LMFDB - Embedded newform 460.2.w.a.167.55

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(3,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([22, 33, 32]))

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

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

chi := DirichletCharacter("460.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.w (of order $44$, degree $20$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$1360$
Relative dimension:	$68$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			167.55
Character	$\chi$	$=$	460.167
Dual form			460.2.w.a.303.55

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.16261 + 0.805194i) q^{2} +(1.05800 + 1.93757i) q^{3} +(0.703326 + 1.87225i) q^{4} +(1.36176 - 1.77359i) q^{5} +(-0.330086 + 3.10453i) q^{6} +(0.469306 + 0.626919i) q^{7} +(-0.689833 + 2.74301i) q^{8} +(-1.01292 + 1.57613i) q^{9} +O(q^{10})$	\(q+(1.16261 + 0.805194i) q^{2} +(1.05800 + 1.93757i) q^{3} +(0.703326 + 1.87225i) q^{4} +(1.36176 - 1.77359i) q^{5} +(-0.330086 + 3.10453i) q^{6} +(0.469306 + 0.626919i) q^{7} +(-0.689833 + 2.74301i) q^{8} +(-1.01292 + 1.57613i) q^{9} +(3.01127 - 0.965517i) q^{10} +(0.247862 - 0.113195i) q^{11} +(-2.88351 + 3.34358i) q^{12} +(-3.81406 - 2.85517i) q^{13} +(0.0408284 + 1.10675i) q^{14} +(4.87719 + 0.762052i) q^{15} +(-3.01067 + 2.63361i) q^{16} +(3.13600 - 0.224291i) q^{17} +(-2.44671 + 1.01683i) q^{18} +(-0.751063 - 0.866772i) q^{19} +(4.27837 + 1.30214i) q^{20} +(-0.718179 + 1.57259i) q^{21} +(0.379311 + 0.0679757i) q^{22} +(-4.69351 - 0.985386i) q^{23} +(-6.04463 + 1.56549i) q^{24} +(-1.29124 - 4.83039i) q^{25} +(-2.13530 - 6.39051i) q^{26} +(2.48044 + 0.177404i) q^{27} +(-0.843677 + 1.31959i) q^{28} +(1.31613 + 1.14043i) q^{29} +(5.05667 + 4.81305i) q^{30} +(-1.79471 - 6.11221i) q^{31} +(-5.62080 + 0.637691i) q^{32} +(0.481561 + 0.360492i) q^{33} +(3.82654 + 2.26432i) q^{34} +(1.75098 + 0.0213545i) q^{35} +(-3.66332 - 0.787903i) q^{36} +(0.595727 + 2.73851i) q^{37} +(-0.175273 - 1.61247i) q^{38} +(1.49684 - 10.4108i) q^{39} +(3.92560 + 4.95880i) q^{40} +(-5.60528 + 3.60229i) q^{41} +(-2.10120 + 1.25004i) q^{42} +(2.89000 + 5.29264i) q^{43} +(0.386258 + 0.384448i) q^{44} +(1.41606 + 3.94280i) q^{45} +(-4.66329 - 4.92480i) q^{46} +(-5.11678 + 5.11678i) q^{47} +(-8.28808 - 3.04704i) q^{48} +(1.79935 - 6.12802i) q^{49} +(2.38819 - 6.65557i) q^{50} +(3.75245 + 5.83892i) q^{51} +(2.66307 - 9.14900i) q^{52} +(-5.98439 - 7.99420i) q^{53} +(2.74094 + 2.20349i) q^{54} +(0.136767 - 0.593750i) q^{55} +(-2.04339 + 0.854843i) q^{56} +(0.884815 - 2.37228i) q^{57} +(0.611878 + 2.38562i) q^{58} +(-0.977381 - 6.79784i) q^{59} +(2.00350 + 9.66731i) q^{60} +(-0.633621 + 0.186048i) q^{61} +(2.83497 - 8.55121i) q^{62} +(-1.46347 + 0.104670i) q^{63} +(-7.04826 - 3.78444i) q^{64} +(-10.2577 + 2.87654i) q^{65} +(0.269602 + 0.806862i) q^{66} +(3.98375 + 10.6808i) q^{67} +(2.62556 + 5.71363i) q^{68} +(-3.05645 - 10.1366i) q^{69} +(2.01851 + 1.43470i) q^{70} +(9.86457 + 4.50500i) q^{71} +(-3.62460 - 3.86571i) q^{72} +(13.9776 + 0.999700i) q^{73} +(-1.51243 + 3.66350i) q^{74} +(7.99311 - 7.61241i) q^{75} +(1.09458 - 2.01580i) q^{76} +(0.187287 + 0.102267i) q^{77} +(10.1229 - 10.8984i) q^{78} +(0.0246843 + 0.171683i) q^{79} +(0.571151 + 8.92602i) q^{80} +(4.61545 + 10.1064i) q^{81} +(-9.41729 - 0.325271i) q^{82} +(1.45734 + 6.69926i) q^{83} +(-3.44941 - 0.238568i) q^{84} +(3.87266 - 5.86740i) q^{85} +(-0.901657 + 8.48029i) q^{86} +(-0.817215 + 3.75668i) q^{87} +(0.139512 + 0.757976i) q^{88} +(4.08868 - 13.9248i) q^{89} +(-1.52839 + 5.72414i) q^{90} -3.73106i q^{91} +(-1.45617 - 9.48048i) q^{92} +(9.94407 - 9.94407i) q^{93} +(-10.0688 + 1.82882i) q^{94} +(-2.56006 + 0.151745i) q^{95} +(-7.18235 - 10.2160i) q^{96} +(8.79636 + 1.91353i) q^{97} +(7.02618 - 5.67567i) q^{98} +(-0.0726540 + 0.505319i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8}+O(q^{10}) $ 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8	$ 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8} - 18 q^{10} - 6 q^{12} - 36 q^{13} - 44 q^{16} - 36 q^{17} - 38 q^{18} - 14 q^{20} - 88 q^{21} - 28 q^{22} - 36 q^{25} - 36 q^{26} - 34 q^{28} + 2 q^{30} + 2 q^{32} - 60 q^{33} - 36 q^{36} - 36 q^{37} - 10 q^{38} + 2 q^{40} - 56 q^{41} - 202 q^{42} - 120 q^{45} - 44 q^{46} - 50 q^{48} - 34 q^{50} - 250 q^{52} - 84 q^{53} - 84 q^{56} - 44 q^{57} - 58 q^{58} - 42 q^{60} - 136 q^{61} - 82 q^{62} - 68 q^{65} - 84 q^{66} - 4 q^{68} + 16 q^{70} - 104 q^{72} - 36 q^{73} + 4 q^{76} - 44 q^{77} - 50 q^{78} + 204 q^{80} + 80 q^{81} - 10 q^{82} - 252 q^{85} + 44 q^{86} - 50 q^{88} + 264 q^{90} - 22 q^{92} - 88 q^{93} + 52 q^{96} - 36 q^{97} + 30 q^{98}+O(q^{100}) $ 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8 - 18 * q^10 - 6 * q^12 - 36 * q^13 - 44 * q^16 - 36 * q^17 - 38 * q^18 - 14 * q^20 - 88 * q^21 - 28 * q^22 - 36 * q^25 - 36 * q^26 - 34 * q^28 + 2 * q^30 + 2 * q^32 - 60 * q^33 - 36 * q^36 - 36 * q^37 - 10 * q^38 + 2 * q^40 - 56 * q^41 - 202 * q^42 - 120 * q^45 - 44 * q^46 - 50 * q^48 - 34 * q^50 - 250 * q^52 - 84 * q^53 - 84 * q^56 - 44 * q^57 - 58 * q^58 - 42 * q^60 - 136 * q^61 - 82 * q^62 - 68 * q^65 - 84 * q^66 - 4 * q^68 + 16 * q^70 - 104 * q^72 - 36 * q^73 + 4 * q^76 - 44 * q^77 - 50 * q^78 + 204 * q^80 + 80 * q^81 - 10 * q^82 - 252 * q^85 + 44 * q^86 - 50 * q^88 + 264 * q^90 - 22 * q^92 - 88 * q^93 + 52 * q^96 - 36 * q^97 + 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{9}{11}\right)$

Coefficient data

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

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

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

$2$	1.16261	+	0.805194i	0.822090	+	0.569358i
$2$	1.16261	+	0.805194i	0.822090	+	0.569358i
$3$	1.05800	+	1.93757i	0.610834	+	1.11866i	0.981783	+	0.190005i	$0.0608506\pi$
$3$	1.05800	+	1.93757i	0.610834	+	1.11866i	−0.370949	+	0.928653i	$0.620968\pi$
$4$	0.703326	+	1.87225i	0.351663	+	0.936127i
$5$	1.36176	−	1.77359i	0.608996	−	0.793174i
$5$	1.36176	−	1.77359i	0.608996	−	0.793174i
$6$	−0.330086	+	3.10453i	−0.134757	+	1.26742i
$7$	0.469306	+	0.626919i	0.177381	+	0.236953i	0.880416	−	0.474202i	$-0.157263\pi$
$7$	0.469306	+	0.626919i	0.177381	+	0.236953i	−0.703035	+	0.711155i	$0.748172\pi$
$8$	−0.689833	+	2.74301i	−0.243893	+	0.969802i
$9$	−1.01292	+	1.57613i	−0.337638	+	0.525376i
$10$	3.01127	−	0.965517i	0.952249	−	0.305323i
$11$	0.247862	−	0.113195i	0.0747333	−	0.0341296i	−0.377698	−	0.925929i	$-0.623284\pi$
$11$	0.247862	−	0.113195i	0.0747333	−	0.0341296i	0.452431	+	0.891799i	$0.350557\pi$
$12$	−2.88351	+	3.34358i	−0.832399	+	0.965209i
$13$	−3.81406	−	2.85517i	−1.05783	−	0.791881i	−0.0790653	−	0.996869i	$-0.525194\pi$
$13$	−3.81406	−	2.85517i	−1.05783	−	0.791881i	−0.978764	+	0.204988i	$0.934284\pi$
$14$	0.0408284	+	1.10675i	0.0109118	+	0.295790i
$15$	4.87719	+	0.762052i	1.25929	+	0.196761i
$16$	−3.01067	+	2.63361i	−0.752666	+	0.658402i
$17$	3.13600	−	0.224291i	0.760591	−	0.0543985i	0.314345	−	0.949309i	$-0.398215\pi$
$17$	3.13600	−	0.224291i	0.760591	−	0.0543985i	0.446246	+	0.894910i	$0.352761\pi$
$18$	−2.44671	+	1.01683i	−0.576696	+	0.239669i
$19$	−0.751063	−	0.866772i	−0.172306	−	0.198851i	0.663028	−	0.748595i	$-0.269271\pi$
$19$	−0.751063	−	0.866772i	−0.172306	−	0.198851i	−0.835334	+	0.549743i	$0.814726\pi$
$20$	4.27837	+	1.30214i	0.956672	+	0.291167i
$21$	−0.718179	+	1.57259i	−0.156719	+	0.343168i
$22$	0.379311	+	0.0679757i	0.0808695	+	0.0144925i
$23$	−4.69351	−	0.985386i	−0.978664	−	0.205467i
$23$	−4.69351	−	0.985386i	−0.978664	−	0.205467i
$24$	−6.04463	+	1.56549i	−1.23386	+	0.319555i
$25$	−1.29124	−	4.83039i	−0.258249	−	0.966078i
$26$	−2.13530	−	6.39051i	−0.418767	−	1.25328i
$27$	2.48044	+	0.177404i	0.477360	+	0.0341415i
$28$	−0.843677	+	1.31959i	−0.159440	+	0.249379i
$29$	1.31613	+	1.14043i	0.244400	+	0.211773i	0.768443	−	0.639918i	$-0.221032\pi$
$29$	1.31613	+	1.14043i	0.244400	+	0.211773i	−0.524044	+	0.851691i	$0.675577\pi$
$30$	5.05667	+	4.81305i	0.923218	+	0.878739i
$31$	−1.79471	−	6.11221i	−0.322339	−	1.09779i	−0.948153	−	0.317814i	$-0.897051\pi$
$31$	−1.79471	−	6.11221i	−0.322339	−	1.09779i	0.625814	−	0.779972i	$-0.284767\pi$
$32$	−5.62080	+	0.637691i	−0.993626	+	0.112729i
$33$	0.481561	+	0.360492i	0.0838290	+	0.0627536i
$34$	3.82654	+	2.26432i	0.656246	+	0.388328i
$35$	1.75098	+	0.0213545i	0.295969	+	0.00360956i
$36$	−3.66332	−	0.787903i	−0.610553	−	0.131317i
$37$	0.595727	+	2.73851i	0.0979369	+	0.450209i	0.999833	+	0.0182563i	$0.00581148\pi$
$37$	0.595727	+	2.73851i	0.0979369	+	0.450209i	−0.901896	+	0.431952i	$0.857825\pi$
$38$	−0.175273	−	1.61247i	−0.0284331	−	0.261577i
$39$	1.49684	−	10.4108i	0.239687	−	1.66706i
$40$	3.92560	+	4.95880i	0.620692	+	0.784055i
$41$	−5.60528	+	3.60229i	−0.875397	+	0.562583i	−0.899399	−	0.437128i	$-0.855996\pi$
$41$	−5.60528	+	3.60229i	−0.875397	+	0.562583i	0.0240021	+	0.999712i	$0.492359\pi$
$42$	−2.10120	+	1.25004i	−0.324223	+	0.192885i
$43$	2.89000	+	5.29264i	0.440721	+	0.807120i	0.999757	−	0.0220229i	$-0.00701066\pi$
$43$	2.89000	+	5.29264i	0.440721	+	0.807120i	−0.559037	+	0.829143i	$0.688829\pi$
$44$	0.386258	+	0.384448i	0.0582305	+	0.0579578i
$45$	1.41606	+	3.94280i	0.211094	+	0.587757i
$46$	−4.66329	−	4.92480i	−0.687565	−	0.726123i
$47$	−5.11678	+	5.11678i	−0.746360	+	0.746360i	−0.973794	−	0.227434i	$-0.926966\pi$
$47$	−5.11678	+	5.11678i	−0.746360	+	0.746360i	0.227434	+	0.973794i	$0.426966\pi$
$48$	−8.28808	−	3.04704i	−1.19628	−	0.439803i
$49$	1.79935	−	6.12802i	0.257050	−	0.875431i
$50$	2.38819	−	6.65557i	0.337741	−	0.941239i
$51$	3.75245	+	5.83892i	0.525448	+	0.817613i
$52$	2.66307	−	9.14900i	0.369302	−	1.26874i
$53$	−5.98439	−	7.99420i	−0.822019	−	1.09809i	−0.993604	−	0.112919i	$-0.963980\pi$
$53$	−5.98439	−	7.99420i	−0.822019	−	1.09809i	0.171586	−	0.985169i	$-0.445111\pi$
$54$	2.74094	+	2.20349i	0.372994	+	0.299856i
