LMFDB - Embedded newform 414.2.i.b.361.1

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:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 138)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			361.1
Root			$-0.841254 - 0.540641i$ of defining polynomial
Character	$\chi$	$=$	414.361
Dual form			414.2.i.b.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.654861 + 0.755750i) q^{2} +(-0.142315 - 0.989821i) q^{4} +(-0.810827 - 1.77546i) q^{5} +(0.439490 - 0.129046i) q^{7} +(0.841254 + 0.540641i) q^{8} +O(q^{10})$	\(q+(-0.654861 + 0.755750i) q^{2} +(-0.142315 - 0.989821i) q^{4} +(-0.810827 - 1.77546i) q^{5} +(0.439490 - 0.129046i) q^{7} +(0.841254 + 0.540641i) q^{8} +(1.87279 + 0.549899i) q^{10} +(0.824822 + 0.951895i) q^{11} +(-5.37459 - 1.57812i) q^{13} +(-0.190279 + 0.416652i) q^{14} +(-0.959493 + 0.281733i) q^{16} +(0.931360 - 6.47775i) q^{17} +(-0.301665 - 2.09813i) q^{19} +(-1.64200 + 1.05525i) q^{20} -1.25954 q^{22} +(-2.94130 - 3.78798i) q^{23} +(0.779471 - 0.899557i) q^{25} +(4.71228 - 3.02840i) q^{26} +(-0.190279 - 0.416652i) q^{28} +(0.720774 - 5.01310i) q^{29} +(-0.0916991 - 0.0589314i) q^{31} +(0.415415 - 0.909632i) q^{32} +(4.28565 + 4.94590i) q^{34} +(-0.585468 - 0.675666i) q^{35} +(-0.384727 + 0.842435i) q^{37} +(1.78321 + 1.14600i) q^{38} +(0.277777 - 1.93198i) q^{40} +(4.08750 + 8.95037i) q^{41} +(5.69889 - 3.66245i) q^{43} +(0.824822 - 0.951895i) q^{44} +(4.78890 + 0.257712i) q^{46} +2.50740 q^{47} +(-5.71228 + 3.67106i) q^{49} +(0.169395 + 1.17817i) q^{50} +(-0.797176 + 5.54448i) q^{52} +(-2.53893 + 0.745497i) q^{53} +(1.02127 - 2.23626i) q^{55} +(0.439490 + 0.129046i) q^{56} +(3.31664 + 3.82760i) q^{58} +(-4.10362 - 1.20493i) q^{59} +(-7.22296 - 4.64192i) q^{61} +(0.104588 - 0.0307097i) q^{62} +(0.415415 + 0.909632i) q^{64} +(1.55597 + 10.8220i) q^{65} +(9.84464 - 11.3613i) q^{67} -6.54436 q^{68} +0.894034 q^{70} +(-0.198713 + 0.229328i) q^{71} +(-0.476214 - 3.31214i) q^{73} +(-0.384727 - 0.842435i) q^{74} +(-2.03384 + 0.597190i) q^{76} +(0.485340 + 0.311909i) q^{77} +(7.72144 + 2.26722i) q^{79} +(1.27819 + 1.47511i) q^{80} +(-9.44098 - 2.77212i) q^{82} +(-4.35855 + 9.54389i) q^{83} +(-12.2562 + 3.59874i) q^{85} +(-0.964080 + 6.70533i) q^{86} +(0.179251 + 1.24672i) q^{88} +(-5.01143 + 3.22065i) q^{89} -2.56573 q^{91} +(-3.33083 + 3.45045i) q^{92} +(-1.64200 + 1.89497i) q^{94} +(-3.48055 + 2.23682i) q^{95} +(7.58500 + 16.6088i) q^{97} +(0.966346 - 6.72108i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - q^{4} - 2 q^{7} - q^{8}+O(q^{10}) $ 10 * q - q^2 - q^4 - 2 * q^7 - q^8	$ 10 q - q^{2} - q^{4} - 2 q^{7} - q^{8} + 11 q^{10} - 11 q^{11} - 13 q^{13} - 13 q^{14} - q^{16} - 2 q^{19} + 11 q^{20} - 22 q^{22} + 10 q^{23} + 5 q^{25} + 9 q^{26} - 13 q^{28} + 27 q^{29} - 18 q^{31} - q^{32} + 33 q^{34} - 44 q^{35} - q^{37} - 13 q^{38} - 11 q^{40} + 16 q^{41} + 20 q^{43} - 11 q^{44} - q^{46} - 19 q^{49} + 27 q^{50} - 2 q^{52} + q^{53} + 33 q^{55} - 2 q^{56} - 17 q^{58} + q^{59} - 34 q^{61} + 4 q^{62} - q^{64} - 11 q^{65} + 8 q^{67} - 22 q^{68} + 22 q^{70} + 22 q^{71} + 31 q^{73} - q^{74} - 2 q^{76} - 22 q^{77} + 32 q^{79} - 28 q^{82} - 33 q^{83} - 11 q^{85} + 20 q^{86} + 22 q^{88} + 23 q^{89} + 18 q^{91} - 23 q^{92} + 11 q^{94} + 22 q^{95} - q^{97} + 14 q^{98}+O(q^{100}) $ 10 * q - q^2 - q^4 - 2 * q^7 - q^8 + 11 * q^10 - 11 * q^11 - 13 * q^13 - 13 * q^14 - q^16 - 2 * q^19 + 11 * q^20 - 22 * q^22 + 10 * q^23 + 5 * q^25 + 9 * q^26 - 13 * q^28 + 27 * q^29 - 18 * q^31 - q^32 + 33 * q^34 - 44 * q^35 - q^37 - 13 * q^38 - 11 * q^40 + 16 * q^41 + 20 * q^43 - 11 * q^44 - q^46 - 19 * q^49 + 27 * q^50 - 2 * q^52 + q^53 + 33 * q^55 - 2 * q^56 - 17 * q^58 + q^59 - 34 * q^61 + 4 * q^62 - q^64 - 11 * q^65 + 8 * q^67 - 22 * q^68 + 22 * q^70 + 22 * q^71 + 31 * q^73 - q^74 - 2 * q^76 - 22 * q^77 + 32 * q^79 - 28 * q^82 - 33 * q^83 - 11 * q^85 + 20 * q^86 + 22 * q^88 + 23 * q^89 + 18 * q^91 - 23 * q^92 + 11 * q^94 + 22 * q^95 - q^97 + 14 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$47$	$235$
$\chi(n)$	$1$	$e\left(\frac{4}{11}\right)$

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 $

$2$	−0.654861	+	0.755750i	−0.463056	+	0.534396i
$2$	−0.654861	+	0.755750i	−0.463056	+	0.534396i
$3$		0			0
$3$		0			0
$4$	−0.142315	−	0.989821i	−0.0711574	−	0.494911i
$5$	−0.810827	−	1.77546i	−0.362613	−	0.794012i	−0.999730	−	0.0232445i	$-0.992600\pi$
$5$	−0.810827	−	1.77546i	−0.362613	−	0.794012i	0.637117	−	0.770767i	$-0.280127\pi$
$6$		0			0
$7$	0.439490	−	0.129046i	0.166112	−	0.0487748i	−0.197619	−	0.980279i	$-0.563321\pi$
$7$	0.439490	−	0.129046i	0.166112	−	0.0487748i	0.363731	+	0.931504i	$0.381503\pi$
$8$	0.841254	+	0.540641i	0.297428	+	0.191145i
$9$		0			0
$10$	1.87279	+	0.549899i	0.592227	+	0.173893i
$11$	0.824822	+	0.951895i	0.248693	+	0.287007i	0.866347	−	0.499443i	$-0.166462\pi$
$11$	0.824822	+	0.951895i	0.248693	+	0.287007i	−0.617654	+	0.786450i	$0.711917\pi$
$12$		0			0
$13$	−5.37459	−	1.57812i	−1.49064	−	0.437693i	−0.567897	−	0.823099i	$-0.692243\pi$
$13$	−5.37459	−	1.57812i	−1.49064	−	0.437693i	−0.922747	+	0.385407i	$0.874061\pi$
$14$	−0.190279	+	0.416652i	−0.0508541	+	0.111355i
$15$		0			0
$16$	−0.959493	+	0.281733i	−0.239873	+	0.0704331i
$17$	0.931360	−	6.47775i	0.225888	−	1.57109i	−0.489276	−	0.872129i	$-0.662739\pi$
$17$	0.931360	−	6.47775i	0.225888	−	1.57109i	0.715164	−	0.698956i	$-0.246352\pi$
$18$		0			0
$19$	−0.301665	−	2.09813i	−0.0692068	−	0.481344i	−0.994720	−	0.102628i	$-0.967275\pi$
$19$	−0.301665	−	2.09813i	−0.0692068	−	0.481344i	0.925513	−	0.378716i	$-0.123634\pi$
$20$	−1.64200	+	1.05525i	−0.367162	+	0.235961i
$21$		0			0
$22$	−1.25954			−0.268534
$23$	−2.94130	−	3.78798i	−0.613303	−	0.789848i
$23$	−2.94130	−	3.78798i	−0.613303	−	0.789848i
$24$		0			0
$25$	0.779471	−	0.899557i	0.155894	−	0.179911i
$26$	4.71228	−	3.02840i	0.924153	−	0.593917i
$27$		0			0
$28$	−0.190279	−	0.416652i	−0.0359593	−	0.0787398i
$29$	0.720774	−	5.01310i	0.133844	−	0.930909i	−0.806633	−	0.591053i	$-0.798713\pi$
$29$	0.720774	−	5.01310i	0.133844	−	0.930909i	0.940477	−	0.339856i	$-0.110378\pi$
$30$		0			0
$31$	−0.0916991	−	0.0589314i	−0.0164696	−	0.0105844i	0.532380	−	0.846505i	$-0.321298\pi$
$31$	−0.0916991	−	0.0589314i	−0.0164696	−	0.0105844i	−0.548850	+	0.835921i	$0.684934\pi$
$32$	0.415415	−	0.909632i	0.0734357	−	0.160802i
$33$		0			0
$34$	4.28565	+	4.94590i	0.734982	+	0.848215i
$35$	−0.585468	−	0.675666i	−0.0989621	−	0.114208i
$36$		0			0
$37$	−0.384727	+	0.842435i	−0.0632488	+	0.138496i	−0.938617	−	0.344962i	$-0.887892\pi$
$37$	−0.384727	+	0.842435i	−0.0632488	+	0.138496i	0.875368	+	0.483457i	$0.160619\pi$
$38$	1.78321	+	1.14600i	0.289275	+	0.185906i
$39$		0			0
$40$	0.277777	−	1.93198i	0.0439204	−	0.305473i
$41$	4.08750	+	8.95037i	0.638360	+	1.39781i	0.901382	+	0.433024i	$0.142553\pi$
$41$	4.08750	+	8.95037i	0.638360	+	1.39781i	−0.263022	+	0.964790i	$0.584719\pi$
$42$		0			0
$43$	5.69889	−	3.66245i	0.869072	−	0.558519i	−0.0283968	−	0.999597i	$-0.509040\pi$
$43$	5.69889	−	3.66245i	0.869072	−	0.558519i	0.897469	+	0.441078i	$0.145404\pi$
$44$	0.824822	−	0.951895i	0.124347	−	0.143504i
$45$		0			0
$46$	4.78890	+	0.257712i	0.706085	+	0.0379976i
$47$	2.50740			0.365742			0.182871	−	0.983137i	$-0.441461\pi$
$47$	2.50740			0.365742			0.182871	+	0.983137i	$0.441461\pi$
$48$		0			0
$49$	−5.71228	+	3.67106i	−0.816039	+	0.524437i
$50$	0.169395	+	1.17817i	0.0239561	+	0.166618i
$51$		0			0
$52$	−0.797176	+	5.54448i	−0.110548	+	0.768881i
$53$	−2.53893	+	0.745497i	−0.348749	+	0.102402i	−0.451415	−	0.892314i	$-0.649081\pi$
$53$	−2.53893	+	0.745497i	−0.348749	+	0.102402i	0.102666	+	0.994716i	$0.467263\pi$
$54$		0			0
$55$	1.02127	−	2.23626i	0.137708	−	0.301538i
$56$	0.439490	+	0.129046i	0.0587294	+	0.0172445i
$57$		0			0
$58$	3.31664	+	3.82760i	0.435496	+	0.502589i
$59$	−4.10362	−	1.20493i	−0.534245	−	0.156869i	0.00347173	−	0.999994i	$-0.498895\pi$
$59$	−4.10362	−	1.20493i	−0.534245	−	0.156869i	−0.537717	+	0.843125i	$0.680713\pi$
