LMFDB - Embedded newform 418.2.n.e.125.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(49,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([12, 20]))

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

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

chi := DirichletCharacter("418.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.n (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$9$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			125.7
Character	$\chi$	$=$	418.125
Dual form			418.2.n.e.311.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.913545 - 0.406737i) q^{2} +(0.927739 + 1.03036i) q^{3} +(0.669131 - 0.743145i) q^{4} +(0.231918 + 2.20655i) q^{5} +(1.26662 + 0.563934i) q^{6} +(-0.102451 - 0.315310i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.112646 - 1.07176i) q^{9} +O(q^{10})$	\(q+(0.913545 - 0.406737i) q^{2} +(0.927739 + 1.03036i) q^{3} +(0.669131 - 0.743145i) q^{4} +(0.231918 + 2.20655i) q^{5} +(1.26662 + 0.563934i) q^{6} +(-0.102451 - 0.315310i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.112646 - 1.07176i) q^{9} +(1.10935 + 1.92145i) q^{10} +(3.15114 - 1.03455i) q^{11} +1.38648 q^{12} +(-0.488750 + 4.65014i) q^{13} +(-0.221841 - 0.246380i) q^{14} +(-2.05838 + 2.28606i) q^{15} +(-0.104528 - 0.994522i) q^{16} +(-0.427284 - 4.06534i) q^{17} +(-0.333016 - 1.02492i) q^{18} +(-1.82993 + 3.95618i) q^{19} +(1.79497 + 1.30412i) q^{20} +(0.229835 - 0.398086i) q^{21} +(2.45793 - 2.22679i) q^{22} +(2.58093 + 4.47030i) q^{23} +(1.26662 - 0.563934i) q^{24} +(0.0756648 - 0.0160831i) q^{25} +(1.44489 + 4.44691i) q^{26} +(4.57387 - 3.32311i) q^{27} +(-0.302874 - 0.134848i) q^{28} +(-4.71354 + 5.23492i) q^{29} +(-0.950597 + 2.92564i) q^{30} +(-7.57417 - 5.50296i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.98939 + 2.28702i) q^{33} +(-2.04387 - 3.54008i) q^{34} +(0.671987 - 0.299188i) q^{35} +(-0.721097 - 0.800860i) q^{36} +(-1.95130 - 6.00548i) q^{37} +(-0.0625972 + 4.35845i) q^{38} +(-5.24474 + 3.81053i) q^{39} +(2.17022 + 0.461294i) q^{40} +(-6.21752 - 6.90526i) q^{41} +(0.0480486 - 0.457152i) q^{42} +(2.52227 - 4.36870i) q^{43} +(1.33971 - 3.03400i) q^{44} +2.39101 q^{45} +(4.17603 + 3.03406i) q^{46} +(-8.87854 + 1.88719i) q^{47} +(0.927739 - 1.03036i) q^{48} +(5.57419 - 4.04989i) q^{49} +(0.0625817 - 0.0454683i) q^{50} +(3.79235 - 4.21183i) q^{51} +(3.12869 + 3.47476i) q^{52} +(1.32706 - 12.6261i) q^{53} +(2.82681 - 4.89617i) q^{54} +(3.01359 + 6.71323i) q^{55} -0.331537 q^{56} +(-5.77398 + 1.78482i) q^{57} +(-2.17680 + 6.69951i) q^{58} +(-0.106629 - 0.0226646i) q^{59} +(0.321550 + 3.05934i) q^{60} +(12.1117 + 5.39248i) q^{61} +(-9.15761 - 1.94651i) q^{62} +(-0.349477 + 0.0742837i) q^{63} +(-0.809017 - 0.587785i) q^{64} -10.3741 q^{65} +(4.57471 + 0.466662i) q^{66} +(-2.37230 - 4.10894i) q^{67} +(-3.30704 - 2.40271i) q^{68} +(-2.21158 + 6.80655i) q^{69} +(0.492200 - 0.546644i) q^{70} +(-0.139024 - 1.32273i) q^{71} +(-0.984494 - 0.438325i) q^{72} +(-9.54220 - 2.02826i) q^{73} +(-4.22525 - 4.69262i) q^{74} +(0.0867685 + 0.0630410i) q^{75} +(1.71556 + 4.00710i) q^{76} +(-0.649040 - 0.887598i) q^{77} +(-3.24143 + 5.61432i) q^{78} +(-2.76317 + 1.23024i) q^{79} +(2.17022 - 0.461294i) q^{80} +(4.50501 + 0.957569i) q^{81} +(-8.48861 - 3.77937i) q^{82} +(-4.71938 + 3.42883i) q^{83} +(-0.142046 - 0.437172i) q^{84} +(8.87128 - 1.88565i) q^{85} +(0.527298 - 5.01691i) q^{86} -9.76678 q^{87} +(-0.0101561 - 3.31661i) q^{88} +(8.87060 + 15.3643i) q^{89} +(2.18430 - 0.972513i) q^{90} +(1.51631 - 0.322302i) q^{91} +(5.04906 + 1.07321i) q^{92} +(-1.35683 - 12.9094i) q^{93} +(-7.34336 + 5.33526i) q^{94} +(-9.15390 - 3.12031i) q^{95} +(0.428447 - 1.31862i) q^{96} +(8.40671 - 3.74291i) q^{97} +(3.44504 - 5.96699i) q^{98} +(-0.753821 - 3.49381i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 9 q^{2} - 2 q^{3} + 9 q^{4} + 8 q^{5} + 3 q^{6} - 20 q^{7} - 18 q^{8} + 9 q^{9}+O(q^{10}) $ 72 * q + 9 * q^2 - 2 * q^3 + 9 * q^4 + 8 * q^5 + 3 * q^6 - 20 * q^7 - 18 * q^8 + 9 * q^9	\( 72 q + 9 q^{2} - 2 q^{3} + 9 q^{4} + 8 q^{5} + 3 q^{6} - 20 q^{7} - 18 q^{8} + 9 q^{9} - 22 q^{10} + 10 q^{11} + 4 q^{12} + 15 q^{13} + 10 q^{14} + 9 q^{15} + 9 q^{16} + 6 q^{17} - 28 q^{18} + 7 q^{19} - 16 q^{20} + 48 q^{21} - 15 q^{22} - 20 q^{23} + 3 q^{24} + 7 q^{25} + 30 q^{26} - 56 q^{27} - 10 q^{28} + 35 q^{29} - 18 q^{30} + 52 q^{31} - 36 q^{32} - 12 q^{33} - 4 q^{34} - 9 q^{35} + 14 q^{36} - 52 q^{37} - 2 q^{38} - 42 q^{39} + 3 q^{40} + 41 q^{41} - 2 q^{42} + 14 q^{43} + 116 q^{45} - 50 q^{46} + 19 q^{47} - 2 q^{48} + 46 q^{49} - 44 q^{50} + 33 q^{51} - 15 q^{52} - 15 q^{53} - 2 q^{54} - 55 q^{55} - 33 q^{57} - 70 q^{58} - 13 q^{59} - 6 q^{60} + 8 q^{61} + 19 q^{62} + 40 q^{63} - 18 q^{64} + 120 q^{65} + 23 q^{66} + 2 q^{67} - 12 q^{68} - 194 q^{69} + q^{70} + 52 q^{71} + 9 q^{72} - 48 q^{73} + 26 q^{74} - 158 q^{75} + 20 q^{76} + 130 q^{77} + 46 q^{78} - 48 q^{79} + 3 q^{80} + 48 q^{81} - 14 q^{82} - 62 q^{83} + 44 q^{84} - 27 q^{85} - 16 q^{86} - 164 q^{87} + 10 q^{88} + 20 q^{89} + 52 q^{90} + 4 q^{91} - 15 q^{92} - 39 q^{93} - 8 q^{94} + 69 q^{95} + 4 q^{96} + 2 q^{97} - 48 q^{98} + 9 q^{99}+O(q^{100}) \) 72 * q + 9 * q^2 - 2 * q^3 + 9 * q^4 + 8 * q^5 + 3 * q^6 - 20 * q^7 - 18 * q^8 + 9 * q^9 - 22 * q^10 + 10 * q^11 + 4 * q^12 + 15 * q^13 + 10 * q^14 + 9 * q^15 + 9 * q^16 + 6 * q^17 - 28 * q^18 + 7 * q^19 - 16 * q^20 + 48 * q^21 - 15 * q^22 - 20 * q^23 + 3 * q^24 + 7 * q^25 + 30 * q^26 - 56 * q^27 - 10 * q^28 + 35 * q^29 - 18 * q^30 + 52 * q^31 - 36 * q^32 - 12 * q^33 - 4 * q^34 - 9 * q^35 + 14 * q^36 - 52 * q^37 - 2 * q^38 - 42 * q^39 + 3 * q^40 + 41 * q^41 - 2 * q^42 + 14 * q^43 + 116 * q^45 - 50 * q^46 + 19 * q^47 - 2 * q^48 + 46 * q^49 - 44 * q^50 + 33 * q^51 - 15 * q^52 - 15 * q^53 - 2 * q^54 - 55 * q^55 - 33 * q^57 - 70 * q^58 - 13 * q^59 - 6 * q^60 + 8 * q^61 + 19 * q^62 + 40 * q^63 - 18 * q^64 + 120 * q^65 + 23 * q^66 + 2 * q^67 - 12 * q^68 - 194 * q^69 + q^70 + 52 * q^71 + 9 * q^72 - 48 * q^73 + 26 * q^74 - 158 * q^75 + 20 * q^76 + 130 * q^77 + 46 * q^78 - 48 * q^79 + 3 * q^80 + 48 * q^81 - 14 * q^82 - 62 * q^83 + 44 * q^84 - 27 * q^85 - 16 * q^86 - 164 * q^87 + 10 * q^88 + 20 * q^89 + 52 * q^90 + 4 * q^91 - 15 * q^92 - 39 * q^93 - 8 * q^94 + 69 * q^95 + 4 * q^96 + 2 * q^97 - 48 * q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	0.913545	−	0.406737i	0.645974	−	0.287606i
$2$	0.913545	−	0.406737i	0.645974	−	0.287606i
$3$	0.927739	+	1.03036i	0.535630	+	0.594878i	0.948840	−	0.315758i	$-0.102259\pi$
$3$	0.927739	+	1.03036i	0.535630	+	0.594878i	−0.413209	+	0.910636i	$0.635592\pi$
$4$	0.669131	−	0.743145i	0.334565	−	0.371572i
$5$	0.231918	+	2.20655i	0.103717	+	0.986799i	0.915358	+	0.402642i	$0.131908\pi$
$5$	0.231918	+	2.20655i	0.103717	+	0.986799i	−0.811641	+	0.584157i	$0.801425\pi$
$6$	1.26662	+	0.563934i	0.517094	+	0.230225i
$7$	−0.102451	−	0.315310i	−0.0387227	−	0.119176i	0.929827	−	0.367998i	$-0.119957\pi$
$7$	−0.102451	−	0.315310i	−0.0387227	−	0.119176i	−0.968549	+	0.248822i	$0.919957\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	0.112646	−	1.07176i	0.0375488	−	0.357253i
$10$	1.10935	+	1.92145i	0.350808	+	0.607617i
$11$	3.15114	−	1.03455i	0.950106	−	0.311928i
$11$	3.15114	−	1.03455i	0.950106	−	0.311928i
$12$	1.38648			0.400243
$13$	−0.488750	+	4.65014i	−0.135555	+	1.28972i	0.689343	+	0.724435i	$0.257899\pi$
$13$	−0.488750	+	4.65014i	−0.135555	+	1.28972i	−0.824898	+	0.565282i	$0.808767\pi$
$14$	−0.221841	−	0.246380i	−0.0592896	−	0.0658478i
$15$	−2.05838	+	2.28606i	−0.531471	+	0.590258i
$16$	−0.104528	−	0.994522i	−0.0261321	−	0.248630i
$17$	−0.427284	−	4.06534i	−0.103632	−	0.985989i	−0.915546	−	0.402213i	$-0.868241\pi$
$17$	−0.427284	−	4.06534i	−0.103632	−	0.985989i	0.811914	−	0.583776i	$-0.198426\pi$
$18$	−0.333016	−	1.02492i	−0.0784927	−	0.241576i
$19$	−1.82993	+	3.95618i	−0.419814	+	0.907610i
$19$	−1.82993	+	3.95618i	−0.419814	+	0.907610i
$20$	1.79497	+	1.30412i	0.401367	+	0.291610i
$21$	0.229835	−	0.398086i	0.0501541	−	0.0868695i
$22$	2.45793	−	2.22679i	0.524031	−	0.474754i
$23$	2.58093	+	4.47030i	0.538161	+	0.932122i	0.999003	+	0.0446398i	$0.0142140\pi$
$23$	2.58093	+	4.47030i	0.538161	+	0.932122i	−0.460842	+	0.887482i	$0.652453\pi$
$24$	1.26662	−	0.563934i	0.258547	−	0.115112i
$25$	0.0756648	−	0.0160831i	0.0151330	−	0.00321661i
$26$	1.44489	+	4.44691i	0.283366	+	0.872110i
$27$	4.57387	−	3.32311i	0.880242	−	0.639533i
$28$	−0.302874	−	0.134848i	−0.0572378	−	0.0254839i
$29$	−4.71354	+	5.23492i	−0.875283	+	0.972100i	−0.999798	−	0.0201174i	$-0.993596\pi$
$29$	−4.71354	+	5.23492i	−0.875283	+	0.972100i	0.124514	+	0.992218i	$0.460263\pi$
$30$	−0.950597	+	2.92564i	−0.173554	+	0.534146i
$31$	−7.57417	−	5.50296i	−1.36036	−	0.988361i	−0.998422	−	0.0561590i	$-0.982115\pi$
$31$	−7.57417	−	5.50296i	−1.36036	−	0.988361i	−0.361940	−	0.932202i	$-0.617885\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	3.98939	+	2.28702i	0.694464	+	0.398119i
$34$	−2.04387	−	3.54008i	−0.350520	−	0.607119i
$35$	0.671987	−	0.299188i	0.113587	−	0.0505720i
$36$	−0.721097	−	0.800860i	−0.120183	−	0.133477i
$37$	−1.95130	−	6.00548i	−0.320792	−	0.987295i	−0.973305	−	0.229517i	$-0.926285\pi$
$37$	−1.95130	−	6.00548i	−0.320792	−	0.987295i	0.652513	−	0.757778i	$-0.273715\pi$
$38$	−0.0625972	+	4.35845i	−0.0101546	+	0.707034i
$39$	−5.24474	+	3.81053i	−0.839831	+	0.610173i
$40$	2.17022	+	0.461294i	0.343142	+	0.0729370i
$41$	−6.21752	−	6.90526i	−0.971014	−	1.07842i	−0.996894	−	0.0787552i	$-0.974905\pi$
$41$	−6.21752	−	6.90526i	−0.971014	−	1.07842i	0.0258800	−	0.999665i	$-0.491761\pi$
$42$	0.0480486	−	0.457152i	0.00741407	−	0.0705401i
$43$	2.52227	−	4.36870i	0.384643	−	0.666221i	−0.607077	−	0.794643i	$-0.707658\pi$
$43$	2.52227	−	4.36870i	0.384643	−	0.666221i	0.991720	+	0.128422i	$0.0409913\pi$
$44$	1.33971	−	3.03400i	0.201969	−	0.457393i
$45$	2.39101			0.356431
$46$	4.17603	+	3.03406i	0.615722	+	0.447348i
$47$	−8.87854	+	1.88719i	−1.29507	+	0.275275i	−0.803365	−	0.595487i	$-0.796959\pi$
