LMFDB - Embedded newform 486.2.e.h.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [486,2,Mod(55,486)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(486, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("486.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$486 = 2 \cdot 3^{5}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	486.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:	$3.88072953823$
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:	$x^{12} - 6 x^{11} + 33 x^{10} - 110 x^{9} + 318 x^{8} - 678 x^{7} + 1225 x^{6} - 1698 x^{5} + 1905 x^{4} + \cdots + 57$ x^12 - 6x^11 + 33x^10 - 110x^9 + 318x^8 - 678x^7 + 1225x^6 - 1698x^5 + 1905x^4 - 1584x^3 + 936x^2 - 342*x + 57
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$3^{3}$
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			109.1
Root			$0.500000 - 1.74095i$ of defining polynomial
Character	$\chi$	$=$	486.109
Dual form			486.2.e.h.379.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 - 0.642788i) q^{2} +(0.173648 - 0.984808i) q^{4} +(-2.97705 + 1.08356i) q^{5} +(0.640018 + 3.62972i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-1.58406 + 2.74367i) q^{10} +(2.14726 + 0.781539i) q^{11} +(2.37495 + 1.99282i) q^{13} +(2.82342 + 2.36913i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(-0.862878 + 1.49455i) q^{17} +(1.69740 + 2.93998i) q^{19} +(0.550137 + 3.11998i) q^{20} +(2.14726 - 0.781539i) q^{22} +(-0.582258 + 3.30215i) q^{23} +(3.85853 - 3.23769i) q^{25} +3.10027 q^{26} +3.68572 q^{28} +(-0.448476 + 0.376316i) q^{29} +(-0.805376 + 4.56751i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(0.299674 + 1.69954i) q^{34} +(-5.83839 - 10.1124i) q^{35} +(3.65360 - 6.32822i) q^{37} +(3.19007 + 1.16109i) q^{38} +(2.42692 + 2.03643i) q^{40} +(-5.42399 - 4.55127i) q^{41} +(-1.55793 - 0.567040i) q^{43} +(1.14253 - 1.97893i) q^{44} +(1.67654 + 2.90386i) q^{46} +(-0.668890 - 3.79346i) q^{47} +(-6.18743 + 2.25204i) q^{49} +(0.874658 - 4.96043i) q^{50} +(2.37495 - 1.99282i) q^{52} -2.58267 q^{53} -7.23936 q^{55} +(2.82342 - 2.36913i) q^{56} +(-0.101661 + 0.576550i) q^{58} +(9.08043 - 3.30500i) q^{59} +(2.27329 + 12.8925i) q^{61} +(2.31899 + 4.01660i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(-9.22969 - 3.35933i) q^{65} +(-6.59469 - 5.53361i) q^{67} +(1.32201 + 1.10929i) q^{68} +(-10.9726 - 3.99369i) q^{70} +(-0.993732 + 1.72119i) q^{71} +(-5.32371 - 9.22094i) q^{73} +(-1.26888 - 7.19618i) q^{74} +(3.19007 - 1.16109i) q^{76} +(-1.46249 + 8.29417i) q^{77} +(10.7960 - 9.05893i) q^{79} +3.16812 q^{80} -7.08052 q^{82} +(-2.37353 + 1.99163i) q^{83} +(0.949403 - 5.38433i) q^{85} +(-1.55793 + 0.567040i) q^{86} +(-0.396798 - 2.25035i) q^{88} +(8.67300 + 15.0221i) q^{89} +(-5.71337 + 9.89585i) q^{91} +(3.15087 + 1.14682i) q^{92} +(-2.95079 - 2.47601i) q^{94} +(-8.23889 - 6.91325i) q^{95} +(-8.63687 - 3.14356i) q^{97} +(-3.29226 + 5.70237i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$12 q + 6 q^{5} - 3 q^{7} - 6 q^{8} - 3 q^{10} + 6 q^{11} - 6 q^{13} + 6 q^{14} - 6 q^{17} - 9 q^{19} - 3 q^{20} + 6 q^{22} - 24 q^{23} + 36 q^{25} + 18 q^{26} + 12 q^{28} - 12 q^{29} + 27 q^{31} + 3 q^{34}+ \cdots - 12 q^{98}+O(q^{100})$ 12 * q + 6 * q^5 - 3 * q^7 - 6 * q^8 - 3 * q^10 + 6 * q^11 - 6 * q^13 + 6 * q^14 - 6 * q^17 - 9 * q^19 - 3 * q^20 + 6 * q^22 - 24 * q^23 + 36 * q^25 + 18 * q^26 + 12 * q^28 - 12 * q^29 + 27 * q^31 + 3 * q^34 + 3 * q^35 - 15 * q^37 + 12 * q^38 - 3 * q^40 - 3 * q^41 - 27 * q^43 - 3 * q^44 + 3 * q^46 + 36 * q^47 - 3 * q^49 - 9 * q^50 - 6 * q^52 - 12 * q^53 + 18 * q^55 + 6 * q^56 + 15 * q^58 + 12 * q^59 + 9 * q^61 - 12 * q^62 - 6 * q^64 - 42 * q^65 - 45 * q^67 + 12 * q^68 - 33 * q^70 + 12 * q^71 - 21 * q^73 - 30 * q^74 + 12 * q^76 + 48 * q^77 + 3 * q^79 + 6 * q^80 + 6 * q^82 - 18 * q^83 - 27 * q^86 + 6 * q^88 + 12 * q^89 - 6 * q^91 + 30 * q^92 - 27 * q^94 - 33 * q^95 - 15 * q^97 - 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/486\mathbb{Z}\right)^\times$ .

$n$	$245$
$\chi(n)$	$e\left(\frac{7}{9}\right)$

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

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$3$		0			0
$3$		0			0
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	−2.97705	+	1.08356i	−1.33138	+	0.484582i	−0.907087	−	0.420943i	$-0.861699\pi$
$5$	−2.97705	+	1.08356i	−1.33138	+	0.484582i	−0.424292	+	0.905525i	$0.639477\pi$
$6$		0			0
$7$	0.640018	+	3.62972i	0.241904	+	1.37191i	0.827574	+	0.561357i	$0.189721\pi$
$7$	0.640018	+	3.62972i	0.241904	+	1.37191i	−0.585670	+	0.810550i	$0.699168\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$		0			0
$10$	−1.58406	+	2.74367i	−0.500923	+	0.867624i
$11$	2.14726	+	0.781539i	0.647424	+	0.235643i	0.644797	−	0.764354i	$-0.276942\pi$
$11$	2.14726	+	0.781539i	0.647424	+	0.235643i	0.00262630	+	0.999997i	$0.499164\pi$
$12$		0			0
$13$	2.37495	+	1.99282i	0.658692	+	0.552708i	0.909694	−	0.415278i	$-0.136316\pi$
$13$	2.37495	+	1.99282i	0.658692	+	0.552708i	−0.251002	+	0.967986i	$0.580760\pi$
$14$	2.82342	+	2.36913i	0.754592	+	0.633178i
$15$		0			0
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	−0.862878	+	1.49455i	−0.209279	+	0.362481i	−0.951487	−	0.307687i	$-0.900445\pi$
$17$	−0.862878	+	1.49455i	−0.209279	+	0.362481i	0.742209	+	0.670169i	$0.233778\pi$
$18$		0			0
$19$	1.69740	+	2.93998i	0.389410	+	0.674478i	0.992370	−	0.123293i	$-0.0393456\pi$
$19$	1.69740	+	2.93998i	0.389410	+	0.674478i	−0.602960	+	0.797771i	$0.706012\pi$
$20$	0.550137	+	3.11998i	0.123014	+	0.697650i
$21$		0			0
$22$	2.14726	−	0.781539i	0.457798	−	0.166625i
$23$	−0.582258	+	3.30215i	−0.121409	+	0.688545i	0.861967	+	0.506965i	$0.169232\pi$
$23$	−0.582258	+	3.30215i	−0.121409	+	0.688545i	−0.983376	+	0.181581i	$0.941879\pi$
$24$		0			0
$25$	3.85853	−	3.23769i	0.771706	−	0.647538i
$26$	3.10027			0.608014
$27$		0			0
$28$	3.68572			0.696535
$29$	−0.448476	+	0.376316i	−0.0832799	+	0.0698802i	−0.683477	−	0.729972i	$-0.739533\pi$
$29$	−0.448476	+	0.376316i	−0.0832799	+	0.0698802i	0.600197	+	0.799852i	$0.295089\pi$
$30$		0			0
$31$	−0.805376	+	4.56751i	−0.144650	+	0.820350i	0.822998	+	0.568044i	$0.192300\pi$
$31$	−0.805376	+	4.56751i	−0.144650	+	0.820350i	−0.967648	+	0.252305i	$0.918811\pi$
$32$	−0.939693	+	0.342020i	−0.166116	+	0.0604612i
$33$		0			0
$34$	0.299674	+	1.69954i	0.0513937	+	0.291468i
$35$	−5.83839	−	10.1124i	−0.986868	−	1.70931i
$36$		0			0
$37$	3.65360	−	6.32822i	0.600648	−	1.04035i	−0.392075	−	0.919933i	$-0.628243\pi$
$37$	3.65360	−	6.32822i	0.600648	−	1.04035i	0.992723	−	0.120420i	$-0.0384240\pi$
$38$	3.19007	+	1.16109i	0.517497	+	0.188353i
$39$		0			0
$40$	2.42692	+	2.03643i	0.383729	+	0.321987i
$41$	−5.42399	−	4.55127i	−0.847085	−	0.710789i	0.112061	−	0.993701i	$-0.464255\pi$
$41$	−5.42399	−	4.55127i	−0.847085	−	0.710789i	−0.959146	+	0.282913i	$0.908699\pi$
$42$		0			0
$43$	−1.55793	−	0.567040i	−0.237582	−	0.0864728i	0.220485	−	0.975390i	$-0.429236\pi$
$43$	−1.55793	−	0.567040i	−0.237582	−	0.0864728i	−0.458067	+	0.888917i	$0.651458\pi$
$44$	1.14253	−	1.97893i	0.172243	−	0.298334i
$45$		0			0
$46$	1.67654	+	2.90386i	0.247193	+	0.428151i
$47$	−0.668890	−	3.79346i	−0.0975676	−	0.553333i	−0.993930	−	0.110012i	$-0.964911\pi$
$47$	−0.668890	−	3.79346i	−0.0975676	−	0.553333i	0.896363	−	0.443321i	$-0.146200\pi$
$48$		0			0
$49$	−6.18743	+	2.25204i	−0.883918	+	0.321720i
$50$	0.874658	−	4.96043i	0.123695	−	0.701511i
$51$		0			0
$52$	2.37495	−	1.99282i	0.329346	−	0.276354i
$53$	−2.58267			−0.354757			−0.177379	−	0.984143i	$-0.556762\pi$
