LMFDB - Embedded newform 961.2.g.f.816.1

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			816.1
Root			$-0.978148 - 0.207912i$ of defining polynomial
Character	$\chi$	$=$	961.816
Dual form			961.2.g.f.338.1

$q$-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} +(0.104528 + 0.994522i) q^{3} +(-0.500000 - 1.53884i) q^{4} +(1.30902 + 2.26728i) q^{5} +(-0.309017 + 0.535233i) q^{6} +(-2.93444 - 0.623735i) q^{7} +(0.690983 - 2.12663i) q^{8} +(1.95630 - 0.415823i) q^{9} +(-0.169131 + 1.60917i) q^{10} +(-0.511170 + 0.567712i) q^{11} +(1.47815 - 0.658114i) q^{12} +(4.43444 + 1.97434i) q^{13} +(-1.24064 - 1.37787i) q^{14} +(-2.11803 + 1.53884i) q^{15} +(-1.50000 + 1.08981i) q^{16} +(0.157960 + 0.175433i) q^{17} +(1.12920 + 0.502754i) q^{18} +(4.56773 - 2.03368i) q^{19} +(2.83448 - 3.14801i) q^{20} +(0.313585 - 2.98357i) q^{21} +(-0.461819 + 0.0981626i) q^{22} +(-1.69098 + 5.20431i) q^{23} +(2.18720 + 0.464905i) q^{24} +(-0.927051 + 1.60570i) q^{25} +(1.50000 + 2.59808i) q^{26} +(1.54508 + 4.75528i) q^{27} +(0.507392 + 4.82751i) q^{28} +(6.97214 + 5.06555i) q^{29} -1.61803 q^{30} -5.61803 q^{32} +(-0.618034 - 0.449028i) q^{33} +(0.0152505 + 0.145099i) q^{34} +(-2.42705 - 7.46969i) q^{35} +(-1.61803 - 2.80252i) q^{36} +(-0.118034 + 0.204441i) q^{37} +(3.02264 + 0.642482i) q^{38} +(-1.50000 + 4.61653i) q^{39} +(5.72618 - 1.21714i) q^{40} +(-0.676522 + 6.43668i) q^{41} +(1.24064 - 1.37787i) q^{42} +(-4.21878 + 1.87832i) q^{43} +(1.12920 + 0.502754i) q^{44} +(3.50361 + 3.89116i) q^{45} +(-2.73607 + 1.98787i) q^{46} +(2.73607 - 1.98787i) q^{47} +(-1.24064 - 1.37787i) q^{48} +(1.82709 + 0.813473i) q^{49} +(-1.04683 + 0.466079i) q^{50} +(-0.157960 + 0.175433i) q^{51} +(0.820977 - 7.81108i) q^{52} +(12.4305 - 2.64218i) q^{53} +(-0.954915 + 2.93893i) q^{54} +(-1.95630 - 0.415823i) q^{55} +(-3.35410 + 5.80948i) q^{56} +(2.50000 + 4.33013i) q^{57} +(1.64590 + 5.06555i) q^{58} +(-0.990108 - 9.42025i) q^{59} +(3.42705 + 2.48990i) q^{60} -6.94427 q^{61} -6.00000 q^{63} +(0.190983 + 0.138757i) q^{64} +(1.32837 + 12.6386i) q^{65} +(-0.145898 - 0.449028i) q^{66} +(2.11803 + 3.66854i) q^{67} +(0.190983 - 0.330792i) q^{68} +(-5.35256 - 1.13772i) q^{69} +(1.50000 - 4.61653i) q^{70} +(-0.0881995 + 0.0187474i) q^{71} +(0.467465 - 4.44764i) q^{72} +(-5.72930 + 6.36303i) q^{73} +(-0.133284 + 0.0593421i) q^{74} +(-1.69381 - 0.754131i) q^{75} +(-5.41338 - 6.01217i) q^{76} +(1.85410 - 1.34708i) q^{77} +(-2.42705 + 1.76336i) q^{78} +(-4.43444 - 1.97434i) q^{80} +(0.913545 - 0.406737i) q^{81} +(-2.67652 + 2.97258i) q^{82} +(0.427539 - 4.06776i) q^{83} +(-4.74803 + 1.00922i) q^{84} +(-0.190983 + 0.587785i) q^{85} +(-2.79173 - 0.593401i) q^{86} +(-4.30902 + 7.46344i) q^{87} +(0.854102 + 1.47935i) q^{88} +(-1.97214 - 6.06961i) q^{89} +(0.338261 + 3.21834i) q^{90} +(-11.7812 - 8.55951i) q^{91} +8.85410 q^{92} +2.09017 q^{94} +(10.5902 + 7.69421i) q^{95} +(-0.587244 - 5.58726i) 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 $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{7}{15}\right)$

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	$0.629881\pi$
$3$	0.104528	+	0.994522i	0.0603495	+	0.574187i	0.982357	+	0.187015i	$0.0598814\pi$
$3$	0.104528	+	0.994522i	0.0603495	+	0.574187i	−0.922007	+	0.387172i	$0.873452\pi$
$4$	−0.500000	−	1.53884i	−0.250000	−	0.769421i
$5$	1.30902	+	2.26728i	0.585410	+	1.01396i	0.994824	+	0.101611i	$0.0323999\pi$
$5$	1.30902	+	2.26728i	0.585410	+	1.01396i	−0.409414	+	0.912349i	$0.634267\pi$
$6$	−0.309017	+	0.535233i	−0.126156	+	0.218508i
$7$	−2.93444	−	0.623735i	−1.10912	−	0.235750i	−0.383289	−	0.923628i	$-0.625209\pi$
$7$	−2.93444	−	0.623735i	−1.10912	−	0.235750i	−0.725826	+	0.687879i	$0.758542\pi$
$8$	0.690983	−	2.12663i	0.244299	−	0.751876i
$9$	1.95630	−	0.415823i	0.652098	−	0.138608i
$10$	−0.169131	+	1.60917i	−0.0534838	+	0.508864i
$11$	−0.511170	+	0.567712i	−0.154124	+	0.171172i	−0.815262	−	0.579092i	$-0.803407\pi$
$11$	−0.511170	+	0.567712i	−0.154124	+	0.171172i	0.661138	+	0.750264i	$0.270074\pi$
$12$	1.47815	−	0.658114i	0.426704	−	0.189981i
$13$	4.43444	+	1.97434i	1.22989	+	0.547584i	0.915733	−	0.401786i	$-0.131611\pi$
$13$	4.43444	+	1.97434i	1.22989	+	0.547584i	0.314160	+	0.949370i	$0.398277\pi$
$14$	−1.24064	−	1.37787i	−0.331574	−	0.368250i
$15$	−2.11803	+	1.53884i	−0.546874	+	0.397327i
$16$	−1.50000	+	1.08981i	−0.375000	+	0.272453i
$17$	0.157960	+	0.175433i	0.0383110	+	0.0425487i	0.761996	−	0.647582i	$-0.224220\pi$
$17$	0.157960	+	0.175433i	0.0383110	+	0.0425487i	−0.723685	+	0.690131i	$0.757553\pi$
$18$	1.12920	+	0.502754i	0.266156	+	0.118500i
$19$	4.56773	−	2.03368i	1.04791	−	0.466559i	0.190765	−	0.981636i	$-0.438903\pi$
$19$	4.56773	−	2.03368i	1.04791	−	0.466559i	0.857144	+	0.515077i	$0.172237\pi$
$20$	2.83448	−	3.14801i	0.633810	−	0.703917i
$21$	0.313585	−	2.98357i	0.0684299	−	0.651067i
$22$	−0.461819	+	0.0981626i	−0.0984601	+	0.0209283i
$23$	−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	$0.906746\pi$
$24$	2.18720	+	0.464905i	0.446461	+	0.0948983i
$25$	−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
$28$	0.507392	+	4.82751i	0.0958880	+	0.912314i
$29$	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
$34$	0.0152505	+	0.145099i	0.00261544	+	0.0248842i
$35$	−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	$-0.839510\pi$
$37$	−0.118034	+	0.204441i	−0.0194047	+	0.0336099i	0.856160	+	0.516711i	$0.172844\pi$
$38$	3.02264	+	0.642482i	0.490337	+	0.104224i
$39$	−1.50000	+	4.61653i	−0.240192	+	0.739236i
$40$	5.72618	−	1.21714i	0.905388	−	0.192446i
$41$	−0.676522	+	6.43668i	−0.105655	+	1.00524i	0.805337	+	0.592817i	$0.201984\pi$
$41$	−0.676522	+	6.43668i	−0.105655	+	1.00524i	−0.910992	+	0.412424i	$0.864682\pi$
$42$	1.24064	−	1.37787i	0.191434	−	0.212609i
$43$	−4.21878	+	1.87832i	−0.643359	+	0.286442i	−0.702366	−	0.711816i	$-0.747873\pi$
