LMFDB - Embedded newform 486.2.e.e.379.2

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			379.2
Root			$0.500000 - 1.74095i$ of defining polynomial
Character	$\chi$	$=$	486.379
Dual form			486.2.e.e.109.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$245$
$\chi(n)$	$e\left(\frac{2}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−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	$-0.138301\pi$
$5$	2.97705	+	1.08356i	1.33138	+	0.484582i	0.424292	+	0.905525i	$0.360523\pi$
$6$		0			0
$7$	0.640018	−	3.62972i	0.241904	−	1.37191i	−0.585670	−	0.810550i	$-0.699168\pi$
$7$	0.640018	−	3.62972i	0.241904	−	1.37191i	0.827574	−	0.561357i	$-0.189721\pi$
$8$	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	$-0.723058\pi$
$11$	−2.14726	+	0.781539i	−0.647424	+	0.235643i	−0.00262630	+	0.999997i	$0.500836\pi$
$12$		0			0
$13$	2.37495	−	1.99282i	0.658692	−	0.552708i	−0.251002	−	0.967986i	$-0.580760\pi$
$13$	2.37495	−	1.99282i	0.658692	−	0.552708i	0.909694	+	0.415278i	$0.136316\pi$
$14$	−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	$-0.0995551\pi$
$17$	0.862878	+	1.49455i	0.209279	+	0.362481i	−0.742209	+	0.670169i	$0.766222\pi$
$18$		0			0
$19$	1.69740	−	2.93998i	0.389410	−	0.674478i	−0.602960	−	0.797771i	$-0.706012\pi$
$19$	1.69740	−	2.93998i	0.389410	−	0.674478i	0.992370	+	0.123293i	$0.0393456\pi$
$20$	−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	0.983376	+	0.181581i	$0.0581214\pi$
$23$	0.582258	+	3.30215i	0.121409	+	0.688545i	−0.861967	+	0.506965i	$0.830768\pi$
$24$		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	$-0.260467\pi$
$29$	0.448476	+	0.376316i	0.0832799	+	0.0698802i	−0.600197	+	0.799852i	$0.704911\pi$
$30$		0			0
$31$	−0.805376	−	4.56751i	−0.144650	−	0.820350i	−0.967648	−	0.252305i	$-0.918811\pi$
$31$	−0.805376	−	4.56751i	−0.144650	−	0.820350i	0.822998	−	0.568044i	$-0.192300\pi$
$32$	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	0.992723	+	0.120420i	$0.0384240\pi$
$37$	3.65360	+	6.32822i	0.600648	+	1.04035i	−0.392075	+	0.919933i	$0.628243\pi$
$38$	−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	$-0.535745\pi$
$41$	5.42399	−	4.55127i	0.847085	−	0.710789i	0.959146	+	0.282913i	$0.0913007\pi$
$42$		0			0
$43$	−1.55793	+	0.567040i	−0.237582	+	0.0864728i	−0.458067	−	0.888917i	$-0.651458\pi$
$43$	−1.55793	+	0.567040i	−0.237582	+	0.0864728i	0.220485	+	0.975390i	$0.429236\pi$
$44$	−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	−0.896363	−	0.443321i	$-0.853800\pi$
$47$	0.668890	−	3.79346i	0.0975676	−	0.553333i	0.993930	−	0.110012i	$-0.0350889\pi$
$48$		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	$-0.443238\pi$
$53$	2.58267			0.354757			0.177379	+	0.984143i	$0.443238\pi$
$54$		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	$-0.605432\pi$
$59$	−9.08043	−	3.30500i	−1.18217	−	0.430275i	−0.856968	+	0.515369i	$0.827655\pi$
$60$		0			0
$61$	2.27329	−	12.8925i	0.291065	−	1.65071i	−0.391716	−	0.920086i	$-0.628119\pi$
$61$	2.27329	−	12.8925i	0.291065	−	1.65071i	0.682781	−	0.730623i	$-0.260770\pi$
$62$	−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	−0.949570	−	0.313555i	$-0.898480\pi$
$67$	−6.59469	+	5.53361i	−0.805670	+	0.676037i	0.143900	+	0.989592i	$0.454036\pi$
$68$	−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	$-0.129039\pi$
$71$	0.993732	+	1.72119i	0.117934	+	0.204268i	−0.801015	+	0.598645i	$0.795706\pi$
$72$		0			0
$73$	−5.32371	+	9.22094i	−0.623094	+	1.07923i	0.365812	+	0.930689i	$0.380791\pi$
$73$	−5.32371	+	9.22094i	−0.623094	+	1.07923i	−0.988906	+	0.148541i	$0.952542\pi$
