LMFDB - Embedded newform 414.2.i.h.289.2

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			289.2
Root			$-0.708869 + 1.55221i$ of defining polynomial
Character	$\chi$	$=$	414.289
Dual form			414.2.i.h.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.654861 + 0.755750i) q^{2} +(-0.142315 + 0.989821i) q^{4} +(0.355945 - 0.779412i) q^{5} +(2.70753 + 0.795003i) q^{7} +(-0.841254 + 0.540641i) q^{8} +O(q^{10})$	\(q+(0.654861 + 0.755750i) q^{2} +(-0.142315 + 0.989821i) q^{4} +(0.355945 - 0.779412i) q^{5} +(2.70753 + 0.795003i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(0.822135 - 0.241401i) q^{10} +(3.69316 - 4.26213i) q^{11} +(-0.549197 + 0.161259i) q^{13} +(1.17223 + 2.56683i) q^{14} +(-0.959493 - 0.281733i) q^{16} +(0.259417 + 1.80429i) q^{17} +(-1.09218 + 7.59627i) q^{19} +(0.720822 + 0.463244i) q^{20} +5.63961 q^{22} +(-4.59874 + 1.36074i) q^{23} +(2.79352 + 3.22389i) q^{25} +(-0.481519 - 0.309453i) q^{26} +(-1.17223 + 2.56683i) q^{28} +(-0.707799 - 4.92285i) q^{29} +(6.83443 - 4.39222i) q^{31} +(-0.415415 - 0.909632i) q^{32} +(-1.19371 + 1.37761i) q^{34} +(1.58337 - 1.82730i) q^{35} +(0.172534 + 0.377797i) q^{37} +(-6.45610 + 4.14909i) q^{38} +(0.121941 + 0.848122i) q^{40} +(1.18061 - 2.58519i) q^{41} +(-4.45929 - 2.86581i) q^{43} +(3.69316 + 4.26213i) q^{44} +(-4.03991 - 2.58440i) q^{46} -6.28555 q^{47} +(0.809915 + 0.520501i) q^{49} +(-0.607089 + 4.22240i) q^{50} +(-0.0814585 - 0.566556i) q^{52} +(0.404800 + 0.118860i) q^{53} +(-2.00739 - 4.39558i) q^{55} +(-2.70753 + 0.795003i) q^{56} +(3.25693 - 3.75870i) q^{58} +(-6.62639 + 1.94569i) q^{59} +(-4.64179 + 2.98310i) q^{61} +(7.79502 + 2.28883i) q^{62} +(0.415415 - 0.909632i) q^{64} +(-0.0697971 + 0.485450i) q^{65} +(-8.17942 - 9.43956i) q^{67} -1.82284 q^{68} +2.41787 q^{70} +(-2.97106 - 3.42878i) q^{71} +(0.375102 - 2.60889i) q^{73} +(-0.172534 + 0.377797i) q^{74} +(-7.36352 - 2.16212i) q^{76} +(13.3877 - 8.60378i) q^{77} +(-4.41367 + 1.29597i) q^{79} +(-0.561113 + 0.647559i) q^{80} +(2.72689 - 0.800687i) q^{82} +(-6.92023 - 15.1532i) q^{83} +(1.49862 + 0.440035i) q^{85} +(-0.754378 - 5.24681i) q^{86} +(-0.802600 + 5.58220i) q^{88} +(10.1439 + 6.51911i) q^{89} -1.61517 q^{91} +(-0.692421 - 4.74558i) q^{92} +(-4.11616 - 4.75030i) q^{94} +(5.53187 + 3.55512i) q^{95} +(-1.32713 + 2.90601i) q^{97} +(0.137013 + 0.952948i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$1$	$e\left(\frac{7}{11}\right)$

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
$5$	0.355945	−	0.779412i	0.159184	−	0.348564i	−0.813188	−	0.582001i	$-0.802270\pi$
$5$	0.355945	−	0.779412i	0.159184	−	0.348564i	0.972372	+	0.233437i	$0.0749973\pi$
$6$		0			0
$7$	2.70753	+	0.795003i	1.02335	+	0.300483i	0.750004	−	0.661433i	$-0.230051\pi$
$7$	2.70753	+	0.795003i	1.02335	+	0.300483i	0.273346	+	0.961916i	$0.411870\pi$
$8$	−0.841254	+	0.540641i	−0.297428	+	0.191145i
$9$		0			0
$10$	0.822135	−	0.241401i	0.259982	−	0.0763376i
$11$	3.69316	−	4.26213i	1.11353	−	1.28508i	0.158896	−	0.987295i	$-0.449207\pi$
$11$	3.69316	−	4.26213i	1.11353	−	1.28508i	0.954633	−	0.297785i	$-0.0962480\pi$
$12$		0			0
$13$	−0.549197	+	0.161259i	−0.152320	+	0.0447251i	−0.357004	−	0.934103i	$-0.616202\pi$
$13$	−0.549197	+	0.161259i	−0.152320	+	0.0447251i	0.204684	+	0.978828i	$0.434383\pi$
$14$	1.17223	+	2.56683i	0.313292	+	0.686014i
$15$		0			0
$16$	−0.959493	−	0.281733i	−0.239873	−	0.0704331i
$17$	0.259417	+	1.80429i	0.0629179	+	0.437604i	0.996794	+	0.0800075i	$0.0254944\pi$
$17$	0.259417	+	1.80429i	0.0629179	+	0.437604i	−0.933876	+	0.357596i	$0.883596\pi$
$18$		0			0
$19$	−1.09218	+	7.59627i	−0.250563	+	1.74270i	0.344284	+	0.938865i	$0.388122\pi$
$19$	−1.09218	+	7.59627i	−0.250563	+	1.74270i	−0.594847	+	0.803839i	$0.702788\pi$
$20$	0.720822	+	0.463244i	0.161181	+	0.103585i
$21$		0			0
$22$	5.63961			1.20237
$23$	−4.59874	+	1.36074i	−0.958903	+	0.283734i
$23$	−4.59874	+	1.36074i	−0.958903	+	0.283734i
$24$		0			0
$25$	2.79352	+	3.22389i	0.558704	+	0.644778i
$26$	−0.481519	−	0.309453i	−0.0944336	−	0.0606888i
$27$		0			0
$28$	−1.17223	+	2.56683i	−0.221531	+	0.485085i
$29$	−0.707799	−	4.92285i	−0.131435	−	0.914150i	−0.943686	−	0.330842i	$-0.892667\pi$
$29$	−0.707799	−	4.92285i	−0.131435	−	0.914150i	0.812251	−	0.583308i	$-0.198242\pi$
$30$		0			0
$31$	6.83443	−	4.39222i	1.22750	−	0.788867i	0.244000	−	0.969775i	$-0.421540\pi$
$31$	6.83443	−	4.39222i	1.22750	−	0.788867i	0.983500	+	0.180909i	$0.0579038\pi$
$32$	−0.415415	−	0.909632i	−0.0734357	−	0.160802i
$33$		0			0
$34$	−1.19371	+	1.37761i	−0.204719	+	0.236258i
$35$	1.58337	−	1.82730i	0.267638	−	0.308871i
$36$		0			0
$37$	0.172534	+	0.377797i	0.0283644	+	0.0621094i	0.923284	−	0.384118i	$-0.125494\pi$
$37$	0.172534	+	0.377797i	0.0283644	+	0.0621094i	−0.894920	+	0.446228i	$0.852767\pi$
$38$	−6.45610	+	4.14909i	−1.04732	+	0.673071i
$39$		0			0
$40$	0.121941	+	0.848122i	0.0192806	+	0.134100i
$41$	1.18061	−	2.58519i	0.184381	−	0.403738i	−0.794759	−	0.606925i	$-0.792403\pi$
$41$	1.18061	−	2.58519i	0.184381	−	0.403738i	0.979140	+	0.203187i	$0.0651300\pi$
$42$		0			0
$43$	−4.45929	−	2.86581i	−0.680035	−	0.437032i	0.154496	−	0.987993i	$-0.450625\pi$
$43$	−4.45929	−	2.86581i	−0.680035	−	0.437032i	−0.834531	+	0.550961i	$0.814261\pi$
$44$	3.69316	+	4.26213i	0.556764	+	0.642540i
$45$		0			0
$46$	−4.03991	−	2.58440i	−0.595652	−	0.381049i
$47$	−6.28555			−0.916841			−0.458421	−	0.888735i	$-0.651585\pi$
$47$	−6.28555			−0.916841			−0.458421	+	0.888735i	$0.651585\pi$
$48$		0			0
$49$	0.809915	+	0.520501i	0.115702	+	0.0743572i
$50$	−0.607089	+	4.22240i	−0.0858554	+	0.597138i
$51$		0			0
$52$	−0.0814585	−	0.566556i	−0.0112963	−	0.0785672i
$53$	0.404800	+	0.118860i	0.0556035	+	0.0163267i	0.309416	−	0.950927i	$-0.399866\pi$
$53$	0.404800	+	0.118860i	0.0556035	+	0.0163267i	−0.253813	+	0.967253i	$0.581685\pi$
$54$		0			0
$55$	−2.00739	−	4.39558i	−0.270677	−	0.592699i
$56$	−2.70753	+	0.795003i	−0.361809	+	0.106237i
$57$		0			0
$58$	3.25693	−	3.75870i	0.427656	−	0.493541i
$59$	−6.62639	+	1.94569i	−0.862683	+	0.253307i	−0.683000	−	0.730418i	$-0.739325\pi$
$59$	−6.62639	+	1.94569i	−0.862683	+	0.253307i	−0.179683	+	0.983725i	$0.557507\pi$
$60$		0			0
$61$	−4.64179	+	2.98310i	−0.594321	+	0.381947i	−0.802949	−	0.596048i	$-0.796737\pi$
$61$	−4.64179	+	2.98310i	−0.594321	+	0.381947i	0.208628	+	0.977995i	$0.433100\pi$
$62$	7.79502	+	2.28883i	0.989969	+	0.290681i
$63$		0			0
$64$	0.415415	−	0.909632i	0.0519269	−	0.113704i
$65$	−0.0697971	+	0.485450i	−0.00865727	+	0.0602126i
$66$		0			0
$67$	−8.17942	−	9.43956i	−0.999276	−	1.15323i	−0.988182	−	0.153287i	$-0.951014\pi$
$67$	−8.17942	−	9.43956i	−0.999276	−	1.15323i	−0.0110941	−	0.999938i	$-0.503531\pi$
$68$	−1.82284			−0.221052
$69$		0			0
$70$	2.41787			0.288991
$71$	−2.97106	−	3.42878i	−0.352599	−	0.406921i	0.551547	−	0.834144i	$-0.314038\pi$
$71$	−2.97106	−	3.42878i	−0.352599	−	0.406921i	−0.904147	+	0.427222i	$0.859492\pi$
$72$		0			0
$73$	0.375102	−	2.60889i	0.0439024	−	0.305348i	−0.956025	−	0.293286i	$-0.905251\pi$
$73$	0.375102	−	2.60889i	0.0439024	−	0.305348i	0.999927	−	0.0120622i	$-0.00383961\pi$
$74$	−0.172534	+	0.377797i	−0.0200567	+	0.0439180i
$75$		0			0
$76$	−7.36352	−	2.16212i	−0.844654	−	0.248013i
$77$	13.3877	−	8.60378i	1.52567	−	0.980491i
$78$		0			0
$79$	−4.41367	+	1.29597i	−0.496576	+	0.145808i	−0.520425	−	0.853908i	$-0.674226\pi$
$79$	−4.41367	+	1.29597i	−0.496576	+	0.145808i	0.0238484	+	0.999716i	$0.492408\pi$
$80$	−0.561113	+	0.647559i	−0.0627343	+	0.0723993i
$81$		0			0
$82$	2.72689	−	0.800687i	0.301135	−	0.0884211i
