LMFDB - Embedded newform 690.2.r.a.49.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(49,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 16]))

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

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

chi := DirichletCharacter("690.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.r (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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$12$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			49.8
Character	$\chi$	$=$	690.49
Dual form			690.2.r.a.169.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.989821 - 0.142315i) q^{2} +(0.909632 + 0.415415i) q^{3} +(0.959493 - 0.281733i) q^{4} +(-1.38916 - 1.75221i) q^{5} +(0.959493 + 0.281733i) q^{6} +(-0.0169454 - 0.0263676i) q^{7} +(0.909632 - 0.415415i) q^{8} +(0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(0.989821 - 0.142315i) q^{2} +(0.909632 + 0.415415i) q^{3} +(0.959493 - 0.281733i) q^{4} +(-1.38916 - 1.75221i) q^{5} +(0.959493 + 0.281733i) q^{6} +(-0.0169454 - 0.0263676i) q^{7} +(0.909632 - 0.415415i) q^{8} +(0.654861 + 0.755750i) q^{9} +(-1.62439 - 1.53668i) q^{10} +(0.838672 - 5.83309i) q^{11} +(0.989821 + 0.142315i) q^{12} +(-0.563617 + 0.877004i) q^{13} +(-0.0205254 - 0.0236876i) q^{14} +(-0.535731 - 2.17094i) q^{15} +(0.841254 - 0.540641i) q^{16} +(0.967380 - 3.29460i) q^{17} +(0.755750 + 0.654861i) q^{18} +(3.93372 - 1.15504i) q^{19} +(-1.82654 - 1.28986i) q^{20} +(-0.00446060 - 0.0310242i) q^{21} -5.89308i q^{22} +(4.10154 + 2.48544i) q^{23} +1.00000 q^{24} +(-1.14047 + 4.86820i) q^{25} +(-0.433069 + 0.948289i) q^{26} +(0.281733 + 0.959493i) q^{27} +(-0.0236876 - 0.0205254i) q^{28} +(1.01582 + 0.298273i) q^{29} +(-0.839235 - 2.07260i) q^{30} +(0.447429 + 0.979733i) q^{31} +(0.755750 - 0.654861i) q^{32} +(3.18604 - 4.95757i) q^{33} +(0.488664 - 3.39873i) q^{34} +(-0.0226616 + 0.0663207i) q^{35} +(0.841254 + 0.540641i) q^{36} +(-6.76119 + 5.85860i) q^{37} +(3.72930 - 1.70312i) q^{38} +(-0.877004 + 0.563617i) q^{39} +(-1.99152 - 1.01679i) q^{40} +(-0.525260 + 0.606183i) q^{41} +(-0.00883040 - 0.0300736i) q^{42} +(-5.04181 - 2.30252i) q^{43} +(-0.838672 - 5.83309i) q^{44} +(0.414525 - 2.19731i) q^{45} +(4.41350 + 1.87643i) q^{46} +6.51753i q^{47} +(0.989821 - 0.142315i) q^{48} +(2.90750 - 6.36653i) q^{49} +(-0.436045 + 4.98095i) q^{50} +(2.24858 - 2.59500i) q^{51} +(-0.293705 + 1.00027i) q^{52} +(0.723111 + 1.12518i) q^{53} +(0.415415 + 0.909632i) q^{54} +(-11.3858 + 6.63357i) q^{55} +(-0.0263676 - 0.0169454i) q^{56} +(4.05806 + 0.583461i) q^{57} +(1.04793 + 0.150670i) q^{58} +(2.38036 + 1.52977i) q^{59} +(-1.12565 - 1.93207i) q^{60} +(0.669151 + 1.46524i) q^{61} +(0.582306 + 0.906085i) q^{62} +(0.00883040 - 0.0300736i) q^{63} +(0.654861 - 0.755750i) q^{64} +(2.31965 - 0.230726i) q^{65} +(2.44807 - 5.36053i) q^{66} +(-13.8191 + 1.98689i) q^{67} -3.43368i q^{68} +(2.69840 + 3.96467i) q^{69} +(-0.0129925 + 0.0688707i) q^{70} +(-0.625522 - 4.35060i) q^{71} +(0.909632 + 0.415415i) q^{72} +(1.29051 + 4.39508i) q^{73} +(-5.85860 + 6.76119i) q^{74} +(-3.05973 + 3.95450i) q^{75} +(3.44896 - 2.21651i) q^{76} +(-0.168016 + 0.0767305i) q^{77} +(-0.787867 + 0.682690i) q^{78} +(9.48726 + 6.09709i) q^{79} +(-2.11595 - 0.723015i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(-0.433645 + 0.674765i) q^{82} +(-3.33508 + 2.88986i) q^{83} +(-0.0130204 - 0.0285108i) q^{84} +(-7.11666 + 2.88167i) q^{85} +(-5.31817 - 1.56156i) q^{86} +(0.800118 + 0.693307i) q^{87} +(-1.66027 - 5.65437i) q^{88} +(-2.96711 + 6.49707i) q^{89} +(0.0975956 - 2.23394i) q^{90} +0.0326752 q^{91} +(4.63562 + 1.22922i) q^{92} +1.07707i q^{93} +(0.927542 + 6.45120i) q^{94} +(-7.48845 - 5.28816i) q^{95} +(0.959493 - 0.281733i) q^{96} +(2.22467 + 1.92768i) q^{97} +(1.97185 - 6.71551i) q^{98} +(4.95757 - 3.18604i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{4} + 12 q^{6} + 12 q^{9}+O(q^{10}) $ 120 * q + 12 * q^4 + 12 * q^6 + 12 * q^9	$ 120 q + 12 q^{4} + 12 q^{6} + 12 q^{9} + 18 q^{10} - 8 q^{14} - 4 q^{15} - 12 q^{16} + 22 q^{20} + 14 q^{21} + 120 q^{24} + 52 q^{25} + 16 q^{29} + 8 q^{31} - 36 q^{34} - 90 q^{35} - 12 q^{36} + 22 q^{39} + 4 q^{40} + 16 q^{41} - 4 q^{49} - 4 q^{50} + 8 q^{51} - 12 q^{54} - 56 q^{55} + 8 q^{56} + 138 q^{59} + 4 q^{60} - 36 q^{61} + 12 q^{64} + 52 q^{65} + 96 q^{70} + 8 q^{71} + 8 q^{74} - 4 q^{75} - 60 q^{79} - 12 q^{81} + 8 q^{84} + 24 q^{85} - 8 q^{86} - 104 q^{89} + 4 q^{90} - 144 q^{91} - 24 q^{94} - 14 q^{95} + 12 q^{96} - 44 q^{99}+O(q^{100}) $ 120 * q + 12 * q^4 + 12 * q^6 + 12 * q^9 + 18 * q^10 - 8 * q^14 - 4 * q^15 - 12 * q^16 + 22 * q^20 + 14 * q^21 + 120 * q^24 + 52 * q^25 + 16 * q^29 + 8 * q^31 - 36 * q^34 - 90 * q^35 - 12 * q^36 + 22 * q^39 + 4 * q^40 + 16 * q^41 - 4 * q^49 - 4 * q^50 + 8 * q^51 - 12 * q^54 - 56 * q^55 + 8 * q^56 + 138 * q^59 + 4 * q^60 - 36 * q^61 + 12 * q^64 + 52 * q^65 + 96 * q^70 + 8 * q^71 + 8 * q^74 - 4 * q^75 - 60 * q^79 - 12 * q^81 + 8 * q^84 + 24 * q^85 - 8 * q^86 - 104 * q^89 + 4 * q^90 - 144 * q^91 - 24 * q^94 - 14 * q^95 + 12 * q^96 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$1$	$e\left(\frac{8}{11}\right)$

Coefficient data

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

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

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

$2$	0.989821	−	0.142315i	0.699909	−	0.100632i
$2$	0.989821	−	0.142315i	0.699909	−	0.100632i
$3$	0.909632	+	0.415415i	0.525176	+	0.239840i
$3$	0.909632	+	0.415415i	0.525176	+	0.239840i
$4$	0.959493	−	0.281733i	0.479746	−	0.140866i
$5$	−1.38916	−	1.75221i	−0.621251	−	0.783611i
$5$	−1.38916	−	1.75221i	−0.621251	−	0.783611i
$6$	0.959493	+	0.281733i	0.391711	+	0.115017i
$7$	−0.0169454	−	0.0263676i	−0.00640477	−	0.00996601i	0.838036	−	0.545614i	$-0.183704\pi$
$7$	−0.0169454	−	0.0263676i	−0.00640477	−	0.00996601i	−0.844441	+	0.535648i	$0.820067\pi$
$8$	0.909632	−	0.415415i	0.321603	−	0.146871i
$9$	0.654861	+	0.755750i	0.218287	+	0.251917i
$10$	−1.62439	−	1.53668i	−0.513676	−	0.485939i
$11$	0.838672	−	5.83309i	0.252869	−	1.75874i	−0.327934	−	0.944701i	$-0.606352\pi$
$11$	0.838672	−	5.83309i	0.252869	−	1.75874i	0.580804	−	0.814044i	$-0.302738\pi$
$12$	0.989821	+	0.142315i	0.285737	+	0.0410828i
$13$	−0.563617	+	0.877004i	−0.156319	+	0.243237i	−0.910576	−	0.413343i	$-0.864361\pi$
$13$	−0.563617	+	0.877004i	−0.156319	+	0.243237i	0.754256	+	0.656580i	$0.227998\pi$
$14$	−0.0205254	−	0.0236876i	−0.00548565	−	0.00633078i
$15$	−0.535731	−	2.17094i	−0.138325	−	0.560535i
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	0.967380	−	3.29460i	0.234624	−	0.799057i	−0.755043	−	0.655675i	$-0.772384\pi$
$17$	0.967380	−	3.29460i	0.234624	−	0.799057i	0.989667	−	0.143382i	$-0.0457977\pi$
$18$	0.755750	+	0.654861i	0.178132	+	0.154352i
$19$	3.93372	−	1.15504i	0.902458	−	0.264985i	0.202595	−	0.979263i	$-0.435063\pi$
$19$	3.93372	−	1.15504i	0.902458	−	0.264985i	0.699863	+	0.714277i	$0.253244\pi$
$20$	−1.82654	−	1.28986i	−0.408428	−	0.288422i
$21$	−0.00446060	−	0.0310242i	−0.000973383	−	0.00677003i
$22$		−	5.89308i		−	1.25641i
$23$	4.10154	+	2.48544i	0.855229	+	0.518250i
$23$	4.10154	+	2.48544i	0.855229	+	0.518250i
$24$	1.00000			0.204124
$25$	−1.14047	+	4.86820i	−0.228094	+	0.973639i
$26$	−0.433069	+	0.948289i	−0.0849318	+	0.185975i
$27$	0.281733	+	0.959493i	0.0542195	+	0.184655i
$28$	−0.0236876	−	0.0205254i	−0.00447654	−	0.00387894i
$29$	1.01582	+	0.298273i	0.188634	+	0.0553878i	0.374685	−	0.927152i	$-0.377751\pi$
$29$	1.01582	+	0.298273i	0.188634	+	0.0553878i	−0.186051	+	0.982540i	$0.559569\pi$
$30$	−0.839235	−	2.07260i	−0.153223	−	0.378404i
$31$	0.447429	+	0.979733i	0.0803606	+	0.175965i	0.945547	−	0.325485i	$-0.105527\pi$
$31$	0.447429	+	0.979733i	0.0803606	+	0.175965i	−0.865187	+	0.501450i	$0.832800\pi$
$32$	0.755750	−	0.654861i	0.133599	−	0.115764i
$33$	3.18604	−	4.95757i	0.554618	−	0.863003i
$34$	0.488664	−	3.39873i	0.0838052	−	0.582878i
$35$	−0.0226616	+	0.0663207i	−0.00383051	+	0.0112102i
$36$	0.841254	+	0.540641i	0.140209	+	0.0901068i
$37$	−6.76119	+	5.85860i	−1.11153	+	0.963148i	−0.999533	−	0.0305604i	$-0.990271\pi$
$37$	−6.76119	+	5.85860i	−1.11153	+	0.963148i	−0.111999	+	0.993708i	$0.535725\pi$
$38$	3.72930	−	1.70312i	0.604973	−	0.276282i
$39$	−0.877004	+	0.563617i	−0.140433	+	0.0902509i
$40$	−1.99152	−	1.01679i	−0.314887	−	0.160768i
$41$	−0.525260	+	0.606183i	−0.0820319	+	0.0946698i	−0.795282	−	0.606240i	$-0.792677\pi$
$41$	−0.525260	+	0.606183i	−0.0820319	+	0.0946698i	0.713250	+	0.700910i	$0.247223\pi$
$42$	−0.00883040	−	0.0300736i	−0.00136256	−	0.00464046i
$43$	−5.04181	−	2.30252i	−0.768869	−	0.351131i	−0.00794202	−	0.999968i	$-0.502528\pi$
$43$	−5.04181	−	2.30252i	−0.768869	−	0.351131i	−0.760927	+	0.648838i	$0.775255\pi$
$44$	−0.838672	−	5.83309i	−0.126435	−	0.879372i
$45$	0.414525	−	2.19731i	0.0617937	−	0.327556i
$46$	4.41350	+	1.87643i	0.650736	+	0.276665i
$47$			6.51753i			0.950680i	0.879802	+	0.475340i	$0.157675\pi$
$47$			6.51753i			0.950680i	−0.879802	+	0.475340i	$0.842325\pi$
$48$	0.989821	−	0.142315i	0.142868	−	0.0205414i
$49$	2.90750	−	6.36653i	0.415357	−	0.909504i
$50$	−0.436045	+	4.98095i	−0.0616660	+	0.704413i
$51$	2.24858	−	2.59500i	0.314865	−	0.363373i
$52$	−0.293705	+	1.00027i	−0.0407296	+	0.138712i
$53$	0.723111	+	1.12518i	0.0993269	+	0.154556i	0.887360	−	0.461077i	$-0.152537\pi$
$53$	0.723111	+	1.12518i	0.0993269	+	0.154556i	−0.788033	+	0.615633i	$0.788900\pi$
$54$	0.415415	+	0.909632i	0.0565308	+	0.123785i
$55$	−11.3858	+	6.63357i	−1.53527	+	0.894471i
$56$	−0.0263676	−	0.0169454i	−0.00352352	−	0.00226443i
$57$	4.05806	+	0.583461i	0.537503	+	0.0772813i
$58$	1.04793	+	0.150670i	0.137600	+	0.0197839i
