LMFDB - Embedded newform 961.2.g.a.846.1

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			846.1
Root			$0.913545 - 0.406737i$ of defining polynomial
Character	$\chi$	$=$	961.846
Dual form			961.2.g.a.844.1

$q$-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} +(-1.20906 - 0.256993i) q^{3} +(1.30902 + 0.951057i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.381966 - 0.661585i) q^{6} +(-3.86984 + 1.72296i) q^{7} +(-1.80902 + 1.31433i) q^{8} +(-1.34486 - 0.598772i) q^{9} +(0.604528 - 0.128496i) q^{10} +(-0.209057 + 1.98904i) q^{11} +(-1.33826 - 1.48629i) q^{12} +(0.827091 - 0.918578i) q^{13} +(-0.273659 - 2.60369i) q^{14} +(0.381966 + 1.17557i) q^{15} +(0.572949 + 1.76336i) q^{16} +(-0.547318 - 5.20738i) q^{17} +(0.608795 - 0.676135i) q^{18} +(1.49622 + 1.66172i) q^{19} +(0.169131 - 1.60917i) q^{20} +(5.12165 - 1.08864i) q^{21} +(-1.12920 - 0.502754i) q^{22} +(6.23607 - 4.53077i) q^{23} +(2.52498 - 1.12419i) q^{24} +(2.00000 - 3.46410i) q^{25} +(0.381966 + 0.661585i) q^{26} +(4.47214 + 3.24920i) q^{27} +(-6.70432 - 1.42505i) q^{28} +(2.23607 - 6.88191i) q^{29} -0.763932 q^{30} -5.61803 q^{32} +(0.763932 - 2.35114i) q^{33} +(3.16535 + 0.672816i) q^{34} +(3.42705 + 2.48990i) q^{35} +(-1.19098 - 2.06284i) q^{36} +(1.00000 - 1.73205i) q^{37} +(-1.26249 + 0.562096i) q^{38} +(-1.23607 + 0.898056i) q^{39} +(2.04275 + 0.909491i) q^{40} +(-6.84703 + 1.45538i) q^{41} +(-0.338261 + 3.21834i) q^{42} +(-2.16535 - 2.40487i) q^{43} +(-2.16535 + 2.40487i) q^{44} +(0.153880 + 1.46407i) q^{45} +(1.47214 + 4.53077i) q^{46} +(-2.00000 - 6.15537i) q^{47} +(-0.239558 - 2.27924i) q^{48} +(7.32315 - 8.13318i) q^{49} +(1.65418 + 1.83716i) q^{50} +(-0.676522 + 6.43668i) q^{51} +(1.95630 - 0.415823i) q^{52} +(-1.39577 - 0.621438i) q^{53} +(-2.76393 + 2.00811i) q^{54} +(1.82709 - 0.813473i) q^{55} +(4.73607 - 8.20311i) q^{56} +(-1.38197 - 2.39364i) q^{57} +(3.61803 + 2.62866i) q^{58} +(2.18720 + 0.464905i) q^{59} +(-0.618034 + 1.90211i) q^{60} -14.1803 q^{61} +6.23607 q^{63} +(-0.0729490 + 0.224514i) q^{64} +(-1.20906 - 0.256993i) q^{65} +(1.23607 + 0.898056i) q^{66} +(-4.00000 - 6.92820i) q^{67} +(4.23607 - 7.33708i) q^{68} +(-8.70414 + 3.87533i) q^{69} +(-2.11803 + 1.53884i) q^{70} +(12.0408 + 5.36093i) q^{71} +(3.21986 - 0.684403i) q^{72} +(0.0493516 - 0.469550i) q^{73} +(0.827091 + 0.918578i) q^{74} +(-3.30836 + 3.67431i) q^{75} +(0.378188 + 3.59821i) q^{76} +(-2.61803 - 8.05748i) q^{77} +(-0.291796 - 0.898056i) q^{78} +(-0.178556 - 1.69885i) q^{79} +(1.24064 - 1.37787i) q^{80} +(-1.61689 - 1.79574i) q^{81} +(0.452215 - 4.30254i) q^{82} +(-2.87993 + 0.612149i) q^{83} +(7.73968 + 3.44593i) q^{84} +(-4.23607 + 3.07768i) q^{85} +(1.82709 - 0.813473i) q^{86} +(-4.47214 + 7.74597i) q^{87} +(-2.23607 - 3.87298i) q^{88} +(1.38197 + 1.00406i) q^{89} +(-0.889948 - 0.189164i) q^{90} +(-1.61803 + 4.97980i) q^{91} +12.4721 q^{92} +4.00000 q^{94} +(0.690983 - 2.12663i) q^{95} +(6.79252 + 1.44380i) 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 $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{15}\right)$

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	$0.170119\pi$
$3$	−1.20906	−	0.256993i	−0.698049	−	0.148375i	−0.154799	−	0.987946i	$-0.549473\pi$
$3$	−1.20906	−	0.256993i	−0.698049	−	0.148375i	−0.543250	+	0.839571i	$0.682806\pi$
$4$	1.30902	+	0.951057i	0.654508	+	0.475528i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	0.732294	−	0.680989i	$-0.238450\pi$
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	−0.955901	+	0.293691i	$0.905116\pi$
$6$	0.381966	−	0.661585i	0.155937	−	0.270091i
$7$	−3.86984	+	1.72296i	−1.46266	+	0.651219i	−0.975079	−	0.221857i	$-0.928788\pi$
$7$	−3.86984	+	1.72296i	−1.46266	+	0.651219i	−0.487583	+	0.873077i	$0.662121\pi$
$8$	−1.80902	+	1.31433i	−0.639584	+	0.464685i
$9$	−1.34486	−	0.598772i	−0.448288	−	0.199591i
$10$	0.604528	−	0.128496i	0.191169	−	0.0406342i
$11$	−0.209057	+	1.98904i	−0.0630330	+	0.599719i	0.916723	+	0.399524i	$0.130824\pi$
$11$	−0.209057	+	1.98904i	−0.0630330	+	0.599719i	−0.979756	+	0.200196i	$0.935842\pi$
$12$	−1.33826	−	1.48629i	−0.386323	−	0.429055i
$13$	0.827091	−	0.918578i	0.229394	−	0.254768i	−0.617449	−	0.786611i	$-0.711834\pi$
$13$	0.827091	−	0.918578i	0.229394	−	0.254768i	0.846843	+	0.531843i	$0.178500\pi$
$14$	−0.273659	−	2.60369i	−0.0731385	−	0.695866i
$15$	0.381966	+	1.17557i	0.0986232	+	0.303531i
$16$	0.572949	+	1.76336i	0.143237	+	0.440839i
$17$	−0.547318	−	5.20738i	−0.132744	−	1.26298i	−0.834680	−	0.550736i	$-0.814347\pi$
$17$	−0.547318	−	5.20738i	−0.132744	−	1.26298i	0.701936	−	0.712240i	$-0.252319\pi$
$18$	0.608795	−	0.676135i	0.143494	−	0.159367i
$19$	1.49622	+	1.66172i	0.343257	+	0.381225i	0.889912	−	0.456133i	$-0.150766\pi$
$19$	1.49622	+	1.66172i	0.343257	+	0.381225i	−0.546655	+	0.837358i	$0.684099\pi$
$20$	0.169131	−	1.60917i	0.0378188	−	0.359821i
$21$	5.12165	−	1.08864i	1.11764	−	0.237561i
$22$	−1.12920	−	0.502754i	−0.240747	−	0.107188i
$23$	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	$0.00289604\pi$
$24$	2.52498	−	1.12419i	0.515409	−	0.229475i
$25$	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
$28$	−6.70432	−	1.42505i	−1.26700	−	0.269309i
$29$	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
$34$	3.16535	+	0.672816i	0.542853	+	0.115387i
$35$	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	−0.772043	−	0.635571i	$-0.780765\pi$
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	0.936442	+	0.350823i	$0.114098\pi$
$38$	−1.26249	+	0.562096i	−0.204803	+	0.0911840i
$39$	−1.23607	+	0.898056i	−0.197929	+	0.143804i
$40$	2.04275	+	0.909491i	0.322987	+	0.143803i
$41$	−6.84703	+	1.45538i	−1.06933	+	0.227292i	−0.708766	−	0.705443i	$-0.750748\pi$
$41$	−6.84703	+	1.45538i	−1.06933	+	0.227292i	−0.360561	+	0.932736i	$0.617415\pi$
$42$	−0.338261	+	3.21834i	−0.0521948	+	0.496601i
