LMFDB - Embedded newform 418.2.u.b.5.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(5,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(90))

chi = DirichletCharacter(H, H._module([36, 80]))

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

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

chi := DirichletCharacter("418.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.u (of order $45$, degree $24$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$264$
Relative dimension:	$11$ over $\Q(\zeta_{45})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{45}]$

Embedding invariants

Embedding label			5.10
Character	$\chi$	$=$	418.5
Dual form			418.2.u.b.251.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.615661 - 0.788011i) q^{2} +(1.73828 - 1.67864i) q^{3} +(-0.241922 + 0.970296i) q^{4} +(2.93245 - 1.83240i) q^{5} +(-2.39298 - 0.336312i) q^{6} +(-1.22803 - 0.546756i) q^{7} +(0.913545 - 0.406737i) q^{8} +(0.0990960 - 2.83774i) q^{9} +O(q^{10})$	\(q+(-0.615661 - 0.788011i) q^{2} +(1.73828 - 1.67864i) q^{3} +(-0.241922 + 0.970296i) q^{4} +(2.93245 - 1.83240i) q^{5} +(-2.39298 - 0.336312i) q^{6} +(-1.22803 - 0.546756i) q^{7} +(0.913545 - 0.406737i) q^{8} +(0.0990960 - 2.83774i) q^{9} +(-3.24934 - 1.18266i) q^{10} +(2.28188 - 2.40687i) q^{11} +(1.20825 + 2.09275i) q^{12} +(-5.44571 + 2.89554i) q^{13} +(0.325204 + 1.30432i) q^{14} +(2.02149 - 8.10775i) q^{15} +(-0.882948 - 0.469472i) q^{16} +(0.195285 + 5.59223i) q^{17} +(-2.29718 + 1.66900i) q^{18} +(4.21427 - 1.11350i) q^{19} +(1.06854 + 3.28864i) q^{20} +(-3.05248 + 1.11101i) q^{21} +(-3.30151 - 0.316324i) q^{22} +(2.00954 - 1.68620i) q^{23} +(0.905237 - 2.24054i) q^{24} +(3.04971 - 6.25283i) q^{25} +(5.63443 + 2.50861i) q^{26} +(0.259572 + 0.288284i) q^{27} +(0.827603 - 1.05928i) q^{28} +(-1.66606 + 0.477735i) q^{29} +(-7.63355 + 3.39867i) q^{30} +(-6.99962 + 7.77386i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-0.0737269 - 8.01428i) q^{33} +(4.28651 - 3.59681i) q^{34} +(-4.60302 + 0.646912i) q^{35} +(2.72947 + 0.782664i) q^{36} +(0.0929429 - 0.0675270i) q^{37} +(-3.47202 - 2.63535i) q^{38} +(-4.60563 + 14.1747i) q^{39} +(1.93362 - 2.86671i) q^{40} +(2.43210 - 2.34866i) q^{41} +(2.75478 + 1.72138i) q^{42} +(0.379529 + 0.318463i) q^{43} +(1.78334 + 2.79637i) q^{44} +(-4.90927 - 8.50310i) q^{45} +(-2.56594 - 0.545408i) q^{46} +(-1.05650 - 1.56633i) q^{47} +(-2.32289 + 0.666077i) q^{48} +(-3.47479 - 3.85914i) q^{49} +(-6.80489 + 1.44642i) q^{50} +(9.72681 + 9.39307i) q^{51} +(-1.49209 - 5.98445i) q^{52} +(-2.20314 - 1.37667i) q^{53} +(0.0673624 - 0.382031i) q^{54} +(2.28114 - 11.2393i) q^{55} -1.34425 q^{56} +(5.45644 - 9.00984i) q^{57} +(1.40219 + 1.01875i) q^{58} +(-6.34925 + 9.41315i) q^{59} +(7.37787 + 3.92288i) q^{60} +(-3.73397 - 9.24190i) q^{61} +(10.4353 + 0.729706i) q^{62} +(-1.67324 + 3.43066i) q^{63} +(0.669131 - 0.743145i) q^{64} +(-10.6635 + 18.4697i) q^{65} +(-6.26995 + 4.99218i) q^{66} +(6.78841 + 2.47078i) q^{67} +(-5.47336 - 1.16340i) q^{68} +(0.662619 - 6.30439i) q^{69} +(3.34367 + 3.22895i) q^{70} +(5.52944 - 3.45518i) q^{71} +(-1.06368 - 2.63271i) q^{72} +(2.05911 + 4.22180i) q^{73} +(-0.110433 - 0.0316662i) q^{74} +(-5.19500 - 15.9886i) q^{75} +(0.0609012 + 4.35847i) q^{76} +(-4.11820 + 1.70809i) q^{77} +(14.0053 - 5.09751i) q^{78} +(13.0973 - 1.84071i) q^{79} +(-3.44945 + 0.241209i) q^{80} +(9.43279 + 0.659605i) q^{81} +(-3.34812 - 0.470547i) q^{82} +(-5.09393 + 1.08275i) q^{83} +(-0.339548 - 3.23059i) q^{84} +(10.8198 + 16.0411i) q^{85} +(0.0172906 - 0.495138i) q^{86} +(-2.09414 + 3.62716i) q^{87} +(1.10563 - 3.12691i) q^{88} +(-1.25206 - 7.10080i) q^{89} +(-3.67809 + 9.10358i) q^{90} +(8.27068 - 0.578342i) q^{91} +(1.14996 + 2.35778i) q^{92} +(0.882205 + 25.2630i) q^{93} +(-0.583838 + 1.79687i) q^{94} +(10.3178 - 10.9875i) q^{95} +(1.95499 + 1.42038i) q^{96} +(4.66743 + 5.97403i) q^{97} +(-0.901753 + 5.11410i) q^{98} +(-6.60395 - 6.71388i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9}+O(q^{10}) $ 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9	$ 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9} + 3 q^{11} - 6 q^{13} + 18 q^{14} - 39 q^{15} - 3 q^{17} - 78 q^{18} - 45 q^{19} - 24 q^{20} + 48 q^{21} + 6 q^{23} - 9 q^{24} + 30 q^{25} + 18 q^{26} - 24 q^{27} + 6 q^{28} - 3 q^{31} - 63 q^{33} - 36 q^{34} + 42 q^{35} - 9 q^{36} + 60 q^{37} - 3 q^{38} + 36 q^{39} + 39 q^{41} + 6 q^{42} - 60 q^{43} + 60 q^{44} - 108 q^{45} - 12 q^{46} - 24 q^{47} - 12 q^{48} + 6 q^{49} + 18 q^{50} + 96 q^{51} + 3 q^{52} - 117 q^{53} + 54 q^{54} + 102 q^{55} - 96 q^{57} - 60 q^{58} - 141 q^{59} + 36 q^{60} + 24 q^{61} - 27 q^{62} - 81 q^{63} + 33 q^{64} - 102 q^{65} + 72 q^{66} + 102 q^{67} - 21 q^{68} - 6 q^{69} - 33 q^{70} - 66 q^{71} - 12 q^{72} + 36 q^{73} + 18 q^{74} + 6 q^{76} - 174 q^{77} + 18 q^{78} + 36 q^{79} + 60 q^{81} - 36 q^{82} - 24 q^{83} + 48 q^{84} + 174 q^{85} - 21 q^{86} + 12 q^{87} + 3 q^{88} + 30 q^{89} - 48 q^{90} - 18 q^{91} + 18 q^{92} - 123 q^{93} - 120 q^{94} - 18 q^{95} - 24 q^{97} - 84 q^{98} - 141 q^{99}+O(q^{100}) $ 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9 + 3 * q^11 - 6 * q^13 + 18 * q^14 - 39 * q^15 - 3 * q^17 - 78 * q^18 - 45 * q^19 - 24 * q^20 + 48 * q^21 + 6 * q^23 - 9 * q^24 + 30 * q^25 + 18 * q^26 - 24 * q^27 + 6 * q^28 - 3 * q^31 - 63 * q^33 - 36 * q^34 + 42 * q^35 - 9 * q^36 + 60 * q^37 - 3 * q^38 + 36 * q^39 + 39 * q^41 + 6 * q^42 - 60 * q^43 + 60 * q^44 - 108 * q^45 - 12 * q^46 - 24 * q^47 - 12 * q^48 + 6 * q^49 + 18 * q^50 + 96 * q^51 + 3 * q^52 - 117 * q^53 + 54 * q^54 + 102 * q^55 - 96 * q^57 - 60 * q^58 - 141 * q^59 + 36 * q^60 + 24 * q^61 - 27 * q^62 - 81 * q^63 + 33 * q^64 - 102 * q^65 + 72 * q^66 + 102 * q^67 - 21 * q^68 - 6 * q^69 - 33 * q^70 - 66 * q^71 - 12 * q^72 + 36 * q^73 + 18 * q^74 + 6 * q^76 - 174 * q^77 + 18 * q^78 + 36 * q^79 + 60 * q^81 - 36 * q^82 - 24 * q^83 + 48 * q^84 + 174 * q^85 - 21 * q^86 + 12 * q^87 + 3 * q^88 + 30 * q^89 - 48 * q^90 - 18 * q^91 + 18 * q^92 - 123 * q^93 - 120 * q^94 - 18 * q^95 - 24 * q^97 - 84 * q^98 - 141 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.615661	−	0.788011i	−0.435338	−	0.557208i
$2$	−0.615661	−	0.788011i	−0.435338	−	0.557208i
$3$	1.73828	−	1.67864i	1.00360	−	0.969164i	0.00407404	−	0.999992i	$-0.498703\pi$
$3$	1.73828	−	1.67864i	1.00360	−	0.969164i	0.999525	+	0.0308276i	$0.00981430\pi$
$4$	−0.241922	+	0.970296i	−0.120961	+	0.485148i
$5$	2.93245	−	1.83240i	1.31143	−	0.819472i	0.319663	−	0.947531i	$-0.396430\pi$
$5$	2.93245	−	1.83240i	1.31143	−	0.819472i	0.991767	+	0.128059i	$0.0408747\pi$
$6$	−2.39298	−	0.336312i	−0.976931	−	0.137299i
$7$	−1.22803	−	0.546756i	−0.464153	−	0.206654i	0.161317	−	0.986903i	$-0.448426\pi$
$7$	−1.22803	−	0.546756i	−0.464153	−	0.206654i	−0.625470	+	0.780248i	$0.715093\pi$
$8$	0.913545	−	0.406737i	0.322987	−	0.143803i
$9$	0.0990960	−	2.83774i	0.0330320	−	0.945913i
$10$	−3.24934	−	1.18266i	−1.02753	−	0.373991i
$11$	2.28188	−	2.40687i	0.688012	−	0.725700i
$11$	2.28188	−	2.40687i	0.688012	−	0.725700i
$12$	1.20825	+	2.09275i	0.348792	+	0.604125i
$13$	−5.44571	+	2.89554i	−1.51037	+	0.803078i	−0.998434	−	0.0559460i	$-0.982183\pi$
$13$	−5.44571	+	2.89554i	−1.51037	+	0.803078i	−0.511936	+	0.859024i	$0.671071\pi$
$14$	0.325204	+	1.30432i	0.0869143	+	0.348594i
$15$	2.02149	−	8.10775i	0.521946	−	2.09341i
$16$	−0.882948	−	0.469472i	−0.220737	−	0.117368i
$17$	0.195285	+	5.59223i	0.0473636	+	1.35632i	0.757769	+	0.652523i	$0.226289\pi$
$17$	0.195285	+	5.59223i	0.0473636	+	1.35632i	−0.710406	+	0.703793i	$0.751488\pi$
$18$	−2.29718	+	1.66900i	−0.541450	+	0.393387i
$19$	4.21427	−	1.11350i	0.966821	−	0.255455i
$19$	4.21427	−	1.11350i	0.966821	−	0.255455i
$20$	1.06854	+	3.28864i	0.238933	+	0.735361i
$21$	−3.05248	+	1.11101i	−0.666106	+	0.242443i
$22$	−3.30151	−	0.316324i	−0.703883	−	0.0674406i
$23$	2.00954	−	1.68620i	0.419018	−	0.351598i	−0.408772	−	0.912637i	$-0.634043\pi$
$23$	2.00954	−	1.68620i	0.419018	−	0.351598i	0.827789	+	0.561039i	$0.189598\pi$
$24$	0.905237	−	2.24054i	0.184781	−	0.457348i
$25$	3.04971	−	6.25283i	0.609942	−	1.25057i
$26$	5.63443	+	2.50861i	1.10500	+	0.491979i
$27$	0.259572	+	0.288284i	0.0499547	+	0.0554803i
$28$	0.827603	−	1.05928i	0.156402	−	0.200186i
$29$	−1.66606	+	0.477735i	−0.309380	+	0.0887132i	−0.426735	−	0.904377i	$-0.640336\pi$
$29$	−1.66606	+	0.477735i	−0.309380	+	0.0887132i	0.117355	+	0.993090i	$0.462558\pi$
$30$	−7.63355	+	3.39867i	−1.39369	+	0.620510i
$31$	−6.99962	+	7.77386i	−1.25717	+	1.39623i	−0.373826	+	0.927499i	$0.621954\pi$
$31$	−6.99962	+	7.77386i	−1.25717	+	1.39623i	−0.883342	+	0.468728i	$0.844712\pi$
$32$	0.173648	+	0.984808i	0.0306970	+	0.174091i
$33$	−0.0737269	−	8.01428i	−0.0128342	−	1.39511i
$34$	4.28651	−	3.59681i	0.735130	−	0.616847i
$35$	−4.60302	+	0.646912i	−0.778052	+	0.109348i
$36$	2.72947	+	0.782664i	0.454912	+	0.130444i
$37$	0.0929429	−	0.0675270i	0.0152797	−	0.0111014i	−0.580119	−	0.814532i	$-0.696994\pi$
$37$	0.0929429	−	0.0675270i	0.0152797	−	0.0111014i	0.595399	+	0.803430i	$0.296994\pi$
$38$	−3.47202	−	2.63535i	−0.563236	−	0.427511i
$39$	−4.60563	+	14.1747i	−0.737491	+	2.26976i
$40$	1.93362	−	2.86671i	0.305732	−	0.453267i
$41$	2.43210	−	2.34866i	0.379831	−	0.366798i	−0.480096	−	0.877216i	$-0.659398\pi$
$41$	2.43210	−	2.34866i	0.379831	−	0.366798i	0.859927	+	0.510418i	$0.170509\pi$
$42$	2.75478	+	1.72138i	0.425072	+	0.265615i
$43$	0.379529	+	0.318463i	0.0578777	+	0.0485651i	0.671268	−	0.741215i	$-0.265750\pi$
$43$	0.379529	+	0.318463i	0.0578777	+	0.0485651i	−0.613390	+	0.789780i	$0.710195\pi$
$44$	1.78334	+	2.79637i	0.268849	+	0.421569i
$45$	−4.90927	−	8.50310i	−0.731830	−	1.26757i
$46$	−2.56594	−	0.545408i	−0.378327	−	0.0804160i
$47$	−1.05650	−	1.56633i	−0.154107	−	0.228473i	0.744076	−	0.668095i	$-0.232890\pi$
$47$	−1.05650	−	1.56633i	−0.154107	−	0.228473i	−0.898183	+	0.439622i	$0.855112\pi$
$48$	−2.32289	+	0.666077i	−0.335280	+	0.0961400i
$49$	−3.47479	−	3.85914i	−0.496398	−	0.551306i
