LMFDB - Embedded newform 87.2.k.a.2.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [87,2,Mod(2,87)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(87, base_ring=CyclotomicField(28))

chi = DirichletCharacter(H, H._module([14, 1]))

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

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

chi := DirichletCharacter("87.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 87 = 3 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	87.k (of order $28$, degree $12$, 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:	$0.694698497585$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$8$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			2.4
Character	$\chi$	$=$	87.2
Dual form			87.2.k.a.44.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.108076 + 0.959202i) q^{2} +(0.843782 - 1.51262i) q^{3} +(1.04147 + 0.237708i) q^{4} +(-1.18935 - 1.49140i) q^{5} +(1.35972 + 0.972836i) q^{6} +(-0.00234208 - 0.0102613i) q^{7} +(-0.978186 + 2.79549i) q^{8} +(-1.57606 - 2.55265i) q^{9} +(1.55910 - 0.979646i) q^{10} +(1.04262 + 2.97964i) q^{11} +(1.23833 - 1.37477i) q^{12} +(-2.37674 + 4.93536i) q^{13} +(0.0100958 - 0.00113753i) q^{14} +(-3.25949 + 0.540627i) q^{15} +(-0.650805 - 0.313411i) q^{16} +(-1.33041 - 1.33041i) q^{17} +(2.61884 - 1.23588i) q^{18} +(-3.58912 - 5.71205i) q^{19} +(-0.884155 - 1.83597i) q^{20} +(-0.0174978 - 0.00511564i) q^{21} +(-2.97076 + 0.678057i) q^{22} +(1.51439 + 1.20769i) q^{23} +(3.40316 + 3.83842i) q^{24} +(0.302886 - 1.32703i) q^{25} +(-4.47714 - 2.81317i) q^{26} +(-5.19105 + 0.230112i) q^{27} -0.0112436i q^{28} +(5.18457 - 1.45609i) q^{29} +(-0.166298 - 3.18494i) q^{30} +(-4.73194 - 0.533162i) q^{31} +(-2.78047 + 4.42510i) q^{32} +(5.38683 + 0.937074i) q^{33} +(1.41992 - 1.13235i) q^{34} +(-0.0125182 + 0.0156973i) q^{35} +(-1.03463 - 3.03315i) q^{36} +(6.27435 + 2.19549i) q^{37} +(5.86691 - 2.82535i) q^{38} +(5.45989 + 7.75949i) q^{39} +(5.33262 - 1.86596i) q^{40} +(-1.30214 + 1.30214i) q^{41} +(0.00679802 - 0.0162310i) q^{42} +(0.496740 + 4.40869i) q^{43} +(0.377572 + 3.35104i) q^{44} +(-1.93253 + 5.38655i) q^{45} +(-1.32209 + 1.32209i) q^{46} +(-3.15765 + 1.10491i) q^{47} +(-1.02321 + 0.719973i) q^{48} +(6.30668 - 3.03714i) q^{49} +(1.24016 + 0.433949i) q^{50} +(-3.13499 + 0.889834i) q^{51} +(-3.64848 + 4.57504i) q^{52} +(5.78058 - 4.60986i) q^{53} +(0.340305 - 5.00414i) q^{54} +(3.20380 - 5.09882i) q^{55} +(0.0309765 + 0.00349021i) q^{56} +(-11.6686 + 0.609263i) q^{57} +(0.836360 + 5.13042i) q^{58} -13.5690i q^{59} +(-3.52316 - 0.211761i) q^{60} +(7.66936 + 4.81898i) q^{61} +(1.02282 - 4.48127i) q^{62} +(-0.0225023 + 0.0221510i) q^{63} +(-5.07355 - 4.04603i) q^{64} +(10.1874 - 2.32521i) q^{65} +(-1.48103 + 5.06578i) q^{66} +(-0.974487 - 2.02354i) q^{67} +(-1.06933 - 1.70183i) q^{68} +(3.10460 - 1.27168i) q^{69} +(-0.0137040 - 0.0137040i) q^{70} +(-9.47597 - 4.56339i) q^{71} +(8.67760 - 1.90891i) q^{72} +(-9.08130 + 1.02322i) q^{73} +(-2.78403 + 5.78109i) q^{74} +(-1.75173 - 1.57788i) q^{75} +(-2.38015 - 6.80207i) q^{76} +(0.0281332 - 0.0176773i) q^{77} +(-8.03300 + 4.39852i) q^{78} +(-0.743076 + 2.12359i) q^{79} +(0.306615 + 1.34337i) q^{80} +(-4.03205 + 8.04628i) q^{81} +(-1.10829 - 1.38975i) q^{82} +(8.26757 + 1.88702i) q^{83} +(-0.0170073 - 0.00948713i) q^{84} +(-0.401848 + 3.56650i) q^{85} -4.28251 q^{86} +(2.17213 - 9.07094i) q^{87} -9.34946 q^{88} +(-1.09875 + 9.75169i) q^{89} +(-4.95793 - 2.43585i) q^{90} +(0.0562099 + 0.0128295i) q^{91} +(1.29011 + 1.61775i) q^{92} +(-4.79920 + 6.70778i) q^{93} +(-0.718566 - 3.14824i) q^{94} +(-4.25023 + 12.1465i) q^{95} +(4.34740 + 7.93963i) q^{96} +(-2.33549 + 1.46749i) q^{97} +(2.23163 + 6.37763i) q^{98} +(5.96275 - 7.35756i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 12 q^{3} - 28 q^{4} - 14 q^{6} - 20 q^{7} - 14 q^{9} - 4 q^{10} - 8 q^{12} - 28 q^{13} - 16 q^{15} - 48 q^{16} - 28 q^{18} - 20 q^{19} + 26 q^{21} - 28 q^{22} + 58 q^{24} - 20 q^{25} + 36 q^{27}+ \cdots + 82 q^{99}+O(q^{100}) $ 96 * q - 12 * q^3 - 28 * q^4 - 14 * q^6 - 20 * q^7 - 14 * q^9 - 4 * q^10 - 8 * q^12 - 28 * q^13 - 16 * q^15 - 48 * q^16 - 28 * q^18 - 20 * q^19 + 26 * q^21 - 28 * q^22 + 58 * q^24 - 20 * q^25 + 36 * q^27 + 96 * q^30 - 32 * q^31 + 28 * q^33 - 28 * q^34 + 22 * q^36 - 4 * q^37 - 40 * q^39 - 48 * q^40 - 14 * q^42 - 32 * q^43 + 42 * q^45 + 120 * q^46 - 20 * q^48 + 4 * q^49 - 14 * q^51 + 72 * q^52 - 30 * q^54 + 148 * q^55 + 112 * q^58 + 20 * q^60 + 12 * q^61 - 14 * q^63 + 224 * q^64 - 32 * q^66 + 28 * q^67 + 10 * q^69 + 52 * q^70 - 44 * q^72 + 16 * q^73 - 144 * q^75 - 100 * q^76 - 102 * q^78 - 60 * q^79 - 146 * q^81 - 108 * q^82 - 64 * q^84 - 104 * q^85 - 70 * q^87 - 312 * q^88 - 96 * q^90 - 112 * q^91 - 70 * q^93 + 56 * q^94 - 168 * q^96 + 32 * q^97 + 82 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/87\mathbb{Z}\right)^\times$.

$n$	$31$	$59$
$\chi(n)$	$e\left(\frac{1}{28}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.108076	+	0.959202i	−0.0764214	+	0.678258i	0.895842	+	0.444372i	$0.146573\pi$
$2$	−0.108076	+	0.959202i	−0.0764214	+	0.678258i	−0.972264	+	0.233887i	$0.924856\pi$
$3$	0.843782	−	1.51262i	0.487158	−	0.873314i
$3$	0.843782	−	1.51262i	0.487158	−	0.873314i
$4$	1.04147	+	0.237708i	0.520734	+	0.118854i
$5$	−1.18935	−	1.49140i	−0.531895	−	0.666975i	0.441192	−	0.897413i	$-0.354556\pi$
$5$	−1.18935	−	1.49140i	−0.531895	−	0.666975i	−0.973087	+	0.230437i	$0.925984\pi$
$6$	1.35972	+	0.972836i	0.555103	+	0.397159i
$7$	−0.00234208	−	0.0102613i	−0.000885224	−	0.00387842i	0.974483	−	0.224460i	$-0.0720617\pi$
$7$	−0.00234208	−	0.0102613i	−0.000885224	−	0.00387842i	−0.975369	+	0.220581i	$0.929205\pi$
$8$	−0.978186	+	2.79549i	−0.345841	+	0.988357i
$9$	−1.57606	−	2.55265i	−0.525355	−	0.850883i
$10$	1.55910	−	0.979646i	0.493030	−	0.309791i
$11$	1.04262	+	2.97964i	0.314362	+	0.898396i	0.987324	+	0.158719i	$0.0507363\pi$
$11$	1.04262	+	2.97964i	0.314362	+	0.898396i	−0.672961	+	0.739678i	$0.734978\pi$
$12$	1.23833	−	1.37477i	0.357476	−	0.396863i
$13$	−2.37674	+	4.93536i	−0.659190	+	1.36882i	0.256345	+	0.966585i	$0.417482\pi$
$13$	−2.37674	+	4.93536i	−0.659190	+	1.36882i	−0.915535	+	0.402237i	$0.868233\pi$
$14$	0.0100958	−	0.00113753i	0.00269822	−	0.000304017i
$15$	−3.25949	+	0.540627i	−0.841596	+	0.139589i
$16$	−0.650805	−	0.313411i	−0.162701	−	0.0783528i
$17$	−1.33041	−	1.33041i	−0.322672	−	0.322672i	0.527119	−	0.849791i	$-0.323272\pi$
$17$	−1.33041	−	1.33041i	−0.322672	−	0.322672i	−0.849791	+	0.527119i	$0.823272\pi$
$18$	2.61884	−	1.23588i	0.617267	−	0.291301i
$19$	−3.58912	−	5.71205i	−0.823400	−	1.31043i	−0.948014	−	0.318228i	$-0.896912\pi$
$19$	−3.58912	−	5.71205i	−0.823400	−	1.31043i	0.124614	−	0.992205i	$-0.460231\pi$
$20$	−0.884155	−	1.83597i	−0.197703	−	0.410534i
$21$	−0.0174978	−	0.00511564i	−0.00381832	−	0.00111632i
$22$	−2.97076	+	0.678057i	−0.633369	+	0.144562i
$23$	1.51439	+	1.20769i	0.315773	+	0.251820i	0.768530	−	0.639813i	$-0.220988\pi$
$23$	1.51439	+	1.20769i	0.315773	+	0.251820i	−0.452758	+	0.891634i	$0.649560\pi$
$24$	3.40316	+	3.83842i	0.694667	+	0.783513i
$25$	0.302886	−	1.32703i	0.0605772	−	0.265406i
$26$	−4.47714	−	2.81317i	−0.878039	−	0.551709i
$27$	−5.19105	+	0.230112i	−0.999019	+	0.0442851i
$28$		−	0.0112436i		−	0.00212484i
$29$	5.18457	−	1.45609i	0.962751	−	0.270390i
$29$	5.18457	−	1.45609i	0.962751	−	0.270390i
$30$	−0.166298	−	3.18494i	−0.0303616	−	0.581487i
$31$	−4.73194	−	0.533162i	−0.849882	−	0.0957587i	−0.323730	−	0.946149i	$-0.604937\pi$
$31$	−4.73194	−	0.533162i	−0.849882	−	0.0957587i	−0.526152	+	0.850391i	$0.676366\pi$
$32$	−2.78047	+	4.42510i	−0.491523	+	0.782254i
$33$	5.38683	+	0.937074i	0.937726	+	0.163124i
$34$	1.41992	−	1.13235i	0.243514	−	0.194196i
$35$	−0.0125182	+	0.0156973i	−0.00211596	+	0.00265334i
$36$	−1.03463	−	3.03315i	−0.172439	−	0.505524i
$37$	6.27435	+	2.19549i	1.03150	+	0.360936i	0.792363	−	0.610050i	$-0.208851\pi$
$37$	6.27435	+	2.19549i	1.03150	+	0.360936i	0.239134	+	0.970986i	$0.423136\pi$
$38$	5.86691	−	2.82535i	0.951738	−	0.458333i
$39$	5.45989	+	7.75949i	0.874282	+	1.24251i
$40$	5.33262	−	1.86596i	0.843161	−	0.295035i
$41$	−1.30214	+	1.30214i	−0.203361	+	0.203361i	−0.801438	−	0.598078i	$-0.795931\pi$
$41$	−1.30214	+	1.30214i	−0.203361	+	0.203361i	0.598078	+	0.801438i	$0.295931\pi$
$42$	0.00679802	−	0.0162310i	0.00104896	−	0.00250450i
$43$	0.496740	+	4.40869i	0.0757522	+	0.672319i	0.973002	+	0.230796i	$0.0741330\pi$
$43$	0.496740	+	4.40869i	0.0757522	+	0.672319i	−0.897250	+	0.441523i	$0.854438\pi$
$44$	0.377572	+	3.35104i	0.0569211	+	0.505188i
$45$	−1.93253	+	5.38655i	−0.288085	+	0.802979i
$46$	−1.32209	+	1.32209i	−0.194931	+	0.194931i
$47$	−3.15765	+	1.10491i	−0.460591	+	0.161168i	−0.550593	−	0.834774i	$-0.685598\pi$
$47$	−3.15765	+	1.10491i	−0.460591	+	0.161168i	0.0900020	+	0.995942i	$0.471313\pi$
$48$	−1.02321	+	0.719973i	−0.147688	+	0.103919i
$49$	6.30668	−	3.03714i	0.900955	−	0.433877i
$50$	1.24016	+	0.433949i	0.175384	+	0.0613697i
$51$	−3.13499	+	0.889834i	−0.438986	+	0.124602i
$52$	−3.64848	+	4.57504i	−0.505953	+	0.634445i
$53$	5.78058	−	4.60986i	0.794024	−	0.633213i	−0.140110	−	0.990136i	$-0.544746\pi$
$53$	5.78058	−	4.60986i	0.794024	−	0.633213i	0.934134	+	0.356923i	$0.116174\pi$
$54$	0.340305	−	5.00414i	0.0463097	−	0.680977i
$55$	3.20380	−	5.09882i	0.432000	−	0.687525i
$56$	0.0309765	+	0.00349021i	0.00413941	+	0.000466400i
$57$	−11.6686	+	0.609263i	−1.54555	+	0.0806988i
$58$	0.836360	+	5.13042i	0.109819	+	0.673657i
$59$		−	13.5690i		−	1.76653i	−0.468870	−	0.883267i	$-0.655339\pi$
$59$		−	13.5690i		−	1.76653i	0.468870	−	0.883267i	$-0.344661\pi$
$60$	−3.52316	−	0.211761i	−0.454838	−	0.0273383i
