LMFDB - Embedded newform 425.2.q.a.84.17

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			84.17
Character	$\chi$	$=$	425.84
Dual form			425.2.q.a.339.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.568609 + 0.782624i) q^{2} +(-0.724084 - 2.22850i) q^{3} +(0.328851 + 1.01210i) q^{4} +(-1.46866 + 1.68613i) q^{5} +(2.15580 + 0.700461i) q^{6} -0.961359 q^{7} +(-2.81914 - 0.915994i) q^{8} +(-2.01486 + 1.46388i) q^{9} +(-0.484512 - 2.10816i) q^{10} +(3.16360 - 4.35432i) q^{11} +(2.01735 - 1.46569i) q^{12} +(-0.0411761 - 0.0566741i) q^{13} +(0.546637 - 0.752382i) q^{14} +(4.82098 + 2.05201i) q^{15} +(0.597981 - 0.434459i) q^{16} +(2.53031 - 3.25539i) q^{17} -2.40926i q^{18} +(0.700717 - 2.15658i) q^{19} +(-2.18950 - 0.931944i) q^{20} +(0.696104 + 2.14239i) q^{21} +(1.60894 + 4.95181i) q^{22} +(-4.45324 - 3.23547i) q^{23} +6.94571i q^{24} +(-0.686075 - 4.95271i) q^{25} +0.0677676 q^{26} +(-0.965828 - 0.701715i) q^{27} +(-0.316144 - 0.972990i) q^{28} +(5.43761 - 1.76679i) q^{29} +(-4.34720 + 2.60622i) q^{30} +(3.78449 + 1.22965i) q^{31} -5.21340i q^{32} +(-11.9943 - 3.89718i) q^{33} +(1.10898 + 3.83132i) q^{34} +(1.41191 - 1.62098i) q^{35} +(-2.14419 - 1.55784i) q^{36} +(-7.21286 + 5.24045i) q^{37} +(1.28936 + 1.77465i) q^{38} +(-0.0964832 + 0.132798i) q^{39} +(5.68484 - 3.40815i) q^{40} +(-3.96838 - 5.46201i) q^{41} +(-2.07249 - 0.673394i) q^{42} -7.97907i q^{43} +(5.44735 + 1.76995i) q^{44} +(0.490850 - 5.54728i) q^{45} +(5.06430 - 1.64549i) q^{46} +(10.1712 - 3.30482i) q^{47} +(-1.40118 - 1.01802i) q^{48} -6.07579 q^{49} +(4.26621 + 2.27922i) q^{50} +(-9.08678 - 3.28163i) q^{51} +(0.0438190 - 0.0603116i) q^{52} +(-1.39170 + 0.452190i) q^{53} +(1.09836 - 0.356878i) q^{54} +(2.69570 + 11.7292i) q^{55} +(2.71020 + 0.880598i) q^{56} -5.31333 q^{57} +(-1.70915 + 5.26021i) q^{58} +(2.12346 - 1.54279i) q^{59} +(-0.491455 + 5.55411i) q^{60} +(-4.11921 + 5.66960i) q^{61} +(-3.11425 + 2.26264i) q^{62} +(1.93701 - 1.40732i) q^{63} +(5.27610 + 3.83331i) q^{64} +(0.156034 + 0.0138066i) q^{65} +(9.87010 - 7.17105i) q^{66} +(13.5466 + 4.40156i) q^{67} +(4.12687 + 1.49039i) q^{68} +(-3.98572 + 12.2668i) q^{69} +(0.465790 + 2.02670i) q^{70} +(-3.77479 + 1.22651i) q^{71} +(7.02109 - 2.28129i) q^{72} +(8.90514 + 6.46996i) q^{73} -8.62472i q^{74} +(-10.5403 + 5.11509i) q^{75} +2.41311 q^{76} +(-3.04135 + 4.18606i) q^{77} +(-0.0490694 - 0.151020i) q^{78} +(-5.56411 + 1.80789i) q^{79} +(-0.145677 + 1.64635i) q^{80} +(-3.17326 + 9.76629i) q^{81} +6.53116 q^{82} +(-1.02862 - 0.334220i) q^{83} +(-1.93939 + 1.40905i) q^{84} +(1.77284 + 9.04749i) q^{85} +(6.24461 + 4.53698i) q^{86} +(-7.87456 - 10.8384i) q^{87} +(-12.9071 + 9.37758i) q^{88} +(-11.0652 - 8.03934i) q^{89} +(4.06233 + 3.53838i) q^{90} +(0.0395850 + 0.0544841i) q^{91} +(1.81016 - 5.57110i) q^{92} -9.32410i q^{93} +(-3.19700 + 9.83936i) q^{94} +(2.60717 + 4.34879i) q^{95} +(-11.6181 + 3.77494i) q^{96} +(-0.704269 - 2.16752i) q^{97} +(3.45475 - 4.75506i) q^{98} +13.4045i 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 $

$2$	−0.568609	+	0.782624i	−0.402068	+	0.553398i	−0.961261	−	0.275638i	$-0.911111\pi$
$2$	−0.568609	+	0.782624i	−0.402068	+	0.553398i	0.559194	+	0.829037i	$0.311111\pi$
$3$	−0.724084	−	2.22850i	−0.418050	−	1.28663i	−0.909494	−	0.415716i	$-0.863531\pi$
$3$	−0.724084	−	2.22850i	−0.418050	−	1.28663i	0.491445	−	0.870909i	$-0.336469\pi$
$4$	0.328851	+	1.01210i	0.164425	+	0.506049i
$5$	−1.46866	+	1.68613i	−0.656805	+	0.754061i
$5$	−1.46866	+	1.68613i	−0.656805	+	0.754061i
$6$	2.15580	+	0.700461i	0.880101	+	0.285962i
$7$	−0.961359			−0.363359			−0.181680	−	0.983358i	$-0.558153\pi$
$7$	−0.961359			−0.363359			−0.181680	+	0.983358i	$0.558153\pi$
$8$	−2.81914	−	0.915994i	−0.996716	−	0.323853i
$9$	−2.01486	+	1.46388i	−0.671622	+	0.487962i
$10$	−0.484512	−	2.10816i	−0.153216	−	0.666658i
$11$	3.16360	−	4.35432i	0.953860	−	1.31288i	0.00406835	−	0.999992i	$-0.498705\pi$
$11$	3.16360	−	4.35432i	0.953860	−	1.31288i	0.949791	−	0.312884i	$-0.101295\pi$
$12$	2.01735	−	1.46569i	0.582358	−	0.423108i
$13$	−0.0411761	−	0.0566741i	−0.0114202	−	0.0157186i	0.803269	−	0.595617i	$-0.203092\pi$
$13$	−0.0411761	−	0.0566741i	−0.0114202	−	0.0157186i	−0.814689	+	0.579898i	$0.803092\pi$
$14$	0.546637	−	0.752382i	0.146095	−	0.201083i
$15$	4.82098	+	2.05201i	1.24477	+	0.529827i
$16$	0.597981	−	0.434459i	0.149495	−	0.108615i
$17$	2.53031	−	3.25539i	0.613690	−	0.789547i
$17$	2.53031	−	3.25539i	0.613690	−	0.789547i
$18$		−	2.40926i		−	0.567868i
$19$	0.700717	−	2.15658i	0.160755	−	0.494754i	−0.837943	−	0.545758i	$-0.816242\pi$
$19$	0.700717	−	2.15658i	0.160755	−	0.494754i	0.998698	+	0.0510033i	$0.0162419\pi$
$20$	−2.18950	−	0.931944i	−0.489587	−	0.208389i
$21$	0.696104	+	2.14239i	0.151902	+	0.467507i
$22$	1.60894	+	4.95181i	0.343027	+	1.05573i
$23$	−4.45324	−	3.23547i	−0.928564	−	0.674641i	0.0170768	−	0.999854i	$-0.494564\pi$
$23$	−4.45324	−	3.23547i	−0.928564	−	0.674641i	−0.945641	+	0.325213i	$0.894564\pi$
$24$			6.94571i			1.41779i
$25$	−0.686075	−	4.95271i	−0.137215	−	0.990541i
$26$	0.0677676			0.0132903
$27$	−0.965828	−	0.701715i	−0.185874	−	0.135045i
$28$	−0.316144	−	0.972990i	−0.0597455	−	0.183878i
$29$	5.43761	−	1.76679i	1.00974	−	0.328084i	0.242988	−	0.970029i	$-0.421872\pi$
$29$	5.43761	−	1.76679i	1.00974	−	0.328084i	0.766750	+	0.641945i	$0.221872\pi$
$30$	−4.34720	+	2.60622i	−0.793687	+	0.475828i
$31$	3.78449	+	1.22965i	0.679714	+	0.220852i	0.628470	−	0.777834i	$-0.283681\pi$
$31$	3.78449	+	1.22965i	0.679714	+	0.220852i	0.0512438	+	0.998686i	$0.483681\pi$
$32$		−	5.21340i		−	0.921608i
$33$	−11.9943	−	3.89718i	−2.08794	−	0.678413i
$34$	1.10898	+	3.83132i	0.190189	+	0.657066i
$35$	1.41191	−	1.62098i	0.238656	−	0.273995i
$36$	−2.14419	−	1.55784i	−0.357364	−	0.259640i
$37$	−7.21286	+	5.24045i	−1.18579	+	0.861525i	−0.992813	−	0.119679i	$-0.961813\pi$
$37$	−7.21286	+	5.24045i	−1.18579	+	0.861525i	−0.192974	+	0.981204i	$0.561813\pi$
$38$	1.28936	+	1.77465i	0.209162	+	0.287887i
$39$	−0.0964832	+	0.132798i	−0.0154497	+	0.0212647i
$40$	5.68484	−	3.40815i	0.898852	−	0.538876i
$41$	−3.96838	−	5.46201i	−0.619757	−	0.853022i	0.377578	−	0.925978i	$-0.376757\pi$
$41$	−3.96838	−	5.46201i	−0.619757	−	0.853022i	−0.997335	+	0.0729553i	$0.976757\pi$
$42$	−2.07249	−	0.673394i	−0.319793	−	0.103907i
$43$		−	7.97907i		−	1.21680i	−0.793632	−	0.608399i	$-0.791812\pi$
$43$		−	7.97907i		−	1.21680i	0.793632	−	0.608399i	$-0.208188\pi$
$44$	5.44735	+	1.76995i	0.821219	+	0.266830i
$45$	0.490850	−	5.54728i	0.0731716	−	0.826939i
$46$	5.06430	−	1.64549i	0.746691	−	0.242615i
$47$	10.1712	−	3.30482i	1.48362	−	0.482058i	0.548428	−	0.836198i	$-0.315226\pi$
$47$	10.1712	−	3.30482i	1.48362	−	0.482058i	0.935192	+	0.354140i	$0.115226\pi$
$48$	−1.40118	−	1.01802i	−0.202243	−	0.146938i
$49$	−6.07579			−0.867970
$50$	4.26621	+	2.27922i	0.603334	+	0.322330i
$51$	−9.08678	−	3.28163i	−1.27240	−	0.459519i
$52$	0.0438190	−	0.0603116i	0.00607660	−	0.00836372i
$53$	−1.39170	+	0.452190i	−0.191164	+	0.0621131i	−0.403035	−	0.915185i	$-0.632045\pi$
$53$	−1.39170	+	0.452190i	−0.191164	+	0.0621131i	0.211870	+	0.977298i	$0.432045\pi$
$54$	1.09836	−	0.356878i	0.149468	−	0.0485649i