$59$	2.38036	+	1.52977i	0.309897	+	0.199159i	0.686340	−	0.727281i	$-0.259216\pi$
$59$	2.38036	+	1.52977i	0.309897	+	0.199159i	−0.376443	+	0.926440i	$0.622853\pi$
$60$	−1.12565	−	1.93207i	−0.145321	−	0.249429i
$61$	0.669151	+	1.46524i	0.0856761	+	0.187604i	0.947621	−	0.319398i	$-0.103481\pi$
$61$	0.669151	+	1.46524i	0.0856761	+	0.187604i	−0.861945	+	0.507003i	$0.830753\pi$
$62$	0.582306	+	0.906085i	0.0739529	+	0.115073i
$63$	0.00883040	−	0.0300736i	0.00111253	−	0.00378892i
$64$	0.654861	−	0.755750i	0.0818576	−	0.0944687i
$65$	2.31965	−	0.230726i	0.287717	−	0.0286180i
$66$	2.44807	−	5.36053i	0.301337	−	0.659836i
$67$	−13.8191	+	1.98689i	−1.68828	+	0.242737i	−0.918456	−	0.395524i	$-0.870563\pi$
$67$	−13.8191	+	1.98689i	−1.68828	+	0.242737i	−0.769820	+	0.638261i	$0.779654\pi$
$68$		−	3.43368i		−	0.416395i
$69$	2.69840	+	3.96467i	0.324849	+	0.477291i
$70$	−0.0129925	+	0.0688707i	−0.00155290	+	0.00823163i
$71$	−0.625522	−	4.35060i	−0.0742358	−	0.516321i	−0.992680	−	0.120772i	$-0.961463\pi$
$71$	−0.625522	−	4.35060i	−0.0742358	−	0.516321i	0.918445	−	0.395550i	$-0.129446\pi$
$72$	0.909632	+	0.415415i	0.107201	+	0.0489571i
$73$	1.29051	+	4.39508i	0.151043	+	0.514406i	0.999899	−	0.0142189i	$-0.00452617\pi$
$73$	1.29051	+	4.39508i	0.151043	+	0.514406i	−0.848856	+	0.528624i	$0.822708\pi$
$74$	−5.85860	+	6.76119i	−0.681048	+	0.785972i
$75$	−3.05973	+	3.95450i	−0.353307	+	0.456626i
$76$	3.44896	−	2.21651i	0.395623	−	0.254252i
$77$	−0.168016	+	0.0767305i	−0.0191472	+	0.00874425i
$78$	−0.787867	+	0.682690i	−0.0892083	+	0.0772995i
$79$	9.48726	+	6.09709i	1.06740	+	0.685977i	0.951614	−	0.307297i	$-0.0994246\pi$
$79$	9.48726	+	6.09709i	1.06740	+	0.685977i	0.115787	+	0.993274i	$0.463061\pi$
$80$	−2.11595	−	0.723015i	−0.236571	−	0.0808355i
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$	−0.433645	+	0.674765i	−0.0478881	+	0.0745153i
$83$	−3.33508	+	2.88986i	−0.366073	+	0.317204i	−0.818401	−	0.574648i	$-0.805139\pi$
$83$	−3.33508	+	2.88986i	−0.366073	+	0.317204i	0.452328	+	0.891852i	$0.350594\pi$
$84$	−0.0130204	−	0.0285108i	−0.00142065	−	0.00311078i
$85$	−7.11666	+	2.88167i	−0.771911	+	0.312561i
$86$	−5.31817	−	1.56156i	−0.573473	−	0.168387i
$87$	0.800118	+	0.693307i	0.0857817	+	0.0743303i
$88$	−1.66027	−	5.65437i	−0.176986	−	0.602758i
$89$	−2.96711	+	6.49707i	−0.314513	+	0.688688i	−0.999193	−	0.0401555i	$-0.987215\pi$
$89$	−2.96711	+	6.49707i	−0.314513	+	0.688688i	0.684680	+	0.728844i	$0.259942\pi$
$90$	0.0975956	−	2.23394i	0.0102875	−	0.235478i
$91$	0.0326752			0.00342529
$92$	4.63562	+	1.22922i	0.483297	+	0.128155i
$93$			1.07707i			0.111686i
$94$	0.927542	+	6.45120i	0.0956686	+	0.665390i
$95$	−7.48845	−	5.28816i	−0.768299	−	0.542554i
$96$	0.959493	−	0.281733i	0.0979278	−	0.0287542i
$97$	2.22467	+	1.92768i	0.225881	+	0.195727i	0.760447	−	0.649400i	$-0.224980\pi$
$97$	2.22467	+	1.92768i	0.225881	+	0.195727i	−0.534567	+	0.845126i	$0.679525\pi$
$98$	1.97185	−	6.71551i	0.199187	−	0.678369i
$99$	4.95757	−	3.18604i	0.498255	−	0.320209i
$100$	0.277257	+	4.99231i	0.0277257	+	0.499231i
$101$	4.45584	+	5.14231i	0.443373	+	0.511679i	0.932815	−	0.360356i	$-0.117345\pi$
$101$	4.45584	+	5.14231i	0.443373	+	0.511679i	−0.489442	+	0.872036i	$0.662799\pi$
$102$	1.85639	−	2.88860i	0.183810	−	0.286014i
$103$	12.9804	+	1.86630i	1.27900	+	0.183892i	0.748124	−	0.663559i	$-0.230955\pi$
$103$	12.9804	+	1.86630i	1.27900	+	0.183892i	0.530874	+	0.847451i	$0.321864\pi$
$104$	−0.148363	+	1.03189i	−0.0145482	+	0.101185i
$105$	−0.0481643	+	0.0509135i	−0.00470036	+	0.00496864i
$106$	0.875881	+	1.01082i	0.0850731	+	0.0981796i
$107$	−5.53153	+	2.52616i	−0.534753	+	0.244213i	−0.664440	−	0.747341i	$-0.731330\pi$
$107$	−5.53153	+	2.52616i	−0.534753	+	0.244213i	0.129687	+	0.991555i	$0.458603\pi$
$108$	0.540641	+	0.841254i	0.0520232	+	0.0809497i
$109$	6.05077	+	1.77667i	0.579558	+	0.170174i	0.558356	−	0.829602i	$-0.311432\pi$
$109$	6.05077	+	1.77667i	0.579558	+	0.170174i	0.0212024	+	0.999775i	$0.493251\pi$
$110$	−10.3259	+	8.18643i	−0.984536	+	0.780545i
$111$	−8.58394	+	2.52047i	−0.814752	+	0.239233i
$112$	−0.0285108	−	0.0130204i	−0.00269402	−	0.00123032i
$113$	15.0097	−	2.15807i	1.41200	−	0.203014i	0.606249	−	0.795275i	$-0.292673\pi$
$113$	15.0097	−	2.15807i	1.41200	−	0.203014i	0.805747	+	0.592261i	$0.201764\pi$
$114$	4.09979			0.383981
$115$	−1.34268	−	10.6394i	−0.125206	−	0.992131i
$116$	1.05871			0.0982986
$117$	−1.03189	+	0.148363i	−0.0953979	+	0.0137161i
$118$	2.57384	+	1.17544i	0.236942	+	0.108208i
$119$	−0.103263	+	0.0303208i	−0.00946612	+	0.00277950i
$120$	−1.38916	−	1.75221i	−0.126812	−	0.159954i
$121$	−22.7672	−	6.68505i	−2.06975	−	0.607732i
$122$	0.870865	+	1.35509i	0.0788445	+	0.122684i
$123$	−0.729611	+	0.333202i	−0.0657868	+	0.0300438i
$124$	0.705328	+	0.813992i	0.0633403	+	0.0730986i
$125$	10.1144	−	4.76436i	0.904658	−	0.426137i
$126$	0.00446060	−	0.0310242i	0.000397382	−	0.00276385i
$127$	−13.1482	−	1.89043i	−1.16671	−	0.167748i	−0.468385	−	0.883524i	$-0.655164\pi$
$127$	−13.1482	−	1.89043i	−1.16671	−	0.167748i	−0.698330	+	0.715776i	$0.746073\pi$
$128$	0.540641	−	0.841254i	0.0477863	−	0.0743570i
$129$	−3.62969	−	4.18889i	−0.319576	−	0.368811i
$130$	2.26320	−	0.558498i	0.198496	−	0.0489835i
$131$	−13.6380	+	8.76463i	−1.19156	+	0.765769i	−0.977476	−	0.211046i	$-0.932313\pi$
$131$	−13.6380	+	8.76463i	−1.19156	+	0.765769i	−0.214084	+	0.976815i	$0.568677\pi$
$132$	1.66027	−	5.65437i	0.144508	−	0.492149i
$133$	−0.0971143	−	0.0841500i	−0.00842088	−	0.00729673i
$134$	−13.3957	+	3.93334i	−1.15721	+	0.339788i
$135$	1.28986	−	1.82654i	0.111013	−	0.157204i
$136$	−0.488664	−	3.39873i	−0.0419026	−	0.291439i
$137$		−	11.5113i		−	0.983474i	−0.870744	−	0.491737i	$-0.836362\pi$
$137$		−	11.5113i		−	0.983474i	0.870744	−	0.491737i	$-0.163638\pi$
$138$	3.23517	+	3.54030i	0.275396	+	0.301370i
$139$	−22.3408			−1.89492			−0.947461	−	0.319872i	$-0.896360\pi$
$139$	−22.3408			−1.89492			−0.947461	+	0.319872i	$0.896360\pi$
$140$	−0.00305896	+	0.0700188i	−0.000258529	+	0.00591766i
$141$	−2.70748	+	5.92856i	−0.228011	+	0.499275i
$142$	−1.23831	−	4.21730i	−0.103917	−	0.353908i
$143$	4.64296	+	4.02315i	0.388264	+	0.336433i
$144$	0.959493	+	0.281733i	0.0799577	+	0.0234777i
$145$	−0.888505	−	2.19428i	−0.0737863	−	0.182225i
$146$	1.90286	+	4.16669i	0.157482	+	0.344838i
$147$	5.28950	−	4.58338i	0.436271	−	0.378031i
$148$	−4.83675	+	7.52613i	−0.397579	+	0.618644i
$149$	2.93977	−	20.4466i	0.240835	−	1.67505i	−0.407124	−	0.913373i	$-0.633468\pi$
$149$	2.93977	−	20.4466i	0.240835	−	1.67505i	0.647960	−	0.761675i	$-0.275623\pi$
$150$	−2.46580	+	4.34969i	−0.201332	+	0.355151i
$151$	8.46512	+	5.44020i	0.688882	+	0.442718i	0.837688	−	0.546149i	$-0.183907\pi$
$151$	8.46512	+	5.44020i	0.688882	+	0.442718i	−0.148806	+	0.988866i	$0.547543\pi$
$152$	3.09842	−	2.68479i	0.251315	−	0.217765i
$153$	3.12339	−	1.42640i	0.252511	−	0.115318i
$154$	−0.155386	+	0.0998607i	−0.0125214	+	0.00804700i
$155$	1.09515	−	2.14500i	0.0879643	−	0.172290i
$156$	−0.682690	+	0.787867i	−0.0546590	+	0.0630798i
$157$	−1.64743	−	5.61063i	−0.131479	−	0.447777i	0.867267	−	0.497844i	$-0.165875\pi$
$157$	−1.64743	−	5.61063i	−0.131479	−	0.447777i	−0.998746	+	0.0500669i	$0.984057\pi$
$158$	10.2584	+	4.68486i	0.816115	+	0.372707i
$159$	0.190347	+	1.32389i	0.0150955	+	0.104992i
$160$	−2.19731	−	0.414525i	−0.173713	−	0.0327710i
$161$	−0.00396726	−	0.150264i	−0.000312664	−	0.0118425i
$162$			1.00000i			0.0785674i
$163$	17.6574	−	2.53875i	1.38303	−	0.198850i	0.589692	−	0.807628i	$-0.299249\pi$
$163$	17.6574	−	2.53875i	1.38303	−	0.198850i	0.793340	+	0.608779i	$0.208340\pi$
$164$	−0.333202	+	0.729611i	−0.0260187	+	0.0569731i
$165$	−13.1126	+	1.30426i	−1.02082	+	0.101536i
$166$	−2.88986	+	3.33508i	−0.224297	+	0.258853i
$167$	−3.77870	+	12.8691i	−0.292404	+	0.995838i	0.673983	+	0.738747i	$0.264582\pi$
$167$	−3.77870	+	12.8691i	−0.292404	+	0.995838i	−0.966387	+	0.257091i	$0.917236\pi$
$168$	−0.0169454	−	0.0263676i	−0.00130737	−	0.00203430i
$169$	4.94892	+	10.8366i	0.380686	+	0.833587i
$170$	−6.63412	+	3.86514i	−0.508814	+	0.296443i
$171$	3.44896	+	2.21651i	0.263749	+	0.169501i
$172$	−5.48627	−	0.788807i	−0.418325	−	0.0601460i
$173$	3.35938	+	0.483005i	0.255409	+	0.0367222i	0.268830	−	0.963188i	$-0.413363\pi$
$173$	3.35938	+	0.483005i	0.255409	+	0.0367222i	−0.0134211	+	0.999910i	$0.504272\pi$
$174$	0.890642	+	0.572381i	0.0675194	+	0.0433921i
$175$	0.147688	−	0.0524222i	0.0111642	−	0.00396274i
$176$	−2.44807	−	5.36053i	−0.184530	−	0.404065i
$177$	1.52977	+	2.38036i	0.114984	+	0.178919i
$178$	−2.01228	+	6.85321i	−0.150827	+	0.513669i
$179$	1.09590	−	1.26474i	0.0819118	−	0.0945312i	−0.713314	−	0.700844i	$-0.752807\pi$
$179$	1.09590	−	1.26474i	0.0819118	−	0.0945312i	0.795226	+	0.606313i	$0.207352\pi$
$180$	−0.221320	−	2.22509i	−0.0164962	−	0.165848i
$181$	−9.21791	+	20.1844i	−0.685162	+	1.50029i	0.171918	+	0.985111i	$0.445004\pi$
$181$	−9.21791	+	20.1844i	−0.685162	+	1.50029i	−0.857080	+	0.515184i	$0.827724\pi$
$182$	0.0323426	−	0.00465017i	0.00239739	−	0.000344693i
$183$			1.61080i			0.119074i
$184$	4.76338	+	0.556994i	0.351161	+	0.0410621i
$185$	19.6579	+	3.70847i	1.44527	+	0.272652i
$186$	0.153282	+	1.06610i	0.0112392	+	0.0781704i
$187$	−18.4064	−	8.40591i	−1.34601	−	0.614701i
$188$	1.83620	+	6.25353i	0.133919	+	0.456085i
$189$	0.0205254	−	0.0236876i	0.00149301	−	0.00172302i
$190$	−8.16481	−	4.16862i	−0.592338	−	0.302423i
$191$	4.16000	−	2.67347i	0.301007	−	0.193446i	−0.381415	−	0.924404i	$-0.624563\pi$
$191$	4.16000	−	2.67347i	0.301007	−	0.193446i	0.682422	+	0.730958i	$0.260927\pi$
$192$	0.909632	−	0.415415i	0.0656470	−	0.0299800i
$193$	−2.81146	+	2.43614i	−0.202373	+	0.175357i	−0.750151	−	0.661266i	$-0.770019\pi$
$193$	−2.81146	+	2.43614i	−0.202373	+	0.175357i	0.547778	+	0.836624i	$0.315474\pi$
