LMFDB - Embedded newform 234.2.z.a.227.5

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			227.5
Character	$\chi$	$=$	234.227
Dual form			234.2.z.a.167.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(0.675780 - 1.59478i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.435860 - 1.62665i) q^{5} +(1.36553 + 1.06551i) q^{6} +(-0.212562 - 0.212562i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.08664 - 2.15544i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(0.675780 - 1.59478i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.435860 - 1.62665i) q^{5} +(1.36553 + 1.06551i) q^{6} +(-0.212562 - 0.212562i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.08664 - 2.15544i) q^{9} +(1.45842 + 0.842018i) q^{10} +(-1.53531 - 0.411385i) q^{11} +(-1.38263 + 1.04323i) q^{12} +(2.24619 - 2.82039i) q^{13} +(0.260334 - 0.150304i) q^{14} +(-2.29961 - 1.79436i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.26545 - 2.19182i) q^{17} +(2.62206 - 1.45767i) q^{18} +(4.16702 + 1.11655i) q^{19} +(-1.19079 + 1.19079i) q^{20} +(-0.482634 + 0.195344i) q^{21} +(0.794734 - 1.37652i) q^{22} +1.32190 q^{23} +(-0.649831 - 1.60553i) q^{24} +(1.87410 + 1.08201i) q^{25} +(2.14293 + 2.89963i) q^{26} +(-4.84756 + 1.87113i) q^{27} +(0.0778030 + 0.290365i) q^{28} +(-6.48106 + 3.74184i) q^{29} +(2.32840 - 1.75684i) q^{30} +(10.3807 + 2.78151i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-1.69360 + 2.17047i) q^{33} +(2.44466 - 0.655045i) q^{34} +(-0.438411 + 0.253117i) q^{35} +(0.729366 + 2.90999i) q^{36} +(-2.37887 + 0.637416i) q^{37} +(-2.15701 + 3.73605i) q^{38} +(-2.97998 - 5.48815i) q^{39} +(-0.842018 - 1.45842i) q^{40} +(2.66186 + 2.66186i) q^{41} +(-0.0637730 - 0.516747i) q^{42} +7.42377i q^{43} +(1.12392 + 1.12392i) q^{44} +(-4.41564 + 2.45477i) q^{45} +(-0.342133 + 1.27686i) q^{46} +(0.928739 + 3.46610i) q^{47} +(1.71901 - 0.212147i) q^{48} -6.90964i q^{49} +(-1.53020 + 1.53020i) q^{50} +(-4.35064 + 0.536923i) q^{51} +(-3.35546 + 1.31944i) q^{52} -3.63112i q^{53} +(-0.552733 - 5.16667i) q^{54} +(-1.33836 + 2.31811i) q^{55} -0.300608 q^{56} +(4.59664 - 5.89093i) q^{57} +(-1.93692 - 7.22868i) q^{58} +(0.187561 + 0.699986i) q^{59} +(1.09434 + 2.70377i) q^{60} -11.2570 q^{61} +(-5.37346 + 9.30710i) q^{62} +(-0.0146237 + 0.901704i) q^{63} -1.00000i q^{64} +(-3.60878 - 4.88307i) q^{65} +(-1.65818 - 2.19765i) q^{66} +(-0.690972 + 0.690972i) q^{67} +2.53090i q^{68} +(0.893313 - 2.10814i) q^{69} +(-0.131023 - 0.488984i) q^{70} +(-1.84126 + 6.87167i) q^{71} +(-2.99961 - 0.0486470i) q^{72} +(3.38109 + 3.38109i) q^{73} -2.46279i q^{74} +(2.99205 - 2.25758i) q^{75} +(-3.05047 - 3.05047i) q^{76} +(0.238903 + 0.413792i) q^{77} +(6.07242 - 1.45800i) q^{78} +(-3.69530 + 6.40045i) q^{79} +(1.62665 - 0.435860i) q^{80} +(-0.291844 + 8.99527i) q^{81} +(-3.26010 + 1.88222i) q^{82} +(11.8761 - 3.18219i) q^{83} +(0.515645 + 0.0721440i) q^{84} +(-4.11690 + 1.10312i) q^{85} +(-7.17081 - 1.92141i) q^{86} +(1.58764 + 12.8645i) q^{87} +(-1.37652 + 0.794734i) q^{88} +(-0.512119 - 1.91125i) q^{89} +(-1.22828 - 4.90052i) q^{90} +(-1.07696 + 0.122054i) q^{91} +(-1.14480 - 0.660949i) q^{92} +(11.4510 - 14.6753i) q^{93} -3.58837 q^{94} +(3.63248 - 6.29163i) q^{95} +(-0.239994 + 1.71534i) q^{96} +(4.41623 - 4.41623i) q^{97} +(6.67419 + 1.78835i) q^{98} +(2.31693 + 4.16768i) 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
$3$	0.675780	−	1.59478i	0.390162	−	0.920746i
$3$	0.675780	−	1.59478i	0.390162	−	0.920746i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	0.435860	−	1.62665i	0.194923	−	0.727461i	−0.797364	−	0.603498i	$-0.793773\pi$
$5$	0.435860	−	1.62665i	0.194923	−	0.727461i	0.992287	−	0.123963i	$-0.0395604\pi$
$6$	1.36553	+	1.06551i	0.557477	+	0.434994i
$7$	−0.212562	−	0.212562i	−0.0803408	−	0.0803408i	0.665794	−	0.746135i	$-0.268093\pi$
$7$	−0.212562	−	0.212562i	−0.0803408	−	0.0803408i	−0.746135	+	0.665794i	$0.768093\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−2.08664	−	2.15544i	−0.695548	−	0.718480i
$10$	1.45842	+	0.842018i	0.461192	+	0.266269i
$11$	−1.53531	−	0.411385i	−0.462913	−	0.124037i	0.0198222	−	0.999804i	$-0.493690\pi$
$11$	−1.53531	−	0.411385i	−0.462913	−	0.124037i	−0.482735	+	0.875766i	$0.660357\pi$
$12$	−1.38263	+	1.04323i	−0.399132	+	0.301154i
$13$	2.24619	−	2.82039i	0.622981	−	0.782237i
$13$	2.24619	−	2.82039i	0.622981	−	0.782237i
$14$	0.260334	−	0.150304i	0.0695771	−	0.0401704i
$15$	−2.29961	−	1.79436i	−0.593756	−	0.463302i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−1.26545	−	2.19182i	−0.306917	−	0.531595i	0.670770	−	0.741666i	$-0.265964\pi$
$17$	−1.26545	−	2.19182i	−0.306917	−	0.531595i	−0.977686	+	0.210071i	$0.932631\pi$
$18$	2.62206	−	1.45767i	0.618025	−	0.343577i
$19$	4.16702	+	1.11655i	0.955980	+	0.256154i	0.702898	−	0.711291i	$-0.251889\pi$
$19$	4.16702	+	1.11655i	0.955980	+	0.256154i	0.253082	+	0.967445i	$0.418556\pi$
$20$	−1.19079	+	1.19079i	−0.266269	+	0.266269i
$21$	−0.482634	+	0.195344i	−0.105319	+	0.0426276i
$22$	0.794734	−	1.37652i	0.169438	−	0.293475i
$23$	1.32190			0.275635			0.137817	−	0.990458i	$-0.455991\pi$
$23$	1.32190			0.275635			0.137817	+	0.990458i	$0.455991\pi$
$24$	−0.649831	−	1.60553i	−0.132646	−	0.327727i
$25$	1.87410	+	1.08201i	0.374820	+	0.216403i
$26$	2.14293	+	2.89963i	0.420264	+	0.568663i
$27$	−4.84756	+	1.87113i	−0.932914	+	0.360099i
$28$	0.0778030	+	0.290365i	0.0147034	+	0.0548738i
$29$	−6.48106	+	3.74184i	−1.20350	+	0.694843i	−0.961332	−	0.275391i	$-0.911193\pi$
$29$	−6.48106	+	3.74184i	−1.20350	+	0.694843i	−0.242170	+	0.970234i	$0.577859\pi$
$30$	2.32840	−	1.75684i	0.425106	−	0.320753i
$31$	10.3807	+	2.78151i	1.86443	+	0.499573i	0.999995	−	0.00316697i	$-0.00100808\pi$
$31$	10.3807	+	2.78151i	1.86443	+	0.499573i	0.864438	+	0.502740i	$0.167675\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	−1.69360	+	2.17047i	−0.294818	+	0.377831i
$34$	2.44466	−	0.655045i	0.419256	−	0.112339i
$35$	−0.438411	+	0.253117i	−0.0741050	+	0.0427846i
$36$	0.729366	+	2.90999i	0.121561	+	0.484998i
$37$	−2.37887	+	0.637416i	−0.391084	+	0.104791i	−0.449002	−	0.893531i	$-0.648220\pi$
$37$	−2.37887	+	0.637416i	−0.391084	+	0.104791i	0.0579183	+	0.998321i	$0.481554\pi$
$38$	−2.15701	+	3.73605i	−0.349913	+	0.606067i
$39$	−2.97998	−	5.48815i	−0.477178	−	0.878807i
$40$	−0.842018	−	1.45842i	−0.133135	−	0.230596i
$41$	2.66186	+	2.66186i	0.415713	+	0.415713i	0.883723	−	0.468010i	$-0.155029\pi$
$41$	2.66186	+	2.66186i	0.415713	+	0.415713i	−0.468010	+	0.883723i	$0.655029\pi$
$42$	−0.0637730	−	0.516747i	−0.00984039	−	0.0797358i
$43$			7.42377i			1.13211i	0.824366	+	0.566057i	$0.191532\pi$
$43$			7.42377i			1.13211i	−0.824366	+	0.566057i	$0.808468\pi$
$44$	1.12392	+	1.12392i	0.169438	+	0.169438i
$45$	−4.41564	+	2.45477i	−0.658244	+	0.365936i
$46$	−0.342133	+	1.27686i	−0.0504447	+	0.188262i
$47$	0.928739	+	3.46610i	0.135470	+	0.505583i	0.999996	+	0.00299296i	$0.000952690\pi$
$47$	0.928739	+	3.46610i	0.135470	+	0.505583i	−0.864525	+	0.502590i	$0.832381\pi$
$48$	1.71901	−	0.212147i	0.248118	−	0.0306208i
$49$		−	6.90964i		−	0.987091i
$50$	−1.53020	+	1.53020i	−0.216403	+	0.216403i
$51$	−4.35064	+	0.536923i	−0.609212	+	0.0751843i
$52$	−3.35546	+	1.31944i	−0.465318	+	0.182973i
