LMFDB - Embedded newform 414.2.m.a.265.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(13,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([22, 42]))

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

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

chi := DirichletCharacter("414.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.m (of order $33$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			265.4
Character	$\chi$	$=$	414.265
Dual form			414.2.m.a.25.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.888835 + 0.458227i) q^{2} +(-0.818784 - 1.52630i) q^{3} +(0.580057 + 0.814576i) q^{4} +(-0.448629 + 1.84927i) q^{5} +(-0.0283727 - 1.73182i) q^{6} +(-1.08663 + 3.13963i) q^{7} +(0.142315 + 0.989821i) q^{8} +(-1.65919 + 2.49942i) q^{9} +O(q^{10})$	\(q+(0.888835 + 0.458227i) q^{2} +(-0.818784 - 1.52630i) q^{3} +(0.580057 + 0.814576i) q^{4} +(-0.448629 + 1.84927i) q^{5} +(-0.0283727 - 1.73182i) q^{6} +(-1.08663 + 3.13963i) q^{7} +(0.142315 + 0.989821i) q^{8} +(-1.65919 + 2.49942i) q^{9} +(-1.24614 + 1.43813i) q^{10} +(-0.0584621 + 1.22727i) q^{11} +(0.768346 - 1.55230i) q^{12} +(0.00414324 + 0.0119711i) q^{13} +(-2.40450 + 2.29269i) q^{14} +(3.18988 - 0.829413i) q^{15} +(-0.327068 + 0.945001i) q^{16} +(-1.33487 - 2.92296i) q^{17} +(-2.62004 + 1.46129i) q^{18} +(-1.95710 + 4.28545i) q^{19} +(-1.76661 + 0.707242i) q^{20} +(5.68173 - 0.912143i) q^{21} +(-0.614331 + 1.06405i) q^{22} +(3.64396 + 3.11794i) q^{23} +(1.39424 - 1.02766i) q^{24} +(1.22563 + 0.631856i) q^{25} +(-0.00180282 + 0.0125389i) q^{26} +(5.17338 + 0.485932i) q^{27} +(-3.18777 + 0.936015i) q^{28} +(1.34969 - 1.89538i) q^{29} +(3.21534 + 0.724475i) q^{30} +(-0.618422 - 0.247579i) q^{31} +(-0.723734 + 0.690079i) q^{32} +(1.92105 - 0.915639i) q^{33} +(0.152897 - 3.20970i) q^{34} +(-5.31853 - 3.41801i) q^{35} +(-2.99839 + 0.0982726i) q^{36} +(8.14302 + 2.39101i) q^{37} +(-3.70325 + 2.91227i) q^{38} +(0.0148791 - 0.0161256i) q^{39} +(-1.89430 - 0.180884i) q^{40} +(2.08042 - 8.57560i) q^{41} +(5.46809 + 1.79277i) q^{42} +(-8.50931 + 3.40661i) q^{43} +(-1.03362 + 0.664265i) q^{44} +(-3.87775 - 4.18960i) q^{45} +(1.81016 + 4.44109i) q^{46} +(1.21841 + 2.11034i) q^{47} +(1.71015 - 0.274547i) q^{48} +(-3.17410 - 2.49614i) q^{49} +(0.799849 + 1.12323i) q^{50} +(-3.36834 + 4.43068i) q^{51} +(-0.00734805 + 0.0103189i) q^{52} +(-4.34014 - 5.00879i) q^{53} +(4.37562 + 2.80249i) q^{54} +(-2.24333 - 0.658702i) q^{55} +(-3.26231 - 0.628759i) q^{56} +(8.14333 - 0.521735i) q^{57} +(2.06817 - 1.06621i) q^{58} +(-3.28457 - 9.49014i) q^{59} +(2.52593 + 2.11729i) q^{60} +(1.83790 - 1.44534i) q^{61} +(-0.436228 - 0.503434i) q^{62} +(-6.04431 - 7.92518i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(-0.0239966 + 0.00229140i) q^{65} +(2.12707 + 0.0664248i) q^{66} +(-0.0474064 - 0.995182i) q^{67} +(1.60667 - 2.78284i) q^{68} +(1.77530 - 8.11470i) q^{69} +(-3.16108 - 5.47514i) q^{70} +(2.29094 - 1.47230i) q^{71} +(-2.71011 - 1.28659i) q^{72} +(-0.782583 + 1.71362i) q^{73} +(6.14218 + 5.85656i) q^{74} +(-0.0391235 - 2.38803i) q^{75} +(-4.62606 + 0.891599i) q^{76} +(-3.78964 - 1.51714i) q^{77} +(0.0206142 - 0.00751498i) q^{78} +(-3.42674 - 0.660450i) q^{79} +(-1.60083 - 1.02879i) q^{80} +(-3.49420 - 8.29401i) q^{81} +(5.77872 - 6.66899i) q^{82} +(3.06742 + 12.6441i) q^{83} +(4.03874 + 4.09911i) q^{84} +(6.00421 - 1.15722i) q^{85} +(-9.12437 - 0.871272i) q^{86} +(-3.99802 - 0.508132i) q^{87} +(-1.22310 + 0.116792i) q^{88} +(-0.0118057 + 0.0821103i) q^{89} +(-1.52690 - 5.50076i) q^{90} -0.0420869 q^{91} +(-0.426094 + 4.77687i) q^{92} +(0.128474 + 1.14661i) q^{93} +(0.115948 + 2.43406i) q^{94} +(-7.04696 - 5.54179i) q^{95} +(1.64585 + 0.539610i) q^{96} +(8.25966 + 7.87557i) q^{97} +(-1.67746 - 3.67311i) q^{98} +(-2.97047 - 2.18239i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 12 q^{2} + 12 q^{4} - 13 q^{7} + 24 q^{8} - 36 q^{9}+O(q^{10}) $ 240 * q - 12 * q^2 + 12 * q^4 - 13 * q^7 + 24 * q^8 - 36 * q^9	\( 240 q - 12 q^{2} + 12 q^{4} - 13 q^{7} + 24 q^{8} - 36 q^{9} + 2 q^{11} + 11 q^{12} + 4 q^{13} + 2 q^{14} + 6 q^{15} + 12 q^{16} - 8 q^{17} - 18 q^{18} + 12 q^{19} - 29 q^{21} + 20 q^{22} + 10 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} - 8 q^{29} - 18 q^{30} - 12 q^{32} + 50 q^{33} - 4 q^{34} - 12 q^{35} - 4 q^{36} + 92 q^{37} + 6 q^{38} + 44 q^{39} + 2 q^{41} + 42 q^{42} - 14 q^{43} - 4 q^{44} - 2 q^{45} - 44 q^{46} + 10 q^{47} - 22 q^{48} + 43 q^{49} - 43 q^{50} - 90 q^{51} - 18 q^{52} + 16 q^{53} - 29 q^{54} - 8 q^{55} + 13 q^{56} + 7 q^{57} + 8 q^{58} - 84 q^{59} + 9 q^{60} - 53 q^{61} - 66 q^{62} + 11 q^{63} - 24 q^{64} + 79 q^{65} - 110 q^{66} + 46 q^{67} - 40 q^{68} - 55 q^{69} - 6 q^{70} - 14 q^{71} - 19 q^{72} + 16 q^{73} + 46 q^{74} - 44 q^{75} - 6 q^{76} - 96 q^{77} + 20 q^{78} + 20 q^{79} - 22 q^{80} - 56 q^{81} + 26 q^{82} + 57 q^{83} + 5 q^{84} - 2 q^{85} - 8 q^{86} - 198 q^{87} - 2 q^{88} + 60 q^{89} - 22 q^{90} - 252 q^{91} - 218 q^{93} - 10 q^{94} + 6 q^{95} - q^{97} + 20 q^{98} + 84 q^{99}+O(q^{100}) \) 240 * q - 12 * q^2 + 12 * q^4 - 13 * q^7 + 24 * q^8 - 36 * q^9 + 2 * q^11 + 11 * q^12 + 4 * q^13 + 2 * q^14 + 6 * q^15 + 12 * q^16 - 8 * q^17 - 18 * q^18 + 12 * q^19 - 29 * q^21 + 20 * q^22 + 10 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 - 8 * q^29 - 18 * q^30 - 12 * q^32 + 50 * q^33 - 4 * q^34 - 12 * q^35 - 4 * q^36 + 92 * q^37 + 6 * q^38 + 44 * q^39 + 2 * q^41 + 42 * q^42 - 14 * q^43 - 4 * q^44 - 2 * q^45 - 44 * q^46 + 10 * q^47 - 22 * q^48 + 43 * q^49 - 43 * q^50 - 90 * q^51 - 18 * q^52 + 16 * q^53 - 29 * q^54 - 8 * q^55 + 13 * q^56 + 7 * q^57 + 8 * q^58 - 84 * q^59 + 9 * q^60 - 53 * q^61 - 66 * q^62 + 11 * q^63 - 24 * q^64 + 79 * q^65 - 110 * q^66 + 46 * q^67 - 40 * q^68 - 55 * q^69 - 6 * q^70 - 14 * q^71 - 19 * q^72 + 16 * q^73 + 46 * q^74 - 44 * q^75 - 6 * q^76 - 96 * q^77 + 20 * q^78 + 20 * q^79 - 22 * q^80 - 56 * q^81 + 26 * q^82 + 57 * q^83 + 5 * q^84 - 2 * q^85 - 8 * q^86 - 198 * q^87 - 2 * q^88 + 60 * q^89 - 22 * q^90 - 252 * q^91 - 218 * q^93 - 10 * q^94 + 6 * q^95 - q^97 + 20 * q^98 + 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{10}{11}\right)$

Coefficient data

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

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

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

$2$	0.888835	+	0.458227i	0.628502	+	0.324015i
$2$	0.888835	+	0.458227i	0.628502	+	0.324015i
$3$	−0.818784	−	1.52630i	−0.472725	−	0.881210i
$3$	−0.818784	−	1.52630i	−0.472725	−	0.881210i
$4$	0.580057	+	0.814576i	0.290028	+	0.407288i
$5$	−0.448629	+	1.84927i	−0.200633	+	0.827021i	0.779130	+	0.626862i	$0.215661\pi$
$5$	−0.448629	+	1.84927i	−0.200633	+	0.827021i	−0.979763	+	0.200159i	$0.935854\pi$
$6$	−0.0283727	−	1.73182i	−0.0115831	−	0.707012i
$7$	−1.08663	+	3.13963i	−0.410709	+	1.18667i	0.530160	+	0.847898i	$0.322132\pi$
$7$	−1.08663	+	3.13963i	−0.410709	+	1.18667i	−0.940869	+	0.338769i	$0.889989\pi$
$8$	0.142315	+	0.989821i	0.0503159	+	0.349955i
$9$	−1.65919	+	2.49942i	−0.553062	+	0.833140i
$10$	−1.24614	+	1.43813i	−0.394065	+	0.454776i
$11$	−0.0584621	+	1.22727i	−0.0176270	+	0.370036i	0.972769	+	0.231777i	$0.0744538\pi$
$11$	−0.0584621	+	1.22727i	−0.0176270	+	0.370036i	−0.990396	+	0.138260i	$0.955849\pi$
$12$	0.768346	−	1.55230i	0.221803	−	0.448111i
$13$	0.00414324	+	0.0119711i	0.00114913	+	0.00332018i	0.945574	−	0.325407i	$-0.105501\pi$
$13$	0.00414324	+	0.0119711i	0.00114913	+	0.00332018i	−0.944425	+	0.328728i	$0.893380\pi$
$14$	−2.40450	+	2.29269i	−0.642629	+	0.612746i
$15$	3.18988	−	0.829413i	0.823623	−	0.214154i
$16$	−0.327068	+	0.945001i	−0.0817670	+	0.236250i
$17$	−1.33487	−	2.92296i	−0.323754	−	0.708921i	0.675851	−	0.737038i	$-0.263776\pi$
$17$	−1.33487	−	2.92296i	−0.323754	−	0.708921i	−0.999605	+	0.0281167i	$0.991049\pi$
$18$	−2.62004	+	1.46129i	−0.617550	+	0.344429i
$19$	−1.95710	+	4.28545i	−0.448990	+	0.983150i	0.540871	+	0.841106i	$0.318095\pi$
$19$	−1.95710	+	4.28545i	−0.448990	+	0.983150i	−0.989860	+	0.142044i	$0.954632\pi$
$20$	−1.76661	+	0.707242i	−0.395025	+	0.158144i
$21$	5.68173	−	0.912143i	1.23986	−	0.199046i
$22$	−0.614331	+	1.06405i	−0.130976	+	0.226857i
$23$	3.64396	+	3.11794i	0.759818	+	0.650135i
$23$	3.64396	+	3.11794i	0.759818	+	0.650135i
$24$	1.39424	−	1.02766i	0.284598	−	0.209771i
$25$	1.22563	+	0.631856i	0.245126	+	0.126371i
$26$	−0.00180282	+	0.0125389i	−0.000353562	+	0.00245907i
$27$	5.17338	+	0.485932i	0.995618	+	0.0935177i
$28$	−3.18777	+	0.936015i	−0.602433	+	0.176890i
$29$	1.34969	−	1.89538i	0.250632	−	0.351963i	−0.670023	−	0.742340i	$-0.733716\pi$
$29$	1.34969	−	1.89538i	0.250632	−	0.351963i	0.920655	+	0.390377i	$0.127655\pi$
$30$	3.21534	+	0.724475i	0.587037	+	0.132271i
$31$	−0.618422	−	0.247579i	−0.111072	−	0.0444664i	0.315461	−	0.948939i	$-0.397841\pi$
$31$	−0.618422	−	0.247579i	−0.111072	−	0.0444664i	−0.426533	+	0.904472i	$0.640265\pi$
$32$	−0.723734	+	0.690079i	−0.127939	+	0.121990i
$33$	1.92105	−	0.915639i	0.334412	−	0.159392i
$34$	0.152897	−	3.20970i	0.0262216	−	0.550459i
$35$	−5.31853	−	3.41801i	−0.898996	−	0.577750i
$36$	−2.99839	+	0.0982726i	−0.499732	+	0.0163788i
$37$	8.14302	+	2.39101i	1.33870	+	0.393079i	0.871207	−	0.490916i	$-0.163338\pi$
$37$	8.14302	+	2.39101i	1.33870	+	0.393079i	0.467497	+	0.883995i	$0.345156\pi$
$38$	−3.70325	+	2.91227i	−0.600746	+	0.472432i
$39$	0.0148791	−	0.0161256i	0.00238256	−	0.00258216i
$40$	−1.89430	−	0.180884i	−0.299515	−	0.0286002i
$41$	2.08042	−	8.57560i	0.324907	−	1.33928i	−0.541818	−	0.840496i	$-0.682264\pi$
$41$	2.08042	−	8.57560i	0.324907	−	1.33928i	0.866724	−	0.498787i	$-0.166221\pi$
$42$	5.46809	+	1.79277i	0.843745	+	0.276631i
$43$	−8.50931	+	3.40661i	−1.29766	+	0.519503i	−0.914652	−	0.404243i	$-0.867535\pi$
$43$	−8.50931	+	3.40661i	−1.29766	+	0.519503i	−0.383005	+	0.923746i	$0.625111\pi$
$44$	−1.03362	+	0.664265i	−0.155824	+	0.100142i
$45$	−3.87775	−	4.18960i	−0.578062	−	0.624549i
$46$	1.81016	+	4.44109i	0.266893	+	0.654804i
$47$	1.21841	+	2.11034i	0.177723	+	0.307825i	0.941100	−	0.338128i	$-0.109794\pi$
$47$	1.21841	+	2.11034i	0.177723	+	0.307825i	−0.763377	+	0.645953i	$0.776460\pi$
