LMFDB - Embedded newform 234.2.z.a.227.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,2,Mod(41,234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 1]))

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

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

chi := DirichletCharacter("234.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.z (of order $12$, degree $4$, 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:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			227.4
Character	$\chi$	$=$	234.227
Dual form			234.2.z.a.167.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(-0.408561 + 1.68317i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.179629 + 0.670386i) q^{5} +(-1.52008 - 0.830278i) q^{6} +(3.24572 + 3.24572i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.66616 - 1.37536i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.408561 + 1.68317i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.179629 + 0.670386i) q^{5} +(-1.52008 - 0.830278i) q^{6} +(3.24572 + 3.24572i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.66616 - 1.37536i) q^{9} +(-0.601052 - 0.347017i) q^{10} +(-2.17356 - 0.582403i) q^{11} +(1.19541 - 1.25339i) q^{12} +(-1.78196 + 3.13442i) q^{13} +(-3.97518 + 2.29507i) q^{14} +(-1.05499 - 0.576241i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-2.32181 - 4.02149i) q^{17} +(2.01855 - 2.21934i) q^{18} +(-2.81042 - 0.753050i) q^{19} +(0.490757 - 0.490757i) q^{20} +(-6.78919 + 4.13704i) q^{21} +(1.12512 - 1.94876i) q^{22} +4.74503 q^{23} +(0.901288 + 1.47908i) q^{24} +(3.91298 + 2.25916i) q^{25} +(-2.56642 - 2.53249i) q^{26} +(3.40426 - 3.92569i) q^{27} +(-1.18802 - 4.43374i) q^{28} +(-4.22816 + 2.44113i) q^{29} +(0.829657 - 0.869897i) q^{30} +(6.51808 + 1.74651i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(1.86832 - 3.42053i) q^{33} +(4.48539 - 1.20186i) q^{34} +(-2.75891 + 1.59286i) q^{35} +(1.62128 + 2.52417i) q^{36} +(3.44953 - 0.924299i) q^{37} +(1.45478 - 2.51976i) q^{38} +(-4.54775 - 4.27995i) q^{39} +(0.347017 + 0.601052i) q^{40} +(4.05999 + 4.05999i) q^{41} +(-2.23890 - 7.62860i) q^{42} -5.30657i q^{43} +(1.59115 + 1.59115i) q^{44} +(1.40094 - 1.54030i) q^{45} +(-1.22810 + 4.58334i) q^{46} +(3.12430 + 11.6601i) q^{47} +(-1.66195 + 0.487763i) q^{48} +14.0694i q^{49} +(-3.19493 + 3.19493i) q^{50} +(7.71746 - 2.26498i) q^{51} +(3.11043 - 1.82351i) q^{52} +5.06576i q^{53} +(2.91083 + 4.30431i) q^{54} +(0.780869 - 1.35250i) q^{55} +4.59014 q^{56} +(2.41575 - 4.42276i) q^{57} +(-1.26362 - 4.71590i) q^{58} +(-1.38984 - 5.18694i) q^{59} +(0.625525 + 1.02653i) q^{60} +3.12110 q^{61} +(-3.37401 + 5.84395i) q^{62} +(-4.18956 - 13.1176i) q^{63} -1.00000i q^{64} +(-1.78118 - 1.75764i) q^{65} +(2.82042 + 2.68995i) q^{66} +(9.25140 - 9.25140i) q^{67} +4.64361i q^{68} +(-1.93864 + 7.98671i) q^{69} +(-0.824524 - 3.07717i) q^{70} +(4.16970 - 15.5615i) q^{71} +(-2.85778 + 0.912729i) q^{72} +(-5.55110 - 5.55110i) q^{73} +3.57122i q^{74} +(-5.40125 + 5.66322i) q^{75} +(2.05737 + 2.05737i) q^{76} +(-5.16444 - 8.94507i) q^{77} +(5.31116 - 3.28505i) q^{78} +(-1.55400 + 2.69161i) q^{79} +(-0.670386 + 0.179629i) q^{80} +(5.21677 + 7.33385i) q^{81} +(-4.97245 + 2.87085i) q^{82} +(9.17998 - 2.45977i) q^{83} +(7.94813 - 0.188185i) q^{84} +(3.11301 - 0.834129i) q^{85} +(5.12575 + 1.37344i) q^{86} +(-2.38139 - 8.11409i) q^{87} +(-1.94876 + 1.12512i) q^{88} +(0.648204 + 2.41913i) q^{89} +(1.12522 + 1.75186i) q^{90} +(-15.9572 + 4.38972i) q^{91} +(-4.10931 - 2.37251i) q^{92} +(-5.60272 + 10.2575i) q^{93} -12.0714 q^{94} +(1.00967 - 1.74880i) q^{95} +(-0.0409976 - 1.73157i) q^{96} +(-0.868150 + 0.868150i) q^{97} +(-13.5900 - 3.64143i) q^{98} +(4.99402 + 4.54220i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{7}+O(q^{10}) $ 56 * q - 8 * q^7	$ 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47} - 24 q^{50} + 8 q^{52} - 36 q^{54} + 36 q^{57} + 24 q^{60} - 48 q^{63} - 36 q^{65} + 28 q^{67} + 84 q^{69} - 24 q^{71} - 24 q^{72} + 28 q^{73} + 4 q^{76} + 24 q^{77} - 60 q^{78} - 24 q^{79} + 24 q^{81} - 96 q^{83} - 72 q^{85} + 4 q^{91} - 24 q^{92} - 36 q^{93} - 52 q^{97} + 48 q^{98} + 60 q^{99}+O(q^{100}) $ 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$	−0.408561	+	1.68317i	−0.235883	+	0.971781i
$3$	−0.408561	+	1.68317i	−0.235883	+	0.971781i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	−0.179629	+	0.670386i	−0.0803327	+	0.299806i	−0.994390	−	0.105780i	$-0.966266\pi$
$5$	−0.179629	+	0.670386i	−0.0803327	+	0.299806i	0.914057	+	0.405586i	$0.132933\pi$
$6$	−1.52008	−	0.830278i	−0.620569	−	0.338959i
$7$	3.24572	+	3.24572i	1.22677	+	1.22677i	0.965180	+	0.261587i	$0.0842458\pi$
$7$	3.24572	+	3.24572i	1.22677	+	1.22677i	0.261587	+	0.965180i	$0.415754\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−2.66616	−	1.37536i	−0.888718	−	0.458454i
$10$	−0.601052	−	0.347017i	−0.190069	−	0.109736i
$11$	−2.17356	−	0.582403i	−0.655352	−	0.175601i	−0.0842044	−	0.996449i	$-0.526835\pi$
$11$	−2.17356	−	0.582403i	−0.655352	−	0.175601i	−0.571147	+	0.820848i	$0.693502\pi$
$12$	1.19541	−	1.25339i	0.345086	−	0.361823i
$13$	−1.78196	+	3.13442i	−0.494227	+	0.869333i
$13$	−1.78196	+	3.13442i	−0.494227	+	0.869333i
$14$	−3.97518	+	2.29507i	−1.06241	+	0.613383i
$15$	−1.05499	−	0.576241i	−0.272396	−	0.148785i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−2.32181	−	4.02149i	−0.563121	−	0.975354i	−0.997222	−	0.0744895i	$-0.976267\pi$
$17$	−2.32181	−	4.02149i	−0.563121	−	0.975354i	0.434101	−	0.900864i	$-0.357066\pi$
$18$	2.01855	−	2.21934i	0.475776	−	0.523103i
$19$	−2.81042	−	0.753050i	−0.644755	−	0.172762i	−0.0783988	−	0.996922i	$-0.524981\pi$
$19$	−2.81042	−	0.753050i	−0.644755	−	0.172762i	−0.566356	+	0.824160i	$0.691647\pi$
$20$	0.490757	−	0.490757i	0.109736	−	0.109736i
$21$	−6.78919	+	4.13704i	−1.48152	+	0.902776i
$22$	1.12512	−	1.94876i	0.239875	−	0.415476i
$23$	4.74503			0.989407			0.494703	−	0.869062i	$-0.335277\pi$
$23$	4.74503			0.989407			0.494703	+	0.869062i	$0.335277\pi$
$24$	0.901288	+	1.47908i	0.183975	+	0.301916i
$25$	3.91298	+	2.25916i	0.782595	+	0.451832i
$26$	−2.56642	−	2.53249i	−0.503316	−	0.496662i
$27$	3.40426	−	3.92569i	0.655150	−	0.755499i
$28$	−1.18802	−	4.43374i	−0.224514	−	0.837897i
$29$	−4.22816	+	2.44113i	−0.785150	+	0.453307i	−0.838252	−	0.545282i	$-0.816422\pi$
$29$	−4.22816	+	2.44113i	−0.785150	+	0.453307i	0.0531023	+	0.998589i	$0.483089\pi$
$30$	0.829657	−	0.869897i	0.151474	−	0.158821i
$31$	6.51808	+	1.74651i	1.17068	+	0.313683i	0.791224	−	0.611526i	$-0.209444\pi$
$31$	6.51808	+	1.74651i	1.17068	+	0.313683i	0.379457	+	0.925209i	$0.376111\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	1.86832	−	3.42053i	0.325232	−	0.595437i
$34$	4.48539	−	1.20186i	0.769237	−	0.206116i
$35$	−2.75891	+	1.59286i	−0.466341	+	0.269242i
$36$	1.62128	+	2.52417i	0.270213	+	0.420696i
$37$	3.44953	−	0.924299i	0.567099	−	0.151954i	0.0361333	−	0.999347i	$-0.488496\pi$
$37$	3.44953	−	0.924299i	0.567099	−	0.151954i	0.530966	+	0.847393i	$0.321829\pi$
$38$	1.45478	−	2.51976i	0.235997	−	0.408758i
$39$	−4.54775	−	4.27995i	−0.728222	−	0.685341i
$40$	0.347017	+	0.601052i	0.0548682	+	0.0950346i
$41$	4.05999	+	4.05999i	0.634064	+	0.634064i	0.949085	−	0.315021i	$-0.102012\pi$
$41$	4.05999	+	4.05999i	0.634064	+	0.634064i	−0.315021	+	0.949085i	$0.602012\pi$
$42$	−2.23890	−	7.62860i	−0.345470	−	1.17712i
