LMFDB - Embedded newform 729.2.e.j.406.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(82,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.e (of order $9$, degree $6$, not 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:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 105x^{8} + 266x^{6} + 306x^{4} + 132x^{2} + 1 $ x^12 + 18x^10 + 105x^8 + 266x^6 + 306x^4 + 132*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			406.1
Root			$1.37340i$ of defining polynomial
Character	$\chi$	$=$	729.406
Dual form			729.2.e.j.325.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.07220 - 1.73878i) q^{2} +(0.923353 + 5.23659i) q^{4} +(-1.57153 - 0.571989i) q^{5} +(0.0869267 - 0.492986i) q^{7} +(4.48686 - 7.77147i) q^{8} +O(q^{10})$	\(q+(-2.07220 - 1.73878i) q^{2} +(0.923353 + 5.23659i) q^{4} +(-1.57153 - 0.571989i) q^{5} +(0.0869267 - 0.492986i) q^{7} +(4.48686 - 7.77147i) q^{8} +(2.26195 + 3.91782i) q^{10} +(-1.80207 + 0.655898i) q^{11} +(2.38426 - 2.00063i) q^{13} +(-1.03732 + 0.870419i) q^{14} +(-12.8172 + 4.66506i) q^{16} +(1.33234 + 2.30767i) q^{17} +(-2.89832 + 5.02003i) q^{19} +(1.54420 - 8.75760i) q^{20} +(4.87470 + 1.77425i) q^{22} +(0.806747 + 4.57529i) q^{23} +(-1.68769 - 1.41614i) q^{25} -8.41934 q^{26} +2.66183 q^{28} +(2.00326 + 1.68093i) q^{29} +(-0.801317 - 4.54450i) q^{31} +(17.8062 + 6.48092i) q^{32} +(1.25168 - 7.09860i) q^{34} +(-0.418591 + 0.725020i) q^{35} +(2.42934 + 4.20773i) q^{37} +(14.7346 - 5.36297i) q^{38} +(-11.4964 + 9.64664i) q^{40} +(8.84640 - 7.42301i) q^{41} +(8.46131 - 3.07966i) q^{43} +(-5.09861 - 8.83106i) q^{44} +(6.28369 - 10.8837i) q^{46} +(-1.18641 + 6.72844i) q^{47} +(6.34237 + 2.30843i) q^{49} +(1.03487 + 5.86907i) q^{50} +(12.6780 + 10.6381i) q^{52} +5.43322 q^{53} +3.20716 q^{55} +(-3.44120 - 2.88751i) q^{56} +(-1.22838 - 6.96647i) q^{58} +(-2.05916 - 0.749473i) q^{59} +(1.18781 - 6.73642i) q^{61} +(-6.24140 + 10.8104i) q^{62} +(-11.9893 - 20.7661i) q^{64} +(-4.89128 + 1.78028i) q^{65} +(9.56299 - 8.02430i) q^{67} +(-10.8541 + 9.10770i) q^{68} +(2.12806 - 0.774549i) q^{70} +(-1.41784 - 2.45578i) q^{71} +(-4.96749 + 8.60394i) q^{73} +(2.28226 - 12.9434i) q^{74} +(-28.9640 - 10.5421i) q^{76} +(0.166701 + 0.945408i) q^{77} +(4.06862 + 3.41398i) q^{79} +22.8109 q^{80} -31.2385 q^{82} +(2.08988 + 1.75362i) q^{83} +(-0.773838 - 4.38865i) q^{85} +(-22.8884 - 8.33069i) q^{86} +(-2.98832 + 16.9476i) q^{88} +(5.60945 - 9.71585i) q^{89} +(-0.779029 - 1.34932i) q^{91} +(-23.2140 + 8.44921i) q^{92} +(14.1578 - 11.8798i) q^{94} +(7.42619 - 6.23132i) q^{95} +(6.47368 - 2.35623i) q^{97} +(-9.12879 - 15.8115i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} + 6 q^{4} + 6 q^{5} - 3 q^{7} + 6 q^{8}+O(q^{10}) $ 12 * q - 6 * q^2 + 6 * q^4 + 6 * q^5 - 3 * q^7 + 6 * q^8	$ 12 q - 6 q^{2} + 6 q^{4} + 6 q^{5} - 3 q^{7} + 6 q^{8} - 6 q^{10} + 12 q^{11} - 3 q^{13} + 15 q^{14} - 36 q^{16} - 9 q^{17} - 12 q^{19} + 42 q^{20} + 6 q^{22} + 6 q^{23} + 6 q^{25} - 48 q^{26} + 6 q^{28} + 12 q^{29} + 6 q^{31} + 54 q^{32} - 9 q^{34} + 30 q^{35} - 3 q^{37} + 42 q^{38} - 57 q^{40} + 24 q^{41} + 6 q^{43} - 33 q^{44} + 3 q^{46} + 21 q^{47} + 33 q^{49} + 21 q^{50} + 45 q^{52} + 18 q^{53} + 30 q^{55} + 3 q^{56} + 33 q^{58} + 15 q^{59} + 33 q^{61} - 30 q^{62} - 6 q^{64} - 6 q^{65} + 42 q^{67} - 18 q^{68} + 24 q^{70} - 12 q^{73} - 3 q^{74} - 87 q^{76} - 57 q^{77} - 48 q^{79} + 42 q^{80} - 42 q^{82} + 12 q^{83} - 36 q^{85} - 30 q^{86} + 30 q^{88} - 9 q^{89} - 18 q^{91} - 48 q^{92} + 33 q^{94} + 30 q^{95} - 3 q^{97} + 18 q^{98}+O(q^{100}) $ 12 * q - 6 * q^2 + 6 * q^4 + 6 * q^5 - 3 * q^7 + 6 * q^8 - 6 * q^10 + 12 * q^11 - 3 * q^13 + 15 * q^14 - 36 * q^16 - 9 * q^17 - 12 * q^19 + 42 * q^20 + 6 * q^22 + 6 * q^23 + 6 * q^25 - 48 * q^26 + 6 * q^28 + 12 * q^29 + 6 * q^31 + 54 * q^32 - 9 * q^34 + 30 * q^35 - 3 * q^37 + 42 * q^38 - 57 * q^40 + 24 * q^41 + 6 * q^43 - 33 * q^44 + 3 * q^46 + 21 * q^47 + 33 * q^49 + 21 * q^50 + 45 * q^52 + 18 * q^53 + 30 * q^55 + 3 * q^56 + 33 * q^58 + 15 * q^59 + 33 * q^61 - 30 * q^62 - 6 * q^64 - 6 * q^65 + 42 * q^67 - 18 * q^68 + 24 * q^70 - 12 * q^73 - 3 * q^74 - 87 * q^76 - 57 * q^77 - 48 * q^79 + 42 * q^80 - 42 * q^82 + 12 * q^83 - 36 * q^85 - 30 * q^86 + 30 * q^88 - 9 * q^89 - 18 * q^91 - 48 * q^92 + 33 * q^94 + 30 * q^95 - 3 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{9}\right)$

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 $

$2$	−2.07220	−	1.73878i	−1.46527	−	1.22950i	−0.920398	−	0.390983i	$-0.872135\pi$
$2$	−2.07220	−	1.73878i	−1.46527	−	1.22950i	−0.544869	−	0.838521i	$-0.683421\pi$
$3$		0			0
$3$		0			0
$4$	0.923353	+	5.23659i	0.461676	+	2.61830i
$5$	−1.57153	−	0.571989i	−0.702809	−	0.255801i	−0.0341990	−	0.999415i	$-0.510888\pi$
$5$	−1.57153	−	0.571989i	−0.702809	−	0.255801i	−0.668610	+	0.743614i	$0.733110\pi$
$6$		0			0
$7$	0.0869267	−	0.492986i	0.0328552	−	0.186331i	−0.963963	−	0.266035i	$-0.914286\pi$
$7$	0.0869267	−	0.492986i	0.0328552	−	0.186331i	0.996819	+	0.0797038i	$0.0253974\pi$
$8$	4.48686	−	7.77147i	1.58634	−	2.74763i
$9$		0			0
$10$	2.26195	+	3.91782i	0.715293	+	1.23892i
$11$	−1.80207	+	0.655898i	−0.543343	+	0.197761i	−0.599086	−	0.800684i	$-0.704469\pi$
$11$	−1.80207	+	0.655898i	−0.543343	+	0.197761i	0.0557432	+	0.998445i	$0.482247\pi$
$12$		0			0
$13$	2.38426	−	2.00063i	0.661276	−	0.554876i	−0.249193	−	0.968454i	$-0.580165\pi$
$13$	2.38426	−	2.00063i	0.661276	−	0.554876i	0.910469	+	0.413578i	$0.135721\pi$
$14$	−1.03732	+	0.870419i	−0.277237	+	0.232629i
$15$		0			0
$16$	−12.8172	+	4.66506i	−3.20429	+	1.16627i
$17$	1.33234	+	2.30767i	0.323139	+	0.559693i	0.981134	−	0.193329i	$-0.0619285\pi$
$17$	1.33234	+	2.30767i	0.323139	+	0.559693i	−0.657995	+	0.753022i	$0.728595\pi$
$18$		0			0
$19$	−2.89832	+	5.02003i	−0.664920	+	1.15167i	0.314387	+	0.949295i	$0.398201\pi$
$19$	−2.89832	+	5.02003i	−0.664920	+	1.15167i	−0.979307	+	0.202380i	$0.935132\pi$
$20$	1.54420	−	8.75760i	0.345294	−	1.95826i
$21$		0			0
$22$	4.87470	+	1.77425i	1.03929	+	0.378271i
$23$	0.806747	+	4.57529i	0.168218	+	0.954013i	0.945684	+	0.325088i	$0.105394\pi$
$23$	0.806747	+	4.57529i	0.168218	+	0.954013i	−0.777466	+	0.628926i	$0.783495\pi$
$24$		0			0
$25$	−1.68769	−	1.41614i	−0.337539	−	0.283229i
$26$	−8.41934			−1.65117
$27$		0			0
$28$	2.66183			0.503039
$29$	2.00326	+	1.68093i	0.371996	+	0.312142i	0.809551	−	0.587050i	$-0.199711\pi$