$55$	0.136767	−	0.593750i	0.0184416	−	0.0800613i
$56$	−2.04339	+	0.854843i	−0.273060	+	0.114233i
$57$	0.884815	−	2.37228i	0.117197	−	0.314216i
$58$	0.611878	+	2.38562i	0.0803435	+	0.313248i
$59$	−0.977381	−	6.79784i	−0.127244	−	0.885003i	−0.949025	−	0.315200i	$-0.897929\pi$
$59$	−0.977381	−	6.79784i	−0.127244	−	0.885003i	0.821781	−	0.569803i	$-0.192981\pi$
$60$	2.00350	+	9.66731i	0.258651	+	1.24804i
$61$	−0.633621	+	0.186048i	−0.0811268	+	0.0238210i	−0.322044	−	0.946725i	$-0.604370\pi$
$61$	−0.633621	+	0.186048i	−0.0811268	+	0.0238210i	0.240917	+	0.970546i	$0.422552\pi$
$62$	2.83497	−	8.55121i	0.360042	−	1.08600i
$63$	−1.46347	+	0.104670i	−0.184380	+	0.0131871i
$64$	−7.04826	−	3.78444i	−0.881033	−	0.473056i
$65$	−10.2577	+	2.87654i	−1.27231	+	0.356790i
$66$	0.269602	+	0.806862i	0.0331857	+	0.0993178i
$67$	3.98375	+	10.6808i	0.486692	+	1.30487i	0.915806	+	0.401621i	$0.131553\pi$
$67$	3.98375	+	10.6808i	0.486692	+	1.30487i	−0.429114	+	0.903250i	$0.641174\pi$
$68$	2.62556	+	5.71363i	0.318395	+	0.692879i
$69$	−3.05645	−	10.1366i	−0.367953	−	1.22030i
$70$	2.01851	+	1.43470i	0.241258	+	0.171480i
$71$	9.86457	+	4.50500i	1.17071	+	0.534645i	0.903330	−	0.428947i	$-0.141115\pi$
$71$	9.86457	+	4.50500i	1.17071	+	0.534645i	0.267379	+	0.963591i	$0.413842\pi$
$72$	−3.62460	−	3.86571i	−0.427163	−	0.455578i
$73$	13.9776	+	0.999700i	1.63596	+	0.117006i	0.858804	−	0.512305i	$-0.171208\pi$
$73$	13.9776	+	0.999700i	1.63596	+	0.117006i	0.777154	+	0.629311i	$0.216663\pi$
$74$	−1.51243	+	3.66350i	−0.175817	+	0.425873i
$75$	7.99311	−	7.61241i	0.922965	−	0.879006i
$76$	1.09458	−	2.01580i	0.125556	−	0.231228i
$77$	0.187287	+	0.102267i	0.0213434	+	0.0116544i
$78$	10.1229	−	10.8984i	1.14620	−	1.23400i
$79$	0.0246843	+	0.171683i	0.00277721	+	0.0193159i	0.991163	−	0.132650i	$-0.0423487\pi$
$79$	0.0246843	+	0.171683i	0.00277721	+	0.0193159i	−0.988386	+	0.151966i	$0.951440\pi$
$80$	0.571151	+	8.92602i	0.0638566	+	0.997959i
$81$	4.61545	+	10.1064i	0.512828	+	1.12294i
$82$	−9.41729	−	0.325271i	−1.03997	−	0.0359202i
$83$	1.45734	+	6.69926i	0.159963	+	0.735340i	0.985319	+	0.170726i	$0.0546112\pi$
$83$	1.45734	+	6.69926i	0.159963	+	0.735340i	−0.825355	+	0.564614i	$0.809025\pi$
$84$	−3.44941	−	0.238568i	−0.376361	−	0.0260299i
$85$	3.87266	−	5.86740i	0.420049	−	0.636409i
$86$	−0.901657	+	8.48029i	−0.0972282	+	0.914453i
$87$	−0.817215	+	3.75668i	−0.0876147	+	0.402758i
$88$	0.139512	+	0.757976i	0.0148720	+	0.0808005i
$89$	4.08868	−	13.9248i	0.433399	−	1.47602i	−0.396462	−	0.918051i	$-0.629762\pi$
$89$	4.08868	−	13.9248i	0.433399	−	1.47602i	0.829861	−	0.557970i	$-0.188420\pi$
$90$	−1.52839	+	5.72414i	−0.161106	+	0.603377i
$91$		−	3.73106i		−	0.391121i
$92$	−1.45617	−	9.48048i	−0.151816	−	0.988409i
$93$	9.94407	−	9.94407i	1.03115	−	1.03115i
$94$	−10.0688	+	1.82882i	−1.03852	+	0.188629i
$95$	−2.56006	+	0.151745i	−0.262657	+	0.0155687i
$96$	−7.18235	−	10.2160i	−0.733045	−	1.04267i
$97$	8.79636	+	1.91353i	0.893135	+	0.194290i	0.635636	−	0.771989i	$-0.280738\pi$
$97$	8.79636	+	1.91353i	0.893135	+	0.194290i	0.257499	+	0.966279i	$0.417102\pi$
$98$	7.02618	−	5.67567i	0.709752	−	0.573329i
$99$	−0.0726540	+	0.505319i	−0.00730200	+	0.0507865i
$100$	8.13555	−	5.81488i	0.813555	−	0.581488i
$101$	−4.79991	−	3.08471i	−0.477609	−	0.306940i	0.279596	−	0.960118i	$-0.409799\pi$
$101$	−4.79991	−	3.08471i	−0.477609	−	0.306940i	−0.757205	+	0.653177i	$0.773436\pi$
$102$	−0.338830	+	9.80984i	−0.0335492	+	0.971319i
$103$	−0.619794	+	1.66173i	−0.0610702	+	0.163735i	−0.963901	−	0.266260i	$-0.914212\pi$
$103$	−0.619794	+	1.66173i	−0.0610702	+	0.163735i	0.902831	+	0.429995i	$0.141485\pi$
$104$	10.4628	−	8.49243i	1.02597	−	0.832751i
$105$	1.81115	+	3.41524i	0.176750	+	0.333293i
$106$	−0.520626	−	14.1127i	−0.0505676	−	1.37075i
$107$	3.05789	−	5.60011i	0.295617	−	0.541383i	−0.687084	−	0.726578i	$-0.741110\pi$
$107$	3.05789	−	5.60011i	0.295617	−	0.541383i	0.982702	+	0.185195i	$0.0592916\pi$
$108$	1.41241	+	4.76878i	0.135909	+	0.458876i
$109$	−3.75589	−	3.25450i	−0.359749	−	0.311724i	0.456168	−	0.889894i	$-0.349222\pi$
$109$	−3.75589	−	3.25450i	−0.359749	−	0.311724i	−0.815917	+	0.578170i	$0.803767\pi$
$110$	0.637090	−	0.580177i	0.0607442	−	0.0553177i
$111$	−4.67579	+	4.05160i	−0.443807	+	0.384561i
$112$	−3.06398	−	0.651477i	−0.289519	−	0.0615588i
$113$	5.73274	+	15.3701i	0.539291	+	1.44590i	0.865650	+	0.500649i	$0.166905\pi$
$113$	5.73274	+	15.3701i	0.539291	+	1.44590i	−0.326359	+	0.945246i	$0.605822\pi$
$114$	2.93884	−	2.04559i	0.275248	−	0.191587i
$115$	−8.13908	+	6.98250i	−0.758973	+	0.651122i
$116$	−1.20951	+	3.26623i	−0.112301	+	0.303262i
$117$	8.36343	−	3.11940i	0.773199	−	0.288388i
$118$	4.33726	−	8.69022i	0.399277	−	0.799999i
$119$	1.61235	+	1.86076i	0.147804	+	0.170575i
$120$	−5.45477	+	12.8525i	−0.497950	+	1.17327i
$121$	−7.15485	+	8.25713i	−0.650440	+	0.750648i
$122$	−0.886459	−	0.293886i	−0.0802562	−	0.0266072i
$123$	−12.9101	−	7.04943i	−1.16406	−	0.635625i
$124$	10.1813	−	7.65903i	0.914312	−	0.687801i
$125$	−10.3255	−	4.28768i	−0.923540	−	0.383501i
$126$	−1.78573	−	1.05669i	−0.159085	−	0.0941373i
$127$	5.30456	+	1.97850i	0.470704	+	0.175563i	0.573612	−	0.819127i	$-0.305542\pi$
$127$	5.30456	+	1.97850i	0.470704	+	0.175563i	−0.102908	+	0.994691i	$0.532815\pi$
$128$	−5.14717	−	10.0751i	−0.454950	−	0.890517i
$129$	−7.19727	+	11.1992i	−0.633685	+	0.986033i
$130$	−14.2419	−	4.91516i	−1.24910	−	0.431088i
$131$	5.82763	+	0.837887i	0.509163	+	0.0732066i	0.392109	−	0.919919i	$-0.371746\pi$
$131$	5.82763	+	0.837887i	0.509163	+	0.0732066i	0.117054	+	0.993126i	$0.462655\pi$
$132$	−0.336238	+	1.15515i	−0.0292658	+	0.100543i
$133$	0.190918	−	0.877637i	0.0165547	−	0.0761008i
$134$	−3.96860	+	15.6253i	−0.342835	+	1.34982i
$135$	3.69239	−	4.15770i	0.317791	−	0.357838i
$136$	−1.54808	+	8.75681i	−0.132747	+	0.750890i
$137$	−8.05574	−	8.05574i	−0.688248	−	0.688248i	0.273596	−	0.961845i	$-0.411787\pi$
$137$	−8.05574	−	8.05574i	−0.688248	−	0.688248i	−0.961845	+	0.273596i	$0.911787\pi$
$138$	4.60843	−	14.2459i	0.392295	−	1.21269i
$139$	−20.3665			−1.72746			−0.863732	−	0.503951i	$-0.831879\pi$
$139$	−20.3665			−1.72746			−0.863732	+	0.503951i	$0.831879\pi$
$140$	1.19153	+	3.29329i	0.100702	+	0.278334i
$141$	−15.3277	−	4.50061i	−1.29082	−	0.379020i
$142$	7.84125	+	13.1804i	0.658023	+	1.10608i
$143$	−1.26855	−	0.275957i	−0.106082	−	0.0230767i
$144$	−1.10135	−	7.41281i	−0.0917793	−	0.617734i
$145$	3.81491	−	0.781285i	0.316811	−	0.0648822i
$146$	15.4456	+	12.4170i	1.27829	+	1.02764i
$147$	13.7772	−	2.99704i	1.13632	−	0.247192i
$148$	−4.70820	+	3.04142i	−0.387011	+	0.250003i
$149$	0.427465	−	0.195217i	0.0350193	−	0.0159928i	−0.397828	−	0.917460i	$-0.630236\pi$
$149$	0.427465	−	0.195217i	0.0350193	−	0.0159928i	0.432848	+	0.901467i	$0.357509\pi$
$150$	15.4223	−	2.41427i	1.25923	−	0.197124i
$151$	−12.1075	+	1.74080i	−0.985295	+	0.141664i	−0.616083	−	0.787681i	$-0.711281\pi$
$151$	−12.1075	+	1.74080i	−0.985295	+	0.141664i	−0.369212	+	0.929345i	$0.620372\pi$
$152$	2.89568	−	1.46225i	0.234870	−	0.118604i
$153$	−2.82299	+	5.16991i	−0.228225	+	0.417963i
$154$	0.135398	+	0.269699i	0.0109107	+	0.0217330i
$155$	−13.2845	−	5.14026i	−1.06704	−	0.412876i
$156$	20.5444	−	4.51970i	1.64487	−	0.361865i
$157$	−0.870197	+	12.1669i	−0.0694493	+	0.971027i	0.836589	+	0.547831i	$0.184546\pi$
$157$	−0.870197	+	12.1669i	−0.0694493	+	0.971027i	−0.906038	+	0.423196i	$0.860908\pi$
$158$	−0.109540	+	0.219477i	−0.00871454	+	0.0174606i
$159$	9.15791	−	20.0530i	0.726269	−	1.59031i
$160$	−6.52315	+	10.8374i	−0.515700	+	0.856769i
$161$	−1.58493	−	3.40490i	−0.124910	−	0.268344i
$162$	−2.77166	+	15.4662i	−0.217762	+	1.21514i
$163$	−16.6372	+	6.20536i	−1.30313	+	0.486042i	−0.902694	−	0.430284i	$-0.858413\pi$
$163$	−16.6372	+	6.20536i	−1.30313	+	0.486042i	−0.400434	+	0.916325i	$0.631141\pi$
$164$	−10.6867	−	7.96091i	−0.834494	−	0.621643i
$165$	1.29513	−	0.363190i	0.100826	−	0.0282743i
$166$	−3.69989	+	8.96207i	−0.287167	+	0.695591i
$167$	−0.891386	−	12.4632i	−0.0689775	−	0.964432i	−0.907632	−	0.419767i	$-0.862112\pi$
$167$	−0.891386	−	12.4632i	−0.0689775	−	0.964432i	0.838654	−	0.544664i	$-0.183343\pi$
$168$	−3.81822	−	3.05480i	−0.294582	−	0.235683i
$169$	2.73254	+	9.30616i	0.210195	+	0.715859i
$170$	9.22679	−	3.70326i	0.707662	−	0.284027i
$171$	2.12691	−	0.305803i	0.162649	−	0.0233853i
$172$	−7.87655	+	9.13326i	−0.600582	+	0.696405i
$173$	−2.82419	−	1.05337i	−0.214719	−	0.0800862i	0.239803	−	0.970822i	$-0.422917\pi$
$173$	−2.82419	−	1.05337i	−0.214719	−	0.0800862i	−0.454522	+	0.890735i	$0.650190\pi$
$174$	−3.97496	+	3.70954i	−0.301341	+	0.281219i
$175$	2.42228	−	3.07644i	0.183107	−	0.232557i
$176$	−0.448120	+	0.993565i	−0.0337783	+	0.0748928i
$177$	12.1372	−	9.08583i	0.912291	−	0.682933i
$178$	15.9657	−	12.8969i	1.19668	−	0.966663i
$179$	−8.88274	+	5.70859i	−0.663928	+	0.426680i	−0.828732	−	0.559646i	$-0.810937\pi$
$179$	−8.88274	+	5.70859i	−0.663928	+	0.426680i	0.164804	+	0.986326i	$0.447301\pi$
$180$	−6.38596	+	5.42429i	−0.475981	+	0.404303i
$181$	19.2569	+	5.65435i	1.43136	+	0.420284i	0.903331	−	0.428944i	$-0.141114\pi$
$181$	19.2569	+	5.65435i	1.43136	+	0.420284i	0.528026	+	0.849228i	$0.322932\pi$
$182$	3.00422	−	4.33776i	0.222688	−	0.321536i
$183$	−1.03085	−	1.03085i	−0.0762026	−	0.0762026i
$184$	5.94067	−	12.1946i	0.437952	−	0.898999i
$185$	5.66823	+	2.67261i	0.416737	+	0.196494i
$186$	19.5680	−	3.55418i	1.43479	−	0.260605i
$187$	0.751907	−	0.410572i	0.0549849	−	0.0300240i
$188$	−13.1787	−	5.98115i	−0.961154	−	0.436220i
$189$	1.05287	+	1.63829i	0.0765847	+	0.119168i
$190$	−3.09854	−	1.88493i	−0.224792	−	0.136747i
$191$	−11.5794	−	1.66486i	−0.837853	−	0.120465i	−0.289986	−	0.957031i	$-0.593651\pi$
$191$	−11.5794	−	1.66486i	−0.837853	−	0.120465i	−0.547867	+	0.836566i	$0.684560\pi$
$192$	−0.124386	−	17.6604i	−0.00897675	−	1.27453i
$193$	−10.1236	+	2.20226i	−0.728713	+	0.158522i	−0.561592	−	0.827415i	$-0.689811\pi$
