LMFDB - Embedded newform 234.2.t.a.25.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [234,2,Mod(25,234)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(234, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("234.25"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.t (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			25.12
Character	$\chi$	$=$	234.25
Dual form			234.2.t.a.103.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{2} +(0.523143 - 1.65116i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.419378 + 0.242128i) q^{5} +(1.27863 - 1.16837i) q^{6} +(4.37722 + 2.52719i) q^{7} +1.00000i q^{8} +(-2.45264 - 1.72758i) q^{9} -0.484256 q^{10} +(-2.78126 - 1.60576i) q^{11} +(1.69152 - 0.372524i) q^{12} +(-0.722307 - 3.53246i) q^{13} +(2.52719 + 4.37722i) q^{14} +(0.180397 + 0.819127i) q^{15} +(-0.500000 + 0.866025i) q^{16} +4.20245 q^{17} +(-1.26026 - 2.72245i) q^{18} +3.21153i q^{19} +(-0.419378 - 0.242128i) q^{20} +(6.46270 - 5.90540i) q^{21} +(-1.60576 - 2.78126i) q^{22} +(-3.13608 - 5.43186i) q^{23} +(1.65116 + 0.523143i) q^{24} +(-2.38275 + 4.12704i) q^{25} +(1.14069 - 3.42035i) q^{26} +(-4.13559 + 3.14593i) q^{27} +5.05438i q^{28} +(-2.29627 + 3.97725i) q^{29} +(-0.253335 + 0.799583i) q^{30} +(-5.61504 + 3.24185i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-4.10637 + 3.75226i) q^{33} +(3.63943 + 2.10123i) q^{34} -2.44761 q^{35} +(0.269808 - 2.98784i) q^{36} -2.08429i q^{37} +(-1.60576 + 2.78126i) q^{38} +(-6.21052 - 0.655337i) q^{39} +(-0.242128 - 0.419378i) q^{40} +(-9.57301 + 5.52698i) q^{41} +(8.54956 - 1.88288i) q^{42} +(4.73367 - 8.19896i) q^{43} -3.21153i q^{44} +(1.44688 + 0.130656i) q^{45} -6.27217i q^{46} +(-4.57369 - 2.64062i) q^{47} +(1.16837 + 1.27863i) q^{48} +(9.27337 + 16.0619i) q^{49} +(-4.12704 + 2.38275i) q^{50} +(2.19848 - 6.93891i) q^{51} +(2.69805 - 2.39177i) q^{52} +6.41990 q^{53} +(-5.15449 + 0.656660i) q^{54} +1.55520 q^{55} +(-2.52719 + 4.37722i) q^{56} +(5.30274 + 1.68009i) q^{57} +(-3.97725 + 2.29627i) q^{58} +(3.13771 - 1.81156i) q^{59} +(-0.619186 + 0.565792i) q^{60} +(0.500864 - 0.867521i) q^{61} -6.48369 q^{62} +(-6.36984 - 13.7603i) q^{63} -1.00000 q^{64} +(1.15823 + 1.30655i) q^{65} +(-5.43235 + 1.19637i) q^{66} +(0.936987 - 0.540970i) q^{67} +(2.10123 + 3.63943i) q^{68} +(-10.6095 + 2.33653i) q^{69} +(-2.11969 - 1.22381i) q^{70} +4.63041i q^{71} +(1.72758 - 2.45264i) q^{72} -0.325525i q^{73} +(1.04214 - 1.80504i) q^{74} +(5.56788 + 6.09332i) q^{75} +(-2.78126 + 1.60576i) q^{76} +(-8.11614 - 14.0576i) q^{77} +(-5.05080 - 3.67280i) q^{78} +(3.91818 - 6.78649i) q^{79} -0.484256i q^{80} +(3.03092 + 8.47428i) q^{81} -11.0540 q^{82} +(-5.08022 - 2.93306i) q^{83} +(8.34557 + 2.64416i) q^{84} +(-1.76242 + 1.01753i) q^{85} +(8.19896 - 4.73367i) q^{86} +(5.36580 + 5.87217i) q^{87} +(1.60576 - 2.78126i) q^{88} -8.42912i q^{89} +(1.18771 + 0.836592i) q^{90} +(5.76550 - 17.2878i) q^{91} +(3.13608 - 5.43186i) q^{92} +(2.41533 + 10.9673i) q^{93} +(-2.64062 - 4.57369i) q^{94} +(-0.777601 - 1.34684i) q^{95} +(0.372524 + 1.69152i) q^{96} +(11.3021 + 6.52525i) q^{97} +18.5467i q^{98} +(4.04736 + 8.74323i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 14 q^{4} - 16 q^{9} + 2 q^{13} + 8 q^{14} - 14 q^{16} + 16 q^{17} - 8 q^{23} + 14 q^{25} + 8 q^{26} + 18 q^{27} - 16 q^{29} - 8 q^{30} - 68 q^{35} - 8 q^{36} - 8 q^{39} - 10 q^{42} - 4 q^{43} + 10 q^{49}+ \cdots + 8 q^{92}+O(q^{100}) $ 28 * q + 14 * q^4 - 16 * q^9 + 2 * q^13 + 8 * q^14 - 14 * q^16 + 16 * q^17 - 8 * q^23 + 14 * q^25 + 8 * q^26 + 18 * q^27 - 16 * q^29 - 8 * q^30 - 68 * q^35 - 8 * q^36 - 8 * q^39 - 10 * q^42 - 4 * q^43 + 10 * q^49 + 58 * q^51 - 2 * q^52 - 120 * q^53 - 8 * q^56 + 28 * q^61 + 68 * q^62 - 28 * q^64 - 8 * q^65 - 24 * q^66 + 8 * q^68 - 92 * q^69 + 16 * q^74 + 32 * q^75 - 24 * q^77 - 22 * q^78 + 28 * q^79 + 8 * q^81 - 48 * q^82 + 68 * q^87 - 50 * q^90 + 8 * q^92

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	0.523143	−	1.65116i	0.302036	−	0.953296i
$3$	0.523143	−	1.65116i	0.302036	−	0.953296i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.419378	+	0.242128i	−0.187552	+	0.108283i	−0.590836	−	0.806792i	$-0.701202\pi$
$5$	−0.419378	+	0.242128i	−0.187552	+	0.108283i	0.403284	+	0.915075i	$0.367869\pi$
$6$	1.27863	−	1.16837i	0.522000	−	0.476986i
$7$	4.37722	+	2.52719i	1.65443	+	0.955188i	0.975217	+	0.221249i	$0.0710134\pi$
$7$	4.37722	+	2.52719i	1.65443	+	0.955188i	0.679216	+	0.733938i	$0.262320\pi$
$8$			1.00000i			0.353553i
$9$	−2.45264	−	1.72758i	−0.817548	−	0.575861i
$10$	−0.484256			−0.153135
$11$	−2.78126	−	1.60576i	−0.838583	−	0.484156i	0.0181994	−	0.999834i	$-0.494207\pi$
$11$	−2.78126	−	1.60576i	−0.838583	−	0.484156i	−0.856782	+	0.515678i	$0.827540\pi$
$12$	1.69152	−	0.372524i	0.488299	−	0.107538i
$13$	−0.722307	−	3.53246i	−0.200332	−	0.979728i
$13$	−0.722307	−	3.53246i	−0.200332	−	0.979728i
$14$	2.52719	+	4.37722i	0.675420	+	1.16986i
$15$	0.180397	+	0.819127i	0.0465783	+	0.211498i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	4.20245			1.01924			0.509622	−	0.860398i	$-0.329785\pi$
$17$	4.20245			1.01924			0.509622	+	0.860398i	$0.329785\pi$
$18$	−1.26026	−	2.72245i	−0.297046	−	0.641688i
$19$			3.21153i			0.736775i	0.929672	+	0.368388i	$0.120090\pi$
$19$			3.21153i			0.736775i	−0.929672	+	0.368388i	$0.879910\pi$
$20$	−0.419378	−	0.242128i	−0.0937758	−	0.0541415i
$21$	6.46270	−	5.90540i	1.41028	−	1.28866i
$22$	−1.60576	−	2.78126i	−0.342350	−	0.592968i
$23$	−3.13608	−	5.43186i	−0.653919	−	1.13262i	−0.982164	−	0.188028i	$-0.939791\pi$
$23$	−3.13608	−	5.43186i	−0.653919	−	1.13262i	0.328245	−	0.944593i	$-0.393543\pi$
$24$	1.65116	+	0.523143i	0.337041	+	0.106786i
$25$	−2.38275	+	4.12704i	−0.476550	+	0.825408i
$26$	1.14069	−	3.42035i	0.223708	−	0.670787i
$27$	−4.13559	+	3.14593i	−0.795895	+	0.605435i
$28$			5.05438i			0.955188i
$29$	−2.29627	+	3.97725i	−0.426406	+	0.738557i	−0.996551	−	0.0829873i	$-0.973554\pi$
$29$	−2.29627	+	3.97725i	−0.426406	+	0.738557i	0.570144	+	0.821544i	$0.306887\pi$
$30$	−0.253335	+	0.799583i	−0.0462524	+	0.145983i
$31$	−5.61504	+	3.24185i	−1.00849	+	0.582253i	−0.910750	−	0.412959i	$-0.864495\pi$
$31$	−5.61504	+	3.24185i	−1.00849	+	0.582253i	−0.0977420	+	0.995212i	$0.531162\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−4.10637	+	3.75226i	−0.714827	+	0.653185i
$34$	3.63943	+	2.10123i	0.624157	+	0.360357i
$35$	−2.44761			−0.413722
$36$	0.269808	−	2.98784i	0.0449679	−	0.497974i
$37$		−	2.08429i		−	0.342654i	−0.985214	−	0.171327i	$-0.945194\pi$
$37$		−	2.08429i		−	0.342654i	0.985214	−	0.171327i	$-0.0548055\pi$
$38$	−1.60576	+	2.78126i	−0.260489	+	0.451181i
$39$	−6.21052	−	0.655337i	−0.994479	−	0.104938i
$40$	−0.242128	−	0.419378i	−0.0382838	−	0.0663095i
$41$	−9.57301	+	5.52698i	−1.49505	+	0.863169i	−0.999984	−	0.00568392i	$-0.998191\pi$
$41$	−9.57301	+	5.52698i	−1.49505	+	0.863169i	−0.495070	+	0.868853i	$0.664857\pi$
$42$	8.54956	−	1.88288i	1.31923	−	0.290534i
$43$	4.73367	−	8.19896i	0.721879	−	1.25033i	−0.238367	−	0.971175i	$-0.576612\pi$
$43$	4.73367	−	8.19896i	0.721879	−	1.25033i	0.960246	−	0.279155i	$-0.0900544\pi$
$44$		−	3.21153i		−	0.484156i
$45$	1.44688	+	0.130656i	0.215688	+	0.0194770i
$46$		−	6.27217i		−	0.924780i
$47$	−4.57369	−	2.64062i	−0.667141	−	0.385174i	0.127851	−	0.991793i	$-0.459192\pi$
$47$	−4.57369	−	2.64062i	−0.667141	−	0.385174i	−0.794992	+	0.606619i	$0.792525\pi$
$48$	1.16837	+	1.27863i	0.168640	+	0.184555i
$49$	9.27337	+	16.0619i	1.32477	+	2.29456i
$50$	−4.12704	+	2.38275i	−0.583652	+	0.336971i
$51$	2.19848	−	6.93891i	0.307849	−	0.971642i
$52$	2.69805	−	2.39177i	0.374152	−	0.331678i
$53$	6.41990			0.881841			0.440921	−	0.897546i	$-0.354652\pi$
$53$	6.41990			0.881841			0.440921	+	0.897546i	$0.354652\pi$
$54$	−5.15449	+	0.656660i	−0.701438	+	0.0893601i
$55$	1.55520			0.209703
$56$	−2.52719	+	4.37722i	−0.337710	+	0.584931i
$57$	5.30274	+	1.68009i	0.702365	+	0.222533i
$58$	−3.97725	+	2.29627i	−0.522239	+	0.301515i
$59$	3.13771	−	1.81156i	0.408495	−	0.235844i	−0.281648	−	0.959518i	$-0.590881\pi$
$59$	3.13771	−	1.81156i	0.408495	−	0.235844i	0.690143	+	0.723673i	$0.257548\pi$
$60$	−0.619186	+	0.565792i	−0.0799366	+	0.0730434i
$61$	0.500864	−	0.867521i	0.0641290	−	0.111075i	−0.832178	−	0.554508i	$-0.812906\pi$
$61$	0.500864	−	0.867521i	0.0641290	−	0.111075i	0.896307	+	0.443433i	$0.146240\pi$
$62$	−6.48369			−0.823430
$63$	−6.36984	−	13.7603i	−0.802524	−	1.73363i
$64$	−1.00000			−0.125000
$65$	1.15823	+	1.30655i	0.143660	+	0.162057i
$66$	−5.43235	+	1.19637i	−0.668676	+	0.147263i
$67$	0.936987	−	0.540970i	0.114471	−	0.0660900i	−0.441671	−	0.897177i	$-0.645614\pi$
$67$	0.936987	−	0.540970i	0.114471	−	0.0660900i	0.556142	+	0.831087i	$0.312281\pi$
$68$	2.10123	+	3.63943i	0.254811	+	0.441346i
$69$	−10.6095	+	2.33653i	−1.27723	+	0.281286i
$70$	−2.11969	−	1.22381i	−0.253352	−	0.146273i
$71$			4.63041i			0.549529i	0.961512	+	0.274764i	$0.0885999\pi$
