LMFDB - Embedded newform 234.2.z.a.227.8

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			227.8
Character	$\chi$	$=$	234.227
Dual form			234.2.z.a.167.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(-1.53353 + 0.805162i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.0908752 - 0.339151i) q^{5} +(0.380820 + 1.68967i) q^{6} +(-2.17921 - 2.17921i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.70343 - 2.46948i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(-1.53353 + 0.805162i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.0908752 - 0.339151i) q^{5} +(0.380820 + 1.68967i) q^{6} +(-2.17921 - 2.17921i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.70343 - 2.46948i) q^{9} +(-0.304074 - 0.175557i) q^{10} +(-3.21508 - 0.861478i) q^{11} +(1.73066 + 0.0694742i) q^{12} +(-3.46037 + 1.01285i) q^{13} +(-2.66897 + 1.54093i) q^{14} +(0.133712 + 0.593267i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-3.87756 - 6.71613i) q^{17} +(-1.94445 - 2.28453i) q^{18} +(3.67410 + 0.984473i) q^{19} +(-0.248276 + 0.248276i) q^{20} +(5.09649 + 1.58726i) q^{21} +(-1.66425 + 2.88256i) q^{22} -6.68501 q^{23} +(0.515034 - 1.65370i) q^{24} +(4.22336 + 2.43836i) q^{25} +(0.0827293 + 3.60460i) q^{26} +(-0.623927 + 5.15856i) q^{27} +(0.797644 + 2.97685i) q^{28} +(4.92745 - 2.84486i) q^{29} +(0.607659 + 0.0243934i) q^{30} +(-1.09596 - 0.293661i) q^{31} +(0.965926 - 0.258819i) q^{32} +(5.62405 - 1.26756i) q^{33} +(-7.49087 + 2.00717i) q^{34} +(-0.937115 + 0.541044i) q^{35} +(-2.70995 + 1.28692i) q^{36} +(8.90068 - 2.38493i) q^{37} +(1.90186 - 3.29411i) q^{38} +(4.49107 - 4.33939i) q^{39} +(0.175557 + 0.304074i) q^{40} +(1.85391 + 1.85391i) q^{41} +(2.85225 - 4.51202i) q^{42} +4.25976i q^{43} +(2.35360 + 2.35360i) q^{44} +(-0.682727 - 0.802134i) q^{45} +(-1.73021 + 6.45722i) q^{46} +(-1.11876 - 4.17527i) q^{47} +(-1.46406 - 0.925495i) q^{48} +2.49787i q^{49} +(3.44836 - 3.44836i) q^{50} +(11.3539 + 7.17732i) q^{51} +(3.50319 + 0.853029i) q^{52} +5.65439i q^{53} +(4.82130 + 1.93780i) q^{54} +(-0.584342 + 1.01211i) q^{55} +3.08186 q^{56} +(-6.42701 + 1.44853i) q^{57} +(-1.47261 - 5.49586i) q^{58} +(-2.84022 - 10.5998i) q^{59} +(0.180836 - 0.580640i) q^{60} -10.0348 q^{61} +(-0.567309 + 0.982608i) q^{62} +(-9.09362 + 1.66938i) q^{63} -1.00000i q^{64} +(0.0290475 + 1.26563i) q^{65} +(0.231245 - 5.76048i) q^{66} +(9.74949 - 9.74949i) q^{67} +7.75512i q^{68} +(10.2517 - 5.38251i) q^{69} +(0.280065 + 1.04522i) q^{70} +(0.343507 - 1.28199i) q^{71} +(0.541680 + 2.95069i) q^{72} +(-2.19140 - 2.19140i) q^{73} -9.21466i q^{74} +(-8.43993 - 0.338806i) q^{75} +(-2.68963 - 2.68963i) q^{76} +(5.12898 + 8.88365i) q^{77} +(-3.02916 - 5.46115i) q^{78} +(-6.22990 + 10.7905i) q^{79} +(0.339151 - 0.0908752i) q^{80} +(-3.19666 - 8.41316i) q^{81} +(2.27056 - 1.31091i) q^{82} +(-3.92483 + 1.05166i) q^{83} +(-3.62006 - 3.92286i) q^{84} +(-2.63016 + 0.704748i) q^{85} +(4.11462 + 1.10251i) q^{86} +(-5.26582 + 8.33008i) q^{87} +(2.88256 - 1.66425i) q^{88} +(-1.43929 - 5.37149i) q^{89} +(-0.951504 + 0.451856i) q^{90} +(9.74806 + 5.33364i) q^{91} +(5.78938 + 3.34250i) q^{92} +(1.91713 - 0.432085i) q^{93} -4.32256 q^{94} +(0.667770 - 1.15661i) q^{95} +(-1.27288 + 1.17463i) q^{96} +(-0.597770 + 0.597770i) q^{97} +(2.41276 + 0.646496i) q^{98} +(-7.60406 + 6.47211i) 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
$3$	−1.53353	+	0.805162i	−0.885384	+	0.464860i
$3$	−1.53353	+	0.805162i	−0.885384	+	0.464860i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	0.0908752	−	0.339151i	0.0406406	−	0.151673i	−0.942624	−	0.333857i	$-0.891650\pi$
$5$	0.0908752	−	0.339151i	0.0406406	−	0.151673i	0.983265	+	0.182184i	$0.0583165\pi$
$6$	0.380820	+	1.68967i	0.155469	+	0.689804i
$7$	−2.17921	−	2.17921i	−0.823662	−	0.823662i	0.162969	−	0.986631i	$-0.447893\pi$
$7$	−2.17921	−	2.17921i	−0.823662	−	0.823662i	−0.986631	+	0.162969i	$0.947893\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	1.70343	−	2.46948i	0.567809	−	0.823160i
$10$	−0.304074	−	0.175557i	−0.0961568	−	0.0555161i
$11$	−3.21508	−	0.861478i	−0.969383	−	0.259745i	−0.260816	−	0.965389i	$-0.583991\pi$
$11$	−3.21508	−	0.861478i	−0.969383	−	0.259745i	−0.708567	+	0.705643i	$0.750658\pi$
$12$	1.73066	+	0.0694742i	0.499598	+	0.0200555i
$13$	−3.46037	+	1.01285i	−0.959733	+	0.280914i
$13$	−3.46037	+	1.01285i	−0.959733	+	0.280914i
$14$	−2.66897	+	1.54093i	−0.713312	+	0.411831i
$15$	0.133712	+	0.593267i	0.0345242	+	0.153181i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−3.87756	−	6.71613i	−0.940446	−	1.62890i	−0.764622	−	0.644479i	$-0.777074\pi$
$17$	−3.87756	−	6.71613i	−0.940446	−	1.62890i	−0.175824	−	0.984422i	$-0.556259\pi$
$18$	−1.94445	−	2.28453i	−0.458312	−	0.538470i
$19$	3.67410	+	0.984473i	0.842897	+	0.225854i	0.654332	−	0.756207i	$-0.272950\pi$
$19$	3.67410	+	0.984473i	0.842897	+	0.225854i	0.188565	+	0.982061i	$0.439616\pi$
$20$	−0.248276	+	0.248276i	−0.0555161	+	0.0555161i
$21$	5.09649	+	1.58726i	1.11215	+	0.346369i
$22$	−1.66425	+	2.88256i	−0.354819	+	0.614564i
$23$	−6.68501			−1.39392			−0.696960	−	0.717110i	$-0.745464\pi$
$23$	−6.68501			−1.39392			−0.696960	+	0.717110i	$0.745464\pi$
$24$	0.515034	−	1.65370i	0.105131	−	0.337561i
$25$	4.22336	+	2.43836i	0.844672	+	0.487672i
$26$	0.0827293	+	3.60460i	0.0162246	+	0.706921i
$27$	−0.623927	+	5.15856i	−0.120075	+	0.992765i
$28$	0.797644	+	2.97685i	0.150741	+	0.562572i
$29$	4.92745	−	2.84486i	0.915005	−	0.528278i	0.0329666	−	0.999456i	$-0.489505\pi$
$29$	4.92745	−	2.84486i	0.915005	−	0.528278i	0.882038	+	0.471178i	$0.156171\pi$
$30$	0.607659	+	0.0243934i	0.110943	+	0.00445361i
$31$	−1.09596	−	0.293661i	−0.196840	−	0.0527430i	0.159052	−	0.987270i	$-0.449156\pi$
$31$	−1.09596	−	0.293661i	−0.196840	−	0.0527430i	−0.355892	+	0.934527i	$0.615823\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	5.62405	−	1.26756i	0.979021	−	0.220653i
$34$	−7.49087	+	2.00717i	−1.28467	+	0.344227i
$35$	−0.937115	+	0.541044i	−0.158401	+	0.0914531i
$36$	−2.70995	+	1.28692i	−0.451659	+	0.214486i
$37$	8.90068	−	2.38493i	1.46326	−	0.392080i	0.562647	−	0.826697i	$-0.309783\pi$
$37$	8.90068	−	2.38493i	1.46326	−	0.392080i	0.900615	+	0.434617i	$0.143116\pi$
$38$	1.90186	−	3.29411i	0.308522	−	0.534375i
$39$	4.49107	−	4.33939i	0.719146	−	0.694859i
$40$	0.175557	+	0.304074i	0.0277581	+	0.0480784i
$41$	1.85391	+	1.85391i	0.289532	+	0.289532i	0.836895	−	0.547363i	$-0.184368\pi$
$41$	1.85391	+	1.85391i	0.289532	+	0.289532i	−0.547363	+	0.836895i	$0.684368\pi$
$42$	2.85225	−	4.51202i	0.440111	−	0.696219i
$43$			4.25976i			0.649608i	0.945781	+	0.324804i	$0.105298\pi$
$43$			4.25976i			0.649608i	−0.945781	+	0.324804i	$0.894702\pi$
$44$	2.35360	+	2.35360i	0.354819	+	0.354819i
$45$	−0.682727	−	0.802134i	−0.101775	−	0.119575i
$46$	−1.73021	+	6.45722i	−0.255105	+	0.952065i
$47$	−1.11876	−	4.17527i	−0.163188	−	0.609026i	−0.998264	−	0.0588917i	$-0.981243\pi$
$47$	−1.11876	−	4.17527i	−0.163188	−	0.609026i	0.835076	−	0.550134i	$-0.185423\pi$
$48$	−1.46406	−	0.925495i	−0.211318	−	0.133584i
$49$			2.49787i			0.356839i
$50$	3.44836	−	3.44836i	0.487672	−	0.487672i
$51$	11.3539	+	7.17732i	1.58987	+	1.00503i
$52$	3.50319	+	0.853029i	0.485805	+	0.118294i