$43$	−2.16535	−	2.40487i	−0.330213	−	0.366739i	0.555060	−	0.831810i	$-0.312695\pi$
$43$	−2.16535	−	2.40487i	−0.330213	−	0.366739i	−0.885273	+	0.465071i	$0.846029\pi$
$44$	−2.16535	+	2.40487i	−0.326439	+	0.362547i
$45$	0.153880	+	1.46407i	0.0229391	+	0.218251i
$46$	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	$-0.256478\pi$
$48$	−0.239558	−	2.27924i	−0.0345772	−	0.328980i
$49$	7.32315	−	8.13318i	1.04616	−	1.16188i
$50$	1.65418	+	1.83716i	0.233937	+	0.259813i
$51$	−0.676522	+	6.43668i	−0.0947321	+	0.901316i
$52$	1.95630	−	0.415823i	0.271289	−	0.0576643i
$53$	−1.39577	−	0.621438i	−0.191724	−	0.0853611i	0.308629	−	0.951182i	$-0.400130\pi$
$53$	−1.39577	−	0.621438i	−0.191724	−	0.0853611i	−0.500353	+	0.865821i	$0.666797\pi$
$54$	−2.76393	+	2.00811i	−0.376124	+	0.273270i
$55$	1.82709	−	0.813473i	0.246365	−	0.109689i
$56$	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
$59$	2.18720	+	0.464905i	0.284750	+	0.0605254i	0.348072	−	0.937468i	$-0.386836\pi$
$59$	2.18720	+	0.464905i	0.284750	+	0.0605254i	−0.0633226	+	0.997993i	$0.520170\pi$
$60$	−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
$65$	−1.20906	−	0.256993i	−0.149965	−	0.0318761i
$66$	1.23607	+	0.898056i	0.152149	+	0.110543i
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	0.511237	−	0.859440i	$-0.329187\pi$
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	−0.999915	+	0.0130248i	$0.995854\pi$
$68$	4.23607	−	7.33708i	0.513699	−	0.889752i
$69$	−8.70414	+	3.87533i	−1.04785	+	0.466535i
$70$	−2.11803	+	1.53884i	−0.253153	+	0.183927i
$71$	12.0408	+	5.36093i	1.42898	+	0.636225i	0.967947	−	0.251155i	$-0.0808105\pi$
$71$	12.0408	+	5.36093i	1.42898	+	0.636225i	0.461038	+	0.887380i	$0.347477\pi$
$72$	3.21986	−	0.684403i	0.379464	−	0.0806577i
$73$	0.0493516	−	0.469550i	0.00577617	−	0.0549566i	−0.991254	−	0.131967i	$-0.957871\pi$
$73$	0.0493516	−	0.469550i	0.00577617	−	0.0549566i	0.997030	+	0.0770102i	$0.0245374\pi$
$74$	0.827091	+	0.918578i	0.0961474	+	0.106782i
$75$	−3.30836	+	3.67431i	−0.382017	+	0.424273i
$76$	0.378188	+	3.59821i	0.0433811	+	0.412743i
$77$	−2.61803	−	8.05748i	−0.298353	−	0.918235i
$78$	−0.291796	−	0.898056i	−0.0330394	−	0.101685i
$79$	−0.178556	−	1.69885i	−0.0200891	−	0.191135i	0.979875	−	0.199612i	$-0.0639683\pi$
$79$	−0.178556	−	1.69885i	−0.0200891	−	0.191135i	−0.999964	+	0.00847717i	$0.997302\pi$
$80$	1.24064	−	1.37787i	0.138707	−	0.154050i
$81$	−1.61689	−	1.79574i	−0.179655	−	0.199527i
$82$	0.452215	−	4.30254i	0.0499388	−	0.475136i
$83$	−2.87993	+	0.612149i	−0.316114	+	0.0671920i	−0.363236	−	0.931697i	$-0.618328\pi$
$83$	−2.87993	+	0.612149i	−0.316114	+	0.0671920i	0.0471226	+	0.998889i	$0.484995\pi$
$84$	7.73968	+	3.44593i	0.844468	+	0.375982i
$85$	−4.23607	+	3.07768i	−0.459466	+	0.333822i
$86$	1.82709	−	0.813473i	0.197020	−	0.0877191i
$87$	−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	$0.671142\pi$
$90$	−0.889948	−	0.189164i	−0.0938088	−	0.0199397i
$91$	−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
$96$	6.79252	+	1.44380i	0.693259	+	0.147357i
$97$	−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
$100$	5.91259	−	2.63245i	0.591259	−	0.263245i
$101$	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	$0.252312\pi$
$102$	−3.65418	−	1.62695i	−0.361818	−	0.161092i
$103$	−1.72539	+	0.366742i	−0.170007	+	0.0361362i	−0.292129	−	0.956379i	$-0.594364\pi$
$103$	−1.72539	+	0.366742i	−0.170007	+	0.0361362i	0.122121	+	0.992515i	$0.461030\pi$
$104$	−0.288910	+	2.74879i	−0.0283299	+	0.269541i
$105$	−3.50361	−	3.89116i	−0.341918	−	0.379738i
$106$	0.631841	−	0.701731i	0.0613698	−	0.0681581i
$107$	−1.06996	−	10.1800i	−0.103437	−	0.984137i	−0.915977	−	0.401231i	$-0.868582\pi$
$107$	−1.06996	−	10.1800i	−0.103437	−	0.984137i	0.812540	−	0.582906i	$-0.198084\pi$
$108$	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	$0.839509\pi$
$110$	0.129204	+	1.22930i	0.0123191	+	0.117209i
$111$	−1.65418	+	1.83716i	−0.157008	+	0.174375i
$112$	−5.25542	−	5.83674i	−0.496591	−	0.551520i
$113$	0.571994	−	5.44216i	0.0538087	−	0.511955i	−0.934110	−	0.356984i	$-0.883805\pi$
$113$	0.571994	−	5.44216i	0.0538087	−	0.511955i	0.987919	−	0.154971i	$-0.0495284\pi$
$114$	1.67088	−	0.355156i	0.156492	−	0.0332634i
$115$	−7.04179	−	3.13521i	−0.656651	−	0.292360i
$116$	9.47214	−	6.88191i	0.879466	−	0.638969i
$117$	−1.66234	+	0.740122i	−0.153684	+	0.0684243i
$118$	−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
$121$	6.84703	+	1.45538i	0.622458	+	0.132307i
$122$	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
$127$	−3.45077	−	0.733484i	−0.306206	−	0.0650862i	0.0522458	−	0.998634i	$-0.483362\pi$
$127$	−3.45077	−	0.733484i	−0.306206	−	0.0650862i	−0.358452	+	0.933548i	$0.616695\pi$
$128$	−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
$131$	10.9625	−	4.88084i	0.957802	−	0.426441i	0.132532	−	0.991179i	$-0.457689\pi$
$131$	10.9625	−	4.88084i	0.957802	−	0.426441i	0.825270	+	0.564738i	$0.191023\pi$
$132$	3.23607	−	2.35114i	0.281664	−	0.204641i
$133$	−8.65323	−	3.85266i	−0.750330	−	0.334068i
$134$	4.83623	−	1.02797i	0.417786	−	0.0888032i
$135$	0.577819	−	5.49758i	0.0497308	−	0.473157i
$136$	7.83432	+	8.70089i	0.671787	+	0.746095i
$137$	13.1874	−	14.6460i	1.12667	−	1.25130i	0.162302	−	0.986741i	$-0.448108\pi$
$137$	13.1874	−	14.6460i	1.12667	−	1.25130i	0.964371	−	0.264555i	$-0.0852252\pi$
$138$	−0.615520	−	5.85629i	−0.0523966	−	0.498520i
$139$	−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
$141$	0.836228	+	7.95618i	0.0704231	+	0.670031i
$142$	−5.45067	+	6.05358i	−0.457410	+	0.508005i
$143$	1.65418	+	1.83716i	0.138330	+	0.153631i
$144$	0.285309	−	2.71454i	0.0237758	−	0.226211i
$145$	−7.07794	+	1.50446i	−0.587791	+	0.124939i
$146$	0.266569	+	0.118684i	0.0220614	+	0.00982237i
$147$	−10.9443	+	7.95148i	−0.902668	+	0.655827i
$148$	2.95630	−	1.31623i	0.243006	−	0.108193i
$149$	−5.00000	+	8.66025i	−0.409616	+	0.709476i	−0.994847	−	0.101391i	$-0.967671\pi$