$48$	1.71015	−	0.274547i	0.246839	−	0.0396275i
$49$	−3.17410	−	2.49614i	−0.453443	−	0.356591i
$50$	0.799849	+	1.12323i	0.113116	+	0.158849i
$51$	−3.36834	+	4.43068i	−0.471662	+	0.620420i
$52$	−0.00734805	+	0.0103189i	−0.00101899	+	0.00143097i
$53$	−4.34014	−	5.00879i	−0.596164	−	0.688010i	0.374835	−	0.927091i	$-0.377699\pi$
$53$	−4.34014	−	5.00879i	−0.596164	−	0.688010i	−0.971000	+	0.239081i	$0.923154\pi$
$54$	4.37562	+	2.80249i	0.595446	+	0.381371i
$55$	−2.24333	−	0.658702i	−0.302491	−	0.0888194i
$56$	−3.26231	−	0.628759i	−0.435945	−	0.0840215i
$57$	8.14333	−	0.521735i	1.07861	−	0.0691055i
$58$	2.06817	−	1.06621i	0.271564	−	0.140001i
$59$	−3.28457	−	9.49014i	−0.427614	−	1.23551i	−0.928933	−	0.370248i	$-0.879273\pi$
$59$	−3.28457	−	9.49014i	−0.427614	−	1.23551i	0.501319	−	0.865263i	$-0.332848\pi$
$60$	2.52593	+	2.11729i	0.326096	+	0.273341i
$61$	1.83790	−	1.44534i	0.235319	−	0.185057i	−0.493535	−	0.869726i	$-0.664296\pi$
$61$	1.83790	−	1.44534i	0.235319	−	0.185057i	0.728854	+	0.684669i	$0.240053\pi$
$62$	−0.436228	−	0.503434i	−0.0554010	−	0.0639362i
$63$	−6.04431	−	7.92518i	−0.761512	−	0.998479i
$64$	−0.959493	+	0.281733i	−0.119937	+	0.0352166i
$65$	−0.0239966	+	0.00229140i	−0.00297641	+	0.000284213i
$66$	2.12707	+	0.0664248i	0.261824	+	0.00817633i
$67$	−0.0474064	−	0.995182i	−0.00579161	−	0.121581i	−0.999912	−	0.0132967i	$-0.995767\pi$
$67$	−0.0474064	−	0.995182i	−0.00579161	−	0.121581i	0.994120	−	0.108284i	$-0.0345356\pi$
$68$	1.60667	−	2.78284i	0.194837	−	0.337468i
$69$	1.77530	−	8.11470i	0.213721	−	0.976895i
$70$	−3.16108	−	5.47514i	−0.377821	−	0.654405i
$71$	2.29094	−	1.47230i	0.271884	−	0.174730i	−0.397593	−	0.917562i	$-0.630154\pi$
$71$	2.29094	−	1.47230i	0.271884	−	0.174730i	0.669478	+	0.742832i	$0.266518\pi$
$72$	−2.71011	−	1.28659i	−0.319389	−	0.151627i
$73$	−0.782583	+	1.71362i	−0.0915944	+	0.200564i	−0.949885	−	0.312601i	$-0.898800\pi$
$73$	−0.782583	+	1.71362i	−0.0915944	+	0.200564i	0.858290	+	0.513165i	$0.171527\pi$
$74$	6.14218	+	5.85656i	0.714014	+	0.680811i
$75$	−0.0391235	−	2.38803i	−0.00451759	−	0.275746i
$76$	−4.62606	+	0.891599i	−0.530645	+	0.102273i
$77$	−3.78964	−	1.51714i	−0.431870	−	0.172895i
$78$	0.0206142	−	0.00751498i	0.00233410	−	0.000850904i
$79$	−3.42674	−	0.660450i	−0.385538	−	0.0743064i	−0.00720054	−	0.999974i	$-0.502292\pi$
$79$	−3.42674	−	0.660450i	−0.385538	−	0.0743064i	−0.378338	+	0.925668i	$0.623504\pi$
$80$	−1.60083	−	1.02879i	−0.178979	−	0.115023i
$81$	−3.49420	−	8.29401i	−0.388245	−	0.921556i
$82$	5.77872	−	6.66899i	0.638152	−	0.736467i
$83$	3.06742	+	12.6441i	0.336693	+	1.38787i	0.848695	+	0.528883i	$0.177389\pi$
$83$	3.06742	+	12.6441i	0.336693	+	1.38787i	−0.512002	+	0.858984i	$0.671096\pi$
$84$	4.03874	+	4.09911i	0.440662	+	0.447249i
$85$	6.00421	−	1.15722i	0.651248	−	0.125518i
$86$	−9.12437	−	0.871272i	−0.983906	−	0.0939517i
$87$	−3.99802	−	0.508132i	−0.428633	−	0.0544774i
$88$	−1.22310	+	0.116792i	−0.130383	+	0.0124500i
$89$	−0.0118057	+	0.0821103i	−0.00125140	+	0.00870367i	−0.990438	−	0.137962i	$-0.955945\pi$
$89$	−0.0118057	+	0.0821103i	−0.00125140	+	0.00870367i	0.989186	+	0.146665i	$0.0468540\pi$
$90$	−1.52690	−	5.50076i	−0.160949	−	0.579831i
$91$	−0.0420869			−0.00441191
$92$	−0.426094	+	4.77687i	−0.0444233	+	0.498023i
$93$	0.128474	+	1.14661i	0.0133221	+	0.118898i
$94$	0.115948	+	2.43406i	0.0119592	+	0.251054i
$95$	−7.04696	−	5.54179i	−0.723003	−	0.568576i
$96$	1.64585	+	0.539610i	0.167979	+	0.0550737i
$97$	8.25966	+	7.87557i	0.838641	+	0.799643i	0.981772	−	0.190061i	$-0.0608685\pi$
$97$	8.25966	+	7.87557i	0.838641	+	0.799643i	−0.143131	+	0.989704i	$0.545717\pi$
$98$	−1.67746	−	3.67311i	−0.169449	−	0.371041i
$99$	−2.97047	−	2.18239i	−0.298543	−	0.219339i
$100$	0.196240	+	1.36488i	0.0196240	+	0.136488i
$101$	−2.69527	−	11.1101i	−0.268190	−	1.10549i	−0.933400	−	0.358837i	$-0.883173\pi$
$101$	−2.69527	−	11.1101i	−0.268190	−	1.10549i	0.665210	−	0.746656i	$-0.268342\pi$
$102$	−5.02416	+	2.39469i	−0.497466	+	0.237109i
$103$	7.76429	−	4.00277i	0.765038	−	0.394404i	−0.0311026	−	0.999516i	$-0.509902\pi$
$103$	7.76429	−	4.00277i	0.765038	−	0.394404i	0.796141	+	0.605112i	$0.206872\pi$
$104$	−0.0112596	+	0.00580473i	−0.00110409	+	0.000569200i
$105$	−0.862187	+	10.9163i	−0.0841409	+	1.06532i
$106$	−1.56251	−	6.44076i	−0.151764	−	0.625582i
$107$	−0.284874	−	1.98134i	−0.0275398	−	0.191543i	0.971407	−	0.237419i	$-0.0763014\pi$
$107$	−0.284874	−	1.98134i	−0.0275398	−	0.191543i	−0.998947	+	0.0458754i	$0.985392\pi$
$108$	2.60503	+	4.49598i	0.250669	+	0.432626i
$109$	8.13531	+	17.8138i	0.779221	+	1.70626i	0.705210	+	0.708999i	$0.250853\pi$
$109$	8.13531	+	17.8138i	0.779221	+	1.70626i	0.0740114	+	0.997257i	$0.476420\pi$
$110$	−1.69212	−	1.61343i	−0.161337	−	0.153835i
$111$	−3.01798	−	14.3864i	−0.286454	−	1.36550i
$112$	−2.61155	−	2.05374i	−0.246768	−	0.194060i
$113$	−0.625573	−	13.1324i	−0.0588490	−	1.23539i	−0.814401	−	0.580303i	$-0.802934\pi$
$113$	−0.625573	−	13.1324i	−0.0588490	−	1.23539i	0.755552	−	0.655089i	$-0.227369\pi$
$114$	7.47715	+	3.26775i	0.700299	+	0.306053i
$115$	−7.40071	+	5.33989i	−0.690120	+	0.497947i
$116$	2.32683			0.216041
$117$	−0.0367952	−	0.00950659i	−0.00340172	−	0.000878884i
$118$	1.42919	−	9.94025i	0.131568	−	0.915074i
$119$	10.6275	−	1.01480i	0.974222	−	0.0930269i
$120$	1.27494	+	3.03937i	0.116385	+	0.277456i
$121$	9.44742	+	0.902119i	0.858856	+	0.0820108i
$122$	2.29588	−	0.442495i	0.207860	−	0.0400616i
$123$	−14.7924	+	3.84622i	−1.33378	+	0.346802i
$124$	−0.157048	−	0.647361i	−0.0141033	−	0.0581347i
$125$	−7.94905	+	9.17369i	−0.710984	+	0.820520i
$126$	−1.74087	−	9.81385i	−0.155089	−	0.874287i
$127$	9.73349	+	6.25534i	0.863708	+	0.555071i	0.895822	−	0.444413i	$-0.146588\pi$
$127$	9.73349	+	6.25534i	0.863708	+	0.555071i	−0.0321141	+	0.999484i	$0.510224\pi$
$128$	−0.981929	−	0.189251i	−0.0867911	−	0.0167276i
$129$	12.1668	+	10.1985i	1.07123	+	0.897926i
$130$	−0.0223790	−	0.00895921i	−0.00196277	−	0.000785775i
$131$	11.1981	−	2.15826i	0.978386	−	0.188568i	0.325100	−	0.945680i	$-0.394602\pi$
$131$	11.1981	−	2.15826i	0.978386	−	0.188568i	0.653286	+	0.757111i	$0.273390\pi$
$132$	1.86018	+	1.03372i	0.161908	+	0.0899738i
$133$	−11.3281	−	10.8013i	−0.982267	−	0.936590i
$134$	0.413882	−	0.906276i	0.0357540	−	0.0782903i
$135$	−3.21955	+	9.34900i	−0.277095	+	0.804634i
$136$	2.70323	−	1.73726i	0.231800	−	0.148969i
$137$	9.07990	+	15.7268i	0.775748	+	1.34364i	0.934373	+	0.356296i	$0.115961\pi$
$137$	9.07990	+	15.7268i	0.775748	+	1.34364i	−0.158625	+	0.987339i	$0.550706\pi$
$138$	5.29632	−	6.39914i	0.450852	−	0.544731i
$139$	−9.47880	+	16.4178i	−0.803981	+	1.39254i	0.112996	+	0.993595i	$0.463955\pi$
$139$	−9.47880	+	16.4178i	−0.803981	+	1.39254i	−0.916977	+	0.398941i	$0.869378\pi$
$140$	−0.300820	−	6.31499i	−0.0254239	−	0.533714i
$141$	2.22341	−	3.58757i	0.187245	−	0.302128i
$142$	2.71091	−	0.258861i	0.227495	−	0.0217231i
$143$	−0.0149340	+	0.00438502i	−0.00124884	+	0.000366693i
$144$	−1.81929	−	2.38541i	−0.151607	−	0.198784i
$145$	2.89956	+	3.34627i	0.240796	+	0.277893i
$146$	−1.48081	+	1.16452i	−0.122553	+	0.0963767i
$147$	−1.21096	+	6.88843i	−0.0998781	+	0.568148i
$148$	2.77576	+	8.02003i	0.228166	+	0.659242i
$149$	15.8849	−	8.18924i	1.30134	−	0.670889i	0.338504	−	0.940965i	$-0.390079\pi$
$149$	15.8849	−	8.18924i	1.30134	−	0.670889i	0.962839	+	0.270077i	$0.0870490\pi$
$150$	1.05948	−	2.14049i	0.0865066	−	0.174771i
$151$	20.8839	+	4.02505i	1.69951	+	0.327554i	0.944587	−	0.328260i	$-0.106462\pi$
$151$	20.8839	+	4.02505i	1.69951	+	0.327554i	0.754923	+	0.655814i	$0.227674\pi$
$152$	−4.52036	−	1.32730i	−0.366649	−	0.107658i
$153$	9.52050	+	1.51333i	0.769687	+	0.122346i
$154$	−2.67317	−	3.08501i	−0.215410	−	0.248597i
$155$	0.735283	−	1.03256i	0.0590593	−	0.0829372i
$156$	0.0217662	+	0.00276639i	0.00174269	+	0.000221489i
$157$	−6.78855	−	9.53319i	−0.541785	−	0.760831i	0.449398	−	0.893332i	$-0.351639\pi$
$157$	−6.78855	−	9.53319i	−0.541785	−	0.760831i	−0.991183	+	0.132501i	$0.957699\pi$
$158$	−2.74317	−	2.15725i	−0.218235	−	0.171622i
$159$	−4.09128	+	10.7255i	−0.324460	+	0.850585i
$160$	−0.951457	−	1.64797i	−0.0752193	−	0.130284i
$161$	−13.7488	+	8.05261i	−1.08356	+	0.634635i
$162$	0.694764	−	8.97314i	0.0545858	−	0.704997i
$163$	−9.62300	+	6.18433i	−0.753732	+	0.484394i	−0.860222	−	0.509920i	$-0.829675\pi$
$163$	−9.62300	+	6.18433i	−0.753732	+	0.484394i	0.106490	+	0.994314i	$0.466039\pi$
$164$	8.19224	−	3.27968i	0.639706	−	0.256100i
$165$	0.831427	+	3.96333i	0.0647265	+	0.308545i
$166$	−3.06742	+	12.6441i	−0.238078	+	0.981371i
$167$	−0.682245	−	0.0651465i	−0.0527937	−	0.00504119i	0.0686258	−	0.997642i	$-0.478139\pi$
$167$	−0.682245	−	0.0651465i	−0.0527937	−	0.00504119i	−0.121419	+	0.992601i	$0.538745\pi$
$168$	1.71145	+	5.49409i	0.132041	+	0.423878i
$169$	10.2186	−	8.03597i	0.786043	−	0.618151i
$170$	5.86703	+	1.72271i	0.449980	+	0.132126i
$171$	−7.46395	−	12.0020i	−0.570783	−	0.917814i
$172$	−7.71083	−	4.95545i	−0.587945	−	0.377849i
$173$	1.02458	−	21.5087i	0.0778976	−	1.63527i	−0.534817	−	0.844968i	$-0.679619\pi$
$173$	1.02458	−	21.5087i	0.0778976	−	1.63527i	0.612714	−	0.790305i	$-0.290078\pi$
$174$	−3.32075	−	2.28365i	−0.251745	−	0.173123i
$175$	−3.31560	+	3.16142i	−0.250636	+	0.238981i
$176$	−1.14065	−	0.456648i	−0.0859798	−	0.0344211i
$177$	−11.7955	+	12.7836i	−0.886600	+	0.960875i
$178$	−0.0481184	+	0.0675728i	−0.00360663	+	0.00506480i
$179$	−5.46624	+	1.60503i	−0.408566	+	0.119966i	−0.479556	−	0.877511i	$-0.659202\pi$
$179$	−5.46624	+	1.60503i	−0.408566	+	0.119966i	0.0709901	+	0.997477i	$0.477384\pi$
$180$	1.16343	−	5.58893i	0.0867171	−	0.416575i
$181$	0.219899	−	1.52943i	0.0163449	−	0.113682i	−0.980016	−	0.198921i	$-0.936256\pi$
$181$	0.219899	−	1.52943i	0.0163449	−	0.113682i	0.996361	+	0.0852392i	$0.0271654\pi$
$182$	−0.0374084	−	0.0192853i	−0.00277289	−	0.00142952i
$183$	−3.71087	−	1.62177i	−0.274315	−	0.119884i
$184$	−2.56761	+	4.05060i	−0.189287	+	0.298614i
$185$	−8.07482	+	13.9860i	−0.593673	+	1.02827i
$186$	−0.411215	+	1.07802i	−0.0301517	+	0.0790441i
$187$	3.66530	−	1.46737i	0.268033	−	0.107304i
$188$	−1.01229	+	2.21661i	−0.0738288	+	0.161663i