$53$			5.65439i			0.776690i	0.921514	+	0.388345i	$0.126953\pi$
$53$			5.65439i			0.776690i	−0.921514	+	0.388345i	$0.873047\pi$
$54$	4.82130	+	1.93780i	0.656096	+	0.263701i
$55$	−0.584342	+	1.01211i	−0.0787927	+	0.136473i
$56$	3.08186			0.411831
$57$	−6.42701	+	1.44853i	−0.851278	+	0.191862i
$58$	−1.47261	−	5.49586i	−0.193363	−	0.721641i
$59$	−2.84022	−	10.5998i	−0.369765	−	1.37998i	−0.860845	−	0.508867i	$-0.830065\pi$
$59$	−2.84022	−	10.5998i	−0.369765	−	1.37998i	0.491080	−	0.871114i	$-0.336602\pi$
$60$	0.180836	−	0.580640i	0.0233458	−	0.0749603i
$61$	−10.0348			−1.28483			−0.642415	−	0.766357i	$-0.722067\pi$
$61$	−10.0348			−1.28483			−0.642415	+	0.766357i	$0.722067\pi$
$62$	−0.567309	+	0.982608i	−0.0720483	+	0.124791i
$63$	−9.09362	+	1.66938i	−1.14569	+	0.210323i
$64$		−	1.00000i		−	0.125000i
$65$	0.0290475	+	1.26563i	0.00360290	+	0.156982i
$66$	0.231245	−	5.76048i	0.0284642	−	0.709066i
$67$	9.74949	−	9.74949i	1.19109	−	1.19109i	0.214328	−	0.976762i	$-0.431244\pi$
$67$	9.74949	−	9.74949i	1.19109	−	1.19109i	0.976762	−	0.214328i	$-0.0687561\pi$
$68$			7.75512i			0.940446i
$69$	10.2517	−	5.38251i	1.23415	−	0.647978i
$70$	0.280065	+	1.04522i	0.0334741	+	0.124927i
$71$	0.343507	−	1.28199i	0.0407668	−	0.152144i	−0.942542	−	0.334087i	$-0.891572\pi$
$71$	0.343507	−	1.28199i	0.0407668	−	0.152144i	0.983309	+	0.181943i	$0.0582387\pi$
$72$	0.541680	+	2.95069i	0.0638376	+	0.347742i
$73$	−2.19140	−	2.19140i	−0.256484	−	0.256484i	0.567138	−	0.823622i	$-0.308050\pi$
$73$	−2.19140	−	2.19140i	−0.256484	−	0.256484i	−0.823622	+	0.567138i	$0.808050\pi$
$74$		−	9.21466i		−	1.07118i
$75$	−8.43993	−	0.338806i	−0.974559	−	0.0391220i
$76$	−2.68963	−	2.68963i	−0.308522	−	0.308522i
$77$	5.12898	+	8.88365i	0.584502	+	1.01239i
$78$	−3.02916	−	5.46115i	−0.342984	−	0.618354i
$79$	−6.22990	+	10.7905i	−0.700919	+	1.21403i	0.267225	+	0.963634i	$0.413893\pi$
$79$	−6.22990	+	10.7905i	−0.700919	+	1.21403i	−0.968144	+	0.250393i	$0.919440\pi$
$80$	0.339151	−	0.0908752i	0.0379182	−	0.0101602i
$81$	−3.19666	−	8.41316i	−0.355185	−	0.934796i
$82$	2.27056	−	1.31091i	0.250742	−	0.144766i
$83$	−3.92483	+	1.05166i	−0.430806	+	0.115434i	−0.467705	−	0.883885i	$-0.654919\pi$
$83$	−3.92483	+	1.05166i	−0.430806	+	0.115434i	0.0368984	+	0.999319i	$0.488252\pi$
$84$	−3.62006	−	3.92286i	−0.394981	−	0.428019i
$85$	−2.63016	+	0.704748i	−0.285280	+	0.0764406i
$86$	4.11462	+	1.10251i	0.443691	+	0.118887i
$87$	−5.26582	+	8.33008i	−0.564555	+	0.893078i
$88$	2.88256	−	1.66425i	0.307282	−	0.177409i
$89$	−1.43929	−	5.37149i	−0.152564	−	0.569377i	−0.999302	−	0.0373662i	$-0.988103\pi$
$89$	−1.43929	−	5.37149i	−0.152564	−	0.569377i	0.846737	−	0.532011i	$-0.178563\pi$
$90$	−0.951504	+	0.451856i	−0.100297	+	0.0476298i
$91$	9.74806	+	5.33364i	1.02187	+	0.559117i
$92$	5.78938	+	3.34250i	0.603585	+	0.348480i
$93$	1.91713	−	0.432085i	0.198797	−	0.0448052i
$94$	−4.32256			−0.445838
$95$	0.667770	−	1.15661i	0.0685117	−	0.118666i
$96$	−1.27288	+	1.17463i	−0.129913	+	0.119886i
$97$	−0.597770	+	0.597770i	−0.0606944	+	0.0606944i	−0.736802	−	0.676108i	$-0.763665\pi$
$97$	−0.597770	+	0.597770i	−0.0606944	+	0.0606944i	0.676108	+	0.736802i	$0.263665\pi$
$98$	2.41276	+	0.646496i	0.243725	+	0.0653060i
$99$	−7.60406	+	6.47211i	−0.764237	+	0.650471i
$100$	−2.43836	−	4.22336i	−0.243836	−	0.422336i
$101$	5.25696	+	9.10532i	0.523087	+	0.906013i	0.999639	+	0.0268670i	$0.00855306\pi$
$101$	5.25696	+	9.10532i	0.523087	+	0.906013i	−0.476552	+	0.879146i	$0.658114\pi$
$102$	9.87137	−	9.10942i	0.977412	−	0.901967i
$103$	1.30284	−	0.752193i	0.128372	−	0.0741158i	−0.434439	−	0.900701i	$-0.643053\pi$
$103$	1.30284	−	0.752193i	0.128372	−	0.0741158i	0.562811	+	0.826586i	$0.309720\pi$
$104$	1.73066	−	3.16304i	0.169705	−	0.310162i
$105$	1.00147	−	1.58424i	0.0977331	−	0.154606i
$106$	5.46172	+	1.46346i	0.530489	+	0.142144i
$107$	−4.75429	−	2.74489i	−0.459615	−	0.265359i	0.252267	−	0.967658i	$-0.418824\pi$
$107$	−4.75429	−	2.74489i	−0.459615	−	0.265359i	−0.711882	+	0.702299i	$0.752157\pi$
$108$	3.11962	−	4.15548i	0.300185	−	0.399861i
$109$	2.22967	−	2.22967i	0.213564	−	0.213564i	−0.592216	−	0.805780i	$-0.701747\pi$
$109$	2.22967	−	2.22967i	0.213564	−	0.213564i	0.805780	+	0.592216i	$0.201747\pi$
$110$	0.826384	+	0.826384i	0.0787927	+	0.0787927i
$111$	−11.7292	+	10.8238i	−1.11329	+	1.02735i
$112$	0.797644	−	2.97685i	0.0753703	−	0.281286i
$113$	−5.79150	−	3.34372i	−0.544818	−	0.314551i	0.202211	−	0.979342i	$-0.435187\pi$
$113$	−5.79150	−	3.34372i	−0.544818	−	0.314551i	−0.747029	+	0.664791i	$0.768521\pi$
$114$	−0.264260	+	6.58292i	−0.0247502	+	0.616547i
$115$	−0.607501	+	2.26723i	−0.0566498	+	0.211420i
$116$	−5.68973			−0.528278
$117$	−3.39327	+	10.2706i	−0.313708	+	0.949519i
$118$	−10.9738			−1.01022
$119$	−6.18583	+	23.0858i	−0.567054	+	2.11627i
$120$	−0.514052	−	0.324955i	−0.0469263	−	0.0296642i
$121$	0.0683098	+	0.0394387i	0.00620998	+	0.00358534i
$122$	−2.59721	+	9.69291i	−0.235140	+	0.877555i
$123$	−4.33572	−	1.35033i	−0.390939	−	0.121755i
$124$	0.802296	+	0.802296i	0.0720483	+	0.0720483i
$125$	2.45215	−	2.45215i	0.219327	−	0.219327i
$126$	−0.741102	+	9.21583i	−0.0660226	+	0.821012i
$127$	−10.6922	−	6.17316i	−0.948782	−	0.547780i	−0.0560797	−	0.998426i	$-0.517860\pi$
$127$	−10.6922	−	6.17316i	−0.948782	−	0.547780i	−0.892702	+	0.450647i	$0.851193\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$	−3.42980	−	6.53248i	−0.301977	−	0.575153i
$130$	1.23002	+	0.299511i	0.107880	+	0.0262689i
$131$	4.12094	−	2.37922i	0.360048	−	0.207874i	−0.309054	−	0.951045i	$-0.600012\pi$
$131$	4.12094	−	2.37922i	0.360048	−	0.207874i	0.669102	+	0.743171i	$0.266679\pi$
$132$	−5.50435	−	1.71429i	−0.479092	−	0.149210i
$133$	−5.86126	−	10.1520i	−0.508235	−	0.880289i
$134$	−6.89393	−	11.9406i	−0.595545	−	1.03151i
$135$	1.69283	+	0.680390i	0.145696	+	0.0585587i
$136$	7.49087	+	2.00717i	0.642337	+	0.172114i
$137$	3.48302	−	3.48302i	0.297575	−	0.297575i	−0.542489	−	0.840063i	$-0.682518\pi$
$137$	3.48302	−	3.48302i	0.297575	−	0.297575i	0.840063	+	0.542489i	$0.182518\pi$
$138$	−2.54578	−	11.2954i	−0.216711	−	0.961531i
$139$	−2.05018	+	3.55102i	−0.173894	+	0.301194i	−0.939778	−	0.341785i	$-0.888968\pi$
$139$	−2.05018	+	3.55102i	−0.173894	+	0.301194i	0.765884	+	0.642979i	$0.222302\pi$
$140$	1.08209			0.0914531
$141$	5.07742	+	5.50212i	0.427596	+	0.463362i
$142$	−1.14940	−	0.663605i	−0.0964553	−	0.0556885i
$143$	11.9979	−	0.275364i	1.00331	−	0.0230271i
$144$	2.99035	+	0.240472i	0.249196	+	0.0200393i
$145$	−0.517055	−	1.92968i	−0.0429391	−	0.160251i
$146$	−2.68391	+	1.54955i	−0.222122	+	0.128242i
$147$	−2.01119	−	3.83056i	−0.165880	−	0.315939i
$148$	−8.90068	−	2.38493i	−0.731631	−	0.196040i
$149$	7.33212	−	1.96463i	0.600670	−	0.160949i	0.0543451	−	0.998522i	$-0.482693\pi$
$149$	7.33212	−	1.96463i	0.600670	−	0.160949i	0.546325	+	0.837573i	$0.316026\pi$
$150$	−2.51168	+	8.06465i	−0.205077	+	0.658476i
$151$	14.0837	−	3.77372i	1.14612	−	0.307101i	0.364709	−	0.931122i	$-0.381169\pi$
$151$	14.0837	−	3.77372i	1.14612	−	0.307101i	0.781408	+	0.624021i	$0.214502\pi$
$152$	−3.29411	+	1.90186i	−0.267188	+	0.154261i
$153$	−23.1905	−	1.86489i	−1.87484	−	0.150767i
$154$	9.90843	−	2.65496i	0.798444	−	0.213942i
$155$	−0.199191	+	0.345008i	−0.0159994	+	0.0277117i
