LMFDB - Embedded newform 234.2.t.a.103.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,2,Mod(25,234)]

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

lf = mfeigenbasis(mf)

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")

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

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

Self dual:	no
Analytic conductor:	$1.86849940730$
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			103.12
Character	$\chi$	$=$	234.103
Dual form			234.2.t.a.25.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.523143 + 1.65116i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.419378 - 0.242128i) q^{5} +(1.27863 + 1.16837i) q^{6} +(4.37722 - 2.52719i) q^{7} -1.00000i q^{8} +(-2.45264 + 1.72758i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 28 * q + 14 * q^4 - 16 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

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

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	0.403284	−	0.915075i	$-0.367869\pi$
$5$	−0.419378	−	0.242128i	−0.187552	−	0.108283i	−0.590836	+	0.806792i	$0.701202\pi$
$6$	1.27863	+	1.16837i	0.522000	+	0.476986i
$7$	4.37722	−	2.52719i	1.65443	−	0.955188i	0.679216	−	0.733938i	$-0.262320\pi$
$7$	4.37722	−	2.52719i	1.65443	−	0.955188i	0.975217	−	0.221249i	$-0.0710134\pi$
$8$		−	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	−0.856782	−	0.515678i	$-0.827540\pi$
$11$	−2.78126	+	1.60576i	−0.838583	+	0.484156i	0.0181994	+	0.999834i	$0.494207\pi$
$12$	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	$-0.879910\pi$
$19$		−	3.21153i		−	0.736775i	0.929672	−	0.368388i	$-0.120090\pi$
$20$	−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	0.328245	+	0.944593i	$0.393543\pi$
$23$	−3.13608	+	5.43186i	−0.653919	+	1.13262i	−0.982164	+	0.188028i	$0.939791\pi$
$24$	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	0.570144	−	0.821544i	$-0.306887\pi$
$29$	−2.29627	−	3.97725i	−0.426406	−	0.738557i	−0.996551	+	0.0829873i	$0.973554\pi$
$30$	−0.253335	−	0.799583i	−0.0462524	−	0.145983i
$31$	−5.61504	−	3.24185i	−1.00849	−	0.582253i	−0.0977420	−	0.995212i	$-0.531162\pi$
$31$	−5.61504	−	3.24185i	−1.00849	−	0.582253i	−0.910750	+	0.412959i	$0.864495\pi$
$32$	−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	$0.0548055\pi$
$37$			2.08429i			0.342654i	−0.985214	+	0.171327i	$0.945194\pi$
$38$	−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	−0.495070	−	0.868853i	$-0.664857\pi$
$41$	−9.57301	−	5.52698i	−1.49505	−	0.863169i	−0.999984	+	0.00568392i	$0.998191\pi$
$42$	8.54956	+	1.88288i	1.31923	+	0.290534i
$43$	4.73367	+	8.19896i	0.721879	+	1.25033i	0.960246	+	0.279155i	$0.0900544\pi$
$43$	4.73367	+	8.19896i	0.721879	+	1.25033i	−0.238367	+	0.971175i	$0.576612\pi$
$44$			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	−0.794992	−	0.606619i	$-0.792525\pi$
$47$	−4.57369	+	2.64062i	−0.667141	+	0.385174i	0.127851	+	0.991793i	$0.459192\pi$
$48$	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	0.690143	−	0.723673i	$-0.257548\pi$
$59$	3.13771	+	1.81156i	0.408495	+	0.235844i	−0.281648	+	0.959518i	$0.590881\pi$
$60$	−0.619186	−	0.565792i	−0.0799366	−	0.0730434i
$61$	0.500864	+	0.867521i	0.0641290	+	0.111075i	0.896307	−	0.443433i	$-0.146240\pi$
$61$	0.500864	+	0.867521i	0.0641290	+	0.111075i	−0.832178	+	0.554508i	$0.812906\pi$
$62$	−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	0.556142	−	0.831087i	$-0.312281\pi$
$67$	0.936987	+	0.540970i	0.114471	+	0.0660900i	−0.441671	+	0.897177i	$0.645614\pi$
$68$	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	$-0.911400\pi$