$149$	−5.00000	+	8.66025i	−0.409616	+	0.709476i	0.585231	+	0.810867i	$0.301004\pi$
$150$	−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	$0.808011\pi$
$152$	−4.89074	−	1.03956i	−0.396691	−	0.0843193i
$153$	−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	$0.897501\pi$
$158$	1.03266	+	0.219498i	0.0821539	+	0.0174623i
$159$	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
$162$	1.36431	−	0.607430i	0.107190	−	0.0477242i
$163$	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	$0.266176\pi$
$164$	−10.3470	−	4.60680i	−0.807968	−	0.359730i
$165$	−2.41811	+	0.513986i	−0.188250	+	0.0400138i
$166$	0.190206	−	1.80969i	0.0147629	−	0.140459i
$167$	1.65418	+	1.83716i	0.128004	+	0.142163i	0.803740	−	0.594981i	$-0.202840\pi$
$167$	1.65418	+	1.83716i	0.128004	+	0.142163i	−0.675735	+	0.737144i	$0.736174\pi$
$168$	−7.83432	+	8.70089i	−0.604431	+	0.671288i
$169$	1.19916	+	11.4093i	0.0922434	+	0.877638i
$170$	−1.00000	−	3.07768i	−0.0766965	−	0.236048i
$171$	−1.01722	−	3.13068i	−0.0777888	−	0.239409i
$172$	−0.547318	−	5.20738i	−0.0417326	−	0.397059i
$173$	−9.99967	+	11.1058i	−0.760261	+	0.844355i	−0.991711	−	0.128492i	$-0.958986\pi$
$173$	−9.99967	+	11.1058i	−0.760261	+	0.844355i	0.231450	+	0.972847i	$0.425653\pi$
$174$	−3.69886	−	4.10800i	−0.280410	−	0.311427i
$175$	−1.77116	+	16.8514i	−0.133887	+	1.27385i
$176$	−3.62717	+	0.770979i	−0.273408	+	0.0581147i
$177$	−2.52498	−	1.12419i	−0.189789	−	0.0844995i
$178$	−0.854102	+	0.620541i	−0.0640176	+	0.0465115i
$179$	−10.6960	+	4.76216i	−0.799455	+	0.355940i	−0.765461	−	0.643482i	$-0.777489\pi$
$179$	−10.6960	+	4.76216i	−0.799455	+	0.355940i	−0.0339934	+	0.999422i	$0.510823\pi$
$180$	−1.19098	+	2.06284i	−0.0887706	+	0.153755i
$181$	−9.09017	−	15.7446i	−0.675667	−	1.17029i	−0.976273	−	0.216541i	$-0.930522\pi$
$181$	−9.09017	−	15.7446i	−0.675667	−	1.17029i	0.300606	−	0.953748i	$-0.402811\pi$
$182$	−2.61803	−	1.90211i	−0.194062	−	0.140994i
$183$	17.1448	+	3.64425i	1.26738	+	0.269391i
$184$	−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
$189$	−22.9047	−	4.86854i	−1.66607	−	0.354135i
$190$	1.11803	+	0.812299i	0.0811107	+	0.0589304i
$191$	−1.59017	−	2.75426i	−0.115061	−	0.199291i	0.802743	−	0.596325i	$-0.203373\pi$
$191$	−1.59017	−	2.75426i	−0.115061	−	0.199291i	−0.917804	+	0.397034i	$0.870040\pi$
$192$	0.145898	−	0.252703i	0.0105293	−	0.0182373i
$193$	−4.99904	+	2.22572i	−0.359839	+	0.160211i	−0.578690	−	0.815548i	$-0.696436\pi$
$193$	−4.99904	+	2.22572i	−0.359839	+	0.160211i	0.218851	+	0.975758i	$0.429769\pi$
$194$	0.972136	−	0.706298i	0.0697953	−	0.0507092i
$195$	1.39577	+	0.621438i	0.0999534	+	0.0445021i
$196$	17.3212	−	3.68174i	1.23723	−	0.262982i
$197$	1.61145	−	15.3320i	0.114811	−	1.09236i	−0.773716	−	0.633533i	$-0.781604\pi$
$197$	1.61145	−	15.3320i	0.114811	−	1.09236i	0.888527	−	0.458824i	$-0.151729\pi$
$198$	1.21759	+	1.35227i	0.0865304	+	0.0961017i
$199$	−0.706420	+	0.784559i	−0.0500768	+	0.0556159i	−0.767663	−	0.640854i	$-0.778580\pi$
$199$	−0.706420	+	0.784559i	−0.0500768	+	0.0556159i	0.717586	+	0.696470i	$0.245247\pi$
$200$	0.934931	+	8.89527i	0.0661096	+	0.628991i
$201$	3.05573	+	9.40456i	0.215534	+	0.663347i
$202$	0.572949	+	1.76336i	0.0403126	+	0.124069i
$203$	3.20406	+	30.4846i	0.224881	+	2.13960i
$204$	−7.00723	+	7.78231i	−0.490604	+	0.544871i
$205$	4.68391	+	5.20201i	0.327139	+	0.363324i
$206$	0.113954	−	1.08420i	0.00793954	−	0.0755396i
$207$	−11.0996	+	2.35928i	−0.771472	+	0.163981i
$208$	2.09366	+	0.932157i	0.145169	+	0.0646335i
$209$	−3.61803	+	2.62866i	−0.250265	+	0.181828i
$210$	2.95630	−	1.31623i	0.204004	−	0.0908283i
$211$	−0.409830	+	0.709846i	−0.0282139	+	0.0488678i	−0.879788	−	0.475367i	$-0.842315\pi$
$211$	−0.409830	+	0.709846i	−0.0282139	+	0.0488678i	0.851574	+	0.524235i	$0.175649\pi$
$212$	−1.23607	−	2.14093i	−0.0848935	−	0.147040i
$213$	−13.1803	−	9.57608i	−0.903102	−	0.656142i
$214$	6.18799	+	1.31530i	0.423003	+	0.0899120i
$215$	−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
$220$	3.16535	+	0.672816i	0.213408	+	0.0453613i
$221$	−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	−0.925188	−	0.379509i	$-0.876093\pi$
$223$	−2.00000	+	3.46410i	−0.133930	+	0.231973i	0.791258	+	0.611482i	$0.209426\pi$
$224$	21.7409	−	9.67967i	1.45262	−	0.646750i
$225$	−4.76393	+	3.46120i	−0.317595	+	0.230747i
$226$	3.08958	+	1.37557i	0.205516	+	0.0915015i
$227$	−2.41811	+	0.513986i	−0.160496	+	0.0341144i	−0.287459	−	0.957793i	$-0.592810\pi$
$227$	−2.41811	+	0.513986i	−0.160496	+	0.0341144i	0.126963	+	0.991907i	$0.459477\pi$
$228$	0.467465	−	4.44764i	0.0309587	−	0.294552i
$229$	8.97733	+	9.97033i	0.593239	+	0.658858i	0.962758	−	0.270365i	$-0.0871443\pi$
$229$	8.97733	+	9.97033i	0.593239	+	0.658858i	−0.369519	+	0.929223i	$0.620478\pi$
$230$	3.18769	−	3.54029i	0.210190	−	0.233440i
$231$	1.09464	+	10.4148i	0.0720218	+	0.685241i
$232$	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	$0.899419\pi$
$234$	−0.117554	−	1.11845i	−0.00768474	−	0.0731154i
$235$	−4.33070	+	4.80973i	−0.282504	+	0.313752i
$236$	2.42094	+	2.68872i	0.157590	+	0.175021i
$237$	−0.220707	+	2.09989i	−0.0143365	+	0.136402i
$238$	−13.4086	+	2.85010i	−0.869153	+	0.184744i
$239$	1.56052	+	0.694789i	0.100942	+	0.0449422i	0.456586	−	0.889679i	$-0.349072\pi$
$239$	1.56052	+	0.694789i	0.100942	+	0.0449422i	−0.355645	+	0.934621i	$0.615739\pi$
$240$	−1.85410	+	1.34708i	−0.119682	+	0.0869539i
$241$	−27.7359	+	12.3488i	−1.78662	+	0.795456i	−0.808182	+	0.588932i	$0.799548\pi$
$241$	−27.7359	+	12.3488i	−1.78662	+	0.795456i	−0.978442	+	0.206524i	$0.933785\pi$
$242$	−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
$245$	−10.7051	−	2.27544i	−0.683925	−	0.145373i
$246$	−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
$251$	23.6519	+	5.02738i	1.49290	+	0.317325i	0.880812	−	0.473466i	$-0.156998\pi$