$156$	−6.05907	+	1.51249i	−0.485114	+	0.121096i
$157$	−8.20325	−	14.2085i	−0.654691	−	1.13396i	−0.981971	−	0.189031i	$-0.939465\pi$
$157$	−8.20325	−	14.2085i	−0.654691	−	1.13396i	0.327280	−	0.944927i	$-0.393868\pi$
$158$	8.81041	+	8.81041i	0.700919	+	0.700919i
$159$	−4.55270	−	8.67117i	−0.361052	−	0.687669i
$160$		−	0.351115i		−	0.0277581i
$161$	14.5680	+	14.5680i	1.14812	+	1.14812i
$162$	−8.95385	+	0.910253i	−0.703481	+	0.0715162i
$163$	4.81720	−	17.9780i	0.377312	−	1.40815i	−0.472625	−	0.881263i	$-0.656694\pi$
$163$	4.81720	−	17.9780i	0.377312	−	1.40815i	0.849937	−	0.526884i	$-0.176640\pi$
$164$	−0.678577	−	2.53248i	−0.0529880	−	0.197754i
$165$	0.0811934	−	2.02259i	0.00632090	−	0.157458i
$166$			4.06328i			0.315372i
$167$	−0.609298	+	0.609298i	−0.0471489	+	0.0471489i	−0.730288	−	0.683139i	$-0.760614\pi$
$167$	−0.609298	+	0.609298i	−0.0471489	+	0.0471489i	0.683139	+	0.730288i	$0.260614\pi$
$168$	−4.72613	+	2.48140i	−0.364629	+	0.191444i
$169$	10.9483	−	7.00966i	0.842175	−	0.539205i
$170$			2.72294i			0.208840i
$171$	8.68971	−	7.39614i	0.664518	−	0.565597i
$172$	2.12988	−	3.68906i	0.162402	−	0.281289i
$173$	−23.8779			−1.81540			−0.907702	−	0.419615i	$-0.862165\pi$
$173$	−23.8779			−1.81540			−0.907702	+	0.419615i	$0.862165\pi$
$174$	6.68335	+	7.24237i	0.506663	+	0.549043i
$175$	−3.88989	−	14.5173i	−0.294048	−	1.09740i
$176$	−0.861478	−	3.21508i	−0.0649363	−	0.242346i
$177$	12.8901	+	13.9683i	0.968882	+	1.04992i
$178$	−5.56098			−0.416813
$179$	5.19785	−	9.00294i	0.388506	−	0.672912i	−0.603743	−	0.797179i	$-0.706325\pi$
$179$	5.19785	−	9.00294i	0.388506	−	0.672912i	0.992249	+	0.124267i	$0.0396581\pi$
$180$	0.190192	+	1.03603i	0.0141761	+	0.0772212i
$181$			0.635701i			0.0472513i	0.999721	+	0.0236256i	$0.00752097\pi$
$181$			0.635701i			0.0472513i	−0.999721	+	0.0236256i	$0.992479\pi$
$182$	7.67488	−	8.03545i	0.568900	−	0.595627i
$183$	15.3887	−	8.07967i	1.13757	−	0.597266i
$184$	4.72701	−	4.72701i	0.348480	−	0.348480i
$185$		−	3.23540i		−	0.237872i
$186$	0.0788267	−	1.96363i	0.00577986	−	0.143981i
$187$	6.68086	+	24.9333i	0.488553	+	1.82330i
$188$	−1.11876	+	4.17527i	−0.0815940	+	0.304513i
$189$	12.6012	−	9.88189i	0.916604	−	0.718802i
$190$	−0.944369	−	0.944369i	−0.0685117	−	0.0685117i
$191$			0.149085i			0.0107874i	0.999985	+	0.00539372i	$0.00171688\pi$
$191$			0.149085i			0.0107874i	−0.999985	+	0.00539372i	$0.998283\pi$
$192$	0.805162	+	1.53353i	0.0581076	+	0.110673i
$193$	−3.01679	−	3.01679i	−0.217153	−	0.217153i	0.590144	−	0.807298i	$-0.299071\pi$
$193$	−3.01679	−	3.01679i	−0.217153	−	0.217153i	−0.807298	+	0.590144i	$0.799071\pi$
$194$	0.422687	+	0.732116i	0.0303472	+	0.0525629i
$195$	−1.06358	−	1.91749i	−0.0761647	−	0.137314i
$196$	1.24894	−	2.16322i	0.0892097	−	0.154516i
$197$	−18.4733	+	4.94991i	−1.31617	+	0.352667i	−0.847542	−	0.530729i	$-0.821918\pi$
$197$	−18.4733	+	4.94991i	−1.31617	+	0.352667i	−0.468629	+	0.883395i	$0.655252\pi$
$198$	4.28350	+	9.02006i	0.304415	+	0.641028i
$199$	−4.55185	+	2.62801i	−0.322672	+	0.186295i	−0.652583	−	0.757717i	$-0.726315\pi$
$199$	−4.55185	+	2.62801i	−0.322672	+	0.186295i	0.329911	+	0.944012i	$0.392981\pi$
$200$	−4.71055	+	1.26219i	−0.333086	+	0.0892501i
$201$	−7.10121	+	22.8010i	−0.500881	+	1.60826i
$202$	10.1557	−	2.72120i	0.714550	−	0.191463i
$203$	−16.9375	−	4.53838i	−1.18878	−	0.318532i
$204$	−6.24413	−	11.8927i	−0.437176	−	0.832656i
$205$	0.797228	−	0.460280i	0.0556809	−	0.0321474i
$206$	−0.389364	−	1.45313i	−0.0271283	−	0.101244i
$207$	−11.3874	+	16.5085i	−0.791481	+	1.14742i
$208$	−2.60734	−	2.49034i	−0.180786	−	0.172674i
$209$	−10.9644	−	6.33032i	−0.758425	−	0.437877i
$210$	−1.27106	−	1.37737i	−0.0877112	−	0.0950477i
$211$	23.8676			1.64311			0.821556	−	0.570128i	$-0.193107\pi$
$211$	23.8676			1.64311			0.821556	+	0.570128i	$0.193107\pi$
$212$	2.82719	−	4.89684i	0.194172	−	0.336317i
$213$	0.505428	+	2.24254i	0.0346314	+	0.153657i
$214$	−3.88186	+	3.88186i	−0.265359	+	0.265359i
$215$	1.44470	+	0.387107i	0.0985279	+	0.0264005i
$216$	−3.20647	−	4.08883i	−0.218173	−	0.278210i
$217$	1.74837	+	3.02826i	0.118687	+	0.205572i
$218$	−1.57662	−	2.73078i	−0.106782	−	0.184952i
$219$	5.12501	+	1.59615i	0.346316	+	0.107858i
$220$	1.01211	−	0.584342i	0.0682364	−	0.0393963i
$221$	20.2202	+	19.3129i	1.36016	+	1.29912i
$222$	7.41929	+	14.1310i	0.497950	+	0.948408i
$223$	21.3815	+	5.72916i	1.43181	+	0.383653i	0.889659	−	0.456626i	$-0.150942\pi$
$223$	21.3815	+	5.72916i	1.43181	+	0.383653i	0.542154	+	0.840279i	$0.317609\pi$
$224$	−2.66897	−	1.54093i	−0.178328	−	0.102958i
$225$	13.2157	−	6.27594i	0.881045	−	0.418396i
$226$	−4.72874	+	4.72874i	−0.314551	+	0.314551i
$227$	15.7959	+	15.7959i	1.04841	+	1.04841i	0.998767	+	0.0496444i	$0.0158088\pi$
$227$	15.7959	+	15.7959i	1.04841	+	1.04841i	0.0496444	+	0.998767i	$0.484191\pi$
$228$	6.29022	+	1.95904i	0.416580	+	0.129741i
$229$	−2.40948	+	8.99230i	−0.159223	+	0.594228i	0.839484	+	0.543385i	$0.182858\pi$
$229$	−2.40948	+	8.99230i	−0.159223	+	0.594228i	−0.998707	+	0.0508431i	$0.983809\pi$
$230$	2.03274	+	1.17360i	0.134035	+	0.0773850i
$231$	−15.0182	−	9.49369i	−0.988127	−	0.624639i
$232$	−1.47261	+	5.49586i	−0.0966816	+	0.360821i
$233$	28.4945			1.86674			0.933370	−	0.358917i	$-0.116854\pi$
$233$	28.4945			1.86674			0.933370	+	0.358917i	$0.116854\pi$
$234$	9.04242	+	5.93588i	0.591121	+	0.388041i
$235$	−1.51771			−0.0990047
$236$	−2.84022	+	10.5998i	−0.184882	+	0.689990i
$237$	0.865636	−	21.5637i	0.0562291	−	1.40071i
$238$	20.6982	+	11.9501i	1.34166	+	0.774610i
$239$	3.73860	−	13.9526i	0.241830	−	0.902521i	−0.733121	−	0.680099i	$-0.761937\pi$
$239$	3.73860	−	13.9526i	0.241830	−	0.902521i	0.974950	−	0.222422i	$-0.0713964\pi$
$240$	−0.446929	+	0.412431i	−0.0288491	+	0.0266223i
$241$	−21.5804	−	21.5804i	−1.39012	−	1.39012i	−0.825034	−	0.565083i	$-0.808844\pi$
$241$	−21.5804	−	21.5804i	−1.39012	−	1.39012i	−0.565083	−	0.825034i	$-0.691156\pi$
$242$	0.0557747	−	0.0557747i	0.00358534	−	0.00358534i
$243$	11.6761	+	10.3280i	0.749025	+	0.662542i
$244$	8.69042	+	5.01742i	0.556347	+	0.321207i
$245$	0.847155	+	0.226994i	0.0541227	+	0.0145021i
$246$	−2.42648	+	3.83849i	−0.154707	+	0.244733i
$247$	−13.7109	+	0.314678i	−0.872401	+	0.0200225i
$248$	0.982608	−	0.567309i	0.0623957	−	0.0360242i
$249$	5.17209	−	4.77287i	0.327768	−	0.302468i
$250$	−1.73393	−	3.00326i	−0.109663	−	0.189943i
$251$	8.22674	+	14.2491i	0.519267	+	0.899397i	0.999749	+	0.0223928i	$0.00712844\pi$
$251$	8.22674	+	14.2491i	0.519267	+	0.899397i	−0.480482	+	0.877005i	$0.659538\pi$
$252$	8.71000	+	3.10108i	0.548678	+	0.195350i
$253$	21.4928	+	5.75898i	1.35124	+	0.362064i
$254$	−8.73017	+	8.73017i	−0.547780	+	0.547780i
$255$	3.46599	−	3.19845i	0.217048	−	0.200295i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−12.1545			−0.758178			−0.379089	−	0.925360i	$-0.623763\pi$
$257$	−12.1545			−0.758178			−0.379089	+	0.925360i	$0.623763\pi$
$258$	−7.19759	+	1.62220i	−0.448102	+	0.100994i
$259$	−24.5936	−	14.1991i	−1.52818	−	0.882292i
$260$	0.607659	−	1.11059i	0.0376854	−	0.0688759i
$261$	1.36822	−	17.0143i	0.0846908	−	1.05316i
$262$	−1.23158	−	4.59631i	−0.0760871	−	0.283961i
$263$	7.18878	−	4.15044i	0.443279	−	0.255927i	−0.261709	−	0.965147i	$-0.584286\pi$
$263$	7.18878	−	4.15044i	0.443279	−	0.255927i	0.704988	+	0.709220i	$0.250953\pi$
