LMFDB - Embedded newform 425.2.q.a.84.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(84,425)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([7, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("425.84");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.q (of order $10$, degree $4$, 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:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$44$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			84.12
Character	$\chi$	$=$	425.84
Dual form			425.2.q.a.339.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.857096 + 1.17969i) q^{2} +(0.707067 + 2.17613i) q^{3} +(-0.0390246 - 0.120105i) q^{4} +(1.58143 + 1.58085i) q^{5} +(-3.17318 - 1.03103i) q^{6} -2.12040 q^{7} +(-2.59849 - 0.844299i) q^{8} +(-1.80854 + 1.31398i) q^{9} +(-3.22035 + 0.510657i) q^{10} +(0.204272 - 0.281156i) q^{11} +(0.233772 - 0.169845i) q^{12} +(-0.627105 - 0.863136i) q^{13} +(1.81739 - 2.50142i) q^{14} +(-2.32196 + 4.55916i) q^{15} +(3.42750 - 2.49023i) q^{16} +(-3.82748 - 1.53311i) q^{17} -3.25973i q^{18} +(-1.34178 + 4.12958i) q^{19} +(0.128154 - 0.251630i) q^{20} +(-1.49927 - 4.61427i) q^{21} +(0.156597 + 0.481955i) q^{22} +(3.42202 + 2.48625i) q^{23} -6.25162i q^{24} +(0.00182737 + 5.00000i) q^{25} +1.55572 q^{26} +(1.41523 + 1.02822i) q^{27} +(0.0827479 + 0.254672i) q^{28} +(4.63792 - 1.50695i) q^{29} +(-3.38826 - 6.64683i) q^{30} +(9.91655 + 3.22208i) q^{31} +0.713336i q^{32} +(0.756265 + 0.245725i) q^{33} +(5.08911 - 3.20122i) q^{34} +(-3.35327 - 3.35204i) q^{35} +(0.228394 + 0.165938i) q^{36} +(-4.75225 + 3.45271i) q^{37} +(-3.72159 - 5.12233i) q^{38} +(1.43489 - 1.97496i) q^{39} +(-2.77461 - 5.44302i) q^{40} +(-2.15281 - 2.96309i) q^{41} +(6.72844 + 2.18620i) q^{42} -3.26028i q^{43} +(-0.0417399 - 0.0135621i) q^{44} +(-4.93728 - 0.781064i) q^{45} +(-5.86601 + 1.90598i) q^{46} +(-10.2608 + 3.33393i) q^{47} +(7.84252 + 5.69793i) q^{48} -2.50388 q^{49} +(-5.90002 - 4.28332i) q^{50} +(0.629968 - 9.41309i) q^{51} +(-0.0791947 + 0.109002i) q^{52} +(2.85480 - 0.927580i) q^{53} +(-2.42597 + 0.788245i) q^{54} +(0.767506 - 0.121705i) q^{55} +(5.50984 + 1.79026i) q^{56} -9.93522 q^{57} +(-2.19741 + 6.76292i) q^{58} +(9.15031 - 6.64809i) q^{59} +(0.638192 + 0.100960i) q^{60} +(0.507392 - 0.698365i) q^{61} +(-12.3005 + 8.93684i) q^{62} +(3.83484 - 2.78617i) q^{63} +(6.01349 + 4.36905i) q^{64} +(0.372767 - 2.35635i) q^{65} +(-0.938072 + 0.681549i) q^{66} +(6.30092 + 2.04729i) q^{67} +(-0.0347693 + 0.519529i) q^{68} +(-2.99079 + 9.20471i) q^{69} +(6.82845 - 1.08280i) q^{70} +(-13.0325 + 4.23452i) q^{71} +(5.80886 - 1.88741i) q^{72} +(9.94242 + 7.22359i) q^{73} -8.56550i q^{74} +(-10.8793 + 3.53931i) q^{75} +0.548346 q^{76} +(-0.433139 + 0.596164i) q^{77} +(1.10000 + 3.38545i) q^{78} +(8.36725 - 2.71868i) q^{79} +(9.35702 + 1.48025i) q^{80} +(-3.30929 + 10.1849i) q^{81} +5.34069 q^{82} +(6.43351 + 2.09038i) q^{83} +(-0.495690 + 0.360140i) q^{84} +(-3.62925 - 8.47517i) q^{85} +(3.84613 + 2.79437i) q^{86} +(6.55865 + 9.02720i) q^{87} +(-0.768177 + 0.558113i) q^{88} +(-3.90634 - 2.83812i) q^{89} +(5.15314 - 5.15502i) q^{90} +(1.32972 + 1.83020i) q^{91} +(0.165068 - 0.508028i) q^{92} +23.8579i q^{93} +(4.86146 - 14.9620i) q^{94} +(-8.65017 + 4.40947i) q^{95} +(-1.55231 + 0.504376i) q^{96} +(0.345614 + 1.06369i) q^{97} +(2.14607 - 2.95381i) q^{98} +0.776891i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q - 10 q^{2} + 38 q^{4} - 10 q^{8} - 50 q^{9} - 10 q^{13} + 6 q^{15} - 58 q^{16} - 8 q^{19} - 44 q^{21} - 20 q^{25} - 64 q^{26} + 78 q^{30} - 20 q^{33} - 23 q^{34} - 46 q^{35} + 52 q^{36} - 10 q^{38}+ \cdots - 250 q^{98}+O(q^{100}) $ 176 * q - 10 * q^2 + 38 * q^4 - 10 * q^8 - 50 * q^9 - 10 * q^13 + 6 * q^15 - 58 * q^16 - 8 * q^19 - 44 * q^21 - 20 * q^25 - 64 * q^26 + 78 * q^30 - 20 * q^33 - 23 * q^34 - 46 * q^35 + 52 * q^36 - 10 * q^38 - 20 * q^42 + 40 * q^47 + 164 * q^49 + 84 * q^50 + 20 * q^51 - 30 * q^52 - 40 * q^53 - 18 * q^55 - 18 * q^59 - 48 * q^60 + 66 * q^64 + 80 * q^66 - 50 * q^67 + 68 * q^69 - 152 * q^70 + 60 * q^72 - 72 * q^76 - 40 * q^77 - 38 * q^81 + 50 * q^83 - 52 * q^84 + 47 * q^85 - 94 * q^86 - 120 * q^87 + 60 * q^89 + 50 * q^94 - 250 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$

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 $

$2$	−0.857096	+	1.17969i	−0.606058	+	0.834168i	−0.996246	−	0.0865675i	$-0.972410\pi$
$2$	−0.857096	+	1.17969i	−0.606058	+	0.834168i	0.390187	+	0.920735i	$0.372410\pi$
$3$	0.707067	+	2.17613i	0.408225	+	1.25639i	0.918172	+	0.396182i	$0.129665\pi$
$3$	0.707067	+	2.17613i	0.408225	+	1.25639i	−0.509947	+	0.860206i	$0.670335\pi$
$4$	−0.0390246	−	0.120105i	−0.0195123	−	0.0600526i
$5$	1.58143	+	1.58085i	0.707236	+	0.706978i
$5$	1.58143	+	1.58085i	0.707236	+	0.706978i
$6$	−3.17318	−	1.03103i	−1.29545	−	0.420916i
$7$	−2.12040			−0.801438			−0.400719	−	0.916201i	$-0.631240\pi$
$7$	−2.12040			−0.801438			−0.400719	+	0.916201i	$0.631240\pi$
$8$	−2.59849	−	0.844299i	−0.918704	−	0.298505i
$9$	−1.80854	+	1.31398i	−0.602847	+	0.437994i
$10$	−3.22035	+	0.510657i	−1.01836	+	0.161484i
$11$	0.204272	−	0.281156i	0.0615902	−	0.0847717i	−0.777111	−	0.629364i	$-0.783316\pi$
$11$	0.204272	−	0.281156i	0.0615902	−	0.0847717i	0.838701	+	0.544592i	$0.183316\pi$
$12$	0.233772	−	0.169845i	0.0674840	−	0.0490300i
$13$	−0.627105	−	0.863136i	−0.173928	−	0.239391i	0.713150	−	0.701012i	$-0.247268\pi$
$13$	−0.627105	−	0.863136i	−0.173928	−	0.239391i	−0.887077	+	0.461621i	$0.847268\pi$
$14$	1.81739	−	2.50142i	0.485718	−	0.668534i
$15$	−2.32196	+	4.55916i	−0.599527	+	1.17717i
$16$	3.42750	−	2.49023i	0.856875	−	0.622556i
$17$	−3.82748	−	1.53311i	−0.928299	−	0.371834i
$17$	−3.82748	−	1.53311i	−0.928299	−	0.371834i
$18$		−	3.25973i		−	0.768325i
$19$	−1.34178	+	4.12958i	−0.307826	+	0.947390i	0.670782	+	0.741655i	$0.265959\pi$
$19$	−1.34178	+	4.12958i	−0.307826	+	0.947390i	−0.978608	+	0.205735i	$0.934041\pi$
$20$	0.128154	−	0.251630i	0.0286561	−	0.0562661i
$21$	−1.49927	−	4.61427i	−0.327167	−	1.00692i
$22$	0.156597	+	0.481955i	0.0333865	+	0.102753i
$23$	3.42202	+	2.48625i	0.713541	+	0.518418i	0.884314	−	0.466892i	$-0.154626\pi$
$23$	3.42202	+	2.48625i	0.713541	+	0.518418i	−0.170773	+	0.985310i	$0.554626\pi$
$24$		−	6.25162i		−	1.27611i
$25$	0.00182737	+	5.00000i	0.000365475	+	1.00000i
$26$	1.55572			0.305102
$27$	1.41523	+	1.02822i	0.272360	+	0.197881i
$28$	0.0827479	+	0.254672i	0.0156379	+	0.0481285i
$29$	4.63792	−	1.50695i	0.861241	−	0.279834i	0.155094	−	0.987900i	$-0.450432\pi$
$29$	4.63792	−	1.50695i	0.861241	−	0.279834i	0.706147	+	0.708066i	$0.250432\pi$
$30$	−3.38826	−	6.64683i	−0.618609	−	1.21354i
$31$	9.91655	+	3.22208i	1.78106	+	0.578703i	0.999009	−	0.0445058i	$-0.0141713\pi$
$31$	9.91655	+	3.22208i	1.78106	+	0.578703i	0.782056	+	0.623209i	$0.214171\pi$
$32$			0.713336i			0.126101i
$33$	0.756265	+	0.245725i	0.131649	+	0.0427753i
$34$	5.08911	−	3.20122i	0.872776	−	0.549004i
$35$	−3.35327	−	3.35204i	−0.566806	−	0.566598i
$36$	0.228394	+	0.165938i	0.0380656	+	0.0276563i
$37$	−4.75225	+	3.45271i	−0.781266	+	0.567623i	−0.905359	−	0.424648i	$-0.860398\pi$
$37$	−4.75225	+	3.45271i	−0.781266	+	0.567623i	0.124093	+	0.992271i	$0.460398\pi$
$38$	−3.72159	−	5.12233i	−0.603722	−	0.830952i
$39$	1.43489	−	1.97496i	0.229766	−	0.316246i
$40$	−2.77461	−	5.44302i	−0.438704	−	0.860616i
