LMFDB - Embedded newform 414.2.i.h.325.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(55,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([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("414.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.i (of order $11$, degree $10$, 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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 8 x^{18} + 53 x^{16} + 358 x^{14} + 1753 x^{12} + 7149 x^{10} + 23268 x^{8} + 37292 x^{6} + \cdots + 58081 $ x^20 + 8x^18 + 53x^16 + 358x^14 + 1753x^12 + 7149x^10 + 23268x^8 + 37292x^6 + 19057x^4 - 81217*x^2 + 58081
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			325.1
Root			$-1.36939 + 1.58036i$ of defining polynomial
Character	$\chi$	$=$	414.325
Dual form			414.2.i.h.307.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.142315 + 0.989821i) q^{2} +(-0.959493 + 0.281733i) q^{4} +(0.144371 - 0.166613i) q^{5} +(-2.90511 + 1.86700i) q^{7} +(-0.415415 - 0.909632i) q^{8} +O(q^{10})$	\(q+(0.142315 + 0.989821i) q^{2} +(-0.959493 + 0.281733i) q^{4} +(0.144371 - 0.166613i) q^{5} +(-2.90511 + 1.86700i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(0.185463 + 0.119190i) q^{10} +(-0.752921 + 5.23668i) q^{11} +(-5.58133 - 3.58690i) q^{13} +(-2.26144 - 2.60984i) q^{14} +(0.841254 - 0.540641i) q^{16} +(4.80693 + 1.41144i) q^{17} +(-3.97286 + 1.16654i) q^{19} +(-0.0915825 + 0.200538i) q^{20} -5.29053 q^{22} +(1.48083 + 4.56148i) q^{23} +(0.704657 + 4.90100i) q^{25} +(2.75609 - 6.03499i) q^{26} +(2.26144 - 2.60984i) q^{28} +(-9.00371 - 2.64373i) q^{29} +(0.780797 + 1.70971i) q^{31} +(0.654861 + 0.755750i) q^{32} +(-0.712978 + 4.95887i) q^{34} +(-0.108347 + 0.753569i) q^{35} +(-0.918627 - 1.06015i) q^{37} +(-1.72006 - 3.76641i) q^{38} +(-0.211530 - 0.0621109i) q^{40} +(5.30573 - 6.12314i) q^{41} +(3.51819 - 7.70376i) q^{43} +(-0.752921 - 5.23668i) q^{44} +(-4.30431 + 2.11493i) q^{46} +4.00642 q^{47} +(2.04607 - 4.48027i) q^{49} +(-4.75083 + 1.39497i) q^{50} +(6.36579 + 1.86917i) q^{52} +(-5.79150 + 3.72197i) q^{53} +(0.763799 + 0.881471i) q^{55} +(2.90511 + 1.86700i) q^{56} +(1.33546 - 9.28831i) q^{58} +(10.8267 + 6.95787i) q^{59} +(5.14249 + 11.2605i) q^{61} +(-1.58119 + 1.01617i) q^{62} +(-0.654861 + 0.755750i) q^{64} +(-1.40340 + 0.412077i) q^{65} +(-0.339613 - 2.36206i) q^{67} -5.00987 q^{68} -0.761318 q^{70} +(-0.489545 - 3.40486i) q^{71} +(-1.30659 + 0.383649i) q^{73} +(0.918627 - 1.06015i) q^{74} +(3.48328 - 2.23857i) q^{76} +(-7.58958 - 16.6189i) q^{77} +(0.440420 + 0.283041i) q^{79} +(0.0313748 - 0.218216i) q^{80} +(6.81590 + 4.38031i) q^{82} +(4.44952 + 5.13502i) q^{83} +(0.929145 - 0.597125i) q^{85} +(8.12604 + 2.38602i) q^{86} +(5.07623 - 1.49052i) q^{88} +(-4.40900 + 9.65436i) q^{89} +22.9111 q^{91} +(-2.70597 - 3.95951i) q^{92} +(0.570173 + 3.96564i) q^{94} +(-0.379205 + 0.830343i) q^{95} +(6.92412 - 7.99086i) q^{97} +(4.72585 + 1.38764i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{7} + 2 q^{8}+O(q^{10}) $ 20 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 4 * q^7 + 2 * q^8	$ 20 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{7} + 2 q^{8} - 2 q^{10} - 2 q^{11} - 18 q^{14} - 2 q^{16} + 18 q^{17} + 16 q^{19} + 2 q^{20} + 24 q^{22} - 2 q^{23} + 38 q^{25} + 18 q^{28} - 30 q^{29} + 14 q^{31} + 2 q^{32} + 4 q^{34} + 48 q^{35} - 20 q^{37} - 16 q^{38} - 2 q^{40} - 12 q^{41} - 28 q^{43} - 2 q^{44} + 2 q^{46} + 32 q^{47} + 6 q^{49} + 6 q^{50} - 46 q^{53} - 28 q^{55} + 4 q^{56} - 14 q^{58} - 50 q^{61} + 8 q^{62} - 2 q^{64} + 16 q^{65} - 8 q^{67} - 48 q^{68} - 48 q^{70} + 12 q^{71} - 18 q^{73} + 20 q^{74} - 6 q^{76} - 4 q^{77} - 18 q^{79} + 2 q^{80} - 10 q^{82} - 44 q^{83} + 32 q^{85} + 28 q^{86} + 2 q^{88} + 44 q^{91} - 2 q^{92} + 12 q^{94} + 64 q^{95} + 14 q^{97} - 28 q^{98}+O(q^{100}) $ 20 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 4 * q^7 + 2 * q^8 - 2 * q^10 - 2 * q^11 - 18 * q^14 - 2 * q^16 + 18 * q^17 + 16 * q^19 + 2 * q^20 + 24 * q^22 - 2 * q^23 + 38 * q^25 + 18 * q^28 - 30 * q^29 + 14 * q^31 + 2 * q^32 + 4 * q^34 + 48 * q^35 - 20 * q^37 - 16 * q^38 - 2 * q^40 - 12 * q^41 - 28 * q^43 - 2 * q^44 + 2 * q^46 + 32 * q^47 + 6 * q^49 + 6 * q^50 - 46 * q^53 - 28 * q^55 + 4 * q^56 - 14 * q^58 - 50 * q^61 + 8 * q^62 - 2 * q^64 + 16 * q^65 - 8 * q^67 - 48 * q^68 - 48 * q^70 + 12 * q^71 - 18 * q^73 + 20 * q^74 - 6 * q^76 - 4 * q^77 - 18 * q^79 + 2 * q^80 - 10 * q^82 - 44 * q^83 + 32 * q^85 + 28 * q^86 + 2 * q^88 + 44 * q^91 - 2 * q^92 + 12 * q^94 + 64 * q^95 + 14 * q^97 - 28 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$1$	$e\left(\frac{8}{11}\right)$

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 $

$2$	0.142315	+	0.989821i	0.100632	+	0.699909i
$2$	0.142315	+	0.989821i	0.100632	+	0.699909i
$3$		0			0
$3$		0			0
$4$	−0.959493	+	0.281733i	−0.479746	+	0.140866i
$5$	0.144371	−	0.166613i	0.0645646	−	0.0745115i	−0.722548	−	0.691320i	$-0.757029\pi$
$5$	0.144371	−	0.166613i	0.0645646	−	0.0745115i	0.787113	+	0.616809i	$0.211575\pi$
$6$		0			0
$7$	−2.90511	+	1.86700i	−1.09803	+	0.705660i	−0.958653	−	0.284579i	$-0.908146\pi$
$7$	−2.90511	+	1.86700i	−1.09803	+	0.705660i	−0.139376	+	0.990239i	$0.544510\pi$
$8$	−0.415415	−	0.909632i	−0.146871	−	0.321603i
$9$		0			0
$10$	0.185463	+	0.119190i	0.0586486	+	0.0376911i
$11$	−0.752921	+	5.23668i	−0.227014	+	1.57892i	0.483569	+	0.875306i	$0.339340\pi$
$11$	−0.752921	+	5.23668i	−0.227014	+	1.57892i	−0.710583	+	0.703613i	$0.751569\pi$
$12$		0			0
$13$	−5.58133	−	3.58690i	−1.54798	−	0.994828i	−0.985821	−	0.167800i	$-0.946334\pi$
$13$	−5.58133	−	3.58690i	−1.54798	−	0.994828i	−0.562161	−	0.827028i	$-0.690030\pi$
$14$	−2.26144	−	2.60984i	−0.604395	−	0.697509i
$15$		0			0
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	4.80693	+	1.41144i	1.16585	+	0.342325i	0.806704	−	0.590956i	$-0.201249\pi$
$17$	4.80693	+	1.41144i	1.16585	+	0.342325i	0.359148	+	0.933281i	$0.383067\pi$
$18$		0			0
$19$	−3.97286	+	1.16654i	−0.911437	+	0.267622i	−0.703646	−	0.710551i	$-0.748446\pi$
$19$	−3.97286	+	1.16654i	−0.911437	+	0.267622i	−0.207791	+	0.978173i	$0.566627\pi$
$20$	−0.0915825	+	0.200538i	−0.0204785	+	0.0448416i
$21$		0			0
$22$	−5.29053			−1.12795
$23$	1.48083	+	4.56148i	0.308775	+	0.951135i
$23$	1.48083	+	4.56148i	0.308775	+	0.951135i
$24$		0			0
$25$	0.704657	+	4.90100i	0.140931	+	0.980200i
$26$	2.75609	−	6.03499i	0.540513	−	1.18356i
$27$		0			0
$28$	2.26144	−	2.60984i	0.427372	−	0.493213i
$29$	−9.00371	−	2.64373i	−1.67195	−	0.490928i	−0.697696	−	0.716394i	$-0.745792\pi$
$29$	−9.00371	−	2.64373i	−1.67195	−	0.490928i	−0.974251	+	0.225465i	$0.927610\pi$
$30$		0			0
$31$	0.780797	+	1.70971i	0.140235	+	0.307073i	0.966698	−	0.255918i	$-0.0823778\pi$
$31$	0.780797	+	1.70971i	0.140235	+	0.307073i	−0.826463	+	0.562991i	$0.809651\pi$
$32$	0.654861	+	0.755750i	0.115764	+	0.133599i
$33$		0			0
$34$	−0.712978	+	4.95887i	−0.122275	+	0.850440i
$35$	−0.108347	+	0.753569i	−0.0183140	+	0.127376i
$36$		0			0
$37$	−0.918627	−	1.06015i	−0.151021	−	0.174288i	0.675198	−	0.737637i	$-0.264058\pi$
$37$	−0.918627	−	1.06015i	−0.151021	−	0.174288i	−0.826219	+	0.563349i	$0.809513\pi$
$38$	−1.72006	−	3.76641i	−0.279031	−	0.610992i
$39$		0			0
$40$	−0.211530	−	0.0621109i	−0.0334459	−	0.00982059i
$41$	5.30573	−	6.12314i	0.828616	−	0.956273i	−0.170964	−	0.985277i	$-0.554688\pi$
$41$	5.30573	−	6.12314i	0.828616	−	0.956273i	0.999579	+	0.0290040i	$0.00923356\pi$
$42$		0			0
$43$	3.51819	−	7.70376i	0.536519	−	1.17481i	−0.426279	−	0.904592i	$-0.640176\pi$
$43$	3.51819	−	7.70376i	0.536519	−	1.17481i	0.962798	−	0.270221i	$-0.0870968\pi$
$44$	−0.752921	−	5.23668i	−0.113507	−	0.789460i
$45$		0			0
$46$	−4.30431	+	2.11493i	−0.634636	+	0.311829i
$47$	4.00642			0.584397			0.292198	−	0.956358i	$-0.405613\pi$
$47$	4.00642			0.584397			0.292198	+	0.956358i	$0.405613\pi$
$48$		0			0
$49$	2.04607	−	4.48027i	0.292296	−	0.640038i
$50$	−4.75083	+	1.39497i	−0.671869	+	0.197279i
$51$		0			0
$52$	6.36579	+	1.86917i	0.882777	+	0.259207i
