LMFDB - Embedded newform 855.2.bs.b.271.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(226,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 10]))

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

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

chi := DirichletCharacter("855.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.bs (of order $9$, degree $6$, 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:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 12 x^{16} - 8 x^{15} + 96 x^{14} - 75 x^{13} + 448 x^{12} - 405 x^{11} + 1521 x^{10} + \cdots + 361 $ x^18 + 12x^16 - 8x^15 + 96x^14 - 75x^13 + 448x^12 - 405x^11 + 1521x^10 - 1294x^9 + 3333x^8 - 2616x^7 + 5113x^6 - 3126x^5 + 4032x^4 - 1359x^3 + 1698x^2 - 513x + 361
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			271.3
Root			$-0.841804 + 1.45805i$ of defining polynomial
Character	$\chi$	$=$	855.271
Dual form			855.2.bs.b.631.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.58207 - 0.575828i) q^{2} +(0.639290 - 0.536428i) q^{4} +(0.766044 + 0.642788i) q^{5} +(0.274194 + 0.474919i) q^{7} +(-0.981094 + 1.69930i) q^{8} +O(q^{10})$	\(q+(1.58207 - 0.575828i) q^{2} +(0.639290 - 0.536428i) q^{4} +(0.766044 + 0.642788i) q^{5} +(0.274194 + 0.474919i) q^{7} +(-0.981094 + 1.69930i) q^{8} +(1.58207 + 0.575828i) q^{10} +(0.165601 - 0.286829i) q^{11} +(0.837254 + 4.74830i) q^{13} +(0.707267 + 0.593468i) q^{14} +(-0.863487 + 4.89708i) q^{16} +(4.96227 - 1.80612i) q^{17} +(4.30704 - 0.670409i) q^{19} +0.834534 q^{20} +(0.0968286 - 0.549142i) q^{22} +(0.850350 - 0.713529i) q^{23} +(0.173648 + 0.984808i) q^{25} +(4.05880 + 7.03005i) q^{26} +(0.430050 + 0.156525i) q^{28} +(-3.01199 - 1.09627i) q^{29} +(3.01060 + 5.21452i) q^{31} +(0.772312 + 4.38000i) q^{32} +(6.81067 - 5.71483i) q^{34} +(-0.0952268 + 0.540058i) q^{35} -6.67261 q^{37} +(6.42801 - 3.54075i) q^{38} +(-1.84385 + 0.671108i) q^{40} +(1.37380 - 7.79121i) q^{41} +(1.25559 + 1.05356i) q^{43} +(-0.0479962 - 0.272200i) q^{44} +(0.934447 - 1.61851i) q^{46} +(-4.32380 - 1.57373i) q^{47} +(3.34963 - 5.80174i) q^{49} +(0.841804 + 1.45805i) q^{50} +(3.08237 + 2.58642i) q^{52} +(-5.15257 + 4.32352i) q^{53} +(0.311228 - 0.113278i) q^{55} -1.07604 q^{56} -5.39645 q^{58} +(-6.39331 + 2.32697i) q^{59} +(0.520640 - 0.436869i) q^{61} +(7.76566 + 6.51616i) q^{62} +(-1.22864 - 2.12807i) q^{64} +(-2.41078 + 4.17559i) q^{65} +(7.30324 + 2.65816i) q^{67} +(2.20348 - 3.81654i) q^{68} +(0.160324 + 0.909245i) q^{70} +(0.832574 + 0.698612i) q^{71} +(2.42261 - 13.7393i) q^{73} +(-10.5566 + 3.84227i) q^{74} +(2.39382 - 2.73900i) q^{76} +0.181627 q^{77} +(-0.243868 + 1.38304i) q^{79} +(-3.80925 + 3.19634i) q^{80} +(-2.31294 - 13.1173i) q^{82} +(-0.427439 - 0.740346i) q^{83} +(4.96227 + 1.80612i) q^{85} +(2.59310 + 0.943812i) q^{86} +(0.324940 + 0.562813i) q^{88} +(-2.52694 - 14.3310i) q^{89} +(-2.02549 + 1.69959i) q^{91} +(0.160864 - 0.912304i) q^{92} -7.74677 q^{94} +(3.73031 + 2.25495i) q^{95} +(6.59799 - 2.40147i) q^{97} +(1.95857 - 11.1076i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 3 q^{2} - 3 q^{4} + 12 q^{8}+O(q^{10}) $ 18 * q - 3 * q^2 - 3 * q^4 + 12 * q^8	$ 18 q - 3 q^{2} - 3 q^{4} + 12 q^{8} - 3 q^{10} - 3 q^{13} - 24 q^{14} + 21 q^{16} + 24 q^{17} - 12 q^{19} + 12 q^{20} + 15 q^{22} - 21 q^{23} + 21 q^{26} - 24 q^{28} + 9 q^{29} + 30 q^{31} - 45 q^{32} + 24 q^{34} + 6 q^{35} - 60 q^{37} + 15 q^{38} - 6 q^{40} + 6 q^{41} - 6 q^{43} + 30 q^{44} + 21 q^{46} - 33 q^{47} - 3 q^{49} + 9 q^{52} - 24 q^{53} - 3 q^{55} + 72 q^{56} + 36 q^{58} - 18 q^{59} + 6 q^{61} - 12 q^{62} - 24 q^{64} - 3 q^{65} - 24 q^{67} + 3 q^{68} + 39 q^{70} - 24 q^{71} + 6 q^{73} + 39 q^{74} + 27 q^{76} - 24 q^{77} + 9 q^{79} - 33 q^{80} - 57 q^{82} + 24 q^{85} + 33 q^{86} + 39 q^{88} + 6 q^{89} - 6 q^{91} + 66 q^{92} - 66 q^{94} + 15 q^{95} - 87 q^{97} - 39 q^{98}+O(q^{100}) $ 18 * q - 3 * q^2 - 3 * q^4 + 12 * q^8 - 3 * q^10 - 3 * q^13 - 24 * q^14 + 21 * q^16 + 24 * q^17 - 12 * q^19 + 12 * q^20 + 15 * q^22 - 21 * q^23 + 21 * q^26 - 24 * q^28 + 9 * q^29 + 30 * q^31 - 45 * q^32 + 24 * q^34 + 6 * q^35 - 60 * q^37 + 15 * q^38 - 6 * q^40 + 6 * q^41 - 6 * q^43 + 30 * q^44 + 21 * q^46 - 33 * q^47 - 3 * q^49 + 9 * q^52 - 24 * q^53 - 3 * q^55 + 72 * q^56 + 36 * q^58 - 18 * q^59 + 6 * q^61 - 12 * q^62 - 24 * q^64 - 3 * q^65 - 24 * q^67 + 3 * q^68 + 39 * q^70 - 24 * q^71 + 6 * q^73 + 39 * q^74 + 27 * q^76 - 24 * q^77 + 9 * q^79 - 33 * q^80 - 57 * q^82 + 24 * q^85 + 33 * q^86 + 39 * q^88 + 6 * q^89 - 6 * q^91 + 66 * q^92 - 66 * q^94 + 15 * q^95 - 87 * q^97 - 39 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{8}{9}\right)$

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 $

$2$	1.58207	−	0.575828i	1.11869	−	0.407172i	0.284519	−	0.958670i	$-0.408166\pi$
$2$	1.58207	−	0.575828i	1.11869	−	0.407172i	0.834176	+	0.551499i	$0.185944\pi$
$3$		0			0
$3$		0			0
$4$	0.639290	−	0.536428i	0.319645	−	0.268214i
$5$	0.766044	+	0.642788i	0.342585	+	0.287463i
$5$	0.766044	+	0.642788i	0.342585	+	0.287463i
$6$		0			0
$7$	0.274194	+	0.474919i	0.103636	+	0.179502i	0.913180	−	0.407556i	$-0.133619\pi$
$7$	0.274194	+	0.474919i	0.103636	+	0.179502i	−0.809544	+	0.587059i	$0.800286\pi$
$8$	−0.981094	+	1.69930i	−0.346869	+	0.600795i
$9$		0			0
$10$	1.58207	+	0.575828i	0.500296	+	0.182093i
$11$	0.165601	−	0.286829i	0.0499306	−	0.0864823i	−0.839980	−	0.542617i	$-0.817433\pi$
$11$	0.165601	−	0.286829i	0.0499306	−	0.0864823i	0.889910	+	0.456135i	$0.150767\pi$
$12$		0			0
$13$	0.837254	+	4.74830i	0.232212	+	1.31694i	0.848406	+	0.529347i	$0.177563\pi$
$13$	0.837254	+	4.74830i	0.232212	+	1.31694i	−0.616193	+	0.787595i	$0.711326\pi$
$14$	0.707267	+	0.593468i	0.189025	+	0.158611i
$15$		0			0
$16$	−0.863487	+	4.89708i	−0.215872	+	1.22427i
$17$	4.96227	−	1.80612i	1.20353	−	0.438048i	0.339074	−	0.940760i	$-0.389886\pi$
$17$	4.96227	−	1.80612i	1.20353	−	0.438048i	0.864454	+	0.502711i	$0.167664\pi$
$18$		0			0
$19$	4.30704	−	0.670409i	0.988102	−	0.153802i
$19$	4.30704	−	0.670409i	0.988102	−	0.153802i
$20$	0.834534			0.186607
$21$		0			0
$22$	0.0968286	−	0.549142i	0.0206439	−	0.117078i
$23$	0.850350	−	0.713529i	0.177310	−	0.148781i	−0.549813	−	0.835288i	$-0.685301\pi$
$23$	0.850350	−	0.713529i	0.177310	−	0.148781i	0.727124	+	0.686507i	$0.240857\pi$
$24$		0			0
$25$	0.173648	+	0.984808i	0.0347296	+	0.196962i
$26$	4.05880	+	7.03005i	0.795996	+	1.37871i
$27$		0			0
$28$	0.430050	+	0.156525i	0.0812717	+	0.0295805i
$29$	−3.01199	−	1.09627i	−0.559312	−	0.203573i	0.0468671	−	0.998901i	$-0.485076\pi$
$29$	−3.01199	−	1.09627i	−0.559312	−	0.203573i	−0.606179	+	0.795328i	$0.707298\pi$
$30$		0			0
$31$	3.01060	+	5.21452i	0.540720	+	0.936555i	0.998863	+	0.0476765i	$0.0151816\pi$
$31$	3.01060	+	5.21452i	0.540720	+	0.936555i	−0.458142	+	0.888879i	$0.651485\pi$
$32$	0.772312	+	4.38000i	0.136527	+	0.774282i
$33$		0			0
$34$	6.81067	−	5.71483i	1.16802	−	0.980085i
$35$	−0.0952268	+	0.540058i	−0.0160963	+	0.0912864i
$36$		0			0
$37$	−6.67261			−1.09697			−0.548485	−	0.836161i	$-0.684795\pi$
$37$	−6.67261			−1.09697			−0.548485	+	0.836161i	$0.684795\pi$
$38$	6.42801	−	3.54075i	1.04276	−	0.574385i
$39$		0			0
$40$	−1.84385	+	0.671108i	−0.291539	+	0.106111i
$41$	1.37380	−	7.79121i	0.214552	−	1.21678i	−0.667131	−	0.744940i	$-0.732478\pi$
$41$	1.37380	−	7.79121i	0.214552	−	1.21678i	0.881683	−	0.471842i	$-0.156411\pi$
$42$		0			0
$43$	1.25559	+	1.05356i	0.191475	+	0.160667i	0.733486	−	0.679705i	$-0.237892\pi$
$43$	1.25559	+	1.05356i	0.191475	+	0.160667i	−0.542010	+	0.840372i	$0.682337\pi$
$44$	−0.0479962	−	0.272200i	−0.00723570	−	0.0410357i
$45$		0			0
$46$	0.934447	−	1.61851i	0.137777	−	0.238636i
$47$	−4.32380	−	1.57373i	−0.630691	−	0.229553i	0.00684117	−	0.999977i	$-0.497822\pi$
$47$	−4.32380	−	1.57373i	−0.630691	−	0.229553i	−0.637532	+	0.770424i	$0.720045\pi$
$48$		0			0
$49$	3.34963	−	5.80174i	0.478519	−	0.828820i
$50$	0.841804	+	1.45805i	0.119049	+	0.206199i
$51$		0			0
$52$	3.08237	+	2.58642i	0.427448	+	0.358671i
$53$	−5.15257	+	4.32352i	−0.707759	+	0.593881i	−0.923970	−	0.382466i	$-0.875075\pi$