$83$	−6.92023	−	15.1532i	−0.759594	−	1.66328i	−0.748317	−	0.663342i	$-0.769138\pi$
$83$	−6.92023	−	15.1532i	−0.759594	−	1.66328i	−0.0112769	−	0.999936i	$-0.503590\pi$
$84$		0			0
$85$	1.49862	+	0.440035i	0.162548	+	0.0477284i
$86$	−0.754378	−	5.24681i	−0.0813466	−	0.565778i
$87$		0			0
$88$	−0.802600	+	5.58220i	−0.0855574	+	0.595065i
$89$	10.1439	+	6.51911i	1.07525	+	0.691024i	0.953456	−	0.301531i	$-0.0974977\pi$
$89$	10.1439	+	6.51911i	1.07525	+	0.691024i	0.121798	+	0.992555i	$0.461134\pi$
$90$		0			0
$91$	−1.61517			−0.169316
$92$	−0.692421	−	4.74558i	−0.0721898	−	0.494761i
$93$		0			0
$94$	−4.11616	−	4.75030i	−0.424549	−	0.489956i
$95$	5.53187	+	3.55512i	0.567558	+	0.364747i
$96$		0			0
$97$	−1.32713	+	2.90601i	−0.134750	+	0.295061i	−0.964963	−	0.262385i	$-0.915491\pi$
$97$	−1.32713	+	2.90601i	−0.134750	+	0.295061i	0.830214	+	0.557445i	$0.188218\pi$
$98$	0.137013	+	0.952948i	0.0138404	+	0.0962623i
$99$		0			0
$100$	−3.58864	+	2.30628i	−0.358864	+	0.230628i
$101$	6.19890	+	13.5737i	0.616814	+	1.35063i	0.917814	+	0.397010i	$0.129952\pi$
$101$	6.19890	+	13.5737i	0.616814	+	1.35063i	−0.301000	+	0.953624i	$0.597320\pi$
$102$		0			0
$103$	1.19423	−	1.37822i	0.117671	−	0.135800i	−0.693858	−	0.720112i	$-0.744090\pi$
$103$	1.19423	−	1.37822i	0.117671	−	0.135800i	0.811529	+	0.584312i	$0.198636\pi$
$104$	0.374831	−	0.432578i	0.0367552	−	0.0424177i
$105$		0			0
$106$	0.175259	+	0.383764i	0.0170227	+	0.0372744i
$107$	−12.9319	+	8.31081i	−1.25017	+	0.803436i	−0.986907	−	0.161288i	$-0.948435\pi$
$107$	−12.9319	+	8.31081i	−1.25017	+	0.803436i	−0.263264	+	0.964724i	$0.584799\pi$
$108$		0			0
$109$	−2.21886	−	15.4325i	−0.212528	−	1.47817i	−0.764673	−	0.644419i	$-0.777099\pi$
$109$	−2.21886	−	15.4325i	−0.212528	−	1.47817i	0.552144	−	0.833749i	$-0.313810\pi$
$110$	2.00739	−	4.39558i	0.191397	−	0.419102i
$111$		0			0
$112$	−2.37388	−	1.52560i	−0.224310	−	0.144156i
$113$	8.31182	+	9.59235i	0.781910	+	0.902373i	0.997246	−	0.0741676i	$-0.0236300\pi$
$113$	8.31182	+	9.59235i	0.781910	+	0.902373i	−0.215336	+	0.976540i	$0.569085\pi$
$114$		0			0
$115$	−0.576323	+	4.06866i	−0.0537424	+	0.379404i
$116$	4.97347			0.461775
$117$		0			0
$118$	−5.80982	−	3.73374i	−0.534837	−	0.343719i
$119$	−0.732032	+	5.09139i	−0.0671053	+	0.466727i
$120$		0			0
$121$	−2.96088	−	20.5934i	−0.269171	−	1.87213i
$122$	−5.29420	−	1.55452i	−0.479315	−	0.140740i
$123$		0			0
$124$	3.37488	+	7.38995i	0.303073	+	0.663637i
$125$	7.61775	−	2.23677i	0.681353	−	0.200063i
$126$		0			0
$127$	−5.91119	+	6.82188i	−0.524533	+	0.605344i	−0.954760	−	0.297377i	$-0.903888\pi$
$127$	−5.91119	+	6.82188i	−0.524533	+	0.605344i	0.430227	+	0.902721i	$0.358434\pi$
$128$	0.959493	−	0.281733i	0.0848080	−	0.0249019i
$129$		0			0
$130$	−0.412586	+	0.265153i	−0.0361862	+	0.0232554i
$131$	−5.80376	−	1.70414i	−0.507077	−	0.148891i	0.0181804	−	0.999835i	$-0.494213\pi$
$131$	−5.80376	−	1.70414i	−0.507077	−	0.148891i	−0.525257	+	0.850944i	$0.676031\pi$
$132$		0			0
$133$	−8.99616	+	19.6988i	−0.780066	+	1.70811i
$134$	1.77756	−	12.3632i	0.153558	−	1.06802i
$135$		0			0
$136$	−1.19371	−	1.37761i	−0.102359	−	0.118129i
$137$	−2.57420			−0.219929			−0.109964	−	0.993936i	$-0.535074\pi$
$137$	−2.57420			−0.219929			−0.109964	+	0.993936i	$0.535074\pi$
$138$		0			0
$139$	11.0030			0.933266			0.466633	−	0.884451i	$-0.345467\pi$
$139$	11.0030			0.933266			0.466633	+	0.884451i	$0.345467\pi$
$140$	1.58337	+	1.82730i	0.133819	+	0.154435i
$141$		0			0
$142$	0.645672	−	4.49075i	0.0541836	−	0.376855i
$143$	−1.34096	+	2.93630i	−0.112137	+	0.245546i
$144$		0			0
$145$	−4.08886	−	1.20060i	−0.339562	−	0.0997043i
$146$	2.21731	−	1.42498i	0.183506	−	0.117932i
$147$		0			0
$148$	−0.398506	+	0.117012i	−0.0327570	+	0.00961831i
$149$	5.77471	−	6.66437i	0.473083	−	0.545967i	−0.468184	−	0.883631i	$-0.655091\pi$
$149$	5.77471	−	6.66437i	0.473083	−	0.545967i	0.941267	+	0.337664i	$0.109637\pi$
$150$		0			0
$151$	5.42483	−	1.59287i	0.441466	−	0.129626i	−0.0534429	−	0.998571i	$-0.517020\pi$
$151$	5.42483	−	1.59287i	0.441466	−	0.129626i	0.494909	+	0.868945i	$0.335201\pi$
$152$	−3.18805	−	6.98087i	−0.258585	−	0.566223i
$153$		0			0
$154$	15.2694	+	4.48350i	1.23044	+	0.361291i
$155$	−0.990665	−	6.89023i	−0.0795722	−	0.553437i
$156$		0			0
$157$	2.90881	−	20.2312i	0.232148	−	1.61463i	−0.456631	−	0.889656i	$-0.650944\pi$
$157$	2.90881	−	20.2312i	0.232148	−	1.61463i	0.688779	−	0.724971i	$-0.258147\pi$
$158$	−3.86976	−	2.48695i	−0.307862	−	0.197851i
$159$		0			0
$160$	−0.856843			−0.0677394
$161$	−13.5330	+	0.0282349i	−1.06655	+	0.00222522i
$162$		0			0
$163$	7.45217	+	8.60027i	0.583699	+	0.673625i	0.968396	−	0.249418i	$-0.0802394\pi$
$163$	7.45217	+	8.60027i	0.583699	+	0.673625i	−0.384697	+	0.923043i	$0.625694\pi$
$164$	2.39085	+	1.53651i	0.186694	+	0.119981i
$165$		0			0
$166$	6.92023	−	15.1532i	0.537114	−	1.17612i
$167$	2.40760	+	16.7452i	0.186306	+	1.29579i	0.841472	+	0.540301i	$0.181690\pi$
$167$	2.40760	+	16.7452i	0.186306	+	1.29579i	−0.655166	+	0.755485i	$0.727401\pi$
$168$		0			0
$169$	−10.6607	+	6.85121i	−0.820053	+	0.527016i
$170$	0.648831	+	1.42074i	0.0497631	+	0.108966i
$171$		0			0
$172$	3.47126	−	4.00605i	0.264681	−	0.305459i
$173$	10.1253	−	11.6852i	0.769809	−	0.888407i	−0.226520	−	0.974006i	$-0.572735\pi$
$173$	10.1253	−	11.6852i	0.769809	−	0.888407i	0.996330	+	0.0855990i	$0.0272804\pi$
$174$		0			0
$175$	5.00053	+	10.9496i	0.378005	+	0.827715i
$176$	−4.74434	+	3.04900i	−0.357618	+	0.229827i
$177$		0			0
$178$	1.71605	+	11.9354i	0.128623	+	0.894594i
$179$	−9.30979	+	20.3856i	−0.695846	+	1.52369i	0.149090	+	0.988824i	$0.452366\pi$
$179$	−9.30979	+	20.3856i	−0.695846	+	1.52369i	−0.844936	+	0.534867i	$0.820362\pi$
$180$		0			0
$181$	15.1607	+	9.74316i	1.12688	+	0.724204i	0.964907	−	0.262591i	$-0.0845770\pi$
$181$	15.1607	+	9.74316i	1.12688	+	0.724204i	0.161976	+	0.986795i	$0.448213\pi$
$182$	−1.05771	−	1.22066i	−0.0784027	−	0.0904815i
$183$		0			0
$184$	3.13303	−	3.63099i	0.230970	−	0.267680i
$185$	0.355872			0.0261642
$186$		0			0
$187$	8.64817	+	5.55784i	0.632417	+	0.406430i
$188$	0.894527	−	6.22157i	0.0652401	−	0.453755i
$189$		0			0
$190$	0.935826	+	6.50881i	0.0678919	+	0.472199i
$191$	−12.2943	−	3.60993i	−0.889585	−	0.261206i	−0.195160	−	0.980771i	$-0.562523\pi$
$191$	−12.2943	−	3.60993i	−0.889585	−	0.261206i	−0.694424	+	0.719566i	$0.744341\pi$
$192$		0			0
$193$	9.54623	+	20.9033i	0.687153	+	1.50465i	0.854883	+	0.518821i	$0.173629\pi$
$193$	9.54623	+	20.9033i	0.687153	+	1.50465i	−0.167730	+	0.985833i	$0.553644\pi$
$194$	−3.06530	+	0.900054i	−0.220076	+	0.0646201i
$195$		0			0
$196$	−0.630466	+	0.727596i	−0.0450333	+	0.0519712i
$197$	−21.6273	+	6.35034i	−1.54088	+	0.452443i	−0.938360	−	0.345661i	$-0.887655\pi$
$197$	−21.6273	+	6.35034i	−1.54088	+	0.452443i	−0.602520	+	0.798104i	$0.705837\pi$
$198$		0			0
$199$	−10.0099	+	6.43300i	−0.709586	+	0.456024i	−0.845000	−	0.534766i	$-0.820400\pi$
$199$	−10.0099	+	6.43300i	−0.709586	+	0.456024i	0.135414	+	0.990789i	$0.456764\pi$
$200$	−4.09302	−	1.20182i	−0.289421	−	0.0849815i
$201$		0			0
$202$	−6.19890	+	13.5737i	−0.436153	+	0.955043i
$203$	1.99729	−	13.8915i	0.140182	−	0.974989i
$204$		0			0
$205$	−1.59469	−	1.84037i	−0.111378	−	0.128537i
$206$	1.82365			0.127059
$207$		0			0
$208$	0.572382			0.0396876
$209$	28.3427	+	32.7092i	1.96051	+	2.26254i
$210$		0			0
$211$	2.38030	−	16.5553i	0.163866	−	1.13972i	−0.727393	−	0.686222i	$-0.759268\pi$
$211$	2.38030	−	16.5553i	0.163866	−	1.13972i	0.891259	−	0.453495i	$-0.149823\pi$
$212$	−0.175259	+	0.383764i	−0.0120368	+	0.0263570i