$29$	2.00326	+	1.68093i	0.371996	+	0.312142i	−0.437555	+	0.899192i	$0.644155\pi$
$30$		0			0
$31$	−0.801317	−	4.54450i	−0.143921	−	0.816216i	−0.968227	−	0.250072i	$-0.919546\pi$
$31$	−0.801317	−	4.54450i	−0.143921	−	0.816216i	0.824306	−	0.566144i	$-0.191565\pi$
$32$	17.8062	+	6.48092i	3.14772	+	1.14567i
$33$		0			0
$34$	1.25168	−	7.09860i	0.214661	−	1.21740i
$35$	−0.418591	+	0.725020i	−0.0707547	+	0.122551i
$36$		0			0
$37$	2.42934	+	4.20773i	0.399381	+	0.691747i	0.993650	−	0.112519i	$-0.0358919\pi$
$37$	2.42934	+	4.20773i	0.399381	+	0.691747i	−0.594269	+	0.804266i	$0.702559\pi$
$38$	14.7346	−	5.36297i	2.39027	−	0.869989i
$39$		0			0
$40$	−11.4964	+	9.64664i	−1.81774	+	1.52527i
$41$	8.84640	−	7.42301i	1.38158	−	1.15928i	0.412951	−	0.910753i	$-0.364498\pi$
$41$	8.84640	−	7.42301i	1.38158	−	1.15928i	0.968625	−	0.248527i	$-0.0799465\pi$
$42$		0			0
$43$	8.46131	−	3.07966i	1.29034	−	0.469644i	0.396500	−	0.918035i	$-0.370225\pi$
$43$	8.46131	−	3.07966i	1.29034	−	0.469644i	0.893838	+	0.448390i	$0.148003\pi$
$44$	−5.09861	−	8.83106i	−0.768645	−	1.33133i
$45$		0			0
$46$	6.28369	−	10.8837i	0.926479	−	1.60471i
$47$	−1.18641	+	6.72844i	−0.173055	+	0.981444i	0.767310	+	0.641277i	$0.221595\pi$
$47$	−1.18641	+	6.72844i	−0.173055	+	0.981444i	−0.940365	+	0.340167i	$0.889516\pi$
$48$		0			0
$49$	6.34237	+	2.30843i	0.906053	+	0.329776i
$50$	1.03487	+	5.86907i	0.146353	+	0.830011i
$51$		0			0
$52$	12.6780	+	10.6381i	1.75813	+	1.47524i
$53$	5.43322			0.746309			0.373155	−	0.927769i	$-0.378276\pi$
$53$	5.43322			0.746309			0.373155	+	0.927769i	$0.378276\pi$
$54$		0			0
$55$	3.20716			0.432454
$56$	−3.44120	−	2.88751i	−0.459849	−	0.385859i
$57$		0			0
$58$	−1.22838	−	6.96647i	−0.161294	−	0.914742i
$59$	−2.05916	−	0.749473i	−0.268080	−	0.0975731i	0.204483	−	0.978870i	$-0.434449\pi$
$59$	−2.05916	−	0.749473i	−0.268080	−	0.0975731i	−0.472563	+	0.881297i	$0.656671\pi$
$60$		0			0
$61$	1.18781	−	6.73642i	0.152084	−	0.862510i	−0.809320	−	0.587368i	$-0.800164\pi$
$61$	1.18781	−	6.73642i	0.152084	−	0.862510i	0.961404	−	0.275142i	$-0.0887248\pi$
$62$	−6.24140	+	10.8104i	−0.792659	+	1.37293i
$63$		0			0
$64$	−11.9893	−	20.7661i	−1.49866	−	2.59576i
$65$	−4.89128	+	1.78028i	−0.606688	+	0.220816i
$66$		0			0
$67$	9.56299	−	8.02430i	1.16831	−	0.980324i	0.168320	−	0.985732i	$-0.446166\pi$
$67$	9.56299	−	8.02430i	1.16831	−	0.980324i	0.999985	+	0.00540797i	$0.00172142\pi$
$68$	−10.8541	+	9.10770i	−1.31626	+	1.10447i
$69$		0			0
$70$	2.12806	−	0.774549i	0.254351	−	0.0925763i
$71$	−1.41784	−	2.45578i	−0.168267	−	0.291447i	0.769544	−	0.638594i	$-0.220484\pi$
$71$	−1.41784	−	2.45578i	−0.168267	−	0.291447i	−0.937811	+	0.347147i	$0.887150\pi$
$72$		0			0
$73$	−4.96749	+	8.60394i	−0.581400	+	1.00701i	0.413913	+	0.910316i	$0.364162\pi$
$73$	−4.96749	+	8.60394i	−0.581400	+	1.00701i	−0.995314	+	0.0966986i	$0.969172\pi$
$74$	2.28226	−	12.9434i	0.265308	−	1.50463i
$75$		0			0
$76$	−28.9640	−	10.5421i	−3.32240	−	1.20926i
$77$	0.166701	+	0.945408i	0.0189973	+	0.107739i
$78$		0			0
$79$	4.06862	+	3.41398i	0.457756	+	0.384103i	0.842305	−	0.539002i	$-0.181198\pi$
$79$	4.06862	+	3.41398i	0.457756	+	0.384103i	−0.384549	+	0.923105i	$0.625643\pi$
$80$	22.8109			2.55033
$81$		0			0
$82$	−31.2385			−3.44972
$83$	2.08988	+	1.75362i	0.229395	+	0.192485i	0.750239	−	0.661167i	$-0.229938\pi$
$83$	2.08988	+	1.75362i	0.229395	+	0.192485i	−0.520844	+	0.853652i	$0.674383\pi$
$84$		0			0
$85$	−0.773838	−	4.38865i	−0.0839345	−	0.476016i
$86$	−22.8884	−	8.33069i	−2.46812	−	0.898322i
$87$		0			0
$88$	−2.98832	+	16.9476i	−0.318556	+	1.80662i
$89$	5.60945	−	9.71585i	0.594600	−	1.02988i	−0.399003	−	0.916950i	$-0.630644\pi$
$89$	5.60945	−	9.71585i	0.594600	−	1.02988i	0.993603	−	0.112928i	$-0.0360230\pi$
$90$		0			0
$91$	−0.779029	−	1.34932i	−0.0816644	−	0.141447i
$92$	−23.2140	+	8.44921i	−2.42023	+	0.880891i
$93$		0			0
$94$	14.1578	−	11.8798i	1.46026	−	1.22531i
$95$	7.42619	−	6.23132i	0.761911	−	0.639320i
$96$		0			0
$97$	6.47368	−	2.35623i	0.657302	−	0.239238i	0.00823103	−	0.999966i	$-0.497380\pi$
$97$	6.47368	−	2.35623i	0.657302	−	0.239238i	0.649071	+	0.760728i	$0.275158\pi$
$98$	−9.12879	−	15.8115i	−0.922147	−	1.59721i
$99$		0			0
$100$	5.85743	−	10.1454i	0.585743	−	1.01454i
$101$	−0.647646	+	3.67298i	−0.0644432	+	0.365476i	0.935484	+	0.353370i	$0.114964\pi$
$101$	−0.647646	+	3.67298i	−0.0644432	+	0.365476i	−0.999927	+	0.0121053i	$0.996147\pi$
$102$		0			0
$103$	−7.21759	−	2.62699i	−0.711170	−	0.258845i	−0.0389976	−	0.999239i	$-0.512416\pi$
$103$	−7.21759	−	2.62699i	−0.711170	−	0.258845i	−0.672173	+	0.740395i	$0.734639\pi$
$104$	−4.85001	−	27.5058i	−0.475583	−	2.69716i
$105$		0			0
$106$	−11.2587	−	9.44718i	−1.09354	−	0.917591i
$107$	10.7658			1.04077			0.520383	−	0.853933i	$-0.325789\pi$
$107$	10.7658			1.04077			0.520383	+	0.853933i	$0.325789\pi$
$108$		0			0
$109$	12.2298			1.17141			0.585703	−	0.810526i	$-0.300819\pi$
$109$	12.2298			1.17141			0.585703	+	0.810526i	$0.300819\pi$
$110$	−6.64588	−	5.57656i	−0.633660	−	0.531704i
$111$		0			0
$112$	1.18566	+	6.72420i	0.112034	+	0.635377i
$113$	−1.82671	−	0.664870i	−0.171843	−	0.0625457i	0.254666	−	0.967029i	$-0.418034\pi$
$113$	−1.82671	−	0.664870i	−0.171843	−	0.0625457i	−0.426509	+	0.904483i	$0.640257\pi$
$114$		0			0
$115$	1.34919	−	7.65164i	0.125813	−	0.713519i
$116$	−6.95266	+	12.0424i	−0.645538	+	1.11810i
$117$		0			0
$118$	2.96382	+	5.13349i	0.272842	+	0.472576i
$119$	1.25347	−	0.456225i	0.114905	−	0.0418220i
$120$		0			0
$121$	−5.60925	+	4.70672i	−0.509932	+	0.427884i
$122$	−14.1745	+	11.8939i	−1.28330	+	1.07682i
$123$		0			0
$124$	23.0578	−	8.39235i	2.07065	−	0.753655i
$125$	6.02320	+	10.4325i	0.538732	+	0.933110i
$126$		0			0
$127$	−1.17217	+	2.03025i	−0.104013	+	0.180156i	−0.913335	−	0.407210i	$-0.866502\pi$
$127$	−1.17217	+	2.03025i	−0.104013	+	0.180156i	0.809322	+	0.587366i	$0.199835\pi$
$128$	−4.68257	+	26.5562i	−0.413885	+	2.34726i
$129$		0			0
$130$	13.2312	+	4.81577i	1.16046	+	0.422371i
$131$	2.96980	+	16.8426i	0.259472	+	1.47154i	0.784326	+	0.620349i	$0.213009\pi$
$131$	2.96980	+	16.8426i	0.259472	+	1.47154i	−0.524854	+	0.851193i	$0.675880\pi$
$132$		0			0
$133$	2.22287	+	1.86521i	0.192747	+	0.161734i
$134$	−33.7689			−2.91719
$135$		0			0
$136$	23.9120			2.05044
$137$	−10.6688	−	8.95221i	−0.911499	−	0.764839i	0.0609045	−	0.998144i	$-0.480601\pi$
$137$	−10.6688	−	8.95221i	−0.911499	−	0.764839i	−0.972404	+	0.233305i	$0.925046\pi$
