LMFDB - Embedded newform 961.2.g.f.732.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,2,Mod(235,961)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(961, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([26]))

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

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

chi := DirichletCharacter("961.235");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$961 = 31^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	961.g (of order $15$ , degree $8$ , 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:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1$ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			732.1
Root			$0.669131 - 0.743145i$ of defining polynomial
Character	$\chi$	$=$	961.732
Dual form			961.2.g.f.235.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.363271i) q^{2} +(-0.913545 - 0.406737i) q^{3} +(-0.500000 - 1.53884i) q^{4} +(1.30902 - 2.26728i) q^{5} +(-0.309017 - 0.535233i) q^{6} +(2.00739 - 2.22943i) q^{7} +(0.690983 - 2.12663i) q^{8} +(-1.33826 - 1.48629i) q^{9} +(1.47815 - 0.658114i) q^{10} +(0.747238 + 0.158830i) q^{11} +(-0.169131 + 1.60917i) q^{12} +(-0.507392 - 4.82751i) q^{13} +(1.81359 - 0.385489i) q^{14} +(-2.11803 + 1.53884i) q^{15} +(-1.50000 + 1.08981i) q^{16} +(-0.230909 + 0.0490813i) q^{17} +(-0.129204 - 1.22930i) q^{18} +(-0.522642 + 4.97261i) q^{19} +(-4.14350 - 0.880728i) q^{20} +(-2.74064 + 1.22021i) q^{21} +(0.315921 + 0.350865i) q^{22} +(-1.69098 + 5.20431i) q^{23} +(-1.49622 + 1.66172i) q^{24} +(-0.927051 - 1.60570i) q^{25} +(1.50000 - 2.59808i) q^{26} +(1.54508 + 4.75528i) q^{27} +(-4.43444 - 1.97434i) q^{28} +(6.97214 + 5.06555i) q^{29} -1.61803 q^{30} -5.61803 q^{32} +(-0.618034 - 0.449028i) q^{33} +(-0.133284 - 0.0593421i) q^{34} +(-2.42705 - 7.46969i) q^{35} +(-1.61803 + 2.80252i) q^{36} +(-0.118034 - 0.204441i) q^{37} +(-2.06773 + 2.29644i) q^{38} +(-1.50000 + 4.61653i) q^{39} +(-3.91716 - 4.35045i) q^{40} +(5.91259 - 2.63245i) q^{41} +(-1.81359 - 0.385489i) q^{42} +(0.482716 - 4.59274i) q^{43} +(-0.129204 - 1.22930i) q^{44} +(-5.12165 + 1.08864i) q^{45} +(-2.73607 + 1.98787i) q^{46} +(2.73607 - 1.98787i) q^{47} +(1.81359 - 0.385489i) q^{48} +(-0.209057 - 1.98904i) q^{49} +(0.119779 - 1.13962i) q^{50} +(0.230909 + 0.0490813i) q^{51} +(-7.17508 + 3.19455i) q^{52} +(-8.50345 - 9.44404i) q^{53} +(-0.954915 + 2.93893i) q^{54} +(1.33826 - 1.48629i) q^{55} +(-3.35410 - 5.80948i) q^{56} +(2.50000 - 4.33013i) q^{57} +(1.64590 + 5.06555i) q^{58} +(8.65323 + 3.85266i) q^{59} +(3.42705 + 2.48990i) q^{60} -6.94427 q^{61} -6.00000 q^{63} +(0.190983 + 0.138757i) q^{64} +(-11.6095 - 5.16889i) q^{65} +(-0.145898 - 0.449028i) q^{66} +(2.11803 - 3.66854i) q^{67} +(0.190983 + 0.330792i) q^{68} +(3.66157 - 4.06659i) q^{69} +(1.50000 - 4.61653i) q^{70} +(0.0603355 + 0.0670093i) q^{71} +(-4.08550 + 1.81898i) q^{72} +(8.37520 + 1.78020i) q^{73} +(0.0152505 - 0.145099i) q^{74} +(0.193806 + 1.84395i) q^{75} +(7.91338 - 1.68204i) q^{76} +(1.85410 - 1.34708i) q^{77} +(-2.42705 + 1.76336i) q^{78} +(0.507392 + 4.82751i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(3.91259 + 0.831647i) q^{82} +(-3.73656 + 1.66362i) q^{83} +(3.24803 + 3.60730i) q^{84} +(-0.190983 + 0.587785i) q^{85} +(1.90977 - 2.12101i) q^{86} +(-4.30902 - 7.46344i) q^{87} +(0.854102 - 1.47935i) q^{88} +(-1.97214 - 6.06961i) q^{89} +(-2.95630 - 1.31623i) q^{90} +(-11.7812 - 8.55951i) q^{91} +8.85410 q^{92} +2.09017 q^{94} +(10.5902 + 7.69421i) q^{95} +(5.13233 + 2.28506i) q^{96} +(-1.63525 - 5.03280i) q^{97} +(0.618034 - 1.07047i) q^{98} +(-0.763932 - 1.32317i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$8 q + 4 q^{2} - q^{3} - 4 q^{4} + 6 q^{5} + 2 q^{6} + 3 q^{7} + 10 q^{8} - 2 q^{9} + 3 q^{10} - 8 q^{11} + 3 q^{12} + 9 q^{13} + 9 q^{14} - 8 q^{15} - 12 q^{16} - 7 q^{17} + 4 q^{18} + 5 q^{19} - 3 q^{20}+ \cdots - 24 q^{99}+O(q^{100})$ 8 * q + 4 * q^2 - q^3 - 4 * q^4 + 6 * q^5 + 2 * q^6 + 3 * q^7 + 10 * q^8 - 2 * q^9 + 3 * q^10 - 8 * q^11 + 3 * q^12 + 9 * q^13 + 9 * q^14 - 8 * q^15 - 12 * q^16 - 7 * q^17 + 4 * q^18 + 5 * q^19 - 3 * q^20 - 3 * q^21 - 14 * q^22 - 18 * q^23 + 5 * q^24 + 6 * q^25 + 12 * q^26 - 10 * q^27 - 9 * q^28 + 20 * q^29 - 4 * q^30 - 36 * q^32 + 4 * q^33 + 4 * q^34 - 6 * q^35 - 4 * q^36 + 8 * q^37 + 15 * q^38 - 12 * q^39 + 5 * q^40 + 12 * q^41 - 9 * q^42 - 6 * q^43 + 4 * q^44 - 2 * q^45 - 4 * q^46 + 4 * q^47 + 9 * q^48 + 2 * q^49 + 3 * q^50 + 7 * q^51 - 12 * q^52 + 9 * q^53 - 30 * q^54 + 2 * q^55 + 20 * q^57 + 40 * q^58 + 15 * q^59 + 14 * q^60 + 16 * q^61 - 48 * q^63 + 6 * q^64 - 21 * q^65 - 28 * q^66 + 8 * q^67 + 6 * q^68 - 9 * q^69 + 12 * q^70 - 18 * q^71 - 10 * q^72 + 24 * q^73 + 4 * q^74 - 6 * q^75 + 10 * q^76 - 12 * q^77 - 6 * q^78 - 9 * q^80 + q^81 - 4 * q^82 - 11 * q^83 - 6 * q^84 - 6 * q^85 - 8 * q^86 - 30 * q^87 - 20 * q^88 + 20 * q^89 - 6 * q^90 - 54 * q^91 + 44 * q^92 - 28 * q^94 + 40 * q^95 + 7 * q^96 + 54 * q^97 - 4 * q^98 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$ .

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{15}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	0.500000	+	0.363271i	0.353553	+	0.256872i	0.750358	−	0.661031i	$-0.229881\pi$
$2$	0.500000	+	0.363271i	0.353553	+	0.256872i	−0.396805	+	0.917903i	$0.629881\pi$
$3$	−0.913545	−	0.406737i	−0.527436	−	0.234830i	0.125703	−	0.992068i	$-0.459881\pi$
$3$	−0.913545	−	0.406737i	−0.527436	−	0.234830i	−0.653139	+	0.757238i	$0.726548\pi$
$4$	−0.500000	−	1.53884i	−0.250000	−	0.769421i
$5$	1.30902	−	2.26728i	0.585410	−	1.01396i	−0.409414	−	0.912349i	$-0.634267\pi$
$5$	1.30902	−	2.26728i	0.585410	−	1.01396i	0.994824	−	0.101611i	$-0.0323999\pi$
$6$	−0.309017	−	0.535233i	−0.126156	−	0.218508i
$7$	2.00739	−	2.22943i	0.758723	−	0.842647i	−0.232807	−	0.972523i	$-0.574791\pi$
$7$	2.00739	−	2.22943i	0.758723	−	0.842647i	0.991530	+	0.129876i	$0.0414579\pi$
$8$	0.690983	−	2.12663i	0.244299	−	0.751876i
$9$	−1.33826	−	1.48629i	−0.446087	−	0.495430i
$10$	1.47815	−	0.658114i	0.467431	−	0.208114i
$11$	0.747238	+	0.158830i	0.225301	+	0.0478892i	0.319179	−	0.947695i	$-0.396593\pi$
$11$	0.747238	+	0.158830i	0.225301	+	0.0478892i	−0.0938779	+	0.995584i	$0.529926\pi$
$12$	−0.169131	+	1.60917i	−0.0488238	+	0.464527i
$13$	−0.507392	−	4.82751i	−0.140725	−	1.33891i	−0.805824	−	0.592155i	$-0.798277\pi$
$13$	−0.507392	−	4.82751i	−0.140725	−	1.33891i	0.665099	−	0.746755i	$-0.268389\pi$
$14$	1.81359	−	0.385489i	0.484701	−	0.103026i
$15$	−2.11803	+	1.53884i	−0.546874	+	0.397327i
$16$	−1.50000	+	1.08981i	−0.375000	+	0.272453i
$17$	−0.230909	+	0.0490813i	−0.0560037	+	0.0119040i	−0.235828	−	0.971795i	$-0.575780\pi$
$17$	−0.230909	+	0.0490813i	−0.0560037	+	0.0119040i	0.179825	+	0.983699i	$0.442447\pi$
$18$	−0.129204	−	1.22930i	−0.0304537	−	0.289748i
$19$	−0.522642	+	4.97261i	−0.119902	+	1.14079i	0.754739	+	0.656025i	$0.227763\pi$
$19$	−0.522642	+	4.97261i	−0.119902	+	1.14079i	−0.874642	+	0.484770i	$0.838903\pi$
$20$	−4.14350	−	0.880728i	−0.926515	−	0.196937i
$21$	−2.74064	+	1.22021i	−0.598056	+	0.266272i
$22$	0.315921	+	0.350865i	0.0673545	+	0.0748048i
$23$	−1.69098	+	5.20431i	−0.352594	+	1.08517i	0.604797	+	0.796380i	$0.293254\pi$
$23$	−1.69098	+	5.20431i	−0.352594	+	1.08517i	−0.957391	+	0.288794i	$0.906746\pi$
$24$	−1.49622	+	1.66172i	−0.305415	+	0.339198i
$25$	−0.927051	−	1.60570i	−0.185410	−	0.321140i
$26$	1.50000	−	2.59808i	0.294174	−	0.509525i
$27$	1.54508	+	4.75528i	0.297352	+	0.915155i
$28$	−4.43444	−	1.97434i	−0.838031	−	0.373115i
$29$	6.97214	+	5.06555i	1.29469	+	0.940650i	0.999889	−	0.0149080i	$-0.00474555\pi$
$29$	6.97214	+	5.06555i	1.29469	+	0.940650i	0.294804	+	0.955558i	$0.404746\pi$
$30$	−1.61803			−0.295411
$31$		0			0
$31$		0			0
$32$	−5.61803			−0.993137
$33$	−0.618034	−	0.449028i	−0.107586	−	0.0781657i
$34$	−0.133284	−	0.0593421i	−0.0228581	−	0.0101771i
$35$	−2.42705	−	7.46969i	−0.410246	−	1.26261i
$36$	−1.61803	+	2.80252i	−0.269672	+	0.467086i
$37$	−0.118034	−	0.204441i	−0.0194047	−	0.0336099i	0.856160	−	0.516711i	$-0.172844\pi$
$37$	−0.118034	−	0.204441i	−0.0194047	−	0.0336099i	−0.875565	+	0.483101i	$0.839510\pi$
$38$	−2.06773	+	2.29644i	−0.335430	+	0.372532i
$39$	−1.50000	+	4.61653i	−0.240192	+	0.739236i
$40$	−3.91716	−	4.35045i	−0.619357	−	0.687866i
$41$	5.91259	−	2.63245i	0.923391	−	0.411120i	0.110726	−	0.993851i	$-0.464682\pi$
$41$	5.91259	−	2.63245i	0.923391	−	0.411120i	0.812665	+	0.582731i	$0.198016\pi$
$42$	−1.81359	−	0.385489i	−0.279842	−	0.0594823i
$43$	0.482716	−	4.59274i	0.0736135	−	0.700386i	−0.894020	−	0.448027i	$-0.852127\pi$
$43$	0.482716	−	4.59274i	0.0736135	−	0.700386i	0.967634	−	0.252359i	$-0.0812064\pi$
$44$	−0.129204	−	1.22930i	−0.0194783	−	0.185323i
$45$	−5.12165	+	1.08864i	−0.763490	+	0.162285i
$46$	−2.73607	+	1.98787i	−0.403411	+	0.293095i
$47$	2.73607	−	1.98787i	0.399097	−	0.289961i	−0.370076	−	0.929001i	$-0.620668\pi$
$47$	2.73607	−	1.98787i	0.399097	−	0.289961i	0.769173	+	0.639041i	$0.220668\pi$
$48$	1.81359	−	0.385489i	0.261769	−	0.0556406i
$49$	−0.209057	−	1.98904i	−0.0298653	−	0.284149i
$50$	0.119779	−	1.13962i	0.0169393	−	0.161167i
$51$	0.230909	+	0.0490813i	0.0323338	+	0.00687276i
$52$	−7.17508	+	3.19455i	−0.995004	+	0.443005i
$53$	−8.50345	−	9.44404i	−1.16804	−	1.29724i	−0.946728	−	0.322035i	$-0.895633\pi$
