LMFDB - Embedded newform 234.2.t.a.103.5

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			103.5
Character	$\chi$	$=$	234.103
Dual form			234.2.t.a.25.5

$q$-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} +(-2.69805 + 2.39177i) 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} +(-5.36065 - 3.20367i) 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} +(0.722307 + 3.53246i) 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} +(-1.71061 + 0.349781i) 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} +(6.24429 + 0.0941329i) 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	0.590836	−	0.806792i	$-0.298798\pi$
$5$	0.419378	+	0.242128i	0.187552	+	0.108283i	−0.403284	+	0.915075i	$0.632131\pi$
$6$	−1.27863	−	1.16837i	−0.522000	−	0.476986i
$7$	−4.37722	+	2.52719i	−1.65443	+	0.955188i	−0.679216	+	0.733938i	$0.737680\pi$
$7$	−4.37722	+	2.52719i	−1.65443	+	0.955188i	−0.975217	+	0.221249i	$0.928987\pi$
$8$			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	$-0.505793\pi$
$11$	2.78126	−	1.60576i	0.838583	−	0.484156i	0.856782	+	0.515678i	$0.172460\pi$
$12$	1.69152	+	0.372524i	0.488299	+	0.107538i
$13$	−2.69805	+	2.39177i	−0.748303	+	0.663357i
$13$	−2.69805	+	2.39177i	−0.748303	+	0.663357i
$14$	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	0.328245	+	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	0.910750	−	0.412959i	$-0.135505\pi$
$31$	5.61504	+	3.24185i	1.00849	+	0.582253i	0.0977420	+	0.995212i	$0.468838\pi$
$32$	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
$39$	−5.36065	−	3.20367i	−0.858390	−	0.512997i
$40$	−0.242128	+	0.419378i	−0.0382838	+	0.0663095i
$41$	9.57301	+	5.52698i	1.49505	+	0.863169i	0.999984	−	0.00568392i	$-0.00180926\pi$
$41$	9.57301	+	5.52698i	1.49505	+	0.863169i	0.495070	+	0.868853i	$0.335143\pi$
$42$	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	−0.127851	−	0.991793i	$-0.540808\pi$
$47$	4.57369	−	2.64062i	0.667141	−	0.385174i	0.794992	+	0.606619i	$0.207475\pi$
$48$	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
$52$	0.722307	+	3.53246i	0.100166	+	0.489864i
$53$	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	$-0.409119\pi$
$59$	−3.13771	−	1.81156i	−0.408495	−	0.235844i	−0.690143	+	0.723673i	$0.742452\pi$
$60$	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
$65$	−1.71061	+	0.349781i	−0.212176	+	0.0433851i
$66$	−5.43235	−	1.19637i	−0.668676	−	0.147263i
$67$	−0.936987	−	0.540970i	−0.114471	−	0.0660900i	0.441671	−	0.897177i	$-0.354386\pi$
$67$	−0.936987	−	0.540970i	−0.114471	−	0.0660900i	−0.556142	+	0.831087i	$0.687719\pi$
$68$	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
$78$	6.24429	+	0.0941329i	0.707026	+	0.0106584i
$79$	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	−0.194566	−	0.980889i	$-0.562330\pi$
$83$	5.08022	−	2.93306i	0.557626	−	0.321946i	0.752192	+	0.658944i	$0.228997\pi$
$84$	−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	$-0.897188\pi$
$97$	−11.3021	+	6.52525i	−1.14755	+	0.662539i	−0.199262	+	0.979946i	$0.563855\pi$
$98$			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	$0.222708\pi$
$104$	−2.39177	−	2.69805i	−0.234532	−	0.264565i
$105$	−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	−0.374653	−	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
$117$	2.48538	−	10.5272i	0.229773	−	0.973244i
$118$	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
$130$	1.30655	−	1.15823i	0.114592	−	0.101583i
$131$	−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	−0.998536	−	0.0540880i	$-0.982775\pi$
$137$	−16.9831	+	9.80519i	−1.45096	+	0.837714i	−0.452427	+	0.891802i	$0.649442\pi$
$138$	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	0.125409	−	0.992105i	$-0.459976\pi$
$149$	−8.19151	−	4.72937i	−0.671075	−	0.387445i	−0.796484	+	0.604660i	$0.793309\pi$
$150$	−1.77526	+	8.06091i	−0.144950	+	0.658171i
$151$	−1.15323	+	0.665819i	−0.0938487	+	0.0541836i	−0.546190	−	0.837661i	$-0.683922\pi$
$151$	−1.15323	+	0.665819i	−0.0938487	+	0.0541836i	0.452341	+	0.891845i	$0.350589\pi$
