LMFDB - Embedded newform 961.2.g.g.844.1

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			844.1
Root			$0.913545 + 0.406737i$ of defining polynomial
Character	$\chi$	$=$	961.844
Dual form			961.2.g.g.846.1

$q$-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 + 1.53884i) q^{2} +(-0.978148 + 0.207912i) q^{3} +(-0.500000 + 0.363271i) q^{4} +(0.190983 - 0.330792i) q^{5} +(-0.809017 - 1.40126i) q^{6} +(2.74064 + 1.22021i) q^{7} +(1.80902 + 1.31433i) q^{8} +(-1.82709 + 0.813473i) q^{9} +(0.604528 + 0.128496i) q^{10} +(-0.547318 - 5.20738i) q^{11} +(0.413545 - 0.459289i) q^{12} +(1.24064 + 1.37787i) q^{13} +(-0.507392 + 4.82751i) q^{14} +(-0.118034 + 0.363271i) q^{15} +(-1.50000 + 4.61653i) q^{16} +(-0.442790 + 4.21286i) q^{17} +(-2.16535 - 2.40487i) q^{18} +(3.34565 - 3.71572i) q^{19} +(0.0246758 + 0.234775i) q^{20} +(-2.93444 - 0.623735i) q^{21} +(7.73968 - 3.44593i) q^{22} +(2.80902 + 2.04087i) q^{23} +(-2.04275 - 0.909491i) q^{24} +(2.42705 + 4.20378i) q^{25} +(-1.50000 + 2.59808i) q^{26} +(4.04508 - 2.93893i) q^{27} +(-1.81359 + 0.385489i) q^{28} +(1.97214 + 6.06961i) q^{29} -0.618034 q^{30} -3.38197 q^{32} +(1.61803 + 4.97980i) q^{33} +(-6.70432 + 1.42505i) q^{34} +(0.927051 - 0.673542i) q^{35} +(0.618034 - 1.07047i) q^{36} +(-2.11803 - 3.66854i) q^{37} +(7.39074 + 3.29057i) q^{38} +(-1.50000 - 1.08981i) q^{39} +(0.780261 - 0.347395i) q^{40} +(2.41811 + 0.513986i) q^{41} +(-0.507392 - 4.82751i) q^{42} +(1.59385 - 1.77015i) q^{43} +(2.16535 + 2.40487i) q^{44} +(-0.0798526 + 0.759747i) q^{45} +(-1.73607 + 5.34307i) q^{46} +(-1.73607 + 5.34307i) q^{47} +(0.507392 - 4.82751i) q^{48} +(1.33826 + 1.48629i) q^{49} +(-5.25542 + 5.83674i) q^{50} +(-0.442790 - 4.21286i) q^{51} +(-1.12086 - 0.238246i) q^{52} +(-0.646976 + 0.288052i) q^{53} +(6.54508 + 4.75528i) q^{54} +(-1.82709 - 0.813473i) q^{55} +(3.35410 + 5.80948i) q^{56} +(-2.50000 + 4.33013i) q^{57} +(-8.35410 + 6.06961i) q^{58} +(-0.516329 + 0.109749i) q^{59} +(-0.0729490 - 0.224514i) q^{60} -10.9443 q^{61} -6.00000 q^{63} +(1.30902 + 4.02874i) q^{64} +(0.692728 - 0.147244i) q^{65} +(-6.85410 + 4.97980i) q^{66} +(-0.118034 + 0.204441i) q^{67} +(-1.30902 - 2.26728i) q^{68} +(-3.17195 - 1.41224i) q^{69} +(1.50000 + 1.08981i) q^{70} +(-10.1314 + 4.51078i) q^{71} +(-4.37441 - 0.929809i) q^{72} +(1.20859 + 11.4990i) q^{73} +(4.58629 - 5.09359i) q^{74} +(-3.24803 - 3.60730i) q^{75} +(-0.323011 + 3.07324i) q^{76} +(4.85410 - 14.9394i) q^{77} +(0.927051 - 2.85317i) q^{78} +(1.24064 + 1.37787i) q^{80} +(0.669131 - 0.743145i) q^{81} +(0.418114 + 3.97809i) q^{82} +(6.93523 + 1.47413i) q^{83} +(1.69381 - 0.754131i) q^{84} +(1.30902 + 0.951057i) q^{85} +(3.52090 + 1.56760i) q^{86} +(-3.19098 - 5.52694i) q^{87} +(5.85410 - 10.1396i) q^{88} +(-6.97214 + 5.06555i) q^{89} +(-1.20906 + 0.256993i) q^{90} +(1.71885 + 5.29007i) q^{91} -2.14590 q^{92} -9.09017 q^{94} +(-0.590170 - 1.81636i) q^{95} +(3.30806 - 0.703150i) q^{96} +(15.1353 - 10.9964i) q^{97} +(-1.61803 + 2.80252i) q^{98} +(5.23607 + 9.06914i) 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 $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{14}{15}\right)$

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	+	1.53884i	0.353553	+	1.08813i	0.956844	+	0.290604i	$0.0938561\pi$
$2$	0.500000	+	1.53884i	0.353553	+	1.08813i	−0.603290	+	0.797522i	$0.706144\pi$
$3$	−0.978148	+	0.207912i	−0.564734	+	0.120038i	−0.481427	−	0.876486i	$-0.659881\pi$
$3$	−0.978148	+	0.207912i	−0.564734	+	0.120038i	−0.0833066	+	0.996524i	$0.526548\pi$
$4$	−0.500000	+	0.363271i	−0.250000	+	0.181636i
$5$	0.190983	−	0.330792i	0.0854102	−	0.147935i	−0.820156	−	0.572140i	$-0.806113\pi$
$5$	0.190983	−	0.330792i	0.0854102	−	0.147935i	0.905566	+	0.424206i	$0.139447\pi$
$6$	−0.809017	−	1.40126i	−0.330280	−	0.572061i
$7$	2.74064	+	1.22021i	1.03586	+	0.461196i	0.852983	−	0.521939i	$-0.174791\pi$
$7$	2.74064	+	1.22021i	1.03586	+	0.461196i	0.182880	+	0.983135i	$0.441458\pi$
$8$	1.80902	+	1.31433i	0.639584	+	0.464685i
$9$	−1.82709	+	0.813473i	−0.609030	+	0.271158i
$10$	0.604528	+	0.128496i	0.191169	+	0.0406342i
$11$	−0.547318	−	5.20738i	−0.165023	−	1.57009i	−0.693070	−	0.720870i	$-0.743742\pi$
$11$	−0.547318	−	5.20738i	−0.165023	−	1.57009i	0.528047	−	0.849215i	$-0.322924\pi$
$12$	0.413545	−	0.459289i	0.119380	−	0.132585i
$13$	1.24064	+	1.37787i	0.344091	+	0.382151i	0.890206	−	0.455559i	$-0.150561\pi$
$13$	1.24064	+	1.37787i	0.344091	+	0.382151i	−0.546115	+	0.837710i	$0.683894\pi$
$14$	−0.507392	+	4.82751i	−0.135606	+	1.29021i
$15$	−0.118034	+	0.363271i	−0.0304762	+	0.0937962i
$16$	−1.50000	+	4.61653i	−0.375000	+	1.15413i
$17$	−0.442790	+	4.21286i	−0.107392	+	1.02177i	0.799574	+	0.600567i	$0.205058\pi$
$17$	−0.442790	+	4.21286i	−0.107392	+	1.02177i	−0.906967	+	0.421202i	$0.861608\pi$
$18$	−2.16535	−	2.40487i	−0.510378	−	0.566833i
$19$	3.34565	−	3.71572i	0.767545	−	0.852446i	−0.224995	−	0.974360i	$-0.572237\pi$
$19$	3.34565	−	3.71572i	0.767545	−	0.852446i	0.992541	+	0.121914i	$0.0389033\pi$
$20$	0.0246758	+	0.234775i	0.00551768	+	0.0524972i
$21$	−2.93444	−	0.623735i	−0.640348	−	0.136110i
$22$	7.73968	−	3.44593i	1.65011	−	0.734674i
$23$	2.80902	+	2.04087i	0.585721	+	0.425551i	0.840782	−	0.541374i	$-0.182096\pi$
$23$	2.80902	+	2.04087i	0.585721	+	0.425551i	−0.255061	+	0.966925i	$0.582096\pi$
$24$	−2.04275	−	0.909491i	−0.416975	−	0.185649i
$25$	2.42705	+	4.20378i	0.485410	+	0.840755i
$26$	−1.50000	+	2.59808i	−0.294174	+	0.509525i
$27$	4.04508	−	2.93893i	0.778477	−	0.565597i
$28$	−1.81359	+	0.385489i	−0.342735	+	0.0728507i
$29$	1.97214	+	6.06961i	0.366216	+	1.12710i	0.949216	+	0.314626i	$0.101879\pi$
$29$	1.97214	+	6.06961i	0.366216	+	1.12710i	−0.582999	+	0.812473i	$0.698121\pi$
$30$	−0.618034			−0.112837
$31$		0			0
$31$		0			0
$32$	−3.38197			−0.597853
$33$	1.61803	+	4.97980i	0.281664	+	0.866871i
$34$	−6.70432	+	1.42505i	−1.14978	+	0.244394i
$35$	0.927051	−	0.673542i	0.156700	−	0.113849i
$36$	0.618034	−	1.07047i	0.103006	−	0.178411i
$37$	−2.11803	−	3.66854i	−0.348203	−	0.603105i	0.637728	−	0.770262i	$-0.279875\pi$
$37$	−2.11803	−	3.66854i	−0.348203	−	0.603105i	−0.985930	+	0.167157i	$0.946541\pi$
$38$	7.39074	+	3.29057i	1.19894	+	0.533801i
$39$	−1.50000	−	1.08981i	−0.240192	−	0.174510i
$40$	0.780261	−	0.347395i	0.123370	−	0.0549279i
$41$	2.41811	+	0.513986i	0.377646	+	0.0802711i	0.392824	−	0.919614i	$-0.371498\pi$
$41$	2.41811	+	0.513986i	0.377646	+	0.0802711i	−0.0151780	+	0.999885i	$0.504832\pi$
$42$	−0.507392	−	4.82751i	−0.0782923	−	0.744901i
$43$	1.59385	−	1.77015i	0.243059	−	0.269945i	−0.609255	−	0.792974i	$-0.708532\pi$
$43$	1.59385	−	1.77015i	0.243059	−	0.269945i	0.852315	+	0.523029i	$0.175198\pi$
$44$	2.16535	+	2.40487i	0.326439	+	0.362547i
$45$	−0.0798526	+	0.759747i	−0.0119037	+	0.113256i
$46$	−1.73607	+	5.34307i	−0.255969	+	0.787792i
$47$	−1.73607	+	5.34307i	−0.253232	+	0.779367i	0.740941	+	0.671570i	$0.234380\pi$
$47$	−1.73607	+	5.34307i	−0.253232	+	0.779367i	−0.994173	+	0.107797i	$0.965620\pi$
$48$	0.507392	−	4.82751i	0.0732357	−	0.696791i
$49$	1.33826	+	1.48629i	0.191180	+	0.212327i
