LMFDB - Embedded newform 729.2.e.u.325.2

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			325.2
Root			$1.37340i$ of defining polynomial
Character	$\chi$	$=$	729.325
Dual form			729.2.e.u.406.2

$q$-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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{9}\right)$

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	0.544869	−	0.838521i	$-0.316579\pi$
$2$	2.07220	−	1.73878i	1.46527	−	1.22950i	0.920398	−	0.390983i	$-0.127865\pi$
$3$		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	$-0.489112\pi$
$5$	1.57153	−	0.571989i	0.702809	−	0.255801i	0.668610	+	0.743614i	$0.266890\pi$
$6$		0			0
$7$	0.0869267	+	0.492986i	0.0328552	+	0.186331i	0.996819	−	0.0797038i	$-0.0253974\pi$
$7$	0.0869267	+	0.492986i	0.0328552	+	0.186331i	−0.963963	+	0.266035i	$0.914286\pi$
$8$	−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	$-0.295531\pi$
$11$	1.80207	+	0.655898i	0.543343	+	0.197761i	−0.0557432	+	0.998445i	$0.517753\pi$
$12$		0			0
$13$	2.38426	+	2.00063i	0.661276	+	0.554876i	0.910469	−	0.413578i	$-0.135721\pi$
$13$	2.38426	+	2.00063i	0.661276	+	0.554876i	−0.249193	+	0.968454i	$0.580165\pi$
$14$	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	$-0.938071\pi$
$17$	−1.33234	+	2.30767i	−0.323139	+	0.559693i	0.657995	+	0.753022i	$0.271405\pi$
$18$		0			0
$19$	−2.89832	−	5.02003i	−0.664920	−	1.15167i	−0.979307	−	0.202380i	$-0.935132\pi$
$19$	−2.89832	−	5.02003i	−0.664920	−	1.15167i	0.314387	−	0.949295i	$-0.398201\pi$
$20$	−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	0.777466	+	0.628926i	$0.216505\pi$
$23$	−0.806747	+	4.57529i	−0.168218	+	0.954013i	−0.945684	+	0.325088i	$0.894606\pi$
$24$		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	$-0.800289\pi$
$29$	−2.00326	+	1.68093i	−0.371996	+	0.312142i	0.437555	+	0.899192i	$0.355845\pi$
$30$		0			0
$31$	−0.801317	+	4.54450i	−0.143921	+	0.816216i	0.824306	+	0.566144i	$0.191565\pi$
$31$	−0.801317	+	4.54450i	−0.143921	+	0.816216i	−0.968227	+	0.250072i	$0.919546\pi$
$32$	−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	−0.594269	−	0.804266i	$-0.702559\pi$
$37$	2.42934	−	4.20773i	0.399381	−	0.691747i	0.993650	+	0.112519i	$0.0358919\pi$
$38$	−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	−0.968625	−	0.248527i	$-0.920054\pi$
$41$	−8.84640	−	7.42301i	−1.38158	−	1.15928i	−0.412951	−	0.910753i	$-0.635502\pi$
$42$		0			0
$43$	8.46131	+	3.07966i	1.29034	+	0.469644i	0.893838	−	0.448390i	$-0.148003\pi$
$43$	8.46131	+	3.07966i	1.29034	+	0.469644i	0.396500	+	0.918035i	$0.370225\pi$
$44$	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	0.940365	+	0.340167i	$0.110484\pi$
$47$	1.18641	+	6.72844i	0.173055	+	0.981444i	−0.767310	+	0.641277i	$0.778405\pi$
$48$		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	$-0.621724\pi$
$53$	−5.43322			−0.746309			−0.373155	+	0.927769i	$0.621724\pi$
$54$		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	$-0.565551\pi$
$59$	2.05916	−	0.749473i	0.268080	−	0.0975731i	0.472563	+	0.881297i	$0.343329\pi$
$60$		0			0
$61$	1.18781	+	6.73642i	0.152084	+	0.862510i	0.961404	+	0.275142i	$0.0887248\pi$
$61$	1.18781	+	6.73642i	0.152084	+	0.862510i	−0.809320	+	0.587368i	$0.800164\pi$