$71$			4.63041i			0.549529i	−0.961512	+	0.274764i	$0.911400\pi$
$72$	1.72758	−	2.45264i	0.203597	−	0.289047i
$73$		−	0.325525i		−	0.0380998i	−0.999819	−	0.0190499i	$-0.993936\pi$
$73$		−	0.325525i		−	0.0380998i	0.999819	−	0.0190499i	$-0.00606414\pi$
$74$	1.04214	−	1.80504i	0.121147	−	0.209832i
$75$	5.56788	+	6.09332i	0.642923	+	0.703596i
$76$	−2.78126	+	1.60576i	−0.319033	+	0.184194i
$77$	−8.11614	−	14.0576i	−0.924920	−	1.60201i
$78$	−5.05080	−	3.67280i	−0.571890	−	0.415862i
$79$	3.91818	−	6.78649i	0.440830	−	0.763540i	−0.556921	−	0.830565i	$-0.688017\pi$
$79$	3.91818	−	6.78649i	0.440830	−	0.763540i	0.997751	+	0.0670253i	$0.0213508\pi$
$80$		−	0.484256i		−	0.0541415i
$81$	3.03092	+	8.47428i	0.336769	+	0.941587i
$82$	−11.0540			−1.22071
$83$	−5.08022	−	2.93306i	−0.557626	−	0.321946i	0.194566	−	0.980889i	$-0.437670\pi$
$83$	−5.08022	−	2.93306i	−0.557626	−	0.321946i	−0.752192	+	0.658944i	$0.771003\pi$
$84$	8.34557	+	2.64416i	0.910577	+	0.288501i
$85$	−1.76242	+	1.01753i	−0.191161	+	0.110367i
$86$	8.19896	−	4.73367i	0.884117	−	0.510445i
$87$	5.36580	+	5.87217i	0.575274	+	0.629563i
$88$	1.60576	−	2.78126i	0.171175	−	0.296484i
$89$		−	8.42912i		−	0.893485i	−0.894662	−	0.446743i	$-0.852584\pi$
$89$		−	8.42912i		−	0.893485i	0.894662	−	0.446743i	$-0.147416\pi$
$90$	1.18771	+	0.836592i	0.125195	+	0.0881845i
$91$	5.76550	−	17.2878i	0.604388	−	1.81225i
$92$	3.13608	−	5.43186i	0.326959	−	0.566310i
$93$	2.41533	+	10.9673i	0.250458	+	1.13725i
$94$	−2.64062	−	4.57369i	−0.272359	−	0.471740i
$95$	−0.777601	−	1.34684i	−0.0797802	−	0.138183i
$96$	0.372524	+	1.69152i	0.0380206	+	0.172640i
$97$	11.3021	+	6.52525i	1.14755	+	0.662539i	0.948289	−	0.317407i	$-0.102812\pi$
$97$	11.3021	+	6.52525i	1.14755	+	0.662539i	0.199262	+	0.979946i	$0.436145\pi$
$98$			18.5467i			1.87350i
$99$	4.04736	+	8.74323i	0.406775	+	0.878728i
$100$	−4.76550			−0.476550
$101$	3.42351	−	5.92969i	0.340652	−	0.590027i	−0.643902	−	0.765108i	$-0.722686\pi$
$101$	3.42351	−	5.92969i	0.340652	−	0.590027i	0.984554	+	0.175081i	$0.0560189\pi$
$102$	5.37340	−	4.91003i	0.532046	−	0.486166i
$103$	−1.77760	−	3.07889i	−0.175152	−	0.303373i	0.765062	−	0.643957i	$-0.222708\pi$
$103$	−1.77760	−	3.07889i	−0.175152	−	0.303373i	−0.940214	+	0.340584i	$0.889375\pi$
$104$	3.53246	−	0.722307i	0.346386	−	0.0708280i
$105$	−1.28045	+	4.04139i	−0.124959	+	0.394400i
$106$	5.55980	+	3.20995i	0.540015	+	0.311778i
$107$	1.41392			0.136689			0.0683445	−	0.997662i	$-0.478228\pi$
$107$	1.41392			0.136689			0.0683445	+	0.997662i	$0.478228\pi$
$108$	−4.79225	−	2.00856i	−0.461135	−	0.193274i
$109$		−	4.97525i		−	0.476543i	−0.971199	−	0.238271i	$-0.923419\pi$
$109$		−	4.97525i		−	0.476543i	0.971199	−	0.238271i	$-0.0765808\pi$
$110$	1.34684	+	0.777601i	0.128417	+	0.0741413i
$111$	−3.44148	−	1.09038i	−0.326651	−	0.103494i
$112$	−4.37722	+	2.52719i	−0.413608	+	0.238797i
$113$	6.54415	+	11.3348i	0.615622	+	1.06629i	0.990275	+	0.139124i	$0.0444286\pi$
$113$	6.54415	+	11.3348i	0.615622	+	1.06629i	−0.374653	+	0.927165i	$0.622238\pi$
$114$	3.75226	+	4.10637i	0.351432	+	0.384597i
$115$	2.63041	+	1.51867i	0.245287	+	0.141616i
$116$	−4.59254			−0.426406
$117$	−4.33105	+	9.91171i	−0.400406	+	0.916338i
$118$	3.62311			0.333534
$119$	18.3951	+	10.6204i	1.68627	+	0.973570i
$120$	−0.819127	+	0.180397i	−0.0747757	+	0.0164679i
$121$	−0.343044	−	0.594169i	−0.0311858	−	0.0540154i
$122$	0.867521	−	0.500864i	0.0785417	−	0.0453461i
$123$	4.11787	+	18.6980i	0.371296	+	1.68594i
$124$	−5.61504	−	3.24185i	−0.504246	−	0.291126i
$125$		−	4.72900i		−	0.422975i
$126$	1.36371	−	15.1017i	0.121489	−	1.34536i
$127$	−4.56300			−0.404901			−0.202450	−	0.979293i	$-0.564890\pi$
$127$	−4.56300			−0.404901			−0.202450	+	0.979293i	$0.564890\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−11.0614	−	12.1053i	−0.973902	−	1.06581i
$130$	0.349781	+	1.71061i	0.0306779	+	0.150031i
$131$	−1.23473	−	2.13862i	−0.107879	−	0.186852i	0.807032	−	0.590508i	$-0.201073\pi$
$131$	−1.23473	−	2.13862i	−0.107879	−	0.186852i	−0.914911	+	0.403656i	$0.867739\pi$
$132$	−5.30274	−	1.68009i	−0.461544	−	0.146233i
$133$	−8.11614	+	14.0576i	−0.703758	+	1.21895i
$134$	1.08194			0.0934654
$135$	0.972658	−	2.32068i	0.0837131	−	0.199732i
$136$			4.20245i			0.360357i
$137$	16.9831	+	9.80519i	1.45096	+	0.837714i	0.998536	−	0.0540880i	$-0.0172251\pi$
$137$	16.9831	+	9.80519i	1.45096	+	0.837714i	0.452427	+	0.891802i	$0.350558\pi$
$138$	−10.3563	−	3.28124i	−0.881590	−	0.279317i
$139$	0.193698	+	0.335495i	0.0164293	+	0.0284563i	0.874123	−	0.485704i	$-0.161437\pi$
$139$	0.193698	+	0.335495i	0.0164293	+	0.0284563i	−0.857694	+	0.514161i	$0.828104\pi$
$140$	−1.22381	−	2.11969i	−0.103430	−	0.179147i
$141$	−6.75277	+	6.17046i	−0.568686	+	0.519646i
$142$	−2.31521	+	4.01005i	−0.194288	+	0.336516i
$143$	−3.66337	+	10.9846i	−0.306346	+	0.918575i
$144$	2.72245	−	1.26026i	0.226871	−	0.105022i
$145$		−	2.22396i		−	0.184690i
$146$	0.162762	−	0.281913i	0.0134703	−	0.0233313i
$147$	31.3721	−	6.90911i	2.58753	−	0.569853i
$148$	1.80504	−	1.04214i	0.148374	−	0.0856636i
$149$	8.19151	−	4.72937i	0.671075	−	0.387445i	−0.125409	−	0.992105i	$-0.540024\pi$
$149$	8.19151	−	4.72937i	0.671075	−	0.387445i	0.796484	+	0.604660i	$0.206691\pi$
$150$	1.77526	+	8.06091i	0.144950	+	0.658171i
$151$	1.15323	+	0.665819i	0.0938487	+	0.0541836i	0.546190	−	0.837661i	$-0.316078\pi$
$151$	1.15323	+	0.665819i	0.0938487	+	0.0541836i	−0.452341	+	0.891845i	$0.649411\pi$
$152$	−3.21153			−0.260489
$153$	−10.3071	−	7.26008i	−0.833281	−	0.586943i
$154$		−	16.2323i		−	1.30803i
$155$	1.56988	−	2.71912i	0.126096	−	0.218405i
$156$	−2.53772	−	5.70613i	−0.203180	−	0.456856i
$157$	2.92122	+	5.05970i	0.233139	+	0.403808i	0.958730	−	0.284318i	$-0.0917671\pi$
$157$	2.92122	+	5.05970i	0.233139	+	0.403808i	−0.725592	+	0.688126i	$0.758434\pi$
$158$	6.78649	−	3.91818i	0.539904	−	0.311714i
$159$	3.35852	−	10.6003i	0.266348	−	0.840656i
$160$	0.242128	−	0.419378i	0.0191419	−	0.0331547i
$161$		−	31.7019i		−	2.49846i
$162$	−1.61229	+	8.85441i	−0.126673	+	0.695668i
$163$		−	15.1340i		−	1.18538i	−0.805430	−	0.592691i	$-0.798065\pi$
$163$		−	15.1340i		−	1.18538i	0.805430	−	0.592691i	$-0.201935\pi$
$164$	−9.57301	−	5.52698i	−0.747527	−	0.431585i
$165$	0.813592	−	2.56788i	0.0633381	−	0.199909i
$166$	−2.93306	−	5.08022i	−0.227650	−	0.394301i
$167$	10.4155	−	6.01341i	0.805978	−	0.465331i	−0.0395794	−	0.999216i	$-0.512602\pi$
$167$	10.4155	−	6.01341i	0.805978	−	0.465331i	0.845557	+	0.533885i	$0.179268\pi$
$168$	5.90540	+	6.46270i	0.455611	+	0.498608i
$169$	−11.9565	+	5.10304i	−0.919734	+	0.392542i
$170$	−2.03506			−0.156082
$171$	5.54818	−	7.87673i	0.424280	−	0.602349i
$172$	9.46735			0.721879
$173$	−4.42932	+	7.67180i	−0.336755	+	0.583276i	−0.983820	−	0.179158i	$-0.942663\pi$
$173$	−4.42932	+	7.67180i	−0.336755	+	0.583276i	0.647066	+	0.762434i	$0.275996\pi$
$174$	1.71083	+	7.76835i	0.129698	+	0.588917i
$175$	−20.8596	+	12.0433i	−1.57684	+	0.910389i
$176$	2.78126	−	1.60576i	0.209646	−	0.121039i
$177$	−1.34970	−	6.12855i	−0.101449	−	0.460650i
$178$	4.21456	−	7.29984i	0.315895	−	0.547146i
$179$	10.3704			0.775121			0.387561	−	0.921844i	$-0.373318\pi$
$179$	10.3704			0.775121			0.387561	+	0.921844i	$0.373318\pi$
$180$	0.610289	+	1.31836i	0.0454883	+	0.0982650i
$181$	10.8407			0.805783			0.402892	−	0.915248i	$-0.368005\pi$
$181$	10.8407			0.805783			0.402892	+	0.915248i	$0.368005\pi$
$182$	13.6369	−	12.0889i	1.01084	−	0.896088i
$183$	−1.17039	−	1.28084i	−0.0865178	−	0.0946826i
$184$	5.43186	−	3.13608i	0.400442	−	0.231195i
$185$	0.504664	+	0.874103i	0.0371036	+	0.0642653i
$186$	−3.39190	+	10.7056i	−0.248706	+	0.784973i
$187$	−11.6881	−	6.74815i	−0.854721	−	0.493474i
$188$		−	5.28124i		−	0.385174i
$189$	−26.0528	+	3.31901i	−1.89506	+	0.241422i
$190$		−	1.55520i		−	0.112826i
$191$	−5.62900	+	9.74971i	−0.407300	+	0.705464i	−0.994586	−	0.103915i	$-0.966863\pi$
$191$	−5.62900	+	9.74971i	−0.407300	+	0.705464i	0.587286	+	0.809379i	$0.300196\pi$
$192$	−0.523143	+	1.65116i	−0.0377546	+	0.119162i
$193$	6.60401	−	3.81283i	0.475367	−	0.274453i	−0.243117	−	0.969997i	$-0.578170\pi$
$193$	6.60401	−	3.81283i	0.475367	−	0.274453i	0.718484	+	0.695544i	$0.244836\pi$
$194$	6.52525	+	11.3021i	0.468486	+	0.811441i
$195$	2.76323	−	1.22891i	0.197879	−	0.0880038i
$196$	−9.27337	+	16.0619i	−0.662383	+	1.14728i
$197$			24.5170i			1.74677i	0.487035	+	0.873383i	$0.338079\pi$
$197$			24.5170i			1.74677i	−0.487035	+	0.873383i	$0.661921\pi$
$198$	−0.866495	+	9.59554i	−0.0615791	+	0.681925i
$199$	−13.5310			−0.959187			−0.479593	−	0.877491i	$-0.659216\pi$
$199$	−13.5310			−0.959187			−0.479593	+	0.877491i	$0.659216\pi$
$200$	−4.12704	−	2.38275i	−0.291826	−	0.168486i
$201$	−0.403049	−	1.83012i	−0.0284289	−	0.129087i
$202$	5.92969	−	3.42351i	0.417212	−	0.240877i
$203$	−20.1025	+	11.6062i	−1.41092	+	0.814596i
$204$	7.10852	−	1.56552i	0.497696	−	0.109608i
$205$	2.67647	−	4.63579i	0.186933	−	0.323777i
$206$		−	3.55520i		−	0.247703i
