LMFDB - Embedded newform 228.2.w.b.67.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [228,2,Mod(67,228)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("228.67"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(228, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 0, 17])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	228.w (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [60,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$1.82058916609$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			67.1
Character	$\chi$	$=$	228.67
Dual form			228.2.w.b.211.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41419 + 0.00878762i) q^{2} +(0.766044 - 0.642788i) q^{3} +(1.99985 - 0.0248547i) q^{4} +(3.39140 + 1.23437i) q^{5} +(-1.07768 + 0.915753i) q^{6} +(1.70277 + 0.983096i) q^{7} +(-2.82794 + 0.0527230i) q^{8} +(0.173648 - 0.984808i) q^{9} +(-4.80692 - 1.71582i) q^{10} +(-4.83466 + 2.79129i) q^{11} +(1.51599 - 1.30452i) q^{12} +(0.0739637 - 0.0881465i) q^{13} +(-2.41668 - 1.37532i) q^{14} +(3.39140 - 1.23437i) q^{15} +(3.99876 - 0.0994110i) q^{16} +(0.580442 + 3.29185i) q^{17} +(-0.236917 + 1.39423i) q^{18} +(1.02155 - 4.23750i) q^{19} +(6.81295 + 2.38425i) q^{20} +(1.93632 - 0.341426i) q^{21} +(6.81258 - 3.98989i) q^{22} +(-2.16818 - 5.95703i) q^{23} +(-2.13243 + 1.85815i) q^{24} +(6.14770 + 5.15853i) q^{25} +(-0.103824 + 0.125306i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(3.42972 + 1.92372i) q^{28} +(1.55282 + 0.273805i) q^{29} +(-4.78522 + 1.77543i) q^{30} +(-0.653262 + 1.13148i) q^{31} +(-5.65412 + 0.175725i) q^{32} +(-1.90935 + 5.24591i) q^{33} +(-0.849781 - 4.65019i) q^{34} +(4.56128 + 5.43592i) q^{35} +(0.322792 - 1.97378i) q^{36} -7.12135i q^{37} +(-1.40742 + 6.00160i) q^{38} -0.115067i q^{39} +(-9.65574 - 3.31191i) q^{40} +(-4.70052 - 5.60186i) q^{41} +(-2.73532 + 0.499855i) q^{42} +(-1.14640 + 3.14970i) q^{43} +(-9.59919 + 5.70231i) q^{44} +(1.80453 - 3.12553i) q^{45} +(3.11856 + 8.40530i) q^{46} +(5.87946 + 1.03671i) q^{47} +(2.99933 - 2.64651i) q^{48} +(-1.56704 - 2.71420i) q^{49} +(-8.73932 - 7.24110i) q^{50} +(2.56060 + 2.14860i) q^{51} +(0.145725 - 0.178118i) q^{52} +(0.762548 + 2.09508i) q^{53} +(0.714703 + 1.22033i) q^{54} +(-19.8417 + 3.49863i) q^{55} +(-4.86716 - 2.69036i) q^{56} +(-1.94126 - 3.90276i) q^{57} +(-2.19839 - 0.373565i) q^{58} +(-2.03426 - 11.5368i) q^{59} +(6.75159 - 2.55284i) q^{60} +(-10.4409 + 3.80016i) q^{61} +(0.913891 - 1.60587i) q^{62} +(1.26384 - 1.50619i) q^{63} +(7.99444 - 0.298194i) q^{64} +(0.359646 - 0.207642i) q^{65} +(2.65408 - 7.43547i) q^{66} +(-0.935414 + 5.30500i) q^{67} +(1.24261 + 6.56876i) q^{68} +(-5.49003 - 3.16967i) q^{69} +(-6.49826 - 7.64732i) q^{70} +(-2.08825 - 0.760061i) q^{71} +(-0.439144 + 2.79413i) q^{72} +(2.21674 - 1.86006i) q^{73} +(0.0625797 + 10.0709i) q^{74} +8.02525 q^{75} +(1.93762 - 8.49974i) q^{76} -10.9764 q^{77} +(0.00101117 + 0.162726i) q^{78} +(-8.78604 + 7.37237i) q^{79} +(13.6841 + 4.59881i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(6.69664 + 7.88077i) q^{82} +(15.2741 + 8.81848i) q^{83} +(3.86386 - 0.730925i) q^{84} +(-2.09484 + 11.8805i) q^{85} +(1.59354 - 4.46433i) q^{86} +(1.36553 - 0.788389i) q^{87} +(13.5249 - 8.14849i) q^{88} +(7.41292 - 8.83438i) q^{89} +(-2.52447 + 4.43594i) q^{90} +(0.212600 - 0.0773800i) q^{91} +(-4.48409 - 11.8592i) q^{92} +(0.226876 + 1.28668i) q^{93} +(-8.32376 - 1.41443i) q^{94} +(8.69512 - 13.1101i) q^{95} +(-4.21836 + 3.76901i) q^{96} +(-5.32239 + 0.938482i) q^{97} +(2.23994 + 3.82462i) q^{98} +(1.90935 + 5.24591i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 3 q^{2} - 3 q^{4} + 3 q^{6} - 3 q^{8} - 6 q^{10} - 6 q^{13} - 9 q^{14} + 21 q^{16} + 18 q^{19} + 30 q^{20} - 6 q^{21} - 12 q^{22} - 18 q^{24} - 30 q^{27} - 18 q^{28} - 12 q^{31} + 33 q^{32} - 15 q^{34}+ \cdots - 105 q^{98}+O(q^{100}) $ 60 * q + 3 * q^2 - 3 * q^4 + 3 * q^6 - 3 * q^8 - 6 * q^10 - 6 * q^13 - 9 * q^14 + 21 * q^16 + 18 * q^19 + 30 * q^20 - 6 * q^21 - 12 * q^22 - 18 * q^24 - 30 * q^27 - 18 * q^28 - 12 * q^31 + 33 * q^32 - 15 * q^34 - 3 * q^36 - 84 * q^38 - 87 * q^40 - 12 * q^41 + 9 * q^42 - 18 * q^43 - 51 * q^44 - 21 * q^46 + 18 * q^48 + 30 * q^49 - 27 * q^50 - 3 * q^52 + 12 * q^53 + 3 * q^54 + 42 * q^56 - 36 * q^58 + 15 * q^60 + 105 * q^62 - 12 * q^63 + 21 * q^64 - 36 * q^65 + 24 * q^66 + 42 * q^67 - 15 * q^68 - 72 * q^69 - 96 * q^70 + 24 * q^71 + 18 * q^72 + 18 * q^73 + 69 * q^74 + 60 * q^75 + 54 * q^76 - 72 * q^77 + 57 * q^78 + 12 * q^79 - 12 * q^80 + 75 * q^82 + 39 * q^84 - 60 * q^85 + 21 * q^86 + 36 * q^88 - 12 * q^89 + 15 * q^90 - 84 * q^91 + 99 * q^92 - 12 * q^93 - 24 * q^95 + 12 * q^97 - 105 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

$n$	$77$	$97$	$115$
$\chi(n)$	$1$	$e\left(\frac{17}{18}\right)$	$-1$

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 $

$2$	−1.41419	+	0.00878762i	−0.999981	+	0.00621378i
$2$	−1.41419	+	0.00878762i	−0.999981	+	0.00621378i
$3$	0.766044	−	0.642788i	0.442276	−	0.371114i
$3$	0.766044	−	0.642788i	0.442276	−	0.371114i
$4$	1.99985	−	0.0248547i	0.999923	−	0.0124273i
$5$	3.39140	+	1.23437i	1.51668	+	0.552026i	0.960316	−	0.278913i	$-0.0899741\pi$
$5$	3.39140	+	1.23437i	1.51668	+	0.552026i	0.556363	+	0.830939i	$0.312196\pi$
$6$	−1.07768	+	0.915753i	−0.439961	+	0.373855i
$7$	1.70277	+	0.983096i	0.643587	+	0.371575i	0.785995	−	0.618233i	$-0.212151\pi$
$7$	1.70277	+	0.983096i	0.643587	+	0.371575i	−0.142408	+	0.989808i	$0.545484\pi$
$8$	−2.82794	+	0.0527230i	−0.999826	+	0.0186404i
$9$	0.173648	−	0.984808i	0.0578827	−	0.328269i
$10$	−4.80692	−	1.71582i	−1.52008	−	0.542591i
$11$	−4.83466	+	2.79129i	−1.45770	+	0.841606i	−0.998898	−	0.0469311i	$-0.985056\pi$
$11$	−4.83466	+	2.79129i	−1.45770	+	0.841606i	−0.458806	+	0.888537i	$0.651723\pi$
$12$	1.51599	−	1.30452i	0.437630	−	0.376581i
$13$	0.0739637	−	0.0881465i	0.0205138	−	0.0244475i	−0.755690	−	0.654929i	$-0.772698\pi$
$13$	0.0739637	−	0.0881465i	0.0205138	−	0.0244475i	0.776204	+	0.630482i	$0.217143\pi$
$14$	−2.41668	−	1.37532i	−0.645884	−	0.367569i
$15$	3.39140	−	1.23437i	0.875655	−	0.318713i
$16$	3.99876	−	0.0994110i	0.999691	−	0.0248527i
$17$	0.580442	+	3.29185i	0.140778	+	0.798391i	0.970661	+	0.240453i	$0.0772961\pi$
$17$	0.580442	+	3.29185i	0.140778	+	0.798391i	−0.829883	+	0.557938i	$0.811593\pi$
$18$	−0.236917	+	1.39423i	−0.0558418	+	0.328623i
$19$	1.02155	−	4.23750i	0.234360	−	0.972150i
$19$	1.02155	−	4.23750i	0.234360	−	0.972150i
$20$	6.81295	+	2.38425i	1.52342	+	0.533135i
$21$	1.93632	−	0.341426i	0.422540	−	0.0745052i
$22$	6.81258	−	3.98989i	1.45245	−	0.850647i
$23$	−2.16818	−	5.95703i	−0.452097	−	1.24213i	−0.931245	−	0.364393i	$-0.881277\pi$
$23$	−2.16818	−	5.95703i	−0.452097	−	1.24213i	0.479148	−	0.877734i	$-0.340946\pi$
$24$	−2.13243	+	1.85815i	−0.435281	+	0.379293i
$25$	6.14770	+	5.15853i	1.22954	+	1.03171i
$26$	−0.103824	+	0.125306i	−0.0203615	+	0.0245744i
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$	3.42972	+	1.92372i	0.648155	+	0.363549i
$29$	1.55282	+	0.273805i	0.288352	+	0.0508442i	0.315953	−	0.948775i	$-0.397676\pi$
$29$	1.55282	+	0.273805i	0.288352	+	0.0508442i	−0.0276012	+	0.999619i	$0.508787\pi$
$30$	−4.78522	+	1.77543i	−0.873658	+	0.324147i
$31$	−0.653262	+	1.13148i	−0.117329	+	0.203220i	−0.918708	−	0.394936i	$-0.870767\pi$
$31$	−0.653262	+	1.13148i	−0.117329	+	0.203220i	0.801379	+	0.598157i	$0.204100\pi$
$32$	−5.65412	+	0.175725i	−0.999517	+	0.0310641i
$33$	−1.90935	+	5.24591i	−0.332376	+	0.913196i
$34$	−0.849781	−	4.65019i	−0.145736	−	0.797501i
$35$	4.56128	+	5.43592i	0.770997	+	0.918838i
$36$	0.322792	−	1.97378i	0.0537987	−	0.328963i
$37$		−	7.12135i		−	1.17074i	−0.810766	−	0.585371i	$-0.800949\pi$
$37$		−	7.12135i		−	1.17074i	0.810766	−	0.585371i	$-0.199051\pi$
$38$	−1.40742	+	6.00160i	−0.228314	+	0.973587i
$39$		−	0.115067i		−	0.0184255i
$40$	−9.65574	−	3.31191i	−1.52671	−	0.523659i
$41$	−4.70052	−	5.60186i	−0.734098	−	0.874864i	0.261821	−	0.965116i	$-0.415677\pi$
$41$	−4.70052	−	5.60186i	−0.734098	−	0.874864i	−0.995919	+	0.0902527i	$0.971233\pi$
$42$	−2.73532	+	0.499855i	−0.422069	+	0.0771293i
$43$	−1.14640	+	3.14970i	−0.174824	+	0.480324i	−0.995897	−	0.0904992i	$-0.971154\pi$
$43$	−1.14640	+	3.14970i	−0.174824	+	0.480324i	0.821073	+	0.570824i	$0.193376\pi$
$44$	−9.59919	+	5.70231i	−1.44713	+	0.859656i
$45$	1.80453	−	3.12553i	0.269003	−	0.465927i
$46$	3.11856	+	8.40530i	0.459807	+	1.23929i
$47$	5.87946	+	1.03671i	0.857607	+	0.151219i	0.585127	−	0.810942i	$-0.301045\pi$
$47$	5.87946	+	1.03671i	0.857607	+	0.151219i	0.272481	+	0.962161i	$0.412156\pi$
$48$	2.99933	−	2.64651i	0.432916	−	0.381991i
$49$	−1.56704	−	2.71420i	−0.223864	−	0.387743i
$50$	−8.73932	−	7.24110i	−1.23593	−	1.02405i
$51$	2.56060	+	2.14860i	0.358556	+	0.300865i
$52$	0.145725	−	0.178118i	0.0202084	−	0.0247005i
$53$	0.762548	+	2.09508i	0.104744	+	0.287782i	0.980983	−	0.194096i	$-0.0621773\pi$
$53$	0.762548	+	2.09508i	0.104744	+	0.287782i	−0.876239	+	0.481877i	$0.839955\pi$
$54$	0.714703	+	1.22033i	0.0972588	+	0.166066i
$55$	−19.8417	+	3.49863i	−2.67546	+	0.471755i
$56$	−4.86716	−	2.69036i	−0.650402	−	0.359514i
$57$	−1.94126	−	3.90276i	−0.257126	−	0.516933i
$58$	−2.19839	−	0.373565i	−0.288662	−	0.0490515i
$59$	−2.03426	−	11.5368i	−0.264838	−	1.50197i	−0.769497	−	0.638651i	$-0.779493\pi$
$59$	−2.03426	−	11.5368i	−0.264838	−	1.50197i	0.504659	−	0.863319i	$-0.331618\pi$
$60$	6.75159	−	2.55284i	0.871627	−	0.329570i
$61$	−10.4409	+	3.80016i	−1.33682	+	0.486561i	−0.908808	−	0.417214i	$-0.863007\pi$
$61$	−10.4409	+	3.80016i	−1.33682	+	0.486561i	−0.428008	+	0.903775i	$0.640784\pi$
