LMFDB - Embedded newform 552.2.t.a.451.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(19,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 0, 15]))

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

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

chi := DirichletCharacter("552.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.t (of order $22$, degree $10$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			451.13
Character	$\chi$	$=$	552.451
Dual form			552.2.t.a.235.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.347362 + 1.37089i) q^{2} +(0.654861 + 0.755750i) q^{3} +(-1.75868 + 0.952390i) q^{4} +(0.441718 + 3.07221i) q^{5} +(-0.808576 + 1.16026i) q^{6} +(-1.53367 + 3.35827i) q^{7} +(-1.91652 - 2.08013i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(0.347362 + 1.37089i) q^{2} +(0.654861 + 0.755750i) q^{3} +(-1.75868 + 0.952390i) q^{4} +(0.441718 + 3.07221i) q^{5} +(-0.808576 + 1.16026i) q^{6} +(-1.53367 + 3.35827i) q^{7} +(-1.91652 - 2.08013i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(-4.05823 + 1.67272i) q^{10} +(0.0724295 - 0.246672i) q^{11} +(-1.87146 - 0.705438i) q^{12} +(5.35488 - 2.44549i) q^{13} +(-5.13655 - 0.935958i) q^{14} +(-2.03256 + 2.34570i) q^{15} +(2.18591 - 3.34990i) q^{16} +(1.69694 - 2.64049i) q^{17} +(-1.40637 + 0.148728i) q^{18} +(-1.92513 - 2.99556i) q^{19} +(-3.70279 - 4.98235i) q^{20} +(-3.54235 + 1.04013i) q^{21} +(0.363320 + 0.0136083i) q^{22} +(-1.99173 - 4.36268i) q^{23} +(0.317005 - 2.81061i) q^{24} +(-4.44592 + 1.30544i) q^{25} +(5.21258 + 6.49148i) q^{26} +(-0.841254 + 0.540641i) q^{27} +(-0.501148 - 7.36676i) q^{28} +(-4.01055 + 6.24053i) q^{29} +(-3.92173 - 1.97161i) q^{30} +(7.88409 + 6.83161i) q^{31} +(5.35164 + 1.83301i) q^{32} +(0.233854 - 0.106797i) q^{33} +(4.20928 + 1.40911i) q^{34} +(-10.9948 - 3.22835i) q^{35} +(-0.692410 - 1.87632i) q^{36} +(0.699014 - 4.86175i) q^{37} +(3.43787 - 3.67968i) q^{38} +(5.35488 + 2.44549i) q^{39} +(5.54405 - 6.80679i) q^{40} +(0.377327 + 2.62437i) q^{41} +(-2.65638 - 4.49487i) q^{42} +(-4.72925 + 4.09791i) q^{43} +(0.107548 + 0.502798i) q^{44} -3.10381 q^{45} +(5.28891 - 4.24588i) q^{46} +12.3891i q^{47} +(3.96315 - 0.541718i) q^{48} +(-4.34179 - 5.01069i) q^{49} +(-3.33396 - 5.64141i) q^{50} +(3.10681 - 0.446692i) q^{51} +(-7.08845 + 9.40076i) q^{52} +(-2.05165 + 4.49249i) q^{53} +(-1.03338 - 0.965468i) q^{54} +(0.789823 + 0.113559i) q^{55} +(9.92495 - 3.24595i) q^{56} +(1.00320 - 3.41659i) q^{57} +(-9.94820 - 3.33030i) q^{58} +(2.01001 + 4.40132i) q^{59} +(1.34060 - 6.06113i) q^{60} +(1.41239 - 1.62998i) q^{61} +(-6.62675 + 13.1813i) q^{62} +(-3.10582 - 1.99599i) q^{63} +(-0.653900 + 7.97323i) q^{64} +(9.87841 + 15.3711i) q^{65} +(0.227639 + 0.283490i) q^{66} +(-2.74344 - 9.34331i) q^{67} +(-0.469597 + 6.25993i) q^{68} +(1.99279 - 4.36220i) q^{69} +(0.606556 - 16.1940i) q^{70} +(-2.77882 - 9.46378i) q^{71} +(2.33171 - 1.60098i) q^{72} +(9.51353 - 6.11398i) q^{73} +(6.90774 - 0.730515i) q^{74} +(-3.89805 - 2.50512i) q^{75} +(6.23863 + 3.43475i) q^{76} +(0.717308 + 0.621551i) q^{77} +(-1.49242 + 8.19042i) q^{78} +(-3.04965 - 6.67779i) q^{79} +(11.2572 + 5.23586i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-3.46665 + 1.42888i) q^{82} +(-2.47700 - 0.356138i) q^{83} +(5.23925 - 5.20295i) q^{84} +(8.86173 + 4.04702i) q^{85} +(-7.26055 - 5.05982i) q^{86} +(-7.34263 + 1.05571i) q^{87} +(-0.651923 + 0.322089i) q^{88} +(12.0123 - 10.4087i) q^{89} +(-1.07814 - 4.25498i) q^{90} +21.7337i q^{91} +(7.65779 + 5.77566i) q^{92} +10.4322i q^{93} +(-16.9841 + 4.30350i) q^{94} +(8.35264 - 7.23760i) q^{95} +(2.11928 + 5.24487i) q^{96} +(14.6695 - 2.10915i) q^{97} +(5.36093 - 7.69264i) q^{98} +(0.233854 + 0.106797i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9}+O(q^{10}) $ 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9	$ 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9} + 4 q^{12} - 4 q^{16} + 44 q^{17} - 55 q^{20} - 24 q^{25} + 24 q^{27} + 33 q^{34} + 7 q^{36} - 132 q^{38} + 11 q^{40} - 66 q^{42} + 77 q^{44} + 37 q^{48} - 56 q^{49} - 37 q^{50} - 55 q^{52} - 11 q^{54} + 132 q^{56} + 37 q^{58} + 11 q^{60} + 51 q^{62} - 4 q^{64} - 55 q^{66} - 132 q^{70} + 144 q^{73} + 44 q^{74} + 24 q^{75} - 55 q^{76} - 198 q^{80} - 24 q^{81} - 26 q^{82} + 44 q^{84} - 110 q^{86} + 22 q^{88} - 139 q^{92} - 117 q^{94} - 209 q^{98}+O(q^{100}) $ 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9 + 4 * q^12 - 4 * q^16 + 44 * q^17 - 55 * q^20 - 24 * q^25 + 24 * q^27 + 33 * q^34 + 7 * q^36 - 132 * q^38 + 11 * q^40 - 66 * q^42 + 77 * q^44 + 37 * q^48 - 56 * q^49 - 37 * q^50 - 55 * q^52 - 11 * q^54 + 132 * q^56 + 37 * q^58 + 11 * q^60 + 51 * q^62 - 4 * q^64 - 55 * q^66 - 132 * q^70 + 144 * q^73 + 44 * q^74 + 24 * q^75 - 55 * q^76 - 198 * q^80 - 24 * q^81 - 26 * q^82 + 44 * q^84 - 110 * q^86 + 22 * q^88 - 139 * q^92 - 117 * q^94 - 209 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{21}{22}\right)$	$1$	$-1$	$-1$

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 $

$2$	0.347362	+	1.37089i	0.245622	+	0.969366i
$2$	0.347362	+	1.37089i	0.245622	+	0.969366i
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$4$	−1.75868	+	0.952390i	−0.879340	+	0.476195i
$5$	0.441718	+	3.07221i	0.197542	+	1.37394i	0.811387	+	0.584509i	$0.198713\pi$
$5$	0.441718	+	3.07221i	0.197542	+	1.37394i	−0.613845	+	0.789427i	$0.710378\pi$
$6$	−0.808576	+	1.16026i	−0.330100	+	0.473674i
$7$	−1.53367	+	3.35827i	−0.579672	+	1.26931i	0.361813	+	0.932251i	$0.382158\pi$
$7$	−1.53367	+	3.35827i	−0.579672	+	1.26931i	−0.941485	+	0.337055i	$0.890569\pi$
$8$	−1.91652	−	2.08013i	−0.677592	−	0.735438i
$9$	−0.142315	+	0.989821i	−0.0474383	+	0.329940i
$10$	−4.05823	+	1.67272i	−1.28333	+	0.528960i
$11$	0.0724295	−	0.246672i	0.0218383	−	0.0743745i	−0.947853	−	0.318708i	$-0.896751\pi$
$11$	0.0724295	−	0.246672i	0.0218383	−	0.0743745i	0.969691	+	0.244334i	$0.0785692\pi$
$12$	−1.87146	−	0.705438i	−0.540244	−	0.203643i
$13$	5.35488	−	2.44549i	1.48518	−	0.678257i	0.502668	−	0.864480i	$-0.332352\pi$
$13$	5.35488	−	2.44549i	1.48518	−	0.678257i	0.982508	+	0.186223i	$0.0596247\pi$
$14$	−5.13655	−	0.935958i	−1.37280	−	0.250145i
$15$	−2.03256	+	2.34570i	−0.524805	+	0.605657i
$16$	2.18591	−	3.34990i	0.546477	−	0.837474i
$17$	1.69694	−	2.64049i	0.411569	−	0.640413i	−0.572146	−	0.820152i	$-0.693889\pi$
$17$	1.69694	−	2.64049i	0.411569	−	0.640413i	0.983714	+	0.179739i	$0.0575252\pi$
$18$	−1.40637	+	0.148728i	−0.331485	+	0.0350556i
$19$	−1.92513	−	2.99556i	−0.441655	−	0.687228i	0.547051	−	0.837099i	$-0.315750\pi$
$19$	−1.92513	−	2.99556i	−0.441655	−	0.687228i	−0.988706	+	0.149871i	$0.952114\pi$
$20$	−3.70279	−	4.98235i	−0.827968	−	1.11409i
$21$	−3.54235	+	1.04013i	−0.773004	+	0.226974i
$22$	0.363320	+	0.0136083i	0.0774600	+	0.00290131i
$23$	−1.99173	−	4.36268i	−0.415305	−	0.909682i
$23$	−1.99173	−	4.36268i	−0.415305	−	0.909682i
$24$	0.317005	−	2.81061i	0.0647084	−	0.573713i
$25$	−4.44592	+	1.30544i	−0.889185	+	0.261088i
$26$	5.21258	+	6.49148i	1.02227	+	1.27308i
$27$	−0.841254	+	0.540641i	−0.161899	+	0.104046i
$28$	−0.501148	−	7.36676i	−0.0947080	−	1.39219i
$29$	−4.01055	+	6.24053i	−0.744740	+	1.15884i	0.237533	+	0.971380i	$0.423661\pi$
$29$	−4.01055	+	6.24053i	−0.744740	+	1.15884i	−0.982273	+	0.187458i	$0.939975\pi$
$30$	−3.92173	−	1.97161i	−0.716007	−	0.359965i
$31$	7.88409	+	6.83161i	1.41603	+	1.22699i	0.937064	+	0.349156i	$0.113532\pi$
$31$	7.88409	+	6.83161i	1.41603	+	1.22699i	0.478961	+	0.877836i	$0.341014\pi$
$32$	5.35164	+	1.83301i	0.946046	+	0.324034i
$33$	0.233854	−	0.106797i	0.0407087	−	0.0185910i
$34$	4.20928	+	1.40911i	0.721885	+	0.241661i
$35$	−10.9948	−	3.22835i	−1.85845	−	0.545691i
$36$	−0.692410	−	1.87632i	−0.115402	−	0.312720i
$37$	0.699014	−	4.86175i	0.114917	−	0.799267i	−0.848102	−	0.529833i	$-0.822254\pi$
$37$	0.699014	−	4.86175i	0.114917	−	0.799267i	0.963019	−	0.269434i	$-0.0868365\pi$
$38$	3.43787	−	3.67968i	0.557696	−	0.596923i
$39$	5.35488	+	2.44549i	0.857466	+	0.391592i
$40$	5.54405	−	6.80679i	0.876592	−	1.07625i
$41$	0.377327	+	2.62437i	0.0589286	+	0.409858i	0.997840	+	0.0656975i	$0.0209272\pi$
$41$	0.377327	+	2.62437i	0.0589286	+	0.409858i	−0.938911	+	0.344160i	$0.888164\pi$
$42$	−2.65638	−	4.49487i	−0.409888	−	0.693573i
$43$	−4.72925	+	4.09791i	−0.721203	+	0.624926i	−0.936110	−	0.351709i	$-0.885601\pi$
$43$	−4.72925	+	4.09791i	−0.721203	+	0.624926i	0.214906	+	0.976635i	$0.431055\pi$
$44$	0.107548	+	0.502798i	0.0162135	+	0.0757997i
$45$	−3.10381			−0.462688
$46$	5.28891	−	4.24588i	0.779807	−	0.626020i
$47$			12.3891i			1.80713i	0.428446	+	0.903567i	$0.359061\pi$
$47$			12.3891i			1.80713i	−0.428446	+	0.903567i	$0.640939\pi$
$48$	3.96315	−	0.541718i	0.572031	−	0.0781903i
$49$	−4.34179	−	5.01069i	−0.620255	−	0.715813i
$50$	−3.33396	−	5.64141i	−0.471493	−	0.797816i
$51$	3.10681	−	0.446692i	0.435041	−	0.0625494i
$52$	−7.08845	+	9.40076i	−0.982991	+	1.30365i
$53$	−2.05165	+	4.49249i	−0.281816	+	0.617091i	−0.996612	−	0.0822417i	$-0.973792\pi$
$53$	−2.05165	+	4.49249i	−0.281816	+	0.617091i	0.714796	+	0.699333i	$0.246519\pi$
$54$	−1.03338	−	0.965468i	−0.140625	−	0.131384i
$55$	0.789823	+	0.113559i	0.106500	+	0.0153124i
$56$	9.92495	−	3.24595i	1.32628	−	0.433759i
$57$	1.00320	−	3.41659i	0.132877	−	0.452538i
$58$	−9.94820	−	3.33030i	−1.30626	−	0.437289i
$59$	2.01001	+	4.40132i	0.261681	+	0.573003i	0.994176	−	0.107771i	$-0.0343712\pi$
$59$	2.01001	+	4.40132i	0.261681	+	0.573003i	−0.732494	+	0.680773i	$0.761644\pi$
$60$	1.34060	−	6.06113i	0.173071	−	0.782488i
$61$	1.41239	−	1.62998i	0.180837	−	0.208697i	−0.658092	−	0.752937i	$-0.728636\pi$