$61$	7.66936	+	4.81898i	0.981961	+	0.617007i	0.924436	−	0.381337i	$-0.124536\pi$
$61$	7.66936	+	4.81898i	0.981961	+	0.617007i	0.0575249	+	0.998344i	$0.481679\pi$
$62$	1.02282	−	4.48127i	0.129898	−	0.569122i
$63$	−0.0225023	+	0.0221510i	−0.00283503	+	0.00279077i
$64$	−5.07355	−	4.04603i	−0.634194	−	0.505753i
$65$	10.1874	−	2.32521i	1.26359	−	0.288406i
$66$	−1.48103	+	5.06578i	−0.182302	+	0.623555i
$67$	−0.974487	−	2.02354i	−0.119052	−	0.247215i	0.832923	−	0.553389i	$-0.186666\pi$
$67$	−0.974487	−	2.02354i	−0.119052	−	0.247215i	−0.951976	+	0.306173i	$0.900951\pi$
$68$	−1.06933	−	1.70183i	−0.129675	−	0.206377i
$69$	3.10460	−	1.27168i	0.373750	−	0.153093i
$70$	−0.0137040	−	0.0137040i	−0.00163794	−	0.00163794i
$71$	−9.47597	−	4.56339i	−1.12459	−	0.541575i	−0.223283	−	0.974754i	$-0.571678\pi$
$71$	−9.47597	−	4.56339i	−1.12459	−	0.541575i	−0.901308	+	0.433179i	$0.857392\pi$
$72$	8.67760	−	1.90891i	1.02267	−	0.224967i
$73$	−9.08130	+	1.02322i	−1.06289	+	0.119758i	−0.626050	−	0.779783i	$-0.715329\pi$
$73$	−9.08130	+	1.02322i	−1.06289	+	0.119758i	−0.436836	+	0.899541i	$0.643901\pi$
$74$	−2.78403	+	5.78109i	−0.323637	+	0.672038i
$75$	−1.75173	−	1.57788i	−0.202272	−	0.182198i
$76$	−2.38015	−	6.80207i	−0.273022	−	0.780251i
$77$	0.0281332	−	0.0176773i	0.00320608	−	0.00201451i
$78$	−8.03300	+	4.39852i	−0.909558	+	0.498035i
$79$	−0.743076	+	2.12359i	−0.0836026	+	0.238923i	−0.978094	−	0.208162i	$-0.933252\pi$
$79$	−0.743076	+	2.12359i	−0.0836026	+	0.238923i	0.894492	+	0.447084i	$0.147538\pi$
$80$	0.306615	+	1.34337i	0.0342806	+	0.150193i
$81$	−4.03205	+	8.04628i	−0.448005	+	0.894031i
$82$	−1.10829	−	1.38975i	−0.122390	−	0.153472i
$83$	8.26757	+	1.88702i	0.907484	+	0.207127i	0.650694	−	0.759340i	$-0.274478\pi$
$83$	8.26757	+	1.88702i	0.907484	+	0.207127i	0.256790	+	0.966467i	$0.417335\pi$
$84$	−0.0170073	−	0.00948713i	−0.00185565	−	0.00103513i
$85$	−0.401848	+	3.56650i	−0.0435866	+	0.386842i
$86$	−4.28251			−0.461795
$87$	2.17213	−	9.07094i	0.232876	−	0.972506i
$88$	−9.34946			−0.996655
$89$	−1.09875	+	9.75169i	−0.116467	+	1.03368i	0.790496	+	0.612467i	$0.209823\pi$
$89$	−1.09875	+	9.75169i	−0.116467	+	1.03368i	−0.906963	+	0.421210i	$0.861606\pi$
$90$	−4.95793	−	2.43585i	−0.522612	−	0.256761i
$91$	0.0562099	+	0.0128295i	0.00589240	+	0.00134490i
$92$	1.29011	+	1.61775i	0.134504	+	0.168662i
$93$	−4.79920	+	6.70778i	−0.497654	+	0.695564i
$94$	−0.718566	−	3.14824i	−0.0741144	−	0.324716i
$95$	−4.25023	+	12.1465i	−0.436064	+	1.24620i
$96$	4.34740	+	7.93963i	0.443704	+	0.810335i
$97$	−2.33549	+	1.46749i	−0.237133	+	0.149001i	−0.645357	−	0.763881i	$-0.723291\pi$
$97$	−2.33549	+	1.46749i	−0.237133	+	0.149001i	0.408223	+	0.912882i	$0.366148\pi$
$98$	2.23163	+	6.37763i	0.225428	+	0.644237i
$99$	5.96275	−	7.35756i	0.599279	−	0.739462i
$100$	0.630892	−	1.31006i	0.0630892	−	0.131006i
$101$	13.9657	−	1.57355i	1.38963	−	0.156574i	0.614773	−	0.788704i	$-0.289248\pi$
$101$	13.9657	−	1.57355i	1.38963	−	0.156574i	0.774862	+	0.632130i	$0.217819\pi$
$102$	−0.514714	−	3.10326i	−0.0509643	−	0.307268i
$103$	0.960655	+	0.462627i	0.0946561	+	0.0455840i	0.480613	−	0.876933i	$-0.340414\pi$
$103$	0.960655	+	0.462627i	0.0946561	+	0.0455840i	−0.385957	+	0.922517i	$0.626129\pi$
$104$	−11.4719	−	11.4719i	−1.12491	−	1.12491i
$105$	0.0131815	+	0.0321805i	0.00128639	+	0.00314049i
$106$	3.79705	+	6.04296i	0.368802	+	0.586944i
$107$	−2.05971	−	4.27703i	−0.199119	−	0.413476i	0.777369	−	0.629045i	$-0.216554\pi$
$107$	−2.05971	−	4.27703i	−0.199119	−	0.413476i	−0.976489	+	0.215569i	$0.930839\pi$
$108$	−5.46101	−	0.994302i	−0.525486	−	0.0956767i
$109$	12.2855	−	2.80408i	1.17674	−	0.268582i	0.410938	−	0.911663i	$-0.365201\pi$
$109$	12.2855	−	2.80408i	1.17674	−	0.268582i	0.765798	+	0.643081i	$0.222344\pi$
$110$	4.54454	+	3.62415i	0.433305	+	0.345549i
$111$	8.61514	−	7.63822i	0.817713	−	0.724988i
$112$	−0.00169178	+	0.00741217i	−0.000159858	+	0.000700384i
$113$	−15.0759	−	9.47284i	−1.41822	−	0.891130i	−0.418372	−	0.908276i	$-0.637399\pi$
$113$	−15.0759	−	9.47284i	−1.41822	−	0.891130i	−0.999853	+	0.0171460i	$0.994542\pi$
$114$	0.676692	−	11.2584i	0.0633781	−	1.05445i
$115$		−	3.69494i		−	0.344555i
$116$	5.74569	−	0.284060i	0.533474	−	0.0263743i
$117$	16.3441	−	1.71145i	1.51102	−	0.158223i
$118$	13.0154	+	1.46649i	1.19817	+	0.135001i
$119$	−0.0105359	+	0.0167677i	−0.000965820	+	0.00153709i
$120$	1.67706	−	9.64071i	0.153094	−	0.880072i
$121$	0.808932	−	0.645102i	0.0735393	−	0.0586456i
$122$	−5.45125	+	6.83565i	−0.493533	+	0.618871i
$123$	0.870929	+	3.06838i	0.0785290	+	0.276667i
$124$	−4.80143	−	1.68009i	−0.431181	−	0.150877i
$125$	−10.9327	+	5.26491i	−0.977851	+	0.470908i
$126$	−0.0188154	−	0.0239783i	−0.00167621	−	0.00213616i
$127$	−20.0239	+	7.00667i	−1.77683	+	0.621741i	−0.999969	−	0.00792407i	$-0.997478\pi$
$127$	−20.0239	+	7.00667i	−1.77683	+	0.621741i	−0.776866	+	0.629666i	$0.783192\pi$
$128$	−2.96159	+	2.96159i	−0.261770	+	0.261770i
$129$	7.08783	+	2.96859i	0.624049	+	0.261370i
$130$	1.12933	+	10.0231i	0.0990487	+	0.879082i
$131$	0.371859	+	3.30034i	0.0324894	+	0.288352i	0.999442	+	0.0333961i	$0.0106323\pi$
$131$	0.371859	+	3.30034i	0.0324894	+	0.288352i	−0.966953	+	0.254956i	$0.917939\pi$
$132$	5.38745	+	2.25642i	0.468918	+	0.196397i
$133$	−0.0502072	+	0.0502072i	−0.00435352	+	0.00435352i
$134$	2.04631	−	0.716033i	0.176774	−	0.0618558i
$135$	6.51719	+	7.46827i	0.560910	+	0.642766i
$136$	5.02054	−	2.41777i	0.430508	−	0.207322i
$137$	14.4370	+	5.05173i	1.23344	+	0.431598i	0.866748	−	0.498746i	$-0.166206\pi$
$137$	14.4370	+	5.05173i	1.23344	+	0.431598i	0.366688	+	0.930344i	$0.380492\pi$
$138$	0.884268	+	3.11537i	0.0752739	+	0.265198i
$139$	8.97557	−	11.2550i	0.761298	−	0.954638i	−0.238566	−	0.971126i	$-0.576677\pi$
$139$	8.97557	−	11.2550i	0.761298	−	0.954638i	0.999864	+	0.0164886i	$0.00524871\pi$
$140$	−0.0167687	+	0.0133726i	−0.00141721	+	0.00113019i
$141$	−0.993056	+	5.70865i	−0.0836304	+	0.480755i
$142$	5.40134	−	8.59618i	0.453270	−	0.721376i
$143$	−17.1837	−	1.93613i	−1.43697	−	0.161908i
$144$	0.225681	+	2.15523i	0.0188068	+	0.179603i
$145$	−8.33791	−	6.00047i	−0.692426	−	0.498312i
$146$		−	8.82139i		−	0.730063i
$147$	0.727417	−	12.1023i	0.0599963	−	0.998183i
$148$	6.01265	+	3.77800i	0.494237	+	0.310549i
$149$	−1.87094	+	8.19713i	−0.153274	+	0.671535i	0.838647	+	0.544675i	$0.183347\pi$
$149$	−1.87094	+	8.19713i	−0.153274	+	0.671535i	−0.991921	+	0.126860i	$0.959510\pi$
$150$	1.70282	−	1.50973i	0.139035	−	0.123269i
$151$	−1.02137	−	0.814517i	−0.0831181	−	0.0662844i	0.581049	−	0.813868i	$-0.302642\pi$
$151$	−1.02137	−	0.814517i	−0.0831181	−	0.0662844i	−0.664167	+	0.747584i	$0.731214\pi$
$152$	19.4788	−	4.44591i	1.57994	−	0.360611i
$153$	−1.29926	+	5.49288i	−0.105039	+	0.444073i
$154$	0.0139156	+	0.0288959i	0.00112135	+	0.00232850i
$155$	4.83280	+	7.69135i	0.388179	+	0.617784i
$156$	3.84180	+	9.37911i	0.307591	+	0.750930i
$157$	−1.96964	−	1.96964i	−0.157194	−	0.157194i	0.624128	−	0.781322i	$-0.285454\pi$
$157$	−1.96964	−	1.96964i	−0.157194	−	0.157194i	−0.781322	+	0.624128i	$0.785454\pi$
$158$	−1.95664	−	0.942270i	−0.155662	−	0.0749630i
$159$	−2.09544	−	12.6336i	−0.166179	−	1.00191i
$160$	9.90656	−	1.11620i	0.783183	−	0.0882435i
$161$	0.00884566	−	0.0183682i	0.000697136	−	0.00144762i
$162$	−7.28224	−	4.73716i	−0.572147	−	0.372186i
$163$	4.19472	+	11.9878i	0.328556	+	0.938959i	0.983122	+	0.182954i	$0.0585658\pi$
$163$	4.19472	+	11.9878i	0.328556	+	0.938959i	−0.654566	+	0.756005i	$0.727148\pi$
$164$	−1.66567	+	1.04661i	−0.130067	+	0.0817265i
$165$	−5.00929	−	9.14844i	−0.389973	−	0.712205i
$166$	−2.70356	+	7.72633i	−0.209837	+	0.599680i
$167$	4.29738	+	18.8280i	0.332541	+	1.45696i	0.814192	+	0.580595i	$0.197180\pi$
$167$	4.29738	+	18.8280i	0.332541	+	1.45696i	−0.481651	+	0.876363i	$0.659963\pi$
$168$	0.0314168	−	0.0439108i	0.00242386	−	0.00338779i
$169$	−10.6035	−	13.2964i	−0.815653	−	1.02280i
$170$	−3.37757	−	0.770908i	−0.259048	−	0.0591259i
$171$	−8.92418	+	18.1643i	−0.682449	+	1.38906i
$172$	−0.530643	+	4.70959i	−0.0404611	+	0.359103i
$173$	−17.2438			−1.31102			−0.655511	−	0.755186i	$-0.727547\pi$
$173$	−17.2438			−1.31102			−0.655511	+	0.755186i	$0.727547\pi$
$174$	8.46611	+	3.06386i	0.641814	+	0.232271i
$175$	−0.0143265			−0.00108298
$176$	0.255310	−	2.26594i	0.0192447	−	0.170801i
$177$	−20.5248	−	11.4493i	−1.54274	−	0.860581i
$178$	−9.23509	−	2.10785i	−0.692199	−	0.157990i
$179$	−6.70948	−	8.41342i	−0.501490	−	0.628849i	0.465075	−	0.885271i	$-0.346027\pi$
$179$	−6.70948	−	8.41342i	−0.501490	−	0.628849i	−0.966565	+	0.256423i	$0.917456\pi$
$180$	−3.29309	+	5.15054i	−0.245453	+	0.383898i
$181$	2.35283	+	10.3084i	0.174885	+	0.766219i	0.983942	+	0.178489i	$0.0571210\pi$
$181$	2.35283	+	10.3084i	0.174885	+	0.766219i	−0.809057	+	0.587730i	$0.800022\pi$
$182$	−0.0183811	+	0.0525301i	−0.00136250	+	0.00389379i
$183$	13.7606	−	7.53469i	1.01721	−	0.556980i
$184$	−4.85745	+	3.05214i	−0.358096	+	0.225006i
$185$	−4.18806	−	11.9688i	−0.307913	−	0.879964i
$186$	−5.91544	−	5.32836i	−0.433741	−	0.390694i
$187$	2.57703	−	5.35126i	0.188451	−	0.391323i
$188$	−3.55124	+	0.400129i	−0.259001	+	0.0291824i
$189$	0.0145191	+	0.0527282i	0.00105611	+	0.00383541i
$190$	−11.1916	−	5.38957i	−0.811921	−	0.391001i
$191$	3.62170	+	3.62170i	0.262057	+	0.262057i	0.825889	−	0.563832i	$-0.190674\pi$
$191$	3.62170	+	3.62170i	0.262057	+	0.262057i	−0.563832	+	0.825889i	$0.690674\pi$
$192$	−10.4011	+	4.26042i	−0.750634	+	0.307469i
$193$	−6.48683	−	10.3237i	−0.466932	−	0.743118i	0.527379	−	0.849630i	$-0.323175\pi$
$193$	−6.48683	−	10.3237i	−0.466932	−	0.743118i	−0.994311	+	0.106512i	$0.966032\pi$
$194$	−1.15521	−	2.39881i	−0.0829390	−	0.172225i
$195$	5.07878	−	17.3717i	0.363699	−	1.24401i