$62$	0.913891	−	1.60587i	0.116064	−	0.203946i
$63$	1.26384	−	1.50619i	0.159229	−	0.189762i
$64$	7.99444	−	0.298194i	0.999305	−	0.0372743i
$65$	0.359646	−	0.207642i	0.0446086	−	0.0257548i
$66$	2.65408	−	7.43547i	0.326695	−	0.915243i
$67$	−0.935414	+	5.30500i	−0.114279	+	0.648108i	0.872826	+	0.488032i	$0.162285\pi$
$67$	−0.935414	+	5.30500i	−0.114279	+	0.648108i	−0.987105	+	0.160076i	$0.948826\pi$
$68$	1.24261	+	6.56876i	0.150689	+	0.796580i
$69$	−5.49003	−	3.16967i	−0.660922	−	0.381583i
$70$	−6.49826	−	7.64732i	−0.776691	−	0.914029i
$71$	−2.08825	−	0.760061i	−0.247830	−	0.0902027i	0.215118	−	0.976588i	$-0.430986\pi$
$71$	−2.08825	−	0.760061i	−0.247830	−	0.0902027i	−0.462948	+	0.886385i	$0.653208\pi$
$72$	−0.439144	+	2.79413i	−0.0517536	+	0.329291i
$73$	2.21674	−	1.86006i	0.259449	−	0.217704i	−0.503779	−	0.863832i	$-0.668057\pi$
$73$	2.21674	−	1.86006i	0.259449	−	0.217704i	0.763229	+	0.646129i	$0.223613\pi$
$74$	0.0625797	+	10.0709i	0.00727474	+	1.17072i
$75$	8.02525			0.926676
$76$	1.93762	−	8.49974i	0.222260	−	0.974987i
$77$	−10.9764			−1.25088
$78$	0.00101117	+	0.162726i	0.000114492	+	0.0184251i
$79$	−8.78604	+	7.37237i	−0.988507	+	0.829456i	−0.985351	−	0.170539i	$-0.945449\pi$
$79$	−8.78604	+	7.37237i	−0.988507	+	0.829456i	−0.00315617	+	0.999995i	$0.501005\pi$
$80$	13.6841	+	4.59881i	1.52993	+	0.514162i
$81$	−0.939693	−	0.342020i	−0.104410	−	0.0380022i
$82$	6.69664	+	7.88077i	0.739520	+	0.870285i
$83$	15.2741	+	8.81848i	1.67655	+	0.967954i	0.963836	+	0.266495i	$0.0858656\pi$
$83$	15.2741	+	8.81848i	1.67655	+	0.967954i	0.712710	+	0.701459i	$0.247468\pi$
$84$	3.86386	−	0.730925i	0.421581	−	0.0797505i
$85$	−2.09484	+	11.8805i	−0.227218	+	1.28862i
$86$	1.59354	−	4.46433i	0.171836	−	0.481401i
$87$	1.36553	−	0.788389i	0.146400	−	0.0845241i
$88$	13.5249	−	8.14849i	1.44176	−	0.868632i
$89$	7.41292	−	8.83438i	0.785768	−	0.936442i	−0.213411	−	0.976963i	$-0.568457\pi$
$89$	7.41292	−	8.83438i	0.785768	−	0.936442i	0.999179	+	0.0405206i	$0.0129016\pi$
$90$	−2.52447	+	4.43594i	−0.266102	+	0.467589i
$91$	0.212600	−	0.0773800i	0.0222865	−	0.00811163i
$92$	−4.48409	−	11.8592i	−0.467498	−	1.23641i
$93$	0.226876	+	1.28668i	0.0235259	+	0.133422i
$94$	−8.32376	−	1.41443i	−0.858530	−	0.145887i
$95$	8.69512	−	13.1101i	0.892101	−	1.34507i
$96$	−4.21836	+	3.76901i	−0.430534	+	0.384673i
$97$	−5.32239	+	0.938482i	−0.540407	+	0.0952884i	−0.437188	−	0.899370i	$-0.644025\pi$
$97$	−5.32239	+	0.938482i	−0.540407	+	0.0952884i	−0.103219	+	0.994659i	$0.532914\pi$
$98$	2.23994	+	3.82462i	0.226269	+	0.386345i
$99$	1.90935	+	5.24591i	0.191897	+	0.527234i
$100$	12.4227	+	10.1635i	1.24227	+	1.01635i
$101$	−13.7940	−	11.5745i	−1.37255	−	1.15171i	−0.971878	−	0.235484i	$-0.924332\pi$
$101$	−13.7940	−	11.5745i	−1.37255	−	1.15171i	−0.400672	−	0.916222i	$-0.631223\pi$
$102$	−3.64005	−	3.01602i	−0.360419	−	0.298631i
$103$	4.46091	+	7.72652i	0.439546	+	0.761317i	0.997654	−	0.0684516i	$-0.0218059\pi$
$103$	4.46091	+	7.72652i	0.439546	+	0.761317i	−0.558108	+	0.829768i	$0.688473\pi$
$104$	−0.204517	+	0.253172i	−0.0200546	+	0.0248256i
$105$	6.98828	+	1.23222i	0.681986	+	0.120253i
$106$	−1.09680	−	2.95614i	−0.106530	−	0.287125i
$107$	−3.26682	+	5.65831i	−0.315816	+	0.547009i	−0.979611	−	0.200906i	$-0.935612\pi$
$107$	−3.26682	+	5.65831i	−0.315816	+	0.547009i	0.663795	+	0.747915i	$0.268945\pi$
$108$	−1.02145	−	1.71949i	−0.0982888	−	0.165458i
$109$	−3.67153	+	10.0875i	−0.351669	+	0.966203i	0.630165	+	0.776461i	$0.282987\pi$
$109$	−3.67153	+	10.0875i	−0.351669	+	0.966203i	−0.981834	+	0.189741i	$0.939235\pi$
$110$	28.0292	−	5.12208i	2.67247	−	0.488371i
$111$	−4.57751	−	5.45527i	−0.434478	−	0.517791i
$112$	6.90672	+	3.76189i	0.652623	+	0.355466i
$113$			14.9055i			1.40219i	0.713066	+	0.701097i	$0.247306\pi$
$113$			14.9055i			1.40219i	−0.713066	+	0.701097i	$0.752694\pi$
$114$	2.77960	+	5.50216i	0.260334	+	0.515325i
$115$		−	22.8790i		−	2.13348i
$116$	3.11221	+	0.508972i	0.288962	+	0.0472569i
$117$	−0.0739637	−	0.0881465i	−0.00683795	−	0.00814915i
$118$	2.97820	+	16.2974i	0.274166	+	1.50029i
$119$	−2.24784	+	6.17590i	−0.206060	+	0.566144i
$120$	−9.52558	+	3.66952i	−0.869562	+	0.334980i
$121$	10.0826	−	17.4636i	0.916600	−	1.58760i
$122$	14.7319	−	5.46589i	1.33377	−	0.494858i
$123$	−7.20161	−	1.26984i	−0.649348	−	0.114498i
$124$	−1.27830	+	2.27903i	−0.114795	+	0.204663i
$125$	5.45914	+	9.45551i	0.488281	+	0.845727i
$126$	−1.77407	+	2.14114i	−0.158047	+	0.190748i
$127$	0.891348	+	0.747930i	0.0790943	+	0.0663680i	0.681478	−	0.731839i	$-0.261338\pi$
$127$	0.891348	+	0.747930i	0.0790943	+	0.0663680i	−0.602383	+	0.798207i	$0.705782\pi$
$128$	−11.3030	+	0.491955i	−0.999054	+	0.0434831i
$129$	1.14640	+	3.14970i	0.100935	+	0.277315i
$130$	−0.506782	+	0.296804i	−0.0444477	+	0.0260315i
$131$	−13.9279	+	2.45587i	−1.21689	+	0.214570i	−0.744986	−	0.667081i	$-0.767544\pi$
$131$	−13.9279	+	2.45587i	−1.21689	+	0.214570i	−0.471902	+	0.881651i	$0.656433\pi$
$132$	−3.68803	+	10.5385i	−0.321002	+	0.917256i
$133$	5.90534	−	6.21122i	0.512058	−	0.538581i
$134$	1.27623	−	7.51047i	0.110250	−	0.648806i
$135$	−0.626705	−	3.55422i	−0.0539382	−	0.305899i
$136$	−1.81501	−	9.27854i	−0.155636	−	0.795628i
$137$	17.6840	−	6.43644i	1.51084	−	0.549902i	0.552002	−	0.833843i	$-0.313864\pi$
$137$	17.6840	−	6.43644i	1.51084	−	0.549902i	0.958842	+	0.283941i	$0.0916418\pi$
$138$	7.79178	+	4.43426i	0.663280	+	0.377469i
$139$	4.98537	−	5.94134i	0.422854	−	0.503938i	−0.511993	−	0.858990i	$-0.671092\pi$
$139$	4.98537	−	5.94134i	0.422854	−	0.503938i	0.934846	+	0.355052i	$0.115537\pi$
$140$	9.25696	+	10.7576i	0.782356	+	0.909185i
$141$	5.17031	−	2.98508i	0.435419	−	0.251389i
$142$	2.95986	+	1.05652i	0.248386	+	0.0886610i
$143$	−0.111547	+	0.632612i	−0.00932800	+	0.0529017i
$144$	0.596477	−	3.95528i	0.0497065	−	0.329606i
$145$	4.92827	+	2.84534i	0.409270	+	0.236292i
$146$	−3.11853	+	2.64996i	−0.258092	+	0.219312i
$147$	−2.94508	−	1.07192i	−0.242906	−	0.0884106i
$148$	−0.176999	−	14.2416i	−0.0145492	−	1.17065i
$149$	−9.40224	+	7.88942i	−0.770261	+	0.646326i	−0.940776	−	0.339029i	$-0.889901\pi$
$149$	−9.40224	+	7.88942i	−0.770261	+	0.646326i	0.170514	+	0.985355i	$0.445457\pi$
$150$	−11.3492	+	0.0705228i	−0.926658	+	0.00575817i
$151$	5.39650			0.439161			0.219580	−	0.975594i	$-0.429531\pi$
$151$	5.39650			0.439161			0.219580	+	0.975594i	$0.429531\pi$
$152$	−2.66546	+	12.0372i	−0.216198	+	0.976350i
$153$	3.34263			0.270236
$154$	15.5227	−	0.0964566i	1.25086	−	0.00777270i
$155$	−3.61214	+	3.03095i	−0.290134	+	0.243451i
$156$	−0.00285995	−	0.230117i	−0.000228980	−	0.0184241i
$157$	−8.88411	−	3.23355i	−0.709029	−	0.258066i	−0.0377683	−	0.999287i	$-0.512025\pi$
$157$	−8.88411	−	3.23355i	−0.709029	−	0.258066i	−0.671261	+	0.741221i	$0.734247\pi$
$158$	12.3603	−	10.5031i	0.983334	−	0.835582i
$159$	1.93084	+	1.11477i	0.153125	+	0.0884070i
$160$	−19.3923	−	6.38332i	−1.53310	−	0.504646i
$161$	2.16441	−	12.2750i	0.170580	−	0.967405i
$162$	1.33191	+	0.475423i	0.104644	+	0.0373527i
$163$	−1.61949	+	0.935013i	−0.126848	+	0.0732359i	−0.562081	−	0.827082i	$-0.689999\pi$
$163$	−1.61949	+	0.935013i	−0.126848	+	0.0732359i	0.435233	+	0.900318i	$0.356666\pi$
$164$	−9.53955	−	11.0860i	−0.744913	−	0.865673i
$165$	−12.9508	+	15.4341i	−1.00822	+	1.20154i
$166$	−21.6779	−	12.3368i	−1.68253	−	0.957518i
$167$	14.4659	−	5.26515i	1.11940	−	0.407429i	0.284969	−	0.958537i	$-0.408017\pi$
$167$	14.4659	−	5.26515i	1.11940	−	0.407429i	0.834434	+	0.551108i	$0.185795\pi$
$168$	−5.45779	+	1.06762i	−0.421078	+	0.0823685i
$169$	2.25513	+	12.7895i	0.173471	+	0.983805i
$170$	2.85810	−	16.8196i	0.219206	−	1.29000i
$171$	−3.99574	−	1.74187i	−0.305562	−	0.133204i
$172$	−2.21433	+	6.32740i	−0.168841	+	0.482460i
$173$	−16.6499	+	2.93583i	−1.26587	+	0.223207i	−0.765970	−	0.642877i	$-0.777741\pi$
$173$	−16.6499	+	2.93583i	−1.26587	+	0.223207i	−0.499899	+	0.866084i	$0.666630\pi$
$174$	−1.92418	+	1.12693i	−0.145872	+	0.0854322i
$175$	5.39680	+	14.8276i	0.407960	+	1.12086i
$176$	−19.0552	+	11.6423i	−1.43634	+	0.877574i
$177$	−8.97407	−	7.53014i	−0.674533	−	0.566000i
$178$	−10.4056	+	12.5586i	−0.779934	+	0.941307i
$179$	4.45014	+	7.70786i	0.332619	+	0.576113i	0.983024	−	0.183474i	$-0.0587345\pi$
$179$	4.45014	+	7.70786i	0.332619	+	0.576113i	−0.650406	+	0.759587i	$0.725401\pi$
$180$	3.53109	−	6.29543i	0.263192	−	0.469234i
$181$	−9.01732	−	1.59000i	−0.670252	−	0.118184i	−0.171842	−	0.985125i	$-0.554972\pi$
$181$	−9.01732	−	1.59000i	−0.670252	−	0.118184i	−0.498411	+	0.866941i	$0.666083\pi$
$182$	−0.299976	+	0.111298i	−0.0222357	+	0.00824996i
$183$	−5.55547	+	9.62235i	−0.410672	+	0.711305i
$184$	6.44555	+	16.7318i	0.475172	+	1.23348i
$185$	8.79036	−	24.1513i	0.646280	−	1.77564i
$186$	−0.332151	−	1.81761i	−0.0243545	−	0.133273i
$187$	−11.9947	−	14.2948i	−0.877143	−	1.04534i
$188$	11.7838	+	1.92712i	0.859420	+	0.140550i
$189$		−	1.96619i		−	0.143019i
$190$	−12.1813	+	18.6165i	−0.883726	+	1.35058i
$191$		−	15.5280i		−	1.12356i	−0.827286	−	0.561782i	$-0.810116\pi$
$191$		−	15.5280i		−	1.12356i	0.827286	−	0.561782i	$-0.189884\pi$
$192$	5.93242	−	5.36716i	0.428136	−	0.387341i
$193$	3.71827	+	4.43126i	0.267647	+	0.318969i	0.883082	−	0.469218i	$-0.155464\pi$
$193$	3.71827	+	4.43126i	0.267647	+	0.318969i	−0.615435	+	0.788187i	$0.711020\pi$
$194$	7.51861	−	1.37396i	0.539805	−	0.0986445i
$195$	0.142035	−	0.390239i	0.0101714	−	0.0279456i
$196$	−3.20131	−	5.38903i	−0.228665	−	0.384931i
$197$	−2.17496	+	3.76714i	−0.154959	+	0.268398i	−0.933044	−	0.359762i	$-0.882858\pi$
$197$	−2.17496	+	3.76714i	−0.154959	+	0.268398i	0.778085	+	0.628159i	$0.216191\pi$