$43$		−	5.30657i		−	0.809244i	−0.914484	−	0.404622i	$-0.867403\pi$
$43$		−	5.30657i		−	0.809244i	0.914484	−	0.404622i	$-0.132597\pi$
$44$	1.59115	+	1.59115i	0.239875	+	0.239875i
$45$	1.40094	−	1.54030i	0.208840	−	0.229614i
$46$	−1.22810	+	4.58334i	−0.181074	+	0.675777i
$47$	3.12430	+	11.6601i	0.455727	+	1.70080i	0.685943	+	0.727656i	$0.259390\pi$
$47$	3.12430	+	11.6601i	0.455727	+	1.70080i	−0.230216	+	0.973140i	$0.573943\pi$
$48$	−1.66195	+	0.487763i	−0.239882	+	0.0704025i
$49$			14.0694i			2.00991i
$50$	−3.19493	+	3.19493i	−0.451832	+	0.451832i
$51$	7.71746	−	2.26498i	1.08066	−	0.317161i
$52$	3.11043	−	1.82351i	0.431340	−	0.252876i
$53$			5.06576i			0.695835i	0.937525	+	0.347918i	$0.113111\pi$
$53$			5.06576i			0.695835i	−0.937525	+	0.347918i	$0.886889\pi$
$54$	2.91083	+	4.30431i	0.396114	+	0.585742i
$55$	0.780869	−	1.35250i	0.105292	−	0.182372i
$56$	4.59014			0.613383
$57$	2.41575	−	4.42276i	0.319973	−	0.585810i
$58$	−1.26362	−	4.71590i	−0.165922	−	0.619228i
$59$	−1.38984	−	5.18694i	−0.180941	−	0.675282i	−0.995463	−	0.0951492i	$-0.969667\pi$
$59$	−1.38984	−	5.18694i	−0.180941	−	0.675282i	0.814522	−	0.580133i	$-0.196999\pi$
$60$	0.625525	+	1.02653i	0.0807549	+	0.132525i
$61$	3.12110			0.399616			0.199808	−	0.979835i	$-0.435968\pi$
$61$	3.12110			0.399616			0.199808	+	0.979835i	$0.435968\pi$
$62$	−3.37401	+	5.84395i	−0.428499	+	0.742182i
$63$	−4.18956	−	13.1176i	−0.527834	−	1.65267i
$64$		−	1.00000i		−	0.125000i
$65$	−1.78118	−	1.75764i	−0.220928	−	0.218008i
$66$	2.82042	+	2.68995i	0.347170	+	0.331110i
$67$	9.25140	−	9.25140i	1.13024	−	1.13024i	0.140102	−	0.990137i	$-0.455257\pi$
$67$	9.25140	−	9.25140i	1.13024	−	1.13024i	0.990137	−	0.140102i	$-0.0447429\pi$
$68$			4.64361i			0.563121i
$69$	−1.93864	+	7.98671i	−0.233384	+	0.961487i
$70$	−0.824524	−	3.07717i	−0.0985495	−	0.367792i
$71$	4.16970	−	15.5615i	0.494852	−	1.84681i	−0.0360054	−	0.999352i	$-0.511463\pi$
$71$	4.16970	−	15.5615i	0.494852	−	1.84681i	0.530857	−	0.847461i	$-0.321870\pi$
$72$	−2.85778	+	0.912729i	−0.336793	+	0.107566i
$73$	−5.55110	−	5.55110i	−0.649707	−	0.649707i	0.303215	−	0.952922i	$-0.401940\pi$
$73$	−5.55110	−	5.55110i	−0.649707	−	0.649707i	−0.952922	+	0.303215i	$0.901940\pi$
$74$			3.57122i			0.415145i
$75$	−5.40125	+	5.66322i	−0.623683	+	0.653932i
$76$	2.05737	+	2.05737i	0.235997	+	0.235997i
$77$	−5.16444	−	8.94507i	−0.588542	−	1.01939i
$78$	5.31116	−	3.28505i	0.601371	−	0.371959i
$79$	−1.55400	+	2.69161i	−0.174839	+	0.302829i	−0.940105	−	0.340884i	$-0.889274\pi$
$79$	−1.55400	+	2.69161i	−0.174839	+	0.302829i	0.765267	+	0.643713i	$0.222607\pi$
$80$	−0.670386	+	0.179629i	−0.0749514	+	0.0200832i
$81$	5.21677	+	7.33385i	0.579641	+	0.814872i
$82$	−4.97245	+	2.87085i	−0.549115	+	0.317032i
$83$	9.17998	−	2.45977i	1.00763	−	0.269995i	0.282993	−	0.959122i	$-0.408673\pi$
$83$	9.17998	−	2.45977i	1.00763	−	0.269995i	0.724640	+	0.689127i	$0.242006\pi$
$84$	7.94813	−	0.188185i	0.867212	−	0.0205326i
$85$	3.11301	−	0.834129i	0.337654	−	0.0904740i
$86$	5.12575	+	1.37344i	0.552724	+	0.148102i
$87$	−2.38139	−	8.11409i	−0.255311	−	0.869922i
$88$	−1.94876	+	1.12512i	−0.207738	+	0.119938i
$89$	0.648204	+	2.41913i	0.0687095	+	0.256427i	0.991733	−	0.128315i	$-0.0409569\pi$
$89$	0.648204	+	2.41913i	0.0687095	+	0.256427i	−0.923024	+	0.384743i	$0.874290\pi$
$90$	1.12522	+	1.75186i	0.118609	+	0.184663i
$91$	−15.9572	+	4.38972i	−1.67277	+	0.460168i
$92$	−4.10931	−	2.37251i	−0.428426	−	0.247352i
$93$	−5.60272	+	10.2575i	−0.580975	+	1.06365i
$94$	−12.0714			−1.24507
$95$	1.00967	−	1.74880i	0.103590	−	0.179423i
$96$	−0.0409976	−	1.73157i	−0.00418430	−	0.176727i
$97$	−0.868150	+	0.868150i	−0.0881473	+	0.0881473i	−0.749806	−	0.661658i	$-0.769853\pi$
$97$	−0.868150	+	0.868150i	−0.0881473	+	0.0881473i	0.661658	+	0.749806i	$0.269853\pi$
$98$	−13.5900	−	3.64143i	−1.37280	−	0.367840i
$99$	4.99402	+	4.54220i	0.501918	+	0.456508i
$100$	−2.25916	−	3.91298i	−0.225916	−	0.391298i
$101$	−1.88220	−	3.26007i	−0.187286	−	0.324389i	0.757058	−	0.653347i	$-0.226636\pi$
$101$	−1.88220	−	3.26007i	−0.187286	−	0.324389i	−0.944345	+	0.328958i	$0.893302\pi$
$102$	0.190377	+	8.04072i	0.0188501	+	0.796150i
$103$	−13.1567	+	7.59604i	−1.29637	+	0.748460i	−0.979775	−	0.200100i	$-0.935873\pi$
$103$	−13.1567	+	7.59604i	−1.29637	+	0.748460i	−0.316596	+	0.948561i	$0.602540\pi$
$104$	0.956337	+	3.47641i	0.0937766	+	0.340890i
$105$	−1.55387	−	5.29451i	−0.151643	−	0.516691i
$106$	−4.89315	−	1.31111i	−0.475264	−	0.127347i
$107$	4.73458	+	2.73351i	0.457709	+	0.264259i	0.711081	−	0.703111i	$-0.248206\pi$
$107$	4.73458	+	2.73351i	0.457709	+	0.264259i	−0.253371	+	0.967369i	$0.581539\pi$
$108$	−4.91102	+	1.69761i	−0.472563	+	0.163353i
$109$	5.10130	−	5.10130i	0.488616	−	0.488616i	−0.419253	−	0.907869i	$-0.637708\pi$
$109$	5.10130	−	5.10130i	0.488616	−	0.488616i	0.907869	+	0.419253i	$0.137708\pi$
$110$	1.10432	+	1.10432i	0.105292	+	0.105292i
$111$	0.146411	+	6.18379i	0.0138967	+	0.586940i
$112$	−1.18802	+	4.43374i	−0.112257	+	0.418949i
$113$	0.409538	+	0.236447i	0.0385261	+	0.0222430i	0.519139	−	0.854690i	$-0.326253\pi$
$113$	0.409538	+	0.236447i	0.0385261	+	0.0222430i	−0.480613	+	0.876933i	$0.659586\pi$
$114$	3.64682	+	3.47813i	0.341556	+	0.325756i
$115$	−0.852346	+	3.18100i	−0.0794817	+	0.296630i
$116$	4.88226			0.453307
$117$	9.06195	−	5.90603i	0.837777	−	0.546012i
$118$	5.36992			0.494341
$119$	5.51668	−	20.5885i	0.505714	−	1.88735i
$120$	−1.15345	+	0.338524i	−0.105295	+	0.0309029i
$121$	−5.14113	−	2.96823i	−0.467375	−	0.269839i
$122$	−0.807800	+	3.01475i	−0.0731348	+	0.272943i
$123$	−8.49243	+	5.17492i	−0.765736	+	0.466607i
$124$	−4.77157	−	4.77157i	−0.428499	−	0.428499i
$125$	−4.67118	+	4.67118i	−0.417803	+	0.417803i
$126$	13.7550	−	0.651708i	1.22539	−	0.0580588i
$127$	−0.377096	−	0.217716i	−0.0334618	−	0.0193192i	0.483176	−	0.875523i	$-0.339483\pi$
$127$	−0.377096	−	0.217716i	−0.0334618	−	0.0193192i	−0.516638	+	0.856204i	$0.672817\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	8.93188	+	2.16806i	0.786408	+	0.190887i
$130$	2.15875	−	1.26558i	0.189335	−	0.110999i
$131$	−9.02321	+	5.20955i	−0.788361	+	0.455161i	−0.839385	−	0.543537i	$-0.817085\pi$
$131$	−9.02321	+	5.20955i	−0.788361	+	0.455161i	0.0510241	+	0.998697i	$0.483751\pi$
$132$	−3.32827	+	2.02811i	−0.289689	+	0.176524i
$133$	−6.67765	−	11.5660i	−0.579026	−	1.00290i
$134$	6.54173	+	11.3306i	0.565119	+	0.978815i
$135$	2.02022	+	2.98734i	0.173873	+	0.257109i
$136$	−4.48539	−	1.20186i	−0.384619	−	0.103058i
$137$	−5.40791	+	5.40791i	−0.462029	+	0.462029i	−0.899320	−	0.437291i	$-0.855938\pi$
$137$	−5.40791	+	5.40791i	−0.462029	+	0.462029i	0.437291	+	0.899320i	$0.355938\pi$
$138$	−7.21281	−	3.93969i	−0.613996	−	0.335369i
$139$	−5.58662	+	9.67631i	−0.473851	+	0.820734i	−0.999552	−	0.0299353i	$-0.990470\pi$
$139$	−5.58662	+	9.67631i	−0.473851	+	0.820734i	0.525701	+	0.850670i	$0.323803\pi$
$140$	3.18572			0.269242
$141$	−20.9024	+	0.494898i	−1.76030	+	0.0416779i
$142$	13.9521	+	8.05524i	1.17083	+	0.675980i
$143$	5.69869	−	5.77503i	0.476548	−	0.482932i
$144$	−0.141980	−	2.99664i	−0.0118317	−	0.249720i
$145$	−0.876997	−	3.27300i	−0.0728307	−	0.271808i
$146$	6.79868	−	3.92522i	0.562663	−	0.324853i
$147$	−23.6812	−	5.74821i	−1.95320	−	0.474105i
$148$	−3.44953	−	0.924299i	−0.283550	−	0.0759769i
$149$	−7.14709	+	1.91506i	−0.585513	+	0.156888i	−0.539401	−	0.842049i	$-0.681349\pi$