$264$	−3.08050	+	4.87310i	−0.189592	+	0.299919i
$265$	1.91769	+	0.513844i	0.117803	+	0.0315652i
$266$	−11.3231	+	3.03401i	−0.694262	+	0.186027i
$267$	6.53211	+	7.07849i	0.399759	+	0.433196i
$268$	−13.3180	+	3.56856i	−0.813529	+	0.217985i
$269$	15.3432	−	8.85839i	0.935490	−	0.540105i	0.0469463	−	0.998897i	$-0.485051\pi$
$269$	15.3432	−	8.85839i	0.935490	−	0.540105i	0.888544	+	0.458792i	$0.151718\pi$
$270$	1.09534	−	1.45905i	0.0666605	−	0.0887950i
$271$	−6.44584	+	1.72716i	−0.391557	+	0.104917i	−0.449226	−	0.893418i	$-0.648300\pi$
$271$	−6.44584	+	1.72716i	−0.391557	+	0.104917i	0.0576685	+	0.998336i	$0.481633\pi$
$272$	3.87756	−	6.71613i	0.235112	−	0.407225i
$273$	−19.2434	−	0.330532i	−1.16466	−	0.0200047i
$274$	−2.46287	−	4.26581i	−0.148787	−	0.257707i
$275$	−11.4779	−	11.4779i	−0.692140	−	0.692140i
$276$	−11.5695	−	0.464436i	−0.696399	−	0.0279557i
$277$			17.4707i			1.04971i	0.851191	+	0.524856i	$0.175881\pi$
$277$			17.4707i			1.04971i	−0.851191	+	0.524856i	$0.824119\pi$
$278$	2.89940	+	2.89940i	0.173894	+	0.173894i
$279$	−2.59207	+	2.20621i	−0.155183	+	0.132083i
$280$	0.280065	−	1.04522i	0.0167371	−	0.0624636i
$281$	3.74231	+	13.9665i	0.223248	+	0.833172i	0.983099	+	0.183075i	$0.0586051\pi$
$281$	3.74231	+	13.9665i	0.223248	+	0.833172i	−0.759851	+	0.650097i	$0.774728\pi$
$282$	6.62877	−	3.48036i	0.394738	−	0.207252i
$283$			3.57156i			0.212307i	0.994350	+	0.106154i	$0.0338535\pi$
$283$			3.57156i			0.212307i	−0.994350	+	0.106154i	$0.966146\pi$
$284$	−0.938479	+	0.938479i	−0.0556885	+	0.0556885i
$285$	−0.0927856	+	2.31136i	−0.00549614	+	0.136913i
$286$	2.83930	−	11.6603i	0.167892	−	0.689491i
$287$		−	8.08009i		−	0.476953i
$288$	1.00624	−	2.82621i	0.0592931	−	0.166536i
$289$	−21.5709	+	37.3619i	−1.26888	+	2.19776i
$290$	−1.99775			−0.117312
$291$	0.435397	−	1.39800i	0.0255234	−	0.0819522i
$292$	0.802108	+	2.99351i	0.0469398	+	0.175182i
$293$	1.77421	+	6.62145i	0.103651	+	0.386829i	0.998189	−	0.0601627i	$-0.0191619\pi$
$293$	1.77421	+	6.62145i	0.103651	+	0.386829i	−0.894538	+	0.446992i	$0.852495\pi$
$294$	−4.22057	+	0.951239i	−0.246149	+	0.0554774i
$295$	−3.85305			−0.224333
$296$	−4.60733	+	7.98013i	−0.267796	+	0.463836i
$297$	6.44996	−	16.0477i	0.374264	−	0.931180i
$298$		−	7.59077i		−	0.439721i
$299$	23.1326	−	6.77091i	1.33779	−	0.391572i
$300$	7.13979	+	4.51338i	0.412216	+	0.260580i
$301$	9.28290	−	9.28290i	0.535058	−	0.535058i
$302$		−	14.5805i		−	0.839015i
$303$	−15.3930	−	9.73058i	−0.884303	−	0.559007i
$304$	0.984473	+	3.67410i	0.0564634	+	0.210724i
$305$	−0.911918	+	3.40332i	−0.0522163	+	0.194874i
$306$	−7.80349	+	21.9176i	−0.446096	+	1.25295i
$307$	2.89643	+	2.89643i	0.165308	+	0.165308i	0.784913	−	0.619605i	$-0.212707\pi$
$307$	2.89643	+	2.89643i	0.165308	+	0.165308i	−0.619605	+	0.784913i	$0.712707\pi$
$308$		−	10.2580i		−	0.584502i
$309$	−1.39230	+	2.20251i	−0.0792053	+	0.125296i
$310$	0.281698	+	0.281698i	0.0159994	+	0.0159994i
$311$	−14.2341	−	24.6543i	−0.807144	−	1.39801i	−0.914834	−	0.403830i	$-0.867679\pi$
$311$	−14.2341	−	24.6543i	−0.807144	−	1.39801i	0.107690	−	0.994185i	$-0.465655\pi$
$312$	−0.107251	+	6.24408i	−0.00607189	+	0.353501i
$313$	−2.79680	+	4.84421i	−0.158085	+	0.273811i	−0.934178	−	0.356807i	$-0.883865\pi$
$313$	−2.79680	+	4.84421i	−0.158085	+	0.273811i	0.776093	+	0.630618i	$0.217199\pi$
$314$	−15.8475	+	4.24632i	−0.894324	+	0.239634i
$315$	−0.260212	+	3.23582i	−0.0146613	+	0.182318i
$316$	10.7905	−	6.22990i	0.607014	−	0.350459i
$317$	1.99822	−	0.535423i	0.112231	−	0.0300723i	−0.202266	−	0.979331i	$-0.564831\pi$
$317$	1.99822	−	0.535423i	0.112231	−	0.0300723i	0.314498	+	0.949258i	$0.398164\pi$
$318$	−9.55404	+	2.15330i	−0.535764	+	0.120751i
$319$	−18.2929	+	4.90158i	−1.02421	+	0.274436i
$320$	−0.339151	−	0.0908752i	−0.0189591	−	0.00508008i
$321$	9.50093	+	0.381399i	0.530290	+	0.0212876i
$322$	17.8421	−	10.3011i	0.994300	−	0.574060i
$323$	−7.63470	−	28.4931i	−0.424806	−	1.58540i
$324$	−1.43819	+	8.88435i	−0.0798995	+	0.493575i
$325$	−17.0841	−	4.15998i	−0.947654	−	0.230754i
$326$	−16.1187	−	9.30611i	−0.892730	−	0.515418i
$327$	−1.62402	+	5.21452i	−0.0898087	+	0.288364i
$328$	−2.62182			−0.144766
$329$	−6.66076	+	11.5368i	−0.367220	+	0.636043i
$330$	−1.93266	−	0.601912i	−0.106389	−	0.0331342i
$331$	17.1726	−	17.1726i	0.943890	−	0.943890i	−0.0546177	−	0.998507i	$-0.517394\pi$
$331$	17.1726	−	17.1726i	0.943890	−	0.943890i	0.998507	+	0.0546177i	$0.0173940\pi$
$332$	3.92483	+	1.05166i	0.215403	+	0.0577171i
$333$	9.27213	−	26.0426i	0.508110	−	1.42713i
$334$	0.430839	+	0.746235i	0.0235745	+	0.0408322i
$335$	−2.42056	−	4.19253i	−0.132249	−	0.229063i
$336$	1.17363	+	5.20732i	0.0640270	+	0.284083i
$337$	−23.9772	+	13.8433i	−1.30612	+	0.754090i	−0.981447	−	0.191735i	$-0.938589\pi$
$337$	−23.9772	+	13.8433i	−1.30612	+	0.754090i	−0.324676	+	0.945825i	$0.605255\pi$
$338$	−3.93720	−	12.3895i	−0.214155	−	0.673897i
$339$	11.5737	+	0.464605i	0.628596	+	0.0252339i
$340$	2.63016	+	0.704748i	0.142640	+	0.0382203i
$341$	3.27061	+	1.88829i	0.177113	+	0.102256i
$342$	−4.89507	−	10.3079i	−0.264695	−	0.557386i
$343$	−9.81106	+	9.81106i	−0.529748	+	0.529748i
$344$	−3.01211	−	3.01211i	−0.162402	−	0.162402i
$345$	−0.893862	−	3.96600i	−0.0481239	−	0.213522i
$346$	−6.18006	+	23.0643i	−0.332242	+	1.23994i
$347$	1.89409	+	1.09355i	0.101680	+	0.0587049i	0.549978	−	0.835179i	$-0.314636\pi$
$347$	1.89409	+	1.09355i	0.101680	+	0.0587049i	−0.448298	+	0.893884i	$0.647970\pi$
$348$	8.72537	−	4.58115i	0.467729	−	0.245576i
$349$	−7.52759	+	28.0933i	−0.402942	+	1.50380i	0.404877	+	0.914371i	$0.367314\pi$
$349$	−7.52759	+	28.0933i	−0.402942	+	1.50380i	−0.807819	+	0.589430i	$0.799352\pi$
$350$	−15.0294			−0.803354
$351$	−3.06583	−	18.4824i	−0.163642	−	0.986520i
$352$	−3.32849			−0.177409
$353$	1.88114	−	7.02050i	0.100123	−	0.373664i	−0.897623	−	0.440763i	$-0.854708\pi$
$353$	1.88114	−	7.02050i	0.100123	−	0.373664i	0.997746	+	0.0670996i	$0.0213745\pi$
$354$	16.8286	−	8.83565i	0.894429	−	0.469610i
$355$	−0.403571	−	0.233002i	−0.0214193	−	0.0123664i
$356$	−1.43929	+	5.37149i	−0.0762821	+	0.284689i
$357$	−9.10167	−	40.3834i	−0.481712	−	2.13732i
$358$	−7.35087	−	7.35087i	−0.388506	−	0.388506i
$359$	−5.00179	+	5.00179i	−0.263985	+	0.263985i	−0.826671	−	0.562686i	$-0.809768\pi$
$359$	−5.00179	+	5.00179i	−0.263985	+	0.263985i	0.562686	+	0.826671i	$0.309768\pi$
$360$	1.04996	+	0.0844333i	0.0553375	+	0.00445003i
$361$	−3.92464	−	2.26589i	−0.206560	−	0.119257i
$362$	0.614040	+	0.164531i	0.0322732	+	0.00864758i
$363$	−0.136510	−	0.00547995i	−0.00716490	−	0.000287623i
$364$	−5.77524	−	9.49310i	−0.302705	−	0.497573i
$365$	−0.942359	+	0.544071i	−0.0493253	+	0.0284780i
$366$	−3.82147	−	16.9555i	−0.199751	−	0.886280i
$367$	−8.76307	−	15.1781i	−0.457428	−	0.792289i	0.541396	−	0.840768i	$-0.317896\pi$
$367$	−8.76307	−	15.1781i	−0.457428	−	0.792289i	−0.998824	+	0.0484787i	$0.984563\pi$
$368$	−3.34250	−	5.78938i	−0.174240	−	0.301793i
$369$	7.73619	−	1.42019i	0.402730	−	0.0739321i
$370$	−3.12516	−	0.837384i	−0.162469	−	0.0435335i
$371$	12.3221	−	12.3221i	0.639730	−	0.639730i
$372$	−1.87632	−	0.584367i	−0.0972829	−	0.0302980i
$373$	−6.06364	+	10.5025i	−0.313963	+	0.543801i	−0.979217	−	0.202817i	$-0.934990\pi$