$71$		−	4.63041i		−	0.549529i	0.961512	−	0.274764i	$-0.0885999\pi$
$72$	1.72758	+	2.45264i	0.203597	+	0.289047i
$73$			0.325525i			0.0380998i	0.999819	+	0.0190499i	$0.00606414\pi$
$73$			0.325525i			0.0380998i	−0.999819	+	0.0190499i	$0.993936\pi$
$74$	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	0.997751	−	0.0670253i	$-0.0213508\pi$
$79$	3.91818	+	6.78649i	0.440830	+	0.763540i	−0.556921	+	0.830565i	$0.688017\pi$
$80$			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	−0.752192	−	0.658944i	$-0.771003\pi$
$83$	−5.08022	+	2.93306i	−0.557626	+	0.321946i	0.194566	+	0.980889i	$0.437670\pi$
$84$	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	$0.147416\pi$
$89$			8.42912i			0.893485i	−0.894662	+	0.446743i	$0.852584\pi$
$90$	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	0.199262	−	0.979946i	$-0.436145\pi$
$97$	11.3021	−	6.52525i	1.14755	−	0.662539i	0.948289	+	0.317407i	$0.102812\pi$
$98$		−	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	0.984554	−	0.175081i	$-0.0560189\pi$
$101$	3.42351	+	5.92969i	0.340652	+	0.590027i	−0.643902	+	0.765108i	$0.722686\pi$
$102$	5.37340	+	4.91003i	0.532046	+	0.486166i
$103$	−1.77760	+	3.07889i	−0.175152	+	0.303373i	−0.940214	−	0.340584i	$-0.889375\pi$
$103$	−1.77760	+	3.07889i	−0.175152	+	0.303373i	0.765062	+	0.643957i	$0.222708\pi$
$104$	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	$0.0765808\pi$
$109$			4.97525i			0.476543i	−0.971199	+	0.238271i	$0.923419\pi$
$110$	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	−0.374653	−	0.927165i	$-0.622238\pi$
$113$	6.54415	−	11.3348i	0.615622	−	1.06629i	0.990275	−	0.139124i	$-0.0444286\pi$
$114$	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	−0.914911	−	0.403656i	$-0.867739\pi$
$131$	−1.23473	+	2.13862i	−0.107879	+	0.186852i	0.807032	+	0.590508i	$0.201073\pi$
$132$	−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	0.452427	−	0.891802i	$-0.350558\pi$
$137$	16.9831	−	9.80519i	1.45096	−	0.837714i	0.998536	+	0.0540880i	$0.0172251\pi$
$138$	−10.3563	+	3.28124i	−0.881590	+	0.279317i
$139$	0.193698	−	0.335495i	0.0164293	−	0.0284563i	−0.857694	−	0.514161i	$-0.828104\pi$
$139$	0.193698	−	0.335495i	0.0164293	−	0.0284563i	0.874123	+	0.485704i	$0.161437\pi$
$140$	−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	0.796484	−	0.604660i	$-0.206691\pi$
$149$	8.19151	+	4.72937i	0.671075	+	0.387445i	−0.125409	+	0.992105i	$0.540024\pi$
$150$	1.77526	−	8.06091i	0.144950	−	0.658171i
$151$	1.15323	−	0.665819i	0.0938487	−	0.0541836i	−0.452341	−	0.891845i	$-0.649411\pi$
$151$	1.15323	−	0.665819i	0.0938487	−	0.0541836i	0.546190	+	0.837661i	$0.316078\pi$
$152$	−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	−0.725592	−	0.688126i	$-0.758434\pi$
$157$	2.92122	−	5.05970i	0.233139	−	0.403808i	0.958730	+	0.284318i	$0.0917671\pi$
$158$	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	$0.201935\pi$
$163$			15.1340i			1.18538i	−0.805430	+	0.592691i	$0.798065\pi$
$164$	−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	0.845557	−	0.533885i	$-0.179268\pi$
$167$	10.4155	+	6.01341i	0.805978	+	0.465331i	−0.0395794	+	0.999216i	$0.512602\pi$
$168$	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	0.647066	−	0.762434i	$-0.275996\pi$
$173$	−4.42932	−	7.67180i	−0.336755	−	0.583276i	−0.983820	+	0.179158i	$0.942663\pi$
$174$	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	0.587286	−	0.809379i	$-0.300196\pi$
$191$	−5.62900	−	9.74971i	−0.407300	−	0.705464i	−0.994586	+	0.103915i	$0.966863\pi$
$192$	−0.523143	−	1.65116i	−0.0377546	−	0.119162i
