LMFDB - Embedded newform 462.2.y.d.37.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(25,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 20, 24]))

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

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

chi := DirichletCharacter("462.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.y (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			37.3
Character	$\chi$	$=$	462.37
Dual form			462.2.y.d.25.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.913545 - 0.406737i) q^{2} +(0.978148 - 0.207912i) q^{3} +(0.669131 - 0.743145i) q^{4} +(0.0926977 + 0.881959i) q^{5} +(0.809017 - 0.587785i) q^{6} +(1.77880 + 1.95854i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.913545 - 0.406737i) q^{9} +(0.443409 + 0.768006i) q^{10} +(3.02915 + 1.35064i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-3.78905 - 2.75291i) q^{13} +(2.42163 + 1.06571i) q^{14} +(0.274042 + 0.843413i) q^{15} +(-0.104528 - 0.994522i) q^{16} +(-3.02484 - 1.34675i) q^{17} +(0.669131 - 0.743145i) q^{18} +(2.58762 + 2.87385i) q^{19} +(0.717450 + 0.521258i) q^{20} +(2.14713 + 1.54590i) q^{21} +(3.31662 + 0.00180404i) q^{22} +(-2.93144 + 5.07740i) q^{23} +(0.104528 - 0.994522i) q^{24} +(4.12148 - 0.876047i) q^{25} +(-4.58118 - 0.973759i) q^{26} +(0.809017 - 0.587785i) q^{27} +(2.64573 - 0.0113917i) q^{28} +(-2.05746 - 6.33220i) q^{29} +(0.593397 + 0.659034i) q^{30} +(1.02698 - 9.77111i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.24377 + 0.691330i) q^{33} -3.31110 q^{34} +(-1.56246 + 1.75038i) q^{35} +(0.309017 - 0.951057i) q^{36} +(-0.203413 - 0.0432367i) q^{37} +(3.53281 + 1.57291i) q^{38} +(-4.27861 - 1.90496i) q^{39} +(0.867438 + 0.184380i) q^{40} +(-1.71512 + 5.27861i) q^{41} +(2.59028 + 0.538935i) q^{42} -6.38498 q^{43} +(3.03062 - 1.34734i) q^{44} +(0.443409 + 0.768006i) q^{45} +(-0.612837 + 5.83076i) q^{46} +(-7.44880 - 8.27273i) q^{47} +(-0.309017 - 0.951057i) q^{48} +(-0.671724 + 6.96770i) q^{49} +(3.40884 - 2.47667i) q^{50} +(-3.23875 - 0.688417i) q^{51} +(-4.58118 + 0.973759i) q^{52} +(-1.23855 + 11.7840i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-0.910415 + 2.79679i) q^{55} +(2.41236 - 1.08652i) q^{56} +(3.12859 + 2.27305i) q^{57} +(-4.45512 - 4.94791i) q^{58} +(1.40745 - 1.56313i) q^{59} +(0.810148 + 0.360701i) q^{60} +(-0.992796 - 9.44582i) q^{61} +(-3.03607 - 9.34406i) q^{62} +(2.42163 + 1.06571i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(2.07671 - 3.59698i) q^{65} +(3.24452 - 0.687800i) q^{66} +(0.784736 + 1.35920i) q^{67} +(-3.02484 + 1.34675i) q^{68} +(-1.81173 + 5.57593i) q^{69} +(-0.715431 + 2.23456i) q^{70} +(-3.69033 + 2.68118i) q^{71} +(-0.104528 - 0.994522i) q^{72} +(-7.69078 + 8.54147i) q^{73} +(-0.203413 + 0.0432367i) q^{74} +(3.84927 - 1.71381i) q^{75} +3.86714 q^{76} +(2.74299 + 8.33523i) q^{77} -4.68352 q^{78} +(13.9917 - 6.22952i) q^{79} +(0.867438 - 0.184380i) q^{80} +(0.669131 - 0.743145i) q^{81} +(0.580160 + 5.51985i) q^{82} +(-13.5913 + 9.87464i) q^{83} +(2.58554 - 0.561220i) q^{84} +(0.907380 - 2.79263i) q^{85} +(-5.83297 + 2.59700i) q^{86} +(-3.32904 - 5.76606i) q^{87} +(2.22060 - 2.46353i) q^{88} +(-5.12492 + 8.87662i) q^{89} +(0.717450 + 0.521258i) q^{90} +(-1.34831 - 12.3179i) q^{91} +(1.81173 + 5.57593i) q^{92} +(-1.02698 - 9.77111i) q^{93} +(-10.1696 - 4.52781i) q^{94} +(-2.29475 + 2.54858i) q^{95} +(-0.669131 - 0.743145i) q^{96} +(-2.58883 - 1.88089i) q^{97} +(2.22037 + 6.63852i) q^{98} +(3.31662 + 0.00180404i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 3 q^{5} + 10 q^{6} - 7 q^{7} - 10 q^{8} + 5 q^{9} + 12 q^{10} + 2 q^{11} + 20 q^{12} + 10 q^{13} + 5 q^{14} - 6 q^{15} + 5 q^{16} + 5 q^{18} - 13 q^{19} + 6 q^{20} - 2 q^{21}+ \cdots - 4 q^{99}+O(q^{100}) $ 40 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 3 * q^5 + 10 * q^6 - 7 * q^7 - 10 * q^8 + 5 * q^9 + 12 * q^10 + 2 * q^11 + 20 * q^12 + 10 * q^13 + 5 * q^14 - 6 * q^15 + 5 * q^16 + 5 * q^18 - 13 * q^19 + 6 * q^20 - 2 * q^21 - 4 * q^22 - 20 * q^23 - 5 * q^24 + 12 * q^25 + 10 * q^27 - 3 * q^28 + 12 * q^29 + 3 * q^30 - 10 * q^31 - 20 * q^32 + 8 * q^33 - 13 * q^35 - 10 * q^36 + 3 * q^37 + 2 * q^38 + 5 * q^39 - 3 * q^40 - 44 * q^41 - 3 * q^42 + 36 * q^43 - 3 * q^44 + 12 * q^45 + 11 * q^47 + 10 * q^48 + 33 * q^49 - 4 * q^50 + 26 * q^53 + 20 * q^54 - 20 * q^55 + 8 * q^56 + 4 * q^57 - 6 * q^58 + 4 * q^59 + 3 * q^60 - 23 * q^61 + 5 * q^63 - 10 * q^64 - 50 * q^65 - 7 * q^66 - 108 * q^67 + 20 * q^69 - 86 * q^71 + 5 * q^72 - 35 * q^73 + 3 * q^74 - 2 * q^75 - 44 * q^76 - 37 * q^77 + 20 * q^78 + 3 * q^79 - 3 * q^80 + 5 * q^81 - 28 * q^82 - 88 * q^83 - 5 * q^84 + 96 * q^85 - 13 * q^86 + 6 * q^87 - 8 * q^88 + 6 * q^89 + 6 * q^90 + 40 * q^91 - 20 * q^92 + 10 * q^93 - 24 * q^94 + 36 * q^95 - 5 * q^96 + 60 * q^97 + 2 * q^98 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	0.913545	−	0.406737i	0.645974	−	0.287606i
$2$	0.913545	−	0.406737i	0.645974	−	0.287606i
$3$	0.978148	−	0.207912i	0.564734	−	0.120038i
$3$	0.978148	−	0.207912i	0.564734	−	0.120038i
$4$	0.669131	−	0.743145i	0.334565	−	0.371572i
$5$	0.0926977	+	0.881959i	0.0414557	+	0.394424i	0.995500	+	0.0947594i	$0.0302082\pi$
$5$	0.0926977	+	0.881959i	0.0414557	+	0.394424i	−0.954045	+	0.299665i	$0.903125\pi$
$6$	0.809017	−	0.587785i	0.330280	−	0.239962i
$7$	1.77880	+	1.95854i	0.672324	+	0.740257i
$7$	1.77880	+	1.95854i	0.672324	+	0.740257i
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	0.913545	−	0.406737i	0.304515	−	0.135579i
$10$	0.443409	+	0.768006i	0.140218	+	0.242865i
$11$	3.02915	+	1.35064i	0.913324	+	0.407233i
$11$	3.02915	+	1.35064i	0.913324	+	0.407233i
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−3.78905	−	2.75291i	−1.05089	−	0.763519i	−0.0785112	−	0.996913i	$-0.525017\pi$
$13$	−3.78905	−	2.75291i	−1.05089	−	0.763519i	−0.972382	+	0.233394i	$0.925017\pi$
$14$	2.42163	+	1.06571i	0.647207	+	0.284822i
$15$	0.274042	+	0.843413i	0.0707572	+	0.217768i
$16$	−0.104528	−	0.994522i	−0.0261321	−	0.248630i
$17$	−3.02484	−	1.34675i	−0.733632	−	0.326634i	0.00569197	−	0.999984i	$-0.498188\pi$
$17$	−3.02484	−	1.34675i	−0.733632	−	0.326634i	−0.739324	+	0.673350i	$0.764855\pi$
$18$	0.669131	−	0.743145i	0.157716	−	0.175161i
$19$	2.58762	+	2.87385i	0.593642	+	0.659306i	0.962849	−	0.270041i	$-0.0870373\pi$
$19$	2.58762	+	2.87385i	0.593642	+	0.659306i	−0.369207	+	0.929347i	$0.620371\pi$
$20$	0.717450	+	0.521258i	0.160427	+	0.116557i
$21$	2.14713	+	1.54590i	0.468543	+	0.337344i
$22$	3.31662	+	0.00180404i	0.707107	+	0.000384623i
$23$	−2.93144	+	5.07740i	−0.611247	+	1.05871i	0.379783	+	0.925075i	$0.375998\pi$
$23$	−2.93144	+	5.07740i	−0.611247	+	1.05871i	−0.991031	+	0.133636i	$0.957335\pi$
$24$	0.104528	−	0.994522i	0.0213368	−	0.203006i
$25$	4.12148	−	0.876047i	0.824296	−	0.175209i
$26$	−4.58118	−	0.973759i	−0.898443	−	0.190970i
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$	2.64573	−	0.0113917i	0.499995	−	0.00215283i
$29$	−2.05746	−	6.33220i	−0.382060	−	1.17586i	−0.938590	−	0.345033i	$-0.887868\pi$
$29$	−2.05746	−	6.33220i	−0.382060	−	1.17586i	0.556530	−	0.830827i	$-0.312132\pi$
$30$	0.593397	+	0.659034i	0.108339	+	0.120323i
$31$	1.02698	−	9.77111i	0.184452	−	1.75494i	−0.375874	−	0.926671i	$-0.622658\pi$
$31$	1.02698	−	9.77111i	0.184452	−	1.75494i	0.560326	−	0.828272i	$-0.310676\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	3.24377	+	0.691330i	0.564668	+	0.120345i
$34$	−3.31110			−0.567849
$35$	−1.56246	+	1.75038i	−0.264104	+	0.295869i
$36$	0.309017	−	0.951057i	0.0515028	−	0.158509i
$37$	−0.203413	−	0.0432367i	−0.0334409	−	0.00710808i	0.191161	−	0.981559i	$-0.438775\pi$
$37$	−0.203413	−	0.0432367i	−0.0334409	−	0.00710808i	−0.224602	+	0.974451i	$0.572108\pi$
$38$	3.53281	+	1.57291i	0.573098	+	0.255160i
$39$	−4.27861	−	1.90496i	−0.685126	−	0.305038i
$40$	0.867438	+	0.184380i	0.137154	+	0.0291530i
$41$	−1.71512	+	5.27861i	−0.267857	+	0.824380i	0.723164	+	0.690676i	$0.242687\pi$
$41$	−1.71512	+	5.27861i	−0.267857	+	0.824380i	−0.991021	+	0.133704i	$0.957313\pi$
$42$	2.59028	+	0.538935i	0.399689	+	0.0831594i
$43$	−6.38498			−0.973700			−0.486850	−	0.873486i	$-0.661854\pi$
$43$	−6.38498			−0.973700			−0.486850	+	0.873486i	$0.661854\pi$
$44$	3.03062	−	1.34734i	0.456883	−	0.203120i
$45$	0.443409	+	0.768006i	0.0660995	+	0.114488i
$46$	−0.612837	+	5.83076i	−0.0903579	+	0.859698i
$47$	−7.44880	−	8.27273i	−1.08652	−	1.20670i	−0.977117	−	0.212704i	$-0.931773\pi$
$47$	−7.44880	−	8.27273i	−1.08652	−	1.20670i	−0.109402	−	0.993998i	$-0.534894\pi$
$48$	−0.309017	−	0.951057i	−0.0446028	−	0.137273i
$49$	−0.671724	+	6.96770i	−0.0959605	+	0.995385i
$50$	3.40884	−	2.47667i	0.482082	−	0.350253i
$51$	−3.23875	−	0.688417i	−0.453515	−	0.0963977i
$52$	−4.58118	+	0.973759i	−0.635295	+	0.135036i
$53$	−1.23855	+	11.7840i	−0.170127	+	1.61865i	0.492918	+	0.870075i	$0.335930\pi$
$53$	−1.23855	+	11.7840i	−0.170127	+	1.61865i	−0.663046	+	0.748579i	$0.730737\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	−0.910415	+	2.79679i	−0.122760	+	0.377119i
$56$	2.41236	−	1.08652i	0.322365	−	0.145192i
$57$	3.12859	+	2.27305i	0.414391	+	0.301073i
$58$	−4.45512	−	4.94791i	−0.584986	−	0.649693i
$59$	1.40745	−	1.56313i	0.183234	−	0.203502i	−0.644529	−	0.764580i	$-0.722946\pi$
$59$	1.40745	−	1.56313i	0.183234	−	0.203502i	0.827763	+	0.561078i	$0.189613\pi$
$60$	0.810148	+	0.360701i	0.104590	+	0.0465663i
$61$	−0.992796	−	9.44582i	−0.127115	−	1.20941i	−0.853116	−	0.521721i	$-0.825290\pi$
$61$	−0.992796	−	9.44582i	−0.127115	−	1.20941i	0.726002	−	0.687693i	$-0.241376\pi$
$62$	−3.03607	−	9.34406i	−0.385581	−	1.18670i