$55$	2.69570	+	11.7292i	0.363488	+	1.58157i
$56$	2.71020	+	0.880598i	0.362166	+	0.117675i
$57$	−5.31333			−0.703767
$58$	−1.70915	+	5.26021i	−0.224422	+	0.690699i
$59$	2.12346	−	1.54279i	0.276451	−	0.200854i	−0.440917	−	0.897548i	$-0.645347\pi$
$59$	2.12346	−	1.54279i	0.276451	−	0.200854i	0.717368	+	0.696694i	$0.245347\pi$
$60$	−0.491455	+	5.55411i	−0.0634465	+	0.717032i
$61$	−4.11921	+	5.66960i	−0.527411	+	0.725918i	−0.986733	−	0.162351i	$-0.948092\pi$
$61$	−4.11921	+	5.66960i	−0.527411	+	0.725918i	0.459322	+	0.888270i	$0.348092\pi$
$62$	−3.11425	+	2.26264i	−0.395510	+	0.287355i
$63$	1.93701	−	1.40732i	0.244040	−	0.177305i
$64$	5.27610	+	3.83331i	0.659512	+	0.479163i
$65$	0.156034	+	0.0138066i	0.0193536	+	0.00171250i
$66$	9.87010	−	7.17105i	1.21493	−	0.882695i
$67$	13.5466	+	4.40156i	1.65498	+	0.537736i	0.979811	−	0.199926i	$-0.0640700\pi$
$67$	13.5466	+	4.40156i	1.65498	+	0.537736i	0.675171	+	0.737662i	$0.264070\pi$
$68$	4.12687	+	1.49039i	0.500456	+	0.180736i
$69$	−3.98572	+	12.2668i	−0.479824	+	1.47675i
$70$	0.465790	+	2.02670i	0.0556725	+	0.242236i
$71$	−3.77479	+	1.22651i	−0.447986	+	0.145559i	−0.524317	−	0.851523i	$-0.675679\pi$
$71$	−3.77479	+	1.22651i	−0.447986	+	0.145559i	0.0763313	+	0.997083i	$0.475679\pi$
$72$	7.02109	−	2.28129i	0.827444	−	0.268853i
$73$	8.90514	+	6.46996i	1.04227	+	0.757252i	0.970727	−	0.240186i	$-0.0772085\pi$
$73$	8.90514	+	6.46996i	1.04227	+	0.757252i	0.0715406	+	0.997438i	$0.477208\pi$
$74$		−	8.62472i		−	1.00260i
$75$	−10.5403	+	5.11509i	−1.21709	+	0.590640i
$76$	2.41311			0.276803
$77$	−3.04135	+	4.18606i	−0.346594	+	0.477046i
$78$	−0.0490694	−	0.151020i	−0.00555601	−	0.0170997i
$79$	−5.56411	+	1.80789i	−0.626012	+	0.203404i	−0.604808	−	0.796372i	$-0.706750\pi$
$79$	−5.56411	+	1.80789i	−0.626012	+	0.203404i	−0.0212042	+	0.999775i	$0.506750\pi$
$80$	−0.145677	+	1.64635i	−0.0162872	+	0.184067i
$81$	−3.17326	+	9.76629i	−0.352585	+	1.08514i
$82$	6.53116			0.721245
$83$	−1.02862	−	0.334220i	−0.112906	−	0.0366854i	0.252019	−	0.967722i	$-0.418905\pi$
$83$	−1.02862	−	0.334220i	−0.112906	−	0.0366854i	−0.364925	+	0.931037i	$0.618905\pi$
$84$	−1.93939	+	1.40905i	−0.211605	+	0.153740i
$85$	1.77284	+	9.04749i	0.192292	+	0.981338i
$86$	6.24461	+	4.53698i	0.673374	+	0.489235i
$87$	−7.87456	−	10.8384i	−0.844242	−	1.16200i
$88$	−12.9071	+	9.37758i	−1.37591	+	0.999654i
$89$	−11.0652	−	8.03934i	−1.17291	−	0.852168i	−0.181555	−	0.983381i	$-0.558113\pi$
$89$	−11.0652	−	8.03934i	−1.17291	−	0.852168i	−0.991354	+	0.131213i	$0.958113\pi$
$90$	4.06233	+	3.53838i	0.428207	+	0.372978i
$91$	0.0395850	+	0.0544841i	0.00414964	+	0.00571148i
$92$	1.81016	−	5.57110i	0.188722	−	0.580827i
$93$		−	9.32410i		−	0.966864i
$94$	−3.19700	+	9.83936i	−0.329746	+	1.01485i
$95$	2.60717	+	4.34879i	0.267490	+	0.446176i
$96$	−11.6181	+	3.77494i	−1.18576	+	0.385278i
$97$	−0.704269	−	2.16752i	−0.0715077	−	0.220078i	0.908915	−	0.416981i	$-0.136912\pi$
$97$	−0.704269	−	2.16752i	−0.0715077	−	0.220078i	−0.980423	+	0.196903i	$0.936912\pi$
$98$	3.45475	−	4.75506i	0.348983	−	0.480333i
$99$			13.4045i			1.34720i
$100$	4.78701	−	2.32308i	0.478701	−	0.232308i
$101$	9.00362			0.895894			0.447947	−	0.894060i	$-0.352155\pi$
$101$	9.00362			0.895894			0.447947	+	0.894060i	$0.352155\pi$
$102$	7.73511	−	5.24557i	0.765890	−	0.519389i
$103$	−1.36177	+	0.442465i	−0.134179	+	0.0435974i	−0.375337	−	0.926889i	$-0.622473\pi$
$103$	−1.36177	+	0.442465i	−0.134179	+	0.0435974i	0.241158	+	0.970486i	$0.422473\pi$
$104$	0.0641681	+	0.197489i	0.00629220	+	0.0193654i
$105$	−4.63469	−	1.97272i	−0.452299	−	0.192517i
$106$	0.437438	−	1.34629i	0.0424877	−	0.130764i
$107$	−8.27819			−0.800283			−0.400141	−	0.916453i	$-0.631039\pi$
$107$	−8.27819			−0.800283			−0.400141	+	0.916453i	$0.631039\pi$
$108$	0.392592	−	1.20827i	0.0377772	−	0.116266i
$109$	−6.91345	−	9.51555i	−0.662189	−	0.911425i	0.337363	−	0.941375i	$-0.390465\pi$
$109$	−6.91345	−	9.51555i	−0.662189	−	0.911425i	−0.999551	+	0.0299500i	$0.990465\pi$
$110$	−10.7124	−	4.55964i	−1.02139	−	0.434745i
$111$	16.9011	+	12.2793i	1.60418	+	1.16550i
$112$	−0.574874	+	0.417671i	−0.0543205	+	0.0394662i
$113$	0.730866	−	0.531005i	0.0687541	−	0.0499528i	−0.552877	−	0.833263i	$-0.686470\pi$
$113$	0.730866	−	0.531005i	0.0687541	−	0.0499528i	0.621631	+	0.783310i	$0.286470\pi$
$114$	3.02121	−	4.15834i	0.282962	−	0.389464i
$115$	11.9957	−	2.75694i	1.11861	−	0.257086i
$116$	3.57632	+	4.92239i	0.332053	+	0.457032i
$117$	0.165929	+	0.0539135i	0.0153401	+	0.00498430i
$118$			2.53912i			0.233745i
$119$	−2.43254	+	3.12959i	−0.222990	+	0.286889i
$120$	−11.7114	−	10.2009i	−1.06910	−	0.931209i
$121$	−5.55254	−	17.0890i	−0.504776	−	1.55354i
$122$	−2.09495	−	6.44758i	−0.189667	−	0.583736i
$123$	−9.29865	+	12.7985i	−0.838431	+	1.15400i
$124$			4.23465i			0.380283i
$125$	9.35852	+	6.11703i	0.837052	+	0.547124i
$126$			2.31616i			0.206340i
$127$	−5.32629	+	7.33101i	−0.472632	+	0.650522i	−0.977068	−	0.212927i	$-0.931700\pi$
$127$	−5.32629	+	7.33101i	−0.472632	+	0.650522i	0.504436	+	0.863449i	$0.331700\pi$
$128$	3.91641	−	1.27252i	0.346165	−	0.112476i
$129$	−17.7814	+	5.77752i	−1.56556	+	0.508682i
$130$	−0.0995275	+	0.114265i	−0.00872914	+	0.0100217i
$131$	9.82000	+	3.19071i	0.857978	+	0.278774i	0.704784	−	0.709422i	$-0.251044\pi$
$131$	9.82000	+	3.19071i	0.857978	+	0.278774i	0.153194	+	0.988196i	$0.451044\pi$
$132$		−	13.4210i		−	1.16815i
$133$	−0.673640	+	2.07325i	−0.0584120	+	0.179774i
$134$	−11.1475	+	8.09913i	−0.962997	+	0.699658i
$135$	2.60166	−	0.597931i	0.223915	−	0.0514617i
$136$	−10.1152	+	6.85963i	−0.867372	+	0.588209i
$137$	−3.04381	−	4.18944i	−0.260050	−	0.357928i	0.658949	−	0.752187i	$-0.271001\pi$
$137$	−3.04381	−	4.18944i	−0.260050	−	0.357928i	−0.918999	+	0.394259i	$0.871001\pi$
$138$	−7.33396	−	10.0943i	−0.624308	−	0.859286i
$139$	1.00657	−	1.38542i	0.0853760	−	0.117510i	−0.764193	−	0.644988i	$-0.776862\pi$
$139$	1.00657	−	1.38542i	0.0853760	−	0.117510i	0.849569	+	0.527478i	$0.176862\pi$
$140$	2.10490	+	0.895932i	0.177896	+	0.0757201i
$141$	−14.7296	−	20.2735i	−1.24045	−	1.70734i
$142$	1.18649	−	3.65165i	0.0995682	−	0.306439i
$143$	−0.377041			−0.0315298
$144$	−0.568854	+	1.75075i	−0.0474045	+	0.145896i
$145$	−5.00696	+	11.7633i	−0.415806	+	0.976891i
$146$	−10.1271	+	3.29049i	−0.838124	+	0.272323i
$147$	4.39938	+	13.5399i	0.362855	+	1.11675i
$148$	−7.67581	−	5.57680i	−0.630948	−	0.458410i
$149$	−13.1934			−1.08084			−0.540421	−	0.841395i	$-0.681735\pi$
$149$	−13.1934			−1.08084			−0.540421	+	0.841395i	$0.681735\pi$
$150$	1.99014	−	11.1576i	0.162494	−	0.911014i
$151$	9.65520			0.785729			0.392865	−	0.919596i	$-0.371484\pi$
$151$	9.65520			0.785729			0.392865	+	0.919596i	$0.371484\pi$
$152$	−3.95084	+	5.43786i	−0.320455	+	0.441069i
$153$	−0.332723	+	10.2632i	−0.0268991	+	0.829734i
$154$	−1.54677	−	4.76046i	−0.124642	−	0.383609i
$155$	−7.63148	+	4.57520i	−0.612975	+	0.367489i
$156$	−0.166133	−	0.0539799i	−0.0133013	−	0.00432185i
$157$			5.82777i			0.465107i	0.972584	+	0.232553i	$0.0747080\pi$
$157$			5.82777i			0.465107i	−0.972584	+	0.232553i	$0.925292\pi$
$158$	1.74891	−	5.38259i	0.139136	−	0.428216i
$159$	2.01541	+	2.77397i	0.159832	+	0.219991i