$60$		0			0
$61$	−7.22296	−	4.64192i	−0.924805	−	0.594336i	−0.0107573	−	0.999942i	$-0.503424\pi$
$61$	−7.22296	−	4.64192i	−0.924805	−	0.594336i	−0.914048	+	0.405606i	$0.867061\pi$
$62$	0.104588	−	0.0307097i	0.0132826	−	0.00390013i
$63$		0			0
$64$	0.415415	+	0.909632i	0.0519269	+	0.113704i
$65$	1.55597	+	10.8220i	0.192994	+	1.34230i
$66$		0			0
$67$	9.84464	−	11.3613i	1.20271	−	1.38801i	0.302164	−	0.953256i	$-0.402291\pi$
$67$	9.84464	−	11.3613i	1.20271	−	1.38801i	0.900551	−	0.434751i	$-0.143163\pi$
$68$	−6.54436			−0.793621
$69$		0			0
$70$	0.894034			0.106857
$71$	−0.198713	+	0.229328i	−0.0235830	+	0.0272162i	−0.767419	−	0.641146i	$-0.778459\pi$
$71$	−0.198713	+	0.229328i	−0.0235830	+	0.0272162i	0.743836	+	0.668363i	$0.233005\pi$
$72$		0			0
$73$	−0.476214	−	3.31214i	−0.0557366	−	0.387657i	−0.998526	−	0.0542688i	$-0.982717\pi$
$73$	−0.476214	−	3.31214i	−0.0557366	−	0.387657i	0.942790	−	0.333388i	$-0.108192\pi$
$74$	−0.384727	−	0.842435i	−0.0447237	−	0.0979311i
$75$		0			0
$76$	−2.03384	+	0.597190i	−0.233298	+	0.0685024i
$77$	0.485340	+	0.311909i	0.0553096	+	0.0355453i
$78$		0			0
$79$	7.72144	+	2.26722i	0.868730	+	0.255082i	0.685575	−	0.728002i	$-0.259551\pi$
$79$	7.72144	+	2.26722i	0.868730	+	0.255082i	0.183155	+	0.983084i	$0.441369\pi$
$80$	1.27819	+	1.47511i	0.142906	+	0.164922i
$81$		0			0
$82$	−9.44098	−	2.77212i	−1.04258	−	0.306130i
$83$	−4.35855	+	9.54389i	−0.478413	+	1.04758i	0.504484	+	0.863421i	$0.331683\pi$
$83$	−4.35855	+	9.54389i	−0.478413	+	1.04758i	−0.982897	+	0.184157i	$0.941044\pi$
$84$		0			0
$85$	−12.2562	+	3.59874i	−1.32937	+	0.390338i
$86$	−0.964080	+	6.70533i	−0.103959	+	0.723054i
$87$		0			0
$88$	0.179251	+	1.24672i	0.0191082	+	0.132901i
$89$	−5.01143	+	3.22065i	−0.531210	+	0.341388i	−0.778593	−	0.627530i	$-0.784066\pi$
$89$	−5.01143	+	3.22065i	−0.531210	+	0.341388i	0.247382	+	0.968918i	$0.420430\pi$
$90$		0			0
$91$	−2.56573			−0.268962
$92$	−3.33083	+	3.45045i	−0.347263	+	0.359734i
$93$		0			0
$94$	−1.64200	+	1.89497i	−0.169359	+	0.195451i
$95$	−3.48055	+	2.23682i	−0.357097	+	0.229493i
$96$		0			0
$97$	7.58500	+	16.6088i	0.770140	+	1.68637i	0.726344	+	0.687332i	$0.241218\pi$
$97$	7.58500	+	16.6088i	0.770140	+	1.68637i	0.0437969	+	0.999040i	$0.486055\pi$
$98$	0.966346	−	6.72108i	0.0976156	−	0.678932i
$99$		0			0
$100$	−1.00133	−	0.643516i	−0.100133	−	0.0643516i
$101$	−4.42821	+	9.69642i	−0.440623	+	0.964830i	0.550861	+	0.834597i	$0.314300\pi$
$101$	−4.42821	+	9.69642i	−0.440623	+	0.964830i	−0.991483	+	0.130232i	$0.958428\pi$
$102$		0			0
$103$	−4.63291	−	5.34666i	−0.456494	−	0.526822i	0.480112	−	0.877207i	$-0.340596\pi$
$103$	−4.63291	−	5.34666i	−0.456494	−	0.526822i	−0.936606	+	0.350385i	$0.886051\pi$
$104$	−3.66820	−	4.23333i	−0.359696	−	0.415112i
$105$		0			0
$106$	1.09924	−	2.40699i	0.106767	−	0.233788i
$107$	2.32502	+	1.49420i	0.224768	+	0.144450i	0.648179	−	0.761488i	$-0.275531\pi$
$107$	2.32502	+	1.49420i	0.224768	+	0.144450i	−0.423411	+	0.905938i	$0.639167\pi$
$108$		0			0
$109$	−2.34762	+	16.3281i	−0.224861	+	1.56394i	0.494419	+	0.869224i	$0.335381\pi$
$109$	−2.34762	+	16.3281i	−0.224861	+	1.56394i	−0.719280	+	0.694720i	$0.755528\pi$
$110$	1.02127	+	2.23626i	0.0973741	+	0.213219i
$111$		0			0
$112$	−0.385331	+	0.247638i	−0.0364104	+	0.0233995i
$113$	10.0429	−	11.5901i	0.944757	−	1.09031i	−0.0510375	−	0.998697i	$-0.516253\pi$
$113$	10.0429	−	11.5901i	0.944757	−	1.09031i	0.995795	−	0.0916114i	$-0.0292017\pi$
$114$		0			0
$115$	−4.34053	+	8.29357i	−0.404757	+	0.773379i
$116$	−5.06465			−0.470241
$117$		0			0
$118$	3.59792	−	2.31224i	0.331216	−	0.212859i
$119$	−0.426604	−	2.96710i	−0.0391067	−	0.271993i
$120$		0			0
$121$	1.33969	−	9.31775i	0.121790	−	0.847068i
$122$	8.23816	−	2.41894i	0.745848	−	0.219001i
$123$		0			0
$124$	−0.0452815	+	0.0991526i	−0.00406639	+	0.00890416i
$125$	−11.5931	−	3.40403i	−1.03692	−	0.304466i
$126$		0			0
$127$	14.1865	+	16.3721i	1.25885	+	1.45278i	0.838017	+	0.545645i	$0.183715\pi$
$127$	14.1865	+	16.3721i	1.25885	+	1.45278i	0.420828	+	0.907140i	$0.361739\pi$
$128$	−0.959493	−	0.281733i	−0.0848080	−	0.0249019i
$129$		0			0
$130$	−9.19765	−	5.91097i	−0.806687	−	0.518427i
$131$	16.4522	−	4.83081i	1.43744	−	0.422070i	0.532072	−	0.846699i	$-0.321414\pi$
$131$	16.4522	−	4.83081i	1.43744	−	0.422070i	0.905367	+	0.424629i	$0.139596\pi$
$132$		0			0
$133$	−0.403334	−	0.883179i	−0.0349735	−	0.0765813i
$134$	2.13945	+	14.8802i	0.184820	+	1.28545i
$135$		0			0
$136$	4.28565	−	4.94590i	0.367491	−	0.424107i
$137$	3.10334			0.265136			0.132568	−	0.991174i	$-0.457678\pi$
$137$	3.10334			0.265136			0.132568	+	0.991174i	$0.457678\pi$
$138$		0			0
$139$	−22.4485			−1.90406			−0.952028	−	0.306011i	$-0.901006\pi$
$139$	−22.4485			−1.90406			−0.952028	+	0.306011i	$0.901006\pi$
$140$	−0.585468	+	0.675666i	−0.0494810	+	0.0571042i
$141$		0			0
$142$	−0.0431846	−	0.300355i	−0.00362397	−	0.0252053i
$143$	−2.93087	−	6.41772i	−0.245092	−	0.536677i
$144$		0			0
$145$	−9.48500	+	2.78505i	−0.787686	+	0.231286i
$146$	2.81500	+	1.80909i	0.232971	+	0.149722i
$147$		0			0
$148$	0.888613	+	0.260920i	0.0730435	+	0.0214475i
$149$	10.2879	+	11.8728i	0.842815	+	0.972661i	0.999889	−	0.0149262i	$-0.00475134\pi$
$149$	10.2879	+	11.8728i	0.842815	+	0.972661i	−0.157073	+	0.987587i	$0.550206\pi$
$150$		0			0
$151$	5.34933	+	1.57070i	0.435322	+	0.127822i	0.492049	−	0.870568i	$-0.336248\pi$
$151$	5.34933	+	1.57070i	0.435322	+	0.127822i	−0.0567266	+	0.998390i	$0.518066\pi$
$152$	0.880557	−	1.92815i	0.0714226	−	0.156394i
$153$		0			0
$154$	−0.553555	+	0.162538i	−0.0446067	+	0.0130977i
$155$	−0.0302785	+	0.210592i	−0.00243203	+	0.0169151i
$156$		0			0
$157$	1.16229	+	8.08389i	0.0927606	+	0.645164i	0.982162	+	0.188037i	$0.0602125\pi$
$157$	1.16229	+	8.08389i	0.0927606	+	0.645164i	−0.889401	+	0.457127i	$0.848878\pi$
$158$	−6.76992	+	4.35076i	−0.538586	+	0.346128i
$159$		0			0
$160$	−1.95185			−0.154307
$161$	−1.78150	−	1.28522i	−0.140402	−	0.101289i
$162$		0			0
$163$	11.1729	−	12.8942i	0.875131	−	1.00995i	−0.124712	−	0.992193i	$-0.539801\pi$
$163$	11.1729	−	12.8942i	0.875131	−	1.00995i	0.999842	−	0.0177615i	$-0.00565395\pi$
$164$	8.27756	−	5.31966i	0.646369	−	0.415396i
$165$		0			0
$166$	−4.35855	−	9.54389i	−0.338289	−	0.740750i
$167$	2.57153	−	17.8854i	0.198991	−	1.38401i	−0.608228	−	0.793762i	$-0.708119\pi$
$167$	2.57153	−	17.8854i	0.198991	−	1.38401i	0.807219	−	0.590252i	$-0.200971\pi$
$168$		0			0
$169$	15.4595	+	9.93521i	1.18919	+	0.764247i
$170$	5.30635	−	11.6193i	0.406978	−	0.891158i
$171$		0			0
$172$	−4.43621	−	5.11966i	−0.338258	−	0.390370i
$173$	−10.4523	−	12.0626i	−0.794676	−	0.917105i	0.203401	−	0.979096i	$-0.434801\pi$
$173$	−10.4523	−	12.0626i	−0.794676	−	0.917105i	−0.998077	+	0.0619905i	$0.980255\pi$
$174$		0			0
$175$	0.226486	−	0.495934i	0.0171207	−	0.0374891i
$176$	−1.05959	−	0.680958i	−0.0798697	−	0.0513291i
$177$		0			0
$178$	0.847783	−	5.89646i	0.0635441	−	0.441959i
$179$	6.51851	+	14.2736i	0.487216	+	1.06686i	0.980416	+	0.196939i	$0.0631001\pi$
$179$	6.51851	+	14.2736i	0.487216	+	1.06686i	−0.493199	+	0.869916i	$0.664173\pi$
$180$		0			0
$181$	−1.53050	+	0.983590i	−0.113761	+	0.0731097i	−0.596284	−	0.802774i	$-0.703357\pi$
$181$	−1.53050	+	0.983590i	−0.113761	+	0.0731097i	0.482523	+	0.875883i	$0.339720\pi$
$182$	1.68020	−	1.93905i	0.124545	−	0.143732i
$183$		0			0
$184$	−0.426443	−	4.77683i	−0.0314378	−	0.352153i
$185$	1.80766			0.132902
$186$		0			0
$187$	6.93435	−	4.45643i	0.507090	−	0.325887i
$188$	−0.356841	−	2.48188i	−0.0260253	−	0.181010i
$189$		0			0
$190$	0.588805	−	4.09523i	0.0427164	−	0.297099i
$191$	4.07639	−	1.19694i	0.294957	−	0.0866073i	−0.130906	−	0.991395i	$-0.541789\pi$
$191$	4.07639	−	1.19694i	0.294957	−	0.0866073i	0.425863	+	0.904787i	$0.359970\pi$
$192$		0			0
$193$	5.44695	−	11.9272i	0.392080	−	0.858536i	−0.605932	−	0.795516i	$-0.707200\pi$
$193$	5.44695	−	11.9272i	0.392080	−	0.858536i	0.998012	−	0.0630197i	$-0.0200731\pi$