$50$	−5.25542	+	5.83674i	−0.743229	+	0.825439i
$51$	−0.442790	−	4.21286i	−0.0620030	−	0.589919i
$52$	−1.12086	−	0.238246i	−0.155435	−	0.0330387i
$53$	−0.646976	+	0.288052i	−0.0888691	+	0.0395671i	−0.450690	−	0.892681i	$-0.648822\pi$
$53$	−0.646976	+	0.288052i	−0.0888691	+	0.0395671i	0.361821	+	0.932248i	$0.382155\pi$
$54$	6.54508	+	4.75528i	0.890673	+	0.647112i
$55$	−1.82709	−	0.813473i	−0.246365	−	0.109689i
$56$	3.35410	+	5.80948i	0.448211	+	0.776324i
$57$	−2.50000	+	4.33013i	−0.331133	+	0.573539i
$58$	−8.35410	+	6.06961i	−1.09695	+	0.796979i
$59$	−0.516329	+	0.109749i	−0.0672203	+	0.0142881i	−0.241399	−	0.970426i	$-0.577606\pi$
$59$	−0.516329	+	0.109749i	−0.0672203	+	0.0142881i	0.174179	+	0.984714i	$0.444273\pi$
$60$	−0.0729490	−	0.224514i	−0.00941768	−	0.0289846i
$61$	−10.9443			−1.40127			−0.700635	−	0.713520i	$-0.747100\pi$
$61$	−10.9443			−1.40127			−0.700635	+	0.713520i	$0.747100\pi$
$62$		0			0
$63$	−6.00000			−0.755929
$64$	1.30902	+	4.02874i	0.163627	+	0.503593i
$65$	0.692728	−	0.147244i	0.0859223	−	0.0182634i
$66$	−6.85410	+	4.97980i	−0.843682	+	0.612971i
$67$	−0.118034	+	0.204441i	−0.0144201	+	0.0249764i	−0.873145	−	0.487460i	$-0.837924\pi$
$67$	−0.118034	+	0.204441i	−0.0144201	+	0.0249764i	0.858725	+	0.512436i	$0.171257\pi$
$68$	−1.30902	−	2.26728i	−0.158742	−	0.274949i
$69$	−3.17195	−	1.41224i	−0.381858	−	0.170014i
$70$	1.50000	+	1.08981i	0.179284	+	0.130258i
$71$	−10.1314	+	4.51078i	−1.20237	+	0.535331i	−0.907438	−	0.420186i	$-0.861965\pi$
$71$	−10.1314	+	4.51078i	−1.20237	+	0.535331i	−0.294935	+	0.955517i	$0.595298\pi$
$72$	−4.37441	−	0.929809i	−0.515529	−	0.109579i
$73$	1.20859	+	11.4990i	0.141455	+	1.34585i	0.803014	+	0.595960i	$0.203228\pi$
$73$	1.20859	+	11.4990i	0.141455	+	1.34585i	−0.661560	+	0.749893i	$0.730105\pi$
$74$	4.58629	−	5.09359i	0.533145	−	0.592118i
$75$	−3.24803	−	3.60730i	−0.375050	−	0.416535i
$76$	−0.323011	+	3.07324i	−0.0370519	+	0.352525i
$77$	4.85410	−	14.9394i	0.553176	−	1.70250i
$78$	0.927051	−	2.85317i	0.104968	−	0.323058i
$79$		0			0		−0.994522	−	0.104528i	$-0.966667\pi$
$79$		0			0		0.994522	+	0.104528i	$0.0333333\pi$
$80$	1.24064	+	1.37787i	0.138707	+	0.154050i
$81$	0.669131	−	0.743145i	0.0743478	−	0.0825716i
$82$	0.418114	+	3.97809i	0.0461730	+	0.439306i
$83$	6.93523	+	1.47413i	0.761241	+	0.161807i	0.572146	−	0.820152i	$-0.306111\pi$
$83$	6.93523	+	1.47413i	0.761241	+	0.161807i	0.189095	+	0.981959i	$0.439445\pi$
$84$	1.69381	−	0.754131i	0.184809	−	0.0822825i
$85$	1.30902	+	0.951057i	0.141983	+	0.103157i
$86$	3.52090	+	1.56760i	0.379668	+	0.169039i
$87$	−3.19098	−	5.52694i	−0.342109	−	0.592551i
$88$	5.85410	−	10.1396i	0.624049	−	1.08089i
$89$	−6.97214	+	5.06555i	−0.739045	+	0.536948i	−0.892412	−	0.451222i	$-0.850988\pi$
$89$	−6.97214	+	5.06555i	−0.739045	+	0.536948i	0.153367	+	0.988169i	$0.450988\pi$
$90$	−1.20906	+	0.256993i	−0.127446	+	0.0270894i
$91$	1.71885	+	5.29007i	0.180184	+	0.554550i
$92$	−2.14590			−0.223725
$93$		0			0
$94$	−9.09017			−0.937579
$95$	−0.590170	−	1.81636i	−0.0605502	−	0.186354i
$96$	3.30806	−	0.703150i	0.337628	−	0.0717650i
$97$	15.1353	−	10.9964i	1.53675	−	1.11652i	0.584421	−	0.811451i	$-0.301322\pi$
$97$	15.1353	−	10.9964i	1.53675	−	1.11652i	0.952331	−	0.305065i	$-0.0986782\pi$
$98$	−1.61803	+	2.80252i	−0.163446	+	0.283097i
$99$	5.23607	+	9.06914i	0.526245	+	0.911482i
$100$	−2.74064	−	1.22021i	−0.274064	−	0.122021i
$101$	−7.47214	−	5.42882i	−0.743505	−	0.540188i	0.150302	−	0.988640i	$-0.451976\pi$
$101$	−7.47214	−	5.42882i	−0.743505	−	0.540188i	−0.893807	+	0.448452i	$0.851976\pi$
$102$	6.26153	−	2.78781i	0.619984	−	0.276035i
$103$	6.70432	+	1.42505i	0.660597	+	0.140414i	0.525998	−	0.850486i	$-0.323692\pi$
$103$	6.70432	+	1.42505i	0.660597	+	0.140414i	0.134599	+	0.990900i	$0.457025\pi$
$104$	0.433364	+	4.12319i	0.0424949	+	0.404312i
$105$	−0.766755	+	0.851568i	−0.0748277	+	0.0831045i
$106$	−0.766755	−	0.851568i	−0.0744739	−	0.0827116i
$107$	1.05471	−	10.0349i	0.101963	−	0.970110i	−0.817233	−	0.576308i	$-0.804493\pi$
$107$	1.05471	−	10.0349i	0.101963	−	0.970110i	0.919195	−	0.393802i	$-0.128840\pi$
$108$	−0.954915	+	2.93893i	−0.0918867	+	0.282798i
$109$	5.69098	−	17.5150i	0.545097	−	1.67764i	−0.175661	−	0.984451i	$-0.556206\pi$
$109$	5.69098	−	17.5150i	0.545097	−	1.67764i	0.720758	−	0.693186i	$-0.243794\pi$
$110$	0.338261	−	3.21834i	0.0322519	−	0.306857i
$111$	2.83448	+	3.14801i	0.269037	+	0.298796i
$112$	−9.74408	+	10.8219i	−0.920729	+	1.02257i
$113$	−0.507392	−	4.82751i	−0.0477314	−	0.454134i	−0.992119	−	0.125299i	$-0.960011\pi$
$113$	−0.507392	−	4.82751i	−0.0477314	−	0.454134i	0.944388	−	0.328835i	$-0.106656\pi$
$114$	−7.91338	−	1.68204i	−0.741156	−	0.157538i
$115$	1.21158	−	0.539430i	0.112980	−	0.0503021i
$116$	−3.19098	−	2.31838i	−0.296275	−	0.215257i
$117$	−3.38761	−	1.50826i	−0.313185	−	0.139439i
$118$	−0.427051	−	0.739674i	−0.0393132	−	0.0680925i
$119$	−6.35410	+	11.0056i	−0.582480	+	1.00888i
$120$	−0.690983	+	0.502029i	−0.0630778	+	0.0458287i
$121$	−16.0577	+	3.41316i	−1.45979	+	0.310288i
$122$	−5.47214	−	16.8415i	−0.495424	−	1.52476i
$123$	−2.47214			−0.222905
$124$		0			0
$125$	3.76393			0.336656
$126$	−3.00000	−	9.23305i	−0.267261	−	0.822546i
$127$	5.63798	−	1.19839i	0.500289	−	0.106340i	0.0491467	−	0.998792i	$-0.484350\pi$
$127$	5.63798	−	1.19839i	0.500289	−	0.106340i	0.451143	+	0.892452i	$0.351016\pi$
$128$	−11.0172	+	8.00448i	−0.973794	+	0.707503i
$129$	−1.19098	+	2.06284i	−0.104860	+	0.181623i
$130$	0.572949	+	0.992377i	0.0502510	+	0.0870372i
$131$	−10.1314	−	4.51078i	−0.885182	−	0.394109i	−0.0867762	−	0.996228i	$-0.527656\pi$
$131$	−10.1314	−	4.51078i	−0.885182	−	0.394109i	−0.798406	+	0.602119i	$0.794323\pi$
$132$	−2.61803	−	1.90211i	−0.227871	−	0.165558i
$133$	13.7032	−	6.10105i	1.18822	−	0.529028i
$134$	−0.373619	−	0.0794152i	−0.0322758	−	0.00686043i
$135$	−0.199632	−	1.89937i	−0.0171816	−	0.163472i
$136$	−6.33810	+	7.03917i	−0.543487	+	0.603604i
$137$	−1.65418	−	1.83716i	−0.141326	−	0.156959i	0.668326	−	0.743868i	$-0.267011\pi$
$137$	−1.65418	−	1.83716i	−0.141326	−	0.156959i	−0.809652	+	0.586910i	$0.800344\pi$
$138$	0.587244	−	5.58726i	0.0499896	−	0.475619i
$139$	0.263932	−	0.812299i	0.0223864	−	0.0688983i	−0.939239	−	0.343263i	$-0.888468\pi$
$139$	0.263932	−	0.812299i	0.0223864	−	0.0688983i	0.961626	+	0.274365i	$0.0884677\pi$
$140$	−0.218847	+	0.673542i	−0.0184960	+	0.0569247i
$141$	0.587244	−	5.58726i	0.0494549	−	0.470532i
$142$	−12.0071	−	13.3352i	−1.00761	−	1.11906i
$143$	6.49606	−	7.21460i	0.543228	−	0.603315i
$144$	−1.01478	−	9.65502i	−0.0845653	−	0.804585i
$145$	2.38442	+	0.506825i	0.198016	+	0.0420895i
$146$	−17.0908	+	7.60931i	−1.41444	+	0.629751i
$147$	−1.61803	−	1.17557i	−0.133453	−	0.0969594i
$148$	2.39169	+	1.06485i	0.196596	+	0.0875302i
$149$	−6.01722	−	10.4221i	−0.492950	−	0.853814i	0.507017	−	0.861936i	$-0.330748\pi$
$149$	−6.01722	−	10.4221i	−0.492950	−	0.853814i	−0.999967	+	0.00812166i	$0.997415\pi$
$150$	3.92705	−	6.80185i	0.320642	−	0.555369i
$151$	14.9721	−	10.8779i	1.21842	−	0.885230i	0.222448	−	0.974945i	$-0.428595\pi$
$151$	14.9721	−	10.8779i	1.21842	−	0.885230i	0.995968	+	0.0897142i	$0.0285954\pi$
