LMFDB - Embedded newform 216.2.v.b.11.29

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(11,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 13]))

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

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

chi := DirichletCharacter("216.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.v (of order $18$, degree $6$, 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:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$32$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			11.29
Character	$\chi$	$=$	216.11
Dual form			216.2.v.b.59.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.35595 - 0.401734i) q^{2} +(-1.03533 - 1.38855i) q^{3} +(1.67722 - 1.08946i) q^{4} +(1.93709 + 0.705042i) q^{5} +(-1.96169 - 1.46689i) q^{6} +(-0.744451 - 0.131267i) q^{7} +(1.83656 - 2.15106i) q^{8} +(-0.856167 + 2.87524i) q^{9} +O(q^{10})$	\(q+(1.35595 - 0.401734i) q^{2} +(-1.03533 - 1.38855i) q^{3} +(1.67722 - 1.08946i) q^{4} +(1.93709 + 0.705042i) q^{5} +(-1.96169 - 1.46689i) q^{6} +(-0.744451 - 0.131267i) q^{7} +(1.83656 - 2.15106i) q^{8} +(-0.856167 + 2.87524i) q^{9} +(2.90984 + 0.177811i) q^{10} +(-0.949342 - 2.60830i) q^{11} +(-3.24926 - 1.20095i) q^{12} +(0.421307 + 0.502095i) q^{13} +(-1.06217 + 0.121079i) q^{14} +(-1.02654 - 3.41970i) q^{15} +(1.62614 - 3.65454i) q^{16} +(-3.79256 + 2.18964i) q^{17} +(-0.00584395 + 4.24264i) q^{18} +(0.155896 - 0.270019i) q^{19} +(4.01704 - 0.927876i) q^{20} +(0.588484 + 1.16962i) q^{21} +(-2.33510 - 3.15535i) q^{22} +(1.32831 + 7.53324i) q^{23} +(-4.88831 - 0.323097i) q^{24} +(-0.575004 - 0.482485i) q^{25} +(0.772981 + 0.511564i) q^{26} +(4.87884 - 1.78799i) q^{27} +(-1.39162 + 0.590889i) q^{28} +(5.89474 + 4.94627i) q^{29} +(-2.76575 - 4.22456i) q^{30} +(-4.16197 + 0.733867i) q^{31} +(0.736811 - 5.60866i) q^{32} +(-2.63888 + 4.01867i) q^{33} +(-4.26289 + 4.49265i) q^{34} +(-1.34952 - 0.779144i) q^{35} +(1.69649 + 5.75517i) q^{36} +(2.70478 - 1.56160i) q^{37} +(0.102912 - 0.428762i) q^{38} +(0.260992 - 1.10484i) q^{39} +(5.07416 - 2.87194i) q^{40} +(4.31331 + 5.14040i) q^{41} +(1.26783 + 1.34953i) q^{42} +(-3.00565 + 1.09397i) q^{43} +(-4.43390 - 3.34041i) q^{44} +(-3.68563 + 4.96594i) q^{45} +(4.82749 + 9.68110i) q^{46} +(-1.89499 + 10.7470i) q^{47} +(-6.75813 + 1.52570i) q^{48} +(-6.04087 - 2.19870i) q^{49} +(-0.973509 - 0.423229i) q^{50} +(6.96700 + 2.99917i) q^{51} +(1.25364 + 0.383124i) q^{52} -0.876371 q^{53} +(5.89718 - 4.38443i) q^{54} -5.72182i q^{55} +(-1.64959 + 1.36028i) q^{56} +(-0.536341 + 0.0630905i) q^{57} +(9.98008 + 4.33880i) q^{58} +(2.94714 - 8.09720i) q^{59} +(-5.44738 - 4.61721i) q^{60} +(-12.1748 - 2.14675i) q^{61} +(-5.34862 + 2.66709i) q^{62} +(1.01480 - 2.02808i) q^{63} +(-1.25411 - 7.90109i) q^{64} +(0.462111 + 1.26964i) q^{65} +(-1.96376 + 6.50926i) q^{66} +(3.32854 - 2.79298i) q^{67} +(-3.97543 + 7.80437i) q^{68} +(9.08507 - 9.64386i) q^{69} +(-2.14289 - 0.514337i) q^{70} +(-7.08002 - 12.2629i) q^{71} +(4.61240 + 7.12220i) q^{72} +(7.17342 - 12.4247i) q^{73} +(3.04020 - 3.20406i) q^{74} +(-0.0746363 + 1.29796i) q^{75} +(-0.0327049 - 0.622725i) q^{76} +(0.364356 + 2.06636i) q^{77} +(-0.0899601 - 1.60297i) q^{78} +(7.09014 - 8.44970i) q^{79} +(5.72657 - 5.93267i) q^{80} +(-7.53396 - 4.92336i) q^{81} +(7.91372 + 5.23734i) q^{82} +(-7.10823 + 8.47125i) q^{83} +(2.26127 + 1.32057i) q^{84} +(-8.89031 + 1.56760i) q^{85} +(-3.63604 + 2.69084i) q^{86} +(0.765146 - 13.3062i) q^{87} +(-7.35412 - 2.74820i) q^{88} +(5.55986 + 3.20999i) q^{89} +(-3.00256 + 8.21423i) q^{90} +(-0.247734 - 0.429088i) q^{91} +(10.4351 + 11.1878i) q^{92} +(5.32804 + 5.01932i) q^{93} +(1.74792 + 15.3337i) q^{94} +(0.492358 - 0.413138i) q^{95} +(-8.55078 + 4.78374i) q^{96} +(1.59192 - 0.579411i) q^{97} +(-9.07443 - 0.554511i) q^{98} +(8.31226 - 0.496445i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) $ 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9	$ 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 30 q^{11} - 3 q^{12} + 9 q^{14} - 6 q^{16} - 18 q^{17} + 63 q^{18} - 6 q^{19} - 27 q^{20} - 18 q^{22} - 30 q^{24} - 12 q^{25} + 18 q^{27} - 12 q^{28} - 21 q^{30} - 36 q^{32} - 30 q^{33} + 12 q^{34} - 18 q^{35} - 36 q^{36} - 102 q^{38} + 9 q^{40} + 18 q^{41} - 6 q^{42} - 42 q^{43} - 81 q^{44} - 3 q^{46} - 81 q^{48} - 12 q^{49} + 57 q^{50} - 18 q^{51} + 21 q^{52} + 78 q^{54} - 69 q^{56} - 36 q^{57} - 33 q^{58} - 84 q^{59} - 54 q^{60} + 90 q^{62} - 51 q^{64} - 12 q^{65} + 87 q^{66} + 30 q^{67} + 63 q^{68} - 33 q^{70} + 12 q^{72} - 6 q^{73} + 51 q^{74} - 96 q^{75} + 30 q^{76} + 90 q^{78} - 12 q^{81} - 12 q^{82} - 72 q^{83} - 48 q^{84} + 42 q^{86} - 78 q^{88} + 144 q^{89} + 120 q^{90} - 6 q^{91} - 3 q^{92} - 33 q^{94} - 78 q^{96} - 42 q^{97} + 162 q^{98} - 12 q^{99}+O(q^{100}) $ 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 30 * q^11 - 3 * q^12 + 9 * q^14 - 6 * q^16 - 18 * q^17 + 63 * q^18 - 6 * q^19 - 27 * q^20 - 18 * q^22 - 30 * q^24 - 12 * q^25 + 18 * q^27 - 12 * q^28 - 21 * q^30 - 36 * q^32 - 30 * q^33 + 12 * q^34 - 18 * q^35 - 36 * q^36 - 102 * q^38 + 9 * q^40 + 18 * q^41 - 6 * q^42 - 42 * q^43 - 81 * q^44 - 3 * q^46 - 81 * q^48 - 12 * q^49 + 57 * q^50 - 18 * q^51 + 21 * q^52 + 78 * q^54 - 69 * q^56 - 36 * q^57 - 33 * q^58 - 84 * q^59 - 54 * q^60 + 90 * q^62 - 51 * q^64 - 12 * q^65 + 87 * q^66 + 30 * q^67 + 63 * q^68 - 33 * q^70 + 12 * q^72 - 6 * q^73 + 51 * q^74 - 96 * q^75 + 30 * q^76 + 90 * q^78 - 12 * q^81 - 12 * q^82 - 72 * q^83 - 48 * q^84 + 42 * q^86 - 78 * q^88 + 144 * q^89 + 120 * q^90 - 6 * q^91 - 3 * q^92 - 33 * q^94 - 78 * q^96 - 42 * q^97 + 162 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{13}{18}\right)$

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 $

$2$	1.35595	−	0.401734i	0.958804	−	0.284069i
$2$	1.35595	−	0.401734i	0.958804	−	0.284069i
$3$	−1.03533	−	1.38855i	−0.597750	−	0.801682i
$3$	−1.03533	−	1.38855i	−0.597750	−	0.801682i
$4$	1.67722	−	1.08946i	0.838610	−	0.544732i
$5$	1.93709	+	0.705042i	0.866291	+	0.315304i	0.736664	−	0.676259i	$-0.236400\pi$
$5$	1.93709	+	0.705042i	0.866291	+	0.315304i	0.129627	+	0.991563i	$0.458622\pi$
$6$	−1.96169	−	1.46689i	−0.800858	−	0.598854i
$7$	−0.744451	−	0.131267i	−0.281376	−	0.0496142i	0.0311792	−	0.999514i	$-0.490074\pi$
$7$	−0.744451	−	0.131267i	−0.281376	−	0.0496142i	−0.312555	+	0.949900i	$0.601185\pi$
$8$	1.83656	−	2.15106i	0.649321	−	0.760514i
$9$	−0.856167	+	2.87524i	−0.285389	+	0.958412i
$10$	2.90984	+	0.177811i	0.920171	+	0.0562288i
$11$	−0.949342	−	2.60830i	−0.286237	−	0.786431i	−0.996584	−	0.0825793i	$-0.973684\pi$
$11$	−0.949342	−	2.60830i	−0.286237	−	0.786431i	0.710347	−	0.703852i	$-0.248538\pi$
$12$	−3.24926	−	1.20095i	−0.937982	−	0.346685i
$13$	0.421307	+	0.502095i	0.116850	+	0.139256i	0.821298	−	0.570499i	$-0.193250\pi$
$13$	0.421307	+	0.502095i	0.116850	+	0.139256i	−0.704449	+	0.709755i	$0.748806\pi$
$14$	−1.06217	+	0.121079i	−0.283878	+	0.0323598i
$15$	−1.02654	−	3.41970i	−0.265052	−	0.882964i
$16$	1.62614	−	3.65454i	0.406534	−	0.913636i
$17$	−3.79256	+	2.18964i	−0.919832	+	0.531065i	−0.883581	−	0.468278i	$-0.844875\pi$
$17$	−3.79256	+	2.18964i	−0.919832	+	0.531065i	−0.0362504	+	0.999343i	$0.511541\pi$
$18$	−0.00584395	+	4.24264i	−0.00137743	+	0.999999i
$19$	0.155896	−	0.270019i	0.0357649	−	0.0619467i	−0.847589	−	0.530653i	$-0.821947\pi$
$19$	0.155896	−	0.270019i	0.0357649	−	0.0619467i	0.883354	+	0.468707i	$0.155280\pi$
$20$	4.01704	−	0.927876i	0.898237	−	0.207479i
$21$	0.588484	+	1.16962i	0.128418	+	0.255231i
$22$	−2.33510	−	3.15535i	−0.497846	−	0.672722i
$23$	1.32831	+	7.53324i	0.276973	+	1.57079i	0.732626	+	0.680632i	$0.238295\pi$
$23$	1.32831	+	7.53324i	0.276973	+	1.57079i	−0.455653	+	0.890157i	$0.650594\pi$
$24$	−4.88831	−	0.323097i	−0.997823	−	0.0659519i
$25$	−0.575004	−	0.482485i	−0.115001	−	0.0964971i
$26$	0.772981	+	0.511564i	0.151594	+	0.100326i
$27$	4.87884	−	1.78799i	0.938933	−	0.344100i
$28$	−1.39162	+	0.590889i	−0.262991	+	0.111668i
$29$	5.89474	+	4.94627i	1.09463	+	0.918500i	0.997052	−	0.0767286i	$-0.0244475\pi$
$29$	5.89474	+	4.94627i	1.09463	+	0.918500i	0.0975734	+	0.995228i	$0.468892\pi$
$30$	−2.76575	−	4.22456i	−0.504955	−	0.771296i
$31$	−4.16197	+	0.733867i	−0.747511	+	0.131806i	−0.534412	−	0.845224i	$-0.679467\pi$
$31$	−4.16197	+	0.733867i	−0.747511	+	0.131806i	−0.213099	+	0.977031i	$0.568356\pi$
$32$	0.736811	−	5.60866i	0.130251	−	0.991481i
$33$	−2.63888	+	4.01867i	−0.459369	+	0.699561i
$34$	−4.26289	+	4.49265i	−0.731079	+	0.770483i
$35$	−1.34952	−	0.779144i	−0.228110	−	0.131699i
$36$	1.69649	+	5.75517i	0.282748	+	0.959194i
$37$	2.70478	−	1.56160i	0.444662	−	0.256726i	−0.260911	−	0.965363i	$-0.584023\pi$
$37$	2.70478	−	1.56160i	0.444662	−	0.256726i	0.705573	+	0.708637i	$0.250690\pi$
$38$	0.102912	−	0.428762i	0.0166945	−	0.0695544i
$39$	0.260992	−	1.10484i	0.0417921	−	0.176917i
$40$	5.07416	−	2.87194i	0.802295	−	0.454093i
$41$	4.31331	+	5.14040i	0.673626	+	0.802796i	0.989273	−	0.146081i	$-0.0466660\pi$
$41$	4.31331	+	5.14040i	0.673626	+	0.802796i	−0.315647	+	0.948877i	$0.602222\pi$
$42$	1.26783	+	1.34953i	0.195631	+	0.208237i
$43$	−3.00565	+	1.09397i	−0.458358	+	0.166829i	−0.560871	−	0.827903i	$-0.689534\pi$
$43$	−3.00565	+	1.09397i	−0.458358	+	0.166829i	0.102513	+	0.994732i	$0.467312\pi$
$44$	−4.43390	−	3.34041i	−0.668436	−	0.503586i
$45$	−3.68563	+	4.96594i	−0.549421	+	0.740279i
$46$	4.82749	+	9.68110i	0.711774	+	1.42740i
$47$	−1.89499	+	10.7470i	−0.276412	+	1.56761i	0.458028	+	0.888938i	$0.348556\pi$
$47$	−1.89499	+	10.7470i	−0.276412	+	1.56761i	−0.734440	+	0.678673i	$0.762555\pi$
$48$	−6.75813	+	1.52570i	−0.975451	+	0.220215i
$49$	−6.04087	−	2.19870i	−0.862982	−	0.314100i
$50$	−0.973509	−	0.423229i	−0.137675	−	0.0598537i
$51$	6.96700	+	2.99917i	0.975575	+	0.419968i
$52$	1.25364	+	0.383124i	0.173848	+	0.0531297i