$149$	−7.14709	+	1.91506i	−0.585513	+	0.156888i	−0.0461110	+	0.998936i	$0.514683\pi$
$150$	−4.07230	−	6.68296i	−0.332502	−	0.545661i
$151$	13.8415	−	3.70881i	1.12640	−	0.301818i	0.352930	−	0.935650i	$-0.385185\pi$
$151$	13.8415	−	3.70881i	1.12640	−	0.301818i	0.773471	+	0.633831i	$0.218519\pi$
$152$	−2.51976	+	1.45478i	−0.204379	+	0.117998i
$153$	0.659300	+	13.9152i	0.0533013	+	1.12498i
$154$	9.97693	−	2.67331i	0.803964	−	0.215421i
$155$	−2.34168	+	4.05590i	−0.188088	+	0.325778i
$156$	1.79849	+	5.98042i	0.143994	+	0.478817i
$157$	−2.86104	−	4.95546i	−0.228336	−	0.395489i	0.728979	−	0.684536i	$-0.239995\pi$
$157$	−2.86104	−	4.95546i	−0.228336	−	0.395489i	−0.957315	+	0.289047i	$0.906662\pi$
$158$	−2.19769	−	2.19769i	−0.174839	−	0.174839i
$159$	−8.52656	−	2.06967i	−0.676200	−	0.164136i
$160$		−	0.694035i		−	0.0548682i
$161$	15.4010	+	15.4010i	1.21377	+	1.21377i
$162$	−8.43415	+	3.14087i	−0.662650	+	0.246770i
$163$	−1.44621	+	5.39731i	−0.113276	+	0.422750i	−0.999152	−	0.0411708i	$-0.986891\pi$
$163$	−1.44621	+	5.39731i	−0.113276	+	0.422750i	0.885877	+	0.463921i	$0.153558\pi$
$164$	−1.48606	−	5.54605i	−0.116042	−	0.433074i
$165$	1.95747	+	1.86692i	0.152389	+	0.145340i
$166$			9.50381i			0.737639i
$167$	17.3166	−	17.3166i	1.34000	−	1.34000i	0.443945	−	0.896054i	$-0.353579\pi$
$167$	17.3166	−	17.3166i	1.34000	−	1.34000i	0.896054	−	0.443945i	$-0.146421\pi$
$168$	−1.87535	+	7.72601i	−0.144687	+	0.596075i
$169$	−6.64924	−	11.1708i	−0.511480	−	0.859295i
$170$			3.22283i			0.247180i
$171$	6.45731	+	5.87309i	0.493803	+	0.449127i
$172$	−2.65328	+	4.59562i	−0.202311	+	0.350413i
$173$	−10.5940			−0.805445			−0.402722	−	0.915322i	$-0.631936\pi$
$173$	−10.5940			−0.805445			−0.402722	+	0.915322i	$0.631936\pi$
$174$	8.45396	−	0.200161i	0.640893	−	0.0151742i
$175$	5.36783	+	20.0330i	0.405770	+	1.51435i
$176$	−0.582403	−	2.17356i	−0.0439002	−	0.163838i
$177$	9.29836	−	0.220154i	0.698908	−	0.0165478i
$178$	−2.50447			−0.187718
$179$	6.22591	−	10.7836i	0.465346	−	0.806003i	−0.533871	−	0.845566i	$-0.679263\pi$
$179$	6.22591	−	10.7836i	0.465346	−	0.806003i	0.999217	+	0.0395630i	$0.0125966\pi$
$180$	−1.98340	+	0.633466i	−0.147834	+	0.0472157i
$181$		−	18.4465i		−	1.37112i	−0.728018	−	0.685558i	$-0.759558\pi$
$181$		−	18.4465i		−	1.37112i	0.728018	−	0.685558i	$-0.240442\pi$
$182$	−0.110118	−	16.5496i	−0.00816251	−	1.22674i
$183$	−1.27516	+	5.25336i	−0.0942627	+	0.388339i
$184$	3.35524	−	3.35524i	0.247352	−	0.247352i
$185$			2.47855i			0.182226i
$186$	−8.45790	−	8.06666i	−0.620163	−	0.591476i
$187$	2.70445	+	10.0932i	0.197769	+	0.738084i
$188$	3.12430	−	11.6601i	0.227863	−	0.850398i
$189$	23.7910	−	1.69240i	1.73054	−	0.123104i
$190$	1.42789	+	1.42789i	0.103590	+	0.103590i
$191$			8.51565i			0.616171i	0.951359	+	0.308085i	$0.0996883\pi$
$191$			8.51565i			0.616171i	−0.951359	+	0.308085i	$0.900312\pi$
$192$	1.68317	+	0.408561i	0.121473	+	0.0294854i
$193$	−13.3856	−	13.3856i	−0.963516	−	0.963516i	0.0358411	−	0.999358i	$-0.488589\pi$
$193$	−13.3856	−	13.3856i	−0.963516	−	0.963516i	−0.999358	+	0.0358411i	$0.988589\pi$
$194$	−0.613875	−	1.06326i	−0.0440736	−	0.0763378i
$195$	3.68613	−	2.27994i	0.263969	−	0.163270i
$196$	7.03470	−	12.1845i	0.502478	−	0.870318i
$197$	16.8453	−	4.51369i	1.20018	−	0.321587i	0.397278	−	0.917698i	$-0.369955\pi$
$197$	16.8453	−	4.51369i	1.20018	−	0.321587i	0.802902	+	0.596111i	$0.203288\pi$
$198$	−5.67998	+	3.64825i	−0.403658	+	0.259270i
$199$	20.0170	−	11.5568i	1.41897	−	0.819243i	0.422761	−	0.906241i	$-0.361061\pi$
$199$	20.0170	−	11.5568i	1.41897	−	0.819243i	0.996208	+	0.0869986i	$0.0277276\pi$
$200$	4.36436	−	1.16943i	0.308607	−	0.0826909i
$201$	11.7920	+	19.3515i	0.831741	+	1.36495i
$202$	3.63614	−	0.974300i	0.255838	−	0.0685515i
$203$	−21.6467	−	5.80020i	−1.51930	−	0.407095i
$204$	−7.81601	−	1.89720i	−0.547230	−	0.132831i
$205$	−3.45105	+	1.99247i	−0.241032	+	0.139160i
$206$	−3.93200	−	14.6744i	−0.273955	−	1.02242i
$207$	−12.6510	−	6.52613i	−0.879304	−	0.453597i
$208$	−3.60547	+	0.0239902i	−0.249994	+	0.00166342i
$209$	5.67003	+	3.27359i	0.392204	+	0.226439i
$210$	5.51628	−	0.130607i	0.380659	−	0.00901272i
$211$	−10.3885			−0.715172			−0.357586	−	0.933880i	$-0.616400\pi$
$211$	−10.3885			−0.715172			−0.357586	+	0.933880i	$0.616400\pi$
$212$	2.53288	−	4.38707i	0.173959	−	0.301306i
$213$	24.4892	+	13.3762i	1.67797	+	0.916520i
$214$	−3.86577	+	3.86577i	−0.264259	+	0.264259i
$215$	3.55745	+	0.953215i	0.242616	+	0.0650087i
$216$	−0.368703	−	5.18305i	−0.0250870	−	0.352662i
$217$	15.4872	+	26.8246i	1.05134	+	1.82097i
$218$	3.60717	+	6.24779i	0.244308	+	0.423154i
$219$	11.6114	−	7.07550i	0.784628	−	0.478118i
$220$	−1.35250	+	0.780869i	−0.0911858	+	0.0526462i
$221$	16.7424	−	0.111401i	1.12622	−	0.00749365i
$222$	−6.01098	−	1.45906i	−0.403431	−	0.0979258i
$223$	−15.3255	−	4.10646i	−1.02627	−	0.274989i	−0.293859	−	0.955849i	$-0.594940\pi$
$223$	−15.3255	−	4.10646i	−1.02627	−	0.274989i	−0.732414	+	0.680860i	$0.761606\pi$
$224$	−3.97518	−	2.29507i	−0.265603	−	0.153346i
$225$	−7.32544	−	11.4050i	−0.488363	−	0.760335i
$226$	−0.334386	+	0.334386i	−0.0222430	+	0.0222430i
$227$	4.50740	+	4.50740i	0.299167	+	0.299167i	0.840687	−	0.541521i	$-0.182151\pi$
$227$	4.50740	+	4.50740i	0.299167	+	0.299167i	−0.541521	+	0.840687i	$0.682151\pi$
$228$	−4.30348	+	2.62235i	−0.285005	+	0.173670i
$229$	−3.31118	+	12.3575i	−0.218809	+	0.816606i	0.765982	+	0.642862i	$0.222253\pi$
$229$	−3.31118	+	12.3575i	−0.218809	+	0.816606i	−0.984791	+	0.173744i	$0.944414\pi$
$230$	−2.85201	−	1.64661i	−0.188056	−	0.108574i
$231$	17.1661	−	5.03804i	1.12945	−	0.331479i
$232$	−1.26362	+	4.71590i	−0.0829609	+	0.309614i
$233$	−18.2644			−1.19654			−0.598271	−	0.801294i	$-0.704145\pi$
$233$	−18.2644			−1.19654			−0.598271	+	0.801294i	$0.704145\pi$
$234$	3.35938	+	10.2818i	0.219609	+	0.672140i
$235$	−8.37796			−0.546518
$236$	−1.38984	+	5.18694i	−0.0904707	+	0.337641i
$237$	−3.89554	−	3.71534i	−0.253042	−	0.241337i
$238$	18.4592	+	10.6574i	1.19653	+	0.690818i
$239$	5.17656	−	19.3192i	0.334844	−	1.24965i	−0.569195	−	0.822203i	$-0.692745\pi$
$239$	5.17656	−	19.3192i	0.334844	−	1.24965i	0.904039	−	0.427451i	$-0.140588\pi$
$240$	−0.0284537	−	1.20177i	−0.00183668	−	0.0775737i
$241$	10.6459	+	10.6459i	0.685762	+	0.685762i	0.961292	−	0.275530i	$-0.0888534\pi$
$241$	10.6459	+	10.6459i	0.685762	+	0.685762i	−0.275530	+	0.961292i	$0.588853\pi$
$242$	4.19771	−	4.19771i	0.269839	−	0.269839i
$243$	−14.4755	+	5.78440i	−0.928605	+	0.371069i
$244$	−2.70295	−	1.56055i	−0.173039	−	0.0999040i
$245$	−9.43192	−	2.52728i	−0.602583	−	0.161462i
$246$	−2.80058	−	9.54242i	−0.178559	−	0.608403i
$247$	7.36844	−	7.46715i	0.468843	−	0.475124i
$248$	5.84395	−	3.37401i	0.371091	−	0.214250i
$249$	0.389633	+	16.4565i	0.0246920	+	1.04289i
$250$	−3.30302	−	5.72100i	−0.208901	−	0.361828i
$251$	13.1431	+	22.7645i	0.829586	+	1.43689i	0.898363	+	0.439253i	$0.144757\pi$
$251$	13.1431	+	22.7645i	0.829586	+	1.43689i	−0.0687771	+	0.997632i	$0.521910\pi$
$252$	−2.93055	+	13.4550i	−0.184607	+	0.847584i
$253$	−10.3136	−	2.76352i	−0.648409	−	0.173741i
$254$	0.307897	−	0.307897i	0.0193192	−	0.0193192i
$255$	0.132128	+	5.58054i	0.00827419	+	0.349467i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	13.6658			0.852450			0.426225	−	0.904617i	$-0.359843\pi$
$257$	13.6658			0.852450			0.426225	+	0.904617i	$0.359843\pi$