$251$	23.6519	+	5.02738i	1.49290	+	0.317325i	0.612085	+	0.790792i	$0.290331\pi$
$252$	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
$255$	5.91259	−	2.63245i	0.370261	−	0.164851i
$256$	5.30902	−	3.85723i	0.331814	−	0.241077i
$257$	−14.5658	−	6.48512i	−0.908591	−	0.404531i	−0.101417	−	0.994844i	$-0.532337\pi$
$257$	−14.5658	−	6.48512i	−0.908591	−	0.404531i	−0.807174	+	0.590313i	$0.799004\pi$
$258$	−2.41811	+	0.513986i	−0.150545	+	0.0319994i
$259$	−0.885579	+	8.42572i	−0.0550272	+	0.523549i
$260$	−1.33826	−	1.48629i	−0.0829954	−	0.0921758i
$261$	−7.12790	+	7.91633i	−0.441206	+	0.490009i
$262$	0.775226	+	7.37578i	0.0478936	+	0.455677i
$263$	−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
$265$	0.159705	+	1.51949i	0.00981062	+	0.0933418i
$266$	3.91716	−	4.35045i	0.240176	−	0.266743i
$267$	−1.41284	−	1.56912i	−0.0864644	−	0.0960284i
$268$	1.35304	−	12.8734i	0.0826504	−	0.786366i
$269$	28.3118	−	6.01785i	1.72620	−	0.366915i	0.765270	−	0.643709i	$-0.222605\pi$
$269$	28.3118	−	6.01785i	1.72620	−	0.366915i	0.960929	+	0.276795i	$0.0892721\pi$
$270$	3.12104	+	1.38958i	0.189941	+	0.0845670i
$271$	−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	$0.379924\pi$
$272$	8.86889	−	3.94868i	0.537755	−	0.239424i
$273$	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
$276$	−15.0795	−	3.20525i	−0.907681	−	0.192933i
$277$	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	$-0.0692705\pi$
$282$	−4.83623	−	1.02797i	−0.287993	−	0.0612148i
$283$	−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
$286$	−1.39577	+	0.621438i	−0.0825338	+	0.0367464i
$287$	23.9894	−	17.4293i	1.41605	−	1.02882i
$288$	7.55549	+	3.36392i	0.445211	+	0.198221i
$289$	−10.1888	+	2.16569i	−0.599340	+	0.127394i
$290$	0.467465	−	4.44764i	0.0274505	−	0.261174i
$291$	1.60809	+	1.78596i	0.0942679	+	0.104695i
$292$	0.511170	−	0.567712i	0.0299140	−	0.0332228i
$293$	−0.885579	−	8.42572i	−0.0517361	−	0.492236i	−0.989455	−	0.144841i	$-0.953733\pi$
$293$	−0.885579	−	8.42572i	−0.0517361	−	0.492236i	0.937719	−	0.347395i	$-0.112934\pi$
$294$	−2.58359	−	7.95148i	−0.150678	−	0.463740i
$295$	−0.690983	−	2.12663i	−0.0402306	−	0.123817i
$296$	0.467465	+	4.44764i	0.0271709	+	0.258514i
$297$	−7.39773	+	8.21601i	−0.429260	+	0.476741i
$298$	−4.13545	−	4.59289i	−0.239560	−	0.266059i
$299$	0.995933	−	9.47567i	0.0575963	−	0.547992i
$300$	−7.82518	+	1.66329i	−0.451787	+	0.0960303i
$301$	12.5231	+	5.57563i	0.721818	+	0.321374i
$302$	4.09017	−	2.97168i	0.235363	−	0.171001i
$303$	−3.38761	+	1.50826i	−0.194613	+	0.0866474i
$304$	−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
$307$	14.9576	+	3.17934i	0.853677	+	0.181455i	0.613910	−	0.789376i	$-0.289596\pi$
$307$	14.9576	+	3.17934i	0.853677	+	0.181455i	0.239767	+	0.970830i	$0.422929\pi$
$308$	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
$313$	−20.7720	−	4.41523i	−1.17410	−	0.249563i	−0.420748	−	0.907177i	$-0.638232\pi$
$313$	−20.7720	−	4.41523i	−1.17410	−	0.249563i	−0.753355	+	0.657614i	$0.771566\pi$
$314$	−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
$317$	20.0471	−	8.92554i	1.12596	−	0.501308i	0.242655	−	0.970113i	$-0.421982\pi$
$317$	20.0471	−	8.92554i	1.12596	−	0.501308i	0.883302	+	0.468804i	$0.155315\pi$
$318$	−0.944272	+	0.686054i	−0.0529521	+	0.0384720i
$319$	13.2210	+	5.88635i	0.740231	+	0.329572i
$320$	0.230909	−	0.0490813i	0.0129082	−	0.00274373i
$321$	−1.32254	+	12.5832i	−0.0738172	+	0.702324i
$322$	−13.5033	−	14.9969i	−0.752509	−	0.835745i
$323$	7.83432	−	8.70089i	0.435913	−	0.484131i
$324$	−0.408689	−	3.88841i	−0.0227049	−	0.216023i
$325$	−1.52786	−	4.70228i	−0.0847506	−	0.260836i
$326$	0.517221	+	1.59184i	0.0286462	+	0.0881640i
$327$	−0.509617	−	4.84868i	−0.0281819	−	0.268133i
$328$	10.4736	−	11.6321i	0.578305	−	0.642273i
$329$	18.3452	+	20.3744i	1.01140	+	1.12327i
$330$	0.159705	−	1.51949i	0.00879149	−	0.0836454i
$331$	−1.95630	+	0.415823i	−0.107528	+	0.0228557i	−0.261361	−	0.965241i	$-0.584171\pi$
$331$	−1.95630	+	0.415823i	−0.107528	+	0.0228557i	0.153834	+	0.988097i	$0.450838\pi$
$332$	−4.35207	−	1.93767i	−0.238851	−	0.106343i
$333$	−2.38197	+	1.73060i	−0.130531	+	0.0948363i
$334$	−1.39577	+	0.621438i	−0.0763733	+	0.0340036i
$335$	−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	$0.524466\pi$
$338$	−6.93523	−	1.47413i	−0.377227	−	0.0801821i
$339$	−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
$344$	7.07794	+	1.50446i	0.381617	+	0.0811152i
$345$	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	−0.889413	−	0.457105i	$-0.848886\pi$
$347$	−0.909830	+	1.57587i	−0.0488422	+	0.0845972i	0.840571	+	0.541702i	$0.182220\pi$
$348$	−13.2210	+	5.88635i	−0.708718	+	0.315541i
$349$	−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	$0.568229\pi$
$350$	−9.56677	−	4.25940i	−0.511365	−	0.227675i
$351$	6.68350	−	1.42062i	0.356739	−	0.0758272i
$352$	1.17449	−	11.1745i	0.0626005	−	0.595604i
$353$	−12.9921	−	14.4292i	−0.691500	−	0.767989i	0.290499	−	0.956875i	$-0.406179\pi$
$353$	−12.9921	−	14.4292i	−0.691500	−	0.767989i	−0.981999	+	0.188886i	$0.939512\pi$
$354$	1.14301	−	1.26944i	0.0607504	−	0.0674701i
$355$	−1.37772	−	13.1081i	−0.0731218	−	0.695708i
$356$	0.854102	+	2.62866i	0.0452673	+	0.139318i
$357$	−8.47214	−	26.0746i	−0.448393	−	1.38001i
$358$	−0.756375	−	7.19643i	−0.0399757	−	0.380343i
$359$	11.8864	−	13.2012i	0.627340	−	0.696731i	−0.342764	−	0.939421i	$-0.611363\pi$
$359$	11.8864	−	13.2012i	0.627340	−	0.696731i	0.970104	+	0.242690i	$0.0780298\pi$
$360$	−2.20264	−	2.44628i	−0.116089	−	0.128930i
$361$	1.46340	−	13.9233i	0.0770210	−	0.732806i
$362$	10.9905	−	2.33611i	0.577650	−	0.122783i
$363$	−7.90443	−	3.51928i	−0.414875	−	0.184714i
$364$	−6.85410	+	4.97980i	−0.359253	+	0.261012i
$365$	−0.431318	+	0.192035i	−0.0225762	+	0.0100516i
$366$	−5.41641	+	9.38149i	−0.283120	+	0.490379i
$367$	−9.00000	−	15.5885i	−0.469796	−	0.813711i	0.529607	−	0.848243i	$-0.322339\pi$