$213$		0			0
$214$	−14.7495	−	4.33083i	−1.00825	−	0.296050i
$215$	−3.82091	+	2.45555i	−0.260584	+	0.167467i
$216$		0			0
$217$	21.9963	−	6.45868i	1.49320	−	0.438444i
$218$	10.2101	−	11.7831i	0.691514	−	0.798049i
$219$		0			0
$220$	4.63652	−	1.36140i	0.312594	−	0.0917859i
$221$	−0.433428	−	0.949075i	−0.0291555	−	0.0638417i
$222$		0			0
$223$	2.27882	+	0.669123i	0.152601	+	0.0448078i	0.357141	−	0.934050i	$-0.383752\pi$
$223$	2.27882	+	0.669123i	0.152601	+	0.0448078i	−0.204540	+	0.978858i	$0.565570\pi$
$224$	−0.401589	−	2.79311i	−0.0268323	−	0.186623i
$225$		0			0
$226$	−1.80633	+	12.5633i	−0.120155	+	0.835699i
$227$	−11.3480	−	7.29290i	−0.753191	−	0.484047i	0.106847	−	0.994275i	$-0.465924\pi$
$227$	−11.3480	−	7.29290i	−0.753191	−	0.484047i	−0.860039	+	0.510229i	$0.829561\pi$
$228$		0			0
$229$	2.39089			0.157995			0.0789973	−	0.996875i	$-0.474828\pi$
$229$	2.39089			0.157995			0.0789973	+	0.996875i	$0.474828\pi$
$230$	−3.45230	+	2.22885i	−0.227638	+	0.146966i
$231$		0			0
$232$	3.25693	+	3.75870i	0.213828	+	0.246771i
$233$	−11.0222	−	7.08355i	−0.722089	−	0.464059i	0.127274	−	0.991868i	$-0.459377\pi$
$233$	−11.0222	−	7.08355i	−0.722089	−	0.464059i	−0.849363	+	0.527809i	$0.823014\pi$
$234$		0			0
$235$	−2.23731	+	4.89903i	−0.145946	+	0.319577i
$236$	−0.982847	−	6.83585i	−0.0639779	−	0.444976i
$237$		0			0
$238$	−4.32720	+	2.78092i	−0.280491	+	0.180260i
$239$	−3.59643	−	7.87508i	−0.232634	−	0.509397i	0.756929	−	0.653497i	$-0.226699\pi$
$239$	−3.59643	−	7.87508i	−0.232634	−	0.509397i	−0.989563	+	0.144100i	$0.953971\pi$
$240$		0			0
$241$	0.714663	−	0.824765i	0.0460355	−	0.0531278i	−0.732265	−	0.681020i	$-0.761537\pi$
$241$	0.714663	−	0.824765i	0.0460355	−	0.0531278i	0.778300	+	0.627892i	$0.216082\pi$
$242$	13.6245	−	15.7235i	0.875815	−	1.01074i
$243$		0			0
$244$	−2.29214	−	5.01909i	−0.146739	−	0.321314i
$245$	0.693970	−	0.445987i	0.0443361	−	0.0284931i
$246$		0			0
$247$	−0.625144	−	4.34797i	−0.0397769	−	0.276655i
$248$	−3.37488	+	7.38995i	−0.214305	+	0.469262i
$249$		0			0
$250$	6.67901	+	4.29234i	0.422418	+	0.271471i
$251$	9.71008	+	11.2060i	0.612895	+	0.707319i	0.974342	−	0.225074i	$-0.0722624\pi$
$251$	9.71008	+	11.2060i	0.612895	+	0.707319i	−0.361447	+	0.932393i	$0.617717\pi$
$252$		0			0
$253$	−11.1842	+	24.6258i	−0.703145	+	1.54821i
$254$	−9.02664			−0.566382
$255$		0			0
$256$	0.841254	+	0.540641i	0.0525783	+	0.0337901i
$257$	−1.05099	+	7.30982i	−0.0655592	+	0.455974i	0.930428	+	0.366475i	$0.119436\pi$
$257$	−1.05099	+	7.30982i	−0.0655592	+	0.455974i	−0.995987	+	0.0894986i	$0.971474\pi$
$258$		0			0
$259$	0.166792	+	1.16006i	0.0103639	+	0.0720827i
$260$	−0.470575	−	0.138173i	−0.0291838	−	0.00856915i
$261$		0			0
$262$	−2.51275	−	5.50216i	−0.155238	−	0.339925i
$263$	−2.13706	+	0.627498i	−0.131777	+	0.0386932i	−0.346956	−	0.937881i	$-0.612785\pi$
$263$	−2.13706	+	0.627498i	−0.131777	+	0.0386932i	0.215179	+	0.976575i	$0.430966\pi$
$264$		0			0
$265$	0.236727	−	0.273198i	0.0145420	−	0.0167824i
$266$	−20.7786	+	6.10116i	−1.27402	+	0.374086i
$267$		0			0
$268$	10.5075	−	6.75278i	0.641850	−	0.412492i
$269$	20.3924	+	5.98774i	1.24335	+	0.365079i	0.836271	−	0.548316i	$-0.184731\pi$
$269$	20.3924	+	5.98774i	1.24335	+	0.365079i	0.407074	+	0.913395i	$0.366549\pi$
$270$		0			0
$271$	−0.724827	+	1.58715i	−0.0440301	+	0.0964125i	−0.930369	−	0.366625i	$-0.880513\pi$
$271$	−0.724827	+	1.58715i	−0.0440301	+	0.0964125i	0.886339	+	0.463038i	$0.153240\pi$
$272$	0.259417	−	1.80429i	0.0157295	−	0.109401i
$273$		0			0
$274$	−1.68574	−	1.94545i	−0.101839	−	0.117529i
$275$	24.0575			1.45072
$276$		0			0
$277$	8.34410			0.501348			0.250674	−	0.968072i	$-0.419348\pi$
$277$	8.34410			0.501348			0.250674	+	0.968072i	$0.419348\pi$
$278$	7.20546	+	8.31555i	0.432155	+	0.498733i
$279$		0			0
$280$	−0.344099	+	2.39326i	−0.0205638	+	0.143025i
$281$	−12.6455	+	27.6897i	−0.754365	+	1.65183i	0.00399528	+	0.999992i	$0.498728\pi$
$281$	−12.6455	+	27.6897i	−0.754365	+	1.65183i	−0.758360	+	0.651836i	$0.773999\pi$
$282$		0			0
$283$	2.72983	+	0.801551i	0.162272	+	0.0476473i	0.361859	−	0.932233i	$-0.382142\pi$
$283$	2.72983	+	0.801551i	0.162272	+	0.0476473i	−0.199588	+	0.979880i	$0.563960\pi$
$284$	3.81671	−	2.45285i	0.226480	−	0.145550i
$285$		0			0
$286$	−3.09725	+	0.909436i	−0.183144	+	0.0537761i
$287$	5.25178	−	6.06088i	0.310003	−	0.357762i
$288$		0			0
$289$	13.1232	−	3.85333i	0.771955	−	0.226666i
$290$	−1.77028	−	3.87638i	−0.103955	−	0.227629i
$291$		0			0
$292$	2.52896	+	0.742568i	0.147996	+	0.0434555i
$293$	−2.47962	−	17.2462i	−0.144861	−	1.00753i	−0.924467	−	0.381261i	$-0.875490\pi$
$293$	−2.47962	−	17.2462i	−0.144861	−	1.00753i	0.779606	−	0.626270i	$-0.215419\pi$
$294$		0			0
$295$	−0.842145	+	5.85725i	−0.0490316	+	0.341022i
$296$	−0.349397	−	0.224544i	−0.0203083	−	0.0130514i
$297$		0			0
$298$	8.81823			0.510826
$299$	2.30618	−	1.48890i	0.133370	−	0.0861053i
$300$		0			0
$301$	−9.79533	−	11.3044i	−0.564593	−	0.651576i
$302$	4.75632	+	3.05670i	0.273695	+	0.175893i
$303$		0			0
$304$	3.18805	−	6.98087i	0.182847	−	0.400380i
$305$	0.672838	+	4.67969i	0.0385266	+	0.267958i
$306$		0			0
$307$	15.3698	−	9.87754i	0.877199	−	0.563741i	−0.0227481	−	0.999741i	$-0.507242\pi$
$307$	15.3698	−	9.87754i	0.877199	−	0.563741i	0.899947	+	0.436000i	$0.143605\pi$
$308$	6.61093	+	14.4759i	0.376693	+	0.824842i
$309$		0			0
$310$	4.55854	−	5.26084i	0.258908	−	0.298795i
$311$	19.0664	−	22.0038i	1.08116	−	1.24772i	0.114015	−	0.993479i	$-0.463629\pi$
$311$	19.0664	−	22.0038i	1.08116	−	1.24772i	0.967141	−	0.254241i	$-0.0818257\pi$
$312$		0			0
$313$	7.14017	+	15.6348i	0.403586	+	0.883730i	0.996894	+	0.0787546i	$0.0250943\pi$
$313$	7.14017	+	15.6348i	0.403586	+	0.883730i	−0.593308	+	0.804976i	$0.702178\pi$
$314$	17.1946	−	11.0503i	0.970348	−	0.623605i
$315$		0			0
$316$	−0.654648	−	4.55318i	−0.0368268	−	0.256136i
$317$	4.73917	−	10.3773i	0.266178	−	0.582849i	−0.728597	−	0.684943i	$-0.759827\pi$
$317$	4.73917	−	10.3773i	0.266178	−	0.582849i	0.994775	+	0.102094i	$0.0325544\pi$
$318$		0			0
$319$	−23.5958	−	15.1641i	−1.32111	−	0.849028i
$320$	−0.561113	−	0.647559i	−0.0313672	−	0.0361996i
$321$		0			0
$322$	−8.88358	−	10.2091i	−0.495062	−	0.568930i
$323$	−13.9892			−0.778378
$324$		0			0
$325$	−2.05407	−	1.32007i	−0.113939	−	0.0732244i
$326$	−1.61951	+	11.2640i	−0.0896965	+	0.623853i
$327$		0			0
$328$	0.404461	+	2.81308i	0.0223326	+	0.155327i
$329$	−17.0183	−	4.99703i	−0.938250	−	0.275495i
$330$		0			0
$331$	−5.26686	−	11.5328i	−0.289493	−	0.633900i	0.707881	−	0.706332i	$-0.249651\pi$
$331$	−5.26686	−	11.5328i	−0.289493	−	0.633900i	−0.997373	+	0.0724316i	$0.976924\pi$
$332$	15.9838	−	4.69327i	0.877225	−	0.257576i
$333$		0			0
$334$	−11.0786	+	12.7854i	−0.606192	+	0.699583i
$335$	−10.2687	+	3.01517i	−0.561041	+	0.164736i
$336$		0			0
$337$	−12.7081	+	8.16702i	−0.692256	+	0.444886i	−0.838887	−	0.544305i	$-0.816793\pi$
$337$	−12.7081	+	8.16702i	−0.692256	+	0.444886i	0.146631	+	0.989191i	$0.453157\pi$
$338$	−12.1591	−	3.57022i	−0.661366	−	0.194194i
$339$		0			0
$340$	−0.648831	+	1.42074i	−0.0351878	+	0.0770506i
$341$	6.52040	−	45.3504i	0.353100	−	2.45586i
$342$		0			0
$343$	−11.1563	−	12.8750i	−0.602383	−	0.695187i
$344$	5.30077			0.285798
$345$		0			0
$346$	15.4617			0.831226
$347$	21.2172	+	24.4860i	1.13900	+	1.31448i	0.942590	+	0.333953i	$0.108383\pi$
$347$	21.2172	+	24.4860i	1.13900	+	1.31448i	0.196410	+	0.980522i	$0.437072\pi$
$348$		0			0
$349$	1.83316	−	12.7499i	0.0981267	−	0.682486i	−0.880076	−	0.474833i	$-0.842508\pi$
$349$	1.83316	−	12.7499i	0.0981267	−	0.682486i	0.978203	−	0.207653i	$-0.0665825\pi$