$53$	−2.58267			−0.354757			−0.177379	+	0.984143i	$0.556762\pi$
$54$		0			0
$55$	−7.23936			−0.976155
$56$	2.82342	−	2.36913i	0.377296	−	0.316589i
$57$		0			0
$58$	−0.101661	+	0.576550i	−0.0133488	+	0.0757047i
$59$	9.08043	−	3.30500i	1.18217	−	0.430275i	0.325203	−	0.945644i	$-0.394568\pi$
$59$	9.08043	−	3.30500i	1.18217	−	0.430275i	0.856968	+	0.515369i	$0.172345\pi$
$60$		0			0
$61$	2.27329	+	12.8925i	0.291065	+	1.65071i	0.682781	+	0.730623i	$0.260770\pi$
$61$	2.27329	+	12.8925i	0.291065	+	1.65071i	−0.391716	+	0.920086i	$0.628119\pi$
$62$	2.31899	+	4.01660i	0.294512	+	0.510109i
$63$		0			0
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−9.22969	−	3.35933i	−1.14480	−	0.416674i
$66$		0			0
$67$	−6.59469	−	5.53361i	−0.805670	−	0.676037i	0.143900	−	0.989592i	$-0.454036\pi$
$67$	−6.59469	−	5.53361i	−0.805670	−	0.676037i	−0.949570	+	0.313555i	$0.898480\pi$
$68$	1.32201	+	1.10929i	0.160317	+	0.134522i
$69$		0			0
$70$	−10.9726	−	3.99369i	−1.31147	−	0.477338i
$71$	−0.993732	+	1.72119i	−0.117934	+	0.204268i	−0.918949	−	0.394377i	$-0.870961\pi$
$71$	−0.993732	+	1.72119i	−0.117934	+	0.204268i	0.801015	+	0.598645i	$0.204294\pi$
$72$		0			0
$73$	−5.32371	−	9.22094i	−0.623094	−	1.07923i	−0.988906	−	0.148541i	$-0.952542\pi$
$73$	−5.32371	−	9.22094i	−0.623094	−	1.07923i	0.365812	−	0.930689i	$-0.380791\pi$
$74$	−1.26888	−	7.19618i	−0.147504	−	0.836539i
$75$		0			0
$76$	3.19007	−	1.16109i	0.365926	−	0.133186i
$77$	−1.46249	+	8.29417i	−0.166666	+	0.945208i
$78$		0			0
$79$	10.7960	−	9.05893i	1.21465	−	1.01921i	0.215559	−	0.976491i	$-0.430843\pi$
$79$	10.7960	−	9.05893i	1.21465	−	1.01921i	0.999087	−	0.0427183i	$-0.0136018\pi$
$80$	3.16812			0.354206
$81$		0			0
$82$	−7.08052			−0.781912
$83$	−2.37353	+	1.99163i	−0.260529	+	0.218609i	−0.763690	−	0.645583i	$-0.776615\pi$
$83$	−2.37353	+	1.99163i	−0.260529	+	0.218609i	0.503162	+	0.864192i	$0.332170\pi$
$84$		0			0
$85$	0.949403	−	5.38433i	0.102977	−	0.584013i
$86$	−1.55793	+	0.567040i	−0.167996	+	0.0611455i
$87$		0			0
$88$	−0.396798	−	2.25035i	−0.0422988	−	0.239888i
$89$	8.67300	+	15.0221i	0.919336	+	1.59234i	0.800425	+	0.599432i	$0.204607\pi$
$89$	8.67300	+	15.0221i	0.919336	+	1.59234i	0.118911	+	0.992905i	$0.462060\pi$
$90$		0			0
$91$	−5.71337	+	9.89585i	−0.598924	+	1.03737i
$92$	3.15087	+	1.14682i	0.328501	+	0.119565i
$93$		0			0
$94$	−2.95079	−	2.47601i	−0.304351	−	0.255381i
$95$	−8.23889	−	6.91325i	−0.845292	−	0.709284i
$96$		0			0
$97$	−8.63687	−	3.14356i	−0.876941	−	0.319181i	−0.135967	−	0.990713i	$-0.543414\pi$
$97$	−8.63687	−	3.14356i	−0.876941	−	0.319181i	−0.740975	+	0.671533i	$0.765636\pi$
$98$	−3.29226	+	5.70237i	−0.332569	+	0.576026i
$99$		0			0
$100$	−2.51848	−	4.36213i	−0.251848	−	0.436213i
$101$	2.07686	+	11.7785i	0.206656	+	1.17200i	0.894813	+	0.446441i	$0.147309\pi$
$101$	2.07686	+	11.7785i	0.206656	+	1.17200i	−0.688158	+	0.725561i	$0.741580\pi$
$102$		0			0
$103$	11.9778	−	4.35955i	1.18020	−	0.429559i	0.323930	−	0.946081i	$-0.394996\pi$
$103$	11.9778	−	4.35955i	1.18020	−	0.429559i	0.856274	+	0.516522i	$0.172773\pi$
$104$	0.538357	−	3.05317i	0.0527903	−	0.299388i
$105$		0			0
$106$	−1.97844	+	1.66011i	−0.192163	+	0.161244i
$107$	6.09894			0.589607			0.294803	−	0.955558i	$-0.404746\pi$
$107$	6.09894			0.589607			0.294803	+	0.955558i	$0.404746\pi$
$108$		0			0
$109$	11.2390			1.07650			0.538250	−	0.842785i	$-0.319086\pi$
$109$	11.2390			1.07650			0.538250	+	0.842785i	$0.319086\pi$
$110$	−5.54567	+	4.65337i	−0.528759	+	0.443681i
$111$		0			0
$112$	0.640018	−	3.62972i	0.0604761	−	0.342977i
$113$	6.61257	−	2.40678i	0.622059	−	0.226411i	−0.0117125	−	0.999931i	$-0.503728\pi$
$113$	6.61257	−	2.40678i	0.622059	−	0.226411i	0.633771	+	0.773521i	$0.281506\pi$
$114$		0			0
$115$	−1.84466	−	10.4616i	−0.172015	−	0.975548i
$116$	0.292722	+	0.507009i	0.0271786	+	0.0470746i
$117$		0			0
$118$	4.83159	−	8.36857i	0.444784	−	0.770389i
$119$	−5.97705	−	2.17547i	−0.547916	−	0.199425i
$120$		0			0
$121$	−4.42656	−	3.71433i	−0.402415	−	0.337666i
$122$	10.0285	+	8.41495i	0.907942	+	0.761854i
$123$		0			0
$124$	4.35827	+	1.58628i	0.391384	+	0.142452i
$125$	−0.0585380	+	0.101391i	−0.00523579	+	0.00906866i
$126$		0			0
$127$	−2.99250	−	5.18316i	−0.265541	−	0.459931i	0.702164	−	0.712015i	$-0.252217\pi$
$127$	−2.99250	−	5.18316i	−0.265541	−	0.459931i	−0.967705	+	0.252084i	$0.918884\pi$
$128$	0.173648	+	0.984808i	0.0153485	+	0.0870455i
$129$		0			0
$130$	−9.22969	+	3.35933i	−0.809497	+	0.294633i
$131$	2.85044	−	16.1657i	0.249044	−	1.41240i	−0.561866	−	0.827228i	$-0.689916\pi$
$131$	2.85044	−	16.1657i	0.249044	−	1.41240i	0.810910	−	0.585171i	$-0.198973\pi$
$132$		0			0
$133$	−9.58495	+	8.04273i	−0.831121	+	0.697393i
$134$	−8.60876			−0.743684
$135$		0			0
$136$	1.72576			0.147982
$137$	−0.161757	+	0.135730i	−0.0138198	+	0.0115962i	−0.649671	−	0.760215i	$-0.725093\pi$
$137$	−0.161757	+	0.135730i	−0.0138198	+	0.0115962i	0.635852	+	0.771811i	$0.280649\pi$
$138$		0			0
$139$	0.637551	−	3.61573i	0.0540764	−	0.306682i	−0.945758	−	0.324871i	$-0.894679\pi$
$139$	0.637551	−	3.61573i	0.0540764	−	0.306682i	0.999835	+	0.0181891i	$0.00579008\pi$
$140$	−10.9726	+	3.99369i	−0.927353	+	0.337529i
$141$		0			0
$142$	0.345119	+	1.95727i	0.0289618	+	0.164250i
$143$	3.54217	+	6.13522i	0.296211	+	0.513053i
$144$		0			0
$145$	0.927377	−	1.60626i	0.0770145	−	0.133393i
$146$	−10.0053	−	3.64164i	−0.828045	−	0.301384i
$147$		0			0
$148$	−5.59764	−	4.69698i	−0.460123	−	0.386089i
$149$	11.8541	+	9.94675i	0.971123	+	0.814869i	0.982727	−	0.185063i	$-0.0592490\pi$
$149$	11.8541	+	9.94675i	0.971123	+	0.814869i	−0.0116031	+	0.999933i	$0.503693\pi$
$150$		0			0
$151$	−18.9308	−	6.89024i	−1.54057	−	0.560720i	−0.574385	−	0.818585i	$-0.694759\pi$
$151$	−18.9308	−	6.89024i	−1.54057	−	0.560720i	−0.966181	+	0.257865i	$0.916981\pi$
$152$	1.69740	−	2.93998i	0.137677	−	0.238464i
$153$		0			0
$154$	4.21106	+	7.29377i	0.339337	+	0.587748i
$155$	−2.55152	−	14.4704i	−0.204943	−	1.16229i
$156$		0			0
$157$	−16.9121	+	6.15549i	−1.34973	+	0.491261i	−0.912863	−	0.408265i	$-0.866134\pi$
$157$	−16.9121	+	6.15549i	−1.34973	+	0.491261i	−0.436866	+	0.899527i	$0.643912\pi$
$158$	2.44726	−	13.8791i	0.194693	−	1.10416i
$159$		0			0
$160$	2.42692	−	2.03643i	0.191865	−	0.160994i
$161$	−12.3585			−0.973989
$162$		0			0
$163$	3.05289			0.239121			0.119560	−	0.992827i	$-0.461851\pi$
$163$	3.05289			0.239121			0.119560	+	0.992827i	$0.461851\pi$
$164$	−5.42399	+	4.55127i	−0.423542	+	0.355394i
$165$		0			0
$166$	−0.538035	+	3.05135i	−0.0417596	+	0.236831i
$167$	3.85386	−	1.40269i	0.298221	−	0.108544i	−0.188576	−	0.982059i	$-0.560387\pi$
$167$	3.85386	−	1.40269i	0.298221	−	0.108544i	0.486797	+	0.873515i	$0.338165\pi$
$168$		0			0
$169$	−0.588371	−	3.33682i	−0.0452593	−	0.256678i
$170$	−2.73370	−	4.73490i	−0.209665	−	0.363150i
$171$		0			0
$172$	−0.828957	+	1.43580i	−0.0632074	+	0.109478i
$173$	16.0002	+	5.82361i	1.21648	+	0.442761i	0.868945	−	0.494908i	$-0.164798\pi$
$173$	16.0002	+	5.82361i	1.21648	+	0.442761i	0.347530	+	0.937669i	$0.387020\pi$
$174$		0			0
$175$	14.2215	+	11.9332i	1.07504	+	0.902067i
$176$	−1.75046	−	1.46881i	−0.131946	−	0.110716i
$177$		0			0
$178$	16.2999	+	5.93268i	1.22173	+	0.444673i
$179$	7.27802	−	12.6059i	0.543985	−	0.942210i	−0.454685	−	0.890652i	$-0.650248\pi$
$179$	7.27802	−	12.6059i	0.543985	−	0.942210i	0.998670	−	0.0515575i	$-0.0164185\pi$
$180$		0			0
$181$	6.51190	+	11.2789i	0.484026	+	0.838357i	0.999832	−	0.0183482i	$-0.00584075\pi$
$181$	6.51190	+	11.2789i	0.484026	+	0.838357i	−0.515806	+	0.856706i	$0.672507\pi$
$182$	1.98423	+	11.2531i	0.147081	+	0.834139i