$53$	−0.876371			−0.120379			−0.0601894	−	0.998187i	$-0.519170\pi$
$53$	−0.876371			−0.120379			−0.0601894	+	0.998187i	$0.519170\pi$
$54$	5.89718	−	4.38443i	0.802505	−	0.596646i
$55$		−	5.72182i		−	0.771530i
$56$	−1.64959	+	1.36028i	−0.220436	+	0.181775i
$57$	−0.536341	+	0.0630905i	−0.0710401	+	0.00835654i
$58$	9.98008	+	4.33880i	1.31045	+	0.569713i
$59$	2.94714	−	8.09720i	0.383685	−	1.05417i	−0.586107	−	0.810233i	$-0.699340\pi$
$59$	2.94714	−	8.09720i	0.383685	−	1.05417i	0.969792	−	0.243932i	$-0.0784374\pi$
$60$	−5.44738	−	4.61721i	−0.703254	−	0.596080i
$61$	−12.1748	−	2.14675i	−1.55883	−	0.274863i	−0.673271	−	0.739395i	$-0.735111\pi$
$61$	−12.1748	−	2.14675i	−1.55883	−	0.274863i	−0.885556	+	0.464532i	$0.846223\pi$
$62$	−5.34862	+	2.66709i	−0.679275	+	0.338721i
$63$	1.01480	−	2.02808i	0.127852	−	0.255515i
$64$	−1.25411	−	7.90109i	−0.156763	−	0.987636i
$65$	0.462111	+	1.26964i	0.0573178	+	0.157479i
$66$	−1.96376	+	6.50926i	−0.241722	+	0.801234i
$67$	3.32854	−	2.79298i	0.406646	−	0.341216i	−0.416410	−	0.909177i	$-0.636712\pi$
$67$	3.32854	−	2.79298i	0.406646	−	0.341216i	0.823056	+	0.567961i	$0.192267\pi$
$68$	−3.97543	+	7.80437i	−0.482092	+	0.946419i
$69$	9.08507	−	9.64386i	1.09371	−	1.16098i
$70$	−2.14289	−	0.514337i	−0.256124	−	0.0614750i
$71$	−7.08002	−	12.2629i	−0.840243	−	1.45534i	−0.889689	−	0.456567i	$-0.849079\pi$
$71$	−7.08002	−	12.2629i	−0.840243	−	1.45534i	0.0494456	−	0.998777i	$-0.484255\pi$
$72$	4.61240	+	7.12220i	0.543576	+	0.839360i
$73$	7.17342	−	12.4247i	0.839585	−	1.45420i	−0.0506575	−	0.998716i	$-0.516132\pi$
$73$	7.17342	−	12.4247i	0.839585	−	1.45420i	0.890242	−	0.455487i	$-0.150535\pi$
$74$	3.04020	−	3.20406i	0.353416	−	0.372464i
$75$	−0.0746363	+	1.29796i	−0.00861826	+	0.149875i
$76$	−0.0327049	−	0.622725i	−0.00375151	−	0.0714314i
$77$	0.364356	+	2.06636i	0.0415222	+	0.235484i
$78$	−0.0899601	−	1.60297i	−0.0101860	−	0.181500i
$79$	7.09014	−	8.44970i	0.797703	−	0.950666i	−0.201883	−	0.979410i	$-0.564706\pi$
$79$	7.09014	−	8.44970i	0.797703	−	0.950666i	0.999587	+	0.0287437i	$0.00915065\pi$
$80$	5.72657	−	5.93267i	0.640250	−	0.663293i
$81$	−7.53396	−	4.92336i	−0.837106	−	0.547040i
$82$	7.91372	+	5.23734i	0.873924	+	0.578368i
$83$	−7.10823	+	8.47125i	−0.780229	+	0.929841i	−0.998944	−	0.0459479i	$-0.985369\pi$
$83$	−7.10823	+	8.47125i	−0.780229	+	0.929841i	0.218715	+	0.975789i	$0.429814\pi$
$84$	2.26127	+	1.32057i	0.246725	+	0.144086i
$85$	−8.89031	+	1.56760i	−0.964289	+	0.170030i
$86$	−3.63604	+	2.69084i	−0.392085	+	0.290161i
$87$	0.765146	−	13.3062i	0.0820322	−	1.42658i
$88$	−7.35412	−	2.74820i	−0.783952	−	0.292959i
$89$	5.55986	+	3.20999i	0.589344	+	0.340258i	0.764838	−	0.644222i	$-0.222819\pi$
$89$	5.55986	+	3.20999i	0.589344	+	0.340258i	−0.175494	+	0.984481i	$0.556152\pi$
$90$	−3.00256	+	8.21423i	−0.316497	+	0.865856i
$91$	−0.247734	−	0.429088i	−0.0259696	−	0.0449807i
$92$	10.4351	+	11.1878i	1.08793	+	1.16640i
$93$	5.32804	+	5.01932i	0.552492	+	0.520479i
$94$	1.74792	+	15.3337i	0.180284	+	1.58155i
$95$	0.492358	−	0.413138i	0.0505149	−	0.0423870i
$96$	−8.55078	+	4.78374i	−0.872710	+	0.488238i
$97$	1.59192	−	0.579411i	0.161635	−	0.0588303i	−0.259935	−	0.965626i	$-0.583701\pi$
$97$	1.59192	−	0.579411i	0.161635	−	0.0588303i	0.421570	+	0.906796i	$0.361479\pi$
$98$	−9.07443	−	0.554511i	−0.916656	−	0.0560140i
$99$	8.31226	−	0.496445i	0.835414	−	0.0498946i
$100$	−1.49006	−	0.182788i	−0.149006	−	0.0182788i
$101$	0.0772824	−	0.438290i	0.00768988	−	0.0436115i	−0.980721	−	0.195411i	$-0.937396\pi$
$101$	0.0772824	−	0.438290i	0.00768988	−	0.0436115i	0.988411	+	0.151800i	$0.0485069\pi$
$102$	10.6518	+	1.26786i	1.05469	+	0.125537i
$103$	−4.31107	+	11.8446i	−0.424782	+	1.16708i	0.524157	+	0.851621i	$0.324380\pi$
$103$	−4.31107	+	11.8446i	−0.424782	+	1.16708i	−0.948940	+	0.315458i	$0.897842\pi$
$104$	1.85379	+	0.0158691i	0.181779	+	0.00155610i
$105$	0.315317	+	2.68055i	0.0307718	+	0.261595i
$106$	−1.18832	+	0.352068i	−0.115420	+	0.0341958i
$107$		−	9.16557i		−	0.886069i	−0.896505	−	0.443034i	$-0.853902\pi$
$107$		−	9.16557i		−	0.886069i	0.896505	−	0.443034i	$-0.146098\pi$
$108$	6.23493	−	8.31418i	0.599957	−	0.800033i
$109$		−	12.6300i		−	1.20973i	−0.796327	−	0.604867i	$-0.793226\pi$
$109$		−	12.6300i		−	1.20973i	0.796327	−	0.604867i	$-0.206774\pi$
$110$	−2.29865	−	7.75852i	−0.219167	−	0.739746i
$111$	−4.96872	−	2.13895i	−0.471610	−	0.203020i
$112$	−1.69030	+	2.50717i	−0.159718	+	0.236905i
$113$	−4.39773	+	12.0827i	−0.413703	+	1.13664i	0.541503	+	0.840699i	$0.317856\pi$
$113$	−4.39773	+	12.0827i	−0.413703	+	1.13664i	−0.955206	+	0.295942i	$0.904367\pi$
$114$	−0.701908	+	0.301014i	−0.0657397	+	0.0281925i
$115$	−2.73819	+	15.5291i	−0.255338	+	1.44809i
$116$	15.2756	+	1.87388i	1.41830	+	0.173986i
$117$	−1.80435	+	0.781481i	−0.166812	+	0.0722479i
$118$	0.743267	−	12.1634i	0.0684233	−	1.11973i
$119$	3.11080	−	1.13224i	0.285167	−	0.103792i
$120$	−9.24129	−	4.07233i	−0.843610	−	0.371751i
$121$	2.52453	−	2.11833i	0.229503	−	0.192576i
$122$	−17.3709	+	1.98014i	−1.57269	+	0.179274i
$123$	2.67201	−	11.3113i	0.240927	−	1.01991i
$124$	−6.18101	+	5.76517i	−0.555071	+	0.517728i
$125$	−5.92717	−	10.2662i	−0.530142	−	0.918233i
$126$	0.561268	−	3.15767i	0.0500017	−	0.281307i
$127$	3.31139	+	1.91183i	0.293838	+	0.169648i	0.639671	−	0.768648i	$-0.279070\pi$
$127$	3.31139	+	1.91183i	0.293838	+	0.169648i	−0.345833	+	0.938296i	$0.612404\pi$
$128$	−4.87464	−	10.2097i	−0.430862	−	0.902418i
$129$	4.63089	+	3.04089i	0.407727	+	0.267736i
$130$	1.13666	+	1.53593i	0.0996915	+	0.134710i
$131$	−13.1264	+	2.31454i	−1.14686	+	0.202222i	−0.714604	−	0.699529i	$-0.753393\pi$
$131$	−13.1264	+	2.31454i	−1.14686	+	0.202222i	−0.432255	+	0.901751i	$0.642282\pi$
$132$	−0.0477761	+	9.61516i	−0.00415838	+	0.836892i
$133$	−0.151501	+	0.180552i	−0.0131368	+	0.0156559i
$134$	3.39131	−	5.12433i	0.292965	−	0.442675i
$135$	10.7113	−	0.0237142i	0.921886	−	0.00204099i
$136$	−2.25523	+	12.1794i	−0.193384	+	1.04438i
$137$	8.71665	−	10.3881i	0.744714	−	0.887516i	−0.252065	−	0.967710i	$-0.581110\pi$
$137$	8.71665	−	10.3881i	0.744714	−	0.887516i	0.996779	+	0.0801947i	$0.0255542\pi$
$138$	8.44467	−	16.7264i	0.718858	−	1.42385i
$139$	0.183415	+	1.04020i	0.0155571	+	0.0882286i	0.991598	−	0.129360i	$-0.0412921\pi$
$139$	0.183415	+	1.04020i	0.0155571	+	0.0882286i	−0.976041	+	0.217588i	$0.930181\pi$
$140$	−3.11229	+	0.163454i	−0.263036	+	0.0138144i
$141$	16.8847	−	8.49544i	1.42195	−	0.715445i
$142$	−14.5266	−	13.7837i	−1.21905	−	1.15670i
$143$	0.909646	−	1.57555i	0.0760685	−	0.131754i
$144$	9.11543	+	7.80442i	0.759619	+	0.650368i
$145$	7.93129	+	13.7374i	0.658658	+	1.14083i
$146$	4.73539	−	19.7291i	0.391904	−	1.63280i
$147$	3.20131	+	10.6645i	0.264040	+	0.879590i
$148$	2.83519	−	5.56591i	0.233052	−	0.457515i
$149$	17.2009	−	14.4333i	1.40915	−	1.18242i	0.452294	−	0.891869i	$-0.350606\pi$
$149$	17.2009	−	14.4333i	1.40915	−	1.18242i	0.956859	−	0.290551i	$-0.0938387\pi$
$150$	0.420230	+	1.78995i	0.0343116	+	0.146149i
$151$	6.78428	+	18.6396i	0.552097	+	1.51687i	0.830842	+	0.556508i	$0.187859\pi$
$151$	6.78428	+	18.6396i	0.552097	+	1.51687i	−0.278746	+	0.960365i	$0.589919\pi$
$152$	−0.294516	−	0.831247i	−0.0238884	−	0.0674230i
$153$	−3.04866	−	12.7792i	−0.246469	−	1.03314i
$154$	1.32418	+	2.65552i	0.106705	+	0.213988i
$155$	−8.57950	−	1.51280i	−0.689122	−	0.121511i
$156$	−0.765947	−	2.13741i	−0.0613248	−	0.171130i
$157$	−5.37486	+	14.7673i	−0.428960	+	1.17856i	0.517485	+	0.855693i	$0.326868\pi$
$157$	−5.37486	+	14.7673i	−0.428960	+	1.17856i	−0.946445	+	0.322866i	$0.895354\pi$
$158$	6.21938	−	14.3058i	0.494787	−	1.13810i
$159$	0.907337	+	1.21689i	0.0719565	+	0.0965055i
$160$	5.38161	−	10.3450i	0.425454	−	0.817843i
$161$		−	5.78249i		−	0.455724i
$162$	−12.1936	−	3.64921i	−0.958018	−	0.286709i
$163$	−11.3706			−0.890618			−0.445309	−	0.895377i	$-0.646906\pi$
$163$	−11.3706			−0.890618			−0.445309	+	0.895377i	$0.646906\pi$
$164$	12.8347	+	3.92239i	1.00222	+	0.306287i
$165$	−7.94506	+	5.92400i	−0.618522	+	0.461182i
$166$	−6.23524	+	14.3422i	−0.483948	+	1.11317i
$167$	−10.8721	−	3.95710i	−0.841305	−	0.306210i	−0.114815	−	0.993387i	$-0.536627\pi$
$167$	−10.8721	−	3.95710i	−0.841305	−	0.306210i	−0.726490	+	0.687177i	$0.758850\pi$
$168$	3.59670	+	0.882203i	0.277491	+	0.0680634i
$169$	2.18283	−	12.3794i	0.167910	−	0.952264i
$170$	−11.4251	+	5.69713i	−0.876264	+	0.436950i
$171$	0.642896	+	0.679419i	0.0491635	+	0.0519564i
$172$	−3.84930	+	5.10938i	−0.293507	+	0.389586i
$173$	−6.70079	+	2.43889i	−0.509452	+	0.185425i	−0.583940	−	0.811797i	$-0.698490\pi$
$173$	−6.70079	+	2.43889i	−0.509452	+	0.185425i	0.0744886	+	0.997222i	$0.476268\pi$
$174$	−4.30805	−	18.3500i	−0.326592	−	1.39111i
$175$	0.364728	+	0.434665i	0.0275708	+	0.0328576i
$176$	−11.0759	−	0.772031i	−0.834877	−	0.0581940i
$177$	−14.2947	+	4.29104i	−1.07445	+	0.322535i
$178$	8.82848	+	2.11901i	0.661722	+	0.158827i
$179$	5.44606	−	3.14429i	0.407058	−	0.235015i	−0.282467	−	0.959277i	$-0.591153\pi$
$179$	5.44606	−	3.14429i	0.407058	−	0.235015i	0.689525	+	0.724262i	$0.257819\pi$
$180$	−0.771393	+	12.3443i	−0.0574963	+	0.920093i
$181$	−12.3575	−	7.13460i	−0.918525	−	0.530311i	−0.0353608	−	0.999375i	$-0.511258\pi$
$181$	−12.3575	−	7.13460i	−0.918525	−	0.530311i	−0.883164	+	0.469064i	$0.844591\pi$
$182$	−0.508295	−	0.482301i	−0.0376773	−	0.0357505i
$183$	9.62414	+	19.1280i	0.711437	+	1.41398i
$184$	18.6440	+	10.9780i	1.37445	+	0.809306i
$185$	6.34038	−	1.11798i	0.466154	−	0.0821955i
$186$	9.24101	+	4.66551i	0.677583	+	0.342092i
$187$	9.31166	+	7.81341i	0.680936	+	0.571373i
$188$	8.53016	+	20.0896i	0.622126	+	1.46519i
$189$	−3.86676	+	0.690644i	−0.281265	+	0.0502370i
$190$	0.501644	−	0.757992i	0.0363931	−	0.0549905i
$191$	7.59946	+	6.37671i	0.549878	+	0.461402i	0.874900	−	0.484304i	$-0.160927\pi$
$191$	7.59946	+	6.37671i	0.549878	+	0.461402i	−0.325022	+	0.945706i	$0.605372\pi$
$192$	−9.67267	+	9.92166i	−0.698065	+	0.716034i