$43$	−4.21878	+	1.87832i	−0.643359	+	0.286442i	0.0590076	+	0.998258i	$0.481206\pi$
$44$	1.12920	+	0.502754i	0.170234	+	0.0757930i
$45$	3.50361	+	3.89116i	0.522288	+	0.580059i
$46$	−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	$0.220668\pi$
$48$	−1.24064	−	1.37787i	−0.179070	−	0.198878i
$49$	1.82709	+	0.813473i	0.261013	+	0.116210i
$50$	−1.04683	+	0.466079i	−0.148044	+	0.0659135i
$51$	−0.157960	+	0.175433i	−0.0221189	+	0.0245655i
$52$	0.820977	−	7.81108i	0.113849	−	1.08320i
$53$	12.4305	−	2.64218i	1.70746	−	0.362932i	0.752254	−	0.658873i	$-0.228967\pi$
$53$	12.4305	−	2.64218i	1.70746	−	0.362932i	0.955206	+	0.295941i	$0.0956332\pi$
$54$	−0.954915	+	2.93893i	−0.129947	+	0.399937i
$55$	−1.95630	−	0.415823i	−0.263787	−	0.0560696i
$56$	−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
$59$	−0.990108	−	9.42025i	−0.128901	−	1.22641i	−0.847427	−	0.530912i	$-0.821850\pi$
$59$	−0.990108	−	9.42025i	−0.128901	−	1.22641i	0.718526	−	0.695500i	$-0.244817\pi$
$60$	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
$65$	1.32837	+	12.6386i	0.164764	+	1.56762i
$66$	−0.145898	−	0.449028i	−0.0179588	−	0.0552715i
$67$	2.11803	+	3.66854i	0.258759	+	0.448184i	0.965910	−	0.258879i	$-0.0833531\pi$
$67$	2.11803	+	3.66854i	0.258759	+	0.448184i	−0.707151	+	0.707063i	$0.750020\pi$
$68$	0.190983	−	0.330792i	0.0231601	−	0.0401145i
$69$	−5.35256	−	1.13772i	−0.644372	−	0.136966i
$70$	1.50000	−	4.61653i	0.179284	−	0.551780i
$71$	−0.0881995	+	0.0187474i	−0.0104674	+	0.00222491i	−0.213142	−	0.977021i	$-0.568370\pi$
$71$	−0.0881995	+	0.0187474i	−0.0104674	+	0.00222491i	0.202675	+	0.979246i	$0.435036\pi$
$72$	0.467465	−	4.44764i	0.0550913	−	0.524159i
$73$	−5.72930	+	6.36303i	−0.670564	+	0.744737i	−0.978404	−	0.206701i	$-0.933727\pi$
$73$	−5.72930	+	6.36303i	−0.670564	+	0.744737i	0.307840	+	0.951438i	$0.400394\pi$
$74$	−0.133284	+	0.0593421i	−0.0154940	+	0.00689838i
$75$	−1.69381	−	0.754131i	−0.195584	−	0.0870796i
$76$	−5.41338	−	6.01217i	−0.620957	−	0.689643i
$77$	1.85410	−	1.34708i	0.211295	−	0.153514i
$78$	−2.42705	+	1.76336i	−0.274809	+	0.199661i
$79$		0			0		0.743145	−	0.669131i	$-0.233333\pi$
$79$		0			0		−0.743145	+	0.669131i	$0.766667\pi$
$80$	−4.43444	−	1.97434i	−0.495786	−	0.220738i
$81$	0.913545	−	0.406737i	0.101505	−	0.0451930i
$82$	−2.67652	+	2.97258i	−0.295572	+	0.328266i
$83$	0.427539	−	4.06776i	0.0469285	−	0.446495i	−0.945677	−	0.325108i	$-0.894599\pi$
$83$	0.427539	−	4.06776i	0.0469285	−	0.446495i	0.992605	−	0.121387i	$-0.0387341\pi$
$84$	−4.74803	+	1.00922i	−0.518052	+	0.110115i
$85$	−0.190983	+	0.587785i	−0.0207150	+	0.0637543i
$86$	−2.79173	−	0.593401i	−0.301040	−	0.0639881i
$87$	−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	$-0.209833\pi$
$90$	0.338261	+	3.21834i	0.0356559	+	0.339243i
$91$	−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
$96$	−0.587244	−	5.58726i	−0.0599354	−	0.570247i
$97$	−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
$100$	2.93444	+	0.623735i	0.293444	+	0.0623735i
$101$	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	$0.0238311\pi$
$102$	−0.142710	+	0.0303339i	−0.0141304	+	0.00300350i
$103$	0.0152505	−	0.145099i	0.00150268	−	0.0142970i	−0.993745	−	0.111674i	$-0.964379\pi$
$103$	0.0152505	−	0.145099i	0.00150268	−	0.0142970i	0.995248	+	0.0973773i	$0.0310453\pi$
$104$	7.26281	−	8.06617i	0.712177	−	0.790953i
$105$	7.17508	−	3.19455i	0.700216	−	0.311756i
$106$	7.17508	+	3.19455i	0.696905	+	0.310282i
$107$	0.729466	+	0.810154i	0.0705201	+	0.0783206i	0.777372	−	0.629041i	$-0.216552\pi$
$107$	0.729466	+	0.810154i	0.0705201	+	0.0783206i	−0.706852	+	0.707361i	$0.749885\pi$
$108$	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	$0.167942\pi$
$110$	−0.827091	−	0.918578i	−0.0788600	−	0.0875829i
$111$	−0.215659	−	0.0960175i	−0.0204694	−	0.00911358i
$112$	5.08142	−	2.26239i	0.480149	−	0.213776i
$113$	−1.24064	+	1.37787i	−0.116709	+	0.129619i	−0.798668	−	0.601772i	$-0.794462\pi$
$113$	−1.24064	+	1.37787i	−0.116709	+	0.129619i	0.681959	+	0.731391i	$0.261128\pi$
$114$	−0.323011	+	3.07324i	−0.0302527	+	0.287835i
$115$	−14.0132	+	2.97859i	−1.30674	+	0.277755i
$116$	4.30902	−	13.2618i	0.400082	−	1.23133i
$117$	9.49606	+	2.01845i	0.877911	+	0.186606i
$118$	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
$121$	1.08881	+	10.3593i	0.0989828	+	0.941759i
$122$	−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
$127$	−1.06996	−	10.1800i	−0.0949436	−	0.903328i	−0.933515	−	0.358537i	$-0.883276\pi$
$127$	−1.06996	−	10.1800i	−0.0949436	−	0.903328i	0.838572	−	0.544791i	$-0.183391\pi$
$128$	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
$131$	−0.0881995	−	0.0187474i	−0.00770603	−	0.00163797i	0.204057	−	0.978959i	$-0.434587\pi$
$131$	−0.0881995	−	0.0187474i	−0.00770603	−	0.00163797i	−0.211763	+	0.977321i	$0.567921\pi$
$132$	−0.381966	+	1.17557i	−0.0332459	+	0.102320i
$133$	−14.6722	+	3.11868i	−1.27224	+	0.270423i
$134$	−0.273659	+	2.60369i	−0.0236405	+	0.224925i
$135$	−8.75903	+	9.72789i	−0.753858	+	0.837244i
$136$	0.482228	−	0.214702i	0.0413507	−	0.0184105i
$137$	−5.91259	−	2.63245i	−0.505147	−	0.224906i	0.138309	−	0.990389i	$-0.455833\pi$
$137$	−5.91259	−	2.63245i	−0.505147	−	0.224906i	−0.643456	+	0.765483i	$0.722500\pi$
$138$	−2.26298	−	2.51329i	−0.192637	−	0.213945i
$139$	−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
$141$	2.26298	+	2.51329i	0.190577	+	0.211657i
$142$	−0.0509101	−	0.0226667i	−0.00427228	−	0.00190214i
$143$	−3.38761	+	1.50826i	−0.283286	+	0.126127i
$144$	−2.48127	+	2.75573i	−0.206773	+	0.229644i
$145$	−2.35840	+	22.4387i	−0.195855	+	1.86343i
$146$	−5.17616	+	1.10023i	−0.428382	+	0.0910554i
$147$	−0.618034	+	1.90211i	−0.0509746	+	0.156884i
$148$	0.373619	+	0.0794152i	0.0307113	+	0.00652789i
$149$	8.51722	−	14.7523i	0.697758	−	1.20855i	−0.271484	−	0.962443i	$-0.587514\pi$
