LMFDB - Embedded newform 300.2.w.a.223.29

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(67,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 13]))

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

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

chi := DirichletCharacter("300.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.w (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			223.29
Character	$\chi$	$=$	300.223
Dual form			300.2.w.a.187.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.40559 - 0.155946i) q^{2} +(-0.453990 - 0.891007i) q^{3} +(1.95136 - 0.438391i) q^{4} +(-1.39750 - 1.74556i) q^{5} +(-0.777073 - 1.18159i) q^{6} +(-2.75918 - 2.75918i) q^{7} +(2.67445 - 0.920504i) q^{8} +(-0.587785 + 0.809017i) q^{9} +(-2.23652 - 2.23561i) q^{10} +(-0.189562 - 0.260910i) q^{11} +(-1.27651 - 1.53965i) q^{12} +(0.0568939 + 0.359214i) q^{13} +(-4.30856 - 3.44799i) q^{14} +(-0.920857 + 2.03765i) q^{15} +(3.61563 - 1.71092i) q^{16} +(6.81039 + 3.47007i) q^{17} +(-0.700022 + 1.22881i) q^{18} +(1.52937 + 4.70692i) q^{19} +(-3.49227 - 2.79357i) q^{20} +(-1.20581 + 3.71109i) q^{21} +(-0.307135 - 0.337171i) q^{22} +(1.39600 - 8.81398i) q^{23} +(-2.03435 - 1.96505i) q^{24} +(-1.09399 + 4.87885i) q^{25} +(0.135987 + 0.496035i) q^{26} +(0.987688 + 0.156434i) q^{27} +(-6.59376 - 4.17456i) q^{28} +(6.53236 + 2.12249i) q^{29} +(-0.976583 + 3.00770i) q^{30} +(-5.16506 + 1.67823i) q^{31} +(4.81527 - 2.96869i) q^{32} +(-0.146413 + 0.287352i) q^{33} +(10.1138 + 3.81544i) q^{34} +(-0.960370 + 8.67228i) q^{35} +(-0.792316 + 1.83636i) q^{36} +(5.02172 - 0.795363i) q^{37} +(2.88369 + 6.37749i) q^{38} +(0.294233 - 0.213773i) q^{39} +(-5.34434 - 3.38201i) q^{40} +(-7.28627 - 5.29378i) q^{41} +(-1.11614 + 5.40431i) q^{42} +(-1.45559 + 1.45559i) q^{43} +(-0.484286 - 0.426028i) q^{44} +(2.23362 - 0.104585i) q^{45} +(0.587697 - 12.6065i) q^{46} +(-0.891709 + 0.454348i) q^{47} +(-3.16590 - 2.44481i) q^{48} +8.22616i q^{49} +(-0.776859 + 7.02826i) q^{50} -7.64348i q^{51} +(0.268497 + 0.676015i) q^{52} +(-2.04487 + 1.04191i) q^{53} +(1.41268 + 0.0658569i) q^{54} +(-0.190522 + 0.695515i) q^{55} +(-9.91913 - 4.83945i) q^{56} +(3.49957 - 3.49957i) q^{57} +(9.51281 + 1.96466i) q^{58} +(5.88836 + 4.27814i) q^{59} +(-0.903637 + 4.37989i) q^{60} +(-3.66737 + 2.66450i) q^{61} +(-6.99824 + 3.16437i) q^{62} +(3.85403 - 0.610418i) q^{63} +(6.30534 - 4.92368i) q^{64} +(0.547522 - 0.601314i) q^{65} +(-0.160986 + 0.426732i) q^{66} +(-0.984607 + 1.93240i) q^{67} +(14.8108 + 3.78574i) q^{68} +(-8.48708 + 2.75762i) q^{69} +(0.00251926 + 12.3394i) q^{70} +(8.42272 + 2.73671i) q^{71} +(-0.827297 + 2.70473i) q^{72} +(-12.8742 - 2.03907i) q^{73} +(6.93444 - 1.90107i) q^{74} +(4.84375 - 1.24020i) q^{75} +(5.04782 + 8.51443i) q^{76} +(-0.196862 + 1.24294i) q^{77} +(0.380233 - 0.346361i) q^{78} +(-3.45409 + 10.6306i) q^{79} +(-8.03936 - 3.92030i) q^{80} +(-0.309017 - 0.951057i) q^{81} +(-11.0670 - 6.30462i) q^{82} +(4.05203 + 2.06461i) q^{83} +(-0.726055 + 7.77030i) q^{84} +(-3.46030 - 16.7374i) q^{85} +(-1.81897 + 2.27296i) q^{86} +(-1.07447 - 6.78397i) q^{87} +(-0.747144 - 0.523298i) q^{88} +(-2.42940 - 3.34378i) q^{89} +(3.12324 - 0.495327i) q^{90} +(0.834156 - 1.14812i) q^{91} +(-1.13988 - 17.8113i) q^{92} +(3.84020 + 3.84020i) q^{93} +(-1.18252 + 0.777685i) q^{94} +(6.07893 - 9.24753i) q^{95} +(-4.83121 - 2.94268i) q^{96} +(1.13559 + 2.22872i) q^{97} +(1.28283 + 11.5626i) q^{98} +0.322503 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44}+ \cdots + 256 q^{98}+O(q^{100}) $ 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{20}\right)$

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 $

$2$	1.40559	−	0.155946i	0.993902	−	0.110270i
$2$	1.40559	−	0.155946i	0.993902	−	0.110270i
$3$	−0.453990	−	0.891007i	−0.262112	−	0.514423i
$3$	−0.453990	−	0.891007i	−0.262112	−	0.514423i
$4$	1.95136	−	0.438391i	0.975681	−	0.219196i
$5$	−1.39750	−	1.74556i	−0.624981	−	0.780640i
$5$	−1.39750	−	1.74556i	−0.624981	−	0.780640i
$6$	−0.777073	−	1.18159i	−0.317239	−	0.482383i
$7$	−2.75918	−	2.75918i	−1.04287	−	1.04287i	−0.999039	−	0.0438337i	$-0.986043\pi$
$7$	−2.75918	−	2.75918i	−1.04287	−	1.04287i	−0.0438337	−	0.999039i	$-0.513957\pi$
$8$	2.67445	−	0.920504i	0.945560	−	0.325447i
$9$	−0.587785	+	0.809017i	−0.195928	+	0.269672i
$10$	−2.23652	−	2.23561i	−0.707251	−	0.706962i
$11$	−0.189562	−	0.260910i	−0.0571552	−	0.0786674i	0.779483	−	0.626424i	$-0.215482\pi$
$11$	−0.189562	−	0.260910i	−0.0571552	−	0.0786674i	−0.836638	+	0.547756i	$0.815482\pi$
$12$	−1.27651	−	1.53965i	−0.368496	−	0.444459i
$13$	0.0568939	+	0.359214i	0.0157795	+	0.0996280i	0.994321	−	0.106421i	$-0.0339392\pi$
$13$	0.0568939	+	0.359214i	0.0157795	+	0.0996280i	−0.978542	+	0.206049i	$0.933939\pi$
$14$	−4.30856	−	3.44799i	−1.15151	−	0.921515i
$15$	−0.920857	+	2.03765i	−0.237764	+	0.526119i
$16$	3.61563	−	1.71092i	0.903907	−	0.427730i
$17$	6.81039	+	3.47007i	1.65176	+	0.841615i	0.996259	+	0.0864233i	$0.0275437\pi$
$17$	6.81039	+	3.47007i	1.65176	+	0.841615i	0.655504	+	0.755192i	$0.272456\pi$
$18$	−0.700022	+	1.22881i	−0.164997	+	0.289633i
$19$	1.52937	+	4.70692i	0.350861	+	1.07984i	0.958370	+	0.285528i	$0.0921689\pi$
$19$	1.52937	+	4.70692i	0.350861	+	1.07984i	−0.607509	+	0.794313i	$0.707831\pi$
$20$	−3.49227	−	2.79357i	−0.780895	−	0.624662i
$21$	−1.20581	+	3.71109i	−0.263129	+	0.809826i
$22$	−0.307135	−	0.337171i	−0.0654813	−	0.0718851i
$23$	1.39600	−	8.81398i	0.291086	−	1.83784i	−0.216552	−	0.976271i	$-0.569481\pi$
$23$	1.39600	−	8.81398i	0.291086	−	1.83784i	0.507637	−	0.861571i	$-0.330519\pi$
$24$	−2.03435	−	1.96505i	−0.415260	−	0.401114i
$25$	−1.09399	+	4.87885i	−0.218797	+	0.975770i
$26$	0.135987	+	0.496035i	0.0266693	+	0.0972804i
$27$	0.987688	+	0.156434i	0.190081	+	0.0301058i
$28$	−6.59376	−	4.17456i	−1.24610	−	0.788918i
$29$	6.53236	+	2.12249i	1.21303	+	0.394137i	0.844539	−	0.535495i	$-0.179875\pi$
$29$	6.53236	+	2.12249i	1.21303	+	0.394137i	0.368490	+	0.929632i	$0.379875\pi$
$30$	−0.976583	+	3.00770i	−0.178299	+	0.549129i
$31$	−5.16506	+	1.67823i	−0.927672	+	0.301419i	−0.733610	−	0.679570i	$-0.762166\pi$
$31$	−5.16506	+	1.67823i	−0.927672	+	0.301419i	−0.194062	+	0.980989i	$0.562166\pi$
$32$	4.81527	−	2.96869i	0.851228	−	0.524795i
$33$	−0.146413	+	0.287352i	−0.0254873	+	0.0500216i
$34$	10.1138	+	3.81544i	1.73449	+	0.654342i
$35$	−0.960370	+	8.67228i	−0.162332	+	1.46588i
$36$	−0.792316	+	1.83636i	−0.132053	+	0.306061i
$37$	5.02172	−	0.795363i	0.825566	−	0.130757i	0.270665	−	0.962673i	$-0.412756\pi$
$37$	5.02172	−	0.795363i	0.825566	−	0.130757i	0.554901	+	0.831917i	$0.312756\pi$
$38$	2.88369	+	6.37749i	0.467796	+	1.03457i
$39$	0.294233	−	0.213773i	0.0471149	−	0.0342310i
$40$	−5.34434	−	3.38201i	−0.845014	−	0.534743i
$41$	−7.28627	−	5.29378i	−1.13792	−	0.826750i	−0.151095	−	0.988519i	$-0.548280\pi$
$41$	−7.28627	−	5.29378i	−1.13792	−	0.826750i	−0.986829	+	0.161769i	$0.948280\pi$
$42$	−1.11614	+	5.40431i	−0.172224	+	0.833903i
$43$	−1.45559	+	1.45559i	−0.221976	+	0.221976i	−0.809330	−	0.587354i	$-0.800170\pi$
$43$	−1.45559	+	1.45559i	−0.221976	+	0.221976i	0.587354	+	0.809330i	$0.300170\pi$
$44$	−0.484286	−	0.426028i	−0.0730088	−	0.0642261i
$45$	2.23362	−	0.104585i	0.332969	−	0.0155906i
$46$	0.587697	−	12.6065i	0.0866511	−	1.85873i
$47$	−0.891709	+	0.454348i	−0.130069	+	0.0662735i	−0.517814	−	0.855493i	$-0.673254\pi$
$47$	−0.891709	+	0.454348i	−0.130069	+	0.0662735i	0.387745	+	0.921767i	$0.373254\pi$
$48$	−3.16590	−	2.44481i	−0.456958	−	0.352877i
$49$			8.22616i			1.17517i
$50$	−0.776859	+	7.02826i	−0.109864	+	0.993947i
$51$		−	7.64348i		−	1.07030i
$52$	0.268497	+	0.676015i	0.0372338	+	0.0937464i
$53$	−2.04487	+	1.04191i	−0.280885	+	0.143118i	−0.588758	−	0.808310i	$-0.700383\pi$
$53$	−2.04487	+	1.04191i	−0.280885	+	0.143118i	0.307873	+	0.951427i	$0.400383\pi$
$54$	1.41268	+	0.0658569i	0.192241	+	0.00896198i
$55$	−0.190522	+	0.695515i	−0.0256900	+	0.0937833i
$56$	−9.91913	−	4.83945i	−1.32550	−	0.646698i
$57$	3.49957	−	3.49957i	0.463530	−	0.463530i
$58$	9.51281	+	1.96466i	1.24909	+	0.257972i
$59$	5.88836	+	4.27814i	0.766599	+	0.556967i	0.900927	−	0.433970i	$-0.142888\pi$
$59$	5.88836	+	4.27814i	0.766599	+	0.556967i	−0.134328	+	0.990937i	$0.542888\pi$
$60$	−0.903637	+	4.37989i	−0.116659	+	0.565441i
$61$	−3.66737	+	2.66450i	−0.469559	+	0.341155i	−0.797269	−	0.603624i	$-0.793723\pi$
$61$	−3.66737	+	2.66450i	−0.469559	+	0.341155i	0.327710	+	0.944778i	$0.393723\pi$
$62$	−6.99824	+	3.16437i	−0.888777	+	0.401875i
$63$	3.85403	−	0.610418i	0.485562	−	0.0769055i
$64$	6.30534	−	4.92368i	0.788168	−	0.615460i
$65$	0.547522	−	0.601314i	0.0679117	−	0.0745838i
$66$	−0.160986	+	0.426732i	−0.0198159	+	0.0525270i
$67$	−0.984607	+	1.93240i	−0.120289	+	0.236080i	−0.943297	−	0.331949i	$-0.892294\pi$
$67$	−0.984607	+	1.93240i	−0.120289	+	0.236080i	0.823009	+	0.568029i	$0.192294\pi$
$68$	14.8108	+	3.78574i	1.79607	+	0.459089i
$69$	−8.48708	+	2.75762i	−1.02172	+	0.331979i
$70$	0.00251926	+	12.3394i	0.000301110	+	1.47484i
$71$	8.42272	+	2.73671i	0.999593	+	0.324787i	0.762703	−	0.646749i	$-0.223872\pi$
$71$	8.42272	+	2.73671i	0.999593	+	0.324787i	0.236890	+	0.971536i	$0.423872\pi$
$72$	−0.827297	+	2.70473i	−0.0974979	+	0.318756i
$73$	−12.8742	−	2.03907i	−1.50681	−	0.238656i	−0.652250	−	0.758004i	$-0.726175\pi$
$73$	−12.8742	−	2.03907i	−1.50681	−	0.238656i	−0.854562	+	0.519349i	$0.826175\pi$