$152$	10.9360	−	2.32452i	0.887029	−	0.188544i
$153$	−2.61803	−	8.05748i	−0.211656	−	0.651409i
$154$	25.4164			2.04811
$155$		0			0
$156$	1.14590			0.0917453
$157$	−1.14590	−	3.52671i	−0.0914526	−	0.281462i	0.894860	−	0.446346i	$-0.147275\pi$
$157$	−1.14590	−	3.52671i	−0.0914526	−	0.281462i	−0.986313	+	0.164884i	$0.947275\pi$
$158$		0			0
$159$	0.572949	−	0.416272i	0.0454378	−	0.0330125i
$160$	−0.645898	+	1.11873i	−0.0510627	+	0.0884432i
$161$	5.20820	+	9.02087i	0.410464	+	0.710944i
$162$	1.47815	+	0.658114i	0.116134	+	0.0517063i
$163$	−0.572949	−	0.416272i	−0.0448768	−	0.0326049i	0.565121	−	0.825008i	$-0.308830\pi$
$163$	−0.572949	−	0.416272i	−0.0448768	−	0.0326049i	−0.609998	+	0.792403i	$0.708830\pi$
$164$	−1.39577	+	0.621438i	−0.108992	+	0.0485262i
$165$	1.95630	+	0.415823i	0.152297	+	0.0323718i
$166$	1.19916	+	11.4093i	0.0930732	+	0.885533i
$167$	3.18769	−	3.54029i	0.246671	−	0.273956i	−0.607076	−	0.794644i	$-0.707658\pi$
$167$	3.18769	−	3.54029i	0.246671	−	0.273956i	0.853747	+	0.520688i	$0.174324\pi$
$168$	−4.48866	−	4.98517i	−0.346308	−	0.384614i
$169$	0.999533	−	9.50992i	0.0768872	−	0.731533i
$170$	−0.809017	+	2.48990i	−0.0620488	+	0.190966i
$171$	−3.09017	+	9.51057i	−0.236311	+	0.727291i
$172$	−0.153880	+	1.46407i	−0.0117332	+	0.111634i
$173$	8.08990	+	8.98475i	0.615064	+	0.683098i	0.967538	−	0.252724i	$-0.0813264\pi$
$173$	8.08990	+	8.98475i	0.615064	+	0.683098i	−0.352475	+	0.935821i	$0.614660\pi$
$174$	6.90960	−	7.67389i	0.523816	−	0.581756i
$175$	1.52218	+	14.4825i	0.115066	+	1.09478i
$176$	24.8610	+	5.28437i	1.87397	+	0.398324i
$177$	0.482228	−	0.214702i	0.0362465	−	0.0161380i
$178$	−11.2812	−	8.19624i	−0.845558	−	0.614334i
$179$	4.38353	+	1.95167i	0.327641	+	0.145875i	0.563964	−	0.825800i	$-0.309276\pi$
$179$	4.38353	+	1.95167i	0.327641	+	0.145875i	−0.236323	+	0.971675i	$0.575942\pi$
$180$	−0.236068	−	0.408882i	−0.0175955	−	0.0304762i
$181$	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	$-0.0510169\pi$
$182$	−7.28115	+	5.29007i	−0.539715	+	0.392126i
$183$	10.7051	−	2.27544i	0.791345	−	0.168206i
$184$	2.39919	+	7.38394i	0.176870	+	0.544351i
$185$	−1.61803			−0.118960
$186$		0			0
$187$	22.1803			1.62199
$188$	−1.07295	−	3.30220i	−0.0782528	−	0.240838i
$189$	14.6722	−	3.11868i	1.06725	−	0.226850i
$190$	2.50000	−	1.81636i	0.181369	−	0.131772i
$191$	2.45492	−	4.25204i	0.177631	−	0.307667i	−0.763437	−	0.645882i	$-0.776490\pi$
$191$	2.45492	−	4.25204i	0.177631	−	0.307667i	0.941069	+	0.338215i	$0.109823\pi$
$192$	−2.11803	−	3.66854i	−0.152856	−	0.264754i
$193$	−4.21878	−	1.87832i	−0.303675	−	0.135205i	0.249242	−	0.968441i	$-0.419819\pi$
$193$	−4.21878	−	1.87832i	−0.303675	−	0.135205i	−0.552917	+	0.833237i	$0.686485\pi$
$194$	24.4894	+	17.7926i	1.75823	+	1.27743i
$195$	−0.646976	+	0.288052i	−0.0463309	+	0.0206279i
$196$	−1.20906	−	0.256993i	−0.0863612	−	0.0183566i
$197$	−1.08881	−	10.3593i	−0.0775746	−	0.738073i	−0.962306	−	0.271971i	$-0.912325\pi$
$197$	−1.08881	−	10.3593i	−0.0775746	−	0.738073i	0.884731	−	0.466102i	$-0.154342\pi$
$198$	−11.3379	+	12.5920i	−0.805752	+	0.894878i
$199$	8.89395	+	9.87773i	0.630475	+	0.700214i	0.970745	−	0.240114i	$-0.0771849\pi$
$199$	8.89395	+	9.87773i	0.630475	+	0.700214i	−0.340269	+	0.940328i	$0.610518\pi$
$200$	−1.13456	+	10.7946i	−0.0802257	+	0.763296i
$201$	0.0729490	−	0.224514i	0.00514543	−	0.0158360i
$202$	4.61803	−	14.2128i	0.324924	−	1.00001i
$203$	−2.00129	+	19.0410i	−0.140463	+	1.33642i
$204$	1.75181	+	1.94558i	0.122651	+	0.136218i
$205$	0.631841	−	0.701731i	0.0441297	−	0.0490110i
$206$	1.15924	+	11.0294i	0.0807680	+	0.768456i
$207$	−6.79252	−	1.44380i	−0.472113	−	0.100351i
$208$	−8.22191	+	3.66063i	−0.570087	+	0.253819i
$209$	−21.1803	−	15.3884i	−1.46507	−	1.06444i
$210$	−1.69381	−	0.754131i	−0.116884	−	0.0520400i
$211$	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	$0.744533\pi$
$212$	0.218847	−	0.379054i	0.0150305	−	0.0260336i
$213$	8.97214	−	6.51864i	0.614761	−	0.446650i
$214$	15.9695	−	3.39442i	1.09165	−	0.232037i
$215$	−0.281153	−	0.865300i	−0.0191745	−	0.0590130i
$216$	11.1803			0.760726
$217$		0			0
$218$	29.7984			2.01820
$219$	−3.57295	−	10.9964i	−0.241438	−	0.743068i
$220$	1.20906	−	0.256993i	0.0815146	−	0.0173265i
$221$	−6.35410	+	4.61653i	−0.427423	+	0.310541i
$222$	−3.42705	+	5.93583i	−0.230009	+	0.398387i
$223$	−6.35410	−	11.0056i	−0.425502	−	0.736991i	0.570965	−	0.820974i	$-0.306569\pi$
$223$	−6.35410	−	11.0056i	−0.425502	−	0.736991i	−0.996467	+	0.0839830i	$0.973236\pi$
$224$	−9.26874	−	4.12671i	−0.619294	−	0.275727i
$225$	−7.85410	−	5.70634i	−0.523607	−	0.380423i
$226$	7.17508	−	3.19455i	0.477279	−	0.212498i
$227$	−21.2675	−	4.52055i	−1.41157	−	0.300039i	−0.561838	−	0.827247i	$-0.689906\pi$
$227$	−21.2675	−	4.52055i	−1.41157	−	0.300039i	−0.849736	+	0.527208i	$0.823239\pi$
$228$	−0.323011	−	3.07324i	−0.0213919	−	0.203530i
$229$	1.84943	−	2.05400i	0.122214	−	0.135732i	−0.678933	−	0.734201i	$-0.737557\pi$
$229$	1.84943	−	2.05400i	0.122214	−	0.135732i	0.801146	+	0.598468i	$0.204224\pi$
$230$	1.43589	+	1.59471i	0.0946795	+	0.105152i
$231$	−1.64195	+	15.6222i	−0.108033	+	1.02786i
$232$	−4.40983	+	13.5721i	−0.289520	+	0.891049i
$233$	−1.79180	+	5.51458i	−0.117384	+	0.361272i	−0.992437	−	0.122756i	$-0.960827\pi$
$233$	−1.79180	+	5.51458i	−0.117384	+	0.361272i	0.875052	+	0.484028i	$0.160827\pi$
$234$	0.627171	−	5.96713i	0.0409994	−	0.390084i
$235$	1.43589	+	1.59471i	0.0936669	+	0.104028i
$236$	0.218296	−	0.242442i	0.0142098	−	0.0157816i
$237$		0			0
$238$	−20.1130	−	4.27514i	−1.30373	−	0.277116i
$239$	−12.2565	+	5.45694i	−0.792807	+	0.352980i	−0.762854	−	0.646571i	$-0.776202\pi$
$239$	−12.2565	+	5.45694i	−0.792807	+	0.352980i	−0.0299531	+	0.999551i	$0.509536\pi$
$240$	−1.50000	−	1.08981i	−0.0968246	−	0.0703472i
$241$	15.9616	+	7.10656i	1.02818	+	0.457774i	0.850311	−	0.526281i	$-0.176414\pi$
$241$	15.9616	+	7.10656i	1.02818	+	0.457774i	0.177866	+	0.984055i	$0.443081\pi$
$242$	−13.2812	−	23.0036i	−0.853745	−	1.47873i
$243$	−8.00000	+	13.8564i	−0.513200	+	0.888889i
$244$	5.47214	−	3.97574i	0.350318	−	0.254521i
$245$	0.747238	−	0.158830i	0.0477393	−	0.0101473i
$246$	−1.23607	−	3.80423i	−0.0788088	−	0.242549i
$247$	9.27051			0.589868
$248$		0			0
$249$	−7.09017			−0.449321
$250$	1.88197	+	5.79210i	0.119026	+	0.366324i
$251$	−16.5740	+	3.52291i	−1.04614	+	0.222364i	−0.698757	−	0.715359i	$-0.746263\pi$
$251$	−16.5740	+	3.52291i	−1.04614	+	0.222364i	−0.347384	+	0.937723i	$0.612930\pi$
$252$	3.00000	−	2.17963i	0.188982	−	0.137304i
$253$	9.09017	−	15.7446i	0.571494	−	0.989857i
$254$	4.66312	+	8.07676i	0.292590	+	0.506781i
$255$	−1.47815	−	0.658114i	−0.0925652	−	0.0412127i
$256$	−10.9721	−	7.97172i	−0.685758	−	0.498233i
$257$	−23.2190	+	10.3378i	−1.44836	+	0.644853i	−0.972125	−	0.234463i	$-0.924667\pi$
$257$	−23.2190	+	10.3378i	−1.44836	+	0.644853i	−0.476239	+	0.879316i	$0.658000\pi$
$258$	−3.76988	−	0.801313i	−0.234703	−	0.0498876i
$259$	−1.32837	−	12.6386i	−0.0825408	−	0.785324i
$260$	−0.292875	+	0.325270i	−0.0181633	+	0.0201724i
$261$	−8.54074	−	9.48545i	−0.528658	−	0.587135i
