LMFDB - Embedded newform 961.2.g.g.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.g.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	0.653139	−	0.757238i	$-0.273452\pi$
$3$	0.913545	+	0.406737i	0.527436	+	0.234830i	−0.125703	+	0.992068i	$0.540119\pi$
$4$	−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	0.0938779	−	0.995584i	$-0.470074\pi$
$11$	−0.747238	−	0.158830i	−0.225301	−	0.0478892i	−0.319179	+	0.947695i	$0.603407\pi$
$12$	0.169131	−	1.60917i	0.0488238	−	0.464527i
$13$	0.507392	+	4.82751i	0.140725	+	1.33891i	0.805824	+	0.592155i	$0.201723\pi$
$13$	0.507392	+	4.82751i	0.140725	+	1.33891i	−0.665099	+	0.746755i	$0.731611\pi$
$14$	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	−0.179825	−	0.983699i	$-0.557553\pi$
$17$	0.230909	−	0.0490813i	0.0560037	−	0.0119040i	0.235828	+	0.971795i	$0.424220\pi$
$18$	−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	$-0.706746\pi$
$23$	1.69098	−	5.20431i	0.352594	−	1.08517i	0.957391	−	0.288794i	$-0.0932543\pi$
$24$	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	−0.294804	−	0.955558i	$-0.595254\pi$
$29$	−6.97214	−	5.06555i	−1.29469	−	0.940650i	−0.999889	+	0.0149080i	$0.995254\pi$
$30$	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	0.875565	−	0.483101i	$-0.160490\pi$
$37$	0.118034	+	0.204441i	0.0194047	+	0.0336099i	−0.856160	+	0.516711i	$0.827156\pi$
$38$	−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	$0.147873\pi$
$43$	−0.482716	+	4.59274i	−0.0736135	+	0.700386i	−0.967634	+	0.252359i	$0.918794\pi$
$44$	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	$0.104367\pi$
$53$	8.50345	+	9.44404i	1.16804	+	1.29724i	0.221311	+	0.975203i	$0.428967\pi$
$54$	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	$-0.353360\pi$
$61$	6.94427			0.889123			0.444561	+	0.895748i	$0.353360\pi$
$62$		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	−0.310193	−	0.950673i	$-0.600394\pi$
$73$	−8.37520	−	1.78020i	−0.980243	−	0.208357i	−0.670050	+	0.742316i	$0.733727\pi$
$74$	−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	−0.191286	−	0.981534i	$-0.561266\pi$
$83$	3.73656	−	1.66362i	0.410140	−	0.182606i	0.601427	+	0.798928i	$0.294599\pi$
$84$	−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	$0.00983276\pi$
$89$	1.97214	+	6.06961i	0.209046	+	0.643377i	−0.790477	+	0.612492i	$0.790167\pi$
$90$	−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	−0.0525171	−	0.998620i	$-0.516724\pi$
$127$	−9.35111	−	4.16338i	−0.829777	−	0.369441i	−0.777260	+	0.629179i	$0.783391\pi$
$128$	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	$-0.944167\pi$
$137$	−0.676522	−	6.43668i	−0.0577992	−	0.549923i	0.926857	−	0.375415i	$-0.122500\pi$
$138$	3.30806	−	0.703150i	0.281601	−	0.0598561i
$139$	4.73607	−	3.44095i	0.401708	−	0.291858i	−0.368528	−	0.929617i	$-0.620138\pi$
$139$	4.73607	−	3.44095i	0.401708	−	0.291858i	0.770236	+	0.637759i	$0.220138\pi$
$140$	−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	$0.191854\pi$
$151$	6.02786	+	18.5519i	0.490541	+	1.50973i	−0.333252	+	0.942838i	$0.608146\pi$
$152$	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	$0.149654\pi$
$167$	−0.965432	+	9.18547i	−0.0747074	+	0.710793i	−0.966206	+	0.257770i	$0.917012\pi$