$189$	−7.14722	+	15.7144i	−0.519884	+	1.14306i
$190$	−3.72419	−	8.15485i	−0.270182	−	0.591615i
$191$	−0.679607	+	1.96360i	−0.0491747	+	0.142081i	−0.966914	−	0.255102i	$-0.917891\pi$
$191$	−0.679607	+	1.96360i	−0.0491747	+	0.142081i	0.917739	+	0.397183i	$0.130012\pi$
$192$	1.21563	+	1.23380i	0.0877302	+	0.0890416i
$193$	−11.6071	+	11.0673i	−0.835497	+	0.796645i	−0.981263	−	0.192674i	$-0.938284\pi$
$193$	−11.6071	+	11.0673i	−0.835497	+	0.796645i	0.145766	+	0.989319i	$0.453435\pi$
$194$	3.73268	+	10.7849i	0.267991	+	0.774309i
$195$	0.0231454	+	0.0347499i	0.00165748	+	0.00248849i
$196$	0.192137	−	4.03345i	0.0137241	−	0.288103i
$197$	−11.2295	+	12.9595i	−0.800070	+	0.923330i	−0.998385	−	0.0568087i	$-0.981907\pi$
$197$	−11.2295	+	12.9595i	−0.800070	+	0.923330i	0.198315	+	0.980138i	$0.436453\pi$
$198$	−1.64023	−	3.30093i	−0.116566	−	0.234587i
$199$	−3.14880	−	21.9004i	−0.223212	−	1.55248i	−0.725773	−	0.687934i	$-0.758518\pi$
$199$	−3.14880	−	21.9004i	−0.223212	−	1.55248i	0.502561	−	0.864542i	$-0.332391\pi$
$200$	−0.450999	+	1.30308i	−0.0318904	+	0.0921414i
$201$	−1.48013	+	0.887195i	−0.104400	+	0.0625779i
$202$	2.69527	−	11.1101i	0.189639	−	0.781702i
$203$	4.48415	+	6.29711i	0.314726	+	0.441971i
$204$	−5.56296	−	0.173722i	−0.389485	−	0.0121630i
$205$	14.9253	+	7.69453i	1.04243	+	0.537409i
$206$	8.73535			0.608621
$207$	−13.8391	+	3.93455i	−0.961881	+	0.273470i
$208$	−0.0126678			−0.000878355
$209$	−5.14499	−	2.65243i	−0.355887	−	0.183472i
$210$	−5.76848	+	9.30771i	−0.398063	+	0.642293i
$211$	−9.31874	−	13.0863i	−0.641528	−	0.900900i	0.357932	−	0.933748i	$-0.383482\pi$
$211$	−9.31874	−	13.0863i	−0.641528	−	0.900900i	−0.999460	+	0.0328472i	$0.989543\pi$
$212$	1.56251	−	6.44076i	0.107314	−	0.442353i
$213$	−4.12295	−	2.29117i	−0.282500	−	0.156988i
$214$	0.654697	−	1.89162i	0.0447542	−	0.129309i
$215$	−2.48224	−	17.2643i	−0.169287	−	1.17742i
$216$	0.255263	+	5.18988i	0.0173684	+	0.353127i
$217$	1.44930	−	1.67258i	0.0983851	−	0.113542i
$218$	−0.931824	+	19.5614i	−0.0631111	+	1.32486i
$219$	3.25626	−	0.208626i	0.220038	−	0.0140976i
$220$	−0.764698	−	2.20945i	−0.0515559	−	0.148961i
$221$	0.0294603	−	0.0280904i	0.00198172	−	0.00188956i
$222$	3.90975	−	14.1701i	0.262405	−	0.951033i
$223$	5.03775	−	14.5556i	0.337353	−	0.974716i	−0.640959	−	0.767575i	$-0.721463\pi$
$223$	5.03775	−	14.5556i	0.337353	−	0.974716i	0.978311	−	0.207141i	$-0.0664158\pi$
$224$	−1.38015	−	3.02212i	−0.0922155	−	0.201924i
$225$	−3.61282	+	2.01500i	−0.240855	+	0.134333i
$226$	5.46158	−	11.9592i	0.363299	−	0.795513i
$227$	−14.6887	+	5.88048i	−0.974925	+	0.390301i	−0.803768	−	0.594943i	$-0.797175\pi$
$227$	−14.6887	+	5.88048i	−0.974925	+	0.390301i	−0.171157	+	0.985244i	$0.554750\pi$
$228$	5.14859	+	6.33072i	0.340974	+	0.419262i
$229$	−1.70844	+	2.95911i	−0.112897	+	0.195543i	−0.916937	−	0.399032i	$-0.869346\pi$
$229$	−1.70844	+	2.95911i	−0.112897	+	0.195543i	0.804040	+	0.594575i	$0.202680\pi$
$230$	−9.02489	+	1.35508i	−0.595084	+	0.0893511i
$231$	0.787280	+	7.02635i	0.0517992	+	0.462300i
$232$	2.06817	+	1.06621i	0.135782	+	0.0700004i
$233$	−3.32025	+	23.0929i	−0.217517	+	1.51286i	0.529644	+	0.848220i	$0.322326\pi$
$233$	−3.32025	+	23.0929i	−0.217517	+	1.51286i	−0.747161	+	0.664643i	$0.768583\pi$
$234$	−0.0283487	−	0.0253103i	−0.00185321	−	0.00165459i
$235$	−4.44922	+	1.30641i	−0.290235	+	0.0852207i
$236$	5.82520	−	8.18035i	0.379188	−	0.532495i
$237$	1.79771	+	5.77100i	0.116774	+	0.374867i
$238$	9.91112	+	3.96781i	0.642442	+	0.257195i
$239$	2.72146	−	2.59491i	0.176037	−	0.167851i	−0.596938	−	0.802287i	$-0.703616\pi$
$239$	2.72146	−	2.59491i	0.176037	−	0.167851i	0.772975	+	0.634436i	$0.218768\pi$
$240$	−0.259511	+	3.28571i	−0.0167514	+	0.212092i
$241$	0.861372	−	18.0824i	0.0554859	−	1.16479i	−0.783769	−	0.621053i	$-0.786705\pi$
$241$	0.861372	−	18.0824i	0.0554859	−	1.16479i	0.839255	−	0.543739i	$-0.182992\pi$
$242$	7.98382	+	5.13089i	0.513220	+	0.329826i
$243$	−9.79815	+	12.1242i	−0.628552	+	0.777768i
$244$	2.24343	+	0.658729i	0.143621	+	0.0421708i
$245$	6.04004	−	4.74994i	0.385884	−	0.303463i
$246$	−14.9104	−	3.35959i	−0.950653	−	0.214200i
$247$	−0.0594103	−	0.00567299i	−0.00378018	−	0.000360964i
$248$	0.157048	−	0.647361i	0.00997256	−	0.0411075i
$249$	16.7871	−	15.0346i	1.06384	−	0.952777i
$250$	−11.2690	+	4.51144i	−0.712716	+	0.285328i
$251$	13.4985	−	8.67497i	0.852019	−	0.547559i	−0.0401850	−	0.999192i	$-0.512795\pi$
$251$	13.4985	−	8.67497i	0.852019	−	0.547559i	0.892204	+	0.451633i	$0.149158\pi$
$252$	2.94962	−	9.52061i	0.185808	−	0.599742i
$253$	−4.03959	+	4.28985i	−0.253967	+	0.269700i
$254$	5.78511	+	10.0201i	0.362990	+	0.628718i
$255$	−6.68241	−	8.21672i	−0.418469	−	0.514551i
$256$	−0.786053	−	0.618159i	−0.0491283	−	0.0386349i
$257$	16.4140	+	23.0502i	1.02387	+	1.43783i	0.894945	+	0.446177i	$0.147215\pi$
$257$	16.4140	+	23.0502i	1.02387	+	1.43783i	0.128930	+	0.991654i	$0.458846\pi$
$258$	6.14107	+	14.6399i	0.382326	+	0.911441i
$259$	−16.3554	+	22.9679i	−1.01627	+	1.42715i
$260$	−0.0157859	−	0.0182179i	−0.000979001	−	0.00112983i
$261$	2.49796	+	6.51824i	0.154620	+	0.403469i
$262$	10.9423	+	3.21294i	0.676016	+	0.198496i
$263$	2.00980	+	0.387358i	0.123930	+	0.0238855i	0.250839	−	0.968029i	$-0.419294\pi$
$263$	2.00980	+	0.387358i	0.123930	+	0.0238855i	−0.126909	+	0.991914i	$0.540506\pi$
$264$	1.17971	+	1.77119i	0.0726063	+	0.109009i
$265$	11.2097	−	5.77902i	0.688609	−	0.355003i
$266$	−5.11935	−	14.7914i	−0.313887	−	0.906918i
$267$	0.134991	−	0.0492115i	0.00826133	−	0.00301170i
$268$	0.783153	−	0.615878i	0.0478387	−	0.0376207i
$269$	−5.79256	−	6.68497i	−0.353179	−	0.407590i	0.551164	−	0.834397i	$-0.314184\pi$
$269$	−5.79256	−	6.68497i	−0.353179	−	0.407590i	−0.904343	+	0.426807i	$0.859638\pi$
$270$	−7.14561	+	6.83444i	−0.434868	+	0.415931i
$271$	−29.1796	+	8.56789i	−1.77253	+	0.520462i	−0.994215	−	0.107410i	$-0.965744\pi$
$271$	−29.1796	+	8.56789i	−1.77253	+	0.520462i	−0.778317	+	0.627872i	$0.783926\pi$
$272$	3.19879	−	0.305448i	0.193955	−	0.0185205i
$273$	0.0344601	+	0.0642373i	0.00208562	+	0.00388782i
$274$	0.864078	+	18.1392i	0.0522009	+	1.09583i
$275$	−0.847111	+	1.46724i	−0.0510827	+	0.0884778i
$276$	7.63981	−	3.26087i	0.459863	−	0.196281i
$277$	−2.30303	−	3.98896i	−0.138376	−	0.239673i	0.788506	−	0.615027i	$-0.210855\pi$
$277$	−2.30303	−	3.98896i	−0.138376	−	0.239673i	−0.926882	+	0.375353i	$0.877521\pi$
$278$	−15.9481	+	10.2492i	−0.956506	+	0.614709i
$279$	1.64488	−	1.13492i	0.0984764	−	0.0679456i
$280$	2.62632	−	5.75083i	0.156952	−	0.343678i
$281$	19.6141	+	18.7020i	1.17008	+	1.11567i	0.991279	+	0.131782i	$0.0420698\pi$
$281$	19.6141	+	18.7020i	1.17008	+	1.11567i	0.178799	+	0.983886i	$0.442779\pi$
$282$	3.62016	−	2.16994i	0.215578	−	0.129218i
$283$	9.85986	−	1.90033i	0.586108	−	0.112963i	0.112428	−	0.993660i	$-0.464137\pi$
$283$	9.85986	−	1.90033i	0.586108	−	0.112963i	0.473680	+	0.880697i	$0.342925\pi$
$284$	2.52817	+	1.01213i	0.150019	+	0.0600587i
$285$	−2.68850	+	15.2933i	−0.159253	+	0.905898i
$286$	−0.0152832	−	0.00294559i	−0.000903714	−	0.000174177i
$287$	24.6635	+	15.8503i	1.45584	+	0.935612i
$288$	−0.523988	−	2.95389i	−0.0308763	−	0.174059i
$289$	4.37083	−	5.04420i	0.257107	−	0.296718i
$290$	1.04388	+	4.30294i	0.0612989	+	0.252678i
$291$	5.25761	−	19.0551i	0.308207	−	1.11703i
$292$	−1.84982	+	0.356523i	−0.108252	+	0.0208639i
$293$	31.1543	+	2.97488i	1.82006	+	0.173794i	0.948558	−	0.316604i	$-0.102543\pi$
$293$	31.1543	+	2.97488i	1.82006	+	0.173794i	0.871498	+	0.490398i	$0.163149\pi$
$294$	−4.23280	+	5.56779i	−0.246862	+	0.324720i
$295$	19.0234	−	1.81652i	1.10759	−	0.105762i
$296$	−1.20780	+	8.40041i	−0.0702017	+	0.488264i
$297$	−0.898817	+	6.32073i	−0.0521547	+	0.366766i
$298$	17.8716			1.03527
$299$	−0.0222274	+	0.0565405i	−0.00128544	+	0.00326982i
$300$	1.92254	−	1.41706i	0.110998	−	0.0818142i
$301$	−1.44898	−	30.4178i	−0.0835177	−	1.75325i
$302$	16.7180	+	13.1472i	0.962012	+	0.756535i
$303$	−14.7505	+	13.2105i	−0.847392	+	0.758926i
$304$	−3.40965	−	3.25110i	−0.195557	−	0.186463i
$305$	1.84830	+	4.04720i	0.105833	+	0.231742i
$306$	7.76871	+	5.70765i	0.444108	+	0.326284i
$307$	−3.29463	−	22.9147i	−0.188035	−	1.30781i	−0.837089	−	0.547067i	$-0.815744\pi$
$307$	−3.29463	−	22.9147i	−0.188035	−	1.30781i	0.649054	−	0.760742i	$-0.275165\pi$
$308$	−0.962380	−	3.96698i	−0.0548367	−	0.226040i
$309$	−12.4667	−	8.57323i	−0.709206	−	0.487714i
$310$	1.12669	−	0.580850i	0.0639918	−	0.0329901i
$311$	1.68331	−	0.867805i	0.0954516	−	0.0492087i	−0.409840	−	0.912158i	$-0.634415\pi$
$311$	1.68331	−	0.867805i	0.0954516	−	0.0492087i	0.505291	+	0.862949i	$0.331385\pi$
$312$	0.0180789	+	0.0124327i	0.00102352	+	0.000703864i
$313$	−0.222297	−	0.916320i	−0.0125650	−	0.0517935i	0.965184	−	0.261572i	$-0.0842409\pi$
$313$	−0.222297	−	0.916320i	−0.0125650	−	0.0517935i	−0.977749	+	0.209778i	$0.932726\pi$
$314$	−1.66555	−	11.5841i	−0.0939922	−	0.653730i
$315$	17.3675	−	7.62213i	0.978547	−	0.429458i
$316$	−1.44972	−	3.17444i	−0.0815529	−	0.178576i
$317$	−6.43062	−	6.13158i	−0.361179	−	0.344384i	0.487661	−	0.873033i	$-0.337850\pi$
$317$	−6.43062	−	6.13158i	−0.361179	−	0.344384i	−0.848840	+	0.528649i	$0.822699\pi$
$318$	−8.55117	+	7.65845i	−0.479526	+	0.429464i
$319$	2.24724	+	1.76725i	0.125821	+	0.0989468i
$320$	−0.0905443	−	1.90076i	−0.00506158	−	0.106256i
$321$	−2.79087	+	2.05709i	−0.155771	+	0.114816i
$322$	−15.9104	+	0.857373i	−0.886649	+	0.0477796i
$323$	15.1387			0.842338
$324$	4.72926	−	7.65729i	0.262737	−	0.425405i
$325$	−0.00248593	+	0.0172900i	−0.000137895	+	0.000959079i
$326$	−11.3871	+	1.08733i	−0.630672	+	0.0602219i
$327$	20.5282	−	27.0026i	1.13521	−	1.49325i
$328$	8.78438	+	0.838807i	0.485037	+	0.0463154i
$329$	−7.94966	+	1.53217i	−0.438279	+	0.0844713i
$330$	−1.07710	+	3.90373i	−0.0592926	+	0.214894i
$331$	4.24265	+	17.4884i	0.233197	+	0.961251i	0.961239	+	0.275718i	$0.0889156\pi$
$331$	4.24265	+	17.4884i	0.233197	+	0.961251i	−0.728042	+	0.685533i	$0.759569\pi$
$332$	−8.52028	+	9.83293i	−0.467611	+	0.539652i
$333$	−19.4869	+	16.3857i	−1.06788	+	0.897931i
$334$	−0.576552	−	0.370527i	−0.0315475	−	0.0202744i
$335$	1.86163	+	0.358800i	0.101712	+	0.0196034i
