 * q^41 + 68 * q^42 - 26 * q^43 - 52 * q^44 - 50 * q^46 - 4 * q^47 - 105 * q^48 + 93 * q^49 - 42 * q^51 - 15 * q^52 - 13 * q^53 + 102 * q^54 + 5 * q^56 + 36 * q^57 + 37 * q^58 + 31 * q^59 + 68 * q^61 - 47 * q^62 + 10 * q^63 - 23 * q^64 + 2 * q^67 + 28 * q^68 - 48 * q^69 - 30 * q^71 - 39 * q^72 - 25 * q^73 + 50 * q^74 + 14 * q^76 + 64 * q^77 + 22 * q^78 + 49 * q^79 + 25 * q^81 + 66 * q^82 + 18 * q^83 - 18 * q^84 + 163 * q^86 + 36 * q^87 + 124 * q^88 + 4 * q^89 - 37 * q^91 - 110 * q^92 - 7 * q^93 - 94 * q^94 + 22 * q^96 - 46 * q^97 + 13 * q^98 + 17 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/775\mathbb{Z}\right)^\times$.

$n$	$251$	$652$
$\chi(n)$	$e\left(\frac{7}{15}\right)$	$1$

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 $

$2$	−2.03762	−	1.48042i	−1.44081	−	1.04681i	−0.987872	−	0.155272i	$-0.950375\pi$
$2$	−2.03762	−	1.48042i	−1.44081	−	1.04681i	−0.452942	−	0.891540i	$-0.649625\pi$
$3$	0.203052	+	1.93191i	0.117232	+	1.11539i	0.882055	+	0.471147i	$0.156160\pi$
$3$	0.203052	+	1.93191i	0.117232	+	1.11539i	−0.764823	+	0.644240i	$0.777174\pi$
$4$	1.34222	+	4.13093i	0.671111	+	2.06547i
$5$		0			0
$5$		0			0
$6$	2.44628	−	4.23709i	0.998692	−	1.72978i
$7$	−0.816826	−	0.173622i	−0.308731	−	0.0656229i	0.0509406	−	0.998702i	$-0.483778\pi$
$7$	−0.816826	−	0.173622i	−0.308731	−	0.0656229i	−0.359672	+	0.933079i	$0.617111\pi$
$8$	1.82396	−	5.61358i	0.644868	−	1.98470i
$9$	−0.756592	+	0.160819i	−0.252197	+	0.0536062i
$10$		0			0
$11$	−3.03538	+	3.37113i	−0.915201	+	1.01643i	0.0845988	+	0.996415i	$0.473039\pi$
$11$	−3.03538	+	3.37113i	−0.915201	+	1.01643i	−0.999800	+	0.0200184i	$0.993628\pi$
$12$	−7.70804	+	3.43184i	−2.22512	+	0.990687i
$13$	5.75194	+	2.56093i	1.59530	+	0.710274i	0.995924	−	0.0901931i	$-0.0287484\pi$
$13$	5.75194	+	2.56093i	1.59530	+	0.710274i	0.599377	+	0.800467i	$0.295415\pi$
$14$	1.40735	+	1.56302i	0.376129	+	0.417734i
$15$		0			0
$16$	−4.99902	+	3.63200i	−1.24975	+	0.907999i
$17$	−0.865839	−	0.961611i	−0.209997	−	0.233225i	0.628940	−	0.777454i	$-0.283489\pi$
$17$	−0.865839	−	0.961611i	−0.209997	−	0.233225i	−0.838937	+	0.544229i	$0.816822\pi$
$18$	1.77972	+	0.792384i	0.419485	+	0.186767i
$19$	0.526383	−	0.234361i	0.120761	−	0.0537661i	−0.345467	−	0.938431i	$-0.612279\pi$
$19$	0.526383	−	0.234361i	0.120761	−	0.0537661i	0.466228	+	0.884665i	$0.345613\pi$
$20$		0			0
$21$	0.169563	−	1.61329i	0.0370017	−	0.352048i
$22$	11.1756	−	2.37545i	2.38265	−	0.506448i
$23$	−0.729749	+	2.24594i	−0.152163	+	0.468310i	−0.997862	−	0.0653498i	$-0.979184\pi$
$23$	−0.729749	+	2.24594i	−0.152163	+	0.468310i	0.845699	+	0.533660i	$0.179184\pi$
$24$	11.2153	+	2.38388i	2.28931	+	0.486608i
$25$		0			0
$26$	−7.92902	−	13.7335i	−1.55501	−	2.69335i
$27$	1.33653	+	4.11341i	0.257215	+	0.791626i
$28$	−0.379142	−	3.60729i	−0.0716511	−	0.681714i
$29$	−0.640127	−	0.465079i	−0.118869	−	0.0863630i	0.526763	−	0.850012i	$-0.323406\pi$
$29$	−0.640127	−	0.465079i	−0.118869	−	0.0863630i	−0.645631	+	0.763649i	$0.723406\pi$
$30$		0			0
$31$	4.56993	−	3.18053i	0.820783	−	0.571240i
$31$	4.56993	−	3.18053i	0.820783	−	0.571240i
$32$	3.75801			0.664329
$33$	−7.12905	−	5.17955i	−1.24101	−	0.901645i
$34$	0.340664	+	3.24120i	0.0584233	+	0.555861i
$35$		0			0
$36$	−1.67985	−	2.90958i	−0.279974	−	0.484930i
$37$	5.64427	−	9.77616i	0.927912	−	1.60719i	0.141102	−	0.989995i	$-0.454935\pi$
$37$	5.64427	−	9.77616i	0.927912	−	1.60719i	0.786810	−	0.617196i	$-0.211731\pi$
$38$	−1.41952	−	0.301728i	−0.230276	−	0.0489468i
$39$	−3.77954	+	11.6322i	−0.605210	+	1.86265i
$40$		0			0
$41$	−1.17622	+	11.1910i	−0.183695	+	1.74774i	0.382944	+	0.923771i	$0.374910\pi$
$41$	−1.17622	+	11.1910i	−0.183695	+	1.74774i	−0.566639	+	0.823966i	$0.691757\pi$
$42$	−2.73384	+	3.03624i	−0.421841	+	0.468502i
$43$	−10.2075	+	4.54466i	−1.55663	+	0.693054i	−0.991277	−	0.131797i	$-0.957925\pi$
$43$	−10.2075	+	4.54466i	−1.55663	+	0.693054i	−0.565349	+	0.824852i	$0.691259\pi$
$44$	−18.0001	−	8.01414i	−2.71361	−	1.20818i
$45$		0			0
$46$	4.81187	−	3.49603i	0.709471	−	0.515461i
$47$	−6.73909	+	4.89623i	−0.982997	+	0.714189i	−0.958376	−	0.285508i	$-0.907838\pi$
$47$	−6.73909	+	4.89623i	−0.982997	+	0.714189i	−0.0246207	+	0.999697i	$0.507838\pi$
$48$	−8.03174	−	8.92015i	−1.15928	−	1.28751i
$49$	−5.75776	−	2.56352i	−0.822537	−	0.366217i
$50$		0			0
$51$	1.68193	−	1.86798i	0.235518	−	0.261569i
$52$	−2.85865	+	27.1982i	−0.396423	+	3.77171i
$53$	−5.22161	+	1.10989i	−0.717244	+	0.152455i	−0.552056	−	0.833807i	$-0.686156\pi$
$53$	−5.22161	+	1.10989i	−0.717244	+	0.152455i	−0.165188	+	0.986262i	$0.552823\pi$
$54$	3.36622	−	10.3602i	0.458085	−	1.40984i
$55$		0			0
$56$	−2.46450	+	4.26864i	−0.329333	+	0.570421i
$57$	0.559646	+	0.969336i	0.0741270	+	0.128392i
$58$	0.615823	+	1.89531i	0.0808615	+	0.248866i
$59$	0.557834	+	5.30744i	0.0726238	+	0.690969i	0.968897	+	0.247466i	$0.0795979\pi$
$59$	0.557834	+	5.30744i	0.0726238	+	0.690969i	−0.896273	+	0.443503i	$0.853735\pi$
$60$		0			0
$61$	−4.18717			−0.536112			−0.268056	−	0.963403i	$-0.586381\pi$
$61$	−4.18717			−0.536112			−0.268056	+	0.963403i	$0.586381\pi$
$62$	−14.0203	−	0.284685i	−1.78058	−	0.0361551i
$63$	0.645926			0.0813790
$64$	2.34063	+	1.70057i	0.292579	+	0.212571i
$65$		0			0
$66$	6.85838	+	21.1079i	0.844208	+	2.59820i
$67$	3.52238	+	6.10094i	0.430327	+	0.745348i	0.996901	−	0.0786623i	$-0.0250649\pi$
$67$	3.52238	+	6.10094i	0.430327	+	0.745348i	−0.566574	+	0.824011i	$0.691732\pi$
$68$	2.81020	−	4.86742i	0.340787	−	0.590261i
$69$	−4.48712	−	0.953766i	−0.540185	−	0.114820i
$70$		0			0
$71$	2.94921	−	0.626874i	0.350007	−	0.0743962i	−0.0295537	−	0.999563i	$-0.509409\pi$
$71$	2.94921	−	0.626874i	0.350007	−	0.0743962i	0.379560	+	0.925167i	$0.376075\pi$
$72$	−0.477228	+	4.54052i	−0.0562418	+	0.535105i
$73$	−6.92763	+	7.69391i	−0.810818	+	0.900504i	−0.996626	−	0.0820820i	$-0.973843\pi$
$73$	−6.92763	+	7.69391i	−0.810818	+	0.900504i	0.185808	+	0.982586i	$0.440510\pi$
$74$	−25.9736	+	11.5642i	−3.01938	+	1.34431i
$75$		0			0
$76$	1.67465	+	1.85989i	0.192096	+	0.213344i
$77$	3.06468	−	2.22662i	0.349252	−	0.253747i
$78$	24.9218	−	18.1067i	2.82183	−	2.05018i
$79$	0.856267	+	0.950981i	0.0963375	+	0.106994i	0.789386	−	0.613898i	$-0.210399\pi$
$79$	0.856267	+	0.950981i	0.0963375	+	0.106994i	−0.693048	+	0.720891i	$0.743733\pi$
$80$		0			0
$81$	−9.79521	+	4.36111i	−1.08836	+	0.484568i
$82$	18.9640	−	21.0616i	2.09422	−	2.32587i
$83$	1.37104	−	13.0446i	0.150492	−	1.43183i	−0.615071	−	0.788472i	$-0.710873\pi$
$83$	1.37104	−	13.0446i	0.150492	−	1.43183i	0.765563	−	0.643361i	$-0.222461\pi$
$84$	6.89197	−	1.46493i	0.751976	−	0.159837i
$85$		0			0
$86$	27.5269	+	5.85103i	2.96831	+	0.630933i
$87$	0.768511	−	1.33110i	0.0823930	−	0.142709i
$88$	13.3877	+	23.1882i	1.42713	+	2.47187i
$89$	1.14268	+	3.51681i	0.121124	+	0.372782i	0.993175	−	0.116634i	$-0.0372103\pi$
$89$	1.14268	+	3.51681i	0.121124	+	0.372782i	−0.872051	+	0.489415i	$0.837210\pi$
$90$		0			0
$91$	−4.25370	−	3.09050i	−0.445909	−	0.323972i
$92$	−10.2573			−1.06940
$93$	7.07242	+	8.18286i	0.733376	+	0.848523i
$94$	20.9802			2.16394
$95$		0			0
$96$	0.763071	+	7.26013i	0.0778806	+	0.740984i
$97$	1.67517	+	5.15563i	0.170087	+	0.523475i	0.999375	−	0.0353469i	$-0.0112536\pi$
$97$	1.67517	+	5.15563i	0.170087	+	0.523475i	−0.829288	+	0.558822i	$0.811254\pi$
$98$	7.93704	+	13.7473i	0.801762	+	1.38869i
$99$	1.75440	−	3.03871i	0.176324	−	0.305402i
$100$		0			0
$101$	0.705882	−	2.17248i	0.0702379	−	0.216170i	−0.909776	−	0.415100i	$-0.863747\pi$
$101$	0.705882	−	2.17248i	0.0702379	−	0.216170i	0.980014	+	0.198930i	$0.0637466\pi$
$102$	−6.19252	+	1.31626i	−0.613151	+	0.130329i
$103$	−0.684777	+	6.51522i	−0.0674731	+	0.641963i	0.907563	+	0.419916i	$0.137941\pi$
$103$	−0.684777	+	6.51522i	−0.0674731	+	0.641963i	−0.975036	+	0.222047i	$0.928726\pi$
$104$	24.8673	−	27.6179i	2.43844	−	2.70816i
$105$		0			0
$106$	12.2828	+	5.46863i	1.19301	+	0.531161i
$107$	3.10153	+	3.44460i	0.299836	+	0.333002i	0.874171	−	0.485619i	$-0.161406\pi$
$107$	3.10153	+	3.44460i	0.299836	+	0.333002i	−0.574334	+	0.818621i	$0.694739\pi$
$108$	−15.1983	+	11.0422i	−1.46246	+	1.06254i
