LMFDB - Embedded newform 547.2.h.a.13.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,2,Mod(13,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, base_ring=CyclotomicField(42))

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

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

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

chi := DirichletCharacter("547.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	547.h (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.36781699056$
Analytic rank:	$0$
Dimension:	$540$
Relative dimension:	$45$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			13.19
Character	$\chi$	$=$	547.13
Dual form			547.2.h.a.505.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0370969 + 0.495024i) q^{2} +(-0.0486951 + 0.0610617i) q^{3} +(1.73399 + 0.261357i) q^{4} +(2.75036 - 2.55197i) q^{5} +(-0.0284205 - 0.0263704i) q^{6} +(1.13879 - 0.171645i) q^{7} +(-0.414627 + 1.81660i) q^{8} +(0.666205 + 2.91884i) q^{9} +O(q^{10})$	\(q+(-0.0370969 + 0.495024i) q^{2} +(-0.0486951 + 0.0610617i) q^{3} +(1.73399 + 0.261357i) q^{4} +(2.75036 - 2.55197i) q^{5} +(-0.0284205 - 0.0263704i) q^{6} +(1.13879 - 0.171645i) q^{7} +(-0.414627 + 1.81660i) q^{8} +(0.666205 + 2.91884i) q^{9} +(1.16125 + 1.45617i) q^{10} +(-1.01210 + 1.75301i) q^{11} +(-0.100396 + 0.0931535i) q^{12} +(-2.28013 + 1.55456i) q^{13} +(0.0427228 + 0.570097i) q^{14} +(0.0218981 + 0.292210i) q^{15} +(2.46746 + 0.761110i) q^{16} +(-0.485233 - 0.149675i) q^{17} +(-1.46961 + 0.221508i) q^{18} +(-0.187840 - 2.50655i) q^{19} +(5.43608 - 3.70625i) q^{20} +(-0.0449726 + 0.0778949i) q^{21} +(-0.830236 - 0.566046i) q^{22} +(-0.627333 - 8.37118i) q^{23} +(-0.0907344 - 0.113777i) q^{24} +(0.678327 - 9.05165i) q^{25} +(-0.684960 - 1.18639i) q^{26} +(-0.421769 - 0.203113i) q^{27} +2.01952 q^{28} +(-0.386423 + 1.69303i) q^{29} -0.145463 q^{30} +(-3.69788 + 4.63699i) q^{31} +(-1.82980 + 4.66224i) q^{32} +(-0.0577575 - 0.147164i) q^{33} +(0.0920930 - 0.234649i) q^{34} +(2.69406 - 3.37825i) q^{35} +(0.392335 + 5.23535i) q^{36} +(3.44410 + 1.06237i) q^{37} +1.24777 q^{38} +(0.0161066 - 0.214928i) q^{39} +(3.49553 + 6.05443i) q^{40} +(-0.703221 + 1.21801i) q^{41} +(-0.0368915 - 0.0251522i) q^{42} +(-0.0799067 + 0.0120440i) q^{43} +(-2.21314 + 2.77519i) q^{44} +(9.28108 + 6.32773i) q^{45} +4.16720 q^{46} +(-4.46958 - 7.74155i) q^{47} +(-0.166628 + 0.113605i) q^{48} +(-5.42162 + 1.67235i) q^{49} +(4.45562 + 0.671576i) q^{50} +(0.0327678 - 0.0223407i) q^{51} +(-4.36001 + 2.09967i) q^{52} +(4.06431 - 2.77100i) q^{53} +(0.116192 - 0.201251i) q^{54} +(1.68998 + 7.40427i) q^{55} +(-0.160363 + 2.13990i) q^{56} +(0.162201 + 0.110587i) q^{57} +(-0.823754 - 0.254095i) q^{58} +(-0.702793 + 1.21727i) q^{59} +(-0.0384000 + 0.512412i) q^{60} +(-6.38081 - 1.96822i) q^{61} +(-2.15824 - 2.00256i) q^{62} +(1.25967 + 3.20960i) q^{63} +(2.41288 + 1.16198i) q^{64} +(-2.30399 + 10.0944i) q^{65} +(0.0749921 - 0.0231320i) q^{66} +(9.48688 + 2.92632i) q^{67} +(-0.802270 - 0.386353i) q^{68} +(0.541706 + 0.369329i) q^{69} +(1.57237 + 1.45895i) q^{70} +(-5.80228 - 1.78977i) q^{71} -5.57859 q^{72} +(0.000648877 - 0.00865866i) q^{73} +(-0.653661 + 1.66550i) q^{74} +(0.519678 + 0.482191i) q^{75} +(0.329391 - 4.39542i) q^{76} +(-0.851678 + 2.17004i) q^{77} +(0.105797 + 0.0159463i) q^{78} +(-2.41088 - 3.02314i) q^{79} +(8.72874 - 4.20354i) q^{80} +(-8.05929 + 3.88115i) q^{81} +(-0.576858 - 0.393295i) q^{82} +(6.02451 - 10.4348i) q^{83} +(-0.0983404 + 0.123315i) q^{84} +(-1.71653 + 0.826638i) q^{85} +(-0.00299777 - 0.0400025i) q^{86} +(-0.0845623 - 0.106038i) q^{87} +(-2.76488 - 2.56543i) q^{88} +(3.10489 - 13.6034i) q^{89} +(-3.47668 + 4.35961i) q^{90} +(-2.32976 + 2.16170i) q^{91} +(1.10008 - 14.6795i) q^{92} +(-0.103074 - 0.451597i) q^{93} +(3.99806 - 1.92536i) q^{94} +(-6.91325 - 6.41456i) q^{95} +(-0.195582 - 0.338759i) q^{96} +(0.0894676 + 1.19386i) q^{97} +(-0.626727 - 2.74587i) q^{98} +(-5.79102 - 1.78629i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 540 q - 13 q^{2} - 10 q^{3} + 33 q^{4} - 15 q^{5} + 10 q^{6} - 2 q^{7} - 26 q^{8} - 96 q^{9}+O(q^{10}) $ 540 * q - 13 * q^2 - 10 * q^3 + 33 * q^4 - 15 * q^5 + 10 * q^6 - 2 * q^7 - 26 * q^8 - 96 * q^9	\( 540 q - 13 q^{2} - 10 q^{3} + 33 q^{4} - 15 q^{5} + 10 q^{6} - 2 q^{7} - 26 q^{8} - 96 q^{9} - 4 q^{10} - 8 q^{11} - 18 q^{12} - 11 q^{13} + 5 q^{14} - 7 q^{15} + 53 q^{16} - 10 q^{17} - 59 q^{18} - 12 q^{19} - 18 q^{20} + 20 q^{21} + 70 q^{22} - 15 q^{23} - 46 q^{24} + 26 q^{25} - 39 q^{26} - q^{27} - 56 q^{28} - 40 q^{29} - 100 q^{30} + 59 q^{31} - 5 q^{32} - 15 q^{33} - 8 q^{34} + 36 q^{35} + 43 q^{36} - 32 q^{37} - 108 q^{38} + 34 q^{39} - 27 q^{40} + 39 q^{41} + 46 q^{42} - 16 q^{43} - 110 q^{44} - 103 q^{45} + 12 q^{46} - 60 q^{47} + 42 q^{48} + 57 q^{49} - 168 q^{50} + 57 q^{51} - 46 q^{52} - 30 q^{53} + 113 q^{54} + 38 q^{55} + 64 q^{56} + 22 q^{57} - 88 q^{58} + 55 q^{59} + 9 q^{60} + 26 q^{61} - 32 q^{62} + 6 q^{63} - 50 q^{64} + 73 q^{65} + 72 q^{66} - 104 q^{67} - 181 q^{68} - 125 q^{69} - 50 q^{70} + 39 q^{71} - 434 q^{72} + 46 q^{73} - 178 q^{74} + 248 q^{75} - 126 q^{76} - 52 q^{77} - 82 q^{78} + 86 q^{79} + 208 q^{80} - 4 q^{81} + 177 q^{82} + 39 q^{83} + 124 q^{84} - 12 q^{85} + 2 q^{86} + 162 q^{87} - 34 q^{88} + 63 q^{89} + 121 q^{90} + 21 q^{91} + q^{92} - 57 q^{93} + 67 q^{94} - 143 q^{95} + 489 q^{96} + 119 q^{97} - 10 q^{98} - 120 q^{99}+O(q^{100}) \) 540 * q - 13 * q^2 - 10 * q^3 + 33 * q^4 - 15 * q^5 + 10 * q^6 - 2 * q^7 - 26 * q^8 - 96 * q^9 - 4 * q^10 - 8 * q^11 - 18 * q^12 - 11 * q^13 + 5 * q^14 - 7 * q^15 + 53 * q^16 - 10 * q^17 - 59 * q^18 - 12 * q^19 - 18 * q^20 + 20 * q^21 + 70 * q^22 - 15 * q^23 - 46 * q^24 + 26 * q^25 - 39 * q^26 - q^27 - 56 * q^28 - 40 * q^29 - 100 * q^30 + 59 * q^31 - 5 * q^32 - 15 * q^33 - 8 * q^34 + 36 * q^35 + 43 * q^36 - 32 * q^37 - 108 * q^38 + 34 * q^39 - 27 * q^40 + 39 * q^41 + 46 * q^42 - 16 * q^43 - 110 * q^44 - 103 * q^45 + 12 * q^46 - 60 * q^47 + 42 * q^48 + 57 * q^49 - 168 * q^50 + 57 * q^51 - 46 * q^52 - 30 * q^53 + 113 * q^54 + 38 * q^55 + 64 * q^56 + 22 * q^57 - 88 * q^58 + 55 * q^59 + 9 * q^60 + 26 * q^61 - 32 * q^62 + 6 * q^63 - 50 * q^64 + 73 * q^65 + 72 * q^66 - 104 * q^67 - 181 * q^68 - 125 * q^69 - 50 * q^70 + 39 * q^71 - 434 * q^72 + 46 * q^73 - 178 * q^74 + 248 * q^75 - 126 * q^76 - 52 * q^77 - 82 * q^78 + 86 * q^79 + 208 * q^80 - 4 * q^81 + 177 * q^82 + 39 * q^83 + 124 * q^84 - 12 * q^85 + 2 * q^86 + 162 * q^87 - 34 * q^88 + 63 * q^89 + 121 * q^90 + 21 * q^91 + q^92 - 57 * q^93 + 67 * q^94 - 143 * q^95 + 489 * q^96 + 119 * q^97 - 10 * q^98 - 120 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/547\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{11}{21}\right)$

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 $

$2$	−0.0370969	+	0.495024i	−0.0262315	+	0.350034i	0.968609	+	0.248587i	$0.0799663\pi$
$2$	−0.0370969	+	0.495024i	−0.0262315	+	0.350034i	−0.994841	+	0.101447i	$0.967653\pi$
$3$	−0.0486951	+	0.0610617i	−0.0281141	+	0.0352540i	−0.795690	−	0.605704i	$-0.792891\pi$
$3$	−0.0486951	+	0.0610617i	−0.0281141	+	0.0352540i	0.767576	+	0.640958i	$0.221463\pi$
$4$	1.73399	+	0.261357i	0.866995	+	0.130678i
$5$	2.75036	−	2.55197i	1.23000	−	1.14127i	0.244853	−	0.969560i	$-0.421260\pi$
$5$	2.75036	−	2.55197i	1.23000	−	1.14127i	0.985147	−	0.171713i	$-0.0549303\pi$
$6$	−0.0284205	−	0.0263704i	−0.0116026	−	0.0107657i
$7$	1.13879	−	0.171645i	0.430423	−	0.0648759i	0.0697421	−	0.997565i	$-0.477782\pi$
$7$	1.13879	−	0.171645i	0.430423	−	0.0648759i	0.360681	+	0.932689i	$0.382544\pi$
$8$	−0.414627	+	1.81660i	−0.146593	+	0.642265i
$9$	0.666205	+	2.91884i	0.222068	+	0.972946i
$10$	1.16125	+	1.45617i	0.367220	+	0.460480i
$11$	−1.01210	+	1.75301i	−0.305160	+	0.528553i	−0.977297	−	0.211874i	$-0.932043\pi$
$11$	−1.01210	+	1.75301i	−0.305160	+	0.528553i	0.672137	+	0.740427i	$0.265377\pi$
$12$	−0.100396	+	0.0931535i	−0.0289817	+	0.0268911i
$13$	−2.28013	+	1.55456i	−0.632394	+	0.431159i	−0.836634	−	0.547762i	$-0.815480\pi$
$13$	−2.28013	+	1.55456i	−0.632394	+	0.431159i	0.204241	+	0.978921i	$0.434528\pi$
$14$	0.0427228	+	0.570097i	0.0114182	+	0.152365i
$15$	0.0218981	+	0.292210i	0.00565407	+	0.0754483i
$16$	2.46746	+	0.761110i	0.616865	+	0.190278i
$17$	−0.485233	−	0.149675i	−0.117686	−	0.0363014i	0.235353	−	0.971910i	$-0.424375\pi$
$17$	−0.485233	−	0.149675i	−0.117686	−	0.0363014i	−0.353039	+	0.935609i	$0.614852\pi$
$18$	−1.46961	+	0.221508i	−0.346390	+	0.0522099i
$19$	−0.187840	−	2.50655i	−0.0430934	−	0.575042i	−0.976401	−	0.215964i	$-0.930710\pi$
$19$	−0.187840	−	2.50655i	−0.0430934	−	0.575042i	0.933308	−	0.359077i	$-0.116909\pi$
$20$	5.43608	−	3.70625i	1.21554	−	0.828744i
$21$	−0.0449726	+	0.0778949i	−0.00981383	+	0.0169981i
$22$	−0.830236	−	0.566046i	−0.177007	−	0.120681i
$23$	−0.627333	−	8.37118i	−0.130808	−	1.74551i	−0.547807	−	0.836605i	$-0.684537\pi$
$23$	−0.627333	−	8.37118i	−0.130808	−	1.74551i	0.416999	−	0.908907i	$-0.363082\pi$
$24$	−0.0907344	−	0.113777i	−0.0185211	−	0.0232247i
$25$	0.678327	−	9.05165i	0.135665	−	1.81033i
$26$	−0.684960	−	1.18639i	−0.134332	−	0.232669i
$27$	−0.421769	−	0.203113i	−0.0811695	−	0.0390892i
$28$	2.01952			0.381653
$29$	−0.386423	+	1.69303i	−0.0717569	+	0.314388i	−0.998050	−	0.0624156i	$-0.980120\pi$
$29$	−0.386423	+	1.69303i	−0.0717569	+	0.314388i	0.926293	+	0.376803i	$0.122977\pi$
$30$	−0.145463			−0.0265578
$31$	−3.69788	+	4.63699i	−0.664159	+	0.832829i	−0.993789	−	0.111282i	$-0.964504\pi$
$31$	−3.69788	+	4.63699i	−0.664159	+	0.832829i	0.329630	+	0.944110i	$0.393076\pi$
$32$	−1.82980	+	4.66224i	−0.323465	+	0.824176i
$33$	−0.0577575	−	0.147164i	−0.0100543	−	0.0256179i
$34$	0.0920930	−	0.234649i	0.0157938	−	0.0402420i
$35$	2.69406	−	3.37825i	0.455380	−	0.571028i
$36$	0.392335	+	5.23535i	0.0653892	+	0.872558i
$37$	3.44410	+	1.06237i	0.566207	+	0.174652i	0.564626	−	0.825347i	$-0.309020\pi$
$37$	3.44410	+	1.06237i	0.566207	+	0.174652i	0.00158133	+	0.999999i	$0.499497\pi$
$38$	1.24777			0.202415
$39$	0.0161066	−	0.214928i	0.00257913	−	0.0344160i
$40$	3.49553	+	6.05443i	0.552691	+	0.957289i
$41$	−0.703221	+	1.21801i	−0.109825	+	0.190222i	−0.915699	−	0.401865i	$-0.868362\pi$