$373$	−6.06364	+	10.5025i	−0.313963	+	0.543801i	0.665253	+	0.746618i	$0.268324\pi$
$374$	25.8129			1.33475
$375$	−1.78607	+	5.73482i	−0.0922321	+	0.296145i
$376$	3.74344	+	2.16128i	0.193053	+	0.111459i
$377$	−14.1694	+	14.8350i	−0.729759	+	0.764044i
$378$	−6.28374	−	14.7295i	−0.323201	−	0.757602i
$379$	1.59520	+	5.95337i	0.0819399	+	0.305804i	0.994717	−	0.102654i	$-0.0327334\pi$
$379$	1.59520	+	5.95337i	0.0819399	+	0.305804i	−0.912777	+	0.408458i	$0.866067\pi$
$380$	−1.15661	+	0.667770i	−0.0593329	+	0.0342559i
$381$	21.3673	+	0.857752i	1.09468	+	0.0439439i
$382$	0.144006	+	0.0385862i	0.00736796	+	0.00197424i
$383$	−14.1096	+	3.78066i	−0.720967	+	0.193183i	−0.600603	−	0.799547i	$-0.705073\pi$
$383$	−14.1096	+	3.78066i	−0.720967	+	0.193183i	−0.120364	+	0.992730i	$0.538406\pi$
$384$	1.68967	−	0.380820i	0.0862255	−	0.0194336i
$385$	3.47900	−	0.932194i	0.177306	−	0.0475090i
$386$	−3.69480	+	2.13319i	−0.188060	+	0.108577i
$387$	10.5194	+	7.25620i	0.534731	+	0.368854i
$388$	0.816569	−	0.218799i	0.0414550	−	0.0111078i
$389$	−2.49669	+	4.32440i	−0.126587	+	0.219256i	−0.922352	−	0.386350i	$-0.873736\pi$
$389$	−2.49669	+	4.32440i	−0.126587	+	0.219256i	0.795765	+	0.605606i	$0.207069\pi$
$390$	−2.12743	+	0.531058i	−0.107727	+	0.0268911i
$391$	25.9215	+	44.8974i	1.31091	+	2.27056i
$392$	−1.76626	−	1.76626i	−0.0892097	−	0.0892097i
$393$	−4.40392	+	6.96663i	−0.222148	+	0.351420i
$394$			19.1250i			0.963504i
$395$	3.09347	+	3.09347i	0.155649	+	0.155649i
$396$	9.82136	−	1.80298i	0.493542	−	0.0906032i
$397$	−1.56112	+	5.82617i	−0.0783503	+	0.292407i	−0.993972	−	0.109634i	$-0.965032\pi$
$397$	−1.56112	+	5.82617i	−0.0783503	+	0.292407i	0.915622	+	0.402041i	$0.131699\pi$
$398$	1.36036	+	5.07693i	0.0681886	+	0.254483i
$399$	17.1624	+	10.8491i	0.859195	+	0.543136i
$400$			4.87672i			0.243836i
$401$	5.39583	−	5.39583i	0.269455	−	0.269455i	−0.559426	−	0.828881i	$-0.688978\pi$
$401$	5.39583	−	5.39583i	0.269455	−	0.269455i	0.828881	+	0.559426i	$0.188978\pi$
$402$	20.1862	+	12.7606i	1.00680	+	0.636441i
$403$	4.08985	−	0.0938662i	0.203730	−	0.00467581i
$404$		−	10.5139i		−	0.523087i
$405$	−3.14383	+	0.319603i	−0.156218	+	0.0158812i
$406$	−8.76748	+	15.1857i	−0.435123	+	0.753655i
$407$	−30.6709			−1.52030
$408$	−13.1036	+	2.95330i	−0.648723	+	0.146210i
$409$	−1.21890	−	4.54898i	−0.0602705	−	0.224933i	0.929221	−	0.369525i	$-0.120480\pi$
$409$	−1.21890	−	4.54898i	−0.0602705	−	0.224933i	−0.989491	+	0.144592i	$0.953813\pi$
$410$	−0.238259	−	0.889193i	−0.0117667	−	0.0439141i
$411$	−2.53692	+	8.14571i	−0.125137	+	0.401798i
$412$	−1.50439			−0.0741158
$413$	−16.9098	+	29.2886i	−0.832077	+	1.44120i
$414$	12.9987	+	15.2721i	0.638851	+	0.750584i
$415$			1.42668i			0.0700329i
$416$	−3.08031	+	1.87395i	−0.151025	+	0.0918778i
$417$	0.284870	−	7.09633i	0.0139501	−	0.347509i
$418$	−8.95242	+	8.95242i	−0.437877	+	0.437877i
$419$			14.0661i			0.687174i	0.939121	+	0.343587i	$0.111642\pi$
$419$			14.0661i			0.687174i	−0.939121	+	0.343587i	$0.888358\pi$
$420$	−1.65941	+	0.871256i	−0.0809711	+	0.0425129i
$421$	−7.95186	−	29.6767i	−0.387550	−	1.44636i	−0.834108	−	0.551601i	$-0.814017\pi$
$421$	−7.95186	−	29.6767i	−0.387550	−	1.44636i	0.446558	−	0.894755i	$-0.352650\pi$
$422$	6.17738	−	23.0543i	0.300710	−	1.12227i
$423$	−12.2165	−	4.34952i	−0.593985	−	0.211481i
$424$	−3.99826	−	3.99826i	−0.194172	−	0.194172i
$425$		−	37.8195i		−	1.83452i
$426$	2.29695	+	0.0922069i	0.111287	+	0.00446744i
$427$	21.8680	+	21.8680i	1.05827	+	1.05827i
$428$	2.74489	+	4.75429i	0.132679	+	0.229807i
$429$	−18.1774	+	10.0825i	−0.877614	+	0.486789i
$430$	0.747833	−	1.29529i	0.0360637	−	0.0624642i
$431$	−37.7065	+	10.1034i	−1.81626	+	0.486665i	−0.996314	−	0.0857790i	$-0.972662\pi$
$431$	−37.7065	+	10.1034i	−1.81626	+	0.486665i	−0.819944	+	0.572444i	$0.805995\pi$
$432$	−4.77941	+	2.03894i	−0.229949	+	0.0980987i
$433$	−1.12288	+	0.648297i	−0.0539623	+	0.0311552i	−0.526738	−	0.850027i	$-0.676585\pi$
$433$	−1.12288	+	0.648297i	−0.0539623	+	0.0311552i	0.472776	+	0.881183i	$0.343252\pi$
$434$	3.37759	−	0.905022i	0.162129	−	0.0434424i
$435$	2.34662	+	2.54290i	0.112512	+	0.121923i
$436$	−3.04579	+	0.816118i	−0.145867	+	0.0390849i
$437$	−24.5614	−	6.58121i	−1.17493	−	0.314822i
$438$	2.86821	−	4.53727i	0.137048	−	0.216799i
$439$	16.2821	−	9.40048i	0.777103	−	0.448660i	−0.0582998	−	0.998299i	$-0.518568\pi$
$439$	16.2821	−	9.40048i	0.777103	−	0.448660i	0.835403	+	0.549639i	$0.185235\pi$
$440$	−0.302478	−	1.12886i	−0.0144201	−	0.0538164i
$441$	6.16844	+	4.25494i	0.293735	+	0.202616i
$442$	23.8882	−	14.5327i	1.13625	−	0.691249i
$443$	18.8039	+	10.8564i	0.893400	+	0.515805i	0.875053	−	0.484027i	$-0.160826\pi$
$443$	18.8039	+	10.8564i	0.893400	+	0.515805i	0.0183470	+	0.999832i	$0.494160\pi$
$444$	15.5697	−	3.50913i	0.738906	−	0.166536i
$445$	−1.95254			−0.0925594
$446$	11.0679	−	19.1702i	0.524080	−	0.907733i
$447$	−9.66217	+	8.91637i	−0.457005	+	0.421730i
$448$	−2.17921	+	2.17921i	−0.102958	+	0.102958i
$449$	21.9490	+	5.88123i	1.03584	+	0.277552i	0.736388	−	0.676559i	$-0.236530\pi$
$449$	21.9490	+	5.88123i	1.03584	+	0.277552i	0.299451	+	0.954112i	$0.403196\pi$
$450$	−2.64162	−	14.3897i	−0.124527	−	0.678337i
$451$	−4.36336	−	7.55756i	−0.205463	−	0.355872i
$452$	3.34372	+	5.79150i	0.157275	+	0.272409i
$453$	−18.5593	+	17.1268i	−0.871994	+	0.804686i
$454$	19.3460	−	11.1694i	0.907951	−	0.524206i
$455$	2.69477	−	2.82137i	0.126333	−	0.132268i
$456$	3.52032	−	5.56884i	0.164854	−	0.260785i
$457$	28.0487	+	7.51563i	1.31206	+	0.351567i	0.845999	−	0.533184i	$-0.179005\pi$
$457$	28.0487	+	7.51563i	1.31206	+	0.351567i	0.466065	+	0.884751i	$0.345671\pi$
$458$	8.06228	+	4.65476i	0.376725	+	0.217503i
$459$	37.0649	−	15.8122i	1.73004	−	0.738052i
$460$	1.65972	−	1.65972i	0.0773850	−	0.0773850i
$461$	8.27821	+	8.27821i	0.385555	+	0.385555i	0.873099	−	0.487544i	$-0.162107\pi$
$461$	8.27821	+	8.27821i	0.385555	+	0.385555i	−0.487544	+	0.873099i	$0.662107\pi$
$462$	−13.0572	+	12.0493i	−0.607476	+	0.560586i
$463$	4.77229	−	17.8104i	0.221787	−	0.827722i	−0.761879	−	0.647720i	$-0.775723\pi$
$463$	4.77229	−	17.8104i	0.221787	−	0.827722i	0.983666	−	0.180002i	$-0.0576105\pi$
$464$	4.92745	+	2.84486i	0.228751	+	0.132070i
$465$	0.0276772	−	0.689461i	0.00128350	−	0.0319730i
$466$	7.37493	−	27.5236i	0.341637	−	1.27501i
$467$	15.3781			0.711613			0.355807	−	0.934560i	$-0.384206\pi$
$467$	15.3781			0.711613			0.355807	+	0.934560i	$0.384206\pi$
$468$	8.07397	−	7.19798i	0.373219	−	0.332727i
$469$	−42.4923			−1.96211
$470$	−0.392813	+	1.46600i	−0.0181191	+	0.0676215i
$471$	24.0200	+	15.1841i	1.10679	+	0.699648i
$472$	9.50355	+	5.48688i	0.437436	+	0.252554i
$473$	3.66969	−	13.6955i	0.168733	−	0.629719i
$474$	−20.6048	−	6.41722i	−0.946412	−	0.294753i
$475$	13.1166	+	13.1166i	0.601829	+	0.601829i
$476$	16.9000	−	16.9000i	0.774610	−	0.774610i
$477$	13.9634	+	9.63184i	0.639340	+	0.441012i
$478$	−12.5096	−	7.22241i	−0.572175	−	0.330346i
$479$	−15.0199	−	4.02458i	−0.686279	−	0.183888i	−0.101202	−	0.994866i	$-0.532269\pi$
$479$	−15.0199	−	4.02458i	−0.686279	−	0.183888i	−0.585077	+	0.810978i	$0.698936\pi$
$480$	0.282704	+	0.538445i	0.0129036	+	0.0245765i
$481$	−28.3840	+	17.2678i	−1.29420	+	0.787343i
$482$	−26.4305	+	15.2597i	−1.20388	+	0.695058i