$74$	6.93444	−	1.90107i	0.806113	−	0.220995i
$75$	4.84375	−	1.24020i	0.559308	−	0.143206i
$76$	5.04782	+	8.51443i	0.579025	+	0.976673i
$77$	−0.196862	+	1.24294i	−0.0224345	+	0.141646i
$78$	0.380233	−	0.346361i	0.0430530	−	0.0392176i
$79$	−3.45409	+	10.6306i	−0.388615	+	1.19603i	0.545208	+	0.838301i	$0.316451\pi$
$79$	−3.45409	+	10.6306i	−0.388615	+	1.19603i	−0.933823	+	0.357734i	$0.883549\pi$
$80$	−8.03936	−	3.92030i	−0.898828	−	0.438302i
$81$	−0.309017	−	0.951057i	−0.0343352	−	0.105673i
$82$	−11.0670	−	6.30462i	−1.22215	−	0.696229i
$83$	4.05203	+	2.06461i	0.444768	+	0.226621i	0.662007	−	0.749498i	$-0.269705\pi$
$83$	4.05203	+	2.06461i	0.444768	+	0.226621i	−0.217239	+	0.976119i	$0.569705\pi$
$84$	−0.726055	+	7.77030i	−0.0792191	+	0.847809i
$85$	−3.46030	−	16.7374i	−0.375322	−	1.81543i
$86$	−1.81897	+	2.27296i	−0.196145	+	0.245100i
$87$	−1.07447	−	6.78397i	−0.115196	−	0.727318i
$88$	−0.747144	−	0.523298i	−0.0796458	−	0.0557837i
$89$	−2.42940	−	3.34378i	−0.257516	−	0.354440i	0.660610	−	0.750729i	$-0.270298\pi$
$89$	−2.42940	−	3.34378i	−0.257516	−	0.354440i	−0.918126	+	0.396289i	$0.870298\pi$
$90$	3.12324	−	0.495327i	0.329219	−	0.0522120i
$91$	0.834156	−	1.14812i	0.0874433	−	0.120355i
$92$	−1.13988	−	17.8113i	−0.118840	−	1.85695i
$93$	3.84020	+	3.84020i	0.398210	+	0.398210i
$94$	−1.18252	+	0.777685i	−0.121968	+	0.0802121i
$95$	6.07893	−	9.24753i	0.623685	−	0.948776i
$96$	−4.83121	−	2.94268i	−0.493084	−	0.300336i
$97$	1.13559	+	2.22872i	0.115302	+	0.226292i	0.941444	−	0.337169i	$-0.109469\pi$
$97$	1.13559	+	2.22872i	0.115302	+	0.226292i	−0.826142	+	0.563461i	$0.809469\pi$
$98$	1.28283	+	11.5626i	0.129586	+	1.16800i
$99$	0.322503			0.0324128
$100$	0.00408327	+	10.0000i	0.000408327	+	1.00000i
$101$	1.62632			0.161825			0.0809123	−	0.996721i	$-0.474217\pi$
$101$	1.62632			0.161825			0.0809123	+	0.996721i	$0.474217\pi$
$102$	−1.19197	−	10.7436i	−0.118022	−	1.06377i
$103$	0.899683	+	1.76573i	0.0886484	+	0.173982i	0.931074	−	0.364830i	$-0.118873\pi$
$103$	0.899683	+	1.76573i	0.0886484	+	0.173982i	−0.842426	+	0.538813i	$0.818873\pi$
$104$	0.482818	+	0.908328i	0.0473442	+	0.0890689i
$105$	8.16306	−	3.08144i	0.796633	−	0.300718i
$106$	−2.71177	+	1.78339i	−0.263390	+	0.173218i
$107$	2.76146	+	2.76146i	0.266960	+	0.266960i	0.827874	−	0.560914i	$-0.189550\pi$
$107$	2.76146	+	2.76146i	0.266960	+	0.266960i	−0.560914	+	0.827874i	$0.689550\pi$
$108$	1.99592	−	0.127734i	0.192057	−	0.0122912i
$109$	−5.43848	+	7.48543i	−0.520912	+	0.716974i	−0.985712	−	0.168442i	$-0.946126\pi$
$109$	−5.43848	+	7.48543i	−0.520912	+	0.716974i	0.464799	+	0.885416i	$0.346126\pi$
$110$	−0.159333	+	1.00732i	−0.0151918	+	0.0960442i
$111$	−2.98849	−	4.11330i	−0.283655	−	0.390417i
$112$	−14.6969	−	5.25543i	−1.38873	−	0.496592i
$113$	−1.93191	−	12.1976i	−0.181739	−	1.14745i	−0.894838	−	0.446391i	$-0.852709\pi$
$113$	−1.93191	−	12.1976i	−0.181739	−	1.14745i	0.713099	−	0.701063i	$-0.247291\pi$
$114$	4.37322	−	5.46471i	0.409589	−	0.511817i
$115$	−17.3363	+	9.88074i	−1.61662	+	0.921384i
$116$	13.6775	+	1.27802i	1.26992	+	0.118661i
$117$	−0.324052	−	0.165113i	−0.0299586	−	0.0152647i
$118$	8.94377	+	5.09505i	0.823341	+	0.469037i
$119$	−9.21656	−	28.3656i	−0.844880	−	2.60027i
$120$	−0.587117	+	6.29724i	−0.0535962	+	0.574857i
$121$	3.36705	−	10.3627i	0.306095	−	0.942064i
$122$	−4.73930	+	4.31711i	−0.429076	+	0.390853i
$123$	−1.40890	+	8.89544i	−0.127036	+	0.802075i
$124$	−9.34318	+	5.53915i	−0.839042	+	0.497430i
$125$	10.0452	−	4.90857i	0.898469	−	0.439036i
$126$	5.32199	−	1.45902i	0.474121	−	0.129980i
$127$	−0.984224	−	0.155886i	−0.0873358	−	0.0138326i	0.112614	−	0.993639i	$-0.464078\pi$
$127$	−0.984224	−	0.155886i	−0.0873358	−	0.0138326i	−0.199949	+	0.979806i	$0.564078\pi$
$128$	8.09490	−	7.90397i	0.715494	−	0.698618i
$129$	1.95777	+	0.636118i	0.172372	+	0.0560070i
$130$	0.675818	−	0.930583i	0.0592732	−	0.0816176i
$131$	−16.5622	+	5.38139i	−1.44705	+	0.470174i	−0.924087	−	0.382183i	$-0.875172\pi$
$131$	−16.5622	+	5.38139i	−1.44705	+	0.470174i	−0.522960	+	0.852357i	$0.675172\pi$
$132$	−0.159733	+	0.624914i	−0.0139029	+	0.0543918i
$133$	8.76743	−	17.2070i	0.760232	−	1.49204i
$134$	−1.08260	+	2.86970i	−0.0935227	+	0.247905i
$135$	−1.10723	−	1.94269i	−0.0952950	−	0.167200i
$136$	21.4082	+	3.01152i	1.83574	+	0.258236i
$137$	8.21802	−	1.30161i	0.702113	−	0.111204i	0.204837	−	0.978796i	$-0.434334\pi$
$137$	8.21802	−	1.30161i	0.702113	−	0.111204i	0.497276	+	0.867592i	$0.334334\pi$
$138$	−11.4993	+	5.19961i	−0.978887	+	0.442620i
$139$	−6.67504	+	4.84970i	−0.566170	+	0.411346i	−0.833712	−	0.552200i	$-0.813789\pi$
$139$	−6.67504	+	4.84970i	−0.566170	+	0.411346i	0.267542	+	0.963546i	$0.413789\pi$
$140$	1.92782	+	17.3438i	0.162931	+	1.46582i
$141$	0.809655	+	0.588249i	0.0681852	+	0.0495395i
$142$	12.2657	+	2.53320i	1.02931	+	0.212581i
$143$	0.0829377	−	0.0829377i	0.00693560	−	0.00693560i
$144$	−0.741049	+	3.93076i	−0.0617541	+	0.327563i
$145$	−5.42403	−	14.3688i	−0.450441	−	1.19327i
$146$	−18.4138	−	0.858423i	−1.52394	−	0.0710436i
$147$	7.32956	−	3.73460i	0.604532	−	0.308025i
$148$	9.45052	−	3.75352i	0.776828	−	0.308537i
$149$			15.6909i			1.28545i	0.766097	+	0.642725i	$0.222196\pi$
$149$			15.6909i			1.28545i	−0.766097	+	0.642725i	$0.777804\pi$
$150$	6.61492	−	2.49858i	0.540106	−	0.204008i
$151$		−	8.75664i		−	0.712605i	−0.934371	−	0.356303i	$-0.884037\pi$
$151$		−	8.75664i		−	0.712605i	0.934371	−	0.356303i	$-0.115963\pi$
$152$	8.42296	+	11.1806i	0.683192	+	0.906867i
$153$	−6.81039	+	3.47007i	−0.550587	+	0.280538i
$154$	−0.0828762	+	1.77776i	−0.00667835	+	0.143256i
$155$	10.1476	+	6.67061i	0.815077	+	0.535797i
$156$	0.480438	−	0.546137i	0.0384659	−	0.0437259i
$157$	−3.89141	+	3.89141i	−0.310568	+	0.310568i	−0.845130	−	0.534562i	$-0.820477\pi$
$157$	−3.89141	+	3.89141i	−0.310568	+	0.310568i	0.534562	+	0.845130i	$0.320477\pi$
$158$	−3.19723	+	15.4809i	−0.254358	+	1.23159i
$159$	1.85670	+	1.34897i	0.147246	+	0.106981i
$160$	−11.9114	−	4.25662i	−0.941678	−	0.336516i
$161$	−28.1712	+	20.4676i	−2.22020	+	1.61307i
$162$	−0.582664	−	1.28860i	−0.0457784	−	0.101242i
$163$	15.5572	−	2.46402i	1.21854	−	0.192997i	0.486144	−	0.873879i	$-0.338403\pi$
$163$	15.5572	−	2.46402i	1.21854	−	0.192997i	0.732393	+	0.680882i	$0.238403\pi$
$164$	−16.5389	−	7.13585i	−1.29147	−	0.557216i
$165$	0.706204	−	0.146001i	0.0549779	−	0.0113662i
$166$	6.01746	+	2.27010i	0.467045	+	0.176194i
$167$	−1.25530	+	2.46366i	−0.0971380	+	0.190644i	−0.934462	−	0.356063i	$-0.884119\pi$
$167$	−1.25530	+	2.46366i	−0.0971380	+	0.190644i	0.837324	+	0.546707i	$0.184119\pi$
$168$	0.191208	+	11.0351i	0.0147521	+	0.851374i
$169$	12.2379	−	3.97635i	0.941380	−	0.305873i
$170$	−7.47388	−	22.9863i	−0.573221	−	1.76297i
$171$	−4.70692	−	1.52937i	−0.359947	−	0.116954i
$172$	−2.20227	+	3.47851i	−0.167922	+	0.265234i
$173$	11.8456	+	1.87616i	0.900605	+	0.142642i	0.589533	−	0.807744i	$-0.299312\pi$
$173$	11.8456	+	1.87616i	0.900605	+	0.142642i	0.311072	+	0.950386i	$0.399312\pi$
$174$	−2.56820	−	9.36791i	−0.194695	−	0.710180i
$175$	16.4801	−	10.4431i	1.24578	−	0.789427i
$176$	−1.13178	−	0.619028i	−0.0853114	−	0.0466610i
$177$	1.13859	−	7.18880i	0.0855820	−	0.540343i
$178$	−3.93618	−	4.32112i	−0.295029	−	0.323882i
$179$	−0.191592	+	0.589661i	−0.0143203	+	0.0440733i	−0.957961	−	0.286897i	$-0.907376\pi$
$179$	−0.191592	+	0.589661i	−0.0143203	+	0.0440733i	0.943641	+	0.330971i	$0.107376\pi$
$180$	4.31275	−	1.18328i	0.321454	−	0.0881967i
$181$	−0.378454	−	1.16476i	−0.0281303	−	0.0865761i	0.936006	−	0.351985i	$-0.114493\pi$
$181$	−0.378454	−	1.16476i	−0.0281303	−	0.0865761i	−0.964136	+	0.265409i	$0.914493\pi$
$182$	0.993437	−	1.74386i	0.0736384	−	0.129264i
$183$	4.03904	+	2.05800i	0.298575	+	0.152131i
$184$	−4.37979	−	24.8576i	−0.322882	−	1.83252i
$185$	−8.40621	−	7.65422i	−0.618037	−	0.562749i
$186$	5.99661	+	4.79888i	0.439693	+	0.351871i
$187$	−0.385618	−	2.43470i	−0.0281992	−	0.178043i
$188$	−1.54086	+	1.27752i	−0.112379	+	0.0931724i
$189$	−2.29358	−	3.15684i	−0.166833	−	0.229626i
$190$	7.10236	−	13.9462i	0.515259	−	1.01176i
$191$	−0.928379	+	1.27780i	−0.0671751	+	0.0924586i	−0.841283	−	0.540596i	$-0.818199\pi$
$191$	−0.928379	+	1.27780i	−0.0671751	+	0.0924586i	0.774108	+	0.633054i	$0.218199\pi$
$192$	−7.24960	−	3.38280i	−0.523195	−	0.244132i
$193$	−11.7970	−	11.7970i	−0.849166	−	0.849166i	0.140863	−	0.990029i	$-0.455012\pi$
$193$	−11.7970	−	11.7970i	−0.849166	−	0.849166i	−0.990029	+	0.140863i	$0.955012\pi$
$194$	1.94373	+	2.95558i	0.139552	+	0.212198i
$195$	−0.784344	−	0.214855i	−0.0561680	−	0.0153861i
$196$	3.60628	+	16.0522i	0.257591	+	1.14659i
$197$	−7.02214	−	13.7817i	−0.500307	−	0.981908i	−0.993697	−	0.112100i	$-0.964242\pi$
$197$	−7.02214	−	13.7817i	−0.500307	−	0.981908i	0.493390	−	0.869808i	$-0.335758\pi$
$198$	0.453306	−	0.0502929i	0.0322151	−	0.00357416i
$199$	3.88395			0.275326			0.137663	−	0.990479i	$-0.456041\pi$
$199$	3.88395			0.275326			0.137663	+	0.990479i	$0.456041\pi$
$200$	1.56520	+	14.0553i	0.110676	+	0.993857i
$201$	2.16878			0.152974
$202$	2.28593	−	0.253617i	0.160838	−	0.0178444i
$203$	−12.1676	−	23.8803i	−0.854000	−	1.67607i
$204$	−3.35083	−	14.9152i	−0.234605	−	1.04427i
$205$	0.941925	+	20.1167i	0.0657869	+	1.40501i
$206$	1.53994	+	2.34159i	0.107293	+	0.163146i
$207$	6.31011	+	6.31011i	0.438583	+	0.438583i
$208$	0.820293	+	1.20144i	0.0568771	+	0.0833051i