$41$	−0.703221	+	1.21801i	−0.109825	+	0.190222i	0.805874	+	0.592086i	$0.201696\pi$
$42$	−0.0368915	−	0.0251522i	−0.00569248	−	0.00388106i
$43$	−0.0799067	+	0.0120440i	−0.0121857	+	0.00183669i	−0.155132	−	0.987894i	$-0.549580\pi$
$43$	−0.0799067	+	0.0120440i	−0.0121857	+	0.00183669i	0.142947	+	0.989730i	$0.454342\pi$
$44$	−2.21314	+	2.77519i	−0.333643	+	0.418375i
$45$	9.28108	+	6.32773i	1.38354	+	0.943283i
$46$	4.16720			0.614421
$47$	−4.46958	−	7.74155i	−0.651956	−	1.12922i	−0.982648	−	0.185482i	$-0.940615\pi$
$47$	−4.46958	−	7.74155i	−0.651956	−	1.12922i	0.330692	−	0.943739i	$-0.392718\pi$
$48$	−0.166628	+	0.113605i	−0.0240506	+	0.0163975i
$49$	−5.42162	+	1.67235i	−0.774518	+	0.238907i
$50$	4.45562	+	0.671576i	0.630119	+	0.0949752i
$51$	0.0327678	−	0.0223407i	0.00458841	−	0.00312833i
$52$	−4.36001	+	2.09967i	−0.604625	+	0.291172i
$53$	4.06431	−	2.77100i	0.558276	−	0.380626i	−0.251060	−	0.967971i	$-0.580779\pi$
$53$	4.06431	−	2.77100i	0.558276	−	0.380626i	0.809337	+	0.587345i	$0.199827\pi$
$54$	0.116192	−	0.201251i	0.0158118	−	0.0273868i
$55$	1.68998	+	7.40427i	0.227876	+	0.998392i
$56$	−0.160363	+	2.13990i	−0.0214295	+	0.285956i
$57$	0.162201	+	0.110587i	0.0214840	+	0.0146476i
$58$	−0.823754	−	0.254095i	−0.108164	−	0.0333642i
$59$	−0.702793	+	1.21727i	−0.0914959	+	0.158475i	−0.908141	−	0.418665i	$-0.862498\pi$
$59$	−0.702793	+	1.21727i	−0.0914959	+	0.158475i	0.816645	+	0.577140i	$0.195831\pi$
$60$	−0.0384000	+	0.512412i	−0.00495742	+	0.0661521i
$61$	−6.38081	−	1.96822i	−0.816979	−	0.252005i	−0.142023	−	0.989863i	$-0.545361\pi$
$61$	−6.38081	−	1.96822i	−0.816979	−	0.252005i	−0.674955	+	0.737859i	$0.735837\pi$
$62$	−2.15824	−	2.00256i	−0.274097	−	0.254325i
$63$	1.25967	+	3.20960i	0.158704	+	0.404371i
$64$	2.41288	+	1.16198i	0.301610	+	0.145248i
$65$	−2.30399	+	10.0944i	−0.285774	+	1.25206i
$66$	0.0749921	−	0.0231320i	0.00923089	−	0.00284735i
$67$	9.48688	+	2.92632i	1.15901	+	0.357506i	0.813871	−	0.581046i	$-0.197356\pi$
$67$	9.48688	+	2.92632i	1.15901	+	0.357506i	0.345137	+	0.938552i	$0.387833\pi$
$68$	−0.802270	−	0.386353i	−0.0972895	−	0.0468522i
$69$	0.541706	+	0.369329i	0.0652138	+	0.0444620i
$70$	1.57237	+	1.45895i	0.187934	+	0.174377i
$71$	−5.80228	−	1.78977i	−0.688604	−	0.212406i	−0.0693449	−	0.997593i	$-0.522091\pi$
$71$	−5.80228	−	1.78977i	−0.688604	−	0.212406i	−0.619259	+	0.785186i	$0.712567\pi$
$72$	−5.57859			−0.657443
$73$	0.000648877	−	0.00865866i	7.59453e−5	−	0.00101342i	−0.997166	−	0.0752368i	$-0.976029\pi$
$73$	0.000648877	−	0.00865866i	7.59453e−5	−	0.00101342i	0.997242	+	0.0742234i	$0.0236478\pi$
$74$	−0.653661	+	1.66550i	−0.0759866	+	0.193611i
$75$	0.519678	+	0.482191i	0.0600072	+	0.0556786i
$76$	0.329391	−	4.39542i	0.0377838	−	0.504190i
$77$	−0.851678	+	2.17004i	−0.0970577	+	0.247299i
$78$	0.105797	+	0.0159463i	0.0119791	+	0.00180557i
$79$	−2.41088	−	3.02314i	−0.271245	−	0.340130i	0.627488	−	0.778626i	$-0.284083\pi$
$79$	−2.41088	−	3.02314i	−0.271245	−	0.340130i	−0.898733	+	0.438495i	$0.855512\pi$
$80$	8.72874	−	4.20354i	0.975903	−	0.469970i
$81$	−8.05929	+	3.88115i	−0.895477	+	0.431239i
$82$	−0.576858	−	0.393295i	−0.0637033	−	0.0434322i
$83$	6.02451	−	10.4348i	0.661276	−	1.14536i	−0.319005	−	0.947753i	$-0.603349\pi$
$83$	6.02451	−	10.4348i	0.661276	−	1.14536i	0.980281	−	0.197610i	$-0.0633180\pi$
$84$	−0.0983404	+	0.123315i	−0.0107298	+	0.0134548i
$85$	−1.71653	+	0.826638i	−0.186184	+	0.0896615i
$86$	−0.00299777	−	0.0400025i	−0.000323258	−	0.00431358i
$87$	−0.0845623	−	0.106038i	−0.00906603	−	0.0113684i
$88$	−2.76488	−	2.56543i	−0.294737	−	0.273476i
$89$	3.10489	−	13.6034i	0.329118	−	1.44196i	−0.491698	−	0.870766i	$-0.663624\pi$
$89$	3.10489	−	13.6034i	0.329118	−	1.44196i	0.820816	−	0.571193i	$-0.193519\pi$
$90$	−3.47668	+	4.35961i	−0.366474	+	0.459544i
$91$	−2.32976	+	2.16170i	−0.244225	+	0.226608i
$92$	1.10008	−	14.6795i	0.114691	−	1.53044i
$93$	−0.103074	−	0.451597i	−0.0106883	−	0.0468285i
$94$	3.99806	−	1.92536i	0.412368	−	0.198586i
$95$	−6.91325	−	6.41456i	−0.709285	−	0.658120i
$96$	−0.195582	−	0.338759i	−0.0199615	−	0.0345744i
$97$	0.0894676	+	1.19386i	0.00908406	+	0.121218i	0.999902	−	0.0139827i	$-0.00445099\pi$
$97$	0.0894676	+	1.19386i	0.00908406	+	0.121218i	−0.990818	+	0.135201i	$0.956832\pi$
$98$	−0.626727	−	2.74587i	−0.0633090	−	0.277375i
$99$	−5.79102	−	1.78629i	−0.582020	−	0.179529i
$100$	3.54192	−	15.5182i	0.354192	−	1.55182i
$101$	3.05888	+	13.4018i	0.304370	+	1.33353i	0.863457	+	0.504423i	$0.168295\pi$
$101$	3.05888	+	13.4018i	0.304370	+	1.33353i	−0.559087	+	0.829109i	$0.688848\pi$
$102$	0.00984360	+	0.0170496i	0.000974662	+	0.00168816i
$103$	−1.77159	+	0.853151i	−0.174560	+	0.0840635i	−0.519123	−	0.854700i	$-0.673741\pi$
$103$	−1.77159	+	0.853151i	−0.174560	+	0.0840635i	0.344563	+	0.938763i	$0.388027\pi$
$104$	−1.87862	−	4.78665i	−0.184214	−	0.469369i
$105$	0.0750939	+	0.329008i	0.00732842	+	0.0321079i
$106$	1.22094	+	2.11473i	0.118588	+	0.205400i
$107$	−17.0556			−1.64883			−0.824413	−	0.565988i	$-0.808495\pi$
$107$	−17.0556			−1.64883			−0.824413	+	0.565988i	$0.808495\pi$
$108$	−0.678258	−	0.462429i	−0.0652654	−	0.0444972i
$109$	−6.28192	+	5.82877i	−0.601699	+	0.558295i	−0.921101	−	0.389324i	$-0.872709\pi$
$109$	−6.28192	+	5.82877i	−0.601699	+	0.558295i	0.319402	+	0.947619i	$0.396518\pi$
$110$	−3.72798	+	0.561903i	−0.355449	+	0.0535753i
$111$	−0.232581	+	0.158571i	−0.0220756	+	0.0150509i
$112$	2.94057	+	0.443219i	0.277857	+	0.0418803i
$113$	16.9996	+	11.5901i	1.59919	+	1.09031i	0.941496	+	0.337025i	$0.109421\pi$
$113$	16.9996	+	11.5901i	1.59919	+	1.09031i	0.657694	+	0.753285i	$0.271532\pi$
$114$	−0.0607602	+	0.0761909i	−0.00569071	+	0.00713593i
$115$	−23.0884	−	21.4229i	−2.15300	−	1.99769i
$116$	−1.11254	+	2.83470i	−0.103297	+	0.263195i
$117$	−6.05655	−	5.61966i	−0.559929	−	0.519538i
$118$	−0.576507	−	0.393056i	−0.0530718	−	0.0361837i
$119$	−0.578271	−	0.0871603i	−0.0530100	−	0.00798997i
$120$	−0.539909	−	0.0813781i	−0.0492867	−	0.00742877i
$121$	3.45130	+	5.97782i	0.313754	+	0.543439i
$122$	1.21102	−	3.08563i	0.109641	−	0.279360i
$123$	−0.0401306	−	0.102251i	−0.00361846	−	0.00921967i
$124$	−7.62399	+	7.07403i	−0.684655	+	0.635267i
$125$	−9.53738	−	11.9595i	−0.853049	−	1.06969i
$126$	−1.63556	+	0.504503i	−0.145707	+	0.0449447i
$127$	0.941935	+	12.5692i	0.0835832	+	1.11534i	0.868484	+	0.495718i	$0.165095\pi$
$127$	0.941935	+	12.5692i	0.0835832	+	1.11534i	−0.784900	+	0.619622i	$0.787286\pi$
$128$	−5.67318	+	9.82624i	−0.501443	+	0.868525i
$129$	0.00315564	−	0.00546572i	0.000277838	−	0.000481230i
$130$	−4.91151	−	1.51500i	−0.430768	−	0.132874i
$131$	−3.94354	−	17.2778i	−0.344549	−	1.50957i	−0.789353	−	0.613939i	$-0.789584\pi$
$131$	−3.94354	−	17.2778i	−0.344549	−	1.50957i	0.444804	−	0.895628i	$-0.353273\pi$
$132$	−0.0616887	−	0.270276i	−0.00536931	−	0.0235245i
$133$	−0.644148	−	2.82220i	−0.0558547	−	0.244716i
$134$	−1.80053	+	4.58767i	−0.155542	+	0.396315i
$135$	−1.67836	+	0.517705i	−0.144450	+	0.0445569i
$136$	0.473090	−	0.819415i	0.0405671	−	0.0702643i
$137$	5.43641	−	0.819408i	0.464464	−	0.0700067i	0.0873585	−	0.996177i	$-0.472157\pi$
$137$	5.43641	−	0.819408i	0.464464	−	0.0700067i	0.377106	+	0.926170i	$0.376919\pi$
$138$	−0.202922	+	0.254456i	−0.0172739	+	0.0216608i
$139$	−4.31244	−	10.9879i	−0.365777	−	0.931984i	−0.988728	−	0.149723i	$-0.952162\pi$
$139$	−4.31244	−	10.9879i	−0.365777	−	0.931984i	0.622951	−	0.782261i	$-0.285933\pi$
$140$	5.55440	−	5.15373i	0.469433	−	0.435570i
$141$	0.690359	+	0.104055i	0.0581387	+	0.00876300i
$142$	1.10122	−	2.80587i	0.0924126	−	0.235464i
$143$	−0.417449	−	5.57047i	−0.0349088	−	0.465826i
$144$	−0.577722	+	7.70917i	−0.0481435	+	0.642431i
$145$	3.25775	+	5.64258i	0.270541	+	0.468591i
$146$	0.00426217		0.000642418i	0.000352739		5.31669e-5i
$147$	0.161890	−	0.412489i	0.0133524	−	0.0340215i
$148$	5.69438	+	2.74227i	0.468075	+	0.225413i
$149$	−10.3013	+	4.96082i	−0.843912	+	0.406407i	−0.805314	−	0.592848i	$-0.798003\pi$
$149$	−10.3013	+	4.96082i	−0.843912	+	0.406407i	−0.0385978	+	0.999255i	$0.512289\pi$
$150$	−0.257974	+	0.239365i	−0.0210635	+	0.0195441i
$151$	5.77676	+	2.78194i	0.470106	+	0.226391i	0.653911	−	0.756572i	$-0.273127\pi$
$151$	5.77676	+	2.78194i	0.470106	+	0.226391i	−0.183805	+	0.982963i	$0.558841\pi$
$152$	4.63128	+	0.698054i	0.375647	+	0.0566196i
$153$	0.113611	−	1.51603i	0.00918488	−	0.122564i
$154$	−1.04263	−	0.502102i	−0.0840172	−	0.0404606i
$155$	1.66293	+	22.1903i	0.133570	+	1.78237i
$156$	0.0841017	−	0.368473i	0.00673352	−	0.0295015i
$157$	−8.14767	+	5.55499i	−0.650255	+	0.443336i	−0.843001	−	0.537913i	$-0.819213\pi$
$157$	−8.14767	+	5.55499i	−0.650255	+	0.443336i	0.192746	+	0.981249i	$0.438261\pi$
$158$	1.58596	−	1.08129i	0.126173	−	0.0860230i
$159$	−0.0287100	+	0.383108i	−0.00227685	+	0.0303824i
$160$	6.86528	+	17.4924i	0.542748	+	1.38290i
$161$	−2.15128	−	9.42536i	−0.169544	−	0.742823i
$162$	−1.62229	−	4.13352i	−0.127459	−	0.324760i
$163$	−2.13985	−	5.45226i	−0.167606	−	0.427054i	0.822250	−	0.569127i	$-0.192719\pi$
$163$	−2.13985	−	5.45226i	−0.167606	−	0.427054i	−0.989856	+	0.142073i	$0.954623\pi$
$164$	−1.53771	+	1.92823i	−0.120075	+	0.150570i
$165$	−0.534411	−	0.257359i	−0.0416038	−	0.0200353i
$166$	4.94196	+	3.36937i	0.383570	+	0.261514i
$167$	−4.55820	−	5.71580i	−0.352724	−	0.442302i	0.573540	−	0.819178i	$-0.305570\pi$
$167$	−4.55820	−	5.71580i	−0.352724	−	0.442302i	−0.926264	+	0.376876i	$0.876998\pi$
$168$	−0.122857	−	0.113995i	−0.00947863	−	0.00879488i
$169$	−1.96712	+	5.01215i	−0.151317	+	0.385550i
$170$	−0.345527	−	0.880389i	−0.0265007	−	0.0675228i
$171$	7.19107	−	2.21815i	0.549915	−	0.169626i
$172$	−0.141705			−0.0108049
$173$	3.65166	+	4.57904i	0.277631	+	0.348138i	0.901023	−	0.433771i	$-0.142817\pi$
$173$	3.65166	+	4.57904i	0.277631	+	0.348138i	−0.623392	+	0.781909i	$0.714246\pi$
$174$	0.0556282	−	0.0379267i	0.00421716	−	0.00287521i
$175$	−0.781200	−	10.4244i	−0.0590531	−	0.788009i
$176$	−3.83156	+	3.55516i	−0.288814	+	0.267981i
$177$	−0.0401062	−	0.102189i	−0.00301457	−	0.00768099i
$178$	6.61883	+	2.04164i	0.496102	+	0.153027i
$179$	1.04101	−	4.56096i	0.0778086	−	0.340902i	−0.921008	−	0.389545i	$-0.872632\pi$
$179$	1.04101	−	4.56096i	0.0778086	−	0.340902i	0.998816	+	0.0486427i	$0.0154896\pi$