$483$	−34.0701	−	10.6109i	−1.55024	−	0.482811i
$484$	−0.0394387	−	0.0683098i	−0.00179267	−	0.00310499i
$485$	0.148412	+	0.257057i	0.00673903	+	0.0116723i
$486$	12.9981	−	8.60520i	0.589606	−	0.390340i
$487$	16.7862	+	4.49786i	0.760656	+	0.203817i	0.618240	−	0.785990i	$-0.287846\pi$
$487$	16.7862	+	4.49786i	0.760656	+	0.203817i	0.142417	+	0.989807i	$0.454513\pi$
$488$	7.09570	−	7.09570i	0.321207	−	0.321207i
$489$	7.08790	+	31.4485i	0.320526	+	1.42215i
$490$	0.438520	−	0.759538i	0.0198103	−	0.0343124i
$491$	8.08082			0.364682			0.182341	−	0.983235i	$-0.441632\pi$
$491$	8.08082			0.364682			0.182341	+	0.983235i	$0.441632\pi$
$492$	3.07968	+	3.33728i	0.138843	+	0.150456i
$493$	−38.2130	−	22.0623i	−1.72103	−	0.993634i
$494$	−3.24468	+	13.3251i	−0.145985	+	0.599526i
$495$	1.50400	+	3.16708i	0.0675998	+	0.142350i
$496$	−0.293661	−	1.09596i	−0.0131858	−	0.0492099i
$497$	−3.54228	+	2.04514i	−0.158893	+	0.0917370i
$498$	−3.27160	−	6.23117i	−0.146604	−	0.279225i
$499$	−12.6704	−	3.39501i	−0.567203	−	0.151982i	−0.0361895	−	0.999345i	$-0.511522\pi$
$499$	−12.6704	−	3.39501i	−0.567203	−	0.151982i	−0.531014	+	0.847363i	$0.678189\pi$
$500$	−3.34970	+	0.897549i	−0.149803	+	0.0401396i
$501$	0.443793	−	1.42496i	0.0198272	−	0.0636626i
$502$	15.8928	−	4.25847i	0.709332	−	0.190065i
$503$	17.8854	−	10.3261i	0.797470	−	0.460419i	−0.0451158	−	0.998982i	$-0.514366\pi$
$503$	17.8854	−	10.3261i	0.797470	−	0.460419i	0.842586	+	0.538562i	$0.181032\pi$
$504$	5.24973	−	7.61060i	0.233842	−	0.339003i
$505$	3.56580	−	0.955455i	0.158676	−	0.0425172i
$506$	11.1255	−	19.2699i	0.494589	−	0.856653i
$507$	−11.1456	+	19.5647i	−0.494993	+	0.868897i
$508$	6.17316	+	10.6922i	0.273890	+	0.474391i
$509$	24.3229	+	24.3229i	1.07809	+	1.07809i	0.996680	+	0.0814135i	$0.0259434\pi$
$509$	24.3229	+	24.3229i	1.07809	+	1.07809i	0.0814135	+	0.996680i	$0.474057\pi$
$510$	−2.19241	−	4.17571i	−0.0970813	−	0.184903i
$511$			9.55102i			0.422512i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−7.37083	+	18.3388i	−0.325430	+	0.809679i
$514$	−3.14582	+	11.7404i	−0.138756	+	0.517845i
$515$	−0.136711	−	0.510214i	−0.00602423	−	0.0224827i
$516$	−0.295944	+	7.37219i	−0.0130282	+	0.324543i
$517$			14.3876i			0.632766i
$518$	−20.0806	+	20.0806i	−0.882292	+	0.882292i
$519$	36.6175	−	19.2256i	1.60733	−	0.843910i
$520$	−0.915475	−	0.874395i	−0.0401462	−	0.0383448i
$521$		−	10.8135i		−	0.473747i	−0.971540	−	0.236874i	$-0.923877\pi$
$521$		−	10.8135i		−	0.473747i	0.971540	−	0.236874i	$-0.0761227\pi$
$522$	−16.0804	−	5.72522i	−0.703820	−	0.250586i
$523$	12.9411	−	22.4147i	0.565876	−	0.980126i	−0.431091	−	0.902308i	$-0.641871\pi$
$523$	12.9411	−	22.4147i	0.565876	−	0.980126i	0.996968	−	0.0778180i	$-0.0247953\pi$
$524$	−4.75845			−0.207874
$525$	17.6540	+	19.1307i	0.770484	+	0.834930i
$526$	−2.14843	−	8.01804i	−0.0936759	−	0.349603i
$527$	2.27737	+	8.49928i	0.0992040	+	0.370234i
$528$	3.90976	+	4.23679i	0.170151	+	0.184383i
$529$	21.6893			0.943013
$530$	0.992670	−	1.71935i	0.0431188	−	0.0746840i
$531$	−31.0142	−	11.0422i	−1.34590	−	0.479191i
$532$			11.7225i			0.508235i
$533$	−8.29293	−	4.53747i	−0.359207	−	0.196540i
$534$	8.52793	−	4.47749i	0.369040	−	0.193760i
$535$	−1.36298	+	1.36298i	−0.0589268	+	0.0589268i
$536$			13.7879i			0.595545i
$537$	−0.722234	+	17.9914i	−0.0311667	+	0.776386i
$538$	−4.58544	−	17.1131i	−0.197692	−	0.737798i
$539$	2.15186	−	8.03085i	0.0926872	−	0.345913i
$540$	−1.12584	−	1.43565i	−0.0484484	−	0.0617806i
$541$	−20.8711	−	20.8711i	−0.897318	−	0.897318i	0.0978806	−	0.995198i	$-0.468794\pi$
$541$	−20.8711	−	20.8711i	−0.897318	−	0.897318i	−0.995198	+	0.0978806i	$0.968794\pi$
$542$			6.67323i			0.286640i
$543$	−0.511842	−	0.974866i	−0.0219652	−	0.0418355i
$544$	−5.48370	−	5.48370i	−0.235112	−	0.235112i
$545$	−0.553574	−	0.958818i	−0.0237125	−	0.0410713i
$546$	−5.29982	+	18.5021i	−0.226811	+	0.791818i
$547$	8.21466	−	14.2282i	0.351233	−	0.608354i	−0.635233	−	0.772321i	$-0.719096\pi$
$547$	8.21466	−	14.2282i	0.351233	−	0.608354i	0.986466	+	0.163967i	$0.0524291\pi$
$548$	−4.75789	+	1.27487i	−0.203247	+	0.0544599i
$549$	−17.0936	+	24.7808i	−0.729538	+	1.05762i
$550$	−14.0574	+	8.11607i	−0.599411	+	0.346070i
$551$	20.9047	−	5.60138i	0.890568	−	0.238627i
$552$	−3.44300	+	11.0550i	−0.146544	+	0.470533i
$553$	37.0910	−	9.93850i	1.57727	−	0.422628i
$554$	16.8754	+	4.52175i	0.716967	+	0.192111i
$555$	2.60502	+	4.96159i	0.110577	+	0.210608i
$556$	3.55102	−	2.05018i	0.150597	−	0.0869472i
$557$	6.82819	+	25.4831i	0.289320	+	1.07976i	0.945625	+	0.325260i	$0.105452\pi$
$557$	6.82819	+	25.4831i	0.289320	+	1.07976i	−0.656305	+	0.754496i	$0.727882\pi$
$558$	1.46016	+	3.07476i	0.0618135	+	0.130165i
$559$	−4.31450	−	14.7403i	−0.182484	−	0.623450i
$560$	−0.937115	−	0.541044i	−0.0396003	−	0.0228633i
$561$	−30.3207	−	32.8568i	−1.28014	−	1.38722i
$562$	14.4592			0.609924
$563$	−13.9450	+	24.1535i	−0.587712	+	1.01795i	0.406819	+	0.913509i	$0.366638\pi$
$563$	−13.9450	+	24.1535i	−0.587712	+	1.01795i	−0.994531	+	0.104438i	$0.966695\pi$
$564$	−1.64612	−	7.30368i	−0.0693140	−	0.307541i
$565$	−1.66033	+	1.66033i	−0.0698506	+	0.0698506i
$566$	3.44986	+	0.924387i	0.145008	+	0.0388549i
$567$	−11.3678	+	25.3002i	−0.477404	+	1.06251i
$568$	0.663605	+	1.14940i	0.0278442	+	0.0482277i
$569$	−0.201415	−	0.348862i	−0.00844377	−	0.0146250i	0.861773	−	0.507295i	$-0.169354\pi$
$569$	−0.201415	−	0.348862i	−0.00844377	−	0.0146250i	−0.870216	+	0.492670i	$0.836021\pi$
$570$	2.20859	+	0.687848i	0.0925076	+	0.0288108i
$571$	30.8570	−	17.8153i	1.29133	−	0.745548i	0.312437	−	0.949938i	$-0.398855\pi$
$571$	30.8570	−	17.8153i	1.29133	−	0.745548i	0.978889	+	0.204390i	$0.0655212\pi$
$572$	−10.5282	−	5.76048i	−0.440205	−	0.240858i
$573$	−0.120038	−	0.228627i	−0.00501466	−	0.00955103i
$574$	−7.80477	−	2.09128i	−0.325765	−	0.0872884i
$575$	−28.2332	−	16.3004i	−1.17741	−	0.679775i
$576$	−2.46948	−	1.70343i	−0.102895	−	0.0709762i
$577$	33.2996	−	33.2996i	1.38628	−	1.38628i	0.553294	−	0.832986i	$-0.313371\pi$
$577$	33.2996	−	33.2996i	1.38628	−	1.38628i	0.832986	−	0.553294i	$-0.186629\pi$
$578$	30.5059	+	30.5059i	1.26888	+	1.26888i
$579$	7.05535	+	2.19733i	0.293210	+	0.0913181i
$580$	−0.517055	+	1.92968i	−0.0214696	+	0.0801255i
$581$	10.8448	+	6.26124i	0.449917	+	0.259760i
$582$	−1.23768	−	0.782390i	−0.0513033	−	0.0324311i
$583$	4.87113	−	18.1793i	0.201742	−	0.752910i
$584$	3.09911			0.128242
$585$	3.17493	+	2.08418i	0.131267	+	0.0861701i
$586$	6.85503			0.283179
$587$	−1.58077	+	5.89951i	−0.0652453	+	0.243499i	−0.990845	−	0.135005i	$-0.956895\pi$
$587$	−1.58077	+	5.89951i	−0.0652453	+	0.243499i	0.925600	+	0.378504i	$0.123561\pi$
$588$	−0.173538	+	4.32296i	−0.00715657	+	0.178276i
$589$	−3.73756	−	2.15788i	−0.154003	−	0.0889139i
$590$	−0.997242	+	3.72176i	−0.0410558	+	0.153222i
$591$	24.3439	−	22.4649i	1.00138	−	0.924081i
$592$	6.51575	+	6.51575i	0.267796	+	0.267796i
$593$	5.57423	−	5.57423i	0.228906	−	0.228906i	−0.583329	−	0.812236i	$-0.698250\pi$
$593$	5.57423	−	5.57423i	0.228906	−	0.228906i	0.812236	+	0.583329i	$0.198250\pi$
$594$	−13.8315	−	10.3836i	−0.567513	−	0.426045i
$595$	7.26744	+	4.19586i	0.297936	+	0.172013i
$596$	−7.33212	−	1.96463i	−0.300335	−	0.0804746i
$597$	4.86442	−	7.69511i	0.199088	−	0.314940i