$53$	−8.50345	−	9.44404i	−1.16804	−	1.29724i	−0.221311	−	0.975203i	$-0.571033\pi$
$54$	−0.954915	+	2.93893i	−0.129947	+	0.399937i
$55$	1.33826	−	1.48629i	0.180451	−	0.200411i
$56$	−3.35410	−	5.80948i	−0.448211	−	0.776324i
$57$	2.50000	−	4.33013i	0.331133	−	0.573539i
$58$	1.64590	+	5.06555i	0.216117	+	0.665140i
$59$	8.65323	+	3.85266i	1.12655	+	0.501574i	0.883497	−	0.468438i	$-0.155183\pi$
$59$	8.65323	+	3.85266i	1.12655	+	0.501574i	0.243058	+	0.970012i	$0.421850\pi$
$60$	3.42705	+	2.48990i	0.442430	+	0.321444i
$61$	−6.94427			−0.889123			−0.444561	−	0.895748i	$-0.646640\pi$
$61$	−6.94427			−0.889123			−0.444561	+	0.895748i	$0.646640\pi$
$62$		0			0
$63$	−6.00000			−0.755929
$64$	0.190983	+	0.138757i	0.0238729	+	0.0173447i
$65$	−11.6095	−	5.16889i	−1.43998	−	0.641122i
$66$	−0.145898	−	0.449028i	−0.0179588	−	0.0552715i
$67$	2.11803	−	3.66854i	0.258759	−	0.448184i	−0.707151	−	0.707063i	$-0.750020\pi$
$67$	2.11803	−	3.66854i	0.258759	−	0.448184i	0.965910	+	0.258879i	$0.0833531\pi$
$68$	0.190983	+	0.330792i	0.0231601	+	0.0401145i
$69$	3.66157	−	4.06659i	0.440802	−	0.489560i
$70$	1.50000	−	4.61653i	0.179284	−	0.551780i
$71$	0.0603355	+	0.0670093i	0.00716050	+	0.00795254i	0.746714	−	0.665145i	$-0.231630\pi$
$71$	0.0603355	+	0.0670093i	0.00716050	+	0.00795254i	−0.739554	+	0.673097i	$0.764964\pi$
$72$	−4.08550	+	1.81898i	−0.481481	+	0.214369i
$73$	8.37520	+	1.78020i	0.980243	+	0.208357i	0.670050	−	0.742316i	$-0.266273\pi$
$73$	8.37520	+	1.78020i	0.980243	+	0.208357i	0.310193	+	0.950673i	$0.399606\pi$
$74$	0.0152505	−	0.145099i	0.00177283	−	0.0168674i
$75$	0.193806	+	1.84395i	0.0223788	+	0.212920i
$76$	7.91338	−	1.68204i	0.907727	−	0.192943i
$77$	1.85410	−	1.34708i	0.211295	−	0.153514i
$78$	−2.42705	+	1.76336i	−0.274809	+	0.199661i
$79$		0			0		−0.207912	−	0.978148i	$-0.566667\pi$
$79$		0			0		0.207912	+	0.978148i	$0.433333\pi$
$80$	0.507392	+	4.82751i	0.0567281	+	0.539732i
$81$	−0.104528	+	0.994522i	−0.0116143	+	0.110502i
$82$	3.91259	+	0.831647i	0.432073	+	0.0918400i
$83$	−3.73656	+	1.66362i	−0.410140	+	0.182606i	−0.601427	−	0.798928i	$-0.705401\pi$
$83$	−3.73656	+	1.66362i	−0.410140	+	0.182606i	0.191286	+	0.981534i	$0.438734\pi$
$84$	3.24803	+	3.60730i	0.354389	+	0.393589i
$85$	−0.190983	+	0.587785i	−0.0207150	+	0.0637543i
$86$	1.90977	−	2.12101i	0.205935	−	0.228715i
$87$	−4.30902	−	7.46344i	−0.461975	−	0.800164i
$88$	0.854102	−	1.47935i	0.0910476	−	0.157699i
$89$	−1.97214	−	6.06961i	−0.209046	−	0.643377i	−0.999523	−	0.0308856i	$-0.990167\pi$
$89$	−1.97214	−	6.06961i	−0.209046	−	0.643377i	0.790477	−	0.612492i	$-0.209833\pi$
$90$	−2.95630	−	1.31623i	−0.311621	−	0.138743i
$91$	−11.7812	−	8.55951i	−1.23500	−	0.897280i
$92$	8.85410			0.923104
$93$		0			0
$94$	2.09017			0.215585
$95$	10.5902	+	7.69421i	1.08653	+	0.789409i
$96$	5.13233	+	2.28506i	0.523816	+	0.233218i
$97$	−1.63525	−	5.03280i	−0.166035	−	0.511003i	0.833076	−	0.553158i	$-0.186578\pi$
$97$	−1.63525	−	5.03280i	−0.166035	−	0.511003i	−0.999111	+	0.0421553i	$0.986578\pi$
$98$	0.618034	−	1.07047i	0.0624309	−	0.108133i
$99$	−0.763932	−	1.32317i	−0.0767781	−	0.132983i
$100$	−2.00739	+	2.22943i	−0.200739	+	0.222943i
$101$	1.47214	−	4.53077i	0.146483	−	0.450828i	−0.850716	−	0.525626i	$-0.823831\pi$
$101$	1.47214	−	4.53077i	0.146483	−	0.450828i	0.997199	+	0.0747977i	$0.0238311\pi$
$102$	0.0976248	+	0.108423i	0.00966630	+	0.0107355i
$103$	−0.133284	+	0.0593421i	−0.0131329	+	0.00584715i	−0.413293	−	0.910598i	$-0.635621\pi$
$103$	−0.133284	+	0.0593421i	−0.0131329	+	0.00584715i	0.400160	+	0.916445i	$0.368955\pi$
$104$	−10.6169	−	2.25669i	−1.04107	−	0.221287i
$105$	−0.820977	+	7.81108i	−0.0801192	+	0.762283i
$106$	−0.820977	−	7.81108i	−0.0797404	−	0.758679i
$107$	−1.06635	+	0.226659i	−0.103088	+	0.0219120i	−0.259167	−	0.965833i	$-0.583448\pi$
$107$	−1.06635	+	0.226659i	−0.103088	+	0.0219120i	0.156079	+	0.987745i	$0.450115\pi$
$108$	6.54508	−	4.75528i	0.629801	−	0.457577i
$109$	6.80902	−	4.94704i	0.652186	−	0.473841i	−0.211829	−	0.977307i	$-0.567942\pi$
$109$	6.80902	−	4.94704i	0.652186	−	0.473841i	0.864015	+	0.503466i	$0.167942\pi$
$110$	1.20906	−	0.256993i	0.115279	−	0.0245033i
$111$	0.0246758	+	0.234775i	0.00234213	+	0.0222838i
$112$	−0.581419	+	5.53184i	−0.0549390	+	0.522709i
$113$	1.81359	+	0.385489i	0.170608	+	0.0362638i	0.292423	−	0.956289i	$-0.405538\pi$
$113$	1.81359	+	0.385489i	0.170608	+	0.0362638i	−0.121816	+	0.992553i	$0.538872\pi$
$114$	2.82301	−	1.25689i	0.264399	−	0.117718i
$115$	9.58612	+	10.6465i	0.893911	+	0.992788i
$116$	4.30902	−	13.2618i	0.400082	−	1.23133i
$117$	−6.49606	+	7.21460i	−0.600561	+	0.666990i
$118$	2.92705	+	5.06980i	0.269457	+	0.466713i
$119$	−0.354102	+	0.613323i	−0.0324605	+	0.0562232i
$120$	1.80902	+	5.56758i	0.165140	+	0.508248i
$121$	−9.51586	−	4.23673i	−0.865078	−	0.385158i
$122$	−3.47214	−	2.52265i	−0.314352	−	0.228390i
$123$	−6.47214			−0.583573
$124$		0			0
$125$	8.23607			0.736656
$126$	−3.00000	−	2.17963i	−0.267261	−	0.194177i
$127$	9.35111	+	4.16338i	0.829777	+	0.369441i	0.777260	−	0.629179i	$-0.216609\pi$
$127$	9.35111	+	4.16338i	0.829777	+	0.369441i	0.0525171	+	0.998620i	$0.483276\pi$
$128$	3.51722	+	10.8249i	0.310881	+	0.956794i
$129$	−2.30902	+	3.99933i	−0.203298	+	0.352122i
$130$	−3.92705	−	6.80185i	−0.344425	−	0.596562i
$131$	0.0603355	−	0.0670093i	0.00527153	−	0.00585463i	−0.740503	−	0.672053i	$-0.765413\pi$
$131$	0.0603355	−	0.0670093i	0.00527153	−	0.00585463i	0.745775	+	0.666198i	$0.232079\pi$
$132$	−0.381966	+	1.17557i	−0.0332459	+	0.102320i
$133$	10.0370	+	11.1472i	0.870315	+	0.966582i
$134$	2.39169	−	1.06485i	0.206611	−	0.0919891i
$135$	12.8041	+	2.72160i	1.10200	+	0.234238i
$136$	−0.0551768	+	0.524972i	−0.00473137	+	0.0450160i
$137$	0.676522	+	6.43668i	0.0577992	+	0.549923i	0.984656	+	0.174507i	$0.0558333\pi$
$137$	0.676522	+	6.43668i	0.0577992	+	0.549923i	−0.926857	+	0.375415i	$0.877500\pi$
$138$	3.30806	−	0.703150i	0.281601	−	0.0598561i
$139$	−4.73607	+	3.44095i	−0.401708	+	0.291858i	−0.770236	−	0.637759i	$-0.779862\pi$
$139$	−4.73607	+	3.44095i	−0.401708	+	0.291858i	0.368528	+	0.929617i	$0.379862\pi$
$140$	−10.2812	+	7.46969i	−0.868916	+	0.631304i
$141$	−3.30806	+	0.703150i	−0.278589	+	0.0592159i
$142$	0.00582517	+	0.0554228i	0.000488838	+	0.00465098i
$143$	0.387613	−	3.68789i	0.0324138	−	0.308397i
$144$	3.62717	+	0.770979i	0.302264	+	0.0642482i
$145$	20.6117	−	9.17692i	1.71171	−	0.762101i
$146$	3.54090	+	3.93257i	0.293047	+	0.325462i
$147$	−0.618034	+	1.90211i	−0.0509746	+	0.156884i
$148$	−0.255585	+	0.283856i	−0.0210090	+	0.0233328i
$149$	8.51722	+	14.7523i	0.697758	+	1.20855i	0.969242	+	0.246109i	$0.0791522\pi$
$149$	8.51722	+	14.7523i	0.697758	+	1.20855i	−0.271484	+	0.962443i	$0.587514\pi$
$150$	−0.572949	+	0.992377i	−0.0467811	+	0.0810272i
$151$	−6.02786	−	18.5519i	−0.490541	−	1.50973i	−0.823793	−	0.566891i	$-0.808146\pi$
$151$	−6.02786	−	18.5519i	−0.490541	−	1.50973i	0.333252	−	0.942838i	$-0.391854\pi$
$152$	10.2137	+	4.54745i	0.828444	+	0.368847i
$153$	0.381966	+	0.277515i	0.0308801	+	0.0224357i
$154$	1.41641			0.114137
$155$		0			0
$156$	7.85410			0.628831
$157$	−7.85410	−	5.70634i	−0.626826	−	0.455415i	0.228473	−	0.973550i	$-0.426627\pi$
$157$	−7.85410	−	5.70634i	−0.626826	−	0.455415i	−0.855299	+	0.518135i	$0.826627\pi$
$158$		0			0
$159$	3.92705	+	12.0862i	0.311435	+	0.958500i
$160$	−7.35410	+	12.7377i	−0.581393	+	1.00700i
$161$	8.20820	+	14.2170i	0.646897	+	1.12046i
$162$	−0.413545	+	0.459289i	−0.0324912	+	0.0360851i
$163$	−3.92705	+	12.0862i	−0.307590	+	0.946666i	0.671108	+	0.741360i	$0.265819\pi$
$163$	−3.92705	+	12.0862i	−0.307590	+	0.946666i	−0.978698	+	0.205306i	$0.934181\pi$
$164$	−7.00723	−	7.78231i	−0.547172	−	0.607697i
$165$	−1.82709	+	0.813473i	−0.142239	+	0.0633288i
$166$	−2.47262	−	0.525572i	−0.191913	−	0.0407923i
$167$	0.965432	−	9.18547i	0.0747074	−	0.710793i	−0.891499	−	0.453023i	$-0.850346\pi$
$167$	0.965432	−	9.18547i	0.0747074	−	0.710793i	0.966206	−	0.257770i	$-0.0829878\pi$
$168$	0.701198	+	6.67146i	0.0540986	+	0.514714i
$169$	−10.3315	+	2.19603i	−0.794730	+	0.168925i
$170$	−0.309017	+	0.224514i	−0.0237005	+	0.0172194i
$171$	8.09017	−	5.87785i	0.618671	−	0.449491i
$172$	−7.30885	+	1.55354i	−0.557295	+	0.118457i
$173$	−0.0951031	−	0.904846i	−0.00723056	−	0.0687942i	0.990312	−	0.138863i	$-0.0443448\pi$
$173$	−0.0951031	−	0.904846i	−0.00723056	−	0.0687942i	−0.997542	+	0.0700688i	$0.977678\pi$
$174$	0.556743	−	5.29706i	0.0422066	−	0.401569i
$175$	−5.44076	−	1.15647i	−0.411283	−	0.0874208i
$176$	−1.29395	+	0.576105i	−0.0975354	+	0.0434255i
$177$	−6.33810	−	7.03917i	−0.476400	−	0.529096i
$178$	1.21885	−	3.75123i	0.0913564	−	0.281166i
$179$	13.2477	−	14.7131i	0.990179	−	1.09971i	−0.00483637	−	0.999988i	$-0.501539\pi$
$179$	13.2477	−	14.7131i	0.990179	−	1.09971i	0.995016	−	0.0997174i	$-0.0317939\pi$
$180$	4.23607	+	7.33708i	0.315738	+	0.546874i
$181$	−8.50000	+	14.7224i	−0.631800	+	1.09431i	0.355383	+	0.934721i	$0.384350\pi$
$181$	−8.50000	+	14.7224i	−0.631800	+	1.09431i	−0.987184	+	0.159589i	$0.948983\pi$
$182$	−2.78115	−	8.55951i	−0.206153	−	0.634473i
$183$	6.34391	+	2.82449i	0.468955	+	0.208792i
$184$	9.89919	+	7.19218i	0.729778	+	0.530215i
$185$	−0.618034			−0.0454388
$186$		0			0
$187$	−0.180340			−0.0131878
