LMFDB - Embedded newform 961.2.g.a.448.1

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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			448.1
Root			$-0.104528 + 0.994522i$ of defining polynomial
Character	$\chi$	$=$	961.448
Dual form			961.2.g.a.547.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.190983 + 0.587785i) q^{2} +(0.827091 - 0.918578i) q^{3} +(1.30902 + 0.951057i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.381966 + 0.661585i) q^{6} +(0.442790 - 4.21286i) q^{7} +(-1.80902 + 1.31433i) q^{8} +(0.153880 + 1.46407i) q^{9} +(-0.413545 - 0.459289i) q^{10} +(1.82709 - 0.813473i) q^{11} +(1.95630 - 0.415823i) q^{12} +(-1.20906 - 0.256993i) q^{13} +(2.39169 + 1.06485i) q^{14} +(0.381966 + 1.17557i) q^{15} +(0.572949 + 1.76336i) q^{16} +(4.78339 + 2.12970i) q^{17} +(-0.889948 - 0.189164i) q^{18} +(-2.18720 + 0.464905i) q^{19} +(-1.47815 + 0.658114i) q^{20} +(-3.50361 - 3.89116i) q^{21} +(0.129204 + 1.22930i) q^{22} +(6.23607 - 4.53077i) q^{23} +(-0.288910 + 2.74879i) q^{24} +(2.00000 + 3.46410i) q^{25} +(0.381966 - 0.661585i) q^{26} +(4.47214 + 3.24920i) q^{27} +(4.58629 - 5.09359i) q^{28} +(2.23607 - 6.88191i) q^{29} -0.763932 q^{30} -5.61803 q^{32} +(0.763932 - 2.35114i) q^{33} +(-2.16535 + 2.40487i) q^{34} +(3.42705 + 2.48990i) q^{35} +(-1.19098 + 2.06284i) q^{36} +(1.00000 + 1.73205i) q^{37} +(0.144455 - 1.37440i) q^{38} +(-1.23607 + 0.898056i) q^{39} +(-0.233733 - 2.22382i) q^{40} +(4.68391 + 5.20201i) q^{41} +(2.95630 - 1.31623i) q^{42} +(3.16535 - 0.672816i) q^{43} +(3.16535 + 0.672816i) q^{44} +(-1.34486 - 0.598772i) q^{45} +(1.47214 + 4.53077i) q^{46} +(-2.00000 - 6.15537i) q^{47} +(2.09366 + 0.932157i) q^{48} +(-10.7051 - 2.27544i) q^{49} +(-2.41811 + 0.513986i) q^{50} +(5.91259 - 2.63245i) q^{51} +(-1.33826 - 1.48629i) q^{52} +(0.159705 + 1.51949i) q^{53} +(-2.76393 + 2.00811i) q^{54} +(-0.209057 + 1.98904i) q^{55} +(4.73607 + 8.20311i) q^{56} +(-1.38197 + 2.39364i) q^{57} +(3.61803 + 2.62866i) q^{58} +(-1.49622 + 1.66172i) q^{59} +(-0.618034 + 1.90211i) q^{60} -14.1803 q^{61} +6.23607 q^{63} +(-0.0729490 + 0.224514i) q^{64} +(0.827091 - 0.918578i) q^{65} +(1.23607 + 0.898056i) q^{66} +(-4.00000 + 6.92820i) q^{67} +(4.23607 + 7.33708i) q^{68} +(0.995933 - 9.47567i) q^{69} +(-2.11803 + 1.53884i) q^{70} +(-1.37772 - 13.1081i) q^{71} +(-2.20264 - 2.44628i) q^{72} +(-0.431318 + 0.192035i) q^{73} +(-1.20906 + 0.256993i) q^{74} +(4.83623 + 1.02797i) q^{75} +(-3.30524 - 1.47159i) q^{76} +(-2.61803 - 8.05748i) q^{77} +(-0.291796 - 0.898056i) q^{78} +(1.56052 + 0.694789i) q^{79} +(-1.81359 - 0.385489i) q^{80} +(2.36360 - 0.502399i) q^{81} +(-3.95222 + 1.75964i) q^{82} +(1.97010 + 2.18802i) q^{83} +(-0.885579 - 8.42572i) q^{84} +(-4.23607 + 3.07768i) q^{85} +(-0.209057 + 1.98904i) q^{86} +(-4.47214 - 7.74597i) q^{87} +(-2.23607 + 3.87298i) q^{88} +(1.38197 + 1.00406i) q^{89} +(0.608795 - 0.676135i) q^{90} +(-1.61803 + 4.97980i) q^{91} +12.4721 q^{92} +4.00000 q^{94} +(0.690983 - 2.12663i) q^{95} +(-4.64662 + 5.16060i) q^{96} +(-1.57295 - 1.14281i) q^{97} +(3.38197 - 5.85774i) q^{98} +(1.47214 + 2.54981i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{2} - 6 q^{3} + 6 q^{4} - 4 q^{5} + 12 q^{6} - 7 q^{7} - 10 q^{8} - 7 q^{9} + 3 q^{10} + 2 q^{11} - 2 q^{12} - 6 q^{13} + 4 q^{14} + 12 q^{15} + 18 q^{16} + 8 q^{17} + 19 q^{18} - 5 q^{19} - 3 q^{20}+ \cdots - 24 q^{99}+O(q^{100}) $ 8 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 - 4 * q^5 + 12 * q^6 - 7 * q^7 - 10 * q^8 - 7 * q^9 + 3 * q^10 + 2 * q^11 - 2 * q^12 - 6 * q^13 + 4 * q^14 + 12 * q^15 + 18 * q^16 + 8 * q^17 + 19 * q^18 - 5 * q^19 - 3 * q^20 + 2 * q^21 - 4 * q^22 + 32 * q^23 + 16 * q^25 + 12 * q^26 - 4 * q^28 - 24 * q^30 - 36 * q^32 + 24 * q^33 + 4 * q^34 + 14 * q^35 - 14 * q^36 + 8 * q^37 + 8 * q^39 + 5 * q^40 + 7 * q^41 + 6 * q^42 + 4 * q^43 + 4 * q^44 - 7 * q^45 - 24 * q^46 - 16 * q^47 - 6 * q^48 - 18 * q^49 - 12 * q^50 + 12 * q^51 - 2 * q^52 + 4 * q^53 - 40 * q^54 + 2 * q^55 + 20 * q^56 - 20 * q^57 + 20 * q^58 + 5 * q^59 + 4 * q^60 - 24 * q^61 + 32 * q^63 - 14 * q^64 - 6 * q^65 - 8 * q^66 - 32 * q^67 + 16 * q^68 - 4 * q^69 - 8 * q^70 + 27 * q^71 - 25 * q^72 - 6 * q^73 - 6 * q^74 + 24 * q^75 - 5 * q^76 - 12 * q^77 - 56 * q^78 + 10 * q^79 - 9 * q^80 + 41 * q^81 - 14 * q^82 - 26 * q^83 + 14 * q^84 - 16 * q^85 + 2 * q^86 + 20 * q^89 + 19 * q^90 - 4 * q^91 + 64 * q^92 + 32 * q^94 + 10 * q^95 + 22 * q^96 - 26 * q^97 + 36 * q^98 - 24 * q^99

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{11}{15}\right)$

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 $

$2$	−0.190983	+	0.587785i	−0.135045	+	0.415627i	−0.995597	−	0.0937362i	$-0.970119\pi$
$2$	−0.190983	+	0.587785i	−0.135045	+	0.415627i	0.860552	+	0.509363i	$0.170119\pi$
$3$	0.827091	−	0.918578i	0.477521	−	0.530341i	−0.455465	−	0.890254i	$-0.650527\pi$
$3$	0.827091	−	0.918578i	0.477521	−	0.530341i	0.932986	+	0.359913i	$0.117194\pi$
$4$	1.30902	+	0.951057i	0.654508	+	0.475528i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	−0.955901	−	0.293691i	$-0.905116\pi$
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	0.732294	+	0.680989i	$0.238450\pi$
$6$	0.381966	+	0.661585i	0.155937	+	0.270091i
$7$	0.442790	−	4.21286i	0.167359	−	1.59231i	−0.512315	−	0.858798i	$-0.671212\pi$
$7$	0.442790	−	4.21286i	0.167359	−	1.59231i	0.679674	−	0.733515i	$-0.262121\pi$
$8$	−1.80902	+	1.31433i	−0.639584	+	0.464685i
$9$	0.153880	+	1.46407i	0.0512934	+	0.488024i
$10$	−0.413545	−	0.459289i	−0.130775	−	0.145240i
$11$	1.82709	−	0.813473i	0.550889	−	0.245271i	−0.112364	−	0.993667i	$-0.535842\pi$
$11$	1.82709	−	0.813473i	0.550889	−	0.245271i	0.663252	+	0.748396i	$0.269176\pi$
$12$	1.95630	−	0.415823i	0.564734	−	0.120038i
$13$	−1.20906	−	0.256993i	−0.335332	−	0.0712770i	0.0371685	−	0.999309i	$-0.488166\pi$
$13$	−1.20906	−	0.256993i	−0.335332	−	0.0712770i	−0.372501	+	0.928032i	$0.621500\pi$
$14$	2.39169	+	1.06485i	0.639207	+	0.284593i
$15$	0.381966	+	1.17557i	0.0986232	+	0.303531i
$16$	0.572949	+	1.76336i	0.143237	+	0.440839i
$17$	4.78339	+	2.12970i	1.16014	+	0.516528i	0.894291	−	0.447486i	$-0.147681\pi$
$17$	4.78339	+	2.12970i	1.16014	+	0.516528i	0.265851	+	0.964014i	$0.414347\pi$
$18$	−0.889948	−	0.189164i	−0.209763	−	0.0445865i
$19$	−2.18720	+	0.464905i	−0.501779	+	0.106656i	−0.451846	−	0.892096i	$-0.649234\pi$
$19$	−2.18720	+	0.464905i	−0.501779	+	0.106656i	−0.0499334	+	0.998753i	$0.515901\pi$
$20$	−1.47815	+	0.658114i	−0.330524	+	0.147159i
$21$	−3.50361	−	3.89116i	−0.764551	−	0.849120i
$22$	0.129204	+	1.22930i	0.0275464	+	0.262087i
$23$	6.23607	−	4.53077i	1.30031	−	0.944731i	0.300351	−	0.953829i	$-0.402896\pi$
$23$	6.23607	−	4.53077i	1.30031	−	0.944731i	0.999959	+	0.00909805i	$0.00289604\pi$
$24$	−0.288910	+	2.74879i	−0.0589734	+	0.561095i
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$	0.381966	−	0.661585i	0.0749097	−	0.129747i
$27$	4.47214	+	3.24920i	0.860663	+	0.625308i
$28$	4.58629	−	5.09359i	0.866727	−	0.962598i
$29$	2.23607	−	6.88191i	0.415227	−	1.27794i	−0.496820	−	0.867854i	$-0.665499\pi$
$29$	2.23607	−	6.88191i	0.415227	−	1.27794i	0.912047	−	0.410085i	$-0.134501\pi$
$30$	−0.763932			−0.139474
$31$		0			0
$31$		0			0
$32$	−5.61803			−0.993137
$33$	0.763932	−	2.35114i	0.132983	−	0.409281i
$34$	−2.16535	+	2.40487i	−0.371355	+	0.412431i
$35$	3.42705	+	2.48990i	0.579277	+	0.420870i
$36$	−1.19098	+	2.06284i	−0.198497	+	0.343807i
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	0.936442	−	0.350823i	$-0.114098\pi$