$47$	−8.87854	+	1.88719i	−1.29507	+	0.275275i	−0.491704	+	0.870763i	$0.663626\pi$
$48$	0.927739	−	1.03036i	0.133908	−	0.148719i
$49$	5.57419	−	4.04989i	0.796314	−	0.578556i
$50$	0.0625817	−	0.0454683i	0.00885039	−	0.00643018i
$51$	3.79235	−	4.21183i	0.531035	−	0.589774i
$52$	3.12869	+	3.47476i	0.433871	+	0.481863i
$53$	1.32706	−	12.6261i	0.182285	−	1.73433i	−0.395788	−	0.918342i	$-0.629529\pi$
$53$	1.32706	−	12.6261i	0.182285	−	1.73433i	0.578074	−	0.815985i	$-0.303805\pi$
$54$	2.82681	−	4.89617i	0.384680	−	0.666285i
$55$	3.01359	+	6.71323i	0.406352	+	0.905211i
$56$	−0.331537			−0.0443035
$57$	−5.77398	+	1.78482i	−0.764782	+	0.236406i
$58$	−2.17680	+	6.69951i	−0.285828	+	0.879689i
$59$	−0.106629	−	0.0226646i	−0.0138819	−	0.00295068i	0.200966	−	0.979598i	$-0.435592\pi$
$59$	−0.106629	−	0.0226646i	−0.0138819	−	0.00295068i	−0.214847	+	0.976648i	$0.568925\pi$
$60$	0.321550	+	3.05934i	0.0415119	+	0.394960i
$61$	12.1117	+	5.39248i	1.55075	+	0.690437i	0.990452	−	0.137857i	$-0.0440213\pi$
$61$	12.1117	+	5.39248i	1.55075	+	0.690437i	0.560294	+	0.828293i	$0.310688\pi$
$62$	−9.15761	−	1.94651i	−1.16302	−	0.247207i
$63$	−0.349477	+	0.0742837i	−0.0440300	+	0.00935887i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−10.3741			−1.28675
$66$	4.57471	+	0.466662i	0.563107	+	0.0574421i
$67$	−2.37230	−	4.10894i	−0.289822	−	0.501987i	0.683945	−	0.729534i	$-0.260263\pi$
$67$	−2.37230	−	4.10894i	−0.289822	−	0.501987i	−0.973767	+	0.227547i	$0.926930\pi$
$68$	−3.30704	−	2.40271i	−0.401038	−	0.291371i
$69$	−2.21158	+	6.80655i	−0.266243	+	0.819412i
$70$	0.492200	−	0.546644i	0.0588292	−	0.0653364i
$71$	−0.139024	−	1.32273i	−0.0164992	−	0.156979i	0.983170	−	0.182692i	$-0.0584811\pi$
$71$	−0.139024	−	1.32273i	−0.0164992	−	0.156979i	−0.999669	+	0.0257129i	$0.991814\pi$
$72$	−0.984494	−	0.438325i	−0.116024	−	0.0516571i
$73$	−9.54220	−	2.02826i	−1.11683	−	0.237390i	−0.387714	−	0.921780i	$-0.626735\pi$
$73$	−9.54220	−	2.02826i	−1.11683	−	0.237390i	−0.729116	+	0.684390i	$0.760069\pi$
$74$	−4.22525	−	4.69262i	−0.491175	−	0.545505i
$75$	0.0867685	+	0.0630410i	0.0100192	+	0.00727935i
$76$	1.71556	+	4.00710i	0.196788	+	0.459646i
$77$	−0.649040	−	0.887598i	−0.0739649	−	0.101151i
$78$	−3.24143	+	5.61432i	−0.367020	+	0.635697i
$79$	−2.76317	+	1.23024i	−0.310881	+	0.138413i	−0.556246	−	0.831018i	$-0.687759\pi$
$79$	−2.76317	+	1.23024i	−0.310881	+	0.138413i	0.245365	+	0.969431i	$0.421092\pi$
$80$	2.17022	−	0.461294i	0.242638	−	0.0515743i
$81$	4.50501	+	0.957569i	0.500557	+	0.106397i
$82$	−8.48861	−	3.77937i	−0.937410	−	0.417362i
$83$	−4.71938	+	3.42883i	−0.518019	+	0.376363i	−0.815857	−	0.578254i	$-0.803734\pi$
$83$	−4.71938	+	3.42883i	−0.518019	+	0.376363i	0.297838	+	0.954616i	$0.403734\pi$
$84$	−0.142046	−	0.437172i	−0.0154985	−	0.0476994i
$85$	8.87128	−	1.88565i	0.962225	−	0.204527i
$86$	0.527298	−	5.01691i	0.0568601	−	0.540987i
$87$	−9.76678			−1.04711
$88$	−0.0101561	−	3.31661i	−0.00108264	−	0.353552i
$89$	8.87060	+	15.3643i	0.940282	+	1.62862i	0.764933	+	0.644110i	$0.222772\pi$
$89$	8.87060	+	15.3643i	0.940282	+	1.62862i	0.175349	+	0.984506i	$0.443895\pi$
$90$	2.18430	−	0.972513i	0.230245	−	0.102512i
$91$	1.51631	−	0.322302i	0.158952	−	0.0337864i
$92$	5.04906	+	1.07321i	0.526401	+	0.111890i
$93$	−1.35683	−	12.9094i	−0.140697	−	1.33864i
$94$	−7.34336	+	5.33526i	−0.757410	+	0.550290i
$95$	−9.15390	−	3.12031i	−0.939170	−	0.320138i
$96$	0.428447	−	1.31862i	0.0437282	−	0.134582i
$97$	8.40671	−	3.74291i	0.853572	−	0.380035i	0.0671638	−	0.997742i	$-0.478605\pi$
$97$	8.40671	−	3.74291i	0.853572	−	0.380035i	0.786408	+	0.617707i	$0.211938\pi$
$98$	3.44504	−	5.96699i	0.348002	−	0.602757i
$99$	−0.753821	−	3.49381i	−0.0757619	−	0.351141i
$100$	0.0386776	−	0.0669916i	0.00386776	−	0.00669916i
$101$	−0.856882	+	8.15269i	−0.0852629	+	0.811223i	0.865418	+	0.501051i	$0.167053\pi$
$101$	−0.856882	+	8.15269i	−0.0852629	+	0.811223i	−0.950681	+	0.310171i	$0.899614\pi$
$102$	1.75138	−	5.39018i	0.173412	−	0.533708i
$103$	−2.59350	−	7.98196i	−0.255545	−	0.786486i	−0.993722	−	0.111879i	$-0.964313\pi$
$103$	−2.59350	−	7.98196i	−0.255545	−	0.786486i	0.738177	−	0.674607i	$-0.235687\pi$
$104$	4.27151	+	1.90180i	0.418856	+	0.186487i
$105$	0.931700	+	0.414819i	0.0909246	+	0.0404822i
$106$	−3.92317	−	12.0743i	−0.381052	−	1.17276i
$107$	−5.80473	+	17.8651i	−0.561164	+	1.72709i	0.117918	+	0.993023i	$0.462378\pi$
$107$	−5.80473	+	17.8651i	−0.561164	+	1.72709i	−0.679082	+	0.734062i	$0.737622\pi$
$108$	0.590964	−	5.62264i	0.0568655	−	0.541039i
$109$	−2.80945	+	4.86611i	−0.269097	+	0.466089i	−0.968629	−	0.248512i	$-0.920058\pi$
$109$	−2.80945	+	4.86611i	−0.269097	+	0.466089i	0.699532	+	0.714601i	$0.253392\pi$
$110$	5.48356	+	4.90710i	0.522837	+	0.467874i
$111$	4.37750	−	7.58205i	0.415494	−	0.719657i
$112$	−0.302874	+	0.134848i	−0.0286189	+	0.0127420i
$113$	1.80476	−	5.55448i	0.169777	−	0.522521i	−0.829579	−	0.558389i	$-0.811420\pi$
$113$	1.80476	−	5.55448i	0.169777	−	0.522521i	0.999357	+	0.0358680i	$0.0114196\pi$
$114$	−4.54884	+	3.97900i	−0.426038	+	0.372668i
$115$	−9.26537	+	6.73169i	−0.864000	+	0.627733i
$116$	0.736328	+	7.00569i	0.0683663	+	0.650462i
$117$	4.92878	+	1.04764i	0.455666	+	0.0968547i
$118$	−0.106629	+	0.0226646i	−0.00981596	+	0.00208645i
$119$	−1.23807	+	0.551223i	−0.113493	+	0.0505305i
$120$	1.53810	+	2.66406i	0.140408	+	0.243195i
$121$	8.85942	−	6.52002i	0.805402	−	0.592729i
$122$	13.2579			1.20032
$123$	1.34665	−	12.8126i	0.121424	−	1.15527i
$124$	−9.15761	+	1.94651i	−0.822377	+	0.174802i
$125$	3.48112	+	10.7138i	0.311361	+	0.958270i
$126$	−0.289050	+	0.210007i	−0.0257506	+	0.0187089i
$127$	−11.2598	−	5.01320i	−0.999148	−	0.444849i	−0.159042	−	0.987272i	$-0.550841\pi$
$127$	−11.2598	−	5.01320i	−0.999148	−	0.444849i	−0.840106	+	0.542422i	$0.817507\pi$
$128$	−0.978148	−	0.207912i	−0.0864569	−	0.0183770i
$129$	6.84134	−	1.45417i	0.602346	−	0.128033i
$130$	−9.47722	+	4.21953i	−0.831208	+	0.370077i
$131$	−7.07232	+	12.2496i	−0.617912	+	1.07025i	0.371955	+	0.928251i	$0.378688\pi$
$131$	−7.07232	+	12.2496i	−0.617912	+	1.07025i	−0.989866	+	0.142003i	$0.954646\pi$
$132$	4.36901	−	1.43438i	0.380274	−	0.124847i
$133$	1.43490	+	0.171682i	0.124422	+	0.0148867i
$134$	−3.83846	−	2.78880i	−0.331592	−	0.240916i
$135$	8.39337	+	9.32178i	0.722386	+	0.802291i
$136$	−3.99841	−	0.849887i	−0.342860	−	0.0728772i
$137$	−4.88207	−	2.17364i	−0.417103	−	0.185706i	0.187445	−	0.982275i	$-0.439979\pi$
$137$	−4.88207	−	2.17364i	−0.417103	−	0.185706i	−0.604548	+	0.796569i	$0.706646\pi$
$138$	0.748093	+	7.11762i	0.0636819	+	0.605892i
$139$	3.66485	−	4.07023i	0.310849	−	0.345233i	−0.567395	−	0.823446i	$-0.692049\pi$
$139$	3.66485	−	4.07023i	0.310849	−	0.345233i	0.878244	+	0.478213i	$0.158715\pi$
$140$	0.227307	−	0.699580i	0.0192110	−	0.0591253i
$141$	−10.1815	−	7.39726i	−0.857433	−	0.622961i
$142$	−0.665007	−	1.15183i	−0.0558062	−	0.0966591i
$143$	3.27067	+	15.1589i	0.273507	+	1.26765i
$144$	−1.07766			−0.0898052
$145$	−12.6443	−	9.18660i	−1.05005	−	0.762905i
$146$	−9.54220	+	2.02826i	−0.789718	+	0.167860i
$147$	9.34423	+	1.98618i	0.770699	+	0.163817i
$148$	−5.76862	−	2.56835i	−0.474177	−	0.211117i
$149$	−2.42024	−	23.0270i	−0.198273	−	1.88645i	−0.414422	−	0.910085i	$-0.636016\pi$
$149$	−2.42024	−	23.0270i	−0.198273	−	1.88645i	0.216149	−	0.976360i	$-0.430650\pi$
$150$	0.104908	+	0.0222989i	0.00856571	+	0.00182070i
$151$	−2.52743	+	7.77863i	−0.205679	+	0.633016i	0.794005	+	0.607911i	$0.207992\pi$
$151$	−2.52743	+	7.77863i	−0.205679	+	0.633016i	−0.999685	+	0.0251054i	$0.992008\pi$
$152$	3.19707	+	2.96289i	0.259317	+	0.240322i
$153$	−4.40520			−0.356139
$154$	−0.953946	−	0.546873i	−0.0768712	−	0.0440683i
$155$	10.3860	−	17.9890i	0.834221	−	1.44491i
$156$	−0.677643	+	6.44734i	−0.0542549	+	0.516201i
$157$	5.23104	+	5.80966i	0.417483	+	0.463662i	0.914800	−	0.403907i	$-0.132348\pi$
$157$	5.23104	+	5.80966i	0.417483	+	0.463662i	−0.497317	+	0.867569i	$0.665681\pi$
$158$	−2.02390	+	2.24776i	−0.161013	+	0.178823i
$159$	14.2406	−	10.3464i	1.12935	−	0.820520i
$160$	1.79497	−	1.30412i	0.141905	−	0.103100i
$161$	1.14511	−	1.27178i	0.0902476	−	0.100230i
$162$	4.50501	−	0.957569i	0.353947	−	0.0752337i
$163$	3.03874	+	2.20777i	0.238012	+	0.172926i	0.700397	−	0.713753i	$-0.253006\pi$
$163$	3.03874	+	2.20777i	0.238012	+	0.172926i	−0.462385	+	0.886679i	$0.653006\pi$
$164$	−9.29194			−0.725579
$165$	−4.12121	+	9.33319i	−0.320835	+	0.726588i
$166$	−2.91674	+	5.05193i	−0.226383	+	0.392106i
$167$	−1.09634	+	10.4310i	−0.0848376	+	0.807176i	0.866532	+	0.499122i	$0.166344\pi$
$167$	−1.09634	+	10.4310i	−0.0848376	+	0.807176i	−0.951369	+	0.308053i	$0.900323\pi$
$168$	−0.307580	−	0.341602i	−0.0237303	−	0.0263551i
$169$	−8.66902	−	1.84266i	−0.666847	−	0.141743i
$170$	7.33735	−	5.33090i	0.562749	−	0.408861i
$171$	4.03394	+	2.40689i	0.308483	+	0.184060i
$172$	−1.55885	−	4.79765i	−0.118861	−	0.365817i
$173$	14.1294	+	15.6923i	1.07424	+	1.19307i	0.980305	+	0.197487i	$0.0632781\pi$
$173$	14.1294	+	15.6923i	1.07424	+	1.19307i	0.0939355	+	0.995578i	$0.470055\pi$
$174$	−8.92240	+	3.97251i	−0.676405	+	0.301155i
$175$	−0.0128231	−	0.0222102i	−0.000969332	−	0.00167893i
$176$	−1.35826	−	3.02574i	−0.102383	−	0.228074i
$177$	−0.0755708	−	0.130893i	−0.00568025	−	0.00983848i
$178$	14.3529	+	10.4280i	1.07580	+	0.781613i
$179$	−7.59963	+	23.3893i	−0.568023	+	1.74820i	0.0907706	+	0.995872i	$0.471067\pi$
$179$	−7.59963	+	23.3893i	−0.568023	+	1.74820i	−0.658794	+	0.752324i	$0.728933\pi$
$180$	1.59990	−	1.77687i	0.119250	−	0.132440i
$181$	3.44432	+	1.53351i	0.256015	+	0.113985i	0.530731	−	0.847540i	$-0.321917\pi$
$181$	3.44432	+	1.53351i	0.256015	+	0.113985i	−0.274717	+	0.961525i	$0.588584\pi$
$182$	1.25413	−	0.911176i	0.0929620	−	0.0675408i
$183$	5.68032	+	17.4822i	0.419901	+	1.29232i
$184$	5.04906	−	1.07321i	0.372222	−	0.0791181i
$185$	12.7988	−	5.69841i	0.940990	−	0.418956i
$186$	−6.49026	−	11.2415i	−0.475889	−	0.824264i
$187$	−5.55222	−	12.3684i	−0.406019	−	0.904469i