$188$	−4.42705	−	3.21644i	−0.322876	−	0.234583i
$189$	13.7032	+	6.10105i	0.996760	+	0.443786i
$190$	2.50000	+	7.69421i	0.181369	+	0.558197i
$191$	8.04508	−	13.9345i	0.582122	−	1.00826i	−0.413106	−	0.910683i	$-0.635556\pi$
$191$	8.04508	−	13.9345i	0.582122	−	1.00826i	0.995228	−	0.0975816i	$-0.0311107\pi$
$192$	−0.118034	−	0.204441i	−0.00851837	−	0.0147542i
$193$	−1.59385	+	1.77015i	−0.114728	+	0.127418i	−0.797773	−	0.602958i	$-0.793989\pi$
$193$	−1.59385	+	1.77015i	−0.114728	+	0.127418i	0.683045	+	0.730376i	$0.260655\pi$
$194$	1.01064	−	3.11044i	0.0725599	−	0.223317i
$195$	8.50345	+	9.44404i	0.608945	+	0.676301i
$196$	−2.95630	+	1.31623i	−0.211164	+	0.0940162i
$197$	−16.0577	−	3.41316i	−1.14406	−	0.243178i	−0.403379	−	0.915033i	$-0.632164\pi$
$197$	−16.0577	−	3.41316i	−1.14406	−	0.243178i	−0.740683	+	0.671855i	$0.765498\pi$
$198$	0.0987033	−	0.939099i	0.00701454	−	0.0667389i
$199$	2.79177	+	26.5619i	0.197903	+	1.88292i	0.419458	+	0.907775i	$0.362220\pi$
$199$	2.79177	+	26.5619i	0.197903	+	1.88292i	−0.221555	+	0.975148i	$0.571113\pi$
$200$	−4.05530	+	0.861981i	−0.286753	+	0.0609512i
$201$	−3.42705	+	2.48990i	−0.241726	+	0.175624i
$202$	2.38197	−	1.73060i	0.167595	−	0.121765i
$203$	25.2891	−	5.37537i	1.77495	−	0.377277i
$204$	−0.0399263	−	0.379874i	−0.00279540	−	0.0265965i
$205$	1.77116	−	16.8514i	0.123703	−	1.17696i
$206$	−0.0881995	−	0.0187474i	−0.00614515	−	0.00130619i
$207$	9.99809	−	4.45144i	0.694915	−	0.309396i
$208$	6.02218	+	6.68830i	0.417563	+	0.463750i
$209$	−1.18034	+	3.63271i	−0.0816458	+	0.251280i
$210$	−3.24803	+	3.60730i	−0.224135	+	0.248927i
$211$	4.00000	+	6.92820i	0.275371	+	0.476957i	0.970229	−	0.242190i	$-0.0778659\pi$
$211$	4.00000	+	6.92820i	0.275371	+	0.476957i	−0.694857	+	0.719148i	$0.744533\pi$
$212$	−10.2812	+	17.8075i	−0.706112	+	1.22302i
$213$	−0.0278640	−	0.0857567i	−0.00190921	−	0.00587595i
$214$	−0.615512	−	0.274044i	−0.0420756	−	0.0187332i
$215$	−9.78115	−	7.10642i	−0.667069	−	0.484654i
$216$	11.1803			0.760726
$217$		0			0
$218$	5.20163			0.352299
$219$	−6.92705	−	5.03280i	−0.468087	−	0.340085i
$220$	−2.95630	−	1.31623i	−0.199313	−	0.0887400i
$221$	0.354102	+	1.08981i	0.0238195	+	0.0733088i
$222$	−0.0729490	+	0.126351i	−0.00489602	+	0.00848015i
$223$	−0.354102	−	0.613323i	−0.0237124	−	0.0410711i	0.853926	−	0.520395i	$-0.174215\pi$
$223$	−0.354102	−	0.613323i	−0.0237124	−	0.0410711i	−0.877638	+	0.479324i	$0.840882\pi$
$224$	−11.2776	+	12.5250i	−0.753516	+	0.836864i
$225$	−1.14590	+	3.52671i	−0.0763932	+	0.235114i
$226$	0.766755	+	0.851568i	0.0510038	+	0.0566455i
$227$	−18.9493	+	8.43679i	−1.25771	+	0.559970i	−0.923887	−	0.382665i	$-0.875006\pi$
$227$	−18.9493	+	8.43679i	−1.25771	+	0.559970i	−0.333825	+	0.942635i	$0.608340\pi$
$228$	−7.91338	−	1.68204i	−0.524076	−	0.111396i
$229$	0.756375	−	7.19643i	0.0499827	−	0.475553i	−0.940688	−	0.339274i	$-0.889819\pi$
$229$	0.756375	−	7.19643i	0.0499827	−	0.475553i	0.990670	−	0.136280i	$-0.0435146\pi$
$230$	0.925506	+	8.80560i	0.0610260	+	0.580624i
$231$	−2.24171	+	0.476491i	−0.147494	+	0.0313508i
$232$	15.5902	−	11.3269i	1.02354	−	0.743649i
$233$	−15.2082	+	11.0494i	−0.996323	+	0.723871i	−0.961297	−	0.275516i	$-0.911151\pi$
$233$	−15.2082	+	11.0494i	−0.996323	+	0.723871i	−0.0350260	+	0.999386i	$0.511151\pi$
$234$	−5.86889	+	1.24747i	−0.383661	+	0.0815497i
$235$	−0.925506	−	8.80560i	−0.0603733	−	0.574414i
$236$	1.60203	−	15.2423i	0.104283	−	0.992188i
$237$		0			0
$238$	−0.399853	+	0.178026i	−0.0259187	+	0.0115397i
$239$	−8.97733	−	9.97033i	−0.580695	−	0.644927i	0.379191	−	0.925319i	$-0.376202\pi$
$239$	−8.97733	−	9.97033i	−0.580695	−	0.644927i	−0.959886	+	0.280391i	$0.909536\pi$
$240$	1.50000	−	4.61653i	0.0968246	−	0.297995i
$241$	−5.70625	+	6.33744i	−0.367572	+	0.408230i	−0.898350	−	0.439281i	$-0.855233\pi$
$241$	−5.70625	+	6.33744i	−0.367572	+	0.408230i	0.530778	+	0.847511i	$0.321900\pi$
$242$	−3.21885	−	5.57521i	−0.206915	−	0.358388i
$243$	8.00000	−	13.8564i	0.513200	−	0.888889i
$244$	3.47214	+	10.6861i	0.222281	+	0.684110i
$245$	−4.78339	−	2.12970i	−0.305599	−	0.136062i
$246$	−3.23607	−	2.35114i	−0.206324	−	0.149903i
$247$	24.2705			1.54430
$248$		0			0
$249$	4.09017			0.259204
$250$	4.11803	+	2.99193i	0.260447	+	0.189226i
$251$	0.862635	+	0.384070i	0.0544491	+	0.0242423i	0.433781	−	0.901019i	$-0.357179\pi$
$251$	0.862635	+	0.384070i	0.0544491	+	0.0242423i	−0.379331	+	0.925261i	$0.623846\pi$
$252$	3.00000	+	9.23305i	0.188982	+	0.581628i
$253$	−2.09017	+	3.62028i	−0.131408	+	0.227605i
$254$	3.16312	+	5.47868i	0.198472	+	0.343763i
$255$	0.413545	−	0.459289i	0.0258972	−	0.0287618i
$256$	−2.02786	+	6.24112i	−0.126742	+	0.390070i
$257$	0.947762	+	1.05260i	0.0591198	+	0.0656591i	0.771979	−	0.635648i	$-0.219267\pi$
$257$	0.947762	+	1.05260i	0.0591198	+	0.0656591i	−0.712859	+	0.701307i	$0.752600\pi$
$258$	−2.60735	+	1.16087i	−0.162327	+	0.0722725i
$259$	−0.692728	−	0.147244i	−0.0430440	−	0.00914929i
$260$	−2.14935	+	20.4497i	−0.133297	+	1.26823i
$261$	−1.80166	−	17.1416i	−0.111520	−	1.06104i
$262$	0.0545103	−	0.0115865i	0.00336766	−	0.000715818i
$263$	8.73607	−	6.34712i	0.538689	−	0.391380i	−0.284909	−	0.958555i	$-0.591963\pi$
$263$	8.73607	−	6.34712i	0.538689	−	0.391380i	0.823598	+	0.567174i	$0.191963\pi$
$264$	−1.38197	+	1.00406i	−0.0850541	+	0.0617954i
$265$	−32.5435	+	6.91733i	−1.99913	+	0.424928i
$266$	0.969032	+	9.21973i	0.0594152	+	0.565298i
$267$	−0.667097	+	6.34700i	−0.0408257	+	0.388430i
$268$	−6.70432	−	1.42505i	−0.409532	−	0.0870487i
$269$	−1.26249	+	0.562096i	−0.0769753	+	0.0342716i	−0.444863	−	0.895599i	$-0.646748\pi$
$269$	−1.26249	+	0.562096i	−0.0769753	+	0.0342716i	0.367888	+	0.929870i	$0.380081\pi$
$270$	5.41338	+	6.01217i	0.329448	+	0.365889i
$271$	2.95492	−	9.09429i	0.179498	−	0.552439i	−0.820312	−	0.571916i	$-0.806200\pi$
$271$	2.95492	−	9.09429i	0.179498	−	0.552439i	0.999810	+	0.0194773i	$0.00620021\pi$
$272$	0.292875	−	0.325270i	0.0177581	−	0.0197224i
$273$	7.28115	+	12.6113i	0.440675	+	0.763272i
$274$	−2.00000	+	3.46410i	−0.120824	+	0.209274i
$275$	−0.437694	−	1.34708i	−0.0263939	−	0.0812322i
$276$	−8.08862	−	3.60129i	−0.486878	−	0.216772i
$277$	−10.7812	−	7.83297i	−0.647777	−	0.470637i	0.214736	−	0.976672i	$-0.431111\pi$
$277$	−10.7812	−	7.83297i	−0.647777	−	0.470637i	−0.862513	+	0.506035i	$0.831111\pi$
$278$	−3.61803			−0.216995
$279$		0			0
$280$	−17.5623			−1.04955
$281$	−15.3992	−	11.1882i	−0.918638	−	0.667430i	0.0245463	−	0.999699i	$-0.492186\pi$
$281$	−15.3992	−	11.1882i	−0.918638	−	0.667430i	−0.943185	+	0.332269i	$0.892186\pi$
$282$	−1.90947	−	0.850149i	−0.113707	−	0.0506256i
$283$	2.02786	+	6.24112i	0.120544	+	0.370996i	0.993063	−	0.117584i	$-0.0375149\pi$
$283$	2.02786	+	6.24112i	0.120544	+	0.370996i	−0.872519	+	0.488580i	$0.837515\pi$
$284$	0.0729490	−	0.126351i	0.00432873	−	0.00749758i
$285$	−6.54508	−	11.3364i	−0.387697	−	0.671512i
$286$	1.53351	−	1.70314i	0.0906784	−	0.100709i
$287$	6.00000	−	18.4661i	0.354169	−	1.09002i
$288$	7.51840	+	8.35003i	0.443026	+	0.492030i
$289$	−15.4794	+	6.89186i	−0.910551	+	0.405403i
$290$	13.6396	+	2.89918i	0.800942	+	0.170246i
$291$	−0.553143	+	5.26281i	−0.0324258	+	0.308511i
$292$	−1.44815	−	13.7782i	−0.0847465	−	0.806309i
$293$	8.05609	−	1.71237i	0.470642	−	0.100038i	0.0335156	−	0.999438i	$-0.489330\pi$
$293$	8.05609	−	1.71237i	0.470642	−	0.100038i	0.437126	+	0.899400i	$0.355996\pi$
$294$	−1.00000	+	0.726543i	−0.0583212	+	0.0423728i
$295$	20.0623	−	14.5761i	1.16807	−	0.848654i
$296$	−0.516329	+	0.109749i	−0.0300110	+	0.00637904i
$297$	0.399263	+	3.79874i	0.0231676	+	0.220425i
$298$	−1.10046	+	10.4702i	−0.0637480	+	0.606522i
$299$	25.9819	+	5.52261i	1.50257	+	0.319381i
$300$	2.74064	−	1.22021i	0.158231	−	0.0704489i
$301$	−9.27020	−	10.2956i	−0.534326	−	0.593429i
$302$	3.72542	−	11.4657i	0.214374	−	0.659776i
$303$	−3.18769	+	3.54029i	−0.183128	+	0.203384i
$304$	−4.63525	−	8.02850i	−0.265850	−	0.460466i
$305$	−9.09017	+	15.7446i	−0.520502	+	0.901535i
$306$	0.0901699	+	0.277515i	0.00515467	+	0.0158645i
$307$	5.56365	+	2.47710i	0.317534	+	0.141375i	0.559314	−	0.828956i	$-0.311065\pi$
$307$	5.56365	+	2.47710i	0.317534	+	0.141375i	−0.241780	+	0.970331i	$0.577731\pi$
$308$	−3.00000	−	2.17963i	−0.170941	−	0.124196i
$309$	0.145898			0.00829985
$310$		0			0
$311$	16.4721			0.934049			0.467025	−	0.884244i	$-0.345326\pi$
$311$	16.4721			0.934049			0.467025	+	0.884244i	$0.345326\pi$
$312$	8.78115	+	6.37988i	0.497135	+	0.361190i
$313$	1.12920	+	0.502754i	0.0638264	+	0.0284173i	0.438402	−	0.898779i	$-0.355545\pi$
$313$	1.12920	+	0.502754i	0.0638264	+	0.0284173i	−0.374575	+	0.927197i	$0.622211\pi$
$314$	−1.85410	−	5.70634i	−0.104633	−	0.322027i
$315$	−7.85410	+	13.6037i	−0.442529	+	0.766482i
$316$		0			0
$317$	17.3228	−	19.2389i	0.972946	−	1.08057i	−0.0237800	−	0.999717i	$-0.507570\pi$
$317$	17.3228	−	19.2389i	0.972946	−	1.08057i	0.996726	−	0.0808492i	$-0.0257632\pi$
$318$	−2.42705	+	7.46969i	−0.136102	+	0.418880i
$319$	4.40528	+	4.89256i	0.246648	+	0.273931i
$320$	0.564602	−	0.251377i	0.0315622	−	0.0140524i
$321$	1.06635	+	0.226659i	0.0595177	+	0.0126509i
$322$	−1.06054	+	10.0903i	−0.0591013	+	0.562311i
$323$	−0.123379	−	1.17387i	−0.00686500	−	0.0653161i
$324$	1.58268	−	0.336408i	0.0879264	−	0.0186893i
$325$	−7.28115	+	5.29007i	−0.403886	+	0.293440i
$326$	−6.35410	+	4.61653i	−0.351921	+	0.255686i