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	−0.772043	+	0.635571i	$0.780765\pi$
$38$	0.144455	−	1.37440i	0.0234337	−	0.222956i
$39$	−1.23607	+	0.898056i	−0.197929	+	0.143804i
$40$	−0.233733	−	2.22382i	−0.0369564	−	0.351617i
$41$	4.68391	+	5.20201i	0.731505	+	0.812418i	0.988053	−	0.154113i	$-0.0492521\pi$
$41$	4.68391	+	5.20201i	0.731505	+	0.812418i	−0.256549	+	0.966531i	$0.582585\pi$
$42$	2.95630	−	1.31623i	0.456166	−	0.203098i
$43$	3.16535	−	0.672816i	0.482712	−	0.102604i	0.0398728	−	0.999205i	$-0.487305\pi$
$43$	3.16535	−	0.672816i	0.482712	−	0.102604i	0.442839	+	0.896601i	$0.353971\pi$
$44$	3.16535	+	0.672816i	0.477195	+	0.101431i
$45$	−1.34486	−	0.598772i	−0.200480	−	0.0892596i
$46$	1.47214	+	4.53077i	0.217055	+	0.668025i
$47$	−2.00000	−	6.15537i	−0.291730	−	0.897853i	−0.984300	−	0.176502i	$-0.943522\pi$
$47$	−2.00000	−	6.15537i	−0.291730	−	0.897853i	0.692570	−	0.721350i	$-0.256478\pi$
$48$	2.09366	+	0.932157i	0.302194	+	0.134545i
$49$	−10.7051	−	2.27544i	−1.52930	−	0.325063i
$50$	−2.41811	+	0.513986i	−0.341973	+	0.0726886i
$51$	5.91259	−	2.63245i	0.827928	−	0.368617i
$52$	−1.33826	−	1.48629i	−0.185583	−	0.206111i
$53$	0.159705	+	1.51949i	0.0219372	+	0.208719i	1.00000		0.000407913i	$0.000129843\pi$
$53$	0.159705	+	1.51949i	0.0219372	+	0.208719i	−0.978063	+	0.208311i	$0.933203\pi$
$54$	−2.76393	+	2.00811i	−0.376124	+	0.273270i
$55$	−0.209057	+	1.98904i	−0.0281892	+	0.268203i
$56$	4.73607	+	8.20311i	0.632884	+	1.09619i
$57$	−1.38197	+	2.39364i	−0.183046	+	0.317045i
$58$	3.61803	+	2.62866i	0.475071	+	0.345159i
$59$	−1.49622	+	1.66172i	−0.194791	+	0.216338i	−0.832626	−	0.553836i	$-0.813164\pi$
$59$	−1.49622	+	1.66172i	−0.194791	+	0.216338i	0.637835	+	0.770173i	$0.279830\pi$
$60$	−0.618034	+	1.90211i	−0.0797878	+	0.245562i
$61$	−14.1803			−1.81561			−0.907803	−	0.419396i	$-0.862242\pi$
$61$	−14.1803			−1.81561			−0.907803	+	0.419396i	$0.862242\pi$
$62$		0			0
$63$	6.23607			0.785671
$64$	−0.0729490	+	0.224514i	−0.00911863	+	0.0280642i
$65$	0.827091	−	0.918578i	0.102588	−	0.113936i
$66$	1.23607	+	0.898056i	0.152149	+	0.110543i
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	−0.999915	−	0.0130248i	$-0.995854\pi$
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	0.511237	+	0.859440i	$0.329187\pi$
$68$	4.23607	+	7.33708i	0.513699	+	0.889752i
$69$	0.995933	−	9.47567i	0.119896	−	1.14074i
$70$	−2.11803	+	1.53884i	−0.253153	+	0.183927i
$71$	−1.37772	−	13.1081i	−0.163505	−	1.55565i	−0.701480	−	0.712689i	$-0.747477\pi$
$71$	−1.37772	−	13.1081i	−0.163505	−	1.55565i	0.537975	−	0.842961i	$-0.319189\pi$
$72$	−2.20264	−	2.44628i	−0.259584	−	0.288297i
$73$	−0.431318	+	0.192035i	−0.0504819	+	0.0224760i	−0.431822	−	0.901959i	$-0.642129\pi$
$73$	−0.431318	+	0.192035i	−0.0504819	+	0.0224760i	0.381340	+	0.924435i	$0.375463\pi$
$74$	−1.20906	+	0.256993i	−0.140550	+	0.0298748i
$75$	4.83623	+	1.02797i	0.558439	+	0.118700i
$76$	−3.30524	−	1.47159i	−0.379137	−	0.168803i
$77$	−2.61803	−	8.05748i	−0.298353	−	0.918235i
$78$	−0.291796	−	0.898056i	−0.0330394	−	0.101685i
$79$	1.56052	+	0.694789i	0.175572	+	0.0781699i	0.492641	−	0.870233i	$-0.336032\pi$
$79$	1.56052	+	0.694789i	0.175572	+	0.0781699i	−0.317068	+	0.948403i	$0.602698\pi$
$80$	−1.81359	−	0.385489i	−0.202765	−	0.0430990i
$81$	2.36360	−	0.502399i	0.262623	−	0.0558222i
$82$	−3.95222	+	1.75964i	−0.436449	+	0.194320i
$83$	1.97010	+	2.18802i	0.216247	+	0.240166i	0.841502	−	0.540254i	$-0.181672\pi$
$83$	1.97010	+	2.18802i	0.216247	+	0.240166i	−0.625255	+	0.780420i	$0.715005\pi$
$84$	−0.885579	−	8.42572i	−0.0966246	−	0.919322i
$85$	−4.23607	+	3.07768i	−0.459466	+	0.333822i
$86$	−0.209057	+	1.98904i	−0.0225432	+	0.214484i
$87$	−4.47214	−	7.74597i	−0.479463	−	0.830455i
$88$	−2.23607	+	3.87298i	−0.238366	+	0.412861i
$89$	1.38197	+	1.00406i	0.146488	+	0.106430i	0.658615	−	0.752480i	$-0.271142\pi$
$89$	1.38197	+	1.00406i	0.146488	+	0.106430i	−0.512127	+	0.858910i	$0.671142\pi$
$90$	0.608795	−	0.676135i	0.0641726	−	0.0712709i
$91$	−1.61803	+	4.97980i	−0.169616	+	0.522025i
$92$	12.4721			1.30031
$93$		0			0
$94$	4.00000			0.412568
$95$	0.690983	−	2.12663i	0.0708934	−	0.218187i
$96$	−4.64662	+	5.16060i	−0.474244	+	0.526702i
$97$	−1.57295	−	1.14281i	−0.159709	−	0.116035i	0.505061	−	0.863084i	$-0.331470\pi$
$97$	−1.57295	−	1.14281i	−0.159709	−	0.116035i	−0.664769	+	0.747049i	$0.731470\pi$
$98$	3.38197	−	5.85774i	0.341630	−	0.591721i
$99$	1.47214	+	2.54981i	0.147955	+	0.256266i
$100$	−0.676522	+	6.43668i	−0.0676522	+	0.643668i
$101$	2.42705	−	1.76336i	0.241501	−	0.175460i	−0.460451	−	0.887685i	$-0.652312\pi$
$101$	2.42705	−	1.76336i	0.241501	−	0.175460i	0.701952	+	0.712225i	$0.252312\pi$
$102$	0.418114	+	3.97809i	0.0413994	+	0.393889i
$103$	1.18030	+	1.31086i	0.116299	+	0.129163i	0.798483	−	0.602018i	$-0.205636\pi$
$103$	1.18030	+	1.31086i	0.116299	+	0.129163i	−0.682184	+	0.731180i	$0.738970\pi$
$104$	2.52498	−	1.12419i	0.247594	−	0.110236i
$105$	5.12165	−	1.08864i	0.499822	−	0.106240i
$106$	−0.923637	−	0.196325i	−0.0897116	−	0.0190688i
$107$	9.35111	+	4.16338i	0.904006	+	0.402490i	0.805465	−	0.592643i	$-0.201916\pi$
$107$	9.35111	+	4.16338i	0.904006	+	0.402490i	0.0985413	+	0.995133i	$0.468582\pi$
$108$	2.76393	+	8.50651i	0.265959	+	0.818539i
$109$	1.21885	+	3.75123i	0.116744	+	0.359302i	0.992307	−	0.123803i	$-0.0395090\pi$
$109$	1.21885	+	3.75123i	0.116744	+	0.359302i	−0.875562	+	0.483105i	$0.839509\pi$
$110$	−1.12920	−	0.502754i	−0.107665	−	0.0479357i
$111$	2.41811	+	0.513986i	0.229517	+	0.0487854i
$112$	7.68247	−	1.63296i	0.725925	−	0.154300i
$113$	−4.99904	+	2.22572i	−0.470271	+	0.209378i	−0.628168	−	0.778078i	$-0.716195\pi$
$113$	−4.99904	+	2.22572i	−0.470271	+	0.209378i	0.157898	+	0.987455i	$0.449528\pi$
$114$	−1.14301	−	1.26944i	−0.107053	−	0.118894i
$115$	0.805727	+	7.66598i	0.0751344	+	0.714856i
$116$	9.47214	−	6.88191i	0.879466	−	0.638969i
$117$	0.190206	−	1.80969i	0.0175846	−	0.167306i
$118$	−0.690983	−	1.19682i	−0.0636101	−	0.110176i
$119$	11.0902	−	19.2087i	1.01663	−	1.76086i
$120$	−2.23607	−	1.62460i	−0.204124	−	0.148305i
$121$	−4.68391	+	5.20201i	−0.425810	+	0.472910i
$122$	2.70820	−	8.33499i	0.245189	−	0.754615i
$123$	8.65248			0.780167
$124$		0			0
$125$	−9.00000			−0.804984
$126$	−1.19098	+	3.66547i	−0.106101	+	0.326546i
$127$	2.36060	−	2.62171i	0.209470	−	0.232639i	−0.629250	−	0.777203i	$-0.716638\pi$
$127$	2.36060	−	2.62171i	0.209470	−	0.232639i	0.838720	+	0.544563i	$0.183305\pi$
$128$	−9.20820	−	6.69015i	−0.813898	−	0.591331i
$129$	2.00000	−	3.46410i	0.176090	−	0.304997i
$130$	0.381966	+	0.661585i	0.0335006	+	0.0580248i
$131$	−1.25434	+	11.9343i	−0.109592	+	1.04270i	0.792120	+	0.610365i	$0.208977\pi$
$131$	−1.25434	+	11.9343i	−0.109592	+	1.04270i	−0.901712	+	0.432336i	$0.857689\pi$
$132$	3.23607	−	2.35114i	0.281664	−	0.204641i
$133$	0.990108	+	9.42025i	0.0858532	+	0.816839i
$134$	−3.30836	−	3.67431i	−0.285799	−	0.317412i
$135$	−5.04996	+	2.24838i	−0.434631	+	0.193510i
$136$	−11.4524	+	2.43427i	−0.982031	+	0.208737i
$137$	−19.2775	−	4.09757i	−1.64699	−	0.350079i	−0.711297	−	0.702892i	$-0.751892\pi$
$137$	−19.2775	−	4.09757i	−1.64699	−	0.350079i	−0.935694	+	0.352813i	$0.885225\pi$
$138$	5.37945	+	2.39509i	0.457929	+	0.203883i
$139$	−4.14590	−	12.7598i	−0.351650	−	1.08227i	−0.957926	−	0.287014i	$-0.907337\pi$
$139$	−4.14590	−	12.7598i	−0.351650	−	1.08227i	0.606276	−	0.795254i	$-0.292663\pi$
$140$	2.11803	+	6.51864i	0.179007	+	0.550925i
$141$	−7.30836	−	3.25389i	−0.615475	−	0.274027i
$142$	7.96789	+	1.69363i	0.668651	+	0.142126i