$196$	7.29016	−	1.66393i	0.520725	−	0.118852i
$197$	7.20267	+	5.74393i	0.513169	+	0.409238i	0.845541	−	0.533910i	$-0.179278\pi$
$197$	7.20267	+	5.74393i	0.513169	+	0.409238i	−0.332373	+	0.943148i	$0.607849\pi$
$198$	6.41296	+	6.51466i	0.455749	+	0.462977i
$199$	−4.61512	+	20.2202i	−0.327157	+	1.43337i	0.497365	+	0.867541i	$0.334301\pi$
$199$	−4.61512	+	20.2202i	−0.327157	+	1.43337i	−0.824522	+	0.565829i	$0.808556\pi$
$200$	3.41343	+	2.14480i	0.241366	+	0.151660i
$201$	−3.88311	−	0.233397i	−0.273894	−	0.0164625i
$202$			13.5660i			0.954497i
$203$	−0.0270842	−	0.0497904i	−0.00190094	−	0.00349460i
$204$	−3.47651	+	0.181522i	−0.243404	+	0.0127091i
$205$	3.49073	+	0.393311i	0.243803	+	0.0274700i
$206$	−0.547577	+	0.871463i	−0.0381515	+	0.0607177i
$207$	0.696025	−	5.76911i	0.0483771	−	0.400981i
$208$	3.09359	−	2.46706i	0.214502	−	0.171060i
$209$	13.2778	−	16.6498i	0.918442	−	1.15169i
$210$	−0.0322922	+	0.00916582i	−0.00222837	+	0.000632502i
$211$	−18.0480	−	6.31528i	−1.24248	−	0.434762i	−0.372583	−	0.927999i	$-0.621528\pi$
$211$	−18.0480	−	6.31528i	−1.24248	−	0.434762i	−0.869895	+	0.493237i	$0.835813\pi$
$212$	7.11609	−	3.42693i	0.488735	−	0.235362i
$213$	−14.8983	+	10.4831i	−1.02082	+	0.718289i
$214$	4.32514	−	1.51343i	0.295660	−	0.103456i
$215$	5.98433	−	5.98433i	0.408128	−	0.408128i
$216$	4.43454	−	14.7367i	0.301732	−	1.00270i
$217$	0.00561165	+	0.0498048i	0.000380944	+	0.00338097i
$218$	1.36191	+	12.0873i	0.0922405	+	0.818657i
$219$	−6.11489	+	14.6000i	−0.413206	+	0.986574i
$220$	4.54868	−	4.54868i	0.306672	−	0.306672i
$221$	9.72809	−	3.40401i	0.654382	−	0.228978i
$222$	6.39551	+	9.08917i	0.429238	+	0.610025i
$223$	6.08242	−	2.92914i	0.407309	−	0.196150i	−0.218999	−	0.975725i	$-0.570279\pi$
$223$	6.08242	−	2.92914i	0.407309	−	0.196150i	0.626309	+	0.779575i	$0.284565\pi$
$224$	0.0519195	+	0.0181674i	0.00346902	+	0.00121386i
$225$	−3.86481	+	1.31832i	−0.257654	+	0.0878882i
$226$	10.7157	−	13.4371i	0.712799	−	0.893822i
$227$	−4.06313	+	3.24024i	−0.269680	+	0.215062i	−0.748987	−	0.662585i	$-0.769459\pi$
$227$	−4.06313	+	3.24024i	−0.269680	+	0.215062i	0.479307	+	0.877647i	$0.340888\pi$
$228$	−12.2973	−	2.13920i	−0.814409	−	0.141672i
$229$	−2.02600	+	3.22436i	−0.133882	+	0.213072i	−0.906936	−	0.421268i	$-0.861585\pi$
$229$	−2.02600	+	3.22436i	−0.133882	+	0.213072i	0.773054	+	0.634340i	$0.218728\pi$
$230$	3.54419	+	0.399335i	0.233697	+	0.0263313i
$231$	−0.00300077	−	0.0574708i	−0.000197436	−	0.00378130i
$232$	−1.00097	+	15.9178i	−0.0657170	+	1.04505i
$233$		−	8.32635i		−	0.545477i	−0.962088	−	0.272739i	$-0.912071\pi$
$233$		−	8.32635i		−	0.545477i	0.962088	−	0.272739i	$-0.0879294\pi$
$234$	−0.124789	+	15.8623i	−0.00815774	+	1.03695i
$235$	5.40343	+	3.39520i	0.352481	+	0.221479i
$236$	3.22546	−	14.1317i	0.209960	−	0.919894i
$237$	2.58520	+	2.91584i	0.167927	+	0.189404i
$238$	−0.0149450	−	0.0119182i	−0.000968738	−	0.000772542i
$239$	−15.8176	+	3.61027i	−1.02316	+	0.233529i	−0.701003	−	0.713158i	$-0.747264\pi$
$239$	−15.8176	+	3.61027i	−1.02316	+	0.233529i	−0.322154	+	0.946687i	$0.604407\pi$
$240$	2.29073	+	0.669717i	0.147866	+	0.0432300i
$241$	2.12766	+	4.41813i	0.137055	+	0.284597i	0.958188	−	0.286140i	$-0.0923721\pi$
$241$	2.12766	+	4.41813i	0.137055	+	0.284597i	−0.821133	+	0.570736i	$0.806658\pi$
$242$	0.531357	+	0.845650i	0.0341569	+	0.0543604i
$243$	8.76883	+	12.8883i	0.562521	+	0.826783i
$244$	6.84188	+	6.84188i	0.438006	+	0.438006i
$245$	−12.0305	−	5.79357i	−0.768599	−	0.370138i
$246$	−3.03732	+	0.503778i	−0.193653	+	0.0321197i
$247$	36.7214	−	4.13751i	2.33653	−	0.263263i
$248$	6.11917	−	12.7066i	0.388568	−	0.806869i
$249$	9.83038	−	10.9135i	0.622975	−	0.691615i
$250$	−3.86855	−	11.0557i	−0.244669	−	0.699223i
$251$	−13.0995	+	8.23098i	−0.826835	+	0.519535i	−0.877722	−	0.479170i	$-0.840938\pi$
$251$	−13.0995	+	8.23098i	−0.826835	+	0.519535i	0.0508877	+	0.998704i	$0.483795\pi$
$252$	−0.0287009	+	0.0177206i	−0.00180799	+	0.00111629i
$253$	−2.01954	+	5.77152i	−0.126967	+	0.362852i
$254$	−4.55671	−	19.9642i	−0.285913	−	1.25267i
$255$	5.05571	+	3.61720i	0.316601	+	0.226518i
$256$	−10.6127	−	13.3079i	−0.663296	−	0.831747i
$257$	20.4103	+	4.65852i	1.27316	+	0.290591i	0.805118	−	0.593115i	$-0.202102\pi$
$257$	20.4103	+	4.65852i	1.27316	+	0.290591i	0.468043	+	0.883706i	$0.344959\pi$
$258$	−3.61351	+	6.47783i	−0.224967	+	0.403292i
$259$	0.00783362	−	0.0695253i	0.000486757	−	0.00432009i
$260$	11.1626			0.692273
$261$	−11.8881	−	10.9395i	−0.735856	−	0.677138i
$262$	−3.20588			−0.198060
$263$	−0.116740	+	1.03609i	−0.00719847	+	0.0638882i	−0.996798	−	0.0799625i	$-0.974520\pi$
$263$	−0.116740	+	1.03609i	−0.00719847	+	0.0638882i	0.989599	+	0.143851i	$0.0459485\pi$
$264$	−7.88890	+	14.1422i	−0.485528	+	0.870393i
$265$	−13.7503	−	3.13842i	−0.844675	−	0.192792i
$266$	−0.0427327	−	0.0535851i	−0.00262011	−	0.00328551i
$267$	13.8235	+	9.89030i	0.845986	+	0.605276i
$268$	−0.533884	−	2.33910i	−0.0326121	−	0.142883i
$269$	0.173542	−	0.495955i	0.0105810	−	0.0302389i	−0.938472	−	0.345356i	$-0.887758\pi$
$269$	0.173542	−	0.495955i	0.0105810	−	0.0302389i	0.949053	+	0.315117i	$0.102044\pi$
$270$	−7.86793	+	5.44416i	−0.478827	+	0.331321i
$271$	14.3636	−	9.02526i	0.872528	−	0.548246i	−0.0197129	−	0.999806i	$-0.506275\pi$
$271$	14.3636	−	9.02526i	0.872528	−	0.548246i	0.892241	+	0.451560i	$0.149132\pi$
$272$	0.448872	+	1.28280i	0.0272169	+	0.0777813i
$273$	0.0668352	−	0.0741991i	0.00404505	−	0.00449074i
$274$	−6.40592	+	13.3020i	−0.386996	+	0.803605i
$275$	4.26987	−	0.481099i	0.257483	−	0.0290114i
$276$	3.53563	−	0.586428i	0.212820	−	0.0352988i
$277$	4.15853	+	2.00264i	0.249862	+	0.120327i	0.554623	−	0.832102i	$-0.312862\pi$
$277$	4.15853	+	2.00264i	0.249862	+	0.120327i	−0.304761	+	0.952429i	$0.598577\pi$
$278$	9.82579	+	9.82579i	0.589312	+	0.589312i
$279$	6.09687	+	12.9193i	0.365010	+	0.773458i
$280$	−0.0316367	−	0.0503495i	−0.00189066	−	0.00300896i
$281$	9.61324	+	19.9621i	0.573478	+	1.19084i	0.962920	+	0.269788i	$0.0869537\pi$
$281$	9.61324	+	19.9621i	0.573478	+	1.19084i	−0.389442	+	0.921051i	$0.627332\pi$
$282$	−5.36842	−	1.56951i	−0.319685	−	0.0934630i
$283$	2.75082	−	0.627856i	0.163519	−	0.0373222i	−0.139978	−	0.990155i	$-0.544703\pi$
$283$	2.75082	−	0.627856i	0.163519	−	0.0373222i	0.303497	+	0.952833i	$0.401846\pi$
$284$	−8.78416	−	7.00514i	−0.521244	−	0.415678i
$285$	14.7868	+	16.6780i	0.875892	+	0.987917i
$286$	3.71429	−	16.2734i	0.219630	−	0.962264i
$287$	0.0164115	+	0.0103120i	0.000968739	+	0.000608699i
$288$	15.6779	+	0.123339i	0.923831	+	0.00726781i
$289$		−	13.4600i		−	0.791766i
$290$	6.65680	−	7.34924i	0.390900	−	0.431562i
$291$	0.249110	+	4.77096i	0.0146031	+	0.279679i
$292$	−9.70110	−	1.09305i	−0.567714	−	0.0639660i
$293$	6.53890	−	10.4066i	0.382006	−	0.607960i	−0.599274	−	0.800544i	$-0.704544\pi$
$293$	6.53890	−	10.4066i	0.382006	−	0.607960i	0.981280	+	0.192584i	$0.0616869\pi$
$294$	11.5300	+	2.00571i	0.672441	+	0.116975i
$295$	−20.2368	+	16.1383i	−1.17823	+	0.939611i
$296$	−12.2750	+	15.3923i	−0.713468	+	0.894661i
$297$	−6.09796	−	15.2276i	−0.353840	−	0.883593i
$298$	−7.66050	−	2.68053i	−0.443761	−	0.155279i
$299$	−9.55970	+	4.60371i	−0.552852	+	0.266239i
$300$	−1.44929	−	2.05971i	−0.0836750	−	0.118917i
$301$	0.0440757	−	0.0154227i	0.00254048	−	0.000888952i
$302$	0.891672	−	0.891672i	0.0513100	−	0.0513100i
$303$	9.40378	−	22.4525i	0.540233	−	1.28986i
$304$	0.545596	+	4.84230i	0.0312921	+	0.277725i
$305$	−1.93455	−	17.1696i	−0.110772	−	0.983127i
$306$	−5.12836	−	1.83990i	−0.293169	−	0.105180i
$307$	−3.00770	+	3.00770i	−0.171659	+	0.171659i	−0.787708	−	0.616049i	$-0.788732\pi$
$307$	−3.00770	+	3.00770i	−0.171659	+	0.171659i	0.616049	+	0.787708i	$0.288732\pi$
$308$	0.0335019	−	0.0117228i	0.00190895	−	0.000667969i
$309$	1.51036	−	1.06275i	0.0859216	−	0.0604579i
$310$	−7.89987	+	3.80438i	−0.448682	+	0.216074i
$311$	−4.17180	−	1.45978i	−0.236561	−	0.0827764i	0.209395	−	0.977831i	$-0.432851\pi$
$311$	−4.17180	−	1.45978i	−0.236561	−	0.0827764i	−0.445956	+	0.895055i	$0.647136\pi$
$312$	−27.0324	+	7.67287i	−1.53041	+	0.434391i
$313$	3.57654	−	4.48484i	0.202158	−	0.253498i	−0.670410	−	0.741991i	$-0.733882\pi$
$313$	3.57654	−	4.48484i	0.202158	−	0.253498i	0.872568	+	0.488493i	$0.162453\pi$
$314$	2.10215	−	1.67641i	0.118631	−	0.0946054i
$315$	0.0597993	+	0.00721461i	0.00336931	+	0.000406497i
$316$	−1.27868	+	2.03501i	−0.0719316	+	0.114479i
$317$	−2.26036	−	0.254682i	−0.126955	−	0.0143043i	0.0482585	−	0.998835i	$-0.484633\pi$
$317$	−2.26036	−	0.254682i	−0.126955	−	0.0143043i	−0.175213	+	0.984531i	$0.556061\pi$
$318$	12.3446	−	0.644559i	0.692251	−	0.0361451i
$319$	9.74419	+	13.9300i	0.545570	+	0.779931i
$320$			12.3789i			0.692000i
$321$	−8.20748	−	0.493315i	−0.458097	−	0.0275341i
$322$	0.0166628	+	0.0104699i	0.000928583	+	0.000583467i
$323$	−2.82437	+	12.3744i	−0.157152	+	0.688528i
$324$	−6.11191	+	7.42149i	−0.339551	+	0.412305i
$325$	5.82949	+	4.64886i	0.323362	+	0.257872i
$326$	−11.9521	+	2.72799i	−0.661965	+	0.151089i
$327$	6.12475	−	20.9494i	0.338700	−	1.15850i
$328$	−2.36640	−	4.91388i	−0.130662	−	0.271323i
$329$	0.0187333	+	0.0298140i	0.00103280	+	0.00164370i
$330$	9.31659	−	3.81619i	0.512861	−	0.210074i
$331$	15.8631	+	15.8631i	0.871916	+	0.871916i	0.992681	−	0.120765i	$-0.0385347\pi$
$331$	15.8631	+	15.8631i	0.871916	+	0.871916i	−0.120765	+	0.992681i	$0.538535\pi$
$332$	8.16185	+	3.93054i	0.447939	+	0.215716i
$333$	−4.28446	−	19.4765i	−0.234787	−	1.06730i
$334$	−18.5243	+	2.08719i	−1.01361	+	0.114206i
$335$	−1.85891	+	3.86006i	−0.101563	+	0.210898i
$336$	0.00978433	+	0.00881328i	0.000533779	+	0.000480804i
$337$	−7.66711	−	21.9114i	−0.417654	−	1.19359i	−0.940095	−	0.340912i	$-0.889264\pi$