$350$	−5.00053	+	10.9496i	−0.267290	+	0.585283i
$351$		0			0
$352$	−5.41116	−	1.58886i	−0.288416	−	0.0846866i
$353$	13.6929	−	8.79987i	0.728797	−	0.468370i	−0.122890	−	0.992420i	$-0.539216\pi$
$353$	13.6929	−	8.79987i	0.728797	−	0.468370i	0.851687	+	0.524051i	$0.175580\pi$
$354$		0			0
$355$	−3.72997	+	1.09522i	−0.197966	+	0.0581281i
$356$	−7.89638	+	9.11291i	−0.418507	+	0.482983i
$357$		0			0
$358$	−21.5030	+	6.31386i	−1.13647	+	0.333698i
$359$	−12.6056	−	27.6025i	−0.665300	−	1.45680i	−0.877500	−	0.479577i	$-0.840790\pi$
$359$	−12.6056	−	27.6025i	−0.665300	−	1.45680i	0.212200	−	0.977226i	$-0.431937\pi$
$360$		0			0
$361$	−38.2801	−	11.2401i	−2.01474	−	0.591582i
$362$	2.56473	+	17.8381i	0.134799	+	0.937548i
$363$		0			0
$364$	0.229862	−	1.59873i	0.0120481	−	0.0837961i
$365$	−1.89989	−	1.22098i	−0.0994446	−	0.0639092i
$366$		0			0
$367$	−3.34854			−0.174793			−0.0873963	−	0.996174i	$-0.527855\pi$
$367$	−3.34854			−0.174793			−0.0873963	+	0.996174i	$0.527855\pi$
$368$	4.79582	−	0.0100059i	0.249999	−	0.000521592i
$369$		0			0
$370$	0.233047	+	0.268950i	0.0121155	+	0.0139820i
$371$	1.00151	+	0.643634i	0.0519960	+	0.0334158i
$372$		0			0
$373$	−1.36501	+	2.98896i	−0.0706776	+	0.154762i	−0.941673	−	0.336528i	$-0.890747\pi$
$373$	−1.36501	+	2.98896i	−0.0706776	+	0.154762i	0.870996	+	0.491290i	$0.163475\pi$
$374$	1.46301	+	10.1755i	0.0756505	+	0.526161i
$375$		0			0
$376$	5.28774	−	3.39822i	0.272694	−	0.175250i
$377$	1.18257	+	2.58947i	0.0609056	+	0.133365i
$378$		0			0
$379$	5.25100	−	6.05998i	0.269726	−	0.311280i	−0.604687	−	0.796463i	$-0.706702\pi$
$379$	5.25100	−	6.05998i	0.269726	−	0.311280i	0.874412	+	0.485183i	$0.161247\pi$
$380$	−4.30620	+	4.96962i	−0.220903	+	0.254936i
$381$		0			0
$382$	−5.32285	−	11.6554i	−0.272341	−	0.596343i
$383$	−23.4400	+	15.0640i	−1.19773	+	0.769733i	−0.978562	−	0.205955i	$-0.933970\pi$
$383$	−23.4400	+	15.0640i	−1.19773	+	0.769733i	−0.219166	+	0.975688i	$0.570334\pi$
$384$		0			0
$385$	−1.94058	−	13.4970i	−0.0989012	−	0.687873i
$386$	−9.54623	+	20.9033i	−0.485890	+	1.06395i
$387$		0			0
$388$	−2.68756	−	1.72719i	−0.136440	−	0.0876849i
$389$	3.35223	+	3.86867i	0.169965	+	0.196150i	0.834341	−	0.551248i	$-0.185848\pi$
$389$	3.35223	+	3.86867i	0.169965	+	0.196150i	−0.664377	+	0.747398i	$0.731303\pi$
$390$		0			0
$391$	−3.64815	−	7.94444i	−0.184495	−	0.401767i
$392$	−0.962748			−0.0486261
$393$		0			0
$394$	−18.9621	−	12.1862i	−0.955298	−	0.613933i
$395$	−0.560931	+	3.90136i	−0.0282235	+	0.196299i
$396$		0			0
$397$	0.955783	+	6.64762i	0.0479694	+	0.333634i	0.999648	+	0.0265380i	$0.00844829\pi$
$397$	0.955783	+	6.64762i	0.0479694	+	0.333634i	−0.951678	+	0.307096i	$0.900643\pi$
$398$	−11.4169	−	3.35229i	−0.572276	−	0.168035i
$399$		0			0
$400$	−1.77209	−	3.88033i	−0.0886043	−	0.194016i
$401$	23.8422	−	7.00070i	1.19062	−	0.349598i	0.374362	−	0.927283i	$-0.377862\pi$
$401$	23.8422	−	7.00070i	1.19062	−	0.349598i	0.816260	+	0.577685i	$0.196044\pi$
$402$		0			0
$403$	−3.04516	+	3.51431i	−0.151690	+	0.175060i
$404$	−14.3177	+	4.20407i	−0.712334	+	0.209160i
$405$		0			0
$406$	11.8064	−	7.58752i	0.585942	−	0.376562i
$407$	2.24741	+	0.659900i	0.111400	+	0.0327100i
$408$		0			0
$409$	10.8041	−	23.6578i	0.534230	−	1.16980i	−0.429535	−	0.903050i	$-0.641323\pi$
$409$	10.8041	−	23.6578i	0.534230	−	1.16980i	0.963765	−	0.266751i	$-0.0859501\pi$
$410$	0.346559	−	2.41037i	0.0171153	−	0.119040i
$411$		0			0
$412$	1.19423	+	1.37822i	0.0588357	+	0.0679000i
$413$	−19.4880			−0.958941
$414$		0			0
$415$	−14.2738			−0.700673
$416$	0.374831	+	0.432578i	0.0183776	+	0.0212089i
$417$		0			0
$418$	−6.15946	+	42.8400i	−0.301269	+	2.09537i
$419$	−2.88790	+	6.32362i	−0.141083	+	0.308929i	−0.966963	−	0.254917i	$-0.917952\pi$
$419$	−2.88790	+	6.32362i	−0.141083	+	0.308929i	0.825880	+	0.563846i	$0.190679\pi$
$420$		0			0
$421$	3.81214	+	1.11935i	0.185792	+	0.0545536i	0.373305	−	0.927709i	$-0.378224\pi$
$421$	3.81214	+	1.11935i	0.185792	+	0.0545536i	−0.187513	+	0.982262i	$0.560043\pi$
$422$	14.0704	−	9.04253i	0.684939	−	0.440183i
$423$		0			0
$424$	−0.404800	+	0.118860i	−0.0196588	+	0.00577235i
$425$	−5.09214	+	5.87664i	−0.247005	+	0.285059i
$426$		0			0
$427$	−14.9394	+	4.38659i	−0.722967	+	0.212282i
$428$	−6.38582	−	13.9830i	−0.308670	−	0.675894i
$429$		0			0
$430$	−4.35794	−	1.27961i	−0.210159	−	0.0617082i
$431$	−3.54839	−	24.6796i	−0.170920	−	1.18877i	−0.876946	−	0.480589i	$-0.840423\pi$
$431$	−3.54839	−	24.6796i	−0.170920	−	1.18877i	0.706026	−	0.708186i	$-0.250486\pi$
$432$		0			0
$433$	−4.87979	+	33.9397i	−0.234508	+	1.63104i	0.443705	+	0.896173i	$0.353664\pi$
$433$	−4.87979	+	33.9397i	−0.234508	+	1.63104i	−0.678213	+	0.734866i	$0.737245\pi$
$434$	19.2856	+	12.3941i	0.925740	+	0.594937i
$435$		0			0
$436$	15.5912			0.746684
$437$	−5.31390	−	36.4194i	−0.254198	−	1.74218i
$438$		0			0
$439$	19.5636	+	22.5776i	0.933719	+	1.07757i	0.996830	+	0.0795627i	$0.0253524\pi$
$439$	19.5636	+	22.5776i	0.933719	+	1.07757i	−0.0631108	+	0.998007i	$0.520102\pi$
$440$	4.06515	+	2.61252i	0.193799	+	0.124547i
$441$		0			0
$442$	0.433428	−	0.949075i	0.0206161	−	0.0451429i
$443$	2.57453	+	17.9062i	0.122319	+	0.850751i	0.954917	+	0.296872i	$0.0959436\pi$
$443$	2.57453	+	17.9062i	0.122319	+	0.850751i	−0.832598	+	0.553878i	$0.813147\pi$
$444$		0			0
$445$	8.69175	−	5.58585i	0.412029	−	0.264795i
$446$	0.986623	+	2.16040i	0.0467179	+	0.102298i
$447$		0			0
$448$	1.84791	−	2.13260i	0.0873055	−	0.100756i
$449$	−20.8580	+	24.0714i	−0.984348	+	1.13600i	0.00635782	+	0.999980i	$0.497976\pi$
$449$	−20.8580	+	24.0714i	−0.984348	+	1.13600i	−0.990706	+	0.136019i	$0.956569\pi$
$450$		0			0
$451$	−6.65820	−	14.5794i	−0.313522	−	0.686518i
$452$	−10.6776	+	6.86208i	−0.502233	+	0.322765i
$453$		0			0
$454$	−1.91974	−	13.3521i	−0.0900977	−	0.626643i
$455$	−0.574912	+	1.25888i	−0.0269523	+	0.0590172i
$456$		0			0
$457$	−25.7404	−	16.5424i	−1.20409	−	0.773819i	−0.224428	−	0.974491i	$-0.572051\pi$
$457$	−25.7404	−	16.5424i	−1.20409	−	0.773819i	−0.979659	+	0.200671i	$0.935688\pi$
$458$	1.56570	+	1.80691i	0.0731604	+	0.0844316i
$459$		0			0
$460$	−3.94523	−	1.14949i	−0.183947	−	0.0535951i
$461$	19.9053			0.927080			0.463540	−	0.886076i	$-0.346579\pi$
$461$	19.9053			0.927080			0.463540	+	0.886076i	$0.346579\pi$
$462$		0			0
$463$	33.9003	+	21.7864i	1.57548	+	1.01250i	0.977487	+	0.210997i	$0.0676710\pi$
$463$	33.9003	+	21.7864i	1.57548	+	1.01250i	0.597992	+	0.801502i	$0.295965\pi$
$464$	−0.707799	+	4.92285i	−0.0328587	+	0.228537i
$465$		0			0
$466$	−1.86463	−	12.9688i	−0.0863772	−	0.600767i
$467$	−30.5902	−	8.98209i	−1.41554	−	0.415641i	−0.517552	−	0.855652i	$-0.673157\pi$
$467$	−30.5902	−	8.98209i	−1.41554	−	0.415641i	−0.897993	+	0.440010i	$0.854975\pi$
$468$		0			0
$469$	−14.6416	−	32.0606i	−0.676085	−	1.48042i
$470$	−5.16757	+	1.51733i	−0.238362	+	0.0699894i
$471$		0			0
$472$	4.52256	−	5.21931i	0.208168	−	0.240238i
$473$	−28.6833	+	8.42218i	−1.31886	+	0.387252i
$474$		0			0
$475$	−27.5406	+	17.6993i	−1.26365	+	0.812097i
$476$	−4.93539	−	1.44916i	−0.226213	−	0.0664222i
$477$		0			0
$478$	3.59643	−	7.87508i	0.164497	−	0.360198i
$479$	5.05428	−	35.1533i	0.230936	−	1.60619i	−0.463135	−	0.886288i	$-0.653276\pi$
$479$	5.05428	−	35.1533i	0.230936	−	1.60619i	0.694071	−	0.719907i	$-0.255815\pi$
$480$		0			0
$481$	−0.155678	−	0.179662i	−0.00709831	−	0.00819189i
$482$	1.09132			0.0497083
$483$		0			0
$484$	20.8052			0.945689
$485$	1.79259	+	2.06876i	0.0813975	+	0.0939377i
$486$		0			0
$487$	5.31361	−	36.9570i	0.240783	−	1.67468i	−0.407441	−	0.913232i	$-0.633579\pi$
