LMFDB - Embedded Newform 31.2.g.a.7.2

Newspace parameters

Level:	$ N $	=	$ 31 $
Weight:	$ k $	=	$ 2 $
Character orbit:	$[\chi]$	=	31.g (of order $15$ and degree $8$)

Newform invariants

Self dual:	No
Analytic conductor:	$0.247536246266$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			7.2
Root			$0.176392i$
Character	$\chi$	=	31.7
Dual form			31.2.g.a.9.2

$q$-expansion

$f(q)$	$=$	$q$$+(0.380762 + 1.17187i) q^{2}$ $+(-2.02963 + 0.431412i) q^{3}$ $+(0.389745 - 0.283166i) q^{4}$ $+(0.772811 - 1.33855i) q^{5}$ $+(-1.27836 - 2.21419i) q^{6}$ $+(-3.47491 - 1.54713i) q^{7}$ $+(2.47393 + 1.79742i) q^{8}$ $+(1.19265 - 0.531003i) q^{9}$ $+O(q^{10})$	$q$$+(0.380762 + 1.17187i) q^{2}$ $+(-2.02963 + 0.431412i) q^{3}$ $+(0.389745 - 0.283166i) q^{4}$ $+(0.772811 - 1.33855i) q^{5}$ $+(-1.27836 - 2.21419i) q^{6}$ $+(-3.47491 - 1.54713i) q^{7}$ $+(2.47393 + 1.79742i) q^{8}$ $+(1.19265 - 0.531003i) q^{9}$ $+(1.86286 + 0.395962i) q^{10}$ $+(0.393186 + 3.74092i) q^{11}$ $+(-0.668878 + 0.742864i) q^{12}$ $+(-1.76320 - 1.95823i) q^{13}$ $+(0.489913 - 4.66121i) q^{14}$ $+(-0.991057 + 3.05016i) q^{15}$ $+(-0.866611 + 2.66715i) q^{16}$ $+(-0.394526 + 3.75366i) q^{17}$ $+(1.07638 + 1.19544i) q^{18}$ $+(4.08057 - 4.53193i) q^{19}$ $+(-0.0778325 - 0.740527i) q^{20}$ $+(7.72023 + 1.64099i) q^{21}$ $+(-4.23414 + 1.88516i) q^{22}$ $+(-0.736082 - 0.534795i) q^{23}$ $+(-5.79659 - 2.58081i) q^{24}$ $+(1.30553 + 2.26124i) q^{25}$ $+(1.62343 - 2.81186i) q^{26}$ $+(2.84451 - 2.06665i) q^{27}$ $+(-1.79242 + 0.380991i) q^{28}$ $+(-2.10397 - 6.47535i) q^{29}$ $-3.95173 q^{30}$ $+(-3.88819 + 3.98522i) q^{31}$ $+2.66037 q^{32}$ $+(-2.41190 - 7.42306i) q^{33}$ $+(-4.54901 + 0.966922i) q^{34}$ $+(-4.75635 + 3.45569i) q^{35}$ $+(0.314468 - 0.544675i) q^{36}$ $+(0.907032 + 1.57103i) q^{37}$ $+(6.86454 + 3.05629i) q^{38}$ $+(4.42345 + 3.21383i) q^{39}$ $+(4.31781 - 1.92241i) q^{40}$ $+(-0.329777 - 0.0700963i) q^{41}$ $+(1.01656 + 9.67189i) q^{42}$ $+(2.59890 - 2.88637i) q^{43}$ $+(1.21255 + 1.34667i) q^{44}$ $+(0.210922 - 2.00679i) q^{45}$ $+(0.346435 - 1.06622i) q^{46}$ $+(-0.367467 + 1.13095i) q^{47}$ $+(0.608260 - 5.78721i) q^{48}$ $+(4.99745 + 5.55023i) q^{49}$ $+(-2.15277 + 2.39089i) q^{50}$ $+(-0.818631 - 7.78876i) q^{51}$ $+(-1.24171 - 0.263933i) q^{52}$ $+(-2.14147 + 0.953442i) q^{53}$ $+(3.50492 + 2.54647i) q^{54}$ $+(5.31126 + 2.36473i) q^{55}$ $+(-5.81584 - 10.0733i) q^{56}$ $+(-6.32692 + 10.9586i) q^{57}$ $+(6.78713 - 4.93114i) q^{58}$ $+(-7.60885 + 1.61731i) q^{59}$ $+(0.477443 + 1.46942i) q^{60}$ $-2.72343 q^{61}$ $+(-6.15062 - 3.03901i) q^{62}$ $-4.96588 q^{63}$ $+(2.74619 + 8.45191i) q^{64}$ $+(-3.98381 + 0.846786i) q^{65}$ $+(7.78047 - 5.65284i) q^{66}$ $+(3.71059 - 6.42693i) q^{67}$ $+(0.909147 + 1.57469i) q^{68}$ $+(1.72469 + 0.767882i) q^{69}$ $+(-5.86065 - 4.25801i) q^{70}$ $+(-4.65742 + 2.07362i) q^{71}$ $+(3.90497 + 0.830027i) q^{72}$ $+(-0.563591 - 5.36221i) q^{73}$ $+(-1.49567 + 1.66111i) q^{74}$ $+(-3.62526 - 4.02626i) q^{75}$ $+(0.307091 - 2.92178i) q^{76}$ $+(4.42139 - 13.6076i) q^{77}$ $+(-2.08189 + 6.40740i) q^{78}$ $+(1.01782 - 9.68388i) q^{79}$ $+(2.90039 + 3.22121i) q^{80}$ $+(-7.50241 + 8.33227i) q^{81}$ $+(-0.0434232 - 0.413145i) q^{82}$ $+(8.21169 + 1.74545i) q^{83}$ $+(3.47359 - 1.54654i) q^{84}$ $+(4.71957 + 3.42897i) q^{85}$ $+(4.37200 + 1.94654i) q^{86}$ $+(7.06383 + 12.2349i) q^{87}$ $+(-5.75127 + 9.96149i) q^{88}$ $+(-4.12243 + 2.99512i) q^{89}$ $+(2.43200 - 0.516937i) q^{90}$ $+(3.09732 + 9.53258i) q^{91}$ $-0.438320 q^{92}$ $+(6.17231 - 9.76595i) q^{93}$ $-1.46523 q^{94}$ $+(-2.91270 - 8.96437i) q^{95}$ $+(-5.39957 + 1.14771i) q^{96}$ $+(-8.82979 + 6.41522i) q^{97}$ $+(-4.60129 + 7.96966i) q^{98}$ $+(2.45537 + 4.25283i) q^{99}$ $+O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$16q $ $\mathstrut -\mathstrut 6q^{2} $ $\mathstrut -\mathstrut 12q^{3} $ $\mathstrut -\mathstrut 14q^{4} $ $\mathstrut -\mathstrut 3q^{5} $ $\mathstrut +\mathstrut 11q^{6} $ $\mathstrut +\mathstrut 2q^{7} $ $\mathstrut +\mathstrut 17q^{8} $ $\mathstrut -\mathstrut 10q^{9} $ $\mathstrut +\mathstrut O(q^{10}) $	$16q $ $\mathstrut -\mathstrut 6q^{2} $ $\mathstrut -\mathstrut 12q^{3} $ $\mathstrut -\mathstrut 14q^{4} $ $\mathstrut -\mathstrut 3q^{5} $ $\mathstrut +\mathstrut 11q^{6} $ $\mathstrut +\mathstrut 2q^{7} $ $\mathstrut +\mathstrut 17q^{8} $ $\mathstrut -\mathstrut 10q^{9} $ $\mathstrut -\mathstrut 2q^{10} $ $\mathstrut -\mathstrut 7q^{11} $ $\mathstrut +\mathstrut 5q^{12} $ $\mathstrut -\mathstrut 7q^{13} $ $\mathstrut -\mathstrut 6q^{14} $ $\mathstrut +\mathstrut 14q^{15} $ $\mathstrut -\mathstrut 2q^{16} $ $\mathstrut -\mathstrut 6q^{17} $ $\mathstrut -\mathstrut 3q^{18} $ $\mathstrut +\mathstrut 16q^{19} $ $\mathstrut +\mathstrut 37q^{20} $ $\mathstrut +\mathstrut 9q^{21} $ $\mathstrut +\mathstrut 9q^{22} $ $\mathstrut +\mathstrut q^{23} $ $\mathstrut -\mathstrut 20q^{24} $ $\mathstrut -\mathstrut 13q^{25} $ $\mathstrut +\mathstrut 9q^{26} $ $\mathstrut +\mathstrut 9q^{27} $ $\mathstrut -\mathstrut 30q^{28} $ $\mathstrut -\mathstrut 14q^{29} $ $\mathstrut -\mathstrut 22q^{30} $ $\mathstrut +\mathstrut 15q^{31} $ $\mathstrut -\mathstrut 42q^{32} $ $\mathstrut -\mathstrut 13q^{33} $ $\mathstrut -\mathstrut 32q^{34} $ $\mathstrut -\mathstrut 9q^{35} $ $\mathstrut +\mathstrut q^{36} $ $\mathstrut -\mathstrut 8q^{37} $ $\mathstrut +\mathstrut 8q^{38} $ $\mathstrut -\mathstrut 3q^{39} $ $\mathstrut -\mathstrut q^{40} $ $\mathstrut -\mathstrut 8q^{41} $ $\mathstrut +\mathstrut 69q^{42} $ $\mathstrut +\mathstrut 23q^{43} $ $\mathstrut +\mathstrut 39q^{44} $ $\mathstrut +\mathstrut 65q^{45} $ $\mathstrut +\mathstrut 34q^{46} $ $\mathstrut +\mathstrut 14q^{47} $ $\mathstrut +\mathstrut 34q^{48} $ $\mathstrut +\mathstrut 2q^{49} $ $\mathstrut +\mathstrut 3q^{50} $ $\mathstrut -\mathstrut 42q^{51} $ $\mathstrut +\mathstrut 29q^{52} $ $\mathstrut +\mathstrut 6q^{53} $ $\mathstrut -\mathstrut 46q^{54} $ $\mathstrut -\mathstrut 7q^{55} $ $\mathstrut -\mathstrut 30q^{56} $ $\mathstrut -\mathstrut 17q^{57} $ $\mathstrut -\mathstrut 15q^{58} $ $\mathstrut +\mathstrut 4q^{59} $ $\mathstrut -\mathstrut 75q^{60} $ $\mathstrut -\mathstrut 60q^{61} $ $\mathstrut -\mathstrut 25q^{62} $ $\mathstrut -\mathstrut 46q^{63} $ $\mathstrut +\mathstrut 23q^{64} $ $\mathstrut -\mathstrut 12q^{65} $ $\mathstrut -\mathstrut 30q^{66} $ $\mathstrut +\mathstrut 13q^{67} $ $\mathstrut +\mathstrut 30q^{68} $ $\mathstrut +\mathstrut 38q^{69} $ $\mathstrut +\mathstrut 12q^{70} $ $\mathstrut -\mathstrut 14q^{71} $ $\mathstrut +\mathstrut 37q^{72} $ $\mathstrut +\mathstrut 2q^{73} $ $\mathstrut +\mathstrut 13q^{74} $ $\mathstrut +\mathstrut 13q^{75} $ $\mathstrut -\mathstrut 12q^{76} $ $\mathstrut +\mathstrut 18q^{77} $ $\mathstrut -\mathstrut 15q^{78} $ $\mathstrut +\mathstrut 18q^{79} $ $\mathstrut +\mathstrut 36q^{80} $ $\mathstrut +\mathstrut 23q^{81} $ $\mathstrut +\mathstrut 14q^{82} $ $\mathstrut -\mathstrut 16q^{83} $ $\mathstrut +\mathstrut 8q^{84} $ $\mathstrut +\mathstrut 37q^{85} $ $\mathstrut -\mathstrut 26q^{86} $ $\mathstrut +\mathstrut 15q^{87} $ $\mathstrut -\mathstrut 17q^{88} $ $\mathstrut +\mathstrut q^{89} $ $\mathstrut -\mathstrut 23q^{90} $ $\mathstrut +\mathstrut 8q^{91} $ $\mathstrut -\mathstrut 64q^{92} $ $\mathstrut +\mathstrut 17q^{93} $ $\mathstrut +\mathstrut 44q^{94} $ $\mathstrut -\mathstrut 22q^{95} $ $\mathstrut +\mathstrut 8q^{96} $ $\mathstrut +\mathstrut 3q^{97} $ $\mathstrut -\mathstrut 10q^{98} $ $\mathstrut +\mathstrut 6q^{99} $ $\mathstrut +\mathstrut O(q^{100}) $

Display 100 coefficients 10 coefficients

Character Values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{14}{15}\right)$