$41$	−2.15281	−	2.96309i	−0.336212	−	0.462756i	0.607118	−	0.794612i	$-0.292325\pi$
$41$	−2.15281	−	2.96309i	−0.336212	−	0.462756i	−0.943330	+	0.331855i	$0.892325\pi$
$42$	6.72844	+	2.18620i	1.03822	+	0.337338i
$43$		−	3.26028i		−	0.497188i	−0.968608	−	0.248594i	$-0.920032\pi$
$43$		−	3.26028i		−	0.497188i	0.968608	−	0.248594i	$-0.0799685\pi$
$44$	−0.0417399	−	0.0135621i	−0.00629253	−	0.00204457i
$45$	−4.93728	−	0.781064i	−0.736007	−	0.116434i
$46$	−5.86601	+	1.90598i	−0.864896	+	0.281022i
$47$	−10.2608	+	3.33393i	−1.49669	+	0.486303i	−0.939050	−	0.343781i	$-0.888292\pi$
$47$	−10.2608	+	3.33393i	−1.49669	+	0.486303i	−0.557638	+	0.830085i	$0.688292\pi$
$48$	7.84252	+	5.69793i	1.13197	+	0.822425i
$49$	−2.50388			−0.357698
$50$	−5.90002	−	4.28332i	−0.834389	−	0.605754i
$51$	0.629968	−	9.41309i	0.0882132	−	1.31810i
$52$	−0.0791947	+	0.109002i	−0.0109823	+	0.0151159i
$53$	2.85480	−	0.927580i	0.392137	−	0.127413i	−0.106311	−	0.994333i	$-0.533904\pi$
$53$	2.85480	−	0.927580i	0.392137	−	0.127413i	0.498447	+	0.866920i	$0.333904\pi$
$54$	−2.42597	+	0.788245i	−0.330132	+	0.107267i
$55$	0.767506	−	0.121705i	0.103490	−	0.0164107i
$56$	5.50984	+	1.79026i	0.736284	+	0.239233i
$57$	−9.93522			−1.31595
$58$	−2.19741	+	6.76292i	−0.288534	+	0.888015i
$59$	9.15031	−	6.64809i	1.19127	−	0.865507i	0.197871	−	0.980228i	$-0.436597\pi$
$59$	9.15031	−	6.64809i	1.19127	−	0.865507i	0.993398	+	0.114721i	$0.0365973\pi$
$60$	0.638192	+	0.100960i	0.0823903	+	0.0130339i
$61$	0.507392	−	0.698365i	0.0649649	−	0.0894165i	−0.775298	−	0.631595i	$-0.782400\pi$
$61$	0.507392	−	0.698365i	0.0649649	−	0.0894165i	0.840263	+	0.542179i	$0.182400\pi$
$62$	−12.3005	+	8.93684i	−1.56216	+	1.13498i
$63$	3.83484	−	2.78617i	0.483144	−	0.351025i
$64$	6.01349	+	4.36905i	0.751686	+	0.546132i
$65$	0.372767	−	2.35635i	0.0462361	−	0.292269i
$66$	−0.938072	+	0.681549i	−0.115469	+	0.0838929i
$67$	6.30092	+	2.04729i	0.769780	+	0.250117i	0.667471	−	0.744636i	$-0.267377\pi$
$67$	6.30092	+	2.04729i	0.769780	+	0.250117i	0.102309	+	0.994753i	$0.467377\pi$
$68$	−0.0347693	+	0.519529i	−0.00421640	+	0.0630022i
$69$	−2.99079	+	9.20471i	−0.360049	+	1.10812i
$70$	6.82845	−	1.08280i	0.816156	−	0.129419i
$71$	−13.0325	+	4.23452i	−1.54667	+	0.502545i	−0.953208	−	0.302315i	$-0.902241\pi$
$71$	−13.0325	+	4.23452i	−1.54667	+	0.502545i	−0.593465	+	0.804860i	$0.702241\pi$
$72$	5.80886	−	1.88741i	0.684581	−	0.222434i
$73$	9.94242	+	7.22359i	1.16367	+	0.845458i	0.990238	−	0.139388i	$-0.0445134\pi$
$73$	9.94242	+	7.22359i	1.16367	+	0.845458i	0.173435	+	0.984845i	$0.444513\pi$
$74$		−	8.56550i		−	0.995720i
$75$	−10.8793	+	3.53931i	−1.25624	+	0.408684i
$76$	0.548346			0.0628997
$77$	−0.433139	+	0.596164i	−0.0493607	+	0.0679392i
$78$	1.10000	+	3.38545i	0.124551	+	0.383327i
$79$	8.36725	−	2.71868i	0.941389	−	0.305876i	0.202178	−	0.979349i	$-0.435198\pi$
$79$	8.36725	−	2.71868i	0.941389	−	0.305876i	0.739212	+	0.673473i	$0.235198\pi$
$80$	9.35702	+	1.48025i	1.04615	+	0.165497i
$81$	−3.30929	+	10.1849i	−0.367698	+	1.13166i
$82$	5.34069			0.589781
$83$	6.43351	+	2.09038i	0.706170	+	0.229449i	0.640017	−	0.768361i	$-0.278927\pi$
$83$	6.43351	+	2.09038i	0.706170	+	0.229449i	0.0661532	+	0.997809i	$0.478927\pi$
$84$	−0.495690	+	0.360140i	−0.0540842	+	0.0392945i
$85$	−3.62925	−	8.47517i	−0.393648	−	0.919261i
$86$	3.84613	+	2.79437i	0.414738	+	0.301325i
$87$	6.55865	+	9.02720i	0.703161	+	0.967818i
$88$	−0.768177	+	0.558113i	−0.0818879	+	0.0594951i
$89$	−3.90634	−	2.83812i	−0.414071	−	0.300840i	0.361177	−	0.932497i	$-0.382375\pi$
$89$	−3.90634	−	2.83812i	−0.414071	−	0.300840i	−0.775248	+	0.631657i	$0.782375\pi$
$90$	5.15314	−	5.15502i	0.543189	−	0.543387i
$91$	1.32972	+	1.83020i	0.139392	+	0.191857i
$92$	0.165068	−	0.508028i	0.0172096	−	0.0529656i
$93$			23.8579i			2.47395i
$94$	4.86146	−	14.9620i	0.501422	−	1.54322i
$95$	−8.65017	+	4.40947i	−0.887489	+	0.452402i
$96$	−1.55231	+	0.504376i	−0.158432	+	0.0514777i
$97$	0.345614	+	1.06369i	0.0350918	+	0.108002i	0.967068	−	0.254518i	$-0.0819167\pi$
$97$	0.345614	+	1.06369i	0.0350918	+	0.108002i	−0.931976	+	0.362519i	$0.881917\pi$
$98$	2.14607	−	2.95381i	0.216786	−	0.298380i
$99$			0.776891i			0.0780805i
$100$	0.600455	−	0.195342i	0.0600455	−	0.0195342i
$101$	−6.00719			−0.597738			−0.298869	−	0.954294i	$-0.596609\pi$
$101$	−6.00719			−0.597738			−0.298869	+	0.954294i	$0.596609\pi$
$102$	10.5646	+	8.81109i	1.04605	+	0.872428i
$103$	13.0463	−	4.23901i	1.28549	−	0.417682i	0.414982	−	0.909830i	$-0.363788\pi$
$103$	13.0463	−	4.23901i	1.28549	−	0.417682i	0.870512	+	0.492148i	$0.163788\pi$
$104$	0.900779	+	2.77231i	0.0883286	+	0.271848i
$105$	4.92349	−	9.66726i	0.480483	−	0.943428i
$106$	−1.35258	+	4.16281i	−0.131374	+	0.404327i
$107$	1.28241			0.123975			0.0619875	−	0.998077i	$-0.480256\pi$
$107$	1.28241			0.123975			0.0619875	+	0.998077i	$0.480256\pi$
$108$	0.0682663	−	0.210102i	0.00656892	−	0.0202171i
$109$	−0.734955	−	1.01158i	−0.0703959	−	0.0968917i	0.772367	−	0.635176i	$-0.219073\pi$
$109$	−0.734955	−	1.01158i	−0.0703959	−	0.0968917i	−0.842763	+	0.538285i	$0.819073\pi$
$110$	−0.514252	+	1.00973i	−0.0490320	+	0.0962743i
$111$	−10.8737	−	7.90021i	−1.03209	−	0.749855i
$112$	−7.26769	+	5.28029i	−0.686732	+	0.498940i
$113$	3.48165	−	2.52957i	0.327526	−	0.237962i	−0.411854	−	0.911250i	$-0.635119\pi$
$113$	3.48165	−	2.52957i	0.327526	−	0.237962i	0.739380	+	0.673288i	$0.235119\pi$
$114$	8.51544	−	11.7205i	0.797544	−	1.09772i
$115$	1.48130	+	9.34152i	0.138132	+	0.871102i
$116$	−0.361986	−	0.498231i	−0.0336096	−	0.0462596i
$117$	2.26829	+	0.737012i	0.209703	+	0.0681368i
$118$			16.4926i			1.51827i
$119$	8.11580	+	3.25082i	0.743974	+	0.298002i
$120$	9.88287	−	9.88648i	0.902178	−	0.902508i
$121$	3.36187	+	10.3468i	0.305624	+	0.940614i
$122$	0.388972	+	1.19713i	0.0352158	+	0.108383i
$123$	4.92588	−	6.77989i	0.444151	−	0.611322i
$124$		−	1.31677i		−	0.118249i
$125$	−7.90136	+	7.91003i	−0.706719	+	0.707494i
$126$			6.91194i			0.615765i
$127$	−1.05357	+	1.45011i	−0.0934889	+	0.128676i	−0.853199	−	0.521585i	$-0.825341\pi$
$127$	−1.05357	+	1.45011i	−0.0934889	+	0.128676i	0.759710	+	0.650262i	$0.225341\pi$
$128$	−11.6651	+	3.79023i	−1.03106	+	0.335012i
$129$	7.09479	−	2.30524i	0.624661	−	0.202965i
$130$	2.46026	+	2.45937i	0.215779	+	0.215701i
$131$	−1.52878	−	0.496730i	−0.133570	−	0.0433995i	0.241469	−	0.970408i	$-0.422371\pi$
$131$	−1.52878	−	0.496730i	−0.133570	−	0.0433995i	−0.375039	+	0.927009i	$0.622371\pi$
$132$		−	0.100421i		−	0.00874050i
$133$	2.84512	−	8.75637i	0.246703	−	0.759274i
$134$	−7.81567	+	5.67841i	−0.675171	+	0.490540i
$135$	0.612613	+	3.86332i	0.0527253	+	0.332501i
$136$	8.65124	+	7.21531i	0.741837	+	0.618707i
$137$	−5.92841	−	8.15976i	−0.506498	−	0.697135i	0.476825	−	0.878998i	$-0.341787\pi$
$137$	−5.92841	−	8.15976i	−0.506498	−	0.697135i	−0.983324	+	0.181863i	$0.941787\pi$
$138$	−8.29532	−	11.4175i	−0.706145	−	0.971925i
$139$	−8.02399	+	11.0441i	−0.680586	+	0.936746i	−0.999941	−	0.0108891i	$-0.996534\pi$
$139$	−8.02399	+	11.0441i	−0.680586	+	0.936746i	0.319355	+	0.947635i	$0.396534\pi$
$140$	−0.271738	+	0.533557i	−0.0229661	+	0.0450938i
$141$	−14.5101	−	19.9714i	−1.22197	−	1.68190i
$142$	6.17468	−	19.0037i	0.518168	−	1.59476i
$143$	−0.370775			−0.0310058
$144$	−2.92666	+	9.00734i	−0.243889	+	0.750612i
$145$	9.71681	+	4.94872i	0.806937	+	0.410969i
$146$	−17.0432	+	5.53768i	−1.41051	+	0.458302i