$194$	2.47636	+	1.59146i	0.177792	+	0.114260i
$195$	2.20587	+	0.753741i	0.157966	+	0.0539765i
$196$	0.996064	−	6.92778i	0.0711474	−	0.494841i
$197$	4.34534	−	6.76148i	0.309593	−	0.481736i	−0.651237	−	0.758874i	$-0.725750\pi$
$197$	4.34534	−	6.76148i	0.309593	−	0.481736i	0.960830	+	0.277139i	$0.0893861\pi$
$198$	4.45369	−	3.85915i	0.316510	−	0.274258i
$199$	9.89731	+	21.6721i	0.701602	+	1.53629i	0.838018	+	0.545642i	$0.183714\pi$
$199$	9.89731	+	21.6721i	0.701602	+	1.53629i	−0.136416	+	0.990652i	$0.543558\pi$
$200$	0.984914	+	4.90203i	0.0696439	+	0.346626i
$201$	−13.3957	−	3.93334i	−0.944861	−	0.277436i
$202$	5.14231	+	4.45584i	0.361812	+	0.313512i
$203$	−0.00934882	−	0.0318392i	−0.000656159	−	0.00223467i
$204$	1.42640	−	3.12339i	0.0998682	−	0.218681i
$205$	1.79183	+	0.0782809i	0.125147	+	0.00546738i
$206$	13.1139			0.913688
$207$	0.807567	+	4.72735i	0.0561298	+	0.328574i
$208$			1.04250i			0.0722842i
$209$	−3.43838	−	23.9145i	−0.237838	−	1.65420i
$210$	−0.0404284	+	0.0572497i	−0.00278982	+	0.00395061i
$211$	−16.5007	+	4.84505i	−1.13596	+	0.333547i	−0.795046	−	0.606549i	$-0.792553\pi$
$211$	−16.5007	+	4.84505i	−1.13596	+	0.333547i	−0.340910	+	0.940096i	$0.610735\pi$
$212$	1.01082	+	0.875881i	0.0694234	+	0.0601558i
$213$	1.23831	−	4.21730i	0.0848476	−	0.288964i
$214$	−5.11571	+	3.28767i	−0.349703	+	0.224740i
$215$	2.96939	+	12.0329i	0.202511	+	0.820635i
$216$	0.654861	+	0.755750i	0.0445576	+	0.0514222i
$217$	0.0182513	−	0.0283996i	0.00123898	−	0.00192789i
$218$	6.24202	+	0.897468i	0.422763	+	0.0607842i
$219$	−0.651892	+	4.53401i	−0.0440508	+	0.306380i
$220$	−9.05575	+	9.57263i	−0.610538	+	0.645387i
$221$	2.34414	+	2.70529i	0.157684	+	0.181977i
$222$	−8.13787	+	3.71644i	−0.546178	+	0.249431i
$223$	13.6259	+	21.2023i	0.912456	+	1.41981i	0.907607	+	0.419821i	$0.137907\pi$
$223$	13.6259	+	21.2023i	0.912456	+	1.41981i	0.00484895	+	0.999988i	$0.498457\pi$
$224$	−0.0300736	−	0.00883040i	−0.00200938	−	0.000590006i
$225$	−4.42599	+	2.32608i	−0.295066	+	0.155072i
$226$	14.5498	−	4.27221i	0.967839	−	0.284183i
$227$	20.9112	+	9.54981i	1.38792	+	0.633843i	0.962532	−	0.271166i	$-0.0874094\pi$
$227$	20.9112	+	9.54981i	1.38792	+	0.633843i	0.425391	+	0.905010i	$0.360137\pi$
$228$	4.05806	−	0.583461i	0.268752	−	0.0386407i
$229$	−16.7178			−1.10475			−0.552373	−	0.833597i	$-0.686277\pi$
$229$	−16.7178			−1.10475			−0.552373	+	0.833597i	$0.686277\pi$
$230$	−2.84316	−	10.3400i	−0.187473	−	0.681802i
$231$	−0.184708			−0.0121529
$232$	1.04793	−	0.150670i	0.0688001	−	0.00989196i
$233$	−12.2788	−	5.60756i	−0.804414	−	0.367364i	−0.0296072	−	0.999562i	$-0.509426\pi$
$233$	−12.2788	−	5.60756i	−0.804414	−	0.367364i	−0.774807	+	0.632198i	$0.782153\pi$
$234$	−1.00027	+	0.293705i	−0.0653896	+	0.0192001i
$235$	11.4201	−	9.05390i	0.744964	−	0.590611i
$236$	2.71493	+	0.797175i	0.176727	+	0.0518917i
$237$	6.09709	+	9.48726i	0.396049	+	0.616264i
$238$	−0.0978970	+	0.0447081i	−0.00634572	+	0.00289799i
$239$	3.74253	+	4.31911i	0.242084	+	0.279380i	0.863770	−	0.503887i	$-0.168097\pi$
$239$	3.74253	+	4.31911i	0.242084	+	0.279380i	−0.621685	+	0.783267i	$0.713552\pi$
$240$	−1.62439	−	1.53668i	−0.104854	−	0.0991920i
$241$	1.77647	−	12.3556i	0.114433	−	0.795896i	−0.849086	−	0.528255i	$-0.822847\pi$
$241$	1.77647	−	12.3556i	0.114433	−	0.795896i	0.963519	−	0.267642i	$-0.0862443\pi$
$242$	−23.4868	−	3.37690i	−1.50979	−	0.217075i
$243$	−0.540641	+	0.841254i	−0.0346821	+	0.0539664i
$244$	1.05485	+	1.21736i	0.0675299	+	0.0779337i
$245$	−15.1945	+	3.74959i	−0.970739	+	0.239552i
$246$	−0.674765	+	0.433645i	−0.0430214	+	0.0276482i
$247$	−1.20413	+	4.10089i	−0.0766170	+	0.260934i
$248$	0.813992	+	0.705328i	0.0516885	+	0.0447884i
$249$	−4.23419	+	1.24327i	−0.268331	+	0.0787891i
$250$	9.33340	−	6.15529i	0.590296	−	0.389295i
$251$	−0.0224910	−	0.156428i	−0.00141962	−	0.00987366i	0.989099	−	0.147250i	$-0.0470422\pi$
$251$	−0.0224910	−	0.156428i	−0.00141962	−	0.00987366i	−0.990519	+	0.137376i	$0.956133\pi$
$252$		−	0.0313432i		−	0.00197444i
$253$	17.9376	−	21.8402i	1.12773	−	1.37308i
$254$	−13.2834			−0.833475
$255$	−7.67063	−	0.335112i	−0.480354	−	0.0209855i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	−5.04684	−	17.1880i	−0.314813	−	1.07216i	−0.953175	−	0.302419i	$-0.902206\pi$
$257$	−5.04684	−	17.1880i	−0.314813	−	1.07216i	0.638362	−	0.769737i	$-0.279612\pi$
$258$	−4.18889	−	3.62969i	−0.260789	−	0.225975i
$259$	0.269048	+	0.0789997i	0.0167178	+	0.00490880i
$260$	2.16068	−	0.874900i	0.134000	−	0.0542590i
$261$	0.439803	+	0.963035i	0.0272231	+	0.0596104i
$262$	−12.2519	+	10.6163i	−0.756923	+	0.655878i
$263$	10.7046	−	16.6567i	0.660075	−	1.02710i	−0.336277	−	0.941763i	$-0.609168\pi$
$263$	10.7046	−	16.6567i	0.660075	−	1.02710i	0.996352	−	0.0853339i	$-0.0271957\pi$
$264$	0.838672	−	5.83309i	0.0516167	−	0.359002i
$265$	0.967038	−	2.83010i	0.0594047	−	0.173852i
$266$	−0.108102	−	0.0694727i	−0.00662813	−	0.00425964i
$267$	−5.39796	+	4.67736i	−0.330350	+	0.286250i
$268$	−12.6996	+	5.79971i	−0.775751	+	0.354274i
$269$	3.28404	−	2.11053i	0.200232	−	0.128681i	−0.436683	−	0.899616i	$-0.643847\pi$
$269$	3.28404	−	2.11053i	0.200232	−	0.128681i	0.636914	+	0.770934i	$0.280210\pi$
$270$	1.01679	−	1.99152i	0.0618797	−	0.121200i
$271$	−1.70799	+	1.97113i	−0.103753	+	0.119737i	−0.805251	−	0.592934i	$-0.797969\pi$
$271$	−1.70799	+	1.97113i	−0.103753	+	0.119737i	0.701498	+	0.712671i	$0.252515\pi$
$272$	−0.967380	−	3.29460i	−0.0586561	−	0.199764i
$273$	0.0297224	+	0.0135738i	0.00179888	+	0.000821522i
$274$	−1.63822	−	11.3941i	−0.0989688	−	0.688343i
$275$	27.4402	+	10.7353i	1.65470	+	0.647362i
$276$	3.70607	+	3.04385i	0.223079	+	0.183218i
$277$		−	14.9221i		−	0.896579i	−0.893888	−	0.448290i	$-0.852033\pi$
$277$		−	14.9221i		−	0.896579i	0.893888	−	0.448290i	$-0.147967\pi$
$278$	−22.1134	+	3.17943i	−1.32627	+	0.190689i
$279$	−0.447429	+	0.979733i	−0.0267869	+	0.0586551i
$280$	0.00693688	+	0.0697414i	0.000414558	+	0.00416785i
$281$	12.4596	−	14.3791i	0.743275	−	0.857785i	−0.250623	−	0.968085i	$-0.580636\pi$
$281$	12.4596	−	14.3791i	0.743275	−	0.857785i	0.993898	+	0.110299i	$0.0351810\pi$
$282$	−1.83620	+	6.25353i	−0.109344	+	0.372392i
$283$	1.69331	+	2.63485i	0.100657	+	0.156625i	0.887929	−	0.459981i	$-0.152144\pi$
$283$	1.69331	+	2.63485i	0.100657	+	0.156625i	−0.787272	+	0.616606i	$0.788507\pi$
$284$	−1.82589	−	3.99814i	−0.108347	−	0.237246i
$285$	−4.61495	−	7.92109i	−0.273366	−	0.469205i
$286$	5.16826	+	3.32144i	0.305605	+	0.196401i
$287$	0.0248843	+	0.00357783i	0.00146888	+	0.000211192i
$288$	0.989821	+	0.142315i	0.0583258	+	0.00838598i
$289$	4.38278	+	2.81664i	0.257810	+	0.165685i
$290$	−1.19174	−	2.04550i	−0.0699814	−	0.120116i
$291$	1.22284	+	2.67764i	0.0716841	+	0.156966i
$292$	2.47648	+	3.85347i	0.144925	+	0.225507i
$293$	4.07702	−	13.8850i	0.238182	−	0.811173i	−0.750464	−	0.660911i	$-0.770170\pi$
$293$	4.07702	−	13.8850i	0.238182	−	0.811173i	0.988646	−	0.150262i	$-0.0480117\pi$
$294$	4.58338	−	5.28950i	0.267308	−	0.308490i
$295$	−0.626235	−	6.29599i	−0.0364608	−	0.366566i
$296$	−3.71644	+	8.13787i	−0.216014	+	0.473004i
$297$	5.83309	−	0.838672i	0.338470	−	0.0486647i
$298$		−	20.6568i		−	1.19662i
$299$	−4.49143	+	2.19623i	−0.259746	+	0.127011i
$300$	−1.82168	+	4.65634i	−0.105175	+	0.268834i
$301$	0.0247237	+	0.171957i	0.00142505	+	0.00991146i
$302$	9.15318	+	4.18012i	0.526706	+	0.240539i
$303$	1.91698	+	6.52864i	0.110128	+	0.375060i
$304$	2.68479	−	3.09842i	0.153983	−	0.177706i
$305$	1.63784	−	3.20794i	0.0937826	−	0.183686i
$306$	2.88860	−	1.85639i	0.165130	−	0.106123i
$307$	22.1729	−	10.1260i	1.26548	−	0.577924i	0.334291	−	0.942470i	$-0.391503\pi$
$307$	22.1729	−	10.1260i	1.26548	−	0.577924i	0.931185	+	0.364546i	$0.118776\pi$
$308$	−0.139593	+	0.120958i	−0.00795405	+	0.00689222i
$309$	11.0321	+	7.08991i	0.627595	+	0.403331i
$310$	0.778735	−	2.27902i	0.0442291	−	0.129440i
$311$	−2.33406	+	16.2337i	−0.132352	+	0.920531i	0.810124	+	0.586258i	$0.199400\pi$
$311$	−2.33406	+	16.2337i	−0.132352	+	0.920531i	−0.942477	+	0.334272i	$0.891509\pi$
$312$	−0.563617	+	0.877004i	−0.0319085	+	0.0496506i
$313$	9.17784	−	7.95264i	0.518762	−	0.449510i	−0.355703	−	0.934599i	$-0.615758\pi$
$313$	9.17784	−	7.95264i	0.518762	−	0.449510i	0.874465	+	0.485089i	$0.161213\pi$
$314$	−2.42914	−	5.31907i	−0.137084	−	0.300172i
$315$	−0.0649620	+	0.0263043i	−0.00366020	+	0.00148208i
$316$	10.8207	+	3.17725i	0.608713	+	0.178734i
$317$	−6.84573	−	5.93186i	−0.384494	−	0.333166i	0.441072	−	0.897472i	$-0.354598\pi$
$317$	−6.84573	−	5.93186i	−0.384494	−	0.333166i	−0.825566	+	0.564306i	$0.809144\pi$
$318$	0.376819	+	1.28333i	0.0211310	+	0.0719655i
$319$	2.59180	−	5.67524i	0.145113	−	0.317752i
$320$	−2.23394	−	0.0975956i	−0.124881	−	0.00545576i
$321$	−6.08106			−0.339412
$322$	−0.0253117	−	0.148170i	−0.00141057	−	0.00825721i
$323$		−	14.0774i		−	0.783287i
$324$	0.142315	+	0.989821i	0.00790638	+	0.0549901i
$325$	−3.62664	−	3.74399i	−0.201170	−	0.207679i
$326$	17.1163	−	5.02581i	0.947986	−	0.278354i
$327$	4.76592	+	4.12969i	0.263556	+	0.228372i
$328$	−0.225976	+	0.769604i	−0.0124774	+	0.0424943i
$329$	0.171852	−	0.110442i	0.00947449	−	0.00608888i
$330$	−12.7935	+	3.15710i	−0.704261	+	0.173793i
$331$	−21.0571	−	24.3011i	−1.15740	−	1.33571i	−0.932432	−	0.361346i	$-0.882317\pi$
$331$	−21.0571	−	24.3011i	−1.15740	−	1.33571i	−0.224969	−	0.974366i	$-0.572228\pi$
$332$	−2.38582	+	3.71241i	−0.130939	+	0.203745i
$333$	−8.85527	−	1.27320i	−0.485266	−	0.0697707i
$334$	−1.90878	+	13.2758i	−0.104444	+	0.726422i
$335$	22.6784	+	21.4539i	1.23906	+	1.17215i
$336$	−0.0205254	−	0.0236876i	−0.00111975	−	0.00129227i
$337$	−22.1096	+	10.0971i	−1.20438	+	0.550024i	−0.913541	−	0.406747i	$-0.866663\pi$
