LMFDB - Embedded newform 225.2.h.c.136.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(46,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("225.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.h (of order $5$, degree $4$, 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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.26265625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 2x^{6} + x^{4} + 8x^{2} - 24x + 16 $ x^8 - 3x^7 + 2x^6 + x^4 + 8x^2 - 24x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			136.2
Root			$1.33631 - 0.462894i$ of defining polynomial
Character	$\chi$	$=$	225.136
Dual form			225.2.h.c.91.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.18949 - 1.59076i) q^{2} +(1.64533 - 5.06380i) q^{4} +(-0.336312 + 2.21063i) q^{5} +0.470294 q^{7} +(-2.78023 - 8.55667i) q^{8} +O(q^{10})$	\(q+(2.18949 - 1.59076i) q^{2} +(1.64533 - 5.06380i) q^{4} +(-0.336312 + 2.21063i) q^{5} +0.470294 q^{7} +(-2.78023 - 8.55667i) q^{8} +(2.78023 + 5.37515i) q^{10} +(-2.57387 + 1.87003i) q^{11} +(-0.455836 - 0.331184i) q^{13} +(1.02971 - 0.748125i) q^{14} +(-11.0839 - 8.05289i) q^{16} +(0.527295 + 1.62285i) q^{17} +(1.15575 + 3.55705i) q^{19} +(10.6409 + 5.34023i) q^{20} +(-2.66071 + 8.18882i) q^{22} +(-1.83631 + 1.33416i) q^{23} +(-4.77379 - 1.48692i) q^{25} -1.52488 q^{26} +(0.773789 - 2.38148i) q^{28} +(2.57238 - 7.91697i) q^{29} +(1.67999 + 5.17047i) q^{31} -19.0842 q^{32} +(3.73607 + 2.71441i) q^{34} +(-0.158166 + 1.03965i) q^{35} +(-0.825886 - 0.600041i) q^{37} +(8.18892 + 5.94960i) q^{38} +(19.8507 - 3.26836i) q^{40} +(1.19098 + 0.865300i) q^{41} +6.72721 q^{43} +(5.23458 + 16.1104i) q^{44} +(-1.89827 + 5.84226i) q^{46} +(1.37005 - 4.21658i) q^{47} -6.77882 q^{49} +(-12.8175 + 4.33834i) q^{50} +(-2.42705 + 1.76336i) q^{52} +(2.17907 - 6.70648i) q^{53} +(-3.26832 - 6.31879i) q^{55} +(-1.30753 - 4.02415i) q^{56} +(-6.96179 - 21.4262i) q^{58} +(-10.4136 - 7.56596i) q^{59} +(-0.102655 + 0.0745831i) q^{61} +(11.9033 + 8.64825i) q^{62} +(-19.6170 + 14.2526i) q^{64} +(0.885429 - 0.896304i) q^{65} +(-0.863607 - 2.65791i) q^{67} +9.08535 q^{68} +(1.30753 + 2.52790i) q^{70} +(-4.95838 + 15.2603i) q^{71} +(7.91925 - 5.75367i) q^{73} -2.76279 q^{74} +19.9138 q^{76} +(-1.21048 + 0.879462i) q^{77} +(-1.46937 + 4.52227i) q^{79} +(21.5296 - 21.7940i) q^{80} +3.98413 q^{82} +(-3.61256 - 11.1183i) q^{83} +(-3.76485 + 0.619872i) q^{85} +(14.7292 - 10.7014i) q^{86} +(23.1572 + 16.8247i) q^{88} +(-5.01630 + 3.64456i) q^{89} +(-0.214377 - 0.155754i) q^{91} +(3.73458 + 11.4938i) q^{92} +(-3.70785 - 11.4116i) q^{94} +(-8.25202 + 1.35867i) q^{95} +(2.61256 - 8.04064i) q^{97} +(-14.8422 + 10.7835i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + q^{4} + 5 q^{5} + 4 q^{7}+O(q^{10}) $ 8 * q + q^2 + q^4 + 5 * q^5 + 4 * q^7	$ 8 q + q^{2} + q^{4} + 5 q^{5} + 4 q^{7} - 16 q^{11} - 8 q^{13} + 8 q^{14} - 17 q^{16} + q^{17} - 5 q^{19} + 10 q^{20} + 13 q^{22} - 7 q^{23} - 15 q^{25} - 6 q^{26} - 17 q^{28} - 5 q^{29} - 19 q^{31} - 24 q^{32} + 12 q^{34} + 10 q^{35} - q^{37} + 10 q^{38} + 25 q^{40} + 14 q^{41} + 32 q^{43} + 3 q^{44} + 16 q^{46} + q^{47} + 16 q^{49} - 10 q^{50} - 6 q^{52} + 3 q^{53} + 15 q^{55} + 15 q^{56} + 5 q^{58} - 30 q^{59} - 14 q^{61} + 17 q^{62} - 44 q^{64} - 25 q^{65} + 4 q^{67} + 22 q^{68} - 15 q^{70} - 21 q^{71} + 2 q^{73} + 38 q^{74} + 80 q^{76} + 37 q^{77} - 30 q^{79} + 50 q^{80} - 12 q^{82} - 2 q^{83} - 30 q^{85} + 34 q^{86} + 70 q^{88} + 21 q^{91} - 9 q^{92} - 33 q^{94} - 65 q^{95} - 6 q^{97} - 73 q^{98}+O(q^{100}) $ 8 * q + q^2 + q^4 + 5 * q^5 + 4 * q^7 - 16 * q^11 - 8 * q^13 + 8 * q^14 - 17 * q^16 + q^17 - 5 * q^19 + 10 * q^20 + 13 * q^22 - 7 * q^23 - 15 * q^25 - 6 * q^26 - 17 * q^28 - 5 * q^29 - 19 * q^31 - 24 * q^32 + 12 * q^34 + 10 * q^35 - q^37 + 10 * q^38 + 25 * q^40 + 14 * q^41 + 32 * q^43 + 3 * q^44 + 16 * q^46 + q^47 + 16 * q^49 - 10 * q^50 - 6 * q^52 + 3 * q^53 + 15 * q^55 + 15 * q^56 + 5 * q^58 - 30 * q^59 - 14 * q^61 + 17 * q^62 - 44 * q^64 - 25 * q^65 + 4 * q^67 + 22 * q^68 - 15 * q^70 - 21 * q^71 + 2 * q^73 + 38 * q^74 + 80 * q^76 + 37 * q^77 - 30 * q^79 + 50 * q^80 - 12 * q^82 - 2 * q^83 - 30 * q^85 + 34 * q^86 + 70 * q^88 + 21 * q^91 - 9 * q^92 - 33 * q^94 - 65 * q^95 - 6 * q^97 - 73 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	2.18949	−	1.59076i	1.54821	−	1.12484i	0.603290	−	0.797522i	$-0.293856\pi$
$2$	2.18949	−	1.59076i	1.54821	−	1.12484i	0.944915	−	0.327315i	$-0.106144\pi$
$3$		0			0
$3$		0			0
$4$	1.64533	−	5.06380i	0.822664	−	2.53190i
$5$	−0.336312	+	2.21063i	−0.150403	+	0.988625i
$5$	−0.336312	+	2.21063i	−0.150403	+	0.988625i
$6$		0			0
$7$	0.470294			0.177754			0.0888772	−	0.996043i	$-0.471672\pi$
$7$	0.470294			0.177754			0.0888772	+	0.996043i	$0.471672\pi$
$8$	−2.78023	−	8.55667i	−0.982960	−	3.02524i
$9$		0			0
$10$	2.78023	+	5.37515i	0.879187	+	1.69977i