$53$	−5.15257	+	4.32352i	−0.707759	+	0.593881i	0.216210	+	0.976347i	$0.430630\pi$
$54$		0			0
$55$	0.311228	−	0.113278i	0.0419660	−	0.0152744i
$56$	−1.07604			−0.143792
$57$		0			0
$58$	−5.39645			−0.708588
$59$	−6.39331	+	2.32697i	−0.832338	+	0.302946i	−0.722818	−	0.691038i	$-0.757154\pi$
$59$	−6.39331	+	2.32697i	−0.832338	+	0.302946i	−0.109520	+	0.993985i	$0.534931\pi$
$60$		0			0
$61$	0.520640	−	0.436869i	0.0666612	−	0.0559354i	−0.608848	−	0.793287i	$-0.708368\pi$
$61$	0.520640	−	0.436869i	0.0666612	−	0.0559354i	0.675509	+	0.737351i	$0.263924\pi$
$62$	7.76566	+	6.51616i	0.986240	+	0.827554i
$63$		0			0
$64$	−1.22864	−	2.12807i	−0.153580	−	0.266009i
$65$	−2.41078	+	4.17559i	−0.299020	+	0.517918i
$66$		0			0
$67$	7.30324	+	2.65816i	0.892232	+	0.324746i	0.747136	−	0.664672i	$-0.231429\pi$
$67$	7.30324	+	2.65816i	0.892232	+	0.324746i	0.145097	+	0.989418i	$0.453651\pi$
$68$	2.20348	−	3.81654i	0.267211	−	0.462823i
$69$		0			0
$70$	0.160324	+	0.909245i	0.0191624	+	0.108676i
$71$	0.832574	+	0.698612i	0.0988083	+	0.0829101i	0.690854	−	0.722995i	$-0.257235\pi$
$71$	0.832574	+	0.698612i	0.0988083	+	0.0829101i	−0.592045	+	0.805905i	$0.701679\pi$
$72$		0			0
$73$	2.42261	−	13.7393i	0.283545	−	1.60806i	−0.426892	−	0.904302i	$-0.640392\pi$
$73$	2.42261	−	13.7393i	0.283545	−	1.60806i	0.710437	−	0.703761i	$-0.248497\pi$
$74$	−10.5566	+	3.84227i	−1.22717	+	0.446655i
$75$		0			0
$76$	2.39382	−	2.73900i	0.274590	−	0.314185i
$77$	0.181627			0.0206984
$78$		0			0
$79$	−0.243868	+	1.38304i	−0.0274373	+	0.155605i	−0.995448	−	0.0953032i	$-0.969618\pi$
$79$	−0.243868	+	1.38304i	−0.0274373	+	0.155605i	0.968011	+	0.250908i	$0.0807291\pi$
$80$	−3.80925	+	3.19634i	−0.425887	+	0.357362i
$81$		0			0
$82$	−2.31294	−	13.1173i	−0.255422	−	1.44857i
$83$	−0.427439	−	0.740346i	−0.0469176	−	0.0812636i	0.841613	−	0.540081i	$-0.181606\pi$
$83$	−0.427439	−	0.740346i	−0.0469176	−	0.0812636i	−0.888530	+	0.458818i	$0.848273\pi$
$84$		0			0
$85$	4.96227	+	1.80612i	0.538234	+	0.195901i
$86$	2.59310	+	0.943812i	0.279621	+	0.101774i
$87$		0			0
$88$	0.324940	+	0.562813i	0.0346387	+	0.0599960i
$89$	−2.52694	−	14.3310i	−0.267855	−	1.51908i	−0.760781	−	0.649009i	$-0.775184\pi$
$89$	−2.52694	−	14.3310i	−0.267855	−	1.51908i	0.492926	−	0.870071i	$-0.335927\pi$
$90$		0			0
$91$	−2.02549	+	1.69959i	−0.212329	+	0.178165i
$92$	0.160864	−	0.912304i	0.0167712	−	0.0951142i
$93$		0			0
$94$	−7.74677			−0.799018
$95$	3.73031	+	2.25495i	0.382722	+	0.231353i
$96$		0			0
$97$	6.59799	−	2.40147i	0.669924	−	0.243832i	0.0154088	−	0.999881i	$-0.495095\pi$
$97$	6.59799	−	2.40147i	0.669924	−	0.243832i	0.654515	+	0.756049i	$0.272873\pi$
$98$	1.95857	−	11.1076i	0.197845	−	1.12204i
$99$		0			0
$100$	0.639290	+	0.536428i	0.0639290	+	0.0536428i
$101$	1.25144	+	7.09728i	0.124523	+	0.706206i	0.981590	+	0.191000i	$0.0611732\pi$
$101$	1.25144	+	7.09728i	0.124523	+	0.706206i	−0.857067	+	0.515205i	$0.827716\pi$
$102$		0			0
$103$	−3.53759	+	6.12729i	−0.348569	+	0.603739i	−0.985996	−	0.166772i	$-0.946666\pi$
$103$	−3.53759	+	6.12729i	−0.348569	+	0.603739i	0.637426	+	0.770511i	$0.279999\pi$
$104$	−8.89023	−	3.23578i	−0.871759	−	0.317294i
$105$		0			0
$106$	−5.66214	+	9.80711i	−0.549956	+	0.952551i
$107$	−3.25053	−	5.63008i	−0.314241	−	0.544281i	0.665035	−	0.746812i	$-0.268417\pi$
$107$	−3.25053	−	5.63008i	−0.314241	−	0.544281i	−0.979276	+	0.202531i	$0.935083\pi$
$108$		0			0
$109$	−13.5289	−	11.3521i	−1.29583	−	1.08733i	−0.990850	−	0.134971i	$-0.956906\pi$
$109$	−13.5289	−	11.3521i	−1.29583	−	1.08733i	−0.304980	−	0.952359i	$-0.598650\pi$
$110$	0.427157	−	0.358427i	0.0407278	−	0.0341747i
$111$		0			0
$112$	−2.56248	+	0.932665i	−0.242131	+	0.0881286i
$113$	4.86487			0.457649			0.228824	−	0.973468i	$-0.426512\pi$
$113$	4.86487			0.457649			0.228824	+	0.973468i	$0.426512\pi$
$114$		0			0
$115$	1.11005			0.103513
$116$	−2.51360	+	0.914877i	−0.233382	+	0.0849442i
$117$		0			0
$118$	−8.77475	+	7.36289i	−0.807781	+	0.677809i
$119$	2.21839	+	1.86145i	0.203359	+	0.170639i
$120$		0			0
$121$	5.44515	+	9.43128i	0.495014	+	0.857389i
$122$	0.572130	−	0.990958i	0.0517982	−	0.0897171i
$123$		0			0
$124$	4.72186	+	1.71862i	0.424036	+	0.154336i
$125$	−0.500000	+	0.866025i	−0.0447214	+	0.0774597i
$126$		0			0
$127$	−0.515613	−	2.92418i	−0.0457532	−	0.259479i	0.953348	−	0.301874i	$-0.0976123\pi$
$127$	−0.515613	−	2.92418i	−0.0457532	−	0.259479i	−0.999101	+	0.0423950i	$0.986501\pi$
$128$	−9.98327	−	8.37696i	−0.882405	−	0.740426i
$129$		0			0
$130$	−1.40961	+	7.99427i	−0.123631	+	0.701144i
$131$	−7.51285	+	2.73445i	−0.656400	+	0.238910i	−0.648682	−	0.761060i	$-0.724679\pi$
$131$	−7.51285	+	2.73445i	−0.656400	+	0.238910i	−0.00771895	+	0.999970i	$0.502457\pi$
$132$		0			0
$133$	1.49936	+	1.86167i	0.130011	+	0.161427i
$134$	13.0849			1.13036
$135$		0			0
$136$	−1.79931	+	10.2044i	−0.154289	+	0.875019i
$137$	−0.705354	+	0.591862i	−0.0602625	+	0.0505662i	−0.672421	−	0.740169i	$-0.734746\pi$
$137$	−0.705354	+	0.591862i	−0.0602625	+	0.0505662i	0.612159	+	0.790735i	$0.290301\pi$
$138$		0			0
$139$	−0.0173742	−	0.0985339i	−0.00147366	−	0.00835754i	0.984062	−	0.177825i	$-0.0569062\pi$
$139$	−0.0173742	−	0.0985339i	−0.00147366	−	0.00835754i	−0.985536	+	0.169468i	$0.945795\pi$
$140$	0.228825	+	0.396336i	0.0193392	+	0.0334965i
$141$		0			0
$142$	1.71947	+	0.625837i	0.144295	+	0.0525191i
$143$	1.50060	+	0.546174i	0.125487	+	0.0456734i
$144$		0			0
$145$	−1.60264	−	2.77586i	−0.133092	−	0.230523i
$146$	−4.07872	−	23.1316i	−0.337557	−	1.91438i
$147$		0			0
$148$	−4.26573	+	3.57937i	−0.350641	+	0.294223i
$149$	3.00368	−	17.0347i	0.246071	−	1.39554i	−0.571922	−	0.820308i	$-0.693802\pi$
$149$	3.00368	−	17.0347i	0.246071	−	1.39554i	0.817992	−	0.575229i	$-0.195087\pi$
$150$		0			0
$151$	−19.2178			−1.56393			−0.781963	−	0.623325i	$-0.785781\pi$
$151$	−19.2178			−1.56393			−0.781963	+	0.623325i	$0.785781\pi$
$152$	−3.08638	+	7.97670i	−0.250338	+	0.646996i
$153$		0			0
$154$	0.287348	−	0.104586i	0.0231552	−	0.00842779i
$155$	−1.04557	+	5.92973i	−0.0839823	+	0.476288i
$156$		0			0
$157$	−5.04261	−	4.23125i	−0.402444	−	0.337690i	0.418994	−	0.907989i	$-0.362383\pi$
$157$	−5.04261	−	4.23125i	−0.402444	−	0.337690i	−0.821437	+	0.570299i	$0.806827\pi$
$158$	0.410578	+	2.32850i	0.0326638	+	0.185246i
$159$		0			0
$160$	−2.22378	+	3.85171i	−0.175806	+	0.304504i
$161$	0.572030	+	0.208202i	0.0450822	+	0.0164086i
$162$		0			0
$163$	7.29637	−	12.6377i	0.571496	−	0.989860i	−0.424917	−	0.905232i	$-0.639697\pi$
$163$	7.29637	−	12.6377i	0.571496	−	0.989860i	0.996413	−	0.0846275i	$-0.0269700\pi$
$164$	−3.30117	−	5.71779i	−0.257778	−	0.446484i
$165$		0			0
$166$	−1.10255	−	0.925151i	−0.0855746	−	0.0718057i
$167$	−2.68854	+	2.25595i	−0.208045	+	0.174571i	−0.740856	−	0.671664i	$-0.765580\pi$
$167$	−2.68854	+	2.25595i	−0.208045	+	0.174571i	0.532811	+	0.846234i	$0.321136\pi$
$168$		0			0
$169$	−9.62936	+	3.50480i	−0.740720	+	0.269600i
$170$	8.89069			0.681885
$171$		0			0
$172$	1.36784			0.104297
$173$	2.35200	−	0.856059i	0.178819	−	0.0650849i	−0.251059	−	0.967972i	$-0.580779\pi$
$173$	2.35200	−	0.856059i	0.178819	−	0.0650849i	0.429878	+	0.902887i	$0.358557\pi$
$174$		0			0
$175$	−0.420090	+	0.352498i	−0.0317558	+	0.0266463i
$176$	1.26163	+	1.05863i	0.0950990	+	0.0797975i
$177$		0			0
$178$	−12.2500	−	21.2176i	−0.918174	−	1.59032i
$179$	−2.51029	+	4.34795i	−0.187628	+	0.324981i	−0.944459	−	0.328630i	$-0.893413\pi$
$179$	−2.51029	+	4.34795i	−0.187628	+	0.324981i	0.756831	+	0.653610i	$0.226747\pi$
$180$		0			0
$181$	5.09429	+	1.85417i	0.378656	+	0.137819i	0.524334	−	0.851513i	$-0.324314\pi$
$181$	5.09429	+	1.85417i	0.378656	+	0.137819i	−0.145678	+	0.989332i	$0.546536\pi$
$182$	−2.22580	+	3.85520i	−0.164987	+	0.285766i
$183$		0			0
$184$	0.378229	+	2.14504i	0.0278834	+	0.158135i
$185$	−5.11151	−	4.28907i	−0.375806	−	0.315339i
$186$		0			0
$187$	0.303709	−	1.72242i	0.0222094	−	0.125956i
$188$	−3.60836	+	1.31333i	−0.263166	+	0.0957847i
$189$		0			0
$190$	7.20009	+	1.41947i	0.522349	+	0.102979i