$168$	−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	$0.498461\pi$
$179$	−13.2477	+	14.7131i	−0.990179	+	1.09971i	−0.995016	+	0.0997174i	$0.968206\pi$
$180$	4.23607	+	7.33708i	0.315738	+	0.546874i
$181$	8.50000	−	14.7224i	0.631800	−	1.09431i	−0.355383	−	0.934721i	$-0.615650\pi$
$181$	8.50000	−	14.7224i	0.631800	−	1.09431i	0.987184	−	0.159589i	$-0.0510169\pi$
$182$	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	0.740683	−	0.671855i	$-0.234502\pi$
$197$	16.0577	+	3.41316i	1.14406	+	0.243178i	0.403379	+	0.915033i	$0.367836\pi$
$198$	−0.0987033	+	0.939099i	−0.00701454	+	0.0667389i
$199$	−2.79177	−	26.5619i	−0.197903	−	1.88292i	−0.419458	−	0.907775i	$-0.637780\pi$
$199$	−2.79177	−	26.5619i	−0.197903	−	1.88292i	0.221555	−	0.975148i	$-0.428887\pi$
$200$	−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	0.877638	−	0.479324i	$-0.159118\pi$
$223$	0.354102	+	0.613323i	0.0237124	+	0.0410711i	−0.853926	+	0.520395i	$0.825785\pi$
$224$	−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	$0.110181\pi$
$229$	−0.756375	+	7.19643i	−0.0499827	+	0.475553i	−0.990670	+	0.136280i	$0.956485\pi$
$230$	−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	0.959886	−	0.280391i	$-0.0904642\pi$
$239$	8.97733	+	9.97033i	0.580695	+	0.644927i	−0.379191	+	0.925319i	$0.623798\pi$
$240$	−1.50000	+	4.61653i	−0.0968246	+	0.297995i
$241$	5.70625	−	6.33744i	0.367572	−	0.408230i	−0.530778	−	0.847511i	$-0.678100\pi$
$241$	5.70625	−	6.33744i	0.367572	−	0.408230i	0.898350	+	0.439281i	$0.144767\pi$
$242$	−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	0.379331	−	0.925261i	$-0.376154\pi$
$251$	−0.862635	−	0.384070i	−0.0544491	−	0.0242423i	−0.433781	+	0.901019i	$0.642821\pi$
$252$	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	−0.823598	−	0.567174i	$-0.808037\pi$
$263$	−8.73607	+	6.34712i	−0.538689	+	0.391380i	0.284909	+	0.958555i	$0.408037\pi$
$264$	−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	−0.367888	−	0.929870i	$-0.619919\pi$
$269$	1.26249	−	0.562096i	0.0769753	−	0.0342716i	0.444863	+	0.895599i	$0.353252\pi$
$270$	−5.41338	−	6.01217i	−0.329448	−	0.365889i
$271$	−2.95492	+	9.09429i	−0.179498	+	0.552439i	−0.999810	−	0.0194773i	$-0.993800\pi$
$271$	−2.95492	+	9.09429i	−0.179498	+	0.552439i	0.820312	+	0.571916i	$0.193800\pi$
$272$	−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	0.862513	−	0.506035i	$-0.168889\pi$
$277$	10.7812	+	7.83297i	0.647777	+	0.470637i	−0.214736	+	0.976672i	$0.568889\pi$
$278$	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	0.374575	−	0.927197i	$-0.377789\pi$
$313$	−1.12920	−	0.502754i	−0.0638264	−	0.0284173i	−0.438402	+	0.898779i	$0.644455\pi$
$314$	−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	−0.669697	−	0.742635i	$-0.733576\pi$
$331$	−10.2961	+	4.58413i	−0.565926	+	0.251967i	0.103771	+	0.994601i	$0.466909\pi$
$332$	−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	$-0.927079\pi$
$337$	−5.86475	−	18.0498i	−0.319473	−	0.983237i	0.654401	−	0.756148i	$-0.272921\pi$
$338$	−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	0.954220	−	0.299107i	$-0.0966886\pi$