$194$	−17.5192	−	5.14411i	−1.25781	−	0.369326i
$195$		0			0
$196$	4.44663	+	5.13169i	0.317617	+	0.366549i
$197$	−9.52183	−	2.79586i	−0.678402	−	0.199197i	−0.0756609	−	0.997134i	$-0.524107\pi$
$197$	−9.52183	−	2.79586i	−0.678402	−	0.199197i	−0.602741	+	0.797937i	$0.705925\pi$
$198$		0			0
$199$	5.30457	+	3.40904i	0.376031	+	0.241660i	0.714981	−	0.699144i	$-0.246435\pi$
$199$	5.30457	+	3.40904i	0.376031	+	0.241660i	−0.338950	+	0.940804i	$0.610072\pi$
$200$	1.14207	−	0.335342i	0.0807565	−	0.0237123i
$201$		0			0
$202$	−4.42821	−	9.69642i	−0.311567	−	0.682238i
$203$	−0.330147	−	2.29622i	−0.0231718	−	0.161163i
$204$		0			0
$205$	12.5768	−	14.5144i	0.878403	−	1.01373i
$206$	7.07465			0.492914
$207$		0			0
$208$	5.60149			0.388394
$209$	1.74838	−	2.01774i	0.120938	−	0.139570i
$210$		0			0
$211$	−3.56564	−	24.7996i	−0.245469	−	1.70727i	−0.623784	−	0.781597i	$-0.714405\pi$
$211$	−3.56564	−	24.7996i	−0.245469	−	1.70727i	0.378315	−	0.925677i	$-0.376504\pi$
$212$	1.09924	+	2.40699i	0.0754959	+	0.165313i
$213$		0			0
$214$	−2.65180	+	0.778640i	−0.181274	+	0.0532267i
$215$	−11.1234	−	7.14855i	−0.758607	−	0.487527i
$216$		0			0
$217$	−0.0479057	−	0.0140664i	−0.00325205	−	0.000954889i
$218$	−10.8026	−	12.4668i	−0.731641	−	0.844359i
$219$		0			0
$220$	−2.35884	−	0.692619i	−0.159033	−	0.0466964i
$221$	−15.2284	+	33.3455i	−1.02437	+	2.24306i
$222$		0			0
$223$	−1.70893	+	0.501787i	−0.114438	+	0.0336022i	−0.338450	−	0.940984i	$-0.609903\pi$
$223$	−1.70893	+	0.501787i	−0.114438	+	0.0336022i	0.224012	+	0.974586i	$0.428085\pi$
$224$	0.0651865	−	0.453382i	0.00435546	−	0.0302929i
$225$		0			0
$226$	2.18253	+	15.1798i	0.145180	+	1.00975i
$227$	17.4218	−	11.1963i	1.15633	−	0.743126i	0.185437	−	0.982656i	$-0.440630\pi$
$227$	17.4218	−	11.1963i	1.15633	−	0.743126i	0.970889	+	0.239531i	$0.0769935\pi$
$228$		0			0
$229$	8.62288			0.569816			0.284908	−	0.958555i	$-0.408037\pi$
$229$	8.62288			0.569816			0.284908	+	0.958555i	$0.408037\pi$
$230$	−3.42541	−	8.71149i	−0.225865	−	0.574418i
$231$		0			0
$232$	3.31664	−	3.82760i	0.217748	−	0.251295i
$233$	−4.01814	+	2.58230i	−0.263237	+	0.169172i	−0.665601	−	0.746307i	$-0.731825\pi$
$233$	−4.01814	+	2.58230i	−0.263237	+	0.169172i	0.402364	+	0.915480i	$0.368189\pi$
$234$		0			0
$235$	−2.03307	−	4.45181i	−0.132623	−	0.290404i
$236$	−0.608660	+	4.23333i	−0.0396204	+	0.275566i
$237$		0			0
$238$	2.52175	+	1.62063i	0.163461	+	0.105050i
$239$	9.93216	−	21.7484i	0.642458	−	1.40679i	−0.255544	−	0.966797i	$-0.582255\pi$
$239$	9.93216	−	21.7484i	0.642458	−	1.40679i	0.898003	−	0.439990i	$-0.145018\pi$
$240$		0			0
$241$	15.0945	+	17.4200i	0.972323	+	1.12212i	0.992490	+	0.122324i	$0.0390346\pi$
$241$	15.0945	+	17.4200i	0.972323	+	1.12212i	−0.0201674	+	0.999797i	$0.506420\pi$
$242$	6.16457	+	7.11430i	0.396274	+	0.457324i
$243$		0			0
$244$	−3.56673	+	7.81005i	−0.228337	+	0.499988i
$245$	11.1495	+	7.16535i	0.712315	+	0.457777i
$246$		0			0
$247$	−1.68978	+	11.7527i	−0.107518	+	0.747804i
$248$	−0.0452815	−	0.0991526i	−0.00287538	−	0.00629619i
$249$		0			0
$250$	10.1644	−	6.53229i	0.642856	−	0.413139i
$251$	−0.144891	+	0.167213i	−0.00914544	+	0.0105544i	−0.760304	−	0.649568i	$-0.774950\pi$
$251$	−0.144891	+	0.167213i	−0.00914544	+	0.0105544i	0.751158	+	0.660122i	$0.229495\pi$
$252$		0			0
$253$	1.17971	−	5.92421i	0.0741677	−	0.372452i
$254$	−21.6633			−1.35928
$255$		0			0
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	−0.0775605	−	0.539445i	−0.00483809	−	0.0336496i	0.987259	−	0.159119i	$-0.0508654\pi$
$257$	−0.0775605	−	0.539445i	−0.00483809	−	0.0336496i	−0.992097	+	0.125469i	$0.959956\pi$
$258$		0			0
$259$	−0.0603710	+	0.419890i	−0.00375127	+	0.0260907i
$260$	10.4904	−	3.08026i	0.650587	−	0.191029i
$261$		0			0
$262$	−7.12304	+	15.5973i	−0.440063	+	0.963604i
$263$	14.1304	+	4.14907i	0.871320	+	0.255842i	0.686676	−	0.726963i	$-0.259069\pi$
$263$	14.1304	+	4.14907i	0.871320	+	0.255842i	0.184643	+	0.982806i	$0.440887\pi$
$264$		0			0
$265$	3.38224	+	3.90331i	0.207769	+	0.239779i
$266$	0.931590	+	0.273539i	0.0571194	+	0.0167718i
$267$		0			0
$268$	−12.6467	−	8.12755i	−0.772521	−	0.496469i
$269$	0.966365	−	0.283750i	0.0589203	−	0.0173006i	−0.252140	−	0.967691i	$-0.581134\pi$
$269$	0.966365	−	0.283750i	0.0589203	−	0.0173006i	0.311060	+	0.950390i	$0.399316\pi$
$270$		0			0
$271$	−8.27279	−	18.1149i	−0.502536	−	1.10040i	−0.975637	−	0.219392i	$-0.929593\pi$
$271$	−8.27279	−	18.1149i	−0.502536	−	1.10040i	0.473101	−	0.881008i	$-0.343135\pi$
$272$	0.931360	+	6.47775i	0.0564720	+	0.392771i
$273$		0			0
$274$	−2.03225	+	2.34535i	−0.122773	+	0.141688i
$275$	1.49921			0.0904057
$276$		0			0
$277$	−24.4934			−1.47167			−0.735834	−	0.677162i	$-0.763209\pi$
$277$	−24.4934			−1.47167			−0.735834	+	0.677162i	$0.763209\pi$
$278$	14.7006	−	16.9654i	0.881686	−	1.01752i
$279$		0			0
$280$	−0.127234	−	0.884934i	−0.00760370	−	0.0528849i
$281$	−9.22652	−	20.2033i	−0.550408	−	1.20523i	−0.956591	−	0.291434i	$-0.905868\pi$
$281$	−9.22652	−	20.2033i	−0.550408	−	1.20523i	0.406183	−	0.913792i	$-0.366859\pi$
$282$		0			0
$283$	−15.7568	+	4.62661i	−0.936643	+	0.275023i	−0.714215	−	0.699926i	$-0.753216\pi$
$283$	−15.7568	+	4.62661i	−0.936643	+	0.275023i	−0.222428	+	0.974949i	$0.571398\pi$
$284$	0.255273	+	0.164054i	0.0151477	+	0.00973482i
$285$		0			0
$286$	6.76950	+	1.98771i	0.400289	+	0.117535i
$287$	2.95143	+	3.40613i	0.174217	+	0.201057i
$288$		0			0
$289$	−24.7824	−	7.27678i	−1.45779	−	0.428046i
$290$	4.10655	−	8.99210i	0.241145	−	0.528034i
$291$		0			0
$292$	−3.21066	+	0.942733i	−0.187889	+	0.0551693i
$293$	3.48627	−	24.2475i	0.203670	−	1.41656i	−0.589605	−	0.807692i	$-0.700717\pi$
$293$	3.48627	−	24.2475i	0.203670	−	1.41656i	0.793275	−	0.608864i	$-0.208374\pi$
$294$		0			0
$295$	1.18801	+	8.26281i	0.0691688	+	0.481080i
$296$	−0.779108	+	0.500702i	−0.0452847	+	0.0291027i
$297$		0			0
$298$	−15.7100			−0.910057
$299$	9.83039	+	25.0006i	0.568506	+	1.44582i
$300$		0			0
$301$	2.03198	−	2.34503i	0.117121	−	0.135165i
$302$	−4.69013	+	3.01416i	−0.269886	+	0.173445i
$303$		0			0
$304$	0.880557	+	1.92815i	0.0505034	+	0.110587i
$305$	−2.38498	+	16.5879i	−0.136564	+	0.949821i
$306$		0			0
$307$	12.3453	+	7.93383i	0.704582	+	0.452808i	0.843243	−	0.537532i	$-0.180643\pi$
$307$	12.3453	+	7.93383i	0.704582	+	0.452808i	−0.138661	+	0.990340i	$0.544280\pi$
$308$	0.239663	−	0.524789i	0.0136561	−	0.0299026i
$309$		0			0
$310$	−0.139326	−	0.160791i	−0.00791321	−	0.00913233i
$311$	21.7671	+	25.1206i	1.23430	+	1.42446i	0.869910	+	0.493211i	$0.164177\pi$
$311$	21.7671	+	25.1206i	1.23430	+	1.42446i	0.364390	+	0.931246i	$0.381277\pi$
$312$		0			0
$313$	−8.51331	+	18.6415i	−0.481201	+	1.05368i	0.500931	+	0.865487i	$0.332991\pi$
$313$	−8.51331	+	18.6415i	−0.481201	+	1.05368i	−0.982132	+	0.188195i	$0.939736\pi$
$314$	−6.87053	−	4.41542i	−0.387726	−	0.249177i
$315$		0			0
$316$	1.14527	−	7.96550i	0.0644263	−	0.448095i
$317$	−9.51318	−	20.8310i	−0.534314	−	1.16998i	−0.963731	−	0.266877i	$-0.914008\pi$
$317$	−9.51318	−	20.8310i	−0.534314	−	1.16998i	0.429417	−	0.903106i	$-0.358719\pi$
$318$		0			0
$319$	5.36645	−	3.44881i	0.300464	−	0.193096i
$320$	1.27819	−	1.47511i	0.0714530	−	0.0824611i
$321$		0			0
$322$	2.13793	−	0.504727i	0.119142	−	0.0281273i
$323$	−13.8721			−0.771865
$324$		0			0
$325$	−5.60895	+	3.60465i	−0.311129	+	0.199950i
$326$	2.42811	+	16.8879i	0.134480	+	0.935332i
$327$		0			0
$328$	−1.40031	+	9.73940i	−0.0773194	+	0.537769i
$329$	1.10198	−	0.323570i	0.0607541	−	0.0178390i
$330$		0			0
$331$	−4.26889	+	9.34757i	−0.234639	+	0.513789i	−0.989923	−	0.141610i	$-0.954772\pi$
$331$	−4.26889	+	9.34757i	−0.234639	+	0.513789i	0.755283	+	0.655399i	$0.227499\pi$
$332$	10.0670	+	2.95595i	0.552501	+	0.162229i
$333$		0			0
$334$	11.8329	+	13.6559i	0.647467	+	0.747217i
$335$	−28.1539	−	8.26674i	−1.53821	−	0.451660i
$336$		0			0
$337$	9.77214	+	6.28017i	0.532322	+	0.342103i	0.779029	−	0.626987i	$-0.215712\pi$
$337$	9.77214	+	6.28017i	0.532322	+	0.342103i	−0.246707	+	0.969090i	$0.579349\pi$
