LMFDB - Embedded newform 177.2.e.b.16.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,2,Mod(4,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("177.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	177.e (of order $29$, degree $28$, 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:	$1.41335211578$
Analytic rank:	$0$
Dimension:	$140$
Relative dimension:	$5$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			16.1
Character	$\chi$	$=$	177.16
Dual form			177.2.e.b.166.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.69139 - 0.592420i) q^{2} +(0.161782 + 0.986827i) q^{3} +(5.07747 + 2.34909i) q^{4} +(0.982969 + 3.54033i) q^{5} +(0.149197 - 2.75178i) q^{6} +(-0.252139 - 0.238838i) q^{7} +(-7.88603 - 5.99480i) q^{8} +(-0.947653 + 0.319302i) q^{9} +O(q^{10})$	\(q+(-2.69139 - 0.592420i) q^{2} +(0.161782 + 0.986827i) q^{3} +(5.07747 + 2.34909i) q^{4} +(0.982969 + 3.54033i) q^{5} +(0.149197 - 2.75178i) q^{6} +(-0.252139 - 0.238838i) q^{7} +(-7.88603 - 5.99480i) q^{8} +(-0.947653 + 0.319302i) q^{9} +(-0.548189 - 10.1108i) q^{10} +(-1.52137 + 1.79109i) q^{11} +(-1.49670 + 5.39062i) q^{12} +(-2.19043 - 0.738042i) q^{13} +(0.537111 + 0.792179i) q^{14} +(-3.33467 + 1.54278i) q^{15} +(10.4293 + 12.2783i) q^{16} +(4.07791 - 3.86280i) q^{17} +(2.73967 - 0.297957i) q^{18} +(-2.39674 + 6.01536i) q^{19} +(-3.32556 + 20.2850i) q^{20} +(0.194901 - 0.287457i) q^{21} +(5.15567 - 3.91924i) q^{22} +(-1.10609 - 0.120294i) q^{23} +(4.64001 - 8.75199i) q^{24} +(-7.28345 + 4.38231i) q^{25} +(5.45807 + 3.28401i) q^{26} +(-0.468408 - 0.883512i) q^{27} +(-0.719174 - 1.80499i) q^{28} +(-1.18664 + 0.261199i) q^{29} +(9.88887 - 2.17671i) q^{30} +(1.25816 + 3.15775i) q^{31} +(-11.5153 - 21.7202i) q^{32} +(-2.01363 - 1.21156i) q^{33} +(-13.2637 + 7.98048i) q^{34} +(0.597723 - 1.12743i) q^{35} +(-5.56175 - 0.604876i) q^{36} +(1.05578 - 0.802581i) q^{37} +(10.0142 - 14.7698i) q^{38} +(0.373947 - 2.28098i) q^{39} +(13.4719 - 33.8119i) q^{40} +(6.99835 - 0.761116i) q^{41} +(-0.694849 + 0.658196i) q^{42} +(1.46267 + 1.72199i) q^{43} +(-11.9321 + 5.52039i) q^{44} +(-2.06195 - 3.04115i) q^{45} +(2.90565 + 0.979027i) q^{46} +(-1.55893 + 5.61475i) q^{47} +(-10.4293 + 12.2783i) q^{48} +(-0.372442 - 6.86929i) q^{49} +(22.1988 - 7.47964i) q^{50} +(4.47165 + 3.39926i) q^{51} +(-9.38812 - 8.89290i) q^{52} +(-0.252680 + 4.66041i) q^{53} +(0.737260 + 2.65537i) q^{54} +(-7.83652 - 3.62556i) q^{55} +(0.556583 + 3.39501i) q^{56} +(-6.32386 - 1.39199i) q^{57} +3.34845 q^{58} +(2.69004 + 7.19470i) q^{59} -20.5558 q^{60} +(5.80648 + 1.27810i) q^{61} +(-1.51549 - 9.24411i) q^{62} +(0.315201 + 0.145828i) q^{63} +(9.50509 + 34.2342i) q^{64} +(0.459790 - 8.48033i) q^{65} +(4.70171 + 4.45369i) q^{66} +(-4.15186 - 3.15616i) q^{67} +(29.7795 - 10.0339i) q^{68} +(-0.0602355 - 1.11098i) q^{69} +(-2.27662 + 2.68024i) q^{70} +(3.03779 - 10.9411i) q^{71} +(9.38737 + 3.16297i) q^{72} +(6.15590 + 9.07927i) q^{73} +(-3.31697 + 1.53460i) q^{74} +(-5.50291 - 6.47853i) q^{75} +(-26.3000 + 24.9127i) q^{76} +(0.811377 - 0.0882426i) q^{77} +(-2.35773 + 5.91746i) q^{78} +(2.21624 - 13.5185i) q^{79} +(-33.2176 + 48.9923i) q^{80} +(0.796093 - 0.605174i) q^{81} +(-19.2862 - 2.09750i) q^{82} +(-4.20069 + 7.92334i) q^{83} +(1.66486 - 1.00171i) q^{84} +(17.6841 + 10.6402i) q^{85} +(-2.91648 - 5.50107i) q^{86} +(-0.449735 - 1.12875i) q^{87} +(22.7348 - 5.00431i) q^{88} +(15.4400 - 3.39860i) q^{89} +(3.74787 + 9.40645i) q^{90} +(0.376019 + 0.709248i) q^{91} +(-5.33355 - 3.20909i) q^{92} +(-2.91261 + 1.75246i) q^{93} +(7.52197 - 14.1879i) q^{94} +(-23.6523 - 2.57234i) q^{95} +(19.5711 - 14.8776i) q^{96} +(6.21596 - 9.16785i) q^{97} +(-3.06712 + 18.7086i) q^{98} +(0.869830 - 2.18311i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q + q^{2} + 5 q^{3} - q^{4} + 2 q^{5} - q^{6} - 2 q^{7} - 3 q^{8} - 5 q^{9}+O(q^{10}) $ 140 * q + q^2 + 5 * q^3 - q^4 + 2 * q^5 - q^6 - 2 * q^7 - 3 * q^8 - 5 * q^9	\( 140 q + q^{2} + 5 q^{3} - q^{4} + 2 q^{5} - q^{6} - 2 q^{7} - 3 q^{8} - 5 q^{9} - 116 q^{10} + 2 q^{11} + q^{12} + 4 q^{13} - 43 q^{14} - 2 q^{15} + 7 q^{16} + q^{18} - 2 q^{19} + 4 q^{20} - 27 q^{21} + 6 q^{22} + 6 q^{23} + 3 q^{24} - 57 q^{25} + 12 q^{26} + 5 q^{27} - 10 q^{28} - 4 q^{29} - 12 q^{31} - 150 q^{32} - 2 q^{33} - 2 q^{34} + 6 q^{35} - q^{36} + 12 q^{37} - 12 q^{38} - 4 q^{39} - 66 q^{40} - 4 q^{41} + 14 q^{42} - 60 q^{43} + 20 q^{44} + 2 q^{45} + 76 q^{46} - 25 q^{47} - 7 q^{48} + 31 q^{49} + 137 q^{50} + 118 q^{52} + 48 q^{53} - q^{54} + 93 q^{55} + 228 q^{56} + 2 q^{57} - 120 q^{58} + 57 q^{59} - 4 q^{60} + 72 q^{61} - 179 q^{62} - 2 q^{63} + 249 q^{64} - 39 q^{65} - 6 q^{66} + 40 q^{67} + 94 q^{68} - 64 q^{69} + 94 q^{70} + 30 q^{71} - 3 q^{72} - 205 q^{73} + 66 q^{74} - q^{75} - 216 q^{76} - 46 q^{77} - 12 q^{78} + 4 q^{79} - 356 q^{80} - 5 q^{81} - 28 q^{82} + 4 q^{83} - 135 q^{84} + 50 q^{85} - 18 q^{86} - 54 q^{87} - 162 q^{88} + 26 q^{89} - 198 q^{91} + 10 q^{92} + 12 q^{93} - 4 q^{94} - 326 q^{95} + 5 q^{96} - 20 q^{97} - 143 q^{98} + 2 q^{99}+O(q^{100}) \) 140 * q + q^2 + 5 * q^3 - q^4 + 2 * q^5 - q^6 - 2 * q^7 - 3 * q^8 - 5 * q^9 - 116 * q^10 + 2 * q^11 + q^12 + 4 * q^13 - 43 * q^14 - 2 * q^15 + 7 * q^16 + q^18 - 2 * q^19 + 4 * q^20 - 27 * q^21 + 6 * q^22 + 6 * q^23 + 3 * q^24 - 57 * q^25 + 12 * q^26 + 5 * q^27 - 10 * q^28 - 4 * q^29 - 12 * q^31 - 150 * q^32 - 2 * q^33 - 2 * q^34 + 6 * q^35 - q^36 + 12 * q^37 - 12 * q^38 - 4 * q^39 - 66 * q^40 - 4 * q^41 + 14 * q^42 - 60 * q^43 + 20 * q^44 + 2 * q^45 + 76 * q^46 - 25 * q^47 - 7 * q^48 + 31 * q^49 + 137 * q^50 + 118 * q^52 + 48 * q^53 - q^54 + 93 * q^55 + 228 * q^56 + 2 * q^57 - 120 * q^58 + 57 * q^59 - 4 * q^60 + 72 * q^61 - 179 * q^62 - 2 * q^63 + 249 * q^64 - 39 * q^65 - 6 * q^66 + 40 * q^67 + 94 * q^68 - 64 * q^69 + 94 * q^70 + 30 * q^71 - 3 * q^72 - 205 * q^73 + 66 * q^74 - q^75 - 216 * q^76 - 46 * q^77 - 12 * q^78 + 4 * q^79 - 356 * q^80 - 5 * q^81 - 28 * q^82 + 4 * q^83 - 135 * q^84 + 50 * q^85 - 18 * q^86 - 54 * q^87 - 162 * q^88 + 26 * q^89 - 198 * q^91 + 10 * q^92 + 12 * q^93 - 4 * q^94 - 326 * q^95 + 5 * q^96 - 20 * q^97 - 143 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{2}{29}\right)$	$1$

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 $

$2$	−2.69139	−	0.592420i	−1.90310	−	0.418904i	−0.903155	−	0.429316i	$-0.858755\pi$
$2$	−2.69139	−	0.592420i	−1.90310	−	0.418904i	−0.999946	+	0.0104116i	$0.996686\pi$
$3$	0.161782	+	0.986827i	0.0934049	+	0.569745i
$3$	0.161782	+	0.986827i	0.0934049	+	0.569745i
$4$	5.07747	+	2.34909i	2.53873	+	1.17454i
$5$	0.982969	+	3.54033i	0.439597	+	1.58329i	0.769098	+	0.639130i	$0.220706\pi$
$5$	0.982969	+	3.54033i	0.439597	+	1.58329i	−0.329501	+	0.944155i	$0.606881\pi$
$6$	0.149197	−	2.75178i	0.0609095	−	1.12341i
$7$	−0.252139	−	0.238838i	−0.0952995	−	0.0902724i	0.638567	−	0.769566i	$-0.279528\pi$
$7$	−0.252139	−	0.238838i	−0.0952995	−	0.0902724i	−0.733866	+	0.679294i	$0.762286\pi$
$8$	−7.88603	−	5.99480i	−2.78813	−	2.11948i
$9$	−0.947653	+	0.319302i	−0.315884	+	0.106434i
$10$	−0.548189	−	10.1108i	−0.173353	−	3.19730i
$11$	−1.52137	+	1.79109i	−0.458710	+	0.540035i	−0.942083	−	0.335380i	$-0.891135\pi$
$11$	−1.52137	+	1.79109i	−0.458710	+	0.540035i	0.483374	+	0.875414i	$0.339411\pi$
$12$	−1.49670	+	5.39062i	−0.432060	+	1.55614i
$13$	−2.19043	−	0.738042i	−0.607516	−	0.204696i	−0.00130405	−	0.999999i	$-0.500415\pi$
$13$	−2.19043	−	0.738042i	−0.607516	−	0.204696i	−0.606212	+	0.795303i	$0.707312\pi$
$14$	0.537111	+	0.792179i	0.143549	+	0.211719i
$15$	−3.33467	+	1.54278i	−0.861008	+	0.398345i
$16$	10.4293	+	12.2783i	2.60732	+	3.06957i
$17$	4.07791	−	3.86280i	0.989039	−	0.936868i	−0.00896856	−	0.999960i	$-0.502855\pi$
$17$	4.07791	−	3.86280i	0.989039	−	0.936868i	0.998008	+	0.0630921i	$0.0200962\pi$
$18$	2.73967	−	0.297957i	0.645745	−	0.0702290i
$19$	−2.39674	+	6.01536i	−0.549849	+	1.38002i	0.347076	+	0.937837i	$0.387174\pi$
$19$	−2.39674	+	6.01536i	−0.549849	+	1.38002i	−0.896926	+	0.442181i	$0.854205\pi$
$20$	−3.32556	+	20.2850i	−0.743618	+	4.53587i
$21$	0.194901	−	0.287457i	0.0425308	−	0.0627282i
$22$	5.15567	−	3.91924i	1.09919	−	0.835585i
$23$	−1.10609	−	0.120294i	−0.230635	−	0.0250831i	−0.00792848	−	0.999969i	$-0.502524\pi$
$23$	−1.10609	−	0.120294i	−0.230635	−	0.0250831i	−0.222707	+	0.974885i	$0.571489\pi$
$24$	4.64001	−	8.75199i	0.947139	−	1.78649i
$25$	−7.28345	+	4.38231i	−1.45669	+	0.876462i
$26$	5.45807	+	3.28401i	1.07042	+	0.644048i
$27$	−0.468408	−	0.883512i	−0.0901452	−	0.170032i
$28$	−0.719174	−	1.80499i	−0.135911	−	0.341111i
$29$	−1.18664	+	0.261199i	−0.220354	+	0.0485035i	−0.323775	−	0.946134i	$-0.604952\pi$
$29$	−1.18664	+	0.261199i	−0.220354	+	0.0485035i	0.103421	+	0.994638i	$0.467021\pi$
$30$	9.88887	−	2.17671i	1.80545	−	0.397410i
$31$	1.25816	+	3.15775i	0.225973	+	0.567149i	0.997624	−	0.0688970i	$-0.0219480\pi$
$31$	1.25816	+	3.15775i	0.225973	+	0.567149i	−0.771651	+	0.636046i	$0.780569\pi$
$32$	−11.5153	−	21.7202i	−2.03564	−	3.83963i
$33$	−2.01363	−	1.21156i	−0.350528	−	0.210905i
$34$	−13.2637	+	7.98048i	−2.27470	+	1.36864i
$35$	0.597723	−	1.12743i	0.101034	−	0.190570i
$36$	−5.56175	−	0.604876i	−0.926958	−	0.100813i
$37$	1.05578	−	0.802581i	0.173569	−	0.131943i	−0.514783	−	0.857320i	$-0.672128\pi$
$37$	1.05578	−	0.802581i	0.173569	−	0.131943i	0.688352	+	0.725377i	$0.258334\pi$
$38$	10.0142	−	14.7698i	1.62451	−	2.39598i
$39$	0.373947	−	2.28098i	0.0598794	−	0.365248i
$40$	13.4719	−	33.8119i	2.13009	−	5.34613i
$41$	6.99835	−	0.761116i	1.09296	−	0.118866i	0.456161	−	0.889897i	$-0.349224\pi$
$41$	6.99835	−	0.761116i	1.09296	−	0.118866i	0.636798	+	0.771031i	$0.280259\pi$
$42$	−0.694849	+	0.658196i	−0.107217	+	0.101562i
$43$	1.46267	+	1.72199i	0.223056	+	0.262602i	0.862295	−	0.506406i	$-0.169026\pi$
$43$	1.46267	+	1.72199i	0.223056	+	0.262602i	−0.639239	+	0.769008i	$0.720751\pi$
$44$	−11.9321	+	5.52039i	−1.79884	+	0.832230i
$45$	−2.06195	−	3.04115i	−0.307377	−	0.453347i
