LMFDB - Embedded newform 61.2.g.a.41.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [61,2,Mod(3,61)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(61, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("61.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	61.g (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:	$0.487087452330$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 17x^{14} + 111x^{12} + 361x^{10} + 624x^{8} + 558x^{6} + 229x^{4} + 34x^{2} + 1 $ x^16 + 17x^14 + 111x^12 + 361x^10 + 624x^8 + 558x^6 + 229x^4 + 34*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			41.3
Root			$0.196205i$ of defining polynomial
Character	$\chi$	$=$	61.41
Dual form			61.2.g.a.3.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.186602 + 0.0606307i) q^{2} +(-0.865057 - 2.66237i) q^{3} +(-1.58689 + 1.15294i) q^{4} +(2.93210 - 2.13030i) q^{5} +(0.322843 + 0.444355i) q^{6} +(-0.222647 - 0.0723423i) q^{7} +(0.456866 - 0.628822i) q^{8} +(-3.91286 + 2.84286i) q^{9} +O(q^{10})$	\(q+(-0.186602 + 0.0606307i) q^{2} +(-0.865057 - 2.66237i) q^{3} +(-1.58689 + 1.15294i) q^{4} +(2.93210 - 2.13030i) q^{5} +(0.322843 + 0.444355i) q^{6} +(-0.222647 - 0.0723423i) q^{7} +(0.456866 - 0.628822i) q^{8} +(-3.91286 + 2.84286i) q^{9} +(-0.417975 + 0.575293i) q^{10} +5.67170i q^{11} +(4.44232 + 3.22753i) q^{12} +2.04020 q^{13} +0.0459325 q^{14} +(-8.20809 - 5.96352i) q^{15} +(1.16515 - 3.58596i) q^{16} +(1.75528 + 2.41593i) q^{17} +(0.557783 - 0.767722i) q^{18} +(-0.260434 - 0.801534i) q^{19} +(-2.19681 + 6.76110i) q^{20} +0.655349i q^{21} +(-0.343879 - 1.05835i) q^{22} +(-2.06434 - 2.84132i) q^{23} +(-2.06937 - 0.672381i) q^{24} +(2.51398 - 7.73723i) q^{25} +(-0.380706 + 0.123699i) q^{26} +(4.15934 + 3.02194i) q^{27} +(0.436722 - 0.141900i) q^{28} +3.91037i q^{29} +(1.89322 + 0.615144i) q^{30} +(-3.42153 - 1.11172i) q^{31} +2.29433i q^{32} +(15.1002 - 4.90635i) q^{33} +(-0.474018 - 0.344394i) q^{34} +(-0.806934 + 0.262189i) q^{35} +(2.93162 - 9.02260i) q^{36} +(-1.13466 - 0.368672i) q^{37} +(0.0971952 + 0.133778i) q^{38} +(-1.76489 - 5.43177i) q^{39} -2.81703i q^{40} +(-1.18684 + 3.65272i) q^{41} +(-0.0397343 - 0.122289i) q^{42} +(-5.62586 + 7.74333i) q^{43} +(-6.53915 - 9.00037i) q^{44} +(-5.41677 + 16.6711i) q^{45} +(0.557481 + 0.405034i) q^{46} +6.21907 q^{47} -10.5551 q^{48} +(-5.61878 - 4.08228i) q^{49} +1.59621i q^{50} +(4.91370 - 6.76312i) q^{51} +(-3.23757 + 2.35223i) q^{52} +(-1.35820 + 1.86940i) q^{53} +(-0.959363 - 0.311716i) q^{54} +(12.0824 + 16.6300i) q^{55} +(-0.147210 + 0.106954i) q^{56} +(-1.90869 + 1.38675i) q^{57} +(-0.237088 - 0.729682i) q^{58} +(4.75809 - 1.54600i) q^{59} +19.9009 q^{60} +(-7.54478 - 2.01897i) q^{61} +0.705868 q^{62} +(1.07684 - 0.349888i) q^{63} +(2.19119 + 6.74380i) q^{64} +(5.98208 - 4.34623i) q^{65} +(-2.52025 + 1.83107i) q^{66} +(-1.99679 - 2.74834i) q^{67} +(-5.57086 - 1.81008i) q^{68} +(-5.77888 + 7.95394i) q^{69} +(0.134679 - 0.0978499i) q^{70} +(-1.12923 + 1.55426i) q^{71} +3.75929i q^{72} +(-4.14393 - 3.01074i) q^{73} +0.234082 q^{74} -22.7741 q^{75} +(1.33740 + 0.971681i) q^{76} +(0.410304 - 1.26279i) q^{77} +(0.658664 + 0.906574i) q^{78} +(6.05463 - 8.33349i) q^{79} +(-4.22283 - 12.9965i) q^{80} +(-0.0362779 + 0.111652i) q^{81} -0.753565i q^{82} +(-3.02904 - 9.32242i) q^{83} +(-0.755580 - 1.03997i) q^{84} +(10.2933 + 3.34450i) q^{85} +(0.580314 - 1.78602i) q^{86} +(10.4109 - 3.38269i) q^{87} +(3.56649 + 2.59121i) q^{88} +(6.67476 - 2.16876i) q^{89} -3.43928i q^{90} +(-0.454244 - 0.147593i) q^{91} +(6.55176 + 2.12879i) q^{92} +10.0711i q^{93} +(-1.16049 + 0.377067i) q^{94} +(-2.47113 - 1.79538i) q^{95} +(6.10835 - 1.98472i) q^{96} +(3.58986 - 11.0485i) q^{97} +(1.29599 + 0.421092i) q^{98} +(-16.1238 - 22.1926i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 5 q^{2} - q^{3} + 3 q^{4} - 15 q^{6} + 10 q^{7} - 5 q^{8} + q^{9}+O(q^{10}) $ 16 * q - 5 * q^2 - q^3 + 3 * q^4 - 15 * q^6 + 10 * q^7 - 5 * q^8 + q^9	$ 16 q - 5 q^{2} - q^{3} + 3 q^{4} - 15 q^{6} + 10 q^{7} - 5 q^{8} + q^{9} - 5 q^{10} - 12 q^{13} - 18 q^{14} - 13 q^{15} + 19 q^{16} - 10 q^{18} + 3 q^{19} - 13 q^{20} + 19 q^{22} - 15 q^{23} + 10 q^{24} - 2 q^{25} + 10 q^{26} - 4 q^{27} + 35 q^{28} + 45 q^{30} - 15 q^{31} + 25 q^{33} - 14 q^{34} + 10 q^{35} + 37 q^{36} - 5 q^{37} - 15 q^{38} - 3 q^{39} + 12 q^{41} - 15 q^{42} - 25 q^{43} - 50 q^{44} + 36 q^{45} + 27 q^{46} + 6 q^{47} - 20 q^{48} - 30 q^{49} + 50 q^{51} - 46 q^{52} - 20 q^{53} - 20 q^{54} + 20 q^{55} - 28 q^{56} - 11 q^{57} - 41 q^{58} + 5 q^{59} + 14 q^{60} - 53 q^{61} + 16 q^{62} - 5 q^{63} + 17 q^{64} + 20 q^{65} + 13 q^{66} - 55 q^{67} + 80 q^{68} - 15 q^{69} - 17 q^{70} - 50 q^{71} - 11 q^{73} + 24 q^{74} - 88 q^{75} - 19 q^{76} + 63 q^{77} + 50 q^{78} + 40 q^{79} - 49 q^{80} - 19 q^{81} + 31 q^{83} - 25 q^{84} + 55 q^{85} + 35 q^{86} + 25 q^{87} + 27 q^{88} + 60 q^{89} - 15 q^{91} - 5 q^{92} + 65 q^{94} + 48 q^{95} - 25 q^{96} + 45 q^{97} + 10 q^{98} - 5 q^{99}+O(q^{100}) $ 16 * q - 5 * q^2 - q^3 + 3 * q^4 - 15 * q^6 + 10 * q^7 - 5 * q^8 + q^9 - 5 * q^10 - 12 * q^13 - 18 * q^14 - 13 * q^15 + 19 * q^16 - 10 * q^18 + 3 * q^19 - 13 * q^20 + 19 * q^22 - 15 * q^23 + 10 * q^24 - 2 * q^25 + 10 * q^26 - 4 * q^27 + 35 * q^28 + 45 * q^30 - 15 * q^31 + 25 * q^33 - 14 * q^34 + 10 * q^35 + 37 * q^36 - 5 * q^37 - 15 * q^38 - 3 * q^39 + 12 * q^41 - 15 * q^42 - 25 * q^43 - 50 * q^44 + 36 * q^45 + 27 * q^46 + 6 * q^47 - 20 * q^48 - 30 * q^49 + 50 * q^51 - 46 * q^52 - 20 * q^53 - 20 * q^54 + 20 * q^55 - 28 * q^56 - 11 * q^57 - 41 * q^58 + 5 * q^59 + 14 * q^60 - 53 * q^61 + 16 * q^62 - 5 * q^63 + 17 * q^64 + 20 * q^65 + 13 * q^66 - 55 * q^67 + 80 * q^68 - 15 * q^69 - 17 * q^70 - 50 * q^71 - 11 * q^73 + 24 * q^74 - 88 * q^75 - 19 * q^76 + 63 * q^77 + 50 * q^78 + 40 * q^79 - 49 * q^80 - 19 * q^81 + 31 * q^83 - 25 * q^84 + 55 * q^85 + 35 * q^86 + 25 * q^87 + 27 * q^88 + 60 * q^89 - 15 * q^91 - 5 * q^92 + 65 * q^94 + 48 * q^95 - 25 * q^96 + 45 * q^97 + 10 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/61\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{9}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.186602	+	0.0606307i	−0.131948	+	0.0428724i	−0.374246	−	0.927329i	$-0.622099\pi$
$2$	−0.186602	+	0.0606307i	−0.131948	+	0.0428724i	0.242299	+	0.970202i	$0.422099\pi$
$3$	−0.865057	−	2.66237i	−0.499441	−	1.53712i	−0.809919	−	0.586541i	$-0.800489\pi$
$3$	−0.865057	−	2.66237i	−0.499441	−	1.53712i	0.310478	−	0.950581i	$-0.399511\pi$
$4$	−1.58689	+	1.15294i	−0.793445	+	0.576471i
$5$	2.93210	−	2.13030i	1.31128	−	0.952698i	0.311280	−	0.950318i	$-0.399242\pi$
$5$	2.93210	−	2.13030i	1.31128	−	0.952698i	0.999997	−	0.00237986i	$-0.000757534\pi$
$6$	0.322843	+	0.444355i	0.131800	+	0.181407i
$7$	−0.222647	−	0.0723423i	−0.0841525	−	0.0273428i	0.266638	−	0.963797i	$-0.414087\pi$
$7$	−0.222647	−	0.0723423i	−0.0841525	−	0.0273428i	−0.350791	+	0.936454i	$0.614087\pi$
$8$	0.456866	−	0.628822i	0.161527	−	0.222322i
$9$	−3.91286	+	2.84286i	−1.30429	+	0.947619i
$10$	−0.417975	+	0.575293i	−0.132175	+	0.181924i
$11$			5.67170i			1.71008i	0.518560	+	0.855041i	$0.326468\pi$
$11$			5.67170i			1.71008i	−0.518560	+	0.855041i	$0.673532\pi$
$12$	4.44232	+	3.22753i	1.28239	+	0.931708i
$13$	2.04020			0.565850			0.282925	−	0.959142i	$-0.408695\pi$
$13$	2.04020			0.565850			0.282925	+	0.959142i	$0.408695\pi$
$14$	0.0459325			0.0122760
$15$	−8.20809	−	5.96352i	−2.11932	−	1.53978i
$16$	1.16515	−	3.58596i	0.291287	−	0.896490i
$17$	1.75528	+	2.41593i	0.425717	+	0.585950i	0.966964	−	0.254915i	$-0.0820473\pi$
$17$	1.75528	+	2.41593i	0.425717	+	0.585950i	−0.541246	+	0.840864i	$0.682047\pi$
$18$	0.557783	−	0.767722i	0.131471	−	0.180954i
$19$	−0.260434	−	0.801534i	−0.0597477	−	0.183885i	0.916728	−	0.399512i	$-0.130820\pi$
$19$	−0.260434	−	0.801534i	−0.0597477	−	0.183885i	−0.976476	+	0.215627i	$0.930820\pi$
$20$	−2.19681	+	6.76110i	−0.491222	+	1.51183i
$21$			0.655349i			0.143009i
$22$	−0.343879	−	1.05835i	−0.0733153	−	0.225641i
$23$	−2.06434	−	2.84132i	−0.430444	−	0.592456i	0.537611	−	0.843193i	$-0.319327\pi$
$23$	−2.06434	−	2.84132i	−0.430444	−	0.592456i	−0.968055	+	0.250737i	$0.919327\pi$
$24$	−2.06937	−	0.672381i	−0.422409	−	0.137249i
$25$	2.51398	−	7.73723i	0.502796	−	1.54745i
$26$	−0.380706	+	0.123699i	−0.0746625	+	0.0242593i
$27$	4.15934	+	3.02194i	0.800465	+	0.581572i
$28$	0.436722	−	0.141900i	0.0825328	−	0.0268165i
$29$			3.91037i			0.726137i	0.931762	+	0.363068i	$0.118271\pi$
$29$			3.91037i			0.726137i	−0.931762	+	0.363068i	$0.881729\pi$
$30$	1.89322	+	0.615144i	0.345653	+	0.112309i
$31$	−3.42153	−	1.11172i	−0.614524	−	0.199671i	−0.0148166	−	0.999890i	$-0.504716\pi$
$31$	−3.42153	−	1.11172i	−0.614524	−	0.199671i	−0.599708	+	0.800219i	$0.704716\pi$
$32$			2.29433i			0.405583i
$33$	15.1002	−	4.90635i	2.62861	−	0.854086i
$34$	−0.474018	−	0.344394i	−0.0812934	−	0.0590631i
$35$	−0.806934	+	0.262189i	−0.136397	+	0.0443180i
$36$	2.93162	−	9.02260i	0.488603	−	1.50377i
$37$	−1.13466	−	0.368672i	−0.186536	−	0.0606094i	0.214259	−	0.976777i	$-0.431266\pi$
$37$	−1.13466	−	0.368672i	−0.186536	−	0.0606094i	−0.400796	+	0.916167i	$0.631266\pi$
$38$	0.0971952	+	0.133778i	0.0157671	+	0.0217016i
$39$	−1.76489	−	5.43177i	−0.282609	−	0.869780i
$40$		−	2.81703i		−	0.445412i
$41$	−1.18684	+	3.65272i	−0.185354	+	0.570460i	−0.999954	−	0.00956255i	$-0.996956\pi$
$41$	−1.18684	+	3.65272i	−0.185354	+	0.570460i	0.814601	+	0.580022i	$0.196956\pi$
$42$	−0.0397343	−	0.122289i	−0.00613113	−	0.0188697i