$337$	−22.1096	+	10.0971i	−1.20438	+	0.550024i	−0.290843	+	0.956771i	$0.593936\pi$
$338$	6.44076	+	10.0220i	0.350331	+	0.545126i
$339$	14.5498	+	4.27221i	0.790237	+	0.232035i
$340$	−6.01653	+	4.76994i	−0.326292	+	0.258686i
$341$	6.09012	−	1.78822i	0.329799	−	0.0968376i
$342$	3.72930	+	1.70312i	0.201658	+	0.0920939i
$343$	−0.434308	+	0.0624441i	−0.0234504	+	0.00337166i
$344$	−5.54269			−0.298842
$345$	3.19842	−	10.2357i	0.172197	−	0.551073i
$346$	3.39392			0.182458
$347$	−18.2226	+	2.62001i	−0.978238	+	0.140649i	−0.612845	−	0.790204i	$-0.709975\pi$
$347$	−18.2226	+	2.62001i	−0.978238	+	0.140649i	−0.365394	+	0.930853i	$0.619066\pi$
$348$	0.963035	+	0.439803i	0.0516241	+	0.0235759i
$349$	17.0145	−	4.99592i	0.910768	−	0.267426i	0.207404	−	0.978255i	$-0.433499\pi$
$349$	17.0145	−	4.99592i	0.910768	−	0.267426i	0.703364	+	0.710830i	$0.251680\pi$
$350$	0.138725	−	0.0729068i	0.00741514	−	0.00389703i
$351$	−1.00027	−	0.293705i	−0.0533904	−	0.0156768i
$352$	−3.18604	−	4.95757i	−0.169816	−	0.264240i
$353$	5.69687	−	2.60167i	0.303214	−	0.138473i	−0.257998	−	0.966146i	$-0.583063\pi$
$353$	5.69687	−	2.60167i	0.303214	−	0.138473i	0.561212	+	0.827672i	$0.310335\pi$
$354$	1.85296	+	2.13843i	0.0984836	+	0.113656i
$355$	−6.75421	+	7.13973i	−0.358476	+	0.378937i
$356$	−1.01649	+	7.06983i	−0.0538737	+	0.374700i
$357$	−0.106527	−	0.0153163i	−0.00563802	−	0.000810625i
$358$	0.904759	−	1.40783i	0.0478180	−	0.0744062i
$359$	−18.5465	−	21.4038i	−0.978846	−	1.12965i	−0.991549	−	0.129730i	$-0.958589\pi$
$359$	−18.5465	−	21.4038i	−0.978846	−	1.12965i	0.0127030	−	0.999919i	$-0.495956\pi$
$360$	−0.535731	−	2.17094i	−0.0282355	−	0.114419i
$361$	−1.84378	+	1.18493i	−0.0970411	+	0.0623645i
$362$	−6.25154	+	21.2908i	−0.328574	+	1.11902i
$363$	−17.9327	−	15.5388i	−0.941223	−	0.815574i
$364$	0.0313516	−	0.00920567i	0.00164327	−	0.000482508i
$365$	5.90837	−	8.36672i	0.309258	−	0.437934i
$366$	0.229241	+	1.59441i	0.0119826	+	0.0833410i
$367$		−	7.03965i		−	0.367467i	−0.982976	−	0.183733i	$-0.941182\pi$
$367$		−	7.03965i		−	0.367467i	0.982976	−	0.183733i	$-0.0588183\pi$
$368$	4.79416	−	0.126575i	0.249913	−	0.00659816i
$369$	−0.802095			−0.0417554
$370$	19.9855	+	0.873122i	1.03900	+	0.0453915i
$371$	0.0174149	−	0.0381334i	0.000904138	−	0.00197979i
$372$	0.303444	+	1.03344i	0.0157329	+	0.0535812i
$373$	16.8402	+	14.5921i	0.871950	+	0.755549i	0.970885	−	0.239545i	$-0.0769982\pi$
$373$	16.8402	+	14.5921i	0.871950	+	0.755549i	−0.0989353	+	0.995094i	$0.531544\pi$
$374$	−19.4153	−	5.70085i	−1.00394	−	0.294784i
$375$	11.1796	−	0.132147i	0.577310	−	0.00682403i
$376$	2.70748	+	5.92856i	0.139628	+	0.305742i
$377$	−0.834121	+	0.722770i	−0.0429594	+	0.0372246i
$378$	0.0169454	−	0.0263676i	0.000871578	−	0.00135620i
$379$	2.39972	−	16.6904i	0.123266	−	0.857331i	−0.830551	−	0.556942i	$-0.811975\pi$
$379$	2.39972	−	16.6904i	0.123266	−	0.857331i	0.953817	−	0.300389i	$-0.0971164\pi$
$380$	−8.67496	−	2.96421i	−0.445016	−	0.152061i
$381$	−11.1747	−	7.18156i	−0.572498	−	0.367922i
$382$	3.73719	−	3.23829i	0.191211	−	0.165685i
$383$	−31.7658	+	14.5069i	−1.62316	+	0.741270i	−0.999192	−	0.0401838i	$-0.987206\pi$
$383$	−31.7658	+	14.5069i	−1.62316	+	0.741270i	−0.623963	+	0.781454i	$0.714478\pi$
$384$	0.841254	−	0.540641i	0.0429300	−	0.0275895i
$385$	0.367849	+	0.187809i	0.0187473	+	0.00957162i
$386$	−2.43614	+	2.81146i	−0.123996	+	0.143100i
$387$	−1.56156	−	5.31817i	−0.0793784	−	0.270338i
$388$	2.67764	+	1.22284i	0.135937	+	0.0620802i
$389$	−2.37291	−	16.5040i	−0.120311	−	0.836784i	−0.957203	−	0.289416i	$-0.906539\pi$
$389$	−2.37291	−	16.5040i	−0.120311	−	0.836784i	0.836892	−	0.547368i	$-0.184370\pi$
$390$	2.29069	+	0.432141i	0.115994	+	0.0218823i
$391$	12.1563	−	11.1085i	0.614768	−	0.561783i
$392$		−	6.99902i		−	0.353504i
$393$	−16.0465	+	2.30714i	−0.809441	+	0.116380i
$394$	3.33885	−	7.31107i	0.168209	−	0.368326i
$395$	−2.49595	−	25.0935i	−0.125585	−	1.26259i
$396$	3.85915	−	4.45369i	0.193929	−	0.223806i
$397$	7.92824	−	27.0011i	0.397907	−	1.35515i	−0.480400	−	0.877050i	$-0.659508\pi$
$397$	7.92824	−	27.0011i	0.397907	−	1.35515i	0.878307	−	0.478097i	$-0.158673\pi$
$398$	12.8808	+	20.0430i	0.645658	+	1.00466i
$399$	−0.0533811	−	0.116888i	−0.00267240	−	0.00585173i
$400$	1.67252	+	4.71197i	0.0836261	+	0.235599i
$401$	−33.4502	−	21.4972i	−1.67042	−	1.07352i	−0.899888	−	0.436122i	$-0.856352\pi$
$401$	−33.4502	−	21.4972i	−1.67042	−	1.07352i	−0.770537	−	0.637395i	$-0.780012\pi$
$402$	−13.8191	−	1.98689i	−0.689236	−	0.0990971i
$403$	−1.11141	−	0.159796i	−0.0553632	−	0.00796003i
$404$	5.72411	+	3.67866i	0.284785	+	0.183020i
$405$	1.93207	−	1.12565i	0.0960054	−	0.0559342i
$406$	−0.0137848	−	0.0301846i	−0.000684131	−	0.00149804i
$407$	28.5034	+	44.3521i	1.41286	+	2.19845i
$408$	0.967380	−	3.29460i	0.0478925	−	0.163107i
$409$	13.9389	−	16.0863i	0.689232	−	0.795417i	−0.298023	−	0.954559i	$-0.596327\pi$
$409$	13.9389	−	16.0863i	0.689232	−	0.795417i	0.987256	+	0.159142i	$0.0508728\pi$
$410$	1.78473	−	0.177520i	0.0881416	−	0.00876708i
$411$	4.78195	−	10.4710i	0.235876	−	0.516497i
$412$	12.9804	−	1.86630i	0.639499	−	0.0919461i
$413$		−	0.0886870i		−	0.00436400i
$414$	1.47212	+	4.56430i	0.0723507	+	0.224323i
$415$	9.69661	+	1.82927i	0.475988	+	0.0897956i
$416$	0.148363	+	1.03189i	0.00727409	+	0.0505924i
$417$	−20.3219	−	9.28070i	−0.995168	−	0.454478i
$418$	−6.80677	−	23.1817i	−0.332930	−	1.13386i
$419$	−22.9085	+	26.4379i	−1.11916	+	1.29157i	−0.167001	+	0.985957i	$0.553408\pi$
$419$	−22.9085	+	26.4379i	−1.11916	+	1.29157i	−0.952154	+	0.305618i	$0.901137\pi$
$420$	−0.0318694	+	0.0624206i	−0.00155507	+	0.00304581i
$421$	4.11019	−	2.64146i	0.200318	−	0.128737i	−0.436636	−	0.899638i	$-0.643830\pi$
$421$	4.11019	−	2.64146i	0.200318	−	0.128737i	0.636954	+	0.770901i	$0.280194\pi$
$422$	−15.6432	+	7.14403i	−0.761501	+	0.347766i
$423$	−4.92562	+	4.26808i	−0.239492	+	0.207521i
$424$	1.12518	+	0.723111i	0.0546437	+	0.0351174i
$425$	14.9355	+	8.46678i	0.724476	+	0.410699i
$426$	0.625522	−	4.35060i	0.0303066	−	0.210787i
$427$	0.0272957	−	0.0424730i	0.00132093	−	0.00205541i
$428$	−4.59576	+	3.98225i	−0.222144	+	0.192489i
$429$	2.55211	+	5.58834i	0.123217	+	0.269808i
$430$	4.65162	+	11.4878i	0.224321	+	0.553991i
$431$	10.7745	+	3.16367i	0.518987	+	0.152388i	0.530727	−	0.847543i	$-0.321919\pi$
$431$	10.7745	+	3.16367i	0.518987	+	0.152388i	−0.0117400	+	0.999931i	$0.503737\pi$
$432$	0.755750	+	0.654861i	0.0363610	+	0.0315070i
$433$	4.74614	+	16.1639i	0.228085	+	0.776785i	0.991412	+	0.130774i	$0.0417461\pi$
$433$	4.74614	+	16.1639i	0.228085	+	0.776785i	−0.763328	+	0.646012i	$0.776436\pi$
$434$	0.0140239	−	0.0307080i	0.000673167	−	0.00147403i
$435$	0.103325	−	2.36509i	0.00495407	−	0.113397i
$436$	6.30621			0.302013
$437$	19.0051	+	5.03956i	0.909137	+	0.241075i
$438$			4.58063i			0.218871i
$439$	−2.72052	−	18.9216i	−0.129843	−	0.903079i	−0.945750	−	0.324895i	$-0.894671\pi$
$439$	−2.72052	−	18.9216i	−0.129843	−	0.903079i	0.815907	−	0.578183i	$-0.196238\pi$
$440$	−7.60125	+	10.7640i	−0.362375	+	0.513152i
$441$	6.71551	−	1.97185i	0.319786	−	0.0938977i
$442$	2.70529	+	2.34414i	0.128677	+	0.111500i
$443$	1.95061	−	6.64316i	0.0926762	−	0.315626i	−0.900088	−	0.435709i	$-0.856498\pi$
$443$	1.95061	−	6.64316i	0.0926762	−	0.315626i	0.992764	+	0.120083i	$0.0383160\pi$
$444$	−7.52613	+	4.83675i	−0.357174	+	0.229542i
$445$	15.5060	−	3.82647i	0.735056	−	0.181392i
$446$	16.5046	+	19.0473i	0.781514	+	0.901916i
$447$	11.1679	−	17.3776i	0.528224	−	0.821933i
$448$	−0.0310242	−	0.00446060i	−0.00146575	−	0.000210744i
$449$	−2.31880	+	16.1276i	−0.109431	+	0.761110i	0.859027	+	0.511931i	$0.171070\pi$
$449$	−2.31880	+	16.1276i	−0.109431	+	0.761110i	−0.968458	+	0.249179i	$0.919839\pi$
$450$	−4.04990	+	2.93229i	−0.190914	+	0.138229i
$451$	3.09540	+	3.57228i	0.145757	+	0.168212i
$452$	13.7937	−	6.29938i	0.648802	−	0.296298i
$453$	5.44020	+	8.46512i	0.255603	+	0.397726i
$454$	22.0574	+	6.47664i	1.03521	+	0.303964i
$455$	−0.0453911	−	0.0572538i	−0.00212797	−	0.00268410i
$456$	3.93372	−	1.15504i	0.184213	−	0.0540899i
$457$	16.1234	+	7.36332i	0.754222	+	0.344442i	0.755145	−	0.655558i	$-0.227566\pi$
$457$	16.1234	+	7.36332i	0.754222	+	0.344442i	−0.000922809		1.00000i	$0.500294\pi$
$458$	−16.5477	+	2.37920i	−0.773222	+	0.111173i
$459$	3.43368			0.160271
$460$	−4.28577	−	9.83017i	−0.199825	−	0.458334i
$461$	32.3645			1.50736			0.753682	−	0.657240i	$-0.228276\pi$
$461$	32.3645			1.50736			0.753682	+	0.657240i	$0.228276\pi$
$462$	−0.182828	+	0.0262867i	−0.00850592	+	0.00122297i
$463$	14.4610	+	6.60410i	0.672058	+	0.306918i	0.722060	−	0.691831i	$-0.243196\pi$
$463$	14.4610	+	6.60410i	0.672058	+	0.306918i	−0.0500022	+	0.998749i	$0.515923\pi$
$464$	1.01582	−	0.298273i	0.0471584	−	0.0138470i
$465$	1.88724	−	1.49622i	0.0875188	−	0.0693854i
$466$	−12.9519	−	3.80302i	−0.599985	−	0.176172i
$467$	−7.39382	−	11.5050i	−0.342145	−	0.532388i	0.626955	−	0.779055i	$-0.284301\pi$
$467$	−7.39382	−	11.5050i	−0.342145	−	0.532388i	−0.969100	+	0.246667i	$0.920665\pi$
$468$	−0.948289	+	0.433069i	−0.0438347	+	0.0200186i
$469$	0.286561	+	0.330708i	0.0132321	+	0.0152707i
$470$	10.0153	−	10.5870i	0.461973	−	0.488341i
$471$	0.832185	−	5.78797i	0.0383451	−	0.266696i
$472$	2.80074	+	0.402686i	0.128915	+	0.0185351i
$473$	−17.6592	+	27.4783i	−0.811972	+	1.26345i
$474$	7.38521	+	8.52299i	0.339214	+	0.391474i
$475$	1.13669	+	20.4674i	0.0521551	+	0.939110i
$476$	−0.0905379	+	0.0581852i	−0.00414980	+	0.00266691i
$477$	−0.376819	+	1.28333i	−0.0172534	+	0.0587596i
$478$	4.31911	+	3.74253i	0.197552	+	0.171179i
$479$	−38.3174	+	11.2510i	−1.75077	+	0.514072i	−0.990735	−	0.135811i	$-0.956636\pi$
$479$	−38.3174	+	11.2510i	−1.75077	+	0.514072i	−0.760034	+	0.649883i	$0.774818\pi$
$480$	−1.82654	−	1.28986i	−0.0833699	−	0.0588738i