$149$	8.51722	−	14.7523i	0.697758	−	1.20855i	0.969242	−	0.246109i	$-0.0791522\pi$
$150$	−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	$-0.391854\pi$
$152$	−1.16866	−	11.1191i	−0.0947911	−	0.901878i
$153$	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
$162$	0.604528	+	0.128496i	0.0474962	+	0.0100956i
$163$	−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	$0.934181\pi$
$164$	10.2433	−	2.17728i	0.799867	−	0.170017i
$165$	0.209057	−	1.98904i	0.0162751	−	0.154847i
$166$	1.69147	−	1.87857i	0.131284	−	0.145805i
$167$	−8.43757	+	3.75665i	−0.652919	+	0.290698i	−0.706339	−	0.707874i	$-0.749654\pi$
$167$	−8.43757	+	3.75665i	−0.652919	+	0.290698i	0.0534201	+	0.998572i	$0.482988\pi$
$168$	−6.12825	−	2.72847i	−0.472805	−	0.210506i
$169$	7.06756	+	7.84932i	0.543659	+	0.603794i
$170$	−0.309017	+	0.224514i	−0.0237005	+	0.0172194i
$171$	8.09017	−	5.87785i	0.618671	−	0.449491i
$172$	4.99983	+	5.55288i	0.381234	+	0.423403i
$173$	0.831171	+	0.370061i	0.0631928	+	0.0281352i	0.438090	−	0.898931i	$-0.355655\pi$
$173$	0.831171	+	0.370061i	0.0631928	+	0.0281352i	−0.374897	+	0.927067i	$0.622322\pi$
$174$	−4.86576	+	2.16638i	−0.368872	+	0.164233i
$175$	3.72191	−	4.13360i	0.281350	−	0.312471i
$176$	0.148055	−	1.40865i	0.0111601	−	0.106181i
$177$	9.26515	−	1.96937i	0.696411	−	0.148027i
$178$	1.21885	−	3.75123i	0.0913564	−	0.281166i
$179$	−19.3657	−	4.11631i	−1.44746	−	0.307668i	−0.583866	−	0.811850i	$-0.698461\pi$
$179$	−19.3657	−	4.11631i	−1.44746	−	0.307668i	−0.863597	+	0.504183i	$0.831794\pi$
$180$	4.23607	−	7.33708i	0.315738	−	0.546874i
$181$	−8.50000	−	14.7224i	−0.631800	−	1.09431i	−0.987184	−	0.159589i	$-0.948983\pi$
$181$	−8.50000	−	14.7224i	−0.631800	−	1.09431i	0.355383	−	0.934721i	$-0.384350\pi$
$182$	−2.78115	−	8.55951i	−0.206153	−	0.634473i
$183$	−0.725874	−	6.90623i	−0.0536582	−	0.510523i
$184$	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
$189$	−1.56793	−	14.9178i	−0.114050	−	1.08511i
$190$	2.50000	+	7.69421i	0.181369	+	0.558197i
$191$	8.04508	+	13.9345i	0.582122	+	1.00826i	0.995228	+	0.0975816i	$0.0311107\pi$
$191$	8.04508	+	13.9345i	0.582122	+	1.00826i	−0.413106	+	0.910683i	$0.635556\pi$
$192$	−0.118034	+	0.204441i	−0.00851837	+	0.0147542i
$193$	2.32991	+	0.495239i	0.167711	+	0.0356481i	0.291002	−	0.956723i	$-0.406011\pi$
$193$	2.32991	+	0.495239i	0.167711	+	0.0356481i	−0.123291	+	0.992371i	$0.539345\pi$
$194$	1.01064	−	3.11044i	0.0725599	−	0.223317i
$195$	−12.4305	+	2.64218i	−0.890167	+	0.189211i
$196$	0.338261	−	3.21834i	0.0241615	−	0.229881i
$197$	10.9847	−	12.1998i	0.782629	−	0.869198i	−0.211502	−	0.977377i	$-0.567836\pi$
$197$	10.9847	−	12.1998i	0.782629	−	0.869198i	0.994131	+	0.108180i	$0.0345023\pi$
$198$	−0.862635	+	0.384070i	−0.0613048	+	0.0272947i
$199$	−24.3992	−	10.8632i	−1.72961	−	0.770072i	−0.995885	−	0.0906262i	$-0.971113\pi$
$199$	−24.3992	−	10.8632i	−1.72961	−	0.770072i	−0.733725	−	0.679446i	$-0.762220\pi$
$200$	2.77415	+	3.08100i	0.196162	+	0.217860i
$201$	−3.42705	+	2.48990i	−0.241726	+	0.175624i
$202$	2.38197	−	1.73060i	0.167595	−	0.121765i
$203$	−17.2998	−	19.2133i	−1.21421	−	1.34851i
$204$	0.348943	+	0.155360i	0.0244309	+	0.0108773i
$205$	−15.4794	+	6.89186i	−1.08113	+	0.481348i
$206$	0.0603355	−	0.0670093i	0.00420377	−	0.00466876i
$207$	−1.14399	+	10.8843i	−0.0795127	+	0.756512i
$208$	−8.80333	+	1.87121i	−0.610401	+	0.129745i
$209$	−1.18034	+	3.63271i	−0.0816458	+	0.251280i
$210$	4.74803	+	1.00922i	0.327645	+	0.0696431i
$211$	4.00000	−	6.92820i	0.275371	−	0.476957i	−0.694857	−	0.719148i	$-0.744533\pi$
$211$	4.00000	−	6.92820i	0.275371	−	0.476957i	0.970229	+	0.242190i	$0.0778659\pi$
$212$	−10.2812	−	17.8075i	−0.706112	−	1.22302i
$213$	−0.0278640	−	0.0857567i	−0.00190921	−	0.00587595i
$214$	0.0704273	+	0.670071i	0.00481431	+	0.0458051i
$215$	−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
$220$	0.338261	+	3.21834i	0.0228056	+	0.216980i
$221$	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	$-0.840882\pi$
$223$	−0.354102	+	0.613323i	−0.0237124	+	0.0410711i	0.853926	+	0.520395i	$0.174215\pi$
$224$	16.4858	+	3.50416i	1.10150	+	0.234132i
$225$	−1.14590	+	3.52671i	−0.0763932	+	0.235114i
$226$	−1.12086	+	0.238246i	−0.0745583	+	0.0158479i
$227$	2.16820	−	20.6290i	0.143908	−	1.36920i	−0.649433	−	0.760419i	$-0.724994\pi$
$227$	2.16820	−	20.6290i	0.143908	−	1.36920i	0.793341	−	0.608777i	$-0.208340\pi$
$228$	5.41338	−	6.01217i	0.358510	−	0.398166i
$229$	−6.61048	+	2.94317i	−0.436833	+	0.194490i	−0.613357	−	0.789806i	$-0.710181\pi$
$229$	−6.61048	+	2.94317i	−0.436833	+	0.194490i	0.176524	+	0.984296i	$0.443515\pi$
$230$	−8.08862	−	3.60129i	−0.533348	−	0.237462i
$231$	1.53351	+	1.70314i	0.100898	+	0.112058i
$232$	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	$0.511151\pi$
$234$	4.01478	+	4.45887i	0.262455	+	0.291485i
$235$	8.08862	+	3.60129i	0.527644	+	0.234922i
$236$	−14.0012	+	6.23374i	−0.911401	+	0.405782i
$237$		0			0
$238$	0.0457515	−	0.435296i	0.00296563	−	0.0282161i
$239$	13.1232	−	2.78943i	0.848871	−	0.180433i	0.237117	−	0.971481i	$-0.423798\pi$
$239$	13.1232	−	2.78943i	0.848871	−	0.180433i	0.611754	+	0.791048i	$0.290464\pi$
$240$	1.50000	−	4.61653i	0.0968246	−	0.297995i
$241$	8.34151	+	1.77304i	0.537324	+	0.114212i	0.468577	−	0.883422i	$-0.344767\pi$
$241$	8.34151	+	1.77304i	0.537324	+	0.114212i	0.0687465	+	0.997634i	$0.478100\pi$
$242$	−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
$245$	0.547318	+	5.20738i	0.0349669	+	0.332688i
$246$	−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
$251$	−0.0987033	−	0.939099i	−0.00623010	−	0.0592754i	0.990965	−	0.134120i	$-0.0428207\pi$
$251$	−0.0987033	−	0.939099i	−0.00623010	−	0.0592754i	−0.997195	+	0.0748443i	$0.976154\pi$
$252$	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
$255$	−0.604528	−	0.128496i	−0.0378570	−	0.00804676i
$256$	−2.02786	+	6.24112i	−0.126742	+	0.390070i