$209$	0.938172	−	1.29128i	0.0648947	−	0.0893199i
$210$	10.9934	−	5.60423i	0.758615	−	0.386729i
$211$	7.41164	+	10.2012i	0.510238	+	0.702283i	0.983959	−	0.178392i	$-0.0570896\pi$
$211$	7.41164	+	10.2012i	0.510238	+	0.702283i	−0.473721	+	0.880675i	$0.657090\pi$
$212$	−3.53352	+	2.92960i	−0.242683	+	0.201206i
$213$	−1.38541	−	8.74714i	−0.0949268	−	0.599344i
$214$	4.31212	+	3.45084i	0.294770	+	0.235895i
$215$	4.57502	+	0.506639i	0.312014	+	0.0345525i
$216$	2.78552	−	0.490796i	0.189531	−	0.0333944i
$217$	18.8819	+	9.62080i	1.28179	+	0.653102i
$218$	−6.47695	+	11.3695i	−0.438675	+	0.770043i
$219$	4.02794	+	12.3967i	0.272183	+	0.837693i
$220$	−0.0668695	+	1.44073i	−0.00450834	+	0.0971337i
$221$	−0.859027	+	2.64381i	−0.0577844	+	0.177842i
$222$	−4.84204	−	5.31557i	−0.324976	−	0.356758i
$223$	0.458345	−	2.89388i	0.0306930	−	0.193788i	−0.967578	−	0.252574i	$-0.918723\pi$
$223$	0.458345	−	2.89388i	0.0306930	−	0.193788i	0.998271	+	0.0587857i	$0.0187229\pi$
$224$	−21.4774	−	5.09506i	−1.43502	−	0.340428i
$225$	−3.30405	−	3.75277i	−0.220270	−	0.250185i
$226$	−4.61764	−	16.8436i	−0.307161	−	1.12042i
$227$	−17.0941	−	2.70744i	−1.13457	−	0.179699i	−0.439229	−	0.898375i	$-0.644748\pi$
$227$	−17.0941	−	2.70744i	−1.13457	−	0.179699i	−0.695345	+	0.718676i	$0.744748\pi$
$228$	5.29475	−	8.36312i	0.350654	−	0.553861i
$229$	−3.66300	−	1.19018i	−0.242058	−	0.0786494i	0.185476	−	0.982649i	$-0.440617\pi$
$229$	−3.66300	−	1.19018i	−0.242058	−	0.0786494i	−0.427534	+	0.903999i	$0.640617\pi$
$230$	−22.8268	+	16.5918i	−1.50516	+	1.09403i
$231$	1.19684	−	0.388876i	0.0787461	−	0.0255862i
$232$	19.4242	−	0.336570i	1.27526	−	0.0220969i
$233$	−9.42750	+	18.5025i	−0.617616	+	1.21214i	0.344316	+	0.938854i	$0.388111\pi$
$233$	−9.42750	+	18.5025i	−0.617616	+	1.21214i	−0.961933	+	0.273287i	$0.911889\pi$
$234$	−0.481232	−	0.181546i	−0.0314591	−	0.0118680i
$235$	2.03926	+	0.921583i	0.133027	+	0.0601174i
$236$	13.3658	+	5.76680i	0.870041	+	0.375387i
$237$	11.0400	−	1.74857i	0.717128	−	0.113582i
$238$	−17.3782	−	38.4332i	−1.12646	−	2.49125i
$239$	14.8348	−	10.7781i	0.959580	−	0.697176i	0.00652706	−	0.999979i	$-0.497922\pi$
$239$	14.8348	−	10.7781i	0.959580	−	0.697176i	0.953053	+	0.302803i	$0.0979224\pi$
$240$	0.156783	+	8.94290i	0.0101203	+	0.577262i
$241$	3.52121	+	2.55831i	0.226821	+	0.164795i	0.695392	−	0.718631i	$-0.255231\pi$
$241$	3.52121	+	2.55831i	0.226821	+	0.164795i	−0.468571	+	0.883426i	$0.655231\pi$
$242$	3.11667	−	15.0908i	0.200347	−	0.970072i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	−5.98828	+	6.80715i	−0.383360	+	0.435783i
$245$	14.3593	−	11.4961i	0.917382	−	0.734457i
$246$	−0.593128	+	12.7230i	−0.0378165	+	0.811192i
$247$	−1.60378	+	0.817166i	−0.102046	+	0.0519950i
$248$	−12.2689	+	9.24280i	−0.779074	+	0.586918i
$249$		−	4.54770i		−	0.288199i
$250$	13.3539	−	8.46594i	0.844577	−	0.535433i
$251$			9.82650i			0.620243i	0.950697	+	0.310121i	$0.100370\pi$
$251$			9.82650i			0.620243i	−0.950697	+	0.310121i	$0.899630\pi$
$252$	7.25301	−	2.88072i	0.456896	−	0.181468i
$253$	−2.56429	+	1.30657i	−0.161215	+	0.0821433i
$254$	−1.40772	−	0.0656259i	−0.0883285	−	0.00411773i
$255$	−13.3422	+	10.6818i	−0.835520	+	0.668918i
$256$	10.1455	−	12.3721i	0.634094	−	0.773256i
$257$	−2.73807	+	2.73807i	−0.170796	+	0.170796i	−0.787329	−	0.616533i	$-0.788537\pi$
$257$	−2.73807	+	2.73807i	−0.170796	+	0.170796i	0.616533	+	0.787329i	$0.288537\pi$
$258$	2.85102	+	0.588815i	0.177497	+	0.0366580i
$259$	−16.0504	−	11.6613i	−0.997323	−	0.724597i
$260$	0.804802	−	1.41341i	0.0499117	−	0.0876559i
$261$	−5.55676	+	4.03722i	−0.343955	+	0.249898i
$262$	−22.4405	+	10.1468i	−1.38638	+	0.626873i
$263$	−23.9430	+	3.79219i	−1.47639	+	0.233837i	−0.842125	−	0.539282i	$-0.818696\pi$
$263$	−23.9430	+	3.79219i	−1.47639	+	0.233837i	−0.634262	+	0.773118i	$0.718696\pi$
$264$	−0.127066	+	0.903282i	−0.00782035	+	0.0555932i
$265$	4.67643	+	2.11338i	0.287271	+	0.129824i
$266$	9.64003	−	25.5533i	0.591068	−	1.56677i
$267$	−1.87641	+	3.68265i	−0.114834	+	0.225375i
$268$	−1.07418	+	4.20245i	−0.0656158	+	0.256706i
$269$	−9.75063	+	3.16817i	−0.594506	+	0.193167i	−0.590789	−	0.806826i	$-0.701183\pi$
$269$	−9.75063	+	3.16817i	−0.594506	+	0.193167i	−0.00371752	+	0.999993i	$0.501183\pi$
$270$	−1.85926	−	2.55796i	−0.113151	−	0.155672i
$271$	−10.8353	−	3.52061i	−0.658199	−	0.213862i	−0.0391730	−	0.999232i	$-0.512472\pi$
$271$	−10.8353	−	3.52061i	−0.658199	−	0.213862i	−0.619026	+	0.785371i	$0.712472\pi$
$272$	30.5608	+	0.894437i	1.85302	+	0.0542332i
$273$	−1.40168	−	0.222004i	−0.0848334	−	0.0134363i
$274$	11.3482	−	3.11109i	0.685569	−	0.187948i
$275$	1.48032	−	0.639415i	0.0892667	−	0.0385582i
$276$	−15.3525	+	9.10178i	−0.924109	+	0.547863i
$277$	−3.73932	+	23.6091i	−0.224674	+	1.41853i	0.575027	+	0.818135i	$0.304992\pi$
$277$	−3.73932	+	23.6091i	−0.224674	+	1.41853i	−0.799700	+	0.600399i	$0.795008\pi$
$278$	−8.62608	+	7.85763i	−0.517358	+	0.471270i
$279$	1.67823	−	5.16506i	0.100473	−	0.309224i
$280$	5.41441	+	24.0776i	0.323573	+	1.43891i
$281$	4.94655	+	15.2239i	0.295087	+	0.908184i	0.983192	+	0.182573i	$0.0584426\pi$
$281$	4.94655	+	15.2239i	0.295087	+	0.908184i	−0.688106	+	0.725611i	$0.741557\pi$
$282$	1.22978	+	0.700574i	0.0732322	+	0.0417186i
$283$	26.1393	+	13.3186i	1.55382	+	0.791710i	0.999184	−	0.0403832i	$-0.0128579\pi$
$283$	26.1393	+	13.3186i	1.55382	+	0.791710i	0.554635	+	0.832094i	$0.312858\pi$
$284$	17.6355	+	1.64786i	1.04648	+	0.0977826i
$285$	−10.9994	−	1.21807i	−0.651547	−	0.0721525i
$286$	0.103643	−	0.129510i	0.00612851	−	0.00765809i
$287$	5.49762	+	34.7106i	0.324515	+	2.04890i
$288$	−0.428626	+	5.64059i	−0.0252570	+	0.332375i
$289$	24.3477	+	33.5117i	1.43222	+	1.97128i
$290$	−9.86472	−	19.3508i	−0.579276	−	1.13632i
$291$	1.47026	−	2.02364i	0.0861881	−	0.118628i
$292$	−26.0161	+	1.66497i	−1.52248	+	0.0974348i
$293$	7.72111	+	7.72111i	0.451072	+	0.451072i	0.895710	−	0.444638i	$-0.146668\pi$
$293$	7.72111	+	7.72111i	0.451072	+	0.451072i	−0.444638	+	0.895710i	$0.646668\pi$
$294$	9.71996	−	6.39233i	0.566880	−	0.372808i
$295$	−0.761212	−	16.2572i	−0.0443194	−	0.946531i
$296$	12.6982	−	6.74967i	0.738068	−	0.392317i
$297$	−0.146413	−	0.287352i	−0.00849576	−	0.0166739i
$298$	2.44693	+	22.0550i	0.141747	+	1.27761i
$299$	3.24553			0.187694
$300$	8.90821	−	4.54354i	0.514316	−	0.262322i
$301$	8.03249			0.462985
$302$	−1.36556	−	12.3082i	−0.0785791	−	0.708259i
$303$	−0.738332	−	1.44906i	−0.0424161	−	0.0832463i
$304$	13.5828	+	14.4018i	0.779026	+	0.826001i
$305$	9.77622	+	2.67799i	0.559785	+	0.153341i
$306$	−9.03147	+	5.93954i	−0.516295	+	0.339541i
$307$	2.29404	+	2.29404i	0.130928	+	0.130928i	0.769534	−	0.638606i	$-0.220489\pi$
$307$	2.29404	+	2.29404i	0.130928	+	0.130928i	−0.638606	+	0.769534i	$0.720489\pi$
$308$	0.160744	+	2.51172i	0.00915922	+	0.143119i
$309$	1.16483	−	1.60325i	0.0662647	−	0.0912055i
$310$	15.3036	+	7.79366i	0.869189	+	0.442650i
$311$	12.6963	+	17.4750i	0.719941	+	0.990914i	0.999526	+	0.0307932i	$0.00980334\pi$
$311$	12.6963	+	17.4750i	0.719941	+	0.990914i	−0.279584	+	0.960121i	$0.590197\pi$
$312$	0.590131	−	0.842566i	0.0334096	−	0.0477009i
$313$	0.769705	+	4.85973i	0.0435063	+	0.274688i	0.999846	−	0.0175706i	$-0.00559320\pi$
$313$	0.769705	+	4.85973i	0.0435063	+	0.274688i	−0.956339	+	0.292259i	$0.905593\pi$
$314$	−4.86287	+	6.07656i	−0.274428	+	0.342920i
$315$	−6.45153	−	5.87440i	−0.363503	−	0.330985i
$316$	−2.07982	+	22.2584i	−0.116999	+	1.25213i
$317$	−23.3476	−	11.8962i	−1.31133	−	0.668158i	−0.348261	−	0.937398i	$-0.613228\pi$
$317$	−23.3476	−	11.8962i	−1.31133	−	0.668158i	−0.963073	+	0.269239i	$0.913228\pi$
$318$	2.82013	+	1.60656i	0.158145	+	0.0900913i
$319$	−0.684510	−	2.10670i	−0.0383252	−	0.117953i
$320$	−17.4063	−	4.12553i	−0.973043	−	0.230624i
$321$	1.20680	−	3.71416i	0.0673571	−	0.207304i
$322$	−36.4053	+	33.1622i	−2.02879	+	1.84805i
$323$	−5.91771	+	37.3630i	−0.329270	+	2.07893i
$324$	−1.01994	−	1.72039i	−0.0566633	−	0.0955770i
$325$	−1.81479	−	0.115398i	−0.100667	−	0.00640113i
$326$	21.4828	−	5.88949i	1.18982	−	0.326189i
$327$	9.13859	+	1.44741i	0.505365	+	0.0800420i
$328$	−24.3597	−	7.45091i	−1.34504	−	0.411407i
$329$	3.71402	+	1.20676i	0.204760	+	0.0665307i
$330$	0.969864	−	0.315347i	0.0533893	−	0.0173593i
$331$	−2.14095	+	0.695636i	−0.117677	+	0.0382356i	−0.367264	−	0.930117i	$-0.619705\pi$
$331$	−2.14095	+	0.695636i	−0.117677	+	0.0382356i	0.249587	+	0.968353i	$0.419705\pi$
$332$	8.81208	+	2.25243i	0.483626	+	0.123618i
$333$	−2.30823	+	4.53016i	−0.126490	+	0.248251i
$334$	−1.38024	+	3.65866i	−0.0755233	+	0.200193i
$335$	4.74911	−	0.981835i	0.259472	−	0.0536434i
$336$	1.98963	+	15.4810i	0.108543	+	0.844555i
$337$	5.30073	−	0.839553i	0.288749	−	0.0457334i	−0.0103796	−	0.999946i	$-0.503304\pi$
$337$	5.30073	−	0.839553i	0.288749	−	0.0457334i	0.299129	+	0.954213i	$0.403304\pi$
$338$	16.5814	−	7.49756i	0.901910	−	0.407814i
$339$	−9.99108	+	7.25895i	−0.542641	+	0.394252i
$340$	−14.0898	−	31.1437i	−0.764128	−	1.68901i
$341$	1.41697	+	1.02949i	0.0767331	+	0.0557499i
$342$	−6.85449	−	1.41564i	−0.370648	−	0.0765492i
$343$	3.38321	−	3.38321i	0.182676	−	0.182676i
$344$	−2.55303	+	5.23279i	−0.137650	+	0.282133i
$345$	16.6743	+	10.9610i	0.897714	+	0.590119i
$346$	16.9426	+	0.789839i	0.910842	+	0.0424620i
$347$	−2.28048	+	1.16196i	−0.122422	+	0.0623773i	−0.514129	−	0.857713i	$-0.671885\pi$