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 $

$2$	0.380762	+	1.17187i	0.269240	+	0.828634i	0.990686	+	0.136164i	$0.0434774\pi$
$2$	0.380762	+	1.17187i	0.269240	+	0.828634i	−0.721447	+	0.692470i	$0.756523\pi$
$3$	−2.02963	+	0.431412i	−1.17181	+	0.249076i	−0.752390	−	0.658718i	$-0.771099\pi$
$3$	−2.02963	+	0.431412i	−1.17181	+	0.249076i	−0.419418	+	0.907793i	$0.637766\pi$
$4$	0.389745	−	0.283166i	0.194873	−	0.141583i
$5$	0.772811	−	1.33855i	0.345612	−	0.598617i	−0.639853	−	0.768497i	$-0.721005\pi$
$5$	0.772811	−	1.33855i	0.345612	−	0.598617i	0.985465	+	0.169880i	$0.0543381\pi$
$6$	−1.27836	−	2.21419i	−0.521890	−	0.903939i
$7$	−3.47491	−	1.54713i	−1.31339	−	0.584759i	−0.373943	−	0.927452i	$-0.621995\pi$
$7$	−3.47491	−	1.54713i	−1.31339	−	0.584759i	−0.939448	+	0.342692i	$0.888661\pi$
$8$	2.47393	+	1.79742i	0.874666	+	0.635482i
$9$	1.19265	−	0.531003i	0.397551	−	0.177001i
$10$	1.86286	+	0.395962i	0.589087	+	0.125214i
$11$	0.393186	+	3.74092i	0.118550	+	1.12793i	0.878432	+	0.477868i	$0.158590\pi$
$11$	0.393186	+	3.74092i	0.118550	+	1.12793i	−0.759882	+	0.650061i	$0.774743\pi$
$12$	−0.668878	+	0.742864i	−0.193088	+	0.214446i
$13$	−1.76320	−	1.95823i	−0.489024	−	0.543116i	0.447240	−	0.894414i	$-0.352407\pi$
$13$	−1.76320	−	1.95823i	−0.489024	−	0.543116i	−0.936264	+	0.351298i	$0.885740\pi$
$14$	0.489913	−	4.66121i	0.130935	−	1.24576i
$15$	−0.991057	+	3.05016i	−0.255890	+	0.787548i
$16$	−0.866611	+	2.66715i	−0.216653	+	0.666789i
$17$	−0.394526	+	3.75366i	−0.0956866	+	0.910397i	0.836390	+	0.548135i	$0.184662\pi$
$17$	−0.394526	+	3.75366i	−0.0956866	+	0.910397i	−0.932076	+	0.362262i	$0.882005\pi$
$18$	1.07638	+	1.19544i	0.253705	+	0.281768i
$19$	4.08057	−	4.53193i	0.936147	−	1.03970i	−0.0629842	−	0.998015i	$-0.520062\pi$
$19$	4.08057	−	4.53193i	0.936147	−	1.03970i	0.999131	−	0.0416817i	$-0.0132716\pi$
$20$	−0.0778325	−	0.740527i	−0.0174039	−	0.165587i
$21$	7.72023	+	1.64099i	1.68469	+	0.358092i
$22$	−4.23414	+	1.88516i	−0.902722	+	0.401918i
$23$	−0.736082	−	0.534795i	−0.153484	−	0.111512i	0.508393	−	0.861125i	$-0.330240\pi$
$23$	−0.736082	−	0.534795i	−0.153484	−	0.111512i	−0.661877	+	0.749613i	$0.730240\pi$
$24$	−5.79659	−	2.58081i	−1.18322	−	0.526805i
$25$	1.30553	+	2.26124i	0.261105	+	0.452247i
$26$	1.62343	−	2.81186i	0.318380	−	0.551450i
$27$	2.84451	−	2.06665i	0.547425	−	0.397728i
$28$	−1.79242	+	0.380991i	−0.338736	+	0.0720006i
$29$	−2.10397	−	6.47535i	−0.390697	−	1.20244i	−0.932262	−	0.361784i	$-0.882168\pi$
$29$	−2.10397	−	6.47535i	−0.390697	−	1.20244i	0.541565	−	0.840659i	$-0.317832\pi$
$30$	−3.95173			−0.721485
$31$	−3.88819	+	3.98522i	−0.698339	+	0.715767i
$31$	−3.88819	+	3.98522i	−0.698339	+	0.715767i
$32$	2.66037			0.470292
$33$	−2.41190	−	7.42306i	−0.419858	−	1.29219i
$34$	−4.54901	+	0.966922i	−0.780149	+	0.165826i
$35$	−4.75635	+	3.45569i	−0.803970	+	0.584119i
$36$	0.314468	−	0.544675i	0.0524114	−	0.0907792i
$37$	0.907032	+	1.57103i	0.149115	+	0.258275i	0.930901	−	0.365272i	$-0.119024\pi$
$37$	0.907032	+	1.57103i	0.149115	+	0.258275i	−0.781786	+	0.623547i	$0.785691\pi$
$38$	6.86454	+	3.05629i	1.11358	+	0.495796i
$39$	4.42345	+	3.21383i	0.708320	+	0.514624i
$40$	4.31781	−	1.92241i	0.682705	−	0.303960i
$41$	−0.329777	−	0.0700963i	−0.0515026	−	0.0109472i	0.182088	−	0.983282i	$-0.441714\pi$
$41$	−0.329777	−	0.0700963i	−0.0515026	−	0.0109472i	−0.233591	+	0.972335i	$0.575048\pi$
$42$	1.01656	+	9.67189i	0.156858	+	1.49241i
$43$	2.59890	−	2.88637i	0.396329	−	0.440167i	−0.511644	−	0.859198i	$-0.670963\pi$
$43$	2.59890	−	2.88637i	0.396329	−	0.440167i	0.907972	+	0.419030i	$0.137630\pi$
$44$	1.21255	+	1.34667i	0.182798	+	0.203018i
$45$	0.210922	−	2.00679i	0.0314424	−	0.299154i
$46$	0.346435	−	1.06622i	0.0510791	−	0.157205i
$47$	−0.367467	+	1.13095i	−0.0536005	+	0.164965i	−0.974273	−	0.225370i	$-0.927641\pi$
$47$	−0.367467	+	1.13095i	−0.0536005	+	0.164965i	0.920673	+	0.390335i	$0.127641\pi$
$48$	0.608260	−	5.78721i	0.0877948	−	0.835311i
$49$	4.99745	+	5.55023i	0.713922	+	0.792890i
$50$	−2.15277	+	2.39089i	−0.304448	+	0.338123i
$51$	−0.818631	−	7.78876i	−0.114631	−	1.09064i
$52$	−1.24171	−	0.263933i	−0.172194	−	0.0366009i
$53$	−2.14147	+	0.953442i	−0.294153	+	0.130965i	−0.548507	−	0.836146i	$-0.684804\pi$
$53$	−2.14147	+	0.953442i	−0.294153	+	0.130965i	0.254354	+	0.967111i	$0.418137\pi$
$54$	3.50492	+	2.54647i	0.476959	+	0.346531i
$55$	5.31126	+	2.36473i	0.716170	+	0.318859i
$56$	−5.81584	−	10.0733i	−0.777175	−	1.34611i
$57$	−6.32692	+	10.9586i	−0.838022	+	1.45150i
$58$	6.78713	−	4.93114i	0.891194	−	0.647490i
$59$	−7.60885	+	1.61731i	−0.990587	+	0.210556i	−0.674581	−	0.738201i	$-0.735676\pi$
$59$	−7.60885	+	1.61731i	−0.990587	+	0.210556i	−0.316007	+	0.948757i	$0.602342\pi$
$60$	0.477443	+	1.46942i	0.0616377	+	0.189701i
$61$	−2.72343			−0.348700			−0.174350	−	0.984684i	$-0.555782\pi$
$61$	−2.72343			−0.348700			−0.174350	+	0.984684i	$0.555782\pi$
$62$	−6.15062	−	3.03901i	−0.781130	−	0.385954i
$63$	−4.96588			−0.625642
$64$	2.74619	+	8.45191i	0.343274	+	1.05649i
$65$	−3.98381	+	0.846786i	−0.494131	+	0.105031i
$66$	7.78047	−	5.65284i	0.957709	−	0.695817i
$67$	3.71059	−	6.42693i	0.453321	−	0.785175i	−0.545269	−	0.838261i	$-0.683573\pi$
$67$	3.71059	−	6.42693i	0.453321	−	0.785175i	0.998590	+	0.0530864i	$0.0169059\pi$
$68$	0.909147	+	1.57469i	0.110250	+	0.190959i
$69$	1.72469	+	0.767882i	0.207628	+	0.0924421i
$70$	−5.86065	−	4.25801i	−0.700481	−	0.508929i
$71$	−4.65742	+	2.07362i	−0.552734	+	0.246093i	−0.664045	−	0.747693i	$-0.731162\pi$
$71$	−4.65742	+	2.07362i	−0.552734	+	0.246093i	0.111311	+	0.993786i	$0.464495\pi$
$72$	3.90497	+	0.830027i	0.460205	+	0.0978196i
$73$	−0.563591	−	5.36221i	−0.0659633	−	0.627599i	−0.976700	−	0.214611i	$-0.931152\pi$
$73$	−0.563591	−	5.36221i	−0.0659633	−	0.627599i	0.910736	−	0.412988i	$-0.135515\pi$
$74$	−1.49567	+	1.66111i	−0.173868	+	0.193100i
$75$	−3.62526	−	4.02626i	−0.418609	−	0.464912i
$76$	0.307091	−	2.92178i	0.0352258	−	0.335151i
$77$	4.42139	−	13.6076i	0.503865	−	1.55074i
$78$	−2.08189	+	6.40740i	−0.235728	+	0.725495i
$79$	1.01782	−	9.68388i	0.114513	−	1.08952i	−0.774795	−	0.632213i	$-0.782147\pi$
$79$	1.01782	−	9.68388i	0.114513	−	1.08952i	0.889308	−	0.457309i	$-0.151187\pi$
$80$	2.90039	+	3.22121i	0.324273	+	0.360142i
$81$	−7.50241	+	8.33227i	−0.833601	+	0.925808i
$82$	−0.0434232	−	0.413145i	−0.00479530	−	0.0456242i
$83$	8.21169	+	1.74545i	0.901350	+	0.191588i	0.635204	−	0.772345i	$-0.280916\pi$
$83$	8.21169	+	1.74545i	0.901350	+	0.191588i	0.266147	+	0.963933i	$0.414249\pi$
$84$	3.47359	−	1.54654i	0.379000	−	0.168742i
$85$	4.71957	+	3.42897i	0.511909	+	0.371924i
$86$	4.37200	+	1.94654i	0.471445	+	0.209901i
$87$	7.06383	+	12.2349i	0.757322	+	1.31172i
$88$	−5.75127	+	9.96149i	−0.613087	+	1.06190i
$89$	−4.12243	+	2.99512i	−0.436976	+	0.317482i	−0.784432	−	0.620214i	$-0.787046\pi$
$89$	−4.12243	+	2.99512i	−0.436976	+	0.317482i	0.347456	+	0.937696i	$0.387046\pi$
$90$	2.43200	−	0.516937i	0.256355	−	0.0544899i
$91$	3.09732	+	9.53258i	0.324688	+	0.999285i
$92$	−0.438320			−0.0456980
$93$	6.17231	−	9.76595i	0.640039	−	1.01268i
$94$	−1.46523			−0.151127
$95$	−2.91270	−	8.96437i	−0.298837	−	0.919725i
$96$	−5.39957	+	1.14771i	−0.551092	+	0.117138i
$97$	−8.82979	+	6.41522i	−0.896530	+	0.651367i	−0.937572	−	0.347791i	$-0.886932\pi$
$97$	−8.82979	+	6.41522i	−0.896530	+	0.651367i	0.0410427	+	0.999157i	$0.486932\pi$
$98$	−4.60129	+	7.96966i	−0.464800	+	0.805057i
$99$	2.45537	+	4.25283i	0.246774	+	0.427426i
$100$	1.14913	+	0.511625i	0.114913	+	0.0511625i
$101$	0.322577	+	0.234366i	0.0320976	+	0.0233203i	0.603718	−	0.797198i	$-0.293685\pi$
$101$	0.322577	+	0.234366i	0.0320976	+	0.0233203i	−0.571621	+	0.820518i	$0.693685\pi$
$102$	8.81567	−	3.92499i	0.872881	−	0.388632i
$103$	−3.20520	−	0.681286i	−0.315817	−	0.0671291i	0.0472758	−	0.998882i	$-0.484946\pi$
$103$	−3.20520	−	0.681286i	−0.315817	−	0.0671291i	−0.363093	+	0.931753i	$0.618279\pi$
$104$	−0.842278	−	8.01374i	−0.0825921	−	0.785812i
$105$	8.16282	−	9.06573i	0.796609	−	0.884724i
$106$	−1.93269	−	2.14647i	−0.187720	−	0.208484i
$107$	−0.329980	+	3.13955i	−0.0319004	+	0.303512i	0.966925	+	0.255060i	$0.0820953\pi$
$107$	−0.329980	+	3.13955i	−0.0319004	+	0.303512i	−0.998826	+	0.0484517i	$0.984571\pi$
$108$	0.523425	−	1.61094i	0.0503666	−	0.155013i
$109$	2.14959	−	6.61576i	0.205893	−	0.633675i	−0.793782	−	0.608202i	$-0.791891\pi$
$109$	2.14959	−	6.61576i	0.205893	−	0.633675i	0.999676	−	0.0254724i	$-0.00810899\pi$
$110$	−0.748813	+	7.12448i	−0.0713965	+	0.679292i
$111$	−2.51870	−	2.79730i	−0.239064	−	0.265508i
$112$	7.13782	−	7.92735i	0.674461	−	0.749064i