$338$	−17.6323	+	5.17732i	−0.959073	+	0.281609i
$339$		0			0
$340$	5.30635	+	11.6193i	0.287777	+	0.630144i
$341$	−0.0195389	−	0.135896i	−0.00105809	−	0.00735917i
$342$		0			0
$343$	−4.13644	+	4.77371i	−0.223347	+	0.257756i
$344$	6.77428			0.365245
$345$		0			0
$346$	15.9612			0.858077
$347$	−8.44667	+	9.74798i	−0.453441	+	0.523299i	−0.935732	−	0.352712i	$-0.885259\pi$
$347$	−8.44667	+	9.74798i	−0.453441	+	0.523299i	0.482291	+	0.876011i	$0.339805\pi$
$348$		0			0
$349$	−2.25739	−	15.7005i	−0.120835	−	0.840428i	−0.956613	−	0.291360i	$-0.905892\pi$
$349$	−2.25739	−	15.7005i	−0.120835	−	0.840428i	0.835778	−	0.549067i	$-0.185017\pi$
$350$	0.226486	+	0.495934i	0.0121062	+	0.0265088i
$351$		0			0
$352$	1.20852	−	0.354853i	0.0644142	−	0.0189137i
$353$	1.51007	+	0.970465i	0.0803731	+	0.0516526i	0.580210	−	0.814467i	$-0.302970\pi$
$353$	1.51007	+	0.970465i	0.0803731	+	0.0516526i	−0.499837	+	0.866119i	$0.666607\pi$
$354$		0			0
$355$	0.568285	+	0.166864i	0.0301615	+	0.00885620i
$356$	3.90107	+	4.50207i	0.206756	+	0.238609i
$357$		0			0
$358$	−15.0559	−	4.42082i	−0.795732	−	0.233648i
$359$	−7.91279	+	17.3266i	−0.417621	+	0.914462i	0.577555	+	0.816352i	$0.304007\pi$
$359$	−7.91279	+	17.3266i	−0.417621	+	0.914462i	−0.995176	+	0.0981103i	$0.968720\pi$
$360$		0			0
$361$	13.9192	−	4.08705i	0.732591	−	0.215108i
$362$	0.258914	−	1.80079i	0.0136082	−	0.0946472i
$363$		0			0
$364$	0.365142	+	2.53962i	0.0191386	+	0.133112i
$365$	−5.49446	+	3.53108i	−0.287593	+	0.184825i
$366$		0			0
$367$	−3.88864			−0.202985			−0.101493	−	0.994836i	$-0.532362\pi$
$367$	−3.88864			−0.202985			−0.101493	+	0.994836i	$0.532362\pi$
$368$	3.88935	+	2.80588i	0.202746	+	0.146266i
$369$		0			0
$370$	−1.18377	+	1.36614i	−0.0615411	+	0.0710222i
$371$	−1.01963	+	0.655278i	−0.0529367	+	0.0340203i
$372$		0			0
$373$	−12.9840	−	28.4310i	−0.672287	−	1.47210i	−0.870614	−	0.491967i	$-0.836278\pi$
$373$	−12.9840	−	28.4310i	−0.672287	−	1.47210i	0.198327	−	0.980136i	$-0.436449\pi$
$374$	−1.17308	+	8.15897i	−0.0606587	+	0.421890i
$375$		0			0
$376$	2.10936	+	1.35560i	0.108782	+	0.0699100i
$377$	−11.7852	+	25.8059i	−0.606966	+	1.32907i
$378$		0			0
$379$	4.79446	+	5.53310i	0.246275	+	0.284216i	0.865406	−	0.501071i	$-0.167061\pi$
$379$	4.79446	+	5.53310i	0.246275	+	0.284216i	−0.619131	+	0.785287i	$0.712515\pi$
$380$	2.70938	+	3.12680i	0.138988	+	0.160401i
$381$		0			0
$382$	−1.76488	+	3.86456i	−0.0902994	+	0.197728i
$383$	−16.1879	−	10.4034i	−0.827165	−	0.531587i	0.0572106	−	0.998362i	$-0.481779\pi$
$383$	−16.1879	−	10.4034i	−0.827165	−	0.531587i	−0.884376	+	0.466775i	$0.845416\pi$
$384$		0			0
$385$	0.160256	−	1.11461i	0.00816742	−	0.0568057i
$386$	5.44695	+	11.9272i	0.277243	+	0.607077i
$387$		0			0
$388$	15.3603	−	9.87148i	0.779803	−	0.501149i
$389$	5.40793	−	6.24108i	0.274193	−	0.316435i	−0.601906	−	0.798567i	$-0.705592\pi$
$389$	5.40793	−	6.24108i	0.274193	−	0.316435i	0.876099	+	0.482132i	$0.160137\pi$
$390$		0			0
$391$	−27.2770	+	15.5250i	−1.37946	+	0.785134i
$392$	−6.79020			−0.342957
$393$		0			0
$394$	8.34844	−	5.36522i	0.420588	−	0.270296i
$395$	−2.23539	−	15.5475i	−0.112475	−	0.782278i
$396$		0			0
$397$	1.61805	−	11.2538i	0.0812076	−	0.564811i	−0.908076	−	0.418805i	$-0.862449\pi$
$397$	1.61805	−	11.2538i	0.0812076	−	0.564811i	0.989284	−	0.146006i	$-0.0466419\pi$
$398$	−6.05013	+	1.77648i	−0.303266	+	0.0890468i
$399$		0			0
$400$	−0.494462	+	1.08272i	−0.0247231	+	0.0541361i
$401$	14.5973	+	4.28615i	0.728954	+	0.214040i	0.625092	−	0.780551i	$-0.285062\pi$
$401$	14.5973	+	4.28615i	0.728954	+	0.214040i	0.103862	+	0.994592i	$0.466880\pi$
$402$		0			0
$403$	0.399844	+	0.461445i	0.0199177	+	0.0229862i
$404$	10.2279	+	3.00319i	0.508858	+	0.149414i
$405$		0			0
$406$	1.95157	+	1.25420i	0.0968547	+	0.0622447i
$407$	−1.11924	+	0.328639i	−0.0554788	+	0.0162900i
$408$		0			0
$409$	0.637100	+	1.39506i	0.0315026	+	0.0689810i	0.924729	−	0.380626i	$-0.124291\pi$
$409$	0.637100	+	1.39506i	0.0315026	+	0.0689810i	−0.893227	+	0.449607i	$0.851564\pi$
$410$	2.73320	+	19.0098i	0.134983	+	0.938829i
$411$		0			0
$412$	−4.63291	+	5.34666i	−0.228247	+	0.263411i
$413$	−1.95899			−0.0963956
$414$		0			0
$415$	20.4789			1.00527
$416$	−3.66820	+	4.23333i	−0.179848	+	0.207556i
$417$		0			0
$418$	0.379959	+	2.64267i	0.0185844	+	0.129257i
$419$	−1.92376	−	4.21245i	−0.0939818	−	0.205792i	0.856803	−	0.515644i	$-0.172447\pi$
$419$	−1.92376	−	4.21245i	−0.0939818	−	0.205792i	−0.950784	+	0.309853i	$0.899720\pi$
$420$		0			0
$421$	2.49164	−	0.731612i	0.121435	−	0.0356566i	−0.220450	−	0.975398i	$-0.570753\pi$
$421$	2.49164	−	0.731612i	0.121435	−	0.0356566i	0.341885	+	0.939742i	$0.388935\pi$
$422$	21.0773	+	13.5455i	1.02603	+	0.659387i
$423$		0			0
$424$	−2.53893	−	0.745497i	−0.123301	−	0.0362046i
$425$	−5.10114	−	5.88703i	−0.247442	−	0.285563i
$426$		0			0
$427$	−3.77344	−	1.10798i	−0.182610	−	0.0536190i
$428$	1.14811	−	2.51400i	0.0554958	−	0.121519i
$429$		0			0
$430$	12.6868	−	3.72517i	0.611810	−	0.179644i
$431$	−1.41485	+	9.84047i	−0.0681507	+	0.473999i	0.926954	+	0.375175i	$0.122417\pi$
$431$	−1.41485	+	9.84047i	−0.0681507	+	0.473999i	−0.995105	+	0.0988242i	$0.968492\pi$
$432$		0			0
$433$	3.06166	+	21.2943i	0.147134	+	1.02334i	0.920881	+	0.389845i	$0.127471\pi$
$433$	3.06166	+	21.2943i	0.147134	+	1.02334i	−0.773747	+	0.633495i	$0.781620\pi$
$434$	0.0420023	−	0.0269932i	0.00201617	−	0.00129572i
$435$		0			0
$436$	16.4960			0.790013
$437$	−7.06038	+	7.31392i	−0.337744	+	0.349872i
$438$		0			0
$439$	16.6027	−	19.1606i	0.792406	−	0.914485i	−0.205533	−	0.978650i	$-0.565893\pi$
$439$	16.6027	−	19.1606i	0.792406	−	0.914485i	0.997939	+	0.0641650i	$0.0204384\pi$
$440$	2.06816	−	1.32913i	0.0985957	−	0.0633636i
$441$		0			0
$442$	−15.2284	−	33.3455i	−0.724340	−	1.58608i
$443$	−0.962025	+	6.69103i	−0.0457072	+	0.317901i	0.954122	+	0.299418i	$0.0967926\pi$
$443$	−0.962025	+	6.69103i	−0.0457072	+	0.317901i	−0.999829	+	0.0184824i	$0.994117\pi$
$444$		0			0
$445$	9.78155	+	6.28622i	0.463690	+	0.297996i
$446$	0.739886	−	1.62012i	0.0350346	−	0.0767151i
$447$		0			0
$448$	0.299955	+	0.346167i	0.0141716	+	0.0163548i
$449$	5.11113	+	5.89855i	0.241209	+	0.278370i	0.863427	−	0.504474i	$-0.168314\pi$
$449$	5.11113	+	5.89855i	0.241209	+	0.278370i	−0.622218	+	0.782844i	$0.713768\pi$
$450$		0			0
$451$	−5.14836	+	11.2733i	−0.242427	+	0.530841i
$452$	−12.9014	−	8.29124i	−0.606832	−	0.389987i
$453$		0			0
$454$	−2.94725	+	20.4986i	−0.138321	+	0.962045i
$455$	2.08037	+	4.55537i	0.0975291	+	0.213559i
$456$		0			0
$457$	7.82254	−	5.02724i	0.365923	−	0.235164i	−0.344738	−	0.938699i	$-0.612032\pi$
$457$	7.82254	−	5.02724i	0.365923	−	0.235164i	0.710661	+	0.703535i	$0.248396\pi$
$458$	−5.64678	+	6.51674i	−0.263857	+	0.304507i
$459$		0			0
$460$	8.82687	+	3.11605i	0.411555	+	0.145287i
$461$	17.2422			0.803049			0.401525	−	0.915848i	$-0.368480\pi$
$461$	17.2422			0.803049			0.401525	+	0.915848i	$0.368480\pi$
$462$		0			0
$463$	−7.60089	+	4.88480i	−0.353243	+	0.227016i	−0.705213	−	0.708996i	$-0.749149\pi$
$463$	−7.60089	+	4.88480i	−0.353243	+	0.227016i	0.351969	+	0.936012i	$0.385512\pi$
$464$	0.720774	+	5.01310i	0.0334611	+	0.232727i
$465$		0			0
$466$	0.679749	−	4.72775i	0.0314887	−	0.219009i
$467$	−10.1185	+	2.97106i	−0.468228	+	0.137484i	−0.507332	−	0.861751i	$-0.669368\pi$
$467$	−10.1185	+	2.97106i	−0.468228	+	0.137484i	0.0391032	+	0.999235i	$0.487550\pi$
$468$		0			0
$469$	2.86049	−	6.26361i	0.132085	−	0.289226i
$470$	4.69583	+	1.37882i	0.216602	+	0.0636002i
$471$		0			0
$472$	−2.80075	−	3.23223i	−0.128915	−	0.148776i
$473$	8.18684	+	2.40387i	0.376431	+	0.110530i
$474$		0			0
$475$	−2.12253	−	1.36406i	−0.0973882	−	0.0625876i
$476$	−2.87618	+	0.844524i	−0.131830	+	0.0387087i
$477$		0			0
$478$	9.93216	+	21.7484i	0.454287	+	0.994749i
$479$	−1.87403	−	13.0342i	−0.0856265	−	0.595546i	−0.986782	−	0.162051i	$-0.948189\pi$
$479$	−1.87403	−	13.0342i	−0.0856265	−	0.595546i	0.901156	−	0.433495i	$-0.142720\pi$
$480$		0			0