$53$	−5.79150	+	3.72197i	−0.795524	+	0.511252i	−0.874152	−	0.485652i	$-0.838582\pi$
$53$	−5.79150	+	3.72197i	−0.795524	+	0.511252i	0.0786285	+	0.996904i	$0.474946\pi$
$54$		0			0
$55$	0.763799	+	0.881471i	0.102991	+	0.118857i
$56$	2.90511	+	1.86700i	0.388212	+	0.249489i
$57$		0			0
$58$	1.33546	−	9.28831i	0.175354	−	1.21961i
$59$	10.8267	+	6.95787i	1.40951	+	0.905838i	0.999979	−	0.00645778i	$-0.00205559\pi$
$59$	10.8267	+	6.95787i	1.40951	+	0.905838i	0.409532	+	0.912296i	$0.365692\pi$
$60$		0			0
$61$	5.14249	+	11.2605i	0.658429	+	1.44176i	0.883979	+	0.467526i	$0.154855\pi$
$61$	5.14249	+	11.2605i	0.658429	+	1.44176i	−0.225551	+	0.974231i	$0.572418\pi$
$62$	−1.58119	+	1.01617i	−0.200811	+	0.129053i
$63$		0			0
$64$	−0.654861	+	0.755750i	−0.0818576	+	0.0944687i
$65$	−1.40340	+	0.412077i	−0.174071	+	0.0511118i
$66$		0			0
$67$	−0.339613	−	2.36206i	−0.0414903	−	0.288572i	−0.999994	−	0.00349110i	$-0.998889\pi$
$67$	−0.339613	−	2.36206i	−0.0414903	−	0.288572i	0.958504	−	0.285081i	$-0.0920203\pi$
$68$	−5.00987			−0.607536
$69$		0			0
$70$	−0.761318			−0.0909949
$71$	−0.489545	−	3.40486i	−0.0580984	−	0.404083i	−0.998031	−	0.0627229i	$-0.980022\pi$
$71$	−0.489545	−	3.40486i	−0.0580984	−	0.404083i	0.939933	−	0.341360i	$-0.110888\pi$
$72$		0			0
$73$	−1.30659	+	0.383649i	−0.152925	+	0.0449027i	−0.357299	−	0.933990i	$-0.616302\pi$
$73$	−1.30659	+	0.383649i	−0.152925	+	0.0449027i	0.204374	+	0.978893i	$0.434484\pi$
$74$	0.918627	−	1.06015i	0.106788	−	0.123240i
$75$		0			0
$76$	3.48328	−	2.23857i	0.399560	−	0.256781i
$77$	−7.58958	−	16.6189i	−0.864912	−	1.89389i
$78$		0			0
$79$	0.440420	+	0.283041i	0.0495511	+	0.0318446i	0.565182	−	0.824966i	$-0.308806\pi$
$79$	0.440420	+	0.283041i	0.0495511	+	0.0318446i	−0.515631	+	0.856811i	$0.672442\pi$
$80$	0.0313748	−	0.218216i	0.00350781	−	0.0243973i
$81$		0			0
$82$	6.81590	+	4.38031i	0.752690	+	0.483724i
$83$	4.44952	+	5.13502i	0.488398	+	0.563642i	0.945437	−	0.325805i	$-0.105635\pi$
$83$	4.44952	+	5.13502i	0.488398	+	0.563642i	−0.457039	+	0.889447i	$0.651090\pi$
$84$		0			0
$85$	0.929145	−	0.597125i	0.100780	−	0.0647673i
$86$	8.12604	+	2.38602i	0.876253	+	0.257291i
$87$		0			0
$88$	5.07623	−	1.49052i	0.541128	−	0.158889i
$89$	−4.40900	+	9.65436i	−0.467353	+	1.02336i	0.518396	+	0.855140i	$0.326529\pi$
$89$	−4.40900	+	9.65436i	−0.467353	+	1.02336i	−0.985749	+	0.168220i	$0.946198\pi$
$90$		0			0
$91$	22.9111			2.40174
$92$	−2.70597	−	3.95951i	−0.282117	−	0.412808i
$93$		0			0
$94$	0.570173	+	3.96564i	0.0588089	+	0.409025i
$95$	−0.379205	+	0.830343i	−0.0389056	+	0.0851914i
$96$		0			0
$97$	6.92412	−	7.99086i	0.703038	−	0.811349i	−0.286121	−	0.958193i	$-0.592366\pi$
$97$	6.92412	−	7.99086i	0.703038	−	0.811349i	0.989160	+	0.146844i	$0.0469115\pi$
$98$	4.72585	+	1.38764i	0.477383	+	0.140172i
$99$		0			0
$100$	−2.05688	−	4.50395i	−0.205688	−	0.450395i
$101$	3.98647	+	4.60064i	0.396669	+	0.457780i	0.918589	−	0.395214i	$-0.129330\pi$
$101$	3.98647	+	4.60064i	0.396669	+	0.457780i	−0.521920	+	0.852994i	$0.674784\pi$
$102$		0			0
$103$	0.344276	−	2.39450i	0.0339226	−	0.235937i	−0.965805	−	0.259269i	$-0.916518\pi$
$103$	0.344276	−	2.39450i	0.0339226	−	0.235937i	0.999728	+	0.0233322i	$0.00742753\pi$
$104$	−0.944193	+	6.56701i	−0.0925858	+	0.643948i
$105$		0			0
$106$	−4.50830	−	5.20286i	−0.437885	−	0.505346i
$107$	2.11933	+	4.64068i	0.204883	+	0.448632i	0.983982	−	0.178270i	$-0.0570500\pi$
$107$	2.11933	+	4.64068i	0.204883	+	0.448632i	−0.779098	+	0.626902i	$0.784323\pi$
$108$		0			0
$109$	3.31586	+	0.973624i	0.317602	+	0.0932562i	0.436648	−	0.899632i	$-0.356166\pi$
$109$	3.31586	+	0.973624i	0.317602	+	0.0932562i	−0.119046	+	0.992889i	$0.537984\pi$
$110$	−0.763799	+	0.881471i	−0.0728253	+	0.0840449i
$111$		0			0
$112$	−1.43456	+	3.14124i	−0.135553	+	0.296820i
$113$	0.574492	+	3.99568i	0.0540437	+	0.375882i	0.998837	+	0.0482151i	$0.0153533\pi$
$113$	0.574492	+	3.99568i	0.0540437	+	0.375882i	−0.944793	+	0.327667i	$0.893738\pi$
$114$		0			0
$115$	0.973791	+	0.411819i	0.0908064	+	0.0384024i
$116$	9.38382			0.871266
$117$		0			0
$118$	−5.34626	+	11.7067i	−0.492163	+	1.07769i
$119$	−16.5998	+	4.87415i	−1.52170	+	0.446813i
$120$		0			0
$121$	−16.3015	−	4.78656i	−1.48196	−	0.435142i
$122$	−10.4140	+	6.69268i	−0.942841	+	0.605927i
$123$		0			0
$124$	−1.23085	−	1.42048i	−0.110534	−	0.127563i
$125$	1.84562	+	1.18611i	0.165077	+	0.106089i
$126$		0			0
$127$	−2.09947	+	14.6022i	−0.186298	+	1.29573i	0.655193	+	0.755461i	$0.272587\pi$
$127$	−2.09947	+	14.6022i	−0.186298	+	1.29573i	−0.841491	+	0.540271i	$0.818322\pi$
$128$	−0.841254	−	0.540641i	−0.0743570	−	0.0477863i
$129$		0			0
$130$	−0.607608	−	1.33048i	−0.0532907	−	0.116690i
$131$	−9.78066	+	6.28565i	−0.854541	+	0.549180i	−0.892988	−	0.450081i	$-0.851395\pi$
$131$	−9.78066	+	6.28565i	−0.854541	+	0.549180i	0.0384473	+	0.999261i	$0.487759\pi$
$132$		0			0
$133$	9.36368	−	10.8063i	0.811934	−	0.937021i
$134$	2.28969	−	0.672313i	0.197799	−	0.0580790i
$135$		0			0
$136$	−0.712978	−	4.95887i	−0.0611374	−	0.425220i
$137$	4.73449			0.404495			0.202247	−	0.979334i	$-0.435176\pi$
$137$	4.73449			0.404495			0.202247	+	0.979334i	$0.435176\pi$
$138$		0			0
$139$	−12.2073			−1.03541			−0.517706	−	0.855559i	$-0.673214\pi$
$139$	−12.2073			−1.03541			−0.517706	+	0.855559i	$0.673214\pi$
$140$	−0.108347	−	0.753569i	−0.00915698	−	0.0636882i
$141$		0			0
$142$	3.30054	−	0.969125i	0.276975	−	0.0813272i
$143$	22.9858	−	26.5270i	1.92217	−	2.21830i
$144$		0			0
$145$	−1.74035	+	1.11846i	−0.144528	+	0.0928828i
$146$	−0.565691	−	1.23869i	−0.0468169	−	0.102515i
$147$		0			0
$148$	1.18009	+	0.758401i	0.0970032	+	0.0623402i
$149$	2.45008	−	17.0407i	0.200718	−	1.39603i	−0.601441	−	0.798917i	$-0.705407\pi$
$149$	2.45008	−	17.0407i	0.200718	−	1.39603i	0.802160	−	0.597110i	$-0.203684\pi$
$150$		0			0
$151$	2.96138	+	1.90316i	0.240994	+	0.154877i	0.655563	−	0.755141i	$-0.272431\pi$
$151$	2.96138	+	1.90316i	0.240994	+	0.154877i	−0.414569	+	0.910018i	$0.636068\pi$
$152$	2.71151	+	3.12924i	0.219932	+	0.253815i
$153$		0			0
$154$	15.3696	−	9.87743i	1.23852	−	0.795946i
$155$	0.397584	+	0.116741i	0.0319347	+	0.00937687i
$156$		0			0
$157$	7.67026	−	2.25219i	0.612153	−	0.179744i	0.0390632	−	0.999237i	$-0.487563\pi$
$157$	7.67026	−	2.25219i	0.612153	−	0.179744i	0.573090	+	0.819492i	$0.305744\pi$
$158$	−0.217481	+	0.476218i	−0.0173019	+	0.0378859i
$159$		0			0
$160$	0.220460			0.0174289
$161$	−12.8183	−	10.4869i	−1.01022	−	0.826483i
$162$		0			0
$163$	−1.65406	−	11.5042i	−0.129556	−	0.901082i	−0.946118	−	0.323823i	$-0.895032\pi$
$163$	−1.65406	−	11.5042i	−0.129556	−	0.901082i	0.816562	−	0.577258i	$-0.195877\pi$
$164$	−3.36572	+	7.36990i	−0.262819	+	0.575493i
$165$		0			0
$166$	−4.44952	+	5.13502i	−0.345350	+	0.398555i
$167$	−4.53761	−	1.33236i	−0.351131	−	0.103101i	0.101411	−	0.994845i	$-0.467664\pi$
$167$	−4.53761	−	1.33236i	−0.351131	−	0.103101i	−0.452542	+	0.891743i	$0.649483\pi$
$168$		0			0
$169$	12.8850	+	28.2141i	0.991151	+	2.17032i
$170$	0.723279	+	0.834708i	0.0554729	+	0.0640192i
$171$		0			0
$172$	−1.20528	+	8.38289i	−0.0919016	+	0.639190i
$173$	1.58917	−	11.0529i	0.120823	−	0.840339i	−0.835805	−	0.549026i	$-0.814999\pi$
$173$	1.58917	−	11.0529i	0.120823	−	0.840339i	0.956628	−	0.291313i	$-0.0940921\pi$
$174$		0			0
$175$	−11.1973	−	12.9224i	−0.846435	−	0.976838i
$176$	2.19777	+	4.81244i	0.165663	+	0.362751i
$177$		0			0
$178$	−10.1836	−	2.99016i	−0.763290	−	0.224122i
$179$	−5.66522	+	6.53801i	−0.423438	+	0.488674i	−0.926881	−	0.375355i	$-0.877521\pi$
$179$	−5.66522	+	6.53801i	−0.423438	+	0.488674i	0.503443	+	0.864028i	$0.332066\pi$
$180$		0			0
$181$	−4.15569	+	9.09969i	−0.308890	+	0.676375i	−0.998874	−	0.0474504i	$-0.984890\pi$
$181$	−4.15569	+	9.09969i	−0.308890	+	0.676375i	0.689984	+	0.723825i	$0.257618\pi$
$182$	3.26059	+	22.6779i	0.241691	+	1.68100i
$183$		0			0
$184$	3.53411	−	3.24192i	0.260538	−	0.238998i
$185$	−0.309258			−0.0227371
$186$		0			0
$187$	−11.0105	+	24.1097i	−0.805169	+	1.76307i
$188$	−3.84413	+	1.12874i	−0.280362	+	0.0823218i
$189$		0			0
$190$	−0.875858	−	0.257175i	−0.0635414	−	0.0186575i