$138$		0			0
$139$	1.37471	+	7.79636i	0.116601	+	0.661279i	0.985945	+	0.167071i	$0.0534308\pi$
$139$	1.37471	+	7.79636i	0.116601	+	0.661279i	−0.869344	+	0.494208i	$0.835458\pi$
$140$	−4.18314	−	1.52254i	−0.353540	−	0.128678i
$141$		0			0
$142$	−1.33200	+	7.55418i	−0.111779	+	0.633932i
$143$	−2.98439	+	5.16911i	−0.249567	+	0.432263i
$144$		0			0
$145$	−2.18670	−	3.78748i	−0.181596	−	0.314533i
$146$	25.2540	−	9.19170i	2.09004	−	0.760711i
$147$		0			0
$148$	−19.7911	+	16.6067i	−1.62682	+	1.36506i
$149$	−0.557783	+	0.468036i	−0.0456954	+	0.0383430i	−0.665349	−	0.746532i	$-0.731717\pi$
$149$	−0.557783	+	0.468036i	−0.0456954	+	0.0383430i	0.619654	+	0.784875i	$0.287273\pi$
$150$		0			0
$151$	−4.08023	+	1.48508i	−0.332044	+	0.120854i	−0.502662	−	0.864483i	$-0.667646\pi$
$151$	−4.08023	+	1.48508i	−0.332044	+	0.120854i	0.170618	+	0.985337i	$0.445424\pi$
$152$	26.0087	+	45.0484i	2.10958	+	3.65390i
$153$		0			0
$154$	1.29842	−	2.24893i	0.104630	−	0.181224i
$155$	−1.34011	+	7.60015i	−0.107640	+	0.610459i
$156$		0			0
$157$	14.5871	+	5.30927i	1.16418	+	0.423726i	0.850588	−	0.525833i	$-0.176246\pi$
$157$	14.5871	+	5.30927i	1.16418	+	0.423726i	0.313589	+	0.949559i	$0.398469\pi$
$158$	−2.49483	−	14.1489i	−0.198478	−	1.12563i
$159$		0			0
$160$	−24.2759	−	20.3699i	−1.91918	−	1.61038i
$161$	2.32568			0.183289
$162$		0			0
$163$	8.49738			0.665566			0.332783	−	0.943003i	$-0.392012\pi$
$163$	8.49738			0.665566			0.332783	+	0.943003i	$0.392012\pi$
$164$	47.0397	+	39.4710i	3.67318	+	3.08216i
$165$		0			0
$166$	−1.28149	−	7.26771i	−0.0994631	−	0.564083i
$167$	21.7463	+	7.91501i	1.68278	+	0.612482i	0.993687	−	0.112190i	$-0.0357867\pi$
$167$	21.7463	+	7.91501i	1.68278	+	0.612482i	0.689094	+	0.724672i	$0.258009\pi$
$168$		0			0
$169$	−0.575253	+	3.26242i	−0.0442502	+	0.250955i
$170$	−6.02737	+	10.4397i	−0.462278	+	0.800689i
$171$		0			0
$172$	23.9397	+	41.4648i	1.82539	+	3.16166i
$173$	−2.42298	+	0.881892i	−0.184216	+	0.0670490i	−0.432481	−	0.901643i	$-0.642362\pi$
$173$	−2.42298	+	0.881892i	−0.184216	+	0.0670490i	0.248265	+	0.968692i	$0.420139\pi$
$174$		0			0
$175$	−0.844845	+	0.708909i	−0.0638643	+	0.0535885i
$176$	20.0375	−	16.8135i	1.51039	−	1.26737i
$177$		0			0
$178$	−28.5176	+	10.3796i	−2.13749	+	0.777982i
$179$	−4.44806	−	7.70427i	−0.332464	−	0.575844i	0.650530	−	0.759480i	$-0.274547\pi$
$179$	−4.44806	−	7.70427i	−0.332464	−	0.575844i	−0.982994	+	0.183636i	$0.941213\pi$
$180$		0			0
$181$	−3.95592	+	6.85185i	−0.294041	+	0.509294i	−0.974761	−	0.223250i	$-0.928334\pi$
$181$	−3.95592	+	6.85185i	−0.294041	+	0.509294i	0.680720	+	0.732543i	$0.261667\pi$
$182$	−0.731866	+	4.15062i	−0.0542495	+	0.307664i
$183$		0			0
$184$	39.1764	+	14.2591i	2.88813	+	1.05119i
$185$	−1.41099	−	8.00213i	−0.103738	−	0.588328i
$186$		0			0
$187$	−3.91456	−	3.28470i	−0.286261	−	0.240201i
$188$	−36.3296			−2.64961
$189$		0			0
$190$	−26.2235			−1.90245
$191$	12.1781	+	10.2186i	0.881175	+	0.739393i	0.966420	−	0.256967i	$-0.0827230\pi$
$191$	12.1781	+	10.2186i	0.881175	+	0.739393i	−0.0852456	+	0.996360i	$0.527167\pi$
$192$		0			0
$193$	−0.796139	−	4.51513i	−0.0573073	−	0.325006i	0.942654	−	0.333771i	$-0.108321\pi$
$193$	−0.796139	−	4.51513i	−0.0573073	−	0.325006i	−0.999962	+	0.00876483i	$0.997210\pi$
$194$	−17.5117	−	6.37374i	−1.25727	−	0.457608i
$195$		0			0
$196$	−6.23208	+	35.3439i	−0.445149	+	2.52456i
$197$	1.49708	−	2.59303i	0.106663	−	0.184745i	−0.807754	−	0.589520i	$-0.799317\pi$
$197$	1.49708	−	2.59303i	0.106663	−	0.184745i	0.914416	+	0.404775i	$0.132650\pi$
$198$		0			0
$199$	−7.44425	−	12.8938i	−0.527709	−	0.914018i	−0.999478	−	0.0322965i	$-0.989718\pi$
$199$	−7.44425	−	12.8938i	−0.527709	−	0.914018i	0.471770	−	0.881722i	$-0.343615\pi$
$200$	−18.5780	+	6.76183i	−1.31366	+	0.478133i
$201$		0			0
$202$	7.72857	−	6.48504i	0.543781	−	0.456286i
$203$	1.00281	−	0.841461i	0.0703838	−	0.0590590i
$204$		0			0
$205$	−18.1483	+	6.60542i	−1.26753	+	0.461343i
$206$	10.3885	+	17.9935i	0.723803	+	1.25366i
$207$		0			0
$208$	−21.2264	+	36.7652i	−1.47179	+	2.54921i
$209$	1.93033	−	10.9474i	0.133524	−	0.757250i
$210$		0			0
$211$	−13.0420	−	4.74688i	−0.897845	−	0.326789i	−0.148456	−	0.988919i	$-0.547430\pi$
$211$	−13.0420	−	4.74688i	−0.897845	−	0.326789i	−0.749389	+	0.662130i	$0.769653\pi$
$212$	5.01677	+	28.4515i	0.344553	+	1.95406i
$213$		0			0
$214$	−22.3088	−	18.7193i	−1.52500	−	1.27963i
$215$	−15.0587			−1.02700
$216$		0			0
$217$	−2.31003			−0.156815
$218$	−25.3427	−	21.2650i	−1.71642	−	1.44025i
$219$		0			0
$220$	2.96134	+	16.7946i	0.199654	+	1.13229i
$221$	7.79345	+	2.83658i	0.524244	+	0.190809i
$222$		0			0
$223$	−1.18289	+	6.70849i	−0.0792120	+	0.449234i	0.919244	+	0.393688i	$0.128801\pi$
$223$	−1.18289	+	6.70849i	−0.0792120	+	0.449234i	−0.998456	+	0.0555457i	$0.982310\pi$
$224$	4.74283	−	8.21483i	0.316894	−	0.548876i
$225$		0			0
$226$	2.62925	+	4.55400i	0.174895	+	0.302928i
$227$	−9.15340	+	3.33156i	−0.607532	+	0.221124i	−0.627423	−	0.778678i	$-0.715890\pi$
$227$	−9.15340	+	3.33156i	−0.607532	+	0.221124i	0.0198908	+	0.999802i	$0.493668\pi$
$228$		0			0
$229$	−10.7590	+	9.02785i	−0.710973	+	0.596577i	−0.924872	−	0.380279i	$-0.875828\pi$
$229$	−10.7590	+	9.02785i	−0.710973	+	0.596577i	0.213899	+	0.976856i	$0.431384\pi$
$230$	−16.1003	+	13.5098i	−1.06162	+	0.890809i
$231$		0			0
$232$	22.0517	−	8.02615i	1.44776	−	0.526943i
$233$	2.66167	+	4.61014i	0.174372	+	0.302020i	0.939944	−	0.341330i	$-0.110877\pi$
$233$	2.66167	+	4.61014i	0.174372	+	0.302020i	−0.765572	+	0.643350i	$0.777544\pi$
$234$		0			0
$235$	5.71307	−	9.89532i	0.372679	−	0.645499i
$236$	2.02335	−	11.4750i	0.131709	−	0.746960i
$237$		0			0
$238$	−3.39071	−	1.23412i	−0.219787	−	0.0799959i
$239$	−3.08634	−	17.5035i	−0.199639	−	1.13221i	−0.905656	−	0.424012i	$-0.860621\pi$
$239$	−3.08634	−	17.5035i	−0.199639	−	1.13221i	0.706018	−	0.708194i	$-0.250490\pi$
$240$		0			0
$241$	−1.53729	−	1.28994i	−0.0990257	−	0.0830924i	0.591931	−	0.805989i	$-0.298366\pi$
$241$	−1.53729	−	1.28994i	−0.0990257	−	0.0830924i	−0.690956	+	0.722896i	$0.742810\pi$
$242$	19.8075			1.27327
$243$		0			0
$244$	36.3726			2.32852
$245$	−8.64681	−	7.25553i	−0.552424	−	0.463539i
$246$		0			0
$247$	3.13290	+	17.7676i	0.199342	+	1.13052i
$248$	−38.9128	−	14.1631i	−2.47097	−	0.899358i
$249$		0			0
$250$	5.65855	−	32.0912i	0.357878	−	2.02963i
$251$	11.7822	−	20.4073i	0.743683	−	1.28810i	−0.207125	−	0.978314i	$-0.566411\pi$