$61$	1.41239	−	1.62998i	0.180837	−	0.208697i	0.838930	+	0.544240i	$0.183182\pi$
$62$	−6.62675	+	13.1813i	−0.841598	+	1.67402i
$63$	−3.10582	−	1.99599i	−0.391297	−	0.251471i
$64$	−0.653900	+	7.97323i	−0.0817375	+	0.996654i
$65$	9.87841	+	15.3711i	1.22527	+	1.90655i
$66$	0.227639	+	0.283490i	0.0280205	+	0.0348952i
$67$	−2.74344	−	9.34331i	−0.335165	−	1.14147i	−0.938874	−	0.344262i	$-0.888129\pi$
$67$	−2.74344	−	9.34331i	−0.335165	−	1.14147i	0.603709	−	0.797205i	$-0.293689\pi$
$68$	−0.469597	+	6.25993i	−0.0569470	+	0.759128i
$69$	1.99279	−	4.36220i	0.239904	−	0.525147i
$70$	0.606556	−	16.1940i	0.0724974	−	1.93556i
$71$	−2.77882	−	9.46378i	−0.329785	−	1.12314i	−0.942879	−	0.333134i	$-0.891894\pi$
$71$	−2.77882	−	9.46378i	−0.329785	−	1.12314i	0.613095	−	0.790009i	$-0.289924\pi$
$72$	2.33171	−	1.60098i	0.274795	−	0.188677i
$73$	9.51353	−	6.11398i	1.11347	−	0.715587i	0.151427	−	0.988468i	$-0.451613\pi$
$73$	9.51353	−	6.11398i	1.11347	−	0.715587i	0.962048	+	0.272882i	$0.0879767\pi$
$74$	6.90774	−	0.730515i	0.803008	−	0.0849207i
$75$	−3.89805	−	2.50512i	−0.450108	−	0.289267i
$76$	6.23863	+	3.43475i	0.715619	+	0.393993i
$77$	0.717308	+	0.621551i	0.0817448	+	0.0708323i
$78$	−1.49242	+	8.19042i	−0.168983	+	0.927382i
$79$	−3.04965	−	6.67779i	−0.343112	−	0.751310i	0.656885	−	0.753991i	$-0.271874\pi$
$79$	−3.04965	−	6.67779i	−0.343112	−	0.751310i	−0.999996	+	0.00268099i	$0.999147\pi$
$80$	11.2572	+	5.23586i	1.25859	+	0.585387i
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$	−3.46665	+	1.42888i	−0.382828	+	0.157793i
$83$	−2.47700	−	0.356138i	−0.271886	−	0.0390913i	0.00502342	−	0.999987i	$-0.498401\pi$
$83$	−2.47700	−	0.356138i	−0.271886	−	0.0390913i	−0.276909	+	0.960896i	$0.589310\pi$
$84$	5.23925	−	5.20295i	0.571649	−	0.567688i
$85$	8.86173	+	4.04702i	0.961189	+	0.438961i
$86$	−7.26055	−	5.05982i	−0.782925	−	0.545614i
$87$	−7.34263	+	1.05571i	−0.787212	+	0.113184i
$88$	−0.651923	+	0.322089i	−0.0694953	+	0.0343348i
$89$	12.0123	−	10.4087i	1.27330	−	1.10332i	0.283785	−	0.958888i	$-0.408410\pi$
$89$	12.0123	−	10.4087i	1.27330	−	1.10332i	0.989515	−	0.144432i	$-0.0461356\pi$
$90$	−1.07814	−	4.25498i	−0.113646	−	0.448514i
$91$			21.7337i			2.27831i
$92$	7.65779	+	5.77566i	0.798380	+	0.602154i
$93$			10.4322i			1.08176i
$94$	−16.9841	+	4.30350i	−1.75177	+	0.443872i
$95$	8.35264	−	7.23760i	0.856962	−	0.742562i
$96$	2.11928	+	5.24487i	0.216298	+	0.535302i
$97$	14.6695	−	2.10915i	1.48946	−	0.214152i	0.650985	−	0.759090i	$-0.274356\pi$
$97$	14.6695	−	2.10915i	1.48946	−	0.214152i	0.838476	+	0.544938i	$0.183447\pi$
$98$	5.36093	−	7.69264i	0.541536	−	0.777074i
$99$	0.233854	+	0.106797i	0.0235032	+	0.0107335i
$100$	6.57566	−	6.53010i	0.657566	−	0.653010i
$101$	−2.04888	−	0.294585i	−0.203871	−	0.0293123i	0.0396225	−	0.999215i	$-0.487384\pi$
$101$	−2.04888	−	0.294585i	−0.203871	−	0.0293123i	−0.243494	+	0.969902i	$0.578294\pi$
$102$	1.69155	+	4.10393i	0.167489	+	0.406350i
$103$	−10.3649	−	3.04341i	−1.02129	−	0.299876i	−0.272123	−	0.962263i	$-0.587726\pi$
$103$	−10.3649	−	3.04341i	−1.02129	−	0.299876i	−0.749163	+	0.662386i	$0.769544\pi$
$104$	−15.3497	−	6.45202i	−1.50516	−	0.632672i
$105$	−4.76021	−	10.4234i	−0.464549	−	1.01722i
$106$	−6.87137	−	1.25207i	−0.667407	−	0.121612i
$107$	1.95540	+	1.69436i	0.189035	+	0.163800i	0.744237	−	0.667916i	$-0.232813\pi$
$107$	1.95540	+	1.69436i	0.189035	+	0.163800i	−0.555202	+	0.831716i	$0.687359\pi$
$108$	0.964594	−	1.75202i	0.0928181	−	0.168588i
$109$	−8.17194	−	5.25179i	−0.782730	−	0.503030i	0.0872086	−	0.996190i	$-0.472205\pi$
$109$	−8.17194	−	5.25179i	−0.782730	−	0.503030i	−0.869939	+	0.493160i	$0.835842\pi$
$110$	0.118677	+	1.12221i	0.0113154	+	0.106998i
$111$	4.13202	−	2.65549i	0.392194	−	0.252048i
$112$	7.89739	+	12.4785i	0.746233	+	1.17911i
$113$	4.52936	+	15.4256i	0.426086	+	1.45112i	0.840891	+	0.541205i	$0.182032\pi$
$113$	4.52936	+	15.4256i	0.426086	+	1.45112i	−0.414805	+	0.909911i	$0.636150\pi$
$114$	5.03224	+	0.188486i	0.471313	+	0.0176533i
$115$	12.5233	−	8.04610i	1.16781	−	0.750303i
$116$	1.10985	−	14.7947i	0.103047	−	1.37365i
$117$	1.65852	+	5.64840i	0.153330	+	0.522195i
$118$	−5.33552	+	4.28436i	−0.491174	+	0.394407i
$119$	6.26493	+	9.74842i	0.574305	+	0.893636i
$120$	8.77481	−	0.267587i	0.801027	−	0.0244272i
$121$	9.19819	+	5.91132i	0.836199	+	0.537392i
$122$	2.72513	+	1.37003i	0.246722	+	0.124037i
$123$	−1.73627	+	2.00376i	−0.156554	+	0.180673i
$124$	−20.3719	−	4.50587i	−1.82945	−	0.404639i
$125$	0.472402	+	1.03442i	0.0422529	+	0.0925210i
$126$	1.65744	−	4.95107i	0.147656	−	0.441076i
$127$	−1.37688	+	4.68924i	−0.122179	+	0.416103i	−0.997754	−	0.0669783i	$-0.978664\pi$
$127$	−1.37688	+	4.68924i	−0.122179	+	0.416103i	0.875576	+	0.483081i	$0.160482\pi$
$128$	−11.1576	+	1.87317i	−0.986199	+	0.165567i
$129$	−6.19399	−	0.890562i	−0.545351	−	0.0784096i
$130$	−17.6407	+	18.8816i	−1.54719	+	1.65602i
$131$	−2.57745	+	5.64384i	−0.225193	+	0.493104i	−0.988178	−	0.153312i	$-0.951006\pi$
$131$	−2.57745	+	5.64384i	−0.225193	+	0.493104i	0.762985	+	0.646417i	$0.223733\pi$
$132$	−0.309561	+	0.410542i	−0.0269438	+	0.0357331i
$133$	13.0124	−	1.87090i	1.12832	−	0.162228i
$134$	11.8557	−	7.00647i	1.02417	−	0.605267i
$135$	−2.03256	−	2.34570i	−0.174935	−	0.201886i
$136$	−8.74480	+	1.53069i	−0.749860	+	0.131256i
$137$		−	3.13781i		−	0.268081i	−0.990976	−	0.134041i	$-0.957205\pi$
$137$		−	3.13781i		−	0.268081i	0.990976	−	0.134041i	$-0.0427953\pi$
$138$	6.67232	+	1.21663i	0.567985	+	0.103567i
$139$	−2.13658			−0.181222			−0.0906110	−	0.995886i	$-0.528882\pi$
$139$	−2.13658			−0.181222			−0.0906110	+	0.995886i	$0.528882\pi$
$140$	22.4109	−	4.79366i	1.89407	−	0.405139i
$141$	−9.36305	+	8.11313i	−0.788511	+	0.683249i
$142$	12.0085	−	7.09681i	1.00773	−	0.595551i
$143$	−0.215383	−	1.49802i	−0.0180113	−	0.125271i
$144$	3.00471	+	2.64040i	0.250393	+	0.220033i
$145$	−20.9438	−	9.56471i	−1.73929	−	0.794306i
$146$	11.6862	+	10.9182i	0.967159	+	0.903600i
$147$	0.943561	−	6.56261i	0.0778236	−	0.541275i
$148$	3.40094	+	9.21600i	0.279556	+	0.757550i
$149$	−13.2654	−	3.89509i	−1.08675	−	0.319098i	−0.311173	−	0.950353i	$-0.600722\pi$
$149$	−13.2654	−	3.89509i	−1.08675	−	0.319098i	−0.775575	+	0.631255i	$0.782540\pi$
$150$	2.08021	−	6.21398i	0.169849	−	0.507369i
$151$	7.45411	−	3.40418i	0.606607	−	0.277028i	−0.0883387	−	0.996090i	$-0.528156\pi$
$151$	7.45411	−	3.40418i	0.606607	−	0.277028i	0.694945	+	0.719062i	$0.255429\pi$
$152$	−2.54161	+	9.74557i	−0.206152	+	0.790470i
$153$	2.37212	+	2.05545i	0.191774	+	0.166173i
$154$	−0.602913	+	1.19925i	−0.0485841	+	0.0966386i
$155$	−17.5056	+	27.2393i	−1.40609	+	2.18791i
$156$	−11.7466	+	0.799098i	−0.940478	+	0.0639790i
$157$	0.318954	−	0.204979i	0.0254553	−	0.0163591i	−0.527851	−	0.849337i	$-0.677002\pi$
$157$	0.318954	−	0.204979i	0.0254553	−	0.0163591i	0.553307	+	0.832978i	$0.313366\pi$
$158$	8.09519	−	6.50034i	0.644019	−	0.517139i
$159$	−4.73874	+	1.39142i	−0.375807	+	0.110347i
$160$	−3.26749	+	17.2511i	−0.258318	+	1.36382i
$161$	17.7057	+	0.00214493i	1.39541	+	0.000169044i
$162$	0.0529331	−	1.41322i	0.00415881	−	0.111033i
$163$	−3.13869	+	0.921603i	−0.245841	+	0.0721855i	−0.402332	−	0.915494i	$-0.631800\pi$
$163$	−3.13869	+	0.921603i	−0.245841	+	0.0721855i	0.156490	+	0.987679i	$0.449982\pi$
$164$	−3.16302	−	4.25606i	−0.246990	−	0.332343i
$165$	0.431402	+	0.671274i	0.0335846	+	0.0522586i
$166$	−0.372188	−	3.51940i	−0.0288874	−	0.273158i
$167$	−9.54486	+	14.8521i	−0.738603	+	1.14929i	0.245102	+	0.969497i	$0.421179\pi$
$167$	−9.54486	+	14.8521i	−0.738603	+	1.14929i	−0.983705	+	0.179792i	$0.942458\pi$
$168$	8.95258	+	5.37513i	0.690707	+	0.414700i
$169$	14.1811	−	16.3658i	1.09085	−	1.25891i
$170$	−2.46979	+	13.5542i	−0.189424	+	1.03956i
$171$	3.23904	−	1.47922i	0.247696	−	0.113119i
$172$	4.41441	−	11.7110i	0.336596	−	0.892956i
$173$	0.270361	−	0.920764i	0.0205551	−	0.0700044i	−0.948577	−	0.316547i	$-0.897476\pi$
$173$	0.270361	−	0.920764i	0.0205551	−	0.0700044i	0.969132	+	0.246543i	$0.0792946\pi$
$174$	−3.99781	−	9.69922i	−0.303073	−	0.735296i
$175$	2.43456	−	16.9327i	0.184035	−	1.27999i
$176$	−0.668002	−	0.781834i	−0.0503526	−	0.0589329i
$177$	−2.01001	+	4.40132i	−0.151082	+	0.330823i
$178$	18.4418	+	12.8519i	1.38227	+	0.963293i
$179$	−1.06604	−	7.41445i	−0.0796794	−	0.554182i	−0.990085	−	0.140466i	$-0.955140\pi$
$179$	−1.06604	−	7.41445i	−0.0796794	−	0.554182i	0.910406	−	0.413716i	$-0.135769\pi$
$180$	5.45860	−	2.95603i	0.406860	−	0.220330i
$181$	0.711059	+	0.820606i	0.0528526	+	0.0609952i	0.781560	−	0.623830i	$-0.214424\pi$
$181$	0.711059	+	0.820606i	0.0528526	+	0.0609952i	−0.728708	+	0.684825i	$0.759879\pi$
$182$	−29.7945	+	7.54945i	−2.20851	+	0.559602i
$183$	2.15677			0.159433
$184$	−5.25776	+	12.5042i	−0.387607	+	0.921825i
$185$	15.2451			1.12084
$186$	−14.3013	+	3.62373i	−1.04862	+	0.265705i
$187$	−0.528427	−	0.609838i	−0.0386424	−	0.0445958i
$188$	−11.7992	−	21.7884i	−0.860548	−	1.58909i
$189$	−0.525412	−	3.65432i	−0.0382181	−	0.265812i
$190$	12.8233	+	8.93648i	0.930303	+	0.648320i
$191$	−5.66127	+	12.3965i	−0.409635	+	0.896976i	0.586566	+	0.809901i	$0.300479\pi$
$191$	−5.66127	+	12.3965i	−0.409635	+	0.896976i	−0.996202	+	0.0870752i	$0.972248\pi$
$192$	−6.45398	+	4.72717i	−0.465776	+	0.341154i
$193$	−0.241471	+	1.67947i	−0.0173814	+	0.120891i	−0.996665	−	0.0816039i	$-0.973996\pi$
$193$	−0.241471	+	1.67947i	−0.0173814	+	0.120891i	0.979283	+	0.202495i	$0.0649048\pi$
$194$	7.98704	+	19.3776i	0.573436	+	1.39123i
$195$	−5.14773	+	17.5315i	−0.368636	+	1.25546i
$196$	12.4079	+	4.67712i	0.886282	+	0.334080i
$197$	18.0552	−	8.24555i	1.28638	−	0.587471i	0.349441	−	0.936958i	$-0.386371\pi$