$337$	−7.66711	−	21.9114i	−0.417654	−	1.19359i	0.522441	−	0.852675i	$-0.325022\pi$
$338$	13.8999	−	8.73388i	0.756054	−	0.475060i
$339$	−27.0497	+	14.8112i	−1.46914	+	0.804435i
$340$	−1.26630	+	3.61887i	−0.0686747	+	0.196261i
$341$	−3.34500	−	14.6554i	−0.181142	−	0.793634i
$342$	−16.4588	−	10.5232i	−0.889988	−	0.569031i
$343$	−0.0918725	−	0.115204i	−0.00496065	−	0.00622046i
$344$	−12.8104	−	2.92388i	−0.690689	−	0.157645i
$345$	−5.58905	−	3.11772i	−0.300905	−	0.167853i
$346$	1.86364	−	16.5403i	0.100190	−	0.889212i
$347$	−1.67185			−0.0897495			−0.0448748	−	0.998993i	$-0.514289\pi$
$347$	−1.67185			−0.0897495			−0.0448748	+	0.998993i	$0.514289\pi$
$348$	4.41843	−	8.93075i	0.236853	−	0.478739i
$349$	−16.7492			−0.896564			−0.448282	−	0.893892i	$-0.647964\pi$
$349$	−16.7492			−0.896564			−0.448282	+	0.893892i	$0.647964\pi$
$350$	0.00154835	−	0.0137420i	8.27629e−5	−	0.000734541i
$351$	11.2021	−	26.1666i	0.597925	−	1.39667i
$352$	−16.0842	−	3.67111i	−0.857290	−	0.195671i
$353$	−2.54703	−	3.19387i	−0.135565	−	0.169993i	0.709415	−	0.704791i	$-0.248959\pi$
$353$	−2.54703	−	3.19387i	−0.135565	−	0.169993i	−0.844980	+	0.534798i	$0.820388\pi$
$354$	13.2004	−	18.4500i	0.701594	−	0.980609i
$355$	4.46444	+	19.5600i	0.236948	+	1.03814i
$356$	−3.46237	+	9.89488i	−0.183505	+	0.524428i
$357$	0.0164733	+	0.0300851i	0.000871859	+	0.00159227i
$358$	8.79531	−	5.52646i	0.464846	−	0.292082i
$359$	−6.56170	−	18.7523i	−0.346314	−	0.989707i	−0.976920	−	0.213605i	$-0.931480\pi$
$359$	−6.56170	−	18.7523i	−0.346314	−	0.989707i	0.630607	−	0.776103i	$-0.282806\pi$
$360$	−13.1677	−	10.6714i	−0.693998	−	0.562434i
$361$	−11.5019	+	23.8840i	−0.605365	+	1.25705i
$362$	−10.1421	+	1.14275i	−0.533060	+	0.0600614i
$363$	−0.293234	−	1.76794i	−0.0153908	−	0.0927926i
$364$	0.0554911	+	0.0267231i	0.00290852	+	0.00140067i
$365$	12.3269	+	12.3269i	0.645220	+	0.645220i
$366$	5.74010	+	14.0135i	0.300040	+	0.732497i
$367$	−5.03322	−	8.01032i	−0.262732	−	0.418136i	0.689142	−	0.724627i	$-0.257988\pi$
$367$	−5.03322	−	8.01032i	−0.262732	−	0.418136i	−0.951873	+	0.306491i	$0.900845\pi$
$368$	−0.607072	−	1.26060i	−0.0316458	−	0.0657132i
$369$	5.37618	+	1.27166i	0.279873	+	0.0661998i
$370$	11.9331	−	2.72366i	0.620374	−	0.141596i
$371$	−0.0608419	−	0.0485198i	−0.00315876	−	0.00251902i
$372$	−6.59271	+	5.84512i	−0.341816	+	0.303056i
$373$	1.78879	−	7.83720i	0.0926200	−	0.405795i	−0.907271	−	0.420546i	$-0.861838\pi$
$373$	1.78879	−	7.83720i	0.0926200	−	0.405795i	0.999891	+	0.0147512i	$0.00469563\pi$
$374$	4.85443	+	3.05024i	0.251016	+	0.157724i
$375$	−1.26098	+	20.9795i	−0.0651170	+	1.08338i
$376$		−	9.90801i		−	0.510967i
$377$	−5.13605	+	29.0485i	−0.264520	+	1.49607i
$378$	−0.0521462	+	0.00822813i	−0.00268211	+	0.000423209i
$379$	17.0276	+	1.91855i	0.874648	+	0.0985491i	0.537863	−	0.843032i	$-0.319232\pi$
$379$	17.0276	+	1.91855i	0.874648	+	0.0985491i	0.336785	+	0.941582i	$0.390660\pi$
$380$	−7.31379	+	11.6398i	−0.375189	+	0.597111i
$381$	−6.29736	+	36.2008i	−0.322623	+	1.85462i
$382$	−3.86536	+	3.08252i	−0.197769	+	0.157715i
$383$	4.63776	−	5.81556i	0.236978	−	0.297161i	−0.649094	−	0.760708i	$-0.724852\pi$
$383$	4.63776	−	5.81556i	0.236978	−	0.297161i	0.886073	+	0.463547i	$0.153423\pi$
$384$	1.98083	+	6.97870i	0.101084	+	0.356130i
$385$	−0.0598243	−	0.0209334i	−0.00304893	−	0.00106687i
$386$	10.6036	−	5.10643i	0.539710	−	0.259911i
$387$	10.4710	−	8.21638i	0.532268	−	0.417662i
$388$	−2.78117	+	0.973175i	−0.141193	+	0.0494055i
$389$	−21.6166	+	21.6166i	−1.09601	+	1.09601i	−0.101132	+	0.994873i	$0.532247\pi$
$389$	−21.6166	+	21.6166i	−1.09601	+	1.09601i	−0.994873	+	0.101132i	$0.967753\pi$
$390$	16.1140	+	6.74904i	0.815967	+	0.341751i
$391$	−0.408043	−	3.62148i	−0.0206356	−	0.183146i
$392$	2.32120	+	20.6012i	0.117238	+	1.04052i
$393$	5.30594	+	2.22228i	0.267649	+	0.112099i
$394$	−6.28803	+	6.28803i	−0.316786	+	0.316786i
$395$	4.05091	−	1.41747i	0.203823	−	0.0713209i
$396$	7.95896	−	6.24526i	0.399953	−	0.313836i
$397$	19.8798	−	9.57359i	0.997737	−	0.480485i	0.137567	−	0.990492i	$-0.456072\pi$
$397$	19.8798	−	9.57359i	0.997737	−	0.480485i	0.860170	+	0.510008i	$0.170357\pi$
$398$	−18.8965	−	6.61216i	−0.947194	−	0.331437i
$399$	0.0335807	+	0.118309i	0.00168114	+	0.00592284i
$400$	−0.613026	+	0.768710i	−0.0306513	+	0.0384355i
$401$	−6.83289	+	5.44905i	−0.341218	+	0.272112i	−0.779073	−	0.626933i	$-0.784310\pi$
$401$	−6.83289	+	5.44905i	−0.341218	+	0.272112i	0.437855	+	0.899046i	$0.355738\pi$
$402$	0.643546	−	3.69947i	0.0320972	−	0.184513i
$403$	13.8780	−	22.0867i	0.691311	−	1.10021i
$404$	14.9188	+	1.68095i	0.742239	+	0.0836303i
$405$	16.7958	−	3.55647i	0.834588	−	0.176722i
$406$	0.0506862	−	0.0205981i	0.00251551	−	0.00102226i
$407$			20.9844i			1.04016i
$408$	0.579072	−	9.63426i	0.0286684	−	0.476967i
$409$	16.8140	+	10.5650i	0.831400	+	0.522403i	0.879200	−	0.476454i	$-0.158078\pi$
$409$	16.8140	+	10.5650i	0.831400	+	0.522403i	−0.0477995	+	0.998857i	$0.515221\pi$
$410$	−0.754529	+	3.30581i	−0.0372635	+	0.163262i
$411$	19.8230	−	17.5752i	0.977799	−	0.866921i
$412$	0.890520	+	0.710166i	0.0438728	+	0.0349874i
$413$	−0.139236	+	0.0317797i	−0.00685136	+	0.00156378i
$414$	5.45852	+	1.29113i	0.268272	+	0.0634557i
$415$	−7.01876	−	14.5746i	−0.344537	−	0.715439i
$416$	−15.2310	−	24.2400i	−0.746760	−	1.18846i
$417$	−9.45118	−	23.0734i	−0.462826	−	1.12991i
$418$	14.5355	+	14.5355i	0.710955	+	0.710955i
$419$	34.2011	+	16.4704i	1.67083	+	0.804630i	0.997889	+	0.0649360i	$0.0206843\pi$
$419$	34.2011	+	16.4704i	1.67083	+	0.804630i	0.672943	+	0.739694i	$0.265030\pi$
$420$	0.00607858	+	0.0366483i	0.000296604	+	0.00178825i
$421$	−13.0553	+	1.47098i	−0.636278	+	0.0716913i	−0.424210	−	0.905564i	$-0.639448\pi$
$421$	−13.0553	+	1.47098i	−0.636278	+	0.0716913i	−0.212068	+	0.977255i	$0.568020\pi$
$422$	8.00819	−	16.6292i	0.389833	−	0.809496i
$423$	7.79711	+	6.31897i	0.379109	+	0.307239i
$424$	7.23236	+	20.6689i	0.351234	+	1.00377i
$425$	−2.16846	+	1.36253i	−0.105186	+	0.0660925i
$426$	−8.44524	−	15.4235i	−0.409173	−	0.747271i
$427$	0.0314869	−	0.0899843i	0.00152376	−	0.00435465i
$428$	−1.12843	−	4.94399i	−0.0545449	−	0.238977i
$429$	−17.4279	+	24.3587i	−0.841427	+	1.17605i
$430$	5.09342	+	6.38695i	0.245627	+	0.308006i
$431$	−21.1180	−	4.82004i	−1.01722	−	0.232173i	−0.318768	−	0.947833i	$-0.603269\pi$
$431$	−21.1180	−	4.82004i	−1.01722	−	0.232173i	−0.698449	+	0.715660i	$0.746126\pi$
$432$	3.45048	+	1.47718i	0.166012	+	0.0710707i
$433$	−1.77682	+	15.7697i	−0.0853884	+	0.757843i	0.875937	+	0.482426i	$0.160244\pi$
$433$	−1.77682	+	15.7697i	−0.0853884	+	0.757843i	−0.961325	+	0.275416i	$0.911184\pi$
$434$	−0.0483793			−0.00232228
$435$	−16.1118	+	7.54904i	−0.772504	+	0.361949i
$436$	13.4615			0.644689
$437$	1.46304	−	12.9848i	0.0699866	−	0.621148i
$438$	−13.3434	−	7.44333i	−0.637574	−	0.355656i
$439$	7.32542	+	1.67198i	0.349623	+	0.0797993i	0.393726	−	0.919228i	$-0.371186\pi$
$439$	7.32542	+	1.67198i	0.349623	+	0.0797993i	−0.0441029	+	0.999027i	$0.514043\pi$
$440$	11.1198	+	13.9438i	0.530116	+	0.664745i
$441$	−17.6925	−	11.3120i	−0.842499	−	0.538668i
$442$	2.21376	+	9.69910i	0.105298	+	0.461339i
$443$	10.8730	−	31.0733i	0.516593	−	1.47634i	−0.329939	−	0.944002i	$-0.607028\pi$
$443$	10.8730	−	31.0733i	0.516593	−	1.47634i	0.846532	−	0.532337i	$-0.178686\pi$
$444$	10.7881	−	5.90707i	0.511978	−	0.280337i
$445$	15.8505	−	9.95953i	0.751385	−	0.472127i
$446$	2.15227	+	6.15084i	0.101913	+	0.291251i
$447$	10.8205	+	9.74662i	0.511793	+	0.461000i
$448$	−0.0296349	+	0.0615376i	−0.00140012	+	0.00290738i
$449$	−24.9954	+	2.81630i	−1.17960	+	0.132909i	−0.679912	−	0.733294i	$-0.737982\pi$
$449$	−24.9954	+	2.81630i	−1.17960	+	0.132909i	−0.499692	+	0.866203i	$0.666554\pi$
$450$	−0.846844	−	3.84962i	−0.0399206	−	0.181473i
$451$	−5.23757	−	2.52228i	−0.246628	−	0.118770i
$452$	−13.4493	−	13.4493i	−0.632603	−	0.632603i
$453$	−2.09387	+	0.857677i	−0.0983787	+	0.0402972i
$454$	−2.66892	−	4.24756i	−0.125259	−	0.199348i
$455$	−0.0477195	−	0.0990905i	−0.00223712	−	0.00464543i
$456$	9.71088	−	33.2155i	0.454754	−	1.55546i
$457$	−11.7002	+	2.67049i	−0.547312	+	0.124920i	−0.487231	−	0.873273i	$-0.661993\pi$
$457$	−11.7002	+	2.67049i	−0.547312	+	0.124920i	−0.0600809	+	0.998194i	$0.519136\pi$
$458$	−2.87385	−	2.29182i	−0.134286	−	0.107090i
$459$	7.21237	+	6.60009i	0.336645	+	0.308066i
$460$	0.878317	−	3.84816i	0.0409517	−	0.179421i
$461$	22.9487	+	14.4197i	1.06883	+	0.671590i	0.947089	−	0.320972i	$-0.104009\pi$
$461$	22.9487	+	14.4197i	1.06883	+	0.671590i	0.121741	+	0.992562i	$0.461152\pi$
$462$	0.0554504	+	0.00333287i	0.00257979	+	0.000155059i
$463$		−	21.3059i		−	0.990167i	−0.868845	−	0.495084i	$-0.835137\pi$
$463$		−	21.3059i		−	0.990167i	0.868845	−	0.495084i	$-0.164863\pi$
$464$	−3.83050	−	0.677270i	−0.177827	−	0.0314414i
$465$	15.7119	−	0.820381i	0.728624	−	0.0380442i
$466$	7.98665	+	0.899879i	0.369974	+	0.0416861i
$467$	4.01023	−	6.38225i	0.185571	−	0.295335i	−0.740963	−	0.671546i	$-0.765630\pi$
$467$	4.01023	−	6.38225i	0.185571	−	0.295335i	0.926534	+	0.376211i	$0.122773\pi$
$468$	17.4287	+	2.10272i	0.805643	+	0.0971983i
$469$	−0.0184819	+	0.0147388i	−0.000853416	+	0.000680576i
$470$	−3.84067	+	4.81604i	−0.177157	+	0.222148i
$471$	−4.64127	+	1.31738i	−0.213858	+	0.0607016i
$472$	37.9321	+	13.2730i	1.74597	+	0.610940i
$473$	−12.6184	+	6.07671i	−0.580195	+	0.279407i
$474$	−3.07628	+	2.16460i	−0.141298	+	0.0994232i
$475$	−8.66715	+	3.03277i	−0.397676	+	0.139153i
$476$	−0.0149586	+	0.0149586i	−0.000685625	+	0.000685625i
$477$	−20.8779	−	7.49037i	−0.955935	−	0.342960i
$478$	−1.75347	−	15.5625i	−0.0802019	−	0.711812i
$479$	−4.26564	−	37.8586i	−0.194902	−	1.72980i	−0.586746	−	0.809771i	$-0.699591\pi$
$479$	−4.26564	−	37.8586i	−0.194902	−	1.72980i	0.391844	−	0.920032i	$-0.371837\pi$