$152$	−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
$156$	−5.45478	+	3.04062i	−0.436732	+	0.243445i
$157$	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	$-0.798065\pi$
$163$		−	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	$-0.487398\pi$
$167$	−10.4155	−	6.01341i	−0.805978	−	0.465331i	−0.845557	+	0.533885i	$0.820732\pi$
$168$	5.90540	−	6.46270i	0.455611	−	0.498608i
$169$	1.55891	−	12.9062i	0.119916	−	0.992784i
$170$	−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	$0.368005\pi$
$182$	3.65081	+	17.8544i	0.270616	+	1.32346i
$183$	−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	0.243117	−	0.969997i	$-0.421830\pi$
$193$	−6.60401	−	3.81283i	−0.475367	−	0.274453i	−0.718484	+	0.695544i	$0.755164\pi$
$194$	6.52525	−	11.3021i	0.468486	−	0.811441i
$195$	−1.47244	−	2.64151i	−0.105444	−	0.189162i
$196$	−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	0.0828724	+	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
$221$	−11.3384	+	10.0513i	−0.762704	+	0.676123i
$222$	−2.43522	+	2.66504i	−0.163441	+	0.178866i
$223$	11.1456	−	6.43490i	0.746363	−	0.430913i	−0.0780155	−	0.996952i	$-0.524858\pi$
$223$	11.1456	−	6.43490i	0.746363	−	0.430913i	0.824378	+	0.566040i	$0.191525\pi$
$224$	−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	$-0.462159\pi$
$227$	15.6362	−	9.02759i	1.03781	−	0.599182i	0.919213	+	0.393760i	$0.128826\pi$
$228$	−1.19637	+	5.43235i	−0.0792317	+	0.359766i
$229$	18.3370	+	10.5869i	1.21174	+	0.699599i	0.963138	−	0.269006i	$-0.0866953\pi$
$229$	18.3370	+	10.5869i	1.21174	+	0.699599i	0.248603	+	0.968606i	$0.420029\pi$
$230$	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	$0.0991033\pi$
$234$	3.11122	+	10.3596i	0.203387	+	0.677225i
$235$	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	$-0.408874\pi$
$239$	−6.29516	−	3.63451i	−0.407200	−	0.235097i	−0.689586	+	0.724204i	$0.742207\pi$
$240$	0.799583	−	0.253335i	0.0516129	−	0.0163527i
$241$	−15.5109	+	8.95521i	−0.999144	+	0.576856i	−0.907995	−	0.418981i	$-0.862387\pi$
$241$	−15.5109	+	8.95521i	−0.999144	+	0.576856i	−0.0911491	+	0.995837i	$0.529054\pi$
$242$		−	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
$247$	−7.68122	−	8.66485i	−0.488745	−	0.551331i
$248$	−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	$0.0347335\pi$
$271$			3.58551i			0.217804i	−0.994052	+	0.108902i	$0.965266\pi$
$272$	−2.10123	−	3.63943i	−0.127406	−	0.220673i
$273$	31.5610	+	0.475783i	1.91016	+	0.0287957i
$274$	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	−0.861674	−	0.507462i	$-0.830584\pi$
$281$	−14.2995	+	8.25582i	−0.853037	+	0.492501i	0.00863764	+	0.999963i	$0.497251\pi$
$282$	−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
$286$	−2.31971	−	11.3446i	−0.137167	−	0.670820i
$287$	−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	$-0.139416\pi$
$293$	16.9651	+	9.79482i	0.991113	+	0.572220i	0.0855065	+	0.996338i	$0.472749\pi$
$294$	−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
$299$	−4.53043	−	22.1562i	−0.262002	−	1.28132i
$300$	−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	−0.501438	−	0.865194i	$-0.667195\pi$
$311$	8.79222	−	15.2286i	0.498561	−	0.863533i	0.999999	+	0.00166095i	$0.000528697\pi$
$312$	3.20367	−	5.36065i	0.181372	−	0.303487i
$313$	−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	0.00897641	−	0.999960i	$-0.497143\pi$
$317$	15.6583	−	9.04030i	0.879455	−	0.507754i	0.870479	+	0.492206i	$0.163809\pi$
$318$	−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	$-0.703446\pi$
$331$	−3.63300	+	2.09751i	−0.199688	+	0.115290i	0.396822	+	0.917896i	$0.370113\pi$
$332$		−	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	$0.288955\pi$
$338$	5.10304	+	11.9565i	0.277569	+	0.650350i
$339$	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	0.0207153	−	0.999785i	$-0.493406\pi$
$349$	16.7557	−	9.67391i	0.896913	−	0.517833i	0.876197	+	0.481953i	$0.160072\pi$
$350$	−24.0866			−1.28748
$351$	18.6823	−	1.40350i	0.997190	−	0.0749134i
$352$	3.21153			0.171175