$207$	−1.69228	+	18.7402i	−0.117621	+	1.30254i
$208$	3.42035	+	1.14069i	0.237159	+	0.0790929i
$209$	5.15696	−	8.93211i	0.356714	−	0.617847i
$210$	−3.12960	+	2.85972i	−0.215963	+	0.197340i
$211$	−11.9346	−	20.6713i	−0.821610	−	1.42307i	−0.904483	−	0.426511i	$-0.859743\pi$
$211$	−11.9346	−	20.6713i	−0.821610	−	1.42307i	0.0828724	−	0.996560i	$-0.473591\pi$
$212$	3.20995	+	5.55980i	0.220460	+	0.381849i
$213$	7.64554	+	2.42237i	0.523864	+	0.165978i
$214$	1.22449	+	0.706961i	0.0837045	+	0.0483268i
$215$			4.58462i			0.312668i
$216$	−3.14593	−	4.13559i	−0.214053	−	0.281391i
$217$	−32.7710			−2.22464
$218$	2.48763	−	4.30869i	0.168483	−	0.291822i
$219$	−0.537493	−	0.170296i	−0.0363204	−	0.0115075i
$220$	0.777601	+	1.34684i	0.0524258	+	0.0908042i
$221$	−3.03546	−	14.8450i	−0.204187	−	0.998583i
$222$	−2.43522	−	2.66504i	−0.163441	−	0.178866i
$223$	−11.1456	−	6.43490i	−0.746363	−	0.430913i	0.0780155	−	0.996952i	$-0.475142\pi$
$223$	−11.1456	−	6.43490i	−0.746363	−	0.430913i	−0.824378	+	0.566040i	$0.808475\pi$
$224$	−5.05438			−0.337710
$225$	12.9738	−	6.00577i	0.864922	−	0.400385i
$226$			13.0883i			0.870621i
$227$	−15.6362	−	9.02759i	−1.03781	−	0.599182i	−0.118600	−	0.992942i	$-0.537841\pi$
$227$	−15.6362	−	9.02759i	−1.03781	−	0.599182i	−0.919213	+	0.393760i	$0.871174\pi$
$228$	1.19637	+	5.43235i	0.0792317	+	0.359766i
$229$	−18.3370	+	10.5869i	−1.21174	+	0.699599i	−0.963138	−	0.269006i	$-0.913305\pi$
$229$	−18.3370	+	10.5869i	−1.21174	+	0.699599i	−0.248603	+	0.968606i	$0.579971\pi$
$230$	1.51867	+	2.63041i	0.100138	+	0.173444i
$231$	−27.4571	+	6.04691i	−1.80655	+	0.397858i
$232$	−3.97725	−	2.29627i	−0.261119	−	0.150757i
$233$	29.0610			1.90385			0.951923	−	0.306337i	$-0.0991033\pi$
$233$	29.0610			1.90385			0.951923	+	0.306337i	$0.0991033\pi$
$234$	−8.70666	+	6.41827i	−0.569172	+	0.419575i
$235$	2.55747			0.166831
$236$	3.13771	+	1.81156i	0.204247	+	0.117922i
$237$	−9.15580	−	10.0198i	−0.594733	−	0.650859i
$238$	10.6204	+	18.3951i	0.688418	+	1.19237i
$239$	6.29516	−	3.63451i	0.407200	−	0.235097i	−0.282386	−	0.959301i	$-0.591126\pi$
$239$	6.29516	−	3.63451i	0.407200	−	0.235097i	0.689586	+	0.724204i	$0.257793\pi$
$240$	−0.799583	−	0.253335i	−0.0516129	−	0.0163527i
$241$	15.5109	+	8.95521i	0.999144	+	0.576856i	0.907995	−	0.418981i	$-0.137613\pi$
$241$	15.5109	+	8.95521i	0.999144	+	0.576856i	0.0911491	+	0.995837i	$0.470946\pi$
$242$		−	0.686087i		−	0.0441034i
$243$	15.5780	−	0.571274i	0.999328	−	0.0366473i
$244$	1.00173			0.0641290
$245$	−7.77809	−	4.49068i	−0.496924	−	0.286899i
$246$	−5.78280	+	18.2518i	−0.368698	+	1.16369i
$247$	11.3446	−	2.31971i	0.721839	−	0.147600i
$248$	−3.24185	−	5.61504i	−0.205857	−	0.356556i
$249$	−7.50063	+	6.85383i	−0.475333	+	0.434344i
$250$	2.36450	−	4.09543i	0.149544	−	0.259018i
$251$	−3.84702			−0.242822			−0.121411	−	0.992602i	$-0.538742\pi$
$251$	−3.84702			−0.242822			−0.121411	+	0.992602i	$0.538742\pi$
$252$	8.73185	−	12.3966i	0.550055	−	0.780912i
$253$			20.1432i			1.26639i
$254$	−3.95167	−	2.28150i	−0.247950	−	0.143154i
$255$	0.758110	+	3.44234i	0.0474747	+	0.215568i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	7.38375	+	12.7890i	0.460586	+	0.797758i	0.998990	−	0.0449285i	$-0.0143060\pi$
$257$	7.38375	+	12.7890i	0.460586	+	0.797758i	−0.538404	+	0.842687i	$0.680973\pi$
$258$	−3.52682	−	16.0142i	−0.219570	−	0.996999i
$259$	5.26738	−	9.12337i	0.327299	−	0.566899i
$260$	−0.552388	+	1.65633i	−0.0342576	+	0.102721i
$261$	12.5030	−	5.78779i	0.773913	−	0.358255i
$262$		−	2.46946i		−	0.152564i
$263$	−4.38124	+	7.58853i	−0.270159	+	0.467929i	−0.968902	−	0.247443i	$-0.920410\pi$
$263$	−4.38124	+	7.58853i	−0.270159	+	0.467929i	0.698743	+	0.715372i	$0.253743\pi$
$264$	−3.75226	−	4.10637i	−0.230936	−	0.252729i
$265$	−2.69237	+	1.55444i	−0.165391	+	0.0954884i
$266$	−14.0576	+	8.11614i	−0.861924	+	0.497632i
$267$	−13.9178	−	4.40963i	−0.851756	−	0.269865i
$268$	0.936987	+	0.540970i	0.0572356	+	0.0330450i
$269$	−8.90736			−0.543091			−0.271546	−	0.962426i	$-0.587535\pi$
$269$	−8.90736			−0.543091			−0.271546	+	0.962426i	$0.587535\pi$
$270$	2.00269	−	1.52344i	0.121880	−	0.0927133i
$271$			3.58551i			0.217804i	0.994052	+	0.108902i	$0.0347335\pi$
$271$			3.58551i			0.217804i	−0.994052	+	0.108902i	$0.965266\pi$
$272$	−2.10123	+	3.63943i	−0.127406	+	0.220673i
$273$	−25.5286	−	18.5637i	−1.54506	−	1.12353i
$274$	9.80519	+	16.9831i	0.592353	+	1.02599i
$275$	13.2541	−	7.65226i	0.799253	−	0.461449i
$276$	−7.32823	−	8.01980i	−0.441108	−	0.482735i
$277$	7.43966	−	12.8859i	0.447006	−	0.774237i	−0.551183	−	0.834384i	$-0.685824\pi$
$277$	7.43966	−	12.8859i	0.447006	−	0.774237i	0.998190	+	0.0601468i	$0.0191569\pi$
$278$			0.387396i			0.0232345i
$279$	19.3723	+	1.74935i	1.15979	+	0.104731i
$280$		−	2.44761i		−	0.146273i
$281$	14.2995	+	8.25582i	0.853037	+	0.492501i	0.861674	−	0.507462i	$-0.169416\pi$
$281$	14.2995	+	8.25582i	0.853037	+	0.492501i	−0.00863764	+	0.999963i	$0.502749\pi$
$282$	−8.93330	+	1.96739i	−0.531970	+	0.117156i
$283$	0.267833	+	0.463900i	0.0159210	+	0.0275760i	0.873876	−	0.486149i	$-0.161599\pi$
$283$	0.267833	+	0.463900i	0.0159210	+	0.0275760i	−0.857955	+	0.513725i	$0.828265\pi$
$284$	−4.01005	+	2.31521i	−0.237953	+	0.137382i
$285$	−2.63065	+	0.579350i	−0.155826	+	0.0343177i
$286$	−8.66485	+	7.68122i	−0.512363	+	0.454200i
$287$	−55.8709			−3.29795
$288$	2.98784	+	0.269808i	0.176060	+	0.0158986i
$289$	0.660618			0.0388599
$290$	1.11198	−	1.92601i	0.0652978	−	0.113099i
$291$	16.6868	−	15.2479i	0.978199	−	0.893846i
$292$	0.281913	−	0.162762i	0.0164977	−	0.00952495i
$293$	−16.9651	+	9.79482i	−0.991113	+	0.572220i	−0.905607	−	0.424118i	$-0.860584\pi$
$293$	−16.9651	+	9.79482i	−0.991113	+	0.572220i	−0.0855065	+	0.996338i	$0.527251\pi$
$294$	30.6236	+	9.70258i	1.78600	+	0.565866i
$295$	−0.877257	+	1.51945i	−0.0510758	+	0.0884660i
$296$	2.08429			0.121147
$297$	16.5538	−	2.10888i	0.960549	−	0.122370i
$298$	9.45874			0.547930
$299$	−16.9226	+	15.0016i	−0.978659	+	0.867562i
$300$	−2.49303	+	7.86859i	−0.143935	+	0.454293i
$301$	41.4407	−	23.9258i	2.38860	−	1.37906i
$302$	0.665819	+	1.15323i	0.0383136	+	0.0663611i
$303$	−7.99988	−	8.75483i	−0.459581	−	0.502952i
$304$	−2.78126	−	1.60576i	−0.159516	−	0.0920969i
$305$			0.485092i			0.0277763i
$306$	−5.29619	−	11.4410i	−0.302763	−	0.654037i
$307$		−	1.26064i		−	0.0719485i	−0.999353	−	0.0359743i	$-0.988547\pi$
$307$		−	1.26064i		−	0.0719485i	0.999353	−	0.0359743i	$-0.0114534\pi$
$308$	8.11614	−	14.0576i	0.462460	−	0.801004i
$309$	−6.01368	+	1.32440i	−0.342106	+	0.0753424i
$310$	2.71912	−	1.56988i	0.154436	−	0.0891634i
$311$	8.79222	+	15.2286i	0.498561	+	0.863533i	0.999999	−	0.00166095i	$-0.000528697\pi$
$311$	8.79222	+	15.2286i	0.498561	+	0.863533i	−0.501438	+	0.865194i	$0.667195\pi$
$312$	0.655337	−	6.21052i	0.0371011	−	0.351601i
$313$	−0.102706	+	0.177891i	−0.00580526	+	0.0100550i	−0.868913	−	0.494964i	$-0.835181\pi$
$313$	−0.102706	+	0.177891i	−0.00580526	+	0.0100550i	0.863108	+	0.505019i	$0.168515\pi$
$314$			5.84243i			0.329708i
$315$	6.00312	+	4.22845i	0.338238	+	0.238246i
$316$	7.83637			0.440830
$317$	−15.6583	−	9.04030i	−0.879455	−	0.507754i	−0.00897641	−	0.999960i	$-0.502857\pi$
$317$	−15.6583	−	9.04030i	−0.879455	−	0.507754i	−0.870479	+	0.492206i	$0.836191\pi$
$318$	8.20870	−	7.50084i	0.460321	−	0.420626i
$319$	12.7731	−	7.37453i	0.715154	−	0.412894i
$320$	0.419378	−	0.242128i	0.0234439	−	0.0135354i
$321$	0.739682	−	2.33461i	0.0412850	−	0.130305i
$322$	15.8509	−	27.4546i	0.883339	−	1.52999i
$323$			13.4963i			0.750954i
$324$	−5.82348	+	6.86200i	−0.323527	+	0.381222i
$325$	16.2997	+	5.43597i	0.904144	+	0.301533i
$326$	7.56698	−	13.1064i	0.419096	−	0.725896i
$327$	−8.21492	−	2.60277i	−0.454286	−	0.143933i
$328$	−5.52698	−	9.57301i	−0.305176	−	0.528581i
$329$	−13.3467	−	23.1171i	−0.735827	−	1.27449i
$330$	1.98853	−	1.81706i	0.109465	−	0.100026i
$331$	3.63300	+	2.09751i	0.199688	+	0.115290i	0.596510	−	0.802606i	$-0.296554\pi$
$331$	3.63300	+	2.09751i	0.199688	+	0.115290i	−0.396822	+	0.917896i	$0.629887\pi$
$332$		−	5.86613i		−	0.321946i
$333$	−3.60077	+	5.11201i	−0.197321	+	0.280136i
$334$	12.0268			0.658078
$335$	−0.261968	+	0.453742i	−0.0143128	+	0.0247906i
$336$	1.88288	+	8.54956i	0.102719	+	0.466417i
$337$	−6.88041	−	11.9172i	−0.374800	−	0.649172i	0.615497	−	0.788139i	$-0.288955\pi$
$337$	−6.88041	−	11.9172i	−0.374800	−	0.649172i	−0.990297	+	0.138967i	$0.955622\pi$
$338$	−12.9062	−	1.55891i	−0.702004	−	0.0847935i
$339$	22.1391	−	4.87571i	1.20243	−	0.264812i
$340$	−1.76242	−	1.01753i	−0.0955805	−	0.0551834i
$341$	20.8226			1.12761
$342$	8.74323	−	4.04736i	0.472780	−	0.218856i
$343$			58.3615i			3.15123i
$344$	8.19896	+	4.73367i	0.442059	+	0.255223i
$345$	3.88364	−	3.54874i	0.209088	−	0.191058i
$346$	−7.67180	+	4.42932i	−0.412439	+	0.238122i
$347$	11.9351	+	20.6722i	0.640710	+	1.10974i	0.985275	+	0.170979i	$0.0546931\pi$
$347$	11.9351	+	20.6722i	0.640710	+	1.10974i	−0.344565	+	0.938763i	$0.611974\pi$