$183$		0			0
$184$	3.15087	−	1.14682i	0.232285	−	0.0845450i
$185$	−4.01996	+	22.7983i	−0.295554	+	1.67617i
$186$		0			0
$187$	−3.02087	+	2.53481i	−0.220908	+	0.185364i
$188$	−3.85198			−0.280935
$189$		0			0
$190$	−10.7551			−0.780258
$191$	2.75996	−	2.31588i	0.199704	−	0.167571i	−0.537452	−	0.843295i	$-0.680613\pi$
$191$	2.75996	−	2.31588i	0.199704	−	0.167571i	0.737155	+	0.675723i	$0.236169\pi$
$192$		0			0
$193$	0.256108	−	1.45246i	0.0184351	−	0.104551i	−0.974202	−	0.225679i	$-0.927540\pi$
$193$	0.256108	−	1.45246i	0.0184351	−	0.104551i	0.992637	+	0.121128i	$0.0386512\pi$
$194$	−8.63687	+	3.14356i	−0.620091	+	0.225695i
$195$		0			0
$196$	1.14339	+	6.48449i	0.0816708	+	0.463178i
$197$	−1.26931	−	2.19851i	−0.0904346	−	0.156637i	0.817259	−	0.576270i	$-0.195492\pi$
$197$	−1.26931	−	2.19851i	−0.0904346	−	0.156637i	−0.907694	+	0.419633i	$0.862159\pi$
$198$		0			0
$199$	0.925891	−	1.60369i	0.0656347	−	0.113683i	−0.831341	−	0.555763i	$-0.812426\pi$
$199$	0.925891	−	1.60369i	0.0656347	−	0.113683i	0.896975	+	0.442081i	$0.145759\pi$
$200$	−4.73319	−	1.72274i	−0.334687	−	0.121816i
$201$		0			0
$202$	9.16203	+	7.68785i	0.644638	+	0.540916i
$203$	−1.65296	−	1.38700i	−0.116015	−	0.0973480i
$204$		0			0
$205$	21.0791	+	7.67216i	1.47223	+	0.535847i
$206$	6.37324	−	11.0388i	0.444045	−	0.769108i
$207$		0			0
$208$	−1.55014	−	2.68492i	−0.107483	−	0.186165i
$209$	1.34705	+	7.63949i	0.0931773	+	0.528434i
$210$		0			0
$211$	17.8432	−	6.49438i	1.22837	−	0.447091i	0.355333	−	0.934740i	$-0.384367\pi$
$211$	17.8432	−	6.49438i	1.22837	−	0.447091i	0.873040	+	0.487648i	$0.162145\pi$
$212$	−0.448476	+	2.54343i	−0.0308015	+	0.174684i
$213$		0			0
$214$	4.67206	−	3.92032i	0.319375	−	0.267988i
$215$	5.25247			0.358215
$216$		0			0
$217$	−17.0943			−1.16043
$218$	8.60957	−	7.22429i	0.583114	−	0.489290i
$219$		0			0
$220$	−1.25710	+	7.12937i	−0.0847537	+	0.480662i
$221$	−5.02765	+	1.82992i	−0.338196	+	0.123093i
$222$		0			0
$223$	−1.25971	−	7.14415i	−0.0843562	−	0.478408i	−0.997494	−	0.0707560i	$-0.977459\pi$
$223$	−1.25971	−	7.14415i	−0.0843562	−	0.478408i	0.913137	−	0.407652i	$-0.133652\pi$
$224$	−1.84286	−	3.19193i	−0.123131	−	0.213270i
$225$		0			0
$226$	3.51848	−	6.09418i	0.234046	−	0.405379i
$227$	26.8068	+	9.75687i	1.77923	+	0.647586i	0.999777	+	0.0211232i	$0.00672422\pi$
$227$	26.8068	+	9.75687i	1.77923	+	0.647586i	0.779451	+	0.626463i	$0.215498\pi$
$228$		0			0
$229$	1.42131	+	1.19262i	0.0939225	+	0.0788104i	0.688540	−	0.725198i	$-0.258252\pi$
$229$	1.42131	+	1.19262i	0.0939225	+	0.0788104i	−0.594617	+	0.804009i	$0.702696\pi$
$230$	−8.13767	−	6.82831i	−0.536582	−	0.450246i
$231$		0			0
$232$	0.550137	+	0.200234i	0.0361183	+	0.0131460i
$233$	−4.26735	+	7.39126i	−0.279563	+	0.484218i	−0.971276	−	0.237955i	$-0.923523\pi$
$233$	−4.26735	+	7.39126i	−0.279563	+	0.484218i	0.691713	+	0.722172i	$0.256856\pi$
$234$		0			0
$235$	6.10176	+	10.5686i	0.398035	+	0.689417i
$236$	−1.67799	−	9.51638i	−0.109228	−	0.619464i
$237$		0			0
$238$	−5.97705	+	2.17547i	−0.387435	+	0.141015i
$239$	−1.26554	+	7.17724i	−0.0818611	+	0.464257i	0.916129	+	0.400884i	$0.131297\pi$
$239$	−1.26554	+	7.17724i	−0.0818611	+	0.464257i	−0.997990	+	0.0633733i	$0.979814\pi$
$240$		0			0
$241$	−1.02261	+	0.858069i	−0.0658719	+	0.0552731i	−0.675129	−	0.737700i	$-0.735912\pi$
$241$	−1.02261	+	0.858069i	−0.0658719	+	0.0552731i	0.609257	+	0.792973i	$0.291468\pi$
$242$	−5.77847			−0.371454
$243$		0			0
$244$	13.0913			0.838087
$245$	15.9801	−	13.4089i	1.02093	−	0.856663i
$246$		0			0
$247$	−1.82761	+	10.3649i	−0.116288	+	0.659503i
$248$	4.35827	−	1.58628i	0.276750	−	0.100729i
$249$		0			0
$250$	0.0203300	+	0.115297i	0.00128578	+	0.00729204i
$251$	1.43928	+	2.49291i	0.0908466	+	0.157351i	0.907868	−	0.419257i	$-0.137709\pi$
$251$	1.43928	+	2.49291i	0.0908466	+	0.157351i	−0.817021	+	0.576608i	$0.804376\pi$
$252$		0			0
$253$	−3.83102	+	6.63552i	−0.240854	+	0.417171i
$254$	−5.62406	−	2.04699i	−0.352885	−	0.128440i
$255$		0			0
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−19.7470	−	16.5697i	−1.23179	−	1.03359i	−0.998121	−	0.0612737i	$-0.980484\pi$
$257$	−19.7470	−	16.5697i	−1.23179	−	1.03359i	−0.233665	−	0.972317i	$-0.575072\pi$
$258$		0			0
$259$	25.3081	+	9.21138i	1.57257	+	0.572367i
$260$	−4.91101	+	8.50613i	−0.304568	+	0.527528i
$261$		0			0
$262$	−8.20752	−	14.2158i	−0.507062	−	0.878257i
$263$	−2.61682	−	14.8408i	−0.161360	−	0.915120i	−0.952738	−	0.303793i	$-0.901747\pi$
$263$	−2.61682	−	14.8408i	−0.161360	−	0.915120i	0.791378	−	0.611327i	$-0.209364\pi$
$264$		0			0
$265$	7.68875	−	2.79848i	0.472316	−	0.171909i
$266$	−2.17273	+	12.3222i	−0.133219	+	0.755521i
$267$		0			0
$268$	−6.59469	+	5.53361i	−0.402835	+	0.338019i
$269$	16.0615			0.979286			0.489643	−	0.871923i	$-0.337127\pi$
$269$	16.0615			0.979286			0.489643	+	0.871923i	$0.337127\pi$
$270$		0			0
$271$	9.41446			0.571888			0.285944	−	0.958246i	$-0.407693\pi$
$271$	9.41446			0.571888			0.285944	+	0.958246i	$0.407693\pi$
$272$	1.32201	−	1.10929i	0.0801583	−	0.0672608i
$273$		0			0
$274$	−0.0366673	+	0.207951i	−0.00221515	+	0.0125628i
$275$	10.8157	−	3.93658i	0.652209	−	0.237385i
$276$		0			0
$277$	0.968047	+	5.49007i	0.0581643	+	0.329866i	0.999980	−	0.00626247i	$-0.00199342\pi$
$277$	0.968047	+	5.49007i	0.0581643	+	0.329866i	−0.941816	+	0.336129i	$0.890882\pi$
$278$	−1.83576	−	3.17962i	−0.110101	−	0.190701i
$279$		0			0
$280$	−5.83839	+	10.1124i	−0.348911	+	0.604331i
$281$	−26.3159	−	9.57821i	−1.56988	−	0.571388i	−0.596904	−	0.802313i	$-0.703603\pi$
$281$	−26.3159	−	9.57821i	−1.56988	−	0.571388i	−0.972972	+	0.230925i	$0.925825\pi$
$282$		0			0
$283$	4.71517	+	3.95650i	0.280288	+	0.235189i	0.772083	−	0.635521i	$-0.219215\pi$
$283$	4.71517	+	3.95650i	0.280288	+	0.235189i	−0.491796	+	0.870711i	$0.663659\pi$
$284$	1.52249	+	1.27752i	0.0903429	+	0.0758067i
$285$		0			0
$286$	6.65710	+	2.42299i	0.393643	+	0.143274i
$287$	13.0484	−	22.6005i	0.770222	−	1.33406i
$288$		0			0
$289$	7.01088	+	12.1432i	0.412405	+	0.714306i
$290$	−0.322075	−	1.82658i	−0.0189129	−	0.107260i
$291$		0			0
$292$	−10.0053	+	3.64164i	−0.585517	+	0.213111i
$293$	0.405486	−	2.29962i	0.0236887	−	0.134345i	−0.970670	−	0.240416i	$-0.922716\pi$
$293$	0.405486	−	2.29962i	0.0236887	−	0.134345i	0.994359	+	0.106071i	$0.0338271\pi$
$294$		0			0
$295$	−23.4518	+	19.6784i	−1.36541	+	1.14572i
$296$	−7.30720			−0.424722
$297$		0			0
$298$	15.4744			0.896408
$299$	−7.96341	+	6.68210i	−0.460536	+	0.386436i
$300$		0			0
$301$	1.06110	−	6.01777i	0.0611606	−	0.346859i
$302$	−18.9308	+	6.89024i	−1.08934	+	0.396489i
$303$		0			0
$304$	−0.589500	−	3.34322i	−0.0338102	−	0.191747i
$305$	−20.7374	−	35.9183i	−1.18742	−	2.05668i
$306$		0			0
$307$	−3.41265	+	5.91088i	−0.194770	+	0.337351i	−0.946825	−	0.321749i	$-0.895729\pi$
$307$	−3.41265	+	5.91088i	−0.194770	+	0.337351i	0.752055	+	0.659100i	$0.229063\pi$
$308$	7.91420	+	2.88053i	0.450953	+	0.164134i
$309$		0			0
$310$	−11.2560	−	9.44489i	−0.639297	−	0.536434i
$311$	6.58432	+	5.52490i	0.373362	+	0.313288i	0.810090	−	0.586306i	$-0.199418\pi$
$311$	6.58432	+	5.52490i	0.373362	+	0.313288i	−0.436728	+	0.899594i	$0.643863\pi$
$312$		0			0
$313$	20.3621	+	7.41120i	1.15093	+	0.418906i	0.845851	−	0.533420i	$-0.179093\pi$
$313$	20.3621	+	7.41120i	1.15093	+	0.418906i	0.305083	+	0.952326i	$0.401316\pi$
$314$	−8.99872	+	15.5862i	−0.507827	+	0.879582i
$315$		0			0
$316$	−7.04660	−	12.2051i	−0.396402	−	0.686588i
$317$	6.13325	+	34.7834i	0.344477	+	1.95363i	0.297460	+	0.954734i	$0.403861\pi$