$63$	2.42163	+	1.06571i	0.305096	+	0.134266i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	2.07671	−	3.59698i	0.257585	−	0.446150i
$66$	3.24452	−	0.687800i	0.399373	−	0.0846624i
$67$	0.784736	+	1.35920i	0.0958708	+	0.166053i	0.909972	−	0.414670i	$-0.136103\pi$
$67$	0.784736	+	1.35920i	0.0958708	+	0.166053i	−0.814101	+	0.580723i	$0.802770\pi$
$68$	−3.02484	+	1.34675i	−0.366816	+	0.163317i
$69$	−1.81173	+	5.57593i	−0.218106	+	0.671263i
$70$	−0.715431	+	2.23456i	−0.0855104	+	0.267081i
$71$	−3.69033	+	2.68118i	−0.437961	+	0.318197i	−0.784824	−	0.619718i	$-0.787247\pi$
$71$	−3.69033	+	2.68118i	−0.437961	+	0.318197i	0.346863	+	0.937916i	$0.387247\pi$
$72$	−0.104528	−	0.994522i	−0.0123188	−	0.117206i
$73$	−7.69078	+	8.54147i	−0.900137	+	0.999704i	0.0998515	+	0.995002i	$0.468163\pi$
$73$	−7.69078	+	8.54147i	−0.900137	+	0.999704i	−0.999989	+	0.00470161i	$0.998503\pi$
$74$	−0.203413	+	0.0432367i	−0.0236463	+	0.00502617i
$75$	3.84927	−	1.71381i	0.444476	−	0.197893i
$76$	3.86714			0.443592
$77$	2.74299	+	8.33523i	0.312592	+	0.949887i
$78$	−4.68352			−0.530305
$79$	13.9917	−	6.22952i	1.57419	−	0.700875i	0.580630	−	0.814167i	$-0.302806\pi$
$79$	13.9917	−	6.22952i	1.57419	−	0.700875i	0.993562	+	0.113292i	$0.0361395\pi$
$80$	0.867438	−	0.184380i	0.0969825	−	0.0206143i
$81$	0.669131	−	0.743145i	0.0743478	−	0.0825716i
$82$	0.580160	+	5.51985i	0.0640679	+	0.609566i
$83$	−13.5913	+	9.87464i	−1.49184	+	1.08388i	−0.518342	+	0.855174i	$0.673450\pi$
$83$	−13.5913	+	9.87464i	−1.49184	+	1.08388i	−0.973495	+	0.228709i	$0.926550\pi$
$84$	2.58554	−	0.561220i	0.282106	−	0.0612342i
$85$	0.907380	−	2.79263i	0.0984192	−	0.302903i
$86$	−5.83297	+	2.59700i	−0.628985	+	0.280042i
$87$	−3.32904	−	5.76606i	−0.356910	−	0.618187i
$88$	2.22060	−	2.46353i	0.236716	−	0.262613i
$89$	−5.12492	+	8.87662i	−0.543240	+	0.940920i	0.455475	+	0.890249i	$0.349469\pi$
$89$	−5.12492	+	8.87662i	−0.543240	+	0.940920i	−0.998715	+	0.0506715i	$0.983864\pi$
$90$	0.717450	+	0.521258i	0.0756259	+	0.0549454i
$91$	−1.34831	−	12.3179i	−0.141341	−	1.29126i
$92$	1.81173	+	5.57593i	0.188886	+	0.581331i
$93$	−1.02698	−	9.77111i	−0.106493	−	1.01322i
$94$	−10.1696	−	4.52781i	−1.04892	−	0.467008i
$95$	−2.29475	+	2.54858i	−0.235436	+	0.261479i
$96$	−0.669131	−	0.743145i	−0.0682929	−	0.0758469i
$97$	−2.58883	−	1.88089i	−0.262856	−	0.190976i	0.448549	−	0.893758i	$-0.351941\pi$
$97$	−2.58883	−	1.88089i	−0.262856	−	0.190976i	−0.711405	+	0.702782i	$0.751941\pi$
$98$	2.22037	+	6.63852i	0.224291	+	0.670592i
$99$	3.31662	+	0.00180404i	0.333333	+	0.000181313i
$100$	2.10678	−	3.64905i	0.210678	−	0.364905i
$101$	0.214554	−	2.04135i	0.0213490	−	0.203122i	−0.978648	−	0.205543i	$-0.934104\pi$
$101$	0.214554	−	2.04135i	0.0213490	−	0.203122i	0.999997	+	0.00242105i	$0.000770646\pi$
$102$	−3.23875	+	0.688417i	−0.320684	+	0.0681634i
$103$	10.7018	+	2.27473i	1.05448	+	0.224136i	0.702362	−	0.711820i	$-0.252129\pi$
$103$	10.7018	+	2.27473i	1.05448	+	0.224136i	0.352116	+	0.935956i	$0.385462\pi$
$104$	−3.78905	+	2.75291i	−0.371547	+	0.269945i
$105$	−1.16439	+	2.03699i	−0.113633	+	0.198789i
$106$	3.66151	+	11.2690i	0.355637	+	1.09454i
$107$	−2.28018	−	2.53240i	−0.220433	−	0.244816i	0.622778	−	0.782399i	$-0.286004\pi$
$107$	−2.28018	−	2.53240i	−0.220433	−	0.244816i	−0.843211	+	0.537583i	$0.819337\pi$
$108$	0.104528	−	0.994522i	0.0100583	−	0.0956979i
$109$	1.99726	+	3.45935i	0.191303	+	0.331346i	0.945682	−	0.325093i	$-0.105396\pi$
$109$	1.99726	+	3.45935i	0.191303	+	0.331346i	−0.754380	+	0.656438i	$0.772062\pi$
$110$	0.305852	+	2.92529i	0.0291619	+	0.278916i
$111$	−0.207957			−0.0197384
$112$	1.76187	−	1.97378i	0.166481	−	0.186505i
$113$	2.19366	−	6.75141i	0.206363	−	0.635119i	−0.793292	−	0.608841i	$-0.791635\pi$
$113$	2.19366	−	6.75141i	0.206363	−	0.635119i	0.999655	−	0.0262776i	$-0.00836537\pi$
$114$	3.78264	+	0.804024i	0.354276	+	0.0753038i
$115$	−4.74980	−	2.11475i	−0.442921	−	0.197201i
$116$	−6.08245	−	2.70808i	−0.564741	−	0.251439i
$117$	−4.58118	−	0.973759i	−0.423530	−	0.0900241i
$118$	0.649986	−	2.00045i	0.0598360	−	0.184156i
$119$	−2.74295	−	8.31986i	−0.251445	−	0.762680i
$120$	0.886817			0.0809550
$121$	7.35154	+	8.18260i	0.668322	+	0.743872i
$122$	−4.74893	−	8.22538i	−0.429948	−	0.744691i
$123$	−0.580160	+	5.51985i	−0.0523112	+	0.497708i
$124$	−6.57416	−	7.30135i	−0.590377	−	0.655680i
$125$	2.52490	+	7.77084i	0.225834	+	0.695045i
$126$	2.64573	−	0.0113917i	0.235700	−	0.00101486i
$127$	6.91701	−	5.02550i	0.613785	−	0.445941i	−0.236960	−	0.971519i	$-0.576151\pi$
$127$	6.91701	−	5.02550i	0.613785	−	0.445941i	0.850745	+	0.525578i	$0.176151\pi$
$128$	−0.978148	−	0.207912i	−0.0864569	−	0.0183770i
$129$	−6.24545	+	1.32751i	−0.549881	+	0.116881i
$130$	0.434152	−	4.13068i	0.0380776	−	0.362284i
$131$	−6.51819	+	11.2898i	−0.569497	+	0.986398i	0.427119	+	0.904196i	$0.359529\pi$
$131$	−6.51819	+	11.2898i	−0.569497	+	0.986398i	−0.996616	+	0.0822023i	$0.973805\pi$
$132$	2.68427	−	1.94800i	0.233635	−	0.169552i
$133$	−1.02566	+	10.1800i	−0.0889361	+	0.882715i
$134$	1.26973	+	0.922513i	0.109688	+	0.0796930i
$135$	0.593397	+	0.659034i	0.0510714	+	0.0567206i
$136$	−2.21556	+	2.46063i	−0.189983	+	0.210997i
$137$	7.21762	+	3.21349i	0.616643	+	0.274547i	0.691193	−	0.722670i	$-0.257085\pi$
$137$	7.21762	+	3.21349i	0.616643	+	0.274547i	−0.0745502	+	0.997217i	$0.523752\pi$
$138$	0.612837	+	5.83076i	0.0521682	+	0.496347i
$139$	−2.95946	−	9.10829i	−0.251018	−	0.772555i	−0.994588	−	0.103897i	$-0.966869\pi$
$139$	−2.95946	−	9.10829i	−0.251018	−	0.772555i	0.743570	−	0.668658i	$-0.233131\pi$
$140$	0.255300	+	2.33237i	0.0215768	+	0.197121i
$141$	−9.00602	−	6.54326i	−0.758444	−	0.551042i
$142$	−2.28075	+	3.95037i	−0.191396	+	0.331508i
$143$	−7.75943	−	13.4566i	−0.648876	−	1.12530i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	5.39402	−	2.40157i	0.447949	−	0.199440i
$146$	−3.55174	+	10.9311i	−0.293944	+	0.904668i
$147$	0.791621	+	6.95509i	0.0652918	+	0.573647i
$148$	−0.168241	+	0.122234i	−0.0138293	+	0.0100476i
$149$	−2.06548	−	19.6517i	−0.169211	−	1.60993i	−0.668646	−	0.743581i	$-0.733126\pi$
$149$	−2.06548	−	19.6517i	−0.169211	−	1.60993i	0.499436	−	0.866351i	$-0.333541\pi$
$150$	2.81942	−	3.13128i	0.230205	−	0.255668i
$151$	−16.4875	+	3.50453i	−1.34173	+	0.285194i	−0.822172	−	0.569239i	$-0.807238\pi$
$151$	−16.4875	+	3.50453i	−1.34173	+	0.285194i	−0.519562	+	0.854433i	$0.673905\pi$
$152$	3.53281	−	1.57291i	0.286549	−	0.127580i
$153$	−3.31110			−0.267687
$154$	5.89609	+	6.49894i	0.475120	+	0.523699i
$155$	8.71292			0.699838
$156$	−4.27861	+	1.90496i	−0.342563	+	0.152519i
$157$	8.46503	−	1.79930i	0.675583	−	0.143600i	0.142671	−	0.989770i	$-0.454431\pi$
$157$	8.46503	−	1.79930i	0.675583	−	0.143600i	0.532912	+	0.846171i	$0.321098\pi$
$158$	10.2483	−	11.3819i	0.815311	−	0.905495i
$159$	1.23855	+	11.7840i	0.0982231	+	0.934530i
$160$	0.717450	−	0.521258i	0.0567194	−	0.0412091i
$161$	−15.1587	+	3.29037i	−1.19467	+	0.259317i
$162$	0.309017	−	0.951057i	0.0242787	−	0.0747221i
$163$	15.1914	−	6.76367i	1.18989	−	0.529771i	0.286284	−	0.958145i	$-0.407580\pi$
$163$	15.1914	−	6.76367i	1.18989	−	0.529771i	0.903602	+	0.428374i	$0.140913\pi$
$164$	2.77513	+	4.80666i	0.216701	+	0.375337i
$165$	−0.309034	+	2.92496i	−0.0240583	+	0.227708i
$166$	−8.39987	+	14.5490i	−0.651956	+	1.12922i
$167$	−0.958932	−	0.696705i	−0.0742044	−	0.0539126i	0.550065	−	0.835122i	$-0.314603\pi$
$167$	−0.958932	−	0.696705i	−0.0742044	−	0.0539126i	−0.624269	+	0.781209i	$0.714603\pi$
$168$	2.13374	−	1.56434i	0.164622	−	0.120691i
$169$	2.76119	+	8.49806i	0.212399	+	0.653697i
$170$	−0.306931	−	2.92026i	−0.0235406	−	0.223974i
$171$	3.53281	+	1.57291i	0.270161	+	0.120283i
$172$	−4.27238	+	4.74496i	−0.325766	+	0.361800i
$173$	−5.56110	−	6.17622i	−0.422802	−	0.469569i	0.493681	−	0.869643i	$-0.335651\pi$
$173$	−5.56110	−	6.17622i	−0.422802	−	0.469569i	−0.916483	+	0.400074i	$0.868984\pi$
$174$	−5.38649	−	3.91352i	−0.408349	−	0.296683i
$175$	9.04707	+	6.51375i	0.683894	+	0.492393i
$176$	1.02661	−	3.15374i	0.0773836	−	0.237722i
$177$	1.05170	−	1.82160i	0.0790505	−	0.136920i
$178$	−1.07140	+	10.1937i	−0.0803048	+	0.764049i
$179$	11.5236	−	2.44943i	0.861318	−	0.183079i	0.243983	−	0.969779i	$-0.421546\pi$
$179$	11.5236	−	2.44943i	0.861318	−	0.183079i	0.617334	+	0.786701i	$0.288213\pi$
$180$	0.867438	+	0.184380i	0.0646550	+	0.0137429i
$181$	−4.76867	+	3.46464i	−0.354452	+	0.257525i	−0.750734	−	0.660604i	$-0.770300\pi$
$181$	−4.76867	+	3.46464i	−0.354452	+	0.257525i	0.396282	+	0.918129i	$0.370300\pi$
$182$	−6.24187	−	10.7045i	−0.462678	−	0.793472i
$183$	−2.93500	−	9.03300i	−0.216961	−	0.667738i
$184$	3.92303	+	4.35697i	0.289210	+	0.321200i
$185$	0.0192771	−	0.183410i	0.00141728	−	0.0134846i
$186$	−4.91246	−	8.50864i	−0.360199	−	0.623884i
$187$	−7.34374	−	8.16498i	−0.537028	−	0.597082i
$188$	−11.1321			−0.811888
$189$	2.59028	+	0.538935i	0.188415	+	0.0392017i
$190$	−1.05976	+	3.26160i	−0.0768830	+	0.236621i
$191$	23.6211	+	5.02081i	1.70916	+	0.363293i	0.955732	−	0.294238i	$-0.0950657\pi$
$191$	23.6211	+	5.02081i	1.70916	+	0.363293i	0.753428	+	0.657531i	$0.228399\pi$
$192$	−0.913545	−	0.406737i	−0.0659295	−	0.0293537i
$193$	11.9409	+	5.31642i	0.859524	+	0.382685i	0.788681	−	0.614803i	$-0.210764\pi$
$193$	11.9409	+	5.31642i	0.859524	+	0.382685i	0.0708429	+	0.997487i	$0.477431\pi$
$194$	−3.13004	−	0.665310i	−0.224724	−	0.0477665i
$195$	1.28348	−	3.95015i	0.0919119	−	0.282876i
$196$	4.72854	+	5.16149i	0.337753	+	0.368678i
$197$	−3.54632			−0.252665			−0.126332	−	0.991988i	$-0.540321\pi$
$197$	−3.54632			−0.252665			−0.126332	+	0.991988i	$0.540321\pi$