$113$	1.59372	+	15.1633i	0.149925	+	1.42644i	0.768065	+	0.640372i	$0.221220\pi$
$113$	1.59372	+	15.1633i	0.149925	+	1.42644i	−0.618140	+	0.786068i	$0.712114\pi$
$114$	−15.2510	−	3.24170i	−1.42839	−	0.303613i
$115$	−1.28470	+	0.571986i	−0.119799	+	0.0533379i
$116$	−2.65362	−	1.92796i	−0.246382	−	0.179007i
$117$	−3.14271	−	1.39923i	−0.290544	−	0.129359i
$118$	−4.79243	−	8.30073i	−0.441179	−	0.764144i
$119$	7.17834	−	12.4332i	0.658037	−	1.13975i
$120$	−7.93421	+	5.76454i	−0.724291	+	0.526228i
$121$	−3.08025	+	0.654727i	−0.280023	+	0.0595207i
$122$	−1.03698	−	3.19150i	−0.0938838	−	0.288945i
$123$	0.699567			0.0630778
$124$	−0.386920	+	2.65423i	−0.0347464	+	0.238357i
$125$	11.7638			1.05219
$126$	−1.89082	−	5.81935i	−0.168448	−	0.518429i
$127$	19.7844	−	4.20530i	1.75558	−	0.373160i	0.786055	−	0.618156i	$-0.212120\pi$
$127$	19.7844	−	4.20530i	1.75558	−	0.373160i	0.969524	+	0.244996i	$0.0787867\pi$
$128$	−4.55428	+	3.30888i	−0.402545	+	0.292466i
$129$	−4.02960	+	6.97946i	−0.354786	+	0.614508i
$130$	−2.50920	−	4.34607i	−0.220072	−	0.381175i
$131$	11.5575	+	5.14574i	1.00979	+	0.449585i	0.843866	−	0.536554i	$-0.180274\pi$
$131$	11.5575	+	5.14574i	1.00979	+	0.449585i	0.165919	+	0.986139i	$0.446941\pi$
$132$	−3.04199	−	2.21013i	−0.264771	−	0.192367i
$133$	−21.1911	+	9.43487i	−1.83750	+	0.818107i
$134$	8.94435	+	1.90118i	0.772674	+	0.164237i
$135$	−0.568051	−	5.40464i	−0.0488900	−	0.465158i
$136$	−7.72292	+	8.57717i	−0.662235	+	0.735486i
$137$	−6.60968	−	7.34079i	−0.564703	−	0.627166i	0.391392	−	0.920224i	$-0.371994\pi$
$137$	−6.60968	−	7.34079i	−0.564703	−	0.627166i	−0.956095	+	0.293058i	$0.905327\pi$
$138$	−0.243157	+	2.31349i	−0.0206989	+	0.196937i
$139$	−4.78945	+	14.7404i	−0.406236	+	1.25026i	0.513623	+	0.858016i	$0.328303\pi$
$139$	−4.78945	+	14.7404i	−0.406236	+	1.25026i	−0.919859	+	0.392249i	$0.871697\pi$
$140$	−0.875229	+	2.69368i	−0.0739704	+	0.227657i
$141$	0.257919	−	2.45393i	0.0217207	−	0.206658i
$142$	−4.20337	−	4.66831i	−0.352739	−	0.391756i
$143$	6.63233	−	7.36594i	0.554623	−	0.615971i
$144$	0.382701	+	3.64116i	0.0318918	+	0.303430i
$145$	−10.2935	−	2.18796i	−0.854833	−	0.181700i
$146$	6.06919	−	2.70218i	0.502290	−	0.223634i
$147$	−12.5374	−	9.10897i	−1.03407	−	0.751295i
$148$	0.798373	+	0.355459i	0.0656259	+	0.0292185i
$149$	7.62162	+	13.2010i	0.624388	+	1.08147i	0.988659	+	0.150178i	$0.0479848\pi$
$149$	7.62162	+	13.2010i	0.624388	+	1.08147i	−0.364271	+	0.931293i	$0.618682\pi$
$150$	3.33787	−	5.78136i	0.272536	−	0.472046i
$151$	0.211823	−	0.153899i	0.0172379	−	0.0125241i	−0.579133	−	0.815233i	$-0.696609\pi$
$151$	0.211823	−	0.153899i	0.0172379	−	0.0125241i	0.596371	+	0.802709i	$0.296609\pi$
$152$	18.2408	−	3.87720i	1.47952	−	0.314483i
$153$	1.52267	+	4.68631i	0.123101	+	0.378866i
$154$	17.6298			1.42065
$155$	2.32958	+	8.28435i	0.187117	+	0.665415i
$156$	2.63407			0.210894
$157$	4.92157	+	15.1470i	0.392784	+	1.20886i	0.930674	+	0.365850i	$0.119222\pi$
$157$	4.92157	+	15.1470i	0.392784	+	1.20886i	−0.537890	+	0.843015i	$0.680778\pi$
$158$	11.7358	−	2.49451i	0.933647	−	0.198453i
$159$	3.93506	−	2.85899i	0.312071	−	0.226733i
$160$	2.05597	−	3.56104i	0.162538	−	0.281525i
$161$	1.73042	+	2.99717i	0.136376	+	0.236210i
$162$	−12.6209	−	5.61920i	−0.991594	−	0.441486i
$163$	0.107741	+	0.0782785i	0.00843894	+	0.00613125i	0.591997	−	0.805940i	$-0.298340\pi$
$163$	0.107741	+	0.0782785i	0.00843894	+	0.00613125i	−0.583558	+	0.812072i	$0.698340\pi$
$164$	−0.148378	+	0.0660621i	−0.0115864	+	0.00515859i
$165$	−11.8001	−	2.50818i	−0.918634	−	0.195262i
$166$	1.08127	+	10.2876i	0.0839228	+	0.798472i
$167$	−2.64225	+	2.93451i	−0.204463	+	0.227080i	−0.836652	−	0.547735i	$-0.815490\pi$
$167$	−2.64225	+	2.93451i	−0.204463	+	0.227080i	0.632188	+	0.774815i	$0.282157\pi$
$168$	16.1498	+	17.9361i	1.24598	+	1.38380i
$169$	0.633070	−	6.02326i	0.0486977	−	0.463328i
$170$	−2.22125	+	6.83632i	−0.170362	+	0.524322i
$171$	2.46023	−	7.57181i	0.188139	−	0.579031i
$172$	0.195585	−	1.86087i	0.0149132	−	0.141890i
$173$	−9.67358	−	10.7436i	−0.735469	−	0.816821i	0.253124	−	0.967434i	$-0.418542\pi$
$173$	−9.67358	−	10.7436i	−0.735469	−	0.816821i	−0.988593	+	0.150613i	$0.951875\pi$
$174$	−11.6480	+	12.9364i	−0.883035	+	0.980709i
$175$	−1.03816	−	9.87740i	−0.0784772	−	0.746661i
$176$	−10.3183	−	2.19323i	−0.777775	−	0.165321i
$177$	14.7454	−	6.56509i	1.10833	−	0.493462i
$178$	−5.07954	−	3.69050i	−0.380727	−	0.276615i
$179$	−16.1879	−	7.20733i	−1.20994	−	0.538701i	−0.300201	−	0.953876i	$-0.597054\pi$
$179$	−16.1879	−	7.20733i	−1.20994	−	0.538701i	−0.909741	+	0.415175i	$0.863720\pi$
$180$	−0.486049	−	0.841862i	−0.0362280	−	0.0627487i
$181$	6.02958	−	10.4435i	0.448175	−	0.776262i	−0.550092	−	0.835104i	$-0.685407\pi$
$181$	6.02958	−	10.4435i	0.448175	−	0.776262i	0.998267	+	0.0588418i	$0.0187408\pi$
$182$	−9.99155	+	7.25929i	−0.740623	+	0.538094i
$183$	5.52757	−	1.17492i	0.408609	−	0.0868526i
$184$	−0.859766	−	2.64609i	−0.0633828	−	0.195072i
$185$	2.80386			0.206144
$186$	13.7946	+	3.51462i	1.01147	+	0.257704i
$187$	−14.1973			−1.03821
$188$	0.177028	+	0.544835i	0.0129111	+	0.0397362i
$189$	−13.0818	+	2.78062i	−0.951559	+	0.202260i
$190$	9.39599	−	6.82658i	0.681656	−	0.495252i
$191$	−2.53576	+	4.39207i	−0.183481	+	0.317799i	−0.943064	−	0.332612i	$-0.892070\pi$
$191$	−2.53576	+	4.39207i	−0.183481	+	0.317799i	0.759583	+	0.650411i	$0.225403\pi$
$192$	−9.22001	−	15.9695i	−0.665397	−	1.15250i
$193$	−18.3090	−	8.15171i	−1.31791	−	0.586773i	−0.377250	−	0.926112i	$-0.623130\pi$
$193$	−18.3090	−	8.15171i	−1.31791	−	0.586773i	−0.940664	+	0.339339i	$0.889797\pi$
$194$	−10.8798	−	7.90466i	−0.781126	−	0.567521i
$195$	7.72036	−	3.43733i	0.552866	−	0.246152i
$196$	3.51937	+	0.748066i	0.251384	+	0.0534333i
$197$	−2.26914	−	21.5894i	−0.161670	−	1.53818i	−0.711367	−	0.702820i	$-0.751924\pi$
$197$	−2.26914	−	21.5894i	−0.161670	−	1.53818i	0.549698	−	0.835364i	$-0.314743\pi$
$198$	−4.04883	+	4.49668i	−0.287738	+	0.319565i
$199$	10.1477	+	11.2702i	0.719352	+	0.798921i	0.986330	−	0.164781i	$-0.0526919\pi$
$199$	10.1477	+	11.2702i	0.719352	+	0.798921i	−0.266978	+	0.963703i	$0.586025\pi$
$200$	−0.834602	+	7.94071i	−0.0590153	+	0.561493i
$201$	−4.75848	+	14.6451i	−0.335637	+	1.03299i
$202$	−0.151820	+	0.467255i	−0.0106820	+	0.0328759i
$203$	−2.70710	+	25.7564i	−0.190001	+	1.80774i
$204$	−2.52457	−	2.80382i	−0.176755	−	0.196307i
$205$	−0.348683	+	0.387252i	−0.0243531	+	0.0270468i
$206$	−0.422043	−	4.01547i	−0.0294051	−	0.279771i
$207$	−1.16187	−	0.246962i	−0.0807553	−	0.0171651i
$208$	6.75092	−	3.00570i	0.468092	−	0.208408i
$209$	18.5580	+	13.4832i	1.28368	+	0.932651i
$210$	13.7319	+	6.11384i	0.947591	+	0.421895i
$211$	−3.15220	−	5.45978i	−0.217007	−	0.375867i	0.736885	−	0.676018i	$-0.236296\pi$
$211$	−3.15220	−	5.45978i	−0.217007	−	0.375867i	−0.953891	+	0.300152i	$0.902963\pi$
$212$	−0.564643	+	0.977990i	−0.0387798	+	0.0671687i
$213$	8.55826	−	6.21794i	0.586403	−	0.426046i
$214$	−3.80478	+	0.808730i	−0.260089	+	0.0552837i
$215$	−1.85509	−	5.70937i	−0.126516	−	0.389376i
$216$	10.7517			0.731564
$217$	19.6767	−	7.83276i	1.33574	−	0.531722i
$218$	8.57126			0.580519
$219$	3.45720	+	10.6402i	0.233616	+	0.718996i
$220$	2.73965	−	0.582330i	0.184707	−	0.0392607i
$221$	8.04618	−	5.84589i	0.541245	−	0.393237i
$222$	2.31903	−	4.01668i	0.155643	−	0.269582i
$223$	−3.69455	−	6.39915i	−0.247406	−	0.428519i	0.715400	−	0.698716i	$-0.246245\pi$
$223$	−3.69455	−	6.39915i	−0.247406	−	0.428519i	−0.962805	+	0.270196i	$0.912911\pi$
$224$	−9.24454	−	4.11594i	−0.617677	−	0.275007i
$225$	2.75776	+	2.00363i	0.183851	+	0.133575i
$226$	−17.1625	+	7.64123i	−1.14163	+	0.508287i
$227$	−18.8193	−	4.00018i	−1.24908	−	0.265501i	−0.464528	−	0.885559i	$-0.653776\pi$
$227$	−18.8193	−	4.00018i	−1.24908	−	0.265501i	−0.784556	+	0.620058i	$0.787109\pi$
$228$	0.637207	+	6.06262i	0.0422000	+	0.401507i
$229$	−4.07307	+	4.52360i	−0.269156	+	0.298928i	−0.862537	−	0.505994i	$-0.831126\pi$
$229$	−4.07307	+	4.52360i	−0.269156	+	0.298928i	0.593381	+	0.804921i	$0.297793\pi$
$230$	−1.15946	−	1.28771i	−0.0764523	−	0.0849088i
$231$	−3.10330	+	29.5260i	−0.204182	+	1.94267i
$232$	6.43383	−	19.8013i	0.422401	−	1.30002i
$233$	5.41646	−	16.6702i	0.354844	−	1.09210i	−0.601255	−	0.799057i	$-0.705333\pi$
$233$	5.41646	−	16.6702i	0.354844	−	1.09210i	0.956100	−	0.293042i	$-0.0946675\pi$
$234$	0.443078	−	4.21561i	0.0289649	−	0.275583i
$235$	1.22984	+	1.36588i	0.0802262	+	0.0891002i
$236$	−2.50754	+	2.78491i	−0.163227	+	0.181282i
$237$	2.11195	+	20.0938i	0.137186	+	1.30523i
$238$	17.3033	+	3.67794i	1.12161	+	0.238405i
$239$	−25.4989	+	11.3529i	−1.64939	+	0.734355i	−0.999667	−	0.0258176i	$-0.991781\pi$