$74$	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	0.999087	+	0.0427183i	$0.0136018\pi$
$79$	10.7960	+	9.05893i	1.21465	+	1.01921i	0.215559	+	0.976491i	$0.430843\pi$
$80$	−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	$-0.223385\pi$
$83$	2.37353	+	1.99163i	0.260529	+	0.218609i	−0.503162	+	0.864192i	$0.667830\pi$
$84$		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	−0.118911	+	0.992905i	$0.537940\pi$
$89$	−8.67300	+	15.0221i	−0.919336	+	1.59234i	−0.800425	+	0.599432i	$0.795393\pi$
$90$		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	−0.740975	−	0.671533i	$-0.765636\pi$
$97$	−8.63687	+	3.14356i	−0.876941	+	0.319181i	−0.135967	+	0.990713i	$0.543414\pi$
$98$	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	0.688158	+	0.725561i	$0.258420\pi$
$101$	−2.07686	+	11.7785i	−0.206656	+	1.17200i	−0.894813	+	0.446441i	$0.852691\pi$
$102$		0			0
$103$	11.9778	+	4.35955i	1.18020	+	0.429559i	0.856274	−	0.516522i	$-0.172773\pi$
$103$	11.9778	+	4.35955i	1.18020	+	0.429559i	0.323930	+	0.946081i	$0.394996\pi$
$104$	−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	$-0.595254\pi$
$107$	−6.09894			−0.589607			−0.294803	+	0.955558i	$0.595254\pi$
$108$		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	$-0.496272\pi$
$113$	−6.61257	−	2.40678i	−0.622059	−	0.226411i	−0.633771	+	0.773521i	$0.718494\pi$
$114$		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	−0.967705	−	0.252084i	$-0.918884\pi$
$127$	−2.99250	+	5.18316i	−0.265541	+	0.459931i	0.702164	+	0.712015i	$0.252217\pi$
$128$	−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	−0.810910	−	0.585171i	$-0.801027\pi$
$131$	−2.85044	−	16.1657i	−0.249044	−	1.41240i	0.561866	−	0.827228i	$-0.310084\pi$
$132$		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	$-0.274907\pi$
$137$	0.161757	+	0.135730i	0.0138198	+	0.0115962i	−0.635852	+	0.771811i	$0.719351\pi$
$138$		0			0
$139$	0.637551	+	3.61573i	0.0540764	+	0.306682i	0.999835	−	0.0181891i	$-0.00579008\pi$
$139$	0.637551	+	3.61573i	0.0540764	+	0.306682i	−0.945758	+	0.324871i	$0.894679\pi$
$140$	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	$-0.940751\pi$
$149$	−11.8541	+	9.94675i	−0.971123	+	0.814869i	0.0116031	+	0.999933i	$0.496307\pi$
$150$		0			0
$151$	−18.9308	+	6.89024i	−1.54057	+	0.560720i	−0.966181	−	0.257865i	$-0.916981\pi$
$151$	−18.9308	+	6.89024i	−1.54057	+	0.560720i	−0.574385	+	0.818585i	$0.694759\pi$
$152$	−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	−0.436866	−	0.899527i	$-0.643912\pi$
$157$	−16.9121	−	6.15549i	−1.34973	−	0.491261i	−0.912863	+	0.408265i	$0.866134\pi$
$158$	−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	$-0.439613\pi$
$167$	−3.85386	−	1.40269i	−0.298221	−	0.108544i	−0.486797	+	0.873515i	$0.661835\pi$
$168$		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	$-0.835202\pi$
$173$	−16.0002	+	5.82361i	−1.21648	+	0.442761i	−0.347530	+	0.937669i	$0.612980\pi$
$174$		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	−0.998670	−	0.0515575i	$-0.983581\pi$
$179$	−7.27802	−	12.6059i	−0.543985	−	0.942210i	0.454685	−	0.890652i	$-0.349752\pi$
$180$		0			0
$181$	6.51190	−	11.2789i	0.484026	−	0.838357i	−0.515806	−	0.856706i	$-0.672507\pi$
$181$	6.51190	−	11.2789i	0.484026	−	0.838357i	0.999832	+	0.0183482i	$0.00584075\pi$
$182$	−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	$-0.319387\pi$
$191$	−2.75996	−	2.31588i	−0.199704	−	0.167571i	−0.737155	+	0.675723i	$0.763831\pi$
$192$		0			0