$188$	−4.53845	+	7.86082i	−0.331000	+	0.573309i
$189$	−1.51641	−	1.10173i	−0.110302	−	0.0801393i
$190$	−9.63165	+	0.872678i	−0.698753	+	0.0633107i
$191$	2.34272	+	7.21017i	0.169514	+	0.521709i	0.999341	−	0.0363116i	$-0.0115609\pi$
$191$	2.34272	+	7.21017i	0.169514	+	0.521709i	−0.829827	+	0.558021i	$0.811561\pi$
$192$	−0.144927	−	1.37889i	−0.0104592	−	0.0995127i
$193$	−0.833366	−	7.92894i	−0.0599870	−	0.570738i	−0.982694	−	0.185236i	$-0.940695\pi$
$193$	−0.833366	−	7.92894i	−0.0599870	−	0.570738i	0.922707	−	0.385502i	$-0.125972\pi$
$194$	6.15753	−	6.83863i	0.442085	−	0.490985i
$195$	−9.62447	−	10.6891i	−0.689222	−	0.765459i
$196$	0.720210	−	6.85234i	0.0514436	−	0.489453i
$197$	12.3889			0.882672			0.441336	−	0.897342i	$-0.354505\pi$
$197$	12.3889			0.882672			0.441336	+	0.897342i	$0.354505\pi$
$198$	−2.10971	−	2.88514i	−0.149930	−	0.205038i
$199$	9.32784	+	16.1563i	0.661233	+	1.14529i	0.980292	+	0.197554i	$0.0632999\pi$
$199$	9.32784	+	16.1563i	0.661233	+	1.14529i	−0.319059	+	0.947735i	$0.603367\pi$
$200$	0.00808582	−	0.0769315i	0.000571754	−	0.00543988i
$201$	2.03281	−	6.25634i	0.143383	−	0.441288i
$202$	2.53320	+	7.79637i	0.178235	+	0.548551i
$203$	2.13353	+	0.949908i	0.149744	+	0.0666705i
$204$	−0.592423	−	5.63653i	−0.0414779	−	0.394636i
$205$	13.7948	−	15.3207i	0.963473	−	1.07005i
$206$	−5.61583	−	6.23701i	−0.391274	−	0.434553i
$207$	5.08182	−	2.26257i	0.353211	−	0.157260i
$208$	4.67576			0.324205
$209$	−1.67350	+	14.3596i	−0.115759	+	0.993277i
$210$	1.01987			0.0703779
$211$	16.1199	−	7.17706i	1.10974	−	0.494089i	0.231755	−	0.972774i	$-0.425553\pi$
$211$	16.1199	−	7.17706i	1.10974	−	0.494089i	0.877987	+	0.478685i	$0.158886\pi$
$212$	−8.49504	−	9.43470i	−0.583442	−	0.647978i
$213$	1.23391	−	1.37039i	0.0845459	−	0.0938977i
$214$	1.96351	+	18.6816i	0.134223	+	1.27705i
$215$	10.2247	+	4.55234i	0.697320	+	0.310467i
$216$	−1.74706	−	5.37691i	−0.118873	−	0.365852i
$217$	−0.959161	+	2.95199i	−0.0651121	+	0.200394i
$218$	−0.587335	+	5.58812i	−0.0397794	+	0.378475i
$219$	−6.76284	−	11.7136i	−0.456990	−	0.791530i
$220$	7.00538	+	2.25249i	0.472303	+	0.151863i
$221$	19.1132			1.28570
$222$	0.915147	−	8.70704i	0.0614206	−	0.584378i
$223$	4.72889	+	5.25196i	0.316670	+	0.351697i	0.880375	−	0.474279i	$-0.157291\pi$
$223$	4.72889	+	5.25196i	0.316670	+	0.351697i	−0.563705	+	0.825976i	$0.690625\pi$
$224$	−0.221841	+	0.246380i	−0.0148224	+	0.0164619i
$225$	−0.00871379	−	0.0829062i	−0.000580920	−	0.00552708i
$226$	−0.610480	−	5.80833i	−0.0406085	−	0.386364i
$227$	−5.92405	−	18.2323i	−0.393193	−	1.21012i	−0.930360	−	0.366647i	$-0.880506\pi$
$227$	−5.92405	−	18.2323i	−0.393193	−	1.21012i	0.537167	−	0.843476i	$-0.319494\pi$
$228$	−2.53716	+	5.48518i	−0.168028	+	0.363265i
$229$	−1.37981	−	1.00249i	−0.0911801	−	0.0662462i	0.541261	−	0.840855i	$-0.317947\pi$
$229$	−1.37981	−	1.00249i	−0.0911801	−	0.0662462i	−0.632441	+	0.774608i	$0.717947\pi$
$230$	−5.72631	+	9.91827i	−0.377582	+	0.653991i
$231$	0.312405	−	1.49220i	0.0205547	−	0.0981797i
$232$	3.52214	+	6.10053i	0.231240	+	0.400519i
$233$	9.90495	−	4.40997i	0.648895	−	0.288907i	−0.0557733	−	0.998443i	$-0.517762\pi$
$233$	9.90495	−	4.40997i	0.648895	−	0.288907i	0.704668	+	0.709537i	$0.251096\pi$
$234$	4.92878	−	1.04764i	0.322204	−	0.0684866i
$235$	−6.22327	−	19.1533i	−0.405962	−	1.24942i
$236$	−0.0881916	+	0.0640749i	−0.00574078	+	0.00417092i
$237$	−3.83109	−	1.70571i	−0.248856	−	0.110798i
$238$	−0.906828	+	1.00713i	−0.0587809	+	0.0652829i
$239$	4.77374	−	14.6921i	0.308788	−	0.950351i	−0.669449	−	0.742858i	$-0.733470\pi$
$239$	4.77374	−	14.6921i	0.308788	−	0.950351i	0.978236	−	0.207493i	$-0.0665304\pi$
$240$	2.48869	+	1.80814i	0.160645	+	0.116715i
$241$	−9.14409	−	15.8380i	−0.589023	−	1.02022i	−0.994361	−	0.106050i	$-0.966180\pi$
$241$	−9.14409	−	15.8380i	−0.589023	−	1.02022i	0.405338	−	0.914167i	$-0.367154\pi$
$242$	5.44155	−	9.55978i	0.349796	−	0.614526i
$243$	−5.28759	−	9.15837i	−0.339199	−	0.587510i
$244$	12.1117	−	5.39248i	0.775373	−	0.345218i
$245$	10.2290	+	11.3605i	0.653509	+	0.725795i
$246$	−3.98111	−	12.2526i	−0.253826	−	0.781196i
$247$	−17.5024	−	10.4430i	−1.11365	−	0.664472i
$248$	−7.57417	+	5.50296i	−0.480960	+	0.349438i
$249$	−7.91127	−	1.68159i	−0.501356	−	0.106567i
$250$	7.53785	+	8.37163i	0.476736	+	0.529469i
$251$	−2.47439	+	23.5422i	−0.156182	+	1.48597i	0.583004	+	0.812469i	$0.301877\pi$
$251$	−2.47439	+	23.5422i	−0.156182	+	1.48597i	−0.739186	+	0.673502i	$0.764789\pi$
$252$	−0.178642	+	0.309418i	−0.0112534	+	0.0194915i
$253$	12.7576	+	11.4165i	0.802064	+	0.717747i
$254$	−12.3254			−0.773365
$255$	10.1731	+	7.39120i	0.637065	+	0.462855i
$256$	−0.978148	+	0.207912i	−0.0611342	+	0.0129945i
$257$	−6.73787	+	7.48316i	−0.420297	+	0.466787i	−0.915692	−	0.401881i	$-0.868357\pi$
$257$	−6.73787	+	7.48316i	−0.420297	+	0.466787i	0.495395	+	0.868668i	$0.335023\pi$
$258$	5.65841	−	4.11107i	0.352277	−	0.255944i
$259$	−1.69368	+	1.23053i	−0.105240	+	0.0764614i
$260$	−6.94164	+	7.70947i	−0.430502	+	0.478121i
$261$	5.07961	+	5.64148i	0.314420	+	0.349199i
$262$	−1.47852	+	14.0672i	−0.0913431	+	0.869072i
$263$	−13.0469	+	22.5979i	−0.804505	+	1.39344i	0.112119	+	0.993695i	$0.464236\pi$
$263$	−13.0469	+	22.5979i	−0.804505	+	1.39344i	−0.916625	+	0.399749i	$0.869097\pi$
$264$	3.40787	−	3.08741i	0.209740	−	0.190017i
$265$	28.1678			1.73034
$266$	1.38068	−	0.426788i	0.0846547	−	0.0261680i
$267$	−7.60117	+	23.3940i	−0.465184	+	1.43169i
$268$	−4.64091	−	0.986456i	−0.283489	−	0.0602574i
$269$	−1.80432	−	17.1670i	−0.110012	−	1.04669i	−0.900691	−	0.434460i	$-0.856939\pi$
$269$	−1.80432	−	17.1670i	−0.110012	−	1.04669i	0.790679	−	0.612230i	$-0.209728\pi$
$270$	11.4592	+	5.10198i	0.697387	+	0.310497i
$271$	9.54486	+	2.02882i	0.579809	+	0.123242i	0.488475	−	0.872578i	$-0.337553\pi$
$271$	9.54486	+	2.02882i	0.579809	+	0.123242i	0.0913344	+	0.995820i	$0.470887\pi$
$272$	−3.99841	+	0.849887i	−0.242439	+	0.0515320i
$273$	1.73883	+	1.26333i	0.105238	+	0.0764602i
$274$	−5.34409			−0.322848
$275$	0.221792	−	0.128959i	0.0133746	−	0.00777652i
$276$	3.57842	+	6.19800i	0.215395	+	0.373076i
$277$	−0.0457436	−	0.0332347i	−0.00274847	−	0.00199688i	0.586410	−	0.810014i	$-0.300541\pi$
$277$	−0.0457436	−	0.0332347i	−0.00274847	−	0.00199688i	−0.589159	+	0.808017i	$0.700541\pi$
$278$	1.69250	−	5.20897i	0.101509	−	0.312414i
$279$	−6.75105	+	7.49780i	−0.404175	+	0.448882i
$280$	−0.0768892	−	0.731552i	−0.00459501	−	0.0437186i
$281$	14.5232	+	6.46615i	0.866382	+	0.385738i	0.791292	−	0.611439i	$-0.209409\pi$
$281$	14.5232	+	6.46615i	0.866382	+	0.385738i	0.0750901	+	0.997177i	$0.476076\pi$
$282$	−12.3100	−	2.61656i	−0.733047	−	0.155814i
$283$	2.58677	+	2.87290i	0.153768	+	0.170776i	0.815107	−	0.579311i	$-0.196678\pi$
$283$	2.58677	+	2.87290i	0.153768	+	0.170776i	−0.661339	+	0.750087i	$0.730012\pi$
$284$	−1.07600	−	0.781763i	−0.0638491	−	0.0463891i
$285$	−5.27739	−	12.3266i	−0.312605	−	0.730167i
$286$	9.15359	+	12.5180i	0.541263	+	0.740207i
$287$	−1.54031	+	2.66790i	−0.0909216	+	0.157481i
$288$	−0.984494	+	0.438325i	−0.0580119	+	0.0258285i
$289$	0.284101	−	0.0603876i	0.0167118	−	0.00355221i
$290$	−15.2876	−	3.24949i	−0.897721	−	0.190816i
$291$	11.6558	+	5.18948i	0.683273	+	0.304213i
$292$	−7.89227	+	5.73407i	−0.461860	+	0.335561i
$293$	−4.44900	−	13.6926i	−0.259913	−	0.799931i	−0.992822	−	0.119604i	$-0.961838\pi$
$293$	−4.44900	−	13.6926i	−0.259913	−	0.799931i	0.732908	−	0.680327i	$-0.238162\pi$
$294$	9.34423	−	1.98618i	0.544967	−	0.115836i
$295$	0.0252815	−	0.240538i	0.00147195	−	0.0140046i
$296$	−6.31454			−0.367025
$297$	10.9750	−	15.2035i	0.636834	−	0.882196i
$298$	−11.5769	−	20.0518i	−0.670633	−	1.16157i
$299$	−22.0489	+	9.81682i	−1.27512	+	0.567722i
$300$	0.104908	−	0.0222989i	0.00605687	−	0.00128743i
$301$	−1.63590	−	0.347722i	−0.0942920	−	0.0200424i
$302$	0.854932	+	8.13413i	0.0491958	+	0.468067i
$303$	−9.19515	+	6.68067i	−0.528248	+	0.383794i
$304$	4.12579	+	1.40637i	0.236630	+	0.0806608i
$305$	−9.08986	+	27.9757i	−0.520484	+	1.60188i
$306$	−4.02435	+	1.79176i	−0.230057	+	0.102428i
$307$	0.749180	−	1.29762i	0.0427580	−	0.0740590i	−0.843854	−	0.536572i	$-0.819719\pi$
$307$	0.749180	−	1.29762i	0.0427580	−	0.0740590i	0.886612	+	0.462513i	$0.153052\pi$
$308$	−1.09391	−	0.111589i	−0.0623311	−	0.00635835i
$309$	5.81819	−	10.0774i	0.330985	−	0.573284i
$310$	2.17126	−	20.6581i	0.123319	−	1.17330i
$311$	4.60304	−	14.1667i	0.261015	−	0.803320i	−0.731570	−	0.681766i	$-0.761212\pi$
$311$	4.60304	−	14.1667i	0.261015	−	0.803320i	0.992585	−	0.121554i	$-0.0387878\pi$
$312$	2.00331	+	6.16556i	0.113415	+	0.349056i
$313$	9.25208	+	4.11929i	0.522959	+	0.232836i	0.651199	−	0.758907i	$-0.274266\pi$
$313$	9.25208	+	4.11929i	0.522959	+	0.232836i	−0.128241	+	0.991743i	$0.540933\pi$
$314$	7.14180	+	3.17973i	0.403035	+	0.179443i
$315$	−0.244961	−	0.753911i	−0.0138020	−	0.0424781i
$316$	−0.934673	+	2.87663i	−0.0525795	+	0.161823i
$317$	0.791100	−	7.52681i	0.0444326	−	0.422748i	−0.949584	−	0.313514i	$-0.898494\pi$
$317$	0.791100	−	7.52681i	0.0444326	−	0.422748i	0.994016	−	0.109234i	$-0.0348397\pi$
$318$	8.80115	−	15.2440i	0.493544	−	0.854843i
$319$	−9.43728	+	21.3724i	−0.528386	+	1.19662i
$320$	1.10935	−	1.92145i	0.0620146	−	0.107413i
$321$	−23.7927	+	10.5932i	−1.32798	+	0.591255i
$322$	0.528835	−	1.62759i	0.0294708	−	0.0907018i
$323$	16.8651	+	5.74886i	0.938400	+	0.319875i
$324$	3.72605	−	2.70714i	0.207003	−	0.150396i
$325$	0.0378073	+	0.359713i	0.00209717	+	0.0199533i
$326$	3.67400	+	0.780934i	0.203484	+	0.0432519i
$327$	−7.62028	+	1.61974i	−0.421402	+	0.0895718i
$328$	−8.48861	+	3.77937i	−0.468705	+	0.208681i
$329$	1.50466	+	2.60615i	0.0829547	+	0.143682i
$330$	0.0312421	+	10.2025i	0.00171982	+	0.561631i
$331$	−16.6202			−0.913528			−0.456764	−	0.889588i	$-0.650992\pi$
$331$	−16.6202			−0.913528			−0.456764	+	0.889588i	$0.650992\pi$
$332$	−0.609764	+	5.80151i	−0.0334651	+	0.318399i
$333$	−6.65624	+	1.41483i	−0.364760	+	0.0775320i
$334$	3.24111	+	9.97512i	0.177346	+	0.545814i
$335$	8.51640	−	6.18752i	0.465300	−	0.338061i