$191$	−10.0986	+	6.49000i	−0.730712	+	0.469600i	−0.852348	−	0.522975i	$-0.824822\pi$
$191$	−10.0986	+	6.49000i	−0.730712	+	0.469600i	0.121636	+	0.992575i	$0.461186\pi$
$192$		0			0
$193$	−12.8340	−	14.8112i	−0.923808	−	1.06613i	−0.997626	−	0.0688598i	$-0.978064\pi$
$193$	−12.8340	−	14.8112i	−0.923808	−	1.06613i	0.0738182	−	0.997272i	$-0.476482\pi$
$194$	8.89493	+	5.71643i	0.638619	+	0.410416i
$195$		0			0
$196$	−0.700952	+	4.87523i	−0.0500680	+	0.348231i
$197$	−8.50925	−	5.46856i	−0.606259	−	0.389619i	0.201194	−	0.979551i	$-0.435518\pi$
$197$	−8.50925	−	5.46856i	−0.606259	−	0.389619i	−0.807452	+	0.589933i	$0.799154\pi$
$198$		0			0
$199$	−7.59783	−	16.6369i	−0.538596	−	1.17936i	−0.961907	−	0.273377i	$-0.911860\pi$
$199$	−7.59783	−	16.6369i	−0.538596	−	1.17936i	0.423311	−	0.905984i	$-0.360868\pi$
$200$	4.16538	−	2.67693i	0.294537	−	0.189287i
$201$		0			0
$202$	−3.98647	+	4.60064i	−0.280487	+	0.323700i
$203$	31.0926	−	9.12962i	2.18228	−	0.640774i
$204$		0			0
$205$	−0.254201	−	1.76800i	−0.0177541	−	0.123483i
$206$	2.41912			0.168548
$207$		0			0
$208$	−6.63454			−0.460022
$209$	−3.11753	−	21.6829i	−0.215644	−	1.49984i
$210$		0			0
$211$	−24.8128	+	7.28568i	−1.70818	+	0.501567i	−0.982468	−	0.186431i	$-0.940308\pi$
$211$	−24.8128	+	7.28568i	−1.70818	+	0.501567i	−0.725713	+	0.687998i	$0.758490\pi$
$212$	4.50830	−	5.20286i	0.309632	−	0.357334i
$213$		0			0
$214$	−4.29184	+	2.75820i	−0.293384	+	0.188546i
$215$	−0.775621	−	1.69837i	−0.0528969	−	0.115828i
$216$		0			0
$217$	−5.46033	−	3.50914i	−0.370671	−	0.238216i
$218$	−0.491818	+	3.42067i	−0.0333101	+	0.231677i
$219$		0			0
$220$	−0.981198	−	0.630578i	−0.0661524	−	0.0425136i
$221$	−21.7664	−	25.1197i	−1.46416	−	1.68973i
$222$		0			0
$223$	1.85783	−	1.19395i	0.124409	−	0.0799530i	−0.476956	−	0.878927i	$-0.658260\pi$
$223$	1.85783	−	1.19395i	0.124409	−	0.0799530i	0.601365	+	0.798974i	$0.294624\pi$
$224$	−3.31343	−	0.972910i	−0.221388	−	0.0650053i
$225$		0			0
$226$	−3.87325	+	1.13729i	−0.257645	+	0.0756514i
$227$	0.733691	−	1.60656i	0.0486968	−	0.106631i	−0.883720	−	0.468016i	$-0.844969\pi$
$227$	0.733691	−	1.60656i	0.0486968	−	0.106631i	0.932417	+	0.361385i	$0.117696\pi$
$228$		0			0
$229$	−11.6895			−0.772465			−0.386232	−	0.922402i	$-0.626224\pi$
$229$	−11.6895			−0.772465			−0.386232	+	0.922402i	$0.626224\pi$
$230$	−0.269043	+	1.02249i	−0.0177402	+	0.0674208i
$231$		0			0
$232$	1.33546	+	9.28831i	0.0876771	+	0.609807i
$233$	−0.799821	+	1.75136i	−0.0523980	+	0.114736i	−0.934020	−	0.357220i	$-0.883725\pi$
$233$	−0.799821	+	1.75136i	−0.0523980	+	0.114736i	0.881622	+	0.471956i	$0.156452\pi$
$234$		0			0
$235$	0.578411	−	0.667521i	0.0377313	−	0.0435443i
$236$	−12.3484	−	3.62581i	−0.803810	−	0.236020i
$237$		0			0
$238$	−7.18694	−	15.7372i	−0.465860	−	1.02009i
$239$	10.1573	+	11.7221i	0.657019	+	0.758240i	0.982287	−	0.187381i	$-0.0600001\pi$
$239$	10.1573	+	11.7221i	0.657019	+	0.758240i	−0.325268	+	0.945622i	$0.605455\pi$
$240$		0			0
$241$	1.59314	−	11.0805i	0.102623	−	0.713758i	−0.871935	−	0.489622i	$-0.837135\pi$
$241$	1.59314	−	11.0805i	0.102623	−	0.713758i	0.974558	−	0.224136i	$-0.0719561\pi$
$242$	2.41789	−	16.8168i	0.155428	−	1.08103i
$243$		0			0
$244$	−8.10663	−	9.35555i	−0.518974	−	0.598928i
$245$	−0.451077	−	0.987722i	−0.0288183	−	0.0631032i
$246$		0			0
$247$	26.3581	+	7.73944i	1.67713	+	0.492448i
$248$	1.23085	−	1.42048i	0.0781590	−	0.0902003i
$249$		0			0
$250$	−0.911374	+	1.99563i	−0.0576404	+	0.126215i
$251$	4.28941	+	29.8335i	0.270745	+	1.88307i	0.440748	+	0.897631i	$0.354713\pi$
$251$	4.28941	+	29.8335i	0.270745	+	1.88307i	−0.170003	+	0.985443i	$0.554378\pi$
$252$		0			0
$253$	−25.0020	+	4.32021i	−1.57186	+	0.271610i
$254$	−14.7523			−0.925642
$255$		0			0
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	3.01139	−	0.884225i	0.187846	−	0.0551564i	−0.186457	−	0.982463i	$-0.559700\pi$
$257$	3.01139	−	0.884225i	0.187846	−	0.0551564i	0.374302	+	0.927307i	$0.377882\pi$
$258$		0			0
$259$	4.64802	+	1.36478i	0.288814	+	0.0848034i
$260$	1.23046	−	0.790770i	0.0763100	−	0.0490414i
$261$		0			0
$262$	−7.61361	−	8.78657i	−0.470370	−	0.542836i
$263$	22.4598	+	14.4340i	1.38493	+	0.890039i	0.999466	−	0.0326849i	$-0.0104058\pi$
$263$	22.4598	+	14.4340i	1.38493	+	0.890039i	0.385462	+	0.922724i	$0.374042\pi$
$264$		0			0
$265$	−0.215996	+	1.50228i	−0.0132685	+	0.0922845i
$266$	12.0289	+	7.73048i	0.737536	+	0.473986i
$267$		0			0
$268$	0.991326	+	2.17070i	0.0605549	+	0.132597i
$269$	−19.9599	+	12.8274i	−1.21698	+	0.782102i	−0.981812	−	0.189854i	$-0.939199\pi$
$269$	−19.9599	+	12.8274i	−1.21698	+	0.782102i	−0.235163	+	0.971956i	$0.575562\pi$
$270$		0			0
$271$	−5.35158	+	6.17605i	−0.325085	+	0.375169i	−0.894642	−	0.446783i	$-0.852569\pi$
$271$	−5.35158	+	6.17605i	−0.325085	+	0.375169i	0.569557	+	0.821952i	$0.307115\pi$
$272$	4.80693	−	1.41144i	0.291463	−	0.0855813i
$273$		0			0
$274$	0.673788	+	4.68630i	0.0407050	+	0.283110i
$275$	−26.1955			−1.57965
$276$		0			0
$277$	−13.4046			−0.805404			−0.402702	−	0.915331i	$-0.631929\pi$
$277$	−13.4046			−0.805404			−0.402702	+	0.915331i	$0.631929\pi$
$278$	−1.73728	−	12.0831i	−0.104195	−	0.724694i
$279$		0			0
$280$	0.730480	−	0.214488i	0.0436545	−	0.0128181i
$281$	4.20358	−	4.85119i	0.250765	−	0.289398i	−0.616385	−	0.787445i	$-0.711404\pi$
$281$	4.20358	−	4.85119i	0.250765	−	0.289398i	0.867150	+	0.498047i	$0.165949\pi$
$282$		0			0
$283$	4.04108	−	2.59705i	0.240217	−	0.154378i	−0.414993	−	0.909824i	$-0.636216\pi$
$283$	4.04108	−	2.59705i	0.240217	−	0.154378i	0.655211	+	0.755446i	$0.272580\pi$
$284$	1.42898	+	3.12902i	0.0847941	+	0.185673i
$285$		0			0
$286$	29.5282	+	18.9766i	1.74604	+	1.12211i
$287$	−3.98182	+	27.6942i	−0.235040	+	1.63474i
$288$		0			0
$289$	6.81311	+	4.37852i	0.400771	+	0.257560i
$290$	−1.35475	−	1.56347i	−0.0795537	−	0.0918098i
$291$		0			0
$292$	1.14558	−	0.736217i	0.0670398	−	0.0430838i
$293$	17.5106	+	5.14156i	1.02298	+	0.300373i	0.749852	−	0.661605i	$-0.230125\pi$
$293$	17.5106	+	5.14156i	1.02298	+	0.300373i	0.273125	+	0.961979i	$0.411943\pi$
$294$		0			0
$295$	2.72232	−	0.799347i	0.158500	−	0.0465398i
$296$	−0.582737	+	1.27601i	−0.0338709	+	0.0741669i
$297$		0			0
$298$	17.2159			0.997291
$299$	8.09658	−	30.7707i	0.468237	−	1.77952i
$300$		0			0
$301$	4.16220	+	28.9488i	0.239905	+	1.66858i
$302$	−1.46234	+	3.20208i	−0.0841484	+	0.184259i
$303$		0			0
$304$	−2.71151	+	3.12924i	−0.155516	+	0.179474i
$305$	2.61857	+	0.768881i	0.149939	+	0.0440260i
$306$		0			0
$307$	2.65435	+	5.81221i	0.151492	+	0.331720i	0.970129	−	0.242591i	$-0.0779973\pi$
$307$	2.65435	+	5.81221i	0.151492	+	0.331720i	−0.818637	+	0.574311i	$0.805270\pi$
$308$	11.9642	+	13.8074i	0.681724	+	0.786752i
$309$		0			0
$310$	−0.0589708	+	0.410151i	−0.00334931	+	0.0232950i
$311$	−3.15823	+	21.9660i	−0.179087	+	1.24558i	0.679795	+	0.733402i	$0.262069\pi$
$311$	−3.15823	+	21.9660i	−0.179087	+	1.24558i	−0.858882	+	0.512174i	$0.828840\pi$
$312$		0			0
$313$	0.669900	+	0.773106i	0.0378650	+	0.0436986i	0.774366	−	0.632738i	$-0.218069\pi$
$313$	0.669900	+	0.773106i	0.0378650	+	0.0436986i	−0.736501	+	0.676436i	$0.763523\pi$
$314$	3.32086	+	7.27167i	0.187407	+	0.410364i
$315$		0			0
$316$	−0.502322	−	0.147495i	−0.0282578	−	0.00829724i
$317$	17.7847	−	20.5246i	0.998886	−	1.15278i	0.0106333	−	0.999943i	$-0.496615\pi$
$317$	17.7847	−	20.5246i	0.998886	−	1.15278i	0.988252	−	0.152832i	$-0.0488393\pi$
$318$		0			0
$319$	20.6235	−	45.1591i	1.15469	−	2.52842i
$320$	0.0313748	+	0.218216i	0.00175390	+	0.0121987i
$321$		0			0
$322$	8.55593	−	14.1803i	0.476803	−	0.790234i
$323$	−20.7438			−1.15421
$324$		0			0
$325$	13.6465	−	29.8816i	0.756970	−	1.65753i
$326$	11.1517	−	3.27445i	0.617638	−	0.181355i
$327$		0			0
$328$	−7.77388	−	2.28262i	−0.429241	−	0.126036i
$329$	−11.6391	+	7.48000i	−0.641685	+	0.412386i
$330$		0			0
$331$	15.0842	+	17.4081i	0.829102	+	0.956835i	0.999593	−	0.0285243i	$-0.00908080\pi$
$331$	15.0842	+	17.4081i	0.829102	+	0.956835i	−0.170491	+	0.985359i	$0.554535\pi$
$332$	−5.71598	−	3.67344i	−0.313705	−	0.201606i