$109$	0.480316	−	0.348970i	0.0460059	−	0.0334252i	−0.564545	−	0.825403i	$-0.690948\pi$
$109$	0.480316	−	0.348970i	0.0460059	−	0.0334252i	0.610551	+	0.791977i	$0.290948\pi$
$110$		0			0
$111$	20.0327	+	8.91914i	1.90142	+	0.846567i
$112$	4.71392	−	2.09877i	0.445424	−	0.198315i
$113$	6.46109	−	7.17577i	0.607808	−	0.675039i	−0.358172	−	0.933656i	$-0.616600\pi$
$113$	6.46109	−	7.17577i	0.607808	−	0.675039i	0.965980	+	0.258616i	$0.0832665\pi$
$114$	0.294675	−	2.80365i	0.0275988	−	0.262585i
$115$		0			0
$116$	1.06202	−	3.26856i	0.0986060	−	0.303478i
$117$	−4.76372	−	1.01256i	−0.440406	−	0.0936112i
$118$	6.72056	−	11.6404i	0.618678	−	1.07158i
$119$	0.540283	+	0.935798i	0.0495277	+	0.0857844i
$120$		0			0
$121$	−1.00118	−	9.52556i	−0.0910160	−	0.865960i
$122$	8.53186	+	6.19876i	0.772438	+	0.561209i
$123$	−21.8588			−1.97094
$124$	19.2724	+	14.6091i	1.73071	+	1.31193i
$125$		0			0
$126$	−1.31615	−	0.956239i	−0.117252	−	0.0851886i
$127$	1.28296	+	12.2066i	0.113845	+	1.08316i	0.891048	+	0.453910i	$0.149971\pi$
$127$	1.28296	+	12.2066i	0.113845	+	1.08316i	−0.777203	+	0.629250i	$0.783362\pi$
$128$	−4.57435	−	14.0784i	−0.404319	−	1.24437i
$129$	−10.8525	−	18.7971i	−0.955510	−	1.65499i
$130$		0			0
$131$	−16.2500	−	3.45404i	−1.41977	−	0.301781i	−0.566847	−	0.823823i	$-0.691837\pi$
$131$	−16.2500	−	3.45404i	−1.41977	−	0.301781i	−0.852919	+	0.522042i	$0.825170\pi$
$132$	11.8276	−	36.4017i	1.02946	−	3.16836i
$133$	−0.470654	+	0.100041i	−0.0408108	+	0.00867461i
$134$	1.85467	−	17.6460i	0.160219	−	1.52438i
$135$		0			0
$136$	−6.97734	+	3.10651i	−0.598302	+	0.266381i
$137$	−2.67643	−	1.19162i	−0.228663	−	0.101807i	0.289207	−	0.957266i	$-0.406608\pi$
$137$	−2.67643	−	1.19162i	−0.228663	−	0.101807i	−0.517870	+	0.855459i	$0.673275\pi$
$138$	7.73106	+	8.58621i	0.658111	+	0.730907i
$139$	−17.3423	+	12.6000i	−1.47096	+	1.06871i	−0.490624	+	0.871371i	$0.663231\pi$
$139$	−17.3423	+	12.6000i	−1.47096	+	1.06871i	−0.980335	+	0.197342i	$0.936769\pi$
$140$		0			0
$141$	−10.8275	−	12.0251i	−0.911836	−	1.01270i
$142$	−6.93739	−	3.08873i	−0.582173	−	0.259200i
$143$	−26.0925	+	11.6171i	−2.18197	+	0.971474i
$144$	3.19812	−	3.55188i	0.266510	−	0.295990i
$145$		0			0
$146$	25.5060	−	5.42148i	2.11090	−	0.448685i
$147$	3.78336	−	11.6440i	0.312046	−	0.960379i
$148$	47.9605	+	10.1943i	3.94233	+	0.837968i
$149$	3.94968	−	6.84105i	0.323571	−	0.560441i	−0.657651	−	0.753322i	$-0.728450\pi$
$149$	3.94968	−	6.84105i	0.323571	−	0.560441i	0.981222	+	0.192882i	$0.0617834\pi$
$150$		0			0
$151$	−0.686047	−	2.11144i	−0.0558297	−	0.171826i	0.919253	−	0.393667i	$-0.128794\pi$
$151$	−0.686047	−	2.11144i	−0.0558297	−	0.171826i	−0.975083	+	0.221840i	$0.928794\pi$
$152$	−0.355500	−	3.38236i	−0.0288349	−	0.274346i
$153$	0.809732	+	0.588305i	0.0654629	+	0.0475616i
$154$	−9.54097			−0.768833
$155$		0			0
$156$	−53.1249			−4.25339
$157$	4.23067	+	3.07376i	0.337644	+	0.245313i	0.743667	−	0.668550i	$-0.233085\pi$
$157$	4.23067	+	3.07376i	0.337644	+	0.245313i	−0.406023	+	0.913863i	$0.633085\pi$
$158$	−0.336898	−	3.20537i	−0.0268021	−	0.255005i
$159$	−3.20446	−	9.86231i	−0.254130	−	0.782132i
$160$		0			0
$161$	0.986021	−	1.70784i	0.0777094	−	0.134597i
$162$	26.4151	+	5.61471i	2.07537	+	0.441134i
$163$	−4.10314	+	12.6282i	−0.321382	+	0.989113i	0.651665	+	0.758507i	$0.274071\pi$
$163$	−4.10314	+	12.6282i	−0.321382	+	0.989113i	−0.973047	+	0.230606i	$0.925929\pi$
$164$	−47.8079	+	10.1619i	−3.73317	+	0.793510i
$165$		0			0
$166$	−22.1051	+	24.5502i	−1.71569	+	1.90547i
$167$	−5.80350	+	2.58388i	−0.449088	+	0.199947i	−0.618803	−	0.785546i	$-0.712382\pi$
$167$	−5.80350	+	2.58388i	−0.449088	+	0.199947i	0.169715	+	0.985493i	$0.445715\pi$
$168$	−8.74704	−	3.89443i	−0.674849	−	0.300462i
$169$	17.8278	+	19.7997i	1.37137	+	1.52306i
$170$		0			0
$171$	−0.360568	+	0.261968i	−0.0275733	+	0.0200332i
$172$	−32.4744	−	36.0665i	−2.47615	−	2.75004i
$173$	−2.30333	−	1.02551i	−0.175119	−	0.0779679i	0.317305	−	0.948324i	$-0.397222\pi$
$173$	−2.30333	−	1.02551i	−0.175119	−	0.0779679i	−0.492423	+	0.870356i	$0.663889\pi$
$174$	−3.53651	+	1.57456i	−0.268102	+	0.119367i
$175$		0			0
$176$	2.92997	−	27.8768i	0.220855	−	2.10129i
$177$	−10.1402	+	2.15537i	−0.762184	+	0.162007i
$178$	2.87800	−	8.85757i	0.215715	−	0.663903i
$179$	11.6906	+	2.48491i	0.873795	+	0.185731i	0.622917	−	0.782288i	$-0.285947\pi$
$179$	11.6906	+	2.48491i	0.873795	+	0.185731i	0.250878	+	0.968019i	$0.419281\pi$
$180$		0			0
$181$	−7.04742	−	12.2065i	−0.523830	−	0.907301i	−0.999615	−	0.0277391i	$-0.991169\pi$
$181$	−7.04742	−	12.2065i	−0.523830	−	0.907301i	0.475785	−	0.879562i	$-0.342164\pi$
$182$	4.09220	+	12.5945i	0.303334	+	0.933567i
$183$	−0.850212	−	8.08923i	−0.0628495	−	0.597973i
$184$	11.2767	+	8.19301i	0.831330	+	0.603997i
$185$		0			0
$186$	−2.29685	−	27.1437i	−0.168413	−	1.99027i
$187$	5.86986			0.429247
$188$	−29.2714	−	21.2669i	−2.13483	−	1.55105i
$189$	−0.377533	−	3.59199i	−0.0274615	−	0.261279i
$190$		0			0
$191$	−0.140704	−	0.243707i	−0.0101810	−	0.0176340i	0.860890	−	0.508791i	$-0.169907\pi$
$191$	−0.140704	−	0.243707i	−0.0101810	−	0.0176340i	−0.871071	+	0.491157i	$0.836574\pi$
$192$	−2.81007	+	4.86719i	−0.202800	+	0.351259i
$193$	23.6610	+	5.02930i	1.70316	+	0.362017i	0.953868	−	0.300226i	$-0.0970621\pi$
$193$	23.6610	+	5.02930i	1.70316	+	0.362017i	0.749289	+	0.662243i	$0.230395\pi$
$194$	4.21913	−	12.9851i	0.302916	−	0.932279i
$195$		0			0
$196$	2.86154	−	27.2257i	0.204396	−	1.94469i
$197$	8.52507	−	9.46805i	0.607386	−	0.674571i	−0.358502	−	0.933529i	$-0.616713\pi$
$197$	8.52507	−	9.46805i	0.607386	−	0.674571i	0.965889	+	0.258958i	$0.0833792\pi$
$198$	−8.07337	+	3.59449i	−0.573749	+	0.255450i
$199$	9.87056	+	4.39466i	0.699705	+	0.311529i	0.725582	−	0.688136i	$-0.241571\pi$
$199$	9.87056	+	4.39466i	0.699705	+	0.311529i	−0.0258761	+	0.999665i	$0.508238\pi$
$200$		0			0
$201$	−11.0712	+	8.04371i	−0.780904	+	0.567360i
$202$	−4.65449	+	3.38169i	−0.327489	+	0.237935i
$203$	0.442124	+	0.491029i	0.0310310	+	0.0344635i
$204$	9.97401	+	4.44072i	0.698320	+	0.310912i
$205$		0			0
$206$	11.0405	−	12.2618i	0.769231	−	0.854318i
$207$	0.190934	−	1.81661i	0.0132708	−	0.126263i
$208$	−38.0553	+	8.08891i	−2.63866	+	0.560865i
$209$	−0.807711	+	2.48588i	−0.0558705	+	0.171952i
$210$		0			0
$211$	2.19907	−	3.80891i	0.151391	−	0.262216i	−0.780348	−	0.625345i	$-0.784958\pi$
$211$	2.19907	−	3.80891i	0.151391	−	0.262216i	0.931739	+	0.363129i	$0.118292\pi$
$212$	−11.5934	−	20.0804i	−0.796241	−	1.37913i
$213$	1.80990	+	5.57031i	0.124013	+	0.381671i
$214$	−1.22030	−	11.6103i	−0.0834177	−	0.793667i
$215$		0			0
$216$	25.5287			1.73701
$217$	−4.28505	+	1.80450i	−0.290888	+	0.122498i
$218$	−1.49532			−0.101276
$219$	−16.2706	−	11.8213i	−1.09946	−	0.798808i
$220$		0			0
$221$	−2.51763	−	7.74848i	−0.169354	−	0.521219i
$222$	−27.6150	−	47.8305i	−1.85340	−	3.21018i
$223$	8.79878	−	15.2399i	0.589210	−	1.02054i	−0.405126	−	0.914261i	$-0.632772\pi$
$223$	8.79878	−	15.2399i	0.589210	−	1.02054i	0.994336	−	0.106281i	$-0.0338943\pi$
$224$	−3.06964	−	0.652473i	−0.205099	−	0.0435952i
$225$		0			0
$226$	−23.7884	+	5.05637i	−1.58238	+	0.336345i
$227$	2.33539	−	22.2197i	0.155005	−	1.47477i	−0.589831	−	0.807527i	$-0.700806\pi$
$227$	2.33539	−	22.2197i	0.155005	−	1.47477i	0.744836	−	0.667248i	$-0.232528\pi$
$228$	−3.25309	+	3.61292i	−0.215441	+	0.239272i
$229$	0.133599	−	0.0594822i	0.00882849	−	0.00393070i	−0.402318	−	0.915500i	$-0.631795\pi$
$229$	0.133599	−	0.0594822i	0.00882849	−	0.00393070i	0.411146	+	0.911569i	$0.365129\pi$
$230$		0			0
$231$	4.92391	+	5.46855i	0.323969	+	0.359804i
$232$	−3.77833	+	2.74512i	−0.248059	+	0.180226i
$233$	7.02994	−	5.10755i	0.460547	−	0.334607i	−0.333199	−	0.942856i	$-0.608128\pi$
$233$	7.02994	−	5.10755i	0.460547	−	0.334607i	0.793746	+	0.608250i	$0.208128\pi$
$234$	8.20763	+	9.11550i	0.536549	+	0.595899i
$235$		0			0
$236$	−21.1759	+	9.42813i	−1.37844	+	0.613719i
$237$	−1.66334	+	1.84733i	−0.108046	+	0.119997i
$238$	0.284480	−	2.70664i	0.0184401	−	0.175446i
$239$	10.2336	−	2.17521i	0.661954	−	0.140703i	0.135329	−	0.990801i	$-0.456791\pi$
$239$	10.2336	−	2.17521i	0.661954	−	0.140703i	0.526624	+	0.850098i	$0.323457\pi$