$251$	11.7822	−	20.4073i	0.743683	−	1.28810i	0.950808	−	0.309782i	$-0.100256\pi$
$252$		0			0
$253$	−4.45473	−	7.71582i	−0.280067	−	0.485090i
$254$	5.95913	−	2.16895i	0.373909	−	0.136092i
$255$		0			0
$256$	19.1413	−	16.0614i	1.19633	−	1.00384i
$257$	−4.50018	+	3.77610i	−0.280713	+	0.235547i	−0.772263	−	0.635303i	$-0.780875\pi$
$257$	−4.50018	+	3.77610i	−0.280713	+	0.235547i	0.491549	+	0.870850i	$0.336431\pi$
$258$		0			0
$259$	2.28553	−	0.831864i	0.142016	−	0.0516895i
$260$	−13.8390	−	23.9698i	−0.858257	−	1.48654i
$261$		0			0
$262$	23.1315	−	40.0650i	1.42907	−	2.47522i
$263$	−3.81646	+	21.6442i	−0.235333	+	1.33464i	0.606578	+	0.795024i	$0.292542\pi$
$263$	−3.81646	+	21.6442i	−0.235333	+	1.33464i	−0.841911	+	0.539617i	$0.818569\pi$
$264$		0			0
$265$	−8.53845	−	3.10774i	−0.524513	−	0.190907i
$266$	−1.36304	−	7.73016i	−0.0835731	−	0.473966i
$267$		0			0
$268$	50.8500	+	42.6682i	3.10616	+	2.60638i
$269$	30.6026			1.86587			0.932937	−	0.360041i	$-0.117237\pi$
$269$	30.6026			1.86587			0.932937	+	0.360041i	$0.117237\pi$
$270$		0			0
$271$	−16.0823			−0.976928			−0.488464	−	0.872584i	$-0.662443\pi$
$271$	−16.0823			−0.976928			−0.488464	+	0.872584i	$0.662443\pi$
$272$	−27.8422	−	23.3624i	−1.68818	−	1.41655i
$273$		0			0
$274$	6.54200	+	37.1015i	0.395217	+	2.24138i
$275$	3.97018	+	1.44503i	0.239411	+	0.0871385i
$276$		0			0
$277$	−3.61424	+	20.4974i	−0.217159	+	1.23157i	0.659963	+	0.751298i	$0.270572\pi$
$277$	−3.61424	+	20.4974i	−0.217159	+	1.23157i	−0.877121	+	0.480269i	$0.840539\pi$
$278$	10.7075	−	18.5459i	0.642194	−	1.11231i
$279$		0			0
$280$	3.75631	+	6.50612i	0.224483	+	0.388815i
$281$	11.5209	−	4.19326i	0.687279	−	0.250149i	0.0253092	−	0.999680i	$-0.491943\pi$
$281$	11.5209	−	4.19326i	0.687279	−	0.250149i	0.661970	+	0.749531i	$0.269721\pi$
$282$		0			0
$283$	3.50280	−	2.93920i	0.208220	−	0.174717i	−0.532714	−	0.846295i	$-0.678828\pi$
$283$	3.50280	−	2.93920i	0.208220	−	0.174717i	0.740934	+	0.671578i	$0.234383\pi$
$284$	11.5507	−	9.69221i	0.685409	−	0.575127i
$285$		0			0
$286$	15.1722	−	5.52223i	0.897151	−	0.326536i
$287$	−2.89045	−	5.00641i	−0.170618	−	0.295519i
$288$		0			0
$289$	4.94976	−	8.57324i	0.291162	−	0.504308i
$290$	−2.05432	+	11.6506i	−0.120634	+	0.684147i
$291$		0			0
$292$	−49.6421	−	18.0682i	−2.90508	−	1.05736i
$293$	−4.53628	−	25.7265i	−0.265013	−	1.50296i	−0.769000	−	0.639249i	$-0.779245\pi$
$293$	−4.53628	−	25.7265i	−0.265013	−	1.50296i	0.503987	−	0.863711i	$-0.331866\pi$
$294$		0			0
$295$	2.80734	+	2.35564i	0.163449	+	0.137150i
$296$	43.6004			2.53422
$297$		0			0
$298$	1.96965			0.114099
$299$	11.0770	+	9.29469i	0.640598	+	0.537526i
$300$		0			0
$301$	−0.782718	−	4.43901i	−0.0451151	−	0.255860i
$302$	11.0373	+	4.01724i	0.635125	+	0.231166i
$303$		0			0
$304$	13.7294	−	77.8634i	0.787436	−	4.46577i
$305$	−5.71984	+	9.90705i	−0.327517	+	0.567276i
$306$		0			0
$307$	−1.64638	−	2.85162i	−0.0939641	−	0.162751i	0.815212	−	0.579163i	$-0.196621\pi$
$307$	−1.64638	−	2.85162i	−0.0939641	−	0.162751i	−0.909176	+	0.416412i	$0.863287\pi$
$308$	−4.79679	+	1.74589i	−0.273323	+	0.0994813i
$309$		0			0
$310$	15.9920	−	13.4189i	0.908283	−	0.762140i
$311$	−26.6527	+	22.3643i	−1.51134	+	1.26816i	−0.650229	+	0.759738i	$0.725327\pi$
$311$	−26.6527	+	22.3643i	−1.51134	+	1.26816i	−0.861107	+	0.508424i	$0.830228\pi$
$312$		0			0
$313$	−9.98690	+	3.63493i	−0.564493	+	0.205459i	−0.608474	−	0.793574i	$-0.708218\pi$
$313$	−9.98690	+	3.63493i	−0.564493	+	0.205459i	0.0439812	+	0.999032i	$0.485996\pi$
$314$	−20.9957	−	36.3657i	−1.18486	−	2.05223i
$315$		0			0
$316$	−14.1209	+	24.4580i	−0.794360	+	1.37587i
$317$	2.69159	−	15.2647i	0.151175	−	0.857353i	−0.811026	−	0.585010i	$-0.801090\pi$
$317$	2.69159	−	15.2647i	0.151175	−	0.857353i	0.962200	−	0.272343i	$-0.0877985\pi$
$318$		0			0
$319$	−4.71253	−	1.71522i	−0.263851	−	0.0960339i
$320$	6.96355	+	39.4922i	0.389274	+	2.20768i
$321$		0			0
$322$	−4.81928	−	4.04385i	−0.268568	−	0.225355i
$323$	−15.4461			−0.859446
$324$		0			0
$325$	−6.85710			−0.380363
$326$	−17.6083	−	14.7751i	−0.975232	−	0.818317i
$327$		0			0
$328$	−17.9951	−	102.056i	−0.993616	−	5.63508i
$329$	3.21390	+	1.16976i	0.177188	+	0.0644911i
$330$		0			0
$331$	−2.53010	+	14.3489i	−0.139067	+	0.788688i	0.832874	+	0.553463i	$0.186694\pi$
$331$	−2.53010	+	14.3489i	−0.139067	+	0.788688i	−0.971941	+	0.235225i	$0.924417\pi$
$332$	−7.25330	+	12.5631i	−0.398077	+	0.689489i
$333$		0			0
$334$	−31.3002	−	54.2136i	−1.71267	−	2.96644i
$335$	−19.6183	+	7.14048i	−1.07186	+	0.390126i
$336$		0			0
$337$	−15.7918	+	13.2509i	−0.860236	+	0.721824i	−0.962019	−	0.272983i	$-0.911990\pi$
$337$	−15.7918	+	13.2509i	−0.860236	+	0.721824i	0.101783	+	0.994807i	$0.467545\pi$
$338$	6.86468	−	5.76015i	0.373389	−	0.313311i
$339$		0			0
$340$	22.2671	−	8.10455i	1.20760	−	0.439531i
$341$	4.42475	+	7.66390i	0.239614	+	0.415023i
$342$		0			0
$343$	3.44142	−	5.96071i	0.185819	−	0.321848i
$344$	14.0312	−	79.5748i	0.756511	−	4.29039i
$345$		0			0
$346$	6.55431	+	2.38557i	0.352362	+	0.128249i
$347$	3.67848	+	20.8617i	0.197471	+	1.11992i	0.908855	+	0.417112i	$0.136958\pi$
$347$	3.67848	+	20.8617i	0.197471	+	1.11992i	−0.711384	+	0.702804i	$0.751931\pi$
$348$		0			0
$349$	−3.54370	−	2.97352i	−0.189690	−	0.159169i	0.542997	−	0.839735i	$-0.317290\pi$
$349$	−3.54370	−	2.97352i	−0.189690	−	0.159169i	−0.732687	+	0.680566i	$0.761734\pi$
$350$	2.98333			0.159466
$351$		0			0
$352$	−36.3387			−1.93686
$353$	10.4515	+	8.76982i	0.556275	+	0.466770i	0.877059	−	0.480382i	$-0.159502\pi$
$353$	10.4515	+	8.76982i	0.556275	+	0.466770i	−0.320784	+	0.947152i	$0.603946\pi$
$354$		0			0
$355$	0.823501	+	4.67031i	0.0437069	+	0.247874i
$356$	56.0574	+	20.4032i	2.97104	+	1.08137i
$357$		0			0
$358$	−4.17877	+	23.6990i	−0.220855	+	1.25253i
$359$	−14.1223	+	24.4606i	−0.745349	+	1.29098i	0.204683	+	0.978828i	$0.434384\pi$
$359$	−14.1223	+	24.4606i	−0.745349	+	1.29098i	−0.950032	+	0.312153i	$0.898950\pi$
$360$		0			0
$361$	−7.30050	−	12.6448i	−0.384237	−	0.665517i
$362$	20.1113	−	7.31992i	1.05703	−	0.384726i
$363$		0			0
$364$	6.34651	−	5.32535i	0.332647	−	0.279124i
$365$	12.7279	−	10.6800i	0.666209	−	0.559016i
$366$		0			0
$367$	−32.7767	+	11.9297i	−1.71093	+	0.622727i	−0.996994	−	0.0774850i	$-0.975311\pi$
$367$	−32.7767	+	11.9297i	−1.71093	+	0.622727i	−0.713935	+	0.700212i	$0.753089\pi$
$368$	−31.6842	−	54.8786i	−1.65165	−	2.86075i
$369$		0			0