$258$	−4.40593	+	8.06640i	−0.274301	+	0.502192i
$259$	14.1962	+	8.19619i	0.882110	+	0.509286i
$260$	0.663731	+	2.41275i	0.0411629	+	0.149632i
$261$	14.6304	−	0.693184i	0.905597	−	0.0429070i
$262$	−2.69666	−	10.0641i	−0.166600	−	0.621761i
$263$	−4.15346	+	2.39800i	−0.256113	+	0.147867i	−0.622560	−	0.782572i	$-0.713907\pi$
$263$	−4.15346	+	2.39800i	−0.256113	+	0.147867i	0.366447	+	0.930439i	$0.380574\pi$
$264$	−1.09758	−	3.73978i	−0.0675513	−	0.230167i
$265$	−3.39601	−	0.909959i	−0.208615	−	0.0558983i
$266$	12.9002	−	3.45661i	0.790964	−	0.211938i
$267$	−4.33665	+	0.102677i	−0.265399	+	0.00628375i
$268$	−12.6377	+	3.38625i	−0.771967	+	0.206848i
$269$	−21.5499	+	12.4418i	−1.31392	+	0.758591i	−0.982743	−	0.184978i	$-0.940779\pi$
$269$	−21.5499	+	12.4418i	−1.31392	+	0.758591i	−0.331176	+	0.943569i	$0.607445\pi$
$270$	−3.40842	+	1.17820i	−0.207430	+	0.0717031i
$271$	−0.766787	+	0.205460i	−0.0465790	+	0.0124808i	−0.282033	−	0.959405i	$-0.591009\pi$
$271$	−0.766787	+	0.205460i	−0.0465790	+	0.0124808i	0.235454	+	0.971885i	$0.424342\pi$
$272$	2.32181	−	4.02149i	0.140780	−	0.243838i
$273$	−0.869172	−	28.6522i	−0.0526047	−	1.73411i
$274$	−3.82397	−	6.62331i	−0.231015	−	0.400129i
$275$	−7.18933	−	7.18933i	−0.433533	−	0.433533i
$276$	5.67226	−	5.94738i	0.341430	−	0.357990i
$277$		−	32.9502i		−	1.97979i	−0.141813	−	0.989893i	$-0.545293\pi$
$277$		−	32.9502i		−	1.97979i	0.141813	−	0.989893i	$-0.454707\pi$
$278$	−7.90068	−	7.90068i	−0.473851	−	0.473851i
$279$	−14.9761	−	13.6212i	−0.896597	−	0.815479i
$280$	−0.824524	+	3.07717i	−0.0492747	+	0.183896i
$281$	−4.70802	−	17.5706i	−0.280857	−	1.04817i	−0.951814	−	0.306676i	$-0.900783\pi$
$281$	−4.70802	−	17.5706i	−0.280857	−	1.04817i	0.670957	−	0.741496i	$-0.265883\pi$
$282$	4.93190	−	20.3183i	0.293691	−	1.20993i
$283$		−	24.4025i		−	1.45058i	−0.688446	−	0.725288i	$-0.741707\pi$
$283$		−	24.4025i		−	1.45058i	0.688446	−	0.725288i	$-0.258293\pi$
$284$	−11.3918	+	11.3918i	−0.675980	+	0.675980i
$285$	2.53102	+	2.41394i	0.149925	+	0.142989i
$286$	4.10332	+	6.99920i	0.242635	+	0.413871i
$287$			26.3552i			1.55570i
$288$	2.93128	+	0.638445i	0.172727	+	0.0376207i
$289$	−2.28157	+	3.95179i	−0.134210	+	0.232458i
$290$	3.38846			0.198977
$291$	−1.10656	−	1.81594i	−0.0648674	−	0.106452i
$292$	2.03184	+	7.58294i	0.118905	+	0.443758i
$293$	−0.941471	−	3.51362i	−0.0550013	−	0.205268i	0.932957	−	0.359988i	$-0.117219\pi$
$293$	−0.941471	−	3.51362i	−0.0550013	−	0.205268i	−0.987958	+	0.154720i	$0.950552\pi$
$294$	11.6815	−	21.3866i	0.681279	−	1.24729i
$295$	3.72691			0.216989
$296$	1.78561	−	3.09276i	0.103786	−	0.179763i
$297$	−9.68568	+	6.55005i	−0.562020	+	0.380072i
$298$		−	7.39921i		−	0.428625i
$299$	−8.45545	+	14.8729i	−0.488991	+	0.860124i
$300$	7.50923	−	2.20387i	0.433546	−	0.127240i
$301$	17.2236	−	17.2236i	0.992754	−	0.992754i
$302$			14.3297i			0.824583i
$303$	6.25626	−	1.83614i	0.359413	−	0.105483i
$304$	−0.753050	−	2.81042i	−0.0431904	−	0.161189i
$305$	−0.560641	+	2.09234i	−0.0321022	+	0.119807i
$306$	−13.6117	−	2.96469i	−0.778130	−	0.169480i
$307$	10.8993	+	10.8993i	0.622055	+	0.622055i	0.946057	−	0.324001i	$-0.105028\pi$
$307$	10.8993	+	10.8993i	0.622055	+	0.622055i	−0.324001	+	0.946057i	$0.605028\pi$
$308$			10.3289i			0.588542i
$309$	−7.41013	−	25.2485i	−0.421548	−	1.43634i
$310$	−3.31163	−	3.31163i	−0.188088	−	0.188088i
$311$	5.37895	+	9.31661i	0.305012	+	0.528296i	0.977264	−	0.212026i	$-0.0680062\pi$
$311$	5.37895	+	9.31661i	0.305012	+	0.528296i	−0.672252	+	0.740322i	$0.734673\pi$
$312$	−6.24213	+	0.189356i	−0.353391	+	0.0107202i
$313$	6.34655	−	10.9926i	0.358728	−	0.621336i	−0.629020	−	0.777389i	$-0.716544\pi$
$313$	6.34655	−	10.9926i	0.358728	−	0.621336i	0.987749	+	0.156053i	$0.0498771\pi$
$314$	5.52710	−	1.48098i	0.311912	−	0.0835766i
$315$	9.54644	−	0.452308i	0.537881	−	0.0254847i
$316$	2.69161	−	1.55400i	0.151415	−	0.0874193i
$317$	−25.1552	+	6.74033i	−1.41286	+	0.378574i	−0.882945	−	0.469477i	$-0.844443\pi$
$317$	−25.1552	+	6.74033i	−1.41286	+	0.378574i	−0.529914	+	0.848051i	$0.677776\pi$
$318$	4.20599	−	7.70035i	0.235860	−	0.431814i
$319$	10.6119	−	2.84344i	0.594151	−	0.159202i
$320$	0.670386	+	0.179629i	0.0374757	+	0.0100416i
$321$	−6.53535	+	6.85232i	−0.364767	+	0.382459i
$322$	−18.8623	+	10.8902i	−1.05116	+	0.606886i
$323$	3.49687	+	13.0505i	0.194571	+	0.726150i
$324$	−0.850926	−	8.95968i	−0.0472737	−	0.497760i
$325$	−14.0539	+	8.23920i	−0.779572	+	0.457029i
$326$	−4.83910	−	2.79386i	−0.268013	−	0.154737i
$327$	6.50219	+	10.6706i	0.359572	+	0.590084i
$328$	5.74169			0.317032
$329$	−27.7047	+	47.9859i	−1.52741	+	2.64555i
$330$	−2.30994	+	1.40758i	−0.127158	+	0.0774845i
$331$	−14.3286	+	14.3286i	−0.787571	+	0.787571i	−0.981095	−	0.193525i	$-0.938008\pi$
$331$	−14.3286	+	14.3286i	−0.787571	+	0.787571i	0.193525	+	0.981095i	$0.438008\pi$
$332$	−9.17998	−	2.45977i	−0.503817	−	0.134997i
$333$	−10.4682	−	2.28002i	−0.573655	−	0.124945i
$334$	12.2447	+	21.2084i	0.670000	+	1.16047i
$335$	4.54019	+	7.86383i	0.248057	+	0.429647i
$336$	−6.97737	−	3.81109i	−0.380647	−	0.207912i
$337$	6.82932	−	3.94291i	0.372017	−	0.214784i	−0.302322	−	0.953206i	$-0.597762\pi$
$337$	6.82932	−	3.94291i	0.372017	−	0.214784i	0.674339	+	0.738422i	$0.264429\pi$
$338$	12.5112	−	3.53145i	0.680517	−	0.192085i
$339$	−0.565302	+	0.592720i	−0.0307030	+	0.0321922i
$340$	−3.11301	−	0.834129i	−0.168827	−	0.0452370i
$341$	−13.1502	−	7.59229i	−0.712125	−	0.411146i
$342$	−7.34425	+	4.71721i	−0.397131	+	0.255077i
$343$	−22.9453	+	22.9453i	−1.23893	+	1.23893i
$344$	−3.75231	−	3.75231i	−0.202311	−	0.202311i
$345$	−5.00594	−	2.73428i	−0.269511	−	0.147209i
$346$	2.74192	−	10.2330i	0.147407	−	0.550129i
$347$	−14.7186	−	8.49778i	−0.790135	−	0.456185i	0.0498748	−	0.998755i	$-0.484118\pi$
$347$	−14.7186	−	8.49778i	−0.790135	−	0.456185i	−0.840010	+	0.542571i	$0.817451\pi$
$348$	−1.99470	+	8.21770i	−0.106927	+	0.440515i
$349$	−3.76269	+	14.0426i	−0.201412	+	0.751681i	0.789101	+	0.614264i	$0.210547\pi$
$349$	−3.76269	+	14.0426i	−0.201412	+	0.751681i	−0.990513	+	0.137418i	$0.956120\pi$
$350$	−20.7397			−1.10858
$351$	6.23851	+	17.6658i	0.332987	+	0.942931i
$352$	2.25023			0.119938
$353$	2.20358	−	8.22389i	0.117285	−	0.437713i	−0.882163	−	0.470945i	$-0.843913\pi$
$353$	2.20358	−	8.22389i	0.117285	−	0.437713i	0.999448	+	0.0332313i	$0.0105798\pi$
$354$	−2.19394	+	9.03851i	−0.116607	+	0.480391i
$355$	9.68322	+	5.59061i	0.513932	+	0.296719i
$356$	0.648204	−	2.41913i	0.0343548	−	0.128214i
$357$	32.4002	+	17.6972i	1.71480	+	0.936637i
$358$	8.80476	+	8.80476i	0.465346	+	0.465346i
$359$	−2.80645	+	2.80645i	−0.148119	+	0.148119i	−0.777277	−	0.629158i	$-0.783400\pi$
$359$	−2.80645	+	2.80645i	−0.148119	+	0.148119i	0.629158	+	0.777277i	$0.283400\pi$
$360$	−0.0985391	−	2.07977i	−0.00519346	−	0.109614i
$361$	−9.12309	−	5.26722i	−0.480163	−	0.277222i
$362$	17.8179	+	4.77430i	0.936489	+	0.250932i
$363$	7.09652	−	7.44071i	0.372471	−	0.390536i
$364$	16.0142	+	4.17699i	0.839373	+	0.218934i
$365$	4.71852	−	2.72424i	0.246979	−	0.142593i
$366$	−4.74432	−	2.59138i	−0.247990	−	0.135454i
$367$	12.1791	+	21.0948i	0.635742	+	1.10114i	0.986357	+	0.164618i	$0.0526392\pi$
$367$	12.1791	+	21.0948i	0.635742	+	1.10114i	−0.350615	+	0.936520i	$0.614027\pi$
$368$	2.37251	+	4.10931i	0.123676	+	0.214213i
$369$	−5.24061	−	16.4085i	−0.272815	−	0.854193i
$370$	−2.39409	−	0.641495i	−0.124463	−	0.0333497i