$487$	5.31361	−	36.9570i	0.240783	−	1.67468i	0.648224	−	0.761450i	$-0.275512\pi$
$488$	2.29214	−	5.01909i	0.103760	−	0.227203i
$489$		0			0
$490$	0.791508	+	0.232408i	0.0357567	+	0.0104991i
$491$	14.5916	−	9.37746i	0.658510	−	0.423199i	−0.168257	−	0.985743i	$-0.553814\pi$
$491$	14.5916	−	9.37746i	0.658510	−	0.423199i	0.826767	+	0.562544i	$0.190177\pi$
$492$		0			0
$493$	8.69861	−	2.55414i	0.391766	−	0.115033i
$494$	2.87659	−	3.31977i	0.129424	−	0.149363i
$495$		0			0
$496$	−7.79502	+	2.28883i	−0.350007	+	0.102771i
$497$	−5.31833	−	11.6455i	−0.238560	−	0.522373i
$498$		0			0
$499$	14.1201	+	4.14604i	0.632103	+	0.185602i	0.582061	−	0.813145i	$-0.302246\pi$
$499$	14.1201	+	4.14604i	0.632103	+	0.185602i	0.0500418	+	0.998747i	$0.484065\pi$
$500$	1.12989	+	7.85854i	0.0505301	+	0.351445i
$501$		0			0
$502$	−2.11020	+	14.6768i	−0.0941830	+	0.655057i
$503$	25.4281	+	16.3417i	1.13378	+	0.728639i	0.966347	−	0.257243i	$-0.0828142\pi$
$503$	25.4281	+	16.3417i	1.13378	+	0.728639i	0.167438	+	0.985883i	$0.446451\pi$
$504$		0			0
$505$	12.7860			0.568969
$506$	−25.9351	+	7.67404i	−1.15295	+	0.341153i
$507$		0			0
$508$	−5.91119	−	6.82188i	−0.262267	−	0.302672i
$509$	12.6406	+	8.12364i	0.560286	+	0.360074i	0.789926	−	0.613202i	$-0.210119\pi$
$509$	12.6406	+	8.12364i	0.560286	+	0.360074i	−0.229640	+	0.973276i	$0.573755\pi$
$510$		0			0
$511$	3.08968	−	6.76545i	0.136679	−	0.299286i
$512$	0.142315	+	0.989821i	0.00628949	+	0.0437443i
$513$		0			0
$514$	−6.21265	+	3.99263i	−0.274028	+	0.176107i
$515$	−0.649118	−	1.42137i	−0.0286036	−	0.0626331i
$516$		0			0
$517$	−23.2135	+	26.7898i	−1.02093	+	1.17821i
$518$	−0.767490	+	0.885731i	−0.0337216	+	0.0389168i
$519$		0			0
$520$	−0.203737	−	0.446122i	−0.00893445	−	0.0195637i
$521$	−12.7048	+	8.16485i	−0.556606	+	0.357709i	−0.788502	−	0.615032i	$-0.789143\pi$
$521$	−12.7048	+	8.16485i	−0.556606	+	0.357709i	0.231897	+	0.972740i	$0.425507\pi$
$522$		0			0
$523$	5.70422	+	39.6737i	0.249428	+	1.73481i	0.601532	+	0.798849i	$0.294557\pi$
$523$	5.70422	+	39.6737i	0.249428	+	1.73481i	−0.352104	+	0.935961i	$0.614534\pi$
$524$	2.51275	−	5.50216i	0.109770	−	0.240363i
$525$		0			0
$526$	−1.87371	−	1.20416i	−0.0816976	−	0.0525038i
$527$	9.69779	+	11.1919i	0.422443	+	0.487525i
$528$		0			0
$529$	19.2968	−	12.5154i	0.838990	−	0.544146i
$530$	0.361493			0.0157022
$531$		0			0
$532$	−18.2181	−	11.7080i	−0.789853	−	0.507608i
$533$	−0.231506	+	1.61016i	−0.0100276	+	0.0697438i
$534$		0			0
$535$	1.87450	+	13.0374i	0.0810418	+	0.563658i
$536$	11.9844	+	3.51893i	0.517646	+	0.151995i
$537$		0			0
$538$	8.82893	+	19.3327i	0.380642	+	0.833491i
$539$	5.20958	−	1.52967i	0.224393	−	0.0658876i
$540$		0			0
$541$	17.3053	−	19.9714i	0.744015	−	0.858639i	−0.249959	−	0.968256i	$-0.580417\pi$
$541$	17.3053	−	19.9714i	0.744015	−	0.858639i	0.993974	+	0.109617i	$0.0349625\pi$
$542$	−1.67415	+	0.491575i	−0.0719109	+	0.0211149i
$543$		0			0
$544$	1.53347	−	0.985501i	0.0657470	−	0.0422530i
$545$	−12.8181	−	3.76373i	−0.549066	−	0.161220i
$546$		0			0
$547$	6.88022	−	15.0656i	0.294177	−	0.644158i	−0.703614	−	0.710582i	$-0.748432\pi$
$547$	6.88022	−	15.0656i	0.294177	−	0.644158i	0.997791	+	0.0664241i	$0.0211590\pi$
$548$	0.366347	−	2.54800i	0.0156496	−	0.108845i
$549$		0			0
$550$	15.7543	+	18.1815i	0.671767	+	0.775261i
$551$	38.1683			1.62603
$552$		0			0
$553$	−12.9804			−0.551984
$554$	5.46422	+	6.30605i	0.232153	+	0.267918i
$555$		0			0
$556$	−1.56590	+	10.8910i	−0.0664088	+	0.461883i
$557$	−0.837062	+	1.83291i	−0.0354675	+	0.0776629i	−0.926537	−	0.376205i	$-0.877229\pi$
$557$	−0.837062	+	1.83291i	−0.0354675	+	0.0776629i	0.891069	+	0.453868i	$0.149956\pi$
$558$		0			0
$559$	2.91116	+	0.854795i	0.123129	+	0.0361540i
$560$	−2.03404	+	1.30720i	−0.0859539	+	0.0552392i
$561$		0			0
$562$	−29.2075	+	8.57609i	−1.23204	+	0.361761i
$563$	7.93081	−	9.15265i	0.334244	−	0.385738i	−0.563603	−	0.826046i	$-0.690585\pi$
$563$	7.93081	−	9.15265i	0.334244	−	0.385738i	0.897847	+	0.440308i	$0.145131\pi$
$564$		0			0
$565$	10.4349	−	3.06398i	0.439002	−	0.128902i
$566$	1.18189	+	2.58797i	0.0496785	+	0.108781i
$567$		0			0
$568$	4.35315	+	1.27820i	0.182654	+	0.0536321i
$569$	−0.568652	−	3.95506i	−0.0238391	−	0.165805i	0.974424	−	0.224717i	$-0.0721458\pi$
$569$	−0.568652	−	3.95506i	−0.0238391	−	0.165805i	−0.998263	+	0.0589123i	$0.981237\pi$
$570$		0			0
$571$	3.64276	−	25.3360i	0.152445	−	1.06028i	−0.759660	−	0.650320i	$-0.774635\pi$
$571$	3.64276	−	25.3360i	0.152445	−	1.06028i	0.912105	−	0.409957i	$-0.134456\pi$
$572$	−2.71558	−	1.74519i	−0.113544	−	0.0729702i
$573$		0			0
$574$	8.01969			0.334735
$575$	−17.2335	−	11.0246i	−0.718688	−	0.459757i
$576$		0			0
$577$	−4.35685	−	5.02808i	−0.181378	−	0.209322i	0.657778	−	0.753212i	$-0.271496\pi$
$577$	−4.35685	−	5.02808i	−0.181378	−	0.209322i	−0.839157	+	0.543890i	$0.816951\pi$
$578$	11.5060	+	7.39448i	0.478588	+	0.307570i
$579$		0			0
$580$	1.77028	−	3.87638i	0.0735071	−	0.160958i
$581$	−6.68990	−	46.5293i	−0.277544	−	1.93036i
$582$		0			0
$583$	2.00159	−	1.28634i	0.0828972	−	0.0532748i
$584$	1.09492	+	2.39754i	0.0453080	+	0.0992108i
$585$		0			0
$586$	11.4100	−	13.1678i	0.471341	−	0.543957i
$587$	13.2259	−	15.2635i	0.545890	−	0.629991i	−0.414030	−	0.910263i	$-0.635879\pi$
$587$	13.2259	−	15.2635i	0.545890	−	0.629991i	0.959921	+	0.280272i	$0.0904248\pi$
$588$		0			0
$589$	25.9001	+	56.7133i	1.06719	+	2.33683i
$590$	−4.97810	+	3.19923i	−0.204945	+	0.131710i
$591$		0			0
$592$	−0.0591075	−	0.411102i	−0.00242930	−	0.0168962i
$593$	−7.15919	+	15.6764i	−0.293993	+	0.643754i	−0.997776	−	0.0666608i	$-0.978765\pi$
$593$	−7.15919	+	15.6764i	−0.293993	+	0.643754i	0.703783	+	0.710415i	$0.251493\pi$
$594$		0			0
$595$	3.70773	+	2.38281i	0.152002	+	0.0976858i
$596$	5.77471	+	6.66437i	0.236541	+	0.272983i
$597$		0			0
$598$	2.63546	+	0.767873i	0.107772	+	0.0314007i
$599$	−14.1802			−0.579389			−0.289694	−	0.957119i	$-0.593554\pi$
$599$	−14.1802			−0.579389			−0.289694	+	0.957119i	$0.593554\pi$
$600$		0			0
$601$	31.7753	+	20.4207i	1.29614	+	0.832978i	0.992786	−	0.119900i	$-0.0382572\pi$
$601$	31.7753	+	20.4207i	1.29614	+	0.832978i	0.303354	+	0.952878i	$0.401894\pi$
$602$	2.12873	−	14.8056i	0.0867605	−	0.603433i
$603$		0			0
$604$	0.804627	+	5.59630i	0.0327398	+	0.227710i
$605$	−17.1047	−	5.02238i	−0.695403	−	0.204189i
$606$		0			0
$607$	12.0125	+	26.3037i	0.487572	+	1.06763i	0.980311	+	0.197458i	$0.0632685\pi$
$607$	12.0125	+	26.3037i	0.487572	+	1.06763i	−0.492739	+	0.870177i	$0.664004\pi$
$608$	7.36352	−	2.16212i	0.298630	−	0.0876857i
$609$		0			0
$610$	−3.09606	+	3.57304i	−0.125356	+	0.144668i
$611$	3.45200	−	1.01360i	0.139653	−	0.0410058i
$612$		0			0
$613$	−0.0141916	+	0.00912036i	−0.000573191	+	0.000368368i	−0.540927	−	0.841069i	$-0.681927\pi$
$613$	−0.0141916	+	0.00912036i	−0.000573191	+	0.000368368i	0.540354	+	0.841438i	$0.318290\pi$
$614$	17.5300	+	5.14727i	0.707453	+	0.207727i
$615$		0			0
$616$	−6.61093	+	14.4759i	−0.266362	+	0.583251i
$617$	−3.26990	+	22.7426i	−0.131641	+	0.915583i	0.811775	+	0.583971i	$0.198502\pi$
$617$	−3.26990	+	22.7426i	−0.131641	+	0.915583i	−0.943416	+	0.331613i	$0.892407\pi$
$618$		0			0
$619$	9.73944	+	11.2399i	0.391461	+	0.451770i	0.916933	−	0.399041i	$-0.130657\pi$
$619$	9.73944	+	11.2399i	0.391461	+	0.451770i	−0.525472	+	0.850811i	$0.676111\pi$
$620$	6.96108			0.279564
$621$		0			0
$622$	29.1152			1.16741
$623$	22.2823	+	25.7151i	0.892721	+	1.03025i
$624$		0			0
$625$	−2.06731	+	14.3785i	−0.0826924	+	0.575139i
$626$	−7.14017	+	15.6348i	−0.285378	+	0.624892i