$53$		−	3.63112i		−	0.498772i	−0.968404	−	0.249386i	$-0.919771\pi$
$53$		−	3.63112i		−	0.498772i	0.968404	−	0.249386i	$-0.0802288\pi$
$54$	−0.552733	−	5.16667i	−0.0752174	−	0.703095i
$55$	−1.33836	+	2.31811i	−0.180464	+	0.312574i
$56$	−0.300608			−0.0401704
$57$	4.59664	−	5.89093i	0.608840	−	0.780273i
$58$	−1.93692	−	7.22868i	−0.254330	−	0.949173i
$59$	0.187561	+	0.699986i	0.0244183	+	0.0911304i	0.977060	−	0.212966i	$-0.0683123\pi$
$59$	0.187561	+	0.699986i	0.0244183	+	0.0911304i	−0.952641	+	0.304096i	$0.901646\pi$
$60$	1.09434	+	2.70377i	0.141278	+	0.349055i
$61$	−11.2570			−1.44132			−0.720658	−	0.693291i	$-0.756160\pi$
$61$	−11.2570			−1.44132			−0.720658	+	0.693291i	$0.756160\pi$
$62$	−5.37346	+	9.30710i	−0.682430	+	1.18200i
$63$	−0.0146237	+	0.901704i	−0.00184241	+	0.113604i
$64$		−	1.00000i		−	0.125000i
$65$	−3.60878	−	4.88307i	−0.447614	−	0.605671i
$66$	−1.65818	−	2.19765i	−0.204108	−	0.270512i
$67$	−0.690972	+	0.690972i	−0.0844157	+	0.0844157i	−0.748054	−	0.663638i	$-0.769012\pi$
$67$	−0.690972	+	0.690972i	−0.0844157	+	0.0844157i	0.663638	+	0.748054i	$0.269012\pi$
$68$			2.53090i			0.306917i
$69$	0.893313	−	2.10814i	0.107542	−	0.253790i
$70$	−0.131023	−	0.488984i	−0.0156602	−	0.0584448i
$71$	−1.84126	+	6.87167i	−0.218517	+	0.815518i	0.766381	+	0.642386i	$0.222055\pi$
$71$	−1.84126	+	6.87167i	−0.218517	+	0.815518i	−0.984899	+	0.173132i	$0.944611\pi$
$72$	−2.99961	−	0.0486470i	−0.353507	−	0.00573310i
$73$	3.38109	+	3.38109i	0.395727	+	0.395727i	0.876723	−	0.480996i	$-0.159725\pi$
$73$	3.38109	+	3.38109i	0.395727	+	0.395727i	−0.480996	+	0.876723i	$0.659725\pi$
$74$		−	2.46279i		−	0.286293i
$75$	2.99205	−	2.25758i	0.345492	−	0.260682i
$76$	−3.05047	−	3.05047i	−0.349913	−	0.349913i
$77$	0.238903	+	0.413792i	0.0272255	+	0.0471560i
$78$	6.07242	−	1.45800i	0.687566	−	0.165086i
$79$	−3.69530	+	6.40045i	−0.415754	+	0.720107i	−0.995507	−	0.0946854i	$-0.969815\pi$
$79$	−3.69530	+	6.40045i	−0.415754	+	0.720107i	0.579754	+	0.814792i	$0.303149\pi$
$80$	1.62665	−	0.435860i	0.181865	−	0.0487307i
$81$	−0.291844	+	8.99527i	−0.0324271	+	0.999474i
$82$	−3.26010	+	1.88222i	−0.360018	+	0.207856i
$83$	11.8761	−	3.18219i	1.30357	−	0.349291i	0.460773	−	0.887518i	$-0.347572\pi$
$83$	11.8761	−	3.18219i	1.30357	−	0.349291i	0.842800	+	0.538227i	$0.180906\pi$
$84$	0.515645	+	0.0721440i	0.0562615	+	0.00787156i
$85$	−4.11690	+	1.10312i	−0.446540	+	0.119650i
$86$	−7.17081	−	1.92141i	−0.773248	−	0.207191i
$87$	1.58764	+	12.8645i	0.170213	+	1.37922i
$88$	−1.37652	+	0.794734i	−0.146738	+	0.0847190i
$89$	−0.512119	−	1.91125i	−0.0542845	−	0.202592i	0.933457	−	0.358688i	$-0.116776\pi$
$89$	−0.512119	−	1.91125i	−0.0542845	−	0.202592i	−0.987742	+	0.156096i	$0.950109\pi$
$90$	−1.22828	−	4.90052i	−0.129472	−	0.516560i
$91$	−1.07696	+	0.122054i	−0.112896	+	0.0127947i
$92$	−1.14480	−	0.660949i	−0.119353	−	0.0689087i
$93$	11.4510	−	14.6753i	1.18741	−	1.52176i
$94$	−3.58837			−0.370112
$95$	3.63248	−	6.29163i	0.372684	−	0.645508i
$96$	−0.239994	+	1.71534i	−0.0244943	+	0.175071i
$97$	4.41623	−	4.41623i	0.448400	−	0.448400i	−0.446422	−	0.894822i	$-0.647302\pi$
$97$	4.41623	−	4.41623i	0.448400	−	0.448400i	0.894822	+	0.446422i	$0.147302\pi$
$98$	6.67419	+	1.78835i	0.674196	+	0.180650i
$99$	2.31693	+	4.16768i	0.232860	+	0.418868i
$100$	−1.08201	−	1.87410i	−0.108201	−	0.187410i
$101$	4.29630	+	7.44140i	0.427498	+	0.740447i	0.996650	−	0.0817846i	$-0.0260619\pi$
$101$	4.29630	+	7.44140i	0.427498	+	0.740447i	−0.569153	+	0.822232i	$0.692729\pi$
$102$	0.607401	−	4.34136i	0.0601417	−	0.429859i
$103$	−0.228107	+	0.131698i	−0.0224761	+	0.0129766i	−0.511196	−	0.859464i	$-0.670797\pi$
$103$	−0.228107	+	0.131698i	−0.0224761	+	0.0129766i	0.488720	+	0.872441i	$0.337464\pi$
$104$	−0.406023	−	3.58262i	−0.0398138	−	0.351305i
$105$	0.107396	+	0.870221i	0.0104808	+	0.0849248i
$106$	3.50739	+	0.939802i	0.340668	+	0.0912817i
$107$	−11.4443	−	6.60737i	−1.10636	−	0.638759i	−0.168478	−	0.985705i	$-0.553885\pi$
$107$	−11.4443	−	6.60737i	−1.10636	−	0.638759i	−0.937885	+	0.346947i	$0.887218\pi$
$108$	5.13368	+	0.803334i	0.493988	+	0.0773008i
$109$	11.1164	−	11.1164i	1.06475	−	1.06475i	0.0670011	−	0.997753i	$-0.478657\pi$
$109$	11.1164	−	11.1164i	1.06475	−	1.06475i	0.997753	−	0.0670011i	$-0.0213431\pi$
$110$	−1.89273	−	1.89273i	−0.180464	−	0.180464i
$111$	−0.591054	+	4.22452i	−0.0561004	+	0.400974i
$112$	0.0778030	−	0.290365i	0.00735169	−	0.0274369i
$113$	8.43567	+	4.87034i	0.793561	+	0.458163i	0.841215	−	0.540701i	$-0.181841\pi$
$113$	8.43567	+	4.87034i	0.793561	+	0.458163i	−0.0476538	+	0.998864i	$0.515174\pi$
$114$	4.50051	+	5.96470i	0.421511	+	0.558645i
$115$	0.576163	−	2.15027i	0.0537275	−	0.200514i
$116$	7.48368			0.694843
$117$	−10.7662	+	1.04363i	−0.995335	+	0.0964832i
$118$	−0.724678			−0.0667121
$119$	−0.196912	+	0.734884i	−0.0180509	+	0.0673667i
$120$	−2.89487	+	0.357263i	−0.264264	+	0.0326135i
$121$	−7.33834	−	4.23679i	−0.667122	−	0.385163i
$122$	2.91354	−	10.8735i	0.263779	−	0.984437i
$123$	6.04391	−	2.44625i	0.544961	−	0.220571i
$124$	−7.59922	−	7.59922i	−0.682430	−	0.682430i
$125$	8.53087	−	8.53087i	0.763024	−	0.763024i
$126$	−0.867194	−	0.247504i	−0.0772558	−	0.0220494i
$127$	15.1666	+	8.75644i	1.34582	+	0.777009i	0.987654	−	0.156650i	$-0.0500694\pi$
$127$	15.1666	+	8.75644i	1.34582	+	0.777009i	0.358164	+	0.933659i	$0.383403\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	11.8393	+	5.01683i	1.04239	+	0.441708i
$130$	5.65071	−	2.22198i	0.495600	−	0.194880i
$131$	13.4168	−	7.74619i	1.17223	−	0.676788i	0.218027	−	0.975943i	$-0.430038\pi$
$131$	13.4168	−	7.74619i	1.17223	−	0.676788i	0.954205	+	0.299155i	$0.0967047\pi$
$132$	2.55194	−	1.03289i	0.222118	−	0.0899012i
$133$	−0.648413	−	1.12308i	−0.0562245	−	0.0973837i
$134$	−0.488591	−	0.846265i	−0.0422079	−	0.0731062i
$135$	0.930822	+	8.70085i	0.0801124	+	0.748850i
$136$	−2.44466	−	0.655045i	−0.209628	−	0.0561697i
$137$	15.1254	−	15.1254i	1.29225	−	1.29225i	0.358861	−	0.933391i	$-0.383165\pi$
$137$	15.1254	−	15.1254i	1.29225	−	1.29225i	0.933391	−	0.358861i	$-0.116835\pi$
$138$	1.80510	+	1.40850i	0.153660	+	0.119899i
$139$	−4.61459	+	7.99271i	−0.391405	+	0.677933i	−0.992635	−	0.121143i	$-0.961344\pi$
$139$	−4.61459	+	7.99271i	−0.391405	+	0.677933i	0.601230	+	0.799076i	$0.294677\pi$
$140$	0.506234			0.0427846
$141$	6.15529	+	0.861188i	0.518369	+	0.0725251i
$142$	−6.16098	−	3.55704i	−0.517018	−	0.298500i
$143$	−4.60886	+	3.40613i	−0.385413	+	0.284835i
$144$	0.823344	−	2.88481i	0.0686120	−	0.240400i
$145$	3.26184	+	12.1734i	0.270881	+	1.01094i
$146$	−4.14098	+	2.39079i	−0.342710	+	0.197864i
$147$	−11.0193	−	4.66939i	−0.908860	−	0.385125i
$148$	2.37887	+	0.637416i	0.195542	+	0.0523953i
$149$	−21.4547	+	5.74878i	−1.75764	+	0.470958i	−0.986230	−	0.165381i	$-0.947115\pi$
$149$	−21.4547	+	5.74878i	−1.75764	+	0.470958i	−0.771410	+	0.636339i	$0.780448\pi$
$150$	1.40625	+	3.47440i	0.114820	+	0.283684i
$151$	−16.6660	+	4.46564i	−1.35626	+	0.363409i	−0.862441	−	0.506157i	$-0.831066\pi$
$151$	−16.6660	+	4.46564i	−1.35626	+	0.363409i	−0.493818	+	0.869565i	$0.664399\pi$
$152$	3.73605	−	2.15701i	0.303033	−	0.174956i
$153$	−2.08380	+	7.30115i	−0.168465	+	0.590263i
$154$	−0.461525	+	0.123665i	−0.0371908	+	0.00996524i
$155$	9.04909	−	15.6735i	0.726840	−	1.25892i