$11$	−2.57387	+	1.87003i	−0.776051	+	0.563834i	−0.903791	−	0.427974i	$-0.859228\pi$
$11$	−2.57387	+	1.87003i	−0.776051	+	0.563834i	0.127740	+	0.991808i	$0.459228\pi$
$12$		0			0
$13$	−0.455836	−	0.331184i	−0.126426	−	0.0918540i	0.522775	−	0.852471i	$-0.324897\pi$
$13$	−0.455836	−	0.331184i	−0.126426	−	0.0918540i	−0.649201	+	0.760617i	$0.724897\pi$
$14$	1.02971	−	0.748125i	0.275200	−	0.199945i
$15$		0			0
$16$	−11.0839	−	8.05289i	−2.77096	−	2.01322i
$17$	0.527295	+	1.62285i	0.127888	+	0.393598i	0.994416	−	0.105530i	$-0.0336538\pi$
$17$	0.527295	+	1.62285i	0.127888	+	0.393598i	−0.866528	+	0.499128i	$0.833654\pi$
$18$		0			0
$19$	1.15575	+	3.55705i	0.265148	+	0.816043i	0.991659	+	0.128888i	$0.0411406\pi$
$19$	1.15575	+	3.55705i	0.265148	+	0.816043i	−0.726511	+	0.687155i	$0.758859\pi$
$20$	10.6409	+	5.34023i	2.37937	+	1.19411i
$21$		0			0
$22$	−2.66071	+	8.18882i	−0.567265	+	1.74586i
$23$	−1.83631	+	1.33416i	−0.382898	+	0.278191i	−0.762539	−	0.646942i	$-0.776047\pi$
$23$	−1.83631	+	1.33416i	−0.382898	+	0.278191i	0.379641	+	0.925134i	$0.376047\pi$
$24$		0			0
$25$	−4.77379	−	1.48692i	−0.954758	−	0.297385i
$26$	−1.52488			−0.299054
$27$		0			0
$28$	0.773789	−	2.38148i	0.146232	−	0.450057i
$29$	2.57238	−	7.91697i	0.477679	−	1.47014i	−0.364631	−	0.931152i	$-0.618805\pi$
$29$	2.57238	−	7.91697i	0.477679	−	1.47014i	0.842310	−	0.538993i	$-0.181195\pi$
$30$		0			0
$31$	1.67999	+	5.17047i	0.301735	+	0.928644i	0.980876	+	0.194636i	$0.0623526\pi$
$31$	1.67999	+	5.17047i	0.301735	+	0.928644i	−0.679141	+	0.734008i	$0.737647\pi$
$32$	−19.0842			−3.37364
$33$		0			0
$34$	3.73607	+	2.71441i	0.640730	+	0.465518i
$35$	−0.158166	+	1.03965i	−0.0267349	+	0.175732i
$36$		0			0
$37$	−0.825886	−	0.600041i	−0.135775	−	0.0986462i	0.517825	−	0.855487i	$-0.326742\pi$
$37$	−0.825886	−	0.600041i	−0.135775	−	0.0986462i	−0.653600	+	0.756841i	$0.726742\pi$
$38$	8.18892	+	5.94960i	1.32842	+	0.965153i
$39$		0			0
$40$	19.8507	−	3.26836i	3.13867	−	0.516773i
$41$	1.19098	+	0.865300i	0.186000	+	0.135137i	0.676889	−	0.736085i	$-0.263328\pi$
$41$	1.19098	+	0.865300i	0.186000	+	0.135137i	−0.490889	+	0.871222i	$0.663328\pi$
$42$		0			0
$43$	6.72721			1.02589			0.512945	−	0.858421i	$-0.328554\pi$
$43$	6.72721			1.02589			0.512945	+	0.858421i	$0.328554\pi$
$44$	5.23458	+	16.1104i	0.789142	+	2.42873i
$45$		0			0
$46$	−1.89827	+	5.84226i	−0.279884	+	0.861395i
$47$	1.37005	−	4.21658i	0.199842	−	0.615052i	−0.800043	−	0.599942i	$-0.795190\pi$