$370$	−10.9901	+	19.0354i	−0.571348	+	0.989604i
$371$	0.472292	−	2.67850i	0.0245202	−	0.139061i
$372$		0			0
$373$	−2.87493	−	1.04639i	−0.148858	−	0.0541800i	0.266516	−	0.963830i	$-0.414127\pi$
$373$	−2.87493	−	1.04639i	−0.148858	−	0.0541800i	−0.415375	+	0.909650i	$0.636350\pi$
$374$	2.40036	+	13.6131i	0.124120	+	0.703918i
$375$		0			0
$376$	46.9666	+	39.4097i	2.42212	+	2.03240i
$377$	8.13924			0.419192
$378$		0			0
$379$	−7.67705			−0.394344			−0.197172	−	0.980369i	$-0.563176\pi$
$379$	−7.67705			−0.394344			−0.197172	+	0.980369i	$0.563176\pi$
$380$	39.4879	+	33.1342i	2.02568	+	1.69975i
$381$		0			0
$382$	−7.46746	−	42.3500i	−0.382068	−	2.16682i
$383$	9.73704	+	3.54399i	0.497539	+	0.181090i	0.578587	−	0.815621i	$-0.303604\pi$
$383$	9.73704	+	3.54399i	0.497539	+	0.181090i	−0.0810475	+	0.996710i	$0.525827\pi$
$384$		0			0
$385$	0.278788	−	1.58109i	0.0142084	−	0.0805796i
$386$	−6.20106	+	10.7406i	−0.315626	+	0.546680i
$387$		0			0
$388$	18.3161	+	31.7244i	0.929858	+	1.61056i
$389$	−0.401203	+	0.146026i	−0.0203418	+	0.00740381i	−0.352171	−	0.935936i	$-0.614556\pi$
$389$	−0.401203	+	0.146026i	−0.0203418	+	0.00740381i	0.331829	+	0.943339i	$0.392334\pi$
$390$		0			0
$391$	−9.48341	+	7.95753i	−0.479597	+	0.402429i
$392$	46.3972	−	38.9319i	2.34341	−	1.96636i
$393$		0			0
$394$	−7.61097	+	2.77017i	−0.383435	+	0.139559i
$395$	−4.44119	−	7.69238i	−0.223461	−	0.387045i
$396$		0			0
$397$	13.5445	−	23.4598i	0.679781	−	1.17741i	−0.295266	−	0.955415i	$-0.595408\pi$
$397$	13.5445	−	23.4598i	0.679781	−	1.17741i	0.975047	−	0.221999i	$-0.0712583\pi$
$398$	−6.99357	+	39.6625i	−0.350556	+	1.98810i
$399$		0			0
$400$	28.2379	+	10.2777i	1.41189	+	0.513887i
$401$	−5.09839	−	28.9144i	−0.254602	−	1.44392i	−0.797093	−	0.603856i	$-0.793630\pi$
$401$	−5.09839	−	28.9144i	−0.254602	−	1.44392i	0.542492	−	0.840061i	$-0.317481\pi$
$402$		0			0
$403$	−11.0024	−	9.23214i	−0.548070	−	0.459885i
$404$	−19.8319			−0.986675
$405$		0			0
$406$	−3.54115			−0.175744
$407$	−7.13767	−	5.98922i	−0.353801	−	0.296874i
$408$		0			0
$409$	−3.50490	−	19.8773i	−0.173306	−	0.982869i	−0.940081	−	0.340952i	$-0.889251\pi$
$409$	−3.50490	−	19.8773i	−0.173306	−	0.982869i	0.766774	−	0.641917i	$-0.221860\pi$
$410$	49.0922	+	17.8681i	2.42449	+	0.882443i
$411$		0			0
$412$	7.09208	−	40.2212i	0.349402	−	1.98156i
$413$	−0.548476	+	0.949988i	−0.0269887	+	0.0467459i
$414$		0			0
$415$	−2.28126	−	3.95126i	−0.111983	−	0.193960i
$416$	55.4205	−	20.1714i	2.71722	−	0.988986i
$417$		0			0
$418$	−23.0352	+	19.3289i	−1.12669	+	0.945405i
$419$	−18.6688	+	15.6649i	−0.912028	+	0.765282i	−0.972504	−	0.232887i	$-0.925183\pi$
$419$	−18.6688	+	15.6649i	−0.912028	+	0.765282i	0.0604756	+	0.998170i	$0.480738\pi$
$420$		0			0
$421$	24.5960	−	8.95222i	1.19874	−	0.436305i	0.335954	−	0.941879i	$-0.390941\pi$
$421$	24.5960	−	8.95222i	1.19874	−	0.436305i	0.862783	+	0.505574i	$0.168719\pi$
$422$	18.7717	+	32.5136i	0.913794	+	1.58274i
$423$		0			0
$424$	24.3781	−	42.2240i	1.18390	−	2.05058i
$425$	1.01942	−	5.78143i	0.0494492	−	0.280440i
$426$		0			0
$427$	−3.21771	−	1.17115i	−0.155716	−	0.0566759i
$428$	9.94059	+	56.3759i	0.480497	+	2.72503i
$429$		0			0
$430$	31.2047	+	26.1838i	1.50482	+	1.26270i
$431$	−31.9185			−1.53746			−0.768731	−	0.639572i	$-0.779111\pi$
$431$	−31.9185			−1.53746			−0.768731	+	0.639572i	$0.779111\pi$
$432$		0			0
$433$	0.0123080			0.000591484			0.000295742	−	1.00000i	$-0.499906\pi$
$433$	0.0123080			0.000591484			0.000295742		1.00000i	$0.499906\pi$
$434$	4.78684	+	4.01664i	0.229776	+	0.192805i
$435$		0			0
$436$	11.2925	+	64.0427i	0.540810	+	3.06709i
$437$	−25.3063	−	9.21074i	−1.21056	−	0.440610i
$438$		0			0
$439$	0.921170	−	5.22421i	0.0439650	−	0.249338i	−0.954902	−	0.296920i	$-0.904040\pi$
$439$	0.921170	−	5.22421i	0.0439650	−	0.249338i	0.998867	+	0.0475821i	$0.0151516\pi$
$440$	14.3901	−	24.9244i	0.686020	−	1.18822i
$441$		0			0
$442$	−11.2174	−	19.4291i	−0.533557	−	0.924147i
$443$	38.2420	−	13.9190i	1.81693	−	0.661310i	0.821031	−	0.570883i	$-0.193399\pi$
$443$	38.2420	−	13.9190i	1.81693	−	0.661310i	0.995903	−	0.0904272i	$-0.0288232\pi$
$444$		0			0
$445$	−14.3728	+	12.0602i	−0.681334	+	0.571707i
$446$	14.1158	−	11.8445i	0.668402	−	0.560856i
$447$		0			0
$448$	−11.2796	+	4.10543i	−0.532910	+	0.193963i
$449$	7.71401	+	13.3611i	0.364047	+	0.630547i	0.988623	−	0.150417i	$-0.0480615\pi$
$449$	7.71401	+	13.3611i	0.364047	+	0.630547i	−0.624576	+	0.780964i	$0.714728\pi$
$450$		0			0
$451$	−11.0731	+	19.1791i	−0.521410	+	0.903109i
$452$	1.79495	−	10.1797i	0.0844274	−	0.478811i
$453$		0			0
$454$	24.7605	+	9.01210i	1.16207	+	0.422959i
$455$	0.452470	+	2.56609i	0.0212121	+	0.120300i
$456$		0			0
$457$	1.82989	+	1.53546i	0.0855985	+	0.0718256i	0.684583	−	0.728935i	$-0.259984\pi$
$457$	1.82989	+	1.53546i	0.0855985	+	0.0718256i	−0.598984	+	0.800761i	$0.704429\pi$
$458$	37.9922			1.77526
$459$		0			0
$460$	41.3143			1.92629
$461$	−24.8841	−	20.8802i	−1.15897	−	0.972489i	−0.159076	−	0.987266i	$-0.550852\pi$
$461$	−24.8841	−	20.8802i	−1.15897	−	0.972489i	−0.999891	+	0.0147772i	$0.995296\pi$
$462$		0			0
$463$	5.88295	+	33.3638i	0.273404	+	1.55055i	0.743987	+	0.668194i	$0.232932\pi$
$463$	5.88295	+	33.3638i	0.273404	+	1.55055i	−0.470584	+	0.882355i	$0.655957\pi$
$464$	−33.5178	−	12.1995i	−1.55602	−	0.566346i
$465$		0			0
$466$	2.50053	−	14.1812i	0.115835	−	0.656931i
$467$	−6.90133	+	11.9535i	−0.319356	+	0.553140i	−0.980354	−	0.197247i	$-0.936800\pi$
$467$	−6.90133	+	11.9535i	−0.319356	+	0.553140i	0.660998	+	0.750388i	$0.270133\pi$
$468$		0			0
$469$	−3.12459	−	5.41195i	−0.144280	−	0.249901i
$470$	−29.0444	+	10.5713i	−1.33972	+	0.487618i
$471$		0			0
$472$	−15.0637	+	12.6399i	−0.693361	+	0.581799i
$473$	−13.2279	+	11.0995i	−0.608219	+	0.510356i
$474$		0			0
$475$	12.0006	−	4.36785i	0.550624	−	0.200411i
$476$	3.54645	+	6.14264i	0.162551	+	0.281547i
$477$		0			0
$478$	−24.0392	+	41.6372i	−1.09953	+	1.90444i
$479$	−1.02298	+	5.80162i	−0.0467412	+	0.265083i	−0.999219	−	0.0395270i	$-0.987415\pi$
$479$	−1.02298	+	5.80162i	−0.0467412	+	0.265083i	0.952477	+	0.304610i	$0.0985260\pi$
$480$		0			0
$481$	14.2103	+	5.17213i	0.647935	+	0.235829i
$482$	0.942650	+	5.34603i	0.0429365	+	0.243505i
$483$		0			0
$484$	−29.8265	−	25.0274i	−1.35575	−	1.13761i
$485$	−11.5213			−0.523155
$486$		0			0
$487$	29.0299			1.31547			0.657736	−	0.753249i	$-0.271514\pi$
$487$	29.0299			1.31547			0.657736	+	0.753249i	$0.271514\pi$