$191$	−5.98517			−0.433071			−0.216536	−	0.976275i	$-0.569476\pi$
$191$	−5.98517			−0.433071			−0.216536	+	0.976275i	$0.569476\pi$
$192$		0			0
$193$	0.376572	−	2.13565i	0.0271063	−	0.153727i	−0.968250	−	0.249982i	$-0.919575\pi$
$193$	0.376572	−	2.13565i	0.0271063	−	0.153727i	0.995357	+	0.0962548i	$0.0306864\pi$
$194$	9.05567	−	7.59861i	0.650159	−	0.545548i
$195$		0			0
$196$	−0.970827	−	5.50583i	−0.0693448	−	0.393274i
$197$	8.28327	+	14.3471i	0.590159	+	1.02219i	0.994211	+	0.107449i	$0.0342682\pi$
$197$	8.28327	+	14.3471i	0.590159	+	1.02219i	−0.404052	+	0.914736i	$0.632398\pi$
$198$		0			0
$199$	−13.1370	−	4.78149i	−0.931259	−	0.338951i	−0.168551	−	0.985693i	$-0.553909\pi$
$199$	−13.1370	−	4.78149i	−0.931259	−	0.338951i	−0.762709	+	0.646742i	$0.776131\pi$
$200$	−1.84385	−	0.671108i	−0.130380	−	0.0474545i
$201$		0			0
$202$	6.06668	+	10.5078i	0.426850	+	0.739327i
$203$	−0.305229	−	1.73104i	−0.0214229	−	0.121495i
$204$		0			0
$205$	6.06049	−	5.08535i	0.423283	−	0.355176i
$206$	−2.06847	+	11.7309i	−0.144117	+	0.817328i
$207$		0			0
$208$	−23.9757			−1.66242
$209$	0.520956	−	1.34640i	0.0360353	−	0.0931327i
$210$		0			0
$211$	16.9908	−	6.18415i	1.16970	−	0.425735i	0.317145	−	0.948377i	$-0.397276\pi$
$211$	16.9908	−	6.18415i	1.16970	−	0.425735i	0.852552	+	0.522643i	$0.175054\pi$
$212$	−0.974729	+	5.52796i	−0.0669447	+	0.379662i
$213$		0			0
$214$	−8.38453	−	7.03546i	−0.573155	−	0.480934i
$215$	0.284618	+	1.61415i	0.0194108	+	0.110084i
$216$		0			0
$217$	−1.65098	+	2.85958i	−0.112076	+	0.194121i
$218$	−27.9405	−	10.1695i	−1.89237	−	0.688766i
$219$		0			0
$220$	0.138200	−	0.239369i	0.00931741	−	0.0161382i
$221$	12.7307	+	22.0502i	0.856358	+	1.48326i
$222$		0			0
$223$	20.1214	+	16.8838i	1.34743	+	1.13062i	0.979651	+	0.200710i	$0.0643250\pi$
$223$	20.1214	+	16.8838i	1.34743	+	1.13062i	0.367775	+	0.929915i	$0.380119\pi$
$224$	−1.86838	+	1.56776i	−0.124836	+	0.104750i
$225$		0			0
$226$	7.69659	−	2.80133i	0.511969	−	0.186342i
$227$	−6.97401			−0.462881			−0.231441	−	0.972849i	$-0.574344\pi$
$227$	−6.97401			−0.462881			−0.231441	+	0.972849i	$0.574344\pi$
$228$		0			0
$229$	2.62489			0.173458			0.0867288	−	0.996232i	$-0.472359\pi$
$229$	2.62489			0.173458			0.0867288	+	0.996232i	$0.472359\pi$
$230$	1.75619	−	0.639200i	0.115799	−	0.0421476i
$231$		0			0
$232$	4.81794	−	4.04273i	0.316313	−	0.265419i
$233$	20.4217	+	17.1358i	1.33787	+	1.12260i	0.982168	+	0.188004i	$0.0602019\pi$
$233$	20.4217	+	17.1358i	1.33787	+	1.12260i	0.355700	+	0.934600i	$0.384243\pi$
$234$		0			0
$235$	−2.30064	−	3.98483i	−0.150078	−	0.259942i
$236$	−2.83892	+	4.91716i	−0.184798	+	0.320080i
$237$		0			0
$238$	4.58153	+	1.66754i	0.296976	+	0.108091i
$239$	6.55369	−	11.3513i	0.423923	−	0.734256i	−0.572396	−	0.819977i	$-0.693986\pi$
$239$	6.55369	−	11.3513i	0.423923	−	0.734256i	0.996319	+	0.0857211i	$0.0273194\pi$
$240$		0			0
$241$	−2.63284	−	14.9316i	−0.169596	−	0.961828i	−0.944198	−	0.329379i	$-0.893161\pi$
$241$	−2.63284	−	14.9316i	−0.169596	−	0.961828i	0.774602	−	0.632449i	$-0.217950\pi$
$242$	14.0454	+	11.7855i	0.902874	+	0.757601i
$243$		0			0
$244$	0.0984913	−	0.558572i	0.00630526	−	0.0357589i
$245$	6.29525	−	2.29129i	0.402189	−	0.146385i
$246$		0			0
$247$	6.78939	+	19.8898i	0.431998	+	1.26556i
$248$	−11.8147			−0.750237
$249$		0			0
$250$	−0.292355	+	1.65803i	−0.0184902	+	0.104863i
$251$	−14.5597	+	12.2170i	−0.919001	+	0.771133i	−0.973810	−	0.227364i	$-0.926989\pi$
$251$	−14.5597	+	12.2170i	−0.919001	+	0.771133i	0.0548090	+	0.998497i	$0.482545\pi$
$252$		0			0
$253$	−0.0638421	−	0.362066i	−0.00401372	−	0.0227629i
$254$	−2.49956	−	4.32937i	−0.156837	−	0.271649i
$255$		0			0
$256$	−15.9998	−	5.82344i	−0.999986	−	0.363965i
$257$	20.5212	+	7.46911i	1.28008	+	0.465910i	0.890458	−	0.455066i	$-0.150384\pi$
$257$	20.5212	+	7.46911i	1.28008	+	0.465910i	0.389620	+	0.920976i	$0.372606\pi$
$258$		0			0
$259$	−1.82959	−	3.16895i	−0.113685	−	0.196909i
$260$	0.698716	+	3.96262i	0.0433326	+	0.245751i
$261$		0			0
$262$	−10.3113	+	8.65221i	−0.637034	+	0.534535i
$263$	3.40719	−	19.3231i	0.210096	−	1.19152i	−0.679119	−	0.734028i	$-0.737638\pi$
$263$	3.40719	−	19.3231i	0.210096	−	1.19152i	0.889216	−	0.457488i	$-0.151251\pi$
$264$		0			0
$265$	−6.72620			−0.413187
$266$	3.44409	+	2.08193i	0.211171	+	0.127651i
$267$		0			0
$268$	6.09480	−	2.21832i	0.372299	−	0.135506i
$269$	0.293697	−	1.66564i	0.0179070	−	0.101556i	−0.974544	−	0.224195i	$-0.928025\pi$
$269$	0.293697	−	1.66564i	0.0179070	−	0.101556i	0.992451	+	0.122639i	$0.0391359\pi$
$270$		0			0
$271$	−6.08215	−	5.10353i	−0.369465	−	0.310018i	0.439085	−	0.898445i	$-0.355303\pi$
$271$	−6.08215	−	5.10353i	−0.369465	−	0.310018i	−0.808550	+	0.588428i	$0.799747\pi$
$272$	4.55985	+	25.8602i	0.276481	+	1.56800i
$273$		0			0
$274$	−0.775111	+	1.34253i	−0.0468262	+	0.0811053i
$275$	0.311228	+	0.113278i	0.0187678	+	0.00683090i
$276$		0			0
$277$	4.73698	−	8.20468i	0.284617	−	0.492972i	−0.687899	−	0.725806i	$-0.741467\pi$
$277$	4.73698	−	8.20468i	0.284617	−	0.492972i	0.972516	+	0.232835i	$0.0748002\pi$
$278$	−0.0842258	−	0.145883i	−0.00505153	−	0.00874950i
$279$		0			0
$280$	−0.824296	−	0.691666i	−0.0492611	−	0.0413350i
$281$	9.62922	−	8.07988i	0.574431	−	0.482005i	−0.308682	−	0.951165i	$-0.599888\pi$
$281$	9.62922	−	8.07988i	0.574431	−	0.482005i	0.883113	+	0.469160i	$0.155443\pi$
$282$		0			0
$283$	17.4632	−	6.35609i	1.03808	−	0.377830i	0.233928	−	0.972254i	$-0.424842\pi$
$283$	17.4632	−	6.35609i	1.03808	−	0.377830i	0.804152	+	0.594424i	$0.202620\pi$
$284$	0.907012			0.0538212
$285$		0			0
$286$	2.68856			0.158978
$287$	4.07688	−	1.48386i	0.240651	−	0.0875897i
$288$		0			0
$289$	8.33933	−	6.99753i	0.490549	−	0.411619i
$290$	−4.13392	−	3.46877i	−0.242752	−	0.203693i
$291$		0			0
$292$	−5.82139	−	10.0830i	−0.340671	−	0.590060i
$293$	−8.68253	+	15.0386i	−0.507239	+	0.878563i	0.492726	+	0.870184i	$0.336000\pi$
$293$	−8.68253	+	15.0386i	−0.507239	+	0.878563i	−0.999965	+	0.00837865i	$0.997333\pi$
$294$		0			0
$295$	−6.39331	−	2.32697i	−0.372233	−	0.135482i
$296$	6.54645	−	11.3388i	0.380505	−	0.659054i
$297$		0			0
$298$	−5.05701	−	28.6798i	−0.292945	−	1.66137i
$299$	4.10001	+	3.44032i	0.237110	+	0.198959i
$300$		0			0
$301$	−0.156082	+	0.885183i	−0.00899639	+	0.0510211i
$302$	−30.4040	+	11.0662i	−1.74956	+	0.636786i
$303$		0			0
$304$	−0.436022	+	21.6708i	−0.0250076	+	1.24290i
$305$	0.679648			0.0389165
$306$		0			0
$307$	−4.34996	+	24.6698i	−0.248265	+	1.40798i	0.564521	+	0.825419i	$0.309061\pi$
$307$	−4.34996	+	24.6698i	−0.248265	+	1.40798i	−0.812786	+	0.582563i	$0.802050\pi$
$308$	0.116113	−	0.0974301i	0.00661613	−	0.00555159i
$309$		0			0
$310$	1.76033	+	9.98334i	0.0999802	+	0.567016i
$311$	−2.79206	−	4.83598i	−0.158323	−	0.274223i	0.775941	−	0.630805i	$-0.217275\pi$
$311$	−2.79206	−	4.83598i	−0.158323	−	0.274223i	−0.934264	+	0.356582i	$0.883942\pi$
$312$		0			0
$313$	0.771588	+	0.280835i	0.0436127	+	0.0158737i	0.363734	−	0.931503i	$-0.381502\pi$
$313$	0.771588	+	0.280835i	0.0436127	+	0.0158737i	−0.320122	+	0.947376i	$0.603724\pi$
$314$	−10.4142	−	3.79048i	−0.587710	−	0.213909i
$315$		0			0
$316$	0.586001	+	1.01498i	0.0329651	+	0.0570973i
$317$	−5.82285	−	33.0230i	−0.327044	−	1.85476i	−0.494904	−	0.868948i	$-0.664797\pi$
$317$	−5.82285	−	33.0230i	−0.327044	−	1.85476i	0.167860	−	0.985811i	$-0.446314\pi$
$318$		0			0
$319$	−0.813231	+	0.682382i	−0.0455322	+	0.0382061i
$320$	0.426703	−	2.41995i	0.0238534	−	0.135280i
$321$		0			0
$322$	1.02488			0.0571144
$323$	20.1618	−	11.1058i	1.12184	−	0.617942i
$324$		0			0
$325$	−4.53078	+	1.64907i	−0.251322	+	0.0914738i
$326$	4.26627	−	24.1952i	0.236287	−	1.34005i
$327$		0			0
$328$	11.8918	+	9.97841i	0.656615	+	0.550966i
$329$	−0.438166	−	2.48496i	−0.0241569	−	0.137000i
$330$		0			0
$331$	−5.63364	+	9.75775i	−0.309653	+	0.536334i	−0.978286	−	0.207258i	$-0.933546\pi$
$331$	−5.63364	+	9.75775i	−0.309653	+	0.536334i	0.668634	+	0.743592i	$0.266879\pi$
$332$	−0.670400	−	0.244006i	−0.0367930	−	0.0133916i
$333$		0			0
$334$	−2.95442	+	5.11721i	−0.161659	+	0.280001i