$198$	3.03062	−	1.34734i	0.215377	−	0.0957516i
$199$	1.36352	+	2.36169i	0.0966573	+	0.167415i	0.910299	−	0.413951i	$-0.135852\pi$
$199$	1.36352	+	2.36169i	0.0966573	+	0.167415i	−0.813642	+	0.581367i	$0.802518\pi$
$200$	0.440436	−	4.19047i	0.0311436	−	0.296311i
$201$	1.05018	+	1.16635i	0.0740741	+	0.0822677i
$202$	−0.634286	−	1.95213i	−0.0446282	−	0.137352i
$203$	8.74203	−	15.2933i	0.613571	−	1.07338i
$204$	−2.67874	+	1.94622i	−0.187549	+	0.136262i
$205$	−4.81450	−	1.02335i	−0.336260	−	0.0714742i
$206$	10.7018	−	2.27473i	0.745628	−	0.158488i
$207$	−0.612837	+	5.83076i	−0.0425951	+	0.405266i
$208$	−2.34176	+	4.05605i	−0.162372	+	0.281236i
$209$	3.95677	+	12.2003i	0.273696	+	0.843911i
$210$	−0.235206	+	2.33448i	−0.0162307	+	0.161094i
$211$	−18.9851	−	13.7935i	−1.30699	−	0.949583i	−0.306991	−	0.951713i	$-0.599322\pi$
$211$	−18.9851	−	13.7935i	−1.30699	−	0.949583i	−0.999998	+	0.00212990i	$0.999322\pi$
$212$	7.92846	+	8.80544i	0.544529	+	0.604760i
$213$	−3.05224	+	3.38985i	−0.209136	+	0.232269i
$214$	−3.11307	−	1.38603i	−0.212805	−	0.0947468i
$215$	−0.591872	−	5.63129i	−0.0403654	−	0.384051i
$216$	−0.309017	−	0.951057i	−0.0210259	−	0.0647112i
$217$	20.9639	−	15.3695i	1.42312	−	1.04335i
$218$	3.23163	+	2.34792i	0.218874	+	0.159021i
$219$	−5.74684	+	9.95383i	−0.388336	+	0.672617i
$220$	1.46923	+	2.54799i	0.0990558	+	0.171785i
$221$	7.75381	+	13.4300i	0.521578	+	0.903399i
$222$	−0.189978	+	0.0845838i	−0.0127505	+	0.00567690i
$223$	9.11850	−	28.0638i	0.610620	−	1.87929i	0.158436	−	0.987369i	$-0.449355\pi$
$223$	9.11850	−	28.0638i	0.610620	−	1.87929i	0.452184	−	0.891925i	$-0.350645\pi$
$224$	0.806740	−	2.51976i	0.0539026	−	0.168358i
$225$	3.40884	−	2.47667i	0.227256	−	0.165111i
$226$	−0.742032	−	7.05996i	−0.0493592	−	0.469622i
$227$	10.9923	−	12.2082i	0.729585	−	0.810286i	−0.258203	−	0.966091i	$-0.583130\pi$
$227$	10.9923	−	12.2082i	0.729585	−	0.810286i	0.987788	+	0.155804i	$0.0497970\pi$
$228$	3.78264	−	0.804024i	0.250511	−	0.0532478i
$229$	11.3084	−	5.03484i	0.747282	−	0.332711i	0.00247991	−	0.999997i	$-0.499211\pi$
$229$	11.3084	−	5.03484i	0.747282	−	0.332711i	0.744802	+	0.667286i	$0.232544\pi$
$230$	−5.19930			−0.342832
$231$	4.41604	+	7.58278i	0.290554	+	0.498911i
$232$	−6.65807			−0.437124
$233$	−9.25351	+	4.11993i	−0.606217	+	0.269905i	−0.686804	−	0.726842i	$-0.740987\pi$
$233$	−9.25351	+	4.11993i	−0.606217	+	0.269905i	0.0805872	+	0.996748i	$0.474320\pi$
$234$	−4.58118	+	0.973759i	−0.299481	+	0.0636566i
$235$	6.60572	−	7.33640i	0.430910	−	0.478574i
$236$	−0.219865	−	2.09188i	−0.0143120	−	0.136170i
$237$	12.3908	−	9.00243i	0.804868	−	0.584771i
$238$	−5.88980	−	6.48491i	−0.381779	−	0.420354i
$239$	0.395305	−	1.21662i	0.0255701	−	0.0786968i	−0.937457	−	0.348101i	$-0.886827\pi$
$239$	0.395305	−	1.21662i	0.0255701	−	0.0786968i	0.963027	+	0.269404i	$0.0868267\pi$
$240$	0.810148	−	0.360701i	0.0522948	−	0.0232832i
$241$	6.63535	+	11.4928i	0.427420	+	0.740314i	0.996643	−	0.0818696i	$-0.0260891\pi$
$241$	6.63535	+	11.4928i	0.427420	+	0.740314i	−0.569223	+	0.822183i	$0.692756\pi$
$242$	10.0441	+	4.48503i	0.645661	+	0.288309i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−7.68393	−	5.58270i	−0.491913	−	0.357396i
$245$	−6.20749	+	0.0534562i	−0.396582	+	0.00341519i
$246$	1.71512	+	5.27861i	0.109352	+	0.336552i
$247$	−1.89320	−	18.0126i	−0.120462	−	1.14612i
$248$	−8.97552	−	3.99616i	−0.569946	−	0.253756i
$249$	−11.2412	+	12.4846i	−0.712383	+	0.791182i
$250$	5.46729	+	6.07204i	0.345782	+	0.384030i
$251$	4.08757	+	2.96979i	0.258005	+	0.187452i	0.709267	−	0.704940i	$-0.249026\pi$
$251$	4.08757	+	2.96979i	0.258005	+	0.187452i	−0.451262	+	0.892391i	$0.649026\pi$
$252$	2.41236	−	1.08652i	0.151964	−	0.0684444i
$253$	−15.7375	+	11.4209i	−0.989409	+	0.718026i
$254$	4.27495	−	7.40443i	0.268234	−	0.464595i
$255$	0.306931	−	2.92026i	0.0192208	−	0.182874i
$256$	−0.978148	+	0.207912i	−0.0611342	+	0.0129945i
$257$	17.1272	+	3.64051i	1.06837	+	0.227089i	0.708353	−	0.705858i	$-0.249438\pi$
$257$	17.1272	+	3.64051i	1.06837	+	0.227089i	0.360015	+	0.932947i	$0.382772\pi$
$258$	−5.16555	+	3.75299i	−0.321593	+	0.233651i
$259$	−0.277151	−	0.475301i	−0.0172213	−	0.0295338i
$260$	−1.28348	−	3.95015i	−0.0795981	−	0.244978i
$261$	−4.45512	−	4.94791i	−0.275765	−	0.306268i
$262$	−1.36267	+	12.9650i	−0.0841862	+	0.800979i
$263$	4.15053	+	7.18893i	0.255933	+	0.443288i	0.965148	−	0.261703i	$-0.0842842\pi$
$263$	4.15053	+	7.18893i	0.255933	+	0.443288i	−0.709216	+	0.704991i	$0.750951\pi$
$264$	1.65987	−	2.87138i	0.102158	−	0.176721i
$265$	−10.5078			−0.645489
$266$	3.20358	+	9.71703i	0.196424	+	0.595789i
$267$	−3.16737	+	9.74818i	−0.193840	+	0.596579i
$268$	1.53518	+	0.326312i	0.0937758	+	0.0199327i
$269$	6.34277	+	2.82398i	0.386725	+	0.172181i	0.590884	−	0.806757i	$-0.298779\pi$
$269$	6.34277	+	2.82398i	0.386725	+	0.172181i	−0.204159	+	0.978938i	$0.565446\pi$
$270$	0.810148	+	0.360701i	0.0493040	+	0.0219516i
$271$	5.11728	+	1.08771i	0.310852	+	0.0660737i	0.360696	−	0.932683i	$-0.382539\pi$
$271$	5.11728	+	1.08771i	0.310852	+	0.0660737i	−0.0498439	+	0.998757i	$0.515872\pi$
$272$	−1.02319	+	3.14905i	−0.0620398	+	0.190939i
$273$	−3.87987	−	11.7684i	−0.234821	−	0.712254i
$274$	7.90067			0.477297
$275$	13.6678	+	2.91296i	0.824200	+	0.175658i
$276$	2.93144	+	5.07740i	0.176452	+	0.305624i
$277$	−2.55531	+	24.3122i	−0.153534	+	1.46078i	0.598219	+	0.801333i	$0.295875\pi$
$277$	−2.55531	+	24.3122i	−0.153534	+	1.46078i	−0.751753	+	0.659445i	$0.770791\pi$
$278$	−6.40828	−	7.11711i	−0.384343	−	0.426856i
$279$	−3.03607	−	9.34406i	−0.181765	−	0.559414i
$280$	1.18189	+	2.02688i	0.0706313	+	0.121129i
$281$	2.28490	−	1.66008i	0.136306	−	0.0990319i	−0.517543	−	0.855657i	$-0.673153\pi$
$281$	2.28490	−	1.66008i	0.136306	−	0.0990319i	0.653849	+	0.756625i	$0.273153\pi$
$282$	−10.8888	−	2.31448i	−0.648418	−	0.137826i
$283$	4.68816	−	0.996500i	0.278682	−	0.0592358i	−0.0664501	−	0.997790i	$-0.521167\pi$
$283$	4.68816	−	0.996500i	0.278682	−	0.0592358i	0.345132	+	0.938554i	$0.387834\pi$
$284$	−0.476806	+	4.53651i	−0.0282932	+	0.269192i
$285$	−1.71473	+	2.96999i	−0.101572	+	0.175927i
$286$	−12.5619	−	9.13719i	−0.742800	−	0.540293i
$287$	−13.3892	+	6.03047i	−0.790340	+	0.355967i
$288$	−0.809017	−	0.587785i	−0.0476718	−	0.0346356i
$289$	−4.03927	−	4.48607i	−0.237604	−	0.263886i
$290$	3.95088	−	4.38789i	0.232004	−	0.257666i
$291$	−2.92331	−	1.30154i	−0.171368	−	0.0762978i
$292$	1.20142	+	11.4307i	0.0703076	+	0.668933i
$293$	−1.69435	−	5.21468i	−0.0989851	−	0.304645i	0.889287	−	0.457350i	$-0.151201\pi$
$293$	−1.69435	−	5.21468i	−0.0989851	−	0.304645i	−0.988272	+	0.152705i	$0.951201\pi$
$294$	3.55207	+	6.03181i	0.207161	+	0.351783i
$295$	1.50908	+	1.09641i	0.0878622	+	0.0638357i
$296$	−0.103979	+	0.180096i	−0.00604364	+	0.0104679i
$297$	3.24452	−	0.687800i	0.188266	−	0.0399102i
$298$	−9.87998	−	17.1126i	−0.572332	−	0.991308i
$299$	25.0850	−	11.1685i	1.45070	−	0.645894i
$300$	1.30206	−	4.00733i	0.0751745	−	0.231363i
$301$	−11.3576	−	12.5052i	−0.654642	−	0.720788i
$302$	−13.6367	+	9.90762i	−0.784702	+	0.570119i
$303$	−0.214554	−	2.04135i	−0.0123258	−	0.117272i
$304$	2.58762	−	2.87385i	0.148410	−	0.164826i
$305$	8.23880	−	1.75121i	0.471752	−	0.100274i
$306$	−3.02484	+	1.34675i	−0.172919	+	0.0769884i
$307$	3.12569			0.178393			0.0891964	−	0.996014i	$-0.471570\pi$
$307$	3.12569			0.178393			0.0891964	+	0.996014i	$0.471570\pi$
$308$	8.02970	+	3.53892i	0.457535	+	0.201649i
$309$	10.9409			0.622404
$310$	7.95965	−	3.54386i	0.452078	−	0.201278i
$311$	10.1789	−	2.16359i	0.577191	−	0.122686i	0.0899392	−	0.995947i	$-0.471333\pi$
$311$	10.1789	−	2.16359i	0.577191	−	0.122686i	0.487252	+	0.873262i	$0.337999\pi$
$312$	−3.13389	+	3.48054i	−0.177422	+	0.197047i
$313$	2.38652	+	22.7062i	0.134894	+	1.28343i	0.827233	+	0.561859i	$0.189914\pi$
$313$	2.38652	+	22.7062i	0.134894	+	1.28343i	−0.692339	+	0.721572i	$0.743420\pi$
$314$	7.00135	−	5.08678i	0.395109	−	0.287064i
$315$	−0.715431	+	2.23456i	−0.0403100	+	0.125903i
$316$	4.73286	−	14.5662i	0.266244	−	0.819415i
$317$	24.6348	−	10.9681i	1.38363	−	0.616032i	0.426182	−	0.904637i	$-0.359858\pi$
$317$	24.6348	−	10.9681i	1.38363	−	0.616032i	0.957448	+	0.288605i	$0.0931915\pi$
$318$	5.92445	+	10.2614i	0.332226	+	0.575433i
$319$	2.32018	−	21.9601i	0.129905	−	1.22953i
$320$	0.443409	−	0.768006i	0.0247873	−	0.0429329i
$321$	−2.75687	−	2.00298i	−0.153873	−	0.111795i
$322$	−12.5099	+	9.17150i	−0.697148	+	0.511108i
$323$	−3.95681	−	12.1778i	−0.220163	−	0.677592i
$324$	−0.104528	−	0.994522i	−0.00580714	−	0.0552512i
$325$	−18.0282	−	8.02666i	−1.00002	−	0.445239i
$326$	11.1270	−	12.3578i	0.616270	−	0.684437i
$327$	2.67285	+	2.96850i	0.147809	+	0.164159i
$328$	4.49025	+	3.26236i	0.247933	+	0.180134i
$329$	2.95249	−	29.3043i	0.162776	−	1.61560i
$330$	0.907372	+	2.79778i	0.0499492	+	0.154013i
$331$	−10.5986	+	18.3573i	−0.582552	+	1.00901i	0.412623	+	0.910902i	$0.364613\pi$
$331$	−10.5986	+	18.3573i	−0.582552	+	1.00901i	−0.995176	+	0.0981085i	$0.968721\pi$
$332$	−1.75605	+	16.7077i	−0.0963758	+	0.916955i
$333$	−0.203413	+	0.0432367i	−0.0111470	+	0.00236936i
$334$	−1.15940	−	0.246439i	−0.0634397	−	0.0134845i
$335$	−1.12602	+	0.818100i	−0.0615210	+	0.0446976i
$336$	1.31300	−	2.29696i	0.0716299	−	0.125310i
$337$	9.15405	+	28.1733i	0.498653	+	1.53470i	0.811185	+	0.584789i	$0.198823\pi$
$337$	9.15405	+	28.1733i	0.498653	+	1.53470i	−0.312532	+	0.949907i	$0.601177\pi$
$338$	5.97894	+	6.64029i	0.325212	+	0.361184i
$339$	0.742032	−	7.05996i	0.0403016	−	0.383444i
$340$	−1.46817	−	2.54295i	−0.0796228	−	0.137911i
$341$	16.3082	−	28.2111i	0.883136	−	1.52772i
$342$	3.86714			0.209111