$481$	3.39722	−	3.92060i	0.154900	−	0.178764i
$482$	−23.0500			−1.04990
$483$		0			0
$484$	−9.41356			−0.427889
$485$	23.3383	−	26.9338i	1.05974	−	1.22300i
$486$		0			0
$487$	0.431388	+	3.00037i	0.0195480	+	0.135960i	0.997258	−	0.0739990i	$-0.0235762\pi$
$487$	0.431388	+	3.00037i	0.0195480	+	0.135960i	−0.977710	+	0.209959i	$0.932667\pi$
$488$	−3.56673	−	7.81005i	−0.161458	−	0.353545i
$489$		0			0
$490$	−12.7166	+	3.73392i	−0.574477	+	0.168682i
$491$	−5.30467	−	3.40910i	−0.239396	−	0.153851i	0.415442	−	0.909620i	$-0.363627\pi$
$491$	−5.30467	−	3.40910i	−0.239396	−	0.153851i	−0.654838	+	0.755769i	$0.727263\pi$
$492$		0			0
$493$	−31.8023	−	9.33799i	−1.43230	−	0.420562i
$494$	−7.77550	−	8.97340i	−0.349836	−	0.403732i
$495$		0			0
$496$	0.104588	+	0.0307097i	0.00469612	+	0.00137891i
$497$	−0.0577389	+	0.126430i	−0.00258994	+	0.00567118i
$498$		0			0
$499$	6.51009	−	1.91154i	0.291432	−	0.0855721i	−0.132749	−	0.991150i	$-0.542380\pi$
$499$	6.51009	−	1.91154i	0.291432	−	0.0855721i	0.424181	+	0.905578i	$0.360562\pi$
$500$	−1.71952	+	11.9595i	−0.0768992	+	0.534846i
$501$		0			0
$502$	−0.0314878	−	0.219003i	−0.00140537	−	0.00977456i
$503$	30.2665	−	19.4511i	1.34952	−	0.867283i	0.351885	−	0.936043i	$-0.385541\pi$
$503$	30.2665	−	19.4511i	1.34952	−	0.867283i	0.997633	+	0.0687603i	$0.0219044\pi$
$504$		0			0
$505$	20.8062			0.925862
$506$	3.70468	+	4.77110i	0.164693	+	0.212101i
$507$		0			0
$508$	14.1865	−	16.3721i	0.629423	−	0.726392i
$509$	−10.1506	+	6.52339i	−0.449917	+	0.289144i	−0.745911	−	0.666046i	$-0.767986\pi$
$509$	−10.1506	+	6.52339i	−0.449917	+	0.289144i	0.295994	+	0.955190i	$0.404349\pi$
$510$		0			0
$511$	−0.636710	−	1.39420i	−0.0281664	−	0.0616758i
$512$	−0.142315	+	0.989821i	−0.00628949	+	0.0437443i
$513$		0			0
$514$	0.458477	+	0.294645i	0.0202225	+	0.0129962i
$515$	−5.73632	+	12.5608i	−0.252772	+	0.553494i
$516$		0			0
$517$	2.06816	+	2.38679i	0.0909576	+	0.104971i
$518$	−0.277797	−	0.320595i	−0.0122057	−	0.0140861i
$519$		0			0
$520$	−4.54184	+	9.94525i	−0.199173	+	0.436128i
$521$	0.550395	+	0.353718i	0.0241133	+	0.0154967i	0.552642	−	0.833419i	$-0.313620\pi$
$521$	0.550395	+	0.353718i	0.0241133	+	0.0154967i	−0.528529	+	0.848915i	$0.677256\pi$
$522$		0			0
$523$	5.32600	−	37.0432i	0.232890	−	1.61978i	−0.452608	−	0.891709i	$-0.649506\pi$
$523$	5.32600	−	37.0432i	0.232890	−	1.61978i	0.685498	−	0.728074i	$-0.259584\pi$
$524$	−7.12304	−	15.5973i	−0.311172	−	0.681371i
$525$		0			0
$526$	−12.3891	+	7.96200i	−0.540191	+	0.347160i
$527$	−0.467148	+	0.539118i	−0.0203493	+	0.0234843i
$528$		0			0
$529$	−5.69753	+	22.2831i	−0.247719	+	0.968832i
$530$	−5.16482			−0.224346
$531$		0			0
$532$	−0.816789	+	0.524918i	−0.0354123	+	0.0227581i
$533$	−7.84385	−	54.5552i	−0.339755	−	2.36305i
$534$		0			0
$535$	0.767708	−	5.33953i	0.0331909	−	0.230848i
$536$	14.4242	−	4.23534i	0.623032	−	0.182939i
$537$		0			0
$538$	−0.418390	+	0.916147i	−0.0180381	+	0.0394979i
$539$	−8.20607	−	2.40952i	−0.353461	−	0.103785i
$540$		0			0
$541$	−17.3382	−	20.0094i	−0.745429	−	0.860271i	0.248688	−	0.968584i	$-0.420001\pi$
$541$	−17.3382	−	20.0094i	−0.745429	−	0.860271i	−0.994117	+	0.108313i	$0.965455\pi$
$542$	19.1078	+	5.61057i	0.820752	+	0.240994i
$543$		0			0
$544$	−5.50547	−	3.53815i	−0.236045	−	0.151697i
$545$	30.8934	−	9.07112i	1.32333	−	0.388564i
$546$		0			0
$547$	−2.80031	−	6.13182i	−0.119733	−	0.262178i	0.840270	−	0.542168i	$-0.182396\pi$
$547$	−2.80031	−	6.13182i	−0.119733	−	0.262178i	−0.960003	+	0.279990i	$0.909669\pi$
$548$	−0.441651	−	3.07175i	−0.0188664	−	0.131219i
$549$		0			0
$550$	−0.981773	+	1.13303i	−0.0418629	+	0.0483124i
$551$	−10.7356			−0.457350
$552$		0			0
$553$	3.68607			0.156748
$554$	16.0398	−	18.5109i	0.681465	−	0.786453i
$555$		0			0
$556$	3.19475	+	22.2200i	0.135488	+	0.942338i
$557$	7.84417	+	17.1763i	0.332368	+	0.727785i	0.999858	−	0.0168340i	$-0.00535867\pi$
$557$	7.84417	+	17.1763i	0.332368	+	0.727785i	−0.667490	+	0.744619i	$0.732631\pi$
$558$		0			0
$559$	−36.4090	+	10.6906i	−1.53994	+	0.452166i
$560$	0.752109	+	0.483351i	0.0317824	+	0.0204253i
$561$		0			0
$562$	21.3107	+	6.25738i	0.898937	+	0.263952i
$563$	−2.49813	−	2.88300i	−0.105284	−	0.121504i	0.700662	−	0.713493i	$-0.252888\pi$
$563$	−2.49813	−	2.88300i	−0.105284	−	0.121504i	−0.805946	+	0.591989i	$0.798343\pi$
$564$		0			0
$565$	−28.7209	−	8.43323i	−1.20830	−	0.354789i
$566$	6.82194	−	14.9380i	0.286747	−	0.627889i
$567$		0			0
$568$	−0.291152	+	0.0854900i	−0.0122165	+	0.00358708i
$569$	−2.64794	+	18.4168i	−0.111008	+	0.772074i	0.855936	+	0.517082i	$0.172982\pi$
$569$	−2.64794	+	18.4168i	−0.111008	+	0.772074i	−0.966943	+	0.254992i	$0.917927\pi$
$570$		0			0
$571$	6.10845	+	42.4852i	0.255631	+	1.77795i	0.563096	+	0.826391i	$0.309610\pi$
$571$	6.10845	+	42.4852i	0.255631	+	1.77795i	−0.307465	+	0.951559i	$0.599481\pi$
$572$	−5.93529	+	3.81438i	−0.248167	+	0.159487i
$573$		0			0
$574$	−4.50695			−0.188117
$575$	−5.70016	−	0.306751i	−0.237713	−	0.0127924i
$576$		0			0
$577$	7.51277	−	8.67019i	0.312761	−	0.360945i	−0.577505	−	0.816387i	$-0.695973\pi$
$577$	7.51277	−	8.67019i	0.312761	−	0.360945i	0.890265	+	0.455442i	$0.150519\pi$
$578$	21.7285	−	13.9640i	0.903785	−	0.580827i
$579$		0			0
$580$	4.10655	+	8.99210i	0.170515	+	0.373377i
$581$	−0.683940	+	4.75690i	−0.0283746	+	0.197350i
$582$		0			0
$583$	−2.80380	−	1.80189i	−0.116122	−	0.0746268i
$584$	1.39006	−	3.04381i	0.0575212	−	0.125954i
$585$		0			0
$586$	16.0420	+	18.5135i	0.662690	+	0.764785i
$587$	7.21008	+	8.32088i	0.297592	+	0.343439i	0.884778	−	0.466012i	$-0.154310\pi$
$587$	7.21008	+	8.32088i	0.297592	+	0.343439i	−0.587186	+	0.809452i	$0.699764\pi$
$588$		0			0
$589$	−0.0959833	+	0.210174i	−0.00395492	+	0.00866007i
$590$	−7.02260	−	4.51315i	−0.289116	−	0.185804i
$591$		0			0
$592$	0.131802	−	0.916701i	0.00541702	−	0.0376762i
$593$	−7.24210	−	15.8580i	−0.297397	−	0.651209i	0.700661	−	0.713494i	$-0.252888\pi$
$593$	−7.24210	−	15.8580i	−0.297397	−	0.651209i	−0.998058	+	0.0622851i	$0.980161\pi$
$594$		0			0
$595$	−4.92207	+	3.16322i	−0.201785	+	0.129680i
$596$	10.2879	−	11.8728i	0.421408	−	0.486330i
$597$		0			0
$598$	−25.3317	−	8.94258i	−1.03589	−	0.365689i
$599$	11.8571			0.484470			0.242235	−	0.970218i	$-0.422120\pi$
$599$	11.8571			0.484470			0.242235	+	0.970218i	$0.422120\pi$
$600$		0			0
$601$	4.21154	−	2.70659i	0.171792	−	0.110404i	−0.451919	−	0.892059i	$-0.649260\pi$
$601$	4.21154	−	2.70659i	0.171792	−	0.110404i	0.623711	+	0.781655i	$0.285624\pi$
$602$	0.441592	+	3.07134i	0.0179979	+	0.125178i
$603$		0			0
$604$	0.793428	−	5.51842i	0.0322841	−	0.224541i
$605$	−17.6296	+	5.17651i	−0.716745	+	0.210455i
$606$		0			0
$607$	13.2717	−	29.0610i	0.538683	−	1.17955i	−0.423186	−	0.906043i	$-0.639088\pi$
$607$	13.2717	−	29.0610i	0.538683	−	1.17955i	0.961869	−	0.273509i	$-0.0881843\pi$
$608$	−2.03384	−	0.597190i	−0.0824832	−	0.0242192i
$609$		0			0
$610$	−10.9745	−	12.6652i	−0.444343	−	0.512800i
$611$	−13.4763	−	3.95699i	−0.545192	−	0.160083i
$612$		0			0
$613$	−25.5158	−	16.3980i	−1.03057	−	0.662309i	−0.0879349	−	0.996126i	$-0.528027\pi$
$613$	−25.5158	−	16.3980i	−1.03057	−	0.662309i	−0.942638	+	0.333817i	$0.891663\pi$
$614$	−14.0804	+	4.13439i	−0.568240	+	0.166850i
$615$		0			0
$616$	0.239663	+	0.524789i	0.00965630	+	0.0211443i
$617$	1.56352	+	10.8745i	0.0629450	+	0.437792i	0.996786	+	0.0801048i	$0.0255255\pi$
$617$	1.56352	+	10.8745i	0.0629450	+	0.437792i	−0.933841	+	0.357687i	$0.883565\pi$
$618$		0			0
$619$	7.71335	−	8.90168i	0.310026	−	0.357789i	−0.579258	−	0.815144i	$-0.696658\pi$
$619$	7.71335	−	8.90168i	0.310026	−	0.357789i	0.889284	+	0.457355i	$0.151203\pi$
$620$	0.212757			0.00854454
$621$		0			0
$622$	−33.2393			−1.33277
$623$	−1.78686	+	2.06215i	−0.0715892	+	0.0826183i
$624$		0			0
$625$	2.50927	+	17.4523i	0.100371	+	0.698093i
$626$	−8.51331	−	18.6415i	−0.340260	−	0.745066i
$627$		0			0
$628$	7.83619	−	2.30091i	0.312698	−	0.0918164i
$629$	5.09877	+	3.27678i	0.203301	+	0.130654i
$630$		0			0