$335$	3.88597	+	6.73070i	0.212313	+	0.367737i
$336$		0			0
$337$	4.82284	+	4.04684i	0.262717	+	0.220445i	0.764625	−	0.644475i	$-0.222924\pi$
$337$	4.82284	+	4.04684i	0.262717	+	0.220445i	−0.501909	+	0.864921i	$0.667369\pi$
$338$	−13.2162	+	11.0897i	−0.718866	+	0.603201i
$339$		0			0
$340$	4.14118	−	1.50727i	0.224587	−	0.0817431i
$341$	1.99424			0.107994
$342$		0			0
$343$	7.51253			0.405638
$344$	−3.02217	+	1.09998i	−0.162945	+	0.0593070i
$345$		0			0
$346$	3.22810	−	2.70870i	0.173544	−	0.145620i
$347$	13.4490	+	11.2851i	0.721981	+	0.605814i	0.927932	−	0.372749i	$-0.121585\pi$
$347$	13.4490	+	11.2851i	0.721981	+	0.605814i	−0.205952	+	0.978562i	$0.566029\pi$
$348$		0			0
$349$	−6.25844	−	10.8399i	−0.335007	−	0.580248i	0.648480	−	0.761232i	$-0.275405\pi$
$349$	−6.25844	−	10.8399i	−0.335007	−	0.580248i	−0.983486	+	0.180984i	$0.942072\pi$
$350$	−0.461636	+	0.799577i	−0.0246755	+	0.0427392i
$351$		0			0
$352$	1.38421	+	0.503810i	0.0737785	+	0.0268532i
$353$	2.91409	−	5.04735i	0.155101	−	0.268643i	−0.777995	−	0.628271i	$-0.783763\pi$
$353$	2.91409	−	5.04735i	0.155101	−	0.268643i	0.933096	+	0.359628i	$0.117096\pi$
$354$		0			0
$355$	0.188729	+	1.07034i	0.0100167	+	0.0568076i
$356$	−9.30298	−	7.80613i	−0.493057	−	0.413724i
$357$		0			0
$358$	−1.46779	+	8.32426i	−0.0775752	+	0.439951i
$359$	0.544588	−	0.198214i	0.0287423	−	0.0104613i	−0.327609	−	0.944813i	$-0.606243\pi$
$359$	0.544588	−	0.198214i	0.0287423	−	0.0104613i	0.356351	+	0.934352i	$0.384021\pi$
$360$		0			0
$361$	18.1011	−	5.77495i	0.952690	−	0.303945i
$362$	9.12723			0.479717
$363$		0			0
$364$	−0.383168	+	2.17306i	−0.0200835	+	0.113899i
$365$	10.6873	−	8.96769i	0.559398	−	0.469390i
$366$		0			0
$367$	−1.37291	−	7.78614i	−0.0716651	−	0.406433i	−0.999445	−	0.0333057i	$-0.989397\pi$
$367$	−1.37291	−	7.78614i	−0.0716651	−	0.406433i	0.927780	−	0.373127i	$-0.121715\pi$
$368$	2.75994	+	4.78035i	0.143872	+	0.249193i
$369$		0			0
$370$	−10.5566	−	3.84227i	−0.548809	−	0.199750i
$371$	−3.46613	−	1.26157i	−0.179952	−	0.0654973i
$372$		0			0
$373$	4.15310	+	7.19338i	0.215039	+	0.372459i	0.953285	−	0.302073i	$-0.0976787\pi$
$373$	4.15310	+	7.19338i	0.215039	+	0.372459i	−0.738245	+	0.674532i	$0.764345\pi$
$374$	−0.511327	−	2.89988i	−0.0264401	−	0.149949i
$375$		0			0
$376$	6.91630	−	5.80347i	0.356681	−	0.299291i
$377$	2.68364	−	15.2197i	0.138214	−	0.783853i
$378$		0			0
$379$	10.2928			0.528707			0.264354	−	0.964426i	$-0.414841\pi$
$379$	10.2928			0.528707			0.264354	+	0.964426i	$0.414841\pi$
$380$	3.59437	−	0.559479i	0.184387	−	0.0287007i
$381$		0			0
$382$	−9.46897	+	3.44642i	−0.484475	+	0.176334i
$383$	−5.56168	+	31.5418i	−0.284188	+	1.61171i	0.423981	+	0.905671i	$0.360632\pi$
$383$	−5.56168	+	31.5418i	−0.284188	+	1.61171i	−0.708170	+	0.706042i	$0.750479\pi$
$384$		0			0
$385$	0.139135	+	0.116748i	0.00709096	+	0.00595002i
$386$	−0.634000	−	3.59559i	−0.0322698	−	0.183011i
$387$		0			0
$388$	2.92981	−	5.07458i	0.148739	−	0.257623i
$389$	−28.7624	−	10.4686i	−1.45831	−	0.530781i	−0.513411	−	0.858143i	$-0.671618\pi$
$389$	−28.7624	−	10.4686i	−1.45831	−	0.530781i	−0.944899	+	0.327362i	$0.893840\pi$
$390$		0			0
$391$	2.93095	−	5.07656i	0.148225	−	0.256733i
$392$	6.57261	+	11.3841i	0.331967	+	0.574984i
$393$		0			0
$394$	21.3662	+	17.9284i	1.07641	+	0.903217i
$395$	−1.07582	+	0.902717i	−0.0541302	+	0.0454206i
$396$		0			0
$397$	−9.97995	+	3.63241i	−0.500880	+	0.182305i	−0.580090	−	0.814553i	$-0.696982\pi$
$397$	−9.97995	+	3.63241i	−0.500880	+	0.182305i	0.0792100	+	0.996858i	$0.474760\pi$
$398$	−23.5371			−1.17981
$399$		0			0
$400$	−4.97262			−0.248631
$401$	−14.3159	+	5.21056i	−0.714901	+	0.260203i	−0.673760	−	0.738950i	$-0.735322\pi$
$401$	−14.3159	+	5.21056i	−0.714901	+	0.260203i	−0.0411417	+	0.999153i	$0.513099\pi$
$402$		0			0
$403$	−22.2395	+	18.6611i	−1.10783	+	0.929577i
$404$	4.60721	+	3.86591i	0.229217	+	0.192336i
$405$		0			0
$406$	−1.47968	−	2.56287i	−0.0734351	−	0.127193i
$407$	−1.10499	+	1.91390i	−0.0547723	+	0.0948684i
$408$		0			0
$409$	10.9607	+	3.98936i	0.541971	+	0.197261i	0.598476	−	0.801141i	$-0.295773\pi$
$409$	10.9607	+	3.98936i	0.541971	+	0.197261i	−0.0565046	+	0.998402i	$0.517996\pi$
$410$	6.65985	−	11.5352i	0.328906	−	0.569683i
$411$		0			0
$412$	1.02530	+	5.81478i	0.0505130	+	0.286473i
$413$	−2.85813	−	2.39826i	−0.140640	−	0.118011i
$414$		0			0
$415$	0.148448	−	0.841891i	0.00728703	−	0.0413268i
$416$	−20.1509	+	7.33434i	−0.987981	+	0.359595i
$417$		0			0
$418$	0.0488942	−	2.43009i	0.00239149	−	0.118860i
$419$	−17.7028			−0.864840			−0.432420	−	0.901672i	$-0.642340\pi$
$419$	−17.7028			−0.864840			−0.432420	+	0.901672i	$0.642340\pi$
$420$		0			0
$421$	3.57756	−	20.2893i	0.174359	−	0.988841i	−0.764521	−	0.644599i	$-0.777025\pi$
$421$	3.57756	−	20.2893i	0.174359	−	0.988841i	0.938881	−	0.344243i	$-0.111864\pi$
$422$	23.3197	−	19.5676i	1.13519	−	0.952534i
$423$		0			0
$424$	−2.29182	−	12.9976i	−0.111301	−	0.631217i
$425$	2.64037	+	4.57326i	0.128077	+	0.221835i
$426$		0			0
$427$	0.350234	+	0.127475i	0.0169490	+	0.00616894i
$428$	−5.09817	−	1.85558i	−0.246429	−	0.0896929i
$429$		0			0
$430$	1.37976	+	2.38981i	0.0665379	+	0.115247i
$431$	−1.44676	−	8.20498i	−0.0696879	−	0.395220i	−0.999622	−	0.0274936i	$-0.991247\pi$
$431$	−1.44676	−	8.20498i	−0.0696879	−	0.395220i	0.929934	−	0.367726i	$-0.119864\pi$
$432$		0			0
$433$	21.5979	−	18.1228i	1.03793	−	0.870926i	0.0461560	−	0.998934i	$-0.485303\pi$
$433$	21.5979	−	18.1228i	1.03793	−	0.870926i	0.991773	+	0.128008i	$0.0408584\pi$
$434$	−0.965347	+	5.47475i	−0.0463381	+	0.262797i
$435$		0			0
$436$	−14.7384			−0.705843
$437$	3.18413	−	3.64328i	0.152318	−	0.174282i
$438$		0			0
$439$	−28.5501	+	10.3914i	−1.36262	+	0.495954i	−0.916864	−	0.399199i	$-0.869288\pi$
$439$	−28.5501	+	10.3914i	−1.36262	+	0.495954i	−0.445759	+	0.895153i	$0.647066\pi$
$440$	−0.112850	+	0.640007i	−0.00537994	+	0.0305111i
$441$		0			0
$442$	32.8380	+	27.5543i	1.56194	+	1.31063i
$443$	−4.25799	−	24.1482i	−0.202303	−	1.14732i	−0.901628	−	0.432513i	$-0.857627\pi$
$443$	−4.25799	−	24.1482i	−0.202303	−	1.14732i	0.699325	−	0.714804i	$-0.253484\pi$
$444$		0			0
$445$	7.27602	−	12.6024i	0.344917	−	0.597413i
$446$	41.5556	+	15.1250i	1.96772	+	0.716190i
$447$		0			0
$448$	0.673774	−	1.16701i	0.0318328	−	0.0551361i
$449$	12.3444	+	21.3812i	0.582570	+	1.00904i	0.995174	+	0.0981300i	$0.0312861\pi$
$449$	12.3444	+	21.3812i	0.582570	+	1.00904i	−0.412604	+	0.910911i	$0.635381\pi$
$450$		0			0
$451$	−2.00724	−	1.68428i	−0.0945174	−	0.0793095i
$452$	3.11007	−	2.60965i	0.146285	−	0.122748i
$453$		0			0
$454$	−11.0334	+	4.01583i	−0.517823	+	0.188472i
$455$	−2.64409			−0.123957
$456$		0			0
$457$	7.16480			0.335155			0.167578	−	0.985859i	$-0.446406\pi$
$457$	7.16480			0.335155			0.167578	+	0.985859i	$0.446406\pi$
$458$	4.15277	−	1.51148i	0.194046	−	0.0706270i
$459$		0			0
$460$	0.709646	−	0.595464i	0.0330874	−	0.0277636i
$461$	−16.6388	−	13.9616i	−0.774947	−	0.650258i	0.167024	−	0.985953i	$-0.446584\pi$
$461$	−16.6388	−	13.9616i	−0.774947	−	0.650258i	−0.941971	+	0.335695i	$0.891029\pi$
$462$		0			0
$463$	15.9642	+	27.6508i	0.741918	+	1.28504i	0.951621	+	0.307274i	$0.0994169\pi$
$463$	15.9642	+	27.6508i	0.741918	+	1.28504i	−0.209703	+	0.977765i	$0.567250\pi$
$464$	7.96934	−	13.8033i	0.369968	−	0.640803i
$465$		0			0
$466$	42.1759	+	15.3508i	1.95376	+	0.711110i
$467$	−9.76911	+	16.9206i	−0.452061	+	0.782992i	−0.998514	−	0.0544977i	$-0.982644\pi$
$467$	−9.76911	+	16.9206i	−0.452061	+	0.782992i	0.546453	+	0.837490i	$0.315978\pi$
$468$		0			0
$469$	0.740097	+	4.19730i	0.0341745	+	0.193813i
$470$	−5.93437	−	4.97952i	−0.273732	−	0.229688i
$471$		0			0
$472$	2.31820	−	13.1472i	0.106704	−	0.605147i
$473$	0.510119	−	0.185668i	0.0234553	−	0.00853703i
$474$		0			0
$475$	1.40813	+	4.12519i	0.0646096	+	0.189277i
$476$	2.41673			0.110770
$477$		0			0
$478$	3.83201	−	21.7324i	0.175272	−	0.994018i
$479$	9.37543	−	7.86692i	0.428374	−	0.359449i	−0.402964	−	0.915216i	$-0.632020\pi$
$479$	9.37543	−	7.86692i	0.428374	−	0.359449i	0.831338	+	0.555767i	$0.187575\pi$
$480$		0			0