$480$	6.67059	−	15.9267i	0.304469	−	0.726953i
$481$	−25.7481	+	25.7481i	−1.17401	+	1.17401i
$482$	−4.46783	+	1.56336i	−0.203504	+	0.0712092i
$483$	−0.0203204	−	0.0288789i	−0.000924610	−	0.00131404i
$484$	0.995823	−	0.479563i	0.0452647	−	0.0217983i
$485$	4.96634	+	1.73780i	0.225510	+	0.0789093i
$486$	−13.3102	+	7.01817i	−0.603761	+	0.318350i
$487$	−2.55768	+	3.20723i	−0.115900	+	0.145334i	−0.836397	−	0.548124i	$-0.815342\pi$
$487$	−2.55768	+	3.20723i	−0.115900	+	0.145334i	0.720497	+	0.693458i	$0.243914\pi$
$488$	−20.9735	+	16.7258i	−0.949425	+	0.757141i
$489$	21.6725	+	3.77007i	0.980064	+	0.170489i
$490$	6.85741	−	10.9135i	0.309786	−	0.493022i
$491$	20.3753	+	2.29574i	0.919522	+	0.103605i	0.559021	−	0.829153i	$-0.311177\pi$
$491$	20.3753	+	2.29574i	0.919522	+	0.103605i	0.360501	+	0.932759i	$0.382606\pi$
$492$	0.177665	+	3.40265i	0.00800976	+	0.153403i
$493$	−8.83481	−	4.96040i	−0.397900	−	0.223405i
$494$			35.6704i			1.60489i
$495$	−18.0649	−	0.142117i	−0.811957	−	0.00638769i
$496$	2.91247	+	1.83003i	0.130774	+	0.0821707i
$497$	−0.0246330	+	0.107924i	−0.00110494	+	0.00484105i
$498$	9.40582	+	10.6088i	0.421485	+	0.475392i
$499$	−18.1915	−	14.5072i	−0.814362	−	0.649432i	0.125077	−	0.992147i	$-0.460082\pi$
$499$	−18.1915	−	14.5072i	−0.814362	−	0.649432i	−0.939439	+	0.342715i	$0.888654\pi$
$500$	−12.6376	+	2.88444i	−0.565169	+	0.128996i
$501$	32.1058	+	9.38645i	1.43438	+	0.419356i
$502$	−6.47942	−	13.4547i	−0.289191	−	0.600511i
$503$	5.19094	+	8.26133i	0.231452	+	0.368354i	0.942177	−	0.335116i	$-0.108776\pi$
$503$	5.19094	+	8.26133i	0.231452	+	0.368354i	−0.710724	+	0.703471i	$0.751633\pi$
$504$	−0.0399117	−	0.0845730i	−0.00177781	−	0.00376718i
$505$	−18.9569	−	18.9569i	−0.843571	−	0.843571i
$506$	−5.31779	−	2.56091i	−0.236404	−	0.113846i
$507$	−29.0594	+	4.81987i	−1.29057	+	0.214058i
$508$	−22.5198	+	2.53737i	−0.999154	+	0.112578i
$509$	11.2858	−	23.4351i	0.500232	−	1.03874i	−0.486089	−	0.873909i	$-0.661577\pi$
$509$	11.2858	−	23.4351i	0.500232	−	1.03874i	0.986321	−	0.164834i	$-0.0527088\pi$
$510$	−4.01602	+	4.45851i	−0.177833	+	0.197426i
$511$	0.0317687	+	0.0907898i	0.00140537	+	0.00401631i
$512$	6.81930	−	4.28485i	0.301373	−	0.189365i
$513$	19.9457	+	28.8256i	0.880625	+	1.27268i
$514$	−6.67434	+	19.0742i	−0.294392	+	0.841325i
$515$	−0.452595	−	1.98295i	−0.0199437	−	0.0873792i
$516$	6.67609	+	4.77653i	0.293898	+	0.210275i
$517$	−6.58448	−	8.25668i	−0.289585	−	0.363128i
$518$	0.0658422	+	0.0150280i	0.00289294	+	0.000660294i
$519$	−14.5500	+	26.0834i	−0.638675	+	1.14493i
$520$	−3.46506	+	30.7533i	−0.151953	+	1.34862i
$521$	44.6310			1.95532			0.977660	−	0.210194i	$-0.0674095\pi$
$521$	44.6310			1.95532			0.977660	+	0.210194i	$0.0674095\pi$
$522$	11.7780	−	10.2208i	0.515510	−	0.447353i
$523$	−34.1462			−1.49311			−0.746554	−	0.665325i	$-0.768293\pi$
$523$	−34.1462			−1.49311			−0.746554	+	0.665325i	$0.768293\pi$
$524$	−0.397238	+	3.52559i	−0.0173534	+	0.154016i
$525$	−0.0120884	+	0.0216706i	−0.000527583	+	0.000945782i
$526$	−0.981205	−	0.223954i	−0.0427826	−	0.00976485i
$527$	5.58610	+	7.00475i	0.243334	+	0.305132i
$528$	−3.21209	−	2.29814i	−0.139788	−	0.100014i
$529$	−4.28311	−	18.7655i	−0.186222	−	0.815892i
$530$	4.49646	−	12.8501i	0.195314	−	0.558175i
$531$	−34.6369	+	21.3856i	−1.50311	+	0.928057i
$532$	−0.0642239	+	0.0403545i	−0.00278446	+	0.00174959i
$533$	−3.33169	−	9.52141i	−0.144311	−	0.412418i
$534$	−10.9808	+	12.1907i	−0.475185	+	0.527541i
$535$	−3.92905	+	8.15875i	−0.169867	+	0.352733i
$536$	6.61003	−	0.744772i	0.285510	−	0.0321692i
$537$	−18.3877	+	3.04983i	−0.793487	+	0.131610i
$538$	0.456965	+	0.220063i	0.0197012	+	0.00948758i
$539$	15.6251	+	15.6251i	0.673020	+	0.673020i
$540$	5.01217	+	9.32714i	0.215690	+	0.401376i
$541$	−10.5017	−	16.7133i	−0.451503	−	0.718563i	0.540968	−	0.841043i	$-0.318058\pi$
$541$	−10.5017	−	16.7133i	−0.451503	−	0.718563i	−0.992471	+	0.122480i	$0.960915\pi$
$542$	7.10469	+	14.7530i	0.305172	+	0.633697i
$543$	17.5780	+	5.13911i	0.754346	+	0.220541i
$544$	9.58636	−	2.18802i	0.411012	−	0.0938108i
$545$	−18.7938	−	14.9876i	−0.805038	−	0.641997i
$546$	0.0639487	+	0.0721276i	0.00273675	+	0.00308678i
$547$	2.08842	−	9.14998i	0.0892945	−	0.391225i	−0.910455	−	0.413608i	$-0.864268\pi$
$547$	2.08842	−	9.14998i	0.0892945	−	0.391225i	0.999749	+	0.0223834i	$0.00712546\pi$
$548$	13.8348	+	8.69300i	0.590995	+	0.371347i
$549$	0.213765	−	27.1722i	0.00912326	−	1.15968i
$550$			4.14767i			0.176857i
$551$	−26.9253	−	24.3884i	−1.14706	−	1.03898i
$552$	0.518108	+	9.92283i	0.0220522	+	0.422344i
$553$	0.0235312	+	0.00265133i	0.00100065	+	0.000112746i
$554$	−2.37038	+	3.77244i	−0.100708	+	0.160275i
$555$	−21.6381	−	3.76409i	−0.918487	−	0.159777i
$556$	12.0232	−	9.58816i	0.509896	−	0.406629i
$557$	11.8992	−	14.9211i	0.504185	−	0.632228i	−0.462983	−	0.886367i	$-0.653221\pi$
$557$	11.8992	−	14.9211i	0.504185	−	0.632228i	0.967168	+	0.254139i	$0.0817922\pi$
$558$	−13.0511	+	4.45186i	−0.552499	+	0.188462i
$559$	−22.9391	−	8.02674i	−0.970220	−	0.339495i
$560$	0.0130666	−	0.00629256i	0.000552167	−	0.000265909i
$561$	−5.91999	−	8.41338i	−0.249942	−	0.355213i
$562$	−20.1867	+	7.06362i	−0.851523	+	0.297961i
$563$	22.5711	−	22.5711i	0.951260	−	0.951260i	−0.0476064	−	0.998866i	$-0.515159\pi$
$563$	22.5711	−	22.5711i	0.951260	−	0.951260i	0.998866	+	0.0476064i	$0.0151593\pi$
$564$	−2.39123	+	5.70931i	−0.100689	+	0.240405i
$565$	3.80281	+	33.7508i	0.159985	+	1.41991i
$566$	0.304943	+	2.70645i	0.0128177	+	0.113760i
$567$	0.0920090	+	0.0225291i	0.00386401	+	0.000946134i
$568$	22.0262	−	22.0262i	0.924199	−	0.924199i
$569$	−9.54511	+	3.33998i	−0.400152	+	0.140019i	−0.522850	−	0.852425i	$-0.675131\pi$
$569$	−9.54511	+	3.33998i	−0.400152	+	0.140019i	0.122698	+	0.992444i	$0.460845\pi$
$570$	−17.5956	+	12.3810i	−0.737000	+	0.518583i
$571$	−7.86857	+	3.78930i	−0.329289	+	0.158577i	−0.591222	−	0.806509i	$-0.701354\pi$
$571$	−7.86857	+	3.78930i	−0.329289	+	0.158577i	0.261933	+	0.965086i	$0.415640\pi$
$572$	−17.4360	−	6.10111i	−0.729035	−	0.255100i
$573$	8.53419	−	2.42234i	0.356521	−	0.101195i
$574$	−0.0116650	+	0.0146274i	−0.000486887	+	0.000610537i
$575$	2.06133	−	1.64385i	0.0859633	−	0.0685535i
$576$	−2.33184	+	19.3278i	−0.0971600	+	0.805325i
$577$	19.8326	−	31.5634i	0.825643	−	1.31400i	−0.121305	−	0.992615i	$-0.538708\pi$
$577$	19.8326	−	31.5634i	0.825643	−	1.31400i	0.946948	−	0.321387i	$-0.104149\pi$
$578$	12.9109	+	1.45471i	0.537022	+	0.0605078i
$579$	−21.0894	+	1.10116i	−0.876445	+	0.0457625i
$580$	−7.25730	−	8.23129i	−0.301343	−	0.341786i
$581$		−	0.0892559i		−	0.00370296i
$582$	−4.60324	−	0.276680i	−0.190810	−	0.0114688i
$583$	19.7627	+	12.4177i	0.818488	+	0.514290i
$584$	6.02280	−	26.3876i	0.249225	−	1.09193i
$585$	−21.9914	−	22.3402i	−0.909233	−	0.923653i
$586$	9.27533	+	7.39683i	0.383160	+	0.305560i
$587$	−21.6451	+	4.94034i	−0.893387	+	0.203910i	−0.644483	−	0.764618i	$-0.722927\pi$
$587$	−21.6451	+	4.94034i	−0.893387	+	0.203910i	−0.248904	+	0.968528i	$0.580070\pi$
$588$	3.63440	−	12.4313i	0.149880	−	0.512657i
$589$	13.9381	+	28.9427i	0.574307	+	1.19256i
$590$	−13.2928	−	21.1554i	−0.547257	−	0.870954i
$591$	14.7659	−	6.04830i	0.607388	−	0.248794i
$592$	−3.39529	−	3.39529i	−0.139546	−	0.139546i
$593$	−17.9106	−	8.62531i	−0.735501	−	0.354199i	0.0283438	−	0.999598i	$-0.490977\pi$
$593$	−17.9106	−	8.62531i	−0.735501	−	0.354199i	−0.763845	+	0.645399i	$0.776691\pi$
$594$	15.2654	−	4.20344i	0.626346	−	0.172469i
$595$	0.0375383	−	0.00422955i	0.00153892	−	0.000173394i
$596$	−3.89705	+	8.09231i	−0.159629	+	0.331474i
$597$	26.6914	+	24.0424i	1.09241	+	0.983989i
$598$	−3.38271	−	9.66724i	−0.138329	−	0.395323i
$599$	4.39216	−	2.75978i	0.179459	−	0.112762i	−0.439307	−	0.898337i	$-0.644776\pi$
$599$	4.39216	−	2.75978i	0.179459	−	0.112762i	0.618766	+	0.785576i	$0.287633\pi$
$600$	6.12446	−	3.35349i	0.250030	−	0.136906i
$601$	−5.11864	+	14.6282i	−0.208794	+	0.596698i	−0.999888	−	0.0149966i	$-0.995226\pi$
$601$	−5.11864	+	14.6282i	−0.208794	+	0.596698i	0.791094	+	0.611695i	$0.209512\pi$
$602$	0.0100300	+	0.0439443i	0.000408792	+	0.00179104i
$603$	−3.62954	+	5.67676i	−0.147806	+	0.231175i
$604$	−0.870108	−	1.09108i	−0.0354042	−	0.0443955i
$605$	−1.92421	−	0.439189i	−0.0782304	−	0.0178556i
$606$	20.5202	+	11.4467i	0.833576	+	0.464991i
$607$	1.53053	−	13.5838i	0.0621221	−	0.551349i	−0.923647	−	0.383244i	$-0.874807\pi$
$607$	1.53053	−	13.5838i	0.0621221	−	0.551349i	0.985769	−	0.168105i	$-0.0537647\pi$
$608$	35.2558			1.42981
$609$	−0.0981672	−	0.00104402i	−0.00397794	−	4.23060e-5i
$610$	16.6782			0.675279
$611$	2.05180	−	18.2102i	0.0830070	−	0.736708i
$612$	−2.65884	+	5.41181i	−0.107477	+	0.218760i
$613$	42.3898	+	9.67520i	1.71211	+	0.390777i	0.962538	−	0.271148i	$-0.0874031\pi$
$613$	42.3898	+	9.67520i	1.71211	+	0.390777i	0.749570	+	0.661925i	$0.230260\pi$
$614$	−2.55993	−	3.21005i	−0.103310	−	0.129547i
$615$	3.54035	−	4.94829i	0.142761	−	0.199535i
$616$	0.0218972	+	0.0959379i	0.000882264	+	0.00386545i
$617$	7.07061	−	20.2066i	0.284652	−	0.813489i	−0.709422	−	0.704784i	$-0.751044\pi$
$617$	7.07061	−	20.2066i	0.284652	−	0.813489i	0.994074	−	0.108705i	$-0.0346703\pi$
$618$	0.856161	+	1.56360i	0.0344398	+	0.0628973i
$619$	−15.4524	+	9.70941i	−0.621086	+	0.390254i	−0.805501	−	0.592594i	$-0.798104\pi$
$619$	−15.4524	+	9.70941i	−0.621086	+	0.390254i	0.184415	+	0.982848i	$0.440961\pi$
$620$	3.20490	+	9.15908i	0.128712	+	0.367838i
$621$	−8.13920	−	5.92070i	−0.326615	−	0.237589i
$622$	1.85109	−	3.84384i	0.0742221	−	0.154124i
$623$	0.102639	−	0.0115646i	0.00411213	−	0.000463326i
$624$	−1.12141	−	6.76111i	−0.0448925	−	0.270661i
$625$	14.7232	+	7.09030i	0.588926	+	0.283612i
$626$	3.91533	+	3.91533i	0.156488	+	0.156488i