$50$	−6.80489	+	1.44642i	−0.962356	+	0.204555i
$51$	9.72681	+	9.39307i	1.36203	+	1.31529i
$52$	−1.49209	−	5.98445i	−0.206916	−	0.829894i
$53$	−2.20314	−	1.37667i	−0.302624	−	0.189100i	0.370104	−	0.928990i	$-0.379322\pi$
$53$	−2.20314	−	1.37667i	−0.302624	−	0.189100i	−0.672728	+	0.739890i	$0.734878\pi$
$54$	0.0673624	−	0.382031i	0.00916687	−	0.0519879i
$55$	2.28114	−	11.2393i	0.307588	−	1.51551i
$56$	−1.34425			−0.179633
$57$	5.45644	−	9.00984i	0.722723	−	1.19338i
$58$	1.40219	+	1.01875i	0.184117	+	0.133769i
$59$	−6.34925	+	9.41315i	−0.826602	+	1.22549i	0.145133	+	0.989412i	$0.453639\pi$
$59$	−6.34925	+	9.41315i	−0.826602	+	1.22549i	−0.971735	+	0.236076i	$0.924139\pi$
$60$	7.37787	+	3.92288i	0.952479	+	0.506442i
$61$	−3.73397	−	9.24190i	−0.478086	−	1.18330i	−0.952918	−	0.303228i	$-0.901936\pi$
$61$	−3.73397	−	9.24190i	−0.478086	−	1.18330i	0.474832	−	0.880076i	$-0.342509\pi$
$62$	10.4353	+	0.729706i	1.32528	+	0.0926728i
$63$	−1.67324	+	3.43066i	−0.210809	+	0.432222i
$64$	0.669131	−	0.743145i	0.0836413	−	0.0928931i
$65$	−10.6635	+	18.4697i	−1.32264	+	2.29089i
$66$	−6.26995	+	4.99218i	−0.771777	+	0.614495i
$67$	6.78841	+	2.47078i	0.829336	+	0.301854i	0.721586	−	0.692324i	$-0.243413\pi$
$67$	6.78841	+	2.47078i	0.829336	+	0.301854i	0.107750	+	0.994178i	$0.465636\pi$
$68$	−5.47336	−	1.16340i	−0.663743	−	0.141083i
$69$	0.662619	−	6.30439i	0.0797699	−	0.758960i
$70$	3.34367	+	3.22895i	0.399645	+	0.385933i
$71$	5.52944	−	3.45518i	0.656224	−	0.410054i	−0.160537	−	0.987030i	$-0.551323\pi$
$71$	5.52944	−	3.45518i	0.656224	−	0.410054i	0.816762	+	0.576975i	$0.195767\pi$
$72$	−1.06368	−	2.63271i	−0.125356	−	0.310268i
$73$	2.05911	+	4.22180i	0.241001	+	0.494125i	0.984671	−	0.174422i	$-0.0558056\pi$
$73$	2.05911	+	4.22180i	0.241001	+	0.494125i	−0.743670	+	0.668547i	$0.766917\pi$
$74$	−0.110433	−	0.0316662i	−0.0128376	−	0.00368113i
$75$	−5.19500	−	15.9886i	−0.599867	−	1.84620i
$76$	0.0609012	+	4.35847i	0.00698585	+	0.499951i
$77$	−4.11820	+	1.70809i	−0.469312	+	0.194655i
$78$	14.0053	−	5.09751i	1.58579	−	0.577180i
$79$	13.0973	−	1.84071i	1.47356	−	0.207096i	0.643791	−	0.765201i	$-0.277360\pi$
$79$	13.0973	−	1.84071i	1.47356	−	0.207096i	0.829770	+	0.558105i	$0.188472\pi$
$80$	−3.44945	+	0.241209i	−0.385661	+	0.0269680i
$81$	9.43279	+	0.659605i	1.04809	+	0.0732894i
$82$	−3.34812	−	0.470547i	−0.369738	−	0.0519633i
$83$	−5.09393	+	1.08275i	−0.559132	+	0.118847i	−0.478805	−	0.877921i	$-0.658930\pi$
$83$	−5.09393	+	1.08275i	−0.559132	+	0.118847i	−0.0803272	+	0.996769i	$0.525597\pi$
$84$	−0.339548	−	3.23059i	−0.0370478	−	0.352486i
$85$	10.8198	+	16.0411i	1.17358	+	1.73990i
$86$	0.0172906	−	0.495138i	0.00186449	−	0.0533921i
$87$	−2.09414	+	3.62716i	−0.224515	+	0.388872i
$88$	1.10563	−	3.12691i	0.117861	−	0.333330i
$89$	−1.25206	−	7.10080i	−0.132718	−	0.752684i	−0.976421	−	0.215873i	$-0.930740\pi$
$89$	−1.25206	−	7.10080i	−0.132718	−	0.752684i	0.843703	−	0.536810i	$-0.180371\pi$
$90$	−3.67809	+	9.10358i	−0.387704	+	0.959602i
$91$	8.27068	−	0.578342i	0.867003	−	0.0606267i
$92$	1.14996	+	2.35778i	0.119892	+	0.245815i
$93$	0.882205	+	25.2630i	0.0914803	+	2.61965i
$94$	−0.583838	+	1.79687i	−0.0602183	+	0.185333i
$95$	10.3178	−	10.9875i	1.05858	−	1.12729i
$96$	1.95499	+	1.42038i	0.199530	+	0.144967i
$97$	4.66743	+	5.97403i	0.473905	+	0.606571i	0.964262	−	0.264951i	$-0.0853557\pi$
$97$	4.66743	+	5.97403i	0.473905	+	0.606571i	−0.490357	+	0.871522i	$0.663133\pi$
$98$	−0.901753	+	5.11410i	−0.0910908	+	0.516602i
$99$	−6.60395	−	6.71388i	−0.663722	−	0.674770i
$100$	5.32930	+	4.47182i	0.532930	+	0.447182i
$101$	−7.11950	+	3.78551i	−0.708417	+	0.376672i	−0.784247	−	0.620449i	$-0.786950\pi$
$101$	−7.11950	+	3.78551i	−0.708417	+	0.376672i	0.0758300	+	0.997121i	$0.475839\pi$
$102$	1.41342	−	13.4478i	0.139949	−	1.33153i
$103$	1.62648	+	15.4749i	0.160262	+	1.52479i	0.718745	+	0.695274i	$0.244717\pi$
$103$	1.62648	+	15.4749i	0.160262	+	1.52479i	−0.558483	+	0.829516i	$0.688616\pi$
$104$	−3.79719	+	4.86018i	−0.372345	+	0.476580i
$105$	−6.91542	+	8.85133i	−0.674876	+	0.863802i
$106$	0.271553	+	2.58366i	0.0263756	+	0.250947i
$107$	−0.560783	+	5.33550i	−0.0542130	+	0.515802i	0.933394	+	0.358854i	$0.116832\pi$
$107$	−0.560783	+	5.33550i	−0.0542130	+	0.515802i	−0.987607	+	0.156948i	$0.949834\pi$
$108$	−0.342517	+	0.182120i	−0.0329587	+	0.0175245i
$109$	−1.53506	−	1.28807i	−0.147032	−	0.123375i	0.566305	−	0.824196i	$-0.308373\pi$
$109$	−1.53506	−	1.28807i	−0.147032	−	0.123375i	−0.713337	+	0.700821i	$0.752817\pi$
$110$	−10.2611	+	5.12206i	−0.978359	+	0.488369i
$111$	0.0482076	−	0.273399i	0.00457566	−	0.0259499i
$112$	0.827603	+	1.05928i	0.0782012	+	0.100093i
$113$	−0.986997	−	0.717095i	−0.0928489	−	0.0674587i	0.540392	−	0.841413i	$-0.318276\pi$
$113$	−0.986997	−	0.717095i	−0.0928489	−	0.0674587i	−0.633241	+	0.773955i	$0.718276\pi$
$114$	−10.4592	+	1.24728i	−0.979591	+	0.116819i
$115$	2.80307	−	8.62697i	0.261388	−	0.804469i
$116$	−0.0604879	−	1.73215i	−0.00561616	−	0.160826i
$117$	7.67713	+	15.7405i	0.709751	+	1.45521i
$118$	11.3267	−	0.792037i	1.04270	−	0.0729129i
$119$	2.81777	−	6.97422i	0.258305	−	0.639326i
$120$	−1.45100	−	8.22901i	−0.132457	−	0.751202i
$121$	−0.586077	−	10.9844i	−0.0532797	−	0.998580i
$122$	−4.98386	+	8.63229i	−0.451217	+	0.781531i
$123$	0.285137	−	8.16526i	0.0257100	−	0.736237i
$124$	−5.84959	−	8.67237i	−0.525308	−	0.778802i
$125$	−0.707319	−	6.72969i	−0.0632645	−	0.601922i
$126$	3.73355	−	0.793590i	0.332611	−	0.0706986i
$127$	15.3555	+	2.15807i	1.36258	+	0.191498i	0.782291	−	0.622913i	$-0.214051\pi$
$127$	15.3555	+	2.15807i	1.36258	+	0.191498i	0.580289	+	0.814411i	$0.302940\pi$
$128$	−0.997564	−	0.0697565i	−0.0881730	−	0.00616566i
$129$	1.19431	−	0.0835146i	0.105154	−	0.00735305i
$130$	21.1194	−	2.96814i	1.85230	−	0.260323i
$131$	18.0753	−	6.57887i	1.57925	−	0.574799i	0.604207	−	0.796828i	$-0.293490\pi$
$131$	18.0753	−	6.57887i	1.57925	−	0.574799i	0.975040	+	0.222029i	$0.0712679\pi$
$132$	7.79406	+	1.86729i	0.678386	+	0.162527i
$133$	−5.78409	−	0.936761i	−0.501544	−	0.0812275i
$134$	−2.23236	−	6.87050i	−0.192847	−	0.593521i
$135$	1.28943	+	0.369739i	0.110977	+	0.0318221i
$136$	2.45297	+	5.02933i	0.210340	+	0.431261i
$137$	7.92890	+	19.6247i	0.677411	+	1.67665i	0.734786	+	0.678299i	$0.237283\pi$
$137$	7.92890	+	19.6247i	0.677411	+	1.67665i	−0.0573743	+	0.998353i	$0.518273\pi$
$138$	−5.37588	+	3.35922i	−0.457625	+	0.285956i
$139$	−12.4588	−	12.0314i	−1.05675	−	1.02049i	−0.999755	−	0.0221122i	$-0.992961\pi$
$139$	−12.4588	−	12.0314i	−1.05675	−	1.02049i	−0.0569897	−	0.998375i	$-0.518150\pi$
$140$	0.485875	−	4.62279i	0.0410639	−	0.390697i
$141$	−4.46582	−	0.949239i	−0.376090	−	0.0799403i
$142$	−6.12698	−	2.23004i	−0.514165	−	0.187141i
$143$	−5.45726	+	19.7144i	−0.456359	+	1.64860i
$144$	−1.41973	+	2.45905i	−0.118311	+	0.204921i
$145$	−4.01023	+	4.45382i	−0.333032	+	0.369869i
$146$	2.05911	−	4.22180i	0.170413	−	0.349399i
$147$	−12.5183	−	0.875364i	−1.03249	−	0.0721988i
$148$	0.0430362	+	0.106518i	0.00353755	+	0.00875575i
$149$	−14.1670	−	7.53272i	−1.16060	−	0.617105i	−0.226468	−	0.974019i	$-0.572718\pi$
$149$	−14.1670	−	7.53272i	−1.16060	−	0.617105i	−0.934137	+	0.356914i	$0.883829\pi$
$150$	−9.40080	+	13.9373i	−0.767572	+	1.13797i
$151$	6.39387	+	4.64542i	0.520326	+	0.378039i	0.816727	−	0.577025i	$-0.195786\pi$
$151$	6.39387	+	4.64542i	0.520326	+	0.378039i	−0.296401	+	0.955064i	$0.595786\pi$
$152$	3.39703	−	2.73134i	0.275535	−	0.221541i
$153$	15.8886			1.28452
$154$	3.88141	+	2.19358i	0.312773	+	0.176763i
$155$	−6.28121	+	35.6225i	−0.504519	+	2.86127i
$156$	−12.6394	−	7.89799i	−1.01196	−	0.632345i
$157$	−2.15273	−	8.63411i	−0.171806	−	0.689077i	−0.992968	−	0.118382i	$-0.962229\pi$
$157$	−2.15273	−	8.63411i	−0.171806	−	0.689077i	0.821162	−	0.570695i	$-0.193326\pi$
$158$	−9.51400	−	9.18756i	−0.756893	−	0.730923i
$159$	−6.14061	+	1.30523i	−0.486982	+	0.103511i
$160$	2.31377	+	2.56970i	0.182920	+	0.203153i
$161$	−3.38972	+	0.971988i	−0.267148	+	0.0766034i
$162$	−5.28763	−	7.83923i	−0.415435	−	0.615908i
$163$	−6.25000	−	1.32848i	−0.489538	−	0.104055i	−0.0434721	−	0.999055i	$-0.513842\pi$
$163$	−6.25000	−	1.32848i	−0.489538	−	0.104055i	−0.446066	+	0.895000i	$0.647175\pi$
$164$	1.69051	+	2.92805i	0.132007	+	0.228642i
$165$	−14.9015	−	23.3663i	−1.16008	−	1.81907i
$166$	3.98936	+	3.34747i	0.309634	+	0.259814i
$167$	3.71634	+	2.32223i	0.287579	+	0.179699i	0.666036	−	0.745920i	$-0.267990\pi$
$167$	3.71634	+	2.32223i	0.287579	+	0.179699i	−0.378457	+	0.925619i	$0.623545\pi$
$168$	−2.33669	+	2.25652i	−0.180280	+	0.174094i
$169$	14.0022	−	20.7591i	1.07709	−	1.59685i
$170$	5.97918	−	18.4020i	0.458582	−	1.41137i
$171$	−2.74221	−	12.0694i	−0.209702	−	0.922967i
$172$	−0.400819	+	0.291212i	−0.0305622	+	0.0222047i
$173$	−17.4802	−	5.01238i	−1.32900	−	0.381084i	−0.465326	−	0.885139i	$-0.654063\pi$
$173$	−17.4802	−	5.01238i	−1.32900	−	0.381084i	−0.863671	+	0.504055i	$0.831841\pi$
$174$	4.14752	−	0.582896i	0.314423	−	0.0441892i
$175$	−7.16392	+	6.01124i	−0.541541	+	0.454407i
$176$	−3.14474	+	1.05387i	−0.237043	+	0.0794382i
$177$	4.76450	+	27.0208i	0.358122	+	2.03101i
$178$	−4.82466	+	5.35833i	−0.361624	+	0.401624i
$179$	−17.0867	+	7.60750i	−1.27712	+	0.568611i	−0.929430	−	0.368997i	$-0.879701\pi$
$179$	−17.0867	+	7.60750i	−1.27712	+	0.568611i	−0.347692	+	0.937609i	$0.613034\pi$
$180$	9.43818	−	2.70635i	0.703480	−	0.201720i
$181$	−7.35697	+	9.41649i	−0.546839	+	0.699922i	−0.979457	−	0.201655i	$-0.935368\pi$
$181$	−7.35697	+	9.41649i	−0.546839	+	0.699922i	0.432617	+	0.901578i	$0.357590\pi$
$182$	−5.54768	−	6.16132i	−0.411221	−	0.456707i
$183$	−22.0045	−	9.79705i	−1.62662	−	0.724219i
$184$	1.14996	−	2.35778i	0.0847765	−	0.173818i
$185$	0.148814	−	0.368327i	0.0109410	−	0.0270800i
$186$	19.3644	−	16.2487i	1.41987	−	1.19141i
$187$	13.9054	+	12.2908i	1.01686	+	0.898789i
$188$	1.77540	−	0.646192i	0.129484	−	0.0471284i
$189$	−0.161143	−	0.495946i	−0.0117214	−	0.0360747i
$190$	−15.0105	−	1.36592i	−1.08898	−	0.0990942i