$343$	−14.8413	+	11.0786i	−0.801357	+	0.598186i
$344$	−1.97307	+	6.07247i	−0.106381	+	0.327406i
$345$	−5.08568	−	1.08100i	−0.273804	−	0.0581988i
$346$	−7.59241	−	3.38036i	−0.408170	−	0.181729i
$347$	0.313829	+	0.139726i	0.0168472	+	0.00750087i	0.415143	−	0.909756i	$-0.363732\pi$
$347$	0.313829	+	0.139726i	0.0168472	+	0.00750087i	−0.398296	+	0.917257i	$0.630398\pi$
$348$	−6.51258	−	1.38429i	−0.349111	−	0.0742058i
$349$	−4.98126	+	15.3307i	−0.266641	+	0.820635i	0.724670	+	0.689096i	$0.241992\pi$
$349$	−4.98126	+	15.3307i	−0.266641	+	0.820635i	−0.991311	+	0.131540i	$0.958008\pi$
$350$	10.9143	+	2.27083i	0.583393	+	0.121381i
$351$	−4.68352			−0.249988
$352$	−0.344887	−	3.29864i	−0.0183826	−	0.175818i
$353$	7.96645	+	13.7983i	0.424012	+	0.734410i	0.996328	−	0.0856236i	$-0.0272882\pi$
$353$	7.96645	+	13.7983i	0.424012	+	0.734410i	−0.572316	+	0.820033i	$0.693955\pi$
$354$	0.219865	−	2.09188i	0.0116857	−	0.111182i
$355$	−2.70678	−	3.00618i	−0.143661	−	0.159551i
$356$	3.16737	+	9.74818i	0.167871	+	0.516652i
$357$	−4.41280	−	7.56776i	−0.233550	−	0.400528i
$358$	9.53110	−	6.92475i	0.503734	−	0.365984i
$359$	−2.12218	−	0.451084i	−0.112005	−	0.0238073i	0.151568	−	0.988447i	$-0.451568\pi$
$359$	−2.12218	−	0.451084i	−0.112005	−	0.0238073i	−0.263573	+	0.964639i	$0.584901\pi$
$360$	0.867438	−	0.184380i	0.0457180	−	0.00971766i
$361$	0.422838	−	4.02304i	0.0222546	−	0.211739i
$362$	−2.94720	+	5.10470i	−0.154901	+	0.268297i
$363$	8.89215	+	6.47532i	0.466717	+	0.339866i
$364$	−10.0562	−	7.24027i	−0.527086	−	0.379493i
$365$	−8.24615	−	5.99118i	−0.431623	−	0.313593i
$366$	−6.35530	−	7.05828i	−0.332197	−	0.368942i
$367$	−3.35229	+	3.72309i	−0.174988	+	0.194344i	−0.824258	−	0.566214i	$-0.808408\pi$
$367$	−3.35229	+	3.72309i	−0.174988	+	0.194344i	0.649270	+	0.760558i	$0.275074\pi$
$368$	5.35600	+	2.38465i	0.279201	+	0.124308i
$369$	0.580160	+	5.51985i	0.0302019	+	0.287352i
$370$	−0.0569889	−	0.175394i	−0.00296271	−	0.00911830i
$371$	−25.2825	+	18.5356i	−1.31260	+	0.962322i
$372$	−7.94854	−	5.77495i	−0.412112	−	0.299417i
$373$	−2.12278	+	3.67676i	−0.109913	+	0.190375i	−0.915735	−	0.401783i	$-0.868391\pi$
$373$	−2.12278	+	3.67676i	−0.109913	+	0.190375i	0.805822	+	0.592158i	$0.201724\pi$
$374$	−10.0298	−	4.47211i	−0.518631	−	0.231247i
$375$	4.08537	+	7.07607i	0.210968	+	0.365407i
$376$	−10.1696	+	4.52781i	−0.524459	+	0.233504i
$377$	−9.63615	+	29.6570i	−0.496287	+	1.52741i
$378$	2.58554	−	0.561220i	0.132986	−	0.0288661i
$379$	−23.9822	+	17.4241i	−1.23188	+	0.895015i	−0.997030	−	0.0770166i	$-0.975461\pi$
$379$	−23.9822	+	17.4241i	−1.23188	+	0.895015i	−0.234852	+	0.972031i	$0.575461\pi$
$380$	0.358475	+	3.41066i	0.0183894	+	0.174963i
$381$	5.72100	−	6.35381i	0.293096	−	0.325516i
$382$	23.6211	−	5.02081i	1.20856	−	0.256887i
$383$	−26.3259	+	11.7210i	−1.34519	+	0.598916i	−0.947839	−	0.318751i	$-0.896737\pi$
$383$	−26.3259	+	11.7210i	−1.34519	+	0.598916i	−0.397350	+	0.917667i	$0.630070\pi$
$384$	−1.00000			−0.0510310
$385$	−7.09706	+	3.19186i	−0.361700	+	0.162672i
$386$	13.0709			0.665293
$387$	−5.83297	+	2.59700i	−0.296506	+	0.132013i
$388$	−3.13004	+	0.665310i	−0.158904	+	0.0337760i
$389$	13.0786	−	14.5252i	0.663109	−	0.736458i	−0.313947	−	0.949441i	$-0.601651\pi$
$389$	13.0786	−	14.5252i	0.663109	−	0.736458i	0.977056	+	0.212983i	$0.0683179\pi$
$390$	−0.434152	−	4.13068i	−0.0219841	−	0.209165i
$391$	15.7051	−	11.4104i	0.794242	−	0.577050i
$392$	6.41910	+	2.79198i	0.324213	+	0.141016i
$393$	−4.02846	+	12.3983i	−0.203209	+	0.625413i
$394$	−3.23972	+	1.44242i	−0.163215	+	0.0726680i
$395$	6.79118	+	11.7627i	0.341701	+	0.591844i
$396$	2.22060	−	2.46353i	0.111589	−	0.123797i
$397$	−9.24531	+	16.0133i	−0.464009	+	0.803687i	−0.999156	−	0.0410720i	$-0.986923\pi$
$397$	−9.24531	+	16.0133i	−0.464009	+	0.803687i	0.535147	+	0.844759i	$0.320256\pi$
$398$	2.20622	+	1.60291i	0.110588	+	0.0803468i
$399$	1.11329	+	10.1708i	0.0557340	+	0.509175i
$400$	−1.30206	−	4.00733i	−0.0651030	−	0.200366i
$401$	0.352902	+	3.35764i	0.0176231	+	0.167673i	0.999794	−	0.0203201i	$-0.00646853\pi$
$401$	0.352902	+	3.35764i	0.0176231	+	0.167673i	−0.982170	+	0.187993i	$0.939802\pi$
$402$	1.43378	+	0.638362i	0.0715107	+	0.0318386i
$403$	−30.7902	+	34.1960i	−1.53377	+	1.70343i
$404$	−1.37345	−	1.52537i	−0.0683319	−	0.0758902i
$405$	0.717450	+	0.521258i	0.0356504	+	0.0259015i
$406$	1.76588	−	17.5269i	0.0876393	−	0.869844i
$407$	−0.557772	−	0.405708i	−0.0276477	−	0.0201102i
$408$	−1.65555	+	2.86750i	−0.0819620	+	0.141962i
$409$	1.46692	−	13.9568i	0.0725346	−	0.690121i	−0.896474	−	0.443095i	$-0.853880\pi$
$409$	1.46692	−	13.9568i	0.0725346	−	0.690121i	0.969009	−	0.247025i	$-0.0794531\pi$
$410$	−4.81450	+	1.02335i	−0.237771	+	0.0505399i
$411$	7.72802	+	1.64264i	0.381195	+	0.0810255i
$412$	8.85134	−	6.43088i	0.436074	−	0.316827i
$413$	5.56502	−	0.0239613i	0.273837	−	0.00117906i
$414$	1.81173	+	5.57593i	0.0890416	+	0.274042i
$415$	−9.96891	−	11.0716i	−0.489355	−	0.543483i
$416$	−0.489561	+	4.65787i	−0.0240027	+	0.228371i
$417$	−4.78851	−	8.29394i	−0.234494	−	0.406156i
$418$	8.57699	+	9.53614i	0.419514	+	0.466428i
$419$	29.6993			1.45090			0.725452	−	0.688273i	$-0.241631\pi$
$419$	29.6993			1.45090			0.725452	+	0.688273i	$0.241631\pi$
$420$	0.734647	+	2.22832i	0.0358471	+	0.108731i
$421$	−5.96630	+	18.3624i	−0.290780	+	0.894928i	0.693827	+	0.720142i	$0.255923\pi$
$421$	−5.96630	+	18.3624i	−0.290780	+	0.894928i	−0.984606	+	0.174786i	$0.944077\pi$
$422$	−22.9541	−	4.87904i	−1.11739	−	0.237508i
$423$	−10.1696	−	4.52781i	−0.494465	−	0.220150i
$424$	10.8245	+	4.81938i	0.525684	+	0.234050i
$425$	−13.6466	−	2.90068i	−0.661959	−	0.140704i
$426$	−1.40958	+	4.33824i	−0.0682943	+	0.210188i
$427$	16.7340	−	18.7467i	0.809815	−	0.907215i
$428$	−3.40767			−0.164716
$429$	−10.3877	−	11.5493i	−0.501521	−	0.557605i
$430$	−2.83115	−	4.90370i	−0.136530	−	0.236478i
$431$	0.921764	−	8.77000i	0.0443998	−	0.422436i	−0.949634	−	0.313362i	$-0.898545\pi$
$431$	0.921764	−	8.77000i	0.0443998	−	0.422436i	0.994034	−	0.109074i	$-0.0347886\pi$
$432$	−0.669131	−	0.743145i	−0.0321936	−	0.0357546i
$433$	−1.39773	−	4.30178i	−0.0671708	−	0.206730i	0.911837	−	0.410552i	$-0.134664\pi$
$433$	−1.39773	−	4.30178i	−0.0671708	−	0.206730i	−0.979008	+	0.203821i	$0.934664\pi$
$434$	12.9001	−	22.5675i	0.619225	−	1.08327i
$435$	4.77684	−	3.47057i	0.229032	−	0.166401i
$436$	3.90722	+	0.830506i	0.187122	+	0.0397740i
$437$	−22.1771	+	4.71390i	−1.06088	+	0.225496i
$438$	−1.20142	+	11.4307i	−0.0574059	+	0.546181i
$439$	0.950968	−	1.64713i	0.0453872	−	0.0786130i	−0.842439	−	0.538791i	$-0.818881\pi$
$439$	0.950968	−	1.64713i	0.0453872	−	0.0786130i	0.887827	+	0.460178i	$0.152214\pi$
$440$	2.37857	+	1.73011i	0.113394	+	0.0824798i
$441$	2.22037	+	6.63852i	0.105732	+	0.316120i
$442$	12.5459	+	9.11515i	0.596749	+	0.433564i
$443$	−13.9999	−	15.5484i	−0.665154	−	0.738728i	0.312276	−	0.949992i	$-0.398909\pi$
$443$	−13.9999	−	15.5484i	−0.665154	−	0.738728i	−0.977429	+	0.211264i	$0.932242\pi$
$444$	−0.139151	+	0.154542i	−0.00660379	+	0.00733426i
$445$	−8.30389	−	3.69713i	−0.393642	−	0.175261i
$446$	−3.08443	−	29.3464i	−0.146052	−	1.38959i
$447$	−6.10617	−	18.7928i	−0.288812	−	0.888871i
$448$	−0.287883	−	2.63004i	−0.0136012	−	0.124258i
$449$	−8.61063	−	6.25599i	−0.406361	−	0.295238i	0.365766	−	0.930707i	$-0.380807\pi$
$449$	−8.61063	−	6.25599i	−0.406361	−	0.295238i	−0.772127	+	0.635468i	$0.780807\pi$
$450$	2.10678	−	3.64905i	0.0993144	−	0.172018i
$451$	−12.3249	+	13.6732i	−0.580356	+	0.643846i
$452$	−3.54942	−	6.14778i	−0.166951	−	0.289167i
$453$	−15.3986	+	6.85589i	−0.723488	+	0.322118i
$454$	5.07645	−	15.6237i	0.238250	−	0.733257i
$455$	10.7389	−	2.33099i	0.503446	−	0.109278i
$456$	3.12859	−	2.27305i	0.146509	−	0.106445i
$457$	−0.0742647	−	0.706582i	−0.00347396	−	0.0330525i	0.992648	−	0.121040i	$-0.0386230\pi$
$457$	−0.0742647	−	0.706582i	−0.00347396	−	0.0330525i	−0.996122	+	0.0879878i	$0.971956\pi$
$458$	8.28291	−	9.19910i	0.387035	−	0.429846i
$459$	−3.23875	+	0.688417i	−0.151172	+	0.0321326i
$460$	−4.74980	+	2.11475i	−0.221460	+	0.0986005i
$461$	−19.8752			−0.925681			−0.462841	−	0.886442i	$-0.653170\pi$
$461$	−19.8752			−0.925681			−0.462841	+	0.886442i	$0.653170\pi$
$462$	7.11845	+	5.13105i	0.331180	+	0.238718i
$463$	−25.7387			−1.19618			−0.598090	−	0.801429i	$-0.704073\pi$
$463$	−25.7387			−1.19618			−0.598090	+	0.801429i	$0.704073\pi$
$464$	−6.08245	+	2.70808i	−0.282371	+	0.125720i
$465$	8.52252	−	1.81152i	0.395222	−	0.0840071i
$466$	−6.77777	+	7.52748i	−0.313974	+	0.348704i
$467$	0.515619	+	4.90579i	0.0238600	+	0.227013i	0.999953	+	0.00966102i	$0.00307525\pi$
$467$	0.515619	+	4.90579i	0.0238600	+	0.227013i	−0.976093	+	0.217352i	$0.930258\pi$
$468$	−3.78905	+	2.75291i	−0.175149	+	0.127253i
$469$	−1.26616	+	3.95469i	−0.0584657	+	0.182611i
$470$	3.05065	−	9.38892i	0.140716	−	0.433079i
$471$	7.90596	−	3.51996i	0.364287	−	0.162191i
$472$	−1.05170	−	1.82160i	−0.0484084	−	0.0838458i
$473$	−19.3411	−	8.62381i	−0.889303	−	0.396523i
$474$	7.65792	−	13.2639i	0.351740	−	0.609232i
$475$	13.1825	+	9.57762i	0.604853	+	0.439451i
$476$	−8.01825	−	3.52867i	−0.367516	−	0.161736i
$477$	3.66151	+	11.2690i	0.167649	+	0.515970i
$478$	−0.133716	−	1.27222i	−0.00611604	−	0.0581902i
$479$	−0.968735	−	0.431309i	−0.0442626	−	0.0197070i	0.384486	−	0.923131i	$-0.374379\pi$
$479$	−0.968735	−	0.431309i	−0.0442626	−	0.0197070i	−0.428749	+	0.903424i	$0.641045\pi$
$480$	0.593397	−	0.659034i	0.0270847	−	0.0300806i
$481$	0.651715	+	0.723803i	0.0297156	+	0.0330026i
$482$	10.7362	+	7.80032i	0.489021	+	0.355295i
$483$	−14.1434	+	6.37014i	−0.643545	+	0.289851i