$147$	−1.77041	−	5.44877i	−0.146021	−	0.449407i
$148$	0.600144	+	0.436030i	0.0493315	+	0.0358415i
$149$	−10.1701			−0.833167			−0.416584	−	0.909097i	$-0.636773\pi$
$149$	−10.1701			−0.833167			−0.416584	+	0.909097i	$0.636773\pi$
$150$	5.14935	−	15.8678i	0.420443	−	1.29560i
$151$	15.4371			1.25625			0.628126	−	0.778112i	$-0.283822\pi$
$151$	15.4371			1.25625			0.628126	+	0.778112i	$0.283822\pi$
$152$	6.97320	−	9.59778i	0.565601	−	0.778483i
$153$	8.93662	−	2.25654i	0.722483	−	0.182430i
$154$	−0.332048	−	1.02194i	−0.0267572	−	0.0823503i
$155$	10.5887	+	20.7721i	0.850503	+	1.66845i
$156$	−0.293199	−	0.0952660i	−0.0234747	−	0.00762738i
$157$		−	14.7442i		−	1.17672i	−0.808600	−	0.588359i	$-0.799774\pi$
$157$		−	14.7442i		−	1.17672i	0.808600	−	0.588359i	$-0.200226\pi$
$158$	−3.96433	+	12.2010i	−0.315385	+	0.970656i
$159$	4.03707	+	5.55654i	0.320160	+	0.440663i
$160$	−1.12768	+	1.12809i	−0.0891507	+	0.0891833i
$161$	−7.25608	−	5.27185i	−0.571859	−	0.415480i
$162$	−9.17870	−	12.6334i	−0.721147	−	0.992574i
$163$	−0.538689	+	0.391380i	−0.0421934	+	0.0306553i	−0.608682	−	0.793414i	$-0.708301\pi$
$163$	−0.538689	+	0.391380i	−0.0421934	+	0.0306553i	0.566489	+	0.824070i	$0.308301\pi$
$164$	−0.271870	+	0.374197i	−0.0212295	+	0.0292199i
$165$	0.807523	+	1.58414i	0.0628656	+	0.123325i
$166$	−7.98014	+	5.79791i	−0.619379	+	0.450005i
$167$	−1.89057	+	5.81858i	−0.146297	+	0.450255i	−0.997175	−	0.0751070i	$-0.976070\pi$
$167$	−1.89057	+	5.81858i	−0.146297	+	0.450255i	0.850879	+	0.525362i	$0.176070\pi$
$168$			13.2560i			1.02272i
$169$	3.66548	−	11.2812i	0.281960	−	0.867783i
$170$	13.1087	+	2.98263i	1.00539	+	0.228758i
$171$	−2.99952	−	9.23158i	−0.229379	−	0.705957i
$172$	−0.391577	+	0.127231i	−0.0298575	+	0.00970128i
$173$	−6.54721	−	4.75682i	−0.497775	−	0.361655i	0.310392	−	0.950609i	$-0.399540\pi$
$173$	−6.54721	−	4.75682i	−0.497775	−	0.361655i	−0.808166	+	0.588954i	$0.799540\pi$
$174$	−16.2707			−1.23348
$175$	−0.00387477	−	10.6020i	−0.000292905	−	0.801438i
$176$		−	1.47234i		−	0.110982i
$177$	20.9370	+	15.2116i	1.57372	+	1.14337i
$178$	6.69622	−	2.17573i	0.501903	−	0.163078i
$179$	−6.30163	−	19.3944i	−0.471006	−	1.44961i	−0.851269	−	0.524729i	$-0.824167\pi$
$179$	−6.30163	−	19.3944i	−0.471006	−	1.44961i	0.380263	−	0.924878i	$-0.375833\pi$
$180$	0.0988654	+	0.623474i	0.00736900	+	0.0464710i
$181$	−1.98460	−	0.644837i	−0.147514	−	0.0479304i	0.234329	−	0.972157i	$-0.424711\pi$
$181$	−1.98460	−	0.644837i	−0.147514	−	0.0479304i	−0.381844	+	0.924227i	$0.624711\pi$
$182$	−3.29876			−0.244521
$183$	1.87849	+	0.610359i	0.138862	+	0.0451190i
$184$	−6.79295	−	9.34969i	−0.500783	−	0.689268i
$185$	−12.9736	−	2.05238i	−0.953836	−	0.150894i
$186$	−28.1450	−	20.4485i	−2.06369	−	1.49936i
$187$	−1.21289	+	0.762945i	−0.0886952	+	0.0557921i
$188$	0.800844	+	1.10227i	0.0584076	+	0.0803911i
$189$	−3.00085	−	2.18025i	−0.218280	−	0.158590i
$190$	2.21221	−	13.9839i	0.160491	−	1.01450i
$191$	16.9661	−	12.3266i	1.22762	−	0.891919i	0.230911	−	0.972975i	$-0.425829\pi$
$191$	16.9661	−	12.3266i	1.22762	−	0.891919i	0.996710	+	0.0810559i	$0.0258292\pi$
$192$	−5.25568	+	16.1753i	−0.379296	+	1.16735i
$193$	15.6848			1.12902			0.564509	−	0.825427i	$-0.309066\pi$
$193$	15.6848			1.12902			0.564509	+	0.825427i	$0.309066\pi$
$194$	−1.55105	−	0.503968i	−0.111359	−	0.0361828i
$195$	5.39128	−	0.854905i	0.386078	−	0.0612210i
$196$	0.0977130	+	0.300730i	0.00697950	+	0.0214807i
$197$	0.124522	+	0.383239i	0.00887182	+	0.0273046i	0.955394	−	0.295333i	$-0.0954305\pi$
$197$	0.124522	+	0.383239i	0.00887182	+	0.0273046i	−0.946523	+	0.322637i	$0.895431\pi$
$198$	−0.916492	−	0.665870i	−0.0651322	−	0.0473213i
$199$			24.0542i			1.70516i	0.522599	+	0.852578i	$0.324962\pi$
$199$			24.0542i			1.70516i	−0.522599	+	0.852578i	$0.675038\pi$
$200$	4.21675	−	12.9940i	0.298169	−	0.918813i
$201$			15.1592i			1.06925i
$202$	5.14874	−	7.08663i	0.362264	−	0.498614i
$203$	−9.83428	+	3.19535i	−0.690231	+	0.224270i
$204$	−1.15515	+	0.291679i	−0.0808764	+	0.0204216i
$205$	1.27968	−	8.08918i	0.0893770	−	0.564973i
$206$	−6.18124	+	19.0239i	−0.430667	+	1.32546i
$207$	−9.45575			−0.657220
$208$	−4.29881	−	1.39677i	−0.298069	−	0.0968483i
$209$	0.886967	+	1.22081i	0.0613528	+	0.0844449i
$210$	7.18448	+	14.0940i	0.495776	+	0.972576i
$211$	−0.109363	+	0.150525i	−0.00752886	+	0.0103626i	−0.812765	−	0.582592i	$-0.802039\pi$
$211$	−0.109363	+	0.150525i	−0.00752886	+	0.0103626i	0.805236	+	0.592954i	$0.202039\pi$
$212$	−0.222815	−	0.306678i	−0.0153030	−	0.0210627i
$213$	−18.4297	−	25.3663i	−1.26278	−	1.73807i
$214$	−1.09915	+	1.51285i	−0.0751361	+	0.103416i
$215$	5.15401	−	5.15590i	0.351501	−	0.351629i
$216$	−2.80932	−	3.86669i	−0.191150	−	0.263095i
$217$	−21.0271	−	6.83212i	−1.42741	−	0.463794i
$218$	1.82328			0.123488
$219$	−8.68951	+	26.7436i	−0.587183	+	1.80716i
$220$	−0.0445690	−	0.0874321i	−0.00300484	−	0.00589467i
$221$	1.07694	+	4.26505i	0.0724431	+	0.286899i
$222$	18.6396	−	6.05638i	1.25101	−	0.406478i
$223$	−9.56879	+	13.1703i	−0.640774	+	0.881949i	−0.998657	−	0.0518172i	$-0.983499\pi$
$223$	−9.56879	+	13.1703i	−0.640774	+	0.881949i	0.357883	+	0.933766i	$0.383499\pi$
$224$		−	1.51256i		−	0.101062i
$225$	−6.57321	−	9.04030i	−0.438214	−	0.602687i
$226$			6.27535i			0.417430i
$227$	20.4882	+	14.8856i	1.35985	+	0.987989i	0.998454	+	0.0555772i	$0.0176999\pi$
$227$	20.4882	+	14.8856i	1.35985	+	0.987989i	0.361396	+	0.932412i	$0.382300\pi$
$228$	0.387718	+	1.19327i	0.0256772	+	0.0790264i
$229$	−7.01209	−	21.5810i	−0.463372	−	1.42611i	−0.861018	−	0.508574i	$-0.830173\pi$
$229$	−7.01209	−	21.5810i	−0.463372	−	1.42611i	0.397646	−	0.917539i	$-0.369827\pi$
$230$	−12.2897	−	6.25911i	−0.810361	−	0.412713i
$231$	−1.60359	−	0.521037i	−0.105508	−	0.0342817i
$232$	−13.3239			−0.874757
$233$	6.42610	−	19.7775i	0.420988	−	1.29567i	−0.485796	−	0.874072i	$-0.661470\pi$
$233$	6.42610	−	19.7775i	0.420988	−	1.29567i	0.906784	−	0.421596i	$-0.138530\pi$
$234$	−2.81359	+	2.04419i	−0.183930	+	0.133633i
$235$	−21.4971	−	10.9484i	−1.40232	−	0.714193i
$236$	−1.15556	−	0.839562i	−0.0752204	−	0.0546508i
$237$	11.8324	+	16.2859i	0.768598	+	1.05788i
$238$	−10.7910	+	6.78787i	−0.699475	+	0.439992i
$239$	5.27668	+	3.83373i	0.341320	+	0.247984i	0.745219	−	0.666820i	$-0.232345\pi$
$239$	5.27668	+	3.83373i	0.341320	+	0.247984i	−0.403899	+	0.914804i	$0.632345\pi$
$240$	3.39482	+	21.4087i	0.219134	+	1.38193i
$241$	0.469675	+	0.646452i	0.0302544	+	0.0416416i	0.823876	−	0.566770i	$-0.191807\pi$
$241$	0.469675	+	0.646452i	0.0302544	+	0.0416416i	−0.793622	+	0.608411i	$0.791807\pi$
$242$	−15.0874	−	4.90220i	−0.969856	−	0.315125i
$243$	−19.2557			−1.23525
$244$	−0.103678	−	0.0336870i	−0.00663731	−	0.00215659i
$245$	−3.95971	−	3.95826i	−0.252977	−	0.252884i
$246$	3.77623	+	11.6220i	0.240763	+	0.740994i
$247$	4.40582	−	1.43154i	0.280336	−	0.0910866i
$248$	−23.0476	−	16.7451i	−1.46352	−	1.06331i
$249$			15.4782i			0.980890i
$250$	−2.55917	−	16.1008i	−0.161856	−	1.01831i
$251$	22.2681			1.40555			0.702776	−	0.711412i	$-0.251944\pi$
$251$	22.2681			1.40555			0.702776	+	0.711412i	$0.251944\pi$
$252$	−0.484287	−	0.351855i	−0.0305072	−	0.0221648i
$253$	1.39805	−	0.454252i	0.0878943	−	0.0285586i
$254$	−0.807675	−	2.48577i	−0.0506780	−	0.155971i
$255$	15.8769	−	13.8902i	0.994252	−	0.869840i
$256$	0.932934	−	2.87128i	0.0583084	−	0.179455i