$193$	−10.1236	+	2.20226i	−0.728713	+	0.158522i	−0.167121	+	0.985936i	$0.553447\pi$
$194$	8.68597	+	9.30746i	0.623616	+	0.668237i
$195$	−16.4261	−	16.8317i	−1.17630	−	1.20534i
$196$	12.7387	−	0.941156i	0.909909	−	0.0672255i
$197$	6.90184	−	9.21978i	0.491736	−	0.656882i	−0.484196	−	0.874960i	$-0.660888\pi$
$197$	6.90184	−	9.21978i	0.491736	−	0.656882i	0.975931	+	0.218078i	$0.0699786\pi$
$198$	−0.491348	+	0.528989i	−0.0349186	+	0.0375936i
$199$	−4.27981	+	1.25667i	−0.303388	+	0.0890826i	−0.429883	−	0.902885i	$-0.641445\pi$
$199$	−4.27981	+	1.25667i	−0.303388	+	0.0890826i	0.126496	+	0.991967i	$0.459627\pi$
$200$	14.1406	−	0.209737i	0.999890	−	0.0148306i
$201$	−16.4801	+	19.0191i	−1.16242	+	1.34150i
$202$	−3.09663	−	7.45118i	−0.217878	−	0.524263i
$203$	−0.0972921	+	1.36032i	−0.00682857	+	0.0954759i
$204$	−8.29275	+	11.1322i	−0.580609	+	0.779410i
$205$	−1.24403	+	14.8469i	−0.0868865	+	1.03695i
$206$	−2.05860	+	1.43289i	−0.143429	+	0.0998344i
$207$	6.30722	−	6.39945i	0.438382	−	0.444793i
$208$	19.0023	−	1.44878i	1.31757	−	0.100455i
$209$	−0.284275	−	0.129824i	−0.0196637	−	0.00898010i
$210$	−0.644269	+	5.42892i	−0.0444588	+	0.374631i
$211$	−8.14645	+	7.05894i	−0.560825	+	0.485957i	−0.888527	−	0.458824i	$-0.848271\pi$
$211$	−8.14645	+	7.05894i	−0.560825	+	0.485957i	0.327703	+	0.944781i	$0.393726\pi$
$212$	10.7582	−	16.8268i	0.738876	−	1.15567i
$213$	1.70790	+	23.8796i	0.117024	+	1.63620i
$214$	8.06431	−	4.04855i	0.551265	−	0.276753i
$215$	13.3225	+	2.08161i	0.908584	+	0.141964i
$216$	−2.19771	+	6.68150i	−0.149535	+	0.454618i
$217$	2.98960	−	3.99364i	0.202947	−	0.271106i
$218$	−1.74613	−	6.80793i	−0.118263	−	0.461091i
$219$	12.8513	+	28.1404i	0.868409	+	1.90155i
$220$	1.20784	−	0.161538i	0.0814327	−	0.0108909i
$221$	−12.6013	−	8.09834i	−0.847653	−	0.544753i
$222$	−8.69844	+	0.945510i	−0.583801	+	0.0634584i
$223$	13.7930	−	10.3253i	0.923651	−	0.691436i	−0.0276770	−	0.999617i	$-0.508811\pi$
$223$	13.7930	−	10.3253i	0.923651	−	0.691436i	0.951328	+	0.308181i	$0.0997201\pi$
$224$	−3.03765	−	3.22451i	−0.202962	−	0.215447i
$225$	8.92123	+	2.85761i	0.594749	+	0.190508i
$226$	−5.71095	+	22.4854i	−0.379886	+	1.49571i
$227$	−17.2357	+	9.41140i	−1.14397	+	0.624656i	−0.935484	−	0.353368i	$-0.885036\pi$
$227$	−17.2357	+	9.41140i	−1.14397	+	0.624656i	−0.208489	+	0.978025i	$0.566854\pi$
$228$	5.06382	−	0.0118883i	0.335360	−	0.000787320i
$229$			16.9000i			1.11678i	0.829577	+	0.558392i	$0.188582\pi$
$229$			16.9000i			1.11678i	−0.829577	+	0.558392i	$0.811418\pi$
$230$	−15.0848	+	1.56439i	−0.994665	+	0.103153i
$231$			0.471081i			0.0309948i
$232$	−4.03614	+	2.82346i	−0.264986	+	0.185369i
$233$	11.2898	−	6.16468i	0.739617	−	0.403861i	−0.0648220	−	0.997897i	$-0.520648\pi$
$233$	11.2898	−	6.16468i	0.739617	−	0.403861i	0.804439	+	0.594036i	$0.202466\pi$
$234$	12.2351	+	3.10754i	0.799835	+	0.203146i
$235$	2.10727	+	16.0429i	0.137463	+	1.04652i
$236$	12.0399	−	6.61100i	0.783728	−	0.430339i
$237$	−0.306533	+	0.229468i	−0.0199115	+	0.0149055i
$238$	0.376270	+	3.46159i	0.0243900	+	0.224382i
$239$	5.46723	+	3.51357i	0.353645	+	0.227274i	0.705386	−	0.708823i	$-0.250774\pi$
$239$	5.46723	+	3.51357i	0.353645	+	0.227274i	−0.351740	+	0.936098i	$0.614410\pi$
$240$	−16.6905	+	10.5503i	−1.07737	+	0.681021i
$241$	9.61869	+	21.0620i	0.619594	+	1.35672i	0.915814	+	0.401602i	$0.131547\pi$
$241$	9.61869	+	21.0620i	0.619594	+	1.35672i	−0.296220	+	0.955120i	$0.595726\pi$
$242$	−14.9669	+	3.83879i	−0.962108	+	0.246767i
$243$	−10.2280	+	13.6630i	−0.656128	+	0.876485i
$244$	−0.793970	−	1.05545i	−0.0508287	−	0.0675680i
$245$	−8.41832	−	11.5362i	−0.537827	−	0.737019i
$246$	−9.33322	−	18.5908i	−0.595064	−	1.18531i
$247$	0.389815	+	5.45033i	0.0248034	+	0.346796i
$248$	18.0039	−	0.706503i	1.14325	−	0.0448630i
$249$	−11.4385	+	9.91148i	−0.724883	+	0.628115i
$250$	−8.55212	−	13.2989i	−0.540883	−	0.841098i
$251$	−23.8260	−	10.8810i	−1.50388	−	0.686801i	−0.518177	−	0.855273i	$-0.673389\pi$
$251$	−23.8260	−	10.8810i	−1.50388	−	0.686801i	−0.985706	+	0.168473i	$0.946117\pi$
$252$	−1.22526	−	2.66637i	−0.0771844	−	0.167966i
$253$	−1.27489	+	0.287041i	−0.0801513	+	0.0180461i
$254$	4.57406	+	6.57143i	0.287002	+	0.412328i
$255$	15.4658	+	1.29588i	0.968504	+	0.0811512i
$256$	2.12822	−	15.8578i	0.133014	−	0.991114i
$257$	1.12949	−	15.7923i	0.0704556	−	0.985098i	−0.832128	−	0.554584i	$-0.812878\pi$
$257$	1.12949	−	15.7923i	0.0704556	−	0.985098i	0.902584	−	0.430515i	$-0.141668\pi$
$258$	−17.3851	+	7.22508i	−1.08235	+	0.449814i
$259$	−1.43725	+	1.65867i	−0.0893062	+	0.103065i
$260$	−12.6001	−	17.1819i	−0.781426	−	1.06558i
$261$	−3.13060	+	0.919227i	−0.193779	+	0.0568987i
$262$	6.10061	+	5.66651i	0.376897	+	0.350078i
$263$	13.4404	−	17.9542i	0.828769	−	1.10711i	−0.163928	−	0.986472i	$-0.552417\pi$
$263$	13.4404	−	17.9542i	0.828769	−	1.10711i	0.992697	−	0.120633i	$-0.0384926\pi$
$264$	−1.32103	+	1.07225i	−0.0813039	+	0.0659924i
$265$	−22.3277	−	0.272303i	−1.37158	−	0.0167274i
$266$	0.928632	−	0.866624i	0.0569381	−	0.0531361i
$267$	31.3060	−	6.81021i	1.91590	−	0.416778i
$268$	−17.1954	+	14.9707i	−1.05037	+	0.914480i
$269$	−14.4886	−	2.08315i	−0.883388	−	0.127012i	−0.314334	−	0.949312i	$-0.601781\pi$
$269$	−14.4886	−	2.08315i	−0.883388	−	0.127012i	−0.569054	+	0.822300i	$0.692690\pi$
$270$	7.64057	−	1.86069i	0.464990	−	0.113238i
$271$	−3.66638	−	5.70500i	−0.222717	−	0.346554i	0.711856	−	0.702325i	$-0.247855\pi$
$271$	−3.66638	−	5.70500i	−0.222717	−	0.346554i	−0.934573	+	0.355771i	$0.884218\pi$
$272$	−8.85074	+	8.93425i	−0.536655	+	0.541718i
$273$	7.22920	−	3.94744i	0.437531	−	0.238910i
$274$	−2.87925	−	15.8521i	−0.173942	−	0.957662i
$275$	−0.866827	−	1.05111i	−0.0522716	−	0.0633843i
$276$	16.8285	−	12.8517i	1.01296	−	0.773584i
$277$	14.0770	+	14.0770i	0.845806	+	0.845806i	0.989607	−	0.143800i	$-0.0459323\pi$
$277$	14.0770	+	14.0770i	0.845806	+	0.845806i	−0.143800	+	0.989607i	$0.545932\pi$
$278$	−23.6783	−	16.3990i	−1.42013	−	0.983546i
$279$	11.4515	+	3.36247i	0.685584	+	0.201306i
$280$	−1.26646	+	4.78823i	−0.0756854	+	0.286151i
$281$	6.54181	−	4.20417i	0.390252	−	0.250800i	−0.330771	−	0.943711i	$-0.607309\pi$
$281$	6.54181	−	4.20417i	0.390252	−	0.250800i	0.721023	+	0.692912i	$0.243672\pi$
$282$	−14.1963	−	17.5742i	−0.845375	−	1.04653i
$283$	13.8895	−	10.3976i	0.825647	−	0.618071i	−0.100626	−	0.994924i	$-0.532085\pi$
$283$	13.8895	−	10.3976i	0.825647	−	0.618071i	0.926273	+	0.376853i	$0.122994\pi$
$284$	−1.49649	+	21.6375i	−0.0888005	+	1.28395i
$285$	−3.00255	−	4.79976i	−0.177856	−	0.284313i
$286$	−1.25263	−	1.34226i	−0.0740698	−	0.0793696i
$287$	−4.88894	−	1.82348i	−0.288585	−	0.107637i
$288$	4.68831	−	9.50501i	0.276261	−	0.560088i
$289$	−7.04280	+	1.01260i	−0.414282	+	0.0595648i
$290$	5.06434	+	2.16341i	0.297389	+	0.127040i
$291$	5.59890	+	19.0681i	0.328213	+	1.11779i
$292$	7.95914	+	26.8728i	0.465773	+	1.57261i
$293$	2.20567	+	30.8393i	0.128857	+	1.80165i	0.492709	+	0.870194i	$0.336007\pi$
$293$	2.20567	+	30.8393i	0.128857	+	1.80165i	−0.363852	+	0.931457i	$0.618539\pi$
$294$	18.4307	+	7.60891i	1.07490	+	0.443761i
$295$	−13.3875	−	7.52352i	−0.779452	−	0.438036i
$296$	−7.92273	−	0.255029i	−0.460499	−	0.0148232i
$297$	0.634889	−	0.236801i	0.0368400	−	0.0137406i
$298$	0.654163	+	0.117231i	0.0378946	+	0.00679102i
$299$	15.0879	+	17.1591i	0.872554	+	0.992335i
$300$	19.8741	+	9.61112i	1.14743	+	0.554898i
$301$	−1.96176	+	4.29567i	−0.113074	+	0.247598i
$302$	−15.4780	−	7.72502i	−0.890658	−	0.444525i
$303$	0.898580	−	12.5638i	0.0516221	−	0.721771i
$304$	4.54394	+	0.631558i	0.260613	+	0.0362223i
$305$	−0.532864	+	1.37714i	−0.0305117	+	0.0788545i
$306$	−7.44482	+	3.73754i	−0.425592	+	0.213661i
$307$	−11.8779	+	21.7527i	−0.677906	+	1.24149i	0.281527	+	0.959553i	$0.409159\pi$
$307$	−11.8779	+	21.7527i	−0.677906	+	1.24149i	−0.959433	+	0.281938i	$0.909023\pi$
$308$	−0.0597451	+	0.422576i	−0.00340429	+	0.0240785i
$309$	−3.87547	+	0.557208i	−0.220468	+	0.0316985i
$310$	−11.3058	−	16.6727i	−0.642127	−	0.946948i
$311$	−4.57853	+	2.09094i	−0.259624	+	0.118566i	−0.540975	−	0.841038i	$-0.681945\pi$
$311$	−4.57853	+	2.09094i	−0.259624	+	0.118566i	0.281351	+	0.959605i	$0.409217\pi$
$312$	27.5243	+	11.2876i	1.55826	+	0.639032i
$313$	0.811050	−	0.176433i	0.0458432	−	0.00997259i	−0.189585	−	0.981864i	$-0.560714\pi$
$313$	0.811050	−	0.176433i	0.0458432	−	0.00997259i	0.235428	+	0.971892i	$0.424351\pi$
$314$	−10.8084	+	13.4447i	−0.609956	+	0.758730i
$315$	−1.80725	+	2.73813i	−0.101827	+	0.154276i
$316$	−0.304074	+	0.166965i	−0.0171055	+	0.00939250i
$317$	−28.0052	−	6.09215i	−1.57293	−	0.342169i	−0.660313	−	0.750991i	$-0.729576\pi$
$317$	−28.0052	−	6.09215i	−1.57293	−	0.342169i	−0.912614	+	0.408822i	$0.865940\pi$
$318$	26.7936	−	15.9400i	1.50251	−	0.893868i
$319$	0.455311	+	0.133691i	0.0254925	+	0.00748528i
$320$	−16.3101	+	7.34724i	−0.911760	+	0.410723i
$321$	14.0859			0.786196
$322$	0.898943	−	5.23475i	0.0500961	−	0.291721i
$323$	−2.54974	−	2.54974i	−0.141871	−	0.141871i
$324$	−15.6756	+	15.7494i	−0.870869	+	0.874967i
$325$	−8.86671	+	22.1101i	−0.491836	+	1.22645i
$326$	−24.3391	−	6.18177i	−1.34802	−	0.342377i
$327$	2.33211	−	10.7205i	0.128966	−	0.592848i
$328$	−6.01444	−	17.8603i	−0.332092	−	0.986172i
$329$	−5.60915	−	0.806474i	−0.309242	−	0.0444623i
$330$	1.79817	+	0.620585i	0.0989862	+	0.0341621i
$331$	6.20132	−	9.64944i	0.340855	−	0.530381i	−0.627934	−	0.778267i	$-0.716099\pi$
$331$	6.20132	−	9.64944i	0.340855	−	0.530381i	0.968789	+	0.247885i	$0.0797356\pi$
$332$	−11.5177	+	7.44026i	−0.632118	+	0.408338i
$333$	−4.91966	−	1.83494i	−0.269596	−	0.100554i
$334$	8.99896	−	15.2076i	0.492401	−	0.832122i
$335$	24.3683	+	7.47915i	1.33138	+	0.408630i
$336$	−1.97940	−	6.62595i	−0.107985	−	0.361475i
$337$	20.3012	+	11.0853i	1.10587	+	0.603853i	0.925120	−	0.379675i	$-0.123964\pi$
$337$	20.3012	+	11.0853i	1.10587	+	0.603853i	0.180754	+	0.983528i	$0.442146\pi$
