LMFDB - Embedded newform 425.2.q.a.84.11

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			84.11
Character	$\chi$	$=$	425.84
Dual form			425.2.q.a.339.11

$q$-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} +(-3.99763 - 1.00942i) 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} +(4.61716 - 3.85081i) 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} +(4.72623 + 7.91598i) 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	$-0.870335\pi$
$3$	−0.707067	−	2.17613i	−0.408225	−	1.25639i	0.509947	−	0.860206i	$-0.329665\pi$
$4$	−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	$-0.368760\pi$
$7$	2.12040			0.801438			0.400719	+	0.916201i	$0.368760\pi$
$8$	−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	−0.838701	−	0.544592i	$-0.816684\pi$
$11$	−0.204272	+	0.281156i	−0.0615902	+	0.0847717i	0.777111	+	0.629364i	$0.216684\pi$
$12$	−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
$17$	−3.99763	−	1.00942i	−0.969569	−	0.244820i
$17$	−3.99763	−	1.00942i	−0.969569	−	0.244820i
$18$		−	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	0.170773	−	0.985310i	$-0.445374\pi$
$23$	−3.42202	−	2.48625i	−0.713541	−	0.518418i	−0.884314	+	0.466892i	$0.845374\pi$
$24$			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	−0.706147	−	0.708066i	$-0.749568\pi$
$29$	−4.63792	+	1.50695i	−0.861241	+	0.279834i	−0.155094	+	0.987900i	$0.549568\pi$
$30$	−3.38826	−	6.64683i	−0.618609	−	1.21354i
$31$	−9.91655	−	3.22208i	−1.78106	−	0.578703i	−0.782056	−	0.623209i	$-0.785829\pi$
$31$	−9.91655	−	3.22208i	−1.78106	−	0.578703i	−0.999009	+	0.0445058i	$0.985829\pi$
$32$			0.713336i			0.126101i
$33$	0.756265	+	0.245725i	0.131649	+	0.0427753i
$34$	4.61716	−	3.85081i	0.791836	−	0.660408i
$35$	−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	−0.124093	−	0.992271i	$-0.539602\pi$
$37$	4.75225	−	3.45271i	0.781266	−	0.567623i	0.905359	+	0.424648i	$0.139602\pi$
$38$	−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	0.943330	−	0.331855i	$-0.107675\pi$
$41$	2.15281	+	2.96309i	0.336212	+	0.462756i	−0.607118	+	0.794612i	$0.707675\pi$
$42$	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	−0.840263	−	0.542179i	$-0.817600\pi$
$61$	−0.507392	+	0.698365i	−0.0649649	+	0.0894165i	0.775298	+	0.631595i	$0.217600\pi$
$62$	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	0.593465	−	0.804860i	$-0.297759\pi$
$71$	13.0325	−	4.23452i	1.54667	−	0.502545i	0.953208	+	0.302315i	$0.0977594\pi$
$72$	5.80886	−	1.88741i	0.684581	−	0.222434i
$73$	−9.94242	−	7.22359i	−1.16367	−	0.845458i	−0.173435	−	0.984845i	$-0.555487\pi$
$73$	−9.94242	−	7.22359i	−1.16367	−	0.845458i	−0.990238	+	0.139388i	$0.955487\pi$
$74$			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	−0.739212	−	0.673473i	$-0.764802\pi$
$79$	−8.36725	+	2.71868i	−0.941389	+	0.305876i	−0.202178	+	0.979349i	$0.564802\pi$
$80$	−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
$85$	4.72623	+	7.91598i	0.512631	+	0.858609i
$86$	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	0.931976	−	0.362519i	$-0.118083\pi$
$97$	−0.345614	−	1.06369i	−0.0350918	−	0.108002i	−0.967068	+	0.254518i	$0.918083\pi$
$98$	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	$0.596609\pi$
$102$	−11.6445	−	7.32476i	−1.15298	−	0.725259i
$103$	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	$-0.519744\pi$
$107$	−1.28241			−0.123975			−0.0619875	+	0.998077i	$0.519744\pi$
$108$	−0.0682663	+	0.210102i	−0.00656892	+	0.0202171i
$109$	0.734955	+	1.01158i	0.0703959	+	0.0968917i	0.842763	−	0.538285i	$-0.180927\pi$
$109$	0.734955	+	1.01158i	0.0703959	+	0.0968917i	−0.772367	+	0.635176i	$0.780927\pi$
$110$	−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	−0.739380	−	0.673288i	$-0.764881\pi$
$113$	−3.48165	+	2.52957i	−0.327526	+	0.237962i	0.411854	+	0.911250i	$0.364881\pi$
$114$	−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
$119$	−8.47660	−	2.14038i	−0.777049	−	0.196208i
$120$	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	0.375039	−	0.927009i	$-0.377629\pi$