$481$	−5.58666	−	31.6835i	−0.254730	−	1.44464i
$482$	−12.7634	−	22.1068i	−0.581356	−	1.00694i
$483$		0			0
$484$	8.54024	+	3.10839i	0.388193	+	0.141291i
$485$	6.59799	+	2.40147i	0.299599	+	0.109045i
$486$		0			0
$487$	7.05086	+	12.2125i	0.319505	+	0.553399i	0.980385	−	0.197093i	$-0.0631500\pi$
$487$	7.05086	+	12.2125i	0.319505	+	0.553399i	−0.660880	+	0.750492i	$0.729817\pi$
$488$	0.231577	+	1.31334i	0.0104830	+	0.0594519i
$489$		0			0
$490$	8.64017	−	7.24996i	0.390323	−	0.327520i
$491$	3.45329	−	19.5846i	0.155845	−	0.883839i	−0.802165	−	0.597103i	$-0.796318\pi$
$491$	3.45329	−	19.5846i	0.155845	−	0.883839i	0.958009	−	0.286737i	$-0.0925704\pi$
$492$		0			0
$493$	−16.9263			−0.762322
$494$	22.1944	+	27.5576i	0.998573	+	1.23988i
$495$		0			0
$496$	−28.1355	+	10.2405i	−1.26332	+	0.459812i
$497$	−0.103497	+	0.586961i	−0.00464248	+	0.0263288i
$498$		0			0
$499$	−5.69739	−	4.78068i	−0.255050	−	0.214013i	0.506293	−	0.862362i	$-0.331015\pi$
$499$	−5.69739	−	4.78068i	−0.255050	−	0.214013i	−0.761343	+	0.648349i	$0.775460\pi$
$500$	0.144915	+	0.821855i	0.00648081	+	0.0367545i
$501$		0			0
$502$	−15.9996	+	27.7122i	−0.714098	+	1.23685i
$503$	−12.6972	−	4.62141i	−0.566141	−	0.206059i	0.0430624	−	0.999072i	$-0.486289\pi$
$503$	−12.6972	−	4.62141i	−0.566141	−	0.206059i	−0.609204	+	0.793014i	$0.708511\pi$
$504$		0			0
$505$	−3.60338	+	6.24124i	−0.160348	+	0.277732i
$506$	−0.309491	−	0.536054i	−0.0137585	−	0.0238305i
$507$		0			0
$508$	−1.89824	−	1.59281i	−0.0842208	−	0.0706696i
$509$	26.9446	−	22.6092i	1.19430	−	1.00214i	0.194525	−	0.980898i	$-0.437684\pi$
$509$	26.9446	−	22.6092i	1.19430	−	1.00214i	0.999774	−	0.0212383i	$-0.00676087\pi$
$510$		0			0
$511$	7.18932	−	2.61670i	0.318037	−	0.115756i
$512$	−2.60163			−0.114977
$513$		0			0
$514$	36.7670			1.62172
$515$	−6.64850	+	2.41985i	−0.292968	+	0.106632i
$516$		0			0
$517$	−1.16742	+	0.979580i	−0.0513430	+	0.0430819i
$518$	−4.71931	−	3.95998i	−0.207355	−	0.173991i
$519$		0			0
$520$	−4.73039	−	8.19328i	−0.207441	−	0.359299i
$521$	−2.92797	+	5.07140i	−0.128277	+	0.222182i	−0.923009	−	0.384778i	$-0.874278\pi$
$521$	−2.92797	+	5.07140i	−0.128277	+	0.222182i	0.794732	+	0.606960i	$0.207611\pi$
$522$		0			0
$523$	−10.8529	−	3.95014i	−0.474565	−	0.172727i	0.0936543	−	0.995605i	$-0.470145\pi$
$523$	−10.8529	−	3.95014i	−0.474565	−	0.172727i	−0.568219	+	0.822877i	$0.692367\pi$
$524$	−3.33605	+	5.77821i	−0.145736	+	0.252422i
$525$		0			0
$526$	−5.73637	−	32.5326i	−0.250118	−	1.41849i
$527$	24.3575	+	20.4384i	1.06103	+	0.890309i
$528$		0			0
$529$	−3.77994	+	21.4371i	−0.164345	+	0.932047i
$530$	−10.6413	+	3.87313i	−0.462230	+	0.168238i
$531$		0			0
$532$	1.95717	+	0.385851i	0.0848543	+	0.0167287i
$533$	38.1452			1.65225
$534$		0			0
$535$	1.12890	−	6.40229i	0.0488065	−	0.276795i
$536$	−11.6822	+	9.80251i	−0.504593	+	0.423404i
$537$		0			0
$538$	−0.494470	−	2.80428i	−0.0213181	−	0.120901i
$539$	−1.10941	−	1.92155i	−0.0477855	−	0.0827669i
$540$		0			0
$541$	−11.0424	−	4.01909i	−0.474748	−	0.172794i	0.0935540	−	0.995614i	$-0.470177\pi$
$541$	−11.0424	−	4.01909i	−0.474748	−	0.172794i	−0.568302	+	0.822820i	$0.692399\pi$
$542$	−12.5612	−	4.57189i	−0.539548	−	0.196380i
$543$		0			0
$544$	11.7432	+	20.3399i	0.503487	+	0.872064i
$545$	−3.06674	−	17.3924i	−0.131365	−	0.745007i
$546$		0			0
$547$	−22.1845	+	18.6150i	−0.948541	+	0.795920i	−0.979051	−	0.203614i	$-0.934731\pi$
$547$	−22.1845	+	18.6150i	−0.948541	+	0.795920i	0.0305106	+	0.999534i	$0.490287\pi$
$548$	−0.133434	+	0.756743i	−0.00570003	+	0.0323265i
$549$		0			0
$550$	0.557614			0.0237767
$551$	−13.7077	−	2.70242i	−0.583967	−	0.115127i
$552$		0			0
$553$	−0.723700	+	0.263405i	−0.0307749	+	0.0112011i
$554$	2.76976	−	15.7081i	0.117676	−	0.667373i
$555$		0			0
$556$	−0.0639635	−	0.0536718i	−0.00271266	−	0.00227619i
$557$	4.20497	+	23.8476i	0.178170	+	1.01045i	0.934421	+	0.356171i	$0.115918\pi$
$557$	4.20497	+	23.8476i	0.178170	+	1.01045i	−0.756250	+	0.654282i	$0.772971\pi$
$558$		0			0
$559$	−3.95139	+	6.84400i	−0.167126	+	0.289470i
$560$	−2.56248	−	0.932665i	−0.108284	−	0.0394123i
$561$		0			0
$562$	10.5815	−	18.3277i	0.446355	−	0.773109i
$563$	22.7232	+	39.3578i	0.957669	+	1.65873i	0.728138	+	0.685431i	$0.240386\pi$
$563$	22.7232	+	39.3578i	0.957669	+	1.65873i	0.229531	+	0.973301i	$0.426281\pi$
$564$		0			0
$565$	3.72671	+	3.12708i	0.156784	+	0.131557i
$566$	23.9681	−	20.1116i	1.00745	−	0.845354i
$567$		0			0
$568$	−2.00399	+	0.729392i	−0.0840855	+	0.0306046i
$569$	−28.1695			−1.18093			−0.590463	−	0.807065i	$-0.701055\pi$
$569$	−28.1695			−1.18093			−0.590463	+	0.807065i	$0.701055\pi$
$570$		0			0
$571$	18.2742			0.764752			0.382376	−	0.924007i	$-0.375106\pi$
$571$	18.2742			0.764752			0.382376	+	0.924007i	$0.375106\pi$
$572$	1.25230	−	0.455801i	0.0523614	−	0.0190580i
$573$		0			0
$574$	5.59547	−	4.69516i	0.233551	−	0.195972i
$575$	0.850350	+	0.713529i	0.0354621	+	0.0297562i
$576$		0			0
$577$	10.0919	+	17.4797i	0.420132	+	0.727689i	0.995952	−	0.0898868i	$-0.0286505\pi$
$577$	10.0919	+	17.4797i	0.420132	+	0.727689i	−0.575820	+	0.817576i	$0.695317\pi$
$578$	9.16406	−	15.8726i	0.381175	−	0.660214i
$579$		0			0
$580$	−2.51360	−	0.914877i	−0.104372	−	0.0379882i
$581$	0.234403	−	0.405998i	0.00972467	−	0.0168436i
$582$		0			0
$583$	0.386841	+	2.19389i	0.0160213	+	0.0908614i
$584$	20.9704	+	17.5963i	0.867763	+	0.728140i
$585$		0			0
$586$	−5.07677	+	28.7918i	−0.209719	+	1.18938i
$587$	−17.3771	+	6.32474i	−0.717229	+	0.261050i	−0.674749	−	0.738047i	$-0.735748\pi$
$587$	−17.3771	+	6.32474i	−0.717229	+	0.261050i	−0.0424803	+	0.999097i	$0.513526\pi$
$588$		0			0
$589$	16.4626	+	20.4408i	0.678331	+	0.842248i
$590$	−11.4546			−0.471579
$591$		0			0
$592$	5.76170	−	32.6763i	0.236805	−	1.34299i
$593$	3.91012	−	3.28098i	0.160569	−	0.134734i	−0.558963	−	0.829193i	$-0.688801\pi$
$593$	3.91012	−	3.28098i	0.160569	−	0.134734i	0.719532	+	0.694459i	$0.244356\pi$
$594$		0			0
$595$	0.502868	+	2.85190i	0.0206156	+	0.116917i
$596$	−7.21767	−	12.5014i	−0.295647	−	0.512076i
$597$		0			0
$598$	8.46754	+	3.08193i	0.346264	+	0.126030i
$599$	33.6127	+	12.2340i	1.37338	+	0.499869i	0.920164	−	0.391532i	$-0.128055\pi$
$599$	33.6127	+	12.2340i	1.37338	+	0.499869i	0.453215	+	0.891401i	$0.350277\pi$
$600$		0			0
$601$	−17.1676	−	29.7352i	−0.700281	−	1.21292i	−0.968368	−	0.249528i	$-0.919725\pi$
$601$	−17.1676	−	29.7352i	−0.700281	−	1.21292i	0.268087	−	0.963395i	$-0.413609\pi$
$602$	0.262780	+	1.49030i	0.0107101	+	0.0607401i
$603$		0			0
$604$	−12.2858	+	10.3090i	−0.499901	+	0.419467i
$605$	−1.89108	+	10.7249i	−0.0768834	+	0.436027i
$606$		0			0
$607$	−3.43239			−0.139316			−0.0696582	−	0.997571i	$-0.522191\pi$
$607$	−3.43239			−0.139316			−0.0696582	+	0.997571i	$0.522191\pi$
$608$	6.26277	+	18.3470i	0.253989	+	0.744071i
$609$		0			0
$610$	1.07525	−	0.391360i	0.0435357	−	0.0158457i
$611$	3.85245	−	21.8483i	0.155853	−	0.883888i
$612$		0			0
$613$	21.5266	+	18.0630i	0.869451	+	0.729556i	0.963982	−	0.265966i	$-0.0856908\pi$
$613$	21.5266	+	18.0630i	0.869451	+	0.729556i	−0.0945313	+	0.995522i	$0.530135\pi$
$614$	7.32362	+	41.5343i	0.295557	+	1.67619i
$615$		0			0
$616$	−0.178194	+	0.308640i	−0.00717962	+	0.0124355i
$617$	−11.2044	−	4.07805i	−0.451070	−	0.164176i	0.106488	−	0.994314i	$-0.466039\pi$
$617$	−11.2044	−	4.07805i	−0.451070	−	0.164176i	−0.557558	+	0.830138i	$0.688262\pi$
$618$		0			0
$619$	13.9457	−	24.1547i	0.560525	−	0.970858i	−0.436926	−	0.899498i	$-0.643933\pi$
$619$	13.9457	−	24.1547i	0.560525	−	0.970858i	0.997451	−	0.0713602i	$-0.0227340\pi$
$620$	2.51245	+	4.35169i	0.100902	+	0.174768i
$621$		0			0
$622$	−7.20193	−	6.04314i	−0.288771	−	0.242308i
$623$	6.11318	−	5.12956i	0.244919	−	0.205512i
$624$		0			0
$625$	−0.939693	+	0.342020i	−0.0375877	+	0.0136808i
$626$	1.38242			0.0552527
$627$		0			0
$628$	−5.49345			−0.219212
$629$	−33.1113	+	12.0515i	−1.32023	+	0.480526i
$630$		0			0
$631$	14.3666	−	12.0550i	0.571927	−	0.479904i	−0.310358	−	0.950620i	$-0.600449\pi$
$631$	14.3666	−	12.0550i	0.571927	−	0.479904i	0.882285	+	0.470716i	$0.156004\pi$