$240$		0			0
$241$	−5.32178	−	1.13118i	−0.342806	−	0.0728657i	0.0332916	−	0.999446i	$-0.489401\pi$
$241$	−5.32178	−	1.13118i	−0.342806	−	0.0728657i	−0.376098	+	0.926580i	$0.622734\pi$
$242$	−12.0618	+	20.8916i	−0.775360	+	1.34296i
$243$	−3.92655	−	6.80098i	−0.251888	−	0.436283i
$244$	−5.62011	−	17.2969i	−0.359791	−	1.10732i
$245$		0			0
$246$	44.5398	+	32.3601i	2.83976	+	2.06320i
$247$	3.62790			0.230838
$248$	−9.51879	−	31.4548i	−0.604444	−	1.99738i
$249$	25.4794			1.61469
$250$		0			0
$251$	1.20823	+	11.4955i	0.0762626	+	0.725590i	0.964119	+	0.265470i	$0.0855270\pi$
$251$	1.20823	+	11.4955i	0.0762626	+	0.725590i	−0.887857	+	0.460120i	$0.847806\pi$
$252$	0.866976	+	2.66828i	0.0546143	+	0.168086i
$253$	−5.35627	−	9.27734i	−0.336746	−	0.583261i
$254$	15.4566	−	26.7717i	0.969836	−	1.67981i
$255$		0			0
$256$	−9.73302	+	29.9552i	−0.608314	+	1.87220i
$257$	18.5574	−	3.94450i	1.15758	−	0.246051i	0.411184	−	0.911552i	$-0.365115\pi$
$257$	18.5574	−	3.94450i	1.15758	−	0.246051i	0.746397	+	0.665501i	$0.231782\pi$
$258$	−5.71426	+	54.3675i	−0.355754	+	3.38477i
$259$	−6.30774	+	7.00546i	−0.391944	+	0.435298i
$260$		0			0
$261$	0.559108	+	0.248931i	0.0346079	+	0.0154084i
$262$	27.9978	+	31.0947i	1.72971	+	1.92104i
$263$	4.21884	−	3.06516i	0.260145	−	0.189006i	−0.450066	−	0.892995i	$-0.648600\pi$
$263$	4.21884	−	3.06516i	0.260145	−	0.189006i	0.710211	+	0.703989i	$0.248600\pi$
$264$	−42.0790	+	30.5722i	−2.58978	+	1.88159i
$265$		0			0
$266$	1.10711	+	0.492919i	0.0678815	+	0.0302228i
$267$	−6.56213	+	2.92165i	−0.401596	+	0.178802i
$268$	−20.4748	+	22.7395i	−1.25069	+	1.38904i
$269$	−0.120184	+	1.14347i	−0.00732773	+	0.0697187i	−0.997575	−	0.0696049i	$-0.977826\pi$
$269$	−0.120184	+	1.14347i	−0.00732773	+	0.0697187i	0.990247	+	0.139324i	$0.0444928\pi$
$270$		0			0
$271$	3.88599	−	11.9599i	0.236057	−	0.726509i	−0.760922	−	0.648843i	$-0.775253\pi$
$271$	3.88599	−	11.9599i	0.236057	−	0.726509i	0.996979	−	0.0776663i	$-0.0247469\pi$
$272$	7.82091	+	1.66239i	0.474212	+	0.100797i
$273$	5.10683	−	8.84529i	0.309079	−	0.535341i
$274$	3.68944	+	6.39030i	0.222887	+	0.386052i
$275$		0			0
$276$	−2.08276	−	19.8161i	−0.125367	−	1.19279i
$277$	−17.6504	−	12.8237i	−1.06051	−	0.770503i	−0.0863249	−	0.996267i	$-0.527512\pi$
$277$	−17.6504	−	12.8237i	−1.06051	−	0.770503i	−0.974182	+	0.225764i	$0.927512\pi$
$278$	53.9902			3.23812
$279$	−2.94608	+	3.14129i	−0.176377	+	0.188064i
$280$		0			0
$281$	25.1753	+	18.2909i	1.50183	+	1.09114i	0.969645	+	0.244515i	$0.0786289\pi$
$281$	25.1753	+	18.2909i	1.50183	+	1.09114i	0.532185	+	0.846628i	$0.321371\pi$
$282$	4.26005	+	40.5317i	0.253683	+	2.41363i
$283$	−5.60243	−	17.2425i	−0.333030	−	1.02496i	−0.967684	−	0.252165i	$-0.918858\pi$
$283$	−5.60243	−	17.2425i	−0.333030	−	1.02496i	0.634654	−	0.772796i	$-0.281142\pi$
$284$	6.54806	+	11.3416i	0.388556	+	0.672999i
$285$		0			0
$286$	70.3648	+	14.9565i	4.16076	+	0.884397i
$287$	2.90377	−	8.93687i	0.171404	−	0.527527i
$288$	−2.84328	+	0.604359i	−0.167542	+	0.0356122i
$289$	1.60196	−	15.2417i	0.0942332	−	0.896569i
$290$		0			0
$291$	−9.62005	+	4.28312i	−0.563937	+	0.251081i
$292$	−41.0814	−	18.2906i	−2.40411	−	1.07038i
$293$	7.83301	+	8.69944i	0.457609	+	0.508226i	0.927153	−	0.374683i	$-0.122248\pi$
$293$	7.83301	+	8.69944i	0.457609	+	0.508226i	−0.469544	+	0.882909i	$0.655582\pi$
$294$	−24.9470	+	18.1250i	−1.45494	+	1.05707i
$295$		0			0
$296$	−44.5843	−	49.5159i	−2.59141	−	2.87805i
$297$	−17.9237	−	7.98014i	−1.04004	−	0.463055i
$298$	−18.1755	+	8.09227i	−1.05288	+	0.468773i
$299$	−9.94915	+	11.0497i	−0.575374	+	0.639018i
$300$		0			0
$301$	9.12679	−	1.93996i	0.526059	−	0.111817i
$302$	−1.72790	+	5.31794i	−0.0994296	+	0.306013i
$303$	4.34036	+	0.922572i	0.249347	+	0.0530004i
$304$	−1.78020	+	3.08339i	−0.102101	+	0.176845i
$305$		0			0
$306$	−0.778988	−	2.39748i	−0.0445318	−	0.137055i
$307$	−1.22753	−	11.6792i	−0.0700591	−	0.666568i	−0.972044	−	0.234800i	$-0.924557\pi$
$307$	−1.22753	−	11.6792i	−0.0700591	−	0.666568i	0.901985	−	0.431768i	$-0.142110\pi$
$308$	13.3115	+	9.67136i	0.758492	+	0.551077i
$309$	−12.7258			−0.723947
$310$		0			0
$311$	−0.833220			−0.0472476			−0.0236238	−	0.999721i	$-0.507520\pi$
$311$	−0.833220			−0.0472476			−0.0236238	+	0.999721i	$0.507520\pi$
$312$	58.4047	+	42.4335i	3.30651	+	2.40232i
$313$	1.10756	+	10.5377i	0.0626029	+	0.595627i	0.980186	+	0.198082i	$0.0634711\pi$
$313$	1.10756	+	10.5377i	0.0626029	+	0.595627i	−0.917583	+	0.397545i	$0.869862\pi$
$314$	−4.07004	−	12.5263i	−0.229686	−	0.706900i
$315$		0			0
$316$	−2.77914	+	4.81361i	−0.156339	+	0.270787i
$317$	30.4268	+	6.46741i	1.70894	+	0.363246i	0.955663	−	0.294461i	$-0.0951403\pi$
$317$	30.4268	+	6.46741i	1.70894	+	0.363246i	0.753274	+	0.657707i	$0.228474\pi$
$318$	−8.07086	+	24.8396i	−0.452591	+	1.39293i
$319$	3.51087	−	0.746258i	0.196571	−	0.0417824i
$320$		0			0
$321$	−6.02488	+	6.69130i	−0.336276	+	0.373472i
$322$	−4.53745	+	2.02020i	−0.252862	+	0.112581i
$323$	−0.681127	−	0.303257i	−0.0378989	−	0.0168737i
$324$	−31.1628	−	34.6098i	−1.73127	−	1.92277i
$325$		0			0
$326$	27.0555	−	19.6570i	1.49847	−	1.08870i
$327$	0.771706	+	0.857067i	0.0426755	+	0.0473959i
$328$	60.6761	+	27.0147i	3.35028	+	1.49164i
$329$	6.35476	−	2.82932i	0.350349	−	0.155986i
$330$		0			0
$331$	0.934022	−	8.88662i	0.0513385	−	0.488453i	−0.938399	−	0.345554i	$-0.887691\pi$
$331$	0.934022	−	8.88662i	0.0513385	−	0.488453i	0.989737	−	0.142899i	$-0.0456424\pi$
$332$	55.7267	−	11.8451i	3.05840	−	0.650083i
$333$	−2.69822	+	8.30427i	−0.147862	+	0.455071i
$334$	15.6505	+	3.32662i	0.856359	+	0.182025i
$335$		0			0
$336$	5.01180	+	8.68070i	0.273416	+	0.473571i
$337$	−7.20064	−	22.1613i	−0.392244	−	1.20720i	−0.931087	−	0.364796i	$-0.881139\pi$
$337$	−7.20064	−	22.1613i	−0.392244	−	1.20720i	0.538843	−	0.842406i	$-0.318861\pi$
$338$	−7.01432	−	66.7368i	−0.381529	−	3.63000i
$339$	15.1749	+	11.0252i	0.824185	+	0.598805i
$340$		0			0
$341$	−3.14947	+	25.0599i	−0.170554	+	1.35707i
$342$	1.12252			0.0606990
$343$	8.98713	+	6.52953i	0.485260	+	0.352562i
$344$	6.89377	+	65.5898i	0.371687	+	3.53637i
$345$		0			0
$346$	3.17512	+	5.49947i	0.170696	+	0.295654i
$347$	−9.63256	+	16.6841i	−0.517103	+	0.895648i	0.482700	+	0.875786i	$0.339656\pi$
$347$	−9.63256	+	16.6841i	−0.517103	+	0.895648i	−0.999803	+	0.0198624i	$0.993677\pi$
$348$	6.53020	+	1.38804i	0.350055	+	0.0744065i
$349$	10.0809	−	31.0259i	0.539619	−	1.66078i	−0.193832	−	0.981035i	$-0.562092\pi$
$349$	10.0809	−	31.0259i	0.539619	−	1.66078i	0.733451	−	0.679743i	$-0.237908\pi$
$350$		0			0
$351$	−2.84652	+	27.0828i	−0.151936	+	1.44557i
$352$	−11.4070	+	12.6687i	−0.607995	+	0.675247i
$353$	11.6241	−	5.17536i	0.618686	−	0.275457i	−0.0733652	−	0.997305i	$-0.523374\pi$
$353$	11.6241	−	5.17536i	0.618686	−	0.275457i	0.692051	+	0.721848i	$0.256707\pi$
$354$	23.8527	+	10.6199i	1.26776	+	0.564442i
$355$		0			0
$356$	−12.9940	+	9.44069i	−0.688680	+	0.500355i
$357$	−1.69817	+	1.23379i	−0.0898766	+	0.0652992i
$358$	−20.1422	−	22.3702i	−1.06455	−	1.18230i
$359$	−5.85762	−	2.60798i	−0.309153	−	0.137644i	0.246295	−	0.969195i	$-0.420787\pi$
$359$	−5.85762	−	2.60798i	−0.309153	−	0.137644i	−0.555449	+	0.831551i	$0.687453\pi$
$360$		0			0
$361$	−12.4913	+	13.8730i	−0.657438	+	0.730159i
$362$	−3.71073	+	35.3053i	−0.195032	+	1.85560i
$363$	18.1992	−	3.86836i	0.955210	−	0.203036i
$364$	7.05722	−	21.7199i	0.369899	−	1.13843i
$365$		0			0
$366$	−10.2430	+	17.7414i	−0.535411	+	0.927359i
$367$	10.9471	+	18.9610i	0.571435	+	0.989754i	0.996419	+	0.0845536i	$0.0269464\pi$
$367$	10.9471	+	18.9610i	0.571435	+	0.989754i	−0.424984	+	0.905201i	$0.639720\pi$
$368$	−4.50921	−	13.8779i	−0.235059	−	0.723436i
$369$	−0.909800	−	8.65617i	−0.0473623	−	0.450622i
$370$		0			0
$371$	4.45785			0.231440
$372$	−24.3101	+	40.1989i	−1.26042	+	2.08422i
$373$	−4.62775			−0.239616			−0.119808	−	0.992797i	$-0.538228\pi$
$373$	−4.62775			−0.239616			−0.119808	+	0.992797i	$0.538228\pi$
$374$	−11.9605	−	8.68984i	−0.618465	−	0.449341i
$375$		0			0
$376$	15.1936	+	46.7610i	0.783548	+	2.41151i
$377$	−2.49093	−	4.31443i	−0.128290	−	0.222204i