$197$	18.0552	−	8.24555i	1.28638	−	0.587471i	0.936941	+	0.349487i	$0.113644\pi$
$198$	−0.0651756	+	0.357685i	−0.00463183	+	0.0254196i
$199$	17.7732	−	20.5113i	1.25991	−	1.45401i	0.423502	−	0.905895i	$-0.360801\pi$
$199$	17.7732	−	20.5113i	1.25991	−	1.45401i	0.836404	−	0.548114i	$-0.184654\pi$
$200$	11.2362	+	6.74620i	0.794519	+	0.477029i
$201$	5.26463	−	8.19192i	0.371338	−	0.577814i
$202$	−0.307860	−	2.91112i	−0.0216610	−	0.204826i
$203$	−14.8065	−	23.0394i	−1.03921	−	1.61705i
$204$	−5.03846	+	3.74448i	−0.352763	+	0.262166i
$205$	−7.89595	+	2.31846i	−0.551477	+	0.161928i
$206$	0.571809	−	15.2663i	0.0398398	−	1.06366i
$207$	4.60173	−	1.35058i	0.319842	−	0.0938721i
$208$	3.51312	−	23.2839i	0.243591	−	1.61445i
$209$	−0.878357	+	0.257909i	−0.0607572	+	0.0178399i
$210$	12.6358	−	10.1464i	0.871955	−	0.700170i
$211$	6.70532	−	4.30925i	0.461613	−	0.296661i	−0.289088	−	0.957302i	$-0.593352\pi$
$211$	6.70532	−	4.30925i	0.461613	−	0.296661i	0.750701	+	0.660642i	$0.229716\pi$
$212$	−0.670405	−	9.85482i	−0.0460436	−	0.676832i
$213$	5.33251	−	8.29754i	0.365377	−	0.568538i
$214$	−1.64355	+	3.26919i	−0.112351	+	0.223477i
$215$	−14.6787	−	12.7191i	−1.00108	−	0.867438i
$216$	2.73688	+	0.713769i	0.186221	+	0.0485659i
$217$	−35.0339	+	15.9995i	−2.37826	+	1.08611i
$218$	4.36100	−	13.0271i	0.295364	−	0.882307i
$219$	10.8507	+	3.18605i	0.733221	+	0.215293i
$220$	−1.49720	+	0.552505i	−0.100941	+	0.0372499i
$221$	2.62961	−	18.2894i	0.176887	−	1.23028i
$222$	5.07569	+	4.74213i	0.340658	+	0.318271i
$223$	13.7396	+	6.27465i	0.920069	+	0.420182i	0.818408	−	0.574638i	$-0.194857\pi$
$223$	13.7396	+	6.27465i	0.920069	+	0.420182i	0.101661	+	0.994819i	$0.467584\pi$
$224$	−14.3634	+	15.1610i	−0.959694	+	1.01299i
$225$	−0.659433	−	4.58645i	−0.0439622	−	0.305764i
$226$	−19.5734	+	11.5675i	−1.30201	+	0.769459i
$227$	10.2302	−	8.86455i	0.679004	−	0.588361i	−0.245562	−	0.969381i	$-0.578973\pi$
$227$	10.2302	−	8.86455i	0.679004	−	0.588361i	0.924567	+	0.381020i	$0.124427\pi$
$228$	1.48962	+	6.96412i	0.0986523	+	0.461210i
$229$	−1.58326			−0.104625			−0.0523124	−	0.998631i	$-0.516659\pi$
$229$	−1.58326			−0.104625			−0.0523124	+	0.998631i	$0.516659\pi$
$230$	15.3804	+	14.3732i	1.01416	+	0.947739i
$231$			0.949135i			0.0624485i
$232$	20.6674	−	3.61764i	1.35688	−	0.237510i
$233$	−1.87628	−	2.16534i	−0.122919	−	0.141856i	0.690954	−	0.722899i	$-0.257191\pi$
$233$	−1.87628	−	2.16534i	−0.122919	−	0.141856i	−0.813873	+	0.581042i	$0.802645\pi$
$234$	−7.16723	+	4.23569i	−0.468536	+	0.276896i
$235$	−38.0619	+	5.47248i	−2.48289	+	0.356985i
$236$	−7.72674	−	5.82619i	−0.502968	−	0.379252i
$237$	3.04965	−	6.67779i	0.198096	−	0.433769i
$238$	−11.1878	+	11.9748i	−0.725199	+	0.776209i
$239$	−6.62612	−	0.952693i	−0.428608	−	0.0616246i	−0.0753649	−	0.997156i	$-0.524012\pi$
$239$	−6.62612	−	0.952693i	−0.428608	−	0.0616246i	−0.353243	+	0.935531i	$0.614921\pi$
$240$	3.41487	+	11.9364i	0.220429	+	0.770488i
$241$	−0.703431	+	2.39567i	−0.0453120	+	0.154318i	−0.979041	−	0.203661i	$-0.934716\pi$
$241$	−0.703431	+	2.39567i	−0.0453120	+	0.154318i	0.933730	+	0.357979i	$0.116534\pi$
$242$	−4.90867	+	14.6631i	−0.315541	+	0.942578i
$243$	−0.415415	−	0.909632i	−0.0266489	−	0.0583529i
$244$	−0.931557	+	4.21175i	−0.0596368	+	0.269630i
$245$	13.4761	−	15.5522i	0.860955	−	0.993595i
$246$	−3.35005	−	1.68420i	−0.213591	−	0.107381i
$247$	−17.6344	−	11.3330i	−1.12205	−	0.721099i
$248$	−0.899382	−	29.4929i	−0.0571108	−	1.87280i
$249$	−1.35294	−	2.10521i	−0.0857388	−	0.133412i
$250$	−1.25398	+	1.00693i	−0.0793084	+	0.0636837i
$251$	−5.69412	−	19.3924i	−0.359410	−	1.22404i	−0.918664	−	0.395041i	$-0.870730\pi$
$251$	−5.69412	−	19.3924i	−0.359410	−	1.22404i	0.559254	−	0.828996i	$-0.311088\pi$
$252$	7.36310	+	0.552353i	0.463832	+	0.0347950i
$253$	−1.22041	+	0.175318i	−0.0767267	+	0.0110221i
$254$	−6.90671	−	0.258695i	−0.433365	−	0.0162320i
$255$	2.74467	+	9.34748i	0.171878	+	0.585362i
$256$	−6.44363	−	14.6451i	−0.402727	−	0.915320i
$257$	7.01099	−	4.50569i	0.437334	−	0.281057i	−0.303391	−	0.952866i	$-0.598119\pi$
$257$	7.01099	−	4.50569i	0.437334	−	0.281057i	0.740725	+	0.671809i	$0.234482\pi$
$258$	−0.930695	−	8.80063i	−0.0579426	−	0.547903i
$259$	15.2550	+	9.80379i	0.947900	+	0.609178i
$260$	−32.0123	−	17.6248i	−1.98532	−	1.09304i
$261$	−5.60625	−	4.85785i	−0.347018	−	0.300693i
$262$	−8.63239	−	1.57295i	−0.533311	−	0.0971773i
$263$	8.00809	+	17.5353i	0.493800	+	1.08127i	0.978435	+	0.206554i	$0.0662250\pi$
$263$	8.00809	+	17.5353i	0.493800	+	1.08127i	−0.484635	+	0.874716i	$0.661048\pi$
$264$	−0.670338	−	0.281767i	−0.0412564	−	0.0173416i
$265$	−14.7081	−	4.31870i	−0.903514	−	0.265296i
$266$	7.08481	+	17.1887i	0.434398	+	1.05391i
$267$	15.7327	+	2.26203i	0.962828	+	0.138434i
$268$	13.7233	+	13.8191i	0.838284	+	0.844133i
$269$	8.56519	+	3.91159i	0.522229	+	0.238494i	0.659046	−	0.752102i	$-0.270960\pi$
$269$	8.56519	+	3.91159i	0.522229	+	0.238494i	−0.136817	+	0.990596i	$0.543687\pi$
$270$	2.50966	−	3.60123i	0.152733	−	0.219164i
$271$	24.5332	−	3.52734i	1.49029	−	0.214271i	0.651465	−	0.758679i	$-0.274155\pi$
$271$	24.5332	−	3.52734i	1.49029	−	0.214271i	0.838820	+	0.544408i	$0.183246\pi$
$272$	−5.13602	−	11.4564i	−0.311417	−	0.694649i
$273$	−16.4252	+	14.2325i	−0.994099	+	0.861392i
$274$	4.30160	−	1.08996i	0.259869	−	0.0658467i
$275$			1.19124i			0.0718344i
$276$	0.649839	+	9.56962i	0.0391157	+	0.576024i
$277$		−	16.7284i		−	1.00511i	−0.864544	−	0.502557i	$-0.832393\pi$
$277$		−	16.7284i		−	1.00511i	0.864544	−	0.502557i	$-0.167607\pi$
$278$	−0.742165	−	2.92901i	−0.0445121	−	0.175670i
$279$	−7.88409	+	6.83161i	−0.472008	+	0.408998i
$280$	14.3563	+	29.0578i	0.857952	+	1.73653i
$281$	−16.4468	+	2.36469i	−0.981131	+	0.141065i	−0.614173	−	0.789172i	$-0.710510\pi$
$281$	−16.4468	+	2.36469i	−0.981131	+	0.141065i	−0.366959	+	0.930237i	$0.619601\pi$
$282$	−14.3746	−	10.0175i	−0.855993	−	0.596535i
$283$	12.8540	+	5.87022i	0.764090	+	0.348948i	0.759044	−	0.651039i	$-0.225667\pi$
$283$	12.8540	+	5.87022i	0.764090	+	0.348948i	0.00504600	+	0.999987i	$0.498394\pi$
$284$	13.9003	+	13.9972i	0.824828	+	0.830583i
$285$	10.9396	+	1.57288i	0.648008	+	0.0931694i
$286$	1.97881	−	0.815624i	0.117010	−	0.0482288i
$287$	−9.39203	−	2.75775i	−0.554394	−	0.162785i
$288$	−2.57597	+	5.03631i	−0.151791	+	0.296767i
$289$	2.96947	+	6.50222i	0.174674	+	0.382484i
$290$	5.83709	−	32.0340i	0.342766	−	1.88110i
$291$	11.2005	+	9.70526i	0.656583	+	0.568932i
$292$	−10.9084	+	19.8131i	−0.638364	+	1.15947i
$293$	−16.4223	−	10.5540i	−0.959400	−	0.616569i	−0.0355678	−	0.999367i	$-0.511324\pi$
$293$	−16.4223	−	10.5540i	−0.959400	−	0.616569i	−0.923832	+	0.382799i	$0.874960\pi$
$294$	9.32437	−	0.986082i	0.543808	−	0.0575095i
$295$	−12.6339	+	8.11933i	−0.735576	+	0.472726i
$296$	−11.4528	+	7.86360i	−0.665678	+	0.457063i
$297$	0.0724295	+	0.246672i	0.00420279	+	0.0143134i
$298$	0.731825	−	19.5385i	0.0423935	−	1.13183i
$299$	−21.3344	−	18.4909i	−1.23380	−	1.06935i
$300$	9.24127	+	0.693247i	0.533545	+	0.0400246i
$301$	−6.50879	−	22.1669i	−0.375161	−	1.27768i
$302$	7.25603	+	9.03628i	0.417537	+	0.519980i
$303$	−1.11910	−	1.74135i	−0.0642906	−	0.100038i
$304$	−14.2430	−	0.0990277i	−0.816890	−	0.00567963i
$305$	5.63152	+	3.61916i	0.322460	+	0.207232i
$306$	−1.99381	+	3.96590i	−0.113979	+	0.226715i
$307$	−8.70813	+	10.0497i	−0.496999	+	0.573568i	−0.947722	−	0.319096i	$-0.896621\pi$
$307$	−8.70813	+	10.0497i	−0.496999	+	0.573568i	0.450723	+	0.892664i	$0.351166\pi$
$308$	−1.85347	−	0.409952i	−0.105611	−	0.0233592i
$309$	−4.48752	−	9.82629i	−0.255286	−	0.558998i
$310$	−43.4228	−	14.5364i	−2.46625	−	0.825612i
$311$	3.71494	−	12.6519i	0.210655	−	0.717424i	−0.784590	−	0.620015i	$-0.787126\pi$
$311$	3.71494	−	12.6519i	0.210655	−	0.717424i	0.995244	−	0.0974089i	$-0.0310555\pi$
$312$	−5.17579	−	15.8257i	−0.293021	−	0.895953i
$313$	11.0836	+	1.59358i	0.626480	+	0.0900743i	0.448241	−	0.893913i	$-0.352051\pi$
$313$	11.0836	+	1.59358i	0.626480	+	0.0900743i	0.178240	+	0.983987i	$0.442960\pi$
$314$	0.391797	+	0.366049i	0.0221104	+	0.0206573i
$315$	4.76021	−	10.4234i	0.268208	−	0.587293i
$316$	11.7232	+	8.83964i	0.659482	+	0.497269i
$317$	−28.3218	+	4.07206i	−1.59071	+	0.228710i	−0.880070	−	0.474845i	$-0.842504\pi$
$317$	−28.3218	+	4.07206i	−1.59071	+	0.228710i	−0.710641	+	0.703555i	$0.751595\pi$
$318$	−3.55354	−	6.01297i	−0.199273	−	0.337191i
$319$	1.24888	+	1.44129i	0.0699241	+	0.0806967i
$320$	−24.7843	+	1.51300i	−1.38549	+	0.0845791i
$321$			2.58736i			0.144412i
$322$	6.14735	+	24.2733i	0.342578	+	1.35270i
$323$	−11.1766			−0.621882
$324$	1.95576	−	0.418334i	0.108653	−	0.0232408i
$325$	−20.6149	+	17.8629i	−1.14351	+	0.990857i
$326$	−2.35368	−	3.98267i	−0.130358	−	0.220580i
$327$	−1.38245	−	9.61513i	−0.0764495	−	0.531718i
$328$	4.73588	−	5.81455i	0.261495	−	0.321055i
$329$	−41.6059	−	19.0008i	−2.29381	−	1.04755i
$330$	−0.770391	+	0.824580i	−0.0424086	+	0.0453916i
$331$	2.28936	−	15.9229i	0.125835	−	0.875201i	−0.824918	−	0.565252i	$-0.808779\pi$
$331$	2.28936	−	15.9229i	0.125835	−	0.875201i	0.950753	−	0.309949i	$-0.100312\pi$
$332$	4.69542	−	1.73273i	0.257695	−	0.0950961i
$333$	4.71279	+	1.38380i	0.258259	+	0.0758317i
$334$	−23.6761	−	7.92590i	−1.29550	−	0.433686i
$335$	27.4928	−	12.5555i	1.50209	−	0.685983i
$336$	−4.25892	+	14.1401i	−0.232343	+	0.771407i
$337$	−13.9806	−	12.1143i	−0.761574	−	0.659907i	0.184875	−	0.982762i	$-0.440812\pi$
$337$	−13.9806	−	12.1143i	−0.761574	−	0.659907i	−0.946449	+	0.322855i	$0.895357\pi$
$338$	27.3617	+	13.7558i	1.48828	+	0.748219i
$339$	−8.69177	+	13.5247i	−0.472072	+	0.734559i
$340$	−19.4393	+	1.32242i	−1.05424	+	0.0717182i