$47$	1.37005	−	4.21658i	0.199842	−	0.615052i	0.999886	−	0.0151095i	$-0.00480970\pi$
$48$		0			0
$49$	−6.77882			−0.968403
$50$	−12.8175	+	4.33834i	−1.81267	+	0.613534i
$51$		0			0
$52$	−2.42705	+	1.76336i	−0.336571	+	0.244533i
$53$	2.17907	−	6.70648i	0.299318	−	0.921206i	−0.682419	−	0.730961i	$-0.739072\pi$
$53$	2.17907	−	6.70648i	0.299318	−	0.921206i	0.981737	−	0.190244i	$-0.0609281\pi$
$54$		0			0
$55$	−3.26832	−	6.31879i	−0.440700	−	0.852026i
$56$	−1.30753	−	4.02415i	−0.174726	−	0.537750i
$57$		0			0
$58$	−6.96179	−	21.4262i	−0.914128	−	2.81340i
$59$	−10.4136	−	7.56596i	−1.35574	−	0.985004i	−0.998703	−	0.0509138i	$-0.983787\pi$
$59$	−10.4136	−	7.56596i	−1.35574	−	0.985004i	−0.357038	−	0.934090i	$-0.616213\pi$
$60$		0			0
$61$	−0.102655	+	0.0745831i	−0.0131436	+	0.00954939i	−0.594338	−	0.804216i	$-0.702586\pi$
$61$	−0.102655	+	0.0745831i	−0.0131436	+	0.00954939i	0.581194	+	0.813765i	$0.302586\pi$
$62$	11.9033	+	8.64825i	1.51172	+	1.09833i
$63$		0			0
$64$	−19.6170	+	14.2526i	−2.45213	+	1.78158i
$65$	0.885429	−	0.896304i	0.109824	−	0.111173i
$66$		0			0
$67$	−0.863607	−	2.65791i	−0.105506	−	0.324715i	0.884343	−	0.466838i	$-0.154607\pi$
$67$	−0.863607	−	2.65791i	−0.105506	−	0.324715i	−0.989849	+	0.142123i	$0.954607\pi$
$68$	9.08535			1.10176
$69$		0			0
$70$	1.30753	+	2.52790i	0.156279	+	0.302142i
$71$	−4.95838	+	15.2603i	−0.588451	+	1.81107i	−0.00350617	+	0.999994i	$0.501116\pi$
$71$	−4.95838	+	15.2603i	−0.588451	+	1.81107i	−0.584945	+	0.811073i	$0.698884\pi$
$72$		0			0
$73$	7.91925	−	5.75367i	0.926878	−	0.673416i	−0.0183484	−	0.999832i	$-0.505841\pi$
$73$	7.91925	−	5.75367i	0.926878	−	0.673416i	0.945226	+	0.326415i	$0.105841\pi$
$74$	−2.76279			−0.321168
$75$		0			0
$76$	19.9138			2.28427
$77$	−1.21048	+	0.879462i	−0.137947	+	0.100224i
$78$		0			0
$79$	−1.46937	+	4.52227i	−0.165317	+	0.508795i	−0.999060	−	0.0433593i	$-0.986194\pi$
$79$	−1.46937	+	4.52227i	−0.165317	+	0.508795i	0.833742	+	0.552154i	$0.186194\pi$
$80$	21.5296	−	21.7940i	2.40708	−	2.43665i
$81$		0			0
$82$	3.98413			0.439974
$83$	−3.61256	−	11.1183i	−0.396530	−	1.22039i	−0.927763	−	0.373169i	$-0.878271\pi$
$83$	−3.61256	−	11.1183i	−0.396530	−	1.22039i	0.531233	−	0.847226i	$-0.321729\pi$
$84$		0			0
$85$	−3.76485	+	0.619872i	−0.408356	+	0.0672346i
$86$	14.7292	−	10.7014i	1.58829	−	1.15396i
$87$		0			0
$88$	23.1572	+	16.8247i	2.46856	+	1.79351i
$89$	−5.01630	+	3.64456i	−0.531727	+	0.386322i	−0.821003	−	0.570923i	$-0.806585\pi$