$481$	−1.32730	−	9.23159i	−0.0605198	−	0.420924i
$482$		−	12.4827i		−	0.568571i
$483$	0.0588133	−	0.138333i	0.00267610	−	0.00629439i
$484$	−23.7284			−1.07856
$485$	0.287288	−	6.57594i	0.0130451	−	0.298598i
$486$	−0.415415	+	0.909632i	−0.0188436	+	0.0412617i
$487$	−3.93389	−	13.3976i	−0.178261	−	0.607103i	−0.999341	−	0.0362895i	$-0.988446\pi$
$487$	−3.93389	−	13.3976i	−0.178261	−	0.607103i	0.821080	−	0.570813i	$-0.193372\pi$
$488$	1.21736	+	1.05485i	0.0551074	+	0.0477509i
$489$	17.1163	+	5.02581i	0.774028	+	0.227275i
$490$	−14.5062	+	5.87382i	−0.655323	+	0.265352i
$491$	13.8866	+	30.4075i	0.626695	+	1.37227i	0.910548	+	0.413404i	$0.135660\pi$
$491$	13.8866	+	30.4075i	0.626695	+	1.37227i	−0.283852	+	0.958868i	$0.591613\pi$
$492$	−0.606183	+	0.525260i	−0.0273288	+	0.0236806i
$493$	1.96538	−	3.05818i	0.0885160	−	0.137734i
$494$	−0.608257	+	4.23052i	−0.0273668	+	0.190340i
$495$	−12.4695	−	4.26078i	−0.560461	−	0.191508i
$496$	0.906085	+	0.582306i	0.0406844	+	0.0261463i
$497$	−0.104115	+	0.0902163i	−0.00467020	+	0.00404675i
$498$	−4.01416	+	1.83320i	−0.179879	+	0.0821478i
$499$	5.75885	−	3.70099i	0.257802	−	0.165679i	−0.405356	−	0.914159i	$-0.632852\pi$
$499$	5.75885	−	3.70099i	0.257802	−	0.165679i	0.663157	+	0.748480i	$0.269216\pi$
$500$	8.36241	−	7.42092i	0.373978	−	0.331874i
$501$	−8.78323	+	10.1364i	−0.392406	+	0.452860i
$502$	−0.0445241	−	0.151635i	−0.00198721	−	0.00676781i
$503$	−29.7300	−	13.5773i	−1.32560	−	0.605380i	−0.378284	−	0.925690i	$-0.623486\pi$
$503$	−29.7300	−	13.5773i	−1.32560	−	0.605380i	−0.947313	+	0.320310i	$0.896213\pi$
$504$	−0.00446060	−	0.0310242i	−0.000198691	−	0.00138193i
$505$	2.82053	−	14.9511i	0.125512	−	0.665313i
$506$	14.6469	−	24.1707i	0.651133	−	1.07452i
$507$			11.9132i			0.529084i
$508$	−13.1482	+	1.89043i	−0.583357	+	0.0838741i
$509$	7.21088	−	15.7896i	0.319617	−	0.699863i	−0.679821	−	0.733378i	$-0.737943\pi$
$509$	7.21088	−	15.7896i	0.319617	−	0.699863i	0.999438	+	0.0335145i	$0.0106700\pi$
$510$	−7.64025	+	0.759943i	−0.338316	+	0.0336509i
$511$	0.0940194	−	0.108504i	0.00415918	−	0.00479994i
$512$	0.281733	−	0.959493i	0.0124509	−	0.0424040i
$513$	2.21651	+	3.44896i	0.0978615	+	0.152276i
$514$	−7.44157	−	16.2948i	−0.328234	−	0.718732i
$515$	−14.7617	−	25.3370i	−0.650479	−	1.11648i
$516$	−4.66281	−	2.99661i	−0.205269	−	0.131918i
$517$	38.0174	+	5.46608i	1.67200	+	0.240398i
$518$	0.277553	+	0.0399060i	0.0121950	+	0.00175337i
$519$	2.85515	+	1.83489i	0.125327	+	0.0805428i
$520$	2.01418	−	1.17349i	0.0883276	−	0.0514610i
$521$	1.24899	+	2.73490i	0.0547191	+	0.119818i	0.935017	−	0.354604i	$-0.115384\pi$
$521$	1.24899	+	2.73490i	0.0547191	+	0.119818i	−0.880297	+	0.474422i	$0.842657\pi$
$522$	0.572381	+	0.890642i	0.0250524	+	0.0389823i
$523$	0.698044	−	2.37732i	0.0305234	−	0.103953i	−0.942822	−	0.333295i	$-0.891839\pi$
$523$	0.698044	−	2.37732i	0.0305234	−	0.103953i	0.973346	+	0.229342i	$0.0736575\pi$
$524$	−10.6163	+	12.2519i	−0.463776	+	0.535226i
$525$	0.156119	+	0.0136670i	0.00681359	+	0.000596479i
$526$	8.22516	−	18.0106i	0.358634	−	0.785299i
$527$	3.66066	−	0.526323i	0.159461	−	0.0229270i
$528$		−	5.89308i		−	0.256463i
$529$	10.6452	+	20.3882i	0.462835	+	0.886445i
$530$	0.554430	−	2.93892i	0.0240829	−	0.127658i
$531$	0.402686	+	2.80074i	0.0174751	+	0.121542i
$532$	−0.116888	−	0.0533811i	−0.00506775	−	0.00231436i
$533$	−0.235580	−	0.802310i	−0.0102041	−	0.0347519i
$534$	−4.67736	+	5.39796i	−0.202409	+	0.233593i
$535$	12.1105	+	6.18314i	0.523584	+	0.267321i
$536$	−11.7449	+	7.54802i	−0.507304	+	0.326025i
$537$	1.52226	−	0.695194i	0.0656905	−	0.0299998i
$538$	2.95026	−	2.55641i	0.127195	−	0.110215i
$539$	−34.6981	−	22.2991i	−1.49455	−	0.960492i
$540$	0.723015	−	2.11595i	0.0311136	−	0.0910560i
$541$	−3.52835	+	24.5402i	−0.151696	+	1.05507i	0.761681	+	0.647952i	$0.224374\pi$
$541$	−3.52835	+	24.5402i	−0.151696	+	1.05507i	−0.913377	+	0.407115i	$0.866535\pi$
$542$	−1.41009	+	2.19414i	−0.0605684	+	0.0942463i
$543$	−16.7698	+	14.5311i	−0.719661	+	0.623590i
$544$	−1.42640	−	3.12339i	−0.0611566	−	0.133914i
$545$	−5.29239	−	13.0703i	−0.226701	−	0.559869i
$546$	0.0313516	+	0.00920567i	0.00134173	+	0.000393966i
$547$	9.72526	+	8.42698i	0.415822	+	0.360312i	0.837503	−	0.546432i	$-0.184014\pi$
$547$	9.72526	+	8.42698i	0.415822	+	0.360312i	−0.421681	+	0.906744i	$0.638560\pi$
$548$	−3.24310	−	11.0450i	−0.138538	−	0.471818i
$549$	−0.669151	+	1.46524i	−0.0285587	+	0.0625348i
$550$	28.6887	+	6.72088i	1.22329	+	0.286579i
$551$	4.34048			0.184911
$552$	4.10154	+	2.48544i	0.174573	+	0.105787i
$553$		−	0.353474i		−	0.0150312i
$554$	−2.12363	−	14.7702i	−0.0902244	−	0.627524i
$555$	16.3409	+	11.5395i	0.693631	+	0.489825i
$556$	−21.4358	+	6.29413i	−0.909082	+	0.266931i
$557$	−19.8379	−	17.1896i	−0.840557	−	0.728347i	0.123983	−	0.992284i	$-0.460433\pi$
$557$	−19.8379	−	17.1896i	−0.840557	−	0.728347i	−0.964540	+	0.263938i	$0.914979\pi$
$558$	−0.303444	+	1.03344i	−0.0128458	+	0.0437489i
$559$	4.86096	−	3.12395i	0.205597	−	0.132129i
$560$	0.0167915	+	0.0680443i	0.000709571	+	0.00287540i
$561$	−13.2511	−	15.2926i	−0.559461	−	0.645653i
$562$	10.2864	−	16.0059i	0.433905	−	0.675169i
$563$	−0.496190	−	0.0713414i	−0.0209119	−	0.00300668i	0.131851	−	0.991270i	$-0.457908\pi$
$563$	−0.496190	−	0.0713414i	−0.0209119	−	0.00300668i	−0.152763	+	0.988263i	$0.548817\pi$
$564$	−0.927542	+	6.45120i	−0.0390566	+	0.271644i
$565$	−24.6323	−	23.3023i	−1.03629	−	0.980333i
$566$	2.05105	+	2.36704i	0.0862123	+	0.0994943i
$567$	0.0285108	−	0.0130204i	0.00119734	−	0.000546807i
$568$	−2.37630	−	3.69760i	−0.0997073	−	0.155148i
$569$	−2.03114	−	0.596398i	−0.0851500	−	0.0250023i	0.238880	−	0.971049i	$-0.423220\pi$
$569$	−2.03114	−	0.596398i	−0.0851500	−	0.0250023i	−0.324030	+	0.946047i	$0.605038\pi$
$570$	−5.69527	−	7.18369i	−0.238548	−	0.300892i
$571$	−19.3399	+	5.67872i	−0.809351	+	0.237647i	−0.660125	−	0.751156i	$-0.729497\pi$
$571$	−19.3399	+	5.67872i	−0.809351	+	0.237647i	−0.149226	+	0.988803i	$0.547678\pi$
$572$	5.58834	+	2.55211i	0.233660	+	0.106709i
$573$	4.89467	−	0.703748i	0.204478	−	0.0293995i
$574$	0.0251402			0.00104933
$575$	−16.7773	+	17.1325i	−0.699661	+	0.714475i
$576$	1.00000			0.0416667
$577$	42.0772	−	6.04978i	1.75170	−	0.251856i	0.809548	−	0.587054i	$-0.199713\pi$
$577$	42.0772	−	6.04978i	1.75170	−	0.251856i	0.942147	+	0.335199i	$0.108803\pi$
$578$	4.73902	+	2.16424i	0.197117	+	0.0900204i
$579$	−3.56940	+	1.04807i	−0.148339	+	0.0435564i
$580$	−1.47072	−	1.85508i	−0.0610681	−	0.0770279i
$581$	0.132713	+	0.0389681i	0.00550587	+	0.00161667i
$582$	1.59146	+	2.47636i	0.0659682	+	0.102648i
$583$	7.16975	−	3.27432i	0.296941	−	0.135608i
$584$	2.99968	+	3.46181i	0.124127	+	0.143251i
$585$	1.69342	+	1.60198i	0.0700142	+	0.0662337i
$586$	2.05947	−	14.3239i	0.0850759	−	0.591716i
$587$	10.9066	+	1.56813i	0.450162	+	0.0647235i	0.363667	−	0.931529i	$-0.381524\pi$
$587$	10.9066	+	1.56813i	0.450162	+	0.0647235i	0.0864943	+	0.996252i	$0.472434\pi$
$588$	3.78395	−	5.88795i	0.156048	−	0.242815i
$589$	2.89170	+	3.33720i	0.119150	+	0.137507i
$590$	−1.51587	−	6.14278i	−0.0624075	−	0.252894i
$591$	6.76148	−	4.34534i	0.278130	−	0.178743i
$592$	−2.52047	+	8.58394i	−0.103591	+	0.352798i
$593$	−23.8915	−	20.7021i	−0.981108	−	0.850135i	0.00760271	−	0.999971i	$-0.497580\pi$
$593$	−23.8915	−	20.7021i	−0.981108	−	0.850135i	−0.988711	+	0.149836i	$0.952125\pi$
$594$	5.65437	−	1.66027i	0.232001	−	0.0681218i
$595$	0.196577	+	0.138818i	0.00805889	+	0.00569099i
$596$	−2.93977	−	20.4466i	−0.120418	−	0.837524i
$597$			23.8251i			0.975097i
$598$	−4.13316	+	2.81307i	−0.169018	+	0.115035i
$599$	−40.3122			−1.64711			−0.823557	−	0.567234i	$-0.808014\pi$
$599$	−40.3122			−1.64711			−0.823557	+	0.567234i	$0.808014\pi$
$600$	−1.14047	+	4.86820i	−0.0465595	+	0.198743i
$601$	−8.92712	+	19.5477i	−0.364145	+	0.797366i	0.635535	+	0.772072i	$0.280779\pi$
$601$	−8.92712	+	19.5477i	−0.364145	+	0.797366i	−0.999680	+	0.0252941i	$0.991948\pi$
$602$	0.0489442	+	0.166689i	0.00199482	+	0.00679372i
$603$	−10.5512	−	9.14267i	−0.429678	−	0.372318i
$604$	9.65491	+	2.83494i	0.392853	+	0.115352i
$605$	19.9137	+	49.1795i	0.809606	+	1.99943i
$606$	2.82659	+	6.18937i	0.114822	+	0.251426i
$607$	−31.2653	+	27.0915i	−1.26902	+	1.09961i	−0.278762	+	0.960360i	$0.589924\pi$
$607$	−31.2653	+	27.0915i	−1.26902	+	1.09961i	−0.990257	+	0.139251i	$0.955530\pi$
$608$	2.21651	−	3.44896i	0.0898915	−	0.139874i
$609$	0.00472248	−	0.0328456i	0.000191364	−	0.00133097i
$610$	1.16463	−	3.40838i	0.0471547	−	0.138001i
$611$	−5.71591	−	3.67339i	−0.231241	−	0.148609i
$612$	2.59500	−	2.24858i	0.104897	−	0.0908936i
$613$	−37.0409	+	16.9160i	−1.49607	+	0.683232i	−0.984399	−	0.175950i	$-0.943700\pi$
$613$	−37.0409	+	16.9160i	−1.49607	+	0.683232i	−0.511670	+	0.859182i	$0.670973\pi$
$614$	20.5062	−	13.1785i	0.827561	−	0.531841i
$615$	1.59739	+	0.815560i	0.0644128	+	0.0328865i
$616$	−0.120958	+	0.139593i	−0.00487354	+	0.00562436i
$617$	−10.1893	−	34.7017i	−0.410207	−	1.39704i	−0.862902	−	0.505372i	$-0.831355\pi$
$617$	−10.1893	−	34.7017i	−0.410207	−	1.39704i	0.452695	−	0.891666i	$-0.350463\pi$
$618$	11.9288	+	5.44771i	0.479847	+	0.219139i
$619$	4.71752	+	32.8111i	0.189613	+	1.31879i	0.833011	+	0.553257i	$0.186615\pi$
$619$	4.71752	+	32.8111i	0.189613	+	1.31879i	−0.643397	+	0.765532i	$0.722476\pi$
$620$	0.446470	−	2.36665i	0.0179307	−	0.0950468i
$621$	−1.22922	+	4.63562i	−0.0493270	+	0.186021i
$622$			16.4007i			0.657607i
$623$	0.221591	−	0.0318600i	0.00887786	−	0.00127644i
$624$	−0.433069	+	0.948289i	−0.0173366	+	0.0379619i
$625$	−22.3987	−	11.1041i	−0.895946	−	0.444162i
$626$	7.95264	−	9.17784i	0.317851	−	0.366820i
$627$	6.80677	−	23.1817i	0.271836	−	0.925789i
$628$	−3.16139	−	4.91922i	−0.126153	−	0.196298i
$629$	12.7611	+	27.9429i	0.508817	+	1.11415i