$336$	−0.419930	−	0.186965i	−0.0229090	−	0.0101998i
$337$	−8.03375	−	1.70763i	−0.437626	−	0.0930204i	−0.0161705	−	0.999869i	$-0.505147\pi$
$337$	−8.03375	−	1.70763i	−0.437626	−	0.0930204i	−0.421456	+	0.906849i	$0.638481\pi$
$338$	−8.66902	+	1.84266i	−0.471532	+	0.100227i
$339$	7.39744	−	3.29355i	0.401774	−	0.178881i
$340$	4.53473	−	7.85439i	0.245930	−	0.425964i
$341$	−29.5604	−	9.50477i	−1.60078	−	0.514712i
$342$	4.66416	+	0.558053i	0.252209	+	0.0301761i
$343$	−3.72558	−	2.70679i	−0.201163	−	0.146153i
$344$	−3.37546	−	3.74883i	−0.181993	−	0.202123i
$345$	−15.5319	−	3.30141i	−0.836209	−	0.177742i
$346$	19.2905	+	8.58869i	1.03706	+	0.461731i
$347$	0.561569	+	5.34297i	0.0301466	+	0.286826i	0.999201	+	0.0399770i	$0.0127285\pi$
$347$	0.561569	+	5.34297i	0.0301466	+	0.286826i	−0.969054	+	0.246849i	$0.920605\pi$
$348$	−6.53525	+	7.25813i	−0.350326	+	0.389077i
$349$	1.36683	−	4.20668i	0.0731649	−	0.225178i	−0.907786	−	0.419433i	$-0.862229\pi$
$349$	1.36683	−	4.20668i	0.0731649	−	0.225178i	0.980951	+	0.194255i	$0.0622288\pi$
$350$	−0.0207481	−	0.0150744i	−0.00110903	−	0.000805761i
$351$	13.2175	+	22.8933i	0.705496	+	1.22195i
$352$	−2.47152	−	2.21170i	−0.131732	−	0.117884i
$353$	−2.20618			−0.117423			−0.0587116	−	0.998275i	$-0.518699\pi$
$353$	−2.20618			−0.117423			−0.0587116	+	0.998275i	$0.518699\pi$
$354$	−0.122276	−	0.0888388i	−0.00649891	−	0.00472173i
$355$	2.88642	−	0.613528i	0.153195	−	0.0325627i
$356$	17.3535	+	3.68860i	0.919735	+	0.195496i
$357$	−1.71656	−	0.764262i	−0.0908500	−	0.0404490i
$358$	2.57066	+	24.4582i	0.135864	+	1.29266i
$359$	1.25301	+	0.266335i	0.0661313	+	0.0140566i	0.240859	−	0.970560i	$-0.422571\pi$
$359$	1.25301	+	0.266335i	0.0661313	+	0.0140566i	−0.174727	+	0.984617i	$0.555904\pi$
$360$	0.738864	−	2.27399i	0.0389416	−	0.119850i
$361$	−12.3027	−	14.4790i	−0.647513	−	0.762055i
$362$	3.77028			0.198162
$363$	14.9372	+	3.07951i	0.783999	+	0.161632i
$364$	0.775092	−	1.34250i	0.0406259	−	0.0703661i
$365$	2.26245	−	21.5257i	0.118422	−	1.12671i
$366$	12.2999	+	13.6604i	0.642926	+	0.714041i
$367$	2.11725	−	2.35145i	0.110520	−	0.122745i	−0.685346	−	0.728217i	$-0.740349\pi$
$367$	2.11725	−	2.35145i	0.110520	−	0.122745i	0.795866	+	0.605473i	$0.207016\pi$
$368$	4.17603	−	3.03406i	0.217691	−	0.158161i
$369$	−8.10116	+	5.88584i	−0.421729	+	0.306404i
$370$	9.37458	−	10.4115i	0.487361	−	0.541269i
$371$	−4.11709	+	0.875115i	−0.213749	+	0.0454337i
$372$	−10.5015	−	7.62976i	−0.544476	−	0.395585i
$373$	−26.2649			−1.35994			−0.679972	−	0.733238i	$-0.738008\pi$
$373$	−26.2649			−1.35994			−0.679972	+	0.733238i	$0.738008\pi$
$374$	−10.1029	−	9.04083i	−0.522408	−	0.467490i
$375$	−7.80947	+	13.5264i	−0.403279	+	0.698500i
$376$	−0.948794	+	9.02717i	−0.0489303	+	0.465541i
$377$	−22.0394	−	24.4772i	−1.13509	−	1.26064i
$378$	−1.83342	−	0.389706i	−0.0943010	−	0.0200443i
$379$	10.2464	−	7.44444i	0.526322	−	0.382395i	−0.292658	−	0.956217i	$-0.594540\pi$
$379$	10.2464	−	7.44444i	0.526322	−	0.382395i	0.818980	+	0.573822i	$0.194540\pi$
$380$	−8.44400	+	4.71478i	−0.433168	+	0.241863i
$381$	−5.28079	−	16.2526i	−0.270543	−	0.832645i
$382$	5.07282	+	5.63394i	0.259548	+	0.288258i
$383$	−7.37386	+	3.28306i	−0.376787	+	0.167756i	−0.586387	−	0.810031i	$-0.699450\pi$
$383$	−7.37386	+	3.28306i	−0.376787	+	0.167756i	0.209600	+	0.977787i	$0.432784\pi$
$384$	−0.693242	−	1.20073i	−0.0353768	−	0.0612745i
$385$	1.80801	−	1.63799i	0.0921445	−	0.0834796i
$386$	−3.98631	−	6.90449i	−0.202898	−	0.351429i
$387$	−4.39807	−	3.19539i	−0.223567	−	0.162431i
$388$	2.84366	−	8.75190i	0.144365	−	0.444310i
$389$	−7.21960	+	8.01818i	−0.366048	+	0.406538i	−0.897829	−	0.440344i	$-0.854856\pi$
$389$	−7.21960	+	8.01818i	−0.366048	+	0.406538i	0.531781	+	0.846882i	$0.321523\pi$
$390$	−13.1400	−	5.85031i	−0.665371	−	0.296242i
$391$	17.0705	−	12.4024i	0.863292	−	0.627218i
$392$	−2.12915	−	6.55286i	−0.107538	−	0.330969i
$393$	−19.1828	+	4.07742i	−0.967642	+	0.205679i
$394$	11.3178	−	5.03902i	0.570184	−	0.253862i
$395$	−3.35542	−	5.81176i	−0.168829	−	0.292421i
$396$	−3.10081	−	1.77761i	−0.155822	−	0.0893285i
$397$	10.7415	−	18.6048i	0.539099	−	0.933746i	−0.459854	−	0.887994i	$-0.652098\pi$
$397$	10.7415	−	18.6048i	0.539099	−	0.933746i	0.998953	−	0.0457518i	$-0.0145683\pi$
$398$	15.0928	+	10.9655i	0.756532	+	0.549652i
$399$	1.15432	+	1.63774i	0.0577883	+	0.0819895i
$400$	−0.0239041	−	0.0735692i	−0.00119520	−	0.00367846i
$401$	1.51715	+	14.4347i	0.0757627	+	0.720834i	0.964797	+	0.262994i	$0.0847100\pi$
$401$	1.51715	+	14.4347i	0.0757627	+	0.720834i	−0.889035	+	0.457840i	$0.848623\pi$
$402$	−0.687620	−	6.54227i	−0.0342954	−	0.326299i
$403$	29.2914	−	32.5314i	1.45911	−	1.62050i
$404$	5.48526	+	6.09200i	0.272902	+	0.303088i
$405$	−1.06813	+	10.1626i	−0.0530759	+	0.504984i
$406$	2.33544			0.115906
$407$	−12.3618	−	16.9054i	−0.612751	−	0.837971i
$408$	−2.83379	−	4.90826i	−0.140293	−	0.242995i
$409$	1.22169	−	11.6236i	0.0604087	−	0.574750i	−0.921893	−	0.387444i	$-0.873358\pi$
$409$	1.22169	−	11.6236i	0.0604087	−	0.574750i	0.982302	−	0.187306i	$-0.0599754\pi$
$410$	6.37071	−	19.6070i	0.314627	−	0.968323i
$411$	−2.28966	−	7.04684i	−0.112941	−	0.347595i
$412$	−7.66714	−	3.41363i	−0.377733	−	0.168178i
$413$	0.00377777	+	0.0359431i	0.000185892	+	0.00176864i
$414$	3.72220	−	4.13392i	0.182936	−	0.203171i
$415$	−8.66038	−	9.61833i	−0.425122	−	0.472145i
$416$	4.27151	−	1.90180i	0.209428	−	0.0932435i
$417$	7.59383			0.371871
$418$	4.31177	+	13.7989i	0.210896	+	0.674924i
$419$	−39.8186			−1.94527			−0.972633	−	0.232348i	$-0.925359\pi$
$419$	−39.8186			−1.94527			−0.972633	+	0.232348i	$0.925359\pi$
$420$	0.931700	−	0.414819i	0.0454623	−	0.0202411i
$421$	19.1439	+	21.2614i	0.933016	+	1.03622i	0.999262	+	0.0384158i	$0.0122311\pi$
$421$	19.1439	+	21.2614i	0.933016	+	1.03622i	−0.0662460	+	0.997803i	$0.521102\pi$
$422$	11.8071	−	13.1131i	0.574762	−	0.638337i
$423$	1.02248	+	9.72825i	0.0497147	+	0.473004i
$424$	−11.5980	−	5.16378i	−0.563251	−	0.250775i
$425$	−0.0977135	−	0.300731i	−0.00473980	−	0.0145876i
$426$	0.569841	−	1.75379i	0.0276089	−	0.0849714i
$427$	0.459454	−	4.37141i	0.0222345	−	0.211547i
$428$	9.39224	+	16.2678i	0.453991	+	0.786336i
$429$	−12.5848	+	17.4335i	−0.607598	+	0.841695i
$430$	11.1923			0.539743
$431$	0.205853	−	1.95856i	0.00991561	−	0.0943407i	−0.988445	−	0.151581i	$-0.951564\pi$
$431$	0.205853	−	1.95856i	0.00991561	−	0.0943407i	0.998360	+	0.0572405i	$0.0182302\pi$
$432$	−3.78301	−	4.20145i	−0.182010	−	0.202143i
$433$	−5.26740	+	5.85005i	−0.253135	+	0.281135i	−0.856297	−	0.516484i	$-0.827241\pi$
$433$	−5.26740	+	5.85005i	−0.253135	+	0.281135i	0.603162	+	0.797619i	$0.293907\pi$
$434$	0.324447	+	3.08691i	0.0155740	+	0.148176i
$435$	−2.26509	−	21.5509i	−0.108603	−	1.03329i
$436$	1.73634	+	5.34390i	0.0831555	+	0.255926i
$437$	−22.4082	+	2.03030i	−1.07193	+	0.0971225i
$438$	−10.9425	−	7.95019i	−0.522853	−	0.379875i
$439$	4.49767	−	7.79020i	0.214662	−	0.371806i	−0.738506	−	0.674247i	$-0.764468\pi$
$439$	4.49767	−	7.79020i	0.214662	−	0.371806i	0.953168	+	0.302441i	$0.0978016\pi$
$440$	7.31591	−	0.791590i	0.348772	−	0.0377376i
$441$	−3.71259	−	6.43040i	−0.176790	−	0.306210i
$442$	17.4608	−	7.77405i	0.830526	−	0.369774i
$443$	−5.54537	+	1.17870i	−0.263469	+	0.0560020i	−0.337752	−	0.941235i	$-0.609666\pi$
$443$	−5.54537	+	1.17870i	−0.263469	+	0.0560020i	0.0742833	+	0.997237i	$0.476333\pi$
$444$	−2.70544	−	8.32650i	−0.128395	−	0.395158i
$445$	−31.8449	+	23.1367i	−1.50959	+	1.09678i
$446$	6.45622	+	2.87449i	0.305711	+	0.136111i
$447$	21.4807	−	23.8567i	1.01600	−	1.12839i
$448$	−0.102451	+	0.315310i	−0.00484033	+	0.0148970i
$449$	−3.59183	−	2.60962i	−0.169509	−	0.123156i	0.499796	−	0.866143i	$-0.333408\pi$
$449$	−3.59183	−	2.60962i	−0.169509	−	0.123156i	−0.669305	+	0.742987i	$0.733408\pi$
$450$	−0.0416814	−	0.0721944i	−0.00196488	−	0.00340327i
$451$	−26.7361	−	15.3271i	−1.25896	−	0.721727i
$452$	−2.92016	−	5.05787i	−0.137353	−	0.237902i
$453$	−10.3596	+	4.61238i	−0.486735	+	0.216708i
$454$	−12.8276	−	14.2465i	−0.602031	−	0.668623i
$455$	1.06283	+	3.27106i	0.0498264	+	0.153350i
$456$	−0.0867900	+	6.04292i	−0.00406432	+	0.282986i
$457$	−13.9888	+	10.1635i	−0.654370	+	0.475428i	−0.864757	−	0.502191i	$-0.832528\pi$
$457$	−13.9888	+	10.1635i	−0.654370	+	0.475428i	0.210387	+	0.977618i	$0.432528\pi$
$458$	−1.66826	−	0.354600i	−0.0779528	−	0.0165694i
$459$	−15.4639	−	17.1744i	−0.721794	−	0.801633i
$460$	−1.19713	+	11.3899i	−0.0558163	+	0.531056i
$461$	−2.75861	+	4.77805i	−0.128481	+	0.222536i	−0.923088	−	0.384588i	$-0.874343\pi$
$461$	−2.75861	+	4.77805i	−0.128481	+	0.222536i	0.794607	+	0.607124i	$0.207677\pi$
$462$	−0.321538	−	1.49026i	−0.0149593	−	0.0693332i
$463$	22.6200			1.05124			0.525621	−	0.850719i	$-0.323833\pi$
$463$	22.6200			1.05124			0.525621	+	0.850719i	$0.323833\pi$
$464$	5.69894	+	4.14052i	0.264567	+	0.192219i
$465$	28.1706	−	5.98784i	1.30638	−	0.277680i
$466$	7.25493	−	8.05742i	0.336078	−	0.373253i
$467$	−16.1314	+	11.7202i	−0.746473	+	0.542345i	−0.894732	−	0.446604i	$-0.852633\pi$
$467$	−16.1314	+	11.7202i	−0.746473	+	0.542345i	0.148258	+	0.988949i	$0.452633\pi$
$468$	4.07655	−	2.96178i	0.188438	−	0.136909i
$469$	−1.05255	+	1.16897i	−0.0486021	+	0.0539781i
$470$	−13.4756	−	14.9661i	−0.621582	−	0.690337i
$471$	−1.13299	+	10.7797i	−0.0522055	+	0.496702i
$472$	−0.0545054	+	0.0944061i	−0.00250881	+	0.00434539i
$473$	3.42841	−	16.3758i	0.157639	−	0.752961i
$474$	−4.19365			−0.192621
$475$	−0.0748336	+	0.328775i	−0.00343360	+	0.0150852i
$476$	−0.418790	+	1.28890i	−0.0191952	+	0.0590768i
$477$	−13.3826	−	2.84457i	−0.612749	−	0.130244i
$478$	−1.61477	−	15.3635i	−0.0738580	−	0.702712i
$479$	0.712407	+	0.317184i	0.0325507	+	0.0144925i	0.422947	−	0.906154i	$-0.360995\pi$
$479$	0.712407	+	0.317184i	0.0325507	+	0.0144925i	−0.390397	+	0.920647i	$0.627662\pi$
$480$	3.00897	+	0.639577i	0.137340	+	0.0291926i
$481$	28.8800	−	6.13864i	1.31682	−	0.279898i
$482$	−14.7955	−	10.7495i	−0.673914	−	0.489627i
$483$	2.37275			0.107964