$46$	2.90565	+	0.979027i	0.428415	+	0.144350i
$47$	−1.55893	+	5.61475i	−0.227393	+	0.818995i	0.758508	+	0.651664i	$0.225929\pi$
$47$	−1.55893	+	5.61475i	−0.227393	+	0.818995i	−0.985901	+	0.167331i	$0.946485\pi$
$48$	−10.4293	+	12.2783i	−1.50534	+	1.77222i
$49$	−0.372442	−	6.86929i	−0.0532060	−	0.981328i
$50$	22.1988	−	7.47964i	3.13938	−	1.05778i
$51$	4.47165	+	3.39926i	0.626156	+	0.475992i
$52$	−9.38812	−	8.89290i	−1.30190	−	1.23322i
$53$	−0.252680	+	4.66041i	−0.0347083	+	0.640156i	0.928489	+	0.371360i	$0.121109\pi$
$53$	−0.252680	+	4.66041i	−0.0347083	+	0.640156i	−0.963197	+	0.268796i	$0.913374\pi$
$54$	0.737260	+	2.65537i	0.100328	+	0.361350i
$55$	−7.83652	−	3.62556i	−1.05668	−	0.488871i
$56$	0.556583	+	3.39501i	0.0743766	+	0.453677i
$57$	−6.32386	−	1.39199i	−0.837616	−	0.184373i
$58$	3.34845			0.439673
$59$	2.69004	+	7.19470i	0.350213	+	0.936670i
$59$	2.69004	+	7.19470i	0.350213	+	0.936670i
$60$	−20.5558			−2.65374
$61$	5.80648	+	1.27810i	0.743444	+	0.163644i	0.570512	−	0.821289i	$-0.306745\pi$
$61$	5.80648	+	1.27810i	0.743444	+	0.163644i	0.172932	+	0.984934i	$0.444676\pi$
$62$	−1.51549	−	9.24411i	−0.192468	−	1.17400i
$63$	0.315201	+	0.145828i	0.0397117	+	0.0183726i
$64$	9.50509	+	34.2342i	1.18814	+	4.27928i
$65$	0.459790	−	8.48033i	0.0570299	−	1.05185i
$66$	4.70171	+	4.45369i	0.578740	+	0.548212i
$67$	−4.15186	−	3.15616i	−0.507231	−	0.385587i	0.320028	−	0.947408i	$-0.396308\pi$
$67$	−4.15186	−	3.15616i	−0.507231	−	0.385587i	−0.827259	+	0.561821i	$0.810101\pi$
$68$	29.7795	−	10.0339i	3.61130	−	1.21679i
$69$	−0.0602355	−	1.11098i	−0.00725150	−	0.133746i
$70$	−2.27662	+	2.68024i	−0.272108	+	0.320350i
$71$	3.03779	−	10.9411i	0.360519	−	1.29847i	−0.531724	−	0.846918i	$-0.678456\pi$
$71$	3.03779	−	10.9411i	0.360519	−	1.29847i	0.892243	−	0.451555i	$-0.149130\pi$
$72$	9.38737	+	3.16297i	1.10631	+	0.372760i
$73$	6.15590	+	9.07927i	0.720493	+	1.06265i	0.994883	+	0.101029i	$0.0322136\pi$
$73$	6.15590	+	9.07927i	0.720493	+	1.06265i	−0.274390	+	0.961618i	$0.588476\pi$
$74$	−3.31697	+	1.53460i	−0.385590	+	0.178393i
$75$	−5.50291	−	6.47853i	−0.635421	−	0.748076i
$76$	−26.3000	+	24.9127i	−3.01681	+	2.85768i
$77$	0.811377	−	0.0882426i	0.0924650	−	0.0100562i
$78$	−2.35773	+	5.91746i	−0.266961	+	0.670021i
$79$	2.21624	−	13.5185i	0.249347	−	1.52095i	−0.504218	−	0.863576i	$-0.668219\pi$
$79$	2.21624	−	13.5185i	0.249347	−	1.52095i	0.753565	−	0.657373i	$-0.228333\pi$
$80$	−33.2176	+	48.9923i	−3.71384	+	5.47751i
$81$	0.796093	−	0.605174i	0.0884548	−	0.0672416i
$82$	−19.2862	−	2.09750i	−2.12980	−	0.231630i
$83$	−4.20069	+	7.92334i	−0.461085	+	0.869699i	0.538547	+	0.842595i	$0.318973\pi$
$83$	−4.20069	+	7.92334i	−0.461085	+	0.869699i	−0.999633	+	0.0271041i	$0.991371\pi$
$84$	1.66486	−	1.00171i	0.181651	−	0.109296i
$85$	17.6841	+	10.6402i	1.91811	+	1.15409i
$86$	−2.91648	−	5.50107i	−0.314493	−	0.593196i
$87$	−0.449735	−	1.12875i	−0.0482167	−	0.121015i
$88$	22.7348	−	5.00431i	2.42354	−	0.533461i
$89$	15.4400	−	3.39860i	1.63664	−	0.360251i	0.700986	−	0.713175i	$-0.252744\pi$
$89$	15.4400	−	3.39860i	1.63664	−	0.360251i	0.935652	+	0.352924i	$0.114813\pi$
$90$	3.74787	+	9.40645i	0.395060	+	0.991527i
$91$	0.376019	+	0.709248i	0.0394175	+	0.0743494i
$92$	−5.33355	−	3.20909i	−0.556061	−	0.334571i
$93$	−2.91261	+	1.75246i	−0.302023	+	0.181721i
$94$	7.52197	−	14.1879i	0.775832	−	1.46337i
$95$	−23.6523	−	2.57234i	−2.42667	−	0.263917i
$96$	19.5711	−	14.8776i	1.99747	−	1.51844i
$97$	6.21596	−	9.16785i	0.631135	−	0.930854i	−0.368864	−	0.929483i	$-0.620253\pi$
$97$	6.21596	−	9.16785i	0.631135	−	0.930854i	0.999999	−	0.00137091i	$-0.000436374\pi$
$98$	−3.06712	+	18.7086i	−0.309826	+	1.88985i
$99$	0.869830	−	2.18311i	0.0874212	−	0.219411i
$100$	−47.2759	+	5.14157i	−4.72759	+	0.514157i
$101$	3.25870	−	3.08681i	0.324253	−	0.307149i	−0.508206	−	0.861236i	$-0.669691\pi$
$101$	3.25870	−	3.08681i	0.324253	−	0.307149i	0.832459	+	0.554087i	$0.186932\pi$
$102$	−10.0212	−	11.7978i	−0.992243	−	1.16816i
$103$	9.02780	−	4.17670i	0.889535	−	0.411543i	0.0787555	−	0.996894i	$-0.474905\pi$
$103$	9.02780	−	4.17670i	0.889535	−	0.411543i	0.810780	+	0.585351i	$0.199043\pi$
$104$	12.8494	+	18.9514i	1.25998	+	1.85834i
$105$	1.20927	+	0.407452i	0.118013	+	0.0397633i
$106$	3.44098	−	12.3933i	0.334217	−	1.20374i
$107$	−0.216261	+	0.254602i	−0.0209067	+	0.0246133i	−0.772516	−	0.634995i	$-0.781002\pi$
$107$	−0.216261	+	0.254602i	−0.0209067	+	0.0246133i	0.751609	+	0.659609i	$0.229278\pi$
$108$	−0.302882	−	5.58634i	−0.0291449	−	0.537546i
$109$	0.180039	−	0.0606622i	0.0172446	−	0.00581039i	−0.310666	−	0.950519i	$-0.600552\pi$
$109$	0.180039	−	0.0606622i	0.0172446	−	0.00581039i	0.327911	+	0.944709i	$0.393656\pi$
$110$	18.9433	+	14.4003i	1.80617	+	1.37302i
$111$	0.962814	+	0.912026i	0.0913862	+	0.0865657i
$112$	0.302905	−	5.58675i	0.0286218	−	0.527898i
$113$	1.12856	+	4.06472i	0.106166	+	0.382377i	0.997475	−	0.0710206i	$-0.0226256\pi$
$113$	1.12856	+	4.06472i	0.106166	+	0.382377i	−0.891308	+	0.453397i	$0.850212\pi$
$114$	16.1953	+	7.49276i	1.51683	+	0.701762i
$115$	−0.661368	−	4.03417i	−0.0616729	−	0.376188i
$116$	−6.63871	−	1.46129i	−0.616389	−	0.135677i
$117$	2.31143			0.213691
$118$	−2.97765	−	20.9574i	−0.274115	−	1.92928i
$119$	−1.95079			−0.178828
$120$	35.5460	+	7.82426i	3.24489	+	0.714254i
$121$	0.886149	+	5.40527i	0.0805590	+	0.491388i
$122$	−14.8703	−	6.87975i	−1.34630	−	0.622863i
$123$	1.88330	+	6.78302i	0.169811	+	0.611605i
$124$	−1.02955	+	18.9889i	−0.0924563	+	1.70526i
$125$	−9.33676	−	8.84425i	−0.835105	−	0.791054i
$126$	−0.761939	−	0.579211i	−0.0678789	−	0.0516002i
$127$	−0.873493	+	0.294314i	−0.0775100	+	0.0261162i	−0.357789	−	0.933802i	$-0.616469\pi$
$127$	−0.873493	+	0.294314i	−0.0775100	+	0.0261162i	0.280279	+	0.959918i	$0.409573\pi$
$128$	−2.63897	−	48.6729i	−0.233254	−	4.30212i
$129$	−1.46267	+	1.72199i	−0.128781	+	0.151613i
$130$	−6.26139	+	22.5515i	−0.549160	+	1.97790i
$131$	−3.60870	−	1.21591i	−0.315294	−	0.106235i	0.157205	−	0.987566i	$-0.449752\pi$
$131$	−3.60870	−	1.21591i	−0.315294	−	0.106235i	−0.472499	+	0.881331i	$0.656648\pi$
$132$	−7.37807	−	10.8818i	−0.642179	−	0.947143i
$133$	2.04101	−	0.944271i	0.176978	−	0.0818787i
$134$	9.30451	+	10.9541i	0.803787	+	0.946291i
$135$	2.66750	−	2.52679i	0.229582	−	0.217471i
$136$	−55.3153	+	6.01590i	−4.74325	+	0.515859i
$137$	0.587191	−	1.47374i	0.0501671	−	0.125910i	−0.901758	−	0.432242i	$-0.857723\pi$
$137$	0.587191	−	1.47374i	0.0501671	−	0.125910i	0.951925	+	0.306332i	$0.0991019\pi$
$138$	−0.496048	+	3.02576i	−0.0422264	+	0.257570i
$139$	3.12285	−	4.60586i	0.264877	−	0.390664i	−0.671872	−	0.740668i	$-0.734509\pi$
$139$	3.12285	−	4.60586i	0.264877	−	0.390664i	0.936748	+	0.350004i	$0.113820\pi$
$140$	5.68334	−	4.32037i	0.480330	−	0.365138i
$141$	−5.79299	−	0.630026i	−0.487858	−	0.0530577i
$142$	−14.6576	+	27.6472i	−1.23004	+	2.32010i
$143$	4.65435	−	2.80043i	0.389216	−	0.234184i
$144$	−13.8038	−	8.30548i	−1.15032	−	0.692123i
$145$	−2.09116	−	3.94435i	−0.173662	−	0.327561i
$146$	−11.1892	−	28.0827i	−0.926023	−	2.32414i
$147$	6.71855	−	1.47886i	0.554136	−	0.121975i
$148$	7.24601	−	1.59497i	0.595618	−	0.131105i
$149$	1.51495	+	3.80225i	0.124110	+	0.311492i	0.977883	−	0.209153i	$-0.0670707\pi$
$149$	1.51495	+	3.80225i	0.124110	+	0.311492i	−0.853773	+	0.520645i	$0.825691\pi$
$150$	10.9725	+	20.6963i	0.895898	+	1.68984i
$151$	−8.78832	−	5.28776i	−0.715184	−	0.430312i	0.110921	−	0.993829i	$-0.464620\pi$
$151$	−8.78832	−	5.28776i	−0.715184	−	0.430312i	−0.826104	+	0.563518i	$0.809448\pi$
$152$	54.9616	−	33.0693i	4.45798	−	2.68228i
$153$	−2.63105	+	4.96268i	−0.212708	+	0.401209i
$154$	−2.23601	−	0.243181i	−0.180183	−	0.0195961i
$155$	−9.94277	+	7.55830i	−0.798622	+	0.607097i
$156$	7.25692	−	10.7032i	0.581018	−	0.856938i
$157$	−0.339348	+	2.06993i	−0.0270829	+	0.165198i	−0.996905	−	0.0786151i	$-0.974950\pi$
$157$	−0.339348	+	2.06993i	−0.0270829	+	0.165198i	0.969822	+	0.243813i	$0.0783985\pi$
$158$	−13.9734	+	35.0706i	−1.11166	+	2.79007i
$159$	−4.63989	+	0.504619i	−0.367967	+	0.0400189i
$160$	65.5776	−	62.1184i	5.18437	−	4.91089i
$161$	0.250157	+	0.294507i	0.0197151	+	0.0232104i
$162$	−2.50111	+	1.15714i	−0.196506	+	0.0909134i
$163$	6.25952	+	9.23210i	0.490283	+	0.723114i	0.989686	−	0.143257i	$-0.0457574\pi$
$163$	6.25952	+	9.23210i	0.490283	+	0.723114i	−0.499402	+	0.866370i	$0.666447\pi$
$164$	37.3218	+	12.5752i	2.91435	+	0.981957i
$165$	2.30999	−	8.31984i	0.179833	−	0.647699i
$166$	15.9996	−	18.8362i	1.24181	−	1.46197i
$167$	0.0335603	+	0.618983i	0.00259697	+	0.0478984i	0.999545	−	0.0301741i	$-0.00960619\pi$
$167$	0.0335603	+	0.618983i	0.00259697	+	0.0478984i	−0.996948	+	0.0780725i	$0.975123\pi$
$168$	−3.26024	+	1.09850i	−0.251533	+	0.0847513i
$169$	−6.09593	−	4.63401i	−0.468918	−	0.356462i
$170$	−41.2913	−	39.1132i	−3.16690	−	2.99985i
$171$	0.350563	−	6.46576i	0.0268082	−	0.494449i
$172$	3.38157	+	12.1793i	0.257842	+	0.928664i
$173$	−18.0955	−	8.37185i	−1.37577	−	0.636500i	−0.413982	−	0.910285i	$-0.635862\pi$
$173$	−18.0955	−	8.37185i	−1.37577	−	0.636500i	−0.961791	+	0.273785i	$0.911724\pi$
$174$	0.541719	+	3.30434i	0.0410676	+	0.250501i
$175$	2.88310	+	0.634619i	0.217942	+	0.0479727i
$176$	−37.8583			−2.85368
$177$	−6.66472	+	3.81857i	−0.500951	+	0.287021i
$178$	−43.5685			−3.26560
$179$	5.29608	+	1.16575i	0.395847	+	0.0871326i	0.408433	−	0.912788i	$-0.366075\pi$
$179$	5.29608	+	1.16575i	0.395847	+	0.0871326i	−0.0125859	+	0.999921i	$0.504006\pi$
$180$	−3.32556	−	20.2850i	−0.247873	−	1.51196i
$181$	11.8942	+	5.50283i	0.884087	+	0.409022i	0.808761	−	0.588137i	$-0.200138\pi$
$181$	11.8942	+	5.50283i	0.884087	+	0.409022i	0.0753255	+	0.997159i	$0.476000\pi$
$182$	−0.591842	−	2.13162i	−0.0438703	−	0.158006i
$183$	−0.321882	+	5.93677i	−0.0237942	+	0.438858i
$184$	8.00150	+	7.57942i	0.589878	+	0.558762i
$185$	3.87920	+	2.94889i	0.285205	+	0.216807i
$186$	8.87715	−	2.99106i	0.650904	−	0.219315i
$187$	0.714635	+	13.1807i	0.0522593	+	0.963866i
$188$	−21.1049	+	24.8467i	−1.53924	+	1.81213i