$378$	−4.54837	+	7.87801i	−0.233943	+	0.405201i
$379$	14.1342	+	3.00432i	0.726025	+	0.154321i	0.556076	−	0.831131i	$-0.312306\pi$
$379$	14.1342	+	3.00432i	0.726025	+	0.154321i	0.169949	+	0.985453i	$0.445640\pi$
$380$		0			0
$381$	−23.3215	+	4.95714i	−1.19480	+	0.253962i
$382$	−0.0740861	+	0.704882i	−0.00379057	+	0.0360649i
$383$	−13.6515	+	15.1615i	−0.697560	+	0.774718i	−0.982986	−	0.183682i	$-0.941198\pi$
$383$	−13.6515	+	15.1615i	−0.697560	+	0.774718i	0.285426	+	0.958401i	$0.407865\pi$
$384$	26.2693	−	11.6959i	1.34055	−	0.596852i
$385$		0			0
$386$	−40.7666	−	45.2759i	−2.07497	−	2.30449i
$387$	6.99203	−	5.08001i	0.355425	−	0.258231i
$388$	−19.0491	+	13.8400i	−0.967072	+	0.702619i
$389$	4.17983	+	4.64217i	0.211926	+	0.235367i	0.839730	−	0.543004i	$-0.182713\pi$
$389$	4.17983	+	4.64217i	0.211926	+	0.235367i	−0.627805	+	0.778371i	$0.716046\pi$
$390$		0			0
$391$	2.79156	−	1.24288i	0.141175	−	0.0628553i
$392$	−24.8925	+	27.6459i	−1.25726	+	1.39633i
$393$	3.37330	−	32.0948i	0.170160	−	1.61897i
$394$	−31.3875	+	6.67162i	−1.58128	+	0.336111i
$395$		0			0
$396$	14.9075	+	3.16869i	0.749131	+	0.159233i
$397$	−15.7955	+	27.3586i	−0.792753	+	1.37309i	0.131503	+	0.991316i	$0.458020\pi$
$397$	−15.7955	+	27.3586i	−0.792753	+	1.37309i	−0.924256	+	0.381773i	$0.875314\pi$
$398$	−13.6065	−	23.5672i	−0.682033	−	1.18132i
$399$	−0.288836	−	0.888946i	−0.0144599	−	0.0445030i
$400$		0			0
$401$	−1.67599	−	1.21768i	−0.0836950	−	0.0608080i	0.545151	−	0.838338i	$-0.316472\pi$
$401$	−1.67599	−	1.21768i	−0.0836950	−	0.0608080i	−0.628846	+	0.777530i	$0.716472\pi$
$402$	34.4670			1.71906
$403$	34.4311	−	6.59097i	1.71513	−	0.328320i
$404$	9.92182			0.493629
$405$		0			0
$406$	−0.173954	−	1.65506i	−0.00863317	−	0.0821391i
$407$	15.8242	+	48.7019i	0.784377	+	2.41406i
$408$	−7.41825	−	12.8488i	−0.367258	−	0.636110i
$409$	−11.9560	+	20.7083i	−0.591184	+	1.02396i	0.402890	+	0.915249i	$0.368006\pi$
$409$	−11.9560	+	20.7083i	−0.591184	+	1.02396i	−0.994073	+	0.108712i	$0.965327\pi$
$410$		0			0
$411$	1.75865	−	5.41258i	0.0867479	−	0.266983i
$412$	−27.8330	+	5.91609i	−1.37124	+	0.291465i
$413$	0.465833	−	4.43211i	0.0229221	−	0.218090i
$414$	−3.07840	+	3.41891i	−0.151295	+	0.168030i
$415$		0			0
$416$	21.6159	+	9.62401i	1.05981	+	0.471856i
$417$	−27.8633	−	30.9454i	−1.36447	−	1.51540i
$418$	5.32594	−	3.86952i	0.260500	−	0.189265i
$419$	24.7274	−	17.9655i	1.20801	−	0.877673i	0.212965	−	0.977060i	$-0.431688\pi$
$419$	24.7274	−	17.9655i	1.20801	−	0.877673i	0.995049	+	0.0993864i	$0.0316880\pi$
$420$		0			0
$421$	20.5099	+	9.13160i	0.999592	+	0.445047i	0.840263	−	0.542178i	$-0.182400\pi$
$421$	20.5099	+	9.13160i	0.999592	+	0.445047i	0.159329	+	0.987226i	$0.449067\pi$
$422$	−10.1196	+	4.50555i	−0.492616	+	0.219327i
$423$	4.31134	−	4.78822i	0.209624	−	0.232811i
$424$	−3.29358	+	31.3364i	−0.159951	+	1.52183i
$425$		0			0
$426$	4.55848	−	14.0296i	0.220859	−	0.679735i
$427$	3.42019	+	0.726984i	0.165515	+	0.0351812i
$428$	−10.0665	+	17.4356i	−0.486581	+	0.842783i
$429$	−27.7414	−	48.0495i	−1.33937	−	2.31985i
$430$		0			0
$431$	1.72251	+	16.3886i	0.0829704	+	0.789411i	0.954328	+	0.298762i	$0.0965736\pi$
$431$	1.72251	+	16.3886i	0.0829704	+	0.789411i	−0.871357	+	0.490649i	$0.836760\pi$
$432$	−21.6212	−	15.7087i	−1.04025	−	0.755787i
$433$	−30.3372			−1.45791			−0.728957	−	0.684560i	$-0.759994\pi$
$433$	−30.3372			−1.45791			−0.728957	+	0.684560i	$0.759994\pi$
$434$	11.4027	+	2.66676i	0.547347	+	0.128009i
$435$		0			0
$436$	2.08626	+	1.51576i	0.0999138	+	0.0725916i
$437$	0.142232	+	1.35325i	0.00680388	+	0.0647346i
$438$	15.6528	+	48.1745i	0.747921	+	2.30187i
$439$	8.25197	+	14.2928i	0.393845	+	0.682160i	0.992953	−	0.118508i	$-0.0378113\pi$
$439$	8.25197	+	14.2928i	0.393845	+	0.682160i	−0.599108	+	0.800668i	$0.704478\pi$
$440$		0			0
$441$	4.76854	+	1.01358i	0.227073	+	0.0482659i
$442$	−6.34100	+	19.5156i	−0.301611	+	0.928262i
$443$	−24.6936	+	5.24879i	−1.17323	+	0.249377i	−0.752987	−	0.658035i	$-0.771388\pi$
$443$	−24.6936	+	5.24879i	−1.17323	+	0.249377i	−0.420241	+	0.907413i	$0.638054\pi$
$444$	−9.95602	+	94.7252i	−0.472492	+	4.49546i
$445$		0			0
$446$	−40.4900	+	18.0273i	−1.91726	+	0.853618i
$447$	14.0183	+	6.24133i	0.663041	+	0.295205i
$448$	−1.61664	−	1.79546i	−0.0763788	−	0.0848273i
$449$	−2.11185	+	1.53435i	−0.0996644	+	0.0724104i	−0.636501	−	0.771276i	$-0.719619\pi$
$449$	−2.11185	+	1.53435i	−0.0996644	+	0.0724104i	0.536837	+	0.843686i	$0.319619\pi$
$450$		0			0
$451$	−34.1560	−	37.9340i	−1.60834	−	1.78624i
$452$	38.3148	+	17.0589i	1.80218	+	0.802381i
$453$	3.93980	−	1.75411i	0.185108	−	0.0824153i
$454$	−37.6531	+	41.8180i	−1.76715	+	1.96261i
$455$		0			0
$456$	6.46222	−	1.37359i	0.302621	−	0.0643241i
$457$	2.89306	−	8.90392i	0.135332	−	0.416508i	−0.860310	−	0.509771i	$-0.829730\pi$
$457$	2.89306	−	8.90392i	0.135332	−	0.416508i	0.995641	+	0.0932637i	$0.0297300\pi$
$458$	−0.360283	−	0.0765805i	−0.0168349	−	0.00357837i
$459$	2.79828	−	4.84677i	0.130613	−	0.226228i
$460$		0			0
$461$	−5.44913	−	16.7707i	−0.253791	−	0.781089i	−0.994065	−	0.108784i	$-0.965304\pi$
$461$	−5.44913	−	16.7707i	−0.253791	−	0.781089i	0.740274	−	0.672305i	$-0.234696\pi$
$462$	−1.93731	−	18.4323i	−0.0901318	−	0.857546i
$463$	4.70265	+	3.41667i	0.218551	+	0.158786i	0.691674	−	0.722210i	$-0.256874\pi$
$463$	4.70265	+	3.41667i	0.218551	+	0.158786i	−0.473123	+	0.880996i	$0.656874\pi$
$464$	4.88917			0.226974
$465$		0			0
$466$	−21.8856			−1.01383
$467$	6.54431	+	4.75472i	0.302834	+	0.220022i	0.728816	−	0.684710i	$-0.240071\pi$
$467$	6.54431	+	4.75472i	0.302834	+	0.220022i	−0.425981	+	0.904732i	$0.640071\pi$
$468$	−2.21115	−	21.0377i	−0.102210	−	0.972467i
$469$	−1.81792	−	5.59497i	−0.0839436	−	0.258352i
$470$		0			0
$471$	−5.07918	+	8.79739i	−0.234036	+	0.405362i
$472$	30.8112	+	6.54912i	1.41820	+	0.301448i
$473$	15.6629	−	48.2055i	0.720181	−	2.21649i
$474$	6.12406	−	1.30171i	0.281287	−	0.0597895i
$475$		0			0
$476$	−3.14054	+	3.48792i	−0.143946	+	0.159869i
$477$	3.77214	−	1.67947i	0.172715	−	0.0768975i
$478$	−24.0723	−	10.7177i	−1.10104	−	0.490215i
$479$	6.09262	+	6.76654i	0.278379	+	0.309171i	0.866078	−	0.499908i	$-0.166633\pi$
$479$	6.09262	+	6.76654i	0.278379	+	0.309171i	−0.587700	+	0.809079i	$0.699966\pi$
$480$		0			0
$481$	57.5015	−	41.7773i	2.62184	−	1.90488i
$482$	9.16915	+	10.1834i	0.417643	+	0.463840i
$483$	3.49960	+	1.55812i	0.159237	+	0.0708970i
$484$	38.0056	−	16.9212i	1.72753	−	0.769145i
$485$		0			0
$486$	−2.06748	+	19.6707i	−0.0937826	+	0.892282i
$487$	40.2479	−	8.55495i	1.82381	−	0.387662i	0.836691	−	0.547675i	$-0.184487\pi$
$487$	40.2479	−	8.55495i	1.82381	−	0.387662i	0.987115	+	0.160013i	$0.0511537\pi$
$488$	−7.63725	+	23.5050i	−0.345722	+	1.06402i
$489$	−25.2296	−	5.36271i	−1.14092	−	0.242510i
$490$		0			0
$491$	−9.46138	−	16.3876i	−0.426986	−	0.739562i	0.569617	−	0.821910i	$-0.307091\pi$
$491$	−9.46138	−	16.3876i	−0.426986	−	0.739562i	−0.996604	+	0.0823481i	$0.973758\pi$
$492$	−29.3393	−	90.2971i	−1.32272	−	4.07091i
$493$	0.107021	+	1.01824i	0.00481998	+	0.0458591i
$494$	−7.39228	−	5.37081i	−0.332595	−	0.241644i
$495$		0			0
$496$	−11.2935	+	32.4975i	−0.507091	+	1.45918i
$497$	−2.51783			−0.112940
$498$	−51.9172	−	37.7201i	−2.32647	−	1.69028i
$499$	−0.831837	−	7.91440i	−0.0372382	−	0.354297i	−0.997237	−	0.0742919i	$-0.976330\pi$
$499$	−0.831837	−	7.91440i	−0.0372382	−	0.354297i	0.959998	−	0.280006i	$-0.0903363\pi$
$500$		0			0
$501$	−6.17023	−	10.6872i	−0.275666	−	0.477467i
$502$	14.5562	−	25.2121i	0.649676	−	1.12527i
$503$	−7.35909	−	1.56422i	−0.328125	−	0.0697452i	0.0409035	−	0.999163i	$-0.486976\pi$
$503$	−7.35909	−	1.56422i	−0.328125	−	0.0697452i	−0.369029	+	0.929418i	$0.620310\pi$
$504$	1.17815	−	3.62596i	0.0524788	−	0.161513i
$505$		0			0
$506$	−2.82028	+	26.8332i	−0.125377	+	1.19288i
$507$	−34.6313	+	38.4619i	−1.53803	+	1.70816i
$508$	−48.7026	+	21.6838i	−2.16083	+	0.962062i
$509$	12.2699	+	5.46290i	0.543852	+	0.242139i	0.660226	−	0.751067i	$-0.270460\pi$
$509$	12.2699	+	5.46290i	0.543852	+	0.242139i	−0.116374	+	0.993205i	$0.537127\pi$
$510$		0			0
$511$	6.99450	−	5.08180i	0.309418	−	0.224806i