$627$		0			0
$628$	19.6113	+	5.75841i	0.782578	+	0.229785i
$629$	−0.636895	+	0.409308i	−0.0253947	+	0.0163202i
$630$		0			0
$631$	17.4413	−	5.12122i	0.694325	−	0.203872i	0.0845180	−	0.996422i	$-0.473065\pi$
$631$	17.4413	−	5.12122i	0.694325	−	0.203872i	0.609807	+	0.792550i	$0.291247\pi$
$632$	3.01236	−	3.47645i	0.119825	−	0.138286i
$633$		0			0
$634$	10.9462	−	3.21408i	0.434727	−	0.127647i
$635$	3.21299	+	7.03547i	0.127504	+	0.279194i
$636$		0			0
$637$	−0.528738	−	0.155251i	−0.0209494	−	0.00615129i
$638$	−3.99171	−	27.7629i	−0.158033	−	1.09914i
$639$		0			0
$640$	0.121941	−	0.848122i	0.00482016	−	0.0335249i
$641$	12.4722	+	8.01542i	0.492624	+	0.316590i	0.763260	−	0.646092i	$-0.223598\pi$
$641$	12.4722	+	8.01542i	0.492624	+	0.316590i	−0.270636	+	0.962682i	$0.587234\pi$
$642$		0			0
$643$	−21.6321			−0.853087			−0.426544	−	0.904467i	$-0.640269\pi$
$643$	−21.6321			−0.853087			−0.426544	+	0.904467i	$0.640269\pi$
$644$	1.89800	−	13.3993i	0.0747917	−	0.528006i
$645$		0			0
$646$	−9.16096	−	10.5723i	−0.360433	−	0.415962i
$647$	40.8722	+	26.2670i	1.60685	+	1.03266i	0.963723	+	0.266904i	$0.0860008\pi$
$647$	40.8722	+	26.2670i	1.60685	+	1.03266i	0.643130	+	0.765757i	$0.277636\pi$
$648$		0			0
$649$	−16.1796	+	35.4283i	−0.635103	+	1.39068i
$650$	−0.347487	−	2.41683i	−0.0136296	−	0.0947958i
$651$		0			0
$652$	−9.57328	+	6.15238i	−0.374919	+	0.240946i
$653$	−6.12227	−	13.4059i	−0.239583	−	0.524613i	0.751200	−	0.660075i	$-0.229475\pi$
$653$	−6.12227	−	13.4059i	−0.239583	−	0.524613i	−0.990783	+	0.135462i	$0.956748\pi$
$654$		0			0
$655$	−3.39405	+	3.91694i	−0.132616	+	0.153047i
$656$	−1.86112	+	2.14785i	−0.0726646	+	0.0838594i
$657$		0			0
$658$	−7.36812	−	16.1339i	−0.287239	−	0.628966i
$659$	−0.898508	+	0.577436i	−0.0350009	+	0.0224937i	−0.558024	−	0.829825i	$-0.688440\pi$
$659$	−0.898508	+	0.577436i	−0.0350009	+	0.0224937i	0.523023	+	0.852318i	$0.324804\pi$
$660$		0			0
$661$	−0.618566	−	4.30222i	−0.0240594	−	0.167337i	0.974249	−	0.225474i	$-0.0723931\pi$
$661$	−0.618566	−	4.30222i	−0.0240594	−	0.167337i	−0.998309	+	0.0581369i	$0.981484\pi$
$662$	5.26686	−	11.5328i	0.204702	−	0.448235i
$663$		0			0
$664$	14.0141	+	9.00631i	0.543852	+	0.349513i
$665$	12.1514	+	14.0234i	0.471210	+	0.543805i
$666$		0			0
$667$	9.95369	+	21.6758i	0.385409	+	0.839289i
$668$	−16.9174			−0.654556
$669$		0			0
$670$	−9.00330	−	5.78607i	−0.347828	−	0.223535i
$671$	−4.42851	+	30.8010i	−0.170961	+	1.18906i
$672$		0			0
$673$	−1.40385	−	9.76399i	−0.0541144	−	0.376374i	−0.998825	−	0.0484679i	$-0.984566\pi$
$673$	−1.40385	−	9.76399i	−0.0541144	−	0.376374i	0.944710	−	0.327906i	$-0.106343\pi$
$674$	−14.4943	−	4.25590i	−0.558299	−	0.163931i
$675$		0			0
$676$	−5.26430	−	11.5272i	−0.202473	−	0.443354i
$677$	−33.4468	+	9.82086i	−1.28546	+	0.377446i	−0.851913	−	0.523683i	$-0.824558\pi$
$677$	−33.4468	+	9.82086i	−1.28546	+	0.377446i	−0.433551	+	0.901129i	$0.642740\pi$
$678$		0			0
$679$	−5.90354	+	6.81304i	−0.226557	+	0.261461i
$680$	−1.49862	+	0.440035i	−0.0574695	+	0.0168746i
$681$		0			0
$682$	38.5435	−	24.7704i	1.47591	−	0.948508i
$683$	23.5785	+	6.92326i	0.902204	+	0.264911i	0.699756	−	0.714382i	$-0.253292\pi$
$683$	23.5785	+	6.92326i	0.902204	+	0.264911i	0.202448	+	0.979293i	$0.435110\pi$
$684$		0			0
$685$	−0.916275	+	2.00636i	−0.0350091	+	0.0766592i
$686$	2.42449	−	16.8627i	0.0925676	−	0.643822i
$687$		0			0
$688$	3.47126	+	4.00605i	0.132341	+	0.152729i
$689$	−0.241482			−0.00919973
$690$		0			0
$691$	−47.0341			−1.78926			−0.894631	−	0.446806i	$-0.852561\pi$
$691$	−47.0341			−1.78926			−0.894631	+	0.446806i	$0.852561\pi$
$692$	10.1253	+	11.6852i	0.384905	+	0.444204i
$693$		0			0
$694$	−4.61094	+	32.0698i	−0.175029	+	1.21735i
$695$	3.91648	−	8.57590i	0.148561	−	0.325303i
$696$		0			0
$697$	4.97068	+	1.45952i	0.188278	+	0.0552834i
$698$	10.8362	−	6.96399i	0.410156	−	0.263591i
$699$		0			0
$700$	−11.5498	+	3.39134i	−0.436543	+	0.128181i
$701$	28.7960	−	33.2324i	1.08761	−	1.25517i	0.122743	−	0.992439i	$-0.460831\pi$
$701$	28.7960	−	33.2324i	1.08761	−	1.25517i	0.964869	−	0.262732i	$-0.0846236\pi$
$702$		0			0
$703$	−3.05828	+	0.897993i	−0.115345	+	0.0338685i
$704$	−2.34278	−	5.12997i	−0.0882967	−	0.193343i
$705$		0			0
$706$	15.6174	+	4.58569i	0.587769	+	0.172585i
$707$	5.99259	+	41.6794i	0.225374	+	1.56751i
$708$		0			0
$709$	6.34742	−	44.1472i	0.238382	−	1.65798i	−0.421658	−	0.906755i	$-0.638552\pi$
$709$	6.34742	−	44.1472i	0.238382	−	1.65798i	0.660041	−	0.751230i	$-0.270539\pi$
$710$	−3.27032	−	2.10171i	−0.122733	−	0.0788756i
$711$		0			0
$712$	−12.0581			−0.451897
$713$	−25.4531	+	29.4986i	−0.953226	+	1.10473i
$714$		0			0
$715$	1.81128	+	2.09033i	0.0677380	+	0.0781738i
$716$	−18.8532	−	12.1162i	−0.704576	−	0.452804i
$717$		0			0
$718$	12.6056	−	27.6025i	0.470438	−	1.03012i
$719$	−3.57484	−	24.8636i	−0.133319	−	0.927254i	−0.941186	−	0.337889i	$-0.890287\pi$
$719$	−3.57484	−	24.8636i	−0.133319	−	0.927254i	0.807867	−	0.589365i	$-0.200622\pi$
$720$		0			0
$721$	4.32911	−	2.78215i	0.161225	−	0.103613i
$722$	−16.5735	−	36.2908i	−0.616801	−	1.35061i
$723$		0			0
$724$	−11.8016	+	13.6197i	−0.438602	+	0.506174i
$725$	13.8935	−	16.0339i	0.515991	−	0.595485i
$726$		0			0
$727$	−13.5696	−	29.7133i	−0.503270	−	1.10201i	−0.975393	−	0.220474i	$-0.929239\pi$
$727$	−13.5696	−	29.7133i	−0.503270	−	1.10201i	0.472123	−	0.881533i	$-0.343488\pi$
$728$	1.35877	−	0.873226i	0.0503592	−	0.0323639i
$729$		0			0
$730$	−0.321404	−	2.23541i	−0.0118957	−	0.0827363i
$731$	4.01393	−	8.78927i	0.148460	−	0.325083i
$732$		0			0
$733$	31.1064	+	19.9909i	1.14894	+	0.738379i	0.969428	−	0.245376i	$-0.0789115\pi$
$733$	31.1064	+	19.9909i	1.14894	+	0.738379i	0.179513	+	0.983756i	$0.442548\pi$
$734$	−2.19283	−	2.53066i	−0.0809388	−	0.0934084i
$735$		0			0
$736$	3.14816	+	3.61789i	0.116043	+	0.133357i
$737$	−70.4405			−2.59471
$738$		0			0
$739$	1.90154	+	1.22205i	0.0699494	+	0.0449537i	0.575148	−	0.818049i	$-0.304944\pi$
$739$	1.90154	+	1.22205i	0.0699494	+	0.0449537i	−0.505199	+	0.863003i	$0.668581\pi$
$740$	−0.0506459	+	0.352250i	−0.00186178	+	0.0129490i
$741$		0			0
$742$	0.169426	+	1.17838i	0.00621982	+	0.0432598i
$743$	22.6991	+	6.66507i	0.832750	+	0.244518i	0.670198	−	0.742182i	$-0.266209\pi$
$743$	22.6991	+	6.66507i	0.832750	+	0.244518i	0.162552	+	0.986700i	$0.448027\pi$
$744$		0			0
$745$	−3.13881	−	6.87303i	−0.114997	−	0.251808i
$746$	−3.15279	+	0.925744i	−0.115432	+	0.0338939i
$747$		0			0
$748$	−6.73203	+	7.76918i	−0.246148	+	0.284069i
$749$	−41.6205	+	12.2209i	−1.52078	+	0.446542i
$750$		0			0
$751$	15.9559	−	10.2542i	0.582240	−	0.374183i	−0.216117	−	0.976367i	$-0.569339\pi$
$751$	15.9559	−	10.2542i	0.582240	−	0.374183i	0.798357	+	0.602185i	$0.205703\pi$
$752$	6.03094	+	1.77084i	0.219926	+	0.0645760i
$753$		0			0
$754$	−1.18257	+	2.58947i	−0.0430668	+	0.0943031i
$755$	0.689439	−	4.79515i	0.0250912	−	0.174513i
$756$		0			0
$757$	5.80868	+	6.70358i	0.211120	+	0.243646i	0.851426	−	0.524474i	$-0.175738\pi$
$757$	5.80868	+	6.70358i	0.211120	+	0.243646i	−0.640306	+	0.768120i	$0.721193\pi$
$758$	8.01850			0.291245
$759$		0			0
$760$	−6.57574			−0.238527
$761$	−2.10882	−	2.43371i	−0.0764447	−	0.0882218i	0.716239	−	0.697855i	$-0.245862\pi$
$761$	−2.10882	−	2.43371i	−0.0764447	−	0.0882218i	−0.792683	+	0.609633i	$0.791317\pi$
$762$		0			0
$763$	6.26126	−	43.5480i	0.226673	−	1.57654i
$764$	5.32285	−	11.6554i	0.192574	−	0.421678i
$765$		0			0
$766$	−26.7345	−	7.84996i	−0.965958	−	0.283631i
$767$	3.32544	−	2.13713i	0.120075	−	0.0771672i
$768$		0			0