$156$	−0.163338	+	6.24286i	−0.0130775	+	0.499829i
$157$	0.300573	+	0.520608i	0.0239884	+	0.0415490i	0.877770	−	0.479082i	$-0.159030\pi$
$157$	0.300573	+	0.520608i	0.0239884	+	0.0415490i	−0.853782	+	0.520631i	$0.825697\pi$
$158$	−5.22594	−	5.22594i	−0.415754	−	0.415754i
$159$	−5.79083	−	2.45384i	−0.459243	−	0.194602i
$160$			1.68404i			0.133135i
$161$	−0.280985	−	0.280985i	−0.0221447	−	0.0221447i
$162$	−8.61323	−	2.61005i	−0.676719	−	0.205065i
$163$	0.929908	−	3.47046i	0.0728360	−	0.271828i	−0.919898	−	0.392158i	$-0.871729\pi$
$163$	0.929908	−	3.47046i	0.0728360	−	0.271828i	0.992734	+	0.120330i	$0.0383953\pi$
$164$	−0.974309	−	3.63617i	−0.0760807	−	0.283937i
$165$	2.79243	+	3.70092i	0.217391	+	0.288116i
$166$			12.2951i			0.954282i
$167$	−6.38449	+	6.38449i	−0.494047	+	0.494047i	−0.909579	−	0.415532i	$-0.863596\pi$
$167$	−6.38449	+	6.38449i	−0.494047	+	0.494047i	0.415532	+	0.909579i	$0.363596\pi$
$168$	−0.203145	+	0.479403i	−0.0156729	+	0.0369867i
$169$	−2.90925	−	12.6703i	−0.223788	−	0.974638i
$170$		−	4.26212i		−	0.326890i
$171$	−6.28842	−	11.3116i	−0.480888	−	0.865020i
$172$	3.71188	−	6.42917i	0.283028	−	0.490220i
$173$	−15.7320			−1.19608			−0.598041	−	0.801466i	$-0.704054\pi$
$173$	−15.7320			−1.19608			−0.598041	+	0.801466i	$0.704054\pi$
$174$	−12.8371	−	1.79604i	−0.973177	−	0.136157i
$175$	−0.168368	−	0.628357i	−0.0127274	−	0.0474993i
$176$	−0.411385	−	1.53531i	−0.0310093	−	0.115728i
$177$	1.24307	+	0.173919i	0.0934350	+	0.0130725i
$178$	1.97868			0.148308
$179$	−3.29562	+	5.70819i	−0.246326	+	0.426650i	−0.962504	−	0.271268i	$-0.912557\pi$
$179$	−3.29562	+	5.70819i	−0.246326	+	0.426650i	0.716177	+	0.697918i	$0.245890\pi$
$180$	5.05144	+	0.0819233i	0.376512	+	0.00610620i
$181$		−	11.2750i		−	0.838063i	−0.907972	−	0.419031i	$-0.862370\pi$
$181$		−	11.2750i		−	0.838063i	0.907972	−	0.419031i	$-0.137630\pi$
$182$	0.160844	−	1.07186i	0.0119225	−	0.0794512i
$183$	−7.60728	+	17.9525i	−0.562346	+	1.32709i
$184$	0.934723	−	0.934723i	0.0689087	−	0.0689087i
$185$			4.14742i			0.304924i
$186$	11.2115	+	14.8590i	0.822067	+	1.08952i
$187$	1.04117	+	3.88571i	0.0761382	+	0.284151i
$188$	0.928739	−	3.46610i	0.0677352	−	0.252791i
$189$	1.42814	+	0.632675i	0.103882	+	0.0460203i
$190$	5.13710	+	5.13710i	0.372684	+	0.372684i
$191$		−	10.9652i		−	0.793418i	−0.917945	−	0.396709i	$-0.870152\pi$
$191$		−	10.9652i		−	0.793418i	0.917945	−	0.396709i	$-0.129848\pi$
$192$	−1.59478	−	0.675780i	−0.115093	−	0.0487702i
$193$	−9.87885	−	9.87885i	−0.711095	−	0.711095i	0.255669	−	0.966764i	$-0.417704\pi$
$193$	−9.87885	−	9.87885i	−0.711095	−	0.711095i	−0.966764	+	0.255669i	$0.917704\pi$
$194$	3.12275	+	5.40876i	0.224200	+	0.388326i
$195$	−10.2262	+	2.45532i	−0.732311	+	0.175829i
$196$	−3.45482	+	5.98392i	−0.246773	+	0.427423i
$197$	−4.59113	+	1.23019i	−0.327105	+	0.0876474i	−0.418634	−	0.908155i	$-0.637491\pi$
$197$	−4.59113	+	1.23019i	−0.327105	+	0.0876474i	0.0915295	+	0.995802i	$0.470824\pi$
$198$	−4.62533	+	1.15930i	−0.328708	+	0.0823881i
$199$	−20.1187	+	11.6155i	−1.42618	+	0.823403i	−0.996816	−	0.0797315i	$-0.974594\pi$
$199$	−20.1187	+	11.6155i	−1.42618	+	0.823403i	−0.429359	+	0.903134i	$0.641260\pi$
$200$	2.09029	−	0.560091i	0.147806	−	0.0396044i
$201$	0.635003	+	1.56889i	0.0447897	+	0.110661i
$202$	−8.29981	+	2.22393i	−0.583972	+	0.156475i
$203$	2.17300	+	0.582253i	0.152514	+	0.0408661i
$204$	4.03623	+	1.71033i	0.282592	+	0.119747i
$205$	5.49012	−	3.16973i	0.383447	−	0.221383i
$206$	−0.0681718	−	0.254421i	−0.00474975	−	0.0177263i
$207$	−2.75833	−	2.84927i	−0.191717	−	0.198038i
$208$	3.56563	+	0.535061i	0.247232	+	0.0370998i
$209$	−5.93833	−	3.42850i	−0.410763	−	0.237154i
$210$	−0.868365	−	0.121493i	−0.0599229	−	0.00838382i
$211$	−2.05342			−0.141363			−0.0706817	−	0.997499i	$-0.522517\pi$
$211$	−2.05342			−0.141363			−0.0706817	+	0.997499i	$0.522517\pi$
$212$	−1.81556	+	3.14464i	−0.124693	+	0.215975i
$213$	9.71452	+	7.58014i	0.665628	+	0.519383i
$214$	9.34423	−	9.34423i	0.638759	−	0.638759i
$215$	12.0759	+	3.23573i	0.823569	+	0.220675i
$216$	−2.10465	+	4.75083i	−0.143204	+	0.323253i
$217$	−1.61530	−	2.79778i	−0.109654	−	0.189926i
$218$	7.86045	+	13.6147i	0.532377	+	0.922104i
$219$	7.67697	−	3.10722i	0.518762	−	0.209967i
$220$	2.31811	−	1.33836i	0.156287	−	0.0902322i
$221$	−9.02425	−	1.35419i	−0.607037	−	0.0910925i
$222$	−3.92760	−	1.66430i	−0.263603	−	0.111701i
$223$	0.574743	+	0.154002i	0.0384876	+	0.0103127i	0.278011	−	0.960578i	$-0.410325\pi$
$223$	0.574743	+	0.154002i	0.0384876	+	0.0103127i	−0.239524	+	0.970890i	$0.576991\pi$
$224$	0.260334	+	0.150304i	0.0173943	+	0.0100426i
$225$	−1.57837	−	6.29729i	−0.105224	−	0.419819i
$226$	−6.88769	+	6.88769i	−0.458163	+	0.458163i
$227$	12.9035	+	12.9035i	0.856432	+	0.856432i	0.990916	−	0.134484i	$-0.0429376\pi$
$227$	12.9035	+	12.9035i	0.856432	+	0.856432i	−0.134484	+	0.990916i	$0.542938\pi$
$228$	−6.92627	+	2.80338i	−0.458704	+	0.185658i
$229$	−2.66237	+	9.93612i	−0.175935	+	0.656597i	0.820456	+	0.571710i	$0.193720\pi$
$229$	−2.66237	+	9.93612i	−0.175935	+	0.656597i	−0.996391	+	0.0848872i	$0.972947\pi$
$230$	1.92788	+	1.11306i	0.127121	+	0.0733931i
$231$	0.821354	−	0.101365i	0.0540411	−	0.00666934i
$232$	−1.93692	+	7.22868i	−0.127165	+	0.474586i
$233$	21.7770			1.42666			0.713328	−	0.700830i	$-0.247187\pi$
$233$	21.7770			1.42666			0.713328	+	0.700830i	$0.247187\pi$
$234$	1.77843	−	10.6695i	0.116260	−	0.697484i
$235$	6.04294			0.394198
$236$	0.187561	−	0.699986i	0.0122092	−	0.0455652i
$237$	7.71009	+	10.2185i	0.500824	+	0.663762i
$238$	−0.658879	−	0.380404i	−0.0427088	−	0.0246579i
$239$	−4.84819	+	18.0937i	−0.313603	+	1.17038i	0.611679	+	0.791106i	$0.290494\pi$
$239$	−4.84819	+	18.0937i	−0.313603	+	1.17038i	−0.925283	+	0.379278i	$0.876172\pi$
$240$	0.404158	−	2.88870i	0.0260883	−	0.186465i
$241$	−3.12996	−	3.12996i	−0.201618	−	0.201618i	0.599075	−	0.800693i	$-0.295535\pi$
$241$	−3.12996	−	3.12996i	−0.201618	−	0.201618i	−0.800693	+	0.599075i	$0.795535\pi$
$242$	5.99173	−	5.99173i	0.385163	−	0.385163i
$243$	14.1482	+	6.54425i	0.907610	+	0.419814i
$244$	9.74888	+	5.62852i	0.624108	+	0.360329i
$245$	−11.2396	−	3.01164i	−0.718070	−	0.192406i
$246$	0.798615	+	6.47111i	0.0509178	+	0.412583i
$247$	12.5090	−	9.24465i	0.795930	−	0.588223i
$248$	9.30710	−	5.37346i	0.591001	−	0.341215i
$249$	2.95074	−	21.0902i	0.186996	−	1.33654i
$250$	6.03224	+	10.4481i	0.381512	+	0.660798i
$251$	−14.8094	−	25.6507i	−0.934763	−	1.61906i	−0.775057	−	0.631892i	$-0.782279\pi$
$251$	−14.8094	−	25.6507i	−0.934763	−	1.61906i	−0.159706	−	0.987165i	$-0.551055\pi$
$252$	0.463517	−	0.773587i	0.0291988	−	0.0487314i
$253$	−2.02952	−	0.543809i	−0.127595	−	0.0341890i
$254$	−12.3835	+	12.3835i	−0.777009	+	0.777009i
$255$	−1.02288	+	7.31101i	−0.0640555	+	0.457833i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−16.6485			−1.03851			−0.519253	−	0.854620i	$-0.673790\pi$
$257$	−16.6485			−1.03851			−0.519253	+	0.854620i	$0.673790\pi$
$258$	−7.91012	+	10.1374i	−0.492462	+	0.631127i
$259$	0.641147	+	0.370166i	0.0398389	+	0.0230010i
$260$	0.683757	+	6.03325i	0.0424048	+	0.374166i
$261$	21.5890	+	6.16165i	1.33632	+	0.381397i
$262$	4.00972	+	14.9645i	0.247722	+	0.924510i
$263$	24.3103	−	14.0355i	1.49904	−	0.865469i	0.499037	−	0.866581i	$-0.333687\pi$