$371$	−16.4420	+	16.4420i	−0.853628	+	0.853628i
$372$	9.98086	−	6.08190i	0.517483	−	0.315332i
$373$	4.62903	−	8.01772i	0.239682	−	0.415142i	−0.720941	−	0.692997i	$-0.756290\pi$
$373$	4.62903	−	8.01772i	0.239682	−	0.415142i	0.960623	+	0.277855i	$0.0896234\pi$
$374$	−10.4492			−0.540315
$375$	−5.95394	−	9.77087i	−0.307460	−	0.504565i
$376$	10.4541	+	6.03569i	0.539130	+	0.311267i
$377$	−0.117126	−	17.6029i	−0.00603231	−	0.906593i
$378$	−4.52282	+	23.4183i	−0.232629	+	1.20451i
$379$	−3.58050	−	13.3626i	−0.183918	−	0.686391i	−0.994860	−	0.101264i	$-0.967711\pi$
$379$	−3.58050	−	13.3626i	−0.183918	−	0.686391i	0.810942	−	0.585127i	$-0.198955\pi$
$380$	−1.74880	+	1.00967i	−0.0897114	+	0.0517949i
$381$	0.520521	−	0.545768i	0.0266671	−	0.0279605i
$382$	−8.22549	−	2.20401i	−0.420853	−	0.112767i
$383$	17.2004	−	4.60883i	0.878898	−	0.235500i	0.208967	−	0.977923i	$-0.432990\pi$
$383$	17.2004	−	4.60883i	0.878898	−	0.235500i	0.669932	+	0.742423i	$0.266323\pi$
$384$	−0.830278	+	1.52008i	−0.0423699	+	0.0775712i
$385$	6.92433	−	1.85537i	0.352897	−	0.0945584i
$386$	16.3939	−	9.46505i	0.834430	−	0.481758i
$387$	−7.29845	+	14.1481i	−0.371001	+	0.719190i
$388$	1.18591	−	0.317765i	0.0602057	−	0.0161321i
$389$	−7.46970	+	12.9379i	−0.378729	+	0.655978i	−0.990878	−	0.134765i	$-0.956972\pi$
$389$	−7.46970	+	12.9379i	−0.378729	+	0.655978i	0.612149	+	0.790743i	$0.290305\pi$
$390$	1.24821	+	4.15062i	0.0632056	+	0.210175i
$391$	−11.0170	−	19.0821i	−0.557155	−	0.965021i
$392$	9.94856	+	9.94856i	0.502478	+	0.502478i
$393$	−5.08205	−	17.3161i	−0.256356	−	0.873480i
$394$			17.4396i			0.878593i
$395$	−1.52527	−	1.52527i	−0.0767447	−	0.0767447i
$396$	−2.05385	−	6.43067i	−0.103210	−	0.323153i
$397$	0.691339	−	2.58011i	0.0346973	−	0.129492i	−0.946405	−	0.322983i	$-0.895314\pi$
$397$	0.691339	−	2.58011i	0.0346973	−	0.129492i	0.981102	+	0.193491i	$0.0619810\pi$
$398$	5.98226	+	22.3261i	0.299864	+	1.11911i
$399$	22.1959	−	6.51422i	1.11118	−	0.326119i
$400$			4.51832i			0.225916i
$401$	−0.0475983	+	0.0475983i	−0.00237694	+	0.00237694i	−0.708294	−	0.705917i	$-0.750535\pi$
$401$	−0.0475983	+	0.0475983i	−0.00237694	+	0.00237694i	0.705917	+	0.708294i	$0.250535\pi$
$402$	−21.7441	+	6.38162i	−1.08450	+	0.318287i
$403$	−17.0893	+	17.3182i	−0.851277	+	0.862682i
$404$			3.76440i			0.187286i
$405$	−5.85359	+	2.17987i	−0.290867	+	0.108319i
$406$	11.2051	−	19.4079i	0.556101	−	0.963196i
$407$	−8.03606			−0.398333
$408$	3.85549	−	7.05866i	0.190875	−	0.349456i
$409$	−5.28660	−	19.7298i	−0.261405	−	0.975578i	−0.964414	−	0.264397i	$-0.914827\pi$
$409$	−5.28660	−	19.7298i	−0.261405	−	0.975578i	0.703009	−	0.711181i	$-0.251840\pi$
$410$	−1.03138	−	3.84915i	−0.0509361	−	0.190096i
$411$	−6.89300	−	11.3119i	−0.340006	−	0.557976i
$412$	15.1921			0.748460
$413$	12.3243	−	21.3464i	0.606441	−	1.05039i
$414$	9.57807	−	10.5308i	0.470736	−	0.517562i
$415$			6.59597i			0.323784i
$416$	0.909992	−	3.48883i	0.0446160	−	0.171054i
$417$	−14.0045	−	13.3566i	−0.685801	−	0.654077i
$418$	−4.62956	+	4.62956i	−0.226439	+	0.226439i
$419$			22.9596i			1.12165i	0.827934	+	0.560826i	$0.189516\pi$
$419$			22.9596i			1.12165i	−0.827934	+	0.560826i	$0.810484\pi$
$420$	−1.30156	+	5.36212i	−0.0635097	+	0.261645i
$421$	−2.92242	−	10.9066i	−0.142430	−	0.531556i	−0.999856	−	0.0169495i	$-0.994605\pi$
$421$	−2.92242	−	10.9066i	−0.142430	−	0.531556i	0.857426	−	0.514607i	$-0.172062\pi$
$422$	2.68874	−	10.0345i	0.130886	−	0.488472i
$423$	7.70691	−	35.3846i	0.374723	−	1.72046i
$424$	3.58203	+	3.58203i	0.173959	+	0.173959i
$425$		−	20.9813i		−	1.01774i
$426$	−19.2587	+	20.1927i	−0.933085	+	0.978341i
$427$	10.1302	+	10.1302i	0.490236	+	0.490236i
$428$	−2.73351	−	4.73458i	−0.132129	−	0.228855i
$429$	7.39212	+	11.9513i	0.356895	+	0.577016i
$430$	−1.84147	+	3.18952i	−0.0888036	+	0.153812i
$431$	−8.79469	+	2.35653i	−0.423625	+	0.113510i	−0.464332	−	0.885661i	$-0.653706\pi$
$431$	−8.79469	+	2.35653i	−0.423625	+	0.113510i	0.0407069	+	0.999171i	$0.487039\pi$
$432$	5.10187	+	0.985334i	0.245464	+	0.0474069i
$433$	19.6096	−	11.3216i	0.942379	−	0.544083i	0.0516737	−	0.998664i	$-0.483544\pi$
$433$	19.6096	−	11.3216i	0.942379	−	0.544083i	0.890705	+	0.454581i	$0.150211\pi$
$434$	−29.9189	+	8.01675i	−1.43615	+	0.384816i
$435$	5.86734	−	0.138919i	0.281317	−	0.00666064i
$436$	−6.96851	+	1.86721i	−0.333731	+	0.0894230i
$437$	−13.3355	−	3.57325i	−0.637925	−	0.170931i
$438$	3.82915	+	13.0471i	0.182964	+	0.623413i
$439$	−18.5237	+	10.6947i	−0.884090	+	0.510430i	−0.872005	−	0.489497i	$-0.837180\pi$
$439$	−18.5237	+	10.6947i	−0.884090	+	0.510430i	−0.0120853	+	0.999927i	$0.503847\pi$
$440$	−0.404207	−	1.50852i	−0.0192698	−	0.0719160i
$441$	19.3505	−	37.5112i	0.921452	−	1.78625i
$442$	−4.22565	+	16.2008i	−0.200994	+	0.770592i
$443$	27.1059	+	15.6496i	1.28784	+	0.743535i	0.978269	−	0.207341i	$-0.0664811\pi$
$443$	27.1059	+	15.6496i	1.28784	+	0.743535i	0.309571	+	0.950876i	$0.399814\pi$
$444$	2.96510	−	5.42853i	0.140717	−	0.257627i
$445$	−1.73819			−0.0823980
$446$	7.93307	−	13.7405i	0.375642	−	0.650631i
$447$	−0.303350	−	12.8122i	−0.0143480	−	0.605997i
$448$	3.24572	−	3.24572i	0.153346	−	0.153346i
$449$	−12.7731	−	3.42254i	−0.602800	−	0.161520i	−0.0555034	−	0.998458i	$-0.517676\pi$
$449$	−12.7731	−	3.42254i	−0.602800	−	0.161520i	−0.547297	+	0.836939i	$0.684343\pi$
$450$	12.9124	−	4.12400i	0.608695	−	0.194407i
$451$	−6.46007	−	11.1892i	−0.304193	−	0.526877i
$452$	−0.236447	−	0.409538i	−0.0111215	−	0.0192630i
$453$	0.587484	+	24.8129i	0.0276024	+	1.16581i
$454$	−5.52042	+	3.18721i	−0.259086	+	0.149583i
$455$	−0.0764259	−	11.4860i	−0.00358290	−	0.538472i
$456$	−1.41918	−	4.83556i	−0.0664590	−	0.226446i
$457$	−11.3132	−	3.03137i	−0.529210	−	0.141801i	−0.0156865	−	0.999877i	$-0.504993\pi$
$457$	−11.3132	−	3.03137i	−0.529210	−	0.141801i	−0.513523	+	0.858076i	$0.671660\pi$
$458$	−11.0794	−	6.39671i	−0.517707	−	0.298898i
$459$	−23.6911	−	4.57551i	−1.10581	−	0.213566i
$460$	2.32865	−	2.32865i	0.108574	−	0.108574i
$461$	5.18033	+	5.18033i	0.241272	+	0.241272i	0.817376	−	0.576104i	$-0.195428\pi$
$461$	5.18033	+	5.18033i	0.241272	+	0.241272i	−0.576104	+	0.817376i	$0.695428\pi$
$462$	0.423459	+	17.8851i	0.0197011	+	0.832091i
$463$	3.79457	−	14.1615i	0.176349	−	0.658142i	−0.819969	−	0.572407i	$-0.806010\pi$
$463$	3.79457	−	14.1615i	0.176349	−	0.658142i	0.996318	−	0.0857346i	$-0.0273237\pi$
$464$	−4.22816	−	2.44113i	−0.196288	−	0.113327i
$465$	−5.87007	−	5.59854i	−0.272218	−	0.259626i
$466$	4.72718	−	17.6421i	0.218982	−	0.817253i
$467$	18.0118			0.833488			0.416744	−	0.909024i	$-0.363171\pi$
$467$	18.0118			0.833488			0.416744	+	0.909024i	$0.363171\pi$
$468$	−10.8009	+	0.583795i	−0.499271	+	0.0269859i
$469$	60.0549			2.77308
$470$	2.16838	−	8.09249i	0.100020	−	0.373279i
$471$	9.50982	−	2.79101i	0.438189	−	0.128603i
$472$	−4.65048	−	2.68496i	−0.214056	−	0.123585i
$473$	−3.09056	+	11.5341i	−0.142104	+	0.530339i
$474$	4.59698	−	2.80120i	0.211146	−	0.128663i
$475$	−9.29586	−	9.29586i	−0.426523	−	0.426523i
$476$	−15.0719	+	15.0719i	−0.690818	+	0.690818i
$477$	6.96724	−	13.5061i	0.319008	−	0.618402i
$478$	17.3211	+	10.0003i	0.792249	+	0.457405i
$479$	−6.94673	−	1.86137i	−0.317404	−	0.0850482i	0.0965997	−	0.995323i	$-0.469203\pi$
$479$	−6.94673	−	1.86137i	−0.317404	−	0.0850482i	−0.414004	+	0.910275i	$0.635870\pi$
$480$	1.16818	+	0.283556i	0.0533199	+	0.0129425i