$62$	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	0.999985	−	0.00540797i	$-0.00172142\pi$
$67$	9.56299	+	8.02430i	1.16831	+	0.980324i	0.168320	+	0.985732i	$0.446166\pi$
$68$	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	$-0.779516\pi$
$71$	1.41784	−	2.45578i	0.168267	−	0.291447i	0.937811	+	0.347147i	$0.112850\pi$
$72$		0			0
$73$	−4.96749	−	8.60394i	−0.581400	−	1.00701i	−0.995314	−	0.0966986i	$-0.969172\pi$
$73$	−4.96749	−	8.60394i	−0.581400	−	1.00701i	0.413913	−	0.910316i	$-0.364162\pi$
$74$	−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	−0.384549	−	0.923105i	$-0.625643\pi$
$79$	4.06862	−	3.41398i	0.457756	−	0.384103i	0.842305	+	0.539002i	$0.181198\pi$
$80$	−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	$-0.770062\pi$
$83$	−2.08988	+	1.75362i	−0.229395	+	0.192485i	0.520844	+	0.853652i	$0.325617\pi$
$84$		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	−0.993603	−	0.112928i	$-0.963977\pi$
$89$	−5.60945	−	9.71585i	−0.594600	−	1.02988i	0.399003	−	0.916950i	$-0.369356\pi$
$90$		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	0.649071	−	0.760728i	$-0.275158\pi$
$97$	6.47368	+	2.35623i	0.657302	+	0.239238i	0.00823103	+	0.999966i	$0.497380\pi$
$98$	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	0.999927	+	0.0121053i	$0.00385333\pi$
$101$	0.647646	+	3.67298i	0.0644432	+	0.365476i	−0.935484	+	0.353370i	$0.885036\pi$
$102$		0			0
$103$	−7.21759	+	2.62699i	−0.711170	+	0.258845i	−0.672173	−	0.740395i	$-0.734639\pi$
$103$	−7.21759	+	2.62699i	−0.711170	+	0.258845i	−0.0389976	+	0.999239i	$0.512416\pi$
$104$	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	$-0.674211\pi$
$107$	−10.7658			−1.04077			−0.520383	+	0.853933i	$0.674211\pi$
$108$		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	$-0.581966\pi$
$113$	1.82671	−	0.664870i	0.171843	−	0.0625457i	0.426509	+	0.904483i	$0.359743\pi$
$114$		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	0.809322	−	0.587366i	$-0.199835\pi$
$127$	−1.17217	−	2.03025i	−0.104013	−	0.180156i	−0.913335	+	0.407210i	$0.866502\pi$
$128$	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	0.524854	+	0.851193i	$0.324120\pi$
$131$	−2.96980	+	16.8426i	−0.259472	+	1.47154i	−0.784326	+	0.620349i	$0.786991\pi$
$132$		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	$-0.519399\pi$
$137$	10.6688	−	8.95221i	0.911499	−	0.764839i	0.972404	+	0.233305i	$0.0749541\pi$
$138$		0			0
$139$	1.37471	−	7.79636i	0.116601	−	0.661279i	−0.869344	−	0.494208i	$-0.835458\pi$
$139$	1.37471	−	7.79636i	0.116601	−	0.661279i	0.985945	−	0.167071i	$-0.0534308\pi$
$140$	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	$-0.268283\pi$
$149$	0.557783	+	0.468036i	0.0456954	+	0.0383430i	−0.619654	+	0.784875i	$0.712727\pi$
$150$		0			0
$151$	−4.08023	−	1.48508i	−0.332044	−	0.120854i	0.170618	−	0.985337i	$-0.445424\pi$
$151$	−4.08023	−	1.48508i	−0.332044	−	0.120854i	−0.502662	+	0.864483i	$0.667646\pi$
$152$	−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	0.313589	−	0.949559i	$-0.398469\pi$
$157$	14.5871	−	5.30927i	1.16418	−	0.423726i	0.850588	+	0.525833i	$0.176246\pi$
$158$	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	$-0.964213\pi$
$167$	−21.7463	+	7.91501i	−1.68278	+	0.612482i	−0.689094	+	0.724672i	$0.741991\pi$