$333$		0			0
$334$	0.673032	−	4.68104i	0.0368267	−	0.256135i
$335$	−0.442580	−	0.284429i	−0.0241807	−	0.0155400i
$336$		0			0
$337$	7.32476	+	16.0390i	0.399005	+	0.873700i	0.997370	+	0.0724758i	$0.0230900\pi$
$337$	7.32476	+	16.0390i	0.399005	+	0.873700i	−0.598365	+	0.801224i	$0.704183\pi$
$338$	−26.0932	+	16.7691i	−1.41929	+	0.912119i
$339$		0			0
$340$	−0.723279	+	0.834708i	−0.0392253	+	0.0452684i
$341$	−9.54108	+	2.80151i	−0.516678	+	0.151710i
$342$		0			0
$343$	−1.01960	−	7.09144i	−0.0550530	−	0.382902i
$344$	−8.46910			−0.456623
$345$		0			0
$346$	11.1666			0.600320
$347$	−1.70297	−	11.8444i	−0.0914200	−	0.635840i	−0.983086	−	0.183146i	$-0.941372\pi$
$347$	−1.70297	−	11.8444i	−0.0914200	−	0.635840i	0.891666	−	0.452694i	$-0.149537\pi$
$348$		0			0
$349$	3.24084	−	0.951597i	0.173478	−	0.0509378i	−0.193840	−	0.981033i	$-0.562094\pi$
$349$	3.24084	−	0.951597i	0.173478	−	0.0509378i	0.367318	+	0.930095i	$0.380276\pi$
$350$	11.1973	−	12.9224i	0.598520	−	0.690729i
$351$		0			0
$352$	−4.45068	+	2.86028i	−0.237222	+	0.152453i
$353$	7.87774	+	17.2498i	0.419290	+	0.918116i	0.994945	+	0.100424i	$0.0320198\pi$
$353$	7.87774	+	17.2498i	0.419290	+	0.918116i	−0.575655	+	0.817693i	$0.695253\pi$
$354$		0			0
$355$	−0.637970	−	0.409998i	−0.0338599	−	0.0217605i
$356$	1.51046	−	10.5055i	0.0800540	−	0.556788i
$357$		0			0
$358$	−7.27771	−	4.67710i	−0.384639	−	0.247192i
$359$	−0.0880312	−	0.101593i	−0.00464611	−	0.00536189i	0.753422	−	0.657538i	$-0.228402\pi$
$359$	−0.0880312	−	0.101593i	−0.00464611	−	0.00536189i	−0.758068	+	0.652176i	$0.773856\pi$
$360$		0			0
$361$	−1.56100	+	1.00319i	−0.0821579	+	0.0527997i
$362$	−9.59848	−	2.81837i	−0.504485	−	0.148130i
$363$		0			0
$364$	−21.9831	+	6.45481i	−1.15223	+	0.338324i
$365$	−0.124712	+	0.273082i	−0.00652775	+	0.0142938i
$366$		0			0
$367$	−1.49129			−0.0778447			−0.0389224	−	0.999242i	$-0.512393\pi$
$367$	−1.49129			−0.0778447			−0.0389224	+	0.999242i	$0.512393\pi$
$368$	3.71188	+	3.03677i	0.193495	+	0.158302i
$369$		0			0
$370$	−0.0440120	−	0.306110i	−0.00228807	−	0.0159139i
$371$	9.87603	−	21.6255i	0.512738	−	1.12274i
$372$		0			0
$373$	10.7829	−	12.4441i	0.558316	−	0.644331i	−0.404484	−	0.914545i	$-0.632549\pi$
$373$	10.7829	−	12.4441i	0.558316	−	0.644331i	0.962800	+	0.270214i	$0.0870943\pi$
$374$	−25.4312	−	7.46728i	−1.31502	−	0.386124i
$375$		0			0
$376$	−1.66433	−	3.64437i	−0.0858312	−	0.187944i
$377$	40.7699	+	47.0510i	2.09976	+	2.42325i
$378$		0			0
$379$	−0.553053	+	3.84657i	−0.0284084	+	0.197585i	−0.999083	−	0.0428117i	$-0.986368\pi$
$379$	−0.553053	+	3.84657i	−0.0284084	+	0.197585i	0.970675	+	0.240397i	$0.0772775\pi$
$380$	0.129910	−	0.903543i	0.00666424	−	0.0463508i
$381$		0			0
$382$	−7.86113	−	9.07222i	−0.402210	−	0.464175i
$383$	−5.90892	−	12.9387i	−0.301932	−	0.661139i	0.696474	−	0.717582i	$-0.254751\pi$
$383$	−5.90892	−	12.9387i	−0.301932	−	0.661139i	−0.998406	+	0.0564436i	$0.982024\pi$
$384$		0			0
$385$	−3.86463	−	1.13476i	−0.196960	−	0.0578326i
$386$	12.8340	−	14.8112i	0.653231	−	0.753869i
$387$		0			0
$388$	−4.39236	+	9.61793i	−0.222988	+	0.488276i
$389$	2.55428	+	17.7654i	0.129507	+	0.900743i	0.946180	+	0.323641i	$0.104907\pi$
$389$	2.55428	+	17.7654i	0.129507	+	0.900743i	−0.816673	+	0.577101i	$0.804184\pi$
$390$		0			0
$391$	0.679991	+	24.0169i	0.0343886	+	1.21458i
$392$	−4.92536			−0.248768
$393$		0			0
$394$	4.20191	−	9.20089i	0.211689	−	0.463534i
$395$	0.110742	−	0.0325168i	0.00557203	−	0.00163610i
$396$		0			0
$397$	19.8789	+	5.83698i	0.997695	+	0.292950i	0.739510	−	0.673146i	$-0.235057\pi$
$397$	19.8789	+	5.83698i	0.997695	+	0.292950i	0.258185	+	0.966095i	$0.416876\pi$
$398$	15.3863	−	9.88818i	0.771246	−	0.495650i
$399$		0			0
$400$	3.24248	+	3.74202i	0.162124	+	0.187101i
$401$	23.6737	+	15.2141i	1.18221	+	0.759758i	0.975791	−	0.218706i	$-0.0701835\pi$
$401$	23.6737	+	15.2141i	1.18221	+	0.759758i	0.206416	+	0.978464i	$0.433820\pi$
$402$		0			0
$403$	1.77467	−	12.3431i	0.0884025	−	0.614853i
$404$	−5.12114	−	3.29116i	−0.254786	−	0.163741i
$405$		0			0
$406$	13.4616	+	29.4769i	0.668090	+	1.46291i
$407$	6.24333	−	4.01235i	0.309470	−	0.198885i
$408$		0			0
$409$	14.7514	−	17.0240i	0.729410	−	0.841784i	−0.262995	−	0.964797i	$-0.584710\pi$
$409$	14.7514	−	17.0240i	0.729410	−	0.841784i	0.992405	+	0.123013i	$0.0392557\pi$
$410$	1.71383	−	0.503227i	0.0846401	−	0.0248526i
$411$		0			0
$412$	0.344276	+	2.39450i	0.0169613	+	0.117968i
$413$	−44.4430			−2.18690
$414$		0			0
$415$	1.49794			0.0735310
$416$	−0.944193	−	6.56701i	−0.0462929	−	0.321974i
$417$		0			0
$418$	21.0186	−	6.17160i	1.02805	−	0.301863i
$419$	13.1138	−	15.1342i	0.640653	−	0.739353i	−0.338837	−	0.940845i	$-0.610034\pi$
$419$	13.1138	−	15.1342i	0.640653	−	0.739353i	0.979490	+	0.201492i	$0.0645791\pi$
$420$		0			0
$421$	16.8469	−	10.8269i	0.821070	−	0.527669i	−0.0613590	−	0.998116i	$-0.519543\pi$
$421$	16.8469	−	10.8269i	0.821070	−	0.527669i	0.882429	+	0.470446i	$0.155907\pi$
$422$	−10.7427	−	23.5233i	−0.522949	−	1.14510i
$423$		0			0
$424$	5.79150	+	3.72197i	0.281260	+	0.180755i
$425$	−3.53024	+	24.5534i	−0.171242	+	1.19101i
$426$		0			0
$427$	−35.9629	−	23.1119i	−1.74036	−	1.11846i
$428$	−3.34091	−	3.85562i	−0.161489	−	0.186368i
$429$		0			0
$430$	1.57070	−	1.00943i	0.0757461	−	0.0486791i
$431$	0.895958	+	0.263077i	0.0431568	+	0.0126720i	0.303240	−	0.952914i	$-0.401932\pi$
$431$	0.895958	+	0.263077i	0.0431568	+	0.0126720i	−0.260083	+	0.965586i	$0.583750\pi$
$432$		0			0
$433$	23.9187	−	7.02317i	1.14946	−	0.337512i	0.349132	−	0.937074i	$-0.386477\pi$
$433$	23.9187	−	7.02317i	1.14946	−	0.337512i	0.800329	+	0.599562i	$0.204658\pi$
$434$	2.69634	−	5.90415i	0.129428	−	0.283408i
$435$		0			0
$436$	−3.45584			−0.165505
$437$	−11.2043	−	16.3947i	−0.535974	−	0.784265i
$438$		0			0
$439$	1.46226	+	10.1703i	0.0697899	+	0.485400i	0.994501	+	0.104729i	$0.0333976\pi$
$439$	1.46226	+	10.1703i	0.0697899	+	0.485400i	−0.924711	+	0.380670i	$0.875693\pi$
$440$	0.484520	−	1.06095i	0.0230986	−	0.0505789i
$441$		0			0
$442$	21.7664	−	25.1197i	1.03532	−	1.19482i
$443$	−27.6225	−	8.11070i	−1.31238	−	0.385351i	−0.450646	−	0.892703i	$-0.648806\pi$
$443$	−27.6225	−	8.11070i	−1.31238	−	0.385351i	−0.861739	+	0.507352i	$0.830624\pi$
$444$		0			0
$445$	0.972010	+	2.12840i	0.0460777	+	0.100896i
$446$	1.44620	+	1.66900i	0.0684794	+	0.0790295i
$447$		0			0
$448$	0.491458	−	3.41816i	0.0232192	−	0.161493i
$449$	3.57436	−	24.8602i	0.168684	−	1.17323i	−0.712923	−	0.701242i	$-0.752629\pi$
$449$	3.57436	−	24.8602i	0.168684	−	1.17323i	0.881607	−	0.471983i	$-0.156462\pi$
$450$		0			0
$451$	28.0701	+	32.3947i	1.32177	+	1.52540i
$452$	−1.67693	−	3.67197i	−0.0788764	−	0.172715i
$453$		0			0
$454$	1.69462	+	0.497586i	0.0795325	+	0.0233529i
$455$	3.30770	−	3.81729i	0.155067	−	0.178957i
$456$		0			0
$457$	−2.54867	+	5.58081i	−0.119222	+	0.261059i	−0.959829	−	0.280586i	$-0.909471\pi$
$457$	−2.54867	+	5.58081i	−0.119222	+	0.261059i	0.840607	+	0.541645i	$0.182198\pi$
$458$	−1.66359	−	11.5705i	−0.0777345	−	0.540655i
$459$		0			0
$460$	−1.05037	−	0.120789i	−0.0489737	−	0.00563183i
$461$	9.53306			0.443999			0.222000	−	0.975047i	$-0.428742\pi$
$461$	9.53306			0.443999			0.222000	+	0.975047i	$0.428742\pi$
$462$		0			0
$463$	−11.4095	+	24.9834i	−0.530245	+	1.16107i	0.435168	+	0.900349i	$0.356689\pi$
$463$	−11.4095	+	24.9834i	−0.530245	+	1.16107i	−0.965413	+	0.260726i	$0.916038\pi$
$464$	−9.00371	+	2.64373i	−0.417987	+	0.122732i
$465$		0			0
$466$	−1.84736	−	0.542435i	−0.0855775	−	0.0251278i
$467$	−10.5006	+	6.74831i	−0.485909	+	0.312275i	−0.760558	−	0.649270i	$-0.775075\pi$
$467$	−10.5006	+	6.74831i	−0.485909	+	0.312275i	0.274649	+	0.961544i	$0.411438\pi$
$468$		0			0
$469$	5.39658	+	6.22799i	0.249191	+	0.287582i
$470$	0.743043	+	0.477525i	0.0342740	+	0.0220266i
$471$		0			0
$472$	1.83155	−	12.7387i	0.0843037	−	0.586345i
$473$	37.6932	+	24.2240i	1.73314	+	1.11382i
$474$		0			0
$475$	−8.51670	−	18.6490i	−0.390773	−	0.855674i
$476$	14.5542	−	9.35343i	0.667091	−	0.428714i
$477$		0			0
$478$	−10.1573	+	11.7221i	−0.464583	+	0.536157i