$180$	14.4395	+	13.3979i	1.07626	+	0.998620i
$181$	−2.98361	−	5.16777i	−0.221770	−	0.384117i	0.733575	−	0.679608i	$-0.237850\pi$
$181$	−2.98361	−	5.16777i	−0.221770	−	0.384117i	−0.955346	+	0.295491i	$0.904517\pi$
$182$	−0.983666	−	1.23348i	−0.0729142	−	0.0914315i
$183$	0.430897	−	0.293780i	0.0318528	−	0.0217169i
$184$	15.4672	+	2.33131i	1.14026	+	0.171866i
$185$	12.1837	−	5.86734i	0.895761	−	0.431376i
$186$	0.227375	−	0.0342713i	0.0166719	−	0.00251289i
$187$	0.753486	−	0.699133i	0.0551004	−	0.0511257i
$188$	−5.72691	−	14.5919i	−0.417678	−	1.06422i
$189$	−0.515171	−	0.158909i	−0.0374732	−	0.0115589i
$190$	3.43182	−	3.18426i	0.248970	−	0.231011i
$191$	4.56013	−	11.6190i	0.329960	−	0.840723i	−0.665575	−	0.746331i	$-0.731814\pi$
$191$	4.56013	−	11.6190i	0.329960	−	0.840723i	0.995535	−	0.0943927i	$-0.0300909\pi$
$192$	−0.188448	+	0.0907519i	−0.0136001	+	0.00654945i
$193$	−9.91095	+	3.05712i	−0.713406	+	0.220057i	−0.630152	−	0.776472i	$-0.717007\pi$
$193$	−9.91095	+	3.05712i	−0.713406	+	0.220057i	−0.0832538	+	0.996528i	$0.526531\pi$
$194$	−0.594309			−0.0426689
$195$	−0.504190	−	0.632234i	−0.0361058	−	0.0452752i
$196$	−9.83812	+	1.48286i	−0.702723	+	0.105918i
$197$	−6.31278			−0.449767			−0.224884	−	0.974386i	$-0.572200\pi$
$197$	−6.31278			−0.449767			−0.224884	+	0.974386i	$0.572200\pi$
$198$	1.09909	−	2.80043i	0.0781087	−	0.199018i
$199$	5.01207	+	8.68115i	0.355296	+	0.615391i	0.987169	−	0.159682i	$-0.0510468\pi$
$199$	5.01207	+	8.68115i	0.355296	+	0.615391i	−0.631873	+	0.775072i	$0.717713\pi$
$200$	16.1620	+	4.98531i	1.14282	+	0.352515i
$201$	−0.640650	+	0.436788i	−0.0451880	+	0.0308086i
$202$	−6.74769	+	1.01705i	−0.474766	+	0.0715595i
$203$	−0.149455	+	1.99434i	−0.0104897	+	0.139975i
$204$	0.0626580	−	0.0301745i	0.00438693	−	0.00211264i
$205$	1.17422	+	5.14458i	0.0820108	+	0.359313i
$206$	−0.356609	−	0.908626i	−0.0248462	−	0.0633070i
$207$	24.0162	−	7.40801i	1.66924	−	0.514892i
$208$	−6.80932	+	2.10040i	−0.472141	+	0.145636i
$209$	4.58412	+	2.20760i	0.317091	+	0.152703i
$210$	−0.165652	+	0.0249681i	−0.0114311	+	0.00172296i
$211$	−13.0462	+	12.1051i	−0.898135	+	0.833348i	−0.986671	−	0.162725i	$-0.947972\pi$
$211$	−13.0462	+	12.1051i	−0.898135	+	0.833348i	0.0885362	+	0.996073i	$0.471781\pi$
$212$	7.77170	−	3.74265i	0.533762	−	0.257046i
$213$	0.391829	−	0.267144i	0.0268477	−	0.0183044i
$214$	0.632709	−	8.44292i	0.0432511	−	0.577146i
$215$	−0.189037	+	0.237044i	−0.0128922	+	0.0161663i
$216$	0.543853	−	0.681970i	0.0370045	−	0.0464022i
$217$	−3.41520	+	5.91530i	−0.231839	+	0.401557i
$218$	−2.65234	−	3.32593i	−0.179639	−	0.225260i
$219$	0.000497115	0	0.000461255i	3.35919e−5	0	3.11688e-5i
$220$	0.995245	+	13.2806i	0.0670994	+	0.895379i
$221$	1.33907	−	0.413049i	0.0900757	−	0.0277847i
$222$	−0.0698683	−	0.121015i	−0.00468925	−	0.00812202i
$223$	−23.1383	+	7.13723i	−1.54946	+	0.477944i	−0.947277	−	0.320416i	$-0.896177\pi$
$223$	−23.1383	+	7.13723i	−1.54946	+	0.477944i	−0.602180	+	0.798360i	$0.705701\pi$
$224$	−1.28351	+	5.62341i	−0.0857578	+	0.375730i
$225$	26.8722	−	4.05033i	1.79148	−	0.270022i
$226$	−6.36803	+	7.98526i	−0.423595	+	0.531171i
$227$	25.3190	−	7.80989i	1.68048	−	0.518360i	0.699863	−	0.714277i	$-0.253245\pi$
$227$	25.3190	−	7.80989i	1.68048	−	0.518360i	0.980620	+	0.195917i	$0.0627683\pi$
$228$	0.252352	+	0.234149i	0.0167124	+	0.0155069i
$229$	−1.95044	−	0.293981i	−0.128889	−	0.0194268i	0.0842811	−	0.996442i	$-0.473141\pi$
$229$	−1.95044	−	0.293981i	−0.128889	−	0.0194268i	−0.213170	+	0.977015i	$0.568379\pi$
$230$	11.4613	−	10.6346i	0.755738	−	0.701222i
$231$	−0.0910338	−	0.157675i	−0.00598958	−	0.0103743i
$232$	−2.91534	−	1.40395i	−0.191401	−	0.0921740i
$233$	−7.70819	−	13.3510i	−0.504980	−	0.874652i	−0.999983	−	0.00576039i	$-0.998166\pi$
$233$	−7.70819	−	13.3510i	−0.504980	−	0.874652i	0.495003	−	0.868891i	$-0.335167\pi$
$234$	3.00654	−	2.78966i	0.196544	−	0.182366i
$235$	−32.0491	−	9.88585i	−2.09066	−	0.644882i
$236$	−1.53678	+	1.92706i	−0.100036	+	0.125441i
$237$	0.301996			0.0196168
$238$	0.0645984	−	0.283024i	0.00418729	−	0.0183457i
$239$	−9.42706	+	16.3281i	−0.609786	+	1.05618i	0.381490	+	0.924373i	$0.375411\pi$
$239$	−9.42706	+	16.3281i	−0.609786	+	1.05618i	−0.991275	+	0.131807i	$0.957922\pi$
$240$	−0.168371	+	0.737683i	−0.0108683	+	0.0476172i
$241$	6.51016	+	0.981248i	0.419356	+	0.0632078i	0.355331	−	0.934741i	$-0.384368\pi$
$241$	6.51016	+	0.981248i	0.419356	+	0.0632078i	0.0640251	+	0.997948i	$0.479606\pi$
$242$	−3.08720	+	1.48672i	−0.198452	+	0.0955697i
$243$	0.467963	−	2.05028i	0.0300199	−	0.131526i
$244$	−10.5498	−	5.08054i	−0.675385	−	0.325248i
$245$	−10.6437	+	18.4354i	−0.679999	+	1.17779i
$246$	0.0521054	−	0.0160724i	0.00332212	−	0.00102474i
$247$	4.32489	+	5.42324i	0.275186	+	0.345073i
$248$	−6.89033	−	8.64020i	−0.437536	−	0.548653i
$249$	0.343800	+	0.875988i	0.0217874	+	0.0555135i
$250$	6.27404	−	4.27757i	0.396805	−	0.270537i
$251$	9.06017	−	15.6927i	0.571873	−	0.990513i	−0.424501	−	0.905428i	$-0.639550\pi$
$251$	9.06017	−	15.6927i	0.571873	−	0.990513i	0.996374	−	0.0850854i	$-0.0271163\pi$
$252$	1.34541	+	5.89464i	0.0847530	+	0.371327i
$253$	15.3097	+	7.37277i	0.962513	+	0.463522i
$254$	−6.25701			−0.392600
$255$	0.0331107	−	0.145067i	0.00207347	−	0.00908448i
$256$	−0.228263	−	0.155627i	−0.0142664	−	0.00972668i
$257$	15.8870	−	7.65079i	0.991006	−	0.477243i	0.133129	−	0.991099i	$-0.457498\pi$
$257$	15.8870	−	7.65079i	0.991006	−	0.477243i	0.857877	+	0.513855i	$0.171783\pi$
$258$	0.00258860	+	0.00176487i	0.000161159	+	0.000109876i
$259$	4.10447	+	0.618649i	0.255039	+	0.0384410i
$260$	−6.63334	+	16.9015i	−0.411382	+	1.04818i
$261$	−5.19911			−0.321817
$262$	8.69920	−	1.31119i	0.537439	−	0.0810058i
$263$	−6.69131	−	3.22236i	−0.412604	−	0.198699i	0.216054	−	0.976381i	$-0.430681\pi$
$263$	−6.69131	−	3.22236i	−0.412604	−	0.198699i	−0.628658	+	0.777682i	$0.716395\pi$
$264$	0.291286	−	0.0439042i	0.0179274	−	0.00270212i
$265$	4.10684	−	17.9932i	0.252281	−	1.10532i
$266$	1.42095	−	0.214174i	0.0871241	−	0.0131318i
$267$	0.679454	+	0.852009i	0.0415819	+	0.0521421i
$268$	15.6853	+	7.55366i	0.958135	+	0.461413i
$269$	16.7830	−	5.17686i	1.02328	−	0.315639i	0.262693	−	0.964880i	$-0.415389\pi$
$269$	16.7830	−	5.17686i	1.02328	−	0.315639i	0.760583	+	0.649241i	$0.224913\pi$
$270$	−0.194014	−	0.850032i	−0.0118073	−	0.0517313i
$271$	5.58583	+	5.18290i	0.339315	+	0.314839i	0.831363	−	0.555730i	$-0.187561\pi$
$271$	5.58583	+	5.18290i	0.339315	+	0.314839i	−0.492048	+	0.870568i	$0.663752\pi$
$272$	−1.08337	−	0.738631i	−0.0656892	−	0.0447861i
$273$	−0.0185493	−	0.247523i	−0.00112265	−	0.0149808i
$274$	0.203952	+	2.72155i	0.0123212	+	0.164415i
$275$	15.1811	+	10.3503i	0.915456	+	0.624147i
$276$	0.842787	+	0.781992i	0.0507298	+	0.0470704i
$277$	6.83438	+	29.9434i	0.410638	+	1.79912i	0.581183	+	0.813773i	$0.302590\pi$
$277$	6.83438	+	29.9434i	0.410638	+	1.79912i	−0.170545	+	0.985350i	$0.554553\pi$
$278$	5.59926	−	1.72714i	0.335821	−	0.103587i
$279$	−15.9982	−	7.70431i	−0.957786	−	0.461245i
$280$	5.01990	+	6.29475i	0.299996	+	0.376183i
$281$	29.8852	−	4.50447i	1.78280	−	0.268714i	0.826890	−	0.562364i	$-0.190108\pi$
$281$	29.8852	−	4.50447i	1.78280	−	0.268714i	0.955913	+	0.293650i	$0.0948700\pi$
$282$	−0.0771197	+	0.337884i	−0.00459241	+	0.0201207i
$283$	1.09518	−	0.165072i	0.0651018	−	0.00981251i	−0.116411	−	0.993201i	$-0.537139\pi$
$283$	1.09518	−	0.165072i	0.0651018	−	0.00981251i	0.181512	+	0.983389i	$0.441901\pi$
$284$	−9.59333	−	4.61990i	−0.569259	−	0.274141i
$285$	0.728325	−	0.109777i	0.0431423	−	0.00650265i
$286$	2.77300			0.163971
$287$	−0.591756	+	1.50777i	−0.0349303	+	0.0890009i
$288$	−14.8274	−	2.23486i	−0.873710	−	0.131691i
$289$	−13.8330	−	9.43119i	−0.813707	−	0.554776i
$290$	−2.91406	+	1.40334i	−0.171120	+	0.0824069i
$291$	−0.0772559	−	0.0526722i	−0.00452882	−	0.00308770i
$292$	0.00338814	−	0.0148444i	0.000198276	−	0.000868705i
$293$	−9.27337			−0.541756			−0.270878	−	0.962614i	$-0.587314\pi$
$293$	−9.27337			−0.541756			−0.270878	+	0.962614i	$0.587314\pi$
$294$	0.198186	+	0.0954413i	0.0115584	+	0.00556625i
$295$	1.17350	+	5.14145i	0.0683239	+	0.299347i
$296$	−3.35791	+	5.81608i	−0.195175	+	0.338053i
$297$	0.782934	−	0.533795i	0.0454304	−	0.0309739i
$298$	−2.07358	−	5.28340i	−0.120119	−	0.306059i
$299$	14.4439	+	18.1121i	0.835315	+	1.04745i
$300$	0.775092	+	0.971935i	0.0447500	+	0.0561147i
$301$	−0.0889299	+	0.0274312i	−0.00512583	+	0.00158111i
$302$	−1.59143	+	2.75643i	−0.0915762	+	0.158615i
$303$	−0.967290	−	0.465822i	−0.0555694	−	0.0267608i
$304$	1.44427	−	6.32777i	0.0828348	−	0.362923i
$305$	−22.5724	+	10.8703i	−1.29249	+	0.622430i
$306$	0.746256	+	0.112480i	0.0426606	+	0.00643005i
$307$	−0.736210	+	3.22555i	−0.0420177	+	0.184092i	−0.991582	−	0.129481i	$-0.958669\pi$
$307$	−0.736210	+	3.22555i	−0.0420177	+	0.184092i	0.949564	+	0.313573i	$0.101526\pi$
$308$	−2.04396	+	3.54024i	−0.116465	+	0.201724i
$309$	0.0341727	−	0.149720i	0.00194402	−	0.00851729i
$310$	−11.0464			−0.627393
$311$	−14.0036	+	17.5599i	−0.794070	+	0.995733i	0.205783	+	0.978598i	$0.434026\pi$
$311$	−14.0036	+	17.5599i	−0.794070	+	0.995733i	−0.999853	+	0.0171350i	$0.994545\pi$
$312$	0.383760	+	0.118374i	0.0217261	+	0.00670163i
$313$	24.3123	−	22.5585i	1.37421	−	1.27508i	0.450093	−	0.892982i	$-0.351391\pi$
$313$	24.3123	−	22.5585i	1.37421	−	1.27508i	0.924120	−	0.382102i	$-0.124800\pi$
$314$	−2.44760	−	4.23936i	−0.138126	−	0.239241i
$315$	11.6554	+	5.61292i	0.656705	+	0.316252i
$316$	−3.39032	−	5.87220i	−0.190720	−	0.330337i
$317$	−0.242941	+	0.225417i	−0.0136450	+	0.0126607i	−0.686966	−	0.726690i	$-0.741058\pi$
$317$	−0.242941	+	0.225417i	−0.0136450	+	0.0126607i	0.673321	+	0.739350i	$0.264867\pi$
$318$	−0.188582	−	0.0284242i	−0.0105752	−	0.00159395i
$319$	−2.57680	−	2.39092i	−0.144273	−	0.133866i
$320$	9.60165	−	2.96172i	0.536749	−	0.165565i
$321$	0.830523	−	1.04144i	0.0463553	−	0.0581277i
$322$	4.74558	−	0.715281i	0.264461	−	0.0398611i
$323$	−0.284020	+	1.24437i	−0.0158033	+	0.0692389i
$324$	−14.9891	+	4.62352i	−0.832727	+	0.256862i
$325$	12.5247	+	21.6934i	0.694745	+	1.20333i
$326$	2.77838	−	0.857016i	0.153880	−	0.0474657i
$327$	−0.0500160	−	0.667417i	−0.00276589	−	0.0369083i
$328$	−1.92107	−	1.78249i	−0.106073	−	0.0984217i