$484$	11.0000	+	0.0119667i	0.500000	+	0.000543939i
$485$	1.41889	−	2.45759i	0.0644286	−	0.111594i
$486$	0.104528	−	0.994522i	0.00474151	−	0.0451124i
$487$	−21.9911	+	4.67435i	−0.996511	+	0.211815i	−0.677171	−	0.735825i	$-0.736794\pi$
$487$	−21.9911	+	4.67435i	−0.996511	+	0.211815i	−0.319340	+	0.947640i	$0.603461\pi$
$488$	−9.29030	−	1.97471i	−0.420552	−	0.0893911i
$489$	13.4532	−	9.77434i	0.608376	−	0.442011i
$490$	−5.64908	+	2.57365i	−0.255200	+	0.116266i
$491$	0.0242648	+	0.0746795i	0.00109506	+	0.00337024i	0.951603	−	0.307331i	$-0.0994360\pi$
$491$	0.0242648	+	0.0746795i	0.00109506	+	0.00337024i	−0.950507	+	0.310702i	$0.899436\pi$
$492$	3.71385	+	4.12464i	0.167433	+	0.185953i
$493$	−2.30439	+	21.9248i	−0.103784	+	0.987443i
$494$	−9.05593	−	15.6853i	−0.407446	−	0.705716i
$495$	0.305852	+	2.92529i	0.0137470	+	0.131482i
$496$	−9.82493			−0.441152
$497$	−11.8155	−	2.45835i	−0.530000	−	0.110272i
$498$	−5.19141	+	15.9775i	−0.232632	+	0.715969i
$499$	−3.68515	−	0.783302i	−0.164970	−	0.0350654i	0.124686	−	0.992196i	$-0.460208\pi$
$499$	−3.68515	−	0.783302i	−0.164970	−	0.0350654i	−0.289656	+	0.957131i	$0.593541\pi$
$500$	7.46434	+	3.32334i	0.333816	+	0.148624i
$501$	−1.08283	−	0.482107i	−0.0483773	−	0.0215389i
$502$	4.94210	+	1.05048i	0.220577	+	0.0468850i
$503$	−10.8432	+	33.3718i	−0.483473	+	1.48798i	0.350708	+	0.936485i	$0.385941\pi$
$503$	−10.8432	+	33.3718i	−0.483473	+	1.48798i	−0.834181	+	0.551491i	$0.814059\pi$
$504$	1.76187	−	1.97378i	0.0784800	−	0.0879192i
$505$	1.82028			0.0810012
$506$	−9.73164	+	16.8345i	−0.432624	+	0.748386i
$507$	4.46770	+	7.73828i	0.198417	+	0.343669i
$508$	0.893707	−	8.50306i	0.0396519	−	0.377262i
$509$	−6.91750	−	7.68266i	−0.306613	−	0.340528i	0.570071	−	0.821596i	$-0.306916\pi$
$509$	−6.91750	−	7.68266i	−0.306613	−	0.340528i	−0.876683	+	0.481068i	$0.840249\pi$
$510$	−0.907380	−	2.79263i	−0.0401795	−	0.123660i
$511$	−30.4092	+	0.130933i	−1.34522	+	0.00579213i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	3.78264	+	0.804024i	0.167008	+	0.0354985i
$514$	17.1272	−	3.64051i	0.755450	−	0.160576i
$515$	−1.01419	+	9.64939i	−0.0446906	+	0.425203i
$516$	−3.19249	+	5.52955i	−0.140541	+	0.243425i
$517$	−11.3901	−	35.1200i	−0.500935	−	1.54458i
$518$	−0.446512	−	0.321482i	−0.0196186	−	0.0141251i
$519$	−6.72368	−	4.88504i	−0.295137	−	0.214429i
$520$	−2.77919	−	3.08660i	−0.121875	−	0.135356i
$521$	2.86441	−	3.18126i	0.125492	−	0.139373i	−0.677124	−	0.735869i	$-0.736774\pi$
$521$	2.86441	−	3.18126i	0.125492	−	0.139373i	0.802616	+	0.596496i	$0.203441\pi$
$522$	−6.08245	−	2.70808i	−0.266222	−	0.118530i
$523$	−3.60306	−	34.2808i	−0.157551	−	1.49899i	−0.732479	−	0.680790i	$-0.761637\pi$
$523$	−3.60306	−	34.2808i	−0.157551	−	1.49899i	0.574928	−	0.818204i	$-0.305030\pi$
$524$	4.02846	+	12.3983i	0.175984	+	0.541624i
$525$	10.2037	+	4.49042i	0.445324	+	0.195978i
$526$	6.71570	+	4.87924i	0.292818	+	0.212745i
$527$	−16.2657	+	28.1730i	−0.708544	+	1.22723i
$528$	0.348476	−	3.29827i	0.0151655	−	0.143539i
$529$	−5.68666	−	9.84958i	−0.247246	−	0.428243i
$530$	−9.59935	+	4.27391i	−0.416969	+	0.185647i
$531$	0.649986	−	2.00045i	0.0282070	−	0.0868122i
$532$	6.87889	+	7.57394i	0.298238	+	0.328372i
$533$	21.0302	−	15.2793i	0.910919	−	0.661821i
$534$	1.07140	+	10.1937i	0.0463640	+	0.441124i
$535$	2.02210	−	2.24577i	0.0874231	−	0.0970932i
$536$	1.53518	−	0.326312i	0.0663095	−	0.0140945i
$537$	10.7626	−	4.79180i	0.464439	−	0.206781i
$538$	6.94302			0.299335
$539$	−11.4456	+	20.1990i	−0.492997	+	0.870031i
$540$	0.886817			0.0381625
$541$	−21.8940	+	9.74785i	−0.941298	+	0.419093i	−0.819253	−	0.573432i	$-0.805612\pi$
$541$	−21.8940	+	9.74785i	−0.941298	+	0.419093i	−0.122044	+	0.992525i	$0.538945\pi$
$542$	5.11728	−	1.08771i	0.219806	−	0.0467212i
$543$	−3.94412	+	4.38039i	−0.169258	+	0.187980i
$544$	0.346104	+	3.29296i	0.0148391	+	0.141185i
$545$	−2.86587	+	2.08217i	−0.122760	+	0.0891905i
$546$	−8.33106	−	9.17285i	−0.356537	−	0.392562i
$547$	13.5206	−	41.6121i	0.578098	−	1.77920i	−0.0472809	−	0.998882i	$-0.515056\pi$
$547$	13.5206	−	41.6121i	0.578098	−	1.77920i	0.625379	−	0.780321i	$-0.284944\pi$
$548$	7.21762	−	3.21349i	0.308321	−	0.137274i
$549$	−4.74893	−	8.22538i	−0.202679	−	0.351051i
$550$	13.6710	−	2.89808i	0.582932	−	0.123575i
$551$	12.8739	−	22.2982i	0.548445	−	0.949935i
$552$	4.74317	+	3.44611i	0.201883	+	0.146676i
$553$	37.0892	+	16.3222i	1.57720	+	0.694091i
$554$	7.55426	+	23.2496i	0.320950	+	0.987782i
$555$	−0.0192771	−	0.183410i	−0.000818269	−	0.00778531i
$556$	−8.74904	−	3.89533i	−0.371042	−	0.165199i
$557$	5.22649	−	5.80460i	0.221453	−	0.245949i	−0.622173	−	0.782880i	$-0.713750\pi$
$557$	5.22649	−	5.80460i	0.221453	−	0.245949i	0.843626	+	0.536931i	$0.180416\pi$
$558$	−6.57416	−	7.30135i	−0.278306	−	0.309091i
$559$	24.1930	+	17.5772i	1.02325	+	0.743438i
$560$	1.90412	+	1.37093i	0.0804636	+	0.0579325i
$561$	−8.88086	−	6.45970i	−0.374950	−	0.272729i
$562$	1.41215	−	2.44591i	0.0595678	−	0.103174i
$563$	1.44277	−	13.7270i	0.0608054	−	0.578524i	−0.921123	−	0.389272i	$-0.872727\pi$
$563$	1.44277	−	13.7270i	0.0608054	−	0.578524i	0.981928	−	0.189253i	$-0.0606066\pi$
$564$	−10.8888	+	2.31448i	−0.458501	+	0.0974574i
$565$	6.15781	+	1.30888i	0.259061	+	0.0550651i
$566$	3.87754	−	2.81720i	0.162985	−	0.118416i
$567$	2.64573	−	0.0113917i	0.111110	−	0.000478407i
$568$	1.40958	+	4.33824i	0.0591446	+	0.182028i
$569$	15.2896	+	16.9808i	0.640973	+	0.711872i	0.972846	−	0.231452i	$-0.0743475\pi$
$569$	15.2896	+	16.9808i	0.640973	+	0.711872i	−0.331874	+	0.943324i	$0.607681\pi$
$570$	−0.358475	+	3.41066i	−0.0150149	+	0.142857i
$571$	−2.50063	−	4.33122i	−0.104648	−	0.181256i	0.808946	−	0.587883i	$-0.200038\pi$
$571$	−2.50063	−	4.33122i	−0.104648	−	0.181256i	−0.913594	+	0.406627i	$0.866705\pi$
$572$	−15.1923	−	3.23786i	−0.635221	−	0.135382i
$573$	24.1488			1.00883
$574$	−9.77884	+	10.9550i	−0.408161	+	0.457252i
$575$	−7.63382	+	23.4945i	−0.318352	+	0.979787i
$576$	−0.978148	−	0.207912i	−0.0407562	−	0.00866299i
$577$	33.2617	+	14.8091i	1.38470	+	0.616510i	0.957708	−	0.287743i	$-0.0929049\pi$
$577$	33.2617	+	14.8091i	1.38470	+	0.616510i	0.426997	+	0.904253i	$0.359572\pi$
$578$	−5.51471	−	2.45531i	−0.229382	−	0.102127i
$579$	12.7853	+	2.71760i	0.531339	+	0.112940i
$580$	1.82459	−	5.61551i	0.0757619	−	0.233171i
$581$	−43.5160	−	9.05396i	−1.80535	−	0.375622i
$582$	−3.19997			−0.132643
$583$	−19.6677	+	34.0227i	−0.814552	+	1.40907i
$584$	5.74684	+	9.95383i	0.237806	+	0.411892i
$585$	0.434152	−	4.13068i	0.0179500	−	0.170782i
$586$	−3.66887	−	4.07469i	−0.151560	−	0.168324i
$587$	−4.71211	−	14.5024i	−0.194490	−	0.598578i	−0.999982	−	0.00597171i	$-0.998099\pi$
$587$	−4.71211	−	14.5024i	−0.194490	−	0.598578i	0.805492	−	0.592606i	$-0.201901\pi$
$588$	5.69834	+	4.06558i	0.234996	+	0.167662i
$589$	30.7381	−	22.3326i	1.26654	−	0.920197i
$590$	1.82457	+	0.387824i	0.0751163	+	0.0159665i
$591$	−3.46882	+	0.737321i	−0.142688	+	0.0303293i
$592$	−0.0217375	+	0.206818i	−0.000893404	+	0.00850017i
$593$	−1.91891	+	3.32366i	−0.0788004	+	0.136486i	−0.902733	−	0.430202i	$-0.858442\pi$
$593$	−1.91891	+	3.32366i	−0.0788004	+	0.136486i	0.823932	+	0.566688i	$0.191776\pi$
$594$	2.68427	−	1.94800i	0.110137	−	0.0799275i
$595$	7.08351	−	3.19040i	0.290396	−	0.130794i
$596$	−15.9861	−	11.6146i	−0.654818	−	0.475753i
$597$	1.82475	+	2.02658i	0.0746819	+	0.0829426i
$598$	18.3736	−	20.4060i	0.751352	−	0.834461i
$599$	17.7630	+	7.90862i	0.725778	+	0.323137i	0.736159	−	0.676809i	$-0.236638\pi$
$599$	17.7630	+	7.90862i	0.725778	+	0.323137i	−0.0103806	+	0.999946i	$0.503304\pi$
$600$	−0.440436	−	4.19047i	−0.0179807	−	0.171075i
$601$	10.1730	+	31.3093i	0.414966	+	1.27713i	0.912282	+	0.409563i	$0.134319\pi$
$601$	10.1730	+	31.3093i	0.414966	+	1.27713i	−0.497316	+	0.867569i	$0.665681\pi$
$602$	−15.4620	−	6.80451i	−0.630185	−	0.277331i
$603$	1.26973	+	0.922513i	0.0517074	+	0.0375676i
$604$	−8.42792	+	14.5976i	−0.342927	+	0.593968i
$605$	−6.53525	+	7.24227i	−0.265696	+	0.294440i
$606$	−1.02630	−	1.77760i	−0.0416905	−	0.0722100i
$607$	12.7338	−	5.66946i	0.516850	−	0.230116i	−0.131699	−	0.991290i	$-0.542043\pi$
$607$	12.7338	−	5.66946i	0.516850	−	0.230116i	0.648548	+	0.761173i	$0.275376\pi$
$608$	1.19501	−	3.67787i	0.0484642	−	0.149157i
$609$	5.37134	−	16.7767i	0.217658	−	0.679827i
$610$	6.81424	−	4.95083i	0.275900	−	0.200453i
$611$	5.44983	+	51.8516i	0.220476	+	2.09769i
$612$	−2.21556	+	2.46063i	−0.0895587	+	0.0994650i
$613$	−39.6628	+	8.43058i	−1.60196	+	0.340508i	−0.920317	−	0.391173i	$-0.872069\pi$
$613$	−39.6628	+	8.43058i	−1.60196	+	0.340508i	−0.681647	+	0.731681i	$0.738736\pi$
$614$	2.85546	−	1.27133i	0.115237	−	0.0513069i
$615$	−4.92206			−0.198477
$616$	8.77490	−	0.0330091i	0.353551	−	0.00132997i
$617$	−18.2266			−0.733774			−0.366887	−	0.930266i	$-0.619576\pi$
$617$	−18.2266			−0.733774			−0.366887	+	0.930266i	$0.619576\pi$
$618$	9.99497	−	4.45005i	0.402057	−	0.179007i
$619$	3.74982	−	0.797049i	0.150718	−	0.0320361i	−0.131935	−	0.991258i	$-0.542119\pi$
$619$	3.74982	−	0.797049i	0.150718	−	0.0320361i	0.282653	+	0.959222i	$0.408786\pi$
$620$	5.83008	−	6.47496i	0.234142	−	0.260041i
$621$	0.612837	+	5.83076i	0.0245923	+	0.233980i
$622$	8.41885	−	6.11665i	0.337565	−	0.245256i
$623$	−26.5014	+	5.75242i	−1.06176	+	0.230466i
$624$	−1.44729	+	4.45430i	−0.0579379	+	0.178315i
$625$	12.6269	−	5.62184i	0.505074	−	0.224874i
$626$	11.4156	+	19.7725i	0.456261	+	0.790267i
$627$	6.40689	+	11.1110i	0.255867	+	0.443731i
$628$	4.32707	−	7.49471i	0.172669	−	0.299072i
$629$	0.557063	+	0.404730i	0.0222116	+	0.0161376i
$630$	0.255300	+	2.33237i	0.0101714	+	0.0929237i