$189$	−0.0929128	+	0.334641i	−0.00675841	+	0.0243416i
$190$	62.1337	+	20.9353i	4.50765	+	1.51880i
$191$	13.1059	+	19.3298i	0.948310	+	1.39865i	0.916887	+	0.399147i	$0.130694\pi$
$191$	13.1059	+	19.3298i	0.948310	+	1.39865i	0.0314233	+	0.999506i	$0.489996\pi$
$192$	−32.2455	+	14.9184i	−2.32712	+	1.07664i
$193$	13.5523	+	15.9550i	0.975517	+	1.14847i	0.988904	+	0.148557i	$0.0474630\pi$
$193$	13.5523	+	15.9550i	0.975517	+	1.14847i	−0.0133864	+	0.999910i	$0.504261\pi$
$194$	−22.1608	+	20.9918i	−1.59105	+	1.50712i
$195$	8.44300	−	0.918231i	0.604615	−	0.0657559i
$196$	14.2455	−	35.7535i	1.01754	−	2.55382i
$197$	2.67230	−	16.3003i	0.190393	−	1.16135i	−0.702703	−	0.711483i	$-0.748024\pi$
$197$	2.67230	−	16.3003i	0.190393	−	1.16135i	0.893097	−	0.449865i	$-0.148528\pi$
$198$	−3.63437	+	5.36029i	−0.258283	+	0.380940i
$199$	−16.6942	+	12.6906i	−1.18342	+	0.899611i	−0.996568	−	0.0827779i	$-0.973621\pi$
$199$	−16.6942	+	12.6906i	−1.18342	+	0.899611i	−0.186850	+	0.982389i	$0.559828\pi$
$200$	83.7086	+	9.10386i	5.91909	+	0.643740i
$201$	2.44289	−	4.60778i	0.172308	−	0.325008i
$202$	−10.5991	+	6.37729i	−0.745752	+	0.448704i
$203$	0.361582	+	0.217557i	0.0253781	+	0.0152695i
$204$	14.7195	+	27.7639i	1.03057	+	1.94386i
$205$	9.57377	+	24.0283i	0.668661	+	1.67821i
$206$	−26.7717	+	5.89290i	−1.86527	+	0.410577i
$207$	1.08660	−	0.239178i	0.0755238	−	0.0166240i
$208$	−13.7827	−	34.5920i	−0.955659	−	2.39852i
$209$	−7.12774	−	13.4443i	−0.493036	−	0.929965i
$210$	−3.01325	−	1.81301i	−0.207934	−	0.125110i
$211$	0.462192	−	0.278092i	0.0318186	−	0.0191446i	−0.499556	−	0.866282i	$-0.666503\pi$
$211$	0.462192	−	0.278092i	0.0318186	−	0.0191446i	0.531374	+	0.847137i	$0.321676\pi$
$212$	−12.2307	+	23.0695i	−0.840007	+	1.58442i
$213$	11.2885	+	1.22769i	0.773472	+	0.0841201i
$214$	0.732872	−	0.557115i	0.0500981	−	0.0380836i
$215$	−4.65867	+	6.87102i	−0.317719	+	0.468600i
$216$	−1.60260	+	9.77542i	−0.109043	+	0.665133i
$217$	0.436961	−	1.09669i	0.0296629	−	0.0744482i
$218$	−0.520493	+	0.0566070i	−0.0352522	+	0.00383391i
$219$	−7.96375	+	7.54366i	−0.538140	+	0.509754i
$220$	−31.2729	−	36.8174i	−2.10842	−	2.48223i
$221$	−11.7833	+	5.45153i	−0.792630	+	0.366710i
$222$	−2.05101	−	3.02501i	−0.137654	−	0.203025i
$223$	−1.21950	−	0.410898i	−0.0816639	−	0.0275158i	0.278173	−	0.960531i	$-0.410271\pi$
$223$	−1.21950	−	0.410898i	−0.0816639	−	0.0275158i	−0.359837	+	0.933015i	$0.617168\pi$
$224$	−2.28416	+	8.22681i	−0.152617	+	0.549677i
$225$	5.50291	−	6.47853i	0.366861	−	0.431902i
$226$	−0.629386	−	11.6083i	−0.0418661	−	0.772175i
$227$	−6.47688	+	2.18232i	−0.429886	+	0.144845i	−0.525923	−	0.850532i	$-0.676280\pi$
$227$	−6.47688	+	2.18232i	−0.429886	+	0.144845i	0.0960369	+	0.995378i	$0.469383\pi$
$228$	−28.8393	−	21.9231i	−1.90993	−	1.45189i
$229$	3.47853	+	3.29504i	0.229868	+	0.217742i	0.793961	−	0.607969i	$-0.208015\pi$
$229$	3.47853	+	3.29504i	0.229868	+	0.217742i	−0.564093	+	0.825711i	$0.690774\pi$
$230$	−0.609921	+	11.2493i	−0.0402170	+	0.741758i
$231$	0.218346	+	0.786413i	0.0143661	+	0.0517421i
$232$	10.9237	+	5.05385i	0.717177	+	0.331801i
$233$	2.65608	+	16.2014i	0.174005	+	1.06139i	0.918983	+	0.394297i	$0.129012\pi$
$233$	2.65608	+	16.2014i	0.174005	+	1.06139i	−0.744978	+	0.667089i	$0.767540\pi$
$234$	−6.22095	−	1.36933i	−0.406676	−	0.0895162i
$235$	−21.4105			−1.39666
$236$	−3.24241	+	42.8500i	−0.211063	+	2.78930i
$237$	13.6990			0.889843
$238$	5.25033	+	1.15568i	0.340328	+	0.0749119i
$239$	−2.32396	−	14.1755i	−0.150324	−	0.916938i	−0.949023	−	0.315207i	$-0.897926\pi$
$239$	−2.32396	−	14.1755i	−0.150324	−	0.916938i	0.798699	−	0.601731i	$-0.205522\pi$
$240$	−53.7209	−	24.8540i	−3.46767	−	1.60432i
$241$	−7.76737	−	27.9755i	−0.500340	−	1.80206i	−0.591595	−	0.806235i	$-0.701502\pi$
$241$	−7.76737	−	27.9755i	−0.500340	−	1.80206i	0.0912553	−	0.995828i	$-0.470912\pi$
$242$	0.817216	−	15.0727i	0.0525327	−	0.968908i
$243$	0.725995	+	0.687699i	0.0465726	+	0.0441159i
$244$	26.4799	+	20.1295i	1.69520	+	1.28866i
$245$	23.9535	−	8.07087i	1.53033	−	0.515629i
$246$	−1.05029	−	19.3715i	−0.0669641	−	1.23508i
$247$	9.68947	−	11.4073i	0.616526	−	0.725831i
$248$	9.00819	−	32.4446i	0.572021	−	2.06023i
$249$	−8.49856	−	2.86350i	−0.538574	−	0.181467i
$250$	19.8894	+	29.3346i	1.25791	+	1.85528i
$251$	2.49472	−	1.15418i	0.157466	−	0.0728513i	−0.339573	−	0.940580i	$-0.610283\pi$
$251$	2.49472	−	1.15418i	0.157466	−	0.0728513i	0.497039	+	0.867728i	$0.334421\pi$
$252$	1.25786	+	1.48087i	0.0792380	+	0.0932862i
$253$	1.89822	−	1.79809i	0.119340	−	0.113045i
$254$	2.52527	−	0.274640i	0.158449	−	0.0172324i
$255$	−7.63902	+	19.1725i	−0.478374	+	1.20063i
$256$	−10.2363	+	62.4387i	−0.639769	+	3.90242i
$257$	12.5934	−	18.5738i	0.785552	−	1.15860i	−0.198392	−	0.980123i	$-0.563572\pi$
$257$	12.5934	−	18.5738i	0.785552	−	1.15860i	0.983944	−	0.178479i	$-0.0571178\pi$
$258$	4.95677	−	3.76804i	0.308595	−	0.234588i
$259$	−0.457889	−	0.0497985i	−0.0284519	−	0.00309433i
$260$	22.2556	−	41.9785i	1.38023	−	2.60340i
$261$	1.04112	−	0.626422i	0.0644438	−	0.0387746i
$262$	8.99210	+	5.41037i	0.555534	+	0.334254i
$263$	−6.05104	−	11.4135i	−0.373123	−	0.703785i	0.623849	−	0.781545i	$-0.285568\pi$
$263$	−6.05104	−	11.4135i	−0.373123	−	0.703785i	−0.996972	+	0.0777601i	$0.975223\pi$
$264$	8.61646	+	21.6257i	0.530307	+	1.33097i
$265$	−16.7478	+	3.68647i	−1.02881	+	0.226458i
$266$	−6.05256	+	1.33227i	−0.371106	+	0.0816866i
$267$	5.85175	+	14.6868i	0.358121	+	0.898816i
$268$	−13.6668	−	25.7784i	−0.834835	−	1.57467i
$269$	−15.0846	−	9.07611i	−0.919725	−	0.553380i	−0.0248470	−	0.999691i	$-0.507910\pi$
$269$	−15.0846	−	9.07611i	−0.919725	−	0.553380i	−0.894878	+	0.446311i	$0.852737\pi$
$270$	−8.67619	+	5.22029i	−0.528016	+	0.317697i
$271$	−4.70270	+	8.87024i	−0.285669	+	0.538829i	−0.984267	−	0.176685i	$-0.943463\pi$
$271$	−4.70270	+	8.87024i	−0.285669	+	0.538829i	0.698599	+	0.715514i	$0.253807\pi$
$272$	89.9583	+	9.78356i	5.45453	+	0.593215i
$273$	−0.639071	+	0.485809i	−0.0386784	+	0.0294025i
$274$	−2.45343	+	3.61854i	−0.148217	+	0.218604i
$275$	3.23169	−	19.7124i	0.194878	−	1.18870i
$276$	2.30394	−	5.78246i	0.138681	−	0.348063i
$277$	−17.3790	+	1.89008i	−1.04420	+	0.113564i	−0.614111	−	0.789220i	$-0.710485\pi$
$277$	−17.3790	+	1.89008i	−1.04420	+	0.113564i	−0.430094	+	0.902784i	$0.641520\pi$
$278$	−11.1334	+	10.5461i	−0.667738	+	0.632515i
$279$	−2.20058	−	2.59072i	−0.131745	−	0.155102i
$280$	−11.4724	+	5.30768i	−0.685605	+	0.317194i
$281$	−4.01969	−	5.92859i	−0.239794	−	0.353670i	0.688681	−	0.725065i	$-0.258190\pi$
$281$	−4.01969	−	5.92859i	−0.239794	−	0.353670i	−0.928475	+	0.371394i	$0.878880\pi$
$282$	15.2180	+	5.12753i	0.906216	+	0.305340i
$283$	8.45628	−	30.4568i	0.502674	−	1.81047i	−0.0787845	−	0.996892i	$-0.525104\pi$
$283$	8.45628	−	30.4568i	0.502674	−	1.81047i	0.581458	−	0.813576i	$-0.302482\pi$
$284$	41.1259	−	48.4172i	2.44038	−	2.87303i
$285$	−1.28806	−	23.7569i	−0.0762981	−	1.40724i
$286$	−14.1857	+	4.77972i	−0.838818	+	0.282631i
$287$	−1.94634	−	1.47957i	−0.114889	−	0.0873361i
$288$	17.8478	+	16.9064i	1.05169	+	0.996217i
$289$	0.787755	−	14.5293i	0.0463385	−	0.854664i
$290$	3.29142	+	11.8546i	0.193279	+	0.696128i
$291$	10.0527	+	4.65088i	0.589300	+	0.272639i
$292$	9.92838	+	60.5604i	0.581015	+	3.54403i
$293$	−31.2596	−	6.88076i	−1.82621	−	0.401978i	−0.836842	−	0.547444i	$-0.815601\pi$
$293$	−31.2596	−	6.88076i	−1.82621	−	0.401978i	−0.989363	+	0.145466i	$0.953532\pi$
$294$	−18.9583			−1.10567
$295$	−22.8274	+	16.5958i	−1.32906	+	0.966244i
$296$	−13.1372			−0.763584
$297$	2.29507	+	0.505184i	0.133174	+	0.0293137i
$298$	−1.82481	−	11.1308i	−0.105708	−	0.644791i
$299$	2.33403	+	1.07984i	0.134980	+	0.0624485i
$300$	−12.7222	−	45.8213i	−0.734518	−	2.64550i
$301$	0.0424814	−	0.783524i	0.00244859	−	0.0451616i
$302$	20.5202	+	19.4378i	1.18081	+	1.11852i
$303$	3.57334	+	2.71639i	0.205283	+	0.156052i
$304$	−98.8546	+	33.3080i	−5.66970	+	1.91034i
$305$	1.18268	+	21.8132i	0.0677200	+	1.24902i
$306$	10.0212	−	11.7978i	0.572872	−	0.674437i
$307$	3.17609	−	11.4392i	0.181269	−	0.652871i	−0.815935	−	0.578144i	$-0.803777\pi$
$307$	3.17609	−	11.4392i	0.181269	−	0.652871i	0.997204	−	0.0747279i	$-0.0238088\pi$
$308$	4.32703	+	1.45795i	0.246556	+	0.0830742i
$309$	5.58222	+	8.23316i	0.317561	+	0.468368i
$310$	31.2376	−	14.4520i	1.77417	−	0.820820i
$311$	−2.81549	−	3.31466i	−0.159652	−	0.187957i	0.676520	−	0.736424i	$-0.263487\pi$
$311$	−2.81549	−	3.31466i	−0.159652	−	0.187957i	−0.836172	+	0.548468i	$0.815211\pi$
$312$	−16.6230	+	15.7461i	−0.941090	+	0.891447i
$313$	21.3833	−	2.32557i	1.20865	−	0.131449i	0.518478	−	0.855091i	$-0.326499\pi$
$313$	21.3833	−	2.32557i	1.20865	−	0.131449i	0.690176	+	0.723642i	$0.257533\pi$
$314$	2.13958	−	5.36995i	0.120744	−	0.303044i
$315$	−0.206446	+	1.25926i	−0.0116319	+	0.0709514i
$316$	43.0090	−	63.4336i	2.41945	−	3.56842i
$317$	−11.1552	+	8.47996i	−0.626538	+	0.476282i	−0.869619	−	0.493724i	$-0.835635\pi$
$317$	−11.1552	+	8.47996i	−0.626538	+	0.476282i	0.243080	+	0.970006i	$0.421842\pi$
$318$	12.7867	+	1.39064i	0.717043	+	0.0779831i
$319$	1.33748	−	2.52276i	0.0748847	−	0.141248i
$320$	−111.857	+	67.3024i	−6.25302	+	3.76232i
$321$	−0.286235	−	0.172222i	−0.0159761	−	0.00961248i
$322$	−0.498797	−	0.940831i	−0.0277969	−	0.0524305i
$323$	13.4625	+	33.7882i	0.749072	+	1.88003i
$324$	5.46375	−	1.20266i	0.303541	−	0.0668145i
$325$	19.1882	−	4.22365i	1.06437	−	0.234286i
$326$	−11.3775	−	28.5554i	−0.630143	−	1.58154i
$327$	0.0889902	+	0.167853i	0.00492117	+	0.00928231i
$328$	−59.7519	−	35.9515i	−3.29925	−	1.98509i
$329$	1.73408	−	1.04336i	0.0956031	−	0.0575225i
$330$	−11.1459	+	21.0234i	−0.613563	+	1.15730i
$331$	1.81518	+	0.197413i	0.0997713	+	0.0108508i	0.157868	−	0.987460i	$-0.449538\pi$
$331$	1.81518	+	0.197413i	0.0997713	+	0.0108508i	−0.0580972	+	0.998311i	$0.518503\pi$
$332$	−39.9415	+	30.3627i	−2.19207	+	1.66637i
$333$	−0.744245	+	1.09768i	−0.0407844	+	0.0601525i
$334$	0.276374	−	1.68581i	0.0151225	−	0.0922433i