$769$	−8.12962	+	2.38707i	−0.293162	+	0.0860801i	−0.425006	−	0.905190i	$-0.639728\pi$
$769$	−8.12962	+	2.38707i	−0.293162	+	0.0860801i	0.131845	+	0.991270i	$0.457910\pi$
$770$	8.92957	−	10.3053i	0.321799	−	0.371376i
$771$		0			0
$772$	−22.0491	+	6.47421i	−0.793566	+	0.233012i
$773$	2.53123	+	5.54261i	0.0910419	+	0.199354i	0.949675	−	0.313236i	$-0.101413\pi$
$773$	2.53123	+	5.54261i	0.0910419	+	0.199354i	−0.858633	+	0.512590i	$0.828686\pi$
$774$		0			0
$775$	33.2522	+	9.76372i	1.19445	+	0.350723i
$776$	−0.454655	−	3.16219i	−0.0163212	−	0.113516i
$777$		0			0
$778$	−0.728508	+	5.06689i	−0.0261183	+	0.181657i
$779$	18.3483	+	11.7918i	0.657397	+	0.422483i
$780$		0			0
$781$	−25.5865			−0.915557
$782$	3.61497	−	7.95959i	0.129271	−	0.284634i
$783$		0			0
$784$	−0.630466	−	0.727596i	−0.0225166	−	0.0259856i
$785$	−14.7331	−	9.46838i	−0.525846	−	0.337941i
$786$		0			0
$787$	−8.50165	+	18.6160i	−0.303051	+	0.663589i	−0.998486	−	0.0549995i	$-0.982484\pi$
$787$	−8.50165	+	18.6160i	−0.303051	+	0.663589i	0.695435	+	0.718589i	$0.255212\pi$
$788$	−3.20782	−	22.3109i	−0.114274	−	0.794792i
$789$		0			0
$790$	−3.31578	+	2.13092i	−0.117970	+	0.0758148i
$791$	14.8786	+	32.5795i	0.529021	+	1.15839i
$792$		0			0
$793$	2.06821	−	2.38684i	0.0734442	−	0.0847591i
$794$	−4.39803	+	5.07560i	−0.156080	+	0.180126i
$795$		0			0
$796$	−4.94296	−	10.8236i	−0.175199	−	0.383631i
$797$	−15.2450	+	9.79736i	−0.540005	+	0.347040i	−0.782041	−	0.623227i	$-0.785821\pi$
$797$	−15.2450	+	9.79736i	−0.540005	+	0.347040i	0.242036	+	0.970267i	$0.422185\pi$
$798$		0			0
$799$	−1.63058	−	11.3409i	−0.0576857	−	0.401213i
$800$	1.77209	−	3.88033i	0.0626527	−	0.137190i
$801$		0			0
$802$	20.9041	+	13.4342i	0.738149	+	0.474379i
$803$	−9.73413	−	11.2338i	−0.343510	−	0.396432i
$804$		0			0
$805$	−4.79501	+	10.5578i	−0.169002	+	0.372115i
$806$	−4.65009			−0.163793
$807$		0			0
$808$	−12.5534	−	8.06755i	−0.441625	−	0.283815i
$809$	−5.28187	+	36.7362i	−0.185701	+	1.29158i	0.657285	+	0.753642i	$0.271705\pi$
$809$	−5.28187	+	36.7362i	−0.185701	+	1.29158i	−0.842986	+	0.537935i	$0.819204\pi$
$810$		0			0
$811$	−1.31503	−	9.14621i	−0.0461768	−	0.321167i	−0.999797	−	0.0201540i	$-0.993584\pi$
$811$	−1.31503	−	9.14621i	−0.0461768	−	0.321167i	0.953620	−	0.301013i	$-0.0973247\pi$
$812$	13.4658	+	3.95392i	0.472558	+	0.138755i
$813$		0			0
$814$	0.973024	+	2.13063i	0.0341045	+	0.0746784i
$815$	9.35572	−	2.74709i	0.327716	−	0.0962262i
$816$		0			0
$817$	26.6398	−	30.7440i	0.932009	−	1.07560i
$818$	24.9546	−	7.32732i	0.872515	−	0.256194i
$819$		0			0
$820$	2.04859	−	1.31655i	0.0715397	−	0.0459758i
$821$	−19.7878	−	5.81024i	−0.690601	−	0.202779i	−0.0824440	−	0.996596i	$-0.526273\pi$
$821$	−19.7878	−	5.81024i	−0.690601	−	0.202779i	−0.608157	+	0.793817i	$0.708091\pi$
$822$		0			0
$823$	−6.12463	+	13.4111i	−0.213491	+	0.467481i	−0.985834	−	0.167726i	$-0.946358\pi$
$823$	−6.12463	+	13.4111i	−0.213491	+	0.467481i	0.772342	+	0.635206i	$0.219085\pi$
$824$	−0.259532	+	1.80508i	−0.00904122	+	0.0628830i
$825$		0			0
$826$	−12.7619	−	14.7280i	−0.444044	−	0.512454i
$827$	−7.95122			−0.276491			−0.138245	−	0.990398i	$-0.544146\pi$
$827$	−7.95122			−0.276491			−0.138245	+	0.990398i	$0.544146\pi$
$828$		0			0
$829$	−21.0393			−0.730725			−0.365363	−	0.930865i	$-0.619055\pi$
$829$	−21.0393			−0.730725			−0.365363	+	0.930865i	$0.619055\pi$
$830$	−9.34735	−	10.7874i	−0.324451	−	0.374437i
$831$		0			0
$832$	−0.0814585	+	0.566556i	−0.00282406	+	0.0196418i
$833$	−0.729026	+	1.59634i	−0.0252593	+	0.0553101i
$834$		0			0
$835$	13.9084	+	4.08388i	0.481321	+	0.141329i
$836$	−36.4099	+	23.3992i	−1.25926	+	0.809279i
$837$		0			0
$838$	−6.67024	+	1.95856i	−0.230420	+	0.0676574i
$839$	−5.15416	+	5.94821i	−0.177941	+	0.205355i	−0.837713	−	0.546111i	$-0.816108\pi$
$839$	−5.15416	+	5.94821i	−0.177941	+	0.205355i	0.659771	+	0.751466i	$0.270653\pi$
$840$		0			0
$841$	4.09184	−	1.20147i	0.141098	−	0.0414301i
$842$	1.65048	+	3.61404i	0.0568792	+	0.124548i
$843$		0			0
$844$	16.0481	+	4.71214i	0.552397	+	0.162199i
$845$	1.54529	+	10.7477i	0.0531595	+	0.369733i
$846$		0			0
$847$	8.35512	−	58.1112i	0.287085	−	1.99672i
$848$	−0.354916	−	0.228090i	−0.0121879	−	0.00783266i
$849$		0			0
$850$	−7.77591			−0.266711
$851$	−1.30752	−	1.50261i	−0.0448213	−	0.0515090i
$852$		0			0
$853$	−24.1768	−	27.9015i	−0.827797	−	0.955328i	0.171759	−	0.985139i	$-0.445055\pi$
$853$	−24.1768	−	27.9015i	−0.827797	−	0.955328i	−0.999556	+	0.0298108i	$0.990510\pi$
$854$	−13.0984	−	8.41781i	−0.448217	−	0.288052i
$855$		0			0
$856$	6.38582	−	13.9830i	0.218263	−	0.477929i
$857$	5.88775	+	40.9502i	0.201122	+	1.39883i	0.800963	+	0.598713i	$0.204321\pi$
$857$	5.88775	+	40.9502i	0.201122	+	1.39883i	−0.599842	+	0.800119i	$0.704770\pi$
$858$		0			0
$859$	−40.5569	+	26.0643i	−1.38378	+	0.889303i	−0.999426	−	0.0338809i	$-0.989213\pi$
$859$	−40.5569	+	26.0643i	−1.38378	+	0.889303i	−0.384357	+	0.923184i	$0.625577\pi$
$860$	−1.88678	−	4.13148i	−0.0643388	−	0.140882i
$861$		0			0
$862$	16.3279	−	18.8434i	0.556131	−	0.641809i
$863$	−10.4133	+	12.0176i	−0.354473	+	0.409084i	−0.904780	−	0.425878i	$-0.859965\pi$
$863$	−10.4133	+	12.0176i	−0.354473	+	0.409084i	0.550307	+	0.834962i	$0.314511\pi$
$864$		0			0
$865$	−5.50352	−	12.0510i	−0.187125	−	0.409747i
$866$	−28.8455	+	18.5379i	−0.980210	+	0.629943i
$867$		0			0
$868$	3.26255	+	22.6915i	0.110738	+	0.770201i
$869$	−10.7768	+	23.5978i	−0.365577	+	0.800502i
$870$		0			0
$871$	6.01432	+	3.86517i	0.203788	+	0.130966i
$872$	10.2101	+	11.7831i	0.345757	+	0.399025i
$873$		0			0
$874$	24.0441	−	27.8656i	0.813304	−	0.942569i
$875$	22.4035			0.757378
$876$		0			0
$877$	−23.5748	−	15.1506i	−0.796064	−	0.511599i	0.0782651	−	0.996933i	$-0.475062\pi$
$877$	−23.5748	−	15.1506i	−0.796064	−	0.511599i	−0.874329	+	0.485333i	$0.838698\pi$
$878$	−4.25157	+	29.5703i	−0.143484	+	0.997951i
$879$		0			0
$880$	0.687702	+	4.78307i	0.0231824	+	0.161237i
$881$	13.0293	+	3.82575i	0.438968	+	0.128893i	0.493747	−	0.869606i	$-0.335627\pi$
$881$	13.0293	+	3.82575i	0.438968	+	0.128893i	−0.0547783	+	0.998499i	$0.517445\pi$
$882$		0			0
$883$	7.94493	+	17.3970i	0.267368	+	0.585454i	0.994928	−	0.100590i	$-0.0320729\pi$
$883$	7.94493	+	17.3970i	0.267368	+	0.585454i	−0.727560	+	0.686044i	$0.759346\pi$
$884$	1.00110	−	0.293949i	0.0336706	−	0.00988657i
$885$		0			0
$886$	−11.8467	+	13.6718i	−0.397997	+	0.459313i
$887$	−2.28277	+	0.670283i	−0.0766480	+	0.0225059i	−0.319832	−	0.947474i	$-0.603626\pi$
$887$	−2.28277	+	0.670283i	−0.0766480	+	0.0225059i	0.243184	+	0.969980i	$0.421808\pi$
$888$		0			0
$889$	−21.4281	+	13.7710i	−0.718677	+	0.461865i
$890$	9.91339	+	2.91083i	0.332298	+	0.0975714i
$891$		0			0
$892$	−0.986623	+	2.16040i	−0.0330346	+	0.0723356i
$893$	6.86494	−	47.7467i	0.229726	−	1.59778i
$894$		0			0
$895$	12.5750	+	14.5123i	0.420336	+	0.485093i
$896$	2.82183			0.0942709
$897$		0			0
$898$	−31.8510			−1.06288
$899$	−26.4596	−	30.5361i	−0.882479	−	1.01843i
$900$		0			0
$901$	−0.109445	+	0.761209i	−0.00364615	+	0.0253595i
$902$	6.65820	−	14.5794i	0.221694	−	0.485442i
$903$		0			0
$904$	−12.1784	−	3.57589i	−0.405046	−	0.118932i
$905$	12.9903	−	8.34836i	0.431812	−	0.277509i
$906$		0			0
$907$	5.57373	−	1.63660i	0.185073	−	0.0543423i	−0.187883	−	0.982191i	$-0.560163\pi$
$907$	5.57373	−	1.63660i	0.185073	−	0.0543423i	0.372956	+	0.927849i	$0.378344\pi$
$908$	8.83365	−	10.1946i	0.293155	−	0.338319i
$909$		0			0
$910$	−1.32789	+	0.389902i	−0.0440190	+	0.0129251i
$911$	−4.38987	−	9.61247i	−0.145443	−	0.318475i	0.822864	−	0.568238i	$-0.192375\pi$