$191$	17.9013	−	13.0060i	1.29529	−	0.941083i	0.295392	−	0.955376i	$-0.404550\pi$
$191$	17.9013	−	13.0060i	1.29529	−	0.941083i	0.999898	+	0.0142931i	$0.00454978\pi$
$192$	−0.0843346	−	2.41503i	−0.00608633	−	0.174290i
$193$	−17.7815	−	9.45457i	−1.27994	−	0.680555i	−0.316526	−	0.948584i	$-0.602517\pi$
$193$	−17.7815	−	9.45457i	−1.27994	−	0.680555i	−0.963411	+	0.268029i	$0.913628\pi$
$194$	1.83405	−	7.35597i	0.131677	−	0.528128i
$195$	12.4678	+	50.0058i	0.892841	+	3.58099i
$196$	4.58514	−	2.43796i	0.327510	−	0.174140i
$197$	4.10601	+	7.11182i	0.292541	+	0.506696i	0.974410	−	0.224778i	$-0.0721658\pi$
$197$	4.10601	+	7.11182i	0.292541	+	0.506696i	−0.681869	+	0.731475i	$0.738832\pi$
$198$	−1.22481	+	9.33746i	−0.0870436	+	0.663585i
$199$	−7.51534	−	2.73536i	−0.532748	−	0.193904i	0.0616168	−	0.998100i	$-0.480374\pi$
$199$	−7.51534	−	2.73536i	−0.532748	−	0.193904i	−0.594365	+	0.804195i	$0.702597\pi$
$200$	0.242793	−	6.95267i	0.0171680	−	0.491628i
$201$	15.9477	−	7.10039i	1.12487	−	0.500823i
$202$	7.36622	+	3.27965i	0.518286	+	0.230756i
$203$	2.30718	+	0.324254i	0.161933	+	0.0227581i
$204$	−11.4672	+	7.16549i	−0.802864	+	0.501685i
$205$	2.82835	−	11.3439i	0.197540	−	0.792291i
$206$	11.1931	−	10.8090i	0.779857	−	0.753099i
$207$	−4.58587	−	5.86964i	−0.318740	−	0.407968i
$208$	6.16765			0.427650
$209$	6.93640	−	12.6841i	0.479801	−	0.877378i
$210$	11.2325			0.775116
$211$	−13.7721	−	17.6274i	−0.948108	−	1.21352i	−0.976848	−	0.213936i	$-0.931372\pi$
$211$	−13.7721	−	17.6274i	−0.948108	−	1.21352i	0.0287397	−	0.999587i	$-0.490851\pi$
$212$	1.86877	−	1.80465i	0.128347	−	0.123944i
$213$	3.81173	−	15.2880i	0.261176	−	1.04752i
$214$	4.54968	−	2.84296i	0.311010	−	0.194340i
$215$	1.69650	+	0.238427i	0.115700	+	0.0162606i
$216$	0.354387	+	0.157783i	0.0241130	+	0.0107358i
$217$	12.8462	−	5.71949i	0.872055	−	0.388264i
$218$	−0.0699345	+	2.00266i	−0.00473656	+	0.135637i
$219$	10.6662	+	3.88219i	0.720756	+	0.262334i
$220$	10.3536	+	4.93242i	0.698040	+	0.332543i
$221$	−17.2560	−	29.8882i	−1.16076	−	2.01050i
$222$	−0.245121	+	0.130333i	−0.0164514	+	0.00874738i
$223$	−6.20074	−	24.8698i	−0.415232	−	1.66540i	−0.705693	−	0.708518i	$-0.749364\pi$
$223$	−6.20074	−	24.8698i	−0.415232	−	1.66540i	0.290461	−	0.956887i	$-0.406191\pi$
$224$	0.325204	−	1.30432i	0.0217286	−	0.0871486i
$225$	−17.4417	−	9.27391i	−1.16278	−	0.618260i
$226$	0.0425772	+	1.21925i	0.00283220	+	0.0811035i
$227$	1.46441	−	1.06396i	0.0971964	−	0.0706173i	−0.538126	−	0.842865i	$-0.680867\pi$
$227$	1.46441	−	1.06396i	0.0971964	−	0.0706173i	0.635322	+	0.772247i	$0.280867\pi$
$228$	7.42218	+	7.47403i	0.491546	+	0.494980i
$229$	−2.66850	−	8.21281i	−0.176340	−	0.542718i	0.823352	−	0.567530i	$-0.192101\pi$
$229$	−2.66850	−	8.21281i	−0.176340	−	0.542718i	−0.999692	+	0.0248126i	$0.992101\pi$
$230$	−8.52389	+	3.10244i	−0.562048	+	0.204569i
$231$	−4.29132	+	9.88212i	−0.282348	+	0.650196i
$232$	−1.32771	+	1.11408i	−0.0871684	+	0.0731430i
$233$	0.209974	−	0.519705i	0.0137559	−	0.0340470i	−0.920150	−	0.391567i	$-0.871933\pi$
$233$	0.209974	−	0.519705i	0.0137559	−	0.0340470i	0.933906	+	0.357520i	$0.116378\pi$
$234$	7.67713	−	15.7405i	0.501870	−	1.02899i
$235$	−5.96828	−	2.65725i	−0.389328	−	0.173340i
$236$	−7.59752	−	8.43790i	−0.494556	−	0.549260i
$237$	19.6769	−	25.1853i	1.27815	−	1.63596i
$238$	−7.23056	+	2.07333i	−0.468687	+	0.134394i
$239$	−19.4690	+	8.66814i	−1.25934	+	0.560695i	−0.924357	−	0.381528i	$-0.875398\pi$
$239$	−19.4690	+	8.66814i	−1.25934	+	0.560695i	−0.334985	+	0.942223i	$0.608731\pi$
$240$	−5.59123	+	6.20969i	−0.360912	+	0.400833i
$241$	3.43863	+	19.5014i	0.221502	+	1.25620i	0.869261	+	0.494354i	$0.164595\pi$
$241$	3.43863	+	19.5014i	0.221502	+	1.25620i	−0.647759	+	0.761845i	$0.724294\pi$
$242$	−8.29498	+	7.22449i	−0.533222	+	0.464408i
$243$	16.6126	−	13.9396i	1.06570	−	0.894228i
$244$	9.87071	−	1.38724i	0.631907	−	0.0888088i
$245$	−17.2611	−	4.94954i	−1.10277	−	0.316215i
$246$	−6.60986	+	4.80235i	−0.421429	+	0.306186i
$247$	−19.7256	+	18.2664i	−1.25511	+	1.16226i
$248$	−3.23255	+	9.94878i	−0.205267	+	0.631748i
$249$	−7.03716	+	10.4330i	−0.445962	+	0.661166i
$250$	−4.86760	+	4.70058i	−0.307854	+	0.297291i
$251$	14.9240	+	9.32554i	0.941994	+	0.588623i	0.911673	−	0.410917i	$-0.134791\pi$
$251$	14.9240	+	9.32554i	0.941994	+	0.588623i	0.0303212	+	0.999540i	$0.490347\pi$
$252$	−2.92396	−	2.45349i	−0.184192	−	0.154556i
$253$	0.527042	−	8.68441i	0.0331349	−	0.545984i
$254$	−7.75320	−	13.4289i	−0.486479	−	0.842607i
$255$	45.7352	+	9.72131i	2.86405	+	0.608772i
$256$	0.559193	+	0.829038i	0.0349496	+	0.0518148i
$257$	7.03027	−	2.01590i	0.438536	−	0.125748i	−0.0491027	−	0.998794i	$-0.515636\pi$
$257$	7.03027	−	2.01590i	0.438536	−	0.125748i	0.487639	+	0.873046i	$0.337858\pi$
$258$	−0.801104	−	0.889716i	−0.0498745	−	0.0553913i
$259$	−0.151058	+	0.0321083i	−0.00938628	+	0.00199511i
$260$	−15.3413	−	14.8150i	−0.951430	−	0.918785i
$261$	1.19059	+	4.77519i	0.0736955	+	0.295577i
$262$	−16.3125	−	10.1932i	−1.00779	−	0.629737i
$263$	0.355862	−	2.01819i	0.0219434	−	0.124447i	−0.971868	−	0.235525i	$-0.924319\pi$
$263$	0.355862	−	2.01819i	0.0219434	−	0.124447i	0.993812	+	0.111078i	$0.0354302\pi$
$264$	−3.32706	−	7.29142i	−0.204766	−	0.448756i
$265$	−8.98318			−0.551832
$266$	2.82286	+	5.13465i	0.173081	+	0.314826i
$267$	−14.0961	−	10.2414i	−0.862670	−	0.626766i
$268$	−4.03965	+	5.98903i	−0.246761	+	0.365838i
$269$	−18.3537	−	9.75881i	−1.11904	−	0.595005i	−0.196347	−	0.980535i	$-0.562908\pi$
$269$	−18.3537	−	9.75881i	−1.11904	−	0.595005i	−0.922696	+	0.385529i	$0.874019\pi$
$270$	−0.502496	−	1.24372i	−0.0305809	−	0.0756904i
$271$	−0.358202	−	0.0250479i	−0.0217592	−	0.00152155i	0.0588727	−	0.998265i	$-0.481249\pi$
$271$	−0.358202	−	0.0250479i	−0.0217592	−	0.00152155i	−0.0806319	+	0.996744i	$0.525694\pi$
$272$	2.45297	−	5.02933i	0.148733	−	0.304948i
$273$	13.4060	−	14.8888i	0.811365	−	0.901113i
$274$	10.5830	−	18.3302i	0.639340	−	1.10737i
$275$	−8.09071	−	21.6085i	−0.487888	−	1.30304i
$276$	5.95683	+	2.16811i	0.358559	+	0.130505i
$277$	−5.92142	−	1.25864i	−0.355783	−	0.0756241i	0.0265527	−	0.999647i	$-0.491547\pi$
$277$	−5.92142	−	1.25864i	−0.355783	−	0.0756241i	−0.382336	+	0.924023i	$0.624880\pi$
$278$	−1.81042	+	17.2249i	−0.108581	+	1.03308i
$279$	21.3666	+	20.6334i	1.27918	+	1.23529i
$280$	−3.94194	+	2.46320i	−0.235576	+	0.147204i
$281$	0.703857	+	1.74211i	0.0419886	+	0.103925i	0.946721	−	0.322055i	$-0.104374\pi$
$281$	0.703857	+	1.74211i	0.0419886	+	0.103925i	−0.904732	+	0.425981i	$0.859929\pi$
$282$	2.00142	+	4.10352i	0.119183	+	0.244361i
$283$	3.59150	+	1.02985i	0.213492	+	0.0612180i	0.380679	−	0.924707i	$-0.375690\pi$
$283$	3.59150	+	1.02985i	0.213492	+	0.0612180i	−0.167186	+	0.985925i	$0.553468\pi$
$284$	2.01485	+	6.20108i	0.119559	+	0.367966i
$285$	−0.508888	−	36.4192i	−0.0301439	−	2.15729i
$286$	18.8950	−	7.83702i	1.11728	−	0.463413i
$287$	−4.27085	+	1.55446i	−0.252100	+	0.0917570i
$288$	2.81183	−	0.395178i	0.165689	−	0.0232861i
$289$	−14.2763	+	0.998298i	−0.839784	+	0.0587234i
$290$	5.97860	+	0.418065i	0.351076	+	0.0245496i
$291$	18.1416	+	2.54963i	1.06348	+	0.149462i
$292$	−4.59454	+	0.976600i	−0.268875	+	0.0571512i
$293$	1.68339	+	16.0163i	0.0983444	+	0.935685i	0.926781	+	0.375602i	$0.122564\pi$
$293$	1.68339	+	16.0163i	0.0983444	+	0.935685i	−0.828437	+	0.560083i	$0.810769\pi$
$294$	7.01723	+	10.4035i	0.409253	+	0.606743i
$295$	−1.37022	+	39.2379i	−0.0797771	+	2.28452i
$296$	0.0574419	−	0.0994922i	0.00333874	−	0.00578287i
$297$	1.28618	+	0.0330715i	0.0746315	+	0.00191900i
$298$	2.78620	+	15.8013i	0.161400	+	0.915347i
$299$	−6.06091	+	15.0013i	−0.350511	+	0.867546i
$300$	16.7704	−	1.17270i	0.968241	−	0.0677060i
$301$	−0.291953	−	0.598593i	−0.0168279	−	0.0345023i
$302$	−0.275820	−	7.89844i	−0.0158716	−	0.454504i
$303$	−6.02121	+	18.5314i	−0.345909	+	1.06460i
$304$	−4.24374	−	0.995318i	−0.243395	−	0.0570854i
$305$	−27.8845	−	20.2593i	−1.59666	−	1.16004i
$306$	−9.78202	−	12.5204i	−0.559201	−	0.715745i
$307$	0.661526	−	3.75170i	0.0377553	−	0.214121i	−0.960093	−	0.279680i	$-0.909772\pi$
$307$	0.661526	−	3.75170i	0.0377553	−	0.214121i	0.997849	+	0.0655585i	$0.0208829\pi$
$308$	−0.661073	−	4.40909i	−0.0376682	−	0.251231i
$309$	28.8041	+	24.1695i	1.63861	+	1.37496i
$310$	31.9380	−	16.9817i	1.81396	−	0.964498i
$311$	−0.433085	+	4.12052i	−0.0245580	+	0.233654i	0.975357	+	0.220632i	$0.0708118\pi$
$311$	−0.433085	+	4.12052i	−0.0245580	+	0.233654i	−0.999915	+	0.0130220i	$0.995855\pi$
$312$	1.55791	+	14.8225i	0.0881990	+	0.839158i
$313$	−8.48570	+	10.8612i	−0.479640	+	0.613911i	−0.965588	−	0.260076i	$-0.916252\pi$
$313$	−8.48570	+	10.8612i	−0.479640	+	0.613911i	0.485948	+	0.873988i	$0.338474\pi$
$314$	−5.47842	+	7.01206i	−0.309165	+	0.395713i
$315$	1.37963	+	13.1263i	0.0777331	+	0.739581i
$316$	−1.38250	+	13.1536i	−0.0777714	+	0.739946i
$317$	−24.8185	+	13.1962i	−1.39395	+	0.741175i	−0.985190	−	0.171468i	$-0.945149\pi$
$317$	−24.8185	+	13.1962i	−1.39395	+	0.741175i	−0.408757	+	0.912643i	$0.634038\pi$
$318$	4.80907	+	4.03529i	0.269679	+	0.226288i
$319$	−2.65190	+	5.10013i	−0.148478	+	0.285553i
$320$	0.600454	−	3.40534i	0.0335664	−	0.190365i
$321$	7.98158	+	10.2160i	0.445489	+	0.570199i
$322$	2.85286	+	2.07272i	0.158984	+	0.115508i
$323$	7.04995	+	23.3497i	0.392270	+	1.29921i
$324$	−2.92201	+	8.99302i	−0.162334	+	0.499612i
$325$	1.49746	+	42.8817i	0.0830642	+	2.37865i
$326$	2.80103	+	5.74296i	0.155135	+	0.318073i
$327$	−4.83058	+	0.337787i	−0.267132	+	0.0186797i
$328$	1.26655	−	3.13483i	0.0699337	−	0.173092i
$329$	0.441022	+	2.50116i	0.0243143	+	0.137893i
$330$	−9.23863	+	26.1283i	−0.508570	+	1.43832i
$331$	4.71208	−	8.16157i	0.259000	−	0.448600i	−0.706975	−	0.707239i	$-0.749940\pi$
$331$	4.71208	−	8.16157i	0.259000	−	0.448600i	0.965974	+	0.258638i	$0.0832738\pi$
$332$	0.181747	−	5.20456i	0.00997468	−	0.285638i
$333$	−0.182414	−	0.270439i	−0.00999620	−	0.0148200i
$334$	−0.458068	−	4.35822i	−0.0250643	−	0.238471i
$335$	24.4341	−	5.19362i	1.33498	−	0.283758i