$347$	4.06231	+	7.03612i	0.218076	+	0.377719i	−0.736144	+	0.676825i	$0.763355\pi$
$348$	−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	$0.363970\pi$
$353$	−3.38484	+	32.2046i	−0.180157	+	1.71408i	−0.594617	+	0.804009i	$0.702696\pi$
$354$	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	$0.562226\pi$
$367$	−18.1353	+	31.4112i	−0.946653	+	1.63965i	−0.752408	+	0.658697i	$0.771108\pi$
$368$	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	−0.233544	−	0.972346i	$-0.575032\pi$
$383$	−16.4858	−	3.50416i	−0.842385	−	0.179054i	−0.608841	+	0.793292i	$0.708365\pi$
$384$	−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	−0.861365	−	0.507987i	$-0.830390\pi$
$389$	−28.4337	+	6.04376i	−1.44164	+	0.306431i	−0.580279	+	0.814418i	$0.697056\pi$
$390$	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	−0.210466	−	0.977601i	$-0.567498\pi$
$401$	−24.1353	−	17.5353i	−1.20526	−	0.875671i	−0.994792	+	0.101931i	$0.967498\pi$
$402$	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	0.779456	−	0.626457i	$-0.215495\pi$
$409$	−3.09017	−	5.35233i	−0.152799	−	0.264656i	−0.932255	+	0.361801i	$0.882162\pi$
$410$	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	$-0.504464\pi$
$433$	−0.583592			−0.0280456			−0.0140228	+	0.999902i	$0.504464\pi$
$434$		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	−0.0243148	−	0.999704i	$-0.507740\pi$
$449$	19.4721	−	14.1473i	0.918947	−	0.667654i	0.943262	+	0.332050i	$0.107740\pi$
$450$	−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	$-0.779972\pi$
$457$	4.86475	−	14.9721i	0.227563	−	0.700367i	0.998021	−	0.0628768i	$-0.0200275\pi$
$458$	−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	0.843509	−	0.537114i	$-0.180486\pi$
$461$	−3.31966	−	10.2169i	−0.154612	−	0.475847i	−0.998121	+	0.0612677i	$0.980486\pi$
$462$	−1.29395	−	0.576105i	−0.0602001	−	0.0268028i
$463$	−25.1803	−	18.2946i	−1.17023	−	0.850222i	−0.179193	−	0.983814i	$-0.557349\pi$
$463$	−25.1803	−	18.2946i	−1.17023	−	0.850222i	−0.991036	+	0.133592i	$0.957349\pi$
$464$	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	0.287528	−	0.957772i	$-0.407167\pi$
$487$	−15.3385	−	17.0351i	−0.695052	−	0.771934i	−0.982580	+	0.185838i	$0.940500\pi$
$488$	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	$0.380636\pi$
$491$	−13.7984	+	23.8995i	−0.622712	+	1.07857i	−0.988979	+	0.148059i	$0.952698\pi$
$492$	−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	0.320206	−	0.947348i	$-0.396248\pi$
$499$	−3.78747	−	1.68629i	−0.169550	−	0.0754886i	−0.489757	+	0.871859i	$0.662914\pi$
$500$	−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	0.989206	−	0.146529i	$-0.0468101\pi$
$509$	−0.199632	−	1.89937i	−0.00884852	−	0.0841880i	−0.998055	+	0.0623408i	$0.980143\pi$
$510$	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	$-0.831932\pi$
$523$	−10.5451	−	32.4544i	−0.461104	−	1.41913i	0.402712	−	0.915327i	$-0.368068\pi$
$524$	−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	$-0.774959\pi$
$557$	−35.8885			−1.52065			−0.760323	+	0.649545i	$0.774959\pi$
$558$		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	0.514959	−	0.857215i	$-0.327807\pi$
$569$	15.1885	+	3.22842i	0.636737	+	0.135343i	0.121778	+	0.992557i	$0.461140\pi$