$131$	1.52878	+	0.496730i	0.133570	+	0.0433995i	−0.241469	+	0.970408i	$0.577629\pi$
$132$		−	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
$136$	9.53554	+	5.99816i	0.817666	+	0.514338i
$137$	−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	−0.319355	−	0.947635i	$-0.603466\pi$
$139$	8.02399	−	11.0441i	0.680586	−	0.936746i	0.999941	+	0.0108891i	$0.00346617\pi$
$140$	−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
$153$	8.55624	−	3.42724i	0.691731	−	0.277076i
$154$	−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	−0.566489	−	0.824070i	$-0.691699\pi$
$163$	0.538689	−	0.391380i	0.0421934	−	0.0306553i	0.608682	+	0.793414i	$0.291699\pi$
$164$	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	−0.850879	−	0.525362i	$-0.823930\pi$
$167$	1.89057	−	5.81858i	0.146297	−	0.450255i	0.997175	+	0.0751070i	$0.0239298\pi$
$168$			13.2560i			1.02272i
$169$	3.66548	−	11.2812i	0.281960	−	0.867783i
$170$	−13.3892	−	1.20927i	−1.02691	−	0.0927465i
$171$	−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	0.808166	−	0.588954i	$-0.200460\pi$
$173$	6.54721	+	4.75682i	0.497775	+	0.361655i	−0.310392	+	0.950609i	$0.600460\pi$
$174$	−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	0.381844	−	0.924227i	$-0.375289\pi$
$181$	1.98460	+	0.644837i	0.147514	+	0.0479304i	−0.234329	+	0.972157i	$0.575289\pi$
$182$	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
$187$	1.10041	−	0.917762i	0.0804698	−	0.0671134i
$188$	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	$-0.690934\pi$
$193$	−15.6848			−1.12902			−0.564509	+	0.825427i	$0.690934\pi$
$194$	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	0.946523	−	0.322637i	$-0.104569\pi$
$197$	−0.124522	−	0.383239i	−0.00887182	−	0.0273046i	−0.955394	+	0.295333i	$0.904569\pi$
$198$	0.916492	+	0.665870i	0.0651322	+	0.0473213i
$199$		−	24.0542i		−	1.70516i	−0.522599	−	0.852578i	$-0.675038\pi$
$199$		−	24.0542i		−	1.70516i	0.522599	−	0.852578i	$-0.324962\pi$
$200$	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
$204$	1.10598	−	0.443004i	0.0774339	−	0.0310165i
$205$	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	−0.805236	−	0.592954i	$-0.797961\pi$
$211$	0.109363	−	0.150525i	0.00752886	−	0.0103626i	0.812765	+	0.582592i	$0.197961\pi$
$212$	−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
$221$	1.63567	+	4.08351i	0.110027	+	0.274687i
$222$	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	$-0.982300\pi$
$227$	−20.4882	−	14.8856i	−1.35985	−	0.987989i	−0.361396	−	0.932412i	$-0.617700\pi$
$228$	−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	$0.338530\pi$
$233$	−6.42610	+	19.7775i	−0.420988	+	1.29567i	−0.906784	+	0.421596i	$0.861470\pi$
$234$	−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
$238$	9.79025	−	8.16527i	0.634607	−	0.529276i
$239$	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	0.793622	−	0.608411i	$-0.208193\pi$
$241$	−0.469675	−	0.646452i	−0.0302544	−	0.0416416i	−0.823876	+	0.566770i	$0.808193\pi$
$242$	−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
$255$	13.8844	−	15.8820i	0.869477	−	0.994570i
$256$	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	0.617579	−	0.786509i	$-0.288113\pi$
$269$	10.7414	+	3.49009i	0.654913	+	0.212794i	0.0373340	+	0.999303i	$0.488113\pi$
$270$	−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	$-0.431480\pi$
$272$	−16.2156	+	6.49522i	−0.983214	+	0.393831i
$273$	−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	0.927612	−	0.373546i	$-0.121858\pi$
$277$	14.2965	+	10.3870i	0.858996	+	0.624097i	−0.0686156	+	0.997643i	$0.521858\pi$
$278$	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	−0.947932	−	0.318473i	$-0.896830\pi$
$283$	0.103543	−	0.318671i	0.00615496	−	0.0189430i	0.954087	+	0.299530i	$0.0968299\pi$
$284$	−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
$289$	14.9621	+	8.07058i	0.880126	+	0.474740i
$290$	−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
$306$	−3.29043	+	13.0312i	−0.188102	+	0.744944i