$348$	−2.40255	+	7.58300i	−0.128790	+	0.406491i
$349$	−16.7557	−	9.67391i	−0.896913	−	0.517833i	−0.0207153	−	0.999785i	$-0.506594\pi$
$349$	−16.7557	−	9.67391i	−0.896913	−	0.517833i	−0.876197	+	0.481953i	$0.839928\pi$
$350$	−24.0866			−1.28748
$351$	14.1000	+	12.3365i	0.752604	+	0.658473i
$352$	3.21153			0.171175
$353$	−24.0606	−	13.8914i	−1.28062	−	0.739365i	−0.303656	−	0.952782i	$-0.598207\pi$
$353$	−24.0606	−	13.8914i	−1.28062	−	0.739365i	−0.976961	+	0.213417i	$0.931541\pi$
$354$	1.89540	−	5.98233i	0.100740	−	0.317957i
$355$	−1.12115	−	1.94189i	−0.0595046	−	0.103065i
$356$	7.29984	−	4.21456i	0.386891	−	0.223371i
$357$	27.1592	−	24.8172i	1.43742	−	1.31346i
$358$	8.98104	+	5.18521i	0.474663	+	0.274047i
$359$		−	23.8304i		−	1.25772i	−0.777517	−	0.628861i	$-0.783521\pi$
$359$		−	23.8304i		−	1.25772i	0.777517	−	0.628861i	$-0.216479\pi$
$360$	−0.130656	+	1.44688i	−0.00688617	+	0.0762573i
$361$	8.68609			0.457162
$362$	9.38833	+	5.42035i	0.493440	+	0.284887i
$363$	−1.16053	+	0.255584i	−0.0609119	+	0.0134147i
$364$	17.8544	−	3.65081i	0.935824	−	0.191355i
$365$	0.0788187	+	0.136518i	0.00412556	+	0.00714568i
$366$	−0.373168	−	1.69444i	−0.0195058	−	0.0885697i
$367$	5.04643	−	8.74067i	0.263421	−	0.456259i	−0.703728	−	0.710470i	$-0.748482\pi$
$367$	5.04643	−	8.74067i	0.263421	−	0.456259i	0.967149	+	0.254211i	$0.0818157\pi$
$368$	6.27217			0.326959
$369$	33.0275	+	2.98244i	1.71934	+	0.155260i
$370$			1.00933i			0.0524724i
$371$	28.1013	+	16.2243i	1.45895	+	0.842324i
$372$	−8.29027	+	7.57538i	−0.429830	+	0.392765i
$373$	4.27370	+	7.40227i	0.221284	+	0.383275i	0.955198	−	0.295967i	$-0.0956419\pi$
$373$	4.27370	+	7.40227i	0.221284	+	0.383275i	−0.733914	+	0.679242i	$0.762309\pi$
$374$	−6.74815	−	11.6881i	−0.348938	−	0.604379i
$375$	−7.80832	−	2.47394i	−0.403220	−	0.127754i
$376$	2.64062	−	4.57369i	0.136180	−	0.235870i
$377$	15.7081	+	5.23868i	0.809008	+	0.269806i
$378$	−24.2218	−	10.1520i	−1.24584	−	0.522164i
$379$			30.7125i			1.57760i	0.614653	+	0.788798i	$0.289296\pi$
$379$			30.7125i			1.57760i	−0.614653	+	0.788798i	$0.710704\pi$
$380$	0.777601	−	1.34684i	0.0398901	−	0.0690916i
$381$	−2.38710	+	7.53423i	−0.122295	+	0.385990i
$382$	−9.74971	+	5.62900i	−0.498839	+	0.288005i
$383$	−2.49892	+	1.44275i	−0.127689	+	0.0737212i	−0.562484	−	0.826808i	$-0.690154\pi$
$383$	−2.49892	+	1.44275i	−0.127689	+	0.0737212i	0.434795	+	0.900529i	$0.356821\pi$
$384$	−1.27863	+	1.16837i	−0.0652500	+	0.0596233i
$385$	6.80746	+	3.93029i	0.346940	+	0.200306i
$386$	7.62566			0.388136
$387$	−25.7744	+	11.9313i	−1.31019	+	0.606504i
$388$			13.0505i			0.662539i
$389$	5.94776	−	10.3018i	0.301564	−	0.522323i	−0.674927	−	0.737885i	$-0.735825\pi$
$389$	5.94776	−	10.3018i	0.301564	−	0.522323i	0.976490	+	0.215561i	$0.0691581\pi$
$390$	3.00748	+	0.317351i	0.152290	+	0.0160697i
$391$	−13.1792	−	22.8271i	−0.666503	−	1.15442i
$392$	−16.0619	+	9.27337i	−0.811250	+	0.468376i
$393$	−4.17714	+	0.919935i	−0.210709	+	0.0464046i
$394$	−12.2585	+	21.2324i	−0.617575	+	1.06967i
$395$			3.79481i			0.190937i
$396$	−5.54818	+	7.87673i	−0.278806	+	0.395821i
$397$		−	23.8021i		−	1.19459i	−0.802020	−	0.597297i	$-0.796241\pi$
$397$		−	23.8021i		−	1.19459i	0.802020	−	0.597297i	$-0.203759\pi$
$398$	−11.7182	−	6.76550i	−0.587379	−	0.339124i
$399$	18.9654	+	20.7551i	0.949455	+	1.03906i
$400$	−2.38275	−	4.12704i	−0.119137	−	0.206352i
$401$	−7.79168	+	4.49853i	−0.389098	+	0.224646i	−0.681769	−	0.731567i	$-0.738789\pi$
$401$	−7.79168	+	4.49853i	−0.389098	+	0.224646i	0.292671	+	0.956213i	$0.405456\pi$
$402$	0.566009	−	1.78645i	0.0282300	−	0.0891002i
$403$	15.5075	+	17.4933i	0.772483	+	0.871404i
$404$	6.84702			0.340652
$405$	−3.32296	−	2.82006i	−0.165119	−	0.140130i
$406$	−23.2124			−1.15201
$407$	−3.34687	+	5.79695i	−0.165898	+	0.287344i
$408$	6.93891	+	2.19848i	0.343527	+	0.108841i
$409$	−27.8344	+	16.0702i	−1.37632	+	0.794620i	−0.991715	−	0.128460i	$-0.958997\pi$
$409$	−27.8344	+	16.0702i	−1.37632	+	0.794620i	−0.384608	+	0.923080i	$0.625663\pi$
$410$	4.63579	−	2.67647i	0.228945	−	0.132182i
$411$	25.0745	−	22.9122i	1.23683	−	1.13018i
$412$	1.77760	−	3.07889i	0.0875761	−	0.151686i
$413$	18.3126			0.901103
$414$	−10.8357	+	15.3834i	−0.532545	+	0.756052i
$415$	2.84071			0.139445
$416$	2.39177	+	2.69805i	0.117266	+	0.132283i
$417$	0.655287	−	0.144314i	0.0320895	−	0.00706711i
$418$	8.93211	−	5.15696i	0.436884	−	0.252235i
$419$	−1.68689	−	2.92177i	−0.0824098	−	0.142738i	0.821875	−	0.569668i	$-0.192928\pi$
$419$	−1.68689	−	2.92177i	−0.0824098	−	0.142738i	−0.904285	+	0.426930i	$0.859595\pi$
$420$	−4.14017	+	0.911795i	−0.202020	+	0.0444910i
$421$	−2.26626	−	1.30842i	−0.110451	−	0.0637687i	0.443757	−	0.896147i	$-0.353645\pi$
$421$	−2.26626	−	1.30842i	−0.110451	−	0.0637687i	−0.554208	+	0.832378i	$0.686979\pi$
$422$		−	23.8692i		−	1.16193i
$423$	6.65574	+	14.3779i	0.323613	+	0.699078i
$424$			6.41990i			0.311778i
$425$	−10.0134	+	17.3437i	−0.485721	+	0.841293i
$426$	5.41005	+	5.92060i	0.262118	+	0.286854i
$427$	4.38478	−	2.53155i	0.212194	−	0.122510i
$428$	0.706961	+	1.22449i	0.0341722	+	0.0591880i
$429$	16.2208	+	11.7953i	0.783147	+	0.569482i
$430$	−2.29231	+	3.97040i	−0.110545	+	0.191470i
$431$		−	1.25113i		−	0.0602647i	−0.999546	−	0.0301324i	$-0.990407\pi$
$431$		−	1.25113i		−	0.0602647i	0.999546	−	0.0301324i	$-0.00959288\pi$
$432$	−0.656660	−	5.15449i	−0.0315936	−	0.247996i
$433$	−4.77117			−0.229288			−0.114644	−	0.993407i	$-0.536573\pi$
$433$	−4.77117			−0.229288			−0.114644	+	0.993407i	$0.536573\pi$
$434$	−28.3806	−	16.3855i	−1.36231	−	0.786530i
$435$	−3.67211	−	1.16345i	−0.176064	−	0.0557831i
$436$	4.30869	−	2.48763i	0.206349	−	0.119136i
$437$	17.4446	−	10.0716i	0.834486	−	0.481791i
$438$	−0.380335	−	0.416227i	−0.0181731	−	0.0198881i
$439$	−16.8509	+	29.1867i	−0.804252	+	1.39300i	0.112543	+	0.993647i	$0.464100\pi$
$439$	−16.8509	+	29.1867i	−0.804252	+	1.39300i	−0.916795	+	0.399358i	$0.869233\pi$
$440$			1.55520i			0.0741413i
$441$	5.00405	−	55.4147i	0.238288	−	2.63880i
$442$	4.79371	−	14.3739i	0.228014	−	0.683696i
$443$	2.68876	−	4.65706i	0.127747	−	0.221264i	−0.795057	−	0.606535i	$-0.792559\pi$
$443$	2.68876	−	4.65706i	0.127747	−	0.221264i	0.922803	+	0.385272i	$0.125892\pi$
$444$	−0.776447	−	3.52560i	−0.0368485	−	0.167318i
$445$	2.04093	+	3.53499i	0.0967492	+	0.167575i
$446$	−6.43490	−	11.1456i	−0.304701	−	0.527758i
$447$	−3.52361	−	15.9996i	−0.166661	−	0.756756i
$448$	−4.37722	−	2.52719i	−0.206804	−	0.119398i
$449$			16.7813i			0.791958i	0.918260	+	0.395979i	$0.129595\pi$
$449$			16.7813i			0.791958i	−0.918260	+	0.395979i	$0.870405\pi$
$450$	14.2386	+	1.28577i	0.671212	+	0.0606116i
$451$	35.5001			1.67163
$452$	−6.54415	+	11.3348i	−0.307811	+	0.533145i
$453$	1.70268	−	1.55585i	0.0799988	−	0.0731002i
$454$	−9.02759	−	15.6362i	−0.423686	−	0.733845i
$455$	1.76793	+	8.64609i	0.0828817	+	0.405335i
$456$	−1.68009	+	5.30274i	−0.0786773	+	0.248324i
$457$	−20.5067	−	11.8396i	−0.959263	−	0.553831i	−0.0633172	−	0.997993i	$-0.520168\pi$
$457$	−20.5067	−	11.8396i	−0.959263	−	0.553831i	−0.895946	+	0.444162i	$0.853501\pi$
$458$	−21.1737			−0.989383
$459$	−17.3796	+	13.2206i	−0.811212	+	0.617086i
$460$			3.03733i			0.141616i
$461$	−29.8451	−	17.2311i	−1.39003	−	0.802533i	−0.396709	−	0.917944i	$-0.629848\pi$
$461$	−29.8451	−	17.2311i	−1.39003	−	0.802533i	−0.993318	+	0.115412i	$0.963181\pi$
$462$	−26.8020	−	8.49179i	−1.24694	−	0.395074i
$463$	19.4659	−	11.2386i	0.904657	−	0.522304i	0.0259487	−	0.999663i	$-0.491739\pi$
$463$	19.4659	−	11.2386i	0.904657	−	0.522304i	0.878708	+	0.477359i	$0.158406\pi$
$464$	−2.29627	−	3.97725i	−0.106602	−	0.184639i
$465$	−3.66842	−	4.01461i	−0.170119	−	0.186173i
$466$	25.1675	+	14.5305i	1.16586	+	0.673111i
$467$	−4.43632			−0.205288			−0.102644	−	0.994718i	$-0.532730\pi$
$467$	−4.43632			−0.205288			−0.102644	+	0.994718i	$0.532730\pi$
$468$	−10.7493	+	1.20506i	−0.496887	+	0.0557037i
$469$	5.46853			0.252513
$470$	2.21484	+	1.27874i	0.102163	+	0.0589837i
$471$	9.88257	−	2.17645i	0.455365	−	0.100285i
$472$	1.81156	+	3.13771i	0.0833836	+	0.144425i
$473$	−26.3312	+	15.2023i	−1.21071	+	0.699004i
$474$	−2.91924	−	13.2553i	−0.134085	−	0.608838i
$475$	−13.2541	−	7.65226i	−0.608140	−	0.351110i
$476$			21.2408i			0.973570i
$477$	−15.7457	−	11.0909i	−0.720948	−	0.507818i
$478$	7.26902			0.332477
$479$	10.2334	+	5.90827i	0.467577	+	0.269956i	0.715225	−	0.698894i	$-0.246324\pi$
$479$	10.2334	+	5.90827i	0.467577	+	0.269956i	−0.247648	+	0.968850i	$0.579658\pi$
$480$	−0.565792	−	0.619186i	−0.0258247	−	0.0282618i
$481$	−7.36265	+	1.50549i	−0.335708	+	0.0686446i
$482$	8.95521	+	15.5109i	0.407899	+	0.706501i
$483$	−52.3448	−	16.5846i	−2.38177	−	0.754626i
$484$	0.343044	−	0.594169i	0.0155929	−	0.0270077i
$485$	−6.31979			−0.286967
$486$	13.7766	+	7.29425i	0.624918	+	0.330874i
$487$		−	25.8373i		−	1.17080i	−0.810745	−	0.585400i	$-0.800938\pi$
$487$		−	25.8373i		−	1.17080i	0.810745	−	0.585400i	$-0.199062\pi$
$488$	0.867521	+	0.500864i	0.0392708	+	0.0226730i