$911$	−4.38987	−	9.61247i	−0.145443	−	0.318475i	−0.968307	+	0.249763i	$0.919647\pi$
$912$		0			0
$913$	−90.1423	−	26.4682i	−2.98328	−	0.875969i
$914$	−4.35451	−	30.2863i	−0.144034	−	1.00178i
$915$		0			0
$916$	−0.340259	+	2.36656i	−0.0112425	+	0.0781932i
$917$	−14.3591	−	9.22801i	−0.474178	−	0.304736i
$918$		0			0
$919$	−44.4966			−1.46781			−0.733904	−	0.679253i	$-0.762304\pi$
$919$	−44.4966			−1.46781			−0.733904	+	0.679253i	$0.762304\pi$
$920$	−1.71485	−	3.73436i	−0.0565369	−	0.123118i
$921$		0			0
$922$	13.0352	+	15.0434i	0.429291	+	0.495428i
$923$	2.18461	+	1.40397i	0.0719075	+	0.0462121i
$924$		0			0
$925$	−0.735999	+	1.61161i	−0.0241995	+	0.0529895i
$926$	5.73491	+	39.8872i	0.188461	+	1.31077i
$927$		0			0
$928$	−4.18395	+	2.68886i	−0.137345	+	0.0882662i
$929$	3.72377	+	8.15391i	0.122173	+	0.267521i	0.960830	−	0.277139i	$-0.0893861\pi$
$929$	3.72377	+	8.15391i	0.122173	+	0.267521i	−0.838657	+	0.544660i	$0.816659\pi$
$930$		0			0
$931$	−4.83844	+	5.58385i	−0.158573	+	0.183003i
$932$	8.58007	−	9.90193i	0.281050	−	0.324348i
$933$		0			0
$934$	−13.2441	−	29.0005i	−0.433360	−	0.948926i
$935$	7.41012	−	4.76220i	0.242337	−	0.155740i
$936$		0			0
$937$	0.251751	+	1.75097i	0.00822435	+	0.0572016i	0.993520	−	0.113655i	$-0.0362557\pi$
$937$	0.251751	+	1.75097i	0.00822435	+	0.0572016i	−0.985296	+	0.170856i	$0.945347\pi$
$938$	14.6416	−	32.0606i	0.478064	−	1.04681i
$939$		0			0
$940$	−4.53076	−	2.91174i	−0.147777	−	0.0949706i
$941$	−14.6401	−	16.8956i	−0.477253	−	0.550779i	0.465162	−	0.885226i	$-0.345996\pi$
$941$	−14.6401	−	16.8956i	−0.477253	−	0.550779i	−0.942415	+	0.334446i	$0.891451\pi$
$942$		0			0
$943$	−1.91157	+	13.4951i	−0.0622494	+	0.439461i
$944$	6.90614			0.224776
$945$		0			0
$946$	−25.1486	−	16.1620i	−0.817653	−	0.525473i
$947$	6.69948	−	46.5959i	0.217704	−	1.51416i	−0.528779	−	0.848759i	$-0.677350\pi$
$947$	6.69948	−	46.5959i	0.217704	−	1.51416i	0.746483	−	0.665404i	$-0.231741\pi$
$948$		0			0
$949$	0.214702	+	1.49328i	0.00696952	+	0.0484741i
$950$	−31.4114	−	9.22323i	−1.01912	−	0.299241i
$951$		0			0
$952$	−2.13679	−	4.67892i	−0.0692538	−	0.151645i
$953$	22.2979	−	6.54726i	0.722300	−	0.212086i	0.100136	−	0.994974i	$-0.468072\pi$
$953$	22.2979	−	6.54726i	0.722300	−	0.212086i	0.622164	+	0.782887i	$0.286254\pi$
$954$		0			0
$955$	−7.18973	+	8.29739i	−0.232654	+	0.268497i
$956$	8.30675	−	2.43908i	0.268660	−	0.0788856i
$957$		0			0
$958$	29.8769	−	19.2007i	0.965280	−	0.620347i
$959$	−6.96973	−	2.04650i	−0.225064	−	0.0660848i
$960$		0			0
$961$	14.5400	−	31.8381i	0.469032	−	1.02704i
$962$	0.0338321	−	0.235307i	0.00109079	−	0.00758661i
$963$		0			0
$964$	0.714663	+	0.824765i	0.0230177	+	0.0265639i
$965$	19.6902			0.633851
$966$		0			0
$967$	−55.2673			−1.77728			−0.888638	−	0.458610i	$-0.848347\pi$
$967$	−55.2673			−1.77728			−0.888638	+	0.458610i	$0.848347\pi$
$968$	13.6245	+	15.7235i	0.437908	+	0.505372i
$969$		0			0
$970$	−0.389568	+	2.70950i	−0.0125083	+	0.0869969i
$971$	−6.92361	+	15.1606i	−0.222189	+	0.486527i	−0.987595	−	0.157021i	$-0.949811\pi$
$971$	−6.92361	+	15.1606i	−0.222189	+	0.486527i	0.765406	+	0.643548i	$0.222538\pi$
$972$		0			0
$973$	29.7911	+	8.74745i	0.955058	+	0.280430i
$974$	31.4099	−	20.1859i	1.00644	−	0.646799i
$975$		0			0
$976$	5.29420	−	1.55452i	0.169463	−	0.0497589i
$977$	−6.35399	+	7.33289i	−0.203282	+	0.234600i	−0.848232	−	0.529625i	$-0.822333\pi$
$977$	−6.35399	+	7.33289i	−0.203282	+	0.234600i	0.644950	+	0.764225i	$0.276878\pi$
$978$		0			0
$979$	65.2484	−	19.1587i	2.08535	−	0.612313i
$980$	0.342686	+	0.750377i	0.0109467	+	0.0239699i
$981$		0			0
$982$	16.6425	+	4.88668i	0.531083	+	0.155940i
$983$	5.05373	+	35.1495i	0.161189	+	1.12109i	0.896397	+	0.443253i	$0.146175\pi$
$983$	5.05373	+	35.1495i	0.161189	+	1.12109i	−0.735208	+	0.677842i	$0.762915\pi$
$984$		0			0
$985$	−2.74860	+	19.1169i	−0.0875777	+	0.609116i
$986$	7.62667	+	4.90136i	0.242883	+	0.156091i
$987$		0			0
$988$	4.39268			0.139750
$989$	24.4067	+	7.11118i	0.776089	+	0.226122i
$990$		0			0
$991$	−19.1801	−	22.1350i	−0.609277	−	0.703143i	0.364357	−	0.931259i	$-0.381289\pi$
$991$	−19.1801	−	22.1350i	−0.609277	−	0.703143i	−0.973634	+	0.228117i	$0.926743\pi$
$992$	−6.83443	−	4.39222i	−0.216993	−	0.139453i
$993$		0			0
$994$	5.31833	−	11.6455i	0.168687	−	0.369374i
$995$	1.45096	+	10.0917i	0.0459986	+	0.319927i
$996$		0			0
$997$	17.4446	−	11.2110i	0.552476	−	0.355055i	−0.234425	−	0.972134i	$-0.575321\pi$
$997$	17.4446	−	11.2110i	0.552476	−	0.355055i	0.786901	+	0.617080i	$0.211684\pi$
$998$	6.11334	+	13.3863i	0.193514	+	0.423737i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.i.h.289.2	yes	20
3.2	odd	2		414.2.i.g.289.1	✓	20
23.4	even	11		9522.2.a.cg.1.8		10
23.16	even	11	inner	414.2.i.h.361.2	yes	20
23.19	odd	22		9522.2.a.ch.1.3		10
69.50	odd	22		9522.2.a.cj.1.3		10
69.62	odd	22		414.2.i.g.361.1	yes	20
69.65	even	22		9522.2.a.ci.1.8		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.i.g.289.1	✓	20	3.2	odd	2
414.2.i.g.361.1	yes	20	69.62	odd	22
414.2.i.h.289.2	yes	20	1.1	even	1	trivial
414.2.i.h.361.2	yes	20	23.16	even	11	inner
9522.2.a.cg.1.8		10	23.4	even	11
9522.2.a.ch.1.3		10	23.19	odd	22
9522.2.a.ci.1.8		10	69.65	even	22
9522.2.a.cj.1.3		10	69.50	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)

\(f(q)\)	\(=\)	\(q+(0.654861 + 0.755750i) q^{2} +(-0.142315 + 0.989821i) q^{4} +(0.355945 - 0.779412i) q^{5} +(2.70753 + 0.795003i) q^{7} +(-0.841254 + 0.540641i) q^{8} +O(q^{10})\)	\(q+(0.654861 + 0.755750i) q^{2} +(-0.142315 + 0.989821i) q^{4} +(0.355945 - 0.779412i) q^{5} +(2.70753 + 0.795003i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(0.822135 - 0.241401i) q^{10} +(3.69316 - 4.26213i) q^{11} +(-0.549197 + 0.161259i) q^{13} +(1.17223 + 2.56683i) q^{14} +(-0.959493 - 0.281733i) q^{16} +(0.259417 + 1.80429i) q^{17} +(-1.09218 + 7.59627i) q^{19} +(0.720822 + 0.463244i) q^{20} +5.63961 q^{22} +(-4.59874 + 1.36074i) q^{23} +(2.79352 + 3.22389i) q^{25} +(-0.481519 - 0.309453i) q^{26} +(-1.17223 + 2.56683i) q^{28} +(-0.707799 - 4.92285i) q^{29} +(6.83443 - 4.39222i) q^{31} +(-0.415415 - 0.909632i) q^{32} +(-1.19371 + 1.37761i) q^{34} +(1.58337 - 1.82730i) q^{35} +(0.172534 + 0.377797i) q^{37} +(-6.45610 + 4.14909i) q^{38} +(0.121941 + 0.848122i) q^{40} +(1.18061 - 2.58519i) q^{41} +(-4.45929 - 2.86581i) q^{43} +(3.69316 + 4.26213i) q^{44} +(-4.03991 - 2.58440i) q^{46} -6.28555 q^{47} +(0.809915 + 0.520501i) q^{49} +(-0.607089 + 4.22240i) q^{50} +(-0.0814585 - 0.566556i) q^{52} +(0.404800 + 0.118860i) q^{53} +(-2.00739 - 4.39558i) q^{55} +(-2.70753 + 0.795003i) q^{56} +(3.25693 - 3.75870i) q^{58} +(-6.62639 + 1.94569i) q^{59} +(-4.64179 + 2.98310i) q^{61} +(7.79502 + 2.28883i) q^{62} +(0.415415 - 0.909632i) q^{64} +(-0.0697971 + 0.485450i) q^{65} +(-8.17942 - 9.43956i) q^{67} -1.82284 q^{68} +2.41787 q^{70} +(-2.97106 - 3.42878i) q^{71} +(0.375102 - 2.60889i) q^{73} +(-0.172534 + 0.377797i) q^{74} +(-7.36352 - 2.16212i) q^{76} +(13.3877 - 8.60378i) q^{77} +(-4.41367 + 1.29597i) q^{79} +(-0.561113 + 0.647559i) q^{80} +(2.72689 - 0.800687i) q^{82} +(-6.92023 - 15.1532i) q^{83} +(1.49862 + 0.440035i) q^{85} +(-0.754378 - 5.24681i) q^{86} +(-0.802600 + 5.58220i) q^{88} +(10.1439 + 6.51911i) q^{89} -1.61517 q^{91} +(-0.692421 - 4.74558i) q^{92} +(-4.11616 - 4.75030i) q^{94} +(5.53187 + 3.55512i) q^{95} +(-1.32713 + 2.90601i) q^{97} +(0.137013 + 0.952948i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{7} + 2 q^{8}+O(q^{10}) \) 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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