$598$	−0.553046	−	24.0968i	−0.0226157	−	0.985391i
$599$	12.2562	−	7.07612i	0.500775	−	0.289122i	−0.228259	−	0.973601i	$-0.573303\pi$
$599$	12.2562	−	7.07612i	0.500775	−	0.289122i	0.729033	+	0.684478i	$0.239970\pi$
$600$	6.20750	−	5.72836i	0.253420	−	0.233859i
$601$	19.8095	+	34.3110i	0.808044	+	1.39957i	0.914216	+	0.405226i	$0.132807\pi$
$601$	19.8095	+	34.3110i	0.808044	+	1.39957i	−0.106172	+	0.994348i	$0.533859\pi$
$602$	−6.56400	−	11.3692i	−0.267529	−	0.463373i
$603$	−7.46861	−	40.6837i	−0.304145	−	1.65677i
$604$	−14.0837	−	3.77372i	−0.573058	−	0.153550i
$605$	0.0195833	−	0.0195833i	0.000796176	−	0.000796176i
$606$	−13.3830	+	12.3500i	−0.543648	+	0.501685i
$607$	3.42680	−	5.93539i	0.139090	−	0.240910i	−0.788063	−	0.615595i	$-0.788916\pi$
$607$	3.42680	−	5.93539i	0.139090	−	0.240910i	0.927152	+	0.374685i	$0.122249\pi$
$608$	3.80371			0.154261
$609$	29.6282	−	6.67766i	1.20060	−	0.270593i
$610$	3.05134	+	1.76169i	0.123545	+	0.0713288i
$611$	8.10024	+	13.3148i	0.327701	+	0.538660i
$612$	19.1511	+	13.2103i	0.774138	+	0.533994i
$613$	−5.58884	−	20.8578i	−0.225731	−	0.842440i	−0.982110	−	0.188307i	$-0.939700\pi$
$613$	−5.58884	−	20.8578i	−0.225731	−	0.842440i	0.756379	−	0.654134i	$-0.226967\pi$
$614$	3.54739	−	2.04809i	0.143161	−	0.0826541i
$615$	−0.851974	+	1.34775i	−0.0343549	+	0.0543466i
$616$	−9.90843	−	2.65496i	−0.399222	−	0.106971i
$617$	26.9973	−	7.23390i	1.08687	−	0.291226i	0.329463	−	0.944169i	$-0.393132\pi$
$617$	26.9973	−	7.23390i	1.08687	−	0.291226i	0.757407	+	0.652943i	$0.226466\pi$
$618$	1.76710	+	1.91491i	0.0710833	+	0.0770290i
$619$	−17.5683	+	4.70742i	−0.706130	+	0.189207i	−0.593975	−	0.804484i	$-0.702442\pi$
$619$	−17.5683	+	4.70742i	−0.706130	+	0.189207i	−0.112155	+	0.993691i	$0.535775\pi$
$620$	0.345008	−	0.199191i	0.0138559	−	0.00799969i
$621$	4.17095	−	34.4850i	0.167375	−	1.38383i
$622$	−27.4983	+	7.36814i	−1.10258	+	0.295435i
$623$	−8.56908	+	14.8421i	−0.343313	+	0.594636i
$624$	6.00356	+	1.71968i	0.240335	+	0.0688424i
$625$	11.5830	+	20.0623i	0.463319	+	0.802493i
$626$	3.95528	+	3.95528i	0.158085	+	0.158085i
$627$	21.9112	+	0.879588i	0.875049	+	0.0351274i
$628$			16.4065i			0.654691i
$629$	−50.5304	−	50.5304i	−2.01478	−	2.01478i
$630$	3.05821	+	1.08884i	0.121842	+	0.0433803i
$631$	−2.24267	+	8.36975i	−0.0892792	+	0.333195i	−0.996090	−	0.0883431i	$-0.971843\pi$
$631$	−2.24267	+	8.36975i	−0.0892792	+	0.333195i	0.906811	+	0.421538i	$0.138509\pi$
$632$	−3.22484	−	12.0353i	−0.128277	−	0.478737i
$633$	−36.6016	+	19.2173i	−1.45478	+	0.763818i
$634$		−	2.06871i		−	0.0821591i
$635$	−3.06529	+	3.06529i	−0.121642	+	0.121642i
$636$	−0.392834	+	9.78581i	−0.0155769	+	0.388032i
$637$	−2.52997	−	8.64355i	−0.100241	−	0.342470i
$638$			18.9382i			0.749772i
$639$	−2.58070	−	3.03206i	−0.102091	−	0.119946i
$640$	−0.175557	+	0.304074i	−0.00693952	+	0.0120196i
$641$	−26.5547			−1.04885			−0.524424	−	0.851457i	$-0.675719\pi$
$641$	−26.5547			−1.04885			−0.524424	+	0.851457i	$0.675719\pi$
$642$	2.82742	−	9.07848i	0.111590	−	0.358299i
$643$	−8.63840	−	32.2390i	−0.340665	−	1.27138i	−0.897595	−	0.440821i	$-0.854687\pi$
$643$	−8.63840	−	32.2390i	−0.340665	−	1.27138i	0.556930	−	0.830560i	$-0.311979\pi$
$644$	−5.33226	−	19.9003i	−0.210120	−	0.784180i
$645$	−2.52718	+	0.569580i	−0.0995076	+	0.0224272i
$646$	−29.4982			−1.16059
$647$	11.9267	−	20.6576i	0.468886	−	0.812134i	−0.530482	−	0.847696i	$-0.677989\pi$
$647$	11.9267	−	20.6576i	0.468886	−	0.812134i	0.999367	+	0.0355623i	$0.0113222\pi$
$648$	8.20939	+	3.68862i	0.322495	+	0.144903i
$649$			36.5261i			1.43377i
$650$	−8.43992	+	15.4253i	−0.331041	+	0.605029i
$651$	−5.11942	−	3.23621i	−0.200646	−	0.126837i
$652$	−13.1608	+	13.1608i	−0.515418	+	0.515418i
$653$			29.8988i			1.17003i	0.811023	+	0.585014i	$0.198911\pi$
$653$			29.8988i			1.17003i	−0.811023	+	0.585014i	$0.801089\pi$
$654$	4.61651	+	2.91830i	0.180520	+	0.114115i
$655$	−0.432425	−	1.61383i	−0.0168962	−	0.0630576i
$656$	−0.678577	+	2.53248i	−0.0264940	+	0.0988769i
$657$	−9.14451	+	1.67873i	−0.356761	+	0.0654933i
$658$	9.41974	+	9.41974i	0.367220	+	0.367220i
$659$			23.8172i			0.927786i	0.885891	+	0.463893i	$0.153548\pi$
$659$			23.8172i			0.927786i	−0.885891	+	0.463893i	$0.846452\pi$
$660$	−1.08161	+	1.71102i	−0.0421017	+	0.0666013i
$661$	9.16721	+	9.16721i	0.356563	+	0.356563i	0.862544	−	0.505981i	$-0.168870\pi$
$661$	9.16721	+	9.16721i	0.356563	+	0.356563i	−0.505981	+	0.862544i	$0.668870\pi$
$662$	−12.1428	−	21.0320i	−0.471945	−	0.817432i
$663$	−46.5583	−	13.3363i	−1.80817	−	0.517941i
$664$	2.03164	−	3.51891i	0.0788430	−	0.136560i
$665$	−3.97570	+	1.06529i	−0.154171	+	0.0413100i
$666$	−22.7554	−	15.6965i	−0.881754	−	0.608227i
$667$	−32.9400	+	19.0179i	−1.27544	+	0.736377i
$668$	0.832317	−	0.223019i	0.0322033	−	0.00862885i
$669$	−37.4021	+	8.42975i	−1.44605	+	0.325913i
$670$	−4.67616	+	1.25297i	−0.180656	+	0.0484066i
$671$	32.2628	+	8.64479i	1.24549	+	0.333728i
$672$	5.33364	+	0.214110i	0.205750	+	0.00825947i
$673$	40.1881	−	23.2026i	1.54914	−	0.894396i	0.550931	−	0.834551i	$-0.314273\pi$
$673$	40.1881	−	23.2026i	1.54914	−	0.894396i	0.998208	−	0.0598451i	$-0.0190607\pi$
$674$	7.16580	+	26.7431i	0.276016	+	1.03011i
$675$	−15.2135	+	20.2651i	−0.585567	+	0.780004i
$676$	−12.9863	+	0.596413i	−0.499474	+	0.0229389i
$677$	−28.9400	−	16.7085i	−1.11225	−	0.642159i	−0.172841	−	0.984950i	$-0.555295\pi$
$677$	−28.9400	−	16.7085i	−1.11225	−	0.642159i	−0.939412	+	0.342790i	$0.888628\pi$
$678$	3.44426	−	11.0591i	0.132276	−	0.424721i
$679$	2.60533			0.0999833
$680$	1.36147	−	2.35813i	0.0522099	−	0.0904303i
$681$	−36.9418	−	11.5052i	−1.41561	−	0.440882i
$682$	2.67044	−	2.67044i	0.102256	−	0.102256i
$683$	4.57669	+	1.22632i	0.175122	+	0.0469238i	0.345314	−	0.938487i	$-0.387772\pi$
$683$	4.57669	+	1.22632i	0.175122	+	0.0469238i	−0.170192	+	0.985411i	$0.554439\pi$
$684$	−11.2236	+	2.06040i	−0.429144	+	0.0787812i
$685$	−0.864749	−	1.49779i	−0.0330404	−	0.0572276i
$686$	6.93747	+	12.0161i	0.264874	+	0.458775i
$687$	−3.54525	−	15.7300i	−0.135260	−	0.600136i
$688$	−3.68906	+	2.12988i	−0.140644	+	0.0812010i
$689$	−5.72705	−	19.5663i	−0.218183	−	0.745415i
$690$	−4.06221	−	0.163070i	−0.154646	−	0.00620798i
$691$	−4.68742	−	1.25599i	−0.178318	−	0.0477801i	0.168555	−	0.985692i	$-0.446090\pi$
$691$	−4.68742	−	1.25599i	−0.178318	−	0.0477801i	−0.346873	+	0.937912i	$0.612757\pi$
$692$	20.6789	+	11.9390i	0.786093	+	0.453851i
$693$	30.6749	+	2.46675i	1.16524	+	0.0937042i
$694$	1.54652	−	1.54652i	0.0587049	−	0.0587049i
$695$	1.01802	+	1.01802i	0.0386158	+	0.0386158i
$696$	−2.16676	−	9.61375i	−0.0821309	−	0.364408i
$697$	5.26245	−	19.6397i	0.199329	−	0.743907i
$698$	25.1878	+	14.5422i	0.953372	+	0.550430i
$699$	−43.6972	+	22.9427i	−1.65278	+	0.867773i
$700$	−3.88989	+	14.5173i	−0.147024	+	0.548701i
$701$	−1.76335			−0.0666009			−0.0333004	−	0.999445i	$-0.510602\pi$
$701$	−1.76335			−0.0666009			−0.0333004	+	0.999445i	$0.510602\pi$
$702$	−18.6462	−	1.82224i	−0.703754	−	0.0687762i
$703$	35.0499			1.32193
$704$	−0.861478	+	3.21508i	−0.0324682	+	0.121173i
$705$	2.32746	−	1.22201i	0.0876572	−	0.0460234i
$706$	−6.29441	−	3.63408i	−0.236893	−	0.136770i
$707$	8.38637	−	31.2984i	0.315402	−	1.17710i
$708$	−4.17903	−	18.5420i	−0.157057	−	0.696851i
