LMFDB - Embedded newform 71.2.g.a.10.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [71,2,Mod(2,71)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(71, base_ring=CyclotomicField(70))

chi = DirichletCharacter(H, H._module([6]))

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

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

chi := DirichletCharacter("71.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	71.g (of order $35$, degree $24$, 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:	$0.566937854351$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$5$ over $\Q(\zeta_{35})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{35}]$

Embedding invariants

Embedding label			10.2
Character	$\chi$	$=$	71.10
Dual form			71.2.g.a.64.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.713225 + 0.196838i) q^{2} +(-0.487143 + 1.13973i) q^{3} +(-1.24695 + 0.745020i) q^{4} +(-0.623421 + 1.91869i) q^{5} +(0.123101 - 0.908769i) q^{6} +(0.0146541 + 0.326298i) q^{7} +(1.76533 - 1.84639i) q^{8} +(1.01152 + 1.05797i) q^{9} +O(q^{10})$	\(q+(-0.713225 + 0.196838i) q^{2} +(-0.487143 + 1.13973i) q^{3} +(-1.24695 + 0.745020i) q^{4} +(-0.623421 + 1.91869i) q^{5} +(0.123101 - 0.908769i) q^{6} +(0.0146541 + 0.326298i) q^{7} +(1.76533 - 1.84639i) q^{8} +(1.01152 + 1.05797i) q^{9} +(0.0669687 - 1.49117i) q^{10} +(-1.35338 - 0.245602i) q^{11} +(-0.241675 - 1.78412i) q^{12} +(3.64635 - 0.661714i) q^{13} +(-0.0746794 - 0.229840i) q^{14} +(-1.88309 - 1.64521i) q^{15} +(0.481013 - 0.893871i) q^{16} +(-3.50350 + 2.54544i) q^{17} +(-0.929688 - 0.555463i) q^{18} +(5.46579 - 4.77532i) q^{19} +(-0.652088 - 2.85698i) q^{20} +(-0.379029 - 0.142252i) q^{21} +(1.01361 - 0.0912262i) q^{22} +(0.550786 + 0.690664i) q^{23} +(1.24441 + 2.91145i) q^{24} +(0.752353 + 0.546616i) q^{25} +(-2.47042 + 1.18969i) q^{26} +(-5.17985 + 1.94403i) q^{27} +(-0.261371 - 0.395961i) q^{28} +(0.505362 + 0.0454834i) q^{29} +(1.66691 + 0.802740i) q^{30} +(0.738057 + 1.37154i) q^{31} +(-1.30399 + 5.71314i) q^{32} +(0.939207 - 1.42284i) q^{33} +(1.99774 - 2.50509i) q^{34} +(-0.635202 - 0.175305i) q^{35} +(-2.04952 - 0.565632i) q^{36} +(-3.02816 + 3.79719i) q^{37} +(-2.95837 + 4.48175i) q^{38} +(-1.02212 + 4.47819i) q^{39} +(2.44211 + 4.53820i) q^{40} +(9.08603 + 4.37560i) q^{41} +(0.298334 + 0.0268505i) q^{42} +(-4.02244 - 6.09374i) q^{43} +(1.87058 - 0.702039i) q^{44} +(-2.66051 + 1.28124i) q^{45} +(-0.528783 - 0.384183i) q^{46} +(-3.12104 - 7.30203i) q^{47} +(0.784447 + 0.983666i) q^{48} +(6.86556 - 0.617912i) q^{49} +(-0.644191 - 0.241769i) q^{50} +(-1.19440 - 5.23302i) q^{51} +(-4.05383 + 3.54173i) q^{52} +(-5.92634 - 3.54082i) q^{53} +(3.31174 - 2.40612i) q^{54} +(1.31496 - 2.44360i) q^{55} +(0.628343 + 0.548966i) q^{56} +(2.77994 + 8.55576i) q^{57} +(-0.369389 + 0.0670343i) q^{58} +(-1.20842 - 8.92089i) q^{59} +(3.57384 + 0.648556i) q^{60} +(0.513091 - 11.4249i) q^{61} +(-0.796371 - 0.832939i) q^{62} +(-0.330389 + 0.345560i) q^{63} +(-0.103442 - 2.30332i) q^{64} +(-1.00358 + 7.40875i) q^{65} +(-0.389798 + 1.19967i) q^{66} +(-5.32861 + 3.18370i) q^{67} +(2.47229 - 5.78422i) q^{68} +(-1.05548 + 0.291294i) q^{69} +0.487548 q^{70} +(5.80097 - 6.11136i) q^{71} +3.73908 q^{72} +(11.7349 - 3.23862i) q^{73} +(1.41233 - 3.30431i) q^{74} +(-0.989496 + 0.591197i) q^{75} +(-3.25788 + 10.0267i) q^{76} +(0.0603069 - 0.445204i) q^{77} +(-0.152476 - 3.39515i) q^{78} +(-6.41959 + 6.71436i) q^{79} +(1.41519 + 1.48017i) q^{80} +(0.110654 - 2.46391i) q^{81} +(-7.34166 - 1.33232i) q^{82} +(0.581031 + 4.28934i) q^{83} +(0.578612 - 0.105003i) q^{84} +(-2.69977 - 8.30902i) q^{85} +(4.06838 + 3.55444i) q^{86} +(-0.298022 + 0.553817i) q^{87} +(-2.84263 + 2.06529i) q^{88} +(-8.69518 - 5.19513i) q^{89} +(1.64535 - 1.43750i) q^{90} +(0.269350 + 1.18010i) q^{91} +(-1.20136 - 0.450879i) q^{92} +(-1.92272 + 0.173048i) q^{93} +(3.66331 + 4.59365i) q^{94} +(5.75488 + 13.4642i) q^{95} +(-5.87620 - 4.26931i) q^{96} +(-2.76730 + 1.33266i) q^{97} +(-4.77506 + 1.79211i) q^{98} +(-1.10913 - 1.68026i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9}+O(q^{10}) $ 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9	\( 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9} - 8 q^{10} - 27 q^{11} + 3 q^{12} - 31 q^{13} + 2 q^{14} + 12 q^{15} + 30 q^{16} + 9 q^{17} + 27 q^{18} - 31 q^{19} + 72 q^{20} - 32 q^{21} - 24 q^{22} - 6 q^{23} - 47 q^{24} - 42 q^{25} + 77 q^{26} - 2 q^{27} - 18 q^{28} + q^{29} + 15 q^{30} + 15 q^{31} - 10 q^{32} - 24 q^{33} + 20 q^{34} + 74 q^{35} + 8 q^{36} - 22 q^{37} - 39 q^{38} + 86 q^{39} - 30 q^{40} + 39 q^{41} - 34 q^{42} + 33 q^{43} - 23 q^{44} + 121 q^{45} + 124 q^{46} + 6 q^{47} + 131 q^{48} - 22 q^{49} - 15 q^{50} + 29 q^{51} + 83 q^{52} - 30 q^{53} - 25 q^{54} + 32 q^{55} + 11 q^{56} - 10 q^{57} + 12 q^{58} - 80 q^{59} + 80 q^{60} - 12 q^{61} - 68 q^{62} - 79 q^{63} - 117 q^{64} - 89 q^{65} - 39 q^{66} - 74 q^{67} - 67 q^{68} - 95 q^{69} - 64 q^{70} - 115 q^{71} - 144 q^{72} - 14 q^{73} - 70 q^{74} - 13 q^{75} + 8 q^{76} + 47 q^{77} - 218 q^{78} - 25 q^{79} - 103 q^{80} - 28 q^{81} - 88 q^{82} - 20 q^{83} - 142 q^{84} + 22 q^{85} + 159 q^{86} - 105 q^{87} + 43 q^{88} + 33 q^{89} + 33 q^{90} + 60 q^{91} - 2 q^{92} + 63 q^{93} + 174 q^{94} + 20 q^{95} - 30 q^{96} + 121 q^{97} + 128 q^{98} - 2 q^{99}+O(q^{100}) \) 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9 - 8 * q^10 - 27 * q^11 + 3 * q^12 - 31 * q^13 + 2 * q^14 + 12 * q^15 + 30 * q^16 + 9 * q^17 + 27 * q^18 - 31 * q^19 + 72 * q^20 - 32 * q^21 - 24 * q^22 - 6 * q^23 - 47 * q^24 - 42 * q^25 + 77 * q^26 - 2 * q^27 - 18 * q^28 + q^29 + 15 * q^30 + 15 * q^31 - 10 * q^32 - 24 * q^33 + 20 * q^34 + 74 * q^35 + 8 * q^36 - 22 * q^37 - 39 * q^38 + 86 * q^39 - 30 * q^40 + 39 * q^41 - 34 * q^42 + 33 * q^43 - 23 * q^44 + 121 * q^45 + 124 * q^46 + 6 * q^47 + 131 * q^48 - 22 * q^49 - 15 * q^50 + 29 * q^51 + 83 * q^52 - 30 * q^53 - 25 * q^54 + 32 * q^55 + 11 * q^56 - 10 * q^57 + 12 * q^58 - 80 * q^59 + 80 * q^60 - 12 * q^61 - 68 * q^62 - 79 * q^63 - 117 * q^64 - 89 * q^65 - 39 * q^66 - 74 * q^67 - 67 * q^68 - 95 * q^69 - 64 * q^70 - 115 * q^71 - 144 * q^72 - 14 * q^73 - 70 * q^74 - 13 * q^75 + 8 * q^76 + 47 * q^77 - 218 * q^78 - 25 * q^79 - 103 * q^80 - 28 * q^81 - 88 * q^82 - 20 * q^83 - 142 * q^84 + 22 * q^85 + 159 * q^86 - 105 * q^87 + 43 * q^88 + 33 * q^89 + 33 * q^90 + 60 * q^91 - 2 * q^92 + 63 * q^93 + 174 * q^94 + 20 * q^95 - 30 * q^96 + 121 * q^97 + 128 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/71\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{17}{35}\right)$

Coefficient data

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

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

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

$2$	−0.713225	+	0.196838i	−0.504326	+	0.139185i	−0.508936	−	0.860804i	$-0.669961\pi$
$2$	−0.713225	+	0.196838i	−0.504326	+	0.139185i	0.00461011	+	0.999989i	$0.498533\pi$
$3$	−0.487143	+	1.13973i	−0.281252	+	0.658022i	−0.999278	−	0.0379947i	$-0.987903\pi$
$3$	−0.487143	+	1.13973i	−0.281252	+	0.658022i	0.718026	+	0.696016i	$0.245046\pi$
$4$	−1.24695	+	0.745020i	−0.623476	+	0.372510i
$5$	−0.623421	+	1.91869i	−0.278803	+	0.858066i	0.709386	+	0.704821i	$0.248973\pi$
$5$	−0.623421	+	1.91869i	−0.278803	+	0.858066i	−0.988188	+	0.153245i	$0.951027\pi$
$6$	0.123101	−	0.908769i	0.0502559	−	0.371004i
$7$	0.0146541	+	0.326298i	0.00553872	+	0.123329i	0.999857	+	0.0168853i	$0.00537501\pi$
$7$	0.0146541	+	0.326298i	0.00553872	+	0.123329i	−0.994319	+	0.106444i	$0.966054\pi$
$8$	1.76533	−	1.84639i	0.624138	−	0.652797i
$9$	1.01152	+	1.05797i	0.337173	+	0.352655i
$10$	0.0669687	−	1.49117i	0.0211773	−	0.471550i
$11$	−1.35338	−	0.245602i	−0.408059	−	0.0740517i	−0.0293534	−	0.999569i	$-0.509345\pi$
$11$	−1.35338	−	0.245602i	−0.408059	−	0.0740517i	−0.378705	+	0.925517i	$0.623631\pi$
$12$	−0.241675	−	1.78412i	−0.0697656	−	0.515030i
$13$	3.64635	−	0.661714i	1.01131	−	0.183527i	0.352484	−	0.935818i	$-0.385337\pi$
$13$	3.64635	−	0.661714i	1.01131	−	0.183527i	0.658831	+	0.752291i	$0.271051\pi$
$14$	−0.0746794	−	0.229840i	−0.0199589	−	0.0614272i
$15$	−1.88309	−	1.64521i	−0.486212	−	0.424791i
$16$	0.481013	−	0.893871i	0.120253	−	0.223468i
$17$	−3.50350	+	2.54544i	−0.849723	+	0.617360i	−0.925070	−	0.379797i	$-0.875994\pi$
$17$	−3.50350	+	2.54544i	−0.849723	+	0.617360i	0.0753465	+	0.997157i	$0.475994\pi$
$18$	−0.929688	−	0.555463i	−0.219130	−	0.130924i
$19$	5.46579	−	4.77532i	1.25394	−	1.09553i	0.262503	−	0.964931i	$-0.415452\pi$
$19$	5.46579	−	4.77532i	1.25394	−	1.09553i	0.991435	−	0.130601i	$-0.0416908\pi$
$20$	−0.652088	−	2.85698i	−0.145811	−	0.638841i
$21$	−0.379029	−	0.142252i	−0.0827110	−	0.0310420i
$22$	1.01361	−	0.0912262i	0.216102	−	0.0194495i
$23$	0.550786	+	0.690664i	0.114847	+	0.144013i	0.835932	−	0.548833i	$-0.184928\pi$
$23$	0.550786	+	0.690664i	0.114847	+	0.144013i	−0.721085	+	0.692847i	$0.756356\pi$
$24$	1.24441	+	2.91145i	0.254015	+	0.594297i
$25$	0.752353	+	0.546616i	0.150471	+	0.109323i
$26$	−2.47042	+	1.18969i	−0.484488	+	0.233317i
$27$	−5.17985	+	1.94403i	−0.996863	+	0.374129i
$28$	−0.261371	−	0.395961i	−0.0493946	−	0.0748296i
$29$	0.505362	+	0.0454834i	0.0938433	+	0.00844605i	0.136461	−	0.990645i	$-0.456427\pi$
$29$	0.505362	+	0.0454834i	0.0938433	+	0.00844605i	−0.0426181	+	0.999091i	$0.513570\pi$
$30$	1.66691	+	0.802740i	0.304334	+	0.146560i
$31$	0.738057	+	1.37154i	0.132559	+	0.246336i	0.938219	−	0.346043i	$-0.112475\pi$
$31$	0.738057	+	1.37154i	0.132559	+	0.246336i	−0.805660	+	0.592378i	$0.798189\pi$
$32$	−1.30399	+	5.71314i	−0.230515	+	1.00995i
$33$	0.939207	−	1.42284i	0.163495	−	0.247684i
$34$	1.99774	−	2.50509i	0.342610	−	0.429620i
$35$	−0.635202	−	0.175305i	−0.107369	−	0.0296319i
$36$	−2.04952	−	0.565632i	−0.341587	−	0.0942720i
$37$	−3.02816	+	3.79719i	−0.497826	+	0.624255i	−0.965737	−	0.259521i	$-0.916435\pi$
$37$	−3.02816	+	3.79719i	−0.497826	+	0.624255i	0.467911	+	0.883776i	$0.345007\pi$
$38$	−2.95837	+	4.48175i	−0.479912	+	0.727035i
$39$	−1.02212	+	4.47819i	−0.163670	+	0.717084i
$40$	2.44211	+	4.53820i	0.386132	+	0.717553i