$160$	8.79048	+	7.65672i	0.694949	+	0.605317i
$161$	4.28116	+	3.11044i	0.337402	+	0.245137i
$162$	−5.83899	−	8.03668i	−0.458754	−	0.631421i
$163$	−19.3284	+	14.0429i	−1.51392	+	1.09993i	−0.549515	+	0.835484i	$0.685188\pi$
$163$	−19.3284	+	14.0429i	−1.51392	+	1.09993i	−0.964402	+	0.264441i	$0.914812\pi$
$164$	4.22309	−	5.81258i	0.329768	−	0.453886i
$165$	24.1867	−	14.5003i	1.88293	−	1.12885i
$166$	0.846453	−	0.614984i	0.0656975	−	0.0477320i
$167$	3.83475	−	11.8021i	0.296741	−	0.913276i	−0.685889	−	0.727706i	$-0.740587\pi$
$167$	3.83475	−	11.8021i	0.296741	−	0.913276i	0.982631	−	0.185571i	$-0.0594133\pi$
$168$		−	6.67731i		−	0.515166i
$169$	4.01570	−	12.3591i	0.308900	−	0.950697i
$170$	−8.08883	−	3.75702i	−0.620385	−	0.288150i
$171$	1.74514	+	5.37100i	0.133454	+	0.410730i
$172$	8.07561	−	2.62393i	0.615760	−	0.200072i
$173$	10.3927	+	7.55075i	0.790144	+	0.574073i	0.908006	−	0.418957i	$-0.137604\pi$
$173$	10.3927	+	7.55075i	0.790144	+	0.574073i	−0.117862	+	0.993030i	$0.537604\pi$
$174$	12.9599			0.982491
$175$	0.659564	+	4.76133i	0.0498584	+	0.359922i
$176$		−	3.97825i		−	0.299872i
$177$	−4.97567	−	3.61503i	−0.373994	−	0.271722i
$178$	12.5836	−	4.08864i	0.943177	−	0.306457i
$179$	7.73540	+	23.8071i	0.578171	+	1.77943i	0.625118	+	0.780531i	$0.285051\pi$
$179$	7.73540	+	23.8071i	0.578171	+	1.77943i	−0.0469463	+	0.998897i	$0.514949\pi$
$180$	5.77581	−	1.32744i	0.430503	−	0.0989414i
$181$	12.5529	+	4.07868i	0.933049	+	0.303166i	0.735809	−	0.677189i	$-0.236802\pi$
$181$	12.5529	+	4.07868i	0.933049	+	0.303166i	0.197240	+	0.980355i	$0.436802\pi$
$182$	−0.0651489			−0.00482916
$183$	15.6174	+	5.07439i	1.15447	+	0.375110i
$184$	9.59062	+	13.2004i	0.707030	+	0.973144i
$185$	1.75716	−	19.8583i	0.129189	−	1.46001i
$186$	7.29726	+	5.30177i	0.535061	+	0.388745i
$187$	−6.17010	−	21.3165i	−0.451202	−	1.55882i
$188$	6.68961	+	9.20746i	0.487890	+	0.671523i
$189$	0.928507	+	0.674600i	0.0675389	+	0.0490699i
$190$	−4.88593	−	0.432330i	−0.354462	−	0.0313646i
$191$	0.386781	−	0.281013i	0.0279865	−	0.0203334i	−0.573704	−	0.819063i	$-0.694494\pi$
$191$	0.386781	−	0.281013i	0.0279865	−	0.0203334i	0.601691	+	0.798729i	$0.294494\pi$
$192$	4.72219	−	14.5334i	0.340795	−	1.04886i
$193$	18.8179			1.35454			0.677269	−	0.735735i	$-0.263163\pi$
$193$	18.8179			1.35454			0.677269	+	0.735735i	$0.263163\pi$
$194$	2.09680	+	0.681293i	0.150542	+	0.0489140i
$195$	−0.0822133	−	0.357718i	−0.00588742	−	0.0256167i
$196$	−1.99803	−	6.14930i	−0.142716	−	0.439236i
$197$	−7.56833	−	23.2929i	−0.539221	−	1.65955i	−0.734347	−	0.678775i	$-0.762511\pi$
$197$	−7.56833	−	23.2929i	−0.539221	−	1.65955i	0.195125	−	0.980778i	$-0.437489\pi$
$198$	−10.4907	−	7.62192i	−0.745540	−	0.541666i
$199$		−	14.7272i		−	1.04399i	−0.852950	−	0.521993i	$-0.825189\pi$
$199$		−	14.7272i		−	1.04399i	0.852950	−	0.521993i	$-0.174811\pi$
$200$	−2.60251	+	14.5908i	−0.184025	+	1.03173i
$201$		−	33.3757i		−	2.35414i
$202$	−5.11954	+	7.04645i	−0.360210	+	0.495786i
$203$	−5.22749	+	1.69851i	−0.366898	+	0.119212i
$204$	0.333133	−	10.2759i	0.0233240	−	0.719456i
$205$	15.0379	+	1.33062i	1.05029	+	0.0929348i
$206$	0.428030	−	1.31734i	0.0298223	−	0.0917835i
$207$	13.7090			0.952843
$208$	−0.0492451	−	0.0160007i	−0.00341453	−	0.00110945i
$209$	−7.17367	−	9.87370i	−0.496213	−	0.682978i
$210$	4.17922	−	2.50551i	0.288394	−	0.172897i
$211$	0.0911097	−	0.125402i	0.00627225	−	0.00863301i	−0.805869	−	0.592093i	$-0.798302\pi$
$211$	0.0911097	−	0.125402i	0.00627225	−	0.00863301i	0.812142	+	0.583460i	$0.198302\pi$
$212$	−0.915322	−	1.25983i	−0.0628646	−	0.0865257i
$213$	5.46653	+	7.52404i	0.374561	+	0.515539i
$214$	4.70705	−	6.47870i	0.321768	−	0.442875i
$215$	13.4538	+	11.7185i	0.917539	+	0.799198i
$216$	2.08004	+	2.86292i	0.141529	+	0.194797i
$217$	−3.63825	−	1.18214i	−0.246980	−	0.0802488i
$218$	11.3782			0.770626
$219$	7.97024	−	24.5299i	0.538579	−	1.65758i
$220$	−10.9847	+	6.58549i	−0.740586	+	0.443993i
$221$	−0.288684	−	0.00935883i	−0.0194190	−	0.000629543i
$222$	−19.2202	+	6.24502i	−1.28998	+	0.419138i
$223$	3.25387	−	4.47857i	0.217895	−	0.299907i	−0.686051	−	0.727554i	$-0.740657\pi$
$223$	3.25387	−	4.47857i	0.217895	−	0.299907i	0.903946	+	0.427647i	$0.140657\pi$
$224$			5.01195i			0.334875i
$225$	8.63254	+	8.97470i	0.575503	+	0.598313i
$226$			0.873928i			0.0581328i
$227$	9.00814	+	6.54480i	0.597891	+	0.434394i	0.845130	−	0.534561i	$-0.179523\pi$
$227$	9.00814	+	6.54480i	0.597891	+	0.434394i	−0.247238	+	0.968955i	$0.579523\pi$
$228$	−1.74729	−	5.37761i	−0.115717	−	0.356141i
$229$	−0.0215994	−	0.0664762i	−0.00142733	−	0.00439287i	0.950340	−	0.311213i	$-0.100735\pi$
$229$	−0.0215994	−	0.0664762i	−0.00142733	−	0.00439287i	−0.951768	+	0.306820i	$0.900735\pi$
$230$	−4.66323	+	10.9557i	−0.307484	+	0.722401i
$231$	11.5308	+	3.74659i	0.758672	+	0.246508i
$232$	−16.9477			−1.11267
$233$	−4.76687	+	14.6709i	−0.312288	+	0.961125i	0.664568	+	0.747228i	$0.268616\pi$
$233$	−4.76687	+	14.6709i	−0.312288	+	0.961125i	−0.976856	+	0.213897i	$0.931384\pi$
$234$	−0.136543	+	0.0992039i	−0.00892606	+	0.00648516i
$235$	−9.36566	+	22.0036i	−0.610948	+	1.43536i
$236$	2.25976	+	1.64181i	0.147098	+	0.106873i
$237$	8.05777	+	11.0906i	0.523408	+	0.720410i
$238$	−1.06613	−	3.68327i	−0.0691070	−	0.238751i
$239$	−24.1160	−	17.5213i	−1.55994	−	1.13336i	−0.936061	−	0.351838i	$-0.885557\pi$
$239$	−24.1160	−	17.5213i	−1.55994	−	1.13336i	−0.623876	−	0.781523i	$-0.714443\pi$
$240$	3.77437	−	0.867452i	0.243634	−	0.0559938i
$241$	8.89748	+	12.2463i	0.573137	+	0.788856i	0.992922	−	0.118768i	$-0.0378945\pi$
$241$	8.89748	+	12.2463i	0.573137	+	0.788856i	−0.419785	+	0.907624i	$0.637894\pi$
$242$	16.5314	+	5.37139i	1.06268	+	0.345286i
$243$	20.4804			1.31382
$244$	−7.09280	−	2.30459i	−0.454070	−	0.147536i
$245$	8.92327	−	10.2446i	0.570087	−	0.654502i
$246$	−4.72910	−	14.5547i	−0.301517	−	0.927973i
$247$	−0.151075	+	0.0490873i	−0.00961269	+	0.00312335i
$248$	−9.54264	−	6.93313i	−0.605958	−	0.440254i
$249$			2.53429i			0.160604i
$250$	−10.1087	+	3.84600i	−0.639329	+	0.243242i
$251$	−13.8762			−0.875858			−0.437929	−	0.899010i	$-0.644288\pi$
$251$	−13.8762			−0.875858			−0.437929	+	0.899010i	$0.644288\pi$
$252$	2.06133	+	1.49765i	0.129852	+	0.0943428i
$253$	−28.1765	+	9.15509i	−1.77144	+	0.575576i
$254$	−2.70884	−	8.33696i	−0.169968	−	0.523107i
$255$	18.8786	−	10.5019i	1.18223	−	0.657655i
$256$	−5.26158	+	16.1935i	−0.328849	+	1.01209i
$257$		−	28.9043i		−	1.80300i	−0.432778	−	0.901501i	$-0.642466\pi$
$257$		−	28.9043i		−	1.80300i	0.432778	−	0.901501i	$-0.357534\pi$
$258$	5.58903	−	17.2013i	0.347958	−	1.07090i
$259$	6.93415	−	5.03795i	0.430867	−	0.313043i
$260$	0.0373381	+	0.162462i	0.00231561	+	0.0100754i
$261$	−8.36967	+	11.5199i	−0.518070	+	0.713062i
$262$	−8.08087	+	5.87110i	−0.499238	+	0.362718i
$263$	−10.3025	−	14.1802i	−0.635282	−	0.874391i	0.363071	−	0.931762i	$-0.381728\pi$
$263$	−10.3025	−	14.1802i	−0.635282	−	0.874391i	−0.998353	+	0.0573708i	$0.981728\pi$
$264$	30.2438	+	21.9734i	1.86138	+	1.35237i
$265$	1.28148	−	3.01070i	0.0787206	−	0.184946i
$266$	−1.23954	−	1.70608i	−0.0760009	−	0.104606i
$267$	−9.90354	+	30.4799i	−0.606087	+	1.86534i
$268$			15.1580i			0.925920i