$631$	11.2044	+	3.28990i	0.446039	+	0.130969i	0.497036	−	0.867730i	$-0.334422\pi$
$631$	11.2044	+	3.28990i	0.446039	+	0.130969i	−0.0509968	+	0.998699i	$0.516240\pi$
$632$	5.26994	+	6.08183i	0.209627	+	0.241922i
$633$		0			0
$634$	21.9728	+	6.45180i	0.872651	+	0.256234i
$635$	17.5652	−	38.4625i	0.697055	−	1.52634i
$636$		0			0
$637$	36.4945	−	10.7158i	1.44597	−	0.424574i
$638$	−0.907843	+	6.31418i	−0.0359418	+	0.249981i
$639$		0			0
$640$	0.277777	+	1.93198i	0.0109801	+	0.0763683i
$641$	3.95916	−	2.54440i	0.156377	−	0.100498i	−0.460112	−	0.887861i	$-0.652191\pi$
$641$	3.95916	−	2.54440i	0.156377	−	0.100498i	0.616489	+	0.787363i	$0.288554\pi$
$642$		0			0
$643$	38.9574			1.53633			0.768165	−	0.640252i	$-0.221170\pi$
$643$	38.9574			1.53633			0.768165	+	0.640252i	$0.221170\pi$
$644$	−1.01860	+	1.94627i	−0.0401385	+	0.0766937i
$645$		0			0
$646$	9.08430	−	10.4838i	0.357417	−	0.412481i
$647$	−36.0078	+	23.1408i	−1.41561	+	0.909759i	−0.415613	+	0.909541i	$0.636433\pi$
$647$	−36.0078	+	23.1408i	−1.41561	+	0.909759i	−1.00000		0.000218133i	$0.999931\pi$
$648$		0			0
$649$	−2.23778	−	4.90006i	−0.0878407	−	0.192344i
$650$	0.948866	−	6.59951i	0.0372176	−	0.258854i
$651$		0			0
$652$	−14.3531	−	9.22415i	−0.562109	−	0.361246i
$653$	8.81058	−	19.2925i	0.344785	−	0.754973i	−0.655215	−	0.755442i	$-0.727422\pi$
$653$	8.81058	−	19.2925i	0.344785	−	0.754973i	1.00000		0.000469115i	$0.000149324\pi$
$654$		0			0
$655$	−21.9169	−	25.2934i	−0.856363	−	0.988295i
$656$	−6.44354	−	7.43624i	−0.251578	−	0.290336i
$657$		0			0
$658$	−0.477105	+	1.04471i	−0.0185995	+	0.0407272i
$659$	8.59977	+	5.52674i	0.335000	+	0.215291i	0.697316	−	0.716764i	$-0.254378\pi$
$659$	8.59977	+	5.52674i	0.335000	+	0.215291i	−0.362316	+	0.932055i	$0.618014\pi$
$660$		0			0
$661$	−5.68969	+	39.5727i	−0.221303	+	1.53920i	0.511814	+	0.859096i	$0.328974\pi$
$661$	−5.68969	+	39.5727i	−0.221303	+	1.53920i	−0.733117	+	0.680102i	$0.761935\pi$
$662$	−4.26889	−	9.34757i	−0.165915	−	0.363303i
$663$		0			0
$664$	−8.82647	+	5.67242i	−0.342533	+	0.220133i
$665$	−1.24102	+	1.43221i	−0.0481246	+	0.0555388i
$666$		0			0
$667$	−21.1095	+	12.0147i	−0.817363	+	0.465212i
$668$	−18.0693			−0.699123
$669$		0			0
$670$	24.6845	−	15.8638i	0.953645	−	0.612871i
$671$	−1.53904	−	10.7043i	−0.0594140	−	0.413233i
$672$		0			0
$673$	0.982285	−	6.83195i	0.0378643	−	0.263352i	−0.962092	−	0.272726i	$-0.912075\pi$
$673$	0.982285	−	6.83195i	0.0378643	−	0.263352i	0.999956	+	0.00937387i	$0.00298384\pi$
$674$	−11.1456	+	3.27265i	−0.429313	+	0.126058i
$675$		0			0
$676$	7.63397	−	16.7161i	0.293614	−	0.642925i
$677$	17.0823	+	5.01583i	0.656528	+	0.192774i	0.592995	−	0.805206i	$-0.297945\pi$
$677$	17.0823	+	5.01583i	0.656528	+	0.192774i	0.0635324	+	0.997980i	$0.479763\pi$
$678$		0			0
$679$	5.47684	+	6.32061i	0.210182	+	0.242563i
$680$	−12.2562	−	3.59874i	−0.470003	−	0.138005i
$681$		0			0
$682$	0.115498	+	0.0742264i	0.00442267	+	0.00284227i
$683$	−49.8638	+	14.6413i	−1.90799	+	0.560236i	−0.923873	+	0.382700i	$0.874994\pi$
$683$	−49.8638	+	14.6413i	−1.90799	+	0.560236i	−0.984114	+	0.177536i	$0.943188\pi$
$684$		0			0
$685$	−2.51627	−	5.50986i	−0.0961418	−	0.210521i
$686$	−0.898935	−	6.25223i	−0.0343215	−	0.238711i
$687$		0			0
$688$	−4.43621	+	5.11966i	−0.169129	+	0.195185i
$689$	14.8222			0.564681
$690$		0			0
$691$	−26.8796			−1.02255			−0.511274	−	0.859418i	$-0.670826\pi$
$691$	−26.8796			−1.02255			−0.511274	+	0.859418i	$0.670826\pi$
$692$	−10.4523	+	12.0626i	−0.397338	+	0.458553i
$693$		0			0
$694$	−1.83564	−	12.7671i	−0.0696799	−	0.484634i
$695$	18.2019	+	39.8565i	0.690436	+	1.51184i
$696$		0			0
$697$	61.7852	−	18.1418i	2.34028	−	0.687169i
$698$	13.3439	+	8.57561i	0.505074	+	0.324592i
$699$		0			0
$700$	−0.523119	−	0.153602i	−0.0197720	−	0.00580559i
$701$	3.33803	+	3.85229i	0.126076	+	0.145499i	0.815278	−	0.579070i	$-0.196584\pi$
$701$	3.33803	+	3.85229i	0.126076	+	0.145499i	−0.689202	+	0.724569i	$0.742039\pi$
$702$		0			0
$703$	1.88360	+	0.553074i	0.0710412	+	0.0208596i
$704$	−0.523231	+	1.14572i	−0.0197200	+	0.0431808i
$705$		0			0
$706$	−1.72232	+	0.505718i	−0.0648202	+	0.0190329i
$707$	−0.694870	+	4.83293i	−0.0261333	+	0.181761i
$708$		0			0
$709$	−0.117874	−	0.819831i	−0.00442684	−	0.0307894i	0.987488	−	0.157692i	$-0.0504054\pi$
$709$	−0.117874	−	0.819831i	−0.00442684	−	0.0307894i	−0.991915	+	0.126903i	$0.959496\pi$
$710$	−0.498255	+	0.320209i	−0.0186992	+	0.0120172i
$711$		0			0
$712$	−5.95710			−0.223252
$713$	0.0464835	+	0.520689i	0.00174082	+	0.0195000i
$714$		0			0
$715$	−9.01800	+	10.4073i	−0.337254	+	0.389212i
$716$	13.2006	−	8.48350i	0.493329	−	0.317043i
$717$		0			0
$718$	−7.91279	−	17.3266i	−0.295303	−	0.646623i
$719$	0.676000	−	4.70168i	0.0252105	−	0.175343i	−0.973326	−	0.229427i	$-0.926315\pi$
$719$	0.676000	−	4.70168i	0.0252105	−	0.175343i	0.998536	+	0.0540839i	$0.0172239\pi$
$720$		0			0
$721$	−2.72608	−	1.75195i	−0.101525	−	0.0652459i
$722$	−6.02636	+	13.1959i	−0.224278	+	0.491100i
$723$		0			0
$724$	1.19139	+	1.37494i	0.0442777	+	0.0510992i
$725$	−3.94774	−	4.55594i	−0.146616	−	0.169203i
$726$		0			0
$727$	−13.0271	+	28.5254i	−0.483149	+	1.05795i	0.498436	+	0.866926i	$0.333908\pi$
$727$	−13.0271	+	28.5254i	−0.483149	+	1.05795i	−0.981586	+	0.191023i	$0.938819\pi$
$728$	−2.15843	−	1.38714i	−0.0799968	−	0.0514108i
$729$		0			0
$730$	0.929498	−	6.46480i	0.0344023	−	0.239273i
$731$	−18.4167	−	40.3270i	−0.681167	−	1.49155i
$732$		0			0
$733$	9.54503	−	6.13422i	0.352554	−	0.226572i	−0.352362	−	0.935864i	$-0.614621\pi$
$733$	9.54503	−	6.13422i	0.352554	−	0.226572i	0.704915	+	0.709291i	$0.250985\pi$
$734$	2.54652	−	2.93884i	0.0939936	−	0.108474i
$735$		0			0
$736$	−4.66752	+	1.10192i	−0.172047	+	0.0406172i
$737$	18.9349			0.697475
$738$		0			0
$739$	23.0716	−	14.8272i	0.848703	−	0.545428i	−0.0424673	−	0.999098i	$-0.513522\pi$
$739$	23.0716	−	14.8272i	0.848703	−	0.545428i	0.891170	+	0.453670i	$0.149885\pi$
$740$	−0.257257	−	1.78926i	−0.00945696	−	0.0657746i
$741$		0			0
$742$	0.172491	−	1.19970i	0.00633235	−	0.0440425i
$743$	−50.6452	+	14.8708i	−1.85799	+	0.545556i	−0.858530	+	0.512763i	$0.828622\pi$
$743$	−50.6452	+	14.8708i	−1.85799	+	0.545556i	−0.999462	+	0.0327922i	$0.989560\pi$
$744$		0			0
$745$	12.7381	−	27.8926i	0.466688	−	1.02190i
$746$	29.9895	+	8.80570i	1.09799	+	0.322400i
$747$		0			0
$748$	−5.39793	−	6.22955i	−0.197368	−	0.227775i
$749$	1.21464	+	0.356652i	0.0443821	+	0.0130318i
$750$		0			0
$751$	14.6669	+	9.42585i	0.535203	+	0.343954i	0.780160	−	0.625580i	$-0.215138\pi$
$751$	14.6669	+	9.42585i	0.535203	+	0.343954i	−0.244957	+	0.969534i	$0.578774\pi$
$752$	−2.40584	+	0.706417i	−0.0877318	+	0.0257604i
$753$		0			0
$754$	−11.7852	−	25.8059i	−0.429190	−	0.939795i
$755$	−1.54865	−	10.7711i	−0.0563612	−	0.392001i
$756$		0			0
$757$	−11.8757	+	13.7053i	−0.431630	+	0.498128i	−0.929345	−	0.369213i	$-0.879627\pi$
$757$	−11.8757	+	13.7053i	−0.431630	+	0.498128i	0.497714	+	0.867341i	$0.334173\pi$
$758$	−7.32134			−0.265923
$759$		0			0
$760$	−4.13734			−0.150077
$761$	2.86350	−	3.30466i	0.103802	−	0.119794i	−0.701471	−	0.712698i	$-0.747473\pi$
$761$	2.86350	−	3.30466i	0.103802	−	0.119794i	0.805273	+	0.592904i	$0.202019\pi$
$762$		0			0
$763$	1.07531	+	7.47897i	0.0389290	+	0.270757i
$764$	−1.76488	−	3.86456i	−0.0638513	−	0.139815i
$765$		0			0
$766$	18.4632	−	5.42128i	0.667102	−	0.195879i
$767$	20.1537	+	12.9520i	0.727709	+	0.467670i
$768$		0			0
$769$	−26.6389	−	7.82187i	−0.960622	−	0.282064i	−0.236419	−	0.971651i	$-0.575974\pi$
$769$	−26.6389	−	7.82187i	−0.960622	−	0.282064i	−0.724203	+	0.689587i	$0.757792\pi$
$770$	0.737419	+	0.851026i	0.0265747	+	0.0306689i
$771$		0			0
$772$	−12.5809	−	3.69410i	−0.452798	−	0.132954i
$773$	−0.0667830	+	0.146234i	−0.00240202	+	0.00525969i	−0.910829	−	0.412783i	$-0.864557\pi$
$773$	−0.0667830	+	0.146234i	−0.00240202	+	0.00525969i	0.908427	+	0.418043i	$0.137284\pi$
$774$		0			0
$775$	−0.124489	+	0.0365533i	−0.00447178	+	0.00131303i