$327$	−8.23249	+	1.74987i	−0.455258	+	0.0967680i
$328$	−1.51275	−	14.3929i	−0.0835277	−	0.794713i
$329$	1.06054	−	10.0903i	0.0584692	−	0.556297i
$330$	−1.20906	−	0.256993i	−0.0665564	−	0.0141470i
$331$	10.2961	−	4.58413i	0.565926	−	0.251967i	−0.103771	−	0.994601i	$-0.533091\pi$
$331$	10.2961	−	4.58413i	0.565926	−	0.251967i	0.669697	+	0.742635i	$0.266424\pi$
$332$	4.42833	+	4.91816i	0.243036	+	0.269919i
$333$	−0.145898	+	0.449028i	−0.00799516	+	0.0246066i
$334$	3.81953	−	4.24202i	0.208996	−	0.232113i
$335$	−5.54508	−	9.60437i	−0.302960	−	0.524743i
$336$	2.78115	−	4.81710i	0.151724	−	0.262794i
$337$	5.86475	+	18.0498i	0.319473	+	0.983237i	0.973874	+	0.227089i	$0.0729209\pi$
$337$	5.86475	+	18.0498i	0.319473	+	0.983237i	−0.654401	+	0.756148i	$0.727079\pi$
$338$	−5.96350	−	2.65512i	−0.324372	−	0.144420i
$339$	−1.50000	−	1.08981i	−0.0814688	−	0.0591906i
$340$	1.00000			0.0542326
$341$		0			0
$342$	6.18034			0.334195
$343$	12.1353	+	8.81678i	0.655242	+	0.476061i
$344$	−9.43349	−	4.20006i	−0.508620	−	0.226452i
$345$	−4.42705	−	13.6251i	−0.238344	−	0.733549i
$346$	0.281153	−	0.486971i	0.0151149	−	0.0261797i
$347$	−4.06231	−	7.03612i	−0.218076	−	0.377719i	0.736144	−	0.676825i	$-0.236645\pi$
$347$	−4.06231	−	7.03612i	−0.218076	−	0.377719i	−0.954220	+	0.299107i	$0.903311\pi$
$348$	−9.33054	+	10.3626i	−0.500169	+	0.555494i
$349$	−5.16312	+	15.8904i	−0.276375	+	0.850596i	0.712477	+	0.701696i	$0.247573\pi$
$349$	−5.16312	+	15.8904i	−0.276375	+	0.850596i	−0.988852	+	0.148900i	$0.952427\pi$
$350$	−2.30027	−	2.55470i	−0.122954	−	0.136555i
$351$	22.1722	−	9.87171i	1.18347	−	0.526913i
$352$	−4.19801	−	0.892315i	−0.223755	−	0.0475605i
$353$	3.38484	−	32.2046i	0.180157	−	1.71408i	−0.414460	−	0.910067i	$-0.636030\pi$
$353$	3.38484	−	32.2046i	0.180157	−	1.71408i	0.594617	−	0.804009i	$-0.297304\pi$
$354$	−0.611920	−	5.82203i	−0.0325232	−	0.309438i
$355$	0.230909	−	0.0490813i	0.0122554	−	0.00260496i
$356$	−8.35410	+	6.06961i	−0.442767	+	0.321689i
$357$	0.572949	−	0.416272i	0.0303237	−	0.0220314i
$358$	11.9687	−	2.54402i	0.632564	−	0.134456i
$359$	2.64731	+	25.1875i	0.139720	+	1.32935i	0.809646	+	0.586918i	$0.199659\pi$
$359$	2.64731	+	25.1875i	0.139720	+	1.32935i	−0.669927	+	0.742427i	$0.733674\pi$
$360$	−1.22384	+	11.6441i	−0.0645021	+	0.613696i
$361$	−5.86889	−	1.24747i	−0.308889	−	0.0656563i
$362$	−9.59824	+	4.27341i	−0.504472	+	0.224605i
$363$	6.96994	+	7.74090i	0.365827	+	0.406292i
$364$	−7.28115	+	22.4091i	−0.381636	+	1.17456i
$365$	14.9995	−	16.6586i	0.785110	−	0.871953i
$366$	2.14590	+	3.71680i	0.112168	+	0.194280i
$367$	18.1353	−	31.4112i	0.946653	−	1.63965i	0.194245	−	0.980953i	$-0.437774\pi$
$367$	18.1353	−	31.4112i	0.946653	−	1.63965i	0.752408	−	0.658697i	$-0.228892\pi$
$368$	−3.13525	−	9.64932i	−0.163436	−	0.503006i
$369$	−11.8252	−	5.26491i	−0.615594	−	0.274080i
$370$	−0.309017	−	0.224514i	−0.0160650	−	0.0116719i
$371$	−38.1246			−1.97933
$372$		0			0
$373$	−0.347524			−0.0179941			−0.00899706	−	0.999960i	$-0.502864\pi$
$373$	−0.347524			−0.0179941			−0.00899706	+	0.999960i	$0.502864\pi$
$374$	−0.0901699	−	0.0655123i	−0.00466258	−	0.00338756i
$375$	−7.52402	−	3.34991i	−0.388539	−	0.172989i
$376$	−2.33688	−	7.19218i	−0.120515	−	0.370908i
$377$	20.9164	−	36.2283i	1.07725	−	1.86585i
$378$	4.63525	+	8.02850i	0.238412	+	0.412941i
$379$	−12.3230	+	13.6861i	−0.632989	+	0.703006i	−0.971254	−	0.238045i	$-0.923493\pi$
$379$	−12.3230	+	13.6861i	−0.632989	+	0.703006i	0.338265	+	0.941051i	$0.390160\pi$
$380$	6.54508	−	20.1437i	0.335756	−	1.03335i
$381$	−6.84927	−	7.60688i	−0.350899	−	0.389712i
$382$	9.08454	−	4.04470i	0.464806	−	0.206945i
$383$	16.4858	+	3.50416i	0.842385	+	0.179054i	0.608841	−	0.793292i	$-0.291635\pi$
$383$	16.4858	+	3.50416i	0.842385	+	0.179054i	0.233544	+	0.972346i	$0.424968\pi$
$384$	1.18974	−	11.3196i	0.0607136	−	0.577652i
$385$	−0.627171	−	5.96713i	−0.0319636	−	0.304113i
$386$	−1.43997	+	0.306074i	−0.0732924	+	0.0155788i
$387$	−7.47214	+	5.42882i	−0.379830	+	0.275963i
$388$	−6.92705	+	5.03280i	−0.351668	+	0.255502i
$389$	28.4337	−	6.04376i	1.44164	−	0.306431i	0.580279	−	0.814418i	$-0.302944\pi$
$389$	28.4337	−	6.04376i	1.44164	−	0.306431i	0.861365	+	0.507987i	$0.169610\pi$
$390$	0.820977	+	7.81108i	0.0415718	+	0.395529i
$391$	0.135029	−	1.28472i	0.00682873	−	0.0649711i
$392$	−4.37441	−	0.929809i	−0.220941	−	0.0469625i
$393$	−0.0823743	+	0.0366754i	−0.00415524	+	0.00185003i
$394$	−6.78893	−	7.53987i	−0.342021	−	0.379853i
$395$		0			0
$396$	−1.65418	+	1.83716i	−0.0831258	+	0.0923205i
$397$	−8.14590	−	14.1091i	−0.408831	−	0.708116i	0.585928	−	0.810363i	$-0.300730\pi$
$397$	−8.14590	−	14.1091i	−0.408831	−	0.708116i	−0.994759	+	0.102247i	$0.967397\pi$
$398$	−8.25329	+	14.2951i	−0.413700	+	0.716549i
$399$	−4.63525	−	14.2658i	−0.232053	−	0.714186i
$400$	3.14049	+	1.39824i	0.157024	+	0.0699118i
$401$	24.1353	+	17.5353i	1.20526	+	0.875671i	0.994792	−	0.101931i	$-0.0325020\pi$
$401$	24.1353	+	17.5353i	1.20526	+	0.875671i	0.210466	+	0.977601i	$0.432502\pi$
$402$	−2.61803			−0.130576
$403$		0			0
$404$	−7.70820			−0.383497
$405$	2.11803	+	1.53884i	0.105246	+	0.0764657i
$406$	14.5973	+	6.49913i	0.724451	+	0.322546i
$407$	−0.0557281	−	0.171513i	−0.00276234	−	0.00850160i
$408$	0.263932	−	0.457144i	0.0130666	−	0.0226320i
$409$	3.09017	+	5.35233i	0.152799	+	0.264656i	0.932255	−	0.361801i	$-0.117838\pi$
$409$	3.09017	+	5.35233i	0.152799	+	0.264656i	−0.779456	+	0.626457i	$0.784505\pi$
$410$	7.00723	−	7.78231i	0.346062	−	0.384341i
$411$	2.00000	−	6.15537i	0.0986527	−	0.303622i
$412$	0.157960	+	0.175433i	0.00778215	+	0.00864295i
$413$	25.9597	−	11.5580i	1.27739	−	0.568732i
$414$	6.61612	+	1.40630i	0.325165	+	0.0691159i
$415$	−1.11931	+	10.6495i	−0.0549449	+	0.522766i
$416$	2.85054	+	27.1211i	0.139759	+	1.32972i
$417$	5.72618	−	1.21714i	0.280412	−	0.0596034i
$418$	−1.90983	+	1.38757i	−0.0934128	+	0.0678684i
$419$	−3.61803	+	2.62866i	−0.176753	+	0.128418i	−0.672644	−	0.739966i	$-0.734841\pi$
$419$	−3.61803	+	2.62866i	−0.176753	+	0.128418i	0.495891	+	0.868385i	$0.334841\pi$
$420$	12.4305	−	2.64218i	0.606546	−	0.128925i
$421$	−1.54325	−	14.6831i	−0.0752135	−	0.715608i	−0.965535	−	0.260275i	$-0.916187\pi$
$421$	−1.54325	−	14.6831i	−0.0752135	−	0.715608i	0.890321	−	0.455333i	$-0.150480\pi$
$422$	−0.516817	+	4.91719i	−0.0251583	+	0.239365i
$423$	−6.61612	−	1.40630i	−0.321687	−	0.0683767i
$424$	−25.9597	+	11.5580i	−1.26071	+	0.561306i
$425$	0.292875	+	0.325270i	0.0142065	+	0.0157779i
$426$	0.0172209	−	0.0530006i	0.000834357	−	0.00256789i
$427$	−13.9399	+	15.4818i	−0.674598	+	0.749217i
$428$	0.881966	+	1.52761i	0.0426314	+	0.0738398i
$429$	−1.85410	+	3.21140i	−0.0895169	+	0.155048i
$430$	−2.30902	−	7.10642i	−0.111351	−	0.342702i
$431$	26.7085	+	11.8914i	1.28650	+	0.572788i	0.932065	−	0.362292i	$-0.118006\pi$
$431$	26.7085	+	11.8914i	1.28650	+	0.572788i	0.354437	+	0.935080i	$0.384672\pi$
$432$	−7.50000	−	5.44907i	−0.360844	−	0.262168i
$433$	0.583592			0.0280456			0.0140228	−	0.999902i	$-0.495536\pi$
$433$	0.583592			0.0280456			0.0140228	+	0.999902i	$0.495536\pi$
$434$		0			0
$435$	−22.5623			−1.08178
$436$	−11.0172	−	8.00448i	−0.527629	−	0.383345i
$437$	−24.9952	−	11.1286i	−1.19568	−	0.532353i
$438$	−1.63525	−	5.03280i	−0.0781355	−	0.240476i
$439$	−20.9164	+	36.2283i	−0.998286	+	1.72908i	−0.448455	+	0.893805i	$0.648026\pi$
$439$	−20.9164	+	36.2283i	−0.998286	+	1.72908i	−0.549831	+	0.835276i	$0.685308\pi$
$440$	−2.23607	−	3.87298i	−0.106600	−	0.184637i
$441$	−2.67652	+	2.97258i	−0.127453	+	0.141551i
$442$	−0.218847	+	0.673542i	−0.0104095	+	0.0320371i
$443$	−27.5177	−	30.5615i	−1.30741	−	1.45202i	−0.812360	−	0.583157i	$-0.801817\pi$
$443$	−27.5177	−	30.5615i	−1.30741	−	1.45202i	−0.495047	−	0.868866i	$-0.664849\pi$
$444$	0.348943	−	0.155360i	0.0165601	−	0.00737304i
$445$	−16.3431	−	3.47383i	−0.774737	−	0.164675i
$446$	0.0457515	−	0.435296i	0.00216640	−	0.0206119i
$447$	−1.78058	−	16.9411i	−0.0842187	−	0.801288i
$448$	0.692728	−	0.147244i	0.0327283	−	0.00695662i
$449$	−19.4721	+	14.1473i	−0.918947	+	0.667654i	−0.943262	−	0.332050i	$-0.892260\pi$
$449$	−19.4721	+	14.1473i	−0.918947	+	0.667654i	0.0243148	+	0.999704i	$0.492260\pi$
$450$	−1.85410	+	1.34708i	−0.0874032	+	0.0635021i
$451$	4.83623	−	1.02797i	0.227729	−	0.0484053i
$452$	−0.313585	−	2.98357i	−0.0147498	−	0.140335i
$453$	−2.03899	+	19.3997i	−0.0958002	+	0.911478i
$454$	−12.5395	−	2.66536i	−0.588509	−	0.125091i
$455$	−34.8286	+	15.5067i	−1.63279	+	0.726964i
$456$	−7.48111	−	8.30861i	−0.350335	−	0.389086i
$457$	−4.86475	+	14.9721i	−0.227563	+	0.700367i	0.770458	+	0.637491i	$0.220028\pi$
$457$	−4.86475	+	14.9721i	−0.227563	+	0.700367i	−0.998021	+	0.0628768i	$0.979972\pi$
$458$	2.99244	−	3.32344i	0.139828	−	0.155294i
$459$	−0.590170	−	1.02220i	−0.0275468	−	0.0477124i
$460$	11.5902	−	20.0748i	0.540394	−	0.935991i
$461$	3.31966	+	10.2169i	0.154612	+	0.475847i	0.998121	−	0.0612677i	$-0.0195143\pi$
$461$	3.31966	+	10.2169i	0.154612	+	0.475847i	−0.843509	+	0.537114i	$0.819514\pi$
$462$	−1.29395	−	0.576105i	−0.0602001	−	0.0268028i
$463$	25.1803	+	18.2946i	1.17023	+	0.850222i	0.991036	−	0.133592i	$-0.0426513\pi$
$463$	25.1803	+	18.2946i	1.17023	+	0.850222i	0.179193	+	0.983814i	$0.442651\pi$
$464$	−15.9787			−0.741793
$465$		0			0
$466$	−11.6180			−0.538195