$347$	−2.28048	+	1.16196i	−0.122422	+	0.0623773i	0.391707	+	0.920090i	$0.371885\pi$
$348$	−5.07072	−	12.7669i	−0.271819	−	0.684380i
$349$		−	14.1549i		−	0.757693i	−0.925459	−	0.378847i	$-0.876321\pi$
$349$		−	14.1549i		−	0.757693i	0.925459	−	0.378847i	$-0.123679\pi$
$350$	21.5357	−	17.2488i	1.15113	−	0.921985i
$351$			0.363692i			0.0194124i
$352$	−1.68736	−	0.693602i	−0.0899364	−	0.0369691i
$353$	8.61001	−	4.38702i	0.458265	−	0.233498i	−0.209590	−	0.977789i	$-0.567213\pi$
$353$	8.61001	−	4.38702i	0.458265	−	0.233498i	0.667854	+	0.744292i	$0.267213\pi$
$354$	0.479333	−	10.2821i	0.0254763	−	0.546485i
$355$	−6.99366	−	18.5269i	−0.371185	−	0.983308i
$356$	−6.20652	−	5.45990i	−0.328945	−	0.289374i
$357$	−21.0897	+	21.0897i	−1.11619	+	1.11619i
$358$	−0.177345	+	0.858699i	−0.00937299	+	0.0453837i
$359$	−12.7349	−	9.25247i	−0.672124	−	0.488327i	0.198612	−	0.980078i	$-0.436357\pi$
$359$	−12.7349	−	9.25247i	−0.672124	−	0.488327i	−0.870735	+	0.491752i	$0.836357\pi$
$360$	5.87743	−	2.33576i	0.309768	−	0.123106i
$361$	−4.44476	+	3.22931i	−0.233935	+	0.169964i
$362$	−0.713590	−	1.57816i	−0.0375055	−	0.0829462i
$363$	−10.7618	+	1.70451i	−0.564850	+	0.0894635i
$364$	1.12442	−	2.60608i	0.0589354	−	0.136596i
$365$	14.4324	+	25.3224i	0.755425	+	1.32543i
$366$	5.99817	+	2.26282i	0.313529	+	0.118280i
$367$	−2.56797	+	5.03993i	−0.134047	+	0.263082i	−0.948267	−	0.317475i	$-0.897165\pi$
$367$	−2.56797	+	5.03993i	−0.134047	+	0.263082i	0.814220	+	0.580557i	$0.197165\pi$
$368$	−10.0326	−	34.2565i	−0.522986	−	1.78574i
$369$	8.56552	−	2.78311i	0.445903	−	0.144883i
$370$	−13.0093	−	9.44777i	−0.676323	−	0.491166i
$371$	8.51700	+	2.76734i	0.442181	+	0.143673i
$372$	9.17713	+	5.81011i	0.475812	+	0.301240i
$373$	−36.5755	−	5.79298i	−1.89381	−	0.299949i	−0.902413	−	0.430872i	$-0.858206\pi$
$373$	−36.5755	−	5.79298i	−1.89381	−	0.299949i	−0.991393	+	0.130922i	$0.958206\pi$
$374$	−0.921700	−	3.36205i	−0.0476600	−	0.173847i
$375$	−8.93399	−	6.72189i	−0.461349	−	0.347117i
$376$	−1.96660	+	2.03595i	−0.101420	+	0.104996i
$377$	−0.390778	+	2.46727i	−0.0201261	+	0.127071i
$378$	−3.71613	−	4.07955i	−0.191137	−	0.209829i
$379$	−7.06358	+	21.7395i	−0.362832	+	1.11668i	0.588496	+	0.808500i	$0.299720\pi$
$379$	−7.06358	+	21.7395i	−0.362832	+	1.11668i	−0.951328	+	0.308181i	$0.900280\pi$
$380$	7.80815	−	20.7102i	0.400550	−	1.06241i
$381$	0.307933	+	0.947721i	0.0157759	+	0.0485532i
$382$	−1.10565	+	1.94084i	−0.0565700	+	0.0993022i
$383$	−28.9397	−	14.7455i	−1.47875	−	0.753461i	−0.486035	−	0.873939i	$-0.661557\pi$
$383$	−28.9397	−	14.7455i	−1.47875	−	0.753461i	−0.992716	+	0.120478i	$0.961557\pi$
$384$	−10.7175	−	3.62428i	−0.546925	−	0.184951i
$385$	2.44474	−	1.39337i	0.124595	−	0.0710126i
$386$	−18.4214	−	14.7420i	−0.937625	−	0.750349i
$387$	−0.322024	−	2.03318i	−0.0163694	−	0.103352i
$388$	3.19300	+	3.85121i	0.162100	+	0.195516i
$389$	−13.0849	−	18.0098i	−0.663429	−	0.913132i	0.336160	−	0.941805i	$-0.390872\pi$
$389$	−13.0849	−	18.0098i	−0.663429	−	0.913132i	−0.999589	+	0.0286732i	$0.990872\pi$
$390$	−1.13597	−	0.179682i	−0.0575221	−	0.00909857i
$391$	40.0924	−	55.1825i	2.02756	−	2.79070i
$392$	7.57222	+	22.0004i	0.382455	+	1.11119i
$393$	12.3139	+	12.3139i	0.621156	+	0.621156i
$394$	−12.0195	−	18.2764i	−0.605531	−	0.920751i
$395$	23.3835	−	8.82692i	1.17655	−	0.444131i
$396$	0.629320	−	0.141382i	0.0316245	−	0.00710473i
$397$	−10.2521	−	20.1209i	−0.514540	−	1.00984i	−0.991401	−	0.130862i	$-0.958225\pi$
$397$	−10.2521	−	20.1209i	−0.514540	−	1.00984i	0.476861	−	0.878979i	$-0.341775\pi$
$398$	5.45924	−	0.605685i	0.273647	−	0.0303603i
$399$	−19.3119			−0.966805
$400$	4.39188	+	19.5118i	0.219594	+	0.975591i
$401$	6.32448			0.315829			0.157915	−	0.987453i	$-0.449523\pi$
$401$	6.32448			0.315829			0.157915	+	0.987453i	$0.449523\pi$
$402$	3.04842	−	0.338212i	0.152041	−	0.0168685i
$403$	−0.896704	−	1.75988i	−0.0446680	−	0.0876659i
$404$	3.17353	−	0.712963i	0.157889	−	0.0354712i
$405$	−1.22828	+	1.86851i	−0.0610336	+	0.0928470i
$406$	−20.8267	−	31.6684i	−1.03361	−	1.57168i
$407$	−1.15945	−	1.15945i	−0.0574717	−	0.0574717i
$408$	−7.03586	−	20.4421i	−0.348327	−	1.01203i
$409$	16.0583	−	22.1024i	0.794033	−	1.09289i	−0.199561	−	0.979885i	$-0.563952\pi$
$409$	16.0583	−	22.1024i	0.794033	−	1.09289i	0.993594	−	0.113008i	$-0.0360485\pi$
$410$	4.46107	+	28.1289i	0.220317	+	1.38919i
$411$	−4.89064	−	6.73140i	−0.241238	−	0.332035i
$412$	2.52969	+	3.05116i	0.124629	+	0.150320i
$413$	−4.44288	−	28.0512i	−0.218620	−	1.38031i
$414$	9.85346	+	7.88539i	0.484271	+	0.387546i
$415$	−2.05880	−	9.95837i	−0.101063	−	0.488837i
$416$	1.34036	+	1.56081i	0.0657163	+	0.0765252i
$417$	7.35152	+	3.74579i	0.360006	+	0.183432i
$418$	1.11731	−	1.96132i	0.0546496	−	0.0959311i
$419$	1.49679	+	4.60666i	0.0731232	+	0.225050i	0.980938	−	0.194322i	$-0.0622505\pi$
$419$	1.49679	+	4.60666i	0.0731232	+	0.225050i	−0.907815	+	0.419371i	$0.862251\pi$
$420$	14.5782	−	9.59161i	0.711344	−	0.468023i
$421$	5.13224	−	15.7954i	0.250130	−	0.769821i	−0.744620	−	0.667489i	$-0.767369\pi$
$421$	5.13224	−	15.7954i	0.250130	−	0.769821i	0.994750	−	0.102333i	$-0.0326307\pi$
$422$	12.0086	+	13.1829i	0.584568	+	0.641736i
$423$	0.156558	−	0.988467i	0.00761210	−	0.0480609i
$424$	−4.50981	+	4.66886i	−0.219016	+	0.226740i
$425$	−24.3804	+	29.4307i	−1.18262	+	1.42760i
$426$	−3.31140	−	12.0788i	−0.160438	−	0.585221i
$427$	17.4708	+	2.76710i	0.845471	+	0.133909i
$428$	6.59921	+	4.17801i	0.318985	+	0.201952i
$429$	−0.111551	−	0.0362451i	−0.00538573	−	0.00174993i
$430$	6.50961	−	0.00132903i	0.313921	−	6.40913e-5i
$431$	6.07264	−	1.97312i	0.292509	−	0.0950418i	−0.159087	−	0.987265i	$-0.550855\pi$
$431$	6.07264	−	1.97312i	0.292509	−	0.0950418i	0.451596	+	0.892223i	$0.350855\pi$
$432$	3.83876	−	1.12425i	0.184692	−	0.0540903i
$433$	−0.330445	+	0.648535i	−0.0158802	+	0.0311666i	−0.898810	−	0.438338i	$-0.855567\pi$
$433$	−0.330445	+	0.648535i	−0.0158802	+	0.0311666i	0.882930	+	0.469504i	$0.155567\pi$
$434$	28.0405	+	10.5783i	1.34599	+	0.507777i
$435$	−10.3403	+	11.3562i	−0.495778	+	0.544486i
$436$	−7.33090	+	16.9910i	−0.351087	+	0.813720i
$437$	43.6217	−	6.90899i	2.08671	−	0.330502i
$438$	7.59484	+	16.7966i	0.362896	+	0.802571i
$439$	3.95205	−	2.87133i	0.188621	−	0.137041i	−0.489467	−	0.872022i	$-0.662809\pi$
$439$	3.95205	−	2.87133i	0.188621	−	0.137041i	0.678088	+	0.734980i	$0.262809\pi$
$440$	0.130684	+	2.03550i	0.00623011	+	0.0970385i
$441$	−6.65511	−	4.83522i	−0.316910	−	0.230248i
$442$	−0.795148	+	3.85008i	−0.0378213	+	0.183129i
$443$	10.1012	−	10.1012i	0.479921	−	0.479921i	−0.425185	−	0.905106i	$-0.639791\pi$
$443$	10.1012	−	10.1012i	0.479921	−	0.479921i	0.905106	+	0.425185i	$0.139791\pi$
$444$	−7.63485	−	6.71641i	−0.362334	−	0.318747i
$445$	−2.44170	+	8.91360i	−0.115747	+	0.422545i
$446$	0.192957	−	4.13908i	0.00913679	−	0.195991i
$447$	13.9807	−	7.12352i	0.661265	−	0.336931i
$448$	−30.9829	−	3.81226i	−1.46381	−	0.180112i
$449$		−	1.32766i		−	0.0626560i	−0.999509	−	0.0313280i	$-0.990026\pi$
$449$		−	1.32766i		−	0.0626560i	0.999509	−	0.0313280i	$-0.00997364\pi$
$450$	−5.22936	−	4.75960i	−0.246514	−	0.224370i
$451$			2.90456i			0.136771i
$452$	−9.11718	−	22.9550i	−0.428836	−	1.07971i
$453$	−7.80222	+	3.97543i	−0.366580	+	0.186782i
$454$	−24.4495	−	1.13980i	−1.14747	−	0.0534932i
$455$	−3.16984	+	0.148422i	−0.148605	+	0.00695812i
$456$	6.13805	−	12.5808i	0.287441	−	0.589150i
$457$	−25.8996	+	25.8996i	−1.21153	+	1.21153i	−0.241012	+	0.970522i	$0.577479\pi$
$457$	−25.8996	+	25.8996i	−1.21153	+	1.21153i	−0.970522	+	0.241012i	$0.922521\pi$
$458$	−5.33428	−	1.10168i	−0.249255	−	0.0514780i
$459$	6.18371	+	4.49273i	0.288631	+	0.209702i
$460$	−29.4977	+	26.8810i	−1.37534	+	1.25333i
$461$	17.2942	−	12.5650i	0.805473	−	0.585210i	−0.107042	−	0.994255i	$-0.534138\pi$
$461$	17.2942	−	12.5650i	0.805473	−	0.585210i	0.912515	+	0.409044i	$0.134138\pi$
$462$	1.62162	−	0.733241i	0.0754445	−	0.0341135i
$463$	−38.1896	+	6.04864i	−1.77482	+	0.281104i	−0.956091	−	0.293071i	$-0.905323\pi$
$463$	−38.1896	+	6.04864i	−1.77482	+	0.281104i	−0.818732	+	0.574175i	$0.805323\pi$
$464$	27.2500	−	3.50220i	1.26505	−	0.162586i
$465$	1.33663	−	12.0700i	0.0619849	−	0.559733i
$466$	−10.3658	+	27.4771i	−0.480187	+	1.27285i
$467$	−11.0351	+	21.6575i	−0.510642	+	1.00219i	0.481425	+	0.876487i	$0.340119\pi$
$467$	−11.0351	+	21.6575i	−0.510642	+	1.00219i	−0.992068	+	0.125705i	$0.959881\pi$
$468$	−0.704726	−	0.180133i	−0.0325760	−	0.00832665i
$469$	8.04855	−	2.61513i	0.371647	−	0.120756i
$470$	3.01008	+	0.977354i	0.138844	+	0.0450820i
$471$	5.23393	+	1.70061i	0.241167	+	0.0783598i
$472$	19.6862	+	6.02141i	0.906129	+	0.277158i
$473$	0.655705	+	0.103853i	0.0301494	+	0.00477519i
$474$	15.2451	−	4.17942i	0.700230	−	0.191967i
$475$	−24.6375	+	2.31227i	−1.13044	+	0.106094i
$476$	−30.4201	−	51.3112i	−1.39430	−	2.35184i
$477$	0.359019	−	2.26676i	0.0164384	−	0.103788i
$478$	19.1708	−	17.4630i	0.876851	−	0.798737i
$479$	4.52864	−	13.9377i	0.206919	−	0.636831i	−0.792710	−	0.609599i	$-0.791331\pi$
$479$	4.52864	−	13.9377i	0.206919	−	0.636831i	0.999629	−	0.0272324i	$-0.00866942\pi$
$480$	1.61498	+	12.5456i	0.0737134	+	0.572625i
$481$	0.571411	+	1.75862i	0.0260541	+	0.0801862i
$482$	5.34833	+	3.04682i	0.243610	+	0.138779i
$483$	31.0262	+	15.8086i	1.41174	+	0.719317i
$484$	2.02741	−	21.6975i	0.0921549	−	0.986249i
$485$	2.30339	−	5.09689i	0.104591	−	0.231438i
$486$	−0.883631	+	1.10417i	−0.0400823	+	0.0500863i