$367$	−9.00000	−	15.5885i	−0.469796	−	0.813711i	−0.999404	+	0.0345320i	$0.989006\pi$
$368$	11.5623	+	8.40051i	0.602727	+	0.437907i
$369$	10.0798	+	2.14252i	0.524732	+	0.111535i
$370$	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
$375$	10.8815	+	2.31294i	0.561919	+	0.119440i
$376$	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
$379$	−34.6129	+	15.4107i	−1.77795	+	0.791592i	−0.795271	+	0.606254i	$0.792671\pi$
$379$	−34.6129	+	15.4107i	−1.77795	+	0.791592i	−0.982675	+	0.185338i	$0.940662\pi$
$380$	2.92705	−	2.12663i	0.150155	−	0.109094i
$381$	3.98368	+	1.77365i	0.204090	+	0.0908668i
$382$	1.92261	−	0.408663i	0.0983691	−	0.0209090i
$383$	−1.24269	+	11.8234i	−0.0634986	+	0.604148i	0.915787	+	0.401664i	$0.131568\pi$
$383$	−1.24269	+	11.8234i	−0.0634986	+	0.604148i	−0.979286	+	0.202484i	$0.935099\pi$
$384$	9.41392	+	10.4552i	0.480402	+	0.533541i
$385$	−5.66897	+	6.29602i	−0.288917	+	0.320875i
$386$	−0.353512	−	3.36344i	−0.0179933	−	0.171195i
$387$	1.47214	+	4.53077i	0.0748329	+	0.230312i
$388$	−0.972136	−	2.99193i	−0.0493527	−	0.151892i
$389$	−1.86986	−	17.7905i	−0.0948058	−	0.902017i	−0.933781	−	0.357846i	$-0.883511\pi$
$389$	−1.86986	−	17.7905i	−0.0948058	−	0.902017i	0.838975	−	0.544170i	$-0.183155\pi$
$390$	−0.631841	+	0.701731i	−0.0319945	+	0.0355335i
$391$	−27.0066	−	29.9938i	−1.36578	−	1.51685i
$392$	−2.55803	+	24.3381i	−0.129200	+	1.22926i
$393$	−14.5087	+	3.08392i	−0.731866	+	0.155563i
$394$	8.70414	+	3.87533i	0.438508	+	0.195236i
$395$	−1.38197	+	1.00406i	−0.0695343	+	0.0505196i
$396$	4.35207	−	1.93767i	0.218700	−	0.0973714i
$397$	3.50000	−	6.06218i	0.175660	−	0.304252i	−0.764730	−	0.644351i	$-0.777127\pi$
$397$	3.50000	−	6.06218i	0.175660	−	0.304252i	0.940389	+	0.340099i	$0.110461\pi$
$398$	−0.326238	−	0.565061i	−0.0163528	−	0.0283239i
$399$	9.47214	+	6.88191i	0.474200	+	0.344526i
$400$	7.25434	+	1.54196i	0.362717	+	0.0770979i
$401$	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
$406$	−18.5303	−	3.93874i	−0.919643	−	0.195476i
$407$	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	−0.336506	−	0.941681i	$-0.609245\pi$
$409$	13.0902	−	22.6728i	0.647267	−	1.12110i	0.983773	−	0.179418i	$-0.0574216\pi$
$410$	−3.95222	+	1.75964i	−0.195186	+	0.0869024i
$411$	−19.7082	+	14.3188i	−0.972134	+	0.706297i
$412$	−2.60735	−	1.16087i	−0.128455	−	0.0571919i
$413$	−9.26515	+	1.96937i	−0.455908	+	0.0969063i
$414$	0.733074	−	6.97474i	0.0360286	−	0.342790i
$415$	1.97010	+	2.18802i	0.0967085	+	0.107406i
$416$	−4.64662	+	5.16060i	−0.227820	+	0.253019i
$417$	1.73346	+	16.4927i	0.0848878	+	0.807653i
$418$	−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	$0.636787\pi$
$420$	−0.885579	−	8.42572i	−0.0432118	−	0.411133i
$421$	−10.2783	+	11.4152i	−0.500934	+	0.556343i	−0.939586	−	0.342314i	$-0.888789\pi$
$421$	−10.2783	+	11.4152i	−0.500934	+	0.556343i	0.438652	+	0.898657i	$0.355456\pi$
$422$	−0.338967	−	0.376461i	−0.0165006	−	0.0183258i
$423$	−0.995933	+	9.47567i	−0.0484239	+	0.460723i
$424$	3.34175	−	0.710311i	0.162290	−	0.0344958i
$425$	−19.1335	−	8.51880i	−0.928113	−	0.413223i
$426$	8.14590	−	5.91834i	0.394670	−	0.286745i
$427$	54.8757	−	24.4322i	2.65562	−	1.18236i
$428$	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
$431$	−11.7378	−	2.49494i	−0.565389	−	0.120177i	−0.0836550	−	0.996495i	$-0.526659\pi$
$431$	−11.7378	−	2.49494i	−0.565389	−	0.120177i	−0.481734	+	0.876318i	$0.659993\pi$
$432$	−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
$437$	16.8594	+	3.58358i	0.806495	+	0.171426i
$438$	−0.291796	−	0.212002i	−0.0139426	−	0.0101299i
$439$	−10.5902	−	18.3427i	−0.505441	−	0.875450i	−0.999980	−	0.00629443i	$-0.997996\pi$
$439$	−10.5902	−	18.3427i	−0.505441	−	0.875450i	0.494539	−	0.869155i	$-0.335337\pi$
$440$	−2.23607	+	3.87298i	−0.106600	+	0.184637i
$441$	−14.7185	+	6.55312i	−0.700883	+	0.312053i
$442$	3.23607	−	2.35114i	0.153924	−	0.111832i
$443$	15.7968	+	7.03321i	0.750531	+	0.334158i	0.746101	−	0.665832i	$-0.231923\pi$
$443$	15.7968	+	7.03321i	0.750531	+	0.334158i	0.00442929	+	0.999990i	$0.498590\pi$
$444$	−3.91259	+	0.831647i	−0.185683	+	0.0394682i
$445$	0.178556	−	1.69885i	0.00846436	−	0.0805330i
$446$	−1.65418	−	1.83716i	−0.0783278	−	0.0869918i
$447$	8.27091	−	9.18578i	0.391201	−	0.434472i
$448$	−0.104528	−	0.994522i	−0.00493851	−	0.0469867i
$449$	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
$451$	−1.46340	−	13.9233i	−0.0689087	−	0.655623i
$452$	5.92455	−	6.57988i	0.278667	−	0.309492i
$453$	6.76588	+	7.51428i	0.317889	+	0.353052i
$454$	0.159705	−	1.51949i	0.00749534	−	0.0713134i
$455$	5.12165	−	1.08864i	0.240107	−	0.0510362i
$456$	5.64602	+	2.51377i	0.264399	+	0.117718i
$457$	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	$0.137046\pi$
$458$	−7.57493	+	3.37258i	−0.353953	+	0.157590i
$459$	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	$0.622435\pi$
$462$	−6.33070	−	1.34563i	−0.294531	−	0.0626045i
$463$	−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	$0.164576\pi$
$468$	−2.87993	−	0.612149i	−0.133125	−	0.0282966i
$469$	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
$472$	−4.56773	+	2.03368i	−0.210247	+	0.0936079i
$473$	5.23607	−	3.80423i	0.240755	−	0.174919i
$474$	−1.19213	−	0.530772i	−0.0547565	−	0.0243792i
$475$	8.74882	−	1.85962i	0.401423	−	0.0853252i
$476$	−3.75137	+	35.6919i	−0.171944	+	1.63594i
$477$	1.50502	+	1.67150i	0.0689103	+	0.0765327i
$478$	−0.706420	+	0.784559i	−0.0323109	+	0.0358849i
$479$	−3.83705	−	36.5071i	−0.175319	−	1.66805i	−0.629392	−	0.777088i	$-0.716696\pi$
$479$	−3.83705	−	36.5071i	−0.175319	−	1.66805i	0.454073	−	0.890965i	$-0.349971\pi$
$480$	−2.14590	−	6.60440i	−0.0979464	−	0.301448i
$481$	−0.763932	−	2.35114i	−0.0348323	−	0.107203i
$482$	−1.96136	−	18.6611i	−0.0893377	−	0.849992i
$483$	27.0066	−	29.9938i	1.22884	−	1.36477i
$484$	7.57873	+	8.41704i	0.344488	+	0.382593i