$709$	−24.2601	−	24.2601i	−0.911109	−	0.911109i	0.0852508	−	0.996360i	$-0.472831\pi$
$709$	−24.2601	−	24.2601i	−0.911109	−	0.911109i	−0.996360	+	0.0852508i	$0.972831\pi$
$710$	−0.329514	+	0.329514i	−0.0123664	+	0.0123664i
$711$	16.0348	+	33.7655i	0.601350	+	1.26630i
$712$	4.81595	+	2.78049i	0.180485	+	0.104203i
$713$	7.32648	+	1.96312i	0.274379	+	0.0735196i
$714$	−41.3630	−	1.66045i	−1.54797	−	0.0621407i
$715$	0.996922	−	4.09412i	0.0372828	−	0.153111i
$716$	−9.00294	+	5.19785i	−0.336456	+	0.194253i
$717$	5.50088	+	24.4070i	0.205434	+	0.911494i
$718$	3.53680	+	6.12592i	0.131992	+	0.228617i
$719$	−15.1571	−	26.2528i	−0.565264	−	0.979065i	−0.997025	−	0.0770774i	$-0.975441\pi$
$719$	−15.1571	−	26.2528i	−0.565264	−	0.979065i	0.431762	−	0.901988i	$-0.357892\pi$
$720$	0.353305	−	0.992326i	0.0131669	−	0.0369818i
$721$	−4.47833	−	1.19997i	−0.166782	−	0.0446891i
$722$	−3.20445	+	3.20445i	−0.119257	+	0.119257i
$723$	50.4700	+	15.7185i	1.87700	+	0.584577i
$724$	0.317850	−	0.550533i	0.0118128	−	0.0204604i
$725$	27.7472			1.03051
$726$	−0.0406245	+	0.130440i	−0.00150772	+	0.00484108i
$727$	−19.2180	−	11.0955i	−0.712758	−	0.411511i	0.0993236	−	0.995055i	$-0.468332\pi$
$727$	−19.2180	−	11.0955i	−0.712758	−	0.411511i	−0.812081	+	0.583544i	$0.801665\pi$
$728$	−10.6644	+	3.12146i	−0.395248	+	0.115689i
$729$	−26.2214	−	6.43713i	−0.971164	−	0.238412i
$730$	0.281632	+	1.05107i	0.0104237	+	0.0389017i
$731$	28.6091	−	16.5175i	1.05815	−	0.610921i
$732$	−17.3669	−	0.697163i	−0.641898	−	0.0257679i
$733$	−1.03372	−	0.276984i	−0.0381813	−	0.0102306i	0.239678	−	0.970852i	$-0.422958\pi$
$733$	−1.03372	−	0.276984i	−0.0381813	−	0.0102306i	−0.277859	+	0.960622i	$0.589625\pi$
$734$	−16.9289	+	4.53610i	−0.624859	+	0.167430i
$735$	−1.48190	+	0.333994i	−0.0546609	+	0.0123196i
$736$	−6.45722	+	1.73021i	−0.238016	+	0.0637763i
$737$	−39.7443	+	22.9464i	−1.46400	+	0.845242i
$738$	0.630475	−	7.84015i	0.0232081	−	0.288600i
$739$	−44.6085	+	11.9528i	−1.64095	+	0.439691i	−0.957059	−	0.289894i	$-0.906380\pi$
$739$	−44.6085	+	11.9528i	−1.64095	+	0.439691i	−0.683890	+	0.729585i	$0.739713\pi$
$740$	−1.61770	+	2.80194i	−0.0594679	+	0.103001i
$741$	20.7727	−	11.5220i	0.763103	−	0.423273i
$742$	−8.71302	−	15.0914i	−0.319865	−	0.554022i
$743$	−2.28791	−	2.28791i	−0.0839351	−	0.0839351i	0.663893	−	0.747828i	$-0.268903\pi$
$743$	−2.28791	−	2.28791i	−0.0839351	−	0.0839351i	−0.747828	+	0.663893i	$0.768903\pi$
$744$	−1.05008	+	1.66114i	−0.0384979	+	0.0609005i
$745$		−	2.66523i		−	0.0976465i
$746$	8.57528	+	8.57528i	0.313963	+	0.313963i
$747$	−4.08863	+	11.4837i	−0.149595	+	0.420167i
$748$	6.68086	−	24.9333i	0.244277	−	0.911652i
$749$	4.37890	+	16.3423i	0.160001	+	0.597133i
$750$	5.07714	+	3.20949i	0.185391	+	0.117194i
$751$		−	22.0806i		−	0.805733i	−0.915259	−	0.402866i	$-0.868014\pi$
$751$		−	22.0806i		−	0.805733i	0.915259	−	0.402866i	$-0.131986\pi$
$752$	3.05651	−	3.05651i	0.111459	−	0.111459i
$753$	−24.0888	−	15.2276i	−0.877845	−	0.554925i
$754$	10.6623	+	17.5261i	0.388296	+	0.638265i
$755$		−	5.11944i		−	0.186316i
$756$	−15.8539	+	2.25736i	−0.576602	+	0.0820993i
$757$	7.92964	−	13.7345i	0.288208	−	0.499190i	−0.685174	−	0.728379i	$-0.740274\pi$
$757$	7.92964	−	13.7345i	0.288208	−	0.499190i	0.973382	+	0.229189i	$0.0736074\pi$
$758$	6.16338			0.223864
$759$	−37.5968	+	8.47363i	−1.36468	+	0.307573i
$760$	0.345663	+	1.29003i	0.0125385	+	0.0467944i
$761$	3.46597	+	12.9352i	0.125641	+	0.468900i	0.999862	−	0.0166293i	$-0.00529352\pi$
$761$	3.46597	+	12.9352i	0.125641	+	0.468900i	−0.874220	+	0.485529i	$0.838627\pi$
$762$	6.35878	−	20.4172i	0.230354	−	0.739636i
$763$	−9.71784			−0.351809
$764$	0.0745427	−	0.129112i	0.00269686	−	0.00467110i
$765$	−2.73992	+	7.69560i	−0.0990620	+	0.278235i
$766$			14.6073i			0.527785i
$767$	20.5642	+	33.8026i	0.742531	+	1.22054i
$768$	0.0694742	−	1.73066i	0.00250694	−	0.0624497i
$769$	29.6908	−	29.6908i

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)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(-1.53353 + 0.805162i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.0908752 - 0.339151i) q^{5} +(0.380820 + 1.68967i) q^{6} +(-2.17921 - 2.17921i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.70343 - 2.46948i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(-1.53353 + 0.805162i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.0908752 - 0.339151i) q^{5} +(0.380820 + 1.68967i) q^{6} +(-2.17921 - 2.17921i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.70343 - 2.46948i) q^{9} +(-0.304074 - 0.175557i) q^{10} +(-3.21508 - 0.861478i) q^{11} +(1.73066 + 0.0694742i) q^{12} +(-3.46037 + 1.01285i) q^{13} +(-2.66897 + 1.54093i) q^{14} +(0.133712 + 0.593267i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-3.87756 - 6.71613i) q^{17} +(-1.94445 - 2.28453i) q^{18} +(3.67410 + 0.984473i) q^{19} +(-0.248276 + 0.248276i) q^{20} +(5.09649 + 1.58726i) q^{21} +(-1.66425 + 2.88256i) q^{22} -6.68501 q^{23} +(0.515034 - 1.65370i) q^{24} +(4.22336 + 2.43836i) q^{25} +(0.0827293 + 3.60460i) q^{26} +(-0.623927 + 5.15856i) q^{27} +(0.797644 + 2.97685i) q^{28} +(4.92745 - 2.84486i) q^{29} +(0.607659 + 0.0243934i) q^{30} +(-1.09596 - 0.293661i) q^{31} +(0.965926 - 0.258819i) q^{32} +(5.62405 - 1.26756i) q^{33} +(-7.49087 + 2.00717i) q^{34} +(-0.937115 + 0.541044i) q^{35} +(-2.70995 + 1.28692i) q^{36} +(8.90068 - 2.38493i) q^{37} +(1.90186 - 3.29411i) q^{38} +(4.49107 - 4.33939i) q^{39} +(0.175557 + 0.304074i) q^{40} +(1.85391 + 1.85391i) q^{41} +(2.85225 - 4.51202i) q^{42} +4.25976i q^{43} +(2.35360 + 2.35360i) q^{44} +(-0.682727 - 0.802134i) q^{45} +(-1.73021 + 6.45722i) q^{46} +(-1.11876 - 4.17527i) q^{47} +(-1.46406 - 0.925495i) q^{48} +2.49787i q^{49} +(3.44836 - 3.44836i) q^{50} +(11.3539 + 7.17732i) q^{51} +(3.50319 + 0.853029i) q^{52} +5.65439i q^{53} +(4.82130 + 1.93780i) q^{54} +(-0.584342 + 1.01211i) q^{55} +3.08186 q^{56} +(-6.42701 + 1.44853i) q^{57} +(-1.47261 - 5.49586i) q^{58} +(-2.84022 - 10.5998i) q^{59} +(0.180836 - 0.580640i) q^{60} -10.0348 q^{61} +(-0.567309 + 0.982608i) q^{62} +(-9.09362 + 1.66938i) q^{63} -1.00000i q^{64} +(0.0290475 + 1.26563i) q^{65} +(0.231245 - 5.76048i) q^{66} +(9.74949 - 9.74949i) q^{67} +7.75512i q^{68} +(10.2517 - 5.38251i) q^{69} +(0.280065 + 1.04522i) q^{70} +(0.343507 - 1.28199i) q^{71} +(0.541680 + 2.95069i) q^{72} +(-2.19140 - 2.19140i) q^{73} -9.21466i q^{74} +(-8.43993 - 0.338806i) q^{75} +(-2.68963 - 2.68963i) q^{76} +(5.12898 + 8.88365i) q^{77} +(-3.02916 - 5.46115i) q^{78} +(-6.22990 + 10.7905i) q^{79} +(0.339151 - 0.0908752i) q^{80} +(-3.19666 - 8.41316i) q^{81} +(2.27056 - 1.31091i) q^{82} +(-3.92483 + 1.05166i) q^{83} +(-3.62006 - 3.92286i) q^{84} +(-2.63016 + 0.704748i) q^{85} +(4.11462 + 1.10251i) q^{86} +(-5.26582 + 8.33008i) q^{87} +(2.88256 - 1.66425i) q^{88} +(-1.43929 - 5.37149i) q^{89} +(-0.951504 + 0.451856i) q^{90} +(9.74806 + 5.33364i) q^{91} +(5.78938 + 3.34250i) q^{92} +(1.91713 - 0.432085i) q^{93} -4.32256 q^{94} +(0.667770 - 1.15661i) q^{95} +(-1.27288 + 1.17463i) q^{96} +(-0.597770 + 0.597770i) q^{97} +(2.41276 + 0.646496i) q^{98} +(-7.60406 + 6.47211i) 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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