$336$	−0.996336	+	5.66757i	−0.0543546	+	0.309191i
$337$	−31.4815	−	12.6033i	−1.71491	−	0.686545i	−0.714985	−	0.699140i	$-0.753566\pi$
$337$	−31.4815	−	12.6033i	−1.71491	−	0.686545i	−0.999921	+	0.0125956i	$0.995991\pi$
$338$	12.7649	−	2.46024i	0.694320	−	0.133819i
$339$	−19.5318	+	11.7074i	−1.06082	+	0.635859i
$340$	4.42543	+	4.21964i	0.240002	+	0.228842i
$341$	0.340000	−	0.744497i	0.0184120	−	0.0403168i
$342$	−1.13460	−	14.0880i	−0.0613521	−	0.761790i
$343$	−8.27855	+	5.32030i	−0.447000	+	0.287269i
$344$	−4.58294	−	7.93788i	−0.247095	−	0.427982i
$345$	14.2099	+	6.92350i	0.765033	+	0.372749i
$346$	10.7665	−	18.6482i	0.578812	−	1.00253i
$347$	−0.116681	−	2.44945i	−0.00626379	−	0.131493i	−0.999833	−	0.0182678i	$-0.994185\pi$
$347$	−0.116681	−	2.44945i	−0.00626379	−	0.131493i	0.993569	−	0.113225i	$-0.0361182\pi$
$348$	−1.90517	−	3.55144i	−0.102128	−	0.190377i
$349$	−17.2023	+	1.64262i	−0.920818	+	0.0879275i	−0.544688	−	0.838639i	$-0.683352\pi$
$349$	−17.2023	+	1.64262i	−0.920818	+	0.0879275i	−0.376131	+	0.926567i	$0.622746\pi$
$350$	−4.39567	+	1.29068i	−0.234958	+	0.0689900i
$351$	0.0156174	+	0.0639443i	0.000833595	+	0.00341310i
$352$	−0.804603	−	0.928561i	−0.0428855	−	0.0494925i
$353$	−6.60328	+	5.19287i	−0.351457	+	0.276389i	−0.778242	−	0.627964i	$-0.783888\pi$
$353$	−6.60328	+	5.19287i	−0.351457	+	0.276389i	0.426785	+	0.904353i	$0.359646\pi$
$354$	−16.3420	+	5.95754i	−0.868568	+	0.316640i
$355$	1.69490	+	4.89709i	0.0899559	+	0.259911i
$356$	−0.0737330	+	0.0380120i	−0.00390784	+	0.00201463i
$357$	−10.2505	−	15.3899i	−0.542516	−	0.814518i
$358$	−5.59406	−	1.07817i	−0.295655	−	0.0569828i
$359$	−14.0458	−	4.12421i	−0.741307	−	0.217668i	−0.110791	−	0.993844i	$-0.535339\pi$
$359$	−14.0458	−	4.12421i	−0.741307	−	0.217668i	−0.630516	+	0.776176i	$0.717157\pi$
$360$	3.59510	−	4.43453i	0.189478	−	0.233720i
$361$	−2.09250	−	2.41487i	−0.110132	−	0.127099i
$362$	0.896279	−	1.25865i	0.0471074	−	0.0661530i
$363$	−6.35849	−	15.1582i	−0.333734	−	0.795601i
$364$	−0.0244128	−	0.0342830i	−0.00127958	−	0.00179692i
$365$	−2.81786	−	2.21599i	−0.147494	−	0.115990i
$366$	−2.55521	−	3.14190i	−0.133563	−	0.164230i
$367$	11.0555	+	19.1486i	0.577090	+	0.999550i	0.995811	+	0.0914349i	$0.0291453\pi$
$367$	11.0555	+	19.1486i	0.577090	+	0.999550i	−0.418721	+	0.908115i	$0.637521\pi$
$368$	−4.13828	+	2.42377i	−0.215723	+	0.126348i
$369$	17.9822	+	19.4284i	0.936117	+	1.01140i
$370$	−13.5859	+	8.73116i	−0.706300	+	0.453911i
$371$	20.4419	−	8.18369i	1.06129	−	0.424876i
$372$	−0.859479	+	0.769751i	−0.0445619	+	0.0399097i
$373$	2.73157	−	11.2597i	0.141435	−	0.583003i	−0.856345	−	0.516405i	$-0.827270\pi$
$373$	2.73157	−	11.2597i	0.141435	−	0.583003i	0.997780	−	0.0665988i	$-0.0212148\pi$
$374$	3.93023	+	0.375292i	0.203228	+	0.0194059i
$375$	20.5104	+	4.62137i	1.05915	+	0.238646i
$376$	−1.91547	+	1.50634i	−0.0987827	+	0.0776835i
$377$	0.0282818	+	0.00830430i	0.00145659	+	0.000427693i
$378$	−13.5535	+	10.6925i	−0.697116	+	0.549963i
$379$	−16.2635	−	10.4519i	−0.835400	−	0.536879i	0.0515894	−	0.998668i	$-0.483571\pi$
$379$	−16.2635	−	10.4519i	−0.835400	−	0.536879i	−0.886990	+	0.461789i	$0.847208\pi$
$380$	0.426572	−	8.95484i	0.0218827	−	0.459374i
$381$	1.57790	−	19.9780i	0.0808381	−	1.02350i
$382$	−1.50383	+	1.43390i	−0.0769427	+	0.0733647i
$383$	15.5404	+	6.22144i	0.794077	+	0.317901i	0.732997	−	0.680232i	$-0.238121\pi$
$383$	15.5404	+	6.22144i	0.794077	+	0.317901i	0.0610807	+	0.998133i	$0.480545\pi$
$384$	0.515133	+	1.65367i	0.0262878	+	0.0843887i
$385$	4.50576	−	6.32746i	0.229635	−	0.322477i
$386$	−15.3882	+	4.51837i	−0.783236	+	0.229979i
$387$	5.60397	−	26.9205i	0.284866	−	1.36845i
$388$	−1.62418	+	11.2964i	−0.0824551	+	0.573488i
$389$	−17.2092	−	8.87194i	−0.872539	−	0.449825i	−0.0370379	−	0.999314i	$-0.511792\pi$
$389$	−17.2092	−	8.87194i	−0.872539	−	0.449825i	−0.835501	+	0.549489i	$0.814823\pi$
$390$	0.00464913	+	0.0414928i	0.000235418	+	0.00210107i
$391$	4.24939	−	14.8132i	0.214901	−	0.749135i
$392$	2.01901	−	3.49703i	0.101975	−	0.176627i
$393$	−12.4630	−	15.3246i	−0.628676	−	0.773022i
$394$	−15.9196	+	6.37325i	−0.802018	+	0.321079i
$395$	2.75869	−	6.04068i	0.138805	−	0.303940i
$396$	0.0546851	−	3.68558i	0.00274803	−	0.185207i
$397$	−5.43553	−	11.9021i	−0.272801	−	0.597351i	0.722799	−	0.691059i	$-0.242855\pi$
$397$	−5.43553	−	11.9021i	−0.272801	−	0.597351i	−0.995600	+	0.0937075i	$0.970128\pi$
$398$	7.23657	−	20.9087i	0.362736	−	1.04806i
$399$	−7.21077	+	26.1339i	−0.360990	+	1.30833i
$400$	−0.997968	+	0.951560i	−0.0498984	+	0.0475780i
$401$	−4.45860	−	12.8823i	−0.222652	−	0.643310i	−0.999900	−	0.0141163i	$-0.995506\pi$
$401$	−4.45860	−	12.8823i	−0.222652	−	0.643310i	0.777249	−	0.629194i	$-0.216615\pi$
$402$	−1.72213	+	0.110335i	−0.0858920	+	0.00550302i
$403$	0.000401521	−	0.00842896i	2.00012e−5	−	0.000419876i
$404$	7.48659	−	8.63998i	0.372472	−	0.429855i
$405$	16.9055	−	2.74080i	0.840041	−	0.136192i
$406$	1.10017	+	7.65186i	0.0546006	+	0.379755i
$407$	−3.41047	+	9.85391i	−0.169051	+	0.488440i
$408$	−4.86495	−	2.70351i	−0.240851	−	0.133843i
$409$	6.10733	−	25.1748i	0.301988	−	1.24481i	−0.595349	−	0.803467i	$-0.702986\pi$
$409$	6.10733	−	25.1748i	0.301988	−	1.24481i	0.897337	−	0.441345i	$-0.145499\pi$
$410$	9.74030	+	13.6783i	0.481039	+	0.675525i
$411$	16.5694	−	26.7355i	0.817309	−	1.31877i
$412$	7.76429	+	4.00277i	0.382519	+	0.197202i
$413$	33.3646			1.64176
$414$	−14.1036	−	2.84426i	−0.693152	−	0.139788i
$415$	−24.7585			−1.21535
$416$	−0.0112596	−	0.00580473i	−0.000552047	−	0.000284600i
$417$	32.8195	+	1.02490i	1.60718	+	0.0501895i
$418$	−3.35764	−	4.71515i	−0.164228	−	0.230625i
$419$	3.32089	−	13.6889i	0.162236	−	0.668746i	−0.831358	−	0.555737i	$-0.812436\pi$
$419$	3.32089	−	13.6889i	0.162236	−	0.668746i	0.993594	−	0.113009i	$-0.0360488\pi$
$420$	−9.39227	+	5.62975i	−0.458296	+	0.274704i
$421$	6.46763	−	18.6870i	0.315213	−	0.910749i	−0.670440	−	0.741964i	$-0.733895\pi$
$421$	6.46763	−	18.6870i	0.315213	−	0.910749i	0.985653	−	0.168785i	$-0.0539843\pi$
$422$	−2.28632	−	15.9017i	−0.111296	−	0.774082i
$423$	−7.29620	−	0.456141i	−0.354754	−	0.0221784i
$424$	4.34014	−	5.00879i	0.210776	−	0.243248i
$425$	0.210832	−	4.42591i	0.0102269	−	0.214688i
$426$	−2.61475	−	3.92572i	−0.126685	−	0.190202i
$427$	2.54070	+	7.34087i	0.122953	+	0.355250i
$428$	1.44871	−	1.38134i	0.0700260	−	0.0667697i
$429$	0.0189206	+	0.0192034i	0.000913493	+	0.000927148i
$430$	5.70468	−	16.4826i	0.275104	−	0.794861i
$431$	−3.69879	−	8.09922i	−0.178164	−	0.390126i	0.799389	−	0.600814i	$-0.205157\pi$
$431$	−3.69879	−	8.09922i	−0.178164	−	0.390126i	−0.977553	+	0.210688i	$0.932430\pi$
$432$	−2.15125	+	4.72992i	−0.103502	+	0.227568i
$433$	1.32532	−	2.90204i	0.0636906	−	0.139463i	−0.875110	−	0.483924i	$-0.839211\pi$
$433$	1.32532	−	2.90204i	0.0636906	−	0.139463i	0.938801	+	0.344461i	$0.111938\pi$
$434$	2.05461	−	0.822543i	0.0986246	−	0.0394833i
$435$	2.73331	−	7.16548i	0.131052	−	0.343559i
$436$	−9.79178	+	16.9599i	−0.468941	+	0.812230i
$437$	−20.4934	+	9.51390i	−0.980331	+	0.455112i
$438$	2.98988	+	1.30667i	0.142862	+	0.0624352i
$439$	27.5351	+	14.1953i	1.31418	+	0.677505i	0.965663	−	0.259798i	$-0.0836561\pi$
$439$	27.5351	+	14.1953i	1.31418	+	0.677505i	0.348514	+	0.937304i	$0.386686\pi$
$440$	0.332738	−	2.31424i	0.0158627	−	0.110327i
$441$	11.5053	−	3.79185i	0.547873	−	0.180564i
$442$	0.0390571	−	0.0114682i	0.00185776	−	0.000545487i
$443$	−17.7813	+	24.9704i	−0.844816	+	1.18638i	0.135858	+	0.990728i	$0.456621\pi$
$443$	−17.7813	+	24.9704i	−0.844816	+	1.18638i	−0.980674	+	0.195650i	$0.937318\pi$
$444$	9.96822	−	10.8033i	0.473071	−	0.512702i
$445$	−0.146548	−	0.0586690i	−0.00694704	−	0.00278118i
$446$	11.1475	−	10.6291i	0.527849	−	0.503303i
$447$	−25.5055	−	17.5399i	−1.20637	−	0.829610i
$448$	0.158084	−	3.31859i	0.00746876	−	0.156789i
$449$	−16.3436	−	10.5034i	−0.771302	−	0.495686i	0.0948345	−	0.995493i	$-0.469768\pi$
$449$	−16.3436	−	10.5034i	−0.771302	−	0.495686i	−0.866137	+	0.499807i	$0.833404\pi$
$450$	−4.13453	+	0.135510i	−0.194903	+	0.00638798i
$451$	10.4030	+	3.05458i	0.489856	+	0.143835i
$452$	10.3345	−	8.12711i	0.486092	−	0.382267i
$453$	−10.9560	−	35.1708i	−0.514757	−	1.65247i
$454$	−15.7505	−	1.50399i	−0.739205	−	0.0705855i
$455$	0.0188814	−	0.0778303i	0.000885175	−	0.00364874i
$456$	1.67534	+	7.98619i	0.0784550	+	0.373988i
$457$	−18.4054	+	7.36840i	−0.860968	+	0.344679i	−0.759774	−	0.650187i	$-0.774690\pi$
$457$	−18.4054	+	7.36840i	−0.860968	+	0.344679i	−0.101194	+	0.994867i	$0.532266\pi$
$458$	−2.87446	+	1.84731i	−0.134315	+	0.0863189i
$459$	−5.48543	−	15.7702i	−0.256038	−	0.736091i
$460$	−8.64258	−	2.93101i	−0.402962	−	0.136659i
$461$	−5.26173	−	9.11358i	−0.245063	−	0.424462i	0.717086	−	0.696984i	$-0.245475\pi$
$461$	−5.26173	−	9.11358i	−0.245063	−	0.424462i	−0.962149	+	0.272523i	$0.912142\pi$
$462$	−2.51990	+	6.60602i	−0.117236	+	0.307340i
$463$	28.0157	+	22.0318i	1.30200	+	1.02390i	0.997447	+	0.0714076i	$0.0227491\pi$
$463$	28.0157	+	22.0318i	1.30200	+	1.02390i	0.304552	+	0.952496i	$0.401493\pi$
$464$	1.34969	+	1.89538i	0.0626579	+	0.0879907i
$465$	−2.17803	−	0.276819i	−0.101004	−	0.0128372i
$466$	−13.5329	+	19.0043i	−0.626900	+	0.880358i
$467$	−8.15025	−	9.40589i	−0.377148	−	0.435252i	0.535163	−	0.844749i	$-0.320250\pi$
$467$	−8.15025	−	9.40589i	−0.377148	−	0.435252i	−0.912312	+	0.409496i	$0.865705\pi$
$468$	−0.0135995	−	0.0354868i	−0.000628635	−	0.00164038i
$469$	3.17601	+	0.932561i	0.146655	+	0.0430617i
$470$	−4.55326	−	0.877568i	−0.210026	−	0.0404792i
$471$	−8.99215	+	18.1670i	−0.414336	+	0.837091i
$472$	8.92610	−	4.60172i	0.410857	−	0.211812i
$473$	−3.68336	−	10.6424i	−0.169361	−	0.489337i
$474$	−1.04655	+	5.95323i	−0.0480698	+	0.273441i
$475$	−5.10646	+	4.01577i	−0.234301	+	0.184256i
$476$	6.99120	+	8.06827i	0.320441	+	0.369809i
$477$	19.7202	−	2.53732i	0.902924	−	0.116176i
$478$	3.60799	−	1.05940i	0.165026	−	0.0484559i
$479$	−4.39060	+	0.419251i	−0.200611	+	0.0191561i	−0.194878	−	0.980827i	$-0.562431\pi$
$479$	−4.39060	+	0.419251i	−0.200611	+	0.0191561i	−0.00573348	+	0.999984i	$0.501825\pi$
$480$	−1.73626	+	2.80154i	−0.0792492	+	0.127872i