$317$	6.13325	+	34.7834i	0.344477	+	1.95363i	0.0470178	+	0.998894i	$0.485028\pi$
$318$		0			0
$319$	−1.25710	+	0.457547i	−0.0703842	+	0.0256177i
$320$	0.550137	−	3.11998i	0.0307536	−	0.174412i
$321$		0			0
$322$	−9.46719	+	7.94392i	−0.527586	+	0.442697i
$323$	−5.85859			−0.325981
$324$		0			0
$325$	15.6159			0.866217
$326$	2.33865	−	1.96236i	0.129526	−	0.108685i
$327$		0			0
$328$	−1.22952	+	6.97295i	−0.0678888	+	0.385017i
$329$	13.3411	−	4.85577i	0.735520	−	0.267707i
$330$		0			0
$331$	−4.48249	−	25.4215i	−0.246380	−	1.39729i	−0.817265	−	0.576261i	$-0.804511\pi$
$331$	−4.48249	−	25.4215i	−0.246380	−	1.39729i	0.570885	−	0.821030i	$-0.306600\pi$
$332$	1.54921	+	2.68331i	0.0850240	+	0.147266i
$333$		0			0
$334$	2.05060	−	3.55174i	0.112204	−	0.194343i
$335$	25.6288	+	9.32810i	1.40025	+	0.509649i
$336$		0			0
$337$	−2.59274	−	2.17557i	−0.141236	−	0.118511i	0.569433	−	0.822038i	$-0.307163\pi$
$337$	−2.59274	−	2.17557i	−0.141236	−	0.118511i	−0.710668	+	0.703527i	$0.751607\pi$
$338$	−2.59559	−	2.17795i	−0.141181	−	0.118465i
$339$		0			0
$340$	−5.13767	−	1.86996i	−0.278629	−	0.101413i
$341$	−5.29904	+	9.17821i	−0.286959	+	0.497028i
$342$		0			0
$343$	0.765664	+	1.32617i	0.0413420	+	0.0716064i
$344$	0.287894	+	1.63273i	0.0155222	+	0.0880308i
$345$		0			0
$346$	16.0002	−	5.82361i	0.860178	−	0.313079i
$347$	−2.81310	+	15.9539i	−0.151015	+	0.856451i	0.811323	+	0.584598i	$0.198748\pi$
$347$	−2.81310	+	15.9539i	−0.151015	+	0.856451i	−0.962339	+	0.271853i	$0.912364\pi$
$348$		0			0
$349$	3.44148	−	2.88774i	0.184218	−	0.154577i	−0.546015	−	0.837775i	$-0.683856\pi$
$349$	3.44148	−	2.88774i	0.184218	−	0.154577i	0.730233	+	0.683198i	$0.239411\pi$
$350$	18.5648			0.992330
$351$		0			0
$352$	−2.28507			−0.121795
$353$	−17.7927	+	14.9298i	−0.947008	+	0.794634i	−0.978791	−	0.204861i	$-0.934326\pi$
$353$	−17.7927	+	14.9298i	−0.947008	+	0.794634i	0.0317832	+	0.999495i	$0.489881\pi$
$354$		0			0
$355$	1.09338	−	6.20086i	0.0580305	−	0.329107i
$356$	16.2999	−	5.93268i	0.863894	−	0.314432i
$357$		0			0
$358$	−2.52763	−	14.3349i	−0.133589	−	0.757624i
$359$	5.77697	+	10.0060i	0.304897	+	0.528097i	0.977238	−	0.212144i	$-0.0680447\pi$
$359$	5.77697	+	10.0060i	0.304897	+	0.528097i	−0.672341	+	0.740241i	$0.734711\pi$
$360$		0			0
$361$	3.73768	−	6.47385i	0.196720	−	0.340729i
$362$	12.2384	+	4.45440i	0.643234	+	0.234118i
$363$		0			0
$364$	8.75339	+	7.34497i	0.458802	+	0.384981i
$365$	25.8404	+	21.6827i	1.35255	+	1.13492i
$366$		0			0
$367$	−14.6307	−	5.32516i	−0.763719	−	0.277971i	−0.0693521	−	0.997592i	$-0.522093\pi$
$367$	−14.6307	−	5.32516i	−0.763719	−	0.277971i	−0.694367	+	0.719621i	$0.744315\pi$
$368$	1.67654	−	2.90386i	0.0873959	−	0.151374i
$369$		0			0
$370$	11.5750	+	20.0485i	0.601757	+	1.04227i
$371$	−1.65296	−	9.37439i	−0.0858173	−	0.486694i
$372$		0			0
$373$	9.16883	−	3.33718i	0.474744	−	0.172793i	−0.0935562	−	0.995614i	$-0.529823\pi$
$373$	9.16883	−	3.33718i	0.474744	−	0.172793i	0.568300	+	0.822821i	$0.307601\pi$
$374$	−0.684776	+	3.88356i	−0.0354089	+	0.200814i
$375$		0			0
$376$	−2.95079	+	2.47601i	−0.152175	+	0.127690i
$377$	−1.81504			−0.0934792
$378$		0			0
$379$	−18.7904			−0.965197			−0.482599	−	0.875842i	$-0.660307\pi$
$379$	−18.7904			−0.965197			−0.482599	+	0.875842i	$0.660307\pi$
$380$	−8.23889	+	6.91325i	−0.422646	+	0.354642i
$381$		0			0
$382$	0.625632	−	3.54814i	0.0320101	−	0.181539i
$383$	−28.9125	+	10.5233i	−1.47736	+	0.537715i	−0.950088	−	0.311982i	$-0.899007\pi$
$383$	−28.9125	+	10.5233i	−1.47736	+	0.537715i	−0.527271	+	0.849697i	$0.676785\pi$
$384$		0			0
$385$	−4.63332	−	26.2769i	−0.236136	−	1.33919i
$386$	−0.737435	−	1.27727i	−0.0375344	−	0.0650116i
$387$		0			0
$388$	−4.59558	+	7.95978i	−0.233305	+	0.404097i
$389$	−27.8155	−	10.1240i	−1.41030	−	0.513308i	−0.479085	−	0.877769i	$-0.659031\pi$
$389$	−27.8155	−	10.1240i	−1.41030	−	0.513308i	−0.931219	+	0.364460i	$0.881253\pi$
$390$		0			0
$391$	−4.43280	−	3.71956i	−0.224176	−	0.188106i
$392$	5.04404	+	4.23245i	0.254762	+	0.213771i
$393$		0			0
$394$	−2.38552	−	0.868259i	−0.120181	−	0.0437423i
$395$	−22.3244	+	38.6670i	−1.12326	+	1.94555i
$396$		0			0
$397$	−8.07134	−	13.9800i	−0.405089	−	0.701635i	0.589243	−	0.807956i	$-0.299426\pi$
$397$	−8.07134	−	13.9800i	−0.405089	−	0.701635i	−0.994332	+	0.106321i	$0.966093\pi$
$398$	−0.321559	−	1.82365i	−0.0161183	−	0.0914113i
$399$		0			0
$400$	−4.73319	+	1.72274i	−0.236659	+	0.0861370i
$401$	4.40413	−	24.9771i	0.219932	−	1.24730i	−0.652209	−	0.758039i	$-0.726157\pi$
$401$	4.40413	−	24.9771i	0.219932	−	1.24730i	0.872140	−	0.489256i	$-0.162731\pi$
$402$		0			0
$403$	−11.0150	+	9.24264i	−0.548694	+	0.460409i
$404$	11.9602			0.595041
$405$		0			0
$406$	−2.15778			−0.107089
$407$	12.7910	−	10.7329i	0.634025	−	0.532010i
$408$		0			0
$409$	−3.95420	+	22.4254i	−0.195522	+	1.10886i	0.716150	+	0.697946i	$0.245902\pi$
$409$	−3.95420	+	22.4254i	−0.195522	+	1.10886i	−0.911673	+	0.410917i	$0.865209\pi$
$410$	21.0791	−	7.67216i	1.04102	−	0.378901i
$411$		0			0
$412$	−2.21340	−	12.5528i	−0.109047	−	0.618433i
$413$	17.8079	+	30.8442i	0.876269	+	1.51774i
$414$		0			0
$415$	4.90808	−	8.50104i	0.240928	−	0.417300i
$416$	−2.91331	−	1.06036i	−0.142837	−	0.0519883i
$417$		0			0
$418$	5.94247	+	4.98632i	0.290656	+	0.243889i
$419$	−3.77105	−	3.16429i	−0.184228	−	0.154586i	0.546010	−	0.837779i	$-0.316146\pi$
$419$	−3.77105	−	3.16429i	−0.184228	−	0.154586i	−0.730238	+	0.683193i	$0.760591\pi$
$420$		0			0
$421$	−18.5285	−	6.74382i	−0.903023	−	0.328674i	−0.151560	−	0.988448i	$-0.548430\pi$
$421$	−18.5285	−	6.74382i	−0.903023	−	0.328674i	−0.751464	+	0.659775i	$0.770652\pi$
$422$	9.49415	−	16.4443i	0.462168	−	0.800498i
$423$		0			0
$424$	1.29134	+	2.23666i	0.0627128	+	0.108622i
$425$	1.50945	+	8.56049i	0.0732189	+	0.415245i
$426$		0			0
$427$	−45.3411	+	16.5028i	−2.19421	+	0.798627i
$428$	1.05907	−	6.00628i	0.0511921	−	0.290325i
$429$		0			0
$430$	4.02362	−	3.37622i	0.194036	−	0.162816i
$431$	−6.16323			−0.296873			−0.148436	−	0.988922i	$-0.547424\pi$
$431$	−6.16323			−0.296873			−0.148436	+	0.988922i	$0.547424\pi$
$432$		0			0
$433$	−14.7838			−0.710466			−0.355233	−	0.934778i	$-0.615599\pi$
$433$	−14.7838			−0.710466			−0.355233	+	0.934778i	$0.615599\pi$
$434$	−13.0950	+	10.9880i	−0.628579	+	0.527440i
$435$		0			0
$436$	1.95163	−	11.0683i	0.0934662	−	0.530073i
$437$	−10.6966	+	3.89323i	−0.511686	+	0.186239i
$438$		0			0
$439$	5.16899	+	29.3148i	0.246703	+	1.39912i	0.816505	+	0.577338i	$0.195909\pi$
$439$	5.16899	+	29.3148i	0.246703	+	1.39912i	−0.569803	+	0.821782i	$0.692980\pi$
$440$	3.61968	+	6.26947i	0.172561	+	0.298885i
$441$		0			0
$442$	−2.67516	+	4.63351i	−0.127244	+	0.220394i
$443$	−28.6365	−	10.4228i	−1.36056	−	0.495204i	−0.444335	−	0.895861i	$-0.646560\pi$
$443$	−28.6365	−	10.4228i	−1.36056	−	0.495204i	−0.916228	+	0.400656i	$0.868782\pi$
$444$		0			0
$445$	−42.0973	−	35.3238i	−1.99560	−	1.67451i
$446$	−5.55716	−	4.66301i	−0.263139	−	0.220800i
$447$		0			0
$448$	−3.46344	−	1.26059i	−0.163632	−	0.0595573i
$449$	−5.92055	+	10.2547i	−0.279408	+	0.483949i	−0.971238	−	0.238112i	$-0.923472\pi$
$449$	−5.92055	+	10.2547i	−0.279408	+	0.483949i	0.691830	+	0.722061i	$0.256805\pi$
$450$		0			0
$451$	−8.08973	−	14.0118i	−0.380930	−	0.659791i
$452$	−1.22195	−	6.93005i	−0.0574759	−	0.325962i
$453$		0			0
$454$	26.8068	−	9.75687i	1.25810	−	0.457913i
$455$	6.28628	−	35.6513i	0.294705	−	1.67136i
$456$		0			0
$457$	−0.142785	+	0.119811i	−0.00667922	+	0.00560453i	−0.646121	−	0.763235i	$-0.723610\pi$
$457$	−0.142785	+	0.119811i	−0.00667922	+	0.00560453i	0.639442	+	0.768839i	$0.279165\pi$