$262$	1.87569	−	17.8460i	0.115880	−	1.10253i
$263$	−4.26393	+	13.1230i	−0.262925	+	0.809201i	0.729239	+	0.684259i	$0.239874\pi$
$263$	−4.26393	+	13.1230i	−0.262925	+	0.809201i	−0.992164	+	0.124942i	$0.960126\pi$
$264$	−3.61803	+	11.1352i	−0.222675	+	0.685322i
$265$	−0.0282760	+	0.269028i	−0.00173698	+	0.0165263i
$266$	16.2401	+	18.0365i	0.995747	+	1.10589i
$267$	5.76659	−	6.40445i	0.352910	−	0.391946i
$268$	−0.0152505	−	0.145099i	−0.000931572	−	0.00886332i
$269$	−3.53897	−	0.752232i	−0.215775	−	0.0458644i	0.0987557	−	0.995112i	$-0.468514\pi$
$269$	−3.53897	−	0.752232i	−0.215775	−	0.0458644i	−0.314531	+	0.949247i	$0.601847\pi$
$270$	2.82301	−	1.25689i	0.171803	−	0.0764916i
$271$	−8.54508	−	6.20837i	−0.519077	−	0.377131i	0.297179	−	0.954822i	$-0.403954\pi$
$271$	−8.54508	−	6.20837i	−0.519077	−	0.377131i	−0.816256	+	0.577690i	$0.803954\pi$
$272$	−18.7846	−	8.36344i	−1.13898	−	0.507108i
$273$	−2.78115	−	4.81710i	−0.168323	−	0.291544i
$274$	2.00000	−	3.46410i	0.120824	−	0.209274i
$275$	20.5623	−	14.9394i	1.23995	−	0.900879i
$276$	2.09901	−	0.446157i	0.126345	−	0.0268555i
$277$	0.718847	+	2.21238i	0.0431913	+	0.132929i	0.970327	−	0.241797i	$-0.0777368\pi$
$277$	0.718847	+	2.21238i	0.0431913	+	0.132929i	−0.927136	+	0.374726i	$0.877737\pi$
$278$	1.38197			0.0828848
$279$		0			0
$280$	2.56231			0.153127
$281$	−3.10081	−	9.54332i	−0.184979	−	0.569307i	0.814969	−	0.579505i	$-0.196754\pi$
$281$	−3.10081	−	9.54332i	−0.184979	−	0.569307i	−0.999948	+	0.0101977i	$0.996754\pi$
$282$	8.89153	−	1.88995i	0.529483	−	0.112545i
$283$	10.9721	−	7.97172i	0.652226	−	0.473870i	−0.211803	−	0.977312i	$-0.567933\pi$
$283$	10.9721	−	7.97172i	0.652226	−	0.473870i	0.864029	+	0.503443i	$0.167933\pi$
$284$	3.42705	−	5.93583i	0.203358	−	0.352226i
$285$	0.954915	+	1.65396i	0.0565643	+	0.0979722i
$286$	14.3502	+	6.38910i	0.848543	+	0.377796i
$287$	6.00000	+	4.35926i	0.354169	+	0.257319i
$288$	6.17916	−	2.75114i	0.364110	−	0.162112i
$289$	−0.923637	−	0.196325i	−0.0543316	−	0.0115485i
$290$	0.412289	+	3.92266i	0.0242104	+	0.230347i
$291$	−12.5182	+	13.9029i	−0.733832	+	0.815003i
$292$	−4.78154	−	5.31044i	−0.279818	−	0.310770i
$293$	0.393438	−	3.74331i	0.0229849	−	0.218687i	−0.977000	−	0.213238i	$-0.931599\pi$
$293$	0.393438	−	3.74331i	0.0229849	−	0.218687i	0.999985	−	0.00544856i	$-0.00173434\pi$
$294$	1.00000	−	3.07768i	0.0583212	−	0.179494i
$295$	−0.0623059	+	0.191758i	−0.00362759	+	0.0111646i
$296$	0.990108	−	9.42025i	0.0575488	−	0.547541i
$297$	−17.5181	−	19.4558i	−1.01650	−	1.12894i
$298$	13.0294	−	14.4706i	0.754773	−	0.838260i
$299$	0.672922	+	6.40243i	0.0389161	+	0.370262i
$300$	2.93444	+	0.623735i	0.169420	+	0.0360114i
$301$	6.52810	−	2.90650i	0.376274	−	0.167528i
$302$	24.2254	+	17.6008i	1.39402	+	1.01281i
$303$	8.43757	+	3.75665i	0.484726	+	0.215814i
$304$	12.1353	+	21.0189i	0.696005	+	1.20552i
$305$	−2.09017	+	3.62028i	−0.119683	+	0.207297i
$306$	11.0902	−	8.05748i	0.633983	−	0.460615i
$307$	4.97894	−	1.05831i	0.284163	−	0.0604007i	−0.0636251	−	0.997974i	$-0.520266\pi$
$307$	4.97894	−	1.05831i	0.284163	−	0.0604007i	0.347788	+	0.937573i	$0.386933\pi$
$308$	3.00000	+	9.23305i	0.170941	+	0.526102i
$309$	−6.85410			−0.389916
$310$		0			0
$311$	7.52786			0.426866			0.213433	−	0.976958i	$-0.431535\pi$
$311$	7.52786			0.426866			0.213433	+	0.976958i	$0.431535\pi$
$312$	−1.28115	−	3.94298i	−0.0725310	−	0.223227i
$313$	−3.16535	+	0.672816i	−0.178916	+	0.0380298i	−0.296498	−	0.955033i	$-0.595819\pi$
$313$	−3.16535	+	0.672816i	−0.178916	+	0.0380298i	0.117582	+	0.993063i	$0.462486\pi$
$314$	4.85410	−	3.52671i	0.273933	−	0.199024i
$315$	−1.14590	+	1.98475i	−0.0645640	+	0.111828i
$316$		0			0
$317$	−9.03363	−	4.02203i	−0.507379	−	0.225900i	0.137049	−	0.990564i	$-0.456238\pi$
$317$	−9.03363	−	4.02203i	−0.507379	−	0.225900i	−0.644429	+	0.764664i	$0.722905\pi$
$318$	0.927051	+	0.673542i	0.0519864	+	0.0377704i
$319$	30.5274	−	13.5917i	1.70921	−	0.760988i
$320$	1.58268	+	0.336408i	0.0884743	+	0.0188058i
$321$	1.05471	+	10.0349i	0.0588682	+	0.560093i
$322$	−11.2776	+	12.5250i	−0.628476	+	0.697993i
$323$	14.1724	+	15.7401i	0.788574	+	0.875800i
$324$	−0.0646021	+	0.614648i	−0.00358901	+	0.0341471i
$325$	−2.78115	+	8.55951i	−0.154271	+	0.474796i
$326$	0.354102	−	1.08981i	0.0196119	−	0.0603592i
$327$	−1.92504	+	18.3155i	−0.106455	+	1.01285i
$328$	3.69886	+	4.10800i	0.204236	+	0.226827i
$329$	−11.2776	+	12.5250i	−0.621754	+	0.690528i
$330$	0.338261	+	3.21834i	0.0186207	+	0.177164i
$331$	−21.7838	−	4.63030i	−1.19735	−	0.254504i	−0.434254	−	0.900791i	$-0.642988\pi$
$331$	−21.7838	−	4.63030i	−1.19735	−	0.254504i	−0.763095	+	0.646286i	$0.776321\pi$
$332$	−4.00313	+	1.78231i	−0.219700	+	0.0978168i
$333$	6.85410	+	4.97980i	0.375602	+	0.272891i
$334$	7.04179	+	3.13521i	0.385310	+	0.171551i
$335$	0.0450850	+	0.0780895i	0.00246326	+	0.00426648i
$336$	7.28115	−	12.6113i	0.397219	−	0.688004i
$337$	−22.6353	+	16.4455i	−1.23302	+	0.895842i	−0.997113	−	0.0759333i	$-0.975806\pi$
$337$	−22.6353	+	16.4455i	−1.23302	+	0.895842i	−0.235908	+	0.971775i	$0.575806\pi$
$338$	15.1340	−	3.21684i	0.823183	−	0.174973i
$339$	1.50000	+	4.61653i	0.0814688	+	0.250735i
$340$	−1.00000			−0.0542326
$341$		0			0
$342$	−16.1803			−0.874933
$343$	−4.63525	−	14.2658i	−0.250280	−	0.770283i
$344$	5.20985	−	1.10739i	0.280896	−	0.0597063i
$345$	−1.07295	+	0.779543i	−0.0577656	+	0.0419692i
$346$	−9.78115	+	16.9415i	−0.525838	+	0.910778i
$347$	−16.0623	−	27.8207i	−0.862270	−	1.49350i	−0.869733	−	0.493523i	$-0.835709\pi$
$347$	−16.0623	−	27.8207i	−0.862270	−	1.49350i	0.00746305	−	0.999972i	$-0.497624\pi$
$348$	3.60327	+	1.60428i	0.193156	+	0.0859984i
$349$	2.66312	+	1.93487i	0.142553	+	0.103571i	0.656776	−	0.754085i	$-0.271920\pi$
$349$	2.66312	+	1.93487i	0.142553	+	0.103571i	−0.514223	+	0.857657i	$0.671920\pi$
$350$	−21.5252	+	9.58365i	−1.15057	+	0.512268i
$351$	9.06793	+	1.92745i	0.484010	+	0.102880i
$352$	1.85101	+	17.6112i	0.0986592	+	0.938680i
$353$	23.1640	−	25.7262i	1.23289	−	1.36927i	0.327414	−	0.944881i	$-0.393823\pi$
$353$	23.1640	−	25.7262i	1.23289	−	1.36927i	0.905481	−	0.424387i	$-0.139510\pi$
$354$	0.571506	+	0.634721i	0.0303752	+	0.0337351i
$355$	−0.442790	+	4.21286i	−0.0235008	+	0.223596i
$356$	1.64590	−	5.06555i	0.0872324	−	0.268474i
$357$	3.92705	−	12.0862i	0.207842	−	0.639671i
$358$	−0.811552	+	7.72140i	−0.0428918	+	0.408089i
$359$	−6.47301	−	7.18901i	−0.341632	−	0.379421i	0.547706	−	0.836671i	$-0.315501\pi$
$359$	−6.47301	−	7.18901i	−0.341632	−	0.379421i	−0.889338	+	0.457250i	$0.848835\pi$
$360$	−1.14301	+	1.26944i	−0.0602420	+	0.0669055i
$361$	−0.627171	−	5.96713i	−0.0330090	−	0.314060i
$362$	26.9055	+	5.71894i	1.41412	+	0.300581i
$363$	14.9971	−	6.67715i	0.787145	−	0.350460i
$364$	−2.78115	−	2.02063i	−0.145772	−	0.105910i
$365$	4.03459	+	1.79631i	0.211180	+	0.0940234i
$366$	8.85410	+	15.3358i	0.462811	+	0.801613i
$367$	−1.36475	+	2.36381i	−0.0712391	+	0.123390i	−0.899445	−	0.437035i	$-0.856029\pi$
$367$	−1.36475	+	2.36381i	−0.0712391	+	0.123390i	0.828206	+	0.560425i	$0.189362\pi$
$368$	−13.6353	+	9.90659i	−0.710787	+	0.516417i
$369$	−4.83623	+	1.02797i	−0.251764	+	0.0535141i