$257$		−	0.529757i		−	0.0330453i	−0.999863	−	0.0165227i	$-0.994740\pi$
$257$		−	0.529757i		−	0.0330453i	0.999863	−	0.0165227i	$-0.00525957\pi$
$258$	−3.36145	+	10.3455i	−0.209275	+	0.644081i
$259$	10.0767	−	7.32115i	0.626136	−	0.454914i
$260$	−0.297557	+	0.0471841i	−0.0184537	+	0.00292623i
$261$	−6.40776	+	8.81953i	−0.396631	+	0.545915i
$262$	1.89630	−	1.37774i	0.117154	−	0.0851170i
$263$	−6.06576	−	8.34881i	−0.374031	−	0.514810i	0.579960	−	0.814645i	$-0.303068\pi$
$263$	−6.06576	−	8.34881i	−0.374031	−	0.514810i	−0.953991	+	0.299835i	$0.903068\pi$
$264$	−1.75768	−	1.27703i	−0.108178	−	0.0785956i
$265$	5.98102	+	3.04611i	0.367411	+	0.187121i
$266$	7.89128	+	10.8614i	0.483846	+	0.665956i
$267$	3.41408	−	10.5074i	0.208938	−	0.643045i
$268$		−	0.836668i		−	0.0511076i
$269$	−10.7414	−	3.49009i	−0.654913	−	0.212794i	−0.0373340	−	0.999303i	$-0.511887\pi$
$269$	−10.7414	−	3.49009i	−0.654913	−	0.212794i	−0.617579	+	0.786509i	$0.711887\pi$
$270$	−5.08259	−	2.58854i	−0.309317	−	0.157533i
$271$	−8.78128	−	27.0260i	−0.533425	−	1.64171i	−0.747028	−	0.664792i	$-0.768520\pi$
$271$	−8.78128	−	27.0260i	−0.533425	−	1.64171i	0.213604	−	0.976920i	$-0.431480\pi$
$272$	−16.9365	+	4.27653i	−1.02692	+	0.259303i
$273$	−3.04255	+	4.18771i	−0.184143	+	0.253452i
$274$	14.7072			0.888496
$275$	1.40615	+	1.02084i	0.0847942	+	0.0615592i
$276$	1.22225			0.0735707
$277$	−14.2965	−	10.3870i	−0.858996	−	0.624097i	0.0686156	−	0.997643i	$-0.478142\pi$
$277$	−14.2965	−	10.3870i	−0.858996	−	0.624097i	−0.927612	+	0.373546i	$0.878142\pi$
$278$	−6.15127	−	18.9317i	−0.368929	−	1.13545i
$279$	−22.1682	+	7.20289i	−1.32718	+	0.431226i
$280$	5.88329	+	11.5414i	0.351594	+	0.689730i
$281$	−6.52451	+	20.0804i	−0.389220	+	1.19790i	0.544153	+	0.838986i	$0.316851\pi$
$281$	−6.52451	+	20.0804i	−0.389220	+	1.19790i	−0.933372	+	0.358909i	$0.883149\pi$
$282$	35.9967			2.14357
$283$	−0.103543	+	0.318671i	−0.00615496	+	0.0189430i	−0.954087	−	0.299530i	$-0.903170\pi$
$283$	−0.103543	+	0.318671i	−0.00615496	+	0.0189430i	0.947932	+	0.318473i	$0.103170\pi$
$284$	1.01718	+	1.40002i	0.0603583	+	0.0830760i
$285$	−15.7118	−	15.7061i	−0.930688	−	0.930348i
$286$	0.317790	−	0.437401i	0.0187913	−	0.0258640i
$287$	4.56483	+	6.28294i	0.269453	+	0.370870i
$288$	−0.937310	−	1.29010i	−0.0552315	−	0.0760197i
$289$	12.2991	+	11.7359i	0.723478	+	0.690347i
$290$	−14.1662	+	7.22130i	−0.831868	+	0.424050i
$291$	−2.07036	+	1.50420i	−0.121367	+	0.0881779i
$292$	0.479593	−	1.47604i	0.0280661	−	0.0863784i
$293$			11.7077i			0.683971i	0.939705	+	0.341986i	$0.111099\pi$
$293$			11.7077i			0.683971i	−0.939705	+	0.341986i	$0.888901\pi$
$294$	7.94529	+	2.58158i	0.463378	+	0.150561i
$295$	24.9802	+	3.95179i	1.45440	+	0.230082i
$296$	15.2638	−	4.95951i	0.887190	−	0.288265i
$297$	0.578181	−	0.187862i	0.0335495	−	0.0109009i
$298$	8.71676	−	11.9976i	0.504948	−	0.695001i
$299$		−	4.51281i		−	0.260983i
$300$	0.849652	+	1.16855i	0.0490547	+	0.0674661i
$301$			6.91311i			0.398465i
$302$	−13.2311	+	18.2110i	−0.761362	+	1.04793i
$303$	−4.24749	−	13.0724i	−0.244012	−	0.750991i
$304$	5.68462	+	17.4955i	0.326035	+	1.00343i
$305$	1.90641	−	0.302303i	0.109161	−	0.0173098i
$306$	−4.99753	+	12.4765i	−0.285690	+	0.713236i
$307$			19.3881i			1.10654i	0.833002	+	0.553269i	$0.186620\pi$
$307$			19.3881i			1.10654i	−0.833002	+	0.553269i	$0.813380\pi$
$308$	0.0885055	+	0.0287572i	0.00504307	+	0.00163859i
$309$	18.4493	+	25.3932i	1.04954	+	1.44457i
$310$	−33.5801	−	5.31228i	−1.90722	−	0.301717i
$311$	17.1872	−	23.6562i	0.974598	−	1.34142i	0.0349090	−	0.999390i	$-0.488886\pi$
$311$	17.1872	−	23.6562i	0.974598	−	1.34142i	0.939689	−	0.342029i	$-0.111114\pi$
$312$	−5.39599	+	3.92042i	−0.305488	+	0.221950i
$313$	19.4894	−	14.1599i	1.10161	−	0.800364i	0.120285	−	0.992739i	$-0.461619\pi$
$313$	19.4894	−	14.1599i	1.10161	−	0.800364i	0.981321	+	0.192376i	$0.0616192\pi$
$314$	17.3937	+	12.6372i	0.981581	+	0.713160i
$315$	10.4690	+	1.65617i	0.589863	+	0.0933147i
$316$	−0.653057	−	0.898856i	−0.0367373	−	0.0505646i
$317$	8.45266	−	26.0146i	0.474749	−	1.46113i	−0.371548	−	0.928414i	$-0.621173\pi$
$317$	8.45266	−	26.0146i	0.474749	−	1.46113i	0.846296	−	0.532713i	$-0.178827\pi$
$318$	−10.0152			−0.561622
$319$	0.523708	−	1.61181i	0.0293220	−	0.0902439i
$320$	2.60308	+	16.4158i	0.145516	+	0.917669i
$321$	0.906748	+	2.79068i	0.0506098	+	0.155761i
$322$	12.4383	−	4.04145i	0.693160	−	0.225221i
$323$	11.4667	−	13.7488i	0.638026	−	0.765001i
$324$	1.35241			0.0751338
$325$	4.31453	−	3.13710i	0.239327	−	0.174015i
$326$		−	0.970938i		−	0.0537753i
$327$	1.68166	−	2.31461i	0.0929962	−	0.127998i
$328$	3.09231	+	9.51716i	0.170744	+	0.525497i
$329$	21.7570	−	7.06927i	1.19950	−	0.389742i
$330$	−2.56092	−	0.405130i	−0.140974	−	0.0223017i
$331$	−0.0379631	+	0.116838i	−0.00208664	+	0.00642202i	−0.952094	−	0.305804i	$-0.901075\pi$
$331$	−0.0379631	+	0.116838i	−0.00208664	+	0.00642202i	0.950008	+	0.312226i	$0.101075\pi$
$332$		−	0.854275i		−	0.0468844i
$333$	4.05784	−	12.4887i	0.222368	−	0.684379i
$334$	−5.24373	−	7.21737i	−0.286924	−	0.394917i
$335$	6.72798	+	13.1984i	0.367589	+	0.721108i
$336$	−16.6293	−	12.0819i	−0.907204	−	0.659122i
$337$	15.9516	−	11.5895i	0.868937	−	0.631320i	−0.0613641	−	0.998115i	$-0.519545\pi$
$337$	15.9516	−	11.5895i	0.868937	−	0.631320i	0.930302	+	0.366795i	$0.119545\pi$
$338$	10.1666	+	13.9932i	0.552993	+	0.761129i
$339$	7.96642	+	5.78794i	0.432677	+	0.314358i
$340$	−0.876283	+	0.766633i	−0.0475231	+	0.0415765i
$341$	2.93158	−	2.12992i	0.158754	−	0.115341i
$342$	13.4613	+	4.37384i	0.727904	+	0.236510i
$343$	20.1521			1.08811
$344$	−2.75265	+	8.47179i	−0.148413	+	0.456769i
$345$	−19.2810	+	9.82859i	−1.03805	+	0.529153i
$346$	11.2232	−	3.64663i	0.603361	−	0.196044i
$347$	−2.94244	−	9.05591i	−0.157959	−	0.486147i	0.840490	−	0.541827i	$-0.182267\pi$
$347$	−2.94244	−	9.05591i	−0.157959	−	0.486147i	−0.998449	+	0.0556803i	$0.982267\pi$
$348$	0.828266	−	1.14001i	0.0443997	−	0.0611110i
$349$	3.64657			0.195197			0.0975983	−	0.995226i	$-0.468884\pi$
$349$	3.64657			0.195197			0.0975983	+	0.995226i	$0.468884\pi$
$350$	12.5104	+	9.08238i	0.668711	+	0.485474i
$351$		−	1.86633i		−	0.0996176i
$352$	0.200559	+	0.145714i	0.0106898	+	0.00776660i
$353$	11.1896	−	3.63574i	0.595565	−	0.193511i	0.00430348	−	0.999991i	$-0.498630\pi$
$353$	11.1896	−	3.63574i	0.595565	−	0.193511i	0.591261	+	0.806480i	$0.298630\pi$
$354$	−35.8900	+	11.6614i	−1.90753	+	0.619795i
$355$	−27.3041	−	13.9058i	−1.44915	−	0.738046i
$356$	−0.188430	+	0.579929i	−0.00998679	+	0.0307362i
$357$	−1.33579	+	19.9596i	−0.0706974	+	1.05637i
$358$	28.2806	+	9.18891i	1.49467	+	0.485649i
$359$	23.7459	−	17.2524i	1.25326	−	0.910547i	0.254854	−	0.966979i	$-0.417972\pi$
$359$	23.7459	−	17.2524i	1.25326	−	0.910547i	0.998406	+	0.0564321i	$0.0179724\pi$
$360$	12.1700	+	6.19813i	0.641416	+	0.326670i
$361$	0.118294	+	0.0859455i	0.00622599	+	0.00452345i
$362$	2.46171	−	1.78853i	0.129384	−	0.0940032i
$363$	−20.1388	+	14.6317i	−1.05701	+	0.767965i
$364$	0.167925	−	0.231129i	0.00880165	−	0.0121144i
$365$	4.30381	+	27.1411i	0.225272	+	1.42063i
$366$	−2.33008	+	1.69290i	−0.121795	+	0.0884895i
$367$	2.17309	−	6.68808i	0.113434	−	0.349115i	−0.878183	−	0.478325i	$-0.841244\pi$
$367$	2.17309	−	6.68808i	0.113434	−	0.349115i	0.991617	+	0.129210i	$0.0412441\pi$
$368$	17.9203			0.934160
$369$	7.78688	+	2.53011i	0.405369	+	0.131712i