$631$	12.6954	+	39.0724i	0.505395	+	1.55545i	0.800105	+	0.599859i	$0.204777\pi$
$631$	12.6954	+	39.0724i	0.505395	+	1.55545i	−0.294710	+	0.955587i	$0.595223\pi$
$632$	−1.60094	−	15.2319i	−0.0636821	−	0.605894i
$633$	−21.4381	−	9.54484i	−0.852086	−	0.379373i
$634$	18.0439	−	20.0398i	0.716615	−	0.795882i
$635$	5.07348	+	5.63467i	0.201335	+	0.223605i
$636$	9.58595	+	6.96460i	0.380108	+	0.276164i
$637$	21.7266	−	24.5518i	0.860839	−	0.972776i
$638$	−6.81239	−	21.0053i	−0.269705	−	0.831606i
$639$	−2.28075	+	3.95037i	−0.0902250	+	0.156274i
$640$	0.0926977	−	0.881959i	0.00366420	−	0.0348625i
$641$	40.4554	−	8.59907i	1.59789	−	0.339643i	0.678997	−	0.734141i	$-0.262415\pi$
$641$	40.4554	−	8.59907i	1.59789	−	0.339643i	0.918897	+	0.394499i	$0.129082\pi$
$642$	−3.33321	−	0.708495i	−0.131551	−	0.0279621i
$643$	−5.13239	+	3.72890i	−0.202402	+	0.147053i	−0.684369	−	0.729136i	$-0.739922\pi$
$643$	−5.13239	+	3.72890i	−0.202402	+	0.147053i	0.481968	+	0.876189i	$0.339922\pi$
$644$	−7.69794	+	13.4668i	−0.303341	+	0.530666i
$645$	−1.74975	−	5.38517i	−0.0688963	−	0.212041i
$646$	−8.56789	−	9.51561i	−0.337099	−	0.374387i
$647$	−0.0950776	+	0.904603i	−0.00373789	+	0.0355636i	−0.996232	−	0.0867300i	$-0.972358\pi$
$647$	−0.0950776	+	0.904603i	−0.00373789	+	0.0355636i	0.992494	+	0.122294i	$0.0390249\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	6.37460	−	2.83400i	0.250225	−	0.111244i
$650$	−19.7343			−0.774042
$651$	17.3103	−	19.3923i	0.678443	−	0.760042i
$652$	5.13868	−	15.8152i	0.201246	−	0.619372i
$653$	−44.7759	−	9.51741i	−1.75222	−	0.372445i	−0.783650	−	0.621203i	$-0.786644\pi$
$653$	−44.7759	−	9.51741i	−1.75222	−	0.372445i	−0.968566	+	0.248758i	$0.919978\pi$
$654$	3.64917	+	1.62472i	0.142694	+	0.0635314i
$655$	−10.5614	−	4.70224i	−0.412668	−	0.183732i
$656$	5.42897	+	1.15396i	0.211966	+	0.0450547i
$657$	−3.55174	+	10.9311i	−0.138567	+	0.426465i
$658$	−9.22189	−	27.9717i	−0.359507	−	1.09045i
$659$	−14.3786			−0.560109			−0.280054	−	0.959984i	$-0.590353\pi$
$659$	−14.3786			−0.560109			−0.280054	+	0.959984i	$0.590353\pi$
$660$	1.96688	+	2.18684i	0.0765609	+	0.0851225i
$661$	−1.26394	−	2.18920i	−0.0491614	−	0.0851500i	0.840398	−	0.541970i	$-0.182322\pi$
$661$	−1.26394	−	2.18920i	−0.0491614	−	0.0851500i	−0.889559	+	0.456820i	$0.848988\pi$
$662$	−2.21571	+	21.0811i	−0.0861161	+	0.819340i
$663$	10.3766	+	11.5244i	0.402995	+	0.447571i
$664$	5.19141	+	15.9775i	0.201466	+	0.620047i
$665$	−9.07339	+	0.0390673i	−0.351851	+	0.00151497i
$666$	−0.168241	+	0.122234i	−0.00651920	+	0.00473648i
$667$	38.1824	+	8.11593i	1.47843	+	0.314250i
$668$	−1.15940	+	0.246439i	−0.0448586	+	0.00953500i
$669$	3.08443	−	29.3464i	0.119251	−	1.13460i
$670$	−0.695918	+	1.20536i	−0.0268856	+	0.0465673i
$671$	9.75058	−	29.9538i	0.376417	−	1.15635i
$672$	0.265224	−	2.63242i	0.0102313	−	0.101548i
$673$	−10.3577	−	7.52529i	−0.399259	−	0.290079i	0.369980	−	0.929040i	$-0.379365\pi$
$673$	−10.3577	−	7.52529i	−0.399259	−	0.290079i	−0.769239	+	0.638961i	$0.779365\pi$
$674$	19.8217	+	22.0143i	0.763505	+	0.847959i
$675$	2.81942	−	3.13128i	0.108519	−	0.120523i
$676$	8.16289	+	3.63435i	0.313957	+	0.139783i
$677$	2.45637	+	23.3708i	0.0944059	+	0.898212i	0.934546	+	0.355842i	$0.115806\pi$
$677$	2.45637	+	23.3708i	0.0944059	+	0.898212i	−0.840140	+	0.542369i	$0.817527\pi$
$678$	−2.19366	−	6.75141i	−0.0842472	−	0.259286i
$679$	−0.921216	−	8.41605i	−0.0353530	−	0.322978i
$680$	−2.37555	−	1.72594i	−0.0910982	−	0.0661867i
$681$	8.21387	−	14.2268i	0.314756	−	0.545174i
$682$	3.42375	−	32.4052i	0.131102	−	1.24086i
$683$	8.51883	+	14.7550i	0.325964	+	0.564586i	0.981707	−	0.190398i	$-0.0609779\pi$
$683$	8.51883	+	14.7550i	0.325964	+	0.564586i	−0.655743	+	0.754984i	$0.727645\pi$
$684$	3.53281	−	1.57291i	0.135080	−	0.0601417i
$685$	−2.16511	+	6.66353i	−0.0827247	+	0.254600i
$686$	−9.05219	+	16.1573i	−0.345614	+	0.616888i
$687$	10.0145	−	7.27597i	0.382077	−	0.277595i
$688$	0.667412	+	6.35000i	0.0254448	+	0.242091i
$689$	37.1331	−	41.2405i	1.41466	−	1.57114i
$690$	−5.08568	+	1.08100i	−0.193609	+	0.0411528i
$691$	−10.6410	+	4.73767i	−0.404802	+	0.180229i	−0.599029	−	0.800727i	$-0.704447\pi$
$691$	−10.6410	+	4.73767i	−0.404802	+	0.180229i	0.194228	+	0.980957i	$0.437780\pi$
$692$	−8.31093			−0.315934
$693$	5.89609	+	6.49894i	0.223974	+	0.246874i
$694$	0.343529			0.0130402
$695$	7.75880	−	3.45444i	0.294308	−	0.131034i
$696$	−6.51258	+	1.38429i	−0.246859	+	0.0524714i
$697$	12.2969	−	13.6571i	0.465779	−	0.517300i
$698$	1.68497	+	16.0314i	0.0637769	+	0.606797i
$699$	−8.19471	+	5.95381i	−0.309953	+	0.225194i
$700$	10.8943	−	2.36473i	0.411767	−	0.0893785i
$701$	11.9324	−	36.7243i	0.450682	−	1.38706i	−0.425448	−	0.904983i	$-0.639883\pi$
$701$	11.9324	−	36.7243i	0.450682	−	1.38706i	0.876130	−	0.482074i	$-0.160117\pi$
$702$	−4.27861	+	1.90496i	−0.161486	+	0.0718981i
$703$	−0.402100	−	0.696458i	−0.0151655	−	0.0262674i
$704$	−1.65675	−	2.87318i	−0.0624411	−	0.108287i
$705$	4.93605	−	8.54949i	0.185902	−	0.321992i
$706$	12.8900	+	9.36513i	0.485121	+	0.352461i
$707$	4.37971	−	3.21095i	0.164716	−	0.120760i
$708$	−0.649986	−	2.00045i	−0.0244280	−	0.0751815i
$709$	−2.76540	−	26.3110i	−0.103857	−	0.988131i	−0.915047	−	0.403348i	$-0.867846\pi$
$709$	−2.76540	−	26.3110i	−0.103857	−	0.988131i	0.811190	−	0.584783i	$-0.198820\pi$
$710$	−3.69549	−	1.64534i	−0.138689	−	0.0617484i
$711$	10.2483	−	11.3819i	0.384341	−	0.426854i
$712$	6.85848	+	7.61712i	0.257032	+	0.285463i
$713$	46.6013	+	33.8578i	1.74523	+	1.26798i
$714$	−7.10938	−	5.11864i	−0.266062	−	0.191560i
$715$	11.1489	−	8.09089i	0.416946	−	0.302582i
$716$	5.89054	−	10.2027i	0.220140	−	0.381294i
$717$	0.133716	−	1.27222i	0.00499372	−	0.0475121i
$718$	−2.12218	+	0.451084i	−0.0791992	+	0.0168343i
$719$	−8.87106	−	1.88560i	−0.330835	−	0.0703211i	0.0394997	−	0.999220i	$-0.487424\pi$
$719$	−8.87106	−	1.88560i	−0.330835	−	0.0703211i	−0.370334	+	0.928898i	$0.620757\pi$
$720$	0.717450	−	0.521258i	0.0267378	−	0.0194261i
$721$	14.5812	+	25.0061i	0.543032	+	0.931276i
$722$	−1.25003	−	3.84721i	−0.0465215	−	0.143178i
$723$	8.87983	+	9.86205i	0.330244	+	0.366774i
$724$	−0.616132	+	5.86210i	−0.0228984	+	0.217863i
$725$	−14.0271	−	24.2956i	−0.520953	−	0.902316i
$726$	10.7571	+	2.29873i	0.399235	+	0.0853140i
$727$	46.6030			1.72841			0.864204	−	0.503141i	$-0.167822\pi$
$727$	46.6030			1.72841			0.864204	+	0.503141i	$0.167822\pi$
$728$	−12.1316	−	2.52411i	−0.449628	−	0.0935499i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	−9.97006	−	2.11920i	−0.369009	−	0.0784352i
$731$	19.3135	+	8.59895i	0.714337	+	0.318044i
$732$	−8.67672	−	3.86313i	−0.320701	−	0.142785i
$733$	28.3466	+	6.02525i	1.04700	+	0.222548i	0.699131	−	0.714994i	$-0.253570\pi$
$733$	28.3466	+	6.02525i	1.04700	+	0.222548i	0.347874	+	0.937541i	$0.386904\pi$
$734$	−1.54815	+	4.76472i	−0.0571433	+	0.175869i
$735$	−6.06073	+	1.34290i	−0.223553	+	0.0495335i
$736$	5.86288			0.216108
$737$	0.541291	+	5.17713i	0.0199387	+	0.190702i
$738$	2.77513	+	4.80666i	0.102154	+	0.176936i
$739$	2.94631	−	28.0322i	0.108382	−	1.03118i	−0.796244	−	0.604975i	$-0.793183\pi$
$739$	2.94631	−	28.0322i	0.108382	−	1.03118i	0.904626	−	0.426207i	$-0.140150\pi$
$740$	−0.123401	−	0.137051i	−0.00453632	−	0.00503809i
$741$	−5.59687	−	17.2254i	−0.205606	−	0.632791i
$742$	−15.5576	+	27.2165i	−0.571136	+	0.999148i
$743$	40.6753	−	29.5523i	1.49223	−	1.08417i	0.518881	−	0.854847i	$-0.326349\pi$
$743$	40.6753	−	29.5523i	1.49223	−	1.08417i	0.973350	−	0.229323i	$-0.0736511\pi$
$744$	−9.61023	−	2.04272i	−0.352328	−	0.0748897i
$745$	17.1406	−	3.64334i	0.627981	−	0.133482i
$746$	−0.443781	+	4.22229i	−0.0162480	+	0.154589i
$747$	−8.39987	+	14.5490i	−0.307335	+	0.532320i
$748$	−10.9817	−	0.00597337i	−0.401530	−	0.000218408i
$749$	0.903798	−	8.97044i	0.0330241	−	0.327773i
$750$	6.61027	+	4.80264i	0.241373	+	0.175368i
$751$	3.48930	+	3.87526i	0.127326	+	0.141410i	0.803437	−	0.595390i	$-0.203002\pi$
$751$	3.48930	+	3.87526i	0.127326	+	0.141410i	−0.676110	+	0.736800i	$0.736336\pi$
$752$	−7.44880	+	8.27273i	−0.271630	+	0.301675i
$753$	4.61570	+	2.05504i	0.168205	+	0.0748899i
$754$	3.25954	+	31.0124i	0.118705	+	1.12941i
$755$	−4.61920	−	14.2164i	−0.168110	−	0.517389i
$756$	2.13374	−	1.56434i	0.0776034	−	0.0568943i
$757$	−31.8757	−	23.1590i	−1.15854	−	0.841730i	−0.168949	−	0.985625i	$-0.554037\pi$
$757$	−31.8757	−	23.1590i	−1.15854	−	0.841730i	−0.989593	+	0.143895i	$0.954037\pi$
$758$	−14.8218	+	25.6721i	−0.538352	+	0.932453i
$759$	−13.0191	+	14.4433i	−0.472563	+	0.524260i
$760$	1.71473	+	2.96999i	0.0621996	+	0.107733i
$761$	31.5439	−	14.0442i	1.14346	−	0.509103i	0.254497	−	0.967074i	$-0.418090\pi$
$761$	31.5439	−	14.0442i	1.14346	−	0.509103i	0.888967	+	0.457971i	$0.151424\pi$
$762$	2.64206	−	8.13143i	0.0957118	−	0.294571i
$763$	−3.22254	+	10.0652i	−0.116664	+	0.364385i
$764$	19.5368	−	14.1943i	0.706815	−	0.513531i
$765$	−0.306931	−	2.92026i	−0.0110971	−	0.105582i
$766$	−19.2825	+	21.4154i	−0.696705	+	0.773769i
$767$	−9.63604	+	2.04820i	−0.347937	+	0.0739563i
$768$	−0.913545	+	0.406737i	−0.0329647	+	0.0146768i
$769$	12.1041			0.436484			0.218242	−	0.975895i	$-0.429968\pi$
$769$	12.1041			0.436484			0.218242	+	0.975895i	$0.429968\pi$
$770$	−5.18524	+	5.80254i	−0.186863	+	0.209109i
$771$	17.5099			0.630603
$772$	11.9409	−	5.31642i	0.429762	−	0.191342i
$773$	−29.6317	+	6.29841i	−1.06578	+	0.226538i	−0.707237	−	0.706976i	$-0.750059\pi$
$773$	−29.6317	+	6.29841i	−1.06578	+	0.226538i	−0.358540	+	0.933514i	$0.616725\pi$
$774$	−4.27238	+	4.74496i	−0.153568	+	0.170554i
$775$	−4.32726	−	41.1711i	−0.155440	−	1.47891i
$776$	−2.58883	+	1.88089i	−0.0929335	+	0.0675201i
$777$	−0.369915	−	0.407292i	−0.0132706	−	0.0146115i