$481$	0.00511549	+	0.107387i	0.000233246	+	0.00489644i
$482$	9.05147	−	15.6776i	0.412283	−	0.714095i
$483$	23.5480	+	14.3915i	1.07147	+	0.654835i
$484$	4.74519	+	8.21892i	0.215691	+	0.373587i
$485$	−18.2696	+	11.7412i	−0.829580	+	0.533139i
$486$	−14.2646	+	6.28665i	−0.647054	+	0.285168i
$487$	3.18710	−	6.97877i	0.144421	−	0.316238i	−0.823573	−	0.567210i	$-0.808023\pi$
$487$	3.18710	−	6.97877i	0.144421	−	0.316238i	0.967994	+	0.250972i	$0.0807501\pi$
$488$	1.69219	+	1.61350i	0.0766018	+	0.0730397i
$489$	17.3183	+	9.62396i	0.783161	+	0.435211i
$490$	7.54515	−	1.45421i	0.340855	−	0.0656945i
$491$	−28.4174	−	11.3766i	−1.28246	−	0.513420i	−0.372469	−	0.928045i	$-0.621489\pi$
$491$	−28.4174	−	11.3766i	−1.28246	−	0.513420i	−0.909992	+	0.414625i	$0.863913\pi$
$492$	−11.7134	−	9.81847i	−0.528083	−	0.442651i
$493$	−7.34178	−	1.41501i	−0.330657	−	0.0637289i
$494$	−0.0502064	−	0.0322657i	−0.00225889	−	0.00145170i
$495$	5.36848	−	4.51412i	0.241295	−	0.202895i
$496$	0.436228	−	0.503434i	0.0195872	−	0.0226048i
$497$	2.13305	+	8.79254i	0.0956802	+	0.394399i
$498$	21.8102	−	5.67096i	0.977339	−	0.254122i
$499$	30.4819	−	5.87490i	1.36456	−	0.262997i	0.546175	−	0.837671i	$-0.316083\pi$
$499$	30.4819	−	5.87490i	1.36456	−	0.262997i	0.818382	+	0.574674i	$0.194871\pi$
$500$	−12.0836	−	1.15384i	−0.540394	−	0.0516013i
$501$	0.459178	+	1.09465i	0.0205146	+	0.0489055i
$502$	15.9731	−	1.52524i	0.712913	−	0.0680749i
$503$	−2.24362	+	15.6047i	−0.100038	+	0.695780i	0.876652	+	0.481125i	$0.159772\pi$
$503$	−2.24362	+	15.6047i	−0.100038	+	0.695780i	−0.976690	+	0.214655i	$0.931137\pi$
$504$	6.98432	−	7.11066i	0.311106	−	0.316734i
$505$	21.7548			0.968074
$506$	−5.55625	+	1.96192i	−0.247006	+	0.0872180i
$507$	−20.6321	−	9.01688i	−0.916304	−	0.400454i
$508$	0.550534	+	11.5571i	0.0244260	+	0.512764i
$509$	−9.06479	−	7.12863i	−0.401790	−	0.315971i	0.396735	−	0.917933i	$-0.370143\pi$
$509$	−9.06479	−	7.12863i	−0.401790	−	0.315971i	−0.798524	+	0.601962i	$0.794386\pi$
$510$	−2.17445	−	10.3654i	−0.0962861	−	0.458987i
$511$	−4.52974	−	4.31910i	−0.200384	−	0.191066i
$512$	−0.415415	−	0.909632i	−0.0183589	−	0.0402004i
$513$	−12.2073	+	21.2193i	−0.538964	+	0.936853i
$514$	4.02710	+	28.0091i	0.177628	+	1.23543i
$515$	3.91893	+	16.1541i	0.172689	+	0.711833i
$516$	−1.25000	+	15.8265i	−0.0550283	+	0.696722i
$517$	−2.66120	+	1.37194i	−0.117039	+	0.0603379i
$518$	−25.0617	+	12.9202i	−1.10115	+	0.567681i
$519$	−33.6676	+	16.0471i	−1.47784	+	0.704390i
$520$	−0.00568315	−	0.0234263i	−0.000249223	−	0.00102731i
$521$	−0.218672	−	1.52090i	−0.00958020	−	0.0666318i	0.984471	−	0.175550i	$-0.0561704\pi$
$521$	−0.218672	−	1.52090i	−0.00958020	−	0.0666318i	−0.994051	+	0.108918i	$0.965261\pi$
$522$	−0.766557	+	6.93827i	−0.0335513	+	0.303680i
$523$	2.06382	+	4.51915i	0.0902448	+	0.197608i	0.949372	−	0.314153i	$-0.101720\pi$
$523$	2.06382	+	4.51915i	0.0902448	+	0.197608i	−0.859128	+	0.511761i	$0.828993\pi$
$524$	8.25363	+	7.86982i	0.360561	+	0.343795i
$525$	7.54003	+	2.47208i	0.329074	+	0.107891i
$526$	1.60889	+	1.26524i	0.0701508	+	0.0551672i
$527$	0.101851	+	2.13811i	0.00443668	+	0.0931373i
$528$	0.236965	+	2.11487i	0.0103126	+	0.0920380i
$529$	3.55691	+	22.7233i	0.154648	+	0.987970i
$530$	12.6117			0.547818
$531$	29.1696	+	7.53639i	1.26585	+	0.327051i
$532$	2.22755	−	15.4929i	0.0965764	−	0.671703i
$533$	0.111279	−	0.0106258i	0.00482003	−	0.000460257i
$534$	0.142535	+	0.0181156i	0.00616809	+	0.000783939i
$535$	3.79185	+	0.362077i	0.163936	+	0.0156540i
$536$	0.978306	−	0.188553i	0.0422564	−	0.00814425i
$537$	6.92543	+	7.02895i	0.298854	+	0.303322i
$538$	−2.08540	−	8.59614i	−0.0899081	−	0.370606i
$539$	3.24900	−	3.74955i	0.139945	−	0.161505i
$540$	−9.48299	+	2.80038i	−0.408083	+	0.120509i
$541$	−19.8077	−	12.7296i	−0.851600	−	0.547290i	0.0404737	−	0.999181i	$-0.487113\pi$
$541$	−19.8077	−	12.7296i	−0.851600	−	0.547290i	−0.892073	+	0.451891i	$0.850750\pi$
$542$	−29.8619	−	5.75540i	−1.28268	−	0.247216i
$543$	−2.51442	+	0.916640i	−0.107904	+	0.0393368i
$544$	2.98316	+	1.19428i	0.127902	+	0.0512043i
$545$	−36.5924	+	7.05261i	−1.56745	+	0.302101i
$546$	0.00119412	+	0.0728869i	5.11035e−5	+	0.00311927i
$547$	−29.6035	−	28.2269i	−1.26576	−	1.20690i	−0.967631	−	0.252369i	$-0.918790\pi$
$547$	−29.6035	−	28.2269i	−1.26576	−	1.20690i	−0.298125	−	0.954527i	$-0.596361\pi$
$548$	−7.54385	+	16.5187i	−0.322257	+	0.705645i
$549$	0.563095	+	6.99177i	0.0240323	+	0.298402i
$550$	−1.42527	+	0.915965i	−0.0607737	+	0.0390569i
$551$	5.48107	+	9.49349i	0.233501	+	0.404436i
$552$	8.28475	+	0.602384i	0.352623	+	0.0256392i
$553$	5.79718	−	10.0410i	0.246521	−	0.426987i
$554$	−0.219165	−	4.60084i	−0.00931143	−	0.195471i
$555$	27.9584	+	0.873093i	1.18677	+	0.0370608i
$556$	−18.8718	+	1.80203i	−0.800341	+	0.0764233i
$557$	14.9381	−	4.38622i	0.632948	−	0.185850i	0.0505074	−	0.998724i	$-0.483916\pi$
$557$	14.9381	−	4.38622i	0.632948	−	0.185850i	0.582440	+	0.812873i	$0.302098\pi$
$558$	1.98208	−	0.255026i	0.0839080	−	0.0107961i
$559$	−0.0760369	−	0.0877513i	−0.00321602	−	0.00371148i
$560$	4.96955	−	3.90810i	0.210002	−	0.165147i
$561$	−5.24073	−	4.39290i	−0.221264	−	0.185468i
$562$	8.86395	+	25.6107i	0.373903	+	1.08032i
$563$	−6.53127	+	3.36711i	−0.275260	+	0.141907i	−0.590330	−	0.807162i	$-0.701002\pi$
$563$	−6.53127	+	3.36711i	−0.275260	+	0.141907i	0.315070	+	0.949069i	$0.397972\pi$
$564$	4.21205	−	0.269862i	0.177359	−	0.0113632i
$565$	24.5660	+	4.73472i	1.03350	+	0.199191i
$566$	9.63457	+	2.82897i	0.404971	+	0.118910i
$567$	29.8370	−	1.95793i	1.25304	−	0.0822252i
$568$	1.78335	+	2.05809i	0.0748275	+	0.0863556i
$569$	−7.42233	+	10.4232i	−0.311160	+	0.436963i	−0.940309	−	0.340321i	$-0.889464\pi$
$569$	−7.42233	+	10.4232i	−0.311160	+	0.436963i	0.629149	+	0.777285i	$0.283404\pi$
$570$	−9.39744	+	12.3613i	−0.393615	+	0.517758i
$571$	10.4743	+	14.7091i	0.438337	+	0.615559i	0.973361	−	0.229278i	$-0.0736366\pi$
$571$	10.4743	+	14.7091i	0.438337	+	0.615559i	−0.535023	+	0.844837i	$0.679697\pi$
$572$	−0.0122345	−	0.00962131i	−0.000511550	−	0.000402287i
$573$	3.55349	−	0.570476i	0.148449	−	0.0238320i
$574$	14.6588	+	25.3898i	0.611846	+	1.05975i
$575$	2.49606	+	6.12389i	0.104093	+	0.255384i
$576$	0.887810	−	2.86562i	0.0369921	−	0.119401i
$577$	−0.487133	+	0.313061i	−0.0202796	+	0.0130329i	−0.550741	−	0.834676i	$-0.685655\pi$
$577$	−0.487133	+	0.313061i	−0.0202796	+	0.0130329i	0.530462	+	0.847709i	$0.322019\pi$
$578$	6.19633	−	2.48064i	0.257733	−	0.103181i
$579$	26.3958	+	8.65416i	1.09697	+	0.359654i
$580$	−1.04388	+	4.30294i	−0.0433449	+	0.178670i
$581$	−43.0308	−	4.10895i	−1.78522	−	0.170468i
$582$	13.4047	−	14.5277i	0.555643	−	0.602192i
$583$	6.40087	−	5.03370i	0.265097	−	0.208475i
$584$	−1.80755	−	0.530744i	−0.0747969	−	0.0219624i
$585$	0.0340877	−	0.0637795i	0.00140935	−	0.00263696i
$586$	26.3279	+	16.9199i	1.08760	+	0.698956i
$587$	0.830978	−	17.4444i	0.0342981	−	0.720006i	−0.914588	−	0.404387i	$-0.867485\pi$
$587$	0.830978	−	17.4444i	0.0342981	−	0.720006i	0.948886	−	0.315619i	$-0.102212\pi$
$588$	−6.31357	+	3.00926i	−0.260367	+	0.124100i
$589$	2.27130	−	2.16568i	0.0935873	−	0.0892353i
$590$	17.7411	+	7.10245i	0.730388	+	0.292403i
$591$	28.9747	+	6.52854i	1.19186	+	0.268548i
$592$	−4.92282	+	6.91314i	−0.202327	+	0.284128i
$593$	5.06976	−	1.48862i	0.208190	−	0.0611301i	−0.175975	−	0.984395i	$-0.556308\pi$
$593$	5.06976	−	1.48862i	0.208190	−	0.0611301i	0.384165	+	0.923265i	$0.374489\pi$
$594$	−3.69523	+	5.20623i	−0.151617	+	0.213614i
$595$	−2.89116	+	20.1085i	−0.118526	+	0.824366i
$596$	15.8849	+	8.18924i	0.650671	+	0.335444i
$597$	−30.8484	+	22.7377i	−1.26254	+	0.930591i
$598$	−0.0456648	+	0.0400701i	−0.00186737	+	0.00163859i
$599$	−4.80939	+	8.33011i	−0.196506	+	0.340359i	−0.947393	−	0.320072i	$-0.896293\pi$
$599$	−4.80939	+	8.33011i	−0.196506	+	0.340359i	0.750887	+	0.660431i	$0.229626\pi$
$600$	2.35816	−	0.378577i	0.0962713	−	0.0154554i
$601$	25.5528	−	10.2298i	1.04232	−	0.417283i	0.213587	−	0.976924i	$-0.431485\pi$
$601$	25.5528	−	10.2298i	1.04232	−	0.417283i	0.828735	+	0.559641i	$0.189061\pi$
$602$	12.6503	−	27.7004i	0.515589	−	1.12898i
$603$	2.56603	+	1.53270i	0.104497	+	0.0624165i
$604$	8.83516	+	19.3463i	0.359498	+	0.787190i
$605$	−5.90665	+	17.0661i	−0.240140	+	0.693838i
$606$	−19.1642	+	4.98295i	−0.778491	+	0.202418i
$607$	−18.9349	+	18.0544i	−0.768543	+	0.732805i	−0.969044	−	0.246889i	$-0.920592\pi$
$607$	−18.9349	+	18.0544i	−0.768543	+	0.732805i	0.200500	+	0.979694i	$0.435743\pi$
$608$	−1.54088	−	4.45208i	−0.0624909	−	0.180556i
$609$	5.93974	−	12.0001i	0.240690	−	0.486270i
$610$	−0.211705	+	4.44424i	−0.00857169	+	0.179942i
$611$	−0.0202150	+	0.0233293i	−0.000817811	+	0.000943804i
$612$	4.28971	+	8.63299i	0.173401	+	0.348968i
$613$	2.36031	+	16.4163i	0.0953321	+	0.663049i	0.980317	+	0.197430i	$0.0632594\pi$
$613$	2.36031	+	16.4163i	0.0953321	+	0.663049i	−0.884985	+	0.465620i	$0.845831\pi$
$614$	7.57172	−	21.8771i	0.305570	−	0.882886i
$615$	−0.476433	−	29.0806i	−0.0192116	−	1.17264i
$616$	0.962380	−	3.96698i	0.0387754	−	0.159834i
$617$	10.9813	+	15.4210i	0.442089	+	0.620827i	0.974156	−	0.225875i	$-0.0725240\pi$
$617$	10.9813	+	15.4210i	0.442089	+	0.620827i	−0.532067	+	0.846702i	$0.678585\pi$
$618$	−7.15236	−	13.3328i	−0.287710	−	0.536323i
$619$	−1.65843	−	0.854980i	−0.0666579	−	0.0343646i	0.424575	−	0.905393i	$-0.360423\pi$
$619$	−1.65843	−	0.854980i	−0.0666579	−	0.0343646i	−0.491233	+	0.871028i	$0.663454\pi$
$620$	1.26760			0.0509082
$621$	17.3365	+	17.9010i	0.695689	+	0.718343i
$622$	1.89383			0.0759358
$623$	−0.244967	−	0.126289i	−0.00981440	−	0.00505967i
$624$	0.0103722	+	0.0193349i	0.000415220	+	0.000774015i
$625$	−9.39925	−	13.1994i	−0.375970	−	0.527976i
$626$	0.222297	−	0.916320i	0.00888477	−	0.0366235i
$627$	0.164234	+	10.0246i	0.00655888	+	0.400343i
$628$	3.82776	−	11.0596i	0.152744	−	0.441325i
$629$	−3.88106	−	26.9934i	−0.154748	−	1.07630i
$630$	18.9295	+	1.18343i	0.754169	+	0.0471489i
$631$	17.1524	−	19.7949i	0.682826	−	0.788023i	−0.303500	−	0.952831i	$-0.598155\pi$
$631$	17.1524	−	19.7949i	0.682826	−	0.788023i	0.986326	+	0.164809i	$0.0527007\pi$
$632$	0.166052	−	3.48585i	0.00660517	−	0.138660i