$627$	−13.9813	−	34.1331i	−0.558361	−	1.36314i
$628$	−1.58312	−	2.51951i	−0.0631732	−	0.100540i
$629$	−5.42656	−	11.2684i	−0.216371	−	0.449299i
$630$	−0.0133831	+	0.0565799i	−0.000533197	+	0.00225420i
$631$	7.85535	−	1.79293i	0.312716	−	0.0713755i	−0.0632823	−	0.997996i	$-0.520157\pi$
$631$	7.85535	−	1.79293i	0.312716	−	0.0713755i	0.375999	+	0.926620i	$0.377300\pi$
$632$	−5.20962	−	4.15453i	−0.207228	−	0.165258i
$633$	−24.7813	+	21.9712i	−0.984966	+	0.873276i
$634$	0.488582	−	2.14062i	0.0194041	−	0.0850148i
$635$	34.2653	+	21.5303i	1.35978	+	0.854404i
$636$	0.820774	−	13.6555i	0.0325458	−	0.541478i
$637$			38.3442i			1.51925i
$638$	−14.4148	+	7.84115i	−0.570688	+	0.310434i
$639$	3.28601	+	31.3810i	0.129992	+	1.24141i
$640$	7.93929	+	0.894544i	0.313828	+	0.0353599i
$641$	4.64897	−	7.39879i	0.183623	−	0.292235i	−0.742210	−	0.670168i	$-0.766222\pi$
$641$	4.64897	−	7.39879i	0.183623	−	0.292235i	0.925833	+	0.377933i	$0.123365\pi$
$642$	1.36022	−	7.81932i	0.0536836	−	0.308604i
$643$	0.523650	−	0.417597i	0.0206508	−	0.0164684i	−0.613110	−	0.789998i	$-0.710082\pi$
$643$	0.523650	−	0.417597i	0.0206508	−	0.0164684i	0.633761	+	0.773529i	$0.281510\pi$
$644$	0.0135787	−	0.0170272i	0.000535077	−	0.000670966i
$645$	−4.00257	−	14.1015i	−0.157601	−	0.555247i
$646$	−11.5643	−	4.04651i	−0.454990	−	0.159208i
$647$	4.91969	−	2.36920i	0.193413	−	0.0931428i	−0.334671	−	0.942335i	$-0.608625\pi$
$647$	4.91969	−	2.36920i	0.193413	−	0.0931428i	0.528084	+	0.849192i	$0.322911\pi$
$648$	−18.5492	−	19.1423i	−0.728683	−	0.751981i
$649$	40.4308	−	14.1474i	1.58705	−	0.555332i
$650$	−5.08923	+	5.08923i	−0.199616	+	0.199616i
$651$	0.0800709	+	0.0335361i	0.00313823	+	0.00131438i
$652$	1.51906	+	13.4820i	0.0594911	+	0.527998i
$653$	2.66777	+	23.6772i	0.104398	+	0.926559i	0.931310	+	0.364227i	$0.118667\pi$
$653$	2.66777	+	23.6772i	0.104398	+	0.926559i	−0.826912	+	0.562331i	$0.809905\pi$
$654$	19.4327	+	8.13900i	0.759880	+	0.318260i
$655$	4.47986	−	4.47986i	0.175042	−	0.175042i
$656$	1.25555	−	0.439336i	0.0490209	−	0.0171532i
$657$	16.9246	+	21.5687i	0.660292	+	0.841476i
$658$	−0.0306222	+	0.0147469i	−0.00119378	+	0.000574894i
$659$	11.8923	+	4.16129i	0.463257	+	0.162101i	0.551808	−	0.833971i	$-0.313938\pi$
$659$	11.8923	+	4.16129i	0.463257	+	0.162101i	−0.0885512	+	0.996072i	$0.528224\pi$
$660$	−3.04235	−	10.7185i	−0.118423	−	0.417219i
$661$	−7.23040	+	9.06664i	−0.281230	+	0.352651i	−0.902304	−	0.431101i	$-0.858125\pi$
$661$	−7.23040	+	9.06664i	−0.281230	+	0.352651i	0.621074	+	0.783752i	$0.286697\pi$
$662$	−16.9304	+	13.5015i	−0.658018	+	0.524751i
$663$	3.05941	−	17.5872i	0.118818	−	0.683030i
$664$	−13.3624	+	21.2661i	−0.518561	+	0.825285i
$665$	0.134593	+	0.0151650i	0.00521931	+	0.000588074i
$666$	19.1449	−	2.00472i	0.741850	−	0.0776814i
$667$	9.60999	+	4.05625i	0.372100	+	0.157059i
$668$			20.6303i			0.798211i
$669$	0.701550	−	11.6720i	0.0271235	−	0.451265i
$670$	−3.50167	−	2.20025i	−0.135281	−	0.0850030i
$671$	−6.36259	+	27.8763i	−0.245625	+	1.07615i
$672$	0.0712892	−	0.0632054i	0.00275004	−	0.00243820i
$673$	20.5691	+	16.4033i	0.792879	+	0.632300i	0.933830	−	0.357717i	$-0.116445\pi$
$673$	20.5691	+	16.4033i	0.792879	+	0.632300i	−0.140951	+	0.990017i	$0.545016\pi$
$674$	21.8460	−	4.98622i	0.841478	−	0.192062i
$675$	−1.26693	+	6.95838i	−0.0487642	+	0.267828i
$676$	−7.88254	−	16.3683i	−0.303175	−	0.629549i
$677$	3.21411	+	5.11523i	0.123528	+	0.196594i	0.902763	−	0.430138i	$-0.141535\pi$
$677$	3.21411	+	5.11523i	0.123528	+	0.196594i	−0.779235	+	0.626732i	$0.784392\pi$
$678$	−11.2835	−	27.5468i	−0.433341	−	1.05793i
$679$	0.0205283	+	0.0205283i	0.000787804	+	0.000787804i
$680$	−9.57706	−	4.61207i	−0.367263	−	0.176865i
$681$	1.47287	+	8.88005i	0.0564404	+	0.340284i
$682$	14.4190	−	1.62463i	0.552132	−	0.0622103i
$683$	−13.5951	+	28.2305i	−0.520202	+	1.08021i	0.461030	+	0.887384i	$0.347480\pi$
$683$	−13.5951	+	28.2305i	−0.520202	+	1.08021i	−0.981233	+	0.192827i	$0.938234\pi$
$684$	−13.6120	+	16.7962i	−0.520470	+	0.642218i
$685$	−9.63655	−	27.5397i	−0.368194	−	1.05224i
$686$	0.120434	−	0.0756734i	0.00459818	−	0.00288923i
$687$	3.16775	+	5.78524i	0.120857	+	0.220721i
$688$	1.05845	−	3.02488i	0.0403531	−	0.115323i
$689$	9.01236	+	39.4857i	0.343343	+	1.50429i
$690$	3.59457	−	5.02408i	0.136843	−	0.191263i
$691$	−3.06844	−	3.84770i	−0.116729	−	0.146373i	0.720034	−	0.693939i	$-0.244126\pi$
$691$	−3.06844	−	3.84770i	−0.116729	−	0.146373i	−0.836763	+	0.547565i	$0.815555\pi$
$692$	−17.9589	−	4.09899i	−0.682693	−	0.155820i
$693$	−0.0894636	−	0.0439538i	−0.00339844	−	0.00166967i
$694$	0.180687	−	1.60364i	0.00685878	−	0.0608734i
$695$	−27.4609			−1.04165
$696$	23.2330	+	14.9452i	0.880645	+	0.566497i
$697$	3.46477			0.131238
$698$	1.81019	−	16.0659i	0.0685167	−	0.608102i
$699$	−12.5946	−	7.02562i	−0.476373	−	0.265733i
$700$	−0.0149206	−	0.00340552i	−0.000563945	−	0.000128717i
$701$	7.95466	+	9.97483i	0.300443	+	0.376744i	0.909021	−	0.416750i	$-0.136831\pi$
$701$	7.95466	+	9.97483i	0.300443	+	0.376744i	−0.608578	+	0.793494i	$0.708260\pi$
$702$	23.8884	+	13.5731i	0.901610	+	0.512283i
$703$	−9.97864	−	43.7193i	−0.376351	−	1.64890i
$704$	6.76591	−	19.3359i	0.255000	−	0.728748i
$705$	9.69498	−	5.30855i	0.365134	−	0.199932i
$706$	3.33884	−	2.09793i	0.125659	−	0.0789568i
$707$	−0.0488555	−	0.139621i	−0.00183740	−	0.00525099i
$708$	−18.6543	−	16.8030i	−0.701073	−	0.631494i
$709$	−0.857294	+	1.78019i	−0.0321964	+	0.0668564i	−0.916447	−	0.400157i	$-0.868956\pi$
$709$	−0.857294	+	1.78019i	−0.0321964	+	0.0668564i	0.884250	+	0.467013i	$0.154670\pi$
$710$	−19.2445	+	2.16833i	−0.722232	+	0.0813760i
$711$	6.59192	−	1.45010i	0.247216	−	0.0543830i
$712$	−26.1860	−	12.6105i	−0.981362	−	0.472599i
$713$	−6.52213	−	6.52213i	−0.244256	−	0.244256i
$714$	−0.0306380	+	0.0125497i	−0.00114660	+	0.000469662i
$715$	17.5499	+	27.9305i	0.656329	+	1.04454i
$716$	−4.98776	−	10.3572i	−0.186402	−	0.387067i
$717$	−7.88565	+	26.9724i	−0.294495	+	1.00730i
$718$	18.6964	−	4.26733i	0.697743	−	0.159255i
$719$	−13.3016	−	10.6077i	−0.496067	−	0.395600i	0.343249	−	0.939244i	$-0.388473\pi$
$719$	−13.3016	−	10.6077i	−0.496067	−	0.395600i	−0.839316	+	0.543645i	$0.817044\pi$
$720$	2.94591	−	2.89992i	0.109787	−	0.108074i
$721$	0.00249724	−	0.0109411i	9.30020e−5	−	0.000407468i
$722$	−21.6665	−	13.6140i	−0.806344	−	0.506659i
$723$	8.47825	+	0.509590i	0.315310	+	0.0189519i
$724$			11.2952i			0.419782i
$725$	−0.361947	−	7.32112i	−0.0134424	−	0.271899i
$726$	1.72750	−	0.0901993i	0.0641135	−	0.00334761i
$727$	−23.1590	−	2.60939i	−0.858918	−	0.0967769i	−0.328491	−	0.944507i	$-0.606540\pi$
$727$	−23.1590	−	2.60939i	−0.858918	−	0.0967769i	−0.530428	+	0.847730i	$0.677969\pi$
$728$	−0.0908487	+	0.144585i	−0.00336708	+	0.00535867i
$729$	26.8941	−	2.38905i	0.996078	−	0.0884832i
$730$	−13.1562	+	10.4917i	−0.486934	+	0.388317i
$731$	5.20450	−	6.52623i	0.192495	−	0.241381i
$732$	16.1222	−	4.57614i	0.595895	−	0.169139i
$733$	−8.94489	−	3.12995i	−0.330387	−	0.115607i	0.159988	−	0.987119i	$-0.448854\pi$
$733$	−8.94489	−	3.12995i	−0.330387	−	0.115607i	−0.490375	+	0.871512i	$0.663140\pi$
$734$	8.22749	−	3.96215i	0.303682	−	0.146246i
$735$	−18.9146	+	13.3091i	−0.697675	+	0.490912i
$736$	−9.55487	+	3.34339i	−0.352197	+	0.123239i
$737$	5.01341	−	5.01341i	0.184671	−	0.184671i
$738$	−1.80081	+	5.01941i	−0.0662888	+	0.184767i
$739$	1.12270	+	9.96427i	0.0412993	+	0.366542i	0.997315	+	0.0732270i	$0.0233298\pi$
$739$	1.12270	+	9.96427i	0.0412993	+	0.366542i	−0.956016	+	0.293315i	$0.905242\pi$
$740$	−1.51665	−	13.4607i	−0.0557532	−	0.494823i
$741$	24.7264	−	59.0369i	0.908346	−	2.16877i
$742$	0.0531159	−	0.0531159i	0.00194995	−	0.00194995i
$743$	−22.9403	+	8.02715i	−0.841597	+	0.294488i	−0.716439	−	0.697649i	$-0.754229\pi$
$743$	−22.9403	+	8.02715i	−0.841597	+	0.294488i	−0.125158	+	0.992137i	$0.539944\pi$
$744$	−14.0571	−	19.9776i	−0.515357	−	0.732414i
$745$	14.4504	−	6.95896i	0.529423	−	0.254957i
$746$	7.32414	+	2.56283i	0.268156	+	0.0938317i
$747$	−8.21332	−	24.0783i	−0.300510	−	0.880978i
$748$	3.95593	−	4.96058i	0.144643	−	0.181377i
$749$	−0.0390640	+	0.0311525i	−0.00142737	+	0.00113829i
$750$	−19.9873	−	3.47692i	−0.729833	−	0.126959i
$751$	−9.11788	+	14.5110i	−0.332716	+	0.529515i	−0.970625	−	0.240597i	$-0.922657\pi$
$751$	−9.11788	+	14.5110i	−0.332716	+	0.529515i	0.637909	+	0.770112i	$0.279800\pi$
$752$	2.40131	+	0.270562i	0.0875667	+	0.00986640i
$753$	1.39723	+	26.7598i	0.0509179	+	0.975182i
$754$	−27.3083	−	8.06596i	−0.994509	−	0.293745i
$755$			2.49202i			0.0906941i
$756$	0.00258728	+	0.0583660i	9.40986e−5	+	0.00212275i
$757$	11.8448	+	7.44260i	0.430507	+	0.270506i	0.729807	−	0.683654i	$-0.239610\pi$
$757$	11.8448	+	7.44260i	0.430507	+	0.270506i	−0.299299	+	0.954159i	$0.596753\pi$
$758$	−3.68055	+	16.1255i	−0.133684	+	0.585706i
$759$	7.02608	+	7.92471i	0.255031	+	0.287649i
$760$	−29.7979	−	23.7630i	−1.08088	−	0.861974i
$761$	−24.4664	+	5.58429i	−0.886905	+	0.202430i	−0.641622	−	0.767021i	$-0.721738\pi$
$761$	−24.4664	+	5.58429i	−0.886905	+	0.202430i	−0.245283	+	0.969451i	$0.578881\pi$
$762$	−34.0433	−	9.95288i	−1.23326	−	0.360555i
$763$	−0.0575473	−	0.119498i	−0.00208335	−	0.00432613i
$764$	2.91097	+	4.63279i	0.105315	+	0.167608i
$765$	9.73737	−	4.59526i	0.352056	−	0.166142i
$766$	5.07707	+	5.07707i	0.183442	+	0.183442i
$767$	66.9679	+	32.2501i	2.41807	+	1.16448i
$768$	−29.0848	+	4.82407i	−1.04951	+	0.174074i
$769$	9.25720	−	1.04304i	0.333823	−	0.0376128i	0.0565378	−	0.998400i	$-0.481994\pi$
$769$	9.25720	−	1.04304i	0.333823	−	0.0376128i	0.277285	+	0.960788i	$0.410565\pi$
$770$	0.0265450	−	0.0551212i	0.000956614	−	0.00198643i
$771$	24.2685	−	26.9424i	0.874007	−	0.970306i
$772$	−4.30179	−	12.2938i	−0.154825	−	0.442464i