$570$	−0.845653	+	8.04585i	−0.0354205	+	0.337004i
$571$	0.731699	+	6.96165i	0.0306207	+	0.291336i	0.999106	+	0.0422669i	$0.0134580\pi$
$571$	0.731699	+	6.96165i	0.0306207	+	0.291336i	−0.968486	+	0.249069i	$0.919875\pi$
$572$	−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	0.994532	−	0.104430i	$-0.0333018\pi$
$587$	29.1353	+	21.1680i	1.20254	+	0.873697i	0.208008	+	0.978127i	$0.433302\pi$
$588$	−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	$-0.818554\pi$
$601$	2.29963	−	21.8795i	0.0938037	−	0.892483i	0.935689	−	0.352826i	$-0.114779\pi$
$602$	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	−0.979566	−	0.201121i	$-0.935541\pi$
$613$	−16.7656	+	18.6200i	−0.677154	+	0.752056i	0.302412	+	0.953177i	$0.402208\pi$
$614$	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	$-0.202772\pi$
$619$	40.0000			1.60774			0.803868	+	0.594808i	$0.202772\pi$
$620$		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	0.0347883	−	0.999395i	$-0.488924\pi$
$631$	−8.53873	−	1.81496i	−0.339921	−	0.0722525i	−0.374710	+	0.927142i	$0.622258\pi$
$632$		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	0.503638	−	0.863915i	$-0.331995\pi$
$641$	37.5377	−	16.7129i	1.48265	−	0.660119i	0.979013	+	0.203796i	$0.0653278\pi$
$642$	−0.450835	−	0.500703i	−0.0177930	−	0.0197612i
$643$	−2.51722	+	7.74721i	−0.0992695	+	0.305520i	−0.988343	−	0.152245i	$-0.951350\pi$
$643$	−2.51722	+	7.74721i	−0.0992695	+	0.305520i	0.889073	+	0.457765i	$0.151350\pi$
$644$	−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	$0.0998956\pi$
$647$	9.23607	+	28.4257i	0.363107	+	1.11753i	−0.588050	+	0.808824i	$0.700104\pi$
$648$	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	0.797404	−	0.603446i	$-0.206206\pi$
$673$	2.95515	+	3.28203i	0.113913	+	0.126513i	−0.683491	+	0.729959i	$0.739539\pi$
$674$	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	$-0.647732\pi$
$677$	14.3262	−	24.8138i	0.550602	−	0.953671i	0.998231	−	0.0594514i	$-0.0189351\pi$
$678$	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	0.924113	−	0.382120i	$-0.124806\pi$
$709$	−1.28115	−	3.94298i	−0.0481147	−	0.148082i	−0.972227	+	0.234038i	$0.924806\pi$
$710$	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	$-0.886102\pi$
$719$	−20.6910	−	35.8378i	−0.771643	−	1.33653i	0.165018	−	0.986290i	$-0.447232\pi$
$720$	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	−0.594362	−	0.804198i	$-0.702595\pi$
$739$	10.8541	−	18.7999i	0.399275	−	0.691564i	0.993637	+	0.112634i	$0.0359287\pi$
$740$	−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	$-0.479915\pi$
$743$	3.43769			0.126117			0.0630584	+	0.998010i	$0.479915\pi$
$744$		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	$0.253334\pi$
$757$	4.50775	+	42.8884i	0.163837	+	1.55880i	−0.535824	+	0.844330i	$0.679999\pi$
$758$	−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	−0.145324	−	0.989384i	$-0.546422\pi$
$761$	3.42995	−	0.729059i	0.124336	−	0.0264284i	0.269659	+	0.962956i	$0.413089\pi$
$762$	−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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.g (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more