$263$	24.3103	−	14.0355i	1.49904	−	0.865469i	0.999999	+	0.00111197i	$0.000353950\pi$
$264$	0.337201	+	2.73231i	0.0207533	+	0.168162i
$265$	−5.90657	−	1.58266i	−0.362838	−	0.0972220i
$266$	1.25264	−	0.335643i	0.0768041	−	0.0205796i
$267$	−3.39411	−	0.474870i	−0.207716	−	0.0290616i
$268$	0.943886	−	0.252913i	0.0576570	−	0.0154491i
$269$	−16.1655	+	9.33318i	−0.985631	+	0.569054i	−0.903965	−	0.427606i	$-0.859357\pi$
$269$	−16.1655	+	9.33318i	−0.985631	+	0.569054i	−0.0816654	+	0.996660i	$0.526024\pi$
$270$	−8.64529	−	1.35284i	−0.526136	−	0.0823314i
$271$	−24.6548	+	6.60622i	−1.49767	+	0.401299i	−0.912319	−	0.409481i	$-0.865710\pi$
$271$	−24.6548	+	6.60622i	−1.49767	+	0.401299i	−0.585351	+	0.810780i	$0.699043\pi$
$272$	1.26545	−	2.19182i	0.0767292	−	0.132899i
$273$	−0.533141	+	1.80000i	−0.0322671	+	0.108941i
$274$	10.6953	+	18.5248i	0.646126	+	1.11912i
$275$	−2.43220	−	2.43220i	−0.146667	−	0.146667i
$276$	−1.82770	+	1.37904i	−0.110015	+	0.0830087i
$277$			15.8023i			0.949470i	0.880129	+	0.474735i	$0.157456\pi$
$277$			15.8023i			0.949470i	−0.880129	+	0.474735i	$0.842544\pi$
$278$	−6.52602	−	6.52602i	−0.391405	−	0.391405i
$279$	−15.6655	−	28.1790i	−0.937868	−	1.68703i
$280$	−0.131023	+	0.488984i	−0.00783012	+	0.0292224i
$281$	6.96981	+	26.0117i	0.415784	+	1.55173i	0.783261	+	0.621694i	$0.213555\pi$
$281$	6.96981	+	26.0117i	0.415784	+	1.55173i	−0.367477	+	0.930033i	$0.619778\pi$
$282$	−2.42495	+	5.72266i	−0.144404	+	0.340779i
$283$		−	23.2762i		−	1.38363i	−0.722077	−	0.691813i	$-0.756812\pi$
$283$		−	23.2762i		−	1.38363i	0.722077	−	0.691813i	$-0.243188\pi$
$284$	5.03042	−	5.03042i	0.298500	−	0.298500i
$285$	−7.57901	−	10.0448i	−0.448942	−	0.595000i
$286$	−2.09720	−	5.33339i	−0.124010	−	0.315370i
$287$		−	1.13162i		−	0.0667974i
$288$	2.57341	+	1.54193i	0.151640	+	0.0908592i
$289$	5.29727	−	9.17515i	0.311604	−	0.539714i
$290$	−12.6028			−0.740061
$291$	−4.05851	−	10.0273i	−0.237914	−	0.587811i
$292$	−1.23757	−	4.61866i	−0.0724231	−	0.270287i
$293$	6.07527	+	22.6732i	0.354921	+	1.32458i	0.880584	+	0.473890i	$0.157151\pi$
$293$	6.07527	+	22.6732i	0.354921	+	1.32458i	−0.525663	+	0.850693i	$0.676183\pi$
$294$	7.36230	−	9.43534i	0.429378	−	0.550280i
$295$	1.22038			0.0710535
$296$	−1.23139	+	2.13284i	−0.0715733	+	0.123969i
$297$	8.21226	−	0.878552i	0.476524	−	0.0509787i
$298$		−	22.2116i		−	1.28668i
$299$	2.96924	−	3.72828i	0.171715	−	0.215612i
$300$	−3.71998	+	0.459092i	−0.214773	+	0.0265057i
$301$	1.57801	−	1.57801i	0.0909549	−	0.0909549i
$302$		−	17.2539i		−	0.992851i
$303$	14.7708	−	1.82289i	0.848557	−	0.104722i
$304$	1.11655	+	4.16702i	0.0640385	+	0.238995i
$305$	−4.90650	+	18.3113i	−0.280945	+	1.04850i
$306$	−6.51305	−	3.90248i	−0.372326	−	0.223090i
$307$	−15.1916	−	15.1916i	−0.867028	−	0.867028i	0.125115	−	0.992142i	$-0.460070\pi$
$307$	−15.1916	−	15.1916i	−0.867028	−	0.867028i	−0.992142	+	0.125115i	$0.960070\pi$
$308$		−	0.477806i		−	0.0272255i
$309$	0.0558786	+	0.452779i	0.00317882	+	0.0257577i
$310$	12.7973	+	12.7973i	0.726840	+	0.726840i
$311$	−5.02062	−	8.69597i	−0.284693	−	0.493103i	0.687841	−	0.725861i	$-0.258558\pi$
$311$	−5.02062	−	8.69597i	−0.284693	−	0.493103i	−0.972535	+	0.232758i	$0.925225\pi$
$312$	−5.98787	−	1.77354i	−0.338996	−	0.100407i
$313$	−3.93637	+	6.81799i	−0.222497	+	0.385376i	−0.955565	−	0.294779i	$-0.904754\pi$
$313$	−3.93637	+	6.81799i	−0.222497	+	0.385376i	0.733069	+	0.680154i	$0.238087\pi$
$314$	−0.580663	+	0.155588i	−0.0327687	+	0.00878035i
$315$	1.46039	+	0.416805i	0.0822834	+	0.0234843i
$316$	6.40045	−	3.69530i	0.360053	−	0.207877i
$317$	−10.6249	+	2.84693i	−0.596753	+	0.159900i	−0.544538	−	0.838736i	$-0.683295\pi$
$317$	−10.6249	+	2.84693i	−0.596753	+	0.159900i	−0.0522155	+	0.998636i	$0.516628\pi$
$318$	3.86900	−	4.95841i	0.216963	−	0.278054i
$319$	11.4898	−	3.07867i	0.643303	−	0.172373i
$320$	−1.62665	−	0.435860i	−0.0909327	−	0.0243653i
$321$	−18.2711	+	13.7860i	−1.01979	+	0.769460i
$322$	0.344135	−	0.198686i	0.0191779	−	0.0110724i
$323$	−2.82587	−	10.5463i	−0.157236	−	0.586812i
$324$	4.75038	−	7.64421i	0.263910	−	0.424678i
$325$	7.26129	−	2.85530i	0.402784	−	0.158383i
$326$	3.11153	+	1.79644i	0.172332	+	0.0994958i
$327$	−10.2159	−	25.2404i	−0.564942	−	1.39579i
$328$	3.76444			0.207856
$329$	0.539346	−	0.934174i	0.0297351	−	0.0515027i
$330$	−4.29755	+	1.73942i	−0.236572	+	0.0957517i
$331$	15.9202	−	15.9202i	0.875053	−	0.875053i	−0.117965	−	0.993018i	$-0.537637\pi$
$331$	15.9202	−	15.9202i	0.875053	−	0.875053i	0.993018	+	0.117965i	$0.0376370\pi$
$332$	−11.8761	−	3.18219i	−0.651786	−	0.174646i
$333$	6.33776	+	3.79745i	0.347307	+	0.208099i
$334$	−4.51452	−	7.81938i	−0.247023	−	0.427857i
$335$	0.822805	+	1.42514i	0.0449546	+	0.0778637i
$336$	−0.410490	−	0.320301i	−0.0223941	−	0.0174739i
$337$	−12.2213	+	7.05595i	−0.665734	+	0.384362i	−0.794458	−	0.607318i	$-0.792245\pi$
$337$	−12.2213	+	7.05595i	−0.665734	+	0.384362i	0.128724	+	0.991680i	$0.458912\pi$
$338$	12.9915	+	0.469193i	0.706646	+	0.0255207i
$339$	13.4678	−	10.1618i	0.731469	−	0.551911i
$340$	4.11690	+	1.10312i	0.223270	+	0.0598250i
$341$	−14.7933	−	8.54094i	−0.801105	−	0.462518i
$342$	12.5537	−	3.14649i	0.678828	−	0.170143i
$343$	−2.95666	+	2.95666i	−0.159644	+	0.159644i
$344$	5.24940	+	5.24940i	0.283028	+	0.283028i
$345$	−3.03985	−	2.37196i	−0.163660	−	0.127702i
$346$	4.07174	−	15.1959i	0.218898	−	0.816939i
$347$	21.3155	+	12.3065i	1.14428	+	0.660648i	0.947486	−	0.319798i	$-0.103615\pi$
$347$	21.3155	+	12.3065i	1.14428	+	0.660648i	0.196789	+	0.980446i	$0.436948\pi$
$348$	5.05732	−	11.9348i	0.271101	−	0.639774i
$349$	5.79845	−	21.6401i	0.310384	−	1.15837i	−0.617827	−	0.786314i	$-0.711987\pi$
$349$	5.79845	−	21.6401i	0.310384	−	1.15837i	0.928211	−	0.372054i	$-0.121346\pi$
$350$	0.650523			0.0347719
$351$	−5.61122	+	17.8750i	−0.299505	+	0.954095i
$352$	1.58947			0.0847190
$353$	−4.59982	+	17.1668i	−0.244824	+	0.913694i	0.728648	+	0.684888i	$0.240149\pi$
$353$	−4.59982	+	17.1668i	−0.244824	+	0.913694i	−0.973472	+	0.228806i	$0.926518\pi$
$354$	−0.489723	+	1.15570i	−0.0260285	+	0.0614249i
$355$	10.3753	+	5.99018i	0.550664	+	0.317926i
$356$	−0.512119	+	1.91125i	−0.0271422	+	0.101296i
$357$	1.03891	+	0.810650i	0.0549849	+	0.0429042i
$358$	−4.66072	−	4.66072i	−0.246326	−	0.246326i
$359$	−9.00574	+	9.00574i	−0.475305	+	0.475305i	−0.903626	−	0.428322i	$-0.859105\pi$
$359$	−9.00574	+	9.00574i	−0.475305	+	0.475305i	0.428322	+	0.903626i	$0.359105\pi$
$360$	−1.38654	+	4.85811i	−0.0730771	+	0.256045i
$361$	−0.337122	−	0.194638i	−0.0177433	−	0.0102441i
$362$	10.8908	+	2.91818i	0.572408	+	0.153376i
$363$	−11.7159	+	8.83990i	−0.614923	+	0.463974i
$364$	0.993703	+	0.432779i	0.0520842	+	0.0226838i
$365$	6.97355	−	4.02618i	0.365012	−	0.210740i
$366$	−15.3719	−	11.9945i	−0.803500	−	0.626963i
$367$	17.8604	+	30.9352i	0.932308	+	1.61480i	0.779366	+	0.626569i	$0.215541\pi$
$367$	17.8604	+	30.9352i	0.932308	+	1.61480i	0.152941	+	0.988235i	$0.451125\pi$
$368$	0.660949	+	1.14480i	0.0344544	+	0.0596767i
$369$	0.183129	−	11.2918i	0.00953330	−	0.587830i
$370$	−4.00610	−	1.07343i	−0.208267	−	0.0558050i
$371$	−0.771836	+	0.771836i	−0.0400717	+	0.0400717i
$372$	−17.2545	+	6.98367i	−0.894603	+	0.362087i