$336$	3.21677	+	0.452087i	0.175489	+	0.0246634i
$337$	0.979921	+	0.0685227i	0.0533797	+	0.00373267i	0.0964213	−	0.995341i	$-0.469260\pi$
$337$	0.979921	+	0.0685227i	0.0533797	+	0.00373267i	−0.0430417	+	0.999073i	$0.513705\pi$
$338$	−24.9790	+	1.74670i	−1.35868	+	0.0950079i
$339$	−2.91943	+	0.410299i	−0.158562	+	0.0222844i
$340$	−18.1821	+	6.61776i	−0.986065	+	0.358898i
$341$	2.73844	+	34.5862i	0.148295	+	1.87295i
$342$	−7.82251	+	9.59153i	−0.422993	+	0.518650i
$343$	5.06492	+	15.5882i	0.273480	+	0.841685i
$344$	0.476248	+	0.136562i	0.0256775	+	0.00736292i
$345$	−9.60905	−	19.7015i	−0.517334	−	1.06069i
$346$	6.81210	+	16.8605i	0.366221	+	0.906428i
$347$	4.53525	−	2.83394i	0.243465	−	0.152134i	−0.402699	−	0.915333i	$-0.631928\pi$
$347$	4.53525	−	2.83394i	0.243465	−	0.152134i	0.646164	+	0.763199i	$0.276372\pi$
$348$	−3.01280	−	2.90943i	−0.161503	−	0.155962i
$349$	−3.38839	+	32.2384i	−0.181377	+	1.72568i	0.403861	+	0.914820i	$0.367668\pi$
$349$	−3.38839	+	32.2384i	−0.181377	+	1.72568i	−0.585238	+	0.810862i	$0.698999\pi$
$350$	9.14747	+	1.94436i	0.488953	+	0.103930i
$351$	−2.24829	−	0.818312i	−0.120005	−	0.0436783i
$352$	2.76655	+	1.82926i	0.147458	+	0.0974999i
$353$	−8.32083	+	14.4121i	−0.442873	+	0.767079i	−0.997901	−	0.0647526i	$-0.979374\pi$
$353$	−8.32083	+	14.4121i	−0.442873	+	0.767079i	0.555028	+	0.831832i	$0.312707\pi$
$354$	18.3594	−	20.3902i	0.975791	−	1.08373i
$355$	9.88354	−	20.2643i	0.524564	−	1.07551i
$356$	7.19278	+	0.502968i	0.381217	+	0.0266573i
$357$	−6.80914	−	16.8532i	−0.360378	−	0.891966i
$358$	16.5144	+	8.78088i	0.872815	+	0.464084i
$359$	−1.46259	+	2.16838i	−0.0771924	+	0.114442i	−0.865657	−	0.500638i	$-0.833099\pi$
$359$	−1.46259	+	2.16838i	−0.0771924	+	0.114442i	0.788464	+	0.615081i	$0.210877\pi$
$360$	−7.94336	−	5.77119i	−0.418652	−	0.304168i
$361$	16.5202	−	9.38521i	0.869486	−	0.493958i
$362$	11.9497			0.628062
$363$	−19.4576	−	18.1102i	−1.02126	−	0.950536i
$364$	−1.43970	+	8.16492i	−0.0754605	+	0.427958i
$365$	13.7742	+	8.60711i	0.720977	+	0.450516i
$366$	5.82716	+	23.3715i	0.304591	+	1.22165i
$367$	−23.0735	−	22.2818i	−1.20443	−	1.16310i	−0.982146	−	0.188119i	$-0.939761\pi$
$367$	−23.0735	−	22.2818i	−1.20443	−	1.16310i	−0.222281	−	0.974983i	$-0.571350\pi$
$368$	−2.56594	+	0.545408i	−0.133759	+	0.0284313i
$369$	−6.42386	−	7.13442i	−0.334413	−	0.371403i
$370$	−0.381865	+	0.109498i	−0.0198522	+	0.00569253i
$371$	1.95282	+	2.89518i	0.101385	+	0.150310i
$372$	−24.7260	−	5.25568i	−1.28199	−	0.272494i
$373$	−5.55153	−	9.61552i	−0.287447	−	0.497873i	0.685753	−	0.727835i	$-0.259473\pi$
$373$	−5.55153	−	9.61552i	−0.287447	−	0.497873i	−0.973200	+	0.229962i	$0.926140\pi$
$374$	1.12422	−	18.5246i	0.0581323	−	0.957882i
$375$	−12.5263	−	10.5108i	−0.646853	−	0.542774i
$376$	−1.60225	−	1.00120i	−0.0826297	−	0.0516328i
$377$	7.68959	−	7.42575i	0.396034	−	0.382446i
$378$	−0.291601	+	0.432317i	−0.0149984	+	0.0222360i
$379$	2.89114	−	8.89801i	0.148508	−	0.457060i	−0.848938	−	0.528493i	$-0.822757\pi$
$379$	2.89114	−	8.89801i	0.148508	−	0.457060i	0.997445	+	0.0714330i	$0.0227572\pi$
$380$	8.16504	+	12.6694i	0.418858	+	0.649926i
$381$	30.3148	−	22.0250i	1.55308	−	1.12838i
$382$	−21.2700	−	6.09908i	−1.08827	−	0.312056i
$383$	4.13677	−	0.581384i	0.211379	−	0.0297074i	−0.0326888	−	0.999466i	$-0.510407\pi$
$383$	4.13677	−	0.581384i	0.211379	−	0.0297074i	0.244068	+	0.969758i	$0.421518\pi$
$384$	−1.85115	+	1.55330i	−0.0944659	+	0.0792663i
$385$	−8.94648	+	12.5551i	−0.455955	+	0.639865i
$386$	3.49706	+	19.8328i	0.177995	+	1.00946i
$387$	0.941324	−	1.04545i	0.0478502	−	0.0531430i
$388$	−6.92573	+	3.08354i	−0.351601	+	0.156543i
$389$	17.3366	−	4.97118i	0.878998	−	0.252049i	0.194359	−	0.980931i	$-0.437737\pi$
$389$	17.3366	−	4.97118i	0.878998	−	0.252049i	0.684639	+	0.728882i	$0.259960\pi$
$390$	31.7291	−	40.6114i	1.60667	−	2.05644i
$391$	9.82207	+	10.9085i	0.496723	+	0.551667i
$392$	−4.74403	−	2.11218i	−0.239610	−	0.106681i
$393$	20.3764	−	41.7779i	1.02786	−	2.10742i
$394$	3.07628	−	7.61406i	0.154981	−	0.383591i
$395$	35.0342	−	29.3972i	1.76276	−	1.47913i
$396$	8.11209	−	4.78355i	0.407648	−	0.240383i
$397$	−5.03506	+	1.83261i	−0.252702	+	0.0919761i	−0.465265	−	0.885171i	$-0.654041\pi$
$397$	−5.03506	+	1.83261i	−0.252702	+	0.0919761i	0.212563	+	0.977147i	$0.431819\pi$
$398$	2.47141	+	7.60622i	0.123881	+	0.381265i
$399$	−11.6269	+	8.08105i	−0.582072	+	0.404559i
$400$	−5.62826	+	4.08917i	−0.281413	+	0.204458i
$401$	−0.576477	−	16.5081i	−0.0287879	−	0.824377i	−0.924824	−	0.380396i	$-0.875788\pi$
$401$	−0.576477	−	16.5081i	−0.0287879	−	0.824377i	0.896036	−	0.443982i	$-0.146434\pi$
$402$	−15.4136	−	8.19555i	−0.768760	−	0.408757i
$403$	15.6084	−	62.6019i	0.777510	−	3.11842i
$404$	−1.95070	−	7.82382i	−0.0970508	−	0.389250i
$405$	28.8698	−	15.3503i	1.43455	−	0.762765i
$406$	−1.16493	−	2.01772i	−0.0578145	−	0.100138i
$407$	0.0495554	−	0.377790i	0.00245637	−	0.0187264i
$408$	12.7064	+	4.62475i	0.629060	+	0.228959i
$409$	0.945630	−	27.0793i	0.0467584	−	1.33899i	−0.718619	−	0.695404i	$-0.755225\pi$
$409$	0.945630	−	27.0793i	0.0467584	−	1.33899i	0.765377	−	0.643582i	$-0.222552\pi$
$410$	−10.6804	+	4.75522i	−0.527468	+	0.234844i
$411$	46.7255	+	20.8035i	2.30480	+	1.02616i
$412$	−15.4087	−	2.16556i	−0.759134	−	0.106689i
$413$	12.9438	−	8.08818i	0.636922	−	0.397993i
$414$	−1.80200	+	7.22742i	−0.0885634	+	0.355209i
$415$	−12.9537	+	12.5092i	−0.635870	+	0.614053i
$416$	−3.79719	−	4.86018i	−0.186172	−	0.238290i
$417$	−41.8534			−2.04957
$418$	−14.2657	+	2.34316i	−0.697757	+	0.114608i
$419$	−2.97097			−0.145141			−0.0725706	−	0.997363i	$-0.523120\pi$
$419$	−2.97097			−0.145141			−0.0725706	+	0.997363i	$0.523120\pi$
$420$	−6.91542	−	8.85133i	−0.337438	−	0.431901i
$421$	−25.0601	+	24.2003i	−1.22136	+	1.17945i	−0.243560	+	0.969886i	$0.578315\pi$
$421$	−25.0601	+	24.2003i	−1.22136	+	1.17945i	−0.977795	+	0.209563i	$0.932796\pi$
$422$	−5.41168	+	21.7051i	−0.263437	+	1.05659i
$423$	−4.54954	+	2.84287i	−0.221206	+	0.138225i
$424$	−2.57261	−	0.361556i	−0.124937	−	0.0175587i
$425$	35.5628	+	15.8336i	1.72505	+	0.768042i
$426$	−14.3939	+	6.40857i	−0.697385	+	0.310496i
$427$	−0.467622	+	13.3909i	−0.0226298	+	0.648033i
$428$	−5.04134	−	1.83490i	−0.243683	−	0.0886932i
$429$	23.6072	+	43.4300i	1.13976	+	2.09682i
$430$	−0.856585	−	1.48365i	−0.0413082	−	0.0715479i
$431$	0.672675	−	0.357668i	0.0324016	−	0.0172283i	−0.453192	−	0.891413i	$-0.649715\pi$
$431$	0.672675	−	0.357668i	0.0324016	−	0.0172283i	0.485593	+	0.874185i	$0.338604\pi$
$432$	−0.0938475	−	0.376402i	−0.00451524	−	0.0181096i
$433$	−3.73507	+	14.9805i	−0.179496	+	0.719918i	0.811309	+	0.584618i	$0.198756\pi$
$433$	−3.73507	+	14.9805i	−0.179496	+	0.719918i	−0.990805	+	0.135301i	$0.956800\pi$
$434$	−12.4159	−	6.60166i	−0.595983	−	0.316890i
$435$	0.505434	+	14.4737i	0.0242337	+	0.693963i
$436$	1.62117	−	1.17785i	0.0776402	−	0.0564089i
$437$	6.59116	−	9.34375i	0.315298	−	0.446972i
$438$	−3.50757	−	10.7952i	−0.167598	−	0.515815i
$439$	−13.2169	+	4.81057i	−0.630810	+	0.229596i	−0.637584	−	0.770381i	$-0.720066\pi$
$439$	−13.2169	+	4.81057i	−0.630810	+	0.229596i	0.00677392	+	0.999977i	$0.497844\pi$
$440$	−2.48752	−	11.1955i	−0.118588	−	0.533722i
$441$	−11.2956	+	9.47812i	−0.537885	+	0.451339i
$442$	−12.9284	+	31.9989i	−0.614942	+	1.52203i
$443$	−5.73164	+	11.7516i	−0.272318	+	0.558335i	−0.990499	−	0.137522i	$-0.956086\pi$
$443$	−5.73164	+	11.7516i	−0.272318	+	0.558335i	0.718181	+	0.695857i	$0.244975\pi$
$444$	0.253615	+	0.112917i	0.0120360	+	0.00535879i
$445$	−16.6831	−	18.5284i	−0.790854	−	0.878332i
$446$	−15.7801	+	20.1976i	−0.747210	+	0.956385i
$447$	−37.2710	+	10.6873i	−1.76286	+	0.505491i
$448$	−1.22803	+	0.546756i	−0.0580192	+	0.0258318i
$449$	21.8679	−	24.2868i	1.03201	−	1.14616i	0.0428862	−	0.999080i	$-0.486345\pi$
$449$	21.8679	−	24.2868i	1.03201	−	1.14616i	0.989124	−	0.147084i	$-0.0469886\pi$
$450$	3.43023	+	19.4538i	0.161703	+	0.917062i
$451$	−0.103154	−	11.2131i	−0.00485735	−	0.528005i
$452$	0.934571	−	0.784198i	0.0439585	−	0.0368856i
$453$	18.9124	−	2.65796i	0.888580	−	0.124882i
$454$	−1.73999	−	0.498934i	−0.0816618	−	0.0234162i
$455$	23.1936	−	16.8511i	1.08733	−	0.789992i
$456$	1.32007	−	10.4502i	0.0618179	−	0.489377i
$457$	5.76631	−	17.7469i	0.269737	−	0.830165i	−0.720827	−	0.693115i	$-0.756238\pi$
$457$	5.76631	−	17.7469i	0.269737	−	0.830165i	0.990564	−	0.137050i	$-0.0437621\pi$
$458$	−4.82889	+	7.15912i	−0.225639	+	0.334524i
$459$	−1.56146	+	1.50789i	−0.0728828	+	0.0703821i
$460$	7.69259	+	4.80686i	0.358669	+	0.224121i
$461$	−13.4691	−	11.3019i	−0.627320	−	0.526384i	0.272775	−	0.962078i	$-0.412059\pi$
$461$	−13.4691	−	11.3019i	−0.627320	−	0.526384i	−0.900095	+	0.435694i	$0.856503\pi$
$462$	10.4292	−	2.70244i	0.485211	−	0.125729i
$463$	−1.80647	−	3.12890i	−0.0839539	−	0.145412i	0.820991	−	0.570941i	$-0.193422\pi$
$463$	−1.80647	−	3.12890i	−0.0839539	−	0.145412i	−0.904945	+	0.425529i	$0.860088\pi$
$464$	1.69533	+	0.360353i	0.0787036	+	0.0167290i
$465$	48.8789	+	72.4659i	2.26670	+	3.36053i
$466$	−0.538806	+	0.154500i	−0.0249597	+	0.00715708i
$467$	4.02154	+	4.46638i	0.186095	+	0.206679i	0.828972	−	0.559290i	$-0.188926\pi$
$467$	4.02154	+	4.46638i	0.186095	+	0.206679i	−0.642877	+	0.765969i	$0.722259\pi$
$468$	−17.1302	+	3.64113i	−0.791842	+	0.168311i
$469$	−6.98548	−	6.74580i	−0.322560	−	0.311492i
$470$	1.58050	+	6.33904i	0.0729030	+	0.292398i
$471$	−18.2356	−	11.3949i	−0.840253	−	0.525048i
$472$	−1.97166	+	11.1818i	−0.0907528	+	0.514685i
$473$	1.63254	−	0.186786i	0.0750642	−	0.00858842i
$474$	−31.9607			−1.46800
$475$	5.88977	−	29.7470i	0.270241	−	1.36489i
$476$	6.08538	+	4.42129i	0.278923	+	0.202649i
$477$	−4.12496	+	6.11550i	−0.188869	+	0.280009i
$478$	18.8169	+	10.0051i	0.860664	+	0.457623i
$479$	−7.99277	−	19.7828i	−0.365199	−	0.903899i	−0.992174	−	0.124860i	$-0.960152\pi$
$479$	−7.99277	−	19.7828i	−0.365199	−	0.903899i	0.626975	−	0.779039i	$-0.284293\pi$
$480$	8.33560	+	0.582882i	0.380466	+	0.0266048i
$481$	−0.310614	+	0.636852i	−0.0141628	+	0.0290380i