$41$	9.08603	+	4.37560i	1.41900	+	0.683354i	0.976917	−	0.213621i	$-0.0685257\pi$
$41$	9.08603	+	4.37560i	1.41900	+	0.683354i	0.442082	+	0.896975i	$0.354240\pi$
$42$	0.298334	+	0.0268505i	0.0460339	+	0.00414313i
$43$	−4.02244	−	6.09374i	−0.613417	−	0.929287i	−0.999975	−	0.00702182i	$-0.997765\pi$
$43$	−4.02244	−	6.09374i	−0.613417	−	0.929287i	0.386559	−	0.922265i	$-0.373664\pi$
$44$	1.87058	−	0.702039i	0.282000	−	0.105836i
$45$	−2.66051	+	1.28124i	−0.396606	+	0.190995i
$46$	−0.528783	−	0.384183i	−0.0779648	−	0.0566447i
$47$	−3.12104	−	7.30203i	−0.455250	−	1.06511i	−0.977236	−	0.212156i	$-0.931951\pi$
$47$	−3.12104	−	7.30203i	−0.455250	−	1.06511i	0.521986	−	0.852954i	$-0.325191\pi$
$48$	0.784447	+	0.983666i	0.113225	+	0.141980i
$49$	6.86556	−	0.617912i	0.980795	−	0.0882731i
$50$	−0.644191	−	0.241769i	−0.0911024	−	0.0341913i
$51$	−1.19440	−	5.23302i	−0.167250	−	0.732770i
$52$	−4.05383	+	3.54173i	−0.562165	+	0.491149i
$53$	−5.92634	−	3.54082i	−0.814046	−	0.486370i	0.0445598	−	0.999007i	$-0.485811\pi$
$53$	−5.92634	−	3.54082i	−0.814046	−	0.486370i	−0.858605	+	0.512637i	$0.828669\pi$
$54$	3.31174	−	2.40612i	0.450671	−	0.327431i
$55$	1.31496	−	2.44360i	0.177309	−	0.329495i
$56$	0.628343	+	0.548966i	0.0839658	+	0.0733587i
$57$	2.77994	+	8.55576i	0.368212	+	1.13324i
$58$	−0.369389	+	0.0670343i	−0.0485032	+	0.00880203i
$59$	−1.20842	−	8.92089i	−0.157322	−	1.16140i	−0.881636	−	0.471930i	$-0.843558\pi$
$59$	−1.20842	−	8.92089i	−0.157322	−	1.16140i	0.724314	−	0.689471i	$-0.242157\pi$
$60$	3.57384	+	0.648556i	0.461381	+	0.0837282i
$61$	0.513091	−	11.4249i	0.0656946	−	1.46280i	−0.647622	−	0.761962i	$-0.724236\pi$
$61$	0.513091	−	11.4249i	0.0656946	−	1.46280i	0.713316	−	0.700842i	$-0.247192\pi$
$62$	−0.796371	−	0.832939i	−0.101139	−	0.105783i
$63$	−0.330389	+	0.345560i	−0.0416252	+	0.0435365i
$64$	−0.103442	−	2.30332i	−0.0129303	−	0.287915i
$65$	−1.00358	+	7.40875i	−0.124479	+	0.918942i
$66$	−0.389798	+	1.19967i	−0.0479808	+	0.147670i
$67$	−5.32861	+	3.18370i	−0.650993	+	0.388950i	−0.800096	−	0.599871i	$-0.795218\pi$
$67$	−5.32861	+	3.18370i	−0.650993	+	0.388950i	0.149103	+	0.988822i	$0.452361\pi$
$68$	2.47229	−	5.78422i	0.299810	−	0.701440i
$69$	−1.05548	+	0.291294i	−0.127065	+	0.0350677i
$70$	0.487548			0.0582732
$71$	5.80097	−	6.11136i	0.688449	−	0.725285i
$71$	5.80097	−	6.11136i	0.688449	−	0.725285i
$72$	3.73908			0.440655
$73$	11.7349	−	3.23862i	1.37346	−	0.379052i	0.500036	−	0.866005i	$-0.333320\pi$
$73$	11.7349	−	3.23862i	1.37346	−	0.379052i	0.873429	+	0.486952i	$0.161891\pi$
$74$	1.41233	−	3.30431i	0.164180	−	0.384118i
$75$	−0.989496	+	0.591197i	−0.114257	+	0.0682655i
$76$	−3.25788	+	10.0267i	−0.373704	+	1.15014i
$77$	0.0603069	−	0.445204i	0.00687261	−	0.0507357i
$78$	−0.152476	−	3.39515i	−0.0172645	−	0.384425i
$79$	−6.41959	+	6.71436i	−0.722260	+	0.755425i	−0.977381	−	0.211484i	$-0.932170\pi$
$79$	−6.41959	+	6.71436i	−0.722260	+	0.755425i	0.255121	+	0.966909i	$0.417885\pi$
$80$	1.41519	+	1.48017i	0.158223	+	0.165489i
$81$	0.110654	−	2.46391i	0.0122949	−	0.273768i
$82$	−7.34166	−	1.33232i	−0.810751	−	0.147130i
$83$	0.581031	+	4.28934i	0.0637765	+	0.470817i	0.994470	+	0.105018i	$0.0334899\pi$
$83$	0.581031	+	4.28934i	0.0637765	+	0.470817i	−0.930694	+	0.365799i	$0.880796\pi$
$84$	0.578612	−	0.105003i	0.0631318	−	0.0114567i
$85$	−2.69977	−	8.30902i	−0.292831	−	0.901240i
$86$	4.06838	+	3.55444i	0.438705	+	0.383285i
$87$	−0.298022	+	0.553817i	−0.0319513	+	0.0593755i
$88$	−2.84263	+	2.06529i	−0.303026	+	0.220161i
$89$	−8.69518	−	5.19513i	−0.921688	−	0.550683i	−0.0281167	−	0.999605i	$-0.508951\pi$
$89$	−8.69518	−	5.19513i	−0.921688	−	0.550683i	−0.893571	+	0.448922i	$0.851808\pi$
$90$	1.64535	−	1.43750i	0.173435	−	0.151526i
$91$	0.269350	+	1.18010i	0.0282356	+	0.123708i
$92$	−1.20136	−	0.450879i	−0.125251	−	0.0470074i
$93$	−1.92272	+	0.173048i	−0.199377	+	0.0179442i
$94$	3.66331	+	4.59365i	0.377842	+	0.473799i
$95$	5.75488	+	13.4642i	0.590438	+	1.38140i
$96$	−5.87620	−	4.26931i	−0.599737	−	0.435734i
$97$	−2.76730	+	1.33266i	−0.280976	+	0.135311i	−0.569065	−	0.822293i	$-0.692695\pi$
$97$	−2.76730	+	1.33266i	−0.280976	+	0.135311i	0.288088	+	0.957604i	$0.406980\pi$
$98$	−4.77506	+	1.79211i	−0.482354	+	0.181031i
$99$	−1.10913	−	1.68026i	−0.111472	−	0.168872i
$100$	−1.34539	−	0.121087i	−0.134539	−	0.0121087i
$101$	2.09118	+	1.00706i	0.208080	+	0.100206i	0.535021	−	0.844838i	$-0.320304\pi$
$101$	2.09118	+	1.00706i	0.208080	+	0.100206i	−0.326941	+	0.945045i	$0.606018\pi$
$102$	1.88193	+	3.49722i	0.186339	+	0.346276i
$103$	−3.02144	+	13.2378i	−0.297711	+	1.30436i	0.575815	+	0.817580i	$0.304685\pi$
$103$	−3.02144	+	13.2378i	−0.297711	+	1.30436i	−0.873526	+	0.486778i	$0.838172\pi$
$104$	5.21522	−	7.90072i	0.511394	−	0.774729i
$105$	0.509233	−	0.638558i	0.0496961	−	0.0623169i
$106$	4.92378	+	1.35888i	0.478240	+	0.131986i
$107$	6.19017	+	1.70838i	0.598426	+	0.165155i	0.552109	−	0.833772i	$-0.313823\pi$
$107$	6.19017	+	1.70838i	0.598426	+	0.165155i	0.0463168	+	0.998927i	$0.485252\pi$
$108$	5.01069	−	6.28320i	0.482154	−	0.604602i
$109$	−4.89491	+	7.41547i	−0.468848	+	0.710274i	−0.989666	−	0.143394i	$-0.954198\pi$
$109$	−4.89491	+	7.41547i	−0.468848	+	0.710274i	0.520818	+	0.853668i	$0.325627\pi$
$110$	−0.456869	+	2.00167i	−0.0435607	+	0.190852i
$111$	−2.85262	−	5.30105i	−0.270758	−	0.503153i
$112$	0.298717	+	0.143855i	0.0282261	+	0.0135930i
$113$	18.5115	+	1.66607i	1.74142	+	0.156731i	0.914231	−	0.405193i	$-0.132796\pi$
$113$	18.5115	+	1.66607i	1.74142	+	0.156731i	0.827189	+	0.561924i	$0.189939\pi$
$114$	−3.66682	−	5.55499i	−0.343429	−	0.520272i
$115$	−1.66854	+	0.626215i	−0.155593	+	0.0583949i
$116$	−0.664048	+	0.319789i	−0.0616553	+	0.0296916i
$117$	4.38842	+	3.18837i	0.405710	+	0.294765i
$118$	2.61784	+	6.12474i	0.240992	+	0.563828i
$119$	−0.881913	−	1.10588i	−0.0808448	−	0.101376i
$120$	−6.36197	+	0.572587i	−0.580766	+	0.0522698i
$121$	−8.52727	−	3.20034i	−0.775207	−	0.290940i
$122$	1.88289	+	8.24950i	0.170469	+	0.746874i
$123$	−9.41318	+	8.22405i	−0.848758	+	0.741537i
$124$	−1.94215	−	1.16038i	−0.174410	−	0.104205i
$125$	−9.67852	+	7.03185i	−0.865673	+	0.628948i
$126$	0.167623	−	0.311495i	0.0149330	−	0.0277502i
$127$	−10.1316	−	8.85175i	−0.899038	−	0.785466i	0.0783486	−	0.996926i	$-0.475035\pi$
$127$	−10.1316	−	8.85175i	−0.899038	−	0.785466i	−0.977387	+	0.211460i	$0.932178\pi$
$128$	−3.09456	−	9.52409i	−0.273523	−	0.841818i
$129$	8.90470	−	1.61597i	0.784015	−	0.142278i
$130$	−0.742540	−	5.48165i	−0.0651250	−	0.480772i
$131$	12.9449	+	2.34915i	1.13100	+	0.205246i	0.711619	−	0.702565i	$-0.247962\pi$
$131$	12.9449	+	2.34915i	1.13100	+	0.205246i	0.419379	+	0.907811i	$0.362248\pi$
$132$	−0.111105	+	2.47394i	−0.00967042	+	0.215329i
$133$	1.63827	+	1.71350i	0.142056	+	0.148579i
$134$	3.17383	−	3.31956i	0.274177	−	0.286766i
$135$	−0.500769	−	11.1505i	−0.0430994	−	0.959682i
$136$	−1.48495	+	10.9624i	−0.127334	+	0.940015i
$137$	1.63870	−	5.04341i	0.140004	−	0.430888i	−0.856331	−	0.516428i	$-0.827261\pi$
$137$	1.63870	−	5.04341i	0.140004	−	0.430888i	0.996335	+	0.0855398i	$0.0272615\pi$
$138$	0.695457	−	0.415516i	0.0592012	−	0.0353711i
$139$	6.78148	−	15.8661i	0.575197	−	1.34574i	−0.339120	−	0.940743i	$-0.610129\pi$
$139$	6.78148	−	15.8661i	0.575197	−	1.34574i	0.914318	−	0.404998i	$-0.132728\pi$
$140$	0.922672	−	0.254641i	0.0779800	−	0.0215211i
$141$	9.84271			0.828905
$142$	−2.93445	+	5.50062i	−0.246254	+	0.461602i
$143$	−5.09740			−0.426266
$144$	1.43224	−	0.395273i	0.119353	−	0.0329394i
$145$	−0.402322	+	0.941279i	−0.0334110	+	0.0781690i
$146$	−7.73213	+	4.61973i	−0.639916	+	0.382332i
$147$	−2.64026	+	8.12588i	−0.217765	+	0.670211i
$148$	0.946990	−	6.99096i	0.0778421	−	0.574653i
$149$	0.367171	+	8.17570i	0.0300798	+	0.669779i	0.956229	+	0.292621i	$0.0945274\pi$
$149$	0.367171	+	8.17570i	0.0300798	+	0.669779i	−0.926149	+	0.377158i	$0.876901\pi$
$150$	0.589364	−	0.616426i	0.0481214	−	0.0503310i
$151$	10.1153	+	10.5798i	0.823172	+	0.860970i	0.992202	−	0.124641i	$-0.0397779\pi$
$151$	10.1153	+	10.5798i	0.823172	+	0.860970i	−0.169030	+	0.985611i	$0.554064\pi$
$152$	0.831823	−	18.5220i	0.0674697	−	1.50233i
$153$	−6.23684	−	1.13182i	−0.504219	−	0.0915022i
$154$	0.0446204	+	0.329401i	0.00359561	+	0.0265439i
$155$	−3.09168	+	0.561058i	−0.248330	+	0.0450653i
$156$	−2.06181	−	6.34559i	−0.165077	−	0.508054i
$157$	−10.7908	−	9.42767i	−0.861202	−	0.752410i	0.109170	−	0.994023i	$-0.465181\pi$
$157$	−10.7908	−	9.42767i	−0.861202	−	0.752410i	−0.970373	+	0.241613i	$0.922323\pi$
$158$	3.25697	−	6.05247i	0.259111	−	0.481508i
$159$	6.92254	−	5.02952i	0.548994	−	0.398867i
$160$	−10.1488	−	6.06365i	−0.802336	−	0.479374i
$161$	−0.217291	+	0.189842i	−0.0171249	+	0.0149616i
$162$	0.406069	+	1.77910i	0.0319038	+	0.139780i
$163$	12.2960	+	4.61475i	0.963094	+	0.361455i	0.782880	−	0.622172i	$-0.213750\pi$
$163$	12.2960	+	4.61475i	0.963094	+	0.361455i	0.180214	+	0.983627i	$0.442321\pi$
$164$	−14.5898	+	1.31310i	−1.13927	+	0.102536i
$165$	2.14447	+	2.68908i	0.166947	+	0.209344i
$166$	−1.25871	−	2.94490i	−0.0976948	−	0.228568i
$167$	−3.88170	−	2.82022i	−0.300375	−	0.218235i	0.427381	−	0.904072i	$-0.359436\pi$
$167$	−3.88170	−	2.82022i	−0.300375	−	0.218235i	−0.727756	+	0.685837i	$0.759436\pi$
$168$	−0.931764	+	0.448714i	−0.0718872	+	0.0346190i
$169$	0.686926	−	0.257808i	0.0528404	−	0.0198314i
$170$	3.56107	+	5.39479i	0.273121	+	0.413761i
$171$	10.5809	+	0.952295i	0.809139	+	0.0728238i
$172$	9.55575	+	4.60181i	0.728619	+	0.350885i
$173$	−10.5576	−	19.6193i	−0.802680	−	1.49163i	−0.869537	−	0.493867i	$-0.835583\pi$
$173$	−10.5576	−	19.6193i	−0.802680	−	1.49163i	0.0668572	−	0.997763i	$-0.478703\pi$
$174$	0.103545	−	0.453658i	0.00784969	−	0.0343917i
$175$	−0.167335	+	0.253502i	−0.0126493	+	0.0191629i
$176$	−0.870528	+	1.09161i	−0.0656185	+	0.0822830i
$177$	10.7560	+	2.96848i	0.808474	+	0.223125i
$178$	7.22422	+	1.99376i	0.541478	+	0.149438i
$179$	1.47239	−	1.84632i	0.110052	−	0.138001i	−0.723755	−	0.690057i	$-0.757585\pi$
$179$	1.47239	−	1.84632i	0.110052	−	0.138001i	0.833807	+	0.552057i	$0.186157\pi$
$180$	2.36299	−	3.57978i	0.176127	−	0.266821i
$181$	0.682290	−	2.98931i	0.0507142	−	0.222194i	−0.943220	−	0.332168i	$-0.892220\pi$