$43$	−5.62586	+	7.74333i	−0.857936	+	1.18085i	0.124122	+	0.992267i	$0.460388\pi$
$43$	−5.62586	+	7.74333i	−0.857936	+	1.18085i	−0.982058	+	0.188580i	$0.939612\pi$
$44$	−6.53915	−	9.00037i	−0.985814	−	1.35686i
$45$	−5.41677	+	16.6711i	−0.807484	+	2.48518i
$46$	0.557481	+	0.405034i	0.0821961	+	0.0597190i
$47$	6.21907			0.907145			0.453573	−	0.891219i	$-0.350149\pi$
$47$	6.21907			0.907145			0.453573	+	0.891219i	$0.350149\pi$
$48$	−10.5551			−1.52350
$49$	−5.61878	−	4.08228i	−0.802683	−	0.583183i
$50$			1.59621i			0.225738i
$51$	4.91370	−	6.76312i	0.688055	−	0.947027i
$52$	−3.23757	+	2.35223i	−0.448971	+	0.326196i
$53$	−1.35820	+	1.86940i	−0.186563	+	0.256781i	−0.892046	−	0.451945i	$-0.850730\pi$
$53$	−1.35820	+	1.86940i	−0.186563	+	0.256781i	0.705483	+	0.708727i	$0.250730\pi$
$54$	−0.959363	−	0.311716i	−0.130553	−	0.0424192i
$55$	12.0824	+	16.6300i	1.62919	+	2.24239i
$56$	−0.147210	+	0.106954i	−0.0196718	+	0.0142924i
$57$	−1.90869	+	1.38675i	−0.252813	+	0.183679i
$58$	−0.237088	−	0.729682i	−0.0311312	−	0.0958120i
$59$	4.75809	−	1.54600i	0.619451	−	0.201272i	0.0175545	−	0.999846i	$-0.494412\pi$
$59$	4.75809	−	1.54600i	0.619451	−	0.201272i	0.601897	+	0.798574i	$0.294412\pi$
$60$	19.9009			2.56920
$61$	−7.54478	−	2.01897i	−0.966011	−	0.258502i
$61$	−7.54478	−	2.01897i	−0.966011	−	0.258502i
$62$	0.705868			0.0896453
$63$	1.07684	−	0.349888i	0.135669	−	0.0440817i
$64$	2.19119	+	6.74380i	0.273899	+	0.842975i
$65$	5.98208	−	4.34623i	0.741986	−	0.539084i
$66$	−2.52025	+	1.83107i	−0.310222	+	0.225389i
$67$	−1.99679	−	2.74834i	−0.243947	−	0.335764i	0.669433	−	0.742872i	$-0.266537\pi$
$67$	−1.99679	−	2.74834i	−0.243947	−	0.335764i	−0.913380	+	0.407109i	$0.866537\pi$
$68$	−5.57086	−	1.81008i	−0.675566	−	0.219505i
$69$	−5.77888	+	7.95394i	−0.695695	+	0.957542i
$70$	0.134679	−	0.0978499i	0.0160972	−	0.0116953i
$71$	−1.12923	+	1.55426i	−0.134015	+	0.184456i	−0.870751	−	0.491725i	$-0.836367\pi$
$71$	−1.12923	+	1.55426i	−0.134015	+	0.184456i	0.736735	+	0.676182i	$0.236367\pi$
$72$			3.75929i			0.443037i
$73$	−4.14393	−	3.01074i	−0.485011	−	0.352381i	0.318252	−	0.948006i	$-0.396904\pi$
$73$	−4.14393	−	3.01074i	−0.485011	−	0.352381i	−0.803262	+	0.595625i	$0.796904\pi$
$74$	0.234082			0.0272115
$75$	−22.7741			−2.62973
$76$	1.33740	+	0.971681i	0.153411	+	0.111459i
$77$	0.410304	−	1.26279i	0.0467585	−	0.143908i
$78$	0.658664	+	0.906574i	0.0745791	+	0.102649i
$79$	6.05463	−	8.33349i	0.681199	−	0.937590i	−0.318748	−	0.947839i	$-0.603262\pi$
$79$	6.05463	−	8.33349i	0.681199	−	0.937590i	0.999947	+	0.0102491i	$0.00326244\pi$
$80$	−4.22283	−	12.9965i	−0.472127	−	1.45306i
$81$	−0.0362779	+	0.111652i	−0.00403087	+	0.0124058i
$82$		−	0.753565i		−	0.0832173i
$83$	−3.02904	−	9.32242i	−0.332480	−	1.02327i	−0.967950	−	0.251143i	$-0.919194\pi$
$83$	−3.02904	−	9.32242i	−0.332480	−	1.02327i	0.635470	−	0.772125i	$-0.280806\pi$
$84$	−0.755580	−	1.03997i	−0.0824405	−	0.113470i
$85$	10.2933	+	3.34450i	1.11647	+	0.362762i
$86$	0.580314	−	1.78602i	0.0625768	−	0.192592i
$87$	10.4109	−	3.38269i	1.11616	−	0.362663i
$88$	3.56649	+	2.59121i	0.380189	+	0.276224i
$89$	6.67476	−	2.16876i	0.707523	−	0.229888i	0.0669175	−	0.997759i	$-0.478684\pi$
$89$	6.67476	−	2.16876i	0.707523	−	0.229888i	0.640605	+	0.767870i	$0.278684\pi$
$90$		−	3.43928i		−	0.362532i
$91$	−0.454244	−	0.147593i	−0.0476177	−	0.0154719i
$92$	6.55176	+	2.12879i	0.683068	+	0.221942i
$93$			10.0711i			1.04432i
$94$	−1.16049	+	0.377067i	−0.119696	+	0.0388915i
$95$	−2.47113	−	1.79538i	−0.253532	−	0.184202i
$96$	6.10835	−	1.98472i	0.623431	−	0.202565i
$97$	3.58986	−	11.0485i	0.364495	−	1.12180i	−0.585801	−	0.810455i	$-0.699220\pi$
$97$	3.58986	−	11.0485i	0.364495	−	1.12180i	0.950297	−	0.311346i	$-0.100780\pi$
$98$	1.29599	+	0.421092i	0.130915	+	0.0425367i
$99$	−16.1238	−	22.1926i	−1.62051	−	2.23044i
$100$	4.93118	+	15.1766i	0.493118	+	1.51766i
$101$			9.61575i			0.956803i	0.878141	+	0.478402i	$0.158784\pi$
$101$			9.61575i			0.956803i	−0.878141	+	0.478402i	$0.841216\pi$
$102$	−0.506853	+	1.55993i	−0.0501859	+	0.154456i
$103$	0.415686	+	1.27935i	0.0409588	+	0.126058i	0.969445	−	0.245309i	$-0.0788893\pi$
$103$	0.415686	+	1.27935i	0.0409588	+	0.126058i	−0.928486	+	0.371367i	$0.878889\pi$
$104$	0.932098	−	1.28292i	0.0913997	−	0.125801i
$105$	1.39609	+	1.92155i	0.136244	+	0.187524i
$106$	0.140099	−	0.431182i	0.0136077	−	0.0418801i
$107$	14.5954	+	10.6041i	1.41099	+	1.02514i	0.993178	+	0.116606i	$0.0372015\pi$
$107$	14.5954	+	10.6041i	1.41099	+	1.02514i	0.417808	+	0.908535i	$0.362799\pi$
$108$	−10.0845			−0.970385
$109$	13.3997			1.28346			0.641731	−	0.766930i	$-0.278217\pi$
$109$	13.3997			1.28346			0.641731	+	0.766930i	$0.278217\pi$
$110$	−3.26289	−	2.37063i	−0.311105	−	0.226031i
$111$			3.33980i			0.317000i
$112$	−0.518833	+	0.714113i	−0.0490252	+	0.0674773i
$113$	−9.44394	+	6.86142i	−0.888411	+	0.645469i	−0.935463	−	0.353424i	$-0.885017\pi$
$113$	−9.44394	+	6.86142i	−0.888411	+	0.645469i	0.0470520	+	0.998892i	$0.485017\pi$
$114$	0.272087	−	0.374495i	0.0254833	−	0.0350747i
$115$	−12.1057	−	3.93338i	−1.12886	−	0.366790i
$116$	−4.50843	−	6.20532i	−0.418597	−	0.576150i
$117$	−7.98301	+	5.80000i	−0.738029	+	0.536210i
$118$	−0.794135	+	0.576973i	−0.0731061	+	0.0531147i
$119$	−0.216033	−	0.664880i	−0.0198037	−	0.0609495i
$120$	−7.49999	+	2.43690i	−0.684652	+	0.222457i
$121$	−21.1682			−1.92438
$122$	1.53028	−	0.0807019i	0.138545	−	0.00730640i
$123$	10.7516			0.969439
$124$	6.71133	−	2.18064i	0.602696	−	0.195828i
$125$	−3.51154	−	10.8074i	−0.314081	−	0.966643i
$126$	−0.179727	+	0.130579i	−0.0160114	+	0.0116329i
$127$	8.38899	−	6.09496i	0.744403	−	0.540840i	−0.149684	−	0.988734i	$-0.547826\pi$
$127$	8.38899	−	6.09496i	0.744403	−	0.540840i	0.894087	+	0.447894i	$0.147826\pi$
$128$	−3.51490	−	4.83785i	−0.310677	−	0.427610i
$129$	25.4823	+	8.27971i	2.24359	+	0.728988i
$130$	−0.852753	+	1.17371i	−0.0747914	+	0.102942i
$131$	−1.05388	+	0.765691i	−0.0920782	+	0.0668987i	−0.632872	−	0.774257i	$-0.718124\pi$
$131$	−1.05388	+	0.765691i	−0.0920782	+	0.0668987i	0.540794	+	0.841155i	$0.318124\pi$
$132$	−18.3056	+	25.1955i	−1.59330	+	2.19299i
$133$			0.197299i			0.0171080i
$134$	0.539239	+	0.391780i	0.0465831	+	0.0338446i
$135$	18.6332			1.60369
$136$	2.32112			0.199034
$137$	−6.44428	−	4.68204i	−0.550572	−	0.400014i	0.277425	−	0.960747i	$-0.410519\pi$
$137$	−6.44428	−	4.68204i	−0.550572	−	0.400014i	−0.827996	+	0.560734i	$0.810519\pi$
$138$	0.596098	−	1.83460i	0.0507432	−	0.156172i
$139$	−8.70163	−	11.9768i	−0.738063	−	1.01586i	−0.998728	−	0.0504268i	$-0.983942\pi$
$139$	−8.70163	−	11.9768i	−0.738063	−	1.01586i	0.260665	−	0.965429i	$-0.416058\pi$
$140$	0.978227	−	1.34641i	0.0826752	−	0.113793i
$141$	−5.37986	−	16.5575i	−0.453066	−	1.39439i
$142$	0.116482	−	0.358494i	0.00977493	−	0.0300841i
$143$			11.5714i			0.967650i
$144$	5.63531	+	17.3437i	0.469609	+	1.44531i
$145$	8.33025	+	11.4656i	0.691789	+	0.952166i
$146$	0.955810	+	0.310561i	0.0791034	+	0.0257022i
$147$	−6.00799	+	18.4907i	−0.495531	+	1.52509i
$148$	2.22563	−	0.723152i	0.182946	−	0.0594427i
$149$	−12.8814	−	9.35889i	−1.05529	−	0.766710i	−0.0820758	−	0.996626i	$-0.526155\pi$
$149$	−12.8814	−	9.35889i	−1.05529	−	0.766710i	−0.973211	+	0.229916i	$0.926155\pi$
$150$	4.24970	−	1.38081i	0.346986	−	0.112743i
$151$			14.2978i			1.16354i	0.813354	+	0.581769i	$0.197639\pi$
$151$			14.2978i			1.16354i	−0.813354	+	0.581769i	$0.802361\pi$
$152$	−0.623006	−	0.202427i	−0.0505325	−	0.0164190i
$153$	−13.7363	−	4.46319i	−1.11051	−	0.360828i
$154$			0.260516i			0.0209929i
$155$	−12.4006	+	4.02919i	−0.996037	+	0.323632i
$156$	9.06321	+	6.58481i	0.725638	+	0.527207i
$157$	−1.45961	+	0.474257i	−0.116490	+	0.0378499i	−0.366682	−	0.930346i	$-0.619506\pi$
$157$	−1.45961	+	0.474257i	−0.116490	+	0.0378499i	0.250192	+	0.968196i	$0.419506\pi$
$158$	−0.624542	+	1.92214i	−0.0496859	+	0.152917i
$159$	6.15195	+	1.99889i	0.487882	+	0.158522i
$160$	4.88760	+	6.72720i	0.386398	+	0.531832i
$161$	0.254071	+	0.781949i	0.0200236	+	0.0616262i
$162$		−	0.0230340i		−	0.00180972i
$163$	−3.88891	+	11.9688i	−0.304603	+	0.937471i	0.675223	+	0.737614i	$0.264048\pi$
$163$	−3.88891	+	11.9688i	−0.304603	+	0.937471i	−0.979825	+	0.199856i	$0.935952\pi$
$164$	−2.32799	−	7.16483i	−0.181786	−	0.559479i
$165$	33.8233	−	46.5538i	2.63314	−	3.62421i
$166$	1.13045	+	1.55593i	0.0877399	+	0.120764i
$167$	3.27928	−	10.0926i	0.253758	−	0.780988i	−0.740313	−	0.672262i	$-0.765323\pi$
$167$	3.27928	−	10.0926i	0.253758	−	0.780988i	0.994072	−	0.108726i	$-0.0346771\pi$
$168$	0.412098	+	0.299407i	0.0317940	+	0.0230997i
$169$	−8.83758			−0.679814
$170$	−2.12353			−0.162867
$171$	3.29769	+	2.39591i	0.252181	+	0.183220i
$172$		−	18.7741i		−	1.43151i
$173$	11.4963	−	15.8233i	0.874045	−	1.20302i	−0.103989	−	0.994578i	$-0.533161\pi$
$173$	11.4963	−	15.8233i	0.874045	−	1.20302i	0.978035	−	0.208442i	$-0.0668392\pi$
$174$	−1.73759	+	1.26243i	−0.131727	+	0.0957049i
$175$	−1.11946	+	1.54080i	−0.0846230	+	0.116474i
$176$	20.3385	+	6.60838i	1.53307	+	0.498126i
$177$	−8.23205	−	11.3304i	−0.618759	−	0.851648i
$178$	−1.11403	+	0.809390i	−0.0835001	+	0.0606663i
$179$	−0.388965	+	0.282599i	−0.0290726	+	0.0211225i	−0.602227	−	0.798325i	$-0.705720\pi$
$179$	−0.388965	+	0.282599i	−0.0290726	+	0.0211225i	0.573154	+	0.819448i	$0.305720\pi$
$180$	−10.6250	−	32.7004i	−0.791941	−	2.43735i
$181$	−19.0605	+	6.19313i	−1.41676	+	0.460332i	−0.914570	−	0.404428i	$-0.867471\pi$
$181$	−19.0605	+	6.19313i	−1.41676	+	0.460332i	−0.502186	+	0.864760i	$0.667471\pi$
$182$	0.0937115			0.00694636
$183$	1.15143	+	21.8336i	0.0851159	+	1.61398i