$467$	26.5172	+	19.2659i	1.22707	+	0.891519i	0.996667	−	0.0815762i	$-0.0259954\pi$
$467$	26.5172	+	19.2659i	1.22707	+	0.891519i	0.230404	+	0.973095i	$0.425995\pi$
$468$	14.3502	+	6.38910i	0.663336	+	0.295336i
$469$	−3.92705	−	12.0862i	−0.181334	−	0.558090i
$470$	2.73607	−	4.73901i	0.126205	−	0.218594i
$471$	4.85410	+	8.40755i	0.223665	+	0.387400i
$472$	14.1724	−	15.7401i	0.652338	−	0.724495i
$473$	1.09017	−	3.35520i	0.0501261	−	0.154272i
$474$		0			0
$475$	8.46903	−	3.77066i	0.388586	−	0.173010i
$476$	1.12086	+	0.238246i	0.0513744	+	0.0109200i
$477$	−2.65674	+	25.2772i	−0.121644	+	1.15736i
$478$	−0.866729	−	8.24637i	−0.0396432	−	0.377180i
$479$	8.74882	−	1.85962i	0.399744	−	0.0849681i	−0.00365302	−	0.999993i	$-0.501163\pi$
$479$	8.74882	−	1.85962i	0.399744	−	0.0849681i	0.403397	+	0.915025i	$0.367829\pi$
$480$	11.8992	−	8.64527i	0.543121	−	0.394601i
$481$	−0.927051	+	0.673542i	−0.0422699	+	0.0307109i
$482$	−5.15534	+	1.09580i	−0.234819	+	0.0499124i
$483$	−1.71598	−	16.3265i	−0.0780799	−	0.742880i
$484$	−1.76173	+	16.7618i	−0.0800788	+	0.761899i
$485$	−13.5514	−	2.88043i	−0.615335	−	0.130794i
$486$	9.03363	−	4.02203i	0.409774	−	0.182443i
$487$	15.3385	+	17.0351i	0.695052	+	0.771934i	0.982580	−	0.185838i	$-0.0595001\pi$
$487$	15.3385	+	17.0351i	0.695052	+	0.771934i	−0.287528	+	0.957772i	$0.592833\pi$
$488$	−4.79837	+	14.7679i	−0.217212	+	0.668510i
$489$	8.50345	−	9.44404i	0.384539	−	0.427074i
$490$	−1.61803	−	2.80252i	−0.0730953	−	0.126605i
$491$	13.7984	−	23.8995i	0.622712	−	1.07857i	−0.366267	−	0.930510i	$-0.619364\pi$
$491$	13.7984	−	23.8995i	0.622712	−	1.07857i	0.988979	−	0.148059i	$-0.0473025\pi$
$492$	3.23607	+	9.95959i	0.145893	+	0.449013i
$493$	−1.85856	−	0.827482i	−0.0837051	−	0.0372679i
$494$	12.1353	+	8.81678i	0.545991	+	0.396686i
$495$	−4.00000			−0.179787
$496$		0			0
$497$	0.270510			0.0121340
$498$	2.04508	+	1.48584i	0.0916424	+	0.0665821i
$499$	3.78747	+	1.68629i	0.169550	+	0.0754886i	0.489757	−	0.871859i	$-0.337086\pi$
$499$	3.78747	+	1.68629i	0.169550	+	0.0754886i	−0.320206	+	0.947348i	$0.603752\pi$
$500$	−4.11803	−	12.6740i	−0.184164	−	0.566799i
$501$	−4.61803	+	7.99867i	−0.206319	+	0.357354i
$502$	0.291796	+	0.505406i	0.0130235	+	0.0225574i
$503$	8.79632	−	9.76931i	0.392209	−	0.435592i	−0.514409	−	0.857545i	$-0.671989\pi$
$503$	8.79632	−	9.76931i	0.392209	−	0.435592i	0.906618	+	0.421953i	$0.138655\pi$
$504$	−4.14590	+	12.7598i	−0.184673	+	0.568365i
$505$	−8.34549	−	9.26860i	−0.371369	−	0.412447i
$506$	−2.36023	+	1.05084i	−0.104925	+	0.0467156i
$507$	10.3315	+	2.19603i	0.458838	+	0.0975290i
$508$	1.73123	−	16.4716i	0.0768110	−	0.730808i
$509$	0.199632	+	1.89937i	0.00884852	+	0.0841880i	0.998055	−	0.0623408i	$-0.0198566\pi$
$509$	0.199632	+	1.89937i	0.00884852	+	0.0841880i	−0.989206	+	0.146529i	$0.953190\pi$
$510$	0.373619	−	0.0794152i	0.0165441	−	0.00351656i
$511$	20.7812	−	15.0984i	0.919304	−	0.667914i
$512$	15.1353	−	10.9964i	0.668890	−	0.485977i
$513$	−24.4537	+	5.19779i	−1.07966	+	0.229488i
$514$	0.0915030	+	0.870593i	0.00403602	+	0.0384002i
$515$	−0.0399263	+	0.379874i	−0.00175936	+	0.0167392i
$516$	7.30885	+	1.55354i	0.321754	+	0.0683910i
$517$	2.36023	−	1.05084i	0.103803	−	0.0462160i
$518$	−0.292875	−	0.325270i	−0.0128682	−	0.0142915i
$519$	−0.281153	+	0.865300i	−0.0123412	+	0.0379824i
$520$	−19.0143	+	21.1175i	−0.833832	+	0.926064i
$521$	−15.5344	−	26.9064i	−0.680576	−	1.17879i	−0.974805	−	0.223058i	$-0.928396\pi$
$521$	−15.5344	−	26.9064i	−0.680576	−	1.17879i	0.294229	−	0.955735i	$-0.404937\pi$
$522$	5.32624	−	9.22531i	0.233123	−	0.403781i
$523$	10.5451	+	32.4544i	0.461104	+	1.41913i	0.863816	+	0.503807i	$0.168068\pi$
$523$	10.5451	+	32.4544i	0.461104	+	1.41913i	−0.402712	+	0.915327i	$0.631932\pi$
$524$	−0.133284	−	0.0593421i	−0.00582256	−	0.00259237i
$525$	4.50000	+	3.26944i	0.196396	+	0.142690i
$526$	6.67376			0.290990
$527$		0			0
$528$	1.41641			0.0616412
$529$	−5.61803	−	4.08174i	−0.244262	−	0.177467i
$530$	−18.7846	−	8.36344i	−0.815951	−	0.363285i
$531$	−5.85410	−	18.0171i	−0.254046	−	0.781874i
$532$	12.1353	−	21.0189i	0.526130	−	0.911284i
$533$	−15.7082	−	27.2074i	−0.680398	−	1.17848i
$534$	−2.63923	+	2.93117i	−0.114211	+	0.126844i
$535$	−0.881966	+	2.71441i	−0.0381307	+	0.117354i
$536$	−6.33810	−	7.03917i	−0.273764	−	0.304046i
$537$	−18.0867	+	8.05272i	−0.780499	+	0.347501i
$538$	−0.835438	−	0.177578i	−0.0360183	−	0.00765592i
$539$	0.159705	−	1.51949i	0.00687899	−	0.0654493i
$540$	−2.21395	−	21.0643i	−0.0952732	−	0.906464i
$541$	−21.5192	+	4.57406i	−0.925185	+	0.196654i	−0.645784	−	0.763520i	$-0.723469\pi$
$541$	−21.5192	+	4.57406i	−0.925185	+	0.196654i	−0.279401	+	0.960175i	$0.590136\pi$
$542$	4.78115	−	3.47371i	0.205368	−	0.149209i
$543$	13.7533	−	9.99235i	0.590210	−	0.428813i
$544$	1.29726	−	0.275740i	0.0556194	−	0.0118223i
$545$	−2.30323	−	21.9137i	−0.0986594	−	0.938681i
$546$	−0.940756	+	8.95070i	−0.0402606	+	0.383054i
$547$	23.1901	+	4.92921i	0.991538	+	0.210758i	0.674997	−	0.737821i	$-0.264145\pi$
$547$	23.1901	+	4.92921i	0.991538	+	0.210758i	0.316541	+	0.948579i	$0.397478\pi$
$548$	9.56677	−	4.25940i	0.408672	−	0.181953i
$549$	9.29325	+	10.3212i	0.396626	+	0.440498i
$550$	0.270510	−	0.832544i	0.0115346	−	0.0354998i
$551$	−28.8330	+	32.0222i	−1.22833	+	1.36419i
$552$	−6.11803	−	10.5967i	−0.260401	−	0.451027i
$553$		0			0
$554$	−2.54508	−	7.83297i	−0.108130	−	0.332791i
$555$	0.564602	+	0.251377i	0.0239660	+	0.0106704i
$556$	7.66312	+	5.56758i	0.324989	+	0.236118i
$557$	35.8885			1.52065			0.760323	−	0.649545i	$-0.225041\pi$
$557$	35.8885			1.52065			0.760323	+	0.649545i	$0.225041\pi$
$558$		0			0
$559$	−22.4164			−0.948113
$560$	11.7812	+	8.55951i	0.497845	+	0.361705i
$561$	0.164749	+	0.0733508i	0.00695569	+	0.00309687i
$562$	−3.63525	−	11.1882i	−0.153344	−	0.471944i
$563$	4.28115	−	7.41517i	0.180429	−	0.312512i	−0.761598	−	0.648050i	$-0.775585\pi$
$563$	4.28115	−	7.41517i	0.180429	−	0.312512i	0.942027	+	0.335538i	$0.108918\pi$
$564$	2.73607	+	4.73901i	0.115209	+	0.199548i
$565$	3.24803	−	3.60730i	0.136646	−	0.151760i
$566$	−1.25329	+	3.85723i	−0.0526797	+	0.162131i
$567$	2.00739	+	2.22943i	0.0843025	+	0.0936274i
$568$	0.184195	−	0.0820087i	0.00772863	−	0.00344101i
$569$	−15.1885	−	3.22842i	−0.636737	−	0.135343i	−0.121778	−	0.992557i	$-0.538860\pi$
$569$	−15.1885	−	3.22842i	−0.636737	−	0.135343i	−0.514959	+	0.857215i	$0.672193\pi$
$570$	0.845653	−	8.04585i	0.0354205	−	0.337004i
$571$	−0.731699	−	6.96165i	−0.0306207	−	0.291336i	−0.999106	−	0.0422669i	$-0.986542\pi$
$571$	−0.731699	−	6.96165i	−0.0306207	−	0.291336i	0.968486	−	0.249069i	$-0.0801247\pi$
$572$	−5.86889	+	1.24747i	−0.245390	+	0.0521593i
$573$	−13.0172	+	9.45756i	−0.543802	+	0.395095i
$574$	9.70820	−	7.05342i	0.405213	−	0.294404i
$575$	9.92419	−	2.10945i	0.413867	−	0.0879702i
$576$	−0.0493516	−	0.469550i	−0.00205632	−	0.0195646i
$577$	−4.07439	+	38.7652i	−0.169619	+	1.61382i	0.496545	+	0.868011i	$0.334602\pi$
$577$	−4.07439	+	38.7652i	−0.169619	+	1.61382i	−0.666164	+	0.745805i	$0.732065\pi$
$578$	−10.2433	−	2.17728i	−0.426065	−	0.0905629i
$579$	2.17603	−	0.968833i	0.0904329	−	0.0402633i
$580$	−24.4277	−	27.1297i	−1.01430	−	1.12650i
$581$	−3.79180	+	11.6699i	−0.157310	+	0.484151i
$582$	−2.18840	+	2.43046i	−0.0907120	+	0.100746i
$583$	−4.85410	−	8.40755i	−0.201036	−	0.348205i
$584$	9.57295	−	16.5808i	0.396131	−	0.686120i
$585$	7.85410	+	24.1724i	0.324727	+	0.999407i
$586$	4.65010	+	2.07036i	0.192094	+	0.0855257i
$587$	−29.1353	−	21.1680i	−1.20254	−	0.873697i	−0.208008	−	0.978127i	$-0.566698\pi$
$587$	−29.1353	−	21.1680i	−1.20254	−	0.873697i	−0.994532	+	0.104430i	$0.966698\pi$
$588$	3.23607			0.133453
$589$		0			0
$590$	15.3262			0.630971
$591$	13.2812	+	9.64932i	0.546314	+	0.396920i
$592$	0.399853	+	0.178026i	0.0164339	+	0.00731683i
$593$	1.88854	+	5.81234i	0.0775532	+	0.238684i	0.982316	−	0.187232i	$-0.0599517\pi$
$593$	1.88854	+	5.81234i	0.0775532	+	0.238684i	−0.904762	+	0.425917i	$0.859952\pi$
$594$	−1.18034	+	2.04441i	−0.0484299	+	0.0838831i
$595$	0.927051	+	1.60570i	0.0380054	+	0.0658273i
$596$	18.4428	−	20.4828i	0.755446	−	0.839008i
$597$	8.25329	−	25.4010i	0.337785	−	1.03959i
$598$	10.9847	+	12.1998i	0.449199	+	0.498886i
$599$	27.2222	−	12.1201i	1.11227	−	0.495213i	0.233449	−	0.972369i	$-0.424999\pi$
$599$	27.2222	−	12.1201i	1.11227	−	0.495213i	0.878819	+	0.477156i	$0.158332\pi$
$600$	4.05530	+	0.861981i	0.165557	+	0.0351902i
$601$	−2.29963	+	21.8795i	−0.0938037	+	0.892483i	0.841885	+	0.539657i	$0.181446\pi$
$601$	−2.29963	+	21.8795i	−0.0938037	+	0.892483i	−0.935689	+	0.352826i	$0.885221\pi$
$602$	−0.895005	−	8.51540i	−0.0364777	−	0.347062i
$603$	−8.28700	+	1.76146i	−0.337473	+	0.0717320i
$604$	−25.5344	+	18.5519i	−1.03898	+	0.754864i
$605$	−22.0623	+	16.0292i	−0.896960	+	0.651680i
$606$	−2.87993	+	0.612149i	−0.116989	+	0.0248668i
$607$	2.65674	+	25.2772i	0.107834	+	1.02597i	0.905927	+	0.423435i	$0.139176\pi$
$607$	2.65674	+	25.2772i	0.107834	+	1.02597i	−0.798093	+	0.602534i	$0.794158\pi$
$608$	2.93622	−	27.9363i	0.119080	−	1.13297i
$609$	−25.2891	−	5.37537i	−1.02477	−	0.217821i
$610$	−10.2647	+	4.57012i	−0.415604	+	0.185039i
$611$	−10.9847	−	12.1998i	−0.444394	−	0.493550i
$612$	0.236068	−	0.726543i	0.00954248	−	0.0293687i
$613$	16.7656	−	18.6200i	0.677154	−	0.752056i	−0.302412	−	0.953177i	$-0.597792\pi$