$307$			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	$0.511114\pi$
$311$	−17.1872	+	23.6562i	−0.974598	+	1.34142i	−0.939689	+	0.342029i	$0.888886\pi$
$312$	5.39599	−	3.92042i	0.305488	−	0.221950i
$313$	−19.4894	+	14.1599i	−1.10161	+	0.800364i	−0.981321	−	0.192376i	$-0.938381\pi$
$313$	−19.4894	+	14.1599i	−1.10161	+	0.800364i	−0.120285	+	0.992739i	$0.538381\pi$
$314$	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	$0.378827\pi$
$317$	−8.45266	+	26.0146i	−0.474749	+	1.46113i	−0.846296	+	0.532713i	$0.821173\pi$
$318$	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
$323$	9.53242	−	15.1541i	0.530398	−	0.843197i
$324$	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	−0.930302	−	0.366795i	$-0.880455\pi$
$337$	−15.9516	+	11.5895i	−0.868937	+	0.631320i	0.0613641	+	0.998115i	$0.480455\pi$
$338$	10.1666	+	13.9932i	0.552993	+	0.761129i
$339$	7.96642	+	5.78794i	0.432677	+	0.314358i
$340$	0.766312	−	0.876563i	0.0415591	−	0.0475383i
$341$	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	0.998449	−	0.0556803i	$-0.0177328\pi$
$347$	2.94244	+	9.05591i	0.157959	+	0.486147i	−0.840490	+	0.541827i	$0.817733\pi$
$348$	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	−0.991617	−	0.129210i	$-0.958756\pi$
$367$	−2.17309	+	6.68808i	−0.113434	+	0.349115i	0.878183	+	0.478325i	$0.158756\pi$
$368$	−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	−0.121404	−	0.992603i	$-0.538740\pi$
$379$	7.08275	−	2.30132i	0.363816	−	0.118211i	0.485220	+	0.874392i	$0.338740\pi$
$380$	−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
$391$	11.1703	+	13.3934i	0.564908	+	0.677331i
$392$	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	$-0.942957\pi$
$397$	−5.83193	−	17.9488i	−0.292696	−	0.900827i	0.691289	−	0.722578i	$-0.257043\pi$
$398$	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	$-0.866197\pi$
$401$		−	16.3437i		−	0.816167i	0.912945	−	0.408083i	$-0.133803\pi$
$402$	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
$408$	6.31050	−	24.9917i	0.312416	−	1.23727i
$409$	−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	0.125059	−	0.992149i	$-0.460088\pi$
$419$	−7.30633	−	2.37397i	−0.356938	−	0.115976i	−0.481996	+	0.876173i	$0.660088\pi$
$420$	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
$425$	5.03979	−	19.9900i	0.244466	−	0.969658i
$426$	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	0.589288	−	0.807923i	$-0.299408\pi$
$431$	12.2725	+	3.98759i	0.591148	+	0.192076i	0.00185934	+	0.999998i	$0.499408\pi$
$432$	−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	$-0.426366\pi$
$439$	22.7154	−	31.2650i	1.08415	−	1.49220i	0.854874	−	0.518835i	$-0.173634\pi$
$440$	−2.09711	−	0.331757i	−0.0999758	−	0.0158159i
$441$	4.52837	−	3.29006i	0.215637	−	0.156669i
$442$	−6.21921	−	1.57038i	−0.295818	−	0.0746952i
$443$			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	$0.142101\pi$
$449$			18.2969i			0.863484i	−0.901997	+	0.431742i	$0.857899\pi$
$450$	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
$459$	4.61964	+	5.53901i	0.215627	+	0.258539i
$460$	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	−0.692237	−	0.721671i	$-0.743375\pi$
$479$	−18.1234	+	5.88866i	−0.828081	+	0.269060i	−0.135844	+	0.990730i	$0.543375\pi$
$480$	−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	−0.556963	−	0.830538i	$-0.688033\pi$
$487$	1.34206	−	0.975065i	0.0608146	−	0.0441844i	0.617777	+	0.786353i	$0.288033\pi$
$488$	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	$-0.969000\pi$
$499$		−	4.34411i		−	0.194469i	0.995261	−	0.0972345i	$-0.0309997\pi$
$500$	−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	0.865251	−	0.501339i	$-0.167159\pi$
$503$	−2.90285	−	8.93406i	−0.129432	−	0.398350i	−0.994682	+	0.102989i	$0.967159\pi$
$504$	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	$0.501091\pi$
$510$	6.83558	+	29.9918i	0.302684	+	1.32806i
$511$	−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	−0.523089	−	0.852278i	$-0.675221\pi$