$373$	5.42959	−	9.40433i	0.281134	−	0.486938i	−0.690531	−	0.723303i	$-0.742623\pi$
$373$	5.42959	−	9.40433i	0.281134	−	0.486938i	0.971664	+	0.236365i	$0.0759562\pi$
$374$	−4.02279			−0.208013
$375$	−7.83986	−	19.3698i	−0.404849	−	1.00025i
$376$	3.10762	+	1.79419i	0.160263	+	0.0925281i
$377$	−4.00423	+	26.6840i	−0.206228	+	1.37430i
$378$	−0.980746	+	1.21573i	−0.0504441	+	0.0625302i
$379$	3.41411	+	12.7416i	0.175371	+	0.654494i	0.996488	+	0.0837342i	$0.0266847\pi$
$379$	3.41411	+	12.7416i	0.175371	+	0.654494i	−0.821117	+	0.570760i	$0.806649\pi$
$380$	−6.29163	+	3.63248i	−0.322754	+	0.186342i
$381$	24.2139	−	18.2700i	1.24051	−	0.935998i
$382$	10.5916	+	2.83802i	0.541914	+	0.145206i
$383$	13.3086	−	3.56602i	0.680035	−	0.182215i	0.0977643	−	0.995210i	$-0.468831\pi$
$383$	13.3086	−	3.56602i	0.680035	−	0.182215i	0.582271	+	0.812995i	$0.302164\pi$
$384$	1.06551	−	1.36553i	0.0543742	−	0.0696846i
$385$	0.777225	−	0.208257i	0.0396111	−	0.0106138i
$386$	12.0991	−	6.98540i	0.615826	−	0.355548i
$387$	16.0015	−	15.4907i	0.813401	−	0.787439i
$388$	−6.03268	+	1.61645i	−0.306263	+	0.0820629i
$389$	−10.3218	+	17.8779i	−0.523336	+	0.906445i	0.476295	+	0.879286i	$0.341980\pi$
$389$	−10.3218	+	17.8779i	−0.523336	+	0.906445i	−0.999631	+	0.0271595i	$0.991354\pi$
$390$	0.275067	−	10.5132i	0.0139286	−	0.532356i
$391$	−1.67280	−	2.89737i	−0.0845970	−	0.146526i
$392$	−4.88585	−	4.88585i	−0.246773	−	0.246773i
$393$	−3.28666	−	26.6316i	−0.165790	−	1.34338i
$394$		−	4.75309i		−	0.239457i
$395$	8.80067	+	8.80067i	0.442810	+	0.442810i
$396$	0.0773229	−	4.76778i	0.00388562	−	0.239590i
$397$	2.46047	−	9.18259i	0.123487	−	0.460861i	−0.876294	−	0.481777i	$-0.839992\pi$
$397$	2.46047	−	9.18259i	0.123487	−	0.460861i	0.999781	+	0.0209159i	$0.00665821\pi$
$398$	−6.01264	−	22.4395i	−0.301386	−	1.12479i
$399$	−2.22926	+	0.275118i	−0.111602	+	0.0137731i
$400$			2.16403i			0.108201i
$401$	−8.37540	+	8.37540i	−0.418248	+	0.418248i	−0.884599	−	0.466352i	$-0.845568\pi$
$401$	−8.37540	+	8.37540i	−0.418248	+	0.418248i	0.466352	+	0.884599i	$0.345568\pi$
$402$	−1.67979	+	0.207306i	−0.0837801	+	0.0103395i
$403$	31.1620	−	23.0299i	1.55229	−	1.14720i
$404$		−	8.59259i		−	0.427498i
$405$	14.5050	+	4.39541i	0.720758	+	0.218410i
$406$	−1.12483	+	1.94826i	−0.0558242	+	0.0966903i
$407$	3.91452			0.194036
$408$	−2.69671	+	3.45603i	−0.133507	+	0.171099i
$409$	9.94664	+	37.1214i	0.491830	+	1.83553i	0.547107	+	0.837062i	$0.315729\pi$
$409$	9.94664	+	37.1214i	0.491830	+	1.83553i	−0.0552778	+	0.998471i	$0.517604\pi$
$410$	1.64077	+	6.12344i	0.0810319	+	0.302415i
$411$	−13.9003	−	34.3432i	−0.685649	−	1.69402i
$412$	0.263395			0.0129766
$413$	0.108922	−	0.188658i	0.00535970	−	0.00928327i
$414$	3.46609	−	1.92690i	0.170349	−	0.0947018i
$415$		−	20.7053i		−	1.01638i
$416$	−1.43968	+	3.30565i	−0.0705862	+	0.162073i
$417$	9.62816	+	12.7606i	0.471493	+	0.624888i
$418$	4.84863	−	4.84863i	0.237154	−	0.237154i
$419$			21.0347i			1.02761i	0.857907	+	0.513805i	$0.171765\pi$
$419$			21.0347i			1.02761i	−0.857907	+	0.513805i	$0.828235\pi$
$420$	0.342103	−	0.807331i	0.0166929	−	0.0393937i
$421$	−6.90262	−	25.7609i	−0.336413	−	1.25551i	−0.902329	−	0.431048i	$-0.858144\pi$
$421$	−6.90262	−	25.7609i	−0.336413	−	1.25551i	0.565916	−	0.824463i	$-0.308523\pi$
$422$	0.531465	−	1.98345i	0.0258713	−	0.0965530i
$423$	5.53303	−	9.23435i	0.269025	−	0.448990i
$424$	−2.56759	−	2.56759i	−0.124693	−	0.124693i
$425$		−	5.47693i		−	0.265670i
$426$	−9.83616	+	7.42162i	−0.476563	+	0.359579i
$427$	2.39281	+	2.39281i	0.115796	+	0.115796i
$428$	6.60737	+	11.4443i	0.319379	+	0.553181i
$429$	2.31744	+	9.65192i	0.111887	+	0.465999i
$430$	−6.25094	+	10.8269i	−0.301447	+	0.522122i
$431$	−30.6200	+	8.20459i	−1.47491	+	0.395201i	−0.904612	−	0.426236i	$-0.859839\pi$
$431$	−30.6200	+	8.20459i	−1.47491	+	0.395201i	−0.570299	+	0.821437i	$0.693173\pi$
$432$	−4.04423	−	3.26255i	−0.194578	−	0.156969i
$433$	−32.6337	+	18.8411i	−1.56827	+	0.905444i	−0.571904	+	0.820320i	$0.693795\pi$
$433$	−32.6337	+	18.8411i	−1.56827	+	0.905444i	−0.996370	+	0.0851235i	$0.972872\pi$
$434$	3.12052	−	0.836142i	0.149790	−	0.0401361i
$435$	21.6181	+	3.02459i	1.03651	+	0.145018i
$436$	−15.1852	+	4.06887i	−0.727240	+	0.194864i
$437$	5.50838	+	1.47596i	0.263501	+	0.0706050i
$438$	1.01440	+	8.21959i	0.0484699	+	0.392747i
$439$	−2.56493	+	1.48087i	−0.122418	+	0.0706779i	−0.559958	−	0.828521i	$-0.689183\pi$
$439$	−2.56493	+	1.48087i	−0.122418	+	0.0706779i	0.437541	+	0.899199i	$0.355850\pi$
$440$	0.692786	+	2.58551i	0.0330273	+	0.123260i
$441$	−14.8933	+	14.4179i	−0.709205	+	0.686569i
$442$	3.64369	−	8.36627i	0.173313	−	0.397943i
$443$	−23.4384	−	13.5322i	−1.11359	−	0.642933i	−0.173835	−	0.984775i	$-0.555616\pi$
$443$	−23.4384	−	13.5322i	−1.11359	−	0.642933i	−0.939757	+	0.341842i	$0.888949\pi$
$444$	2.62413	−	3.36302i	0.124536	−	0.159602i
$445$	−3.33216			−0.157959
$446$	−0.297509	+	0.515300i	−0.0140875	+	0.0244002i
$447$	−5.33064	+	38.1005i	−0.252131	+	1.80209i
$448$	−0.212562	+	0.212562i	−0.0100426	+	0.0100426i
$449$	38.6090	+	10.3453i	1.82207	+	0.488223i	0.997041	−	0.0768655i	$-0.0244912\pi$
$449$	38.6090	+	10.3453i	1.82207	+	0.488223i	0.825030	+	0.565088i	$0.191158\pi$
$450$	6.49122	+	0.105273i	0.305999	+	0.00496263i
$451$	−2.99173	−	5.18183i	−0.140875	−	0.244003i
$452$	−4.87034	−	8.43567i	−0.229081	−	0.396780i
$453$	−4.14083	+	29.5964i	−0.194553	+	1.39056i
$454$	−15.8034	+	9.12412i	−0.741692	+	0.428216i
$455$	−0.270866	+	1.80504i	−0.0126984	+	0.0846217i
$456$	−0.915206	−	7.41583i	−0.0428584	−	0.347278i
$457$	31.2261	+	8.36700i	1.46069	+	0.391392i	0.899729	−	0.436449i	$-0.143764\pi$
$457$	31.2261	+	8.36700i	1.46069	+	0.391392i	0.560964	+	0.827840i	$0.310431\pi$
$458$	−8.90848	−	5.14331i	−0.416266	−	0.240331i
$459$	10.2355	+	8.25718i	0.477754	+	0.385412i
$460$	−1.57411	+	1.57411i	−0.0733931	+	0.0733931i
$461$	7.36533	+	7.36533i	0.343038	+	0.343038i	0.857508	−	0.514470i	$-0.172011\pi$
$461$	7.36533	+	7.36533i	0.343038	+	0.343038i	−0.514470	+	0.857508i	$0.672011\pi$
$462$	−0.114671	+	0.819602i	−0.00533496	+	0.0381313i
$463$	−3.39310	+	12.6632i	−0.157691	+	0.588509i	0.841169	+	0.540772i	$0.181868\pi$
$463$	−3.39310	+	12.6632i	−0.157691	+	0.588509i	−0.998860	+	0.0477376i	$0.984799\pi$
$464$	−6.48106	−	3.74184i	−0.300876	−	0.173711i
$465$	−18.8806	−	25.0231i	−0.875565	−	1.16042i
$466$	−5.63630	+	21.0349i	−0.261096	+	0.974425i
$467$	−1.37176			−0.0634775			−0.0317388	−	0.999496i	$-0.510104\pi$
$467$	−1.37176			−0.0634775			−0.0317388	+	0.999496i	$0.510104\pi$
$468$	9.84561	+	4.47929i	0.455113	+	0.207055i
$469$	0.293749			0.0135640
$470$	−1.56403	+	5.83703i	−0.0721433	+	0.269242i
$471$	1.03338	−	0.127531i	0.0476155	−	0.00587634i
$472$	0.627590	+	0.362339i	0.0288872	+	0.0166780i
$473$	3.05402	−	11.3978i	0.140424	−	0.524070i
$474$	−11.8658	+	4.80264i	−0.545015	+	0.220592i
$475$	6.60129	+	6.60129i	0.302888	+	0.302888i
$476$	0.537972	−	0.537972i	0.0246579	−	0.0246579i
$477$	−7.82665	+	7.57684i	−0.358358	+	0.346920i
$478$	−16.2224	−	9.36599i	−0.741994	−	0.428390i
$479$	−8.97190	−	2.40401i	−0.409936	−	0.109842i	0.0479566	−	0.998849i	$-0.484729\pi$
$479$	−8.97190	−	2.40401i	−0.409936	−	0.109842i	−0.457893	+	0.889007i	$0.651396\pi$
$480$	2.68566	+	1.13804i	0.122583	+	0.0519441i
$481$	−3.54563	+	8.14111i	−0.161667	+	0.371203i