$193$	−1.18184	−	6.70255i	−0.0850707	−	0.482460i	−0.997341	−	0.0728719i	$-0.976784\pi$
$193$	−1.18184	−	6.70255i	−0.0850707	−	0.482460i	0.912271	−	0.409588i	$-0.134328\pi$
$194$	1.92580	−	1.42518i	0.138264	−	0.102322i
$195$	1.28452	−	1.95617i	0.0919867	−	0.140084i
$196$	−12.5273	+	2.89361i	−0.894805	+	0.206687i
$197$	−3.08336	+	5.34054i	−0.219681	+	0.380498i	−0.954710	−	0.297537i	$-0.903835\pi$
$197$	−3.08336	+	5.34054i	−0.219681	+	0.380498i	0.735030	+	0.678035i	$0.237168\pi$
$198$	11.0716	−	4.01247i	0.786824	−	0.285154i
$199$	−2.83677	+	1.63781i	−0.201093	+	0.116101i	−0.597165	−	0.802118i	$-0.703706\pi$
$199$	−2.83677	+	1.63781i	−0.201093	+	0.116101i	0.396072	+	0.918219i	$0.370373\pi$
$200$	−2.09388	+	0.350754i	−0.148060	+	0.0248021i
$201$	−7.32435	−	1.73019i	−0.516620	−	0.122038i
$202$	−0.0712845	−	0.625348i	−0.00501556	−	0.0439993i
$203$	−3.73906	−	4.45604i	−0.262431	−	0.312753i
$204$	14.9527	−	2.56002i	1.04690	−	0.179237i
$205$	4.73105	+	12.9985i	0.330431	+	0.907852i
$206$	−1.08725	+	17.7926i	−0.0757523	+	1.23967i
$207$	−22.7971	−	2.63050i	−1.58451	−	0.182832i
$208$	2.52003	−	0.723212i	0.174733	−	0.0501457i
$209$	−0.852289	−	0.150282i	−0.0589541	−	0.0103952i
$210$	1.50442	+	3.50803i	0.103815	+	0.242077i
$211$	6.00891	+	2.18706i	0.413670	+	0.150564i	0.540467	−	0.841365i	$-0.318247\pi$
$211$	6.00891	+	2.18706i	0.413670	+	0.150564i	−0.126797	+	0.991929i	$0.540470\pi$
$212$	−1.46987	+	0.954775i	−0.100951	+	0.0655742i
$213$	−9.69759	+	22.5272i	−0.664468	+	1.54354i
$214$	−3.68212	−	12.4281i	−0.251704	−	0.849566i
$215$	−6.59350			−0.449673
$216$	5.11419	−	13.7784i	0.347977	−	0.937503i
$217$	3.19471			0.216871
$218$	−5.07389	−	17.1257i	−0.343647	−	1.15990i
$219$	−24.6793	+	2.90306i	−1.66767	+	0.196170i
$220$	−6.23372	−	9.59675i	−0.420277	−	0.647013i
$221$	−2.69724	−	0.981715i	−0.181436	−	0.0660373i
$222$	−7.59664	−	0.904213i	−0.509853	−	0.0606868i
$223$	16.3621	+	2.88507i	1.09568	+	0.193199i	0.692141	−	0.721762i	$-0.256667\pi$
$223$	16.3621	+	2.88507i	1.09568	+	0.193199i	0.403543	+	0.914961i	$0.367779\pi$
$224$	−1.28475	+	4.07865i	−0.0858410	+	0.272517i
$225$	1.87956	−	1.24018i	0.125304	−	0.0826789i
$226$	−1.10911	+	18.1502i	−0.0737766	+	1.20734i
$227$	0.151200	+	0.415419i	0.0100355	+	0.0275724i	0.944609	−	0.328197i	$-0.106441\pi$
$227$	0.151200	+	0.415419i	0.0100355	+	0.0275724i	−0.934574	+	0.355770i	$0.884219\pi$
$228$	−0.830827	+	0.690141i	−0.0550228	+	0.0457057i
$229$	6.21678	+	7.40887i	0.410817	+	0.489592i	0.931286	−	0.364288i	$-0.118688\pi$
$229$	6.21678	+	7.40887i	0.410817	+	0.489592i	−0.520470	+	0.853880i	$0.674243\pi$
$230$	2.52568	+	22.1567i	0.166539	+	1.46097i
$231$	2.49203	−	2.64531i	0.163964	−	0.174048i
$232$	21.4658	−	3.59581i	1.40930	−	0.236076i
$233$	1.49279	−	0.861864i	0.0977961	−	0.0564626i	−0.450304	−	0.892875i	$-0.648685\pi$
$233$	1.49279	−	0.861864i	0.0977961	−	0.0564626i	0.548100	+	0.836413i	$0.315351\pi$
$234$	−2.13267	+	1.78452i	−0.139417	+	0.116658i
$235$	−11.2478	+	19.4818i	−0.733728	+	1.27085i
$236$	−3.87861	−	16.7916i	−0.252476	−	1.09304i
$237$	−19.0735	−	1.09678i	−1.23896	−	0.0712438i
$238$	3.76325	−	2.78498i	0.243935	−	0.180523i
$239$	1.11054	+	6.29821i	0.0718351	+	0.407397i	0.999428	+	0.0338057i	$0.0107627\pi$
$239$	1.11054	+	6.29821i	0.0718351	+	0.407397i	−0.927593	+	0.373592i	$0.878126\pi$
$240$	−14.1667	−	1.80936i	−0.914460	−	0.116793i
$241$	−13.9890	−	11.7382i	−0.901114	−	0.756124i	0.0692941	−	0.997596i	$-0.477925\pi$
$241$	−13.9890	−	11.7382i	−0.901114	−	0.756124i	−0.970408	+	0.241472i	$0.922370\pi$
$242$	2.57214	−	3.88655i	0.165343	−	0.249837i
$243$	0.963804	+	15.5586i	0.0618281	+	0.998087i
$244$	−22.7587	+	9.66347i	−1.45698	+	0.618640i
$245$	−10.1515	−	8.51813i	−0.648557	−	0.544204i
$246$	−0.921004	−	16.4110i	−0.0587211	−	1.04633i
$247$	0.201255	−	0.0354867i	0.0128056	−	0.00225797i
$248$	−6.06510	+	10.3004i	−0.385135	+	0.654078i
$249$	19.1222	+	1.09958i	1.21182	+	0.0696832i
$250$	−12.1612	−	11.5393i	−0.769144	−	0.729809i
$251$	22.9769	+	13.2657i	1.45029	+	0.837325i	0.998497	−	0.0547989i	$-0.0174518\pi$
$251$	22.9769	+	13.2657i	1.45029	+	0.837325i	0.451791	+	0.892124i	$0.350785\pi$
$252$	−0.507488	−	4.50713i	−0.0319687	−	0.283922i
$253$	18.3879	−	10.6163i	1.15604	−	0.667438i
$254$	5.25814	+	1.26206i	0.329925	+	0.0791886i
$255$	11.3811	+	10.7217i	0.712714	+	0.671418i
$256$	−10.7114	−	11.8856i	−0.669460	−	0.742848i
$257$	14.9145	+	17.7744i	0.930341	+	1.10874i	0.993848	+	0.110755i	$0.0353270\pi$
$257$	14.9145	+	17.7744i	0.930341	+	1.10874i	−0.0635070	+	0.997981i	$0.520229\pi$
$258$	7.50090	+	2.26292i	0.466986	+	0.140883i
$259$	−2.21856	+	0.807489i	−0.137855	+	0.0501749i
$260$	2.15829	+	1.62601i	0.133851	+	0.100841i
$261$	−19.2686	+	12.7139i	−1.19270	+	0.786972i
$262$	−16.8690	+	8.41173i	−1.04217	+	0.519678i
$263$	−2.19804	+	12.4657i	−0.135537	+	0.768669i	0.838947	+	0.544213i	$0.183172\pi$
$263$	−2.19804	+	12.4657i	−0.135537	+	0.768669i	−0.974484	+	0.224456i	$0.927939\pi$
$264$	3.79795	+	13.0569i	0.233748	+	0.803597i
$265$	−1.69761	−	0.617878i	−0.104283	−	0.0379559i
$266$	−0.132895	+	0.305683i	−0.00814830	+	0.0187427i
$267$	−1.29907	−	11.0436i	−0.0795019	−	0.675856i
$268$	2.53984	−	8.31076i	0.155146	−	0.507660i
$269$	−1.20091			−0.0732208			−0.0366104	−	0.999330i	$-0.511656\pi$
$269$	−1.20091			−0.0732208			−0.0366104	+	0.999330i	$0.511656\pi$
$270$	14.5146	−	4.33526i	0.883328	−	0.263836i
$271$		−	5.81199i		−	0.353053i	−0.984296	−	0.176527i	$-0.943514\pi$
$271$		−	5.81199i		−	0.353053i	0.984296	−	0.176527i	$-0.0564862\pi$
$272$	1.83490	+	17.4207i	0.111257	+	1.05629i
$273$	−0.339325	+	0.788242i	−0.0205369	+	0.0477066i
$274$	7.64613	−	17.5876i	0.461919	−	1.06250i
$275$	−0.712590	+	1.95782i	−0.0429708	+	0.118061i
$276$	4.73102	−	26.0727i	0.284774	−	1.56939i
$277$	14.3435	+	2.52915i	0.861817	+	0.151962i	0.587051	−	0.809550i	$-0.300289\pi$
$277$	14.3435	+	2.52915i	0.861817	+	0.151962i	0.274766	+	0.961511i	$0.411400\pi$
$278$	0.666586	+	1.33678i	0.0399792	+	0.0801746i
$279$	1.45330	−	12.5949i	0.0870067	−	0.754040i
$280$	−4.15445	+	1.47195i	−0.248276	+	0.0879656i
$281$	−3.34759	−	9.19743i	−0.199701	−	0.548673i	0.798905	−	0.601457i	$-0.205413\pi$
$281$	−3.34759	−	9.19743i	−0.199701	−	0.548673i	−0.998606	+	0.0527839i	$0.983191\pi$
$282$	19.4820	−	18.3026i	1.16014	−	1.08990i
$283$	−1.06126	+	0.890502i	−0.0630853	+	0.0529348i	−0.673785	−	0.738927i	$-0.735333\pi$
$283$	−1.06126	+	0.890502i	−0.0630853	+	0.0529348i	0.610700	+	0.791862i	$0.290888\pi$
$284$	−25.2348	−	12.8542i	−1.49741	−	0.762759i
$285$	−1.08342	−	0.255931i	−0.0641762	−	0.0151600i
$286$	0.600485	−	2.50181i	0.0355074	−	0.147935i
$287$	−2.53628	−	4.39297i	−0.149712	−	0.259309i
$288$	15.4954	+	6.92046i	0.913075	+	0.407792i
$289$	1.08903	−	1.88625i	0.0640603	−	0.110956i
$290$	16.2732	+	15.4410i	0.955597	+	0.906727i
$291$	−2.45271	−	1.61058i	−0.143781	−	0.0944140i
$292$	−1.50489	−	28.6542i	−0.0880671	−	1.67686i
$293$	0.541790	+	3.07264i	0.0316517	+	0.179506i	0.996535	−	0.0831727i	$-0.0265053\pi$
$293$	0.541790	+	3.07264i	0.0316517	+	0.179506i	−0.964883	+	0.262678i	$0.915394\pi$
$294$	8.62510	+	13.1744i	0.503026	+	0.768349i
$295$	11.4177	−	13.6071i	0.664766	−	0.792237i
$296$	1.60838	−	8.68611i	0.0934851	−	0.504870i
$297$	−9.29531	−	11.0280i	−0.539368	−	0.639912i
$298$	17.5253	−	26.4810i	1.01521	−	1.53401i
$299$	−3.22277	+	3.84075i	−0.186378	+	0.222116i
$300$	1.28890	+	2.25827i	0.0744145	+	0.130382i
$301$	2.38116	−	0.419863i	0.137248	−	0.0242005i
$302$	16.6873	+	22.5490i	0.960248	+	1.29755i
$303$	−0.688603	+	0.346466i	−0.0395592	+	0.0199039i
$304$	−0.733290	−	1.00882i	−0.0420570	−	0.0578595i
$305$	−22.0702	−	12.7422i	−1.26373	−	0.729617i
$306$	−9.26767	−	16.1033i	−0.529798	−	0.920562i
$307$	−13.5864	−	23.5323i	−0.775415	−	1.34306i	−0.934561	−	0.355803i	$-0.884207\pi$
$307$	−13.5864	−	23.5323i	−0.775415	−	1.34306i	0.159146	−	0.987255i	$-0.449126\pi$
$308$	2.86234	+	3.06880i	0.163097	+	0.174861i
$309$	20.9102	−	6.27693i	1.18954	−	0.357082i
$310$	−12.2411	+	1.39539i	−0.695250	+	0.0792528i
$311$	15.0893	−	12.6614i	0.855634	−	0.717962i	−0.105389	−	0.994431i	$-0.533609\pi$
$311$	15.0893	−	12.6614i	0.855634	−	0.717962i	0.961023	+	0.276469i	$0.0891644\pi$
$312$	−1.89726	−	2.59052i	−0.107411	−	0.146659i
$313$	12.9477	−	4.71256i	0.731845	−	0.266370i	0.0508993	−	0.998704i	$-0.483791\pi$
$313$	12.9477	−	4.71256i	0.731845	−	0.266370i	0.680946	+	0.732334i	$0.261569\pi$
$314$	−1.35554	+	22.1830i	−0.0764973	+	1.25186i
$315$	3.39563	−	3.21310i	0.191322	−	0.181038i
$316$	2.68608	−	21.8965i	0.151104	−	1.23177i
$317$	1.93237	−	10.9590i	0.108533	−	0.615521i	−0.881217	−	0.472711i	$-0.843275\pi$
$317$	1.93237	−	10.9590i	0.108533	−	0.615521i	0.989750	−	0.142809i	$-0.0456135\pi$
$318$	1.71917	+	1.28554i	0.0964063	+	0.0720893i
$319$	7.30522	−	20.0709i	0.409014	−	1.12376i
$320$	3.14128	−	16.1893i	0.175603	−	0.905009i
$321$	−12.7269	+	9.48942i	−0.710346	+	0.529648i
$322$	−2.32302	−	7.84079i	−0.129457	−	0.436950i
$323$			1.36542i			0.0759740i
$324$	−17.9999	−	0.0495875i	−0.999996	−	0.00275486i
$325$		−	0.491981i		−	0.0272902i
$326$	−15.4181	+	4.56797i	−0.853928	+	0.252997i
$327$	−17.5374	+	13.0763i	−0.969822	+	0.723119i
$328$	18.9789	+	0.162467i	1.04794	+	0.00897073i
$329$	2.82145	−	7.75186i	0.155551	−	0.427374i
$330$	−8.39326	+	11.2245i	−0.462034	+	0.617886i
$331$	−3.55339	+	20.1523i	−0.195312	+	1.10767i	0.716661	+	0.697421i	$0.245669\pi$
$331$	−3.55339	+	20.1523i	−0.195312	+	1.10767i	−0.911973	+	0.410249i	$0.865442\pi$
$332$	−2.69293	+	21.9523i	−0.147794	+	1.20479i
$333$	2.17424	+	9.11386i	0.119147	+	0.499436i
$334$	−16.3317	−	0.997980i	−0.893631	−	0.0546070i
$335$	8.41683	−	3.06348i	0.459860	−	0.167376i
$336$	5.23136	−	0.248688i	0.285394	−	0.0135670i
$337$	−27.2025	+	22.8256i	−1.48181	+	1.24339i	−0.577591	+	0.816326i	$0.696007\pi$
$337$	−27.2025	+	22.8256i	−1.48181	+	1.24339i	−0.904222	+	0.427062i	$0.859548\pi$