$485$	−0.203232	+	1.93362i	−0.00922828	+	0.0878012i
$486$	8.21962	−	1.74713i	0.372850	−	0.0792516i
$487$	−13.4875	−	6.00503i	−0.611178	−	0.272114i	0.0777166	−	0.996975i	$-0.475237\pi$
$487$	−13.4875	−	6.00503i	−0.611178	−	0.272114i	−0.688895	+	0.724862i	$0.741904\pi$
$488$	25.6525	−	18.6376i	1.16123	−	0.843685i
$489$	−3.05812	+	1.36156i	−0.138293	+	0.0615719i
$490$	3.38197	−	5.85774i	0.152782	−	0.264626i
$491$	20.1803	+	34.9534i	0.910726	+	1.57742i	0.813041	+	0.582206i	$0.197810\pi$
$491$	20.1803	+	34.9534i	0.910726	+	1.57742i	0.0976849	+	0.995217i	$0.468856\pi$
$492$	11.3262	+	8.22899i	0.510626	+	0.370992i
$493$	−37.0606	−	7.87747i	−1.66912	−	0.354783i
$494$	−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
$499$	32.6862	+	6.94766i	1.46323	+	0.311020i	0.869617	−	0.493727i	$-0.164366\pi$
$499$	32.6862	+	6.94766i	1.46323	+	0.311020i	0.593618	+	0.804747i	$0.297699\pi$
$500$	−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
$503$	−1.50961	+	0.672122i	−0.0673103	+	0.0299685i	−0.440116	−	0.897941i	$-0.645063\pi$
$503$	−1.50961	+	0.672122i	−0.0673103	+	0.0299685i	0.372805	+	0.927910i	$0.378396\pi$
$504$	−11.2812	+	8.19624i	−0.502502	+	0.365089i
$505$	−2.74064	−	1.22021i	−0.121957	−	0.0542986i
$506$	−9.31966	+	1.98095i	−0.414309	+	0.0880642i
$507$	1.48225	−	14.1027i	0.0658290	−	0.626321i
$508$	−3.81953	−	4.24202i	−0.169464	−	0.188209i
$509$	−13.1128	+	14.5632i	−0.581214	+	0.645503i	−0.960006	−	0.279978i	$-0.909673\pi$
$509$	−13.1128	+	14.5632i	−0.581214	+	0.645503i	0.378792	+	0.925482i	$0.376339\pi$
$510$	0.418114	+	3.97809i	0.0185144	+	0.176153i
$511$	0.618034	+	1.90211i	0.0273402	+	0.0841445i
$512$	−5.78115	−	17.7926i	−0.255493	−	0.786327i
$513$	1.29204	+	12.2930i	0.0570451	+	0.542748i
$514$	6.59368	−	7.32302i	0.290835	−	0.323005i
$515$	1.18030	+	1.31086i	0.0520103	+	0.0577633i
$516$	−0.676522	+	6.43668i	−0.0297822	+	0.283359i
$517$	12.6614	−	2.69127i	0.556848	−	0.118362i
$518$	−4.78339	−	2.12970i	−0.210170	−	0.0935737i
$519$	14.9443	−	10.8576i	0.655981	−	0.476598i
$520$	2.52498	−	1.12419i	0.110728	−	0.0492991i
$521$	−1.00000	+	1.73205i	−0.0438108	+	0.0758825i	−0.887099	−	0.461579i	$-0.847283\pi$
$521$	−1.00000	+	1.73205i	−0.0438108	+	0.0758825i	0.843288	+	0.537461i	$0.180617\pi$
$522$	−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	$0.670088\pi$
$524$	18.9921	+	4.03690i	0.829674	+	0.176353i
$525$	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
$530$	−0.923637	−	0.196325i	−0.0401202	−	0.00852782i
$531$	−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
$534$	1.19213	−	0.530772i	0.0515886	−	0.0229687i
$535$	−8.28115	+	6.01661i	−0.358025	+	0.260121i
$536$	16.3420	+	7.27593i	0.705867	+	0.314272i
$537$	14.1559	−	3.00893i	0.610872	−	0.129845i
$538$	−1.86986	+	17.7905i	−0.0806155	+	0.767005i
$539$	14.6463	+	16.2664i	0.630861	+	0.700642i
$540$	5.98489	−	6.64689i	0.257548	−	0.286037i
$541$	−2.02374	−	19.2546i	−0.0870075	−	0.827821i	−0.947800	−	0.318865i	$-0.896698\pi$
$541$	−2.02374	−	19.2546i	−0.0870075	−	0.827821i	0.860793	−	0.508956i	$-0.169968\pi$
$542$	−1.56231	−	4.80828i	−0.0671068	−	0.206533i
$543$	6.94427	+	21.3723i	0.298007	+	0.917172i
$544$	3.07485	+	29.2553i	0.131833	+	1.25431i
$545$	2.63923	−	2.93117i	0.113052	−	0.125557i
$546$	2.67652	+	2.97258i	0.114545	+	0.127215i
$547$	−2.93982	+	27.9705i	−0.125698	+	1.19593i	0.731827	+	0.681491i	$0.238668\pi$
$547$	−2.93982	+	27.9705i	−0.125698	+	1.19593i	−0.857524	+	0.514443i	$0.827999\pi$
$548$	31.1917	−	6.63000i	1.33244	−	0.283220i
$549$	19.0706	+	8.49079i	0.813914	+	0.362378i
$550$	−4.00000	+	2.90617i	−0.170561	+	0.123920i
$551$	14.7815	−	6.58114i	0.629712	−	0.280366i
$552$	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
$555$	2.41811	+	0.513986i	0.102643	+	0.0218175i
$556$	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
$561$	−12.6614	−	2.69127i	−0.534565	−	0.113625i
$562$	8.50000	+	6.17561i	0.358551	+	0.260502i
$563$	19.7705	+	34.2435i	0.833228	+	1.44319i	0.895465	+	0.445131i	$0.146843\pi$
$563$	19.7705	+	34.2435i	0.833228	+	1.44319i	−0.0622377	+	0.998061i	$0.519824\pi$
$564$	−6.47214	+	11.2101i	−0.272526	+	0.472029i
$565$	−4.99904	+	2.22572i	−0.210311	+	0.0936367i
$566$	10.9443	−	7.95148i	0.460022	−	0.334226i
$567$	9.35111	+	4.16338i	0.392710	+	0.174846i
$568$	−28.8281	+	6.12760i	−1.20960	+	0.257108i
$569$	−1.51275	+	14.3929i	−0.0634178	+	0.603380i	0.915950	+	0.401293i	$0.131439\pi$
$569$	−1.51275	+	14.3929i	−0.0634178	+	0.603380i	−0.979368	+	0.202087i	$0.935228\pi$
$570$	−1.14301	−	1.26944i	−0.0478755	−	0.0531711i
$571$	3.89411	−	4.32485i	0.162964	−	0.180989i	−0.656133	−	0.754646i	$-0.727809\pi$
$571$	3.89411	−	4.32485i	0.162964	−	0.180989i	0.819096	+	0.573656i	$0.194475\pi$
$572$	0.418114	+	3.97809i	0.0174822	+	0.166332i
$573$	1.21478	+	3.73871i	0.0507482	+	0.156187i
$574$	5.66312	+	17.4293i	0.236374	+	0.727484i
$575$	−3.22291	−	30.6639i	−0.134405	−	1.27877i
$576$	0.232539	−	0.258261i	0.00968913	−	0.0107609i
$577$	16.6164	+	18.4544i	0.691750	+	0.768266i	0.982040	−	0.188673i	$-0.0604186\pi$
$577$	16.6164	+	18.4544i	0.691750	+	0.768266i	−0.290290	+	0.956939i	$0.593752\pi$
$578$	0.672922	−	6.40243i	0.0279899	−	0.266306i
$579$	6.61612	−	1.40630i	0.274957	−	0.0584439i
$580$	−10.6960	−	4.76216i	−0.444126	−	0.197738i
$581$	10.0902	−	7.33094i	0.418611	−	0.304139i
$582$	−1.35688	+	0.604123i	−0.0562445	+	0.0250417i
$583$	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
$586$	5.12165	+	1.08864i	0.211573	+	0.0449713i
$587$	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
$592$	3.62717	+	0.770979i	0.149076	+	0.0316870i
$593$	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
$596$	−14.7815	+	6.58114i	−0.605473	+	0.269574i
$597$	1.05573	−	0.767031i	0.0432081	−	0.0313925i
$598$	5.37945	+	2.39509i	0.219982	+	0.0979424i
$599$	−33.8407	+	7.19307i	−1.38269	+	0.293901i	−0.838428	−	0.545012i	$-0.816525\pi$