$521$	−10.1646	+	3.30269i	−0.445321	+	0.144693i	0.0777685	+	0.996971i	$0.475221\pi$
$522$	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
$527$	36.3903	+	22.8907i	1.58519	+	0.997133i
$528$	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	0.574304	−	0.818642i	$-0.305273\pi$
$541$	−8.87905	−	12.2210i	−0.381740	−	0.525420i	−0.956045	+	0.293221i	$0.905273\pi$
$542$	39.4087	+	12.8047i	1.69275	+	0.550008i
$543$		−	4.77470i		−	0.204902i
$544$	0.720055	−	2.85166i	0.0308721	−	0.122264i
$545$	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	$0.153572\pi$
$547$	10.3350	+	31.8078i	0.441892	+	1.36000i	−0.443964	+	0.896044i	$0.646428\pi$
$548$	−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
$561$	−2.77523	−	1.74571i	−0.117170	−	0.0737039i
$562$	−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	−0.748806	−	0.662790i	$-0.769372\pi$
$571$	−23.0598	+	7.49260i	−0.965024	+	0.313555i	−0.216219	+	0.976345i	$0.569372\pi$
$572$	−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	$-0.0932491\pi$
$578$	−22.3448	+	10.7335i	−0.929421	+	0.446453i
$579$	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
$595$	10.0215	+	16.7851i	0.410842	+	0.688121i
$596$	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	$0.328273\pi$
$601$			42.0667i			1.71594i	−0.513704	+	0.857968i	$0.671727\pi$
$602$	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	$-0.231132\pi$
$607$	36.8455			1.49551			0.747755	+	0.663974i	$0.231132\pi$
$608$	−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
$612$	−0.745533	−	0.893903i	−0.0301364	−	0.0361339i
$613$	−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	$-0.605672\pi$
$617$	12.2570	−	37.7232i	0.493448	−	1.51868i	0.819361	−	0.573277i	$-0.194328\pi$
$618$	45.7690			1.84110
$619$	45.0899	+	14.6506i	1.81231	+	0.588857i	0.999984	+	0.00565963i	$0.00180153\pi$
$619$	45.0899	+	14.6506i	1.81231	+	0.588857i	0.812331	+	0.583197i	$0.198198\pi$
$620$	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
$629$	−22.4830	+	9.00567i	−0.896456	+	0.359080i
$630$	−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	0.692035	−	0.721864i	$-0.256715\pi$
$641$	−5.27499	−	7.26040i	−0.208350	−	0.286768i	−0.900384	+	0.435096i	$0.856715\pi$
$642$	−4.06932	−	1.32220i	−0.160603	−	0.0521831i
$643$	−19.8985			−0.784719			−0.392360	−	0.919812i	$-0.628341\pi$
$643$	−19.8985			−0.784719			−0.392360	+	0.919812i	$0.628341\pi$
$644$	−0.350012	+	1.07722i	−0.0137924	+	0.0424486i
$645$	14.8641	+	7.57023i	0.585274	+	0.298078i
$646$	9.70698	+	24.2339i	0.381916	+	0.953468i
$647$	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	$0.0559393\pi$
$653$	7.43124	+	22.8710i	0.290807	+	0.895012i	−0.693791	+	0.720177i	$0.744061\pi$
$654$	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
$663$	7.72972	−	6.44674i	0.300197	−	0.250371i
$664$	−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	0.454520	−	0.890737i	$-0.349811\pi$
$673$	−6.54178	−	4.75288i	−0.252167	−	0.183210i	−0.706687	+	0.707527i	$0.749811\pi$
$674$		−	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	$0.0196548\pi$
$677$	35.5217	+	25.8080i	1.36521	+	0.991883i	0.367116	+	0.930175i	$0.380345\pi$
$678$	−13.6560	+	4.43710i	−0.524455	+	0.170406i
$679$	−0.732843	−	2.25546i	−0.0281239	−	0.0865565i
$680$	−5.59758	−	24.5599i	−0.214657	−	0.941830i
$681$	−17.9064	+	55.1101i	−0.686173	+	2.11182i
$682$			5.28390i			0.202331i
$683$	1.05304	−	3.24091i	0.0402933	−	0.124010i	−0.928886	−	0.370365i	$-0.879233\pi$
$683$	1.05304	−	3.24091i	0.0402933	−	0.124010i	0.969180	+	0.246355i	$0.0792328\pi$
$684$	−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	0.401789	−	0.915732i	$-0.368388\pi$
$691$	−15.5956	−	21.4655i	−0.593283	−	0.816585i	−0.995073	+	0.0991476i	$0.968388\pi$
$692$	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
$697$	−5.61514	−	14.0184i	−0.212689	−	0.530986i
$698$	−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	0.666148	−	0.745819i	$-0.267942\pi$
$709$	−6.63065	−	9.12630i	−0.249019	−	0.342746i	−0.915167	+	0.403074i	$0.867942\pi$