$269$	−7.14869	−	2.32275i	−0.435863	−	0.141621i	0.0828630	−	0.996561i	$-0.473594\pi$
$269$	−7.14869	−	2.32275i	−0.435863	−	0.141621i	−0.518726	+	0.854940i	$0.673594\pi$
$270$	−1.01137	+	2.37611i	−0.0615501	+	0.144605i
$271$	−0.864226	−	2.65982i	−0.0524980	−	0.161572i	0.921370	−	0.388686i	$-0.127071\pi$
$271$	−0.864226	−	2.65982i	−0.0524980	−	0.161572i	−0.973868	+	0.227114i	$0.927071\pi$
$272$	0.0987472	−	3.04597i	0.00598743	−	0.184689i
$273$	0.0927549	−	0.127666i	0.00561378	−	0.00772671i
$274$	5.00949			0.302634
$275$	−23.7361	−	12.6810i	−1.43134	−	0.764691i
$276$	−13.7259			−0.826203
$277$	4.39506	+	3.19320i	0.264073	+	0.191861i	0.711941	−	0.702239i	$-0.247816\pi$
$277$	4.39506	+	3.19320i	0.264073	+	0.191861i	−0.447868	+	0.894100i	$0.647816\pi$
$278$	0.511920	+	1.57553i	0.0307029	+	0.0944938i
$279$	−9.42530	+	3.06247i	−0.564278	+	0.183345i
$280$	−5.46517	+	3.27646i	−0.326606	+	0.195806i
$281$	1.89506	−	5.83239i	0.113050	−	0.347931i	−0.878486	−	0.477769i	$-0.841446\pi$
$281$	1.89506	−	5.83239i	0.113050	−	0.347931i	0.991535	+	0.129838i	$0.0414457\pi$
$282$	24.2419			1.44359
$283$	5.24266	−	16.1353i	0.311644	−	0.959141i	−0.665470	−	0.746425i	$-0.731769\pi$
$283$	5.24266	−	16.1353i	0.311644	−	0.959141i	0.977114	−	0.212717i	$-0.0682311\pi$
$284$	−2.48269	−	3.41713i	−0.147320	−	0.202769i
$285$	7.80347	−	8.95897i	0.462238	−	0.530683i
$286$	0.214389	−	0.295081i	0.0126771	−	0.0174485i
$287$	3.81504	+	5.25095i	0.225195	+	0.309954i
$288$	7.63182	+	10.5043i	0.449710	+	0.618972i
$289$	−4.19506	−	16.4743i	−0.246768	−	0.969074i
$290$	−6.35925	−	10.6073i	−0.373428	−	0.622882i
$291$	−4.32036	+	3.13893i	−0.253264	+	0.184007i
$292$	−3.61978	+	11.1405i	−0.211831	+	0.651950i
$293$			15.4345i			0.901694i	0.892601	+	0.450847i	$0.148878\pi$
$293$			15.4345i			0.901694i	−0.892601	+	0.450847i	$0.851122\pi$
$294$	−13.0982	−	4.25585i	−0.763901	−	0.248206i
$295$	−0.517306	+	5.84627i	−0.0301187	+	0.340383i
$296$	25.1343	−	8.16662i	1.46090	−	0.474675i
$297$	−6.11098	+	1.98558i	−0.354595	+	0.115215i
$298$	7.50186	−	10.3254i	0.434571	−	0.598136i
$299$			0.385607i			0.0223002i
$300$	−8.64318	−	8.98576i	−0.499014	−	0.518793i
$301$			7.67075i			0.442135i
$302$	−5.49004	+	7.55639i	−0.315916	+	0.434821i
$303$	−6.51937	−	20.0646i	−0.374528	−	1.15268i
$304$	−0.517932	−	1.59403i	−0.0297054	−	0.0914239i
$305$	−3.50998	−	15.2722i	−0.200981	−	0.874486i
$306$	−7.84307	−	6.09617i	−0.448358	−	0.348495i
$307$			7.69750i			0.439320i	0.975577	+	0.219660i	$0.0704947\pi$
$307$			7.69750i			0.439320i	−0.975577	+	0.219660i	$0.929505\pi$
$308$	−5.23686	−	1.70156i	−0.298398	−	0.0969552i
$309$	1.97207	+	2.71432i	0.112187	+	0.154412i
$310$	0.758676	−	8.57408i	0.0430899	−	0.486975i
$311$	−4.33183	+	5.96225i	−0.245635	+	0.338088i	−0.913977	−	0.405767i	$-0.867005\pi$
$311$	−4.33183	+	5.96225i	−0.245635	+	0.338088i	0.668341	+	0.743855i	$0.267005\pi$
$312$	0.393641	−	0.285997i	0.0222856	−	0.0161914i
$313$	1.10518	−	0.802958i	0.0624683	−	0.0453859i	−0.556113	−	0.831107i	$-0.687708\pi$
$313$	1.10518	−	0.802958i	0.0624683	−	0.0453859i	0.618581	+	0.785721i	$0.287708\pi$
$314$	−4.56095	−	3.31372i	−0.257389	−	0.187004i
$315$	−0.471883	+	5.33292i	−0.0265876	+	0.300476i
$316$	−3.65953	−	5.03691i	−0.205865	−	0.283348i
$317$	−7.45404	+	22.9412i	−0.418661	+	1.28851i	0.490274	+	0.871568i	$0.336897\pi$
$317$	−7.45404	+	22.9412i	−0.418661	+	1.28851i	−0.908935	+	0.416937i	$0.863103\pi$
$318$	−3.31696			−0.186006
$319$	9.50925	−	29.2665i	0.532416	−	1.63861i
$320$	−14.2122	+	3.26636i	−0.794489	+	0.182595i
$321$	5.99410	+	18.4479i	0.334558	+	1.02966i
$322$	−4.86861	+	1.58191i	−0.271317	+	0.0881563i
$323$	−5.24748	−	7.73793i	−0.291978	−	0.430550i
$324$	−10.9280			−0.607110
$325$	−0.252440	+	0.242816i	−0.0140029	+	0.0134690i
$326$		−	23.1118i		−	1.28004i
$327$	−16.1995	+	22.2967i	−0.895834	+	1.23301i
$328$	6.18425	+	19.0332i	0.341468	+	1.05093i
$329$	−9.77816	+	3.17712i	−0.539087	+	0.175160i
$330$	−2.40450	+	27.1741i	−0.132363	+	1.49589i
$331$	6.65338	−	20.4770i	0.365703	−	1.12552i	−0.583837	−	0.811871i	$-0.698449\pi$
$331$	6.65338	−	20.4770i	0.365703	−	1.12552i	0.949540	−	0.313646i	$-0.101551\pi$
$332$		−	1.15098i		−	0.0631681i
$333$	6.86152	−	21.1176i	0.376009	−	1.15724i
$334$	7.05615	+	9.71196i	0.386096	+	0.531415i
$335$	−27.3170	+	16.3770i	−1.49249	+	0.894769i
$336$	1.34704	+	0.978679i	0.0734868	+	0.0533913i
$337$	0.963320	−	0.699893i	0.0524754	−	0.0381256i	−0.561238	−	0.827654i	$-0.689675\pi$
$337$	0.963320	−	0.699893i	0.0524754	−	0.0381256i	0.613714	+	0.789529i	$0.289675\pi$
$338$	7.38913	+	10.1703i	0.401916	+	0.553190i
$339$	−1.71255	−	1.24424i	−0.0930131	−	0.0675780i
$340$	−8.57395	+	4.76956i	−0.464988	+	0.258666i
$341$	17.3269	−	12.5887i	0.938303	−	0.681717i
$342$	−5.19577	−	1.68821i	−0.280955	−	0.0912879i
$343$	12.5705			0.678744
$344$	−7.30878	+	22.4941i	−0.394063	+	1.21280i
$345$	−14.8297	−	24.7362i	−0.798406	−	1.33175i
$346$	−11.8188	+	3.84016i	−0.635382	+	0.206448i
$347$	0.892690	+	2.74742i	0.0479221	+	0.147489i	0.972154	−	0.234342i	$-0.0752936\pi$
$347$	0.892690	+	2.74742i	0.0479221	+	0.147489i	−0.924232	+	0.381831i	$0.875294\pi$
$348$	8.37998	−	11.5341i	0.449214	−	0.618290i
$349$	25.6994			1.37566			0.687828	−	0.725874i	$-0.258564\pi$
$349$	25.6994			1.37566			0.687828	+	0.725874i	$0.258564\pi$
$350$	−4.10136	−	2.19114i	−0.219227	−	0.117122i
$351$			0.0836313i			0.00446391i
$352$	−22.7008	−	16.4931i	−1.20996	−	0.879085i
$353$	21.6417	−	7.03182i	1.15187	−	0.374266i	0.330024	−	0.943973i	$-0.392943\pi$
$353$	21.6417	−	7.03182i	1.15187	−	0.374266i	0.821848	+	0.569707i	$0.192943\pi$
$354$	5.65842	−	1.83853i	0.300742	−	0.0977169i
$355$	3.47584	−	8.16612i	0.184479	−	0.433412i
$356$	4.49780	−	13.8428i	0.238383	−	0.733668i
$357$	8.73566	+	3.15482i	0.462340	+	0.166971i
$358$	−23.0304	−	7.48304i	−1.21720	−	0.395491i
$359$	13.9746	−	10.1531i	0.737549	−	0.535861i	−0.154393	−	0.988009i	$-0.549342\pi$
$359$	13.9746	−	10.1531i	0.737549	−	0.535861i	0.891943	+	0.452148i	$0.149342\pi$
$360$	−6.46504	+	15.1889i	−0.340738	+	0.800527i
$361$	11.2115	+	8.14561i	0.590077	+	0.428716i
$362$	−10.3298	+	7.50501i	−0.542920	+	0.394455i
$363$	−34.0622	+	24.7477i	−1.78780	+	1.29892i
$364$	−0.0421257	+	0.0579811i	−0.00220799	+	0.00303903i
$365$	−23.9878	+	5.51305i	−1.25558	+	0.288566i
$366$	−12.8515	+	9.33717i	−0.671759	+	0.488062i
$367$	−5.07085	+	15.6065i	−0.264696	+	0.814651i	0.727067	+	0.686566i	$0.240883\pi$
$367$	−5.07085	+	15.6065i	−0.264696	+	0.814651i	−0.991763	+	0.128084i	$0.959117\pi$
$368$	−4.06863			−0.212092
$369$	15.9915	+	5.19595i	0.832485	+	0.270491i
$370$	14.5424	+	12.6668i	0.756024	+	0.658515i
$371$	1.33792	−	0.434717i	0.0694614	−	0.0225694i
$372$	9.43691	−	3.06624i	0.489281	−	0.158977i
$373$	−14.5858	+	20.0756i	−0.755223	+	1.03948i	0.242373	+	0.970183i	$0.422074\pi$
$373$	−14.5858	+	20.0756i	−0.755223	+	1.03948i	−0.997596	+	0.0692927i	$0.977926\pi$
$374$	20.1912	+	7.29189i	1.04406	+	0.377055i
$375$	6.85545	−	25.2847i	0.354014	−	1.30570i
$376$	−31.7012			−1.63486
$377$	−0.324030	−	0.235422i	−0.0166884	−	0.0121248i
$378$	−1.05592	+	0.343088i	−0.0543104	+	0.0176465i
$379$	16.3171	−	5.30174i	0.838152	−	0.272332i	0.141677	−	0.989913i	$-0.454751\pi$