$341$	2.25621	−	1.44998i	0.122181	−	0.0785207i
$342$	3.15297	+	3.92655i	0.170493	+	0.212323i
$343$	−1.31034	+	0.384750i	−0.0707516	+	0.0207745i
$344$	17.5879	+	1.98372i	0.948276	+	0.106955i
$345$	14.2819	+	4.19541i	0.768910	+	0.225873i
$346$	1.35618	+	0.0507965i	0.0729086	+	0.00273084i
$347$	11.9643	−	3.51304i	0.642278	−	0.188590i	0.0556550	−	0.998450i	$-0.482275\pi$
$347$	11.9643	−	3.51304i	0.642278	−	0.188590i	0.586623	+	0.809860i	$0.300457\pi$
$348$	11.9079	−	8.84970i	0.638329	−	0.474394i
$349$	−11.6040	−	18.0563i	−0.621150	−	0.966529i	−0.999170	−	0.0407315i	$-0.987031\pi$
$349$	−11.6040	−	18.0563i	−0.621150	−	0.966529i	0.378020	−	0.925798i	$-0.376605\pi$
$350$	24.0586	−	2.54427i	1.28598	−	0.135997i
$351$	−3.18268	+	4.95234i	−0.169879	+	0.264336i
$352$	0.839770	−	1.18734i	0.0447599	−	0.0632853i
$353$	4.80991	−	5.55093i	0.256006	−	0.295446i	−0.613169	−	0.789952i	$-0.710105\pi$
$353$	4.80991	−	5.55093i	0.256006	−	0.295446i	0.869174	+	0.494506i	$0.164651\pi$
$354$	−6.73192	−	1.22666i	−0.357798	−	0.0651962i
$355$	27.8473	−	12.7174i	1.47798	−	0.674971i
$356$	−11.2126	+	29.7459i	−0.594267	+	1.57653i
$357$	−3.26471	+	11.1186i	−0.172787	+	0.588458i
$358$	9.79410	−	4.03692i	0.517634	−	0.213358i
$359$	0.681472	−	4.73974i	0.0359667	−	0.250154i	−0.963904	−	0.266251i	$-0.914215\pi$
$359$	0.681472	−	4.73974i	0.0359667	−	0.250154i	0.999870	+	0.0160970i	$0.00512405\pi$
$360$	5.94851	+	6.45633i	0.313514	+	0.340278i
$361$	2.62563	−	5.74933i	0.138191	−	0.302596i
$362$	−0.877966	+	1.25983i	−0.0461448	+	0.0662152i
$363$	1.55606	+	10.8226i	0.0816718	+	0.568040i
$364$	−20.6989	−	38.2226i	−1.08492	−	2.00341i
$365$	22.9857	+	26.5270i	1.20313	+	1.38848i
$366$	0.749180	+	2.95670i	0.0391603	+	0.154549i
$367$	18.9007			0.986610			0.493305	−	0.869856i	$-0.335789\pi$
$367$	18.9007			0.986610			0.493305	+	0.869856i	$0.335789\pi$
$368$	−18.9683	−	2.86432i	−0.988790	−	0.149313i
$369$	−2.65136			−0.138024
$370$	5.29557	+	20.8994i	0.275304	+	1.08651i
$371$	−11.9404	−	13.7800i	−0.619916	−	0.715421i
$372$	−9.93548	−	18.3468i	−0.515131	−	0.951238i
$373$	5.17752	+	36.0104i	0.268082	+	1.86455i	0.466622	+	0.884457i	$0.345471\pi$
$373$	5.17752	+	36.0104i	0.268082	+	1.86455i	−0.198540	+	0.980093i	$0.563620\pi$
$374$	0.652465	−	0.936250i	0.0337382	−	0.0484124i
$375$	−0.472402	+	1.03442i	−0.0243947	+	0.0534170i
$376$	25.7709	−	23.7439i	1.32903	−	1.22450i
$377$	−6.21482	+	43.2250i	−0.320080	+	2.22620i
$378$	4.82716	−	1.98965i	0.248282	−	0.102337i
$379$	−0.361190	+	1.23010i	−0.0185531	+	0.0631860i	−0.968249	−	0.249987i	$-0.919574\pi$
$379$	−0.361190	+	1.23010i	−0.0185531	+	0.0631860i	0.949696	+	0.313173i	$0.101392\pi$
$380$	−7.79659	+	20.6836i	−0.399957	+	1.06105i
$381$	−4.44556	+	2.03022i	−0.227753	+	0.104011i
$382$	−18.9607	−	3.45493i	−0.970113	−	0.176769i
$383$	−3.74504	+	4.32201i	−0.191363	+	0.220844i	−0.843321	−	0.537411i	$-0.819402\pi$
$383$	−3.74504	+	4.32201i	−0.191363	+	0.220844i	0.651958	+	0.758255i	$0.273948\pi$
$384$	−8.72230	−	7.20566i	−0.445108	−	0.367712i
$385$	−1.59269	+	2.47827i	−0.0811710	+	0.126305i
$386$	−2.38624	+	0.252353i	−0.121456	+	0.0128444i
$387$	−3.38316	−	5.26430i	−0.171976	−	0.267600i
$388$	−23.7902	+	17.6804i	−1.20776	+	0.897587i
$389$	10.0216	−	2.94261i	0.508115	−	0.149196i	−0.0176194	−	0.999845i	$-0.505609\pi$
$389$	10.0216	−	2.94261i	0.508115	−	0.149196i	0.525734	+	0.850649i	$0.323791\pi$
$390$	−25.8219	−	0.967176i	−1.30754	−	0.0489748i
$391$	−14.8995	−	2.14406i	−0.753499	−	0.108430i
$392$	−2.10177	+	18.6346i	−0.106156	+	0.941189i
$393$	−5.95320	+	1.74802i	−0.300299	+	0.0881758i
$394$	17.5754	+	21.8876i	0.885438	+	1.10268i
$395$	19.1685	−	12.3189i	0.964473	−	0.619829i
$396$	−0.512986	+	0.0348975i	−0.0257785	+	0.00175367i
$397$	−15.9295	+	24.7868i	−0.799479	+	1.24401i	0.166666	+	0.986013i	$0.446700\pi$
$397$	−15.9295	+	24.7868i	−0.799479	+	1.24401i	−0.966145	+	0.258000i	$0.916937\pi$
$398$	34.2925	+	17.2402i	1.71893	+	0.864173i
$399$	9.93524	+	8.60893i	0.497384	+	0.430986i
$400$	−5.34528	+	17.7470i	−0.267264	+	0.887348i
$401$	20.5430	−	9.38169i	1.02587	−	0.468499i	0.169866	−	0.985467i	$-0.445667\pi$
$401$	20.5430	−	9.38169i	1.02587	−	0.468499i	0.856005	+	0.516968i	$0.172939\pi$
$402$	13.0590	+	4.37166i	0.651321	+	0.218039i
$403$	58.9250	+	17.3019i	2.93526	+	0.861871i
$404$	3.88388	−	1.43325i	0.193230	−	0.0713070i
$405$	0.441718	−	3.07221i	0.0219491	−	0.152660i
$406$	26.4413	−	28.3011i	1.31226	−	1.40456i
$407$	−1.14863	−	0.524562i	−0.0569355	−	0.0260016i
$408$	−6.88345	−	5.60648i	−0.340781	−	0.277562i
$409$	4.99311	+	34.7279i	0.246893	+	1.71718i	0.615959	+	0.787778i	$0.288769\pi$
$409$	4.99311	+	34.7279i	0.246893	+	1.71718i	−0.369065	+	0.929403i	$0.620322\pi$
$410$	−5.92111	−	10.0191i	−0.292423	−	0.494810i
$411$	2.37140	−	2.05483i	0.116973	−	0.101357i
$412$	21.1271	−	4.51905i	1.04086	−	0.222638i
$413$	−17.8635			−0.879005
$414$	3.44997	+	5.83932i	0.169557	+	0.286987i
$415$		−	7.76718i		−	0.381276i
$416$	33.1400	−	3.27184i	1.62482	−	0.160415i
$417$	−1.39916	−	1.61472i	−0.0685172	−	0.0790730i
$418$	−0.658673	−	1.11454i	−0.0322167	−	0.0545141i
$419$	−6.34748	+	0.912630i	−0.310095	+	0.0445849i	−0.295605	−	0.955310i	$-0.595521\pi$
$419$	−6.34748	+	0.912630i	−0.310095	+	0.0445849i	−0.0144893	+	0.999895i	$0.504612\pi$
$420$	18.2988	+	13.7979i	0.892892	+	0.673267i
$421$	14.0742	−	30.8181i	0.685933	−	1.50198i	−0.170300	−	0.985392i	$-0.554474\pi$
$421$	14.0742	−	30.8181i	0.685933	−	1.50198i	0.856233	−	0.516591i	$-0.172799\pi$
$422$	8.23668	+	7.69539i	0.400955	+	0.374606i
$423$	−12.2630	−	1.76315i	−0.596247	−	0.0857274i
$424$	13.2770	−	4.34224i	0.644788	−	0.210878i
$425$	−4.09746	+	13.9547i	−0.198756	+	0.676902i
$426$	13.2273	+	4.42803i	0.640866	+	0.214539i
$427$	3.30777	+	7.24301i	0.160074	+	0.350514i
$428$	−5.05260	−	1.11754i	−0.244227	−	0.0540182i
$429$	0.991085	−	1.14377i	0.0478500	−	0.0552219i
$430$	12.3377	−	24.5410i	0.594978	−	1.18347i
$431$	−4.43816	−	2.85223i	−0.213779	−	0.137387i	0.429370	−	0.903129i	$-0.358736\pi$
$431$	−4.43816	−	2.85223i	−0.213779	−	0.137387i	−0.643148	+	0.765742i	$0.722372\pi$
$432$	−0.0278103	+	3.99990i	−0.00133802	+	0.192445i
$433$	1.65915	+	2.58169i	0.0797337	+	0.124068i	0.878830	−	0.477135i	$-0.158325\pi$
$433$	1.65915	+	2.58169i	0.0797337	+	0.124068i	−0.799096	+	0.601203i	$0.794688\pi$
$434$	−34.1030	−	42.4701i	−1.63699	−	2.03863i
$435$	−6.48674	−	22.0918i	−0.311015	−	1.05922i
$436$	19.3736	+	1.45334i	0.927826	+	0.0696022i
$437$	−9.23433	+	14.3651i	−0.441738	+	0.687175i
$438$	−0.598607	+	15.9818i	−0.0286026	+	0.763640i
$439$	−7.95864	−	27.1047i	−0.379845	−	1.29363i	−0.898622	−	0.438724i	$-0.855430\pi$
$439$	−7.95864	−	27.1047i	−0.379845	−	1.29363i	0.518776	−	0.854910i	$-0.326388\pi$
$440$	−1.27749	−	1.86058i	−0.0609021	−	0.0886995i
$441$	5.57759	−	3.58450i	0.265600	−	0.170690i
$442$	25.9861	−	2.74812i	1.23603	−	0.130715i
$443$	11.8276	+	7.60112i	0.561945	+	0.361140i	0.790567	−	0.612375i	$-0.209786\pi$
$443$	11.8276	+	7.60112i	0.561945	+	0.361140i	−0.228622	+	0.973515i	$0.573422\pi$
$444$	−4.73784	+	8.60545i	−0.224848	+	0.408397i
$445$	37.2838	+	32.3066i	1.76742	+	1.53148i
$446$	−3.82925	+	21.0150i	−0.181320	+	0.995089i
$447$	−5.74331	−	12.5761i	−0.271649	−	0.594829i
$448$	−25.7734	−	14.4243i	−1.21768	−	0.681483i
$449$	−30.5113	−	8.95892i	−1.43992	−	0.422797i	−0.533722	−	0.845660i	$-0.679207\pi$
$449$	−30.5113	−	8.95892i	−1.43992	−	0.422797i	−0.906194	+	0.422862i	$0.861025\pi$
$450$	6.05846	−	2.49717i	0.285599	−	0.117718i
$451$	0.674689	+	0.0970056i	0.0317698	+	0.00456781i
$452$	−22.6568	−	22.8149i	−1.06569	−	1.07312i
$453$	7.45411	+	3.40418i	0.350225	+	0.159942i
$454$	15.7059	+	10.9453i	0.737115	+	0.513689i
$455$	−66.7705	+	9.60015i	−3.13025	+	0.450062i
$456$	−9.02961	+	4.46117i	−0.422850	+	0.208914i
$457$	−9.25622	+	8.02056i	−0.432988	+	0.375186i	−0.843910	−	0.536484i	$-0.819752\pi$
$457$	−9.25622	+	8.02056i	−0.432988	+	0.375186i	0.410923	+	0.911670i	$0.365207\pi$
$458$	−0.549964	−	2.17048i	−0.0256982	−	0.101420i
$459$			3.13876i			0.146505i
$460$	−14.3615	+	26.0776i	−0.669607	+	1.21587i
$461$		−	10.6525i		−	0.496137i	−0.968743	−	0.248068i	$-0.920204\pi$
$461$		−	10.6525i		−	0.496137i	0.968743	−	0.248068i	$-0.0797958\pi$
$462$	−1.30116	+	0.329693i	−0.0605354	+	0.0153387i
$463$	−1.43037	+	1.23942i	−0.0664747	+	0.0576007i	−0.687464	−	0.726218i	$-0.741276\pi$
$463$	−1.43037	+	1.23942i	−0.0664747	+	0.0576007i	0.620990	+	0.783819i	$0.286731\pi$
$464$	12.1385	+	27.0761i	0.563514	+	1.25698i
$465$	−32.0498	+	4.60807i	−1.48627	+	0.213694i
$466$	2.31670	−	3.32433i	0.107319	−	0.153997i
$467$	−19.6299	−	8.96470i	−0.908366	−	0.414837i	−0.0942561	−	0.995548i	$-0.530047\pi$
$467$	−19.6299	−	8.96470i	−0.908366	−	0.414837i	−0.814110	+	0.580711i	$0.802775\pi$
$468$	−8.29628	−	8.35417i	−0.383496	−	0.386171i
$469$	35.5848	+	5.11633i	1.64316	+	0.236250i
$470$	−20.7234	−	50.2778i	−0.955901	−	2.31914i
$471$	0.363784	+	0.106817i	0.0167623	+	0.00492185i
$472$	5.30309	−	12.6163i	0.244094	−	0.580713i
$473$	0.668305	+	1.46338i	0.0307287	+	0.0672864i
$474$	10.2138	+	1.86112i	0.469138	+	0.0854840i
$475$	12.4695	+	10.8049i	0.572140	+	0.495762i
$476$	−20.3023	−	11.1777i	−0.930555	−	0.512329i
$477$	−4.15478	−	2.67012i	−0.190234	−	0.122256i
$478$	−0.995626	−	9.41462i	−0.0455389	−	0.430615i
$479$	10.8983	−	7.00390i	0.497955	−	0.320016i	−0.267443	−	0.963574i	$-0.586179\pi$
$479$	10.8983	−	7.00390i	0.497955	−	0.320016i	0.765398	+	0.643557i	$0.222542\pi$
$480$	−15.1772	+	8.82764i	−0.692743	+	0.402925i
$481$	−8.14623	−	27.7435i	−0.371436	−	1.26499i
$482$	−3.52854	−	0.132163i	−0.160721	−	0.00601988i