$773$	−12.3565	+	7.76408i	−0.444431	+	0.279255i	−0.735599	−	0.677417i	$-0.763099\pi$
$773$	−12.3565	+	7.76408i	−0.444431	+	0.279255i	0.291168	+	0.956672i	$0.405956\pi$
$774$	6.74951	+	10.9318i	0.242606	+	0.392934i
$775$	−2.14076	+	6.11795i	−0.0768984	+	0.219763i
$776$	−1.81781	−	7.96433i	−0.0652555	−	0.285903i
$777$	−0.0985558	−	0.0705135i	−0.00353567	−	0.00252966i
$778$	−18.3985	−	23.0709i	−0.659617	−	0.827133i
$779$	12.1115	+	2.76436i	0.433938	+	0.0990435i
$780$	9.41877	−	16.8848i	0.337246	−	0.604571i
$781$	3.71741	−	32.9929i	0.133019	−	1.18058i
$782$	3.51784			0.125798
$783$	−26.5783	+	8.75170i	−0.949832	+	0.312760i
$784$	−5.05629			−0.180582
$785$	−0.594927	+	5.28012i	−0.0212339	+	0.188456i
$786$	−2.70506	+	4.84929i	−0.0964864	+	0.172968i
$787$	−41.2995	−	9.42633i	−1.47217	−	0.336013i	−0.590174	−	0.807276i	$-0.700941\pi$
$787$	−41.2995	−	9.42633i	−1.47217	−	0.336013i	−0.881993	+	0.471263i	$0.843798\pi$
$788$	6.13596	+	7.69425i	0.218585	+	0.274096i
$789$	1.46872	+	1.05082i	0.0522877	+	0.0374102i
$790$	0.921838	+	4.03884i	0.0327975	+	0.143695i
$791$	−0.0618949	+	0.176885i	−0.00220073	+	0.00628932i
$792$	14.7353	+	23.8659i	0.523598	+	0.848038i
$793$	−42.0115	+	26.3976i	−1.49187	+	0.937405i
$794$	7.03448	+	20.1034i	0.249644	+	0.713443i
$795$	−16.3495	+	18.1509i	−0.579858	+	0.643747i
$796$	−9.61300	+	19.9616i	−0.340724	+	0.707520i
$797$	−31.5593	+	3.55588i	−1.11789	+	0.125956i	−0.651517	−	0.758634i	$-0.725867\pi$
$797$	−31.5593	+	3.55588i	−1.11789	+	0.125956i	−0.466370	+	0.884590i	$0.654439\pi$
$798$	−0.117111	+	0.0194244i	−0.00414569	+	0.000687615i
$799$	5.67096	+	2.73099i	0.200624	+	0.0966154i
$800$	5.03007	+	5.03007i	0.177840	+	0.177840i
$801$	26.6244	−	12.5646i	0.940725	−	0.443947i
$802$	−4.48827	−	7.14304i	−0.158486	−	0.252229i
$803$	−12.5172	−	25.9922i	−0.441722	−	0.917245i
$804$	−3.98866	−	1.16612i	−0.140669	−	0.0411260i
$805$	−0.0379150	+	0.00865385i	−0.00133633	+	0.000305008i
$806$	19.6857	+	15.6988i	0.693399	+	0.552967i
$807$	−0.603761	−	0.680982i	−0.0212534	−	0.0239717i
$808$	−9.26215	+	40.5801i	−0.325841	+	1.42760i
$809$	−18.9925	−	11.9338i	−0.667741	−	0.419570i	0.155055	−	0.987906i	$-0.450444\pi$
$809$	−18.9925	−	11.9338i	−0.667741	−	0.419570i	−0.822796	+	0.568336i	$0.807587\pi$
$810$	1.59615	+	16.4949i	0.0560831	+	0.579572i
$811$			34.9297i			1.22655i	0.789871	+	0.613273i	$0.210148\pi$
$811$			34.9297i			1.22655i	−0.789871	+	0.613273i	$0.789852\pi$
$812$	−0.0163717	−	0.0582932i	−0.000574535	−	0.00204569i
$813$	−1.53206	−	29.3421i	−0.0537318	−	1.02907i
$814$	−20.1283	−	2.26791i	−0.705496	−	0.0794903i
$815$	12.8897	−	20.5138i	0.451505	−	0.718566i
$816$	2.31915	+	0.403431i	0.0811864	+	0.0141229i
$817$	23.3998	−	18.6607i	0.818655	−	0.652856i
$818$	−11.9511	+	14.9862i	−0.417861	+	0.523981i
$819$	−0.0558411	−	0.163704i	−0.00195125	−	0.00572030i
$820$	3.54199	+	1.23940i	0.123692	+	0.0432816i
$821$	−24.3867	+	11.7440i	−0.851100	+	0.409868i	−0.807986	−	0.589202i	$-0.799442\pi$
$821$	−24.3867	+	11.7440i	−0.851100	+	0.409868i	−0.0431145	+	0.999070i	$0.513728\pi$
$822$	14.7158	+	20.9138i	0.513272	+	0.729452i
$823$	−1.68136	+	0.588334i	−0.0586086	+	0.0205080i	−0.359424	−	0.933174i	$-0.617027\pi$
$823$	−1.68136	+	0.588334i	−0.0586086	+	0.0205080i	0.300816	+	0.953682i	$0.402741\pi$
$824$	−2.23297	+	2.23297i	−0.0777892	+	0.0777892i
$825$	2.87512	−	6.86466i	0.100099	−	0.238997i
$826$	−0.0154351	−	0.136990i	−0.000537056	−	0.00476650i
$827$	−3.62853	−	32.2041i	−0.126176	−	1.11985i	−0.884033	−	0.467425i	$-0.845182\pi$
$827$	−3.62853	−	32.2041i	−0.126176	−	1.11985i	0.757856	−	0.652421i	$-0.226247\pi$
$828$	2.09625	−	5.84289i	0.0728498	−	0.203054i
$829$	5.02270	−	5.02270i	0.174446	−	0.174446i	−0.614484	−	0.788929i	$-0.710636\pi$
$829$	5.02270	−	5.02270i	0.174446	−	0.174446i	0.788929	+	0.614484i	$0.210636\pi$
$830$	14.7386	−	5.15724i	0.511583	−	0.179011i
$831$	6.53814	−	4.60050i	0.226806	−	0.159590i
$832$	32.0271	−	15.4235i	1.11034	−	0.534712i
$833$	−12.4311	−	4.34983i	−0.430712	−	0.150713i
$834$	23.1535	−	6.57190i	0.801742	−	0.227566i
$835$	22.9691	−	28.8023i	0.794878	−	0.996746i
$836$	17.7862	−	14.1840i	0.615147	−	0.490563i
$837$	24.6865	+	1.67880i	0.853289	+	0.0580277i
$838$	−19.4947	+	31.0257i	−0.673435	+	1.07177i
$839$	−11.8776	−	1.33828i	−0.410060	−	0.0462027i	−0.0954748	−	0.995432i	$-0.530437\pi$
$839$	−11.8776	−	1.33828i	−0.410060	−	0.0462027i	−0.314586	+	0.949229i	$0.601866\pi$
$840$	−0.102854	+	0.00537042i	−0.00354881	+	0.000185297i
$841$	24.7596	−	15.0985i	0.853779	−	0.520636i
$842$		−	12.6817i		−	0.437040i
$843$	38.3067	+	2.30244i	1.31935	+	0.0793003i
$844$	−17.2952	−	10.8673i	−0.595327	−	0.374069i
$845$	−7.21892	+	31.6282i	−0.248338	+	1.08804i
$846$	−6.90386	+	6.79608i	−0.237359	+	0.233654i
$847$	−0.00851420	−	0.00678985i	−0.000292551	−	0.000233302i
$848$	−5.20681	+	1.18842i	−0.178803	+	0.0408106i
$849$	1.37138	−	4.69072i	0.0470656	−	0.160985i
$850$	−1.07258	−	2.22725i	−0.0367894	−	0.0763939i
$851$	6.85037	+	10.9023i	0.234828	+	0.373726i
$852$	−18.0081	+	7.37633i	−0.616946	+	0.252709i
$853$	−31.0349	−	31.0349i	−1.06261	−	1.06261i	−0.997904	−	0.0647099i	$-0.979388\pi$
$853$	−31.0349	−	31.0349i	−1.06261	−	1.06261i	−0.0647099	−	0.997904i	$-0.520612\pi$
$854$	0.0829102	+	0.0399274i	0.00283713	+	0.00136629i
$855$	37.7043	−	8.29425i	1.28946	−	0.283657i
$856$	13.9712	−	1.57417i	0.477525	−	0.0538042i
$857$	−6.74481	+	14.0057i	−0.230398	+	0.478427i	−0.983831	−	0.179098i	$-0.942682\pi$
$857$	−6.74481	+	14.0057i	−0.230398	+	0.478427i	0.753433	+	0.657525i	$0.228397\pi$
$858$	−21.4814	−	19.3495i	−0.733364	−	0.660580i
$859$	10.5508	+	30.1524i	0.359988	+	1.02879i	0.971395	+	0.237471i	$0.0763185\pi$
$859$	10.5508	+	30.1524i	0.359988	+	1.02879i	−0.611406	+	0.791317i	$0.709396\pi$
$860$	7.65501	−	4.80996i	0.261034	−	0.164018i
$861$	0.0294459	−	0.0161233i	0.00100351	−	0.000549481i
$862$	6.90574	−	19.7355i	0.235210	−	0.672193i
$863$	−0.601526	−	2.63546i	−0.0204762	−	0.0897120i	0.963657	−	0.267141i	$-0.0860790\pi$
$863$	−0.601526	−	2.63546i	−0.0204762	−	0.0897120i	−0.984134	+	0.177429i	$0.943222\pi$
$864$	13.4153	−	23.6107i	0.456398	−	0.803254i
$865$	20.5090	+	25.7174i	0.697326	+	0.874419i
$866$	−14.9343	−	3.40865i	−0.507488	−	0.115831i
$867$	−20.3600	−	11.3573i	−0.691460	−	0.385715i
$868$	−0.00599465	+	0.0532040i	−0.000203472	+	0.00180586i
$869$	−7.10229			−0.240929
$870$	−5.49975	−	16.2704i	−0.186459	−	0.551618i
$871$	12.3030			0.416872
$872$	−4.17870	+	37.0869i	−0.141508	+	1.25592i
$873$	7.42687	+	3.64884i	0.251361	+	0.123495i
$874$	12.2969	+	2.80670i	0.415951	+	0.0949380i
$875$	0.0796303	+	0.0998533i	0.00269200	+	0.00337566i
$876$	−9.83899	+	13.7518i	−0.332429	+	0.464631i
$877$	6.82277	+	29.8925i	0.230388	+	1.00940i	0.949319	+	0.314315i	$0.101775\pi$
$877$	6.82277	+	29.8925i	0.230388	+	1.00940i	−0.718930	+	0.695082i	$0.755368\pi$
$878$	−2.39547	+	6.84586i	−0.0808432	+	0.231037i
$879$	−10.2239	−	18.6718i	−0.344842	−	0.629784i
$880$	−3.68308	+	2.31423i	−0.124156	+	0.0780127i
$881$	−3.30100	−	9.43372i	−0.111214	−	0.317830i	0.874803	−	0.484479i	$-0.160991\pi$
$881$	−3.30100	−	9.43372i	−0.111214	−	0.317830i	−0.986016	+	0.166649i	$0.946705\pi$
$882$	12.7627	−	15.7481i	0.429741	−	0.530266i
$883$	18.9783	−	39.4088i	0.638670	−	1.32621i	−0.290613	−	0.956841i	$-0.593859\pi$
$883$	18.9783	−	39.4088i	0.638670	−	1.32621i	0.929282	−	0.369370i	$-0.120427\pi$
$884$	10.9407	−	1.23272i	0.367974	−	0.0414607i
$885$	7.33577	+	44.2280i	0.246589	+	1.48671i
$886$	28.6305	+	13.7877i	0.961861	+	0.463208i
$887$	−0.762300	−	0.762300i	−0.0255955	−	0.0255955i	0.694193	−	0.719789i	$-0.255761\pi$
$887$	−0.762300	−	0.762300i	−0.0255955	−	0.0255955i	−0.719789	+	0.694193i	$0.755761\pi$
$888$	12.9254	+	31.5552i	0.433748	+	1.05892i
$889$	0.118795	+	0.189062i	0.00398427	+	0.00634093i
$890$	7.84014	+	16.2802i	0.262802	+	0.545714i
$891$	−28.1789	−	3.62483i	−0.944030	−	0.121436i
$892$	7.03093	−	1.60476i	0.235413	−	0.0537314i
$893$	17.6445	+	14.0710i	0.590450	+	0.470868i
$894$	−10.5184	+	9.32568i	−0.351789	+	0.311897i
$895$	−4.56785	+	20.0131i	−0.152686	+	0.668963i
$896$	0.0373261	+	0.0234536i	0.00124698	+	0.000783529i
$897$	−1.10262	+	18.3448i	−0.0368155	+	0.612514i
$898$		−	24.2800i		−	0.810234i
$899$	−25.3094	+	4.12594i	−0.844117	+	0.137608i
$900$	−4.33845	+	0.454293i	−0.144615	+	0.0151431i
$901$	−13.8235	−	1.55754i	−0.460529	−	0.0518892i
$902$	2.98543	−	4.75129i	0.0994041	−	0.158201i
$903$	0.0138614	−	0.0796833i	0.000461280	−	0.00265170i
$904$	41.2283	−	32.8785i	1.37123	−	1.09352i
$905$	12.5757	−	15.7694i	0.418029	−	0.524192i
$906$	−0.596388	−	2.10114i	−0.0198137	−	0.0698058i
$907$	32.0695	+	11.2216i	1.06485	+	0.372607i	0.805143	−	0.593081i	$-0.202088\pi$
$907$	32.0695	+	11.2216i	1.06485	+	0.372607i	0.259707	+	0.965688i	$0.416374\pi$
$908$	−5.00185	+	2.40877i	−0.165992	+	0.0799377i
$909$	−26.0275	−	33.1694i	−0.863277	−	1.10016i
$910$	0.100205	−	0.0350633i	0.00332177	−	0.00116234i
$911$	−6.24926	+	6.24926i	−0.207047	+	0.207047i	−0.803011	−	0.595964i	$-0.796770\pi$
$911$	−6.24926	+	6.24926i	−0.207047	+	0.207047i	0.595964	+	0.803011i	$0.296770\pi$
$912$	7.78494	+	3.26056i	0.257785	+	0.107968i
$913$	2.99731	+	26.6019i	0.0991965	+	0.880393i
$914$	−1.29703	−	11.5115i	−0.0429020	−	0.380765i
$915$	−27.6034	−	11.5611i	−0.912542	−	0.382199i
$916$	−2.87647	+	2.87647i	−0.0950413	+	0.0950413i
$917$	0.0329949	−	0.0115454i	0.00108959	−	0.000381264i
$918$	−7.11030	+	6.20481i	−0.234675	+	0.204789i
$919$	−10.7052	+	5.15537i	−0.353133	+	0.170060i	−0.602037	−	0.798468i	$-0.705644\pi$
$919$	−10.7052	+	5.15537i	−0.353133	+	0.170060i	0.248904	+	0.968528i	$0.419930\pi$
$920$	10.3292	+	3.61434i	0.340543	+	0.119161i
$921$	2.01168	+	7.08736i	0.0662870	+	0.233537i