$487$	−1.06090	−	6.69827i	−0.0480741	−	0.303528i	0.951922	−	0.306341i	$-0.0991046\pi$
$487$	−1.06090	−	6.69827i	−0.0480741	−	0.303528i	−0.999996	+	0.00281290i	$0.999105\pi$
$488$	−7.35551	+	10.5019i	−0.332969	+	0.475399i
$489$	−9.25830	−	12.7430i	−0.418675	−	0.576257i
$490$	18.3905	−	18.3980i	0.830798	−	0.831138i
$491$	14.5516	−	20.0286i	0.656706	−	0.903879i	−0.342661	−	0.939459i	$-0.611328\pi$
$491$	14.5516	−	20.0286i	0.656706	−	0.903879i	0.999367	+	0.0355807i	$0.0113281\pi$
$492$	1.15041	+	17.9759i	0.0518645	+	0.810415i
$493$	37.1227	+	37.1227i	1.67192	+	1.67192i
$494$	−2.12682	+	1.39870i	−0.0956901	+	0.0629306i
$495$	−0.450698	−	0.562949i	−0.0202574	−	0.0253027i
$496$	−15.8036	+	14.9049i	−0.709603	+	0.669248i
$497$	−15.6887	−	30.7909i	−0.703736	−	1.38116i
$498$	−0.709194	−	6.39220i	−0.0317797	−	0.286441i
$499$	28.7378			1.28648			0.643240	−	0.765665i	$-0.277590\pi$
$499$	28.7378			1.28648			0.643240	+	0.765665i	$0.277590\pi$
$500$	17.4499	−	13.9821i	0.780385	−	0.625300i
$501$	2.76504			0.123533
$502$	1.53240	+	13.8120i	0.0683943	+	0.616460i
$503$	−3.95231	−	7.75685i	−0.176225	−	0.345861i	0.785951	−	0.618288i	$-0.212174\pi$
$503$	−3.95231	−	7.75685i	−0.176225	−	0.345861i	−0.962176	+	0.272427i	$0.912174\pi$
$504$	9.74551	−	5.18018i	0.434100	−	0.230744i
$505$	−2.27278	−	2.83884i	−0.101137	−	0.126327i
$506$	−3.40058	+	2.23639i	−0.151174	+	0.0994196i
$507$	−9.09886	−	9.09886i	−0.404094	−	0.404094i
$508$	−1.98892	+	0.127286i	−0.0882439	+	0.00564739i
$509$	19.9966	−	27.5229i	0.886332	−	1.21993i	−0.0882946	−	0.996094i	$-0.528142\pi$
$509$	19.9966	−	27.5229i	0.886332	−	1.21993i	0.974627	−	0.223837i	$-0.0718583\pi$
$510$	−17.0879	+	17.0948i	−0.756663	+	0.756972i
$511$	29.8961	+	41.1484i	1.32253	+	1.82030i
$512$	12.3310	−	18.9722i	0.544960	−	0.838462i
$513$	0.774217	+	4.88821i	0.0341825	+	0.215820i
$514$	−3.42161	+	4.27559i	−0.150921	+	0.188588i
$515$	1.82488	−	4.03806i	0.0804139	−	0.177938i
$516$	4.09918	+	0.383027i	0.180457	+	0.0168618i
$517$	0.287579	+	0.146529i	0.0126477	+	0.00644432i
$518$	−24.3788	−	13.8880i	−1.07114	−	0.610204i
$519$	−3.70612	−	11.4063i	−0.162681	−	0.500680i
$520$	0.910806	−	2.11218i	0.0399415	−	0.0926251i
$521$	6.36698	−	19.5956i	0.278943	−	0.858497i	−0.709207	−	0.705001i	$-0.750947\pi$
$521$	6.36698	−	19.5956i	0.278943	−	0.858497i	0.988149	−	0.153496i	$-0.0490533\pi$
$522$	−7.18093	+	6.54123i	−0.314301	+	0.286302i
$523$	3.69045	−	23.3006i	0.161372	−	1.01886i	−0.765486	−	0.643453i	$-0.777501\pi$
$523$	3.69045	−	23.3006i	0.161372	−	1.01886i	0.926858	−	0.375412i	$-0.122499\pi$
$524$	−29.9597	+	17.7618i	−1.30880	+	0.775926i
$525$	−16.7867	−	9.94283i	−0.732633	−	0.433941i
$526$	−33.0626	+	9.06407i	−1.44160	+	0.395212i
$527$	−40.9996	−	6.49371i	−1.78597	−	0.282870i
$528$	−0.0377391	+	1.28946i	−0.00164239	+	0.0561165i
$529$	−53.8632	−	17.5012i	−2.34188	−	0.760922i
$530$	6.90272	+	2.24127i	0.299835	+	0.0973546i
$531$	−6.92218	+	2.24915i	−0.300397	+	0.0976049i
$532$	9.56501	−	37.4207i	0.414696	−	1.62239i
$533$	1.48706	−	2.91851i	0.0644116	−	0.126415i
$534$	−2.06316	+	5.46891i	−0.0892817	+	0.236663i
$535$	0.961163	−	8.67944i	0.0415547	−	0.375245i
$536$	−0.854497	+	6.07444i	−0.0369087	+	0.262376i
$537$	0.612373	−	0.0969904i	0.0264258	−	0.00418544i
$538$	−13.2113	+	5.97372i	−0.569580	+	0.257545i
$539$	2.14629	−	1.55937i	0.0924473	−	0.0671669i
$540$	−3.01226	−	3.30549i	−0.129627	−	0.142246i
$541$	−3.14541	−	2.28527i	−0.135232	−	0.0982515i	0.518113	−	0.855312i	$-0.326635\pi$
$541$	−3.14541	−	2.28527i	−0.135232	−	0.0982515i	−0.653345	+	0.757061i	$0.726635\pi$
$542$	−15.7790	−	3.25881i	−0.677767	−	0.139978i
$543$	−0.865996	+	0.865996i	−0.0371634	+	0.0371634i
$544$	43.0955	−	3.50862i	1.84770	−	0.150431i
$545$	20.6666	−	0.967672i	0.885259	−	0.0414505i
$546$	−2.00480	−	0.0934608i	−0.0857977	−	0.00399975i
$547$	39.6114	−	20.1830i	1.69366	−	0.862963i	0.705652	−	0.708558i	$-0.250654\pi$
$547$	39.6114	−	20.1830i	1.69366	−	0.862963i	0.988008	−	0.154405i	$-0.0493460\pi$
$548$	15.4657	−	6.14261i	0.660663	−	0.262400i
$549$		−	4.53312i		−	0.193469i
$550$	1.98101	−	1.12960i	0.0844705	−	0.0481665i
$551$			33.9933i			1.44817i
$552$	−20.1599	+	15.1875i	−0.858061	+	0.646423i
$553$	38.8622	−	19.8013i	1.65259	−	0.842036i
$554$	−1.57420	+	33.7678i	−0.0668815	+	1.43466i
$555$	−3.00362	+	10.9649i	−0.127496	+	0.465436i
$556$	−10.8994	+	12.3898i	−0.462236	+	0.525445i
$557$	−20.4214	+	20.4214i	−0.865283	+	0.865283i	−0.991946	−	0.126663i	$-0.959573\pi$
$557$	−20.4214	+	20.4214i	−0.865283	+	0.865283i	0.126663	+	0.991946i	$0.459573\pi$
$558$	1.55343	−	7.52166i	0.0657620	−	0.318417i
$559$	−0.605684	−	0.440055i	−0.0256177	−	0.0186123i
$560$	11.3652	+	32.9989i	0.480269	+	1.39446i
$561$	−1.99426	+	1.44892i	−0.0841978	+	0.0611733i
$562$	9.32693	+	20.6272i	0.393433	+	0.870106i
$563$	−5.17707	+	0.819967i	−0.218187	+	0.0345575i	−0.264571	−	0.964366i	$-0.585230\pi$
$563$	−5.17707	+	0.819967i	−0.218187	+	0.0345575i	0.0463836	+	0.998924i	$0.485230\pi$
$564$	1.83781	+	0.792941i	0.0773859	+	0.0333888i
$565$	−18.5919	+	20.4184i	−0.782165	+	0.859010i
$566$	38.8181	+	14.6442i	1.63165	+	0.615542i
$567$	−1.77150	+	3.47677i	−0.0743962	+	0.146011i
$568$	25.0453	−	0.433968i	1.05088	−	0.0182089i
$569$	−18.5693	+	6.03353i	−0.778465	+	0.252939i	−0.671185	−	0.741290i	$-0.734214\pi$
$569$	−18.5693	+	6.03353i	−0.778465	+	0.252939i	−0.107280	+	0.994229i	$0.534214\pi$
$570$	−15.6506	+	0.00319528i	−0.655530	+	0.000133835i
$571$	−34.6379	−	11.2545i	−1.44955	−	0.470988i	−0.524691	−	0.851293i	$-0.675819\pi$
$571$	−34.6379	−	11.2545i	−1.44955	−	0.470988i	−0.924861	+	0.380304i	$0.875819\pi$
$572$	0.125482	−	0.198201i	0.00524668	−	0.00828718i
$573$	1.56001	+	0.247081i	0.0651702	+	0.0103219i
$574$	13.1404	+	47.9316i	0.548469	+	2.00062i
$575$	41.4749	+	16.4532i	1.72962	+	0.686147i
$576$	0.277154	+	7.99520i	0.0115481	+	0.333133i
$577$	−0.186710	+	1.17884i	−0.00777283	+	0.0490757i	−0.991270	−	0.131848i	$-0.957909\pi$
$577$	−0.186710	+	1.17884i	−0.00777283	+	0.0490757i	0.983497	+	0.180924i	$0.0579088\pi$
$578$	39.4489	+	43.3068i	1.64086	+	1.80133i
$579$	−5.15547	+	15.8669i	−0.214254	+	0.659406i
$580$	−16.8834	−	25.6610i	−0.701046	−	1.06551i
$581$	−5.48365	−	16.8769i	−0.227500	−	0.700173i
$582$	1.75100	−	3.07368i	0.0725814	−	0.127408i
$583$	0.659477	+	0.336020i	0.0273127	+	0.0139165i
$584$	−36.3084	+	6.39737i	−1.50245	+	0.264725i
$585$	0.164648	+	0.796398i	0.00680735	+	0.0329270i
$586$	12.0568	+	9.64863i	0.498061	+	0.398581i
$587$	−6.21808	−	39.2594i	−0.256648	−	1.62041i	−0.693210	−	0.720736i	$-0.743804\pi$
$587$	−6.21808	−	39.2594i	−0.256648	−	1.62041i	0.436562	−	0.899674i	$-0.356196\pi$
$588$	12.6654	−	10.5008i	0.522313	−	0.433045i
$589$	−15.7986	−	21.7449i	−0.650969	−	0.895982i
$590$	−3.60519	−	22.7323i	−0.148423	−	0.935872i
$591$	−9.09163	+	12.5136i	−0.373980	+	0.514739i
$592$	16.7959	−	11.4675i	0.690306	−	0.471311i
$593$	−32.4961	−	32.4961i	−1.33446	−	1.33446i	−0.901336	−	0.433121i	$-0.857412\pi$
$593$	−32.4961	−	32.4961i	−1.33446	−	1.33446i	−0.433121	−	0.901336i	$-0.642588\pi$
$594$	−0.250608	−	0.381067i	−0.0102826	−	0.0156353i
$595$	−36.6339	+	55.7291i	−1.50184	+	2.28467i
$596$	6.87876	+	30.6186i	0.281765	+	1.25419i
$597$	−1.76328	−	3.46063i	−0.0721661	−	0.141634i
$598$	4.56188	−	0.506126i	0.186549	−	0.0206970i
$599$	−1.39380			−0.0569493			−0.0284746	−	0.999595i	$-0.509065\pi$
$599$	−1.39380			−0.0569493			−0.0284746	+	0.999595i	$0.509065\pi$
$600$	11.8127	−	7.77555i	0.482253	−	0.317436i
$601$	46.9085			1.91344			0.956718	−	0.291017i	$-0.0939936\pi$
$601$	46.9085			1.91344			0.956718	+	0.291017i	$0.0939936\pi$
$602$	11.2904	−	1.25263i	0.460162	−	0.0510535i
$603$	−0.984607	−	1.93240i	−0.0400963	−	0.0786934i
$604$	−3.83883	−	17.0874i	−0.156200	−	0.695275i
$605$	−22.7942	+	8.60449i	−0.926716	+	0.349822i
$606$	−1.26377	−	1.92164i	−0.0513370	−	0.0780614i
$607$	−16.0846	−	16.0846i	−0.652852	−	0.652852i	0.300827	−	0.953679i	$-0.402737\pi$
$607$	−16.0846	−	16.0846i	−0.652852	−	0.652852i	−0.953679	+	0.300827i	$0.902737\pi$
$608$	21.3377	+	18.1249i	0.865359	+	0.735060i
$609$	−15.7535	+	21.6829i	−0.638365	+	0.878634i
$610$	14.1590	+	2.23960i	0.573280	+	0.0906786i
$611$	−0.213941	−	0.294465i	−0.00865513	−	0.0119128i
$612$	−11.7683	+	9.75697i	−0.475705	+	0.394402i
$613$	5.92897	+	37.4340i	0.239469	+	1.51195i	0.755370	+	0.655298i	$0.227457\pi$
$613$	5.92897	+	37.4340i	0.239469	+	1.51195i	−0.515901	+	0.856648i	$0.672543\pi$
$614$	3.58222	+	2.86673i	0.144567	+	0.115692i
$615$	17.4965	−	9.97205i	0.705527	−	0.402112i
$616$	0.617631	+	3.50538i	0.0248851	+	0.141236i
$617$	−22.9501	−	11.6937i	−0.923936	−	0.470769i	−0.0737649	−	0.997276i	$-0.523501\pi$
$617$	−22.9501	−	11.6937i	−0.923936	−	0.470769i	−0.850171	+	0.526507i	$0.823501\pi$
$618$	1.38725	−	2.43516i	0.0558033	−	0.0979564i
$619$	−0.977819	−	3.00942i	−0.0393019	−	0.120959i	0.929481	−	0.368871i	$-0.120256\pi$
$619$	−0.977819	−	3.00942i	−0.0393019	−	0.120959i	−0.968783	+	0.247912i	$0.920256\pi$
$620$	22.7260	+	8.56815i	0.912699	+	0.344105i
$621$	2.75762	−	8.48708i	0.110660	−	0.340575i
$622$	20.5709	+	22.5827i	0.824819	+	0.905483i
$623$	−2.52294	+	15.9292i	−0.101080	+	0.638191i
$624$	0.698088	−	1.27633i	0.0279459	−	0.0510941i
$625$	−22.6064	−	10.6748i	−0.904256	−	0.426992i
$626$	1.83974	+	6.71075i	0.0735309	+	0.268215i
$627$	−1.57646	−	0.249687i	−0.0629578	−	0.00997154i