$630$	−0.0605573	+	0.0352816i	−0.00241266	+	0.00140565i
$631$	17.4220	+	11.1964i	0.693557	+	0.445722i	0.839349	−	0.543593i	$-0.182937\pi$
$631$	17.4220	+	11.1964i	0.693557	+	0.445722i	−0.145792	+	0.989315i	$0.546573\pi$
$632$	11.1627	+	1.60496i	0.444030	+	0.0638419i
$633$	−17.0223	−	2.44744i	−0.676575	−	0.0972768i
$634$	−7.62024	−	4.89723i	−0.302638	−	0.194494i
$635$	14.9525	+	25.6645i	0.593373	+	1.01846i
$636$	0.555621	+	1.21664i	0.0220318	+	0.0482429i
$637$	3.94476	+	6.13817i	0.156297	+	0.243203i
$638$	1.75774	−	5.98633i	0.0695897	−	0.237001i
$639$	2.87834	−	3.32178i	0.113865	−	0.131407i
$640$	−2.22509	+	0.221320i	−0.0879543	+	0.00874845i
$641$	−19.7792	+	43.3105i	−0.781232	+	1.71066i	−0.0810350	+	0.996711i	$0.525823\pi$
$641$	−19.7792	+	43.3105i	−0.781232	+	1.71066i	−0.700197	+	0.713949i	$0.746905\pi$
$642$	−6.01916	+	0.865425i	−0.237557	+	0.0341556i
$643$		−	44.6802i		−	1.76201i	−0.473103	−	0.881007i	$-0.656866\pi$
$643$		−	44.6802i		−	1.76201i	0.473103	−	0.881007i	$-0.343134\pi$
$644$	−0.0461409	−	0.143060i	−0.00181821	−	0.00563735i
$645$	−2.29758	+	12.1790i	−0.0904672	+	0.479548i
$646$	−2.00342	−	13.9341i	−0.0788235	−	0.548230i
$647$	4.07349	+	1.86030i	0.160145	+	0.0731359i	0.493875	−	0.869533i	$-0.335580\pi$
$647$	4.07349	+	1.86030i	0.160145	+	0.0731359i	−0.333730	+	0.942669i	$0.608307\pi$
$648$	0.281733	+	0.959493i	0.0110675	+	0.0376924i
$649$	10.9196	−	12.6019i	0.428633	−	0.494668i
$650$	−4.12255	−	3.18976i	−0.161700	−	0.125113i
$651$	0.0283996	−	0.0182513i	0.00111307	−	0.000715326i
$652$	16.2269	−	7.41056i	0.635493	−	0.290220i
$653$	−24.5669	+	21.2874i	−0.961378	+	0.833039i	−0.986015	−	0.166658i	$-0.946703\pi$
$653$	−24.5669	+	21.2874i	−0.961378	+	0.833039i	0.0246366	+	0.999696i	$0.492157\pi$
$654$	5.30512	+	3.40940i	0.207447	+	0.133318i
$655$	34.3029	+	11.7212i	1.34032	+	0.457985i
$656$	−0.114150	+	0.793931i	−0.00445681	+	0.0309978i
$657$	−2.47648	+	3.85347i	−0.0966165	+	0.150338i
$658$	0.154385	−	0.133775i	0.00601855	−	0.00521510i
$659$	−0.151766	−	0.332320i	−0.00591195	−	0.0129454i	0.906653	−	0.421877i	$-0.138629\pi$
$659$	−0.151766	−	0.332320i	−0.00591195	−	0.0129454i	−0.912565	+	0.408932i	$0.865901\pi$
$660$	−12.2140	+	4.94568i	−0.475430	+	0.192510i
$661$	−14.3267	−	4.20671i	−0.557246	−	0.163622i	−0.00903023	−	0.999959i	$-0.502874\pi$
$661$	−14.3267	−	4.20671i	−0.557246	−	0.163622i	−0.548215	+	0.836337i	$0.684693\pi$
$662$	−24.3011	−	21.0571i	−0.944491	−	0.818406i
$663$	1.00849	+	3.43461i	0.0391666	+	0.133389i
$664$	−1.83320	+	4.01416i	−0.0711421	+	0.155779i
$665$	−0.0125411	+	0.287062i	−0.000486323	+	0.0111318i
$666$	−8.94633			−0.346663
$667$	3.42510	+	3.74814i	0.132620	+	0.145129i
$668$			13.4124i			0.518940i
$669$	3.58679	+	24.9467i	0.138673	+	0.964493i
$670$	25.5008	+	18.0080i	0.985182	+	0.695712i
$671$	9.10807	−	2.67437i	0.351613	−	0.103243i
$672$	−0.0236876	−	0.0205254i	−0.000913770	−	0.000791786i
$673$	2.19619	−	7.47954i	0.0846569	−	0.288315i	−0.906273	−	0.422692i	$-0.861085\pi$
$673$	2.19619	−	7.47954i	0.0846569	−	0.288315i	0.990930	+	0.134377i	$0.0429033\pi$
$674$	−20.4475	+	13.1408i	−0.787610	+	0.506166i
$675$	−4.99231	+	0.277257i	−0.192154	+	0.0106716i
$676$	7.80149	+	9.00340i	0.300057	+	0.346284i
$677$	5.06604	−	7.88291i	0.194704	−	0.302965i	−0.730151	−	0.683286i	$-0.760550\pi$
$677$	5.06604	−	7.88291i	0.194704	−	0.302965i	0.924854	+	0.380321i	$0.124187\pi$
$678$	15.0097	+	2.15807i	0.576445	+	0.0828802i
$679$	0.0131305	−	0.0913245i	0.000503902	−	0.00350471i
$680$	−5.27646	+	5.57763i	−0.202343	+	0.213892i
$681$	15.0543	+	17.3736i	0.576883	+	0.665759i
$682$	5.77364	−	2.63673i	0.221084	−	0.100966i
$683$	8.86212	+	13.7897i	0.339100	+	0.527650i	0.968364	−	0.249542i	$-0.0802800\pi$
$683$	8.86212	+	13.7897i	0.339100	+	0.527650i	−0.629264	+	0.777191i	$0.716644\pi$
$684$	3.93372	+	1.15504i	0.150410	+	0.0441642i
$685$	−20.1701	+	15.9910i	−0.770662	+	0.610984i
$686$	−0.421001	+	0.123617i	−0.0160739	+	0.00471972i
$687$	−15.2071	−	6.94484i	−0.580186	−	0.264962i
$688$	−5.48627	+	0.788807i	−0.209162	+	0.0300730i
$689$	−1.39435			−0.0531204
$690$	1.70917	−	10.5867i	0.0650671	−	0.403030i
$691$	28.8476			1.09742			0.548708	−	0.836014i	$-0.315120\pi$
$691$	28.8476			1.09742			0.548708	+	0.836014i	$0.315120\pi$
$692$	3.35938	−	0.483005i	0.127704	−	0.0183611i
$693$	−0.168016	−	0.0767305i	−0.00638241	−	0.00291475i
$694$	−17.6642	+	5.18668i	−0.670525	+	0.196884i
$695$	31.0349	+	39.1457i	1.17722	+	1.48488i
$696$	1.01582	+	0.298273i	0.0385047	+	0.0113060i
$697$	1.48900	+	2.31693i	0.0563999	+	0.0877600i
$698$	16.1304	−	7.36649i	0.610544	−	0.278826i
$699$	−8.83977	−	10.2016i	−0.334351	−	0.385861i
$700$	0.126937	−	0.0919073i	0.00479776	−	0.00347377i
$701$	−2.45238	+	17.0567i	−0.0926251	+	0.644222i	0.889631	+	0.456679i	$0.150961\pi$
$701$	−2.45238	+	17.0567i	−0.0926251	+	0.644222i	−0.982257	+	0.187542i	$0.939948\pi$
$702$	−1.03189	−	0.148363i	−0.0389460	−	0.00559959i
$703$	−19.8297	+	30.8556i	−0.747890	+	1.16374i
$704$	−3.85915	−	4.45369i	−0.145447	−	0.167855i
$705$	14.1492	−	3.49164i	0.532890	−	0.131503i
$706$	5.26863	−	3.38594i	0.198287	−	0.127432i
$707$	0.0600843	−	0.204628i	0.00225970	−	0.00769584i
$708$	2.13843	+	1.85296i	0.0803670	+	0.0696384i
$709$	−40.8404	+	11.9918i	−1.53379	+	0.450362i	−0.936209	−	0.351444i	$-0.885691\pi$
$709$	−40.8404	+	11.9918i	−1.53379	+	0.450362i	−0.597584	+	0.801806i	$0.703873\pi$
$710$	−5.66937	+	8.02828i	−0.212768	+	0.301296i
$711$	1.60496	+	11.1627i	0.0601907	+	0.418636i
$712$			7.14253i			0.267678i
$713$	−0.599919	+	5.13047i	−0.0224671	+	0.192138i
$714$	−0.107623			−0.00402768
$715$	0.599580	−	13.7242i	0.0224230	−	0.513257i
$716$	0.695194	−	1.52226i	0.0259806	−	0.0568896i
$717$	1.61010	+	5.48351i	0.0601304	+	0.204785i
$718$	−21.4038	−	18.5465i	−0.798782	−	0.692149i
$719$	−26.5550	−	7.79725i	−0.990334	−	0.290788i	−0.253850	−	0.967244i	$-0.581697\pi$
$719$	−26.5550	−	7.79725i	−0.990334	−	0.290788i	−0.736484	+	0.676455i	$0.763515\pi$
$720$	−0.839235	−	2.07260i	−0.0312764	−	0.0772414i
$721$	−0.170749	−	0.373887i	−0.00635901	−	0.0139243i
$722$	−1.65638	+	1.43526i	−0.0616441	+	0.0534149i
$723$	6.74865	−	10.5011i	0.250985	−	0.390540i
$724$	−3.15791	+	21.9638i	−0.117363	+	0.816277i
$725$	−2.61057	+	4.60506i	−0.0969540	+	0.171027i
$726$	−19.9616	−	12.8285i	−0.740843	−	0.476111i
$727$	−28.7373	+	24.9010i	−1.06581	+	0.923528i	−0.997249	−	0.0741191i	$-0.976385\pi$
$727$	−28.7373	+	24.9010i	−1.06581	+	0.923528i	−0.0685587	+	0.997647i	$0.521840\pi$
$728$	0.0297224	−	0.0135738i	0.00110159	−	0.000503077i
$729$	−0.841254	+	0.540641i	−0.0311575	+	0.0200237i
$730$	4.65753	−	9.12241i	0.172383	−	0.337636i
$731$	−12.4632	+	14.3833i	−0.460968	+	0.531986i
$732$	0.453815	+	1.54555i	0.0167735	+	0.0571253i
$733$	−30.9947	−	14.1548i	−1.14482	−	0.522820i	−0.249554	−	0.968361i	$-0.580284\pi$
$733$	−30.9947	−	14.1548i	−1.14482	−	0.522820i	−0.895261	+	0.445541i	$0.853011\pi$
$734$	−1.00185	−	6.96800i	−0.0369788	−	0.257193i
$735$	−15.3790	−	2.90127i	−0.567263	−	0.107015i
$736$	4.72735	−	0.807567i	0.174252	−	0.0297673i
$737$			82.2747i			3.03063i
$738$	−0.793931	+	0.114150i	−0.0292250	+	0.00420192i
$739$	−2.01489	+	4.41199i	−0.0741189	+	0.162298i	−0.943065	−	0.332610i	$-0.892071\pi$
$739$	−2.01489	+	4.41199i	−0.0741189	+	0.162298i	0.868946	+	0.494908i	$0.164798\pi$
$740$	19.9064	−	1.98000i	0.731773	−	0.0727864i
$741$	−2.79889	+	3.23009i	−0.102820	+	0.118660i
$742$	0.0118107	−	0.0402236i	0.000433585	−	0.00147666i
$743$	1.11441	+	1.73406i	0.0408837	+	0.0636163i	0.861094	−	0.508446i	$-0.169780\pi$
$743$	1.11441	+	1.73406i	0.0408837	+	0.0636163i	−0.820210	+	0.572062i	$0.806144\pi$
$744$	0.447429	+	0.979733i	0.0164035	+	0.0359188i
$745$	−39.9105	+	23.2525i	−1.46221	+	0.851904i
$746$	18.7454	+	12.0469i	0.686318	+	0.441070i
$747$	−4.36803	−	0.628028i	−0.159818	−	0.0229783i
$748$	−20.0290	−	2.87974i	−0.732333	−	0.105294i
$749$	0.160343	+	0.103046i	0.00585880	+	0.00376522i
$750$	11.0470	−	1.72182i	0.403378	−	0.0628719i
$751$	−18.7213	−	40.9940i	−0.683151	−	1.49589i	−0.859270	−	0.511523i	$-0.829082\pi$
$751$	−18.7213	−	40.9940i	−0.683151	−	1.49589i	0.176119	−	0.984369i	$-0.443646\pi$
$752$	3.52365	+	5.48290i	0.128494	+	0.199941i
$753$	0.0445241	−	0.151635i	0.00162255	−	0.00552589i
$754$	−0.722770	+	0.834121i	−0.0263217	+	0.0303769i
$755$	−2.22704	−	22.3900i	−0.0810502	−	0.814855i
$756$	0.0130204	−	0.0285108i	0.000473549	−	0.00103693i
$757$	3.85023	−	0.553580i	0.139939	−	0.0201202i	−0.0719893	−	0.997405i	$-0.522935\pi$
$757$	3.85023	−	0.553580i	0.139939	−	0.0201202i	0.211928	+	0.977285i	$0.432026\pi$
$758$		−	16.8621i		−	0.612458i
$759$	25.3894	−	12.4150i	0.921576	−	0.450635i
$760$	−9.00851	−	1.69946i	−0.326773	−	0.0616461i
$761$	−3.52770	−	24.5357i	−0.127879	−	0.889418i	−0.948236	−	0.317566i	$-0.897134\pi$
$761$	−3.52770	−	24.5357i	−0.127879	−	0.889418i	0.820357	−	0.571852i	$-0.193775\pi$
$762$	−12.0830	−	5.51813i	−0.437722	−	0.199901i
$763$	−0.0556864	−	0.189650i	−0.00201598	−	0.00686581i
$764$	3.23829	−	3.73719i	0.117157	−	0.135207i
$765$	−6.83824	−	3.49132i	−0.247237	−	0.126229i
$766$	−29.3779	+	18.8800i	−1.06147	+	0.682163i
$767$	−2.68323	+	1.22539i	−0.0968856	+	0.0442462i
$768$	0.755750	−	0.654861i	0.0272708	−	0.0236303i
$769$	12.6182	+	8.10923i	0.455024	+	0.292426i	0.748006	−	0.663692i	$-0.231011\pi$
$769$	12.6182	+	8.10923i	0.455024	+	0.292426i	−0.292982	+	0.956118i	$0.594648\pi$
$770$	0.390833	+	0.133547i	0.0140846	+	0.00481269i
$771$	2.54937	−	17.7313i	0.0918133	−	0.638576i
$772$	−2.01124	+	3.12954i	−0.0723859	+	0.112635i
$773$	−34.7591	+	30.1189i	−1.25020	+	1.08330i	−0.257056	+	0.966397i	$0.582752\pi$
$773$	−34.7591	+	30.1189i	−1.25020	+	1.08330i	−0.993143	+	0.116907i	$0.962702\pi$
$774$	−2.30252	−	5.04181i	−0.0827623	−	0.181224i