$193$	0.256108	+	1.45246i	0.0184351	+	0.104551i	0.992637	−	0.121128i	$-0.0386512\pi$
$193$	0.256108	+	1.45246i	0.0184351	+	0.104551i	−0.974202	+	0.225679i	$0.927540\pi$
$194$	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	$-0.804508\pi$
$197$	1.26931	−	2.19851i	0.0904346	−	0.156637i	0.907694	+	0.419633i	$0.137841\pi$
$198$		0			0
$199$	0.925891	+	1.60369i	0.0656347	+	0.113683i	0.896975	−	0.442081i	$-0.145759\pi$
$199$	0.925891	+	1.60369i	0.0656347	+	0.113683i	−0.831341	+	0.555763i	$0.812426\pi$
$200$	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	0.873040	−	0.487648i	$-0.162145\pi$
$211$	17.8432	+	6.49438i	1.22837	+	0.447091i	0.355333	+	0.934740i	$0.384367\pi$
$212$	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	0.913137	+	0.407652i	$0.133652\pi$
$223$	−1.25971	+	7.14415i	−0.0843562	+	0.478408i	−0.997494	+	0.0707560i	$0.977459\pi$
$224$	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	−0.779451	+	0.626463i	$0.784502\pi$
$227$	−26.8068	+	9.75687i	−1.77923	+	0.647586i	−0.999777	+	0.0211232i	$0.993276\pi$
$228$		0			0
$229$	1.42131	−	1.19262i	0.0939225	−	0.0788104i	−0.594617	−	0.804009i	$-0.702696\pi$
$229$	1.42131	−	1.19262i	0.0939225	−	0.0788104i	0.688540	+	0.725198i	$0.258252\pi$
$230$	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	$-0.0764770\pi$
$233$	4.26735	+	7.39126i	0.279563	+	0.484218i	−0.691713	+	0.722172i	$0.743144\pi$
$234$		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	0.997990	+	0.0633733i	$0.0201859\pi$
$239$	1.26554	+	7.17724i	0.0818611	+	0.464257i	−0.916129	+	0.400884i	$0.868703\pi$
$240$		0			0
$241$	−1.02261	−	0.858069i	−0.0658719	−	0.0552731i	0.609257	−	0.792973i	$-0.291468\pi$
$241$	−1.02261	−	0.858069i	−0.0658719	−	0.0552731i	−0.675129	+	0.737700i	$0.735912\pi$
$242$	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	$-0.862291\pi$
$251$	−1.43928	+	2.49291i	−0.0908466	+	0.157351i	0.817021	+	0.576608i	$0.195624\pi$
$252$		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	0.233665	−	0.972317i	$-0.424928\pi$
$257$	19.7470	−	16.5697i	1.23179	−	1.03359i	0.998121	−	0.0612737i	$-0.0195162\pi$
$258$		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	−0.791378	−	0.611327i	$-0.790636\pi$
$263$	2.61682	−	14.8408i	0.161360	−	0.915120i	0.952738	−	0.303793i	$-0.0982530\pi$
$264$		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	$-0.662873\pi$
$269$	−16.0615			−0.979286			−0.489643	+	0.871923i	$0.662873\pi$
$270$		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	−0.941816	−	0.336129i	$-0.890882\pi$
$277$	0.968047	−	5.49007i	0.0581643	−	0.329866i	0.999980	+	0.00626247i	$0.00199342\pi$
$278$	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	$-0.296397\pi$
$281$	26.3159	−	9.57821i	1.56988	−	0.571388i	0.972972	+	0.230925i	$0.0741753\pi$
$282$		0			0
$283$	4.71517	−	3.95650i	0.280288	−	0.235189i	−0.491796	−	0.870711i	$-0.663659\pi$
$283$	4.71517	−	3.95650i	0.280288	−	0.235189i	0.772083	+	0.635521i	$0.219215\pi$
$284$	−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	$-0.0772840\pi$
$293$	−0.405486	−	2.29962i	−0.0236887	−	0.134345i	−0.994359	+	0.106071i	$0.966173\pi$
$294$		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	0.752055	−	0.659100i	$-0.229063\pi$
$307$	−3.41265	−	5.91088i	−0.194770	−	0.337351i	−0.946825	+	0.321749i	$0.895729\pi$
$308$	−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	$-0.800582\pi$
$311$	−6.58432	+	5.52490i	−0.373362	+	0.313288i	0.436728	+	0.899594i	$0.356137\pi$
$312$		0			0
$313$	20.3621	−	7.41120i	1.15093	−	0.418906i	0.305083	−	0.952326i	$-0.401316\pi$