$489$	−24.9885	−	7.91721i	−1.13002	−	0.358029i
$490$	−4.49068	−	7.77809i	−0.202868	−	0.351378i
$491$	−5.59995	−	9.69940i	−0.252722	−	0.437728i	0.711552	−	0.702633i	$-0.247993\pi$
$491$	−5.59995	−	9.69940i	−0.252722	−	0.437728i	−0.964274	+	0.264906i	$0.914659\pi$
$492$	−14.1340	+	12.9152i	−0.637208	+	0.582260i
$493$	−9.64996	+	16.7142i	−0.434612	+	0.752771i
$494$	10.9846	+	3.66337i	0.494219	+	0.164823i
$495$	−3.81436	−	2.68674i	−0.171443	−	0.120760i
$496$		−	6.48369i		−	0.291126i
$497$	−11.7019	+	20.2683i	−0.524903	+	0.909159i
$498$	−9.92265	+	2.18527i	−0.444644	+	0.0979245i
$499$	−13.3884	+	7.72982i	−0.599349	+	0.346034i	−0.768786	−	0.639507i	$-0.779139\pi$
$499$	−13.3884	+	7.72982i	−0.599349	+	0.346034i	0.169436	+	0.985541i	$0.445805\pi$
$500$	4.09543	−	2.36450i	0.183153	−	0.105744i
$501$	−4.48028	−	20.3435i	−0.200164	−	0.908883i
$502$	−3.33162	−	1.92351i	−0.148697	−	0.0858505i
$503$	−6.00330			−0.267674			−0.133837	−	0.991003i	$-0.542730\pi$
$503$	−6.00330			−0.267674			−0.133837	+	0.991003i	$0.542730\pi$
$504$	13.7603	−	6.36984i	0.612932	−	0.283735i
$505$			3.31571i			0.147547i
$506$	−10.0716	+	17.4446i	−0.447738	+	0.775505i
$507$	2.17095	+	22.4118i	0.0964153	+	0.995341i
$508$	−2.28150	−	3.95167i	−0.101225	−	0.175327i
$509$	18.6801	−	10.7849i	0.827979	−	0.478034i	−0.0251810	−	0.999683i	$-0.508016\pi$
$509$	18.6801	−	10.7849i	0.827979	−	0.478034i	0.853160	+	0.521649i	$0.174683\pi$
$510$	−1.06463	+	3.36021i	−0.0471425	+	0.148793i
$511$	0.822663	−	1.42489i	0.0363925	−	0.0630336i
$512$		−	1.00000i		−	0.0441942i
$513$	−10.1032	−	13.2816i	−0.446069	−	0.586396i
$514$			14.7675i			0.651367i
$515$	1.49097	+	0.860814i	0.0657001	+	0.0379320i
$516$	4.95277	−	15.6321i	0.218034	−	0.688164i
$517$	8.48043	+	14.6885i	0.372969	+	0.646001i
$518$	9.12337	−	5.26738i	0.400858	−	0.231435i
$519$	10.3502	+	11.3269i	0.454323	+	0.497198i
$520$	−1.30655	+	1.15823i	−0.0572958	+	0.0507916i
$521$	24.0543			1.05384			0.526918	−	0.849916i	$-0.323347\pi$
$521$	24.0543			1.05384			0.526918	+	0.849916i	$0.323347\pi$
$522$	13.7218	+	1.23910i	0.600586	+	0.0542340i
$523$	−10.8449			−0.474215			−0.237107	−	0.971483i	$-0.576199\pi$
$523$	−10.8449			−0.474215			−0.237107	+	0.971483i	$0.576199\pi$
$524$	1.23473	−	2.13862i	0.0539395	−	0.0934260i
$525$	8.97285	+	40.7429i	0.391607	+	1.77817i
$526$	−7.58853	+	4.38124i	−0.330876	+	0.191031i
$527$	−23.5970	+	13.6237i	−1.02790	+	0.593458i
$528$	−1.19637	−	5.43235i	−0.0520654	−	0.236413i
$529$	−8.17003	+	14.1509i	−0.355219	+	0.615257i
$530$	−3.10888			−0.135041
$531$	−10.8253	−	0.977543i	−0.469777	−	0.0424218i
$532$	−16.2323			−0.703758
$533$	26.4385	+	29.8241i	1.14518	+	1.29183i
$534$	−9.84836	−	10.7778i	−0.426180	−	0.466399i
$535$	−0.592967	+	0.342350i	−0.0256362	+	0.0148011i
$536$	0.540970	+	0.936987i	0.0233663	+	0.0404717i
$537$	5.42520	−	17.1232i	0.234115	−	0.738920i
$538$	−7.71400	−	4.45368i	−0.332574	−	0.192012i
$539$		−	59.5633i		−	2.56558i
$540$	2.49609	−	0.317991i	0.107415	−	0.0136842i
$541$			12.2998i			0.528808i	0.964412	+	0.264404i	$0.0851753\pi$
$541$			12.2998i			0.528808i	−0.964412	+	0.264404i	$0.914825\pi$
$542$	−1.79275	+	3.10514i	−0.0770054	+	0.133377i
$543$	5.67123	−	17.8997i	0.243376	−	0.768150i
$544$	−3.63943	+	2.10123i	−0.156039	+	0.0900894i
$545$	1.20465	+	2.08651i	0.0516014	+	0.0893763i
$546$	−12.8266	−	28.8410i	−0.548928	−	1.23428i
$547$	10.3452	−	17.9183i	0.442327	−	0.766133i	−0.555534	−	0.831493i	$-0.687486\pi$
$547$	10.3452	−	17.9183i	0.442327	−	0.766133i	0.997862	+	0.0653602i	$0.0208196\pi$
$548$			19.6104i			0.837714i
$549$	−2.72715	+	1.26244i	−0.116392	+	0.0538795i
$550$	15.3045			0.652587
$551$	−12.7731	−	7.37453i	−0.544151	−	0.314165i
$552$	−2.33653	−	10.6095i	−0.0994495	−	0.451569i
$553$	34.3015	−	19.8040i	1.45865	−	0.842151i
$554$	12.8859	−	7.43966i	0.547468	−	0.316081i
$555$	1.70729	−	0.375999i	0.0724706	−	0.0159603i
$556$	−0.193698	+	0.335495i	−0.00821463	+	0.0142282i
$557$			14.2838i			0.605226i	0.953114	+	0.302613i	$0.0978589\pi$
$557$			14.2838i			0.605226i	−0.953114	+	0.302613i	$0.902141\pi$
$558$	15.9022	+	11.2011i	0.673193	+	0.474181i
$559$	−32.3817	−	10.7993i	−1.36960	−	0.456764i
$560$	1.22381	−	2.11969i	0.0517152	−	0.0895734i
$561$	−17.2568	+	15.7687i	−0.728584	+	0.665756i
$562$	8.25582	+	14.2995i	0.348251	+	0.603188i
$563$	17.9673	+	31.1203i	0.757231	+	1.31156i	0.944257	+	0.329208i	$0.106782\pi$
$563$	17.9673	+	31.1203i	0.757231	+	1.31156i	−0.187026	+	0.982355i	$0.559885\pi$
$564$	−8.72016	−	2.76284i	−0.367185	−	0.116337i
$565$	−5.48895	−	3.16905i	−0.230922	−	0.133323i
$566$			0.535666i			0.0225157i
$567$	−8.14910	+	44.7535i	−0.342230	+	1.87947i
$568$	−4.63041			−0.194288
$569$	18.5315	−	32.0976i	0.776882	−	1.34560i	−0.156848	−	0.987623i	$-0.550133\pi$
$569$	18.5315	−	32.0976i	0.776882	−	1.34560i	0.933730	−	0.357977i	$-0.116533\pi$
$570$	−2.56788	−	0.813592i	−0.107557	−	0.0340776i
$571$	23.1732	+	40.1372i	0.969769	+	1.67969i	0.696217	+	0.717831i	$0.254865\pi$
$571$	23.1732	+	40.1372i	0.969769	+	1.67969i	0.273551	+	0.961857i	$0.411802\pi$
$572$	−11.3446	+	2.31971i	−0.474341	+	0.0969919i
$573$	13.1535	+	14.3949i	0.549497	+	0.601354i
$574$	−48.3856	−	27.9354i	−2.01958	−	1.16600i
$575$	29.8900			1.24650
$576$	2.45264	+	1.72758i	0.102193	+	0.0719826i
$577$			31.4447i			1.30906i	0.756036	+	0.654530i	$0.227134\pi$
$577$			31.4447i			1.30906i	−0.756036	+	0.654530i	$0.772866\pi$
$578$	0.572112	+	0.330309i	0.0237967	+	0.0137390i
$579$	−2.84074	−	12.8989i	−0.118057	−	0.536061i
$580$	1.92601	−	1.11198i	0.0799731	−	0.0461725i
$581$	−14.8248	−	25.6773i	−0.615037	−	1.06527i
$582$	22.0751	−	4.86163i	0.915044	−	0.201521i
$583$	−17.8555	−	10.3088i	−0.739497	−	0.426949i
$584$	0.325525			0.0134703
$585$	−0.583555	−	5.20542i	−0.0241270	−	0.215218i
$586$	−19.5896			−0.809241
$587$	27.0638	+	15.6253i	1.11704	+	0.644924i	0.940644	−	0.339395i	$-0.110222\pi$
$587$	27.0638	+	15.6253i	1.11704	+	0.644924i	0.176397	+	0.984319i	$0.443556\pi$
$588$	21.6695	+	23.7145i	0.893635	+	0.977968i
$589$	−10.4113	−	18.0329i	−0.428989	−	0.743031i
$590$	−1.51945	+	0.877257i	−0.0625549	+	0.0361161i
$591$	40.4815	+	12.8259i	1.66519	+	0.527587i
$592$	1.80504	+	1.04214i	0.0741868	+	0.0428318i
$593$		−	26.3978i		−	1.08403i	−0.840370	−	0.542013i	$-0.817662\pi$
$593$		−	26.3978i		−	1.08403i	0.840370	−	0.542013i	$-0.182338\pi$
$594$	15.3905	+	6.45055i	0.631478	+	0.264669i
$595$	−10.2860			−0.421684
$596$	8.19151	+	4.72937i	0.335537	+	0.193723i
$597$	−7.07864	+	22.3418i	−0.289709	+	0.914389i
$598$	−22.1562	+	4.53043i	−0.906033	+	0.185263i
$599$	3.40524	+	5.89806i	0.139135	+	0.240988i	0.927169	−	0.374643i	$-0.122235\pi$
$599$	3.40524	+	5.89806i	0.139135	+	0.240988i	−0.788035	+	0.615631i	$0.788901\pi$
$600$	−6.09332	+	5.56788i	−0.248759	+	0.227308i
$601$	−4.82516	+	8.35742i	−0.196822	+	0.340906i	−0.947496	−	0.319766i	$-0.896396\pi$
$601$	−4.82516	+	8.35742i	−0.196822	+	0.340906i	0.750674	+	0.660673i	$0.229729\pi$
$602$	47.8516			1.95028
$603$	−3.23267	−	0.291916i	−0.131644	−	0.0118877i
$604$			1.33164i			0.0541836i
$605$	0.287730	+	0.166121i	0.0116979	+	0.00675377i
$606$	−2.55068	−	11.5818i	−0.103614	−	0.470480i
$607$	−13.7896	−	23.8842i	−0.559702	−	0.969432i	−0.997521	−	0.0703688i	$-0.977582\pi$
$607$	−13.7896	−	23.8842i	−0.559702	−	0.969432i	0.437819	−	0.899063i	$-0.355751\pi$
$608$	−1.60576	−	2.78126i	−0.0651223	−	0.112795i
$609$	8.64718	+	39.2642i	0.350402	+	1.59106i
$610$	−0.242546	+	0.420102i	−0.00982041	+	0.0170094i
$611$	−6.02428	+	18.0637i	−0.243716	+	0.730779i
$612$	1.13385	−	12.5563i	0.0458333	−	0.507557i
$613$		−	16.0314i		−	0.647502i	−0.946142	−	0.323751i	$-0.895056\pi$
$613$		−	16.0314i		−	0.647502i	0.946142	−	0.323751i	$-0.104944\pi$
$614$	0.630320	−	1.09175i	0.0254377	−	0.0440593i
$615$	−6.25424	−	6.84446i	−0.252195	−	0.275995i
$616$	14.0576	−	8.11614i	0.566395	−	0.327009i
$617$	11.4362	−	6.60269i	0.460404	−	0.265814i	−0.251810	−	0.967777i	$-0.581026\pi$
$617$	11.4362	−	6.60269i	0.460404	−	0.265814i	0.712214	+	0.701962i	$0.247693\pi$
$618$	−5.87020	−	1.85988i	−0.236134	−	0.0748152i
$619$	1.53649	+	0.887091i	0.0617566	+	0.0356552i	0.530560	−	0.847647i	$-0.321982\pi$
$619$	1.53649	+	0.887091i	0.0617566	+	0.0356552i	−0.468804	+	0.883302i	$0.655315\pi$
$620$	3.13977			0.126096
$621$	30.0578	+	12.5980i	1.20618	+	0.505542i
$622$			17.5844i			0.705072i
$623$	21.3020	−	36.8961i	0.853446	−	1.47821i
$624$	3.67280	−	5.05080i	0.147030	−	0.202194i
$625$	−10.7687	−	18.6520i	−0.430749	−	0.746079i
$626$	−0.177891	+	0.102706i	−0.00710997	+	0.00410494i
$627$	−12.0505	−	13.1877i	−0.481251	−	0.526667i
$628$	−2.92122	+	5.05970i	−0.116569	+	0.201904i
$629$		−	8.75911i		−	0.349249i
$630$	3.08463	+	6.66351i	0.122895	+	0.265480i
$631$		−	30.2211i		−	1.20308i	−0.798841	−	0.601542i	$-0.794553\pi$
$631$		−	30.2211i		−	1.20308i	0.798841	−	0.601542i	$-0.205447\pi$
$632$	6.78649	+	3.91818i	0.269952	+	0.155857i
$633$	−40.3751	+	8.89184i	−1.60476	+	0.353419i