$483$	11.5932	+	13.3825i	0.527507	+	0.608924i
$484$	−21.8065	−	1.63585i	−0.991206	−	0.0743567i
$485$	12.9596	+	44.1362i	0.588463	+	2.00412i
$486$	1.10271	−	0.885460i	0.0500198	−	0.0401653i
$487$	3.04903	+	4.74438i	0.138165	+	0.214988i	0.903440	−	0.428715i	$-0.141033\pi$
$487$	3.04903	+	4.74438i	0.138165	+	0.214988i	−0.765275	+	0.643703i	$0.777397\pi$
$488$	−6.09744	+	0.185941i	−0.276018	+	0.00841714i
$489$	−2.75191	−	1.76854i	−0.124445	−	0.0799763i
$490$	26.0015	+	13.0720i	1.17463	+	0.590531i
$491$	7.34762	−	8.47961i	0.331594	−	0.382679i	−0.565330	−	0.824865i	$-0.691251\pi$
$491$	7.34762	−	8.47961i	0.331594	−	0.382679i	0.896924	+	0.442185i	$0.145797\pi$
$492$	1.14518	−	5.17758i	0.0516286	−	0.233423i
$493$	9.67242	+	21.1796i	0.435624	+	0.953883i
$494$	9.41072	−	28.1115i	0.423408	−	1.26480i
$495$	−0.224807	+	0.765623i	−0.0101043	+	0.0344122i
$496$	40.1191	−	11.4777i	1.80140	−	0.515362i
$497$	36.0437	+	5.18230i	1.61678	+	0.232458i
$498$	2.41605	−	2.58600i	0.108266	−	0.115881i
$499$	1.72421	−	3.77550i	0.0771864	−	0.169015i	−0.867105	−	0.498126i	$-0.834022\pi$
$499$	1.72421	−	3.77550i	0.0771864	−	0.169015i	0.944291	+	0.329111i	$0.106749\pi$
$500$	−1.81597	−	1.36930i	−0.0812127	−	0.0612368i
$501$	−17.4750	+	2.51253i	−0.780726	+	0.112251i
$502$	24.6069	−	14.5422i	1.09826	−	0.649050i
$503$	−5.23047	−	6.03629i	−0.233215	−	0.269145i	0.627064	−	0.778968i	$-0.284256\pi$
$503$	−5.23047	−	6.03629i	−0.233215	−	0.269145i	−0.860279	+	0.509823i	$0.829711\pi$
$504$	1.80045	+	10.2859i	0.0801982	+	0.458169i
$505$		−	6.42472i		−	0.285896i
$506$	−0.664267	−	1.61215i	−0.0295303	−	0.0716689i
$507$	21.6551			0.961737
$508$	−2.04449	−	9.55820i	−0.0907094	−	0.424076i
$509$	−13.9705	+	12.1055i	−0.619231	+	0.536567i	−0.906999	−	0.421134i	$-0.861632\pi$
$509$	−13.9705	+	12.1055i	−0.619231	+	0.536567i	0.287768	+	0.957700i	$0.407087\pi$
$510$	−11.8610	+	7.00960i	−0.525213	+	0.310390i
$511$	5.94175	+	41.3258i	0.262848	+	1.82815i
$512$	17.8386	−	13.9207i	0.788362	−	0.615212i
$513$	3.23904	+	1.47922i	0.143007	+	0.0653092i
$514$	8.61216	+	8.04620i	0.379866	+	0.354903i
$515$	4.77165	−	33.1876i	0.210264	−	1.46242i
$516$	11.7414	−	4.33289i	0.516887	−	0.190745i
$517$	3.05604	+	0.897335i	0.134405	+	0.0394648i
$518$	−8.14092	+	24.3184i	−0.357691	+	1.06849i
$519$	0.872916	−	0.398647i	0.0383167	−	0.0174987i
$520$	13.0418	−	50.0074i	0.571919	−	2.19297i
$521$	−3.55524	−	3.08063i	−0.155758	−	0.134965i	0.573496	−	0.819209i	$-0.305587\pi$
$521$	−3.55524	−	3.08063i	−0.155758	−	0.134965i	−0.729253	+	0.684244i	$0.760132\pi$
$522$	4.71217	−	9.37299i	0.206246	−	0.410244i
$523$	3.76901	−	5.86469i	0.164807	−	0.256445i	−0.749021	−	0.662547i	$-0.769476\pi$
$523$	3.76901	−	5.86469i	0.164807	−	0.256445i	0.913828	+	0.406101i	$0.133112\pi$
$524$	−0.842219	−	12.3804i	−0.0367925	−	0.540842i
$525$	14.3912	−	9.24865i	0.628083	−	0.403644i
$526$	−21.2572	+	17.0693i	−0.926859	+	0.744256i
$527$	31.4177	−	9.22506i	1.36857	−	0.401850i
$528$	0.153422	−	1.01683i	0.00667683	−	0.0442521i
$529$	−15.0660	+	17.3786i	−0.655044	+	0.755591i
$530$	0.811415	−	21.6634i	0.0352456	−	0.940998i
$531$	−4.64257	+	1.36318i	−0.201470	+	0.0591571i
$532$	−21.1028	+	15.6832i	−0.914923	+	0.679953i
$533$	8.43841	+	13.1304i	0.365508	+	0.568742i
$534$	2.36397	+	22.3536i	0.102299	+	0.967335i
$535$	−4.34170	+	6.75582i	−0.187708	+	0.292080i
$536$	−14.1775	+	23.6134i	−0.612373	+	1.01994i
$537$	4.90536	−	5.66109i	0.211682	−	0.244294i
$538$	−2.38714	+	13.1007i	−0.102917	+	0.564810i
$539$	−1.55047	+	0.708077i	−0.0667835	+	0.0304990i
$540$	5.80865	+	2.18954i	0.249964	+	0.0942230i
$541$	1.40137	−	4.77263i	0.0602497	−	0.205192i	−0.923867	−	0.382713i	$-0.874990\pi$
$541$	1.40137	−	4.77263i	0.0602497	−	0.205192i	0.984117	+	0.177522i	$0.0568079\pi$
$542$	13.3575	+	32.4070i	0.573753	+	1.39200i
$543$	−0.154528	+	1.07477i	−0.00663143	+	0.0461226i
$544$	13.9215	−	11.0205i	0.596878	−	0.472498i
$545$	12.5249	−	27.4258i	0.536509	−	1.17479i
$546$	−25.2167	−	17.5733i	−1.07918	−	0.752069i
$547$	−6.45441	−	44.8914i	−0.275971	−	1.91942i	−0.380275	−	0.924873i	$-0.624171\pi$
$547$	−6.45441	−	44.8914i	−0.275971	−	1.91942i	0.104304	−	0.994545i	$-0.466738\pi$
$548$	2.98842	+	5.51841i	0.127659	+	0.235735i
$549$	1.41239	+	1.62998i	0.0602791	+	0.0695658i
$550$	−1.63306	+	0.413791i	−0.0696338	+	0.0176441i
$551$	26.4147			1.12530
$552$	−12.8932	+	4.21498i	−0.548770	+	0.179402i
$553$	27.1029			1.15253
$554$	22.9329	−	5.81082i	0.974324	−	0.246878i
$555$	9.98342	+	11.5215i	0.423773	+	0.489060i
$556$	3.75755	−	2.03485i	0.159356	−	0.0862970i
$557$	−4.50825	−	31.3556i	−0.191021	−	1.32858i	−0.829313	−	0.558784i	$-0.811268\pi$
$557$	−4.50825	−	31.3556i	−0.191021	−	1.32858i	0.638292	−	0.769794i	$-0.279641\pi$
$558$	−12.1040	−	8.43519i	−0.512404	−	0.357090i
$559$	−15.3031	+	33.5091i	−0.647253	+	1.41729i
$560$	−34.8482	+	29.7745i	−1.47260	+	1.25820i
$561$	0.114838	−	0.798718i	0.00484848	−	0.0337219i
$562$	−8.95470	−	21.7253i	−0.377731	−	0.916426i
$563$	−5.10791	+	17.3959i	−0.215273	+	0.733151i	0.779071	+	0.626936i	$0.215691\pi$
$563$	−5.10791	+	17.3959i	−0.215273	+	0.733151i	−0.994343	+	0.106215i	$0.966127\pi$
$564$	8.73974	−	23.1857i	0.368009	−	0.976293i
$565$	−45.3900	+	20.7289i	−1.90957	+	0.872072i
$566$	−3.58244	+	19.6605i	−0.150581	+	0.826392i
$567$	2.41768	−	2.79015i	0.101533	−	0.117175i
$568$	−14.3603	+	23.9178i	−0.602543	+	1.00357i
$569$	−18.5553	+	28.8726i	−0.777879	+	1.21040i	0.195387	+	0.980726i	$0.437404\pi$
$569$	−18.5553	+	28.8726i	−0.777879	+	1.21040i	−0.973267	+	0.229678i	$0.926233\pi$
$570$	1.64376	+	15.5434i	0.0688497	+	0.651041i
$571$	−0.598552	−	0.931365i	−0.0250486	−	0.0389764i	0.828503	−	0.559984i	$-0.189193\pi$
$571$	−0.598552	−	0.931365i	−0.0250486	−	0.0389764i	−0.853552	+	0.521008i	$0.825556\pi$
$572$	1.80549	+	2.42942i	0.0754915	+	0.101579i
$573$	−13.0760	+	3.83945i	−0.546256	+	0.160395i
$574$	0.518137	−	13.8334i	0.0216266	−	0.577394i
$575$	14.5503	+	16.7961i	0.606790	+	0.700444i
$576$	−7.79902	−	1.78195i	−0.324959	−	0.0742481i
$577$	−30.2245	+	8.87473i	−1.25826	+	0.369460i	−0.841848	−	0.539715i	$-0.818532\pi$
$577$	−30.2245	+	8.87473i	−1.25826	+	0.369460i	−0.416416	+	0.909174i	$0.636714\pi$
$578$	−7.88235	+	6.32943i	−0.327863	+	0.263270i
$579$	−1.42739	+	0.917325i	−0.0593201	+	0.0381227i
$580$	45.9427	−	3.12540i	1.90767	−	0.129775i
$581$	4.99490	−	7.77221i	0.207223	−	0.322446i
$582$	−9.41423	+	18.7258i	−0.390232	+	0.776211i
$583$	0.959572	+	0.831474i	0.0397414	+	0.0344361i
$584$	−30.9508	−	8.07185i	−1.28075	−	0.334015i
$585$	−16.6205	+	7.59033i	−0.687173	+	0.313821i
$586$	8.76384	−	26.1792i	0.362031	−	1.08145i
$587$	30.7129	+	9.01813i	1.26766	+	0.372218i	0.845339	−	0.534230i	$-0.179398\pi$
$587$	30.7129	+	9.01813i	1.26766	+	0.372218i	0.422318	+	0.906448i	$0.361216\pi$
$588$	4.59074	+	12.4402i	0.189319	+	0.513024i
$589$	5.28658	−	36.7690i	0.217830	−	1.51504i
$590$	−15.5193	−	14.4994i	−0.638918	−	0.596930i
$591$	18.0552	+	8.24555i	0.742693	+	0.339177i
$592$	−14.7584	−	12.9690i	−0.606566	−	0.533021i
$593$	−2.77032	−	19.2680i	−0.113763	−	0.791242i	−0.964202	−	0.265168i	$-0.914573\pi$
$593$	−2.77032	−	19.2680i	−0.113763	−	0.791242i	0.850439	−	0.526074i	$-0.176336\pi$
$594$	−0.313001	+	0.184977i	−0.0128426	+	0.00758971i
$595$	−27.1819	+	23.5533i	−1.11435	+	0.965590i
$596$	27.0393	−	5.78367i	1.10757	−	0.236908i
$597$	27.1404			1.11078
$598$	17.9382	−	35.6701i	0.733547	−	1.45866i
$599$		−	18.6589i		−	0.762384i	−0.924496	−	0.381192i	$-0.875514\pi$
$599$		−	18.6589i		−	0.762384i	0.924496	−	0.381192i	$-0.124486\pi$
$600$	2.25970	+	12.9096i	0.0922519	+	0.527031i
$601$	−1.92208	−	2.21819i	−0.0784031	−	0.0904820i	0.715193	−	0.698927i	$-0.246339\pi$
$601$	−1.92208	−	2.21819i	−0.0784031	−	0.0904820i	−0.793596	+	0.608445i	$0.791793\pi$
$602$	28.1275	−	16.6228i	1.14639	−	0.677494i
$603$	9.63864	−	1.38583i	0.392516	−	0.0564352i
$604$	−9.86728	+	13.0861i	−0.401494	+	0.532465i
$605$	−14.0978	+	30.8699i	−0.573158	+	1.25504i
$606$	1.99847	−	2.13904i	0.0811823	−	0.0868926i
$607$	−21.5050	−	3.09195i	−0.872861	−	0.125498i	−0.308696	−	0.951161i	$-0.599893\pi$
$607$	−21.5050	−	3.09195i	−0.872861	−	0.125498i	−0.564165	+	0.825662i	$0.690802\pi$
$608$	−4.81171	−	19.5599i	−0.195141	−	0.793260i
$609$	7.71580	−	26.2776i	0.312660	−	1.06482i
$610$	−3.00529	+	8.97736i	−0.121681	+	0.363483i
$611$	30.2974	+	66.3420i	1.22570	+	2.68391i
$612$	−6.12938	−	1.35570i	−0.247766	−	0.0548009i
$613$	11.3607	−	13.1110i	0.458856	−	0.529548i	−0.478422	−	0.878130i	$-0.658791\pi$
$613$	11.3607	−	13.1110i	0.458856	−	0.529548i	0.937278	+	0.348582i	$0.113337\pi$
$614$	−16.8019	−	8.44700i	−0.678071	−	0.340893i
$615$	−6.92293	−	4.44909i	−0.279159	−	0.179405i
$616$	−0.0818273	−	2.68331i	−0.00329691	−	0.108114i
$617$	16.9705	+	26.4066i	0.683207	+	1.06309i	0.993652	+	0.112500i	$0.0358858\pi$
$617$	16.9705	+	26.4066i	0.683207	+	1.06309i	−0.310444	+	0.950592i	$0.600478\pi$
$618$	11.9120	−	9.56517i	0.479170	−	0.384768i
$619$	3.37253	+	11.4858i	0.135553	+	0.461652i	0.999091	−	0.0426325i	$-0.0135745\pi$
$619$	3.37253	+	11.4858i	0.135553	+	0.461652i	−0.863538	+	0.504285i	$0.831756\pi$
$620$	4.84436	−	64.5773i	0.194554	−	2.59349i
$621$	4.03420	+	2.59331i	0.161887	+	0.104066i
$622$	18.6348	+	0.697978i	0.747188	+	0.0279864i
$623$	16.5323	+	56.3039i	0.662354	+	2.25577i
$624$	19.8974	−	12.5927i	0.796533	−	0.504110i
$625$	−22.4595	+	14.4339i	−0.898381	+	0.577354i
$626$	1.66539	+	15.7479i	0.0665624	+	0.629413i
$627$	−0.770116	−	0.494924i	−0.0307555	−	0.0197653i
$628$	−0.365718	+	0.664262i	−0.0145937	+	0.0265069i
$629$	−11.6512	−	10.0958i	−0.464565	−	0.402548i
$630$	15.9429	+	2.90503i	0.635179	+	0.115739i