$313$	20.3621	−	7.41120i	1.15093	−	0.418906i	0.845851	+	0.533420i	$0.179093\pi$
$314$	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	−0.0470178	+	0.998894i	$0.514972\pi$
$317$	−6.13325	+	34.7834i	−0.344477	+	1.95363i	−0.297460	+	0.954734i	$0.596139\pi$
$318$		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	0.570885	+	0.821030i	$0.306600\pi$
$331$	−4.48249	+	25.4215i	−0.246380	+	1.39729i	−0.817265	+	0.576261i	$0.804511\pi$
$332$	−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	−0.710668	−	0.703527i	$-0.751607\pi$
$337$	−2.59274	+	2.17557i	−0.141236	+	0.118511i	0.569433	+	0.822038i	$0.307163\pi$
$338$	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	0.962339	+	0.271853i	$0.0876365\pi$
$347$	2.81310	+	15.9539i	0.151015	+	0.856451i	−0.811323	+	0.584598i	$0.801252\pi$
$348$		0			0
$349$	3.44148	+	2.88774i	0.184218	+	0.154577i	0.730233	−	0.683198i	$-0.239411\pi$
$349$	3.44148	+	2.88774i	0.184218	+	0.154577i	−0.546015	+	0.837775i	$0.683856\pi$
$350$	−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	$-0.0656742\pi$
$353$	17.7927	+	14.9298i	0.947008	+	0.794634i	−0.0317832	+	0.999495i	$0.510119\pi$
$354$		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	$-0.931955\pi$
$359$	−5.77697	+	10.0060i	−0.304897	+	0.528097i	0.672341	+	0.740241i	$0.265289\pi$
$360$		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	−0.694367	−	0.719621i	$-0.744315\pi$
$367$	−14.6307	+	5.32516i	−0.763719	+	0.277971i	−0.0693521	+	0.997592i	$0.522093\pi$
$368$	−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	0.568300	−	0.822821i	$-0.307601\pi$
$373$	9.16883	+	3.33718i	0.474744	+	0.172793i	−0.0935562	+	0.995614i	$0.529823\pi$
$374$	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	$-0.100993\pi$
$383$	28.9125	+	10.5233i	1.47736	+	0.537715i	0.527271	+	0.849697i	$0.323215\pi$
$384$		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	$-0.340969\pi$
$389$	27.8155	−	10.1240i	1.41030	−	0.513308i	0.931219	+	0.364460i	$0.118747\pi$
$390$		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	−0.994332	−	0.106321i	$-0.966093\pi$
$397$	−8.07134	+	13.9800i	−0.405089	+	0.701635i	0.589243	+	0.807956i	$0.299426\pi$
$398$	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	−0.872140	−	0.489256i	$-0.837269\pi$
$401$	−4.40413	−	24.9771i	−0.219932	−	1.24730i	0.652209	−	0.758039i	$-0.273843\pi$
$402$		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	−0.911673	−	0.410917i	$-0.865209\pi$
$409$	−3.95420	−	22.4254i	−0.195522	−	1.10886i	0.716150	−	0.697946i	$-0.245902\pi$
$410$	−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	$-0.683854\pi$
$419$	3.77105	−	3.16429i	0.184228	−	0.154586i	0.730238	+	0.683193i	$0.239409\pi$
$420$		0			0
$421$	−18.5285	+	6.74382i	−0.903023	+	0.328674i	−0.751464	−	0.659775i	$-0.770652\pi$
$421$	−18.5285	+	6.74382i	−0.903023	+	0.328674i	−0.151560	+	0.988448i	$0.548430\pi$
$422$	−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	$-0.452576\pi$
$431$	6.16323			0.296873			0.148436	+	0.988922i	$0.452576\pi$
$432$		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	−0.569803	−	0.821782i	$-0.692980\pi$
$439$	5.16899	−	29.3148i	0.246703	−	1.39912i	0.816505	−	0.577338i	$-0.195909\pi$
$440$	−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	$-0.353440\pi$
$443$	28.6365	−	10.4228i	1.36056	−	0.495204i	0.916228	+	0.400656i	$0.131218\pi$
$444$		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	$-0.0765284\pi$
$449$	5.92055	+	10.2547i	0.279408	+	0.483949i	−0.691830	+	0.722061i	$0.743195\pi$