$239$	−25.4989	+	11.3529i	−1.64939	+	0.734355i	−0.649721	+	0.760172i	$0.725114\pi$
$240$	−7.27639	−	5.28660i	−0.469689	−	0.341249i
$241$	20.7829	+	9.25315i	1.33875	+	0.596048i	0.946169	−	0.323672i	$-0.104917\pi$
$241$	20.7829	+	9.25315i	1.33875	+	0.596048i	0.392576	+	0.919720i	$0.371584\pi$
$242$	−1.94010	−	3.36034i	−0.124714	−	0.216011i
$243$	6.35849	−	11.0132i	0.407897	−	0.706499i
$244$	−1.06144	+	0.771185i	−0.0679520	+	0.0493701i
$245$	11.2913	−	2.40005i	0.721378	−	0.153334i
$246$	0.266369	+	0.819798i	0.0169830	+	0.0522684i
$247$	−16.0694			−1.02247
$248$	−16.7822	+	2.87048i	−1.06567	+	0.182276i
$249$	−17.4197			−1.10393
$250$	4.47921	+	13.7856i	0.283290	+	0.871878i
$251$	15.8797	−	3.37534i	1.00232	−	0.213050i	0.322611	−	0.946532i	$-0.395439\pi$
$251$	15.8797	−	3.37534i	1.00232	−	0.213050i	0.679709	+	0.733482i	$0.262106\pi$
$252$	−1.93543	+	1.40617i	−0.121921	+	0.0885805i
$253$	1.71121	−	2.96390i	0.107583	−	0.186339i
$254$	12.4612	+	21.5834i	0.781884	+	1.35426i
$255$	−11.0583	−	4.92346i	−0.692496	−	0.308319i
$256$	8.76759	+	6.37002i	0.547974	+	0.398126i
$257$	21.3332	−	9.49816i	1.33073	−	0.592479i	0.386659	−	0.922223i	$-0.373629\pi$
$257$	21.3332	−	9.49816i	1.33073	−	0.592479i	0.944070	+	0.329744i	$0.106963\pi$
$258$	−9.71331	−	2.06463i	−0.604724	−	0.128538i
$259$	−0.721274	−	6.86246i	−0.0448178	−	0.426412i
$260$	−1.31289	+	1.45811i	−0.0814220	+	0.0904283i
$261$	−5.94774	−	6.60563i	−0.368156	−	0.408878i
$262$	−1.62945	+	15.5032i	−0.100668	+	0.957789i
$263$	−3.21203	+	9.88562i	−0.198062	+	0.609574i	0.801865	+	0.597506i	$0.203841\pi$
$263$	−3.21203	+	9.88562i	−0.198062	+	0.609574i	−0.999927	+	0.0120680i	$0.996159\pi$
$264$	7.37545	−	22.6993i	0.453928	−	1.39705i
$265$	−0.378721	+	3.60329i	−0.0232646	+	0.221348i
$266$	−19.1252	−	21.2406i	−1.17264	−	1.30235i
$267$	7.07488	−	7.85745i	0.432975	−	0.480868i
$268$	−0.373707	−	3.55558i	−0.0228278	−	0.217192i
$269$	4.32150	+	0.918563i	0.263487	+	0.0560058i	0.337761	−	0.941232i	$-0.390331\pi$
$269$	4.32150	+	0.918563i	0.263487	+	0.0560058i	−0.0742740	+	0.997238i	$0.523664\pi$
$270$	6.11722	−	2.72356i	0.372282	−	0.165751i
$271$	−4.97777	−	3.61656i	−0.302378	−	0.219691i	0.426241	−	0.904610i	$-0.359838\pi$
$271$	−4.97777	−	3.61656i	−0.302378	−	0.219691i	−0.728619	+	0.684919i	$0.759838\pi$
$272$	−9.66970	−	4.30523i	−0.586312	−	0.261043i
$273$	−10.3989	−	18.0114i	−0.629369	−	1.09010i
$274$	6.08571	−	10.5408i	0.367651	−	0.636790i
$275$	−7.94578	+	5.77295i	−0.479149	+	0.348122i
$276$	0.889629	−	0.189096i	0.0535493	−	0.0113823i
$277$	6.81302	+	20.9683i	0.409355	+	1.25987i	0.917204	+	0.398419i	$0.130441\pi$
$277$	6.81302	+	20.9683i	0.409355	+	1.25987i	−0.507849	+	0.861446i	$0.669559\pi$
$278$	−19.0974			−1.14539
$279$	−2.52109	+	6.81762i	−0.150933	+	0.408160i
$280$	−17.9782			−1.07440
$281$	−9.50955	−	29.2674i	−0.567292	−	1.74595i	−0.661040	−	0.750351i	$-0.729885\pi$
$281$	−9.50955	−	29.2674i	−0.567292	−	1.74595i	0.0937474	−	0.995596i	$-0.470115\pi$
$282$	2.97389	−	0.632119i	0.177092	−	0.0376421i
$283$	17.2687	−	12.5464i	1.02652	−	0.745807i	0.0589075	−	0.998263i	$-0.481238\pi$
$283$	17.2687	−	12.5464i	1.02652	−	0.745807i	0.967608	+	0.252456i	$0.0812383\pi$
$284$	−1.22803	+	2.12701i	−0.0728701	+	0.126215i
$285$	9.77904	+	16.9378i	0.579260	+	1.00331i
$286$	11.1572	+	4.96752i	0.659741	+	0.293736i
$287$	1.03750	+	0.753786i	0.0612415	+	0.0444946i
$288$	3.17290	−	1.41267i	0.186965	−	0.0832421i
$289$	2.69417	+	0.572664i	0.158481	+	0.0336861i
$290$	−1.35540	−	12.8957i	−0.0795917	−	0.757264i
$291$	15.1536	−	16.8298i	0.888321	−	0.986581i
$292$	−1.73805	−	1.93030i	−0.101712	−	0.112963i
$293$	0.188050	−	1.78917i	0.0109860	−	0.104525i	−0.987655	−	0.156646i	$-0.949932\pi$
$293$	0.188050	−	1.78917i	0.0109860	−	0.104525i	0.998641	+	0.0521218i	$0.0165984\pi$
$294$	5.90071	−	18.1605i	0.344136	−	1.05914i
$295$	−3.71535	+	11.4347i	−0.216316	+	0.665753i
$296$	−0.579852	+	5.51692i	−0.0337032	+	0.320664i
$297$	8.84961	+	9.82848i	0.513506	+	0.570306i
$298$	−12.5678	+	13.9580i	−0.728034	+	0.808564i
$299$	0.250607	+	2.38437i	0.0144930	+	0.137892i
$300$	−2.55303	−	0.542663i	−0.147399	−	0.0313307i
$301$	−13.4965	+	6.00904i	−0.777926	+	0.346355i
$302$	0.261003	+	0.189630i	0.0150190	+	0.0109120i
$303$	−0.755821	−	0.336513i	−0.0434208	−	0.0193322i
$304$	8.55109	+	14.8109i	0.490439	+	0.849465i
$305$	−2.10470	+	3.64545i	−0.120515	+	0.208738i
$306$	−4.91195	+	3.56874i	−0.280797	+	0.204011i
$307$	−26.1844	+	5.56567i	−1.49442	+	0.317650i	−0.881383	−	0.472402i	$-0.843387\pi$
$307$	−26.1844	+	5.56567i	−1.49442	+	0.317650i	−0.613041	+	0.790051i	$0.710054\pi$
$308$	−2.13001	−	6.55551i	−0.121369	−	0.373535i
$309$	6.79928			0.386798
$310$	−8.82113	+	5.88433i	−0.501006	+	0.334207i
$311$	4.18114			0.237090			0.118545	−	0.992949i	$-0.462177\pi$
$311$	4.18114			0.237090			0.118545	+	0.992949i	$0.462177\pi$
$312$	5.16673	+	15.9016i	0.292509	+	0.900249i
$313$	11.0950	−	2.35831i	0.627124	−	0.133299i	0.116623	−	0.993176i	$-0.462793\pi$
$313$	11.0950	−	2.35831i	0.627124	−	0.133299i	0.510501	+	0.859877i	$0.329460\pi$
$314$	−15.8763	+	11.5348i	−0.895953	+	0.650948i
$315$	−3.83769	+	6.64708i	−0.216229	+	0.374520i
$316$	−2.34546	−	4.06246i	−0.131943	−	0.228531i
$317$	23.6438	+	10.5269i	1.32797	+	0.591249i	0.943341	−	0.331824i	$-0.107664\pi$
$317$	23.6438	+	10.5269i	1.32797	+	0.591249i	0.384626	+	0.923073i	$0.374331\pi$
$318$	4.84867	+	3.52277i	0.271900	+	0.197547i
$319$	23.3965	−	10.4168i	1.30995	−	0.583229i
$320$	13.4356	+	2.85582i	0.751071	+	0.159645i
$321$	−0.684701	−	6.51449i	−0.0382163	−	0.363604i
$322$	−2.85341	+	3.16903i	−0.159014	+	0.176603i
$323$	15.4015	+	17.1050i	0.856960	+	0.951750i
$324$	−0.564609	+	5.37189i	−0.0313672	+	0.298439i
$325$	2.12612	−	6.54354i	0.117936	−	0.362970i
$326$	−0.0507081	+	0.156064i	−0.00280846	+	0.00864356i
$327$	−1.50876	+	14.3549i	−0.0834347	+	0.793828i
$328$	−0.689854	−	0.766160i	−0.0380908	−	0.0423041i
$329$	3.02663	−	3.36141i	0.166864	−	0.185321i
$330$	−1.55377	−	14.7831i	−0.0855321	−	0.813784i
$331$	−0.749053	−	0.159216i	−0.0411717	−	0.00875131i	0.187280	−	0.982307i	$-0.440033\pi$
$331$	−0.749053	−	0.159216i	−0.0411717	−	0.00875131i	−0.228451	+	0.973555i	$0.573366\pi$
$332$	3.69472	−	1.64500i	0.202774	−	0.0902808i
$333$	1.91599	+	1.39205i	0.104996	+	0.0762839i
$334$	−4.44493	−	1.97901i	−0.243215	−	0.108287i
$335$	−5.73517	−	9.93361i	−0.313346	−	0.542731i
$336$	−11.0672	+	19.1689i	−0.603765	+	1.04575i
$337$	−1.93706	+	1.40736i	−0.105519	+	0.0766637i	−0.639293	−	0.768963i	$-0.720773\pi$
$337$	−1.93706	+	1.40736i	−0.105519	+	0.0766637i	0.533775	+	0.845627i	$0.320773\pi$
$338$	7.29950	−	1.55156i	0.397041	−	0.0843936i
$339$	−9.77628	−	30.0883i	−0.530974	−	1.63417i
$340$	2.81040			0.152415
$341$	−16.4372	−	12.9784i	−0.890123	−	0.702822i
$342$	9.80991			0.530459
$343$	−0.550776	−	1.69511i	−0.0297391	−	0.0915276i
$344$	11.6175	−	2.46938i	0.626374	−	0.133140i
$345$	2.36071	−	1.71516i	0.127096	−	0.0923408i
$346$	8.90672	−	15.4269i	0.478828	−	0.829355i
$347$	−2.82890	−	4.89980i	−0.151863	−	0.263035i	0.780049	−	0.625718i	$-0.215194\pi$
$347$	−2.82890	−	4.89980i	−0.151863	−	0.263035i	−0.931912	+	0.362683i	$0.881861\pi$
$348$	6.21761	+	2.76826i	0.333299	+	0.148394i
$349$	−23.5162	−	17.0855i	−1.25879	−	0.914566i	−0.260095	−	0.965583i	$-0.583754\pi$
$349$	−23.5162	−	17.0855i	−1.25879	−	0.914566i	−0.998698	+	0.0510167i	$0.983754\pi$
$350$	11.1797	−	4.97752i	0.597580	−	0.266060i
$351$	−9.06243	−	1.92628i	−0.483717	−	0.102817i
$352$	1.04602	+	9.95223i	0.0557532	+	0.530456i
$353$	−12.8976	+	14.3243i	−0.686471	+	0.762404i	−0.981162	−	0.193189i	$-0.938117\pi$
$353$	−12.8976	+	14.3243i	−0.686471	+	0.762404i	0.294690	+	0.955593i	$0.404784\pi$
$354$	13.3079	+	14.7799i	0.707307	+	0.785544i
$355$	−0.823670	+	7.83670i	−0.0437159	+	0.415929i
$356$	−0.758579	+	2.33467i	−0.0402046	+	0.123737i
$357$	−9.20553	+	28.3317i	−0.487209	+	1.49947i
$358$	2.28227	−	21.7143i	0.120622	−	1.14764i
$359$	6.92167	+	7.68729i	0.365312	+	0.405720i	0.897577	−	0.440858i	$-0.145326\pi$
$359$	6.92167	+	7.68729i	0.365312	+	0.405720i	−0.532265	+	0.846578i	$0.678659\pi$
$360$	4.12884	−	4.58554i	0.217609	−	0.241679i
$361$	−1.90131	−	18.0898i	−0.100069	−	0.952095i
$362$	14.5343	+	3.08935i	0.763904	+	0.162373i
$363$	5.96932	−	2.65771i	0.313308	−	0.139494i
$364$	3.90647	+	2.83822i	0.204755	+	0.148763i
$365$	−7.61312	−	3.38958i	−0.398489	−	0.177419i
$366$	3.48154	+	6.03020i	0.181983	+	0.315203i
$367$	0.0682819	−	0.118268i	0.00356428	−	0.00617352i	−0.864238	−	0.503084i	$-0.832199\pi$
$367$	0.0682819	−	0.118268i	0.00356428	−	0.00617352i	0.867802	+	0.496910i	$0.165532\pi$