$628$	−5.88758	+	9.29950i	−0.234940	+	0.371090i
$629$	36.9599	+	12.0090i	1.47369	+	0.478830i
$630$	−9.98429	−	7.25090i	−0.397784	−	0.288883i
$631$	−30.5823	+	9.93678i	−1.21746	+	0.395577i	−0.846157	−	0.532934i	$-0.821089\pi$
$631$	−30.5823	+	9.93678i	−1.21746	+	0.395577i	−0.371304	+	0.928511i	$0.621089\pi$
$632$	0.547725	+	31.6105i	0.0217873	+	1.25740i
$633$	5.72456	−	11.2351i	0.227531	−	0.446555i
$634$	−34.6724	−	13.0802i	−1.37702	−	0.519482i
$635$	1.10335	+	1.93588i	0.0437849	+	0.0768229i
$636$	4.21448	+	1.81837i	0.167115	+	0.0721032i
$637$	−2.95495	+	0.468019i	−0.117079	+	0.0185436i
$638$	−1.29067	−	2.85442i	−0.0510982	−	0.113007i
$639$	−7.16479	+	5.20553i	−0.283435	+	0.205927i
$640$	−25.1095	−	3.08436i	−0.992540	−	0.121920i
$641$	−3.32274	−	2.41412i	−0.131241	−	0.0953518i	0.520228	−	0.854027i	$-0.325847\pi$
$641$	−3.32274	−	2.41412i	−0.131241	−	0.0953518i	−0.651469	+	0.758675i	$0.725847\pi$
$642$	1.11706	−	5.40877i	0.0440869	−	0.213467i
$643$	3.90717	−	3.90717i	0.154084	−	0.154084i	−0.625855	−	0.779939i	$-0.715250\pi$
$643$	3.90717	−	3.90717i	0.154084	−	0.154084i	0.779939	+	0.625855i	$0.215250\pi$
$644$	−45.9994	+	52.2896i	−1.81263	+	2.06050i
$645$	−1.62560	−	4.30639i	−0.0640079	−	0.169564i
$646$	−2.49128	+	53.4398i	−0.0980180	+	2.10256i
$647$	−3.97759	+	2.02668i	−0.156375	+	0.0796771i	−0.530427	−	0.847731i	$-0.677968\pi$
$647$	−3.97759	+	2.02668i	−0.156375	+	0.0796771i	0.374052	+	0.927408i	$0.377968\pi$
$648$	−1.70190	−	2.25910i	−0.0668570	−	0.0887458i
$649$		−	2.34731i		−	0.0921399i
$650$	−2.56885	+	0.120807i	−0.100759	+	0.00473844i
$651$		−	21.1916i		−	0.830565i
$652$	29.2776	−	11.6284i	1.14660	−	0.455402i
$653$	18.5467	−	9.44999i	0.725787	−	0.369807i	−0.0517368	−	0.998661i	$-0.516476\pi$
$653$	18.5467	−	9.44999i	0.725787	−	0.369807i	0.777523	+	0.628854i	$0.216476\pi$
$654$	13.0708	+	0.609341i	0.511109	+	0.0238271i
$655$	32.5393	+	21.3899i	1.27141	+	0.835773i
$656$	−35.4017	−	6.67412i	−1.38220	−	0.260581i
$657$	9.21691	−	9.21691i	0.359586	−	0.359586i
$658$	5.40857	+	1.11702i	0.210848	+	0.0435460i
$659$	29.6956	+	21.5751i	1.15677	+	0.840446i	0.989367	−	0.145442i	$-0.0464603\pi$
$659$	29.6956	+	21.5751i	1.15677	+	0.840446i	0.167408	+	0.985888i	$0.446460\pi$
$660$	1.31405	−	0.594494i	0.0511495	−	0.0231407i
$661$	−33.2569	+	24.1626i	−1.29354	+	0.939815i	−0.999871	−	0.0160906i	$-0.994878\pi$
$661$	−33.2569	+	24.1626i	−1.29354	+	0.939815i	−0.293674	+	0.955906i	$0.594878\pi$
$662$	−2.90081	+	1.31165i	−0.112743	+	0.0509787i
$663$	2.74565	−	0.434867i	0.106632	−	0.0168889i
$664$	12.7374	+	1.79179i	0.494308	+	0.0695348i
$665$	−42.2885	+	8.74275i	−1.63988	+	0.339029i
$666$	−2.53797	+	6.72750i	−0.0983442	+	0.260685i
$667$	27.8268	−	54.6131i	1.07746	−	2.11463i
$668$	−1.36950	+	5.35781i	−0.0529874	+	0.207300i
$669$	−2.78655	+	0.905404i	−0.107734	+	0.0350049i
$670$	6.52219	−	2.12066i	0.251974	−	0.0819283i
$671$	1.39039	+	0.451766i	0.0536755	+	0.0174402i
$672$	5.21079	+	21.4496i	0.201011	+	0.827436i
$673$	37.3753	+	5.91966i	1.44071	+	0.228186i	0.827381	−	0.561641i	$-0.189830\pi$
$673$	37.3753	+	5.91966i	1.44071	+	0.228186i	0.613330	+	0.789827i	$0.289830\pi$
$674$	7.31972	−	2.00669i	0.281945	−	0.0772949i
$675$	−1.84374	+	4.64765i	−0.0709655	+	0.178888i
$676$	22.1374	−	13.1243i	0.851440	−	0.504781i
$677$	−1.70482	+	10.7638i	−0.0655215	+	0.413687i	0.933026	+	0.359809i	$0.117158\pi$
$677$	−1.70482	+	10.7638i	−0.0655215	+	0.413687i	−0.998548	+	0.0538777i	$0.982842\pi$
$678$	−12.9114	+	11.7612i	−0.495858	+	0.451685i
$679$	3.01615	−	9.28275i	0.115749	−	0.356239i
$680$	−24.6612	−	41.5781i	−0.945715	−	1.59445i
$681$	5.34821	+	16.4601i	0.204944	+	0.630752i
$682$	2.15222	+	1.22607i	0.0824127	+	0.0469485i
$683$	−9.58062	−	4.88157i	−0.366592	−	0.186788i	0.260984	−	0.965343i	$-0.415953\pi$
$683$	−9.58062	−	4.88157i	−0.366592	−	0.186788i	−0.627576	+	0.778555i	$0.715953\pi$
$684$	−9.85536	−	0.920883i	−0.376829	−	0.0352109i
$685$	−13.7567	−	12.5261i	−0.525618	−	0.478597i
$686$	4.22780	−	5.28299i	0.161418	−	0.201706i
$687$	0.602509	+	3.80409i	0.0229871	+	0.145135i
$688$	−2.77248	+	7.75329i	−0.105700	+	0.295591i
$689$	−0.490611	−	0.675268i	−0.0186908	−	0.0257256i
$690$	25.1465	+	12.8063i	0.957312	+	0.487529i
$691$	−10.8307	+	14.9072i	−0.412020	+	0.567097i	−0.963710	−	0.266953i	$-0.913983\pi$
$691$	−10.8307	+	14.9072i	−0.412020	+	0.567097i	0.551690	+	0.834049i	$0.313983\pi$
$692$	23.9376	−	1.53194i	0.909970	−	0.0582357i
$693$	−0.889844	−	0.889844i	−0.0338024	−	0.0338024i
$694$	−3.02421	+	1.98887i	−0.114797	+	0.0754965i
$695$	17.7938	+	4.87425i	0.674959	+	0.184891i
$696$	−9.11830	−	17.1543i	−0.345628	−	0.650232i
$697$	−31.2525	−	61.3366i	−1.18377	−	2.32329i
$698$	−2.20739	−	19.8959i	−0.0835510	−	0.753073i
$699$	20.7659			0.785437
$700$	27.5805	−	27.6031i	1.04245	−	1.04330i
$701$	31.2659			1.18090			0.590448	−	0.807076i	$-0.298951\pi$
$701$	31.2659			1.18090			0.590448	+	0.807076i	$0.298951\pi$
$702$	0.0567161	+	0.511201i	0.00214061	+	0.0192940i
$703$	11.4238	+	22.4204i	0.430856	+	0.845602i
$704$	−2.47990	−	0.711784i	−0.0934646	−	0.0268264i
$705$	−0.104667	−	2.23538i	−0.00394200	−	0.0841894i
$706$	11.4180	−	7.50904i	0.429722	−	0.282607i
$707$	−4.48730	−	4.48730i	−0.168762	−	0.168762i
$708$	−0.929697	−	14.5271i	−0.0349402	−	0.545962i
$709$	−0.510077	+	0.702061i	−0.0191563	+	0.0263665i	−0.818488	−	0.574524i	$-0.805187\pi$
$709$	−0.510077	+	0.702061i	−0.0191563	+	0.0263665i	0.799331	+	0.600890i	$0.205187\pi$
$710$	−12.7194	−	24.9506i	−0.477351	−	0.936381i
$711$	−6.57007	−	9.04292i	−0.246397	−	0.339136i
$712$	−9.57526	−	6.70649i	−0.358848	−	0.251336i
$713$	7.58147	+	47.8675i	0.283928	+	1.79265i
$714$	−26.3547	+	32.9324i	−0.986299	+	1.23246i
$715$	−0.260678	−	0.0288676i	−0.00974882	−	0.00107959i
$716$	−0.115364	+	1.23463i	−0.00431136	+	0.0461405i
$717$	−16.3382	−	8.32472i	−0.610160	−	0.310892i
$718$	−19.3430	−	11.0192i	−0.721873	−	0.411233i
$719$	10.9066	+	33.5672i	0.406749	+	1.25184i	0.919426	+	0.393263i	$0.128654\pi$
$719$	10.9066	+	33.5672i	0.406749	+	1.25184i	−0.512678	+	0.858581i	$0.671346\pi$
$720$	7.89700	−	4.19969i	0.294304	−	0.156513i
$721$	2.38957	−	7.35435i	0.0889924	−	0.273890i
$722$	−5.74391	+	5.23222i	−0.213766	+	0.194723i
$723$	0.680874	−	4.29887i	0.0253220	−	0.159877i
$724$	−1.24912	−	2.10696i	−0.0464233	−	0.0783046i
$725$	−17.5016	+	29.5484i	−0.649995	+	1.09740i
$726$	−14.8609	+	4.07410i	−0.551541	+	0.151204i
$727$	12.0688	+	1.91151i	0.447606	+	0.0708939i	0.376169	−	0.926551i	$-0.377241\pi$
$727$	12.0688	+	1.91151i	0.447606	+	0.0708939i	0.0714377	+	0.997445i	$0.477241\pi$
$728$	1.17406	−	3.83842i	0.0435135	−	0.142261i
$729$	0.951057	+	0.309017i	0.0352243	+	0.0114451i
$730$	24.2349	+	33.3422i	0.896974	+	1.23405i
$731$	−14.9642	+	4.86215i	−0.553470	+	0.179833i
$732$	8.78384	+	2.24521i	0.324660	+	0.0829855i
$733$	−10.7166	+	21.0325i	−0.395827	+	0.776855i	−0.999797	−	0.0201526i	$-0.993585\pi$
$733$	−10.7166	+	21.0325i	−0.395827	+	0.776855i	0.603970	+	0.797007i	$0.293585\pi$
$734$	−2.82356	+	7.48454i	−0.104220	+	0.276259i
$735$	−16.7621	−	7.57512i	−0.618278	−	0.279412i
$736$	−19.4439	−	46.5860i	−0.716711	−	1.71718i
$737$	0.690827	−	0.109416i	0.0254469	−	0.00403040i
$738$	11.6056	−	5.24766i	0.427208	−	0.193169i
$739$	−8.20279	+	5.95967i	−0.301744	+	0.219230i	−0.728346	−	0.685209i	$-0.759711\pi$
$739$	−8.20279	+	5.95967i	−0.301744	+	0.219230i	0.426602	+	0.904440i	$0.359711\pi$
$740$	−19.7591	−	11.2509i	−0.726359	−	0.413593i
$741$	1.45620	+	1.05799i	0.0534948	+	0.0388663i
$742$	12.4030	+	2.56155i	0.455327	+	0.0940376i
$743$	29.3014	−	29.3014i	1.07496	−	1.07496i	0.0780122	−	0.996952i	$-0.475143\pi$
$743$	29.3014	−	29.3014i	1.07496	−	1.07496i	0.996952	−	0.0780122i	$-0.0248573\pi$
$744$	13.8053	+	6.73550i	0.506128	+	0.246935i
$745$	27.3895	−	21.9281i	1.00347	−	0.803382i
$746$	−52.3135	−	2.43877i	−1.91533	−	0.0892897i
$747$	−4.05203	+	2.06461i	−0.148256	+	0.0755402i
$748$	−1.81983	−	4.58192i	−0.0665395	−	0.167532i
$749$		−	15.2387i		−	0.556811i
$750$	−13.6058	−	8.05499i	−0.496813	−	0.294127i
$751$			19.3537i			0.706226i	0.935581	+	0.353113i	$0.114877\pi$
$751$			19.3537i			0.706226i	−0.935581	+	0.353113i	$0.885123\pi$
$752$	−2.44673	+	3.16840i	−0.0892232	+	0.115540i
$753$	8.75547	−	4.46114i	0.319067	−	0.162573i
$754$	−0.164512	+	3.52891i	−0.00599118	+	0.128515i
$755$	−15.2853	+	12.2374i	−0.556288	+	0.445365i
$756$	−5.85954	−	5.15466i	−0.213109	−	0.187473i
$757$	25.7334	−	25.7334i	0.935297	−	0.935297i	−0.0627330	−	0.998030i	$-0.519982\pi$
$757$	25.7334	−	25.7334i	0.935297	−	0.935297i	0.998030	+	0.0627330i	$0.0199816\pi$
$758$	−6.53832	+	31.6583i	−0.237482	+	1.14988i
$759$	2.32832	+	1.69163i	0.0845128	+	0.0614021i
$760$	7.74538	−	30.3277i	0.280955	−	1.10010i
$761$	−0.0820705	+	0.0596277i	−0.00297505	+	0.00216150i	−0.589272	−	0.807935i	$-0.700585\pi$
$761$	−0.0820705	+	0.0596277i	−0.00297505	+	0.00216150i	0.586297	+	0.810096i	$0.300585\pi$
$762$	0.580621	+	1.28409i	0.0210337	+	0.0465175i
$763$	35.6594	−	5.64790i	1.29096	−	0.204468i
$764$	−1.25143	+	2.90045i	−0.0452750	+	0.104935i
$765$	15.5747	+	7.03855i	0.563106	+	0.254479i
$766$	−42.9769	−	16.2131i	−1.55282	−	0.585804i
$767$	−1.20176	+	2.35858i	−0.0433929	+	0.0851634i
$768$	−15.6296	−	3.42290i	−0.563984	−	0.123513i
$769$	6.32553	−	2.05529i	0.228104	−	0.0741156i	−0.192735	−	0.981251i	$-0.561736\pi$
$769$	6.32553	−	2.05529i	0.228104	−	0.0741156i	0.420839	+	0.907135i	$0.361736\pi$