$329$	−6.41873	−	8.04883i	−0.353876	−	0.443747i
$330$	0.147224	−	0.254999i	0.00810439	−	0.0140372i
$331$	−8.89936	+	11.1594i	−0.489153	+	0.613378i	−0.963744	−	0.266828i	$-0.914024\pi$
$331$	−8.89936	+	11.1594i	−0.489153	+	0.613378i	0.474591	+	0.880206i	$0.342596\pi$
$332$	13.1736	−	16.5192i	0.722997	−	0.906610i
$333$	−0.806390	+	10.7605i	−0.0441899	+	0.589674i
$334$	2.99855	−	2.04438i	0.164074	−	0.111863i
$335$	33.5602	−	16.1618i	1.83359	−	0.883012i
$336$	−0.170255	+	0.157973i	−0.00928816	+	0.00861815i
$337$	10.8239	−	1.63143i	0.589613	−	0.0888699i	0.152542	−	0.988297i	$-0.451254\pi$
$337$	10.8239	−	1.63143i	0.589613	−	0.0888699i	0.437071	+	0.899427i	$0.356016\pi$
$338$	−2.40816	−	1.15971i	−0.130986	−	0.0630798i
$339$	−1.53551	+	0.473643i	−0.0833976	+	0.0257247i
$340$	−3.19249	+	0.984754i	−0.173137	+	0.0534058i
$341$	−4.38608	−	11.1755i	−0.237519	−	0.605189i
$342$	0.831271	+	3.64203i	0.0449500	+	0.196939i
$343$	−13.1503	+	6.33285i	−0.710049	+	0.341942i
$344$	0.0112524	−	0.150152i	0.000606687	−	0.00809567i
$345$	2.43241	−	0.366626i	0.130956	−	0.0197385i
$346$	−2.40220	+	1.63779i	−0.129143	+	0.0880481i
$347$	−2.67705	−	0.825759i	−0.143711	−	0.0443291i	0.222065	−	0.975032i	$-0.428720\pi$
$347$	−2.67705	−	0.825759i	−0.143711	−	0.0443291i	−0.365776	+	0.930703i	$0.619196\pi$
$348$	−0.118916	−	0.205969i	−0.00637459	−	0.0110411i
$349$	−10.2840	+	26.2032i	−0.550491	+	1.40263i	0.336870	+	0.941551i	$0.390632\pi$
$349$	−10.2840	+	26.2032i	−0.550491	+	1.40263i	−0.887361	+	0.461076i	$0.847463\pi$
$350$	5.18930			0.277380
$351$	1.27744	−	0.192543i	0.0681847	−	0.0102772i
$352$	−6.32103	−	7.92632i	−0.336912	−	0.422474i
$353$	19.6617			1.04649			0.523243	−	0.852183i	$-0.324722\pi$
$353$	19.6617			1.04649			0.523243	+	0.852183i	$0.324722\pi$
$354$	0.0520737	−	0.0160626i	0.00276769	−	0.000853719i
$355$	−20.5258	+	9.88471i	−1.08940	+	0.524626i
$356$	8.93919	−	22.7767i	0.473776	−	1.20716i
$357$	0.0334811	−	0.0310659i	0.00177201	−	0.00164418i
$358$	2.21916	+	0.684521i	0.117286	+	0.0361781i
$359$	11.9463	+	30.4386i	0.630499	+	1.60649i	0.785704	+	0.618603i	$0.212301\pi$
$359$	11.9463	+	30.4386i	0.630499	+	1.60649i	−0.155205	+	0.987882i	$0.549604\pi$
$360$	−15.3432	+	14.2364i	−0.808655	+	0.750322i
$361$	12.5403	−	1.89014i	0.660015	−	0.0994812i
$362$	2.66885	−	1.28525i	0.140272	−	0.0675513i
$363$	−0.533077	−	0.0803485i	−0.0279793	−	0.00421720i
$364$	−4.60475	+	3.13947i	−0.241355	+	0.164553i
$365$	−0.0203119	−	0.0254704i	−0.00106318	−	0.00133318i
$366$	0.129443	+	0.224202i	0.00676611	+	0.0117192i
$367$	5.30078	+	4.91840i	0.276698	+	0.256738i	0.806298	−	0.591509i	$-0.201468\pi$
$367$	5.30078	+	4.91840i	0.276698	+	0.256738i	−0.529600	+	0.848247i	$0.677658\pi$
$368$	4.82347	−	21.1330i	0.251441	−	1.10163i
$369$	−4.02367	−	1.24114i	−0.209464	−	0.0646111i
$370$	2.45250	+	6.24886i	0.127499	+	0.324863i
$371$	4.15278	−	3.85322i	0.215602	−	0.200049i
$372$	−0.0607014	−	0.810004i	−0.00314722	−	0.0419968i
$373$	24.2772	−	16.5519i	1.25702	−	0.857025i	0.262853	−	0.964836i	$-0.415336\pi$
$373$	24.2772	−	16.5519i	1.25702	−	0.857025i	0.994171	+	0.107811i	$0.0343840\pi$
$374$	0.318135	+	0.398929i	0.0164504	+	0.0206281i
$375$	1.19469			0.0616935
$376$	15.9165	−	4.90959i	0.820832	−	0.253193i
$377$	−1.75083	−	4.46104i	−0.0901723	−	0.229755i
$378$	0.0977751	−	0.249127i	0.00502901	−	0.0128137i
$379$	16.8329	+	15.6186i	0.864647	+	0.802275i	0.981617	−	0.190860i	$-0.0611278\pi$
$379$	16.8329	+	15.6186i	0.864647	+	0.802275i	−0.116970	+	0.993135i	$0.537318\pi$
$380$	−10.3110	−	12.9296i	−0.528944	−	0.663275i
$381$	−0.813367	−	0.554544i	−0.0416700	−	0.0284102i
$382$	5.58252	+	2.68840i	0.285627	+	0.137551i
$383$	−6.81387	+	8.54432i	−0.348172	+	0.436594i	−0.924824	−	0.380396i	$-0.875788\pi$
$383$	−6.81387	+	8.54432i	−0.348172	+	0.436594i	0.576651	+	0.816990i	$0.304359\pi$
$384$	−0.323751	−	0.824903i	−0.0165213	−	0.0420957i
$385$	3.19544	+	8.14185i	0.162855	+	0.414947i
$386$	−1.14568	−	5.01956i	−0.0583137	−	0.255489i
$387$	−0.0883887	−	0.225211i	−0.00449305	−	0.0114481i
$388$	−0.156888	+	2.09353i	−0.00796479	+	0.106283i
$389$	−23.8303	+	16.2472i	−1.20824	+	0.823766i	−0.988415	−	0.151773i	$-0.951502\pi$
$389$	−23.8303	+	16.2472i	−1.20824	+	0.823766i	−0.219827	+	0.975539i	$0.570549\pi$
$390$	0.331675	−	0.226132i	0.0167950	−	0.0114506i
$391$	−0.948550	+	4.15587i	−0.0479702	+	0.210171i
$392$	−0.790038	−	10.5423i	−0.0399030	−	0.532468i
$393$	1.24704	+	0.600544i	0.0629049	+	0.0302934i
$394$	0.234185	−	3.12498i	0.0117981	−	0.157434i
$395$	−14.3458	−	2.16227i	−0.721813	−	0.108796i
$396$	−9.57472	−	4.61094i	−0.481148	−	0.231708i
$397$	28.1242	−	26.0955i	1.41151	−	1.30969i	0.521881	−	0.853019i	$-0.325231\pi$
$397$	28.1242	−	26.0955i	1.41151	−	1.30969i	0.889634	−	0.456675i	$-0.150960\pi$
$398$	−4.48331	+	2.15905i	−0.224728	+	0.108223i
$399$	0.203695	+	0.0980944i	0.0101975	+	0.00491086i
$400$	8.56305	−	21.8183i	0.428153	−	1.09091i
$401$	4.73269	+	0.713338i	0.236339	+	0.0356224i	0.266144	−	0.963933i	$-0.414250\pi$
$401$	4.73269	+	0.713338i	0.236339	+	0.0356224i	−0.0298047	+	0.999556i	$0.509489\pi$
$402$	−0.192454	−	0.333340i	−0.00959874	−	0.0166255i
$403$	1.22313	−	16.3215i	0.0609284	−	0.813033i
$404$	1.80141	+	24.0381i	0.0896233	+	1.19594i
$405$	−12.2614	+	31.2416i	−0.609275	+	1.55241i
$406$	−0.981699	−	0.147967i	−0.0487209	−	0.00734350i
$407$	−5.34812	+	4.96233i	−0.265097	+	0.245974i
$408$	0.0269977	+	0.0687891i	0.00133659	+	0.00340557i
$409$	−10.3692	+	13.0025i	−0.512722	+	0.642933i	−0.969046	−	0.246881i	$-0.920594\pi$
$409$	−10.3692	+	13.0025i	−0.512722	+	0.642933i	0.456324	+	0.889814i	$0.349166\pi$
$410$	−2.59025	+	0.390417i	−0.127923	+	0.0192813i
$411$	−0.214692	+	0.371858i	−0.0105900	+	0.0183424i
$412$	−3.29489	+	1.01634i	−0.162328	+	0.0500714i
$413$	−0.591396	+	1.50685i	−0.0291007	+	0.0741474i
$414$	2.77621	+	12.1634i	0.136443	+	0.597798i
$415$	−10.0595	−	44.0737i	−0.493803	−	2.16349i
$416$	−3.07559	−	13.4750i	−0.150793	−	0.660669i
$417$	0.880936	+	0.271733i	0.0431396	+	0.0133068i
$418$	−1.26287	+	2.18735i	−0.0617690	+	0.106987i
$419$	1.61228	−	2.79255i	0.0787649	−	0.136425i	−0.823952	−	0.566659i	$-0.808236\pi$
$419$	1.61228	−	2.79255i	0.0787649	−	0.136425i	0.902717	+	0.430234i	$0.141569\pi$
$420$	0.0442236	+	0.590123i	0.00215789	+	0.0287950i
$421$	8.30399	−	2.56144i	0.404712	−	0.124837i	−0.0857145	−	0.996320i	$-0.527317\pi$
$421$	8.30399	−	2.56144i	0.404712	−	0.124837i	0.490426	+	0.871483i	$0.336841\pi$
$422$	−5.50832	−	6.90722i	−0.268141	−	0.336238i
$423$	19.6187	−	18.2034i	0.953891	−	0.885082i
$424$	3.34863	+	8.53217i	0.162624	+	0.414359i
$425$	−1.68395	+	4.29063i	−0.0816835	+	0.208126i
$426$	0.117707	+	0.203875i	0.00570293	+	0.00987776i
$427$	−7.60425	−	1.14616i	−0.367996	−	0.0554664i
$428$	−29.5742	−	4.45760i	−1.42952	−	0.215466i
$429$	0.360470	+	0.245764i	0.0174037	+	0.0118656i
$430$	−0.110330	−	0.102371i	−0.00532058	−	0.00493678i
$431$	10.0990	−	25.7319i	0.486453	−	1.23946i	−0.451366	−	0.892339i	$-0.649063\pi$
$431$	10.0990	−	25.7319i	0.486453	−	1.23946i	0.937819	−	0.347124i	$-0.112842\pi$
$432$	−0.886107	−	0.822187i	−0.0426328	−	0.0395575i
$433$	6.77261	−	8.49259i	0.325471	−	0.408128i	−0.591995	−	0.805942i	$-0.701660\pi$
$433$	6.77261	−	8.49259i	0.325471	−	0.408128i	0.917466	+	0.397814i	$0.130231\pi$
$434$	−2.80152	−	1.91004i	−0.134477	−	0.0916850i
$435$	−0.503182	−	0.0758425i	−0.0241257	−	0.00363637i
$436$	−12.4162	+	8.46521i	−0.594627	+	0.405410i
$437$	−20.8649	+	3.14488i	−0.998105	+	0.150440i
$438$	−0.000246774	0	0.000228973i	−1.17913e−5	0	1.09407e-5i
$439$	14.3937	+	9.81344i	0.686972	+	0.468370i	0.855821	−	0.517272i	$-0.173053\pi$
$439$	14.3937	+	9.81344i	0.686972	+	0.468370i	−0.168849	+	0.985642i	$0.554005\pi$
$440$	−14.1513			−0.674638
$441$	−8.49323	−	14.7107i	−0.404439	−	0.700510i
$442$	0.154794	+	0.678195i	0.00736278	+	0.0322584i
$443$	0.119762	+	0.305149i	0.00569007	+	0.0144981i	0.933691	−	0.358081i	$-0.116569\pi$
$443$	0.119762	+	0.305149i	0.00569007	+	0.0144981i	−0.928000	+	0.372579i	$0.878474\pi$
$444$	−0.444736	+	0.214174i	−0.0211062	+	0.0101642i
$445$	−26.1758	−	45.3379i	−1.24085	−	2.14922i
$446$	−2.67474	−	11.7188i	−0.126652	−	0.554901i
$447$	0.198704	−	0.870580i	0.00939839	−	0.0411770i
$448$	2.94722	+	0.909098i	0.139243	+	0.0429508i
$449$	−4.00343	−	17.5402i	−0.188934	−	0.827772i	−0.977180	−	0.212413i	$-0.931868\pi$
$449$	−4.00343	−	17.5402i	−0.188934	−	0.827772i	0.788246	−	0.615360i	$-0.210989\pi$
$450$	1.00813	+	13.4526i	0.0475239	+	0.634163i
$451$	−1.42346	−	2.46551i	−0.0670282	−	0.116096i
$452$	26.4480	+	24.5402i	1.24401	+	1.15427i
$453$	−0.451170	+	0.217272i	−0.0211978	+	0.0102083i
$454$	2.92682	+	12.8232i	0.137362	+	0.601824i
$455$	−0.891102	+	11.8909i	−0.0417755	+	0.557455i
$456$	−0.268145	+	0.248802i	−0.0125570	+	0.0116512i
$457$	9.91710	−	12.4357i	0.463902	−	0.581715i	−0.493764	−	0.869596i	$-0.664379\pi$
$457$	9.91710	−	12.4357i	0.463902	−	0.581715i	0.957666	+	0.287881i	$0.0929507\pi$
$458$	0.217883	−	0.954607i	0.0101810	−	0.0446058i
$459$	0.174255	+	0.161685i	0.00813355	+	0.00754683i
$460$	−34.4360	−	43.1813i	−1.60558	−	2.01334i
$461$	2.43894	+	32.5454i	0.113593	+	1.51579i	0.704878	+	0.709328i	$0.251002\pi$
$461$	2.43894	+	32.5454i	0.113593	+	1.51579i	−0.591285	+	0.806462i	$0.701379\pi$
$462$	0.0814300	−	0.0392146i	0.00378847	−	0.00182443i
$463$	25.3489	−	31.7865i	1.17806	−	1.47724i	0.332713	−	0.943028i	$-0.392036\pi$
$463$	25.3489	−	31.7865i	1.17806	−	1.47724i	0.845349	−	0.534215i	$-0.179393\pi$
$464$	−2.24206	+	3.88337i	−0.104085	+	0.180281i
$465$	−1.43595	−	0.979016i	−0.0665907	−	0.0454008i
$466$	6.89500	−	3.32046i	0.319405	−	0.153817i
$467$	−36.3415	+	17.5011i	−1.68168	+	0.809856i	−0.684994	+	0.728549i	$0.740195\pi$
$467$	−36.3415	+	17.5011i	−1.68168	+	0.809856i	−0.996689	+	0.0813066i	$0.974091\pi$
$468$	−9.03326	−	11.3274i	−0.417563	−	0.523607i
$469$	11.3059	+	1.70409i	0.522057	+	0.0786875i
$470$	6.08265	−	15.4983i	0.280572	−	0.714885i
$471$	0.0575545	−	0.768011i	0.00265197	−	0.0353881i
$472$	−1.91990	−	1.78141i	−0.0883707	−	0.0819960i
$473$	0.0597605	−	0.152267i	0.00274779	−	0.00700125i
$474$	−0.0112031	+	0.149495i	−0.000514576	+	0.00686654i
$475$	−22.8158			−1.04686
$476$	−0.979935	−	0.302270i	−0.0449153	−	0.0138545i