$368$	2.06428	−	1.49978i	0.107608	−	0.0781817i
$369$	−0.430531	+	0.0915122i	−0.0224125	+	0.00476393i
$370$	1.06760	+	3.28574i	0.0555020	+	0.170818i
$371$	8.91649			0.462921
$372$	−0.359759	−	5.55402i	−0.0186527	−	0.287963i
$373$	−7.36393			−0.381290			−0.190645	−	0.981659i	$-0.561058\pi$
$373$	−7.36393			−0.381290			−0.190645	+	0.981659i	$0.561058\pi$
$374$	−5.40578	−	16.6373i	−0.279526	−	0.860294i
$375$	−23.8762	+	5.07504i	−1.23296	+	0.262074i
$376$	−2.94187	+	2.13739i	−0.151715	+	0.110228i
$377$	−8.97053	+	15.5374i	−0.462006	+	0.800218i
$378$	−8.23955	−	14.2713i	−0.423797	−	0.734038i
$379$	−4.20974	−	1.87430i	−0.216240	−	0.0962762i	0.295758	−	0.955263i	$-0.404428\pi$
$379$	−4.20974	−	1.87430i	−0.216240	−	0.0962762i	−0.511998	+	0.858987i	$0.671094\pi$
$380$	−3.67362	−	2.66904i	−0.188453	−	0.136919i
$381$	−38.3408	+	17.0704i	−1.96426	+	0.874544i
$382$	−6.11243	−	1.29924i	−0.312739	−	0.0664748i
$383$	3.37572	+	32.1179i	0.172491	+	1.64115i	0.648147	+	0.761515i	$0.275544\pi$
$383$	3.37572	+	32.1179i	0.172491	+	1.64115i	−0.475656	+	0.879631i	$0.657789\pi$
$384$	7.81602	−	8.68057i	0.398860	−	0.442979i
$385$	−14.7976	−	16.4344i	−0.754155	−	0.837574i
$386$	2.58132	−	24.5596i	0.131386	−	1.25005i
$387$	1.56691	−	4.82246i	0.0796506	−	0.245139i
$388$	−1.62479	+	5.00060i	−0.0824864	+	0.253867i
$389$	3.68685	−	35.0781i	0.186931	−	1.77853i	−0.351825	−	0.936066i	$-0.614439\pi$
$389$	3.68685	−	35.0781i	0.186931	−	1.77853i	0.538756	−	0.842462i	$-0.318895\pi$
$390$	6.96770	+	7.73842i	0.352823	+	0.391850i
$391$	2.29784	−	2.55201i	0.116207	−	0.129061i
$392$	2.38727	+	22.7134i	0.120575	+	1.14720i
$393$	−25.6774	−	5.45791i	−1.29526	−	0.275315i
$394$	24.4359	−	10.8796i	1.23106	−	0.548105i
$395$	−12.1758	−	8.84621i	−0.612629	−	0.445101i
$396$	2.16123	+	0.962241i	0.108606	+	0.0483544i
$397$	2.01701	+	3.49356i	0.101231	+	0.175337i	0.912192	−	0.409763i	$-0.134389\pi$
$397$	2.01701	+	3.49356i	0.101231	+	0.175337i	−0.810961	+	0.585100i	$0.801055\pi$
$398$	−9.34326	+	16.1830i	−0.468335	+	0.811181i
$399$	38.9398	−	28.2914i	1.94943	−	1.41634i
$400$	−7.16245	+	1.52243i	−0.358122	+	0.0761213i
$401$	7.68933	+	23.6653i	0.383987	+	1.18179i	0.937212	+	0.348759i	$0.113397\pi$
$401$	7.68933	+	23.6653i	0.383987	+	1.18179i	−0.553225	+	0.833032i	$0.686603\pi$
$402$	−18.9739			−0.946334
$403$	14.6597	+	0.587221i	0.730249	+	0.0292516i
$404$	0.192087			0.00955671
$405$	5.35520	+	16.4816i	0.266102	+	0.818978i
$406$	−31.2137	+	6.63469i	−1.54911	+	0.329274i
$407$	−5.52044	+	4.01084i	−0.273638	+	0.198810i
$408$	11.9744	−	20.7403i	0.592821	−	1.02680i
$409$	−1.75361	−	3.03734i	−0.0867105	−	0.150187i	0.819408	−	0.573210i	$-0.194302\pi$
$409$	−1.75361	−	3.03734i	−0.0867105	−	0.150187i	−0.906119	+	0.423023i	$0.860969\pi$
$410$	−0.586572	−	0.261159i	−0.0289687	−	0.0128977i
$411$	16.5821	+	12.0476i	0.817936	+	0.594265i
$412$	−1.44213	+	0.642076i	−0.0710485	+	0.0316328i
$413$	28.9422	+	6.15186i	1.42415	+	0.302713i
$414$	−0.152988	−	1.45559i	−0.00751896	−	0.0715381i
$415$	8.68246	−	9.64284i	0.426205	−	0.473349i
$416$	−4.69077	−	5.20963i	−0.229984	−	0.255423i
$417$	3.36163	−	31.9838i	0.164620	−	1.56625i
$418$	−8.73429	+	26.8814i	−0.427208	+	1.31481i
$419$	1.27325	−	3.91865i	0.0622022	−	0.191439i	−0.915126	−	0.403167i	$-0.867909\pi$
$419$	1.27325	−	3.91865i	0.0622022	−	0.191439i	0.977328	+	0.211729i	$0.0679093\pi$
$420$	0.614309	−	5.84476i	0.0299752	−	0.285195i
$421$	18.4689	+	20.5118i	0.900121	+	0.999686i	0.999989	+	0.00468505i	$0.00149130\pi$
$421$	18.4689	+	20.5118i	0.900121	+	0.999686i	−0.0998679	+	0.995001i	$0.531842\pi$
$422$	5.19788	−	5.77283i	0.253029	−	0.281017i
$423$	0.162276	+	1.54395i	0.00789012	+	0.0750695i
$424$	−7.01157	−	1.49035i	−0.340512	−	0.0723780i
$425$	−9.00298	+	4.00839i	−0.436709	+	0.194435i
$426$	10.5453	+	7.66158i	0.510919	+	0.371205i
$427$	9.46367	+	4.21350i	0.457979	+	0.203905i
$428$	0.760408	+	1.31706i	0.0367557	+	0.0636627i
$429$	−10.2834	+	17.8114i	−0.496488	+	0.859943i
$430$	5.98427	−	4.34783i	0.288587	−	0.209671i
$431$	14.5489	−	3.09247i	0.700796	−	0.148959i	0.156284	−	0.987712i	$-0.450048\pi$
$431$	14.5489	−	3.09247i	0.700796	−	0.148959i	0.544512	+	0.838753i	$0.316715\pi$
$432$	3.04701	+	9.37772i	0.146599	+	0.451186i
$433$	9.26195			0.445101			0.222550	−	0.974921i	$-0.428562\pi$
$433$	9.26195			0.445101			0.222550	+	0.974921i	$0.428562\pi$
$434$	16.6711	+	20.0761i	0.800238	+	0.963682i
$435$	21.8360			1.04696
$436$	−1.03557	−	3.18715i	−0.0495947	−	0.152637i
$437$	−5.42728	+	1.15361i	−0.259622	+	0.0551844i
$438$	−11.1525	+	8.10275i	−0.532886	+	0.387164i
$439$	−8.85909	+	15.3444i	−0.422821	+	0.732348i	−0.996214	−	0.0869324i	$-0.972294\pi$
$439$	−8.85909	+	15.3444i	−0.422821	+	0.732348i	0.573393	+	0.819281i	$0.305627\pi$
$440$	8.88929	+	15.3967i	0.423780	+	0.734009i
$441$	8.90741	+	3.96584i	0.424163	+	0.188849i
$442$	9.91428	+	7.20314i	0.471574	+	0.342619i
$443$	−16.8551	+	7.50439i	−0.800811	+	0.356544i	−0.765993	−	0.642850i	$-0.777752\pi$
$443$	−16.8551	+	7.50439i	−0.800811	+	0.356544i	−0.0348187	+	0.999394i	$0.511085\pi$
$444$	−1.77375	−	0.377023i	−0.0841785	−	0.0178927i
$445$	0.823253	+	7.83273i	0.0390259	+	0.371307i
$446$	6.09220	−	6.76608i	0.288474	−	0.320383i
$447$	−21.1642	−	23.5052i	−1.00103	−	1.11176i
$448$	3.53342	−	33.6183i	0.166939	−	1.58831i
$449$	7.01784	−	21.5987i	0.331192	−	1.01931i	−0.637375	−	0.770554i	$-0.719980\pi$
$449$	7.01784	−	21.5987i	0.331192	−	1.01931i	0.968567	−	0.248752i	$-0.0800203\pi$
$450$	−1.29793	+	3.99463i	−0.0611852	+	0.188309i
$451$	0.132561	−	1.26123i	0.00624204	−	0.0593890i
$452$	4.91487	+	5.45852i	0.231176	+	0.256747i
$453$	−0.363530	+	0.403740i	−0.0170801	+	0.0189694i
$454$	−2.47803	−	23.5769i	−0.116300	−	1.10652i
$455$	15.1535	+	3.22097i	0.710405	+	0.151001i
$456$	−35.3494	+	15.7386i	−1.65539	+	0.737027i
$457$	13.0752	+	9.49970i	0.611633	+	0.444377i	0.849989	−	0.526800i	$-0.176608\pi$
$457$	13.0752	+	9.49970i	0.611633	+	0.444377i	−0.238356	+	0.971178i	$0.576608\pi$
$458$	−6.85192	−	3.05067i	−0.320169	−	0.142549i
$459$	6.63529	+	11.4927i	0.309709	+	0.536432i
$460$	−0.338739	+	0.586713i	−0.0157938	+	0.0273556i
$461$	−17.4252	+	12.6602i	−0.811573	+	0.589642i	−0.914286	−	0.405069i	$-0.867248\pi$
$461$	−17.4252	+	12.6602i	−0.811573	+	0.589642i	0.102713	+	0.994711i	$0.467248\pi$
$462$	−35.7821	+	7.60571i	−1.66473	+	0.353850i
$463$	−5.41083	−	16.6528i	−0.251462	−	0.773922i	−0.994506	−	0.104679i	$-0.966619\pi$
$463$	−5.41083	−	16.6528i	−0.251462	−	0.773922i	0.743044	−	0.669243i	$-0.233381\pi$
$464$	19.0941			0.886421
$465$	−8.30216	−	15.8092i	−0.385003	−	0.733133i
$466$	21.5976			1.00049
$467$	−3.64845	−	11.2288i	−0.168830	−	0.519605i	0.830468	−	0.557066i	$-0.188073\pi$
$467$	−3.64845	−	11.2288i	−0.168830	−	0.519605i	−0.999298	+	0.0374608i	$0.988073\pi$
$468$	−1.62107	+	0.344569i	−0.0749341	+	0.0159277i
$469$	−22.8372	+	16.5922i	−1.05453	+	0.766158i
$470$	−1.13235	+	1.96129i	−0.0522314	+	0.0904674i
$471$	−16.5236	−	28.6197i	−0.761366	−	1.31872i
$472$	−21.7307	−	9.67514i	−1.00024	−	0.445335i
$473$	11.8195	+	8.58739i	0.543463	+	0.394849i
$474$	−22.7431	+	10.1259i	−1.04463	+	0.465097i
$475$	15.5751	+	3.31058i	0.714632	+	0.151900i
$476$	−0.722955	−	6.87846i	−0.0331366	−	0.315274i
$477$	−2.04774	+	2.27425i	−0.0937597	+	0.104131i
$478$	−23.0130	−	25.5586i	−1.05259	−	1.16902i
$479$	1.65246	−	15.7221i	0.0755029	−	0.718362i	−0.889644	−	0.456654i	$-0.849048\pi$
$479$	1.65246	−	15.7221i	0.0755029	−	0.718362i	0.965147	−	0.261708i	$-0.0842856\pi$
$480$	−2.63658	+	8.11456i	−0.120343	+	0.370377i
$481$	1.47715	−	4.54621i	0.0673525	−	0.207290i
$482$	−2.93010	+	27.8780i	−0.133462	+	1.26981i
$483$	−4.80513	−	5.33664i	−0.218641	−	0.242825i
$484$	−1.01512	+	1.12740i	−0.0461416	+	0.0512455i
$485$	1.76332	+	16.7769i	0.0800682	+	0.761798i
$486$	15.3271	+	3.25787i	0.695251	+	0.147780i
$487$	11.6857	−	5.20283i	0.529532	−	0.235763i	−0.124514	−	0.992218i	$-0.539737\pi$
$487$	11.6857	−	5.20283i	0.529532	−	0.235763i	0.654046	+	0.756455i	$0.273070\pi$
$488$	−6.73758	−	4.89514i	−0.304996	−	0.221593i
$489$	−0.252445	−	0.112396i	−0.0114160	−	0.00508271i
$490$	7.11185	+	12.3181i	0.321281	+	0.556475i
$491$	9.26410	−	16.0459i	0.418083	−	0.724141i	−0.577664	−	0.816275i	$-0.696036\pi$
$491$	9.26410	−	16.0459i	0.418083	−	0.724141i	0.995747	+	0.0921341i	$0.0293688\pi$
$492$	0.272653	−	0.198094i	0.0122921	−	0.00893076i
$493$	25.1364	−	5.34290i	1.13209	−	0.240632i
$494$	−6.11864	−	18.8312i	−0.275290	−	0.847257i
$495$	7.59016			0.341152
$496$	−7.25967	−	13.8240i	−0.325969	−	0.620717i
$497$	19.3922			0.869861
$498$	−6.63277	−	20.4136i	−0.297221	−	0.914754i