$599$	−33.8407	+	7.19307i	−1.38269	+	0.293901i	−0.544266	+	0.838913i	$0.683192\pi$
$600$	1.15564	−	10.9952i	0.0471787	−	0.448876i
$601$	−24.4507	−	27.1553i	−0.997365	−	1.10769i	−0.994184	−	0.107692i	$-0.965654\pi$
$601$	−24.4507	−	27.1553i	−0.997365	−	1.10769i	−0.00318111	−	0.999995i	$-0.501013\pi$
$602$	−5.66897	+	6.29602i	−0.231050	+	0.256607i
$603$	1.23104	+	11.7126i	0.0501319	+	0.476973i
$604$	−4.09017	−	12.5882i	−0.166427	−	0.512209i
$605$	−2.16312	−	6.65740i	−0.0879433	−	0.270662i
$606$	−0.239558	−	2.27924i	−0.00973138	−	0.0925879i
$607$	9.05191	−	10.0532i	0.367406	−	0.408045i	−0.530887	−	0.847442i	$-0.678141\pi$
$607$	9.05191	−	10.0532i	0.367406	−	0.408045i	0.898293	+	0.439397i	$0.144808\pi$
$608$	−8.40582	−	9.33561i	−0.340901	−	0.378609i
$609$	3.96043	−	37.6810i	0.160485	−	1.52691i
$610$	−8.57242	+	1.82212i	−0.347087	+	0.0737756i
$611$	−7.30836	−	3.25389i	−0.295665	−	0.131638i
$612$	−10.0902	+	7.33094i	−0.407871	+	0.296336i
$613$	−7.41018	+	3.29923i	−0.299295	+	0.133255i	−0.550890	−	0.834578i	$-0.685712\pi$
$613$	−7.41018	+	3.29923i	−0.299295	+	0.133255i	0.251595	+	0.967833i	$0.419045\pi$
$614$	−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
$617$	−23.0137	−	4.89172i	−0.926498	−	0.196933i	−0.280132	−	0.959961i	$-0.590378\pi$
$617$	−23.0137	−	4.89172i	−0.926498	−	0.196933i	−0.646365	+	0.763028i	$0.723712\pi$
$618$	−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
$623$	−7.07794	−	1.50446i	−0.283572	−	0.0602750i
$624$	−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
$627$	5.04996	−	2.24838i	0.201676	−	0.0897918i
$628$	−19.4894	+	14.1598i	−0.777710	+	0.565039i
$629$	−9.56677	−	4.25940i	−0.381452	−	0.169833i
$630$	3.76988	−	0.801313i	0.150196	−	0.0319251i
$631$	1.08299	−	10.3039i	0.0431130	−	0.410193i	−0.951588	−	0.307378i	$-0.900548\pi$
$631$	1.08299	−	10.3039i	0.0431130	−	0.410193i	0.994701	−	0.102815i	$-0.0327849\pi$
$632$	2.55585	+	2.83856i	0.101666	+	0.112912i
$633$	0.677933	−	0.752921i	0.0269454	−	0.0299259i
$634$	1.41765	+	13.4880i	0.0563020	+	0.535677i
$635$	1.09017	+	3.35520i	0.0432621	+	0.133147i
$636$	0.944272	+	2.90617i	0.0374428	+	0.115237i
$637$	−1.41405	−	13.4538i	−0.0560266	−	0.533057i
$638$	−5.98489	+	6.64689i	−0.236944	+	0.263153i
$639$	−12.9833	−	14.4194i	−0.513612	−	0.570424i
$640$	−1.18974	+	11.3196i	−0.0470286	+	0.447447i
$641$	−11.7378	+	2.49494i	−0.463614	+	0.0985442i	−0.433796	−	0.901011i	$-0.642826\pi$
$641$	−11.7378	+	2.49494i	−0.463614	+	0.0985442i	−0.0298181	+	0.999555i	$0.509493\pi$
$642$	−7.14361	−	3.18054i	−0.281936	−	0.125526i
$643$	−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	$0.489743\pi$
$644$	−48.2652	+	21.4890i	−1.90191	+	0.846787i
$645$	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	$0.808086\pi$
$648$	5.28518	+	1.12340i	0.207621	+	0.0441313i
$649$	−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	$0.00319198\pi$
$654$	2.94731	+	0.626470i	0.115249	+	0.0244969i
$655$	−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
$658$	−15.4794	+	6.89186i	−0.603448	+	0.268673i
$659$	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	$0.264885\pi$
$660$	−3.65418	−	1.62695i	−0.142239	−	0.0633288i
$661$	44.3694	−	9.43102i	1.72577	−	0.366824i	0.764971	−	0.644065i	$-0.222753\pi$
$661$	44.3694	−	9.43102i	1.72577	−	0.366824i	0.960800	+	0.277241i	$0.0894200\pi$
$662$	0.129204	−	1.22930i	0.00502167	−	0.0477780i
$663$	5.35304	+	5.94516i	0.207895	+	0.230891i
$664$	4.40528	−	4.89256i	0.170958	−	0.189868i
$665$	0.990108	+	9.42025i	0.0383947	+	0.365301i
$666$	−0.562306	−	1.73060i	−0.0217889	−	0.0670594i
$667$	−17.2361	−	53.0472i	−0.667383	−	2.05399i
$668$	0.418114	+	3.97809i	0.0161773	+	0.153917i
$669$	3.30836	−	3.67431i	0.127909	−	0.142057i
$670$	−3.30836	−	3.67431i	−0.127813	−	0.141951i
$671$	2.96450	−	28.2053i	0.114443	−	1.08885i
$672$	−28.7736	+	6.11602i	−1.10997	+	0.235930i
$673$	42.9487	+	19.1220i	1.65555	+	0.737098i	0.999840	−	0.0179154i	$-0.00570296\pi$
$673$	42.9487	+	19.1220i	1.65555	+	0.737098i	0.655709	+	0.755013i	$0.272370\pi$
$674$	−9.61803	+	6.98791i	−0.370473	+	0.269164i
$675$	20.1998	−	8.99354i	0.777491	−	0.346161i
$676$	−9.28115	+	16.0754i	−0.356967	+	0.618286i
$677$	−21.3607	−	36.9978i	−0.820958	−	1.42194i	−0.904970	−	0.425476i	$-0.860107\pi$
$677$	−21.3607	−	36.9978i	−0.820958	−	1.42194i	0.0840123	−	0.996465i	$-0.473226\pi$
$678$	−3.38197	−	2.45714i	−0.129884	−	0.0943660i
$679$	8.05609	+	1.71237i	0.309164	+	0.0657149i
$680$	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
$685$	−19.2775	−	4.09757i	−0.736557	−	0.156560i
$686$	−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
$689$	−1.72527	+	0.768140i	−0.0657276	+	0.0292638i
$690$	−4.76393	+	3.46120i	−0.181360	+	0.131766i
$691$	−17.5221	−	7.80135i	−0.666573	−	0.296777i	0.0454161	−	0.998968i	$-0.485539\pi$
$691$	−17.5221	−	7.80135i	−0.666573	−	0.296777i	−0.711989	+	0.702191i	$0.752205\pi$
$692$	−23.6519	+	5.02738i	−0.899112	+	0.191112i
$693$	−1.30369	+	12.4038i	−0.0495232	+	0.471182i
$694$	−0.752512	−	0.835749i	−0.0285650	−	0.0317246i
$695$	−8.97733	+	9.97033i	−0.340530	+	0.378196i
$696$	−2.09057	−	19.8904i	−0.0792428	−	0.753945i
$697$	11.3262	+	34.8586i	0.429012	+	1.32036i
$698$	−5.32624	−	16.3925i	−0.201601	−	0.620464i
$699$	−0.00720031	−	0.0685064i	−0.000272341	−	0.00259115i
$700$	−18.3452	+	20.3744i	−0.693382	+	0.770078i
$701$	4.68391	+	5.20201i	0.176909	+	0.196477i	0.825077	−	0.565020i	$-0.191131\pi$
$701$	4.68391	+	5.20201i	0.176909	+	0.196477i	−0.648168	+	0.761497i	$0.724465\pi$
$702$	−0.441415	+	4.19978i	−0.0166601	+	0.158510i
$703$	4.37441	−	0.929809i	0.164984	−	0.0350684i
$704$	−0.431318	−	0.192035i	−0.0162559	−	0.00723759i
$705$	6.47214	−	4.70228i	0.243755	−	0.177098i
$706$	10.9625	−	4.88084i	0.412581	−	0.183693i
$707$	−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	$0.924108\pi$
$710$	7.96789	+	1.69363i	0.299030	+	0.0635607i