$143$	−2.41811	+	0.513986i	−0.202213	+	0.0429817i
$144$	−2.49351	+	1.11018i	−0.207793	+	0.0925153i
$145$	4.84187	+	5.37745i	0.402096	+	0.446573i
$146$	−0.0305010	−	0.290198i	−0.00252428	−	0.0240169i
$147$	−10.9443	+	7.95148i	−0.902668	+	0.655827i
$148$	−0.338261	+	3.21834i	−0.0278049	+	0.264546i
$149$	−5.00000	−	8.66025i	−0.409616	−	0.709476i	0.585231	−	0.810867i	$-0.301004\pi$
$149$	−5.00000	−	8.66025i	−0.409616	−	0.709476i	−0.994847	+	0.101391i	$0.967671\pi$
$150$	−1.52786	+	2.64634i	−0.124750	+	0.216073i
$151$	−6.61803	−	4.80828i	−0.538568	−	0.391293i	0.284985	−	0.958532i	$-0.408011\pi$
$151$	−6.61803	−	4.80828i	−0.538568	−	0.391293i	−0.823553	+	0.567239i	$0.808011\pi$
$152$	3.34565	−	3.71572i	0.271368	−	0.301385i
$153$	−2.38197	+	7.33094i	−0.192571	+	0.592671i
$154$	5.23607			0.421934
$155$		0			0
$156$	−2.47214			−0.197929
$157$	−4.60081	+	14.1598i	−0.367185	+	1.13008i	0.581417	+	0.813606i	$0.302499\pi$
$157$	−4.60081	+	14.1598i	−0.367185	+	1.13008i	−0.948602	+	0.316473i	$0.897501\pi$
$158$	−0.706420	+	0.784559i	−0.0561998	+	0.0624162i
$159$	1.52786	+	1.11006i	0.121168	+	0.0880333i
$160$	2.80902	−	4.86536i	0.222072	−	0.384640i
$161$	−16.3262	−	28.2779i	−1.28669	−	2.22861i
$162$	−0.156105	+	1.48524i	−0.0122648	+	0.116692i
$163$	2.19098	−	1.59184i	0.171611	−	0.124683i	−0.498664	−	0.866795i	$-0.666176\pi$
$163$	2.19098	−	1.59184i	0.171611	−	0.124683i	0.670275	+	0.742112i	$0.266176\pi$
$164$	1.18391	+	11.2642i	0.0924482	+	0.879586i
$165$	1.65418	+	1.83716i	0.128778	+	0.143022i
$166$	−1.66234	+	0.740122i	−0.129023	+	0.0574446i
$167$	−2.41811	+	0.513986i	−0.187119	+	0.0397734i	−0.300518	−	0.953776i	$-0.597160\pi$
$167$	−2.41811	+	0.513986i	−0.187119	+	0.0397734i	0.113399	+	0.993550i	$0.463826\pi$
$168$	11.4524	+	2.43427i	0.883568	+	0.187808i
$169$	−10.4803	−	4.66614i	−0.806178	−	0.358934i
$170$	−1.00000	−	3.07768i	−0.0766965	−	0.236048i
$171$	−1.01722	−	3.13068i	−0.0777888	−	0.239409i
$172$	4.78339	+	2.12970i	0.364730	+	0.162388i
$173$	14.6177	+	3.10709i	1.11136	+	0.236228i	0.726785	−	0.686865i	$-0.241014\pi$
$173$	14.6177	+	3.10709i	1.11136	+	0.236228i	0.384578	+	0.923092i	$0.374347\pi$
$174$	5.40707	−	1.14931i	0.409909	−	0.0871288i
$175$	15.4794	−	6.89186i	1.17013	−	0.520975i
$176$	2.48127	+	2.75573i	0.187033	+	0.207721i
$177$	0.288910	+	2.74879i	0.0217158	+	0.206612i
$178$	−0.854102	+	0.620541i	−0.0640176	+	0.0465115i
$179$	1.22384	−	11.6441i	0.0914741	−	0.870318i	−0.848528	−	0.529150i	$-0.822511\pi$
$179$	1.22384	−	11.6441i	0.0914741	−	0.870318i	0.940002	−	0.341168i	$-0.110823\pi$
$180$	−1.19098	−	2.06284i	−0.0887706	−	0.153755i
$181$	−9.09017	+	15.7446i	−0.675667	+	1.17029i	0.300606	+	0.953748i	$0.402811\pi$
$181$	−9.09017	+	15.7446i	−0.675667	+	1.17029i	−0.976273	+	0.216541i	$0.930522\pi$
$182$	−2.61803	−	1.90211i	−0.194062	−	0.140994i
$183$	−11.7284	+	13.0257i	−0.866991	+	0.962891i
$184$	−5.32624	+	16.3925i	−0.392655	+	1.20847i
$185$	−2.00000			−0.147043
$186$		0			0
$187$	10.4721			0.765798
$188$	3.23607	−	9.95959i	0.236015	−	0.726378i
$189$	15.6686	−	17.4018i	1.13973	−	1.26579i
$190$	1.11803	+	0.812299i	0.0811107	+	0.0589304i
$191$	−1.59017	+	2.75426i	−0.115061	+	0.199291i	−0.917804	−	0.397034i	$-0.870040\pi$
$191$	−1.59017	+	2.75426i	−0.115061	+	0.199291i	0.802743	+	0.596325i	$0.203373\pi$
$192$	0.145898	+	0.252703i	0.0105293	+	0.0182373i
$193$	0.571994	−	5.44216i	0.0411730	−	0.391735i	−0.954457	−	0.298349i	$-0.903564\pi$
$193$	0.571994	−	5.44216i	0.0411730	−	0.391735i	0.995630	−	0.0933864i	$-0.0297692\pi$
$194$	0.972136	−	0.706298i	0.0697953	−	0.0507092i
$195$	−0.159705	−	1.51949i	−0.0114367	−	0.108813i
$196$	−11.8491	−	13.1598i	−0.846364	−	0.939983i
$197$	−14.0836	+	6.27042i	−1.00341	+	0.446749i	−0.841617	−	0.540075i	$-0.818396\pi$
$197$	−14.0836	+	6.27042i	−1.00341	+	0.446749i	−0.161797	+	0.986824i	$0.551729\pi$
$198$	−1.77990	+	0.378329i	−0.126492	+	0.0268866i
$199$	1.03266	+	0.219498i	0.0732032	+	0.0155598i	0.244368	−	0.969683i	$-0.421420\pi$
$199$	1.03266	+	0.219498i	0.0732032	+	0.0155598i	−0.171164	+	0.985242i	$0.554753\pi$
$200$	−8.17100	−	3.63796i	−0.577777	−	0.257243i
$201$	3.05573	+	9.40456i	0.215534	+	0.663347i
$202$	0.572949	+	1.76336i	0.0403126	+	0.124069i
$203$	−28.0024	−	12.4675i	−1.96539	−	0.875046i
$204$	10.2433	+	2.17728i	0.717174	+	0.152440i
$205$	−6.84703	+	1.45538i	−0.478218	+	0.101648i
$206$	−0.995920	+	0.443412i	−0.0693890	+	0.0308940i
$207$	7.59298	+	8.43285i	0.527748	+	0.586124i
$208$	−0.239558	−	2.27924i	−0.0166104	−	0.158037i
$209$	−3.61803	+	2.62866i	−0.250265	+	0.181828i
$210$	−0.338261	+	3.21834i	−0.0233422	+	0.222087i
$211$	−0.409830	−	0.709846i	−0.0282139	−	0.0488678i	0.851574	−	0.524235i	$-0.175649\pi$
$211$	−0.409830	−	0.709846i	−0.0282139	−	0.0488678i	−0.879788	+	0.475367i	$0.842315\pi$
$212$	−1.23607	+	2.14093i	−0.0848935	+	0.147040i
$213$	−13.1803	−	9.57608i	−0.903102	−	0.656142i
$214$	−4.23308	+	4.70131i	−0.289367	+	0.321375i
$215$	−1.00000	+	3.07768i	−0.0681994	+	0.209896i
$216$	−12.3607			−0.841038
$217$		0			0
$218$	−2.43769			−0.165101
$219$	−0.180340	+	0.555029i	−0.0121862	+	0.0375054i
$220$	−2.16535	+	2.40487i	−0.145988	+	0.162136i
$221$	−5.23607	−	3.80423i	−0.352216	−	0.255900i
$222$	−0.763932	+	1.32317i	−0.0512718	+	0.0888053i
$223$	−2.00000	−	3.46410i	−0.133930	−	0.231973i	0.791258	−	0.611482i	$-0.209426\pi$
$223$	−2.00000	−	3.46410i	−0.133930	−	0.231973i	−0.925188	+	0.379509i	$0.876093\pi$
$224$	−2.48761	+	23.6680i	−0.166210	+	1.58139i
$225$	−4.76393	+	3.46120i	−0.317595	+	0.230747i
$226$	−0.353512	−	3.36344i	−0.0235152	−	0.223733i
$227$	1.65418	+	1.83716i	0.109792	+	0.121936i	0.795536	−	0.605907i	$-0.207190\pi$
$227$	1.65418	+	1.83716i	0.109792	+	0.121936i	−0.685744	+	0.727843i	$0.740523\pi$
$228$	−4.08550	+	1.81898i	−0.270569	+	0.120465i
$229$	−13.1232	+	2.78943i	−0.867207	+	0.184331i	−0.619971	−	0.784625i	$-0.712856\pi$
$229$	−13.1232	+	2.78943i	−0.867207	+	0.184331i	−0.247236	+	0.968955i	$0.579522\pi$
$230$	−4.65983	−	0.990477i	−0.307260	−	0.0653101i
$231$	−9.56677	−	4.25940i	−0.629447	−	0.280248i
$232$	5.00000	+	15.3884i	0.328266	+	1.01030i
$233$	0.0172209	+	0.0530006i	0.00112818	+	0.00347218i	0.951619	−	0.307280i	$-0.0994189\pi$
$233$	0.0172209	+	0.0530006i	0.00112818	+	0.00347218i	−0.950491	+	0.310753i	$0.899419\pi$
$234$	1.02738	+	0.457421i	0.0671622	+	0.0299025i
$235$	6.33070	+	1.34563i	0.412970	+	0.0877794i
$236$	−3.53897	+	0.752232i	−0.230367	+	0.0489661i
$237$	1.92891	−	0.858807i	0.125296	−	0.0557855i
$238$	9.17258	+	10.1872i	0.594570	+	0.660337i
$239$	−0.178556	−	1.69885i	−0.0115498	−	0.109889i	0.987228	−	0.159313i	$-0.0509280\pi$
$239$	−0.178556	−	1.69885i	−0.0115498	−	0.109889i	−0.998778	+	0.0494242i	$0.984261\pi$
$240$	−1.85410	+	1.34708i	−0.119682	+	0.0869539i
$241$	3.17356	−	30.1944i	0.204427	−	1.94499i	−0.105939	−	0.994373i	$-0.533785\pi$
$241$	3.17356	−	30.1944i	0.204427	−	1.94499i	0.310366	−	0.950617i	$-0.399548\pi$
$242$	−2.16312	−	3.74663i	−0.139051	−	0.240843i
$243$	−6.79837	+	11.7751i	−0.436116	+	0.755375i
$244$	−18.5623	−	13.4863i	−1.18833	−	0.863372i
$245$	7.32315	−	8.13318i	0.467859	−	0.519610i
$246$	−1.65248	+	5.08580i	−0.105358	+	0.324259i
$247$	2.76393			0.175865
$248$		0			0
$249$	3.63932			0.230633
$250$	1.71885	−	5.29007i	0.108709	−	0.334573i
$251$	−16.1798	+	17.9695i	−1.02126	+	1.13422i	−0.0303719	+	0.999539i	$0.509669\pi$
$251$	−16.1798	+	17.9695i	−1.02126	+	1.13422i	−0.990888	+	0.134686i	$0.956998\pi$
$252$	8.16312	+	5.93085i	0.514228	+	0.373609i