$481$	−3.24978	+	12.4594i	−0.148177	+	0.568098i
$482$	−13.0385	+	7.52778i	−0.593887	+	0.342881i
$483$	−32.2149	+	19.6304i	−1.46583	+	0.893212i
$484$	2.96823	+	5.14113i	0.134920	+	0.233688i
$485$	−0.426050	−	0.737940i	−0.0193459	−	0.0335082i
$486$	−1.84076	−	15.4794i	−0.0834985	−	0.702160i
$487$	0.324094	+	0.0868407i	0.0146861	+	0.00393513i	0.266155	−	0.963930i	$-0.414247\pi$
$487$	0.324094	+	0.0868407i	0.0146861	+	0.00393513i	−0.251469	+	0.967865i	$0.580913\pi$
$488$	2.20695	−	2.20695i	0.0999040	−	0.0999040i
$489$	−8.49376	−	4.63935i	−0.384101	−	0.209799i
$490$	4.88232	−	8.45643i	0.220561	−	0.382023i
$491$	−3.92764			−0.177252			−0.0886260	−	0.996065i	$-0.528248\pi$
$491$	−3.92764			−0.177252			−0.0886260	+	0.996065i	$0.528248\pi$
$492$	9.94212	−	0.235396i	0.448225	−	0.0106125i
$493$	19.6339	+	11.3357i	0.884269	+	0.510533i
$494$	5.30562	+	9.05001i	0.238711	+	0.407179i
$495$	−3.94210	+	2.53201i	−0.177184	+	0.113805i
$496$	1.74651	+	6.51808i	0.0784208	+	0.292670i
$497$	64.0420	−	36.9747i	2.87268	−	1.65854i
$498$	−15.9966	−	3.88289i	−0.716824	−	0.173997i
$499$	19.6072	+	5.25372i	0.877737	+	0.235189i	0.669431	−	0.742875i	$-0.266538\pi$
$499$	19.6072	+	5.25372i	0.877737	+	0.235189i	0.208307	+	0.978064i	$0.433205\pi$
$500$	6.38094	−	1.70977i	0.285365	−	0.0764632i
$501$	22.0720	+	36.2218i	0.986103	+	1.61827i
$502$	−25.3906	+	6.80338i	−1.13324	+	0.303650i
$503$	−24.7833	+	14.3086i	−1.10503	+	0.637991i	−0.937538	−	0.347882i	$-0.886901\pi$
$503$	−24.7833	+	14.3086i	−1.10503	+	0.637991i	−0.167494	+	0.985873i	$0.553568\pi$
$504$	−12.2380	−	6.31310i	−0.545125	−	0.281208i
$505$	2.52360	−	0.676198i	0.112299	−	0.0300904i
$506$	5.33870	−	9.24691i	0.237334	−	0.411075i
$507$	21.5191	−	6.62786i	0.955697	−	0.294354i
$508$	0.217716	+	0.377096i	0.00965960	+	0.0167309i
$509$	11.3503	+	11.3503i	0.503091	+	0.503091i	0.912397	−	0.409306i	$-0.134229\pi$
$509$	11.3503	+	11.3503i	0.503091	+	0.503091i	−0.409306	+	0.912397i	$0.634229\pi$
$510$	−5.42458	−	1.31672i	−0.240205	−	0.0583055i
$511$		−	36.0346i		−	1.59408i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−12.5237	+	8.46925i	−0.552933	+	0.373927i
$514$	−3.53697	+	13.2002i	−0.156009	+	0.582235i
$515$	−2.72894	−	10.1846i	−0.120252	−	0.448785i
$516$	−6.65121	−	6.34353i	−0.292803	−	0.279259i
$517$		−	27.1634i		−	1.19465i
$518$	−11.5912	+	11.5912i	−0.509286	+	0.509286i
$519$	4.32829	−	17.8315i	0.189991	−	0.782716i
$520$	−2.50232	+	0.0166500i	−0.109734	+	0.000730151i
$521$		−	19.3205i		−	0.846448i	−0.906025	−	0.423224i	$-0.860898\pi$
$521$		−	19.3205i		−	0.846448i	0.906025	−	0.423224i	$-0.139102\pi$
$522$	−3.11706	+	14.3113i	−0.136430	+	0.626387i
$523$	4.17667	−	7.23421i	0.182633	−	0.316330i	−0.760143	−	0.649755i	$-0.774871\pi$
$523$	4.17667	−	7.23421i	0.182633	−	0.316330i	0.942776	+	0.333426i	$0.108205\pi$
$524$	10.4191			0.455161
$525$	−35.9122	+	0.850278i	−1.56734	+	0.0371092i
$526$	−1.24130	−	4.63258i	−0.0541231	−	0.201990i
$527$	−8.11013	−	30.2674i	−0.353283	−	1.31847i
$528$	3.89642	−	0.0922541i	0.169570	−	0.00401484i
$529$	−0.484713			−0.0210745
$530$	1.75791	−	3.04478i	0.0763585	−	0.132257i
$531$	−3.42840	+	15.7407i	−0.148780	+	0.683089i
$532$			13.3553i			0.579026i
$533$	−19.9605	+	5.49100i	−0.864584	+	0.237841i
$534$	1.02323	−	4.21546i	0.0442795	−	0.182421i
$535$	−2.68298	+	2.68298i	−0.115995	+	0.115995i
$536$		−	13.0835i		−	0.565119i
$537$	15.6070	+	14.8850i	0.673491	+	0.642337i
$538$	−6.44036	−	24.0358i	−0.277664	−	1.03625i
$539$	8.19405	−	30.5806i	0.352943	−	1.31720i
$540$	−0.255892	−	3.59722i	−0.0110119	−	0.154800i
$541$	18.5480	+	18.5480i	0.797443	+	0.797443i	0.982692	−	0.185249i	$-0.0593092\pi$
$541$	18.5480	+	18.5480i	0.797443	+	0.797443i	−0.185249	+	0.982692i	$0.559309\pi$
$542$		−	0.793836i		−	0.0340982i
$543$	31.0486	+	7.53652i	1.33242	+	0.323423i
$544$	3.28353	+	3.28353i	0.140780	+	0.140780i
$545$	2.50350	+	4.33618i	0.107238	+	0.185742i
$546$	27.9009	+	6.57619i	1.19405	+	0.281435i
$547$	−11.1826	+	19.3688i	−0.478133	+	0.828151i	−0.999686	−	0.0250681i	$-0.992020\pi$
$547$	−11.1826	+	19.3688i	−0.478133	+	0.828151i	0.521552	+	0.853219i	$0.325353\pi$
$548$	7.38734	−	1.97943i	0.315572	−	0.0845572i
$549$	−8.32134	−	4.29264i	−0.355146	−	0.183205i
$550$	8.80510	−	5.08363i	0.375451	−	0.216767i
$551$	13.7212	−	3.67659i	0.584544	−	0.156628i
$552$	4.27664	+	7.01828i	0.182026	+	0.298718i
$553$	−13.7800	+	3.69235i	−0.585987	+	0.157015i
$554$	31.8275	+	8.52814i	1.35222	+	0.362326i
$555$	−4.17183	−	1.01264i	−0.177084	−	0.0429841i
$556$	9.67631	−	5.58662i	0.410367	−	0.236926i
$557$	3.13004	+	11.6815i	0.132624	+	0.494959i	0.999996	−	0.00270033i	$-0.000859542\pi$
$557$	3.13004	+	11.6815i	0.132624	+	0.494959i	−0.867372	+	0.497660i	$0.834193\pi$
$558$	17.0332	−	10.9404i	0.721071	−	0.463144i
$559$	16.6330	+	9.45609i	0.703503	+	0.399950i
$560$	−2.75891	−	1.59286i	−0.116585	−	0.0673105i
$561$	−18.0935	+	0.428392i	−0.763907	+	0.0180867i
$562$	18.1904			0.767315
$563$	17.5904	−	30.4674i	0.741345	−	1.28405i	−0.210538	−	0.977586i	$-0.567521\pi$
$563$	17.5904	−	30.4674i	0.741345	−	1.28405i	0.951883	−	0.306462i	$-0.0991452\pi$
$564$	18.3495	+	10.0226i	0.772651	+	0.422028i
$565$	−0.232075	+	0.232075i	−0.00976349	+	0.00976349i
$566$	23.5710	+	6.31582i	0.990761	+	0.265474i
$567$	−6.87147	+	40.7358i	−0.288574	+	1.71074i
$568$	−8.05524	−	13.9521i	−0.337990	−	0.585416i
$569$	−5.63117	−	9.75346i	−0.236071	−	0.408886i	0.723513	−	0.690311i	$-0.242526\pi$
$569$	−5.63117	−	9.75346i	−0.236071	−	0.408886i	−0.959583	+	0.281425i	$0.909193\pi$
$570$	−2.98676	+	1.82000i	−0.125102	+	0.0762316i
$571$	−27.0909	+	15.6409i	−1.13372	+	0.654553i	−0.944868	−	0.327452i	$-0.893810\pi$
$571$	−27.0909	+	15.6409i	−1.13372	+	0.654553i	−0.188852	+	0.982006i	$0.560477\pi$
$572$	−7.82272	+	2.15198i	−0.327084	+	0.0899788i
$573$	−14.3333	−	3.47917i	−0.598783	−	0.145344i
$574$	−25.4571	−	6.82122i	−1.06256	−	0.284712i
$575$	18.5672	+	10.7198i	0.774305	+	0.447045i
$576$	−1.37536	+	2.66616i	−0.0573067	+	0.111090i
$577$	−26.9790	+	26.9790i	−1.12315	+	1.12315i	−0.131887	+	0.991265i	$0.542103\pi$
$577$	−26.9790	+	26.9790i	−1.12315	+	1.12315i	−0.991265	+	0.131887i	$0.957897\pi$
$578$	−3.22662	−	3.22662i	−0.134210	−	0.134210i
$579$	27.9991	−	17.0615i	1.16360	−	0.709050i
$580$	−0.876997	+	3.27300i	−0.0364153	+	0.135904i
$581$	37.7793	+	21.8119i	1.56735	+	0.904911i
$582$	2.04046	−	0.598850i	0.0845798	−	0.0248231i
$583$	2.95031	−	11.0107i	0.122189	−	0.456017i
$584$	−7.85044			−0.324853
$585$	2.33152	+	7.13590i	0.0963967	+	0.295033i
$586$	3.63756			0.150266
$587$	−0.590896	+	2.20525i	−0.0243889	+	0.0910205i	−0.977048	−	0.213021i	$-0.931670\pi$
$587$	−0.590896	+	2.20525i	−0.0243889	+	0.0910205i	0.952659	+	0.304042i	$0.0983363\pi$
$588$	17.6345	+	16.8187i	0.727233	+	0.693592i
$589$	−17.0033	−	9.81688i	−0.700611	−	0.404498i
$590$	−0.964595	+	3.59992i	−0.0397117	+	0.148206i
$591$	0.714980	+	30.1978i	0.0294104	+	1.24217i
$592$	2.52523	+	2.52523i	0.103786	+	0.103786i
$593$	21.4122	−	21.4122i	0.879295	−	0.879295i	−0.114166	−	0.993462i	$-0.536420\pi$
$593$	21.4122	−	21.4122i	0.879295	−	0.879295i	0.993462	+	0.114166i	$0.0364197\pi$
$594$	−3.82002	−	11.0509i	−0.156737	−	0.453425i
$595$	12.8113	+	7.39662i	0.525213	+	0.303232i
$596$	7.14709	+	1.91506i	0.292756	+	0.0784438i
$597$	11.2740	+	38.4138i	0.461414	+	1.57217i
$598$	−12.1777	−	12.0167i	−0.497984	−	0.491401i