$631$	15.2771	+	33.4522i	0.608171	+	1.33171i	0.923818	+	0.382832i	$0.125051\pi$
$631$	15.2771	+	33.4522i	0.608171	+	1.33171i	−0.315647	+	0.948877i	$0.602221\pi$
$632$	−8.04598	+	19.1418i	−0.320052	+	0.761419i
$633$	7.64776	+	2.24559i	0.303971	+	0.0892540i
$634$	−15.4203	−	37.4116i	−0.612417	−	1.48580i
$635$	−15.0145	−	2.15877i	−0.595834	−	0.0856680i
$636$	7.00875	−	6.96019i	0.277915	−	0.275990i
$637$	−35.5033	−	16.2138i	−1.40669	−	0.642415i
$638$	−1.54203	+	2.21273i	−0.0610497	+	0.0876029i
$639$	9.76292	−	1.40370i	0.386215	−	0.0555293i
$640$	−10.6833	−	33.4510i	−0.422294	−	1.32227i
$641$	12.4654	−	10.8013i	0.492354	−	0.426627i	−0.372968	−	0.927844i	$-0.621660\pi$
$641$	12.4654	−	10.8013i	0.492354	−	0.426627i	0.865321	+	0.501217i	$0.167114\pi$
$642$	−3.54698	+	0.898750i	−0.139988	+	0.0354708i
$643$		−	6.16880i		−	0.243274i	−0.992575	−	0.121637i	$-0.961186\pi$
$643$		−	6.16880i		−	0.243274i	0.992575	−	0.121637i	$-0.0388143\pi$
$644$	−31.1407	+	16.8590i	−1.22712	+	0.664336i
$645$		−	19.4227i		−	0.764766i
$646$	−3.88232	−	15.3219i	−0.152748	−	0.602831i
$647$	30.6613	−	26.5682i	1.20542	−	1.04450i	0.207621	−	0.978209i	$-0.433428\pi$
$647$	30.6613	−	26.5682i	1.20542	−	1.04450i	0.997800	−	0.0662935i	$-0.0211174\pi$
$648$	1.25285	+	2.53582i	0.0492165	+	0.0996164i
$649$	1.23127	−	0.177029i	0.0483314	−	0.00694901i
$650$	−31.6490	−	22.0559i	−1.24137	−	0.865103i
$651$	−35.0339	−	15.9995i	−1.37309	−	0.627069i
$652$	4.64222	−	4.61006i	0.181804	−	0.180544i
$653$	42.8280	+	6.15774i	1.67599	+	0.240971i	0.913736	−	0.406308i	$-0.133184\pi$
$653$	42.8280	+	6.15774i	1.67599	+	0.240971i	0.762254	+	0.647279i	$0.224093\pi$
$654$	12.7011	−	5.23511i	0.496651	−	0.204709i
$655$	−18.4776	−	5.42551i	−0.721979	−	0.211992i
$656$	9.61617	+	4.47262i	0.375448	+	0.174626i
$657$	4.69783	+	10.2868i	0.183280	+	0.401327i
$658$	11.5957	−	63.6372i	0.452046	−	2.48084i
$659$	−3.14663	−	2.72657i	−0.122575	−	0.106212i	0.591416	−	0.806366i	$-0.298569\pi$
$659$	−3.14663	−	2.72657i	−0.122575	−	0.106212i	−0.713992	+	0.700154i	$0.753115\pi$
$660$	−1.39801	−	0.769693i	−0.0544176	−	0.0299603i
$661$	−5.26968	−	3.38662i	−0.204967	−	0.131724i	0.434131	−	0.900850i	$-0.357056\pi$
$661$	−5.26968	−	3.38662i	−0.204967	−	0.131724i	−0.639097	+	0.769126i	$0.720692\pi$
$662$	22.6238	−	2.39254i	0.879297	−	0.0929885i
$663$	15.5442	−	9.98966i	0.603687	−	0.387966i
$664$	4.00640	+	5.83503i	0.155478	+	0.226443i
$665$	11.4956	+	39.1505i	0.445781	+	1.51819i
$666$	−0.259994	+	6.94139i	−0.0100746	+	0.268973i
$667$	35.2134	+	5.06728i	1.36347	+	0.196206i
$668$	2.64136	−	35.2105i	0.102197	−	1.36233i
$669$	4.25544	+	14.4927i	0.164525	+	0.560320i
$670$	26.7622	+	33.3283i	1.03392	+	1.28759i
$671$	−0.299772	−	0.466455i	−0.0115726	−	0.0180073i
$672$	−20.8639	−	0.926774i	−0.804844	−	0.0357511i
$673$	−11.3781	−	7.31228i	−0.438595	−	0.281868i	0.302651	−	0.953101i	$-0.402128\pi$
$673$	−11.3781	−	7.31228i	−0.438595	−	0.281868i	−0.741246	+	0.671234i	$0.765765\pi$
$674$	11.7510	−	23.3740i	0.452632	−	0.900331i
$675$	3.03437	−	3.50185i	0.116793	−	0.134786i
$676$	−9.35331	+	42.2882i	−0.359743	+	1.62647i
$677$	−16.3233	−	35.7431i	−0.627356	−	1.37372i	−0.910046	−	0.414508i	$-0.863954\pi$
$677$	−16.3233	−	35.7431i	−0.627356	−	1.37372i	0.282689	−	0.959211i	$-0.408773\pi$
$678$	−21.5600	−	7.21751i	−0.828007	−	0.277187i
$679$	−15.4150	+	52.4988i	−0.591575	+	2.01472i
$680$	−8.56535	−	26.1898i	−0.328466	−	1.00433i
$681$	13.3988	+	1.92645i	0.513441	+	0.0738217i
$682$	2.77148	+	2.58935i	0.106125	+	0.0991512i
$683$	15.1636	−	33.2037i	0.580220	−	1.27050i	−0.360955	−	0.932583i	$-0.617549\pi$
$683$	15.1636	−	33.2037i	0.580220	−	1.27050i	0.941175	−	0.337921i	$-0.109724\pi$
$684$	−4.28764	+	5.68631i	−0.163942	+	0.217421i
$685$	9.64004	−	1.38603i	0.368327	−	0.0529574i
$686$	−0.982611	−	1.66268i	−0.0375163	−	0.0634815i
$687$	−1.03682	−	1.19655i	−0.0395570	−	0.0456512i
$688$	3.38990	+	24.8001i	0.129239	+	0.945497i
$689$			29.0740i			1.10763i
$690$	−0.790475	+	21.0362i	−0.0300929	+	0.800834i
$691$	−31.5649			−1.20079			−0.600393	−	0.799705i	$-0.704989\pi$
$691$	−31.5649			−1.20079			−0.600393	+	0.799705i	$0.704989\pi$
$692$	0.401449	+	1.87682i	0.0152608	+	0.0713459i
$693$	−0.717308	+	0.621551i	−0.0272483	+	0.0236108i
$694$	8.97194	+	15.1815i	0.340570	+	0.576280i
$695$	−0.943764	−	6.56402i	−0.0357990	−	0.248988i
$696$	16.2683	+	13.2503i	0.616649	+	0.502253i
$697$	7.56993	+	3.45707i	0.286732	+	0.130946i
$698$	20.7223	−	22.1799i	0.784352	−	0.839523i
$699$	0.407755	−	2.83600i	0.0154227	−	0.107267i
$700$	11.8449	+	32.0979i	0.447697	+	1.21318i
$701$	14.9079	+	4.37734i	0.563062	+	0.165330i	0.550863	−	0.834596i	$-0.314299\pi$
$701$	14.9079	+	4.37734i	0.563062	+	0.165330i	0.0121991	+	0.999926i	$0.496117\pi$
$702$	−7.89466	−	2.64284i	−0.297965	−	0.0997478i
$703$	−15.9094	+	7.26556i	−0.600033	+	0.274026i
$704$	1.91941	+	0.738796i	0.0723406	+	0.0278444i
$705$	−29.0611	−	25.1816i	−1.09450	−	0.948393i
$706$	9.28050	+	4.66568i	0.349276	+	0.175595i
$707$	4.13160	−	6.42889i	0.155385	−	0.241783i
$708$	−0.656800	−	9.65482i	−0.0246840	−	0.362850i
$709$	−26.6228	+	17.1094i	−0.999838	+	0.642557i	−0.934744	−	0.355322i	$-0.884371\pi$
$709$	−26.6228	+	17.1094i	−0.999838	+	0.642557i	−0.0650944	+	0.997879i	$0.520735\pi$
$710$	27.1073	+	33.7580i	1.01732	+	1.26692i
$711$	7.04383	−	2.06826i	0.264164	−	0.0775656i
$712$	−44.6733	−	5.03865i	−1.67420	−	0.188831i
$713$	14.1011	−	48.0025i	0.528092	−	1.79771i
$714$	−16.3764	−	0.613387i	−0.612871	−	0.0229554i
$715$	4.50711	−	1.32341i	0.168557	−	0.0494927i
$716$	8.93627	+	12.0244i	0.333964	+	0.449371i
$717$	−3.61919	−	5.63157i	−0.135161	−	0.210315i
$718$	6.73439	−	0.712183i	0.251325	−	0.0265784i
$719$	13.4345	−	20.9045i	0.501022	−	0.779606i	−0.494983	−	0.868903i	$-0.664826\pi$
$719$	13.4345	−	20.9045i	0.501022	−	0.779606i	0.996005	+	0.0892967i	$0.0284619\pi$
$720$	−6.78463	+	10.3974i	−0.252848	+	0.387490i
$721$	26.1169	−	30.1406i	0.972646	−	1.12249i
$722$	8.79375	+	1.60235i	0.327269	+	0.0596334i
$723$	−2.27117	+	1.03721i	−0.0844658	+	0.0385742i
$724$	−2.03206	−	0.765977i	−0.0755210	−	0.0284673i
$725$	9.68394	−	32.9805i	0.359652	−	1.22486i
$726$	−14.2961	+	5.89255i	−0.530578	+	0.218693i
$727$	−6.41278	+	44.6018i	−0.237837	+	1.65419i	0.424828	+	0.905274i	$0.360335\pi$
$727$	−6.41278	+	44.6018i	−0.237837	+	1.65419i	−0.662665	+	0.748916i	$0.730575\pi$
$728$	45.2089	−	41.6530i	1.67555	−	1.54376i
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$	−28.3812	+	40.7254i	−1.05043	+	1.50731i
$731$	2.79526	+	19.4415i	0.103386	+	0.719068i
$732$	−3.79307	+	2.05409i	−0.140196	+	0.0759213i
$733$	−27.0839	−	31.2565i	−1.00037	−	1.15449i	−0.987983	−	0.154563i	$-0.950603\pi$
$733$	−27.0839	−	31.2565i	−1.00037	−	1.15449i	−0.0123854	−	0.999923i	$-0.503942\pi$
$734$	6.56539	+	25.9108i	0.242333	+	0.956386i
$735$	20.5785			0.759051
$736$	−2.66219	−	26.9984i	−0.0981296	−	0.995174i
$737$	−2.50344			−0.0922154
$738$	−0.920980	−	3.63472i	−0.0339018	−	0.133796i
$739$	7.15582	+	8.25826i	0.263231	+	0.303785i	0.871944	−	0.489606i	$-0.162859\pi$
$739$	7.15582	+	8.25826i	0.263231	+	0.303785i	−0.608713	+	0.793391i	$0.708314\pi$
$740$	−26.8113	+	14.5193i	−0.985602	+	0.533740i
$741$	−2.98322	−	20.7487i	−0.109591	−	0.762224i
$742$	14.7432	−	21.1556i	0.541240	−	0.776648i
$743$	2.27141	−	4.97369i	0.0833298	−	0.182467i	−0.863380	−	0.504554i	$-0.831657\pi$
$743$	2.27141	−	4.97369i	0.0833298	−	0.182467i	0.946710	+	0.322087i	$0.104384\pi$
$744$	21.7003	−	19.9934i	0.795570	−	0.732995i
$745$	6.10696	−	42.4748i	0.223742	−	1.55616i
$746$	−47.5679	+	19.6065i	−1.74158	+	0.717844i
$747$	0.705027	−	2.40110i	0.0257956	−	0.0878517i
$748$	1.51014	+	0.569240i	0.0552161	+	0.0208135i
$749$	−8.68904	+	3.96815i	−0.317491	+	0.144993i
$750$	−1.58217	−	0.288295i	−0.0577725	−	0.0105270i
$751$	18.5737	−	21.4352i	0.677763	−	0.782180i	−0.307807	−	0.951449i	$-0.599595\pi$
$751$	18.5737	−	21.4352i	0.677763	−	0.782180i	0.985570	+	0.169269i	$0.0541405\pi$
$752$	41.5022	+	27.0814i	1.51343	+	0.987557i
$753$	10.9269	−	17.0026i	0.398200	−	0.619611i
$754$	−61.4155	+	6.49489i	−2.23662	+	0.236530i
$755$	13.7510	+	21.3969i	0.500449	+	0.778714i
$756$	4.40437	+	5.92638i	0.160185	+	0.215540i
$757$	−28.4818	+	8.36301i	−1.03519	+	0.303959i	−0.754819	−	0.655934i	$-0.772275\pi$
$757$	−28.4818	+	8.36301i	−1.03519	+	0.303959i	−0.280369	+	0.959892i	$0.590457\pi$
$758$	−1.81179	−	0.0678618i	−0.0658073	−	0.00246485i
$759$	−0.931697	−	0.807518i	−0.0338185	−	0.0293110i
$760$	−31.0632	−	3.50358i	−1.12678	−	0.127088i
$761$	−18.2021	+	5.34463i	−0.659827	+	0.193743i	−0.594468	−	0.804119i	$-0.702637\pi$
$761$	−18.2021	+	5.34463i	−0.659827	+	0.193743i	−0.0653590	+	0.997862i	$0.520819\pi$
$762$	−4.32742	−	5.38915i	−0.156766	−	0.195228i
$763$	30.1700	−	19.3891i	1.09223	−	0.701931i
$764$	−1.84990	−	27.1931i	−0.0669270	−	0.983813i
$765$	−5.26698	+	8.19558i	−0.190428	+	0.296312i
$766$	−7.22588	−	3.63274i	−0.261082	−	0.131256i
$767$	21.5267	+	18.6530i	0.777286	+	0.673522i
$768$	6.84837	−	14.4603i	0.247119	−	0.521791i
$769$	−22.0083	+	10.0509i	−0.793639	+	0.362443i	−0.770622	−	0.637292i	$-0.780054\pi$
$769$	−22.0083	+	10.0509i	−0.793639	+	0.362443i	−0.0230170	+	0.999735i	$0.507327\pi$
$770$	−3.95068	−	1.32255i	−0.142373	−	0.0476612i
$771$	7.99640	+	2.34795i	0.287983	+	0.0845595i
$772$	−1.17484	−	3.18362i	−0.0422833	−	0.114581i
$773$	2.28478	−	15.8910i	0.0821778	−	0.571559i	−0.906580	−	0.422034i	$-0.861316\pi$
$773$	2.28478	−	15.8910i	0.0821778	−	0.571559i	0.988758	−	0.149525i	$-0.0477746\pi$
$774$	6.04160	−	6.46656i	0.217161	−	0.232436i
$775$	−43.9703	−	20.0806i	−1.57946	−	0.721316i