$338$	−2.01342	−	17.6628i	−0.109516	−	0.960732i
$339$	21.3305	−	6.40310i	1.15852	−	0.347769i
$340$	−13.2032	+	12.3149i	−0.716042	+	0.667868i
$341$	5.86527	+	10.1590i	0.317622	+	0.550138i
$342$	1.14468	+	0.662987i	0.0618974	+	0.0358502i
$343$	8.79113	+	5.07556i	0.474676	+	0.274054i
$344$	−3.16687	+	8.47447i	−0.170746	+	0.456913i
$345$	24.3979	−	12.2756i	1.31354	−	0.660898i
$346$	−8.10618	+	5.99895i	−0.435791	+	0.322506i
$347$	11.0057	−	1.94061i	0.590818	−	0.104177i	0.129757	−	0.991546i	$-0.458580\pi$
$347$	11.0057	−	1.94061i	0.590818	−	0.104177i	0.461061	+	0.887369i	$0.347469\pi$
$348$	−13.2133	−	23.1510i	−0.708308	−	1.24103i
$349$	18.9269	−	22.5561i	1.01313	−	1.20740i	0.0350059	−	0.999387i	$-0.488855\pi$
$349$	18.9269	−	22.5561i	1.01313	−	1.20740i	0.978125	−	0.208016i	$-0.0667006\pi$
$350$	0.669173	+	0.442863i	0.0357688	+	0.0236720i
$351$	2.95323	+	1.69634i	0.157632	+	0.0905441i
$352$	−15.3285	+	3.40272i	−0.817014	+	0.181366i
$353$	1.05874	−	1.26175i	0.0563508	−	0.0671563i	−0.737133	−	0.675748i	$-0.763821\pi$
$353$	1.05874	−	1.26175i	0.0563508	−	0.0671563i	0.793484	+	0.608592i	$0.208265\pi$
$354$	−17.6591	+	11.5611i	−0.938569	+	0.614466i
$355$	−5.06871	−	28.7461i	−0.269019	−	1.52568i
$356$	12.8223	−	0.673414i	0.679580	−	0.0356909i
$357$	−4.79290	−	3.14727i	−0.253667	−	0.166571i
$358$	6.12144	−	6.45137i	0.323528	−	0.340966i
$359$	5.17384	−	8.96135i	0.273065	−	0.472962i	−0.696580	−	0.717479i	$-0.745296\pi$
$359$	5.17384	−	8.96135i	0.273065	−	0.472962i	0.969645	+	0.244517i	$0.0786293\pi$
$360$	3.91316	+	17.0483i	0.206242	+	0.898522i
$361$	9.45139	+	16.3703i	0.497442	+	0.861594i
$362$	−19.6224	−	4.70977i	−1.03133	−	0.247540i
$363$	−5.55515	−	1.31227i	−0.291570	−	0.0688761i
$364$	−0.882981	−	0.449778i	−0.0462808	−	0.0235748i
$365$	22.6555	−	19.0102i	1.18584	−	0.995039i
$366$	20.7343	+	22.0704i	1.08380	+	1.15364i
$367$	2.26512	+	6.22336i	0.118238	+	0.324857i	0.984667	−	0.174444i	$-0.0558127\pi$
$367$	2.26512	+	6.22336i	0.118238	+	0.324857i	−0.866429	+	0.499300i	$0.833590\pi$
$368$	29.6906	+	7.39569i	1.54773	+	0.385527i
$369$	−18.4728	+	8.00074i	−0.961654	+	0.416502i
$370$	8.14813	−	4.06307i	0.423601	−	0.211229i
$371$	0.652415	+	0.115038i	0.0338717	+	0.00597249i
$372$	14.4047	+	2.61380i	0.746847	+	0.135519i
$373$	3.26986	−	8.98387i	0.169307	−	0.465167i	−0.825801	−	0.563962i	$-0.809277\pi$
$373$	3.26986	−	8.98387i	0.169307	−	0.465167i	0.995108	+	0.0987948i	$0.0314987\pi$
$374$	15.7651	+	6.85382i	0.815194	+	0.354403i
$375$	−8.11852	+	18.8591i	−0.419239	+	0.973880i
$376$	19.6372	+	23.8137i	1.01271	+	1.22810i
$377$			5.04362i			0.259759i
$378$	−4.96569	+	2.48989i	−0.255408	+	0.128066i
$379$	32.8619			1.68800			0.844000	−	0.536343i	$-0.180194\pi$
$379$	32.8619			1.68800			0.844000	+	0.536343i	$0.180194\pi$
$380$	0.375695	−	1.22933i	0.0192727	−	0.0630633i
$381$	−0.773712	−	6.57743i	−0.0396384	−	0.336972i
$382$	12.8663	+	5.59356i	0.658295	+	0.286191i
$383$	−17.7062	−	6.44453i	−0.904744	−	0.329300i	−0.152592	−	0.988289i	$-0.548762\pi$
$383$	−17.7062	−	6.44453i	−0.904744	−	0.329300i	−0.752152	+	0.658989i	$0.770984\pi$
$384$	−9.12983	+	17.3392i	−0.465905	+	0.884835i
$385$	−0.751085	+	4.25961i	−0.0382788	+	0.217090i
$386$	−4.29516	−	8.61356i	−0.218618	−	0.438419i
$387$	−0.572076	−	9.57858i	−0.0290802	−	0.486907i
$388$	2.03875	−	2.70614i	0.103502	−	0.137383i
$389$	−32.5922	+	11.8626i	−1.65249	+	0.601458i	−0.989157	−	0.146865i	$-0.953082\pi$
$389$	−32.5922	+	11.8626i	−1.65249	+	0.601458i	−0.663335	+	0.748323i	$0.730860\pi$
$390$	0.955897	−	3.16851i	0.0484037	−	0.160444i
$391$	−21.5328	−	25.6618i	−1.08896	−	1.29777i
$392$	−15.8239	+	8.95623i	−0.799230	+	0.452358i
$393$	16.8041	+	15.8304i	0.847654	+	0.798538i
$394$	−2.03542	+	8.48022i	−0.102543	+	0.427227i
$395$	19.6916	−	11.3690i	0.990792	−	0.572034i
$396$	13.4006	−	9.88856i	0.673407	−	0.496919i
$397$	−7.71976	−	4.45700i	−0.387444	−	0.223691i	0.293608	−	0.955926i	$-0.405144\pi$
$397$	−7.71976	−	4.45700i	−0.387444	−	0.223691i	−0.681052	+	0.732235i	$0.738477\pi$
$398$	−3.18856	+	3.36041i	−0.159828	+	0.168442i
$399$	0.407561	+	0.0234359i	0.0204036	+	0.00117326i
$400$	−2.69830	+	1.31679i	−0.134915	+	0.0658394i
$401$	−5.23648	+	0.923333i	−0.261497	+	0.0461090i	−0.302860	−	0.953035i	$-0.597941\pi$
$401$	−5.23648	+	0.923333i	−0.261497	+	0.0461090i	0.0413623	+	0.999144i	$0.486830\pi$
$402$	−10.6266	+	0.596373i	−0.530004	+	0.0297444i
$403$	−2.12194	−	1.78052i	−0.105701	−	0.0886939i
$404$	−0.347882	−	0.819305i	−0.0173078	−	0.0407620i
$405$	−11.1227	−	14.8487i	−0.552694	−	0.737839i
$406$	−6.86013	−	4.54008i	−0.340463	−	0.225320i
$407$	−6.64088	−	5.57236i	−0.329176	−	0.276212i
$408$	19.2467	−	9.47827i	0.952854	−	0.469244i
$409$	5.33255	+	30.2424i	0.263678	+	1.49539i	0.772774	+	0.634681i	$0.218869\pi$
$409$	5.33255	+	30.2424i	0.263678	+	1.49539i	−0.509096	+	0.860710i	$0.670020\pi$
$410$	11.6370	+	15.7247i	0.574711	+	0.776587i
$411$	−23.4491	−	1.34839i	−1.15666	−	0.0665112i
$412$	5.67362	+	24.5627i	0.279519	+	1.21012i
$413$	−3.25689	+	5.64110i	−0.160261	+	0.277581i
$414$	−31.9686	+	5.59153i	−1.57117	+	0.274809i
$415$	−19.7418	+	11.3980i	−0.969089	+	0.559504i
$416$	3.12650	−	1.99302i	0.153289	−	0.0977160i
$417$	1.25448	−	1.33164i	0.0614320	−	0.0652105i
$418$	−1.21604	+	0.138618i	−0.0594783	+	0.00678004i
$419$	−6.31758	−	7.52899i	−0.308634	−	0.367815i	0.589324	−	0.807897i	$-0.299394\pi$
$419$	−6.31758	−	7.52899i	−0.308634	−	0.367815i	−0.897958	+	0.440081i	$0.854950\pi$
$420$	3.44922	+	4.15235i	0.168305	+	0.202614i
$421$	5.77588	+	15.8691i	0.281499	+	0.773413i	0.997184	+	0.0749895i	$0.0238923\pi$
$421$	5.77588	+	15.8691i	0.281499	+	0.773413i	−0.715685	+	0.698423i	$0.753885\pi$
$422$	9.02642	+	0.551576i	0.439399	+	0.0268503i
$423$	−29.2777	−	14.6498i	−1.42353	−	0.712296i
$424$	−1.60951	+	1.88513i	−0.0781645	+	0.0915498i
$425$	3.23721	+	0.570807i	0.157028	+	0.0276882i
$426$	−4.09953	+	34.4417i	−0.198623	+	1.66871i
$427$	8.78177	+	3.19630i	0.424979	+	0.154680i
$428$	−9.98556	−	15.3727i	−0.482670	−	0.743066i
$429$	−3.12953	+	0.368131i	−0.151095	+	0.0177735i
$430$	−8.94048	+	2.64883i	−0.431148	+	0.127738i
$431$	−4.98460			−0.240100			−0.120050	−	0.992768i	$-0.538305\pi$
$431$	−4.98460			−0.240100			−0.120050	+	0.992768i	$0.538305\pi$
$432$	1.39935	−	20.7374i	0.0673263	−	0.997731i
$433$	1.51448			0.0727813			0.0363907	−	0.999338i	$-0.488414\pi$
$433$	1.51448			0.0727813			0.0363907	+	0.999338i	$0.488414\pi$
$434$	4.33188	−	1.28342i	0.207937	−	0.0616063i
$435$	10.8636	−	25.2358i	0.520869	−	1.20996i
$436$	−13.7599	−	21.1833i	−0.658981	−	1.01449i
$437$	2.24120	+	0.815730i	0.107211	+	0.0390216i
$438$	−32.2977	+	13.8509i	−1.54324	+	0.661822i
$439$	−11.1514	−	1.96629i	−0.532227	−	0.0938460i	−0.0989253	−	0.995095i	$-0.531540\pi$
$439$	−11.1514	−	1.96629i	−0.532227	−	0.0938460i	−0.433302	+	0.901249i	$0.642652\pi$
$440$	−12.3080	−	10.5085i	−0.586759	−	0.500971i
$441$	11.4938	−	15.4865i	0.547322	−	0.737451i
$442$	−4.05172	−	0.247588i	−0.192721	−	0.0117766i
$443$	1.11491	+	3.06318i	0.0529709	+	0.145536i	0.963356	−	0.268225i	$-0.0864370\pi$
$443$	1.11491	+	3.06318i	0.0529709	+	0.145536i	−0.910385	+	0.413761i	$0.864215\pi$
$444$	−10.6639	+	1.82575i	−0.506088	+	0.0866464i
$445$	8.50676	+	10.1380i	0.403259	+	0.480585i
$446$	23.3452	−	2.66116i	1.10543	−	0.126010i
$447$	−37.8501	−	8.94114i	−1.79025	−	0.422901i
$448$	−0.103530	+	6.04659i	−0.00489132	+	0.285675i
$449$	−19.0431	+	10.9945i	−0.898698	+	0.518864i	−0.876778	−	0.480896i	$-0.840311\pi$
$449$	−19.0431	+	10.9945i	−0.898698	+	0.518864i	−0.0219208	+	0.999760i	$0.506978\pi$
$450$	2.05037	−	2.43671i	0.0966554	−	0.114868i
$451$	9.31288	−	16.1304i	0.438527	−	0.759550i
$452$	5.78767	+	25.0564i	0.272229	+	1.17856i
$453$	18.8582	−	28.7186i	0.886034	−	1.34932i
$454$	0.371908	+	0.502547i	0.0174545	+	0.0235857i
$455$	−0.177357	−	1.00584i	−0.00831464	−	0.0471547i
$456$	−0.849310	+	1.26957i	−0.0397726	+	0.0594530i
$457$	−0.610943	−	0.512642i	−0.0285787	−	0.0239804i	0.628386	−	0.777901i	$-0.283716\pi$
$457$	−0.610943	−	0.512642i	−0.0285787	−	0.0239804i	−0.656965	+	0.753921i	$0.728160\pi$
$458$	11.4061	+	7.54860i	0.532970	+	0.352723i
$459$	−14.5882	+	17.4640i	−0.680921	+	0.815148i
$460$	12.3258	+	29.0288i	0.574693	+	1.35347i
$461$	−2.30805	−	1.93668i	−0.107496	−	0.0902002i	0.587455	−	0.809257i	$-0.300130\pi$
$461$	−2.30805	−	1.93668i	−0.107496	−	0.0902002i	−0.694952	+	0.719056i	$0.744574\pi$
$462$	2.31637	−	4.58804i	0.107767	−	0.213455i
$463$	−9.53305	+	1.68093i	−0.443038	+	0.0781196i	−0.390717	−	0.920511i	$-0.627773\pi$
$463$	−9.53305	+	1.68093i	−0.443038	+	0.0781196i	−0.0523209	+	0.998630i	$0.516662\pi$
$464$	27.6620	−	13.4993i	1.28418	−	0.626688i
$465$	6.78204	+	13.4793i	0.314510	+	0.625090i
$466$	1.67792	−	1.76835i	0.0777280	−	0.0819173i
$467$	4.68978	+	2.70765i	0.217017	+	0.125295i	0.604568	−	0.796553i	$-0.293346\pi$
$467$	4.68978	+	2.70765i	0.217017	+	0.125295i	−0.387551	+	0.921848i	$0.626679\pi$
$468$	−2.17490	+	3.27649i	−0.100535	+	0.151456i
$469$	−2.84456	+	1.64231i	−0.131349	+	0.0758346i
$470$	−7.42504	+	30.9351i	−0.342492	+	1.42693i
$471$	26.0700	−	7.82580i	1.20124	−	0.360594i
$472$	−12.0050	−	21.2105i	−0.552573	−	0.976290i
$473$	5.70679	+	6.80109i	0.262398	+	0.312714i
$474$	−26.3034	+	6.17529i	−1.20816	+	0.283641i
$475$	−0.219921	+	0.0800447i	−0.0100907	+	0.00367270i
$476$	3.98397	−	5.28812i	0.182605	−	0.242381i
$477$	0.750320	−	2.51977i	0.0343548	−	0.115372i
$478$	4.03605	+	8.09394i	0.184605	+	0.370208i
$479$	2.45737	−	13.9364i	0.112280	−	0.636772i	−0.875781	−	0.482709i	$-0.839653\pi$
$479$	2.45737	−	13.9364i	0.112280	−	0.636772i	0.988061	−	0.154063i	$-0.0492359\pi$
$480$	−19.9363	+	3.23785i	−0.909965	+	0.147787i
$481$	1.92361	+	0.700138i	0.0877093	+	0.0319236i
$482$	−23.6841	−	10.2966i	−1.07878	−	0.468997i
$483$	−8.02930	+	5.98681i	−0.365346	+	0.272409i
$484$	1.92635	−	6.30329i	0.0875612	−	0.286513i
$485$	3.49219			0.158572