$710$	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
$714$	−24.6910	−	15.5314i	−0.924038	−	0.581250i
$715$	−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	−0.587863	−	0.808960i	$-0.700031\pi$
$719$	−41.2657	−	13.4080i	−1.53895	−	0.500035i	−0.951086	+	0.308925i	$0.900031\pi$
$720$	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
$731$	−3.29099	+	13.0334i	−0.121722	+	0.482058i
$732$		−	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	$-0.291264\pi$
$743$	33.2420			1.21953			0.609765	+	0.792582i	$0.291264\pi$
$744$	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
$748$	−0.153171	−	0.0963495i	−0.00560049	−	0.00352289i
$749$	−2.71922			−0.0993583
$750$	33.2279	−	16.9534i	1.21331	−	0.619052i
$751$			17.1770i			0.626799i	0.949621	+	0.313399i	$0.101468\pi$
$751$			17.1770i			0.626799i	−0.949621	+	0.313399i	$0.898532\pi$
$752$	−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
$765$	−18.9490	−	8.10620i	−0.685103	−	0.293080i
$766$	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	+	0.374574i	−0.0415178	+	0.0134899i
$772$	0.612093	+	1.88383i	0.0220297	+	0.0678005i
$773$	13.2390	−	18.2219i	0.476174	−	0.655397i	−0.501590	−	0.865105i	$-0.667251\pi$
$773$	13.2390	−	18.2219i	0.476174	−	0.655397i	0.977764	+	0.209708i	$0.0672514\pi$
$774$	−10.6276			−0.382002
$775$	16.0923	−	49.5886i	0.578052	−	1.78128i
$776$			3.05579i			0.109697i
$777$	−23.0567	−	16.7517i	−0.827154	−	0.600962i
$778$	5.15299	−	1.67431i	0.184743	−	0.0600268i
$779$	−15.1249	+	4.91438i	−0.541906	+	0.176076i
$780$	−0.313071	−	0.614159i	−0.0112097	−	0.0219904i
$781$	−1.47161	+	4.52916i	−0.0526584	+	0.162066i
$782$	−25.3741	+	1.69815i	−0.907375	+	0.0607258i
$783$	8.11319	+	2.63613i	0.289942	+	0.0942077i
$784$	−8.58206	+	6.23523i	−0.306502	+	0.222687i
$785$	−23.3084	+	23.3170i	−0.831914	+	0.832218i
$786$	4.33895	+	3.15243i	0.154765	+	0.112443i
$787$	−23.5486	+	17.1090i	−0.839416	+	0.609872i	−0.922208	−	0.386695i	$-0.873617\pi$
$787$	−23.5486	+	17.1090i	−0.839416	+	0.609872i	0.0827912	+	0.996567i	$0.473617\pi$
$788$	−0.0411696	+	0.0299115i	−0.00146661	+	0.00106555i
$789$	−13.8792	+	19.1030i	−0.494112	+	0.680087i
$790$	−25.5572	+	13.0279i	−0.909283	+	0.463512i
$791$	−7.38251	+	5.36371i	−0.262492	+	0.190711i
$792$	−0.655928	+	2.01874i	−0.0233074	+	0.0717328i
$793$	0.920972			0.0327047
$794$	26.1726	+	8.50400i	0.928832	+	0.301796i
$795$	−2.39973	+	15.1693i	−0.0851098	+	0.537999i
$796$	−2.88904	+	0.938705i	−0.102399	+	0.0332715i
$797$	34.9600	−	11.3592i	1.23835	−	0.402364i	0.384616	−	0.923077i	$-0.374334\pi$
$797$	34.9600	−	11.3592i	1.23835	−	0.402364i	0.853732	+	0.520713i	$0.174334\pi$
$798$	−18.0562	+	24.8522i	−0.639182	+	0.879758i
$799$	44.3841	−	2.97040i	1.57020	−	0.105085i
$800$	−3.56668	+	0.00130353i	−0.126101	+	4.60868e-5i
$801$	10.7940			0.381388
$802$	19.2806	+	14.0081i	0.680820	+	0.494645i
$803$	4.06191	−	1.31979i	0.143342	−	0.0465745i
$804$	−1.82070	+	0.591580i	−0.0642111	+	0.0208634i
$805$	3.14096	+	19.8078i	0.110704	+	0.698134i
$806$	−15.4274	−	5.01267i	−0.543407	−	0.176564i
$807$		−	25.8423i		−	0.909694i
$808$	15.6096	+	5.07187i	0.549144	+	0.178428i
$809$	15.0755	+	20.7497i	0.530027	+	0.729520i	0.987135	−	0.159892i	$-0.0511146\pi$
$809$	15.0755	+	20.7497i	0.530027	+	0.729520i	−0.457108	+	0.889411i	$0.651115\pi$
$810$	−5.45606	+	34.4890i	−0.191706	+	1.21182i
$811$	26.4656	−	36.4267i	0.929331	−	1.27911i	−0.0307887	−	0.999526i	$-0.509802\pi$
$811$	26.4656	−	36.4267i	0.929331	−	1.27911i	0.960120	−	0.279589i	$-0.0901981\pi$
$812$	0.767557	+	1.05645i	0.0269360	+	0.0370742i
$813$	−52.6031	+	38.2184i	−1.84487	+	1.34038i
$814$	−2.40824	−	1.74969i	−0.0844088	−	0.0613266i
$815$	−1.47061	−	0.232647i	−0.0515133	−	0.00814925i
$816$	25.5999	+	30.6946i	0.896177	+	1.07453i
$817$	13.4636	+	4.37458i	0.471031	+	0.153047i
$818$		−	48.4393i		−	1.69364i
$819$	4.80969	+	1.56276i	0.168064	+	0.0546074i
$820$	−1.02149	+	0.161980i	−0.0356720	+	0.00565658i
$821$	53.2310	−	17.2958i	1.85777	−	0.603627i	0.862554	−	0.505965i	$-0.168864\pi$