$477$	10.7958	+	10.0170i	0.494304	+	0.458647i
$478$	−7.73310	−	5.27234i	−0.353704	−	0.241151i
$479$	26.0756	+	12.5573i	1.19142	+	0.573760i	0.921220	−	0.389043i	$-0.127194\pi$
$479$	26.0756	+	12.5573i	1.19142	+	0.573760i	0.270205	+	0.962803i	$0.412909\pi$
$480$	−1.40242	−	0.432590i	−0.0640116	−	0.0197450i
$481$	−9.50451	+	2.93175i	−0.433368	+	0.133676i
$482$	−0.727248	+	3.18628i	−0.0331252	+	0.145131i
$483$	0.680285	+	0.327608i	0.0309540	+	0.0149067i
$484$	4.42217	+	11.2675i	0.201008	+	0.512159i
$485$	3.29276	+	3.05524i	0.149517	+	0.138731i
$486$	0.997578	+	0.307712i	0.0452510	+	0.0139581i
$487$	−0.400598	+	5.34561i	−0.0181528	+	0.242233i	0.980745	+	0.195293i	$0.0625659\pi$
$487$	−0.400598	+	5.34561i	−0.0181528	+	0.242233i	−0.998898	+	0.0469396i	$0.985053\pi$
$488$	6.22112	−	10.7753i	0.281617	−	0.487775i
$489$	0.437124	+	0.134835i	0.0197675	+	0.00609745i
$490$	−8.73109	−	5.95276i	−0.394431	−	0.268918i
$491$	2.10252	−	28.0562i	0.0948856	−	1.26616i	−0.723028	−	0.690819i	$-0.757250\pi$
$491$	2.10252	−	28.0562i	0.0948856	−	1.26616i	0.817913	−	0.575341i	$-0.195131\pi$
$492$	−0.0428620	−	0.187791i	−0.00193237	−	0.00846626i
$493$	0.440908	−	0.763676i	0.0198575	−	0.0343942i
$494$	−2.84507	+	1.93974i	−0.128006	+	0.0872729i
$495$	−20.4860	+	9.86553i	−0.920777	+	0.443423i
$496$	−12.6536	+	8.62710i	−0.568165	+	0.387368i
$497$	−6.91480	−	1.04224i	−0.310171	−	0.0467508i
$498$	−0.446389	+	0.137693i	−0.0200031	+	0.00617015i
$499$	−12.7360	+	8.68329i	−0.570144	+	0.388717i	−0.813801	−	0.581144i	$-0.802605\pi$
$499$	−12.7360	+	8.68329i	−0.570144	+	0.388717i	0.243657	+	0.969861i	$0.421653\pi$
$500$	−13.4120	−	23.2303i	−0.599804	−	1.03889i
$501$	0.570979			0.0255094
$502$	7.43214	+	5.06715i	0.331713	+	0.226158i
$503$	6.39683	−	8.02137i	0.285220	−	0.357655i	−0.618495	−	0.785789i	$-0.712257\pi$
$503$	6.39683	−	8.02137i	0.285220	−	0.357655i	0.903715	+	0.428134i	$0.140829\pi$
$504$	−6.35286	+	0.957539i	−0.282979	+	0.0426522i
$505$	42.6140	+	29.0538i	1.89630	+	1.29287i
$506$	−4.21764	+	7.30516i	−0.187497	+	0.324754i
$507$	−0.210261	−	0.364183i	−0.00933802	−	0.0161739i
$508$	−1.65175	+	22.0411i	−0.0732847	+	0.977916i
$509$	−35.6937			−1.58210			−0.791049	−	0.611753i	$-0.790465\pi$
$509$	−35.6937			−1.58210			−0.791049	+	0.611753i	$0.790465\pi$
$510$	0.0705835	+	0.0217721i	0.00312549	+	0.000964086i
$511$	−0.000747282	−	0.00997179i	−3.30578e−5	−	0.000441126i
$512$	−14.0632	+	17.6347i	−0.621510	+	0.779349i
$513$	−0.429889	+	1.09534i	−0.0189800	+	0.0483604i
$514$	3.19796	+	8.14828i	0.141056	+	0.359405i
$515$	−2.69530	+	6.86750i	−0.118769	+	0.302618i
$516$	0.00690034	−	0.00865276i	0.000303771	−	0.000380916i
$517$	18.0947			0.795804
$518$	−0.458509	+	2.00886i	−0.0201457	+	0.0882642i
$519$	−0.457422			−0.0200786
$520$	−17.3822	−	8.37085i	−0.762262	−	0.367086i
$521$	−0.786523	−	1.36230i	−0.0344582	−	0.0596834i	0.848282	−	0.529545i	$-0.177637\pi$
$521$	−0.786523	−	1.36230i	−0.0344582	−	0.0596834i	−0.882740	+	0.469861i	$0.844304\pi$
$522$	0.192871	−	2.57368i	0.00844173	−	0.112647i
$523$	4.77990	+	5.99380i	0.209010	+	0.262091i	0.875276	−	0.483624i	$-0.160680\pi$
$523$	4.77990	+	5.99380i	0.209010	+	0.262091i	−0.666266	+	0.745715i	$0.732108\pi$
$524$	−2.32239	−	30.9902i	−0.101454	−	1.35381i
$525$	0.674571	+	0.459915i	0.0294407	+	0.0200723i
$526$	1.84337	−	3.19282i	0.0803749	−	0.139213i
$527$	2.48837	−	1.69654i	0.108395	−	0.0739026i
$528$	−0.0305065	−	0.407080i	−0.00132762	−	0.0177159i
$529$	−46.9400	+	7.07507i	−2.04087	+	0.307612i
$530$	8.75473	+	2.70048i	0.380281	+	0.117301i
$531$	−4.02123	−	1.24038i	−0.174506	−	0.0538281i
$532$	−0.379346	−	5.06201i	−0.0164467	−	0.219466i
$533$	−0.290049	−	3.87043i	−0.0125634	−	0.167647i
$534$	−0.446970	+	0.304739i	−0.0193423	+	0.0131873i
$535$	−46.9091	+	43.5253i	−2.02806	+	1.88176i
$536$	−9.24947	+	16.0206i	−0.399516	+	0.691983i
$537$	0.227808	+	0.285662i	0.00983063	+	0.0123272i
$538$	1.94007	+	8.50001i	0.0836424	+	0.366461i
$539$	2.55559	−	11.1968i	0.110077	−	0.482279i
$540$	−3.04556	+	0.459044i	−0.131060	+	0.0197541i
$541$	8.28867	+	7.69076i	0.356358	+	0.330652i	0.837953	−	0.545742i	$-0.183752\pi$
$541$	8.28867	+	7.69076i	0.356358	+	0.330652i	−0.481596	+	0.876394i	$0.659943\pi$
$542$	−2.77287	+	2.57285i	−0.119105	+	0.110513i
$543$	0.460840	+	0.0694605i	0.0197765	+	0.00298083i
$544$	1.58570	−	1.98840i	0.0679862	−	0.0852519i
$545$	−2.40275	+	32.0625i	−0.102923	+	1.37341i
$546$	0.123218			0.00527324
$547$	20.1382	−	11.8934i	0.861046	−	0.508526i
$547$	20.1382	−	11.8934i	0.861046	−	0.508526i
$548$	9.64084			0.411836
$549$	1.49398	−	19.9358i	0.0637615	−	0.850838i
$550$	−5.68682	+	7.13105i	−0.242487	+	0.304069i
$551$	4.31625	+	0.650569i	0.183878	+	0.0277152i
$552$	−0.895530	+	0.830931i	−0.0381163	+	0.0353668i
$553$	−3.26440	−	3.02892i	−0.138816	−	0.128803i
$554$	−15.0762	+	2.27237i	−0.640527	+	0.0965439i
$555$	−0.235014	+	1.02967i	−0.00997581	+	0.0437069i
$556$	−4.60596	−	20.1800i	−0.195336	−	0.855824i
$557$	−21.9630	−	27.5408i	−0.930604	−	1.16694i	−0.985709	−	0.168459i	$-0.946121\pi$
$557$	−21.9630	−	27.5408i	−0.930604	−	1.16694i	0.0551050	−	0.998481i	$-0.482451\pi$
$558$	4.40730	−	7.63367i	0.186576	−	0.323159i
$559$	0.163474	−	0.151682i	0.00691423	−	0.00641546i
$560$	9.21871	−	6.28521i	0.389561	−	0.265599i
$561$	0.00599918	+	0.0800535i	0.000253286	+	0.00337986i
$562$	1.12117	+	14.9610i	0.0472937	+	0.631091i
$563$	−3.05255	−	0.941587i	−0.128650	−	0.0396831i	0.229762	−	0.973247i	$-0.426205\pi$
$563$	−3.05255	−	0.941587i	−0.128650	−	0.0396831i	−0.358411	+	0.933564i	$0.616681\pi$
$564$	1.16988	+	0.360860i	0.0492608	+	0.0151949i
$565$	76.3328	−	11.5053i	3.21135	−	0.484033i
$566$	0.0410867	+	0.548264i	0.00172700	+	0.0230453i
$567$	−8.51168	+	5.80317i	−0.357457	+	0.243710i
$568$	5.65708	−	9.79835i	0.237366	−	0.411130i
$569$	30.2541	+	20.6269i	1.26832	+	0.864724i	0.995258	−	0.0972738i	$-0.0310123\pi$
$569$	30.2541	+	20.6269i	1.26832	+	0.864724i	0.273059	+	0.961997i	$0.411965\pi$
$570$	0.0273238	+	0.364611i	0.00114447	+	0.0152719i
$571$	−12.8751	−	16.1449i	−0.538808	−	0.675644i	0.435675	−	0.900104i	$-0.356510\pi$
$571$	−12.8751	−	16.1449i	−0.538808	−	0.675644i	−0.974483	+	0.224460i	$0.927938\pi$
$572$	0.732028	−	9.76824i	0.0306076	−	0.408431i
$573$	0.487421	+	0.844239i	0.0203623	+	0.0352686i
$574$	−0.724429	−	0.348867i	−0.0302371	−	0.0145614i
$575$	−76.1985			−3.17770
$576$	−1.78416	+	7.81693i	−0.0743402	+	0.325706i
$577$	−22.8264			−0.950276			−0.475138	−	0.879911i	$-0.657602\pi$
$577$	−22.8264			−0.950276			−0.475138	+	0.879911i	$0.657602\pi$
$578$	5.18182	−	6.49780i	0.215535	−	0.270273i
$579$	0.295941	−	0.754046i	0.0122989	−	0.0313371i
$580$	4.17417	+	10.6356i	0.173323	+	0.441620i
$581$	5.06959	−	12.9171i	0.210322	−	0.535892i
$582$	0.0289399	−	0.0362895i	0.00119960	−	0.00150425i
$583$	0.744100	+	9.92933i	0.0308175	+	0.411231i
$584$	0.0154603	+	0.00476887i	0.000639751	+	0.000197337i
$585$	−30.9989			−1.28165
$586$	0.344013	−	4.59054i	0.0142110	−	0.189633i
$587$	2.42464	+	4.19961i	0.100076	+	0.173336i	0.911716	−	0.410822i	$-0.134758\pi$
$587$	2.42464	+	4.19961i	0.100076	+	0.173336i	−0.811640	+	0.584158i	$0.801425\pi$
$588$	0.388522	−	0.672940i	0.0160224	−	0.0277516i
$589$	12.3175	+	8.39790i	0.507532	+	0.346030i
$590$	−2.58867	+	0.390179i	−0.106574	+	0.0160634i
$591$	0.307401	−	0.385469i	0.0126448	−	0.0158561i
$592$	7.68961	+	5.24269i	0.316041	+	0.215473i
$593$	10.2801			0.422154			0.211077	−	0.977469i	$-0.432303\pi$
$593$	10.2801			0.422154			0.211077	+	0.977469i	$0.432303\pi$
$594$	0.235197	+	0.407373i	0.00965024	+	0.0167147i
$595$	−1.81288	+	1.23600i	−0.0743210	+	0.0506712i
$596$	−19.1588	+	5.90971i	−0.784776	+	0.242071i
$597$	−0.774149	−	0.116684i	−0.0316838	−	0.00477556i
$598$	−9.50176	+	6.47819i	−0.388556	+	0.264913i
$599$	−17.9659	+	8.65191i	−0.734066	+	0.353507i	−0.763282	−	0.646066i	$-0.776413\pi$
$599$	−17.9659	+	8.65191i	−0.734066	+	0.353507i	0.0292160	+	0.999573i	$0.490699\pi$
$600$	−1.09142	+	0.744118i	−0.0445571	+	0.0303785i
$601$	20.7491	−	35.9384i	0.846372	−	1.46596i	−0.0380524	−	0.999276i	$-0.512115\pi$
$601$	20.7491	−	35.9384i	0.846372	−	1.46596i	0.884424	−	0.466683i	$-0.154551\pi$
$602$	−0.0102801	−	0.0450400i	−0.000418985	−	0.00183569i
$603$	−2.22123	+	29.6402i	−0.0904553	+	1.20704i
$604$	9.28976	+	6.33365i	0.377995	+	0.257713i
$605$	24.7475	+	7.63360i	1.00613	+	0.310350i
$606$	0.266477	−	0.461551i	0.0108249	−	0.0187492i
$607$	−1.78814	+	23.8611i	−0.0725785	+	0.968493i	0.835445	+	0.549574i	$0.185210\pi$
$607$	−1.78814	+	23.8611i	−0.0725785	+	0.968493i	−0.908024	+	0.418919i	$0.862409\pi$
$608$	12.0299	+	3.71072i	0.487875	+	0.150489i
$609$	−0.114500	−	0.106240i	−0.00463977	−	0.00430508i
$610$	−4.54368	−	11.5771i	−0.183968	−	0.468743i
$611$	22.2260	+	10.7035i	0.899166	+	0.433015i
$612$	0.593224	−	2.59909i	0.0239797	−	0.105062i
$613$	21.5538	−	6.64846i	0.870548	−	0.268529i	0.172874	−	0.984944i	$-0.444695\pi$
$613$	21.5538	−	6.64846i	0.870548	−	0.268529i	0.697674	+	0.716415i	$0.254218\pi$
$614$	−1.56941	−	0.484099i	−0.0633363	−	0.0195367i
$615$	−0.371315	−	0.178816i	−0.0149729	−	0.00721056i
$616$	−3.58897	−	2.44692i	−0.144604	−	0.0985891i
$617$	13.6640	+	12.6783i	0.550091	+	0.510410i	0.905526	−	0.424291i	$-0.139477\pi$
$617$	13.6640	+	12.6783i	0.550091	+	0.510410i	−0.355435	+	0.934701i	$0.615667\pi$
$618$	0.0728474	+	0.0224704i	0.00293035	+	0.000903894i
$619$	17.3898			0.698957			0.349478	−	0.936944i	$-0.386359\pi$
$619$	17.3898			0.698957			0.349478	+	0.936944i	$0.386359\pi$
$620$	−2.91608	+	38.9123i	−0.117112	+	1.56276i
$621$	−1.43571	+	3.65813i	−0.0576130	+	0.146796i
$622$	−8.17309	−	7.58352i	−0.327711	−	0.304072i
$623$	1.20086	−	16.0244i	0.0481116	−	0.642004i
$624$	0.203326	−	0.518067i	0.00813957	−	0.0207393i
$625$	−11.8732	−	1.78960i	−0.474929	−	0.0715841i
$626$	10.2651	+	12.8720i	0.410276	+	0.514469i
$627$	−0.358024	+	0.172415i	−0.0142981	+	0.00688560i
$628$	−15.5798	+	7.50284i	−0.621702	+	0.299396i
$629$	−1.51218	−	1.03099i	−0.0602947	−	0.0411082i
$630$	−3.21091	+	5.56145i	−0.127926	+	0.221574i
$631$	14.6377	−	18.3551i	0.582718	−	0.730705i	−0.399856	−	0.916578i	$-0.630940\pi$
$631$	14.6377	−	18.3551i	0.582718	−	0.730705i	0.982574	+	0.185873i	$0.0595114\pi$
$632$	6.49146	−	3.12612i	0.258217	−	0.124351i