$599$	−27.0669	+	15.6271i	−1.10593	+	0.638506i	−0.937771	−	0.347255i	$-0.887114\pi$
$599$	−27.0669	+	15.6271i	−1.10593	+	0.638506i	−0.168154	+	0.985761i	$0.553781\pi$
$600$	0.185240	+	7.82376i	0.00756240	+	0.319404i
$601$	13.9378	+	24.1409i	0.568533	+	0.984728i	0.996711	+	0.0810336i	$0.0258221\pi$
$601$	13.9378	+	24.1409i	0.568533	+	0.984728i	−0.428179	+	0.903694i	$0.640845\pi$
$602$	12.1789	+	21.0946i	0.496377	+	0.859750i
$603$	−37.3897	+	11.9417i	−1.52263	+	0.486302i
$604$	−13.8415	−	3.70881i	−0.563201	−	0.150909i
$605$	2.91336	−	2.91336i	0.118445	−	0.118445i
$606$	0.154332	+	6.51831i	0.00626929	+	0.264788i
$607$	1.42278	−	2.46433i	0.0577490	−	0.100024i	−0.835706	−	0.549178i	$-0.814941\pi$
$607$	1.42278	−	2.46433i	0.0577490	−	0.100024i	0.893455	+	0.449153i	$0.148274\pi$
$608$	2.90956			0.117998
$609$	18.6067	−	34.0654i	0.753984	−	1.38040i
$610$	−1.87594	−	1.08308i	−0.0759547	−	0.0438525i
$611$	−42.1150	−	10.9849i	−1.70379	−	0.444400i
$612$	6.38664	−	12.3806i	0.258165	−	0.500456i
$613$	0.202550	+	0.755928i	0.00818093	+	0.0305316i	0.969896	−	0.243521i	$-0.0783024\pi$
$613$	0.202550	+	0.755928i	0.00818093	+	0.0305316i	−0.961715	+	0.274053i	$0.911636\pi$
$614$	−13.3488	+	7.70696i	−0.538716	+	0.311028i
$615$	−1.94370	−	6.62277i	−0.0783776	−	0.267056i
$616$	−9.97693	−	2.67331i	−0.401982	−	0.107711i
$617$	−26.7737	+	7.17399i	−1.07787	+	0.288814i	−0.753723	−	0.657193i	$-0.771744\pi$
$617$	−26.7737	+	7.17399i	−1.07787	+	0.288814i	−0.324147	+	0.946007i	$0.605077\pi$
$618$	26.3061	−	0.622839i	1.05819	−	0.0250543i
$619$	−6.46639	+	1.73266i	−0.259906	+	0.0696417i	−0.386419	−	0.922323i	$-0.626288\pi$
$619$	−6.46639	+	1.73266i	−0.259906	+	0.0696417i	0.126513	+	0.991965i	$0.459621\pi$
$620$	4.05590	−	2.34168i	0.162889	−	0.0940440i
$621$	16.1533	−	18.6275i	0.648210	−	0.747495i
$622$	−10.3913	+	2.78435i	−0.416654	+	0.111642i
$623$	−5.74793	+	9.95571i	−0.230286	+	0.398867i
$624$	1.43268	−	6.07844i	0.0573530	−	0.243332i
$625$	9.00338	+	15.5943i	0.360135	+	0.623772i
$626$	8.97538	+	8.97538i	0.358728	+	0.358728i
$627$	−7.82659	+	8.20619i	−0.312564	+	0.327724i
$628$			5.72207i			0.228336i
$629$	−11.7262	−	11.7262i	−0.467554	−	0.467554i
$630$	−2.03390	+	9.33822i	−0.0810327	+	0.372044i
$631$	−1.16111	+	4.33331i	−0.0462230	+	0.172506i	−0.985179	−	0.171532i	$-0.945128\pi$
$631$	−1.16111	+	4.33331i	−0.0462230	+	0.172506i	0.938956	+	0.344038i	$0.111795\pi$
$632$	0.804409	+	3.00210i	0.0319977	+	0.119417i
$633$	4.24433	−	17.4856i	0.168697	−	0.694991i
$634$		−	26.0426i		−	1.03428i
$635$	0.213691	−	0.213691i	0.00848008	−	0.00848008i
$636$	6.34938	+	6.05567i	0.251769	+	0.240123i
$637$	−44.0995	−	25.0711i	−1.74728	−	0.993353i
$638$			10.9862i			0.434948i
$639$	−32.5198	+	35.7546i	−1.28646	+	1.41443i
$640$	−0.347017	+	0.601052i	−0.0137171	+	0.0237586i
$641$	42.9821			1.69769			0.848845	−	0.528642i	$-0.177298\pi$
$641$	42.9821			1.69769			0.848845	+	0.528642i	$0.177298\pi$
$642$	−4.92736	−	8.08617i	−0.194467	−	0.319136i
$643$	5.91017	+	22.0571i	0.233074	+	0.869845i	0.979007	+	0.203824i	$0.0653372\pi$
$643$	5.91017	+	22.0571i	0.233074	+	0.869845i	−0.745933	+	0.666021i	$0.767996\pi$
$644$	−5.63717	−	21.0382i	−0.222136	−	0.829021i
$645$	−3.05786	+	5.59836i	−0.120403	+	0.220435i
$646$	−13.5109			−0.531579
$647$	18.2315	−	31.5780i	0.716756	−	1.24146i	−0.245523	−	0.969391i	$-0.578960\pi$
$647$	18.2315	−	31.5780i	0.716756	−	1.24146i	0.962278	−	0.272067i	$-0.0877071\pi$
$648$	8.87463	+	1.49701i	0.348628	+	0.0588079i
$649$			12.0836i			0.474321i
$650$	−4.32103	−	15.7075i	−0.169485	−	0.616099i
$651$	−51.4779	+	15.1081i	−2.01758	+	0.592134i
$652$	3.95111	−	3.95111i	0.154737	−	0.154737i
$653$			3.39452i			0.132838i	0.997792	+	0.0664190i	$0.0211574\pi$
$653$			3.39452i			0.132838i	−0.997792	+	0.0664190i	$0.978843\pi$
$654$	−11.9899	+	3.51888i	−0.468841	+	0.137599i
$655$	−1.87158	−	6.98482i	−0.0731285	−	0.272919i
$656$	−1.48606	+	5.54605i	−0.0580209	+	0.216537i
$657$	7.16533	+	22.4349i	0.279546	+	0.875267i
$658$	−39.1803	−	39.1803i	−1.52741	−	1.52741i
$659$		−	27.3904i		−	1.06698i	−0.845806	−	0.533490i	$-0.820880\pi$
$659$		−	27.3904i		−	1.06698i	0.845806	−	0.533490i	$-0.179120\pi$
$660$	−0.761758	−	2.59553i	−0.0296514	−	0.101031i
$661$	32.4505	+	32.4505i	1.26218	+	1.26218i	0.950035	+	0.312144i	$0.101047\pi$
$661$	32.4505	+	32.4505i	1.26218	+	1.26218i	0.312144	+	0.950035i	$0.398953\pi$
$662$	−10.1318	−	17.5489i	−0.393785	−	0.682056i
$663$	−6.65280	+	28.2259i	−0.258373	+	1.09620i
$664$	4.75191	−	8.23054i	0.184410	−	0.319407i
$665$	8.95321	−	2.39900i	0.347191	−	0.0930294i
$666$	4.91171	−	9.52141i	0.190325	−	0.368947i
$667$	−20.0627	+	11.5832i	−0.776833	+	0.448505i
$668$	−23.6549	+	6.33832i	−0.915236	+	0.245237i
$669$	13.1733	−	24.1178i	0.509309	−	0.932447i
$670$	−8.77097	+	2.35017i	−0.338852	+	0.0907951i
$671$	−6.78389	−	1.81774i	−0.261889	−	0.0701730i
$672$	5.48711	−	5.75324i	0.211670	−	0.221936i
$673$	−17.9179	+	10.3449i	−0.690685	+	0.398767i	−0.803869	−	0.594807i	$-0.797229\pi$
$673$	−17.9179	+	10.3449i	−0.690685	+	0.398767i	0.113183	+	0.993574i	$0.463895\pi$
$674$	2.04100	+	7.61712i	0.0786164	+	0.293401i
$675$	22.1895	−	7.67035i	0.854076	−	0.295232i
$676$	0.172992	+	12.9988i	0.00665353	+	0.499956i
$677$	6.49755	+	3.75136i	0.249721	+	0.144176i	0.619636	−	0.784889i	$-0.287280\pi$
$677$	6.49755	+	3.75136i	0.249721	+	0.144176i	−0.369916	+	0.929065i	$0.620613\pi$
$678$	−0.426213	−	0.699447i	−0.0163686	−	0.0268621i
$679$	−5.63554			−0.216272
$680$	1.61141	−	2.79105i	0.0617949	−	0.107032i
$681$	−9.42830	+	5.74519i	−0.361293	+	0.220156i
$682$	10.7371	−	10.7371i	0.411146	−	0.411146i
$683$	39.9739	+	10.7110i	1.52956	+	0.409844i	0.922875	−	0.385100i	$-0.125833\pi$
$683$	39.9739	+	10.7110i	1.52956	+	0.409844i	0.606683	+	0.794944i	$0.292500\pi$
$684$	−2.65564	−	8.31490i	−0.101541	−	0.317928i
$685$	−2.65397	−	4.59681i	−0.101403	−	0.175635i
$686$	−16.2248	−	28.1021i	−0.619464	−	1.07294i
$687$	−19.4470	−	10.6221i	−0.741949	−	0.405258i
$688$	4.59562	−	2.65328i	0.175206	−	0.101155i
$689$	−15.8782	−	9.02698i	−0.604913	−	0.343900i
$690$	3.93675	−	4.12768i	0.149869	−	0.157138i
$691$	−5.45974	−	1.46293i	−0.207698	−	0.0556526i	0.153470	−	0.988153i	$-0.450955\pi$
$691$	−5.45974	−	1.46293i	−0.207698	−	0.0556526i	−0.361168	+	0.932501i	$0.617622\pi$
$692$	9.17465	+	5.29699i	0.348768	+	0.201361i
$693$	1.46649	+	30.9519i	0.0557075	+	1.17577i
$694$	12.0177	−	12.0177i	0.456185	−	0.456185i
$695$	−5.48334	−	5.48334i	−0.207995	−	0.207995i
$696$	−7.42142	−	4.05363i	−0.281308	−	0.153653i
$697$	6.90068	−	25.7537i	0.261382	−	0.975491i
$698$	−12.5902	−	7.26897i	−0.476547	−	0.275134i
$699$	7.46214	−	30.7422i	0.282244	−	1.16278i
$700$	5.36783	−	20.0330i	0.202885	−	0.757177i
$701$	−40.7022			−1.53730			−0.768651	−	0.639669i	$-0.779072\pi$
$701$	−40.7022			−1.53730			−0.768651	+	0.639669i	$0.779072\pi$
$702$	−18.6785	+	1.45369i	−0.704975	+	0.0548660i
$703$	−10.3907			−0.391892
$704$	−0.582403	+	2.17356i	−0.0219501	+	0.0819190i
$705$	3.42291	−	14.1016i	0.128914	−	0.531096i
$706$	7.37333	+	4.25700i	0.277499	+	0.160214i
$707$	4.47217	−	16.6904i	0.168193	−	0.627706i
$708$	−8.16270	−	4.45852i	−0.306773	−	0.167562i
$709$	−1.21373	−	1.21373i	−0.0455824	−	0.0455824i	0.683948	−	0.729531i	$-0.260261\pi$
$709$	−1.21373	−	1.21373i	−0.0455824	−	0.0455824i	−0.729531	+	0.683948i	$0.760261\pi$
$710$	−7.90632	+	7.90632i	−0.296719	+	0.296719i