$198$	−2.74628	−	7.40191i	−0.195170	−	0.526031i
$199$	3.06985	+	0.541297i	0.217616	+	0.0383715i	0.281393	−	0.959593i	$-0.409204\pi$
$199$	3.06985	+	0.541297i	0.217616	+	0.0383715i	−0.0637771	+	0.997964i	$0.520315\pi$
$200$	−17.6573	−	14.2639i	−1.24856	−	1.00861i
$201$	2.69342	+	4.66513i	0.189979	+	0.329053i
$202$	19.6089	+	16.2473i	1.37968	+	1.14316i
$203$	2.37493	+	1.99280i	0.166687	+	0.139867i
$204$	5.17422	+	4.23323i	0.362268	+	0.296385i
$205$	−9.02658	−	24.8003i	−0.630444	−	1.73213i
$206$	−6.37645	−	10.8875i	−0.444269	−	0.758571i
$207$	−6.24303	+	1.10081i	−0.433921	+	0.0765119i
$208$	0.287001	−	0.359830i	0.0198999	−	0.0249497i
$209$	6.88926	+	23.3383i	0.476540	+	1.61434i
$210$	−9.89356	−	1.68118i	−0.682721	−	0.116013i
$211$	0.910393	+	5.16309i	0.0626740	+	0.355442i	0.999976	+	0.00692381i	$0.00220393\pi$
$211$	0.910393	+	5.16309i	0.0626740	+	0.355442i	−0.937302	+	0.348518i	$0.886685\pi$
$212$	1.57705	+	4.17089i	0.108312	+	0.286458i
$213$	−2.08825	+	0.760061i	−0.143085	+	0.0520785i
$214$	4.57018	−	8.03061i	0.312411	−	0.548961i
$215$	−7.77577	+	9.26680i	−0.530303	+	0.631991i
$216$	1.45963	+	2.42270i	0.0993151	+	0.164844i
$217$	−2.22471	+	1.28444i	−0.151023	+	0.0871934i
$218$	5.10359	−	14.2978i	0.345658	−	0.968369i
$219$	0.502493	−	2.84978i	0.0339554	−	0.192570i
$220$	−39.5934	+	7.48988i	−2.66939	+	0.504968i
$221$	0.333097	+	0.192314i	0.0224065	+	0.0129364i
$222$	6.52139	+	7.67454i	0.437687	+	0.515081i
$223$	6.80645	+	2.47734i	0.455794	+	0.165895i	0.559706	−	0.828691i	$-0.310914\pi$
$223$	6.80645	+	2.47734i	0.455794	+	0.165895i	−0.103913	+	0.994586i	$0.533136\pi$
$224$	−9.80044	−	5.25933i	−0.654819	−	0.351404i
$225$	6.14770	−	5.15853i	0.409847	−	0.343902i
$226$	−0.130984	−	21.0792i	−0.00871293	−	1.40217i
$227$	−12.9028			−0.856391			−0.428195	−	0.903686i	$-0.640851\pi$
$227$	−12.9028			−0.856391			−0.428195	+	0.903686i	$0.640851\pi$
$228$	−3.97923	−	7.75666i	−0.263531	−	0.513697i
$229$	6.50015			0.429542			0.214771	−	0.976664i	$-0.431099\pi$
$229$	6.50015			0.429542			0.214771	+	0.976664i	$0.431099\pi$
$230$	0.201052	+	32.3552i	0.0132570	+	2.13344i
$231$	−8.40843	+	7.05551i	−0.553234	+	0.464218i
$232$	−4.40572	−	0.692432i	−0.289250	−	0.0454604i
$233$	9.80942	+	3.57034i	0.642636	+	0.233901i	0.642722	−	0.766099i	$-0.277805\pi$
$233$	9.80942	+	3.57034i	0.642636	+	0.233901i	−8.56138e−5		1.00000i	$0.500027\pi$
$234$	0.105373	+	0.124006i	0.00688845	+	0.00810650i
$235$	18.6599	+	10.7733i	1.21724	+	0.702773i
$236$	−4.35494	−	23.0213i	−0.283483	−	1.49856i
$237$	−1.99163	+	11.2951i	−0.129371	+	0.733697i
$238$	3.12460	−	8.75363i	0.202538	−	0.567413i
$239$	24.2728	−	14.0139i	1.57008	−	0.906484i	0.573918	−	0.818913i	$-0.305423\pi$
$239$	24.2728	−	14.0139i	1.57008	−	0.906484i	0.996158	−	0.0875716i	$-0.0279107\pi$
$240$	13.4387	−	5.27309i	0.867464	−	0.340377i
$241$	9.48229	−	11.3006i	0.610808	−	0.727933i	−0.368653	−	0.929567i	$-0.620181\pi$
$241$	9.48229	−	11.3006i	0.610808	−	0.727933i	0.979461	+	0.201634i	$0.0646253\pi$
$242$	−14.1052	+	24.7854i	−0.906717	+	1.59326i
$243$	−0.939693	+	0.342020i	−0.0602813	+	0.0219406i
$244$	−20.7857	+	7.85925i	−1.33067	+	0.503137i
$245$	−1.96415	−	11.1392i	−0.125485	−	0.711661i
$246$	10.1956	+	1.73250i	0.650047	+	0.110460i
$247$	−0.297964	−	0.403468i	−0.0189590	−	0.0256720i
$248$	1.78773	−	3.23420i	0.113521	−	0.205372i
$249$	17.3690	−	3.06263i	1.10072	−	0.194086i
$250$	−7.80334	−	13.3239i	−0.493526	−	0.842676i
$251$	5.95225	+	16.3537i	0.375702	+	1.03223i	0.973119	+	0.230303i	$0.0739717\pi$
$251$	5.95225	+	16.3537i	0.375702	+	1.03223i	−0.597417	+	0.801931i	$0.703806\pi$
$252$	2.49006	−	3.04356i	0.156859	−	0.191726i
$253$	27.1102	+	22.7482i	1.70440	+	1.43016i
$254$	−1.26710	−	1.04988i	−0.0795052	−	0.0658753i
$255$	6.03187	+	10.4475i	0.377730	+	0.654248i
$256$	15.9802	−	0.795042i	0.998765	−	0.0496901i
$257$	2.97920	+	0.525313i	0.185837	+	0.0327681i	0.265792	−	0.964030i	$-0.414367\pi$
$257$	2.97920	+	0.525313i	0.185837	+	0.0327681i	−0.0799549	+	0.996798i	$0.525478\pi$
$258$	−1.64890	−	4.44418i	−0.102656	−	0.276683i
$259$	7.00097	−	12.1260i	0.435019	−	0.753475i
$260$	0.714075	−	0.424190i	0.0442851	−	0.0263071i
$261$	0.539290	−	1.48169i	0.0333812	−	0.0917141i
$262$	19.6751	−	3.59545i	1.21553	−	0.222128i
$263$	0.596660	+	0.711072i	0.0367916	+	0.0438465i	0.784126	−	0.620601i	$-0.213111\pi$
$263$	0.596660	+	0.711072i	0.0367916	+	0.0438465i	−0.747335	+	0.664448i	$0.768667\pi$
$264$	5.12295	−	14.9358i	0.315296	−	0.919233i
$265$			8.04652i			0.494294i
$266$	−8.29667	+	8.83572i	−0.508701	+	0.541753i
$267$		−	11.5325i		−	0.705775i
$268$	−1.73883	+	10.6324i	−0.106216	+	0.649478i
$269$	14.4498	+	17.2205i	0.881017	+	1.04995i	0.998382	+	0.0568661i	$0.0181108\pi$
$269$	14.4498	+	17.2205i	0.881017	+	1.04995i	−0.117365	+	0.993089i	$0.537445\pi$
$270$	0.917511	+	5.02082i	0.0558379	+	0.305558i
$271$	−2.63856	+	7.24939i	−0.160281	+	0.440369i	−0.993673	−	0.112314i	$-0.964174\pi$
$271$	−2.63856	+	7.24939i	−0.160281	+	0.440369i	0.833391	+	0.552683i	$0.186396\pi$
$272$	2.64830	+	13.1056i	0.160577	+	0.794646i
$273$	0.113122	−	0.195933i	0.00684646	−	0.0118584i
$274$	−24.9519	+	9.25773i	−1.50740	+	0.559280i
$275$	−44.1210	−	7.77972i	−2.66059	−	0.469135i
$276$	−11.0580	−	6.20240i	−0.665613	−	0.373340i
$277$	−0.803534	−	1.39176i	−0.0482797	−	0.0836229i	0.840876	−	0.541228i	$-0.182041\pi$
$277$	−0.803534	−	1.39176i	−0.0482797	−	0.0836229i	−0.889155	+	0.457605i	$0.848707\pi$
$278$	−6.99804	+	8.44597i	−0.419714	+	0.506555i
$279$	1.00086	+	0.839818i	0.0599197	+	0.0502786i
$280$	−13.1856	−	15.1319i	−0.787990	−	0.904307i
$281$	3.41959	+	9.39526i	0.203996	+	0.560474i	0.998931	−	0.0462199i	$-0.0147175\pi$
$281$	3.41959	+	9.39526i	0.203996	+	0.560474i	−0.794935	+	0.606694i	$0.792495\pi$
$282$	−7.28555	+	4.26689i	−0.433848	+	0.254090i
$283$	10.9910	−	1.93801i	0.653348	−	0.115203i	0.162858	−	0.986650i	$-0.447929\pi$
$283$	10.9910	−	1.93801i	0.653348	−	0.115203i	0.490490	+	0.871447i	$0.336818\pi$
$284$	−4.19507	−	1.46810i	−0.248932	−	0.0871159i
$285$	−1.76616	−	15.6320i	−0.104618	−	0.925962i
$286$	0.152189	−	0.895612i	0.00899910	−	0.0529587i
$287$	−2.49675	−	14.1598i	−0.147378	−	0.835824i
$288$	−0.808773	+	5.59874i	−0.0476574	+	0.329909i
$289$	5.47541	−	1.99289i	0.322083	−	0.117229i
$290$	−6.99449	−	3.98053i	−0.410731	−	0.233745i
$291$	−3.47395	+	4.14009i	−0.203646	+	0.242696i
$292$	4.38690	−	3.77493i	0.256724	−	0.220911i
$293$	1.70034	−	0.981693i	0.0993351	−	0.0573511i	−0.449510	−	0.893276i	$-0.648401\pi$
$293$	1.70034	−	0.981693i	0.0993351	−	0.0573511i	0.548845	+	0.835924i	$0.315068\pi$
$294$	4.17431	+	1.49002i	0.243451	+	0.0868995i
$295$	7.34174	−	41.6371i	0.427453	−	2.42420i
$296$	0.375459	+	20.1387i	0.0218231	+	1.17054i
$297$	4.83466	+	2.79129i	0.280535	+	0.161967i
$298$	13.2272	−	11.2397i	0.766230	−	0.651100i
$299$	−0.685458	−	0.249486i	−0.0396411	−	0.0144282i
$300$	16.0493	−	0.199465i	0.926605	−	0.0115161i
$301$	−5.04851	+	4.23620i	−0.290991	+	0.244170i
$302$	−7.63166	+	0.0474224i	−0.439152	+	0.00272885i
$303$	−18.0067			−1.03446
$304$	3.66368	−	17.0463i	0.210127	−	0.977674i
$305$	−40.0999			−2.29612
$306$	−4.72710	+	0.0293738i	−0.270231	+	0.00167919i
$307$	9.42719	−	7.91035i	0.538038	−	0.451468i	−0.332828	−	0.942987i	$-0.608003\pi$
$307$	9.42719	−	7.91035i	0.538038	−	0.451468i	0.870866	+	0.491520i	$0.163559\pi$
$308$	−21.9512	+	0.272815i	−1.25078	+	0.0155451i
$309$	8.38377	+	3.05144i	0.476936	+	0.173590i
$310$	5.08160	−	4.31806i	0.288616	−	0.245250i
$311$	−8.74451	−	5.04865i	−0.495856	−	0.286283i	0.231145	−	0.972919i	$-0.425753\pi$
$311$	−8.74451	−	5.04865i	−0.495856	−	0.286283i	−0.727001	+	0.686637i	$0.759086\pi$
$312$	0.00606668	+	0.325402i	0.000343458	+	0.0184223i
$313$	0.958695	−	5.43703i	0.0541887	−	0.307319i	−0.945652	−	0.325181i	$-0.894575\pi$
$313$	0.958695	−	5.43703i	0.0541887	−	0.307319i	0.999840	+	0.0178618i	$0.00568589\pi$
$314$	12.5922	+	4.49478i	0.710619	+	0.253655i
$315$	6.14539	−	3.54804i	0.346254	−	0.199910i
$316$	−17.3875	+	14.9620i	−0.978123	+	0.841676i
$317$	16.9033	−	20.1446i	0.949385	−	1.13143i	−0.0418233	−	0.999125i	$-0.513317\pi$
$317$	16.9033	−	20.1446i	0.949385	−	1.13143i	0.991209	−	0.132308i	$-0.0422389\pi$
$318$	−2.74036	−	1.55952i	−0.153672	−	0.0874538i
$319$	−8.27163	+	3.01063i	−0.463122	+	0.168563i
$320$	27.4804	+	8.85679i	1.53620	+	0.495109i
$321$	1.13456	+	6.43439i	0.0633248	+	0.359133i
$322$	−2.95301	+	17.3781i	−0.164565	+	0.968446i
$323$	14.5422	+	0.903165i	0.809148	+	0.0502534i
$324$	−1.88774	−	0.660632i	−0.104874	−	0.0367018i
$325$	0.909414	−	0.160354i	0.0504452	−	0.00889485i
$326$	2.28205	−	1.33651i	0.126391	−	0.0740227i
$327$	3.67153	+	10.0875i	0.203036	+	0.557837i
$328$	13.5881	+	15.5939i	0.750278	+	0.861028i
$329$	8.99220	+	7.54535i	0.495756	+	0.415989i
$330$	18.1792	−	21.9405i	1.00073	−	1.20779i
$331$	17.5645	+	30.4227i	0.965434	+	1.67218i	0.708443	+	0.705768i	$0.249398\pi$
$331$	17.5645	+	30.4227i	0.965434	+	1.67218i	0.256991	+	0.966414i	$0.417269\pi$
$332$	30.7649	+	17.2560i	1.68845	+	0.947045i
$333$	−7.01316	−	1.23661i	−0.384319	−	0.0677657i
$334$	−20.4112	+	7.57302i	−1.11685	+	0.414377i
$335$	−9.72068	+	16.8367i	−0.531097	+	0.919888i
$336$	7.70895	−	1.55777i	0.420558	−	0.0849834i
$337$	−3.15640	+	8.67213i	−0.171940	+	0.472401i	−0.995493	−	0.0948387i	$-0.969766\pi$
$337$	−3.15640	+	8.67213i	−0.171940	+	0.472401i	0.823553	+	0.567240i	$0.191989\pi$
$338$	−3.30156	−	18.0669i	−0.179581	−	0.982708i
$339$	9.58108	+	11.4183i	0.520373	+	0.620156i
$340$	−3.89408	+	23.8111i	−0.211186	+	1.29134i
$341$		−	7.29378i		−	0.394980i