$482$	13.2503	−	14.7160i	0.603535	−	0.670294i
$483$	−4.26068	+	7.37972i	−0.193868	+	0.335789i
$484$	10.7999	+	2.08869i	0.490904	+	0.0949406i
$485$	24.6338	+	8.96596i	1.11856	+	0.407123i
$486$	−21.2123	−	4.50882i	−0.962210	−	0.204524i
$487$	1.61080	−	15.3257i	0.0729922	−	0.694475i	−0.895437	−	0.445188i	$-0.853137\pi$
$487$	1.61080	−	15.3257i	0.0729922	−	0.694475i	0.968430	−	0.249287i	$-0.0801963\pi$
$488$	−7.17017	−	6.92415i	−0.324578	−	0.313442i
$489$	−13.0943	+	8.18224i	−0.592146	+	0.370014i
$490$	6.72670	+	16.6492i	0.303882	+	0.752133i
$491$	−8.84305	−	18.1309i	−0.399081	−	0.818238i	−0.999823	−	0.0187948i	$-0.994017\pi$
$491$	−8.84305	−	18.1309i	−0.399081	−	0.818238i	0.600742	−	0.799443i	$-0.294872\pi$
$492$	7.85374	+	2.25202i	0.354074	+	0.101529i
$493$	−2.99696	−	9.22370i	−0.134976	−	0.415415i
$494$	26.5384	+	4.29802i	1.19402	+	0.193377i
$495$	−31.6682	−	7.58704i	−1.42338	−	0.341012i
$496$	9.82990	−	3.57779i	0.441376	−	0.160648i
$497$	−8.67948	+	1.21982i	−0.389328	+	0.0547165i
$498$	12.5538	−	0.877850i	0.562551	−	0.0393374i
$499$	−9.71143	−	0.679090i	−0.434743	−	0.0304002i	−0.149291	−	0.988793i	$-0.547699\pi$
$499$	−9.71143	−	0.679090i	−0.434743	−	0.0304002i	−0.285452	+	0.958393i	$0.592144\pi$
$500$	6.70090	+	0.941751i	0.299673	+	0.0421164i
$501$	10.3582	−	2.20171i	0.462772	−	0.0983653i
$502$	−1.83950	−	17.5016i	−0.0821008	−	0.781137i
$503$	14.3003	+	21.2011i	0.637619	+	0.945308i	0.999912	+	0.0132444i	$0.00421596\pi$
$503$	14.3003	+	21.2011i	0.637619	+	0.945308i	−0.362294	+	0.932064i	$0.618006\pi$
$504$	−0.133210	+	3.81463i	−0.00593364	+	0.169917i
$505$	−13.9410	+	24.1465i	−0.620367	+	1.07451i
$506$	−7.16789	+	4.93134i	−0.318652	+	0.219225i
$507$	−10.5073	−	59.5898i	−0.466645	−	2.64647i
$508$	−5.80880	+	14.3773i	−0.257724	+	0.637889i
$509$	10.0387	−	0.701974i	0.444957	−	0.0311144i	0.154479	−	0.987996i	$-0.450630\pi$
$509$	10.0387	−	0.701974i	0.444957	−	0.0311144i	0.290478	+	0.956882i	$0.406186\pi$
$510$	−20.4969	−	42.0248i	−0.907617	−	1.86089i
$511$	−0.220362	−	6.31035i	−0.00974826	−	0.279154i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	1.41491	+	0.925875i	0.0624700	+	0.0408784i
$514$	−5.91681	−	4.29881i	−0.260979	−	0.189613i
$515$	33.1258	+	42.3990i	1.45970	+	1.86832i
$516$	−0.207897	+	1.17904i	−0.00915215	+	0.0519044i
$517$	−6.18078	−	1.03131i	−0.271830	−	0.0453568i
$518$	0.118302	+	0.0992673i	0.00519790	+	0.00436156i
$519$	−38.7996	+	20.6301i	−1.70311	+	0.905561i
$520$	−2.22928	+	21.2102i	−0.0977603	+	0.930127i
$521$	−1.57677	−	15.0020i	−0.0690796	−	0.657248i	−0.973198	−	0.229967i	$-0.926138\pi$
$521$	−1.57677	−	15.0020i	−0.0690796	−	0.657248i	0.904119	−	0.427281i	$-0.140529\pi$
$522$	3.02990	−	3.87810i	0.132615	−	0.169740i
$523$	21.0174	−	26.9011i	0.919028	−	1.17630i	−0.0649278	−	0.997890i	$-0.520682\pi$
$523$	21.0174	−	26.9011i	0.919028	−	1.17630i	0.983956	−	0.178412i	$-0.0570961\pi$
$524$	2.01064	+	19.1300i	0.0878352	+	0.835696i
$525$	−2.36221	+	22.4749i	−0.103095	+	0.980885i
$526$	−1.80945	+	0.962101i	−0.0788957	+	0.0419496i
$527$	−44.8402	−	37.6254i	−1.95327	−	1.63899i
$528$	−3.69738	+	7.11080i	−0.160908	+	0.309458i
$529$	−2.79894	+	15.8736i	−0.121693	+	0.690156i
$530$	5.53060	+	7.07884i	0.240234	+	0.307485i
$531$	26.0829	+	18.9503i	1.13190	+	0.822374i
$532$	2.30823	−	5.38565i	0.100075	−	0.233498i
$533$	−6.44392	+	19.8324i	−0.279117	+	0.859035i
$534$	0.608081	+	17.4132i	0.0263143	+	0.753542i
$535$	8.13227	+	16.6736i	0.351589	+	0.720864i
$536$	7.20647	−	0.503926i	0.311272	−	0.0217663i
$537$	−16.9313	+	41.9065i	−0.730641	+	1.80840i
$538$	3.60959	+	20.4710i	0.155621	+	0.882568i
$539$	−17.2175	−	0.442715i	−0.741611	−	0.0190691i
$540$	−0.670698	+	1.16168i	−0.0288622	+	0.0499909i
$541$	1.50631	−	43.1351i	0.0647613	−	1.85452i	−0.340405	−	0.940279i	$-0.610564\pi$
$541$	1.50631	−	43.1351i	0.0647613	−	1.85452i	0.405166	−	0.914243i	$-0.367214\pi$
$542$	0.200793	+	0.297688i	0.00862481	+	0.0127868i
$543$	3.01841	+	28.7182i	0.129532	+	1.23242i
$544$	−5.47336	+	1.16340i	−0.234668	+	0.0498803i
$545$	−6.86174	−	0.964355i	−0.293925	−	0.0413084i
$546$	−19.9861	−	1.39756i	−0.855325	−	0.0598102i
$547$	−24.6142	+	1.72119i	−1.05243	+	0.0735927i	−0.585475	−	0.810691i	$-0.699092\pi$
$547$	−24.6142	+	1.72119i	−1.05243	+	0.0735927i	−0.466951	+	0.884283i	$0.654647\pi$
$548$	−20.9599	+	2.94573i	−0.895364	+	0.125835i
$549$	−26.5961	+	9.68020i	−1.13509	+	0.413141i
$550$	−12.0466	+	19.6791i	−0.513667	+	0.839118i
$551$	−6.48928	+	3.86847i	−0.276453	+	0.164802i
$552$	−1.95890	−	6.02886i	−0.0833762	−	0.256605i
$553$	−17.0904	−	4.90058i	−0.726756	−	0.208394i
$554$	2.65377	+	5.44103i	0.112748	+	0.231167i
$555$	−0.359609	−	0.890063i	−0.0152645	−	0.0377811i
$556$	14.6880	−	9.17811i	0.622912	−	0.389239i
$557$	25.1011	+	24.2398i	1.06357	+	1.02707i	0.999576	+	0.0291242i	$0.00927183\pi$
$557$	25.1011	+	24.2398i	1.06357	+	1.02707i	0.0639911	+	0.997950i	$0.479617\pi$
$558$	3.10481	−	29.5403i	0.131437	−	1.25054i
$559$	−2.98893	−	0.635316i	−0.126418	−	0.0268710i
$560$	4.36793	+	1.58980i	0.184579	+	0.0671812i
$561$	44.8033	−	1.97737i	1.89160	−	0.0834845i
$562$	0.939462	−	1.62720i	0.0396288	−	0.0686391i
$563$	−6.85459	+	7.61280i	−0.288887	+	0.320841i	−0.870067	−	0.492934i	$-0.835924\pi$
$563$	−6.85459	+	7.61280i	−0.288887	+	0.320841i	0.581180	+	0.813775i	$0.302591\pi$
$564$	2.00142	−	4.10352i	0.0842750	−	0.172789i
$565$	−4.20832	−	0.294274i	−0.177045	−	0.0123802i
$566$	−1.39962	−	3.46418i	−0.0588303	−	0.145610i
$567$	−11.2231	−	5.96745i	−0.471328	−	0.250609i
$568$	3.64605	−	5.40549i	0.152985	−	0.226809i
$569$	14.1472	+	10.2785i	0.593080	+	0.430898i	0.843416	−	0.537261i	$-0.180541\pi$
$569$	14.1472	+	10.2785i	0.593080	+	0.430898i	−0.250336	+	0.968159i	$0.580541\pi$
$570$	−28.3854	+	22.8229i	−1.18893	+	0.955947i
$571$	36.9866			1.54784			0.773920	−	0.633283i	$-0.218293\pi$
$571$	36.9866			1.54784			0.773920	+	0.633283i	$0.218293\pi$
$572$	−17.8086	−	10.0645i	−0.744614	−	0.420818i
$573$	9.28502	−	52.6580i	0.387887	−	2.19982i
$574$	3.85433	+	2.40845i	0.160877	+	0.100527i
$575$	−4.41503	−	17.7077i	−0.184120	−	0.738463i
$576$	−2.04254	−	1.97246i	−0.0851059	−	0.0821859i
$577$	13.3693	−	2.84174i	0.556573	−	0.118303i	0.0789667	−	0.996877i	$-0.474838\pi$
$577$	13.3693	−	2.84174i	0.556573	−	0.118303i	0.477606	+	0.878574i	$0.341505\pi$
$578$	9.57605	+	10.6353i	0.398311	+	0.442369i
$579$	−46.7801	+	13.4140i	−1.94411	+	0.557465i
$580$	−3.35135	−	4.96859i	−0.139157	−	0.206309i
$581$	6.84753	+	1.45549i	0.284083	+	0.0603838i
$582$	−9.15993	−	15.8655i	−0.379691	−	0.657645i
$583$	−8.34076	+	2.16127i	−0.345439	+	0.0895107i
$584$	3.59825	+	3.01929i	0.148897	+	0.124939i
$585$	51.3555	+	32.0905i	2.12329	+	1.32678i
$586$	11.5847	−	11.1872i	0.478558	−	0.462138i
$587$	−0.711998	+	1.05558i	−0.0293873	+	0.0435685i	−0.843445	−	0.537216i	$-0.819476\pi$
$587$	−0.711998	+	1.05558i	−0.0293873	+	0.0435685i	0.814058	+	0.580784i	$0.197254\pi$
$588$	3.87781	−	11.9347i	0.159918	−	0.492178i
$589$	−20.8421	+	40.5553i	−0.858784	+	1.67105i
$590$	31.7635	−	23.0775i	1.30768	−	0.950086i
$591$	19.0756	+	5.46984i	0.784666	+	0.224999i
$592$	−0.113766	+	0.0159887i	−0.00467574	+	0.000657133i
$593$	−1.39218	+	1.16818i	−0.0571701	+	0.0479714i	−0.670925	−	0.741525i	$-0.734103\pi$
$593$	−1.39218	+	1.16818i	−0.0571701	+	0.0479714i	0.613755	+	0.789497i	$0.289658\pi$
$594$	−0.765788	−	1.03388i	−0.0314207	−	0.0424207i
$595$	−4.51658	−	25.6148i	−0.185162	−	1.05010i
$596$	10.7363	−	11.9238i	0.439775	−	0.488419i
$597$	−17.6555	+	7.86073i	−0.722591	+	0.321718i
$598$	15.5526	−	4.45965i	0.635995	−	0.182369i
$599$	16.8745	−	21.5984i	0.689473	−	0.882486i	−0.308154	−	0.951337i	$-0.599711\pi$
$599$	16.8745	−	21.5984i	0.689473	−	0.882486i	0.997627	+	0.0688510i	$0.0219333\pi$
$600$	−11.2490	−	12.4933i	−0.459239	−	0.510036i
$601$	−25.4863	−	11.3472i	−1.03961	−	0.462864i	−0.185329	−	0.982677i	$-0.559335\pi$
$601$	−25.4863	−	11.3472i	−1.03961	−	0.462864i	−0.854280	+	0.519813i	$0.826002\pi$
$602$	−0.291953	+	0.598593i	−0.0118991	+	0.0243968i
$603$	7.68413	−	19.0189i	0.312922	−	0.774509i
$604$	−6.05425	+	5.08012i	−0.246344	+	0.206707i
$605$	−21.8464	−	31.1372i	−0.888181	−	1.26591i
$606$	18.3100	−	6.66428i	0.743791	−	0.270718i
$607$	0.366902	+	1.12921i	0.0148921	+	0.0458331i	0.958226	−	0.286011i	$-0.0923293\pi$
$607$	0.366902	+	1.12921i	0.0148921	+	0.0458331i	−0.943334	+	0.331844i	$0.892329\pi$
$608$	1.82839	+	3.95689i	0.0741509	+	0.160473i
$609$	4.55485	−	3.30929i	0.184572	−	0.134099i
$610$	1.20288	+	34.4461i	0.0487034	+	1.39468i
$611$	10.2888	+	5.47065i	0.416240	+	0.221319i
$612$	−3.84381	+	15.4167i	−0.155377	+	0.623182i
$613$	−2.48357	−	9.96105i	−0.100310	−	0.402323i	0.899059	−	0.437827i	$-0.144252\pi$
$613$	−2.48357	−	9.96105i	−0.100310	−	0.402323i	−0.999370	+	0.0355043i	$0.988696\pi$
$614$	−3.36366	+	1.78849i	−0.135746	+	0.0721775i
$615$	−14.1258	−	24.4667i	−0.569609	−	0.986591i
$616$	−3.06741	+	3.23544i	−0.123590	+	0.130360i
$617$	−26.4499	−	9.62698i	−1.06483	−	0.387568i	−0.250591	−	0.968093i	$-0.580625\pi$
$617$	−26.4499	−	9.62698i	−1.06483	−	0.387568i	−0.814242	+	0.580525i	$0.802847\pi$
$618$	1.31226	−	37.5782i	0.0527869	−	1.51162i
$619$	42.1381	−	18.7611i	1.69367	−	0.754072i	0.694265	−	0.719720i	$-0.255730\pi$
$619$	42.1381	−	18.7611i	1.69367	−	0.754072i	0.999410	−	0.0343526i	$-0.0109369\pi$
$620$	−33.0448	−	14.7125i	−1.32711	−	0.590868i
$621$	1.00773	+	0.141627i	0.0404387	+	0.00568328i
$622$	3.51365	−	2.19557i	0.140885	−	0.0880345i
$623$	−2.34483	+	9.40460i	−0.0939437	+	0.376787i
$624$	10.7211	−	10.3533i	0.429189	−	0.414463i
$625$	7.00989	+	8.97225i	0.280396	+	0.358890i
$626$	13.7831			0.550882
$627$	−9.23463	−	33.6923i	−0.368795	−	1.34554i
$628$	8.89843			0.355086
$629$	0.395777	+	0.506571i	0.0157807	+	0.0201983i
$630$	9.49426	−	9.16850i	0.378260	−	0.365282i
$631$	−4.43982	+	17.8071i	−0.176746	+	0.708891i	0.814867	+	0.579648i	$0.196810\pi$
$631$	−4.43982	+	17.8071i	−0.176746	+	0.708891i	−0.991613	+	0.129243i	$0.958745\pi$
$632$	11.2163	−	7.00872i	0.446160	−	0.278792i