$370$	−0.809017	−	2.48990i	−0.0420588	−	0.129444i
$371$	−2.12461			−0.110304
$372$		0			0
$373$	−31.6525			−1.63890			−0.819452	−	0.573148i	$-0.805722\pi$
$373$	−31.6525			−1.63890			−0.819452	+	0.573148i	$0.805722\pi$
$374$	11.0902	+	34.1320i	0.573459	+	1.76493i
$375$	−3.68168	+	0.782565i	−0.190121	+	0.0404115i
$376$	−10.1631	+	7.38394i	−0.524123	+	0.380798i
$377$	−5.91641	+	10.2475i	−0.304711	+	0.527774i
$378$	12.1353	+	21.0189i	0.624170	+	1.08109i
$379$	7.68877	+	3.42326i	0.394946	+	0.175841i	0.594593	−	0.804027i	$-0.297313\pi$
$379$	7.68877	+	3.42326i	0.394946	+	0.175841i	−0.199648	+	0.979868i	$0.563980\pi$
$380$	0.954915	+	0.693786i	0.0489861	+	0.0355905i
$381$	−5.26561	+	2.34440i	−0.269766	+	0.120107i
$382$	7.77067	+	1.65171i	0.397582	+	0.0845087i
$383$	−1.06054	−	10.0903i	−0.0541908	−	0.515591i	−0.987624	−	0.156840i	$-0.949869\pi$
$383$	−1.06054	−	10.0903i	−0.0541908	−	0.515591i	0.933433	−	0.358751i	$-0.116797\pi$
$384$	9.11224	−	10.1202i	0.465007	−	0.516443i
$385$	−4.01478	−	4.45887i	−0.204612	−	0.227245i
$386$	0.781051	−	7.43120i	0.0397544	−	0.378238i
$387$	−1.47214	+	4.53077i	−0.0748329	+	0.230312i
$388$	−3.57295	+	10.9964i	−0.181389	+	0.558258i
$389$	3.03853	−	28.9096i	0.154059	−	1.46578i	−0.595241	−	0.803547i	$-0.702944\pi$
$389$	3.03853	−	28.9096i	0.154059	−	1.46578i	0.749301	−	0.662230i	$-0.230390\pi$
$390$	−0.766755	−	0.851568i	−0.0388262	−	0.0431208i
$391$	−9.84171	+	10.9303i	−0.497717	+	0.552770i
$392$	0.467465	+	4.44764i	0.0236106	+	0.224640i
$393$	10.8478	+	2.30578i	0.547200	+	0.116311i
$394$	15.3970	−	6.85518i	0.775689	−	0.345359i
$395$		0			0
$396$	−5.91259	−	2.63245i	−0.297119	−	0.132286i
$397$	−14.8541	−	25.7281i	−0.745506	−	1.29125i	−0.949958	−	0.312378i	$-0.898875\pi$
$397$	−14.8541	−	25.7281i	−0.745506	−	1.29125i	0.204452	−	0.978877i	$-0.434459\pi$
$398$	−10.7533	+	18.6252i	−0.539014	+	0.933599i
$399$	−12.1353	+	8.81678i	−0.607523	+	0.441391i
$400$	−23.0474	+	4.89888i	−1.15237	+	0.244944i
$401$	−7.36475	−	22.6664i	−0.367778	−	1.13190i	−0.948223	−	0.317605i	$-0.897122\pi$
$401$	−7.36475	−	22.6664i	−0.367778	−	1.13190i	0.580445	−	0.814299i	$-0.302878\pi$
$402$	0.381966			0.0190507
$403$		0			0
$404$	5.70820			0.283994
$405$	−0.118034	−	0.363271i	−0.00586516	−	0.0180511i
$406$	−30.3018	+	6.44084i	−1.50385	+	0.319653i
$407$	−17.9443	+	13.0373i	−0.889465	+	0.646234i
$408$	4.73607	−	8.20311i	0.234470	−	0.406114i
$409$	8.09017	+	14.0126i	0.400033	+	0.692878i	0.993729	−	0.111811i	$-0.0356653\pi$
$409$	8.09017	+	14.0126i	0.400033	+	0.692878i	−0.593696	+	0.804689i	$0.702332\pi$
$410$	1.39577	+	0.621438i	0.0689323	+	0.0306906i
$411$	2.00000	+	1.45309i	0.0986527	+	0.0716754i
$412$	−3.86984	+	1.72296i	−0.190653	+	0.0848843i
$413$	−1.54899	−	0.329247i	−0.0762207	−	0.0162012i
$414$	−1.17449	−	11.1745i	−0.0577230	−	0.549197i
$415$	1.81214	−	2.01259i	0.0889546	−	0.0987940i
$416$	−4.19579	−	4.65990i	−0.205716	−	0.228470i
$417$	−0.0892780	+	0.849423i	−0.00437196	+	0.0415964i
$418$	13.0902	−	40.2874i	0.640261	−	1.97052i
$419$	−1.38197	+	4.25325i	−0.0675135	+	0.207785i	−0.979122	−	0.203275i	$-0.934841\pi$
$419$	−1.38197	+	4.25325i	−0.0675135	+	0.207785i	0.911608	+	0.411060i	$0.134841\pi$
$420$	0.0740275	−	0.704324i	0.00361217	−	0.0343675i
$421$	12.8714	+	14.2952i	0.627316	+	0.696705i	0.970099	−	0.242710i	$-0.0780363\pi$
$421$	12.8714	+	14.2952i	0.627316	+	0.696705i	−0.342783	+	0.939415i	$0.611370\pi$
$422$	−8.66141	+	9.61947i	−0.421631	+	0.468268i
$423$	−1.17449	−	11.1745i	−0.0571056	−	0.543324i
$424$	−1.54899	−	0.329247i	−0.0752255	−	0.0159897i
$425$	−18.7846	+	8.36344i	−0.911187	+	0.405687i
$426$	14.5172	+	10.5474i	0.703362	+	0.511022i
$427$	−29.9943	−	13.3543i	−1.45152	−	0.646260i
$428$	3.11803	+	5.40059i	0.150716	+	0.261048i
$429$	−4.85410	+	8.40755i	−0.234358	+	0.405920i
$430$	1.19098	−	0.865300i	0.0574343	−	0.0417285i
$431$	−24.2228	+	5.14871i	−1.16677	+	0.248005i	−0.750270	−	0.661131i	$-0.770077\pi$
$431$	−24.2228	+	5.14871i	−1.16677	+	0.248005i	−0.416500	+	0.909136i	$0.636743\pi$
$432$	7.50000	+	23.0826i	0.360844	+	1.11056i
$433$	−27.4164			−1.31755			−0.658774	−	0.752341i	$-0.728925\pi$
$433$	−27.4164			−1.31755			−0.658774	+	0.752341i	$0.728925\pi$
$434$		0			0
$435$	−2.43769			−0.116878
$436$	3.51722	+	10.8249i	0.168444	+	0.518418i
$437$	16.9813	−	3.60949i	0.812326	−	0.172665i
$438$	15.1353	−	10.9964i	0.723190	−	0.525429i
$439$	5.91641	−	10.2475i	0.282375	−	0.489087i	−0.689594	−	0.724196i	$-0.742211\pi$
$439$	5.91641	−	10.2475i	0.282375	−	0.489087i	0.971969	+	0.235108i	$0.0755445\pi$
$440$	−2.23607	−	3.87298i	−0.106600	−	0.184637i
$441$	−3.65418	−	1.62695i	−0.174009	−	0.0774736i
$442$	−10.2812	−	7.46969i	−0.489025	−	0.355297i
$443$	−0.799707	+	0.356052i	−0.0379952	+	0.0169166i	−0.425646	−	0.904890i	$-0.639953\pi$
$443$	−0.799707	+	0.356052i	−0.0379952	+	0.0169166i	0.387651	+	0.921806i	$0.373287\pi$
$444$	−2.56082	−	0.544320i	−0.121531	−	0.0258323i
$445$	0.344086	+	3.27376i	0.0163113	+	0.155191i
$446$	13.7589	−	15.2808i	0.651501	−	0.723565i
$447$	8.05261	+	8.94333i	0.380876	+	0.423005i
$448$	−1.32837	+	12.6386i	−0.0627595	+	0.597117i
$449$	10.5279	−	32.4014i	0.496841	−	1.52912i	−0.317228	−	0.948349i	$-0.602752\pi$
$449$	10.5279	−	32.4014i	0.496841	−	1.52912i	0.814069	−	0.580769i	$-0.197248\pi$
$450$	4.85410	−	14.9394i	0.228825	−	0.704250i
$451$	1.35304	−	12.8734i	0.0637124	−	0.606183i
$452$	2.00739	+	2.22943i	0.0944198	+	0.104864i
$453$	−12.3833	+	13.7531i	−0.581819	+	0.646175i
$454$	−3.67735	−	34.9876i	−0.172586	−	1.64205i
$455$	2.07818	+	0.441732i	0.0974268	+	0.0207087i
$456$	−10.2137	+	4.54745i	−0.478303	+	0.212954i
$457$	21.6353	+	15.7189i	1.01205	+	0.735301i	0.964639	−	0.263575i	$-0.0849015\pi$
$457$	21.6353	+	15.7189i	1.01205	+	0.735301i	0.0474155	+	0.998875i	$0.484902\pi$
$458$	4.08550	+	1.81898i	0.190903	+	0.0849954i
$459$	10.5902	+	18.3427i	0.494307	+	0.856164i
$460$	−0.409830	+	0.709846i	−0.0191084	+	0.0330968i
$461$	−25.6803	+	18.6579i	−1.19605	+	0.868983i	−0.993891	−	0.110369i	$-0.964797\pi$
$461$	−25.6803	+	18.6579i	−1.19605	+	0.868983i	−0.202162	+	0.979352i	$0.564797\pi$
$462$	−24.8610	+	5.28437i	−1.15664	+	0.245851i
$463$	−2.81966	−	8.67802i	−0.131041	−	0.403302i	0.863912	−	0.503642i	$-0.168007\pi$
$463$	−2.81966	−	8.67802i	−0.131041	−	0.403302i	−0.994953	+	0.100340i	$0.968007\pi$
$464$	−30.9787			−1.43815
$465$		0			0
$466$	−9.38197			−0.434611
$467$	11.9828	+	36.8792i	0.554497	+	1.70657i	0.697268	+	0.716810i	$0.254399\pi$
$467$	11.9828	+	36.8792i	0.554497	+	1.70657i	−0.142771	+	0.989756i	$0.545601\pi$
$468$	2.24171	−	0.476491i	0.103623	−	0.0220258i
$469$	−0.572949	+	0.416272i	−0.0264563	+	0.0192216i
$470$	−1.73607	+	3.00696i	−0.0800788	+	0.138701i
$471$	1.85410	+	3.21140i	0.0854325	+	0.147973i
$472$	−1.07829	−	0.480087i	−0.0496325	−	0.0220978i
$473$	−10.0902	−	7.33094i	−0.463947	−	0.337077i
$474$		0			0
$475$	23.7401	+	5.04612i	1.08927	+	0.231532i
$476$	−0.820977	−	7.81108i	−0.0376294	−	0.358020i
$477$	0.947762	−	1.05260i	0.0433950	−	0.0481951i
$478$	−14.5256	−	16.1323i	−0.664387	−	0.737876i