$486$	7.55730	+	20.7096i	0.342806	+	0.939406i
$487$			19.4173i			0.879884i	0.898026	+	0.439942i	$0.145001\pi$
$487$			19.4173i			0.879884i	−0.898026	+	0.439942i	$0.854999\pi$
$488$	−26.9776	+	22.2461i	−1.22122	+	1.00704i
$489$	11.7724	+	15.7888i	0.532367	+	0.713993i
$490$	−17.1870	−	7.47199i	−0.776430	−	0.337550i
$491$	8.52216	−	23.4144i	0.384600	−	1.05668i	−0.584797	−	0.811180i	$-0.698826\pi$
$491$	8.52216	−	23.4144i	0.384600	−	1.05668i	0.969397	−	0.245499i	$-0.0789520\pi$
$492$	−7.84170	−	21.8826i	−0.353531	−	0.986544i
$493$	−33.1867	−	5.85171i	−1.49465	−	0.263548i
$494$	0.258637	−	0.128969i	0.0116366	−	0.00580261i
$495$	16.4516	+	4.89883i	0.739444	+	0.220186i
$496$	−4.08597	+	16.4035i	−0.183466	+	0.736537i
$497$	3.66101	+	10.0585i	0.164219	+	0.451187i
$498$	26.3705	−	6.19104i	1.18169	−	0.277427i
$499$	26.2739	−	22.0464i	1.17618	−	0.986934i	0.176185	−	0.984357i	$-0.443624\pi$
$499$	26.2739	−	22.0464i	1.17618	−	0.986934i	0.999997	−	0.00257701i	$-0.000820288\pi$
$500$	−21.1258	−	10.7612i	−0.944774	−	0.481254i
$501$	5.76155	+	19.1934i	0.257407	+	0.857496i
$502$	36.4849	+	8.75711i	1.62840	+	0.390849i
$503$	5.33340	+	9.23771i	0.237804	+	0.411889i	0.960084	−	0.279712i	$-0.0902390\pi$
$503$	5.33340	+	9.23771i	0.237804	+	0.411889i	−0.722280	+	0.691601i	$0.756906\pi$
$504$	−2.49880	−	5.90758i	−0.111305	−	0.263145i
$505$	0.458715	−	0.794518i	0.0204126	−	0.0353556i
$506$	20.6682	−	21.7822i	0.918815	−	0.968336i
$507$	−19.4495	+	9.78587i	−0.863781	+	0.434606i
$508$	7.63680	−	0.401078i	0.338828	−	0.0177949i
$509$	6.89823	+	39.1218i	0.305759	+	1.73404i	0.619911	+	0.784672i	$0.287169\pi$
$509$	6.89823	+	39.1218i	0.305759	+	1.73404i	−0.314152	+	0.949373i	$0.601720\pi$
$510$	19.7396	+	9.96592i	0.874082	+	0.441298i
$511$	−6.97121	+	8.30796i	−0.308388	+	0.367522i
$512$	−19.2989	−	11.8132i	−0.852901	−	0.522073i
$513$	0.277797	−	1.59612i	0.0122650	−	0.0704705i
$514$	27.3639	+	18.1096i	1.20697	+	0.798781i
$515$	−16.7018	+	19.9045i	−0.735970	+	0.877095i
$516$	11.0800	+	0.0550545i	0.487768	+	0.00242364i
$517$	29.8304	−	5.25990i	1.31194	−	0.231330i
$518$	−2.68387	+	1.98619i	−0.117922	+	0.0872681i
$519$	10.3241	+	6.77935i	0.453177	+	0.297580i
$520$	3.57976	+	1.33774i	0.156983	+	0.0586637i
$521$	−15.1484	−	8.74596i	−0.663665	−	0.383167i	0.130007	−	0.991513i	$-0.458500\pi$
$521$	−15.1484	−	8.74596i	−0.663665	−	0.383167i	−0.793672	+	0.608346i	$0.791833\pi$
$522$	−21.0197	+	24.9803i	−0.920007	+	1.09336i
$523$	−19.3217	−	33.4661i	−0.844878	−	1.46337i	−0.885727	−	0.464206i	$-0.846340\pi$
$523$	−19.3217	−	33.4661i	−0.844878	−	1.46337i	0.0408499	−	0.999165i	$-0.486993\pi$
$524$	−19.4943	+	18.1827i	−0.851611	+	0.794317i
$525$	0.225942	−	0.956468i	0.00986090	−	0.0417437i
$526$	2.02746	+	17.7860i	0.0884012	+	0.775505i
$527$	14.1776	−	11.8964i	0.617587	−	0.518217i
$528$	10.3952	+	16.1788i	0.452395	+	0.704091i
$529$	−33.3724	+	12.1465i	−1.45097	+	0.528111i
$530$	−2.55010	−	0.155829i	−0.110769	−	0.00676876i
$531$	20.7581	+	15.4063i	0.900825	+	0.668575i
$532$	−0.0573958	+	0.467881i	−0.00248842	+	0.0202852i
$533$	−0.763739	+	4.33138i	−0.0330812	+	0.187613i
$534$	−6.19806	−	14.4527i	−0.268216	−	0.625430i
$535$	6.46211	−	17.7545i	0.279381	−	0.767594i
$536$	0.105201	−	12.2893i	0.00454400	−	0.530819i
$537$	−10.0045	−	4.30677i	−0.431726	−	0.185851i
$538$	−1.62838	+	0.482446i	−0.0702044	+	0.0207997i
$539$			17.8437i			0.768583i
$540$	17.9394	−	11.7094i	0.771991	−	0.503892i
$541$			34.6309i			1.48890i	0.667679	+	0.744449i	$0.267288\pi$
$541$			34.6309i			1.48890i	−0.667679	+	0.744449i	$0.732712\pi$
$542$	−2.33487	−	7.88079i	−0.100291	−	0.338509i
$543$	2.88735	+	24.5457i	0.123908	+	1.05336i
$544$	9.48654	+	22.8846i	0.406732	+	0.981168i
$545$	8.90467	−	24.4654i	0.381434	−	1.04798i
$546$	−0.143445	+	1.20514i	−0.00613889	+	0.0515751i
$547$	5.81585	−	32.9833i	0.248668	−	1.41027i	−0.563150	−	0.826355i	$-0.690411\pi$
$547$	5.81585	−	32.9833i	0.248668	−	1.41027i	0.811818	−	0.583910i	$-0.198478\pi$
$548$	3.30228	−	26.9196i	0.141066	−	1.14995i
$549$	16.5961	−	33.1675i	0.708305	−	1.41556i
$550$	−0.179715	+	2.94099i	−0.00766306	+	0.125404i
$551$	2.25455	−	0.820590i	0.0960472	−	0.0349583i
$552$	−4.05924	−	37.2540i	−0.172773	−	1.58564i
$553$	−6.38743	+	5.35969i	−0.271621	+	0.227917i
$554$	20.4652	−	2.33286i	0.869481	−	0.0991137i
$555$	−8.11679	−	7.64648i	−0.344538	−	0.324575i
$556$	1.44089	+	1.54482i	0.0611073	+	0.0655149i
$557$	13.2023	+	22.8671i	0.559401	+	0.968911i	0.997547	+	0.0700066i	$0.0223020\pi$
$557$	13.2023	+	22.8671i	0.559401	+	0.968911i	−0.438146	+	0.898904i	$0.644365\pi$
$558$	−3.08921	−	17.6620i	−0.130777	−	0.747692i
$559$	−1.81558	−	1.04823i	−0.0767908	−	0.0443352i
$560$	−5.04191	+	3.66487i	−0.213060	+	0.154869i
$561$	1.20867	−	21.0192i	0.0510300	−	0.887433i
$562$	−8.23410	−	11.1265i	−0.347334	−	0.469341i
$563$	−20.5566	+	3.62468i	−0.866356	+	0.152762i	−0.589126	−	0.808041i	$-0.700528\pi$
$563$	−20.5566	+	3.62468i	−0.866356	+	0.152762i	−0.277231	+	0.960803i	$0.589417\pi$
$564$	19.0639	−	32.6440i	0.802737	−	1.37456i
$565$	−17.0376	+	20.3046i	−0.716775	+	0.854220i
$566$	−1.08127	+	1.63382i	−0.0454493	+	0.0686747i
$567$	4.96238	+	4.65416i	0.208401	+	0.195456i
$568$	−39.3812	−	7.29209i	−1.65240	−	0.305969i
$569$	20.8581	−	24.8577i	0.874418	−	1.04209i	−0.124339	−	0.992240i	$-0.539681\pi$
$569$	20.8581	−	24.8577i	0.874418	−	1.04209i	0.998757	−	0.0498506i	$-0.0158745\pi$
$570$	−1.57188	+	0.0882157i	−0.0658389	+	0.00369495i
$571$	2.23408	+	12.6701i	0.0934935	+	0.530228i	0.995199	+	0.0978764i	$0.0312050\pi$
$571$	2.23408	+	12.6701i	0.0934935	+	0.530228i	−0.901705	+	0.432352i	$0.857684\pi$
$572$	−0.190832	−	3.63358i	−0.00797909	−	0.151928i
$573$	0.986421	−	17.1543i	0.0412083	−	0.716631i
$574$	−5.20388	−	4.93775i	−0.217206	−	0.206098i
$575$	2.87089	−	4.97253i	0.119725	−	0.207369i
$576$	23.7912	+	3.15880i	0.991301	+	0.131617i
$577$	16.5679	+	28.6964i	0.689730	+	1.19465i	0.971925	+	0.235291i	$0.0756043\pi$
$577$	16.5679	+	28.6964i	0.689730	+	1.19465i	−0.282195	+	0.959357i	$0.591062\pi$
$578$	0.718899	−	2.99516i	0.0299023	−	0.124582i
$579$	−8.08325	+	8.58042i	−0.335929	+	0.356590i
$580$	28.2689	+	14.3998i	1.17380	+	0.597918i
$581$	6.40372	−	5.37336i	0.265671	−	0.222924i
$582$	−3.97279	−	1.19854i	−0.164677	−	0.0496810i
$583$	0.831976	+	2.28583i	0.0344569	+	0.0946696i
$584$	−13.5519	−	38.2492i	−0.560782	−	1.58276i
$585$	−4.04616	+	0.241655i	−0.167288	+	0.00999118i
$586$	1.96902	+	3.94870i	0.0813397	+	0.163119i
$587$	27.2988	+	4.81352i	1.12674	+	0.198675i	0.705799	−	0.708412i	$-0.250588\pi$
$587$	27.2988	+	4.81352i	1.12674	+	0.198675i	0.420943	+	0.907087i	$0.361699\pi$
$588$	16.9879	+	14.3989i	0.700567	+	0.593803i
$589$	−0.450675	+	1.23822i	−0.0185697	+	0.0510199i
$590$	10.0155	−	23.0375i	0.412330	−	0.948439i
$591$	10.6079	−	1.24783i	0.436353	−	0.0513287i
$592$	−1.30861	−	12.4241i	−0.0537837	−	0.510627i
$593$		−	3.09941i		−	0.127277i	−0.997973	−	0.0636387i	$-0.979729\pi$
$593$		−	3.09941i		−	0.127277i	0.997973	−	0.0636387i	$-0.0202705\pi$
$594$	−17.0343	−	11.2193i	−0.698927	−	0.460332i
$595$	6.82417			0.279764
$596$	13.1252	−	42.9476i	0.537628	−	1.75920i
$597$	5.21118	+	2.24333i	0.213280	+	0.0918132i
$598$	−2.82697	+	6.50257i	−0.115603	+	0.265910i
$599$	−2.99899	−	1.09154i	−0.122535	−	0.0445992i	0.280025	−	0.959993i	$-0.409657\pi$
$599$	−2.99899	−	1.09154i	−0.122535	−	0.0445992i	−0.402560	+	0.915394i	$0.631880\pi$
$600$	2.65491	+	2.54432i	0.108386	+	0.103871i
$601$	1.48624	−	8.42889i	0.0606251	−	0.343822i	−0.939375	−	0.342893i	$-0.888593\pi$
$601$	1.48624	−	8.42889i	0.0606251	−	0.343822i	1.00000		0.000928888i	$-0.000295674\pi$
$602$	3.06007	−	1.52591i	0.124719	−	0.0621914i
$603$	5.18068	+	11.9616i	0.210973	+	0.487113i
$604$	31.6860	+	23.8716i	1.28928	+	0.971320i
$605$	6.38374	−	2.32349i	0.259536	−	0.0944634i
$606$	−0.794526	+	0.746426i	−0.0322754	+	0.0303215i
$607$	2.15954	+	2.57364i	0.0876531	+	0.104461i	0.808088	−	0.589061i	$-0.200502\pi$
$607$	2.15954	+	2.57364i	0.0876531	+	0.104461i	−0.720435	+	0.693522i	$0.756058\pi$
$608$	−1.39958	−	1.07332i	−0.0567605	−	0.0435289i
$609$	−2.31628	+	9.80538i	−0.0938602	+	0.397334i
$610$	−35.0451	−	8.41152i	−1.41893	−	0.340573i
$611$	−6.19438	+	3.57633i	−0.250598	+	0.144683i
$612$	−19.0358	−	18.1121i	−0.769475	−	0.732140i
$613$	−6.39597	−	3.69272i	−0.258331	−	0.149147i	0.365242	−	0.930913i	$-0.380986\pi$
$613$	−6.39597	−	3.69272i	−0.258331	−	0.149147i	−0.623573	+	0.781765i	$0.714320\pi$
$614$	−27.8762	−	26.4506i	−1.12499	−	1.06746i
$615$	13.1509	−	20.0271i	0.530294	−	0.807570i
$616$	5.11403	+	3.01125i	0.206050	+	0.121327i
$617$	−45.9169	+	8.09638i	−1.84854	+	0.325948i	−0.984215	−	0.176979i	$-0.943367\pi$
$617$	−45.9169	+	8.09638i	−1.84854	+	0.325948i	−0.864329	+	0.502928i	$0.832256\pi$
$618$	25.8316	−	16.9116i	1.03910	−	0.680283i
$619$	12.0986	+	10.1519i	0.486284	+	0.408041i	0.852692	−	0.522414i	$-0.174968\pi$
$619$	12.0986	+	10.1519i	0.486284	+	0.408041i	−0.366408	+	0.930454i	$0.619413\pi$
$620$	−16.0378	+	6.80976i	−0.644095	+	0.273487i
$621$	19.9500	+	34.3785i	0.800567	+	1.37956i
$622$	15.3738	−	23.2301i	0.616435	−	0.931443i
$623$	−3.71768	−	3.11950i	−0.148946	−	0.124980i
$624$	−3.61329	−	2.75043i	−0.144647	−	0.110105i
$625$	−3.59165	−	20.3693i	−0.143666	−	0.814771i
$626$	15.6632	−	11.5915i	0.626029	−	0.463290i
$627$	0.673730	+	1.33904i	0.0269062	+	0.0534761i
$628$	7.07362	+	30.6237i	0.282268	+	1.22202i
$629$	−6.83869	+	11.8450i	−0.272676	+	0.472289i
$630$	3.31351	−	5.72095i	0.132013	−	0.227928i
$631$	−36.1614	+	20.8778i	−1.43956	+	0.831132i	−0.997819	−	0.0660087i	$-0.978973\pi$
$631$	−36.1614	+	20.8778i	−1.43956	+	0.831132i	−0.441744	+	0.897141i	$0.645640\pi$
$632$	−5.15435	−	30.7697i	−0.205029	−	1.22395i
$633$	−3.18437	−	10.6080i	−0.126567	−	0.421632i
$634$	−1.78240	−	15.6362i	−0.0707883	−	0.620994i
$635$	5.06652	+	6.03805i	0.201059	+	0.239613i
$636$	2.84756	+	1.05248i	0.112913	+	0.0417335i