$338$	−4.31639	+	13.0197i	−0.234781	+	0.708176i
$339$	−23.7154	+	27.3691i	−1.28805	+	1.48648i
$340$	13.7090	+	3.12391i	0.743475	+	0.169418i
$341$	−1.13671	−	1.31184i	−0.0615564	−	0.0710399i
$342$	2.71899	+	1.35704i	0.147026	+	0.0733804i
$343$	9.82242	−	3.66357i	0.530361	−	0.197814i
$344$	−16.5114	+	4.27628i	−0.890236	+	0.230561i
$345$	−22.1402	−	8.38261i	−1.19199	−	0.451305i
$346$	−2.43527	−	3.49868i	−0.130921	−	0.188090i
$347$	5.92658	+	15.8898i	0.318155	+	0.853007i	0.993325	+	0.115345i	$0.0367974\pi$
$347$	5.92658	+	15.8898i	0.318155	+	0.853007i	−0.675170	+	0.737662i	$0.735930\pi$
$348$	−7.60822	+	1.11213i	−0.407843	+	0.0596166i
$349$	26.6785	−	23.1170i	1.42807	−	1.23743i	0.499473	−	0.866330i	$-0.333527\pi$
$349$	26.6785	−	23.1170i	1.42807	−	1.23743i	0.928594	−	0.371097i	$-0.121018\pi$
$350$	5.29329	−	1.62630i	0.282938	−	0.0869291i
$351$	−8.95402	−	7.75870i	−0.477930	−	0.414129i
$352$	−1.32100	+	0.794306i	−0.0704096	+	0.0423366i
$353$	−2.76289	+	5.05985i	−0.147054	+	0.269309i	−0.940815	−	0.338921i	$-0.889938\pi$
$353$	−2.76289	+	5.05985i	−0.147054	+	0.269309i	0.793761	+	0.608230i	$0.208120\pi$
$354$	21.4267	−	0.790443i	1.13882	−	0.0420116i
$355$	21.4232	−	11.3610i	1.13702	−	0.602979i
$356$	28.9463	−	2.13860i	1.53415	−	0.113346i
$357$	−1.89949	+	5.09272i	−0.100532	+	0.269536i
$358$	−14.9237	−	0.515461i	−0.788742	−	0.0272430i
$359$	10.4488	+	6.71503i	0.551466	+	0.354406i	0.786509	−	0.617579i	$-0.211887\pi$
$359$	10.4488	+	6.71503i	0.551466	+	0.354406i	−0.235042	+	0.971985i	$0.575523\pi$
$360$	−11.7920	+	1.16440i	−0.621492	+	0.0613694i
$361$	2.51678	−	17.5046i	0.132462	−	0.921295i
$362$	17.8355	+	22.0794i	0.937411	+	1.16047i
$363$	−23.5686	−	5.12703i	−1.23703	−	0.269099i
$364$	6.98548	−	2.62415i	0.366139	−	0.137543i
$365$	20.8072	−	23.4292i	1.08910	−	1.22634i
$366$	−0.368442	−	2.02851i	−0.0192588	−	0.106032i
$367$	−17.3869	+	17.3869i	−0.907590	+	0.907590i	−0.996077	−	0.0884876i	$-0.971797\pi$
$367$	−17.3869	+	17.3869i	−0.907590	+	0.907590i	0.0884876	+	0.996077i	$0.471797\pi$
$368$	16.7257	−	9.39419i	0.871888	−	0.489706i
$369$		−	12.4834i		−	0.649862i
$370$	4.43798	+	7.67123i	0.230719	+	0.398808i
$371$	2.20321	−	7.50345i	0.114385	−	0.389560i
$372$	25.6117	+	11.6239i	1.32791	+	0.602671i
$373$	3.71916	−	17.0967i	0.192571	−	0.885234i	−0.774867	−	0.632125i	$-0.782183\pi$
$373$	3.71916	−	17.0967i	0.192571	−	0.885234i	0.967438	−	0.253110i	$-0.0814533\pi$
$374$	1.20477	+	0.128095i	0.0622969	+	0.00662365i
$375$	−2.61664	−	24.5427i	−0.135123	−	1.26738i
$376$	−10.5057	−	17.5651i	−0.541790	−	0.905853i
$377$	−1.76367	−	8.10747i	−0.0908337	−	0.417556i
$378$	−0.0950693	+	2.75246i	−0.00488984	+	0.141571i
$379$	−6.72391	−	14.7233i	−0.345384	−	0.756286i	−1.00000		0.000323922i	$-0.999897\pi$
$379$	−6.72391	−	14.7233i	−0.345384	−	0.756286i	0.654616	−	0.755962i	$-0.272830\pi$
$380$	−2.08466	−	4.68636i	−0.106941	−	0.240405i
$381$	1.77871	+	12.3712i	0.0911263	+	0.633797i
$382$	−12.1217	−	11.2592i	−0.620202	−	0.576071i
$383$	20.0575	+	10.9522i	1.02489	+	0.559633i	0.901525	−	0.432728i	$-0.142449\pi$
$383$	20.0575	+	10.9522i	1.02489	+	0.559633i	0.123367	+	0.992361i	$0.460631\pi$
$384$	14.0755	−	20.6324i	0.718286	−	1.05289i
$385$	0.436419	−	0.192909i	0.0222420	−	0.00983155i
$386$	−13.5430	−	5.59110i	−0.689323	−	0.284579i
$387$	−11.2692	−	0.805989i	−0.572845	−	0.0409707i
$388$	2.60409	+	17.8148i	0.132203	+	0.904412i
$389$	5.99087	+	2.73594i	0.303749	+	0.138718i	0.561458	−	0.827505i	$-0.310240\pi$
$389$	5.99087	+	2.73594i	0.303749	+	0.138718i	−0.257709	+	0.966222i	$0.582968\pi$
$390$	−5.54438	−	32.7949i	−0.280750	−	1.66064i
$391$	−14.9398	−	2.03746i	−0.755540	−	0.103039i
$392$	15.5680	+	9.16295i	0.786302	+	0.462799i
$393$	4.54214	+	12.1780i	0.229121	+	0.614296i
$394$	15.4479	−	5.16169i	0.778252	−	0.260042i
$395$	0.338110	+	0.190011i	0.0170122	+	0.00956048i
$396$	−0.997186	+	0.219378i	−0.0501105	+	0.0110241i
$397$	19.7299	−	1.41111i	0.990215	−	0.0708215i	0.433177	−	0.901309i	$-0.357392\pi$
$397$	19.7299	−	1.41111i	0.990215	−	0.0708215i	0.557038	+	0.830487i	$0.311938\pi$
$398$	−5.98761	−	1.98506i	−0.300132	−	0.0995022i
$399$	1.90248	−	0.558618i	0.0952430	−	0.0279659i
$400$	16.6089	+	11.1421i	0.830443	+	0.557103i
$401$	−2.91219	−	20.2547i	−0.145428	−	1.01147i	−0.923582	−	0.383401i	$-0.874753\pi$
$401$	−2.91219	−	20.2547i	−0.145428	−	1.01147i	0.778154	−	0.628073i	$-0.216156\pi$
$402$	−34.4740	+	8.84208i	−1.71941	+	0.441003i
$403$	−10.6063	+	28.4365i	−0.528337	+	1.41653i
$404$	2.39947	−	11.1562i	0.119378	−	0.555042i
$405$	24.2098	+	5.57657i	1.20299	+	0.277102i
$406$	−1.20844	+	1.50318i	−0.0599736	+	0.0746018i
$407$	0.457644	+	0.611341i	0.0226846	+	0.0303030i
$408$	−18.6048	+	6.26514i	−0.921076	+	0.310171i
$409$	2.71077	+	4.21804i	0.134039	+	0.208569i	0.901784	−	0.432186i	$-0.142258\pi$
$409$	2.71077	+	4.21804i	0.134039	+	0.208569i	−0.767745	+	0.640755i	$0.778621\pi$
$410$	−13.4010	+	16.2595i	−0.661826	+	0.802998i
$411$	7.08566	−	24.1315i	0.349510	−	1.19032i
$412$	−3.54710	+	0.00832749i	−0.174753	+	0.000410266i
$413$	3.80300	−	3.80300i	0.187134	−	0.187134i
$414$	12.4856	−	2.36153i	0.613635	−	0.116063i
$415$	13.8663	+	6.53804i	0.680669	+	0.320940i
$416$	23.2588	+	13.6161i	1.14035	+	0.667586i
$417$	−21.5477	−	39.4616i	−1.05519	−	1.93244i
$418$	−0.225967	−	0.379831i	−0.0110524	−	0.0185781i
$419$	22.5216	−	14.4738i	1.10025	−	0.707091i	0.141106	−	0.989994i	$-0.454934\pi$
$419$	22.5216	−	14.4738i	1.10025	−	0.707091i	0.959148	+	0.282904i	$0.0912977\pi$
$420$	−5.12037	+	5.79296i	−0.249848	+	0.282668i
$421$	3.13787	−	21.8244i	0.152930	−	1.06365i	−0.758344	−	0.651855i	$-0.773991\pi$
$421$	3.13787	−	21.8244i	0.152930	−	1.06365i	0.911274	−	0.411800i	$-0.135100\pi$
$422$	−15.1550	+	1.64732i	−0.737732	+	0.0801905i
$423$	−2.88183	−	13.2476i	−0.140119	−	0.644119i
$424$	26.0564	−	10.9006i	1.26541	−	0.529380i
$425$	−5.13275	−	14.8585i	−0.248975	−	0.720742i
$426$	−17.2421	+	29.1379i	−0.835381	+	1.41173i
$427$	−0.413999	−	0.309916i	−0.0200348	−	0.0149979i
$428$	12.6355	+	1.78645i	0.610761	+	0.0863511i
$429$	−0.807436	−	2.74988i	−0.0389834	−	0.132765i
$430$	13.8127	+	13.1473i	0.666109	+	0.634017i
$431$	11.1902	+	9.69635i	0.539012	+	0.467057i	0.881312	−	0.472534i	$-0.156661\pi$
$431$	11.1902	+	9.69635i	0.539012	+	0.467057i	−0.342300	+	0.939591i	$0.611206\pi$
$432$	−7.93498	+	5.99840i	−0.381772	+	0.288598i
$433$	−2.37261	−	0.169693i	−0.114020	−	0.00815491i	0.0142123	−	0.999899i	$-0.495476\pi$
$433$	−2.37261	−	0.169693i	−0.114020	−	0.00815491i	−0.128233	+	0.991744i	$0.540930\pi$
$434$	6.69139	−	2.23584i	0.321197	−	0.107324i
$435$	5.54996	+	6.56508i	0.266100	+	0.314772i
$436$	3.45163	−	9.32094i	0.165303	−	0.446392i
$437$	2.67101	+	4.80829i	0.127772	+	0.230012i
$438$	−7.71742	+	43.0640i	−0.368753	+	2.05768i
$439$	14.7444	−	32.2857i	0.703711	−	1.54091i	−0.131701	−	0.991289i	$-0.542044\pi$
$439$	14.7444	−	32.2857i	0.703711	−	1.54091i	0.835413	−	0.549623i	$-0.185229\pi$
$440$	1.53432	+	0.784741i	0.0731458	+	0.0374111i
$441$	7.83594	+	9.04316i	0.373140	+	0.430627i
$442$	−8.12963	−	19.5617i	−0.386687	−	0.930454i
$443$	−35.2724	+	2.52273i	−1.67584	+	0.119859i	−0.876622	−	0.481180i	$-0.840208\pi$
$443$	−35.2724	+	2.52273i	−1.67584	+	0.119859i	−0.799220	+	0.601038i	$0.794754\pi$
$444$	−10.8742	−	5.90468i	−0.516068	−	0.280223i
$445$	−19.1290	−	26.2137i	−0.906803	−	1.24265i
$446$	24.3498	−	0.898278i	1.15300	−	0.0425347i
$447$	0.830503	+	0.621707i	0.0392814	+	0.0294057i
$448$	−0.935249	−	6.19475i	−0.0441864	−	0.292675i
$449$	−16.7501	+	7.64953i	−0.790487	+	0.361004i	−0.769394	−	0.638774i	$-0.779442\pi$
$449$	−16.7501	+	7.64953i	−0.790487	+	0.361004i	−0.0210930	+	0.999778i	$0.506715\pi$
$450$	8.07098	+	10.5056i	0.380470	+	0.495239i
$451$	−0.981576	+	1.52736i	−0.0462206	+	0.0719207i
$452$	−24.7447	+	21.5433i	−1.16389	+	1.01331i
$453$	−16.1826	−	21.6174i	−0.760325	−	1.01568i
$454$	−27.6164	−	2.93628i	−1.29610	−	0.137807i
$455$	−6.61736	−	5.08079i	−0.310227	−	0.238191i
$456$	5.89682	+	4.06354i	0.276144	+	0.190293i
$457$	5.62430	+	10.3001i	0.263094	+	0.481820i	0.975515	−	0.219932i	$-0.0705834\pi$
$457$	5.62430	+	10.3001i	0.263094	+	0.481820i	−0.712422	+	0.701752i	$0.752402\pi$
$458$	−13.6078	+	19.6481i	−0.635850	+	0.918097i
$459$	7.81843			0.364933
$460$	−18.7974	−	10.3274i	−0.876435	−	0.481520i
$461$	−7.89724			−0.367811			−0.183906	−	0.982944i	$-0.558874\pi$
$461$	−7.89724			−0.367811			−0.183906	+	0.982944i	$0.558874\pi$
$462$	−0.379311	+	0.547684i	−0.0176472	+	0.0254805i
$463$	1.10546	+	2.02449i	0.0513749	+	0.0940862i	0.902105	−	0.431517i	$-0.142022\pi$
$463$	1.10546	+	2.02449i	0.0513749	+	0.0940862i	−0.850730	+	0.525603i	$0.823840\pi$
$464$	−6.96589	+	0.0327077i	−0.323383	+	0.00151842i
$465$	−4.09531	−	31.1781i	−0.189916	−	1.44585i
$466$	18.0894	+	1.92333i	0.837973	+	0.0890965i
$467$	−22.1638	−	29.6074i	−1.02562	−	1.37007i	−0.927051	−	0.374936i	$-0.877665\pi$
$467$	−22.1638	−	29.6074i	−1.02562	−	1.37007i	−0.0985680	−	0.995130i	$-0.531426\pi$
$468$	11.7225	+	13.4645i	0.541873	+	0.622397i
$469$	−4.82643	+	7.51007i	−0.222864	+	0.346783i
$470$	−10.4677	+	20.3484i	−0.482839	+	0.938601i
$471$	−24.4950	+	11.1865i	−1.12867	+	0.515446i
$472$	19.3208	+	2.00840i	0.889312	+	0.0924442i
$473$	1.31542	+	0.984713i	0.0604832	+	0.0452772i
$474$	−0.541145	+	0.0199631i	−0.0248556	+	0.000916935i
$475$	−3.21705	+	4.74714i	−0.147608	+	0.217814i
$476$	−2.34980	+	4.32745i	−0.107703	+	0.198348i
$477$	18.6616	−	1.33470i	0.854454	−	0.0611117i
$478$	3.52715	+	8.48709i	0.161328	+	0.388191i
$479$	−14.2420	−	16.4361i	−0.650734	−	0.750987i	0.330501	−	0.943806i	$-0.392782\pi$
$479$	−14.2420	−	16.4361i	−0.650734	−	0.750987i	−0.981234	+	0.192819i	$0.938237\pi$
$480$	−27.8997	−	1.17320i	−1.27344	−	0.0535489i
$481$	5.54678	−	12.1457i	0.252911	−	0.553798i
$482$	−5.77620	+	32.2318i	−0.263099	+	1.46812i
$483$	4.92039	−	6.67329i	0.223885	−	0.303645i
$484$	−20.4916	−	7.58823i	−0.931438	−	0.344920i