$458$	1.85538			0.0866963
$459$		0			0
$460$	−10.6230			−0.495299
$461$	7.97096	−	6.68843i	0.371245	−	0.311511i	−0.438009	−	0.898971i	$-0.644316\pi$
$461$	7.97096	−	6.68843i	0.371245	−	0.311511i	0.809254	+	0.587459i	$0.199872\pi$
$462$		0			0
$463$	4.47811	−	25.3966i	0.208115	−	1.18028i	−0.684346	−	0.729158i	$-0.739912\pi$
$463$	4.47811	−	25.3966i	0.208115	−	1.18028i	0.892461	−	0.451124i	$-0.148977\pi$
$464$	0.550137	−	0.200234i	0.0255395	−	0.00929561i
$465$		0			0
$466$	1.48203	+	8.40503i	0.0686539	+	0.389356i
$467$	−10.8506	−	18.7937i	−0.502104	−	0.869670i	−0.999997	−	0.00243153i	$-0.999226\pi$
$467$	−10.8506	−	18.7937i	−0.502104	−	0.869670i	0.497893	−	0.867239i	$-0.334107\pi$
$468$		0			0
$469$	15.8647	−	27.4785i	0.732566	−	1.26884i
$470$	11.4676	+	4.17385i	0.528959	+	0.192525i
$471$		0			0
$472$	−7.40243	−	6.21138i	−0.340724	−	0.285902i
$473$	−2.90212	−	2.43517i	−0.133440	−	0.111969i
$474$		0			0
$475$	16.0682	+	5.84835i	0.737260	+	0.268341i
$476$	−3.18032	+	5.50848i	−0.145770	+	0.252481i
$477$		0			0
$478$	3.64398	+	6.31156i	0.166672	+	0.288684i
$479$	−6.79333	−	38.5269i	−0.310395	−	1.76034i	−0.596954	−	0.802276i	$-0.703622\pi$
$479$	−6.79333	−	38.5269i	−0.310395	−	1.76034i	0.286559	−	0.958063i	$-0.407489\pi$
$480$		0			0
$481$	21.2881	−	7.74823i	0.970654	−	0.353289i
$482$	−0.231806	+	1.31464i	−0.0105585	+	0.0598801i
$483$		0			0
$484$	−4.42656	+	3.71433i	−0.201207	+	0.168833i
$485$	29.1187			1.32221
$486$		0			0
$487$	−10.4833			−0.475043			−0.237522	−	0.971382i	$-0.576335\pi$
$487$	−10.4833			−0.475043			−0.237522	+	0.971382i	$0.576335\pi$
$488$	10.0285	−	8.41495i	0.453971	−	0.380927i
$489$		0			0
$490$	3.62239	−	20.5436i	0.163643	−	0.928066i
$491$	−6.44349	+	2.34524i	−0.290791	+	0.105839i	−0.483297	−	0.875457i	$-0.660561\pi$
$491$	−6.44349	+	2.34524i	−0.290791	+	0.105839i	0.192506	+	0.981296i	$0.438339\pi$
$492$		0			0
$493$	−0.175443	−	0.994984i	−0.00790153	−	0.0448118i
$494$	5.26240	+	9.11475i	0.236767	+	0.410092i
$495$		0			0
$496$	2.31899	−	4.01660i	0.104126	−	0.180351i
$497$	−6.88347	−	2.50538i	−0.308766	−	0.112382i
$498$		0			0
$499$	14.3815	+	12.0675i	0.643804	+	0.540216i	0.905184	−	0.425020i	$-0.139733\pi$
$499$	14.3815	+	12.0675i	0.643804	+	0.540216i	−0.261380	+	0.965236i	$0.584177\pi$
$500$	0.0896853	+	0.0752549i	0.00401085	+	0.00336550i
$501$		0			0
$502$	2.70496	+	0.984526i	0.120728	+	0.0439415i
$503$	6.21350	−	10.7621i	0.277046	−	0.479858i	−0.693603	−	0.720357i	$-0.743978\pi$
$503$	6.21350	−	10.7621i	0.277046	−	0.479858i	0.970649	+	0.240499i	$0.0773112\pi$
$504$		0			0
$505$	−18.9456	−	32.8148i	−0.843069	−	1.46024i
$506$	1.33050	+	7.54563i	0.0591479	+	0.335444i
$507$		0			0
$508$	−5.62406	+	2.04699i	−0.249527	+	0.0908204i
$509$	5.72652	−	32.4767i	0.253824	−	1.43950i	−0.545251	−	0.838273i	$-0.683566\pi$
$509$	5.72652	−	32.4767i	0.253824	−	1.43950i	0.799075	−	0.601232i	$-0.205323\pi$
$510$		0			0
$511$	30.0622	−	25.2252i	1.32987	−	1.11590i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−25.7779			−1.13702
$515$	−30.9346	+	25.9572i	−1.36314	+	1.14381i
$516$		0			0
$517$	1.52846	−	8.66831i	0.0672215	−	0.381232i
$518$	25.3081	−	9.21138i	1.11197	−	0.404725i
$519$		0			0
$520$	1.70558	+	9.67281i	0.0747945	+	0.424181i
$521$	−7.16598	−	12.4118i	−0.313947	−	0.543773i	0.665266	−	0.746607i	$-0.268318\pi$
$521$	−7.16598	−	12.4118i	−0.313947	−	0.543773i	−0.979213	+	0.202834i	$0.934985\pi$
$522$		0			0
$523$	2.85442	−	4.94400i	0.124815	−	0.216186i	−0.796846	−	0.604183i	$-0.793500\pi$
$523$	2.85442	−	4.94400i	0.124815	−	0.216186i	0.921661	+	0.387997i	$0.126833\pi$
$524$	−15.4251	−	5.61427i	−0.673848	−	0.245261i
$525$		0			0
$526$	−11.5441	−	9.68661i	−0.503345	−	0.422356i
$527$	−6.13143	−	5.14488i	−0.267089	−	0.224114i
$528$		0			0
$529$	11.0478	+	4.02106i	0.480338	+	0.174829i
$530$	4.09110	−	7.08599i	0.177706	−	0.307796i
$531$		0			0
$532$	6.25613	+	10.8359i	0.271238	+	0.469798i
$533$	−3.81185	−	21.6181i	−0.165109	−	0.936382i
$534$		0			0
$535$	−18.1569	+	6.60856i	−0.784990	+	0.285713i
$536$	−1.49490	+	8.47798i	−0.0645697	+	0.366193i
$537$		0			0
$538$	12.3038	−	10.3241i	0.530455	−	0.445104i
$539$	−15.0461			−0.648081
$540$		0			0
$541$	18.0099			0.774305			0.387153	−	0.922016i	$-0.373459\pi$
$541$	18.0099			0.774305			0.387153	+	0.922016i	$0.373459\pi$
$542$	7.21190	−	6.05150i	0.309777	−	0.259934i
$543$		0			0
$544$	0.299674	−	1.69954i	0.0128484	−	0.0728671i
$545$	−33.4591	+	12.1781i	−1.43323	+	0.521653i
$546$		0			0
$547$	−3.58197	−	20.3143i	−0.153154	−	0.868578i	−0.960454	−	0.278438i	$-0.910183\pi$
$547$	−3.58197	−	20.3143i	−0.153154	−	0.868578i	0.807301	−	0.590141i	$-0.200928\pi$
$548$	0.105579	+	0.182869i	0.00451012	+	0.00781176i
$549$		0			0
$550$	5.75489	−	9.96776i	0.245389	−	0.425027i
$551$	−1.86760	−	0.679753i	−0.0795626	−	0.0289584i
$552$		0			0
$553$	39.7911	+	33.3887i	1.69209	+	1.41983i
$554$	4.27051	+	3.58339i	0.181437	+	0.152244i
$555$		0			0
$556$	−3.45009	−	1.25573i	−0.146316	−	0.0532548i
$557$	1.90209	−	3.29452i	0.0805942	−	0.139593i	−0.822911	−	0.568170i	$-0.807652\pi$
$557$	1.90209	−	3.29452i	0.0805942	−	0.139593i	0.903505	+	0.428577i	$0.140985\pi$
$558$		0			0
$559$	−2.57000	−	4.45136i	−0.108699	−	0.188273i
$560$	2.02765	+	11.4994i	0.0856839	+	0.485938i
$561$		0			0
$562$	−26.3159	+	9.57821i	−1.11007	+	0.404032i
$563$	−1.92252	+	10.9032i	−0.0810247	+	0.459514i	0.917119	+	0.398613i	$0.130508\pi$
$563$	−1.92252	+	10.9032i	−0.0810247	+	0.459514i	−0.998144	+	0.0609006i	$0.980603\pi$
$564$		0			0
$565$	−17.0781	+	14.3302i	−0.718481	+	0.602877i
$566$	6.15522			0.258723
$567$		0			0
$568$	1.98746			0.0833921
$569$	35.7860	−	30.0280i	1.50023	−	1.25884i	0.619704	−	0.784836i	$-0.287253\pi$
$569$	35.7860	−	30.0280i	1.50023	−	1.25884i	0.880523	−	0.474004i	$-0.157192\pi$
$570$		0			0
$571$	−5.50225	+	31.2048i	−0.230262	+	1.30588i	0.622104	+	0.782935i	$0.286278\pi$
$571$	−5.50225	+	31.2048i	−0.230262	+	1.30588i	−0.852366	+	0.522946i	$0.824833\pi$
$572$	6.65710	−	2.42299i	0.278347	−	0.101310i
$573$		0			0
$574$	−4.53166	−	25.7003i	−0.189148	−	1.07271i
$575$	8.44468	+	14.6266i	0.352167	+	0.609972i
$576$		0			0
$577$	−22.1642	+	38.3895i	−0.922707	+	1.59818i	−0.127499	+	0.991839i	$0.540695\pi$
$577$	−22.1642	+	38.3895i	−0.922707	+	1.59818i	−0.795208	+	0.606336i	$0.792639\pi$
$578$	13.1762	+	4.79573i	0.548056	+	0.199476i
$579$		0			0
$580$	−1.42082	−	1.19221i	−0.0589965	−	0.0495040i
$581$	−8.74816	−	7.34058i	−0.362935	−	0.304539i
$582$		0			0
$583$	−5.54567	−	2.01846i	−0.229678	−	0.0835960i
$584$	−5.32371	+	9.22094i	−0.220297	+	0.381565i
$585$		0			0
$586$	−1.16755	−	2.02226i	−0.0482310	−	0.0835386i
$587$	7.12733	+	40.4211i	0.294176	+	1.66836i	0.670531	+	0.741882i	$0.266066\pi$
$587$	7.12733	+	40.4211i	0.294176	+	1.66836i	−0.376354	+	0.926476i	$0.622823\pi$
$588$		0			0
$589$	−14.7954	+	5.38510i	−0.609636	+	0.221889i
$590$	−5.31608	+	30.1490i	−0.218860	+	1.24121i
$591$		0			0
$592$	−5.59764	+	4.69698i	−0.230062	+	0.193045i
$593$	−9.69265			−0.398029			−0.199015	−	0.979996i	$-0.563774\pi$
$593$	−9.69265			−0.398029			−0.199015	+	0.979996i	$0.563774\pi$
$594$		0			0
$595$	20.1513			0.826121
$596$	11.8541	−	9.94675i	0.485562	−	0.407435i
$597$		0			0
$598$	−1.80516	+	10.2376i	−0.0738184	+	0.418645i
$599$	28.0385	−	10.2052i	1.14562	−	0.416972i	0.301680	−	0.953409i	$-0.402452\pi$
$599$	28.0385	−	10.2052i	1.14562	−	0.416972i	0.843940	+	0.536437i	$0.180230\pi$
$600$		0			0
$601$	2.17941	+	12.3600i	0.0888998	+	0.504176i	0.996447	+	0.0842252i	$0.0268415\pi$