$922$	−16.3116	+	20.4541i	−0.537193	+	0.673619i
$923$	45.0439	−	35.9213i	1.48264	−	1.18237i
$924$	0.0105361	−	0.0605672i	0.000346611	−	0.00199252i
$925$	4.81390	−	7.66127i	0.158280	−	0.251901i
$926$	20.4366	+	2.30266i	0.671589	+	0.0756699i
$927$	−0.333128	−	3.18135i	−0.0109414	−	0.104489i
$928$	−7.97220	+	26.9909i	−0.261700	+	0.886019i
$929$			18.6915i			0.613249i	0.951831	+	0.306625i	$0.0991996\pi$
$929$			18.6915i			0.613249i	−0.951831	+	0.306625i	$0.900800\pi$
$930$	−0.911176	+	15.1596i	−0.0298786	+	0.497103i
$931$	−39.9837	−	25.1234i	−1.31041	−	0.823387i
$932$	1.97924	−	8.67162i	0.0648322	−	0.284048i
$933$	−5.72819	+	5.07864i	−0.187532	+	0.166267i
$934$	5.68846	+	4.53639i	0.186132	+	0.148435i
$935$	−11.0459	+	2.52115i	−0.361239	+	0.0824505i
$936$	−11.2033	+	47.3641i	−0.366191	+	1.54814i
$937$	16.6396	+	34.5524i	0.543591	+	1.12878i	0.974084	+	0.226185i	$0.0726253\pi$
$937$	16.6396	+	34.5524i	0.543591	+	1.12878i	−0.430493	+	0.902594i	$0.641660\pi$
$938$	−0.0121401	−	0.0193208i	−0.000396387	−	0.000630847i
$939$	−3.76605	−	9.19418i	−0.122901	−	0.300041i
$940$	4.82043	+	4.82043i	0.157225	+	0.157225i
$941$	−43.6825	−	21.0364i	−1.42401	−	0.685766i	−0.446135	−	0.894966i	$-0.647200\pi$
$941$	−43.6825	−	21.0364i	−1.42401	−	0.685766i	−0.977873	+	0.209200i	$0.932914\pi$
$942$	−0.762021	−	4.59429i	−0.0248280	−	0.149690i
$943$	−3.54454	+	0.399374i	−0.115426	+	0.0130054i
$944$	−4.25268	+	8.83078i	−0.138413	+	0.287417i
$945$	0.0613706	−	0.0843664i	0.00199639	−	0.00274444i
$946$	−4.46504	−	12.7604i	−0.145171	−	0.414875i
$947$	34.8959	−	21.9265i	1.13396	−	0.712516i	0.171838	−	0.985125i	$-0.445029\pi$
$947$	34.8959	−	21.9265i	1.13396	−	0.712516i	0.962125	+	0.272609i	$0.0878866\pi$
$948$	1.99928	+	3.65128i	0.0649336	+	0.118588i
$949$	16.5340	−	47.2514i	0.536716	−	1.53385i
$950$	−1.97233	−	8.64132i	−0.0639907	−	0.280361i
$951$	−2.29249	+	3.20418i	−0.0743391	+	0.103903i
$952$	−0.0365680	−	0.0458549i	−0.00118518	−	0.00148616i
$953$	27.3857	+	6.25061i	0.887110	+	0.202477i	0.641712	−	0.766946i	$-0.278224\pi$
$953$	27.3857	+	6.25061i	0.887110	+	0.202477i	0.245397	+	0.969423i	$0.421082\pi$
$954$	9.44118	−	19.2166i	0.305670	−	0.622161i
$955$	1.09393	−	9.70889i	0.0353987	−	0.314172i
$956$	−17.3317			−0.560548
$957$	29.2929	−	2.98540i	0.946904	−	0.0965043i
$958$	36.7750			1.18815
$959$	0.0180248	−	0.159975i	0.000582051	−	0.00516585i
$960$	18.7246	+	10.4451i	0.604333	+	0.337113i
$961$	−8.11574	−	1.85236i	−0.261798	−	0.0597537i
$962$	−21.9149	−	27.4804i	−0.706563	−	0.886002i
$963$	−7.67152	+	11.9986i	−0.247211	+	0.386649i
$964$	1.16566	+	5.10710i	0.0375435	+	0.164489i
$965$	−7.68170	+	21.9530i	−0.247283	+	0.706693i
$966$	0.0298969	−	0.0163702i	0.000961916	−	0.000526704i
$967$	38.9915	−	24.5000i	1.25388	−	0.787867i	0.269346	−	0.963043i	$-0.413192\pi$
$967$	38.9915	−	24.5000i	1.25388	−	0.787867i	0.984537	+	0.175176i	$0.0560496\pi$
$968$	1.01209	+	2.89240i	0.0325299	+	0.0929651i
$969$	16.3346	+	14.7135i	0.524743	+	0.472665i
$970$	−2.20364	+	4.57591i	−0.0707547	+	0.146924i
$971$	40.8711	−	4.60506i	1.31161	−	0.147784i	0.571688	−	0.820471i	$-0.306289\pi$
$971$	40.8711	−	4.60506i	1.31161	−	0.147784i	0.739927	+	0.672687i	$0.234860\pi$
$972$	6.06880	+	15.5071i	0.194657	+	0.497392i
$973$	−0.136513	−	0.0657412i	−0.00437641	−	0.00210757i
$974$	−2.79996	−	2.79996i	−0.0897165	−	0.0897165i
$975$	11.9508	−	4.89520i	0.382732	−	0.156772i
$976$	−3.48094	−	5.53988i	−0.111422	−	0.177327i
$977$	9.79779	+	20.3453i	0.313459	+	0.650904i	0.996864	−	0.0791352i	$-0.0252159\pi$
$977$	9.79779	+	20.3453i	0.313459	+	0.650904i	−0.683405	+	0.730040i	$0.739502\pi$
$978$	−5.95854	+	20.3809i	−0.190533	+	0.651708i
$979$	−30.2021	+	6.89344i	−0.965265	+	0.220315i
$980$	−11.1522	−	8.89355i	−0.356243	−	0.284094i
$981$	−26.5206	−	26.9412i	−0.846736	−	0.860165i
$982$	−4.40416	+	19.2959i	−0.140542	+	0.615756i
$983$	7.59701	+	4.77352i	0.242307	+	0.152252i	0.647711	−	0.761886i	$-0.275726\pi$
$983$	7.59701	+	4.77352i	0.242307	+	0.152252i	−0.405404	+	0.914138i	$0.632869\pi$
$984$	−9.42957	−	0.566769i	−0.300604	−	0.0180680i
$985$		−	17.5736i		−	0.559943i
$986$	5.71286	−	7.93827i	0.181935	−	0.252806i
$987$	0.0609042	−	0.00318004i	0.00193860	−	0.000101222i
$988$	39.2277	+	4.41990i	1.24800	+	0.140616i
$989$	−4.57206	+	7.27640i	−0.145383	+	0.231376i
$990$	2.08870	−	17.3125i	0.0663833	−	0.550228i
$991$	−32.9962	+	26.3136i	−1.04816	+	0.835880i	−0.986752	−	0.162233i	$-0.948130\pi$
$991$	−32.9962	+	26.3136i	−1.04816	+	0.835880i	−0.0614073	+	0.998113i	$0.519559\pi$
$992$	15.5163	−	19.4569i	0.492644	−	0.617756i
$993$	37.3800	−	10.6099i	1.18622	−	0.336696i
$994$	−0.100859	−	0.0352920i	−0.00319904	−	0.00111939i
$995$	35.6454	−	17.1659i	1.13004	−	0.544197i
$996$	12.8322	−	9.02929i	0.406605	−	0.286104i
$997$	−31.1747	+	10.9085i	−0.987313	+	0.345476i	−0.775163	−	0.631761i	$-0.782332\pi$
$997$	−31.1747	+	10.9085i	−0.987313	+	0.345476i	−0.212150	+	0.977237i	$0.568047\pi$
$998$	15.8814	−	15.8814i	0.502717	−	0.502717i
$999$	−33.0757	−	9.95311i	−1.04647	−	0.314902i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	87.2.k.a.2.4	✓	96
3.2	odd	2	inner	87.2.k.a.2.5	yes	96
29.15	odd	28	inner	87.2.k.a.44.5	yes	96
87.44	even	28	inner	87.2.k.a.44.4	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.2.k.a.2.4	✓	96	1.1	even	1	trivial
87.2.k.a.2.5	yes	96	3.2	odd	2	inner
87.2.k.a.44.4	yes	96	87.44	even	28	inner
87.2.k.a.44.5	yes	96	29.15	odd	28	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:	\( N \)	\(=\)	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	87.k (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.108076 + 0.959202i) q^{2} +(0.843782 - 1.51262i) q^{3} +(1.04147 + 0.237708i) q^{4} +(-1.18935 - 1.49140i) q^{5} +(1.35972 + 0.972836i) q^{6} +(-0.00234208 - 0.0102613i) q^{7} +(-0.978186 + 2.79549i) q^{8} +(-1.57606 - 2.55265i) q^{9} +(1.55910 - 0.979646i) q^{10} +(1.04262 + 2.97964i) q^{11} +(1.23833 - 1.37477i) q^{12} +(-2.37674 + 4.93536i) q^{13} +(0.0100958 - 0.00113753i) q^{14} +(-3.25949 + 0.540627i) q^{15} +(-0.650805 - 0.313411i) q^{16} +(-1.33041 - 1.33041i) q^{17} +(2.61884 - 1.23588i) q^{18} +(-3.58912 - 5.71205i) q^{19} +(-0.884155 - 1.83597i) q^{20} +(-0.0174978 - 0.00511564i) q^{21} +(-2.97076 + 0.678057i) q^{22} +(1.51439 + 1.20769i) q^{23} +(3.40316 + 3.83842i) q^{24} +(0.302886 - 1.32703i) q^{25} +(-4.47714 - 2.81317i) q^{26} +(-5.19105 + 0.230112i) q^{27} -0.0112436i q^{28} +(5.18457 - 1.45609i) q^{29} +(-0.166298 - 3.18494i) q^{30} +(-4.73194 - 0.533162i) q^{31} +(-2.78047 + 4.42510i) q^{32} +(5.38683 + 0.937074i) q^{33} +(1.41992 - 1.13235i) q^{34} +(-0.0125182 + 0.0156973i) q^{35} +(-1.03463 - 3.03315i) q^{36} +(6.27435 + 2.19549i) q^{37} +(5.86691 - 2.82535i) q^{38} +(5.45989 + 7.75949i) q^{39} +(5.33262 - 1.86596i) q^{40} +(-1.30214 + 1.30214i) q^{41} +(0.00679802 - 0.0162310i) q^{42} +(0.496740 + 4.40869i) q^{43} +(0.377572 + 3.35104i) q^{44} +(-1.93253 + 5.38655i) q^{45} +(-1.32209 + 1.32209i) q^{46} +(-3.15765 + 1.10491i) q^{47} +(-1.02321 + 0.719973i) q^{48} +(6.30668 - 3.03714i) q^{49} +(1.24016 + 0.433949i) q^{50} +(-3.13499 + 0.889834i) q^{51} +(-3.64848 + 4.57504i) q^{52} +(5.78058 - 4.60986i) q^{53} +(0.340305 - 5.00414i) q^{54} +(3.20380 - 5.09882i) q^{55} +(0.0309765 + 0.00349021i) q^{56} +(-11.6686 + 0.609263i) q^{57} +(0.836360 + 5.13042i) q^{58} -13.5690i q^{59} +(-3.52316 - 0.211761i) q^{60} +(7.66936 + 4.81898i) q^{61} +(1.02282 - 4.48127i) q^{62} +(-0.0225023 + 0.0221510i) q^{63} +(-5.07355 - 4.04603i) q^{64} +(10.1874 - 2.32521i) q^{65} +(-1.48103 + 5.06578i) q^{66} +(-0.974487 - 2.02354i) q^{67} +(-1.06933 - 1.70183i) q^{68} +(3.10460 - 1.27168i) q^{69} +(-0.0137040 - 0.0137040i) q^{70} +(-9.47597 - 4.56339i) q^{71} +(8.67760 - 1.90891i) q^{72} +(-9.08130 + 1.02322i) q^{73} +(-2.78403 + 5.78109i) q^{74} +(-1.75173 - 1.57788i) q^{75} +(-2.38015 - 6.80207i) q^{76} +(0.0281332 - 0.0176773i) q^{77} +(-8.03300 + 4.39852i) q^{78} +(-0.743076 + 2.12359i) q^{79} +(0.306615 + 1.34337i) q^{80} +(-4.03205 + 8.04628i) q^{81} +(-1.10829 - 1.38975i) q^{82} +(8.26757 + 1.88702i) q^{83} +(-0.0170073 - 0.00948713i) q^{84} +(-0.401848 + 3.56650i) q^{85} -4.28251 q^{86} +(2.17213 - 9.07094i) q^{87} -9.34946 q^{88} +(-1.09875 + 9.75169i) q^{89} +(-4.95793 - 2.43585i) q^{90} +(0.0562099 + 0.0128295i) q^{91} +(1.29011 + 1.61775i) q^{92} +(-4.79920 + 6.70778i) q^{93} +(-0.718566 - 3.14824i) q^{94} +(-4.25023 + 12.1465i) q^{95} +(4.34740 + 7.93963i) q^{96} +(-2.33549 + 1.46749i) q^{97} +(2.23163 + 6.37763i) q^{98} +(5.96275 - 7.35756i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 12 q^{3} - 28 q^{4} - 14 q^{6} - 20 q^{7} - 14 q^{9} - 4 q^{10} - 8 q^{12} - 28 q^{13} - 16 q^{15} - 48 q^{16} - 28 q^{18} - 20 q^{19} + 26 q^{21} - 28 q^{22} + 58 q^{24} - 20 q^{25} + 36 q^{27}+ \cdots + 82 q^{99}+O(q^{100}) \) 96 * q - 12 * q^3 - 28 * q^4 - 14 * q^6 - 20 * q^7 - 14 * q^9 - 4 * q^10 - 8 * q^12 - 28 * q^13 - 16 * q^15 - 48 * q^16 - 28 * q^18 - 20 * q^19 + 26 * q^21 - 28 * q^22 + 58 * q^24 - 20 * q^25 + 36 * q^27 + 96 * q^30 - 32 * q^31 + 28 * q^33 - 28 * q^34 + 22 * q^36 - 4 * q^37 - 40 * q^39 - 48 * q^40 - 14 * q^42 - 32 * q^43 + 42 * q^45 + 120 * q^46 - 20 * q^48 + 4 * q^49 - 14 * q^51 + 72 * q^52 - 30 * q^54 + 148 * q^55 + 112 * q^58 + 20 * q^60 + 12 * q^61 - 14 * q^63 + 224 * q^64 - 32 * q^66 + 28 * q^67 + 10 * q^69 + 52 * q^70 - 44 * q^72 + 16 * q^73 - 144 * q^75 - 100 * q^76 - 102 * q^78 - 60 * q^79 - 146 * q^81 - 108 * q^82 - 64 * q^84 - 104 * q^85 - 70 * q^87 - 312 * q^88 - 96 * q^90 - 112 * q^91 - 70 * q^93 + 56 * q^94 - 168 * q^96 + 32 * q^97 + 82 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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