$342$	5.66602	+	2.42821i	0.306383	+	0.131303i
$343$		−	19.9256i		−	1.07588i
$344$	3.07587	−	8.96758i	0.165840	−	0.483500i
$345$	−14.7063	−	17.5263i	−0.791763	−	0.943586i
$346$	23.5203	−	4.29812i	1.26446	−	0.231068i
$347$	−1.33452	+	3.66657i	−0.0716408	+	0.196832i	−0.970345	−	0.241723i	$-0.922287\pi$
$347$	−1.33452	+	3.66657i	−0.0716408	+	0.196832i	0.898704	+	0.438555i	$0.144510\pi$
$348$	2.71125	−	1.61060i	0.145338	−	0.0863370i
$349$	−7.75109	+	13.4253i	−0.414906	+	0.718639i	−0.995419	−	0.0956128i	$-0.969519\pi$
$349$	−7.75109	+	13.4253i	−0.414906	+	0.718639i	0.580512	+	0.814251i	$0.302852\pi$
$350$	−7.76238	−	20.9215i	−0.414917	−	1.11830i
$351$	−0.113319	−	0.0199812i	−0.00604852	−	0.00106652i
$352$	26.8452	−	16.6319i	1.43086	−	0.886482i
$353$	1.90578	+	3.30091i	0.101435	+	0.175690i	0.912276	−	0.409576i	$-0.134323\pi$
$353$	1.90578	+	3.30091i	0.101435	+	0.175690i	−0.810841	+	0.585266i	$0.800990\pi$
$354$	12.7572	+	10.5702i	0.678037	+	0.561798i
$355$	−6.14390	−	5.15534i	−0.326084	−	0.273617i
$356$	14.6051	−	17.8516i	0.774070	−	0.946135i
$357$	2.24784	+	6.17590i	0.118969	+	0.326863i
$358$	−6.36105	−	10.8612i	−0.336192	−	0.574035i
$359$	0.124666	−	0.0219820i	0.00657961	−	0.00116016i	−0.170357	−	0.985382i	$-0.554492\pi$
$359$	0.124666	−	0.0219820i	0.00657961	−	0.00116016i	0.176937	+	0.984222i	$0.443381\pi$
$360$	−4.93830	+	8.93394i	−0.260271	+	0.470860i
$361$	−16.9129	−	8.65764i	−0.890151	−	0.455666i
$362$	12.7661	+	2.16931i	0.670974	+	0.114016i
$363$	−3.50165	−	19.8588i	−0.183789	−	1.04232i
$364$	0.423244	−	0.160032i	0.0221840	−	0.00838797i
$365$	9.81384	−	3.57195i	0.513680	−	0.186964i
$366$	7.77191	−	13.6566i	0.406244	−	0.713843i
$367$	−1.56490	+	1.86497i	−0.0816869	+	0.0973506i	−0.805340	−	0.592813i	$-0.798017\pi$
$367$	−1.56490	+	1.86497i	−0.0816869	+	0.0973506i	0.723653	+	0.690164i	$0.242462\pi$
$368$	−9.26224	−	23.6052i	−0.482828	−	1.23051i
$369$	−6.33299	+	3.65636i	−0.329682	+	0.190342i
$370$	−12.2190	+	34.2317i	−0.635234	+	1.77962i
$371$	−0.761222	+	4.31710i	−0.0395207	+	0.224133i
$372$	0.485696	+	2.56751i	0.0251822	+	0.133119i
$373$	−12.7636	−	7.36906i	−0.660874	−	0.381556i	0.131736	−	0.991285i	$-0.457945\pi$
$373$	−12.7636	−	7.36906i	−0.660874	−	0.381556i	−0.792610	+	0.609729i	$0.791278\pi$
$374$	17.0884	+	20.1101i	0.883621	+	1.03987i
$375$	10.2598	+	3.73427i	0.529815	+	0.192837i
$376$	−16.6814	−	2.62176i	−0.860277	−	0.135207i
$377$	0.138987	−	0.116624i	0.00715822	−	0.00600646i
$378$	0.0172781	+	2.78056i	0.000888692	+	0.143017i
$379$	−27.3596			−1.40537			−0.702683	−	0.711503i	$-0.748015\pi$
$379$	−27.3596			−1.40537			−0.702683	+	0.711503i	$0.748015\pi$
$380$	17.0631	−	26.4343i	0.875316	−	1.35605i
$381$	1.16357			0.0596116
$382$	0.136454	+	21.9594i	0.00698158	+	1.12354i
$383$	−6.78984	+	5.69735i	−0.346945	+	0.291121i	−0.799562	−	0.600584i	$-0.794935\pi$
$383$	−6.78984	+	5.69735i	−0.346945	+	0.291121i	0.452617	+	0.891705i	$0.350490\pi$
$384$	−8.34238	+	7.64229i	−0.425720	+	0.389994i
$385$	−37.2254	−	13.5489i	−1.89718	−	0.690518i
$386$	−5.29726	−	6.23395i	−0.269624	−	0.317300i
$387$	2.90278	+	1.67592i	0.147556	+	0.0851917i
$388$	−10.6206	+	2.00910i	−0.539181	+	0.101997i
$389$	−3.82780	+	21.7085i	−0.194077	+	1.10067i	0.719650	+	0.694337i	$0.244302\pi$
$389$	−3.82780	+	21.7085i	−0.194077	+	1.10067i	−0.913727	+	0.406329i	$0.866809\pi$
$390$	−0.197435	+	0.553118i	−0.00999751	+	0.0280082i
$391$	18.3511	−	10.5950i	0.928057	−	0.535814i
$392$	4.57460	+	7.59297i	0.231052	+	0.383503i
$393$	−9.09080	+	10.8340i	−0.458570	+	0.546503i
$394$	3.04269	−	5.34655i	0.153289	−	0.269355i
$395$	−38.8972	+	14.1574i	−1.95713	+	0.712337i
$396$	3.94880	+	10.4436i	0.198435	+	0.524808i
$397$	−2.58993	−	14.6882i	−0.129985	−	0.737179i	−0.978222	−	0.207563i	$-0.933447\pi$
$397$	−2.58993	−	14.6882i	−0.129985	−	0.737179i	0.848237	−	0.529617i	$-0.177664\pi$
$398$	−4.34610	−	0.738518i	−0.217850	−	0.0370186i
$399$	0.531257	−	8.55395i	0.0265961	−	0.428233i
$400$	25.0960	+	20.0166i	1.25480	+	1.00083i
$401$	−0.0489938	+	0.00863892i	−0.00244663	+	0.000431407i	−0.174871	−	0.984591i	$-0.555951\pi$
$401$	−0.0489938	+	0.00863892i	−0.00244663	+	0.000431407i	0.172425	+	0.985023i	$0.444840\pi$
$402$	−3.84999	−	6.57370i	−0.192020	−	0.327866i
$403$	0.0514186	+	0.141272i	0.00256134	+	0.00703724i
$404$	−27.8735	−	22.8044i	−1.38676	−	1.13456i
$405$	−2.76469	−	2.31985i	−0.137379	−	0.115274i
$406$	−3.37610	−	2.79732i	−0.167553	−	0.138829i
$407$	19.8777	+	34.4293i	0.985303	+	1.70659i
$408$	−7.35451	−	5.94111i	−0.364102	−	0.294129i
$409$	20.3246	+	3.58378i	1.00499	+	0.177206i	0.651836	−	0.758360i	$-0.273999\pi$
$409$	20.3246	+	3.58378i	1.00499	+	0.177206i	0.353151	+	0.935566i	$0.385110\pi$
$410$	12.9832	+	34.9929i	0.641194	+	1.72818i
$411$	9.40945	−	16.2976i	0.464134	−	0.803903i
$412$	9.11317	+	15.3410i	0.448974	+	0.755796i
$413$	7.87795	−	21.6445i	0.387649	−	1.06506i
$414$	8.81913	−	1.61162i	0.433437	−	0.0792067i
$415$	40.9152	+	48.7608i	2.00845	+	2.39357i
$416$	−0.402711	+	0.511389i	−0.0197445	+	0.0250729i
$417$		−	7.75587i		−	0.379806i
$418$	−9.94778	−	32.9442i	−0.486562	−	1.61135i
$419$		−	17.1879i		−	0.839685i	−0.907597	−	0.419843i	$-0.862085\pi$
$419$		−	17.1879i		−	0.839685i	0.907597	−	0.419843i	$-0.137915\pi$
$420$	14.0061	+	2.29056i	0.683428	+	0.111768i
$421$	−1.30377	−	1.55377i	−0.0635417	−	0.0757260i	0.733337	−	0.679865i	$-0.237962\pi$
$421$	−1.30377	−	1.55377i	−0.0635417	−	0.0757260i	−0.796879	+	0.604139i	$0.793517\pi$
$422$	−1.33284	−	7.29358i	−0.0648814	−	0.355046i
$423$	2.04191	−	5.61012i	0.0992813	−	0.272773i
$424$	−2.26689	−	5.88455i	−0.110090	−	0.285779i
$425$	−13.4127	+	23.2315i	−0.650613	+	1.12689i
$426$	2.94650	−	1.09322i	0.142758	−	0.0529666i
$427$	−21.5143	−	3.79356i	−1.04115	−	0.183583i
$428$	−6.39251	+	11.3969i	−0.308994	+	0.550892i
$429$	0.321186	+	0.556310i	0.0155070	+	0.0268589i
$430$	10.9150	−	13.1733i	0.526366	−	0.635274i
$431$	−25.5727	−	21.4580i	−1.23179	−	1.03360i	−0.998120	−	0.0612822i	$-0.980481\pi$
$431$	−25.5727	−	21.4580i	−1.23179	−	1.03360i	−0.233673	−	0.972315i	$-0.575075\pi$
$432$	−2.08547	−	3.41333i	−0.100337	−	0.164224i
$433$	6.88171	+	18.9073i	0.330714	+	0.908629i	0.987926	+	0.154924i	$0.0495132\pi$
$433$	6.88171	+	18.9073i	0.330714	+	0.908629i	−0.657212	+	0.753705i	$0.728265\pi$
$434$	3.13487	−	1.83599i	0.150479	−	0.0881301i
$435$	5.60422	−	0.988175i	0.268702	−	0.0473793i
$436$	−7.09178	+	20.2646i	−0.339634	+	0.970498i
$437$	−27.4578	+	3.10227i	−1.31349	+	0.148402i
$438$	−0.685576	+	4.03454i	−0.0327581	+	0.192778i
$439$	−6.34583	−	35.9890i	−0.302870	−	1.71766i	−0.633365	−	0.773853i	$-0.718327\pi$
$439$	−6.34583	−	35.9890i	−0.302870	−	1.71766i	0.330496	−	0.943808i	$-0.392784\pi$
$440$	55.9267	−	10.9400i	2.66620	−	0.521545i
$441$	−2.94508	+	1.07192i	−0.140242	+	0.0510439i
$442$	−0.472751	−	0.269040i	−0.0224865	−	0.0127969i
$443$	−12.4013	+	14.7793i	−0.589205	+	0.702187i	−0.975453	−	0.220208i	$-0.929327\pi$
$443$	−12.4013	+	14.7793i	−0.589205	+	0.702187i	0.386248	+	0.922395i	$0.373771\pi$
$444$	−9.28991	−	10.7959i	−0.440879	−	0.512352i
$445$	36.0451	−	20.8106i	1.70870	−	0.986518i
$446$	−9.64736	−	3.44361i	−0.456816	−	0.163060i
$447$	−2.13131	+	12.0873i	−0.100808	+	0.571709i
$448$	13.9059	+	7.35154i	0.656990	+	0.347328i
$449$	−10.4202	−	6.01610i	−0.491759	−	0.283917i	0.233545	−	0.972346i	$-0.424967\pi$
$449$	−10.4202	−	6.01610i	−0.491759	−	0.283917i	−0.725304	+	0.688429i	$0.758301\pi$
$450$	−8.64866	+	7.34915i	−0.407702	+	0.346442i
$451$	38.3618	+	13.9626i	1.80639	+	0.657471i
$452$	0.370472	+	29.8087i	0.0174255	+	1.40208i
$453$	4.13396	−	3.46880i	0.194230	−	0.162979i
$454$	18.2470	−	0.113385i	0.856374	−	0.00532143i
$455$	0.816526			0.0382794
$456$	5.69553	+	10.9344i	0.266718	+	0.512050i
$457$	16.6523			0.778960			0.389480	−	0.921035i	$-0.372655\pi$
$457$	16.6523			0.778960			0.389480	+	0.921035i	$0.372655\pi$
$458$	−9.19242	+	0.0571208i	−0.429534	+	0.00266908i
$459$	2.56060	−	2.14860i	0.119519	−	0.100288i
$460$	−0.568650	−	45.7545i	−0.0265134	−	2.13331i
$461$	18.8513	+	6.86133i	0.877995	+	0.319564i	0.741400	−	0.671063i	$-0.234162\pi$
$461$	18.8513	+	6.86133i	0.877995	+	0.319564i	0.136594	+	0.990627i	$0.456384\pi$
$462$	11.8291	−	10.0517i	0.550339	−	0.467647i
$463$	−20.5675	−	11.8747i	−0.955855	−	0.551863i	−0.0609600	−	0.998140i	$-0.519416\pi$
$463$	−20.5675	−	11.8747i	−0.955855	−	0.551863i	−0.894895	+	0.446277i	$0.852750\pi$
$464$	6.23659	+	0.940512i	0.289526	+	0.0436622i
$465$	−0.818806	+	4.64368i	−0.0379712	+	0.215345i
$466$	−13.9037	−	4.96292i	−0.644077	−	0.229903i
$467$	17.3535	−	10.0190i	0.803022	−	0.463625i	−0.0415046	−	0.999138i	$-0.513215\pi$
$467$	17.3535	−	10.0190i	0.803022	−	0.463625i	0.844527	+	0.535513i	$0.179882\pi$
$468$	−0.150107	−	0.174441i	−0.00693869	−	0.00806354i
$469$	−6.80812	+	8.11360i	−0.314370	+	0.374651i
$470$	−26.4833	−	15.0715i	−1.22158	−	0.695196i
$471$	−8.88411	+	3.23355i	−0.409358	+	0.148994i
$472$	6.36101	+	32.5182i	0.292789	+	1.49677i
$473$	−3.24929	−	18.4276i	−0.149402	−	0.847303i
$474$	2.71728	−	15.9909i	0.124809	−	0.734487i
$475$	28.1395	−	20.7812i	1.29113	−	0.953507i
$476$	−4.34184	+	12.4067i	−0.199008	+	0.568661i
$477$	2.19567	−	0.387156i	0.100533	−	0.0177266i
$478$	−34.2031	+	20.0316i	−1.56441	+	0.916223i
$479$	5.26518	+	14.4660i	0.240572	+	0.660966i	0.999947	+	0.0103127i	$0.00328269\pi$
$479$	5.26518	+	14.4660i	0.240572	+	0.660966i	−0.759375	+	0.650653i	$0.774495\pi$
$480$	−18.9585	+	7.57523i	−0.865332	+	0.345760i
$481$	−0.627722	−	0.526721i	−0.0286217	−	0.0240164i
$482$	−13.3104	+	16.0644i	−0.606273	+	0.731714i
$483$	−6.23218	−	10.7944i	−0.283574	−	0.491164i