$193$	6.60401	+	3.81283i	0.475367	+	0.274453i	0.718484	−	0.695544i	$-0.244836\pi$
$193$	6.60401	+	3.81283i	0.475367	+	0.274453i	−0.243117	+	0.969997i	$0.578170\pi$
$194$	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	$-0.661921\pi$
$197$		−	24.5170i		−	1.74677i	0.487035	−	0.873383i	$-0.338079\pi$
$198$	−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	0.0828724	+	0.996560i	$0.473591\pi$
$211$	−11.9346	+	20.6713i	−0.821610	+	1.42307i	−0.904483	+	0.426511i	$0.859743\pi$
$212$	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	−0.824378	−	0.566040i	$-0.808475\pi$
$223$	−11.1456	+	6.43490i	−0.746363	+	0.430913i	0.0780155	+	0.996952i	$0.475142\pi$
$224$	−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	−0.919213	−	0.393760i	$-0.871174\pi$
$227$	−15.6362	+	9.02759i	−1.03781	+	0.599182i	−0.118600	+	0.992942i	$0.537841\pi$
$228$	1.19637	−	5.43235i	0.0792317	−	0.359766i
$229$	−18.3370	−	10.5869i	−1.21174	−	0.699599i	−0.248603	−	0.968606i	$-0.579971\pi$
$229$	−18.3370	−	10.5869i	−1.21174	−	0.699599i	−0.963138	+	0.269006i	$0.913305\pi$
$230$	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	0.689586	−	0.724204i	$-0.257793\pi$
$239$	6.29516	+	3.63451i	0.407200	+	0.235097i	−0.282386	+	0.959301i	$0.591126\pi$
$240$	−0.799583	+	0.253335i	−0.0516129	+	0.0163527i
$241$	15.5109	−	8.95521i	0.999144	−	0.576856i	0.0911491	−	0.995837i	$-0.470946\pi$
$241$	15.5109	−	8.95521i	0.999144	−	0.576856i	0.907995	+	0.418981i	$0.137613\pi$
$242$			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	−0.538404	−	0.842687i	$-0.680973\pi$
$257$	7.38375	−	12.7890i	0.460586	−	0.797758i	0.998990	+	0.0449285i	$0.0143060\pi$
$258$	−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	0.698743	−	0.715372i	$-0.253743\pi$
$263$	−4.38124	−	7.58853i	−0.270159	−	0.467929i	−0.968902	+	0.247443i	$0.920410\pi$
$264$	−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	$-0.965266\pi$
$271$		−	3.58551i		−	0.217804i	0.994052	−	0.108902i	$-0.0347335\pi$
$272$	−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	0.998190	−	0.0601468i	$-0.0191569\pi$
$277$	7.43966	+	12.8859i	0.447006	+	0.774237i	−0.551183	+	0.834384i	$0.685824\pi$
$278$		−	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	−0.00863764	−	0.999963i	$-0.502749\pi$
$281$	14.2995	−	8.25582i	0.853037	−	0.492501i	0.861674	+	0.507462i	$0.169416\pi$
$282$	−8.93330	−	1.96739i	−0.531970	−	0.117156i
$283$	0.267833	−	0.463900i	0.0159210	−	0.0275760i	−0.857955	−	0.513725i	$-0.828265\pi$
$283$	0.267833	−	0.463900i	0.0159210	−	0.0275760i	0.873876	+	0.486149i	$0.161599\pi$
$284$	−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	−0.0855065	−	0.996338i	$-0.527251\pi$
$293$	−16.9651	−	9.79482i	−0.991113	−	0.572220i	−0.905607	+	0.424118i	$0.860584\pi$
$294$	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	$0.0114534\pi$
$307$			1.26064i			0.0719485i	−0.999353	+	0.0359743i	$0.988547\pi$
$308$	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	−0.501438	−	0.865194i	$-0.667195\pi$
$311$	8.79222	−	15.2286i	0.498561	−	0.863533i	0.999999	+	0.00166095i	$0.000528697\pi$
$312$	0.655337	+	6.21052i	0.0371011	+	0.351601i
$313$	−0.102706	−	0.177891i	−0.00580526	−	0.0100550i	0.863108	−	0.505019i	$-0.168515\pi$
$313$	−0.102706	−	0.177891i	−0.00580526	−	0.0100550i	−0.868913	+	0.494964i	$0.835181\pi$
$314$		−	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	−0.870479	−	0.492206i	$-0.836191\pi$
$317$	−15.6583	+	9.04030i	−0.879455	+	0.507754i	−0.00897641	+	0.999960i	$0.502857\pi$
$318$	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	−0.396822	−	0.917896i	$-0.629887\pi$