$821$	53.2310	−	17.2958i	1.85777	−	0.603627i	0.995220	−	0.0976618i	$-0.0311363\pi$
$822$	−10.3990	−	32.0048i	−0.362706	−	1.11630i
$823$	−11.6448	−	8.46044i	−0.405912	−	0.294912i	0.366033	−	0.930602i	$-0.380716\pi$
$823$	−11.6448	−	8.46044i	−0.405912	−	0.294912i	−0.771945	+	0.635690i	$0.780716\pi$
$824$	−37.4797			−1.30567
$825$	−1.22724	+	3.78177i	−0.0427272	+	0.131664i
$826$			34.9710i			1.21680i
$827$	22.1780	+	16.1133i	0.771206	+	0.560314i	0.902327	−	0.431053i	$-0.141858\pi$
$827$	22.1780	+	16.1133i	0.771206	+	0.560314i	−0.131121	+	0.991366i	$0.541858\pi$
$828$	−0.369007	−	1.13569i	−0.0128239	−	0.0394678i
$829$	−5.58149	−	17.1781i	−0.193853	−	0.596618i	−0.999988	−	0.00488670i	$-0.998445\pi$
$829$	−5.58149	−	17.1781i	−0.193853	−	0.596618i	0.806135	−	0.591732i	$-0.201555\pi$
$830$	21.7856	+	3.44643i	0.756191	+	0.119627i
$831$	12.4949	−	38.4555i	0.433444	−	1.33400i
$832$		−	7.93031i		−	0.274934i
$833$	10.0096	+	2.52747i	0.346812	+	0.0875716i
$834$	36.8484	−	26.7719i	1.27595	−	0.927036i
$835$	−12.1881	+	6.21295i	−0.421787	+	0.215008i
$836$	−0.112012	+	0.154171i	−0.00387400	+	0.00533211i
$837$	10.7211	+	14.7564i	0.370577	+	0.510055i
$838$	9.06278	−	6.58450i	0.313069	−	0.227458i
$839$	5.67741	−	7.81429i	0.196006	−	0.269779i	−0.699689	−	0.714447i	$-0.746678\pi$
$839$	5.67741	−	7.81429i	0.196006	−	0.269779i	0.895695	+	0.444668i	$0.146678\pi$
$840$	20.9557	−	20.9633i	0.723040	−	0.723304i
$841$	−4.22206	+	3.06751i	−0.145588	+	0.105776i
$842$	−6.52946	−	2.12155i	−0.225020	−	0.0731135i
$843$	48.3108			1.66391
$844$	−0.0223467	−	0.00726089i	−0.000769206	−	0.000249930i
$845$	−23.6305	+	12.0458i	−0.812915	+	0.414388i
$846$	10.8677	+	33.4473i	0.373639	+	1.14994i
$847$	7.12852	+	21.9393i	0.244939	+	0.753844i
$848$	7.47494	−	10.2884i	0.256690	−	0.353304i
$849$	−0.766681			−0.0263124
$850$	19.2625	+	23.0788i	0.660697	+	0.791595i
$851$	−24.8466			−0.851731
$852$	−2.32742	+	3.20341i	−0.0797360	+	0.109747i
$853$	−8.16172	−	25.1192i	−0.279452	−	0.860065i	−0.988007	−	0.154409i	$-0.950653\pi$
$853$	−8.16172	−	25.1192i	−0.279452	−	0.860065i	0.708555	−	0.705656i	$-0.249347\pi$
$854$	−0.824777	−	2.53840i	−0.0282233	−	0.0868624i
$855$	−9.85021	+	19.3409i	−0.336870	+	0.661444i
$856$	3.33232	+	1.08274i	0.113896	+	0.0370072i
$857$	−35.1893			−1.20204			−0.601022	−	0.799233i	$-0.705239\pi$
$857$	−35.1893			−1.20204			−0.601022	+	0.799233i	$0.705239\pi$
$858$	1.17654	+	0.382281i	0.0401664	+	0.0130508i
$859$	−35.6873	+	25.9284i	−1.21764	+	0.884664i	−0.995902	−	0.0904430i	$-0.971172\pi$
$859$	−35.6873	+	25.9284i	−1.21764	+	0.884664i	−0.221734	+	0.975107i	$0.571172\pi$
$860$	0.820384	+	0.417818i	0.0279749	+	0.0142475i
$861$	10.4449	−	14.3761i	0.355960	−	0.489937i
$862$	−15.2229	+	11.0601i	−0.518493	+	0.376708i
$863$	0.358860	+	0.493929i	0.0122158	+	0.0168135i	0.815081	−	0.579347i	$-0.196692\pi$
$863$	0.358860	+	0.493929i	0.0122158	+	0.0168135i	−0.802865	+	0.596160i	$0.796692\pi$
$864$	0.733467	−	1.00953i	0.0249531	−	0.0343449i
$865$	−2.83411	−	17.8727i	−0.0963626	−	0.607691i
$866$	−0.522056	+	0.379296i	−0.0177402	+	0.0128890i
$867$	6.98337	−	38.2660i	0.237168	−	1.29958i
$868$			2.79209i			0.0947696i
$869$	0.944818	−	2.90785i	0.0320508	−	0.0986421i
$870$	25.7309	+	25.7215i	0.872361	+	0.872042i
$871$	−2.18425	−	6.72242i	−0.0740103	−	0.227780i
$872$	−1.05570	−	3.24910i	−0.0357503	−	0.110028i
$873$	2.02273	+	1.46960i	0.0684590	+	0.0497384i
$874$			26.7815i			0.905899i
$875$	16.7541	−	16.7725i	0.566391	−	0.567013i
$876$	3.55115			0.119982
$877$	−27.0703	−	19.6677i	−0.914100	−	0.664133i	0.0279484	−	0.999609i	$-0.491103\pi$
$877$	−27.0703	−	19.6677i	−0.914100	−	0.664133i	−0.942048	+	0.335477i	$0.891103\pi$
$878$	17.4138	+	53.5942i	0.587688	+	1.80872i
$879$	25.4775	−	8.27813i	0.859333	−	0.279214i
$880$	2.32756	−	2.32841i	0.0784619	−	0.0784906i
$881$	−31.3770	−	10.1950i	−1.05712	−	0.343479i	−0.271660	−	0.962393i	$-0.587573\pi$
$881$	−31.3770	−	10.1950i	−1.05712	−	0.343479i	−0.785458	+	0.618914i	$0.787573\pi$
$882$			8.16198i			0.274828i