$370$	13.5408	−	13.5457i	0.703951	−	0.704209i
$371$	−6.05333	+	1.96684i	−0.314273	+	0.102114i
$372$	2.86546	−	0.931045i	0.148567	−	0.0482724i
$373$	−8.04336	+	11.0707i	−0.416469	+	0.573221i	−0.964781	−	0.263053i	$-0.915271\pi$
$373$	−8.04336	+	11.0707i	−0.416469	+	0.573221i	0.548312	+	0.836274i	$0.315271\pi$
$374$	0.139521	−	2.08475i	0.00721448	−	0.107800i
$375$	−22.8000	−	11.6015i	−1.17739	−	0.599096i
$376$	29.4773			1.52018
$377$	−4.20917	−	3.05814i	−0.216783	−	0.157502i
$378$	5.14403	−	1.67140i	0.264581	−	0.0859674i
$379$	−7.08275	+	2.30132i	−0.363816	+	0.118211i	−0.485220	−	0.874392i	$-0.661260\pi$
$379$	−7.08275	+	2.30132i	−0.363816	+	0.118211i	0.121404	+	0.992603i	$0.461260\pi$
$380$	0.867170	+	0.866853i	0.0444849	+	0.0444686i
$381$	−3.90057	−	1.26737i	−0.199832	−	0.0649294i
$382$			30.5798i			1.56460i
$383$	−25.4648	−	8.27403i	−1.30119	−	0.422783i	−0.425196	−	0.905101i	$-0.639795\pi$
$383$	−25.4648	−	8.27403i	−1.30119	−	0.422783i	−0.875996	+	0.482318i	$0.839795\pi$
$384$	−16.4960	−	22.7048i	−0.841810	−	1.15865i
$385$	−1.62742	+	0.258063i	−0.0829412	+	0.0131521i
$386$	−13.4434	+	18.5032i	−0.684251	+	0.941790i
$387$	4.28395	+	5.89635i	0.217765	+	0.299728i
$388$	0.114268	−	0.0830203i	0.00580106	−	0.00421471i
$389$	−3.00607	−	2.18404i	−0.152414	−	0.110735i	0.508965	−	0.860787i	$-0.330028\pi$
$389$	−3.00607	−	2.18404i	−0.152414	−	0.110735i	−0.661379	+	0.750052i	$0.730028\pi$
$390$	−3.61232	+	7.09279i	−0.182917	+	0.359157i
$391$	−9.28602	−	14.7624i	−0.469614	−	0.746566i
$392$	6.50631	+	2.11403i	0.328618	+	0.106775i
$393$		−	3.67803i		−	0.185532i
$394$	−0.558831	−	0.181575i	−0.0281535	−	0.00914763i
$395$	17.5300	+	8.92797i	0.882032	+	0.449215i
$396$	0.0933087	−	0.0303178i	0.00468894	−	0.00152353i
$397$	5.83193	+	17.9488i	0.292696	+	0.900827i	0.983986	+	0.178248i	$0.0570431\pi$
$397$	5.83193	+	17.9488i	0.292696	+	0.900827i	−0.691289	+	0.722578i	$0.742957\pi$
$398$	−28.3765	−	20.6168i	−1.42239	−	1.03342i
$399$	21.0667			1.05465
$400$	12.4574	+	17.1330i	0.622869	+	0.856648i
$401$			16.3437i			0.816167i	0.912945	+	0.408083i	$0.133803\pi$
$401$			16.3437i			0.816167i	−0.912945	+	0.408083i	$0.866197\pi$
$402$	−17.8832	−	12.9929i	−0.891931	−	0.648026i
$403$	−3.43762	−	10.5799i	−0.171240	−	0.527023i
$404$	0.234428	+	0.721496i	0.0116632	+	0.0358957i
$405$	−21.3342	+	10.8753i	−1.06011	+	0.540396i
$406$	4.65939	−	14.3401i	0.231242	−	0.711689i
$407$			2.04142i			0.101189i
$408$	−9.58443	+	23.9279i	−0.474500	+	1.18461i
$409$	−26.8747	+	19.5256i	−1.32887	+	0.965481i	−0.329095	+	0.944297i	$0.606744\pi$
$409$	−26.8747	+	19.5256i	−1.32887	+	0.965481i	−0.999776	+	0.0211838i	$0.993256\pi$
$410$	8.44592	+	8.44283i	0.417114	+	0.416962i
$411$	13.5649	−	18.6705i	0.669107	−	0.920947i
$412$	−1.01826	−	1.40151i	−0.0501658	−	0.0690473i
$413$	−19.4024	+	14.0966i	−0.954728	+	0.693650i
$414$	8.10449	−	11.1549i	0.398314	−	0.548232i
$415$	6.86957	+	13.4762i	0.337214	+	0.661521i
$416$	0.615706	−	0.447337i	0.0301875	−	0.0219325i
$417$	−29.7068	−	9.65233i	−1.45475	−	0.472677i
$418$	−2.20039			−0.107625
$419$	7.30633	+	2.37397i	0.356938	+	0.115976i	0.481996	−	0.876173i	$-0.339912\pi$
$419$	7.30633	+	2.37397i	0.356938	+	0.115976i	−0.125059	+	0.992149i	$0.539912\pi$
$420$	−1.35323	−	0.214076i	−0.0660307	−	0.0104459i
$421$	1.45493	+	4.47782i	0.0709091	+	0.218236i	0.980231	−	0.197859i	$-0.0633987\pi$
$421$	1.45493	+	4.47782i	0.0709091	+	0.218236i	−0.909322	+	0.416094i	$0.863399\pi$
$422$	−0.0838388	−	0.258029i	−0.00408121	−	0.0125607i
$423$	14.1763	−	19.5120i	0.689275	−	0.948706i
$424$	−8.20131			−0.398291
$425$	7.65857	−	19.1402i	0.371495	−	0.928435i
$426$	45.7205			2.21516
$427$	−1.07588	+	1.48082i	−0.0520653	+	0.0716617i
$428$	−0.0500454	−	0.154024i	−0.00241904	−	0.00744503i
$429$	−0.262163	−	0.806855i	−0.0126574	−	0.0389553i
$430$	1.66488	+	10.4992i	0.0802878	+	0.506319i
$431$	−12.2725	−	3.98759i	−0.591148	−	0.192076i	−0.00185934	−	0.999998i	$-0.500592\pi$
$431$	−12.2725	−	3.98759i	−0.591148	−	0.192076i	−0.589288	+	0.807923i	$0.700592\pi$
$432$	7.41119			0.356571
$433$	0.420877	+	0.136751i	0.0202261	+	0.00657185i	0.319113	−	0.947717i	$-0.396615\pi$
$433$	0.420877	+	0.136751i	0.0202261	+	0.00657185i	−0.298886	+	0.954289i	$0.596615\pi$
$434$	26.0820	−	18.9497i	1.25198	−	0.909615i
$435$	−3.89863	+	24.6441i	−0.186925	+	1.18159i
$436$	−0.0928146	+	0.127748i	−0.00444502	+	0.00611804i
$437$	−14.8588	+	10.7955i	−0.710790	+	0.516419i
$438$	−24.1014	−	33.1727i	−1.15161	−	1.58505i
$439$	−22.7154	+	31.2650i	−1.08415	+	1.49220i	−0.229271	+	0.973363i	$0.573634\pi$
$439$	−22.7154	+	31.2650i	−1.08415	+	1.49220i	−0.854874	+	0.518835i	$0.826366\pi$
$440$	−2.09711	−	0.331757i	−0.0999758	−	0.0158159i
$441$	4.52837	−	3.29006i	0.215637	−	0.156669i
$442$	−5.95449	−	2.38510i	−0.283226	−	0.113448i
$443$			22.6106i			1.07426i	0.843500	+	0.537130i	$0.180492\pi$
$443$			22.6106i			1.07426i	−0.843500	+	0.537130i	$0.819508\pi$
$444$	−0.524516	+	1.61429i	−0.0248924	+	0.0766110i
$445$	−1.69095	−	10.6636i	−0.0801587	−	0.505504i
$446$	−7.33553	−	22.5764i	−0.347347	−	1.06903i
$447$	−7.19094	−	22.1314i	−0.340120	−	1.04678i
$448$	−12.7510	−	9.26416i	−0.602429	−	0.437690i
$449$		−	18.2969i		−	0.863484i	−0.901997	−	0.431742i	$-0.857899\pi$
$449$		−	18.2969i		−	0.863484i	0.901997	−	0.431742i	$-0.142101\pi$
$450$	16.2986	−	0.00595674i	0.768325	−	0.000280804i
$451$	−1.27285			−0.0599360
$452$	−0.439684	−	0.319449i	−0.0206810	−	0.0150256i
$453$	10.9151	+	33.5931i	0.512834	+	1.57834i
$454$	−35.1207	+	11.4114i	−1.64830	+	0.535565i
$455$	−0.790417	+	4.99641i	−0.0370553	+	0.234235i
$456$	25.8165	+	8.38830i	1.20897	+	0.392818i
$457$		−	32.4991i		−	1.52024i	−0.649780	−	0.760122i	$-0.725139\pi$
$457$		−	32.4991i		−	1.52024i	0.649780	−	0.760122i	$-0.274861\pi$
$458$	31.4690	+	10.2249i	1.47045	+	0.477777i
$459$	−3.84036	−	6.10519i	−0.179253	−	0.284966i
$460$	1.06416	−	0.542461i	0.0496167	−	0.0252924i
$461$	13.6519	+	9.91871i	0.635834	+	0.461961i	0.858416	−	0.512953i	$-0.171449\pi$
$461$	13.6519	+	9.91871i	0.635834	+	0.461961i	−0.222582	+	0.974914i	$0.571449\pi$
$462$	1.98909	−	1.44516i	0.0925409	−	0.0672349i
$463$	−17.7617	−	24.4469i	−0.825456	−	1.13614i	−0.988752	−	0.149566i	$-0.952212\pi$
$463$	−17.7617	−	24.4469i	−0.825456	−	1.13614i	0.163296	−	0.986577i	$-0.447788\pi$
$464$	12.1438	−	16.7146i	0.563763	−	0.775954i
$465$	−37.7158	+	37.7296i	−1.74903	+	1.74967i
$466$	17.8236	+	24.5320i	0.825661	+	1.13643i
$467$	21.4425	+	6.96710i	0.992242	+	0.322399i	0.759761	−	0.650202i	$-0.225316\pi$
$467$	21.4425	+	6.96710i	0.992242	+	0.322399i	0.232481	+	0.972601i	$0.425316\pi$
$468$		−	0.301195i		−	0.0139227i
$469$	−13.3605	−	4.34109i	−0.616930	−	0.200453i
$470$	31.3408	−	15.9761i	1.44564	−	0.736925i
$471$	32.0854	−	10.4252i	1.47842	−	0.480366i
$472$	−29.3899	+	9.54937i	−1.35278	+	0.439545i
$473$	−0.916647	−	0.665983i	−0.0421475	−	0.0306219i
$474$	−29.3539			−1.34827
$475$	−20.6503	−	6.70136i	−0.947502	−	0.307479i
$476$	0.0737251	−	1.10161i	0.00337918	−	0.0504923i
$477$	−3.94419	+	5.42872i	−0.180592	+	0.248564i
$478$	−9.04524	+	2.93898i	−0.413720	+	0.134426i
$479$	18.1234	−	5.88866i	0.828081	−	0.269060i	0.135844	−	0.990730i	$-0.456625\pi$
$479$	18.1234	−	5.88866i	0.828081	−	0.269060i	0.692237	+	0.721671i	$0.256625\pi$
$480$	−3.25221	−	1.65634i	−0.148442	−	0.0756010i
$481$	5.96032	+	1.93663i	0.271767	+	0.0883026i
$482$	−1.16517			−0.0530721