$331$	3.63300	−	2.09751i	0.199688	−	0.115290i	0.596510	+	0.802606i	$0.296554\pi$
$332$			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	−0.990297	−	0.138967i	$-0.955622\pi$
$337$	−6.88041	+	11.9172i	−0.374800	+	0.649172i	0.615497	+	0.788139i	$0.288955\pi$
$338$	−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	−0.344565	−	0.938763i	$-0.611974\pi$
$347$	11.9351	−	20.6722i	0.640710	−	1.10974i	0.985275	−	0.170979i	$-0.0546931\pi$
$348$	−2.40255	−	7.58300i	−0.128790	−	0.406491i
$349$	−16.7557	+	9.67391i	−0.896913	+	0.517833i	−0.876197	−	0.481953i	$-0.839928\pi$
$349$	−16.7557	+	9.67391i	−0.896913	+	0.517833i	−0.0207153	+	0.999785i	$0.506594\pi$
$350$	−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	−0.976961	−	0.213417i	$-0.931541\pi$
$353$	−24.0606	+	13.8914i	−1.28062	+	0.739365i	−0.303656	+	0.952782i	$0.598207\pi$
$354$	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	$0.216479\pi$
$359$			23.8304i			1.25772i	−0.777517	+	0.628861i	$0.783521\pi$
$360$	−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	0.967149	−	0.254211i	$-0.0818157\pi$
$367$	5.04643	+	8.74067i	0.263421	+	0.456259i	−0.703728	+	0.710470i	$0.748482\pi$
$368$	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	−0.733914	−	0.679242i	$-0.762309\pi$
$373$	4.27370	−	7.40227i	0.221284	−	0.383275i	0.955198	+	0.295967i	$0.0956419\pi$
$374$	−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	$-0.710704\pi$
$379$		−	30.7125i		−	1.57760i	0.614653	−	0.788798i	$-0.289296\pi$
$380$	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	0.434795	−	0.900529i	$-0.356821\pi$
$383$	−2.49892	−	1.44275i	−0.127689	−	0.0737212i	−0.562484	+	0.826808i	$0.690154\pi$
$384$	−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	0.976490	−	0.215561i	$-0.0691581\pi$
$389$	5.94776	+	10.3018i	0.301564	+	0.522323i	−0.674927	+	0.737885i	$0.735825\pi$
$390$	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	$0.203759\pi$
$397$			23.8021i			1.19459i	−0.802020	+	0.597297i	$0.796241\pi$
$398$	−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	0.292671	−	0.956213i	$-0.405456\pi$
$401$	−7.79168	−	4.49853i	−0.389098	−	0.224646i	−0.681769	+	0.731567i	$0.738789\pi$
$402$	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	−0.384608	−	0.923080i	$-0.625663\pi$
$409$	−27.8344	−	16.0702i	−1.37632	−	0.794620i	−0.991715	+	0.128460i	$0.958997\pi$
$410$	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	−0.904285	−	0.426930i	$-0.859595\pi$
$419$	−1.68689	+	2.92177i	−0.0824098	+	0.142738i	0.821875	+	0.569668i	$0.192928\pi$
$420$	−4.14017	−	0.911795i	−0.202020	−	0.0444910i
$421$	−2.26626	+	1.30842i	−0.110451	+	0.0637687i	−0.554208	−	0.832378i	$-0.686979\pi$
$421$	−2.26626	+	1.30842i	−0.110451	+	0.0637687i	0.443757	+	0.896147i	$0.353645\pi$
$422$			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	$0.00959288\pi$
$431$			1.25113i			0.0602647i	−0.999546	+	0.0301324i	$0.990407\pi$
$432$	−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	−0.916795	−	0.399358i	$-0.869233\pi$
$439$	−16.8509	−	29.1867i	−0.804252	−	1.39300i	0.112543	−	0.993647i	$-0.464100\pi$
$440$		−	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	0.922803	−	0.385272i	$-0.125892\pi$
$443$	2.68876	+	4.65706i	0.127747	+	0.221264i	−0.795057	+	0.606535i	$0.792559\pi$
$444$	−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	$-0.870405\pi$
$449$		−	16.7813i		−	0.791958i	0.918260	−	0.395979i	$-0.129595\pi$
$450$	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	−0.895946	−	0.444162i	$-0.853501\pi$
$457$	−20.5067	+	11.8396i	−0.959263	+	0.553831i	−0.0633172	+	0.997993i	$0.520168\pi$