$450$		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	0.639442	−	0.768839i	$-0.279165\pi$
$457$	−0.142785	−	0.119811i	−0.00667922	−	0.00560453i	−0.646121	+	0.763235i	$0.723610\pi$
$458$	−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	$-0.355684\pi$
$461$	−7.97096	−	6.68843i	−0.371245	−	0.311511i	−0.809254	+	0.587459i	$0.800128\pi$
$462$		0			0
$463$	4.47811	+	25.3966i	0.208115	+	1.18028i	0.892461	+	0.451124i	$0.148977\pi$
$463$	4.47811	+	25.3966i	0.208115	+	1.18028i	−0.684346	+	0.729158i	$0.739912\pi$
$464$	−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	−0.497893	−	0.867239i	$-0.665893\pi$
$467$	10.8506	−	18.7937i	0.502104	−	0.869670i	0.999997	−	0.00243153i	$-0.000773982\pi$
$468$		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	−0.286559	−	0.958063i	$-0.592511\pi$
$479$	6.79333	−	38.5269i	0.310395	−	1.76034i	0.596954	−	0.802276i	$-0.296378\pi$
$480$		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	$-0.339439\pi$
$491$	6.44349	+	2.34524i	0.290791	+	0.105839i	−0.192506	+	0.981296i	$0.561661\pi$
$492$		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	−0.261380	−	0.965236i	$-0.584177\pi$
$499$	14.3815	−	12.0675i	0.643804	−	0.540216i	0.905184	+	0.425020i	$0.139733\pi$
$500$	−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	$-0.256022\pi$
$503$	−6.21350	−	10.7621i	−0.277046	−	0.479858i	−0.970649	+	0.240499i	$0.922689\pi$
$504$		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	−0.799075	−	0.601232i	$-0.794677\pi$
$509$	−5.72652	−	32.4767i	−0.253824	−	1.43950i	0.545251	−	0.838273i	$-0.316434\pi$
$510$		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	$-0.731682\pi$
$521$	7.16598	−	12.4118i	0.313947	−	0.543773i	0.979213	+	0.202834i	$0.0650151\pi$
$522$		0			0
$523$	2.85442	+	4.94400i	0.124815	+	0.216186i	0.921661	−	0.387997i	$-0.126833\pi$
$523$	2.85442	+	4.94400i	0.124815	+	0.216186i	−0.796846	+	0.604183i	$0.793500\pi$
$524$	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	0.807301	+	0.590141i	$0.200928\pi$
$547$	−3.58197	+	20.3143i	−0.153154	+	0.868578i	−0.960454	+	0.278438i	$0.910183\pi$
$548$	−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	$-0.192348\pi$
$557$	−1.90209	−	3.29452i	−0.0805942	−	0.139593i	−0.903505	+	0.428577i	$0.859015\pi$
$558$		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	0.998144	+	0.0609006i	$0.0193973\pi$
$563$	1.92252	+	10.9032i	0.0810247	+	0.459514i	−0.917119	+	0.398613i	$0.869492\pi$
$564$		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	−0.880523	−	0.474004i	$-0.842808\pi$
$569$	−35.7860	−	30.0280i	−1.50023	−	1.25884i	−0.619704	−	0.784836i	$-0.712747\pi$
$570$		0			0
$571$	−5.50225	−	31.2048i	−0.230262	−	1.30588i	−0.852366	−	0.522946i	$-0.824833\pi$
$571$	−5.50225	−	31.2048i	−0.230262	−	1.30588i	0.622104	−	0.782935i	$-0.286278\pi$
$572$	−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	−0.795208	−	0.606336i	$-0.792639\pi$
$577$	−22.1642	−	38.3895i	−0.922707	−	1.59818i	−0.127499	−	0.991839i	$-0.540695\pi$
$578$	−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	0.376354	+	0.926476i	$0.377177\pi$
$587$	−7.12733	+	40.4211i	−0.294176	+	1.66836i	−0.670531	+	0.741882i	$0.733934\pi$
$588$		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	$-0.436226\pi$
$593$	9.69265			0.398029			0.199015	+	0.979996i	$0.436226\pi$
$594$		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	$-0.597548\pi$
$599$	−28.0385	−	10.2052i	−1.14562	−	0.416972i	−0.843940	+	0.536437i	$0.819770\pi$
$600$		0			0
$601$	2.17941	−	12.3600i	0.0888998	−	0.504176i	−0.907547	−	0.419951i	$-0.862047\pi$