$633$	−53.5299	−	7.52314i	−2.12762	−	0.299018i
$634$	25.6786	+	11.4328i	1.01983	+	0.454056i
$635$	48.9836	−	21.8089i	1.94385	−	0.865460i
$636$	0.219092	−	6.27397i	0.00868756	−	0.248779i
$637$	30.0970	+	10.9544i	1.19249	+	0.434030i
$638$	5.65163	−	1.05023i	0.223750	−	0.0415790i
$639$	−9.25695	−	16.0335i	−0.366199	−	0.634276i
$640$	−3.05312	+	1.62337i	−0.120685	+	0.0641695i
$641$	−5.86889	−	23.5388i	−0.231807	−	0.929727i	−0.967593	−	0.252514i	$-0.918743\pi$
$641$	−5.86889	−	23.5388i	−0.231807	−	0.929727i	0.735786	−	0.677214i	$-0.236813\pi$
$642$	3.13633	−	12.5791i	0.123781	−	0.496459i
$643$	−10.7803	−	5.73197i	−0.425132	−	0.226047i	0.243097	−	0.970002i	$-0.421837\pi$
$643$	−10.7803	−	5.73197i	−0.425132	−	0.226047i	−0.668230	+	0.743955i	$0.732948\pi$
$644$	−0.123067	−	3.52418i	−0.00484952	−	0.138872i
$645$	3.34923	−	2.43336i	0.131876	−	0.0958134i
$646$	14.0595	−	19.9310i	0.553163	−	0.784174i
$647$	10.6373	+	32.7383i	0.418196	+	1.28708i	0.909360	+	0.416009i	$0.136572\pi$
$647$	10.6373	+	32.7383i	0.418196	+	1.28708i	−0.491164	+	0.871067i	$0.663428\pi$
$648$	8.88557	−	3.23408i	0.349058	−	0.127047i
$649$	8.16805	+	36.7615i	0.320624	+	1.44301i
$650$	32.8693	−	27.5806i	1.28924	−	1.08180i
$651$	12.7293	−	31.5062i	0.498902	−	1.23483i
$652$	2.80103	−	5.74296i	0.109697	−	0.224912i
$653$	25.0457	+	11.1511i	0.980113	+	0.436374i	0.833319	−	0.552793i	$-0.186438\pi$
$653$	25.0457	+	11.1511i	0.980113	+	0.436374i	0.146794	+	0.989167i	$0.453104\pi$
$654$	3.24018	+	3.59859i	0.126701	+	0.140716i
$655$	40.9498	−	52.4133i	1.60004	−	2.04796i
$656$	−3.25005	+	0.931936i	−0.126893	+	0.0363860i
$657$	12.1844	−	5.42486i	0.475360	−	0.211644i
$658$	1.69942	−	1.88740i	0.0662503	−	0.0735785i
$659$	−0.406613	−	2.30602i	−0.0158394	−	0.0898297i	0.975863	−	0.218382i	$-0.0700780\pi$
$659$	−0.406613	−	2.30602i	−0.0158394	−	0.0898297i	−0.991703	+	0.128553i	$0.958967\pi$
$660$	26.2773	−	8.80606i	1.02284	−	0.342776i
$661$	−19.8990	+	16.6972i	−0.773980	+	0.649446i	−0.941725	−	0.336384i	$-0.890796\pi$
$661$	−19.8990	+	16.6972i	−0.773980	+	0.649446i	0.167745	+	0.985830i	$0.446352\pi$
$662$	−9.33245	+	1.31159i	−0.362716	+	0.0509764i
$663$	−80.1674	−	22.9876i	−3.11345	−	0.892766i
$664$	−4.21315	+	3.06103i	−0.163502	+	0.118791i
$665$	−18.6780	+	7.85173i	−0.724303	+	0.304477i
$666$	−0.100804	+	0.310243i	−0.00390608	+	0.0120217i
$667$	−2.54246	+	3.76934i	−0.0984443	+	0.145950i
$668$	−3.15231	+	3.04415i	−0.121967	+	0.117782i
$669$	−52.5261	−	32.8220i	−2.03078	−	1.26897i
$670$	−19.1358	−	16.0568i	−0.739279	−	0.620328i
$671$	−30.7645	−	12.1017i	−1.18765	−	0.467180i
$672$	−1.62419	−	2.81318i	−0.0626545	−	0.108521i
$673$	−41.8164	−	8.88834i	−1.61190	−	0.342620i	−0.688137	−	0.725581i	$-0.741571\pi$
$673$	−41.8164	−	8.88834i	−1.61190	−	0.342620i	−0.923765	+	0.382960i	$0.874905\pi$
$674$	−0.549303	−	0.814375i	−0.0211584	−	0.0313685i
$675$	2.59421	−	0.743879i	0.0998513	−	0.0286319i
$676$	16.7550	+	18.6083i	0.644423	+	0.715704i
$677$	19.4697	−	4.13841i	0.748281	−	0.159052i	0.182039	−	0.983291i	$-0.441730\pi$
$677$	19.4697	−	4.13841i	0.748281	−	0.159052i	0.566242	+	0.824239i	$0.308397\pi$
$678$	2.12070	+	2.04793i	0.0814449	+	0.0786505i
$679$	−2.46542	−	9.88826i	−0.0946142	−	0.379477i
$680$	16.4089	+	10.2534i	0.629253	+	0.393201i
$681$	0.759560	−	4.30768i	0.0291064	−	0.165071i
$682$	25.5683	−	23.4513i	0.979062	−	0.897997i
$683$	−32.7623			−1.25362			−0.626808	−	0.779174i	$-0.715639\pi$
$683$	−32.7623			−1.25362			−0.626808	+	0.779174i	$0.715639\pi$
$684$	12.3742	+	0.259086i	0.473141	+	0.00990638i
$685$	59.2113	+	43.0195i	2.26235	+	1.64369i
$686$	9.16542	−	13.5883i	0.349937	−	0.518803i
$687$	−18.4250	−	9.79674i	−0.702957	−	0.373769i
$688$	−0.185595	−	0.459364i	−0.00707575	−	0.0175131i
$689$	15.9839	+	1.11770i	0.608936	+	0.0425810i
$690$	−9.60905	+	19.7015i	−0.365810	+	0.750022i
$691$	−7.56381	+	8.40046i	−0.287741	+	0.319569i	−0.869634	−	0.493696i	$-0.835645\pi$
$691$	−7.56381	+	8.40046i	−0.287741	+	0.319569i	0.581893	+	0.813265i	$0.302312\pi$
$692$	9.09234	−	15.7484i	0.345639	−	0.598664i
$693$	4.43902	+	11.8556i	0.168625	+	0.450358i
$694$	−5.02536	−	1.82908i	−0.190760	−	0.0694309i
$695$	−58.5811	−	12.4518i	−2.22211	−	0.472324i
$696$	−0.437795	+	4.16534i	−0.0165946	+	0.157887i
$697$	13.6092	+	13.1422i	0.515484	+	0.497798i
$698$	27.4903	−	17.1779i	1.04052	−	0.650191i
$699$	−0.507403	−	1.25587i	−0.0191917	−	0.0475012i
$700$	−4.09957	−	8.40537i	−0.154949	−	0.317693i
$701$	19.7689	+	5.66863i	0.746660	+	0.214101i	0.627330	−	0.778753i	$-0.284148\pi$
$701$	19.7689	+	5.66863i	0.746660	+	0.214101i	0.119330	+	0.992855i	$0.461925\pi$
$702$	0.739350	+	2.27548i	0.0279050	+	0.0858826i
$703$	0.316495	−	0.388069i	0.0119369	−	0.0146363i
$704$	−0.261782	−	3.30628i	−0.00986627	−	0.124610i
$705$	−14.8351	+	5.39955i	−0.558724	+	0.203359i
$706$	16.4797	−	2.31607i	0.620222	−	0.0871665i
$707$	10.8127	−	0.756100i	0.406655	−	0.0284361i
$708$	−27.3708	−	1.91396i	−1.02866	−	0.0719309i
$709$	−19.5991	−	2.75447i	−0.736060	−	0.103446i	−0.238825	−	0.971063i	$-0.576762\pi$
$709$	−19.5991	−	2.75447i	−0.736060	−	0.103446i	−0.497235	+	0.867616i	$0.665651\pi$
$710$	−22.0534	+	4.68759i	−0.827648	+	0.175922i
$711$	−3.92555	−	37.3491i	−0.147220	−	1.40070i
$712$	−4.03197	−	5.97765i	−0.151105	−	0.224022i
$713$	−0.957690	+	27.4247i	−0.0358658	+	1.02706i
$714$	−9.08839	+	15.7415i	−0.340124	+	0.589113i
$715$	20.1215	+	67.8113i	0.752501	+	2.53600i
$716$	−3.24787	−	18.4196i	−0.121379	−	0.688373i
$717$	−19.2919	+	47.7491i	−0.720469	+	1.78322i
$718$	2.60916	−	0.182450i	0.0973731	−	0.00680899i
$719$	2.08247	+	4.26969i	0.0776629	+	0.159233i	0.934092	−	0.357032i	$-0.116211\pi$
$719$	2.08247	+	4.26969i	0.0776629	+	0.159233i	−0.856429	+	0.516264i	$0.827322\pi$
$720$	0.342662	+	9.81255i	0.0127703	+	0.365692i
$721$	6.46364	−	19.8930i	0.240718	−	0.740855i
$722$	−17.5665	−	7.24000i	−0.653758	−	0.269445i
$723$	38.7133	+	28.1268i	1.43976	+	1.04605i
$724$	−7.35697	−	9.41649i	−0.273420	−	0.349961i
$725$	−2.09380	+	11.8746i	−0.0777619	+	0.441010i
$726$	−2.29170	+	26.4825i	−0.0850531	+	0.982858i
$727$	1.74330	+	1.46281i	0.0646555	+	0.0542524i	0.674543	−	0.738236i	$-0.264341\pi$
$727$	1.74330	+	1.46281i	0.0646555	+	0.0542524i	−0.609887	+	0.792488i	$0.708785\pi$
$728$	7.32041	−	3.89233i	0.271312	−	0.144259i
$729$	2.51258	−	23.9056i	0.0930584	−	0.885392i
$730$	−1.69778	−	16.1533i	−0.0628377	−	0.597861i
$731$	−1.70680	+	2.18461i	−0.0631283	+	0.0808006i
$732$	14.8294	−	18.9808i	0.548111	−	0.701550i
$733$	−1.53007	−	14.5576i	−0.0565143	−	0.537698i	−0.985751	−	0.168212i	$-0.946201\pi$
$733$	−1.53007	−	14.5576i	−0.0565143	−	0.537698i	0.929236	−	0.369486i	$-0.120466\pi$
$734$	−3.35285	+	31.9002i	−0.123756	+	1.17746i
$735$	−38.3132	+	20.3715i	−1.41320	+	0.751414i
$736$	2.00954	+	1.68620i	0.0740726	+	0.0621543i
$737$	21.4372	−	10.7008i	0.789648	−	0.394170i
$738$	−1.66708	+	9.45446i	−0.0613659	+	0.348023i
$739$	14.5499	+	18.6231i	0.535228	+	0.685060i	0.977286	−	0.211926i	$-0.0679737\pi$
$739$	14.5499	+	18.6231i	0.535228	+	0.685060i	−0.442058	+	0.896986i	$0.645751\pi$
$740$	0.321385	+	0.233500i	0.0118143	+	0.00858363i
$741$	−3.62586	+	64.8643i	−0.133199	+	2.38285i
$742$	1.07915	−	3.32129i	0.0396170	−	0.121929i
$743$	−1.34161	−	38.4187i	−0.0492189	−	1.40945i	−0.733233	−	0.679977i	$-0.761990\pi$
$743$	−1.34161	−	38.4187i	−0.0492189	−	1.40945i	0.684015	−	0.729468i	$-0.260232\pi$
$744$	11.0813	+	22.7201i	0.406261	+	0.832959i
$745$	−55.3469	+	3.87023i	−2.02775	+	0.141794i
$746$	−4.15928	+	10.2946i	−0.152282	+	0.376911i
$747$	2.56777	+	14.5626i	0.0939498	+	0.532816i
$748$	−15.2897	+	10.5190i	−0.559046	+	0.384611i
$749$	3.60588	−	6.24556i	0.131756	−	0.228208i
$750$	−0.570672	+	16.3419i	−0.0208380	+	0.596722i
$751$	4.30509	+	6.38256i	0.157095	+	0.232903i	0.899366	−	0.437197i	$-0.144029\pi$
$751$	4.30509	+	6.38256i	0.157095	+	0.232903i	−0.742271	+	0.670100i	$0.766251\pi$
$752$	0.197490	+	1.87899i	0.00720171	+	0.0685197i
$753$	41.5964	−	8.84158i	1.51586	−	0.322205i
$754$	−10.5858	−	1.48773i	−0.385511	−	0.0541800i
$755$	27.2619	+	1.90634i	0.992163	+	0.0693788i
$756$	0.520198	−	0.0363758i	0.0189194	−	0.00132297i
$757$	35.5852	−	5.00117i	1.29337	−	0.181771i	0.541284	−	0.840840i	$-0.317938\pi$
$757$	35.5852	−	5.00117i	1.29337	−	0.181771i	0.752082	+	0.659069i	$0.229050\pi$
$758$	−8.79169	+	3.19991i	−0.319329	+	0.116226i
$759$	−13.6619	−	15.9807i	−0.495894	−	0.580062i
$760$	4.95672	−	14.2342i	0.179799	−	0.516328i
$761$	7.62876	+	23.4789i	0.276542	+	0.851109i	0.988807	+	0.149199i	$0.0476694\pi$
$761$	7.62876	+	23.4789i	0.276542	+	0.851109i	−0.712265	+	0.701911i	$0.752331\pi$
$762$	−36.0196	−	10.3285i	−1.30485	−	0.374161i
$763$	1.18085	+	2.42110i	0.0427496	+	0.0876497i
$764$	8.28899	+	20.5160i	0.299885	+	0.742241i
$765$	46.5926	−	29.1143i	1.68456	−	1.05263i
$766$	−3.00498	−	2.90188i	−0.108574	−	0.104849i
$767$	7.32007	−	69.6458i	0.264312	−	2.51477i
$768$	2.36369	+	0.502418i	0.0852924	+	0.0181295i
$769$	24.3265	+	8.85412i	0.877236	+	0.319288i	0.741094	−	0.671402i	$-0.234307\pi$
$769$	24.3265	+	8.85412i	0.877236	+	0.319288i	0.136142	+	0.990689i	$0.456530\pi$
$770$	15.4015	−	0.679737i	0.555032	−	0.0244960i
$771$	8.83663	−	15.3055i	0.318243	−	0.551214i
$772$	13.4755	−	14.9660i	0.484992	−	0.538638i
$773$	−14.2907	+	29.3003i	−0.514000	+	1.05386i	0.471132	+	0.882062i	$0.343845\pi$
$773$	−14.2907	+	29.3003i	−0.514000	+	1.05386i	−0.985133	+	0.171794i	$0.945044\pi$
$774$	−1.40336	−	0.0981325i	−0.0504427	−	0.00352730i
$775$	27.2619	+	67.4754i	0.979275	+	2.42379i
$776$	6.69377	+	3.55914i	0.240292	+	0.127766i
$777$	−0.208683	+	0.309385i	−0.00748646	+	0.0110991i
$778$	−14.5908	−	10.6008i	−0.523105	−	0.380058i
$779$	7.63432	−	12.6060i	0.273528	−	0.451658i
$780$	−51.5366			−1.84531
$781$	4.30133	−	21.1930i	0.153914	−	0.758344i
$782$	2.54896	−	14.4558i	0.0911505	−	0.516940i
$783$	−0.570187	−	0.356292i	−0.0203768	−	0.0127328i
$784$	1.25630	+	5.03874i	0.0448678	+	0.179955i
$785$	−22.1339	−	21.3744i	−0.789991	−	0.762885i
$786$	−45.4664	+	9.66419i	−1.62173	+	0.344710i