$479$	−20.5218	+	6.02574i	−0.937665	+	0.275323i	−0.714642	−	0.699490i	$-0.753410\pi$
$479$	−20.5218	+	6.02574i	−0.937665	+	0.275323i	−0.223022	+	0.974813i	$0.571592\pi$
$480$		0			0
$481$	1.32450	+	9.21208i	0.0603919	+	0.420035i
$482$	11.1945			0.509893
$483$		0			0
$484$	16.9897			0.772261
$485$	−0.331739	−	2.30730i	−0.0150635	−	0.104769i
$486$		0			0
$487$	0.353352	−	0.103753i	0.0160119	−	0.00470152i	−0.273717	−	0.961810i	$-0.588253\pi$
$487$	0.353352	−	0.103753i	0.0160119	−	0.00470152i	0.289729	+	0.957109i	$0.406435\pi$
$488$	8.10663	−	9.35555i	0.366970	−	0.423506i
$489$		0			0
$490$	0.913473	−	0.587053i	0.0412665	−	0.0265204i
$491$	−1.75794	−	3.84935i	−0.0793346	−	0.173719i	0.865808	−	0.500376i	$-0.166805\pi$
$491$	−1.75794	−	3.84935i	−0.0793346	−	0.173719i	−0.945143	+	0.326658i	$0.894078\pi$
$492$		0			0
$493$	−39.5488	−	25.4164i	−1.78119	−	1.14470i
$494$	−3.90951	+	27.1912i	−0.175897	+	1.22339i
$495$		0			0
$496$	1.58119	+	1.01617i	0.0709974	+	0.0456272i
$497$	7.77907	+	8.97752i	0.348939	+	0.402697i
$498$		0			0
$499$	15.7732	−	10.1368i	0.706105	−	0.453786i	−0.137673	−	0.990478i	$-0.543962\pi$
$499$	15.7732	−	10.1368i	0.706105	−	0.453786i	0.843779	+	0.536691i	$0.180326\pi$
$500$	−2.10502	−	0.618090i	−0.0941394	−	0.0276418i
$501$		0			0
$502$	−28.9194	+	8.49150i	−1.29074	+	0.378994i
$503$	3.41792	−	7.48420i	0.152398	−	0.333704i	−0.818000	−	0.575219i	$-0.804917\pi$
$503$	3.41792	−	7.48420i	0.152398	−	0.333704i	0.970397	+	0.241515i	$0.0776442\pi$
$504$		0			0
$505$	1.34206			0.0597207
$506$	−7.83440	−	24.1327i	−0.348281	−	1.07283i
$507$		0			0
$508$	−2.09947	−	14.6022i	−0.0931491	−	0.647866i
$509$	−2.00919	+	4.39950i	−0.0890556	+	0.195005i	−0.948919	−	0.315519i	$-0.897821\pi$
$509$	−2.00919	+	4.39950i	−0.0890556	+	0.195005i	0.859864	+	0.510524i	$0.170549\pi$
$510$		0			0
$511$	3.07951	−	3.55395i	0.136230	−	0.157217i
$512$	0.959493	+	0.281733i	0.0424040	+	0.0124509i
$513$		0			0
$514$	1.30379	+	2.85490i	0.0575078	+	0.125924i
$515$	−0.349250	−	0.403056i	−0.0153898	−	0.0177608i
$516$		0			0
$517$	−3.01652	+	20.9804i	−0.132666	+	0.922716i
$518$	−0.689408	+	4.79494i	−0.0302908	+	0.210677i
$519$		0			0
$520$	0.957834	+	1.10540i	0.0420038	+	0.0484750i
$521$	3.00410	+	6.57806i	0.131612	+	0.288190i	0.963952	−	0.266075i	$-0.0857268\pi$
$521$	3.00410	+	6.57806i	0.131612	+	0.288190i	−0.832340	+	0.554265i	$0.813000\pi$
$522$		0			0
$523$	−12.1931	−	3.58022i	−0.533168	−	0.156552i	0.00405605	−	0.999992i	$-0.498709\pi$
$523$	−12.1931	−	3.58022i	−0.533168	−	0.156552i	−0.537224	+	0.843439i	$0.680527\pi$
$524$	7.61361	−	8.78657i	0.332602	−	0.383843i
$525$		0			0
$526$	−11.0907	+	24.2853i	−0.483579	+	1.05889i
$527$	1.34009	+	9.32050i	0.0583750	+	0.406007i
$528$		0			0
$529$	−18.6143	+	13.5096i	−0.809316	+	0.587374i
$530$	−1.51773			−0.0659260
$531$		0			0
$532$	−5.93991	+	13.0066i	−0.257528	+	0.563907i
$533$	−51.5761	+	15.1441i	−2.23401	+	0.655964i
$534$		0			0
$535$	1.07917	+	0.316872i	0.0466564	+	0.0136996i
$536$	−2.00753	+	1.29016i	−0.0867119	+	0.0557264i
$537$		0			0
$538$	−15.5375	−	17.9312i	−0.669867	−	0.773068i
$539$	21.9212	+	14.0879i	0.944214	+	0.606809i
$540$		0			0
$541$	0.0106969	−	0.0743986i	0.000459896	−	0.00319865i	−0.989590	−	0.143914i	$-0.954031\pi$
$541$	0.0106969	−	0.0743986i	0.000459896	−	0.00319865i	0.990050	+	0.140715i	$0.0449402\pi$
$542$	−6.87480	−	4.41817i	−0.295298	−	0.189776i
$543$		0			0
$544$	2.08117	+	4.55713i	0.0892296	+	0.195386i
$545$	0.640931	−	0.411902i	0.0274545	−	0.0176439i
$546$		0			0
$547$	19.3741	−	22.3589i	0.828376	−	0.955997i	−0.171197	−	0.985237i	$-0.554763\pi$
$547$	19.3741	−	22.3589i	0.828376	−	0.955997i	0.999572	+	0.0292403i	$0.00930881\pi$
$548$	−4.54271	+	1.33386i	−0.194055	+	0.0569797i
$549$		0			0
$550$	−3.72801	−	25.9289i	−0.158963	−	1.10561i
$551$	38.8545			1.65526
$552$		0			0
$553$	−1.80791			−0.0768800
$554$	−1.90767	−	13.2682i	−0.0810492	−	0.563710i
$555$		0			0
$556$	11.7128	−	3.43920i	0.496735	−	0.145855i
$557$	16.0037	−	18.4693i	0.678099	−	0.782568i	−0.307522	−	0.951541i	$-0.599500\pi$
$557$	16.0037	−	18.4693i	0.678099	−	0.782568i	0.985621	+	0.168973i	$0.0540451\pi$
$558$		0			0
$559$	−47.2688	+	30.3778i	−1.99926	+	1.28484i
$560$	0.316263	+	0.692520i	0.0133646	+	0.0292643i
$561$		0			0
$562$	5.40005	+	3.47040i	0.227787	+	0.146390i
$563$	2.81112	−	19.5518i	0.118475	−	0.824008i	−0.840762	−	0.541405i	$-0.817893\pi$
$563$	2.81112	−	19.5518i	0.118475	−	0.824008i	0.959237	−	0.282604i	$-0.0911982\pi$
$564$		0			0
$565$	0.748671	+	0.481142i	0.0314968	+	0.0202418i
$566$	3.14572	+	3.63035i	0.132224	+	0.152595i
$567$		0			0
$568$	−2.89381	+	1.85974i	−0.121421	+	0.0780329i
$569$	29.4311	+	8.64176i	1.23382	+	0.362281i	0.832689	−	0.553741i	$-0.186800\pi$
$569$	29.4311	+	8.64176i	1.23382	+	0.362281i	0.401128	+	0.916022i	$0.368618\pi$
$570$		0			0
$571$	7.59233	−	2.22931i	0.317729	−	0.0932936i	−0.118980	−	0.992897i	$-0.537962\pi$
$571$	7.59233	−	2.22931i	0.317729	−	0.0932936i	0.436709	+	0.899603i	$0.356144\pi$
$572$	−14.5812	+	31.9283i	−0.609669	+	1.33499i
$573$		0			0
$574$	−27.9790			−1.16782
$575$	−21.3123	+	10.4718i	−0.888786	+	0.436706i
$576$		0			0
$577$	−3.22186	−	22.4086i	−0.134128	−	0.932881i	−0.940093	−	0.340918i	$-0.889262\pi$
$577$	−3.22186	−	22.4086i	−0.134128	−	0.932881i	0.805965	−	0.591963i	$-0.201647\pi$
$578$	−3.36435	+	7.36689i	−0.139938	+	0.306422i
$579$		0			0
$580$	1.35475	−	1.56347i	0.0562529	−	0.0649194i
$581$	−22.5134	−	6.61054i	−0.934015	−	0.274251i
$582$		0			0
$583$	−15.1302	−	33.1306i	−0.626631	−	1.37213i
$584$	0.891756	+	1.02914i	0.0369011	+	0.0425862i
$585$		0			0
$586$	−2.59722	+	18.0640i	−0.107290	+	0.746219i
$587$	−0.0815630	+	0.567283i	−0.00336647	+	0.0234143i	−0.991435	−	0.130598i	$-0.958310\pi$
$587$	−0.0815630	+	0.567283i	−0.00336647	+	0.0234143i	0.988069	+	0.154012i	$0.0492195\pi$
$588$		0			0
$589$	−5.09644	−	5.88160i	−0.209995	−	0.242347i
$590$	1.17864	+	2.58086i	0.0485237	+	0.106252i
$591$		0			0
$592$	−1.34596	−	0.395209i	−0.0553186	−	0.0162430i
$593$	−12.6191	+	14.5632i	−0.518205	+	0.598040i	−0.953180	−	0.302402i	$-0.902211\pi$
$593$	−12.6191	+	14.5632i	−0.518205	+	0.598040i	0.434976	+	0.900442i	$0.356757\pi$
$594$		0			0
$595$	−1.58444	+	3.46943i	−0.0649555	+	0.142233i
$596$	2.45008	+	17.0407i	0.100359	+	0.698013i
$597$		0			0
$598$	31.6098	+	3.63504i	1.29262	+	0.148648i
$599$	8.99662			0.367592			0.183796	−	0.982964i	$-0.441161\pi$
$599$	8.99662			0.367592			0.183796	+	0.982964i	$0.441161\pi$
$600$		0			0
$601$	4.60316	−	10.0795i	0.187767	−	0.411152i	−0.792214	−	0.610243i	$-0.791072\pi$
$601$	4.60316	−	10.0795i	0.187767	−	0.411152i	0.979981	+	0.199091i	$0.0637991\pi$
$602$	−28.0618	+	8.23967i	−1.14371	+	0.335824i
$603$		0			0
$604$	−3.37760	−	0.991754i	−0.137433	−	0.0403539i
$605$	−3.15097	+	2.02500i	−0.128105	+	0.0823282i
$606$		0			0
$607$	28.0949	+	32.4232i	1.14034	+	1.31602i	0.941896	+	0.335904i	$0.109042\pi$
$607$	28.0949	+	32.4232i	1.14034	+	1.31602i	0.198439	+	0.980113i	$0.436413\pi$
$608$	−3.48328	−	2.23857i	−0.141266	−	0.0907859i
$609$		0			0
$610$	−0.388394	+	2.70134i	−0.0157256	+	0.109374i
$611$	−22.3612	−	14.3706i	−0.904636	−	0.581374i
$612$		0			0
$613$	4.72678	+	10.3502i	0.190913	+	0.418041i	0.980748	−	0.195279i	$-0.0625611\pi$
$613$	4.72678	+	10.3502i	0.190913	+	0.418041i	−0.789835	+	0.613319i	$0.789834\pi$
$614$	−5.37530	+	3.45449i	−0.216929	+	0.139412i
$615$		0			0
$616$	−11.9642	+	13.8074i	−0.482052	+	0.556318i
$617$	36.5212	−	10.7236i	1.47029	−	0.431716i	0.554096	−	0.832453i	$-0.313064\pi$
$617$	36.5212	−	10.7236i	1.47029	−	0.431716i	0.916193	+	0.400737i	$0.131246\pi$
$618$		0			0
$619$	2.92551	+	20.3474i	0.117586	+	0.817830i	0.960200	+	0.279312i	$0.0901065\pi$
$619$	2.92551	+	20.3474i	0.117586	+	0.817830i	−0.842614	+	0.538518i	$0.818984\pi$
$620$	−0.414368			−0.0166414
$621$		0			0
$622$	−22.1919			−0.889813
$623$	−5.21608	−	36.2786i	−0.208978	−	1.45347i
$624$		0			0
$625$	−23.2901	+	6.83858i	−0.931603	+	0.273543i
$626$	−0.669900	+	0.773106i	−0.0267746	+	0.0308995i