$634$	−9.04030	−	15.6583i	−0.359036	−	0.621869i
$635$	1.91362	−	1.10483i	0.0759397	−	0.0438438i
$636$	10.8594	−	2.39157i	0.430602	−	0.0948319i
$637$	50.0399	−	44.3594i	1.98265	−	1.75759i
$638$	14.7491			0.583921
$639$	7.99942	−	11.3568i	0.316452	−	0.449266i
$640$	0.484256			0.0191419
$641$	0.301673	−	0.522512i	0.0119154	−	0.0206380i	−0.860006	−	0.510284i	$-0.829540\pi$
$641$	0.301673	−	0.522512i	0.0119154	−	0.0206380i	0.871922	+	0.489646i	$0.162874\pi$
$642$	1.80789	−	1.65199i	0.0713516	−	0.0651988i
$643$	27.0250	−	15.6029i	1.06576	−	0.615317i	0.138740	−	0.990329i	$-0.455695\pi$
$643$	27.0250	−	15.6029i	1.06576	−	0.615317i	0.927020	+	0.375012i	$0.122361\pi$
$644$	27.4546	−	15.8509i	1.08186	−	0.624615i
$645$	7.56993	+	2.39841i	0.298066	+	0.0944373i
$646$	−6.74815	+	11.6881i	−0.265502	+	0.459864i
$647$	−48.8937			−1.92221			−0.961105	−	0.276182i	$-0.910931\pi$
$647$	−48.8937			−1.92221			−0.961105	+	0.276182i	$0.910931\pi$
$648$	−8.47428	+	3.03092i	−0.332901	+	0.119066i
$649$	−11.6357			−0.456742
$650$	11.3980	+	12.8575i	0.447064	+	0.504314i
$651$	−17.1439	+	54.1102i	−0.671923	+	2.12074i
$652$	13.1064	−	7.56698i	0.513286	−	0.296346i
$653$	−19.1944	−	33.2457i	−0.751135	−	1.30100i	−0.947273	−	0.320427i	$-0.896173\pi$
$653$	−19.1944	−	33.2457i	−0.751135	−	1.30100i	0.196138	−	0.980576i	$-0.437160\pi$
$654$	−5.81295	−	6.36152i	−0.227304	−	0.248755i
$655$	1.03564	+	0.597926i	0.0404658	+	0.0233629i
$656$		−	11.0540i		−	0.431585i
$657$	−0.562371	+	0.798397i	−0.0219402	+	0.0311484i
$658$		−	26.6934i		−	1.04062i
$659$	20.9568	−	36.2983i	0.816362	−	1.41398i	−0.0919840	−	0.995760i	$-0.529321\pi$
$659$	20.9568	−	36.2983i	0.816362	−	1.41398i	0.908346	−	0.418220i	$-0.137346\pi$
$660$	2.63065	−	0.579350i	0.102398	−	0.0225512i
$661$	10.5208	−	6.07418i	0.409211	−	0.236258i	−0.281240	−	0.959638i	$-0.590746\pi$
$661$	10.5208	−	6.07418i	0.409211	−	0.236258i	0.690451	+	0.723379i	$0.257412\pi$
$662$	2.09751	+	3.63300i	0.0815221	+	0.141200i
$663$	−26.0994	−	2.75402i	−1.01362	−	0.106957i
$664$	2.93306	−	5.08022i	0.113825	−	0.197151i
$665$		−	7.86058i		−	0.304820i
$666$	−5.67437	+	2.62674i	−0.219877	+	0.101784i
$667$	28.8051			1.11534
$668$	10.4155	+	6.01341i	0.402989	+	0.232666i
$669$	−16.4558	+	15.0367i	−0.636216	+	0.581353i
$670$	−0.453742	+	0.261968i	−0.0175296	+	0.0101207i
$671$	−2.78607	+	1.60854i	−0.107555	+	0.0620969i
$672$	−2.64416	+	8.34557i	−0.102001	+	0.321938i
$673$	−18.3252	+	31.7403i	−0.706386	+	1.22350i	0.259803	+	0.965662i	$0.416342\pi$
$673$	−18.3252	+	31.7403i	−0.706386	+	1.22350i	−0.966189	+	0.257835i	$0.916991\pi$
$674$		−	13.7608i		−	0.530047i
$675$	−3.12931	−	24.5637i	−0.120447	−	0.945458i
$676$	−10.3976	−	7.80315i	−0.399909	−	0.300121i
$677$	−19.2964	+	33.4223i	−0.741620	+	1.28452i	0.210138	+	0.977672i	$0.432609\pi$
$677$	−19.2964	+	33.4223i	−0.741620	+	1.28452i	−0.951757	+	0.306851i	$0.900725\pi$
$678$	21.6109	+	6.84705i	0.829960	+	0.262959i
$679$	32.9811	+	57.1249i	1.26570	+	2.19225i
$680$	−1.01753	−	1.76242i	−0.0390206	−	0.0675856i
$681$	−23.0860	+	21.0952i	−0.884656	+	0.808369i
$682$	18.0329	+	10.4113i	0.690514	+	0.398669i
$683$			31.4038i			1.20163i	0.799387	+	0.600816i	$0.205158\pi$
$683$			31.4038i			1.20163i	−0.799387	+	0.600816i	$0.794842\pi$
$684$	9.59554	+	0.866495i	0.366895	+	0.0331313i
$685$	−9.49644			−0.362840
$686$	−29.1808	+	50.5426i	−1.11413	+	1.92972i
$687$	7.88772	+	35.8157i	0.300935	+	1.36645i
$688$	4.73367	+	8.19896i	0.180470	+	0.312583i
$689$	−4.63714	−	22.6780i	−0.176661	−	0.863965i
$690$	5.13770	−	1.13148i	0.195589	−	0.0430747i
$691$	−16.6786	−	9.62941i	−0.634485	−	0.366320i	0.148002	−	0.988987i	$-0.452716\pi$
$691$	−16.6786	−	9.62941i	−0.634485	−	0.366320i	−0.782487	+	0.622667i	$0.786049\pi$
$692$	−8.85863			−0.336755
$693$	−4.37959	+	48.4995i	−0.166367	+	1.84234i
$694$			23.8702i			0.906100i
$695$	−0.162465	−	0.0937995i	−0.00616266	−	0.00355802i
$696$	−5.87217	+	5.36580i	−0.222584	+	0.203390i
$697$	−40.2301	+	23.2269i	−1.52383	+	0.879781i
$698$	−9.67391	−	16.7557i	−0.366163	−	0.634213i
$699$	15.2030	−	47.9842i	0.575031	−	1.81493i
$700$	−20.8596	−	12.0433i	−0.788420	−	0.455194i
$701$	−26.7781			−1.01139			−0.505697	−	0.862711i	$-0.668765\pi$
$701$	−26.7781			−1.01139			−0.505697	+	0.862711i	$0.668765\pi$
$702$	6.04275	+	17.7337i	0.228069	+	0.669316i
$703$	6.69374			0.252459
$704$	2.78126	+	1.60576i	0.104823	+	0.0605195i
$705$	1.33792	−	4.22279i	0.0503891	−	0.159039i
$706$	−13.8914	−	24.0606i	−0.522810	−	0.905533i
$707$	29.9709	−	17.3037i	1.12717	−	0.650773i
$708$	4.63263	−	4.23315i	0.174105	−	0.159091i
$709$	−40.2439	−	23.2348i	−1.51139	−	0.872602i	−0.999911	−	0.0133058i	$-0.995764\pi$
$709$	−40.2439	−	23.2348i	−1.51139	−	0.872602i	−0.511479	−	0.859296i	$-0.670902\pi$
$710$		−	2.24230i		−	0.0841522i
$711$	−21.3341	+	9.87587i	−0.800092	+	0.370374i
$712$	8.42912			0.315895
$713$	35.2185	+	20.3334i	1.31894	+	0.761492i
$714$	35.9291	−	7.91271i	1.34461	−	0.296126i
$715$	−1.12333	−	5.49369i	−0.0420103	−	0.205452i
$716$	5.18521	+	8.98104i	0.193780	+	0.335637i
$717$	−2.70789	−	12.2957i	−0.101128	−	0.459190i
$718$	11.9152	−	20.6378i	0.444672	−	0.770195i
$719$	−4.81378			−0.179524			−0.0897619	−	0.995963i	$-0.528611\pi$
$719$	−4.81378			−0.179524			−0.0897619	+	0.995963i	$0.528611\pi$
$720$	−0.836592	+	1.18771i	−0.0311779	+	0.0442632i
$721$		−	17.9693i		−	0.669213i
$722$	7.52237	+	4.34304i	0.279954	+	0.161631i
$723$	22.9009	−	20.9261i	0.851693	−	0.778249i
$724$	5.42035	+	9.38833i	0.201446	+	0.348914i
$725$	−10.9429	−	18.9536i	−0.406407	−	0.703918i
$726$	−1.13284	−	0.358921i	−0.0420436	−	0.0133208i
$727$	−6.35915	+	11.0144i	−0.235848	+	0.408501i	−0.959519	−	0.281645i	$-0.909120\pi$
$727$	−6.35915	+	11.0144i	−0.235848	+	0.408501i	0.723671	+	0.690145i	$0.242453\pi$
$728$	17.2878	+	5.76550i	0.640727	+	0.213684i
$729$	7.20624	−	26.0206i	0.266898	−	0.963725i
$730$			0.157637i			0.00583442i
$731$	19.8930	−	34.4558i	0.735771	−	1.27439i
$732$	0.524046	−	1.65401i	0.0193693	−	0.0611340i
$733$	3.68483	−	2.12744i	0.136102	−	0.0785787i	−0.430403	−	0.902637i	$-0.641628\pi$
$733$	3.68483	−	2.12744i	0.136102	−	0.0785787i	0.566505	+	0.824058i	$0.308295\pi$
$734$	8.74067	−	5.04643i	0.322624	−	0.186267i
$735$	−11.4839	+	10.4936i	−0.423589	+	0.387062i
$736$	5.43186	+	3.13608i	0.200221	+	0.115598i
$737$	−3.47468			−0.127991
$738$	27.1114	+	19.0966i	0.997986	+	0.702956i
$739$			9.71484i			0.357366i	0.983907	+	0.178683i	$0.0571837\pi$
$739$			9.71484i			0.357366i	−0.983907	+	0.178683i	$0.942816\pi$
$740$	−0.504664	+	0.874103i	−0.0185518	+	0.0321327i
$741$	2.10463	−	19.9453i	0.0773156	−	0.732707i
$742$	16.2243	+	28.1013i	0.595613	+	1.03163i
$743$	−10.6739	+	6.16261i	−0.391589	+	0.226084i	−0.682848	−	0.730560i	$-0.739259\pi$
$743$	−10.6739	+	6.16261i	−0.391589	+	0.226084i	0.291259	+	0.956644i	$0.405926\pi$
$744$	−10.9673	+	2.41533i	−0.402080	+	0.0885504i
$745$	−2.29023	+	3.96679i	−0.0839074	+	0.145332i
$746$			8.54741i			0.312943i
$747$	7.39285	+	15.9702i	0.270490	+	0.584321i
$748$		−	13.4963i		−	0.493474i
$749$	6.18904	+	3.57325i	0.226143	+	0.130564i
$750$	−5.52524	−	6.04666i	−0.201753	−	0.220793i
$751$	1.43490	+	2.48532i	0.0523603	+	0.0906908i	0.891018	−	0.453969i	$-0.149992\pi$
$751$	1.43490	+	2.48532i	0.0523603	+	0.0906908i	−0.838657	+	0.544660i	$0.816659\pi$
$752$	4.57369	−	2.64062i	0.166785	−	0.0962935i
$753$	−2.01254	+	6.35204i	−0.0733410	+	0.231481i
$754$	10.9843	+	12.3909i	0.400024	+	0.451249i
$755$	−0.644854			−0.0234686
$756$	−15.9007	−	20.9028i	−0.578304	−	0.760229i
$757$	33.1438			1.20463			0.602316	−	0.798258i	$-0.294245\pi$
$757$	33.1438			1.20463			0.602316	+	0.798258i	$0.294245\pi$
$758$	−15.3563	+	26.5978i	−0.557764	+	0.966076i
$759$	33.2597	+	10.5378i	1.20725	+	0.382497i
$760$	1.34684	−	0.777601i	0.0488552	−	0.0282065i
$761$	37.0264	−	21.3772i	1.34221	−	0.774923i	0.355075	−	0.934838i	$-0.384455\pi$
$761$	37.0264	−	21.3772i	1.34221	−	0.774923i	0.987131	+	0.159915i	$0.0511220\pi$
$762$	−5.83440	+	5.33128i	−0.211358	+	0.193132i
$763$	12.5734	−	21.7778i	0.455188	−	0.788408i
$764$	−11.2580			−0.407300
$765$	6.08045	+	0.549076i	0.219839	+	0.0198519i
$766$	−2.88551			−0.104258
$767$	−8.66563	−	9.77532i	−0.312898	−	0.352966i
$768$	−1.69152	+	0.372524i	−0.0610373	+	0.0134423i
$769$	41.6797	−	24.0638i	1.50301	−	0.867762i	0.503014	−	0.864278i	$-0.332224\pi$
$769$	41.6797	−	24.0638i	1.50301	−	0.867762i	0.999994	−	0.00348401i	$-0.00110900\pi$
$770$	3.93029	+	6.80746i	0.141638	+	0.245324i
$771$	24.9795	−	5.50125i	0.899614	−	0.198123i
$772$	6.60401	+	3.81283i	0.237684	+	0.137227i
$773$			21.3661i			0.768484i	0.923232	+	0.384242i	$0.125537\pi$
$773$			21.3661i			0.768484i	−0.923232	+	0.384242i	$0.874463\pi$
$774$	−28.2869	−	2.55436i	−1.01675	−	0.0918147i
$775$		−	30.8980i		−	1.10989i
$776$	−6.52525	+	11.3021i	−0.234243	+	0.405721i
$777$	−12.3085	−	13.4701i	−0.441566	−	0.483237i
$778$	10.3018	−	5.94776i	0.369338	−	0.213238i
$779$	−17.7501	−	30.7440i	−0.635962	−	1.10152i