$482$	3.83340	−	2.21322i	0.174607	−	0.100809i
$483$	−0.637993	+	0.258225i	−0.0290297	+	0.0117496i
$484$	4.23679	+	7.33834i	0.192582	+	0.333561i
$485$	−5.25881	−	9.10853i	−0.238790	−	0.413597i
$486$	−9.98309	+	11.9724i	−0.452842	+	0.543078i
$487$	−11.7546	−	3.14965i	−0.532654	−	0.142724i	−0.0175402	−	0.999846i	$-0.505584\pi$
$487$	−11.7546	−	3.14965i	−0.532654	−	0.142724i	−0.515113	+	0.857122i	$0.672250\pi$
$488$	−7.95993	+	7.95993i	−0.360329	+	0.360329i
$489$	−4.90621	−	3.82827i	−0.221866	−	0.173120i
$490$	5.81803	−	10.0771i	0.262832	−	0.455238i
$491$	−7.44632			−0.336048			−0.168024	−	0.985783i	$-0.553739\pi$
$491$	−7.44632			−0.336048			−0.168024	+	0.985783i	$0.553739\pi$
$492$	−6.45731	−	0.903443i	−0.291118	−	0.0407304i
$493$	16.4029	+	9.47023i	0.738750	+	0.426518i
$494$	5.69207	+	14.4755i	0.256098	+	0.651283i
$495$	7.78922	−	1.95231i	0.350100	−	0.0877497i
$496$	2.78151	+	10.3807i	0.124893	+	0.466108i
$497$	1.85204	−	1.06927i	0.0830752	−	0.0479635i
$498$	19.6079	+	8.30875i	0.878651	+	0.372324i
$499$	4.74819	+	1.27227i	0.212558	+	0.0569548i	0.363527	−	0.931584i	$-0.381573\pi$
$499$	4.74819	+	1.27227i	0.212558	+	0.0569548i	−0.150968	+	0.988539i	$0.548239\pi$
$500$	−11.6534	+	3.12251i	−0.521155	+	0.139643i
$501$	5.86735	+	14.4964i	0.262134	+	0.647650i
$502$	28.6096	−	7.66592i	1.27691	−	0.342147i
$503$	24.0111	−	13.8628i	1.07060	−	0.618112i	0.142255	−	0.989830i	$-0.454565\pi$
$503$	24.0111	−	13.8628i	1.07060	−	0.618112i	0.928346	+	0.371718i	$0.121231\pi$
$504$	0.627261	+	0.647942i	0.0279404	+	0.0288616i
$505$	13.9772	−	3.74517i	0.621976	−	0.166658i
$506$	1.05056	−	1.81962i	0.0467030	−	0.0808920i
$507$	−22.1723	−	3.92272i	−0.984708	−	0.174214i
$508$	−8.75644	−	15.1666i	−0.388504	−	0.672909i
$509$	6.49162	+	6.49162i	0.287736	+	0.287736i	0.836184	−	0.548448i	$-0.184781\pi$
$509$	6.49162	+	6.49162i	0.287736	+	0.287736i	−0.548448	+	0.836184i	$0.684781\pi$
$510$	−6.79715	−	2.88026i	−0.300983	−	0.127540i
$511$		−	1.43738i		−	0.0635860i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−22.2891	+	2.38450i	−0.984088	+	0.105278i
$514$	4.30896	−	16.0812i	0.190060	−	0.709313i
$515$	0.114804	+	0.428453i	0.00505885	+	0.0188799i
$516$	−7.74469	−	10.2643i	−0.340941	−	0.451862i
$517$		−	5.70360i		−	0.250844i
$518$	−0.523494	+	0.523494i	−0.0230010	+	0.0230010i
$519$	−10.6314	+	25.0891i	−0.466665	+	1.10129i
$520$	−6.00464	−	0.901062i	−0.263321	−	0.0395142i
$521$		−	29.1318i		−	1.27629i	−0.769918	−	0.638143i	$-0.779703\pi$
$521$		−	29.1318i		−	1.27629i	0.769918	−	0.638143i	$-0.220297\pi$
$522$	−11.5393	+	19.2586i	−0.505063	+	0.842926i
$523$	1.29854	−	2.24913i	0.0567811	−	0.0983478i	−0.836238	−	0.548367i	$-0.815250\pi$
$523$	1.29854	−	2.24913i	0.0567811	−	0.0983478i	0.893019	+	0.450019i	$0.148583\pi$
$524$	−15.4924			−0.676788
$525$	−1.11587	−	0.156122i	−0.0487005	−	0.00681370i
$526$	7.26533	+	27.1146i	0.316784	+	1.18225i
$527$	−7.03971	−	26.2726i	−0.306655	−	1.14445i
$528$	−2.72648	−	0.381463i	−0.118655	−	0.0166010i
$529$	−21.2526			−0.924025
$530$	3.05746	−	5.29568i	0.132808	−	0.230030i
$531$	1.11741	−	1.86490i	0.0484912	−	0.0809296i
$532$			1.29683i			0.0562245i
$533$	13.4866	−	1.52845i	0.584167	−	0.0662045i
$534$	1.33715	−	3.15555i	0.0578641	−	0.136554i
$535$	−15.7360	+	15.7360i	−0.680327	+	0.680327i
$536$			0.977183i			0.0422079i
$537$	6.87618	+	9.11327i	0.296729	+	0.393267i
$538$	−4.83121	−	18.0303i	−0.208288	−	0.777343i
$539$	−2.84252	+	10.6084i	−0.122436	+	0.456937i
$540$	3.54431	−	8.00057i	0.152523	−	0.344290i
$541$	−4.52095	−	4.52095i	−0.194371	−	0.194371i	0.603211	−	0.797582i	$-0.293888\pi$
$541$	−4.52095	−	4.52095i	−0.194371	−	0.194371i	−0.797582	+	0.603211i	$0.793888\pi$
$542$		−	25.5245i		−	1.09637i
$543$	−17.9811	−	7.61941i	−0.771643	−	0.326980i
$544$	1.78962	+	1.78962i	0.0767292	+	0.0767292i
$545$	−13.2373	−	22.9276i	−0.567023	−	0.982112i
$546$	−1.60068	−	0.980848i	−0.0685027	−	0.0419764i
$547$	−7.08272	+	12.2676i	−0.302835	+	0.524526i	−0.976777	−	0.214259i	$-0.931267\pi$
$547$	−7.08272	+	12.2676i	−0.302835	+	0.524526i	0.673942	+	0.738784i	$0.264600\pi$
$548$	−20.6617	+	5.53629i	−0.882624	+	0.236498i
$549$	23.4894	+	24.2639i	1.00250	+	1.03556i
$550$	2.97883	−	1.71983i	0.127018	−	0.0733336i
$551$	−31.1846	+	8.35590i	−1.32851	+	0.355973i
$552$	−0.859010	−	2.12235i	−0.0365619	−	0.0903330i
$553$	2.14597	−	0.575011i	0.0912559	−	0.0244519i
$554$	−15.2639	−	4.08995i	−0.648500	−	0.173765i
$555$	6.61422	+	2.80274i	0.280758	+	0.118970i
$556$	7.99271	−	4.61459i	0.338966	−	0.195702i
$557$	2.54976	+	9.51584i	0.108037	+	0.403199i	0.998672	−	0.0515195i	$-0.0164064\pi$
$557$	2.54976	+	9.51584i	0.108037	+	0.403199i	−0.890635	+	0.454719i	$0.849740\pi$
$558$	31.2734	−	7.83843i	1.32391	−	0.331827i
$559$	20.9380	+	16.6752i	0.885581	+	0.705286i
$560$	−0.438411	−	0.253117i	−0.0185263	−	0.0106961i
$561$	6.90046	+	0.965445i	0.291338	+	0.0407611i
$562$	−26.9293			−1.13594
$563$	16.7341	−	28.9843i	0.705257	−	1.22154i	−0.261341	−	0.965246i	$-0.584165\pi$
$563$	16.7341	−	28.9843i	0.705257	−	1.22154i	0.966599	−	0.256295i	$-0.0825019\pi$
$564$	−4.90004	−	3.82345i	−0.206329	−	0.160996i
$565$	11.5991	−	11.5991i	0.487979	−	0.487979i
$566$	22.4831	+	6.02432i	0.945034	+	0.253221i
$567$	1.97408	−	1.85001i	0.0829037	−	0.0776933i
$568$	3.55704	+	6.16098i	0.149250	+	0.258509i
$569$	−5.33533	−	9.24106i	−0.223669	−	0.387406i	0.732250	−	0.681035i	$-0.238470\pi$
$569$	−5.33533	−	9.24106i	−0.223669	−	0.387406i	−0.955919	+	0.293630i	$0.905137\pi$
$570$	11.6641	−	4.72099i	0.488555	−	0.197740i
$571$	−31.5424	+	18.2110i	−1.32001	+	0.762107i	−0.983730	−	0.179656i	$-0.942502\pi$
$571$	−31.5424	+	18.2110i	−1.32001	+	0.762107i	−0.336279	+	0.941763i	$0.609168\pi$
$572$	5.69446	−	0.645361i	0.238097	−	0.0269839i
$573$	−17.4872	−	7.41010i	−0.730536	−	0.309561i
$574$	1.09306	+	0.292885i	0.0456235	+	0.0122248i
$575$	2.47737	+	1.43031i	0.103314	+	0.0596481i
$576$	−2.15544	+	2.08664i	−0.0898100	+	0.0869434i
$577$	−17.7894	+	17.7894i	−0.740581	+	0.740581i	−0.972690	−	0.232109i	$-0.925437\pi$
$577$	−17.7894	+	17.7894i	−0.740581	+	0.740581i	0.232109	+	0.972690i	$0.425437\pi$
$578$	7.49147	+	7.49147i	0.311604	+	0.311604i
$579$	−22.4305	+	9.07866i	−0.932180	+	0.377296i
$580$	3.26184	−	12.1734i	0.135441	−	0.505471i
$581$	−3.20082	−	1.84799i	−0.132792	−	0.0766677i
$582$	10.7361	−	1.32496i	0.445024	−	0.0549215i
$583$	−1.49379	+	5.57489i	−0.0618663	+	0.230888i
$584$	4.78159			0.197864
$585$	−2.99494	+	17.9677i	−0.123826	+	0.742874i
$586$	−23.4730			−0.969662
$587$	5.36801	−	20.0337i	0.221562	−	0.826879i	−0.762191	−	0.647352i	$-0.775877\pi$
$587$	5.36801	−	20.0337i	0.221562	−	0.826879i	0.983753	−	0.179527i	$-0.0574568\pi$
$588$	7.20834	+	9.55349i	0.297267	+	0.393979i
$589$	40.1510	+	23.1812i	1.65439	+	0.955164i
$590$	−0.315859	+	1.17880i	−0.0130037	+	0.0485304i
$591$	−1.14071	+	8.15318i	−0.0469227	+	0.335377i
$592$	−1.74145	−	1.74145i	−0.0715733	−	0.0715733i
$593$	25.1984	−	25.1984i	1.03477	−	1.03477i	0.0353990	−	0.999373i	$-0.488730\pi$
$593$	25.1984	−	25.1984i	1.03477	−	1.03477i	0.999373	−	0.0353990i	$-0.0112702\pi$
$594$	−1.27687	+	8.15982i	−0.0523908	+	0.334802i
$595$	1.10958	+	0.640613i	0.0454881	+	0.0262626i
$596$	21.4547	+	5.74878i	0.878820	+	0.235479i