$253$	7.70820	−	13.3510i	0.484611	−	0.839370i
$254$	1.09017	+	1.88823i	0.0684033	+	0.118478i
$255$	−0.676522	+	6.43668i	−0.0423655	+	0.403081i
$256$	5.30902	−	3.85723i	0.331814	−	0.241077i
$257$	1.66663	+	15.8569i	0.103962	+	0.989128i	0.914813	+	0.403877i	$0.132337\pi$
$257$	1.66663	+	15.8569i	0.103962	+	0.989128i	−0.810852	+	0.585251i	$0.800996\pi$
$258$	1.65418	+	1.83716i	0.102985	+	0.114376i
$259$	7.73968	−	3.44593i	0.480920	−	0.214120i
$260$	1.95630	−	0.415823i	0.121324	−	0.0257883i
$261$	10.4197	+	2.21477i	0.644963	+	0.137091i
$262$	−6.77523	−	3.01652i	−0.418575	−	0.186362i
$263$	−5.79837	−	17.8456i	−0.357543	−	1.10040i	−0.954520	−	0.298146i	$-0.903632\pi$
$263$	−5.79837	−	17.8456i	−0.357543	−	1.10040i	0.596977	−	0.802258i	$-0.296368\pi$
$264$	1.70820	+	5.25731i	0.105133	+	0.323565i
$265$	−1.39577	−	0.621438i	−0.0857417	−	0.0381747i
$266$	−5.72618	−	1.21714i	−0.351094	−	0.0746274i
$267$	2.06532	−	0.438996i	0.126395	−	0.0268661i
$268$	−11.8252	+	5.26491i	−0.722338	+	0.321606i
$269$	−19.3675	−	21.5098i	−1.18086	−	1.31147i	−0.940104	−	0.340888i	$-0.889272\pi$
$269$	−19.3675	−	21.5098i	−1.18086	−	1.31147i	−0.240753	−	0.970586i	$-0.577395\pi$
$270$	−0.357112	−	3.39769i	−0.0217331	−	0.206777i
$271$	−6.61803	+	4.80828i	−0.402017	+	0.292082i	−0.770362	−	0.637607i	$-0.779924\pi$
$271$	−6.61803	+	4.80828i	−0.402017	+	0.292082i	0.368345	+	0.929689i	$0.379924\pi$
$272$	−1.01478	+	9.65502i	−0.0615303	+	0.585422i
$273$	3.23607	+	5.60503i	0.195856	+	0.339232i
$274$	6.09017	−	10.5485i	0.367921	−	0.637257i
$275$	6.47214	+	4.70228i	0.390284	+	0.283558i
$276$	10.3156	−	11.4566i	0.620926	−	0.689608i
$277$	5.76393	−	17.7396i	0.346321	−	1.06587i	−0.614552	−	0.788877i	$-0.710663\pi$
$277$	5.76393	−	17.7396i	0.346321	−	1.06587i	0.960873	−	0.276990i	$-0.0893370\pi$
$278$	8.29180			0.497309
$279$		0			0
$280$	−9.47214			−0.566068
$281$	5.25329	−	16.1680i	0.313385	−	0.964500i	−0.663029	−	0.748594i	$-0.730729\pi$
$281$	5.25329	−	16.1680i	0.313385	−	0.964500i	0.976414	−	0.215906i	$-0.0692705\pi$
$282$	3.30836	−	3.67431i	0.197010	−	0.218802i
$283$	−17.7082	−	12.8658i	−1.05264	−	0.764790i	−0.0799301	−	0.996800i	$-0.525470\pi$
$283$	−17.7082	−	12.8658i	−1.05264	−	0.764790i	−0.972713	+	0.232010i	$0.925470\pi$
$284$	10.6631	−	18.4691i	0.632740	−	1.09594i
$285$	−1.38197	−	2.39364i	−0.0818606	−	0.141787i
$286$	0.159705	−	1.51949i	0.00944357	−	0.0898496i
$287$	23.9894	−	17.4293i	1.41605	−	1.02882i
$288$	−0.864504	−	8.22520i	−0.0509414	−	0.484675i
$289$	6.96994	+	7.74090i	0.409996	+	0.455347i
$290$	−4.08550	+	1.81898i	−0.239909	+	0.106814i
$291$	−2.35074	+	0.499664i	−0.137803	+	0.0292908i
$292$	−0.747238	−	0.158830i	−0.0437288	−	0.00929485i
$293$	7.73968	+	3.44593i	0.452157	+	0.201313i	0.620163	−	0.784473i	$-0.287066\pi$
$293$	7.73968	+	3.44593i	0.452157	+	0.201313i	−0.168006	+	0.985786i	$0.553733\pi$
$294$	−2.58359	−	7.95148i	−0.150678	−	0.463740i
$295$	−0.690983	−	2.12663i	−0.0402306	−	0.123817i
$296$	−4.08550	−	1.81898i	−0.237465	−	0.105726i
$297$	10.8141	+	2.29862i	0.627500	+	0.133379i
$298$	6.04528	−	1.28496i	0.350194	−	0.0744360i
$299$	−8.70414	+	3.87533i	−0.503373	+	0.224116i
$300$	5.35304	+	5.94516i	0.309058	+	0.343244i
$301$	−1.43290	−	13.6331i	−0.0825908	−	0.785799i
$302$	4.09017	−	2.97168i	0.235363	−	0.171001i
$303$	0.387613	−	3.68789i	0.0222678	−	0.211864i
$304$	−2.07295	−	3.59045i	−0.118892	−	0.205927i
$305$	7.09017	−	12.2805i	0.405982	−	0.703181i
$306$	−3.85410	−	2.80017i	−0.220324	−	0.160075i
$307$	−10.2322	+	11.3640i	−0.583983	+	0.648579i	−0.960647	−	0.277771i	$-0.910404\pi$
$307$	−10.2322	+	11.3640i	−0.583983	+	0.648579i	0.376664	+	0.926350i	$0.377071\pi$
$308$	4.23607	−	13.0373i	0.241372	−	0.742868i
$309$	2.18034			0.124035
$310$		0			0
$311$	−6.81966			−0.386707			−0.193354	−	0.981129i	$-0.561936\pi$
$311$	−6.81966			−0.386707			−0.193354	+	0.981129i	$0.561936\pi$
$312$	1.05573	−	3.24920i	0.0597688	−	0.183950i
$313$	14.2097	−	15.7815i	0.803180	−	0.892022i	−0.192833	−	0.981232i	$-0.561768\pi$
$313$	14.2097	−	15.7815i	0.803180	−	0.892022i	0.996013	+	0.0892099i	$0.0284342\pi$
$314$	−7.44427	−	5.40858i	−0.420105	−	0.305224i
$315$	−3.11803	+	5.40059i	−0.175681	+	0.304289i
$316$	1.38197	+	2.39364i	0.0777417	+	0.134653i
$317$	−2.29380	+	21.8241i	−0.128833	+	1.22576i	0.718815	+	0.695202i	$0.244685\pi$
$317$	−2.29380	+	21.8241i	−0.128833	+	1.22576i	−0.847648	+	0.530560i	$0.821982\pi$
$318$	−0.944272	+	0.686054i	−0.0529521	+	0.0384720i
$319$	−1.51275	−	14.3929i	−0.0846977	−	0.805845i
$320$	−0.157960	−	0.175433i	−0.00883025	−	0.00980699i
$321$	11.5586	−	5.14623i	0.645139	−	0.287234i
$322$	19.7394	−	4.19573i	1.10003	−	0.233819i
$323$	−11.4524	−	2.43427i	−0.637226	−	0.135447i
$324$	3.57181	+	1.59027i	0.198434	+	0.0883484i
$325$	−1.52786	−	4.70228i	−0.0847506	−	0.260836i
$326$	0.517221	+	1.59184i	0.0286462	+	0.0881640i
$327$	4.45389	+	1.98300i	0.246301	+	0.109660i
$328$	−15.3104	−	3.25433i	−0.845377	−	0.179690i
$329$	−26.8173	+	5.70019i	−1.47849	+	0.314262i
$330$	−1.39577	+	0.621438i	−0.0768348	+	0.0342091i
$331$	1.33826	+	1.48629i	0.0735575	+	0.0816939i	0.778800	−	0.627272i	$-0.215829\pi$
$331$	1.33826	+	1.48629i	0.0735575	+	0.0816939i	−0.705243	+	0.708966i	$0.749162\pi$
$332$	0.497966	+	4.73783i	0.0273295	+	0.260022i
$333$	−2.38197	+	1.73060i	−0.130531	+	0.0948363i
$334$	0.159705	−	1.51949i	0.00873868	−	0.0831430i
$335$	−4.00000	−	6.92820i	−0.218543	−	0.378528i
$336$	4.85410	−	8.40755i	0.264813	−	0.458670i
$337$	15.5623	+	11.3067i	0.847733	+	0.615914i	0.924520	−	0.381134i	$-0.124466\pi$
$337$	15.5623	+	11.3067i	0.847733	+	0.615914i	−0.0767872	+	0.997048i	$0.524466\pi$
$338$	4.74425	−	5.26902i	0.258053	−	0.286597i
$339$	−2.09017	+	6.43288i	−0.113522	+	0.349386i
$340$	−8.47214			−0.459466
$341$		0			0
$342$	2.03444			0.110010
$343$	−5.16312	+	15.8904i	−0.278782	+	0.858003i
$344$	−4.84187	+	5.37745i	−0.261056	+	0.289932i
$345$	7.70820	+	5.60034i	0.414996	+	0.301512i
$346$	−4.61803	+	7.99867i	−0.248267	+	0.430011i
$347$	−0.909830	−	1.57587i	−0.0488422	−	0.0845972i	0.840571	−	0.541702i	$-0.182220\pi$
$347$	−0.909830	−	1.57587i	−0.0488422	−	0.0845972i	−0.889413	+	0.457105i	$0.848886\pi$
$348$	1.51275	−	14.3929i	0.0810919	−	0.771538i
$349$	−22.5623	+	16.3925i	−1.20773	+	0.877469i	−0.995023	−	0.0996464i	$-0.968229\pi$
$349$	−22.5623	+	16.3925i	−1.20773	+	0.877469i	−0.212710	+	0.977115i	$0.568229\pi$
$350$	1.09464	+	10.4148i	0.0585108	+	0.556693i
$351$	−4.57205	−	5.07777i	−0.244038	−	0.271031i
$352$	−10.2647	+	4.57012i	−0.547108	+	0.243588i
$353$	18.9921	−	4.03690i	1.01085	−	0.214862i	0.327419	−	0.944879i	$-0.393821\pi$
$353$	18.9921	−	4.03690i	1.01085	−	0.214862i	0.683429	+	0.730017i	$0.260488\pi$
$354$	−1.67088	−	0.355156i	−0.0888060	−	0.0188763i
$355$	12.0408	+	5.36093i	0.639061	+	0.284528i
$356$	0.854102	+	2.62866i	0.0452673	+	0.139318i
$357$	−8.47214	−	26.0746i	−0.448393	−	1.38001i
$358$	6.61048	+	2.94317i	0.349375	+	0.155552i
$359$	−17.3757	−	3.69333i	−0.917057	−	0.194926i	−0.274876	−	0.961480i	$-0.588637\pi$
$359$	−17.3757	−	3.69333i	−0.917057	−	0.194926i	−0.642181	+	0.766553i	$0.721970\pi$
$360$	3.21986	−	0.684403i	0.169702	−	0.0360712i
$361$	−12.7896	+	5.69431i	−0.673139	+	0.299701i
$362$	−7.51840	−	8.35003i	−0.395158	−	0.438868i
$363$	0.904430	+	8.60508i	0.0474703	+	0.451649i
$364$	−6.85410	+	4.97980i	−0.359253	+	0.261012i
$365$	0.0493516	−	0.469550i	0.00258318	−	0.0245773i
$366$	−5.41641	−	9.38149i	−0.283120	−	0.490379i
$367$	−9.00000	+	15.5885i	−0.469796	+	0.813711i	−0.999404	−	0.0345320i	$-0.989006\pi$