$787$	−15.0933	−	16.7628i	−0.538018	−	0.597529i	0.411435	−	0.911439i	$-0.365028\pi$
$787$	−15.0933	−	16.7628i	−0.538018	−	0.597529i	−0.949453	+	0.313910i	$0.898361\pi$
$788$	−7.89390	+	2.26354i	−0.281209	+	0.0806353i
$789$	−2.76923	−	4.10556i	−0.0985873	−	0.146162i
$790$	−44.7345	−	9.50862i	−1.59158	−	0.338301i
$791$	0.819990	+	1.42026i	0.0291555	+	0.0504988i
$792$	−8.76379	−	3.44737i	−0.311408	−	0.122497i
$793$	47.0944	+	39.5169i	1.67237	+	1.40329i
$794$	4.54401	+	2.83941i	0.161261	+	0.100767i
$795$	−15.6153	+	15.0795i	−0.553818	+	0.534816i
$796$	4.47223	−	6.63036i	0.158514	−	0.235007i
$797$	−14.2580	+	43.8815i	−0.505043	+	1.55436i	0.295656	+	0.955295i	$0.404462\pi$
$797$	−14.2580	+	43.8815i	−0.505043	+	1.55436i	−0.800699	+	0.599067i	$0.795538\pi$
$798$	13.5262	+	4.18691i	0.478821	+	0.148215i
$799$	8.55298	−	6.21410i	0.302583	−	0.219839i
$800$	6.68741	+	1.91758i	0.236436	+	0.0677969i
$801$	−20.2743	+	2.84937i	−0.716357	+	0.100677i
$802$	−12.6537	+	10.6177i	−0.446817	+	0.374924i
$803$	14.8600	+	4.67762i	0.524398	+	0.165070i
$804$	3.03137	+	17.1918i	0.106908	+	0.606306i
$805$	−8.15912	+	9.06162i	−0.287571	+	0.319380i
$806$	−58.9405	+	26.2420i	−2.07609	+	0.924335i
$807$	−48.2854	+	13.8456i	−1.69973	+	0.487389i
$808$	−4.96428	+	6.35399i	−0.174643	+	0.223533i
$809$	10.6999	+	11.8834i	0.376188	+	0.417799i	0.901274	−	0.433250i	$-0.142633\pi$
$809$	10.6999	+	11.8834i	0.376188	+	0.417799i	−0.525086	+	0.851049i	$0.675967\pi$
$810$	−29.8703	−	13.2991i	−1.04953	−	0.467283i
$811$	−0.882048	+	1.80847i	−0.0309729	+	0.0635039i	−0.913719	−	0.406346i	$-0.866803\pi$
$811$	−0.882048	+	1.80847i	−0.0309729	+	0.0635039i	0.882747	+	0.469849i	$0.155692\pi$
$812$	−0.872780	+	2.16021i	−0.0306286	+	0.0758084i
$813$	−0.664704	+	0.557753i	−0.0233122	+	0.0195612i
$814$	−0.328212	+	0.193541i	−0.0115038	+	0.00678359i
$815$	−20.7621	+	7.55678i	−0.727264	+	0.264703i
$816$	−4.17848	−	12.8601i	−0.146276	−	0.450192i
$817$	1.95405	+	0.919483i	0.0683635	+	0.0321686i
$818$	−21.9210	+	15.9265i	−0.766449	+	0.556858i
$819$	−0.821592	−	23.5273i	−0.0287088	−	0.822111i
$820$	10.3227	+	5.48867i	0.360484	+	0.191673i
$821$	−9.20398	+	36.9152i	−0.321221	+	1.28835i	0.565002	+	0.825089i	$0.308875\pi$
$821$	−9.20398	+	36.9152i	−0.321221	+	1.28835i	−0.886223	+	0.463258i	$0.846680\pi$
$822$	−12.3737	−	49.6282i	−0.431582	−	1.73098i
$823$	37.7018	−	20.0464i	1.31420	−	0.698773i	0.343520	−	0.939145i	$-0.388381\pi$
$823$	37.7018	−	20.0464i	1.31420	−	0.698773i	0.970681	+	0.240372i	$0.0772695\pi$
$824$	7.78009	+	13.4755i	0.271032	+	0.469441i
$825$	−50.3368	−	23.9802i	−1.75250	−	0.834884i
$826$	−14.3426	−	5.22027i	−0.499042	−	0.181636i
$827$	−1.07538	+	30.7947i	−0.0373945	+	1.07084i	0.825168	+	0.564887i	$0.191080\pi$
$827$	−1.07538	+	30.7947i	−0.0373945	+	1.07084i	−0.862563	+	0.505950i	$0.831142\pi$
$828$	6.80471	−	3.02965i	0.236480	−	0.105288i
$829$	−11.3945	−	5.07315i	−0.395747	−	0.176198i	0.199208	−	0.979957i	$-0.436163\pi$
$829$	−11.3945	−	5.07315i	−0.395747	−	0.176198i	−0.594954	+	0.803760i	$0.702830\pi$
$830$	17.8325	+	2.50619i	0.618974	+	0.0869911i
$831$	−12.4059	+	7.75207i	−0.430356	+	0.268916i
$832$	−1.49209	+	5.98445i	−0.0517289	+	0.207473i
$833$	20.9026	−	20.1855i	0.724234	−	0.699384i
$834$	25.7675	+	32.9809i	0.892255	+	1.14203i
$835$	15.1532			0.524398
$836$	10.6293	+	9.79892i	0.367621	+	0.338903i
$837$	−4.05799			−0.140265
$838$	1.82911	+	2.34115i	0.0631855	+	0.0808738i
$839$	0.488826	−	0.472054i	0.0168762	−	0.0162971i	−0.686172	−	0.727439i	$-0.740710\pi$
$839$	0.488826	−	0.472054i	0.0168762	−	0.0162971i	0.703049	+	0.711142i	$0.251822\pi$
$840$	−2.71739	+	10.8988i	−0.0937588	+	0.376046i
$841$	−22.0459	+	13.7758i	−0.760202	+	0.475027i
$842$	34.4986	+	4.84847i	1.18890	+	0.167089i
$843$	4.14788	+	1.84675i	0.142861	+	0.0636056i
$844$	20.4356	−	9.09851i	0.703422	−	0.313184i
$845$	3.02177	−	86.5323i	0.103952	−	2.97680i
$846$	5.04119	+	1.83484i	0.173320	+	0.0630832i
$847$	−5.28605	+	13.8096i	−0.181631	+	0.474505i
$848$	1.29894	+	2.24984i	0.0446059	+	0.0772598i
$849$	7.97179	−	4.23867i	0.273591	−	0.145471i
$850$	−9.41762	−	37.7720i	−0.323022	−	1.29557i
$851$	0.0729082	−	0.292419i	0.00249926	−	0.0100240i
$852$	13.9118	+	7.39702i	0.476609	+	0.253418i
$853$	−0.296835	−	8.50024i	−0.0101634	−	0.291043i	−0.993821	−	0.110994i	$-0.964597\pi$
$853$	−0.296835	−	8.50024i	−0.0101634	−	0.291043i	0.983658	−	0.180049i	$-0.0576256\pi$
$854$	10.8401	−	7.87580i	0.370941	−	0.269504i
$855$	−30.1572	−	30.3679i	−1.03135	−	1.03856i
$856$	1.65784	+	5.10231i	0.0566638	+	0.174393i
$857$	40.9917	−	14.9198i	1.40025	−	0.509649i	0.471998	−	0.881600i	$-0.343533\pi$
$857$	40.9917	−	14.9198i	1.40025	−	0.509649i	0.928253	+	0.371950i	$0.121311\pi$
$858$	19.6893	−	45.3409i	0.672182	−	1.54791i
$859$	0.227624	−	0.190999i	0.00776643	−	0.00651681i	−0.638896	−	0.769293i	$-0.720609\pi$
$859$	0.227624	−	0.190999i	0.00776643	−	0.00651681i	0.646663	+	0.762776i	$0.276164\pi$
$860$	−0.641765	+	1.58842i	−0.0218840	+	0.0541648i
$861$	−4.81456	+	9.87132i	−0.164080	+	0.336414i
$862$	−0.695986	−	0.309873i	−0.0237054	−	0.0105543i
$863$	2.37551	+	2.63827i	0.0808632	+	0.0898077i	0.782219	−	0.623004i	$-0.214088\pi$
$863$	2.37551	+	2.63827i	0.0808632	+	0.0898077i	−0.701355	+	0.712812i	$0.747421\pi$
$864$	−0.238830	+	0.305689i	−0.00812517	+	0.0103997i
$865$	−60.4445	+	17.3322i	−2.05517	+	0.589312i
$866$	14.1044	−	6.27966i	0.479286	−	0.213392i
$867$	−23.1405	+	25.7002i	−0.785893	+	0.872823i
$868$	2.44182	+	13.8483i	0.0828808	+	0.470041i
$869$	25.4561	−	35.7238i	0.863538	−	1.21185i
$870$	11.0943	−	9.30921i	0.376132	−	0.315612i
$871$	−44.1220	+	6.20094i	−1.49502	+	0.210111i
$872$	−1.92625	−	0.552345i	−0.0652312	−	0.0187048i
$873$	17.4153	−	12.6529i	0.589418	−	0.428237i
$874$	−11.4209	+	0.558684i	−0.386318	+	0.0188978i
$875$	−2.81089	+	8.65102i	−0.0950253	+	0.292458i
$876$	−6.34726	+	9.41020i	−0.214454	+	0.317941i
$877$	26.8862	−	25.9637i	0.907883	−	0.876733i	−0.0849322	−	0.996387i	$-0.527067\pi$
$877$	26.8862	−	25.9637i	0.907883	−	0.876733i	0.992816	+	0.119654i	$0.0381785\pi$
$878$	11.9279	+	7.45340i	0.402548	+	0.251540i
$879$	29.8119	+	25.0152i	1.00553	+	0.843740i
$880$	−7.29067	+	8.85281i	−0.245768	+	0.298428i
$881$	16.8173	+	29.1284i	0.566589	+	0.981361i	0.996900	+	0.0786802i	$0.0250706\pi$
$881$	16.8173	+	29.1284i	0.566589	+	0.981361i	−0.430311	+	0.902681i	$0.641596\pi$
$882$	14.4231	+	3.06573i	0.485651	+	0.103228i
$883$	−0.894542	−	1.32621i	−0.0301037	−	0.0446306i	0.813685	−	0.581306i	$-0.197458\pi$
$883$	−0.894542	−	1.32621i	−0.0301037	−	0.0446306i	−0.843789	+	0.536675i	$0.819680\pi$
$884$	33.1750	−	9.51279i	1.11580	−	0.319950i
$885$	63.4845	+	70.5067i	2.13401	+	2.37006i
$886$	12.7891	−	2.71841i	0.429659	−	0.0913269i
$887$	4.04576	+	3.90695i	0.135843	+	0.131182i	0.759476	−	0.650535i	$-0.225455\pi$
$887$	4.04576	+	3.90695i	0.135843	+	0.131182i	−0.623633	+	0.781717i	$0.714344\pi$
$888$	−0.0671615	−	0.269370i	−0.00225379	−	0.00903947i
$889$	−17.6771	−	11.0459i	−0.592872	−	0.370468i
$890$	−4.32948	+	24.5537i	−0.145124	+	0.823042i
$891$	23.1121	−	21.1984i	0.774283	−	0.710173i
$892$	25.6312			0.858194
$893$	−6.19652	−	5.42454i	−0.207359	−	0.181525i
$894$	31.3680	+	22.7902i	1.04910	+	0.762218i
$895$	−36.1660	+	53.6182i	−1.20889	+	1.79226i
$896$	1.18690	+	0.631088i	0.0396516	+	0.0210832i
$897$	14.6462	+	36.2506i	0.489022	+	1.21037i
$898$	−32.6015	−	2.27972i	−1.08792	−	0.0760751i
$899$	7.94794	−	16.2957i	0.265079	−	0.543492i
$900$	13.2180	−	14.6800i	0.440599	−	0.489334i
$901$	7.26843	−	12.5893i	0.242146	−	0.419410i
$902$	−8.77254	+	6.98477i	−0.292094	+	0.232567i
$903$	−1.51232	−	0.550440i	−0.0503269	−	0.0183175i
$904$	−1.19334	−	0.253651i	−0.0396898	−	0.00843632i
$905$	−4.31918	+	41.0942i	−0.143574	+	1.36602i
$906$	−13.7381	−	13.2667i	−0.456418	−	0.440758i
$907$	24.6841	−	15.4244i	0.819624	−	0.512158i	−0.0541258	−	0.998534i	$-0.517237\pi$
$907$	24.6841	−	15.4244i	0.819624	−	0.512158i	0.873749	+	0.486376i	$0.161682\pi$
$908$	0.678080	+	1.67831i	0.0225029	+	0.0556966i
$909$	10.0368	+	20.5784i	0.332898	+	0.682543i
$910$	−27.5582	−	7.90220i	−0.913547	−	0.261955i
$911$	12.5975	+	38.7710i	0.417373	+	1.28454i	0.910111	+	0.414364i	$0.135996\pi$
$911$	12.5975	+	38.7710i	0.417373	+	1.28454i	−0.492739	+	0.870177i	$0.664004\pi$
$912$	−9.04761	+	5.39357i	−0.299596	+	0.178599i
$913$	−9.01769	+	14.7312i	−0.298442	+	0.487530i
$914$	−17.5348	+	6.38216i	−0.580001	+	0.211103i
$915$	−82.4792	+	11.5917i	−2.72668	+	0.383210i
$916$	8.61443	−	0.602379i	0.284629	−	0.0199032i
$917$	−25.7941	−	1.80370i	−0.851797	−	0.0595635i
$918$	2.14956	+	0.302101i	0.0709461	+	0.00997083i
$919$	−11.0244	+	2.34331i	−0.363662	+	0.0772988i	−0.386119	−	0.922449i	$-0.626185\pi$
$919$	−11.0244	+	2.34331i	−0.363662	+	0.0772988i	0.0224566	+	0.999748i	$0.492851\pi$
$920$	−0.948171	−	9.02124i	−0.0312603	−	0.297421i
$921$	−5.14784	−	7.63199i	−0.169627	−	0.251483i
$922$	−0.613628	+	17.5720i	−0.0202088	+	0.578703i
$923$	−20.1072	+	34.8266i	−0.661835	+	1.14633i
$924$	−8.55042	−	6.55455i	−0.281288	−	0.215629i
$925$	−0.138786	−	0.787094i	−0.00456325	−	0.0258795i
$926$	−1.35343	+	3.34987i	−0.0444766	+	0.110083i
$927$	44.0750	−	3.08202i	1.44761	−	0.101227i
$928$	−0.759786	−	1.55779i	−0.0249412	−	0.0511370i
$929$	−0.970847	−	27.8014i	−0.0318525	−	0.912135i	−0.905187	−	0.425014i	$-0.860269\pi$
$929$	−0.970847	−	27.8014i	−0.0318525	−	0.912135i	0.873334	−	0.487121i	$-0.161953\pi$
$930$	27.0111	−	83.1316i	0.885728	−	2.72599i
$931$	−18.9409	−	12.3943i	−0.620762	−	0.406207i
$932$	0.453470	+	0.329465i	0.0148539	+	0.0107920i
$933$	6.16406	+	7.88964i	0.201802	+	0.258295i
$934$	1.04364	−	5.91879i	0.0341490	−	0.193669i
$935$	63.2984	+	10.5618i	2.07008	+	0.345407i
$936$	13.4156	+	11.2570i	0.438503	+	0.367948i
$937$	−41.6277	+	22.1338i	−1.35992	+	0.723080i	−0.979445	−	0.201712i	$-0.935349\pi$
$937$	−41.6277	+	22.1338i	−1.35992	+	0.723080i	−0.380471	+	0.924793i	$0.624238\pi$
$938$	−1.01507	+	9.65777i	−0.0331433	+	0.315337i
$939$	3.48150	+	33.1243i	0.113615	+	1.08097i