$633$	−12.3436	+	24.9381i	−0.490616	+	0.991199i
$634$	−2.90611	−	8.39665i	−0.115416	−	0.333473i
$635$	−15.9346	+	15.1936i	−0.632344	+	0.602939i
$636$	−11.1099	+	2.88873i	−0.440536	+	0.114545i
$637$	0.0167305	−	0.0483395i	0.000662886	−	0.00191528i
$638$	1.18762	+	2.60053i	0.0470185	+	0.102956i
$639$	−0.121206	+	8.16884i	−0.00479482	+	0.323154i
$640$	0.790499	−	1.73095i	0.0312472	−	0.0684219i
$641$	−5.14156	+	2.05837i	−0.203079	+	0.0813007i	−0.470972	−	0.882148i	$-0.656097\pi$
$641$	−5.14156	+	2.05837i	−0.203079	+	0.0813007i	0.267893	+	0.963449i	$0.413673\pi$
$642$	−3.42324	+	0.549566i	−0.135104	+	0.0216896i
$643$	−24.5543	+	42.5294i	−0.968328	+	1.67719i	−0.267935	+	0.963437i	$0.586341\pi$
$643$	−24.5543	+	42.5294i	−0.968328	+	1.67719i	−0.700393	+	0.713757i	$0.746992\pi$
$644$	−14.5346	−	6.52848i	−0.572742	−	0.257258i
$645$	−24.3182	+	17.9244i	−0.957527	+	0.705773i
$646$	13.4558	+	6.93694i	0.529411	+	0.272930i
$647$	4.65745	−	32.3933i	0.183103	−	1.27351i	−0.666267	−	0.745713i	$-0.732109\pi$
$647$	4.65745	−	32.3933i	0.183103	−	1.27351i	0.849370	−	0.527797i	$-0.176982\pi$
$648$	7.71231	−	4.63900i	0.302968	−	0.182237i
$649$	11.8390	−	3.47624i	0.464721	−	0.136454i
$650$	−0.0101323	+	0.0142289i	−0.000397423	+	0.000558103i
$651$	−3.73953	−	0.842586i	−0.146564	−	0.0330236i
$652$	−10.6195	−	4.25140i	−0.415891	−	0.166498i
$653$	−16.8889	+	16.1035i	−0.660913	+	0.630180i	−0.944401	−	0.328796i	$-0.893357\pi$
$653$	−16.8889	+	16.1035i	−0.660913	+	0.630180i	0.283487	+	0.958976i	$0.408509\pi$
$654$	30.6195	−	14.5943i	1.19732	−	0.570682i
$655$	−1.03259	+	21.6767i	−0.0403466	+	0.846979i
$656$	7.42351	+	4.77080i	0.289839	+	0.186268i
$657$	−2.98460	−	4.79922i	−0.116440	−	0.187235i
$658$	−7.76802	−	2.28090i	−0.302829	−	0.0889186i
$659$	32.5454	−	25.5940i	1.26779	−	0.996999i	0.268354	−	0.963320i	$-0.413520\pi$
$659$	32.5454	−	25.5940i	1.26779	−	0.996999i	0.999433	−	0.0336786i	$-0.0107223\pi$
$660$	−2.74616	+	2.97622i	−0.106894	+	0.115849i
$661$	13.2546	+	1.26566i	0.515545	+	0.0492286i	0.349586	−	0.936904i	$-0.386322\pi$
$661$	13.2546	+	1.26566i	0.515545	+	0.0492286i	0.165958	+	0.986133i	$0.446928\pi$
$662$	−4.24265	+	17.4884i	−0.164895	+	0.679707i
$663$	−0.0669960	−	0.0219654i	−0.00260191	−	0.000853064i
$664$	−12.0788	+	4.83564i	−0.468750	+	0.187659i
$665$	25.0566	−	16.1029i	0.971655	−	0.624445i
$666$	−24.8290	+	5.63477i	−0.962105	+	0.218343i
$667$	10.8279	−	2.69842i	0.419258	−	0.104483i
$668$	−0.342674	−	0.593529i	−0.0132585	−	0.0229643i
$669$	−26.3411	+	4.22879i	−1.01840	+	0.163494i
$670$	1.49027	+	1.17196i	0.0575743	+	0.0452769i
$671$	1.66638	+	2.34010i	0.0643298	+	0.0903385i
$672$	−3.48261	+	4.58099i	−0.134345	+	0.176716i
$673$	9.45950	−	13.2840i	0.364637	−	0.512061i	−0.590975	−	0.806690i	$-0.701257\pi$
$673$	9.45950	−	13.2840i	0.364637	−	0.512061i	0.955612	+	0.294629i	$0.0951961\pi$
$674$	−22.2067	−	25.6279i	−0.855370	−	0.987150i
$675$	6.03361	+	3.86440i	0.232234	+	0.148741i
$676$	12.4733	+	3.66248i	0.479741	+	0.140865i
$677$	−44.4943	−	8.57557i	−1.71005	−	0.329586i	−0.761971	−	0.647611i	$-0.775768\pi$
$677$	−44.4943	−	8.57557i	−1.71005	−	0.329586i	−0.948082	+	0.318025i	$0.896980\pi$
$678$	−22.7252	+	1.45598i	−0.872755	+	0.0559166i
$679$	−33.7016	+	17.3744i	−1.29335	+	0.666767i
$680$	1.99993	+	5.77841i	0.0766937	+	0.221592i
$681$	21.0023	+	17.6046i	0.804809	+	0.674609i
$682$	0.643352	−	0.505938i	0.0246352	−	0.0193734i
$683$	19.4323	+	22.4261i	0.743557	+	0.858111i	0.993927	−	0.110039i	$-0.0350977\pi$
$683$	19.4323	+	22.4261i	0.743557	+	0.858111i	−0.250370	+	0.968150i	$0.580552\pi$
$684$	5.44701	−	13.0418i	0.208272	−	0.498665i
$685$	−33.1568	+	9.73570i	−1.26685	+	0.371982i
$686$	−9.79617	+	0.935421i	−0.374020	+	0.0357145i
$687$	5.91533	+	0.184726i	0.225684	+	0.00704773i
$688$	−0.436130	−	9.15549i	−0.0166273	−	0.349050i
$689$	0.0419784	−	0.0727088i	0.00159925	−	0.00276998i
$690$	9.45769	+	12.6652i	0.360048	+	0.482155i
$691$	6.09678	+	10.5599i	0.231932	+	0.401719i	0.958377	−	0.285507i	$-0.0921618\pi$
$691$	6.09678	+	10.5599i	0.231932	+	0.401719i	−0.726444	+	0.687225i	$0.758829\pi$
$692$	18.1148	−	11.6416i	0.688619	−	0.442549i
$693$	10.0797	−	6.95469i	0.382896	−	0.264187i
$694$	1.01869	−	2.23062i	0.0386690	−	0.0846732i
$695$	−26.1085	−	24.8944i	−0.990351	−	0.944298i
$696$	−0.0660183	−	4.02964i	−0.00250242	−	0.152743i
$697$	−27.8432	+	5.36634i	−1.05464	+	0.203265i
$698$	−16.0427	−	6.42253i	−0.607226	−	0.243096i
$699$	37.9652	−	13.8404i	1.43598	−	0.523490i
$700$	−4.49845	−	0.867006i	−0.170026	−	0.0327697i
$701$	−2.31407	−	1.48716i	−0.0874011	−	0.0561693i	0.496210	−	0.868202i	$-0.334724\pi$
$701$	−2.31407	−	1.48716i	−0.0874011	−	0.0561693i	−0.583611	+	0.812033i	$0.698361\pi$
$702$	−0.0154197	+	0.0639923i	−0.000581979	+	0.00241523i
$703$	−26.1832	+	30.2171i	−0.987520	+	1.13966i
$704$	−0.289668	−	1.19403i	−0.0109173	−	0.0450016i
$705$	5.63692	+	5.72118i	0.212299	+	0.215472i
$706$	−8.24874	+	1.58981i	−0.310445	+	0.0598335i
$707$	37.8102	+	3.61044i	1.42200	+	0.135785i
$708$	−17.2553	−	2.19307i	−0.648492	−	0.0824206i
$709$	−38.3138	+	3.65853i	−1.43891	+	0.137399i	−0.785149	−	0.619306i	$-0.787414\pi$
$709$	−38.3138	+	3.65853i	−1.43891	+	0.137399i	−0.653756	+	0.756705i	$0.726808\pi$
$710$	−0.737490	+	5.12936i	−0.0276775	+	0.192501i
$711$	7.33634	−	7.46905i	0.275134	−	0.280111i
$712$	−0.0829546			−0.00310886
$713$	−1.48157	−	2.83037i	−0.0554852	−	0.105998i
$714$	−2.05899	−	18.3761i	−0.0770557	−	0.687709i
$715$	−0.00140927	−	0.0295843i	−5.27039e−5	−	0.00110639i
$716$	−4.47815	−	3.52166i	−0.167356	−	0.131611i
$717$	−6.18890	−	2.02910i	−0.231129	−	0.0757782i
$718$	−10.5946	−	10.1019i	−0.395385	−	0.376999i
$719$	−16.3241	−	35.7448i	−0.608787	−	1.33306i	−0.923401	−	0.383837i	$-0.874602\pi$
$719$	−16.3241	−	35.7448i	−0.608787	−	1.33306i	0.314614	−	0.949220i	$-0.398125\pi$
$720$	5.22747	−	2.29420i	0.194816	−	0.0854996i
$721$	4.13025	+	28.7265i	0.153818	+	1.06983i
$722$	−0.753329	−	3.10527i	−0.0280360	−	0.115566i
$723$	−28.3045	+	13.4909i	−1.05266	+	0.501731i
$724$	1.37339	−	0.708032i	0.0510416	−	0.0263138i
$725$	2.85183	−	1.47022i	0.105914	−	0.0546026i
$726$	1.29426	−	16.3868i	0.0480344	−	0.608171i
$727$	−10.4116	−	42.9171i	−0.386144	−	1.59171i	−0.750777	−	0.660556i	$-0.770321\pi$
$727$	−10.4116	−	42.9171i	−0.386144	−	1.59171i	0.364633	−	0.931151i	$-0.381194\pi$
$728$	−0.00598959	−	0.0416585i	−0.000221989	−	0.00154397i
$729$	26.5277	+	5.02783i	0.982509	+	0.186216i
$730$	−1.48919	−	3.26087i	−0.0551174	−	0.120690i
$731$	21.3162	+	20.3250i	0.788408	+	0.751746i
$732$	−0.831462	−	3.96350i	−0.0307317	−	0.146495i
$733$	8.92065	+	7.01527i	0.329492	+	0.259115i	0.769176	−	0.639037i	$-0.220667\pi$
$733$	8.92065	+	7.01527i	0.329492	+	0.259115i	−0.439684	+	0.898153i	$0.644910\pi$
$734$	1.05208	+	22.0859i	0.0388330	+	0.815205i
$735$	−12.1953	−	5.32974i	−0.449831	−	0.196591i
$736$	−4.78888	+	0.258062i	−0.176521	+	0.00951230i
$737$	1.22413			0.0450914
$738$	7.08065	+	25.5085i	0.260642	+	0.938982i
$739$	−2.71855	+	18.9080i	−0.100004	+	0.695540i	0.876714	+	0.481012i	$0.159731\pi$
$739$	−2.71855	+	18.9080i	−0.100004	+	0.695540i	−0.976718	+	0.214528i	$0.931179\pi$
$740$	−16.0765	+	1.53512i	−0.590985	+	0.0564322i
$741$	0.0399855	+	0.0953229i	0.00146890	+	0.00350177i
$742$	21.9194	+	2.09305i	0.804688	+	0.0768384i
$743$	−37.5100	+	7.22945i	−1.37611	+	0.265223i	−0.823073	−	0.567936i	$-0.807742\pi$
$743$	−37.5100	+	7.22945i	−1.37611	+	0.265223i	−0.553034	+	0.833159i	$0.686530\pi$
$744$	−1.11666	+	0.290346i	−0.0409386	+	0.0106446i
$745$	8.01772	+	33.0495i	0.293747	+	1.21084i
$746$	7.58739	−	8.75632i	0.277794	−	0.320591i
$747$	−36.6923	−	13.3121i	−1.34250	−	0.487065i
$748$	3.32136	+	2.13451i	0.121441	+	0.0780454i
$749$	6.53022	+	1.25860i	0.238609	+	0.0459881i
$750$	16.1127	+	13.5060i	0.588353	+	0.493170i
$751$	18.0543	+	7.22787i	0.658813	+	0.263749i	0.676886	−	0.736088i	$-0.263329\pi$
$751$	18.0543	+	7.22787i	0.658813	+	0.263749i	−0.0180734	+	0.999837i	$0.505753\pi$
$752$	−2.39278	+	0.461171i	−0.0872557	+	0.0168172i
$753$	−24.2930	−	13.4999i	−0.885285	−	0.491963i
$754$	0.0213327	+	0.0203406i	0.000776890	+	0.000740763i
$755$	−16.8126	+	36.8144i	−0.611872	+	1.33981i
$756$	−16.9464	+	3.29332i	−0.616335	+	0.119777i
$757$	−14.6658	+	9.42511i	−0.533036	+	0.342561i	−0.779310	−	0.626639i	$-0.784430\pi$
$757$	−14.6658	+	9.42511i	−0.533036	+	0.342561i	0.246274	+	0.969200i	$0.420794\pi$
$758$	−9.66624	−	16.7424i	−0.351093	−	0.608112i
$759$	9.85514	+	2.65317i	0.357719	+	0.0963040i
$760$	4.48250	−	7.76392i	0.162597	−	0.281627i
$761$	−1.45904	−	30.6291i	−0.0528903	−	1.11030i	−0.856832	−	0.515595i	$-0.827571\pi$
$761$	−1.45904	−	30.6291i	−0.0528903	−	1.11030i	0.803942	−	0.594708i	$-0.202732\pi$
$762$	10.5569	−	17.0341i	0.382438	−	0.617081i
$763$	−64.7689	+	6.18468i	−2.34479	+	0.223900i
$764$	−1.99371	+	0.585406i	−0.0721299	+	0.0211792i
$765$	−7.06974	+	16.9271i	−0.255607	+	0.612000i
$766$	10.9620	+	12.6509i	0.396074	+	0.457094i
$767$	0.0999986	−	0.0786397i	0.00361074	−	0.00283952i
$768$	−0.299889	+	1.70589i	−0.0108213	+	0.0615561i
$769$	6.85691	+	19.8117i	0.247266	+	0.714429i	0.998518	+	0.0544138i	$0.0173290\pi$
$769$	6.85691	+	19.8117i	0.247266	+	0.714429i	−0.751252	+	0.660015i	$0.770550\pi$
$770$	6.90429	−	3.55941i	0.248813	−	0.128272i
$771$	21.7420	−	43.9257i	0.783020	−	1.58195i
$772$	−15.7480	−	3.03517i	−0.566782	−	0.109238i
$773$	−40.3205	−	11.8392i	−1.45023	−	0.425825i	−0.540611	−	0.841273i	$-0.681807\pi$
$773$	−40.3205	−	11.8392i	−1.45023	−	0.425825i	−0.909617	+	0.415448i	$0.863625\pi$
$774$	17.3167	−	21.3600i	0.622436	−	0.767771i
$775$	−0.601521	−	0.694193i	−0.0216073	−	0.0249361i
$776$	−6.61993	+	9.29640i	−0.237642	+	0.333721i
$777$	48.4474	+	6.15746i	1.73804	+	0.220897i
$778$	−11.2308	−	15.7714i	−0.402642	−	0.565432i
$779$	32.6787	+	25.6988i	1.17084	+	0.920756i
$780$	−0.0148808	+	0.0390106i	−0.000532817	+	0.00139680i
$781$	1.67297	+	2.89768i	0.0598637	+	0.103687i
$782$	10.5648	−	11.2193i	0.377797	−	0.401202i
$783$	7.90350	−	9.14966i	0.282448	−	0.326982i
$784$	3.39700	−	2.18312i	0.121321	−	0.0779686i
$785$	20.6750	−	8.27703i	0.737923	−	0.295420i
$786$	−4.05544	−	19.3319i	−0.144653	−	0.689546i