$379$	16.3171	−	5.30174i	0.838152	−	0.272332i	0.696475	+	0.717581i	$0.254751\pi$
$380$	−3.54404	+	4.06882i	−0.181805	+	0.208726i
$381$	20.1938	+	6.56137i	1.03456	+	0.336149i
$382$			0.462491i			0.0236631i
$383$	31.2479	+	10.1531i	1.59669	+	0.518797i	0.966287	−	0.257468i	$-0.0828883\pi$
$383$	31.2479	+	10.1531i	1.59669	+	0.518797i	0.630406	+	0.776265i	$0.282888\pi$
$384$	−5.67162	−	7.80631i	−0.289428	−	0.398364i
$385$	−2.59153	−	11.2760i	−0.132077	−	0.574679i
$386$	−10.7000	+	14.7273i	−0.544616	+	0.749600i
$387$	11.6804	+	16.0768i	0.593750	+	0.817227i
$388$	1.96214	−	1.42558i	0.0996127	−	0.0723728i
$389$	−17.2496	−	12.5326i	−0.874591	−	0.635427i	0.0572240	−	0.998361i	$-0.481775\pi$
$389$	−17.2496	−	12.5326i	−0.874591	−	0.635427i	−0.931815	+	0.362934i	$0.881775\pi$
$390$	0.326706	+	0.139060i	0.0165434	+	0.00704156i
$391$	−21.8008	+	6.31027i	−1.10251	+	0.319124i
$392$	17.1285	+	5.56538i	0.865120	+	0.281094i
$393$		−	24.1942i		−	1.22044i
$394$	22.5330	+	7.32142i	1.13520	+	0.368848i
$395$	5.12345	−	12.0370i	0.257789	−	0.605647i
$396$	−13.5667	+	4.40808i	−0.681751	+	0.221514i
$397$	−0.257360	−	0.792073i	−0.0129165	−	0.0397530i	0.944391	−	0.328826i	$-0.106653\pi$
$397$	−0.257360	−	0.792073i	−0.0129165	−	0.0397530i	−0.957307	+	0.289073i	$0.906653\pi$
$398$	11.5259	+	8.37405i	0.577741	+	0.419753i
$399$	5.10801			0.255720
$400$	−2.56201	−	2.66355i	−0.128100	−	0.133178i
$401$			2.55589i			0.127635i	0.997962	+	0.0638175i	$0.0203275\pi$
$401$			2.55589i			0.127635i	−0.997962	+	0.0638175i	$0.979672\pi$
$402$	26.1206	+	18.9777i	1.30278	+	0.946524i
$403$	−0.0861410	−	0.265115i	−0.00429099	−	0.0132063i
$404$	2.96085	+	9.11255i	0.147308	+	0.453367i
$405$	−11.8068	−	19.6939i	−0.586685	−	0.978598i
$406$	1.64310	−	5.05695i	0.0815458	−	0.250972i
$407$			47.9857i			2.37856i
$408$	22.6109	+	17.5748i	1.11941	+	0.870082i
$409$	10.6749	−	7.75579i	0.527841	−	0.383499i	−0.291708	−	0.956507i	$-0.594224\pi$
$409$	10.6749	−	7.75579i	0.527841	−	0.383499i	0.819550	+	0.573008i	$0.194224\pi$
$410$	−9.59205	+	11.0124i	−0.473717	+	0.543863i
$411$	−7.13220	+	9.81662i	−0.351805	+	0.484218i
$412$	−0.895637	−	1.23274i	−0.0441249	−	0.0607327i
$413$	−2.04141	+	1.48317i	−0.100451	+	0.0729821i
$414$	−7.79508	+	10.7290i	−0.383107	+	0.527302i
$415$	2.07424	−	1.24354i	0.101820	−	0.0610429i
$416$	−0.295465	+	0.214668i	−0.0144864	+	0.0105250i
$417$	−3.81625	−	1.23998i	−0.186883	−	0.0607218i
$418$	11.8064			0.577470
$419$	35.6643	+	11.5880i	1.74231	+	0.566112i	0.995136	−	0.0985106i	$-0.0314078\pi$
$419$	35.6643	+	11.5880i	1.74231	+	0.566112i	0.747179	+	0.664623i	$0.231408\pi$
$420$	0.472464	−	5.33949i	0.0230539	−	0.260540i
$421$	7.88957	+	24.2816i	0.384514	+	1.18341i	0.936832	+	0.349780i	$0.113744\pi$
$421$	7.88957	+	24.2816i	0.384514	+	1.18341i	−0.552318	+	0.833634i	$0.686256\pi$
$422$	0.0463365	+	0.142609i	0.00225563	+	0.00694211i
$423$	−15.6557	+	21.5482i	−0.761206	+	1.04771i
$424$	4.33759			0.210652
$425$	−17.8589	−	10.2984i	−0.866286	−	0.499548i
$426$	−8.99681			−0.435897
$427$	3.96004	−	5.45052i	0.191640	−	0.263769i
$428$	−2.72229	−	8.37834i	−0.131587	−	0.404983i
$429$	0.273009	+	0.840236i	0.0131810	+	0.0405670i
$430$	−16.8211	+	3.86596i	−0.811188	+	0.186433i
$431$	28.7977	+	9.35693i	1.38713	+	0.450707i	0.905008	−	0.425395i	$-0.139865\pi$
$431$	28.7977	+	9.35693i	1.38713	+	0.450707i	0.482126	+	0.876102i	$0.339865\pi$
$432$	−0.882413			−0.0424551
$433$	−0.465212	−	0.151157i	−0.0223567	−	0.00726413i	0.297817	−	0.954623i	$-0.403741\pi$
$433$	−0.465212	−	0.151157i	−0.0223567	−	0.00726413i	−0.320174	+	0.947359i	$0.603741\pi$
$434$	2.99391	−	2.17520i	0.143712	−	0.104413i
$435$	29.8400	+	2.64039i	1.43072	+	0.126597i
$436$	7.35719	−	10.1263i	0.352345	−	0.484962i
$437$	−10.0980	+	7.33664i	−0.483054	+	0.350959i
$438$	14.6657	+	20.1856i	0.700755	+	0.964507i
$439$	−11.7487	+	16.1707i	−0.560735	+	0.771785i	−0.991420	−	0.130717i	$-0.958272\pi$
$439$	−11.7487	+	16.1707i	−0.560735	+	0.771785i	0.430685	+	0.902502i	$0.358272\pi$
$440$	3.14436	−	35.5356i	0.149902	−	1.69409i
$441$	12.2419	−	8.89426i	0.582947	−	0.423536i
$442$	0.171473	−	0.220610i	0.00815614	−	0.0104933i
$443$			17.9836i			0.854428i	0.904150	+	0.427214i	$0.140505\pi$
$443$			17.9836i			0.854428i	−0.904150	+	0.427214i	$0.859495\pi$
$444$	−6.86998	+	21.1436i	−0.326035	+	1.00343i
$445$	29.8064	−	6.85032i	1.41296	−	0.324736i
$446$	1.65485	+	5.09311i	0.0783595	+	0.241166i
$447$	9.55309	+	29.4014i	0.451846	+	1.39064i
$448$	−5.07222	−	3.68518i	−0.239640	−	0.174109i
$449$			17.8886i			0.844214i	0.906546	+	0.422107i	$0.138709\pi$
$449$			17.8886i			0.844214i	−0.906546	+	0.422107i	$0.861291\pi$
$450$	−11.9324	+	1.65293i	−0.562497	+	0.0779200i
$451$	−36.3377			−1.71107
$452$	0.777776	+	0.565087i	0.0365835	+	0.0265795i
$453$	−6.99117	−	21.5166i	−0.328474	−	1.01094i
$454$	−10.2442	+	3.32855i	−0.480785	+	0.156217i
$455$	−0.150004	−	0.0132731i	−0.00703231	−	0.000622253i
$456$	14.9790	+	4.86697i	0.701456	+	0.227917i
$457$			21.8599i			1.02256i	0.859414	+	0.511280i	$0.170829\pi$
$457$			21.8599i			1.02256i	−0.859414	+	0.511280i	$0.829171\pi$
$458$	0.0643074	+	0.0208948i	0.00300489	+	0.000976348i
$459$	−4.72820	+	1.36859i	−0.220693	+	0.0638801i
$460$	6.73510	+	11.2342i	0.314025	+	0.523798i
$461$	−8.24555	−	5.99074i	−0.384034	−	0.279017i	0.378973	−	0.925408i	$-0.376277\pi$
$461$	−8.24555	−	5.99074i	−0.384034	−	0.279017i	−0.763006	+	0.646391i	$0.776277\pi$
$462$	−9.48870	+	6.89395i	−0.441454	+	0.320735i
$463$	−3.30341	−	4.54675i	−0.153522	−	0.211305i	0.725327	−	0.688404i	$-0.241688\pi$
$463$	−3.30341	−	4.54675i	−0.153522	−	0.211305i	−0.878850	+	0.477099i	$0.841688\pi$
$464$	2.48399	−	3.41892i	0.115316	−	0.158719i
$465$	15.7217	+	13.6939i	0.729074	+	0.635041i
$466$	−8.77133	−	12.0727i	−0.406324	−	0.559257i
$467$	−4.51722	−	1.46774i	−0.209032	−	0.0679187i	0.202629	−	0.979256i	$-0.435051\pi$
$467$	−4.51722	−	1.46774i	−0.209032	−	0.0679187i	−0.411661	+	0.911337i	$0.635051\pi$
$468$			0.185666i			0.00858240i
$469$	−13.0231	−	4.23148i	−0.601353	−	0.195391i
$470$	−11.8951	−	19.8412i	−0.548682	−	0.915209i
$471$	12.9872	−	4.21979i	0.598418	−	0.194438i
$472$	−7.39952	+	2.40425i	−0.340591	+	0.110665i
$473$	−34.7434	−	25.2426i	−1.59750	−	1.16065i
$474$	−13.2615			−0.609119
$475$	−11.1617	−	1.99087i	−0.512133	−	0.0913472i
$476$	−3.96740	−	1.43280i	−0.181845	−	0.0656721i
$477$	2.14213	−	2.94839i	0.0980813	−	0.134997i
$478$	27.4252	−	8.91099i	1.25440	−	0.407579i
$479$	19.2544	−	6.25613i	0.879756	−	0.285850i	0.165900	−	0.986143i	$-0.446947\pi$
$479$	19.2544	−	6.25613i	0.879756	−	0.285850i	0.713856	+	0.700293i	$0.246947\pi$
$480$	10.6980	−	25.1337i	0.488293	−	1.14719i
$481$	0.593995	+	0.193001i	0.0270838	+	0.00880008i
$482$	−14.6435			−0.666991
$483$	3.83171	−	11.7928i	0.174349	−	0.536590i
$484$	15.4698	−	11.2394i	0.703171	−	0.510884i
$485$	4.68905	+	1.99586i	0.212919	+	0.0906271i
$486$	−11.6454	+	16.0285i	−0.528244	+	0.727065i
$487$	17.4214	−	12.6574i	0.789441	−	0.573562i	−0.118357	−	0.992971i	$-0.537763\pi$
$487$	17.4214	−	12.6574i	0.789441	−	0.573562i	0.907797	+	0.419409i	$0.137763\pi$
$488$	16.8059	−	12.2102i	0.760769	−	0.552731i
$489$	45.2900	+	32.9051i	2.04808	+	1.48802i