$512$	40.2267	−	29.2264i	1.77779	−	1.29164i
$513$	1.66755	+	1.85200i	0.0736240	+	0.0817677i
$514$	−43.6525	−	19.4353i	−1.92543	−	0.857255i
$515$		0			0
$516$	63.0831	−	70.0608i	2.77708	−	3.08426i
$517$	3.94984	−	37.5803i	0.173714	−	1.65278i
$518$	23.2238	−	4.93636i	1.02039	−	0.216891i
$519$	1.51349	−	4.65804i	0.0664349	−	0.204465i
$520$		0			0
$521$	9.74556	−	16.8798i	0.426961	−	0.739518i	−0.569640	−	0.821894i	$-0.692918\pi$
$521$	9.74556	−	16.8798i	0.426961	−	0.739518i	0.996601	+	0.0823761i	$0.0262509\pi$
$522$	−0.770727	−	1.33494i	−0.0337338	−	0.0584287i
$523$	1.93469	+	5.95438i	0.0845983	+	0.260367i	0.984404	−	0.175925i	$-0.0562916\pi$
$523$	1.93469	+	5.95438i	0.0845983	+	0.260367i	−0.899805	+	0.436292i	$0.856292\pi$
$524$	−7.54266	−	71.7636i	−0.329503	−	3.13501i
$525$		0			0
$526$	−13.1341			−0.572674
$527$	−7.01525	−	1.64067i	−0.305589	−	0.0714685i
$528$	54.4503			2.36965
$529$	14.0957	+	10.2411i	0.612856	+	0.445266i
$530$		0			0
$531$	−1.27559	−	3.92585i	−0.0553558	−	0.170368i
$532$	−1.04498	−	1.80996i	−0.0453057	−	0.0784718i
$533$	−35.4248	+	61.3576i	−1.53442	+	2.65769i
$534$	17.6964	+	3.76148i	0.765797	+	0.162775i
$535$		0			0
$536$	40.6728	−	8.64527i	1.75680	−	0.373419i
$537$	−2.42682	+	23.0897i	−0.104725	+	0.996394i
$538$	1.93770	−	2.15204i	0.0835403	−	0.0927809i
$539$	26.1189	−	11.6289i	1.12502	−	0.500892i
$540$		0			0
$541$	24.4535	+	27.1584i	1.05134	+	1.16763i	0.985478	+	0.169802i	$0.0543127\pi$
$541$	24.4535	+	27.1584i	1.05134	+	1.16763i	0.0658608	+	0.997829i	$0.479021\pi$
$542$	−25.6237	+	18.6167i	−1.10063	+	0.799657i
$543$	22.1508	−	16.0935i	0.950582	−	0.690638i
$544$	−3.25383	−	3.61375i	−0.139507	−	0.154938i
$545$		0			0
$546$	−23.5005	+	10.4631i	−1.00573	+	0.447779i
$547$	−7.61131	+	8.45322i	−0.325436	+	0.361433i	−0.883555	−	0.468328i	$-0.844857\pi$
$547$	−7.61131	+	8.45322i	−0.325436	+	0.361433i	0.558119	+	0.829761i	$0.311523\pi$
$548$	1.33015	−	12.6556i	0.0568214	−	0.540619i
$549$	3.16798	−	0.673375i	0.135206	−	0.0287390i
$550$		0			0
$551$	−0.445948	−	0.0947892i	−0.0189980	−	0.00403815i
$552$	−13.5384	+	23.4492i	−0.576232	+	0.998062i
$553$	−0.534310	−	0.925453i	−0.0227212	−	0.0393542i
$554$	16.9802	+	52.2597i	0.721420	+	2.22030i
$555$		0			0
$556$	−75.3268	−	54.7281i	−3.19457	−	2.32099i
$557$	−17.9263			−0.759560			−0.379780	−	0.925077i	$-0.624000\pi$
$557$	−17.9263			−0.759560			−0.379780	+	0.925077i	$0.624000\pi$
$558$	10.6534	−	2.03933i	0.450995	−	0.0863317i
$559$	−70.3514			−2.97555
$560$		0			0
$561$	1.19188	+	11.3400i	0.0503214	+	0.478776i
$562$	−24.2194	−	74.5397i	−1.02163	−	3.14427i
$563$	16.5969	+	28.7466i	0.699474	+	1.21152i	0.968649	+	0.248433i	$0.0799157\pi$
$563$	16.5969	+	28.7466i	0.699474	+	1.21152i	−0.269175	+	0.963091i	$0.586751\pi$
$564$	35.1421	−	60.8678i	1.47975	−	2.56300i
$565$		0			0
$566$	−14.1105	+	43.4276i	−0.593108	+	1.82540i
$567$	8.75817	−	1.86161i	0.367808	−	0.0781801i
$568$	1.86024	−	17.6990i	0.0780540	−	0.742634i
$569$	18.2648	−	20.2851i	0.765699	−	0.850395i	−0.226635	−	0.973980i	$-0.572772\pi$
$569$	18.2648	−	20.2851i	0.765699	−	0.850395i	0.992334	+	0.123585i	$0.0394391\pi$
$570$		0			0
$571$	27.0994	+	12.0654i	1.13408	+	0.504923i	0.885939	−	0.463802i	$-0.153515\pi$
$571$	27.0994	+	12.0654i	1.13408	+	0.504923i	0.248137	+	0.968725i	$0.420182\pi$
$572$	−83.0116	−	92.1937i	−3.47089	−	3.85481i
$573$	0.442248	−	0.321312i	0.0184752	−	0.0134230i
$574$	−19.1471	+	13.9111i	−0.799182	+	0.580640i
$575$		0			0
$576$	−2.04439	−	0.910221i	−0.0851829	−	0.0379259i
$577$	1.84475	−	0.821336i	0.0767979	−	0.0341926i	−0.367978	−	0.929834i	$-0.619950\pi$
$577$	1.84475	−	0.821336i	0.0767979	−	0.0341926i	0.444776	+	0.895642i	$0.353283\pi$
$578$	−25.8282	+	28.6851i	−1.07431	+	1.19314i
$579$	−4.91174	+	46.7321i	−0.204125	+	1.94212i
$580$		0			0
$581$	−3.38474	+	10.4171i	−0.140422	+	0.432176i
$582$	25.9428	+	5.51431i	1.07536	+	0.228576i
$583$	12.1080	−	20.9717i	0.501462	−	0.868558i
$584$	30.5547	+	52.9222i	1.26436	+	2.18994i
$585$		0			0
$586$	−3.08189	−	29.3222i	−0.127312	−	1.21129i
$587$	2.75988	+	2.00517i	0.113913	+	0.0827623i	0.643283	−	0.765628i	$-0.277572\pi$
$587$	2.75988	+	2.00517i	0.113913	+	0.0827623i	−0.529371	+	0.848391i	$0.677572\pi$
$588$	53.1786			2.19305
$589$	1.66014	−	2.74519i	0.0684049	−	0.113114i
$590$		0			0
$591$	20.0224	+	14.5471i	0.823612	+	0.598389i
$592$	7.29120	+	69.3711i	0.299667	+	2.85114i
$593$	4.48436	+	13.8014i	0.184151	+	0.566757i	0.999933	−	0.0116020i	$-0.00369312\pi$
$593$	4.48436	+	13.8014i	0.184151	+	0.566757i	−0.815782	+	0.578359i	$0.803693\pi$
$594$	24.7077	+	42.7950i	1.01377	+	1.75590i
$595$		0			0
$596$	33.5613	+	7.13367i	1.37472	+	0.292206i
$597$	−6.48584	+	19.9613i	−0.265448	+	0.816964i
$598$	36.6307	−	7.78609i	1.49794	−	0.318397i
$599$	−0.0589838	+	0.561194i	−0.00241001	+	0.0229298i	−0.995661	−	0.0930566i	$-0.970336\pi$
$599$	−0.0589838	+	0.561194i	−0.00241001	+	0.0229298i	0.993251	+	0.115986i	$0.0370029\pi$
$600$		0			0
$601$	−19.9005	+	8.86028i	−0.811759	+	0.361419i	−0.770268	−	0.637720i	$-0.779878\pi$
$601$	−19.9005	+	8.86028i	−0.811759	+	0.361419i	−0.0414913	+	0.999139i	$0.513211\pi$
$602$	−21.4689	−	9.55855i	−0.875005	−	0.389577i
$603$	−3.64615	−	4.04946i	−0.148483	−	0.164907i
$604$	7.80137	−	5.66803i	0.317433	−	0.230629i
$605$		0			0
$606$	−7.47821	−	8.30539i	−0.303781	−	0.337384i
$607$	9.52379	+	4.24026i	0.386559	+	0.172107i	0.590809	−	0.806812i	$-0.298809\pi$
$607$	9.52379	+	4.24026i	0.386559	+	0.172107i	−0.204250	+	0.978919i	$0.565476\pi$
$608$	1.97815	−	0.880731i	0.0802248	−	0.0357184i
$609$	−0.858848	+	0.953847i	−0.0348023	+	0.0386518i
$610$		0			0
$611$	−51.3017	+	10.9045i	−2.07545	+	0.441150i
$612$	−1.34341	+	4.13458i	−0.0543040	+	0.167131i
$613$	−16.2216	−	3.44801i	−0.655184	−	0.139264i	−0.131687	−	0.991291i	$-0.542039\pi$
$613$	−16.2216	−	3.44801i	−0.655184	−	0.139264i	−0.523497	+	0.852028i	$0.675373\pi$
$614$	−14.7888	+	25.6150i	−0.596829	+	1.03374i
$615$		0			0
$616$	−6.90945	−	21.2651i	−0.278390	−	0.856795i
$617$	1.61141	+	15.3315i	0.0648729	+	0.617224i	0.977864	+	0.209244i	$0.0671002\pi$
$617$	1.61141	+	15.3315i	0.0648729	+	0.617224i	−0.912991	+	0.407980i	$0.866233\pi$
$618$	25.9304	+	18.8395i	1.04307	+	0.757837i
$619$	40.5205			1.62866			0.814328	−	0.580406i	$-0.197106\pi$
$619$	40.5205			1.62866			0.814328	+	0.580406i	$0.197106\pi$
$620$		0			0
$621$	−10.2138			−0.409865
$622$	1.69779	+	1.23351i	0.0680750	+	0.0494594i
$623$	−0.322777	−	3.07102i	−0.0129318	−	0.123038i
$624$	−23.3542	−	71.8769i	−0.934917	−	2.87738i
$625$		0			0
$626$	13.3434	−	23.1115i	0.533310	−	0.923721i
$627$	−4.96649	−	1.05566i	−0.198343	−	0.0421590i
$628$	−7.01901	+	21.6023i	−0.280089	+	0.862025i
$629$	−14.2879	+	3.03698i	−0.569695	+	0.121093i
$630$		0			0
$631$	−5.30926	+	5.89653i	−0.211358	+	0.234737i	−0.839497	−	0.543364i	$-0.817150\pi$
$631$	−5.30926	+	5.89653i	−0.211358	+	0.234737i	0.628139	+	0.778101i	$0.283817\pi$
$632$	6.90021	−	3.07217i	0.274475	−	0.122204i
$633$	7.80498	+	3.47500i	0.310220	+	0.138119i
$634$	−52.4237	−	58.2224i	−2.08201	−	2.31231i
$635$		0			0
$636$	36.4394	−	26.4748i	1.44492	−	1.04979i
$637$	−26.5533	−	29.4904i	−1.05208	−	1.16845i
$638$	−8.25858	−	3.67696i	−0.326960	−	0.145572i
$639$	−2.13053	+	0.948575i	−0.0842827	+	0.0375251i
$640$		0			0
$641$	3.39369	−	32.2888i	0.134043	−	1.27533i	−0.696168	−	0.717879i	$-0.745113\pi$
$641$	3.39369	−	32.2888i	0.134043	−	1.27533i	0.830210	−	0.557450i	$-0.188220\pi$
$642$	22.1823	−	4.71500i	0.875466	−	0.186086i
$643$	11.0420	−	33.9837i	0.435453	−	1.34019i	−0.457169	−	0.889380i	$-0.651137\pi$
$643$	11.0420	−	33.9837i	0.435453	−	1.34019i	0.892622	−	0.450806i	$-0.148863\pi$
$644$	8.37843	+	1.78089i	0.330156	+	0.0701769i
$645$		0			0
$646$	0.938929	+	1.62627i	0.0369417	+	0.0639849i
$647$	1.45217	+	4.46933i	0.0570909	+	0.175708i	0.975536	−	0.219842i	$-0.0705542\pi$
$647$	1.45217	+	4.46933i	0.0570909	+	0.175708i	−0.918445	+	0.395550i	$0.870554\pi$
$648$	6.61533	+	62.9407i	0.259875	+	2.47254i
$649$	−19.5853	−	14.2295i	−0.768790	−	0.558558i
$650$		0			0
$651$	−4.35622	−	7.91190i	−0.170734	−	0.310092i
$652$	−57.6734			−2.25866