$488$	−47.0223	−	39.4564i	−2.12860	−	1.78611i
$489$		0			0
$490$	5.30212	+	30.0698i	0.239526	+	1.35842i
$491$	4.11915	+	1.49925i	0.185895	+	0.0676601i	0.433290	−	0.901254i	$-0.357353\pi$
$491$	4.11915	+	1.49925i	0.185895	+	0.0676601i	−0.247396	+	0.968915i	$0.579575\pi$
$492$		0			0
$493$	−1.21003	+	6.86244i	−0.0544972	+	0.309069i
$494$	24.4019	−	42.2654i	1.09789	−	1.90161i
$495$		0			0
$496$	31.4710	+	54.5093i	1.41309	+	2.44754i
$497$	−1.33391	+	0.485504i	−0.0598341	+	0.0217778i
$498$		0			0
$499$	27.0747	−	22.7184i	1.21203	−	1.01701i	0.212827	−	0.977090i	$-0.431733\pi$
$499$	27.0747	−	22.7184i	1.21203	−	1.01701i	0.999203	−	0.0399241i	$-0.0127116\pi$
$500$	−49.0692	+	41.1739i	−2.19444	+	1.84135i
$501$		0			0
$502$	−59.8988	+	21.8014i	−2.67341	+	0.973043i
$503$	−4.18829	−	7.25434i	−0.186747	−	0.323455i	0.757417	−	0.652932i	$-0.226461\pi$
$503$	−4.18829	−	7.25434i	−0.186747	−	0.323455i	−0.944164	+	0.329477i	$0.893128\pi$
$504$		0			0
$505$	3.11870	−	5.40175i	0.138780	−	0.240375i
$506$	−4.18504	+	23.7345i	−0.186048	+	1.05513i
$507$		0			0
$508$	−11.7139	−	4.26352i	−0.519721	−	0.189163i
$509$	0.667325	+	3.78459i	0.0295786	+	0.167749i	0.996019	−	0.0891428i	$-0.0284128\pi$
$509$	0.667325	+	3.78459i	0.0295786	+	0.167749i	−0.966440	+	0.256892i	$0.917302\pi$
$510$		0			0
$511$	3.80981	+	3.19681i	0.168536	+	0.141419i
$512$	−13.6601			−0.603699
$513$		0			0
$514$	15.8911			0.700925
$515$	9.84003	+	8.25677i	0.433604	+	0.363837i
$516$		0			0
$517$	−2.27519	−	12.9033i	−0.100063	−	0.567484i
$518$	−6.18250	−	2.25025i	−0.271644	−	0.0988702i
$519$		0			0
$520$	−8.11109	+	46.0003i	−0.355695	+	2.01724i
$521$	9.82615	−	17.0194i	0.430491	−	0.745633i	−0.566424	−	0.824114i	$-0.691674\pi$
$521$	9.82615	−	17.0194i	0.430491	−	0.745633i	0.996916	+	0.0784810i	$0.0250070\pi$
$522$		0			0
$523$	19.8051	+	34.3035i	0.866018	+	1.49999i	0.866032	+	0.499988i	$0.166662\pi$
$523$	19.8051	+	34.3035i	0.866018	+	1.49999i	−1.41543e−5		1.00000i	$0.500005\pi$
$524$	−85.4555	+	31.1032i	−3.73314	+	1.35875i
$525$		0			0
$526$	45.5431	−	38.2152i	1.98577	−	1.66626i
$527$	9.41959	−	7.90398i	0.410324	−	0.344303i
$528$		0			0
$529$	1.33052	−	0.484268i	0.0578486	−	0.0210552i
$530$	12.2897	+	21.2864i	0.533830	+	0.924620i
$531$		0			0
$532$	−7.71483	+	13.3625i	−0.334480	+	0.579337i
$533$	6.24142	−	35.3968i	0.270346	−	1.53321i
$534$		0			0
$535$	−16.9187	−	6.15790i	−0.731459	−	0.266229i
$536$	−19.4528	−	110.322i	−0.840233	−	4.76520i
$537$		0			0
$538$	−63.4147	−	53.2112i	−2.73400	−	2.29410i
$539$	−12.9435			−0.557514
$540$		0			0
$541$	−41.8257			−1.79823			−0.899115	−	0.437713i	$-0.855788\pi$
$541$	−41.8257			−1.79823			−0.899115	+	0.437713i	$0.855788\pi$
$542$	33.3257	+	27.9636i	1.43146	+	1.20114i
$543$		0			0
$544$	8.76796	+	49.7256i	0.375923	+	2.13197i
$545$	−19.2195	−	6.99533i	−0.823274	−	0.299647i
$546$		0			0
$547$	−2.95798	+	16.7755i	−0.126474	+	0.717270i	0.853947	+	0.520359i	$0.174202\pi$
$547$	−2.95798	+	16.7755i	−0.126474	+	0.717270i	−0.980421	+	0.196911i	$0.936909\pi$
$548$	37.0280	−	64.1343i	1.58176	−	2.73968i
$549$		0			0
$550$	−5.71442	−	9.89767i	−0.243664	−	0.422038i
$551$	−14.2444	+	5.18455i	−0.606833	+	0.220869i
$552$		0			0
$553$	2.03672	−	1.70901i	0.0866100	−	0.0726744i
$554$	43.1299	−	36.1903i	1.83241	−	1.53758i
$555$		0			0
$556$	−39.5570	+	14.3976i	−1.67759	+	0.610594i
$557$	−16.8840	−	29.2439i	−0.715398	−	1.23911i	−0.962806	−	0.270194i	$-0.912912\pi$
$557$	−16.8840	−	29.2439i	−0.715398	−	1.23911i	0.247408	−	0.968911i	$-0.420421\pi$
$558$		0			0
$559$	14.0127	−	24.2707i	0.592674	−	1.02654i
$560$	1.98288	−	11.2454i	0.0837918	−	0.475207i
$561$		0			0
$562$	−31.1648	−	11.3430i	−1.31461	−	0.478477i
$563$	3.94377	+	22.3662i	0.166210	+	0.942624i	0.947808	+	0.318842i	$0.103294\pi$
$563$	3.94377	+	22.3662i	0.166210	+	0.942624i	−0.781598	+	0.623783i	$0.785595\pi$
$564$		0			0
$565$	2.49043	+	2.08972i	0.104773	+	0.0879153i
$566$	−12.3691			−0.519913
$567$		0			0
$568$	−25.4466			−1.06772
$569$	−8.32801	−	6.98803i	−0.349128	−	0.292954i	0.451312	−	0.892366i	$-0.350956\pi$
$569$	−8.32801	−	6.98803i	−0.349128	−	0.292954i	−0.800440	+	0.599413i	$0.795401\pi$
$570$		0			0
$571$	2.58453	+	14.6576i	0.108159	+	0.613401i	0.989911	+	0.141688i	$0.0452530\pi$
$571$	2.58453	+	14.6576i	0.108159	+	0.613401i	−0.881752	+	0.471713i	$0.843636\pi$
$572$	−29.8242	−	10.8551i	−1.24701	−	0.453875i
$573$		0			0
$574$	−2.71546	+	15.4002i	−0.113341	+	0.642790i
$575$	5.11772	−	8.86416i	0.213424	−	0.369661i
$576$		0			0
$577$	18.5582	+	32.1437i	0.772586	+	1.33816i	0.936141	+	0.351624i	$0.114371\pi$
$577$	18.5582	+	32.1437i	0.772586	+	1.33816i	−0.163555	+	0.986534i	$0.552296\pi$
$578$	−25.1639	+	9.15891i	−1.04668	+	0.380960i
$579$		0			0
$580$	17.8144	−	14.9480i	0.739702	−	0.620684i
$581$	1.04618	−	0.877847i	0.0434028	−	0.0364192i
$582$		0			0
$583$	−9.79101	+	3.56364i	−0.405502	+	0.147591i
$584$	44.5768	+	77.2093i	1.84460	+	3.19494i
$585$		0			0
$586$	−35.3328	+	61.1981i	−1.45958	+	2.52807i
$587$	−2.54277	+	14.4208i	−0.104951	+	0.595208i	0.886288	+	0.463134i	$0.153275\pi$
$587$	−2.54277	+	14.4208i	−0.104951	+	0.595208i	−0.991240	+	0.132075i	$0.957836\pi$
$588$		0			0
$589$	25.1360	+	9.14876i	1.03571	+	0.376968i
$590$	−1.72143	−	9.76269i	−0.0708700	−	0.401924i
$591$		0			0
$592$	−50.7665	−	42.5982i	−2.08649	−	1.75077i
$593$	36.4392			1.49638			0.748189	−	0.663485i	$-0.230924\pi$
$593$	36.4392			1.49638			0.748189	+	0.663485i	$0.230924\pi$
$594$		0			0
$595$	−2.23081			−0.0914544
$596$	−2.96594	−	2.48872i	−0.121490	−	0.101942i
$597$		0			0
$598$	−6.79227	−	38.5209i	−0.277757	−	1.57524i
$599$	−25.8368	−	9.40381i	−1.05566	−	0.384229i	−0.244864	−	0.969557i	$-0.578743\pi$
$599$	−25.8368	−	9.40381i	−1.05566	−	0.384229i	−0.810797	+	0.585328i	$0.800966\pi$
$600$		0			0
$601$	7.84490	−	44.4907i	0.320000	−	1.81481i	−0.222702	−	0.974887i	$-0.571488\pi$
$601$	7.84490	−	44.4907i	0.320000	−	1.81481i	0.542702	−	0.839925i	$-0.317401\pi$
$602$	−6.09653	+	10.5595i	−0.248476	+	0.430373i
$603$		0			0
$604$	−11.5443	−	19.9953i	−0.469729	−	0.813595i
$605$	11.5073	−	4.18831i	0.467838	−	0.170279i
$606$		0			0
$607$	13.1278	−	11.0156i	0.532842	−	0.447108i	−0.336239	−	0.941777i	$-0.609155\pi$
$607$	13.1278	−	11.0156i	0.532842	−	0.447108i	0.869082	+	0.494669i	$0.164711\pi$
$608$	−84.1424	+	70.6038i	−3.41242	+	2.86336i
$609$		0			0
$610$	29.0788	−	10.5838i	1.17737	−	0.428527i