$257$	−1.38546	+	0.294488i	−0.0864224	+	0.0183696i	−0.250920	−	0.968008i	$-0.580733\pi$
$257$	−1.38546	+	0.294488i	−0.0864224	+	0.0183696i	0.164498	+	0.986377i	$0.447400\pi$
$258$	0.298335	−	2.83847i	0.0185735	−	0.176715i
$259$	0.473881	−	0.526298i	0.0294455	−	0.0327026i
$260$	18.7846	−	8.36344i	1.16497	−	0.518679i
$261$	15.7459	+	7.01054i	0.974649	+	0.433942i
$262$	−0.0372894	−	0.0414140i	−0.00230375	−	0.00255857i
$263$	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
$265$	22.2623	+	24.7248i	1.36756	+	1.51883i
$266$	−8.46903	−	3.77066i	−0.519270	−	0.231194i
$267$	5.83022	−	2.59578i	0.356803	−	0.158859i
$268$	4.58629	−	5.09359i	0.280152	−	0.311141i
$269$	0.144455	−	1.37440i	0.00880756	−	0.0837984i	−0.989235	−	0.146335i	$-0.953252\pi$
$269$	0.144455	−	1.37440i	0.00880756	−	0.0837984i	0.998043	+	0.0625365i	$0.0199190\pi$
$270$	−7.91338	+	1.68204i	−0.481593	+	0.102366i
$271$	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	$0.00620021\pi$
$272$	−0.428129	−	0.0910017i	−0.0259592	−	0.00551779i
$273$	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
$276$	0.925506	+	8.80560i	0.0557089	+	0.530035i
$277$	−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	$0.892186\pi$
$282$	0.218482	+	2.07872i	0.0130104	+	0.123786i
$283$	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
$286$	−2.24171	−	0.476491i	−0.132555	−	0.0281755i
$287$	6.00000	−	18.4661i	0.354169	−	1.09002i
$288$	−10.9905	+	2.33611i	−0.647623	+	0.137657i
$289$	1.77116	−	16.8514i	0.104186	−	0.991262i
$290$	−9.33054	+	10.3626i	−0.547908	+	0.608514i
$291$	4.83430	−	2.15237i	0.283391	−	0.126174i
$292$	12.6564	+	5.63497i	0.740657	+	0.329762i
$293$	−5.51101	−	6.12059i	−0.321956	−	0.357569i	0.560340	−	0.828262i	$-0.310670\pi$
$293$	−5.51101	−	6.12059i	−0.321956	−	0.357569i	−0.882297	+	0.470694i	$0.844004\pi$
$294$	−1.00000	+	0.726543i	−0.0583212	+	0.0423728i
$295$	20.0623	−	14.5761i	1.16807	−	0.848654i
$296$	0.353210	+	0.392279i	0.0205299	+	0.0228008i
$297$	−3.48943	−	1.55360i	−0.202477	−	0.0901488i
$298$	9.61768	−	4.28207i	0.557137	−	0.248054i
$299$	−17.7737	+	19.7396i	−1.02788	+	1.14157i
$300$	−0.313585	+	2.98357i	−0.0181049	+	0.172256i
$301$	13.5514	−	2.88043i	0.781087	−	0.166025i
$302$	3.72542	−	11.4657i	0.214374	−	0.659776i
$303$	4.65983	+	0.990477i	0.267700	+	0.0569014i
$304$	−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
$307$	−0.636596	−	6.05681i	−0.0363325	−	0.345680i	−0.997554	−	0.0699023i	$-0.977731\pi$
$307$	−0.636596	−	6.05681i	−0.0363325	−	0.345680i	0.961221	−	0.275778i	$-0.0889354\pi$
$308$	−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
$313$	−0.129204	−	1.22930i	−0.00730306	−	0.0694840i	0.990263	−	0.139207i	$-0.0444552\pi$
$313$	−0.129204	−	1.22930i	−0.00730306	−	0.0694840i	−0.997566	+	0.0697227i	$0.977789\pi$
$314$	−1.85410	−	5.70634i	−0.104633	−	0.322027i
$315$	−7.85410	−	13.6037i	−0.442529	−	0.766482i
$316$		0			0
$317$	−25.3228	−	5.38253i	−1.42227	−	0.302313i	−0.568381	−	0.822766i	$-0.692430\pi$
$317$	−25.3228	−	5.38253i	−1.42227	−	0.302313i	−0.853890	+	0.520453i	$0.825763\pi$
$318$	−2.42705	+	7.46969i	−0.136102	+	0.418880i
$319$	−6.43972	+	1.36881i	−0.360555	+	0.0766384i
$320$	−0.0646021	+	0.614648i	−0.00361137	+	0.0343599i
$321$	−0.729466	+	0.810154i	−0.0407148	+	0.0452184i
$322$	9.26874	−	4.12671i	0.516527	−	0.229972i
$323$	1.07829	+	0.480087i	0.0599979	+	0.0267128i
$324$	−1.08268	−	1.20243i	−0.0601487	−	0.0668019i
$325$	−7.28115	+	5.29007i	−0.403886	+	0.293440i
$326$	−6.35410	+	4.61653i	−0.351921	+	0.255686i
$327$	5.63168	+	6.25461i	0.311432	+	0.345881i
$328$	13.2210	+	5.88635i	0.730005	+	0.325019i
$329$	−9.26874	+	4.12671i	−0.511002	+	0.227513i
$330$	0.827091	−	0.918578i	0.0455299	−	0.0505660i
$331$	−1.17809	+	11.2088i	−0.0647536	+	0.616090i	0.913235	+	0.407433i	$0.133576\pi$
$331$	−1.17809	+	11.2088i	−0.0647536	+	0.616090i	−0.977989	+	0.208657i	$0.933091\pi$
$332$	−6.47341	+	1.37597i	−0.355275	+	0.0755160i
$333$	−0.145898	+	0.449028i	−0.00799516	+	0.0246066i
$334$	−5.58347	−	1.18680i	−0.305514	−	0.0649389i
$335$	−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	$0.727079\pi$
$338$	0.682348	+	6.49210i	0.0371148	+	0.353124i
$339$	−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
$344$	1.07939	+	10.2697i	0.0581966	+	0.553703i
$345$	−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	$-0.903311\pi$
$347$	−4.06231	+	7.03612i	−0.218076	+	0.377719i	0.736144	+	0.676825i	$0.236645\pi$
$348$	13.6396	+	2.89918i	0.731157	+	0.155412i
$349$	−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	$0.952427\pi$
$350$	3.36257	−	0.714737i	0.179737	−	0.0382043i
$351$	−2.53696	+	24.1376i	−0.135413	+	1.28837i
$352$	2.87177	−	3.18943i	0.153066	−	0.169997i
$353$	−29.5824	+	13.1709i	−1.57451	+	0.701018i	−0.993601	−	0.112949i	$-0.963970\pi$
$353$	−29.5824	+	13.1709i	−1.57451	+	0.701018i	−0.580911	+	0.813967i	$0.697304\pi$
$354$	5.34799	+	2.38108i	0.284242	+	0.126553i
$355$	−0.157960	−	0.175433i	−0.00838366	−	0.00931100i
$356$	−8.35410	+	6.06961i	−0.442767	+	0.321689i
$357$	0.572949	−	0.416272i	0.0303237	−	0.0220314i
$358$	−8.18753	−	9.09317i	−0.432724	−	0.480589i
$359$	−23.1367	−	10.3011i	−1.22111	−	0.543672i	−0.307998	−	0.951387i	$-0.599659\pi$
$359$	−23.1367	−	10.3011i	−1.22111	−	0.543672i	−0.913109	+	0.407715i	$0.866326\pi$
$360$	10.6960	−	4.76216i	0.563727	−	0.250988i
$361$	4.01478	−	4.45887i	0.211304	−	0.234677i
$362$	1.09824	−	10.4490i	0.0577220	−	0.549188i
$363$	−10.1888	+	2.16569i	−0.534772	+	0.113669i
$364$	−7.28115	+	22.4091i	−0.381636	+	1.17456i
$365$	−21.9266	−	4.66063i	−1.14769	−	0.243949i
$366$	2.14590	−	3.71680i	0.112168	−	0.194280i
$367$	18.1353	+	31.4112i	0.946653	+	1.63965i	0.752408	+	0.658697i	$0.228892\pi$
$367$	18.1353	+	31.4112i	0.946653	+	1.63965i	0.194245	+	0.980953i	$0.437774\pi$
$368$	−3.13525	−	9.64932i	−0.163436	−	0.503006i