$780$	2.44588	+	1.77857i	0.0875765	+	0.0636832i
$781$	7.43535	−	12.8784i	0.266058	−	0.460826i
$782$		−	26.3585i		−	0.942578i
$783$	−3.01573	−	23.6722i	−0.107774	−	0.845975i
$784$	−18.5467			−0.662383
$785$	−2.45019	−	1.41462i	−0.0874510	−	0.0504898i
$786$	−4.07747	−	1.29188i	−0.145439	−	0.0460799i
$787$	−29.5928	+	17.0854i	−1.05487	+	0.609029i	−0.924008	−	0.382372i	$-0.875107\pi$
$787$	−29.5928	+	17.0854i	−1.05487	+	0.609029i	−0.130860	+	0.991401i	$0.541774\pi$
$788$	−21.2324	+	12.2585i	−0.756372	+	0.436691i
$789$	10.2379	+	11.2040i	0.364477	+	0.398873i
$790$	−1.89740	+	3.28640i	−0.0675066	+	0.116925i
$791$			66.1533i			2.35214i
$792$	−8.74323	+	4.04736i	−0.310677	+	0.143817i
$793$	−3.42626	−	1.14266i	−0.121670	−	0.0405772i
$794$	11.9011	−	20.6132i	0.422353	−	0.731537i
$795$	1.15813	+	5.25871i	0.0410747	+	0.186507i
$796$	−6.76550	−	11.7182i	−0.239797	−	0.415340i
$797$	−6.26917	−	10.8585i	−0.222066	−	0.384629i	0.733369	−	0.679830i	$-0.237947\pi$
$797$	−6.26917	−	10.8585i	−0.222066	−	0.384629i	−0.955435	+	0.295201i	$0.904613\pi$
$798$	6.04691	+	27.4571i	0.214058	+	0.971973i
$799$	−19.2207	−	11.0971i	−0.679980	−	0.392587i
$800$		−	4.76550i		−	0.168486i
$801$	−14.5620	+	20.6736i	−0.514523	+	0.730467i
$802$	−8.99705			−0.317697
$803$	−0.522716	+	0.905371i	−0.0184463	+	0.0319498i
$804$	1.38340	−	1.26411i	0.0487889	−	0.0445817i
$805$	7.67592	+	13.2951i	0.270540	+	0.468590i
$806$	4.68322	+	22.9034i	0.164959	+	0.806737i
$807$	−4.65982	+	14.7075i	−0.164033	+	0.517727i
$808$	5.92969	+	3.42351i	0.208606	+	0.120439i
$809$	−23.7653			−0.835543			−0.417772	−	0.908552i	$-0.637189\pi$
$809$	−23.7653			−0.835543			−0.417772	+	0.908552i	$0.637189\pi$
$810$	−1.46774	−	4.10372i	−0.0515712	−	0.144190i
$811$			12.1844i			0.427853i	0.976850	+	0.213926i	$0.0686253\pi$
$811$			12.1844i			0.427853i	−0.976850	+	0.213926i	$0.931375\pi$
$812$	−20.1025	−	11.6062i	−0.705461	−	0.407298i
$813$	5.92024	+	1.87573i	0.207632	+	0.0657848i
$814$	−5.79695	+	3.34687i	−0.203183	+	0.117308i
$815$	3.66435	+	6.34685i	0.128357	+	0.222320i
$816$	4.91003	+	5.37340i	0.171886	+	0.188107i
$817$	26.3312	+	15.2023i	0.921212	+	0.531862i
$818$	−32.1404			−1.12376
$819$	−44.0067	+	32.4403i	−1.53772	+	1.13356i
$820$	5.35295			0.186933
$821$	−14.8532	−	8.57549i	−0.518379	−	0.299287i	0.217892	−	0.975973i	$-0.430082\pi$
$821$	−14.8532	−	8.57549i	−0.518379	−	0.299287i	−0.736271	+	0.676686i	$0.763415\pi$
$822$	33.1713	−	7.30534i	1.15698	−	0.254803i
$823$	−19.0983	−	33.0792i	−0.665725	−	1.15307i	−0.979088	−	0.203436i	$-0.934789\pi$
$823$	−19.0983	−	33.0792i	−0.665725	−	1.15307i	0.313363	−	0.949633i	$-0.398544\pi$
$824$	3.07889	−	1.77760i	0.107258	−	0.0619257i
$825$	−5.70131	−	25.8878i	−0.198494	−	0.901299i
$826$	15.8592	+	9.15629i	0.551810	+	0.318588i
$827$			16.3182i			0.567441i	0.958907	+	0.283721i	$0.0915688\pi$
$827$			16.3182i			0.567441i	−0.958907	+	0.283721i	$0.908431\pi$
$828$	−17.0757	+	7.90457i	−0.593420	+	0.274703i
$829$	13.6052			0.472529			0.236265	−	0.971689i	$-0.424077\pi$
$829$	13.6052			0.472529			0.236265	+	0.971689i	$0.424077\pi$
$830$	2.46012	+	1.42035i	0.0853922	+	0.0493012i
$831$	−17.3846	−	19.0252i	−0.603065	−	0.659977i
$832$	0.722307	+	3.53246i	0.0250415	+	0.122466i
$833$	38.9709	+	67.4996i	1.35026	+	2.33872i
$834$	0.639652	+	0.202663i	0.0221493	+	0.00701766i
$835$	−2.91203	+	5.04378i	−0.100775	+	0.174547i
$836$	10.3139			0.356714
$837$	13.0229	−	31.0715i	0.450137	−	1.07399i
$838$		−	3.37377i		−	0.116545i
$839$	−43.9792	−	25.3914i	−1.51833	−	0.876609i	−0.999767	−	0.0215696i	$-0.993134\pi$
$839$	−43.9792	−	25.3914i	−1.51833	−	0.876609i	−0.518563	−	0.855039i	$-0.673533\pi$
$840$	−4.04139	−	1.28045i	−0.139441	−	0.0441797i
$841$	3.95431	+	6.84907i	0.136356	+	0.236175i
$842$	−1.30842	−	2.26626i	−0.0450913	−	0.0781004i
$843$	21.1123	−	19.2918i	0.727148	−	0.664443i
$844$	11.9346	−	20.6713i	0.410805	−	0.711535i
$845$	3.77872	−	5.03512i	0.129992	−	0.173213i
$846$	−1.42492	+	15.7795i	−0.0489897	+	0.542511i
$847$		−	3.46774i		−	0.119153i
$848$	−3.20995	+	5.55980i	−0.110230	+	0.190924i
$849$	0.906087	−	0.199548i	0.0310968	−	0.00684848i
$850$	−17.3437	+	10.0134i	−0.594884	+	0.343456i
$851$	−11.3215	+	6.53649i	−0.388097	+	0.224068i
$852$	1.72494	+	7.83242i	0.0590955	+	0.268334i
$853$	31.1360	+	17.9764i	1.06608	+	0.615499i	0.927106	−	0.374798i	$-0.122288\pi$
$853$	31.1360	+	17.9764i	1.06608	+	0.615499i	0.138969	+	0.990297i	$0.455621\pi$
$854$	5.06311			0.173256
$855$	−0.419605	+	4.64670i	−0.0143502	+	0.158914i
$856$			1.41392i			0.0483268i
$857$	2.28591	−	3.95932i	0.0780853	−	0.135248i	−0.824339	−	0.566097i	$-0.808453\pi$
$857$	2.28591	−	3.95932i	0.0780853	−	0.135248i	0.902424	+	0.430849i	$0.141786\pi$
$858$	8.14996	+	18.3254i	0.278235	+	0.625619i
$859$	−5.82450	−	10.0883i	−0.198729	−	0.344209i	0.749387	−	0.662132i	$-0.230348\pi$
$859$	−5.82450	−	10.0883i	−0.198729	−	0.344209i	−0.948117	+	0.317923i	$0.897015\pi$
$860$	−3.97040	+	2.29231i	−0.135389	+	0.0781671i
$861$	−29.2284	+	92.2517i	−0.996103	+	3.14393i
$862$	0.625564	−	1.08351i	0.0213068	−	0.0369044i
$863$		−	26.2523i		−	0.893640i	−0.894624	−	0.446820i	$-0.852556\pi$
$863$		−	26.2523i		−	0.893640i	0.894624	−	0.446820i	$-0.147444\pi$
$864$	2.00856	−	4.79225i	0.0683327	−	0.163036i
$865$		−	4.28985i		−	0.145859i
$866$	−4.13195	−	2.38558i	−0.140409	−	0.0810655i
$867$	0.345597	−	1.09078i	0.0117371	−	0.0370450i
$868$	−16.3855	−	28.3806i	−0.556161	−	0.963299i
$869$	−21.7950	+	12.5834i	−0.739345	+	0.426861i
$870$	−2.59842	−	2.84363i	−0.0880946	−	0.0964082i
$871$	−2.58775	−	2.91912i	−0.0876825	−	0.0989107i
$872$	4.97525			0.168483
$873$	−16.4470	−	35.5294i	−0.556648	−	1.20249i
$874$	20.1432			0.681355
$875$	11.9511	−	20.6999i	0.404020	−	0.699783i
$876$	−0.121266	−	0.550630i	−0.00409719	−	0.0186041i
$877$	−40.5146	+	23.3911i	−1.36808	+	0.789862i	−0.990683	−	0.136189i	$-0.956515\pi$
$877$	−40.5146	+	23.3911i	−1.36808	+	0.789862i	−0.377398	+	0.926051i	$0.623181\pi$
$878$	−29.1867	+	16.8509i	−0.985003	+	0.568692i
$879$	7.29762	+	33.1362i	0.246142	+	1.11766i
$880$	−0.777601	+	1.34684i	−0.0262129	+	0.0454021i
$881$	52.3698			1.76438			0.882192	−	0.470889i	$-0.156067\pi$
$881$	52.3698			1.76438			0.882192	+	0.470889i	$0.156067\pi$
$882$	32.0410	−	45.4885i	1.07888	−	1.53168i
$883$	−28.7233			−0.966617			−0.483309	−	0.875450i	$-0.660565\pi$
$883$	−28.7233			−0.966617			−0.483309	+	0.875450i	$0.660565\pi$
$884$	11.3384	−	10.0513i	0.381352	−	0.338061i
$885$	2.04993	+	2.24338i	0.0689075	+	0.0754104i
$886$	4.65706	−	2.68876i	0.156457	−	0.0903305i
$887$	−6.01188	−	10.4129i	−0.201859	−	0.349631i	0.747268	−	0.664523i	$-0.231365\pi$
$887$	−6.01188	−	10.4129i	−0.201859	−	0.349631i	−0.949128	+	0.314892i	$0.898032\pi$
$888$	1.09038	−	3.44148i	0.0365907	−	0.115489i
$889$	−19.9732	−	11.5316i	−0.669881	−	0.386756i
$890$			4.08185i			0.136824i
$891$	5.17790	−	28.4362i	0.173466	−	0.952648i
$892$		−	12.8698i		−	0.430913i
$893$	8.48043	−	14.6885i	0.283787	−	0.491533i
$894$	4.94827	−	15.6179i	0.165495	−	0.522340i
$895$	−4.34912	+	2.51097i	−0.145375	+	0.0839324i
$896$	−2.52719	−	4.37722i	−0.0844274	−	0.146233i
$897$	15.9170	+	35.7898i	0.531453	+	1.19499i
$898$	−8.39064	+	14.5330i	−0.279999	+	0.484973i
$899$		−	29.7766i		−	0.993105i
$900$	11.6881	+	8.23278i	0.389602	+	0.274426i
$901$	26.9793			0.898812
$902$	30.7440	+	17.7501i	1.02366	+	0.591012i
$903$	−17.8259	−	80.9417i	−0.593207	−	2.69357i
$904$	−11.3348	+	6.54415i	−0.376990	+	0.217655i
$905$	−4.54635	+	2.62484i	−0.151126	+	0.0872526i
$906$	2.25249	−	0.496067i	0.0748339	−	0.0164807i
$907$	−13.8974	+	24.0710i	−0.461456	+	0.799265i	−0.999034	−	0.0439492i	$-0.986006\pi$
$907$	−13.8974	+	24.0710i	−0.461456	+	0.799265i	0.537578	+	0.843214i	$0.319339\pi$
$908$		−	18.0552i		−	0.599182i
$909$	−18.6407	+	8.62903i	−0.618272	+	0.286207i
$910$	−2.79198	+	8.37170i	−0.0925531	+	0.277519i
$911$	10.3296	−	17.8914i	0.342235	−	0.592769i	−0.642612	−	0.766191i	$-0.722149\pi$
$911$	10.3296	−	17.8914i	0.342235	−	0.592769i	0.984847	+	0.173423i	$0.0554827\pi$
$912$	−4.10637	+	3.75226i	−0.135975	+	0.124250i
$913$	9.41962	+	16.3153i	0.311744	+	0.539956i
$914$	−11.8396	−	20.5067i	−0.391618	−	0.678302i
$915$	0.800964	+	0.253772i	0.0264791	+	0.00838946i
$916$	−18.3370	−	10.5869i	−0.605871	−	0.349800i
$917$		−	12.4816i		−	0.412179i
$918$	−21.6615	+	2.75958i	−0.714937	+	0.0910798i
$919$	56.3658			1.85933			0.929667	−	0.368400i	$-0.120094\pi$
$919$	56.3658			1.85933			0.929667	+	0.368400i	$0.120094\pi$
$920$	−1.51867	+	2.63041i	−0.0500690	+	0.0867220i
$921$	−2.08152	−	0.659495i	−0.0685883	−	0.0217311i
$922$	−17.2311	−	29.8451i	−0.567476	−	0.982898i
$923$	16.3567	−	3.34458i	0.538389	−	0.110088i
$924$	−18.9654	−	20.7551i	−0.623914	−	0.682794i
$925$	8.60193	+	4.96633i	0.282830	+	0.163292i
$926$	22.4773			0.738649
$927$	−0.959221	+	10.6224i	−0.0315049	+	0.348885i
$928$		−	4.59254i		−	0.150757i
$929$	−1.75111	−	1.01100i	−0.0574520	−	0.0331699i	0.470999	−	0.882134i	$-0.343894\pi$