$479$	−0.934931	+	8.89527i	−0.0427181	+	0.406435i	0.952179	+	0.305541i	$0.0988372\pi$
$479$	−0.934931	+	8.89527i	−0.0427181	+	0.406435i	−0.994897	+	0.100895i	$0.967829\pi$
$480$	0.399187	−	1.22857i	0.0182203	−	0.0560763i
$481$	2.42705	−	7.46969i	0.110664	−	0.340589i
$482$	−2.95507	+	28.1156i	−0.134600	+	1.28063i
$483$	−6.96994	−	7.74090i	−0.317143	−	0.352223i
$484$	6.78893	−	7.53987i	0.308588	−	0.342721i
$485$	−0.746950	−	7.10675i	−0.0339172	−	0.322701i
$486$	−25.3228	−	5.38253i	−1.14867	−	0.244157i
$487$	38.2986	−	17.0516i	1.73547	−	0.772682i	0.740555	−	0.671996i	$-0.234563\pi$
$487$	38.2986	−	17.0516i	1.73547	−	0.772682i	0.994918	−	0.100687i	$-0.0321039\pi$
$488$	−19.7984	−	14.3844i	−0.896230	−	0.651149i
$489$	0.646976	+	0.288052i	0.0292573	+	0.0130262i
$490$	0.618034	+	1.07047i	0.0279199	+	0.0483587i
$491$	10.7984	−	18.7033i	0.487324	−	0.844070i	−0.512570	−	0.858645i	$-0.671306\pi$
$491$	10.7984	−	18.7033i	0.487324	−	0.844070i	0.999894	+	0.0145759i	$0.00463981\pi$
$492$	1.23607	−	0.898056i	0.0557262	−	0.0404875i
$493$	−26.4437	+	5.62078i	−1.19096	+	0.253147i
$494$	4.63525	+	14.2658i	0.208550	+	0.641851i
$495$	4.00000			0.179787
$496$		0			0
$497$	−33.2705			−1.49239
$498$	−3.54508	−	10.9106i	−0.158859	−	0.488918i
$499$	10.6169	−	2.25669i	0.475278	−	0.101024i	0.0359567	−	0.999353i	$-0.488552\pi$
$499$	10.6169	−	2.25669i	0.475278	−	0.101024i	0.439322	+	0.898330i	$0.355219\pi$
$500$	−1.88197	+	1.36733i	−0.0841641	+	0.0611488i
$501$	−2.38197	+	4.12569i	−0.106418	+	0.184322i
$502$	−13.7082	−	23.7433i	−0.611827	−	1.05972i
$503$	18.1376	+	8.07539i	0.808717	+	0.360064i	0.769082	−	0.639150i	$-0.220714\pi$
$503$	18.1376	+	8.07539i	0.808717	+	0.360064i	0.0396349	+	0.999214i	$0.487381\pi$
$504$	−10.8541	−	7.88597i	−0.483480	−	0.351269i
$505$	−3.22286	+	1.43491i	−0.143416	+	0.0638527i
$506$	28.7736	+	6.11602i	1.27914	+	0.271890i
$507$	0.999533	+	9.50992i	0.0443908	+	0.422350i
$508$	−2.38365	+	2.64731i	−0.105757	+	0.117455i
$509$	8.75903	+	9.72789i	0.388237	+	0.431181i	0.905304	−	0.424764i	$-0.139643\pi$
$509$	8.75903	+	9.72789i	0.388237	+	0.431181i	−0.517067	+	0.855945i	$0.672976\pi$
$510$	0.273659	−	2.60369i	0.0121178	−	0.115293i
$511$	−10.7188	+	32.9892i	−0.474174	+	1.45936i
$512$	−1.63525	+	5.03280i	−0.0722687	+	0.222420i
$513$	2.61321	−	24.8630i	0.115376	−	1.09773i
$514$	−27.5177	−	30.5615i	−1.21376	−	1.34801i
$515$	1.75181	−	1.94558i	0.0771938	−	0.0857324i
$516$	−0.153880	−	1.46407i	−0.00677419	−	0.0644522i
$517$	28.7736	+	6.11602i	1.26546	+	0.268982i
$518$	18.7846	−	8.36344i	0.825348	−	0.367469i
$519$	−9.78115	−	7.10642i	−0.429345	−	0.311937i
$520$	1.44668	+	0.644105i	0.0634413	+	0.0282459i
$521$	13.5344	+	23.4423i	0.592955	+	1.02703i	0.993832	+	0.110896i	$0.0353720\pi$
$521$	13.5344	+	23.4423i	0.592955	+	1.02703i	−0.400877	+	0.916132i	$0.631295\pi$
$522$	10.3262	−	17.8856i	0.451967	−	0.782830i
$523$	−4.95492	+	3.59996i	−0.216663	+	0.157415i	−0.690823	−	0.723024i	$-0.742752\pi$
$523$	−4.95492	+	3.59996i	−0.216663	+	0.157415i	0.474160	+	0.880439i	$0.342752\pi$
$524$	6.70432	−	1.42505i	0.292880	−	0.0622535i
$525$	−4.50000	−	13.8496i	−0.196396	−	0.604445i
$526$	−22.3262			−0.973470
$527$		0			0
$528$	−25.4164			−1.10611
$529$	−3.38197	−	10.4086i	−0.147042	−	0.452549i
$530$	−0.428129	+	0.0910017i	−0.0185968	+	0.00395286i
$531$	0.854102	−	0.620541i	0.0370649	−	0.0269292i
$532$	−4.63525	+	8.02850i	−0.200964	+	0.348079i
$533$	2.29180	+	3.96951i	0.0992687	+	0.171938i
$534$	12.7387	+	5.67165i	0.551259	+	0.245436i
$535$	−3.11803	−	2.26538i	−0.134804	−	0.0979411i
$536$	−0.482228	+	0.214702i	−0.0208291	+	0.00927370i
$537$	−4.69352	−	0.997638i	−0.202540	−	0.0430513i
$538$	−0.611920	−	5.82203i	−0.0263818	−	0.251006i
$539$	7.00723	−	7.78231i	0.301823	−	0.335208i
$540$	0.789802	+	0.877163i	0.0339876	+	0.0377471i
$541$	−2.29963	+	21.8795i	−0.0988687	+	0.940672i	0.826841	+	0.562436i	$0.190136\pi$
$541$	−2.29963	+	21.8795i	−0.0988687	+	0.940672i	−0.925709	+	0.378236i	$0.876531\pi$
$542$	5.28115	−	16.2537i	0.226845	−	0.698157i
$543$	−5.25329	+	16.1680i	−0.225440	+	0.693834i
$544$	1.49750	−	14.2478i	0.0642048	−	0.610868i
$545$	−4.70696	−	5.22761i	−0.201624	−	0.223926i
$546$	6.02218	−	6.68830i	0.257725	−	0.286233i
$547$	1.07579	+	10.2354i	0.0459973	+	0.437635i	0.993150	+	0.116850i	$0.0372798\pi$
$547$	1.07579	+	10.2354i	0.0459973	+	0.437635i	−0.947152	+	0.320784i	$0.896054\pi$
$548$	1.49448	+	0.317661i	0.0638409	+	0.0135698i
$549$	19.9962	−	8.90287i	0.853416	−	0.379965i
$550$	33.2705	+	24.1724i	1.41866	+	1.03072i
$551$	29.1511	+	12.9789i	1.24188	+	0.552920i
$552$	−3.88197	−	6.72376i	−0.165227	−	0.286182i
$553$		0			0
$554$	−3.04508	+	2.21238i	−0.129373	+	0.0939952i
$555$	1.58268	−	0.336408i	0.0671809	−	0.0142797i
$556$	0.163119	+	0.502029i	0.00691778	+	0.0212908i
$557$	−0.111456			−0.00472255			−0.00236127	−	0.999997i	$-0.500752\pi$
$557$	−0.111456			−0.00472255			−0.00236127	+	0.999997i	$0.500752\pi$
$558$		0			0
$559$	4.41641			0.186794
$560$	1.71885	+	5.29007i	0.0726345	+	0.223546i
$561$	−21.6956	+	4.61155i	−0.915991	+	0.194700i
$562$	13.1353	−	9.54332i	0.554077	−	0.402561i
$563$	−5.78115	+	10.0133i	−0.243647	+	0.422008i	−0.961750	−	0.273928i	$-0.911677\pi$
$563$	−5.78115	+	10.0133i	−0.243647	+	0.422008i	0.718104	+	0.695936i	$0.245010\pi$
$564$	1.73607	+	3.00696i	0.0731016	+	0.126616i
$565$	−1.69381	−	0.754131i	−0.0712590	−	0.0317265i
$566$	17.7533	+	12.8985i	0.746226	+	0.542165i
$567$	2.74064	−	1.22021i	0.115096	−	0.0512440i
$568$	−24.2565	−	5.15587i	−1.01778	−	0.216336i
$569$	2.55803	+	24.3381i	0.107238	+	1.02031i	0.907328	+	0.420424i	$0.138119\pi$
$569$	2.55803	+	24.3381i	0.107238	+	1.02031i	−0.800089	+	0.599881i	$0.795215\pi$
$570$	−2.06773	+	2.29644i	−0.0866076	+	0.0961874i
$571$	−4.68391	−	5.20201i	−0.196016	−	0.217698i	0.637122	−	0.770763i	$-0.280125\pi$
$571$	−4.68391	−	5.20201i	−0.196016	−	0.217698i	−0.833138	+	0.553065i	$0.813458\pi$
$572$	−0.627171	+	5.96713i	−0.0262233	+	0.249498i
$573$	−1.51722	+	4.66953i	−0.0633828	+	0.195072i
$574$	−3.70820	+	11.4127i	−0.154777	+	0.476356i
$575$	−1.76173	+	16.7618i	−0.0734694	+	0.699014i
$576$	−5.66897	−	6.29602i	−0.236207	−	0.262334i
$577$	−5.33880	+	5.92934i	−0.222257	+	0.246842i	−0.843953	−	0.536417i	$-0.819777\pi$
$577$	−5.33880	+	5.92934i	−0.222257	+	0.246842i	0.621696	+	0.783259i	$0.286444\pi$
$578$	−0.159705	−	1.51949i	−0.00664286	−	0.0632026i
$579$	4.51712	+	0.960143i	0.187725	+	0.0399022i
$580$	−1.37633	+	0.612780i	−0.0571489	+	0.0254443i
$581$	17.2082	+	12.5025i	0.713917	+	0.518691i
$582$	−27.6535	−	12.3121i	−1.14627	−	0.510354i
$583$	1.85410	+	3.21140i	0.0767891	+	0.133003i
$584$	−12.9271	+	22.3903i	−0.534925	+	0.926518i
$585$	−1.14590	+	0.832544i	−0.0473771	+	0.0344214i
$586$	5.95709	−	1.26622i	0.246085	−	0.0523070i
$587$	12.3647	+	38.0548i	0.510348	+	1.57069i	0.791591	+	0.611052i	$0.209253\pi$
$587$	12.3647	+	38.0548i	0.510348	+	1.57069i	−0.281243	+	0.959637i	$0.590747\pi$
$588$	1.23607			0.0509746
$589$		0			0
$590$	−0.326238			−0.0134310
$591$	3.21885	+	9.90659i	0.132406	+	0.407503i
$592$	20.1130	−	4.27514i	0.826638	−	0.175707i