$597$	4.92840	+	39.9344i	0.201706	+	1.63441i
$598$	2.83274	+	3.83301i	0.115839	+	0.156743i
$599$	−27.2170	+	15.7138i	−1.11206	+	0.642047i	−0.939362	−	0.342928i	$-0.888581\pi$
$599$	−27.2170	+	15.7138i	−1.11206	+	0.642047i	−0.172697	+	0.984975i	$0.555248\pi$
$600$	0.519353	−	3.71205i	0.0212025	−	0.151544i
$601$	−12.7413	−	22.0686i	−0.519728	−	0.900195i	−0.999737	−	0.0229318i	$-0.992700\pi$
$601$	−12.7413	−	22.0686i	−0.519728	−	0.900195i	0.480009	−	0.877264i	$-0.340633\pi$
$602$	1.11582	+	1.93266i	0.0454774	+	0.0787692i
$603$	2.93116	+	0.0475370i	0.119366	+	0.00193586i
$604$	16.6660	+	4.46564i	0.678130	+	0.181704i
$605$	−10.0903	+	10.0903i	−0.410229	+	0.410229i
$606$	−2.06217	+	14.7392i	−0.0837700	+	0.598741i
$607$	−7.25626	+	12.5682i	−0.294522	+	0.510128i	−0.974874	−	0.222758i	$-0.928494\pi$
$607$	−7.25626	+	12.5682i	−0.294522	+	0.510128i	0.680351	+	0.732886i	$0.261827\pi$
$608$	−4.31401			−0.174956
$609$	2.39703	−	3.07198i	0.0971327	−	0.124483i
$610$	−16.4175	−	9.47862i	−0.664723	−	0.383778i
$611$	11.8619	+	5.16611i	0.479881	+	0.208999i
$612$	5.45520	−	5.28108i	0.220514	−	0.213475i
$613$	1.08903	+	4.06431i	0.0439855	+	0.164156i	0.984425	−	0.175805i	$-0.0562528\pi$
$613$	1.08903	+	4.06431i	0.0439855	+	0.164156i	−0.940440	+	0.339961i	$0.889586\pi$
$614$	18.6058	−	10.7420i	0.750868	−	0.433514i
$615$	−1.34490	−	10.8976i	−0.0542314	−	0.439433i
$616$	0.461525	+	0.123665i	0.0185954	+	0.00498262i
$617$	2.13165	−	0.571175i	0.0858172	−	0.0229946i	−0.215655	−	0.976470i	$-0.569189\pi$
$617$	2.13165	−	0.571175i	0.0858172	−	0.0229946i	0.301472	+	0.953475i	$0.402522\pi$
$618$	−0.451814	−	0.0632134i	−0.0181746	−	0.00254281i
$619$	−23.7788	+	6.37151i	−0.955750	+	0.256092i	−0.702800	−	0.711387i	$-0.748067\pi$
$619$	−23.7788	+	6.37151i	−0.955750	+	0.256092i	−0.252950	+	0.967479i	$0.581401\pi$
$620$	−15.6735	+	9.04909i	−0.629462	+	0.363420i
$621$	−6.40799	+	2.47345i	−0.257144	+	0.0992560i
$622$	9.69909	−	2.59886i	0.388898	−	0.104205i
$623$	−0.297402	+	0.515116i	−0.0119152	+	0.0206377i
$624$	3.26289	−	5.32481i	0.130620	−	0.213163i
$625$	−4.74843	−	8.22452i	−0.189937	−	0.328981i
$626$	−5.56687	−	5.56687i	−0.222497	−	0.222497i
$627$	−9.48070	+	7.15342i	−0.378623	+	0.285680i
$628$		−	0.601146i		−	0.0239884i
$629$	4.40744	+	4.40744i	0.175736	+	0.175736i
$630$	−0.780578	+	1.30275i	−0.0310990	+	0.0519027i
$631$	9.44199	−	35.2380i	0.375880	−	1.40280i	−0.476176	−	0.879350i	$-0.657977\pi$
$631$	9.44199	−	35.2380i	0.375880	−	1.40280i	0.852055	−	0.523452i	$-0.175356\pi$
$632$	1.91283	+	7.13877i	0.0760882	+	0.283965i
$633$	−1.38766	+	3.27475i	−0.0551546	+	0.130160i
$634$		−	10.9997i		−	0.436854i
$635$	20.8542	−	20.8542i	0.827574	−	0.827574i
$636$	3.78809	+	5.02050i	0.150207	+	0.199076i
$637$	−19.4879	−	15.5204i	−0.772139	−	0.614939i
$638$			11.8951i			0.470931i
$639$	18.6535	−	10.3700i	0.737922	−	0.410231i
$640$	0.842018	−	1.45842i	0.0332837	−	0.0576490i
$641$	20.8637			0.824067			0.412033	−	0.911169i	$-0.364819\pi$
$641$	20.8637			0.824067			0.412033	+	0.911169i	$0.364819\pi$
$642$	−8.58734	−	21.2166i	−0.338915	−	0.837354i
$643$	0.359710	+	1.34246i	0.0141856	+	0.0529413i	0.972656	−	0.232251i	$-0.0746091\pi$
$643$	0.359710	+	1.34246i	0.0141856	+	0.0529413i	−0.958470	+	0.285192i	$0.907942\pi$
$644$	0.102848	+	0.383833i	0.00405276	+	0.0151251i
$645$	13.3209	−	17.0717i	0.524511	−	0.672199i
$646$	10.9183			0.429576
$647$	5.20265	−	9.01126i	0.204537	−	0.354269i	−0.745448	−	0.666564i	$-0.767764\pi$
$647$	5.20265	−	9.01126i	0.204537	−	0.354269i	0.949985	+	0.312295i	$0.101098\pi$
$648$	6.15425	+	6.56698i	0.241762	+	0.257975i
$649$		−	1.15185i		−	0.0452142i
$650$	0.878644	+	7.75288i	0.0344633	+	0.304093i
$651$	−5.55344	+	0.685363i	−0.217656	+	0.0268615i
$652$	−2.54056	+	2.54056i	−0.0994958	+	0.0994958i
$653$		−	27.1775i		−	1.06354i	−0.846890	−	0.531769i	$-0.821528\pi$
$653$		−	27.1775i		−	1.06354i	0.846890	−	0.531769i	$-0.178472\pi$
$654$	27.0244	−	3.33514i	1.05674	−	0.130414i
$655$	−6.75252	−	25.2007i	−0.263843	−	0.984674i
$656$	−0.974309	+	3.63617i	−0.0380404	+	0.141969i
$657$	0.232610	−	14.3429i	0.00907498	−	0.559569i
$658$	0.762750	+	0.762750i	0.0297351	+	0.0297351i
$659$		−	23.3071i		−	0.907914i	−0.891023	−	0.453957i	$-0.850012\pi$
$659$		−	23.3071i		−	0.907914i	0.891023	−	0.453957i	$-0.149988\pi$
$660$	−0.567859	−	4.60131i	−0.0221039	−	0.179106i
$661$	0.359756	+	0.359756i	0.0139929	+	0.0139929i	0.714069	−	0.700076i	$-0.246850\pi$
$661$	0.359756	+	0.359756i	0.0139929	+	0.0139929i	−0.700076	+	0.714069i	$0.746850\pi$
$662$	11.2573	+	19.4982i	0.437526	+	0.757818i
$663$	−8.25804	+	13.4766i	−0.320716	+	0.523386i
$664$	6.14753	−	10.6478i	0.238570	−	0.413216i
$665$	−2.10949	+	0.565235i	−0.0818023	+	0.0219189i
$666$	−5.30839	+	5.13896i	−0.205696	+	0.199131i
$667$	−8.56730	+	4.94634i	−0.331727	+	0.191523i
$668$	8.72138	−	2.33689i	0.337440	−	0.0904169i
$669$	0.633999	−	0.812517i	0.0245118	−	0.0314137i
$670$	−1.58954	+	0.425915i	−0.0614092	+	0.0164545i
$671$	17.2830	+	4.63097i	0.667204	+	0.178777i
$672$	0.415630	−	0.313603i	0.0160333	−	0.0120975i
$673$	−7.28755	+	4.20747i	−0.280914	+	0.162186i	−0.633837	−	0.773466i	$-0.718521\pi$
$673$	−7.28755	+	4.20747i	−0.280914	+	0.162186i	0.352923	+	0.935652i	$0.385188\pi$
$674$	−3.65243	−	13.6310i	−0.140686	−	0.525048i
$675$	−11.1094	−	1.73844i	−0.427602	−	0.0669124i
$676$	−3.81566	+	12.4274i	−0.146756	+	0.477978i
$677$	−17.7008	−	10.2196i	−0.680297	−	0.392770i	0.119670	−	0.992814i	$-0.461816\pi$
$677$	−17.7008	−	10.2196i	−0.680297	−	0.392770i	−0.799967	+	0.600044i	$0.795150\pi$
$678$	6.32979	+	15.6389i	0.243094	+	0.600609i
$679$	−1.87744			−0.0720496
$680$	−2.13106	+	3.69111i	−0.0817225	+	0.141548i
$681$	29.2981	−	11.8583i	1.12270	−	0.454410i
$682$	12.0787	−	12.0787i	0.462518	−	0.462518i
$683$	−16.8568	−	4.51677i	−0.645008	−	0.172829i	−0.0785371	−	0.996911i	$-0.525025\pi$
$683$	−16.8568	−	4.51677i	−0.645008	−	0.172829i	−0.566471	+	0.824082i	$0.691692\pi$
$684$	−0.209864	+	12.9403i	−0.00802435	+	0.494786i
$685$	−18.0112	−	31.1964i	−0.688174	−	1.19195i
$686$	−2.09067	−	3.62115i	−0.0798222	−	0.138256i
$687$	14.0467	+	10.9605i	0.535916	+	0.418170i
$688$	−6.42917	+	3.71188i	−0.245110	+	0.141514i
$689$	−10.2412	−	8.15618i	−0.390158	−	0.310726i
$690$	3.07791	−	2.32236i	0.117174	−	0.0884106i
$691$	−7.22155	−	1.93501i	−0.274721	−	0.0736112i	0.118828	−	0.992915i	$-0.462086\pi$
$691$	−7.22155	−	1.93501i	−0.274721	−	0.0736112i	−0.393549	+	0.919304i	$0.628753\pi$
$692$	13.6243	+	7.86600i	0.517919	+	0.299020i
$693$	0.393399	−	1.37838i	0.0149440	−	0.0523603i
$694$	−17.4040	+	17.4040i	−0.660648	+	0.660648i
$695$	10.9900	+	10.9900i	0.416876	+	0.416876i
$696$	10.2192	+	7.97396i	0.387359	+	0.302252i
$697$	2.46588	−	9.20278i	0.0934018	−	0.348580i
$698$	19.4020	+	11.2017i	0.734376	+	0.423992i
$699$	14.7164	−	34.7295i	0.556627	−	1.31359i
$700$	−0.168368	+	0.628357i	−0.00636370	+	0.0237496i
$701$	31.1840			1.17780			0.588901	−	0.808205i	$-0.299561\pi$
$701$	31.1840			1.17780			0.588901	+	0.808205i	$0.299561\pi$
$702$	−15.8136	−	10.0464i	−0.596846	−	0.379177i
$703$	−10.6245			−0.400711
$704$	−0.411385	+	1.53531i	−0.0155046	+	0.0578641i
$705$	4.08370	−	9.63716i	0.153801	−	0.362956i
$706$	−15.3913	−	8.88616i	−0.579259	−	0.334435i