$601$	2.17941	−	12.3600i	0.0888998	−	0.504176i	0.996447	−	0.0842252i	$-0.0268415\pi$
$602$	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	−0.684985	−	0.728557i	$-0.740191\pi$
$607$	−2.12971	+	1.78704i	−0.0864421	+	0.0725336i	0.598543	+	0.801091i	$0.295747\pi$
$608$	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	−0.766120	−	0.642697i	$-0.777815\pi$
$613$	4.29646	−	7.44168i	0.173532	−	0.300567i	0.939652	+	0.342131i	$0.111149\pi$
$614$	−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	0.970970	+	0.239203i	$0.0768860\pi$
$617$	3.48669	+	19.7740i	0.140369	+	0.796071i	−0.830601	+	0.556868i	$0.812003\pi$
$618$		0			0
$619$	6.42853	+	5.39418i	0.258384	+	0.216810i	0.762773	−	0.646667i	$-0.223838\pi$
$619$	6.42853	+	5.39418i	0.258384	+	0.216810i	−0.504388	+	0.863477i	$0.668282\pi$
$620$	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	0.636588	−	0.771204i	$-0.280345\pi$
$631$	−8.78157	−	15.2101i	−0.349589	−	0.605506i	−0.986176	+	0.165699i	$0.947012\pi$
$632$	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	−0.903617	−	0.428342i	$-0.859098\pi$
$641$	2.32943	−	13.2108i	0.0920069	−	0.521797i	0.995624	−	0.0934548i	$-0.0297910\pi$
$642$		0			0
$643$	9.80578	+	3.56901i	0.386702	+	0.140748i	0.528053	−	0.849211i	$-0.322922\pi$
$643$	9.80578	+	3.56901i	0.386702	+	0.140748i	−0.141351	+	0.989960i	$0.545144\pi$
$644$	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	$-0.231899\pi$
$647$	37.9585			1.49230			0.746152	+	0.665775i	$0.231899\pi$
$648$		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	$-0.568309\pi$
$653$	−25.6595	−	9.33930i	−1.00413	−	0.365475i	−0.791178	+	0.611587i	$0.790532\pi$
$654$		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	$-0.844448\pi$
$659$	−32.2831	+	11.7501i	−1.25757	+	0.457718i	−0.374617	+	0.927180i	$0.622226\pi$
$660$		0			0
$661$	−18.8276	+	15.7982i	−0.732309	+	0.614481i	−0.930760	−	0.365630i	$-0.880853\pi$
$661$	−18.8276	+	15.7982i	−0.732309	+	0.614481i	0.198451	+	0.980111i	$0.436409\pi$
$662$	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	0.995009	+	0.0997881i	$0.0318165\pi$
$673$	32.8445	+	27.5598i	1.26606	+	1.06235i	0.271054	+	0.962564i	$0.412628\pi$
$674$	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	$-0.323737\pi$
$677$	−5.73570	−	4.81283i	−0.220441	−	0.184972i	−0.746320	+	0.665588i	$0.768181\pi$
$678$		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	$-0.729467\pi$
$683$	8.37724	−	14.5098i	0.320546	−	0.555202i	0.980601	+	0.196015i	$0.0628002\pi$
$684$		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	−0.0606190	−	0.998161i	$-0.519307\pi$
$691$	14.0516	−	5.11438i	0.534550	−	0.194560i	0.595169	+	0.803601i	$0.297085\pi$
$692$	−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	$-0.207421\pi$
$701$	42.1025			1.59019			0.795094	+	0.606486i	$0.207421\pi$
$702$		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	−0.739195	−	0.673491i	$-0.764794\pi$
$709$	4.94647	−	28.0528i	0.185769	−	1.05355i	0.924964	−	0.380055i	$-0.124095\pi$
$710$	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	$-0.151615\pi$
$719$	1.26744	+	2.19526i	0.0472674	+	0.0818695i	−0.841424	+	0.540376i	$0.818282\pi$
$720$		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	0.879952	−	0.475063i	$-0.157575\pi$
$727$	15.2316	+	12.7808i	0.564907	+	0.474014i	−0.315044	+	0.949077i	$0.602019\pi$
$728$	−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	−0.999935	−	0.0114203i	$-0.996365\pi$
$733$	−1.73840	−	9.85898i	−0.0642094	−	0.364150i	0.935725	−	0.352729i	$-0.114746\pi$