$778$	6.03992	−	18.5890i	0.216542	−	0.666447i
$779$	−19.6080	+	8.73005i	−0.702530	+	0.312786i
$780$	−2.07671	−	3.59698i	−0.0743583	−	0.128792i
$781$	−14.7999	+	3.13740i	−0.529581	+	0.112265i
$782$	9.70629	−	16.8118i	0.347096	−	0.601188i
$783$	−5.38649	−	3.91352i	−0.192498	−	0.139858i
$784$	6.99974	−	0.0602788i	0.249991	−	0.00215281i
$785$	2.37160	+	7.29902i	0.0846459	+	0.260513i
$786$	1.36267	+	12.9650i	0.0486049	+	0.462445i
$787$	31.3082	+	13.9393i	1.11602	+	0.496883i	0.880052	−	0.474878i	$-0.157508\pi$
$787$	31.3082	+	13.9393i	1.11602	+	0.496883i	0.235966	+	0.971761i	$0.424174\pi$
$788$	−2.37295	+	2.63543i	−0.0845329	+	0.0938832i
$789$	5.55449	+	6.16889i	0.197745	+	0.219618i
$790$	10.9884	+	7.98351i	0.390948	+	0.284041i
$791$	17.1250	−	7.71305i	0.608894	−	0.274244i
$792$	1.02661	−	3.15374i	0.0364790	−	0.112063i
$793$	−22.2417	+	38.5238i	−0.789826	+	1.36802i
$794$	−1.93280	+	18.3893i	−0.0685924	+	0.652613i
$795$	−10.2782	+	2.18469i	−0.364529	+	0.0774831i
$796$	2.66745	+	0.566983i	0.0945451	+	0.0200962i
$797$	−11.5028	+	8.35729i	−0.407451	+	0.296031i	−0.772569	−	0.634931i	$-0.781029\pi$
$797$	−11.5028	+	8.35729i	−0.407451	+	0.296031i	0.365118	+	0.930961i	$0.381029\pi$
$798$	5.15385	+	8.83863i	0.182444	+	0.312884i
$799$	11.3902	+	35.0553i	0.402955	+	1.24017i
$800$	−2.81942	−	3.13128i	−0.0996815	−	0.110708i
$801$	−1.07140	+	10.1937i	−0.0378561	+	0.360176i
$802$	1.68807	+	2.92382i	0.0596078	+	0.103244i
$803$	−34.8330	+	15.4860i	−1.22923	+	0.546488i
$804$	1.56947			0.0553510
$805$	−4.30715	−	13.0644i	−0.151807	−	0.460458i
$806$	−14.2195	+	43.7631i	−0.500861	+	1.54149i
$807$	6.79130	+	1.44354i	0.239065	+	0.0508148i
$808$	−1.87514	−	0.834865i	−0.0659671	−	0.0293705i
$809$	−1.38256	−	0.615557i	−0.0486083	−	0.0216418i	0.382289	−	0.924043i	$-0.375136\pi$
$809$	−1.38256	−	0.615557i	−0.0486083	−	0.0216418i	−0.430897	+	0.902401i	$0.641803\pi$
$810$	0.867438	+	0.184380i	0.0304787	+	0.00647844i
$811$	10.9543	−	33.7140i	0.384659	−	1.18386i	−0.552068	−	0.833799i	$-0.686161\pi$
$811$	10.9543	−	33.7140i	0.384659	−	1.18386i	0.936727	−	0.350060i	$-0.113839\pi$
$812$	−5.51561	−	16.7298i	−0.193560	−	0.587102i
$813$	5.23160			0.183480
$814$	−0.674566	−	0.143767i	−0.0236435	−	0.00503903i
$815$	7.37349	+	12.7713i	0.258282	+	0.447358i
$816$	−0.346104	+	3.29296i	−0.0121161	+	0.115277i
$817$	−16.5219	−	18.3495i	−0.578029	−	0.641966i
$818$	−4.33665	−	13.3468i	−0.151628	−	0.466662i
$819$	−6.24187	−	10.7045i	−0.218108	−	0.374046i
$820$	−3.98203	+	2.89312i	−0.139059	+	0.101032i
$821$	−46.3263	−	9.84696i	−1.61680	−	0.343661i	−0.691346	−	0.722524i	$-0.742982\pi$
$821$	−46.3263	−	9.84696i	−1.61680	−	0.343661i	−0.925453	+	0.378863i	$0.876315\pi$
$822$	7.72802	−	1.64264i	0.269546	−	0.0572937i
$823$	−4.36391	+	41.5199i	−0.152116	+	1.44729i	0.606152	+	0.795349i	$0.292712\pi$
$823$	−4.36391	+	41.5199i	−0.152116	+	1.44729i	−0.758268	+	0.651943i	$0.773954\pi$
$824$	5.47043	−	9.47506i	0.190571	−	0.330079i
$825$	13.9748	+	0.00760143i	0.486539	+	0.000264648i
$826$	5.07415	−	2.28539i	0.176552	−	0.0795188i
$827$	9.08018	+	6.59714i	0.315749	+	0.229405i	0.734359	−	0.678761i	$-0.237483\pi$
$827$	9.08018	+	6.59714i	0.315749	+	0.229405i	−0.418610	+	0.908166i	$0.637483\pi$
$828$	3.92303	+	4.35697i	0.136335	+	0.151415i
$829$	13.0107	−	14.4499i	0.451882	−	0.501866i	−0.473557	−	0.880763i	$-0.657030\pi$
$829$	13.0107	−	14.4499i	0.451882	−	0.501866i	0.925439	+	0.378898i	$0.123697\pi$
$830$	−13.6103	−	6.05969i	−0.472420	−	0.210335i
$831$	2.55531	+	24.3122i	0.0886429	+	0.843381i
$832$	1.44729	+	4.45430i	0.0501757	+	0.154425i
$833$	11.4156	−	20.1715i	0.395526	−	0.698903i
$834$	−7.74797	−	5.62923i	−0.268290	−	0.194924i
$835$	0.525574	−	0.910321i	0.0181883	−	0.0315030i
$836$	11.7142	+	5.22312i	0.405143	+	0.180645i
$837$	−4.91246	−	8.50864i	−0.169800	−	0.294102i
$838$	27.1316	−	12.0798i	0.937247	−	0.417289i
$839$	7.25101	−	22.3163i	0.250333	−	0.770445i	−0.744381	−	0.667755i	$-0.767255\pi$
$839$	7.25101	−	22.3163i	0.250333	−	0.770445i	0.994713	−	0.102689i	$-0.0327448\pi$
$840$	1.57747	+	1.73686i	0.0544280	+	0.0599275i
$841$	−12.4022	+	9.01071i	−0.427661	+	0.310714i
$842$	2.01817	+	19.2016i	0.0695507	+	0.661731i
$843$	1.88982	−	2.09886i	0.0650889	−	0.0722885i
$844$	−22.9541	+	4.87904i	−0.790112	+	0.167943i
$845$	−7.23899	+	3.22301i	−0.249029	+	0.110875i
$846$	−11.1321			−0.382728
$847$	−2.94897	+	28.9535i	−0.101328	+	0.994853i
$848$	11.8489			0.406893
$849$	4.37853	−	1.94945i	0.150271	−	0.0669049i
$850$	−13.6466	+	2.90068i	−0.468076	+	0.0994926i
$851$	0.815823	−	0.906063i	0.0279660	−	0.0310594i
$852$	0.476806	+	4.53651i	0.0163351	+	0.155418i
$853$	−16.6738	+	12.1142i	−0.570899	+	0.414783i	−0.835432	−	0.549594i	$-0.814782\pi$
$853$	−16.6738	+	12.1142i	−0.570899	+	0.414783i	0.264533	+	0.964377i	$0.414782\pi$
$854$	7.66230	−	23.9323i	0.262199	−	0.818946i
$855$	−1.05976	+	3.26160i	−0.0362430	+	0.111544i
$856$	−3.11307	+	1.38603i	−0.106402	+	0.0473734i
$857$	2.22285	+	3.85009i	0.0759312	+	0.131517i	0.901491	−	0.432798i	$-0.142474\pi$
$857$	2.22285	+	3.85009i	0.0759312	+	0.131517i	−0.825560	+	0.564315i	$0.809140\pi$
$858$	−14.1871	−	6.32576i	−0.484340	−	0.215958i
$859$	3.17655	−	5.50195i	0.108383	−	0.187724i	−0.806733	−	0.590917i	$-0.798766\pi$
$859$	3.17655	−	5.50195i	0.108383	−	0.187724i	0.915115	+	0.403193i	$0.132100\pi$
$860$	−4.58090	−	3.32822i	−0.156207	−	0.113491i
$861$	−11.8428	+	8.68246i	−0.403602	+	0.295897i
$862$	−2.72501	−	8.38671i	−0.0928141	−	0.285653i
$863$	5.23927	+	49.8483i	0.178347	+	1.69686i	0.608060	+	0.793891i	$0.291948\pi$
$863$	5.23927	+	49.8483i	0.178347	+	1.69686i	−0.429713	+	0.902965i	$0.641385\pi$
$864$	−0.913545	−	0.406737i	−0.0310794	−	0.0138375i
$865$	4.93168	−	5.47718i	0.167682	−	0.186230i
$866$	−3.02659	−	3.36136i	−0.102848	−	0.114224i
$867$	−4.88371	−	3.54822i	−0.165860	−	0.120504i
$868$	2.60581	−	25.8634i	0.0884470	−	0.877860i
$869$	50.7969	+	0.0276304i	1.72317	+	0.000937298i
$870$	2.95225	−	5.11344i	0.100091	−	0.173362i
$871$	0.768353	−	7.31039i	0.0260347	−	0.247703i
$872$	3.90722	−	0.830506i	0.132315	−	0.0281245i
$873$	−3.13004	−	0.665310i	−0.105936	−	0.0225173i
$874$	−18.3425	+	13.3266i	−0.620445	+	0.450779i
$875$	−10.7282	+	18.7679i	−0.362678	+	0.634470i
$876$	3.55174	+	10.9311i	0.120002	+	0.369329i
$877$	6.05122	+	6.72056i	0.204335	+	0.226937i	0.836599	−	0.547816i	$-0.184541\pi$
$877$	6.05122	+	6.72056i	0.204335	+	0.226937i	−0.632264	+	0.774753i	$0.717874\pi$
$878$	0.198806	−	1.89152i	0.00670939	−	0.0638356i
$879$	−2.74152	−	4.74845i	−0.0924691	−	0.160161i
$880$	2.87663	+	0.613083i	0.0969713	+	0.0206670i
$881$	−6.86988			−0.231452			−0.115726	−	0.993281i	$-0.536919\pi$
$881$	−6.86988			−0.231452			−0.115726	+	0.993281i	$0.536919\pi$
$882$	4.72854	+	5.16149i	0.159218	+	0.173796i
$883$	2.66219	−	8.19336i	0.0895897	−	0.275729i	−0.896216	−	0.443617i	$-0.853695\pi$
$883$	2.66219	−	8.19336i	0.0895897	−	0.275729i	0.985806	+	0.167889i	$0.0536949\pi$
$884$	15.1687	+	3.22422i	0.510180	+	0.108442i
$885$	1.70406	+	0.758698i	0.0572815	+	0.0255034i
$886$	−19.1136	−	8.50993i	−0.642135	−	0.285897i
$887$	−13.1130	−	2.78726i	−0.440293	−	0.0935872i	−0.0175691	−	0.999846i	$-0.505593\pi$
$887$	−13.1130	−	2.78726i	−0.440293	−	0.0935872i	−0.422724	+	0.906258i	$0.638926\pi$
$888$	−0.0642623	+	0.197779i	−0.00215650	+	0.00663703i
$889$	22.1466	+	4.60784i	0.742774	+	0.154542i
$890$	−9.08974			−0.304689
$891$	3.03062	−	1.34734i	0.101530	−	0.0451377i
$892$	−14.7540	−	25.5547i	−0.494002	−	0.855636i
$893$	4.49987	−	42.8134i	0.150582	−	1.43270i
$894$	−13.2220	−	14.6845i	−0.442210	−	0.491124i
$895$	3.22851	+	9.93633i	0.107917	+	0.332135i
$896$	−1.33273	−	2.28557i	−0.0445233	−	0.0763556i
$897$	22.2147	−	16.1399i	0.741728	−	0.538897i
$898$	−10.4107	−	2.21287i	−0.347411	−	0.0738445i
$899$	−63.9856	+	13.6006i	−2.13404	+	0.453604i
$900$	0.440436	−	4.19047i	0.0146812	−	0.139682i
$901$	19.6164	−	33.9767i	0.653519	−	1.13193i
$902$	−5.69794	+	17.5041i	−0.189721	+	0.582822i
$903$	−13.7094	−	9.87055i	−0.456220	−	0.328471i
$904$	−5.74309	−	4.17260i	−0.191012	−	0.138779i
$905$	−3.49771	−	3.88460i	−0.116268	−	0.129129i
$906$	−11.2788	+	12.5263i	−0.374712	+	0.416160i
$907$	−18.5373	−	8.25333i	−0.615520	−	0.274047i	0.0752010	−	0.997168i	$-0.476040\pi$
$907$	−18.5373	−	8.25333i	−0.615520	−	0.274047i	−0.690721	+	0.723121i	$0.742707\pi$
$908$	−1.71717	−	16.3378i	−0.0569862	−	0.542187i
$909$	−0.634286	−	1.95213i	−0.0210380	−	0.0647482i
$910$	8.86235	−	6.49736i	0.293784	−	0.215385i
$911$	−44.5802	−	32.3894i	−1.47701	−	1.07311i	−0.978505	−	0.206223i	$-0.933883\pi$
$911$	−44.5802	−	32.3894i	−1.47701	−	1.07311i	−0.498504	−	0.866887i	$-0.666117\pi$
$912$	1.93357	−	3.34904i	0.0640270	−	0.110898i
$913$	−54.5072	+	11.5549i	−1.80392	+	0.382410i
$914$	−0.355237	−	0.615288i	−0.0117502	−	0.0203519i
$915$	7.69467	−	3.42589i	0.254378	−	0.113256i
$916$	3.82520	−	11.7728i	0.126388	−	0.388983i
$917$	−33.7061	+	7.31628i	−1.11307	+	0.241605i
$918$	−2.67874	+	1.94622i	−0.0884115	+	0.0642347i
$919$	4.48707	+	42.6916i	0.148015	+	1.40827i	0.776339	+	0.630315i	$0.217074\pi$
$919$	4.48707	+	42.6916i	0.148015	+	1.40827i	−0.628325	+	0.777951i	$0.716259\pi$
$920$	−3.47901	+	3.86383i	−0.114700	+	0.127387i
$921$	3.05739	−	0.649868i	0.100744	−	0.0214139i
$922$	−18.1569	+	8.08398i	−0.597966	+	0.266232i
$923$	21.3639			0.703200
$924$	8.59001	+	1.79212i	0.282591	+	0.0589563i
$925$	−0.876239			−0.0288106
$926$	−23.5135	+	10.4689i	−0.772701	+	0.344029i
$927$	10.7018	−	2.27473i	0.351492	−	0.0747120i
$928$	−4.45512	+	4.94791i	−0.146246	+	0.162423i
$929$	−0.793222	−	7.54701i	−0.0260248	−	0.247609i	−0.999798	−	0.0200893i	$-0.993605\pi$