$168$		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	$-0.357638\pi$
$173$	2.42298	+	0.881892i	0.184216	+	0.0670490i	−0.248265	+	0.968692i	$0.579861\pi$
$174$		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	$-0.725453\pi$
$179$	4.44806	−	7.70427i	0.332464	−	0.575844i	0.982994	+	0.183636i	$0.0587867\pi$
$180$		0			0
$181$	−3.95592	−	6.85185i	−0.294041	−	0.509294i	0.680720	−	0.732543i	$-0.261667\pi$
$181$	−3.95592	−	6.85185i	−0.294041	−	0.509294i	−0.974761	+	0.223250i	$0.928334\pi$
$182$	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	$-0.917277\pi$
$191$	−12.1781	+	10.2186i	−0.881175	+	0.739393i	0.0852456	+	0.996360i	$0.472833\pi$
$192$		0			0
$193$	−0.796139	+	4.51513i	−0.0573073	+	0.325006i	−0.999962	−	0.00876483i	$-0.997210\pi$
$193$	−0.796139	+	4.51513i	−0.0573073	+	0.325006i	0.942654	+	0.333771i	$0.108321\pi$
$194$	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	$-0.200683\pi$
$197$	−1.49708	−	2.59303i	−0.106663	−	0.184745i	−0.914416	+	0.404775i	$0.867350\pi$
$198$		0			0
$199$	−7.44425	+	12.8938i	−0.527709	+	0.914018i	0.471770	+	0.881722i	$0.343615\pi$
$199$	−7.44425	+	12.8938i	−0.527709	+	0.914018i	−0.999478	+	0.0322965i	$0.989718\pi$
$200$	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	−0.749389	−	0.662130i	$-0.769653\pi$
$211$	−13.0420	+	4.74688i	−0.897845	+	0.326789i	−0.148456	+	0.988919i	$0.547430\pi$
$212$	−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	−0.998456	−	0.0555457i	$-0.982310\pi$
$223$	−1.18289	−	6.70849i	−0.0792120	−	0.449234i	0.919244	−	0.393688i	$-0.128801\pi$
$224$	−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	$-0.284110\pi$
$227$	9.15340	+	3.33156i	0.607532	+	0.221124i	−0.0198908	+	0.999802i	$0.506332\pi$
$228$		0			0
$229$	−10.7590	−	9.02785i	−0.710973	−	0.596577i	0.213899	−	0.976856i	$-0.431384\pi$
$229$	−10.7590	−	9.02785i	−0.710973	−	0.596577i	−0.924872	+	0.380279i	$0.875828\pi$
$230$	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	$-0.889123\pi$
$233$	−2.66167	+	4.61014i	−0.174372	+	0.302020i	0.765572	+	0.643350i	$0.222456\pi$
$234$		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	−0.706018	−	0.708194i	$-0.749510\pi$
$239$	3.08634	−	17.5035i	0.199639	−	1.13221i	0.905656	−	0.424012i	$-0.139379\pi$
$240$		0			0
$241$	−1.53729	+	1.28994i	−0.0990257	+	0.0830924i	−0.690956	−	0.722896i	$-0.742810\pi$
$241$	−1.53729	+	1.28994i	−0.0990257	+	0.0830924i	0.591931	+	0.805989i	$0.298366\pi$
$242$	−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	−0.950808	−	0.309782i	$-0.899744\pi$
$251$	−11.7822	−	20.4073i	−0.743683	−	1.28810i	0.207125	−	0.978314i	$-0.433589\pi$
$252$		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	$-0.219125\pi$
$257$	4.50018	+	3.77610i	0.280713	+	0.235547i	−0.491549	+	0.870850i	$0.663569\pi$
$258$		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	0.841911	+	0.539617i	$0.181431\pi$
$263$	3.81646	+	21.6442i	0.235333	+	1.33464i	−0.606578	+	0.795024i	$0.707458\pi$
$264$		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	$-0.882763\pi$
$269$	−30.6026			−1.86587			−0.932937	+	0.360041i	$0.882763\pi$
$270$		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	−0.877121	−	0.480269i	$-0.840539\pi$