$369$	1.35304	+	12.8734i	0.0704367	+	0.670160i
$370$	−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
$375$	0.860904	+	8.19095i	0.0444569	+	0.422979i
$376$	−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
$379$	18.0140	+	3.82899i	0.925315	+	0.196682i	0.645842	−	0.763472i	$-0.276507\pi$
$379$	18.0140	+	3.82899i	0.925315	+	0.196682i	0.279474	+	0.960153i	$0.409840\pi$
$380$	6.54508	−	20.1437i	0.335756	−	1.03335i
$381$	10.0124	−	2.12820i	0.512950	−	0.109031i
$382$	−1.03946	+	9.88980i	−0.0531834	+	0.506006i
$383$	−11.2776	+	12.5250i	−0.576258	+	0.640000i	−0.958848	−	0.283919i	$-0.908365\pi$
$383$	−11.2776	+	12.5250i	−0.576258	+	0.640000i	0.382590	+	0.923918i	$0.375032\pi$
$384$	−10.3979	+	4.62946i	−0.530618	+	0.236246i
$385$	5.48127	+	2.44042i	0.279352	+	0.124375i
$386$	0.985051	+	1.09401i	0.0501378	+	0.0556837i
$387$	−7.47214	+	5.42882i	−0.379830	+	0.275963i
$388$	−6.92705	+	5.03280i	−0.351668	+	0.255502i
$389$	−19.4509	−	21.6024i	−0.986199	−	1.09528i	−0.995446	−	0.0953274i	$-0.969610\pi$
$389$	−19.4509	−	21.6024i	−0.986199	−	1.09528i	0.00924722	−	0.999957i	$-0.497056\pi$
$390$	−7.17508	−	3.19455i	−0.363324	−	0.161762i
$391$	−1.18011	+	0.525421i	−0.0596810	+	0.0265717i
$392$	2.99244	−	3.32344i	0.151141	−	0.167859i
$393$	0.00942533	−	0.0896760i	0.000475445	−	0.00452355i
$394$	9.92419	−	2.10945i	0.499973	−	0.106273i
$395$		0			0
$396$	2.41811	+	0.513986i	0.121515	+	0.0258288i
$397$	−8.14590	+	14.1091i	−0.408831	+	0.708116i	−0.994759	−	0.102247i	$-0.967397\pi$
$397$	−8.14590	+	14.1091i	−0.408831	+	0.708116i	0.585928	+	0.810363i	$0.300730\pi$
$398$	−8.25329	−	14.2951i	−0.413700	−	0.716549i
$399$	−4.63525	−	14.2658i	−0.232053	−	0.714186i
$400$	−0.359337	−	3.41886i	−0.0179668	−	0.170943i
$401$	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
$406$	−1.67023	−	15.8912i	−0.0828921	−	0.788666i
$407$	−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	$-0.784505\pi$
$409$	3.09017	−	5.35233i	0.152799	−	0.264656i	0.932255	+	0.361801i	$0.117838\pi$
$410$	−10.2433	−	2.17728i	−0.505880	−	0.107528i
$411$	2.00000	−	6.15537i	0.0986527	−	0.303622i
$412$	−0.230909	+	0.0490813i	−0.0113761	+	0.00241806i
$413$	−2.97032	+	28.2607i	−0.146160	+	1.39062i
$414$	−4.52595	+	5.02658i	−0.222439	+	0.247043i
$415$	9.78243	−	4.35542i	0.480201	−	0.213799i
$416$	−24.9129	−	11.0919i	−1.22145	−	0.543826i
$417$	−3.91716	−	4.35045i	−0.191824	−	0.213042i
$418$	−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	$0.334841\pi$
$420$	−8.50345	−	9.44404i	−0.414926	−	0.460822i
$421$	13.4875	+	6.00503i	0.657342	+	0.292667i	0.708172	−	0.706040i	$-0.249520\pi$
$421$	13.4875	+	6.00503i	0.657342	+	0.292667i	−0.0508304	+	0.998707i	$0.516187\pi$
$422$	4.51682	−	2.01102i	0.219875	−	0.0978948i
$423$	4.52595	−	5.02658i	0.220059	−	0.244401i
$424$	2.97032	−	28.2607i	0.144252	−	1.37246i
$425$	−0.428129	+	0.0910017i	−0.0207673	+	0.00441423i
$426$	0.0172209	−	0.0530006i	0.000834357	−	0.00256789i
$427$	20.3776	+	4.33139i	0.986140	+	0.209610i
$428$	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
$431$	−3.05600	−	29.0759i	−0.147202	−	1.40054i	−0.779786	−	0.626046i	$-0.784672\pi$
$431$	−3.05600	−	29.0759i	−0.147202	−	1.40054i	0.632584	−	0.774492i	$-0.281994\pi$
$432$	−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
$437$	2.85997	+	27.2108i	0.136811	+	1.30167i
$438$	−1.63525	−	5.03280i	−0.0781355	−	0.240476i
$439$	−20.9164	−	36.2283i	−0.998286	−	1.72908i	−0.549831	−	0.835276i	$-0.685308\pi$
$439$	−20.9164	−	36.2283i	−0.998286	−	1.72908i	−0.448455	−	0.893805i	$-0.648026\pi$
$440$	−2.23607	+	3.87298i	−0.106600	+	0.184637i
$441$	3.91259	+	0.831647i	0.186314	+	0.0396022i
$442$	−0.218847	+	0.673542i	−0.0104095	+	0.0320371i
$443$	40.2259	−	8.55029i	1.91119	−	0.406236i	0.911208	−	0.411946i	$-0.135151\pi$
$443$	40.2259	−	8.55029i	1.91119	−	0.406236i	0.999984	+	0.00570927i	$0.00181733\pi$
$444$	−0.0399263	+	0.379874i	−0.00189482	+	0.0180280i
$445$	11.1800	−	12.4166i	0.529981	−	0.588604i
$446$	−0.399853	+	0.178026i	−0.0189336	+	0.00842979i
$447$	15.5617	+	6.92853i	0.736045	+	0.327708i
$448$	−0.473881	−	0.526298i	−0.0223888	−	0.0248652i
$449$	−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
$451$	−3.30836	−	3.67431i	−0.155785	−	0.173017i
$452$	2.74064	+	1.22021i	0.128909	+	0.0573938i
$453$	17.8201	−	7.93404i	0.837263	−	0.372774i
$454$	8.57803	−	9.52686i	0.402587	−	0.447118i
$455$	3.98511	−	37.9158i	0.186825	−	1.77752i
$456$	10.9360	−	2.32452i	0.512126	−	0.108856i
$457$	−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	$0.979972\pi$
$458$	−4.37441	−	0.929809i	−0.204403	−	0.0434471i
$459$	−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	$0.819514\pi$
$462$	0.148055	+	1.40865i	0.00688814	+	0.0655363i
$463$	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	$0.425995\pi$
$468$	−1.64195	−	15.6222i	−0.0758994	−	0.722134i
$469$	−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
$472$	−20.7175	−	4.40364i	−0.953600	−	0.202694i
$473$	1.09017	−	3.35520i	0.0501261	−	0.154272i
$474$		0			0
$475$	−0.969032	+	9.21973i	−0.0444622	+	0.423030i
$476$	−0.766755	+	0.851568i	−0.0351442	+	0.0390316i
$477$	23.2190	−	10.3378i	1.06313	−	0.473335i
$478$	7.57493	+	3.37258i	0.346469	+	0.154258i
$479$	−5.98489	−	6.64689i	−0.273456	−	0.303704i	0.590737	−	0.806864i	$-0.298837\pi$
$479$	−5.98489	−	6.64689i	−0.273456	−	0.303704i	−0.864193	+	0.503160i	$0.832171\pi$
$480$	11.8992	−	8.64527i	0.543121	−	0.394601i
$481$	−0.927051	+	0.673542i	−0.0422699	+	0.0307109i
$482$	3.52666	+	3.91675i	0.160635	+	0.178403i
$483$	14.9971	+	6.67715i	0.682393	+	0.303821i
$484$	15.3970	−	6.85518i	0.699863	−	0.311599i
$485$	9.27020	−	10.2956i	0.420938	−	0.467499i
$486$	−1.03363	+	9.83437i	−0.0468866	+	0.446096i
$487$	−22.4221	+	4.76596i	−1.01604	+	0.215966i	−0.685691	−	0.727893i	$-0.740500\pi$
$487$	−22.4221	+	4.76596i	−1.01604	+	0.215966i	−0.330349	+	0.943859i	$0.607167\pi$