$633$	−0.103872	−	1.38608i	−0.00412855	−	0.0550917i
$634$	−0.102574	−	0.128624i	−0.00407374	−	0.00510831i
$635$	34.6669	+	32.1662i	1.37572	+	1.27648i
$636$	−0.149911	+	0.656801i	−0.00594434	+	0.0260439i
$637$	9.76222	−	12.2414i	0.386793	−	0.485023i
$638$	1.27915	−	1.18688i	0.0506422	−	0.0469891i
$639$	1.35853	−	18.1283i	0.0537425	−	0.717143i
$640$	9.47290	+	41.5035i	0.374449	+	1.64057i
$641$	−15.3701	+	7.40187i	−0.607084	+	0.292356i	−0.712060	−	0.702119i	$-0.752238\pi$
$641$	−15.3701	+	7.40187i	−0.607084	+	0.292356i	0.104976	+	0.994475i	$0.466523\pi$
$642$	0.484729	+	0.449763i	0.0191307	+	0.0177507i
$643$	−12.9217	−	22.3811i	−0.509583	−	0.882624i	−0.999938	−	0.0111015i	$-0.996466\pi$
$643$	−12.9217	−	22.3811i	−0.509583	−	0.882624i	0.490355	−	0.871523i	$-0.336867\pi$
$644$	−1.26691	−	16.9057i	−0.0499232	−	0.666179i
$645$	−0.00526918	−	0.0230858i	−0.000207474	−	0.000909002i
$646$	−0.605459	−	0.186759i	−0.0238214	−	0.00734794i
$647$	5.87011	−	25.7187i	0.230778	−	1.01110i	−0.718218	−	0.695818i	$-0.755042\pi$
$647$	5.87011	−	25.7187i	0.230778	−	1.01110i	0.948996	−	0.315287i	$-0.102101\pi$
$648$	−3.70890	−	16.2498i	−0.145699	−	0.638351i
$649$	−1.42260	−	2.46401i	−0.0558418	−	0.0967208i
$650$	−11.2034	+	5.39526i	−0.439433	+	0.211620i
$651$	−0.194895	−	0.496584i	−0.00763853	−	0.0194626i
$652$	−2.28550	−	10.0134i	−0.0895070	−	0.392156i
$653$	−10.5013	−	18.1888i	−0.410948	−	0.711783i	0.584046	−	0.811721i	$-0.301469\pi$
$653$	−10.5013	−	18.1888i	−0.410948	−	0.711783i	−0.994994	+	0.0999379i	$0.968136\pi$
$654$	0.332243			0.0129917
$655$	−54.9385	−	37.4564i	−2.14662	−	1.46354i
$656$	−2.66221	+	2.47017i	−0.103942	+	0.0964440i
$657$	0.0257055	−	0.00387448i	0.00100287	−	0.000151158i
$658$	4.22248	−	2.87884i	0.164609	−	0.112229i
$659$	−2.76033	−	0.416054i	−0.107527	−	0.0162071i	0.0950581	−	0.995472i	$-0.469696\pi$
$659$	−2.76033	−	0.416054i	−0.107527	−	0.0162071i	−0.202585	+	0.979265i	$0.564934\pi$
$660$	−0.859400	−	0.585929i	−0.0334521	−	0.0228073i
$661$	12.3660	−	15.5064i	0.480980	−	0.603130i	−0.480841	−	0.876808i	$-0.659669\pi$
$661$	12.3660	−	15.5064i	0.480980	−	0.603130i	0.961821	+	0.273678i	$0.0882401\pi$
$662$	−5.19405	−	4.81937i	−0.201872	−	0.187310i
$663$	−0.0399847	+	0.101879i	−0.00155288	+	0.00395667i
$664$	16.4579	+	15.2707i	0.638689	+	0.592617i
$665$	−8.97379	−	6.11823i	−0.347989	−	0.237255i
$666$	−5.29680	−	0.798364i	−0.205247	−	0.0309360i
$667$	14.4151	+	2.17272i	0.558154	+	0.0841281i
$668$	−6.41001	−	11.1025i	−0.248011	−	0.429567i
$669$	0.690911	−	1.76041i	0.0267122	−	0.0680615i
$670$	6.75547	+	17.2127i	0.260987	+	0.664983i
$671$	9.90834	−	9.19359i	0.382507	−	0.354915i
$672$	−0.280874	−	0.352205i	−0.0108350	−	0.0135866i
$673$	35.0363	−	10.8073i	1.35055	−	0.416590i	0.466723	−	0.884403i	$-0.345434\pi$
$673$	35.0363	−	10.8073i	1.35055	−	0.416590i	0.883827	+	0.467814i	$0.154958\pi$
$674$	0.406067	+	5.41859i	0.0156411	+	0.208716i
$675$	−2.12461	+	3.67993i	−0.0817762	+	0.141641i
$676$	−4.72093	+	8.17689i	−0.181574	+	0.314496i
$677$	−42.8069	−	13.2042i	−1.64520	−	0.507478i	−0.672611	−	0.739996i	$-0.734827\pi$
$677$	−42.8069	−	13.2042i	−1.64520	−	0.507478i	−0.972592	+	0.232518i	$0.925303\pi$
$678$	−0.177502	−	0.777685i	−0.00681691	−	0.0298668i
$679$	0.306806	+	1.34421i	0.0117741	+	0.0515859i
$680$	−0.789951	−	3.46100i	−0.0302932	−	0.132723i
$681$	−0.756027	+	1.92633i	−0.0289710	+	0.0738170i
$682$	5.69486	−	1.75663i	0.218068	−	0.0672649i
$683$	−10.2588	+	17.7688i	−0.392544	+	0.679906i	−0.992784	−	0.119914i	$-0.961738\pi$
$683$	−10.2588	+	17.7688i	−0.392544	+	0.679906i	0.600241	+	0.799820i	$0.295072\pi$
$684$	13.0490	−	1.96682i	0.498940	−	0.0752031i
$685$	12.8610	−	16.1272i	0.491394	−	0.616189i
$686$	−2.64707	−	6.74463i	−0.101066	−	0.257511i
$687$	0.112928	−	0.104782i	0.00430846	−	0.00399767i
$688$	−0.206333	−	0.0310997i	−0.00786638	−	0.00118567i
$689$	−4.95945	+	12.6365i	−0.188940	+	0.481411i
$690$	0.0912539	+	1.21770i	0.00347398	+	0.0463570i
$691$	1.62501	−	21.6842i	0.0618182	−	0.824907i	−0.876999	−	0.480492i	$-0.840458\pi$
$691$	1.62501	−	21.6842i	0.0618182	−	0.824907i	0.938817	−	0.344415i	$-0.111923\pi$
$692$	5.13518	+	8.89439i	0.195210	+	0.338114i
$693$	−6.90139	−	1.04022i	−0.262162	−	0.0395146i
$694$	0.508080	−	1.29457i	0.0192865	−	0.0491411i
$695$	−39.9016	−	19.2156i	−1.51355	−	0.728889i
$696$	0.227690	−	0.109650i	0.00863058	−	0.00415627i
$697$	0.523531	−	0.485766i	0.0198302	−	0.0183997i
$698$	−12.5897	−	6.06289i	−0.476528	−	0.229484i
$699$	1.19058	+	0.179452i	0.0450320	+	0.00678749i
$700$	1.36989	−	18.2799i	0.0517771	−	0.690917i
$701$	−11.1768	−	5.38245i	−0.422141	−	0.203292i	0.210739	−	0.977542i	$-0.432413\pi$
$701$	−11.1768	−	5.38245i	−0.422141	−	0.203292i	−0.632880	+	0.774250i	$0.718127\pi$
$702$	0.0479243	+	0.639506i	0.00180879	+	0.0241366i
$703$	2.01593	−	8.83237i	0.0760323	−	0.333119i
$704$	−4.47906	+	3.05377i	−0.168811	+	0.115093i
$705$	2.16428	−	1.47558i	0.0815116	−	0.0555737i
$706$	−0.729388	+	9.73300i	−0.0274509	+	0.366306i
$707$	5.78379	+	14.7369i	0.217522	+	0.554237i
$708$	−0.0428359	−	0.187677i	−0.00160987	−	0.00705332i
$709$	0.388729	+	0.990467i	0.0145990	+	0.0371978i	0.937987	−	0.346669i	$-0.112687\pi$
$709$	0.388729	+	0.990467i	0.0145990	+	0.0371978i	−0.923388	+	0.383867i	$0.874592\pi$
$710$	−4.13172	−	10.5275i	−0.155061	−	0.395088i
$711$	7.21793	−	9.05099i	0.270693	−	0.339439i
$712$	23.4246	+	11.2807i	0.877874	+	0.422762i
$713$	41.1369	+	28.0467i	1.54059	+	1.05036i
$714$	0.0141363	+	0.0177264i	0.000529038	+	0.000663393i
$715$	−15.3638	−	14.2555i	−0.574573	−	0.533126i
$716$	2.99713	−	7.63657i	0.112008	−	0.285392i
$717$	−0.537973	−	1.37073i	−0.0200910	−	0.0511909i
$718$	−15.5110	+	4.78450i	−0.578864	+	0.178556i
$719$	38.7435			1.44489			0.722444	−	0.691429i	$-0.243019\pi$
$719$	38.7435			1.44489			0.722444	+	0.691429i	$0.243019\pi$
$720$	18.0846	+	22.6773i	0.673973	+	0.845135i
$721$	−1.87103	+	1.27565i	−0.0696808	+	0.0475076i
$722$	0.470460	+	6.27785i	0.0175087	+	0.233637i
$723$	−0.376929	+	0.349739i	−0.0140181	+	0.0130069i
$724$	−3.82292	−	9.74065i	−0.142078	−	0.362008i
$725$	15.0626	+	4.64619i	0.559410	+	0.172555i
$726$	0.0595499	−	0.260905i	0.00221010	−	0.00968310i
$727$	8.39955	+	7.79364i	0.311522	+	0.289050i	0.820402	−	0.571787i	$-0.193750\pi$
$727$	8.39955	+	7.79364i	0.311522	+	0.289050i	−0.508880	+	0.860838i	$0.669940\pi$
$728$	−2.96097	−	5.12854i	−0.109741	−	0.190076i
$729$	−16.6292	−	20.8524i	−0.615896	−	0.772310i
$730$	0.0133619	−	0.00911002i	0.000494548	−	0.000337177i
$731$	0.0405760	+	0.00611585i	0.00150076	+	0.000226203i
$732$	0.823952	−	0.396794i	0.0304541	−	0.0146659i
$733$	20.8465	−	3.14210i	0.769981	−	0.116056i	0.247709	−	0.968835i	$-0.420322\pi$
$733$	20.8465	−	3.14210i	0.769981	−	0.116056i	0.522273	+	0.852779i	$0.325084\pi$
$734$	−2.63137	+	2.44155i	−0.0971255	+	0.0901193i
$735$	−0.607401	−	1.54763i	−0.0224043	−	0.0570852i
$736$	40.1764	+	12.3928i	1.48092	+	0.456804i
$737$	−14.7316	+	13.6689i	−0.542644	+	0.503500i
$738$	0.763659	−	1.94577i	0.0281107	−	0.0716248i
$739$	−8.25399	+	3.97491i	−0.303628	+	0.146220i	−0.579494	−	0.814977i	$-0.696750\pi$
$739$	−8.25399	+	3.97491i	−0.303628	+	0.146220i	0.275866	+	0.961196i	$0.411035\pi$
$740$	22.6598	−	6.98963i	0.832991	−	0.256944i
$741$	−0.541753			−0.0199018
$742$	1.75338	+	2.19867i	0.0643685	+	0.0807156i
$743$	31.2219	−	4.70594i	1.14542	−	0.172644i	0.451211	−	0.892418i	$-0.350992\pi$
$743$	31.2219	−	4.70594i	1.14542	−	0.172644i	0.694209	+	0.719773i	$0.255754\pi$
$744$	0.863110			0.0316431
$745$	−15.6724	+	39.9325i	−0.574191	+	1.46301i
$746$	7.29297	+	12.6318i	0.267015	+	0.462483i
$747$	34.4709	+	10.6329i	1.26122	+	0.389036i
$748$	1.48926	−	1.01536i	0.0544528	−	0.0371253i
$749$	−19.4228	+	2.92751i	−0.709693	+	0.106969i
$750$	−0.0443193	+	0.591400i	−0.00161831	+	0.0215949i
$751$	21.6806	−	10.4408i	0.791137	−	0.380991i	0.00573944	−	0.999984i	$-0.498173\pi$
$751$	21.6806	−	10.4408i	0.791137	−	0.380991i	0.785397	+	0.618992i	$0.212459\pi$
$752$	−5.13634	−	22.5038i	−0.187303	−	0.820629i
$753$	0.517036	+	1.31739i	0.0188418	+	0.0480082i
$754$	2.27327	−	0.701211i	0.0827876	−	0.0255366i
$755$	22.9876	−	7.09074i	0.836604	−	0.258058i
$756$	−0.851770	−	0.410191i	−0.0309786	−	0.0149185i
$757$	−42.7558	+	6.44440i	−1.55398	+	0.234226i	−0.869178	−	0.494499i	$-0.835351\pi$
$757$	−42.7558	+	6.44440i	−1.55398	+	0.234226i	−0.684807	+	0.728725i	$0.740113\pi$
$758$	−8.35604	+	7.75327i	−0.303505	+	0.281611i
$759$	−1.19570	+	0.575819i	−0.0434012	+	0.0209009i
$760$	14.5191	−	9.89897i	0.526664	−	0.359074i
$761$	−1.92314	+	25.6625i	−0.0697138	+	0.930266i	0.847224	+	0.531236i	$0.178272\pi$
$761$	−1.92314	+	25.6625i	−0.0697138	+	0.930266i	−0.916938	+	0.399030i	$0.869347\pi$
$762$	0.304686	−	0.382064i	0.0110376	−	0.0138407i
$763$	−6.15333	+	7.71603i	−0.222765	+	0.279339i
$764$	10.9439	−	18.9554i	0.395938	−	0.685784i
$765$	−3.55638	−	4.45956i	−0.128581	−	0.161236i
$766$	−3.97687	−	3.68999i	−0.143690	−	0.133325i
$767$	−0.289872	−	3.86807i	−0.0104667	−	0.139668i
$768$	0.0206181	−	0.00635985i	0.000743992	−	0.000229491i
$769$	15.4286	+	26.7231i	0.556369	+	0.963660i	0.997796	+	0.0663621i	$0.0211393\pi$
$769$	15.4286	+	26.7231i	0.556369	+	0.963660i	−0.441427	+	0.897297i	$0.645527\pi$
$770$	−4.14895	+	1.27978i	−0.149518	+	0.0461201i
$771$	−0.306450	+	1.34264i	−0.0110365	+	0.0483542i
$772$	−17.9845	+	2.71072i	−0.647276	+	0.0975611i
$773$	−27.5987	+	34.6077i	−0.992657	+	1.24475i	−0.0231384	+	0.999732i	$0.507366\pi$
$773$	−27.5987	+	34.6077i	−0.992657	+	1.24475i	−0.969518	+	0.245020i	$0.921206\pi$
$774$	0.114764	−	0.0353999i	0.00412509	−	0.00127242i
$775$	39.4641	+	36.6173i	1.41759	+	1.31533i
$776$	−2.20587	−	0.332481i	−0.0791860	−	0.0119354i
$777$	−0.237643	+	0.220501i	−0.00852540	+	0.00791042i
$778$	−7.15872	−	12.3993i	−0.256653	−	0.444535i
$779$	3.18511	+	1.53387i	0.114118	+	0.0549564i
$780$	−0.709021	−	1.22806i	−0.0253870	−	0.0439716i
$781$	9.00999	−	8.36005i	0.322403	−	0.299146i
$782$	−2.02206	−	0.623724i	−0.0723089	−	0.0223043i
$783$	0.506858	−	0.635580i	0.0181136	−	0.0227138i
$784$	−14.6505			−0.523231
$785$	−8.23293	+	36.0708i	−0.293846	+	1.28742i
$786$	−0.343545	+	0.595037i	−0.0122538	+	0.0212243i
$787$	4.69391	−	20.5654i	0.167320	−	0.733076i	−0.819742	−	0.572734i	$-0.805883\pi$