$89$	−5.01630	+	3.64456i	−0.531727	+	0.386322i	0.289277	+	0.957246i	$0.406585\pi$
$90$		0			0
$91$	−0.214377	−	0.155754i	−0.0224728	−	0.0163275i
$92$	3.73458	+	11.4938i	0.389357	+	1.19832i
$93$		0			0
$94$	−3.70785	−	11.4116i	−0.382436	−	1.17702i
$95$	−8.25202	+	1.35867i	−0.846639	+	0.139397i
$96$		0			0
$97$	2.61256	−	8.04064i	0.265265	−	0.816403i	−0.726367	−	0.687307i	$-0.758793\pi$
$97$	2.61256	−	8.04064i	0.265265	−	0.816403i	0.991632	−	0.129096i	$-0.0412074\pi$
$98$	−14.8422	+	10.7835i	−1.49929	+	1.08930i
$99$		0			0
$100$	−15.3839	+	21.7270i	−1.53839	+	2.17270i
$101$	5.83325			0.580430			0.290215	−	0.956961i	$-0.406273\pi$
$101$	5.83325			0.580430			0.290215	+	0.956961i	$0.406273\pi$
$102$		0			0
$103$	−4.35077	+	13.3903i	−0.428694	+	1.31938i	0.470718	+	0.882284i	$0.343995\pi$
$103$	−4.35077	+	13.3903i	−0.428694	+	1.31938i	−0.899412	+	0.437101i	$0.856005\pi$
$104$	−1.56651	+	4.82121i	−0.153609	+	0.472758i
$105$		0			0
$106$	−5.89735	−	18.1502i	−0.572801	−	1.76290i
$107$	8.61207			0.832561			0.416280	−	0.909236i	$-0.363334\pi$
$107$	8.61207			0.832561			0.416280	+	0.909236i	$0.363334\pi$
$108$		0			0
$109$	−13.5005	−	9.80868i	−1.29311	−	0.939501i	−0.293249	−	0.956036i	$-0.594736\pi$
$109$	−13.5005	−	9.80868i	−1.29311	−	0.939501i	−0.999863	+	0.0165355i	$0.994736\pi$
$110$	−17.2076	−	8.63584i	−1.64068	−	0.823395i
$111$		0			0
$112$	−5.21267	−	3.78723i	−0.492551	−	0.357860i
$113$	9.52686	+	6.92167i	0.896211	+	0.651136i	0.937490	−	0.348012i	$-0.113143\pi$
$113$	9.52686	+	6.92167i	0.896211	+	0.651136i	−0.0412787	+	0.999148i	$0.513143\pi$
$114$		0			0
$115$	−2.33176	−	4.50810i	−0.217438	−	0.420383i
$116$	−35.8576	−	26.0520i	−3.32929	−	2.41887i
$117$		0			0
$118$	−34.8362			−3.20693
$119$	0.247984	+	0.763215i	0.0227326	+	0.0699638i
$120$		0			0
$121$	−0.271378	+	0.835215i	−0.0246707	+	0.0759286i
$122$	−0.106118	+	0.326598i	−0.00960749	+	0.0295688i
$123$		0			0
$124$	28.9464			2.59946
$125$	4.89252	−	10.0530i	0.437601	−	0.899169i
$126$		0			0
$127$	−1.43910	+	1.04557i	−0.127699	+	0.0927790i	−0.649801	−	0.760104i	$-0.725148\pi$
$127$	−1.43910	+	1.04557i	−0.127699	+	0.0927790i	0.522102	+	0.852883i	$0.325148\pi$
$128$	−8.48418	+	26.1116i	−0.749903	+	2.30796i
$129$		0			0
$130$	0.512837	−	3.37096i	0.0449787	−	0.295653i
$131$	1.82895	+	5.62892i	0.159796	+	0.491801i	0.998615	−	0.0526087i	$-0.0167536\pi$
$131$	1.82895	+	5.62892i	0.159796	+	0.491801i	−0.838819	+	0.544410i	$0.816754\pi$