$734$	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	0.951164	+	0.308685i	$0.0998890\pi$
$739$	20.1957	+	34.9800i	0.742911	+	1.28676i	−0.208253	+	0.978075i	$0.566778\pi$
$740$	−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	$-0.949107\pi$
$743$	−27.3096	+	22.9155i	−1.00189	+	0.840688i	−0.0146474	+	0.999893i	$0.504663\pi$
$744$		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	0.499218	−	0.866476i	$-0.333621\pi$
$751$	8.89769	+	3.23850i	0.324681	+	0.118174i	−0.174537	+	0.984651i	$0.555843\pi$
$752$	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	$-0.0864189\pi$
$761$	42.1788	+	15.3518i	1.52898	+	0.556504i	0.565609	+	0.824673i	$0.308641\pi$
$762$		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	0.268140	−	0.963380i	$-0.413591\pi$
$769$	35.0364	−	29.3991i	1.26345	−	1.06016i	0.995306	−	0.0967777i	$-0.0308536\pi$
$770$	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	$-0.287288\pi$
$773$	−10.2853	−	17.8147i	−0.369938	−	0.640752i	−0.989556	+	0.144152i	$0.953954\pi$
$774$		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	0.736271	+	0.676687i	$0.236585\pi$
$787$	7.73837	+	43.8865i	0.275843	+	1.56438i	−0.460427	+	0.887697i	$0.652304\pi$
$788$	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	−0.190274	+	0.981731i	$0.560938\pi$
$797$	−33.5988	+	28.1927i	−1.19013	+	0.998638i	−0.999857	+	0.0169072i	$0.994618\pi$
$798$		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	$-0.411680\pi$
$809$	15.5821			0.547836			0.273918	+	0.961753i	$0.411680\pi$
$810$		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	$-0.621672\pi$
$821$	−1.78637	+	0.650187i	−0.0623448	+	0.0226917i	0.310659	+	0.950521i	$0.399450\pi$
$822$		0			0
$823$	−16.8844	+	14.1677i	−0.588553	+	0.493855i	−0.887743	−	0.460339i	$-0.847728\pi$
$823$	−16.8844	+	14.1677i	−0.588553	+	0.493855i	0.299190	+	0.954194i	$0.403284\pi$
$824$	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	0.887164	+	0.461454i	$0.152672\pi$
$827$	24.2488	+	42.0001i	0.843213	+	1.46049i	−0.0439508	+	0.999034i	$0.513994\pi$
$828$		0			0
$829$	10.1593	−	17.5964i	0.352846	−	0.611148i	−0.633900	−	0.773415i	$-0.718547\pi$
$829$	10.1593	−	17.5964i	0.352846	−	0.611148i	0.986747	+	0.162267i	$0.0518805\pi$
$830$	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	$-0.249904\pi$
$839$	3.88105	+	3.25659i	0.133989	+	0.112430i	−0.573330	+	0.819324i	$0.694349\pi$
$840$		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	−0.730688	−	0.682712i	$-0.760801\pi$
$853$	−24.8716	+	9.05254i	−0.851589	+	0.309953i	−0.120901	+	0.992665i	$0.538578\pi$
$854$	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	−0.881094	−	0.472942i	$-0.843192\pi$
$857$	3.17978	−	18.0334i	0.108619	−	0.616011i	0.989713	−	0.143068i	$-0.0456969\pi$
$858$		0			0
$859$	8.87010	+	3.22845i	0.302644	+	0.110153i	0.488878	−	0.872352i	$-0.337406\pi$
$859$	8.87010	+	3.22845i	0.302644	+	0.110153i	−0.186234	+	0.982505i	$0.559628\pi$
$860$	−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	$-0.422213\pi$
$863$	14.2154			0.483898			0.241949	+	0.970289i	$0.422213\pi$
$864$		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	0.0230156	−	0.999735i	$-0.492673\pi$
$877$	29.9565	−	25.1365i	1.01156	−	0.848799i	0.988544	+	0.150936i	$0.0482288\pi$
$878$	−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	$-0.292692\pi$
$881$	−11.4469	−	19.8266i	−0.385657	−	0.667977i	−0.991860	+	0.127333i	$0.959358\pi$
$882$		0			0
$883$	8.57546	−	14.8531i	0.288587	−	0.499847i	−0.684886	−	0.728651i	$-0.740148\pi$