$632$	−2.11095	−	1.77130i	−0.0839692	−	0.0704586i
$633$		0			0
$634$	−28.2278	−	48.8919i	−1.12107	−	1.94175i
$635$	1.48465	−	2.57148i	0.0589164	−	0.102046i
$636$		0			0
$637$	30.3529	+	11.0475i	1.20263	+	0.437720i
$638$	−0.893657	+	1.54786i	−0.0353802	+	0.0612803i
$639$		0			0
$640$	−2.26302	−	12.8342i	−0.0894539	−	0.507318i
$641$	16.7076	+	14.0193i	0.659909	+	0.553729i	0.910059	−	0.414478i	$-0.136036\pi$
$641$	16.7076	+	14.0193i	0.659909	+	0.553729i	−0.250151	+	0.968207i	$0.580480\pi$
$642$		0			0
$643$	−8.24656	+	46.7686i	−0.325213	+	1.84437i	0.182964	+	0.983120i	$0.441431\pi$
$643$	−8.24656	+	46.7686i	−0.325213	+	1.84437i	−0.508176	+	0.861253i	$0.669680\pi$
$644$	0.477378	−	0.173751i	0.0188113	−	0.00684676i
$645$		0			0
$646$	25.5025	−	29.1799i	1.00338	−	1.14807i
$647$	−35.0985			−1.37986			−0.689932	−	0.723874i	$-0.742360\pi$
$647$	−35.0985			−1.37986			−0.689932	+	0.723874i	$0.742360\pi$
$648$		0			0
$649$	−0.391294	+	2.21914i	−0.0153596	+	0.0871087i
$650$	−6.21844	+	5.21789i	−0.243907	+	0.204663i
$651$		0			0
$652$	−2.11471	−	11.9931i	−0.0828185	−	0.469687i
$653$	23.2582	+	40.2844i	0.910163	+	1.57645i	0.813833	+	0.581099i	$0.197377\pi$
$653$	23.2582	+	40.2844i	0.910163	+	1.57645i	0.0963305	+	0.995349i	$0.469289\pi$
$654$		0			0
$655$	−7.51285	−	2.73445i	−0.293551	−	0.106844i
$656$	36.9679	+	13.4552i	1.44335	+	0.525338i
$657$		0			0
$658$	−2.12412	−	3.67908i	−0.0828068	−	0.143426i
$659$	7.50737	+	42.5764i	0.292445	+	1.65854i	0.677407	+	0.735608i	$0.263103\pi$
$659$	7.50737	+	42.5764i	0.292445	+	1.65854i	−0.384962	+	0.922932i	$0.625785\pi$
$660$		0			0
$661$	−35.9309	+	30.1496i	−1.39755	+	1.17268i	−0.435376	+	0.900249i	$0.643385\pi$
$661$	−35.9309	+	30.1496i	−1.39755	+	1.17268i	−0.962174	+	0.272436i	$0.912171\pi$
$662$	−3.29405	+	18.6815i	−0.128027	+	0.726076i
$663$		0			0
$664$	1.67743			0.0650970
$665$	−0.0480853	+	2.38989i	−0.00186467	+	0.0926759i
$666$		0			0
$667$	−3.34347	+	1.21692i	−0.129460	+	0.0471194i
$668$	−0.508600	+	2.88441i	−0.0196783	+	0.111601i
$669$		0			0
$670$	10.0236	+	8.41081i	0.387246	+	0.324938i
$671$	−0.0390883	−	0.221681i	−0.00150899	−	0.00855789i
$672$		0			0
$673$	−7.15589	+	12.3944i	−0.275839	+	0.477768i	−0.970347	−	0.241718i	$-0.922289\pi$
$673$	−7.15589	+	12.3944i	−0.275839	+	0.477768i	0.694507	+	0.719486i	$0.255622\pi$
$674$	9.96036	+	3.62528i	0.383659	+	0.139640i
$675$		0			0
$676$	−4.27588	+	7.40605i	−0.164457	+	0.284848i
$677$	−13.8430	−	23.9767i	−0.532029	−	0.921501i	−0.999301	−	0.0373874i	$-0.988096\pi$
$677$	−13.8430	−	23.9767i	−0.532029	−	0.921501i	0.467272	−	0.884114i	$-0.345237\pi$
$678$		0			0
$679$	2.94963	+	2.47504i	0.113197	+	0.0949832i
$680$	−7.93760	+	6.66044i	−0.304393	+	0.255416i
$681$		0			0
$682$	3.15503	−	1.14834i	0.120812	−	0.0439721i
$683$	−20.0771			−0.768228			−0.384114	−	0.923286i	$-0.625493\pi$
$683$	−20.0771			−0.768228			−0.384114	+	0.923286i	$0.625493\pi$
$684$		0			0
$685$	−0.920774			−0.0351810
$686$	11.8854	−	4.32592i	0.453786	−	0.165164i
$687$		0			0
$688$	−6.24356	+	5.23897i	−0.238033	+	0.199734i
$689$	−24.8434	−	20.8461i	−0.946457	−	0.794172i
$690$		0			0
$691$	14.3678	+	24.8857i	0.546577	+	0.946698i	0.998506	+	0.0546446i	$0.0174026\pi$
$691$	14.3678	+	24.8857i	0.546577	+	0.946698i	−0.451929	+	0.892054i	$0.649264\pi$
$692$	1.04440	−	1.80895i	0.0397020	−	0.0687659i
$693$		0			0
$694$	27.7756	+	10.1095i	1.05435	+	0.383751i
$695$	0.0500270	−	0.0866493i	0.00189763	−	0.00328680i
$696$		0			0
$697$	−7.25468	−	41.1434i	−0.274791	−	1.55842i
$698$	−16.1432	−	13.5458i	−0.611031	−	0.512716i
$699$		0			0
$700$	−0.0794699	+	0.450696i	−0.00300368	+	0.0170347i
$701$	−25.2861	+	9.20337i	−0.955041	+	0.347607i	−0.772089	−	0.635515i	$-0.780788\pi$
$701$	−25.2861	+	9.20337i	−0.955041	+	0.347607i	−0.182953	+	0.983122i	$0.558566\pi$
$702$		0			0
$703$	−28.7391	+	4.47338i	−1.08392	+	0.168717i
$704$	−0.813858			−0.0306734
$705$		0			0
$706$	1.70390	−	9.66329i	0.0641271	−	0.363683i
$707$	−3.02749	+	2.54037i	−0.113861	+	0.0955404i
$708$		0			0
$709$	−1.74216	−	9.88027i	−0.0654281	−	0.371061i	−0.999888	−	0.0149918i	$-0.995228\pi$
$709$	−1.74216	−	9.88027i	−0.0654281	−	0.371061i	0.934460	−	0.356069i	$-0.115883\pi$
$710$	0.914913	+	1.58468i	0.0343361	+	0.0594718i
$711$		0			0
$712$	26.8318	+	9.76599i	1.00557	+	0.365996i
$713$	6.28078	+	2.28602i	0.235217	+	0.0856120i
$714$		0			0
$715$	0.798453	+	1.38296i	0.0298605	+	0.0517198i
$716$	0.727558	+	4.12619i	0.0271901	+	0.154203i
$717$		0			0
$718$	0.747441	−	0.627178i	0.0278943	−	0.0234061i
$719$	−4.57974	+	25.9730i	−0.170796	+	0.968630i	0.772090	+	0.635513i	$0.219211\pi$
$719$	−4.57974	+	25.9730i	−0.170796	+	0.968630i	−0.942886	+	0.333117i	$0.891900\pi$
$720$		0			0
$721$	−3.87995			−0.144497
$722$	25.3119	−	19.5595i	0.942011	−	0.727930i
$723$		0			0
$724$	4.25136	−	1.54737i	0.158001	−	0.0575075i
$725$	0.556593	−	3.15659i	0.0206713	−	0.117233i
$726$		0			0
$727$	−37.0863	−	31.1191i	−1.37546	−	1.15414i	−0.970860	−	0.239648i	$-0.922968\pi$
$727$	−37.0863	−	31.1191i	−1.37546	−	1.15414i	−0.404595	−	0.914496i	$-0.632588\pi$
$728$	−0.900920	−	5.10937i	−0.0333903	−	0.189366i
$729$		0			0
$730$	11.7442	−	20.3416i	0.434673	−	0.752875i
$731$	8.13342	+	2.96032i	0.300826	+	0.109492i
$732$		0			0
$733$	17.6687	−	30.6031i	0.652610	−	1.13035i	−0.329878	−	0.944024i	$-0.607008\pi$
$733$	17.6687	−	30.6031i	0.652610	−	1.13035i	0.982487	−	0.186329i	$-0.0596591\pi$
$734$	−6.65551	−	11.5277i	−0.245659	−	0.425495i
$735$		0			0
$736$	3.78199	+	3.17347i	0.139406	+	0.116976i
$737$	1.97186	−	1.65459i	0.0726344	−	0.0609475i
$738$		0			0
$739$	−18.2924	+	6.65787i	−0.672895	+	0.244914i	−0.655794	−	0.754940i	$-0.727666\pi$
$739$	−18.2924	+	6.65787i	−0.672895	+	0.244914i	−0.0171013	+	0.999854i	$0.505444\pi$
$740$	−5.56851			−0.204703
$741$		0			0
$742$	−6.21011			−0.227980
$743$	26.8764	−	9.78221i	0.986000	−	0.358875i	0.201830	−	0.979421i	$-0.435311\pi$
$743$	26.8764	−	9.78221i	0.986000	−	0.358875i	0.784170	+	0.620546i	$0.213089\pi$
$744$		0			0
$745$	13.2506	−	11.1186i	0.485466	−	0.407354i
$746$	10.7127	+	8.98899i	0.392218	+	0.329110i
$747$		0			0
$748$	−0.729796	−	1.26404i	−0.0266840	−	0.0462180i
$749$	1.78255	−	3.08748i	0.0651331	−	0.112814i
$750$		0			0
$751$	−44.7071	−	16.2721i	−1.63139	−	0.593776i	−0.645883	−	0.763436i	$-0.723511\pi$
$751$	−44.7071	−	16.2721i	−1.63139	−	0.593776i	−0.985503	+	0.169660i	$0.945733\pi$
$752$	11.4402	−	19.8151i	0.417182	−	0.722581i
$753$		0			0
$754$	−4.51820	−	25.6240i	−0.164543	−	0.933170i
$755$	−14.7217	−	12.3530i	−0.535778	−	0.449571i
$756$		0			0
$757$	2.06236	−	11.6962i	0.0749578	−	0.425107i	−0.924117	−	0.382109i	$-0.875198\pi$
$757$	2.06236	−	11.6962i	0.0749578	−	0.425107i	0.999075	−	0.0429980i	$-0.0136909\pi$
$758$	16.2840	−	5.92689i	0.591462	−	0.215274i
$759$		0			0
$760$	−7.49162	+	4.12662i	−0.271750	+	0.149688i
$761$	−28.1049			−1.01880			−0.509401	−	0.860530i	$-0.670133\pi$
$761$	−28.1049			−1.01880			−0.509401	+	0.860530i	$0.670133\pi$
$762$		0			0
$763$	1.68177	−	9.53778i	0.0608841	−	0.345291i
$764$	−3.82626	+	3.21061i	−0.138429	+	0.116156i
$765$		0			0
$766$	9.36368	+	53.1041i	0.338324	+	1.91873i
$767$	−16.4020	−	28.4091i	−0.592242	−	1.02579i
$768$		0			0
$769$	−52.0340	−	18.9388i	−1.87639	−	0.682952i	−0.957486	−	0.288481i	$-0.906850\pi$
$769$	−52.0340	−	18.9388i	−1.87639	−	0.682952i	−0.918909	−	0.394471i	$-0.870928\pi$
$770$	0.287348	+	0.104586i	0.0103553	+	0.00376902i
$771$		0			0
$772$	−0.904883	−	1.56730i	−0.0325674	−	0.0564085i
$773$	−3.10626	−	17.6165i	−0.111725	−	0.633621i	−0.988320	−	0.152393i	$-0.951302\pi$
$773$	−3.10626	−	17.6165i	−0.111725	−	0.633621i	0.876595	−	0.481228i	$-0.159809\pi$
$774$		0			0
$775$	−4.61251	+	3.87036i	−0.165686	+	0.139027i
$776$	−2.39241	+	13.5681i	−0.0858826	+	0.487065i
$777$		0			0
$778$	−51.5323			−1.84752
$779$	0.693708	−	34.4780i	0.0248547	−	1.23530i
$780$		0			0
$781$	0.338258	−	0.123116i	0.0121038	−	0.00440542i
$782$	1.71376	−	9.71921i	0.0612839	−	0.347558i
$783$		0			0
$784$	25.5192	+	21.4131i	0.911399	+	0.764755i
$785$	−1.14307	−	6.48265i	−0.0407978	−	0.231376i