$488$	−4.79837	+	14.7679i	−0.217212	+	0.668510i
$489$	−12.4305	−	2.64218i	−0.562127	−	0.119484i
$490$	−1.61803	+	2.80252i	−0.0730953	+	0.126605i
$491$	13.7984	+	23.8995i	0.622712	+	1.07857i	0.988979	+	0.148059i	$0.0473025\pi$
$491$	13.7984	+	23.8995i	0.622712	+	1.07857i	−0.366267	+	0.930510i	$0.619364\pi$
$492$	3.23607	+	9.95959i	0.145893	+	0.449013i
$493$	0.212657	+	2.02330i	0.00957759	+	0.0911247i
$494$	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
$499$	−0.433364	−	4.12319i	−0.0194001	−	0.184579i	0.980530	−	0.196367i	$-0.0629144\pi$
$499$	−0.433364	−	4.12319i	−0.0194001	−	0.184579i	−0.999931	+	0.0117878i	$0.996248\pi$
$500$	−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
$503$	−12.8586	−	2.73319i	−0.573338	−	0.121867i	−0.0878867	−	0.996130i	$-0.528011\pi$
$503$	−12.8586	−	2.73319i	−0.573338	−	0.121867i	−0.485451	+	0.874264i	$0.661345\pi$
$504$	−4.14590	+	12.7598i	−0.184673	+	0.568365i
$505$	12.1996	−	2.59310i	0.542875	−	0.115392i
$506$	0.270059	−	2.56944i	0.0120056	−	0.114225i
$507$	−7.06756	+	7.84932i	−0.313881	+	0.348601i
$508$	−15.1304	+	6.73650i	−0.671304	+	0.298884i
$509$	−1.74472	−	0.776798i	−0.0773332	−	0.0344310i	0.367706	−	0.929942i	$-0.380143\pi$
$509$	−1.74472	−	0.776798i	−0.0773332	−	0.0344310i	−0.445039	+	0.895511i	$0.646810\pi$
$510$	−0.255585	−	0.283856i	−0.0113175	−	0.0125694i
$511$	20.7812	−	15.0984i	0.919304	−	0.667914i
$512$	15.1353	−	10.9964i	0.668890	−	0.485977i
$513$	16.7283	+	18.5786i	0.738571	+	0.820266i
$514$	−0.799707	−	0.356052i	−0.0352736	−	0.0157048i
$515$	0.348943	−	0.155360i	0.0153763	−	0.00684596i
$516$	−4.99983	+	5.55288i	−0.220105	+	0.244452i
$517$	−0.270059	+	2.56944i	−0.0118772	+	0.113004i
$518$	0.428129	−	0.0910017i	0.0188109	−	0.00399839i
$519$	−0.281153	+	0.865300i	−0.0123412	+	0.0379824i
$520$	27.7954	+	5.90810i	1.21891	+	0.259087i
$521$	−15.5344	+	26.9064i	−0.680576	+	1.17879i	0.294229	+	0.955735i	$0.404937\pi$
$521$	−15.5344	+	26.9064i	−0.680576	+	1.17879i	−0.974805	+	0.223058i	$0.928396\pi$
$522$	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	$0.631932\pi$
$524$	0.0152505	+	0.145099i	0.000666221	+	0.00633867i
$525$	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
$530$	2.14935	+	20.4497i	0.0933616	+	0.888277i
$531$	−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
$534$	3.85808	+	0.820060i	0.166955	+	0.0354875i
$535$	−0.881966	+	2.71441i	−0.0381307	+	0.117354i
$536$	9.26515	−	1.96937i	0.400193	−	0.0850637i
$537$	2.06949	−	19.6899i	0.0893052	−	0.849683i
$538$	0.571506	−	0.634721i	0.0246394	−	0.0273648i
$539$	−1.39577	+	0.621438i	−0.0601202	+	0.0267672i
$540$	19.3492	+	8.61482i	0.832657	+	0.370723i
$541$	14.7209	+	16.3492i	0.632900	+	0.702906i	0.971236	−	0.238119i	$-0.0765308\pi$
$541$	14.7209	+	16.3492i	0.632900	+	0.702906i	−0.338336	+	0.941025i	$0.609864\pi$
$542$	4.78115	−	3.47371i	0.205368	−	0.149209i
$543$	13.7533	−	9.99235i	0.590210	−	0.428813i
$544$	−0.887426	−	0.985587i	−0.0380481	−	0.0422567i
$545$	20.1295	+	8.96221i	0.862252	+	0.383899i
$546$	8.22191	−	3.66063i	0.351865	−	0.156660i
$547$	−15.8639	+	17.6186i	−0.678291	+	0.753318i	−0.979764	−	0.200156i	$-0.935855\pi$
$547$	−15.8639	+	17.6186i	−0.678291	+	0.753318i	0.301473	+	0.953475i	$0.402522\pi$
$548$	−1.09464	+	10.4148i	−0.0467605	+	0.444897i
$549$	−13.5850	+	2.88759i	−0.579796	+	0.123239i
$550$	0.270510	−	0.832544i	0.0115346	−	0.0354998i
$551$	42.1485	+	8.95895i	1.79559	+	0.381664i
$552$	−6.11803	+	10.5967i	−0.260401	+	0.451027i
$553$		0			0
$554$	−2.54508	−	7.83297i	−0.108130	−	0.332791i
$555$	−0.0646021	−	0.614648i	−0.00274221	−	0.0260904i
$556$	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
$561$	−0.0188507	−	0.179352i	−0.000795875	−	0.00757225i
$562$	−3.63525	−	11.1882i	−0.153344	−	0.471944i
$563$	4.28115	+	7.41517i	0.180429	+	0.312512i	0.942027	−	0.335538i	$-0.108918\pi$
$563$	4.28115	+	7.41517i	0.180429	+	0.312512i	−0.761598	+	0.648050i	$0.775585\pi$
$564$	2.73607	−	4.73901i	0.115209	−	0.199548i
$565$	−4.74803	−	1.00922i	−0.199751	−	0.0424584i
$566$	−1.25329	+	3.85723i	−0.0526797	+	0.162131i
$567$	−2.93444	+	0.623735i	−0.123235	+	0.0261944i
$568$	−0.0210757	+	0.200522i	−0.000884315	+	0.00841370i
$569$	10.3902	−	11.5395i	0.435579	−	0.483759i	−0.484890	−	0.874575i	$-0.661140\pi$
$569$	10.3902	−	11.5395i	0.435579	−	0.483759i	0.920469	+	0.390816i	$0.127807\pi$
$570$	−7.39074	+	3.29057i	−0.309564	+	0.137827i
$571$	6.39482	+	2.84716i	0.267615	+	0.119150i	0.536157	−	0.844118i	$-0.319875\pi$
$571$	6.39482	+	2.84716i	0.267615	+	0.119150i	−0.268543	+	0.963268i	$0.586542\pi$
$572$	4.01478	+	4.45887i	0.167867	+	0.186435i
$573$	−13.0172	+	9.45756i	−0.543802	+	0.395095i
$574$	9.70820	−	7.05342i	0.405213	−	0.294404i
$575$	−6.78893	−	7.53987i	−0.283118	−	0.314434i
$576$	0.431318	+	0.192035i	0.0179716	+	0.00800146i
$577$	35.6088	−	15.8541i	1.48241	−	0.660014i	0.503447	−	0.864026i	$-0.332065\pi$
$577$	35.6088	−	15.8541i	1.48241	−	0.660014i	0.978968	+	0.204013i	$0.0653984\pi$
$578$	7.00723	−	7.78231i	0.291462	−	0.323702i
$579$	−0.248983	+	2.36892i	−0.0103474	+	0.0984488i
$580$	35.7088	−	7.59014i	1.48273	−	0.315164i
$581$	−3.79180	+	11.6699i	−0.157310	+	0.484151i
$582$	3.19904	+	0.679977i	0.132605	+	0.0281860i
$583$	−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
$586$	−0.532068	−	5.06229i	−0.0219795	−	0.209121i
$587$	−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
$592$	−0.0457515	−	0.435296i	−0.00188037	−	0.0178906i
$593$	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
$596$	−26.9600	−	5.73053i	−1.10432	−	0.234731i
$597$	8.25329	−	25.4010i	0.337785	−	1.03959i
$598$	−16.0577	+	3.41316i	−0.656647	+	0.139575i
$599$	−3.11478	+	29.6351i	−0.127266	+	1.21086i	0.725372	+	0.688357i	$0.241668\pi$
$599$	−3.11478	+	29.6351i	−0.127266	+	1.21086i	−0.852638	+	0.522502i	$0.824999\pi$