$601$	2.17941	+	12.3600i	0.0888998	+	0.504176i	−0.907547	+	0.419951i	$0.862047\pi$
$602$	−3.05530	−	5.29194i	−0.124525	−	0.215683i
$603$		0			0
$604$	−10.0729	+	17.4467i	−0.409859	+	0.709896i
$605$	17.2028	+	6.26131i	0.699394	+	0.254558i
$606$		0			0
$607$	−2.12971	−	1.78704i	−0.0864421	−	0.0725336i	0.598543	−	0.801091i	$-0.295747\pi$
$607$	−2.12971	−	1.78704i	−0.0864421	−	0.0725336i	−0.684985	+	0.728557i	$0.740191\pi$
$608$	−2.60057	−	2.18213i	−0.105467	−	0.0884972i
$609$		0			0
$610$	−38.9736	−	14.1852i	−1.57800	−	0.574344i
$611$	5.97110	−	10.3422i	0.241565	−	0.418403i
$612$		0			0
$613$	4.29646	+	7.44168i	0.173532	+	0.300567i	0.939652	−	0.342131i	$-0.111149\pi$
$613$	4.29646	+	7.44168i	0.173532	+	0.300567i	−0.766120	+	0.642697i	$0.777815\pi$
$614$	1.18520	+	6.72160i	0.0478307	+	0.271262i
$615$		0			0
$616$	7.91420	−	2.88053i	0.318872	−	0.116060i
$617$	−3.48669	+	19.7740i	−0.140369	+	0.796071i	0.830601	+	0.556868i	$0.187997\pi$
$617$	−3.48669	+	19.7740i	−0.140369	+	0.796071i	−0.970970	+	0.239203i	$0.923114\pi$
$618$		0			0
$619$	6.42853	−	5.39418i	0.258384	−	0.216810i	−0.504388	−	0.863477i	$-0.668282\pi$
$619$	6.42853	−	5.39418i	0.258384	−	0.216810i	0.762773	+	0.646667i	$0.223838\pi$
$620$	−14.6936			−0.590111
$621$		0			0
$622$	8.59522			0.344637
$623$	−48.9751	+	41.0950i	−1.96215	+	1.64644i
$624$		0			0
$625$	−4.30888	+	24.4369i	−0.172355	+	0.977475i
$626$	20.3621	−	7.41120i	0.813833	−	0.296211i
$627$		0			0
$628$	3.12522	+	17.7240i	0.124710	+	0.707265i
$629$	6.30522	+	10.9210i	0.251405	+	0.435447i
$630$		0			0
$631$	−8.78157	+	15.2101i	−0.349589	+	0.605506i	−0.986176	−	0.165699i	$-0.947012\pi$
$631$	−8.78157	+	15.2101i	−0.349589	+	0.605506i	0.636588	+	0.771204i	$0.280345\pi$
$632$	−13.2433	−	4.82016i	−0.526789	−	0.191735i
$633$		0			0
$634$	27.0567	+	22.7032i	1.07456	+	0.901660i
$635$	14.5251	+	12.1880i	0.576410	+	0.483666i
$636$		0			0
$637$	−19.1827	−	6.98194i	−0.760047	−	0.276635i
$638$	−0.668890	+	1.15855i	−0.0264816	+	0.0458675i
$639$		0			0
$640$	−1.58406	−	2.74367i	−0.0626154	−	0.108453i
$641$	−2.32943	−	13.2108i	−0.0920069	−	0.521797i	−0.995624	−	0.0934548i	$-0.970209\pi$
$641$	−2.32943	−	13.2108i	−0.0920069	−	0.521797i	0.903617	−	0.428342i	$-0.140902\pi$
$642$		0			0
$643$	9.80578	−	3.56901i	0.386702	−	0.140748i	−0.141351	−	0.989960i	$-0.545144\pi$
$643$	9.80578	−	3.56901i	0.386702	−	0.140748i	0.528053	+	0.849211i	$0.322922\pi$
$644$	−2.14604	+	12.1708i	−0.0845657	+	0.479596i
$645$		0			0
$646$	−4.48794	+	3.76583i	−0.176576	+	0.148165i
$647$	−37.9585			−1.49230			−0.746152	−	0.665775i	$-0.768101\pi$
$647$	−37.9585			−1.49230			−0.746152	+	0.665775i	$0.768101\pi$
$648$		0			0
$649$	22.0810			0.866756
$650$	11.9625	−	10.0377i	0.469208	−	0.393712i
$651$		0			0
$652$	0.530129	−	3.00651i	0.0207615	−	0.117744i
$653$	25.6595	−	9.33930i	1.00413	−	0.365475i	0.212957	−	0.977062i	$-0.431691\pi$
$653$	25.6595	−	9.33930i	1.00413	−	0.365475i	0.791178	+	0.611587i	$0.209468\pi$
$654$		0			0
$655$	9.03052	+	51.2146i	0.352852	+	2.00112i
$656$	3.54026	+	6.13191i	0.138224	+	0.239411i
$657$		0			0
$658$	7.09866	−	12.2952i	0.276735	−	0.479318i
$659$	32.2831	+	11.7501i	1.25757	+	0.457718i	0.882953	−	0.469462i	$-0.155552\pi$
$659$	32.2831	+	11.7501i	1.25757	+	0.457718i	0.374617	+	0.927180i	$0.377774\pi$
$660$		0			0
$661$	−18.8276	−	15.7982i	−0.732309	−	0.614481i	0.198451	−	0.980111i	$-0.436409\pi$
$661$	−18.8276	−	15.7982i	−0.732309	−	0.614481i	−0.930760	+	0.365630i	$0.880853\pi$
$662$	−19.7744	−	16.5927i	−0.768554	−	0.644893i
$663$		0			0
$664$	2.91156	+	1.05972i	0.112991	+	0.0411252i
$665$	19.8202	−	34.3295i	0.768593	−	1.33124i
$666$		0			0
$667$	−0.981523	−	1.70005i	−0.0380047	−	0.0658261i
$668$	−0.712165	−	4.03889i	−0.0275545	−	0.156269i
$669$		0			0
$670$	25.6288	−	9.32810i	0.990125	−	0.360376i
$671$	−5.19461	+	29.4601i	−0.200536	+	1.13730i
$672$		0			0
$673$	32.8445	−	27.5598i	1.26606	−	1.06235i	0.271054	−	0.962564i	$-0.412628\pi$
$673$	32.8445	−	27.5598i	1.26606	−	1.06235i	0.995009	−	0.0997881i	$-0.0318165\pi$
$674$	−3.38459			−0.130369
$675$		0			0
$676$	−3.38830			−0.130319
$677$	5.73570	−	4.81283i	0.220441	−	0.184972i	−0.525879	−	0.850560i	$-0.676263\pi$
$677$	5.73570	−	4.81283i	0.220441	−	0.184972i	0.746320	+	0.665588i	$0.231819\pi$
$678$		0			0
$679$	5.88251	−	33.3614i	0.225750	−	1.28029i
$680$	−5.13767	+	1.86996i	−0.197021	+	0.0717096i
$681$		0			0
$682$	1.84034	+	10.4371i	0.0704702	+	0.399656i
$683$	−8.37724	−	14.5098i	−0.320546	−	0.555202i	0.660055	−	0.751218i	$-0.270533\pi$
$683$	−8.37724	−	14.5098i	−0.320546	−	0.555202i	−0.980601	+	0.196015i	$0.937200\pi$
$684$		0			0
$685$	0.334487	−	0.579349i	0.0127801	−	0.0221358i
$686$	1.43898	+	0.523745i	0.0549404	+	0.0199967i
$687$		0			0
$688$	1.27004	+	1.06569i	0.0484197	+	0.0406289i
$689$	−6.13371	−	5.14679i	−0.233676	−	0.196077i
$690$		0			0
$691$	14.0516	+	5.11438i	0.534550	+	0.194560i	0.595169	−	0.803601i	$-0.297085\pi$
$691$	14.0516	+	5.11438i	0.534550	+	0.194560i	−0.0606190	+	0.998161i	$0.519307\pi$
$692$	8.51355	−	14.7459i	0.323637	−	0.560555i
$693$		0			0
$694$	8.10001	+	14.0296i	0.307472	+	0.532558i
$695$	2.01984	+	11.4551i	0.0766167	+	0.434515i
$696$		0			0
$697$	11.4823	−	4.17923i	0.434924	−	0.158299i
$698$	0.780120	−	4.42428i	0.0295280	−	0.167461i
$699$		0			0
$700$	14.2215	−	11.9332i	0.537521	−	0.451033i
$701$	−42.1025			−1.59019			−0.795094	−	0.606486i	$-0.792579\pi$
$701$	−42.1025			−1.59019			−0.795094	+	0.606486i	$0.792579\pi$
$702$		0			0
$703$	24.8065			0.935593
$704$	−1.75046	+	1.46881i	−0.0659731	+	0.0553580i
$705$		0			0
$706$	−4.03327	+	22.8738i	−0.151794	+	0.860867i
$707$	−41.4234	+	15.0769i	−1.55789	+	0.567024i
$708$		0			0
$709$	4.94647	+	28.0528i	0.185769	+	1.05355i	0.924964	+	0.380055i	$0.124095\pi$
$709$	4.94647	+	28.0528i	0.185769	+	1.05355i	−0.739195	+	0.673491i	$0.764794\pi$
$710$	−3.14826	−	5.45294i	−0.118152	−	0.204645i
$711$		0			0
$712$	8.67300	−	15.0221i	0.325035	−	0.562976i
$713$	−14.6137	−	5.31894i	−0.547286	−	0.199196i
$714$		0			0
$715$	−17.1931	−	14.4267i	−0.642985	−	0.539529i
$716$	−11.1506	−	9.35645i	−0.416717	−	0.349667i
$717$		0			0
$718$	10.8572	+	3.95168i	0.405185	+	0.147475i
$719$	−1.26744	+	2.19526i	−0.0472674	+	0.0818695i	−0.888691	−	0.458506i	$-0.848385\pi$
$719$	−1.26744	+	2.19526i	−0.0472674	+	0.0818695i	0.841424	+	0.540376i	$0.181718\pi$
$720$		0			0
$721$	23.4900	+	40.6858i	0.874812	+	1.51522i
$722$	−1.29808	−	7.36179i	−0.0483096	−	0.273977i
$723$		0			0
$724$	12.2384	−	4.45440i	0.454835	−	0.165547i
$725$	−0.512063	+	2.90406i	−0.0190176	+	0.107854i
$726$		0			0
$727$	15.2316	−	12.7808i	0.564907	−	0.474014i	−0.315044	−	0.949077i	$-0.602019\pi$
$727$	15.2316	−	12.7808i	0.564907	−	0.474014i	0.879952	+	0.475063i	$0.157575\pi$
$728$	11.4267			0.423503
$729$		0			0
$730$	33.7323			1.24849
$731$	2.19177	−	1.83912i	0.0810656	−	0.0680221i
$732$		0			0
$733$	−1.73840	+	9.85898i	−0.0642094	+	0.364150i	0.935725	+	0.352729i	$0.114746\pi$
$733$	−1.73840	+	9.85898i	−0.0642094	+	0.364150i	−0.999935	+	0.0114203i	$0.996365\pi$
$734$	−14.6307	+	5.32516i	−0.540031	+	0.196555i
$735$		0			0
$736$	−0.582258	−	3.30215i	−0.0214623	−	0.121719i
$737$	−9.83580	−	17.0361i	−0.362306	−	0.627533i
$738$		0			0
$739$	20.1957	−	34.9800i	0.742911	−	1.28676i	−0.208253	−	0.978075i	$-0.566778\pi$
$739$	20.1957	−	34.9800i	0.742911	−	1.28676i	0.951164	−	0.308685i	$-0.0998890\pi$
$740$	21.7539	+	7.91778i	0.799690	+	0.291063i
$741$		0			0
$742$	−7.29198	−	6.11870i	−0.267697	−	0.224624i
$743$	27.3096	+	22.9155i	1.00189	+	0.840688i	0.987246	−	0.159205i	$-0.0508930\pi$