$335$	7.09272	−	17.8014i	0.387517	−	0.972594i
$336$	5.56215	−	0.604921i	0.303440	−	0.0330011i
$337$	14.3356	−	13.5794i	0.780912	−	0.739719i	−0.189315	−	0.981916i	$-0.560627\pi$
$337$	14.3356	−	13.5794i	0.780912	−	0.739719i	0.970227	+	0.242197i	$0.0778681\pi$
$338$	13.6613	+	16.0833i	0.743074	+	0.874815i
$339$	−3.82859	+	1.77130i	−0.207941	+	0.0962036i
$340$	64.7957	+	95.5665i	3.51404	+	5.18282i
$341$	−7.56996	−	2.55062i	−0.409936	−	0.138124i
$342$	−4.77394	+	17.1942i	−0.258145	+	0.929755i
$343$	−3.12061	+	3.67386i	−0.168497	+	0.198370i
$344$	−1.21168	−	22.3481i	−0.0653294	−	1.20493i
$345$	3.87403	−	1.30531i	0.208571	−	0.0702756i
$346$	43.7423	+	33.2520i	2.35160	+	1.78764i
$347$	25.0057	+	23.6867i	1.34238	+	1.27157i	0.933314	+	0.359061i	$0.116903\pi$
$347$	25.0057	+	23.6867i	1.34238	+	1.27157i	0.409063	+	0.912506i	$0.365856\pi$
$348$	0.368017	−	6.78767i	0.0197278	−	0.363857i
$349$	2.89375	+	10.4223i	0.154899	+	0.557896i	0.999738	+	0.0228755i	$0.00728214\pi$
$349$	2.89375	+	10.4223i	0.154899	+	0.557896i	−0.844839	+	0.535020i	$0.820304\pi$
$350$	−7.38360	−	3.41602i	−0.394670	−	0.182594i
$351$	0.373947	+	2.28098i	0.0199598	+	0.121749i
$352$	56.4220	+	12.4194i	3.00730	+	0.661957i
$353$	−4.48866			−0.238907			−0.119454	−	0.992840i	$-0.538114\pi$
$353$	−4.48866			−0.238907			−0.119454	+	0.992840i	$0.538114\pi$
$354$	20.1996	−	6.32895i	1.07359	−	0.336380i
$355$	41.7213			2.21434
$356$	86.3798	+	19.0136i	4.57812	+	1.00772i
$357$	−0.315602	−	1.92509i	−0.0167034	−	0.101886i
$358$	−13.5632	−	6.27500i	−0.716837	−	0.331644i
$359$	7.93829	+	28.5911i	0.418967	+	1.50898i	0.808793	+	0.588093i	$0.200121\pi$
$359$	7.93829	+	28.5911i	0.418967	+	1.50898i	−0.389826	+	0.920888i	$0.627465\pi$
$360$	−1.97049	+	36.3435i	−0.103854	+	1.91547i
$361$	−16.6463	−	15.7682i	−0.876120	−	0.829904i
$362$	−28.7519	−	21.8566i	−1.51117	−	1.14876i
$363$	−5.19070	+	1.74895i	−0.272441	+	0.0917962i
$364$	0.243142	+	4.48449i	0.0127441	+	0.235051i
$365$	−26.0926	+	30.7186i	−1.36575	+	1.60788i
$366$	4.38337	−	15.7875i	0.229122	−	0.825224i
$367$	−24.1875	−	8.14971i	−1.26258	−	0.425411i	−0.393150	−	0.919474i	$-0.628615\pi$
$367$	−24.1875	−	8.14971i	−1.26258	−	0.425411i	−0.869426	+	0.494063i	$0.835511\pi$
$368$	−10.0587	−	14.8355i	−0.524345	−	0.773352i
$369$	−6.38898	+	2.95586i	−0.332597	+	0.153876i
$370$	−8.69346	−	10.2347i	−0.451952	−	0.532078i
$371$	1.17679	−	1.11472i	0.0610962	−	0.0578733i
$372$	−18.9053	+	2.05608i	−0.980197	+	0.106603i
$373$	−9.78918	+	24.5690i	−0.506864	+	1.27213i	0.423633	+	0.905834i	$0.360755\pi$
$373$	−9.78918	+	24.5690i	−0.506864	+	1.27213i	−0.930497	+	0.366300i	$0.880625\pi$
$374$	5.88512	−	35.8977i	0.304313	−	1.85622i
$375$	7.21722	−	10.6446i	0.372696	−	0.549685i
$376$	45.9531	−	34.9326i	2.36985	−	1.80151i
$377$	2.79203	+	0.303651i	0.143797	+	0.0156388i
$378$	0.448313	−	0.845607i	0.0230587	−	0.0434934i
$379$	6.75822	−	4.06629i	0.347147	−	0.208871i	−0.331292	−	0.943528i	$-0.607485\pi$
$379$	6.75822	−	4.06629i	0.347147	−	0.208871i	0.678439	+	0.734657i	$0.262657\pi$
$380$	−114.051	−	68.6223i	−5.85070	−	3.52025i
$381$	−0.431753	−	0.814372i	−0.0221194	−	0.0417215i
$382$	−23.8218	−	59.7882i	−1.21883	−	3.05903i
$383$	−21.8684	+	4.81360i	−1.11742	+	0.245964i	−0.735029	−	0.678035i	$-0.762832\pi$
$383$	−21.8684	+	4.81360i	−1.11742	+	0.245964i	−0.382395	+	0.923999i	$0.624901\pi$
$384$	47.6048	−	10.4786i	2.42932	−	0.534734i
$385$	1.10997	+	2.78581i	0.0565692	+	0.141978i
$386$	−27.0225	−	50.9699i	−1.37541	−	2.59430i
$387$	−1.93594	−	1.16482i	−0.0984095	−	0.0592110i
$388$	53.0974	−	31.9477i	2.69561	−	1.62190i
$389$	15.4056	−	29.0580i	0.781093	−	1.47330i	−0.0972457	−	0.995260i	$-0.531003\pi$
$389$	15.4056	−	29.0580i	0.781093	−	1.47330i	0.878339	−	0.478038i	$-0.158652\pi$
$390$	−23.2674	−	2.53048i	−1.17819	−	0.128136i
$391$	−4.97520	+	3.78205i	−0.251607	+	0.191267i
$392$	−38.2430	+	56.4042i	−1.93156	+	2.84884i
$393$	0.616073	−	3.75788i	0.0310768	−	0.189560i
$394$	−16.8488	+	42.2873i	−0.848831	+	2.13040i
$395$	50.0385	−	5.44201i	2.51771	−	0.273817i
$396$	9.54485	−	9.04136i	0.479647	−	0.454346i
$397$	−3.63132	−	4.27512i	−0.182251	−	0.214562i	0.663449	−	0.748222i	$-0.269092\pi$
$397$	−3.63132	−	4.27512i	−0.182251	−	0.214562i	−0.845699	+	0.533660i	$0.820816\pi$
$398$	52.4486	−	24.2653i	2.62901	−	1.21631i
$399$	1.26203	+	1.86136i	0.0631806	+	0.0931843i
$400$	−129.768	−	43.7241i	−6.48842	−	2.18620i
$401$	−1.39243	+	5.01509i	−0.0695347	+	0.250442i	−0.990146	−	0.140039i	$-0.955277\pi$
$401$	−1.39243	+	5.01509i	−0.0695347	+	0.250442i	0.920611	+	0.390480i	$0.127691\pi$
$402$	−9.30451	+	10.9541i	−0.464067	+	0.546341i
$403$	−0.425366	−	7.84542i	−0.0211890	−	0.390808i
$404$	23.7972	−	8.01819i	1.18395	−	0.398920i
$405$	2.92505	+	2.22357i	0.145347	+	0.110490i
$406$	−0.844274	−	0.799739i	−0.0419006	−	0.0396904i
$407$	−0.168729	+	3.11201i	−0.00836356	+	0.154257i
$408$	−14.8857	−	53.6133i	−0.736950	−	2.65426i
$409$	8.08013	+	3.73827i	0.399537	+	0.184845i	0.609360	−	0.792894i	$-0.291427\pi$
$409$	8.08013	+	3.73827i	0.399537	+	0.184845i	−0.209823	+	0.977739i	$0.567289\pi$
$410$	−11.5319	−	70.3413i	−0.569519	−	3.47391i
$411$	1.54932	+	0.341031i	0.0764223	+	0.0168218i
$412$	55.6498			2.74167
$413$	1.04011	−	2.45655i	0.0511804	−	0.120879i
$414$	−3.06615			−0.150693
$415$	−32.1804	−	7.08345i	−1.57967	−	0.347713i
$416$	9.19309	+	56.0754i	0.450729	+	2.74932i
$417$	5.05040	+	2.33657i	0.247319	+	0.114422i
$418$	11.2188	+	40.4066i	0.548731	+	1.97635i
$419$	1.70514	−	31.4495i	0.0833015	−	1.53641i	−0.596262	−	0.802790i	$-0.703348\pi$
$419$	1.70514	−	31.4495i	0.0833015	−	1.53641i	0.679564	−	0.733617i	$-0.262169\pi$
$420$	5.18291	+	4.90952i	0.252900	+	0.239560i
$421$	−17.3231	−	13.1687i	−0.844277	−	0.641803i	0.0909483	−	0.995856i	$-0.471010\pi$
$421$	−17.3231	−	13.1687i	−0.844277	−	0.641803i	−0.935225	+	0.354053i	$0.884803\pi$
$422$	−1.40869	+	0.474642i	−0.0685738	+	0.0231052i
$423$	−0.315475	−	5.81860i	−0.0153389	−	0.282910i
$424$	29.9309	−	35.2373i	1.45357	−	1.71128i
$425$	−12.7733	+	46.0052i	−0.619595	+	2.23158i
$426$	−29.6543	−	9.99170i	−1.43676	−	0.484100i
$427$	−1.15878	−	1.70907i	−0.0560772	−	0.0827077i
$428$	−1.69614	+	0.784717i	−0.0819859	+	0.0379307i
$429$	3.51653	+	4.13998i	0.169780	+	0.199880i
$430$	16.6088	−	15.7327i	0.800949	−	0.758699i
$431$	−30.7968	+	3.34936i	−1.48343	+	0.161333i	−0.813706	−	0.581276i	$-0.802554\pi$
$431$	−30.7968	+	3.34936i	−1.48343	+	0.161333i	−0.669725	+	0.742609i	$0.733588\pi$
$432$	5.96286	−	14.9657i	0.286888	−	0.720035i
$433$	−2.62712	+	16.0247i	−0.126251	+	0.770099i	0.845479	+	0.534008i	$0.179315\pi$
$433$	−2.62712	+	16.0247i	−0.126251	+	0.770099i	−0.971731	+	0.236091i	$0.924134\pi$
$434$	−1.82573	+	2.69276i	−0.0876380	+	0.129256i
$435$	3.55408	−	2.70174i	0.170405	−	0.129539i
$436$	1.05664	+	0.114917i	0.0506041	+	0.00550352i
$437$	3.37462	−	6.36520i	0.161430	−	0.304489i
$438$	25.9026	−	15.5851i	1.23767	−	0.744683i
$439$	−5.43305	−	3.26896i	−0.259305	−	0.156019i	0.379965	−	0.925001i	$-0.375936\pi$
$439$	−5.43305	−	3.26896i	−0.259305	−	0.156019i	−0.639270	+	0.768982i	$0.720764\pi$
$440$	40.0645	+	75.5697i	1.91000	+	3.60264i
$441$	2.54632	+	6.39079i	0.121253	+	0.304323i
$442$	34.9430	−	7.69154i	1.66207	−	0.365849i
$443$	14.7111	−	3.23815i	0.698943	−	0.153849i	0.148736	−	0.988877i	$-0.452480\pi$
$443$	14.7111	−	3.23815i	0.698943	−	0.153849i	0.550208	+	0.835028i	$0.314549\pi$
$444$	2.74623	+	6.89252i	0.130330	+	0.327104i
$445$	27.2092	+	51.3221i	1.28984	+	2.43290i
$446$	3.03873	+	1.82834i	0.143888	+	0.0865746i
$447$	−3.50707	+	2.11013i	−0.165879	+	0.0998058i
$448$	5.77985	−	10.9020i	0.273072	−	0.515069i
$449$	−11.2933	−	1.22823i	−0.532966	−	0.0579635i	−0.162321	−	0.986738i	$-0.551898\pi$
$449$	−11.2933	−	1.22823i	−0.532966	−	0.0579635i	−0.370645	+	0.928775i	$0.620863\pi$
$450$	−18.6485	+	14.1762i	−0.879098	+	0.668273i
$451$	−9.28383	+	13.6926i	−0.437159	+	0.644761i
$452$	−3.81814	+	23.2896i	−0.179590	+	1.09545i
$453$	3.79631	−	9.52801i	0.178366	−	0.447665i
$454$	18.7247	−	2.03643i	0.878792	−	0.0955744i
$455$	−2.14136	+	2.02840i	−0.100388	+	0.0950930i
$456$	41.5255	+	48.8876i	1.94461	+	2.28937i
$457$	−20.7251	+	9.58844i	−0.969478	+	0.448528i	−0.839721	−	0.543018i	$-0.817282\pi$
$457$	−20.7251	+	9.58844i	−0.969478	+	0.448528i	−0.129757	+	0.991546i	$0.541420\pi$
$458$	−7.41004	−	10.9290i	−0.346248	−	0.510678i
$459$	−5.32296	−	1.79352i	−0.248455	−	0.0837141i
$460$	6.11853	−	22.0370i	0.285278	−	1.02748i
$461$	−21.2102	+	24.9706i	−0.987857	+	1.16300i	−0.00123059	+	0.999999i	$0.500392\pi$
$461$	−21.2102	+	24.9706i	−0.987857	+	1.16300i	−0.986627	+	0.162996i	$0.947884\pi$
$462$	−0.121769	−	2.24590i	−0.00566520	−	0.104489i
$463$	−21.0783	+	7.10210i	−0.979591	+	0.330063i	−0.763142	−	0.646231i	$-0.776344\pi$
$463$	−21.0783	+	7.10210i	−0.979591	+	0.330063i	−0.216449	+	0.976294i	$0.569448\pi$
$464$	−15.5829	−	11.8458i	−0.723417	−	0.549928i
$465$	−9.06729	−	8.58899i	−0.420485	−	0.398305i
$466$	2.44946	−	45.1777i	0.113469	−	2.09282i
$467$	−9.52067	−	34.2903i	−0.440564	−	1.58677i	−0.767064	−	0.641571i	$-0.778283\pi$
$467$	−9.52067	−	34.2903i	−0.440564	−	1.58677i	0.326500	−	0.945197i	$-0.394131\pi$
$468$	11.7362	+	5.42974i	0.542506	+	0.250990i
$469$	0.293032	+	1.78741i	0.0135309	+	0.0825351i
$470$	57.6239	+	12.6840i	2.65799	+	0.585069i
$471$	−2.09756			−0.0966505
$472$	21.9171	−	72.8638i	1.00882	−	3.35383i
$473$	−5.30951			−0.244132
$474$	−36.8692	−	8.11553i	−1.69346	−	0.372759i
$475$	−8.90463	−	54.3158i	−0.408572	−	2.49218i
$476$	−9.90505	−	4.58257i	−0.453997	−	0.210042i
$477$	−1.24862	−	4.49713i	−0.0571705	−	0.205910i
$478$	−2.14318	+	39.5286i	−0.0980267	+	1.80800i
$479$	5.15150	+	4.87976i	0.235378	+	0.222962i	0.796292	−	0.604912i	$-0.206792\pi$
$479$	5.15150	+	4.87976i	0.235378	+	0.222962i	−0.560914	+	0.827874i	$0.689550\pi$
$480$	71.9094	+	54.6641i	3.28220	+	2.49506i
$481$	−2.90494	+	0.978789i	−0.132454	+	0.0446290i
$482$	4.33176	+	79.8946i	0.197306	+	3.63910i
$483$	−0.250157	+	0.294507i	−0.0113825	+	0.0134005i