$353$	24.0606	−	13.8914i	1.28062	−	0.739365i	0.303656	−	0.952782i	$-0.401793\pi$
$353$	24.0606	−	13.8914i	1.28062	−	0.739365i	0.976961	+	0.213417i	$0.0684593\pi$
$354$	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
$364$	−12.0889	−	13.6369i	−0.633630	−	0.714770i
$365$	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	$0.289296\pi$
$379$			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	$-0.309846\pi$
$383$	2.49892	+	1.44275i	0.127689	+	0.0737212i	−0.434795	+	0.900529i	$0.643179\pi$
$384$	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	$0.735825\pi$
$390$	2.59592	+	1.55139i	0.131450	+	0.0785579i
$391$	−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	$-0.261211\pi$
$401$	7.79168	+	4.49853i	0.389098	+	0.224646i	−0.292671	+	0.956213i	$0.594544\pi$
$402$	0.566009	+	1.78645i	0.0282300	+	0.0891002i
$403$	−22.9034	+	4.68322i	−1.14090	+	0.233288i
$404$	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	$-0.0410033\pi$
$409$	27.8344	+	16.0702i	1.37632	+	0.794620i	0.384608	+	0.923080i	$0.374337\pi$
$410$	−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
$416$	−3.53246	+	0.722307i	−0.173193	+	0.0354140i
$417$	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	−0.443757	−	0.896147i	$-0.646355\pi$
$421$	2.26626	−	1.30842i	0.110451	−	0.0637687i	0.554208	+	0.832378i	$0.313021\pi$
$422$		−	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
$429$	−20.0537	−	0.302310i	−0.968202	−	0.0145957i
$430$	−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	−0.916795	−	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	$0.129595\pi$
$449$			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
$455$	6.60377	−	5.85412i	0.309590	−	0.274445i
$456$	−1.68009	−	5.30274i	−0.0786773	−	0.248324i
$457$	20.5067	−	11.8396i	0.959263	−	0.553831i	0.0633172	−	0.997993i	$-0.479832\pi$
$457$	20.5067	−	11.8396i	0.959263	−	0.553831i	0.895946	+	0.444162i	$0.146499\pi$
$458$	−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	$-0.370152\pi$
$461$	29.8451	−	17.2311i	1.39003	−	0.802533i	0.993318	+	0.115412i	$0.0368188\pi$
$462$	26.8020	−	8.49179i	1.24694	−	0.395074i
$463$	−19.4659	−	11.2386i	−0.904657	−	0.522304i	−0.0259487	−	0.999663i	$-0.508261\pi$
$463$	−19.4659	−	11.2386i	−0.904657	−	0.522304i	−0.878708	+	0.477359i	$0.841594\pi$
$464$	−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	$0.532730\pi$
$468$	−7.87417	−	7.41602i	−0.363984	−	0.342806i
$469$	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	$-0.753676\pi$
$479$	−10.2334	+	5.90827i	−0.467577	+	0.269956i	0.247648	+	0.968850i	$0.420342\pi$
$480$	−0.565792	+	0.619186i	−0.0258247	+	0.0282618i
$481$	4.98512	+	5.62350i	0.227302	+	0.256409i
$482$	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	−0.964274	−	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	0.768786	−	0.639507i	$-0.220861\pi$
$499$	13.3884	+	7.72982i	0.599349	+	0.346034i	−0.169436	+	0.985541i	$0.554195\pi$
$500$	−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
$507$	22.1257	−	4.17777i	0.982636	−	0.185541i
$508$	−2.28150	+	3.95167i	−0.101225	+	0.175327i
$509$	−18.6801	−	10.7849i	−0.827979	−	0.478034i	0.0251810	−	0.999683i	$-0.491984\pi$
$509$	−18.6801	−	10.7849i	−0.827979	−	0.478034i	−0.853160	+	0.521649i	$0.825317\pi$
$510$	−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
$520$	−0.349781	−	1.71061i	−0.0153389	−	0.0750154i
$521$	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
$533$	−39.0477	+	7.98436i	−1.69134	+	0.345841i
$534$	−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
$546$	−27.5705	+	15.3685i	−1.17991	+	0.657709i
$547$	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	$0.0978589\pi$
$557$			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	−0.187026	−	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	$-0.254865\pi$
$572$	7.68122	+	8.66485i	0.321168	+	0.362296i
$573$	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
$585$	3.59125	−	3.81312i	0.148480	−	0.157653i
$586$	−19.5896			−0.809241