$132$		0			0
$133$	0.543545	+	1.67286i	0.0471313	+	0.145055i
$134$	−6.11895	−	4.44568i	−0.528597	−	0.384048i
$135$		0			0
$136$	12.4202	−	9.02378i	1.06502	−	0.773783i
$137$	−4.13902	−	3.00717i	−0.353620	−	0.256920i	0.396766	−	0.917920i	$-0.370132\pi$
$137$	−4.13902	−	3.00717i	−0.353620	−	0.256920i	−0.750386	+	0.661000i	$0.770132\pi$
$138$		0			0
$139$	6.66482	−	4.84228i	0.565303	−	0.410717i	−0.268093	−	0.963393i	$-0.586393\pi$
$139$	6.66482	−	4.84228i	0.565303	−	0.410717i	0.833396	+	0.552676i	$0.186393\pi$
$140$	5.00433	+	2.51148i	0.422943	+	0.212259i
$141$		0			0
$142$	13.4192	+	41.3000i	1.12611	+	3.46581i
$143$	1.79259			0.149904
$144$		0			0
$145$	16.6364	+	8.34916i	1.38158	+	0.693360i
$146$	8.18643	−	25.1952i	0.677514	−	2.08517i
$147$		0			0
$148$	−4.39735	+	3.19486i	−0.361460	+	0.262616i
$149$	10.0585			0.824027			0.412014	−	0.911178i	$-0.364826\pi$
$149$	10.0585			0.824027			0.412014	+	0.911178i	$0.364826\pi$
$150$		0			0
$151$	−11.9810			−0.974999			−0.487500	−	0.873123i	$-0.662091\pi$
$151$	−11.9810			−0.974999			−0.487500	+	0.873123i	$0.662091\pi$
$152$	27.2232	−	19.7788i	2.20810	−	1.60428i
$153$		0			0
$154$	−1.25132	+	3.85115i	−0.100834	+	0.310335i
$155$	−11.9950	+	1.97494i	−0.963462	+	0.158631i
$156$		0			0
$157$	19.5960			1.56393			0.781967	−	0.623319i	$-0.214216\pi$
$157$	19.5960			1.56393			0.781967	+	0.623319i	$0.214216\pi$
$158$	3.97666	+	12.2389i	0.316366	+	0.973674i
$159$		0			0
$160$	6.41825	−	42.1882i	0.507407	−	3.33527i
$161$	−0.863607	+	0.627447i	−0.0680618	+	0.0494498i
$162$		0			0
$163$	−9.62137	−	6.99033i	−0.753604	−	0.547525i	0.143338	−	0.989674i	$-0.454216\pi$
$163$	−9.62137	−	6.99033i	−0.753604	−	0.547525i	−0.896942	+	0.442149i	$0.854216\pi$
$164$	6.34127	−	4.60720i	0.495170	−	0.359762i
$165$		0			0
$166$	−25.5963	−	18.5968i	−1.98665	−	1.44339i
$167$	1.85218	+	5.70042i	0.143326	+	0.441112i	0.996792	−	0.0800367i	$-0.0255038\pi$
$167$	1.85218	+	5.70042i	0.143326	+	0.441112i	−0.853466	+	0.521149i	$0.825504\pi$
$168$		0			0
$169$	−3.91912	−	12.0618i	−0.301471	−	0.927831i
$170$	−7.25705	+	7.34618i	−0.556590	+	0.563426i
$171$		0			0
$172$	11.0685	−	34.0653i	0.843964	−	2.59745i
$173$	14.0157	−	10.1830i	1.06560	−	0.774201i	0.0904807	−	0.995898i	$-0.471160\pi$
$173$	14.0157	−	10.1830i	1.06560	−	0.774201i	0.975116	+	0.221697i	$0.0711596\pi$
$174$		0			0
$175$	−2.24509	−	0.699292i	−0.169712	−	0.0528615i
$176$	43.5875			3.28553
$177$		0			0