$277$	−3.61424	−	20.4974i	−0.217159	−	1.23157i	0.659963	−	0.751298i	$-0.270572\pi$
$278$	−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	$-0.508057\pi$
$281$	−11.5209	−	4.19326i	−0.687279	−	0.250149i	−0.661970	+	0.749531i	$0.730279\pi$
$282$		0			0
$283$	3.50280	+	2.93920i	0.208220	+	0.174717i	0.740934	−	0.671578i	$-0.234383\pi$
$283$	3.50280	+	2.93920i	0.208220	+	0.174717i	−0.532714	+	0.846295i	$0.678828\pi$
$284$	−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	−0.503987	−	0.863711i	$-0.668134\pi$
$293$	4.53628	−	25.7265i	0.265013	−	1.50296i	0.769000	−	0.639249i	$-0.220755\pi$
$294$		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	−0.909176	−	0.416412i	$-0.863287\pi$
$307$	−1.64638	+	2.85162i	−0.0939641	+	0.162751i	0.815212	+	0.579163i	$0.196621\pi$
$308$	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	0.861107	+	0.508424i	$0.169772\pi$
$311$	26.6527	+	22.3643i	1.51134	+	1.26816i	0.650229	+	0.759738i	$0.274673\pi$
$312$		0			0
$313$	−9.98690	−	3.63493i	−0.564493	−	0.205459i	0.0439812	−	0.999032i	$-0.485996\pi$
$313$	−9.98690	−	3.63493i	−0.564493	−	0.205459i	−0.608474	+	0.793574i	$0.708218\pi$
$314$	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	−0.962200	−	0.272343i	$-0.912202\pi$
$317$	−2.69159	−	15.2647i	−0.151175	−	0.857353i	0.811026	−	0.585010i	$-0.198910\pi$
$318$		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	−0.971941	−	0.235225i	$-0.924417\pi$
$331$	−2.53010	−	14.3489i	−0.139067	−	0.788688i	0.832874	−	0.553463i	$-0.186694\pi$
$332$	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	0.101783	−	0.994807i	$-0.467545\pi$
$337$	−15.7918	−	13.2509i	−0.860236	−	0.721824i	−0.962019	+	0.272983i	$0.911990\pi$
$338$	−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	0.711384	+	0.702804i	$0.248069\pi$
$347$	−3.67848	+	20.8617i	−0.197471	+	1.11992i	−0.908855	+	0.417112i	$0.863042\pi$
$348$		0			0
$349$	−3.54370	+	2.97352i	−0.189690	+	0.159169i	−0.732687	−	0.680566i	$-0.761734\pi$
$349$	−3.54370	+	2.97352i	−0.189690	+	0.159169i	0.542997	+	0.839735i	$0.317290\pi$
$350$	−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	$-0.840498\pi$
$353$	−10.4515	+	8.76982i	−0.556275	+	0.466770i	0.320784	+	0.947152i	$0.396054\pi$
$354$		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	0.950032	+	0.312153i	$0.101050\pi$
$359$	14.1223	+	24.4606i	0.745349	+	1.29098i	−0.204683	+	0.978828i	$0.565616\pi$
$360$		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	−0.713935	−	0.700212i	$-0.753089\pi$
$367$	−32.7767	−	11.9297i	−1.71093	−	0.622727i	−0.996994	+	0.0774850i	$0.975311\pi$
$368$	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	−0.415375	−	0.909650i	$-0.636350\pi$
$373$	−2.87493	+	1.04639i	−0.148858	+	0.0541800i	0.266516	+	0.963830i	$0.414127\pi$
$374$	−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	$-0.696396\pi$
$383$	−9.73704	+	3.54399i	−0.497539	+	0.181090i	0.0810475	+	0.996710i	$0.474173\pi$
$384$		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	$-0.385444\pi$
$389$	0.401203	+	0.146026i	0.0203418	+	0.00740381i	−0.331829	+	0.943339i	$0.607666\pi$
$390$		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	0.975047	+	0.221999i	$0.0712583\pi$
$397$	13.5445	+	23.4598i	0.679781	+	1.17741i	−0.295266	+	0.955415i	$0.595408\pi$