$613$	16.7656	−	18.6200i	0.677154	−	0.752056i	0.979566	+	0.201121i	$0.0644585\pi$
$614$	1.88197	+	3.25966i	0.0759500	+	0.131549i
$615$	−8.47214	+	14.6742i	−0.341629	+	0.591720i
$616$	−1.58359	−	4.87380i	−0.0638047	−	0.196371i
$617$	−13.0053	−	5.79033i	−0.523573	−	0.233110i	0.127892	−	0.991788i	$-0.459179\pi$
$617$	−13.0053	−	5.79033i	−0.523573	−	0.233110i	−0.651466	+	0.758678i	$0.725846\pi$
$618$	0.0729490	+	0.0530006i	0.00293444	+	0.00213200i
$619$	−40.0000			−1.60774			−0.803868	−	0.594808i	$-0.797228\pi$
$619$	−40.0000			−1.60774			−0.803868	+	0.594808i	$0.797228\pi$
$620$		0			0
$621$	−27.3607			−1.09795
$622$	8.23607	+	5.98385i	0.330236	+	0.239931i
$623$	−17.4906	−	7.78734i	−0.700748	−	0.311993i
$624$	−2.78115	−	8.55951i	−0.111335	−	0.342655i
$625$	15.4164	−	26.7020i	0.616656	−	1.06808i
$626$	0.381966	+	0.661585i	0.0152664	+	0.0264422i
$627$	2.55585	−	2.83856i	0.102071	−	0.113361i
$628$	−4.85410	+	14.9394i	−0.193700	+	0.596147i
$629$	0.0372894	+	0.0414140i	0.00148682	+	0.00165129i
$630$	−8.86889	+	3.94868i	−0.353345	+	0.157319i
$631$	8.53873	+	1.81496i	0.339921	+	0.0722525i	0.374710	−	0.927142i	$-0.377742\pi$
$631$	8.53873	+	1.81496i	0.339921	+	0.0722525i	−0.0347883	+	0.999395i	$0.511076\pi$
$632$		0			0
$633$	−0.836228	−	7.95618i	−0.0332371	−	0.316230i
$634$	15.6504	−	3.32659i	0.621555	−	0.132116i
$635$	21.6803	−	15.7517i	0.860358	−	0.625087i
$636$	16.6353	−	12.0862i	0.659631	−	0.479250i
$637$	−9.49606	+	2.01845i	−0.376247	+	0.0799739i
$638$	0.425314	+	4.04659i	0.0168383	+	0.160206i
$639$	0.0188507	−	0.179352i	0.000745720	−	0.00709505i
$640$	29.1472	+	6.19543i	1.15214	+	0.244896i
$641$	−37.5377	+	16.7129i	−1.48265	+	0.660119i	−0.979013	−	0.203796i	$-0.934672\pi$
$641$	−37.5377	+	16.7129i	−1.48265	+	0.660119i	−0.503638	+	0.863915i	$0.668005\pi$
$642$	0.450835	+	0.500703i	0.0177930	+	0.0197612i
$643$	2.51722	−	7.74721i	0.0992695	−	0.305520i	−0.889073	−	0.457765i	$-0.848650\pi$
$643$	2.51722	−	7.74721i	0.0992695	−	0.305520i	0.988343	+	0.152245i	$0.0486502\pi$
$644$	17.7737	−	19.7396i	0.700380	−	0.777851i
$645$	6.04508	+	10.4704i	0.238025	+	0.412271i
$646$	0.364745	−	0.631757i	0.0143507	−	0.0248561i
$647$	−9.23607	−	28.4257i	−0.363107	−	1.11753i	−0.951158	−	0.308705i	$-0.900104\pi$
$647$	−9.23607	−	28.4257i	−0.363107	−	1.11753i	0.588050	−	0.808824i	$-0.299896\pi$
$648$	2.04275	+	0.909491i	0.0802468	+	0.0357282i
$649$	5.85410	+	4.25325i	0.229794	+	0.166955i
$650$	−5.56231			−0.218172
$651$		0			0
$652$	20.5623			0.805282
$653$	−32.0795	−	23.3071i	−1.25537	−	0.912079i	−0.256848	−	0.966452i	$-0.582684\pi$
$653$	−32.0795	−	23.3071i	−1.25537	−	0.912079i	−0.998521	+	0.0543729i	$0.982684\pi$
$654$	−4.75192	−	2.11569i	−0.185815	−	0.0827301i
$655$	−0.0729490	−	0.224514i	−0.00285035	−	0.00877249i
$656$	−6.00000	+	10.3923i	−0.234261	+	0.405751i
$657$	−8.56231	−	14.8303i	−0.334047	−	0.578587i
$658$	4.19579	−	4.65990i	0.163569	−	0.181662i
$659$	7.01064	−	21.5765i	0.273096	−	0.840503i	−0.716621	−	0.697463i	$-0.754312\pi$
$659$	7.01064	−	21.5765i	0.273096	−	0.840503i	0.989717	−	0.143040i	$-0.0456877\pi$
$660$	2.16535	+	2.40487i	0.0842862	+	0.0936093i
$661$	−15.1813	+	6.75916i	−0.590485	+	0.262901i	−0.680152	−	0.733071i	$-0.738086\pi$
$661$	−15.1813	+	6.75916i	−0.590485	+	0.262901i	0.0896670	+	0.995972i	$0.471420\pi$
$662$	6.81334	+	1.44822i	0.264808	+	0.0562867i
$663$	0.119779	−	1.13962i	0.00465183	−	0.0442592i
$664$	0.956007	+	9.09580i	0.0371003	+	0.352985i
$665$	38.4124	−	8.16480i	1.48957	−	0.316617i
$666$	−0.236068	+	0.171513i	−0.00914745	+	0.00664601i
$667$	−38.1525	+	27.7194i	−1.47727	+	1.07330i
$668$	−14.6177	+	3.10709i	−0.565576	+	0.120217i
$669$	0.0740275	+	0.704324i	0.00286207	+	0.0272308i
$670$	0.716449	−	6.81655i	0.0276788	−	0.263346i
$671$	−5.18903	−	1.10296i	−0.200320	−	0.0425794i
$672$	15.3970	−	6.85518i	0.593952	−	0.264444i
$673$	−2.95515	−	3.28203i	−0.113913	−	0.126513i	0.683491	−	0.729959i	$-0.260461\pi$
$673$	−2.95515	−	3.28203i	−0.113913	−	0.126513i	−0.797404	+	0.603446i	$0.793794\pi$
$674$	−3.62461	+	11.1554i	−0.139615	+	0.429690i
$675$	6.20318	−	6.88933i	0.238761	−	0.265170i
$676$	8.54508	+	14.8005i	0.328657	+	0.569251i
$677$	−14.3262	+	24.8138i	−0.550602	+	0.953671i	0.447629	+	0.894219i	$0.352268\pi$
$677$	−14.3262	+	24.8138i	−0.550602	+	0.953671i	−0.998231	+	0.0594514i	$0.981065\pi$
$678$	−0.354102	−	1.08981i	−0.0135992	−	0.0418540i
$679$	−14.5029	−	6.45710i	−0.556570	−	0.247801i
$680$	1.11803	+	0.812299i	0.0428746	+	0.0311503i
$681$	20.7426			0.794860
$682$		0			0
$683$	10.0557			0.384772			0.192386	−	0.981319i	$-0.438377\pi$
$683$	10.0557			0.384772			0.192386	+	0.981319i	$0.438377\pi$
$684$	−13.0902	−	9.51057i	−0.500515	−	0.363646i
$685$	15.4794	+	6.89186i	0.591436	+	0.263324i
$686$	2.86475	+	8.81678i	0.109376	+	0.336626i
$687$	−3.61803	+	6.26662i	−0.138037	+	0.239086i
$688$	4.28115	+	7.41517i	0.163217	+	0.282701i
$689$	−41.2766	+	45.8423i	−1.57251	+	1.74645i
$690$	2.73607	−	8.42075i	0.104160	−	0.320573i
$691$	2.56465	+	2.84834i	0.0975640	+	0.108356i	0.789949	−	0.613172i	$-0.210107\pi$
$691$	2.56465	+	2.84834i	0.0975640	+	0.108356i	−0.692385	+	0.721528i	$0.743440\pi$
$692$	−1.34486	+	0.598772i	−0.0511240	+	0.0227619i
$693$	−4.48343	−	0.952982i	−0.170311	−	0.0362008i
$694$	0.524867	−	4.99378i	0.0199237	−	0.189561i
$695$	1.60203	+	15.2423i	0.0607684	+	0.578173i
$696$	−18.8494	+	4.00656i	−0.714485	+	0.151868i
$697$	−1.23607	+	0.898056i	−0.0468194	+	0.0340163i
$698$	−8.35410	+	6.06961i	−0.316207	+	0.229738i
$699$	18.3876	−	3.90840i	0.695482	−	0.147829i
$700$	0.940756	+	8.95070i	0.0355572	+	0.338305i
$701$	3.13945	−	29.8699i	0.118576	−	1.12817i	−0.759786	−	0.650174i	$-0.774696\pi$
$701$	3.13945	−	29.8699i	0.118576	−	1.12817i	0.878361	−	0.477997i	$-0.158637\pi$
$702$	14.6722	+	3.11868i	0.553767	+	0.117707i
$703$	1.07829	−	0.480087i	0.0406686	−	0.0181068i
$704$	0.120671	+	0.134019i	0.00454796	+	0.00505102i
$705$	−2.73607	+	8.42075i	−0.103046	+	0.317144i
$706$	13.3914	−	14.8727i	0.503993	−	0.559740i
$707$	−7.14590	−	12.3771i	−0.268749	−	0.465487i
$708$	−7.66312	+	13.2729i	−0.287998	+	0.498827i
$709$	1.28115	+	3.94298i	0.0481147	+	0.148082i	0.972227	−	0.234038i	$-0.0751941\pi$
$709$	1.28115	+	3.94298i	0.0481147	+	0.148082i	−0.924113	+	0.382120i	$0.875194\pi$
$710$	0.133284	+	0.0593421i	0.00500208	+	0.00222707i
$711$		0			0
$712$	−14.2705			−0.534810
$713$		0			0
$714$	0.437694			0.0163803
$715$	−7.85410	−	5.70634i	−0.293727	−	0.213405i
$716$	−29.2649	−	13.0296i	−1.09368	−	0.486938i
$717$	4.14590	+	12.7598i	0.154831	+	0.476522i
$718$	−7.82624	+	13.5554i	−0.292073	+	0.505885i
$719$	20.6910	+	35.8378i	0.771643	+	1.33653i	0.936662	+	0.350235i	$0.113898\pi$
$719$	20.6910	+	35.8378i	0.771643	+	1.33653i	−0.165018	+	0.986290i	$0.552768\pi$
$720$	6.49606	−	7.21460i	0.242094	−	0.268872i
$721$	−0.135255	+	0.416272i	−0.00503716	+	0.0155028i
$722$	−2.48127	−	2.75573i	−0.0923434	−	0.102558i
$723$	7.79059	−	3.46859i	0.289735	−	0.128998i
$724$	26.9055	+	5.71894i	0.999935	+	0.212543i
$725$	1.67023	−	15.8912i	0.0620308	−	0.590184i
$726$	0.672922	+	6.40243i	0.0249745	+	0.237616i
$727$	23.3120	−	4.95512i	0.864595	−	0.183775i	0.245793	−	0.969322i	$-0.420952\pi$
$727$	23.3120	−	4.95512i	0.864595	−	0.183775i	0.618802	+	0.785547i	$0.287618\pi$
$728$	−26.3435	+	19.1396i	−0.976354	+	0.709362i
$729$	−10.5172	+	7.64121i	−0.389527	+	0.283008i
$730$	13.5514	−	2.88043i	0.501558	−	0.106609i
$731$	0.113954	+	1.08420i	0.00421473	+	0.0401005i
$732$	1.17449	−	11.1745i	0.0434104	−	0.413022i
$733$	−27.3336	−	5.80994i	−1.00959	−	0.214595i	−0.326710	−	0.945125i	$-0.605940\pi$
$733$	−27.3336	−	5.80994i	−1.00959	−	0.214595i	−0.682881	+	0.730530i	$0.739273\pi$
$734$	20.4784	−	9.11757i	0.755872	−	0.336536i
$735$	3.50361	+	3.89116i	0.129233	+	0.143527i
$736$	9.50000	−	29.2380i	0.350175	−	1.07773i
$737$	2.16535	−	2.40487i	0.0797618	−	0.0885844i
$738$	−4.00000	−	6.92820i	−0.147242	−	0.255031i
$739$	−10.8541	+	18.7999i	−0.399275	+	0.691564i	−0.993637	−	0.112634i	$-0.964071\pi$
$739$	−10.8541	+	18.7999i	−0.399275	+	0.691564i	0.594362	+	0.804198i	$0.297405\pi$
$740$	0.309017	+	0.951057i	0.0113597	+	0.0349615i
$741$	−22.1722	−	9.87171i	−0.814517	−	0.362646i
$742$	−19.0623	−	13.8496i	−0.699799	−	0.508434i
$743$	−3.43769			−0.126117			−0.0630584	−	0.998010i	$-0.520085\pi$
$743$	−3.43769			−0.126117			−0.0630584	+	0.998010i	$0.520085\pi$
$744$		0			0
$745$	44.5967			1.63390
$746$	−0.173762	−	0.126246i	−0.00636188	−	0.00462218i
$747$	7.47311	+	3.32724i	0.273427	+	0.121737i
$748$	0.0901699	+	0.277515i	0.00329694	+	0.0101469i
$749$	−1.63525	+	2.83234i	−0.0597509	+	0.103492i
$750$	−2.54508	−	4.40822i	−0.0929334	−	0.160965i
$751$	−26.6534	+	29.6016i	−0.972595	+	1.08018i	0.0241624	+	0.999708i	$0.492308\pi$
$751$	−26.6534	+	29.6016i	−0.972595	+	1.08018i	−0.996757	+	0.0804679i	$0.974359\pi$
$752$	−1.93769	+	5.96361i	−0.0706604	+	0.217470i
$753$	−0.631841	−	0.701731i	−0.0230256	−	0.0255725i
$754$	23.6189	−	10.5158i	0.860150	−	0.382963i
$755$	−49.9529	−	10.6178i	−1.81797	−	0.386422i
$756$	2.53696	−	24.1376i	0.0922683	−	0.877874i
$757$	−4.50775	−	42.8884i	−0.163837	−	1.55880i	−0.699661	−	0.714475i	$-0.746666\pi$
$757$	−4.50775	−	42.8884i	−0.163837	−	1.55880i	0.535824	−	0.844330i	$-0.320001\pi$