$743$	27.3096	+	22.9155i	1.00189	+	0.840688i	0.0146474	+	0.999893i	$0.495337\pi$
$744$		0			0
$745$	−46.0681	−	16.7674i	−1.68781	−	0.614311i
$746$	4.87863	−	8.45004i	0.178619	−	0.309378i
$747$		0			0
$748$	1.97173	+	3.41514i	0.0720937	+	0.124870i
$749$	3.90343	+	22.1375i	0.142628	+	0.808886i
$750$		0			0
$751$	8.89769	−	3.23850i	0.324681	−	0.118174i	−0.174537	−	0.984651i	$-0.555843\pi$
$751$	8.89769	−	3.23850i	0.324681	−	0.118174i	0.499218	+	0.866476i	$0.333621\pi$
$752$	−0.668890	+	3.79346i	−0.0243919	+	0.138333i
$753$		0			0
$754$	−1.39040	+	1.16668i	−0.0506354	+	0.0424881i
$755$	63.8240			2.32279
$756$		0			0
$757$	−37.9651			−1.37987			−0.689933	−	0.723873i	$-0.742360\pi$
$757$	−37.9651			−1.37987			−0.689933	+	0.723873i	$0.742360\pi$
$758$	−14.3943	+	12.0782i	−0.522823	+	0.438701i
$759$		0			0
$760$	−1.86760	+	10.5917i	−0.0677451	+	0.384202i
$761$	−42.1788	+	15.3518i	−1.52898	+	0.556504i	−0.963372	−	0.268170i	$-0.913581\pi$
$761$	−42.1788	+	15.3518i	−1.52898	+	0.556504i	−0.565609	+	0.824673i	$0.691359\pi$
$762$		0			0
$763$	7.19316	+	40.7945i	0.260410	+	1.47686i
$764$	−1.80144	−	3.12018i	−0.0651737	−	0.112884i
$765$		0			0
$766$	−15.3840	+	26.6459i	−0.555847	+	0.962755i
$767$	28.1518	+	10.2464i	1.01650	+	0.369977i
$768$		0			0
$769$	35.0364	+	29.3991i	1.26345	+	1.06016i	0.995306	+	0.0967777i	$0.0308536\pi$
$769$	35.0364	+	29.3991i	1.26345	+	1.06016i	0.268140	+	0.963380i	$0.413591\pi$
$770$	−20.4398	−	17.1510i	−0.736598	−	0.618080i
$771$		0			0
$772$	−1.38592	−	0.504435i	−0.0498805	−	0.0181550i
$773$	10.2853	−	17.8147i	0.369938	−	0.640752i	−0.619617	−	0.784904i	$-0.712712\pi$
$773$	10.2853	−	17.8147i	0.369938	−	0.640752i	0.989556	+	0.144152i	$0.0460455\pi$
$774$		0			0
$775$	11.6806	+	20.2315i	0.419581	+	0.726735i
$776$	1.59603	+	9.05153i	0.0572941	+	0.324931i
$777$		0			0
$778$	−27.8155	+	10.1240i	−0.997235	+	0.362964i
$779$	4.17397	−	23.6717i	0.149548	−	0.848128i
$780$		0			0
$781$	−3.47898	+	2.91921i	−0.124488	+	0.104458i
$782$	−5.78661			−0.206929
$783$		0			0
$784$	6.58452			0.235162
$785$	43.6783	−	36.6504i	1.55894	−	1.30811i
$786$		0			0
$787$	7.73837	−	43.8865i	0.275843	−	1.56438i	−0.460427	−	0.887697i	$-0.652304\pi$
$787$	7.73837	−	43.8865i	0.275843	−	1.56438i	0.736271	−	0.676687i	$-0.236585\pi$
$788$	−2.38552	+	0.868259i	−0.0849807	+	0.0309305i
$789$		0			0
$790$	7.75319	+	43.9705i	0.275846	+	1.56440i
$791$	12.9681	+	22.4614i	0.461093	+	0.798637i
$792$		0			0
$793$	−20.2934	+	35.1492i	−0.720639	+	1.24818i
$794$	−15.1692	−	5.52112i	−0.538333	−	0.195937i
$795$		0			0
$796$	−1.41855	−	1.19030i	−0.0502791	−	0.0421892i
$797$	33.5988	+	28.1927i	1.19013	+	0.998638i	0.999857	+	0.0169072i	$0.00538197\pi$
$797$	33.5988	+	28.1927i	1.19013	+	0.998638i	0.190274	+	0.981731i	$0.439062\pi$
$798$		0			0
$799$	6.24668	+	2.27361i	0.220992	+	0.0804344i
$800$	−2.51848	+	4.36213i	−0.0890416	+	0.154225i
$801$		0			0
$802$	−12.6812	−	21.9645i	−0.447788	−	0.775592i
$803$	−4.22488	−	23.9605i	−0.149093	−	0.845546i
$804$		0			0
$805$	36.7921	−	13.3912i	1.29675	−	0.471978i
$806$	−2.49689	+	14.1605i	−0.0879491	+	0.498784i
$807$		0			0
$808$	9.16203	−	7.68785i	0.322319	−	0.270458i
$809$	−15.5821			−0.547836			−0.273918	−	0.961753i	$-0.588320\pi$
$809$	−15.5821			−0.547836			−0.273918	+	0.961753i	$0.588320\pi$
$810$		0			0
$811$	−30.4691			−1.06992			−0.534958	−	0.844879i	$-0.679673\pi$
$811$	−30.4691			−1.06992			−0.534958	+	0.844879i	$0.679673\pi$
$812$	−1.65296	+	1.38700i	−0.0580074	+	0.0486740i
$813$		0			0
$814$	2.89948	−	16.4438i	0.101627	−	0.576354i
$815$	−9.08863	+	3.30799i	−0.318361	+	0.115874i
$816$		0			0
$817$	−0.977341	−	5.54278i	−0.0341928	−	0.193917i
$818$	11.3857	+	19.7205i	0.398090	+	0.689512i
$819$		0			0
$820$	11.2159	−	19.4266i	0.391678	−	0.678406i
$821$	1.78637	+	0.650187i	0.0623448	+	0.0226917i	0.373004	−	0.927830i	$-0.378328\pi$
$821$	1.78637	+	0.650187i	0.0623448	+	0.0226917i	−0.310659	+	0.950521i	$0.600550\pi$
$822$		0			0
$823$	−16.8844	−	14.1677i	−0.588553	−	0.493855i	0.299190	−	0.954194i	$-0.403284\pi$
$823$	−16.8844	−	14.1677i	−0.588553	−	0.493855i	−0.887743	+	0.460339i	$0.847728\pi$
$824$	−9.76437	−	8.19328i	−0.340158	−	0.285426i
$825$		0			0
$826$	33.4679	+	12.1813i	1.16450	+	0.423842i
$827$	−24.2488	+	42.0001i	−0.843213	+	1.46049i	0.0439508	+	0.999034i	$0.486006\pi$
$827$	−24.2488	+	42.0001i	−0.843213	+	1.46049i	−0.887164	+	0.461454i	$0.847328\pi$
$828$		0			0
$829$	10.1593	+	17.5964i	0.352846	+	0.611148i	0.986747	−	0.162267i	$-0.0518805\pi$
$829$	10.1593	+	17.5964i	0.352846	+	0.611148i	−0.633900	+	0.773415i	$0.718547\pi$
$830$	−1.70456	−	9.66703i	−0.0591661	−	0.335547i
$831$		0			0
$832$	−2.91331	+	1.06036i	−0.101001	+	0.0367612i
$833$	1.97321	−	11.1906i	0.0683678	−	0.387733i
$834$		0			0
$835$	−9.95326	+	8.35178i	−0.344447	+	0.289025i
$836$	7.75734			0.268293
$837$		0			0
$838$	−4.92276			−0.170054
$839$	−3.88105	+	3.25659i	−0.133989	+	0.112430i	−0.707319	−	0.706894i	$-0.750096\pi$
$839$	−3.88105	+	3.25659i	−0.133989	+	0.112430i	0.573330	+	0.819324i	$0.305651\pi$
$840$		0			0
$841$	−4.97628	+	28.2219i	−0.171596	+	0.973169i
$842$	−18.5285	+	6.74382i	−0.638534	+	0.232407i
$843$		0			0
$844$	−3.29728	−	18.6998i	−0.113497	−	0.643674i
$845$	5.36726	+	9.29636i	0.184639	+	0.319804i
$846$		0			0
$847$	10.6489	−	18.4444i	0.365901	−	0.633758i
$848$	2.42692	+	0.883326i	0.0833407	+	0.0303335i
$849$		0			0
$850$	6.65888	+	5.58746i	0.228398	+	0.191648i
$851$	18.7694	+	15.7494i	0.643406	+	0.539882i
$852$		0			0
$853$	−24.8716	−	9.05254i	−0.851589	−	0.309953i	−0.120901	−	0.992665i	$-0.538578\pi$
$853$	−24.8716	−	9.05254i	−0.851589	−	0.309953i	−0.730688	+	0.682712i	$0.760801\pi$
$854$	−24.1255	+	41.7866i	−0.825558	+	1.42991i
$855$		0			0
$856$	−3.04947	−	5.28184i	−0.104229	−	0.180529i
$857$	−3.17978	−	18.0334i	−0.108619	−	0.616011i	−0.989713	−	0.143068i	$-0.954303\pi$
$857$	−3.17978	−	18.0334i	−0.108619	−	0.616011i	0.881094	−	0.472942i	$-0.156808\pi$
$858$		0			0
$859$	8.87010	−	3.22845i	0.302644	−	0.110153i	−0.186234	−	0.982505i	$-0.559628\pi$
$859$	8.87010	−	3.22845i	0.302644	−	0.110153i	0.488878	+	0.872352i	$0.337406\pi$
$860$	0.912081	−	5.17267i	0.0311017	−	0.176387i
$861$		0			0
$862$	−4.72131	+	3.96165i	−0.160809	+	0.134934i
$863$	−14.2154			−0.483898			−0.241949	−	0.970289i	$-0.577787\pi$
$863$	−14.2154			−0.483898			−0.241949	+	0.970289i	$0.577787\pi$
$864$		0			0
$865$	−53.9438			−1.83414
$866$	−11.3251	+	9.50287i	−0.384842	+	0.322921i
$867$		0			0
$868$	−2.96839	+	16.8346i	−0.100754	+	0.571403i
$869$	30.2618	−	11.0144i	1.02656	−	0.373637i
$870$		0			0
$871$	−4.63459	−	26.2841i	−0.157037	−	0.890601i
$872$	−5.61950	−	9.73326i	−0.190300	−	0.329610i
$873$		0			0
$874$	−5.69153	+	9.85801i	−0.192519	+	0.333452i
$875$	−0.405486	−	0.147585i	−0.0137079	−	0.00498927i
$876$		0			0
$877$	29.9565	+	25.1365i	1.01156	+	0.848799i	0.988544	−	0.150936i	$-0.0482288\pi$
$877$	29.9565	+	25.1365i	1.01156	+	0.848799i	0.0230156	+	0.999735i	$0.492673\pi$
$878$	22.8029	+	19.1339i	0.769560	+	0.645737i
$879$		0			0
$880$	6.80277	+	2.47601i	0.229321	+	0.0834661i
$881$	11.4469	−	19.8266i	0.385657	−	0.667977i	−0.606203	−	0.795310i	$-0.707308\pi$
$881$	11.4469	−	19.8266i	0.385657	−	0.667977i	0.991860	+	0.127333i	$0.0406416\pi$
$882$		0			0
$883$	8.57546	+	14.8531i	0.288587	+	0.499847i	0.973473	−	0.228803i	$-0.0734812\pi$
$883$	8.57546	+	14.8531i	0.288587	+	0.499847i	−0.684886	+	0.728651i	$0.740148\pi$
$884$	0.929073	+	5.26903i	0.0312481	+	0.177217i
$885$		0			0
$886$	−28.6365	+	10.4228i	−0.962063	+	0.350162i