$593$	−33.8885	+	24.6215i	−1.39164	+	1.01108i	−0.395952	+	0.918271i	$0.629585\pi$
$593$	−33.8885	+	24.6215i	−1.39164	+	1.01108i	−0.995684	+	0.0928113i	$0.970415\pi$
$594$	21.1803	−	36.6854i	0.869040	−	1.50522i
$595$	2.42705	+	4.20378i	0.0994994	+	0.172338i
$596$	6.79467	+	3.02518i	0.278321	+	0.123916i
$597$	−10.7533	−	7.81272i	−0.440103	−	0.319753i
$598$	−9.51586	+	4.23673i	−0.389133	+	0.173253i
$599$	−5.08796	−	1.08148i	−0.207888	−	0.0441880i	0.102790	−	0.994703i	$-0.467223\pi$
$599$	−5.08796	−	1.08148i	−0.207888	−	0.0441880i	−0.310679	+	0.950515i	$0.600556\pi$
$600$	−1.13456	−	10.7946i	−0.0463183	−	0.440689i
$601$	−14.7209	+	16.3492i	−0.600477	+	0.666897i	−0.964374	−	0.264542i	$-0.914779\pi$
$601$	−14.7209	+	16.3492i	−0.600477	+	0.666897i	0.363897	+	0.931439i	$0.381446\pi$
$602$	7.73669	+	8.59247i	0.315324	+	0.350203i
$603$	0.0493516	−	0.469550i	0.00200975	−	0.0191215i
$604$	−3.53444	+	10.8779i	−0.143814	+	0.442615i
$605$	−1.93769	+	5.96361i	−0.0787785	+	0.242455i
$606$	−1.56210	+	14.8624i	−0.0634560	+	0.603744i
$607$	0.947762	+	1.05260i	0.0384685	+	0.0427236i	0.762072	−	0.647492i	$-0.224182\pi$
$607$	0.947762	+	1.05260i	0.0384685	+	0.0427236i	−0.723604	+	0.690216i	$0.757516\pi$
$608$	−11.3149	+	12.5665i	−0.458879	+	0.509637i
$609$	−2.00129	−	19.0410i	−0.0810964	−	0.771581i
$610$	−6.61612	−	1.40630i	−0.267879	−	0.0569394i
$611$	−9.51586	+	4.23673i	−0.384971	+	0.171400i
$612$	4.23607	+	3.07768i	0.171233	+	0.124408i
$613$	−39.2315	−	17.4670i	−1.58455	−	0.705486i	−0.589771	−	0.807570i	$-0.700782\pi$
$613$	−39.2315	−	17.4670i	−1.58455	−	0.705486i	−0.994776	+	0.102084i	$0.967449\pi$
$614$	4.11803	+	7.13264i	0.166190	+	0.287850i
$615$	−0.472136	+	0.817763i	−0.0190384	+	0.0329754i
$616$	28.4164	−	20.6457i	1.14493	−	0.831840i
$617$	9.55057	−	2.03004i	0.384491	−	0.0817262i	−0.0116108	−	0.999933i	$-0.503696\pi$
$617$	9.55057	−	2.03004i	0.384491	−	0.0817262i	0.396102	+	0.918206i	$0.370363\pi$
$618$	−3.42705	−	10.5474i	−0.137856	−	0.424278i
$619$	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
$621$	17.3607			0.696660
$622$	3.76393	+	11.5842i	0.150920	+	0.464484i
$623$	−25.2891	+	5.37537i	−1.01319	+	0.215360i
$624$	7.28115	−	5.29007i	0.291479	−	0.211772i
$625$	−11.4164	+	19.7738i	−0.456656	+	0.790952i
$626$	−2.61803	−	4.53457i	−0.104638	−	0.181238i
$627$	23.9169	+	10.6485i	0.955150	+	0.425260i
$628$	1.85410	+	1.34708i	0.0739867	+	0.0537545i
$629$	16.3929	−	7.29859i	0.653628	−	0.291014i
$630$	−3.62717	−	0.770979i	−0.144510	−	0.0307165i
$631$	−4.41847	−	42.0389i	−0.175897	−	1.67354i	−0.625430	−	0.780280i	$-0.715076\pi$
$631$	−4.41847	−	42.0389i	−0.175897	−	1.67354i	0.449533	−	0.893264i	$-0.351590\pi$
$632$		0			0
$633$	−5.35304	−	5.94516i	−0.212764	−	0.236299i
$634$	1.67246	−	15.9124i	0.0664217	−	0.631960i
$635$	0.680340	−	2.09387i	0.0269985	−	0.0830927i
$636$	−0.135255	+	0.416272i	−0.00536321	+	0.0165063i
$637$	−0.387613	+	3.68789i	−0.0153578	+	0.146120i
$638$	36.1791	+	40.1810i	1.43235	+	1.59078i
$639$	14.8415	−	16.4832i	0.587122	−	0.652066i
$640$	0.543718	+	5.17313i	0.0214923	+	0.204486i
$641$	−29.2562	−	6.21860i	−1.15555	−	0.245620i	−0.410011	−	0.912081i	$-0.634475\pi$
$641$	−29.2562	−	6.21860i	−1.15555	−	0.245620i	−0.745540	+	0.666460i	$0.767809\pi$
$642$	−14.9148	+	6.64048i	−0.588639	+	0.262079i
$643$	12.0172	+	8.73102i	0.473913	+	0.344318i	0.798964	−	0.601378i	$-0.205382\pi$
$643$	12.0172	+	8.73102i	0.473913	+	0.344318i	−0.325051	+	0.945696i	$0.605382\pi$
$644$	−5.88113	−	2.61845i	−0.231749	−	0.103181i
$645$	0.454915	+	0.787936i	0.0179123	+	0.0310249i
$646$	−17.1353	+	29.6791i	−0.674178	+	1.16771i
$647$	4.76393	−	3.46120i	0.187289	−	0.136074i	−0.490190	−	0.871616i	$-0.663072\pi$
$647$	4.76393	−	3.46120i	0.187289	−	0.136074i	0.677479	+	0.735542i	$0.263072\pi$
$648$	2.18720	−	0.464905i	0.0859215	−	0.0182632i
$649$	0.854102	+	2.62866i	0.0335264	+	0.103184i
$650$	−14.5623			−0.571181
$651$		0			0
$652$	0.437694			0.0171414
$653$	2.57953	+	7.93897i	0.100945	+	0.310676i	0.988757	−	0.149529i	$-0.0477759\pi$
$653$	2.57953	+	7.93897i	0.100945	+	0.310676i	−0.887813	+	0.460205i	$0.847776\pi$
$654$	−29.1472	+	6.19543i	−1.13975	+	0.242260i
$655$	−3.42705	+	2.48990i	−0.133906	+	0.0972884i
$656$	−6.00000	+	10.3923i	−0.234261	+	0.405751i
$657$	−11.5623	−	20.0265i	−0.451089	−	0.781308i
$658$	−24.9129	−	11.0919i	−0.971204	−	0.432408i
$659$	30.4894	+	22.1518i	1.18770	+	0.862912i	0.993019	−	0.117955i	$-0.0376339\pi$
$659$	30.4894	+	22.1518i	1.18770	+	0.862912i	0.194678	+	0.980867i	$0.437634\pi$
$660$	−1.12920	+	0.502754i	−0.0439542	+	0.0195697i
$661$	14.0677	+	2.99018i	0.547170	+	0.116304i	0.473198	−	0.880956i	$-0.343099\pi$
$661$	14.0677	+	2.99018i	0.547170	+	0.116304i	0.0739712	+	0.997260i	$0.476433\pi$
$662$	−3.76662	−	35.8370i	−0.146394	−	1.39285i
$663$	5.25542	−	5.83674i	0.204104	−	0.226680i
$664$	10.6085	+	11.7819i	0.411688	+	0.457226i
$665$	0.598895	−	5.69810i	0.0232241	−	0.220963i
$666$	−4.23607	+	13.0373i	−0.164144	+	0.505184i
$667$	−6.84752	+	21.0745i	−0.265137	+	0.816008i
$668$	−0.307760	+	2.92814i	−0.0119076	+	0.113293i
$669$	8.50345	+	9.44404i	0.328762	+	0.365128i
$670$	−0.0976248	+	0.108423i	−0.00377158	+	0.00418876i
$671$	5.99000	+	56.9910i	0.231241	+	2.20011i
$672$	9.92419	+	2.10945i	0.382834	+	0.0813738i
$673$	−20.4784	+	9.11757i	−0.789385	+	0.351457i	−0.761509	−	0.648155i	$-0.775541\pi$
$673$	−20.4784	+	9.11757i	−0.789385	+	0.351457i	−0.0278759	+	0.999611i	$0.508874\pi$
$674$	−36.6246	−	26.6093i	−1.41073	−	1.02495i
$675$	22.1722	+	9.87171i	0.853409	+	0.379962i
$676$	2.95492	+	5.11806i	0.113651	+	0.196849i
$677$	−1.32624	+	2.29711i	−0.0509715	+	0.0882852i	−0.890385	−	0.455207i	$-0.849565\pi$
$677$	−1.32624	+	2.29711i	−0.0509715	+	0.0882852i	0.839414	+	0.543493i	$0.182898\pi$
$678$	−6.35410	+	4.61653i	−0.244028	+	0.177297i
$679$	54.8982	−	11.6690i	2.10680	−	0.447814i
$680$	1.11803	+	3.44095i	0.0428746	+	0.131955i
$681$	21.7426			0.833180
$682$		0			0
$683$	27.9443			1.06926			0.534629	−	0.845087i	$-0.320451\pi$
$683$	27.9443			1.06926			0.534629	+	0.845087i	$0.320451\pi$
$684$	−1.90983	−	5.87785i	−0.0730242	−	0.224745i
$685$	−0.923637	+	0.196325i	−0.0352904	+	0.00750120i
$686$	19.6353	−	14.2658i	0.749678	−	0.544673i
$687$	−1.38197	+	2.39364i	−0.0527253	+	0.0913229i
$688$	5.78115	+	10.0133i	0.220404	+	0.381752i
$689$	−1.19956	−	0.534079i	−0.0456996	−	0.0203468i
$690$	−1.73607	−	1.26133i	−0.0660910	−	0.0480179i
$691$	−45.5245	+	20.2688i	−1.73184	+	0.771063i	−0.736302	+	0.676653i	$0.763430\pi$
$691$	−45.5245	+	20.2688i	−1.73184	+	0.771063i	−0.995533	+	0.0944094i	$0.969904\pi$
$692$	−7.30885	−	1.55354i	−0.277841	−	0.0590569i
$693$	3.28391	+	31.2443i	0.124745	+	1.18687i
$694$	34.7805	−	38.6277i	1.32025	−	1.46629i
$695$	−0.218296	−	0.242442i	−0.00828043	−	0.00919635i
$696$	1.49167	−	14.1923i	0.0565418	−	0.537959i
$697$	−3.23607	+	9.95959i	−0.122575	+	0.377246i
$698$	−1.64590	+	5.06555i	−0.0622982	+	0.191734i
$699$	0.606095	−	5.76661i	0.0229246	−	0.218113i
$700$	−6.02218	−	6.68830i	−0.227617	−	0.252794i
$701$	−0.646085	+	0.717550i	−0.0244023	+	0.0271015i	−0.755222	−	0.655469i	$-0.772471\pi$