$587$	−27.0638	+	15.6253i	−1.11704	+	0.644924i	−0.940644	−	0.339395i	$-0.889778\pi$
$587$	−27.0638	+	15.6253i	−1.11704	+	0.644924i	−0.176397	+	0.984319i	$0.556444\pi$
$588$	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
$598$	15.0016	+	16.9226i	0.613459	+	0.692016i
$599$	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	$-0.895056\pi$
$613$		−	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	$-0.418974\pi$
$617$	−11.4362	−	6.60269i	−0.460404	−	0.265814i	−0.712214	+	0.701962i	$0.752307\pi$
$618$	5.87020	−	1.85988i	0.236134	−	0.0748152i
$619$	−1.53649	+	0.887091i	−0.0617566	+	0.0356552i	−0.530560	−	0.847647i	$-0.678018\pi$
$619$	−1.53649	+	0.887091i	−0.0617566	+	0.0356552i	0.468804	+	0.883302i	$0.344685\pi$
$620$	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
$624$	−0.0941329	+	6.24429i	−0.00376833	+	0.249972i
$625$	−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
$637$	13.3964	+	65.5156i	0.530786	+	2.59582i
$638$	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	−0.138740	−	0.990329i	$-0.544305\pi$
$643$	−27.0250	−	15.6029i	−1.06576	−	0.615317i	−0.927020	+	0.375012i	$0.877639\pi$
$644$	−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
$650$	−16.8339	+	3.44215i	−0.660281	+	0.135012i
$651$	−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	0.281240	−	0.959638i	$-0.409254\pi$
$661$	−10.5208	−	6.07418i	−0.409211	−	0.236258i	−0.690451	+	0.723379i	$0.742588\pi$
$662$	2.09751	−	3.63300i	0.0815221	−	0.141200i
$663$	−22.5279	−	13.4633i	−0.874910	−	0.522870i
$664$	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	$0.205158\pi$
$683$			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
$689$	−17.3212	+	15.3549i	−0.659885	+	0.584975i
$690$	5.13770	+	1.13148i	0.195589	+	0.0430747i
$691$	16.6786	−	9.62941i	0.634485	−	0.366320i	−0.148002	−	0.988987i	$-0.547284\pi$
$691$	16.6786	−	9.62941i	0.634485	−	0.366320i	0.782487	+	0.622667i	$0.213951\pi$
$692$	−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	$0.668765\pi$
$702$	−15.4776	+	10.5566i	−0.584166	+	0.398435i
$703$	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	$-0.329098\pi$
$709$	40.2439	−	23.2348i	1.51139	−	0.872602i	0.999911	−	0.0133058i	$-0.00423551\pi$
$710$		−	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
$715$	−4.19601	+	3.71968i	−0.156922	+	0.139108i
$716$	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	0.430403	−	0.902637i	$-0.358372\pi$
$733$	−3.68483	−	2.12744i	−0.136102	−	0.0785787i	−0.566505	+	0.824058i	$0.691705\pi$
$734$	−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
$741$	10.2887	−	17.2159i	0.377963	−	0.632441i
$742$	16.2243	−	28.1013i	0.595613	−	1.03163i
$743$	10.6739	+	6.16261i	0.391589	+	0.226084i	0.682848	−	0.730560i	$-0.260741\pi$
$743$	10.6739	+	6.16261i	0.391589	+	0.226084i	−0.291259	+	0.956644i	$0.594074\pi$
$744$	−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
$754$	−16.2229	+	3.31722i	−0.590805	+	0.120806i
$755$	−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	$-0.615545\pi$
$761$	−37.0264	−	21.3772i	−1.34221	−	0.774923i	−0.987131	+	0.159915i	$0.948878\pi$
$762$	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
$767$	12.7985	−	2.61700i	0.462127	−	0.0944943i
$768$	−1.69152	−	0.372524i	−0.0610373	−	0.0134423i
$769$	−41.6797	−	24.0638i	−1.50301	−	0.867762i	−0.999994	−	0.00348401i	$-0.998891\pi$
$769$	−41.6797	−	24.0638i	−1.50301	−	0.867762i	−0.503014	−	0.864278i	$-0.667776\pi$
$770$	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} +(-2.69805 + 2.39177i) 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} +(-5.36065 - 3.20367i) 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} +(0.722307 + 3.53246i) 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} +(-1.71061 + 0.349781i) 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} +(6.24429 + 0.0941329i) 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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Representations

Groups

Database

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