$887$	3.17030	−	17.9797i	0.106448	−	0.603698i	−0.884184	−	0.467139i	$-0.845285\pi$
$887$	3.17030	−	17.9797i	0.106448	−	0.603698i	0.990632	−	0.136559i	$-0.0436043\pi$
$888$		0			0
$889$	16.8982	−	14.1793i	0.566747	−	0.475557i
$890$	−54.9541			−1.84207
$891$		0			0
$892$	−7.25436			−0.242894
$893$	10.0173	−	8.40554i	0.335217	−	0.281281i
$894$		0			0
$895$	−8.00783	+	45.4146i	−0.267672	+	1.51804i
$896$	−3.46344	+	1.26059i	−0.115706	+	0.0421134i
$897$		0			0
$898$	2.05619	+	11.6612i	0.0686158	+	0.389140i
$899$	−1.35764	−	2.35150i	−0.0452797	−	0.0784268i
$900$		0			0
$901$	2.22853	−	3.85993i	0.0742431	−	0.128593i
$902$	−15.2037	−	5.53370i	−0.506228	−	0.184252i
$903$		0			0
$904$	−5.39062	−	4.52327i	−0.179289	−	0.150442i
$905$	−31.6077	−	26.5220i	−1.05068	−	0.881621i
$906$		0			0
$907$	−27.4312	−	9.98413i	−0.910837	−	0.331518i	−0.156250	−	0.987718i	$-0.549941\pi$
$907$	−27.4312	−	9.98413i	−0.910837	−	0.331518i	−0.754587	+	0.656200i	$0.772163\pi$
$908$	14.2636	−	24.7053i	0.473354	−	0.819873i
$909$		0			0
$910$	−18.1006	−	31.3512i	−0.600030	−	1.03928i
$911$	9.48742	+	53.8058i	0.314332	+	1.78267i	0.575939	+	0.817493i	$0.304637\pi$
$911$	9.48742	+	53.8058i	0.314332	+	1.78267i	−0.261607	+	0.965175i	$0.584252\pi$
$912$		0			0
$913$	−6.65312	+	2.42154i	−0.220186	+	0.0801412i
$914$	−0.0323668	+	0.183561i	−0.00107060	+	0.00607167i
$915$		0			0
$916$	1.42131	−	1.19262i	0.0469613	−	0.0394052i
$917$	60.5012			1.99793
$918$		0			0
$919$	41.0995			1.35575			0.677873	−	0.735179i	$-0.262902\pi$
$919$	41.0995			1.35575			0.677873	+	0.735179i	$0.262902\pi$
$920$	−8.13767	+	6.82831i	−0.268291	+	0.225123i
$921$		0			0
$922$	1.80687	−	10.2473i	0.0595061	−	0.337476i
$923$	−5.79009	+	2.10742i	−0.190583	+	0.0693666i
$924$		0			0
$925$	−6.39130	−	36.2469i	−0.210145	−	1.19179i
$926$	−12.8942	−	22.3334i	−0.423730	−	0.733922i
$927$		0			0
$928$	0.292722	−	0.507009i	0.00960907	−	0.0166434i
$929$	−13.7158	−	4.99215i	−0.450002	−	0.163787i	0.107070	−	0.994251i	$-0.465853\pi$
$929$	−13.7158	−	4.99215i	−0.450002	−	0.163787i	−0.557072	+	0.830464i	$0.688075\pi$
$930$		0			0
$931$	−17.1235	−	14.3683i	−0.561200	−	0.470902i
$932$	6.53795	+	5.48600i	0.214158	+	0.179700i
$933$		0			0
$934$	−20.3924	−	7.42222i	−0.667259	−	0.242863i
$935$	6.24668	−	10.8196i	0.204288	−	0.353838i
$936$		0			0
$937$	−12.4641	−	21.5885i	−0.407185	−	0.705265i	0.587388	−	0.809305i	$-0.300156\pi$
$937$	−12.4641	−	21.5885i	−0.407185	−	0.705265i	−0.994573	+	0.104041i	$0.966823\pi$
$938$	−5.50977	−	31.2474i	−0.179900	−	1.02026i
$939$		0			0
$940$	11.4676	−	4.17385i	0.374031	−	0.136136i
$941$	3.61958	−	20.5277i	0.117995	−	0.669182i	−0.867229	−	0.497910i	$-0.834101\pi$
$941$	3.61958	−	20.5277i	0.117995	−	0.669182i	0.985224	−	0.171273i	$-0.0547879\pi$
$942$		0			0
$943$	18.1871	−	15.2608i	0.592254	−	0.496960i
$944$	−9.66319			−0.314510
$945$		0			0
$946$	−3.78845			−0.123173
$947$	27.5110	−	23.0844i	0.893986	−	0.750143i	−0.0750197	−	0.997182i	$-0.523902\pi$
$947$	27.5110	−	23.0844i	0.893986	−	0.750143i	0.969006	+	0.247039i	$0.0794575\pi$
$948$		0			0
$949$	5.73212	−	32.5085i	0.186072	−	1.05527i
$950$	16.0682	−	5.84835i	0.521322	−	0.189746i
$951$		0			0
$952$	1.10452	+	6.26402i	0.0357975	+	0.203018i
$953$	−2.90103	−	5.02474i	−0.0939737	−	0.162767i	0.815206	−	0.579171i	$-0.196624\pi$
$953$	−2.90103	−	5.02474i	−0.0939737	−	0.162767i	−0.909180	+	0.416404i	$0.863290\pi$
$954$		0			0
$955$	−5.70716	+	9.88509i	−0.184679	+	0.319874i
$956$	6.84845	+	2.49263i	0.221495	+	0.0806174i
$957$		0			0
$958$	−29.9686	−	25.1466i	−0.968241	−	0.812451i
$959$	−0.596190	−	0.500263i	−0.0192520	−	0.0161543i
$960$		0			0
$961$	8.91692	+	3.24549i	0.287643	+	0.104693i
$962$	11.3272	−	19.6192i	0.365202	−	0.632549i
$963$		0			0
$964$	0.667459	+	1.15607i	0.0214974	+	0.0372346i
$965$	0.811381	+	4.60157i	0.0261193	+	0.148130i
$966$		0			0
$967$	−27.8702	+	10.1439i	−0.896247	+	0.326207i	−0.748748	−	0.662855i	$-0.769345\pi$
$967$	−27.8702	+	10.1439i	−0.896247	+	0.326207i	−0.147499	+	0.989062i	$0.547122\pi$
$968$	−1.00342	+	5.69068i	−0.0322511	+	0.182905i
$969$		0			0
$970$	22.3062	−	18.7171i	0.716209	−	0.600971i
$971$	47.1522			1.51318			0.756592	−	0.653887i	$-0.226863\pi$
$971$	47.1522			1.51318			0.756592	+	0.653887i	$0.226863\pi$
$972$		0			0
$973$	13.5322			0.433821
$974$	−8.03067	+	6.73853i	−0.257319	+	0.215916i
$975$		0			0
$976$	2.27329	−	12.8925i	0.0727661	−	0.412677i
$977$	22.3675	−	8.14109i	0.715598	−	0.260456i	0.0415422	−	0.999137i	$-0.486773\pi$
$977$	22.3675	−	8.14109i	0.715598	−	0.260456i	0.674056	+	0.738680i	$0.264551\pi$
$978$		0			0
$979$	6.88286	+	39.0346i	0.219977	+	1.24755i
$980$	−10.4303	−	18.0657i	−0.333183	−	0.577089i
$981$		0			0
$982$	−3.42851	+	5.93835i	−0.109408	+	0.189501i
$983$	−10.4139	−	3.79035i	−0.332152	−	0.120894i	0.170560	−	0.985347i	$-0.445442\pi$
$983$	−10.4139	−	3.79035i	−0.332152	−	0.120894i	−0.502712	+	0.864454i	$0.667664\pi$
$984$		0			0
$985$	6.16102	+	5.16971i	0.196306	+	0.164721i
$986$	−0.773960	−	0.649430i	−0.0246479	−	0.0206821i
$987$		0			0
$988$	9.89008	+	3.59969i	0.314645	+	0.114522i
$989$	2.77957	−	4.81435i	0.0883851	−	0.153087i
$990$		0			0
$991$	−5.71846	−	9.90466i	−0.181653	−	0.314632i	0.760791	−	0.648997i	$-0.224811\pi$
$991$	−5.71846	−	9.90466i	−0.181653	−	0.314632i	−0.942443	+	0.334365i	$0.891478\pi$
$992$	−0.805376	−	4.56751i	−0.0255707	−	0.145019i
$993$		0			0
$994$	−6.88347	+	2.50538i	−0.218330	+	0.0794657i
$995$	−1.01874	+	5.77753i	−0.0322961	+	0.183160i
$996$		0			0
$997$	−21.3684	+	17.9303i	−0.676745	+	0.567857i	−0.915053	−	0.403333i	$-0.867852\pi$
$997$	−21.3684	+	17.9303i	−0.676745	+	0.567857i	0.238308	+	0.971190i	$0.423407\pi$
$998$	18.7737			0.594271
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	486.2.e.h.109.1		12
3.2	odd	2		486.2.e.e.109.2		12
9.2	odd	6		486.2.e.g.433.1		12
9.4	even	3		54.2.e.b.13.1	✓	12
9.5	odd	6		162.2.e.b.91.1		12
9.7	even	3		486.2.e.f.433.2		12
27.2	odd	18		486.2.e.g.55.1		12
27.4	even	9		1458.2.a.g.1.5		6
27.5	odd	18		1458.2.c.g.973.5		12
27.7	even	9		54.2.e.b.25.1	yes	12
27.11	odd	18		486.2.e.e.379.2		12
27.13	even	9		1458.2.c.f.487.2		12
27.14	odd	18		1458.2.c.g.487.5		12
27.16	even	9	inner	486.2.e.h.379.1		12
27.20	odd	18		162.2.e.b.73.1		12
27.22	even	9		1458.2.c.f.973.2		12
27.23	odd	18		1458.2.a.f.1.2		6
27.25	even	9		486.2.e.f.55.2		12
36.31	odd	6		432.2.u.b.337.2		12
108.7	odd	18		432.2.u.b.241.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.2.e.b.13.1	✓	12	9.4	even	3
54.2.e.b.25.1	yes	12	27.7	even	9
162.2.e.b.73.1		12	27.20	odd	18
162.2.e.b.91.1		12	9.5	odd	6
432.2.u.b.241.2		12	108.7	odd	18
432.2.u.b.337.2		12	36.31	odd	6
486.2.e.e.109.2		12	3.2	odd	2
486.2.e.e.379.2		12	27.11	odd	18
486.2.e.f.55.2		12	27.25	even	9
486.2.e.f.433.2		12	9.7	even	3
486.2.e.g.55.1		12	27.2	odd	18
486.2.e.g.433.1		12	9.2	odd	6
486.2.e.h.109.1		12	1.1	even	1	trivial
486.2.e.h.379.1		12	27.16	even	9	inner
1458.2.a.f.1.2		6	27.23	odd	18
1458.2.a.g.1.5		6	27.4	even	9
1458.2.c.f.487.2		12	27.13	even	9
1458.2.c.f.973.2		12	27.22	even	9
1458.2.c.g.487.5		12	27.14	odd	18
1458.2.c.g.973.5		12	27.5	odd	18

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
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Abelian varieties over $\F_{q}$
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Newspace parameters

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$q$ -expansion

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	486.2.e.h.109.1

Level	$486$
Weight	$2$
Character	486.109
Analytic conductor	$3.881$
Analytic rank	$0$
Dimension	$12$
Inner twists	$2$