$367$	−9.00000	+	15.5885i	−0.469796	+	0.813711i	0.529607	+	0.848243i	$0.322339\pi$
$368$	11.5623	+	8.40051i	0.602727	+	0.437907i
$369$	−6.89536	+	7.65807i	−0.358958	+	0.398663i
$370$	0.381966	−	1.17557i	0.0198575	−	0.0611150i
$371$	6.47214			0.336017
$372$		0			0
$373$	19.0000			0.983783			0.491891	−	0.870657i	$-0.336306\pi$
$373$	19.0000			0.983783			0.491891	+	0.870657i	$0.336306\pi$
$374$	−2.00000	+	6.15537i	−0.103418	+	0.318286i
$375$	−7.44382	+	8.26720i	−0.384397	+	0.426916i
$376$	11.7082	+	8.50651i	0.603805	+	0.438690i
$377$	−4.47214	+	7.74597i	−0.230327	+	0.398938i
$378$	7.23607	+	12.5332i	0.372183	+	0.644640i
$379$	3.96043	−	37.6810i	0.203434	−	1.93554i	−0.127396	−	0.991852i	$-0.540662\pi$
$379$	3.96043	−	37.6810i	0.203434	−	1.93554i	0.330830	−	0.943690i	$-0.392671\pi$
$380$	2.92705	−	2.12663i	0.150155	−	0.109094i
$381$	−0.455815	−	4.33679i	−0.0233521	−	0.222181i
$382$	−1.31522	−	1.46069i	−0.0672923	−	0.0747356i
$383$	10.8607	−	4.83551i	0.554957	−	0.247083i	−0.110042	−	0.993927i	$-0.535099\pi$
$383$	10.8607	−	4.83551i	0.554957	−	0.247083i	0.664999	+	0.746844i	$0.268432\pi$
$384$	−13.7614	+	2.92509i	−0.702261	+	0.149270i
$385$	8.28700	+	1.76146i	0.422345	+	0.0897721i
$386$	3.08958	+	1.37557i	0.157255	+	0.0700146i
$387$	1.47214	+	4.53077i	0.0748329	+	0.230312i
$388$	−0.972136	−	2.99193i	−0.0493527	−	0.151892i
$389$	16.3420	+	7.27593i	0.828572	+	0.368904i	0.776794	−	0.629755i	$-0.216845\pi$
$389$	16.3420	+	7.27593i	0.828572	+	0.368904i	0.0517780	+	0.998659i	$0.483511\pi$
$390$	0.923637	+	0.196325i	0.0467702	+	0.00994131i
$391$	39.4787	−	8.39146i	1.99652	−	0.424374i
$392$	22.3564	−	9.95371i	1.12917	−	0.502738i
$393$	9.92509	+	11.0229i	0.500655	+	0.556033i
$394$	−0.995933	−	9.47567i	−0.0501744	−	0.477377i
$395$	−1.38197	+	1.00406i	−0.0695343	+	0.0505196i
$396$	−0.497966	+	4.73783i	−0.0250238	+	0.238085i
$397$	3.50000	+	6.06218i	0.175660	+	0.304252i	0.940389	−	0.340099i	$-0.110461\pi$
$397$	3.50000	+	6.06218i	0.175660	+	0.304252i	−0.764730	+	0.644351i	$0.777127\pi$
$398$	−0.326238	+	0.565061i	−0.0163528	+	0.0283239i
$399$	9.47214	+	6.88191i	0.474200	+	0.344526i
$400$	−4.96255	+	5.51147i	−0.248127	+	0.275573i
$401$	4.88854	−	15.0454i	0.244122	−	0.751331i	−0.751657	−	0.659554i	$-0.770745\pi$
$401$	4.88854	−	15.0454i	0.244122	−	0.751331i	0.995780	−	0.0917771i	$-0.0292547\pi$
$402$	−6.11146			−0.304812
$403$		0			0
$404$	4.85410			0.241501
$405$	−0.746711	+	2.29814i	−0.0371044	+	0.114196i
$406$	12.6762	−	14.0783i	0.629109	−	0.698696i
$407$	3.23607	+	2.35114i	0.160406	+	0.116542i
$408$	−7.23607	+	12.5332i	−0.358239	+	0.620488i
$409$	13.0902	+	22.6728i	0.647267	+	1.12110i	0.983773	+	0.179418i	$0.0574216\pi$
$409$	13.0902	+	22.6728i	0.647267	+	1.12110i	−0.336506	+	0.941681i	$0.609245\pi$
$410$	0.452215	−	4.30254i	0.0223333	−	0.212487i
$411$	−19.7082	+	14.3188i	−0.972134	+	0.706297i
$412$	0.298335	+	2.83847i	0.0146979	+	0.139841i
$413$	6.33810	+	7.03917i	0.311877	+	0.346375i
$414$	−6.40684	+	2.85251i	−0.314879	+	0.140193i
$415$	−2.87993	+	0.612149i	−0.141370	+	0.0300492i
$416$	6.79252	+	1.44380i	0.333031	+	0.0707879i
$417$	−15.1499	−	6.74515i	−0.741892	−	0.330312i
$418$	−0.854102	−	2.62866i	−0.0417755	−	0.128572i
$419$	9.30902	+	28.6502i	0.454775	+	1.39965i	0.871399	+	0.490575i	$0.163213\pi$
$419$	9.30902	+	28.6502i	0.454775	+	1.39965i	−0.416624	+	0.909079i	$0.636787\pi$
$420$	7.73968	+	3.44593i	0.377658	+	0.168144i
$421$	15.0250	+	3.19366i	0.732274	+	0.155650i	0.558934	−	0.829212i	$-0.311211\pi$
$421$	15.0250	+	3.19366i	0.732274	+	0.155650i	0.173340	+	0.984862i	$0.444544\pi$
$422$	0.495508	−	0.105323i	0.0241209	−	0.00512707i
$423$	8.70414	−	3.87533i	0.423210	−	0.188425i
$424$	−2.28602	−	2.53889i	−0.111019	−	0.123299i
$425$	2.18927	+	20.8295i	0.106195	+	1.01038i
$426$	8.14590	−	5.91834i	0.394670	−	0.286745i
$427$	−6.27891	+	59.7398i	−0.303858	+	2.89101i
$428$	8.28115	+	14.3434i	0.400285	+	0.693313i
$429$	−1.52786	+	2.64634i	−0.0737660	+	0.127766i
$430$	−1.61803	−	1.17557i	−0.0780285	−	0.0566910i
$431$	8.02957	−	8.91774i	0.386771	−	0.429552i	−0.518047	−	0.855352i	$-0.673341\pi$
$431$	8.02957	−	8.91774i	0.386771	−	0.429552i	0.904817	+	0.425800i	$0.140007\pi$
$432$	−3.16718	+	9.74759i	−0.152381	+	0.468981i
$433$	−12.1803			−0.585350			−0.292675	−	0.956212i	$-0.594545\pi$
$433$	−12.1803			−0.585350			−0.292675	+	0.956212i	$0.594545\pi$
$434$		0			0
$435$	8.94427			0.428845
$436$	−1.97214	+	6.06961i	−0.0944482	+	0.290682i
$437$	−11.5332	+	12.8089i	−0.551707	+	0.612733i
$438$	−0.291796	−	0.212002i	−0.0139426	−	0.0101299i
$439$	−10.5902	+	18.3427i	−0.505441	+	0.875450i	0.494539	+	0.869155i	$0.335337\pi$
$439$	−10.5902	+	18.3427i	−0.505441	+	0.875450i	−0.999980	+	0.00629443i	$0.997996\pi$
$440$	−2.23607	−	3.87298i	−0.106600	−	0.184637i
$441$	1.68411	−	16.0232i	0.0801955	−	0.763009i
$442$	3.23607	−	2.35114i	0.153924	−	0.111832i
$443$	−1.80748	−	17.1971i	−0.0858762	−	0.817057i	−0.949678	−	0.313226i	$-0.898590\pi$
$443$	−1.80748	−	17.1971i	−0.0858762	−	0.817057i	0.863802	−	0.503831i	$-0.168077\pi$
$444$	2.67652	+	2.97258i	0.127022	+	0.141072i
$445$	−1.56052	+	0.694789i	−0.0739758	+	0.0329362i
$446$	2.41811	−	0.513986i	0.114501	−	0.0243379i
$447$	−12.0906	−	2.56993i	−0.571864	−	0.121554i
$448$	0.913545	+	0.406737i	0.0431610	+	0.0192165i
$449$	9.67376	+	29.7728i	0.456533	+	1.40506i	0.869326	+	0.494239i	$0.164553\pi$
$449$	9.67376	+	29.7728i	0.456533	+	1.40506i	−0.412793	+	0.910825i	$0.635447\pi$
$450$	−1.12461	−	3.46120i	−0.0530147	−	0.163162i
$451$	12.7896	+	5.69431i	0.602240	+	0.268135i
$452$	−8.66062	−	1.84087i	−0.407361	−	0.0865873i
$453$	−9.89050	+	2.10229i	−0.464696	+	0.0987742i
$454$	−1.39577	+	0.621438i	−0.0655069	+	0.0291655i
$455$	−3.50361	−	3.89116i	−0.164252	−	0.182420i
$456$	−0.646021	−	6.14648i	−0.0302527	−	0.287835i
$457$	16.9443	−	12.3107i	0.792620	−	0.575872i	−0.116120	−	0.993235i	$-0.537046\pi$
$457$	16.9443	−	12.3107i	0.792620	−	0.575872i	0.908740	+	0.417363i	$0.137046\pi$
$458$	0.866729	−	8.24637i	0.0404996	−	0.385328i
$459$	14.4721	+	25.0665i	0.675501	+	1.17000i
$460$	−6.23607	+	10.8012i	−0.290758	+	0.503608i
$461$	8.38197	+	6.08985i	0.390387	+	0.283633i	0.765614	−	0.643300i	$-0.222435\pi$
$461$	8.38197	+	6.08985i	0.390387	+	0.283633i	−0.375227	+	0.926933i	$0.622435\pi$
$462$	4.33070	−	4.80973i	0.201483	−	0.223769i
$463$	−9.09017	+	27.9767i	−0.422456	+	1.30019i	0.482953	+	0.875646i	$0.339564\pi$
$463$	−9.09017	+	27.9767i	−0.422456	+	1.30019i	−0.905409	+	0.424540i	$0.860436\pi$
$464$	13.4164			0.622841
$465$		0			0
$466$	−0.0344419			−0.00159549
$467$	−2.69098	+	8.28199i	−0.124524	+	0.383245i	−0.993814	−	0.111057i	$-0.964576\pi$
$467$	−2.69098	+	8.28199i	−0.124524	+	0.383245i	0.869290	+	0.494302i	$0.164576\pi$
$468$	1.97010	−	2.18802i	0.0910680	−	0.101141i
$469$	27.4164	+	19.9192i	1.26597	+	0.919783i
$470$	−2.00000	+	3.46410i	−0.0922531	+	0.159787i
$471$	9.20163	+	15.9377i	0.423989	+	0.734370i
$472$	0.522642	−	4.97261i	0.0240566	−	0.228883i
$473$	5.23607	−	3.80423i	0.240755	−	0.174919i
$474$	0.136405	+	1.29780i	0.00626527	+	0.0596101i
$475$	−5.98489	−	6.64689i	−0.274605	−	0.304980i
$476$	32.7858	−	14.5972i	1.50274	−	0.669061i
$477$	−2.20007	+	0.467640i	−0.100734	+	0.0214118i
$478$	1.03266	+	0.219498i	0.0472327	+	0.0100396i
$479$	33.5346	+	14.9306i	1.53224	+	0.682195i	0.987674	−	0.156526i	$-0.0500294\pi$
$479$	33.5346	+	14.9306i	1.53224	+	0.682195i	0.544562	+	0.838721i	$0.316696\pi$
$480$	−2.14590	−	6.60440i	−0.0979464	−	0.301448i