$786$		0			0
$787$	−3.70147	+	6.41114i	−0.131943	+	0.228532i	−0.924426	−	0.381362i	$-0.875455\pi$
$787$	−3.70147	+	6.41114i	−0.131943	+	0.228532i	0.792482	+	0.609895i	$0.208788\pi$
$788$	12.9916	+	4.72855i	0.462806	+	0.168448i
$789$		0			0
$790$	−1.18221	+	2.04765i	−0.0420612	+	0.0728521i
$791$	1.33392	+	2.31042i	0.0474288	+	0.0821491i
$792$		0			0
$793$	2.51029	+	2.10639i	0.0891432	+	0.0748000i
$794$	−13.6974	+	11.4935i	−0.486102	+	0.407888i
$795$		0			0
$796$	−10.9633	+	3.99031i	−0.388584	+	0.141433i
$797$	−45.6568			−1.61725			−0.808624	−	0.588326i	$-0.799787\pi$
$797$	−45.6568			−1.61725			−0.808624	+	0.588326i	$0.799787\pi$
$798$		0			0
$799$	−24.2982			−0.859609
$800$	−4.17935	+	1.52116i	−0.147762	+	0.0537810i
$801$		0			0
$802$	−19.6484	+	16.4870i	−0.693809	+	0.582175i
$803$	−3.53965	−	2.97012i	−0.124911	−	0.104813i
$804$		0			0
$805$	0.304371	+	0.527185i	0.0107277	+	0.0185808i
$806$	−24.4389	+	42.3294i	−0.860823	+	1.49099i
$807$		0			0
$808$	−13.2882	−	4.83652i	−0.467478	−	0.170148i
$809$	−9.67626	+	16.7598i	−0.340199	+	0.589242i	−0.984469	−	0.175556i	$-0.943828\pi$
$809$	−9.67626	+	16.7598i	−0.340199	+	0.589242i	0.644270	+	0.764798i	$0.277161\pi$
$810$		0			0
$811$	3.61818	+	20.5197i	0.127052	+	0.720546i	0.980068	+	0.198662i	$0.0636595\pi$
$811$	3.61818	+	20.5197i	0.127052	+	0.720546i	−0.853016	+	0.521884i	$0.825229\pi$
$812$	−1.12371	−	0.942904i	−0.0394345	−	0.0330894i
$813$		0			0
$814$	−0.646099	+	3.66421i	−0.0226458	+	0.128431i
$815$	13.7127	−	4.99101i	0.480335	−	0.174828i
$816$		0			0
$817$	6.11417	+	3.69597i	0.213908	+	0.129306i
$818$	19.6378			0.686619
$819$		0			0
$820$	1.14648	−	6.50203i	0.0400369	−	0.227061i
$821$	23.4739	−	19.6969i	0.819244	−	0.687427i	−0.133551	−	0.991042i	$-0.542638\pi$
$821$	23.4739	−	19.6969i	0.819244	−	0.687427i	0.952795	+	0.303615i	$0.0981936\pi$
$822$		0			0
$823$	1.40229	+	7.95277i	0.0488807	+	0.277216i	0.999445	−	0.0333116i	$-0.0106054\pi$
$823$	1.40229	+	7.95277i	0.0488807	+	0.277216i	−0.950564	+	0.310528i	$0.899494\pi$
$824$	−6.94142	−	12.0229i	−0.241816	−	0.418837i
$825$		0			0
$826$	−5.90276	−	2.14843i	−0.205383	−	0.0747534i
$827$	−34.3375	−	12.4978i	−1.19403	−	0.434593i	−0.332895	−	0.942964i	$-0.608026\pi$
$827$	−34.3375	−	12.4978i	−1.19403	−	0.434593i	−0.861138	+	0.508371i	$0.830248\pi$
$828$		0			0
$829$	21.3514	+	36.9817i	0.741564	+	1.28443i	0.951783	+	0.306773i	$0.0992491\pi$
$829$	21.3514	+	36.9817i	0.741564	+	1.28443i	−0.210218	+	0.977654i	$0.567418\pi$
$830$	−0.249928	−	1.41741i	−0.00867514	−	0.0491992i
$831$		0			0
$832$	9.07604	−	7.61570i	0.314655	−	0.264027i
$833$	6.14317	−	34.8396i	0.212848	−	1.20712i
$834$		0			0
$835$	−3.50963			−0.121456
$836$	−0.389207	−	1.14020i	−0.0134610	−	0.0394346i
$837$		0			0
$838$	−28.0072	+	10.1938i	−0.967492	+	0.352138i
$839$	−8.35614	+	47.3900i	−0.288486	+	1.63609i	0.404075	+	0.914726i	$0.367594\pi$
$839$	−8.35614	+	47.3900i	−0.288486	+	1.63609i	−0.692561	+	0.721360i	$0.743518\pi$
$840$		0			0
$841$	−14.3450	−	12.0369i	−0.494657	−	0.415066i
$842$	−6.02320	−	34.1593i	−0.207573	−	1.17721i
$843$		0			0
$844$	7.54471	−	13.0678i	0.259700	−	0.449813i
$845$	−9.62936	−	3.50480i	−0.331260	−	0.120569i
$846$		0			0
$847$	−2.98606	+	5.17201i	−0.102602	+	0.177712i
$848$	−16.7234	−	28.9658i	−0.574285	−	0.994690i
$849$		0			0
$850$	6.81067	+	5.71483i	0.233604	+	0.196017i
$851$	−5.67405	+	4.76110i	−0.194504	+	0.163208i
$852$		0			0
$853$	−30.4917	+	11.0981i	−1.04402	+	0.379991i	−0.806402	−	0.591368i	$-0.798588\pi$
$853$	−30.4917	+	11.0981i	−1.04402	+	0.379991i	−0.237615	+	0.971359i	$0.576366\pi$
$854$	0.627500			0.0214726
$855$		0			0
$856$	12.7563			0.436001
$857$	28.3576	−	10.3213i	0.968677	−	0.352569i	0.191249	−	0.981542i	$-0.438746\pi$
$857$	28.3576	−	10.3213i	0.968677	−	0.352569i	0.777428	+	0.628972i	$0.216524\pi$
$858$		0			0
$859$	20.3519	−	17.0772i	0.694396	−	0.582668i	−0.225777	−	0.974179i	$-0.572492\pi$
$859$	20.3519	−	17.0772i	0.694396	−	0.582668i	0.920173	+	0.391511i	$0.128048\pi$
$860$	1.04783	+	0.879234i	0.0357307	+	0.0299816i
$861$		0			0
$862$	−7.01353	−	12.1478i	−0.238882	−	0.413756i
$863$	5.77830	−	10.0083i	0.196696	−	0.340687i	−0.750759	−	0.660576i	$-0.770312\pi$
$863$	5.77830	−	10.0083i	0.196696	−	0.340687i	0.947455	+	0.319889i	$0.103646\pi$
$864$		0			0
$865$	2.35200	+	0.856059i	0.0799705	+	0.0291069i
$866$	23.7339	−	41.1083i	0.806510	−	1.39692i
$867$		0			0
$868$	0.478505	+	2.71374i	0.0162415	+	0.0921102i
$869$	0.356312	+	0.298982i	0.0120871	+	0.0101423i
$870$		0			0
$871$	−6.50709	+	36.9035i	−0.220484	+	1.25043i
$872$	32.5637	−	11.8522i	1.10275	−	0.401366i
$873$		0			0
$874$	2.93963	−	7.59744i	0.0994346	−	0.256987i
$875$	−0.548389			−0.0185389
$876$		0			0
$877$	3.15457	−	17.8905i	0.106522	−	0.604118i	−0.884079	−	0.467338i	$-0.845213\pi$
$877$	3.15457	−	17.8905i	0.106522	−	0.604118i	0.990601	−	0.136781i	$-0.0436756\pi$
$878$	−39.1847	+	32.8799i	−1.32242	+	1.10964i
$879$		0			0
$880$	0.285988	+	1.62192i	0.00964067	+	0.0546749i
$881$	−19.9306	−	34.5209i	−0.671480	−	1.16304i	−0.977484	−	0.211008i	$-0.932326\pi$
$881$	−19.9306	−	34.5209i	−0.671480	−	1.16304i	0.306004	−	0.952030i	$-0.401008\pi$
$882$		0			0
$883$	24.7626	+	9.01286i	0.833329	+	0.303307i	0.723224	−	0.690613i	$-0.242659\pi$
$883$	24.7626	+	9.01286i	0.833329	+	0.303307i	0.110104	+	0.993920i	$0.464882\pi$
$884$	19.9669	+	7.26737i	0.671561	+	0.244428i
$885$		0			0
$886$	−20.6417	−	35.7524i	−0.693470	−	1.20113i
$887$	−9.71703	−	55.1080i	−0.326266	−	1.85035i	−0.500626	−	0.865664i	$-0.666897\pi$
$887$	−9.71703	−	55.1080i	−0.326266	−	1.85035i	0.174360	−	0.984682i	$-0.444214\pi$
$888$		0			0
$889$	1.24737	−	1.04667i	0.0418355	−	0.0351042i
$890$	4.25437	−	24.1277i	0.142607	−	0.808763i
$891$		0			0
$892$	21.9203			0.733947
$893$	−19.6778	−	3.87941i	−0.658492	−	0.129820i
$894$		0			0
$895$	−4.71780	+	1.71714i	−0.157699	+	0.0573976i
$896$	1.24102	−	7.03816i	0.0414595	−	0.235128i
$897$		0			0
$898$	31.8417	+	26.7183i	1.06257	+	0.891603i
$899$	−3.35136	−	19.0065i	−0.111774	−	0.633903i
$900$		0			0
$901$	−17.7597	+	30.7606i	−0.591660	+	1.02479i
$902$	−4.14546	−	1.50882i	−0.138029	−	0.0502384i
$903$		0			0
$904$	−4.77290	+	8.26690i	−0.158744	+	0.274953i
$905$	2.71062	+	4.69493i	0.0901040	+	0.156065i
$906$		0			0
$907$	−35.3239	−	29.6403i	−1.17291	−	0.984188i	−0.172910	−	0.984938i	$-0.555317\pi$
$907$	−35.3239	−	29.6403i	−1.17291	−	0.984188i	−1.00000		0.000749224i	$0.999762\pi$
$908$	−4.45841	+	3.74105i	−0.147958	+	0.124151i
$909$		0			0
$910$	−4.18314	+	1.52254i	−0.138670	+	0.0504716i
$911$	−1.40625			−0.0465912			−0.0232956	−	0.999729i	$-0.507416\pi$
$911$	−1.40625			−0.0465912			−0.0232956	+	0.999729i	$0.507416\pi$
$912$		0			0
$913$	−0.283137			−0.00937048
$914$	11.3352	−	4.12569i	0.374936	−	0.136466i
$915$		0			0
$916$	1.67807	−	1.40807i	0.0554449	−	0.0465238i
$917$	−3.35862	−	2.81822i	−0.110912	−	0.0930658i
$918$		0			0
$919$	−23.5177	−	40.7338i	−0.775777	−	1.34369i	−0.934357	−	0.356339i	$-0.884025\pi$
$919$	−23.5177	−	40.7338i	−0.775777	−	1.34369i	0.158579	−	0.987346i	$-0.449309\pi$
$920$	−1.08907	+	1.88632i	−0.0359055	+	0.0621901i
$921$		0			0
$922$	−34.3633	−	12.5072i	−1.13170	−	0.411903i
$923$	−2.62015	+	4.53823i	−0.0862432	+	0.149378i
$924$		0			0
$925$	−1.15869	−	6.57123i	−0.0380974	−	0.216061i
$926$	41.1786	+	34.5529i	1.35321	+	1.13548i
$927$		0			0
$928$	2.47548	−	14.0392i	0.0812617	−	0.460858i
$929$	−0.927569	+	0.337607i	−0.0304325	+	0.0110765i	−0.357192	−	0.934031i	$-0.616266\pi$
$929$	−0.927569	+	0.337607i	−0.0304325	+	0.0110765i	0.326759	+	0.945108i	$0.394043\pi$
$930$		0			0
$931$	10.5375	−	27.2339i	0.345351	−	0.892555i
$932$	22.2475			0.728741
$933$		0			0
$934$	−5.71210	+	32.3950i	−0.186906	+	1.06000i
$935$	1.33980	−	1.12423i	0.0438163	−	0.0367662i
$936$		0			0
$937$	−1.84463	−	10.4614i	−0.0602615	−	0.341760i	0.939739	−	0.341894i	$-0.111068\pi$
$937$	−1.84463	−	10.4614i	−0.0602615	−	0.341760i	−1.00000		0.000134284i	$0.999957\pi$
$938$	3.58781	+	6.21426i	0.117146	+	0.202903i
$939$		0			0
$940$	−3.60836	−	1.31333i	−0.117692	−	0.0428362i