$483$	6.34169	−	19.5177i	0.288557	−	0.888086i
$484$	1.11150	−	0.807556i	0.0505230	−	0.0367071i
$485$	−1.13497	+	2.22852i	−0.0515365	+	0.101192i
$486$	16.5040	−	22.7157i	0.748635	−	1.03041i
$487$	−1.34206	+	0.975065i	−0.0608146	+	0.0441844i	−0.617777	−	0.786353i	$-0.711967\pi$
$487$	−1.34206	+	0.975065i	−0.0608146	+	0.0441844i	0.556963	+	0.830538i	$0.311967\pi$
$488$	−1.90808	+	1.38630i	−0.0863747	+	0.0627549i
$489$	−1.23258	−	0.895524i	−0.0557394	−	0.0404970i
$490$	8.06338	−	1.27863i	0.364267	−	0.0577624i
$491$	20.5535	−	14.9330i	0.927565	−	0.673915i	−0.0178305	−	0.999841i	$-0.505676\pi$
$491$	20.5535	−	14.9330i	0.927565	−	0.673915i	0.945395	+	0.325926i	$0.105676\pi$
$492$	−1.00653	−	0.327042i	−0.0453779	−	0.0147442i
$493$	−20.0619	−	1.34263i	−0.903541	−	0.0604692i
$494$	−2.08744	+	6.42448i	−0.0939184	+	0.289051i
$495$	−1.22815	+	1.22860i	−0.0552011	+	0.0552213i
$496$	42.0127	−	13.6507i	1.88643	−	0.612937i
$497$	27.6342	−	8.97889i	1.23956	−	0.402758i
$498$	−18.2595	−	13.2663i	−0.818227	−	0.594477i
$499$			4.34411i			0.194469i	0.995261	+	0.0972345i	$0.0309997\pi$
$499$			4.34411i			0.194469i	−0.995261	+	0.0972345i	$0.969000\pi$
$500$	1.25838	+	0.640310i	0.0562766	+	0.0286355i
$501$	−13.9987			−0.625418
$502$	−19.0859	+	26.2695i	−0.851846	+	1.17247i
$503$	2.90285	+	8.93406i	0.129432	+	0.398350i	0.994682	−	0.102989i	$-0.0328408\pi$
$503$	2.90285	+	8.93406i	0.129432	+	0.398350i	−0.865251	+	0.501339i	$0.832841\pi$
$504$	−12.3171	+	4.00208i	−0.548649	+	0.178267i
$505$	−9.49994	−	9.49647i	−0.422742	−	0.422587i
$506$	−0.662381	+	2.03860i	−0.0294464	+	0.0906268i
$507$	27.1410			1.20538
$508$	0.215281	+	0.0699490i	0.00955154	+	0.00310348i
$509$	−21.5579	+	15.6627i	−0.955538	+	0.694239i	−0.952110	−	0.305755i	$-0.901091\pi$
$509$	−21.5579	+	15.6627i	−0.955538	+	0.694239i	−0.00342749	+	0.999994i	$0.501091\pi$
$510$	2.77814	+	30.6352i	0.123018	+	1.35655i
$511$	−21.0820	−	15.3169i	−0.932611	−	0.677582i
$512$	−11.8313	−	16.2843i	−0.522873	−	0.719673i
$513$	−6.14504	+	4.46463i	−0.271310	+	0.197118i
$514$	0.624950	+	0.454053i	0.0275654	+	0.0200274i
$515$	27.3331	+	13.9206i	1.20444	+	0.613415i
$516$	−0.553742	−	0.762161i	−0.0243771	−	0.0335523i
$517$	−1.15863	+	3.56590i	−0.0509566	+	0.156828i
$518$			18.1623i			0.798007i
$519$	5.72215	−	17.6110i	0.251174	−	0.773035i
$520$	−2.95809	+	5.80821i	−0.129721	+	0.254707i
$521$	10.1646	−	3.30269i	0.445321	−	0.144693i	−0.0777685	−	0.996971i	$-0.524779\pi$
$521$	10.1646	−	3.30269i	0.445321	−	0.144693i	0.523089	+	0.852278i	$0.324779\pi$
$522$	−4.91226	−	15.1184i	−0.215004	−	0.661713i
$523$	3.26521	−	4.49417i	0.142778	−	0.196516i	−0.731639	−	0.681692i	$-0.761244\pi$
$523$	3.26521	−	4.49417i	0.142778	−	0.196516i	0.874417	+	0.485176i	$0.161244\pi$
$524$			0.202999i			0.00886804i
$525$	23.0686	−	7.50477i	1.00680	−	0.327535i
$526$	15.0480			0.656122
$527$	−33.0155	−	27.5356i	−1.43818	−	1.19947i
$528$	3.20401	−	1.04105i	0.139437	−	0.0453057i
$529$	−1.57856	−	4.85831i	−0.0686331	−	0.211231i
$530$	−8.71978	+	4.44495i	−0.378763	+	0.193076i
$531$	−7.81324	+	24.0467i	−0.339066	+	1.04354i
$532$	−1.16272			−0.0504102
$533$	−1.20751	+	3.71633i	−0.0523031	+	0.160972i
$534$	9.46935	+	13.0334i	0.409779	+	0.564012i
$535$	2.02804	+	2.02729i	0.0876796	+	0.0876476i
$536$	−14.6443	−	10.6397i	−0.632538	−	0.459566i
$537$	37.7491	−	27.4263i	1.62899	−	1.18353i
$538$	13.3236	−	9.68018i	0.574422	−	0.417342i
$539$	−0.511472	+	0.703981i	−0.0220307	+	0.0303226i
$540$	0.440098	−	0.224342i	0.0189388	−	0.00965416i
$541$	8.87905	+	12.2210i	0.381740	+	0.525420i	0.956045	−	0.293221i	$-0.0947273\pi$
$541$	8.87905	+	12.2210i	0.381740	+	0.525420i	−0.574304	+	0.818642i	$0.694727\pi$
$542$	39.4087	+	12.8047i	1.69275	+	0.550008i
$543$		−	4.77470i		−	0.204902i
$544$	1.09362	−	2.73028i	0.0468888	−	0.117060i
$545$	0.436876	−	2.76159i	0.0187137	−	0.118294i
$546$	−2.33245	−	7.17853i	−0.0998195	−	0.307213i
$547$	−10.3350	−	31.8078i	−0.441892	−	1.36000i	−0.885856	−	0.463959i	$-0.846428\pi$
$547$	−10.3350	−	31.8078i	−0.441892	−	1.36000i	0.443964	−	0.896044i	$-0.353572\pi$
$548$	−0.748677	+	1.03046i	−0.0319819	+	0.0440193i
$549$			1.92972i			0.0823586i
$550$	−2.40949	+	0.783864i	−0.102741	+	0.0334241i
$551$			21.1747i			0.902071i
$552$	15.5431	−	21.3932i	0.661556	−	0.910554i
$553$	−17.7420	+	5.76471i	−0.754465	+	0.245141i
$554$	24.5070	−	7.96281i	1.04120	−	0.338308i
$555$	−4.70694	−	29.6833i	−0.199798	−	1.25999i
$556$	1.63958	+	0.532733i	0.0695339	+	0.0225929i
$557$		−	44.6121i		−	1.89028i	−0.326670	−	0.945138i	$-0.605927\pi$
$557$		−	44.6121i		−	1.89028i	0.326670	−	0.945138i	$-0.394073\pi$
$558$	10.5031	−	32.3252i	0.444632	−	1.36844i
$559$	−2.81407	+	2.04454i	−0.119022	+	0.0864747i
$560$	−19.8407	−	3.13874i	−0.838421	−	0.132636i
$561$	−2.51786	−	2.09995i	−0.106304	−	0.0886598i
$562$	−18.0965	−	24.9077i	−0.763356	−	1.05067i
$563$	5.69200	+	7.83436i	0.239889	+	0.330179i	0.911938	−	0.410328i	$-0.134586\pi$
$563$	5.69200	+	7.83436i	0.239889	+	0.330179i	−0.672049	+	0.740507i	$0.734586\pi$
$564$	−1.83243	+	2.52212i	−0.0771590	+	0.106200i
$565$	9.50484	+	1.50364i	0.399872	+	0.0632586i
$566$	−0.287188	−	0.395280i	−0.0120714	−	0.0166149i
$567$	7.01702	−	21.5962i	0.294687	−	0.906954i
$568$	37.4400			1.57095
$569$	−1.21374	+	3.73552i	−0.0508827	+	0.156601i	−0.973269	−	0.229667i	$-0.926236\pi$
$569$	−1.21374	+	3.73552i	−0.0508827	+	0.156601i	0.922386	+	0.386268i	$0.126236\pi$
$570$	31.9949	−	5.07349i	1.34012	−	0.212505i
$571$	23.0598	−	7.49260i	0.965024	−	0.313555i	0.216219	−	0.976345i	$-0.430628\pi$
$571$	23.0598	−	7.49260i	0.965024	−	0.313555i	0.748806	+	0.662790i	$0.230628\pi$
$572$	0.0144694	+	0.0445321i	0.000604994	+	0.00186198i
$573$	38.8203	+	28.2046i	1.62174	+	1.17826i
$574$	−11.3244			−0.472673
$575$	−12.4250	+	17.1147i	−0.518157	+	0.713731i
$576$	−16.6165			−0.692353
$577$	22.4880	−	30.9521i	0.936189	−	1.28855i	−0.0212068	−	0.999775i	$-0.506751\pi$
$577$	22.4880	−	30.9521i	0.936189	−	1.28855i	0.957396	−	0.288779i	$-0.0932491\pi$
$578$	−24.3863	+	4.45039i	−1.01434	+	0.185112i
$579$	11.0902	+	34.1322i	0.460894	+	1.41848i
$580$	0.215174	−	1.36016i	0.00893460	−	0.0564776i
$581$	−13.6417	−	4.43244i	−0.565951	−	0.183889i
$582$		−	3.73163i		−	0.154681i
$583$	0.322360	−	0.992121i	0.0133508	−	0.0410895i
$584$	−19.7364	−	27.1648i	−0.816697	−	1.12409i
$585$	2.42203	+	4.75136i	0.100139	+	0.196444i
$586$	−13.8115	−	10.0346i	−0.570547	−	0.414526i
$587$	−1.44001	−	1.98201i	−0.0594356	−	0.0818061i	0.778265	−	0.627937i	$-0.216100\pi$
$587$	−1.44001	−	1.98201i	−0.0594356	−	0.0818061i	−0.837700	+	0.546130i	$0.816100\pi$
$588$	−0.585337	+	0.425272i	−0.0241389	+	0.0175379i
$589$	−26.6117	+	36.6278i	−1.09651	+	1.50922i
$590$	−26.0723	+	26.0818i	−1.07338	+	1.07377i
$591$	−0.745932	+	0.541951i	−0.0306835	+	0.0222929i
$592$	−7.69032	+	23.6684i	−0.316070	+	0.972764i
$593$			28.5134i			1.17091i	0.810706	+	0.585453i	$0.199084\pi$
$593$			28.5134i			1.17091i	−0.810706	+	0.585453i	$0.800916\pi$
$594$	−0.273937	+	0.843091i	−0.0112398	+	0.0345924i
$595$	7.69549	+	17.9708i	0.315484	+	0.736731i
$596$	0.396884	+	1.22148i	0.0162570	+	0.0500339i
$597$	−52.3450	+	17.0079i	−2.14234	+	0.696088i
$598$	5.32372	+	3.86791i	0.217703	+	0.158171i
$599$	−30.8954			−1.26235			−0.631176	−	0.775640i	$-0.717427\pi$
$599$	−30.8954			−1.26235			−0.631176	+	0.775640i	$0.717427\pi$