$499$	−39.9938	+	8.50094i	−1.79037	+	0.380554i	−0.978980	−	0.203955i	$-0.934620\pi$
$499$	−39.9938	+	8.50094i	−1.79037	+	0.380554i	−0.811387	+	0.584510i	$0.801287\pi$
$500$	4.58489	−	3.33112i	0.205042	−	0.148972i
$501$	4.09681	−	7.09588i	0.183032	−	0.317021i
$502$	10.0018	+	17.3237i	0.446404	+	0.773195i
$503$	18.3413	+	8.16609i	0.817800	+	0.364108i	0.772618	−	0.634871i	$-0.218947\pi$
$503$	18.3413	+	8.16609i	0.817800	+	0.364108i	0.0451817	+	0.998979i	$0.485613\pi$
$504$	−12.2852	−	8.92575i	−0.547228	−	0.397585i
$505$	0.563001	−	0.250664i	0.0250532	−	0.0111544i
$506$	4.12485	+	0.876764i	0.183372	+	0.0389769i
$507$	1.31361	+	12.4981i	0.0583393	+	0.555061i
$508$	6.52007	−	7.24127i	0.289281	−	0.321279i
$509$	−21.3528	−	23.7147i	−0.946445	−	1.05113i	−0.998621	−	0.0524956i	$-0.983282\pi$
$509$	−21.3528	−	23.7147i	−0.946445	−	1.05113i	0.0521763	−	0.998638i	$-0.483384\pi$
$510$	1.55906	−	14.8335i	0.0690364	−	0.656837i
$511$	−6.33760	+	19.5051i	−0.280359	+	0.862855i
$512$	−7.60561	+	23.4076i	−0.336123	+	1.03448i
$513$	2.24127	−	21.3242i	0.0989544	−	0.941488i
$514$	19.2534	+	21.3831i	0.849233	+	0.943169i
$515$	−3.38895	+	3.76381i	−0.149335	+	0.165853i
$516$	0.405835	+	3.86126i	0.0178659	+	0.169982i
$517$	−4.37526	−	0.929990i	−0.192424	−	0.0409009i
$518$	7.76725	−	3.45820i	0.341273	−	0.151945i
$519$	24.2687	+	17.6323i	1.06528	+	0.773970i
$520$	−11.3777	−	5.06568i	−0.498945	−	0.222145i
$521$	−1.05378	−	1.82520i	−0.0461670	−	0.0799635i	0.842019	−	0.539449i	$-0.181367\pi$
$521$	−1.05378	−	1.82520i	−0.0461670	−	0.0799635i	−0.888185	+	0.459485i	$0.848034\pi$
$522$	5.47624	−	9.48512i	0.239688	−	0.415152i
$523$	−3.97047	+	2.88471i	−0.173616	+	0.126140i	−0.671200	−	0.741276i	$-0.734221\pi$
$523$	−3.97047	+	2.88471i	−0.173616	+	0.126140i	0.497584	+	0.867416i	$0.334221\pi$
$524$	5.96159	−	1.26717i	0.260433	−	0.0553568i
$525$	6.36830	+	19.5996i	0.277935	+	0.855397i
$526$	−12.8076			−0.558440
$527$	−13.4252	−	16.1672i	−0.584811	−	0.704255i
$528$	21.8886			0.952580
$529$	−6.85158	−	21.0870i	−0.297895	−	0.916826i
$530$	−4.36677	+	0.928185i	−0.189680	+	0.0403178i
$531$	−8.21591	+	5.96921i	−0.356540	+	0.259042i
$532$	−5.58748	+	9.67780i	−0.242248	+	0.419586i
$533$	0.444199	+	0.769375i	0.0192404	+	0.0333253i
$534$	11.9017	+	5.29898i	0.515038	+	0.229310i
$535$	3.94743	+	2.86798i	0.170662	+	0.123993i
$536$	20.7316	−	9.23030i	0.895469	−	0.398688i
$537$	35.9648	+	7.64456i	1.55200	+	0.329887i
$538$	0.569031	+	5.41397i	0.0245327	+	0.233413i
$539$	−18.7980	+	20.8773i	−0.809689	+	0.899251i
$540$	−1.75181	−	1.94558i	−0.0753858	−	0.0837245i
$541$	1.30002	−	12.3689i	0.0558923	−	0.531780i	−0.930373	−	0.366613i	$-0.880517\pi$
$541$	1.30002	−	12.3689i	0.0558923	−	0.531780i	0.986266	−	0.165167i	$-0.0528162\pi$
$542$	2.34278	−	7.21033i	0.100631	−	0.309710i
$543$	−7.73236	+	23.7978i	−0.331827	+	1.02126i
$544$	−1.04959	+	9.98614i	−0.0450006	+	0.428152i
$545$	−7.19428	−	7.99006i	−0.308169	−	0.342257i
$546$	17.1474	−	19.0442i	0.733842	−	0.815014i
$547$	1.45974	+	13.8885i	0.0624140	+	0.593830i	0.980373	+	0.197154i	$0.0631697\pi$
$547$	1.45974	+	13.8885i	0.0624140	+	0.593830i	−0.917959	+	0.396676i	$0.870164\pi$
$548$	−4.65476	−	0.989399i	−0.198841	−	0.0422650i
$549$	−3.24811	+	1.44615i	−0.138626	+	0.0617202i
$550$	−9.79058	−	7.11327i	−0.417472	−	0.303311i
$551$	−37.9313	−	16.8881i	−1.61593	−	0.719456i
$552$	2.88656	+	4.99967i	0.122860	+	0.212800i
$553$	−18.5190	+	32.0759i	−0.787509	+	1.36401i
$554$	−21.9779	+	15.9679i	−0.933752	+	0.678411i
$555$	−5.69080	+	1.20962i	−0.241561	+	0.0513454i
$556$	2.30732	+	7.10121i	0.0978523	+	0.301159i
$557$	−37.2207			−1.57709			−0.788546	−	0.614976i	$-0.789166\pi$
$557$	−37.2207			−1.57709			−0.788546	+	0.614976i	$0.789166\pi$
$558$	−8.94927	−	0.358481i	−0.378853	−	0.0151757i
$559$	−10.2346			−0.432876
$560$	−5.09496	−	15.6807i	−0.215301	−	0.662629i
$561$	28.8152	−	6.12487i	1.21658	−	0.258592i
$562$	30.6766	−	22.2878i	1.29401	−	0.940156i
$563$	15.0134	−	26.0039i	0.632738	−	1.09593i	−0.354252	−	0.935150i	$-0.615264\pi$
$563$	15.0134	−	26.0039i	0.632738	−	1.09593i	0.986990	−	0.160784i	$-0.0514023\pi$
$564$	−0.594349	−	1.02944i	−0.0250266	−	0.0433474i
$565$	21.5284	+	9.58507i	0.905707	+	0.403247i
$566$	21.2780	+	15.4594i	0.894380	+	0.649805i
$567$	38.9613	−	17.3467i	1.63622	−	0.728492i
$568$	−15.2493	−	3.24133i	−0.639846	−	0.136003i
$569$	4.21995	+	40.1502i	0.176910	+	1.68318i	0.618359	+	0.785896i	$0.287798\pi$
$569$	4.21995	+	40.1502i	0.176910	+	1.68318i	−0.441449	+	0.897286i	$0.645536\pi$
$570$	−16.1253	+	17.9090i	−0.675415	+	0.750125i
$571$	28.5060	+	31.6591i	1.19294	+	1.32489i	0.933262	+	0.359197i	$0.116949\pi$
$571$	28.5060	+	31.6591i	1.19294	+	1.32489i	0.259677	+	0.965696i	$0.416384\pi$
$572$	0.499129	−	4.74889i	0.0208696	−	0.198561i
$573$	3.25187	−	10.0082i	0.135849	−	0.418100i
$574$	−0.488296	+	1.50282i	−0.0203811	+	0.0627265i
$575$	0.248324	−	2.36264i	0.0103558	−	0.0985290i
$576$	7.76324	+	8.62195i	0.323468	+	0.359248i
$577$	−4.37462	+	4.85851i	−0.182118	+	0.202262i	−0.827290	−	0.561775i	$-0.810119\pi$
$577$	−4.37462	+	4.85851i	−0.182118	+	0.202262i	0.645173	+	0.764037i	$0.276785\pi$
$578$	0.354754	+	3.37526i	0.0147558	+	0.140392i
$579$	40.6774	+	8.64624i	1.69049	+	0.359325i
$580$	−4.63142	+	2.06204i	−0.192309	+	0.0856216i
$581$	−25.8344	−	18.7698i	−1.07179	−	0.778703i
$582$	25.4922	+	11.3499i	1.05669	+	0.470467i
$583$	−4.40874	−	7.63617i	−0.182591	−	0.316258i
$584$	8.24383	−	14.2787i	0.341132	−	0.590858i
$585$	−4.30166	+	3.12534i	−0.177852	+	0.129217i
$586$	2.16827	−	0.460880i	0.0895704	−	0.0190388i
$587$	−6.60607	−	20.3314i	−0.272662	−	0.839167i	−0.989829	−	0.142265i	$-0.954561\pi$
$587$	−6.60607	−	20.3314i	−0.272662	−	0.839167i	0.717167	−	0.696902i	$-0.245439\pi$
$588$	−7.46576			−0.307883
$589$	2.19476	+	33.8830i	0.0904333	+	1.39612i
$590$	−14.8146			−0.609907
$591$	13.9195	+	42.8397i	0.572570	+	1.76219i
$592$	−4.97621	+	1.05773i	−0.204521	+	0.0434723i
$593$	−21.0268	+	15.2769i	−0.863468	+	0.627347i	−0.928826	−	0.370515i	$-0.879181\pi$
$593$	−21.0268	+	15.2769i	−0.863468	+	0.627347i	0.0653579	+	0.997862i	$0.479181\pi$
$594$	−8.14807	+	14.1129i	−0.334319	+	0.579058i
$595$	−11.0950	−	19.2171i	−0.454851	−	0.787824i
$596$	6.70858	+	2.98685i	0.274794	+	0.122346i
$597$	−25.4582	−	18.4965i	−1.04193	−	0.757010i
$598$	−2.69874	+	1.20156i	−0.110360	+	0.0491353i
$599$	8.98718	+	1.91028i	0.367206	+	0.0780521i	0.387819	−	0.921735i	$-0.373228\pi$
$599$	8.98718	+	1.91028i	0.367206	+	0.0780521i	−0.0206131	+	0.999788i	$0.506562\pi$
$600$	−1.73178	−	16.4768i	−0.0706996	−	0.672661i
$601$	22.2948	−	24.7609i	0.909423	−	1.01002i	−0.0904769	−	0.995899i	$-0.528839\pi$
$601$	22.2948	−	24.7609i	0.909423	−	1.01002i	0.999900	−	0.0141185i	$-0.00449419\pi$
$602$	−12.1807	−	13.5281i	−0.496450	−	0.551364i
$603$	1.01272	−	9.63543i	0.0412413	−	0.392385i
$604$	0.0389782	−	0.119962i	0.00158600	−	0.00488120i
$605$	−1.50407	+	4.62905i	−0.0611491	+	0.188197i
$606$	0.106560	−	1.01385i	0.00432871	−	0.0411849i
$607$	−32.5872	−	36.1917i	−1.32267	−	1.46898i	−0.774434	−	0.632654i	$-0.781965\pi$
$607$	−32.5872	−	36.1917i	−1.32267	−	1.46898i	−0.548238	−	0.836322i	$-0.684701\pi$
$608$	10.8558	−	12.0566i	0.440262	−	0.488961i
$609$	−5.61717	−	53.4438i	−0.227619	−	2.16565i
$610$	−5.07336	−	1.07838i	−0.205414	−	0.0436622i
$611$	2.86257	−	1.27450i	0.115807	−	0.0515608i
$612$	1.92046	+	1.39530i	0.0776300	+	0.0564015i
$613$	19.1059	+	8.50649i	0.771680	+	0.343574i	0.754519	−	0.656279i	$-0.227870\pi$
$613$	19.1059	+	8.50649i	0.771680	+	0.343574i	0.0171613	+	0.999853i	$0.494537\pi$
$614$	−16.4923	−	28.5654i	−0.665573	−	1.15281i
$615$	0.540633	−	0.936404i	0.0218004	−	0.0377594i
$616$	35.3968	−	25.7173i	1.42618	−	1.03618i
$617$	−44.3922	+	9.43586i	−1.78716	+	0.379873i	−0.978147	−	0.207913i	$-0.933333\pi$
$617$	−44.3922	+	9.43586i	−1.78716	+	0.379873i	−0.809016	+	0.587787i	$0.799999\pi$
$618$	2.58891	+	7.96784i	0.104141	+	0.320514i
$619$	−10.2462			−0.411832			−0.205916	−	0.978570i	$-0.566017\pi$
$619$	−10.2462			−0.411832			−0.205916	+	0.978570i	$0.566017\pi$
$620$	3.25379	+	2.56913i	0.130676	+	0.103179i
$621$	−3.19902			−0.128372
$622$	1.59202	+	4.89973i	0.0638341	+	0.196461i
$623$	18.9589	−	4.02983i	0.759571	−	0.161452i
$624$	−12.4052	+	9.01290i	−0.496605	+	0.360805i
$625$	2.56358	−	4.44025i	0.102543	−	0.177610i
$626$	6.98816	+	12.1038i	0.279303	+	0.483767i
$627$	−43.4827	−	19.3598i	−1.73653	−	0.773154i
$628$	6.20729	+	4.50986i	0.247698	+	0.179963i
$629$	−6.25495	+	2.78488i	−0.249401	+	0.111041i
$630$	−9.25073	−	1.96630i	−0.368558	−	0.0783394i
$631$	1.11605	+	10.6185i	0.0444291	+	0.422715i	0.994018	+	0.109217i	$0.0348343\pi$