$775$	−5.27981	+	1.06082i	−0.189656	+	0.0381057i
$776$	2.82442	+	0.829324i	0.101391	+	0.0297710i
$777$	0.211917	+	0.183627i	0.00760249	+	0.00658759i
$778$	−4.69752	−	15.9983i	−0.168414	−	0.573566i
$779$	−1.36606	+	2.99125i	−0.0489442	+	0.107173i
$780$	2.32887	+	0.101743i	0.0833870	+	0.00364299i
$781$	−25.9021			−0.926849
$782$	10.4516	−	12.7255i	0.373749	−	0.455062i
$783$			1.05871i			0.0378352i
$784$	−0.996064	−	6.92778i	−0.0355737	−	0.247421i
$785$	−7.54245	+	10.6807i	−0.269202	+	0.381211i
$786$	−15.5549	+	4.56732i	−0.554824	+	0.162911i
$787$	−0.497764	−	0.431315i	−0.0177434	−	0.0153747i	0.645944	−	0.763385i	$-0.276464\pi$
$787$	−0.497764	−	0.431315i	−0.0177434	−	0.0153747i	−0.663687	+	0.748010i	$0.731009\pi$
$788$	2.26439	−	7.71182i	0.0806657	−	0.274722i
$789$	16.6567	−	10.7046i	0.592995	−	0.381095i
$790$	−6.04172	−	24.4829i	−0.214955	−	0.871062i
$791$	−0.311249	−	0.359201i	−0.0110667	−	0.0127717i
$792$	3.18604	−	4.95757i	0.113211	−	0.176160i
$793$	−1.66216	−	0.238983i	−0.0590252	−	0.00848654i
$794$	4.00488	−	27.8546i	0.142128	−	0.988522i
$795$	2.05531	−	2.17263i	0.0728945	−	0.0770552i
$796$	15.6021	+	18.0058i	0.553003	+	0.638200i
$797$	18.4260	−	8.41489i	0.652684	−	0.298071i	−0.0614185	−	0.998112i	$-0.519562\pi$
$797$	18.4260	−	8.41489i	0.652684	−	0.298071i	0.714102	+	0.700041i	$0.246835\pi$
$798$	−0.0694727	−	0.108102i	−0.00245931	−	0.00382676i
$799$	21.4726	+	6.30494i	0.759647	+	0.223053i
$800$	2.32608	+	4.42599i	0.0822394	+	0.156482i
$801$	−6.85321	+	2.01228i	−0.242146	+	0.0711005i
$802$	−36.1691	−	16.5179i	−1.27718	−	0.583267i
$803$	26.7193	−	3.84165i	0.942902	−	0.135569i
$804$	−13.9612			−0.492375
$805$	−0.257783	+	0.215693i	−0.00908567	+	0.00760217i
$806$	−1.12284			−0.0395503
$807$	3.86402	−	0.555562i	0.136020	−	0.0195567i
$808$	6.18937	+	2.82659i	0.217741	+	0.0994391i
$809$	42.4263	−	12.4575i	1.49163	−	0.437981i	0.568568	−	0.822637i	$-0.307498\pi$
$809$	42.4263	−	12.4575i	1.49163	−	0.437981i	0.923060	+	0.384655i	$0.125680\pi$
$810$	1.75221	−	1.38916i	0.0615663	−	0.0488101i
$811$	42.9289	+	12.6051i	1.50744	+	0.442624i	0.928059	−	0.372434i	$-0.121477\pi$
$811$	42.9289	+	12.6051i	1.50744	+	0.442624i	0.579380	+	0.815058i	$0.303295\pi$
$812$	−0.0179403	−	0.0279156i	−0.000629580	−	0.000979645i
$813$	−2.37248	+	1.08348i	−0.0832065	+	0.0379991i
$814$	34.5252	+	39.8442i	1.21011	+	1.39654i
$815$	−28.9773	−	27.4127i	−1.01503	−	0.960224i
$816$	0.488664	−	3.39873i	0.0171067	−	0.118979i
$817$	−22.4926	−	3.23395i	−0.786916	−	0.113141i
$818$	11.5077	−	17.9063i	0.402356	−	0.626078i
$819$	0.0213977	+	0.0246943i	0.000747696	+	0.000862888i
$820$	1.74130	−	0.429707i	0.0608089	−	0.0150060i
$821$	32.3941	−	20.8184i	1.13056	−	0.726568i	0.164884	−	0.986313i	$-0.447275\pi$
$821$	32.3941	−	20.8184i	1.13056	−	0.726568i	0.965677	+	0.259745i	$0.0836385\pi$
$822$	3.24310	−	11.0450i	0.113116	−	0.385238i
$823$	0.778425	+	0.674509i	0.0271342	+	0.0235119i	0.668322	−	0.743872i	$-0.267013\pi$
$823$	0.778425	+	0.674509i	0.0271342	+	0.0235119i	−0.641188	+	0.767384i	$0.721558\pi$
$824$	12.5827	−	3.69461i	0.438339	−	0.128708i
$825$	20.5009	+	21.1642i	0.713748	+	0.736844i
$826$	−0.0126215	−	0.0877843i	−0.000439157	−	0.00305441i
$827$		−	38.1789i		−	1.32761i	−0.747906	−	0.663805i	$-0.768940\pi$
$827$		−	38.1789i		−	1.32761i	0.747906	−	0.663805i	$-0.231060\pi$
$828$	2.10670	+	4.30834i	0.0732130	+	0.149725i
$829$	47.6217			1.65397			0.826984	−	0.562225i	$-0.190054\pi$
$829$	47.6217			1.65397			0.826984	+	0.562225i	$0.190054\pi$
$830$	9.85824	+	0.430684i	0.342185	+	0.0149493i
$831$	6.19884	−	13.5736i	0.215036	−	0.470862i
$832$	0.293705	+	1.00027i	0.0101824	+	0.0346781i
$833$	−18.1625	−	15.7379i	−0.629293	−	0.545285i
$834$	−21.4358	−	6.29413i	−0.742262	−	0.217948i
$835$	27.7985	−	11.2561i	0.962007	−	0.389534i
$836$	−10.0366	−	21.9771i	−0.347123	−	0.760093i
$837$	−0.813992	+	0.705328i	−0.0281357	+	0.0243797i
$838$	−18.9129	+	29.4290i	−0.653334	+	1.01661i
$839$	−7.91805	+	55.0713i	−0.273361	+	1.90127i	0.139070	+	0.990283i	$0.455589\pi$
$839$	−7.91805	+	55.0713i	−0.273361	+	1.90127i	−0.412432	+	0.910988i	$0.635321\pi$
$840$	−0.0226616	+	0.0663207i	−0.000781900	+	0.00228828i
$841$	−23.4534	−	15.0726i	−0.808739	−	0.519745i
$842$	3.69243	−	3.19951i	0.127250	−	0.110262i
$843$	17.3069	−	7.90380i	0.596082	−	0.272221i
$844$	−14.4673	+	9.29758i	−0.497986	+	0.320036i
$845$	12.1132	−	23.7254i	0.416706	−	0.816177i
$846$	−4.26808	+	4.92562i	−0.146740	+	0.169346i
$847$	0.209531	+	0.713597i	0.00719957	+	0.0245195i
$848$	1.21664	+	0.555621i	0.0417796	+	0.0190801i
$849$	0.445737	+	3.10017i	0.0152976	+	0.106397i
$850$	15.9884	+	6.25506i	0.548397	+	0.214547i
$851$	−42.2924	+	7.22476i	−1.44977	+	0.247661i
$852$		−	4.39534i		−	0.150582i
$853$	−15.8427	+	2.27783i	−0.542442	+	0.0779914i	−0.408089	−	0.912942i	$-0.633805\pi$
$853$	−15.8427	+	2.27783i	−0.542442	+	0.0779914i	−0.134353	+	0.990934i	$0.542896\pi$
$854$	0.0209734	−	0.0459252i	0.000717693	−	0.00157153i
$855$	−0.907367	−	9.12240i	−0.0310313	−	0.311979i
$856$	−3.98225	+	4.59576i	−0.136110	+	0.157080i
$857$	−7.35934	+	25.0636i	−0.251390	+	0.856156i	0.733011	+	0.680217i	$0.238114\pi$
$857$	−7.35934	+	25.0636i	−0.251390	+	0.856156i	−0.984401	+	0.175939i	$0.943704\pi$
$858$	3.32144	+	5.16826i	0.113392	+	0.176441i
$859$	−3.64437	−	7.98007i	−0.124344	−	0.272276i	0.837215	−	0.546874i	$-0.184182\pi$
$859$	−3.64437	−	7.98007i	−0.124344	−	0.272276i	−0.961559	+	0.274598i	$0.911455\pi$
$860$	6.23916	+	10.7089i	0.212754	+	0.365170i
$861$	0.0211493	+	0.0135918i	0.000720766	+	0.000463208i
$862$	11.1150	+	1.59810i	0.378579	+	0.0544315i
$863$	−25.5385	−	3.67188i	−0.869339	−	0.124992i	−0.306811	−	0.951770i	$-0.599262\pi$
$863$	−25.5385	−	3.67188i	−0.869339	−	0.124992i	−0.562528	+	0.826778i	$0.690171\pi$
$864$	0.841254	+	0.540641i	0.0286200	+	0.0183930i
$865$	−3.82038	−	6.55730i	−0.129897	−	0.222955i
$866$	6.99818	+	15.3239i	0.237808	+	0.520727i
$867$	2.81664	+	4.38278i	0.0956581	+	0.148847i
$868$	0.00951092	−	0.0323912i	0.000322822	−	0.00109943i
$869$	43.5216	−	50.2266i	1.47637	−	1.70382i
$870$	−0.234314	−	2.35572i	−0.00794397	−	0.0798664i
$871$	6.04618	−	13.2393i	0.204867	−	0.448596i
$872$	6.24202	−	0.897468i	0.211382	−	0.0303921i
$873$			2.94366i			0.0996276i
$874$	19.5289	+	2.28356i	0.660573	+	0.0772425i
$875$	−0.297017	−	0.185958i	−0.0100410	−	0.00628652i
$876$	0.651892	+	4.53401i	0.0220254	+	0.153190i
$877$	−35.3928	−	16.1633i	−1.19513	−	0.545797i	−0.284362	−	0.958717i	$-0.591782\pi$
$877$	−35.3928	−	16.1633i	−1.19513	−	0.545797i	−0.910767	+	0.412920i	$0.864509\pi$
$878$	−5.38565	−	18.3418i	−0.181757	−	0.619007i
$879$	9.47664	−	10.9366i	0.319639	−	0.368883i
$880$	−5.99201	+	11.7362i	−0.201990	+	0.395626i
$881$	−21.2037	+	13.6268i	−0.714372	+	0.459099i	−0.846675	−	0.532111i	$-0.821399\pi$
$881$	−21.2037	+	13.6268i	−0.714372	+	0.459099i	0.132303	+	0.991209i	$0.457763\pi$
$882$	6.36653	−	2.90750i	0.214372	−	0.0979005i
$883$	−24.1204	+	20.9004i	−0.811715	+	0.703355i	−0.958275	−	0.285847i	$-0.907725\pi$
$883$	−24.1204	+	20.9004i	−0.811715	+	0.703355i	0.146561	+	0.989202i	$0.453180\pi$
$884$	3.01136	+	1.93528i	0.101283	+	0.0650905i
$885$	2.04580	−	5.98718i	0.0687689	−	0.201257i
$886$	0.985333	−	6.85314i	0.0331029	−	0.230236i
$887$	−3.64271	+	5.66816i	−0.122310	+	0.190318i	−0.897009	−	0.442012i	$-0.854265\pi$
$887$	−3.64271	+	5.66816i	−0.122310	+	0.190318i	0.774699	+	0.632330i	$0.217901\pi$
$888$	−6.76119	+	5.85860i	−0.226891	+	0.196602i
$889$	0.172956	+	0.378721i	0.00580075	+	0.0127019i
$890$	14.8036	−	5.99426i	0.496219	−	0.200928i
$891$	5.65437	+	1.66027i	0.189428	+	0.0556212i
$892$	19.0473	+	16.5046i	0.637751	+	0.552614i
$893$	7.52804	+	25.6382i	0.251916	+	0.857949i
$894$	8.58115	−	18.7901i	0.286997	−	0.628435i
$895$	−3.73848	−	0.163326i	−0.124964	−	0.00545937i
$896$	−0.0313432			−0.00104710
$897$	−4.99790	+	0.131954i	−0.166875	+	0.00440581i
$898$			16.2935i			0.543720i
$899$	0.162281	+	1.12869i	0.00541239	+	0.0376440i
$900$	−3.59137	+	3.47880i	−0.119712	+	0.115960i
$901$	4.40655	−	1.29388i	0.146803	−	0.0431053i
$902$	3.57228	+	3.09540i	0.118944	+	0.103066i
$903$	−0.0489442	+	0.166689i	−0.00162876	+	0.00554705i
$904$	12.7568	−	8.19831i	0.424286	−	0.272672i
$905$	48.1724	−	11.8877i	1.60131	−	0.395159i
$906$	6.58954	+	7.60474i	0.218923	+	0.252650i
$907$	30.4865	−	47.4378i	1.01229	−	1.57515i	0.210449	−	0.977605i	$-0.432507\pi$
$907$	30.4865	−	47.4378i	1.01229	−	1.57515i	0.801837	−	0.597543i	$-0.203856\pi$
$908$	22.7546	+	3.27162i	0.755138	+	0.108573i
$909$	−0.968347	+	6.73500i	−0.0321180	+	0.223386i
$910$	−0.0530771	−	0.0502112i	−0.00175949	−	0.00166448i
$911$	−19.2458	−	22.2108i	−0.637641	−	0.735877i	0.341315	−	0.939949i	$-0.389128\pi$
$911$	−19.2458	−	22.2108i	−0.637641	−	0.735877i	−0.978956	+	0.204072i	$0.934582\pi$
$912$	3.72930	−	1.70312i	0.123490	−	0.0563958i
$913$	14.0598	+	21.8775i	0.465312	+	0.724039i
$914$	17.0072	+	4.99377i	0.562549	+	0.165179i
$915$	2.82246	−	2.23766i	0.0933077	−	0.0739748i
$916$	−16.0406	+	4.70996i	−0.529998	+	0.155621i
$917$	0.462204	+	0.211082i	0.0152633	+	0.00697053i
$918$	3.39873	−	0.488664i	0.112175	−	0.0161283i
$919$	−44.4260			−1.46548			−0.732740	−	0.680509i	$-0.761759\pi$
$919$	−44.4260			−1.46548			−0.732740	+	0.680509i	$0.761759\pi$
$920$	−5.64112	−	9.12018i	−0.185982	−	0.300684i
$921$	24.3757			0.803207
$922$	32.0350	−	4.60594i	1.05502	−	0.151689i
$923$	4.16805	+	1.90349i	0.137193	+	0.0626540i
$924$	−0.177226	+	0.0520382i	−0.00583031	+	0.00171193i
$925$	−20.8099	−	39.5963i	−0.684225	−	1.30192i
$926$	15.2536	+	4.47887i	0.501265	+	0.147185i
$927$	7.08991	+	11.0321i	0.232863	+	0.362342i
$928$	0.963035	−	0.439803i	0.0316132	−	0.0144373i
$929$	2.09768	+	2.42086i	0.0688228	+	0.0794257i	0.789117	−	0.614243i	$-0.210539\pi$