$701$	−0.646085	+	0.717550i	−0.0244023	+	0.0271015i	0.730820	+	0.682570i	$0.239138\pi$
$702$	1.56793	+	14.9178i	0.0591776	+	0.563037i
$703$	−20.7175	−	4.40364i	−0.781375	−	0.166086i
$704$	20.2627	−	9.02156i	0.763681	−	0.340013i
$705$	−1.73607	−	1.26133i	−0.0653841	−	0.0475043i
$706$	51.1706	+	22.7826i	1.92583	+	0.857435i
$707$	−13.8541	−	23.9960i	−0.521037	−	0.902463i
$708$	−0.163119	+	0.282530i	−0.00613039	+	0.0106181i
$709$	8.78115	−	6.37988i	0.329783	−	0.239601i	−0.410555	−	0.911836i	$-0.634665\pi$
$709$	8.78115	−	6.37988i	0.329783	−	0.239601i	0.740339	+	0.672234i	$0.234665\pi$
$710$	−6.70432	+	1.42505i	−0.251609	+	0.0534811i
$711$		0			0
$712$	−19.2705			−0.722193
$713$		0			0
$714$	20.5623			0.769525
$715$	−1.14590	−	3.52671i	−0.0428542	−	0.131892i
$716$	−2.90075	+	0.616574i	−0.108406	+	0.0230425i
$717$	10.8541	−	7.88597i	0.405354	−	0.294507i
$718$	7.82624	−	13.5554i	0.292073	−	0.505885i
$719$	−21.8090	−	37.7743i	−0.813339	−	1.40874i	−0.910514	−	0.413477i	$-0.864314\pi$
$719$	−21.8090	−	37.7743i	−0.813339	−	1.40874i	0.0971753	−	0.995267i	$-0.469019\pi$
$720$	−3.38761	−	1.50826i	−0.126249	−	0.0562096i
$721$	16.6353	+	12.0862i	0.619529	+	0.450114i
$722$	8.86889	−	3.94868i	0.330066	−	0.146955i
$723$	−17.0903	−	3.63266i	−0.635596	−	0.135100i
$724$	1.09824	+	10.4490i	0.0408156	+	0.388335i
$725$	−20.7288	+	23.0217i	−0.769849	+	0.855003i
$726$	17.7737	+	19.7396i	0.659642	+	0.732607i
$727$	−3.11838	+	29.6694i	−0.115654	+	1.10038i	0.770645	+	0.637264i	$0.219934\pi$
$727$	−3.11838	+	29.6694i	−0.115654	+	1.10038i	−0.886300	+	0.463112i	$0.846733\pi$
$728$	−3.84346	+	11.8290i	−0.142448	+	0.438410i
$729$	4.01722	−	12.3637i	0.148786	−	0.457916i
$730$	−0.746950	+	7.10675i	−0.0276459	+	0.263033i
$731$	6.75164	+	7.49846i	0.249718	+	0.277340i
$732$	−4.52595	+	5.02658i	−0.167284	+	0.185788i
$733$	−1.05111	−	10.0006i	−0.0388236	−	0.369382i	−0.996634	−	0.0819809i	$-0.973875\pi$
$733$	−1.05111	−	10.0006i	−0.0388236	−	0.369382i	0.957810	−	0.287401i	$-0.0927913\pi$
$734$	−4.31990	−	0.918223i	−0.159450	−	0.0338922i
$735$	−0.697887	+	0.310719i	−0.0257419	+	0.0114610i
$736$	−9.50000	−	6.90215i	−0.350175	−	0.254417i
$737$	1.12920	+	0.502754i	0.0415948	+	0.0185192i
$738$	−4.00000	−	6.92820i	−0.147242	−	0.255031i
$739$	4.14590	−	7.18091i	0.152509	−	0.264154i	−0.779640	−	0.626228i	$-0.784598\pi$
$739$	4.14590	−	7.18091i	0.152509	−	0.264154i	0.932149	+	0.362074i	$0.117931\pi$
$740$	0.809017	−	0.587785i	0.0297401	−	0.0216074i
$741$	−9.06793	+	1.92745i	−0.333119	+	0.0708065i
$742$	−1.06231	−	3.26944i	−0.0389985	−	0.120025i
$743$	23.5623			0.864417			0.432209	−	0.901774i	$-0.357734\pi$
$743$	23.5623			0.864417			0.432209	+	0.901774i	$0.357734\pi$
$744$		0			0
$745$	−4.59675			−0.168412
$746$	−15.8262	−	48.7082i	−0.579440	−	1.78333i
$747$	−13.8705	+	2.94826i	−0.507494	+	0.107871i
$748$	−11.0902	+	8.05748i	−0.405497	+	0.294611i
$749$	15.1353	−	26.2150i	0.553030	−	0.957876i
$750$	−3.04508	−	5.27424i	−0.111191	−	0.192588i
$751$	12.6369	+	5.62631i	0.461127	+	0.205307i	0.624133	−	0.781318i	$-0.285452\pi$
$751$	12.6369	+	5.62631i	0.461127	+	0.205307i	−0.163006	+	0.986625i	$0.552119\pi$
$752$	−22.0623	−	16.0292i	−0.804530	−	0.584525i
$753$	15.4794	−	6.89186i	0.564099	−	0.251153i
$754$	−18.7275	−	3.98066i	−0.682016	−	0.144967i
$755$	−0.738900	−	7.03016i	−0.0268913	−	0.255854i
$756$	−6.20318	+	6.88933i	−0.225608	+	0.250563i
$757$	−1.92401	−	2.13683i	−0.0699293	−	0.0776644i	0.707165	−	0.707049i	$-0.249974\pi$
$757$	−1.92401	−	2.13683i	−0.0699293	−	0.0776644i	−0.777094	+	0.629384i	$0.783307\pi$
$758$	−1.42347	+	13.5434i	−0.0517028	+	0.491920i
$759$	−5.61803	+	17.2905i	−0.203922	+	0.627607i
$760$	1.31966	−	4.06150i	0.0478691	−	0.147326i
$761$	−3.60692	+	34.3175i	−0.130751	+	1.24401i	0.710629	+	0.703566i	$0.248410\pi$
$761$	−3.60692	+	34.3175i	−0.130751	+	1.24401i	−0.841380	+	0.540444i	$0.818256\pi$
$762$	−6.24047	−	6.93075i	−0.226068	−	0.251074i
$763$	36.9689	−	41.0582i	1.33837	−	1.48641i
$764$	0.317186	+	3.01782i	0.0114754	+	0.109181i
$765$	−3.16535	−	0.672816i	−0.114444	−	0.0243257i
$766$	14.9971	−	6.67715i	0.541869	−	0.241255i
$767$	−0.791796	−	0.575274i	−0.0285901	−	0.0207719i
$768$	12.3898

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 + 1.53884i) q^{2} +(-0.978148 + 0.207912i) q^{3} +(-0.500000 + 0.363271i) q^{4} +(0.190983 - 0.330792i) q^{5} +(-0.809017 - 1.40126i) q^{6} +(2.74064 + 1.22021i) q^{7} +(1.80902 + 1.31433i) q^{8} +(-1.82709 + 0.813473i) q^{9} +(0.604528 + 0.128496i) q^{10} +(-0.547318 - 5.20738i) q^{11} +(0.413545 - 0.459289i) q^{12} +(1.24064 + 1.37787i) q^{13} +(-0.507392 + 4.82751i) q^{14} +(-0.118034 + 0.363271i) q^{15} +(-1.50000 + 4.61653i) q^{16} +(-0.442790 + 4.21286i) q^{17} +(-2.16535 - 2.40487i) q^{18} +(3.34565 - 3.71572i) q^{19} +(0.0246758 + 0.234775i) q^{20} +(-2.93444 - 0.623735i) q^{21} +(7.73968 - 3.44593i) q^{22} +(2.80902 + 2.04087i) q^{23} +(-2.04275 - 0.909491i) q^{24} +(2.42705 + 4.20378i) q^{25} +(-1.50000 + 2.59808i) q^{26} +(4.04508 - 2.93893i) q^{27} +(-1.81359 + 0.385489i) q^{28} +(1.97214 + 6.06961i) q^{29} -0.618034 q^{30} -3.38197 q^{32} +(1.61803 + 4.97980i) q^{33} +(-6.70432 + 1.42505i) q^{34} +(0.927051 - 0.673542i) q^{35} +(0.618034 - 1.07047i) q^{36} +(-2.11803 - 3.66854i) q^{37} +(7.39074 + 3.29057i) q^{38} +(-1.50000 - 1.08981i) q^{39} +(0.780261 - 0.347395i) q^{40} +(2.41811 + 0.513986i) q^{41} +(-0.507392 - 4.82751i) q^{42} +(1.59385 - 1.77015i) q^{43} +(2.16535 + 2.40487i) q^{44} +(-0.0798526 + 0.759747i) q^{45} +(-1.73607 + 5.34307i) q^{46} +(-1.73607 + 5.34307i) q^{47} +(0.507392 - 4.82751i) q^{48} +(1.33826 + 1.48629i) q^{49} +(-5.25542 + 5.83674i) q^{50} +(-0.442790 - 4.21286i) q^{51} +(-1.12086 - 0.238246i) q^{52} +(-0.646976 + 0.288052i) q^{53} +(6.54508 + 4.75528i) q^{54} +(-1.82709 - 0.813473i) q^{55} +(3.35410 + 5.80948i) q^{56} +(-2.50000 + 4.33013i) q^{57} +(-8.35410 + 6.06961i) q^{58} +(-0.516329 + 0.109749i) q^{59} +(-0.0729490 - 0.224514i) q^{60} -10.9443 q^{61} -6.00000 q^{63} +(1.30902 + 4.02874i) q^{64} +(0.692728 - 0.147244i) q^{65} +(-6.85410 + 4.97980i) q^{66} +(-0.118034 + 0.204441i) q^{67} +(-1.30902 - 2.26728i) q^{68} +(-3.17195 - 1.41224i) q^{69} +(1.50000 + 1.08981i) q^{70} +(-10.1314 + 4.51078i) q^{71} +(-4.37441 - 0.929809i) q^{72} +(1.20859 + 11.4990i) q^{73} +(4.58629 - 5.09359i) q^{74} +(-3.24803 - 3.60730i) q^{75} +(-0.323011 + 3.07324i) q^{76} +(4.85410 - 14.9394i) q^{77} +(0.927051 - 2.85317i) q^{78} +(1.24064 + 1.37787i) q^{80} +(0.669131 - 0.743145i) q^{81} +(0.418114 + 3.97809i) q^{82} +(6.93523 + 1.47413i) q^{83} +(1.69381 - 0.754131i) q^{84} +(1.30902 + 0.951057i) q^{85} +(3.52090 + 1.56760i) q^{86} +(-3.19098 - 5.52694i) q^{87} +(5.85410 - 10.1396i) q^{88} +(-6.97214 + 5.06555i) q^{89} +(-1.20906 + 0.256993i) q^{90} +(1.71885 + 5.29007i) q^{91} -2.14590 q^{92} -9.09017 q^{94} +(-0.590170 - 1.81636i) q^{95} +(3.30806 - 0.703150i) q^{96} +(15.1353 - 10.9964i) q^{97} +(-1.61803 + 2.80252i) q^{98} +(5.23607 + 9.06914i) 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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