$631$	1.11605	+	10.6185i	0.0444291	+	0.422715i	−0.949589	+	0.313498i	$0.898499\pi$
$632$	19.9240	−	22.1278i	0.792533	−	0.880197i
$633$	8.75322	+	9.72144i	0.347909	+	0.386392i
$634$	−3.33344	+	31.7156i	−0.132388	+	1.25959i
$635$	9.66059	−	29.7322i	0.383369	−	1.17989i
$636$	0.724101	−	2.22855i	0.0287125	−	0.0883679i
$637$	2.05714	−	19.5724i	0.0815068	−	0.775485i
$638$	21.1156	+	23.4512i	0.835975	+	0.928444i
$639$	−4.45358	+	4.94621i	−0.176181	+	0.195669i
$640$	0.909495	+	8.65326i	0.0359509	+	0.342050i
$641$	−23.3407	−	4.96121i	−0.921900	−	0.195956i	−0.277572	−	0.960705i	$-0.589530\pi$
$641$	−23.3407	−	4.96121i	−0.921900	−	0.195956i	−0.644328	+	0.764749i	$0.722863\pi$
$642$	7.37340	−	3.28285i	0.291005	−	0.129564i
$643$	6.42300	+	4.66658i	0.253298	+	0.184032i	0.707187	−	0.707026i	$-0.249964\pi$
$643$	6.42300	+	4.66658i	0.253298	+	0.184032i	−0.453889	+	0.891058i	$0.649964\pi$
$644$	1.52312	+	0.678137i	0.0600194	+	0.0267224i
$645$	6.22823	+	10.7876i	0.245237	+	0.424762i
$646$	−14.1805	+	24.5614i	−0.557925	+	0.966355i
$647$	−2.00443	+	1.45630i	−0.0788023	+	0.0572532i	−0.626489	−	0.779430i	$-0.715509\pi$
$647$	−2.00443	+	1.45630i	−0.0788023	+	0.0572532i	0.547687	+	0.836684i	$0.315509\pi$
$648$	−33.5370	+	7.12851i	−1.31746	+	0.280034i
$649$	−9.04192	−	27.8282i	−0.354926	−	1.09235i
$650$	8.47769			0.332523
$651$	−36.5574	+	24.3864i	−1.43280	+	0.955778i
$652$	0.0641574			0.00251260
$653$	6.95104	+	21.3931i	0.272015	+	0.837177i	0.989994	+	0.141112i	$0.0450677\pi$
$653$	6.95104	+	21.3931i	0.272015	+	0.837177i	−0.717978	+	0.696065i	$0.754932\pi$
$654$	−17.3965	+	3.69774i	−0.680257	+	0.144593i
$655$	15.8196	−	11.4936i	0.618123	−	0.449093i
$656$	0.472746	−	0.818821i	0.0184576	−	0.0319696i
$657$	−3.51952	−	6.09598i	−0.137309	−	0.237827i
$658$	5.09155	+	2.26690i	0.198489	+	0.0883731i
$659$	9.67555	+	7.02970i	0.376906	+	0.273838i	0.760069	−	0.649843i	$-0.225165\pi$
$659$	9.67555	+	7.02970i	0.376906	+	0.273838i	−0.383163	+	0.923681i	$0.625165\pi$
$660$	−5.30925	+	2.36383i	−0.206662	+	0.0920120i
$661$	−23.3151	−	4.95578i	−0.906852	−	0.192757i	−0.269202	−	0.963084i	$-0.586760\pi$
$661$	−23.3151	−	4.95578i	−0.906852	−	0.192757i	−0.637650	+	0.770326i	$0.720093\pi$
$662$	−0.0986312	−	0.938413i	−0.00383341	−	0.0364725i
$663$	−13.8088	+	15.3362i	−0.536289	+	0.595609i
$664$	17.1779	+	19.0779i	0.666630	+	0.740368i
$665$	−3.74766	+	35.6567i	−0.145328	+	1.38271i
$666$	−0.901758	+	2.77533i	−0.0349424	+	0.107542i
$667$	−1.91429	+	5.89158i	−0.0741216	+	0.228123i
$668$	−0.198848	+	1.89191i	−0.00769365	+	0.0732002i
$669$	10.2593	+	11.3941i	0.396646	+	0.440520i
$670$	9.45712	−	10.5032i	0.365360	−	0.405774i
$671$	−1.07082	−	10.1881i	−0.0413384	−	0.393309i
$672$	20.5387	+	4.36563i	0.792297	+	0.168408i
$673$	3.19204	−	1.42119i	0.123044	−	0.0547827i	−0.344291	−	0.938863i	$-0.611881\pi$
$673$	3.19204	−	1.42119i	0.123044	−	0.0547827i	0.467335	+	0.884080i	$0.345214\pi$
$674$	−2.38679	−	1.73411i	−0.0919359	−	0.0667953i
$675$	8.38677	+	3.73403i	0.322807	+	0.143723i
$676$	−1.45885	−	2.52680i	−0.0561096	−	0.0971847i
$677$	9.62287	−	16.6673i	0.369837	−	0.640576i	−0.619703	−	0.784836i	$-0.712747\pi$
$677$	9.62287	−	16.6673i	0.369837	−	0.640576i	0.989540	+	0.144260i	$0.0460803\pi$
$678$	31.5370	−	22.9130i	1.21117	−	0.879967i
$679$	40.6079	−	8.63147i	1.55839	−	0.331245i
$680$	5.51260	+	16.9660i	0.211399	+	0.650618i
$681$	39.9221			1.52982
$682$	8.95034	−	24.2039i	0.342726	−	0.926814i
$683$	−39.8738			−1.52573			−0.762865	−	0.646558i	$-0.776208\pi$
$683$	−39.8738			−1.52573			−0.762865	+	0.646558i	$0.776208\pi$
$684$	−1.18522	−	3.64773i	−0.0453180	−	0.139475i
$685$	−14.9340	+	3.17433i	−0.570601	+	0.121285i
$686$	1.77673	−	1.29087i	0.0678359	−	0.0492857i
$687$	6.31529	−	10.9384i	0.240944	−	0.417326i
$688$	5.44616	+	9.43303i	0.207633	+	0.359631i
$689$	5.64290	+	2.51238i	0.214977	+	0.0957140i
$690$	2.90880	+	2.11337i	0.110736	+	0.0804545i
$691$	35.0897	−	15.6229i	1.33487	−	0.594325i	0.389716	−	0.920935i	$-0.372573\pi$
$691$	35.0897	−	15.6229i	1.33487	−	0.594325i	0.945159	+	0.326611i	$0.105907\pi$
$692$	−6.81246	−	1.44803i	−0.258971	−	0.0550459i
$693$	−1.95252	−	18.5770i	−0.0741700	−	0.705680i
$694$	4.66477	−	5.18075i	0.177072	−	0.196659i
$695$	16.0294	+	17.8025i	0.608030	+	0.675286i
$696$	−4.51580	+	42.9649i	−0.171171	+	1.62858i
$697$	0.393224	−	1.21022i	0.0148944	−	0.0458403i
$698$	11.0678	−	34.0633i	0.418924	−	1.28932i
$699$	−3.80173	+	36.1710i	−0.143795	+	1.36811i
$700$	−3.20156	−	3.55570i	−0.121008	−	0.134393i
$701$	−23.7043	+	26.3263i	−0.895298	+	0.994329i	−1.00000		0.000174860i	$-0.999944\pi$
$701$	−23.7043	+	26.3263i	−0.895298	+	0.994329i	0.104702	+	0.994504i	$0.466611\pi$
$702$	−1.19329	−	11.3534i	−0.0450379	−	0.428507i
$703$	10.8210	+	2.30007i	0.408121	+	0.0867488i
$704$	−30.5381	+	13.5965i	−1.15095	+	0.512436i
$705$	−3.08539	−	2.24166i	−0.116202	−	0.0844260i
$706$	−21.6970	−	9.66015i	−0.816579	−	0.363564i
$707$	−0.758331	−	1.31347i	−0.0285200	−	0.0493980i
$708$	3.88795	−	6.73412i	0.146118	−	0.253084i
$709$	20.8801	−	15.1703i	0.784170	−	0.569733i	−0.122057	−	0.992523i	$-0.538949\pi$
$709$	20.8801	−	15.1703i	0.784170	−	0.569733i	0.906228	+	0.422790i	$0.138949\pi$
$710$	−9.49718	+	2.01869i	−0.356423	+	0.0757600i
$711$	−3.92827	−	12.0900i	−0.147322	−	0.453409i
$712$	−15.5821			−0.583962
$713$	4.99330	−	0.854070i	0.187001	−	0.0319852i
$714$	−36.7061			−1.37369
$715$	−4.73414	−	14.5702i	−0.177047	−	0.544894i
$716$	−8.35004	+	1.77486i	−0.312056	+	0.0663295i
$717$	46.8557	−	34.0426i	1.74986	−	1.27135i
$718$	−6.37296	+	11.0383i	−0.237837	+	0.411945i
$719$	19.5234	+	33.8155i	0.728099	+	1.26110i	0.957686	+	0.287816i	$0.0929291\pi$
$719$	19.5234	+	33.8155i	0.728099	+	1.26110i	−0.229587	+	0.973288i	$0.573738\pi$
$720$	5.16963	+	2.30167i	0.192661	+	0.0857780i
$721$	10.0837	+	7.32625i	0.375537	+	0.272844i
$722$	20.4749	−	9.11599i	0.761995	−	0.339262i
$723$	−46.1736	−	9.81450i	−1.71721	−	0.365005i
$724$	−0.607260	−	5.77769i	−0.0225686	−	0.214726i
$725$	11.8955	−	13.2113i	0.441788	−	0.490656i
$726$	5.38737	+	5.98328i	0.199944	+	0.222060i
$727$	−2.61150	+	24.8468i	−0.0968552	+	0.921516i	0.832921	+	0.553391i	$0.186667\pi$
$727$	−2.61150	+	24.8468i	−0.0968552	+	0.921516i	−0.929777	+	0.368124i	$0.880000\pi$
$728$	−9.47144	+	29.1501i	−0.351035	+	1.08037i
$729$	2.24010	−	6.89433i	0.0829668	−	0.255345i
$730$	1.07334	−	10.2122i	0.0397262	−	0.377970i
$731$	9.80913	+	10.8941i	0.362804	+	0.402934i
$732$	1.82164	−	2.02314i	0.0673299	−	0.0747774i
$733$	1.77166	+	16.8562i	0.0654377	+	0.622598i	0.977265	+	0.212023i	$0.0680052\pi$
$733$	1.77166	+	16.8562i	0.0654377	+	0.622598i	−0.911827	+	0.410575i	$0.865328\pi$
$734$	0.164593	+	0.0349853i	0.00607524	+	0.00129133i
$735$	−21.8819	+	9.74243i	−0.807125	+	0.359355i
$736$	−1.95825	−	1.42275i	−0.0721821	−	0.0524434i
$737$	25.5016	+	11.3540i	0.939363	+	0.418231i
$738$	−0.271170	−	0.469680i	−0.00998190	−	0.0172892i
$739$	−7.19107	+	12.4553i	−0.264528	+	0.458175i	−0.967440	−	0.253101i	$-0.918549\pi$
$739$	−7.19107	+	12.4553i	−0.264528	+	0.458175i	0.702912	+	0.711277i	$0.251883\pi$
$740$	1.09279	−	0.793959i	0.0401718	−	0.0291865i
$741$	32.6151	−	6.93254i	1.19814	−	0.254673i
$742$	3.39506	+	10.4489i	0.124637	+	0.383592i
$743$	−27.7705			−1.01880			−0.509400	−	0.860530i	$-0.670133\pi$
$743$	−27.7705			−1.01880			−0.509400	+	0.860530i	$0.670133\pi$
$744$	32.8233	−	13.0661i	1.20336	−	0.479025i
$745$	23.5603			0.863183
$746$	−2.80390	−	8.62953i	−0.102658	−	0.315950i
$747$	10.7205	−	2.27872i	0.392244	−	0.0833740i
$748$	−5.53332	+	4.02019i	−0.202318	+	0.146993i
$749$	6.00394	−	10.3991i	0.219379	−	0.379976i
$750$	−15.0384	−	26.0473i	−0.549126	−	0.951113i
$751$	−39.8034	−	17.7216i	−1.45245	−	0.646670i	−0.479465	−	0.877561i	$-0.659169\pi$
$751$	−39.8034	−	17.7216i	−1.45245	−	0.646670i	−0.972980	+	0.230891i	$0.925836\pi$
$752$	−2.69796	−	1.96018i	−0.0983844	−	0.0714804i
$753$	−30.7739	+	13.7014i	−1.12146	+	0.499307i
$754$	−21.6234	−	4.59620i	−0.787478	−	0.167384i
$755$	−0.0423013	−	0.402470i	−0.00153950	−	0.0146474i
$756$	−4.31118	+	4.78805i	−0.156796	+	0.174140i
$757$	16.8735	+	18.7400i	0.613279	+	0.681115i	0.967158	−	0.254176i	$-0.0818042\pi$
$757$	16.8735	+	18.7400i	0.613279	+	0.681115i	−0.353879	+	0.935291i	$0.615138\pi$
$758$	0.593514	−	5.64691i	0.0215574	−	0.205105i
$759$	−2.19446	+	6.75385i	−0.0796538	+	0.245149i
$760$	8.90688	−	27.4125i	0.323086	−	0.994358i
$761$	0.273439	−	2.60160i	0.00991216	−	0.0943079i	−0.988447	−	0.151565i	$-0.951569\pi$
$761$	0.273439	−	2.60160i	0.00991216	−	0.0943079i	0.998359	+	0.0572569i	$0.0182354\pi$
$762$	−34.6029	−	38.4305i	−1.25353	−	1.39219i