$490$	2.94379	+	12.8087i	0.132987	+	0.578639i
$491$	−0.637512	+	0.463180i	−0.0287705	+	0.0209030i	−0.602078	−	0.798438i	$-0.705660\pi$
$491$	−0.637512	+	0.463180i	−0.0287705	+	0.0209030i	0.573307	+	0.819341i	$0.305660\pi$
$492$	−16.0112	−	5.20236i	−0.721841	−	0.234540i
$493$	8.00726	−	22.1720i	0.360629	−	0.998578i
$494$	0.0474859	−	0.146147i	0.00213649	−	0.00657544i
$495$	−22.6017	−	19.6866i	−1.01587	−	0.884849i
$496$	2.79729	−	0.908893i	0.125602	−	0.0408105i
$497$	3.62893	−	1.17911i	0.162780	−	0.0528904i
$498$	−1.98340	−	1.44102i	−0.0888781	−	0.0645737i
$499$		−	21.3374i		−	0.955194i	−0.878579	−	0.477597i	$-0.841508\pi$
$499$		−	21.3374i		−	0.955194i	0.878579	−	0.477597i	$-0.158492\pi$
$500$	−3.11348	+	11.4833i	−0.139239	+	0.513551i
$501$	−29.0777			−1.29910
$502$	7.89014	−	10.8598i	0.352154	−	0.484698i
$503$	11.4635	+	35.2812i	0.511134	+	1.57311i	0.790207	+	0.612840i	$0.209973\pi$
$503$	11.4635	+	35.2812i	0.511134	+	1.57311i	−0.279073	+	0.960270i	$0.590027\pi$
$504$	−6.74979	+	2.19314i	−0.300659	+	0.0976902i
$505$	−13.2233	+	15.1813i	−0.588427	+	0.675558i
$506$	8.85642	−	27.2572i	0.393716	−	1.21173i
$507$	−30.4499			−1.35233
$508$	−9.17126	−	2.97992i	−0.406909	−	0.132213i
$509$	−15.2895	+	11.1084i	−0.677693	+	0.492373i	−0.872592	−	0.488450i	$-0.837562\pi$
$509$	−15.2895	+	11.1084i	−0.677693	+	0.492373i	0.194898	+	0.980823i	$0.437562\pi$
$510$	−2.51553	+	20.7464i	−0.111389	+	0.918664i
$511$	−8.56103	−	6.21995i	−0.378718	−	0.275154i
$512$	−4.84067	−	6.66261i	−0.213929	−	0.294449i
$513$	−2.19008	+	1.59119i	−0.0966944	+	0.0702526i
$514$	22.6212	+	16.4353i	0.997778	+	0.724928i
$515$	1.25392	−	2.94595i	0.0552543	−	0.129814i
$516$	−11.6948	−	16.0966i	−0.514836	−	0.708612i
$517$	17.7873	−	54.7437i	0.782285	−	2.40762i
$518$			8.29145i			0.364306i
$519$	9.30165	−	28.6275i	0.408297	−	1.25661i
$520$	−0.427234	−	0.181849i	−0.0187354	−	0.00797459i
$521$	−15.7081	+	5.10388i	−0.688186	+	0.223605i	−0.632176	−	0.774825i	$-0.717838\pi$
$521$	−15.7081	+	5.10388i	−0.688186	+	0.223605i	−0.0560101	+	0.998430i	$0.517838\pi$
$522$	−4.25665	−	13.1006i	−0.186308	−	0.573398i
$523$	−6.89931	+	9.49609i	−0.301686	+	0.415235i	−0.932766	−	0.360483i	$-0.882612\pi$
$523$	−6.89931	+	9.49609i	−0.301686	+	0.415235i	0.631080	+	0.775718i	$0.282612\pi$
$524$			10.9881i			0.480017i
$525$	10.1330	−	4.91744i	0.442242	−	0.214615i
$526$	16.9559			0.739313
$527$	13.5789	−	9.20855i	0.591507	−	0.401131i
$528$	−8.86553	+	2.88059i	−0.385823	+	0.125361i
$529$	2.25569	+	6.94229i	0.0980733	+	0.301839i
$530$	1.62758	+	2.71483i	0.0706976	+	0.117925i
$531$	−2.02003	+	6.21701i	−0.0876618	+	0.269795i
$532$	−2.31986			−0.100579
$533$	−0.146152	+	0.449809i	−0.00633053	+	0.0194834i
$534$	−18.2231	−	25.0819i	−0.788590	−	1.08540i
$535$	12.1578	−	13.9581i	0.525629	−	0.603462i
$536$	−34.1580	−	24.8172i	−1.47540	−	1.07194i
$537$	47.4531	−	34.4767i	2.04775	−	1.48778i
$538$	5.88265	−	4.27400i	0.253619	−	0.184265i
$539$	−19.2213	+	26.4559i	−0.827922	+	1.13954i
$540$	1.46072	+	2.43650i	0.0628595	+	0.104850i
$541$	12.3323	+	16.9739i	0.530207	+	0.729767i	0.987162	−	0.159723i	$-0.0510600\pi$
$541$	12.3323	+	16.9739i	0.530207	+	0.729767i	−0.456955	+	0.889490i	$0.651060\pi$
$542$	2.57304	+	0.836032i	0.110522	+	0.0359106i
$543$		−	30.9274i		−	1.32722i
$544$	−16.9716	−	13.1915i	−0.727653	−	0.565582i
$545$	26.1980	+	2.31812i	1.12220	+	0.0992976i
$546$	0.0471733	+	0.145184i	0.00201883	+	0.00621332i
$547$	0.0583069	+	0.179450i	0.00249302	+	0.00767274i	0.952295	−	0.305178i	$-0.0987160\pi$
$547$	0.0583069	+	0.179450i	0.00249302	+	0.00767274i	−0.949802	+	0.312851i	$0.898716\pi$
$548$	3.23917	−	4.45833i	0.138370	−	0.190451i
$549$		−	17.4535i		−	0.744899i
$550$	23.4210	−	11.3659i	0.998675	−	0.484644i
$551$		−	12.9647i		−	0.552314i
$552$	22.4726	−	30.9309i	0.956497	−	1.31651i
$553$	5.34911	−	1.73803i	0.227467	−	0.0739086i
$554$	−4.99814	+	1.62399i	−0.212351	+	0.0689969i
$555$	−45.5265	+	10.4632i	−1.93249	+	0.444139i
$556$	1.73319	+	0.563149i	0.0735038	+	0.0238828i
$557$		−	3.07251i		−	0.130187i	−0.997879	−	0.0650933i	$-0.979266\pi$
$557$		−	3.07251i		−	0.130187i	0.997879	−	0.0650933i	$-0.0207345\pi$
$558$	2.96256	−	9.11781i	0.125415	−	0.385988i
$559$	−0.452207	+	0.328547i	−0.0191263	+	0.0138961i
$560$	0.140048	−	1.58273i	0.00591809	−	0.0668825i
$561$	−43.0361	+	29.1850i	−1.81699	+	1.23219i
$562$	3.48702	+	4.79946i	0.147091	+	0.202453i
$563$	17.6285	+	24.2635i	0.742953	+	1.02259i	0.998443	+	0.0557750i	$0.0177629\pi$
$563$	17.6285	+	24.2635i	0.742953	+	1.02259i	−0.255491	+	0.966811i	$0.582237\pi$
$564$	15.6750	−	21.5748i	0.660036	−	0.908461i
$565$	−0.178049	+	2.01220i	−0.00749059	+	0.0846540i
$566$	9.64680	+	13.2777i	0.405485	+	0.558103i
$567$	3.05064	−	9.38891i	0.128115	−	0.394297i
$568$	11.7651			0.493654
$569$	−5.11350	+	15.7377i	−0.214369	+	0.659760i	0.784829	+	0.619713i	$0.212751\pi$
$569$	−5.11350	+	15.7377i	−0.214369	+	0.659760i	−0.999198	+	0.0400473i	$0.987249\pi$
$570$	2.57437	+	11.2013i	0.107829	+	0.469172i
$571$	7.65599	−	2.48758i	0.320393	−	0.104102i	−0.144405	−	0.989519i	$-0.546127\pi$
$571$	7.65599	−	2.48758i	0.320393	−	0.104102i	0.464798	+	0.885417i	$0.346127\pi$
$572$	−0.123990	−	0.381603i	−0.00518430	−	0.0159556i
$573$	−0.906300	−	0.658465i	−0.0378612	−	0.0275078i
$574$	−6.27878			−0.262071
$575$	−12.9691	+	24.2753i	−0.540847	+	1.01235i
$576$	−16.2421			−0.676756
$577$	−5.76479	+	7.93456i	−0.239992	+	0.330320i	−0.911975	−	0.410246i	$-0.865443\pi$
$577$	−5.76479	+	7.93456i	−0.239992	+	0.330320i	0.671983	+	0.740566i	$0.265443\pi$
$578$	15.2785	+	6.08427i	0.635502	+	0.253072i
$579$	−13.6257	−	41.9356i	−0.566265	−	1.74278i
$580$	−13.5522	−	1.19916i	−0.562724	−	0.0497926i
$581$	0.988876	+	0.321305i	0.0410255	+	0.0133300i
$582$		−	5.16604i		−	0.214139i
$583$	−2.43379	+	7.49044i	−0.100797	+	0.310222i
$584$	−19.1784	−	26.3968i	−0.793607	−	1.09231i
$585$	−0.334598	+	0.200597i	−0.0138339	+	0.00829366i
$586$	−12.0794	−	8.77621i	−0.498996	−	0.362542i
$587$	25.6566	+	35.3133i	1.05896	+	1.45754i	0.880773	+	0.473539i	$0.157024\pi$
$587$	25.6566	+	35.3133i	1.05896	+	1.45754i	0.178189	+	0.983996i	$0.442976\pi$
$588$	−12.2570	+	8.90521i	−0.505469	+	0.367245i
$589$	5.30371	−	7.29993i	0.218535	−	0.300788i
$590$	−4.28128	−	3.72910i	−0.176258	−	0.153525i
$591$	−46.4282	+	33.7321i	−1.90980	+	1.38755i
$592$	−2.03640	+	6.26738i	−0.0836953	+	0.257588i
$593$			10.9894i			0.451282i	0.974211	+	0.225641i	$0.0724476\pi$
$593$			10.9894i			0.451282i	−0.974211	+	0.225641i	$0.927552\pi$
$594$	1.92080	−	5.91161i	0.0788113	−	0.242556i
$595$	−1.70434	−	8.69788i	−0.0698709	−	0.356578i
$596$	−4.33864	−	13.3530i	−0.177718	−	0.546959i
$597$	−32.8197	+	10.6638i	−1.34322	+	0.436439i
$598$	−0.301785	−	0.219260i	−0.0123409	−	0.00896619i
$599$	−32.7717			−1.33902			−0.669508	−	0.742805i	$-0.733495\pi$
$599$	−32.7717			−1.33902			−0.669508	+	0.742805i	$0.733495\pi$
$600$	34.4000	−	4.76528i	1.40438	−	0.194542i
$601$			13.2911i			0.542154i	0.962558	+	0.271077i	$0.0873797\pi$
$601$			13.2911i			0.542154i	−0.962558	+	0.271077i	$0.912620\pi$
$602$	−6.00331	−	4.36166i	−0.244677	−	0.177768i
$603$	−33.7380	+	10.9621i	−1.37392	+	0.446412i
$604$	3.17512	+	9.77202i	0.129194	+	0.397618i