$181$	0.682290	−	2.98931i	0.0507142	−	0.222194i	0.993934	+	0.109975i	$0.0350770\pi$
$182$	−0.424395	−	0.788658i	−0.0314583	−	0.0584592i
$183$	12.7713	+	6.15032i	0.944080	+	0.454645i
$184$	2.24755	+	0.202283i	0.165692	+	0.0149125i
$185$	−5.39783	−	8.17736i	−0.396856	−	0.601212i
$186$	1.33727	−	0.501885i	0.0980533	−	0.0368000i
$187$	5.36672	−	2.58448i	0.392453	−	0.188996i
$188$	9.33194	+	6.78005i	0.680602	+	0.494486i
$189$	−0.710239	−	1.66169i	−0.0516623	−	0.120870i
$190$	−6.75479	−	8.47023i	−0.490044	−	0.614495i
$191$	−13.6426	+	1.22786i	−0.987146	+	0.0888448i	−0.571431	−	0.820650i	$-0.693612\pi$
$191$	−13.6426	+	1.22786i	−0.987146	+	0.0888448i	−0.415715	+	0.909495i	$0.636469\pi$
$192$	2.67555	+	1.00415i	0.193091	+	0.0724683i
$193$	1.68183	+	7.36860i	0.121061	+	0.530403i	0.998695	+	0.0510717i	$0.0162637\pi$
$193$	1.68183	+	7.36860i	0.121061	+	0.530403i	−0.877634	+	0.479332i	$0.840879\pi$
$194$	1.71139	−	1.49519i	0.122870	−	0.107349i
$195$	−7.95506	−	4.75293i	−0.569674	−	0.340364i
$196$	−8.10068	+	5.88549i	−0.578620	+	0.420392i
$197$	−10.3585	+	19.2493i	−0.738011	+	1.37145i	0.183468	+	0.983026i	$0.441267\pi$
$197$	−10.3585	+	19.2493i	−0.738011	+	1.37145i	−0.921479	+	0.388428i	$0.873018\pi$
$198$	1.12180	+	0.980083i	0.0797225	+	0.0696515i
$199$	7.16293	+	22.0452i	0.507767	+	1.56275i	0.796069	+	0.605206i	$0.206909\pi$
$199$	7.16293	+	22.0452i	0.507767	+	1.56275i	−0.288302	+	0.957540i	$0.593091\pi$
$200$	2.33742	−	0.424179i	0.165280	−	0.0299940i
$201$	−1.03275	−	7.62407i	−0.0728446	−	0.537760i
$202$	−1.68971	−	0.306637i	−0.118888	−	0.0215749i
$203$	−0.00743554	+	0.165565i	−0.000521872	+	0.0116204i
$204$	5.38807	+	5.63548i	0.377240	+	0.394562i
$205$	−14.0599	+	14.7055i	−0.981983	+	1.02707i
$206$	−0.450729	−	10.0363i	−0.0314037	−	0.699259i
$207$	−0.173568	+	1.28133i	−0.0120638	+	0.0890587i
$208$	1.16245	−	3.57766i	0.0806015	−	0.248066i
$209$	−8.57010	+	5.12040i	−0.592806	+	0.354185i
$210$	−0.237506	+	0.555672i	−0.0163894	+	0.0383450i
$211$	−24.8592	+	6.86070i	−1.71138	+	0.472310i	−0.978189	−	0.207715i	$-0.933397\pi$
$211$	−24.8592	+	6.86070i	−1.71138	+	0.472310i	−0.733189	+	0.680025i	$0.761969\pi$
$212$	10.0279			0.688716
$213$	4.13938	+	9.58863i	0.283626	+	0.657002i
$214$	−4.75126			−0.324789
$215$	14.1997	−	3.91887i	0.968411	−	0.267265i
$216$	−5.55470	+	12.9959i	−0.377950	+	0.884257i
$217$	−0.436715	+	0.260925i	−0.0296462	+	0.0177128i
$218$	2.03153	−	6.25240i	0.137593	−	0.423466i
$219$	−2.02542	+	14.9522i	−0.136865	+	1.01038i
$220$	0.180841	+	4.02673i	0.0121923	+	0.271482i
$221$	−11.0906	+	11.5999i	−0.746036	+	0.780292i
$222$	3.07800	+	3.21934i	0.206582	+	0.216068i
$223$	0.319669	−	7.11797i	0.0214066	−	0.476655i	−0.959445	−	0.281897i	$-0.909036\pi$
$223$	0.319669	−	7.11797i	0.0214066	−	0.476655i	0.980851	−	0.194758i	$-0.0623922\pi$
$224$	−1.88330	−	0.341768i	−0.125833	−	0.0228353i
$225$	0.182718	+	1.34888i	0.0121812	+	0.0899251i
$226$	−13.5308	+	2.45549i	−0.900058	+	0.163336i
$227$	0.347157	+	1.06844i	0.0230417	+	0.0709149i	0.961916	−	0.273345i	$-0.0881300\pi$
$227$	0.347157	+	1.06844i	0.0230417	+	0.0709149i	−0.938874	+	0.344260i	$0.888130\pi$
$228$	−9.84066	−	8.59753i	−0.651714	−	0.569385i
$229$	7.11283	−	13.2179i	0.470029	−	0.873460i	−0.529652	−	0.848215i	$-0.677678\pi$
$229$	7.11283	−	13.2179i	0.470029	−	0.873460i	0.999681	−	0.0252455i	$-0.00803674\pi$
$230$	1.06678	−	0.775064i	0.0703417	−	0.0511062i
$231$	0.478032	+	0.285611i	0.0314522	+	0.0187918i
$232$	0.976109	−	0.852801i	0.0640847	−	0.0559891i
$233$	3.56716	+	15.6288i	0.233692	+	1.02387i	0.946548	+	0.322563i	$0.104544\pi$
$233$	3.56716	+	15.6288i	0.233692	+	1.02387i	−0.712856	+	0.701311i	$0.752599\pi$
$234$	−3.75752	−	1.41022i	−0.245637	−	0.0921891i
$235$	15.9561	−	1.43607i	1.04086	−	0.0936791i
$236$	8.15307	+	10.2236i	0.530720	+	0.665502i
$237$	−4.52528	−	10.5874i	−0.293949	−	0.687727i
$238$	0.846682	+	0.615150i	0.0548822	+	0.0398743i
$239$	6.71161	−	3.23214i	0.434138	−	0.209070i	−0.204034	−	0.978964i	$-0.565405\pi$
$239$	6.71161	−	3.23214i	0.434138	−	0.209070i	0.638172	+	0.769894i	$0.279691\pi$
$240$	−2.37640	+	0.891876i	−0.153396	+	0.0575703i
$241$	−12.6853	−	19.2174i	−0.817133	−	1.23790i	−0.968398	−	0.249410i	$-0.919763\pi$
$241$	−12.6853	−	19.2174i	−0.817133	−	1.23790i	0.151265	−	0.988493i	$-0.451665\pi$
$242$	6.71181	+	0.604074i	0.431452	+	0.0388313i
$243$	−12.1999	−	5.87518i	−0.782626	−	0.376893i
$244$	7.87195	+	14.6285i	0.503950	+	0.936496i
$245$	−3.09456	+	13.5581i	−0.197704	+	0.866198i
$246$	5.09491	−	7.71846i	0.324840	−	0.492111i
$247$	16.7703	−	21.0292i	1.06707	−	1.33806i
$248$	3.83531	+	1.05848i	0.243542	+	0.0672134i
$249$	−5.17173	−	1.42731i	−0.327745	−	0.0904518i
$250$	5.51883	−	6.92039i	0.349041	−	0.437684i
$251$	9.01757	−	13.6610i	0.569184	−	0.862277i	−0.429993	−	0.902832i	$-0.641484\pi$
$251$	9.01757	−	13.6610i	0.569184	−	0.862277i	0.999177	+	0.0405549i	$0.0129126\pi$
$252$	0.154531	−	0.677044i	0.00973453	−	0.0426498i
$253$	−0.575793	−	1.07000i	−0.0361998	−	0.0672705i
$254$	8.96850	+	4.31900i	0.562734	+	0.270998i
$255$	10.7852	+	0.970684i	0.675395	+	0.0607866i
$256$	6.62216	+	10.0321i	0.413885	+	0.627009i
$257$	22.2098	−	8.33548i	1.38541	−	0.519953i	0.456323	−	0.889814i	$-0.349166\pi$
$257$	22.2098	−	8.33548i	1.38541	−	0.519953i	0.929087	+	0.369861i	$0.120595\pi$
$258$	−6.03297	+	2.90533i	−0.375596	+	0.180878i
$259$	−1.28339	−	0.932439i	−0.0797461	−	0.0579389i
$260$	−4.26824	−	9.98605i	−0.264705	−	0.619309i
$261$	0.463063	+	0.580663i	0.0286629	+	0.0359421i
$262$	−9.69500	+	0.872566i	−0.598959	+	0.0539073i
$263$	−16.8038	−	6.30658i	−1.03617	−	0.388880i	−0.225411	−	0.974264i	$-0.572372\pi$
$263$	−16.8038	−	6.30658i	−1.03617	−	0.388880i	−0.810756	+	0.585384i	$0.800944\pi$
$264$	−0.969102	−	4.24592i	−0.0596441	−	0.261318i
$265$	10.4884	−	9.16341i	0.644295	−	0.562904i
$266$	−1.50574	−	0.899637i	−0.0923227	−	0.0551603i
$267$	10.1568	−	7.37937i	0.621588	−	0.451610i
$268$	4.27261	−	7.93984i	0.260991	−	0.485003i
$269$	−17.6163	−	15.3909i	−1.07408	−	0.938397i	−0.0758077	−	0.997122i	$-0.524154\pi$
$269$	−17.6163	−	15.3909i	−1.07408	−	0.938397i	−0.998274	+	0.0587254i	$0.981296\pi$
$270$	2.55200	+	7.85424i	0.155310	+	0.477994i
$271$	−9.78863	+	1.77638i	−0.594617	+	0.107907i	−0.467519	−	0.883983i	$-0.654852\pi$
$271$	−9.78863	+	1.77638i	−0.594617	+	0.107907i	−0.127098	+	0.991890i	$0.540566\pi$
$272$	0.590069	+	4.35607i	0.0357782	+	0.264125i
$273$	−1.47620	−	0.267891i	−0.0893439	−	0.0162135i
$274$	−0.176032	+	3.91965i	−0.0106345	+	0.236795i
$275$	−0.883967	−	0.924557i	−0.0533052	−	0.0557529i
$276$	1.09911	−	1.14958i	0.0661588	−	0.0691967i
$277$	−1.02965	−	22.9269i	−0.0618657	−	1.37755i	−0.754520	−	0.656277i	$-0.772130\pi$
$277$	−1.02965	−	22.9269i	−0.0618657	−	1.37755i	0.692654	−	0.721270i	$-0.256441\pi$
$278$	−1.71368	+	12.6509i	−0.102780	+	0.758751i
$279$	−0.704483	+	2.16818i	−0.0421763	+	0.129805i
$280$	−1.44502	+	0.863360i	−0.0863565	+	0.0515956i
$281$	4.68469	−	10.9604i	0.279465	−	0.653841i	−0.719717	−	0.694267i	$-0.755729\pi$
$281$	4.68469	−	10.9604i	0.279465	−	0.653841i	0.999183	+	0.0404261i	$0.0128715\pi$
$282$	−7.02006	+	1.93741i	−0.418039	+	0.115371i
$283$	−2.86975			−0.170589			−0.0852945	−	0.996356i	$-0.527183\pi$
$283$	−2.86975			−0.170589			−0.0852945	+	0.996356i	$0.527183\pi$
$284$	−2.68045	+	11.9424i	−0.159056	+	0.708652i
$285$	−18.1490			−1.07505
$286$	3.63559	−	1.00336i	0.214977	−	0.0593299i
$287$	−1.29460	+	3.02887i	−0.0764180	+	0.178789i
$288$	−7.36332	+	4.39938i	−0.433888	+	0.259236i
$289$	0.541944	−	1.66793i	0.0318791	−	0.0981137i
$290$	0.101667	−	0.750536i	0.00597009	−	0.0440730i
$291$	−0.170800	−	3.80316i	−0.0100125	−	0.222945i
$292$	−12.2200	+	12.7811i	−0.715122	+	0.747959i
$293$	−12.3319	−	12.8982i	−0.720440	−	0.753521i	0.256614	−	0.966514i	$-0.417393\pi$
$293$	−12.3319	−	12.8982i	−0.720440	−	0.753521i	−0.977054	+	0.212993i	$0.931679\pi$
$294$	0.283620	−	6.31528i	0.0165410	−	0.368315i
$295$	17.8698	+	3.24289i	1.04042	+	0.188808i
$296$	1.66540	+	12.2945i	0.0967992	+	0.714600i
$297$	7.48775	−	1.35883i	0.434483	−	0.0788471i
$298$	−1.87116	−	5.75884i	−0.108393	−	0.333601i
$299$	2.46538	+	2.15394i	0.142577	+	0.124565i
$300$	0.793402	−	1.47439i	0.0458071	−	0.0851239i
$301$	1.92943	−	1.40181i	0.111211	−	0.0807992i
$302$	−9.29698	−	5.55469i	−0.534981	−	0.319636i
$303$	−2.16648	+	1.89280i	−0.124461	+	0.108738i
$304$	−1.63940	−	7.18270i	−0.0940263	−	0.411956i
$305$	21.6010	+	8.10697i	1.23687	+	0.464204i
$306$	4.67106	−	0.420403i	0.267027	−	0.0240328i
$307$	7.66565	+	9.61243i	0.437502	+	0.548610i	0.950883	−	0.309551i	$-0.100179\pi$
$307$	7.66565	+	9.61243i	0.437502	+	0.548610i	−0.513381	+	0.858161i	$0.671607\pi$
$308$	0.256486	+	0.600078i	0.0146146	+	0.0341926i
$309$	−13.6156	−	9.89230i	−0.774564	−	0.562753i
$310$	2.09463	−	1.00872i	0.118967	−	0.0572915i
$311$	3.65740	−	1.37265i	0.207392	−	0.0778357i	−0.245517	−	0.969392i	$-0.578958\pi$
$311$	3.65740	−	1.37265i	0.207392	−	0.0778357i	0.452909	+	0.891557i	$0.350386\pi$
$312$	6.46410	+	9.79270i	0.365958	+	0.554402i
$313$	−1.02505	−	0.0922557i	−0.0579390	−	0.00521460i	0.0606319	−	0.998160i	$-0.480688\pi$
$313$	−1.02505	−	0.0922557i	−0.0579390	−	0.00521460i	−0.118571	+	0.992946i	$0.537831\pi$
$314$	9.55201	+	4.60001i	0.539051	+	0.259593i
$315$	−0.457052	−	0.849346i	−0.0257520	−	0.0478552i
$316$	3.00259	−	13.1552i	0.168909	−	0.740038i
$317$	6.78490	−	10.2787i	0.381078	−	0.577308i	−0.592526	−	0.805551i	$-0.701869\pi$
$317$	6.78490	−	10.2787i	0.381078	−	0.577308i	0.973604	+	0.228243i	$0.0732979\pi$
$318$	−3.94733	+	4.94980i	−0.221355	+	0.277571i
$319$	−0.672774	−	0.185674i	−0.0376681	−	0.0103957i
$320$	4.48386	+	1.23747i	0.250655	+	0.0691765i
$321$	−4.96258	+	6.22288i	−0.276984	+	0.347327i
$322$	0.117609	−	0.178171i	0.00655412	−	0.00992907i
$323$	−6.99410	+	30.6431i	−0.389162	+	1.70503i
$324$	1.69768	+	3.15482i	0.0943156	+	0.175268i
$325$	3.10504	+	1.49531i	0.172237	+	0.0829449i
$326$	−9.67814	−	0.871049i	−0.536023	−	0.0482429i
$327$	−6.06709	−	9.19126i	−0.335511	−	0.508278i
$328$	24.1189	−	9.05197i	1.33174	−	0.499811i
$329$	2.33690	−	1.12539i	0.128838	−	0.0620449i
$330$	−2.05880	−	1.49581i	−0.113333	−	0.0823414i