$776$	−32.5017	−	26.4722i	−1.16674	−	0.950298i
$777$	2.58069	+	17.9491i	0.0925817	+	0.643920i
$778$	7.51511	+	12.7164i	0.269430	+	0.455903i
$779$	7.13505	−	6.18256i	0.255640	−	0.221513i
$780$	−7.64367	−	35.7350i	−0.273687	−	1.27952i
$781$	−2.53572			−0.0907352
$782$	−2.23624	−	21.1703i	−0.0799676	−	0.757049i
$783$		−	7.41813i		−	0.265103i
$784$	−26.2760	+	3.59164i	−0.938430	+	0.128273i
$785$	0.770629	+	0.889353i	0.0275049	+	0.0317424i
$786$	−4.46425	−	7.55399i	−0.159235	−	0.269442i
$787$	−15.9745	+	2.29678i	−0.569429	+	0.0818715i	−0.421015	−	0.907054i	$-0.638326\pi$
$787$	−15.9745	+	2.29678i	−0.569429	+	0.0818715i	−0.148414	+	0.988925i	$0.547417\pi$
$788$	−23.9004	+	31.6969i	−0.851416	+	1.12916i
$789$	−8.00809	+	17.5353i	−0.285095	+	0.624272i
$790$	23.5462	+	21.9988i	0.837737	+	0.782684i
$791$	−58.7497	−	8.44693i	−2.08890	−	0.300338i
$792$	−0.226033	−	0.691126i	−0.00803172	−	0.0245581i
$793$	3.57705	−	12.1823i	0.127025	−	0.432606i
$794$	−39.5133	−	13.2276i	−1.40227	−	0.469430i
$795$	−6.36793	−	13.9438i	−0.225847	−	0.494536i
$796$	−11.7225	+	52.9998i	−0.415493	+	1.87853i
$797$	−19.1296	+	22.0767i	−0.677605	+	0.781998i	−0.985546	−	0.169407i	$-0.945815\pi$
$797$	−19.1296	+	22.0767i	−0.677605	+	0.781998i	0.307941	+	0.951405i	$0.400360\pi$
$798$	−8.35078	+	16.6105i	−0.295614	+	0.588007i
$799$	32.7133	+	21.0236i	1.15731	+	0.743760i
$800$	−26.1859	−	1.16317i	−0.925811	−	0.0411244i
$801$	8.59323	+	13.3713i	0.303627	+	0.472453i
$802$	19.9971	+	24.9034i	0.706123	+	0.879370i
$803$	−0.819088	−	2.78956i	−0.0289050	−	0.0984413i
$804$	−1.45689	+	19.4209i	−0.0513805	+	0.684924i
$805$	7.81434	+	54.3967i	0.275419	+	1.91723i
$806$	−3.25076	+	86.7897i	−0.114503	+	3.05704i
$807$	2.65282	+	9.03469i	0.0933838	+	0.318036i
$808$	3.31395	+	4.82652i	0.116584	+	0.169796i
$809$	−8.21146	+	5.27718i	−0.288700	+	0.185536i	−0.676972	−	0.736009i	$-0.736708\pi$
$809$	−8.21146	+	5.27718i	−0.288700	+	0.185536i	0.388273	+	0.921545i	$0.373072\pi$
$810$	4.36510	−	0.461624i	0.153374	−	0.0162198i
$811$	−34.4139	−	22.1165i	−1.20844	−	0.776615i	−0.228040	−	0.973652i	$-0.573232\pi$
$811$	−34.4139	−	22.1165i	−1.20844	−	0.776615i	−0.980396	+	0.197037i	$0.936868\pi$
$812$	47.9824	+	26.4173i	1.68385	+	0.927066i
$813$	18.7316	+	16.2310i	0.656946	+	0.569247i
$814$	0.320126	−	1.75686i	0.0112204	−	0.0615778i
$815$	−4.21778	−	9.23564i	−0.147742	−	0.323510i
$816$	5.29483	−	11.3839i	0.185356	−	0.398517i
$817$	21.3800	+	6.27772i	0.747990	+	0.219630i
$818$	−45.8737	+	18.9081i	−1.60393	+	0.661108i
$819$	−21.5125	−	3.09302i	−0.751706	−	0.108079i
$820$	11.6784	−	11.5975i	0.407826	−	0.405001i
$821$	−4.33067	−	1.97775i	−0.151141	−	0.0690240i	0.338408	−	0.940999i	$-0.390112\pi$
$821$	−4.33067	−	1.97775i	−0.151141	−	0.0690240i	−0.489550	+	0.871975i	$0.662839\pi$
$822$	3.64068	+	2.53716i	0.126983	+	0.0884936i
$823$	−36.5440	+	5.25423i	−1.27384	+	0.183151i	−0.745859	−	0.666104i	$-0.767961\pi$
$823$	−36.5440	+	5.25423i	−1.27384	+	0.183151i	−0.527984	+	0.849255i	$0.677052\pi$
$824$	13.5339	+	27.3932i	0.471475	+	0.954286i
$825$	−0.900278	+	0.780095i	−0.0313436	+	0.0271594i
$826$	−6.20509	−	24.4889i	−0.215903	−	0.852077i
$827$			38.8942i			1.35248i	0.736680	+	0.676241i	$0.236392\pi$
$827$			38.8942i			1.35248i	−0.736680	+	0.676241i	$0.763608\pi$
$828$	−6.80669	+	6.75789i	−0.236549	+	0.234853i
$829$		−	31.1378i		−	1.08146i	−0.841196	−	0.540730i	$-0.818148\pi$
$829$		−	31.1378i		−	1.08146i	0.841196	−	0.540730i	$-0.181852\pi$
$830$	10.6479	−	2.69802i	0.369596	−	0.0936497i
$831$	12.6425	−	10.9548i	0.438564	−	0.380018i
$832$	15.9969	+	44.2948i	0.554593	+	1.53564i
$833$	−20.5985	+	2.96161i	−0.713694	+	0.102614i
$834$	1.72758	−	2.47899i	0.0598214	−	0.0858403i
$835$	−49.8449	−	22.7634i	−1.72495	−	0.787760i
$836$	1.29912	−	1.29012i	0.0449310	−	0.0446197i
$837$	−10.3260	−	1.48465i	−0.356918	−	0.0513170i
$838$	−3.45599	−	8.38468i	−0.119385	−	0.289644i
$839$	−32.0663	−	9.41552i	−1.10705	−	0.325060i	−0.323402	−	0.946262i	$-0.604827\pi$
$839$	−32.0663	−	9.41552i	−1.10705	−	0.325060i	−0.783651	+	0.621202i	$0.786645\pi$
$840$	−12.5590	+	29.8785i	−0.433328	+	1.03091i
$841$	−10.8127	−	23.6766i	−0.372853	−	0.816433i
$842$	47.1371	+	8.58909i	1.62445	+	0.296000i
$843$	−12.5574	−	10.8811i	−0.432502	−	0.374765i
$844$	−7.68842	+	13.9647i	−0.264646	+	0.480683i
$845$	56.5434	+	36.3382i	1.94515	+	1.25007i
$846$	−1.84261	−	17.4237i	−0.0633502	−	0.599038i
$847$	−33.9587	+	21.8240i	−1.16684	+	0.749880i
$848$	10.5647	+	16.6930i	0.362792	+	0.573239i
$849$	3.98116	+	13.5586i	0.136633	+	0.465329i
$850$	−20.5536	−	0.769848i	−0.704984	−	0.0264056i
$851$	−22.6025	+	6.63373i	−0.774805	+	0.227401i
$852$	−1.47567	+	19.6713i	−0.0505557	+	0.673929i
$853$	14.2154	+	48.4132i	0.486726	+	1.65763i	0.726776	+	0.686875i	$0.241018\pi$
$853$	14.2154	+	48.4132i	0.486726	+	1.65763i	−0.240050	+	0.970760i	$0.577164\pi$
$854$	−8.78038	+	7.05054i	−0.300458	+	0.241265i
$855$	5.97523	+	9.29764i	0.204349	+	0.317972i
$856$	−0.223063	−	7.31475i	−0.00762412	−	0.250013i
$857$	−43.1954	−	27.7600i	−1.47553	−	0.948263i	−0.997555	−	0.0698871i	$-0.977736\pi$
$857$	−43.1954	−	27.7600i	−1.47553	−	0.948263i	−0.477971	−	0.878376i	$-0.658628\pi$
$858$	1.91225	+	0.961366i	0.0652832	+	0.0328205i
$859$	−10.8504	+	12.5220i	−0.370209	+	0.427244i	−0.910034	−	0.414533i	$-0.863945\pi$
$859$	−10.8504	+	12.5220i	−0.370209	+	0.427244i	0.539825	+	0.841777i	$0.318490\pi$
$860$	37.9286	+	8.38907i	1.29336	+	0.286065i
$861$	−4.06630	−	8.90396i	−0.138579	−	0.303446i
$862$	2.36845	−	7.07499i	0.0806697	−	0.240975i
$863$	−0.260459	+	0.887043i	−0.00886614	+	0.0301953i	−0.963807	−	0.266600i	$-0.914100\pi$
$863$	−0.260459	+	0.887043i	−0.00886614	+	0.0301953i	0.954941	+	0.296795i	$0.0959179\pi$
$864$	−5.49309	+	1.35129i	−0.186879	+	0.0459718i
$865$	2.94821	+	0.423888i	0.100242	+	0.0144126i
$866$	−2.96289	+	3.17129i	−0.100683	+	0.107765i
$867$	−2.96947	+	6.50222i	−0.100848	+	0.220827i
$868$	46.3757	−	61.5039i	1.57410	−	2.08758i
$869$	−1.86811	+	0.268594i	−0.0633713	+	0.00911141i
$870$	28.0322	−	16.5665i	0.950380	−	0.561656i
$871$	−37.5398	−	43.3232i	−1.27199	−	1.46795i
$872$	4.73728	+	27.0639i	0.160424	+	0.916499i
$873$			14.8203i			0.501593i
$874$	−22.9006	−	7.66938i	−0.774624	−	0.259421i
$875$	−4.19835			−0.141930
$876$	−22.1172	+	4.73084i	−0.747271	+	0.159840i
$877$	−0.227647	+	0.197257i	−0.00768710	+	0.00666091i	−0.658696	−	0.752409i	$-0.728892\pi$
$877$	−0.227647	+	0.197257i	−0.00768710	+	0.00666091i	0.651009	+	0.759070i	$0.274346\pi$
$878$	34.3930	−	20.3255i	1.16071	−	0.685954i
$879$	−2.77816	−	19.3225i	−0.0937049	−	0.651732i
$880$	2.10689	−	2.39760i	0.0710233	−	0.0808230i
$881$	9.70204	+	4.43077i	0.326870	+	0.149276i	0.572090	−	0.820191i	$-0.306133\pi$
$881$	9.70204	+	4.43077i	0.326870	+	0.149276i	−0.245220	+	0.969467i	$0.578860\pi$
$882$	6.85140	+	6.40114i	0.230699	+	0.215538i
$883$	−6.23716	+	43.3804i	−0.209897	+	1.45987i	0.563590	+	0.826055i	$0.309420\pi$
$883$	−6.23716	+	43.3804i	−0.209897	+	1.45987i	−0.773487	+	0.633812i	$0.781489\pi$
$884$	12.7940	+	34.6695i	0.430307	+	1.16606i
$885$	−14.4096	−	4.23105i	−0.484375	−	0.142225i
$886$	−6.31185	+	18.8547i	−0.212051	+	0.633434i
$887$	−2.09953	+	0.958825i	−0.0704954	+	0.0321942i	−0.450351	−	0.892852i	$-0.648701\pi$
$887$	−2.09953	+	0.958825i	−0.0704954	+	0.0321942i	0.379855	+	0.925046i	$0.375974\pi$
$888$	−13.4429	−	3.50585i	−0.451113	−	0.117649i
$889$	−13.6360	−	11.8157i	−0.457338	−	0.396285i
$890$	−31.3378	+	62.3341i	−1.05045	+	2.08944i
$891$	−0.138991	+	0.216274i	−0.00465638	+	0.00724547i
$892$	−30.1394	+	2.05033i	−1.00914	+	0.0686501i
$893$	37.1123	−	23.8506i	1.24191	−	0.798130i
$894$	15.2454	−	12.2419i	0.509884	−	0.409431i
$895$	22.3079	−	6.55019i	0.745671	−	0.218949i
$896$	10.8214	−	40.3429i	0.361518	−	1.34776i
$897$	0.00342017	−	28.2324i	0.000114196	−	0.942652i
$898$	1.68324	−	44.9396i	0.0561704	−	1.49965i
$899$	−74.2524	+	21.8025i	−2.47646	+	0.727153i
$900$	5.52782	+	7.43806i	0.184261	+	0.247935i
$901$	8.38085	+	13.0409i	0.279207	+	0.434454i
$902$	0.101377	+	0.958620i	0.00337549	+	0.0319186i
$903$	12.4903	−	19.4353i	0.415651	−	0.646765i
$904$	23.4066	−	38.9851i	0.778493	−	1.29662i
$905$	−2.20699	+	2.54700i	−0.0733628	+	0.0846652i
$906$	−2.07748	+	11.4012i	−0.0690196	+	0.378781i
$907$	16.4224	−	7.49985i	0.545296	−	0.249029i	−0.123667	−	0.992324i	$-0.539465\pi$
$907$	16.4224	−	7.49985i	0.545296	−	0.249029i	0.668964	+	0.743295i	$0.266738\pi$
$908$	−9.54919	+	25.3331i	−0.316901	+	0.840707i
$909$	0.583172	−	1.98610i	0.0193426	−	0.0658749i
$910$	−36.3543	−	88.2003i	−1.20513	−	2.92381i
$911$	2.02575	−	14.0894i	0.0671161	−	0.466803i	−0.928352	−	0.371703i	$-0.878774\pi$
$911$	2.02575	−	14.0894i	0.0671161	−	0.466803i	0.995468	−	0.0950998i	$-0.0303170\pi$
$912$	−9.25232	−	10.8290i	−0.306375	−	0.358583i
$913$	−0.267257	+	0.585211i	−0.00884492	+	0.0193677i
$914$	−14.2106	−	9.90322i	−0.470044	−	0.327569i
$915$	0.952684	+	6.62607i	0.0314948	+	0.219051i
$916$	2.78445	−	1.50788i	0.0920007	−	0.0498218i
$917$	−15.0005	−	17.3116i	−0.495362	−	0.571678i
$918$	−4.30289	+	1.09029i	−0.142017	+	0.0359848i
$919$	1.87892			0.0619798			0.0309899	−	0.999520i	$-0.490134\pi$
$919$	1.87892			0.0619798			0.0309899	+	0.999520i	$0.490134\pi$
$920$	−40.7381	−	10.6296i	−1.34310	−	0.350449i
$921$	−13.2977			−0.438174
$922$	14.6034	−	3.70028i	0.480938	−	0.121862i
$923$	−38.0238	−	43.8818i	−1.25157	−	1.44439i
$924$	−0.903946	−	1.66922i	−0.0297377	−	0.0549134i
$925$	3.23896	+	22.5275i	0.106497	+	0.740700i
$926$	−2.19596	−	1.53035i	−0.0721638	−	0.0502903i
$927$	4.48752	−	9.82629i	0.147389	−	0.322738i
$928$	−32.9020	+	26.0457i	−1.08006	+	0.854993i