$484$	19.7296	−	35.1751i	0.896800	−	1.59887i
$485$	−19.2088	−	3.38703i	−0.872226	−	0.153797i
$486$	1.32589	−	0.491938i	0.0601438	−	0.0223148i
$487$	−11.3873	+	19.7235i	−0.516010	+	0.893755i	0.483817	+	0.875169i	$0.339250\pi$
$487$	−11.3873	+	19.7235i	−0.516010	+	0.893755i	−0.999827	+	0.0185864i	$0.994083\pi$
$488$	29.3257	−	11.2971i	1.32751	−	0.511395i
$489$	−0.639587	+	1.75725i	−0.0289231	+	0.0794656i
$490$	2.87556	+	15.7357i	0.129905	+	0.710867i
$491$	−13.5104	−	16.1011i	−0.609716	−	0.726631i	0.369550	−	0.929211i	$-0.379512\pi$
$491$	−13.5104	−	16.1011i	−0.609716	−	0.726631i	−0.979266	+	0.202580i	$0.935067\pi$
$492$	−14.4337	−	2.36049i	−0.650720	−	0.106419i
$493$			5.27059i			0.237375i
$494$	0.424922	+	0.567960i	0.0191181	+	0.0255537i
$495$			20.1478i			0.905577i
$496$	−2.49976	+	4.58948i	−0.112243	+	0.206074i
$497$	−2.80860	−	3.34716i	−0.125983	−	0.150141i
$498$	−24.5361	+	4.48376i	−1.09949	+	0.200922i
$499$	6.36184	−	17.4790i	0.284795	−	0.782468i	−0.711978	−	0.702201i	$-0.752201\pi$
$499$	6.36184	−	17.4790i	0.284795	−	0.782468i	0.996773	−	0.0802666i	$-0.0255772\pi$
$500$	11.1525	+	18.7739i	0.498753	+	0.839593i
$501$	7.69713	−	13.3318i	0.343882	−	0.595622i
$502$	−8.56129	−	23.0748i	−0.382109	−	1.02988i
$503$	6.21016	+	1.09502i	0.276897	+	0.0488245i	0.310372	−	0.950615i	$-0.399546\pi$
$503$	6.21016	+	1.09502i	0.276897	+	0.0488245i	−0.0334750	+	0.999440i	$0.510657\pi$
$504$	−3.49466	+	4.32604i	−0.155664	+	0.192697i
$505$	−32.4936	−	56.2806i	−1.44595	−	2.50445i
$506$	−38.5388	−	31.9319i	−1.71326	−	1.41955i
$507$	9.94843	+	8.34773i	0.441826	+	0.370736i
$508$	1.80115	+	1.47359i	0.0799130	+	0.0653800i
$509$	−6.21442	−	17.0740i	−0.275449	−	0.756790i	−0.997864	−	0.0653302i	$-0.979190\pi$
$509$	−6.21442	−	17.0740i	−0.275449	−	0.756790i	0.722414	−	0.691460i	$-0.243032\pi$
$510$	−8.62199	−	14.7217i	−0.381788	−	0.651888i
$511$	5.60322	−	0.987998i	0.247872	−	0.0437065i
$512$	−22.5920	+	1.26477i	−0.998437	+	0.0558953i
$513$	−4.18056	+	1.23406i	−0.184576	+	0.0544852i
$514$	−4.21776	−	0.716711i	−0.186037	−	0.0316127i
$515$	5.59135	+	31.7101i	0.246384	+	1.39731i
$516$	2.37090	+	6.27041i	0.104373	+	0.276040i
$517$	−31.3189	+	11.3992i	−1.37740	+	0.501334i
$518$	−9.79411	+	17.2100i	−0.430329	+	0.756163i
$519$	−10.8675	+	12.9513i	−0.477028	+	0.568500i
$520$	−1.00611	+	0.606159i	−0.0441207	+	0.0265818i
$521$	−25.0420	+	14.4580i	−1.09711	+	0.633416i	−0.935460	−	0.353432i	$-0.885014\pi$
$521$	−25.0420	+	14.4580i	−1.09711	+	0.633416i	−0.161649	+	0.986848i	$0.551681\pi$
$522$	−0.749635	+	2.10012i	−0.0328107	+	0.0919197i
$523$	−6.34830	+	36.0030i	−0.277592	+	1.57430i	0.453015	+	0.891503i	$0.350348\pi$
$523$	−6.34830	+	36.0030i	−0.277592	+	1.57430i	−0.730607	+	0.682799i	$0.760763\pi$
$524$	−27.7926	+	5.25753i	−1.21413	+	0.229676i
$525$	13.6652	+	7.88959i	0.596397	+	0.344330i
$526$	−0.850037	−	1.00034i	−0.0370634	−	0.0436171i
$527$	−4.10385	−	1.49368i	−0.178767	−	0.0650658i
$528$	−7.11356	+	21.1670i	−0.309578	+	0.921174i
$529$	−13.1662	+	11.0477i	−0.572442	+	0.480336i
$530$	−0.0707098	−	11.3793i	−0.00307144	−	0.494284i
$531$	−11.7148			−0.508380
$532$	11.6554	−	12.5683i	0.505325	−	0.544903i
$533$	−0.841453			−0.0364474
$534$	0.101343	+	16.3090i	0.00438553	+	0.705761i
$535$	−18.0635	+	15.1571i	−0.780955	+	0.655299i
$536$	2.36559	−	15.0515i	0.102178	−	0.650126i
$537$	8.36352	+	3.04407i	0.360912	+	0.131361i
$538$	−20.5860	−	24.2261i	−0.887524	−	1.04446i
$539$	15.1522	+	8.74815i	0.652653	+	0.376810i
$540$	−1.34165	−	7.09232i	−0.0577355	−	0.305205i
$541$	7.83058	−	44.4094i	0.336663	−	1.90931i	−0.0734954	−	0.997296i	$-0.523415\pi$
$541$	7.83058	−	44.4094i	0.336663	−	1.90931i	0.410158	−	0.912014i	$-0.365473\pi$
$542$	3.66771	−	10.2752i	0.157542	−	0.441357i
$543$	−7.92970	+	4.57821i	−0.340296	+	0.196470i
$544$	−3.86035	−	18.5105i	−0.165511	−	0.793632i
$545$	−24.9033	+	29.6785i	−1.06674	+	1.27129i
$546$	−0.158254	+	0.278080i	−0.00677264	+	0.0119007i
$547$	−26.9570	+	9.81155i	−1.15260	+	0.419512i	−0.846448	−	0.532471i	$-0.821263\pi$
$547$	−26.9570	+	9.81155i	−1.15260	+	0.419512i	−0.306151	+	0.951983i	$0.599041\pi$
$548$	35.2052	−	13.3114i	1.50389	−	0.568636i
$549$	1.92939	+	10.9421i	0.0823445	+	0.466999i
$550$	62.4636	+	10.6143i	2.66346	+	0.452593i
$551$	2.74653	−	6.30039i	0.117006	−	0.268405i
$552$	15.6926	+	8.67417i	0.667920	+	0.369197i
$553$	−22.2084	+	3.91594i	−0.944396	+	0.166522i
$554$	1.14858	+	1.96115i	0.0487984	+	0.0833213i
$555$	−8.79036	−	24.1513i	−0.373130	−	1.02517i
$556$	9.82231	−	12.0057i	0.416559	−	0.509154i
$557$	−14.3725	−	12.0600i	−0.608983	−	0.510998i	0.285336	−	0.958428i	$-0.407895\pi$
$557$	−14.3725	−	12.0600i	−0.608983	−	0.510998i	−0.894319	+	0.447430i	$0.852339\pi$
$558$	−1.42278	−	1.17886i	−0.0602309	−	0.0499053i
$559$	0.192843	+	0.334014i	0.00815640	+	0.0141273i
$560$	18.7799	+	21.2835i	0.793594	+	0.899393i
$561$	−18.3770	−	3.24036i	−0.775878	−	0.136808i
$562$	−4.91851	−	13.2566i	−0.207475	−	0.559196i
$563$	13.6287	−	23.6056i	0.574381	−	0.994857i	−0.421728	−	0.906723i	$-0.638576\pi$
$563$	13.6287	−	23.6056i	0.574381	−	0.994857i	0.996109	−	0.0881344i	$-0.0280905\pi$
$564$	10.2656	−	6.09821i	0.432261	−	0.256781i
$565$	−18.3989	+	50.5506i	−0.774047	+	2.12668i
$566$	−15.5263	+	2.83730i	−0.652620	+	0.119260i
$567$	−1.26384	−	1.50619i	−0.0530764	−	0.0632540i
$568$	5.94551	+	2.03931i	0.249468	+	0.0855674i
$569$		−	13.6814i		−	0.573554i	−0.957997	−	0.286777i	$-0.907416\pi$
$569$		−	13.6814i		−	0.573554i	0.957997	−	0.286777i	$-0.0925839\pi$
$570$	2.63504	+	22.0911i	0.110370	+	0.925294i
$571$		−	4.69406i		−	0.196440i	−0.995165	−	0.0982202i	$-0.968685\pi$
$571$		−	4.69406i		−	0.196440i	0.995165	−	0.0982202i	$-0.0313150\pi$
$572$	−0.207353	+	1.26790i	−0.00866985	+	0.0530136i
$573$	−9.98118	−	11.8951i	−0.416970	−	0.496925i
$574$	3.65530	+	20.0026i	0.152569	+	0.834892i
$575$	17.4002	−	47.8067i	0.725639	−	1.99368i
$576$	1.09456	−	7.92477i	0.0456065	−	0.330199i
$577$	3.24677	−	5.62357i	0.135165	−	0.234112i	−0.790496	−	0.612468i	$-0.790177\pi$
$577$	3.24677	−	5.62357i	0.135165	−	0.234112i	0.925660	+	0.378355i	$0.123510\pi$
$578$	−7.72574	+	2.86643i	−0.321348	+	0.119228i
$579$	5.69672	+	1.00449i	0.236748	+	0.0417450i
$580$	9.92649	+	5.56774i	0.412175	+	0.231188i
$581$	17.3388	+	30.0317i	0.719336	+	1.24593i
$582$	4.87642	−	5.88538i	0.202134	−	0.243957i
$583$	−9.53464	−	8.00051i	−0.394884	−	0.331347i
$584$	−6.17072	+	5.37701i	−0.255346	+	0.222502i
$585$	−0.142035	−	0.390239i	−0.00587243	−	0.0161344i
$586$	−2.39597	+	1.40324i	−0.0989768	+	0.0579673i
$587$	0.243914	−	0.0430085i	0.0100674	−	0.00177515i	−0.168612	−	0.985682i	$-0.553929\pi$
$587$	0.243914	−	0.0430085i	0.0100674	−	0.00177515i	0.178680	+	0.983907i	$0.442817\pi$
$588$	−5.91635	−	2.07048i	−0.243986	−	0.0853851i
$589$	4.12732	+	3.92407i	0.170063	+	0.161688i
$590$	−10.0167	+	58.9471i	−0.412381	+	2.42681i
$591$	0.755355	+	4.28383i	0.0310712	+	0.176213i
$592$	−0.707940	−	28.4766i	−0.0290961	−	1.17038i
$593$	39.5353	−	14.3897i	1.62352	−	0.590913i	0.639473	−	0.768814i	$-0.279153\pi$
$593$	39.5353	−	14.3897i	1.62352	−	0.590913i	0.984048	+	0.177901i	$0.0569305\pi$
$594$	−6.86163	−	3.90492i	−0.281536	−	0.160221i
$595$	−15.2467	+	18.1703i	−0.625053	+	0.744909i
$596$	−18.6069	+	16.0113i	−0.762170	+	0.655848i
$597$	2.69958	−	1.55860i	0.110486	−	0.0637894i
$598$	0.971558	+	0.346797i	0.0397300	+	0.0141816i
$599$	3.30302	−	18.7324i	0.134958	−	0.765384i	−0.839931	−	0.542693i	$-0.817405\pi$
$599$	3.30302	−	18.7324i	0.134958	−	0.765384i	0.974889	−	0.222691i	$-0.0714840\pi$
$600$	−22.6949	+	0.423115i	−0.926515	+	0.0172736i
$601$	35.6278	+	20.5697i	1.45329	+	0.839057i	0.998666	−	0.0516270i	$-0.0164407\pi$
$601$	35.6278	+	20.5697i	1.45329	+	0.839057i	0.454623	+	0.890684i	$0.349774\pi$
$602$	7.10230	−	6.03514i	0.289468	−	0.245974i
$603$	5.06197	+	1.84241i	0.206139	+	0.0750286i
$604$	10.7922	−	0.134128i	0.439127	−	0.00545760i
$605$	55.7506	−	46.7803i	2.26658	−	1.90189i
$606$	25.4649	−	0.158236i	1.03444	−	0.00642791i
$607$	5.25857			0.213439			0.106719	−	0.994289i	$-0.465965\pi$
$607$	5.25857			0.213439			0.106719	+	0.994289i	$0.465965\pi$
$608$	−5.03134	+	24.1389i	−0.204048	+	0.978961i
$609$	3.10025			0.125628
$610$	56.7088	−	0.352383i	2.29607	−	0.0142676i
$611$	0.526249	−	0.441575i	0.0212898	−	0.0178642i
$612$	6.68475	−	0.0830800i	0.270215	−	0.00335831i
$613$	3.19955	+	1.16454i	0.129229	+	0.0470354i	0.405825	−	0.913951i	$-0.366984\pi$
$613$	3.19955	+	1.16454i	0.129229	+	0.0470354i	−0.276596	+	0.960986i	$0.589206\pi$
$614$	−13.2623	+	11.2696i	−0.535222	+	0.454802i
$615$	−22.8561	−	13.1960i	−0.921647	−	0.532113i
$616$	31.0406	−	0.578710i	1.25066	−	0.0233169i
$617$	0.527489	−	2.99154i	0.0212359	−	0.120435i	−0.972347	−	0.233541i	$-0.924969\pi$
$617$	0.527489	−	2.99154i	0.0212359	−	0.120435i	0.993583	+	0.113106i	$0.0360799\pi$
$618$	−11.8830	−	4.24163i	−0.478005	−	0.170624i
$619$	−22.1622	+	12.7953i	−0.890773	+	0.514288i	−0.874195	−	0.485575i	$-0.838610\pi$
$619$	−22.1622	+	12.7953i	−0.890773	+	0.514288i	−0.0165776	+	0.999863i	$0.505277\pi$
$620$	−7.14839	+	6.15120i	−0.287086	+	0.247038i
$621$	−4.07485	+	4.85621i	−0.163518	+	0.194873i
$622$	12.4107	+	7.06288i	0.497625	+	0.283196i
$623$	21.3076	−	7.75532i	0.853669	−	0.310710i
$624$	−0.0114389	−	0.460126i	−0.000457924	−	0.0184198i
$625$	−0.125305	−	0.710638i	−0.00501219	−	0.0284255i
$626$	−1.30800	+	7.69740i	−0.0522780	+	0.307650i
$627$	20.2791	+	13.4499i	0.809868	+	0.537136i
$628$	−17.8472	−	6.24579i	−0.712182	−	0.249234i
$629$	23.4424	−	4.13353i	0.934710	−	0.164815i
$630$	−8.65955	+	5.07160i	−0.345005	+	0.202057i