$758$	−11.1332	+	2.36644i	−0.404378	+	0.0859531i
$759$	3.38197	−	2.45714i	0.122758	−	0.0891886i
$760$	23.6803	−	17.2048i	0.858976	−	0.624083i
$761$	−3.42995	+	0.729059i	−0.124336	+	0.0264284i	−0.269659	−	0.962956i	$-0.586911\pi$
$761$	−3.42995	+	0.729059i	−0.124336	+	0.0264284i	0.145324	+	0.989384i	$0.453578\pi$
$762$	−0.661272	−	6.29158i	−0.0239554	−	0.227920i
$763$	2.63926	−	25.1109i	0.0955477	−	0.909076i
$764$	−25.4655	−	5.41286i	−0.921310	−	0.195831i
$765$	1.12920	−	0.502754i	0.0408265	−	0.0181771i
$766$	6.96994	+	7.74090i	0.251834	+	0.279690i
$767$	14.2082	−	43.7284i	0.513029	−	1.57894i
$768$	4.39104	−	4.87674i	0.158448	−	0.175974i
$769$	26.8713	+	46.5425i	0.969005	+	1.67837i	0.698447	+	0.715662i	$0.253875\pi$
$769$	26.8713	+	46.5425i	0.969005	+	1.67837i	0.270557	+	0.962704i	$0.412792\pi$
$770$	1.85410	−	3.21140i	0.0668172	−	0.115731i
$771$	−0.437694	−	1.34708i	−0.0157632	−	0.0485140i
$772$	3.52090	+	1.56760i	0.126720	+	0.0564193i
$773$	15.4443	+	11.2209i	0.555492	+	0.403588i	0.829806	−	0.558052i	$-0.188451\pi$
$773$	15.4443	+	11.2209i	0.555492	+	0.403588i	−0.274314	+	0.961640i	$0.588451\pi$
$774$	−5.70820			−0.205177
$775$		0			0
$776$	−11.8328			−0.424773
$777$	0.572949	+	0.416272i	0.0205544	+	0.0149337i
$778$	16.4124	+	7.30725i	0.588411	+	0.261978i
$779$	10.0000	+	30.7768i	0.358287	+	1.10269i
$780$	10.2812	−	17.8075i	0.368124	−	0.637610i
$781$	0.0344419	+	0.0596550i	0.00123243	+	0.00213463i
$782$	0.534216	−	0.593307i	0.0191035	−	0.0212166i
$783$	−13.3156	+	40.9812i	−0.475861	+	1.46455i
$784$	2.48127	+	2.75573i	0.0886169	+	0.0984190i
$785$	−23.2190	+	10.3378i	−0.828723	+	0.368971i
$786$	−0.0545103	−	0.0115865i	−0.00194432	−	0.000413278i
$787$	−3.27088	+	31.1204i	−0.116594	+	1.10932i	0.767188	+	0.641423i	$0.221656\pi$
$787$	−3.27088	+	31.1204i	−0.116594	+	1.10932i	−0.883782	+	0.467899i	$0.845011\pi$
$788$	2.77652	+	26.4168i	0.0989093	+	0.941059i
$789$	−10.5624	+	2.24511i	−0.376032	+	0.0799280i
$790$		0			0
$791$	4.50000	−	3.26944i	0.160002	−	0.116248i
$792$	−3.34175	+	0.710311i	−0.118744	+	0.0252398i
$793$	3.52347	+	33.5235i	0.125122	+	1.19046i
$794$	1.05248	−	10.0137i	0.0373513	−	0.355374i
$795$	32.5435	+	6.91733i	1.15420	+	0.245332i
$796$	39.4787	−	17.5770i	1.39928	−	0.623001i
$797$	6.05946	+	6.72972i	0.214637	+	0.238379i	0.840843	−	0.541279i	$-0.182060\pi$
$797$	6.05946	+	6.72972i	0.214637	+	0.238379i	−0.626206	+	0.779658i	$0.715393\pi$
$798$	2.86475	−	8.81678i	0.101411	−	0.312111i
$799$	−0.534216	+	0.593307i	−0.0188992	+	0.0209897i
$800$	5.20820	+	9.02087i	0.184138	+	0.318936i
$801$	−6.38197	+	11.0539i	−0.225496	+	0.390570i
$802$	5.69756	+	17.5353i	0.201188	+	0.619193i
$803$	5.97552	+	2.66047i	0.210871	+	0.0938860i
$804$	5.54508	+	4.02874i	0.195560	+	0.142083i
$805$	42.9787			1.51480
$806$		0			0
$807$	1.38197			0.0486475
$808$	−8.61803	−	6.26137i	−0.303181	−	0.220274i
$809$	50.0608	+	22.2885i	1.76004	+	0.783622i	0.989195	+	0.146604i	$0.0468344\pi$
$809$	50.0608	+	22.2885i	1.76004	+	0.783622i	0.770849	+	0.637018i	$0.219832\pi$
$810$	0.500000	+	1.53884i	0.0175682	+	0.0540694i
$811$	−21.3885	+	37.0460i	−0.751053	+	1.30086i	0.196259	+	0.980552i	$0.437121\pi$
$811$	−21.3885	+	37.0460i	−0.751053	+	1.30086i	−0.947313	+	0.320311i	$0.896213\pi$
$812$	−20.9164	−	36.2283i	−0.734022	−	1.27136i
$813$	−6.39843	+	7.10618i	−0.224403	+	0.249225i
$814$	0.0344419	−	0.106001i	0.00120719	−	0.00371534i
$815$	22.2623	+	24.7248i	0.779815	+	0.866072i
$816$	−0.399853	+	0.178026i	−0.0139977	+	0.00623216i
$817$	22.5856	+	4.80072i	0.790170	+	0.167956i
$818$	−0.399263	+	3.79874i	−0.0139599	+	0.132820i
$819$	3.04435	+	28.9651i	0.106378	+	1.01212i
$820$	−26.8173	+	5.70019i	−0.936501	+	0.199059i
$821$	26.2705	−	19.0866i	0.916847	−	0.666128i	−0.0258901	−	0.999665i	$-0.508242\pi$
$821$	26.2705	−	19.0866i	0.916847	−	0.666128i	0.942737	+	0.333536i	$0.108242\pi$
$822$	3.23607	−	2.35114i	0.112871	−	0.0820055i
$823$	5.99077	−	1.27338i	0.208825	−	0.0443872i	−0.102311	−	0.994752i	$-0.532624\pi$
$823$	5.99077	−	1.27338i	0.208825	−	0.0443872i	0.311136	+	0.950365i	$0.399290\pi$
$824$	0.0341011	+	0.324451i	0.00118797	+	0.0113028i
$825$	−0.148055	+	1.40865i	−0.00515461	+	0.0490429i
$826$	17.1785	+	3.65141i	0.597717	+	0.127049i
$827$	2.44260	−	1.08752i	0.0849376	−	0.0378167i	−0.363828	−	0.931466i	$-0.618530\pi$
$827$	2.44260	−	1.08752i	0.0849376	−	0.0378167i	0.448766	+	0.893649i	$0.351864\pi$
$828$	−11.8491	−	13.1598i	−0.411785	−	0.457333i
$829$	−6.70820	+	20.6457i	−0.232986	+	0.717056i	0.764397	+	0.644746i	$0.223037\pi$
$829$	−6.70820	+	20.6457i	−0.232986	+	0.717056i	−0.997382	+	0.0723096i	$0.976963\pi$
$830$	−4.42833	+	4.91816i	−0.153710	+	0.170712i
$831$	6.66312	+	11.5409i	0.231141	+	0.400348i
$832$	0.572949	−	0.992377i	0.0198634	−	0.0344045i
$833$	0.145898	+	0.449028i	0.00505507	+	0.0155579i
$834$	3.30524	+	1.47159i	0.114451	+	0.0509569i
$835$	−19.5623	−	14.2128i	−0.676982	−	0.491856i
$836$	6.18034			0.213752
$837$		0			0
$838$	−2.76393			−0.0954784
$839$	−9.04508	−	6.57164i	−0.312271	−	0.226878i	0.420599	−	0.907246i	$-0.361820\pi$
$839$	−9.04508	−	6.57164i	−0.312271	−	0.226878i	−0.732870	+	0.680368i	$0.761820\pi$
$840$	16.0440	+	7.14323i	0.553569	+	0.246465i
$841$	13.9894	+	43.0548i	0.482392	+	1.48465i
$842$	4.56231	−	7.90215i	0.157227	−	0.272326i
$843$	9.51722	+	16.4843i	0.327791	+	0.567750i
$844$	8.66141	−	9.61947i	0.298138	−	0.331116i
$845$	−8.54508	+	26.2991i	−0.293960	+	0.904715i
$846$	−2.79719	−	3.10660i	−0.0961695	−	0.106807i
$847$	−28.5476	+	12.7102i	−0.980907	+	0.436728i
$848$	23.0474	+	4.89888i	0.791451	+	0.168228i
$849$	0.685948	−	6.52636i	0.0235417	−	0.223984i
$850$	0.0282760	+	0.269028i	0.000969858	+	0.00922758i
$851$	1.26357	−	0.268580i	0.0433145	−	0.00920679i
$852$	−0.118034	+	0.0857567i	−0.00404378	+	0.00293798i
$853$	−3.23607	+	2.35114i	−0.110801	+	0.0805015i	−0.641806	−	0.766867i	$-0.721815\pi$
$853$	−3.23607	+	2.35114i	−0.110801	+	0.0805015i	0.531005	+	0.847369i	$0.321815\pi$
$854$	−12.5940	+	2.67694i	−0.430959	+	0.0916031i
$855$	−2.73659	−	26.0369i	−0.0935894	−	0.890444i
$856$	−0.254808	+	2.42434i	−0.00870917	+	0.0828622i
$857$	8.00158	+	1.70079i	0.273329	+	0.0580978i	0.342537	−	0.939504i	$-0.388714\pi$
$857$	8.00158	+	1.70079i	0.273329	+	0.0580978i	−0.0692080	+	0.997602i	$0.522047\pi$
$858$	−2.09366	+	0.932157i	−0.0714764	+	0.0318233i
$859$	28.9679	+	32.1721i	0.988371	+	1.09770i	0.995214	+	0.0977204i	$0.0311551\pi$
$859$	28.9679	+	32.1721i	0.988371	+	1.09770i	−0.00684308	+	0.999977i	$0.502178\pi$
$860$	−6.04508	+	18.6049i	−0.206136	+	0.634420i
$861$	−12.9921	+	14.4292i	−0.442770	+	0.491746i
$862$	9.03444	+	15.6481i	0.307714	+	0.532977i
$863$	−1.24671	+	2.15937i	−0.0424385	+	0.0735057i	−0.886464	−	0.462797i	$-0.846846\pi$
$863$	−1.24671	+	2.15937i	−0.0424385	+	0.0735057i	0.844026	+	0.536302i	$0.180179\pi$
$864$	−8.68034	−	26.7153i	−0.295311	−	0.908874i
$865$	−2.17603	−	0.968833i	−0.0739874	−	0.0329413i
$866$	0.291796	+	0.212002i	0.00991563	+	0.00720413i
$867$	16.9443			0.575458
$868$		0			0
$869$		0			0
$870$	−11.2812	−	8.19624i	−0.382467	−	0.277878i
$871$	−18.7846	−	8.36344i	−0.636492	−	0.283384i
$872$	−5.81559	−	17.8986i	−0.196941	−	0.606122i
$873$	−5.29180	+	9.16566i	−0.179100	+	0.310211i
$874$	−8.45492	−	14.6443i	−0.285992	−	0.495352i
$875$	16.5330	−	18.3618i	0.558918	−	0.620741i
$876$	−4.28115	+	13.1760i	−0.144647	+	0.445177i
$877$	10.9013	+	12.1072i	0.368112	+	0.408830i	0.898534	−	0.438904i	$-0.144633\pi$
$877$	10.9013	+	12.1072i	0.368112	+	0.408830i	−0.530422	+	0.847734i	$0.677966\pi$
$878$	−23.6189	+	10.5158i	−0.797099	+	0.354891i
$879$	−8.05609	−	1.71237i	−0.271725	−	0.0577570i
$880$	−0.387613	+	3.68789i	−0.0130664	+	0.124319i
$881$	1.60563	+	15.2765i	0.0540950	+	0.514679i	0.987698	+	0.156371i	$0.0499796\pi$
$881$	1.60563	+	15.2765i	0.0540950	+	0.514679i	−0.933603	+	0.358308i	$0.883354\pi$
$882$	−2.41811	+	0.513986i	−0.0814221	+	0.0173068i
$883$	0.809017	−	0.587785i	0.0272256	−	0.0197805i	−0.574089	−	0.818793i	$-0.694644\pi$
$883$	0.809017	−	0.587785i	0.0272256	−	0.0197805i	0.601315	+	0.799012i	$0.294644\pi$
$884$	1.50000	−	1.08981i	0.0504505	−	0.0366544i
$885$	−24.2565	+	5.15587i	−0.815372	+	0.173313i
$886$	−2.65674	−	25.2772i	−0.0892549	−	0.849203i
$887$	−4.08741	+	38.8891i	−0.137242	+	1.30577i	0.681590	+	0.731735i	$0.261289\pi$
$887$	−4.08741	+	38.8891i	−0.137242	+	1.30577i	−0.818831	+	0.574034i	$0.805378\pi$
$888$	0.516329	+	0.109749i	0.0173269	+	0.00368294i
$889$	28.0533	−	12.4902i	0.940879	−	0.418906i
$890$	−6.90960	−	7.67389i	−0.231610	−	0.257229i
$891$	−0.236068	+	0.726543i	−0.00790857	+	0.0243401i
$892$	−0.766755	+	0.851568i	−0.0256729	+	0.0285126i
$893$	8.45492	+	14.6443i	0.282933	+	0.490054i
$894$	5.26393	−	9.11740i	0.176052	−	0.304931i
$895$	−16.0172	−	49.2959i	−0.535397	−	1.64778i
$896$	31.1938	+	13.8884i	1.04211	+	0.463978i
$897$	−21.4894	−	15.6129i	−0.717509	−	0.521301i
$898$	−14.8754			−0.496398
$899$		0			0
$900$	6.00000			0.200000
$901$	2.42705	+	1.76336i	0.0808568	+	0.0587459i
$902$	2.79155	+	1.24288i	0.0929483	+	0.0413833i
$903$	4.28115	+	13.1760i	0.142468	+	0.438471i
$904$	2.07295	−	3.59045i	0.0689453	−	0.119417i
$905$	22.2533	+	38.5438i	0.739724	+	1.28124i
$906$	−8.06686	+	8.95915i	−0.268003	+	0.297648i
$907$	16.3541	−	50.3328i	0.543029	−	1.67127i	−0.182601	−	0.983187i	$-0.558452\pi$