$600$	−2.77415	+	3.08100i	−0.113254	+	0.125781i
$601$	20.0980	−	8.94821i	0.819815	−	0.365005i	0.0464137	−	0.998922i	$-0.485221\pi$
$601$	20.0980	−	8.94821i	0.819815	−	0.365005i	0.773401	+	0.633917i	$0.218554\pi$
$602$	7.82206	+	3.48260i	0.318803	+	0.141940i
$603$	5.66897	+	6.29602i	0.230858	+	0.256394i
$604$	−25.5344	+	18.5519i	−1.03898	+	0.754864i
$605$	−22.0623	+	16.0292i	−0.896960	+	0.651680i
$606$	1.97010	+	2.18802i	0.0800299	+	0.0888823i
$607$	−23.2190	−	10.3378i	−0.942432	−	0.419598i	−0.122763	−	0.992436i	$-0.539176\pi$
$607$	−23.2190	−	10.3378i	−0.942432	−	0.419598i	−0.819668	+	0.572838i	$0.805842\pi$
$608$	−25.6616	+	11.4253i	−1.04072	+	0.463357i
$609$	17.2998	−	19.2133i	0.701022	−	0.778564i
$610$	1.17449	−	11.1745i	0.0475537	−	0.452443i
$611$	16.0577	−	3.41316i	0.649624	−	0.138082i
$612$	0.236068	−	0.726543i	0.00954248	−	0.0293687i
$613$	−24.5082	−	5.20938i	−0.989877	−	0.210405i	−0.315607	−	0.948890i	$-0.602208\pi$
$613$	−24.5082	−	5.20938i	−0.989877	−	0.210405i	−0.674270	+	0.738485i	$0.735541\pi$
$614$	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
$617$	1.48807	+	14.1581i	0.0599076	+	0.569983i	0.982767	+	0.184847i	$0.0591789\pi$
$617$	1.48807	+	14.1581i	0.0599076	+	0.569983i	−0.922860	+	0.385136i	$0.874154\pi$
$618$	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
$623$	2.00129	+	19.0410i	0.0801800	+	0.762862i
$624$	−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
$627$	−3.73619	−	0.794152i	−0.149209	−	0.0317154i
$628$	−4.85410	+	14.9394i	−0.193700	+	0.596147i
$629$	−0.0545103	+	0.0115865i	−0.00217347	+	0.000461985i
$630$	1.01478	−	9.65502i	0.0404299	−	0.384665i
$631$	−5.84117	+	6.48728i	−0.232533	+	0.258254i	−0.848107	−	0.529825i	$-0.822258\pi$
$631$	−5.84117	+	6.48728i	−0.232533	+	0.258254i	0.615574	+	0.788079i	$0.288924\pi$
$632$		0			0
$633$	7.30836	+	3.25389i	0.290481	+	0.129331i
$634$	−10.7061	−	11.8903i	−0.425193	−	0.472225i
$635$	21.6803	−	15.7517i	0.860358	−	0.625087i
$636$	16.6353	−	12.0862i	0.659631	−	0.479250i
$637$	6.49606	+	7.21460i	0.257383	+	0.285853i
$638$	−3.71711	−	1.65496i	−0.147162	−	0.0655207i
$639$	−0.164749	+	0.0733508i	−0.00651736	+	0.00290171i
$640$	−19.9390	+	22.1445i	−0.788158	+	0.875339i
$641$	4.29509	−	40.8651i	0.169646	−	1.61407i	−0.496353	−	0.868121i	$-0.665328\pi$
$641$	4.29509	−	40.8651i	0.169646	−	1.61407i	0.665999	−	0.745953i	$-0.268005\pi$
$642$	−0.659039	+	0.140083i	−0.0260102	+	0.00552864i
$643$	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	$0.0486502\pi$
$644$	−25.9819	−	5.52261i	−1.02383	−	0.217621i
$645$	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	$-0.299896\pi$
$648$	−0.233733	−	2.22382i	−0.00918189	−	0.0873598i
$649$	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	$0.982684\pi$
$654$	0.543718	+	5.17313i	0.0212611	+	0.202285i
$655$	−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
$658$	−6.13348	−	1.30371i	−0.239108	−	0.0508240i
$659$	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	$-0.0456877\pi$
$660$	−3.16535	+	0.672816i	−0.123211	+	0.0261893i
$661$	1.73706	−	16.5270i	0.0675637	−	0.642826i	−0.907370	−	0.420332i	$-0.861914\pi$
$661$	1.73706	−	16.5270i	0.0675637	−	0.642826i	0.974934	−	0.222494i	$-0.0714197\pi$
$662$	−4.66087	+	5.17642i	−0.181150	+	0.201187i
$663$	−1.04683	+	0.466079i	−0.0406555	+	0.0181010i
$664$	−8.35519	−	3.71997i	−0.324244	−	0.144363i
$665$	−26.2771	−	29.1837i	−1.01898	−	1.13169i
$666$	−0.236068	+	0.171513i	−0.00914745	+	0.00664601i
$667$	−38.1525	+	27.7194i	−1.47727	+	1.07330i
$668$	9.99967	+	11.1058i	0.386899	+	0.429695i
$669$	−0.646976	−	0.288052i	−0.0250136	−	0.0111368i
$670$	−6.26153	+	2.78781i	−0.241904	+	0.107703i
$671$	3.54971	−	3.94235i	0.137035	−	0.152193i
$672$	−1.76173	+	16.7618i	−0.0679603	+	0.646599i
$673$	4.31990	−	0.918223i	0.166520	−	0.0353949i	−0.123897	−	0.992295i	$-0.539539\pi$
$673$	4.31990	−	0.918223i	0.166520	−	0.0353949i	0.290417	+	0.956900i	$0.406206\pi$
$674$	−3.62461	+	11.1554i	−0.139615	+	0.429690i
$675$	−9.06793	−	1.92745i	−0.349025	−	0.0741875i
$676$	8.54508	−	14.8005i	0.328657	−	0.569251i
$677$	−14.3262	−	24.8138i	−0.550602	−	0.953671i	−0.998231	−	0.0594514i	$-0.981065\pi$
$677$	−14.3262	−	24.8138i	−0.550602	−	0.953671i	0.447629	−	0.894219i	$-0.352268\pi$
$678$	−0.354102	−	1.08981i	−0.0135992	−	0.0418540i
$679$	1.65943	+	15.7884i	0.0636831	+	0.605904i
$680$	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
$685$	−1.77116	−	16.8514i	−0.0676725	−	0.643861i
$686$	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
$689$	60.3389	+	12.8254i	2.29873	+	0.488610i
$690$	2.73607	−	8.42075i	0.104160	−	0.320573i
$691$	−3.74906	+	0.796887i	−0.142621	+	0.0303150i	−0.278669	−	0.960387i	$-0.589893\pi$
$691$	−3.74906	+	0.796887i	−0.142621	+	0.0303150i	0.136048	+	0.990702i	$0.456560\pi$
$692$	0.153880	−	1.46407i	0.00584964	−	0.0556556i
$693$	3.06702	−	3.40627i	0.116507	−	0.129394i
$694$	−4.58717	+	2.04234i	−0.174127	+	0.0775262i
$695$	−14.0012	−	6.23374i	−0.531096	−	0.236459i
$696$	12.8945	+	14.3208i	0.488764	+	0.542828i
$697$	−1.23607	+	0.898056i	−0.0468194	+	0.0340163i
$698$	−8.35410	+	6.06961i	−0.316207	+	0.229738i
$699$	−12.5786	−	13.9699i	−0.475765	−	0.528391i
$700$	−8.22191	−	3.66063i	−0.310759	−	0.138359i
$701$	−27.4378	+	12.2161i	−1.03631	+	0.461396i	−0.853139	−	0.521684i	$-0.825304\pi$
$701$	−27.4378	+	12.2161i	−1.03631	+	0.461396i	−0.183174	+	0.983081i	$0.558637\pi$
$702$	−10.0370	+	11.1472i	−0.378821	+	0.420723i
$703$	−0.123379	+	1.17387i	−0.00465333	+	0.0442735i
$704$	−0.176399	+	0.0374948i	−0.00664829	+	0.00141314i
$705$	−2.73607	+	8.42075i	−0.103046	+	0.317144i
$706$	−19.5758	−	4.16097i	−0.736746	−	0.156600i
$707$	−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	$0.875194\pi$
$710$	−0.0152505	−	0.145099i	−0.000572341	−	0.00544546i
$711$		0			0
$712$	−14.2705			−0.534810
$713$		0			0
$714$	0.437694			0.0163803