$184$	−2.72981			−0.201244
$185$	−4.11231	+	1.33617i	−0.302343	+	0.0982373i
$186$	−0.610617	−	1.87928i	−0.0447726	−	0.137796i
$187$	−13.7024	+	9.95541i	−1.00202	+	0.728012i
$188$	−9.86899	+	7.17024i	−0.719770	+	0.522943i
$189$	−0.707449	−	0.973720i	−0.0514594	−	0.0708277i
$190$	0.569973	+	0.185195i	0.0413502	+	0.0134355i
$191$	7.58053	−	10.4337i	0.548508	−	0.754956i	−0.441301	−	0.897359i	$-0.645483\pi$
$191$	7.58053	−	10.4337i	0.548508	−	0.754956i	0.989809	+	0.142403i	$0.0454828\pi$
$192$	16.0590	−	11.6675i	1.15896	−	0.842033i
$193$	12.3347	−	16.9772i	0.887869	−	1.22205i	−0.0863095	−	0.996268i	$-0.527507\pi$
$193$	12.3347	−	16.9772i	0.887869	−	1.22205i	0.974179	−	0.225779i	$-0.0724926\pi$
$194$			2.27932i			0.163646i
$195$	−16.7461	−	12.1668i	−1.19922	−	0.871281i
$196$	13.6230			0.973073
$197$	6.13245			0.436919			0.218459	−	0.975846i	$-0.429897\pi$
$197$	6.13245			0.436919			0.218459	+	0.975846i	$0.429897\pi$
$198$	4.35429	+	3.16358i	0.309446	+	0.224826i
$199$	−5.31897	+	16.3701i	−0.377052	+	1.16045i	0.565032	+	0.825069i	$0.308864\pi$
$199$	−5.31897	+	16.3701i	−0.377052	+	1.16045i	−0.942084	+	0.335377i	$0.891136\pi$
$200$	−3.71679	−	5.11572i	−0.262817	−	0.361736i
$201$	−5.58978	+	7.69367i	−0.394273	+	0.542670i
$202$	−0.583010	−	1.79432i	−0.0410204	−	0.126248i
$203$	0.282885	−	0.870630i	0.0198546	−	0.0611063i
$204$			16.3975i			1.14806i
$205$	4.30145	+	13.2385i	0.300426	+	0.924616i
$206$	−0.155136	−	0.213526i	−0.0108088	−	0.0148771i
$207$	16.1549	+	5.24905i	1.12284	+	0.364834i
$208$	2.37714	−	7.31608i	0.164825	−	0.507279i
$209$	4.54607	−	1.47711i	0.314458	−	0.102174i
$210$	−0.377018	−	0.273920i	−0.0260167	−	0.0189022i
$211$	5.61742	−	1.82521i	0.386719	−	0.125653i	−0.109203	−	0.994019i	$-0.534830\pi$
$211$	5.61742	−	1.82521i	0.386719	−	0.125653i	0.495923	+	0.868367i	$0.334830\pi$
$212$		−	4.53245i		−	0.311290i
$213$	5.11487	+	1.66192i	0.350465	+	0.113873i
$214$	−3.36646	−	1.09383i	−0.230126	−	0.0747726i
$215$			34.6890i			2.36577i
$216$	3.80052	−	1.23486i	0.258593	−	0.0840219i
$217$	0.681367	+	0.495042i	0.0462542	+	0.0336056i
$218$	−2.50042	+	0.812435i	−0.169350	+	0.0550250i
$219$	−4.43098	+	13.6372i	−0.299418	+	0.921514i
$220$	−38.3469	−	12.4597i	−2.58535	−	0.840031i
$221$	3.58112	+	4.92898i	0.240892	+	0.331559i
$222$	−0.202495	−	0.623214i	−0.0135905	−	0.0418274i
$223$		−	27.4756i		−	1.83990i	−0.392034	−	0.919951i	$-0.628228\pi$
$223$		−	27.4756i		−	1.83990i	0.392034	−	0.919951i	$-0.371772\pi$
$224$	0.165977	−	0.510824i	0.0110898	−	0.0341309i
$225$	12.1590	+	37.4215i	0.810599	+	2.49477i
$226$	1.34625	−	1.85295i	0.0895510	−	0.123256i
$227$	−1.17961	−	1.62359i	−0.0782934	−	0.107762i	0.768074	−	0.640361i	$-0.221215\pi$
$227$	−1.17961	−	1.62359i	−0.0782934	−	0.107762i	−0.846367	+	0.532599i	$0.821215\pi$
$228$	1.43005	−	4.40123i	0.0947071	−	0.291478i
$229$	6.75806	+	4.91002i	0.446585	+	0.324463i	0.788246	−	0.615360i	$-0.210989\pi$
$229$	6.75806	+	4.91002i	0.446585	+	0.324463i	−0.341661	+	0.939823i	$0.610989\pi$
$230$	2.49743			0.164676
$231$	−3.71694			−0.244557
$232$	2.45892	+	1.78651i	0.161436	+	0.117290i
$233$		−	18.5006i		−	1.21201i	−0.795460	−	0.606006i	$-0.792771\pi$
$233$		−	18.5006i		−	1.21201i	0.795460	−	0.606006i	$-0.207229\pi$
$234$	1.13799	−	1.56631i	0.0743926	−	0.102393i
$235$	18.2350	−	13.2485i	1.18952	−	0.864236i
$236$	−5.76812	+	7.93914i	−0.375473	+	0.516794i
$237$	−27.4245	−	8.91074i	−1.78141	−	0.578815i
$238$	0.0806243	+	0.110970i	0.00522610	+	0.00719310i
$239$	−8.49551	+	6.17235i	−0.549529	+	0.399256i	−0.827612	−	0.561301i	$-0.810301\pi$
$239$	−8.49551	+	6.17235i	−0.549529	+	0.399256i	0.278083	+	0.960557i	$0.410301\pi$
$240$	−30.9486	+	22.4855i	−1.99772	+	1.45143i
$241$	4.36820	+	13.4439i	0.281381	+	0.866001i	0.987460	+	0.157868i	$0.0504621\pi$
$241$	4.36820	+	13.4439i	0.281381	+	0.866001i	−0.706080	+	0.708133i	$0.749538\pi$
$242$	3.95003	−	1.28344i	0.253918	−	0.0825029i
$243$	15.7523			1.01051
$244$	14.3005	−	5.49483i	0.915495	−	0.351770i
$245$	−25.1713			−1.60814
$246$	−2.00627	+	0.651877i	−0.127915	+	0.0415621i
$247$	−0.531338	−	1.63529i	−0.0338082	−	0.104051i
$248$	−2.26225	+	1.64362i	−0.143653	+	0.104370i
$249$	−22.1995	+	16.1289i	−1.40683	+	1.02212i
$250$	1.31052	+	1.80378i	0.0828846	+	0.114081i
$251$	21.6700	+	7.04100i	1.36780	+	0.444424i	0.898638	−	0.438690i	$-0.144557\pi$
$251$	21.6700	+	7.04100i	1.36780	+	0.444424i	0.469158	+	0.883114i	$0.344557\pi$
$252$	−1.30543	+	1.79677i	−0.0822344	+	0.113186i
$253$	16.1151	−	11.7083i	1.01315	−	0.736096i
$254$	−1.19586	+	1.64596i	−0.0750351	+	0.103277i
$255$		−	30.2978i		−	1.89732i
$256$	−10.5240	−	7.64615i	−0.657751	−	0.477884i
$257$	−7.98748			−0.498245			−0.249123	−	0.968472i	$-0.580142\pi$
$257$	−7.98748			−0.498245			−0.249123	+	0.968472i	$0.580142\pi$
$258$	−5.25706			−0.327290
$259$	0.225957	+	0.164167i	0.0140403	+	0.0102009i
$260$	−4.48194	+	13.7940i	−0.277958	+	0.855467i
$261$	−11.1166	−	15.3007i	−0.688101	−	0.947089i
$262$	0.150232	−	0.206777i	0.00928139	−	0.0127747i
$263$	5.64414	+	17.3709i	0.348033	+	1.07113i	0.959940	+	0.280205i	$0.0904026\pi$
$263$	5.64414	+	17.3709i	0.348033	+	1.07113i	−0.611907	+	0.790930i	$0.709597\pi$
$264$	3.81354	−	11.7369i	0.234707	−	0.722355i
$265$			8.37463i			0.514450i
$266$	−0.0119624	−	0.0368165i	−0.000733462	−	0.00225736i
$267$	−11.5481	−	15.8946i	−0.706732	−	0.972733i
$268$	6.33737	+	2.05914i	0.387116	+	0.125782i
$269$	−5.92188	+	18.2257i	−0.361063	+	1.11124i	0.591347	+	0.806417i	$0.298597\pi$
$269$	−5.92188	+	18.2257i	−0.361063	+	1.11124i	−0.952410	+	0.304821i	$0.901403\pi$
$270$	−3.47700	+	1.12975i	−0.211604	+	0.0687542i
$271$	13.7869	+	10.0167i	0.837492	+	0.608474i	0.921669	−	0.387977i	$-0.126826\pi$
$271$	13.7869	+	10.0167i	0.837492	+	0.608474i	−0.0841768	+	0.996451i	$0.526826\pi$
$272$	10.7086	−	3.47944i	0.649304	−	0.210972i
$273$			1.33704i			0.0809215i
$274$	1.48639	+	0.482958i	0.0897961	+	0.0291765i
$275$	43.8833	+	14.2585i	2.64626	+	0.859822i
$276$		−	19.2847i		−	1.16081i
$277$	−7.67775	+	2.49465i	−0.461311	+	0.149889i	−0.530447	−	0.847718i	$-0.677976\pi$
$277$	−7.67775	+	2.49465i	−0.461311	+	0.149889i	0.0691357	+	0.997607i	$0.477976\pi$
$278$	2.34990	+	1.70730i	0.140938	+	0.102397i
$279$	16.5484	−	5.37690i	0.990727	−	0.321907i
$280$	−0.203791	+	0.627203i	−0.0121788	+	0.0374826i
$281$	17.1860	+	5.58408i	1.02523	+	0.333118i	0.772904	−	0.634523i	$-0.218803\pi$
$281$	17.1860	+	5.58408i	1.02523	+	0.333118i	0.252329	+	0.967642i	$0.418803\pi$
$282$	2.00778	+	2.76348i	0.119562	+	0.164563i
$283$	−4.21538	−	12.9736i	−0.250578	−	0.771201i	−0.994669	−	0.103122i	$-0.967117\pi$
$283$	−4.21538	−	12.9736i	−0.250578	−	0.771201i	0.744091	−	0.668079i	$-0.232883\pi$
$284$		−	3.76838i		−	0.223612i
$285$	−2.64230	+	8.13217i	−0.156516	+	0.481708i
$286$	−0.701583	−	2.15925i	−0.0414854	−	0.127679i
$287$	0.528493	−	0.727408i	0.0311959	−	0.0429375i
$288$	−6.52244	−	8.97736i	−0.384338	−	0.528996i
$289$	2.49756	−	7.68670i	0.146915	−	0.452159i
$290$	−2.24961	−	1.63444i	−0.132102	−	0.0959774i
$291$	−32.5205			−1.90639
$292$	10.0472			0.587967
$293$	3.59005	+	2.60833i	0.209733	+	0.152380i	0.687693	−	0.726002i	$-0.258624\pi$
$293$	3.59005	+	2.60833i	0.209733	+	0.152380i	−0.477960	+	0.878382i	$0.658624\pi$
$294$		−	3.81467i		−	0.222476i
$295$	10.6578	−	14.6692i	0.620520	−	0.854073i
$296$	−0.750216	+	0.545064i	−0.0436054	+	0.0316812i
$297$	−17.1395	+	23.5905i	−0.994536	+	1.36886i
$298$	2.97113	+	0.965380i	0.172113	+	0.0559230i
$299$	−4.21166	−	5.79686i	−0.243567	−	0.335241i
$300$	36.1400	−	26.2573i	2.08655	−	1.51596i
$301$	1.81275	−	1.31704i	0.104485	−	0.0759129i
$302$	−0.866886	−	2.66800i	−0.0498837	−	0.153526i
$303$	25.6007	−	8.31818i	1.47072	−	0.477867i
$304$	−3.17772			−0.182255
$305$	−26.4231	+	10.1528i	−1.51298	+	0.581349i
$306$	2.83383			0.161999
$307$	−30.6130	+	9.94678i	−1.74718	+	0.567693i	−0.995748	−	0.0921196i	$-0.970636\pi$
$307$	−30.6130	+	9.94678i	−1.74718	+	0.567693i	−0.751430	+	0.659812i	$0.770636\pi$
$308$	0.804813	+	2.47696i	0.0458585	+	0.141138i
$309$	3.04652	−	2.21342i	0.173310	−	0.125917i
$310$	2.06968	−	1.50371i	0.117550	−	0.0854050i
$311$	−11.0144	−	15.1600i	−0.624570	−	0.859647i	0.373105	−	0.927789i	$-0.378293\pi$
$311$	−11.0144	−	15.1600i	−0.624570	−	0.859647i	−0.997676	+	0.0681417i	$0.978293\pi$
$312$	−4.22194	−	1.37179i	−0.239020	−	0.0776624i
$313$	−1.14068	+	1.57001i	−0.0644750	+	0.0887422i	−0.840037	−	0.542529i	$-0.817467\pi$
$313$	−1.14068	+	1.57001i	−0.0644750	+	0.0887422i	0.775562	+	0.631272i	$0.217467\pi$
$314$	0.243612	−	0.176995i	0.0137478	−	0.00998840i
$315$	2.41205	−	3.31990i	0.135904	−	0.187055i
$316$			20.2050i			1.13662i
$317$	2.45467	+	1.78342i	0.137868	+	0.100167i	0.654582	−	0.755991i	$-0.272845\pi$
$317$	2.45467	+	1.78342i	0.137868	+	0.100167i	−0.516714	+	0.856158i	$0.672845\pi$
$318$	−1.26916			−0.0711710
$319$	−22.1784			−1.24175
$320$	20.7911	+	15.1056i	1.16226	+	0.844430i
$321$	15.6064	−	48.0315i	0.871063	−	2.68086i
$322$	−0.0948202	−	0.130509i	−0.00528413	−	0.00727297i
$323$	1.47932	−	2.03611i	0.0823115	−	0.113292i
$324$	−0.0711592	−	0.219005i	−0.00395329	−	0.0121670i
$325$	5.12902	−	15.7855i	0.284507	−	0.875622i
$326$		−	2.46919i		−	0.136756i
$327$	−11.5915	−	35.6751i	−0.641013	−	1.97284i
$328$	1.75469	+	2.41512i	0.0968863	+	0.133353i
$329$	−1.38466	−	0.449902i	−0.0763386	−	0.0248039i
$330$	−3.48891	+	10.7378i	−0.192058	+	0.591095i
$331$	−26.8491	+	8.72379i	−1.47576	+	0.479503i	−0.932842	−	0.360284i	$-0.882680\pi$
$331$	−26.8491	+	8.72379i	−1.47576	+	0.479503i	−0.542916	+	0.839787i	$0.682680\pi$