$770$	3.21901	−	2.33975i	0.116005	−	0.0843187i
$771$	3.68269	+	1.19658i	0.132629	+	0.0430937i
$772$	−28.1919	−	17.8485i	−1.01465	−	0.642381i
$773$	31.1382	+	4.93181i	1.11996	+	0.177385i	0.688843	−	0.724910i	$-0.258119\pi$
$773$	31.1382	+	4.93181i	1.11996	+	0.177385i	0.431120	+	0.902295i	$0.358119\pi$
$774$	−0.769698	−	2.80759i	−0.0276662	−	0.100917i
$775$	−2.53733	−	27.0355i	−0.0911436	−	0.971144i
$776$	5.08863	+	4.91528i	0.182671	+	0.176448i
$777$	−3.10356	+	19.5951i	−0.111340	+	0.702971i
$778$	−21.2005	−	23.2738i	−0.760074	−	0.834407i
$779$	13.7740	−	42.3920i	0.493505	−	1.51885i
$780$	−1.62473	−	0.0754099i	−0.0581746	−	0.00270011i
$781$	−0.882596	−	2.71635i	−0.0315818	−	0.0971987i
$782$	47.7480	−	83.8161i	1.70746	−	2.99726i
$783$	6.11991	+	3.11825i	0.218708	+	0.111437i
$784$	14.0743	+	29.7427i	0.502654	+	1.06224i
$785$	12.2309	+	1.35446i	0.436541	+	0.0483426i
$786$	19.2286	+	15.3880i	0.685863	+	0.548873i
$787$	6.82644	+	43.1005i	0.243336	+	1.53637i	0.742493	+	0.669854i	$0.233643\pi$
$787$	6.82644	+	43.1005i	0.243336	+	1.53637i	−0.499156	+	0.866512i	$0.666357\pi$
$788$	−19.7445	−	23.8147i	−0.703370	−	0.848364i
$789$	14.2488	+	19.6117i	0.507269	+	0.698196i
$790$	31.4910	−	16.0536i	1.12040	−	0.571161i
$791$	−28.3249	+	38.9859i	−1.00712	+	1.38618i
$792$	0.862517	−	0.296865i	0.0306482	−	0.0105486i
$793$	−1.16578	−	1.16578i	−0.0413980	−	0.0413980i
$794$	−17.5481	−	26.6830i	−0.622757	−	0.946944i
$795$	−0.240024	−	5.12619i	−0.00851276	−	0.181807i
$796$	7.57899	−	1.70269i	0.268630	−	0.0603502i
$797$	4.98304	+	9.77977i	0.176508	+	0.346417i	0.962263	−	0.272121i	$-0.0877252\pi$
$797$	4.98304	+	9.77977i	0.176508	+	0.346417i	−0.785755	+	0.618538i	$0.787725\pi$
$798$	−27.1446	+	3.01161i	−0.960909	+	0.106610i
$799$	−7.64951			−0.270620
$800$	9.21596	+	26.7407i	0.325833	+	0.945427i
$801$	4.13314			0.146037
$802$	8.88962	−	0.986275i	0.313903	−	0.0348266i
$803$	1.90845	+	3.74554i	0.0673477	+	0.132177i
$804$	4.23208	−	0.950775i	0.149254	−	0.0335313i
$805$	75.0967	+	20.5712i	2.64681	+	0.725038i
$806$	−1.53484	−	2.33383i	−0.0540625	−	0.0822057i
$807$	7.24955	+	7.24955i	0.255196	+	0.255196i
$808$	4.34950	−	1.49703i	0.153015	−	0.0526654i
$809$	−25.7779	+	35.4802i	−0.906301	+	1.24742i	0.0621125	+	0.998069i	$0.480216\pi$
$809$	−25.7779	+	35.4802i	−0.906301	+	1.24742i	−0.968414	+	0.249348i	$0.919784\pi$
$810$	−1.43507	+	2.81790i	−0.0504232	+	0.0990110i
$811$	−24.5130	−	33.7392i	−0.860766	−	1.18474i	−0.981386	−	0.192044i	$-0.938488\pi$
$811$	−24.5130	−	33.7392i	−0.860766	−	1.18474i	0.120620	−	0.992699i	$-0.461512\pi$
$812$	−34.2124	−	41.2649i	−1.20062	−	1.44812i
$813$	1.78225	+	11.2527i	0.0625061	+	0.394648i
$814$	−1.81052	−	1.44890i	−0.0634586	−	0.0507838i
$815$	−26.0424	−	23.7127i	−0.912224	−	0.830619i
$816$	−13.0774	−	27.6360i	−0.457800	−	0.967452i
$817$	−9.07750	−	4.62522i	−0.317581	−	0.161816i
$818$	19.1246	−	33.5711i	0.668677	−	1.17379i
$819$	0.438542	+	1.34969i	0.0153239	+	0.0471621i
$820$	10.6570	+	38.8420i	0.372159	+	1.35642i
$821$	13.9720	−	43.0015i	0.487627	−	1.50076i	−0.340513	−	0.940240i	$-0.610601\pi$
$821$	13.9720	−	43.0015i	0.487627	−	1.50076i	0.828140	−	0.560521i	$-0.189399\pi$
$822$	−7.92397	−	8.69890i	−0.276380	−	0.303409i
$823$	−4.37908	+	27.6484i	−0.152645	+	0.963764i	0.785836	+	0.618434i	$0.212233\pi$
$823$	−4.37908	+	27.6484i	−0.152645	+	0.963764i	−0.938482	+	0.345329i	$0.887767\pi$
$824$	4.03152	+	3.89418i	0.140445	+	0.135660i
$825$	−1.24177	−	1.02869i	−0.0432330	−	0.0358143i
$826$	−10.6193	−	38.7356i	−0.369494	−	1.34779i
$827$	1.80766	+	0.286305i	0.0628585	+	0.00995581i	0.187785	−	0.982210i	$-0.439869\pi$
$827$	1.80766	+	0.286305i	0.0628585	+	0.00995581i	−0.124926	+	0.992166i	$0.539869\pi$
$828$	15.0796	+	9.54702i	0.524053	+	0.331782i
$829$	−22.3135	−	7.25010i	−0.774980	−	0.251806i	−0.105285	−	0.994442i	$-0.533575\pi$
$829$	−22.3135	−	7.25010i	−0.774980	−	0.251806i	−0.669695	+	0.742636i	$0.733575\pi$
$830$	−4.44679	−	13.6763i	−0.154350	−	0.474712i
$831$	22.7335	−	7.38656i	0.788616	−	0.256237i
$832$	2.12739	+	1.98484i	0.0737540	+	0.0688119i
$833$	−28.5453	+	56.0234i	−0.989037	+	1.94110i
$834$	10.9174	+	4.11860i	0.378037	+	0.142615i
$835$	6.05477	−	1.25177i	0.209534	−	0.0433192i
$836$	1.26463	−	2.93105i	0.0437380	−	0.101372i
$837$	−5.36400	+	0.849574i	−0.185407	+	0.0293656i
$838$	2.82227	+	6.24165i	0.0974935	+	0.215614i
$839$	16.3104	−	11.8502i	0.563099	−	0.409116i	−0.269493	−	0.963002i	$-0.586856\pi$
$839$	16.3104	−	11.8502i	0.563099	−	0.409116i	0.832592	+	0.553887i	$0.186856\pi$
$840$	18.9952	−	15.7553i	0.655397	−	0.543609i
$841$	14.7053	+	10.6840i	0.507078	+	0.368414i
$842$	4.75060	−	23.0022i	0.163716	−	0.792709i
$843$	11.3189	−	11.3189i	0.389845	−	0.389845i
$844$	18.9349	+	16.6571i	0.651767	+	0.573362i
$845$	−24.0435	−	15.8052i	−0.827121	−	0.543714i
$846$	0.0659088	−	1.41379i	0.00226599	−	0.0486072i
$847$	−37.8829	+	19.3023i	−1.30167	+	0.663234i
$848$	−5.61086	+	7.26578i	−0.192678	+	0.249508i
$849$		−	29.3368i		−	1.00684i
$850$	−29.6793	+	45.1695i	−1.01799	+	1.54930i
$851$		−	45.3717i		−	1.55532i
$852$	−6.53811	−	16.4615i	−0.223992	−	0.563961i
$853$	−44.0432	+	22.4411i	−1.50801	+	0.768369i	−0.995892	−	0.0905468i	$-0.971139\pi$
$853$	−44.0432	+	22.4411i	−1.50801	+	0.768369i	−0.512117	+	0.858916i	$0.671139\pi$
$854$	24.9883	+	1.16491i	0.855081	+	0.0398625i
$855$	3.90830	+	10.3535i	0.133661	+	0.354083i
$856$	9.92732	+	4.84344i	0.339309	+	0.165546i
$857$	−31.2131	+	31.2131i	−1.06622	+	1.06622i	−0.0685727	+	0.997646i	$0.521844\pi$
$857$	−31.2131	+	31.2131i	−1.06622	+	1.06622i	−0.997646	+	0.0685727i	$0.978156\pi$
$858$	−0.162447	−	0.0335498i	−0.00554585	−	0.00114537i
$859$	9.05606	+	6.57961i	0.308989	+	0.224493i	0.731462	−	0.681882i	$-0.238838\pi$
$859$	9.05606	+	6.57961i	0.308989	+	0.224493i	−0.422474	+	0.906375i	$0.638838\pi$
$860$	9.14963	−	1.01701i	0.312000	−	0.0346799i
$861$	28.4315	−	20.6567i	0.968944	−	0.703979i
$862$	8.22794	−	3.72040i	0.280245	−	0.126717i
$863$	9.69650	−	1.53577i	0.330073	−	0.0522784i	0.0108012	−	0.999942i	$-0.496562\pi$
$863$	9.69650	−	1.53577i	0.330073	−	0.0522784i	0.319271	+	0.947663i	$0.396562\pi$
$864$	5.22040	−	2.17887i	0.177601	−	0.0741266i
$865$	−13.2793	−	23.2992i	−0.451509	−	0.792197i
$866$	−0.363334	+	0.963106i	−0.0123466	+	0.0327277i
$867$	18.8056	−	36.9080i	0.638670	−	1.25346i
$868$	41.0630	+	10.4960i	1.39377	+	0.356258i
$869$	3.42840	−	1.11395i	0.116300	−	0.0377883i
$870$	−12.7632	+	17.5746i	−0.432714	+	0.595835i
$871$	−0.750163	−	0.243743i	−0.0254183	−	0.00825891i
$872$	−7.65457	+	25.0255i	−0.259216	+	0.847472i
$873$	−2.47056	−	0.391298i	−0.0836157	−	0.0132434i
$874$	60.2367	−	16.5138i	2.03754	−	0.558588i
$875$	−41.2602	−	14.1729i	−1.39485	−	0.479130i
$876$	13.2946	+	22.4247i	0.449182	+	0.757660i
$877$	−3.23475	+	20.4234i	−0.109230	+	0.689649i	0.870925	+	0.491416i	$0.163520\pi$
$877$	−3.23475	+	20.4234i	−0.109230	+	0.689649i	−0.980155	+	0.198234i	$0.936480\pi$
$878$	5.10719	−	4.65222i	0.172359	−	0.157005i
$879$	3.37425	−	10.3849i	0.113811	−	0.350273i
$880$	0.501115	+	2.84069i	0.0168926	+	0.0957597i
$881$	5.71719	+	17.5957i	0.192617	+	0.592814i	0.999996	+	0.00278126i	$0.000885305\pi$
$881$	5.71719	+	17.5957i	0.192617	+	0.592814i	−0.807379	+	0.590033i	$0.799115\pi$
$882$	−10.1084	−	5.75849i	−0.340367	−	0.193899i
$883$	−36.1247	−	18.4064i	−1.21569	−	0.619426i	−0.275904	−	0.961185i	$-0.588977\pi$
$883$	−36.1247	−	18.4064i	−1.21569	−	0.619426i	−0.939787	+	0.341759i	$0.888977\pi$
$884$	−0.517248	+	5.53563i	−0.0173969	+	0.186183i
$885$	−14.1397	+	8.05886i	−0.475301	+	0.270896i
$886$	12.6229	−	15.7733i	0.424074	−	0.529916i
$887$	1.89648	+	11.9739i	0.0636775	+	0.402044i	0.998854	+	0.0478619i	$0.0152407\pi$
$887$	1.89648	+	11.9739i	0.0636775	+	0.402044i	−0.935176	+	0.354182i	$0.884759\pi$
$888$	−11.7789	−	8.24989i	−0.395273	−	0.276848i
$889$	2.28554	+	3.14577i	0.0766544	+	0.105506i
$890$	−2.04198	+	12.9096i	−0.0684474	+	0.432732i
$891$	−0.189562	+	0.260910i	−0.00635058	+	0.00874082i
$892$	−0.374253	−	5.84793i	−0.0125309	−	0.195803i
$893$	−3.50233	−	3.50233i	−0.117201	−	0.117201i
$894$	18.5402	−	12.1930i	0.620079	−	0.407794i
$895$	1.29704	−	0.489615i	0.0433553	−	0.0163660i
$896$	−44.1438	−	0.526813i	−1.47474	−	0.0175996i
$897$	−1.47344	−	2.89179i	−0.0491967	−	0.0965540i
$898$	−0.207042	−	1.86614i	−0.00690909	−	0.0622739i
$899$	−37.3021			−1.24409
$900$	−8.09257	−	5.87455i	−0.269752	−	0.195818i
$901$	−17.5419			−0.584405
$902$	0.452954	+	4.08262i	0.0150817	+	0.135936i
$903$	−3.64668	−	7.15700i	−0.121354	−	0.238170i
$904$	−16.3948	−	30.8435i	−0.545281	−	1.02584i
$905$	−1.50428	+	2.28837i	−0.0500038	+	0.0760680i
$906$	−10.3468	+	6.80454i	−0.343748	+	0.226066i
$907$	−25.9154	−	25.9154i	−0.860508	−	0.860508i	0.130889	−	0.991397i	$-0.458217\pi$
$907$	−25.9154	−	25.9154i	−0.860508	−	0.860508i	−0.991397	+	0.130889i	$0.958217\pi$
$908$	−34.5437	+	2.21071i	−1.14637	+	0.0733648i
$909$	−0.955925	+	1.31572i	−0.0317060	+	0.0436396i
$910$	−4.43235	+	0.702943i	−0.146931	+	0.0233024i
$911$	−4.72152	−	6.49861i	−0.156431	−	0.215309i	0.723607	−	0.690212i	$-0.242483\pi$
$911$	−4.72152	−	6.49861i	−0.156431	−	0.215309i	−0.880038	+	0.474904i	$0.842483\pi$
$912$	6.66566	−	18.6406i	0.220722	−	0.617253i
$913$	−0.229434	−	1.44859i	−0.00759316	−	0.0479413i
$914$	−32.3653	+	40.4432i	−1.07055	+	1.33774i
$915$	−2.05220	−	9.92646i	−0.0678437	−	0.328159i