$653$	35.7838	+	25.9985i	1.40033	+	1.01740i	0.994641	+	0.103388i	$0.0329683\pi$
$653$	35.7838	+	25.9985i	1.40033	+	1.01740i	0.405689	+	0.914011i	$0.367032\pi$
$654$	−0.303627	−	2.88882i	−0.0118728	−	0.112962i
$655$		0			0
$656$	−34.7657	−	60.2159i	−1.35737	−	2.35104i
$657$	4.00407	−	6.93524i	0.156213	−	0.270570i
$658$	−17.1371	−	3.64261i	−0.668075	−	0.142004i
$659$	−4.42186	+	13.6091i	−0.172251	+	0.530135i	−0.999497	−	0.0317052i	$-0.989906\pi$
$659$	−4.42186	+	13.6091i	−0.172251	+	0.530135i	0.827246	+	0.561840i	$0.189906\pi$
$660$		0			0
$661$	2.03732	−	19.3838i	0.0792424	−	0.753941i	−0.880687	−	0.473699i	$-0.842919\pi$
$661$	2.03732	−	19.3838i	0.0792424	−	0.753941i	0.959929	−	0.280242i	$-0.0904148\pi$
$662$	−15.0591	+	16.7248i	−0.585288	+	0.650028i
$663$	14.4581	−	6.43718i	0.561507	−	0.249999i
$664$	−70.7263	−	31.4894i	−2.74471	−	1.22202i
$665$		0			0
$666$	17.7917	−	12.9264i	0.689415	−	0.500889i
$667$	1.51167	−	1.09829i	0.0585321	−	0.0425260i
$668$	−18.4634	−	20.5057i	−0.714371	−	0.793390i
$669$	31.2288	+	13.9039i	1.20737	+	0.537557i
$670$		0			0
$671$	12.7096	−	14.1155i	0.490650	−	0.544923i
$672$	0.637221	−	6.06275i	0.0245813	−	0.233876i
$673$	−10.2436	+	2.17735i	−0.394863	+	0.0839307i	−0.401064	−	0.916050i	$-0.631359\pi$
$673$	−10.2436	+	2.17735i	−0.394863	+	0.0839307i	0.00620110	+	0.999981i	$0.498026\pi$
$674$	−18.1358	+	55.8162i	−0.698564	+	2.14996i
$675$		0			0
$676$	−57.8626	+	100.221i	−2.22548	+	3.85465i
$677$	−14.1405	−	24.4920i	−0.543462	−	0.941304i	−0.998702	−	0.0509354i	$-0.983780\pi$
$677$	−14.1405	−	24.4920i	−0.543462	−	0.941304i	0.455240	−	0.890369i	$-0.349554\pi$
$678$	−14.5987	−	44.9302i	−0.560660	−	1.72553i
$679$	−0.473190	−	4.50210i	−0.0181594	−	0.172775i
$680$		0			0
$681$	43.4006			1.66312
$682$	43.5165	−	46.4000i	1.66633	−	1.77675i
$683$	−2.92111			−0.111773			−0.0558866	−	0.998437i	$-0.517799\pi$
$683$	−2.92111			−0.111773			−0.0558866	+	0.998437i	$0.517799\pi$
$684$	−1.56613	−	1.13786i	−0.0598826	−	0.0435072i
$685$		0			0
$686$	−8.64592	−	26.6094i	−0.330103	−	1.01595i
$687$	0.142042	+	0.246023i	0.00541923	+	0.00938638i
$688$	34.5211	−	59.7924i	1.31611	−	2.27956i
$689$	−32.8768	−	6.98817i	−1.25250	−	0.266228i
$690$		0			0
$691$	22.1035	−	4.69823i	0.840855	−	0.178729i	0.232701	−	0.972548i	$-0.425244\pi$
$691$	22.1035	−	4.69823i	0.840855	−	0.178729i	0.608154	+	0.793819i	$0.291910\pi$
$692$	1.14473	−	10.8913i	0.0435160	−	0.414027i
$693$	−1.96063	+	2.17750i	−0.0744782	+	0.0827164i
$694$	44.3268	−	19.7356i	1.68262	−	0.749152i
$695$		0			0
$696$	−6.07050	−	6.74198i	−0.230102	−	0.255554i
$697$	11.7798	−	8.55852i	0.446191	−	0.324177i
$698$	−66.4723	+	48.2949i	−2.51601	+	1.82799i
$699$	11.2948	+	12.5441i	0.427207	+	0.474461i
$700$		0			0
$701$	−25.8525	+	11.5103i	−0.976436	+	0.434737i	−0.831999	−	0.554777i	$-0.812804\pi$
$701$	−25.8525	+	11.5103i	−0.976436	+	0.434737i	−0.144437	+	0.989514i	$0.546137\pi$
$702$	45.8940	−	50.9704i	1.73216	−	1.92376i
$703$	0.679898	−	6.46880i	0.0256428	−	0.243975i
$704$	−12.8375	+	2.72871i	−0.483833	+	0.102842i
$705$		0			0
$706$	−31.3471	−	6.66303i	−1.17976	−	0.250766i
$707$	−0.953773	+	1.65198i	−0.0358703	+	0.0621292i
$708$	−22.5141	−	38.9955i	−0.846131	−	1.46554i
$709$	−4.96572	−	15.2829i	−0.186492	−	0.573962i	0.813479	−	0.581594i	$-0.197571\pi$
$709$	−4.96572	−	15.2829i	−0.186492	−	0.573962i	−0.999971	+	0.00763191i	$0.997571\pi$
$710$		0			0
$711$	−0.800780	−	0.581801i	−0.0300316	−	0.0218192i
$712$	21.8261			0.817969
$713$	3.80837	+	12.5847i	0.142625	+	0.471303i
$714$	5.28675			0.197851
$715$		0			0
$716$	5.42636	+	51.6283i	0.202792	+	1.92944i
$717$	6.28024	+	19.3286i	0.234540	+	0.721840i
$718$	8.07470	+	13.9858i	0.301345	+	0.521945i
$719$	−14.2609	+	24.7007i	−0.531843	+	0.921179i	0.467466	+	0.884011i	$0.345167\pi$
$719$	−14.2609	+	24.7007i	−0.531843	+	0.921179i	−0.999309	+	0.0371679i	$0.988166\pi$
$720$		0			0
$721$	1.69053	−	5.20291i	0.0629585	−	0.193766i
$722$	45.9904	−	9.77556i	1.71159	−	0.363809i
$723$	1.10474	−	10.5109i	0.0410857	−	0.390904i
$724$	40.9650	−	45.4962i	1.52245	−	1.69085i
$725$		0			0
$726$	−42.8098	−	19.0602i	−1.58882	−	0.707389i
$727$	−3.67677	−	4.08346i	−0.136364	−	0.151447i	0.671095	−	0.741371i	$-0.265824\pi$
$727$	−3.67677	−	4.08346i	−0.136364	−	0.151447i	−0.807459	+	0.589924i	$0.799158\pi$
$728$	−25.1074	+	18.2416i	−0.930540	+	0.676077i
$729$	−13.6817	+	9.94036i	−0.506731	+	0.368162i
$730$		0			0
$731$	13.2082	+	5.88068i	0.488524	+	0.217505i
$732$	32.2749	−	14.3697i	1.19291	−	0.531119i
$733$	−27.4651	+	30.5031i	−1.01445	+	1.12666i	−0.0225327	+	0.999746i	$0.507173\pi$
$733$	−27.4651	+	30.5031i	−1.01445	+	1.12666i	−0.991914	+	0.126911i	$0.959494\pi$
$734$	5.76407	−	54.8415i	0.212756	−	2.02424i
$735$		0			0
$736$	−2.74241	+	8.44026i	−0.101086	+	0.311112i
$737$	−31.2588	−	6.64426i	−1.15143	−	0.244745i
$738$	−10.9609	+	18.9848i	−0.403476	+	0.698842i
$739$	6.42893	+	11.1352i	0.236492	+	0.409616i	0.959705	−	0.281009i	$-0.0906689\pi$
$739$	6.42893	+	11.1352i	0.236492	+	0.409616i	−0.723213	+	0.690625i	$0.757336\pi$
$740$		0			0
$741$	0.736652	+	7.00878i	0.0270616	+	0.257474i
$742$	−9.08340	−	6.59948i	−0.333462	−	0.242274i
$743$	−5.08104			−0.186405			−0.0932026	−	0.995647i	$-0.529710\pi$
$743$	−5.08104			−0.186405			−0.0932026	+	0.995647i	$0.529710\pi$
$744$	58.8350	−	24.7764i	2.15700	−	0.908346i
$745$		0			0
$746$	9.42959	+	6.85100i	0.345242	+	0.250833i
$747$	1.06050	+	10.0899i	0.0388015	+	0.369172i
$748$	7.87865	+	24.2480i	0.288072	+	0.886595i
$749$	−1.93536	−	3.35213i	−0.0707164	−	0.122484i
$750$		0			0
$751$	6.81891	+	1.44940i	0.248825	+	0.0528895i	0.330636	−	0.943758i	$-0.392737\pi$
$751$	6.81891	+	1.44940i	0.248825	+	0.0528895i	−0.0818103	+	0.996648i	$0.526070\pi$
$752$	15.9057	−	48.9527i	0.580021	−	1.78512i
$753$	−21.9629	+	4.66836i	−0.800373	+	0.170125i
$754$	−1.31157	+	12.4788i	−0.0477646	+	0.454450i
$755$		0			0
$756$	14.3315	−	6.38081i	0.521233	−	0.232068i
$757$	13.3881	+	5.96076i	0.486598	+	0.216648i	0.635346	−	0.772228i	$-0.280858\pi$
$757$	13.3881	+	5.96076i	0.486598	+	0.216648i	−0.148748	+	0.988875i	$0.547524\pi$
$758$	−24.3525	−	27.0461i	−0.884521	−	0.982360i
$759$	16.8354	−	12.2316i	0.611085	−	0.443979i
$760$		0			0
$761$	21.0905	+	23.4234i	0.764530	+	0.849097i	0.992202	−	0.124641i	$-0.0397779\pi$
$761$	21.0905	+	23.4234i	0.764530	+	0.849097i	−0.227672	+	0.973738i	$0.573111\pi$
$762$	54.8589	+	24.4248i	1.98733	+	0.884816i
$763$	−0.452923	+	0.201654i	−0.0163969	+	0.00730038i
$764$	0.817880	−	0.908348i	0.0295899	−	0.0328629i
$765$		0			0
$766$	50.2619	−	10.6835i	1.81604	−	0.386011i
$767$	−10.3833	+	31.9566i	−0.374921	+	1.15389i
$768$	−59.8469	−	12.7209i	−2.15954	−	0.459024i
$769$	−21.8896	+	37.9139i	−0.789358	+	1.36721i	0.137002	+	0.990571i	$0.456253\pi$
$769$	−21.8896	+	37.9139i	−0.789358	+	1.36721i	−0.926361	+	0.376638i	$0.877080\pi$
$770$		0			0
$771$	11.3885	+	35.0503i	0.410148	+	1.26231i
$772$	10.9826	+	104.492i	0.395273	+	3.76077i
$773$	19.6555	+	14.2806i	0.706960	+	0.513637i	0.882192	−	0.470891i	$-0.156067\pi$
$773$	19.6555	+	14.2806i	0.706960	+	0.513637i	−0.175231	+	0.984527i	$0.556067\pi$
$774$	−21.7676			−0.782421
$775$		0			0
$776$	31.9970			1.14862
$777$	−14.8147	−	10.7635i	−0.531474	−	0.386138i
$778$	−1.64455	−	15.6469i	−0.0589600	−	0.560967i
$779$	2.00359	+	6.16640i	0.0717859	+	0.220934i
$780$		0			0
$781$	−6.83869	+	11.8450i	−0.244708	+	0.423846i
$782$	−7.52812	−	1.60015i	−0.269205	−	0.0572213i
$783$	1.05751	−	3.25469i	0.0377925	−	0.116313i
$784$	38.0938	−	8.09709i	1.36049	−	0.289182i
$785$		0			0
$786$	−54.3871	+	60.4030i	−1.93992	+	2.15450i
$787$	−13.2640	+	5.90552i	−0.472811	+	0.210509i	−0.629287	−	0.777173i	$-0.716653\pi$
$787$	−13.2640	+	5.90552i	−0.472811	+	0.210509i	0.156476	+	0.987682i	$0.449986\pi$
$788$	50.5544	+	22.5083i	1.80093	+	0.801824i
$789$	6.77825	+	7.52801i	0.241312	+	0.268004i
$790$		0			0
$791$	−6.52346	+	4.73957i	−0.231947	+	0.168520i
$792$	−13.8581	−	15.3910i	−0.492426	−	0.546895i
$793$	−24.0844	−	10.7230i	−0.855261	−	0.380787i
$794$	72.6873	−	32.3625i	2.57957	−	1.14850i
$795$		0			0
$796$	−4.90555	+	46.6732i	−0.173873	+	1.65429i