$332$	15.5550	+	11.3013i	0.853689	+	0.620242i
$333$	5.48783	−	1.78310i	0.300731	−	0.0977135i
$334$			2.08212i			0.113929i
$335$	−11.7096	−	3.80467i	−0.639763	−	0.207872i
$336$	2.35006	+	0.763580i	0.128206	+	0.0416567i
$337$		−	28.0471i		−	1.52782i	−0.645322	−	0.763911i	$-0.723277\pi$
$337$		−	28.0471i		−	1.52782i	0.645322	−	0.763911i	$-0.276723\pi$
$338$	1.64911	−	0.535829i	0.0896998	−	0.0291452i
$339$	26.4372	+	19.2078i	1.43587	+	1.04322i
$340$	−20.1904	+	6.56025i	−1.09498	+	0.355779i
$341$	6.30535	−	19.4059i	0.341454	−	1.05089i
$342$	−0.760621	−	0.247141i	−0.0411297	−	0.0133638i
$343$	1.91890	+	2.64114i	0.103611	+	0.142608i
$344$	2.29891	+	7.07533i	0.123949	+	0.381476i
$345$			35.6325i			1.91839i
$346$	−1.18585	+	3.64968i	−0.0637518	+	0.196208i
$347$	−5.22338	−	16.0759i	−0.280406	−	0.863000i	−0.987738	−	0.156119i	$-0.950102\pi$
$347$	−5.22338	−	16.0759i	−0.280406	−	0.863000i	0.707333	−	0.706881i	$-0.249898\pi$
$348$	−12.6208	+	17.3711i	−0.676547	+	0.931188i
$349$	16.8759	+	23.2276i	0.903344	+	1.24335i	0.969389	+	0.245530i	$0.0789621\pi$
$349$	16.8759	+	23.2276i	0.903344	+	1.24335i	−0.0660445	+	0.997817i	$0.521038\pi$
$350$	0.115473	−	0.355390i	0.00617231	−	0.0189964i
$351$	8.48588	+	6.16536i	0.452943	+	0.329082i
$352$	−13.0127			−0.693581
$353$	−25.0218			−1.33178			−0.665888	−	0.746052i	$-0.731947\pi$
$353$	−25.0218			−1.33178			−0.665888	+	0.746052i	$0.731947\pi$
$354$	2.22309	+	1.61517i	0.118156	+	0.0858453i
$355$			6.96285i			0.369550i
$356$	−8.09165	+	11.1372i	−0.428856	+	0.590270i
$357$	−1.58328	+	1.15032i	−0.0837960	+	0.0608813i
$358$	0.0554474	−	0.0763168i	0.00293049	−	0.00403347i
$359$	10.3742	+	3.37080i	0.547532	+	0.177904i	0.569703	−	0.821850i	$-0.307058\pi$
$359$	10.3742	+	3.37080i	0.547532	+	0.177904i	−0.0221718	+	0.999754i	$0.507058\pi$
$360$	8.00842	+	11.0226i	0.422081	+	0.580944i
$361$	14.7967	−	10.7504i	0.778773	−	0.565812i
$362$	3.18124	−	2.31130i	0.167202	−	0.121479i
$363$	18.3117	+	56.3577i	0.961117	+	2.95801i
$364$	0.891001	−	0.289504i	0.0467011	−	0.0151741i
$365$	−18.5642			−0.971696
$366$	−1.53864	−	4.00437i	−0.0804261	−	0.209312i
$367$	22.4321			1.17094			0.585472	−	0.810693i	$-0.300909\pi$
$367$	22.4321			1.17094			0.585472	+	0.810693i	$0.300909\pi$
$368$	−12.5941	+	4.09208i	−0.656514	+	0.213314i
$369$	−5.74023	−	17.6666i	−0.298824	−	0.919686i
$370$	0.686353	−	0.498665i	0.0356818	−	0.0259244i
$371$	0.437635	−	0.317960i	0.0227209	−	0.0165077i
$372$	−11.6114	−	15.9817i	−0.602022	−	0.828612i
$373$	18.7588	+	6.09511i	0.971295	+	0.315593i	0.751338	−	0.659917i	$-0.229409\pi$
$373$	18.7588	+	6.09511i	0.971295	+	0.315593i	0.219956	+	0.975510i	$0.429409\pi$
$374$	1.95330	−	2.68849i	0.101003	−	0.139018i
$375$	−25.7357	+	18.6980i	−1.32898	+	0.965563i
$376$	2.84128	−	3.91069i	0.146528	−	0.201679i
$377$			7.97793i			0.410884i
$378$	0.191049	+	0.138805i	0.00982649	+	0.00713936i
$379$	1.63979			0.0842305			0.0421152	−	0.999113i	$-0.486590\pi$
$379$	1.63979			0.0842305			0.0421152	+	0.999113i	$0.486590\pi$
$380$	5.99138			0.307351
$381$	−23.4840	−	17.0621i	−1.20312	−	0.874120i
$382$	−0.781940	+	2.40656i	−0.0400075	+	0.123131i
$383$	8.73773	+	12.0265i	0.446477	+	0.614523i	0.971636	−	0.236481i	$-0.0759942\pi$
$383$	8.73773	+	12.0265i	0.446477	+	0.614523i	−0.525159	+	0.851004i	$0.675994\pi$
$384$	−9.83957	+	13.5430i	−0.502123	+	0.691114i
$385$	−1.48706	−	4.57669i	−0.0757874	−	0.233250i
$386$	−1.27233	+	3.91584i	−0.0647601	+	0.199311i
$387$		−	46.2920i		−	2.35316i
$388$	7.04153	+	21.6716i	0.357479	+	1.10021i
$389$	14.5755	+	20.0615i	0.739008	+	1.01716i	0.998675	+	0.0514592i	$0.0163872\pi$
$389$	14.5755	+	20.0615i	0.739008	+	1.01716i	−0.259667	+	0.965698i	$0.583613\pi$
$390$	3.86254	+	1.25502i	0.195588	+	0.0635502i
$391$	3.24095	−	9.97460i	0.163902	−	0.504437i
$392$	−5.13406	+	1.66816i	−0.259309	+	0.0842547i
$393$	2.95022	+	2.14346i	0.148819	+	0.108123i
$394$	−1.14433	+	0.371814i	−0.0576504	+	0.0187317i
$395$		−	37.3328i		−	1.87842i
$396$	51.1735	+	16.6273i	2.57157	+	0.835552i
$397$	10.3288	+	3.35605i	0.518390	+	0.168435i	0.556515	−	0.830838i	$-0.312138\pi$
$397$	10.3288	+	3.35605i	0.518390	+	0.168435i	−0.0381245	+	0.999273i	$0.512138\pi$
$398$		−	3.37719i		−	0.169283i
$399$	0.525285	−	0.170675i	0.0262971	−	0.00854445i
$400$	−24.8162	−	18.0301i	−1.24081	−	0.901503i
$401$	−19.3998	+	6.30338i	−0.968780	+	0.314776i	−0.750323	−	0.661071i	$-0.770102\pi$
$401$	−19.3998	+	6.30338i	−0.968780	+	0.314776i	−0.218457	+	0.975847i	$0.570102\pi$
$402$	0.576592	−	1.77457i	0.0287578	−	0.0885074i
$403$	−6.98060	−	2.26813i	−0.347728	−	0.112984i
$404$	−11.0864	−	15.2591i	−0.551570	−	0.759171i
$405$	0.131481	+	0.404657i	0.00653335	+	0.0201076i
$406$			0.179613i			0.00891404i
$407$	2.09100	−	6.43544i	0.103647	−	0.318993i
$408$	−2.00790	−	6.17968i	−0.0994059	−	0.305940i
$409$	−7.08332	+	9.74936i	−0.350248	+	0.482075i	−0.947399	−	0.320054i	$-0.896299\pi$
$409$	−7.08332	+	9.74936i	−0.350248	+	0.482075i	0.597152	+	0.802128i	$0.296299\pi$
$410$	−1.60532	−	2.20953i	−0.0792810	−	0.109121i
$411$	−6.89067	+	21.2073i	−0.339892	+	1.04608i
$412$	−2.13467	−	1.55093i	−0.105167	−	0.0764087i
$413$	−1.17122			−0.0576317
$414$	−3.33279			−0.163798
$415$	−28.7410	−	20.8815i	−1.41084	−	1.02503i
$416$			4.68088i			0.229499i
$417$	−24.3592	+	33.5276i	−1.19288	+	1.64185i
$418$	−0.758747	+	0.551262i	−0.0371115	+	0.0269631i
$419$	11.9002	−	16.3792i	0.581360	−	0.800174i	−0.412483	−	0.910965i	$-0.635338\pi$
$419$	11.9002	−	16.3792i	0.581360	−	0.800174i	0.993844	+	0.110791i	$0.0353385\pi$
$420$	−4.43088	−	1.43968i	−0.216205	−	0.0702492i
$421$	−9.75395	−	13.4252i	−0.475378	−	0.654302i	0.502230	−	0.864734i	$-0.332513\pi$
$421$	−9.75395	−	13.4252i	−0.475378	−	0.654302i	−0.977609	+	0.210432i	$0.932513\pi$
$422$	−0.937559	+	0.681176i	−0.0456397	+	0.0331592i
$423$	−24.3343	+	17.6799i	−1.18318	+	0.859628i
$424$	0.555005	+	1.70813i	0.0269534	+	0.0829540i
$425$	23.1053	−	7.50738i	1.12077	−	0.364161i
$426$	−1.05521			−0.0511250
$427$	1.53376	+	0.995324i	0.0742241	+	0.0481671i
$428$	−35.3872			−1.71050
$429$	30.8074	−	10.0099i	1.48740	−	0.483284i
$430$	−2.10322	−	6.47304i	−0.101426	−	0.312158i
$431$	10.1007	−	7.33861i	0.486535	−	0.353489i	−0.317315	−	0.948320i	$-0.602781\pi$
$431$	10.1007	−	7.33861i	0.486535	−	0.353489i	0.803850	+	0.594832i	$0.202781\pi$
$432$	15.6828	−	11.3942i	0.754539	−	0.548205i
$433$	17.9344	+	24.6846i	0.861873	+	1.18627i	0.981120	+	0.193401i	$0.0619520\pi$
$433$	17.9344	+	24.6846i	0.861873	+	1.18627i	−0.119247	+	0.992865i	$0.538048\pi$
$434$	−0.157159	−	0.0510641i	−0.00754388	−	0.00245116i
$435$	23.3196	−	32.0966i	1.11809	−	1.53892i
$436$	−21.2639	+	15.4491i	−1.01836	+	0.739879i
$437$	−1.73979	+	2.39462i	−0.0832254	+	0.114550i
$438$		−	2.81338i		−	0.134428i
$439$	1.57598	+	1.14501i	0.0752172	+	0.0546485i	0.624758	−	0.780818i	$-0.285197\pi$
$439$	1.57598	+	1.14501i	0.0752172	+	0.0546485i	−0.549541	+	0.835467i	$0.685197\pi$
$440$	15.9774			0.761691
$441$	33.5908			1.59956
$442$	−0.967092	−	0.702633i	−0.0459999	−	0.0334209i
$443$	−3.66131	+	11.2683i	−0.173954	+	0.535375i	−0.999584	−	0.0288365i	$-0.990820\pi$
$443$	−3.66131	+	11.2683i	−0.173954	+	0.535375i	0.825630	+	0.564212i	$0.190820\pi$
$444$	−3.85060	−	5.29990i	−0.182741	−	0.251522i
$445$	14.9510	−	20.5782i	0.708744	−	0.975502i
$446$	1.66586	+	5.12700i	0.0788809	+	0.242771i
$447$	−13.7737	+	42.3911i	−0.651474	+	2.00503i
$448$		−	1.66000i		−	0.0784276i
$449$	−7.04792	−	21.6913i	−0.332612	−	1.02367i	−0.967887	−	0.251387i	$-0.919113\pi$
$449$	−7.04792	−	21.6913i	−0.332612	−	1.02367i	0.635275	−	0.772286i	$-0.280887\pi$
$450$	−4.53779	−	6.24573i	−0.213913	−	0.294426i
$451$	−20.7172	−	6.73141i	−0.975533	−	0.316970i
$452$	7.07566	−	21.7766i	0.332811	−	1.02429i
$453$	38.0661	−	12.3684i	1.78850	−	0.581119i
$454$	0.318557	+	0.231445i	0.0149506	+	0.0108623i
$455$	−1.64631	+	0.534917i	−0.0771801	+	0.0250773i
$456$			1.83379i			0.0858749i
$457$	−2.83822	−	0.922193i	−0.132766	−	0.0431384i	0.241880	−	0.970306i	$-0.422236\pi$
$457$	−2.83822	−	0.922193i	−0.132766	−	0.0431384i	−0.374646	+	0.927168i	$0.622236\pi$
$458$	−1.55877	−	0.506474i	−0.0728364	−	0.0236660i
$459$			15.3530i			0.716617i
$460$	23.7454	−	7.71535i	1.10713	−	0.359730i
$461$	8.38686	+	6.09341i	0.390615	+	0.283798i	0.765707	−	0.643189i	$-0.222389\pi$
$461$	8.38686	+	6.09341i	0.390615	+	0.283798i	−0.375092	+	0.926987i	$0.622389\pi$
$462$	0.693590	−	0.225361i	0.0322687	−	0.0104847i
$463$	−0.561690	+	1.72870i	−0.0261039	+	0.0803397i	−0.963260	−	0.268571i	$-0.913448\pi$
$463$	−0.561690	+	1.72870i	−0.0261039	+	0.0803397i	0.937156	+	0.348911i	$0.113448\pi$
$464$	14.0224	+	4.55616i	0.650975	+	0.211515i
$465$	21.4544	+	29.5295i	0.994924	+	1.36940i
$466$	1.12170	+	3.45224i	0.0519618	+	0.159922i
$467$			13.3142i			0.616110i	0.951369	+	0.308055i	$0.0996780\pi$
$467$			13.3142i			0.616110i	−0.951369	+	0.308055i	$0.900322\pi$
$468$	5.98109	−	18.4079i	0.276476	−	0.850906i
$469$	0.245757	+	0.756362i	0.0113480	+	0.0349256i
$470$	−2.59942	+	3.57779i	−0.119902	+	0.165031i
$471$	2.52530	+	3.47578i	0.116360	+	0.160155i
$472$	1.20165	−	3.69831i	0.0553106	−	0.170228i
$473$	−43.9179	−	31.9082i	−2.01935	−	1.46714i
$474$	5.65772			0.259868
$475$	−6.85638			−0.314592
$476$	1.10939	+	0.806018i	0.0508488	+	0.0369438i
$477$		−	11.1758i		−	0.511707i
$478$	1.21105	−	1.66686i	0.0553920	−	0.0762405i
$479$	0.945134	−	0.686680i	0.0431843	−	0.0313752i	−0.565984	−	0.824416i	$-0.691504\pi$
$479$	0.945134	−	0.686680i	0.0431843	−	0.0313752i	0.609168	+	0.793041i	$0.291504\pi$
$480$	13.6823	−	18.8320i	0.624507	−	0.859560i