$398$	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	−0.542492	−	0.840061i	$-0.682519\pi$
$401$	5.09839	−	28.9144i	0.254602	−	1.44392i	0.797093	−	0.603856i	$-0.206370\pi$
$402$		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	0.766774	+	0.641917i	$0.221860\pi$
$409$	−3.50490	+	19.8773i	−0.173306	+	0.982869i	−0.940081	+	0.340952i	$0.889251\pi$
$410$	−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	$-0.0748173\pi$
$419$	18.6688	+	15.6649i	0.912028	+	0.765282i	−0.0604756	+	0.998170i	$0.519262\pi$
$420$		0			0
$421$	24.5960	+	8.95222i	1.19874	+	0.436305i	0.862783	−	0.505574i	$-0.168719\pi$
$421$	24.5960	+	8.95222i	1.19874	+	0.436305i	0.335954	+	0.941879i	$0.390941\pi$
$422$	−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	$-0.220889\pi$
$431$	31.9185			1.53746			0.768731	+	0.639572i	$0.220889\pi$
$432$		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	0.998867	−	0.0475821i	$-0.0151516\pi$
$439$	0.921170	+	5.22421i	0.0439650	+	0.249338i	−0.954902	+	0.296920i	$0.904040\pi$
$440$	−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	−0.995903	−	0.0904272i	$-0.971177\pi$
$443$	−38.2420	−	13.9190i	−1.81693	−	0.661310i	−0.821031	−	0.570883i	$-0.806601\pi$
$444$		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	$-0.951938\pi$
$449$	−7.71401	+	13.3611i	−0.364047	+	0.630547i	0.624576	+	0.780964i	$0.285272\pi$
$450$		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	−0.598984	−	0.800761i	$-0.704429\pi$
$457$	1.82989	−	1.53546i	0.0855985	−	0.0718256i	0.684583	+	0.728935i	$0.259984\pi$
$458$	−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	$-0.449148\pi$
$461$	24.8841	−	20.8802i	1.15897	−	0.972489i	0.999891	+	0.0147772i	$0.00470391\pi$
$462$		0			0
$463$	5.88295	−	33.3638i	0.273404	−	1.55055i	−0.470584	−	0.882355i	$-0.655957\pi$
$463$	5.88295	−	33.3638i	0.273404	−	1.55055i	0.743987	−	0.668194i	$-0.232932\pi$
$464$	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	$-0.0632002\pi$
$467$	6.90133	+	11.9535i	0.319356	+	0.553140i	−0.660998	+	0.750388i	$0.729867\pi$
$468$		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	$-0.0125851\pi$
$479$	1.02298	+	5.80162i	0.0467412	+	0.265083i	−0.952477	+	0.304610i	$0.901474\pi$
$480$		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	$-0.642647\pi$
$491$	−4.11915	+	1.49925i	−0.185895	+	0.0676601i	0.247396	+	0.968915i	$0.420425\pi$
$492$		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	0.999203	+	0.0399241i	$0.0127116\pi$
$499$	27.0747	+	22.7184i	1.21203	+	1.01701i	0.212827	+	0.977090i	$0.431733\pi$
$500$	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	$-0.773539\pi$
$503$	4.18829	−	7.25434i	0.186747	−	0.323455i	0.944164	+	0.329477i	$0.106872\pi$
$504$		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	$-0.971587\pi$
$509$	−0.667325	+	3.78459i	−0.0295786	+	0.167749i	0.966440	+	0.256892i	$0.0826983\pi$
$510$		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	$-0.308326\pi$
$521$	−9.82615	−	17.0194i	−0.430491	−	0.745633i	−0.996916	+	0.0784810i	$0.974993\pi$
$522$		0			0
$523$	19.8051	−	34.3035i	0.866018	−	1.49999i	−1.41543e−5	−	1.00000i	$-0.500005\pi$
$523$	19.8051	−	34.3035i	0.866018	−	1.49999i	0.866032	−	0.499988i	$-0.166662\pi$