$481$	−0.763932	−	2.35114i	−0.0348323	−	0.107203i
$482$	17.1417	+	7.63198i	0.780783	+	0.347627i
$483$	−39.4787	−	8.39146i	−1.79634	−	0.381825i
$484$	−11.0787	+	2.35486i	−0.503579	+	0.107039i
$485$	1.77618	−	0.790807i	0.0806522	−	0.0359087i
$486$	−5.62287	−	6.24483i	−0.255059	−	0.283271i
$487$	1.54325	+	14.6831i	0.0699314	+	0.665353i	0.972196	+	0.234169i	$0.0752371\pi$
$487$	1.54325	+	14.6831i	0.0699314	+	0.665353i	−0.902264	+	0.431183i	$0.858096\pi$
$488$	25.6525	−	18.6376i	1.16123	−	0.843685i
$489$	0.349912	−	3.32919i	0.0158235	−	0.150551i
$490$	3.38197	+	5.85774i	0.152782	+	0.264626i
$491$	20.1803	−	34.9534i	0.910726	−	1.57742i	0.0976849	−	0.995217i	$-0.468856\pi$
$491$	20.1803	−	34.9534i	0.910726	−	1.57742i	0.813041	−	0.582206i	$-0.197810\pi$
$492$	11.3262	+	8.22899i	0.510626	+	0.370992i
$493$	25.3524	−	28.1567i	1.14181	−	1.26811i
$494$	−0.527864	+	1.62460i	−0.0237497	+	0.0730941i
$495$	−2.94427			−0.132335
$496$		0			0
$497$	−55.8328			−2.50444
$498$	−0.695048	+	2.13914i	−0.0311459	+	0.0958571i
$499$	−22.3599	+	24.8332i	−1.00097	+	1.11169i	−0.00722806	+	0.999974i	$0.502301\pi$
$499$	−22.3599	+	24.8332i	−1.00097	+	1.11169i	−0.993740	+	0.111714i	$0.964366\pi$
$500$	−11.7812	−	8.55951i	−0.526869	−	0.382793i
$501$	−1.52786	+	2.64634i	−0.0682599	+	0.118230i
$502$	−7.47214	−	12.9421i	−0.333498	−	0.577635i
$503$	0.172731	−	1.64342i	0.00770168	−	0.0732766i	−0.989996	−	0.141096i	$-0.954937\pi$
$503$	0.172731	−	1.64342i	0.00770168	−	0.0732766i	0.997698	+	0.0678192i	$0.0216041\pi$
$504$	−11.2812	+	8.19624i	−0.502502	+	0.365089i
$505$	0.313585	+	2.98357i	0.0139544	+	0.132767i
$506$	6.37539	+	7.08058i	0.283420	+	0.314770i
$507$	−12.9544	+	5.76766i	−0.575324	+	0.256151i
$508$	5.58347	−	1.18680i	0.247726	−	0.0526558i
$509$	19.1685	+	4.07439i	0.849629	+	0.180594i	0.612094	−	0.790785i	$-0.290327\pi$
$509$	19.1685	+	4.07439i	0.849629	+	0.180594i	0.237535	+	0.971379i	$0.423661\pi$
$510$	−3.65418	−	1.62695i	−0.161810	−	0.0720424i
$511$	0.618034	+	1.90211i	0.0273402	+	0.0841445i
$512$	−5.78115	−	17.7926i	−0.255493	−	0.786327i
$513$	−11.2920	−	5.02754i	−0.498556	−	0.221971i
$514$	−9.63877	−	2.04878i	−0.425148	−	0.0903679i
$515$	−1.72539	+	0.366742i	−0.0760296	+	0.0161606i
$516$	5.91259	−	2.63245i	0.260287	−	0.115887i
$517$	−8.66141	−	9.61947i	−0.380928	−	0.423064i
$518$	0.547318	+	5.20738i	0.0240478	+	0.228799i
$519$	14.9443	−	10.8576i	0.655981	−	0.476598i
$520$	−0.288910	+	2.74879i	−0.0126695	+	0.120542i
$521$	−1.00000	−	1.73205i	−0.0438108	−	0.0758825i	0.843288	−	0.537461i	$-0.180617\pi$
$521$	−1.00000	−	1.73205i	−0.0438108	−	0.0758825i	−0.887099	+	0.461579i	$0.847283\pi$
$522$	−3.29180	+	5.70156i	−0.144078	+	0.249550i
$523$	3.47214	+	2.52265i	0.151826	+	0.110308i	0.661105	−	0.750294i	$-0.270088\pi$
$523$	3.47214	+	2.52265i	0.151826	+	0.110308i	−0.509279	+	0.860602i	$0.670088\pi$
$524$	−12.9921	+	14.4292i	−0.567563	+	0.630343i
$525$	6.47214	−	19.9192i	0.282467	−	0.869345i
$526$	11.5967			0.505642
$527$		0			0
$528$	4.58359			0.199475
$529$	11.2533	−	34.6341i	0.489273	−	1.50583i
$530$	0.631841	−	0.701731i	0.0274454	−	0.0304812i
$531$	−2.66312	−	1.93487i	−0.115570	−	0.0839662i
$532$	−7.66312	+	13.2729i	−0.332238	+	0.575454i
$533$	−4.32624	−	7.49326i	−0.187390	−	0.324569i
$534$	−0.136405	+	1.29780i	−0.00590280	+	0.0561614i
$535$	−8.28115	+	6.01661i	−0.358025	+	0.260121i
$536$	−1.86986	−	17.7905i	−0.0807657	−	0.768435i
$537$	−9.68375	−	10.7549i	−0.417885	−	0.464108i
$538$	16.3420	−	7.27593i	0.704554	−	0.313687i
$539$	−21.4102	+	4.55088i	−0.922204	+	0.196020i
$540$	−8.74882	−	1.85962i	−0.376489	−	0.0800252i
$541$	17.6869	+	7.87470i	0.760418	+	0.338560i	0.750045	−	0.661387i	$-0.230032\pi$
$541$	17.6869	+	7.87470i	0.760418	+	0.338560i	0.0103723	+	0.999946i	$0.496698\pi$
$542$	−1.56231	−	4.80828i	−0.0671068	−	0.206533i
$543$	6.94427	+	21.3723i	0.298007	+	0.917172i
$544$	−26.8732	−	11.9647i	−1.15218	−	0.512984i
$545$	−3.85808	−	0.820060i	−0.165262	−	0.0351275i
$546$	−3.91259	+	0.831647i	−0.167443	+	0.0355912i
$547$	25.6931	−	11.4393i	1.09856	−	0.489110i	0.224275	−	0.974526i	$-0.427999\pi$
$547$	25.6931	−	11.4393i	1.09856	−	0.489110i	0.874283	+	0.485416i	$0.161332\pi$
$548$	−21.3376	−	23.6978i	−0.911497	−	1.01232i
$549$	−2.18207	−	20.7610i	−0.0931286	−	0.886059i
$550$	−4.00000	+	2.90617i	−0.170561	+	0.123920i
$551$	−1.69131	+	16.0917i	−0.0720521	+	0.685530i
$552$	10.6525	+	18.4506i	0.453399	+	0.785311i
$553$	3.61803	−	6.26662i	0.153854	−	0.266484i
$554$	9.32624	+	6.77591i	0.396234	+	0.287881i
$555$	−1.65418	+	1.83716i	−0.0702161	+	0.0779829i
$556$	6.70820	−	20.6457i	0.284491	−	0.875574i
$557$	−12.0000			−0.508456			−0.254228	−	0.967144i	$-0.581821\pi$
$557$	−12.0000			−0.508456			−0.254228	+	0.967144i	$0.581821\pi$
$558$		0			0
$559$	−4.00000			−0.169182
$560$	−2.42705	+	7.46969i	−0.102562	+	0.315652i
$561$	8.66141	−	9.61947i	0.365685	−	0.406134i
$562$	8.50000	+	6.17561i	0.358551	+	0.260502i
$563$	19.7705	−	34.2435i	0.833228	−	1.44319i	−0.0622377	−	0.998061i	$-0.519824\pi$
$563$	19.7705	−	34.2435i	0.833228	−	1.44319i	0.895465	−	0.445131i	$-0.146843\pi$
$564$	−6.47214	−	11.2101i	−0.272526	−	0.472029i
$565$	0.571994	−	5.44216i	0.0240640	−	0.228953i
$566$	10.9443	−	7.95148i	0.460022	−	0.334226i
$567$	−1.06996	−	10.1800i	−0.0449341	−	0.427520i
$568$	19.7207	+	21.9021i	0.827463	+	0.918990i
$569$	13.2210	−	5.88635i	0.554251	−	0.246769i	−0.110445	−	0.993882i	$-0.535228\pi$
$569$	13.2210	−	5.88635i	0.554251	−	0.246769i	0.664696	+	0.747114i	$0.268561\pi$
$570$	1.67088	−	0.355156i	0.0699853	−	0.0148758i
$571$	−5.69249	−	1.20998i	−0.238223	−	0.0506359i	0.0872528	−	0.996186i	$-0.472191\pi$
$571$	−5.69249	−	1.20998i	−0.238223	−	0.0506359i	−0.325476	+	0.945550i	$0.605525\pi$
$572$	−3.65418	−	1.62695i	−0.152789	−	0.0680261i
$573$	1.21478	+	3.73871i	0.0507482	+	0.156187i
$574$	5.66312	+	17.4293i	0.236374	+	0.727484i
$575$	28.1672	+	12.5408i	1.17465	+	0.522989i
$576$	−0.339930	−	0.0722543i	−0.0141637	−	0.00301060i
$577$	−24.2902	+	5.16303i	−1.01121	+	0.214940i	−0.683588	−	0.729868i	$-0.739581\pi$
$577$	−24.2902	+	5.16303i	−1.01121	+	0.214940i	−0.327625	+	0.944808i	$0.606248\pi$
$578$	−5.88113	+	2.61845i	−0.244623	+	0.108913i
$579$	−4.52595	−	5.02658i	−0.188092	−	0.208898i
$580$	1.22384	+	11.6441i	0.0508172	+	0.483493i
$581$	10.0902	−	7.33094i	0.418611	−	0.304139i
$582$	0.155255	−	1.47715i	0.00643554	−	0.0612300i
$583$	1.52786	+	2.64634i	0.0632777	+	0.109600i
$584$	0.527864	−	0.914287i	0.0218432	−	0.0378335i
$585$	1.47214	+	1.06957i	0.0608653	+	0.0442213i
$586$	−3.50361	+	3.89116i	−0.144733	+	0.160742i
$587$	0.763932	−	2.35114i	0.0315308	−	0.0970420i	−0.934053	−	0.357136i	$-0.883753\pi$
$587$	0.763932	−	2.35114i	0.0315308	−	0.0970420i	0.965583	+	0.260094i	$0.0837534\pi$
$588$	−21.8885			−0.902668
$589$		0			0
$590$	1.38197			0.0568946
$591$	−5.88854	+	18.1231i	−0.242222	+	0.745484i
$592$	−2.48127	+	2.75573i	−0.101980	+	0.113260i
$593$	12.5172	+	9.09429i	0.514021	+	0.373458i	0.814347	−	0.580379i	$-0.197095\pi$
$593$	12.5172	+	9.09429i	0.514021	+	0.373458i	−0.300326	+	0.953837i	$0.597095\pi$
$594$	−3.41641	+	5.91739i	−0.140177	+	0.242794i
$595$	11.0902	+	19.2087i	0.454653	+	0.787481i
$596$	1.69131	−	16.0917i	0.0692786	−	0.659142i
$597$	1.05573	−	0.767031i	0.0432081	−	0.0313925i
$598$	−0.615520	−	5.85629i	−0.0251705	−	0.239481i
$599$	23.1497	+	25.7104i	0.945873	+	1.05050i	0.998653	+	0.0518921i	$0.0165252\pi$
$599$	23.1497	+	25.7104i	0.945873	+	1.05050i	−0.0527799	+	0.998606i	$0.516808\pi$
$600$	−10.0999	+	4.49677i	−0.412327	+	0.183580i