$484$	1.08279	−	10.9466i	0.0492179	−	0.497572i
$485$	10.2086	+	17.6818i	0.463547	+	0.802888i
$486$	−8.55550	−	6.21593i	−0.388085	−	0.281960i
$487$	−5.63001	+	17.3274i	−0.255120	+	0.785179i	0.738686	+	0.674050i	$0.235447\pi$
$487$	−5.63001	+	17.3274i	−0.255120	+	0.785179i	−0.993806	+	0.111129i	$0.964553\pi$
$488$	8.87128	−	9.85256i	0.401584	−	0.446004i
$489$	0.544358	+	5.17922i	0.0246167	+	0.234212i
$490$	13.9654	+	6.21780i	0.630893	+	0.280892i
$491$	4.55035	+	0.967207i	0.205354	+	0.0436494i	0.309440	−	0.950919i	$-0.399858\pi$
$491$	4.55035	+	0.967207i	0.205354	+	0.0436494i	−0.104086	+	0.994568i	$0.533192\pi$
$492$	−8.62049	−	9.57403i	−0.388642	−	0.431631i
$493$	23.2958	+	16.9254i	1.04919	+	0.762280i
$494$	−20.2368	−	2.42128i	−0.910497	−	0.108938i
$495$	7.53443	−	2.47362i	0.338648	−	0.111181i
$496$	−4.68110	+	8.10790i	−0.210187	+	0.364055i
$497$	−0.402827	+	0.179350i	−0.0180693	+	0.00804495i
$498$	−7.91127	+	1.68159i	−0.354512	+	0.0753540i
$499$	4.24602	+	0.902519i	0.190078	+	0.0404023i	0.301967	−	0.953318i	$-0.402357\pi$
$499$	4.24602	+	0.902519i	0.190078	+	0.0404023i	−0.111889	+	0.993721i	$0.535690\pi$
$500$	10.2912	+	4.58195i	0.460237	+	0.204911i
$501$	−11.7648	+	8.54762i	−0.525612	+	0.381880i
$502$	7.31502	+	22.5133i	0.326485	+	1.00482i
$503$	−12.5737	+	2.67262i	−0.560633	+	0.119166i	−0.479507	−	0.877538i	$-0.659185\pi$
$503$	−12.5737	+	2.67262i	−0.560633	+	0.119166i	−0.0811251	+	0.996704i	$0.525851\pi$
$504$	−0.0373464	+	0.355328i	−0.00166354	+	0.0158276i
$505$	−18.1880			−0.809357
$506$	16.2982	+	5.24047i	0.724541	+	0.232967i
$507$	−6.14399	−	10.6417i	−0.272864	−	0.472614i
$508$	−11.2598	+	5.01320i	−0.499574	+	0.222425i
$509$	2.66054	−	0.565514i	0.117926	−	0.0250660i	−0.148571	−	0.988902i	$-0.547467\pi$
$509$	2.66054	−	0.565514i	0.117926	−	0.0250660i	0.266497	+	0.963836i	$0.414134\pi$
$510$	12.2999	+	2.61442i	0.544648	+	0.115768i
$511$	0.338073	+	3.21655i	0.0149555	+	0.142292i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	4.77698	+	24.1761i	0.210909	+	1.06740i
$514$	−3.11167	+	9.57675i	−0.137250	+	0.422412i
$515$	17.0111	−	7.57384i	0.749599	−	0.333743i
$516$	3.49709	−	6.05714i	0.153951	−	0.266651i
$517$	−26.0252	+	15.1321i	−1.14459	+	0.665509i
$518$	−1.04675	+	1.81303i	−0.0459916	+	0.0796598i
$519$	−3.06029	+	29.1168i	−0.134332	+	1.27808i
$520$	−3.20578	+	9.86637i	−0.140583	+	0.432669i
$521$	7.33967	+	22.5892i	0.321557	+	0.989650i	0.972971	+	0.230928i	$0.0741760\pi$
$521$	7.33967	+	22.5892i	0.321557	+	0.989650i	−0.651414	+	0.758722i	$0.725824\pi$
$522$	6.93505	+	3.08768i	0.303539	+	0.135144i
$523$	−7.76706	−	3.45812i	−0.339630	−	0.151213i	0.229833	−	0.973230i	$-0.426182\pi$
$523$	−7.76706	−	3.45812i	−0.339630	−	0.151213i	−0.569463	+	0.822017i	$0.692849\pi$
$524$	4.37094	+	13.4524i	0.190945	+	0.587669i
$525$	0.0109880	−	0.0338176i	0.000479556	−	0.00147592i
$526$	−2.72754	+	25.9508i	−0.118926	+	1.13151i
$527$	−19.1351	+	33.1429i	−0.833537	+	1.44373i
$528$	1.85748	−	4.20660i	0.0808366	−	0.183069i
$529$	−1.82238	+	3.15646i	−0.0792341	+	0.137237i
$530$	25.7326	−	11.4569i	1.11775	−	0.497656i
$531$	−0.0363024	+	0.111727i	−0.00157539	+	0.00484855i
$532$	1.08772	−	0.951462i	0.0471587	−	0.0412511i
$533$	35.1492	−	25.5374i	1.52248	−	1.10615i
$534$	2.57118	+	24.4631i	0.111266	+	1.05862i
$535$	−40.7665	−	8.66518i	−1.76249	−	0.374628i
$536$	−4.64091	+	0.986456i	−0.200457	+	0.0426084i
$537$	−31.1498	+	13.8688i	−1.34421	+	0.598482i
$538$	−8.63078	−	14.9490i	−0.372099	−	0.644495i
$539$	13.3753	−	18.5286i	0.576114	−	0.798081i
$540$	12.5437			0.539795
$541$	−2.00705	+	19.0958i	−0.0862900	+	0.820994i	0.862706	+	0.505706i	$0.168768\pi$
$541$	−2.00705	+	19.0958i	−0.0862900	+	0.820994i	−0.948996	+	0.315288i	$0.897899\pi$
$542$	9.54486	−	2.02882i	0.409987	−	0.0871454i
$543$	1.61537	+	4.97159i	0.0693220	+	0.213351i
$544$	−3.30704	+	2.40271i	−0.141788	+	0.103015i
$545$	−11.3889	−	5.07066i	−0.487846	−	0.217203i
$546$	2.10234	+	0.446866i	0.0899718	+	0.0191241i
$547$	−7.52433	+	1.59934i	−0.321717	+	0.0683830i	−0.365939	−	0.930639i	$-0.619252\pi$
$547$	−7.52433	+	1.59934i	−0.321717	+	0.0683830i	0.0442225	+	0.999022i	$0.485919\pi$
$548$	−4.88207	+	2.17364i	−0.208552	+	0.0928531i
$549$	7.14379	−	12.3734i	0.304889	−	0.528084i
$550$	0.150165	−	0.208021i	0.00640305	−	0.00887004i
$551$	−12.0849	−	28.2272i	−0.514832	−	1.20252i
$552$	5.79000	+	4.20668i	0.246439	+	0.179048i
$553$	0.670996	+	0.745217i	0.0285337	+	0.0316898i
$554$	−0.0553067	−	0.0117558i	−0.00234975	−	0.000499456i
$555$	17.7454	+	7.90076i	0.753250	+	0.335369i
$556$	−0.572507	−	5.44704i	−0.0242797	−	0.231006i
$557$	−1.00269	+	1.11360i	−0.0424853	+	0.0471847i	−0.764013	−	0.645201i	$-0.776774\pi$
$557$	−1.00269	+	1.11360i	−0.0424853	+	0.0471847i	0.721528	+	0.692386i	$0.243440\pi$
$558$	−3.11776	+	9.59548i	−0.131985	+	0.406209i
$559$	19.0823	+	13.8641i	0.807096	+	0.586390i
$560$	−0.367791	−	0.637033i	−0.0155420	−	0.0269195i
$561$	7.59290	−	17.1954i	0.320572	−	0.725992i
$562$	15.8976			0.670601
$563$	10.0243	+	7.28309i	0.422474	+	0.306946i	0.778633	−	0.627480i	$-0.215914\pi$
$563$	10.0243	+	7.28309i	0.422474	+	0.306946i	−0.356158	+	0.934426i	$0.615914\pi$
$564$	−12.3100	+	2.61656i	−0.518343	+	0.110177i
$565$	12.6748	+	2.69411i	0.533232	+	0.113342i
$566$	3.53165	+	1.57239i	0.148446	+	0.0660925i
$567$	−0.159609	−	1.51858i	−0.00670295	−	0.0637743i
$568$	−1.30095	−	0.276526i	−0.0545867	−	0.0116028i
$569$	2.43287	−	7.48760i	0.101991	−	0.313897i	−0.887021	−	0.461729i	$-0.847229\pi$
$569$	2.43287	−	7.48760i	0.101991	−	0.313897i	0.989013	+	0.147832i	$0.0472294\pi$
$570$	−9.83482	−	9.11443i	−0.411935	−	0.381762i
$571$	39.7724			1.66443			0.832213	−	0.554457i	$-0.187074\pi$
$571$	39.7724			1.66443			0.832213	+	0.554457i	$0.187074\pi$
$572$	13.4538	+	7.71270i	0.562530	+	0.322484i
$573$	−5.25562	+	9.10300i	−0.219557	+	0.380283i
$574$	−0.322013	+	3.06374i	−0.0134405	+	0.127878i
$575$	0.267182	+	0.296735i	0.0111422	+	0.0123747i
$576$	−0.721097	+	0.800860i	−0.0300457	+	0.0333692i
$577$	20.2681	−	14.7256i	0.843771	−	0.613036i	−0.0796503	−	0.996823i	$-0.525380\pi$
$577$	20.2681	−	14.7256i	0.843771	−	0.613036i	0.923422	+	0.383787i	$0.125380\pi$
$578$	0.234978	−	0.170721i	0.00977378	−	0.00710107i
$579$	7.39651	−	8.21465i	0.307388	−	0.341389i
$580$	−15.2876	+	3.24949i	−0.634785	+	0.134928i
$581$	1.56465	+	1.13678i	0.0649125	+	0.0471617i
$582$	12.7588			0.528870
$583$	−8.88055	−	41.1595i	−0.367795	−	1.70465i
$584$	−4.87769	+	8.44841i	−0.201840	+	0.349598i
$585$	−1.16861	+	11.1186i	−0.0483160	+	0.459696i
$586$	−9.63365	−	10.6993i	−0.397962	−	0.441982i
$587$	20.5021	+	4.35786i	0.846214	+	0.179868i	0.610561	−	0.791969i	$-0.290944\pi$
$587$	20.5021	+	4.35786i	0.846214	+	0.179868i	0.235652	+	0.971837i	$0.424277\pi$
$588$	7.72853	−	5.61511i	0.318719	−	0.231563i
$589$	35.6309	−	19.8948i	1.46814	−	0.819750i
$590$	−0.0747397	−	0.230025i	−0.00307698	−	0.00946998i
$591$	11.4937	+	12.7650i	0.472786	+	0.525082i
$592$	−5.76862	+	2.56835i	−0.237089	+	0.105559i
$593$	4.20464	+	7.28265i	0.172664	+	0.299062i	0.939350	−	0.342959i	$-0.111429\pi$
$593$	4.20464	+	7.28265i	0.172664	+	0.299062i	−0.766687	+	0.642022i	$0.778096\pi$
$594$	3.84235	−	18.3530i	0.157654	−	0.753033i
$595$	−1.50343	−	2.60402i	−0.0616346	−	0.106754i
$596$	−18.7318	−	13.6095i	−0.767286	−	0.557466i
$597$	−7.99297	+	24.5998i	−0.327130	+	1.00680i
$598$	−16.1499	+	17.9362i	−0.660417	+	0.733467i
$599$	−4.84559	−	2.15740i	−0.197985	−	0.0881488i	0.305349	−	0.952241i	$-0.401227\pi$
$599$	−4.84559	−	2.15740i	−0.197985	−	0.0881488i	−0.503334	+	0.864092i	$0.667894\pi$
$600$	0.0867685	−	0.0630410i	0.00354231	−	0.00257364i
$601$	10.2661	+	31.5957i	0.418761	+	1.28881i	0.908843	+	0.417138i	$0.136967\pi$
$601$	10.2661	+	31.5957i	0.418761	+	1.28881i	−0.490082	+	0.871676i	$0.663033\pi$
$602$	−1.63590	+	0.347722i	−0.0666745	+	0.0141721i
$603$	−4.67102	+	2.07967i	−0.190219	+	0.0846909i
$604$	4.08947	+	7.08317i	0.166398	+	0.288210i
$605$	16.4414	+	18.0366i	0.668438	+	0.733294i
$606$	−5.68291	+	9.84310i	−0.230853	+	0.399848i
$607$	−21.1009	−	15.3307i	−0.856459	−	0.622254i	0.0704602	−	0.997515i	$-0.477553\pi$
$607$	−21.1009	−	15.3307i	−0.856459	−	0.622254i	−0.926919	+	0.375261i	$0.877553\pi$
$608$	4.34112	−	0.393328i	0.176056	−	0.0159515i
$609$	1.00061	+	3.07957i	0.0405468	+	0.124790i
$610$	3.07475	+	29.2543i	0.124493	+	1.18447i
$611$	−4.43633	−	42.2088i	−0.179475	−	1.70759i
$612$	−2.94765	+	3.27370i	−0.119152	+	0.132331i
$613$	−9.70529	−	10.7788i	−0.391993	−	0.435352i	0.514554	−	0.857458i	$-0.327958\pi$
$613$	−9.70529	−	10.7788i	−0.391993	−	0.435352i	−0.906546	+	0.422106i	$0.861291\pi$
$614$	0.156621	−	1.49015i	0.00632072	−	0.0601377i
$615$	28.5838			1.15261
$616$	−1.04472	+	0.342991i	−0.0420930	+	0.0138195i
$617$	−15.4216	−	26.7110i	−0.620850	−	1.07534i	−0.989328	−	0.145707i	$-0.953454\pi$
$617$	−15.4216	−	26.7110i	−0.620850	−	1.07534i	0.368478	−	0.929637i	$-0.379879\pi$
$618$	1.21633	−	11.5726i	0.0489281	−	0.465520i
$619$	10.5398	−	32.4382i	0.423631	−	1.30380i	−0.480669	−	0.876902i	$-0.659606\pi$
$619$	10.5398	−	32.4382i	0.423631	−	1.30380i	0.904299	−	0.426899i	$-0.140394\pi$
$620$	−6.41888	−	19.7553i	−0.257788	−	0.793391i
$621$	26.6601	+	11.8699i	1.06983	+	0.476321i
$622$	−1.55703	−	14.8142i	−0.0624312	−	0.593993i
$623$	3.93573	−	4.37108i	0.157682	−	0.175123i
$624$	4.33788	+	4.81770i	0.173654	+	0.192862i
$625$	−22.4798	+	10.0087i	−0.899193	+	0.400347i
$626$	10.1277			0.404783
$627$	−16.3482	+	11.5977i	−0.652882	+	0.463167i
$628$	7.81767			0.311959
$629$	−23.5806	+	10.4987i	−0.940218	+	0.418612i
$630$	−0.530426	−	0.589098i	−0.0211327	−	0.0234702i
$631$	26.9053	−	29.8813i	1.07108	−	1.18956i	0.0900038	−	0.995941i	$-0.471312\pi$
$631$	26.9053	−	29.8813i	1.07108	−	1.18956i	0.981078	−	0.193615i	$-0.0620213\pi$
$632$	0.316164	+	3.00810i	0.0125763	+	0.119656i
$633$	22.3500	+	9.95087i	0.888334	+	0.395512i
$634$	−2.33872	−	7.19785i	−0.0928826	−	0.285863i
$635$	8.45051	−	26.0080i	0.335348	−	1.03210i
$636$	1.83994	−	17.5059i	0.0729584	−	0.694153i