$883$	8.57546	−	14.8531i	0.288587	−	0.499847i	0.973473	+	0.228803i	$0.0734812\pi$
$884$	−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	−0.990632	−	0.136559i	$-0.956396\pi$
$887$	−3.17030	−	17.9797i	−0.106448	−	0.603698i	0.884184	−	0.467139i	$-0.154715\pi$
$888$		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	−0.754587	−	0.656200i	$-0.772163\pi$
$907$	−27.4312	+	9.98413i	−0.910837	+	0.331518i	−0.156250	+	0.987718i	$0.549941\pi$
$908$	−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	0.261607	+	0.965175i	$0.415748\pi$
$911$	−9.48742	+	53.8058i	−0.314332	+	1.78267i	−0.575939	+	0.817493i	$0.695363\pi$
$912$		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	$-0.534147\pi$
$929$	13.7158	−	4.99215i	0.450002	−	0.163787i	0.557072	+	0.830464i	$0.311925\pi$
$930$		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	−0.994573	−	0.104041i	$-0.966823\pi$
$937$	−12.4641	+	21.5885i	−0.407185	+	0.705265i	0.587388	+	0.809305i	$0.300156\pi$
$938$	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	−0.985224	−	0.171273i	$-0.945212\pi$
$941$	−3.61958	−	20.5277i	−0.117995	−	0.669182i	0.867229	−	0.497910i	$-0.165899\pi$
$942$		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	$-0.476098\pi$
$947$	−27.5110	−	23.0844i	−0.893986	−	0.750143i	−0.969006	+	0.247039i	$0.920542\pi$
$948$		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	$-0.803376\pi$
$953$	2.90103	−	5.02474i	0.0939737	−	0.162767i	0.909180	+	0.416404i	$0.136710\pi$
$954$		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	−0.147499	−	0.989062i	$-0.547122\pi$
$967$	−27.8702	−	10.1439i	−0.896247	−	0.326207i	−0.748748	+	0.662855i	$0.769345\pi$
$968$	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	$-0.773137\pi$
$971$	−47.1522			−1.51318			−0.756592	+	0.653887i	$0.773137\pi$
$972$		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	$-0.513227\pi$
$977$	−22.3675	−	8.14109i	−0.715598	−	0.260456i	−0.674056	+	0.738680i	$0.735449\pi$
$978$		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	$-0.554558\pi$
$983$	10.4139	−	3.79035i	0.332152	−	0.120894i	0.502712	+	0.864454i	$0.332336\pi$
$984$		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	−0.942443	−	0.334365i	$-0.891478\pi$
$991$	−5.71846	+	9.90466i	−0.181653	+	0.314632i	0.760791	+	0.648997i	$0.224811\pi$
$992$	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	0.238308	−	0.971190i	$-0.423407\pi$
$997$	−21.3684	−	17.9303i	−0.676745	−	0.567857i	−0.915053	+	0.403333i	$0.867852\pi$
$998$	−18.7737			−0.594271
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.2.e.b.13.1	✓	12	27.23	odd	18
54.2.e.b.25.1	yes	12	9.2	odd	6
162.2.e.b.73.1		12	9.7	even	3
162.2.e.b.91.1		12	27.4	even	9
432.2.u.b.241.2		12	36.11	even	6
432.2.u.b.337.2		12	108.23	even	18
486.2.e.e.109.2		12	27.22	even	9	inner
486.2.e.e.379.2		12	1.1	even	1	trivial
486.2.e.f.55.2		12	9.5	odd	6
486.2.e.f.433.2		12	27.14	odd	18
486.2.e.g.55.1		12	9.4	even	3
486.2.e.g.433.1		12	27.13	even	9
486.2.e.h.109.1		12	27.5	odd	18
486.2.e.h.379.1		12	3.2	odd	2
1458.2.a.f.1.2		6	27.7	even	9
1458.2.a.g.1.5		6	27.20	odd	18
1458.2.c.f.487.2		12	27.11	odd	18
1458.2.c.f.973.2		12	27.2	odd	18
1458.2.c.g.487.5		12	27.16	even	9
1458.2.c.g.973.5		12	27.25	even	9

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:	\( N \)	\(=\)	\( 486 = 2 \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	486.e (of order \(9\), degree \(6\), not minimal)

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

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