$458$	−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	−0.993318	−	0.115412i	$-0.963181\pi$
$461$	−29.8451	+	17.2311i	−1.39003	+	0.802533i	−0.396709	+	0.917944i	$0.629848\pi$
$462$	−26.8020	+	8.49179i	−1.24694	+	0.395074i
$463$	19.4659	+	11.2386i	0.904657	+	0.522304i	0.878708	−	0.477359i	$-0.158406\pi$
$463$	19.4659	+	11.2386i	0.904657	+	0.522304i	0.0259487	+	0.999663i	$0.491739\pi$
$464$	−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	−0.247648	−	0.968850i	$-0.579658\pi$
$479$	10.2334	−	5.90827i	0.467577	−	0.269956i	0.715225	+	0.698894i	$0.246324\pi$
$480$	−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	$0.199062\pi$
$487$			25.8373i			1.17080i	−0.810745	+	0.585400i	$0.800938\pi$
$488$	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	−0.964274	−	0.264906i	$-0.914659\pi$
$491$	−5.59995	+	9.69940i	−0.252722	+	0.437728i	0.711552	+	0.702633i	$0.247993\pi$
$492$	−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	0.169436	−	0.985541i	$-0.445805\pi$
$499$	−13.3884	−	7.72982i	−0.599349	−	0.346034i	−0.768786	+	0.639507i	$0.779139\pi$
$500$	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	0.853160	−	0.521649i	$-0.174683\pi$
$509$	18.6801	+	10.7849i	0.827979	+	0.478034i	−0.0251810	+	0.999683i	$0.508016\pi$
$510$	−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	$-0.914825\pi$
$541$		−	12.2998i		−	0.528808i	0.964412	−	0.264404i	$-0.0851753\pi$
$542$	−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	0.997862	−	0.0653602i	$-0.0208196\pi$
$547$	10.3452	+	17.9183i	0.442327	+	0.766133i	−0.555534	+	0.831493i	$0.687486\pi$
$548$		−	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	$-0.902141\pi$
$557$		−	14.2838i		−	0.605226i	0.953114	−	0.302613i	$-0.0978589\pi$
$558$	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	−0.187026	−	0.982355i	$-0.559885\pi$
$563$	17.9673	−	31.1203i	0.757231	−	1.31156i	0.944257	−	0.329208i	$-0.106782\pi$
$564$	−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	0.933730	+	0.357977i	$0.116533\pi$
$569$	18.5315	+	32.0976i	0.776882	+	1.34560i	−0.156848	+	0.987623i	$0.550133\pi$
$570$	−2.56788	+	0.813592i	−0.107557	+	0.0340776i
$571$	23.1732	−	40.1372i	0.969769	−	1.67969i	0.273551	−	0.961857i	$-0.411802\pi$
$571$	23.1732	−	40.1372i	0.969769	−	1.67969i	0.696217	−	0.717831i	$-0.254865\pi$
$572$	−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	$-0.772866\pi$
$577$		−	31.4447i		−	1.30906i	0.756036	−	0.654530i	$-0.227134\pi$
$578$	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	0.176397	−	0.984319i	$-0.443556\pi$
$587$	27.0638	−	15.6253i	1.11704	−	0.644924i	0.940644	+	0.339395i	$0.110222\pi$
$588$	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	$0.182338\pi$
$593$			26.3978i			1.08403i	−0.840370	+	0.542013i	$0.817662\pi$
$594$	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	−0.788035	−	0.615631i	$-0.788901\pi$
$599$	3.40524	−	5.89806i	0.139135	−	0.240988i	0.927169	+	0.374643i	$0.122235\pi$
$600$	−6.09332	−	5.56788i	−0.248759	−	0.227308i
$601$	−4.82516	−	8.35742i	−0.196822	−	0.340906i	0.750674	−	0.660673i	$-0.229729\pi$
$601$	−4.82516	−	8.35742i	−0.196822	−	0.340906i	−0.947496	+	0.319766i	$0.896396\pi$
$602$	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	0.437819	+	0.899063i	$0.355751\pi$
$607$	−13.7896	+	23.8842i	−0.559702	+	0.969432i	−0.997521	+	0.0703688i	$0.977582\pi$
$608$	−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	$0.104944\pi$
$613$			16.0314i			0.647502i	−0.946142	+	0.323751i	$0.895056\pi$
$614$	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	0.712214	−	0.701962i	$-0.247693\pi$