$787$	4.69391	−	20.5654i	0.167320	−	0.733076i	0.987061	−	0.160343i	$-0.0512599\pi$
$788$	−10.9463	−	1.64989i	−0.389946	−	0.0587749i
$789$	0.522597	−	0.251669i	0.0186049	−	0.00895966i
$790$	1.60256	−	7.02127i	0.0570165	−	0.249806i
$791$	21.3484	+	10.2809i	0.759063	+	0.365546i
$792$	5.64610	−	9.77934i	0.200626	−	0.347494i
$793$	17.6088	−	5.43159i	0.625306	−	0.192881i
$794$	11.8745	+	14.8902i	0.421412	+	0.528434i
$795$	0.898715	+	1.12695i	0.0318741	+	0.0399689i
$796$	6.42199	+	16.3630i	0.227621	+	0.579970i
$797$	21.7302	−	14.8154i	0.769722	−	0.524788i	−0.113615	−	0.993525i	$-0.536243\pi$
$797$	21.7302	−	14.8154i	0.769722	−	0.524788i	0.883338	+	0.468737i	$0.155291\pi$
$798$	−0.0561155	+	0.0971948i	−0.00198647	+	0.00344066i
$799$	1.01008	+	4.42544i	0.0357339	+	0.156561i
$800$	40.9598	+	19.7252i	1.44815	+	0.697391i
$801$	41.7746			1.47603
$802$	−0.528687	+	2.31633i	−0.0186686	+	0.0817924i
$803$	0.0145220	+	0.00990093i	0.000512470	+	0.000349396i
$804$	−1.22504	+	0.589947i	−0.0432038	+	0.0208058i
$805$	−29.9700	−	20.4332i	−1.05630	−	0.720176i
$806$	8.03417	+	1.21096i	0.282991	+	0.0426541i
$807$	−0.501140	+	1.27688i	−0.0176410	+	0.0449484i
$808$	−25.6141			−0.901100
$809$	22.5333	−	3.39635i	0.792229	−	0.119409i	0.259553	−	0.965729i	$-0.416425\pi$
$809$	22.5333	−	3.39635i	0.792229	−	0.119409i	0.532676	+	0.846320i	$0.321187\pi$
$810$	−15.0105	−	7.22866i	−0.527414	−	0.253989i
$811$	−19.6464	+	2.96122i	−0.689878	+	0.103982i	−0.484619	−	0.874725i	$-0.661042\pi$
$811$	−19.6464	+	2.96122i	−0.689878	+	0.103982i	−0.205259	+	0.978708i	$0.565804\pi$
$812$	−0.780387	+	3.41910i	−0.0273862	+	0.119987i
$813$	−0.588479	+	0.0886989i	−0.0206389	+	0.00311081i
$814$	−2.25807	−	2.83153i	−0.0791454	−	0.0992452i
$815$	−19.7994	−	9.53487i	−0.693541	−	0.333992i
$816$	0.0978570	−	0.0301849i	0.00342568	−	0.00105668i
$817$	0.0451985	+	0.198028i	0.00158130	+	0.00692811i
$818$	−6.05189	−	5.61533i	−0.211599	−	0.196335i
$819$	−7.86175	−	5.36005i	−0.274712	−	0.187295i
$820$	0.691508	+	9.22753i	0.0241485	+	0.322239i
$821$	−1.81351	−	24.1996i	−0.0632918	−	0.844570i	−0.935023	−	0.354586i	$-0.884622\pi$
$821$	−1.81351	−	24.1996i	−0.0632918	−	0.844570i	0.871731	−	0.489984i	$-0.162997\pi$
$822$	−0.176114	−	0.120072i	−0.00614268	−	0.00418801i
$823$	−2.01621	−	1.87077i	−0.0702805	−	0.0652108i	0.644251	−	0.764815i	$-0.277169\pi$
$823$	−2.01621	−	1.87077i	−0.0702805	−	0.0652108i	−0.714531	+	0.699604i	$0.753360\pi$
$824$	−0.815287	−	3.57201i	−0.0284019	−	0.124437i
$825$	−1.37125	+	0.422976i	−0.0477409	+	0.0147261i
$826$	−0.723989	−	0.348655i	−0.0251908	−	0.0121312i
$827$	17.5655	+	22.0265i	0.610814	+	0.765936i	0.987020	−	0.160600i	$-0.0513429\pi$
$827$	17.5655	+	22.0265i	0.610814	+	0.765936i	−0.376206	+	0.926536i	$0.622771\pi$
$828$	43.5799	−	6.56862i	1.51451	−	0.228275i
$829$	−10.6208	+	46.5330i	−0.368877	+	1.61616i	0.360991	+	0.932569i	$0.382439\pi$
$829$	−10.6208	+	46.5330i	−0.368877	+	1.61616i	−0.729868	+	0.683588i	$0.760419\pi$
$830$	22.1907	−	3.34471i	0.770251	−	0.116097i
$831$	−2.16119	−	1.04078i	−0.0749710	−	0.0361041i
$832$	−7.30806	+	1.10151i	−0.253361	+	0.0381881i
$833$	2.88106			0.0998227
$834$	−0.167194	+	0.426004i	−0.00578946	+	0.0147513i
$835$	−27.1233	−	4.08817i	−0.938639	−	0.141477i
$836$	7.37185	+	5.02604i	0.254961	+	0.173829i
$837$	2.50149	−	1.20465i	0.0864640	−	0.0416389i
$838$	1.32257	+	0.901710i	0.0456873	+	0.0311491i
$839$	−6.76959	+	29.6595i	−0.233712	+	1.02396i	0.712819	+	0.701348i	$0.247418\pi$
$839$	−6.76959	+	29.6595i	−0.233712	+	1.02396i	−0.946531	+	0.322612i	$0.895439\pi$
$840$	−0.628812			−0.0216961
$841$	23.4111	+	11.2742i	0.807278	+	0.388765i
$842$	0.959922	+	4.20569i	0.0330811	+	0.144938i
$843$	−1.18021	+	2.04419i	−0.0406487	+	0.0704056i
$844$	−25.7857	+	17.5804i	−0.887579	+	0.605141i
$845$	7.38052	+	18.8053i	0.253898	+	0.646921i
$846$	8.28334	+	10.3870i	0.284787	+	0.357112i
$847$	4.95638	+	6.21510i	0.170303	+	0.213553i
$848$	12.1376	−	3.74394i	0.416806	−	0.128568i
$849$	−0.0432504	+	0.0749118i	−0.00148435	+	0.00257097i
$850$	−2.06149	−	0.992763i	−0.0707086	−	0.0340515i
$851$	6.73265	−	29.4977i	0.230792	−	1.01117i
$852$	0.749247	−	0.360818i	0.0256688	−	0.0123614i
$853$	15.0825	+	2.27332i	0.516415	+	0.0778371i	0.402079	−	0.915605i	$-0.368288\pi$
$853$	15.0825	+	2.27332i	0.516415	+	0.0778371i	0.114336	+	0.993442i	$0.463526\pi$
$854$	0.849469	−	3.72176i	0.0290682	−	0.127356i
$855$	14.1174	−	24.4521i	0.482805	−	0.836244i
$856$	7.07172	−	30.9832i	0.241706	−	1.05898i
$857$	−27.6893			−0.945848			−0.472924	−	0.881103i	$-0.656801\pi$
$857$	−27.6893			−0.945848			−0.472924	+	0.881103i	$0.656801\pi$
$858$	−0.135031	+	0.169324i	−0.00460990	+	0.00578063i
$859$	−9.66631	−	2.98166i	−0.329810	−	0.101733i	0.125428	−	0.992103i	$-0.459970\pi$
$859$	−9.66631	−	2.98166i	−0.329810	−	0.101733i	−0.455238	+	0.890370i	$0.650446\pi$
$860$	−0.389741	+	0.361627i	−0.0132901	+	0.0123314i
$861$	−0.0632514	−	0.109555i	−0.00215560	−	0.00373361i
$862$	12.3633	+	5.95383i	0.421094	+	0.202788i
$863$	−7.81788	−	13.5410i	−0.266124	−	0.460940i	0.701734	−	0.712439i	$-0.252410\pi$
$863$	−7.81788	−	13.5410i	−0.266124	−	0.460940i	−0.967857	+	0.251499i	$0.919076\pi$
$864$	1.71872	−	1.59474i	0.0584719	−	0.0542540i
$865$	21.7289	+	3.27511i	0.738806	+	0.111357i
$866$	3.95279	+	3.66765i	0.134321	+	0.124632i
$867$	1.24948	−	0.385415i	0.0424347	−	0.0130894i
$868$	−7.46792	+	9.36448i	−0.253478	+	0.317851i
$869$	7.73966	−	1.16657i	0.262550	−	0.0395731i
$870$	0.0562103	−	0.246273i	0.00190571	−	0.00834945i
$871$	−26.1805	+	8.07560i	−0.887091	+	0.273631i
$872$	−7.98390	−	13.8285i	−0.270369	−	0.468293i
$873$	−3.42509	+	1.05650i	−0.115922	+	0.0357571i
$874$	−0.782767	−	10.4453i	−0.0264775	−	0.353318i
$875$	−12.9139	−	11.9823i	−0.436569	−	0.405077i
$876$	0.000741440	0	0.000929736i	2.50509e−5	0	3.14129e-5i
$877$	−7.51030	+	13.0082i	−0.253605	+	0.439256i	−0.964516	−	0.264026i	$-0.914950\pi$
$877$	−7.51030	+	13.0082i	−0.253605	+	0.439256i	0.710911	+	0.703282i	$0.248283\pi$
$878$	−5.39184	+	6.76116i	−0.181966	+	0.228178i
$879$	0.451567	−	0.566247i	0.0152310	−	0.0190991i
$880$	−1.46552	+	19.5560i	−0.0494027	+	0.659233i
$881$	30.5844	−	20.8521i	1.03041	−	0.702525i	0.0748161	−	0.997197i	$-0.476163\pi$
$881$	30.5844	−	20.8521i	1.03041	−	0.702525i	0.955598	+	0.294673i	$0.0952106\pi$
$882$	7.59722	−	3.65863i	0.255812	−	0.123192i
$883$	−6.19123	+	5.74463i	−0.208352	+	0.193322i	−0.777445	−	0.628951i	$-0.783485\pi$
$883$	−6.19123	+	5.74463i	−0.208352	+	0.193322i	0.569094	+	0.822273i	$0.307294\pi$
$884$	2.42989	−	0.366247i	0.0817260	−	0.0123182i
$885$	−0.371089	−	0.178707i	−0.0124740	−	0.00600718i
$886$	−0.155499	+	0.0479650i	−0.00522408	+	0.00161141i
$887$	−2.75998	+	0.851341i	−0.0926710	+	0.0285852i	−0.340744	−	0.940156i	$-0.610679\pi$
$887$	−2.75998	+	0.851341i	−0.0926710	+	0.0285852i	0.248073	+	0.968741i	$0.420203\pi$
$888$	−0.191626	−	0.488254i	−0.00643054	−	0.0163847i
$889$	3.23012	+	14.1521i	0.108335	+	0.474646i
$890$	23.4144	−	11.2758i	0.784851	−	0.377965i
$891$	1.35312	−	18.0562i	0.0453313	−	0.604904i
$892$	−41.9870	+	6.32852i	−1.40583	+	0.211894i
$893$	−18.5650	+	12.6574i	−0.621254	+	0.423564i
$894$	0.423586	+	0.130659i	0.0141668	+	0.00436989i
$895$	−8.77625	−	15.2009i	−0.293358	−	0.508110i
$896$	−4.77395	+	12.1638i	−0.159486	+	0.406365i
$897$	−1.80931			−0.0604110
$898$	8.83132	−	1.33111i	0.294705	−	0.0444196i
$899$	−6.42162	−	8.05246i	−0.214173	−	0.268564i
$900$	47.6547			1.58849
$901$	−2.38689	+	0.736257i	−0.0795187	+	0.0245283i
$902$	1.27329	−	0.613185i	0.0423960	−	0.0204168i
$903$	0.00265545	−	0.00676597i	8.83678e−5	−	0.000225157i
$904$	−28.1032	+	26.0759i	−0.934698	+	0.867273i
$905$	−21.3940	−	6.59918i	−0.711161	−	0.219364i
$906$	−0.0908177	−	0.231400i	−0.00301721	−	0.00768774i
$907$	18.9129	−	17.5486i	0.627994	−	0.582693i	−0.300619	−	0.953744i	$-0.597193\pi$
$907$	18.9129	−	17.5486i	0.627994	−	0.582693i	0.928612	+	0.371051i	$0.121003\pi$
$908$	45.9441	−	6.92496i	1.52471	−	0.229813i
$909$	−37.0799	+	17.8567i	−1.22986	+	0.592271i
$910$	−5.85323	−	0.882233i	−0.194033	−	0.0292457i
$911$	6.32326	−	4.31112i	0.209499	−	0.142834i	−0.454025	−	0.890989i	$-0.650012\pi$
$911$	6.32326	−	4.31112i	0.209499	−	0.142834i	0.663524	+	0.748155i	$0.269060\pi$
$912$	0.316056	+	0.396321i	0.0104656	+	0.0131235i
$913$	12.1948	+	21.1221i	0.403590	+	0.699039i
$914$	5.78805	+	5.37052i	0.191452	+	0.177641i
$915$	0.435405	−	1.90764i	0.0143941	−	0.0630645i
$916$	−3.30520	−	1.01952i	−0.109207	−	0.0336859i
$917$	−7.45653	−	18.9989i	−0.246236	−	0.627400i
$918$	−0.0865024	+	0.0802625i	−0.00285500	+	0.00264906i
$919$	−2.32744	−	31.0575i	−0.0767751	−	1.02449i	−0.893969	−	0.448130i	$-0.852090\pi$
$919$	−2.32744	−	31.0575i	−0.0767751	−	1.02449i	0.817193	−	0.576363i	$-0.195529\pi$
$920$	48.4899	−	33.0598i	1.59866	−	1.08995i
$921$	−0.161108	−	0.202023i	−0.00530868	−	0.00665687i
$922$	−16.2012			−0.533559
$923$	16.0123	−	4.93913i	0.527050	−	0.162573i
$924$	−0.116642	−	0.297199i	−0.00383725	−	0.00977714i
$925$	11.9524	−	30.4542i	0.392992	−	1.00133i
$926$	14.7947	+	13.7275i	0.486184	+	0.451113i
$927$	−3.67045	−	4.60260i	−0.120553	−	0.151169i
$928$	−7.18624	−	4.89950i	−0.235900	−	0.160834i
$929$	47.2439	+	22.7514i	1.55002	+	0.746451i	0.996275	−	0.0862350i	$-0.0274836\pi$
$929$	47.2439	+	22.7514i	1.55002	+	0.746451i	0.553746	+	0.832686i	$0.313198\pi$
$930$	0.537905	−	0.674512i	0.0176386	−	0.0221181i
$931$	5.21022	+	13.2754i	0.170758	+	0.435085i
$932$	−9.87655	−	25.1650i	−0.323517	−	0.824308i
$933$	−0.390334	−	1.71016i	−0.0127790	−	0.0559883i
$934$	−7.31532	−	18.6391i	−0.239364	−	0.609891i
$935$	0.288199	−	3.84574i	0.00942510	−	0.125769i
$936$	12.7199	−	8.67228i	0.415763	−	0.283462i
$937$	−8.98498	+	6.12586i	−0.293527	+	0.200123i	−0.701125	−	0.713038i	$-0.747319\pi$
$937$	−8.98498	+	6.12586i	−0.293527	+	0.200123i	0.407599	+	0.913161i	$0.366366\pi$
$938$	−1.26298	+	5.53346i	−0.0412377	+	0.180674i
$939$	0.193572	+	2.58304i	0.00631699	+	0.0842943i
$940$	−52.9891	−	25.5182i	−1.72832	−	0.832313i
$941$	1.24511	−	16.6148i	0.0405893	−	0.541626i	−0.939432	−	0.342735i	$-0.888647\pi$
$941$	1.24511	−	16.6148i	0.0405893	−	0.541626i	0.980022	−	0.198891i	$-0.0637341\pi$
$942$	0.378048	+	0.0569816i	0.0123175	+	0.00185656i