$916$	−7.66961	−	0.716647i	−0.253411	−	0.0236787i
$917$	60.5464	+	30.8499i	1.99942	+	1.01875i
$918$	9.39237	+	5.35060i	0.309994	+	0.176596i
$919$	5.07949	+	15.6331i	0.167557	+	0.515687i	0.999216	−	0.0396000i	$-0.0126084\pi$
$919$	5.07949	+	15.6331i	0.167557	+	0.515687i	−0.831659	+	0.555287i	$0.812608\pi$
$920$	−37.2697	+	42.3836i	−1.22875	+	1.39735i
$921$	1.00253	−	3.08548i	0.0330345	−	0.101670i
$922$	22.3491	−	20.3582i	0.736029	−	0.670461i
$923$	−0.503862	+	3.18126i	−0.0165848	+	0.104712i
$924$	2.16498	−	1.28352i	0.0712227	−	0.0422247i
$925$	−1.61324	+	25.3704i	−0.0530429	+	0.834172i
$926$	−52.7357	+	14.4574i	−1.73300	+	0.475100i
$927$	−1.95732	−	0.310010i	−0.0642870	−	0.0101821i
$928$	37.7561	−	9.17218i	1.23941	−	0.301091i
$929$	16.6330	+	5.40439i	0.545711	+	0.177312i	0.568882	−	0.822419i	$-0.307376\pi$
$929$	16.6330	+	5.40439i	0.545711	+	0.177312i	−0.0231709	+	0.999732i	$0.507376\pi$
$930$	−0.00350629	−	17.1739i	−0.000114976	−	0.563154i
$931$	−38.7199	+	12.5808i	−1.26899	+	0.412320i
$932$	−10.2851	+	40.2380i	−0.336901	+	1.31804i
$933$	9.80631	−	19.2460i	0.321044	−	0.630084i
$934$	−12.1334	+	32.1625i	−0.397016	+	1.05239i
$935$	−3.71101	+	4.07561i	−0.121363	+	0.133287i
$936$	−1.01865	−	0.143294i	−0.0332955	−	0.00468371i
$937$	43.7402	−	6.92777i	1.42893	−	0.226320i	0.606453	−	0.795119i	$-0.292592\pi$
$937$	43.7402	−	6.92777i	1.42893	−	0.226320i	0.822477	+	0.568799i	$0.192592\pi$
$938$	10.9051	−	4.93094i	0.356065	−	0.161001i
$939$	3.98061	−	2.89208i	0.129902	−	0.0943795i
$940$	4.38334	+	0.904349i	0.142969	+	0.0294966i
$941$	1.57111	+	1.14148i	0.0512169	+	0.0372112i	0.613099	−	0.790006i	$-0.289923\pi$
$941$	1.57111	+	1.14148i	0.0512169	+	0.0372112i	−0.561882	+	0.827217i	$0.689923\pi$
$942$	7.62196	+	1.57415i	0.248337	+	0.0512884i
$943$	−56.8309	+	56.8309i	−1.85067	+	1.85067i
$944$	28.6097	+	5.39366i	0.931165	+	0.175549i
$945$	−2.30519	+	8.41528i	−0.0749879	+	0.273749i
$946$	0.937848	+	0.0437210i	0.0304921	+	0.00142149i
$947$	24.4028	−	12.4338i	0.792984	−	0.404045i	−0.0100722	−	0.999949i	$-0.503206\pi$
$947$	24.4028	−	12.4338i	0.792984	−	0.404045i	0.803056	+	0.595904i	$0.203206\pi$
$948$	20.7766	−	8.25196i	0.674792	−	0.268011i
$949$		−	4.74061i		−	0.153887i
$950$	−34.2695	+	7.09220i	−1.11185	+	0.230101i
$951$			26.2037i			0.849712i
$952$	−50.7599	−	67.3786i	−1.64514	−	2.18375i
$953$	19.9787	−	10.1797i	0.647174	−	0.329752i	−0.0994061	−	0.995047i	$-0.531694\pi$
$953$	19.9787	−	10.1797i	0.647174	−	0.329752i	0.746580	+	0.665295i	$0.231694\pi$
$954$	0.151142	−	3.24212i	0.00489341	−	0.104967i
$955$	3.52790	−	0.165187i	0.114160	−	0.00534532i
$956$	24.2230	−	27.5354i	0.783426	−	0.890557i
$957$	−1.56633	+	1.56633i	−0.0506322	+	0.0506322i
$958$	4.19188	−	20.2969i	0.135434	−	0.655765i
$959$	−26.2664	−	19.0836i	−0.848186	−	0.616243i
$960$	4.22643	+	17.3821i	0.136407	+	0.561005i
$961$	−1.21814	+	0.885034i	−0.0392950	+	0.0285495i
$962$	1.07742	+	2.38279i	0.0347374	+	0.0768242i
$963$	−3.85721	+	0.610923i	−0.124297	+	0.0196867i
$964$	7.99270	+	3.44852i	0.257427	+	0.111069i
$965$	−4.10610	+	37.0787i	−0.132180	+	1.19360i
$966$	46.0753	+	17.3820i	1.48245	+	0.559258i
$967$	−12.4805	+	24.4943i	−0.401345	+	0.787684i	−0.999910	−	0.0133900i	$-0.995738\pi$
$967$	−12.4805	+	24.4943i	−0.401345	+	0.787684i	0.598565	+	0.801074i	$0.295738\pi$
$968$	−0.533923	−	30.8139i	−0.0171609	−	0.990396i
$969$	35.9772	−	11.6897i	1.15575	−	0.375527i
$970$	2.44278	−	7.52333i	0.0784329	−	0.241560i
$971$	25.4134	+	8.25731i	0.815555	+	0.264990i	0.686949	−	0.726706i	$-0.258950\pi$
$971$	25.4134	+	8.25731i	0.815555	+	0.264990i	0.128606	+	0.991696i	$0.458950\pi$
$972$	−1.06983	+	1.68981i	−0.0343149	+	0.0542007i
$973$	31.7989	+	5.03644i	1.01942	+	0.161461i
$974$	−2.53576	−	9.24957i	−0.0812510	−	0.296375i
$975$	0.721078	+	1.66938i	0.0230930	+	0.0534630i
$976$	−8.70110	+	15.9084i	−0.278516	+	0.509216i
$977$	0.0626759	−	0.395720i	0.00200518	−	0.0126602i	−0.986665	−	0.162761i	$-0.947960\pi$
$977$	0.0626759	−	0.395720i	0.00200518	−	0.0126602i	0.988671	+	0.150101i	$0.0479599\pi$
$978$	−15.0006	−	16.4676i	−0.479666	−	0.526575i
$979$	−0.411904	+	1.26771i	−0.0131645	+	0.0405162i
$980$	22.9804	−	28.7280i	0.734082	−	0.917681i
$981$	−2.85918	−	8.79965i	−0.0912866	−	0.280951i
$982$	17.3302	−	30.4213i	0.553030	−	0.970782i
$983$	−24.7635	−	12.6176i	−0.789831	−	0.402439i	0.0120463	−	0.999927i	$-0.496165\pi$
$983$	−24.7635	−	12.6176i	−0.789831	−	0.402439i	−0.801878	+	0.597488i	$0.796165\pi$
$984$	4.42026	+	25.0873i	0.140913	+	0.799753i
$985$	−14.2434	+	31.5176i	−0.453834	+	1.00423i
$986$	57.9685	+	46.3902i	1.84609	+	1.47736i
$987$	−0.610900	−	3.85707i	−0.0194452	−	0.122772i
$988$	−2.77131	+	2.29767i	−0.0881672	+	0.0730986i
$989$	10.7976	+	14.8616i	0.343343	+	0.472571i
$990$	−0.721285	−	0.720991i	−0.0229240	−	0.0229146i
$991$	12.1427	−	16.7130i	0.385725	−	0.530906i	−0.571365	−	0.820696i	$-0.693586\pi$
$991$	12.1427	−	16.7130i	0.385725	−	0.530906i	0.957090	+	0.289791i	$0.0935858\pi$
$992$	−19.8890	+	23.4146i	−0.631477	+	0.743414i
$993$	1.59179	+	1.59179i	0.0505138	+	0.0505138i
$994$	−26.8536	−	40.8327i	−0.851745	−	1.29514i
$995$	−5.42782	−	6.77968i	−0.172074	−	0.214930i
$996$	−1.99367	−	8.87421i	−0.0631719	−	0.281190i
$997$	−15.2479	−	29.9257i	−0.482906	−	0.947757i	−0.995994	−	0.0894207i	$-0.971498\pi$
$997$	−15.2479	−	29.9257i	−0.482906	−	0.947757i	0.513088	−	0.858336i	$-0.328502\pi$
$998$	40.3935	−	4.48153i	1.27863	−	0.141861i
$999$	5.08432			0.160861

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.w.a.223.29	yes	240
3.2	odd	2		900.2.bj.f.523.2		240
4.3	odd	2	inner	300.2.w.a.223.5	yes	240
12.11	even	2		900.2.bj.f.523.26		240
25.12	odd	20	inner	300.2.w.a.187.5	✓	240
75.62	even	20		900.2.bj.f.487.26		240
100.87	even	20	inner	300.2.w.a.187.29	yes	240
300.287	odd	20		900.2.bj.f.487.2		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.187.5	✓	240	25.12	odd	20	inner
300.2.w.a.187.29	yes	240	100.87	even	20	inner
300.2.w.a.223.5	yes	240	4.3	odd	2	inner
300.2.w.a.223.29	yes	240	1.1	even	1	trivial
900.2.bj.f.487.2		240	300.287	odd	20
900.2.bj.f.487.26		240	75.62	even	20
900.2.bj.f.523.2		240	3.2	odd	2
900.2.bj.f.523.26		240	12.11	even	2

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40559 - 0.155946i) q^{2} +(-0.453990 - 0.891007i) q^{3} +(1.95136 - 0.438391i) q^{4} +(-1.39750 - 1.74556i) q^{5} +(-0.777073 - 1.18159i) q^{6} +(-2.75918 - 2.75918i) q^{7} +(2.67445 - 0.920504i) q^{8} +(-0.587785 + 0.809017i) q^{9} +(-2.23652 - 2.23561i) q^{10} +(-0.189562 - 0.260910i) q^{11} +(-1.27651 - 1.53965i) q^{12} +(0.0568939 + 0.359214i) q^{13} +(-4.30856 - 3.44799i) q^{14} +(-0.920857 + 2.03765i) q^{15} +(3.61563 - 1.71092i) q^{16} +(6.81039 + 3.47007i) q^{17} +(-0.700022 + 1.22881i) q^{18} +(1.52937 + 4.70692i) q^{19} +(-3.49227 - 2.79357i) q^{20} +(-1.20581 + 3.71109i) q^{21} +(-0.307135 - 0.337171i) q^{22} +(1.39600 - 8.81398i) q^{23} +(-2.03435 - 1.96505i) q^{24} +(-1.09399 + 4.87885i) q^{25} +(0.135987 + 0.496035i) q^{26} +(0.987688 + 0.156434i) q^{27} +(-6.59376 - 4.17456i) q^{28} +(6.53236 + 2.12249i) q^{29} +(-0.976583 + 3.00770i) q^{30} +(-5.16506 + 1.67823i) q^{31} +(4.81527 - 2.96869i) q^{32} +(-0.146413 + 0.287352i) q^{33} +(10.1138 + 3.81544i) q^{34} +(-0.960370 + 8.67228i) q^{35} +(-0.792316 + 1.83636i) q^{36} +(5.02172 - 0.795363i) q^{37} +(2.88369 + 6.37749i) q^{38} +(0.294233 - 0.213773i) q^{39} +(-5.34434 - 3.38201i) q^{40} +(-7.28627 - 5.29378i) q^{41} +(-1.11614 + 5.40431i) q^{42} +(-1.45559 + 1.45559i) q^{43} +(-0.484286 - 0.426028i) q^{44} +(2.23362 - 0.104585i) q^{45} +(0.587697 - 12.6065i) q^{46} +(-0.891709 + 0.454348i) q^{47} +(-3.16590 - 2.44481i) q^{48} +8.22616i q^{49} +(-0.776859 + 7.02826i) q^{50} -7.64348i q^{51} +(0.268497 + 0.676015i) q^{52} +(-2.04487 + 1.04191i) q^{53} +(1.41268 + 0.0658569i) q^{54} +(-0.190522 + 0.695515i) q^{55} +(-9.91913 - 4.83945i) q^{56} +(3.49957 - 3.49957i) q^{57} +(9.51281 + 1.96466i) q^{58} +(5.88836 + 4.27814i) q^{59} +(-0.903637 + 4.37989i) q^{60} +(-3.66737 + 2.66450i) q^{61} +(-6.99824 + 3.16437i) q^{62} +(3.85403 - 0.610418i) q^{63} +(6.30534 - 4.92368i) q^{64} +(0.547522 - 0.601314i) q^{65} +(-0.160986 + 0.426732i) q^{66} +(-0.984607 + 1.93240i) q^{67} +(14.8108 + 3.78574i) q^{68} +(-8.48708 + 2.75762i) q^{69} +(0.00251926 + 12.3394i) q^{70} +(8.42272 + 2.73671i) q^{71} +(-0.827297 + 2.70473i) q^{72} +(-12.8742 - 2.03907i) q^{73} +(6.93444 - 1.90107i) q^{74} +(4.84375 - 1.24020i) q^{75} +(5.04782 + 8.51443i) q^{76} +(-0.196862 + 1.24294i) q^{77} +(0.380233 - 0.346361i) q^{78} +(-3.45409 + 10.6306i) q^{79} +(-8.03936 - 3.92030i) q^{80} +(-0.309017 - 0.951057i) q^{81} +(-11.0670 - 6.30462i) q^{82} +(4.05203 + 2.06461i) q^{83} +(-0.726055 + 7.77030i) q^{84} +(-3.46030 - 16.7374i) q^{85} +(-1.81897 + 2.27296i) q^{86} +(-1.07447 - 6.78397i) q^{87} +(-0.747144 - 0.523298i) q^{88} +(-2.42940 - 3.34378i) q^{89} +(3.12324 - 0.495327i) q^{90} +(0.834156 - 1.14812i) q^{91} +(-1.13988 - 17.8113i) q^{92} +(3.84020 + 3.84020i) q^{93} +(-1.18252 + 0.777685i) q^{94} +(6.07893 - 9.24753i) q^{95} +(-4.83121 - 2.94268i) q^{96} +(1.13559 + 2.22872i) q^{97} +(1.28283 + 11.5626i) q^{98} +0.322503 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44}+ \cdots + 256 q^{98}+O(q^{100}) \) 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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