$485$	15.3723	−	12.9954i	0.698020	−	0.590089i
$486$	−22.8926	+	7.64925i	−1.03843	+	0.346977i
$487$	5.07670	+	0.363093i	0.230047	+	0.0164533i	0.185887	−	0.982571i	$-0.440484\pi$
$487$	5.07670	+	0.363093i	0.230047	+	0.0164533i	0.0441604	+	0.999024i	$0.485939\pi$
$488$	−0.0732394	−	1.86637i	−0.00331539	−	0.0844867i
$489$	−29.6255	−	25.6706i	−1.33971	−	1.16086i
$490$	−0.498374	−	20.1904i	−0.0225142	−	0.912111i
$491$	−4.99690	−	17.0179i	−0.225507	−	0.768007i	−0.992053	−	0.125818i	$-0.959845\pi$
$491$	−4.99690	−	17.0179i	−0.225507	−	0.768007i	0.766546	−	0.642189i	$-0.221974\pi$
$492$	4.11833	−	29.1289i	0.185669	−	1.31323i
$493$	4.38317	+	3.28120i	0.197408	+	0.147778i
$494$	−3.93537	+	6.65049i	−0.177061	+	0.299220i
$495$	0.797293	+	0.816980i	0.0358356	+	0.0367205i
$496$	21.5004	+	13.6753i	0.965398	+	0.614038i
$497$	1.80523	+	8.29851i	0.0809757	+	0.372239i
$498$	−21.2791	+	2.31301i	−0.953541	+	0.103649i
$499$	−1.83411	+	12.7565i	−0.0821059	+	0.571059i	0.906691	+	0.421795i	$0.138600\pi$
$499$	−1.83411	+	12.7565i	−0.0821059	+	0.571059i	−0.988797	+	0.149264i	$0.952309\pi$
$500$	0.765429	−	22.3476i	0.0342310	−	0.999414i
$501$	23.2053	−	14.9131i	1.03674	−	0.666270i
$502$	−18.9391	−	31.8349i	−0.845292	−	1.42086i
$503$	13.0279	+	23.8589i	0.580886	+	1.06381i	0.988580	+	0.150695i	$0.0481513\pi$
$503$	13.0279	+	23.8589i	0.580886	+	1.06381i	−0.407694	+	0.913119i	$0.633667\pi$
$504$	0.722441	−	4.08653i	0.0321801	−	0.182028i
$505$	−12.0073	+	4.31244i	−0.534319	+	0.191901i
$506$	−1.71332	−	0.692812i	−0.0761663	−	0.0307993i
$507$	−15.1404	+	15.1404i	−0.672407	+	0.672407i
$508$	0.0265829	+	11.3230i	0.00117943	+	0.502378i
$509$	−6.53121	+	22.2432i	−0.289491	+	0.985914i	0.678431	+	0.734664i	$0.262660\pi$
$509$	−6.53121	+	22.2432i	−0.289491	+	0.985914i	−0.967922	+	0.251251i	$0.919158\pi$
$510$	16.9372	+	13.9596i	0.749993	+	0.618139i
$511$	5.93305	+	9.23201i	0.262463	+	0.408400i
$512$	15.2429	−	16.7228i	0.673648	−	0.739052i
$513$	−1.70919	−	2.28322i	−0.0754628	−	0.100806i
$514$	14.0290	−	17.4509i	0.618794	−	0.769725i
$515$	2.10323	+	3.36214i	0.0926792	+	0.148153i
$516$	−26.0297	−	5.59845i	−1.14589	−	0.246458i
$517$	−0.689064	+	1.84745i	−0.0303050	+	0.0812509i
$518$	−3.00651	+	0.771127i	−0.132099	+	0.0338814i
$519$	−0.947002	−	6.58654i	−0.0415688	−	0.289117i
$520$	−0.814268	−	30.1214i	−0.0357080	−	1.32091i
$521$	41.2486	−	12.1117i	1.80713	−	0.530622i	0.808787	−	0.588102i	$-0.200125\pi$
$521$	41.2486	−	12.1117i	1.80713	−	0.530622i	0.998347	+	0.0574801i	$0.0183066\pi$
$522$	−4.37982	−	1.45204i	−0.191700	−	0.0635539i
$523$	34.4201	−	2.46178i	1.50509	−	0.107646i	0.705721	−	0.708490i	$-0.250623\pi$
$523$	34.4201	−	2.46178i	1.50509	−	0.107646i	0.799366	+	0.600844i	$0.205169\pi$
$524$	2.52999	+	11.5001i	0.110523	+	0.502385i
$525$	8.52358	+	1.43849i	0.372000	+	0.0627807i
$526$	30.0826	−	10.0517i	1.31166	−	0.438274i
$527$	−6.99911	−	18.7653i	−0.304886	−	0.817431i
$528$	−2.39921	+	0.182922i	−0.104412	+	0.00796065i
$529$	21.0580	+	9.24983i	0.915566	+	0.402167i
$530$	−25.7392	−	18.2947i	−1.11804	−	0.794672i
$531$	11.7043	+	5.34515i	0.507921	+	0.231960i
$532$	1.77744	−	0.259817i	0.0770617	−	0.0112645i
$533$	31.6640	+	2.26465i	1.37152	+	0.0980931i
$534$	41.8803	+	17.2898i	1.81234	+	0.748203i
$535$	−5.76820	−	13.0494i	−0.249381	−	0.564176i
$536$	−32.0458	+	3.55948i	−1.38417	+	0.153746i
$537$	−20.4587	−	11.1713i	−0.882859	−	0.482077i
$538$	−15.1673	−	14.0881i	−0.653909	−	0.607379i
$539$	−0.247670	−	1.72258i	−0.0106679	−	0.0741969i
$540$	10.3812	+	3.98888i	0.446737	+	0.171654i
$541$	3.02022	+	6.61336i	0.129849	+	0.284331i	0.963379	−	0.268145i	$-0.0864106\pi$
$541$	3.02022	+	6.61336i	0.129849	+	0.284331i	−0.833529	+	0.552475i	$0.813683\pi$
$542$	0.331059	−	9.58484i	0.0142202	−	0.411704i
$543$	9.41803	+	43.2940i	0.404167	+	1.85792i
$544$	−17.4838	+	3.26049i	−0.749610	+	0.139792i
$545$	−10.8867	+	2.22958i	−0.466337	+	0.0955047i
$546$	11.5832	+	1.23157i	0.495715	+	0.0527063i
$547$	−5.11355	+	23.5066i	−0.218640	+	1.00507i	0.728698	+	0.684835i	$0.240126\pi$
$547$	−5.11355	+	23.5066i	−0.218640	+	1.00507i	−0.947338	+	0.320235i	$0.896238\pi$
$548$	9.41658	−	20.7482i	0.402256	−	0.886319i
$549$	0.348569	−	1.18712i	0.0148766	−	0.0506649i
$550$	−0.161434	−	1.92000i	−0.00688359	−	0.0818689i
$551$		−	1.99732i		−	0.0850889i
$552$	29.9131	−	1.39136i	1.27319	−	0.0592203i
$553$	−0.0960471	+	0.0960471i	−0.00408434	+	0.00408434i
$554$	5.03136	+	27.7008i	0.213762	+	1.17690i
$555$	0.818587	+	13.8102i	0.0347471	+	0.586211i
$556$	−14.3243	−	38.1313i	−0.607485	−	1.61713i
$557$	−28.1016	−	6.11314i	−1.19071	−	0.259022i	−0.426797	−	0.904347i	$-0.640358\pi$
$557$	−28.1016	−	6.11314i	−1.19071	−	0.259022i	−0.763908	+	0.645325i	$0.776722\pi$
$558$	10.6062	+	13.1299i	0.448997	+	0.555834i
$559$	4.08875	−	28.4379i	0.172936	−	1.20279i
$560$	−5.32785	+	4.54710i	−0.225143	+	0.192150i
$561$	1.59103	+	1.02249i	0.0671733	+	0.0431696i
$562$	10.9907	+	0.379618i	0.463617	+	0.0160132i
$563$	11.3254	−	30.3644i	0.477307	−	1.27971i	−0.445789	−	0.895138i	$-0.647077\pi$
$563$	11.3254	−	30.3644i	0.477307	−	1.27971i	0.923096	−	0.384571i	$-0.125651\pi$
$564$	−2.35406	−	31.8627i	−0.0991240	−	1.34166i
$565$	35.0668	+	10.7628i	1.47527	+	0.452792i
$566$	24.5202	−	0.904561i	1.03066	−	0.0380215i
$567$	−4.16986	+	7.63653i	−0.175118	+	0.320704i
$568$	−19.1622	+	23.9510i	−0.804027	+	1.00496i
$569$	−14.6909	−	12.7297i	−0.615874	−	0.533658i	0.290097	−	0.956997i	$-0.406312\pi$
$569$	−14.6909	−	12.7297i	−0.615874	−	0.533658i	−0.905971	+	0.423339i	$0.860858\pi$
$570$	0.373943	−	7.99789i	0.0156628	−	0.334995i
$571$	8.24750	−	7.14650i	0.345147	−	0.299072i	−0.464986	−	0.885318i	$-0.653940\pi$
$571$	8.24750	−	7.14650i	0.345147	−	0.299072i	0.810133	+	0.586247i	$0.199395\pi$
$572$	−0.375545	−	2.56914i	−0.0157023	−	0.107421i
$573$	−9.02512	−	24.1973i	−0.377030	−	1.01086i
$574$	−4.21567	−	6.05654i	−0.175959	−	0.252795i
$575$	1.30066	+	23.9439i	0.0542414	+	0.998528i
$576$	13.1041	−	7.27563i	0.546002	−	0.303151i
$577$	41.2565	−	15.3879i	1.71753	−	0.640605i	0.719010	−	0.695000i	$-0.244596\pi$
$577$	41.2565	−	15.3879i	1.71753	−	0.640605i	0.998520	+	0.0543945i	$0.0173229\pi$
$578$	−9.00337	−	4.49356i	−0.374491	−	0.186907i
$579$	−14.9778	−	17.2853i	−0.622454	−	0.718351i
$580$	4.14589	+	6.59299i	0.172149	+	0.273759i
$581$	−3.51596	+	4.05764i	−0.145867	+	0.168339i
$582$	−8.84417	+	26.6770i	−0.366603	+	1.10580i
$583$	−2.38821	−	1.30406i	−0.0989095	−	0.0540087i
$584$	−12.3844	+	37.6512i	−0.512471	+	1.55802i
$585$	5.85641	−	19.0811i	0.242133	−	0.788908i
$586$	−22.2673	+	37.6301i	−0.919853	+	1.55448i
$587$	−2.72598	−	1.01674i	−0.112513	−	0.0419652i	0.292577	−	0.956242i	$-0.405487\pi$
$587$	−2.72598	−	1.01674i	−0.112513	−	0.0419652i	−0.405090	+	0.914277i	$0.632760\pi$
$588$	15.3011	+	23.6865i	0.631006	+	0.976814i
$589$	−3.94996	+	6.14626i	−0.162755	+	0.253252i
$590$	−9.50659	−	19.5265i	−0.391380	−	0.803892i
$591$	25.1661	+	3.61834i	1.03520	+	0.148839i
$592$	−9.00570	−	6.67583i	−0.370132	−	0.274375i
$593$	0.0283604	−	0.130371i	0.00116462	−	0.00535368i	−0.976561	−	0.215241i	$-0.930946\pi$
$593$	0.0283604	−	0.130371i	0.00116462	−	0.00535368i	0.977726	+	0.209888i	$0.0673098\pi$
$594$	0.928799	+	0.235901i	0.0381091	+	0.00967913i
$595$	5.49585	−	0.325761i	0.225308	−	0.0133549i
$596$	0.666143	+	0.663022i	0.0272863	+	0.0271584i
$597$	−6.96290	−	6.96290i	−0.284972	−	0.284972i
$598$	3.72493	+	32.0980i	0.152324	+	1.31258i
$599$	−34.1171			−1.39399			−0.696993	−	0.717078i	$-0.745479\pi$
$599$	−34.1171			−1.39399			−0.696993	+	0.717078i	$0.745479\pi$
$600$	15.3670	+	27.1765i	0.627357	+	1.10948i
$601$	31.4302	+	9.22874i	1.28206	+	0.376448i	0.850663	−	0.525712i	$-0.176201\pi$
$601$	31.4302	+	9.22874i	1.28206	+	0.376448i	0.431402	+	0.902160i	$0.358019\pi$
$602$	−5.73961	+	3.41458i	−0.233929	+	0.139168i
$603$	−20.8695	−	4.53989i	−0.849874	−	0.184879i
$604$	−11.7747	−	21.4440i	−0.479107	−	0.872543i
$605$	4.90162	+	23.9340i	0.199279	+	0.973054i
$606$	11.1610	−	13.8833i	0.453384	−	0.563969i
$607$	42.2153	−	9.18337i	1.71347	−	0.372742i	0.754508	−	0.656291i	$-0.227876\pi$
$607$	42.2153	−	9.18337i	1.71347	−	0.372742i	0.958958	+	0.283550i	$0.0915121\pi$
$608$	4.77430	+	4.39301i	0.193624	+	0.178160i
$609$	−2.73866	+	1.25070i	−0.110976	+	0.0506810i
$610$	−1.72837	+	1.17201i	−0.0699798	+	0.0474534i
$611$	34.1250	−	4.90644i	1.38055	−	0.198493i
$612$	−11.6649	−	1.64921i	−0.471524	−	0.0666655i
$613$	−20.8890	+	38.2554i	−0.843699	+	1.54512i	−0.00535042	+	0.999986i	$0.501703\pi$
$613$	−20.8890	+	38.2554i	−0.843699	+	1.54512i	−0.838349	+	0.545134i	$0.816479\pi$
$614$	−31.3245	+	15.7259i	−1.26415	+	0.634646i
$615$	−30.0831	+	13.2976i	−1.21307	+	0.536209i
$616$	−0.409716	+	0.443185i	−0.0165079	+	0.0178564i
$617$	1.31823	−	18.4313i	0.0530700	−	0.742016i	−0.899350	−	0.437229i	$-0.855960\pi$
$617$	1.31823	−	18.4313i	0.0530700	−	0.742016i	0.952420	−	0.304787i	$-0.0985854\pi$
$618$	−4.95432	−	2.47269i	−0.199292	−	0.0994661i
$619$	−11.9564	+	26.1809i	−0.480568	+	1.05230i	0.501739	+	0.865019i	$0.332694\pi$
$619$	−11.9564	+	26.1809i	−0.480568	+	1.05230i	−0.982307	+	0.187278i	$0.940033\pi$
$620$	0.280536	−	28.4873i	0.0112666	−	1.14408i
$621$	−11.4671	−	3.27684i	−0.460161	−	0.131495i
$622$	−7.00665	−	1.25565i	−0.280941	−	0.0503469i
$623$	10.6485	−	3.97170i	0.426625	−	0.159123i
$624$	22.9114	+	35.2855i	0.917190	+	1.41255i
$625$	−21.6654	+	12.4744i	−0.866615	+	0.498977i
$626$	1.08500	+	0.447929i	0.0433652	+	0.0179029i
$627$	−0.0492179	−	0.688156i	−0.00196557	−	0.0274823i
$628$	−23.3916	+	6.92809i	−0.933427	+	0.276461i
$629$	2.48242	+	8.45435i	0.0989806	+	0.337097i
$630$	−4.30585	+	1.72820i	−0.171549	+	0.0688530i
$631$	0.998472	−	0.143559i	0.0397485	−	0.00571498i	−0.122412	−	0.992479i	$-0.539063\pi$
$631$	0.998472	−	0.143559i	0.0397485	−	0.00571498i	0.162160	+	0.986764i	$0.448154\pi$
$632$	−0.487958	−	0.0507234i	−0.0194099	−	0.00201767i