$797$	−21.3661	+	4.54149i	−0.756824	+	0.160868i	−0.570135	−	0.821551i	$-0.693109\pi$
$797$	−21.3661	+	4.54149i	−0.756824	+	0.160868i	−0.186689	+	0.982419i	$0.559776\pi$
$798$	−0.727472	+	2.23893i	−0.0257522	+	0.0792572i
$799$	10.5432	+	2.24103i	0.372993	+	0.0792821i
$800$		0			0
$801$	−1.43011	−	2.47703i	−0.0505306	−	0.0875215i
$802$	1.61236	+	4.96233i	0.0569344	+	0.175226i
$803$	−4.90919	−	46.7078i	−0.173242	−	1.64828i
$804$	−48.0881	−	34.9380i	−1.69594	−	1.23217i
$805$		0			0
$806$	−79.9147	−	37.5424i	−2.81488	−	1.32238i
$807$	−2.23349			−0.0786224
$808$	−10.9079	−	7.92505i	−0.383739	−	0.278802i
$809$	−2.04937	−	19.4984i	−0.0720520	−	0.685529i	−0.969614	−	0.244640i	$-0.921330\pi$
$809$	−2.04937	−	19.4984i	−0.0720520	−	0.685529i	0.897562	−	0.440888i	$-0.145337\pi$
$810$		0			0
$811$	−0.447413	−	0.774942i	−0.0157108	−	0.0272119i	0.858063	−	0.513544i	$-0.171668\pi$
$811$	−0.447413	−	0.774942i	−0.0157108	−	0.0272119i	−0.873774	+	0.486332i	$0.838334\pi$
$812$	−1.43498	+	2.48546i	−0.0503579	+	0.0872224i
$813$	23.8944	+	5.07891i	0.838013	+	0.178125i
$814$	39.8554	−	122.662i	1.39693	−	4.29931i
$815$		0			0
$816$	−1.62353	+	15.4468i	−0.0568348	+	0.540747i
$817$	−4.30795	+	4.78447i	−0.150716	+	0.167387i
$818$	55.0186	−	24.4959i	1.92368	−	0.856477i
$819$	3.71533	+	1.65417i	0.129824	+	0.0578014i
$820$		0			0
$821$	30.2838	−	22.0025i	1.05691	−	0.767892i	0.0833978	−	0.996516i	$-0.473423\pi$
$821$	30.2838	−	22.0025i	1.05691	−	0.767892i	0.973515	+	0.228624i	$0.0734228\pi$
$822$	−11.5963	+	8.42522i	−0.404468	+	0.293863i
$823$	20.4074	+	22.6647i	0.711356	+	0.790041i	0.985141	−	0.171750i	$-0.0549421\pi$
$823$	20.4074	+	22.6647i	0.711356	+	0.790041i	−0.273784	+	0.961791i	$0.588275\pi$
$824$	35.3247	+	15.7276i	1.23059	+	0.547896i
$825$		0			0
$826$	−7.51055	+	8.34131i	−0.261325	+	0.290231i
$827$	2.77030	−	26.3577i	0.0963329	−	0.916546i	−0.834477	−	0.551043i	$-0.814230\pi$
$827$	2.77030	−	26.3577i	0.0963329	−	0.916546i	0.930810	−	0.365504i	$-0.119103\pi$
$828$	7.76059	−	1.64956i	0.269699	−	0.0573263i
$829$	−11.3256	+	34.8565i	−0.393354	+	1.21062i	0.536883	+	0.843657i	$0.319602\pi$
$829$	−11.3256	+	34.8565i	−0.393354	+	1.21062i	−0.930236	+	0.366961i	$0.880398\pi$
$830$		0			0
$831$	21.1903	−	36.7027i	0.735084	−	1.27320i
$832$	9.10815	+	15.7758i	0.315768	+	0.546927i
$833$	2.52018	+	7.75632i	0.0873191	+	0.268740i
$834$	10.9628	+	104.304i	0.379611	+	3.61176i
$835$		0			0
$836$	−11.3531			−0.392656
$837$	19.1907	+	14.5471i	0.663326	+	0.502822i
$838$	−76.9815			−2.65928
$839$	−1.83042	−	1.32988i	−0.0631933	−	0.0459126i	0.555740	−	0.831356i	$-0.312435\pi$
$839$	−1.83042	−	1.32988i	−0.0631933	−	0.0459126i	−0.618933	+	0.785443i	$0.712435\pi$
$840$		0			0
$841$	−8.76803	−	26.9852i	−0.302346	−	0.930525i
$842$	−28.2728	−	48.9699i	−0.974345	−	1.68762i
$843$	−30.2244	+	52.3503i	−1.04098	+	1.80304i
$844$	18.6860	+	3.97183i	0.643198	+	0.136716i
$845$		0			0
$846$	−15.8734	+	3.37400i	−0.545739	+	0.116001i
$847$	−0.836057	+	7.95455i	−0.0287273	+	0.273322i
$848$	22.0718	−	24.5132i	0.757949	−	0.841788i
$849$	32.1733	−	14.3245i	1.10419	−	0.491615i
$850$		0			0
$851$	17.8377	+	19.8108i	0.611469	+	0.679106i
$852$	−20.5813	+	14.9532i	−0.705103	+	0.512287i
$853$	−5.35391	+	3.88984i	−0.183314	+	0.133186i	−0.675658	−	0.737215i	$-0.736140\pi$
$853$	−5.35391	+	3.88984i	−0.183314	+	0.133186i	0.492344	+	0.870401i	$0.336140\pi$
$854$	−5.89281	−	6.54462i	−0.201648	−	0.223952i
$855$		0			0
$856$	24.9936	−	11.1279i	0.854265	−	0.380343i
$857$	25.2061	−	27.9942i	0.861023	−	0.956263i	−0.138395	−	0.990377i	$-0.544194\pi$
$857$	25.2061	−	27.9942i	0.861023	−	0.956263i	0.999418	+	0.0341142i	$0.0108610\pi$
$858$	−14.6069	+	138.975i	−0.498671	+	4.74454i
$859$	−16.0689	+	3.41555i	−0.548264	+	0.116537i	−0.473712	−	0.880680i	$-0.657086\pi$
$859$	−16.0689	+	3.41555i	−0.548264	+	0.116537i	−0.0745524	+	0.997217i	$0.523753\pi$
$860$		0			0
$861$	17.8548	+	3.79516i	0.608491	+	0.129339i
$862$	20.7521	−	35.9437i	0.706820	−	1.22425i
$863$	12.8552	+	22.2659i	0.437598	+	0.757941i	0.997504	−	0.0706147i	$-0.0224961\pi$
$863$	12.8552	+	22.2659i	0.437598	+	0.757941i	−0.559906	+	0.828556i	$0.689163\pi$
$864$	5.02269	+	15.4582i	0.170875	+	0.525900i
$865$		0			0
$866$	61.8156	+	44.9117i	2.10058	+	1.52616i
$867$	29.7708			1.01107
$868$	−13.2058	−	15.2792i	−0.448233	−	0.518610i
$869$	−5.80497			−0.196920
$870$		0			0
$871$	4.63644	+	44.1128i	0.157100	+	1.49471i
$872$	−1.08289	−	3.33280i	−0.0366714	−	0.112863i
$873$	−2.09654	−	3.63131i	−0.0709571	−	0.122901i
$874$	1.71355	−	2.96796i	0.0579618	−	0.100393i
$875$		0			0
$876$	26.9942	−	83.0795i	0.912048	−	2.80699i
$877$	−17.1239	+	3.63980i	−0.578234	+	0.122907i	−0.487739	−	0.872989i	$-0.662178\pi$
$877$	−17.1239	+	3.63980i	−0.578234	+	0.122907i	−0.0904951	+	0.995897i	$0.528845\pi$
$878$	4.34498	−	41.3397i	0.146636	−	1.39515i
$879$	−15.2160	+	16.8991i	−0.513223	+	0.569992i
$880$		0			0
$881$	−8.66292	−	3.85698i	−0.291861	−	0.129945i	0.255583	−	0.966787i	$-0.417733\pi$
$881$	−8.66292	−	3.85698i	−0.291861	−	0.129945i	−0.547444	+	0.836842i	$0.684399\pi$
$882$	−8.21593	−	9.12471i	−0.276645	−	0.307245i
$883$	17.9126	−	13.0142i	0.602806	−	0.437964i	−0.244068	−	0.969758i	$-0.578482\pi$
$883$	17.9126	−	13.0142i	0.602806	−	0.437964i	0.846874	+	0.531794i	$0.178482\pi$
$884$	28.6292	−	20.8004i	0.962905	−	0.699592i
$885$		0			0
$886$	58.0865	+	25.8618i	1.95145	+	0.868843i
$887$	29.2198	−	13.0095i	0.981104	−	0.436816i	0.147430	−	0.989072i	$-0.452900\pi$
$887$	29.2198	−	13.0095i	0.981104	−	0.436816i	0.833674	+	0.552257i	$0.186233\pi$
$888$	86.6072	−	96.1871i	2.90635	−	3.22783i
$889$	1.07137	−	10.1934i	0.0359326	−	0.341876i
$890$		0			0
$891$	15.0303	−	46.2585i	0.503534	−	1.54972i
$892$	74.7651	+	15.8918i	2.50332	+	0.532097i
$893$	−2.39986	+	4.15667i	−0.0803081	+	0.139098i
$894$	−19.3241	−	33.4703i	−0.646294	−	1.11941i
$895$		0			0
$896$	1.29213	+	12.2938i	0.0431671	+	0.410707i
$897$	−23.3671	−	16.9772i	−0.780205	−	0.566852i
$898$	6.57462			0.219398
$899$	−4.40453	−	0.0894351i	−0.146899	−	0.00298283i
$900$		0			0
$901$	5.58836	+	4.06018i	0.186175	+	0.135264i
$902$	13.4386	+	127.860i	0.447458	+	4.25728i
$903$	5.60103	+	17.2382i	0.186391	+	0.573651i
$904$	−28.4970	−	49.3582i	−0.947795	−	1.64163i
$905$		0			0
$906$	−10.6246	−	2.25833i	−0.352979	−	0.0750280i
$907$	10.3373	−	31.8148i	0.343243	−	1.05639i	−0.619275	−	0.785174i	$-0.712573\pi$
$907$	10.3373	−	31.8148i	0.343243	−	1.05639i	0.962518	−	0.271219i	$-0.0874266\pi$
$908$	94.9228	−	20.1765i	3.15012	−	0.669579i
$909$	−0.184689	+	1.75720i	−0.00612576	+	0.0582827i
$910$		0			0
$911$	−40.9176	+	18.2177i	−1.35566	+	0.603579i	−0.950517	−	0.310673i	$-0.899445\pi$
$911$	−40.9176	+	18.2177i	−1.35566	+	0.603579i	−0.405144	+	0.914253i	$0.632779\pi$
$912$	−6.31830	−	2.81309i	−0.209220	−	0.0931507i
$913$	39.8134	+	44.2173i	1.31763	+	1.46338i
$914$	−19.0765	+	13.8599i	−0.630993	+	0.458443i
$915$		0			0
$916$	0.425037	+	0.472051i	0.0140436	+	0.0155970i
$917$	12.6737	+	5.64270i	0.418523	+	0.186338i
$918$	−12.8771	+	5.73324i	−0.425007	+	0.189225i
$919$	−19.0879	+	21.1993i	−0.629652	+	0.699300i	−0.970577	−	0.240791i	$-0.922593\pi$
$919$	−19.0879	+	21.1993i	−0.629652	+	0.699300i	0.340925	+	0.940091i	$0.389260\pi$
$920$		0			0
$921$	22.3139	−	4.74297i	0.735268	−	0.156286i
$922$	−13.7244	+	42.2393i	−0.451988	+	1.39108i
$923$	18.5690	+	3.94697i	0.611208	+	0.129916i
$924$	−15.9813	+	27.6803i	−0.525745	+	0.910616i
$925$		0			0
$926$	−4.52410	−	13.9237i	−0.148671	−	0.457563i
$927$	−0.529671	−	5.03949i	−0.0173967	−	0.165518i
$928$	−2.40560	−	1.74777i	−0.0789678	−	0.0573735i
$929$	−47.0642			−1.54413			−0.772064	−	0.635545i	$-0.780775\pi$
$929$	−47.0642			−1.54413			−0.772064	+	0.635545i	$0.780775\pi$
$930$		0			0
$931$	−3.63157			−0.119020
$932$	30.5347	+	22.1847i	1.00020	+	0.726685i
$933$	−0.169187	−	1.60970i	−0.00553893	−	0.0526994i
$934$	−6.29584	−	19.3766i	−0.206006	−	0.634022i
$935$		0			0
$936$	−14.3729	+	24.8946i	−0.469794	+	0.813707i
$937$	−30.1300	−	6.40434i	−0.984306	−	0.209221i	−0.312476	−	0.949926i	$-0.601158\pi$
$937$	−30.1300	−	6.40434i	−0.984306	−	0.209221i	−0.671830	+	0.740705i	$0.734492\pi$