$637$	16.1082	+	27.9002i	0.638229	+	1.10545i
$638$	0.0715424	+	23.3631i	0.00283239	+	0.924955i
$639$	−1.43331			−0.0567008
$640$	0.231918	−	2.20655i	0.00916735	−	0.0872215i
$641$	31.7300	+	35.2397i	1.25326	+	1.39189i	0.887259	+	0.461271i	$0.152606\pi$
$641$	31.7300	+	35.2397i	1.25326	+	1.39189i	0.366000	+	0.930615i	$0.380727\pi$
$642$	−17.4271	+	19.3548i	−0.687793	+	0.763871i
$643$	−3.31495	−	31.5396i	−0.130729	−	1.24380i	−0.841453	−	0.540330i	$-0.818299\pi$
$643$	−3.31495	−	31.5396i	−0.130729	−	1.24380i	0.710724	−	0.703471i	$-0.248367\pi$
$644$	−0.178884	−	1.70197i	−0.00704903	−	0.0670670i
$645$	4.79533	+	14.7585i	0.188816	+	0.581115i
$646$	17.7453	−	1.60782i	0.698180	−	0.0632588i
$647$	32.5910	+	23.6787i	1.28128	+	0.930907i	0.999591	−	0.0285974i	$-0.00910408\pi$
$647$	32.5910	+	23.6787i	1.28128	+	0.930907i	0.281693	+	0.959505i	$0.409104\pi$
$648$	2.30283	−	3.98861i	0.0904636	−	0.156688i
$649$	−0.359450	+	0.0388929i	−0.0141096	+	0.00152668i
$650$	0.180847	+	0.313236i	0.00709341	+	0.0122861i
$651$	−3.93146	+	1.75040i	−0.154086	+	0.0686036i
$652$	3.67400	−	0.780934i	0.143885	−	0.0305837i
$653$	−5.77555	−	17.7753i	−0.226015	−	0.695602i	−0.998187	−	0.0601886i	$-0.980830\pi$
$653$	−5.77555	−	17.7753i	−0.226015	−	0.695602i	0.772172	−	0.635413i	$-0.219170\pi$
$654$	−6.30266	+	4.57915i	−0.246454	+	0.179059i
$655$	−28.6696	−	12.7645i	−1.12021	−	0.498751i
$656$	−6.21752	+	6.90526i	−0.242753	+	0.269605i
$657$	−3.24870	+	9.99847i	−0.126744	+	0.390077i
$658$	2.43459	+	1.76884i	0.0949104	+	0.0689564i
$659$	−0.607426	−	1.05209i	−0.0236620	−	0.0409837i	0.853952	−	0.520352i	$-0.174199\pi$
$659$	−0.607426	−	1.05209i	−0.0236620	−	0.0409837i	−0.877614	+	0.479368i	$0.840866\pi$
$660$	4.17829	+	9.30778i	0.162640	+	0.362305i
$661$	21.0456	+	36.4520i	0.818577	+	1.41782i	0.906730	+	0.421711i	$0.138570\pi$
$661$	21.0456	+	36.4520i	0.818577	+	1.41782i	−0.0881531	+	0.996107i	$0.528096\pi$
$662$	−15.1833	+	6.76004i	−0.590115	+	0.262736i
$663$	17.7321	+	19.6935i	0.688657	+	0.764831i
$664$	1.80264	+	5.54796i	0.0699561	+	0.215303i
$665$	−0.0460454	+	3.20600i	−0.00178556	+	0.124323i
$666$	−5.50531	+	3.99984i	−0.213327	+	0.154991i
$667$	−35.5670	−	7.56000i	−1.37716	−	0.292724i
$668$	7.01815	+	7.79445i	0.271540	+	0.301576i
$669$	−1.02423	+	9.74489i	−0.0395990	+	0.376759i
$670$	5.26342	−	9.11652i	0.203344	−	0.352202i
$671$	43.7446	+	4.46235i	1.68874	+	0.172267i
$672$	−0.459670			−0.0177322
$673$	9.31314	+	6.76639i	0.358995	+	0.260825i	0.752633	−	0.658440i	$-0.228784\pi$
$673$	9.31314	+	6.76639i	0.358995	+	0.260825i	−0.393638	+	0.919266i	$0.628784\pi$
$674$	−8.03375	+	1.70763i	−0.309449	+	0.0657753i
$675$	0.292635	−	0.325004i	0.0112635	−	0.0125094i
$676$	−7.17006	+	5.20936i	−0.275772	+	0.200360i
$677$	−11.7598	+	8.54396i	−0.451964	+	0.328371i	−0.790371	−	0.612629i	$-0.790112\pi$
$677$	−11.7598	+	8.54396i	−0.451964	+	0.328371i	0.338407	+	0.941000i	$0.390112\pi$
$678$	5.41829	−	6.01762i	0.208088	−	0.231105i
$679$	−2.04145	−	2.26726i	−0.0783436	−	0.0870094i
$680$	0.948017	−	9.01978i	0.0363548	−	0.345893i
$681$	13.2899	−	23.0187i	0.509269	−	0.882080i
$682$	−30.8707	+	3.34025i	−1.18210	+	0.127905i
$683$	−7.27315			−0.278299			−0.139150	−	0.990271i	$-0.544437\pi$
$683$	−7.27315			−0.278299			−0.139150	+	0.990271i	$0.544437\pi$
$684$	4.48790	−	1.38728i	0.171599	−	0.0530439i
$685$	3.66400	−	11.2766i	0.139994	−	0.430858i
$686$	−4.50444	−	0.957449i	−0.171980	−	0.0365556i
$687$	−0.247178	−	2.35174i	−0.00943042	−	0.0897245i
$688$	−4.60842	−	2.05180i	−0.175694	−	0.0782242i
$689$	58.0645	+	12.3420i	2.21208	+	0.470192i
$690$	−15.5319	+	3.30141i	−0.591289	+	0.125682i
$691$	5.82549	+	4.23247i	0.221612	+	0.161011i	0.693052	−	0.720888i	$-0.256266\pi$
$691$	5.82549	+	4.23247i	0.221612	+	0.161011i	−0.471440	+	0.881898i	$0.656266\pi$
$692$	21.1161			0.802714
$693$	−1.02440	+	0.595630i	−0.0389139	+	0.0226261i
$694$	2.68620	+	4.65264i	0.101967	+	0.176612i
$695$	9.83111	+	7.14272i	0.372915	+	0.270939i
$696$	−3.01810	+	9.28876i	−0.114401	+	0.352090i
$697$	−25.4156	+	28.2268i	−0.962683	+	1.06917i
$698$	−0.462347	−	4.39893i	−0.0175001	−	0.166502i
$699$	13.7331	+	6.11435i	0.519432	+	0.231266i
$700$	−0.0250857	−	0.00533213i	−0.000948149	−	0.000201535i
$701$	−4.65529	−	5.17023i	−0.175828	−	0.195277i	0.648789	−	0.760969i	$-0.275276\pi$
$701$	−4.65529	−	5.17023i	−0.175828	−	0.195277i	−0.824617	+	0.565692i	$0.808609\pi$
$702$	21.3863	+	15.5381i	0.807174	+	0.586446i
$703$	27.3295	+	3.26990i	1.03075	+	0.123326i
$704$	−3.15742	−	1.01523i	−0.119000	−	0.0382629i
$705$	13.9612	−	24.1814i	0.525807	−	0.910725i
$706$	−2.01545	+	0.897335i	−0.0758523	+	0.0337716i
$707$	2.65841	−	0.565063i	0.0999799	−	0.0212514i
$708$	−0.147839	−	0.0314241i	−0.00555612	−	0.00118099i
$709$	−47.0877	−	20.9648i	−1.76841	−	0.787349i	−0.986458	−	0.164016i	$-0.947555\pi$
$709$	−47.0877	−	20.9648i	−1.76841	−	0.787349i	−0.781957	−	0.623333i	$-0.785778\pi$
$710$	2.38733	−	1.73450i	0.0895951	−	0.0650946i
$711$	1.00726	+	3.10004i	0.0377753	+	0.116260i
$712$	17.3535	−	3.68860i	0.650351	−	0.138236i
$713$	5.05147	−	48.0616i	0.189179	−	1.79992i
$714$	−1.87901			−0.0703202
$715$	−32.6903	+	10.7325i	−1.22255	+	0.401373i
$716$	12.2965	+	21.2981i	0.459540	+	0.795947i
$717$	19.5669	−	8.71174i	0.730739	−	0.325346i
$718$	1.25301	−	0.266335i	0.0467619	−	0.00993954i
$719$	41.3840	+	8.79643i	1.54336	+	0.328052i	0.899441	−	0.437041i	$-0.143974\pi$
$719$	41.3840	+	8.79643i	1.54336	+	0.328052i	0.643920	+	0.765093i	$0.277307\pi$
$720$	−0.249929	−	2.37792i	−0.00931431	−	0.0886197i
$721$	−2.25109	+	1.63551i	−0.0838349	+	0.0609096i
$722$	−17.1283	−	8.22329i	−0.637448	−	0.306039i
$723$	7.83552	−	24.1152i	0.291406	−	0.896856i
$724$	3.44432	−	1.53351i	0.128007	−	0.0569925i
$725$	−0.272456	+	0.471908i	−0.0101188	+	0.0175262i
$726$	14.8983	−	3.26223i	0.552929	−	0.121073i
$727$	−11.5613	+	20.0247i	−0.428784	+	0.742676i	−0.996765	−	0.0803652i	$-0.974391\pi$
$727$	−11.5613	+	20.0247i	−0.428784	+	0.742676i	0.567981	+	0.823042i	$0.307725\pi$
$728$	0.162038	−	1.54169i	0.00600554	−	0.0571389i
$729$	8.80058	−	27.0854i	0.325947	−	1.00316i
$730$	−6.68846	−	20.5850i	−0.247551	−	0.761883i
$731$	−18.8380	−	8.38721i	−0.696748	−	0.310212i
$732$	16.7927	+	7.47659i	0.620676	+	0.276343i
$733$	7.81820	+	24.0619i	0.288772	+	0.888748i	0.985243	+	0.171163i	$0.0547526\pi$
$733$	7.81820	+	24.0619i	0.288772	+	0.888748i	−0.696471	+	0.717585i	$0.745247\pi$
$734$	0.977787	−	3.00932i	0.0360908	−	0.111076i
$735$	−2.21551	+	21.0791i	−0.0817202	+	0.777516i
$736$	2.58093	−	4.47030i	0.0951343	−	0.164777i
$737$	−11.7263	−	10.4936i	−0.431945	−	0.386537i
$738$	−5.00679	+	8.67202i	−0.184303	+	0.319221i
$739$	18.7690	−	8.35648i	0.690428	−	0.307398i	−0.0313646	−	0.999508i	$-0.509985\pi$
$739$	18.7690	−	8.35648i	0.690428	−	0.307398i	0.721792	+	0.692110i	$0.243319\pi$
$740$	4.32935	−	13.3244i	0.159150	−	0.489814i
$741$	−5.47765	−	27.7221i	−0.201226	−	1.01840i
$742$	−3.40521	+	2.47403i	−0.125009	+	0.0908245i
$743$	−2.35153	−	22.3733i	−0.0862692	−	0.820797i	−0.949030	−	0.315185i	$-0.897933\pi$
$743$	−2.35153	−	22.3733i	−0.0862692	−	0.820797i	0.862761	−	0.505612i	$-0.168733\pi$
$744$	−12.6969	−	2.69880i	−0.465490	−	0.0989429i
$745$	50.2489	−	10.6807i	1.84098	−	0.391312i
$746$	−23.9942	+	10.6829i	−0.878488	+	0.391128i
$747$	3.14326	+	5.44428i	0.115006	+	0.199196i
$748$	−12.9067	−	4.14999i	−0.471915	−	0.151739i
$749$	6.22775			0.227557
$750$	−1.63262	+	15.5334i	−0.0596150	+	0.567199i
$751$	4.64540	−	0.987410i	0.169513	−	0.0360311i	−0.122373	−	0.992484i	$-0.539050\pi$
$751$	4.64540	−	0.987410i	0.169513	−	0.0360311i	0.291886	+	0.956453i	$0.405717\pi$
$752$	2.80491	+	8.63264i	0.102285	+	0.314800i
$753$	−26.5525	+	19.2915i	−0.967627	+	0.703022i
$754$	−30.0898	−	13.3968i	−1.09580	−	0.487883i
$755$	−17.7501	−	3.77290i	−0.645992	−	0.137310i
$756$	−1.83342	+	0.389706i	−0.0666809	+	0.0141735i
$757$	10.1761	−	4.53069i	0.369857	−	0.164671i	−0.213388	−	0.976968i	$-0.568450\pi$
$757$	10.1761	−	4.53069i	0.369857	−	0.164671i	0.583244	+	0.812297i	$0.301783\pi$
$758$	6.33262	−	10.9684i	0.230011	−	0.398391i
$759$	0.0726855	+	23.7364i	0.00263831	+	0.861577i
$760$	−5.79631	+	7.74165i	−0.210254	+	0.280819i
$761$	−13.8793	−	10.0839i	−0.503123	−	0.365540i	0.307086	−	0.951682i	$-0.400646\pi$
$761$	−13.8793	−	10.0839i	−0.503123	−	0.365540i	−0.810209	+	0.586142i	$0.800646\pi$
$762$	−11.4348	−	12.6996i	−0.414238	−	0.460058i
$763$	1.82217	+	0.387313i	0.0659668	+	0.0140217i
$764$	6.92579	+	3.08356i	0.250566	+	0.111559i
$765$	−1.02164	−	9.72028i	−0.0369376	−	0.351438i
$766$	−5.40102	+	5.99844i	−0.195147	+	0.216732i
$767$	0.157508	−	0.484761i	0.00568730	−	0.0175037i
$768$	−1.12169	−	0.814955i	−0.0404755	−	0.0294071i
$769$	−7.30435	−	12.6515i	−0.263402	−	0.456225i	0.703742	−	0.710456i	$-0.251511\pi$
$769$	−7.30435	−	12.6515i	−0.263402	−	0.456225i	−0.967144	+	0.254231i	$0.918178\pi$
$770$	0.985465	−	2.23176i	0.0355137	−	0.0804270i
$771$	−13.9613			−0.502805
$772$	−6.44998	−	4.68619i	−0.232140	−	0.168660i
$773$	−22.5148	+	4.78568i	−0.809803	+	0.172129i	−0.594164	−	0.804344i	$-0.702517\pi$
$773$	−22.5148	+	4.78568i	−0.809803	+	0.172129i	−0.215639	+	0.976473i	$0.569184\pi$
$774$	−5.31752	−	1.13027i	−0.191134	−	0.0406269i
$775$	−0.661603	−	0.294565i	−0.0237655	−	0.0105811i
$776$	−0.961901	−	9.15188i	−0.0345302	−	0.328533i
$777$	−2.83918	−	0.603486i	−0.101855	−	0.0216499i
$778$	−3.33414	+	10.2614i	−0.119535	+	0.367891i
$779$	38.6961	−	11.9615i	1.38643	−	0.428566i
$780$	−14.3835			−0.515013
$781$	−1.80651	−	4.02428i	−0.0646421	−	0.144000i
$782$	10.5501	−	18.2734i	0.377272	−	0.653455i
$783$	−4.16291	+	39.6075i	−0.148770	+	1.41546i
$784$	−4.61037	−	5.12033i	−0.164656	−	0.182869i
$785$	−11.6061	+	12.8899i	−0.414241	+	0.460061i
$786$	−15.8659	+	11.5272i	−0.565918	+	0.411163i
$787$	−29.2743	+	21.2690i	−1.04352	+	0.758159i	−0.970969	−	0.239206i	$-0.923113\pi$
$787$	−29.2743	+	21.2690i	−1.04352	+	0.758159i	−0.0725473	+	0.997365i	$0.523113\pi$
$788$	8.28979	−	9.20675i	0.295312	−	0.327977i