$605$	36.9690	+	15.7356i	1.50300	+	0.639742i
$606$	19.4100	+	6.30669i	0.788477	+	0.256192i
$607$	44.4590			1.80453			0.902267	−	0.431177i	$-0.141902\pi$
$607$	44.4590			1.80453			0.902267	+	0.431177i	$0.141902\pi$
$608$	−11.2431	−	3.65312i	−0.455970	−	0.148154i
$609$	7.57028	+	10.4196i	0.306763	+	0.422223i
$610$	13.9482	+	5.93695i	0.564747	+	0.240380i
$611$	−0.606108	−	0.440363i	−0.0245205	−	0.0178152i
$612$	−10.4968	+	3.03833i	−0.424309	+	0.122817i
$613$	−3.87486	−	5.33329i	−0.156504	−	0.215409i	0.723564	−	0.690258i	$-0.242503\pi$
$613$	−3.87486	−	5.33329i	−0.156504	−	0.215409i	−0.880068	+	0.474848i	$0.842503\pi$
$614$	−6.02425	−	4.37687i	−0.243119	−	0.176636i
$615$	−7.92338	−	34.4754i	−0.319501	−	1.39018i
$616$	12.4084	−	9.01522i	0.499948	−	0.363234i
$617$	13.2911	−	40.9057i	0.535078	−	1.64680i	−0.208402	−	0.978043i	$-0.566826\pi$
$617$	13.2911	−	40.9057i	0.535078	−	1.64680i	0.743480	−	0.668758i	$-0.233174\pi$
$618$	−3.24563			−0.130558
$619$	−1.89136	−	0.614541i	−0.0760203	−	0.0247005i	0.270760	−	0.962647i	$-0.412725\pi$
$619$	−1.89136	−	0.614541i	−0.0760203	−	0.0247005i	−0.346780	+	0.937946i	$0.612725\pi$
$620$	−7.14017	−	6.21926i	−0.286756	−	0.249771i
$621$	2.03068	+	6.24981i	0.0814886	+	0.250796i
$622$	−2.20308	−	6.78038i	−0.0883354	−	0.271868i
$623$	10.6376	+	7.72869i	0.426187	+	0.309643i
$624$			0.121329i			0.00485703i
$625$	−24.0586	+	6.79586i	−0.962344	+	0.271834i
$626$			1.32151i			0.0528181i
$627$	−16.8092	+	23.1359i	−0.671295	+	0.923959i
$628$	−5.89828	+	1.91647i	−0.235367	+	0.0764753i
$629$	−1.19109	+	36.7406i	−0.0474919	+	1.46494i
$630$	−3.90535	−	3.40165i	−0.155593	−	0.135525i
$631$	5.44519	−	16.7586i	0.216770	−	0.667148i	−0.782254	−	0.622960i	$-0.785930\pi$
$631$	5.44519	−	16.7586i	0.216770	−	0.667148i	0.999023	−	0.0441880i	$-0.0140701\pi$
$632$	17.3420			0.689829
$633$	−0.345429	−	0.112237i	−0.0137296	−	0.00446100i
$634$	−13.7159	−	18.8783i	−0.544727	−	0.749752i
$635$	−4.53853	−	19.7476i	−0.180106	−	0.783659i
$636$	−2.14477	+	2.95202i	−0.0850456	+	0.117055i
$637$	0.250177	+	0.344340i	0.00991239	+	0.0136432i
$638$	17.4976	+	24.0833i	0.692735	+	0.953468i
$639$	5.81024	−	7.99711i	0.229849	−	0.316361i
$640$	−3.60624	+	8.47248i	−0.142549	+	0.334904i
$641$	−18.3678	−	25.2811i	−0.725485	−	0.998545i	−0.999324	−	0.0367690i	$-0.988293\pi$
$641$	−18.3678	−	25.2811i	−0.725485	−	0.998545i	0.273839	−	0.961776i	$-0.411707\pi$
$642$	−17.8461	−	5.79855i	−0.704329	−	0.228850i
$643$	−36.6942			−1.44708			−0.723538	−	0.690284i	$-0.757485\pi$
$643$	−36.6942			−1.44708			−0.723538	+	0.690284i	$0.757485\pi$
$644$	−1.74021	+	5.35583i	−0.0685740	+	0.211049i
$645$	16.3731	−	38.4669i	0.644692	−	1.51463i
$646$	9.03966	+	0.293056i	0.355660	+	0.0115301i
$647$	24.5998	−	7.99296i	0.967118	−	0.314236i	0.217466	−	0.976068i	$-0.430221\pi$
$647$	24.5998	−	7.99296i	0.967118	−	0.314236i	0.749652	+	0.661832i	$0.230221\pi$
$648$	17.8917	−	24.6259i	0.702853	−	0.967395i
$649$		−	14.1270i		−	0.554533i
$650$	−0.0464936	−	0.335633i	−0.00182363	−	0.0131646i
$651$			8.96380i			0.351319i
$652$	−20.5690	−	14.9442i	−0.805543	−	0.585261i
$653$	5.77938	+	17.7871i	0.226165	+	0.696063i	0.998171	+	0.0604487i	$0.0192532\pi$
$653$	5.77938	+	17.7871i	0.226165	+	0.696063i	−0.772007	+	0.635614i	$0.780747\pi$
$654$	−8.23873	−	25.3562i	−0.322160	−	0.991506i
$655$	−19.8022	+	11.8717i	−0.773736	+	0.463867i
$656$	−4.74603	−	1.54208i	−0.185302	−	0.0602081i
$657$	−27.4139			−1.06952
$658$	3.07347	−	9.45916i	0.119816	−	0.368756i
$659$	−21.3371	+	15.5023i	−0.831176	+	0.603884i	−0.919892	−	0.392172i	$-0.871724\pi$
$659$	−21.3371	+	15.5023i	−0.831176	+	0.603884i	0.0887160	+	0.996057i	$0.471724\pi$
$660$	22.6296	+	19.7109i	0.880855	+	0.767246i
$661$	30.1545	+	21.9086i	1.17288	+	0.852144i	0.991350	−	0.131242i	$-0.0418965\pi$
$661$	30.1545	+	21.9086i	1.17288	+	0.852144i	0.181526	+	0.983386i	$0.441896\pi$
$662$	12.2426	+	16.8505i	0.475822	+	0.654913i
$663$	0.188175	+	0.650109i	0.00730812	+	0.0252482i
$664$	2.59369	+	1.88442i	0.100655	+	0.0731299i
$665$	−2.50642	−	4.18075i	−0.0971950	−	0.162122i
$666$	12.6256	+	17.3777i	0.489232	+	0.673370i
$667$	−29.9313	−	9.72528i	−1.15895	−	0.376564i
$668$	13.2060			0.510955
$669$	−12.3366	−	4.00839i	−0.476959	−	0.154973i
$670$	2.71569	−	30.6910i	0.104916	−	1.18570i
$671$	11.6557	+	35.8727i	0.449965	+	1.38485i
$672$	11.1691	−	3.62907i	0.430859	−	0.139994i
$673$	17.6327	+	12.8109i	0.679692	+	0.493825i	0.873256	−	0.487262i	$-0.162005\pi$
$673$	17.6327	+	12.8109i	0.679692	+	0.493825i	−0.193563	+	0.981088i	$0.562005\pi$
$674$			1.15188i			0.0443689i
$675$	−2.81276	+	5.26489i	−0.108263	+	0.202646i
$676$	13.8292			0.531891
$677$	14.7406	+	10.7097i	0.566528	+	0.411607i	0.833842	−	0.552003i	$-0.186136\pi$
$677$	14.7406	+	10.7097i	0.566528	+	0.411607i	−0.267314	+	0.963609i	$0.586136\pi$
$678$	1.94755	−	0.632797i	0.0747951	−	0.0243024i
$679$	0.677055	+	2.08376i	0.0259830	+	0.0799674i
$680$	3.28956	−	27.1300i	0.126149	−	1.04039i
$681$	8.06244	−	24.8136i	0.308953	−	0.950860i
$682$			20.7185i			0.793352i
$683$	8.38761	−	25.8144i	0.320943	−	0.987761i	−0.652296	−	0.757965i	$-0.726194\pi$
$683$	8.38761	−	25.8144i	0.320943	−	0.987761i	0.973239	−	0.229797i	$-0.0738061\pi$
$684$	−4.86209	+	3.53251i	−0.185907	+	0.135069i
$685$	11.5343	+	1.02061i	0.440701	+	0.0389954i
$686$	−7.14772	+	9.83799i	−0.272901	+	0.375616i
$687$	−0.132502	+	0.0962686i	−0.00505528	+	0.00367288i
$688$	−3.46658	−	4.77134i	−0.132162	−	0.181905i
$689$	0.0829321	+	0.0602537i	0.00315946	+	0.00229548i
$690$	27.7914	+	2.45912i	1.05800	+	0.0936172i
$691$	−15.1368	−	20.8340i	−0.575829	−	0.792561i	0.417401	−	0.908722i	$-0.362941\pi$
$691$	−15.1368	−	20.8340i	−0.575829	−	0.792561i	−0.993230	+	0.116161i	$0.962941\pi$
$692$	−4.22445	+	13.0015i	−0.160590	+	0.494244i
$693$		−	12.8865i		−	0.489519i
$694$	−2.65779	−	0.863567i	−0.100888	−	0.0327806i
$695$	0.857696	+	3.73192i	0.0325343	+	0.141560i
$696$	12.2716	+	37.7680i	0.465153	+	1.43159i
$697$	−27.8222	−	0.901965i	−1.05384	−	0.0341644i
$698$	−14.6129	+	20.1129i	−0.553106	+	0.761286i
$699$	36.1458			1.36716
$700$	−4.60204	+	2.23331i	−0.173941	+	0.0844112i
$701$	44.6717			1.68723			0.843614	−	0.536950i	$-0.180424\pi$
$701$	44.6717			1.68723			0.843614	+	0.536950i	$0.180424\pi$
$702$	−0.0654518	−	0.0475535i	−0.00247032	−	0.00179479i
$703$	6.24730	+	19.2272i	0.235621	+	0.725168i
$704$	33.3829	−	10.8467i	1.25816	−	0.408802i
$705$	55.8166	+	4.93892i	2.10217	+	0.186011i
$706$	−6.80241	+	20.9357i	−0.256012	+	0.787924i
$707$	−8.65571			−0.325531
$708$	2.02252	−	6.22467i	0.0760109	−	0.233937i
$709$	−17.8388	−	24.5530i	−0.669951	−	0.922109i	0.329808	−	0.944048i	$-0.393016\pi$
$709$	−17.8388	−	24.5530i	−0.669951	−	0.922109i	−0.999759	+	0.0219391i	$0.993016\pi$
$710$	4.41460	+	7.36361i	0.165677	+	0.276351i
$711$	8.56440	−	11.7879i	0.321190	−	0.442080i
$712$	23.8303	+	32.7997i	0.893080	+	1.22922i
$713$	−12.8747	−	17.7205i	−0.482162	−	0.663639i
$714$	−7.43621	+	5.04287i	−0.278293	+	0.188725i
$715$	0.553745	−	0.635741i	0.0207089	−	0.0237754i
$716$	−21.5514	+	15.6580i	−0.805413	+	0.585166i
$717$	−21.5843	+	66.4295i	−0.806079	+	2.48086i
$718$			16.7100i			0.623611i