$707$	0.668529	−	2.49499i	0.0251426	−	0.0938336i
$708$	−0.989573	−	0.772154i	−0.0371904	−	0.0290193i
$709$	5.89289	+	5.89289i	0.221312	+	0.221312i	0.809051	−	0.587739i	$-0.199982\pi$
$709$	5.89289	+	5.89289i	0.221312	+	0.221312i	−0.587739	+	0.809051i	$0.699982\pi$
$710$	−8.47140	+	8.47140i	−0.317926	+	0.317926i
$711$	21.5065	−	5.39045i	0.806559	−	0.202158i
$712$	−1.71358	−	0.989338i	−0.0642192	−	0.0370770i
$713$	13.7223	+	3.67687i	0.513903	+	0.137700i
$714$	−1.05192	+	0.793697i	−0.0393670	+	0.0297034i
$715$	3.53177	+	8.98162i	0.132081	+	0.335894i
$716$	5.70819	−	3.29562i	0.213325	−	0.123163i
$717$	25.5791	+	19.9592i	0.955271	+	0.745388i
$718$	−6.36802	−	11.0297i	−0.237652	−	0.411626i
$719$	5.63051	+	9.75233i	0.209983	+	0.363701i	0.951709	−	0.307002i	$-0.0993259\pi$
$719$	5.63051	+	9.75233i	0.209983	+	0.363701i	−0.741726	+	0.670703i	$0.765993\pi$
$720$	−4.33371	−	2.59667i	−0.161508	−	0.0967721i
$721$	0.0764807	+	0.0204930i	0.00284829	+	0.000763197i
$722$	0.275259	−	0.275259i	0.0102441	−	0.0102441i
$723$	−7.10676	+	2.87643i	−0.264303	+	0.106976i
$724$	−5.63749	+	9.76442i	−0.209516	+	0.362892i
$725$	−16.1949			−0.601463
$726$	−5.50640	−	13.6046i	−0.204362	−	0.504913i
$727$	−5.52426	−	3.18943i	−0.204883	−	0.118290i	0.394048	−	0.919090i	$-0.371074\pi$
$727$	−5.52426	−	3.18943i	−0.204883	−	0.118290i	−0.598931	+	0.800800i	$0.704408\pi$
$728$	−0.675222	+	0.847832i	−0.0250254	+	0.0314227i
$729$	19.9977	−	18.1409i	0.740657	−	0.671884i
$730$	2.08410	+	7.77798i	0.0771362	+	0.287876i
$731$	16.2716	−	9.39441i	0.601826	−	0.347465i
$732$	15.5643	−	11.7437i	0.575275	−	0.434059i
$733$	−24.1919	−	6.48221i	−0.893550	−	0.239426i	−0.217306	−	0.976104i	$-0.569727\pi$
$733$	−24.1919	−	6.48221i	−0.893550	−	0.239426i	−0.676244	+	0.736678i	$0.736394\pi$
$734$	−34.5037	+	9.24525i	−1.27356	+	0.341248i
$735$	−12.3984	+	15.8894i	−0.457321	+	0.586091i
$736$	−1.27686	+	0.342133i	−0.0470655	+	0.0126112i
$737$	1.34511	−	0.776601i	0.0495478	−	0.0286065i
$738$	10.8597	+	3.09943i	0.399750	+	0.114092i
$739$	42.5336	−	11.3968i	1.56462	−	0.419240i	0.630500	−	0.776189i	$-0.282850\pi$
$739$	42.5336	−	11.3968i	1.56462	−	0.419240i	0.934124	+	0.356950i	$0.116183\pi$
$740$	2.07371	−	3.59177i	0.0762311	−	0.132036i
$741$	−6.28983	−	26.1965i	−0.231063	−	0.962352i
$742$	−0.545771	−	0.945302i	−0.0200359	−	0.0347031i
$743$	3.78081	+	3.78081i	0.138704	+	0.138704i	0.773050	−	0.634345i	$-0.218730\pi$
$743$	3.78081	+	3.78081i	0.138704	+	0.138704i	−0.634345	+	0.773050i	$0.718730\pi$
$744$	−2.27993	−	18.4740i	−0.0835861	−	0.677291i
$745$			37.4051i			1.37042i
$746$	7.67860	+	7.67860i	0.281134	+	0.281134i
$747$	−31.6402	−	18.9581i	−1.15766	−	0.693642i
$748$	1.04117	−	3.88571i	0.0380691	−	0.142076i
$749$	1.02815	+	3.83709i	0.0375676	+	0.140204i
$750$	20.7389	−	2.55944i	0.757279	−	0.0934576i
$751$		−	18.9941i		−	0.693104i	−0.938031	−	0.346552i	$-0.887352\pi$
$751$		−	18.9941i		−	0.693104i	0.938031	−	0.346552i	$-0.112648\pi$
$752$	−2.53736	+	2.53736i	−0.0925281	+	0.0925281i
$753$	−50.9151	+	6.28355i	−1.85545	+	0.228985i
$754$	−24.7384	−	10.7741i	−0.900920	−	0.392371i
$755$			29.0562i			1.05746i
$756$	−0.920465	−	1.26198i	−0.0334770	−	0.0458978i
$757$	16.5655	−	28.6922i	0.602082	−	1.04284i	−0.390423	−	0.920636i	$-0.627671\pi$
$757$	16.5655	−	28.6922i	0.602082	−	1.04284i	0.992505	−	0.122202i	$-0.0389954\pi$
$758$	−13.1911			−0.479123
$759$	−2.23877	+	2.86915i	−0.0812621	+	0.104143i
$760$	−1.88031	−	7.01741i	−0.0682059	−	0.254548i
$761$	−11.6052	−	43.3112i	−0.420688	−	1.57003i	−0.773163	−	0.634207i	$-0.781327\pi$
$761$	−11.6052	−	43.3112i	−0.420688	−	1.57003i	0.352475	−	0.935821i	$-0.385340\pi$
$762$	11.3804	+	28.1174i	0.412269	+	1.01859i
$763$	−4.72582			−0.171086
$764$	−5.48262	+	9.49618i	−0.198354	+	0.343560i
$765$	10.9682	+	6.57191i	0.396556	+	0.237608i
$766$			13.7780i			0.497820i
$767$	2.39553	+	1.04331i	0.0864977	+	0.0376716i
$768$	1.04323	+	1.38263i	0.0376443	+	0.0498914i
$769$	5.46734	−

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)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(0.675780 - 1.59478i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.435860 - 1.62665i) q^{5} +(1.36553 + 1.06551i) q^{6} +(-0.212562 - 0.212562i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.08664 - 2.15544i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(0.675780 - 1.59478i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.435860 - 1.62665i) q^{5} +(1.36553 + 1.06551i) q^{6} +(-0.212562 - 0.212562i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.08664 - 2.15544i) q^{9} +(1.45842 + 0.842018i) q^{10} +(-1.53531 - 0.411385i) q^{11} +(-1.38263 + 1.04323i) q^{12} +(2.24619 - 2.82039i) q^{13} +(0.260334 - 0.150304i) q^{14} +(-2.29961 - 1.79436i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.26545 - 2.19182i) q^{17} +(2.62206 - 1.45767i) q^{18} +(4.16702 + 1.11655i) q^{19} +(-1.19079 + 1.19079i) q^{20} +(-0.482634 + 0.195344i) q^{21} +(0.794734 - 1.37652i) q^{22} +1.32190 q^{23} +(-0.649831 - 1.60553i) q^{24} +(1.87410 + 1.08201i) q^{25} +(2.14293 + 2.89963i) q^{26} +(-4.84756 + 1.87113i) q^{27} +(0.0778030 + 0.290365i) q^{28} +(-6.48106 + 3.74184i) q^{29} +(2.32840 - 1.75684i) q^{30} +(10.3807 + 2.78151i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-1.69360 + 2.17047i) q^{33} +(2.44466 - 0.655045i) q^{34} +(-0.438411 + 0.253117i) q^{35} +(0.729366 + 2.90999i) q^{36} +(-2.37887 + 0.637416i) q^{37} +(-2.15701 + 3.73605i) q^{38} +(-2.97998 - 5.48815i) q^{39} +(-0.842018 - 1.45842i) q^{40} +(2.66186 + 2.66186i) q^{41} +(-0.0637730 - 0.516747i) q^{42} +7.42377i q^{43} +(1.12392 + 1.12392i) q^{44} +(-4.41564 + 2.45477i) q^{45} +(-0.342133 + 1.27686i) q^{46} +(0.928739 + 3.46610i) q^{47} +(1.71901 - 0.212147i) q^{48} -6.90964i q^{49} +(-1.53020 + 1.53020i) q^{50} +(-4.35064 + 0.536923i) q^{51} +(-3.35546 + 1.31944i) q^{52} -3.63112i q^{53} +(-0.552733 - 5.16667i) q^{54} +(-1.33836 + 2.31811i) q^{55} -0.300608 q^{56} +(4.59664 - 5.89093i) q^{57} +(-1.93692 - 7.22868i) q^{58} +(0.187561 + 0.699986i) q^{59} +(1.09434 + 2.70377i) q^{60} -11.2570 q^{61} +(-5.37346 + 9.30710i) q^{62} +(-0.0146237 + 0.901704i) q^{63} -1.00000i q^{64} +(-3.60878 - 4.88307i) q^{65} +(-1.65818 - 2.19765i) q^{66} +(-0.690972 + 0.690972i) q^{67} +2.53090i q^{68} +(0.893313 - 2.10814i) q^{69} +(-0.131023 - 0.488984i) q^{70} +(-1.84126 + 6.87167i) q^{71} +(-2.99961 - 0.0486470i) q^{72} +(3.38109 + 3.38109i) q^{73} -2.46279i q^{74} +(2.99205 - 2.25758i) q^{75} +(-3.05047 - 3.05047i) q^{76} +(0.238903 + 0.413792i) q^{77} +(6.07242 - 1.45800i) q^{78} +(-3.69530 + 6.40045i) q^{79} +(1.62665 - 0.435860i) q^{80} +(-0.291844 + 8.99527i) q^{81} +(-3.26010 + 1.88222i) q^{82} +(11.8761 - 3.18219i) q^{83} +(0.515645 + 0.0721440i) q^{84} +(-4.11690 + 1.10312i) q^{85} +(-7.17081 - 1.92141i) q^{86} +(1.58764 + 12.8645i) q^{87} +(-1.37652 + 0.794734i) q^{88} +(-0.512119 - 1.91125i) q^{89} +(-1.22828 - 4.90052i) q^{90} +(-1.07696 + 0.122054i) q^{91} +(-1.14480 - 0.660949i) q^{92} +(11.4510 - 14.6753i) q^{93} -3.58837 q^{94} +(3.63248 - 6.29163i) q^{95} +(-0.239994 + 1.71534i) q^{96} +(4.41623 - 4.41623i) q^{97} +(6.67419 + 1.78835i) q^{98} +(2.31693 + 4.16768i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more