$481$	−2.31493	−	0.752165i	−0.105552	−	0.0342958i
$482$	−1.63023	−	2.24382i	−0.0742550	−	0.102203i
$483$	1.86205	−	1.35286i	0.0847264	−	0.0615574i
$484$	33.5916	−	24.4058i	1.52689	−	1.10935i
$485$	−13.0107	−	40.0427i	−0.590784	−	1.81825i
$486$	−2.93942	+	0.955074i	−0.133335	+	0.0433230i
$487$	19.7482			0.894875			0.447438	−	0.894315i	$-0.352337\pi$
$487$	19.7482			0.894875			0.447438	+	0.894315i	$0.352337\pi$
$488$	−4.71653	+	3.82193i	−0.213507	+	0.173011i
$489$	35.2296			1.59314
$490$	4.69702	−	1.52615i	0.212190	−	0.0689447i
$491$	4.09330	+	12.5979i	0.184728	+	0.568535i	0.999944	−	0.0106229i	$-0.00338143\pi$
$491$	4.09330	+	12.5979i	0.184728	+	0.568535i	−0.815215	+	0.579158i	$0.803381\pi$
$492$	−17.0616	+	12.3960i	−0.769196	+	0.558854i
$493$	−9.44718	+	6.86378i	−0.425480	+	0.309129i
$494$	0.198298	+	0.272933i	0.00892183	+	0.0122798i
$495$	−94.5535	−	30.7223i	−4.24986	−	1.38086i
$496$	−7.97318	+	10.9741i	−0.358006	+	0.492753i
$497$	0.363859	−	0.264359i	0.0163213	−	0.0118581i
$498$	3.16456	−	4.35565i	0.141807	−	0.195181i
$499$			8.33441i			0.373100i	0.982446	+	0.186550i	$0.0597306\pi$
$499$			8.33441i			0.373100i	−0.982446	+	0.186550i	$0.940269\pi$
$500$	18.0327	+	13.1016i	0.806449	+	0.585919i
$501$	−29.7070			−1.32721
$502$	−4.47056			−0.199531
$503$	−31.7639	−	23.0778i	−1.41628	−	1.02899i	−0.992371	−	0.123284i	$-0.960657\pi$
$503$	−31.7639	−	23.0778i	−1.41628	−	1.02899i	−0.423910	−	0.905704i	$-0.639343\pi$
$504$	0.271956	−	0.836995i	0.0121139	−	0.0372827i
$505$	20.4844	+	28.1944i	0.911545	+	1.25463i
$506$	−2.29723	+	3.16187i	−0.102124	+	0.140562i
$507$	7.64502	+	23.5289i	0.339527	+	1.04496i
$508$	−6.28527	+	19.3441i	−0.278864	+	0.858254i
$509$			40.3821i			1.78990i	0.446163	+	0.894952i	$0.352790\pi$
$509$			40.3821i			1.78990i	−0.446163	+	0.894952i	$0.647210\pi$
$510$	1.83698	+	5.65364i	0.0813427	+	0.250347i
$511$	0.704829	+	0.970114i	0.0311798	+	0.0429153i
$512$	13.8019	+	4.48450i	0.609962	+	0.198189i
$513$	1.33895	−	4.12087i	0.0591162	−	0.181941i
$514$	1.49048	−	0.484286i	0.0657422	−	0.0213609i
$515$	3.94423	+	2.86565i	0.173804	+	0.126276i
$516$	−49.9837	+	16.2407i	−2.20041	+	0.714956i
$517$			35.2727i			1.55129i
$518$	−0.0521176	−	0.0169340i	−0.00228992	−	0.000744039i
$519$	−52.0724	−	16.9193i	−2.28572	−	0.742676i
$520$		−	5.74731i		−	0.252036i
$521$	5.92034	−	1.92364i	0.259375	−	0.0842760i	−0.176443	−	0.984311i	$-0.556459\pi$
$521$	5.92034	−	1.92364i	0.259375	−	0.0842760i	0.435818	+	0.900035i	$0.356459\pi$
$522$	3.00207	+	2.18113i	0.131397	+	0.0954657i
$523$	−18.7987	+	6.10806i	−0.822008	+	0.267087i	−0.689675	−	0.724119i	$-0.742247\pi$
$523$	−18.7987	+	6.10806i	−0.822008	+	0.267087i	−0.132333	+	0.991205i	$0.542247\pi$
$524$	0.789598	−	2.43013i	0.0344938	−	0.106161i
$525$	5.07058	+	1.64753i	0.221298	+	0.0719042i
$526$	−2.10642	−	2.89924i	−0.0918442	−	0.126413i
$527$	−3.31988	−	10.2176i	−0.144616	−	0.445084i
$528$		−	59.8653i		−	2.60530i
$529$	3.29579	−	10.1434i	0.143295	−	0.441018i
$530$	−0.507760	−	1.56272i	−0.0220557	−	0.0678804i
$531$	−14.2227	+	19.5758i	−0.617212	+	0.849519i
$532$	−0.227475	−	0.313092i	−0.00986229	−	0.0135743i
$533$	−2.42139	+	7.45229i	−0.104882	+	0.322794i
$534$	3.11860	+	2.26579i	0.134955	+	0.0980505i
$535$	65.3851			2.82684
$536$	−2.64048			−0.114052
$537$	1.08886	+	0.791104i	0.0469878	+	0.0341387i
$538$		−	3.75999i		−	0.162105i
$539$	23.1535	−	31.8681i	0.997292	−	1.37265i
$540$	−29.5689	+	21.4831i	−1.27244	+	0.924484i
$541$	−5.33194	+	7.33879i	−0.229238	+	0.315519i	−0.908105	−	0.418742i	$-0.862471\pi$
$541$	−5.33194	+	7.33879i	−0.229238	+	0.315519i	0.678867	+	0.734261i	$0.262471\pi$
$542$	−3.17998	−	1.03324i	−0.136592	−	0.0443814i
$543$	32.9769	+	45.3888i	1.41517	+	1.94782i
$544$	−5.54293	+	4.02718i	−0.237651	+	0.172664i
$545$	39.2894	−	28.5454i	1.68297	−	1.22275i
$546$	−0.0810658	−	0.249495i	−0.00346930	−	0.0106774i
$547$	−11.8933	+	3.86437i	−0.508521	+	0.165228i	−0.552029	−	0.833825i	$-0.686146\pi$
$547$	−11.8933	+	3.86437i	−0.508521	+	0.165228i	0.0435088	+	0.999053i	$0.486146\pi$
$548$	15.6245			0.667445
$549$	35.2613	−	13.5488i	1.50492	−	0.578249i
$550$	−9.05321			−0.386030
$551$	3.13429	−	1.01839i	0.133525	−	0.0433850i
$552$	2.36144	+	7.26777i	0.100510	+	0.309337i
$553$	−1.95091	+	1.41742i	−0.0829610	+	0.0602747i
$554$	1.28143	−	0.931014i	0.0544428	−	0.0395550i
$555$	7.11478	+	9.79265i	0.302005	+	0.415675i
$556$	27.6171	+	8.97333i	1.17122	+	0.380554i
$557$	−21.8847	+	30.1217i	−0.927284	+	1.27630i	0.0336256	+	0.999434i	$0.489295\pi$
$557$	−21.8847	+	30.1217i	−0.927284	+	1.27630i	−0.960910	+	0.276862i	$0.910705\pi$
$558$	−2.76196	+	2.00668i	−0.116923	+	0.0849496i
$559$	−11.4779	+	15.7979i	−0.485463	+	0.668182i
$560$			3.19912i			0.135188i
$561$	38.3584	+	27.8690i	1.61949	+	1.17663i
$562$	−3.54552			−0.149559
$563$	36.6641			1.54521			0.772603	−	0.634890i	$-0.218954\pi$
$563$	36.6641			1.54521			0.772603	+	0.634890i	$0.218954\pi$
$564$	27.6271	+	20.0723i	1.16331	+	0.845194i
$565$	−13.0737	+	40.2368i	−0.550016	+	1.69278i
$566$	1.57320	+	2.16532i	0.0661264	+	0.0910152i
$567$	0.0161543	−	0.0222345i	0.000678417	−	0.000933761i
$568$	0.461443	+	1.42018i	0.0193617	+	0.0595892i
$569$	8.06929	−	24.8347i	0.338282	−	1.04113i	−0.626800	−	0.779180i	$-0.715636\pi$
$569$	8.06929	−	24.8347i	0.338282	−	1.04113i	0.965083	−	0.261946i	$-0.0843642\pi$
$570$		−	1.67768i		−	0.0702705i
$571$	1.77407	+	5.46001i	0.0742423	+	0.228494i	0.981291	−	0.192532i	$-0.0616699\pi$
$571$	1.77407	+	5.46001i	0.0742423	+	0.228494i	−0.907048	+	0.421026i	$0.861670\pi$
$572$	−13.3412	−	18.3626i	−0.557823	−	0.767777i
$573$	−34.3360	−	11.1564i	−1.43441	−	0.466067i
$574$	−0.0545146	+	0.167779i	−0.00227540	+	0.00700295i
$575$	−27.1736	+	8.82925i	−1.13322	+	0.368205i
$576$	−27.7455	−	20.1583i	−1.15606	−	0.839928i
$577$	8.52870	−	2.77114i	0.355054	−	0.115364i	−0.126059	−	0.992023i	$-0.540233\pi$
$577$	8.52870	−	2.77114i	0.355054	−	0.115364i	0.481113	+	0.876659i	$0.340233\pi$
$578$			1.58578i			0.0659599i
$579$	−55.8699	−	18.1532i	−2.32187	−	0.754423i
$580$	−26.4384	−	8.59035i	−1.09779	−	0.356695i
$581$			2.29473i			0.0952016i
$582$	6.06840	−	1.97174i	0.251543	−	0.0817314i
$583$	−10.6027	−	7.70329i	−0.439118	−	0.319038i
$584$	−3.78644	+	1.23029i	−0.156684	+	0.0509098i
$585$	−11.0513	+	34.0124i	−0.456915	+	1.40624i
$586$	−0.828056	−	0.269052i	−0.0342067	−	0.0111144i
$587$	−4.60895	−	6.34367i	−0.190232	−	0.261831i	0.703238	−	0.710954i	$-0.251737\pi$
$587$	−4.60895	−	6.34367i	−0.190232	−	0.261831i	−0.893470	+	0.449123i	$0.851737\pi$
$588$	−11.7847	−	36.2696i	−0.485993	−	1.49573i
$589$			3.03200i			0.124931i
$590$	−1.09936	+	3.38349i	−0.0452600	+	0.139296i
$591$	−5.30492	−	16.3269i	−0.218215	−	0.671597i
$592$	−2.64409	+	3.63928i	−0.108671	+	0.149573i
$593$	−25.4649	−	35.0494i	−1.04572	−	1.43931i	−0.892462	−	0.451122i	$-0.851024\pi$
$593$	−25.4649	−	35.0494i	−1.04572	−	1.43931i	−0.153256	−	0.988187i	$-0.548976\pi$
$594$	1.76796	−	5.44122i	0.0725403	−	0.223256i
$595$	−2.04982	−	1.48928i	−0.0840345	−	0.0610547i
$596$	31.2317			1.27930
$597$	48.1846			1.97206
$598$	1.13737	+	0.826350i	0.0465106	+	0.0337920i
$599$			25.6723i			1.04894i	0.851428	+	0.524472i	$0.175737\pi$
$599$			25.6723i			1.04894i	−0.851428	+	0.524472i	$0.824263\pi$
$600$	−10.4047	+	14.3209i	−0.424771	+	0.584647i
$601$	27.4022	−	19.9089i	1.11776	−	0.812100i	0.133892	−	0.990996i	$-0.457253\pi$
$601$	27.4022	−	19.9089i	1.11776	−	0.812100i	0.983868	+	0.178896i	$0.0572525\pi$
$602$	−0.258410	+	0.355671i	−0.0105320	+	0.0144961i
$603$	15.6263	+	5.07729i	0.636352	+	0.206763i
$604$	−16.4846	−	22.6890i	−0.670747	−	0.923204i
$605$	−62.0674	+	45.0946i	−2.52340	+	1.83336i
$606$	−4.27281	+	3.10438i	−0.173571	+	0.126107i
$607$	0.862615	+	2.65486i	0.0350125	+	0.107757i	0.967035	−	0.254642i	$-0.0819577\pi$
$607$	0.862615	+	2.65486i	0.0350125	+	0.107757i	−0.932023	+	0.362399i	$0.881958\pi$
$608$	1.83898	−	0.597521i	0.0745805	−	0.0242327i
$609$	−2.56265			−0.103844
$610$	4.31503	−	3.49659i	0.174711	−	0.141573i
$611$	12.6882			0.513308
$612$	26.9438	−	8.75457i	1.08914	−	0.353882i
$613$	5.34073	+	16.4371i	0.215710	+	0.663887i	0.999102	+	0.0423597i	$0.0134875\pi$
$613$	5.34073	+	16.4371i	0.215710	+	0.663887i	−0.783392	+	0.621527i	$0.786512\pi$
$614$	5.10938	−	3.71218i	0.206198	−	0.149811i
$615$	31.5248	−	22.9041i	1.27120	−	0.923583i
$616$	−0.606614	−	0.834932i	−0.0244412	−	0.0336404i
$617$	−24.9816	−	8.11703i	−1.00572	−	0.326779i	−0.240573	−	0.970631i	$-0.577335\pi$
$617$	−24.9816	−	8.11703i	−1.00572	−	0.326779i	−0.765150	+	0.643852i	$0.777335\pi$
$618$	−0.434285	+	0.597742i	−0.0174695	+	0.0240447i
$619$	18.2971	−	13.2936i	0.735422	−	0.534316i	−0.155852	−	0.987780i	$-0.549812\pi$
$619$	18.2971	−	13.2936i	0.735422	−	0.534316i	0.891274	+	0.453465i	$0.149812\pi$
$620$	15.0329	−	20.6910i	0.603736	−	0.830971i
$621$		−	18.0563i		−	0.724575i
$622$	2.97448	+	2.16108i	0.119266	+	0.0866516i
$623$	−1.64301			−0.0658256
$624$	−21.5345			−0.862070
$625$	−0.410787	−	0.298454i	−0.0164315	−	0.0119382i
$626$	0.117662	−	0.362127i	0.00470273	−	0.0144735i
$627$	−7.86522	−	10.8255i	−0.314106	−	0.432330i
$628$	1.76946	−	2.43545i	0.0706089	−	0.0971849i
$629$	−1.10095	−	3.38838i	−0.0438978	−	0.135103i
$630$	−0.248806	+	0.765745i	−0.00991266	+	0.0305080i
$631$		−	42.1014i		−	1.67603i	−0.545648	−	0.838015i	$-0.683716\pi$
$631$		−	42.1014i		−	1.67603i	0.545648	−	0.838015i	$-0.316284\pi$
$632$	−2.47412	−	7.61457i	−0.0984154	−	0.302891i
$633$	−9.71879	−	13.3768i	−0.386287	−	0.531679i
$634$	−0.566177	−	0.183962i	−0.0224858	−	0.00730607i