$484$	−8.19806	+	29.5268i	−0.372639	+	1.34213i
$485$	38.5673	+	12.9949i	1.75125	+	0.590066i
$486$	−1.54653	−	2.28096i	−0.0701520	−	0.103467i
$487$	−15.3679	+	7.10995i	−0.696386	+	0.322183i	−0.735951	−	0.677034i	$-0.763265\pi$
$487$	−15.3679	+	7.10995i	−0.696386	+	0.322183i	0.0395650	+	0.999217i	$0.487403\pi$
$488$	−38.1281	−	44.8879i	−1.72598	−	2.03198i
$489$	−8.09780	+	7.67064i	−0.366195	+	0.346879i
$490$	−69.2495	+	7.53134i	−3.12838	+	0.340231i
$491$	11.2840	−	28.3207i	0.509239	−	1.27809i	−0.419634	−	0.907694i	$-0.637841\pi$
$491$	11.2840	−	28.3207i	0.509239	−	1.27809i	0.928873	−	0.370400i	$-0.120779\pi$
$492$	−6.37153	+	38.8646i	−0.287251	+	1.75215i
$493$	−3.83005	+	5.64891i	−0.172497	+	0.254414i
$494$	−32.8361	+	24.9613i	−1.47736	+	1.12306i
$495$	8.58395	+	0.933561i	0.385820	+	0.0419605i
$496$	−25.6501	+	48.3812i	−1.15172	+	2.17238i
$497$	−3.37910	+	2.03314i	−0.151574	+	0.0911988i
$498$	21.1765	+	12.7415i	0.948944	+	0.570960i
$499$	−0.744408	−	1.40410i	−0.0333243	−	0.0628563i	0.866291	−	0.499540i	$-0.166498\pi$
$499$	−0.744408	−	1.40410i	−0.0333243	−	0.0628563i	−0.899615	+	0.436684i	$0.856153\pi$
$500$	−26.6312	−	66.8393i	−1.19098	−	2.98914i
$501$	−0.605400	+	0.133259i	−0.0270473	+	0.00595355i
$502$	−7.39803	+	1.62843i	−0.330190	+	0.0726804i
$503$	11.5556	+	29.0024i	0.515239	+	1.29315i	0.924656	+	0.380804i	$0.124353\pi$
$503$	11.5556	+	29.0024i	0.515239	+	1.29315i	−0.409417	+	0.912347i	$0.634268\pi$
$504$	−1.61148	−	3.03957i	−0.0717810	−	0.135393i
$505$	14.1315	+	8.50266i	0.628845	+	0.378364i
$506$	−6.17409	+	3.71483i	−0.274472	+	0.165144i
$507$	3.58675	−	6.76533i	0.159293	−	0.300459i
$508$	−5.12651	−	0.557541i	−0.227452	−	0.0247369i
$509$	20.4189	−	15.5220i	0.905050	−	0.688001i	−0.0453702	−	0.998970i	$-0.514447\pi$
$509$	20.4189	−	15.5220i	0.905050	−	0.688001i	0.950420	+	0.310969i	$0.100654\pi$
$510$	31.9178	−	47.0752i	1.41334	−	2.08452i
$511$	0.616339	−	3.75950i	0.0272652	−	0.166310i
$512$	28.4555	−	71.4179i	1.25757	−	3.15626i
$513$	6.43729	−	0.700098i	0.284213	−	0.0309101i
$514$	−44.8971	+	42.5288i	−1.98033	+	1.87587i
$515$	23.6610	+	27.8559i	1.04263	+	1.22748i
$516$	−11.4718	+	5.30742i	−0.505018	+	0.233646i
$517$	−7.68483	−	11.3343i	−0.337979	−	0.498481i
$518$	1.20286	+	0.405290i	0.0528505	+	0.0178074i
$519$	5.33405	−	19.2115i	0.234139	−	0.843291i
$520$	−54.4638	+	64.1197i	−2.38840	+	2.81184i
$521$	1.26197	+	23.2757i	0.0552880	+	1.01973i	0.886194	+	0.463314i	$0.153340\pi$
$521$	1.26197	+	23.2757i	0.0552880	+	1.01973i	−0.830906	+	0.556413i	$0.812177\pi$
$522$	−3.17317	+	1.06917i	−0.138886	+	0.0467961i
$523$	10.1638	+	7.72631i	0.444431	+	0.337848i	0.803336	−	0.595526i	$-0.203057\pi$
$523$	10.1638	+	7.72631i	0.444431	+	0.337848i	−0.358904	+	0.933374i	$0.616850\pi$
$524$	−15.4668	−	14.6509i	−0.675670	−	0.640029i
$525$	−0.159825	+	2.94779i	−0.00697532	+	0.128652i
$526$	9.52414	+	34.3029i	0.415272	+	1.49568i
$527$	17.3285	+	8.01700i	0.754840	+	0.349226i
$528$	−6.12480	−	37.3596i	−0.266548	−	1.62587i
$529$	−21.2533	−	4.67821i	−0.924057	−	0.203400i
$530$	47.2587			2.05279
$531$	−4.84650	−	5.95915i	−0.210320	−	0.258605i
$532$	12.5813			0.545470
$533$	−15.8911	−	3.49790i	−0.688321	−	0.151511i
$534$	−7.04860	−	42.9945i	−0.305023	−	1.86056i
$535$	−1.11395	−	0.515369i	−0.0481603	−	0.0222813i
$536$	13.8211	+	49.7792i	0.596981	+	2.15013i
$537$	−0.293588	+	5.41491i	−0.0126692	+	0.233670i
$538$	35.2217	+	33.3638i	1.51852	+	1.43841i
$539$	12.8702	+	9.78364i	0.554357	+	0.421411i
$540$	19.4798	−	6.56350i	0.838276	−	0.282448i
$541$	−1.56395	−	28.8453i	−0.0672394	−	1.24016i	−0.816289	−	0.577644i	$-0.803972\pi$
$541$	−1.56395	−	28.8453i	−0.0672394	−	1.24016i	0.749050	−	0.662514i	$-0.230510\pi$
$542$	17.9117	−	21.0873i	0.769374	−	0.905777i
$543$	−3.50608	+	12.6277i	−0.150460	+	0.541908i
$544$	−130.859	−	44.0917i	−5.61055	−	1.89042i
$545$	0.391737	+	0.577769i	0.0167802	+	0.0247489i
$546$	2.00779	−	0.928904i	0.0859256	−	0.0397534i
$547$	−0.134843	−	0.158749i	−0.00576545	−	0.00678762i	0.759272	−	0.650774i	$-0.225555\pi$
$547$	−0.134843	−	0.158749i	−0.00576545	−	0.00678762i	−0.765037	+	0.643986i	$0.777279\pi$
$548$	6.44338	−	6.10349i	0.275248	−	0.260728i
$549$	−5.91063	+	0.642820i	−0.252260	+	0.0274349i
$550$	−20.3758	+	51.1393i	−0.868826	+	2.18059i
$551$	1.27286	−	7.76409i	0.0542256	−	0.330761i
$552$	−6.18508	+	9.12231i	−0.263254	+	0.388271i
$553$	−3.78754	+	2.87921i	−0.161062	+	0.122437i
$554$	47.8935	+	5.20873i	2.03480	+	0.221298i
$555$	−2.28246	+	4.30518i	−0.0968850	+	0.182745i
$556$	26.6757	−	16.0503i	1.13130	−	0.680683i
$557$	−13.2118	−	7.94929i	−0.559803	−	0.336822i	0.207370	−	0.978263i	$-0.433510\pi$
$557$	−13.2118	−	7.94929i	−0.559803	−	0.336822i	−0.767173	+	0.641440i	$0.778337\pi$
$558$	4.38782	+	8.27631i	0.185751	+	0.350364i
$559$	−1.93298	−	4.85142i	−0.0817564	−	0.205193i
$560$	20.0767	−	4.41921i	0.848395	−	0.186746i
$561$	−12.8914	+	2.83761i	−0.544276	+	0.119804i
$562$	7.30633	+	18.3375i	0.308199	+	0.773521i
$563$	0.973049	+	1.83537i	0.0410091	+	0.0773514i	0.903170	−	0.429284i	$-0.141234\pi$
$563$	0.973049	+	1.83537i	0.0410091	+	0.0773514i	−0.862161	+	0.506635i	$0.830889\pi$
$564$	−27.9337	−	16.8072i	−1.17622	−	0.707710i
$565$	−13.2811	+	7.99099i	−0.558741	+	0.336184i
$566$	−40.8024	+	76.9614i	−1.71505	+	3.23493i
$567$	−0.345265	−	0.0375498i	−0.0144998	−	0.00157694i
$568$	−89.5460	+	68.0711i	−3.75726	+	2.85620i
$569$	13.9546	−	20.5814i	0.585006	−	0.862819i	−0.413864	−	0.910339i	$-0.635821\pi$
$569$	13.9546	−	20.5814i	0.585006	−	0.862819i	0.998870	+	0.0475194i	$0.0151316\pi$
$570$	−10.6074	+	64.7021i	−0.444294	+	2.71007i
$571$	−3.04954	+	7.65376i	−0.127619	+	0.320300i	−0.978878	−	0.204447i	$-0.934461\pi$
$571$	−3.04954	+	7.65376i	−0.127619	+	0.320300i	0.851259	+	0.524746i	$0.175840\pi$
$572$	30.2108	−	3.28562i	1.26318	−	0.137379i
$573$	−16.9548	+	16.0605i	−0.708298	+	0.670936i
$574$	4.36183	+	5.13514i	0.182059	+	0.214337i
$575$	8.58331	−	3.97106i	0.357949	−	0.165605i
$576$	−19.9386	−	29.4072i	−0.830774	−	1.22530i
$577$	19.8046	+	6.67293i	0.824474	+	0.277798i	0.699745	−	0.714393i	$-0.253297\pi$
$577$	19.8046	+	6.67293i	0.824474	+	0.277798i	0.124730	+	0.992191i	$0.460194\pi$
$578$	−10.7276	+	38.6373i	−0.446209	+	1.60710i
$579$	−13.5523	+	15.9550i	−0.563215	+	0.663068i
$580$	−1.35219	−	24.9397i	−0.0561466	−	1.03556i
$581$	2.95155	−	0.994494i	0.122451	−	0.0412586i
$582$	−24.3005	−	18.4728i	−1.00729	−	0.765720i
$583$	−7.96280	−	7.54277i	−0.329786	−	0.312389i
$584$	5.88285	−	108.503i	0.243434	−	4.48988i
$585$	2.27206	+	8.18322i	0.0939381	+	0.338334i
$586$	80.0555	+	37.0376i	3.30706	+	1.53001i
$587$	−6.97830	−	42.5658i	−0.288025	−	1.75688i	−0.593649	−	0.804724i	$-0.702313\pi$
$587$	−6.97830	−	42.5658i	−0.288025	−	1.75688i	0.305623	−	0.952152i	$-0.401135\pi$
$588$	37.5872	+	8.27357i	1.55007	+	0.341196i
$589$	−22.0105			−0.906927
$590$	71.2692	−	31.1423i	2.93411	−	1.28211i
$591$	16.5179			0.679455
$592$	20.8653	+	4.59280i	0.857559	+	0.188763i
$593$	2.96156	+	18.0647i	0.121617	+	0.741828i	0.975275	+	0.220995i	$0.0709304\pi$
$593$	2.96156	+	18.0647i	0.121617	+	0.741828i	−0.853658	+	0.520833i	$0.825621\pi$
$594$	−5.87766	−	2.71929i	−0.241163	−	0.111574i
$595$	−1.91756	−	6.90643i	−0.0786124	−	0.283136i
$596$	−1.23968	+	22.8646i	−0.0507793	+	0.936569i
$597$	−15.2242	−	14.4211i	−0.623085	−	0.590218i
$598$	−5.64206	−	4.28898i	−0.230721	−	0.175389i
$599$	−1.57750	+	0.531523i	−0.0644550	+	0.0217174i	−0.351344	−	0.936246i	$-0.614275\pi$
$599$	−1.57750	+	0.531523i	−0.0644550	+	0.0217174i	0.286889	+	0.957964i	$0.407379\pi$
$600$	4.55861	+	84.0787i	0.186105	+	3.43250i
$601$	−18.2593	+	21.4965i	−0.744813	+	0.876862i	−0.995840	−	0.0911184i	$-0.970956\pi$
$601$	−18.2593	+	21.4965i	−0.744813	+	0.876862i	0.251027	+	0.967980i	$0.419232\pi$
$602$	−0.578509	+	2.08360i	−0.0235783	+	0.0849213i
$603$	4.94229	+	1.66525i	0.201266	+	0.0678143i
$604$	−32.2010	−	47.4930i	−1.31024	−	1.93246i
$605$	−18.2654	+	8.45048i	−0.742595	+	0.343561i
$606$	−8.00802	−	9.42777i	−0.325304	−	0.382977i
$607$	30.1544	−	28.5638i	1.22393	−	1.15937i	0.241970	−	0.970284i	$-0.422207\pi$
$607$	30.1544	−	28.5638i	1.22393	−	1.15937i	0.981961	−	0.189085i	$-0.0605521\pi$
$608$	158.254	−	17.2112i	6.41805	−	0.698005i
$609$	−0.156193	+	0.392016i	−0.00632927	+	0.0158853i
$610$	9.73954	−	59.4085i	0.394342	−	2.40538i
$611$	7.55864	−	11.1482i	0.305790	−	0.451006i
$612$	−25.0168	+	19.0173i	−1.01125	+	0.768729i
$613$	17.0623	+	1.85563i	0.689138	+	0.0749483i	0.445986	−	0.895040i	$-0.352853\pi$
$613$	17.0623	+	1.85563i	0.689138	+	0.0749483i	0.243152	+	0.969988i	$0.421819\pi$
$614$	−15.3249	+	28.9059i	−0.618463	+	1.16655i
$615$	−22.1629	+	13.3350i	−0.893696	+	0.537719i
$616$	−6.92754	−	4.16816i	−0.279119	−	0.167940i
$617$	−13.6414	−	25.7304i	−0.549182	−	1.03587i	−0.990369	−	0.138452i	$-0.955787\pi$
$617$	−13.6414	−	25.7304i	−0.549182	−	1.03587i	0.441187	−	0.897415i	$-0.354558\pi$
$618$	−10.1464	−	25.4657i	−0.408150	−	1.02438i
$619$	1.18195	−	0.260167i	0.0475066	−	0.0104570i	−0.191154	−	0.981560i	$-0.561223\pi$
$619$	1.18195	−	0.260167i	0.0475066	−	0.0104570i	0.238660	+	0.971103i	$0.423292\pi$
$620$	−68.2392	+	15.0206i	−2.74055	+	0.603241i
$621$	0.411819	+	1.03359i	0.0165257	+	0.0414765i
$622$	5.61393	+	10.5890i	0.225098	+	0.424580i
$623$	−4.70474	−	2.83075i	−0.188491	−	0.113412i
$624$	31.9065	−	19.1975i	1.27728	−	0.768515i
$625$	2.22604	−	4.19875i	0.0890415	−	0.167950i
$626$	−58.9284	−	6.40885i	−2.35525	−	0.256149i
$627$	12.1141	−	9.20890i	0.483791	−	0.367768i
$628$	−6.58547	+	9.71284i	−0.262789	+	0.387585i
$629$	1.20515	−	7.35112i	0.0480526	−	0.293108i
$630$	1.30164	−	3.26687i	0.0518585	−	0.130155i
$631$	29.6293	−	3.22238i	1.17952	−	0.128281i	0.502723	−	0.864447i	$-0.332331\pi$
$631$	29.6293	−	3.22238i	1.17952	−	0.128281i	0.676801	+	0.736166i	$0.263366\pi$
$632$	−98.5181	+	93.3213i	−3.91884	+	3.71212i
$633$	0.349203	+	0.411113i	0.0138796	+	0.0163403i
$634$	35.0467	−	16.2143i	1.39188	−	0.643953i