$627$		0			0
$628$	−6.72505	+	4.32192i	−0.268359	+	0.172464i
$629$	−2.91943	−	6.39266i	−0.116405	−	0.254892i
$630$		0			0
$631$	−37.7583	−	24.2658i	−1.50313	−	0.966005i	−0.994468	−	0.105040i	$-0.966503\pi$
$631$	−37.7583	−	24.2658i	−1.50313	−	0.966005i	−0.508665	−	0.860965i	$-0.669861\pi$
$632$	0.0745058	−	0.518199i	0.00296368	−	0.0206129i
$633$		0			0
$634$	22.8467	+	14.6827i	0.907358	+	0.583124i
$635$	2.12980	+	2.45792i	0.0845187	+	0.0975398i
$636$		0			0
$637$	−27.4901	+	17.6668i	−1.08920	+	0.699984i
$638$	47.6344	+	13.9867i	1.88587	+	0.553740i
$639$		0			0
$640$	−0.211530	+	0.0621109i	−0.00836146	+	0.00245515i
$641$	−20.6359	+	45.1862i	−0.815067	+	1.78475i	−0.231184	+	0.972910i	$0.574260\pi$
$641$	−20.6359	+	45.1862i	−0.815067	+	1.78475i	−0.583883	+	0.811838i	$0.698467\pi$
$642$		0			0
$643$	19.7085			0.777229			0.388614	−	0.921400i	$-0.372954\pi$
$643$	19.7085			0.777229			0.388614	+	0.921400i	$0.372954\pi$
$644$	15.2536	+	6.45078i	0.601074	+	0.254196i
$645$		0			0
$646$	−2.95215	−	20.5326i	−0.116151	−	0.807846i
$647$	7.39110	−	16.1842i	0.290574	−	0.636268i	−0.706899	−	0.707314i	$-0.749907\pi$
$647$	7.39110	−	16.1842i	0.290574	−	0.636268i	0.997473	+	0.0710462i	$0.0226338\pi$
$648$		0			0
$649$	−44.5878	+	51.4571i	−1.75022	+	2.01987i
$650$	31.5196	+	9.25498i	1.23630	+	0.363010i
$651$		0			0
$652$	4.82818	+	10.5722i	0.189086	+	0.414041i
$653$	−8.28660	−	9.56324i	−0.324280	−	0.374239i	0.570079	−	0.821590i	$-0.306913\pi$
$653$	−8.28660	−	9.56324i	−0.324280	−	0.374239i	−0.894358	+	0.447352i	$0.852367\pi$
$654$		0			0
$655$	−0.364772	+	2.53705i	−0.0142528	+	0.0991307i
$656$	1.15304	−	8.01960i	0.0450188	−	0.313113i
$657$		0			0
$658$	−9.06028	−	10.4561i	−0.353206	−	0.407622i
$659$	5.26296	+	11.5243i	0.205016	+	0.448922i	0.984011	−	0.178108i	$-0.0569977\pi$
$659$	5.26296	+	11.5243i	0.205016	+	0.448922i	−0.778995	+	0.627030i	$0.784270\pi$
$660$		0			0
$661$	−23.4934	−	6.89829i	−0.913788	−	0.268312i	−0.209153	−	0.977883i	$-0.567071\pi$
$661$	−23.4934	−	6.89829i	−0.913788	−	0.268312i	−0.704634	+	0.709571i	$0.748889\pi$
$662$	−15.0842	+	17.4081i	−0.586264	+	0.676584i
$663$		0			0
$664$	2.82258	−	6.18059i	0.109537	−	0.239853i
$665$	−0.448619	−	3.12022i	−0.0173967	−	0.120997i
$666$		0			0
$667$	−1.27367	−	44.9852i	−0.0493167	−	1.74183i
$668$	4.72918			0.182977
$669$		0			0
$670$	0.218548	−	0.478553i	0.00844325	−	0.0184881i
$671$	−62.8395	+	18.4513i	−2.42589	+	0.712306i
$672$		0			0
$673$	−29.1581	−	8.56160i	−1.12396	−	0.330026i	−0.333631	−	0.942704i	$-0.608274\pi$
$673$	−29.1581	−	8.56160i	−1.12396	−	0.330026i	−0.790333	+	0.612678i	$0.790092\pi$
$674$	−14.8333	+	9.53279i	−0.571358	+	0.367189i
$675$		0			0
$676$	−20.3119	−	23.4412i	−0.781226	−	0.901583i
$677$	12.7871	+	8.21776i	0.491448	+	0.315834i	0.762787	−	0.646649i	$-0.223830\pi$
$677$	12.7871	+	8.21776i	0.491448	+	0.315834i	−0.271340	+	0.962484i	$0.587467\pi$
$678$		0			0
$679$	−5.19639	+	36.1417i	−0.199419	+	1.38699i
$680$	−0.929145	−	0.597125i	−0.0356311	−	0.0228987i
$681$		0			0
$682$	−4.13083	−	9.04527i	−0.158178	−	0.346361i
$683$	−10.2556	+	6.59089i	−0.392421	+	0.252194i	−0.721940	−	0.691955i	$-0.756750\pi$
$683$	−10.2556	+	6.59089i	−0.392421	+	0.252194i	0.329520	+	0.944149i	$0.393113\pi$
$684$		0			0
$685$	0.683522	−	0.788826i	0.0261160	−	0.0301395i
$686$	6.87416	−	2.01843i	0.262457	−	0.0770642i
$687$		0			0
$688$	−1.20528	−	8.38289i	−0.0459508	−	0.319595i
$689$	45.6746			1.74006
$690$		0			0
$691$	−9.72496			−0.369955			−0.184977	−	0.982743i	$-0.559221\pi$
$691$	−9.72496			−0.369955			−0.184977	+	0.982743i	$0.559221\pi$
$692$	1.58917	+	11.0529i	0.0604113	+	0.420170i
$693$		0			0
$694$	11.4815	−	3.37127i	0.435831	−	0.127972i
$695$	−1.76238	+	2.03390i	−0.0668509	+	0.0771501i
$696$		0			0
$697$	34.1467	−	21.9448i	1.29340	−	0.831217i
$698$	1.40313	+	3.07243i	0.0531093	+	0.116293i
$699$		0			0
$700$	14.3844	+	9.24427i	0.543678	+	0.349400i
$701$	−1.25167	+	8.70558i	−0.0472750	+	0.328805i	0.952435	+	0.304741i	$0.0985698\pi$
$701$	−1.25167	+	8.70558i	−0.0472750	+	0.328805i	−0.999710	+	0.0240645i	$0.992339\pi$
$702$		0			0
$703$	4.88628	+	3.14022i	0.184290	+	0.118436i
$704$	−3.46456	−	3.99832i	−0.130576	−	0.150692i
$705$		0			0
$706$	−15.9531	+	10.2525i	−0.600404	+	0.385856i
$707$	−20.1705	−	5.92260i	−0.758591	−	0.222742i
$708$		0			0
$709$	9.86156	−	2.89561i	0.370359	−	0.108747i	−0.0912565	−	0.995827i	$-0.529088\pi$
$709$	9.86156	−	2.89561i	0.370359	−	0.108747i	0.461615	+	0.887080i	$0.347270\pi$
$710$	0.315033	−	0.689825i	0.0118230	−	0.0258887i
$711$		0			0
$712$	10.6135			0.397757
$713$	−6.64257	+	6.09339i	−0.248766	+	0.228199i
$714$		0			0
$715$	−1.10126	−	7.65945i	−0.0411849	−	0.286447i
$716$	3.59377	−	7.86925i	0.134305	−	0.294088i
$717$		0			0
$718$	0.0880312	−	0.101593i	0.00328529	−	0.00379143i
$719$	−5.31043	−	1.55928i	−0.198046	−	0.0581514i	0.181205	−	0.983445i	$-0.442000\pi$
$719$	−5.31043	−	1.55928i	−0.198046	−	0.0581514i	−0.379251	+	0.925294i	$0.623818\pi$
$720$		0			0
$721$	3.47036	+	7.59904i	0.129243	+	0.283003i
$722$	−1.21514	−	1.40234i	−0.0452227	−	0.0521898i
$723$		0			0
$724$	1.42368	−	9.90188i	0.0529105	−	0.368000i
$725$	6.61238	−	45.9901i	0.245578	−	1.70803i
$726$		0			0
$727$	3.06666	+	3.53911i	0.113736	+	0.131258i	0.809763	−	0.586758i	$-0.199596\pi$
$727$	3.06666	+	3.53911i	0.113736	+	0.131258i	−0.696027	+	0.718016i	$0.745050\pi$
$728$	−9.51763	−	20.8407i	−0.352747	−	0.772408i
$729$		0			0
$730$	−0.288051	−	0.0845794i	−0.0106612	−	0.00313042i
$731$	27.7851	−	32.0657i	1.02767	−	1.18599i
$732$		0			0
$733$	7.75574	−	16.9827i	0.286465	−	0.627270i	−0.710620	−	0.703576i	$-0.751585\pi$
$733$	7.75574	−	16.9827i	0.286465	−	0.627270i	0.997084	+	0.0763061i	$0.0243126\pi$
$734$	−0.212233	−	1.47611i	−0.00783365	−	0.0544842i
$735$		0			0
$736$	−2.47760	+	4.10628i	−0.0913255	+	0.151359i
$737$	12.6251			0.465050
$738$		0			0
$739$	11.5687	−	25.3319i	0.425562	−	0.931851i	−0.568464	−	0.822708i	$-0.692462\pi$
$739$	11.5687	−	25.3319i	0.425562	−	0.931851i	0.994026	−	0.109143i	$-0.0348105\pi$
$740$	0.296731	−	0.0871280i	0.0109080	−	0.00320289i
$741$		0			0
$742$	22.8109	+	6.69788i	0.837413	+	0.245887i
$743$	5.79348	−	3.72324i	0.212542	−	0.136593i	−0.430039	−	0.902810i	$-0.641500\pi$
$743$	5.79348	−	3.72324i	0.212542	−	0.136593i	0.642581	+	0.766218i	$0.277864\pi$
$744$		0			0
$745$	−2.48548	−	2.86839i	−0.0910608	−	0.105090i
$746$	13.8520	+	8.90215i	0.507158	+	0.325931i
$747$		0			0
$748$	3.77204	−	26.2351i	0.137919	−	0.959250i
$749$	−14.8210	−	9.52491i	−0.541549	−	0.348033i
$750$		0			0
$751$	−11.7906	−	25.8177i	−0.430244	−	0.942103i	−0.993287	−	0.115675i	$-0.963097\pi$
$751$	−11.7906	−	25.8177i	−0.430244	−	0.942103i	0.563043	−	0.826428i	$-0.309630\pi$
$752$	3.37042	−	2.16604i	0.122906	−	0.0789872i
$753$		0			0
$754$	−40.7699	+	47.0510i	−1.48475	+	1.71349i
$755$	0.744628	−	0.218642i	0.0270998	−	0.00795721i
$756$		0			0
$757$	5.10040	+	35.4741i	0.185377	+	1.28933i	0.843791	+	0.536672i	$0.180319\pi$
$757$	5.10040	+	35.4741i	0.185377	+	1.28933i	−0.658414	+	0.752656i	$0.728772\pi$
$758$	−3.88613			−0.141150
$759$		0			0
$760$	0.912835			0.0331120
$761$	−0.516440	−	3.59192i	−0.0187209	−	0.130207i	0.978318	−	0.207110i	$-0.0664058\pi$
$761$	−0.516440	−	3.59192i	−0.0187209	−	0.130207i	−0.997039	+	0.0769032i	$0.975497\pi$
$762$		0			0
$763$	−11.4507	+	3.36223i	−0.414543	+	0.121721i
$764$	7.86113	−	9.07222i	0.284406	−	0.328222i
$765$		0			0
$766$	11.9661	−	7.69015i	0.432353	−	0.277856i
$767$	−35.4699	−	77.6683i	−1.28075	−	2.80444i
$768$		0			0
$769$	39.0781	+	25.1140i	1.40919	+	0.905633i	0.999977	−	0.00680480i	$-0.00216605\pi$
$769$	39.0781	+	25.1140i	1.40919	+	0.905633i	0.409216	+	0.912438i	$0.365802\pi$
$770$	0.573213	−	3.98678i	0.0206572	−	0.143674i
$771$		0			0
$772$	16.4869	+	10.5955i	0.593376	+	0.381339i
$773$	34.4794	+	39.7913i	1.24014	+	1.43119i	0.863128	+	0.504985i	$0.168502\pi$
$773$	34.4794	+	39.7913i	1.24014	+	1.43119i	0.377009	+	0.926209i	$0.376952\pi$
$774$		0			0
$775$	−7.82908	+	5.03145i	−0.281229	+	0.180735i