$635$	11.6133	−	35.7421i	0.460860	−	1.41838i
$636$	−12.0671	+	3.92083i	−0.478491	+	0.155471i
$637$	−11.4634	−	8.32867i	−0.454198	−	0.329994i
$638$	4.13854	−	1.34469i	0.163846	−	0.0532369i
$639$		−	9.29184i		−	0.367579i
$640$	−20.6121	−	6.69729i	−0.814766	−	0.264733i
$641$	16.1903	+	5.26056i	0.639480	+	0.207780i	0.610770	−	0.791808i	$-0.290860\pi$
$641$	16.1903	+	5.26056i	0.639480	+	0.207780i	0.0287102	+	0.999588i	$0.490860\pi$
$642$			9.90900i			0.391077i
$643$	10.3498	−	3.36284i	0.408154	−	0.132617i	−0.0977417	−	0.995212i	$-0.531162\pi$
$643$	10.3498	−	3.36284i	0.408154	−	0.132617i	0.505896	+	0.862594i	$0.331162\pi$
$644$	−1.30473	−	0.947938i	−0.0514134	−	0.0373540i
$645$	92.3551	−	30.0080i	3.63648	−	1.18156i
$646$	−0.152593	+	0.469634i	−0.00600370	+	0.0184775i
$647$	7.10510	+	2.30859i	0.279330	+	0.0907599i	0.445332	−	0.895366i	$-0.353086\pi$
$647$	7.10510	+	2.30859i	0.279330	+	0.0907599i	−0.166002	+	0.986125i	$0.553086\pi$
$648$	0.0536350	+	0.0738222i	0.00210698	+	0.00290001i
$649$	8.76845	+	26.9865i	0.344192	+	1.05931i
$650$			3.25658i			0.127734i
$651$	0.728565	−	2.24229i	0.0285547	−	0.0878824i
$652$	−7.62810	−	23.4769i	−0.298740	−	0.919426i
$653$	−8.94924	+	12.3176i	−0.350211	+	0.482024i	−0.947389	−	0.320085i	$-0.896289\pi$
$653$	−8.94924	+	12.3176i	−0.350211	+	0.482024i	0.597178	+	0.802109i	$0.296289\pi$
$654$	4.32601	+	5.95424i	0.169160	+	0.232829i
$655$	−1.45894	+	4.49017i	−0.0570057	+	0.175445i
$656$	11.7157	+	8.51194i	0.457420	+	0.332335i
$657$	24.7737			0.966515
$658$	0.285658			0.0111361
$659$	11.8097	+	8.58022i	0.460039	+	0.334238i	0.793547	−	0.608510i	$-0.208232\pi$
$659$	11.8097	+	8.58022i	0.460039	+	0.334238i	−0.333508	+	0.942747i	$0.608232\pi$
$660$			112.872i			4.39354i
$661$	−11.4308	+	15.7331i	−0.444606	+	0.611948i	−0.971228	−	0.238152i	$-0.923458\pi$
$661$	−11.4308	+	15.7331i	−0.444606	+	0.611948i	0.526622	+	0.850100i	$0.323458\pi$
$662$	4.48116	−	3.25575i	0.174165	−	0.126538i
$663$	10.0249	−	13.7981i	0.389336	−	0.535875i
$664$	−7.24601	−	2.35437i	−0.281200	−	0.0913673i
$665$	0.420307	+	0.578502i	0.0162988	+	0.0224334i
$666$	−0.915930	+	0.665462i	−0.0354916	+	0.0257861i
$667$	11.1106	−	8.07232i	0.430204	−	0.312562i
$668$	6.43232	+	19.7966i	0.248874	+	0.765955i
$669$	−73.1503	+	23.7680i	−2.82815	+	0.918922i
$670$	2.41571			0.0933271
$671$	11.4510	−	42.7918i	0.442060	−	1.65196i
$672$	−1.50358			−0.0580020
$673$	−6.30148	+	2.04748i	−0.242904	+	0.0789244i	−0.427939	−	0.903808i	$-0.640760\pi$
$673$	−6.30148	+	2.04748i	−0.242904	+	0.0789244i	0.185035	+	0.982732i	$0.440760\pi$
$674$	1.70051	+	5.23364i	0.0655013	+	0.201592i
$675$	33.8379	−	24.5847i	1.30242	−	0.946264i
$676$	14.0243	−	10.1892i	0.539395	−	0.391893i
$677$	18.3673	+	25.2805i	0.705915	+	0.971608i	0.999875	+	0.0157906i	$0.00502650\pi$
$677$	18.3673	+	25.2805i	0.705915	+	0.971608i	−0.293961	+	0.955817i	$0.594973\pi$
$678$	−6.09782	−	1.98130i	−0.234185	−	0.0760915i
$679$	−1.59854	+	2.20020i	−0.0613464	+	0.0844361i
$680$	6.80576	−	4.94467i	0.260989	−	0.189620i
$681$	−3.30218	+	4.54506i	−0.126540	+	0.174167i
$682$			4.00347i			0.153301i
$683$	−15.8532	−	11.5180i	−0.606605	−	0.440724i	0.241612	−	0.970373i	$-0.422324\pi$
$683$	−15.8532	−	11.5180i	−0.606605	−	0.440724i	−0.848217	+	0.529648i	$0.822324\pi$
$684$	−7.99542			−0.305712
$685$	−28.8694			−1.10304
$686$	−0.518206	−	0.376499i	−0.0197852	−	0.0143748i
$687$	7.22619	−	22.2399i	0.275696	−	0.848507i
$688$	21.2123	+	29.1963i	0.808712	+	1.11310i
$689$	−2.77099	+	3.81395i	−0.105566	+	0.145300i
$690$	−2.16042	−	6.64910i	−0.0822459	−	0.253127i
$691$	−1.33905	+	4.12116i	−0.0509397	+	0.156776i	−0.973290	−	0.229577i	$-0.926266\pi$
$691$	−1.33905	+	4.12116i	−0.0509397	+	0.156776i	0.922351	+	0.386354i	$0.126266\pi$
$692$			38.3643i			1.45839i
$693$	1.98446	+	6.10754i	0.0753833	+	0.232006i
$694$	1.94939	+	2.68310i	0.0739977	+	0.101849i
$695$	−51.0282	−	16.5801i	−1.93561	−	0.628917i
$696$	2.62925	−	8.09201i	0.0996616	−	0.306727i
$697$	−10.9080	+	3.54421i	−0.413169	+	0.134247i
$698$	−4.55738	−	3.31113i	−0.172499	−	0.125328i
$699$	−49.2554	+	16.0041i	−1.86301	+	0.605329i
$700$		−	3.73575i		−	0.141198i
$701$	−19.4985	−	6.33544i	−0.736447	−	0.239286i	−0.0833078	−	0.996524i	$-0.526548\pi$
$701$	−19.4985	−	6.33544i	−0.736447	−	0.239286i	−0.653139	+	0.757238i	$0.726548\pi$
$702$	−1.95729	−	0.635963i	−0.0738733	−	0.0240029i
$703$			1.00548i			0.0379225i
$704$	−38.2488	+	12.4278i	−1.44156	+	0.468390i
$705$	−51.0467	−	37.0876i	−1.92253	−	1.39680i
$706$	4.66912	−	1.51709i	0.175725	−	0.0570964i
$707$	0.695626	−	2.14092i	0.0261617	−	0.0805174i
$708$	26.1267	+	8.48908i	0.981902	+	0.319039i
$709$	−29.2003	−	40.1908i	−1.09664	−	1.50940i	−0.839764	−	0.542952i	$-0.817307\pi$
$709$	−29.2003	−	40.1908i	−1.09664	−	1.50940i	−0.256876	−	0.966444i	$-0.582693\pi$
$710$	−0.422162	−	1.29928i	−0.0158435	−	0.0487612i
$711$			49.8202i			1.86840i
$712$	1.68571	−	5.18807i	0.0631745	−	0.194431i
$713$	3.90443	+	12.0166i	0.146222	+	0.450026i
$714$	0.225698	−	0.310647i	0.00844655	−	0.0116257i
$715$	24.6506	+	33.9286i	0.921878	+	1.26886i
$716$	0.291423	−	0.896908i	0.0108910	−	0.0335190i
$717$	23.7822	+	17.2788i	0.888163	+	0.645288i
$718$	−2.14023			−0.0798726
$719$	−15.3966			−0.574196			−0.287098	−	0.957901i	$-0.592691\pi$
$719$	−15.3966			−0.574196			−0.287098	+	0.957901i	$0.592691\pi$
$720$	53.4706	+	38.8486i	1.99273	+	1.44780i
$721$		−	0.314915i		−	0.0117280i
$722$	−2.10929	+	2.90319i	−0.0784996	+	0.108045i
$723$	32.0141	−	23.2596i	1.19062	−	0.865033i
$724$	23.1066	−	31.8035i	0.858750	−	1.18197i
$725$	30.2554	+	9.83057i	1.12366	+	0.365098i
$726$	−6.83401	−	9.40621i	−0.253634	−	0.349097i
$727$	14.5568	−	10.5761i	0.539882	−	0.392247i	−0.284159	−	0.958777i	$-0.591714\pi$
$727$	14.5568	−	10.5761i	0.539882	−	0.392247i	0.824041	+	0.566530i	$0.191714\pi$
$728$	−0.300338	+	0.218208i	−0.0111313	+	0.00808734i
$729$	−13.5178	−	41.6036i	−0.500660	−	1.54087i
$730$	3.46412	−	1.12556i	0.128213	−	0.0416589i
$731$	−28.5823			−1.05715
$732$	−27.0000	−	33.3199i	−0.997950	−	1.23154i
$733$	6.80549			0.251366			0.125683	−	0.992070i	$-0.459888\pi$
$733$	6.80549			0.251366			0.125683	+	0.992070i	$0.459888\pi$
$734$	−4.18587	+	1.36007i	−0.154503	+	0.0502012i
$735$	21.7746	+	67.0155i	0.803170	+	2.47190i
$736$	6.51891	−	4.73627i	0.240290	−	0.174581i
$737$	15.5878	−	11.3252i	0.574184	−	0.417169i
$738$	2.14228	+	2.94859i	0.0788583	+	0.108539i
$739$	−20.5631	−	6.68136i	−0.756427	−	0.245778i	−0.0946824	−	0.995508i	$-0.530184\pi$
$739$	−20.5631	−	6.68136i	−0.756427	−	0.245778i	−0.661744	+	0.749730i	$0.730184\pi$
$740$	4.98526	−	6.86162i	0.183262	−	0.252238i
$741$	−3.89412	+	2.82924i	−0.143054	+	0.103935i
$742$	−0.0623854	+	0.0858661i	−0.00229024	+	0.00315224i
$743$			40.0247i			1.46836i	0.678952	+	0.734182i	$0.262434\pi$
$743$			40.0247i			1.46836i	−0.678952	+	0.734182i	$0.737566\pi$
$744$	6.33292	+	4.60113i	0.232176	+	0.168686i
$745$	−57.7069			−2.11422
$746$	−3.86998			−0.141690
$747$	38.3545	+	27.8662i	1.40332	+	1.01957i
$748$	10.2663	−	31.5963i	0.375371	−	1.15527i
$749$	−2.48248	−	3.41684i	−0.0907078	−	0.124849i
$750$	3.66865	−	5.04946i	0.133960	−	0.184380i
$751$	−10.3995	−	32.0063i	−0.379482	−	1.16793i	−0.940405	−	0.340058i	$-0.889553\pi$
$751$	−10.3995	−	32.0063i	−0.379482	−	1.16793i	0.560922	−	0.827868i	$-0.310447\pi$
$752$	7.24615	−	22.3014i	0.264240	−	0.813247i
$753$		−	63.7844i		−	2.32443i
$754$	−0.483707	−	1.48870i	−0.0176156	−	0.0542152i
$755$	30.4586	+	41.9226i	1.10850	+	1.52572i
$756$	2.24529	+	0.729538i	0.0816603	+	0.0265331i
$757$	−8.94756	+	27.5377i	−0.325204	+	1.00088i	0.646144	+	0.763216i	$0.276381\pi$
$757$	−8.94756	+	27.5377i	−0.325204	+	1.00088i	−0.971348	+	0.237661i	$0.923619\pi$
$758$	−0.305989	+	0.0994217i	−0.0111140	+	0.00361116i
$759$	−45.1124	−	32.7761i	−1.63748	−	1.18970i
$760$	−2.25795	+	0.733652i	−0.0819044	+	0.0266124i
$761$			2.00614i			0.0727226i	0.999339	+	0.0363613i	$0.0115767\pi$
$761$			2.00614i			0.0727226i	−0.999339	+	0.0363613i	$0.988423\pi$
$762$	5.41666	+	1.75998i	0.196225	+	0.0637573i
$763$	−2.98341	−	0.969367i	−0.108007	−	0.0350935i
$764$			25.2971i			0.915216i
$765$	−49.7842	+	16.1759i	−1.79995	+	0.584839i
$766$	−2.35965	−	1.71439i	−0.0852576	−	0.0619433i
$767$	9.70746	−	3.15415i	0.350516	−	0.113890i
$768$	−11.2530	+	34.6332i	−0.406058	+	1.24972i
$769$	16.1968	+	5.26267i	0.584073	+	0.189777i	0.586125	−	0.810221i	$-0.300653\pi$
$769$	16.1968	+	5.26267i	0.584073	+	0.189777i	−0.00205127	+	0.999998i	$0.500653\pi$
$770$	0.554976	+	0.763859i	0.0199999	+	0.0275276i
$771$	6.90963	+	21.2656i	0.248844	+	0.765863i
$772$			41.1622i			1.48146i
$773$	−0.212080	+	0.652715i	−0.00762798	+	0.0234765i	−0.954798	−	0.297255i	$-0.903929\pi$
$773$	−0.212080	+	0.652715i	−0.00762798	+	0.0234765i	0.947170	+	0.320732i	$0.103929\pi$
$774$	2.80672	+	8.63819i	0.100885	+	0.310493i
$775$	−17.2033	+	23.6783i	−0.617960	+	0.850549i
$776$	−5.30743	−	7.30505i	−0.190526	−	0.262236i
$777$	0.241609	−	0.743596i	0.00866768	−	0.0266764i
$778$	−3.93616	−	2.85979i	−0.141118	−	0.102528i
$779$	3.23688			0.115973
$780$	40.6019			1.45378
$781$	−8.81529	−	6.40468i	−0.315436	−	0.229178i
$782$			2.05778i			0.0735861i
$783$	−11.8169	+	16.2645i	−0.422301	+	0.581247i
$784$	−21.1856	+	15.3923i	−0.756630	+	0.549724i
$785$	−3.26943	+	4.49999i	−0.116691	+	0.160611i
$786$	−0.680478	−	0.221101i	−0.0242718	−	0.00788640i
$787$	7.75889	+	10.6792i	0.276575	+	0.380672i	0.924596	−	0.380950i	$-0.124403\pi$
$787$	7.75889	+	10.6792i	0.276575	+	0.380672i	−0.648021	+	0.761622i	$0.724403\pi$
$788$	−9.73152	+	7.07036i	−0.346671	+	0.251871i