$711$	−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
$716$	−18.5303	−	3.93874i	−0.692510	−	0.147197i
$717$	−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	−0.301922	−	0.953333i	$-0.597628\pi$
$719$	18.0902	−	31.3331i	0.674649	−	1.16853i	0.976571	−	0.215194i	$-0.0690385\pi$
$720$	−2.49351	+	1.11018i	−0.0929278	+	0.0413741i
$721$	6.04508	−	4.39201i	0.225131	−	0.163567i
$722$	7.90443	+	3.51928i	0.294172	+	0.130974i
$723$	36.7078	−	7.80248i	1.36518	−	0.290177i
$724$	3.07485	−	29.2553i	0.114276	−	1.08726i
$725$	−19.3675	−	21.5098i	−0.719291	−	0.798853i
$726$	3.57819	−	3.97398i	0.132799	−	0.147488i
$727$	4.15646	+	39.5461i	0.154155	+	1.46668i	0.748854	+	0.662735i	$0.230605\pi$
$727$	4.15646	+	39.5461i	0.154155	+	1.46668i	−0.594699	+	0.803948i	$0.702729\pi$
$728$	−3.61803	−	11.1352i	−0.134093	−	0.412697i
$729$	7.43363	+	22.8784i	0.275320	+	0.847347i
$730$	−0.0305010	−	0.290198i	−0.00112889	−	0.0107407i
$731$	−11.3379	+	12.5920i	−0.419349	+	0.465734i
$732$	18.9770	+	21.0761i	0.701410	+	0.778995i
$733$	0.571994	−	5.44216i	0.0211271	−	0.201011i	−0.978867	−	0.204499i	$-0.934444\pi$
$733$	0.571994	−	5.44216i	0.0211271	−	0.201011i	0.999994	+	0.00348796i	$0.00111025\pi$
$734$	10.8815	−	2.31294i	0.401644	−	0.0853721i
$735$	12.3583	+	5.50228i	0.455843	+	0.202955i
$736$	−35.0344	+	25.4540i	−1.29139	+	0.938247i
$737$	14.6167	−	6.50779i	0.538414	−	0.239717i
$738$	−3.18441	+	5.51555i	−0.117220	+	0.203030i
$739$	8.09017	+	14.0126i	0.297602	+	0.515461i	0.975587	−	0.219614i	$-0.0704799\pi$
$739$	8.09017	+	14.0126i	0.297602	+	0.515461i	−0.677985	+	0.735076i	$0.737147\pi$
$740$	−2.61803	−	1.90211i	−0.0962408	−	0.0699231i
$741$	−3.34175	−	0.710311i	−0.122762	−	0.0260939i
$742$	−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
$747$	4.23965	+	0.901166i	0.155121	+	0.0329719i
$748$	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
$751$	41.6038	−	18.5232i	1.51814	−	0.675921i	0.532760	−	0.846267i	$-0.321155\pi$
$751$	41.6038	−	18.5232i	1.51814	−	0.675921i	0.985384	+	0.170345i	$0.0544884\pi$
$752$	9.70820	−	7.05342i	0.354022	−	0.257212i
$753$	−27.3045	−	12.1568i	−0.995033	−	0.443017i
$754$	5.40707	−	1.14931i	0.196914	−	0.0418553i
$755$	−0.855078	+	8.13553i	−0.0311195	+	0.296082i
$756$	−25.3524	−	28.1567i	−0.922057	−	1.02405i
$757$	−15.1575	+	16.8341i	−0.550907	+	0.611845i	−0.952710	−	0.303882i	$-0.901717\pi$
$757$	−15.1575	+	16.8341i	−0.550907	+	0.611845i	0.401802	+	0.915726i	$0.368384\pi$
$758$	−2.44768	−	23.2881i	−0.0889038	−	0.845863i
$759$	−5.88854	−	18.1231i	−0.213741	−	0.657826i
$760$	1.54508	+	4.75528i	0.0560461	+	0.172492i
$761$	−0.209057	−	1.98904i	−0.00757831	−	0.0721028i	0.990079	−	0.140511i	$-0.0448746\pi$
$761$	−0.209057	−	1.98904i	−0.00757831	−	0.0721028i	−0.997657	+	0.0684084i	$0.978208\pi$
$762$	−1.80334	+	2.00281i	−0.0653281	+	0.0725542i
$763$	−11.1800	−	12.4166i	−0.404742	−	0.449512i
$764$	0.537893	−	5.11771i	0.0194603	−	0.185152i
$765$	7.53976	−	1.60263i	0.272601	−	0.0579431i
$766$	−6.71230	−	2.98851i

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} +(-1.20906 - 0.256993i) q^{3} +(1.30902 + 0.951057i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.381966 - 0.661585i) q^{6} +(-3.86984 + 1.72296i) q^{7} +(-1.80902 + 1.31433i) q^{8} +(-1.34486 - 0.598772i) q^{9} +(0.604528 - 0.128496i) q^{10} +(-0.209057 + 1.98904i) q^{11} +(-1.33826 - 1.48629i) q^{12} +(0.827091 - 0.918578i) q^{13} +(-0.273659 - 2.60369i) q^{14} +(0.381966 + 1.17557i) q^{15} +(0.572949 + 1.76336i) q^{16} +(-0.547318 - 5.20738i) q^{17} +(0.608795 - 0.676135i) q^{18} +(1.49622 + 1.66172i) q^{19} +(0.169131 - 1.60917i) q^{20} +(5.12165 - 1.08864i) q^{21} +(-1.12920 - 0.502754i) q^{22} +(6.23607 - 4.53077i) q^{23} +(2.52498 - 1.12419i) q^{24} +(2.00000 - 3.46410i) q^{25} +(0.381966 + 0.661585i) q^{26} +(4.47214 + 3.24920i) q^{27} +(-6.70432 - 1.42505i) q^{28} +(2.23607 - 6.88191i) q^{29} -0.763932 q^{30} -5.61803 q^{32} +(0.763932 - 2.35114i) q^{33} +(3.16535 + 0.672816i) q^{34} +(3.42705 + 2.48990i) q^{35} +(-1.19098 - 2.06284i) q^{36} +(1.00000 - 1.73205i) q^{37} +(-1.26249 + 0.562096i) q^{38} +(-1.23607 + 0.898056i) q^{39} +(2.04275 + 0.909491i) q^{40} +(-6.84703 + 1.45538i) q^{41} +(-0.338261 + 3.21834i) q^{42} +(-2.16535 - 2.40487i) q^{43} +(-2.16535 + 2.40487i) q^{44} +(0.153880 + 1.46407i) q^{45} +(1.47214 + 4.53077i) q^{46} +(-2.00000 - 6.15537i) q^{47} +(-0.239558 - 2.27924i) q^{48} +(7.32315 - 8.13318i) q^{49} +(1.65418 + 1.83716i) q^{50} +(-0.676522 + 6.43668i) q^{51} +(1.95630 - 0.415823i) q^{52} +(-1.39577 - 0.621438i) q^{53} +(-2.76393 + 2.00811i) q^{54} +(1.82709 - 0.813473i) q^{55} +(4.73607 - 8.20311i) q^{56} +(-1.38197 - 2.39364i) q^{57} +(3.61803 + 2.62866i) q^{58} +(2.18720 + 0.464905i) q^{59} +(-0.618034 + 1.90211i) q^{60} -14.1803 q^{61} +6.23607 q^{63} +(-0.0729490 + 0.224514i) q^{64} +(-1.20906 - 0.256993i) q^{65} +(1.23607 + 0.898056i) q^{66} +(-4.00000 - 6.92820i) q^{67} +(4.23607 - 7.33708i) q^{68} +(-8.70414 + 3.87533i) q^{69} +(-2.11803 + 1.53884i) q^{70} +(12.0408 + 5.36093i) q^{71} +(3.21986 - 0.684403i) q^{72} +(0.0493516 - 0.469550i) q^{73} +(0.827091 + 0.918578i) q^{74} +(-3.30836 + 3.67431i) q^{75} +(0.378188 + 3.59821i) q^{76} +(-2.61803 - 8.05748i) q^{77} +(-0.291796 - 0.898056i) q^{78} +(-0.178556 - 1.69885i) q^{79} +(1.24064 - 1.37787i) q^{80} +(-1.61689 - 1.79574i) q^{81} +(0.452215 - 4.30254i) q^{82} +(-2.87993 + 0.612149i) q^{83} +(7.73968 + 3.44593i) q^{84} +(-4.23607 + 3.07768i) q^{85} +(1.82709 - 0.813473i) q^{86} +(-4.47214 + 7.74597i) q^{87} +(-2.23607 - 3.87298i) q^{88} +(1.38197 + 1.00406i) q^{89} +(-0.889948 - 0.189164i) q^{90} +(-1.61803 + 4.97980i) q^{91} +12.4721 q^{92} +4.00000 q^{94} +(0.690983 - 2.12663i) q^{95} +(6.79252 + 1.44380i) 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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