$601$	35.7425	−	7.59731i	1.45797	−	0.309901i	0.590356	−	0.807143i	$-0.298987\pi$
$601$	35.7425	−	7.59731i	1.45797	−	0.309901i	0.867612	+	0.497243i	$0.165654\pi$
$602$	8.28700	+	1.76146i	0.337753	+	0.0717916i
$603$	−10.7589	−	4.79017i	−0.438136	−	0.195071i
$604$	−4.09017	−	12.5882i	−0.166427	−	0.512209i
$605$	−2.16312	−	6.65740i	−0.0879433	−	0.270662i
$606$	2.09366	+	0.932157i	0.0850491	+	0.0378663i
$607$	−13.2322	−	2.81260i	−0.537080	−	0.114160i	−0.0686173	−	0.997643i	$-0.521859\pi$
$607$	−13.2322	−	2.81260i	−0.537080	−	0.114160i	−0.468463	+	0.883483i	$0.655192\pi$
$608$	12.2878	−	2.61185i	0.498336	−	0.105925i
$609$	−34.6129	+	15.4107i	−1.40259	+	0.624471i
$610$	5.86422	+	6.51287i	0.237435	+	0.263698i
$611$	0.836228	+	7.95618i	0.0338302	+	0.321872i
$612$	−10.0902	+	7.33094i	−0.407871	+	0.296336i
$613$	0.847878	−	8.06702i	0.0342455	−	0.325824i	−0.963965	−	0.266028i	$-0.914288\pi$
$613$	0.847878	−	8.06702i	0.0342455	−	0.325824i	0.998211	−	0.0597955i	$-0.0190448\pi$
$614$	−4.72542	−	8.18468i	−0.190703	−	0.330307i
$615$	−4.32624	+	7.49326i	−0.174451	+	0.302158i
$616$	15.3262	+	11.1352i	0.617512	+	0.448649i
$617$	15.7432	−	17.4846i	0.633798	−	0.703904i	−0.337619	−	0.941283i	$-0.609622\pi$
$617$	15.7432	−	17.4846i	0.633798	−	0.703904i	0.971417	+	0.237379i	$0.0762883\pi$
$618$	−0.416408	+	1.28157i	−0.0167504	+	0.0515524i
$619$	−16.1803			−0.650343			−0.325171	−	0.945655i	$-0.605422\pi$
$619$	−16.1803			−0.650343			−0.325171	+	0.945655i	$0.605422\pi$
$620$		0			0
$621$	42.6099			1.70988
$622$	1.30244	−	4.00850i	0.0522231	−	0.160726i
$623$	4.84187	−	5.37745i	0.193986	−	0.215443i
$624$	−2.29180	−	1.66509i	−0.0917453	−	0.0666568i
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$	6.56231	+	11.3662i	0.262282	+	0.454287i
$627$	−0.577819	+	5.49758i	−0.0230759	+	0.219552i
$628$	−19.4894	+	14.1598i	−0.777710	+	0.565039i
$629$	1.09464	+	10.4148i	0.0436460	+	0.415264i
$630$	−2.57890	−	2.86416i	−0.102746	−	0.114111i
$631$	−9.46495	+	4.21407i	−0.376794	+	0.167759i	−0.586390	−	0.810029i	$-0.699452\pi$
$631$	−9.46495	+	4.21407i	−0.376794	+	0.167759i	0.209597	+	0.977788i	$0.432785\pi$
$632$	−3.73619	+	0.794152i	−0.148618	+	0.0315897i
$633$	−0.991016	−	0.210647i	−0.0393893	−	0.00837246i
$634$	−12.3898	−	5.51629i	−0.492061	−	0.219080i
$635$	1.09017	+	3.35520i	0.0432621	+	0.133147i
$636$	0.944272	+	2.90617i	0.0374428	+	0.115237i
$637$	12.3583	+	5.50228i	0.489654	+	0.218008i
$638$	8.74882	+	1.85962i	0.346369	+	0.0736230i
$639$	18.9792	−	4.03416i	0.750807	−	0.159589i
$640$	10.3979	−	4.62946i	0.411015	−	0.182996i
$641$	8.02957	+	8.91774i	0.317149	+	0.352229i	0.880549	−	0.473954i	$-0.157174\pi$
$641$	8.02957	+	8.91774i	0.317149	+	0.352229i	−0.563401	+	0.826184i	$0.690507\pi$
$642$	0.817377	+	7.77682i	0.0322593	+	0.306927i
$643$	−23.0344	+	16.7355i	−0.908390	+	0.659984i	−0.940607	−	0.339497i	$-0.889743\pi$
$643$	−23.0344	+	16.7355i	−0.908390	+	0.659984i	0.0322174	+	0.999481i	$0.489743\pi$
$644$	5.52253	−	52.5434i	0.217618	−	2.07050i
$645$	2.00000	+	3.46410i	0.0787499	+	0.136399i
$646$	3.61803	−	6.26662i	0.142350	−	0.246557i
$647$	−13.7082	−	9.95959i	−0.538925	−	0.391552i	0.284761	−	0.958599i	$-0.408086\pi$
$647$	−13.7082	−	9.95959i	−0.538925	−	0.391552i	−0.823686	+	0.567047i	$0.808086\pi$
$648$	−3.61548	+	4.01540i	−0.142030	+	0.157740i
$649$	−1.38197	+	4.25325i	−0.0542469	+	0.166955i
$650$	3.05573			0.119856
$651$		0			0
$652$	4.38197			0.171611
$653$	4.72949	−	14.5559i	0.185079	−	0.569615i	−0.814870	−	0.579643i	$-0.803192\pi$
$653$	4.72949	−	14.5559i	0.185079	−	0.569615i	0.999950	+	0.0100277i	$0.00319198\pi$
$654$	−2.01619	+	2.23921i	−0.0788394	+	0.0875601i
$655$	−9.70820	−	7.05342i	−0.379331	−	0.275600i
$656$	−6.48936	+	11.2399i	−0.253367	+	0.438844i
$657$	−0.347524	−	0.601929i	−0.0135582	−	0.0234835i
$658$	1.77116	−	16.8514i	0.0690470	−	0.656938i
$659$	4.57295	−	3.32244i	0.178137	−	0.129424i	−0.495144	−	0.868811i	$-0.664885\pi$
$659$	4.57295	−	3.32244i	0.178137	−	0.129424i	0.673281	+	0.739387i	$0.264885\pi$
$660$	0.418114	+	3.97809i	0.0162751	+	0.154847i
$661$	−30.3522	−	33.7096i	−1.18056	−	1.31115i	−0.940262	−	0.340452i	$-0.889420\pi$
$661$	−30.3522	−	33.7096i	−1.18056	−	1.31115i	−0.240302	−	0.970698i	$-0.577247\pi$
$662$	−1.12920	+	0.502754i	−0.0438878	+	0.0195401i
$663$	−7.82518	+	1.66329i	−0.303905	+	0.0645970i
$664$	−6.43972	−	1.36881i	−0.249910	−	0.0531200i
$665$	−8.65323	−	3.85266i	−0.335558	−	0.149400i
$666$	−0.562306	−	1.73060i	−0.0217889	−	0.0670594i
$667$	−17.2361	−	53.0472i	−0.667383	−	2.05399i
$668$	−3.65418	−	1.62695i	−0.141385	−	0.0629485i
$669$	−4.83623	−	1.02797i	−0.186979	−	0.0397437i
$670$	4.83623	−	1.02797i	0.186840	−	0.0397140i
$671$	−25.9088	+	11.5353i	−1.00020	+	0.445316i
$672$	19.6834	+	21.8607i	0.759304	+	0.843293i
$673$	−4.91421	−	46.7556i	−0.189429	−	1.80230i	−0.515435	−	0.856929i	$-0.672370\pi$
$673$	−4.91421	−	46.7556i	−0.189429	−	1.80230i	0.326006	−	0.945368i	$-0.394297\pi$
$674$	−9.61803	+	6.98791i	−0.370473	+	0.269164i
$675$	−2.31128	+	21.9903i	−0.0889611	+	0.846408i
$676$	−9.28115	−	16.0754i	−0.356967	−	0.618286i
$677$	−21.3607	+	36.9978i	−0.820958	+	1.42194i	0.0840123	+	0.996465i	$0.473226\pi$
$677$	−21.3607	+	36.9978i	−0.820958	+	1.42194i	−0.904970	+	0.425476i	$0.860107\pi$
$678$	−3.38197	−	2.45714i	−0.129884	−	0.0943660i
$679$	−5.51101	+	6.12059i	−0.211493	+	0.234887i
$680$	3.61803	−	11.1352i	0.138745	−	0.427014i
$681$	3.05573			0.117096
$682$		0			0
$683$	−17.1803			−0.657387			−0.328694	−	0.944437i	$-0.606608\pi$
$683$	−17.1803			−0.657387			−0.328694	+	0.944437i	$0.606608\pi$
$684$	1.64590	−	5.06555i	0.0629325	−	0.193686i
$685$	13.1874	−	14.6460i	0.503863	−	0.559597i
$686$	−8.35410	−	6.06961i	−0.318961	−	0.231739i
$687$	−8.29180	+	14.3618i	−0.316352	+	0.547937i
$688$	3.00000	+	5.19615i	0.114374	+	0.198101i
$689$	0.197407	−	1.87820i	0.00752059	−	0.0715537i
$690$	−4.76393	+	3.46120i	−0.181360	+	0.131766i
$691$	2.00489	+	19.0753i	0.0762697	+	0.725657i	0.964110	+	0.265505i	$0.0855386\pi$
$691$	2.00489	+	19.0753i	0.0762697	+	0.725657i	−0.887840	+	0.460153i	$0.847795\pi$
$692$	16.1798	+	17.9695i	0.615064	+	0.683098i
$693$	11.3939	−	5.07287i	0.432817	−	0.192703i
$694$	1.10004	−	0.233820i	0.0417568	−	0.00887568i
$695$	13.1232	+	2.78943i	0.497792	+	0.105809i
$696$	18.2709	+	8.13473i	0.692557	+	0.308346i
$697$	11.3262	+	34.8586i	0.429012	+	1.32036i
$698$	−5.32624	−	16.3925i	−0.201601	−	0.620464i
$699$	0.0629284	+	0.0280175i	0.00238017	+	0.00105972i
$700$	26.8173	+	5.70019i	1.01360	+	0.215447i
$701$	−6.84703	+	1.45538i	−0.258609	+	0.0549690i	−0.335391	−	0.942079i	$-0.608869\pi$
$701$	−6.84703	+	1.45538i	−0.258609	+	0.0549690i	0.0767826	+	0.997048i	$0.475535\pi$
$702$	3.85782	−	1.71761i	0.145604	−	0.0648271i
$703$	−2.99244	−	3.32344i	−0.112862	−	0.125346i
$704$	0.0493516	+	0.469550i	0.00186001	+	0.0176968i
$705$	6.47214	−	4.70228i	0.243755	−	0.177098i
$706$	−1.25434	+	11.9343i	−0.0472078	+	0.449152i
$707$	−6.35410	−	11.0056i	−0.238971	−	0.413909i
$708$	−2.23607	+	3.87298i	−0.0840366	+	0.145556i
$709$	−27.8885	−	20.2622i	−1.04738	−	0.760963i	−0.0756645	−	0.997133i	$-0.524108\pi$
$709$	−27.8885	−	20.2622i	−1.04738	−	0.760963i	−0.971712	+	0.236170i	$0.924108\pi$
$710$	−5.45067	+	6.05358i	−0.204560	+	0.227187i
$711$	−0.777088	+	2.39163i	−0.0291431	+	0.0896931i
$712$	−3.81966			−0.143148
$713$		0			0
$714$	16.9443			0.634123
$715$	0.763932	−	2.35114i	0.0285694	−	0.0879277i
$716$	12.6762	−	14.0783i	0.473732	−	0.526132i
$717$	−1.70820	−	1.24108i	−0.0637940	−	0.0463491i