$929$	−0.793222	−	7.54701i	−0.0260248	−	0.247609i	0.973773	−	0.227520i	$-0.0730617\pi$
$930$	7.04890	−	5.12132i	0.231142	−	0.167935i
$931$	−21.7623	+	16.0993i	−0.713230	+	0.527635i
$932$	−3.13010	+	9.63346i	−0.102530	+	0.315555i
$933$	9.50661	−	4.23261i	0.311232	−	0.138570i
$934$	2.46641	+	4.27194i	0.0807033	+	0.139782i
$935$	6.52043	−	7.23376i	0.213241	−	0.236569i
$936$	−2.34176	+	4.05605i	−0.0765429	+	0.132576i
$937$	−34.3436	−	24.9521i	−1.12196	−	0.815148i	−0.137451	−	0.990509i	$-0.543891\pi$
$937$	−34.3436	−	24.9521i	−1.12196	−	0.815148i	−0.984504	+	0.175360i	$0.943891\pi$
$938$	0.451825	+	4.12778i	0.0147526	+	0.134777i
$939$	7.05526	+	21.7138i	0.230240	+	0.708605i
$940$	−1.03192	−	9.81802i	−0.0336574	−	0.320228i
$941$	−19.0198	−	8.46818i	−0.620029	−	0.276055i	0.0725858	−	0.997362i	$-0.476875\pi$
$941$	−19.0198	−	8.46818i	−0.620029	−	0.276055i	−0.692615	+	0.721307i	$0.743542\pi$
$942$	5.79075	−	6.43128i	0.188673	−	0.209543i
$943$	−21.7738	−	24.1823i	−0.709053	−	0.787483i
$944$	−1.70168	−	1.23635i	−0.0553851	−	0.0402397i
$945$	−0.235206	+	2.33448i	−0.00765124	+	0.0759406i
$946$	−21.1766	−	0.0115188i	−0.688510	−	0.000374507i
$947$	4.87390	−	8.44184i	0.158380	−	0.274323i	−0.775904	−	0.630851i	$-0.782706\pi$
$947$	4.87390	−	8.44184i	0.158380	−	0.274323i	0.934285	+	0.356528i	$0.116039\pi$
$948$	1.60094	−	15.2319i	0.0519962	−	0.494711i
$949$	52.6546	−	11.1921i	1.70924	−	0.363310i
$950$	15.9384	+	3.38780i	0.517108	+	0.109915i
$951$	21.8161	−	15.8503i	0.707436	−	0.513982i
$952$	−8.76027	+	0.0377192i	−0.283922	+	0.00122248i
$953$	7.94307	+	24.4463i	0.257301	+	0.791892i	0.993368	+	0.114983i	$0.0366812\pi$
$953$	7.94307	+	24.4463i	0.257301	+	0.791892i	−0.736066	+	0.676910i	$0.763319\pi$
$954$	7.92846	+	8.80544i	0.256693	+	0.285087i
$955$	−2.23853	+	21.2982i	−0.0724373	+	0.689195i
$956$	−0.639616	−	1.10785i	−0.0206867	−	0.0358304i
$957$	−2.29629	−	21.9626i	−0.0742284	−	0.709950i
$958$	−1.06041			−0.0342604
$959$	6.54498	+	19.8521i	0.211348	+	0.641059i
$960$	0.274042	−	0.843413i	0.00884466	−	0.0272211i
$961$	−64.0973	−	13.6243i	−2.06765	−	0.439493i
$962$	0.889768	+	0.396150i	0.0286873	+	0.0127724i
$963$	−3.11307	−	1.38603i	−0.100317	−	0.0446641i
$964$	12.9807	+	2.75913i	0.418080	+	0.0888657i
$965$	−3.58198	+	11.0242i	−0.115308	+	0.354881i
$966$	−10.3296	+	11.5720i	−0.332350	+	0.372324i
$967$	49.0008			1.57576			0.787879	−	0.615830i	$-0.211179\pi$
$967$	49.0008			1.57576			0.787879	+	0.615830i	$0.211179\pi$
$968$	10.0539	−	4.46317i	0.323143	−	0.143452i
$969$	−6.40226	−	11.0890i	−0.205670	−	0.356231i
$970$	0.296629	−	2.82224i	0.00952419	−	0.0906167i
$971$	2.32203	+	2.57888i	0.0745176	+	0.0827601i	0.779251	−	0.626712i	$-0.215600\pi$
$971$	2.32203	+	2.57888i	0.0745176	+	0.0827601i	−0.704733	+	0.709473i	$0.748933\pi$
$972$	−0.309017	−	0.951057i	−0.00991172	−	0.0305052i
$973$	12.5746	−	21.9981i	0.403123	−	0.705225i
$974$	−18.1886	+	13.2148i	−0.582801	+	0.423430i
$975$	−19.3030	−	4.10299i	−0.618192	−	0.131401i
$976$	−9.29030	+	1.97471i	−0.297375	+	0.0632091i
$977$	0.569968	−	5.42288i	0.0182349	−	0.173493i	−0.981614	−	0.190877i	$-0.938867\pi$
$977$	0.569968	−	5.42288i	0.0182349	−	0.173493i	0.999849	+	0.0173834i	$0.00553358\pi$
$978$	8.31455	−	14.4012i	0.265870	−	0.460500i
$979$	−27.5133	+	19.9667i	−0.879329	+	0.638139i
$980$	−4.11390	+	4.64883i	−0.131414	+	0.148502i
$981$	3.23163	+	2.34792i	0.103178	+	0.0749632i
$982$	0.0525419	+	0.0583537i	0.00167668	+	0.00186214i
$983$	−27.1042	+	30.1023i	−0.864491	+	0.960114i	−0.999528	−	0.0307263i	$-0.990218\pi$
$983$	−27.1042	+	30.1023i	−0.864491	+	0.960114i	0.135037	+	0.990841i	$0.456885\pi$
$984$	5.07041	+	2.25749i	0.161639	+	0.0719662i
$985$	−0.328735	−	3.12771i	−0.0104744	−	0.0996571i
$986$	6.81245	+	20.9666i	0.216953	+	0.667712i
$987$	−3.20473	−	29.2778i	−0.102008	−	0.931922i
$988$	−14.6528	−	10.6459i	−0.466168	−	0.338691i
$989$	18.7172	−	32.4191i	0.595171	−	1.03087i
$990$	1.46923	+	2.54799i	0.0466953	+	0.0809804i
$991$	−24.6072	−	42.6209i	−0.781673	−	1.35390i	−0.930967	−	0.365104i	$-0.881033\pi$
$991$	−24.6072	−	42.6209i	−0.781673	−	1.35390i	0.149294	−	0.988793i	$-0.452300\pi$
$992$	−8.97552	+	3.99616i	−0.284973	+	0.126878i
$993$	−6.55030	+	20.1598i	−0.207868	+	0.639751i
$994$	−11.7939	+	2.56000i	−0.374081	+	0.0811984i
$995$	−1.95651	+	1.42149i	−0.0620257	+	0.0450643i
$996$	1.75605	+	16.7077i	0.0556426	+	0.529404i
$997$	−5.91629	+	6.57071i	−0.187371	+	0.208096i	−0.829510	−	0.558491i	$-0.811380\pi$
$997$	−5.91629	+	6.57071i	−0.187371	+	0.208096i	0.642139	+	0.766588i	$0.278047\pi$
$998$	−3.68515	+	0.783302i	−0.116651	+	0.0247950i
$999$	−0.189978	+	0.0845838i	−0.00601065	+	0.00267611i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.y.d.37.3	yes	40
7.4	even	3	inner	462.2.y.d.235.3	yes	40
11.3	even	5	inner	462.2.y.d.289.3	yes	40
77.25	even	15	inner	462.2.y.d.25.3	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.y.d.25.3	✓	40	77.25	even	15	inner
462.2.y.d.37.3	yes	40	1.1	even	1	trivial
462.2.y.d.235.3	yes	40	7.4	even	3	inner
462.2.y.d.289.3	yes	40	11.3	even	5	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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.913545 - 0.406737i) q^{2} +(0.978148 - 0.207912i) q^{3} +(0.669131 - 0.743145i) q^{4} +(0.0926977 + 0.881959i) q^{5} +(0.809017 - 0.587785i) q^{6} +(1.77880 + 1.95854i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.913545 - 0.406737i) q^{9} +(0.443409 + 0.768006i) q^{10} +(3.02915 + 1.35064i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-3.78905 - 2.75291i) q^{13} +(2.42163 + 1.06571i) q^{14} +(0.274042 + 0.843413i) q^{15} +(-0.104528 - 0.994522i) q^{16} +(-3.02484 - 1.34675i) q^{17} +(0.669131 - 0.743145i) q^{18} +(2.58762 + 2.87385i) q^{19} +(0.717450 + 0.521258i) q^{20} +(2.14713 + 1.54590i) q^{21} +(3.31662 + 0.00180404i) q^{22} +(-2.93144 + 5.07740i) q^{23} +(0.104528 - 0.994522i) q^{24} +(4.12148 - 0.876047i) q^{25} +(-4.58118 - 0.973759i) q^{26} +(0.809017 - 0.587785i) q^{27} +(2.64573 - 0.0113917i) q^{28} +(-2.05746 - 6.33220i) q^{29} +(0.593397 + 0.659034i) q^{30} +(1.02698 - 9.77111i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.24377 + 0.691330i) q^{33} -3.31110 q^{34} +(-1.56246 + 1.75038i) q^{35} +(0.309017 - 0.951057i) q^{36} +(-0.203413 - 0.0432367i) q^{37} +(3.53281 + 1.57291i) q^{38} +(-4.27861 - 1.90496i) q^{39} +(0.867438 + 0.184380i) q^{40} +(-1.71512 + 5.27861i) q^{41} +(2.59028 + 0.538935i) q^{42} -6.38498 q^{43} +(3.03062 - 1.34734i) q^{44} +(0.443409 + 0.768006i) q^{45} +(-0.612837 + 5.83076i) q^{46} +(-7.44880 - 8.27273i) q^{47} +(-0.309017 - 0.951057i) q^{48} +(-0.671724 + 6.96770i) q^{49} +(3.40884 - 2.47667i) q^{50} +(-3.23875 - 0.688417i) q^{51} +(-4.58118 + 0.973759i) q^{52} +(-1.23855 + 11.7840i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-0.910415 + 2.79679i) q^{55} +(2.41236 - 1.08652i) q^{56} +(3.12859 + 2.27305i) q^{57} +(-4.45512 - 4.94791i) q^{58} +(1.40745 - 1.56313i) q^{59} +(0.810148 + 0.360701i) q^{60} +(-0.992796 - 9.44582i) q^{61} +(-3.03607 - 9.34406i) q^{62} +(2.42163 + 1.06571i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(2.07671 - 3.59698i) q^{65} +(3.24452 - 0.687800i) q^{66} +(0.784736 + 1.35920i) q^{67} +(-3.02484 + 1.34675i) q^{68} +(-1.81173 + 5.57593i) q^{69} +(-0.715431 + 2.23456i) q^{70} +(-3.69033 + 2.68118i) q^{71} +(-0.104528 - 0.994522i) q^{72} +(-7.69078 + 8.54147i) q^{73} +(-0.203413 + 0.0432367i) q^{74} +(3.84927 - 1.71381i) q^{75} +3.86714 q^{76} +(2.74299 + 8.33523i) q^{77} -4.68352 q^{78} +(13.9917 - 6.22952i) q^{79} +(0.867438 - 0.184380i) q^{80} +(0.669131 - 0.743145i) q^{81} +(0.580160 + 5.51985i) q^{82} +(-13.5913 + 9.87464i) q^{83} +(2.58554 - 0.561220i) q^{84} +(0.907380 - 2.79263i) q^{85} +(-5.83297 + 2.59700i) q^{86} +(-3.32904 - 5.76606i) q^{87} +(2.22060 - 2.46353i) q^{88} +(-5.12492 + 8.87662i) q^{89} +(0.717450 + 0.521258i) q^{90} +(-1.34831 - 12.3179i) q^{91} +(1.81173 + 5.57593i) q^{92} +(-1.02698 - 9.77111i) q^{93} +(-10.1696 - 4.52781i) q^{94} +(-2.29475 + 2.54858i) q^{95} +(-0.669131 - 0.743145i) q^{96} +(-2.58883 - 1.88089i) q^{97} +(2.22037 + 6.63852i) q^{98} +(3.31662 + 0.00180404i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 3 q^{5} + 10 q^{6} - 7 q^{7} - 10 q^{8} + 5 q^{9} + 12 q^{10} + 2 q^{11} + 20 q^{12} + 10 q^{13} + 5 q^{14} - 6 q^{15} + 5 q^{16} + 5 q^{18} - 13 q^{19} + 6 q^{20} - 2 q^{21}+ \cdots - 4 q^{99}+O(q^{100}) \) 40 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 3 * q^5 + 10 * q^6 - 7 * q^7 - 10 * q^8 + 5 * q^9 + 12 * q^10 + 2 * q^11 + 20 * q^12 + 10 * q^13 + 5 * q^14 - 6 * q^15 + 5 * q^16 + 5 * q^18 - 13 * q^19 + 6 * q^20 - 2 * q^21 - 4 * q^22 - 20 * q^23 - 5 * q^24 + 12 * q^25 + 10 * q^27 - 3 * q^28 + 12 * q^29 + 3 * q^30 - 10 * q^31 - 20 * q^32 + 8 * q^33 - 13 * q^35 - 10 * q^36 + 3 * q^37 + 2 * q^38 + 5 * q^39 - 3 * q^40 - 44 * q^41 - 3 * q^42 + 36 * q^43 - 3 * q^44 + 12 * q^45 + 11 * q^47 + 10 * q^48 + 33 * q^49 - 4 * q^50 + 26 * q^53 + 20 * q^54 - 20 * q^55 + 8 * q^56 + 4 * q^57 - 6 * q^58 + 4 * q^59 + 3 * q^60 - 23 * q^61 + 5 * q^63 - 10 * q^64 - 50 * q^65 - 7 * q^66 - 108 * q^67 + 20 * q^69 - 86 * q^71 + 5 * q^72 - 35 * q^73 + 3 * q^74 - 2 * q^75 - 44 * q^76 - 37 * q^77 + 20 * q^78 + 3 * q^79 - 3 * q^80 + 5 * q^81 - 28 * q^82 - 88 * q^83 - 5 * q^84 + 96 * q^85 - 13 * q^86 + 6 * q^87 - 8 * q^88 + 6 * q^89 + 6 * q^90 + 40 * q^91 - 20 * q^92 + 10 * q^93 - 24 * q^94 + 36 * q^95 - 5 * q^96 + 60 * q^97 + 2 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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