$789$	41.3653	−	30.0536i	1.47264	−	1.06994i
$790$	2.26351	+	6.96638i	0.0805322	+	0.247853i
$791$	2.59903	−	0.844477i	0.0924110	−	0.0300262i
$792$	−21.3216			−0.757630
$793$	−15.3929	−	4.11910i	−0.546617	−	0.146273i
$794$	−2.13086			−0.0756215
$795$	22.2964	−	7.24454i	0.790772	−	0.256937i
$796$	−10.4332	−	32.1100i	−0.369794	−	1.13811i
$797$	−3.61052	+	2.62320i	−0.127891	+	0.0929184i	−0.649892	−	0.760027i	$-0.725186\pi$
$797$	−3.61052	+	2.62320i	−0.127891	+	0.0929184i	0.522001	+	0.852945i	$0.325186\pi$
$798$	−0.0876710	+	0.0636967i	−0.00310352	+	0.00225484i
$799$	10.9162	+	15.0249i	0.386187	+	0.531541i
$800$	17.7517	+	5.76788i	0.627618	+	0.203925i
$801$	−19.9519	+	27.4614i	−0.704965	+	0.970301i
$802$	3.23787	−	2.35245i	0.114333	−	0.0830678i
$803$	17.0760	−	23.5032i	0.602600	−	0.829408i
$804$		−	18.6537i		−	0.657865i
$805$	2.41075	+	1.75151i	0.0849677	+	0.0617326i
$806$	1.44011			0.0507258
$807$	53.6463			1.88844
$808$	6.04660	+	4.39311i	0.212719	+	0.154549i
$809$	−11.4375	+	35.2010i	−0.402121	+	1.23760i	0.521155	+	0.853462i	$0.325501\pi$
$809$	−11.4375	+	35.2010i	−0.402121	+	1.23760i	−0.923276	+	0.384138i	$0.874499\pi$
$810$	−0.0490693	−	0.0675381i	−0.00172412	−	0.00237305i
$811$	−6.52324	+	8.97846i	−0.229062	+	0.315276i	−0.908041	−	0.418881i	$-0.862423\pi$
$811$	−6.52324	+	8.97846i	−0.229062	+	0.315276i	0.678979	+	0.734157i	$0.262423\pi$
$812$	0.554880	+	1.70774i	0.0194725	+	0.0599301i
$813$	14.7419	−	45.3708i	0.517020	−	1.59122i
$814$			1.32764i			0.0465339i
$815$	14.0945	+	43.3784i	0.493708	+	1.51948i
$816$	−18.5271	−	25.5004i	−0.648579	−	0.892692i
$817$	7.67171	+	2.49269i	0.268399	+	0.0872082i
$818$	0.730652	−	2.24872i	0.0255467	−	0.0786245i
$819$	2.19698	−	0.713841i	0.0767685	−	0.0249436i
$820$	−22.0891	−	16.0487i	−0.771386	−	0.560445i
$821$	43.9858	−	14.2918i	1.53511	−	0.498789i	0.585091	−	0.810968i	$-0.301059\pi$
$821$	43.9858	−	14.2918i	1.53511	−	0.498789i	0.950023	+	0.312179i	$0.101059\pi$
$822$		−	4.37511i		−	0.152600i
$823$	14.3549	+	4.66419i	0.500380	+	0.162583i	0.548323	−	0.836267i	$-0.315266\pi$
$823$	14.3549	+	4.66419i	0.500380	+	0.162583i	−0.0479425	+	0.998850i	$0.515266\pi$
$824$	0.994397	+	0.323099i	0.0346415	+	0.0112557i
$825$		−	129.168i		−	4.49706i
$826$	0.218551	−	0.0710116i	0.00760437	−	0.00247081i
$827$	2.61979	+	1.90339i	0.0910990	+	0.0661873i	0.632402	−	0.774640i	$-0.282069\pi$
$827$	2.61979	+	1.90339i	0.0910990	+	0.0661873i	−0.541303	+	0.840827i	$0.682069\pi$
$828$	−31.6879	+	10.2960i	−1.10123	+	0.357812i
$829$	6.11721	−	18.8268i	0.212460	−	0.653883i	−0.786865	−	0.617126i	$-0.788297\pi$
$829$	6.11721	−	18.8268i	0.212460	−	0.653883i	0.999324	−	0.0367576i	$-0.0117030\pi$
$830$	6.62919	+	2.15395i	0.230102	+	0.0747648i
$831$	13.2834	+	18.2830i	0.460796	+	0.634231i
$832$	4.47047	+	13.7587i	0.154986	+	0.476997i
$833$		−	20.7401i		−	0.718603i
$834$	2.51268	−	7.73323i	0.0870070	−	0.267780i
$835$	−11.8850	−	36.5784i	−0.411298	−	1.26585i
$836$	−5.51109	+	7.58536i	−0.190605	+	0.262345i
$837$	−10.8717	−	14.9637i	−0.375782	−	0.517220i
$838$	−1.22751	+	3.77790i	−0.0424038	+	0.130505i
$839$	0.0273449	+	0.0198672i	0.000944050	+	0.000685892i	0.588257	−	0.808674i	$-0.299814\pi$
$839$	0.0273449	+	0.0198672i	0.000944050	+	0.000685892i	−0.587313	+	0.809360i	$0.699814\pi$
$840$	1.84614			0.0636979
$841$	13.7090			0.472725
$842$	2.63408	+	1.91377i	0.0907765	+	0.0659530i
$843$		−	50.5862i		−	1.74228i
$844$	−6.80987	+	9.37298i	−0.234405	+	0.322631i
$845$	−25.9127	+	18.8267i	−0.891424	+	0.647658i
$846$	3.46889	−	4.77452i	0.119263	−	0.164151i
$847$	4.71304	+	1.53136i	0.161942	+	0.0526181i
$848$	5.12109	+	7.04857i	0.175859	+	0.242049i
$849$	−30.8940	+	22.4458i	−1.06028	+	0.770339i
$850$	−3.85633	+	2.80179i	−0.132271	+	0.0961005i
$851$	1.29480	+	3.98499i	0.0443852	+	0.136604i
$852$	−10.0328	+	3.25986i	−0.343719	+	0.111681i
$853$	11.0513			0.378390			0.189195	−	0.981940i	$-0.439412\pi$
$853$	11.0513			0.378390			0.189195	+	0.981940i	$0.439412\pi$
$854$	−0.346551	−	0.0927362i	−0.0118587	−	0.00317337i
$855$	14.7732			0.505232
$856$	13.3362	−	4.33321i	0.455823	−	0.148106i
$857$	−5.55617	−	17.1001i	−0.189795	−	0.584129i	0.810203	−	0.586150i	$-0.199357\pi$
$857$	−5.55617	−	17.1001i	−0.189795	−	0.584129i	−0.999998	+	0.00202028i	$0.999357\pi$
$858$	−5.14182	+	3.73575i	−0.175539	+	0.127536i
$859$	−18.5734	+	13.4944i	−0.633716	+	0.460422i	−0.857686	−	0.514174i	$-0.828098\pi$
$859$	−18.5734	+	13.4944i	−0.633716	+	0.460422i	0.223970	+	0.974596i	$0.428098\pi$
$860$	−39.9944	−	55.0476i	−1.36380	−	1.87711i
$861$	−2.39381	−	0.777795i	−0.0815808	−	0.0265072i
$862$	−1.43987	+	1.98182i	−0.0490423	+	0.0675009i
$863$	−17.3296	+	12.5907i	−0.589907	+	0.428592i	−0.842282	−	0.539037i	$-0.818788\pi$
$863$	−17.3296	+	12.5907i	−0.589907	+	0.428592i	0.252375	+	0.967629i	$0.418788\pi$
$864$	−6.93331	+	9.54288i	−0.235876	+	0.324655i
$865$		−	70.8859i		−	2.41019i
$866$	−4.84324	−	3.51882i	−0.164580	−	0.119574i
$867$	−22.6254			−0.768399
$868$	−1.65201			−0.0560729
$869$	47.2651	+	34.3401i	1.60336	+	1.16491i
$870$	−2.40544	+	7.40318i	−0.0815520	+	0.250991i
$871$	−4.07385	−	5.60717i	−0.138037	−	0.189992i
$872$	6.12188	−	8.42605i	0.207313	−	0.285342i
$873$	17.3626	+	53.4365i	0.587634	+	1.80855i
$874$	0.179461	−	0.552325i	0.00607037	−	0.0186827i
$875$			2.66027i			0.0899334i
$876$	−8.69139	−	26.7493i	−0.293655	−	0.903776i
$877$	16.7690	+	23.0806i	0.566251	+	0.779377i	0.992104	−	0.125415i	$-0.0400262\pi$
$877$	16.7690	+	23.0806i	0.566251	+	0.779377i	−0.425854	+	0.904792i	$0.640026\pi$
$878$	−0.363503	−	0.118109i	−0.0122676	−	0.00398600i
$879$	3.83874	−	11.8144i	0.129477	−	0.398490i
$880$	73.7125	−	23.9506i	2.48485	−	0.807376i
$881$	36.8441	+	26.7688i	1.24131	+	0.901865i	0.997685	−	0.0680048i	$-0.0216633\pi$
$881$	36.8441	+	26.7688i	1.24131	+	0.901865i	0.243625	+	0.969869i	$0.421663\pi$
$882$	−6.26812	+	2.03663i	−0.211058	+	0.0685771i
$883$		−	17.7299i		−	0.596658i	−0.954463	−	0.298329i	$-0.903571\pi$
$883$		−	17.7299i		−	0.596658i	0.954463	−	0.298329i	$-0.0964293\pi$
$884$	−11.3657	−	3.69293i	−0.382269	−	0.124207i
$885$	−48.2744	−	15.6853i	−1.62273	−	0.527256i
$886$		−	2.32468i		−	0.0780993i
$887$	−22.4962	+	7.30947i	−0.755349	+	0.245428i	−0.661281	−	0.750138i	$-0.729987\pi$
$887$	−22.4962	+	7.30947i	−0.755349	+	0.245428i	−0.0940679	+	0.995566i	$0.529987\pi$
$888$	2.10014	+	1.52584i	0.0704762	+	0.0512039i
$889$	−2.30871	+	0.750144i	−0.0774315	+	0.0251590i
$890$	−1.54221	+	4.74643i	−0.0516950	+	0.159101i
$891$	−0.633256	−	0.205757i	−0.0212149	−	0.00689313i
$892$	31.6778	+	43.6007i	1.06065	+	1.45986i
$893$	−1.61966	−	4.98480i	−0.0541999	−	0.166810i
$894$		−	8.74538i		−	0.292489i
$895$	−0.538464	+	1.65722i	−0.0179989	+	0.0553948i
$896$	0.432601	+	1.33141i	0.0144522	+	0.0444792i
$897$	−11.7901	+	16.2276i	−0.393659	+	0.541825i
$898$	2.63031	+	3.62031i	0.0877746	+	0.120811i
$899$	4.34724	−	13.3794i	0.144988	−	0.446229i
$900$	−62.4399	−	45.3652i	−2.08133	−	1.51217i
$901$	−6.90035			−0.229884
$902$	4.27400			0.142309
$903$	−5.07458	−	3.68690i	−0.168872	−	0.122692i
$904$			9.07331i			0.301774i
$905$	−42.6942	+	58.7635i	−1.41920	+	1.95336i
$906$	−6.35331	+	4.61595i	−0.211074	+	0.153355i
$907$	18.7335	−	25.7844i	0.622035	−	0.856158i	−0.375464	−	0.926837i	$-0.622517\pi$
$907$	18.7335	−	25.7844i	0.622035	−	0.856158i	0.997499	+	0.0706790i	$0.0225166\pi$
$908$	3.74382	+	1.21644i	0.124243	+	0.0403690i
$909$	−27.3362	−	37.6251i	−0.906684	−	1.24794i
$910$	0.274772	−	0.199633i	0.00910860	−	0.00661778i
$911$	17.6873	−	12.8506i	0.586006	−	0.425758i	−0.254878	−	0.966973i	$-0.582035\pi$
$911$	17.6873	−	12.8506i	0.586006	−	0.425758i	0.840884	+	0.541215i	$0.182035\pi$
$912$	2.74891	+	8.46027i	0.0910254	+	0.280147i
$913$	52.8740	−	17.1798i	1.74987	−	0.568568i
$914$	0.585531			0.0193676
$915$	49.8881	+	61.5654i	1.64925	+	2.03529i
$916$	−16.3853			−0.541385
$917$	0.290035	−	0.0942382i	0.00957781	−	0.00311202i
$918$	−0.930864	−	2.86490i	−0.0307231	−	0.0945559i
$919$	−2.99222	+	2.17398i	−0.0987043	+	0.0717128i	−0.636043	−	0.771654i	$-0.719430\pi$
$919$	−2.99222	+	2.17398i	−0.0987043	+	0.0717128i	0.537338	+	0.843367i	$0.319430\pi$
$920$	−8.00409	+	5.81531i	−0.263887	+	0.191725i
$921$	52.9641	+	72.8988i	1.74523	+	2.40210i
$922$	−1.93445	−	0.628542i	−0.0637078	−	0.0206999i
$923$	−2.30386	+	3.17100i	−0.0758326	+	0.104375i
$924$	5.89838	−	4.28542i	0.194043	−	0.140980i
$925$	−5.70500	+	7.85227i	−0.187579	+	0.258181i
$926$		−	0.356635i		−	0.0117198i
$927$	−5.26353	−	3.82418i	−0.172877	−	0.125603i
$928$	−8.97165			−0.294509
$929$	39.8361			1.30698			0.653491	−	0.756934i	$-0.273304\pi$
$929$	39.8361			1.30698			0.653491	+	0.756934i	$0.273304\pi$
$930$	−5.79383	−	4.20946i	−0.189987	−	0.138034i
$931$	−1.80877	+	5.56681i	−0.0592799	+	0.182445i
$932$	21.3301	+	29.3584i	0.698690	+	0.961665i
$933$	−30.8336	+	42.4388i	−1.00945	+	1.38938i
$934$	−0.807252	−	2.48447i	−0.0264141	−	0.0812942i
$935$	−18.9690	+	58.3806i	−0.620353	+	1.90925i
$936$			7.66971i			0.250692i
$937$	−13.7692	−	42.3771i	−0.449819	−	1.38440i	−0.877111	−	0.480287i	$-0.840532\pi$
$937$	−13.7692	−	42.3771i	−0.449819	−	1.38440i	0.427292	−	0.904114i	$-0.359468\pi$
$938$	−0.0917175	−	0.126238i	−0.00299468	−	0.00412183i
$939$	5.16670	+	1.67876i	0.168609	+	0.0547844i
$940$	−13.6621	+	42.0478i	−0.445610	+	1.37145i
$941$	18.7392	−	6.08873i	0.610880	−	0.198487i	0.0127928	−	0.999918i	$-0.495928\pi$
$941$	18.7392	−	6.08873i	0.610880	−	0.198487i	0.598087	+	0.801431i	$0.295928\pi$
$942$	−0.681965	−	0.495477i	−0.0222196	−	0.0161435i