$617$	11.4362	+	6.60269i	0.460404	+	0.265814i	−0.251810	+	0.967777i	$0.581026\pi$
$618$	−5.87020	+	1.85988i	−0.236134	+	0.0748152i
$619$	1.53649	−	0.887091i	0.0617566	−	0.0356552i	−0.468804	−	0.883302i	$-0.655315\pi$
$619$	1.53649	−	0.887091i	0.0617566	−	0.0356552i	0.530560	+	0.847647i	$0.321982\pi$
$620$	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	$0.205447\pi$
$631$			30.2211i			1.20308i	−0.798841	+	0.601542i	$0.794553\pi$
$632$	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	0.871922	−	0.489646i	$-0.162874\pi$
$641$	0.301673	+	0.522512i	0.0119154	+	0.0206380i	−0.860006	+	0.510284i	$0.829540\pi$
$642$	1.80789	+	1.65199i	0.0713516	+	0.0651988i
$643$	27.0250	+	15.6029i	1.06576	+	0.615317i	0.927020	−	0.375012i	$-0.122361\pi$
$643$	27.0250	+	15.6029i	1.06576	+	0.615317i	0.138740	+	0.990329i	$0.455695\pi$
$644$	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	0.196138	+	0.980576i	$0.437160\pi$
$653$	−19.1944	+	33.2457i	−0.751135	+	1.30100i	−0.947273	+	0.320427i	$0.896173\pi$
$654$	−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	0.908346	+	0.418220i	$0.137346\pi$
$659$	20.9568	+	36.2983i	0.816362	+	1.41398i	−0.0919840	+	0.995760i	$0.529321\pi$
$660$	2.63065	+	0.579350i	0.102398	+	0.0225512i
$661$	10.5208	+	6.07418i	0.409211	+	0.236258i	0.690451	−	0.723379i	$-0.257412\pi$
$661$	10.5208	+	6.07418i	0.409211	+	0.236258i	−0.281240	+	0.959638i	$0.590746\pi$
$662$	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	−0.966189	−	0.257835i	$-0.916991\pi$
$673$	−18.3252	−	31.7403i	−0.706386	−	1.22350i	0.259803	−	0.965662i	$-0.416342\pi$
$674$			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	−0.951757	−	0.306851i	$-0.900725\pi$
$677$	−19.2964	−	33.4223i	−0.741620	−	1.28452i	0.210138	−	0.977672i	$-0.432609\pi$
$678$	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	$-0.794842\pi$
$683$		−	31.4038i		−	1.20163i	0.799387	−	0.600816i	$-0.205158\pi$
$684$	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	−0.782487	−	0.622667i	$-0.786049\pi$
$691$	−16.6786	+	9.62941i	−0.634485	+	0.366320i	0.148002	+	0.988987i	$0.452716\pi$
$692$	−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	−0.511479	+	0.859296i	$0.670902\pi$
$709$	−40.2439	+	23.2348i	−1.51139	+	0.872602i	−0.999911	+	0.0133058i	$0.995764\pi$
$710$			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	0.723671	−	0.690145i	$-0.242453\pi$
$727$	−6.35915	−	11.0144i	−0.235848	−	0.408501i	−0.959519	+	0.281645i	$0.909120\pi$
$728$	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	0.566505	−	0.824058i	$-0.308295\pi$
$733$	3.68483	+	2.12744i	0.136102	+	0.0785787i	−0.430403	+	0.902637i	$0.641628\pi$
$734$	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	$-0.942816\pi$
$739$		−	9.71484i		−	0.357366i	0.983907	−	0.178683i	$-0.0571837\pi$
$740$	−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	0.291259	−	0.956644i	$-0.405926\pi$
$743$	−10.6739	−	6.16261i	−0.391589	−	0.226084i	−0.682848	+	0.730560i	$0.739259\pi$
$744$	−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	−0.838657	−	0.544660i	$-0.816659\pi$
$751$	1.43490	−	2.48532i	0.0523603	−	0.0906908i	0.891018	+	0.453969i	$0.149992\pi$
$752$	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	0.987131	−	0.159915i	$-0.0511220\pi$
$761$	37.0264	+	21.3772i	1.34221	+	0.774923i	0.355075	+	0.934838i	$0.384455\pi$
$762$	−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	0.999994	+	0.00348401i	$0.00110900\pi$
$769$	41.6797	+	24.0638i	1.50301	+	0.867762i	0.503014	+	0.864278i	$0.332224\pi$
$770$	3.93029	−	6.80746i	0.141638	−	0.245324i