$600$	31.2581	−	0.0114240i	1.27611	−	0.000466385i
$601$		−	42.0667i		−	1.71594i	−0.513704	−	0.857968i	$-0.671727\pi$
$601$		−	42.0667i		−	1.71594i	0.513704	−	0.857968i	$-0.328273\pi$
$602$	−8.15534	−	5.92520i	−0.332387	−	0.241493i
$603$	−14.0856	+	4.57668i	−0.573609	+	0.186377i
$604$	−0.602426	−	1.85408i	−0.0245124	−	0.0754413i
$605$	−11.0401	+	21.6773i	−0.448845	+	0.881306i
$606$	19.0619	+	6.19360i	0.774338	+	0.251598i
$607$	−36.8455			−1.49551			−0.747755	−	0.663974i	$-0.768868\pi$
$607$	−36.8455			−1.49551			−0.747755	+	0.663974i	$0.768868\pi$
$608$	−2.94578	−	0.957141i	−0.119467	−	0.0388172i
$609$	−13.9070	−	19.1413i	−0.563539	−	0.775645i
$610$	−1.27736	+	2.50808i	−0.0517186	+	0.101549i
$611$	9.31221	+	6.76572i	0.376732	+	0.273712i
$612$	−0.619770	−	0.985275i	−0.0250527	−	0.0398274i
$613$	−0.125785	−	0.173128i	−0.00508041	−	0.00699259i	0.806469	−	0.591276i	$-0.201376\pi$
$613$	−0.125785	−	0.173128i	−0.00508041	−	0.00699259i	−0.811550	+	0.584283i	$0.801376\pi$
$614$	−22.8720	−	16.6175i	−0.923039	−	0.670627i
$615$	18.5079	−	2.93483i	0.746311	−	0.118344i
$616$	1.62885	−	1.18343i	0.0656281	−	0.0476816i
$617$	−12.2570	+	37.7232i	−0.493448	+	1.51868i	0.325913	+	0.945400i	$0.394328\pi$
$617$	−12.2570	+	37.7232i	−0.493448	+	1.51868i	−0.819361	+	0.573277i	$0.805672\pi$
$618$	−45.7690			−1.84110
$619$	−45.0899	−	14.6506i	−1.81231	−	0.588857i	−0.999984	−	0.00565963i	$-0.998198\pi$
$619$	−45.0899	−	14.6506i	−1.81231	−	0.588857i	−0.812331	−	0.583197i	$-0.801802\pi$
$620$	2.08162	−	2.08238i	0.0835997	−	0.0836303i
$621$	2.28652	+	7.03720i	0.0917550	+	0.282393i
$622$	13.1759	+	40.5513i	0.528306	+	1.62596i
$623$	8.28303	+	6.01797i	0.331852	+	0.241105i
$624$		−	10.3424i		−	0.414026i
$625$	−25.0000	+	0.0182737i	−1.00000	+	0.000730950i
$626$			35.1279i			1.40399i
$627$	−2.02948	+	2.79334i	−0.0810498	+	0.111555i
$628$	−1.77086	+	0.575388i	−0.0706651	+	0.0229605i
$629$	23.4825	−	5.92944i	0.936310	−	0.236422i
$630$	−10.9267	+	10.9307i	−0.435332	+	0.435491i
$631$	−13.8596	+	42.6554i	−0.551741	+	1.69808i	0.152658	+	0.988279i	$0.451217\pi$
$631$	−13.8596	+	42.6554i	−0.551741	+	1.69808i	−0.704398	+	0.709805i	$0.748783\pi$
$632$	−24.0376			−0.956163
$633$	−0.404889	−	0.131556i	−0.0160929	−	0.00522890i
$634$	23.4445	+	32.2686i	0.931099	+	1.28155i
$635$	−3.95854	+	0.627713i	−0.157090	+	0.0249100i
$636$	0.509826	−	0.701715i	0.0202159	−	0.0278248i
$637$	1.57020	+	2.16119i	0.0622135	+	0.0856295i
$638$	1.45257	+	1.99929i	0.0575077	+	0.0791525i
$639$	18.0057	−	24.7828i	0.712296	−	0.980391i
$640$	−24.4393	−	12.4468i	−0.966049	−	0.492004i
$641$	5.27499	+	7.26040i	0.208350	+	0.286768i	0.900384	−	0.435096i	$-0.143285\pi$
$641$	5.27499	+	7.26040i	0.208350	+	0.286768i	−0.692035	+	0.721864i	$0.743285\pi$
$642$	−4.06932	−	1.32220i	−0.160603	−	0.0521831i
$643$	19.8985			0.784719			0.392360	−	0.919812i	$-0.371659\pi$
$643$	19.8985			0.784719			0.392360	+	0.919812i	$0.371659\pi$
$644$	−0.350012	+	1.07722i	−0.0137924	+	0.0424486i
$645$	14.8641	+	7.57023i	0.585274	+	0.298078i
$646$	6.39119	+	25.3112i	0.251458	+	0.995857i
$647$	5.63390	−	1.83056i	0.221491	−	0.0719669i	−0.196169	−	0.980570i	$-0.562850\pi$
$647$	5.63390	−	1.83056i	0.221491	−	0.0719669i	0.417661	+	0.908603i	$0.362850\pi$
$648$	17.1983	−	23.6714i	0.675612	−	0.929900i
$649$		−	3.93068i		−	0.154293i
$650$	0.00284289	+	7.77862i	0.000111507	+	0.305102i
$651$		−	50.5884i		−	1.98272i
$652$	0.0680290	+	0.0494259i	0.00266422	+	0.00193567i
$653$	−7.43124	−	22.8710i	−0.290807	−	0.895012i	−0.984598	−	0.174835i	$-0.944061\pi$
$653$	−7.43124	−	22.8710i	−0.290807	−	0.895012i	0.693791	−	0.720177i	$-0.255939\pi$
$654$	1.28918	+	3.96769i	0.0504109	+	0.155149i
$655$	−1.63239	−	3.20231i	−0.0637829	−	0.125125i
$656$	−14.7575	−	4.79501i	−0.576184	−	0.187213i
$657$	−27.4729			−1.07182
$658$	−10.3083	+	31.7256i	−0.401858	+	1.23679i
$659$	10.1637	−	7.38437i	0.395922	−	0.287654i	−0.371956	−	0.928250i	$-0.621313\pi$
$659$	10.1637	−	7.38437i	0.395922	−	0.287654i	0.767878	+	0.640596i	$0.221313\pi$
$660$	0.158750	−	0.158808i	0.00617934	−	0.00618160i
$661$	−35.5601	−	25.8359i	−1.38313	−	1.00490i	−0.996580	−	0.0826308i	$-0.973668\pi$
$661$	−35.5601	−	25.8359i	−1.38313	−	1.00490i	−0.386547	−	0.922270i	$-0.626332\pi$
$662$	−0.105295	−	0.144926i	−0.00409242	−	0.00563273i
$663$	−8.51983	+	5.35925i	−0.330883	+	0.208136i
$664$	−14.9525	−	10.8636i	−0.580269	−	0.421590i
$665$	18.3419	−	9.34987i	0.711267	−	0.362572i
$666$	11.2549	+	15.4911i	0.436119	+	0.600266i
$667$	19.6177	+	6.37419i	0.759602	+	0.246810i
$668$	0.772621			0.0298936
$669$	−35.4261	−	11.5106i	−1.36965	−	0.445026i
$670$	−21.3366	−	3.37539i	−0.824306	−	0.130403i
$671$	−0.0927036	−	0.285312i	−0.00357878	−	0.0110144i
$672$	3.29153	−	1.06948i	0.126973	−	0.0412562i
$673$	6.54178	+	4.75288i	0.252167	+	0.183210i	0.706687	−	0.707527i	$-0.250189\pi$
$673$	6.54178	+	4.75288i	0.252167	+	0.183210i	−0.454520	+	0.890737i	$0.650189\pi$
$674$			28.7512i			1.10746i
$675$	−5.13852	+	7.07800i	−0.197782	+	0.272433i
$676$	−1.49797			−0.0576144
$677$	−35.5217	−	25.8080i	−1.36521	−	0.991883i	−0.998094	−	0.0617082i	$-0.980345\pi$
$677$	−35.5217	−	25.8080i	−1.36521	−	0.991883i	−0.367116	−	0.930175i	$-0.619655\pi$
$678$	−13.6560	+	4.43710i	−0.524455	+	0.170406i
$679$	−0.732843	−	2.25546i	−0.0281239	−	0.0865565i
$680$	2.27499	+	25.0868i	0.0872418	+	0.962035i
$681$	−17.9064	+	55.1101i	−0.686173	+	2.11182i
$682$			5.28390i			0.202331i
$683$	−1.05304	+	3.24091i	−0.0402933	+	0.124010i	−0.969180	−	0.246355i	$-0.920767\pi$
$683$	−1.05304	+	3.24091i	−0.0402933	+	0.124010i	0.928886	+	0.370365i	$0.120767\pi$
$684$	−0.991707	+	0.720517i	−0.0379188	+	0.0275497i
$685$	3.52400	−	22.2760i	0.134645	−	0.851122i
$686$	−17.2723	+	23.7732i	−0.659458	+	0.907667i
$687$	42.0050	−	30.5184i	1.60259	−	1.16435i
$688$	−8.11883	−	11.1746i	−0.309528	−	0.426028i
$689$	−2.59089	−	1.88239i	−0.0987049	−	0.0717133i
$690$	4.93095	−	31.1697i	0.187718	−	1.18661i
$691$	15.5956	+	21.4655i	0.593283	+	0.816585i	0.995073	−	0.0991476i	$-0.0316116\pi$
$691$	15.5956	+	21.4655i	0.593283	+	0.816585i	−0.401789	+	0.915732i	$0.631612\pi$
$692$	−0.315818	+	0.971987i	−0.0120056	+	0.0369494i
$693$		−	1.64732i		−	0.0625766i
$694$	13.2051	+	4.29061i	0.501260	+	0.162869i
$695$	−30.1484	+	4.78068i	−1.14359	+	0.181342i
$696$	−9.42089	−	28.9945i	−0.357098	−	1.09903i
$697$	3.69708	+	14.6416i	0.140037	+	0.554592i
$698$	−3.12546	+	4.30183i	−0.118301	+	0.162827i
$699$	47.5821			1.79972
$700$	−1.27321	+	0.414205i	−0.0481227	+	0.0156555i
$701$	−34.4647			−1.30172			−0.650858	−	0.759200i	$-0.725591\pi$
$701$	−34.4647			−1.30172			−0.650858	+	0.759200i	$0.725591\pi$
$702$	2.20170	+	1.59963i	0.0830978	+	0.0603741i
$703$	−7.88177	−	24.2576i	−0.297266	−	0.914892i
$704$	2.45677	−	0.798253i	0.0925930	−	0.0300853i
$705$	8.62518	−	54.5217i	0.324843	−	2.05341i
$706$	−5.30156	+	16.3165i	−0.199527	+	0.614080i
$707$	12.7377			0.479050
$708$	1.00994	−	3.10827i	0.0379558	−	0.116816i
$709$	6.63065	+	9.12630i	0.249019	+	0.342746i	0.915167	−	0.403074i	$-0.132058\pi$
$709$	6.63065	+	9.12630i	0.249019	+	0.342746i	−0.666148	+	0.745819i	$0.732058\pi$
$710$	39.8068	−	20.2918i	1.49392	−	0.761536i
$711$	−11.5602	+	15.9113i	−0.433542	+	0.596719i
$712$	7.75435	+	10.6729i	0.290607	+	0.399986i
$713$	25.9238	+	35.6810i	0.970853	+	1.33626i
$714$	−22.4012	−	18.6831i	−0.838345	−	0.699197i
$715$	−0.586355	−	0.586140i	−0.0219284	−	0.0219204i