$635$	−1.90059	−	2.80316i	−0.0754225	−	0.111240i
$636$	−24.7443	−	8.33733i	−0.981176	−	0.330597i
$637$	−4.25402	+	15.3216i	−0.168550	+	0.607063i
$638$	−5.09423	+	5.99739i	−0.201682	+	0.237439i
$639$	0.614748	+	11.3384i	0.0243191	+	0.448539i
$640$	169.724	−	57.1868i	6.70894	−	2.26051i
$641$	29.8186	+	22.6675i	1.17776	+	0.895313i	0.996116	−	0.0880505i	$-0.0280637\pi$
$641$	29.8186	+	22.6675i	1.17776	+	0.895313i	0.181648	+	0.983364i	$0.441857\pi$
$642$	0.668342	+	0.633087i	0.0263773	+	0.0249859i
$643$	2.61335	−	48.2004i	0.103061	−	1.90084i	−0.254691	−	0.967023i	$-0.581974\pi$
$643$	2.61335	−	48.2004i	0.103061	−	1.90084i	0.357751	−	0.933817i	$-0.383544\pi$
$644$	0.578340	+	2.08299i	0.0227898	+	0.0820813i
$645$	−7.53420	−	3.48569i	−0.296659	−	0.137249i
$646$	−16.2159	−	98.9128i	−0.638007	−	3.89167i
$647$	41.5894	+	9.15453i	1.63505	+	0.359902i	0.935126	−	0.354316i	$-0.115286\pi$
$647$	41.5894	+	9.15453i	1.63505	+	0.359902i	0.699924	+	0.714218i	$0.253217\pi$
$648$	−9.90591			−0.389141
$649$	−16.9789	−	6.12768i	−0.666480	−	0.240533i
$650$	−54.1452			−2.12375
$651$	1.15294	+	0.253780i	0.0451871	+	0.00994643i
$652$	10.0955	+	61.5798i	0.395370	+	2.41165i
$653$	38.3592	+	17.7469i	1.50111	+	0.694488i	0.986624	−	0.163010i	$-0.0521203\pi$
$653$	38.3592	+	17.7469i	1.50111	+	0.694488i	0.514487	+	0.857498i	$0.327982\pi$
$654$	−0.140068	−	0.504478i	−0.00547708	−	0.0197267i
$655$	0.757498	−	13.9712i	0.0295979	−	0.545901i
$656$	82.3330	+	77.9899i	3.21456	+	3.04499i
$657$	−8.73268	−	6.63841i	−0.340694	−	0.258989i
$658$	−5.28521	+	1.78079i	−0.206039	+	0.0694225i
$659$	0.879319	+	16.2181i	0.0342534	+	0.631767i	0.964379	+	0.264525i	$0.0852151\pi$
$659$	0.879319	+	16.2181i	0.0342534	+	0.631767i	−0.930125	+	0.367242i	$0.880302\pi$
$660$	31.2729	−	36.8174i	1.21730	−	1.43311i
$661$	1.01008	−	3.63798i	0.0392875	−	0.141501i	−0.941305	−	0.337557i	$-0.890400\pi$
$661$	1.01008	−	3.63798i	0.0392875	−	0.141501i	0.980593	+	0.196056i	$0.0628134\pi$
$662$	−4.76840	−	1.60666i	−0.185329	−	0.0624447i
$663$	−7.28604	−	10.7461i	−0.282966	−	0.417344i
$664$	80.6256	−	37.3014i	3.12888	−	1.44757i
$665$	5.34928	+	6.29767i	0.207436	+	0.244213i
$666$	2.65334	−	2.51338i	0.102815	−	0.0973914i
$667$	1.34395	−	0.146163i	0.0520379	−	0.00565947i
$668$	−1.28364	+	3.22171i	−0.0496657	+	0.124652i
$669$	0.208192	−	1.26991i	0.00804916	−	0.0490977i
$670$	−29.6352	+	43.7086i	−1.14491	+	1.68861i
$671$	−11.1230	+	8.45548i	−0.429398	+	0.326420i
$672$	−8.48797	−	0.923122i	−0.327431	−	0.0356102i
$673$	−20.6795	+	39.0056i	−0.797135	+	1.50356i	0.0655686	+	0.997848i	$0.479114\pi$
$673$	−20.6795	+	39.0056i	−0.797135	+	1.50356i	−0.862704	+	0.505709i	$0.831231\pi$
$674$	−46.6275	+	28.0549i	−1.79603	+	1.08063i
$675$	7.28345	+	4.38231i	0.280340	+	0.168675i
$676$	−20.0662	−	37.8489i	−0.771778	−	1.45573i
$677$	1.27663	+	3.20410i	0.0490649	+	0.123144i	0.951466	−	0.307752i	$-0.0995768\pi$
$677$	1.27663	+	3.20410i	0.0490649	+	0.123144i	−0.902402	+	0.430896i	$0.858198\pi$
$678$	11.3536	−	2.49911i	0.436032	−	0.0959779i
$679$	−3.75692	+	0.826960i	−0.144177	+	0.0317358i
$680$	−75.6715	−	189.921i	−2.90187	−	7.28314i
$681$	−3.20141	−	6.03850i	−0.122678	−	0.231396i
$682$	18.8627	+	11.3493i	0.722289	+	0.434587i
$683$	−10.0229	+	6.03059i	−0.383516	+	0.230754i	−0.694236	−	0.719748i	$-0.744258\pi$
$683$	−10.0229	+	6.03059i	−0.383516	+	0.230754i	0.310720	+	0.950502i	$0.399430\pi$
$684$	16.9686	−	32.0062i	0.648811	−	1.22379i
$685$	5.79471	+	0.630213i	0.221405	+	0.0240792i
$686$	10.5752	−	8.03909i	0.403765	−	0.306934i
$687$	−2.68887	+	3.96579i	−0.102587	+	0.151304i
$688$	−5.88851	+	35.9183i	−0.224497	+	1.36937i
$689$	3.99305	−	10.0218i	0.152123	−	0.381800i
$690$	−11.1998	+	1.21805i	−0.426369	+	0.0463705i
$691$	14.6705	−	13.8967i	0.558094	−	0.528654i	−0.355825	−	0.934553i	$-0.615800\pi$
$691$	14.6705	−	13.8967i	0.558094	−	0.528654i	0.913918	+	0.405898i	$0.133041\pi$
$692$	−72.2129	−	85.0156i	−2.74512	−	3.23181i
$693$	−0.740728	+	0.342697i	−0.0281379	+	0.0130180i
$694$	−53.2677	−	78.5639i	−2.02201	−	2.98225i
$695$	19.3759	+	6.52852i	0.734971	+	0.247641i
$696$	−3.22001	+	11.5974i	−0.122054	+	0.439600i
$697$	25.5986	−	30.1370i	0.969617	−	1.14152i
$698$	−1.61381	−	29.7649i	−0.0610835	−	1.12662i
$699$	−15.5582	+	5.24218i	−0.588466	+	0.198277i
$700$	13.1481	+	9.99492i	0.496951	+	0.377773i
$701$	−28.7192	−	27.2043i	−1.08471	−	1.02749i	−0.999515	−	0.0311268i	$-0.990090\pi$
$701$	−28.7192	−	27.2043i	−1.08471	−	1.02749i	−0.0851938	−	0.996364i	$-0.527151\pi$
$702$	0.344858	−	6.36053i	0.0130158	−	0.240063i
$703$	2.29739	+	8.27445i	0.0866477	+	0.312077i
$704$	−75.7774	−	35.0584i	−2.85597	−	1.32131i
$705$	−3.46383	−	21.1284i	−0.130455	−	0.795742i
$706$	12.0807	+	2.65917i	0.454664	+	0.100079i
$707$	−1.55889			−0.0586282
$708$	−42.8101	+	3.73266i	−1.60890	+	0.140282i
$709$	35.8287			1.34558			0.672788	−	0.739835i	$-0.265097\pi$
$709$	35.8287			1.34558			0.672788	+	0.739835i	$0.265097\pi$
$710$	−112.288	−	24.7165i	−4.21410	−	0.927594i
$711$	2.21624	+	13.5185i	0.0831157	+	0.506983i
$712$	−142.134	−	65.7583i	−5.32671	−	2.46440i
$713$	−1.01178	−	3.64410i	−0.0378915	−	0.136473i
$714$	−0.291052	+	5.36813i	−0.0108923	+	0.200897i
$715$	14.4895	+	13.7252i	0.541878	+	0.513294i
$716$	24.1522	+	18.3600i	0.902610	+	0.686147i
$717$	13.6128	−	4.58669i	0.508379	−	0.171293i
$718$	−4.42708	−	81.6527i	−0.165217	−	3.04725i
$719$	−7.23289	+	8.51522i	−0.269741	+	0.317564i	−0.880310	−	0.474399i	$-0.842665\pi$
$719$	−7.23289	+	8.51522i	−0.269741	+	0.317564i	0.610568	+	0.791964i	$0.290941\pi$
$720$	15.8355	−	57.0342i	0.590153	−	2.12554i
$721$	−3.27381	−	1.10308i	−0.121923	−	0.0410807i
$722$	35.4602	+	52.2999i	1.31969	+	1.94640i
$723$	26.3504	−	12.1910i	0.979981	−	0.453388i
$724$	47.4657	+	55.8809i	1.76405	+	2.07680i
$725$	7.49818	−	7.10266i	0.278476	−	0.263786i
$726$	15.0063	−	1.63204i	0.556937	−	0.0605705i
$727$	−4.55798	+	11.4397i	−0.169046	+	0.424274i	−0.988954	−	0.148222i	$-0.952645\pi$
$727$	−4.55798	+	11.4397i	−0.169046	+	0.424274i	0.819908	+	0.572495i	$0.194024\pi$
$728$	1.28650	−	7.84731i	0.0476809	−	0.290841i
$729$	−0.561187	+	0.827689i	−0.0207847	+	0.0306551i
$730$	88.4236	−	67.2179i	3.27271	−	2.48785i
$731$	12.6164	+	1.37211i	0.466634	+	0.0507495i
$732$	−15.5803	+	29.3876i	−0.575866	+	1.08620i
$733$	4.70843	−	2.83297i	0.173910	−	0.104638i	−0.425937	−	0.904753i	$-0.640056\pi$
$733$	4.70843	−	2.83297i	0.173910	−	0.104638i	0.599847	+	0.800115i	$0.295228\pi$
$734$	60.2699	+	36.2632i	2.22460	+	1.33850i
$735$	11.8398	+	22.3322i	0.436717	+	0.823736i
$736$	10.1241	+	25.4097i	0.373181	+	0.936614i
$737$	11.9695	−	2.63468i	0.440902	−	0.0970498i
$738$	18.9464	−	4.17041i	0.697425	−	0.153515i
$739$	−10.2883	−	25.8216i	−0.378461	−	0.949864i	−0.987627	−	0.156822i	$-0.949875\pi$
$739$	−10.2883	−	25.8216i	−0.378461	−	0.949864i	0.609166	−	0.793042i	$-0.291504\pi$
$740$	12.7693	+	24.0855i	0.469410	+	0.885400i
$741$	12.8246	+	7.71633i	0.471125	+	0.283466i
$742$	−3.82760	+	2.30299i	−0.140515	+	0.0845454i
$743$	4.52464	−	8.53438i	0.165993	−	0.313096i	−0.786536	−	0.617545i	$-0.788127\pi$
$743$	4.52464	−	8.53438i	0.165993	−	0.313096i	0.952529	+	0.304449i	$0.0984722\pi$
$744$	33.4745	+	3.64058i	1.22724	+	0.133470i
$745$	−11.9721	+	9.10094i	−0.438623	+	0.333433i
$746$	40.9017	−	60.3254i	1.49752	−	2.20867i
$747$	1.45086	−	8.84986i	0.0530842	−	0.323800i
$748$	−27.3340	+	68.6032i	−0.999430	+	2.50838i
$749$	0.115336	−	0.0125436i	0.00421430	−	0.000458332i
$750$	−25.7304	+	24.3732i	−0.939542	+	0.889982i
$751$	−3.15863	−	3.71863i	−0.115260	−	0.135695i	0.701506	−	0.712663i	$-0.252511\pi$
$751$	−3.15863	−	3.71863i	−0.115260	−	0.135695i	−0.816766	+	0.576969i	$0.804235\pi$
$752$	−85.1980	+	39.4168i	−3.10685	+	1.43738i
$753$	1.54258	+	2.27513i	0.0562147	+	0.0829104i
$754$	−7.33455	−	2.47130i	−0.267108	−	0.0899993i
$755$	10.0818	−	36.3113i	0.366914	−	1.32150i
$756$	−1.25786	+	1.48087i	−0.0457481	+	0.0538588i
$757$	0.602082	+	11.1047i	0.0218830	+	0.403609i	0.988870	+	0.148783i	$0.0475355\pi$
$757$	0.602082	+	11.1047i	0.0218830	+	0.403609i	−0.966987	+	0.254826i	$0.917982\pi$
$758$	−20.5980	+	6.94026i	−0.748152	+	0.252082i
$759$	2.08151	+	1.58232i	0.0755538	+	0.0574345i
$760$	171.102	+	162.076i	6.20652	+	5.87913i
$761$	0.445580	−	8.21823i	0.0161522	−	0.297911i	−0.979285	−	0.202488i	$-0.935097\pi$
$761$	0.445580	−	8.21823i	0.0161522	−	0.297911i	0.995437	−	0.0954222i	$-0.0304201\pi$
$762$	0.679565	+	2.44757i	0.0246180	+	0.0886661i
$763$	−0.0598833	−	0.0277050i	−0.00216792	−	0.00100299i
$764$	21.1375	+	128.933i	0.764729	+	4.66464i
$765$	−20.1558	−	4.43663i	−0.728734	−	0.160407i
$766$	61.7081			2.22961
$767$	−0.582345	−	17.7448i	−0.0210272	−	0.640729i
$768$	−63.2722			−2.28314
$769$	−14.0229	−	3.08667i	−0.505678	−	0.111308i	−0.0451979	−	0.998978i	$-0.514392\pi$
$769$	−14.0229	−	3.08667i	−0.505678	−	0.111308i	−0.460480	+	0.887670i	$0.652323\pi$
$770$	−1.33699	−	8.15526i	−0.0481817	−	0.293895i
$771$	20.3665	+	9.42255i	0.733482	+	0.339345i
$772$	31.3317	+	112.847i	1.12765	+	4.06144i
$773$	1.43601	−	26.4856i	0.0516497	−	0.952622i	−0.851784	−	0.523894i	$-0.824479\pi$
$773$	1.43601	−	26.4856i	0.0516497	−	0.952622i	0.903433	−	0.428729i	$-0.141038\pi$
$774$	4.52032	+	4.28187i	0.162479	+	0.153909i
$775$	−23.0020	−	17.4857i	−0.826257	−	0.628105i
$776$	−103.979	+	35.0345i	−3.73262	+	1.25766i
$777$	−0.0249358	−	0.459914i	−0.000894567	−	0.0164993i
$778$	−58.6769	+	69.0798i	−2.10367	+	2.47663i
$779$	−12.1948	+	43.9218i	−0.436925	+	1.57366i
$780$	45.0261	+	15.1710i	1.61219	+	0.543211i
$781$	14.9750	+	22.0864i	0.535847	+	0.790315i
$782$	15.6308	−	7.23157i	0.558955	−	0.258600i
$783$	0.786605	+	0.926063i	0.0281110	+	0.0330948i
$784$	80.4589	−	76.2147i	2.87353	−	2.72195i
$785$	−7.66181	+	0.833272i	−0.273462	+	0.0297407i
$786$	−3.88433	+	9.74894i	−0.138550	+	0.347733i
$787$	−3.60048	+	21.9619i	−0.128343	+	0.782858i	0.841704	+	0.539940i	$0.181553\pi$
$787$	−3.60048	+	21.9619i	−0.128343	+	0.782858i	−0.970047	+	0.242919i	$0.921895\pi$