$776$	−2.59851	+	18.0730i	−0.0932809	+	0.648783i
$777$		0			0
$778$	1.17526	+	8.17408i	0.0421349	+	0.293055i
$779$	17.5460	−	11.2761i	0.628650	−	0.404009i
$780$		0			0
$781$	−0.382199			−0.0136762
$782$	6.12959	−	30.7813i	0.219194	−	1.10074i
$783$		0			0
$784$	4.44663	−	5.13169i	0.158808	−	0.183275i
$785$	13.4102	−	8.61824i	0.478632	−	0.307598i
$786$		0			0
$787$	15.6367	+	34.2397i	0.557389	+	1.22051i	0.953245	+	0.302199i	$0.0977209\pi$
$787$	15.6367	+	34.2397i	0.557389	+	1.22051i	−0.395855	+	0.918313i	$0.629552\pi$
$788$	−1.41231	+	9.82280i	−0.0503113	+	0.349923i
$789$		0			0
$790$	13.2139	+	8.49203i	0.470128	+	0.302133i
$791$	2.91810	−	6.38975i	0.103756	−	0.227193i
$792$		0			0
$793$	31.4950	+	36.3471i	1.11842	+	1.29072i
$794$	7.44545	+	8.59251i	0.264229	+	0.304937i
$795$		0			0
$796$	2.61942	−	5.73573i	0.0928429	−	0.203298i
$797$	21.7541	+	13.9805i	0.770568	+	0.495214i	0.865891	−	0.500232i	$-0.166752\pi$
$797$	21.7541	+	13.9805i	0.770568	+	0.495214i	−0.0953230	+	0.995446i	$0.530388\pi$
$798$		0			0
$799$	2.33529	−	16.2423i	0.0826168	−	0.574612i
$800$	−0.494462	−	1.08272i	−0.0174819	−	0.0382800i
$801$		0			0
$802$	−12.7985	+	8.22507i	−0.451929	+	0.290437i
$803$	2.76002	−	3.18523i	0.0973990	−	0.112404i
$804$		0			0
$805$	−0.837371	+	4.20507i	−0.0295134	+	0.148209i
$806$	−0.610579			−0.0215067
$807$		0			0
$808$	−8.96752	+	5.76308i	−0.315476	+	0.202744i
$809$	−1.62366	−	11.2928i	−0.0570847	−	0.397033i	−0.998252	−	0.0590931i	$-0.981179\pi$
$809$	−1.62366	−	11.2928i	−0.0570847	−	0.397033i	0.941168	−	0.337940i	$-0.109730\pi$
$810$		0			0
$811$	−4.70273	+	32.7082i	−0.165135	+	1.14854i	0.723633	+	0.690185i	$0.242471\pi$
$811$	−4.70273	+	32.7082i	−0.165135	+	1.14854i	−0.888768	+	0.458357i	$0.848438\pi$
$812$	−2.22586	+	0.653573i	−0.0781125	+	0.0229359i
$813$		0			0
$814$	0.484579	−	1.06108i	0.0169845	−	0.0371908i
$815$	−31.9526	−	9.38212i	−1.11925	−	0.328641i
$816$		0			0
$817$	−9.40345	−	10.8522i	−0.328985	−	0.379669i
$818$	−1.47152	−	0.432079i	−0.0514506	−	0.0151073i
$819$		0			0
$820$	−16.1565	−	10.3832i	−0.564211	−	0.362596i
$821$	−5.34906	+	1.57063i	−0.186684	+	0.0548152i	−0.373738	−	0.927534i	$-0.621924\pi$
$821$	−5.34906	+	1.57063i	−0.186684	+	0.0548152i	0.187054	+	0.982350i	$0.440106\pi$
$822$		0			0
$823$	13.9557	+	30.5587i	0.486466	+	1.06521i	0.980635	+	0.195845i	$0.0627450\pi$
$823$	13.9557	+	30.5587i	0.486466	+	1.06521i	−0.494169	+	0.869366i	$0.664528\pi$
$824$	−1.00683	−	7.00264i	−0.0350745	−	0.243948i
$825$		0			0
$826$	1.28287	−	1.48051i	0.0446366	−	0.0515134i
$827$	50.3483			1.75078			0.875391	−	0.483416i	$-0.160604\pi$
$827$	50.3483			1.75078			0.875391	+	0.483416i	$0.160604\pi$
$828$		0			0
$829$	43.2992			1.50384			0.751922	−	0.659252i	$-0.229127\pi$
$829$	43.2992			1.50384			0.751922	+	0.659252i	$0.229127\pi$
$830$	−13.4108	+	15.4769i	−0.465496	+	0.537211i
$831$		0			0
$832$	−0.797176	−	5.54448i	−0.0276371	−	0.192220i
$833$	18.4600	+	40.4218i	0.639601	+	1.40053i
$834$		0			0
$835$	−33.8400	+	9.93631i	−1.17108	+	0.343860i
$836$	−2.24602	−	1.44343i	−0.0776802	−	0.0499220i
$837$		0			0
$838$	4.44335	+	1.30469i	0.153493	+	0.0450696i
$839$	31.1856	+	35.9902i	1.07665	+	1.24252i	0.968666	+	0.248365i	$0.0798933\pi$
$839$	31.1856	+	35.9902i	1.07665	+	1.24252i	0.107982	+	0.994153i	$0.465561\pi$
$840$		0			0
$841$	3.21368	+	0.943623i	0.110817	+	0.0325387i
$842$	−1.07876	+	2.36216i	−0.0371766	+	0.0814054i
$843$		0			0
$844$	−24.0397	+	7.05870i	−0.827481	+	0.242970i
$845$	5.10463	−	35.5035i	0.175605	−	1.22136i
$846$		0			0
$847$	−0.613637	−	4.26794i	−0.0210848	−	0.146648i
$848$	2.22606	−	1.43060i	0.0764431	−	0.0491270i
$849$		0			0
$850$	7.78965			0.267183
$851$	4.32272	−	1.02052i	0.148181	−	0.0349828i
$852$		0			0
$853$	31.9979	−	36.9276i	1.09559	−	1.26438i	0.133673	−	0.991026i	$-0.457323\pi$
$853$	31.9979	−	36.9276i	1.09559	−	1.26438i	0.961915	−	0.273350i	$-0.0881317\pi$
$854$	3.30844	−	2.12620i	0.113212	−	0.0727572i
$855$		0			0
$856$	1.14811	+	2.51400i	0.0392414	+	0.0859268i
$857$	0.217270	−	1.51114i	0.00742179	−	0.0516197i	−0.985774	−	0.168076i	$-0.946245\pi$
$857$	0.217270	−	1.51114i	0.00742179	−	0.0516197i	0.993196	+	0.116457i	$0.0371536\pi$
$858$		0			0
$859$	−1.00579	−	0.646382i	−0.0343171	−	0.0220543i	0.523370	−	0.852106i	$-0.324675\pi$
$859$	−1.00579	−	0.646382i	−0.0343171	−	0.0220543i	−0.557687	+	0.830051i	$0.688311\pi$
$860$	−5.49277	+	12.0275i	−0.187302	+	0.410134i
$861$		0			0
$862$	−6.51040	−	7.51341i	−0.221745	−	0.255908i
$863$	32.0983	+	37.0434i	1.09264	+	1.26097i	0.963026	+	0.269407i	$0.0868278\pi$
$863$	32.0983	+	37.0434i	1.09264	+	1.26097i	0.129612	+	0.991565i	$0.458627\pi$
$864$		0			0
$865$	−12.9417	+	28.3385i	−0.440032	+	0.963537i
$866$	−18.0981	−	11.6310i	−0.615000	−	0.395236i
$867$		0			0
$868$	−0.00710552	+	0.0494200i	−0.000241177	+	0.00167742i
$869$	4.21066	+	9.22005i	0.142837	+	0.312769i
$870$		0			0
$871$	−70.8405	+	45.5264i	−2.40034	+	1.54260i
$872$	−10.8026	+	12.4668i	−0.365821	+	0.422180i
$873$		0			0
$874$	−0.903932	−	10.1255i	−0.0305760	−	0.342499i
$875$	−5.53432			−0.187094
$876$		0			0
$877$	0.914461	−	0.587688i	0.0308792	−	0.0198448i	−0.525110	−	0.851034i	$-0.675976\pi$
$877$	0.914461	−	0.587688i	0.0308792	−	0.0198448i	0.555989	+	0.831189i	$0.312340\pi$
$878$	3.60812	+	25.0950i	0.121768	+	0.846917i
$879$		0			0
$880$	−0.349871	+	2.43340i	−0.0117941	+	0.0820301i
$881$	−42.9627	+	12.6150i	−1.44745	+	0.425010i	−0.908698	−	0.417455i	$-0.862922\pi$
$881$	−42.9627	+	12.6150i	−1.44745	+	0.425010i	−0.538752	+	0.842464i	$0.681104\pi$
$882$		0			0
$883$	−20.1171	+	44.0503i	−0.676994	+	1.48241i	0.188802	+	0.982015i	$0.439539\pi$
$883$	−20.1171	+	44.0503i	−0.676994	+	1.48241i	−0.865797	+	0.500396i	$0.833188\pi$
$884$	35.1733	+	10.3278i	1.18301	+	0.347362i
$885$		0			0
$886$	−4.42675	−	5.10875i	−0.148720	−	0.171632i
$887$	−14.4032	−	4.22916i	−0.483612	−	0.142001i	0.0308330	−	0.999525i	$-0.490184\pi$
$887$	−14.4032	−	4.22916i	−0.483612	−	0.142001i	−0.514445	+	0.857523i	$0.672002\pi$
$888$		0			0
$889$	8.34756	+	5.36465i	0.279968	+	0.179925i
$890$	−11.1564	+	3.27580i	−0.373962	+	0.109805i
$891$		0			0
$892$	0.739886	+	1.62012i	0.0247732	+	0.0542458i
$893$	−0.756397	−	5.26086i	−0.0253119	−	0.176048i
$894$		0			0
$895$	20.0568	−	23.1468i	0.670425	−	0.773711i
$896$	−0.458044			−0.0153022
$897$		0			0
$898$	−7.80490			−0.260453
$899$	−0.361523	+	0.417220i	−0.0120575	+	0.0139151i
$900$		0			0
$901$	2.46449	+	17.1409i	0.0821040	+	0.571046i
$902$	−5.14836	−	11.2733i	−0.171422	−	0.375361i
$903$		0			0
$904$	14.7147	−	4.32064i	0.489405	−	0.143702i
$905$	2.98730	+	1.91982i	0.0993011	+	0.0638170i
$906$		0			0
$907$	22.6995	+	6.66518i	0.753725	+	0.221314i	0.635954	−	0.771727i	$-0.280607\pi$
$907$	22.6995	+	6.66518i	0.753725	+	0.221314i	0.117771	+	0.993041i	$0.462425\pi$
$908$	−13.5617	−	15.6511i	−0.450062	−	0.519399i
$909$		0			0
$910$	−4.80507	−	1.41090i	−0.159286	−	0.0467707i
$911$	12.1355	−	26.5730i	0.402066	−	0.880402i	−0.594991	−	0.803733i	$-0.702844\pi$
$911$	12.1355	−	26.5730i	0.402066	−	0.880402i	0.997057	−	0.0766690i	$-0.0244285\pi$
$912$		0			0
$913$	−12.6798	+	3.72313i	−0.419641	+	0.123218i
$914$	−1.32334	+	9.20402i	−0.0437721	+	0.304442i
$915$		0			0
$916$	−1.22716	−	8.53511i	−0.0405466	−	0.282008i
$917$	6.60721	−	4.24619i	0.218189	−	0.140222i
$918$		0			0
$919$	−12.1150			−0.399637			−0.199818	−	0.979833i	$-0.564035\pi$
$919$	−12.1150			−0.399637			−0.199818	+	0.979833i	$0.564035\pi$
$920$	−8.13533	+	4.63032i	−0.268214	+	0.152657i
$921$		0			0
$922$	−11.2912	+	13.0308i	−0.371857	+	0.429146i
$923$	1.42991	−	0.918948i	0.0470661	−	0.0302475i
$924$		0			0
$925$	0.457935	+	1.00274i	0.0150568	+	0.0329698i
$926$	1.28584	−	8.94323i	0.0422554	−	0.293893i
$927$		0			0
$928$	−4.26065	−	2.73815i	−0.139863	−	0.0898843i
$929$	4.21931	−	9.23900i	0.138431	−	0.303122i	−0.827701	−	0.561169i	$-0.810352\pi$
$929$	4.21931	−	9.23900i	0.138431	−	0.303122i	0.966132	+	0.258047i	$0.0830790\pi$
$930$		0			0