$716$	−2.08346	+	1.51372i	−0.0778624	+	0.0565703i
$717$	−4.61173	+	14.1934i	−0.172228	+	0.530064i
$718$			42.7998i			1.59728i
$719$	41.2657	+	13.4080i	1.53895	+	0.500035i	0.951086	−	0.308925i	$-0.0999692\pi$
$719$	41.2657	+	13.4080i	1.53895	+	0.500035i	0.587863	+	0.808960i	$0.299969\pi$
$720$	−18.8676	+	9.61785i	−0.703153	+	0.358436i
$721$	−27.6635	+	8.98842i	−1.03024	+	0.334746i
$722$	−0.202778	+	0.0658867i	−0.00754663	+	0.00245205i
$723$	−1.07467	+	1.47916i	−0.0399675	+	0.0550105i
$724$			0.263526i			0.00979386i
$725$	7.54324	+	23.1869i	0.280149	+	0.861138i
$726$		−	36.2984i		−	1.34716i
$727$	21.3835	−	29.4319i	0.793070	−	1.09157i	−0.200649	−	0.979663i	$-0.564305\pi$
$727$	21.3835	−	29.4319i	0.793070	−	1.09157i	0.993719	−	0.111904i	$-0.0356951\pi$
$728$	−1.91002	−	5.87842i	−0.0707899	−	0.217869i
$729$	−3.68719	−	11.3480i	−0.136563	−	0.420296i
$730$	−35.7069	−	18.1853i	−1.32157	−	0.673070i
$731$	−4.99838	+	12.4786i	−0.184872	+	0.461539i
$732$		−	0.249436i		−	0.00921941i
$733$	16.0293	+	5.20824i	0.592056	+	0.192371i	0.589694	−	0.807627i	$-0.299248\pi$
$733$	16.0293	+	5.20824i	0.592056	+	0.192371i	0.00236159	+	0.999997i	$0.499248\pi$
$734$	6.02733	+	8.29591i	0.222473	+	0.306207i
$735$	5.81391	−	11.4156i	0.214449	−	0.421071i
$736$	−1.77353	+	2.44105i	−0.0653731	+	0.0899784i
$737$	1.86271	−	1.35334i	0.0686137	−	0.0498508i
$738$	−9.65886	+	7.01757i	−0.355547	+	0.258320i
$739$	−16.0949	−	11.6937i	−0.592062	−	0.430158i	0.250990	−	0.967990i	$-0.419244\pi$
$739$	−16.0949	−	11.6937i	−0.592062	−	0.430158i	−0.843053	+	0.537831i	$0.819244\pi$
$740$	0.259786	+	1.63829i	0.00954993	+	0.0602247i
$741$	6.23043	+	8.57544i	0.228880	+	0.315027i
$742$	2.86801	−	8.82683i	0.105288	−	0.324043i
$743$	−33.2420			−1.21953			−0.609765	−	0.792582i	$-0.708736\pi$
$743$	−33.2420			−1.21953			−0.609765	+	0.792582i	$0.708736\pi$
$744$	20.1432	−	61.9945i	0.738486	−	2.27283i
$745$	−16.0833	−	16.0774i	−0.589246	−	0.589031i
$746$	−6.16612	−	18.9774i	−0.225758	−	0.694811i
$747$	−14.3820	+	4.67299i	−0.526209	+	0.170976i
$748$	0.138966	+	0.115901i	0.00508111	+	0.00423775i
$749$	−2.71922			−0.0993583
$750$	33.2279	−	16.9534i	1.21331	−	0.619052i
$751$		−	17.1770i		−	0.626799i	−0.949621	−	0.313399i	$-0.898532\pi$
$751$		−	17.1770i		−	0.626799i	0.949621	−	0.313399i	$-0.101468\pi$
$752$	−26.8666	+	36.9787i	−0.979723	+	1.34847i
$753$	15.7451	+	48.4583i	0.573782	+	1.76592i
$754$	7.21533	−	2.34440i	0.262767	−	0.0853781i
$755$	24.4126	+	24.4037i	0.888467	+	0.888142i
$756$	−0.144752	+	0.445501i	−0.00526458	+	0.0162027i
$757$			5.28399i			0.192050i	0.995379	+	0.0960250i	$0.0306129\pi$
$757$			5.28399i			0.192050i	−0.995379	+	0.0960250i	$0.969387\pi$
$758$	3.35574	−	10.3279i	0.121886	−	0.375127i
$759$	1.97702	+	2.72114i	0.0717614	+	0.0987711i
$760$	26.2003	−	4.15462i	0.950384	−	0.150704i
$761$	1.57522	+	1.14446i	0.0571017	+	0.0414868i	0.615970	−	0.787770i	$-0.288764\pi$
$761$	1.57522	+	1.14446i	0.0571017	+	0.0414868i	−0.558868	+	0.829256i	$0.688764\pi$
$762$	4.83827	−	3.51521i	0.175272	−	0.127343i
$763$	1.55840	+	2.14496i	0.0564179	+	0.0776526i
$764$	−2.14258	−	1.55667i	−0.0775158	−	0.0563185i
$765$	17.6999	+	10.5589i	0.639940	+	0.381758i
$766$	31.5866	−	22.9490i	1.14127	−	0.829182i
$767$	−11.4764	−	3.72891i	−0.414389	−	0.134643i
$768$	6.90791			0.249268
$769$	−10.5394	+	32.4369i	−0.380060	+	1.16970i	0.559941	+	0.828533i	$0.310824\pi$
$769$	−10.5394	+	32.4369i	−0.380060	+	1.16970i	−0.940001	+	0.341172i	$0.889176\pi$
$770$	1.09042	−	2.14104i	0.0392961	−	0.0771578i
$771$	1.15282	−

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.q (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.857096 + 1.17969i) q^{2} +(0.707067 + 2.17613i) q^{3} +(-0.0390246 - 0.120105i) q^{4} +(1.58143 + 1.58085i) q^{5} +(-3.17318 - 1.03103i) q^{6} -2.12040 q^{7} +(-2.59849 - 0.844299i) q^{8} +(-1.80854 + 1.31398i) q^{9} +(-3.22035 + 0.510657i) q^{10} +(0.204272 - 0.281156i) q^{11} +(0.233772 - 0.169845i) q^{12} +(-0.627105 - 0.863136i) q^{13} +(1.81739 - 2.50142i) q^{14} +(-2.32196 + 4.55916i) q^{15} +(3.42750 - 2.49023i) q^{16} +(-3.82748 - 1.53311i) q^{17} -3.25973i q^{18} +(-1.34178 + 4.12958i) q^{19} +(0.128154 - 0.251630i) q^{20} +(-1.49927 - 4.61427i) q^{21} +(0.156597 + 0.481955i) q^{22} +(3.42202 + 2.48625i) q^{23} -6.25162i q^{24} +(0.00182737 + 5.00000i) q^{25} +1.55572 q^{26} +(1.41523 + 1.02822i) q^{27} +(0.0827479 + 0.254672i) q^{28} +(4.63792 - 1.50695i) q^{29} +(-3.38826 - 6.64683i) q^{30} +(9.91655 + 3.22208i) q^{31} +0.713336i q^{32} +(0.756265 + 0.245725i) q^{33} +(5.08911 - 3.20122i) q^{34} +(-3.35327 - 3.35204i) q^{35} +(0.228394 + 0.165938i) q^{36} +(-4.75225 + 3.45271i) q^{37} +(-3.72159 - 5.12233i) q^{38} +(1.43489 - 1.97496i) q^{39} +(-2.77461 - 5.44302i) q^{40} +(-2.15281 - 2.96309i) q^{41} +(6.72844 + 2.18620i) q^{42} -3.26028i q^{43} +(-0.0417399 - 0.0135621i) q^{44} +(-4.93728 - 0.781064i) q^{45} +(-5.86601 + 1.90598i) q^{46} +(-10.2608 + 3.33393i) q^{47} +(7.84252 + 5.69793i) q^{48} -2.50388 q^{49} +(-5.90002 - 4.28332i) q^{50} +(0.629968 - 9.41309i) q^{51} +(-0.0791947 + 0.109002i) q^{52} +(2.85480 - 0.927580i) q^{53} +(-2.42597 + 0.788245i) q^{54} +(0.767506 - 0.121705i) q^{55} +(5.50984 + 1.79026i) q^{56} -9.93522 q^{57} +(-2.19741 + 6.76292i) q^{58} +(9.15031 - 6.64809i) q^{59} +(0.638192 + 0.100960i) q^{60} +(0.507392 - 0.698365i) q^{61} +(-12.3005 + 8.93684i) q^{62} +(3.83484 - 2.78617i) q^{63} +(6.01349 + 4.36905i) q^{64} +(0.372767 - 2.35635i) q^{65} +(-0.938072 + 0.681549i) q^{66} +(6.30092 + 2.04729i) q^{67} +(-0.0347693 + 0.519529i) q^{68} +(-2.99079 + 9.20471i) q^{69} +(6.82845 - 1.08280i) q^{70} +(-13.0325 + 4.23452i) q^{71} +(5.80886 - 1.88741i) q^{72} +(9.94242 + 7.22359i) q^{73} -8.56550i q^{74} +(-10.8793 + 3.53931i) q^{75} +0.548346 q^{76} +(-0.433139 + 0.596164i) q^{77} +(1.10000 + 3.38545i) q^{78} +(8.36725 - 2.71868i) q^{79} +(9.35702 + 1.48025i) q^{80} +(-3.30929 + 10.1849i) q^{81} +5.34069 q^{82} +(6.43351 + 2.09038i) q^{83} +(-0.495690 + 0.360140i) q^{84} +(-3.62925 - 8.47517i) q^{85} +(3.84613 + 2.79437i) q^{86} +(6.55865 + 9.02720i) q^{87} +(-0.768177 + 0.558113i) q^{88} +(-3.90634 - 2.83812i) q^{89} +(5.15314 - 5.15502i) q^{90} +(1.32972 + 1.83020i) q^{91} +(0.165068 - 0.508028i) q^{92} +23.8579i q^{93} +(4.86146 - 14.9620i) q^{94} +(-8.65017 + 4.40947i) q^{95} +(-1.55231 + 0.504376i) q^{96} +(0.345614 + 1.06369i) q^{97} +(2.14607 - 2.95381i) q^{98} +0.776891i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 10 q^{2} + 38 q^{4} - 10 q^{8} - 50 q^{9} - 10 q^{13} + 6 q^{15} - 58 q^{16} - 8 q^{19} - 44 q^{21} - 20 q^{25} - 64 q^{26} + 78 q^{30} - 20 q^{33} - 23 q^{34} - 46 q^{35} + 52 q^{36} - 10 q^{38}+ \cdots - 250 q^{98}+O(q^{100}) \) 176 * q - 10 * q^2 + 38 * q^4 - 10 * q^8 - 50 * q^9 - 10 * q^13 + 6 * q^15 - 58 * q^16 - 8 * q^19 - 44 * q^21 - 20 * q^25 - 64 * q^26 + 78 * q^30 - 20 * q^33 - 23 * q^34 - 46 * q^35 + 52 * q^36 - 10 * q^38 - 20 * q^42 + 40 * q^47 + 164 * q^49 + 84 * q^50 + 20 * q^51 - 30 * q^52 - 40 * q^53 - 18 * q^55 - 18 * q^59 - 48 * q^60 + 66 * q^64 + 80 * q^66 - 50 * q^67 + 68 * q^69 - 152 * q^70 + 60 * q^72 - 72 * q^76 - 40 * q^77 - 38 * q^81 + 50 * q^83 - 52 * q^84 + 47 * q^85 - 94 * q^86 - 120 * q^87 + 60 * q^89 + 50 * q^94 - 250 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more