$788$	51.8593	−	76.4868i	1.84741	−	2.72473i
$789$	10.2842	−	7.81782i	0.366126	−	0.278322i
$790$	−137.897	−	14.9972i	−4.90616	−	0.533577i
$791$	0.686257	−	1.29442i	0.0244005	−	0.0460242i
$792$	−19.9468	+	12.0016i	−0.708779	+	0.426458i
$793$	−11.7754	−	7.08502i	−0.418157	−	0.251597i
$794$	7.24063	+	13.6573i	0.256960	+	0.484678i
$795$	−6.34739	−	15.9307i	−0.225119	−	0.565005i
$796$	−114.575	+	25.2199i	−4.06102	+	0.893897i
$797$	11.8715	−	2.61310i	0.420508	−	0.0925609i	0.000324657	−	1.00000i	$-0.499897\pi$
$797$	11.8715	−	2.61310i	0.420508	−	0.0925609i	0.420184	+	0.907439i	$0.361966\pi$
$798$	−2.29391	−	5.75729i	−0.0812036	−	0.203806i
$799$	15.3315	+	28.9183i	0.542390	+	1.02306i
$800$	179.056	+	107.734i	6.33059	+	3.80899i
$801$	−13.5466	+	8.15072i	−0.478645	+	0.287991i
$802$	6.71862	−	12.6727i	0.237243	−	0.447487i
$803$	−25.6272	−	2.78712i	−0.904364	−	0.0983555i
$804$	23.2278	−	17.6573i	0.819180	−	0.622725i
$805$	−0.796758	+	1.17513i	−0.0280820	+	0.0414179i
$806$	−3.50295	+	21.3671i	−0.123386	+	0.752623i
$807$	6.51613	−	16.3542i	0.229379	−	0.575697i
$808$	−44.2030	+	4.80737i	−1.55506	+	0.169123i
$809$	23.3530	−	22.1211i	0.821046	−	0.777736i	−0.156674	−	0.987650i	$-0.550077\pi$
$809$	23.3530	−	22.1211i	0.821046	−	0.777736i	0.977720	+	0.209914i	$0.0673185\pi$
$810$	−6.55518	−	7.71735i	−0.230325	−	0.271160i
$811$	6.51545	−	3.01437i	0.228788	−	0.105849i	−0.302146	−	0.953262i	$-0.597703\pi$
$811$	6.51545	−	3.01437i	0.228788	−	0.105849i	0.530935	+	0.847413i	$0.321841\pi$
$812$	1.32486	+	1.95403i	0.0464936	+	0.0685729i
$813$	−9.51420	−	3.20571i	−0.333678	−	0.112429i
$814$	2.29773	−	8.27569i	0.0805355	−	0.290063i
$815$	−26.5318	+	31.2356i	−0.929368	+	1.09414i
$816$	4.89896	+	90.3561i	0.171498	+	3.16310i
$817$	−13.8641	+	4.67134i	−0.485042	+	0.163430i
$818$	−19.5322	−	14.8480i	−0.682926	−	0.519147i
$819$	−0.582800	−	0.552057i	−0.0203647	−	0.0192904i
$820$	−7.83417	+	144.493i	−0.273581	+	5.04591i
$821$	−8.12289	−	29.2560i	−0.283491	−	1.02104i	−0.958934	−	0.283629i	$-0.908462\pi$
$821$	−8.12289	−	29.2560i	−0.283491	−	1.02104i	0.675443	−	0.737412i	$-0.263952\pi$
$822$	−3.96779	−	1.83570i	−0.138393	−	0.0640272i
$823$	−3.96648	−	24.1944i	−0.138263	−	0.843365i	−0.961325	−	0.275415i	$-0.911185\pi$
$823$	−3.96648	−	24.1944i	−0.138263	−	0.843365i	0.823063	−	0.567950i	$-0.192263\pi$
$824$	−96.2320	−	21.1823i	−3.35240	−	0.737919i
$825$	19.9756			0.695461
$826$	−4.25465	+	5.99534i	−0.148038	+	0.208605i
$827$	27.2050			0.946012			0.473006	−	0.881059i	$-0.343169\pi$
$827$	27.2050			0.946012			0.473006	+	0.881059i	$0.343169\pi$
$828$	6.07902	+	1.33809i	0.211260	+	0.0465020i
$829$	−1.40419	−	8.56519i	−0.0487696	−	0.297481i	0.951168	−	0.308674i	$-0.0998853\pi$
$829$	−1.40419	−	8.56519i	−0.0487696	−	0.297481i	−0.999937	+	0.0111931i	$0.996437\pi$
$830$	82.4137	+	38.1286i	2.86062	+	1.32346i
$831$	−4.67680	−	16.8443i	−0.162236	−	0.584322i
$832$	4.44607	−	82.0028i	0.154140	−	2.84294i
$833$	−28.0535	−	26.5737i	−0.971997	−	0.920724i
$834$	−12.2084	−	9.28057i	−0.422742	−	0.321360i
$835$	−2.15842	+	0.727256i	−0.0746952	+	0.0251677i
$836$	−4.60894	−	85.0070i	−0.159404	−	2.94003i
$837$	2.20058	−	2.59072i	0.0760631	−	0.0895484i
$838$	−23.2205	+	83.6326i	−0.802138	+	2.88904i
$839$	−11.0750	−	3.73159i	−0.382350	−	0.128829i	0.121562	−	0.992584i	$-0.461210\pi$
$839$	−11.0750	−	3.73159i	−0.382350	−	0.128829i	−0.503912	+	0.863755i	$0.668106\pi$
$840$	−7.09378	−	10.4625i	−0.244759	−	0.360992i
$841$	−24.9798	+	11.5569i	−0.861372	+	0.398513i
$842$	38.8219	+	45.7047i	1.33789	+	1.57509i
$843$	5.20018	−	4.92587i	0.179104	−	0.169656i
$844$	3.00003	−	0.326273i	0.103265	−	0.0112308i
$845$	10.4138	−	26.1367i	0.358246	−	0.899131i
$846$	−2.59799	+	15.8470i	−0.0893207	+	0.544832i
$847$	1.06755	−	1.57452i	0.0366816	−	0.0541013i
$848$	−59.8571	+	45.5022i	−2.05550	+	1.56255i
$849$	31.4236	+	3.41753i	1.07846	+	0.117289i
$850$	61.6323	−	116.251i	2.11397	−	3.98737i
$851$	−1.26433	+	0.760721i	−0.0433406	+	0.0260772i
$852$	54.4328	+	32.7511i	1.86484	+	1.12204i
$853$	1.21109	+	2.28436i	0.0414669	+	0.0782150i	0.903380	−	0.428842i	$-0.141078\pi$
$853$	1.21109	+	2.28436i	0.0414669	+	0.0782150i	−0.861913	+	0.507057i	$0.830733\pi$
$854$	2.10624	+	5.28626i	0.0720740	+	0.180892i
$855$	23.2355	−	5.11453i	0.794638	−	0.174913i
$856$	3.23172	−	0.711356i	0.110458	−	0.0243136i
$857$	0.891021	+	2.23629i	0.0304367	+	0.0763903i	0.943410	−	0.331630i	$-0.107599\pi$
$857$	0.891021	+	2.23629i	0.0304367	+	0.0763903i	−0.912973	+	0.408020i	$0.866219\pi$
$858$	−7.01174	−	13.2256i	−0.239377	−	0.451513i
$859$	20.5090	+	12.3398i	0.699757	+	0.421030i	0.820494	−	0.571655i	$-0.193698\pi$
$859$	20.5090	+	12.3398i	0.699757	+	0.421030i	−0.120738	+	0.992684i	$0.538526\pi$
$860$	−39.7949	+	23.9438i	−1.35699	+	0.816476i
$861$	1.14519	−	2.16007i	0.0390281	−	0.0736148i
$862$	84.8705	+	9.23022i	2.89070	+	0.314383i
$863$	0.0713899	−	0.0542692i	0.00243014	−	0.00184734i	−0.603958	−	0.797016i	$-0.706411\pi$
$863$	0.0713899	−	0.0542692i	0.00243014	−	0.00184734i	0.606389	+	0.795168i	$0.292618\pi$
$864$	−13.7962	+	20.3479i	−0.469356	+	0.692248i
$865$	11.8519	−	72.2933i	0.402976	−	2.45804i
$866$	16.5640	−	41.5724i	0.562867	−	1.41269i
$867$	14.4653	−	1.57320i	0.491268	−	0.0534287i
$868$	4.79488	−	4.54195i	0.162749	−	0.154164i
$869$	20.8412	+	24.5361i	0.706988	+	0.832330i
$870$	−11.1660	+	5.16593i	−0.378562	+	0.175141i
$871$	6.76498	+	9.97760i	0.229223	+	0.338078i
$872$	−1.78345	−	0.600915i	−0.0603953	−	0.0203495i
$873$	−2.96326	+	10.6727i	−0.100291	+	0.361216i
$874$	−12.8533	+	15.1321i	−0.434769	+	0.511849i
$875$	0.241812	+	4.45995i	0.00817473	+	0.150774i
$876$	−58.1564	+	19.5952i	−1.96492	+	0.662060i
$877$	−41.5976	−	31.6216i	−1.40465	−	1.06779i	−0.987270	−	0.159055i	$-0.949155\pi$
$877$	−41.5976	−	31.6216i	−1.40465	−	1.06779i	−0.417380	−	0.908732i	$-0.637051\pi$
$878$	12.6859	+	12.0167i	0.428127	+	0.405543i
$879$	1.73287	−	31.9610i	0.0584484	−	1.07802i
$880$	−37.2136	−	134.031i	−1.25447	−	4.51819i
$881$	−21.2733	−	9.84207i	−0.716715	−	0.331588i	0.0274136	−	0.999624i	$-0.491273\pi$
$881$	−21.2733	−	9.84207i	−0.716715	−	0.331588i	−0.744128	+	0.668037i	$0.767135\pi$
$882$	−3.06712	−	18.7086i	−0.103275	−	0.629951i
$883$	47.6609	+	10.4910i	1.60392	+	0.353049i	0.924643	−	0.380835i	$-0.124363\pi$
$883$	47.6609	+	10.4910i	1.60392	+	0.353049i	0.679275	+	0.733884i	$0.262294\pi$
$884$	−72.6354			−2.44299
$885$	−20.0702	−	19.8418i	−0.674654	−	0.666975i
$886$	−41.5115			−1.39461
$887$	−49.5645	−	10.9100i	−1.66421	−	0.366321i	−0.719569	−	0.694421i	$-0.755660\pi$
$887$	−49.5645	−	10.9100i	−1.66421	−	0.366321i	−0.944643	+	0.328101i	$0.893591\pi$
$888$	−2.12536	−	12.9641i	−0.0713225	−	0.435048i
$889$	0.290535	+	0.134416i	0.00974423	+	0.00450816i
$890$	−42.8265	−	154.247i	−1.43555	−	5.17037i
$891$	−0.127227	+	2.34657i	−0.00426227	+	0.0786130i
$892$	−5.22675	−	4.95104i	−0.175005	−	0.165773i
$893$	−30.0384	−	22.8346i	−1.00520	−	0.764130i
$894$	10.6890	−	3.60153i	0.357493	−	0.120453i
$895$	1.07872	+	19.8958i	0.0360576	+	0.665043i
$896$	−10.9596	+	12.9026i	−0.366134	+	0.431046i
$897$	−0.688007	+	2.47798i	−0.0229719	+	0.0827372i
$898$	29.6672	+	9.99603i	0.990006	+	0.333572i
$899$	−2.31779	−	3.41849i	−0.0773027	−	0.114013i
$900$	43.1595	−	19.9677i	1.43865	−	0.665590i
$901$	16.9718	+	19.9808i	0.565414	+	0.665657i
$902$	33.0982	−	31.3523i	1.10205	−	1.04392i
$903$	0.780075	−	0.0848383i	0.0259593	−	0.00282324i
$904$	15.4673	−	38.8200i	0.514435	−	1.29114i
$905$	−7.79026	+	47.5185i	−0.258957	+	1.57957i
$906$	−15.8619	+	23.3946i	−0.526977	+	0.777233i
$907$	−18.8423	+	14.3236i	−0.625649	+	0.475606i	−0.869319	−	0.494252i	$-0.835442\pi$
$907$	−18.8423	+	14.3236i	−0.625649	+	0.475606i	0.243669	+	0.969858i	$0.421649\pi$
$908$	−38.0126	−	4.13412i	−1.26149	−	0.137196i
$909$	−2.10250	+	3.96573i	−0.0697355	+	0.131535i
$910$	6.96490	−	4.19064i	0.230884	−	0.138918i
$911$	−10.3970	−	6.25567i	−0.344468	−	0.207260i	0.332797	−	0.942998i	$-0.392008\pi$
$911$	−10.3970	−	6.25567i	−0.344468	−	0.207260i	−0.677265	+	0.735739i	$0.736835\pi$
$912$	−48.8621	−	92.1637i	−1.61799	−	3.05185i
$913$	−7.80064	−	19.5781i	−0.258164	−	0.647942i
$914$	61.4596	−	13.5283i	2.03290	−	0.447476i
$915$	−21.3345	+	4.69609i	−0.705298	+	0.155248i
$916$	9.92180	+	24.9018i	0.327826	+	0.822780i
$917$	0.619487	+	1.16848i	0.0204573	+	0.0385865i
$918$	13.2637	+	7.98048i	0.437766	+	0.263395i
$919$	35.1315	−	21.1379i	1.15888	−	0.697276i	0.199642	−	0.979869i	$-0.436022\pi$
$919$	35.1315	−	21.1379i	1.15888	−	0.697276i	0.959240	+	0.282593i	$0.0911945\pi$
$920$	−18.9685	+	35.7783i	−0.625372	+	1.17958i
$921$	11.8024	+	1.28359i	0.388901	+	0.0422956i
$922$	71.8780	−	54.6402i	2.36718	−	1.79948i
$923$	−14.7291	+	21.7237i	−0.484813	+	0.715046i
$924$	−0.738705	+	4.50590i	−0.0243016	+	0.148233i
$925$	−4.17255	+	10.4723i	−0.137192	+	0.344327i
$926$	60.9373	−	6.62733i	2.00252	−	0.217788i
$927$	−7.22159	+	6.84066i	−0.237188	+	0.224677i
$928$	19.3379	+	22.7663i	0.634796	+	0.747340i
$929$	11.8833	−	5.49782i	0.389880	−	0.180378i	−0.215149	−	0.976581i	$-0.569024\pi$
$929$	11.8833	−	5.49782i	0.389880	−	0.180378i	0.605029	+	0.796204i	$0.293162\pi$
$930$	19.3153	+	28.4880i	0.633374	+	0.934157i
$931$	42.2139	+	14.2235i	1.38350	+	0.466157i
$932$	−24.5723	+	88.5013i	−0.804891	+	2.89896i
$933$	2.81549	−	3.31466i	0.0921751	−	0.108517i
$934$	5.30955	+	97.9289i	0.173734	+	3.20433i
$935$	−45.9615	+	15.4862i	−1.50310	+	0.506454i
$936$	−18.2280	−	13.8565i	−0.595800	−	0.452915i
$937$	−9.88927	−	9.36762i	−0.323068	−	0.306027i	0.508926	−	0.860810i	$-0.330043\pi$
$937$	−9.88927	−	9.36762i	−0.323068	−	0.306027i	−0.831995	+	0.554783i	$0.812801\pi$
$938$	0.270237	−	4.98423i	0.00882355	−	0.162741i
$939$	5.75436	+	20.7253i	0.187787	+	0.676346i
$940$	−108.711	−	50.2951i	−3.54576	−	1.64044i
$941$	−3.44080	−	20.9879i	−0.112167	−	0.684187i	−0.981718	−	0.190343i	$-0.939040\pi$
$941$	−3.44080	−	20.9879i	−0.112167	−	0.684187i	0.869551	−	0.493843i	$-0.164408\pi$
$942$	5.64535	+	1.24264i	0.183936	+	0.0404873i