$331$	10.0397	+	23.4891i	0.551832	+	1.29108i	0.930754	+	0.365647i	$0.119152\pi$
$331$	10.0397	+	23.4891i	0.551832	+	1.29108i	−0.378921	+	0.925429i	$0.623705\pi$
$332$	−3.92016	−	4.91573i	−0.215147	−	0.269786i
$333$	−7.08034	+	0.637242i	−0.388000	+	0.0349207i
$334$	3.32365	+	1.24739i	0.181862	+	0.0682540i
$335$	−2.78657	−	12.2088i	−0.152246	−	0.667035i
$336$	−0.309473	+	0.270378i	−0.0168831	+	0.0147504i
$337$	−0.572685	−	0.342163i	−0.0311961	−	0.0186388i	0.497217	−	0.867626i	$-0.334355\pi$
$337$	−0.572685	−	0.342163i	−0.0311961	−	0.0186388i	−0.528413	+	0.848988i	$0.677213\pi$
$338$	−0.439186	+	0.319088i	−0.0238886	+	0.0173561i
$339$	−10.9166	+	20.2865i	−0.592910	+	1.10181i
$340$	9.55687	+	8.34958i	0.518294	+	0.452820i
$341$	−0.662017	−	2.03748i	−0.0358502	−	0.110336i
$342$	−7.73399	+	1.40351i	−0.418206	+	0.0758932i
$343$	0.609142	+	4.49686i	0.0328906	+	0.242808i
$344$	−18.3523	−	3.33046i	−0.989492	−	0.179566i
$345$	0.0991048	−	2.20674i	0.00533562	−	0.118807i
$346$	11.3918	+	11.9149i	0.612425	+	0.640547i
$347$	−5.50138	+	5.75400i	−0.295330	+	0.308891i	−0.853766	−	0.520657i	$-0.825687\pi$
$347$	−5.50138	+	5.75400i	−0.295330	+	0.308891i	0.558436	+	0.829547i	$0.311401\pi$
$348$	−0.0409856	−	0.912616i	−0.00219706	−	0.0489214i
$349$	−0.715291	+	5.28049i	−0.0382887	+	0.282658i	0.961675	+	0.274190i	$0.0884098\pi$
$349$	−0.715291	+	5.28049i	−0.0382887	+	0.282658i	−0.999964	+	0.00846809i	$0.997304\pi$
$350$	0.0694488	−	0.213741i	0.00371219	−	0.0114250i
$351$	−17.6011	+	10.5162i	−0.939479	+	0.561313i
$352$	3.16795	−	7.41178i	0.168852	−	0.395049i
$353$	−10.1224	+	2.79359i	−0.538759	+	0.148688i	−0.524817	−	0.851215i	$-0.675866\pi$
$353$	−10.1224	+	2.79359i	−0.538759	+	0.148688i	−0.0139414	+	0.999903i	$0.504438\pi$
$354$	−8.25579			−0.438790
$355$	8.10938	+	14.9402i	0.430401	+	0.792946i
$356$	14.7130			0.779785
$357$	1.69002	−	0.466417i	0.0894455	−	0.0246854i
$358$	−0.686721	+	1.60666i	−0.0362944	+	0.0849149i
$359$	−19.4807	+	11.6392i	−1.02815	+	0.614291i	−0.924839	−	0.380358i	$-0.875801\pi$
$359$	−19.4807	+	11.6392i	−1.02815	+	0.614291i	−0.103311	+	0.994649i	$0.532944\pi$
$360$	−2.33102	+	7.17415i	−0.122856	+	0.378111i
$361$	4.52077	−	33.3737i	0.237935	−	1.75651i
$362$	0.101782	+	2.26635i	0.00534954	+	0.119117i
$363$	7.80151	−	8.15974i	0.409473	−	0.428275i
$364$	−1.21506	−	1.27086i	−0.0636867	−	0.0666110i
$365$	−1.10185	+	24.5347i	−0.0576737	+	1.28420i
$366$	−10.3194	−	1.87270i	−0.539404	−	0.0978874i
$367$	−0.677207	−	4.99934i	−0.0353499	−	0.260964i	0.964647	−	0.263546i	$-0.0848922\pi$
$367$	−0.677207	−	4.99934i	−0.0353499	−	0.260964i	−0.999997	+	0.00258276i	$0.999178\pi$
$368$	0.882300	−	0.160114i	0.0459930	−	0.00834651i
$369$	4.56145	+	14.0387i	0.237460	+	0.730826i
$370$	5.45948	+	4.76980i	0.283825	+	0.247970i
$371$	1.06852	−	1.98564i	0.0554748	−	0.103089i
$372$	2.26862	−	1.64825i	0.117622	−	0.0854576i
$373$	−2.58982	−	1.54735i	−0.134096	−	0.0801186i	0.444284	−	0.895886i	$-0.353458\pi$
$373$	−2.58982	−	1.54735i	−0.134096	−	0.0801186i	−0.578381	+	0.815767i	$0.696315\pi$
$374$	−3.31896	+	2.89968i	−0.171619	+	0.149939i
$375$	−3.29957	−	14.4564i	−0.170389	−	0.746524i
$376$	−18.9920	−	7.12783i	−0.979439	−	0.367590i
$377$	1.87282	−	0.168557i	0.0964552	−	0.00868112i
$378$	0.833643	+	1.04536i	0.0428780	+	0.0537673i
$379$	9.09798	+	21.2858i	0.467332	+	1.09338i	0.973032	+	0.230668i	$0.0740912\pi$
$379$	9.09798	+	21.2858i	0.467332	+	1.09338i	−0.505700	+	0.862709i	$0.668766\pi$
$380$	−17.2072	−	12.5017i	−0.882709	−	0.641325i
$381$	15.0241	−	7.23524i	0.769710	−	0.370673i
$382$	9.48858	−	3.56112i	0.485478	−	0.182203i
$383$	4.60205	+	6.97181i	0.235154	+	0.356243i	0.932921	−	0.360082i	$-0.117251\pi$
$383$	4.60205	+	6.97181i	0.235154	+	0.356243i	−0.697767	+	0.716325i	$0.745823\pi$
$384$	12.3624	+	1.11263i	0.630864	+	0.0567787i
$385$	0.816613	+	0.393260i	0.0416184	+	0.0200424i
$386$	−2.64994	−	4.92442i	−0.134879	−	0.250646i
$387$	2.37819	−	10.4195i	0.120890	−	0.529655i
$388$	2.45783	−	3.72345i	0.124777	−	0.189030i
$389$	−1.72822	+	2.16712i	−0.0876241	+	0.109877i	−0.823711	−	0.567010i	$-0.808100\pi$
$389$	−1.72822	+	2.16712i	−0.0876241	+	0.109877i	0.736087	+	0.676887i	$0.236672\pi$
$390$	6.60930	+	1.82405i	0.334675	+	0.0923645i
$391$	−3.68772	−	1.01775i	−0.186496	−	0.0514697i
$392$	10.9791	−	13.7673i	0.554527	−	0.695355i
$393$	−8.98338	+	13.6092i	−0.453152	+	0.686495i
$394$	3.59894	−	15.7680i	0.181312	−	0.794380i
$395$	−8.88070	−	16.5031i	−0.446836	−	0.830361i
$396$	2.63486	+	1.26888i	0.132406	+	0.0637636i
$397$	8.09957	+	0.728975i	0.406506	+	0.0365862i	0.291006	−	0.956721i	$-0.406010\pi$
$397$	8.09957	+	0.728975i	0.406506	+	0.0365862i	0.115500	+	0.993307i	$0.463153\pi$
$398$	−9.44811	−	14.3133i	−0.473591	−	0.717460i
$399$	−2.75099	+	1.03246i	−0.137722	+	0.0516879i
$400$	0.850496	−	0.409577i	0.0425248	−	0.0204789i
$401$	14.8424	+	10.7836i	0.741193	+	0.538508i	0.893085	−	0.449889i	$-0.148536\pi$
$401$	14.8424	+	10.7836i	0.741193	+	0.538508i	−0.151891	+	0.988397i	$0.548536\pi$
$402$	2.23729	+	5.23439i	0.111586	+	0.261068i
$403$	3.59878	+	4.51272i	0.179268	+	0.224795i
$404$	−3.35789	+	0.302215i	−0.167061	+	0.0150358i
$405$	4.65850	+	1.74837i	0.231483	+	0.0868770i
$406$	−0.0272862	−	0.119549i	−0.00135419	−	0.00593311i
$407$	5.03084	−	4.39531i	0.249369	−	0.217868i
$408$	−11.7707	−	7.03267i	−0.582737	−	0.348169i
$409$	−14.4787	+	10.5194i	−0.715923	+	0.520149i	−0.885079	−	0.465441i	$-0.845896\pi$
$409$	−14.4787	+	10.5194i	−0.715923	+	0.520149i	0.169156	+	0.985589i	$0.445896\pi$
$410$	7.13325	−	13.2558i	0.352286	−	0.654658i
$411$	4.94983	+	4.32454i	0.244157	+	0.213314i
$412$	−6.09482	−	18.7579i	−0.300270	−	0.924137i
$413$	2.89316	−	0.525031i	0.142363	−	0.0258351i
$414$	−0.128421	−	0.948043i	−0.00631155	−	0.0465938i
$415$	−8.59217	−	1.55925i	−0.421773	−	0.0765405i
$416$	−0.974322	+	21.6950i	−0.0477701	+	1.06368i
$417$	14.7794	+	15.4581i	0.723751	+	0.756985i
$418$	5.10452	−	5.33891i	0.249670	−	0.261135i
$419$	0.354340	+	7.88998i	0.0173106	+	0.385451i	0.988882	+	0.148703i	$0.0475100\pi$
$419$	0.354340	+	7.88998i	0.0173106	+	0.385451i	−0.971571	+	0.236748i	$0.923919\pi$
$420$	−0.159251	+	1.17564i	−0.00777067	+	0.0573654i
$421$	1.53676	−	4.72967i	0.0748972	−	0.230510i	−0.906598	−	0.421994i	$-0.861330\pi$
$421$	1.53676	−	4.72967i	0.0748972	−	0.230510i	0.981496	+	0.191485i	$0.0613302\pi$
$422$	16.3798	−	9.78645i	0.797354	−	0.476397i
$423$	4.56831	−	10.6881i	0.222119	−	0.519673i
$424$	−16.9997	+	4.69161i	−0.825577	+	0.227845i
$425$	−4.02725			−0.195350
$426$	−4.83971	−	6.02406i	−0.234485	−	0.291867i
$427$	3.73543			0.180770
$428$	−8.99162	+	2.48153i	−0.434627	+	0.119949i
$429$	2.48316	−	5.80964i	0.119888	−	0.280492i
$430$	−9.35620	+	5.59007i	−0.451196	+	0.269577i
$431$	−0.174392	+	0.536724i	−0.00840018	+	0.0258531i	−0.955169	−	0.296062i	$-0.904327\pi$
$431$	−0.174392	+	0.536724i	−0.00840018	+	0.0258531i	0.946769	+	0.321915i	$0.104327\pi$
$432$	−0.753861	+	5.56522i	−0.0362701	+	0.267757i
$433$	−0.289036	−	6.43589i	−0.0138902	−	0.309289i	−0.993896	−	0.110321i	$-0.964812\pi$
$433$	−0.289036	−	6.43589i	−0.0138902	−	0.309289i	0.980006	−	0.198969i	$-0.0637592\pi$
$434$	0.260116	−	0.272060i	0.0124860	−	0.0130593i
$435$	−0.876813	−	0.917074i	−0.0420400	−	0.0439703i
$436$	0.579050	−	12.8936i	0.0277315	−	0.617489i
$437$	6.30862	+	1.14485i	0.301782	+	0.0547654i
$438$	−1.49858	−	11.0630i	−0.0716051	−	0.528610i
$439$	2.31490	−	0.420093i	0.110484	−	0.0200499i	−0.123033	−	0.992403i	$-0.539262\pi$
$439$	2.31490	−	0.420093i	0.110484	−	0.0200499i	0.233517	+	0.972353i	$0.424976\pi$
$440$	−2.19051	−	6.74169i	−0.104428	−	0.321397i
$441$	7.59838	+	6.63850i	0.361827	+	0.316119i
$442$	5.62681	−	10.4564i	0.267640	−	0.497359i
$443$	11.1482	−	8.09963i	0.529666	−	0.384825i	−0.290567	−	0.956855i	$-0.593844\pi$
$443$	11.1482	−	8.09963i	0.529666	−	0.384825i	0.820233	+	0.572030i	$0.193844\pi$
$444$	7.50646	+	4.48490i	0.356241	+	0.212844i
$445$	15.3886	−	13.4446i	0.729491	−	0.637337i
$446$	1.17309	+	5.13964i	0.0555474	+	0.243369i
$447$	−9.49693	−	3.56426i	−0.449189	−	0.168584i
$448$	0.750054	−	0.0675061i	0.0354367	−	0.00318936i
$449$	−22.0469	−	27.6459i	−1.04046	−	1.30469i	−0.951164	−	0.308687i	$-0.900110\pi$
$449$	−22.0469	−	27.6459i	−1.04046	−	1.30469i	−0.0892940	−	0.996005i	$-0.528461\pi$
$450$	−0.395828	−	0.926086i	−0.0186595	−	0.0436561i
$451$	−11.2222	−	8.15338i	−0.528431	−	0.383928i
$452$	−24.3243	+	11.7140i	−1.14412	+	0.550978i
$453$	−16.9856	+	6.37482i	−0.798055	+	0.299515i
$454$	−0.457911	−	0.693705i	−0.0214908	−	0.0325572i
$455$	−2.43217	−	0.218899i	−0.114022	−	0.0102621i
$456$	20.7048	+	9.97089i	0.969590	+	0.466930i
$457$	15.1533	+	28.1596i	0.708842	+	1.31725i	0.938940	+	0.344082i	$0.111810\pi$
$457$	15.1533	+	28.1596i	0.708842	+	1.31725i	−0.230098	+	0.973168i	$0.573905\pi$
$458$	−2.47128	+	10.8274i	−0.115475	+	0.505930i
$459$	13.1992	−	19.9959i	0.616085	−	0.933329i
$460$	1.61405	−	2.02396i	0.0752556	−	0.0943676i
$461$	16.4441	+	4.53829i	0.765879	+	0.211369i	0.627084	−	0.778952i	$-0.284248\pi$
$461$	16.4441	+	4.53829i	0.765879	+	0.211369i	0.138795	+	0.990321i	$0.455677\pi$
$462$	−0.397164	−	0.109610i	−0.0184777	−	0.00509953i
$463$	−23.7995	+	29.8436i	−1.10606	+	1.38695i	−0.191984	+	0.981398i	$0.561492\pi$
$463$	−23.7995	+	29.8436i	−1.10606	+	1.38695i	−0.914072	+	0.405552i	$0.867079\pi$
$464$	0.283742	−	0.429850i	0.0131724	−	0.0199553i
$465$	0.866638	−	3.79699i	0.0401894	−	0.176081i
$466$	−5.62051	−	10.4447i	−0.260365	−	0.483840i
$467$	−6.70037	−	3.22673i	−0.310056	−	0.149315i	0.272384	−	0.962189i	$-0.412188\pi$
$467$	−6.70037	−	3.22673i	−0.310056	−	0.149315i	−0.582441	+	0.812873i	$0.697902\pi$
$468$	−7.84755	−	0.706293i	−0.362753	−	0.0326484i
$469$	−1.11692	−	1.69206i	−0.0515746	−	0.0781321i
$470$	−11.0976	+	4.16500i	−0.511894	+	0.192117i
$471$	16.0016	−	7.70598i	0.737317	−	0.355073i
$472$	−18.6047	−	13.5171i	−0.856350	−	0.622174i
$473$	3.94725	+	9.23505i	0.181495	+	0.424628i
$474$	5.31155	+	6.66047i	0.243967	+	0.305926i
$475$	6.72247	−	0.605033i	0.308448	−	0.0277608i
$476$	1.92361	+	0.721943i	0.0881685	+	0.0330902i
$477$	−2.24853	−	9.85148i	−0.102953	−	0.451068i
$478$	−4.15068	+	3.62634i	−0.189848	+	0.165865i