$883$	−11.2042	−	3.64046i	−0.377051	−	0.122511i	0.114360	−	0.993439i	$-0.463518\pi$
$883$	−11.2042	−	3.64046i	−0.377051	−	0.122511i	−0.491410	+	0.870928i	$0.663518\pi$
$884$	0.426620	−	0.355810i	0.0143488	−	0.0119672i
$885$	9.06305	+	57.1543i	0.304651	+	1.92122i
$886$	−26.6735	−	19.3794i	−0.896113	−	0.651064i
$887$	23.2459	−	16.8891i	0.780520	−	0.567081i	−0.124615	−	0.992205i	$-0.539770\pi$
$887$	23.2459	−	16.8891i	0.780520	−	0.567081i	0.905135	+	0.425124i	$0.139770\pi$
$888$	21.5850	+	29.7093i	0.724347	+	0.996978i
$889$	−2.23399	+	3.07482i	−0.0749255	+	0.103126i
$890$	−14.0291	−	7.14495i	−0.470256	−	0.239499i
$891$	−2.18756	−	3.01092i	−0.0732860	−	0.100870i
$892$	1.95524	+	0.635297i	0.0654663	+	0.0212713i
$893$		−	46.8460i		−	1.56764i
$894$	−32.2716	−	10.4857i	−1.07932	−	0.350694i
$895$	−20.6941	+	40.6328i	−0.691728	+	1.35821i
$896$	−24.7348	+	8.03681i	−0.826331	+	0.268491i
$897$	9.82045	−	3.19086i	0.327895	−	0.106540i
$898$	−21.5847	−	15.6822i	−0.720291	−	0.523322i
$899$	50.8477			1.69587
$900$	−0.829271	+	1.14227i	−0.0276424	+	0.0380757i
$901$	−12.3488	+	0.826437i	−0.411397	+	0.0275326i
$902$	1.09095	−	1.50157i	0.0363247	−	0.0499967i
$903$	−15.0438	+	4.88803i	−0.500627	+	0.162664i
$904$	11.1827	−	3.63349i	0.371932	−	0.120848i
$905$	−2.11912	−	4.15712i	−0.0704419	−	0.138187i
$906$	48.9847	+	15.9161i	1.62741	+	0.528777i
$907$	−57.7097			−1.91622			−0.958110	−	0.286399i	$-0.907542\pi$
$907$	−57.7097			−1.91622			−0.958110	+	0.286399i	$0.907542\pi$
$908$	−0.988291	+	3.04165i	−0.0327976	+	0.100941i
$909$	10.8642	−	7.89334i	0.360344	−	0.261806i
$910$	−5.21676	−	5.21485i	−0.172934	−	0.172871i
$911$	21.9813	−	30.2547i	0.728273	−	1.00238i	−0.270935	−	0.962598i	$-0.587333\pi$
$911$	21.9813	−	30.2547i	0.728273	−	1.00238i	0.999208	−	0.0397844i	$-0.0126671\pi$
$912$	34.0530	−	24.7409i	1.12761	−	0.819254i
$913$	−1.90191	+	1.38182i	−0.0629439	+	0.0457314i
$914$	38.3389	+	27.8549i	1.26814	+	0.921357i
$915$	−2.00581	−	3.93485i	−0.0663101	−	0.130082i
$916$	−2.31835	+	1.68438i	−0.0766004	+	0.0556534i
$917$	3.24162	+	1.05327i	0.107048	+	0.0347820i
$918$	−10.4938	+	0.702295i	−0.346347	+	0.0231792i
$919$	−7.46635	+	22.9791i	−0.246292	+	0.758010i	0.749129	+	0.662424i	$0.230472\pi$
$919$	−7.46635	+	22.9791i	−0.246292	+	0.758010i	−0.995421	+	0.0955854i	$0.969528\pi$
$920$	4.03790	−	25.5245i	0.133126	−	0.841517i
$921$	42.1910	−	13.7087i	1.39024	−	0.451717i
$922$	−23.4020	+	7.60379i	−0.770705	+	0.250417i
$923$	−11.8277	−	8.59334i	−0.389314	−	0.282853i
$924$		−	0.212933i		−	0.00700497i
$925$	17.2723	+	23.7550i	0.567908	+	0.781058i
$926$	44.0633			1.44801
$927$	−18.0248	+	24.8091i	−0.592013	+	0.814836i
$928$	−1.07496	−	3.30840i	−0.0352874	−	0.108603i
$929$	−15.5198	+	5.04267i	−0.509187	+	0.165445i	−0.552332	−	0.833624i	$-0.686262\pi$
$929$	−15.5198	+	5.04267i	−0.509187	+	0.165445i	0.0431457	+	0.999069i	$0.486262\pi$
$930$	12.1832	+	76.8308i	0.399503	+	2.51938i
$931$	3.35966	−	10.3400i	0.110109	−	0.338879i
$932$	2.62616			0.0860227
$933$	63.6314	+	20.6751i	2.08320	+	0.676873i
$934$	−26.5973	+	19.3241i	−0.870291	+	0.632304i
$935$	−3.19106	−	0.288204i	−0.104359	−	0.00942529i
$936$	−5.27186	−	3.83023i	−0.172316	−	0.125195i
$937$	5.13906	+	7.07331i	0.167886	+	0.231075i	0.884667	−	0.466223i	$-0.154386\pi$
$937$	5.13906	+	7.07331i	0.167886	+	0.231075i	−0.716782	+	0.697298i	$0.754386\pi$
$938$	−16.5724	+	12.0405i	−0.541107	+	0.393137i
$939$	44.5940	+	32.3995i	1.45527	+	1.05732i
$940$	0.476042	−	3.00917i	0.0155268	−	0.0981484i
$941$	7.78443	+	10.7143i	0.253765	+	0.349278i	0.916825	−	0.399288i	$-0.130743\pi$
$941$	7.78443	+	10.7143i	0.253765	+	0.349278i	−0.663060	+	0.748566i	$0.730743\pi$
$942$	15.2018	−	46.7862i	0.495300	−	1.52438i
$943$		−	15.4922i		−	0.504494i
$944$	14.8075	−	45.5727i	0.481942	−	1.48326i
$945$	1.29899	+	8.19179i	0.0422561	+	0.266479i
$946$	−1.57131	+	0.510549i	−0.0510877	+	0.0165994i
$947$	−4.28683	−	13.1935i	−0.139303	−	0.428731i	0.856931	−	0.515431i	$-0.172368\pi$
$947$	−4.28683	−	13.1935i	−0.139303	−	0.428731i	−0.996235	+	0.0866994i	$0.972368\pi$