$637$	−1.44111	−	3.95942i	−0.0570988	−	0.156878i
$638$	1.84237	−	30.1500i	0.0729403	−	1.19365i
$639$	41.3205	−	9.85758i	1.63462	−	0.389960i
$640$	−2.24434	−	23.2139i	−0.0887155	−	0.917609i
$641$	−20.1746	−	3.55732i	−0.796848	−	0.140506i	−0.239621	−	0.970866i	$-0.577023\pi$
$641$	−20.1746	−	3.55732i	−0.796848	−	0.140506i	−0.557226	+	0.830361i	$0.688134\pi$
$642$	−13.4449	+	17.9800i	−0.530626	+	0.709616i
$643$	−16.7499	−	6.09648i	−0.660553	−	0.240422i	−0.0100781	−	0.999949i	$-0.503208\pi$
$643$	−16.7499	−	6.09648i	−0.660553	−	0.240422i	−0.650475	+	0.759527i	$0.725430\pi$
$644$	−6.29981	−	9.69851i	−0.248247	−	0.382175i
$645$	6.82648	+	9.15544i	0.268792	+	0.360495i
$646$	0.548535	+	1.85145i	0.0215818	+	0.0728442i
$647$	26.7567			1.05192			0.525958	−	0.850511i	$-0.323707\pi$
$647$	26.7567			1.05192			0.525958	+	0.850511i	$0.323707\pi$
$648$	−24.4270	+	7.16394i	−0.959583	+	0.281426i
$649$	−23.9177			−0.938853
$650$	−0.197645	−	0.667103i	−0.00775228	−	0.0261659i
$651$	−3.30759	−	4.43603i	−0.129635	−	0.173862i
$652$	−19.0711	+	12.3879i	−0.746881	+	0.485148i
$653$	−43.1647	−	15.7107i	−1.68916	−	0.614806i	−0.694645	−	0.719353i	$-0.744439\pi$
$653$	−43.1647	−	15.7107i	−1.68916	−	0.614806i	−0.994520	+	0.104547i	$0.966661\pi$
$654$	−18.5268	+	24.7762i	−0.724454	+	0.968825i
$655$	−27.0588	−	4.77120i	−1.05728	−	0.186426i
$656$	25.7998	−	7.40418i	1.00731	−	0.289085i
$657$	29.5824	+	31.2629i	1.15412	+	1.21968i
$658$	0.711568	−	11.6446i	0.0277398	−	0.453955i
$659$	13.8775	+	38.1282i	0.540592	+	1.48526i	0.846074	+	0.533066i	$0.178960\pi$
$659$	13.8775	+	38.1282i	0.540592	+	1.48526i	−0.305482	+	0.952198i	$0.598818\pi$
$660$	−6.87163	+	18.5917i	−0.267478	+	0.723681i
$661$	−16.6703	−	19.8669i	−0.648400	−	0.772733i	0.337272	−	0.941407i	$-0.390496\pi$
$661$	−16.6703	−	19.8669i	−0.648400	−	0.772733i	−0.985672	+	0.168675i	$0.946051\pi$
$662$	3.27762	+	28.7531i	0.127388	+	1.11752i
$663$	1.42938	+	4.76167i	0.0555125	+	0.184928i
$664$	5.16749	+	30.8482i	0.200538	+	1.19714i
$665$	−0.420768	+	0.242930i	−0.0163167	+	0.00942043i
$666$	6.60951	+	11.4845i	0.256113	+	0.445016i
$667$	−29.4314	+	50.9767i	−1.13959	+	1.97382i
$668$	−22.5460	+	5.20778i	−0.872329	+	0.201495i
$669$	−12.9341	−	25.7066i	−0.500062	−	0.993875i
$670$	10.1821	−	7.53525i	0.393370	−	0.291112i
$671$	5.95872	+	33.7936i	0.230034	+	1.30459i
$672$	6.99358	−	2.43882i	0.269783	−	0.0940797i
$673$	7.67968	+	6.44402i	0.296030	+	0.248399i	0.778690	−	0.627409i	$-0.215885\pi$
$673$	7.67968	+	6.44402i	0.296030	+	0.248399i	−0.482660	+	0.875808i	$0.660329\pi$
$674$	−27.7155	+	41.8786i	−1.06756	+	1.61310i
$675$	−3.66803	−	1.32587i	−0.141183	−	0.0510326i
$676$	−9.82586	−	23.1411i	−0.377918	−	0.890044i
$677$	−11.4265	−	9.58797i	−0.439156	−	0.368496i	0.396237	−	0.918148i	$-0.370316\pi$
$677$	−11.4265	−	9.58797i	−0.439156	−	0.368496i	−0.835394	+	0.549652i	$0.814760\pi$
$678$	26.3509	−	17.2515i	1.01200	−	0.662540i
$679$	−1.26116	+	0.222377i	−0.0483990	+	0.00853404i
$680$	−12.9556	+	22.0026i	−0.496823	+	0.843760i
$681$	0.420290	−	0.640048i	0.0161055	−	0.0245267i
$682$	12.0342	+	11.4188i	0.460815	+	0.437248i
$683$	−11.0184	−	6.36145i	−0.421605	−	0.243414i	0.274158	−	0.961685i	$-0.411601\pi$
$683$	−11.0184	−	6.36145i	−0.421605	−	0.243414i	−0.695764	+	0.718270i	$0.744934\pi$
$684$	1.81848	+	0.439122i	0.0695314	+	0.0167902i
$685$	24.2090	−	13.9770i	0.924977	−	0.534035i
$686$	13.9594	+	3.35053i	0.532972	+	0.127924i
$687$	3.85118	−	16.3030i	0.146932	−	0.621998i
$688$	−0.889645	+	12.7632i	−0.0339174	+	0.486594i
$689$	−0.369221	−	0.440021i	−0.0140662	−	0.0167635i
$690$	28.1509	−	26.4466i	1.07168	−	1.00681i
$691$	18.7595	−	6.82789i	0.713644	−	0.259745i	0.0404189	−	0.999183i	$-0.487131\pi$
$691$	18.7595	−	6.82789i	0.713644	−	0.259745i	0.673225	+	0.739438i	$0.264909\pi$
$692$	−8.58162	+	11.3908i	−0.326224	+	0.433014i
$693$	−6.25323	−	0.721544i	−0.237541	−	0.0274092i
$694$	14.1436	−	7.05274i	0.536885	−	0.267718i
$695$	−0.378093	+	2.14427i	−0.0143419	+	0.0813369i
$696$	−27.2172	−	26.0835i	−1.03167	−	0.988693i
$697$	−27.6141	−	10.0507i	−1.04596	−	0.380698i
$698$	16.6024	−	38.1886i	0.628409	−	1.44546i
$699$	−2.74228	−	1.18051i	−0.103723	−	0.0446508i
$700$	1.08528	+	0.331672i	0.0410198	+	0.0125360i
$701$	−23.1054			−0.872679			−0.436340	−	0.899782i	$-0.643725\pi$
$701$	−23.1054			−0.872679			−0.436340	+	0.899782i	$0.643725\pi$
$702$	4.68593	+	1.11375i	0.176859	+	0.0420358i
$703$		−	0.973789i		−	0.0367272i
$704$	−19.4178	+	10.7719i	−0.731836	+	0.405982i
$705$	38.6968	−	4.55196i	1.45741	−	0.171437i
$706$	0.928708	−	2.13621i	0.0349524	−	0.0803972i
$707$	−0.115066	+	0.316141i	−0.00432749	+	0.0118897i
$708$	−19.3004	+	22.7706i	−0.725353	+	0.855770i
$709$	−2.25096	−	0.396904i	−0.0845364	−	0.0149061i	0.131220	−	0.991353i	$-0.458111\pi$
$709$	−2.25096	−	0.396904i	−0.0845364	−	0.0149061i	−0.215756	+	0.976447i	$0.569222\pi$
$710$	−18.4212	−	36.9421i	−0.691336	−	1.38641i
$711$	18.2245	+	27.6202i	0.683474	+	1.03584i
$712$	17.1159	−	6.06426i	0.641445	−	0.227268i
$713$	−11.0568	−	30.3783i	−0.414080	−	1.13768i
$714$	−7.76331	−	2.34209i	−0.290535	−	0.0876505i
$715$	2.87289	−	2.41064i	0.107440	−	0.0901530i
$716$	5.70866	−	11.2070i	0.213343	−	0.418824i
$717$	7.59562	−	8.06280i	0.283664	−	0.301111i
$718$	3.41541	−	14.2297i	0.127462	−	0.531047i
$719$	9.89692	+	17.1420i	0.369093	+	0.639287i	0.989424	−	0.145053i	$-0.0463351\pi$
$719$	9.89692	+	17.1420i	0.369093	+	0.639287i	−0.620331	+	0.784340i	$0.713002\pi$
$720$	12.1549	+	21.5446i	0.452987	+	0.802919i
$721$	4.76417	−	8.25179i	0.177427	−	0.307313i
$722$	19.3921	+	18.4004i	0.721701	+	0.684793i
$723$	−1.81580	+	31.5775i	−0.0675303	+	1.17438i
$724$	−28.4991	+	1.49675i	−1.05916	+	0.0556262i
$725$	−1.00299	−	5.68825i	−0.0372502	−	0.211256i
$726$	−8.05971	+	0.452319i	−0.299124	+	0.0167871i
$727$	11.5970	−	13.8207i	0.430107	−	0.512582i	−0.506846	−	0.862037i	$-0.669189\pi$
$727$	11.5970	−	13.8207i	0.430107	−	0.512582i	0.936953	+	0.349455i	$0.113633\pi$
$728$	−1.37797	−	0.255155i	−0.0510710	−	0.00945666i
$729$	20.6062	−	17.4467i	0.763191	−	0.646173i
$730$	23.0827	−	34.8784i	0.854330	−	1.29091i
$731$	9.00374	−	10.7302i	0.333015	−	0.396872i
$732$	36.9811	+	21.5968i	1.36686	+	0.798239i
$733$	−6.13198	+	1.08123i	−0.226490	+	0.0399362i	−0.285741	−	0.958307i	$-0.592240\pi$
$733$	−6.13198	+	1.08123i	−0.226490	+	0.0399362i	0.0592514	+	0.998243i	$0.481129\pi$
$734$	5.57153	+	7.52861i	0.205649	+	0.277886i
$735$	−1.31768	+	22.9150i	−0.0486034	+	0.845234i
$736$	43.2301	−	1.89949i	1.59348	−	0.0700160i
$737$	−10.4448	−	6.03032i	−0.384740	−	0.222130i
$738$	−21.8341	+	18.2698i	−0.803723	+	0.672519i
$739$	−17.2254	−	29.8353i	−0.633647	−	1.09751i	−0.986800	−	0.161944i	$-0.948224\pi$
$739$	−17.2254	−	29.8353i	−0.633647	−	1.09751i	0.353153	−	0.935566i	$-0.385110\pi$
$740$	9.41621	−	8.78271i	0.346147	−	0.322859i
$741$	−0.257642	−	0.242713i	−0.00946470	−	0.00891629i
$742$	0.930859	−	0.106110i	0.0341729	−	0.00389543i
$743$	−20.9598	+	17.5873i	−0.768939	+	0.645217i	−0.940437	−	0.339968i	$-0.889584\pi$
$743$	−20.9598	+	17.5873i	−0.768939	+	0.645217i	0.171498	+	0.985185i	$0.445139\pi$
$744$	20.5821	−	2.24265i	0.754577	−	0.0822196i
$745$	43.4957	−	15.8311i	1.59356	−	0.580008i
$746$	0.824657	−	13.4953i	0.0301928	−	0.494099i
$747$	−18.2710	−	27.6906i	−0.668502	−	1.01315i
$748$	24.1301	+	2.96009i	0.882286	+	0.108232i
$749$	−1.20313	+	6.82331i	−0.0439616	+	0.249318i
$750$	−3.43200	+	28.8335i	−0.125319	+	1.05285i
$751$	−7.78513	+	21.3895i	−0.284084	+	0.780513i	0.712781	+	0.701387i	$0.247435\pi$
$751$	−7.78513	+	21.3895i	−0.284084	+	0.780513i	−0.996865	+	0.0791265i	$0.974787\pi$
$752$	36.1939	+	24.4014i	1.31985	+	0.889827i
$753$	−5.36859	−	45.6391i	−0.195642	−	1.66318i
$754$	2.02619	+	6.83891i	0.0737895	+	0.249058i
$755$			40.8898i			1.48813i
$756$	−5.73297	+	5.37106i	−0.208506	+	0.195344i
$757$			21.1725i			0.769529i	0.923015	+	0.384765i	$0.125717\pi$
$757$			21.1725i			0.769529i	−0.923015	+	0.384765i	$0.874283\pi$
$758$	44.5592	−	13.2017i	1.61846	−	0.479508i
$759$	−33.7789	−	14.5412i	−1.22610	−	0.527813i
$760$	0.0155614	−	1.81784i	0.000564471	−	0.0659401i
$761$	−7.32872	+	20.1355i	−0.265666	+	0.729911i	0.733094	+	0.680127i	$0.238076\pi$
$761$	−7.32872	+	20.1355i	−0.265666	+	0.729911i	−0.998760	+	0.0497840i	$0.984147\pi$
$762$	−3.69149	−	8.60786i	−0.133729	−	0.311830i
$763$	−1.65790	+	9.40240i	−0.0600199	+	0.340390i
$764$	19.6932	+	2.41580i	0.712474	+	0.0874005i
$765$	3.10437	−	26.9039i	0.112239	−	0.972711i
$766$	−26.5978	−	1.62531i	−0.961016	−	0.0587247i
$767$	5.30721	−	1.93167i	0.191632	−	0.0697485i
$768$	−5.41391	+	27.1788i	−0.195358	+	0.980732i
$769$	23.3889	−	19.6256i	0.843426	−	0.707719i	−0.114905	−	0.993376i	$-0.536656\pi$
$769$	23.3889	−	19.6256i	0.843426	−	0.707719i	0.958332	+	0.285658i	$0.0922120\pi$
$770$	0.692794	+	6.07757i	0.0249665	+	0.219021i
$771$	9.23924	−	39.1120i	0.332743	−	1.40859i
$772$	−9.28439	−	9.95408i	−0.334153	−	0.358255i
$773$	19.2878	+	33.4074i	0.693734	+	1.20158i	0.970606	+	0.240675i	$0.0773689\pi$
$773$	19.2878	+	33.4074i	0.693734	+	1.20158i	−0.276872	+	0.960907i	$0.589298\pi$
$774$	−4.62375	−	12.7583i	−0.166197	−	0.458587i
$775$	2.74723	+	1.58611i	0.0986833	+	0.0569748i
$776$	1.67730	−	4.48843i	0.0602117	−	0.161125i
$777$	3.41819	+	2.24457i	0.122627	+	0.0805234i
$778$	−39.4279	+	29.1785i	−1.41356	+	1.04610i
$779$	2.06043	−	0.363310i	0.0738227	−	0.0130169i
$780$	0.0232560	−	4.68037i	0.000832698	−	0.167584i
$781$	−25.2640	+	30.1085i	−0.904019	+	1.07737i
$782$	−39.5066	−	26.1457i	−1.41275	−	0.934969i
$783$	37.6034	+	13.5923i	1.34384	+	0.485750i
$784$	−17.8585	+	18.5012i	−0.637804	+	0.660759i
$785$	−20.8231	+	24.8160i	−0.743209	+	0.885722i
$786$	29.1452	+	14.7145i	1.03957	+	0.524850i
$787$	0.641604	+	3.63872i	0.0228707	+	0.129706i	0.994105	−	0.108418i	$-0.0345785\pi$
$787$	0.641604	+	3.63872i	0.0228707	+	0.129706i	−0.971235	+	0.238124i	$0.923467\pi$