$631$	−1.29656	−	3.56226i	−0.0516151	−	0.141811i	0.911206	−	0.411951i	$-0.135152\pi$
$631$	−1.29656	−	3.56226i	−0.0516151	−	0.141811i	−0.962821	+	0.270139i	$0.912930\pi$
$632$	24.4577	−	21.3118i	0.972874	−	0.847738i
$633$	4.01617	+	3.36997i	0.159629	+	0.133944i
$634$	−23.7274	+	28.6368i	−0.942337	+	1.13731i
$635$	2.09970	+	3.63678i	0.0833239	+	0.144321i
$636$	3.88909	+	2.18138i	0.154212	+	0.0864972i
$637$	−0.355152	−	0.0626229i	−0.0140716	−	0.00248121i
$638$	11.6712	−	4.33028i	0.462066	−	0.171437i
$639$	−1.11114	+	1.92454i	−0.0439558	+	0.0761337i
$640$	−38.9403	−	12.2837i	−1.53925	−	0.485554i
$641$	−1.34038	+	3.68267i	−0.0529419	+	0.145457i	−0.963345	−	0.268266i	$-0.913549\pi$
$641$	−1.34038	+	3.68267i	−0.0529419	+	0.145457i	0.910403	+	0.413723i	$0.135772\pi$
$642$	−1.66102	−	9.08945i	−0.0655551	−	0.358732i
$643$	−8.07959	−	9.62888i	−0.318628	−	0.379726i	0.582829	−	0.812595i	$-0.301946\pi$
$643$	−8.07959	−	9.62888i	−0.318628	−	0.379726i	−0.901457	+	0.432869i	$0.857501\pi$
$644$	4.02340	−	24.6019i	0.158544	−	0.969450i
$645$			12.0970i			0.476317i
$646$	−20.5733	−	1.14945i	−0.809445	−	0.0452246i
$647$			11.1120i			0.436857i	0.975853	+	0.218429i	$0.0700931\pi$
$647$			11.1120i			0.436857i	−0.975853	+	0.218429i	$0.929907\pi$
$648$	2.67542	+	0.917668i	0.105101	+	0.0360494i
$649$	42.0376	+	50.0985i	1.65012	+	1.96654i
$650$	−1.28467	+	0.234762i	−0.0503889	+	0.00920813i
$651$	−0.878608	+	2.41396i	−0.0344354	+	0.0946104i
$652$	−3.21549	+	1.91013i	−0.125928	+	0.0748066i
$653$	−7.74378	+	13.4126i	−0.303038	+	0.524876i	−0.976822	−	0.214051i	$-0.931334\pi$
$653$	−7.74378	+	13.4126i	−0.303038	+	0.524876i	0.673785	+	0.738928i	$0.264667\pi$
$654$	−5.28087	−	14.2333i	−0.206499	−	0.556565i
$655$	−50.2666	−	8.86335i	−1.96408	−	0.346320i
$656$	−19.3532	−	21.9332i	−0.755614	−	0.856349i
$657$	−1.44687	−	2.50606i	−0.0564479	−	0.0977705i
$658$	−12.7829	−	10.5915i	−0.498331	−	0.412900i
$659$	36.7884	+	30.8692i	1.43307	+	1.20249i	0.943868	+	0.330324i	$0.107158\pi$
$659$	36.7884	+	30.8692i	1.43307	+	1.20249i	0.489207	+	0.872168i	$0.337286\pi$
$660$	−25.5159	+	31.1878i	−0.993206	+	1.21398i
$661$	12.7444	+	35.0149i	0.495699	+	1.36192i	0.895395	+	0.445273i	$0.146894\pi$
$661$	12.7444	+	35.0149i	0.495699	+	1.36192i	−0.399696	+	0.916648i	$0.630884\pi$
$662$	−25.1069	−	42.8690i	−0.975806	−	1.66615i
$663$	0.378784	−	0.0667898i	0.0147107	−	0.00259390i
$664$	−43.6590	−	24.1328i	−1.69430	−	0.936535i
$665$	27.6943	−	13.7754i	1.07394	−	0.534186i
$666$	9.92878	+	1.68717i	0.384732	+	0.0653764i
$667$	−1.73574	−	9.84387i	−0.0672081	−	0.381156i
$668$	28.7986	−	10.8890i	1.11425	−	0.421309i
$669$	6.80645	−	2.47734i	0.263153	−	0.0957797i
$670$	13.5989	−	23.8957i	0.525371	−	0.923170i
$671$	39.8706	−	47.5160i	1.53919	−	1.83433i
$672$	−10.8882	+	2.27072i	−0.420022	+	0.0875951i
$673$	29.1483	−	16.8288i	1.12358	−	0.648701i	0.181270	−	0.983433i	$-0.441979\pi$
$673$	29.1483	−	16.8288i	1.12358	−	0.648701i	0.942313	+	0.334732i	$0.108646\pi$
$674$	4.38753	−	12.2917i	0.169001	−	0.473460i
$675$	1.39357	−	7.90333i	0.0536385	−	0.304199i
$676$	4.82778	+	25.5209i	0.185684	+	0.981573i
$677$	−5.61581	−	3.24229i	−0.215833	−	0.124611i	0.388186	−	0.921581i	$-0.373102\pi$
$677$	−5.61581	−	3.24229i	−0.215833	−	0.124611i	−0.604019	+	0.796970i	$0.706435\pi$
$678$	−13.6498	−	16.0634i	−0.524216	−	0.616911i
$679$	−9.98544	−	3.63440i	−0.383206	−	0.139476i
$680$	5.29771	−	33.7076i	0.203158	−	1.29263i
$681$	−9.88414	+	8.29378i	−0.378761	+	0.317818i
$682$	0.0640949	+	10.3148i	0.00245432	+	0.394973i
$683$	46.0289			1.76125			0.880624	−	0.473815i	$-0.157124\pi$
$683$	46.0289			1.76125			0.880624	+	0.473815i	$0.157124\pi$
$684$	−8.03415	−	3.38415i	−0.307193	−	0.129396i
$685$	67.9183			2.59503
$686$	0.175098	+	28.1785i	0.00668528	+	1.07586i
$687$	4.97940	−	4.17822i	0.189976	−	0.159409i
$688$	−4.27105	+	12.7089i	−0.162832	+	0.484521i
$689$	0.241075	+	0.0877442i	0.00918423	+	0.00334279i
$690$	20.9515	+	24.6563i	0.797610	+	0.938648i
$691$	7.27369	+	4.19947i	0.276704	+	0.159755i	0.631930	−	0.775025i	$-0.282263\pi$
$691$	7.27369	+	4.19947i	0.276704	+	0.159755i	−0.355226	+	0.934780i	$0.615596\pi$
$692$	−33.2243	+	6.28503i	−1.26300	+	0.238921i
$693$	−1.90604	+	10.8097i	−0.0724043	+	0.410625i
$694$	1.85504	−	5.19693i	0.0704164	−	0.197273i
$695$	24.2412	−	13.9957i	0.919521	−	0.530886i
$696$	−3.82006	+	2.30151i	−0.144799	+	0.0872384i
$697$	15.7121	−	18.7250i	0.595139	−	0.709258i
$698$	10.8435	−	19.0540i	0.410433	−	0.721203i
$699$	9.80942	−	3.57034i	0.371026	−	0.135043i
$700$	11.1613	+	29.5187i	0.421857	+	1.11570i
$701$	7.46058	+	42.3111i	0.281782	+	1.59807i	0.716557	+	0.697528i	$0.245717\pi$
$701$	7.46058	+	42.3111i	0.281782	+	1.59807i	−0.434775	+	0.900539i	$0.643172\pi$
$702$	0.160430	+	0.0272613i	0.00605503	+	0.00102891i
$703$	−30.1767	−	7.27481i	−1.13814	−	0.274375i
$704$	−37.8180	+	23.7565i	−1.42532	+	0.895356i
$705$	21.2193	−	3.74153i	0.799164	−	0.140914i
$706$	−2.72414	−	4.65136i	−0.102524	−	0.175056i
$707$	−12.1091	−	33.2695i	−0.455410	−	1.25123i
$708$	−18.1339	−	14.8361i	−0.681514	−	0.557574i
$709$	−10.3902	−	8.71837i	−0.390210	−	0.327425i	0.426485	−	0.904495i	$-0.359752\pi$
$709$	−10.3902	−	8.71837i	−0.390210	−	0.327425i	−0.816695	+	0.577069i	$0.804196\pi$
$710$	8.73392	+	7.23662i	0.327778	+	0.271586i
$711$	5.73468	+	9.93276i	0.215067	+	0.372508i
$712$	−20.4975	+	25.3739i	−0.768176	+	0.950926i
$713$	8.15667	+	1.43824i	0.305470	+	0.0538626i
$714$	−3.23314	−	8.71412i	−0.120997	−	0.326118i
$715$	−1.15918	+	2.00775i	−0.0433507	+	0.0750857i
$716$	9.09116	+	15.3039i	0.339753	+	0.571934i
$717$	9.58608	−	26.3375i	0.357999	−	0.983593i
$718$	−0.176108	+	0.0321821i	−0.00657228	+	0.00120103i
$719$	0.441431	+	0.526077i	0.0164626	+	0.0196193i	0.774213	−	0.632925i	$-0.218146\pi$
$719$	0.441431	+	0.526077i	0.0164626	+	0.0196193i	−0.757750	+	0.652545i	$0.773702\pi$
$720$	6.90516	−	12.6776i	0.257340	−	0.472468i
$721$			17.5420i			0.653298i
$722$	23.9940	+	12.0949i	0.892965	+	0.450125i
$723$		−	14.7518i		−	0.548626i
$724$	−18.0728	−	2.95563i	−0.671669	−	0.109845i
$725$	8.13386	+	9.69355i	0.302084	+	0.360010i
$726$	5.12650	+	28.0533i	0.190262	+	1.04116i
$727$	−13.2285	+	36.3450i	−0.490618	+	1.34796i	0.409498	+	0.912311i	$0.365704\pi$
$727$	−13.2285	+	36.3450i	−0.490618	+	1.34796i	−0.900116	+	0.435651i	$0.856518\pi$
$728$	−0.597139	+	0.230035i	−0.0221314	+	0.00852565i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	−13.8472	+	5.13764i	−0.512508	+	0.190152i
$731$	−11.0337	−	1.94555i	−0.408098	−	0.0719587i
$732$	−10.8709	+	19.3813i	−0.401801	+	0.716353i
$733$	−2.57626	−	4.46222i	−0.0951564	−	0.164816i	0.814517	−	0.580139i	$-0.197002\pi$
$733$	−2.57626	−	4.46222i	−0.0951564	−	0.164816i	−0.909674	+	0.415323i	$0.863668\pi$
$734$	2.19666	−	2.65117i	0.0810804	−	0.0978563i
$735$	−8.66480	−	7.27063i	−0.319606	−	0.268181i
$736$	13.3060	+	33.3008i	0.490464	+	1.22748i
$737$	−10.2854	−	28.2588i	−0.378867	−	1.04093i
$738$	8.92390	−	5.22642i	0.328493	−	0.192387i
$739$	−13.9534	+	2.46035i	−0.513283	+	0.0905056i	−0.424289	−	0.905527i	$-0.639476\pi$
$739$	−13.9534	+	2.46035i	−0.513283	+	0.0905056i	−0.0889933	+	0.996032i	$0.528365\pi$
$740$	16.9791	−	48.5174i	0.624164	−	1.78354i
$741$	−0.487597	−	0.117547i	−0.0179123	−	0.00431819i
$742$	1.03857	−	6.11188i	0.0381272	−	0.224374i
$743$	3.35200	+	19.0101i	0.122973	+	0.697414i	0.982491	+	0.186309i	$0.0596525\pi$
$743$	3.35200	+	19.0101i	0.122973	+	0.697414i	−0.859518	+	0.511105i	$0.829236\pi$
$744$	−0.709427	−	3.62667i	−0.0260089	−	0.132960i
$745$	−41.6252	+	15.1503i	−1.52503	+	0.555065i
$746$	18.1149	+	10.3091i	0.663232	+	0.377442i
$747$	11.3368	−	13.5107i	0.414793	−	0.494331i
$748$	−24.3429	−	28.2892i	−0.890066	−	1.03436i
$749$	−11.1253	+	6.42320i	−0.406510	+	0.234699i
$750$	−14.5421	−	5.19080i	−0.531004	−	0.189541i
$751$	−4.44462	+	25.2067i	−0.162186	+	0.919805i	0.789732	+	0.613453i	$0.210220\pi$
$751$	−4.44462	+	25.2067i	−0.162186	+	0.919805i	−0.951918	+	0.306353i	$0.900891\pi$
$752$	23.6136	+	3.56107i	0.861101	+	0.129859i
$753$	15.0716	+	8.70160i	0.549240	+	0.317104i
$754$	−0.195529	+	0.166150i	−0.00712076	+	0.00605082i
$755$	18.3017	+	6.66127i	0.666066	+	0.242428i
$756$	−0.0488690	−	3.93208i	−0.00177735	−	0.143008i
$757$	−18.0416	+	15.1387i	−0.655735	+	0.550227i	−0.908805	−	0.417221i	$-0.863004\pi$
$757$	−18.0416	+	15.1387i	−0.655735	+	0.550227i	0.253070	+	0.967448i	$0.418560\pi$
$758$	38.6915	−	0.240425i	1.40534	−	0.00873264i
$759$	35.3899			1.28457
$760$	−23.8980	+	37.5329i	−0.866873	+	1.36146i
$761$	18.7562			0.679910			0.339955	−	0.940442i	$-0.389588\pi$
$761$	18.7562			0.679910			0.339955	+	0.940442i	$0.389588\pi$
$762$	−1.64551	+	0.0102250i	−0.0596104	+	0.000370414i
$763$	−16.1687	+	13.5672i	−0.585347	+	0.491164i
$764$	−0.385942	−	31.0535i	−0.0139629	−	1.12348i
$765$	11.3362	+	4.12604i	0.409861	+	0.149177i
$766$	9.55203	−	8.11678i	0.345129	−	0.293271i
$767$	−1.16739	−	0.673995i	−0.0421522	−	0.0243366i
$768$	11.7305	−	10.8809i	0.423289	−	0.392632i
$769$	−0.685755	+	3.88911i	−0.0247289	+	0.140245i	−0.994673	−	0.103085i	$-0.967129\pi$
$769$	−0.685755	+	3.88911i	−0.0247289	+	0.140245i	0.969944	+	0.243330i	$0.0782397\pi$
$770$	52.7628	+	18.8336i	1.90144	+	0.678716i
$771$	2.61986	−	1.51258i	0.0943521	−	0.0544742i
$772$	7.54610	+	8.76942i	0.271590	+	0.315618i
$773$	−20.5063	+	24.4384i	−0.737560	+	0.878990i	−0.996210	−	0.0869812i	$-0.972278\pi$
$773$	−20.5063	+	24.4384i	−0.737560	+	0.878990i	0.258650	+	0.965971i	$0.416722\pi$
$774$	−4.11979	−	2.34455i	−0.148083	−	0.0842732i
$775$	−9.85285	+	3.58615i	−0.353925	+	0.128818i