$776$	−10.1451	−	2.97888i	−0.364189	−	0.106936i
$777$		0			0
$778$	−17.2211	+	5.05657i	−0.617406	+	0.181287i
$779$	−13.9361	+	30.5157i	−0.499311	+	1.09334i
$780$		0			0
$781$	18.1988			0.651204
$782$	−23.6756	+	4.09102i	−0.846638	+	0.146295i
$783$		0			0
$784$	−0.700952	−	4.87523i	−0.0250340	−	0.174115i
$785$	0.732118	−	1.60311i	0.0261304	−	0.0572176i
$786$		0			0
$787$	−29.7760	+	34.3633i	−1.06140	+	1.22492i	−0.0879248	+	0.996127i	$0.528024\pi$
$787$	−29.7760	+	34.3633i	−1.06140	+	1.22492i	−0.973475	+	0.228794i	$0.926522\pi$
$788$	9.70523	+	2.84971i	0.345735	+	0.101517i
$789$		0			0
$790$	0.0479460	+	0.104987i	0.00170584	+	0.00373528i
$791$	−9.12890	−	10.5353i	−0.324586	−	0.374593i
$792$		0			0
$793$	11.6883	−	81.2941i	0.415065	−	2.88684i
$794$	−2.94850	+	20.5073i	−0.104638	+	0.727776i
$795$		0			0
$796$	11.9772	+	13.8225i	0.424522	+	0.489924i
$797$	−10.0784	−	22.0687i	−0.356996	−	0.781713i	−0.999876	−	0.0157455i	$-0.994988\pi$
$797$	−10.0784	−	22.0687i	−0.356996	−	0.781713i	0.642880	−	0.765967i	$-0.277739\pi$
$798$		0			0
$799$	19.2586	+	5.65484i	0.681320	+	0.200054i
$800$	−3.24248	+	3.74202i	−0.114639	+	0.132300i
$801$		0			0
$802$	−11.6902	+	25.5979i	−0.412794	+	0.903894i
$803$	−1.02529	−	7.13105i	−0.0361817	−	0.251649i
$804$		0			0
$805$	−3.59784	+	0.621688i	−0.126807	+	0.0219116i
$806$	12.4700			0.439237
$807$		0			0
$808$	2.52884	−	5.53740i	0.0889644	−	0.194805i
$809$	26.1352	−	7.67399i	0.918865	−	0.269803i	0.212097	−	0.977249i	$-0.431971\pi$
$809$	26.1352	−	7.67399i	0.918865	−	0.269803i	0.706768	+	0.707446i	$0.250153\pi$
$810$		0			0
$811$	18.0145	+	5.28954i	0.632575	+	0.185741i	0.582273	−	0.812993i	$-0.302163\pi$
$811$	18.0145	+	5.28954i	0.632575	+	0.185741i	0.0503020	+	0.998734i	$0.483982\pi$
$812$	−27.2611	+	17.5196i	−0.956675	+	0.614818i
$813$		0			0
$814$	4.86002	+	5.60877i	0.170344	+	0.196587i
$815$	−2.15555	−	1.38529i	−0.0755057	−	0.0485246i
$816$		0			0
$817$	−4.99056	+	34.7101i	−0.174597	+	1.21435i
$818$	18.9501	+	12.1785i	0.662575	+	0.425811i
$819$		0			0
$820$	0.742008	+	1.62477i	0.0259121	+	0.0567395i
$821$	−6.90382	+	4.43682i	−0.240945	+	0.154846i	−0.655541	−	0.755160i	$-0.727559\pi$
$821$	−6.90382	+	4.43682i	−0.240945	+	0.154846i	0.414596	+	0.910006i	$0.363923\pi$
$822$		0			0
$823$	23.0804	−	26.6362i	0.804532	−	0.928479i	−0.194089	−	0.980984i	$-0.562175\pi$
$823$	23.0804	−	26.6362i	0.804532	−	0.928479i	0.998621	+	0.0525047i	$0.0167205\pi$
$824$	−2.32113	+	0.681544i	−0.0808603	+	0.0237427i
$825$		0			0
$826$	−6.32490	−	43.9906i	−0.220071	−	1.53063i
$827$	−28.8088			−1.00178			−0.500890	−	0.865511i	$-0.666994\pi$
$827$	−28.8088			−1.00178			−0.500890	+	0.865511i	$0.666994\pi$
$828$		0			0
$829$	49.1166			1.70589			0.852945	−	0.522001i	$-0.174814\pi$
$829$	49.1166			1.70589			0.852945	+	0.522001i	$0.174814\pi$
$830$	0.213179	+	1.48269i	0.00739956	+	0.0514650i
$831$		0			0
$832$	6.36579	−	1.86917i	0.220694	−	0.0648016i
$833$	16.1590	−	18.6484i	0.559875	−	0.646130i
$834$		0			0
$835$	−0.877087	+	0.563670i	−0.0303529	+	0.0195066i
$836$	9.10004	+	19.9263i	0.314731	+	0.689166i
$837$		0			0
$838$	16.8464	+	10.8265i	0.581950	+	0.373996i
$839$	2.37350	−	16.5080i	0.0819423	−	0.569921i	−0.906944	−	0.421250i	$-0.861591\pi$
$839$	2.37350	−	16.5080i	0.0819423	−	0.569921i	0.988887	−	0.148671i	$-0.0474995\pi$
$840$		0			0
$841$	49.6812	+	31.9282i	1.71314	+	1.10097i
$842$	13.1142	+	15.1346i	0.451946	+	0.521574i
$843$		0			0
$844$	21.7551	−	13.9811i	0.748840	−	0.481250i
$845$	6.56105	+	1.92650i	0.225707	+	0.0662735i
$846$		0			0
$847$	56.2943	−	16.5295i	1.93429	−	0.567960i
$848$	−2.85987	+	6.26224i	−0.0982084	+	0.215046i
$849$		0			0
$850$	−24.8058			−0.850833
$851$	3.47553	−	5.76021i	0.119140	−	0.197457i
$852$		0			0
$853$	−0.294248	−	2.04654i	−0.0100749	−	0.0700722i	0.984164	−	0.177262i	$-0.0567239\pi$
$853$	−0.294248	−	2.04654i	−0.0100749	−	0.0700722i	−0.994239	+	0.107190i	$0.965815\pi$
$854$	17.7586	−	38.8860i	0.607688	−	1.33065i
$855$		0			0
$856$	3.34091	−	3.85562i	0.114190	−	0.131782i
$857$	−7.94775	−	2.33367i	−0.271490	−	0.0797166i	0.143154	−	0.989700i	$-0.454276\pi$
$857$	−7.94775	−	2.33367i	−0.271490	−	0.0797166i	−0.414644	+	0.909984i	$0.636094\pi$
$858$		0			0
$859$	15.4637	+	33.8607i	0.527614	+	1.15531i	0.966476	+	0.256758i	$0.0826544\pi$
$859$	15.4637	+	33.8607i	0.527614	+	1.15531i	−0.438862	+	0.898554i	$0.644618\pi$
$860$	1.22269	+	1.41106i	0.0416934	+	0.0481167i
$861$		0			0
$862$	−0.132891	+	0.924278i	−0.00452629	+	0.0314810i
$863$	4.94121	−	34.3668i	0.168201	−	1.16986i	−0.714400	−	0.699737i	$-0.753300\pi$
$863$	4.94121	−	34.3668i	0.168201	−	1.16986i	0.882601	−	0.470123i	$-0.155791\pi$
$864$		0			0
$865$	−1.61213	−	1.86050i	−0.0548141	−	0.0632588i
$866$	10.3557	+	22.6758i	0.351900	+	0.770554i
$867$		0			0
$868$	6.22779	+	1.82864i	0.211385	+	0.0620682i
$869$	−1.81380	+	2.09323i	−0.0615288	+	0.0710080i
$870$		0			0
$871$	−6.57699	+	14.4016i	−0.222853	+	0.487979i
$872$	−0.491818	−	3.42067i	−0.0166551	−	0.115838i
$873$		0			0
$874$	14.6333	−	13.4234i	0.494978	−	0.454055i
$875$	−7.57618			−0.256122
$876$		0			0
$877$	14.0346	−	30.7315i	0.473915	−	1.03773i	−0.510176	−	0.860070i	$-0.670420\pi$
$877$	14.0346	−	30.7315i	0.473915	−	1.03773i	0.984092	−	0.177660i	$-0.0568528\pi$
$878$	−9.85863	+	2.89476i	−0.332713	+	0.0976933i
$879$		0			0
$880$	1.11911	+	0.328600i	0.0377251	+	0.0110771i
$881$	−7.40682	+	4.76007i	−0.249542	+	0.160371i	−0.659432	−	0.751764i	$-0.729203\pi$
$881$	−7.40682	+	4.76007i	−0.249542	+	0.160371i	0.409890	+	0.912135i	$0.365567\pi$
$882$		0			0
$883$	−9.47371	−	10.9332i	−0.318816	−	0.367933i	0.573609	−	0.819129i	$-0.305543\pi$
$883$	−9.47371	−	10.9332i	−0.318816	−	0.367933i	−0.892425	+	0.451196i	$0.850997\pi$
$884$	27.9617	+	17.9699i	0.940454	+	0.604393i
$885$		0			0
$886$	4.09705	−	28.4956i	0.137643	−	0.957329i
$887$	20.1202	+	12.9304i	0.675569	+	0.434162i	0.832929	−	0.553379i	$-0.186662\pi$
$887$	20.1202	+	12.9304i	0.675569	+	0.434162i	−0.157360	+	0.987541i	$0.550298\pi$
$888$		0			0
$889$	−21.1630	−	46.3406i	−0.709786	−	1.55421i
$890$	−1.96841	+	1.26502i	−0.0659812	+	0.0424035i
$891$		0			0
$892$	−1.44620	+	1.66900i	−0.0484223	+	0.0558823i
$893$	−15.9170	+	4.67364i	−0.532641	+	0.156397i
$894$		0			0
$895$	0.271424	+	1.88780i	0.00907271	+	0.0631021i
$896$	3.45331			0.115367
$897$		0			0
$898$	25.1159			0.838127
$899$	−2.51007	−	17.4579i	−0.0837156	−	0.582255i
$900$		0			0
$901$	−33.0927	+	9.71689i	−1.10248	+	0.323717i
$902$	−28.0701	+	32.3947i	−0.934633	+	1.07862i
$903$		0			0
$904$	3.39595	−	2.18244i	0.112947	−	0.0725869i
$905$	0.916165	+	2.00612i	0.0304543	+	0.0666857i
$906$		0			0
$907$	−17.7025	−	11.3767i	−0.587802	−	0.377758i	0.212673	−	0.977123i	$-0.431783\pi$
$907$	−17.7025	−	11.3767i	−0.587802	−	0.377758i	−0.800475	+	0.599366i	$0.795419\pi$
$908$	−0.251351	+	1.74819i	−0.00834138	+	0.0580156i
$909$		0			0
$910$	4.24917	+	2.73077i	0.140859	+	0.0905243i
$911$	−13.6421	−	15.7438i	−0.451982	−	0.521615i	0.483330	−	0.875438i	$-0.339427\pi$
$911$	−13.6421	−	15.7438i	−0.451982	−	0.521615i	−0.935312	+	0.353823i	$0.884882\pi$
$912$		0			0
$913$	−30.2406	+	19.4345i	−1.00082	+	0.643187i
$914$	−5.88672	−	1.72850i	−0.194715	−	0.0571736i
$915$		0			0
$916$	11.2160	−	3.29332i	0.370587	−	0.108814i
$917$	16.6786	−	36.5210i	0.550776	−	1.20603i
$918$		0			0
$919$	−45.9764			−1.51662			−0.758311	−	0.651893i	$-0.773975\pi$
$919$	−45.9764			−1.51662			−0.758311	+	0.651893i	$0.773975\pi$
$920$	−0.0299232	−	1.05687i	−0.000986537	−	0.0348439i
$921$		0			0
$922$	1.35670	+	9.43603i	0.0446804	+	0.310759i
$923$	−9.48060	+	20.7596i	−0.312058	+	0.683311i
$924$		0			0
$925$	4.54848	−	5.24923i	0.149553	−	0.172594i
$926$	−26.3528	−	7.73788i	−0.866007	−	0.254283i
$927$		0			0
$928$	−3.89818	−	8.53583i	−0.127964	−	0.280202i
$929$	−12.5398	−	14.4718i	−0.411419	−	0.474803i	0.511785	−	0.859114i	$-0.328985\pi$
$929$	−12.5398	−	14.4718i	−0.411419	−	0.474803i	−0.923204	+	0.384311i	$0.874439\pi$
$930$		0			0
$931$	−2.90235	+	20.1863i	−0.0951208	+	0.661579i
$932$	0.274007	−	1.90576i	0.00897538	−	0.0624252i