$788$	0.646850	+	12.3165i	0.0230431	+	0.438756i
$789$	19.5850	−	9.85408i	0.697246	−	0.350815i
$790$	22.1336	−	23.3266i	0.787479	−	0.829922i
$791$	4.85994	−	8.41767i	0.172800	−	0.299298i
$792$	14.1981	−	18.7919i	0.504506	−	0.667742i
$793$	−4.05147	−	7.01736i	−0.143872	−	0.249194i
$794$	−12.2582	−	2.94220i	−0.435026	−	0.104415i
$795$	0.899632	+	2.99693i	0.0319067	+	0.106290i
$796$	−2.97355	+	5.83752i	−0.105395	+	0.206905i
$797$	−20.3153	+	17.0465i	−0.719604	+	0.603820i	−0.927276	−	0.374379i	$-0.877856\pi$
$797$	−20.3153	+	17.0465i	−0.719604	+	0.603820i	0.207672	+	0.978199i	$0.433411\pi$
$798$	0.562049	−	0.131953i	0.0198963	−	0.00467108i
$799$	−16.3452	−	44.9080i	−0.578251	−	1.58873i
$800$	−3.12977	+	2.86950i	−0.110654	+	0.101452i
$801$	−13.9896	+	13.2376i	−0.494300	+	0.467729i
$802$	−6.72949	+	3.35567i	−0.237627	+	0.118493i
$803$	−39.2174	−	6.91508i	−1.38395	−	0.244028i
$804$	−14.1695	+	5.07770i	−0.499721	+	0.179077i
$805$	4.07690	−	11.2012i	0.143692	−	0.394790i
$806$	−3.59254	−	1.56185i	−0.126542	−	0.0550136i
$807$	1.24334	+	1.66753i	0.0437678	+	0.0586998i
$808$	−0.800854	−	0.971184i	−0.0281739	−	0.0341661i
$809$			3.27098i			0.115001i	0.998345	+	0.0575007i	$0.0183131\pi$
$809$			3.27098i			0.115001i	−0.998345	+	0.0575007i	$0.981687\pi$
$810$	−21.0472	−	15.6658i	−0.739522	−	0.550440i
$811$	−1.75903			−0.0617677			−0.0308839	−	0.999523i	$-0.509832\pi$
$811$	−1.75903			−0.0617677			−0.0308839	+	0.999523i	$0.509832\pi$
$812$	−11.1259	−	3.40019i	−0.390443	−	0.119323i
$813$	−8.07027	+	6.01735i	−0.283037	+	0.211038i
$814$	−11.2433	−	4.88800i	−0.394079	−	0.171324i
$815$	−22.0259	−	8.01678i	−0.771534	−	0.280816i
$816$	22.2899	−	20.5841i	0.780303	−	0.720589i
$817$	−0.173176	+	0.982130i	−0.00605866	+	0.0343604i
$818$	19.3801	+	38.8650i	0.677609	+	1.35888i
$819$	1.44583	−	0.344923i	0.0505214	−	0.0120526i
$820$	22.0964	+	16.6470i	0.771639	+	0.581337i
$821$	46.0142	−	16.7478i	1.60591	−	0.584502i	0.625282	−	0.780399i	$-0.284984\pi$
$821$	46.0142	−	16.7478i	1.60591	−	0.584502i	0.980625	+	0.195897i	$0.0627617\pi$
$822$	−32.3376	+	7.59193i	−1.12790	+	0.264799i
$823$	11.6513	+	13.8855i	0.406139	+	0.484017i	0.929882	−	0.367859i	$-0.119909\pi$
$823$	11.6513	+	13.8855i	0.406139	+	0.484017i	−0.523743	+	0.851876i	$0.675465\pi$
$824$	17.5608	+	31.0266i	0.611760	+	1.08086i
$825$	3.45631	−	1.03753i	0.120333	−	0.0361222i
$826$	−2.14997	+	8.95748i	−0.0748072	+	0.311671i
$827$	11.2394	−	6.48908i	0.390833	−	0.225648i	−0.291688	−	0.956514i	$-0.594217\pi$
$827$	11.2394	−	6.48908i	0.390833	−	0.225648i	0.682521	+	0.730866i	$0.260884\pi$
$828$	−41.1016	+	20.4247i	−1.42838	+	0.709807i
$829$	4.97254	+	2.87090i	0.172703	+	0.0997104i	0.583860	−	0.811854i	$-0.301542\pi$
$829$	4.97254	+	2.87090i	0.172703	+	0.0997104i	−0.411157	+	0.911565i	$0.634875\pi$
$830$	−22.1901	+	23.3861i	−0.770229	+	0.811742i
$831$	−11.3385	−	22.5352i	−0.393327	−	0.781739i
$832$	3.43873	−	3.95847i	0.119216	−	0.137235i
$833$	27.7247	−	4.88862i	0.960605	−	0.169381i
$834$	1.16605	−	2.30960i	0.0403770	−	0.0799750i
$835$	−18.2702	−	15.3305i	−0.632266	−	0.530534i
$836$	−1.59320	+	0.676483i	−0.0551021	+	0.0233967i
$837$	−18.9934	+	11.0220i	−0.656509	+	0.380976i
$838$	−11.5910	−	7.67098i	−0.400404	−	0.264990i
$839$	25.0821	+	21.0464i	0.865930	+	0.726602i	0.963237	−	0.268653i	$-0.0865784\pi$
$839$	25.0821	+	21.0464i	0.865930	+	0.726602i	−0.0973069	+	0.995254i	$0.531023\pi$
$840$	6.34512	+	4.24472i	0.218927	+	0.146457i
$841$	5.24653	+	29.7545i	0.180915	+	1.02602i
$842$	14.2070	+	19.1974i	0.489605	+	0.661586i
$843$	−9.30526	+	14.1707i	−0.320490	+	0.488066i
$844$	12.4610	−	2.87830i	0.428925	−	0.0990753i
$845$	12.9563	−	22.4410i	0.445712	−	0.771995i
$846$	−45.5845	−	8.10254i	−1.56723	−	0.278571i
$847$	−2.15745	+	1.24561i	−0.0741310	+	0.0427996i
$848$	−1.42510	+	3.20273i	−0.0489381	+	0.109982i
$849$	2.33527	+	0.551649i	0.0801462	+	0.0189325i
$850$	4.61881	−	0.526507i	0.158424	−	0.0180590i
$851$	15.3567	+	18.3014i	0.526422	+	0.627365i
$852$	8.27762	+	48.3483i	0.283587	+	1.65639i
$853$	−17.3146	−	47.5715i	−0.592842	−	1.62882i	−0.765206	−	0.643785i	$-0.777363\pi$
$853$	−17.3146	−	47.5715i	−0.592842	−	1.62882i	0.172364	−	0.985033i	$-0.444859\pi$
$854$	13.1917	+	0.806106i	0.451412	+	0.0275844i
$855$	0.766327	+	1.76936i	0.0262078	+	0.0605109i
$856$	−19.7157	−	16.8331i	−0.673868	−	0.575344i
$857$	43.9658	+	7.75236i	1.50184	+	0.264816i	0.863269	−	0.504744i	$-0.168413\pi$
$857$	43.9658	+	7.75236i	1.50184	+	0.264816i	0.638575	+	0.769559i	$0.279524\pi$
$858$	−4.09561	+	1.75641i	−0.139822	+	0.0599627i
$859$	21.2132	+	7.72099i	0.723786	+	0.263437i	0.677532	−	0.735493i	$-0.263049\pi$
$859$	21.2132	+	7.72099i	0.723786	+	0.263437i	0.0462539	+	0.998930i	$0.485272\pi$
$860$	−11.0588	+	7.18339i	−0.377100	+	0.244951i
$861$	−3.47398	+	8.06995i	−0.118393	+	0.275023i
$862$	−6.75889	+	2.00248i	−0.230209	+	0.0682048i
$863$	5.45202			0.185589			0.0927945	−	0.995685i	$-0.470420\pi$
$863$	5.45202			0.185589			0.0927945	+	0.995685i	$0.470420\pi$
$864$	−6.43348	−	28.6812i	−0.218871	−	0.975754i
$865$	−14.6995			−0.499799
$866$	2.05357	−	0.608418i	0.0697830	−	0.0206749i
$867$	−3.74666	+	0.440725i	−0.127243	+	0.0149678i
$868$	5.35823	−	3.48052i	0.181870	−	0.118137i
$869$	−28.7703	−	10.4715i	−0.975966	−	0.355222i
$870$	4.59244	−	38.5829i	0.155698	−	1.30808i
$871$	2.80468	+	0.494540i	0.0950328	+	0.0167568i
$872$	−27.1679	−	23.1957i	−0.920020	−	0.785506i
$873$	0.302995	+	5.07321i	0.0102548	+	0.171702i
$874$	3.36667	+	0.205727i	0.113879	+	0.00695881i
$875$	3.06488	+	8.42069i	0.103612	+	0.284671i
$876$	−38.2298	+	31.7563i	−1.29167	+	1.07294i
$877$	17.8965	+	21.3282i	0.604322	+	0.720203i	0.978291	−	0.207238i	$-0.0664475\pi$
$877$	17.8965	+	21.3282i	0.604322	+	0.720203i	−0.373968	+	0.927442i	$0.622003\pi$
$878$	−15.9107	+	1.81369i	−0.536960	+	0.0612091i
$879$	3.70560	−	3.93351i	0.124987	−	0.132674i
$880$	−20.9106	−	9.30445i	−0.704897	−	0.313653i
$881$	15.7703	−	9.10498i	0.531315	−	0.306755i	−0.210237	−	0.977650i	$-0.567424\pi$
$881$	15.7703	−	9.10498i	0.531315	−	0.306755i	0.741552	+	0.670896i	$0.234090\pi$
$882$	9.36358	−	25.6164i	0.315288	−	0.862548i
$883$	−9.43348	+	16.3393i	−0.317462	+	0.549860i	−0.979958	−	0.199206i	$-0.936164\pi$
$883$	−9.43348	+	16.3393i	−0.317462	+	0.549860i	0.662496	+	0.749065i	$0.269497\pi$
$884$	−5.59341	+	1.29199i	−0.188127	+	0.0434545i
$885$	−30.7154	−	1.76622i	−1.03249	−	0.0593710i
$886$	2.74235	+	3.70564i	0.0921310	+	0.124493i
$887$	4.50791	+	25.5656i	0.151361	+	0.858409i	0.962038	+	0.272916i	$0.0879880\pi$
$887$	4.50791	+	25.5656i	0.151361	+	0.858409i	−0.810677	+	0.585493i	$0.800901\pi$
$888$	−13.7263	+	6.75970i	−0.460626	+	0.226841i
$889$	−2.21421	−	1.85794i	−0.0742621	−	0.0623133i
$890$	15.6075	+	10.3291i	0.523165	+	0.346234i
$891$	−5.68929	+	24.3247i	−0.190598	+	0.814910i
$892$	30.5860	−	12.9870i	1.02409	−	0.434836i
$893$	2.60648	+	2.18709i	0.0872224	+	0.0731883i
$894$	−54.9149	+	3.08188i	−1.83663	+	0.103074i
$895$	12.7663	−	2.25105i	0.426732	−	0.0752444i
$896$	2.28874	+	8.24049i	0.0764614	+	0.275295i
$897$	8.66973	+	0.498535i	0.289474	+	0.0166456i
$898$	−21.4047	+	22.5583i	−0.714283	+	0.752781i
$899$	−28.1636	−	16.2603i	−0.939309	−	0.542310i
$900$	1.80130	−	4.12777i	0.0600433	−	0.137592i
$901$	3.32369	−	1.91893i	0.110728	−	0.0639290i
$902$	6.14772	−	25.6134i	0.204697	−	0.852831i
$903$	−3.04830	−	2.87167i	−0.101441	−	0.0955634i
$904$	17.9138	+	31.6503i	0.595805	+	1.05267i
$905$	−18.9073	−	22.5329i	−0.628501	−	0.749018i
$906$	14.0336	−	46.5170i	0.466234	−	1.54543i
$907$	6.38033	−	2.32225i	0.211855	−	0.0771090i	−0.233912	−	0.972258i	$-0.575153\pi$
$907$	6.38033	−	2.32225i	0.211855	−	0.0771090i	0.445768	+	0.895149i	$0.352931\pi$
$908$	0.706181	+	0.532022i	0.0234354	+	0.0176558i
$909$	1.19402	+	0.597454i	0.0396032	+	0.0198163i
$910$	−0.644570	−	1.29263i	−0.0213673	−	0.0428502i
$911$	7.60529	−	43.1317i	0.251974	−	1.42902i	−0.551747	−	0.834012i	$-0.686038\pi$
$911$	7.60529	−	43.1317i	0.251974	−	1.42902i	0.803721	−	0.595006i	$-0.202850\pi$
$912$	−0.641596	+	2.06267i	−0.0212454	+	0.0683020i
$913$	28.8437	+	10.4982i	0.954587	+	0.347441i
$914$	−1.03436	−	0.449682i	−0.0342135	−	0.0148742i
$915$	5.15673	+	43.8381i	0.170476	+	1.44924i
$916$	18.4986	+	5.65335i	0.611211	+	0.186792i
$917$	10.0758			0.332732
$918$	−12.7651	+	29.5409i	−0.421312	+	0.974996i
$919$		−	53.5416i		−	1.76617i	−0.469209	−	0.883087i	$-0.655461\pi$
$919$		−	53.5416i		−	1.76617i	0.469209	−	0.883087i	$-0.344539\pi$
$920$	28.3751	+	34.4100i	0.935498	+	1.13446i
$921$	−18.6094	+	43.2292i	−0.613201	+	1.42445i
$922$	−3.90763	−	1.69883i	−0.128691	−	0.0559480i
$923$	3.17430	−	8.72131i	0.104483	−	0.287065i
$924$	1.29772	−	7.15174i	0.0426918	−	0.235275i
$925$	−2.30871	−	0.407087i	−0.0759098	−	0.0133849i
$926$	−12.2511	+	6.10901i	−0.402595	+	0.200755i
$927$	−30.3649	−	22.5363i	−0.997314	−	0.740188i
$928$	32.0853	−	29.4171i	1.05325	−	0.965665i
$929$	−6.19598	−	17.0233i	−0.203284	−	0.558517i	0.795597	−	0.605827i	$-0.207157\pi$
$929$	−6.19598	−	17.0233i	−0.203284	−	0.558517i	−0.998880	+	0.0473097i	$0.984935\pi$
$930$	14.6112	+	15.5528i	0.479121	+	0.509996i
$931$	−1.53544	+	1.28838i	−0.0503219	+	0.0422251i
$932$	1.56477	−	3.07188i	0.0512558	−	0.100623i
$933$	−33.2035	−	7.84349i	−1.08703	−	0.256784i
$934$	7.44688	+	1.78740i	0.243669	+	0.0584855i
$935$	12.5287	+	21.7004i	0.409733	+	0.709678i
$936$	−1.63278	+	5.31650i	−0.0533691	+	0.173775i
$937$	18.2222	−	31.5618i	0.595294	−	1.03108i	−0.398212	−	0.917294i	$-0.630369\pi$
$937$	18.2222	−	31.5618i	0.595294	−	1.03108i	0.993505	−	0.113785i	$-0.0362976\pi$
$938$	−3.19732	+	3.36964i	−0.104396	+	0.110023i
$939$	−19.9488	−	13.0995i	−0.651004	−	0.427484i
$940$	2.35965	+	44.9294i	0.0769633	+	1.46544i
$941$	1.27775	+	7.24648i	0.0416535	+	0.236229i	0.998526	−	0.0542804i	$-0.0172865\pi$
$941$	1.27775	+	7.24648i	0.0416535	+	0.236229i	−0.956872	+	0.290509i	$0.906175\pi$