$479$	26.2077	+	15.6584i	1.19746	+	0.715450i	0.966288	−	0.257463i	$-0.0828866\pi$
$479$	26.2077	+	15.6584i	1.19746	+	0.715450i	0.231173	+	0.972913i	$0.425744\pi$
$480$	11.8548	−	8.61304i	0.541097	−	0.393130i
$481$	−8.52906	+	15.8497i	−0.388892	+	0.722682i
$482$	12.8302	+	11.2094i	0.584399	+	0.510574i
$483$	−0.110516	−	0.340132i	−0.00502864	−	0.0154766i
$484$	13.0174	−	2.36231i	0.591701	−	0.107378i
$485$	−0.831774	−	6.14040i	−0.0377689	−	0.278821i
$486$	9.85775	+	1.78892i	0.447157	+	0.0811469i
$487$	0.857304	−	19.0894i	0.0388481	−	0.865021i	−0.881088	−	0.472953i	$-0.843188\pi$
$487$	0.857304	−	19.0894i	0.0388481	−	0.865021i	0.919936	−	0.392068i	$-0.128240\pi$
$488$	−20.1890	−	21.1160i	−0.913912	−	0.955877i
$489$	−11.2494	+	11.7660i	−0.508717	+	0.532077i
$490$	−0.461636	−	10.2791i	−0.0208546	−	0.464364i
$491$	5.65337	−	41.7349i	0.255133	−	1.88347i	−0.180847	−	0.983511i	$-0.557884\pi$
$491$	5.65337	−	41.7349i	0.255133	−	1.88347i	0.435980	−	0.899956i	$-0.356402\pi$
$492$	5.61071	−	17.2680i	0.252950	−	0.778501i
$493$	−1.88631	+	1.12702i	−0.0849551	+	0.0507583i
$494$	−7.82162	+	18.2996i	−0.351912	+	0.823338i
$495$	3.91535	−	1.08057i	0.175982	−	0.0485680i
$496$	1.58099			0.0709887
$497$	2.07913	+	1.80329i	0.0932619	+	0.0808886i
$498$	3.96955			0.177880
$499$	−27.9269	+	7.70733i	−1.25018	+	0.345027i	−0.827610	−	0.561303i	$-0.810300\pi$
$499$	−27.9269	+	7.70733i	−1.25018	+	0.345027i	−0.422569	+	0.906331i	$0.638872\pi$
$500$	6.82978	−	15.9791i	0.305437	−	0.714606i
$501$	5.10522	−	3.05023i	0.228084	−	0.136274i
$502$	−3.74255	+	11.5184i	−0.167038	+	0.514091i
$503$	−0.524419	+	3.87142i	−0.0233827	+	0.172618i	−0.998875	−	0.0474142i	$-0.984902\pi$
$503$	−0.524419	+	3.87142i	−0.0233827	+	0.172618i	0.975493	+	0.220032i	$0.0706162\pi$
$504$	0.0547927	+	1.22005i	0.00244066	+	0.0543456i
$505$	−3.23593	+	3.38452i	−0.143997	+	0.150609i
$506$	0.621287	+	0.649815i	0.0276196	+	0.0288878i
$507$	−0.0408006	+	0.908497i	−0.00181202	+	0.0403478i
$508$	19.2284	+	3.48944i	0.853123	+	0.154819i
$509$	4.12322	+	30.4388i	0.182758	+	1.34918i	0.817266	+	0.576261i	$0.195489\pi$
$509$	4.12322	+	30.4388i	0.182758	+	1.34918i	−0.634507	+	0.772917i	$0.718797\pi$
$510$	−7.88333	+	1.43061i	−0.349080	+	0.0633486i
$511$	1.22872	+	3.78161i	0.0543554	+	0.167289i
$512$	8.38505	+	7.32580i	0.370570	+	0.323757i
$513$	−19.0286	+	35.3611i	−0.840133	+	1.56123i
$514$	−14.1999	+	10.3168i	−0.626329	+	0.455055i
$515$	−23.5156	−	14.0499i	−1.03622	−	0.619114i
$516$	−9.89982	+	8.64921i	−0.435815	+	0.380760i
$517$	2.43055	+	10.6489i	0.106895	+	0.468339i
$518$	1.09889	+	0.412419i	0.0482823	+	0.0181206i
$519$	27.5037	−	2.47538i	1.20728	−	0.108657i
$520$	11.9078	+	14.9319i	0.522191	+	0.654806i
$521$	0.613396	+	1.43511i	0.0268734	+	0.0628733i	0.932427	−	0.361359i	$-0.117687\pi$
$521$	0.613396	+	1.43511i	0.0268734	+	0.0628733i	−0.905554	+	0.424232i	$0.860544\pi$
$522$	−0.444564	−	0.322995i	−0.0194580	−	0.0141371i
$523$	−15.2527	+	7.34531i	−0.666954	+	0.321188i	−0.736546	−	0.676388i	$-0.763544\pi$
$523$	−15.2527	+	7.34531i	−0.666954	+	0.321188i	0.0695922	+	0.997576i	$0.477830\pi$
$524$	−17.8918	+	6.71490i	−0.781607	+	0.293342i
$525$	−0.207407	−	0.314207i	−0.00905196	−	0.0137131i
$526$	13.2263	+	1.19039i	0.576693	+	0.0519033i
$527$	−6.07695	−	2.92651i	−0.264716	−	0.127481i
$528$	−0.820063	−	1.52393i	−0.0356887	−	0.0663207i
$529$	4.94433	−	21.6625i	0.214971	−	0.941849i
$530$	−5.67686	+	8.60008i	−0.246587	+	0.373563i
$531$	8.21566	−	10.3021i	0.356529	−	0.447073i
$532$	−3.31944	−	0.916107i	−0.143916	−	0.0397183i
$533$	36.0262	+	9.94260i	1.56047	+	0.430662i
$534$	−5.79156	+	7.26239i	−0.250625	+	0.314274i
$535$	−7.13694	+	10.8120i	−0.308557	+	0.467443i
$536$	−3.52840	+	15.4589i	−0.152404	+	0.667725i
$537$	1.38704	+	2.57755i	0.0598551	+	0.111229i
$538$	15.5938	+	7.50960i	0.672299	+	0.323762i
$539$	−9.44346	−	0.849927i	−0.406759	−	0.0366089i
$540$	8.93177	+	13.5311i	0.384362	+	0.582284i
$541$	−26.3890	+	9.90397i	−1.13455	+	0.425805i	−0.846806	−	0.531901i	$-0.821478\pi$
$541$	−26.3890	+	9.90397i	−1.13455	+	0.425805i	−0.287747	+	0.957706i	$0.592906\pi$
$542$	6.63184	−	3.19373i	0.284862	−	0.137182i
$543$	3.07462	+	2.23384i	0.131945	+	0.0958634i
$544$	−9.97395	−	23.3352i	−0.427630	−	1.00049i
$545$	−11.1764	−	14.0148i	−0.478746	−	0.600328i
$546$	1.10560	−	0.0995054i	0.0473151	−	0.00425844i
$547$	−8.41486	−	3.15815i	−0.359793	−	0.135033i	0.164930	−	0.986305i	$-0.447260\pi$
$547$	−8.41486	−	3.15815i	−0.359793	−	0.135033i	−0.524724	+	0.851272i	$0.675831\pi$
$548$	1.71405	+	7.50977i	0.0732208	+	0.320801i
$549$	12.6061	−	11.0136i	0.538016	−	0.470051i
$550$	0.812455	+	0.485419i	0.0346432	+	0.0206984i
$551$	2.97940	−	2.16466i	0.126927	−	0.0922176i
$552$	−1.32543	+	2.46305i	−0.0564139	+	0.104835i
$553$	−2.28496	−	1.99631i	−0.0971663	−	0.0848916i
$554$	5.24726	+	16.1494i	0.222935	+	0.686122i
$555$	11.9495	−	2.16851i	0.507227	−	0.0920481i
$556$	3.36434	+	24.8366i	0.142680	+	1.05330i
$557$	3.13576	+	0.569057i	0.132867	+	0.0241117i	0.244583	−	0.969628i	$-0.421349\pi$
$557$	3.13576	+	0.569057i	0.132867	+	0.0241117i	−0.111716	+	0.993740i	$0.535635\pi$
$558$	0.0756764	−	1.68507i	0.00320364	−	0.0713345i
$559$	−18.6995	−	19.5582i	−0.790906	−	0.827223i
$560$	−0.462240	+	0.483465i	−0.0195332	+	0.0204301i
$561$	0.331239	+	7.37560i	0.0139849	+	0.311398i
$562$	−1.18382	+	8.73933i	−0.0499366	+	0.368647i
$563$	2.35790	−	7.25687i	0.0993736	−	0.305841i	−0.888995	−	0.457917i	$-0.848596\pi$
$563$	2.35790	−	7.25687i	0.0993736	−	0.305841i	0.988369	+	0.152076i	$0.0485959\pi$
$564$	−12.2734	+	7.33301i	−0.516803	+	0.308775i
$565$	−14.7372	+	34.4793i	−0.619998	+	1.45056i
$566$	2.04678	−	0.564875i	0.0860325	−	0.0237435i
$567$	0.805591			0.0338316
$568$	−1.04333	−	21.4994i	−0.0437772	−	0.902095i
$569$	22.1159			0.927147			0.463573	−	0.886059i	$-0.346567\pi$
$569$	22.1159			0.927147			0.463573	+	0.886059i	$0.346567\pi$
$570$	12.9443	−	3.57240i	0.542177	−	0.149631i
$571$	−3.84327	+	8.99178i	−0.160836	+	0.376294i	−0.980491	−	0.196563i	$-0.937022\pi$
$571$	−3.84327	+	8.99178i	−0.160836	+	0.376294i	0.819655	+	0.572857i	$0.194165\pi$
$572$	6.35622	−	3.79766i	0.265767	−	0.158788i
$573$	5.24648	−	16.1470i	0.219175	−	0.674551i
$574$	0.327147	−	2.41509i	0.0136548	−	0.100804i
$575$	0.0368573	+	0.820692i	0.00153706	+	0.0342252i
$576$	2.33220	−	2.43929i	0.0971751	−	0.101637i
$577$	−14.5169	−	15.1834i	−0.604345	−	0.632095i	0.347863	−	0.937545i	$-0.386907\pi$
$577$	−14.5169	−	15.1834i	−0.604345	−	0.632095i	−0.952208	+	0.305450i	$0.901193\pi$
$578$	−0.0582163	+	1.29629i	−0.00242148	+	0.0539184i
$579$	−9.21748	−	1.67273i	−0.383065	−	0.0695161i
$580$	−0.199595	−	1.47347i	−0.00828773	−	0.0611824i
$581$	−1.39109	+	0.252446i	−0.0577122	+	0.0104732i
$582$	0.870423	+	2.67889i	0.0360802	+	0.111043i
$583$	7.15094	+	6.24759i	0.296162	+	0.258749i
$584$	14.7362	−	27.3844i	0.609787	−	1.13317i
$585$	−8.85335	+	6.43233i	−0.366041	+	0.265944i
$586$	11.3343	+	6.77193i	0.468216	+	0.279746i
$587$	−7.01870	+	6.13205i	−0.289693	+	0.253097i	−0.790500	−	0.612462i	$-0.790179\pi$
$587$	−7.01870	+	6.13205i	−0.289693	+	0.253097i	0.500807	+	0.865559i	$0.333036\pi$
$588$	−2.76166	−	12.0996i	−0.113889	−	0.498980i
$589$	10.5836	+	3.97209i	0.436089	+	0.163667i
$590$	−13.3835	+	1.20454i	−0.550991	+	0.0495900i
$591$	−16.8929	−	21.1830i	−0.694879	−	0.871351i
$592$	1.93762	+	4.53328i	0.0796356	+	0.186317i
$593$	32.5530	+	23.6512i	1.33679	+	0.971237i	0.999555	+	0.0298175i	$0.00949262\pi$
$593$	32.5530	+	23.6512i	1.33679	+	0.971237i	0.337238	+	0.941420i	$0.390507\pi$
$594$	−5.07298	+	2.44302i	−0.208147	+	0.100238i
$595$	2.67166	−	1.00269i	0.109527	−	0.0411063i
$596$	−6.54890	−	9.92116i	−0.268253	−	0.406387i
$597$	−28.6149	−	2.57539i	−1.17113	−	0.105404i
$598$	−2.18235	−	1.05096i	−0.0892427	−	0.0429770i
$599$	−20.0057	−	37.1768i	−0.817411	−	1.51900i	−0.854357	−	0.519687i	$-0.826049\pi$
$599$	−20.0057	−	37.1768i	−0.817411	−	1.51900i	0.0369458	−	0.999317i	$-0.488237\pi$
$600$	−0.655207	+	2.87065i	−0.0267487	+	0.117194i
$601$	−6.62701	+	10.0395i	−0.270321	+	0.409519i	−0.944226	−	0.329299i	$-0.893187\pi$
$601$	−6.62701	+	10.0395i	−0.270321	+	0.409519i	0.673904	+	0.738819i	$0.264616\pi$
$602$	−1.10019	+	1.37959i	−0.0448403	+	0.0562280i
$603$	−8.75823	−	2.41712i	−0.356663	−	0.0984326i
$604$	−20.4954	−	5.65638i	−0.833948	−	0.230155i
$605$	11.4566	−	14.3661i	0.465775	−	0.584064i
$606$	1.17261	−	1.77643i	0.0476342	−	0.0721627i
$607$	−2.69989	+	11.8290i	−0.109585	+	0.480124i	0.890117	+	0.455732i	$0.150622\pi$
$607$	−2.69989	+	11.8290i	−0.109585	+	0.480124i	−0.999702	+	0.0243927i	$0.992235\pi$
$608$	20.1547	+	37.4538i	0.817383	+	1.51895i
$609$	−0.185077	−	0.0891283i	−0.00749969	−	0.00361166i
$610$	−17.0021	−	1.53022i	−0.688395	−	0.0619566i
$611$	−16.2122	−	24.5605i	−0.655877	−	0.993611i
$612$	8.62028	−	3.23524i	0.348454	−	0.130777i
$613$	25.6484	−	12.3516i	1.03593	−	0.498876i	0.162949	−	0.986635i	$-0.447900\pi$
$613$	25.6484	−	12.3516i	1.03593	−	0.498876i	0.872979	+	0.487758i	$0.162185\pi$
$614$	−7.35942	−	5.34693i	−0.297002	−	0.215785i
$615$	−9.91105	−	23.1881i	−0.399652	−	0.935033i
$616$	−0.715557	−	0.897281i	−0.0288306	−	0.0361525i
$617$	13.7414	−	1.23675i	0.553207	−	0.0497896i	0.190491	−	0.981689i	$-0.438992\pi$
$617$	13.7414	−	1.23675i	0.553207	−	0.0497896i	0.362717	+	0.931899i	$0.381849\pi$
$618$	11.6582	+	4.37538i	0.468960	+	0.176004i
$619$	1.31121	+	5.74477i	0.0527019	+	0.230902i	0.994419	−	0.105504i	$-0.0336457\pi$
$619$	1.31121	+	5.74477i	0.0527019	+	0.230902i	−0.941717	+	0.336406i	$0.890789\pi$
$620$	3.43719	−	3.00298i	0.138041	−	0.120603i
$621$	−4.19566	−	2.50679i	−0.168366	−	0.100594i
$622$	−2.33836	+	1.69892i	−0.0937598	+	0.0681205i
$623$	1.56774	−	2.91335i	0.0628103	−	0.116721i
$624$	3.51127	+	3.06771i	0.140563	+	0.122807i
$625$	−6.02131	−	18.5317i	−0.240853	−	0.741268i
$626$	0.749247	−	0.135968i	0.0299459	−	0.00543439i
$627$	−1.66099	−	12.2619i	−0.0663336	−	0.489694i
$628$	20.4795	+	3.71647i	0.817219	+	0.148303i
$629$	0.943626	−	21.0115i	0.0376248	−	0.837782i
$630$	0.493164	+	0.515810i	0.0196481	+	0.0205503i
$631$	0.834404	−	0.872718i	0.0332171	−	0.0347424i	−0.705978	−	0.708234i	$-0.749492\pi$
$631$	0.834404	−	0.872718i	0.0332171	−	0.0347424i	0.739195	+	0.673492i	$0.235206\pi$