$611$	10.6324	+	18.4159i	0.430143	+	0.745029i
$612$		0			0
$613$	0.234380	−	0.405959i	0.00946653	−	0.0163965i	−0.861253	−	0.508176i	$-0.830320\pi$
$613$	0.234380	−	0.405959i	0.00946653	−	0.0163965i	0.870720	+	0.491779i	$0.163653\pi$
$614$	−1.54671	+	8.77183i	−0.0624202	+	0.354002i
$615$		0			0
$616$	8.09517	+	2.94640i	0.326164	+	0.118714i
$617$	−0.370713	−	2.10242i	−0.0149243	−	0.0846401i	0.976436	−	0.215808i	$-0.0692385\pi$
$617$	−0.370713	−	2.10242i	−0.0149243	−	0.0846401i	−0.991360	+	0.131168i	$0.958127\pi$
$618$		0			0
$619$	6.54018	+	5.48786i	0.262872	+	0.220576i	0.764692	−	0.644397i	$-0.222891\pi$
$619$	6.54018	+	5.48786i	0.262872	+	0.220576i	−0.501819	+	0.864972i	$0.667336\pi$
$620$	−41.0363			−1.64806
$621$		0			0
$622$	94.1163			3.77372
$623$	−4.30217	−	3.60995i	−0.172363	−	0.144629i
$624$		0			0
$625$	−1.58551	−	8.99186i	−0.0634203	−	0.359674i
$626$	27.0152	+	9.83273i	1.07974	+	0.392995i
$627$		0			0
$628$	−14.3334	+	81.2890i	−0.571967	+	3.24378i
$629$	−6.47339	+	11.2122i	−0.258111	+	0.447061i
$630$		0			0
$631$	5.93539	+	10.2804i	0.236284	+	0.409256i	0.959645	−	0.281214i	$-0.0907370\pi$
$631$	5.93539	+	10.2804i	0.236284	+	0.409256i	−0.723361	+	0.690470i	$0.757404\pi$
$632$	44.7870	−	16.3011i	1.78153	−	0.648424i
$633$		0			0
$634$	−32.1196	+	26.9515i	−1.27563	+	1.07038i
$635$	3.00337	−	2.52013i	0.119185	−	0.100008i
$636$		0			0
$637$	19.7402	−	7.18485i	0.782136	−	0.284674i
$638$	6.78291	+	11.7483i	0.268538	+	0.465121i
$639$		0			0
$640$	22.5486	−	39.0554i	0.891313	−	1.54380i
$641$	0.920970	−	5.22308i	0.0363761	−	0.206299i	−0.961203	−	0.275843i	$-0.911043\pi$
$641$	0.920970	−	5.22308i	0.0363761	−	0.206299i	0.997579	+	0.0695434i	$0.0221542\pi$
$642$		0			0
$643$	0.774183	+	0.281780i	0.0305308	+	0.0111123i	0.357240	−	0.934012i	$-0.383718\pi$
$643$	0.774183	+	0.281780i	0.0305308	+	0.0111123i	−0.326710	+	0.945125i	$0.605940\pi$
$644$	2.14742	+	12.1786i	0.0846203	+	0.479906i
$645$		0			0
$646$	32.0075	+	26.8575i	1.25932	+	1.05669i
$647$	−40.8373			−1.60548			−0.802740	−	0.596329i	$-0.796626\pi$
$647$	−40.8373			−1.60548			−0.802740	+	0.596329i	$0.796626\pi$
$648$		0			0
$649$	4.20232			0.164955
$650$	14.2093	+	11.9230i	0.557334	+	0.467658i
$651$		0			0
$652$	7.84608	+	44.4973i	0.307276	+	1.74265i
$653$	−1.00487	−	0.365742i	−0.0393235	−	0.0143126i	0.322284	−	0.946643i	$-0.395550\pi$
$653$	−1.00487	−	0.365742i	−0.0393235	−	0.0143126i	−0.361607	+	0.932331i	$0.617772\pi$
$654$		0			0
$655$	4.96665	−	28.1672i	0.194063	−	1.10059i
$656$	−78.7569	+	136.411i	−3.07494	+	5.32595i
$657$		0			0
$658$	−4.62587	−	8.01225i	−0.180335	−	0.312350i
$659$	26.9356	−	9.80376i	1.04926	−	0.381900i	0.240878	−	0.970555i	$-0.422565\pi$
$659$	26.9356	−	9.80376i	1.04926	−	0.381900i	0.808384	+	0.588655i	$0.200342\pi$
$660$		0			0
$661$	−3.44392	+	2.88979i	−0.133953	+	0.112400i	−0.707303	−	0.706911i	$-0.750088\pi$
$661$	−3.44392	+	2.88979i	−0.133953	+	0.112400i	0.573350	+	0.819311i	$0.305644\pi$
$662$	30.1925	−	25.3345i	1.17347	−	0.984655i
$663$		0			0
$664$	23.0052	−	8.37322i	0.892776	−	0.324944i
$665$	−2.42642	−	4.20268i	−0.0940924	−	0.162973i
$666$		0			0
$667$	−6.07464	+	10.5216i	−0.235211	+	0.407397i
$668$	−21.3682	+	121.185i	−0.826759	+	4.68879i
$669$		0			0
$670$	53.0688	+	19.3155i	2.05023	+	0.746222i
$671$	2.27789	+	12.9185i	0.0879369	+	0.498715i
$672$		0			0
$673$	13.8337	+	11.6078i	0.533249	+	0.447449i	0.869222	−	0.494423i	$-0.164621\pi$
$673$	13.8337	+	11.6078i	0.533249	+	0.447449i	−0.335973	+	0.941872i	$0.609065\pi$
$674$	55.7643			2.14796
$675$		0			0
$676$	−17.6151			−0.677505
$677$	12.0569	+	10.1169i	0.463385	+	0.388826i	0.844375	−	0.535753i	$-0.179972\pi$
$677$	12.0569	+	10.1169i	0.463385	+	0.388826i	−0.380990	+	0.924579i	$0.624417\pi$
$678$		0			0
$679$	−0.598851	−	3.39625i	−0.0229818	−	0.130336i
$680$	−37.5784	−	13.6774i	−1.44107	−	0.524505i
$681$		0			0
$682$	4.15688	−	23.5748i	0.159175	−	0.902726i
$683$	1.38059	−	2.39125i	0.0528268	−	0.0914987i	−0.838403	−	0.545051i	$-0.816510\pi$
$683$	1.38059	−	2.39125i	0.0528268	−	0.0914987i	0.891230	+	0.453552i	$0.149844\pi$
$684$		0			0
$685$	11.6458	+	20.1711i	0.444963	+	0.770698i
$686$	−17.4957	+	6.36790i	−0.667988	+	0.243128i
$687$		0			0
$688$	−94.0831	+	78.9451i	−3.58688	+	3.00975i
$689$	12.9542	−	10.8699i	0.493516	−	0.414109i
$690$		0			0
$691$	32.4434	−	11.8084i	1.23421	−	0.449214i	0.359169	−	0.933272i	$-0.383060\pi$
$691$	32.4434	−	11.8084i	1.23421	−	0.449214i	0.875036	+	0.484058i	$0.160838\pi$
$692$	−6.85537	−	11.8738i	−0.260602	−	0.451376i
$693$		0			0
$694$	28.6514	−	49.6257i	1.08759	−	1.88377i
$695$	2.29904	−	13.0385i	0.0872077	−	0.494579i
$696$		0			0
$697$	28.9163	+	10.5247i	1.09528	+	0.398650i
$698$	2.17296	+	12.3234i	0.0822476	+	0.466449i
$699$		0			0
$700$	−4.49236	−	3.76954i	−0.169795	−	0.142475i
$701$	−20.7410			−0.783378			−0.391689	−	0.920098i	$-0.628109\pi$
$701$	−20.7410			−0.783378			−0.391689	+	0.920098i	$0.628109\pi$
$702$		0			0
$703$	−28.1640			−1.06222
$704$	35.2260	+	29.5581i	1.32763	+	1.11401i
$705$		0			0
$706$	−6.40871	−	36.3456i	−0.241195	−	1.36789i
$707$	1.75443	+	0.638561i	0.0659822	+	0.0240156i
$708$		0			0
$709$	4.81129	−	27.2862i	0.180692	−	1.02475i	−0.750675	−	0.660672i	$-0.770271\pi$
$709$	4.81129	−	27.2862i	0.180692	−	1.02475i	0.931367	−	0.364083i	$-0.118617\pi$
$710$	6.41419	−	11.1097i	0.240720	−	0.416940i
$711$		0			0
$712$	−50.3376	−	87.1873i	−1.88648	−	3.26748i
$713$	20.1459	−	7.33252i	0.754471	−	0.274605i
$714$		0			0
$715$	7.64672	−	6.41636i	0.285971	−	0.239958i
$716$	36.2370	−	30.4065i	1.35424	−	1.13634i
$717$		0			0
$718$	71.7960	−	26.1316i	2.67940	−	0.975223i
$719$	−16.5657	−	28.6927i	−0.617797	−	1.07006i	−0.989887	−	0.141859i	$-0.954692\pi$
$719$	−16.5657	−	28.6927i	−0.617797	−	1.07006i	0.372090	−	0.928197i	$-0.378641\pi$
$720$		0			0
$721$	−1.92247	+	3.32981i	−0.0715965	+	0.124009i
$722$	−6.85852	+	38.8966i	−0.255248	+	1.44758i
$723$		0			0
$724$	−39.5330	−	14.3888i	−1.46923	−	0.534757i
$725$	−1.00045	−	5.67381i	−0.0371556	−	0.210720i
$726$		0			0
$727$	−0.0632795	−	0.0530978i	−0.00234691	−	0.00196929i	0.641613	−	0.767028i	$-0.278265\pi$
$727$	−0.0632795	−	0.0530978i	−0.00234691	−	0.00196929i	−0.643960	+	0.765059i	$0.722710\pi$
$728$	−13.9816			−0.518191
$729$		0			0
$730$	−44.9449			−1.66349
$731$	18.3802	+	15.4228i	0.679815	+	0.570433i
$732$		0			0
$733$	−5.54241	−	31.4326i	−0.204714	−	1.16099i	−0.897890	−	0.440221i	$-0.854900\pi$