$776$	15.0019	−	2.93458i	0.538537	−	0.105345i
$777$	−2.43141	−	13.7892i	−0.0872263	−	0.494685i
$778$	5.22245	−	30.7335i	0.187234	−	1.10185i
$779$	−28.5397	+	14.1959i	−1.02254	+	0.508620i
$780$	0.274349	−	0.783947i	0.00982328	−	0.0280698i
$781$	12.2175	−	2.15428i	0.437178	−	0.0770862i
$782$	−25.8588	+	15.1446i	−0.924710	+	0.541570i
$783$	−0.539290	−	1.48169i	−0.0192726	−	0.0529511i
$784$	−6.53606	−	10.6977i	−0.233431	−	0.382060i
$785$	−26.1382	−	21.9325i	−0.932912	−	0.782806i
$786$	12.7609	−	15.4012i	0.455166	−	0.549342i
$787$	−23.6234	−	40.9170i	−0.842084	−	1.45853i	−0.888129	−	0.459594i	$-0.847995\pi$
$787$	−23.6234	−	40.9170i	−0.842084	−	1.45853i	0.0460450	−	0.998939i	$-0.485338\pi$
$788$	−4.25595	+	7.58775i	−0.151612	+	0.270303i
$789$	0.914136	+	0.161187i	0.0325441	+	0.00573840i
$790$	54.8835	−	20.3630i	1.95267	−	0.724485i
$791$	−14.6536	+	25.3807i	−0.521020	+	0.902434i
$792$	−5.67611	−	14.7344i	−0.201692	−	0.523565i
$793$	−0.437274	+	1.20140i	−0.0155281	+	0.0426630i
$794$	3.79171	+	20.7491i	0.134563	+	0.736358i
$795$	5.17221	+	6.16399i	0.183439	+	0.218614i
$796$	6.15268	+	1.00621i	0.218076	+	0.0356642i
$797$		−	11.7621i		−	0.416636i	−0.978061	−	0.208318i	$-0.933201\pi$
$797$		−	11.7621i		−	0.416636i	0.978061	−	0.208318i	$-0.0667988\pi$
$798$	−0.676127	+	12.1015i	−0.0239346	+	0.428390i
$799$			19.9560i			0.705994i
$800$	−35.6663	−	28.0867i	−1.26100	−	0.993014i
$801$	−7.41292	−	8.83438i	−0.261923	−	0.312147i
$802$	0.0692104	−	0.0126476i	0.00244390	−	0.000446602i
$803$	−5.52518	+	15.1803i	−0.194980	+	0.535702i
$804$	5.50237	+	9.26261i	0.194054	+	0.326667i
$805$	22.4922	−	38.9577i	0.792748	−	1.37308i
$806$	−0.0739570	−	0.199332i	−0.00260502	−	0.00702119i
$807$	22.1383	+	3.90358i	0.779305	+	0.137413i
$808$	39.6187	+	32.0047i	1.39378	+	1.12592i
$809$	−2.48471	−	4.30365i	−0.0873578	−	0.151308i	0.819036	−	0.573743i	$-0.194509\pi$
$809$	−2.48471	−	4.30365i	−0.0873578	−	0.151308i	−0.906393	+	0.422434i	$0.861176\pi$
$810$	3.93018	+	3.25641i	0.138092	+	0.114419i
$811$	3.51097	+	2.94606i	0.123287	+	0.103450i	0.702347	−	0.711835i	$-0.252136\pi$
$811$	3.51097	+	2.94606i	0.123287	+	0.103450i	−0.579060	+	0.815285i	$0.696580\pi$
$812$	4.79902	+	3.92626i	0.168412	+	0.137785i
$813$	2.63856	+	7.24939i	0.0925385	+	0.254247i
$814$	−28.4134	−	48.5147i	−0.995888	−	1.70044i
$815$	−6.64649	+	1.17196i	−0.232816	+	0.0410518i
$816$	10.4528	+	8.33720i	0.365923	+	0.291860i
$817$	12.1758	+	8.07543i	0.425976	+	0.282524i
$818$	−28.7743	−	4.88952i	−1.00607	−	0.170958i
$819$	−0.0392869	−	0.222807i	−0.00137279	−	0.00778550i
$820$	−18.6682	−	49.3725i	−0.651921	−	1.72416i
$821$	−13.7267	+	4.99610i	−0.479064	+	0.174365i	−0.570254	−	0.821469i	$-0.693155\pi$
$821$	−13.7267	+	4.99610i	−0.479064	+	0.174365i	0.0911900	+	0.995834i	$0.470933\pi$
$822$	−13.1635	+	23.1306i	−0.459130	+	0.806772i
$823$	33.0057	−	39.3347i	1.15051	−	1.37112i	0.233449	−	0.972369i	$-0.424999\pi$
$823$	33.0057	−	39.3347i	1.15051	−	1.37112i	0.917059	−	0.398753i	$-0.130557\pi$
$824$	−13.0225	−	21.6149i	−0.453661	−	0.752991i
$825$	−38.7993	+	22.4008i	−1.35082	+	0.779896i
$826$	−10.9507	+	30.6786i	−0.381023	+	1.06744i
$827$	−5.61047	+	31.8185i	−0.195095	+	1.10644i	0.717188	+	0.696880i	$0.245429\pi$
$827$	−5.61047	+	31.8185i	−0.195095	+	1.10644i	−0.912283	+	0.409560i	$0.865682\pi$
$828$	−12.4577	+	2.35663i	−0.432936	+	0.0818985i
$829$	−3.43948	−	1.98578i	−0.119458	−	0.0689691i	0.439080	−	0.898448i	$-0.355304\pi$
$829$	−3.43948	−	1.98578i	−0.119458	−	0.0689691i	−0.558538	+	0.829479i	$0.688638\pi$
$830$	−58.2902	−	68.5973i	−2.02328	−	2.38105i
$831$	−1.51015	−	0.549650i	−0.0523865	−	0.0190671i
$832$	0.565014	−	0.726738i	0.0195883	−	0.0251951i
$833$	8.02516	−	6.73391i	0.278055	−	0.233316i
$834$	0.0681556	+	10.9682i	0.00236003	+	0.379799i
$835$	55.5587			1.92269
$836$	14.3575	+	46.5018i	0.496565	+	1.60830i
$837$	1.30652			0.0451601
$838$	0.151041	+	24.3069i	0.00521762	+	0.839669i
$839$	−25.5691	+	21.4550i	−0.882744	+	0.740710i	−0.966741	−	0.255756i	$-0.917676\pi$
$839$	−25.5691	+	21.4550i	−0.882744	+	0.740710i	0.0839976	+	0.996466i	$0.473231\pi$
$840$	−19.8274	−	3.11620i	−0.684110	−	0.107519i
$841$	−24.9148	−	9.06824i	−0.859131	−	0.312698i
$842$	1.85742	+	2.18586i	0.0640110	+	0.0753297i
$843$	8.65872	+	4.99911i	0.298222	+	0.172179i
$844$	1.94897	+	10.3028i	0.0670864	+	0.354636i
$845$	−8.13887	+	46.1578i	−0.279986	+	1.58788i
$846$	−2.83835	+	7.95169i	−0.0975844	+	0.273385i
$847$	34.3367	−	19.8243i	1.17982	−	0.681172i
$848$	3.25752	+	8.30193i	0.111864	+	0.285090i
$849$	7.17388	−	8.54949i	0.246207	−	0.293418i
$850$	18.7639	−	32.9716i	0.643598	−	1.13092i
$851$	−42.4221	+	15.4404i	−1.45421	+	0.529289i
$852$	−4.15729	+	1.57191i	−0.142426	+	0.0538527i
$853$	−2.88646	−	16.3699i	−0.0988304	−	0.560495i	−0.993506	−	0.113779i	$-0.963704\pi$
$853$	−2.88646	−	16.3699i	−0.0988304	−	0.560495i	0.894676	−	0.446716i	$-0.147407\pi$
$854$	30.4586	+	5.17574i	1.04227	+	0.177110i
$855$	−11.4010	−	10.8396i	−0.389907	−	0.370705i
$856$	8.94005	−	16.1736i	0.305565	−	0.552801i
$857$	−34.9234	+	6.15794i	−1.19296	+	0.210351i	−0.734654	−	0.678442i	$-0.762655\pi$
$857$	−34.9234	+	6.15794i	−1.19296	+	0.210351i	−0.458308	+	0.888794i	$0.651544\pi$
$858$	−0.459105	−	0.783904i	−0.0156736	−	0.0267620i
$859$	−3.57775	−	9.82980i	−0.122071	−	0.335388i	0.863573	−	0.504224i	$-0.168221\pi$
$859$	−3.57775	−	9.82980i	−0.122071	−	0.335388i	−0.985644	+	0.168836i	$0.945999\pi$
$860$	−15.3200	+	18.7254i	−0.522408	+	0.638532i
$861$	−11.0143	−	9.24212i	−0.375368	−	0.314971i
$862$	36.3531	+	30.1209i	1.23819	+	1.02592i
$863$	−6.08159	−	10.5336i	−0.207020	−	0.358569i	0.743755	−	0.668453i	$-0.233043\pi$
$863$	−6.08159	−	10.5336i	−0.207020	−	0.358569i	−0.950774	+	0.309884i	$0.899710\pi$
$864$	2.97924	+	4.80875i	0.101356	+	0.163597i
$865$	−60.0904	−	10.5956i	−2.04313	−	0.360260i
$866$	−9.89817	−	26.6780i	−0.336354	−	0.906557i
$867$	2.91341	−	5.04617i	0.0989444	−	0.171377i
$868$	−4.41716	+	2.62397i	−0.149928	+	0.0890635i
$869$	21.8991	−	60.1672i	0.742876	−	2.04103i
$870$	−7.91672	+	1.44671i	−0.268402	+	0.0490481i
$871$	0.398430	+	0.474831i	0.0135003	+	0.0160890i
$872$	9.85102	−	28.7202i	0.333597	−	0.972590i
$873$			5.40450i			0.182915i
$874$	38.8032	−	4.62848i	1.31254	−	0.156561i
$875$			21.4674i			0.725732i
$876$	0.934079	−	5.71161i	0.0315596	−	0.192977i
$877$	−5.18825	−	6.18312i	−0.175195	−	0.208789i	0.671300	−	0.741185i	$-0.265736\pi$
$877$	−5.18825	−	6.18312i	−0.175195	−	0.208789i	−0.846495	+	0.532396i	$0.821292\pi$
$878$	9.29044	+	50.8394i	0.313537	+	1.71575i
$879$	0.671518	−	1.84498i	0.0226497	−	0.0622296i
$880$	−78.9946	+	15.9627i	−2.66291	+	0.538102i
$881$	−12.8256	+	22.2146i	−0.432105	+	0.748427i	−0.997054	−	0.0766980i	$-0.975562\pi$
$881$	−12.8256	+	22.2146i	−0.432105	+	0.748427i	0.564950	+	0.825125i	$0.308896\pi$
$882$	4.15547	−	1.54178i	0.139922	−	0.0519143i
$883$	−13.5357	−	2.38671i	−0.455512	−	0.0803191i	−0.0588155	−	0.998269i	$-0.518732\pi$
$883$	−13.5357	−	2.38671i	−0.455512	−	0.0803191i	−0.396697	+	0.917950i	$0.629843\pi$
$884$	0.670922	+	0.376318i	0.0225656	+	0.0126570i
$885$	−21.1397	−	36.6150i	−0.710603	−	1.23080i
$886$	17.4079	−	21.0097i	0.584831	−	0.705835i
$887$	−16.7033	−	14.0157i	−0.560842	−	0.470603i	0.317750	−	0.948174i	$-0.397073\pi$
$887$	−16.7033	−	14.0157i	−0.560842	−	0.470603i	−0.878593	+	0.477572i	$0.841517\pi$
$888$	13.2325	+	15.1858i	0.444055	+	0.509602i
$889$	0.782476	+	2.14983i	0.0262434	+	0.0721031i
$890$	−50.7915	+	29.7468i	−1.70254	+	0.997116i
$891$	5.49777	−	0.969405i	0.184182	−	0.0324763i
$892$	13.6734	+	4.78513i	0.457820	+	0.160218i
$893$	10.3992	−	23.8552i	0.347996	−	0.798283i
$894$	2.90786	−	17.1124i	0.0972533	−	0.572324i
$895$	5.57785	+	31.6335i	0.186447	+	1.05739i
$896$	−19.7301	−	10.2743i	−0.659136	−	0.343239i
$897$	−0.685458	+	0.249486i	−0.0228868	+	0.00833011i
$898$	14.7890	+	8.41632i	0.493514	+	0.280856i
$899$	−1.32421	+	1.57813i	−0.0441647	+	0.0526335i
$900$	12.1662	−	10.4691i	0.405541	−	0.348969i
$901$	−6.45408	+	3.72627i	−0.215017	+	0.124140i
$902$	−54.3735	−	19.4086i	−1.81044	−	0.646234i
$903$	−1.14440	+	6.49023i	−0.0380834	+	0.215981i
$904$	−0.785864	−	42.1518i	−0.0261374	−	1.40195i
$905$	−28.6187	−	16.5230i	−0.951318	−	0.549244i
$906$	−5.81571	+	4.94186i	−0.193214	+	0.164182i
$907$	17.3624	+	6.31941i	0.576510	+	0.209832i	0.613786	−	0.789473i	$-0.289646\pi$
$907$	17.3624	+	6.31941i	0.576510	+	0.209832i	−0.0372759	+	0.999305i	$0.511868\pi$
$908$	−25.8037	+	0.320695i	−0.856325	+	0.0106427i
$909$	−13.7940	+	11.5745i	−0.457517	+	0.383902i
$910$	−1.15472	+	0.00717532i	−0.0382786	+	0.000237860i
$911$	−7.50876			−0.248776			−0.124388	−	0.992234i	$-0.539697\pi$
$911$	−7.50876			−0.248776			−0.124388	+	0.992234i	$0.539697\pi$
$912$	−8.15063	−	15.4132i	−0.269894	−	0.510383i
$913$	−98.4598			−3.25854
$914$	−23.5494	+	0.146334i	−0.778945	+	0.00484029i
$915$	−30.7183	+	25.7757i	−1.01552	+	0.852120i
$916$	12.9993	−	0.161559i	0.429509	−	0.00533806i
$917$	−26.1304	−	9.51070i	−0.862903	−	0.314071i
$918$	−3.60229	+	3.06103i	−0.118893	+	0.101029i
$919$	−16.6207	−	9.59598i	−0.548267	−	0.316542i	0.200156	−	0.979764i	$-0.435855\pi$
$919$	−16.6207	−	9.59598i	−0.548267	−	0.316542i	−0.748423	+	0.663222i	$0.769189\pi$
$920$	1.20625	+	64.7003i	0.0397689	+	2.13311i
$921$	2.13697	−	12.1194i	0.0704156	−	0.399346i
$922$	−26.7196	−	9.53754i	−0.879963	−	0.314102i
$923$	−0.221452	+	0.127855i	−0.00728917	+	0.00420840i
$924$	−16.6402	+	14.3189i	−0.547422	+	0.471058i
$925$	36.7357	−	43.7799i	1.20786	−	1.43947i
$926$	29.1907	+	16.6123i	0.959265	+	0.545913i
$927$	8.38377	−	3.05144i	0.275359	−	0.100222i