$178$	−5.18554	+	15.9595i	−0.388673	+	1.19621i
$179$	−3.26832	+	10.0588i	−0.244285	+	0.751833i	0.751468	+	0.659770i	$0.229346\pi$
$179$	−3.26832	+	10.0588i	−0.244285	+	0.751833i	−0.995753	+	0.0920634i	$0.970654\pi$
$180$		0			0
$181$	3.70198	+	11.3935i	0.275166	+	0.846873i	0.989175	+	0.146738i	$0.0468773\pi$
$181$	3.70198	+	11.3935i	0.275166	+	0.846873i	−0.714010	+	0.700136i	$0.753123\pi$
$182$	−0.717144			−0.0531583
$183$		0			0
$184$	16.5213	+	12.0035i	1.21797	+	0.884906i
$185$	1.60423	−	1.62393i	0.117945	−	0.119394i
$186$		0			0
$187$	−4.39195	−	3.19094i	−0.321172	−	0.233345i
$188$	−19.0977	−	13.8753i	−1.39285	−	1.01196i
$189$		0			0
$190$	−15.9064	+	16.1018i	−1.15397	+	1.16815i
$191$	14.7773	+	10.7363i	1.06924	+	0.776852i	0.975776	−	0.218771i	$-0.0702047\pi$
$191$	14.7773	+	10.7363i	1.06924	+	0.776852i	0.0934681	+	0.995622i	$0.470205\pi$
$192$		0			0
$193$	25.2063			1.81439			0.907194	−	0.420713i	$-0.138220\pi$
$193$	25.2063			1.81439			0.907194	+	0.420713i	$0.138220\pi$
$194$	−7.07054	−	21.7609i	−0.507635	−	1.56234i
$195$		0			0
$196$	−11.1534	+	34.3266i	−0.796671	+	2.45190i
$197$	−3.73672	+	11.5004i	−0.266230	+	0.819372i	0.725177	+	0.688562i	$0.241758\pi$
$197$	−3.73672	+	11.5004i	−0.266230	+	0.819372i	−0.991407	+	0.130810i	$0.958242\pi$
$198$		0			0
$199$	−0.544434			−0.0385939			−0.0192970	−	0.999814i	$-0.506143\pi$
$199$	−0.544434			−0.0385939			−0.0192970	+	0.999814i	$0.506143\pi$
$200$	0.549118	+	44.9817i	0.0388285	+	3.18069i
$201$		0			0
$202$	12.7719	−	9.27930i	0.898625	−	0.652889i
$203$	1.20978	−	3.72331i	0.0849096	−	0.261325i
$204$		0			0
$205$	−2.31340	+	2.34181i	−0.161575	+	0.163559i
$206$	11.7748	+	36.2390i	0.820386	+	2.52489i
$207$		0			0
$208$	2.38543	+	7.34160i	0.165400	+	0.509048i
$209$	−9.62653	−	6.99409i	−0.665881	−	0.483791i
$210$		0			0
$211$	2.52580	−	1.83510i	0.173884	−	0.126334i	−0.497439	−	0.867499i	$-0.665726\pi$
$211$	2.52580	−	1.83510i	0.173884	−	0.126334i	0.671323	+	0.741165i	$0.265726\pi$
$212$	−30.3750	−	22.0687i	−2.08616	−	1.51569i
$213$		0			0
$214$	18.8561	−	13.6997i	1.28897	−	0.936495i
$215$	−2.26244	+	14.8714i	−0.154297	+	1.01422i
$216$		0			0
$217$	0.790089	+	2.43164i	0.0536347	+	0.165071i
$218$	−45.1625			−3.05879
$219$		0			0
$220$	−37.3746	+	6.15362i	−2.51979	+	0.414877i
$221$	0.297101	−	0.914384i	0.0199852	−	0.0615081i
$222$		0			0
$223$	−0.274358	+	0.199333i	−0.0183724	+	0.0133483i	−0.596934	−	0.802291i	$-0.703614\pi$