$931$	9.42555	+	10.8777i	0.308910	+	0.356501i
$932$	3.12786	+	3.60974i	0.102456	+	0.118241i
$933$		0			0
$934$	4.38083	−	9.59269i	0.143345	−	0.313882i
$935$	−13.5348	−	8.69829i	−0.442635	−	0.284464i
$936$		0			0
$937$	3.12406	−	21.7283i	0.102059	−	0.709834i	−0.872973	−	0.487768i	$-0.837811\pi$
$937$	3.12406	−	21.7283i	0.102059	−	0.709834i	0.975032	−	0.222065i	$-0.0712799\pi$
$938$	2.86049	+	6.26361i	0.0933984	+	0.204514i
$939$		0			0
$940$	−4.11716	+	2.64594i	−0.134287	+	0.0863009i
$941$	−24.8224	+	28.6465i	−0.809186	+	0.933851i	−0.998847	−	0.0479990i	$-0.984716\pi$
$941$	−24.8224	+	28.6465i	−0.809186	+	0.933851i	0.189661	+	0.981850i	$0.439261\pi$
$942$		0			0
$943$	21.8813	−	41.8091i	0.712552	−	1.36149i
$944$	4.27686			0.139200
$945$		0			0
$946$	−7.17796	+	4.61300i	−0.233376	+	0.149981i
$947$	4.91480	+	34.1832i	0.159710	+	1.11081i	0.899168	+	0.437603i	$0.144173\pi$
$947$	4.91480	+	34.1832i	0.159710	+	1.11081i	−0.739459	+	0.673202i	$0.764918\pi$
$948$		0			0
$949$	−2.66751	+	18.5529i	−0.0865910	+	0.602254i
$950$	2.42085	−	0.710826i	0.0785428	−	0.0230622i
$951$		0			0
$952$	1.24525	−	2.72672i	0.0403588	−	0.0883735i
$953$	−44.2608	−	12.9962i	−1.43375	−	0.420987i	−0.529616	−	0.848238i	$-0.677664\pi$
$953$	−44.2608	−	12.9962i	−1.43375	−	0.420987i	−0.904133	+	0.427251i	$0.859482\pi$
$954$		0			0
$955$	−5.43037	−	6.26698i	−0.175723	−	0.202795i
$956$	−22.9405	−	6.73595i	−0.741950	−	0.217856i
$957$		0			0
$958$	11.0778	+	7.11926i	0.357907	+	0.230013i
$959$	1.36389	−	0.400473i	0.0440422	−	0.0129320i
$960$		0			0
$961$	−12.8729	−	28.1878i	−0.415256	−	0.909283i
$962$	0.738286	+	5.13490i	0.0238033	+	0.165556i
$963$		0			0
$964$	15.0945	−	17.4200i	0.486161	−	0.561060i
$965$	−25.5928			−0.823861
$966$		0			0
$967$	32.2668			1.03763			0.518815	−	0.854886i	$-0.326373\pi$
$967$	32.2668			1.03763			0.518815	+	0.854886i	$0.326373\pi$
$968$	6.16457	−	7.11430i	0.198137	−	0.228662i
$969$		0			0
$970$	5.07189	+	35.2758i	0.162849	+	1.13264i
$971$	12.6929	+	27.7936i	0.407335	+	0.891940i	0.996474	+	0.0839078i	$0.0267401\pi$
$971$	12.6929	+	27.7936i	0.407335	+	0.891940i	−0.589138	+	0.808032i	$0.700533\pi$
$972$		0			0
$973$	−9.86590	+	2.89689i	−0.316286	+	0.0928700i
$974$	−2.55002	−	1.63880i	−0.0817081	−	0.0525106i
$975$		0			0
$976$	8.23816	+	2.41894i	0.263697	+	0.0774284i
$977$	−15.9168	−	18.3689i	−0.509223	−	0.587674i	0.441677	−	0.897174i	$-0.354384\pi$
$977$	−15.9168	−	18.3689i	−0.509223	−	0.587674i	−0.950899	+	0.309500i	$0.899838\pi$
$978$		0			0
$979$	−7.19926	−	2.11389i	−0.230089	−	0.0675603i
$980$	5.50568	−	12.0558i	0.175872	−	0.385107i
$981$		0			0
$982$	6.05024	−	1.77651i	0.193071	−	0.0566908i
$983$	−8.29195	+	57.6718i	−0.264472	+	1.83944i	0.233630	+	0.972326i	$0.424940\pi$
$983$	−8.29195	+	57.6718i	−0.264472	+	1.83944i	−0.498102	+	0.867118i	$0.665969\pi$
$984$		0			0
$985$	2.75661	+	19.1726i	0.0878328	+	0.610891i
$986$	27.8832	−	17.9195i	0.887984	−	0.570672i
$987$		0			0
$988$	11.8735			0.377747
$989$	−30.6354	−	10.8149i	−0.974149	−	0.343893i
$990$		0			0
$991$	−23.0895	+	26.6467i	−0.733463	+	0.846461i	−0.992857	−	0.119310i	$-0.961932\pi$
$991$	−23.0895	+	26.6467i	−0.733463	+	0.846461i	0.259394	+	0.965772i	$0.416477\pi$
$992$	−0.0916991	+	0.0589314i	−0.00291145	+	0.00187107i
$993$		0			0
$994$	−0.0577389	−	0.126430i	−0.00183137	−	0.00401013i
$995$	1.75154	−	12.1822i	0.0555275	−	0.386202i
$996$		0			0
$997$	−37.2590	−	23.9449i	−1.18001	−	0.758343i	−0.204618	−	0.978842i	$-0.565595\pi$
$997$	−37.2590	−	23.9449i	−1.18001	−	0.758343i	−0.975387	+	0.220498i	$0.929232\pi$
$998$	−2.81856	+	6.17179i	−0.0892200	+	0.195365i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.i.b.361.1		10
3.2	odd	2		138.2.e.c.85.1	yes	10
23.6	even	11		9522.2.a.bv.1.4		5
23.13	even	11	inner	414.2.i.b.289.1		10
23.17	odd	22		9522.2.a.ca.1.2		5
69.17	even	22		3174.2.a.y.1.4		5
69.29	odd	22		3174.2.a.z.1.2		5
69.59	odd	22		138.2.e.c.13.1	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.e.c.13.1	✓	10	69.59	odd	22
138.2.e.c.85.1	yes	10	3.2	odd	2
414.2.i.b.289.1		10	23.13	even	11	inner
414.2.i.b.361.1		10	1.1	even	1	trivial
3174.2.a.y.1.4		5	69.17	even	22
3174.2.a.z.1.2		5	69.29	odd	22
9522.2.a.bv.1.4		5	23.6	even	11
9522.2.a.ca.1.2		5	23.17	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)

\(f(q)\)	\(=\)	\(q+(-0.654861 + 0.755750i) q^{2} +(-0.142315 - 0.989821i) q^{4} +(-0.810827 - 1.77546i) q^{5} +(0.439490 - 0.129046i) q^{7} +(0.841254 + 0.540641i) q^{8} +O(q^{10})\)	\(q+(-0.654861 + 0.755750i) q^{2} +(-0.142315 - 0.989821i) q^{4} +(-0.810827 - 1.77546i) q^{5} +(0.439490 - 0.129046i) q^{7} +(0.841254 + 0.540641i) q^{8} +(1.87279 + 0.549899i) q^{10} +(0.824822 + 0.951895i) q^{11} +(-5.37459 - 1.57812i) q^{13} +(-0.190279 + 0.416652i) q^{14} +(-0.959493 + 0.281733i) q^{16} +(0.931360 - 6.47775i) q^{17} +(-0.301665 - 2.09813i) q^{19} +(-1.64200 + 1.05525i) q^{20} -1.25954 q^{22} +(-2.94130 - 3.78798i) q^{23} +(0.779471 - 0.899557i) q^{25} +(4.71228 - 3.02840i) q^{26} +(-0.190279 - 0.416652i) q^{28} +(0.720774 - 5.01310i) q^{29} +(-0.0916991 - 0.0589314i) q^{31} +(0.415415 - 0.909632i) q^{32} +(4.28565 + 4.94590i) q^{34} +(-0.585468 - 0.675666i) q^{35} +(-0.384727 + 0.842435i) q^{37} +(1.78321 + 1.14600i) q^{38} +(0.277777 - 1.93198i) q^{40} +(4.08750 + 8.95037i) q^{41} +(5.69889 - 3.66245i) q^{43} +(0.824822 - 0.951895i) q^{44} +(4.78890 + 0.257712i) q^{46} +2.50740 q^{47} +(-5.71228 + 3.67106i) q^{49} +(0.169395 + 1.17817i) q^{50} +(-0.797176 + 5.54448i) q^{52} +(-2.53893 + 0.745497i) q^{53} +(1.02127 - 2.23626i) q^{55} +(0.439490 + 0.129046i) q^{56} +(3.31664 + 3.82760i) q^{58} +(-4.10362 - 1.20493i) q^{59} +(-7.22296 - 4.64192i) q^{61} +(0.104588 - 0.0307097i) q^{62} +(0.415415 + 0.909632i) q^{64} +(1.55597 + 10.8220i) q^{65} +(9.84464 - 11.3613i) q^{67} -6.54436 q^{68} +0.894034 q^{70} +(-0.198713 + 0.229328i) q^{71} +(-0.476214 - 3.31214i) q^{73} +(-0.384727 - 0.842435i) q^{74} +(-2.03384 + 0.597190i) q^{76} +(0.485340 + 0.311909i) q^{77} +(7.72144 + 2.26722i) q^{79} +(1.27819 + 1.47511i) q^{80} +(-9.44098 - 2.77212i) q^{82} +(-4.35855 + 9.54389i) q^{83} +(-12.2562 + 3.59874i) q^{85} +(-0.964080 + 6.70533i) q^{86} +(0.179251 + 1.24672i) q^{88} +(-5.01143 + 3.22065i) q^{89} -2.56573 q^{91} +(-3.33083 + 3.45045i) q^{92} +(-1.64200 + 1.89497i) q^{94} +(-3.48055 + 2.23682i) q^{95} +(7.58500 + 16.6088i) q^{97} +(0.966346 - 6.72108i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - q^{4} - 2 q^{7} - q^{8}+O(q^{10}) \) 10 * q - q^2 - q^4 - 2 * q^7 - q^8	\( 10 q - q^{2} - q^{4} - 2 q^{7} - q^{8} + 11 q^{10} - 11 q^{11} - 13 q^{13} - 13 q^{14} - q^{16} - 2 q^{19} + 11 q^{20} - 22 q^{22} + 10 q^{23} + 5 q^{25} + 9 q^{26} - 13 q^{28} + 27 q^{29} - 18 q^{31} - q^{32} + 33 q^{34} - 44 q^{35} - q^{37} - 13 q^{38} - 11 q^{40} + 16 q^{41} + 20 q^{43} - 11 q^{44} - q^{46} - 19 q^{49} + 27 q^{50} - 2 q^{52} + q^{53} + 33 q^{55} - 2 q^{56} - 17 q^{58} + q^{59} - 34 q^{61} + 4 q^{62} - q^{64} - 11 q^{65} + 8 q^{67} - 22 q^{68} + 22 q^{70} + 22 q^{71} + 31 q^{73} - q^{74} - 2 q^{76} - 22 q^{77} + 32 q^{79} - 28 q^{82} - 33 q^{83} - 11 q^{85} + 20 q^{86} + 22 q^{88} + 23 q^{89} + 18 q^{91} - 23 q^{92} + 11 q^{94} + 22 q^{95} - q^{97} + 14 q^{98}+O(q^{100}) \) 10 * q - q^2 - q^4 - 2 * q^7 - q^8 + 11 * q^10 - 11 * q^11 - 13 * q^13 - 13 * q^14 - q^16 - 2 * q^19 + 11 * q^20 - 22 * q^22 + 10 * q^23 + 5 * q^25 + 9 * q^26 - 13 * q^28 + 27 * q^29 - 18 * q^31 - q^32 + 33 * q^34 - 44 * q^35 - q^37 - 13 * q^38 - 11 * q^40 + 16 * q^41 + 20 * q^43 - 11 * q^44 - q^46 - 19 * q^49 + 27 * q^50 - 2 * q^52 + q^53 + 33 * q^55 - 2 * q^56 - 17 * q^58 + q^59 - 34 * q^61 + 4 * q^62 - q^64 - 11 * q^65 + 8 * q^67 - 22 * q^68 + 22 * q^70 + 22 * q^71 + 31 * q^73 - q^74 - 2 * q^76 - 22 * q^77 + 32 * q^79 - 28 * q^82 - 33 * q^83 - 11 * q^85 + 20 * q^86 + 22 * q^88 + 23 * q^89 + 18 * q^91 - 23 * q^92 + 11 * q^94 + 22 * q^95 - q^97 + 14 * q^98

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