$943$	10.6374	+	5.12269i	0.346400	+	0.166818i
$944$	−2.66059	+	2.46867i	−0.0865949	+	0.0803483i
$945$	−1.82244	+	0.877641i	−0.0592840	+	0.0285497i
$946$	0.0731589	+	0.0352315i	0.00237860	+	0.00114547i
$947$	−18.2732	+	46.5595i	−0.593801	+	1.51298i	0.245547	+	0.969385i	$0.421032\pi$
$947$	−18.2732	+	46.5595i	−0.593801	+	1.51298i	−0.839348	+	0.543595i	$0.817063\pi$
$948$	0.523658	+	0.0789288i	0.0170076	+	0.00256349i
$949$	0.0119809	+	0.0207516i	0.000388917	+	0.000673624i
$950$	0.846396	−	11.2944i	0.0274607	−	0.366438i
$951$	−0.00193427	−	0.0258111i	−6.27231e−5	−	0.000836982i
$952$	0.398102	−	1.01435i	0.0129026	−	0.0328752i
$953$	−44.3530	−	6.68514i	−1.43674	−	0.216553i	−0.615948	−	0.787787i	$-0.711227\pi$
$953$	−44.3530	−	6.68514i	−1.43674	−	0.216553i	−0.820787	+	0.571234i	$0.806465\pi$
$954$	−5.35914	+	4.97256i	−0.173509	+	0.160993i
$955$	−17.1093	−	43.5939i	−0.553645	−	1.41066i
$956$	−20.6139	+	25.8490i	−0.666701	+	0.836016i
$957$	0.271471	−	0.0409177i	0.00877542	−	0.00132268i
$958$	−7.18350	+	12.4422i	−0.232088	+	0.401989i
$959$	6.05030	−	1.86627i	0.195374	−	0.0602650i
$960$	−0.286706	+	0.730514i	−0.00925338	+	0.0235772i
$961$	−0.929250	−	4.07131i	−0.0299758	−	0.131333i
$962$	−1.09870	−	4.81372i	−0.0354235	−	0.155200i
$963$	−11.3625	−	49.7825i	−0.366152	−	1.60422i
$964$	11.0321	+	3.40295i	0.355320	+	0.109602i
$965$	−19.4571	+	33.7006i	−0.626345	+	1.08486i
$966$	−0.187410	+	0.324604i	−0.00602982	+	0.0104440i
$967$	2.51917	+	33.6160i	0.0810110	+	1.08102i	0.878519	+	0.477708i	$0.158532\pi$
$967$	2.51917	+	33.6160i	0.0810110	+	1.08102i	−0.797508	+	0.603309i	$0.793849\pi$
$968$	−12.2903	+	3.79106i	−0.395026	+	0.121849i
$969$	−0.0621532	−	0.0779377i	−0.00199665	−	0.00250372i
$970$	−1.63457	+	1.51666i	−0.0524828	+	0.0486969i
$971$	−0.802647	−	2.04511i	−0.0257582	−	0.0656307i	0.917416	−	0.397929i	$-0.130271\pi$
$971$	−0.802647	−	2.04511i	−0.0257582	−	0.0656307i	−0.943174	+	0.332299i	$0.892176\pi$
$972$	1.34730	−	3.43286i	0.0432146	−	0.110109i
$973$	−6.79701	−	11.7728i	−0.217902	−	0.377417i
$974$	−2.63134	−	0.396611i	−0.0843137	−	0.0127082i
$975$	−1.93453	−	0.291583i	−0.0619545	−	0.00933814i
$976$	−14.2463	−	9.71300i	−0.456015	−	0.310905i
$977$	16.7443	+	15.5364i	0.535696	+	0.497054i	0.900991	−	0.433839i	$-0.142841\pi$
$977$	16.7443	+	15.5364i	0.535696	+	0.497054i	−0.365294	+	0.930892i	$0.619032\pi$
$978$	−0.0829625	+	0.211385i	−0.00265285	+	0.00675934i
$979$	20.7045	+	19.2109i	0.661718	+	0.613984i
$980$	−23.2742	+	29.1849i	−0.743467	+	0.932278i
$981$	−21.1983	−	14.4528i	−0.676809	−	0.461441i
$982$	13.8105	+	2.08160i	0.440711	+	0.0664265i
$983$	−11.5054	+	7.84427i	−0.366966	+	0.250193i	−0.732737	−	0.680512i	$-0.761758\pi$
$983$	−11.5054	+	7.84427i	−0.366966	+	0.250193i	0.365771	+	0.930705i	$0.380805\pi$
$984$	0.202389	−	0.0305052i	0.00645192	−	0.000972470i
$985$	−17.3625	+	16.1100i	−0.553214	+	0.513308i
$986$	0.361681	+	0.246590i	0.0115183	+	0.00785303i
$987$	0.804036			0.0255927
$988$	6.08191	+	10.5342i	0.193491	+	0.335137i
$989$	0.150951	+	0.661358i	0.00479995	+	0.0210300i
$990$	−4.12370	−	10.5070i	−0.131060	−	0.333935i
$991$	48.4012	−	23.3088i	1.53752	−	0.740428i	0.542491	−	0.840061i	$-0.317481\pi$
$991$	48.4012	−	23.3088i	1.53752	−	0.740428i	0.995024	+	0.0996329i	$0.0317668\pi$
$992$	−14.8524	−	25.7252i	−0.471565	−	0.816775i
$993$	−0.248060	−	1.08682i	−0.00787193	−	0.0344892i
$994$	0.772450	−	3.38433i	0.0245006	−	0.107344i
$995$	35.9390	+	11.0857i	1.13934	+	0.351441i
$996$	0.367200	+	1.60881i	0.0116352	+	0.0509770i
$997$	−2.54073	−	33.9037i	−0.0804659	−	1.07374i	−0.880581	−	0.473896i	$-0.842847\pi$
$997$	−2.54073	−	33.9037i	−0.0804659	−	1.07374i	0.800115	−	0.599847i	$-0.204772\pi$
$998$	−3.82596	−	6.62676i	−0.121109	−	0.209767i
$999$	−1.23684	−	1.14762i	−0.0391318	−	0.0363090i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.2.h.a.13.19	✓	540
547.505	even	21	inner	547.2.h.a.505.19	yes	540

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.2.h.a.13.19	✓	540	1.1	even	1	trivial
547.2.h.a.505.19	yes	540	547.505	even	21	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:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	547.h (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0370969 + 0.495024i) q^{2} +(-0.0486951 + 0.0610617i) q^{3} +(1.73399 + 0.261357i) q^{4} +(2.75036 - 2.55197i) q^{5} +(-0.0284205 - 0.0263704i) q^{6} +(1.13879 - 0.171645i) q^{7} +(-0.414627 + 1.81660i) q^{8} +(0.666205 + 2.91884i) q^{9} +O(q^{10})\)	\(q+(-0.0370969 + 0.495024i) q^{2} +(-0.0486951 + 0.0610617i) q^{3} +(1.73399 + 0.261357i) q^{4} +(2.75036 - 2.55197i) q^{5} +(-0.0284205 - 0.0263704i) q^{6} +(1.13879 - 0.171645i) q^{7} +(-0.414627 + 1.81660i) q^{8} +(0.666205 + 2.91884i) q^{9} +(1.16125 + 1.45617i) q^{10} +(-1.01210 + 1.75301i) q^{11} +(-0.100396 + 0.0931535i) q^{12} +(-2.28013 + 1.55456i) q^{13} +(0.0427228 + 0.570097i) q^{14} +(0.0218981 + 0.292210i) q^{15} +(2.46746 + 0.761110i) q^{16} +(-0.485233 - 0.149675i) q^{17} +(-1.46961 + 0.221508i) q^{18} +(-0.187840 - 2.50655i) q^{19} +(5.43608 - 3.70625i) q^{20} +(-0.0449726 + 0.0778949i) q^{21} +(-0.830236 - 0.566046i) q^{22} +(-0.627333 - 8.37118i) q^{23} +(-0.0907344 - 0.113777i) q^{24} +(0.678327 - 9.05165i) q^{25} +(-0.684960 - 1.18639i) q^{26} +(-0.421769 - 0.203113i) q^{27} +2.01952 q^{28} +(-0.386423 + 1.69303i) q^{29} -0.145463 q^{30} +(-3.69788 + 4.63699i) q^{31} +(-1.82980 + 4.66224i) q^{32} +(-0.0577575 - 0.147164i) q^{33} +(0.0920930 - 0.234649i) q^{34} +(2.69406 - 3.37825i) q^{35} +(0.392335 + 5.23535i) q^{36} +(3.44410 + 1.06237i) q^{37} +1.24777 q^{38} +(0.0161066 - 0.214928i) q^{39} +(3.49553 + 6.05443i) q^{40} +(-0.703221 + 1.21801i) q^{41} +(-0.0368915 - 0.0251522i) q^{42} +(-0.0799067 + 0.0120440i) q^{43} +(-2.21314 + 2.77519i) q^{44} +(9.28108 + 6.32773i) q^{45} +4.16720 q^{46} +(-4.46958 - 7.74155i) q^{47} +(-0.166628 + 0.113605i) q^{48} +(-5.42162 + 1.67235i) q^{49} +(4.45562 + 0.671576i) q^{50} +(0.0327678 - 0.0223407i) q^{51} +(-4.36001 + 2.09967i) q^{52} +(4.06431 - 2.77100i) q^{53} +(0.116192 - 0.201251i) q^{54} +(1.68998 + 7.40427i) q^{55} +(-0.160363 + 2.13990i) q^{56} +(0.162201 + 0.110587i) q^{57} +(-0.823754 - 0.254095i) q^{58} +(-0.702793 + 1.21727i) q^{59} +(-0.0384000 + 0.512412i) q^{60} +(-6.38081 - 1.96822i) q^{61} +(-2.15824 - 2.00256i) q^{62} +(1.25967 + 3.20960i) q^{63} +(2.41288 + 1.16198i) q^{64} +(-2.30399 + 10.0944i) q^{65} +(0.0749921 - 0.0231320i) q^{66} +(9.48688 + 2.92632i) q^{67} +(-0.802270 - 0.386353i) q^{68} +(0.541706 + 0.369329i) q^{69} +(1.57237 + 1.45895i) q^{70} +(-5.80228 - 1.78977i) q^{71} -5.57859 q^{72} +(0.000648877 - 0.00865866i) q^{73} +(-0.653661 + 1.66550i) q^{74} +(0.519678 + 0.482191i) q^{75} +(0.329391 - 4.39542i) q^{76} +(-0.851678 + 2.17004i) q^{77} +(0.105797 + 0.0159463i) q^{78} +(-2.41088 - 3.02314i) q^{79} +(8.72874 - 4.20354i) q^{80} +(-8.05929 + 3.88115i) q^{81} +(-0.576858 - 0.393295i) q^{82} +(6.02451 - 10.4348i) q^{83} +(-0.0983404 + 0.123315i) q^{84} +(-1.71653 + 0.826638i) q^{85} +(-0.00299777 - 0.0400025i) q^{86} +(-0.0845623 - 0.106038i) q^{87} +(-2.76488 - 2.56543i) q^{88} +(3.10489 - 13.6034i) q^{89} +(-3.47668 + 4.35961i) q^{90} +(-2.32976 + 2.16170i) q^{91} +(1.10008 - 14.6795i) q^{92} +(-0.103074 - 0.451597i) q^{93} +(3.99806 - 1.92536i) q^{94} +(-6.91325 - 6.41456i) q^{95} +(-0.195582 - 0.338759i) q^{96} +(0.0894676 + 1.19386i) q^{97} +(-0.626727 - 2.74587i) q^{98} +(-5.79102 - 1.78629i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 540 q - 13 q^{2} - 10 q^{3} + 33 q^{4} - 15 q^{5} + 10 q^{6} - 2 q^{7} - 26 q^{8} - 96 q^{9}+O(q^{10}) \) 540 * q - 13 * q^2 - 10 * q^3 + 33 * q^4 - 15 * q^5 + 10 * q^6 - 2 * q^7 - 26 * q^8 - 96 * q^9	\( 540 q - 13 q^{2} - 10 q^{3} + 33 q^{4} - 15 q^{5} + 10 q^{6} - 2 q^{7} - 26 q^{8} - 96 q^{9} - 4 q^{10} - 8 q^{11} - 18 q^{12} - 11 q^{13} + 5 q^{14} - 7 q^{15} + 53 q^{16} - 10 q^{17} - 59 q^{18} - 12 q^{19} - 18 q^{20} + 20 q^{21} + 70 q^{22} - 15 q^{23} - 46 q^{24} + 26 q^{25} - 39 q^{26} - q^{27} - 56 q^{28} - 40 q^{29} - 100 q^{30} + 59 q^{31} - 5 q^{32} - 15 q^{33} - 8 q^{34} + 36 q^{35} + 43 q^{36} - 32 q^{37} - 108 q^{38} + 34 q^{39} - 27 q^{40} + 39 q^{41} + 46 q^{42} - 16 q^{43} - 110 q^{44} - 103 q^{45} + 12 q^{46} - 60 q^{47} + 42 q^{48} + 57 q^{49} - 168 q^{50} + 57 q^{51} - 46 q^{52} - 30 q^{53} + 113 q^{54} + 38 q^{55} + 64 q^{56} + 22 q^{57} - 88 q^{58} + 55 q^{59} + 9 q^{60} + 26 q^{61} - 32 q^{62} + 6 q^{63} - 50 q^{64} + 73 q^{65} + 72 q^{66} - 104 q^{67} - 181 q^{68} - 125 q^{69} - 50 q^{70} + 39 q^{71} - 434 q^{72} + 46 q^{73} - 178 q^{74} + 248 q^{75} - 126 q^{76} - 52 q^{77} - 82 q^{78} + 86 q^{79} + 208 q^{80} - 4 q^{81} + 177 q^{82} + 39 q^{83} + 124 q^{84} - 12 q^{85} + 2 q^{86} + 162 q^{87} - 34 q^{88} + 63 q^{89} + 121 q^{90} + 21 q^{91} + q^{92} - 57 q^{93} + 67 q^{94} - 143 q^{95} + 489 q^{96} + 119 q^{97} - 10 q^{98} - 120 q^{99}+O(q^{100}) \) 540 * q - 13 * q^2 - 10 * q^3 + 33 * q^4 - 15 * q^5 + 10 * q^6 - 2 * q^7 - 26 * q^8 - 96 * q^9 - 4 * q^10 - 8 * q^11 - 18 * q^12 - 11 * q^13 + 5 * q^14 - 7 * q^15 + 53 * q^16 - 10 * q^17 - 59 * q^18 - 12 * q^19 - 18 * q^20 + 20 * q^21 + 70 * q^22 - 15 * q^23 - 46 * q^24 + 26 * q^25 - 39 * q^26 - q^27 - 56 * q^28 - 40 * q^29 - 100 * q^30 + 59 * q^31 - 5 * q^32 - 15 * q^33 - 8 * q^34 + 36 * q^35 + 43 * q^36 - 32 * q^37 - 108 * q^38 + 34 * q^39 - 27 * q^40 + 39 * q^41 + 46 * q^42 - 16 * q^43 - 110 * q^44 - 103 * q^45 + 12 * q^46 - 60 * q^47 + 42 * q^48 + 57 * q^49 - 168 * q^50 + 57 * q^51 - 46 * q^52 - 30 * q^53 + 113 * q^54 + 38 * q^55 + 64 * q^56 + 22 * q^57 - 88 * q^58 + 55 * q^59 + 9 * q^60 + 26 * q^61 - 32 * q^62 + 6 * q^63 - 50 * q^64 + 73 * q^65 + 72 * q^66 - 104 * q^67 - 181 * q^68 - 125 * q^69 - 50 * q^70 + 39 * q^71 - 434 * q^72 + 46 * q^73 - 178 * q^74 + 248 * q^75 - 126 * q^76 - 52 * q^77 - 82 * q^78 + 86 * q^79 + 208 * q^80 - 4 * q^81 + 177 * q^82 + 39 * q^83 + 124 * q^84 - 12 * q^85 + 2 * q^86 + 162 * q^87 - 34 * q^88 + 63 * q^89 + 121 * q^90 + 21 * q^91 + q^92 - 57 * q^93 + 67 * q^94 - 143 * q^95 + 489 * q^96 + 119 * q^97 - 10 * q^98 - 120 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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