$715$	−7.85410	−	5.70634i	−0.293727	−	0.213405i
$716$	3.34851	+	31.8590i	0.125140	+	1.19063i
$717$	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	−0.165018	−	0.986290i	$-0.552768\pi$
$719$	20.6910	−	35.8378i	0.771643	−	1.33653i	0.936662	−	0.350235i	$-0.113898\pi$
$720$	−9.49606	−	2.01845i	−0.353897	−	0.0752232i
$721$	−0.135255	+	0.416272i	−0.00503716	+	0.0155028i
$722$	3.62717	−	0.770979i	0.134989	−	0.0286929i
$723$	−0.891405	+	8.48115i	−0.0331517	+	0.315417i
$724$	−18.4055	+	20.4414i	−0.684035	+	0.759698i
$725$	−14.5973	+	6.49913i	−0.542129	+	0.241372i
$726$	−5.88113	−	2.61845i	−0.218269	−	0.0971796i
$727$	−15.9473	−	17.7112i	−0.591451	−	0.656873i	0.370903	−	0.928672i	$-0.379048\pi$
$727$	−15.9473	−	17.7112i	−0.591451	−	0.656873i	−0.962354	+	0.271798i	$0.912382\pi$
$728$	−26.3435	+	19.1396i	−0.976354	+	0.709362i
$729$	−10.5172	+	7.64121i	−0.389527	+	0.283008i
$730$	−9.27020	−	10.2956i	−0.343106	−	0.381057i
$731$	−0.995920	−	0.443412i	−0.0368354	−	0.0164002i
$732$	−10.2647	+	4.57012i	−0.379393	+	0.168917i
$733$	18.6984	−	20.7666i	0.690640	−	0.767033i	−0.291217	−	0.956657i	$-0.594060\pi$
$733$	18.6984	−	20.7666i	0.690640	−	0.767033i	0.981857	+	0.189624i	$0.0607268\pi$
$734$	−2.34315	+	22.2936i	−0.0864873	+	0.822872i
$735$	−5.12165	+	1.08864i	−0.188915	+	0.0401551i
$736$	9.50000	−	29.2380i	0.350175	−	1.07773i
$737$	−3.16535	−	0.672816i	−0.116597	−	0.0247835i
$738$	−4.00000	+	6.92820i	−0.147242	+	0.255031i
$739$	−10.8541	−	18.7999i	−0.399275	−	0.691564i	0.594362	−	0.804198i	$-0.297405\pi$
$739$	−10.8541	−	18.7999i	−0.399275	−	0.691564i	−0.993637	+	0.112634i	$0.964071\pi$
$740$	0.309017	+	0.951057i	0.0113597	+	0.0349615i
$741$	2.53696	+	24.1376i	0.0931975	+	0.886715i
$742$	−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
$747$	−0.855078	−	8.13553i	−0.0312857	−	0.297663i
$748$	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
$751$	38.9624	+	8.28171i	1.42176	+	0.302204i	0.853691	−	0.520779i	$-0.174359\pi$
$751$	38.9624	+	8.28171i	1.42176	+	0.302204i	0.568066	+	0.822983i	$0.307692\pi$
$752$	−1.93769	+	5.96361i	−0.0706604	+	0.217470i
$753$	0.923637	−	0.196325i	0.0336592	−	0.00715449i
$754$	−2.70249	+	25.7125i	−0.0984189	+	0.936393i
$755$	34.1718	−	37.9516i	1.24364	−	1.38120i
$756$	−22.1722	+	9.87171i	−0.806396	+	0.359030i
$757$	39.3963	+	17.5404i	1.43188	+	0.637515i	0.968584	−	0.248687i	$-0.0799990\pi$
$757$	39.3963	+	17.5404i	1.43188	+	0.637515i	0.463299	+	0.886202i	$0.346666\pi$
$758$	7.61602	+	8.45845i	0.276626	+	0.307225i
$759$	3.38197	−	2.45714i	0.122758	−	0.0891886i
$760$	23.6803	−	17.2048i	0.858976	−	0.624083i
$761$	2.34636	+	2.60590i	0.0850554	+	0.0944636i	0.784170	−	0.620546i	$-0.213089\pi$
$761$	2.34636	+	2.60590i	0.0850554	+	0.0944636i	−0.699115	+	0.715010i	$0.746422\pi$
$762$	5.77931	+	2.57311i	0.209362	+	0.0932140i
$763$	−23.0663	+	10.2698i	−0.835057	+	0.371791i
$764$	17.4204	−	19.3474i	0.630249	−	0.699963i
$765$	−0.129204	+	1.22930i	−0.00467139	+	0.0444453i
$766$	−10.1888	+	2.16569i	−0.368136	+	0.0782497i
$767$	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} +(0.104528 + 0.994522i) q^{3} +(-0.500000 - 1.53884i) q^{4} +(1.30902 + 2.26728i) q^{5} +(-0.309017 + 0.535233i) q^{6} +(-2.93444 - 0.623735i) q^{7} +(0.690983 - 2.12663i) q^{8} +(1.95630 - 0.415823i) q^{9} +(-0.169131 + 1.60917i) q^{10} +(-0.511170 + 0.567712i) q^{11} +(1.47815 - 0.658114i) q^{12} +(4.43444 + 1.97434i) q^{13} +(-1.24064 - 1.37787i) q^{14} +(-2.11803 + 1.53884i) q^{15} +(-1.50000 + 1.08981i) q^{16} +(0.157960 + 0.175433i) q^{17} +(1.12920 + 0.502754i) q^{18} +(4.56773 - 2.03368i) q^{19} +(2.83448 - 3.14801i) q^{20} +(0.313585 - 2.98357i) q^{21} +(-0.461819 + 0.0981626i) q^{22} +(-1.69098 + 5.20431i) q^{23} +(2.18720 + 0.464905i) q^{24} +(-0.927051 + 1.60570i) q^{25} +(1.50000 + 2.59808i) q^{26} +(1.54508 + 4.75528i) q^{27} +(0.507392 + 4.82751i) q^{28} +(6.97214 + 5.06555i) q^{29} -1.61803 q^{30} -5.61803 q^{32} +(-0.618034 - 0.449028i) q^{33} +(0.0152505 + 0.145099i) q^{34} +(-2.42705 - 7.46969i) q^{35} +(-1.61803 - 2.80252i) q^{36} +(-0.118034 + 0.204441i) q^{37} +(3.02264 + 0.642482i) q^{38} +(-1.50000 + 4.61653i) q^{39} +(5.72618 - 1.21714i) q^{40} +(-0.676522 + 6.43668i) q^{41} +(1.24064 - 1.37787i) q^{42} +(-4.21878 + 1.87832i) q^{43} +(1.12920 + 0.502754i) q^{44} +(3.50361 + 3.89116i) q^{45} +(-2.73607 + 1.98787i) q^{46} +(2.73607 - 1.98787i) q^{47} +(-1.24064 - 1.37787i) q^{48} +(1.82709 + 0.813473i) q^{49} +(-1.04683 + 0.466079i) q^{50} +(-0.157960 + 0.175433i) q^{51} +(0.820977 - 7.81108i) q^{52} +(12.4305 - 2.64218i) q^{53} +(-0.954915 + 2.93893i) q^{54} +(-1.95630 - 0.415823i) q^{55} +(-3.35410 + 5.80948i) q^{56} +(2.50000 + 4.33013i) q^{57} +(1.64590 + 5.06555i) q^{58} +(-0.990108 - 9.42025i) q^{59} +(3.42705 + 2.48990i) q^{60} -6.94427 q^{61} -6.00000 q^{63} +(0.190983 + 0.138757i) q^{64} +(1.32837 + 12.6386i) q^{65} +(-0.145898 - 0.449028i) q^{66} +(2.11803 + 3.66854i) q^{67} +(0.190983 - 0.330792i) q^{68} +(-5.35256 - 1.13772i) q^{69} +(1.50000 - 4.61653i) q^{70} +(-0.0881995 + 0.0187474i) q^{71} +(0.467465 - 4.44764i) q^{72} +(-5.72930 + 6.36303i) q^{73} +(-0.133284 + 0.0593421i) q^{74} +(-1.69381 - 0.754131i) q^{75} +(-5.41338 - 6.01217i) q^{76} +(1.85410 - 1.34708i) q^{77} +(-2.42705 + 1.76336i) q^{78} +(-4.43444 - 1.97434i) q^{80} +(0.913545 - 0.406737i) q^{81} +(-2.67652 + 2.97258i) q^{82} +(0.427539 - 4.06776i) q^{83} +(-4.74803 + 1.00922i) q^{84} +(-0.190983 + 0.587785i) q^{85} +(-2.79173 - 0.593401i) q^{86} +(-4.30902 + 7.46344i) q^{87} +(0.854102 + 1.47935i) q^{88} +(-1.97214 - 6.06961i) q^{89} +(0.338261 + 3.21834i) q^{90} +(-11.7812 - 8.55951i) q^{91} +8.85410 q^{92} +2.09017 q^{94} +(10.5902 + 7.69421i) q^{95} +(-0.587244 - 5.58726i) 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

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