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

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.523143 + 1.65116i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.419378 - 0.242128i) q^{5} +(1.27863 + 1.16837i) q^{6} +(4.37722 - 2.52719i) q^{7} -1.00000i q^{8} +(-2.45264 + 1.72758i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 14 q^{4} - 16 q^{9}+O(q^{10}) \) 28 * q + 14 * q^4 - 16 * q^9	\( 28 q + 14 q^{4} - 16 q^{9} + 2 q^{13} + 8 q^{14} - 14 q^{16} + 16 q^{17} - 8 q^{23} + 14 q^{25} + 8 q^{26} + 18 q^{27} - 16 q^{29} - 8 q^{30} - 68 q^{35} - 8 q^{36} - 8 q^{39} - 10 q^{42} - 4 q^{43} + 10 q^{49} + 58 q^{51} - 2 q^{52} - 120 q^{53} - 8 q^{56} + 28 q^{61} + 68 q^{62} - 28 q^{64} - 8 q^{65} - 24 q^{66} + 8 q^{68} - 92 q^{69} + 16 q^{74} + 32 q^{75} - 24 q^{77} - 22 q^{78} + 28 q^{79} + 8 q^{81} - 48 q^{82} + 68 q^{87} - 50 q^{90} + 8 q^{92}+O(q^{100}) \) 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

L-functions

Modular forms

Varieties

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