$719$	14.9116	+	4.84507i	0.556108	+	0.180690i	0.573569	−	0.819157i	$-0.305558\pi$
$719$	14.9116	+	4.84507i	0.556108	+	0.180690i	−0.0174612	+	0.999848i	$0.505558\pi$
$720$	−2.11654	−	3.53042i	−0.0788789	−	0.131571i
$721$	1.30915	−	0.425368i	0.0487552	−	0.0158415i
$722$	−12.7499	+	4.14269i	−0.474502	+	0.154175i
$723$	20.8484	−	28.6954i	0.775362	−	1.06719i
$724$			14.0460i			0.522017i
$725$	−12.4810	−	25.7187i	−0.463532	−	0.955169i
$726$		−	40.7297i		−	1.51162i
$727$	26.0852	−	35.9031i	0.967445	−	1.33157i	0.0241175	−	0.999709i	$-0.492322\pi$
$727$	26.0852	−	35.9031i	0.967445	−	1.33157i	0.943327	−	0.331864i	$-0.107678\pi$
$728$	−0.0616885	−	0.189858i	−0.00228633	−	0.00703660i
$729$	−5.30974	−	16.3417i	−0.196657	−	0.605249i
$730$	9.32505	−	21.9082i	0.345136	−	0.810859i
$731$	−25.9750	−	20.1895i	−0.960719	−	0.746737i
$732$			17.4750i			0.645896i
$733$	−16.8071	−	5.46095i	−0.620783	−	0.201705i	−0.0182952	−	0.999833i	$-0.505824\pi$
$733$	−16.8071	−	5.46095i	−0.620783	−	0.201705i	−0.602488	+	0.798128i	$0.705824\pi$
$734$	−9.33065	−	12.8425i	−0.344401	−	0.474027i
$735$	−29.2912	−	12.4676i	−1.08042	−	0.459874i
$736$	−16.8678	+	23.2165i	−0.621755	+	0.855772i
$737$	62.0218	−	45.0614i	2.28460	−	1.65986i
$738$	−13.1594	+	9.56086i	−0.484404	+	0.351940i
$739$	10.9198	+	7.93370i	0.401691	+	0.291846i	0.770230	−	0.637767i	$-0.220142\pi$
$739$	10.9198	+	7.93370i	0.401691	+	0.291846i	−0.368538	+	0.929613i	$0.620142\pi$
$740$	20.6764	−	4.75199i	0.760079	−	0.174687i
$741$	0.218782	+	0.301128i	0.00803716	+	0.0110622i
$742$	−0.420534	+	1.29427i	−0.0154383	+	0.0475142i
$743$	6.41572			0.235370			0.117685	−	0.993051i	$-0.462453\pi$
$743$	6.41572			0.235370			0.117685	+	0.993051i	$0.462453\pi$
$744$	−8.54082	+	26.2859i	−0.313122	+	0.963689i
$745$	19.3765	−	22.2457i	0.709902	−	0.815020i
$746$	−7.41803	−	22.8304i	−0.271594	−	0.835879i
$747$	2.56180	−	0.832378i	0.0937312	−	0.0304551i
$748$	19.5454	−	13.2547i	0.714649	−	0.484640i
$749$	7.95831			0.290790
$750$	15.8903	+	19.7424i	0.580233	+	0.720889i
$751$		−	37.8138i		−	1.37984i	−0.723884	−	0.689922i	$-0.757645\pi$
$751$		−	37.8138i		−	1.37984i	0.723884	−	0.689922i	$-0.242355\pi$
$752$	4.64637	−	6.39518i	0.169436	−	0.233208i
$753$	10.0475	+	30.9231i	0.366152	+	1.12690i
$754$	0.368493	−	0.119731i	0.0134197	−	0.00436034i
$755$	−14.1802	+	16.2799i	−0.516071	+	0.592487i
$756$	−0.377421	+	1.16158i	−0.0137267	+	0.0422464i
$757$		−	44.8872i		−	1.63145i	−0.578437	−	0.815727i	$-0.696337\pi$
$757$		−	44.8872i		−	1.63145i	0.578437	−	0.815727i	$-0.303663\pi$
$758$	−5.12878	+	15.7848i	−0.186286	+	0.573328i
$759$	40.8042	+	56.1622i	1.48110	+	2.03856i
$760$	−3.36651	−	14.6480i	−0.122116	−	0.531339i
$761$	−5.58737	−	4.05946i	−0.202542	−	0.147155i	0.481891	−	0.876231i	$-0.339950\pi$
$761$	−5.58737	−	4.05946i	−0.202542	−	0.147155i	−0.684433	+	0.729076i	$0.739950\pi$
$762$	−16.6175	+	12.0733i	−0.601988	+	0.437370i
$763$	6.64631	+	9.14786i	0.240613	+	0.331175i
$764$	0.411607	+	0.299050i	0.0148914	+	0.0108192i
$765$	−16.8165	−	15.6342i	−0.608002	−	0.565257i
$766$	−25.7139	+	18.6822i	−0.929080	+	0.675016i
$767$	−0.174872	−	0.0568193i	−0.00631426	−	0.00205163i
$768$	39.8970			1.43966
$769$	13.3329	−	41.0346i	0.480798	−	1.47974i	−0.357177	−	0.934037i	$-0.616261\pi$
$769$	13.3329	−	41.0346i	0.480798	−	1.47974i	0.837976	−	0.545708i	$-0.183739\pi$
$770$	10.2984	+	4.38345i	0.371130	+	0.157969i
$771$	−64.4133	+	20.9291i	−2.31979	+	0.753744i

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+(-0.568609 + 0.782624i) q^{2} +(-0.724084 - 2.22850i) q^{3} +(0.328851 + 1.01210i) q^{4} +(-1.46866 + 1.68613i) q^{5} +(2.15580 + 0.700461i) q^{6} -0.961359 q^{7} +(-2.81914 - 0.915994i) q^{8} +(-2.01486 + 1.46388i) q^{9} +(-0.484512 - 2.10816i) q^{10} +(3.16360 - 4.35432i) q^{11} +(2.01735 - 1.46569i) q^{12} +(-0.0411761 - 0.0566741i) q^{13} +(0.546637 - 0.752382i) q^{14} +(4.82098 + 2.05201i) q^{15} +(0.597981 - 0.434459i) q^{16} +(2.53031 - 3.25539i) q^{17} -2.40926i q^{18} +(0.700717 - 2.15658i) q^{19} +(-2.18950 - 0.931944i) q^{20} +(0.696104 + 2.14239i) q^{21} +(1.60894 + 4.95181i) q^{22} +(-4.45324 - 3.23547i) q^{23} +6.94571i q^{24} +(-0.686075 - 4.95271i) q^{25} +0.0677676 q^{26} +(-0.965828 - 0.701715i) q^{27} +(-0.316144 - 0.972990i) q^{28} +(5.43761 - 1.76679i) q^{29} +(-4.34720 + 2.60622i) q^{30} +(3.78449 + 1.22965i) q^{31} -5.21340i q^{32} +(-11.9943 - 3.89718i) q^{33} +(1.10898 + 3.83132i) q^{34} +(1.41191 - 1.62098i) q^{35} +(-2.14419 - 1.55784i) q^{36} +(-7.21286 + 5.24045i) q^{37} +(1.28936 + 1.77465i) q^{38} +(-0.0964832 + 0.132798i) q^{39} +(5.68484 - 3.40815i) q^{40} +(-3.96838 - 5.46201i) q^{41} +(-2.07249 - 0.673394i) q^{42} -7.97907i q^{43} +(5.44735 + 1.76995i) q^{44} +(0.490850 - 5.54728i) q^{45} +(5.06430 - 1.64549i) q^{46} +(10.1712 - 3.30482i) q^{47} +(-1.40118 - 1.01802i) q^{48} -6.07579 q^{49} +(4.26621 + 2.27922i) q^{50} +(-9.08678 - 3.28163i) q^{51} +(0.0438190 - 0.0603116i) q^{52} +(-1.39170 + 0.452190i) q^{53} +(1.09836 - 0.356878i) q^{54} +(2.69570 + 11.7292i) q^{55} +(2.71020 + 0.880598i) q^{56} -5.31333 q^{57} +(-1.70915 + 5.26021i) q^{58} +(2.12346 - 1.54279i) q^{59} +(-0.491455 + 5.55411i) q^{60} +(-4.11921 + 5.66960i) q^{61} +(-3.11425 + 2.26264i) q^{62} +(1.93701 - 1.40732i) q^{63} +(5.27610 + 3.83331i) q^{64} +(0.156034 + 0.0138066i) q^{65} +(9.87010 - 7.17105i) q^{66} +(13.5466 + 4.40156i) q^{67} +(4.12687 + 1.49039i) q^{68} +(-3.98572 + 12.2668i) q^{69} +(0.465790 + 2.02670i) q^{70} +(-3.77479 + 1.22651i) q^{71} +(7.02109 - 2.28129i) q^{72} +(8.90514 + 6.46996i) q^{73} -8.62472i q^{74} +(-10.5403 + 5.11509i) q^{75} +2.41311 q^{76} +(-3.04135 + 4.18606i) q^{77} +(-0.0490694 - 0.151020i) q^{78} +(-5.56411 + 1.80789i) q^{79} +(-0.145677 + 1.64635i) q^{80} +(-3.17326 + 9.76629i) q^{81} +6.53116 q^{82} +(-1.02862 - 0.334220i) q^{83} +(-1.93939 + 1.40905i) q^{84} +(1.77284 + 9.04749i) q^{85} +(6.24461 + 4.53698i) q^{86} +(-7.87456 - 10.8384i) q^{87} +(-12.9071 + 9.37758i) q^{88} +(-11.0652 - 8.03934i) q^{89} +(4.06233 + 3.53838i) q^{90} +(0.0395850 + 0.0544841i) q^{91} +(1.81016 - 5.57110i) q^{92} -9.32410i q^{93} +(-3.19700 + 9.83936i) q^{94} +(2.60717 + 4.34879i) q^{95} +(-11.6181 + 3.77494i) q^{96} +(-0.704269 - 2.16752i) q^{97} +(3.45475 - 4.75506i) q^{98} +13.4045i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 10 q^{2} + 38 q^{4} - 10 q^{8} - 50 q^{9} - 10 q^{13} + 6 q^{15} - 58 q^{16} - 8 q^{19} - 44 q^{21} - 20 q^{25} - 64 q^{26} + 78 q^{30} - 20 q^{33} - 23 q^{34} - 46 q^{35} + 52 q^{36} - 10 q^{38}+ \cdots - 250 q^{98}+O(q^{100}) \) 176 * q - 10 * q^2 + 38 * q^4 - 10 * q^8 - 50 * q^9 - 10 * q^13 + 6 * q^15 - 58 * q^16 - 8 * q^19 - 44 * q^21 - 20 * q^25 - 64 * q^26 + 78 * q^30 - 20 * q^33 - 23 * q^34 - 46 * q^35 + 52 * q^36 - 10 * q^38 - 20 * q^42 + 40 * q^47 + 164 * q^49 + 84 * q^50 + 20 * q^51 - 30 * q^52 - 40 * q^53 - 18 * q^55 - 18 * q^59 - 48 * q^60 + 66 * q^64 + 80 * q^66 - 50 * q^67 + 68 * q^69 - 152 * q^70 + 60 * q^72 - 72 * q^76 - 40 * q^77 - 38 * q^81 + 50 * q^83 - 52 * q^84 + 47 * q^85 - 94 * q^86 - 120 * q^87 + 60 * q^89 + 50 * q^94 - 250 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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