$633$	−22.2961	−	8.31602i	−0.886191	−	0.330532i
$634$	−27.6537	−	29.6324i	−1.09827	−	1.17685i
$635$	10.7326	−	6.71389i	0.425909	−	0.266433i
$636$	43.9853	+	3.04212i	1.74413	+	0.120628i
$637$	−24.3593	+	18.2352i	−0.965152	+	0.722504i
$638$	0.421702	+	0.522045i	0.0166953	+	0.0206680i
$639$	−17.0924	+	10.9846i	−0.676166	+	0.434545i
$640$	−24.8782	−	4.59079i	−0.983397	−	0.181467i
$641$	−0.793927	−	0.233118i	−0.0313582	−	0.00920761i	0.266016	−	0.963969i	$-0.414293\pi$
$641$	−0.793927	−	0.233118i	−0.0313582	−	0.00920761i	−0.297374	+	0.954761i	$0.596111\pi$
$642$	16.3764	+	11.3418i	0.646323	+	0.447627i
$643$	34.0164	+	34.0164i	1.34148	+	1.34148i	0.894591	+	0.446886i	$0.147467\pi$
$643$	34.0164	+	34.0164i	1.34148	+	1.34148i	0.446886	+	0.894591i	$0.352533\pi$
$644$	5.26011	−	5.36215i	0.207277	−	0.211298i
$645$	10.0618	+	28.0156i	0.396184	+	1.10311i
$646$	−0.911319	−	5.01739i	−0.0358554	−	0.197406i
$647$	33.2107	−	18.1344i	1.30565	−	0.712938i	0.332497	−	0.943104i	$-0.392109\pi$
$647$	33.2107	−	18.1344i	1.30565	−	0.712938i	0.973151	+	0.230166i	$0.0739269\pi$
$648$	−30.9060	+	5.68850i	−1.21410	+	0.223466i
$649$	−1.01174	−	1.57429i	−0.0397142	−	0.0617964i
$650$	−28.1115	+	18.5660i	−1.10262	+	0.728220i
$651$	10.9009	+	1.56732i	0.427242	+	0.0614281i
$652$	−23.3194	−	26.7847i	−0.913258	−	1.04897i
$653$	−35.2246	+	7.66264i	−1.37844	+	0.299862i	−0.839903	−	0.542737i	$-0.817388\pi$
$653$	−35.2246	+	7.66264i	−1.37844	+	0.299862i	−0.538541	+	0.842599i	$0.681024\pi$
$654$	11.3435	−	10.5860i	0.443564	−	0.413946i
$655$	9.42188	−	9.19484i	0.368143	−	0.359272i
$656$	7.38859	−	25.6074i	0.288476	−	0.999801i
$657$	−15.7338	+	21.0179i	−0.613834	+	0.819986i
$658$	−5.87189	−	5.45407i	−0.228910	−	0.212622i
$659$	25.3070	−	7.43080i	0.985820	−	0.289463i	0.251195	−	0.967936i	$-0.419176\pi$
$659$	25.3070	−	7.43080i	0.985820	−	0.289463i	0.734625	+	0.678474i	$0.237358\pi$
$660$	1.59088	+	2.16938i	0.0619251	+	0.0844429i
$661$	8.26986	−	9.54393i	0.321660	−	0.371216i	−0.571773	−	0.820412i	$-0.693744\pi$
$661$	8.26986	−	9.54393i	0.321660	−	0.371216i	0.893433	+	0.449196i	$0.148290\pi$
$662$	14.9794	−	6.22528i	0.582190	−	0.241952i
$663$	2.35905	−	32.9839i	0.0916181	−	1.28099i
$664$	−19.3815	−	0.623881i	−0.752148	−	0.0242113i
$665$	−1.29658	−	1.53374i	−0.0502794	−	0.0594758i
$666$	−4.24217	−	6.09460i	−0.164381	−	0.236161i
$667$	−5.05351	−	6.64954i	−0.195673	−	0.257471i
$668$	22.7073	−	10.4346i	0.878573	−	0.403726i
$669$	34.5991	+	15.8009i	1.33768	+	0.610897i
$670$	22.3087	+	28.3166i	0.861860	+	1.09396i
$671$	−0.135991	+	0.117837i	−0.00524988	+	0.00454905i
$672$	3.03391	−	9.29720i	0.117036	−	0.358647i
$673$	−0.923366	−	12.9103i	−0.0355931	−	0.497657i	−0.983713	−	0.179745i	$-0.942473\pi$
$673$	−0.923366	−	12.9103i	−0.0355931	−	0.497657i	0.948120	−	0.317912i	$-0.102982\pi$
$674$	14.6765	+	29.2342i	0.565319	+	1.12606i
$675$	−2.34592	−	12.2106i	−0.0902944	−	0.469985i
$676$	−15.5016	+	11.6613i	−0.596217	+	0.448510i
$677$	−26.2248	+	35.0323i	−1.00790	+	1.34640i	−0.0707447	+	0.997494i	$0.522538\pi$
$677$	−26.2248	+	35.0323i	−1.00790	+	1.34640i	−0.937158	+	0.348906i	$0.886553\pi$
$678$	−49.6092	+	12.7240i	−1.90523	+	0.488664i
$679$	2.92855	+	6.41264i	0.112388	+	0.246094i
$680$	13.4229	+	14.6703i	0.514744	+	0.562580i
$681$	−36.4706	−	23.4382i	−1.39755	−	0.898154i
$682$	−0.265271	−	2.44043i	−0.0101578	−	0.0934488i
$683$	−26.4047	+	19.7663i	−1.01035	+	0.756336i	−0.970063	−	0.242853i	$-0.921917\pi$
$683$	−26.4047	+	19.7663i	−1.01035	+	0.756336i	−0.0402831	+	0.999188i	$0.512826\pi$
$684$	2.06845	+	3.76703i	0.0790891	+	0.144036i
$685$	−25.2575	+	3.31763i	−0.965041	+	0.126760i
$686$	14.3695	+	3.64964i	0.548631	+	0.139344i
$687$	−32.7450	+	17.8801i	−1.24930	+	0.682170i
$688$	−22.6396	−	8.32324i	−0.863125	−	0.317321i
$689$			47.5768i			1.81253i
$690$	−18.9908	−	27.5729i	−0.722968	−	1.04968i
$691$			27.7309i			1.05493i	0.849575	+	0.527467i	$0.176858\pi$
$691$			27.7309i			1.05493i	−0.849575	+	0.527467i	$0.823142\pi$
$692$	−0.0141530	−	6.02847i	−0.000538015	−	0.229168i
$693$	−0.350892	+	0.191601i	−0.0133293	+	0.00727833i
$694$	−5.90404	+	23.2456i	−0.224114	+	0.882393i
$695$	−27.7342	+	36.1218i	−1.05202	+	1.37018i
$696$	−9.74088	−	4.83311i	−0.369227	−	0.183199i
$697$	−16.7702	+	12.5540i	−0.635215	+	0.475516i
$698$	49.6304	−	5.39476i	1.87854	−	0.204195i
$699$	23.8890	+	15.3525i	0.903566	+	0.580687i
$700$	7.46352	+	2.37138i	0.282095	+	0.0896298i
$701$	13.5785	+	29.7327i	0.512852	+	1.12299i	0.972075	+	0.234668i	$0.0754005\pi$
$701$	13.5785	+	29.7327i	0.512852	+	1.12299i	−0.459223	+	0.888321i	$0.651872\pi$
$702$	−4.16278	−	16.2301i	−0.157114	−	0.612564i
$703$	1.92624	−	2.57315i	0.0726495	−	0.0970483i
$704$	−2.17538	−	0.140194i	−0.0819877	−	0.00528376i
$705$	−28.8548	+	21.0563i	−1.08673	+	0.793026i
$706$	−7.28633	+	3.65798i	−0.274224	+	0.137670i
$707$	−0.318759	−	4.45683i	−0.0119882	−	0.167616i
$708$	25.5474	+	16.3337i	0.960130	+	0.613858i
$709$	20.1011	−	17.4177i	0.754913	−	0.654136i	−0.189878	−	0.981808i	$-0.560809\pi$
$709$	20.1011	−	17.4177i	0.754913	−	0.654136i	0.944792	+	0.327671i	$0.106264\pi$
$710$	34.0546	+	4.04138i	1.27805	+	0.151670i
$711$	−0.295598	−	0.134995i	−0.0110858	−	0.00506271i
$712$	35.3753	+	20.8211i	1.32575	+	0.780302i
$713$	2.40059	+	30.4562i	0.0899026	+	1.14059i
$714$	−6.30900	+	4.39140i	−0.236108	+	0.164344i
$715$	−2.21689	+	1.87411i	−0.0829071	+	0.0700876i
$716$	−16.9354	−	12.6157i	−0.632905	−	0.471473i
$717$	−1.02351	+	14.3105i	−0.0382236	+	0.534435i
$718$	6.74097	+	16.2203i	0.251571	+	0.605335i
$719$	24.8130	−	28.6357i	0.925368	−	1.06793i	−0.0721416	−	0.997394i	$-0.522983\pi$
$719$	24.8130	−	28.6357i	0.925368	−	1.06793i	0.997509	−	0.0705367i	$-0.0224712\pi$
$720$	−14.6471	−	8.14109i	−0.545864	−	0.303401i
$721$	−1.33265	+	0.391300i	−0.0496303	+	0.0145728i
$722$	17.0206	−	18.3245i	0.633443	−	0.681969i
$723$	−30.6326	+	40.9204i	−1.13924	+	1.52185i
$724$	2.95753	+	40.0307i	0.109916	+	1.48773i
$725$	3.80930	−	7.83001i	0.141474	−	0.290799i
$726$	−23.2728	−	24.9380i	−0.863736	−	0.925537i
$727$	45.1809	−	9.82849i	1.67566	−	0.364519i	0.728445	−	0.685104i	$-0.240243\pi$
$727$	45.1809	−	9.82849i	1.67566	−	0.364519i	0.947220	+	0.320585i	$0.103880\pi$
$728$	10.2343	+	2.57381i	0.379310	+	0.0953916i
$729$	−4.30223	−	0.618568i	−0.159342	−	0.0229099i
$730$	43.0557	−	10.4853i	1.59356	−	0.388077i
$731$	10.2501	+	15.9495i	0.379114	+	0.589914i
$732$	1.20499	−	2.65503i	0.0445376	−	0.0981329i
$733$	−30.1333	+	16.4540i	−1.11300	+	0.607744i	−0.927096	−	0.374824i	$-0.877703\pi$
$733$	−30.1333	+	16.4540i	−1.11300	+	0.607744i	−0.185903	+	0.982568i	$0.559521\pi$
$734$	−34.2141	+	6.21437i	−1.26286	+	0.229377i
$735$	13.4456	−	28.5163i	0.495950	−	1.05184i
$736$	27.0096	+	2.54565i	0.995588	+	0.0938339i
$737$	2.19644	+	2.19644i	0.0809068	+	0.0809068i
$738$	10.0516	−	14.5134i	0.370004	−	0.534245i
$739$	−12.8795	−	3.78177i	−0.473781	−	0.139115i	0.0361205	−	0.999347i	$-0.488500\pi$
$739$	−12.8795	−	3.78177i	−0.473781	−	0.139115i	−0.509902	+	0.860233i	$0.670318\pi$
$740$	−1.01719	+	12.4921i	−0.0373925	+	0.459218i
$741$	−10.1480	+	6.52172i	−0.372796	+	0.239581i
$742$	8.60321	−	6.94958i	0.315834	−	0.255127i
$743$	22.1009	−	16.5446i	0.810805	−	0.606961i	−0.111350	−	0.993781i	$-0.535518\pi$
$743$	22.1009	−	16.5446i	0.810805	−	0.606961i	0.922155	+	0.386820i	$0.126427\pi$
$744$	20.4170	+	34.1365i	0.748523	+	1.25150i
$745$	0.235868	−	1.02399i	0.00864155	−	0.0375159i
$746$	18.0901	−	16.8822i	0.662326	−	0.618100i
$747$	−12.0350	−	4.48884i	−0.440339	−	0.164238i
$748$	1.29753	+	1.11899i	0.0474424	+	0.0409145i
$749$	4.94590	−	0.711113i	0.180719	−	0.0259835i
$750$	16.7195	−	30.6406i	0.610511	−	1.11883i
$751$	−3.91724	−	13.3409i	−0.142942	−	0.486816i	0.856634	−	0.515924i	$-0.172551\pi$
$751$	−3.91724	−	13.3409i	−0.142942	−	0.486816i	−0.999576	+	0.0291084i	$0.990733\pi$
$752$	1.92932	−	28.8805i	0.0703552	−	1.05316i
$753$	−4.12511	−	57.6766i	−0.150328	−	2.10185i
$754$	4.47762	−	10.8459i	0.163065	−	0.394985i
$755$	−13.4000	+	23.8443i	−0.487676	+	0.867783i
$756$	−2.32679	+	3.12348i	−0.0846245	+	0.113600i
$757$	−41.1773	+	15.3583i	−1.49661	+	0.558208i	−0.958607	−	0.284733i	$-0.908095\pi$
$757$	−41.1773	+	15.3583i	−1.49661	+	0.558208i	−0.538006	+	0.842941i	$0.680822\pi$
$758$	4.03783	−	22.5315i	0.146661	−	0.818382i
$759$	−1.90499	−	2.16650i	−0.0691466	−	0.0786388i
$760$	1.34978	−	7.12697i	0.0489616	−	0.258522i
$761$	−20.4591	+	44.7991i	−0.741641	+	1.62397i	0.0391964	+	0.999232i	$0.487520\pi$
$761$	−20.4591	+	44.7991i	−0.741641	+	1.62397i	−0.780837	+	0.624735i	$0.785207\pi$
$762$	−7.89328	+	15.8151i	−0.285943	+	0.572922i
$763$	0.277646	−	3.88199i	0.0100514	−	0.140538i
$764$	−5.02702	−	22.8504i	−0.181871	−	0.826700i
$765$	5.32509	+	12.0470i	0.192529	+	0.435559i
$766$	14.5004	+	28.8834i	0.523921	+	1.04360i
$767$	−15.6812	+	28.7179i	−0.566215	+	1.03694i
$768$	32.9774	−	12.6539i	1.18997	−	0.456609i
$769$	41.1524	−	5.91683i	1.48399	−	0.213366i	0.647805	−	0.761806i	$-0.275687\pi$
$769$	41.1524	−	5.91683i	1.48399	−	0.213366i	0.836190	+	0.548440i	$0.184778\pi$
$770$	0.662714	+	0.127124i	0.0238826	+	0.00458123i
$771$	31.7938	−	14.5197i	1.14503	−	0.522915i
$772$	−11.2434	−	17.4050i	−0.404658	−	0.626421i
$773$	−0.631478	+	0.137370i	−0.0227127	+	0.00494084i	−0.223907	−	0.974610i	$-0.571881\pi$
$773$	−0.631478	+	0.137370i	−0.0227127	+	0.00494084i	0.201195	+	0.979551i	$0.435518\pi$
$774$	−12.4527	−	10.0109i	−0.447603	−	0.359836i
$775$	−27.2070	+	16.5615i	−0.977304	+	0.594907i
$776$	−11.3169	+	22.8085i	−0.406252	+	0.818778i
$777$	−4.73440	−	1.02991i	−0.169846	−	0.0369477i
$778$	4.76209	+	8.00464i	0.170729	+	0.286980i
$779$	7.33228	+	2.15295i	0.262706	+	0.0771375i
$780$	19.9603	−	42.5920i	0.714695	−	1.52504i
$781$	2.95500			0.105738
$782$	−15.7287	−	14.3982i	−0.562456	−	0.514880i
$783$	3.06227	+	3.06227i	0.109436	+	0.109436i
$784$	10.7216	+	23.1882i	0.382913	+	0.828150i