$789$	−35.3880	+	7.52195i	−1.25985	+	0.267789i
$790$	−5.42918	−	3.94453i	−0.193162	−	0.140340i
$791$	−1.93628			−0.0688462
$792$	−3.55575	−	0.362719i	−0.126348	−	0.0128887i
$793$	−30.9954	+	53.6856i	−1.10068	+	1.90643i
$794$	2.24558	−	21.3652i	0.0796926	−	0.758224i
$795$	26.1324	+	29.0230i	0.926821	+	1.02934i
$796$	18.2480	+	3.87873i	0.646783	+	0.137478i
$797$	−24.7508	+	17.9825i	−0.876720	+	0.636974i	−0.932382	−	0.361476i	$-0.882273\pi$
$797$	−24.7508	+	17.9825i	−0.876720	+	0.636974i	0.0556620	+	0.998450i	$0.482273\pi$
$798$	1.72065	+	1.02664i	0.0609104	+	0.0363428i
$799$	11.4657	+	35.2879i	0.405629	+	1.24840i
$800$	−0.0517608	−	0.0574861i	−0.00183002	−	0.00203244i
$801$	17.4661	−	7.77641i	0.617135	−	0.274766i
$802$	7.25710	+	12.5697i	0.256257	+	0.443850i
$803$	−32.1672	+	3.48053i	−1.13516	+	0.122825i
$804$	−3.28915	−	5.69698i	−0.115999	−	0.200917i
$805$	3.07181	+	2.23180i	0.108267	+	0.0786607i
$806$	13.5273	−	41.6328i	0.476479	−	1.46645i
$807$	16.0142	−	17.7856i	0.563727	−	0.626083i
$808$	7.48887	+	3.33426i	0.263458	+	0.117299i
$809$	−32.6615	+	23.7300i	−1.14832	+	0.834301i	−0.988256	−	0.152806i	$-0.951169\pi$
$809$	−32.6615	+	23.7300i	−1.14832	+	0.834301i	−0.160061	+	0.987107i	$0.551169\pi$
$810$	3.15771	+	9.71845i	0.110951	+	0.341471i
$811$	40.1634	−	8.53699i	1.41033	−	0.299774i	0.561077	−	0.827764i	$-0.310387\pi$
$811$	40.1634	−	8.53699i	1.41033	−	0.299774i	0.849251	+	0.527990i	$0.177054\pi$
$812$	2.13353	−	0.949908i	0.0748722	−	0.0333352i
$813$	6.76472	+	11.7168i	0.237249	+	0.410928i
$814$	−18.1691	−	10.4159i	−0.636827	−	0.365077i
$815$	−4.16682	+	7.21714i	−0.145957	+	0.252805i
$816$	−4.58516	−	3.33132i	−0.160513	−	0.116619i
$817$	12.6678	+	17.9730i	0.443191	+	0.628795i
$818$	−3.61167	−	11.1156i	−0.126279	−	0.388648i
$819$	−0.174623	−	1.66143i	−0.00610182	−	0.0580549i
$820$	−2.15497	−	20.5031i	−0.0752547	−	0.716000i
$821$	−28.2001	+	31.3194i	−0.984192	+	1.09306i	0.0114629	+	0.999934i	$0.496351\pi$
$821$	−28.2001	+	31.3194i	−0.984192	+	1.09306i	−0.995655	+	0.0931215i	$0.970315\pi$
$822$	−4.95792	−	5.50632i	−0.172927	−	0.192055i
$823$	−1.19695	+	11.3883i	−0.0417232	+	0.396970i	0.953652	+	0.300910i	$0.0972905\pi$
$823$	−1.19695	+	11.3883i	−0.0417232	+	0.396970i	−0.995376	+	0.0960592i	$0.969376\pi$
$824$	−8.39273			−0.292375
$825$	0.338639	+	0.108885i	0.0117899	+	0.00379090i
$826$	0.0180705	+	0.0312991i	0.000628755	+	0.00108903i
$827$	3.54713	−	33.7487i	0.123346	−	1.17356i	−0.741300	−	0.671174i	$-0.765790\pi$
$827$	3.54713	−	33.7487i	0.123346	−	1.17356i	0.864645	−	0.502383i	$-0.167543\pi$
$828$	1.71898	−	5.29048i	0.0597388	−	0.183857i
$829$	−16.6271	−	51.1729i	−0.577483	−	1.77731i	−0.627565	−	0.778564i	$-0.715948\pi$
$829$	−16.6271	−	51.1729i	−0.577483	−	1.77731i	0.0500824	−	0.998745i	$-0.484052\pi$
$830$	−11.8238	−	5.26429i	−0.410409	−	0.182726i
$831$	−0.00819450	−	0.0779654i	−0.000284264	−	0.00270459i
$832$	3.12869	−	3.47476i	0.108468	−	0.120466i
$833$	−18.8459	−	20.9305i	−0.652973	−	0.725200i
$834$	6.93731	−	3.08869i	0.240219	−	0.106952i
$835$	−23.2708			−0.805319
$836$	9.55150	+	10.8521i	0.330346	+	0.375329i
$837$	−52.9302			−1.82954
$838$	−36.3761	+	16.1957i	−1.25659	+	0.559471i
$839$	−20.1069	−	22.3310i	−0.694167	−	0.770951i	0.288269	−	0.957550i	$-0.406920\pi$
$839$	−20.1069	−	22.3310i	−0.694167	−	0.770951i	−0.982436	+	0.186598i	$0.940254\pi$
$840$	0.682428	−	0.757913i	0.0235460	−	0.0261505i
$841$	−2.15558	−	20.5089i	−0.0743302	−	0.707204i
$842$	26.1366	+	11.6368i	0.900727	+	0.401030i
$843$	6.81129	+	20.9630i	0.234593	+	0.722004i
$844$	5.45275	−	16.7818i	0.187691	−	0.577654i
$845$	2.05541	−	19.5560i	0.0707084	−	0.672745i
$846$	4.89092	+	8.47132i	0.168153	+	0.291250i
$847$	−2.96348	−	2.12549i	−0.101826	−	0.0730326i
$848$	−12.6956			−0.435970
$849$	−0.560269	+	5.33060i	−0.0192284	+	0.182946i
$850$	−0.211584	−	0.234988i	−0.00725727	−	0.00806002i
$851$	21.8101	−	24.2226i	0.747642	−	0.830340i
$852$	−0.192755	−	1.83394i	−0.00660368	−	0.0628298i
$853$	−4.32716	−	41.1702i	−0.148159	−	1.40964i	−0.775722	−	0.631074i	$-0.782614\pi$
$853$	−4.32716	−	41.1702i	−0.148159	−	1.40964i	0.627563	−	0.778566i	$-0.284052\pi$
$854$	−1.35828	−	4.18036i	−0.0464794	−	0.143049i
$855$	−4.37538	+	9.45929i	−0.149635	+	0.323501i
$856$	15.1970	+	11.0412i	0.519422	+	0.377382i
$857$	8.92419	−	15.4572i	0.304845	−	0.528006i	−0.672382	−	0.740204i	$-0.734729\pi$
$857$	8.92419	−	15.4572i	0.304845	−	0.528006i	0.977227	+	0.212198i	$0.0680622\pi$
$858$	−4.40593	+	21.0449i	−0.150416	+	0.718463i
$859$	−24.8972	−	43.1233i	−0.849483	−	1.47135i	−0.881670	−	0.471866i	$-0.843581\pi$
$859$	−24.8972	−	43.1233i	−0.849483	−	1.47135i	0.0321876	−	0.999482i	$-0.489753\pi$
$860$	10.2247	−	4.55234i	0.348660	−	0.155233i
$861$	−4.17789	+	0.888039i	−0.142382	+	0.0302643i
$862$	−0.608563	−	1.87297i	−0.0207277	−	0.0637935i
$863$	21.3273	−	15.4952i	0.725991	−	0.527463i	−0.162302	−	0.986741i	$-0.551892\pi$
$863$	21.3273	−	15.4952i	0.725991	−	0.527463i	0.888293	+	0.459278i	$0.151892\pi$
$864$	−5.16483	−	2.29953i	−0.175711	−	0.0782317i
$865$	−31.3490	+	34.8166i	−1.06590	+	1.18380i
$866$	−2.43259	+	7.48673i	−0.0826626	+	0.254409i
$867$	0.325793	+	0.236702i	0.0110645	+	0.00803883i
$868$	1.55196	+	2.68807i	0.0526768	+	0.0912389i
$869$	−7.43440	+	6.73530i	−0.252195	+	0.228480i
$870$	−10.8348	−	18.7664i	−0.367334	−	0.636241i
$871$	20.2666	−	9.02327i	0.686708	−	0.305742i
$872$	3.75978	+	4.17566i	0.127322	+	0.141406i
$873$	−3.06451	−	9.43159i	−0.103718	−	0.319211i
$874$	−19.6451	+	10.9690i	−0.664507	+	0.371033i
$875$	3.02152	−	2.19527i	0.102146	−	0.0742135i
$876$	−13.2301	−	2.81215i	−0.447004	−	0.0950136i
$877$	28.2994	+	31.4297i	0.955604	+	1.06131i	0.998063	+	0.0622071i	$0.0198139\pi$
$877$	28.2994	+	31.4297i	0.955604	+	1.06131i	−0.0424597	+	0.999098i	$0.513519\pi$
$878$	0.940270	−	8.94607i	0.0317326	−	0.301915i
$879$	9.98079	−	17.2872i	0.336644	−	0.583084i
$880$	6.36144	−	3.69880i	0.214444	−	0.124687i
$881$	19.2123			0.647278			0.323639	−	0.946181i	$-0.395094\pi$
$881$	19.2123			0.647278			0.323639	+	0.946181i	$0.395094\pi$
$882$	−6.00710	−	4.36442i	−0.202270	−	0.146958i
$883$	−31.3106	+	6.65528i	−1.05369	+	0.223968i	−0.702020	−	0.712158i	$-0.747718\pi$
$883$	−31.3106	+	6.65528i	−1.05369	+	0.223968i	−0.351666	+	0.936125i	$0.614385\pi$
$884$	12.7892	−	14.2039i	0.430149	−	0.477729i
$885$	0.271295	−	0.197107i	0.00911947	−	0.00662568i
$886$	−4.58653	+	3.33231i	−0.154087	+	0.111951i
$887$	2.70947	−	3.00917i	0.0909752	−	0.101038i	−0.695938	−	0.718102i	$-0.745011\pi$
$887$	2.70947	−	3.00917i	0.0909752	−	0.101038i	0.786913	+	0.617064i	$0.211678\pi$
$888$	−5.85824	−	6.50623i	−0.196590	−	0.218335i
$889$	−0.427138	+	4.06394i	−0.0143257	+	0.136300i
$890$	−19.6812	+	34.0889i	−0.659717	+	1.14266i
$891$	15.1866	−	1.64321i	0.508770	−	0.0550495i
$892$	7.06721			0.236628
$893$	8.78100	−	38.5785i	0.293845	−	1.29098i
$894$	9.92019	−	30.5312i	0.331781	−	1.02112i
$895$	−53.3720	−	11.3446i	−1.78403	−	0.379207i
$896$	0.0346550	+	0.329721i	0.00115774	+	0.0110152i
$897$	−30.5705	−	13.6109i	−1.02072	−	0.454454i
$898$	−4.34273	−	0.923076i	−0.144919	−	0.0308035i
$899$	64.5087	−	13.7118i	2.15149	−	0.457313i
$900$	−0.0674420	−	0.0489995i	−0.00224807	−	0.00163332i
$901$	−51.8964			−1.72892
$902$	−30.6588	−	3.12748i	−1.02083	−	0.104134i
$903$	−1.15941	−	2.00816i	−0.0385829	−	0.0668275i
$904$	−4.72492	−	3.43285i	−0.157148	−	0.114175i
$905$	−2.58497	+	7.95572i	−0.0859273	+	0.264457i
$906$	−7.58792	+	8.42724i	−0.252092	+	0.279976i
$907$	−0.277261	−	2.63797i	−0.00920631	−	0.0875922i	0.988954	−	0.148223i	$-0.0473554\pi$
$907$	−0.277261	−	2.63797i	−0.00920631	−	0.0875922i	−0.998160	+	0.0606310i	$0.980689\pi$
$908$	−17.5132	−	7.79739i	−0.581197	−	0.258766i
$909$	8.64119	+	1.83674i	0.286610	+	0.0609209i
$910$	2.30141	+	2.55597i	0.0762909	+	0.0847297i
$911$	−2.08296	−	1.51336i	−0.0690114	−	0.0501397i	0.552745	−	0.833351i	$-0.313580\pi$
$911$	−2.08296	−	1.51336i	−0.0690114	−	0.0501397i	−0.621756	+	0.783211i	$0.713580\pi$
$912$	2.37859	+	5.55578i	0.0787630	+	0.183970i
$913$	−11.3242	+	15.6872i	−0.374775	+	0.519169i
$914$	−8.64558	+	14.9746i	−0.285970	+	0.495315i
$915$	−37.2580	+	16.5883i	−1.23171	+	0.548394i
$916$	−1.66826	+	0.354600i	−0.0551210	+	0.0117163i
$917$	4.58699	+	0.974996i	0.151476	+	0.0321972i
$918$	−21.1125	−	9.39987i	−0.696815	−	0.310242i
$919$	1.81873	−	1.32138i	0.0599943	−	0.0435884i	−0.557384	−	0.830255i	$-0.688195\pi$
$919$	1.81873	−	1.32138i	0.0599943	−	0.0435884i	0.617378	+	0.786666i	$0.288195\pi$
$920$	3.53906	+	10.8921i	0.116679	+	0.359102i
$921$	2.03206	−	0.431927i	0.0669585	−	0.0142325i
$922$	−0.576706	+	5.48699i	−0.0189928	+	0.180704i
$923$	6.21882			0.204695
$924$	−0.899883	−	1.23064i	−0.0296040	−	0.0404851i
$925$	−0.244231	−	0.423021i	−0.00803027	−	0.0139088i
$926$	20.6644	−	9.20039i	0.679075	−	0.302344i
$927$	−8.84689	+	1.88046i	−0.290570	+	0.0617626i
$928$	6.89035	+	1.46459i	0.226187	+	0.0480775i
$929$	2.03838	+	19.3939i	0.0668771	+	0.636293i	0.975700	+	0.219111i	$0.0703156\pi$
$929$	2.03838	+	19.3939i	0.0668771	+	0.636293i	−0.908823	+	0.417182i	$0.863018\pi$
$930$	23.2996	−	16.9282i	0.764025	−	0.555097i
$931$	5.82173	+	29.4635i	0.190799	+	0.965628i
$932$	3.35046	−	10.3117i	0.109748	−	0.337770i
$933$	18.8672	−	8.40022i	0.617684	−	0.275011i
$934$	−9.96977	+	17.2681i	−0.326221	+	0.565031i
$935$	26.0039	−	15.1197i	0.850418	−	0.494467i
$936$	2.51944	−	4.36381i	0.0823506	−	0.142635i
$937$	2.28133	−	21.7054i	0.0745277	−	0.709084i	−0.891915	−	0.452203i	$-0.850638\pi$
$937$	2.28133	−	21.7054i	0.0745277	−	0.709084i	0.966443	−	0.256881i	$-0.0826949\pi$
$938$	−0.486086	+	1.49602i	−0.0158713	+	0.0488467i
$939$	4.33917	+	13.3546i	0.141603	+	0.435810i
$940$	−18.3978	−	8.19124i	−0.600071	−	0.267169i
$941$	−12.7640	−	5.68290i	−0.416095	−	0.185257i	0.188001	−	0.982169i	$-0.439799\pi$
$941$	−12.7640	−	5.68290i	−0.416095	−	0.185257i	−0.604096	+	0.796911i	$0.706466\pi$
$942$	3.34946	+	10.3086i	0.109131	+	0.335871i
$943$	14.8216	−	45.6162i	0.482657	−	1.48547i
$944$	−0.0113947	+	0.108414i	−0.000370867	+	0.00352856i