$940$	4.02218	−	5.14815i	0.131189	−	0.167914i
$941$	9.33045	−	11.9424i	0.304164	−	0.389312i	−0.611508	−	0.791238i	$-0.709437\pi$
$941$	9.33045	−	11.9424i	0.304164	−	0.389312i	0.915672	+	0.401926i	$0.131659\pi$
$942$	2.24768	+	21.3853i	0.0732334	+	0.696769i
$943$	0.927097	−	8.82074i	0.0301904	−	0.287243i
$944$	10.0253	−	5.33053i	0.326294	−	0.173494i
$945$	−1.38131	−	1.15906i	−0.0449340	−	0.0377041i
$946$	−1.15228	−	1.17146i	−0.0374639	−	0.0380875i
$947$	−3.50982	+	19.9052i	−0.114054	+	0.646831i	0.873161	+	0.487432i	$0.162066\pi$
$947$	−3.50982	+	19.9052i	−0.114054	+	0.646831i	−0.987214	+	0.159398i	$0.949045\pi$
$948$	19.6769	+	25.1853i	0.639077	+	0.817982i
$949$	−23.4377	−	17.0285i	−0.760821	−	0.552769i
$950$	−27.0671	+	13.6729i	−0.878171	+	0.443607i
$951$	−20.9899	+	64.6002i	−0.680644	+	2.09481i
$952$	−0.262512	−	7.51736i	−0.00850806	−	0.243639i
$953$	−0.913666	−	1.87329i	−0.0295965	−	0.0606819i	0.883484	−	0.468462i	$-0.155192\pi$
$953$	−0.913666	−	1.87329i	−0.0295965	−	0.0606819i	−0.913080	+	0.407780i	$0.866303\pi$
$954$	7.35866	−	0.514567i	0.238245	−	0.0166597i
$955$	28.6623	−	70.9417i	0.927490	−	2.29562i
$956$	−3.70069	−	20.9877i	−0.119689	−	0.678789i
$957$	3.95154	+	13.3171i	0.127735	+	0.430479i
$958$	−10.6682	+	18.4779i	−0.344675	+	0.596994i
$959$	0.992972	−	28.4350i	0.0320647	−	0.918214i
$960$	−4.67259	−	6.92740i	−0.150807	−	0.223581i
$961$	−8.19792	−	77.9980i	−0.264449	−	2.51606i
$962$	0.693079	−	0.147319i	0.0223458	−	0.00474974i
$963$	15.0852	+	2.12008i	0.486113	+	0.0683187i
$964$	−19.7541	−	1.38134i	−0.636235	−	0.0444899i
$965$	−69.4677	+	4.85765i	−2.23624	+	0.156373i
$966$	8.43844	−	1.18595i	0.271502	−	0.0381572i
$967$	23.2852	−	8.47513i	0.748802	−	0.272542i	0.0607006	−	0.998156i	$-0.480667\pi$
$967$	23.2852	−	8.47513i	0.748802	−	0.272542i	0.688102	+	0.725614i	$0.258444\pi$
$968$	−5.00316	−	9.79635i	−0.160808	−	0.314867i
$969$	51.4507	+	28.7542i	1.65283	+	0.923717i
$970$	−8.10079	−	24.9317i	−0.260101	−	0.800508i
$971$	33.4792	+	9.60000i	1.07440	+	0.308079i	0.765777	−	0.643106i	$-0.222355\pi$
$971$	33.4792	+	9.60000i	1.07440	+	0.308079i	0.308621	+	0.951185i	$0.400132\pi$
$972$	9.50661	+	19.4914i	0.304925	+	0.625188i
$973$	8.72166	+	21.5869i	0.279604	+	0.692043i
$974$	−13.0685	+	8.16613i	−0.418743	+	0.261660i
$975$	74.5860	+	72.0268i	2.38866	+	2.30670i
$976$	−1.04191	+	9.91311i	−0.0333507	+	0.317311i
$977$	−36.2309	−	7.70111i	−1.15913	−	0.246380i	−0.412079	−	0.911148i	$-0.635197\pi$
$977$	−36.2309	−	7.70111i	−1.15913	−	0.246380i	−0.747050	+	0.664768i	$0.768531\pi$
$978$	14.5094	+	5.28098i	0.463958	+	0.168867i
$979$	−19.9478	−	13.1896i	−0.637534	−	0.421541i
$980$	8.97836	−	15.5510i	0.286803	−	0.496758i
$981$	−3.80733	+	4.22846i	−0.121559	+	0.135004i
$982$	−8.84305	+	18.1309i	−0.282193	+	0.578581i
$983$	−2.38076	−	0.166479i	−0.0759345	−	0.00530986i	0.0317387	−	0.999496i	$-0.489896\pi$
$983$	−2.38076	−	0.166479i	−0.0759345	−	0.00530986i	−0.107673	+	0.994186i	$0.534340\pi$
$984$	−3.06063	−	7.57531i	−0.0975692	−	0.241492i
$985$	25.0723	+	13.3312i	0.798871	+	0.424767i
$986$	−5.42326	+	8.04032i	−0.172712	+	0.256056i
$987$	4.96517	+	3.60741i	0.158043	+	0.114825i
$988$	−12.9518	−	23.5587i	−0.412051	−	0.749501i
$989$	1.29967			0.0413271
$990$	13.5182	+	29.6259i	0.429638	+	0.941574i
$991$	−2.06640	+	11.7192i	−0.0656415	+	0.372271i	0.934237	+	0.356654i	$0.116082\pi$
$991$	−2.06640	+	11.7192i	−0.0656415	+	0.372271i	−0.999878	+	0.0156173i	$0.995029\pi$
$992$	−8.87123	−	5.54336i	−0.281662	−	0.176002i
$993$	−5.50941	−	22.0970i	−0.174836	−	0.701228i
$994$	6.30486	+	6.08853i	0.199978	+	0.193116i
$995$	−27.0506	+	5.74978i	−0.857561	+	0.182280i
$996$	−8.42067	−	9.35210i	−0.266819	−	0.296333i
$997$	36.7192	−	10.5291i	1.16291	−	0.333459i	0.361961	−	0.932193i	$-0.382107\pi$
$997$	36.7192	−	10.5291i	1.16291	−	0.333459i	0.800947	+	0.598735i	$0.204330\pi$
$998$	5.44383	+	8.07080i	0.172321	+	0.255477i
$999$	0.0435924	+	0.00926584i	0.00137920	+	0.000293158i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.u.b.5.10	✓	264
11.9	even	5	inner	418.2.u.b.119.2	yes	264
19.4	even	9	inner	418.2.u.b.137.2	yes	264
209.42	even	45	inner	418.2.u.b.251.10	yes	264

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.u.b.5.10	✓	264	1.1	even	1	trivial
418.2.u.b.119.2	yes	264	11.9	even	5	inner
418.2.u.b.137.2	yes	264	19.4	even	9	inner
418.2.u.b.251.10	yes	264	209.42	even	45	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.u (of order \(45\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.615661 - 0.788011i) q^{2} +(1.73828 - 1.67864i) q^{3} +(-0.241922 + 0.970296i) q^{4} +(2.93245 - 1.83240i) q^{5} +(-2.39298 - 0.336312i) q^{6} +(-1.22803 - 0.546756i) q^{7} +(0.913545 - 0.406737i) q^{8} +(0.0990960 - 2.83774i) q^{9} +O(q^{10})\)	\(q+(-0.615661 - 0.788011i) q^{2} +(1.73828 - 1.67864i) q^{3} +(-0.241922 + 0.970296i) q^{4} +(2.93245 - 1.83240i) q^{5} +(-2.39298 - 0.336312i) q^{6} +(-1.22803 - 0.546756i) q^{7} +(0.913545 - 0.406737i) q^{8} +(0.0990960 - 2.83774i) q^{9} +(-3.24934 - 1.18266i) q^{10} +(2.28188 - 2.40687i) q^{11} +(1.20825 + 2.09275i) q^{12} +(-5.44571 + 2.89554i) q^{13} +(0.325204 + 1.30432i) q^{14} +(2.02149 - 8.10775i) q^{15} +(-0.882948 - 0.469472i) q^{16} +(0.195285 + 5.59223i) q^{17} +(-2.29718 + 1.66900i) q^{18} +(4.21427 - 1.11350i) q^{19} +(1.06854 + 3.28864i) q^{20} +(-3.05248 + 1.11101i) q^{21} +(-3.30151 - 0.316324i) q^{22} +(2.00954 - 1.68620i) q^{23} +(0.905237 - 2.24054i) q^{24} +(3.04971 - 6.25283i) q^{25} +(5.63443 + 2.50861i) q^{26} +(0.259572 + 0.288284i) q^{27} +(0.827603 - 1.05928i) q^{28} +(-1.66606 + 0.477735i) q^{29} +(-7.63355 + 3.39867i) q^{30} +(-6.99962 + 7.77386i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-0.0737269 - 8.01428i) q^{33} +(4.28651 - 3.59681i) q^{34} +(-4.60302 + 0.646912i) q^{35} +(2.72947 + 0.782664i) q^{36} +(0.0929429 - 0.0675270i) q^{37} +(-3.47202 - 2.63535i) q^{38} +(-4.60563 + 14.1747i) q^{39} +(1.93362 - 2.86671i) q^{40} +(2.43210 - 2.34866i) q^{41} +(2.75478 + 1.72138i) q^{42} +(0.379529 + 0.318463i) q^{43} +(1.78334 + 2.79637i) q^{44} +(-4.90927 - 8.50310i) q^{45} +(-2.56594 - 0.545408i) q^{46} +(-1.05650 - 1.56633i) q^{47} +(-2.32289 + 0.666077i) q^{48} +(-3.47479 - 3.85914i) q^{49} +(-6.80489 + 1.44642i) q^{50} +(9.72681 + 9.39307i) q^{51} +(-1.49209 - 5.98445i) q^{52} +(-2.20314 - 1.37667i) q^{53} +(0.0673624 - 0.382031i) q^{54} +(2.28114 - 11.2393i) q^{55} -1.34425 q^{56} +(5.45644 - 9.00984i) q^{57} +(1.40219 + 1.01875i) q^{58} +(-6.34925 + 9.41315i) q^{59} +(7.37787 + 3.92288i) q^{60} +(-3.73397 - 9.24190i) q^{61} +(10.4353 + 0.729706i) q^{62} +(-1.67324 + 3.43066i) q^{63} +(0.669131 - 0.743145i) q^{64} +(-10.6635 + 18.4697i) q^{65} +(-6.26995 + 4.99218i) q^{66} +(6.78841 + 2.47078i) q^{67} +(-5.47336 - 1.16340i) q^{68} +(0.662619 - 6.30439i) q^{69} +(3.34367 + 3.22895i) q^{70} +(5.52944 - 3.45518i) q^{71} +(-1.06368 - 2.63271i) q^{72} +(2.05911 + 4.22180i) q^{73} +(-0.110433 - 0.0316662i) q^{74} +(-5.19500 - 15.9886i) q^{75} +(0.0609012 + 4.35847i) q^{76} +(-4.11820 + 1.70809i) q^{77} +(14.0053 - 5.09751i) q^{78} +(13.0973 - 1.84071i) q^{79} +(-3.44945 + 0.241209i) q^{80} +(9.43279 + 0.659605i) q^{81} +(-3.34812 - 0.470547i) q^{82} +(-5.09393 + 1.08275i) q^{83} +(-0.339548 - 3.23059i) q^{84} +(10.8198 + 16.0411i) q^{85} +(0.0172906 - 0.495138i) q^{86} +(-2.09414 + 3.62716i) q^{87} +(1.10563 - 3.12691i) q^{88} +(-1.25206 - 7.10080i) q^{89} +(-3.67809 + 9.10358i) q^{90} +(8.27068 - 0.578342i) q^{91} +(1.14996 + 2.35778i) q^{92} +(0.882205 + 25.2630i) q^{93} +(-0.583838 + 1.79687i) q^{94} +(10.3178 - 10.9875i) q^{95} +(1.95499 + 1.42038i) q^{96} +(4.66743 + 5.97403i) q^{97} +(-0.901753 + 5.11410i) q^{98} +(-6.60395 - 6.71388i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9}+O(q^{10}) \) 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9	\( 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9} + 3 q^{11} - 6 q^{13} + 18 q^{14} - 39 q^{15} - 3 q^{17} - 78 q^{18} - 45 q^{19} - 24 q^{20} + 48 q^{21} + 6 q^{23} - 9 q^{24} + 30 q^{25} + 18 q^{26} - 24 q^{27} + 6 q^{28} - 3 q^{31} - 63 q^{33} - 36 q^{34} + 42 q^{35} - 9 q^{36} + 60 q^{37} - 3 q^{38} + 36 q^{39} + 39 q^{41} + 6 q^{42} - 60 q^{43} + 60 q^{44} - 108 q^{45} - 12 q^{46} - 24 q^{47} - 12 q^{48} + 6 q^{49} + 18 q^{50} + 96 q^{51} + 3 q^{52} - 117 q^{53} + 54 q^{54} + 102 q^{55} - 96 q^{57} - 60 q^{58} - 141 q^{59} + 36 q^{60} + 24 q^{61} - 27 q^{62} - 81 q^{63} + 33 q^{64} - 102 q^{65} + 72 q^{66} + 102 q^{67} - 21 q^{68} - 6 q^{69} - 33 q^{70} - 66 q^{71} - 12 q^{72} + 36 q^{73} + 18 q^{74} + 6 q^{76} - 174 q^{77} + 18 q^{78} + 36 q^{79} + 60 q^{81} - 36 q^{82} - 24 q^{83} + 48 q^{84} + 174 q^{85} - 21 q^{86} + 12 q^{87} + 3 q^{88} + 30 q^{89} - 48 q^{90} - 18 q^{91} + 18 q^{92} - 123 q^{93} - 120 q^{94} - 18 q^{95} - 24 q^{97} - 84 q^{98} - 141 q^{99}+O(q^{100}) \) 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9 + 3 * q^11 - 6 * q^13 + 18 * q^14 - 39 * q^15 - 3 * q^17 - 78 * q^18 - 45 * q^19 - 24 * q^20 + 48 * q^21 + 6 * q^23 - 9 * q^24 + 30 * q^25 + 18 * q^26 - 24 * q^27 + 6 * q^28 - 3 * q^31 - 63 * q^33 - 36 * q^34 + 42 * q^35 - 9 * q^36 + 60 * q^37 - 3 * q^38 + 36 * q^39 + 39 * q^41 + 6 * q^42 - 60 * q^43 + 60 * q^44 - 108 * q^45 - 12 * q^46 - 24 * q^47 - 12 * q^48 + 6 * q^49 + 18 * q^50 + 96 * q^51 + 3 * q^52 - 117 * q^53 + 54 * q^54 + 102 * q^55 - 96 * q^57 - 60 * q^58 - 141 * q^59 + 36 * q^60 + 24 * q^61 - 27 * q^62 - 81 * q^63 + 33 * q^64 - 102 * q^65 + 72 * q^66 + 102 * q^67 - 21 * q^68 - 6 * q^69 - 33 * q^70 - 66 * q^71 - 12 * q^72 + 36 * q^73 + 18 * q^74 + 6 * q^76 - 174 * q^77 + 18 * q^78 + 36 * q^79 + 60 * q^81 - 36 * q^82 - 24 * q^83 + 48 * q^84 + 174 * q^85 - 21 * q^86 + 12 * q^87 + 3 * q^88 + 30 * q^89 - 48 * q^90 - 18 * q^91 + 18 * q^92 - 123 * q^93 - 120 * q^94 - 18 * q^95 - 24 * q^97 - 84 * q^98 - 141 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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