$785$	20.3942	+	18.1118i	0.727899	+	0.646437i
$786$	−4.52487	+	17.8155i	−0.161397	+	0.635458i
$787$	−2.24561	+	10.3229i	−0.0800472	+	0.367971i	−0.999693	−	0.0247777i	$-0.992112\pi$
$787$	−2.24561	+	10.3229i	−0.0800472	+	0.367971i	0.919646	+	0.392749i	$0.128476\pi$
$788$	22.1160	+	6.43749i	0.787850	+	0.229326i
$789$	49.0075	+	7.04622i	1.74471	+	0.250852i
$790$	0.240095	+	0.493153i	0.00854218	+	0.0175456i
$791$	−6.94539	+	10.8072i	−0.246950	+	0.384261i
$792$	−1.33598	−	0.547877i	−0.0474720	−	0.0194680i
$793$	2.94787	+	1.09950i	0.104682	+	0.0390443i
$794$	24.0744	+	14.2458i	0.854368	+	0.505565i
$795$	−23.0950	−	43.5497i	−0.819095	−	1.54455i
$796$	−5.36290	−	7.12904i	−0.190083	−	0.252682i
$797$	9.96010	+	5.43862i	0.352805	+	0.192646i	0.645872	−	0.763446i	$-0.276494\pi$
$797$	9.96010	+	5.43862i	0.352805	+	0.192646i	−0.293067	+	0.956092i	$0.594676\pi$
$798$	2.66164	+	0.882408i	0.0942209	+	0.0312369i
$799$	−14.8986	+	17.1939i	−0.527073	+	0.608275i
$800$	10.3381	+	26.3272i	0.365508	+	0.930808i
$801$	17.8057	+	20.5489i	0.629133	+	0.726058i
$802$	12.9233	−	25.8933i	0.456336	−	0.914323i
$803$	3.57769	−	1.33441i	0.126254	−	0.0470903i
$804$	−47.1994	−	17.4784i	−1.66460	−	0.616414i
$805$	−8.19719	−	1.82562i	−0.288913	−	0.0643445i
$806$	−35.2279	+	24.5205i	−1.24085	+	0.863698i
$807$	−11.2926	−	30.2768i	−0.397520	−	1.06579i
$808$	11.7725	−	11.0383i	0.414157	−	0.388325i
$809$	13.4865	−	11.6861i	0.474159	−	0.410861i	−0.384725	−	0.923031i	$-0.625704\pi$
$809$	13.4865	−	11.6861i	0.474159	−	0.410861i	0.858884	+	0.512170i	$0.171158\pi$
$810$	23.6563	+	25.9770i	0.831199	+	0.912737i
$811$	0.900139	+	0.779975i	0.0316081	+	0.0273886i	0.670522	−	0.741890i	$-0.266070\pi$
$811$	0.900139	+	0.779975i	0.0316081	+	0.0273886i	−0.638913	+	0.769279i	$0.720616\pi$
$812$	−2.61529	+	0.774594i	−0.0917789	+	0.0271829i
$813$	7.17485	−	13.1398i	0.251633	−	0.460831i
$814$	0.0398138	+	1.07924i	0.00139547	+	0.0378275i
$815$	−11.6501	+	37.9578i	−0.408084	+	1.32960i
$816$	−26.6748	−	7.69657i	−0.933805	−	0.269434i
$817$	2.41694	−	6.48008i	0.0845582	−	0.226709i
$818$	−0.244771	+	7.08664i	−0.00855822	+	0.247779i
$819$	5.88062	+	3.77924i	0.205485	+	0.132057i
$820$	−28.6721	+	8.11308i	−1.00127	+	0.283321i
$821$	3.08638	−	21.4662i	0.107715	−	0.749177i	−0.862346	−	0.506319i	$-0.831006\pi$
$821$	3.08638	−	21.4662i	0.107715	−	0.749177i	0.970062	−	0.242858i	$-0.0780850\pi$
$822$	27.6684	−	22.3502i	0.965047	−	0.779554i
$823$	−30.4135	−	6.61606i	−1.06015	−	0.230621i	−0.351504	−	0.936186i	$-0.614330\pi$
$823$	−30.4135	−	6.61606i	−1.06015	−	0.230621i	−0.708645	+	0.705565i	$0.750693\pi$
$824$	−4.13060	−	2.84642i	−0.143896	−	0.0991599i
$825$	1.11951	−	2.79161i	0.0389762	−	0.0971914i
$826$	7.48357	−	1.35926i	0.260387	−	0.0472946i
$827$	35.5927	−	35.5927i	1.23768	−	1.23768i	0.276731	−	0.960948i	$-0.410749\pi$
$827$	35.5927	−	35.5927i	1.23768	−	1.23768i	0.960948	−	0.276731i	$-0.0892510\pi$
$828$	16.4174	+	7.30781i	0.570545	+	0.253964i
$829$		−	16.7890i		−	0.583105i	−0.956555	−	0.291552i	$-0.905828\pi$
$829$		−	16.7890i		−	0.583105i	0.956555	−	0.291552i	$-0.0941718\pi$
$830$	10.8567	+	18.7662i	0.376841	+	0.651386i
$831$	−12.3818	+	42.1687i	−0.429522	+	1.46282i
$832$	16.0773	+	34.5581i	0.557379	+	1.19809i
$833$	4.26829	−	19.6210i	0.147887	−	0.679828i
$834$	6.72270	−	63.2285i	0.232788	−	2.18942i
$835$	−23.3185	−	15.3909i	−0.806969	−	0.532623i
$836$	0.0431255	−	0.623542i	0.00149153	−	0.0215657i
$837$	−3.36733	−	15.4794i	−0.116392	−	0.535045i
$838$	37.8381	+	1.30692i	1.30710	+	0.0451468i
$839$	−6.32871	−	13.8579i	−0.218491	−	0.478429i	0.768369	−	0.640008i	$-0.221069\pi$
$839$	−6.32871	−	13.8579i	−0.218491	−	0.478429i	−0.986860	+	0.161578i	$0.948342\pi$
$840$	−10.6174	+	2.61207i	−0.366337	+	0.0901248i
$841$	−3.69552	−	25.7029i	−0.127432	−	0.886307i
$842$	21.2210	−	22.8466i	0.731323	−	0.787347i
$843$	15.0671	+	8.22725i	0.518938	+	0.283362i
$844$	−18.9457	−	10.2875i	−0.652139	−	0.354110i
$845$	20.2264	+	7.82632i	0.695808	+	0.269234i
$846$	7.31641	−	17.7222i	0.251543	−	0.609302i
$847$	−8.53437	−	0.610390i	−0.293244	−	0.0209732i
$848$	39.0706	+	8.30735i	1.34169	+	0.285276i
$849$	34.8411	+	15.9114i	1.19574	+	0.546078i
$850$	5.99657	−	21.4075i	0.205681	−	0.734270i
$851$	−0.0975568	−	13.4402i	−0.00334420	−	0.460726i
$852$	−43.5074	+	19.9928i	−1.49054	+	0.684941i
$853$	6.87188	+	18.4242i	0.235289	+	0.630833i	0.999907	−	0.0136502i	$-0.00434514\pi$
$853$	6.87188	+	18.4242i	0.235289	+	0.630833i	−0.764618	+	0.644484i	$0.777072\pi$
$854$	−0.231777	−	0.693661i	−0.00793125	−	0.0237366i
$855$	2.35396	−	4.18869i	0.0805036	−	0.143250i
$856$	13.2517	+	12.2510i	0.452935	+	0.418730i
$857$	18.9501	−	1.35534i	0.647323	−	0.0462975i	0.256183	−	0.966628i	$-0.417535\pi$
$857$	18.9501	−	1.35534i	0.647323	−	0.0462975i	0.391141	+	0.920331i	$0.372081\pi$
$858$	1.27545	−	3.84718i	0.0435431	−	0.131340i
$859$	−8.52907	+	2.50436i	−0.291008	+	0.0854477i	−0.423978	−	0.905672i	$-0.639367\pi$
$859$	−8.52907	+	2.50436i	−0.291008	+	0.0854477i	0.132970	+	0.991120i	$0.457549\pi$
$860$	5.47273	+	26.4071i	0.186618	+	0.900473i
$861$	−1.63935	−	11.4019i	−0.0558688	−	0.388576i
$862$	5.20238	+	20.2833i	0.177194	+	0.690853i
$863$	6.43724	−	17.2589i	0.219126	−	0.587500i	−0.780148	−	0.625595i	$-0.784856\pi$
$863$	6.43724	−	17.2589i	0.219126	−	0.587500i	0.999274	+	0.0380950i	$0.0121289\pi$
$864$	−14.0552	+	0.584598i	−0.478166	+	0.0198884i
$865$	−5.71411	+	3.57453i	−0.194285	+	0.121538i
$866$	−2.62179	−	2.10770i	−0.0890920	−	0.0716225i
$867$	−9.41324	−	12.5746i	−0.319690	−	0.427056i
$868$	9.57976	+	2.78846i	0.325158	+	0.0946465i
$869$	0.0255520	+	0.0397597i	0.000866793	+	0.00134876i
$870$	1.16628	+	12.1014i	0.0395405	+	0.410277i
$871$	15.3014	−	52.1116i	0.518466	−	1.76573i
$872$	11.5181	−	8.05740i	0.390051	−	0.272858i
$873$	−11.9259	+	11.9259i	−0.403631	+	0.403631i
$874$	−0.766258	+	7.74085i	−0.0259191	+	0.261838i
$875$	−2.15779	−	8.48548i	−0.0729466	−	0.286862i
$876$	−43.6473	+	43.8527i	−1.47470	+	1.48164i
$877$	11.1531	+	20.4253i	0.376612	+	0.689713i	0.995396	−	0.0958478i	$-0.0305562\pi$
$877$	11.1531	+	20.4253i	0.376612	+	0.689713i	−0.618784	+	0.785561i	$0.712374\pi$
$878$	43.1382	−	25.6636i	1.45584	−	0.866105i
$879$	−57.4198	+	36.9015i	−1.93672	+	1.24466i
$880$	1.15195	+	2.14777i	0.0388321	+	0.0724014i
$881$	−1.21553	+	8.45418i	−0.0409521	+	0.284828i	0.959047	+	0.283248i	$0.0914121\pi$
$881$	−1.21553	+	8.45418i	−0.0409521	+	0.284828i	−0.999999	+	0.00158012i	$0.999497\pi$
$882$	1.82865	+	16.8231i	0.0615739	+	0.566464i
$883$	1.83864	+	8.45209i	0.0618751	+	0.284435i	0.997680	−	0.0680841i	$-0.0216886\pi$
$883$	1.83864	+	8.45209i	0.0618751	+	0.284435i	−0.935804	+	0.352520i	$0.885325\pi$
$884$	6.29935	−	29.2885i	0.211870	−	0.985080i
$885$	0.413425	−	33.8992i	0.0138971	−	1.13951i
$886$	−43.0393	−	25.4682i	−1.44594	−	0.855620i
$887$	−15.9886	−	11.9689i	−0.536845	−	0.401877i	0.296164	−	0.955137i	$-0.404293\pi$
$887$	−15.9886	−	11.9689i	−0.536845	−	0.401877i	−0.833008	+	0.553260i	$0.813383\pi$
$888$	−7.88807	−	15.6207i	−0.264706	−	0.524196i
$889$	1.24910	+	4.25406i	0.0418936	+	0.142676i
$890$	−1.13246	−	45.8790i	−0.0379601	−	1.53787i
$891$	2.28800	+	1.98256i	0.0766507	+	0.0664182i
$892$	29.0327	+	18.5620i	0.972086	+	0.621502i
$893$	8.27811	+	0.592062i	0.277017	+	0.0198126i
$894$	0.464957	+	1.39152i	0.0155505	+	0.0465394i
$895$	−1.97142	+	23.5281i	−0.0658974	+	0.786456i
$896$	3.90065	−	7.95514i	0.130311	−	0.265763i
$897$	−17.2841	+	47.3881i	−0.577099	+	1.58224i
$898$	−25.6332	−	4.59368i	−0.855392	−	0.153293i
$899$	4.60851	−	10.0912i	0.153702	−	0.336561i
$900$	0.924355	+	18.7126i	0.0308118	+	0.623755i
$901$	−20.5600	−	23.7275i	−0.684954	−	0.790479i
$902$	−2.37101	+	0.985368i	−0.0789461	+	0.0328092i
$903$	−10.3987	+	0.743730i	−0.346047	+	0.0247498i
$904$	−46.1150	+	5.12221i	−1.53376	+	0.170362i
$905$	36.2517	−	26.4541i	1.20505	−	0.879363i
$906$	−1.40784	−	38.1628i	−0.0467725	−	1.26787i
$907$	−44.8658	−	33.5861i	−1.48974	−	1.11521i	−0.964442	−	0.264293i	$-0.914861\pi$
$907$	−44.8658	−	33.5861i	−1.48974	−	1.11521i	−0.525302	−	0.850916i	$-0.676048\pi$
$908$	−29.7428	−	25.6503i	−0.987050	−	0.851235i
$909$	9.72380	−	4.44071i	0.322518	−	0.147289i
$910$	−3.60240	−	11.2352i	−0.119418	−	0.372444i
$911$	−18.1187	+	28.1933i	−0.600300	+	0.934086i	0.399549	+	0.916712i	$0.369167\pi$
$911$	−18.1187	+	28.1933i	−0.600300	+	0.934086i	−0.999849	+	0.0173737i	$0.994470\pi$
$912$	3.58377	+	9.47240i	0.118671	+	0.313662i
$913$	1.11954	+	1.49553i	0.0370514	+	0.0494949i
$914$	−1.75474	+	16.5037i	−0.0580416	+	0.545894i
$915$	−3.23207	+	0.424539i	−0.106849	+	0.0140348i
$916$	−31.6411	+	11.8862i	−1.04545	+	0.392732i
$917$	2.20966	+	4.04668i	0.0729693	+	0.133633i
$918$	9.08979	+	6.29535i	0.300008	+	0.207778i
$919$	13.0630			0.430909			0.215454	−	0.976514i	$-0.430877\pi$
$919$	13.0630			0.430909			0.215454	+	0.976514i	$0.430877\pi$
$920$	−13.5385	−	27.1424i	−0.446351	−	0.894858i
$921$	−54.7142			−1.80289
$922$	−9.18141	−	6.35881i	−0.302374	−	0.209416i
$923$	−24.7615	−	45.3473i	−0.815035	−	1.49263i
$924$	−0.881983	+	0.331323i	−0.0290151	+	0.0108997i
$925$	12.4589	−	6.41368i	0.409645	−	0.210881i
$926$	−0.344894	+	3.24380i	−0.0113339	+	0.106598i
$927$	−1.99130	−	2.66007i	−0.0654030	−	0.0873681i
$928$	−8.12495	−	5.57087i	−0.266715	−	0.182873i
$929$	−2.04954	+	3.18914i	−0.0672431	+	0.104632i	−0.873247	−	0.487278i	$-0.837990\pi$
$929$	−2.04954	+	3.18914i	−0.0672431	+	0.104632i	0.806004	+	0.591911i	$0.201626\pi$
$930$	20.3432	−	39.5455i	0.667079	−	1.29675i
$931$	−6.66302	+	3.04290i	−0.218372	+	0.0997270i
$932$	19.4822	+	16.8015i	0.638161	+	0.550352i
$933$	−8.89541	−	6.65902i	−0.291223	−	0.218007i
$934$	−1.92819	−	52.2680i	−0.0630924	−	1.71026i
$935$	0.295727	−	1.89267i	0.00967129	−	0.0618971i
$936$	2.78718	+	25.0929i	0.0911019	+	0.820186i
$937$	−1.46330	+	0.104657i	−0.0478040	+	0.00341901i	−0.0952207	−	0.995456i	$-0.530356\pi$