$711$	7.84513	−	5.03893i	0.294215	−	0.188975i
$712$	2.16893	+	1.25223i	0.0812843	+	0.0469295i
$713$	30.9285	+	8.28726i	1.15828	+	0.310360i
$714$	−25.4800	+	26.7158i	−0.953565	+	0.999815i
$715$	2.84785	+	4.85768i	0.106503	+	0.181667i
$716$	−10.7836	+	6.22591i	−0.403001	+	0.232673i
$717$	30.4026	+	16.6061i	1.13541	+	0.620167i
$718$	−1.98446	−	3.43719i	−0.0740594	−	0.128275i
$719$	10.3528	+	17.9315i	0.386093	+	0.668732i	0.991920	−	0.126864i	$-0.0404911\pi$
$719$	10.3528	+	17.9315i	0.386093	+	0.668732i	−0.605827	+	0.795596i	$0.707158\pi$
$720$	2.03441	+	0.443103i	0.0758179	+	0.0165135i
$721$	−67.3577	−	18.0484i	−2.50853	−	0.672159i
$722$	7.44897	−	7.44897i	0.277222	−	0.277222i
$723$	−22.2684	+	13.5694i	−0.828171	+	0.504651i
$724$	−9.22324	+	15.9751i	−0.342779	+	0.593711i
$725$	−22.0596			−0.819273
$726$	5.35046	+	8.78051i	0.198574	+	0.325875i
$727$	−38.1761	−	22.0410i	−1.41587	−	0.817455i	−0.419940	−	0.907552i	$-0.637949\pi$
$727$	−38.1761	−	22.0410i	−1.41587	−	0.817455i	−0.995933	+	0.0900971i	$0.971282\pi$
$728$	−8.17945	+	14.3875i	−0.303150	+	0.533234i
$729$	−3.82201	−	26.7281i	−0.141556	−	0.989930i
$730$	1.41017	+	5.26282i	0.0521927	+	0.194786i
$731$	−21.3403	+	12.3208i	−0.789299	+	0.455702i
$732$	3.73100	−	3.91196i	0.137902	−	0.144590i
$733$	19.6173	+	5.25644i	0.724582	+	0.194151i	0.602215	−	0.798334i	$-0.294285\pi$
$733$	19.6173	+	5.25644i	0.724582	+	0.194151i	0.122367	+	0.992485i	$0.460952\pi$
$734$	−23.5282	+	6.30435i	−0.868440	+	0.232698i
$735$	8.10737	−	14.8430i	0.299045	−	0.547493i
$736$	−4.58334	+	1.22810i	−0.168944	+	0.0452685i
$737$	−25.4965	+	14.7204i	−0.939175	+	0.542233i
$738$	17.2058	−	0.815206i	0.633353	−	0.0300081i
$739$	37.8060	−	10.1301i	1.39072	−	0.372642i	0.515715	−	0.856760i	$-0.327526\pi$
$739$	37.8060	−	10.1301i	1.39072	−	0.372642i	0.875002	+	0.484118i	$0.160860\pi$
$740$	1.23927	−	2.14648i	0.0455566	−	0.0789063i
$741$	9.55806	+	15.4532i	0.351124	+	0.567686i
$742$	−11.6263	−	20.1373i	−0.426814	−	0.739263i
$743$	37.3133	+	37.3133i	1.36889	+	1.36889i	0.862024	+	0.506867i	$0.169197\pi$
$743$	37.3133	+	37.3133i	1.36889	+	1.36889i	0.506867	+	0.862024i	$0.330803\pi$
$744$	3.29143	+	11.2149i	0.120670	+	0.411157i
$745$		−	5.13531i		−	0.188143i
$746$	6.54644	+	6.54644i	0.239682	+	0.239682i
$747$	−27.8583	−	6.06766i	−1.01928	−	0.222004i
$748$	2.70445	−	10.0932i	0.0988845	−	0.369042i
$749$	6.49491	+	24.2393i	0.237319	+	0.885686i
$750$	10.9789	−	3.22218i	0.400894	−	0.117657i
$751$		−	28.3546i		−	1.03467i	−0.855782	−	0.517336i	$-0.826924\pi$
$751$		−	28.3546i		−	1.03467i	0.855782	−	0.517336i	$-0.173076\pi$
$752$	−8.53576	+	8.53576i	−0.311267	+	0.311267i
$753$	−43.6865	+	12.8214i	−1.59202	+	0.467239i
$754$	17.0334	+	4.44282i	0.620319	+	0.161798i
$755$			9.94532i			0.361947i
$756$	−21.4498	−	10.4298i	−0.780120	−	0.379329i
$757$	24.6271	−	42.6555i	0.895089	−	1.55034i	0.0613944	−	0.998114i	$-0.480445\pi$
$757$	24.6271	−	42.6555i	0.895089	−	1.55034i	0.833694	−	0.552226i	$-0.186221\pi$
$758$	13.8340			0.502473
$759$	8.86521	−	16.2305i	0.321787	−	0.589130i
$760$	−0.522643	−	1.95053i	−0.0189583	−	0.0707532i
$761$	6.93919	+	25.8974i	0.251545	+	0.938780i	0.969980	+	0.243185i	$0.0781923\pi$
$761$	6.93919	+	25.8974i	0.251545	+	0.938780i	−0.718435	+	0.695595i	$0.755141\pi$
$762$	0.392450	+	0.644040i	0.0142170	+	0.0233311i
$763$	33.1148			1.19884
$764$	4.25783	−	7.37477i	0.154043	−	0.266810i
$765$	−9.44700	−	2.05760i	−0.341557	−	0.0743926i
$766$			17.8071i			0.643398i
$767$	18.7347	+	4.88658i	0.676471	+	0.176444i
$768$	−1.25339	−	1.19541i	−0.0452279	−	0.0431357i
$769$	−30.3153	+	3

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.z (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.408561 + 1.68317i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.179629 + 0.670386i) q^{5} +(-1.52008 - 0.830278i) q^{6} +(3.24572 + 3.24572i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.66616 - 1.37536i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.408561 + 1.68317i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.179629 + 0.670386i) q^{5} +(-1.52008 - 0.830278i) q^{6} +(3.24572 + 3.24572i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.66616 - 1.37536i) q^{9} +(-0.601052 - 0.347017i) q^{10} +(-2.17356 - 0.582403i) q^{11} +(1.19541 - 1.25339i) q^{12} +(-1.78196 + 3.13442i) q^{13} +(-3.97518 + 2.29507i) q^{14} +(-1.05499 - 0.576241i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-2.32181 - 4.02149i) q^{17} +(2.01855 - 2.21934i) q^{18} +(-2.81042 - 0.753050i) q^{19} +(0.490757 - 0.490757i) q^{20} +(-6.78919 + 4.13704i) q^{21} +(1.12512 - 1.94876i) q^{22} +4.74503 q^{23} +(0.901288 + 1.47908i) q^{24} +(3.91298 + 2.25916i) q^{25} +(-2.56642 - 2.53249i) q^{26} +(3.40426 - 3.92569i) q^{27} +(-1.18802 - 4.43374i) q^{28} +(-4.22816 + 2.44113i) q^{29} +(0.829657 - 0.869897i) q^{30} +(6.51808 + 1.74651i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(1.86832 - 3.42053i) q^{33} +(4.48539 - 1.20186i) q^{34} +(-2.75891 + 1.59286i) q^{35} +(1.62128 + 2.52417i) q^{36} +(3.44953 - 0.924299i) q^{37} +(1.45478 - 2.51976i) q^{38} +(-4.54775 - 4.27995i) q^{39} +(0.347017 + 0.601052i) q^{40} +(4.05999 + 4.05999i) q^{41} +(-2.23890 - 7.62860i) q^{42} -5.30657i q^{43} +(1.59115 + 1.59115i) q^{44} +(1.40094 - 1.54030i) q^{45} +(-1.22810 + 4.58334i) q^{46} +(3.12430 + 11.6601i) q^{47} +(-1.66195 + 0.487763i) q^{48} +14.0694i q^{49} +(-3.19493 + 3.19493i) q^{50} +(7.71746 - 2.26498i) q^{51} +(3.11043 - 1.82351i) q^{52} +5.06576i q^{53} +(2.91083 + 4.30431i) q^{54} +(0.780869 - 1.35250i) q^{55} +4.59014 q^{56} +(2.41575 - 4.42276i) q^{57} +(-1.26362 - 4.71590i) q^{58} +(-1.38984 - 5.18694i) q^{59} +(0.625525 + 1.02653i) q^{60} +3.12110 q^{61} +(-3.37401 + 5.84395i) q^{62} +(-4.18956 - 13.1176i) q^{63} -1.00000i q^{64} +(-1.78118 - 1.75764i) q^{65} +(2.82042 + 2.68995i) q^{66} +(9.25140 - 9.25140i) q^{67} +4.64361i q^{68} +(-1.93864 + 7.98671i) q^{69} +(-0.824524 - 3.07717i) q^{70} +(4.16970 - 15.5615i) q^{71} +(-2.85778 + 0.912729i) q^{72} +(-5.55110 - 5.55110i) q^{73} +3.57122i q^{74} +(-5.40125 + 5.66322i) q^{75} +(2.05737 + 2.05737i) q^{76} +(-5.16444 - 8.94507i) q^{77} +(5.31116 - 3.28505i) q^{78} +(-1.55400 + 2.69161i) q^{79} +(-0.670386 + 0.179629i) q^{80} +(5.21677 + 7.33385i) q^{81} +(-4.97245 + 2.87085i) q^{82} +(9.17998 - 2.45977i) q^{83} +(7.94813 - 0.188185i) q^{84} +(3.11301 - 0.834129i) q^{85} +(5.12575 + 1.37344i) q^{86} +(-2.38139 - 8.11409i) q^{87} +(-1.94876 + 1.12512i) q^{88} +(0.648204 + 2.41913i) q^{89} +(1.12522 + 1.75186i) q^{90} +(-15.9572 + 4.38972i) q^{91} +(-4.10931 - 2.37251i) q^{92} +(-5.60272 + 10.2575i) q^{93} -12.0714 q^{94} +(1.00967 - 1.74880i) q^{95} +(-0.0409976 - 1.73157i) q^{96} +(-0.868150 + 0.868150i) q^{97} +(-13.5900 - 3.64143i) q^{98} +(4.99402 + 4.54220i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{7}+O(q^{10}) \) 56 * q - 8 * q^7	\( 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47} - 24 q^{50} + 8 q^{52} - 36 q^{54} + 36 q^{57} + 24 q^{60} - 48 q^{63} - 36 q^{65} + 28 q^{67} + 84 q^{69} - 24 q^{71} - 24 q^{72} + 28 q^{73} + 4 q^{76} + 24 q^{77} - 60 q^{78} - 24 q^{79} + 24 q^{81} - 96 q^{83} - 72 q^{85} + 4 q^{91} - 24 q^{92} - 36 q^{93} - 52 q^{97} + 48 q^{98} + 60 q^{99}+O(q^{100}) \) 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

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