$938$	−4.57867	+	14.0917i	−0.149499	+	0.460110i
$939$	−20.1330	+	4.27940i	−0.657015	+	0.139653i
$940$		0			0
$941$	1.90260	−	2.11305i	0.0620230	−	0.0688835i	−0.711335	−	0.702853i	$-0.751909\pi$
$941$	1.90260	−	2.11305i	0.0620230	−	0.0688835i	0.773358	+	0.633970i	$0.218576\pi$
$942$	23.3732	−	10.4064i	0.761541	−	0.339060i
$943$	−24.2759	−	10.8083i	−0.790531	−	0.351967i
$944$	−22.0652	−	24.5059i	−0.718161	−	0.797599i
$945$		0			0
$946$	−103.279	+	75.0367i	−3.35790	+	2.43965i
$947$	−6.97644	−	7.74812i	−0.226704	−	0.251780i	0.619052	−	0.785350i	$-0.287517\pi$
$947$	−6.97644	−	7.74812i	−0.226704	−	0.251780i	−0.845756	+	0.533570i	$0.820850\pi$
$948$	−9.86375	−	4.39162i	−0.320360	−	0.142633i
$949$	−59.5509	+	26.5138i	−1.93310	+	0.860673i
$950$		0			0
$951$	−6.31623	+	60.0949i	−0.204818	+	1.94871i
$952$	6.23863	−	1.32606i	0.202195	−	0.0429779i
$953$	14.6425	−	45.0649i	0.474316	−	1.45979i	−0.372562	−	0.928007i	$-0.621521\pi$
$953$	14.6425	−	45.0649i	0.474316	−	1.45979i	0.846878	−	0.531788i	$-0.178479\pi$
$954$	−10.1725	−	2.16223i	−0.329347	−	0.0700048i
$955$		0			0
$956$	22.7213	+	39.3545i	0.734861	+	1.27282i
$957$	2.15459	+	6.63114i	0.0696479	+	0.214354i
$958$	−2.39714	−	22.8072i	−0.0774480	−	0.736868i
$959$	1.97929	+	1.43804i	0.0639145	+	0.0464366i
$960$		0			0
$961$	10.7684	−	29.0696i	0.347369	−	0.937728i
$962$	−179.014			−5.77164
$963$	−2.90055	−	2.10737i	−0.0934690	−	0.0679092i
$964$	−2.47018	−	23.5022i	−0.0795593	−	0.756956i
$965$		0			0
$966$	−4.82418	−	8.35572i	−0.155215	−	0.268841i
$967$	−11.3526	+	19.6633i	−0.365075	+	0.632329i	−0.988788	−	0.149325i	$-0.952290\pi$
$967$	−11.3526	+	19.6633i	−0.365075	+	0.632329i	0.623713	+	0.781653i	$0.285623\pi$
$968$	−55.2986	−	11.7541i	−1.77736	−	0.377790i
$969$	0.447561	−	1.37745i	0.0143777	−	0.0442501i
$970$		0			0
$971$	5.75452	−	54.7506i	0.184671	−	1.75703i	−0.373803	−	0.927508i	$-0.621947\pi$
$971$	5.75452	−	54.7506i	0.184671	−	1.75703i	0.558475	−	0.829522i	$-0.311387\pi$
$972$	22.8241	−	25.3487i	0.732083	−	0.813060i
$973$	16.3533	−	7.28096i	0.524263	−	0.233417i
$974$	−94.6747	−	42.1519i	−3.03357	−	1.35063i
$975$		0			0
$976$	20.9317	−	15.2078i	0.670008	−	0.486790i
$977$	11.0724	−	8.04457i	0.354238	−	0.257369i	−0.396407	−	0.918075i	$-0.629743\pi$
$977$	11.0724	−	8.04457i	0.354238	−	0.257369i	0.750645	+	0.660706i	$0.229743\pi$
$978$	43.4692	+	48.2774i	1.38999	+	1.54374i
$979$	−15.3241	−	6.82273i	−0.489761	−	0.218055i
$980$		0			0
$981$	−0.307282	+	0.341272i	−0.00981077	+	0.0108960i
$982$	−4.98178	+	47.3985i	−0.158975	+	1.51255i
$983$	40.3260	−	8.57156i	1.28620	−	0.273390i	0.486443	−	0.873713i	$-0.338294\pi$
$983$	40.3260	−	8.57156i	1.28620	−	0.273390i	0.799758	+	0.600322i	$0.204961\pi$
$984$	−39.8696	+	122.706i	−1.27100	+	3.91172i
$985$		0			0
$986$	1.28935	−	2.23321i	0.0410611	−	0.0711200i
$987$	6.75633	+	11.7023i	0.215056	+	0.372488i
$988$	4.86945	+	14.9866i	0.154918	+	0.476788i
$989$	−2.75812	−	26.2418i	−0.0877032	−	0.834441i
$990$		0			0
$991$	−34.9979			−1.11174			−0.555872	−	0.831268i	$-0.687616\pi$
$991$	−34.9979			−1.11174			−0.555872	+	0.831268i	$0.687616\pi$
$992$	17.1738	−	11.9525i	0.545270	−	0.379492i
$993$	17.3578			0.550833
$994$	5.13038	+	3.72744i	0.162726	+	0.118227i
$995$		0			0
$996$	34.1990	+	105.254i	1.08364	+	3.33509i
$997$	−1.03226	−	1.78793i	−0.0326920	−	0.0566242i	0.849216	−	0.528045i	$-0.177075\pi$
$997$	−1.03226	−	1.78793i	−0.0326920	−	0.0566242i	−0.881908	+	0.471421i	$0.843741\pi$
$998$	−10.0216	+	17.3580i	−0.317230	+	0.549458i
$999$	47.7571	+	10.1511i	1.51097	+	0.321166i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.bl.b.351.1		40
5.2	odd	4		775.2.ck.b.599.10		80
5.3	odd	4		775.2.ck.b.599.1		80
5.4	even	2		155.2.q.b.41.5	✓	40
31.28	even	15	inner	775.2.bl.b.276.1		40
155.28	odd	60		775.2.ck.b.524.10		80
155.59	even	30		155.2.q.b.121.5	yes	40
155.104	odd	30		4805.2.a.z.1.2		20
155.144	even	30		4805.2.a.ba.1.2		20
155.152	odd	60		775.2.ck.b.524.1		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.q.b.41.5	✓	40	5.4	even	2
155.2.q.b.121.5	yes	40	155.59	even	30
775.2.bl.b.276.1		40	31.28	even	15	inner
775.2.bl.b.351.1		40	1.1	even	1	trivial
775.2.ck.b.524.1		80	155.152	odd	60
775.2.ck.b.524.10		80	155.28	odd	60
775.2.ck.b.599.1		80	5.3	odd	4
775.2.ck.b.599.10		80	5.2	odd	4
4805.2.a.z.1.2		20	155.104	odd	30
4805.2.a.ba.1.2		20	155.144	even	30

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:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.bl (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.03762 - 1.48042i) q^{2} +(0.203052 + 1.93191i) q^{3} +(1.34222 + 4.13093i) q^{4} +(2.44628 - 4.23709i) q^{6} +(-0.816826 - 0.173622i) q^{7} +(1.82396 - 5.61358i) q^{8} +(-0.756592 + 0.160819i) q^{9} +(-3.03538 + 3.37113i) q^{11} +(-7.70804 + 3.43184i) q^{12} +(5.75194 + 2.56093i) q^{13} +(1.40735 + 1.56302i) q^{14} +(-4.99902 + 3.63200i) q^{16} +(-0.865839 - 0.961611i) q^{17} +(1.77972 + 0.792384i) q^{18} +(0.526383 - 0.234361i) q^{19} +(0.169563 - 1.61329i) q^{21} +(11.1756 - 2.37545i) q^{22} +(-0.729749 + 2.24594i) q^{23} +(11.2153 + 2.38388i) q^{24} +(-7.92902 - 13.7335i) q^{26} +(1.33653 + 4.11341i) q^{27} +(-0.379142 - 3.60729i) q^{28} +(-0.640127 - 0.465079i) q^{29} +(4.56993 - 3.18053i) q^{31} +3.75801 q^{32} +(-7.12905 - 5.17955i) q^{33} +(0.340664 + 3.24120i) q^{34} +(-1.67985 - 2.90958i) q^{36} +(5.64427 - 9.77616i) q^{37} +(-1.41952 - 0.301728i) q^{38} +(-3.77954 + 11.6322i) q^{39} +(-1.17622 + 11.1910i) q^{41} +(-2.73384 + 3.03624i) q^{42} +(-10.2075 + 4.54466i) q^{43} +(-18.0001 - 8.01414i) q^{44} +(4.81187 - 3.49603i) q^{46} +(-6.73909 + 4.89623i) q^{47} +(-8.03174 - 8.92015i) q^{48} +(-5.75776 - 2.56352i) q^{49} +(1.68193 - 1.86798i) q^{51} +(-2.85865 + 27.1982i) q^{52} +(-5.22161 + 1.10989i) q^{53} +(3.36622 - 10.3602i) q^{54} +(-2.46450 + 4.26864i) q^{56} +(0.559646 + 0.969336i) q^{57} +(0.615823 + 1.89531i) q^{58} +(0.557834 + 5.30744i) q^{59} -4.18717 q^{61} +(-14.0203 - 0.284685i) q^{62} +0.645926 q^{63} +(2.34063 + 1.70057i) q^{64} +(6.85838 + 21.1079i) q^{66} +(3.52238 + 6.10094i) q^{67} +(2.81020 - 4.86742i) q^{68} +(-4.48712 - 0.953766i) q^{69} +(2.94921 - 0.626874i) q^{71} +(-0.477228 + 4.54052i) q^{72} +(-6.92763 + 7.69391i) q^{73} +(-25.9736 + 11.5642i) q^{74} +(1.67465 + 1.85989i) q^{76} +(3.06468 - 2.22662i) q^{77} +(24.9218 - 18.1067i) q^{78} +(0.856267 + 0.950981i) q^{79} +(-9.79521 + 4.36111i) q^{81} +(18.9640 - 21.0616i) q^{82} +(1.37104 - 13.0446i) q^{83} +(6.89197 - 1.46493i) q^{84} +(27.5269 + 5.85103i) q^{86} +(0.768511 - 1.33110i) q^{87} +(13.3877 + 23.1882i) q^{88} +(1.14268 + 3.51681i) q^{89} +(-4.25370 - 3.09050i) q^{91} -10.2573 q^{92} +(7.07242 + 8.18286i) q^{93} +20.9802 q^{94} +(0.763071 + 7.26013i) q^{96} +(1.67517 + 5.15563i) q^{97} +(7.93704 + 13.7473i) q^{98} +(1.75440 - 3.03871i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{2} - 3 q^{3} - 2 q^{4} - 12 q^{6} + 2 q^{7} + 31 q^{8} + 6 q^{9} + 16 q^{11} + q^{12} - 2 q^{13} - 10 q^{14} - 16 q^{16} - 4 q^{17} - 37 q^{18} - 9 q^{19} - 24 q^{21} + 2 q^{22} + 4 q^{23}+ \cdots + 17 q^{99}+O(q^{100}) \) 40 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 - 12 * q^6 + 2 * q^7 + 31 * q^8 + 6 * q^9 + 16 * q^11 + q^12 - 2 * q^13 - 10 * q^14 - 16 * q^16 - 4 * q^17 - 37 * q^18 - 9 * q^19 - 24 * q^21 + 2 * q^22 + 4 * q^23 + 110 * q^24 - 4 * q^26 + 9 * q^27 - 38 * q^28 - 22 * q^29 - 6 * q^31 + 60 * q^32 - 9 * q^33 - 16 * q^34 - q^36 + 38 * q^37 + 32 * q^38 - 55 * q^39 - 24 * q^41 + 68 * q^42 - 26 * q^43 - 52 * q^44 - 50 * q^46 - 4 * q^47 - 105 * q^48 + 93 * q^49 - 42 * q^51 - 15 * q^52 - 13 * q^53 + 102 * q^54 + 5 * q^56 + 36 * q^57 + 37 * q^58 + 31 * q^59 + 68 * q^61 - 47 * q^62 + 10 * q^63 - 23 * q^64 + 2 * q^67 + 28 * q^68 - 48 * q^69 - 30 * q^71 - 39 * q^72 - 25 * q^73 + 50 * q^74 + 14 * q^76 + 64 * q^77 + 22 * q^78 + 49 * q^79 + 25 * q^81 + 66 * q^82 + 18 * q^83 - 18 * q^84 + 163 * q^86 + 36 * q^87 + 124 * q^88 + 4 * q^89 - 37 * q^91 - 110 * q^92 - 7 * q^93 - 94 * q^94 + 22 * q^96 - 46 * q^97 + 13 * q^98 + 17 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more