$943$	12.8286	−	4.16826i	0.417756	−	0.135737i
$944$		−	18.8637i		−	0.613960i
$945$	−4.14863	−	1.34797i	−0.134955	−	0.0438495i
$946$	10.1298	+	3.29137i	0.329348	+	0.107012i
$947$			13.1491i			0.427288i	0.976912	+	0.213644i	$0.0685332\pi$
$947$			13.1491i			0.427288i	−0.976912	+	0.213644i	$0.931467\pi$
$948$	53.7932	−	17.4785i	1.74712	−	0.567674i
$949$	−8.45445	−	6.14252i	−0.274443	−	0.199395i
$950$	1.27941	−	0.415707i	0.0415097	−	0.0134873i
$951$	2.62471	−	8.07802i	0.0851120	−	0.261948i
$952$	−0.516789	−	0.167915i	−0.0167492	−	0.00544216i
$953$	16.1111	+	22.1750i	0.521889	+	0.718319i	0.985867	−	0.167528i	$-0.0535783\pi$
$953$	16.1111	+	22.1750i	0.521889	+	0.718319i	−0.463978	+	0.885847i	$0.653578\pi$
$954$	0.677599	+	2.08543i	0.0219381	+	0.0675184i
$955$		−	46.7415i		−	1.51252i
$956$	6.36507	−	19.5897i	0.205861	−	0.633576i
$957$	19.1856	+	59.0473i	0.620183	+	1.90873i
$958$	−0.134730	+	0.185440i	−0.00435293	+	0.00599130i
$959$	1.09609	+	1.50863i	0.0353945	+	0.0487164i
$960$	22.2313	−	68.4209i	0.717512	−	2.20828i
$961$	−14.6086	−	10.6138i	−0.471246	−	0.342380i
$962$	0.477575			0.0153976
$963$	−87.2556			−2.81177
$964$	−22.4320	−	16.2978i	−0.722485	−	0.524916i
$965$		−	76.0555i		−	2.44831i
$966$	−0.265438	+	0.365345i	−0.00854034	+	0.0117548i
$967$	−25.2418	+	18.3392i	−0.811721	+	0.589750i	−0.914329	−	0.404972i	$-0.867281\pi$
$967$	−25.2418	+	18.3392i	−0.811721	+	0.589750i	0.102608	+	0.994722i	$0.467281\pi$
$968$	−9.67104	+	13.3110i	−0.310839	+	0.427833i
$969$	−6.70057	−	2.17715i	−0.215253	−	0.0699401i
$970$	4.85563	+	6.68320i	0.155905	+	0.214585i
$971$	17.4374	−	12.6690i	0.559593	−	0.406568i	−0.271717	−	0.962377i	$-0.587592\pi$
$971$	17.4374	−	12.6690i	0.559593	−	0.406568i	0.831310	+	0.555809i	$0.187592\pi$
$972$	−24.9972	+	18.1615i	−0.801785	+	0.582531i
$973$	1.07096	+	3.29608i	0.0343335	+	0.105668i
$974$	−3.68505	+	1.19735i	−0.118077	+	0.0383654i
$975$	−46.4638			−1.48803
$976$	−16.0307	+	24.7029i	−0.513132	+	0.790721i
$977$	−55.0844			−1.76231			−0.881153	−	0.472831i	$-0.843232\pi$
$977$	−55.0844			−1.76231			−0.881153	+	0.472831i	$0.843232\pi$
$978$	−6.57392	+	2.13599i	−0.210211	+	0.0683016i
$979$	12.3006	+	37.8572i	0.393128	+	1.20992i
$980$	39.9441	−	29.0211i	1.27597	−	0.927045i
$981$	−52.4312	+	38.0935i	−1.67400	+	1.21623i
$982$	−1.52764	−	2.10261i	−0.0487489	−	0.0670971i
$983$	−39.8976	−	12.9635i	−1.27253	−	0.413472i	−0.406590	−	0.913611i	$-0.633282\pi$
$983$	−39.8976	−	12.9635i	−1.27253	−	0.413472i	−0.865945	+	0.500139i	$0.833282\pi$
$984$	4.91204	−	6.76084i	0.156590	−	0.215528i
$985$	17.9810	−	13.0639i	0.572921	−	0.416252i
$986$	1.34671	−	1.85358i	0.0428879	−	0.0590301i
$987$			4.07566i			0.129730i
$988$	2.72857	+	1.98242i	0.0868074	+	0.0630693i
$989$	33.6150			1.06889
$990$	19.5066			0.619960
$991$	−6.96696	−	5.06180i	−0.221313	−	0.160793i	0.471605	−	0.881810i	$-0.343675\pi$
$991$	−6.96696	−	5.06180i	−0.221313	−	0.160793i	−0.692917	+	0.721017i	$0.743675\pi$
$992$	2.55065	−	7.85009i	0.0809832	−	0.249241i
$993$	46.4520	+	63.9356i	1.47411	+	2.02894i
$994$	−0.0518686	+	0.0713910i	−0.00164517	+	0.00226438i
$995$	19.2774	+	59.3299i	0.611136	+	1.88088i
$996$	16.6325	−	51.1894i	0.527019	−	1.62200i
$997$		−	7.81495i		−	0.247502i	−0.992313	−	0.123751i	$-0.960508\pi$
$997$		−	7.81495i		−	0.247502i	0.992313	−	0.123751i	$-0.0394924\pi$
$998$	−0.505321	−	1.55522i	−0.0159957	−	0.0492296i
$999$	−3.60532	−	4.96229i	−0.114067	−	0.157000i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	61.2.g.a.41.3	yes	16
3.2	odd	2		549.2.y.b.163.2		16
4.3	odd	2		976.2.bd.b.529.4		16
61.3	even	10	inner	61.2.g.a.3.3	✓	16
61.8	odd	20		3721.2.a.k.1.8		16
61.53	odd	20		3721.2.a.k.1.9		16
183.125	odd	10		549.2.y.b.64.2		16
244.3	odd	10		976.2.bd.b.369.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.2.g.a.3.3	✓	16	61.3	even	10	inner
61.2.g.a.41.3	yes	16	1.1	even	1	trivial
549.2.y.b.64.2		16	183.125	odd	10
549.2.y.b.163.2		16	3.2	odd	2
976.2.bd.b.369.4		16	244.3	odd	10
976.2.bd.b.529.4		16	4.3	odd	2
3721.2.a.k.1.8		16	61.8	odd	20
3721.2.a.k.1.9		16	61.53	odd	20

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:	\( N \)	\(=\)	\( 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	61.g (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.186602 + 0.0606307i) q^{2} +(-0.865057 - 2.66237i) q^{3} +(-1.58689 + 1.15294i) q^{4} +(2.93210 - 2.13030i) q^{5} +(0.322843 + 0.444355i) q^{6} +(-0.222647 - 0.0723423i) q^{7} +(0.456866 - 0.628822i) q^{8} +(-3.91286 + 2.84286i) q^{9} +O(q^{10})\)	\(q+(-0.186602 + 0.0606307i) q^{2} +(-0.865057 - 2.66237i) q^{3} +(-1.58689 + 1.15294i) q^{4} +(2.93210 - 2.13030i) q^{5} +(0.322843 + 0.444355i) q^{6} +(-0.222647 - 0.0723423i) q^{7} +(0.456866 - 0.628822i) q^{8} +(-3.91286 + 2.84286i) q^{9} +(-0.417975 + 0.575293i) q^{10} +5.67170i q^{11} +(4.44232 + 3.22753i) q^{12} +2.04020 q^{13} +0.0459325 q^{14} +(-8.20809 - 5.96352i) q^{15} +(1.16515 - 3.58596i) q^{16} +(1.75528 + 2.41593i) q^{17} +(0.557783 - 0.767722i) q^{18} +(-0.260434 - 0.801534i) q^{19} +(-2.19681 + 6.76110i) q^{20} +0.655349i q^{21} +(-0.343879 - 1.05835i) q^{22} +(-2.06434 - 2.84132i) q^{23} +(-2.06937 - 0.672381i) q^{24} +(2.51398 - 7.73723i) q^{25} +(-0.380706 + 0.123699i) q^{26} +(4.15934 + 3.02194i) q^{27} +(0.436722 - 0.141900i) q^{28} +3.91037i q^{29} +(1.89322 + 0.615144i) q^{30} +(-3.42153 - 1.11172i) q^{31} +2.29433i q^{32} +(15.1002 - 4.90635i) q^{33} +(-0.474018 - 0.344394i) q^{34} +(-0.806934 + 0.262189i) q^{35} +(2.93162 - 9.02260i) q^{36} +(-1.13466 - 0.368672i) q^{37} +(0.0971952 + 0.133778i) q^{38} +(-1.76489 - 5.43177i) q^{39} -2.81703i q^{40} +(-1.18684 + 3.65272i) q^{41} +(-0.0397343 - 0.122289i) q^{42} +(-5.62586 + 7.74333i) q^{43} +(-6.53915 - 9.00037i) q^{44} +(-5.41677 + 16.6711i) q^{45} +(0.557481 + 0.405034i) q^{46} +6.21907 q^{47} -10.5551 q^{48} +(-5.61878 - 4.08228i) q^{49} +1.59621i q^{50} +(4.91370 - 6.76312i) q^{51} +(-3.23757 + 2.35223i) q^{52} +(-1.35820 + 1.86940i) q^{53} +(-0.959363 - 0.311716i) q^{54} +(12.0824 + 16.6300i) q^{55} +(-0.147210 + 0.106954i) q^{56} +(-1.90869 + 1.38675i) q^{57} +(-0.237088 - 0.729682i) q^{58} +(4.75809 - 1.54600i) q^{59} +19.9009 q^{60} +(-7.54478 - 2.01897i) q^{61} +0.705868 q^{62} +(1.07684 - 0.349888i) q^{63} +(2.19119 + 6.74380i) q^{64} +(5.98208 - 4.34623i) q^{65} +(-2.52025 + 1.83107i) q^{66} +(-1.99679 - 2.74834i) q^{67} +(-5.57086 - 1.81008i) q^{68} +(-5.77888 + 7.95394i) q^{69} +(0.134679 - 0.0978499i) q^{70} +(-1.12923 + 1.55426i) q^{71} +3.75929i q^{72} +(-4.14393 - 3.01074i) q^{73} +0.234082 q^{74} -22.7741 q^{75} +(1.33740 + 0.971681i) q^{76} +(0.410304 - 1.26279i) q^{77} +(0.658664 + 0.906574i) q^{78} +(6.05463 - 8.33349i) q^{79} +(-4.22283 - 12.9965i) q^{80} +(-0.0362779 + 0.111652i) q^{81} -0.753565i q^{82} +(-3.02904 - 9.32242i) q^{83} +(-0.755580 - 1.03997i) q^{84} +(10.2933 + 3.34450i) q^{85} +(0.580314 - 1.78602i) q^{86} +(10.4109 - 3.38269i) q^{87} +(3.56649 + 2.59121i) q^{88} +(6.67476 - 2.16876i) q^{89} -3.43928i q^{90} +(-0.454244 - 0.147593i) q^{91} +(6.55176 + 2.12879i) q^{92} +10.0711i q^{93} +(-1.16049 + 0.377067i) q^{94} +(-2.47113 - 1.79538i) q^{95} +(6.10835 - 1.98472i) q^{96} +(3.58986 - 11.0485i) q^{97} +(1.29599 + 0.421092i) q^{98} +(-16.1238 - 22.1926i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 5 q^{2} - q^{3} + 3 q^{4} - 15 q^{6} + 10 q^{7} - 5 q^{8} + q^{9}+O(q^{10}) \) 16 * q - 5 * q^2 - q^3 + 3 * q^4 - 15 * q^6 + 10 * q^7 - 5 * q^8 + q^9	\( 16 q - 5 q^{2} - q^{3} + 3 q^{4} - 15 q^{6} + 10 q^{7} - 5 q^{8} + q^{9} - 5 q^{10} - 12 q^{13} - 18 q^{14} - 13 q^{15} + 19 q^{16} - 10 q^{18} + 3 q^{19} - 13 q^{20} + 19 q^{22} - 15 q^{23} + 10 q^{24} - 2 q^{25} + 10 q^{26} - 4 q^{27} + 35 q^{28} + 45 q^{30} - 15 q^{31} + 25 q^{33} - 14 q^{34} + 10 q^{35} + 37 q^{36} - 5 q^{37} - 15 q^{38} - 3 q^{39} + 12 q^{41} - 15 q^{42} - 25 q^{43} - 50 q^{44} + 36 q^{45} + 27 q^{46} + 6 q^{47} - 20 q^{48} - 30 q^{49} + 50 q^{51} - 46 q^{52} - 20 q^{53} - 20 q^{54} + 20 q^{55} - 28 q^{56} - 11 q^{57} - 41 q^{58} + 5 q^{59} + 14 q^{60} - 53 q^{61} + 16 q^{62} - 5 q^{63} + 17 q^{64} + 20 q^{65} + 13 q^{66} - 55 q^{67} + 80 q^{68} - 15 q^{69} - 17 q^{70} - 50 q^{71} - 11 q^{73} + 24 q^{74} - 88 q^{75} - 19 q^{76} + 63 q^{77} + 50 q^{78} + 40 q^{79} - 49 q^{80} - 19 q^{81} + 31 q^{83} - 25 q^{84} + 55 q^{85} + 35 q^{86} + 25 q^{87} + 27 q^{88} + 60 q^{89} - 15 q^{91} - 5 q^{92} + 65 q^{94} + 48 q^{95} - 25 q^{96} + 45 q^{97} + 10 q^{98} - 5 q^{99}+O(q^{100}) \) 16 * q - 5 * q^2 - q^3 + 3 * q^4 - 15 * q^6 + 10 * q^7 - 5 * q^8 + q^9 - 5 * q^10 - 12 * q^13 - 18 * q^14 - 13 * q^15 + 19 * q^16 - 10 * q^18 + 3 * q^19 - 13 * q^20 + 19 * q^22 - 15 * q^23 + 10 * q^24 - 2 * q^25 + 10 * q^26 - 4 * q^27 + 35 * q^28 + 45 * q^30 - 15 * q^31 + 25 * q^33 - 14 * q^34 + 10 * q^35 + 37 * q^36 - 5 * q^37 - 15 * q^38 - 3 * q^39 + 12 * q^41 - 15 * q^42 - 25 * q^43 - 50 * q^44 + 36 * q^45 + 27 * q^46 + 6 * q^47 - 20 * q^48 - 30 * q^49 + 50 * q^51 - 46 * q^52 - 20 * q^53 - 20 * q^54 + 20 * q^55 - 28 * q^56 - 11 * q^57 - 41 * q^58 + 5 * q^59 + 14 * q^60 - 53 * q^61 + 16 * q^62 - 5 * q^63 + 17 * q^64 + 20 * q^65 + 13 * q^66 - 55 * q^67 + 80 * q^68 - 15 * q^69 - 17 * q^70 - 50 * q^71 - 11 * q^73 + 24 * q^74 - 88 * q^75 - 19 * q^76 + 63 * q^77 + 50 * q^78 + 40 * q^79 - 49 * q^80 - 19 * q^81 + 31 * q^83 - 25 * q^84 + 55 * q^85 + 35 * q^86 + 25 * q^87 + 27 * q^88 + 60 * q^89 - 15 * q^91 - 5 * q^92 + 65 * q^94 + 48 * q^95 - 25 * q^96 + 45 * q^97 + 10 * q^98 - 5 * q^99

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