$929$	2.09768	+	2.42086i	0.0688228	+	0.0794257i	−0.720294	+	0.693669i	$0.755993\pi$
$930$	1.65510	−	1.74957i	0.0542729	−	0.0573706i
$931$	4.08366	−	28.4024i	0.133836	−	0.930853i
$932$	−13.3613	−	1.92106i	−0.437664	−	0.0629266i
$933$	−8.86687	+	13.7971i	−0.290288	+	0.451697i
$934$	−8.95589	−	10.3357i	−0.293046	−	0.338193i
$935$	10.8405	+	43.9289i	0.354522	+	1.43663i
$936$	−0.877004	+	0.563617i	−0.0286658	+	0.0184224i
$937$	−14.5345	+	49.5000i	−0.474822	+	1.61710i	0.279190	+	0.960236i	$0.409934\pi$
$937$	−14.5345	+	49.5000i	−0.474822	+	1.61710i	−0.754013	+	0.656860i	$0.771884\pi$
$938$	0.330708	+	0.286561i	0.0107980	+	0.00935653i
$939$	11.6521	−	3.42137i	0.380252	−	0.111652i
$940$	8.40671	−	11.9046i	0.274197	−	0.388284i
$941$	1.81340	+	12.6125i	0.0591153	+	0.411156i	0.997795	+	0.0663664i	$0.0211406\pi$
$941$	1.81340	+	12.6125i	0.0591153	+	0.411156i	−0.938680	+	0.344790i	$0.887950\pi$
$942$		−	5.84749i		−	0.190522i
$943$	−3.66100	+	1.18078i	−0.119219	+	0.0384514i
$944$	2.82954			0.0920938
$945$	−0.0700188	−	0.00305896i	−0.00227771	−	9.95079e-5i
$946$	−13.5689	+	29.7118i	−0.441163	+	0.966013i
$947$	−6.59841	−	22.4721i	−0.214420	−	0.730246i	−0.994516	−	0.104587i	$-0.966648\pi$
$947$	−6.59841	−	22.4721i	−0.214420	−	0.730246i	0.780096	−	0.625660i	$-0.215170\pi$
$948$	8.52299	+	7.38521i	0.276814	+	0.239861i
$949$	−4.58186	−	1.34536i	−0.148734	−	0.0436721i
$950$	4.03794	+	20.0973i	0.131008	+	0.652043i
$951$	−3.76291	−	8.23962i	−0.122021	−	0.267188i
$952$	−0.0813358	+	0.0704778i	−0.00263611	+	0.00228420i
$953$	11.6359	−	18.1057i	0.376922	−	0.586502i	−0.600026	−	0.799981i	$-0.704843\pi$
$953$	11.6359	−	18.1057i	0.376922	−	0.586502i	0.976948	+	0.213478i	$0.0684793\pi$
$954$	−0.190347	+	1.32389i	−0.00616272	+	0.0428626i
$955$	−10.4634	−	3.57531i	−0.338587	−	0.115694i
$956$	4.80777	+	3.08976i	0.155494	+	0.0999301i
$957$	4.71516	−	4.08571i	0.152419	−	0.132072i
$958$	−36.3262	+	16.5896i	−1.17365	+	0.535987i
$959$	−0.303524	+	0.195063i	−0.00980131	+	0.00629892i
$960$	−1.99152	−	1.01679i	−0.0642760	−	0.0328167i
$961$	19.5410	−	22.5515i	0.630355	−	0.727468i
$962$	−2.62759	−	8.94873i	−0.0847168	−	0.288519i
$963$	−5.53153	−	2.52616i	−0.178251	−	0.0814045i
$964$	−1.77647	−	12.3556i	−0.0572163	−	0.397948i
$965$	8.17420	+	1.54207i	0.263137	+	0.0496410i
$966$	0.0385278	−	0.145295i	0.00123961	−	0.00467480i
$967$		−	30.0628i		−	0.966756i	−0.875412	−	0.483378i	$-0.839410\pi$
$967$		−	30.0628i		−	0.966756i	0.875412	−	0.483378i	$-0.160590\pi$
$968$	−23.4868	+	3.37690i	−0.754896	+	0.108538i
$969$	5.84796	−	12.8052i	0.187863	−	0.411364i
$970$	−0.651490	−	6.54989i	−0.0209181	−	0.210304i
$971$	4.45690	−	5.14353i	0.143029	−	0.165064i	−0.679715	−	0.733476i	$-0.737897\pi$
$971$	4.45690	−	5.14353i	0.143029	−	0.165064i	0.822744	+	0.568412i	$0.192442\pi$
$972$	−0.281733	+	0.959493i	−0.00903658	+	0.0307758i
$973$	0.378574	+	0.589073i	0.0121365	+	0.0188848i
$974$	−5.80052	−	12.7014i	−0.185861	−	0.406978i
$975$	−1.74360	−	4.91222i	−0.0558398	−	0.157317i
$976$	1.35509	+	0.870865i	0.0433755	+	0.0278757i
$977$	−11.2628	−	1.61934i	−0.360328	−	0.0518074i	−0.0402267	−	0.999191i	$-0.512808\pi$
$977$	−11.2628	−	1.61934i	−0.360328	−	0.0518074i	−0.320102	+	0.947383i	$0.603717\pi$
$978$	17.6574	+	2.53875i	0.564620	+	0.0811802i
$979$	35.4096	+	22.7564i	1.13170	+	0.727297i
$980$	−13.5226	+	7.87848i	−0.431964	+	0.251669i
$981$	2.61970	+	5.73633i	0.0836404	+	0.183147i
$982$	18.0727	+	28.1217i	0.576724	+	0.897400i
$983$	−2.08329	+	7.09504i	−0.0664467	+	0.226297i	−0.986021	−	0.166618i	$-0.946715\pi$
$983$	−2.08329	+	7.09504i	−0.0664467	+	0.226297i	0.919575	+	0.392915i	$0.128533\pi$
$984$	−0.525260	+	0.606183i	−0.0167447	+	0.0193244i
$985$	−17.8839	+	1.77884i	−0.569828	+	0.0566784i
$986$	1.51015	−	3.30676i	0.0480928	−	0.105309i
$987$	0.202201	−	0.0290721i	0.00643613	−	0.000925376i
$988$			4.27402i			0.135975i
$989$	−14.9564	−	21.9750i	−0.475586	−	0.698763i
$990$	−12.9489	−	2.44283i	−0.411544	−	0.0776381i
$991$	1.13815	+	7.91602i	0.0361546	+	0.251461i	0.999881	−	0.0154318i	$-0.00491228\pi$
$991$	1.13815	+	7.91602i	0.0361546	+	0.251461i	−0.963726	+	0.266892i	$0.914003\pi$
$992$	0.979733	+	0.447429i	0.0311066	+	0.0142059i
$993$	−9.05912	−	30.8525i	−0.287482	−	0.979075i
$994$	−0.0902163	+	0.104115i	−0.00286149	+	0.00330233i
$995$	24.2251	−	47.4482i	0.767987	−	1.50421i
$996$	−3.71241	+	2.38582i	−0.117632	+	0.0755975i
$997$	−11.6247	+	5.30884i	−0.368159	+	0.168133i	−0.590899	−	0.806745i	$-0.701227\pi$
$997$	−11.6247	+	5.30884i	−0.368159	+	0.168133i	0.222740	+	0.974878i	$0.428500\pi$
$998$	5.17353	−	4.48289i	0.163765	−	0.141903i
$999$	−7.52613	−	4.83675i	−0.238116	−	0.153028i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.r.a.49.8	yes	120
5.4	even	2	inner	690.2.r.a.49.6	✓	120
23.8	even	11	inner	690.2.r.a.169.6	yes	120
115.54	even	22	inner	690.2.r.a.169.8	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.r.a.49.6	✓	120	5.4	even	2	inner
690.2.r.a.49.8	yes	120	1.1	even	1	trivial
690.2.r.a.169.6	yes	120	23.8	even	11	inner
690.2.r.a.169.8	yes	120	115.54	even	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.r (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.989821 - 0.142315i) q^{2} +(0.909632 + 0.415415i) q^{3} +(0.959493 - 0.281733i) q^{4} +(-1.38916 - 1.75221i) q^{5} +(0.959493 + 0.281733i) q^{6} +(-0.0169454 - 0.0263676i) q^{7} +(0.909632 - 0.415415i) q^{8} +(0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(0.989821 - 0.142315i) q^{2} +(0.909632 + 0.415415i) q^{3} +(0.959493 - 0.281733i) q^{4} +(-1.38916 - 1.75221i) q^{5} +(0.959493 + 0.281733i) q^{6} +(-0.0169454 - 0.0263676i) q^{7} +(0.909632 - 0.415415i) q^{8} +(0.654861 + 0.755750i) q^{9} +(-1.62439 - 1.53668i) q^{10} +(0.838672 - 5.83309i) q^{11} +(0.989821 + 0.142315i) q^{12} +(-0.563617 + 0.877004i) q^{13} +(-0.0205254 - 0.0236876i) q^{14} +(-0.535731 - 2.17094i) q^{15} +(0.841254 - 0.540641i) q^{16} +(0.967380 - 3.29460i) q^{17} +(0.755750 + 0.654861i) q^{18} +(3.93372 - 1.15504i) q^{19} +(-1.82654 - 1.28986i) q^{20} +(-0.00446060 - 0.0310242i) q^{21} -5.89308i q^{22} +(4.10154 + 2.48544i) q^{23} +1.00000 q^{24} +(-1.14047 + 4.86820i) q^{25} +(-0.433069 + 0.948289i) q^{26} +(0.281733 + 0.959493i) q^{27} +(-0.0236876 - 0.0205254i) q^{28} +(1.01582 + 0.298273i) q^{29} +(-0.839235 - 2.07260i) q^{30} +(0.447429 + 0.979733i) q^{31} +(0.755750 - 0.654861i) q^{32} +(3.18604 - 4.95757i) q^{33} +(0.488664 - 3.39873i) q^{34} +(-0.0226616 + 0.0663207i) q^{35} +(0.841254 + 0.540641i) q^{36} +(-6.76119 + 5.85860i) q^{37} +(3.72930 - 1.70312i) q^{38} +(-0.877004 + 0.563617i) q^{39} +(-1.99152 - 1.01679i) q^{40} +(-0.525260 + 0.606183i) q^{41} +(-0.00883040 - 0.0300736i) q^{42} +(-5.04181 - 2.30252i) q^{43} +(-0.838672 - 5.83309i) q^{44} +(0.414525 - 2.19731i) q^{45} +(4.41350 + 1.87643i) q^{46} +6.51753i q^{47} +(0.989821 - 0.142315i) q^{48} +(2.90750 - 6.36653i) q^{49} +(-0.436045 + 4.98095i) q^{50} +(2.24858 - 2.59500i) q^{51} +(-0.293705 + 1.00027i) q^{52} +(0.723111 + 1.12518i) q^{53} +(0.415415 + 0.909632i) q^{54} +(-11.3858 + 6.63357i) q^{55} +(-0.0263676 - 0.0169454i) q^{56} +(4.05806 + 0.583461i) q^{57} +(1.04793 + 0.150670i) q^{58} +(2.38036 + 1.52977i) q^{59} +(-1.12565 - 1.93207i) q^{60} +(0.669151 + 1.46524i) q^{61} +(0.582306 + 0.906085i) q^{62} +(0.00883040 - 0.0300736i) q^{63} +(0.654861 - 0.755750i) q^{64} +(2.31965 - 0.230726i) q^{65} +(2.44807 - 5.36053i) q^{66} +(-13.8191 + 1.98689i) q^{67} -3.43368i q^{68} +(2.69840 + 3.96467i) q^{69} +(-0.0129925 + 0.0688707i) q^{70} +(-0.625522 - 4.35060i) q^{71} +(0.909632 + 0.415415i) q^{72} +(1.29051 + 4.39508i) q^{73} +(-5.85860 + 6.76119i) q^{74} +(-3.05973 + 3.95450i) q^{75} +(3.44896 - 2.21651i) q^{76} +(-0.168016 + 0.0767305i) q^{77} +(-0.787867 + 0.682690i) q^{78} +(9.48726 + 6.09709i) q^{79} +(-2.11595 - 0.723015i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(-0.433645 + 0.674765i) q^{82} +(-3.33508 + 2.88986i) q^{83} +(-0.0130204 - 0.0285108i) q^{84} +(-7.11666 + 2.88167i) q^{85} +(-5.31817 - 1.56156i) q^{86} +(0.800118 + 0.693307i) q^{87} +(-1.66027 - 5.65437i) q^{88} +(-2.96711 + 6.49707i) q^{89} +(0.0975956 - 2.23394i) q^{90} +0.0326752 q^{91} +(4.63562 + 1.22922i) q^{92} +1.07707i q^{93} +(0.927542 + 6.45120i) q^{94} +(-7.48845 - 5.28816i) q^{95} +(0.959493 - 0.281733i) q^{96} +(2.22467 + 1.92768i) q^{97} +(1.97185 - 6.71551i) q^{98} +(4.95757 - 3.18604i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{4} + 12 q^{6} + 12 q^{9}+O(q^{10}) \) 120 * q + 12 * q^4 + 12 * q^6 + 12 * q^9	\( 120 q + 12 q^{4} + 12 q^{6} + 12 q^{9} + 18 q^{10} - 8 q^{14} - 4 q^{15} - 12 q^{16} + 22 q^{20} + 14 q^{21} + 120 q^{24} + 52 q^{25} + 16 q^{29} + 8 q^{31} - 36 q^{34} - 90 q^{35} - 12 q^{36} + 22 q^{39} + 4 q^{40} + 16 q^{41} - 4 q^{49} - 4 q^{50} + 8 q^{51} - 12 q^{54} - 56 q^{55} + 8 q^{56} + 138 q^{59} + 4 q^{60} - 36 q^{61} + 12 q^{64} + 52 q^{65} + 96 q^{70} + 8 q^{71} + 8 q^{74} - 4 q^{75} - 60 q^{79} - 12 q^{81} + 8 q^{84} + 24 q^{85} - 8 q^{86} - 104 q^{89} + 4 q^{90} - 144 q^{91} - 24 q^{94} - 14 q^{95} + 12 q^{96} - 44 q^{99}+O(q^{100}) \) 120 * q + 12 * q^4 + 12 * q^6 + 12 * q^9 + 18 * q^10 - 8 * q^14 - 4 * q^15 - 12 * q^16 + 22 * q^20 + 14 * q^21 + 120 * q^24 + 52 * q^25 + 16 * q^29 + 8 * q^31 - 36 * q^34 - 90 * q^35 - 12 * q^36 + 22 * q^39 + 4 * q^40 + 16 * q^41 - 4 * q^49 - 4 * q^50 + 8 * q^51 - 12 * q^54 - 56 * q^55 + 8 * q^56 + 138 * q^59 + 4 * q^60 - 36 * q^61 + 12 * q^64 + 52 * q^65 + 96 * q^70 + 8 * q^71 + 8 * q^74 - 4 * q^75 - 60 * q^79 - 12 * q^81 + 8 * q^84 + 24 * q^85 - 8 * q^86 - 104 * q^89 + 4 * q^90 - 144 * q^91 - 24 * q^94 - 14 * q^95 + 12 * q^96 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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