Introduction	Features
Universe	News

Level:	\( N \)	=	\( 31 \)
Weight:	\( k \)	=	\( 2 \)
Character orbit:	\([\chi]\)	=	31.g (of order \(15\) and degree \(8\))

\(f(q)\)	\(=\)	\(q\)\(+(0.380762 + 1.17187i) q^{2}\) \(+(-2.02963 + 0.431412i) q^{3}\) \(+(0.389745 - 0.283166i) q^{4}\) \(+(0.772811 - 1.33855i) q^{5}\) \(+(-1.27836 - 2.21419i) q^{6}\) \(+(-3.47491 - 1.54713i) q^{7}\) \(+(2.47393 + 1.79742i) q^{8}\) \(+(1.19265 - 0.531003i) q^{9}\) \(+O(q^{10})\)	\(q\)\(+(0.380762 + 1.17187i) q^{2}\) \(+(-2.02963 + 0.431412i) q^{3}\) \(+(0.389745 - 0.283166i) q^{4}\) \(+(0.772811 - 1.33855i) q^{5}\) \(+(-1.27836 - 2.21419i) q^{6}\) \(+(-3.47491 - 1.54713i) q^{7}\) \(+(2.47393 + 1.79742i) q^{8}\) \(+(1.19265 - 0.531003i) q^{9}\) \(+(1.86286 + 0.395962i) q^{10}\) \(+(0.393186 + 3.74092i) q^{11}\) \(+(-0.668878 + 0.742864i) q^{12}\) \(+(-1.76320 - 1.95823i) q^{13}\) \(+(0.489913 - 4.66121i) q^{14}\) \(+(-0.991057 + 3.05016i) q^{15}\) \(+(-0.866611 + 2.66715i) q^{16}\) \(+(-0.394526 + 3.75366i) q^{17}\) \(+(1.07638 + 1.19544i) q^{18}\) \(+(4.08057 - 4.53193i) q^{19}\) \(+(-0.0778325 - 0.740527i) q^{20}\) \(+(7.72023 + 1.64099i) q^{21}\) \(+(-4.23414 + 1.88516i) q^{22}\) \(+(-0.736082 - 0.534795i) q^{23}\) \(+(-5.79659 - 2.58081i) q^{24}\) \(+(1.30553 + 2.26124i) q^{25}\) \(+(1.62343 - 2.81186i) q^{26}\) \(+(2.84451 - 2.06665i) q^{27}\) \(+(-1.79242 + 0.380991i) q^{28}\) \(+(-2.10397 - 6.47535i) q^{29}\) \(-3.95173 q^{30}\) \(+(-3.88819 + 3.98522i) q^{31}\) \(+2.66037 q^{32}\) \(+(-2.41190 - 7.42306i) q^{33}\) \(+(-4.54901 + 0.966922i) q^{34}\) \(+(-4.75635 + 3.45569i) q^{35}\) \(+(0.314468 - 0.544675i) q^{36}\) \(+(0.907032 + 1.57103i) q^{37}\) \(+(6.86454 + 3.05629i) q^{38}\) \(+(4.42345 + 3.21383i) q^{39}\) \(+(4.31781 - 1.92241i) q^{40}\) \(+(-0.329777 - 0.0700963i) q^{41}\) \(+(1.01656 + 9.67189i) q^{42}\) \(+(2.59890 - 2.88637i) q^{43}\) \(+(1.21255 + 1.34667i) q^{44}\) \(+(0.210922 - 2.00679i) q^{45}\) \(+(0.346435 - 1.06622i) q^{46}\) \(+(-0.367467 + 1.13095i) q^{47}\) \(+(0.608260 - 5.78721i) q^{48}\) \(+(4.99745 + 5.55023i) q^{49}\) \(+(-2.15277 + 2.39089i) q^{50}\) \(+(-0.818631 - 7.78876i) q^{51}\) \(+(-1.24171 - 0.263933i) q^{52}\) \(+(-2.14147 + 0.953442i) q^{53}\) \(+(3.50492 + 2.54647i) q^{54}\) \(+(5.31126 + 2.36473i) q^{55}\) \(+(-5.81584 - 10.0733i) q^{56}\) \(+(-6.32692 + 10.9586i) q^{57}\) \(+(6.78713 - 4.93114i) q^{58}\) \(+(-7.60885 + 1.61731i) q^{59}\) \(+(0.477443 + 1.46942i) q^{60}\) \(-2.72343 q^{61}\) \(+(-6.15062 - 3.03901i) q^{62}\) \(-4.96588 q^{63}\) \(+(2.74619 + 8.45191i) q^{64}\) \(+(-3.98381 + 0.846786i) q^{65}\) \(+(7.78047 - 5.65284i) q^{66}\) \(+(3.71059 - 6.42693i) q^{67}\) \(+(0.909147 + 1.57469i) q^{68}\) \(+(1.72469 + 0.767882i) q^{69}\) \(+(-5.86065 - 4.25801i) q^{70}\) \(+(-4.65742 + 2.07362i) q^{71}\) \(+(3.90497 + 0.830027i) q^{72}\) \(+(-0.563591 - 5.36221i) q^{73}\) \(+(-1.49567 + 1.66111i) q^{74}\) \(+(-3.62526 - 4.02626i) q^{75}\) \(+(0.307091 - 2.92178i) q^{76}\) \(+(4.42139 - 13.6076i) q^{77}\) \(+(-2.08189 + 6.40740i) q^{78}\) \(+(1.01782 - 9.68388i) q^{79}\) \(+(2.90039 + 3.22121i) q^{80}\) \(+(-7.50241 + 8.33227i) q^{81}\) \(+(-0.0434232 - 0.413145i) q^{82}\) \(+(8.21169 + 1.74545i) q^{83}\) \(+(3.47359 - 1.54654i) q^{84}\) \(+(4.71957 + 3.42897i) q^{85}\) \(+(4.37200 + 1.94654i) q^{86}\) \(+(7.06383 + 12.2349i) q^{87}\) \(+(-5.75127 + 9.96149i) q^{88}\) \(+(-4.12243 + 2.99512i) q^{89}\) \(+(2.43200 - 0.516937i) q^{90}\) \(+(3.09732 + 9.53258i) q^{91}\) \(-0.438320 q^{92}\) \(+(6.17231 - 9.76595i) q^{93}\) \(-1.46523 q^{94}\) \(+(-2.91270 - 8.96437i) q^{95}\) \(+(-5.39957 + 1.14771i) q^{96}\) \(+(-8.82979 + 6.41522i) q^{97}\) \(+(-4.60129 + 7.96966i) q^{98}\) \(+(2.45537 + 4.25283i) q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\(16q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 12q^{3} \) \(\mathstrut -\mathstrut 14q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 11q^{6} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 17q^{8} \) \(\mathstrut -\mathstrut 10q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)	\(16q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 12q^{3} \) \(\mathstrut -\mathstrut 14q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 11q^{6} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 17q^{8} \) \(\mathstrut -\mathstrut 10q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 7q^{11} \) \(\mathstrut +\mathstrut 5q^{12} \) \(\mathstrut -\mathstrut 7q^{13} \) \(\mathstrut -\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 14q^{15} \) \(\mathstrut -\mathstrut 2q^{16} \) \(\mathstrut -\mathstrut 6q^{17} \) \(\mathstrut -\mathstrut 3q^{18} \) \(\mathstrut +\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 37q^{20} \) \(\mathstrut +\mathstrut 9q^{21} \) \(\mathstrut +\mathstrut 9q^{22} \) \(\mathstrut +\mathstrut q^{23} \) \(\mathstrut -\mathstrut 20q^{24} \) \(\mathstrut -\mathstrut 13q^{25} \) \(\mathstrut +\mathstrut 9q^{26} \) \(\mathstrut +\mathstrut 9q^{27} \) \(\mathstrut -\mathstrut 30q^{28} \) \(\mathstrut -\mathstrut 14q^{29} \) \(\mathstrut -\mathstrut 22q^{30} \) \(\mathstrut +\mathstrut 15q^{31} \) \(\mathstrut -\mathstrut 42q^{32} \) \(\mathstrut -\mathstrut 13q^{33} \) \(\mathstrut -\mathstrut 32q^{34} \) \(\mathstrut -\mathstrut 9q^{35} \) \(\mathstrut +\mathstrut q^{36} \) \(\mathstrut -\mathstrut 8q^{37} \) \(\mathstrut +\mathstrut 8q^{38} \) \(\mathstrut -\mathstrut 3q^{39} \) \(\mathstrut -\mathstrut q^{40} \) \(\mathstrut -\mathstrut 8q^{41} \) \(\mathstrut +\mathstrut 69q^{42} \) \(\mathstrut +\mathstrut 23q^{43} \) \(\mathstrut +\mathstrut 39q^{44} \) \(\mathstrut +\mathstrut 65q^{45} \) \(\mathstrut +\mathstrut 34q^{46} \) \(\mathstrut +\mathstrut 14q^{47} \) \(\mathstrut +\mathstrut 34q^{48} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut +\mathstrut 3q^{50} \) \(\mathstrut -\mathstrut 42q^{51} \) \(\mathstrut +\mathstrut 29q^{52} \) \(\mathstrut +\mathstrut 6q^{53} \) \(\mathstrut -\mathstrut 46q^{54} \) \(\mathstrut -\mathstrut 7q^{55} \) \(\mathstrut -\mathstrut 30q^{56} \) \(\mathstrut -\mathstrut 17q^{57} \) \(\mathstrut -\mathstrut 15q^{58} \) \(\mathstrut +\mathstrut 4q^{59} \) \(\mathstrut -\mathstrut 75q^{60} \) \(\mathstrut -\mathstrut 60q^{61} \) \(\mathstrut -\mathstrut 25q^{62} \) \(\mathstrut -\mathstrut 46q^{63} \) \(\mathstrut +\mathstrut 23q^{64} \) \(\mathstrut -\mathstrut 12q^{65} \) \(\mathstrut -\mathstrut 30q^{66} \) \(\mathstrut +\mathstrut 13q^{67} \) \(\mathstrut +\mathstrut 30q^{68} \) \(\mathstrut +\mathstrut 38q^{69} \) \(\mathstrut +\mathstrut 12q^{70} \) \(\mathstrut -\mathstrut 14q^{71} \) \(\mathstrut +\mathstrut 37q^{72} \) \(\mathstrut +\mathstrut 2q^{73} \) \(\mathstrut +\mathstrut 13q^{74} \) \(\mathstrut +\mathstrut 13q^{75} \) \(\mathstrut -\mathstrut 12q^{76} \) \(\mathstrut +\mathstrut 18q^{77} \) \(\mathstrut -\mathstrut 15q^{78} \) \(\mathstrut +\mathstrut 18q^{79} \) \(\mathstrut +\mathstrut 36q^{80} \) \(\mathstrut +\mathstrut 23q^{81} \) \(\mathstrut +\mathstrut 14q^{82} \) \(\mathstrut -\mathstrut 16q^{83} \) \(\mathstrut +\mathstrut 8q^{84} \) \(\mathstrut +\mathstrut 37q^{85} \) \(\mathstrut -\mathstrut 26q^{86} \) \(\mathstrut +\mathstrut 15q^{87} \) \(\mathstrut -\mathstrut 17q^{88} \) \(\mathstrut +\mathstrut q^{89} \) \(\mathstrut -\mathstrut 23q^{90} \) \(\mathstrut +\mathstrut 8q^{91} \) \(\mathstrut -\mathstrut 64q^{92} \) \(\mathstrut +\mathstrut 17q^{93} \) \(\mathstrut +\mathstrut 44q^{94} \) \(\mathstrut -\mathstrut 22q^{95} \) \(\mathstrut +\mathstrut 8q^{96} \) \(\mathstrut +\mathstrut 3q^{97} \) \(\mathstrut -\mathstrut 10q^{98} \) \(\mathstrut +\mathstrut 6q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

\(n\)	\(3\)
\(\chi(n)\)	\(e\left(\frac{14}{15}\right)\)

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