$937$	−1.46330	+	0.104657i	−0.0478040	+	0.00341901i	0.0474167	+	0.998875i	$0.484901\pi$
$938$	−11.6583	+	4.84507i	−0.380657	+	0.158197i
$939$	1.19994	+	1.38480i	0.0391585	+	0.0451913i
$940$	−28.5543	+	15.2287i	−0.931337	+	0.496706i
$941$	11.2056	−	24.5368i	0.365291	−	0.799875i	−0.634349	−	0.773047i	$-0.718732\pi$
$941$	11.2056	−	24.5368i	0.365291	−	0.799875i	0.999640	−	0.0268288i	$-0.00854089\pi$
$942$	−37.4854	−	6.71769i	−1.22134	−	0.218874i
$943$	29.8581	−	11.3840i	0.972312	−	0.370715i
$944$	20.8454	+	17.8920i	0.678460	+	0.582334i
$945$	4.33940	+	0.363600i	0.141161	+	0.0118279i
$946$	0.736439	+	2.20401i	0.0239437	+	0.0716585i
$947$	20.2804	+	1.45048i	0.659024	+	0.0471343i	0.396846	−	0.917885i	$-0.370105\pi$
$947$	20.2804	+	1.45048i	0.659024	+	0.0471343i	0.262178	+	0.965019i	$0.415559\pi$
$948$	−0.645215	−	0.412517i	−0.0209556	−	0.0133979i
$949$	−50.4572	−	43.7214i	−1.63791	−	1.41926i
$950$	−7.56254	+	2.92873i	−0.245361	+	0.0950206i
$951$	−17.8253	−	60.7075i	−0.578026	−	1.96858i
$952$	−6.21634	+	3.13910i	−0.201473	+	0.101739i
$953$	38.5706	+	28.8736i	1.24942	+	0.935308i	0.999457	−	0.0329466i	$-0.0104891\pi$
$953$	38.5706	+	28.8736i	1.24942	+	0.935308i	0.249968	+	0.968254i	$0.419580\pi$
$954$	22.7708	+	13.4744i	0.737232	+	0.436251i
$955$	−18.7210	+	18.2699i	−0.605798	+	0.591200i
$956$	−2.73306	+	12.7072i	−0.0883934	+	0.410981i
$957$	0.222680	+	1.02364i	0.00719823	+	0.0330897i
$958$	−3.32362	−	30.5764i	−0.107381	−	0.987879i
$959$	1.26969	−	8.83091i	0.0410005	−	0.285165i
$960$	−31.4918	−	23.8286i	−1.01639	−	0.769065i
$961$	−8.05933	+	5.17941i	−0.259978	+	0.167078i
$962$	16.2284	−	9.65454i	0.523225	−	0.311275i
$963$	5.72910	+	10.4921i	0.184618	+	0.338102i
$964$	−32.6683	+	32.8221i	−1.05218	+	1.05713i
$965$	−9.87997	+	20.9541i	−0.318048	+	0.674535i
$966$	11.0938	−	3.79657i	0.356937	−	0.122153i
$967$	−9.46925	+	9.46925i	−0.304511	+	0.304511i	−0.842776	−	0.538265i	$-0.819080\pi$
$967$	−9.46925	+	9.46925i	−0.304511	+	0.304511i	0.538265	+	0.842776i	$0.319080\pi$
$968$	−17.7138	−	25.3219i	−0.569343	−	0.813876i
$969$	2.24269	−	7.63792i	0.0720457	−	0.245365i
$970$	28.3358	−	2.73087i	0.909807	−	0.0876829i
$971$	−9.91566	−	15.4291i	−0.318209	−	0.495142i	0.644896	−	0.764271i	$-0.276901\pi$
$971$	−9.91566	−	15.4291i	−0.318209	−	0.495142i	−0.963104	+	0.269128i	$0.913264\pi$
$972$	−32.7743	−	9.53989i	−1.05124	−	0.305992i
$973$	−9.55812	−	12.7682i	−0.306419	−	0.409328i
$974$	5.60987	+	4.50987i	0.179752	+	0.144505i
$975$	−52.2209	+	6.21251i	−1.67241	+	0.198960i
$976$	1.41764	−	2.22884i	0.0453777	−	0.0713433i
$977$	10.0900	−	27.0524i	0.322808	−	0.865483i	−0.669625	−	0.742699i	$-0.733545\pi$
$977$	10.0900	−	27.0524i	0.322808	−	0.865483i	0.992433	−	0.122783i	$-0.0391820\pi$
$978$	−13.7730	−	53.6991i	−0.440414	−	1.71711i
$979$	−0.562783	−	3.91424i	−0.0179866	−	0.125100i
$980$	15.6778	−	23.8749i	0.500809	−	0.762656i
$981$	8.93389	−	2.62323i	0.285237	−	0.0837532i
$982$	7.89325	−	23.8087i	0.251884	−	0.759765i
$983$	−23.1631	+	1.65666i	−0.738788	+	0.0528392i	−0.435661	−	0.900111i	$-0.643485\pi$
$983$	−23.1631	+	1.65666i	−0.738788	+	0.0528392i	−0.303127	+	0.952950i	$0.598031\pi$
$984$	28.2425	−	30.5496i	0.900337	−	0.973884i
$985$	−6.95349	−	24.7961i	−0.221557	−	0.790070i
$986$	2.45392	+	7.34407i	0.0781487	+	0.233883i
$987$	−4.37185	−	11.7214i	−0.139158	−	0.373096i
$988$	−9.93024	+	4.56319i	−0.315923	+	0.145174i
$989$	−8.34895	−	27.6888i	−0.265481	−	0.880453i
$990$	0.269114	+	1.59180i	0.00855299	+	0.0505909i
$991$	−26.0095	−	11.8781i	−0.826219	−	0.377321i	−0.0430056	−	0.999075i	$-0.513693\pi$
$991$	−26.0095	−	11.8781i	−0.826219	−	0.377321i	−0.783213	+	0.621753i	$0.786421\pi$
$992$	13.9854	+	33.2110i	0.444037	+	1.05445i
$993$	25.2575	+	1.80645i	0.801521	+	0.0573259i
$994$	−4.58313	+	11.1015i	−0.145368	+	0.352118i
$995$	−3.59924	+	9.30190i	−0.114104	+	0.294890i
$996$	−26.6018	−	14.4447i	−0.842909	−	0.457698i
$997$	−11.4336	−	6.24324i	−0.362107	−	0.197725i	0.287888	−	0.957664i	$-0.407047\pi$
$997$	−11.4336	−	6.24324i	−0.362107	−	0.197725i	−0.649995	+	0.759939i	$0.725229\pi$
$998$	−12.4038	+	13.3540i	−0.392635	+	0.422714i
$999$	0.991839	+	6.89839i	0.0313804	+	0.218255i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.w.a.167.55	yes	1360
4.3	odd	2	inner	460.2.w.a.167.40	yes	1360
5.3	odd	4	inner	460.2.w.a.443.48	yes	1360
20.3	even	4	inner	460.2.w.a.443.5	yes	1360
23.4	even	11	inner	460.2.w.a.27.5	✓	1360
92.27	odd	22	inner	460.2.w.a.27.48	yes	1360
115.73	odd	44	inner	460.2.w.a.303.40	yes	1360
460.303	even	44	inner	460.2.w.a.303.55	yes	1360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.w.a.27.5	✓	1360	23.4	even	11	inner
460.2.w.a.27.48	yes	1360	92.27	odd	22	inner
460.2.w.a.167.40	yes	1360	4.3	odd	2	inner
460.2.w.a.167.55	yes	1360	1.1	even	1	trivial
460.2.w.a.303.40	yes	1360	115.73	odd	44	inner
460.2.w.a.303.55	yes	1360	460.303	even	44	inner
460.2.w.a.443.5	yes	1360	20.3	even	4	inner
460.2.w.a.443.48	yes	1360	5.3	odd	4	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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(1.16261 + 0.805194i) q^{2} +(1.05800 + 1.93757i) q^{3} +(0.703326 + 1.87225i) q^{4} +(1.36176 - 1.77359i) q^{5} +(-0.330086 + 3.10453i) q^{6} +(0.469306 + 0.626919i) q^{7} +(-0.689833 + 2.74301i) q^{8} +(-1.01292 + 1.57613i) q^{9} +O(q^{10})\)	\(q+(1.16261 + 0.805194i) q^{2} +(1.05800 + 1.93757i) q^{3} +(0.703326 + 1.87225i) q^{4} +(1.36176 - 1.77359i) q^{5} +(-0.330086 + 3.10453i) q^{6} +(0.469306 + 0.626919i) q^{7} +(-0.689833 + 2.74301i) q^{8} +(-1.01292 + 1.57613i) q^{9} +(3.01127 - 0.965517i) q^{10} +(0.247862 - 0.113195i) q^{11} +(-2.88351 + 3.34358i) q^{12} +(-3.81406 - 2.85517i) q^{13} +(0.0408284 + 1.10675i) q^{14} +(4.87719 + 0.762052i) q^{15} +(-3.01067 + 2.63361i) q^{16} +(3.13600 - 0.224291i) q^{17} +(-2.44671 + 1.01683i) q^{18} +(-0.751063 - 0.866772i) q^{19} +(4.27837 + 1.30214i) q^{20} +(-0.718179 + 1.57259i) q^{21} +(0.379311 + 0.0679757i) q^{22} +(-4.69351 - 0.985386i) q^{23} +(-6.04463 + 1.56549i) q^{24} +(-1.29124 - 4.83039i) q^{25} +(-2.13530 - 6.39051i) q^{26} +(2.48044 + 0.177404i) q^{27} +(-0.843677 + 1.31959i) q^{28} +(1.31613 + 1.14043i) q^{29} +(5.05667 + 4.81305i) q^{30} +(-1.79471 - 6.11221i) q^{31} +(-5.62080 + 0.637691i) q^{32} +(0.481561 + 0.360492i) q^{33} +(3.82654 + 2.26432i) q^{34} +(1.75098 + 0.0213545i) q^{35} +(-3.66332 - 0.787903i) q^{36} +(0.595727 + 2.73851i) q^{37} +(-0.175273 - 1.61247i) q^{38} +(1.49684 - 10.4108i) q^{39} +(3.92560 + 4.95880i) q^{40} +(-5.60528 + 3.60229i) q^{41} +(-2.10120 + 1.25004i) q^{42} +(2.89000 + 5.29264i) q^{43} +(0.386258 + 0.384448i) q^{44} +(1.41606 + 3.94280i) q^{45} +(-4.66329 - 4.92480i) q^{46} +(-5.11678 + 5.11678i) q^{47} +(-8.28808 - 3.04704i) q^{48} +(1.79935 - 6.12802i) q^{49} +(2.38819 - 6.65557i) q^{50} +(3.75245 + 5.83892i) q^{51} +(2.66307 - 9.14900i) q^{52} +(-5.98439 - 7.99420i) q^{53} +(2.74094 + 2.20349i) q^{54} +(0.136767 - 0.593750i) q^{55} +(-2.04339 + 0.854843i) q^{56} +(0.884815 - 2.37228i) q^{57} +(0.611878 + 2.38562i) q^{58} +(-0.977381 - 6.79784i) q^{59} +(2.00350 + 9.66731i) q^{60} +(-0.633621 + 0.186048i) q^{61} +(2.83497 - 8.55121i) q^{62} +(-1.46347 + 0.104670i) q^{63} +(-7.04826 - 3.78444i) q^{64} +(-10.2577 + 2.87654i) q^{65} +(0.269602 + 0.806862i) q^{66} +(3.98375 + 10.6808i) q^{67} +(2.62556 + 5.71363i) q^{68} +(-3.05645 - 10.1366i) q^{69} +(2.01851 + 1.43470i) q^{70} +(9.86457 + 4.50500i) q^{71} +(-3.62460 - 3.86571i) q^{72} +(13.9776 + 0.999700i) q^{73} +(-1.51243 + 3.66350i) q^{74} +(7.99311 - 7.61241i) q^{75} +(1.09458 - 2.01580i) q^{76} +(0.187287 + 0.102267i) q^{77} +(10.1229 - 10.8984i) q^{78} +(0.0246843 + 0.171683i) q^{79} +(0.571151 + 8.92602i) q^{80} +(4.61545 + 10.1064i) q^{81} +(-9.41729 - 0.325271i) q^{82} +(1.45734 + 6.69926i) q^{83} +(-3.44941 - 0.238568i) q^{84} +(3.87266 - 5.86740i) q^{85} +(-0.901657 + 8.48029i) q^{86} +(-0.817215 + 3.75668i) q^{87} +(0.139512 + 0.757976i) q^{88} +(4.08868 - 13.9248i) q^{89} +(-1.52839 + 5.72414i) q^{90} -3.73106i q^{91} +(-1.45617 - 9.48048i) q^{92} +(9.94407 - 9.94407i) q^{93} +(-10.0688 + 1.82882i) q^{94} +(-2.56006 + 0.151745i) q^{95} +(-7.18235 - 10.2160i) q^{96} +(8.79636 + 1.91353i) q^{97} +(7.02618 - 5.67567i) q^{98} +(-0.0726540 + 0.505319i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8}+O(q^{10}) \) 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8	\( 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8} - 18 q^{10} - 6 q^{12} - 36 q^{13} - 44 q^{16} - 36 q^{17} - 38 q^{18} - 14 q^{20} - 88 q^{21} - 28 q^{22} - 36 q^{25} - 36 q^{26} - 34 q^{28} + 2 q^{30} + 2 q^{32} - 60 q^{33} - 36 q^{36} - 36 q^{37} - 10 q^{38} + 2 q^{40} - 56 q^{41} - 202 q^{42} - 120 q^{45} - 44 q^{46} - 50 q^{48} - 34 q^{50} - 250 q^{52} - 84 q^{53} - 84 q^{56} - 44 q^{57} - 58 q^{58} - 42 q^{60} - 136 q^{61} - 82 q^{62} - 68 q^{65} - 84 q^{66} - 4 q^{68} + 16 q^{70} - 104 q^{72} - 36 q^{73} + 4 q^{76} - 44 q^{77} - 50 q^{78} + 204 q^{80} + 80 q^{81} - 10 q^{82} - 252 q^{85} + 44 q^{86} - 50 q^{88} + 264 q^{90} - 22 q^{92} - 88 q^{93} + 52 q^{96} - 36 q^{97} + 30 q^{98}+O(q^{100}) \) 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8 - 18 * q^10 - 6 * q^12 - 36 * q^13 - 44 * q^16 - 36 * q^17 - 38 * q^18 - 14 * q^20 - 88 * q^21 - 28 * q^22 - 36 * q^25 - 36 * q^26 - 34 * q^28 + 2 * q^30 + 2 * q^32 - 60 * q^33 - 36 * q^36 - 36 * q^37 - 10 * q^38 + 2 * q^40 - 56 * q^41 - 202 * q^42 - 120 * q^45 - 44 * q^46 - 50 * q^48 - 34 * q^50 - 250 * q^52 - 84 * q^53 - 84 * q^56 - 44 * q^57 - 58 * q^58 - 42 * q^60 - 136 * q^61 - 82 * q^62 - 68 * q^65 - 84 * q^66 - 4 * q^68 + 16 * q^70 - 104 * q^72 - 36 * q^73 + 4 * q^76 - 44 * q^77 - 50 * q^78 + 204 * q^80 + 80 * q^81 - 10 * q^82 - 252 * q^85 + 44 * q^86 - 50 * q^88 + 264 * q^90 - 22 * q^92 - 88 * q^93 + 52 * q^96 - 36 * q^97 + 30 * q^98

Introduction

L-functions

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