$941$	−9.88893	−	3.59928i	−0.322370	−	0.117333i	0.175766	−	0.984432i	$-0.443760\pi$
$941$	−9.88893	−	3.59928i	−0.322370	−	0.117333i	−0.498136	+	0.867099i	$0.665982\pi$
$942$		0			0
$943$	−4.39104	−	7.60550i	−0.142992	−	0.247669i
$944$	−5.87483	−	33.3178i	−0.191210	−	1.08440i
$945$		0			0
$946$	0.700133	−	0.587481i	0.0227633	−	0.0191007i
$947$	−6.09701	+	34.5779i	−0.198126	+	1.12363i	0.709770	+	0.704434i	$0.248799\pi$
$947$	−6.09701	+	34.5779i	−0.198126	+	1.12363i	−0.907896	+	0.419196i	$0.862312\pi$
$948$		0			0
$949$	67.2667			2.18357
$950$	4.60317	+	5.71551i	0.149346	+	0.185435i
$951$		0			0
$952$	−5.33961	+	1.94346i	−0.173058	+	0.0629879i
$953$	−3.66011	+	20.7575i	−0.118563	+	0.672402i	0.866362	+	0.499417i	$0.166452\pi$
$953$	−3.66011	+	20.7575i	−0.118563	+	0.672402i	−0.984924	+	0.172985i	$0.944659\pi$
$954$		0			0
$955$	−4.58490	−	3.84719i	−0.148364	−	0.124492i
$956$	−1.89946	−	10.7724i	−0.0614329	−	0.348403i
$957$		0			0
$958$	10.3026	−	17.8447i	0.332863	−	0.576535i
$959$	−0.474491	−	0.172701i	−0.0153221	−	0.00557679i
$960$		0			0
$961$	−2.62747	+	4.55092i	−0.0847572	+	0.146804i
$962$	−27.0828	−	46.9087i	−0.873183	−	1.51240i
$963$		0			0
$964$	−9.69287	−	8.13329i	−0.312186	−	0.261956i
$965$	1.66124	−	1.39395i	0.0534772	−	0.0448727i
$966$		0			0
$967$	−44.5471	+	16.2138i	−1.43254	+	0.521401i	−0.937658	−	0.347560i	$-0.887010\pi$
$967$	−44.5471	+	16.2138i	−1.43254	+	0.521401i	−0.494881	+	0.868961i	$0.664788\pi$
$968$	−21.3688			−0.686820
$969$		0			0
$970$	11.8213			0.379560
$971$	−30.6348	+	11.1502i	−0.983117	+	0.357825i	−0.783051	−	0.621957i	$-0.786338\pi$
$971$	−30.6348	+	11.1502i	−0.983117	+	0.357825i	−0.200066	+	0.979782i	$0.564116\pi$
$972$		0			0
$973$	0.0420317	−	0.0352688i	0.00134747	−	0.00113067i
$974$	18.1873	+	15.2609i	0.582757	+	0.488991i
$975$		0			0
$976$	1.68982	+	2.92685i	0.0540897	+	0.0936861i
$977$	−11.9957	+	20.7772i	−0.383777	+	0.664721i	−0.991599	−	0.129353i	$-0.958710\pi$
$977$	−11.9957	+	20.7772i	−0.383777	+	0.664721i	0.607822	+	0.794073i	$0.292043\pi$
$978$		0			0
$979$	−4.52900	−	1.64842i	−0.144748	−	0.0526838i
$980$	2.79538	−	4.84175i	0.0892953	−	0.154664i
$981$		0			0
$982$	−5.81398	−	32.9727i	−0.185532	−	1.05220i
$983$	−3.28438	−	2.75592i	−0.104756	−	0.0879003i	0.588906	−	0.808202i	$-0.299559\pi$
$983$	−3.28438	−	2.75592i	−0.104756	−	0.0879003i	−0.693661	+	0.720302i	$0.744003\pi$
$984$		0			0
$985$	−2.87675	+	16.3149i	−0.0916609	+	0.519835i
$986$	−26.7787	+	9.74663i	−0.852806	+	0.310396i
$987$		0			0
$988$	15.0098	+	9.07333i	0.477526	+	0.288661i
$989$	1.81944			0.0578547
$990$		0			0
$991$	−7.94255	+	45.0444i	−0.252303	+	1.43088i	0.550597	+	0.834771i	$0.314400\pi$
$991$	−7.94255	+	45.0444i	−0.252303	+	1.43088i	−0.802901	+	0.596113i	$0.796711\pi$
$992$	−20.5145	+	17.2137i	−0.651335	+	0.546535i
$993$		0			0
$994$	0.174248	+	0.988211i	0.00552682	+	0.0313442i
$995$	−6.99007	−	12.1072i	−0.221600	−	0.383822i
$996$		0			0
$997$	−11.2503	−	4.09478i	−0.356301	−	0.129683i	0.157667	−	0.987492i	$-0.449603\pi$
$997$	−11.2503	−	4.09478i	−0.356301	−	0.129683i	−0.513968	+	0.857809i	$0.671825\pi$
$998$	−11.7665	−	4.28267i	−0.372463	−	0.135566i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.bs.b.271.3		18
3.2	odd	2		95.2.k.b.81.1	yes	18
15.2	even	4		475.2.u.c.24.2		36
15.8	even	4		475.2.u.c.24.5		36
15.14	odd	2		475.2.l.b.176.3		18
19.4	even	9	inner	855.2.bs.b.631.3		18
57.2	even	18		1805.2.a.u.1.3		9
57.17	odd	18		1805.2.a.t.1.7		9
57.23	odd	18		95.2.k.b.61.1	✓	18
285.23	even	36		475.2.u.c.99.2		36
285.59	even	18		9025.2.a.cd.1.7		9
285.74	odd	18		9025.2.a.ce.1.3		9
285.137	even	36		475.2.u.c.99.5		36
285.194	odd	18		475.2.l.b.251.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.b.61.1	✓	18	57.23	odd	18
95.2.k.b.81.1	yes	18	3.2	odd	2
475.2.l.b.176.3		18	15.14	odd	2
475.2.l.b.251.3		18	285.194	odd	18
475.2.u.c.24.2		36	15.2	even	4
475.2.u.c.24.5		36	15.8	even	4
475.2.u.c.99.2		36	285.23	even	36
475.2.u.c.99.5		36	285.137	even	36
855.2.bs.b.271.3		18	1.1	even	1	trivial
855.2.bs.b.631.3		18	19.4	even	9	inner
1805.2.a.t.1.7		9	57.17	odd	18
1805.2.a.u.1.3		9	57.2	even	18
9025.2.a.cd.1.7		9	285.59	even	18
9025.2.a.ce.1.3		9	285.74	odd	18

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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.bs (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.58207 - 0.575828i) q^{2} +(0.639290 - 0.536428i) q^{4} +(0.766044 + 0.642788i) q^{5} +(0.274194 + 0.474919i) q^{7} +(-0.981094 + 1.69930i) q^{8} +O(q^{10})\)	\(q+(1.58207 - 0.575828i) q^{2} +(0.639290 - 0.536428i) q^{4} +(0.766044 + 0.642788i) q^{5} +(0.274194 + 0.474919i) q^{7} +(-0.981094 + 1.69930i) q^{8} +(1.58207 + 0.575828i) q^{10} +(0.165601 - 0.286829i) q^{11} +(0.837254 + 4.74830i) q^{13} +(0.707267 + 0.593468i) q^{14} +(-0.863487 + 4.89708i) q^{16} +(4.96227 - 1.80612i) q^{17} +(4.30704 - 0.670409i) q^{19} +0.834534 q^{20} +(0.0968286 - 0.549142i) q^{22} +(0.850350 - 0.713529i) q^{23} +(0.173648 + 0.984808i) q^{25} +(4.05880 + 7.03005i) q^{26} +(0.430050 + 0.156525i) q^{28} +(-3.01199 - 1.09627i) q^{29} +(3.01060 + 5.21452i) q^{31} +(0.772312 + 4.38000i) q^{32} +(6.81067 - 5.71483i) q^{34} +(-0.0952268 + 0.540058i) q^{35} -6.67261 q^{37} +(6.42801 - 3.54075i) q^{38} +(-1.84385 + 0.671108i) q^{40} +(1.37380 - 7.79121i) q^{41} +(1.25559 + 1.05356i) q^{43} +(-0.0479962 - 0.272200i) q^{44} +(0.934447 - 1.61851i) q^{46} +(-4.32380 - 1.57373i) q^{47} +(3.34963 - 5.80174i) q^{49} +(0.841804 + 1.45805i) q^{50} +(3.08237 + 2.58642i) q^{52} +(-5.15257 + 4.32352i) q^{53} +(0.311228 - 0.113278i) q^{55} -1.07604 q^{56} -5.39645 q^{58} +(-6.39331 + 2.32697i) q^{59} +(0.520640 - 0.436869i) q^{61} +(7.76566 + 6.51616i) q^{62} +(-1.22864 - 2.12807i) q^{64} +(-2.41078 + 4.17559i) q^{65} +(7.30324 + 2.65816i) q^{67} +(2.20348 - 3.81654i) q^{68} +(0.160324 + 0.909245i) q^{70} +(0.832574 + 0.698612i) q^{71} +(2.42261 - 13.7393i) q^{73} +(-10.5566 + 3.84227i) q^{74} +(2.39382 - 2.73900i) q^{76} +0.181627 q^{77} +(-0.243868 + 1.38304i) q^{79} +(-3.80925 + 3.19634i) q^{80} +(-2.31294 - 13.1173i) q^{82} +(-0.427439 - 0.740346i) q^{83} +(4.96227 + 1.80612i) q^{85} +(2.59310 + 0.943812i) q^{86} +(0.324940 + 0.562813i) q^{88} +(-2.52694 - 14.3310i) q^{89} +(-2.02549 + 1.69959i) q^{91} +(0.160864 - 0.912304i) q^{92} -7.74677 q^{94} +(3.73031 + 2.25495i) q^{95} +(6.59799 - 2.40147i) q^{97} +(1.95857 - 11.1076i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 3 q^{2} - 3 q^{4} + 12 q^{8}+O(q^{10}) \) 18 * q - 3 * q^2 - 3 * q^4 + 12 * q^8	\( 18 q - 3 q^{2} - 3 q^{4} + 12 q^{8} - 3 q^{10} - 3 q^{13} - 24 q^{14} + 21 q^{16} + 24 q^{17} - 12 q^{19} + 12 q^{20} + 15 q^{22} - 21 q^{23} + 21 q^{26} - 24 q^{28} + 9 q^{29} + 30 q^{31} - 45 q^{32} + 24 q^{34} + 6 q^{35} - 60 q^{37} + 15 q^{38} - 6 q^{40} + 6 q^{41} - 6 q^{43} + 30 q^{44} + 21 q^{46} - 33 q^{47} - 3 q^{49} + 9 q^{52} - 24 q^{53} - 3 q^{55} + 72 q^{56} + 36 q^{58} - 18 q^{59} + 6 q^{61} - 12 q^{62} - 24 q^{64} - 3 q^{65} - 24 q^{67} + 3 q^{68} + 39 q^{70} - 24 q^{71} + 6 q^{73} + 39 q^{74} + 27 q^{76} - 24 q^{77} + 9 q^{79} - 33 q^{80} - 57 q^{82} + 24 q^{85} + 33 q^{86} + 39 q^{88} + 6 q^{89} - 6 q^{91} + 66 q^{92} - 66 q^{94} + 15 q^{95} - 87 q^{97} - 39 q^{98}+O(q^{100}) \) 18 * q - 3 * q^2 - 3 * q^4 + 12 * q^8 - 3 * q^10 - 3 * q^13 - 24 * q^14 + 21 * q^16 + 24 * q^17 - 12 * q^19 + 12 * q^20 + 15 * q^22 - 21 * q^23 + 21 * q^26 - 24 * q^28 + 9 * q^29 + 30 * q^31 - 45 * q^32 + 24 * q^34 + 6 * q^35 - 60 * q^37 + 15 * q^38 - 6 * q^40 + 6 * q^41 - 6 * q^43 + 30 * q^44 + 21 * q^46 - 33 * q^47 - 3 * q^49 + 9 * q^52 - 24 * q^53 - 3 * q^55 + 72 * q^56 + 36 * q^58 - 18 * q^59 + 6 * q^61 - 12 * q^62 - 24 * q^64 - 3 * q^65 - 24 * q^67 + 3 * q^68 + 39 * q^70 - 24 * q^71 + 6 * q^73 + 39 * q^74 + 27 * q^76 - 24 * q^77 + 9 * q^79 - 33 * q^80 - 57 * q^82 + 24 * q^85 + 33 * q^86 + 39 * q^88 + 6 * q^89 - 6 * q^91 + 66 * q^92 - 66 * q^94 + 15 * q^95 - 87 * q^97 - 39 * q^98

Introduction

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