$524$	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	−0.980421	−	0.196911i	$-0.936909\pi$
$547$	−2.95798	−	16.7755i	−0.126474	−	0.717270i	0.853947	−	0.520359i	$-0.174202\pi$
$548$	−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	−0.247408	−	0.968911i	$-0.579579\pi$
$557$	16.8840	−	29.2439i	0.715398	−	1.23911i	0.962806	−	0.270194i	$-0.0870880\pi$
$558$		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	0.781598	+	0.623783i	$0.214405\pi$
$563$	−3.94377	+	22.3662i	−0.166210	+	0.942624i	−0.947808	+	0.318842i	$0.896706\pi$
$564$		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	$-0.649044\pi$
$569$	8.32801	−	6.98803i	0.349128	−	0.292954i	0.800440	+	0.599413i	$0.204599\pi$
$570$		0			0
$571$	2.58453	−	14.6576i	0.108159	−	0.613401i	−0.881752	−	0.471713i	$-0.843636\pi$
$571$	2.58453	−	14.6576i	0.108159	−	0.613401i	0.989911	−	0.141688i	$-0.0452530\pi$
$572$	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	−0.163555	−	0.986534i	$-0.552296\pi$
$577$	18.5582	−	32.1437i	0.772586	−	1.33816i	0.936141	−	0.351624i	$-0.114371\pi$
$578$	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	0.991240	+	0.132075i	$0.0421639\pi$
$587$	2.54277	+	14.4208i	0.104951	+	0.595208i	−0.886288	+	0.463134i	$0.846725\pi$
$588$		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	$-0.769076\pi$
$593$	−36.4392			−1.49638			−0.748189	+	0.663485i	$0.769076\pi$
$594$		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	$-0.421257\pi$
$599$	25.8368	−	9.40381i	1.05566	−	0.384229i	0.810797	+	0.585328i	$0.199034\pi$
$600$		0			0
$601$	7.84490	+	44.4907i	0.320000	+	1.81481i	0.542702	+	0.839925i	$0.317401\pi$
$601$	7.84490	+	44.4907i	0.320000	+	1.81481i	−0.222702	+	0.974887i	$0.571488\pi$
$602$	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	0.869082	−	0.494669i	$-0.164711\pi$
$607$	13.1278	+	11.0156i	0.532842	+	0.447108i	−0.336239	+	0.941777i	$0.609155\pi$
$608$	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	0.870720	−	0.491779i	$-0.163653\pi$
$613$	0.234380	+	0.405959i	0.00946653	+	0.0163965i	−0.861253	+	0.508176i	$0.830320\pi$
$614$	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	$-0.930762\pi$
$617$	0.370713	−	2.10242i	0.0149243	−	0.0846401i	0.991360	+	0.131168i	$0.0418726\pi$
$618$		0			0
$619$	6.54018	−	5.48786i	0.262872	−	0.220576i	−0.501819	−	0.864972i	$-0.667336\pi$
$619$	6.54018	−	5.48786i	0.262872	−	0.220576i	0.764692	+	0.644397i	$0.222891\pi$
$620$	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	−0.723361	−	0.690470i	$-0.757404\pi$
$631$	5.93539	−	10.2804i	0.236284	−	0.409256i	0.959645	+	0.281214i	$0.0907370\pi$
$632$	−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	$-0.0889569\pi$
$641$	−0.920970	−	5.22308i	−0.0363761	−	0.206299i	−0.997579	+	0.0695434i	$0.977846\pi$
$642$		0			0
$643$	0.774183	−	0.281780i	0.0305308	−	0.0111123i	−0.326710	−	0.945125i	$-0.605940\pi$
$643$	0.774183	−	0.281780i	0.0305308	−	0.0111123i	0.357240	+	0.934012i	$0.383718\pi$
$644$	−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	$-0.203374\pi$
$647$	40.8373			1.60548			0.802740	+	0.596329i	$0.203374\pi$
$648$		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	$-0.604450\pi$