$733$	−5.54241	−	31.4326i	−0.204714	−	1.16099i	0.693176	−	0.720768i	$-0.256211\pi$
$734$	88.6630	+	32.2707i	3.27261	+	1.19113i
$735$		0			0
$736$	−15.2870	+	86.6968i	−0.563486	+	3.19569i
$737$	−11.9700	+	20.7327i	−0.440921	+	0.763698i
$738$		0			0
$739$	17.8960	+	30.9967i	0.658314	+	1.14023i	0.981052	+	0.193745i	$0.0620634\pi$
$739$	17.8960	+	30.9967i	0.658314	+	1.14023i	−0.322738	+	0.946488i	$0.604603\pi$
$740$	40.6010	−	14.7776i	1.49252	−	0.543234i
$741$		0			0
$742$	−5.63601	+	4.72917i	−0.206904	+	0.173613i
$743$	15.1515	−	12.7136i	0.555854	−	0.466417i	−0.321063	−	0.947058i	$-0.604040\pi$
$743$	15.1515	−	12.7136i	0.555854	−	0.466417i	0.876918	+	0.480640i	$0.159596\pi$
$744$		0			0
$745$	1.14428	−	0.416485i	0.0419233	−	0.0152588i
$746$	4.13799	+	7.16721i	0.151503	+	0.262410i
$747$		0			0
$748$	13.5861	−	23.5319i	0.496758	−	0.860411i
$749$	0.935832	−	5.30737i	0.0341946	−	0.193927i
$750$		0			0
$751$	−28.7363	−	10.4592i	−1.04860	−	0.381660i	−0.240468	−	0.970657i	$-0.577301\pi$
$751$	−28.7363	−	10.4592i	−1.04860	−	0.381660i	−0.808135	+	0.588997i	$0.799523\pi$
$752$	−16.1823	−	91.7741i	−0.590106	−	3.34666i
$753$		0			0
$754$	−16.8661	−	14.1524i	−0.614228	−	0.515399i
$755$	7.26165			0.264278
$756$		0			0
$757$	25.4129			0.923647			0.461824	−	0.886972i	$-0.347195\pi$
$757$	25.4129			0.923647			0.461824	+	0.886972i	$0.347195\pi$
$758$	15.9084	+	13.3487i	0.577819	+	0.484847i
$759$		0			0
$760$	−15.1062	−	85.6714i	−0.547959	−	3.10763i
$761$	−43.9945	−	16.0127i	−1.59480	−	0.580460i	−0.616445	−	0.787398i	$-0.711428\pi$
$761$	−43.9945	−	16.0127i	−1.59480	−	0.580460i	−0.978354	+	0.206938i	$0.933650\pi$
$762$		0			0
$763$	1.06310	−	6.02914i	0.0384868	−	0.218269i
$764$	−42.2661	+	73.2070i	−1.52913	+	2.64854i
$765$		0			0
$766$	−14.0149	−	24.2744i	−0.506377	−	0.877071i
$767$	−6.40900	+	2.33269i	−0.231416	+	0.0842284i
$768$		0			0
$769$	11.1578	−	9.36247i	0.402359	−	0.337619i	−0.419046	−	0.907965i	$-0.637635\pi$
$769$	11.1578	−	9.36247i	0.402359	−	0.337619i	0.821405	+	0.570346i	$0.193191\pi$
$770$	−3.32687	+	2.79158i	−0.119892	+	0.100601i
$771$		0			0
$772$	22.9088	−	8.33811i	0.824504	−	0.300095i
$773$	12.1767	+	21.0906i	0.437964	+	0.758576i	0.997532	−	0.0702080i	$-0.0223663\pi$
$773$	12.1767	+	21.0906i	0.437964	+	0.758576i	−0.559568	+	0.828784i	$0.689033\pi$
$774$		0			0
$775$	−5.08328	+	8.80451i	−0.182597	+	0.316267i
$776$	10.7351	−	60.8820i	0.385369	−	2.18554i
$777$		0			0
$778$	1.08528	+	0.395009i	0.0389092	+	0.0141618i
$779$	11.6241	+	65.9235i	0.416476	+	2.36196i
$780$		0

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.07220 - 1.73878i) q^{2} +(0.923353 + 5.23659i) q^{4} +(-1.57153 - 0.571989i) q^{5} +(0.0869267 - 0.492986i) q^{7} +(4.48686 - 7.77147i) q^{8} +O(q^{10})\)	\(q+(-2.07220 - 1.73878i) q^{2} +(0.923353 + 5.23659i) q^{4} +(-1.57153 - 0.571989i) q^{5} +(0.0869267 - 0.492986i) q^{7} +(4.48686 - 7.77147i) q^{8} +(2.26195 + 3.91782i) q^{10} +(-1.80207 + 0.655898i) q^{11} +(2.38426 - 2.00063i) q^{13} +(-1.03732 + 0.870419i) q^{14} +(-12.8172 + 4.66506i) q^{16} +(1.33234 + 2.30767i) q^{17} +(-2.89832 + 5.02003i) q^{19} +(1.54420 - 8.75760i) q^{20} +(4.87470 + 1.77425i) q^{22} +(0.806747 + 4.57529i) q^{23} +(-1.68769 - 1.41614i) q^{25} -8.41934 q^{26} +2.66183 q^{28} +(2.00326 + 1.68093i) q^{29} +(-0.801317 - 4.54450i) q^{31} +(17.8062 + 6.48092i) q^{32} +(1.25168 - 7.09860i) q^{34} +(-0.418591 + 0.725020i) q^{35} +(2.42934 + 4.20773i) q^{37} +(14.7346 - 5.36297i) q^{38} +(-11.4964 + 9.64664i) q^{40} +(8.84640 - 7.42301i) q^{41} +(8.46131 - 3.07966i) q^{43} +(-5.09861 - 8.83106i) q^{44} +(6.28369 - 10.8837i) q^{46} +(-1.18641 + 6.72844i) q^{47} +(6.34237 + 2.30843i) q^{49} +(1.03487 + 5.86907i) q^{50} +(12.6780 + 10.6381i) q^{52} +5.43322 q^{53} +3.20716 q^{55} +(-3.44120 - 2.88751i) q^{56} +(-1.22838 - 6.96647i) q^{58} +(-2.05916 - 0.749473i) q^{59} +(1.18781 - 6.73642i) q^{61} +(-6.24140 + 10.8104i) q^{62} +(-11.9893 - 20.7661i) q^{64} +(-4.89128 + 1.78028i) q^{65} +(9.56299 - 8.02430i) q^{67} +(-10.8541 + 9.10770i) q^{68} +(2.12806 - 0.774549i) q^{70} +(-1.41784 - 2.45578i) q^{71} +(-4.96749 + 8.60394i) q^{73} +(2.28226 - 12.9434i) q^{74} +(-28.9640 - 10.5421i) q^{76} +(0.166701 + 0.945408i) q^{77} +(4.06862 + 3.41398i) q^{79} +22.8109 q^{80} -31.2385 q^{82} +(2.08988 + 1.75362i) q^{83} +(-0.773838 - 4.38865i) q^{85} +(-22.8884 - 8.33069i) q^{86} +(-2.98832 + 16.9476i) q^{88} +(5.60945 - 9.71585i) q^{89} +(-0.779029 - 1.34932i) q^{91} +(-23.2140 + 8.44921i) q^{92} +(14.1578 - 11.8798i) q^{94} +(7.42619 - 6.23132i) q^{95} +(6.47368 - 2.35623i) q^{97} +(-9.12879 - 15.8115i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} + 6 q^{4} + 6 q^{5} - 3 q^{7} + 6 q^{8}+O(q^{10}) \) 12 * q - 6 * q^2 + 6 * q^4 + 6 * q^5 - 3 * q^7 + 6 * q^8	\( 12 q - 6 q^{2} + 6 q^{4} + 6 q^{5} - 3 q^{7} + 6 q^{8} - 6 q^{10} + 12 q^{11} - 3 q^{13} + 15 q^{14} - 36 q^{16} - 9 q^{17} - 12 q^{19} + 42 q^{20} + 6 q^{22} + 6 q^{23} + 6 q^{25} - 48 q^{26} + 6 q^{28} + 12 q^{29} + 6 q^{31} + 54 q^{32} - 9 q^{34} + 30 q^{35} - 3 q^{37} + 42 q^{38} - 57 q^{40} + 24 q^{41} + 6 q^{43} - 33 q^{44} + 3 q^{46} + 21 q^{47} + 33 q^{49} + 21 q^{50} + 45 q^{52} + 18 q^{53} + 30 q^{55} + 3 q^{56} + 33 q^{58} + 15 q^{59} + 33 q^{61} - 30 q^{62} - 6 q^{64} - 6 q^{65} + 42 q^{67} - 18 q^{68} + 24 q^{70} - 12 q^{73} - 3 q^{74} - 87 q^{76} - 57 q^{77} - 48 q^{79} + 42 q^{80} - 42 q^{82} + 12 q^{83} - 36 q^{85} - 30 q^{86} + 30 q^{88} - 9 q^{89} - 18 q^{91} - 48 q^{92} + 33 q^{94} + 30 q^{95} - 3 q^{97} + 18 q^{98}+O(q^{100}) \) 12 * q - 6 * q^2 + 6 * q^4 + 6 * q^5 - 3 * q^7 + 6 * q^8 - 6 * q^10 + 12 * q^11 - 3 * q^13 + 15 * q^14 - 36 * q^16 - 9 * q^17 - 12 * q^19 + 42 * q^20 + 6 * q^22 + 6 * q^23 + 6 * q^25 - 48 * q^26 + 6 * q^28 + 12 * q^29 + 6 * q^31 + 54 * q^32 - 9 * q^34 + 30 * q^35 - 3 * q^37 + 42 * q^38 - 57 * q^40 + 24 * q^41 + 6 * q^43 - 33 * q^44 + 3 * q^46 + 21 * q^47 + 33 * q^49 + 21 * q^50 + 45 * q^52 + 18 * q^53 + 30 * q^55 + 3 * q^56 + 33 * q^58 + 15 * q^59 + 33 * q^61 - 30 * q^62 - 6 * q^64 - 6 * q^65 + 42 * q^67 - 18 * q^68 + 24 * q^70 - 12 * q^73 - 3 * q^74 - 87 * q^76 - 57 * q^77 - 48 * q^79 + 42 * q^80 - 42 * q^82 + 12 * q^83 - 36 * q^85 - 30 * q^86 + 30 * q^88 - 9 * q^89 - 18 * q^91 - 48 * q^92 + 33 * q^94 + 30 * q^95 - 3 * q^97 + 18 * q^98

Introduction

L-functions

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