$632$	1.06464	+	23.7061i	0.0423492	+	0.942978i
$633$	4.29065	−	31.6748i	0.170538	−	1.25896i
$634$	−2.81593	+	8.66654i	−0.111835	+	0.344192i
$635$	23.3001	−	13.9212i	0.924636	−	0.552444i
$636$	−4.88499	+	11.4290i	−0.193703	+	0.453190i
$637$	24.6253	−	6.79616i	0.975692	−	0.269274i
$638$	0.516387			0.0204440
$639$	12.3334	−	0.0445291i	0.487902	−	0.00176154i
$640$	20.2030			0.798595
$641$	5.45228	−	1.50473i	0.215352	−	0.0594334i	−0.156696	−	0.987647i	$-0.550084\pi$
$641$	5.45228	−	1.50473i	0.215352	−	0.0594334i	0.372048	+	0.928214i	$0.378656\pi$
$642$	2.31454	−	5.41513i	0.0913476	−	0.213718i
$643$	7.12833	−	4.25898i	0.281114	−	0.167958i	−0.365421	−	0.930843i	$-0.619075\pi$
$643$	7.12833	−	4.25898i	0.281114	−	0.167958i	0.646534	+	0.762885i	$0.276218\pi$
$644$	0.129516	−	0.398610i	0.00510365	−	0.0157074i
$645$	−2.45084	+	18.0928i	−0.0965017	+	0.712404i
$646$	−1.04336	−	23.2322i	−0.0410503	−	0.914057i
$647$	12.4462	−	13.0177i	0.489309	−	0.511777i	−0.431329	−	0.902195i	$-0.641955\pi$
$647$	12.4462	−	13.0177i	0.489309	−	0.511777i	0.920638	+	0.390418i	$0.127669\pi$
$648$	−4.35399	−	4.55392i	−0.171041	−	0.178895i
$649$	−0.555542	+	12.3701i	−0.0218070	+	0.485569i
$650$	−2.50893	−	0.455303i	−0.0984082	−	0.0178585i
$651$	−0.0846408	−	0.624844i	−0.00331734	−	0.0244896i
$652$	−18.7706	+	3.40636i	−0.735112	+	0.133403i
$653$	−11.1234	−	34.2343i	−0.435292	−	1.33969i	−0.892787	−	0.450479i	$-0.851253\pi$
$653$	−11.1234	−	34.2343i	−0.435292	−	1.33969i	0.457495	−	0.889212i	$-0.348747\pi$
$654$	6.13639	+	5.36120i	0.239952	+	0.209640i
$655$	−12.5774	+	23.3727i	−0.491440	+	0.913248i
$656$	8.28172	−	6.01702i	0.323347	−	0.234925i
$657$	15.2964	+	9.13918i	0.596770	+	0.356553i
$658$	−1.44522	+	1.26265i	−0.0563404	+	0.0492232i
$659$	2.21194	+	9.69114i	0.0861649	+	0.377513i	0.999563	−	0.0295540i	$-0.00940869\pi$
$659$	2.21194	+	9.69114i	0.0861649	+	0.377513i	−0.913398	+	0.407067i	$0.866552\pi$
$660$	−4.67747	−	1.75548i	−0.182070	−	0.0683320i
$661$	8.27421	−	0.744693i	0.321830	−	0.0289652i	0.0724531	−	0.997372i	$-0.476917\pi$
$661$	8.27421	−	0.744693i	0.321830	−	0.0289652i	0.249376	+	0.968407i	$0.419774\pi$
$662$	−11.7841	−	14.7768i	−0.458002	−	0.574316i
$663$	−7.81798	−	18.2911i	−0.303625	−	0.710366i
$664$	8.94551	+	6.49929i	0.347153	+	0.252221i
$665$	−4.30901	+	2.07511i	−0.167096	+	0.0804694i
$666$	4.92444	−	1.84817i	0.190818	−	0.0716153i
$667$	0.246932	+	0.374087i	0.00956126	+	0.0144847i
$668$	6.94142	+	0.624739i	0.268571	+	0.0241719i
$669$	7.95682	+	3.83180i	0.307629	+	0.148146i
$670$	4.39059	+	8.15908i	0.169623	+	0.315213i
$671$	−3.50037	+	15.3361i	−0.135130	+	0.592045i
$672$	1.30696	−	1.97995i	0.0504169	−	0.0763784i
$673$	6.79979	−	8.52666i	0.262113	−	0.328679i	−0.633308	−	0.773900i	$-0.718303\pi$
$673$	6.79979	−	8.52666i	0.262113	−	0.328679i	0.895421	+	0.445221i	$0.146875\pi$
$674$	0.475804	+	0.131313i	0.0183273	+	0.00505801i
$675$	−4.95971	−	1.36879i	−0.190899	−	0.0526849i
$676$	−0.664492	+	0.833247i	−0.0255574	+	0.0320480i
$677$	−0.457358	+	0.692867i	−0.0175777	+	0.0266291i	−0.843256	−	0.537512i	$-0.819364\pi$
$677$	−0.457358	+	0.692867i	−0.0175777	+	0.0266291i	0.825678	+	0.564141i	$0.190793\pi$
$678$	3.79287	−	16.6176i	0.145664	−	0.638196i
$679$	−0.475397	−	0.883435i	−0.0182441	−	0.0339031i
$680$	−20.1077	−	9.68334i	−0.771094	−	0.371339i
$681$	−1.38685	−	0.124818i	−0.0531441	−	0.00478305i
$682$	0.873219	+	1.32287i	0.0334373	+	0.0506553i
$683$	−32.0669	+	12.0349i	−1.22701	+	0.460503i	−0.878924	−	0.476962i	$-0.841738\pi$
$683$	−32.0669	+	12.0349i	−1.22701	+	0.460503i	−0.348081	+	0.937464i	$0.613167\pi$
$684$	−13.9033	+	6.69549i	−0.531607	+	0.256008i
$685$	8.65516	+	6.28834i	0.330697	+	0.240265i
$686$	−1.31961	−	3.08737i	−0.0503828	−	0.117876i
$687$	11.5998	+	14.5457i	0.442559	+	0.554952i
$688$	−7.38187	+	0.664380i	−0.281431	+	0.0253292i
$689$	−23.9525	−	8.98953i	−0.912518	−	0.342474i
$690$	0.363685	+	1.59341i	0.0138453	+	0.0606601i
$691$	−6.11230	+	5.34015i	−0.232523	+	0.203149i	−0.766312	−	0.642468i	$-0.777910\pi$
$691$	−6.11230	+	5.34015i	−0.232523	+	0.203149i	0.533789	+	0.845617i	$0.320767\pi$
$692$	27.7816	+	16.5987i	1.05610	+	0.630990i
$693$	0.532012	−	0.386529i	0.0202095	−	0.0146830i
$694$	2.79112	−	5.18677i	0.105950	−	0.196887i
$695$	26.2144	+	22.9028i	0.994368	+	0.868753i
$696$	0.496456	+	1.52793i	0.0188181	+	0.0579162i
$697$	−42.9707	+	7.79803i	−1.62763	+	0.295372i
$698$	−0.529236	−	3.90698i	−0.0200319	−	0.147881i
$699$	−19.5502	−	3.54784i	−0.739457	−	0.134192i
$700$	0.0197951	−	0.440772i	0.000748185	−	0.0166596i
$701$	4.08756	+	4.27525i	0.154385	+	0.161474i	0.795464	−	0.606001i	$-0.207227\pi$
$701$	4.08756	+	4.27525i	0.154385	+	0.161474i	−0.641079	+	0.767475i	$0.721513\pi$
$702$	10.4836	−	10.9650i	0.395678	−	0.413846i
$703$	1.58151	+	35.2151i	0.0596478	+	1.32816i
$704$	−0.425704	+	3.14267i	−0.0160443	+	0.118444i
$705$	−6.13615	+	18.8851i	−0.231101	+	0.711255i
$706$	6.66964	−	3.98492i	0.251015	−	0.149975i
$707$	−0.297958	+	0.697107i	−0.0112059	+	0.0262174i
$708$	−15.6239	+	4.31191i	−0.587180	+	0.162052i
$709$	−22.4728			−0.843982			−0.421991	−	0.906600i	$-0.638669\pi$
$709$	−22.4728			−0.843982			−0.421991	+	0.906600i	$0.638669\pi$
$710$	−8.72461	−	9.05952i	−0.327429	−	0.339998i
$711$	−13.5971			−0.509931
$712$	−24.9421	+	6.88358i	−0.934744	+	0.257973i
$713$	−0.540761	+	1.26517i	−0.0202517	+	0.0473811i
$714$	−1.11356	+	0.665320i	−0.0416739	+	0.0248990i
$715$	3.17783	−	9.78035i	0.118844	−	0.365764i
$716$	−0.460458	+	3.39924i	−0.0172081	+	0.127035i
$717$	0.414246	+	9.22391i	0.0154703	+	0.344473i
$718$	11.6031	−	12.1359i	0.433023	−	0.452907i
$719$	2.21702	+	2.31883i	0.0826810	+	0.0864776i	0.762841	−	0.646586i	$-0.223804\pi$
$719$	2.21702	+	2.31883i	0.0826810	+	0.0864776i	−0.680160	+	0.733064i	$0.738090\pi$
$720$	−0.134481	+	2.99445i	−0.00501181	+	0.111597i
$721$	−4.36374	−	0.791902i	−0.162514	−	0.0294920i
$722$	3.34487	+	24.6928i	0.124483	+	0.918971i
$723$	28.0822	−	5.09616i	1.04439	−	0.189528i
$724$	1.37631	+	4.23585i	0.0511501	+	0.157424i
$725$	0.355348	+	0.310459i	0.0131973	+	0.0115301i
$726$	−3.95809	+	7.35536i	−0.146898	+	0.272983i
$727$	−0.332383	+	0.241491i	−0.0123274	+	0.00895639i	−0.593932	−	0.804515i	$-0.702425\pi$
$727$	−0.332383	+	0.241491i	−0.0123274	+	0.00895639i	0.581604	+	0.813472i	$0.302425\pi$
$728$	2.65441	+	1.58594i	0.0983791	+	0.0587788i
$729$	18.2113	−	15.9107i	0.674493	−	0.589287i
$730$	−4.04348	−	17.7156i	−0.149656	−	0.655685i
$731$	29.6039	+	11.1105i	1.09494	+	0.410937i
$732$	−20.5073	+	1.84569i	−0.757971	+	0.0682187i
$733$	23.2135	+	29.1088i	0.857411	+	1.07516i	0.996392	+	0.0848648i	$0.0270458\pi$
$733$	23.2135	+	29.1088i	0.857411	+	1.07516i	−0.138981	+	0.990295i	$0.544383\pi$
$734$	1.46706	+	3.43236i	0.0541501	+	0.126691i
$735$	−13.9451	−	10.1317i	−0.514372	−	0.373713i
$736$	−4.66408	+	2.24610i	−0.171920	+	0.0827924i
$737$	7.99354	−	3.00002i	0.294446	−	0.110507i
$738$	−6.01668	−	9.11489i	−0.221477	−	0.335524i
$739$	−4.16758	−	0.375089i	−0.153307	−	0.0137979i	0.0127199	−	0.999919i	$-0.495951\pi$
$739$	−4.16758	−	0.375089i	−0.153307	−	0.0137979i	−0.166027	+	0.986121i	$0.553094\pi$
$740$	12.8231	+	6.17530i	0.471388	+	0.227008i
$741$	15.7981	+	29.3578i	0.580357	+	1.07848i
$742$	−0.371246	+	1.62653i	−0.0136289	+	0.0597119i
$743$	−19.5858	+	29.6712i	−0.718533	+	1.08853i	0.273417	+	0.961896i	$0.411846\pi$
$743$	−19.5858	+	29.6712i	−0.718533	+	1.08853i	−0.991949	+	0.126635i	$0.959582\pi$
$744$	−3.07472	+	3.85557i	−0.112725	+	0.141352i
$745$	−15.9156	−	4.39242i	−0.583101	−	0.160926i
$746$	2.15170	+	0.593832i	0.0787795	+	0.0217418i
$747$	−3.95026	+	4.95346i	−0.144532	+	0.181238i
$748$	−4.76656	+	7.22103i	−0.174283	+	0.264027i
$749$	−0.466729	+	2.04488i	−0.0170539	+	0.0747181i
$750$	5.19890	+	9.66117i	0.189837	+	0.352776i
$751$	−36.2586	−	17.4612i	−1.32309	−	0.637169i	−0.366999	−	0.930222i	$-0.619615\pi$
$751$	−36.2586	−	17.4612i	−1.32309	−	0.637169i	−0.956096	+	0.293053i	$0.905329\pi$
$752$	−8.02833	−	0.722563i	−0.292763	−	0.0263492i
$753$	11.1770	+	16.9324i	0.407313	+	0.617053i
$754$	−1.30256	+	0.488861i	−0.0474366	+	0.0178033i
$755$	−26.6055	+	12.8125i	−0.968271	+	0.466295i
$756$	2.12362	+	1.54290i	0.0772355	+	0.0561149i
$757$	19.5832	+	45.8172i	0.711763	+	1.66525i	0.746092	+	0.665843i	$0.231928\pi$
$757$	19.5832	+	45.8172i	0.711763	+	1.66525i	−0.0343285	+	0.999411i	$0.510929\pi$
$758$	−10.6788	−	13.3907i	−0.387870	−	0.486373i
$759$	1.50000	−	0.135003i	0.0544467	−	0.00490029i
$760$	35.0194	+	13.1430i	1.27029	+	0.476747i
$761$	1.46492	+	6.41825i	0.0531034	+	0.232661i	0.994514	−	0.104601i	$-0.0333564\pi$
$761$	1.46492	+	6.41825i	0.0531034	+	0.232661i	−0.941411	+	0.337262i	$0.890499\pi$
$762$	−9.29142	+	8.11767i	−0.336593	+	0.294072i
$763$	−2.49139	−	1.48853i	−0.0901942	−	0.0538885i
$764$	16.0969	−	11.6951i	0.582367	−	0.423114i
$765$	6.05980	−	11.2610i	0.219092	−	0.407142i
$766$	−4.65461	−	4.06661i	−0.168178	−	0.146933i
$767$	−10.3094	−	31.7290i	−0.372250	−	1.14567i
$768$	−14.6598	+	2.66037i	−0.528992	+	0.0959978i
$769$	−3.64074	−	26.8770i	−0.131288	−	0.969210i	−0.930017	−	0.367518i	$-0.880208\pi$
$769$	−3.64074	−	26.8770i	−0.131288	−	0.969210i	0.798728	−	0.601692i	$-0.205507\pi$
$770$	−0.659837	−	0.119743i	−0.0237789	−	0.00431523i
$771$	−1.31917	+	29.3737i	−0.0475089	+	1.05787i
$772$	−7.58692	−	7.93529i	−0.273059	−	0.285598i
$773$	11.9667	−	12.5162i	0.430411	−	0.450175i	−0.471648	−	0.881787i	$-0.656341\pi$
$773$	11.9667	−	12.5162i	0.430411	−	0.450175i	0.902059	+	0.431612i	$0.142055\pi$
$774$	0.354771	+	7.89959i	0.0127520	+	0.283945i
$775$	−0.194427	+	1.43532i	−0.00698401	+	0.0515581i
$776$	−2.42458	+	7.46209i	−0.0870373	+	0.267873i
$777$	1.68792	−	1.00849i	0.0605538	−	0.0361792i
$778$	0.806038	−	1.88582i	0.0288979	−	0.0676099i
$779$	70.5572	−	19.4725i	2.52797	−	0.697676i
$780$	13.4606			0.481967
$781$	−9.35186	+	6.84625i	−0.334636	+	0.244978i
$782$	2.83051			0.101219
$783$	−2.70612	+	0.746841i	−0.0967088	+	0.0266899i
$784$	2.75009	−	6.43415i	0.0982175	−	0.229791i
$785$	24.8160	−	14.8269i	0.885723	−	0.529195i
$786$	3.72836	−	11.4747i	0.132986	−	0.409290i
$787$	1.40135	−	10.3451i	0.0499526	−	0.368765i	−0.948669	−	0.316271i	$-0.897569\pi$