$933$		0			0
$934$	−8.17401	−	9.43331i	−0.267462	−	0.308667i
$935$	2.42738	+	5.31523i	0.0793839	+	0.173826i
$936$		0			0
$937$	−16.8664	−	4.95241i	−0.551000	−	0.161788i	−0.00563064	−	0.999984i	$-0.501792\pi$
$937$	−16.8664	−	4.95241i	−0.551000	−	0.161788i	−0.545369	+	0.838196i	$0.683610\pi$
$938$	−5.39658	+	6.22799i	−0.176205	+	0.203351i
$939$		0			0
$940$	−0.366918	+	0.803439i	−0.0119676	+	0.0262053i
$941$	1.50432	+	10.4628i	0.0490395	+	0.341078i	0.999539	+	0.0303521i	$0.00966287\pi$
$941$	1.50432	+	10.4628i	0.0490395	+	0.341078i	−0.950500	+	0.310725i	$0.899428\pi$
$942$		0			0
$943$	35.7875	+	15.1347i	1.16540	+	0.492852i
$944$	12.8697			0.418872
$945$		0			0
$946$	−18.6131	+	40.7570i	−0.605164	+	1.32512i
$947$	37.5023	−	11.0117i	1.21866	−	0.357831i	0.391701	−	0.920093i	$-0.371887\pi$
$947$	37.5023	−	11.0117i	1.21866	−	0.357831i	0.826959	+	0.562262i	$0.190069\pi$
$948$		0			0
$949$	8.66861	+	2.54533i	0.281395	+	0.0826250i
$950$	17.2471	−	11.0840i	0.559570	−	0.359614i
$951$		0			0
$952$	11.3295	+	13.0749i	0.367191	+	0.423761i
$953$	−51.1129	−	32.8483i	−1.65571	−	1.06406i	−0.923962	−	0.382484i	$-0.875069\pi$
$953$	−51.1129	−	32.8483i	−1.65571	−	1.06406i	−0.731747	−	0.681576i	$-0.761295\pi$
$954$		0			0
$955$	−0.376631	+	2.61953i	−0.0121875	+	0.0847660i
$956$	−13.0483	−	8.38565i	−0.422013	−	0.271211i
$957$		0			0
$958$	−8.88496	−	19.4554i	−0.287060	−	0.628574i
$959$	−13.7542	+	8.83930i	−0.444147	+	0.285436i
$960$		0			0
$961$	17.9872	−	20.7584i	0.580233	−	0.669625i
$962$	−8.92982	+	2.62203i	−0.287909	+	0.0845377i
$963$		0			0
$964$	1.59314	+	11.0805i	0.0513115	+	0.356879i
$965$	−4.32058			−0.139084
$966$		0			0
$967$	19.5957			0.630155			0.315077	−	0.949066i	$-0.397970\pi$
$967$	19.5957			0.630155			0.315077	+	0.949066i	$0.397970\pi$
$968$	2.41789	+	16.8168i	0.0777140	+	0.540513i
$969$		0			0
$970$	2.23660	−	0.656725i	0.0718129	−	0.0210862i
$971$	15.1705	−	17.5077i	0.486845	−	0.561849i	−0.458175	−	0.888862i	$-0.651497\pi$
$971$	15.1705	−	17.5077i	0.486845	−	0.561849i	0.945020	+	0.327013i	$0.106042\pi$
$972$		0			0
$973$	35.4636	−	22.7911i	1.13691	−	0.730649i
$974$	0.152985	+	0.334990i	0.00490194	+	0.0107338i
$975$		0			0
$976$	10.4140	+	6.69268i	0.333345	+	0.214228i
$977$	−6.72588	+	46.7795i	−0.215180	+	1.49661i	0.540320	+	0.841460i	$0.318303\pi$
$977$	−6.72588	+	46.7795i	−0.215180	+	1.49661i	−0.755500	+	0.655149i	$0.772606\pi$
$978$		0			0
$979$	−47.2372	−	30.3575i	−1.50971	−	0.970230i
$980$	0.711079	+	0.820629i	0.0227146	+	0.0262140i
$981$		0			0
$982$	3.55998	−	2.28786i	0.113604	−	0.0730086i
$983$	42.8628	+	12.5856i	1.36711	+	0.401420i	0.881264	−	0.472624i	$-0.156693\pi$
$983$	42.8628	+	12.5856i	1.36711	+	0.401420i	0.485847	+	0.874044i	$0.338511\pi$
$984$		0			0
$985$	−2.13962	+	0.628249i	−0.0681739	+	0.0200177i
$986$	19.5294	−	42.7634i	0.621942	−	1.36186i
$987$		0			0
$988$	−27.4709			−0.873964
$989$	40.3504	+	4.64018i	1.28307	+	0.147549i
$990$		0			0
$991$	0.281511	+	1.95795i	0.00894250	+	0.0621965i	0.993804	−	0.111146i	$-0.0354522\pi$
$991$	0.281511	+	1.95795i	0.00894250	+	0.0621965i	−0.984862	+	0.173343i	$0.944543\pi$
$992$	−0.780797	+	1.70971i	−0.0247903	+	0.0542833i
$993$		0			0
$994$	−7.77907	+	8.97752i	−0.246737	+	0.284750i
$995$	−3.86883	−	1.13599i	−0.122650	−	0.0360133i
$996$		0			0
$997$	−5.90961	−	12.9402i	−0.187159	−	0.409821i	0.792672	−	0.609648i	$-0.208689\pi$
$997$	−5.90961	−	12.9402i	−0.187159	−	0.409821i	−0.979831	+	0.199827i	$0.935962\pi$
$998$	12.2784	+	14.1700i	0.388666	+	0.448544i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.i.h.325.1	yes	20
3.2	odd	2		414.2.i.g.325.2	yes	20
23.8	even	11	inner	414.2.i.h.307.1	yes	20
23.10	odd	22		9522.2.a.ch.1.5		10
23.13	even	11		9522.2.a.cg.1.6		10
69.8	odd	22		414.2.i.g.307.2	✓	20
69.56	even	22		9522.2.a.ci.1.6		10
69.59	odd	22		9522.2.a.cj.1.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.i.g.307.2	✓	20	69.8	odd	22
414.2.i.g.325.2	yes	20	3.2	odd	2
414.2.i.h.307.1	yes	20	23.8	even	11	inner
414.2.i.h.325.1	yes	20	1.1	even	1	trivial
9522.2.a.cg.1.6		10	23.13	even	11
9522.2.a.ch.1.5		10	23.10	odd	22
9522.2.a.ci.1.6		10	69.56	even	22
9522.2.a.cj.1.5		10	69.59	odd	22

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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.142315 + 0.989821i) q^{2} +(-0.959493 + 0.281733i) q^{4} +(0.144371 - 0.166613i) q^{5} +(-2.90511 + 1.86700i) q^{7} +(-0.415415 - 0.909632i) q^{8} +O(q^{10})\)	\(q+(0.142315 + 0.989821i) q^{2} +(-0.959493 + 0.281733i) q^{4} +(0.144371 - 0.166613i) q^{5} +(-2.90511 + 1.86700i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(0.185463 + 0.119190i) q^{10} +(-0.752921 + 5.23668i) q^{11} +(-5.58133 - 3.58690i) q^{13} +(-2.26144 - 2.60984i) q^{14} +(0.841254 - 0.540641i) q^{16} +(4.80693 + 1.41144i) q^{17} +(-3.97286 + 1.16654i) q^{19} +(-0.0915825 + 0.200538i) q^{20} -5.29053 q^{22} +(1.48083 + 4.56148i) q^{23} +(0.704657 + 4.90100i) q^{25} +(2.75609 - 6.03499i) q^{26} +(2.26144 - 2.60984i) q^{28} +(-9.00371 - 2.64373i) q^{29} +(0.780797 + 1.70971i) q^{31} +(0.654861 + 0.755750i) q^{32} +(-0.712978 + 4.95887i) q^{34} +(-0.108347 + 0.753569i) q^{35} +(-0.918627 - 1.06015i) q^{37} +(-1.72006 - 3.76641i) q^{38} +(-0.211530 - 0.0621109i) q^{40} +(5.30573 - 6.12314i) q^{41} +(3.51819 - 7.70376i) q^{43} +(-0.752921 - 5.23668i) q^{44} +(-4.30431 + 2.11493i) q^{46} +4.00642 q^{47} +(2.04607 - 4.48027i) q^{49} +(-4.75083 + 1.39497i) q^{50} +(6.36579 + 1.86917i) q^{52} +(-5.79150 + 3.72197i) q^{53} +(0.763799 + 0.881471i) q^{55} +(2.90511 + 1.86700i) q^{56} +(1.33546 - 9.28831i) q^{58} +(10.8267 + 6.95787i) q^{59} +(5.14249 + 11.2605i) q^{61} +(-1.58119 + 1.01617i) q^{62} +(-0.654861 + 0.755750i) q^{64} +(-1.40340 + 0.412077i) q^{65} +(-0.339613 - 2.36206i) q^{67} -5.00987 q^{68} -0.761318 q^{70} +(-0.489545 - 3.40486i) q^{71} +(-1.30659 + 0.383649i) q^{73} +(0.918627 - 1.06015i) q^{74} +(3.48328 - 2.23857i) q^{76} +(-7.58958 - 16.6189i) q^{77} +(0.440420 + 0.283041i) q^{79} +(0.0313748 - 0.218216i) q^{80} +(6.81590 + 4.38031i) q^{82} +(4.44952 + 5.13502i) q^{83} +(0.929145 - 0.597125i) q^{85} +(8.12604 + 2.38602i) q^{86} +(5.07623 - 1.49052i) q^{88} +(-4.40900 + 9.65436i) q^{89} +22.9111 q^{91} +(-2.70597 - 3.95951i) q^{92} +(0.570173 + 3.96564i) q^{94} +(-0.379205 + 0.830343i) q^{95} +(6.92412 - 7.99086i) q^{97} +(4.72585 + 1.38764i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{7} + 2 q^{8}+O(q^{10}) \) 20 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 4 * q^7 + 2 * q^8	\( 20 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{7} + 2 q^{8} - 2 q^{10} - 2 q^{11} - 18 q^{14} - 2 q^{16} + 18 q^{17} + 16 q^{19} + 2 q^{20} + 24 q^{22} - 2 q^{23} + 38 q^{25} + 18 q^{28} - 30 q^{29} + 14 q^{31} + 2 q^{32} + 4 q^{34} + 48 q^{35} - 20 q^{37} - 16 q^{38} - 2 q^{40} - 12 q^{41} - 28 q^{43} - 2 q^{44} + 2 q^{46} + 32 q^{47} + 6 q^{49} + 6 q^{50} - 46 q^{53} - 28 q^{55} + 4 q^{56} - 14 q^{58} - 50 q^{61} + 8 q^{62} - 2 q^{64} + 16 q^{65} - 8 q^{67} - 48 q^{68} - 48 q^{70} + 12 q^{71} - 18 q^{73} + 20 q^{74} - 6 q^{76} - 4 q^{77} - 18 q^{79} + 2 q^{80} - 10 q^{82} - 44 q^{83} + 32 q^{85} + 28 q^{86} + 2 q^{88} + 44 q^{91} - 2 q^{92} + 12 q^{94} + 64 q^{95} + 14 q^{97} - 28 q^{98}+O(q^{100}) \) 20 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 4 * q^7 + 2 * q^8 - 2 * q^10 - 2 * q^11 - 18 * q^14 - 2 * q^16 + 18 * q^17 + 16 * q^19 + 2 * q^20 + 24 * q^22 - 2 * q^23 + 38 * q^25 + 18 * q^28 - 30 * q^29 + 14 * q^31 + 2 * q^32 + 4 * q^34 + 48 * q^35 - 20 * q^37 - 16 * q^38 - 2 * q^40 - 12 * q^41 - 28 * q^43 - 2 * q^44 + 2 * q^46 + 32 * q^47 + 6 * q^49 + 6 * q^50 - 46 * q^53 - 28 * q^55 + 4 * q^56 - 14 * q^58 - 50 * q^61 + 8 * q^62 - 2 * q^64 + 16 * q^65 - 8 * q^67 - 48 * q^68 - 48 * q^70 + 12 * q^71 - 18 * q^73 + 20 * q^74 - 6 * q^76 - 4 * q^77 - 18 * q^79 + 2 * q^80 - 10 * q^82 - 44 * q^83 + 32 * q^85 + 28 * q^86 + 2 * q^88 + 44 * q^91 - 2 * q^92 + 12 * q^94 + 64 * q^95 + 14 * q^97 - 28 * q^98

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