$929$	4.58319	−	31.8768i	0.150369	−	1.04584i	−0.765232	−	0.643755i	$-0.777376\pi$
$929$	4.58319	−	31.8768i	0.150369	−	1.04584i	0.915601	−	0.402088i	$-0.131715\pi$
$930$	−17.4500	−	42.3361i	−0.572209	−	1.38826i
$931$	−6.65132	+	22.6523i	−0.217988	+	0.742399i
$932$	5.36203	+	2.02119i	0.175639	+	0.0662064i
$933$	11.9944	−	5.47768i	0.392681	−	0.179331i
$934$	5.47092	−	30.0245i	0.179014	−	0.982432i
$935$	1.64014	−	1.89282i	0.0536382	−	0.0619018i
$936$	8.57083	−	14.2752i	0.280146	−	0.466600i
$937$	−8.76782	+	13.6430i	−0.286432	+	0.445697i	−0.954416	−	0.298478i	$-0.903521\pi$
$937$	−8.76782	+	13.6430i	−0.286432	+	0.445697i	0.667984	+	0.744176i	$0.267157\pi$
$938$	5.34690	+	50.5601i	0.174582	+	1.65085i
$939$	6.05385	+	9.41997i	0.197560	+	0.307409i
$940$	61.7268	−	45.8742i	2.01331	−	1.49625i
$941$	−36.8487	+	10.8197i	−1.20123	+	0.352714i	−0.820324	−	0.571899i	$-0.806207\pi$
$941$	−36.8487	+	10.8197i	−1.20123	+	0.352714i	−0.380908	+	0.924613i	$0.624389\pi$
$942$	−0.0200691	+	0.535811i	−0.000653887	+	0.0174577i
$943$	10.6978	−	6.87320i	0.348367	−	0.223822i
$944$	19.1377	+	2.88753i	0.622878	+	0.0939810i
$945$	10.9948	−	3.22835i	0.357660	−	0.105018i
$946$	−1.77399	+	1.42450i	−0.0576775	+	0.0463144i
$947$	21.0048	−	13.4990i	0.682565	−	0.438658i	−0.152871	−	0.988246i	$-0.548852\pi$
$947$	21.0048	−	13.4990i	0.682565	−	0.438658i	0.835435	+	0.549589i	$0.185216\pi$
$948$	0.996514	+	14.6485i	0.0323653	+	0.475763i
$949$	35.9921	−	56.0048i	1.16835	−	1.81799i
$950$	−10.4809	+	20.8475i	−0.340045	+	0.676383i
$951$	−21.6243	−	18.7376i	−0.701216	−	0.607607i
$952$	8.27114	−	31.7149i	0.268069	−	1.02789i
$953$	4.64218	−	2.12001i	0.150375	−	0.0686739i	−0.338806	−	0.940856i	$-0.610023\pi$
$953$	4.64218	−	2.12001i	0.150375	−	0.0686739i	0.489181	+	0.872182i	$0.337296\pi$
$954$	2.21722	−	6.62325i	0.0717852	−	0.214436i
$955$	−40.5853	−	11.9169i	−1.31331	−	0.385622i
$956$	12.5606	−	4.63517i	0.406238	−	0.149912i
$957$	−0.271408	+	1.88769i	−0.00877339	+	0.0610203i
$958$	13.3872	+	12.5075i	0.432521	+	0.404097i
$959$	10.5376	+	4.81237i	0.340277	+	0.155399i
$960$	−17.3737	−	17.7399i	−0.560734	−	0.572554i
$961$	11.0763	+	77.0376i	0.357301	+	2.48508i
$962$	35.2036	−	20.8046i	1.13501	−	0.670768i
$963$	−1.95540	+	1.69436i	−0.0630117	+	0.0546000i
$964$	−1.04450	−	4.88315i	−0.0336410	−	0.157276i
$965$	−5.26634			−0.169530
$966$	−14.3189	+	20.5415i	−0.460703	+	0.660912i
$967$		−	45.5474i		−	1.46471i	−0.680926	−	0.732353i	$-0.738422\pi$
$967$		−	45.5474i		−	1.46471i	0.680926	−	0.732353i	$-0.261578\pi$
$968$	−5.33219	−	30.4626i	−0.171383	−	0.979105i
$969$	−7.31911	−	8.44670i	−0.235124	−	0.271347i
$970$	−56.0042	+	33.0974i	−1.79819	+	1.06269i
$971$	−9.11993	+	1.31125i	−0.292673	+	0.0420800i	−0.287087	−	0.957904i	$-0.592687\pi$
$971$	−9.11993	+	1.31125i	−0.292673	+	0.0420800i	−0.00558530	+	0.999984i	$0.501778\pi$
$972$	1.59691	+	1.20411i	0.0512208	+	0.0386220i
$973$	3.27680	−	7.17519i	0.105049	−	0.230026i
$974$	−5.44491	+	5.82790i	−0.174466	+	0.186738i
$975$	−26.9998	−	3.88199i	−0.864686	−	0.124323i
$976$	−2.37292	−	8.29433i	−0.0759554	−	0.265495i
$977$	−12.8802	+	43.8658i	−0.412073	+	1.40339i	0.448372	+	0.893847i	$0.352004\pi$
$977$	−12.8802	+	43.8658i	−0.412073	+	1.40339i	−0.860445	+	0.509544i	$0.829814\pi$
$978$	1.46857	−	4.38688i	0.0469597	−	0.140277i
$979$	−1.69749	−	3.71699i	−0.0542521	−	0.118796i
$980$	−8.88831	+	40.1858i	−0.283927	+	1.28369i
$981$	6.36132	−	7.34136i	0.203101	−	0.234391i
$982$	14.1769	+	7.12729i	0.452403	+	0.227441i
$983$	10.0959	+	6.48827i	0.322010	+	0.206944i	0.691652	−	0.722231i	$-0.256883\pi$
$983$	10.0959	+	6.48827i	0.322010	+	0.206944i	−0.369642	+	0.929174i	$0.620520\pi$
$984$	7.49568	−	0.228580i	0.238954	−	0.00728687i
$985$	33.3074	+	51.8274i	1.06126	+	1.65136i
$986$	−25.6751	+	20.6168i	−0.817663	+	0.656573i
$987$	−12.8862	−	43.8865i	−0.410173	−	1.39692i
$988$	41.8067	+	3.13619i	1.33005	+	0.0997755i
$989$	27.2973	+	12.4703i	0.868003	+	0.396531i
$990$	−1.12767	−	0.0422377i	−0.0358398	−	0.00134240i
$991$	−14.0771	−	47.9421i	−0.447172	−	1.52293i	−0.807365	−	0.590052i	$-0.799107\pi$
$991$	−14.0771	−	47.9421i	−0.447172	−	1.52293i	0.360193	−	0.932878i	$-0.382711\pi$
$992$	29.6704	+	51.0119i	0.942037	+	1.61963i
$993$	13.5329	−	8.69708i	0.429454	−	0.275994i
$994$	5.41584	+	51.2120i	0.171780	+	1.62435i
$995$	70.8659	+	45.5427i	2.24660	+	1.44380i
$996$	4.38436	+	2.41387i	0.138924	+	0.0764863i
$997$	17.5252	+	15.1857i	0.555028	+	0.480934i	0.886627	−	0.462486i	$-0.153043\pi$
$997$	17.5252	+	15.1857i	0.555028	+	0.480934i	−0.331599	+	0.943421i	$0.607588\pi$
$998$	5.77472	+	1.05224i	0.182796	+	0.0333081i
$999$	2.04041	+	4.46788i	0.0645558	+	0.141358i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.t.a.451.13	yes	240
8.3	odd	2	inner	552.2.t.a.451.9	yes	240
23.5	odd	22	inner	552.2.t.a.235.9	✓	240
184.51	even	22	inner	552.2.t.a.235.13	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.t.a.235.9	✓	240	23.5	odd	22	inner
552.2.t.a.235.13	yes	240	184.51	even	22	inner
552.2.t.a.451.9	yes	240	8.3	odd	2	inner
552.2.t.a.451.13	yes	240	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.t (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.347362 + 1.37089i) q^{2} +(0.654861 + 0.755750i) q^{3} +(-1.75868 + 0.952390i) q^{4} +(0.441718 + 3.07221i) q^{5} +(-0.808576 + 1.16026i) q^{6} +(-1.53367 + 3.35827i) q^{7} +(-1.91652 - 2.08013i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(0.347362 + 1.37089i) q^{2} +(0.654861 + 0.755750i) q^{3} +(-1.75868 + 0.952390i) q^{4} +(0.441718 + 3.07221i) q^{5} +(-0.808576 + 1.16026i) q^{6} +(-1.53367 + 3.35827i) q^{7} +(-1.91652 - 2.08013i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(-4.05823 + 1.67272i) q^{10} +(0.0724295 - 0.246672i) q^{11} +(-1.87146 - 0.705438i) q^{12} +(5.35488 - 2.44549i) q^{13} +(-5.13655 - 0.935958i) q^{14} +(-2.03256 + 2.34570i) q^{15} +(2.18591 - 3.34990i) q^{16} +(1.69694 - 2.64049i) q^{17} +(-1.40637 + 0.148728i) q^{18} +(-1.92513 - 2.99556i) q^{19} +(-3.70279 - 4.98235i) q^{20} +(-3.54235 + 1.04013i) q^{21} +(0.363320 + 0.0136083i) q^{22} +(-1.99173 - 4.36268i) q^{23} +(0.317005 - 2.81061i) q^{24} +(-4.44592 + 1.30544i) q^{25} +(5.21258 + 6.49148i) q^{26} +(-0.841254 + 0.540641i) q^{27} +(-0.501148 - 7.36676i) q^{28} +(-4.01055 + 6.24053i) q^{29} +(-3.92173 - 1.97161i) q^{30} +(7.88409 + 6.83161i) q^{31} +(5.35164 + 1.83301i) q^{32} +(0.233854 - 0.106797i) q^{33} +(4.20928 + 1.40911i) q^{34} +(-10.9948 - 3.22835i) q^{35} +(-0.692410 - 1.87632i) q^{36} +(0.699014 - 4.86175i) q^{37} +(3.43787 - 3.67968i) q^{38} +(5.35488 + 2.44549i) q^{39} +(5.54405 - 6.80679i) q^{40} +(0.377327 + 2.62437i) q^{41} +(-2.65638 - 4.49487i) q^{42} +(-4.72925 + 4.09791i) q^{43} +(0.107548 + 0.502798i) q^{44} -3.10381 q^{45} +(5.28891 - 4.24588i) q^{46} +12.3891i q^{47} +(3.96315 - 0.541718i) q^{48} +(-4.34179 - 5.01069i) q^{49} +(-3.33396 - 5.64141i) q^{50} +(3.10681 - 0.446692i) q^{51} +(-7.08845 + 9.40076i) q^{52} +(-2.05165 + 4.49249i) q^{53} +(-1.03338 - 0.965468i) q^{54} +(0.789823 + 0.113559i) q^{55} +(9.92495 - 3.24595i) q^{56} +(1.00320 - 3.41659i) q^{57} +(-9.94820 - 3.33030i) q^{58} +(2.01001 + 4.40132i) q^{59} +(1.34060 - 6.06113i) q^{60} +(1.41239 - 1.62998i) q^{61} +(-6.62675 + 13.1813i) q^{62} +(-3.10582 - 1.99599i) q^{63} +(-0.653900 + 7.97323i) q^{64} +(9.87841 + 15.3711i) q^{65} +(0.227639 + 0.283490i) q^{66} +(-2.74344 - 9.34331i) q^{67} +(-0.469597 + 6.25993i) q^{68} +(1.99279 - 4.36220i) q^{69} +(0.606556 - 16.1940i) q^{70} +(-2.77882 - 9.46378i) q^{71} +(2.33171 - 1.60098i) q^{72} +(9.51353 - 6.11398i) q^{73} +(6.90774 - 0.730515i) q^{74} +(-3.89805 - 2.50512i) q^{75} +(6.23863 + 3.43475i) q^{76} +(0.717308 + 0.621551i) q^{77} +(-1.49242 + 8.19042i) q^{78} +(-3.04965 - 6.67779i) q^{79} +(11.2572 + 5.23586i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-3.46665 + 1.42888i) q^{82} +(-2.47700 - 0.356138i) q^{83} +(5.23925 - 5.20295i) q^{84} +(8.86173 + 4.04702i) q^{85} +(-7.26055 - 5.05982i) q^{86} +(-7.34263 + 1.05571i) q^{87} +(-0.651923 + 0.322089i) q^{88} +(12.0123 - 10.4087i) q^{89} +(-1.07814 - 4.25498i) q^{90} +21.7337i q^{91} +(7.65779 + 5.77566i) q^{92} +10.4322i q^{93} +(-16.9841 + 4.30350i) q^{94} +(8.35264 - 7.23760i) q^{95} +(2.11928 + 5.24487i) q^{96} +(14.6695 - 2.10915i) q^{97} +(5.36093 - 7.69264i) q^{98} +(0.233854 + 0.106797i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9}+O(q^{10}) \) 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9	\( 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9} + 4 q^{12} - 4 q^{16} + 44 q^{17} - 55 q^{20} - 24 q^{25} + 24 q^{27} + 33 q^{34} + 7 q^{36} - 132 q^{38} + 11 q^{40} - 66 q^{42} + 77 q^{44} + 37 q^{48} - 56 q^{49} - 37 q^{50} - 55 q^{52} - 11 q^{54} + 132 q^{56} + 37 q^{58} + 11 q^{60} + 51 q^{62} - 4 q^{64} - 55 q^{66} - 132 q^{70} + 144 q^{73} + 44 q^{74} + 24 q^{75} - 55 q^{76} - 198 q^{80} - 24 q^{81} - 26 q^{82} + 44 q^{84} - 110 q^{86} + 22 q^{88} - 139 q^{92} - 117 q^{94} - 209 q^{98}+O(q^{100}) \) 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9 + 4 * q^12 - 4 * q^16 + 44 * q^17 - 55 * q^20 - 24 * q^25 + 24 * q^27 + 33 * q^34 + 7 * q^36 - 132 * q^38 + 11 * q^40 - 66 * q^42 + 77 * q^44 + 37 * q^48 - 56 * q^49 - 37 * q^50 - 55 * q^52 - 11 * q^54 + 132 * q^56 + 37 * q^58 + 11 * q^60 + 51 * q^62 - 4 * q^64 - 55 * q^66 - 132 * q^70 + 144 * q^73 + 44 * q^74 + 24 * q^75 - 55 * q^76 - 198 * q^80 - 24 * q^81 - 26 * q^82 + 44 * q^84 - 110 * q^86 + 22 * q^88 - 139 * q^92 - 117 * q^94 - 209 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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