$787$	1.40135	−	10.3451i	0.0499526	−	0.368765i	0.998621	−	0.0524931i	$-0.0167168\pi$
$788$	−1.42456	−	31.7202i	−0.0507477	−	1.12999i
$789$	15.3736	−	16.0795i	0.547315	−	0.572447i
$790$	9.58236	+	10.0224i	0.340925	+	0.356580i
$791$	−0.272366	+	6.06470i	−0.00968422	+	0.215636i
$792$	−5.06038	−	0.918324i	−0.179813	−	0.0326312i
$793$	−5.68909	−	41.9986i	−0.202026	−	1.49141i
$794$	−5.92031	+	1.07438i	−0.210104	+	0.0381282i
$795$	5.33445	+	16.4178i	0.189194	+	0.582278i
$796$	−25.3560	−	22.1529i	−0.898719	−	0.785187i
$797$	−20.7179	+	38.5003i	−0.733866	+	1.36375i	0.190287	+	0.981729i	$0.439058\pi$
$797$	−20.7179	+	38.5003i	−0.733866	+	1.36375i	−0.924153	+	0.382023i	$0.875227\pi$
$798$	1.75885	−	1.27788i	0.0622626	−	0.0452364i
$799$	29.5214	+	17.6382i	1.04439	+	0.623996i
$800$	−4.10396	+	3.58552i	−0.145097	+	0.126767i
$801$	−3.29907	−	14.4542i	−0.116567	−	0.510713i
$802$	−12.7086	−	4.76961i	−0.448756	−	0.168421i
$803$	−16.6771	+	1.50097i	−0.588524	+	0.0529681i
$804$	6.96787	+	8.73744i	0.245738	+	0.308146i
$805$	−0.228784	−	0.535266i	−0.00806357	−	0.0188657i
$806$	−3.45501	−	2.51021i	−0.121698	−	0.0884185i
$807$	26.1230	−	12.5802i	0.919573	−	0.442843i
$808$	5.55105	−	2.08334i	0.195285	−	0.0732918i
$809$	4.27540	+	6.47695i	0.150315	+	0.227717i	0.901928	−	0.431887i	$-0.142152\pi$
$809$	4.27540	+	6.47695i	0.150315	+	0.227717i	−0.751613	+	0.659605i	$0.770724\pi$
$810$	−3.66671	−	0.330009i	−0.128835	−	0.0115954i
$811$	−33.5375	−	16.1508i	−1.17766	−	0.567132i	−0.260433	−	0.965492i	$-0.583865\pi$
$811$	−33.5375	−	16.1508i	−1.17766	−	0.567132i	−0.917229	+	0.398359i	$0.869580\pi$
$812$	−0.114077	−	0.211992i	−0.00400334	−	0.00743944i
$813$	2.74388	−	12.0217i	0.0962320	−	0.421620i
$814$	−2.72296	+	4.12510i	−0.0954396	+	0.144585i
$815$	−16.5199	+	20.7153i	−0.578666	+	0.725624i
$816$	−5.25217	−	1.44951i	−0.183863	−	0.0507429i
$817$	−51.0853	−	14.0987i	−1.78725	−	0.493250i
$818$	8.25593	−	10.3526i	0.288662	−	0.361970i
$819$	−0.976052	+	1.47866i	−0.0341060	+	0.0516684i
$820$	6.57612	−	28.8119i	0.229648	−	1.00615i
$821$	−4.10430	−	7.62706i	−0.143241	−	0.266186i	0.798859	−	0.601518i	$-0.205437\pi$
$821$	−4.10430	−	7.62706i	−0.143241	−	0.266186i	−0.942100	+	0.335332i	$0.891152\pi$
$822$	−4.38157	−	2.11005i	−0.152825	−	0.0735966i
$823$	37.2732	+	3.35465i	1.29926	+	0.116936i	0.717578	−	0.696478i	$-0.245251\pi$
$823$	37.2732	+	3.35465i	1.29926	+	0.116936i	0.581685	+	0.813414i	$0.302394\pi$
$824$	19.1083	+	28.9478i	0.665668	+	1.00844i
$825$	1.48436	−	0.557090i	0.0516788	−	0.0193954i
$826$	−1.96013	+	0.943948i	−0.0682016	+	0.0328442i
$827$	−19.1092	−	13.8836i	−0.664491	−	0.482781i	0.203685	−	0.979036i	$-0.434708\pi$
$827$	−19.1092	−	13.8836i	−0.664491	−	0.482781i	−0.868177	+	0.496255i	$0.834708\pi$
$828$	−0.738186	−	1.72707i	−0.0256537	−	0.0600199i
$829$	2.19167	+	2.74827i	0.0761199	+	0.0954514i	0.818433	−	0.574601i	$-0.194843\pi$
$829$	2.19167	+	2.74827i	0.0761199	+	0.0954514i	−0.742313	+	0.670053i	$0.766271\pi$
$830$	6.43507	−	0.579166i	0.223364	−	0.0201032i
$831$	26.6320	+	9.99517i	0.923855	+	0.346729i
$832$	−1.90133	−	8.33027i	−0.0659167	−	0.288800i
$833$	−22.4806	+	19.6407i	−0.778908	+	0.680511i
$834$	−13.5838	−	8.11593i	−0.470368	−	0.281032i
$835$	7.83107	−	5.68961i	0.271006	−	0.196897i
$836$	6.87171	−	12.7698i	0.237663	−	0.441652i
$837$	−6.48934	−	5.66956i	−0.224304	−	0.195969i
$838$	−1.80577	−	5.55759i	−0.0623793	−	0.191984i
$839$	39.9512	−	7.25007i	1.37927	−	0.250300i	0.562276	−	0.826950i	$-0.309926\pi$
$839$	39.9512	−	7.25007i	1.37927	−	0.250300i	0.816992	+	0.576649i	$0.195640\pi$
$840$	−0.280063	−	2.06751i	−0.00966309	−	0.0713358i
$841$	−28.2806	−	5.13218i	−0.975194	−	0.176972i
$842$	−0.165081	+	3.67581i	−0.00568906	+	0.126677i
$843$	10.2097	+	10.6785i	0.351641	+	0.367788i
$844$	25.8869	−	27.0756i	0.891064	−	0.931980i
$845$	0.0664095	+	1.47872i	0.00228456	+	0.0508696i
$846$	−1.15441	+	8.52222i	−0.0396896	+	0.293000i
$847$	0.919306	−	2.82933i	0.0315877	−	0.0972170i
$848$	−6.01569	+	3.59421i	−0.206580	+	0.123426i
$849$	1.39798	−	3.27073i	0.0479785	−	0.112251i
$850$	2.87233	−	0.792713i	0.0985202	−	0.0271898i
$851$	−4.29045			−0.147075
$852$	−12.3053	−	8.87264i	−0.421574	−	0.303972i
$853$	7.74679			0.265245			0.132623	−	0.991167i	$-0.457660\pi$
$853$	7.74679			0.265245			0.132623	+	0.991167i	$0.457660\pi$
$854$	−2.66420	+	0.735274i	−0.0911672	+	0.0251605i
$855$	−8.42350	+	19.7078i	−0.288078	+	0.673991i
$856$	14.0820	−	8.41361i	0.481313	−	0.287571i
$857$	6.64729	−	20.4583i	0.227067	−	0.698841i	−0.771008	−	0.636825i	$-0.780247\pi$
$857$	6.64729	−	20.4583i	0.227067	−	0.698841i	0.998075	−	0.0620155i	$-0.0197528\pi$
$858$	−0.627496	+	4.63236i	−0.0214224	+	0.158146i
$859$	1.85389	+	41.2800i	0.0632538	+	1.40845i	0.740182	+	0.672406i	$0.234739\pi$
$859$	1.85389	+	41.2800i	0.0632538	+	1.40845i	−0.676929	+	0.736049i	$0.736689\pi$
$860$	−14.7867	+	15.4657i	−0.504223	+	0.527376i
$861$	−2.82143	−	2.95099i	−0.0961542	−	0.100569i
$862$	0.0187334	−	0.417132i	0.000638063	−	0.0142076i
$863$	−40.0461	−	7.26730i	−1.36319	−	0.247382i	−0.552817	−	0.833303i	$-0.686447\pi$
$863$	−40.0461	−	7.26730i	−1.36319	−	0.247382i	−0.810368	+	0.585921i	$0.800733\pi$
$864$	−4.35206	−	32.1282i	−0.148060	−	1.09302i
$865$	44.2253	−	8.02571i	1.50371	−	0.272882i
$866$	1.47297	+	4.53335i	0.0500537	+	0.154049i
$867$	1.63698	+	1.43019i	0.0555949	+	0.0485718i
$868$	0.350169	−	0.650723i	0.0118855	−	0.0220870i
$869$	10.3372	−	7.51040i	0.350665	−	0.254773i
$870$	0.805879	+	0.481491i	0.0273219	+	0.0163241i
$871$	−17.3233	+	15.1349i	−0.586976	+	0.512826i
$872$	5.05072	+	22.1287i	0.171039	+	0.749371i
$873$	−4.20908	−	1.57969i	−0.142456	−	0.0534646i
$874$	−4.72481	+	0.425241i	−0.159819	+	0.0143840i
$875$	−2.43631	−	3.05504i	−0.0823623	−	0.103279i
$876$	−8.61411	−	20.1537i	−0.291044	−	0.680931i
$877$	36.3604	+	26.4174i	1.22780	+	0.892051i	0.996723	−	0.0808844i	$-0.0257745\pi$
$877$	36.3604	+	26.4174i	1.22780	+	0.892051i	0.231079	+	0.972935i	$0.425774\pi$
$878$	−1.56835	+	0.755280i	−0.0529294	+	0.0254895i
$879$	20.7078	−	7.77178i	0.698458	−	0.262136i
$880$	−1.55176	−	2.35081i	−0.0523097	−	0.0792457i
$881$	−35.1354	−	3.16224i	−1.18374	−	0.106539i	−0.519777	−	0.854302i	$-0.673985\pi$
$881$	−35.1354	−	3.16224i	−1.18374	−	0.106539i	−0.663965	+	0.747763i	$0.731128\pi$
$882$	−6.72606	−	3.23910i	−0.226478	−	0.109066i
$883$	−15.6843	−	29.1463i	−0.527818	−	0.980850i	−0.995299	−	0.0968473i	$-0.969124\pi$
$883$	−15.6843	−	29.1463i	−0.527818	−	0.980850i	0.467481	−	0.884003i	$-0.345162\pi$
$884$	5.18734	−	22.7272i	0.174469	−	0.764399i
$885$	−12.4012	+	18.7869i	−0.416860	+	0.631516i
$886$	−6.35685	+	7.97124i	−0.213563	+	0.267799i
$887$	−17.4052	−	4.80352i	−0.584409	−	0.161287i	−0.0386846	−	0.999251i	$-0.512317\pi$
$887$	−17.4052	−	4.80352i	−0.584409	−	0.161287i	−0.545724	+	0.837965i	$0.683745\pi$
$888$	−14.8236	−	4.09105i	−0.497447	−	0.137287i
$889$	2.73984	−	3.43565i	0.0918913	−	0.115228i
$890$	−8.32914	+	12.6181i	−0.279194	+	0.422960i
$891$	−0.754898	+	3.30742i	−0.0252900	+	0.110803i
$892$	4.90442	+	9.11394i	0.164212	+	0.305157i
$893$	−51.9284	−	25.0074i	−1.73772	−	0.836841i
$894$	7.47502	+	0.672764i	0.250002	+	0.0225006i
$895$	2.62461	+	3.97611i	0.0877309	+	0.132907i
$896$	3.06234	−	1.14932i	0.102306	−	0.0383960i
$897$	−3.65589	+	1.76058i	−0.122067	+	0.0587842i
$898$	21.1662	+	15.3781i	0.706324	+	0.513174i
$899$	0.310603	+	0.726693i	0.0103592	+	0.0242366i
$900$	−1.23278	−	1.54586i	−0.0410927	−	0.0515286i
$901$	29.7759	−	2.67988i	0.991978	−	0.0892797i
$902$	9.60882	+	3.60625i	0.319939	+	0.120075i
$903$	0.657777	+	2.88191i	0.0218894	+	0.0959039i
$904$	35.7552	−	31.2384i	1.18920	−	1.03897i
$905$	5.31021	+	3.17270i	0.176517	+	0.105464i
$906$	10.8598	−	7.89010i	0.360792	−	0.262131i
$907$	19.2227	−	35.7218i	0.638280	−	1.18612i	−0.331803	−	0.943349i	$-0.607657\pi$
$907$	19.2227	−	35.7218i	0.638280	−	1.18612i	0.970083	−	0.242774i	$-0.0780575\pi$
$908$	−1.22890	−	1.07366i	−0.0407824	−	0.0356305i
$909$	1.04984	+	3.23106i	0.0348208	+	0.107168i
$910$	1.77777	−	0.322618i	0.0589325	−	0.0106947i
$911$	4.20748	+	31.0609i	0.139400	+	1.02909i	0.916591	+	0.399827i	$0.130930\pi$
$911$	4.20748	+	31.0609i	0.139400	+	1.02909i	−0.777191	+	0.629265i	$0.783356\pi$
$912$	8.98494	+	1.63053i	0.297521	+	0.0539921i
$913$	0.267116	−	5.94780i	0.00884025	−	0.196844i
$914$	−16.3506	−	17.1014i	−0.540829	−	0.565663i
$915$	−19.7625	+	20.6699i	−0.653327	+	0.683327i
$916$	0.978197	+	21.7812i	0.0323205	+	0.719672i
$917$	−0.576827	+	4.25831i	−0.0190485	+	0.140622i
$918$	−5.47804	+	16.8597i	−0.180802	+	0.556452i
$919$	−1.38446	+	0.827175i	−0.0456690	+	0.0272860i	−0.535552	−	0.844502i	$-0.679897\pi$
$919$	−1.38446	+	0.827175i	−0.0456690	+	0.0272860i	0.489883	+	0.871788i	$0.337039\pi$
$920$	−1.78929	+	4.18626i	−0.0589912	+	0.138017i
$921$	−14.6898	+	4.05413i	−0.484046	+	0.133588i
$922$	−12.6217			−0.415672
$923$	17.1084	−	26.1227i	0.563129	−	0.859840i
$924$	−0.808870			−0.0266099
$925$	−4.35385	+	1.20159i	−0.143154	+	0.0395079i
$926$	11.1000	−	25.9698i	0.364770	−	0.853422i
$927$	−17.0614	+	10.1937i	−0.560369	+	0.334805i
$928$	−0.918839	+	2.82789i	−0.0301624	+	0.0928302i
$929$	−3.88611	+	28.6884i	−0.127499	+	0.941237i	0.808317	+	0.588748i	$0.200379\pi$
$929$	−3.88611	+	28.6884i	−0.127499	+	0.941237i	−0.935816	+	0.352489i	$0.885335\pi$
$930$	0.129282	+	2.87870i	0.00423934	+	0.0943961i
$931$	34.5750	−	36.1626i	1.13315	−	1.18518i
$932$	−16.0918	−	16.8307i	−0.527105	−	0.551308i
$933$	−0.217235	+	4.83712i	−0.00711196	+	0.158360i
$934$	5.41402	+	0.982499i	0.177152	+	0.0321484i
$935$	1.61309	+	11.9083i	0.0527537	+	0.389443i
$936$	13.6340	−	2.47420i	0.445641	−	0.0808718i
$937$	15.4462	+	47.5385i	0.504605	+	1.55301i	0.801433	+	0.598084i	$0.204071\pi$
$937$	15.4462	+	47.5385i	0.504605	+	1.55301i	−0.296828	+	0.954931i	$0.595929\pi$
$938$	1.12968	+	0.986968i	0.0368852	+	0.0322257i
$939$	0.604489	−	1.12333i	0.0197268	−	0.0366585i
$940$	−18.8266	+	13.6783i	−0.614055	+	0.446137i
$941$	22.4029	+	13.3851i	0.730314	+	0.436342i	0.829341	−	0.558743i	$-0.188716\pi$
$941$	22.4029	+	13.3851i	0.730314	+	0.436342i	−0.0990274	+	0.995085i	$0.531573\pi$