$928$	−8.82797	−	1.27525i	−0.289792	−	0.0418623i
$929$	4.66977	+	26.4836i	0.153210	+	0.868899i	0.960404	+	0.278612i	$0.0898743\pi$
$929$	4.66977	+	26.4836i	0.153210	+	0.868899i	−0.807194	+	0.590287i	$0.799015\pi$
$930$	1.11714	−	6.57422i	0.0366324	−	0.215577i
$931$	−13.1023	+	3.86767i	−0.429409	+	0.126758i
$932$	19.7061	+	6.89631i	0.645494	+	0.225896i
$933$	−9.94389	+	1.75338i	−0.325548	+	0.0574030i
$934$	−24.4530	+	14.3213i	−0.800126	+	0.468606i
$935$	−23.0339	−	63.2852i	−0.753290	−	2.06965i
$936$	0.213812	+	0.245373i	0.00698867	+	0.00802027i
$937$	11.2301	+	9.42315i	0.366871	+	0.307841i	0.807522	−	0.589837i	$-0.200808\pi$
$937$	11.2301	+	9.42315i	0.366871	+	0.307841i	−0.440652	+	0.897678i	$0.645253\pi$
$938$	9.55665	−	11.5340i	0.312036	−	0.376597i
$939$	−2.76045	−	4.78125i	−0.0900840	−	0.156030i
$940$	37.5847	+	21.0812i	1.22588	+	0.687592i
$941$	41.2808	+	7.27891i	1.34571	+	0.237286i	0.799655	−	0.600460i	$-0.205016\pi$
$941$	41.2808	+	7.27891i	1.34571	+	0.237286i	0.546060	+	0.837746i	$0.316127\pi$
$942$	12.5354	−	4.65092i	0.408425	−	0.151535i
$943$	−23.1789	+	40.1470i	−0.754808	+	1.30737i
$944$	−9.28140	−	45.9309i	−0.302084	−	1.49492i
$945$	2.42700	−	6.66814i	0.0789505	−	0.216915i
$946$	4.75703	+	26.0315i	0.154664	+	0.846359i
$947$	−33.8066	−	40.2891i	−1.09857	−	1.30922i	−0.947164	−	0.320749i	$-0.896066\pi$
$947$	−33.8066	−	40.2891i	−1.09857	−	1.30922i	−0.151402	−	0.988472i	$-0.548379\pi$
$948$	−3.70222	+	22.6380i	−0.120243	+	0.735248i
$949$		−	0.332975i		−	0.0108088i
$950$	−39.6118	+	29.6358i	−1.28518	+	0.961511i
$951$		−	26.2969i		−	0.852736i
$952$	6.03115	−	17.5836i	0.195471	−	0.569887i
$953$	6.79493	+	8.09789i	0.220109	+	0.262316i	0.864788	−	0.502138i	$-0.167453\pi$
$953$	6.79493	+	8.09789i	0.220109	+	0.262316i	−0.644678	+	0.764454i	$0.723009\pi$
$954$	−3.10168	+	0.566805i	−0.100421	+	0.0183510i
$955$	19.1672	−	52.6615i	0.620236	−	1.70409i
$956$	48.1935	−	28.6289i	1.55869	−	0.925926i
$957$	−4.40124	+	7.62318i	−0.142272	+	0.246422i
$958$	−7.57306	−	20.4113i	−0.244674	−	0.659459i
$959$	36.4394	+	6.42525i	1.17669	+	0.207482i
$960$	26.7443	−	10.8794i	0.863167	−	0.351130i
$961$	14.6465	+	25.3685i	0.472468	+	0.818338i
$962$	0.892344	+	0.739366i	0.0287703	+	0.0238381i
$963$	5.00507	+	4.19975i	0.161286	+	0.135335i
$964$	18.6822	−	22.8350i	0.601715	−	0.735467i
$965$	7.14032	+	19.6179i	0.229855	+	0.631522i
$966$	8.90832	+	15.2106i	0.286620	+	0.489393i
$967$	−39.2804	+	6.92619i	−1.26317	+	0.222731i	−0.764820	−	0.644244i	$-0.777172\pi$
$967$	−39.2804	+	6.92619i	−1.26317	+	0.222731i	−0.498351	+	0.866975i	$0.666061\pi$
$968$	−27.5922	+	49.9175i	−0.886847	+	1.60441i
$969$	11.7205	−	8.65567i	0.376517	−	0.278060i
$970$	27.1946	+	4.62109i	0.873165	+	0.148374i
$971$	−6.74557	−	38.2561i	−0.216476	−	1.22770i	−0.878327	−	0.478060i	$-0.841340\pi$
$971$	−6.74557	−	38.2561i	−0.216476	−	1.22770i	0.661851	−	0.749635i	$-0.269771\pi$
$972$	−1.87074	+	0.707343i	−0.0600040	+	0.0226880i
$973$	14.3299	−	5.21564i	0.459394	−	0.167206i
$974$	15.9305	−	27.9927i	0.510446	−	0.896944i
$975$	0.593578	−	0.707398i	0.0190097	−	0.0226549i
$976$	−41.3728	+	16.2339i	−1.32431	+	0.519634i
$977$	−23.9306	+	13.8163i	−0.765606	+	0.442023i	−0.831305	−	0.555817i	$-0.812406\pi$
$977$	−23.9306	+	13.8163i	−0.765606	+	0.442023i	0.0656987	+	0.997840i	$0.479072\pi$
$978$	0.889053	−	2.49070i	0.0284288	−	0.0796438i
$979$	−11.1796	+	63.4028i	−0.357302	+	2.02636i
$980$	−4.20486	−	22.2280i	−0.134319	−	0.710046i
$981$	9.29664	+	5.36742i	0.296819	+	0.171369i
$982$	19.2477	+	22.6512i	0.614219	+	0.722828i
$983$	55.3082	+	20.1305i	1.76406	+	0.642065i	0.999995	−	0.00307694i	$-0.000979421\pi$
$983$	55.3082	+	20.1305i	1.76406	+	0.642065i	0.764063	+	0.645142i	$0.223202\pi$
$984$	20.4327	+	3.21133i	0.651369	+	0.102374i
$985$	−12.0262	+	10.0912i	−0.383186	+	0.321531i
$986$	−0.0463159	−	7.45359i	−0.00147500	−	0.237371i
$987$	11.7385			0.373640
$988$	−0.605909	−	0.799467i	−0.0192765	−	0.0254344i
$989$	21.2484			0.675661
$990$	−0.177051	−	28.4928i	−0.00562706	−	0.905560i
$991$	32.7089	−	27.4460i	1.03903	−	0.871852i	0.0471344	−	0.998889i	$-0.484991\pi$
$991$	32.7089	−	27.4460i	1.03903	−	0.871852i	0.991898	+	0.127037i	$0.0405467\pi$
$992$	3.49480	−	6.51234i	0.110960	−	0.206767i
$993$	33.0105	+	12.0149i	1.04756	+	0.381280i
$994$	4.00130	+	4.70883i	0.126914	+	0.149355i
$995$	9.74292	+	5.62508i	0.308871	+	0.178327i
$996$	34.6592	−	6.55648i	1.09822	−	0.207750i
$997$	8.78153	−	49.8025i	0.278114	−	1.57726i	−0.450781	−	0.892635i	$-0.648854\pi$
$997$	8.78153	−	49.8025i	0.278114	−	1.57726i	0.728894	−	0.684626i	$-0.240035\pi$
$998$	−8.84323	+	24.7745i	−0.279927	+	0.784223i
$999$	−6.16727	+	3.56067i	−0.195124	+	0.112655i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.2.w.b.67.1	yes	60
3.2	odd	2		684.2.cf.b.523.10		60
4.3	odd	2		228.2.w.a.67.2	✓	60
12.11	even	2		684.2.cf.c.523.9		60
19.2	odd	18		228.2.w.a.211.2	yes	60
57.2	even	18		684.2.cf.c.667.9		60
76.59	even	18	inner	228.2.w.b.211.1	yes	60
228.59	odd	18		684.2.cf.b.667.10		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.w.a.67.2	✓	60	4.3	odd	2
228.2.w.a.211.2	yes	60	19.2	odd	18
228.2.w.b.67.1	yes	60	1.1	even	1	trivial
228.2.w.b.211.1	yes	60	76.59	even	18	inner
684.2.cf.b.523.10		60	3.2	odd	2
684.2.cf.b.667.10		60	228.59	odd	18
684.2.cf.c.523.9		60	12.11	even	2
684.2.cf.c.667.9		60	57.2	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	228.w (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41419 + 0.00878762i) q^{2} +(0.766044 - 0.642788i) q^{3} +(1.99985 - 0.0248547i) q^{4} +(3.39140 + 1.23437i) q^{5} +(-1.07768 + 0.915753i) q^{6} +(1.70277 + 0.983096i) q^{7} +(-2.82794 + 0.0527230i) q^{8} +(0.173648 - 0.984808i) q^{9} +(-4.80692 - 1.71582i) q^{10} +(-4.83466 + 2.79129i) q^{11} +(1.51599 - 1.30452i) q^{12} +(0.0739637 - 0.0881465i) q^{13} +(-2.41668 - 1.37532i) q^{14} +(3.39140 - 1.23437i) q^{15} +(3.99876 - 0.0994110i) q^{16} +(0.580442 + 3.29185i) q^{17} +(-0.236917 + 1.39423i) q^{18} +(1.02155 - 4.23750i) q^{19} +(6.81295 + 2.38425i) q^{20} +(1.93632 - 0.341426i) q^{21} +(6.81258 - 3.98989i) q^{22} +(-2.16818 - 5.95703i) q^{23} +(-2.13243 + 1.85815i) q^{24} +(6.14770 + 5.15853i) q^{25} +(-0.103824 + 0.125306i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(3.42972 + 1.92372i) q^{28} +(1.55282 + 0.273805i) q^{29} +(-4.78522 + 1.77543i) q^{30} +(-0.653262 + 1.13148i) q^{31} +(-5.65412 + 0.175725i) q^{32} +(-1.90935 + 5.24591i) q^{33} +(-0.849781 - 4.65019i) q^{34} +(4.56128 + 5.43592i) q^{35} +(0.322792 - 1.97378i) q^{36} -7.12135i q^{37} +(-1.40742 + 6.00160i) q^{38} -0.115067i q^{39} +(-9.65574 - 3.31191i) q^{40} +(-4.70052 - 5.60186i) q^{41} +(-2.73532 + 0.499855i) q^{42} +(-1.14640 + 3.14970i) q^{43} +(-9.59919 + 5.70231i) q^{44} +(1.80453 - 3.12553i) q^{45} +(3.11856 + 8.40530i) q^{46} +(5.87946 + 1.03671i) q^{47} +(2.99933 - 2.64651i) q^{48} +(-1.56704 - 2.71420i) q^{49} +(-8.73932 - 7.24110i) q^{50} +(2.56060 + 2.14860i) q^{51} +(0.145725 - 0.178118i) q^{52} +(0.762548 + 2.09508i) q^{53} +(0.714703 + 1.22033i) q^{54} +(-19.8417 + 3.49863i) q^{55} +(-4.86716 - 2.69036i) q^{56} +(-1.94126 - 3.90276i) q^{57} +(-2.19839 - 0.373565i) q^{58} +(-2.03426 - 11.5368i) q^{59} +(6.75159 - 2.55284i) q^{60} +(-10.4409 + 3.80016i) q^{61} +(0.913891 - 1.60587i) q^{62} +(1.26384 - 1.50619i) q^{63} +(7.99444 - 0.298194i) q^{64} +(0.359646 - 0.207642i) q^{65} +(2.65408 - 7.43547i) q^{66} +(-0.935414 + 5.30500i) q^{67} +(1.24261 + 6.56876i) q^{68} +(-5.49003 - 3.16967i) q^{69} +(-6.49826 - 7.64732i) q^{70} +(-2.08825 - 0.760061i) q^{71} +(-0.439144 + 2.79413i) q^{72} +(2.21674 - 1.86006i) q^{73} +(0.0625797 + 10.0709i) q^{74} +8.02525 q^{75} +(1.93762 - 8.49974i) q^{76} -10.9764 q^{77} +(0.00101117 + 0.162726i) q^{78} +(-8.78604 + 7.37237i) q^{79} +(13.6841 + 4.59881i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(6.69664 + 7.88077i) q^{82} +(15.2741 + 8.81848i) q^{83} +(3.86386 - 0.730925i) q^{84} +(-2.09484 + 11.8805i) q^{85} +(1.59354 - 4.46433i) q^{86} +(1.36553 - 0.788389i) q^{87} +(13.5249 - 8.14849i) q^{88} +(7.41292 - 8.83438i) q^{89} +(-2.52447 + 4.43594i) q^{90} +(0.212600 - 0.0773800i) q^{91} +(-4.48409 - 11.8592i) q^{92} +(0.226876 + 1.28668i) q^{93} +(-8.32376 - 1.41443i) q^{94} +(8.69512 - 13.1101i) q^{95} +(-4.21836 + 3.76901i) q^{96} +(-5.32239 + 0.938482i) q^{97} +(2.23994 + 3.82462i) q^{98} +(1.90935 + 5.24591i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 3 q^{2} - 3 q^{4} + 3 q^{6} - 3 q^{8} - 6 q^{10} - 6 q^{13} - 9 q^{14} + 21 q^{16} + 18 q^{19} + 30 q^{20} - 6 q^{21} - 12 q^{22} - 18 q^{24} - 30 q^{27} - 18 q^{28} - 12 q^{31} + 33 q^{32} - 15 q^{34}+ \cdots - 105 q^{98}+O(q^{100}) \) 60 * q + 3 * q^2 - 3 * q^4 + 3 * q^6 - 3 * q^8 - 6 * q^10 - 6 * q^13 - 9 * q^14 + 21 * q^16 + 18 * q^19 + 30 * q^20 - 6 * q^21 - 12 * q^22 - 18 * q^24 - 30 * q^27 - 18 * q^28 - 12 * q^31 + 33 * q^32 - 15 * q^34 - 3 * q^36 - 84 * q^38 - 87 * q^40 - 12 * q^41 + 9 * q^42 - 18 * q^43 - 51 * q^44 - 21 * q^46 + 18 * q^48 + 30 * q^49 - 27 * q^50 - 3 * q^52 + 12 * q^53 + 3 * q^54 + 42 * q^56 - 36 * q^58 + 15 * q^60 + 105 * q^62 - 12 * q^63 + 21 * q^64 - 36 * q^65 + 24 * q^66 + 42 * q^67 - 15 * q^68 - 72 * q^69 - 96 * q^70 + 24 * q^71 + 18 * q^72 + 18 * q^73 + 69 * q^74 + 60 * q^75 + 54 * q^76 - 72 * q^77 + 57 * q^78 + 12 * q^79 - 12 * q^80 + 75 * q^82 + 39 * q^84 - 60 * q^85 + 21 * q^86 + 36 * q^88 - 12 * q^89 + 15 * q^90 - 84 * q^91 + 99 * q^92 - 12 * q^93 - 24 * q^95 + 12 * q^97 - 105 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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