$942$	32.2058	−	21.0846i	1.04932	−	0.686974i
$943$	−32.9944	+	39.3213i	−1.07445	+	1.28048i
$944$	−24.7991	−	23.9376i	−0.807142	−	0.779102i
$945$	−7.97718	−	1.38839i	−0.259498	−	0.0451643i
$946$	10.4704	+	6.92935i	0.340421	+	0.225293i
$947$	8.67174	−	10.3346i	0.281794	−	0.335829i	−0.606518	−	0.795070i	$-0.707434\pi$
$947$	8.67174	−	10.3346i	0.281794	−	0.335829i	0.888312	+	0.459241i	$0.151879\pi$
$948$	−33.1854	+	18.9404i	−1.07781	+	0.615155i
$949$	9.26060	−	1.63289i	0.300612	−	0.0530059i
$950$	−0.266046	+	0.196887i	−0.00863167	+	0.00638784i
$951$	−17.2179	+	8.66305i	−0.558328	+	0.280919i
$952$	3.27766	−	8.77094i	0.106229	−	0.284268i
$953$	33.5466	+	19.3681i	1.08668	+	0.627395i	0.932690	−	0.360678i	$-0.117455\pi$
$953$	33.5466	+	19.3681i	1.08668	+	0.627395i	0.153989	+	0.988073i	$0.450788\pi$
$954$	0.00512147	−	3.71812i	0.000165814	−	0.120379i
$955$	10.2250	+	17.7102i	0.330872	+	0.573087i
$956$	8.72430	+	9.35359i	0.282164	+	0.302517i
$957$	−35.4329	+	10.6364i	−1.14538	+	0.343827i
$958$	−2.26665	−	19.8844i	−0.0732323	−	0.642435i
$959$	−7.85273	+	6.58922i	−0.253578	+	0.212777i
$960$	−25.7320	+	12.3995i	−0.830496	+	0.400191i
$961$	−12.3471	+	4.49396i	−0.398292	+	0.144967i
$962$	2.88960	+	0.176575i	0.0931645	+	0.00569299i
$963$	26.3532	+	7.84726i	0.849219	+	0.252874i
$964$	−36.2511	−	4.44699i	−1.16757	−	0.143228i
$965$	2.43625	−	13.8167i	0.0784256	−	0.444774i
$966$	−8.48226	+	11.3435i	−0.272912	+	0.364970i
$967$	5.65523	−	15.5376i	0.181860	−	0.499656i	−0.814944	−	0.579539i	$-0.803233\pi$
$967$	5.65523	−	15.5376i	0.181860	−	0.499656i	0.996804	+	0.0798834i	$0.0254548\pi$
$968$	0.0797899	−	9.32085i	0.00256454	−	0.299584i
$969$	1.89596	−	1.41367i	0.0609070	−	0.0454135i
$970$	4.73525	−	1.40293i	0.152040	−	0.0450454i
$971$		−	54.1911i		−	1.73907i	−0.493868	−	0.869537i	$-0.664417\pi$
$971$		−	54.1911i		−	1.73907i	0.493868	−	0.869537i	$-0.335583\pi$
$972$	18.5671	+	25.0452i	0.595540	+	0.803326i
$973$		−	0.798454i		−	0.0255972i
$974$	7.80060	+	26.3290i	0.249947	+	0.843636i
$975$	−0.683142	+	0.509364i	−0.0218781	+	0.0163127i
$976$	−27.6433	+	41.0025i	−0.884841	+	1.31246i
$977$	6.10992	−	16.7869i	0.195474	−	0.537060i	−0.802771	−	0.596288i	$-0.796642\pi$
$977$	6.10992	−	16.7869i	0.195474	−	0.537060i	0.998244	+	0.0592281i	$0.0188639\pi$
$978$	22.3057	+	16.6795i	0.713259	+	0.533350i
$979$	3.09439	−	17.5491i	0.0988971	−	0.560873i
$980$	−26.3065	−	3.22707i	−0.840331	−	0.103085i
$981$	36.3142	+	10.8134i	1.15942	+	0.345245i
$982$	2.14929	−	35.1725i	0.0685865	−	1.12240i
$983$	−5.24850	+	1.91030i	−0.167401	+	0.0609291i	−0.424361	−	0.905493i	$-0.639501\pi$
$983$	−5.24850	+	1.91030i	−0.167401	+	0.0609291i	0.256960	+	0.966422i	$0.417279\pi$
$984$	−19.4240	−	26.5215i	−0.619213	−	0.845475i
$985$	−9.73805	+	8.17119i	−0.310280	+	0.260356i
$986$	−47.3505	+	5.39757i	−1.50795	+	0.171894i
$987$	−13.6850	+	4.10803i	−0.435599	+	0.130760i
$988$	0.298888	−	0.278779i	0.00950889	−	0.00886916i
$989$	−12.2336	−	21.1892i	−0.389005	−	0.673777i
$990$	24.2756	+	0.0334380i	0.771529	+	0.00106273i
$991$	32.6527	+	18.8521i	1.03725	+	0.598855i	0.919053	−	0.394135i	$-0.128956\pi$
$991$	32.6527	+	18.8521i	1.03725	+	0.598855i	0.118195	+	0.992990i	$0.462289\pi$
$992$	1.04943	+	23.8838i	0.0333194	+	0.758311i
$993$	31.6615	−	15.9303i	1.00475	−	0.505532i
$994$	9.00500	+	12.1681i	0.285621	+	0.385950i
$995$	−6.64978	+	1.17254i	−0.210812	+	0.0371719i
$996$	33.2701	−	18.9887i	1.05420	−	0.601680i
$997$	16.6660	−	19.8617i	0.527817	−	0.629028i	−0.434594	−	0.900627i	$-0.643108\pi$
$997$	16.6660	−	19.8617i	0.527817	−	0.629028i	0.962411	+	0.271599i	$0.0875524\pi$
$998$	26.7694	−	40.4491i	0.847371	−	1.28039i
$999$	10.4040	−	12.4549i	0.329169	−	0.394057i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.v.b.11.29	yes	192
3.2	odd	2		648.2.v.b.35.4		192
4.3	odd	2		864.2.bh.b.335.20		192
8.3	odd	2	inner	216.2.v.b.11.19	✓	192
8.5	even	2		864.2.bh.b.335.19		192
24.11	even	2		648.2.v.b.35.14		192
27.5	odd	18	inner	216.2.v.b.59.19	yes	192
27.22	even	9		648.2.v.b.611.14		192
108.59	even	18		864.2.bh.b.815.19		192
216.5	odd	18		864.2.bh.b.815.20		192
216.59	even	18	inner	216.2.v.b.59.29	yes	192
216.211	odd	18		648.2.v.b.611.4		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.11.19	✓	192	8.3	odd	2	inner
216.2.v.b.11.29	yes	192	1.1	even	1	trivial
216.2.v.b.59.19	yes	192	27.5	odd	18	inner
216.2.v.b.59.29	yes	192	216.59	even	18	inner
648.2.v.b.35.4		192	3.2	odd	2
648.2.v.b.35.14		192	24.11	even	2
648.2.v.b.611.4		192	216.211	odd	18
648.2.v.b.611.14		192	27.22	even	9
864.2.bh.b.335.19		192	8.5	even	2
864.2.bh.b.335.20		192	4.3	odd	2
864.2.bh.b.815.19		192	108.59	even	18
864.2.bh.b.815.20		192	216.5	odd	18

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.v (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.35595 - 0.401734i) q^{2} +(-1.03533 - 1.38855i) q^{3} +(1.67722 - 1.08946i) q^{4} +(1.93709 + 0.705042i) q^{5} +(-1.96169 - 1.46689i) q^{6} +(-0.744451 - 0.131267i) q^{7} +(1.83656 - 2.15106i) q^{8} +(-0.856167 + 2.87524i) q^{9} +O(q^{10})\)	\(q+(1.35595 - 0.401734i) q^{2} +(-1.03533 - 1.38855i) q^{3} +(1.67722 - 1.08946i) q^{4} +(1.93709 + 0.705042i) q^{5} +(-1.96169 - 1.46689i) q^{6} +(-0.744451 - 0.131267i) q^{7} +(1.83656 - 2.15106i) q^{8} +(-0.856167 + 2.87524i) q^{9} +(2.90984 + 0.177811i) q^{10} +(-0.949342 - 2.60830i) q^{11} +(-3.24926 - 1.20095i) q^{12} +(0.421307 + 0.502095i) q^{13} +(-1.06217 + 0.121079i) q^{14} +(-1.02654 - 3.41970i) q^{15} +(1.62614 - 3.65454i) q^{16} +(-3.79256 + 2.18964i) q^{17} +(-0.00584395 + 4.24264i) q^{18} +(0.155896 - 0.270019i) q^{19} +(4.01704 - 0.927876i) q^{20} +(0.588484 + 1.16962i) q^{21} +(-2.33510 - 3.15535i) q^{22} +(1.32831 + 7.53324i) q^{23} +(-4.88831 - 0.323097i) q^{24} +(-0.575004 - 0.482485i) q^{25} +(0.772981 + 0.511564i) q^{26} +(4.87884 - 1.78799i) q^{27} +(-1.39162 + 0.590889i) q^{28} +(5.89474 + 4.94627i) q^{29} +(-2.76575 - 4.22456i) q^{30} +(-4.16197 + 0.733867i) q^{31} +(0.736811 - 5.60866i) q^{32} +(-2.63888 + 4.01867i) q^{33} +(-4.26289 + 4.49265i) q^{34} +(-1.34952 - 0.779144i) q^{35} +(1.69649 + 5.75517i) q^{36} +(2.70478 - 1.56160i) q^{37} +(0.102912 - 0.428762i) q^{38} +(0.260992 - 1.10484i) q^{39} +(5.07416 - 2.87194i) q^{40} +(4.31331 + 5.14040i) q^{41} +(1.26783 + 1.34953i) q^{42} +(-3.00565 + 1.09397i) q^{43} +(-4.43390 - 3.34041i) q^{44} +(-3.68563 + 4.96594i) q^{45} +(4.82749 + 9.68110i) q^{46} +(-1.89499 + 10.7470i) q^{47} +(-6.75813 + 1.52570i) q^{48} +(-6.04087 - 2.19870i) q^{49} +(-0.973509 - 0.423229i) q^{50} +(6.96700 + 2.99917i) q^{51} +(1.25364 + 0.383124i) q^{52} -0.876371 q^{53} +(5.89718 - 4.38443i) q^{54} -5.72182i q^{55} +(-1.64959 + 1.36028i) q^{56} +(-0.536341 + 0.0630905i) q^{57} +(9.98008 + 4.33880i) q^{58} +(2.94714 - 8.09720i) q^{59} +(-5.44738 - 4.61721i) q^{60} +(-12.1748 - 2.14675i) q^{61} +(-5.34862 + 2.66709i) q^{62} +(1.01480 - 2.02808i) q^{63} +(-1.25411 - 7.90109i) q^{64} +(0.462111 + 1.26964i) q^{65} +(-1.96376 + 6.50926i) q^{66} +(3.32854 - 2.79298i) q^{67} +(-3.97543 + 7.80437i) q^{68} +(9.08507 - 9.64386i) q^{69} +(-2.14289 - 0.514337i) q^{70} +(-7.08002 - 12.2629i) q^{71} +(4.61240 + 7.12220i) q^{72} +(7.17342 - 12.4247i) q^{73} +(3.04020 - 3.20406i) q^{74} +(-0.0746363 + 1.29796i) q^{75} +(-0.0327049 - 0.622725i) q^{76} +(0.364356 + 2.06636i) q^{77} +(-0.0899601 - 1.60297i) q^{78} +(7.09014 - 8.44970i) q^{79} +(5.72657 - 5.93267i) q^{80} +(-7.53396 - 4.92336i) q^{81} +(7.91372 + 5.23734i) q^{82} +(-7.10823 + 8.47125i) q^{83} +(2.26127 + 1.32057i) q^{84} +(-8.89031 + 1.56760i) q^{85} +(-3.63604 + 2.69084i) q^{86} +(0.765146 - 13.3062i) q^{87} +(-7.35412 - 2.74820i) q^{88} +(5.55986 + 3.20999i) q^{89} +(-3.00256 + 8.21423i) q^{90} +(-0.247734 - 0.429088i) q^{91} +(10.4351 + 11.1878i) q^{92} +(5.32804 + 5.01932i) q^{93} +(1.74792 + 15.3337i) q^{94} +(0.492358 - 0.413138i) q^{95} +(-8.55078 + 4.78374i) q^{96} +(1.59192 - 0.579411i) q^{97} +(-9.07443 - 0.554511i) q^{98} +(8.31226 - 0.496445i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) \) 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9	\( 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 30 q^{11} - 3 q^{12} + 9 q^{14} - 6 q^{16} - 18 q^{17} + 63 q^{18} - 6 q^{19} - 27 q^{20} - 18 q^{22} - 30 q^{24} - 12 q^{25} + 18 q^{27} - 12 q^{28} - 21 q^{30} - 36 q^{32} - 30 q^{33} + 12 q^{34} - 18 q^{35} - 36 q^{36} - 102 q^{38} + 9 q^{40} + 18 q^{41} - 6 q^{42} - 42 q^{43} - 81 q^{44} - 3 q^{46} - 81 q^{48} - 12 q^{49} + 57 q^{50} - 18 q^{51} + 21 q^{52} + 78 q^{54} - 69 q^{56} - 36 q^{57} - 33 q^{58} - 84 q^{59} - 54 q^{60} + 90 q^{62} - 51 q^{64} - 12 q^{65} + 87 q^{66} + 30 q^{67} + 63 q^{68} - 33 q^{70} + 12 q^{72} - 6 q^{73} + 51 q^{74} - 96 q^{75} + 30 q^{76} + 90 q^{78} - 12 q^{81} - 12 q^{82} - 72 q^{83} - 48 q^{84} + 42 q^{86} - 78 q^{88} + 144 q^{89} + 120 q^{90} - 6 q^{91} - 3 q^{92} - 33 q^{94} - 78 q^{96} - 42 q^{97} + 162 q^{98} - 12 q^{99}+O(q^{100}) \) 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 30 * q^11 - 3 * q^12 + 9 * q^14 - 6 * q^16 - 18 * q^17 + 63 * q^18 - 6 * q^19 - 27 * q^20 - 18 * q^22 - 30 * q^24 - 12 * q^25 + 18 * q^27 - 12 * q^28 - 21 * q^30 - 36 * q^32 - 30 * q^33 + 12 * q^34 - 18 * q^35 - 36 * q^36 - 102 * q^38 + 9 * q^40 + 18 * q^41 - 6 * q^42 - 42 * q^43 - 81 * q^44 - 3 * q^46 - 81 * q^48 - 12 * q^49 + 57 * q^50 - 18 * q^51 + 21 * q^52 + 78 * q^54 - 69 * q^56 - 36 * q^57 - 33 * q^58 - 84 * q^59 - 54 * q^60 + 90 * q^62 - 51 * q^64 - 12 * q^65 + 87 * q^66 + 30 * q^67 + 63 * q^68 - 33 * q^70 + 12 * q^72 - 6 * q^73 + 51 * q^74 - 96 * q^75 + 30 * q^76 + 90 * q^78 - 12 * q^81 - 12 * q^82 - 72 * q^83 - 48 * q^84 + 42 * q^86 - 78 * q^88 + 144 * q^89 + 120 * q^90 - 6 * q^91 - 3 * q^92 - 33 * q^94 - 78 * q^96 - 42 * q^97 + 162 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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