$787$	1.53368	−	6.32190i	0.0546697	−	0.225352i	−0.937923	−	0.346845i	$-0.887253\pi$
$787$	1.53368	−	6.32190i	0.0546697	−	0.225352i	0.992592	+	0.121493i	$0.0387682\pi$
$788$	−17.0703	−	1.63002i	−0.608104	−	0.0580669i
$789$	−1.05437	−	3.38473i	−0.0375366	−	0.120500i
$790$	5.22002	−	4.10507i	0.185720	−	0.146052i
$791$	41.9106	+	12.3061i	1.49017	+	0.437553i
$792$	1.73744	−	3.25082i	0.0617372	−	0.115513i
$793$	0.0249172	+	0.0160133i	0.000884834	+	0.000568648i
$794$	0.622589	−	13.0697i	0.0220948	−	0.463828i
$795$	−17.9989	−	12.3777i	−0.638354	−	0.438990i
$796$	16.0130	−	15.2684i	0.567567	−	0.541174i
$797$	3.99685	+	1.60010i	0.141576	+	0.0566783i	0.441368	−	0.897326i	$-0.354493\pi$
$797$	3.99685	+	1.60010i	0.141576	+	0.0566783i	−0.299793	+	0.954004i	$0.596917\pi$
$798$	−18.3845	+	19.9246i	−0.650803	+	0.705323i
$799$	4.54203	−	6.37839i	0.160686	−	0.225651i
$800$	−1.32306	+	0.388485i	−0.0467772	+	0.0137350i
$801$	−0.185640	−	0.165744i	−0.00655928	−	0.00585626i
$802$	1.94004	−	13.4933i	0.0685051	−	0.476464i
$803$	−2.05732	−	1.06062i	−0.0726013	−	0.0374286i
$804$	−1.58125	−	0.691055i	−0.0557663	−	0.0243716i
$805$	−8.72337	−	29.0380i	−0.307458	−	1.02345i
$806$	0.00421926	−	0.00730797i	0.000148617	−	0.000257412i
$807$	−5.46042	+	14.3147i	−0.192216	+	0.503902i
$808$	10.6134	−	4.24897i	0.373378	−	0.149478i
$809$	3.09397	−	6.77485i	0.108778	−	0.238191i	−0.847413	−	0.530935i	$-0.821841\pi$
$809$	3.09397	−	6.77485i	0.108778	−	0.238191i	0.956191	+	0.292744i	$0.0945682\pi$
$810$	16.2821	+	5.31042i	0.572095	+	0.186589i
$811$	−19.4079	−	42.4973i	−0.681503	−	1.49228i	−0.861043	−	0.508532i	$-0.830188\pi$
$811$	−19.4079	−	42.4973i	−0.681503	−	1.49228i	0.179541	−	0.983751i	$-0.442539\pi$
$812$	−2.52841	+	7.30537i	−0.0887299	+	0.256368i
$813$	36.9689	+	37.5215i	1.29656	+	1.31594i
$814$	−7.54667	+	7.19573i	−0.264511	+	0.252210i
$815$	−7.11936	−	20.5700i	−0.249380	−	0.720537i
$816$	−3.08532	−	4.63222i	−0.108008	−	0.162160i
$817$	2.05469	−	43.1333i	0.0718846	−	1.50904i
$818$	16.9642	−	19.5777i	0.593138	−	0.684518i
$819$	0.0698301	−	0.105193i	0.00244006	−	0.00367574i
$820$	2.38975	+	16.6211i	0.0834536	+	0.580432i
$821$	−0.549469	+	1.58759i	−0.0191766	+	0.0554071i	−0.954183	−	0.299224i	$-0.903272\pi$
$821$	−0.549469	+	1.58759i	−0.0191766	+	0.0554071i	0.935006	+	0.354631i	$0.115393\pi$
$822$	26.9784	−	16.1709i	0.940980	−	0.564027i
$823$	9.27279	−	38.2230i	0.323229	−	1.33237i	−0.545928	−	0.837832i	$-0.683823\pi$
$823$	9.27279	−	38.2230i	0.323229	−	1.33237i	0.869157	−	0.494536i	$-0.164662\pi$
$824$	5.06700	+	7.11560i	0.176517	+	0.247884i
$825$	2.93305	+	0.0915942i	0.102116	+	0.00318890i
$826$	29.6556	+	15.2885i	1.03185	+	0.531957i
$827$	49.5006			1.72130			0.860652	−	0.509194i	$-0.170057\pi$
$827$	49.5006			1.72130			0.860652	+	0.509194i	$0.170057\pi$
$828$	−11.2324	−	8.99070i	−0.390354	−	0.312448i
$829$	34.7967			1.20854			0.604270	−	0.796779i	$-0.293465\pi$
$829$	34.7967			1.20854			0.604270	+	0.796779i	$0.293465\pi$
$830$	−22.0062	−	11.3450i	−0.763848	−	0.393791i
$831$	−4.20267	+	6.78121i	−0.145789	+	0.235238i
$832$	−0.00734805	−	0.0103189i	−0.000254748	−	0.000357743i
$833$	−3.05910	+	12.6098i	−0.105992	+	0.436903i
$834$	28.7015	+	15.9497i	0.993852	+	0.552294i
$835$	0.426549	−	1.23243i	0.0147613	−	0.0426501i
$836$	−0.823785	−	5.72955i	−0.0284912	−	0.198161i
$837$	−3.07902	−	1.58133i	−0.106427	−	0.0546587i
$838$	9.22433	−	10.6454i	0.318649	−	0.367741i
$839$	0.820202	−	17.2182i	0.0283165	−	0.594437i	−0.939465	−	0.342645i	$-0.888677\pi$
$839$	0.820202	−	17.2182i	0.0283165	−	0.594437i	0.967781	−	0.251792i	$-0.0810198\pi$
$840$	−10.9279	+	0.700139i	−0.377048	+	0.0241571i
$841$	7.71418	+	22.2887i	0.266006	+	0.768575i
$842$	14.3115	−	13.6460i	0.493208	−	0.470273i
$843$	12.4852	−	45.2499i	0.430012	−	1.55849i
$844$	5.25442	−	15.1816i	0.180864	−	0.522573i
$845$	10.2764	+	22.5021i	0.353518	+	0.774096i
$846$	−6.27611	−	3.74875i	−0.215777	−	0.128885i
$847$	−13.0982	+	28.6811i	−0.450060	+	0.985493i
$848$	6.15283	−	2.46322i	0.211289	−	0.0845874i
$849$	−10.9736	−	13.4931i	−0.376612	−	0.463084i
$850$	2.21546	−	3.83729i	0.0759897	−	0.131618i
$851$	22.2178	+	34.1022i	0.761617	+	1.16901i
$852$	−0.525216	−	4.68747i	−0.0179936	−	0.160590i
$853$	43.7071	+	22.5326i	1.49650	+	0.771501i	0.995573	−	0.0939867i	$-0.0299611\pi$
$853$	43.7071	+	22.5326i	1.49650	+	0.771501i	0.500930	+	0.865488i	$0.332991\pi$
$854$	−1.10552	+	7.68905i	−0.0378300	+	0.263114i
$855$	25.5435	−	8.41846i	0.873569	−	0.287905i
$856$	1.92063	−	0.563948i	0.0656458	−	0.0192754i
$857$	−25.8023	+	36.2343i	−0.881391	+	1.23774i	0.0889586	+	0.996035i	$0.471646\pi$
$857$	−25.8023	+	36.2343i	−0.881391	+	1.23774i	−0.970350	+	0.241705i	$0.922293\pi$
$858$	0.00801777	+	0.0257386i	0.000273722	+	0.000878700i
$859$	14.4733	+	5.79422i	0.493822	+	0.197696i	0.605187	−	0.796083i	$-0.293098\pi$
$859$	14.4733	+	5.79422i	0.493822	+	0.197696i	−0.111366	+	0.993779i	$0.535522\pi$
$860$	12.6233	−	12.0363i	0.430450	−	0.410434i
$861$	3.99820	−	50.6219i	0.136258	−	1.72519i
$862$	0.423662	−	8.89376i	0.0144300	−	0.302923i
$863$	17.3235	+	11.1331i	0.589698	+	0.378976i	0.801196	−	0.598402i	$-0.204198\pi$
$863$	17.3235	+	11.1331i	0.589698	+	0.378976i	−0.211497	+	0.977379i	$0.567834\pi$
$864$	−4.07948	+	3.21836i	−0.138787	+	0.109491i
$865$	39.3158	+	11.5441i	1.33678	+	0.392513i
$866$	2.50778	−	1.97214i	0.0852178	−	0.0670160i
$867$	−11.2777	−	2.54108i	−0.383012	−	0.0862997i
$868$	2.20312	+	0.210373i	0.0747789	+	0.00714052i
$869$	1.01088	−	4.16692i	0.0342919	−	0.141353i
$870$	5.71287	−	5.11646i	0.193685	−	0.173464i
$871$	0.0117170	−	0.00469078i	0.000397015	−	0.000158941i
$872$	−16.4747	+	10.5877i	−0.557905	+	0.358544i
$873$	−33.3887	+	7.57732i	−1.13004	+	0.256453i
$874$	−22.5748	−	0.934317i	−0.763603	−	0.0316038i
$875$	−20.1642	−	34.9255i	−0.681676	−	1.18070i
$876$	2.05876	+	2.53146i	0.0695590	+	0.0855301i
$877$	−34.2130	−	26.9054i	−1.15529	−	0.908532i	−0.158405	−	0.987374i	$-0.550635\pi$
$877$	−34.2130	−	26.9054i	−1.15529	−	0.908532i	−0.996887	+	0.0788422i	$0.974878\pi$
$878$	17.9695	+	25.2346i	0.606440	+	0.851626i
$879$	−20.9681	−	49.9867i	−0.707237	−	1.68601i
$880$	1.35620	−	1.90451i	0.0457174	−	0.0642011i
$881$	−6.57390	−	7.58669i	−0.221480	−	0.255602i	0.634125	−	0.773230i	$-0.281360\pi$
$881$	−6.57390	−	7.58669i	−0.221480	−	0.255602i	−0.855605	+	0.517628i	$0.826815\pi$
$882$	11.9639	+	1.90172i	0.402844	+	0.0640341i
$883$	33.6840	+	9.89051i	1.13356	+	0.332842i	0.794104	−	0.607781i	$-0.207940\pi$
$883$	33.6840	+	9.89051i	1.13356	+	0.332842i	0.339452	+	0.940623i	$0.389758\pi$
$884$	0.0399704	+	0.00770366i	0.00134435	+	0.000259102i
$885$	−18.3486	−	27.5481i	−0.616782	−	0.926020i
$886$	−27.2468	+	14.0467i	−0.915373	+	0.471907i
$887$	−3.01118	−	8.70023i	−0.101105	−	0.292125i	0.883092	−	0.469200i	$-0.155458\pi$
$887$	−3.01118	−	8.70023i	−0.101105	−	0.292125i	−0.984197	+	0.177075i	$0.943336\pi$
$888$	13.8105	−	5.03466i	0.463449	−	0.168952i
$889$	−30.2162	+	23.7623i	−1.01342	+	0.796961i
$890$	−0.103373	−	0.119299i	−0.00346509	−	0.00399892i
$891$	10.3833	−	3.80345i	0.347853	−	0.127420i
$892$	14.7788	−	4.33946i	0.494832	−	0.145296i
$893$	−11.4283	+	1.09127i	−0.382434	+	0.0365181i
$894$	−14.6330	−	27.2774i	−0.489400	−	0.912294i
$895$	−0.515832	−	10.8286i	−0.0172424	−	0.361962i
$896$	1.66118	−	2.87724i	0.0554960	−	0.0961219i
$897$	0.104497	−	0.0123689i	0.00348906	−	0.000412984i
$898$	−9.71384	−	16.8249i	−0.324155	−	0.561453i
$899$	−1.30393	+	0.837988i	−0.0434886	+	0.0279485i
$900$	−3.73701	−	1.77410i	−0.124567	−	0.0591368i
$901$	−8.84696	+	19.3721i	−0.294735	+	0.645379i
$902$	7.84682	+	7.48193i	0.261271	+	0.249121i
$903$	−45.2403	+	27.1172i	−1.50550	+	0.902402i
$904$	12.9097	−	2.48814i	0.429370	−	0.0827543i
$905$	2.72968	+	1.09280i	0.0907377	+	0.0363259i
$906$	6.37812	−	36.2814i	0.211899	−	1.20537i
$907$	−33.7856	−	6.51164i	−1.12183	−	0.216216i	−0.405582	−	0.914059i	$-0.632931\pi$
$907$	−33.7856	−	6.51164i	−1.12183	−	0.216216i	−0.716251	+	0.697843i	$0.754143\pi$
$908$	−13.3104	−	8.55407i	−0.441721	−	0.283877i
$909$	32.2407	+	11.6971i	1.06936	+	0.387967i
$910$	0.0524464	−	0.0605263i	0.00173858	−	0.00200643i
$911$	7.45079	+	30.7126i	0.246856	+	1.01755i	0.951416	+	0.307909i	$0.0996292\pi$
$911$	7.45079	+	30.7126i	0.246856	+	1.01755i	−0.704560	+	0.709644i	$0.748856\pi$
$912$	−2.17038	+	7.86610i	−0.0718685	+	0.260472i
$913$	−15.6970	+	3.02536i	−0.519496	+	0.100125i
$914$	−19.7358	−	1.88454i	−0.652801	−	0.0623349i
$915$	4.66389	−	6.13484i	0.154184	−	0.202812i
$916$	−3.40141	+	0.324795i	−0.112386	+	0.0107315i
$917$	−5.39215	+	37.5032i	−0.178064	+	1.23846i
$918$	2.35069	−	16.5307i	0.0775844	−	0.545595i
$919$	18.3163			0.604200			0.302100	−	0.953276i	$-0.402312\pi$
$919$	18.3163			0.604200			0.302100	+	0.953276i	$0.402312\pi$
$920$	−6.33877	−	6.56544i	−0.208983	−	0.216456i
$921$	−32.2771	+	23.7908i	−1.06357	+	0.783932i
$922$	−0.500726	−	10.5115i	−0.0164905	−	0.346179i
$923$	0.0271169	+	0.0213250i	0.000892564	+	0.000701920i
$924$	−5.26683	+	4.71698i	−0.173266	+	0.155177i
$925$	8.46955	+	8.07570i	0.278477	+	0.265527i
$926$	14.8058	+	32.4201i	0.486548	+	1.06539i
$927$	−2.87780	+	26.0476i	−0.0945193	+	0.855514i
$928$	0.331142	+	2.30314i	0.0108703	+	0.0756044i
$929$	−13.6994	−	56.4697i	−0.449463	−	1.85271i	−0.518472	−	0.855094i	$-0.673499\pi$
$929$	−13.6994	−	56.4697i	−0.449463	−	1.85271i	0.0690095	−	0.997616i	$-0.478016\pi$
$930$	−1.80907	−	1.24408i	−0.0593217	−	0.0407950i
$931$	16.9091	−	8.71726i	0.554174	−	0.285697i
$932$	−20.7368	+	10.6906i	−0.679257	+	0.350181i
$933$	−2.70280	−	1.85869i	−0.0884855	−	0.0608507i
$934$	−2.93420	−	12.0949i	−0.0960100	−	0.395759i
$935$	1.06920	+	7.43645i	0.0349666	+	0.243198i
$936$	0.00417332	−	0.0377736i	0.000136409	−	0.00123467i
$937$	1.56653	+	3.43023i	0.0511764	+	0.112061i	0.933493	−	0.358596i	$-0.116744\pi$
$937$	1.56653	+	3.43023i	0.0511764	+	0.112061i	−0.882317	+	0.470657i	$0.844017\pi$
$938$	2.39563	+	2.28423i	0.0782200	+	0.0745826i
$939$	−1.21657	+	1.08956i	−0.0397012	+	0.0355564i
$940$	−3.64497	−	2.86644i	−0.118886	−	0.0934929i
$941$	2.14195	+	44.9650i	0.0698255	+	1.46582i	0.713573	+	0.700581i	$0.247076\pi$