$945$	2.07935	−	3.60154i	0.0676412	−	0.117158i
$946$	−3.52864	−	16.3545i	−0.114726	−	0.531731i
$947$	14.3406	−	24.8387i	0.466007	−	0.807148i	−0.533239	−	0.845965i	$-0.679025\pi$
$947$	14.3406	−	24.8387i	0.466007	−	0.807148i	0.999246	+	0.0388164i	$0.0123587\pi$
$948$	−3.83109	+	1.70571i	−0.124428	+	0.0553989i
$949$	14.0954	−	43.3813i	0.457557	−	1.40822i
$950$	0.0653608	+	0.330788i	0.00212058	+	0.0107322i
$951$	8.48924	−	6.16780i	0.275283	−	0.200005i
$952$	0.141660	+	1.34781i	0.00459124	+	0.0436828i
$953$	47.7838	+	10.1568i	1.54787	+	0.329010i	0.901078	−	0.433658i	$-0.142777\pi$
$953$	47.7838	+	10.1568i	1.54787	+	0.329010i	0.646791	+	0.762668i	$0.276111\pi$
$954$	−13.3826	+	2.84457i	−0.433279	+	0.0920963i
$955$	−15.3663	+	6.84150i	−0.497241	+	0.221386i
$956$	−7.72408	−	13.3785i	−0.249815	−	0.432692i
$957$	−30.7765	+	10.1042i	−0.994864	+	0.326622i
$958$	0.779826			0.0251950
$959$	−0.185200	+	1.76206i	−0.00598040	+	0.0568997i
$960$	3.00897	−	0.639577i	0.0971142	−	0.0206423i
$961$	17.5060	+	53.8780i	0.564710	+	1.73800i
$962$	23.8864	−	17.3545i	0.770129	−	0.559531i
$963$	18.4932	+	8.23371i	0.595936	+	0.265328i
$964$	−17.8885	−	3.80233i	−0.576151	−	0.122465i
$965$	17.3023	−	3.67772i	0.556982	−	0.118390i
$966$	2.16762	−	0.965085i	0.0697419	−	0.0310511i
$967$	−19.7876	+	34.2731i	−0.636326	+	1.10215i	0.349906	+	0.936785i	$0.386213\pi$
$967$	−19.7876	+	34.2731i	−0.636326	+	1.10215i	−0.986232	+	0.165365i	$0.947120\pi$
$968$	−3.46319	−	10.4406i	−0.111311	−	0.335574i
$969$	9.72304	+	22.7105i	0.312349	+	0.729568i
$970$	16.5178	+	12.0009i	0.530355	+	0.385326i
$971$	−31.5000	−	34.9843i	−1.01088	−	1.12270i	−0.992423	−	0.122870i	$-0.960790\pi$
$971$	−31.5000	−	34.9843i	−1.01088	−	1.12270i	−0.0184604	−	0.999830i	$-0.505876\pi$
$972$	−10.3441	−	2.19870i	−0.331787	−	0.0705234i
$973$	−1.65885	−	0.738569i	−0.0531804	−	0.0236774i
$974$	1.90441	+	18.1193i	0.0610213	+	0.580579i
$975$	−0.335558	+	0.372675i	−0.0107464	+	0.0119351i
$976$	4.09692	−	12.6090i	0.131139	−	0.403605i
$977$	−18.0040	−	13.0806i	−0.575998	−	0.418487i	0.261281	−	0.965263i	$-0.415855\pi$
$977$	−18.0040	−	13.0806i	−0.575998	−	0.418487i	−0.837279	+	0.546776i	$0.815855\pi$
$978$	2.60387	+	4.51004i	0.0832627	+	0.144215i
$979$	43.8477	+	39.2382i	1.40138	+	1.25406i
$980$	15.2871			0.488327
$981$	4.89883	+	3.55921i	0.156408	+	0.113637i
$982$	4.55035	−	0.967207i	0.145208	−	0.0308648i
$983$	−29.3678	−	6.24231i	−0.936687	−	0.199099i	−0.285813	−	0.958285i	$-0.592264\pi$
$983$	−29.3678	−	6.24231i	−0.936687	−	0.199099i	−0.650873	+	0.759186i	$0.725597\pi$
$984$	−11.7693	−	5.24004i	−0.375192	−	0.167046i
$985$	2.87320	+	27.3367i	0.0915479	+	0.871020i
$986$	28.1659	+	5.98684i	0.896985	+	0.190660i
$987$	−1.28934	+	3.96817i	−0.0410400	+	0.126308i
$988$	−19.4721	+	6.01911i	−0.619489	+	0.191493i
$989$	26.0392			0.827999
$990$	5.87693	−	5.32429i	0.186781	−	0.169217i
$991$	−23.3305	+	40.4096i	−0.741117	+	1.28365i	0.210869	+	0.977514i	$0.432370\pi$
$991$	−23.3305	+	40.4096i	−0.741117	+	1.28365i	−0.951987	+	0.306139i	$0.900963\pi$
$992$	−0.978616	+	9.31090i	−0.0310711	+	0.295622i
$993$	−15.4192	−	17.1247i	−0.489313	−	0.543437i
$994$	−0.295052	+	0.327689i	−0.00935849	+	0.0103937i
$995$	−33.4864	+	24.3293i	−1.06159	+	0.771290i
$996$	−6.54334	+	4.75401i	−0.207334	+	0.150637i
$997$	−5.65539	+	6.28094i	−0.179108	+	0.198919i	−0.826013	−	0.563651i	$-0.809396\pi$
$997$	−5.65539	+	6.28094i	−0.179108	+	0.198919i	0.646905	+	0.762570i	$0.276063\pi$
$998$	4.24602	−	0.902519i	0.134405	−	0.0285688i
$999$	−28.8819	−	20.9839i	−0.913782	−	0.663901i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.n.e.125.7	✓	72
11.3	even	5	inner	418.2.n.e.201.3	yes	72
19.7	even	3	inner	418.2.n.e.235.3	yes	72
209.102	even	15	inner	418.2.n.e.311.7	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.n.e.125.7	✓	72	1.1	even	1	trivial
418.2.n.e.201.3	yes	72	11.3	even	5	inner
418.2.n.e.235.3	yes	72	19.7	even	3	inner
418.2.n.e.311.7	yes	72	209.102	even	15	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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.n (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.913545 - 0.406737i) q^{2} +(0.927739 + 1.03036i) q^{3} +(0.669131 - 0.743145i) q^{4} +(0.231918 + 2.20655i) q^{5} +(1.26662 + 0.563934i) q^{6} +(-0.102451 - 0.315310i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.112646 - 1.07176i) q^{9} +O(q^{10})\)	\(q+(0.913545 - 0.406737i) q^{2} +(0.927739 + 1.03036i) q^{3} +(0.669131 - 0.743145i) q^{4} +(0.231918 + 2.20655i) q^{5} +(1.26662 + 0.563934i) q^{6} +(-0.102451 - 0.315310i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.112646 - 1.07176i) q^{9} +(1.10935 + 1.92145i) q^{10} +(3.15114 - 1.03455i) q^{11} +1.38648 q^{12} +(-0.488750 + 4.65014i) q^{13} +(-0.221841 - 0.246380i) q^{14} +(-2.05838 + 2.28606i) q^{15} +(-0.104528 - 0.994522i) q^{16} +(-0.427284 - 4.06534i) q^{17} +(-0.333016 - 1.02492i) q^{18} +(-1.82993 + 3.95618i) q^{19} +(1.79497 + 1.30412i) q^{20} +(0.229835 - 0.398086i) q^{21} +(2.45793 - 2.22679i) q^{22} +(2.58093 + 4.47030i) q^{23} +(1.26662 - 0.563934i) q^{24} +(0.0756648 - 0.0160831i) q^{25} +(1.44489 + 4.44691i) q^{26} +(4.57387 - 3.32311i) q^{27} +(-0.302874 - 0.134848i) q^{28} +(-4.71354 + 5.23492i) q^{29} +(-0.950597 + 2.92564i) q^{30} +(-7.57417 - 5.50296i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.98939 + 2.28702i) q^{33} +(-2.04387 - 3.54008i) q^{34} +(0.671987 - 0.299188i) q^{35} +(-0.721097 - 0.800860i) q^{36} +(-1.95130 - 6.00548i) q^{37} +(-0.0625972 + 4.35845i) q^{38} +(-5.24474 + 3.81053i) q^{39} +(2.17022 + 0.461294i) q^{40} +(-6.21752 - 6.90526i) q^{41} +(0.0480486 - 0.457152i) q^{42} +(2.52227 - 4.36870i) q^{43} +(1.33971 - 3.03400i) q^{44} +2.39101 q^{45} +(4.17603 + 3.03406i) q^{46} +(-8.87854 + 1.88719i) q^{47} +(0.927739 - 1.03036i) q^{48} +(5.57419 - 4.04989i) q^{49} +(0.0625817 - 0.0454683i) q^{50} +(3.79235 - 4.21183i) q^{51} +(3.12869 + 3.47476i) q^{52} +(1.32706 - 12.6261i) q^{53} +(2.82681 - 4.89617i) q^{54} +(3.01359 + 6.71323i) q^{55} -0.331537 q^{56} +(-5.77398 + 1.78482i) q^{57} +(-2.17680 + 6.69951i) q^{58} +(-0.106629 - 0.0226646i) q^{59} +(0.321550 + 3.05934i) q^{60} +(12.1117 + 5.39248i) q^{61} +(-9.15761 - 1.94651i) q^{62} +(-0.349477 + 0.0742837i) q^{63} +(-0.809017 - 0.587785i) q^{64} -10.3741 q^{65} +(4.57471 + 0.466662i) q^{66} +(-2.37230 - 4.10894i) q^{67} +(-3.30704 - 2.40271i) q^{68} +(-2.21158 + 6.80655i) q^{69} +(0.492200 - 0.546644i) q^{70} +(-0.139024 - 1.32273i) q^{71} +(-0.984494 - 0.438325i) q^{72} +(-9.54220 - 2.02826i) q^{73} +(-4.22525 - 4.69262i) q^{74} +(0.0867685 + 0.0630410i) q^{75} +(1.71556 + 4.00710i) q^{76} +(-0.649040 - 0.887598i) q^{77} +(-3.24143 + 5.61432i) q^{78} +(-2.76317 + 1.23024i) q^{79} +(2.17022 - 0.461294i) q^{80} +(4.50501 + 0.957569i) q^{81} +(-8.48861 - 3.77937i) q^{82} +(-4.71938 + 3.42883i) q^{83} +(-0.142046 - 0.437172i) q^{84} +(8.87128 - 1.88565i) q^{85} +(0.527298 - 5.01691i) q^{86} -9.76678 q^{87} +(-0.0101561 - 3.31661i) q^{88} +(8.87060 + 15.3643i) q^{89} +(2.18430 - 0.972513i) q^{90} +(1.51631 - 0.322302i) q^{91} +(5.04906 + 1.07321i) q^{92} +(-1.35683 - 12.9094i) q^{93} +(-7.34336 + 5.33526i) q^{94} +(-9.15390 - 3.12031i) q^{95} +(0.428447 - 1.31862i) q^{96} +(8.40671 - 3.74291i) q^{97} +(3.44504 - 5.96699i) q^{98} +(-0.753821 - 3.49381i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 9 q^{2} - 2 q^{3} + 9 q^{4} + 8 q^{5} + 3 q^{6} - 20 q^{7} - 18 q^{8} + 9 q^{9}+O(q^{10}) \) 72 * q + 9 * q^2 - 2 * q^3 + 9 * q^4 + 8 * q^5 + 3 * q^6 - 20 * q^7 - 18 * q^8 + 9 * q^9	\( 72 q + 9 q^{2} - 2 q^{3} + 9 q^{4} + 8 q^{5} + 3 q^{6} - 20 q^{7} - 18 q^{8} + 9 q^{9} - 22 q^{10} + 10 q^{11} + 4 q^{12} + 15 q^{13} + 10 q^{14} + 9 q^{15} + 9 q^{16} + 6 q^{17} - 28 q^{18} + 7 q^{19} - 16 q^{20} + 48 q^{21} - 15 q^{22} - 20 q^{23} + 3 q^{24} + 7 q^{25} + 30 q^{26} - 56 q^{27} - 10 q^{28} + 35 q^{29} - 18 q^{30} + 52 q^{31} - 36 q^{32} - 12 q^{33} - 4 q^{34} - 9 q^{35} + 14 q^{36} - 52 q^{37} - 2 q^{38} - 42 q^{39} + 3 q^{40} + 41 q^{41} - 2 q^{42} + 14 q^{43} + 116 q^{45} - 50 q^{46} + 19 q^{47} - 2 q^{48} + 46 q^{49} - 44 q^{50} + 33 q^{51} - 15 q^{52} - 15 q^{53} - 2 q^{54} - 55 q^{55} - 33 q^{57} - 70 q^{58} - 13 q^{59} - 6 q^{60} + 8 q^{61} + 19 q^{62} + 40 q^{63} - 18 q^{64} + 120 q^{65} + 23 q^{66} + 2 q^{67} - 12 q^{68} - 194 q^{69} + q^{70} + 52 q^{71} + 9 q^{72} - 48 q^{73} + 26 q^{74} - 158 q^{75} + 20 q^{76} + 130 q^{77} + 46 q^{78} - 48 q^{79} + 3 q^{80} + 48 q^{81} - 14 q^{82} - 62 q^{83} + 44 q^{84} - 27 q^{85} - 16 q^{86} - 164 q^{87} + 10 q^{88} + 20 q^{89} + 52 q^{90} + 4 q^{91} - 15 q^{92} - 39 q^{93} - 8 q^{94} + 69 q^{95} + 4 q^{96} + 2 q^{97} - 48 q^{98} + 9 q^{99}+O(q^{100}) \) 72 * q + 9 * q^2 - 2 * q^3 + 9 * q^4 + 8 * q^5 + 3 * q^6 - 20 * q^7 - 18 * q^8 + 9 * q^9 - 22 * q^10 + 10 * q^11 + 4 * q^12 + 15 * q^13 + 10 * q^14 + 9 * q^15 + 9 * q^16 + 6 * q^17 - 28 * q^18 + 7 * q^19 - 16 * q^20 + 48 * q^21 - 15 * q^22 - 20 * q^23 + 3 * q^24 + 7 * q^25 + 30 * q^26 - 56 * q^27 - 10 * q^28 + 35 * q^29 - 18 * q^30 + 52 * q^31 - 36 * q^32 - 12 * q^33 - 4 * q^34 - 9 * q^35 + 14 * q^36 - 52 * q^37 - 2 * q^38 - 42 * q^39 + 3 * q^40 + 41 * q^41 - 2 * q^42 + 14 * q^43 + 116 * q^45 - 50 * q^46 + 19 * q^47 - 2 * q^48 + 46 * q^49 - 44 * q^50 + 33 * q^51 - 15 * q^52 - 15 * q^53 - 2 * q^54 - 55 * q^55 - 33 * q^57 - 70 * q^58 - 13 * q^59 - 6 * q^60 + 8 * q^61 + 19 * q^62 + 40 * q^63 - 18 * q^64 + 120 * q^65 + 23 * q^66 + 2 * q^67 - 12 * q^68 - 194 * q^69 + q^70 + 52 * q^71 + 9 * q^72 - 48 * q^73 + 26 * q^74 - 158 * q^75 + 20 * q^76 + 130 * q^77 + 46 * q^78 - 48 * q^79 + 3 * q^80 + 48 * q^81 - 14 * q^82 - 62 * q^83 + 44 * q^84 - 27 * q^85 - 16 * q^86 - 164 * q^87 + 10 * q^88 + 20 * q^89 + 52 * q^90 + 4 * q^91 - 15 * q^92 - 39 * q^93 - 8 * q^94 + 69 * q^95 + 4 * q^96 + 2 * q^97 - 48 * q^98 + 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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