$653$	1.00487	−	0.365742i	0.0393235	−	0.0143126i	0.361607	+	0.932331i	$0.382228\pi$
$654$		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	$-0.577435\pi$
$659$	−26.9356	−	9.80376i	−1.04926	−	0.381900i	−0.808384	+	0.588655i	$0.799658\pi$
$660$		0			0
$661$	−3.44392	−	2.88979i	−0.133953	−	0.112400i	0.573350	−	0.819311i	$-0.305644\pi$
$661$	−3.44392	−	2.88979i	−0.133953	−	0.112400i	−0.707303	+	0.706911i	$0.750088\pi$
$662$	−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	−0.335973	−	0.941872i	$-0.609065\pi$
$673$	13.8337	−	11.6078i	0.533249	−	0.447449i	0.869222	+	0.494423i	$0.164621\pi$
$674$	−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	$-0.820028\pi$
$677$	−12.0569	+	10.1169i	−0.463385	+	0.388826i	0.380990	+	0.924579i	$0.375583\pi$
$678$		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	$-0.183490\pi$
$683$	−1.38059	−	2.39125i	−0.0528268	−	0.0914987i	−0.891230	+	0.453552i	$0.850156\pi$
$684$		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	0.875036	−	0.484058i	$-0.160838\pi$
$691$	32.4434	+	11.8084i	1.23421	+	0.449214i	0.359169	+	0.933272i	$0.383060\pi$
$692$	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	$-0.371891\pi$
$701$	20.7410			0.783378			0.391689	+	0.920098i	$0.371891\pi$
$702$		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	0.931367	+	0.364083i	$0.118617\pi$
$709$	4.81129	+	27.2862i	0.180692	+	1.02475i	−0.750675	+	0.660672i	$0.770271\pi$
$710$	−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	−0.372090	−	0.928197i	$-0.621359\pi$
$719$	16.5657	−	28.6927i	0.617797	−	1.07006i	0.989887	−	0.141859i	$-0.0453081\pi$
$720$		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	−0.643960	−	0.765059i	$-0.722710\pi$
$727$	−0.0632795	+	0.0530978i	−0.00234691	+	0.00196929i	0.641613	+	0.767028i	$0.278265\pi$
$728$	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	0.693176	+	0.720768i	$0.256211\pi$
$733$	−5.54241	+	31.4326i	−0.204714	+	1.16099i	−0.897890	+	0.440221i	$0.854900\pi$
$734$	−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	−0.322738	−	0.946488i	$-0.604603\pi$
$739$	17.8960	−	30.9967i	0.658314	−	1.14023i	0.981052	−	0.193745i	$-0.0620634\pi$
$740$	−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	$-0.395960\pi$
$743$	−15.1515	−	12.7136i	−0.555854	−	0.466417i	−0.876918	+	0.480640i	$0.840404\pi$
$744$		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	−0.808135	−	0.588997i	$-0.799523\pi$
$751$	−28.7363	+	10.4592i	−1.04860	+	0.381660i	−0.240468	+	0.970657i	$0.577301\pi$
$752$	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	$-0.288572\pi$
$761$	43.9945	−	16.0127i	1.59480	−	0.580460i	0.978354	+	0.206938i	$0.0663499\pi$
$762$		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	0.821405	−	0.570346i	$-0.193191\pi$
$769$	11.1578	+	9.36247i	0.402359	+	0.337619i	−0.419046	+	0.907965i	$0.637635\pi$
$770$	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	$-0.977634\pi$
$773$	−12.1767	+	21.0906i	−0.437964	+	0.758576i	0.559568	+	0.828784i	$0.310967\pi$
$774$		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

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

Modular forms

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Database

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