$929$	−1.75111	−	1.01100i	−0.0574520	−	0.0331699i	−0.528451	+	0.848964i	$0.677227\pi$
$930$	−1.16964	−	5.31097i	−0.0383540	−	0.174153i
$931$	−51.5834	+	29.7817i	−1.69058	+	0.976055i
$932$	14.5305	+	25.1675i	0.475962	+	0.824390i
$933$	29.7443	−	6.55063i	0.973786	−	0.214458i
$934$	−3.84196	−	2.21816i	−0.125713	−	0.0725804i
$935$	6.53566			0.213739
$936$	−9.91171	−	4.33105i	−0.323974	−	0.141565i
$937$	−15.3243			−0.500622			−0.250311	−	0.968166i	$-0.580533\pi$
$937$	−15.3243			−0.500622			−0.250311	+	0.968166i	$0.580533\pi$
$938$	4.73589	+	2.73427i	0.154632	+	0.0892770i
$939$	0.239997	+	0.262646i	0.00783200	+	0.00857112i
$940$	1.27874	+	2.21484i	0.0417078	+	0.0722400i
$941$	−35.8714	+	20.7104i	−1.16938	+	0.675139i	−0.953533	−	0.301289i	$-0.902583\pi$
$941$	−35.8714	+	20.7104i	−1.16938	+	0.675139i	−0.215842	+	0.976428i	$0.569250\pi$
$942$	9.64678	+	3.05643i	0.314309	+	0.0995837i
$943$	60.0435	+	34.6661i	1.95529	+	1.12888i
$944$			3.62311i			0.117922i
$945$	10.1223	−	7.70002i	0.329279	−	0.250482i
$946$	−30.4047			−0.988541
$947$	−49.2660	−	28.4437i	−1.60093	−	0.924297i	−0.991302	−	0.131610i	$-0.957985\pi$
$947$	−49.2660	−	28.4437i	−1.60093	−	0.924297i	−0.609628	−	0.792687i	$-0.708681\pi$
$948$	4.09954	−	12.9391i	0.133147	−	0.420242i
$949$	−1.14990	+	0.235129i	−0.0373274	+	0.00763261i
$950$	−7.65226	−	13.2541i	−0.248272	−	0.430020i
$951$	−23.1185	+	21.1249i	−0.749667	+	0.685021i
$952$	−10.6204	+	18.3951i	−0.344209	+	0.596187i
$953$	−40.5931			−1.31494			−0.657470	−	0.753481i	$-0.728373\pi$
$953$	−40.5931			−1.31494			−0.657470	+	0.753481i	$0.728373\pi$
$954$	−8.09075	−	17.4779i	−0.261948	−	0.565867i
$955$		−	5.45175i		−	0.176415i
$956$	6.29516	+	3.63451i	0.203600	+	0.117548i
$957$	−5.49438	−	24.9483i	−0.177608	−	0.806463i
$958$	5.90827	+	10.2334i	0.190888	+	0.330627i
$959$	49.5591	+	85.8389i	1.60035	+	2.77188i
$960$	−0.180397	−	0.819127i	−0.00582229	−	0.0264372i
$961$	5.51914	−	9.55944i	0.178037	−	0.308369i
$962$	−7.12899	−	2.37753i	−0.229848	−	0.0766547i
$963$	−3.46785	−	2.44266i	−0.111750	−	0.0787138i
$964$			17.9104i			0.576856i
$965$	−1.84638	+	3.19803i	−0.0594372	+	0.102948i
$966$	−37.0396	−	40.5351i	−1.19173	−	1.30420i
$967$	43.2958	−	24.9968i	1.39230	−	0.803844i	0.398729	−	0.917069i	$-0.369452\pi$
$967$	43.2958	−	24.9968i	1.39230	−	0.803844i	0.993569	+	0.113225i	$0.0361182\pi$
$968$	0.594169	−	0.343044i	0.0190973	−	0.0110258i
$969$	22.2845	+	7.06049i	0.715882	+	0.226816i
$970$	−5.47310	−	3.15989i	−0.175730	−	0.101458i
$971$	−31.1467			−0.999546			−0.499773	−	0.866156i	$-0.666583\pi$
$971$	−31.1467			−0.999546			−0.499773	+	0.866156i	$0.666583\pi$
$972$	8.28373	+	13.2053i	0.265701	+	0.423560i
$973$			1.95805i			0.0627721i
$974$	12.9186	−	22.3758i	0.413940	−	0.716965i
$975$	17.5027	−	24.0696i	0.560535	−	0.770843i
$976$	0.500864	+	0.867521i	0.0160323	+	0.0277687i
$977$	−5.97565	+	3.45004i	−0.191178	+	0.110377i	−0.592534	−	0.805546i	$-0.701872\pi$
$977$	−5.97565	+	3.45004i	−0.191178	+	0.110377i	0.401356	+	0.915922i	$0.368539\pi$
$978$	−17.6821	−	19.3508i	−0.565411	−	0.618770i
$979$	−13.5352	+	23.4436i	−0.432586	+	0.749262i
$980$		−	8.98136i		−	0.286899i
$981$	−8.59515	+	12.2025i	−0.274422	+	0.389596i
$982$		−	11.1999i		−	0.357403i
$983$	−45.4067	−	26.2156i	−1.44825	−	0.836147i	−0.449872	−	0.893093i	$-0.648530\pi$
$983$	−45.4067	−	26.2156i	−1.44825	−	0.836147i	−0.998377	+	0.0569461i	$0.981864\pi$
$984$	−18.6980	+	4.11787i	−0.596069	+	0.131273i
$985$	−5.93626	−	10.2819i	−0.189145	−	0.327608i
$986$	−16.7142	+	9.64996i	−0.532289	+	0.307317i
$987$	−45.1523	+	9.94393i	−1.43721	+	0.316519i
$988$	7.68122	+	8.66485i	0.244372	+	0.275666i
$989$	−59.3808			−1.88820
$990$	−1.95996	−	4.23396i	−0.0622916	−	0.134564i
$991$	−26.0277			−0.826799			−0.413399	−	0.910550i	$-0.635659\pi$
$991$	−26.0277			−0.826799			−0.413399	+	0.910550i	$0.635659\pi$
$992$	3.24185	−	5.61504i	0.102929	−	0.178278i
$993$	5.36390	−	4.90135i	0.170218	−	0.155540i
$994$	−20.2683	+	11.7019i	−0.642872	+	0.371163i
$995$	5.67460	−	3.27623i	0.179897	−	0.103864i
$996$	−9.68590	−	3.06882i	−0.306910	−	0.0972393i
$997$	−13.6237	+	23.5970i	−0.431468	+	0.747324i	−0.997000	−	0.0774021i	$-0.975337\pi$
$997$	−13.6237	+	23.5970i	−0.431468	+	0.747324i	0.565532	+	0.824726i	$0.308671\pi$
$998$	−15.4596			−0.489367
$999$	6.55702	+	8.61975i	0.207455	+	0.272717i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.2.t.a.25.12	yes	28
3.2	odd	2		702.2.t.a.181.4		28
9.2	odd	6		2106.2.b.d.649.11		14
9.4	even	3	inner	234.2.t.a.103.5	yes	28
9.5	odd	6		702.2.t.a.415.11		28
9.7	even	3		2106.2.b.c.649.4		14
13.12	even	2	inner	234.2.t.a.25.5	✓	28
39.38	odd	2		702.2.t.a.181.11		28
117.25	even	6		2106.2.b.c.649.11		14
117.38	odd	6		2106.2.b.d.649.4		14
117.77	odd	6		702.2.t.a.415.4		28
117.103	even	6	inner	234.2.t.a.103.12	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.t.a.25.5	✓	28	13.12	even	2	inner
234.2.t.a.25.12	yes	28	1.1	even	1	trivial
234.2.t.a.103.5	yes	28	9.4	even	3	inner
234.2.t.a.103.12	yes	28	117.103	even	6	inner
702.2.t.a.181.4		28	3.2	odd	2
702.2.t.a.181.11		28	39.38	odd	2
702.2.t.a.415.4		28	117.77	odd	6
702.2.t.a.415.11		28	9.5	odd	6
2106.2.b.c.649.4		14	9.7	even	3
2106.2.b.c.649.11		14	117.25	even	6
2106.2.b.d.649.4		14	117.38	odd	6
2106.2.b.d.649.11		14	9.2	odd	6

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:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.523143 - 1.65116i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.419378 + 0.242128i) q^{5} +(1.27863 - 1.16837i) q^{6} +(4.37722 + 2.52719i) q^{7} +1.00000i q^{8} +(-2.45264 - 1.72758i) q^{9} -0.484256 q^{10} +(-2.78126 - 1.60576i) q^{11} +(1.69152 - 0.372524i) q^{12} +(-0.722307 - 3.53246i) q^{13} +(2.52719 + 4.37722i) q^{14} +(0.180397 + 0.819127i) q^{15} +(-0.500000 + 0.866025i) q^{16} +4.20245 q^{17} +(-1.26026 - 2.72245i) q^{18} +3.21153i q^{19} +(-0.419378 - 0.242128i) q^{20} +(6.46270 - 5.90540i) q^{21} +(-1.60576 - 2.78126i) q^{22} +(-3.13608 - 5.43186i) q^{23} +(1.65116 + 0.523143i) q^{24} +(-2.38275 + 4.12704i) q^{25} +(1.14069 - 3.42035i) q^{26} +(-4.13559 + 3.14593i) q^{27} +5.05438i q^{28} +(-2.29627 + 3.97725i) q^{29} +(-0.253335 + 0.799583i) q^{30} +(-5.61504 + 3.24185i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-4.10637 + 3.75226i) q^{33} +(3.63943 + 2.10123i) q^{34} -2.44761 q^{35} +(0.269808 - 2.98784i) q^{36} -2.08429i q^{37} +(-1.60576 + 2.78126i) q^{38} +(-6.21052 - 0.655337i) q^{39} +(-0.242128 - 0.419378i) q^{40} +(-9.57301 + 5.52698i) q^{41} +(8.54956 - 1.88288i) q^{42} +(4.73367 - 8.19896i) q^{43} -3.21153i q^{44} +(1.44688 + 0.130656i) q^{45} -6.27217i q^{46} +(-4.57369 - 2.64062i) q^{47} +(1.16837 + 1.27863i) q^{48} +(9.27337 + 16.0619i) q^{49} +(-4.12704 + 2.38275i) q^{50} +(2.19848 - 6.93891i) q^{51} +(2.69805 - 2.39177i) q^{52} +6.41990 q^{53} +(-5.15449 + 0.656660i) q^{54} +1.55520 q^{55} +(-2.52719 + 4.37722i) q^{56} +(5.30274 + 1.68009i) q^{57} +(-3.97725 + 2.29627i) q^{58} +(3.13771 - 1.81156i) q^{59} +(-0.619186 + 0.565792i) q^{60} +(0.500864 - 0.867521i) q^{61} -6.48369 q^{62} +(-6.36984 - 13.7603i) q^{63} -1.00000 q^{64} +(1.15823 + 1.30655i) q^{65} +(-5.43235 + 1.19637i) q^{66} +(0.936987 - 0.540970i) q^{67} +(2.10123 + 3.63943i) q^{68} +(-10.6095 + 2.33653i) q^{69} +(-2.11969 - 1.22381i) q^{70} +4.63041i q^{71} +(1.72758 - 2.45264i) q^{72} -0.325525i q^{73} +(1.04214 - 1.80504i) q^{74} +(5.56788 + 6.09332i) q^{75} +(-2.78126 + 1.60576i) q^{76} +(-8.11614 - 14.0576i) q^{77} +(-5.05080 - 3.67280i) q^{78} +(3.91818 - 6.78649i) q^{79} -0.484256i q^{80} +(3.03092 + 8.47428i) q^{81} -11.0540 q^{82} +(-5.08022 - 2.93306i) q^{83} +(8.34557 + 2.64416i) q^{84} +(-1.76242 + 1.01753i) q^{85} +(8.19896 - 4.73367i) q^{86} +(5.36580 + 5.87217i) q^{87} +(1.60576 - 2.78126i) q^{88} -8.42912i q^{89} +(1.18771 + 0.836592i) q^{90} +(5.76550 - 17.2878i) q^{91} +(3.13608 - 5.43186i) q^{92} +(2.41533 + 10.9673i) q^{93} +(-2.64062 - 4.57369i) q^{94} +(-0.777601 - 1.34684i) q^{95} +(0.372524 + 1.69152i) q^{96} +(11.3021 + 6.52525i) q^{97} +18.5467i q^{98} +(4.04736 + 8.74323i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 14 q^{4} - 16 q^{9} + 2 q^{13} + 8 q^{14} - 14 q^{16} + 16 q^{17} - 8 q^{23} + 14 q^{25} + 8 q^{26} + 18 q^{27} - 16 q^{29} - 8 q^{30} - 68 q^{35} - 8 q^{36} - 8 q^{39} - 10 q^{42} - 4 q^{43} + 10 q^{49}+ \cdots + 8 q^{92}+O(q^{100}) \) 28 * q + 14 * q^4 - 16 * q^9 + 2 * q^13 + 8 * q^14 - 14 * q^16 + 16 * q^17 - 8 * q^23 + 14 * q^25 + 8 * q^26 + 18 * q^27 - 16 * q^29 - 8 * q^30 - 68 * q^35 - 8 * q^36 - 8 * q^39 - 10 * q^42 - 4 * q^43 + 10 * q^49 + 58 * q^51 - 2 * q^52 - 120 * q^53 - 8 * q^56 + 28 * q^61 + 68 * q^62 - 28 * q^64 - 8 * q^65 - 24 * q^66 + 8 * q^68 - 92 * q^69 + 16 * q^74 + 32 * q^75 - 24 * q^77 - 22 * q^78 + 28 * q^79 + 8 * q^81 - 48 * q^82 + 68 * q^87 - 50 * q^90 + 8 * q^92

Introduction

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