$941$	2.14195	+	44.9650i	0.0698255	+	1.46582i	−0.643748	+	0.765238i	$0.722621\pi$
$942$	−16.3171	+	12.0270i	−0.531641	+	0.391861i
$943$	34.3192	−	24.7625i	1.11759	−	0.806379i
$944$	10.0425			0.326854
$945$	−25.8539	−	20.2671i	−0.841027	−	0.659290i
$946$	1.60272	−	11.1471i	0.0521088	−	0.362425i
$947$	−16.9819	+	1.62157i	−0.551837	+	0.0526940i	−0.367250	−	0.930122i	$-0.619701\pi$
$947$	−16.9819	+	1.62157i	−0.551837	+	0.0526940i	−0.184587	+	0.982816i	$0.559095\pi$
$948$	−3.65814	+	4.81188i	−0.118811	+	0.156283i
$949$	−0.0237563	−	0.00226845i	−0.000771162	−	7.36371e-5i
$950$	−6.37894	+	1.22944i	−0.206960	+	0.0398883i
$951$	−4.09335	+	14.8355i	−0.132736	+	0.481074i
$952$	2.51693	+	10.3749i	0.0815741	+	0.336253i
$953$	−1.45669	+	1.68111i	−0.0471869	+	0.0544566i	−0.778852	−	0.627207i	$-0.784198\pi$
$953$	−1.45669	+	1.68111i	−0.0471869	+	0.0544566i	0.731665	+	0.681664i	$0.238743\pi$
$954$	18.6907	+	6.78104i	0.605132	+	0.219544i
$955$	−3.32634	−	2.13771i	−0.107638	−	0.0691746i
$956$	3.69236	+	0.711643i	0.119419	+	0.0230162i
$957$	0.857348	−	4.87695i	0.0277141	−	0.157649i
$958$	−4.09463	−	1.63924i	−0.132291	−	0.0529615i
$959$	−59.2429	+	11.4181i	−1.91305	+	0.368711i
$960$	−2.82699	+	1.69451i	−0.0912408	+	0.0546900i
$961$	−22.1146	−	21.0862i	−0.713374	−	0.680201i
$962$	−0.0446609	+	0.0977937i	−0.00143992	+	0.00315300i
$963$	5.42486	+	2.57539i	0.174814	+	0.0829909i
$964$	15.2292	−	9.78718i	0.490498	−	0.315224i
$965$	−15.2593	−	26.4298i	−0.491214	−	0.850807i
$966$	14.3358	+	23.5820i	0.461245	+	0.758738i
$967$	15.0411	−	26.0519i	0.483689	−	0.837774i	−0.516135	−	0.856507i	$-0.672630\pi$
$967$	15.0411	−	26.0519i	0.483689	−	0.837774i	0.999825	+	0.0187329i	$0.00596322\pi$
$968$	0.451571	+	9.47964i	0.0145140	+	0.304687i
$969$	−12.3953	−	23.1062i	−0.398194	−	0.742277i
$970$	−21.6188	+	2.06434i	−0.694138	+	0.0662821i
$971$	−17.6402	+	5.17964i	−0.566102	+	0.166223i	−0.552246	−	0.833681i	$-0.686229\pi$
$971$	−17.6402	+	5.17964i	−0.566102	+	0.166223i	−0.0138565	+	0.999904i	$0.504411\pi$
$972$	−15.5596	−	0.948613i	−0.499073	−	0.0304268i
$973$	−41.2456	−	47.6000i	−1.32227	−	1.52599i
$974$	6.03066	−	4.74257i	0.193235	−	0.151962i
$975$	0.0284252	−	0.0103625i	0.000910336	−	0.000331866i
$976$	0.764730	+	2.20954i	0.0244784	+	0.0707257i
$977$	24.3352	−	12.5457i	0.778552	−	0.401372i	−0.0226666	−	0.999743i	$-0.507216\pi$
$977$	24.3352	−	12.5457i	0.778552	−	0.401372i	0.801219	+	0.598372i	$0.204185\pi$
$978$	10.9832	+	16.4898i	0.351203	+	0.527286i
$979$	−0.100081	−	0.0192891i	−0.00319861	−	0.000616482i
$980$	7.37276	+	2.16484i	0.235514	+	0.0691532i
$981$	−58.0223	−	9.22293i	−1.85251	−	0.294465i
$982$	−20.0454	−	23.1336i	−0.639673	−	0.738222i
$983$	−6.87715	+	9.65760i	−0.219347	+	0.308030i	−0.909557	−	0.415580i	$-0.863579\pi$
$983$	−6.87715	+	9.65760i	−0.219347	+	0.308030i	0.690210	+	0.723609i	$0.257518\pi$
$984$	−5.91224	−	14.0944i	−0.188475	−	0.449313i
$985$	−18.9279	−	26.5805i	−0.603092	−	0.846925i
$986$	−5.87724	−	4.62191i	−0.187169	−	0.147192i
$987$	8.84760	+	10.8790i	0.281622	+	0.346284i
$988$	−0.0298402	−	0.0516848i	−0.000949345	−	0.00164431i
$989$	−41.6292	−	14.1179i	−1.32373	−	0.448924i
$990$	6.84019	−	1.55233i	0.217395	−	0.0493363i
$991$	34.5549	−	22.2071i	1.09767	−	0.705431i	0.139100	−	0.990278i	$-0.455579\pi$
$991$	34.5549	−	22.2071i	1.09767	−	0.705431i	0.958573	+	0.284847i	$0.0919428\pi$
$992$	0.618422	−	0.247579i	0.0196349	−	0.00786063i
$993$	23.2188	−	20.7948i	0.736826	−	0.659903i
$994$	−2.13305	+	8.79254i	−0.0676561	+	0.278882i
$995$	41.9124	+	4.00215i	1.32871	+	0.126877i
$996$	21.9843	+	4.95347i	0.696598	+	0.156957i
$997$	34.1915	−	26.8885i	1.08285	−	0.851566i	0.0932876	−	0.995639i	$-0.470262\pi$
$997$	34.1915	−	26.8885i	1.08285	−	0.851566i	0.989567	+	0.144073i	$0.0460200\pi$
$998$	29.7854	+	8.74579i	0.942841	+	0.276843i
$999$	40.9651	+	16.3265i	1.29608	+	0.516549i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.m.a.265.4	yes	240
9.7	even	3	inner	414.2.m.a.403.11	yes	240
23.2	even	11	inner	414.2.m.a.301.11	yes	240
207.25	even	33	inner	414.2.m.a.25.4	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.m.a.25.4	✓	240	207.25	even	33	inner
414.2.m.a.265.4	yes	240	1.1	even	1	trivial
414.2.m.a.301.11	yes	240	23.2	even	11	inner
414.2.m.a.403.11	yes	240	9.7	even	3	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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.m (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.888835 + 0.458227i) q^{2} +(-0.818784 - 1.52630i) q^{3} +(0.580057 + 0.814576i) q^{4} +(-0.448629 + 1.84927i) q^{5} +(-0.0283727 - 1.73182i) q^{6} +(-1.08663 + 3.13963i) q^{7} +(0.142315 + 0.989821i) q^{8} +(-1.65919 + 2.49942i) q^{9} +O(q^{10})\)	\(q+(0.888835 + 0.458227i) q^{2} +(-0.818784 - 1.52630i) q^{3} +(0.580057 + 0.814576i) q^{4} +(-0.448629 + 1.84927i) q^{5} +(-0.0283727 - 1.73182i) q^{6} +(-1.08663 + 3.13963i) q^{7} +(0.142315 + 0.989821i) q^{8} +(-1.65919 + 2.49942i) q^{9} +(-1.24614 + 1.43813i) q^{10} +(-0.0584621 + 1.22727i) q^{11} +(0.768346 - 1.55230i) q^{12} +(0.00414324 + 0.0119711i) q^{13} +(-2.40450 + 2.29269i) q^{14} +(3.18988 - 0.829413i) q^{15} +(-0.327068 + 0.945001i) q^{16} +(-1.33487 - 2.92296i) q^{17} +(-2.62004 + 1.46129i) q^{18} +(-1.95710 + 4.28545i) q^{19} +(-1.76661 + 0.707242i) q^{20} +(5.68173 - 0.912143i) q^{21} +(-0.614331 + 1.06405i) q^{22} +(3.64396 + 3.11794i) q^{23} +(1.39424 - 1.02766i) q^{24} +(1.22563 + 0.631856i) q^{25} +(-0.00180282 + 0.0125389i) q^{26} +(5.17338 + 0.485932i) q^{27} +(-3.18777 + 0.936015i) q^{28} +(1.34969 - 1.89538i) q^{29} +(3.21534 + 0.724475i) q^{30} +(-0.618422 - 0.247579i) q^{31} +(-0.723734 + 0.690079i) q^{32} +(1.92105 - 0.915639i) q^{33} +(0.152897 - 3.20970i) q^{34} +(-5.31853 - 3.41801i) q^{35} +(-2.99839 + 0.0982726i) q^{36} +(8.14302 + 2.39101i) q^{37} +(-3.70325 + 2.91227i) q^{38} +(0.0148791 - 0.0161256i) q^{39} +(-1.89430 - 0.180884i) q^{40} +(2.08042 - 8.57560i) q^{41} +(5.46809 + 1.79277i) q^{42} +(-8.50931 + 3.40661i) q^{43} +(-1.03362 + 0.664265i) q^{44} +(-3.87775 - 4.18960i) q^{45} +(1.81016 + 4.44109i) q^{46} +(1.21841 + 2.11034i) q^{47} +(1.71015 - 0.274547i) q^{48} +(-3.17410 - 2.49614i) q^{49} +(0.799849 + 1.12323i) q^{50} +(-3.36834 + 4.43068i) q^{51} +(-0.00734805 + 0.0103189i) q^{52} +(-4.34014 - 5.00879i) q^{53} +(4.37562 + 2.80249i) q^{54} +(-2.24333 - 0.658702i) q^{55} +(-3.26231 - 0.628759i) q^{56} +(8.14333 - 0.521735i) q^{57} +(2.06817 - 1.06621i) q^{58} +(-3.28457 - 9.49014i) q^{59} +(2.52593 + 2.11729i) q^{60} +(1.83790 - 1.44534i) q^{61} +(-0.436228 - 0.503434i) q^{62} +(-6.04431 - 7.92518i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(-0.0239966 + 0.00229140i) q^{65} +(2.12707 + 0.0664248i) q^{66} +(-0.0474064 - 0.995182i) q^{67} +(1.60667 - 2.78284i) q^{68} +(1.77530 - 8.11470i) q^{69} +(-3.16108 - 5.47514i) q^{70} +(2.29094 - 1.47230i) q^{71} +(-2.71011 - 1.28659i) q^{72} +(-0.782583 + 1.71362i) q^{73} +(6.14218 + 5.85656i) q^{74} +(-0.0391235 - 2.38803i) q^{75} +(-4.62606 + 0.891599i) q^{76} +(-3.78964 - 1.51714i) q^{77} +(0.0206142 - 0.00751498i) q^{78} +(-3.42674 - 0.660450i) q^{79} +(-1.60083 - 1.02879i) q^{80} +(-3.49420 - 8.29401i) q^{81} +(5.77872 - 6.66899i) q^{82} +(3.06742 + 12.6441i) q^{83} +(4.03874 + 4.09911i) q^{84} +(6.00421 - 1.15722i) q^{85} +(-9.12437 - 0.871272i) q^{86} +(-3.99802 - 0.508132i) q^{87} +(-1.22310 + 0.116792i) q^{88} +(-0.0118057 + 0.0821103i) q^{89} +(-1.52690 - 5.50076i) q^{90} -0.0420869 q^{91} +(-0.426094 + 4.77687i) q^{92} +(0.128474 + 1.14661i) q^{93} +(0.115948 + 2.43406i) q^{94} +(-7.04696 - 5.54179i) q^{95} +(1.64585 + 0.539610i) q^{96} +(8.25966 + 7.87557i) q^{97} +(-1.67746 - 3.67311i) q^{98} +(-2.97047 - 2.18239i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 12 q^{2} + 12 q^{4} - 13 q^{7} + 24 q^{8} - 36 q^{9}+O(q^{10}) \) 240 * q - 12 * q^2 + 12 * q^4 - 13 * q^7 + 24 * q^8 - 36 * q^9	\( 240 q - 12 q^{2} + 12 q^{4} - 13 q^{7} + 24 q^{8} - 36 q^{9} + 2 q^{11} + 11 q^{12} + 4 q^{13} + 2 q^{14} + 6 q^{15} + 12 q^{16} - 8 q^{17} - 18 q^{18} + 12 q^{19} - 29 q^{21} + 20 q^{22} + 10 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} - 8 q^{29} - 18 q^{30} - 12 q^{32} + 50 q^{33} - 4 q^{34} - 12 q^{35} - 4 q^{36} + 92 q^{37} + 6 q^{38} + 44 q^{39} + 2 q^{41} + 42 q^{42} - 14 q^{43} - 4 q^{44} - 2 q^{45} - 44 q^{46} + 10 q^{47} - 22 q^{48} + 43 q^{49} - 43 q^{50} - 90 q^{51} - 18 q^{52} + 16 q^{53} - 29 q^{54} - 8 q^{55} + 13 q^{56} + 7 q^{57} + 8 q^{58} - 84 q^{59} + 9 q^{60} - 53 q^{61} - 66 q^{62} + 11 q^{63} - 24 q^{64} + 79 q^{65} - 110 q^{66} + 46 q^{67} - 40 q^{68} - 55 q^{69} - 6 q^{70} - 14 q^{71} - 19 q^{72} + 16 q^{73} + 46 q^{74} - 44 q^{75} - 6 q^{76} - 96 q^{77} + 20 q^{78} + 20 q^{79} - 22 q^{80} - 56 q^{81} + 26 q^{82} + 57 q^{83} + 5 q^{84} - 2 q^{85} - 8 q^{86} - 198 q^{87} - 2 q^{88} + 60 q^{89} - 22 q^{90} - 252 q^{91} - 218 q^{93} - 10 q^{94} + 6 q^{95} - q^{97} + 20 q^{98} + 84 q^{99}+O(q^{100}) \) 240 * q - 12 * q^2 + 12 * q^4 - 13 * q^7 + 24 * q^8 - 36 * q^9 + 2 * q^11 + 11 * q^12 + 4 * q^13 + 2 * q^14 + 6 * q^15 + 12 * q^16 - 8 * q^17 - 18 * q^18 + 12 * q^19 - 29 * q^21 + 20 * q^22 + 10 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 - 8 * q^29 - 18 * q^30 - 12 * q^32 + 50 * q^33 - 4 * q^34 - 12 * q^35 - 4 * q^36 + 92 * q^37 + 6 * q^38 + 44 * q^39 + 2 * q^41 + 42 * q^42 - 14 * q^43 - 4 * q^44 - 2 * q^45 - 44 * q^46 + 10 * q^47 - 22 * q^48 + 43 * q^49 - 43 * q^50 - 90 * q^51 - 18 * q^52 + 16 * q^53 - 29 * q^54 - 8 * q^55 + 13 * q^56 + 7 * q^57 + 8 * q^58 - 84 * q^59 + 9 * q^60 - 53 * q^61 - 66 * q^62 + 11 * q^63 - 24 * q^64 + 79 * q^65 - 110 * q^66 + 46 * q^67 - 40 * q^68 - 55 * q^69 - 6 * q^70 - 14 * q^71 - 19 * q^72 + 16 * q^73 + 46 * q^74 - 44 * q^75 - 6 * q^76 - 96 * q^77 + 20 * q^78 + 20 * q^79 - 22 * q^80 - 56 * q^81 + 26 * q^82 + 57 * q^83 + 5 * q^84 - 2 * q^85 - 8 * q^86 - 198 * q^87 - 2 * q^88 + 60 * q^89 - 22 * q^90 - 252 * q^91 - 218 * q^93 - 10 * q^94 + 6 * q^95 - q^97 + 20 * q^98 + 84 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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