$907$	16.3541	−	50.3328i	0.543029	−	1.67127i	0.725631	−	0.688085i	$-0.241548\pi$
$908$	22.4576	+	24.9417i	0.745281	+	0.827718i
$909$	−8.70414	+	3.87533i	−0.288698	+	0.128537i
$910$	−23.0474	−	4.89888i	−0.764014	−	0.162396i
$911$	−0.855078	+	8.13553i	−0.0283300	+	0.269542i	0.971183	+	0.238335i	$0.0766017\pi$
$911$	−0.855078	+	8.13553i	−0.0283300	+	0.269542i	−0.999513	+	0.0312068i	$0.990065\pi$
$912$	0.969032	+	9.21973i	0.0320879	+	0.305296i
$913$	−3.05633	+	0.649643i	−0.101150	+	0.0215001i
$914$	−7.87132	+	5.71885i	−0.260360	+	0.189163i
$915$	14.7082	−	10.6861i	0.486238	−	0.353273i
$916$	−11.4524	+	2.43427i	−0.378396	+	0.0804306i
$917$	−0.0282760	−	0.269028i	−0.000933755	−	0.00888409i
$918$	0.0762525	−	0.725494i	0.00251671	−	0.0239449i
$919$	−9.65959	−	2.05321i	−0.318640	−	0.0677291i	0.0458150	−	0.998950i	$-0.485412\pi$
$919$	−9.65959	−	2.05321i	−0.318640	−	0.0677291i	−0.364455	+	0.931221i	$0.618745\pi$
$920$	29.2649	−	13.0296i	0.964836	−	0.429573i
$921$	−4.07512	−	4.52588i	−0.134280	−	0.149133i
$922$	−2.05166	+	6.31437i	−0.0675679	+	0.207953i
$923$	0.292875	−	0.325270i	0.00964008	−	0.0107064i
$924$	1.85410	+	3.21140i	0.0609955	+	0.105647i
$925$	−0.218847	+	0.379054i	−0.00719565	+	0.0124632i
$926$	5.94427	+	18.2946i	0.195341	+	0.601197i
$927$	0.266569	+	0.118684i	0.00875527	+	0.00389810i
$928$	−39.1697	−	28.4585i	−1.28581	−	0.934194i
$929$	33.5410			1.10045			0.550223	−	0.835018i	$-0.314543\pi$
$929$	33.5410			1.10045			0.550223	+	0.835018i	$0.314543\pi$
$930$		0			0
$931$	10.0000			0.327737
$932$	24.6074	+	17.8783i	0.806042	+	0.585624i
$933$	−15.0480	−	6.69982i	−0.492651	−	0.219342i
$934$	6.25987	+	19.2659i	0.204829	+	0.630399i
$935$	−0.236068	+	0.408882i	−0.00772025	+	0.0133719i
$936$	10.8541	+	18.7999i	0.354777	+	0.614493i
$937$	27.0899	−	30.0864i	0.884990	−	0.982881i	−0.114955	−	0.993371i	$-0.536672\pi$
$937$	27.0899	−	30.0864i	0.884990	−	0.982881i	0.999945	+	0.0104897i	$0.00333904\pi$
$938$	2.42705	−	7.46969i	0.0792460	−	0.243894i
$939$	−0.827091	−	0.918578i	−0.0269911	−	0.0299766i
$940$	−13.0877	+	5.82701i	−0.426873	+	0.190056i
$941$	−27.9590	−	5.94286i	−0.911436	−	0.193732i	−0.271750	−	0.962368i	$-0.587602\pi$
$941$	−27.9590	−	5.94286i	−0.911436	−	0.193732i	−0.639686	+	0.768636i	$0.720936\pi$
$942$	−0.627171	+	5.96713i	−0.0204343	+	0.194420i
$943$	3.70202	+	35.2224i	0.120554	+	1.14700i
$944$	−17.1785	+	3.65141i	−0.559113	+	0.118843i
$945$	31.7705	−	23.0826i	1.03349	−	0.750878i
$946$	1.76393	−	1.28157i	0.0573504	−	0.0416675i
$947$	−21.5866	+	4.58838i	−0.701471	+	0.149102i	−0.544822	−	0.838552i	$-0.683403\pi$
$947$	−21.5866	+	4.58838i	−0.701471	+	0.149102i	−0.156649	+	0.987654i	$0.550069\pi$
$948$		0			0
$949$	4.34444	−	41.3346i	0.141027	−	1.34178i
$950$	5.60429	+	1.19123i	0.181827	+	0.0386485i
$951$	−23.6504	+	10.5298i	−0.766916	+	0.341453i
$952$	1.05963	+	1.17684i	0.0343428	+	0.0381415i
$953$	13.0451	−	40.1486i	0.422572	−	1.30054i	−0.482729	−	0.875770i	$-0.660354\pi$
$953$	13.0451	−	40.1486i	0.422572	−	1.30054i	0.905300	−	0.424772i	$-0.139646\pi$
$954$	−10.5108	+	11.6735i	−0.340301	+	0.377943i
$955$	−21.0623	−	36.4810i	−0.681560	−	1.18050i
$956$	−10.8541	+	18.7999i	−0.351047	+	0.608031i
$957$	−2.03444	−	6.26137i	−0.0657642	−	0.202401i
$958$	5.04996	+	2.24838i	0.163157	+	0.0726420i
$959$	15.7082	+	11.4127i	0.507244	+	0.368535i
$960$	−0.618034			−0.0199470
$961$		0			0
$962$	−0.708204			−0.0228334
$963$	1.76393	+	1.28157i	0.0568419	+	0.0412981i
$964$	12.6054	+	5.61230i	0.405994	+	0.180760i
$965$	1.92705	+	5.93085i	0.0620340	+	0.190921i
$966$	5.07295	−	8.78661i	0.163219	−	0.282704i
$967$	−21.8262	−	37.8042i	−0.701884	−	1.21570i	−0.967804	−	0.251704i	$-0.919009\pi$
$967$	−21.8262	−	37.8042i	−0.701884	−	1.21570i	0.265920	−	0.963995i	$-0.414324\pi$
$968$	−15.5853	+	17.3092i	−0.500929	+	0.556338i
$969$	−0.364745	+	1.12257i	−0.0117173	+	0.0360621i
$970$	−5.72930	−	6.36303i	−0.183957	−	0.204305i
$971$	−18.7846	+	8.36344i	−0.602827	+	0.268396i	−0.685374	−	0.728191i	$-0.740361\pi$
$971$	−18.7846	+	8.36344i	−0.602827	+	0.268396i	0.0825472	+	0.996587i	$0.473694\pi$
$972$	−25.3228	−	5.38253i	−0.812230	−	0.172645i
$973$	−1.83576	+	17.4661i	−0.0588518	+	0.559937i
$974$	1.48087	+	14.0896i	0.0474503	+	0.451459i
$975$	8.80333	−	1.87121i	0.281932	−	0.0599265i
$976$	10.4164	−	7.56796i	0.333421	−	0.242245i
$977$	4.90983	−	3.56720i	0.157079	−	0.114125i	−0.506469	−	0.862258i	$-0.669050\pi$
$977$	4.90983	−	3.56720i	0.157079	−	0.114125i	0.663549	+	0.748133i	$0.269050\pi$
$978$	7.68247	−	1.63296i	0.245658	−	0.0522163i
$979$	−0.509617	−	4.84868i	−0.0162874	−	0.154964i
$980$	−0.885579	+	8.42572i	−0.0282888	+	0.269150i
$981$	−16.4650	−	3.49974i	−0.525686	−	0.111738i
$982$	15.5812	−	6.93719i	0.497216	−	0.221375i
$983$	14.0748	+	15.6316i	0.448916	+	0.498572i	0.924544	−	0.381075i	$-0.124446\pi$
$983$	14.0748	+	15.6316i	0.448916	+	0.498572i	−0.475628	+	0.879646i	$0.657779\pi$
$984$	−4.47214	+	13.7638i	−0.142566	+	0.438775i
$985$	−28.7584	+	31.9394i	−0.916318	+	1.01767i
$986$	−0.628677	−	1.08890i	−0.0200212	−	0.0346777i
$987$	−5.07295	+	8.78661i	−0.161474	+	0.279681i
$988$	−12.1353	−	37.3485i	−0.386074	−	1.18821i
$989$	23.0858	+	10.2784i	0.734084	+	0.326835i
$990$	−2.00000	−	1.45309i	−0.0635642	−	0.0461821i
$991$	−17.2705			−0.548616			−0.274308	−	0.961642i	$-0.588449\pi$
$991$	−17.2705			−0.548616			−0.274308	+	0.961642i	$0.588449\pi$
$992$		0			0
$993$	−11.2705			−0.357659
$994$	0.135255	+	0.0982684i	0.00429003	+	0.00311689i
$995$	63.8778	+	28.4402i	2.02506	+	0.901616i
$996$	−2.04508	−	6.29412i	−0.0648010	−	0.199437i
$997$	13.6246	−	23.5985i	0.431496	−	0.747373i	−0.565507	−	0.824744i	$-0.691319\pi$
$997$	13.6246	−	23.5985i	0.431496	−	0.747373i	0.997002	+	0.0773712i	$0.0246526\pi$
$998$	1.28115	+	2.21902i	0.0405542	+	0.0702419i
$999$	0.789802	−	0.877163i	0.0249882	−	0.0277522i

Display

a_p

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p

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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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.f.732.1		8
31.2	even	5		961.2.g.b.448.1		8
31.3	odd	30		961.2.d.e.388.1		4
31.4	even	5		961.2.c.f.521.1		4
31.5	even	3	inner	961.2.g.f.816.1		8
31.6	odd	6		961.2.d.e.374.1		4
31.7	even	15		961.2.a.d.1.1		2
31.8	even	5		961.2.g.b.844.1		8
31.9	even	15		961.2.g.b.547.1		8
31.10	even	15		961.2.g.b.846.1		8
31.11	odd	30		961.2.c.d.439.1		4
31.12	odd	30		961.2.d.b.628.1		4
31.13	odd	30		961.2.g.g.235.1		8
31.14	even	15		31.2.d.a.4.1	✓	4
31.15	odd	10		961.2.g.g.338.1		8
31.16	even	5	inner	961.2.g.f.338.1		8
31.17	odd	30		961.2.d.b.531.1		4
31.18	even	15	inner	961.2.g.f.235.1		8
31.19	even	15		31.2.d.a.8.1	yes	4
31.20	even	15		961.2.c.f.439.1		4
31.21	odd	30		961.2.g.c.846.1		8
31.22	odd	30		961.2.g.c.547.1		8
31.23	odd	10		961.2.g.c.844.1		8
31.24	odd	30		961.2.a.e.1.1		2
31.25	even	3		961.2.d.f.374.1		4
31.26	odd	6		961.2.g.g.816.1		8
31.27	odd	10		961.2.c.d.521.1		4
31.28	even	15		961.2.d.f.388.1		4
31.29	odd	10		961.2.g.c.448.1		8
31.30	odd	2		961.2.g.g.732.1		8
93.14	odd	30		279.2.i.a.190.1		4
93.38	odd	30		8649.2.a.g.1.2		2
93.50	odd	30		279.2.i.a.163.1		4
93.86	even	30		8649.2.a.f.1.2		2
124.19	odd	30		496.2.n.b.225.1		4
124.107	odd	30		496.2.n.b.97.1		4
155.14	even	30		775.2.k.c.376.1		4
155.19	even	30		775.2.k.c.101.1		4
155.107	odd	60		775.2.bf.a.624.2		8
155.112	odd	60		775.2.bf.a.349.1		8
155.138	odd	60		775.2.bf.a.624.1		8
155.143	odd	60		775.2.bf.a.349.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.d.a.4.1	✓	4	31.14	even	15
31.2.d.a.8.1	yes	4	31.19	even	15
279.2.i.a.163.1		4	93.50	odd	30
279.2.i.a.190.1		4	93.14	odd	30
496.2.n.b.97.1		4	124.107	odd	30
496.2.n.b.225.1		4	124.19	odd	30
775.2.k.c.101.1		4	155.19	even	30
775.2.k.c.376.1		4	155.14	even	30
775.2.bf.a.349.1		8	155.112	odd	60
775.2.bf.a.349.2		8	155.143	odd	60
775.2.bf.a.624.1		8	155.138	odd	60
775.2.bf.a.624.2		8	155.107	odd	60
961.2.a.d.1.1		2	31.7	even	15
961.2.a.e.1.1		2	31.24	odd	30
961.2.c.d.439.1		4	31.11	odd	30
961.2.c.d.521.1		4	31.27	odd	10
961.2.c.f.439.1		4	31.20	even	15
961.2.c.f.521.1		4	31.4	even	5
961.2.d.b.531.1		4	31.17	odd	30
961.2.d.b.628.1		4	31.12	odd	30
961.2.d.e.374.1		4	31.6	odd	6
961.2.d.e.388.1		4	31.3	odd	30
961.2.d.f.374.1		4	31.25	even	3
961.2.d.f.388.1		4	31.28	even	15
961.2.g.b.448.1		8	31.2	even	5
961.2.g.b.547.1		8	31.9	even	15
961.2.g.b.844.1		8	31.8	even	5
961.2.g.b.846.1		8	31.10	even	15
961.2.g.c.448.1		8	31.29	odd	10
961.2.g.c.547.1		8	31.22	odd	30
961.2.g.c.844.1		8	31.23	odd	10
961.2.g.c.846.1		8	31.21	odd	30
961.2.g.f.235.1		8	31.18	even	15	inner
961.2.g.f.338.1		8	31.16	even	5	inner
961.2.g.f.732.1		8	1.1	even	1	trivial
961.2.g.f.816.1		8	31.5	even	3	inner
961.2.g.g.235.1		8	31.13	odd	30
961.2.g.g.338.1		8	31.15	odd	10
961.2.g.g.732.1		8	31.30	odd	2
961.2.g.g.816.1		8	31.26	odd	6
8649.2.a.f.1.2		2	93.86	even	30
8649.2.a.g.1.2		2	93.38	odd	30

Overview	Random
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Classical	Maass
Hilbert	Bianchi

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

Introduction

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	961.2.g.f.732.1

Level	$961$
Weight	$2$
Character	961.732
Analytic conductor	$7.674$
Analytic rank	$0$
Dimension	$8$
Inner twists	$4$