$718$	5.48936	−	9.50785i	0.204861	−	0.354830i
$719$	18.0902	+	31.3331i	0.674649	+	1.16853i	0.976571	+	0.215194i	$0.0690385\pi$
$719$	18.0902	+	31.3331i	0.674649	+	1.16853i	−0.301922	+	0.953333i	$0.597628\pi$
$720$	0.285309	−	2.71454i	0.0106329	−	0.101165i
$721$	6.04508	−	4.39201i	0.225131	−	0.163567i
$722$	−0.904430	−	8.60508i	−0.0336594	−	0.320248i
$723$	−25.1110	−	27.8886i	−0.933890	−	1.03719i
$724$	−26.8732	+	11.9647i	−0.998736	+	0.444666i
$725$	28.3118	−	6.01785i	1.05147	−	0.223497i
$726$	−5.23067	−	1.11181i	−0.194128	−	0.0412632i
$727$	−36.3262	−	16.1734i	−1.34726	−	0.599840i	−0.398890	−	0.916999i	$-0.630605\pi$
$727$	−36.3262	−	16.1734i	−1.34726	−	0.599840i	−0.948372	+	0.317159i	$0.897271\pi$
$728$	−3.61803	−	11.1352i	−0.134093	−	0.412697i
$729$	7.43363	+	22.8784i	0.275320	+	0.847347i
$730$	0.266569	+	0.118684i	0.00986616	+	0.00439270i
$731$	16.5740	+	3.52291i	0.613011	+	0.130300i
$732$	−27.7409	+	5.89652i	−1.02533	+	0.217942i
$733$	−4.99904	+	2.22572i	−0.184644	+	0.0822088i	−0.496976	−	0.867764i	$-0.665556\pi$
$733$	−4.99904	+	2.22572i	−0.184644	+	0.0822088i	0.312332	+	0.949973i	$0.398890\pi$
$734$	−7.44382	−	8.26720i	−0.274756	−	0.305148i
$735$	−1.41405	−	13.4538i	−0.0521579	−	0.496249i
$736$	−35.0344	+	25.4540i	−1.29139	+	0.938247i
$737$	−1.67246	+	15.9124i	−0.0616057	+	0.586139i
$738$	−3.18441	−	5.51555i	−0.117220	−	0.203030i
$739$	8.09017	−	14.0126i	0.297602	−	0.515461i	−0.677985	−	0.735076i	$-0.737147\pi$
$739$	8.09017	−	14.0126i	0.297602	−	0.515461i	0.975587	+	0.219614i	$0.0704799\pi$
$740$	−2.61803	−	1.90211i	−0.0962408	−	0.0699231i
$741$	2.28602	−	2.53889i	0.0839792	−	0.0932683i
$742$	−1.23607	+	3.80423i	−0.0453775	+	0.139658i
$743$	27.8197			1.02060			0.510302	−	0.859995i	$-0.329534\pi$
$743$	27.8197			1.02060			0.510302	+	0.859995i	$0.329534\pi$
$744$		0			0
$745$	10.0000			0.366372
$746$	−3.62868	+	11.1679i	−0.132855	+	0.408887i
$747$	−2.90026	+	3.22106i	−0.106115	+	0.117853i
$748$	13.7082	+	9.95959i	0.501222	+	0.364159i
$749$	21.6803	−	37.5515i	0.792182	−	1.37210i
$750$	−3.43769	−	5.95426i	−0.125527	−	0.217419i
$751$	−4.76033	+	45.2915i	−0.173707	+	1.65271i	0.466509	+	0.884517i	$0.345512\pi$
$751$	−4.76033	+	45.2915i	−0.173707	+	1.65271i	−0.640216	+	0.768195i	$0.721155\pi$
$752$	9.70820	−	7.05342i	0.354022	−	0.257212i
$753$	3.12420	+	29.7248i	0.113852	+	1.08323i
$754$	−3.69886	−	4.10800i	−0.134705	−	0.149605i
$755$	7.47311	−	3.32724i	0.271974	−	0.121091i
$756$	37.0606	−	7.87747i	1.34788	−	0.286501i
$757$	22.1575	+	4.70971i	0.805327	+	0.171177i	0.592141	−	0.805834i	$-0.298283\pi$
$757$	22.1575	+	4.70971i	0.805327	+	0.171177i	0.213186	+	0.977012i	$0.431616\pi$
$758$	21.3920	+	9.52431i	0.776991	+	0.345939i
$759$	−5.88854	−	18.1231i	−0.213741	−	0.657826i
$760$	1.54508	+	4.75528i	0.0560461	+	0.172492i
$761$	1.82709	+	0.813473i	0.0662320	+	0.0294884i	0.439585	−	0.898201i	$-0.355125\pi$
$761$	1.82709	+	0.813473i	0.0662320	+	0.0294884i	−0.373353	+	0.927689i	$0.621792\pi$
$762$	2.63616	+	0.560332i	0.0954978	+	0.0202987i
$763$	16.3431	−	3.47383i	0.591660	−	0.125761i
$764$	−4.70101	+	2.09303i	−0.170077	+	0.0757230i
$765$	−5.15780	−	5.72831i	−0.186480	−	0.207108i
$766$	0.768025	+	7.30727i	0.0277499	+	0.264023i

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+(-0.190983 + 0.587785i) q^{2} +(0.827091 - 0.918578i) q^{3} +(1.30902 + 0.951057i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.381966 + 0.661585i) q^{6} +(0.442790 - 4.21286i) q^{7} +(-1.80902 + 1.31433i) q^{8} +(0.153880 + 1.46407i) q^{9} +(-0.413545 - 0.459289i) q^{10} +(1.82709 - 0.813473i) q^{11} +(1.95630 - 0.415823i) q^{12} +(-1.20906 - 0.256993i) q^{13} +(2.39169 + 1.06485i) q^{14} +(0.381966 + 1.17557i) q^{15} +(0.572949 + 1.76336i) q^{16} +(4.78339 + 2.12970i) q^{17} +(-0.889948 - 0.189164i) q^{18} +(-2.18720 + 0.464905i) q^{19} +(-1.47815 + 0.658114i) q^{20} +(-3.50361 - 3.89116i) q^{21} +(0.129204 + 1.22930i) q^{22} +(6.23607 - 4.53077i) q^{23} +(-0.288910 + 2.74879i) q^{24} +(2.00000 + 3.46410i) q^{25} +(0.381966 - 0.661585i) q^{26} +(4.47214 + 3.24920i) q^{27} +(4.58629 - 5.09359i) q^{28} +(2.23607 - 6.88191i) q^{29} -0.763932 q^{30} -5.61803 q^{32} +(0.763932 - 2.35114i) q^{33} +(-2.16535 + 2.40487i) q^{34} +(3.42705 + 2.48990i) q^{35} +(-1.19098 + 2.06284i) q^{36} +(1.00000 + 1.73205i) q^{37} +(0.144455 - 1.37440i) q^{38} +(-1.23607 + 0.898056i) q^{39} +(-0.233733 - 2.22382i) q^{40} +(4.68391 + 5.20201i) q^{41} +(2.95630 - 1.31623i) q^{42} +(3.16535 - 0.672816i) q^{43} +(3.16535 + 0.672816i) q^{44} +(-1.34486 - 0.598772i) q^{45} +(1.47214 + 4.53077i) q^{46} +(-2.00000 - 6.15537i) q^{47} +(2.09366 + 0.932157i) q^{48} +(-10.7051 - 2.27544i) q^{49} +(-2.41811 + 0.513986i) q^{50} +(5.91259 - 2.63245i) q^{51} +(-1.33826 - 1.48629i) q^{52} +(0.159705 + 1.51949i) q^{53} +(-2.76393 + 2.00811i) q^{54} +(-0.209057 + 1.98904i) q^{55} +(4.73607 + 8.20311i) q^{56} +(-1.38197 + 2.39364i) q^{57} +(3.61803 + 2.62866i) q^{58} +(-1.49622 + 1.66172i) q^{59} +(-0.618034 + 1.90211i) q^{60} -14.1803 q^{61} +6.23607 q^{63} +(-0.0729490 + 0.224514i) q^{64} +(0.827091 - 0.918578i) q^{65} +(1.23607 + 0.898056i) q^{66} +(-4.00000 + 6.92820i) q^{67} +(4.23607 + 7.33708i) q^{68} +(0.995933 - 9.47567i) q^{69} +(-2.11803 + 1.53884i) q^{70} +(-1.37772 - 13.1081i) q^{71} +(-2.20264 - 2.44628i) q^{72} +(-0.431318 + 0.192035i) q^{73} +(-1.20906 + 0.256993i) q^{74} +(4.83623 + 1.02797i) q^{75} +(-3.30524 - 1.47159i) q^{76} +(-2.61803 - 8.05748i) q^{77} +(-0.291796 - 0.898056i) q^{78} +(1.56052 + 0.694789i) q^{79} +(-1.81359 - 0.385489i) q^{80} +(2.36360 - 0.502399i) q^{81} +(-3.95222 + 1.75964i) q^{82} +(1.97010 + 2.18802i) q^{83} +(-0.885579 - 8.42572i) q^{84} +(-4.23607 + 3.07768i) q^{85} +(-0.209057 + 1.98904i) q^{86} +(-4.47214 - 7.74597i) q^{87} +(-2.23607 + 3.87298i) q^{88} +(1.38197 + 1.00406i) q^{89} +(0.608795 - 0.676135i) q^{90} +(-1.61803 + 4.97980i) q^{91} +12.4721 q^{92} +4.00000 q^{94} +(0.690983 - 2.12663i) q^{95} +(-4.64662 + 5.16060i) q^{96} +(-1.57295 - 1.14281i) q^{97} +(3.38197 - 5.85774i) q^{98} +(1.47214 + 2.54981i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{2} - 6 q^{3} + 6 q^{4} - 4 q^{5} + 12 q^{6} - 7 q^{7} - 10 q^{8} - 7 q^{9} + 3 q^{10} + 2 q^{11} - 2 q^{12} - 6 q^{13} + 4 q^{14} + 12 q^{15} + 18 q^{16} + 8 q^{17} + 19 q^{18} - 5 q^{19} - 3 q^{20}+ \cdots - 24 q^{99}+O(q^{100}) \) 8 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 - 4 * q^5 + 12 * q^6 - 7 * q^7 - 10 * q^8 - 7 * q^9 + 3 * q^10 + 2 * q^11 - 2 * q^12 - 6 * q^13 + 4 * q^14 + 12 * q^15 + 18 * q^16 + 8 * q^17 + 19 * q^18 - 5 * q^19 - 3 * q^20 + 2 * q^21 - 4 * q^22 + 32 * q^23 + 16 * q^25 + 12 * q^26 - 4 * q^28 - 24 * q^30 - 36 * q^32 + 24 * q^33 + 4 * q^34 + 14 * q^35 - 14 * q^36 + 8 * q^37 + 8 * q^39 + 5 * q^40 + 7 * q^41 + 6 * q^42 + 4 * q^43 + 4 * q^44 - 7 * q^45 - 24 * q^46 - 16 * q^47 - 6 * q^48 - 18 * q^49 - 12 * q^50 + 12 * q^51 - 2 * q^52 + 4 * q^53 - 40 * q^54 + 2 * q^55 + 20 * q^56 - 20 * q^57 + 20 * q^58 + 5 * q^59 + 4 * q^60 - 24 * q^61 + 32 * q^63 - 14 * q^64 - 6 * q^65 - 8 * q^66 - 32 * q^67 + 16 * q^68 - 4 * q^69 - 8 * q^70 + 27 * q^71 - 25 * q^72 - 6 * q^73 - 6 * q^74 + 24 * q^75 - 5 * q^76 - 12 * q^77 - 56 * q^78 + 10 * q^79 - 9 * q^80 + 41 * q^81 - 14 * q^82 - 26 * q^83 + 14 * q^84 - 16 * q^85 + 2 * q^86 + 20 * q^89 + 19 * q^90 - 4 * q^91 + 64 * q^92 + 32 * q^94 + 10 * q^95 + 22 * q^96 - 26 * q^97 + 36 * q^98 - 24 * q^99

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