$943$	−7.83235			−0.255056
$944$	−60.2835	+	108.065i	−1.96206	+	3.51720i
$945$	−1.27607			−0.0415107
$946$	14.2900	+	3.14546i	0.464607	+	0.102268i
$947$	2.35278	+	14.3513i	0.0764552	+	0.466356i	0.997110	+	0.0759774i	$0.0242077\pi$
$947$	2.35278	+	14.3513i	0.0764552	+	0.466356i	−0.920654	+	0.390379i	$0.872344\pi$
$948$	69.5560	+	32.1801i	2.25908	+	1.04516i
$949$	−6.78318	−	24.4308i	−0.220191	−	0.793057i
$950$	−8.21194	+	151.460i	−0.266431	+	4.91402i
$951$	−10.1730	−	9.63634i	−0.329881	−	0.312480i
$952$	15.3840	+	11.6946i	0.498597	+	0.379023i
$953$	27.3041	−	9.19981i	0.884466	−	0.298011i	0.159831	−	0.987144i	$-0.448905\pi$
$953$	27.3041	−	9.19981i	0.884466	−	0.298011i	0.724635	+	0.689133i	$0.242009\pi$
$954$	0.696341	+	12.8432i	0.0225449	+	0.415815i
$955$	−55.5511	+	65.3999i	−1.79759	+	2.11629i
$956$	21.4997	−	77.4349i	0.695350	−	2.50442i
$957$	2.70591	+	0.911727i	0.0874696	+	0.0294720i
$958$	−10.9738	−	16.1852i	−0.354548	−	0.522920i
$959$	−0.500039	+	0.231342i	−0.0161471	+	0.00747044i
$960$	−84.5123	−	99.4956i	−2.72762	−	3.21121i
$961$	14.1174	−	13.3727i	0.455401	−	0.431379i
$962$	8.39819	−	0.913358i	0.270769	−	0.0294479i
$963$	0.123645	−	0.310326i	0.00398441	−	0.0100001i
$964$	26.2784	−	160.291i	0.846370	−	5.16263i
$965$	−43.1646	+	63.6630i	−1.38952	+	2.04939i
$966$	0.847741	−	0.644436i	0.0272756	−	0.0207344i
$967$	46.2643	+	5.03154i	1.48776	+	0.161804i	0.815606	−	0.578608i	$-0.196404\pi$
$967$	46.2643	+	5.03154i	1.48776	+	0.161804i	0.672153	+	0.740412i	$0.265370\pi$
$968$	25.4153	−	47.9384i	0.816880	−	1.54080i
$969$	−31.1651	+	18.7514i	−1.00117	+	0.602383i
$970$	−96.1014	−	57.8223i	−3.08563	−	1.85656i
$971$	17.4535	+	32.9209i	0.560111	+	1.05648i	0.988261	+	0.152774i	$0.0488206\pi$
$971$	17.4535	+	32.9209i	0.560111	+	1.05648i	−0.428150	+	0.903708i	$0.640835\pi$
$972$	2.07075	+	5.19720i	0.0664195	+	0.166700i
$973$	−1.88745	+	0.415459i	−0.0605088	+	0.0133190i
$974$	45.5731	−	10.0314i	1.46026	−	0.321427i
$975$	7.27231	+	18.2521i	0.232900	+	0.584536i
$976$	44.8645	+	84.6234i	1.43608	+	2.70873i
$977$	−26.5496	−	15.9743i	−0.849396	−	0.511065i	0.0230732	−	0.999734i	$-0.492655\pi$
$977$	−26.5496	−	15.9743i	−0.849396	−	0.511065i	−0.872469	+	0.488669i	$0.837483\pi$
$978$	26.3386	−	15.8474i	0.842215	−	0.506744i
$979$	−17.4027	+	32.8250i	−0.556193	+	1.04909i
$980$	140.582	+	15.2892i	4.49074	+	0.488397i
$981$	−0.151245	+	0.114974i	−0.00482888	+	0.00367082i
$982$	−47.1473	+	69.5371i	−1.50453	+	2.21902i
$983$	5.23429	−	31.9277i	0.166948	−	1.01834i	−0.761851	−	0.647752i	$-0.775709\pi$
$983$	5.23429	−	31.9277i	0.166948	−	1.01834i	0.928799	−	0.370584i	$-0.120843\pi$
$984$	25.8111	−	64.7811i	0.822829	−	2.06515i
$985$	60.3353	−	6.56186i	1.92244	−	0.209078i
$986$	13.6547	−	12.9344i	0.434854	−	0.411916i
$987$	1.31016	+	1.54244i	0.0417029	+	0.0490965i
$988$	75.9948	−	35.1589i	2.41772	−	1.11855i
$989$	−1.41070	−	2.08063i	−0.0448577	−	0.0661601i
$990$	−22.5497	−	7.59788i	−0.716677	−	0.241477i
$991$	3.43086	−	12.3568i	0.108985	−	0.392528i	−0.888858	−	0.458184i	$-0.848500\pi$
$991$	3.43086	−	12.3568i	0.108985	−	0.392528i	0.997842	+	0.0656560i	$0.0209140\pi$
$992$	54.0989	−	63.6902i	1.71764	−	2.02216i
$993$	0.0988513	+	1.82320i	0.00313695	+	0.0578577i
$994$	10.2990	−	3.47012i	0.326663	−	0.110066i
$995$	−61.3387	−	46.6285i	−1.94457	−	1.47822i
$996$	−36.4246	−	34.5032i	−1.15416	−	1.09327i
$997$	−3.11361	+	57.4272i	−0.0986091	+	1.81874i	0.363149	+	0.931731i	$0.381702\pi$
$997$	−3.11361	+	57.4272i	−0.0986091	+	1.81874i	−0.461758	+	0.887006i	$0.652781\pi$
$998$	1.17167	+	4.21999i	0.0370887	+	0.133581i
$999$	−1.20362	−	0.556856i	−0.0380810	−	0.0176181i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.2.e.b.16.1	✓	140
3.2	odd	2		531.2.i.b.370.5		140
59.48	even	29	inner	177.2.e.b.166.1	yes	140
177.107	odd	58		531.2.i.b.343.5		140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.2.e.b.16.1	✓	140	1.1	even	1	trivial
177.2.e.b.166.1	yes	140	59.48	even	29	inner
531.2.i.b.343.5		140	177.107	odd	58
531.2.i.b.370.5		140	3.2	odd	2

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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	177.e (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.69139 - 0.592420i) q^{2} +(0.161782 + 0.986827i) q^{3} +(5.07747 + 2.34909i) q^{4} +(0.982969 + 3.54033i) q^{5} +(0.149197 - 2.75178i) q^{6} +(-0.252139 - 0.238838i) q^{7} +(-7.88603 - 5.99480i) q^{8} +(-0.947653 + 0.319302i) q^{9} +O(q^{10})\)	\(q+(-2.69139 - 0.592420i) q^{2} +(0.161782 + 0.986827i) q^{3} +(5.07747 + 2.34909i) q^{4} +(0.982969 + 3.54033i) q^{5} +(0.149197 - 2.75178i) q^{6} +(-0.252139 - 0.238838i) q^{7} +(-7.88603 - 5.99480i) q^{8} +(-0.947653 + 0.319302i) q^{9} +(-0.548189 - 10.1108i) q^{10} +(-1.52137 + 1.79109i) q^{11} +(-1.49670 + 5.39062i) q^{12} +(-2.19043 - 0.738042i) q^{13} +(0.537111 + 0.792179i) q^{14} +(-3.33467 + 1.54278i) q^{15} +(10.4293 + 12.2783i) q^{16} +(4.07791 - 3.86280i) q^{17} +(2.73967 - 0.297957i) q^{18} +(-2.39674 + 6.01536i) q^{19} +(-3.32556 + 20.2850i) q^{20} +(0.194901 - 0.287457i) q^{21} +(5.15567 - 3.91924i) q^{22} +(-1.10609 - 0.120294i) q^{23} +(4.64001 - 8.75199i) q^{24} +(-7.28345 + 4.38231i) q^{25} +(5.45807 + 3.28401i) q^{26} +(-0.468408 - 0.883512i) q^{27} +(-0.719174 - 1.80499i) q^{28} +(-1.18664 + 0.261199i) q^{29} +(9.88887 - 2.17671i) q^{30} +(1.25816 + 3.15775i) q^{31} +(-11.5153 - 21.7202i) q^{32} +(-2.01363 - 1.21156i) q^{33} +(-13.2637 + 7.98048i) q^{34} +(0.597723 - 1.12743i) q^{35} +(-5.56175 - 0.604876i) q^{36} +(1.05578 - 0.802581i) q^{37} +(10.0142 - 14.7698i) q^{38} +(0.373947 - 2.28098i) q^{39} +(13.4719 - 33.8119i) q^{40} +(6.99835 - 0.761116i) q^{41} +(-0.694849 + 0.658196i) q^{42} +(1.46267 + 1.72199i) q^{43} +(-11.9321 + 5.52039i) q^{44} +(-2.06195 - 3.04115i) q^{45} +(2.90565 + 0.979027i) q^{46} +(-1.55893 + 5.61475i) q^{47} +(-10.4293 + 12.2783i) q^{48} +(-0.372442 - 6.86929i) q^{49} +(22.1988 - 7.47964i) q^{50} +(4.47165 + 3.39926i) q^{51} +(-9.38812 - 8.89290i) q^{52} +(-0.252680 + 4.66041i) q^{53} +(0.737260 + 2.65537i) q^{54} +(-7.83652 - 3.62556i) q^{55} +(0.556583 + 3.39501i) q^{56} +(-6.32386 - 1.39199i) q^{57} +3.34845 q^{58} +(2.69004 + 7.19470i) q^{59} -20.5558 q^{60} +(5.80648 + 1.27810i) q^{61} +(-1.51549 - 9.24411i) q^{62} +(0.315201 + 0.145828i) q^{63} +(9.50509 + 34.2342i) q^{64} +(0.459790 - 8.48033i) q^{65} +(4.70171 + 4.45369i) q^{66} +(-4.15186 - 3.15616i) q^{67} +(29.7795 - 10.0339i) q^{68} +(-0.0602355 - 1.11098i) q^{69} +(-2.27662 + 2.68024i) q^{70} +(3.03779 - 10.9411i) q^{71} +(9.38737 + 3.16297i) q^{72} +(6.15590 + 9.07927i) q^{73} +(-3.31697 + 1.53460i) q^{74} +(-5.50291 - 6.47853i) q^{75} +(-26.3000 + 24.9127i) q^{76} +(0.811377 - 0.0882426i) q^{77} +(-2.35773 + 5.91746i) q^{78} +(2.21624 - 13.5185i) q^{79} +(-33.2176 + 48.9923i) q^{80} +(0.796093 - 0.605174i) q^{81} +(-19.2862 - 2.09750i) q^{82} +(-4.20069 + 7.92334i) q^{83} +(1.66486 - 1.00171i) q^{84} +(17.6841 + 10.6402i) q^{85} +(-2.91648 - 5.50107i) q^{86} +(-0.449735 - 1.12875i) q^{87} +(22.7348 - 5.00431i) q^{88} +(15.4400 - 3.39860i) q^{89} +(3.74787 + 9.40645i) q^{90} +(0.376019 + 0.709248i) q^{91} +(-5.33355 - 3.20909i) q^{92} +(-2.91261 + 1.75246i) q^{93} +(7.52197 - 14.1879i) q^{94} +(-23.6523 - 2.57234i) q^{95} +(19.5711 - 14.8776i) q^{96} +(6.21596 - 9.16785i) q^{97} +(-3.06712 + 18.7086i) q^{98} +(0.869830 - 2.18311i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q + q^{2} + 5 q^{3} - q^{4} + 2 q^{5} - q^{6} - 2 q^{7} - 3 q^{8} - 5 q^{9}+O(q^{10}) \) 140 * q + q^2 + 5 * q^3 - q^4 + 2 * q^5 - q^6 - 2 * q^7 - 3 * q^8 - 5 * q^9	\( 140 q + q^{2} + 5 q^{3} - q^{4} + 2 q^{5} - q^{6} - 2 q^{7} - 3 q^{8} - 5 q^{9} - 116 q^{10} + 2 q^{11} + q^{12} + 4 q^{13} - 43 q^{14} - 2 q^{15} + 7 q^{16} + q^{18} - 2 q^{19} + 4 q^{20} - 27 q^{21} + 6 q^{22} + 6 q^{23} + 3 q^{24} - 57 q^{25} + 12 q^{26} + 5 q^{27} - 10 q^{28} - 4 q^{29} - 12 q^{31} - 150 q^{32} - 2 q^{33} - 2 q^{34} + 6 q^{35} - q^{36} + 12 q^{37} - 12 q^{38} - 4 q^{39} - 66 q^{40} - 4 q^{41} + 14 q^{42} - 60 q^{43} + 20 q^{44} + 2 q^{45} + 76 q^{46} - 25 q^{47} - 7 q^{48} + 31 q^{49} + 137 q^{50} + 118 q^{52} + 48 q^{53} - q^{54} + 93 q^{55} + 228 q^{56} + 2 q^{57} - 120 q^{58} + 57 q^{59} - 4 q^{60} + 72 q^{61} - 179 q^{62} - 2 q^{63} + 249 q^{64} - 39 q^{65} - 6 q^{66} + 40 q^{67} + 94 q^{68} - 64 q^{69} + 94 q^{70} + 30 q^{71} - 3 q^{72} - 205 q^{73} + 66 q^{74} - q^{75} - 216 q^{76} - 46 q^{77} - 12 q^{78} + 4 q^{79} - 356 q^{80} - 5 q^{81} - 28 q^{82} + 4 q^{83} - 135 q^{84} + 50 q^{85} - 18 q^{86} - 54 q^{87} - 162 q^{88} + 26 q^{89} - 198 q^{91} + 10 q^{92} + 12 q^{93} - 4 q^{94} - 326 q^{95} + 5 q^{96} - 20 q^{97} - 143 q^{98} + 2 q^{99}+O(q^{100}) \) 140 * q + q^2 + 5 * q^3 - q^4 + 2 * q^5 - q^6 - 2 * q^7 - 3 * q^8 - 5 * q^9 - 116 * q^10 + 2 * q^11 + q^12 + 4 * q^13 - 43 * q^14 - 2 * q^15 + 7 * q^16 + q^18 - 2 * q^19 + 4 * q^20 - 27 * q^21 + 6 * q^22 + 6 * q^23 + 3 * q^24 - 57 * q^25 + 12 * q^26 + 5 * q^27 - 10 * q^28 - 4 * q^29 - 12 * q^31 - 150 * q^32 - 2 * q^33 - 2 * q^34 + 6 * q^35 - q^36 + 12 * q^37 - 12 * q^38 - 4 * q^39 - 66 * q^40 - 4 * q^41 + 14 * q^42 - 60 * q^43 + 20 * q^44 + 2 * q^45 + 76 * q^46 - 25 * q^47 - 7 * q^48 + 31 * q^49 + 137 * q^50 + 118 * q^52 + 48 * q^53 - q^54 + 93 * q^55 + 228 * q^56 + 2 * q^57 - 120 * q^58 + 57 * q^59 - 4 * q^60 + 72 * q^61 - 179 * q^62 - 2 * q^63 + 249 * q^64 - 39 * q^65 - 6 * q^66 + 40 * q^67 + 94 * q^68 - 64 * q^69 + 94 * q^70 + 30 * q^71 - 3 * q^72 - 205 * q^73 + 66 * q^74 - q^75 - 216 * q^76 - 46 * q^77 - 12 * q^78 + 4 * q^79 - 356 * q^80 - 5 * q^81 - 28 * q^82 + 4 * q^83 - 135 * q^84 + 50 * q^85 - 18 * q^86 - 54 * q^87 - 162 * q^88 + 26 * q^89 - 198 * q^91 + 10 * q^92 + 12 * q^93 - 4 * q^94 - 326 * q^95 + 5 * q^96 - 20 * q^97 - 143 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

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Database

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