$942$	−9.89594	+	8.64582i	−0.322427	+	0.281696i
$943$	1.98239	+	8.68541i	0.0645554	+	0.282836i
$944$	−8.55539	−	3.21089i	−0.278454	−	0.104506i
$945$	3.63105	−	0.326800i	0.118118	−	0.0106308i
$946$	−4.63308	−	5.80970i	−0.150634	−	0.188890i
$947$	−6.39650	−	14.9654i	−0.207858	−	0.486309i	0.782867	−	0.622189i	$-0.213757\pi$
$947$	−6.39650	−	14.9654i	−0.207858	−	0.486309i	−0.990725	+	0.135880i	$0.956614\pi$
$948$	13.5307	+	9.83060i	0.439455	+	0.319283i
$949$	40.6464	−	19.5743i	1.31944	−	0.635408i
$950$	−4.67554	+	1.75476i	−0.151694	+	0.0569319i
$951$	8.40968	+	12.7401i	0.272703	+	0.413127i
$952$	−3.59876	−	0.323894i	−0.116636	−	0.0104975i
$953$	−24.1216	−	11.6164i	−0.781375	−	0.376291i	0.000280912	−	1.00000i	$-0.499911\pi$
$953$	−24.1216	−	11.6164i	−0.781375	−	0.376291i	−0.781656	+	0.623709i	$0.785625\pi$
$954$	3.54285	+	6.58372i	0.114704	+	0.213156i
$955$	6.14922	−	26.9415i	0.198984	−	0.871807i
$956$	−5.96105	+	9.03061i	−0.192794	+	0.292071i
$957$	0.539354	−	0.676329i	0.0174349	−	0.0218626i
$958$	−21.7742	−	6.00928i	−0.703491	−	0.194151i
$959$	1.66967	+	0.460800i	0.0539165	+	0.0148800i
$960$	−3.59465	+	4.50755i	−0.116017	+	0.145481i
$961$	15.7414	−	23.8472i	0.507788	−	0.769265i
$962$	2.96333	−	12.9832i	0.0955417	−	0.418596i
$963$	4.45407	+	8.27704i	0.143530	+	0.266724i
$964$	30.1354	+	14.5124i	0.970594	+	0.467414i
$965$	−15.1866	−	1.36682i	−0.488873	−	0.0439994i
$966$	0.145773	+	0.220837i	0.00469018	+	0.00710532i
$967$	33.6786	−	12.6398i	1.08303	−	0.406468i	0.254879	−	0.966973i	$-0.417964\pi$
$967$	33.6786	−	12.6398i	1.08303	−	0.406468i	0.828151	+	0.560505i	$0.189393\pi$
$968$	−20.9625	+	10.0950i	−0.673761	+	0.324466i
$969$	−31.5177	−	22.8989i	−1.01249	−	0.735620i
$970$	1.80190	+	4.21577i	0.0578557	+	0.135360i
$971$	17.5864	+	22.0526i	0.564373	+	0.707702i	0.979360	−	0.202126i	$-0.0647850\pi$
$971$	17.5864	+	22.0526i	0.564373	+	0.707702i	−0.414986	+	0.909828i	$0.636214\pi$
$972$	19.5899	−	1.76312i	0.628345	−	0.0565521i
$973$	5.27644	+	1.98028i	0.169155	+	0.0634849i
$974$	3.14605	+	13.7837i	0.100806	+	0.441660i
$975$	−3.21684	+	2.81047i	−0.103021	+	0.0900071i
$976$	−9.96556	−	5.95414i	−0.318990	−	0.190588i
$977$	−48.3548	+	35.1318i	−1.54701	+	1.12397i	−0.601265	+	0.799050i	$0.705336\pi$
$977$	−48.3548	+	35.1318i	−1.54701	+	1.12397i	−0.945742	+	0.324917i	$0.894664\pi$
$978$	5.70739	−	10.6061i	0.182502	−	0.339146i
$979$	10.4919	+	9.16652i	0.335324	+	0.292963i
$980$	−6.24231	−	19.2119i	−0.199403	−	0.613700i
$981$	−12.7966	+	2.32224i	−0.408564	+	0.0741435i
$982$	4.18286	+	30.8791i	0.133481	+	0.985393i
$983$	37.3869	+	6.78472i	1.19246	+	0.216399i	0.738269	−	0.674507i	$-0.235644\pi$
$983$	37.3869	+	6.78472i	1.19246	+	0.216399i	0.454188	+	0.890906i	$0.349929\pi$
$984$	−1.43256	+	31.8985i	−0.0456685	+	1.01689i
$985$	−30.4758	−	31.8751i	−0.971038	−	1.01563i
$986$	1.12352	−	1.17511i	0.0357803	−	0.0374232i
$987$	0.144236	+	3.21166i	0.00459107	+	0.102228i
$988$	−5.24453	+	38.7167i	−0.166851	+	1.23174i
$989$	1.99322	−	6.13450i	0.0633807	−	0.195066i
$990$	−2.57983	+	1.54138i	−0.0819924	+	0.0489882i
$991$	−10.3904	+	24.3096i	−0.330063	+	0.772220i	0.669505	+	0.742808i	$0.266506\pi$
$991$	−10.3904	+	24.3096i	−0.330063	+	0.772220i	−0.999567	+	0.0294124i	$0.990636\pi$
$992$	−8.79822	+	2.42815i	−0.279344	+	0.0770940i
$993$	−31.6619			−1.00476
$994$	−1.83785	−	0.876900i	−0.0582929	−	0.0278136i
$995$	−46.7636			−1.48251
$996$	7.51227	−	2.07325i	0.238035	−	0.0656936i
$997$	4.29007	−	10.0371i	0.135868	−	0.317878i	−0.837753	−	0.546049i	$-0.816131\pi$
$997$	4.29007	−	10.0371i	0.135868	−	0.317878i	0.973621	+	0.228170i	$0.0732742\pi$
$998$	18.4011	−	10.9941i	0.582475	−	0.348013i
$999$	8.30356	−	25.5557i	0.262713	−	0.808547i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	71.2.g.a.10.2	✓	120
3.2	odd	2		639.2.v.a.10.4		120
71.8	even	35		5041.2.a.s.1.37		60
71.63	odd	70		5041.2.a.t.1.37		60
71.64	even	35	inner	71.2.g.a.64.2	yes	120
213.206	odd	70		639.2.v.a.64.4		120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
71.2.g.a.10.2	✓	120	1.1	even	1	trivial
71.2.g.a.64.2	yes	120	71.64	even	35	inner
639.2.v.a.10.4		120	3.2	odd	2
639.2.v.a.64.4		120	213.206	odd	70
5041.2.a.s.1.37		60	71.8	even	35
5041.2.a.t.1.37		60	71.63	odd	70

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:	\( N \)	\(=\)	\( 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	71.g (of order \(35\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.713225 + 0.196838i) q^{2} +(-0.487143 + 1.13973i) q^{3} +(-1.24695 + 0.745020i) q^{4} +(-0.623421 + 1.91869i) q^{5} +(0.123101 - 0.908769i) q^{6} +(0.0146541 + 0.326298i) q^{7} +(1.76533 - 1.84639i) q^{8} +(1.01152 + 1.05797i) q^{9} +O(q^{10})\)	\(q+(-0.713225 + 0.196838i) q^{2} +(-0.487143 + 1.13973i) q^{3} +(-1.24695 + 0.745020i) q^{4} +(-0.623421 + 1.91869i) q^{5} +(0.123101 - 0.908769i) q^{6} +(0.0146541 + 0.326298i) q^{7} +(1.76533 - 1.84639i) q^{8} +(1.01152 + 1.05797i) q^{9} +(0.0669687 - 1.49117i) q^{10} +(-1.35338 - 0.245602i) q^{11} +(-0.241675 - 1.78412i) q^{12} +(3.64635 - 0.661714i) q^{13} +(-0.0746794 - 0.229840i) q^{14} +(-1.88309 - 1.64521i) q^{15} +(0.481013 - 0.893871i) q^{16} +(-3.50350 + 2.54544i) q^{17} +(-0.929688 - 0.555463i) q^{18} +(5.46579 - 4.77532i) q^{19} +(-0.652088 - 2.85698i) q^{20} +(-0.379029 - 0.142252i) q^{21} +(1.01361 - 0.0912262i) q^{22} +(0.550786 + 0.690664i) q^{23} +(1.24441 + 2.91145i) q^{24} +(0.752353 + 0.546616i) q^{25} +(-2.47042 + 1.18969i) q^{26} +(-5.17985 + 1.94403i) q^{27} +(-0.261371 - 0.395961i) q^{28} +(0.505362 + 0.0454834i) q^{29} +(1.66691 + 0.802740i) q^{30} +(0.738057 + 1.37154i) q^{31} +(-1.30399 + 5.71314i) q^{32} +(0.939207 - 1.42284i) q^{33} +(1.99774 - 2.50509i) q^{34} +(-0.635202 - 0.175305i) q^{35} +(-2.04952 - 0.565632i) q^{36} +(-3.02816 + 3.79719i) q^{37} +(-2.95837 + 4.48175i) q^{38} +(-1.02212 + 4.47819i) q^{39} +(2.44211 + 4.53820i) q^{40} +(9.08603 + 4.37560i) q^{41} +(0.298334 + 0.0268505i) q^{42} +(-4.02244 - 6.09374i) q^{43} +(1.87058 - 0.702039i) q^{44} +(-2.66051 + 1.28124i) q^{45} +(-0.528783 - 0.384183i) q^{46} +(-3.12104 - 7.30203i) q^{47} +(0.784447 + 0.983666i) q^{48} +(6.86556 - 0.617912i) q^{49} +(-0.644191 - 0.241769i) q^{50} +(-1.19440 - 5.23302i) q^{51} +(-4.05383 + 3.54173i) q^{52} +(-5.92634 - 3.54082i) q^{53} +(3.31174 - 2.40612i) q^{54} +(1.31496 - 2.44360i) q^{55} +(0.628343 + 0.548966i) q^{56} +(2.77994 + 8.55576i) q^{57} +(-0.369389 + 0.0670343i) q^{58} +(-1.20842 - 8.92089i) q^{59} +(3.57384 + 0.648556i) q^{60} +(0.513091 - 11.4249i) q^{61} +(-0.796371 - 0.832939i) q^{62} +(-0.330389 + 0.345560i) q^{63} +(-0.103442 - 2.30332i) q^{64} +(-1.00358 + 7.40875i) q^{65} +(-0.389798 + 1.19967i) q^{66} +(-5.32861 + 3.18370i) q^{67} +(2.47229 - 5.78422i) q^{68} +(-1.05548 + 0.291294i) q^{69} +0.487548 q^{70} +(5.80097 - 6.11136i) q^{71} +3.73908 q^{72} +(11.7349 - 3.23862i) q^{73} +(1.41233 - 3.30431i) q^{74} +(-0.989496 + 0.591197i) q^{75} +(-3.25788 + 10.0267i) q^{76} +(0.0603069 - 0.445204i) q^{77} +(-0.152476 - 3.39515i) q^{78} +(-6.41959 + 6.71436i) q^{79} +(1.41519 + 1.48017i) q^{80} +(0.110654 - 2.46391i) q^{81} +(-7.34166 - 1.33232i) q^{82} +(0.581031 + 4.28934i) q^{83} +(0.578612 - 0.105003i) q^{84} +(-2.69977 - 8.30902i) q^{85} +(4.06838 + 3.55444i) q^{86} +(-0.298022 + 0.553817i) q^{87} +(-2.84263 + 2.06529i) q^{88} +(-8.69518 - 5.19513i) q^{89} +(1.64535 - 1.43750i) q^{90} +(0.269350 + 1.18010i) q^{91} +(-1.20136 - 0.450879i) q^{92} +(-1.92272 + 0.173048i) q^{93} +(3.66331 + 4.59365i) q^{94} +(5.75488 + 13.4642i) q^{95} +(-5.87620 - 4.26931i) q^{96} +(-2.76730 + 1.33266i) q^{97} +(-4.77506 + 1.79211i) q^{98} +(-1.10913 - 1.68026i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9}+O(q^{10}) \) 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9	\( 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9} - 8 q^{10} - 27 q^{11} + 3 q^{12} - 31 q^{13} + 2 q^{14} + 12 q^{15} + 30 q^{16} + 9 q^{17} + 27 q^{18} - 31 q^{19} + 72 q^{20} - 32 q^{21} - 24 q^{22} - 6 q^{23} - 47 q^{24} - 42 q^{25} + 77 q^{26} - 2 q^{27} - 18 q^{28} + q^{29} + 15 q^{30} + 15 q^{31} - 10 q^{32} - 24 q^{33} + 20 q^{34} + 74 q^{35} + 8 q^{36} - 22 q^{37} - 39 q^{38} + 86 q^{39} - 30 q^{40} + 39 q^{41} - 34 q^{42} + 33 q^{43} - 23 q^{44} + 121 q^{45} + 124 q^{46} + 6 q^{47} + 131 q^{48} - 22 q^{49} - 15 q^{50} + 29 q^{51} + 83 q^{52} - 30 q^{53} - 25 q^{54} + 32 q^{55} + 11 q^{56} - 10 q^{57} + 12 q^{58} - 80 q^{59} + 80 q^{60} - 12 q^{61} - 68 q^{62} - 79 q^{63} - 117 q^{64} - 89 q^{65} - 39 q^{66} - 74 q^{67} - 67 q^{68} - 95 q^{69} - 64 q^{70} - 115 q^{71} - 144 q^{72} - 14 q^{73} - 70 q^{74} - 13 q^{75} + 8 q^{76} + 47 q^{77} - 218 q^{78} - 25 q^{79} - 103 q^{80} - 28 q^{81} - 88 q^{82} - 20 q^{83} - 142 q^{84} + 22 q^{85} + 159 q^{86} - 105 q^{87} + 43 q^{88} + 33 q^{89} + 33 q^{90} + 60 q^{91} - 2 q^{92} + 63 q^{93} + 174 q^{94} + 20 q^{95} - 30 q^{96} + 121 q^{97} + 128 q^{98} - 2 q^{99}+O(q^{100}) \) 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9 - 8 * q^10 - 27 * q^11 + 3 * q^12 - 31 * q^13 + 2 * q^14 + 12 * q^15 + 30 * q^16 + 9 * q^17 + 27 * q^18 - 31 * q^19 + 72 * q^20 - 32 * q^21 - 24 * q^22 - 6 * q^23 - 47 * q^24 - 42 * q^25 + 77 * q^26 - 2 * q^27 - 18 * q^28 + q^29 + 15 * q^30 + 15 * q^31 - 10 * q^32 - 24 * q^33 + 20 * q^34 + 74 * q^35 + 8 * q^36 - 22 * q^37 - 39 * q^38 + 86 * q^39 - 30 * q^40 + 39 * q^41 - 34 * q^42 + 33 * q^43 - 23 * q^44 + 121 * q^45 + 124 * q^46 + 6 * q^47 + 131 * q^48 - 22 * q^49 - 15 * q^50 + 29 * q^51 + 83 * q^52 - 30 * q^53 - 25 * q^54 + 32 * q^55 + 11 * q^56 - 10 * q^57 + 12 * q^58 - 80 * q^59 + 80 * q^60 - 12 * q^61 - 68 * q^62 - 79 * q^63 - 117 * q^64 - 89 * q^65 - 39 * q^66 - 74 * q^67 - 67 * q^68 - 95 * q^69 - 64 * q^70 - 115 * q^71 - 144 * q^72 - 14 * q^73 - 70 * q^74 - 13 * q^75 + 8 * q^76 + 47 * q^77 - 218 * q^78 - 25 * q^79 - 103 * q^80 - 28 * q^81 - 88 * q^82 - 20 * q^83 - 142 * q^84 + 22 * q^85 + 159 * q^86 - 105 * q^87 + 43 * q^88 + 33 * q^89 + 33 * q^90 + 60 * q^91 - 2 * q^92 + 63 * q^93 + 174 * q^94 + 20 * q^95 - 30 * q^96 + 121 * q^97 + 128 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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