$948$	1.49427	−	2.05669i	0.0485316	−	0.0667981i
$949$			13.1116i			0.425621i
$950$	25.6049	−	18.6173i	0.830731	−	0.604026i
$951$	62.5877			2.02955
$952$	20.2192	+	12.7185i	0.655308	+	0.412210i
$953$	−31.6213	+	10.2744i	−1.02432	+	0.332820i	−0.772540	−	0.634966i	$-0.781014\pi$
$953$	−31.6213	+	10.2744i	−1.02432	+	0.332820i	−0.251775	+	0.967786i	$0.581014\pi$
$954$	−3.02366	−	9.30586i	−0.0978946	−	0.301288i
$955$	−46.3170	−	7.32722i	−1.49878	−	0.237103i
$956$	0.254531	−	0.783367i	0.00823213	−	0.0253359i
$957$	−3.87780			−0.125351
$958$	8.58672	−	26.4272i	0.277424	−	0.853824i
$959$	−12.5706	−	17.3020i	−0.405927	−	0.558711i
$960$	−33.8822	+	17.2717i	−1.09354	+	0.557441i
$961$	62.8766	+	45.6825i	2.02828	+	1.47363i
$962$	7.39319	−	5.37147i	0.238366	−	0.173183i
$963$	2.31929	−	1.68506i	0.0747380	−	0.0543003i
$964$	−0.0593135	+	0.0816380i	−0.00191036	+	0.00262938i
$965$	24.8044	+	24.7953i	0.798482	+	0.798190i
$966$	−17.5894	−	24.2098i	−0.565931	−	0.778937i
$967$	−38.2217	−	12.4190i	−1.22913	−	0.399367i	−0.378728	−	0.925508i	$-0.623639\pi$
$967$	−38.2217	−	12.4190i	−1.22913	−	0.399367i	−0.850398	+	0.526141i	$0.823639\pi$
$968$		−	29.7243i		−	0.955376i
$969$	−39.7174	−	10.0288i	−1.27591	−	0.322172i
$970$	−1.65618	−	3.24897i	−0.0531768	−	0.104318i
$971$	−12.9284	−	39.7895i	−0.414892	−	1.27691i	−0.912348	−	0.409416i	$-0.865732\pi$
$971$	−12.9284	−	39.7895i	−0.414892	−	1.27691i	0.497456	−	0.867489i	$-0.334268\pi$
$972$	−0.751444	−	2.31271i	−0.0241026	−	0.0741801i
$973$	17.0141	−	23.4179i	0.545447	−	0.750744i
$974$			2.41894i			0.0775080i
$975$	−9.87740	−	7.17084i	−0.316330	−	0.229651i
$976$			3.65717i			0.117063i
$977$	−13.1206	+	18.0589i	−0.419765	+	0.577756i	−0.965566	−	0.260158i	$-0.916225\pi$
$977$	−13.1206	+	18.0589i	−0.419765	+	0.577756i	0.545801	+	0.837915i	$0.316225\pi$
$978$	2.11289	−	0.686518i	0.0675626	−	0.0219524i
$979$	1.59591	−	0.518543i	0.0510055	−	0.0165727i
$980$	0.320882	−	0.630052i	0.0102502	−	0.0201263i
$981$	−2.65839	−	0.863764i	−0.0848759	−	0.0275778i
$982$			37.0457i			1.18218i
$983$	−4.00619	+	12.3298i	−0.127778	+	0.393260i	−0.994397	−	0.105711i	$-0.966288\pi$
$983$	−4.00619	+	12.3298i	−0.127778	+	0.393260i	0.866619	+	0.498970i	$0.166288\pi$
$984$	−18.5241	+	13.4585i	−0.590526	+	0.429042i
$985$	−0.408921	+	0.802915i	−0.0130293	+	0.0255830i
$986$	−15.6111	+	24.8176i	−0.497157	+	0.790353i
$987$	30.7673	+	42.3476i	0.979334	+	1.34794i
$988$	−0.343871	−	0.473298i	−0.0109400	−	0.0150576i
$989$	−8.10586	+	11.1568i	−0.257751	+	0.354764i
$990$	−0.396725	−	2.50186i	−0.0126087	−	0.0795144i
$991$	20.4909	+	28.2033i	0.650915	+	0.895908i	0.999138	−	0.0415038i	$-0.0132149\pi$
$991$	20.4909	+	28.2033i	0.650915	+	0.895908i	−0.348223	+	0.937412i	$0.613215\pi$
$992$	2.29843	−	7.07383i	0.0729751	−	0.224594i
$993$	0.281098			0.00892037
$994$	−13.0928	+	40.2956i	−0.415279	+	1.27810i
$995$	−38.0261	+	38.0400i	−1.20551	+	1.20595i
$996$	−1.85901	+	0.604030i	−0.0589051	+	0.0191394i
$997$	−19.2539	−	59.2575i	−0.609778	−	1.87670i	−0.459820	−	0.888012i	$-0.652086\pi$
$997$	−19.2539	−	59.2575i	−0.609778	−	1.87670i	−0.149959	−	0.988692i	$-0.547914\pi$
$998$	5.12471	+	3.72332i	0.162220	+	0.117860i
$999$	−10.2757			−0.325108

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.q.a.84.11	✓	176
17.16	even	2	inner	425.2.q.a.84.12	yes	176
25.14	even	10	inner	425.2.q.a.339.12	yes	176
425.339	even	10	inner	425.2.q.a.339.11	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.q.a.84.11	✓	176	1.1	even	1	trivial
425.2.q.a.84.12	yes	176	17.16	even	2	inner
425.2.q.a.339.11	yes	176	425.339	even	10	inner
425.2.q.a.339.12	yes	176	25.14	even	10	inner

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} +(-3.99763 - 1.00942i) 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} +(4.61716 - 3.85081i) 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} +(4.72623 + 7.91598i) 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

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