$223$	−0.274358	+	0.199333i	−0.0183724	+	0.0133483i	0.578561	+	0.815639i	$0.303614\pi$
$224$	−8.97519			−0.599680
$225$		0			0
$226$	31.8697			2.11994
$227$	−1.44690	+	1.05123i	−0.0960341	+	0.0697729i	−0.634766	−	0.772704i	$-0.718904\pi$
$227$	−1.44690	+	1.05123i	−0.0960341	+	0.0697729i	0.538732	+	0.842477i	$0.318904\pi$
$228$		0			0
$229$	−8.64730	+	26.6137i	−0.571430	+	1.75868i	0.0765965	+	0.997062i	$0.475595\pi$
$229$	−8.64730	+	26.6137i	−0.571430	+	1.75868i	−0.648026	+	0.761618i	$0.724405\pi$
$230$	−12.2767	−	6.16119i	−0.809500	−	0.406257i
$231$		0			0
$232$	−74.8948			−4.91708
$233$	2.09328	+	6.44246i	0.137135	+	0.422059i	0.995916	−	0.0902840i	$-0.0287775\pi$
$233$	2.09328	+	6.44246i	0.137135	+	0.422059i	−0.858781	+	0.512343i	$0.828777\pi$
$234$		0			0
$235$	8.86055	+	4.44676i	0.577998	+	0.290075i
$236$	−55.4464	+	40.2841i	−3.60925	+	2.62227i
$237$		0			0
$238$	1.75705	+	1.27657i	0.113893	+	0.0827479i
$239$	−5.24514	+	3.81081i	−0.339280	+	0.246501i	−0.744358	−	0.667781i	$-0.767244\pi$
$239$	−5.24514	+	3.81081i	−0.339280	+	0.246501i	0.405078	+	0.914282i	$0.367244\pi$
$240$		0			0
$241$	6.02602	+	4.37816i	0.388170	+	0.282022i	0.764705	−	0.644380i	$-0.222885\pi$
$241$	6.02602	+	4.37816i	0.388170	+	0.282022i	−0.376535	+	0.926402i	$0.622885\pi$
$242$	0.734446	+	2.26039i	0.0472120	+	0.145304i
$243$		0			0
$244$	0.208773	+	0.642537i	0.0133653	+	0.0411342i
$245$	2.27980	−	14.9855i	0.145651	−	0.957387i
$246$		0			0
$247$	0.651203	−	2.00420i	0.0414351	−	0.127524i
$248$	39.5713	−	28.7502i	2.51278	−	1.82564i
$249$		0			0
$250$	−5.27979	−	29.7938i	−0.333924	−	1.88433i
$251$	4.60217			0.290486			0.145243	−	0.989396i	$-0.453604\pi$
$251$	4.60217			0.290486			0.145243	+	0.989396i	$0.453604\pi$
$252$		0			0
$253$	2.23152	−	6.86790i	0.140294	−	0.431781i
$254$	−1.48765	+	4.57852i	−0.0933435	+	0.287282i
$255$		0			0
$256$	7.97520	+	24.5451i	0.498450	+	1.53407i
$257$	5.79485			0.361473			0.180736	−	0.983532i	$-0.442152\pi$
$257$	5.79485			0.361473			0.180736	+	0.983532i	$0.442152\pi$
$258$		0			0
$259$	−0.388409	−	0.282196i	−0.0241346	−	0.0175348i
$260$	−3.08188	−	5.95835i	−0.191130	−	0.369521i
$261$		0			0
$262$	12.9587	+	9.41507i	0.800593	+	0.581665i
$263$	11.5680	+	8.40467i	0.713316	+	0.518254i	0.884242	−	0.467030i	$-0.154676\pi$
$263$	11.5680	+	8.40467i	0.713316	+	0.518254i	−0.170926	+	0.985284i	$0.554676\pi$
$264$		0			0
$265$	14.0927	+	7.07258i	0.865708	+	0.434465i
$266$	3.85120	+	2.79806i	0.236132	+	0.171560i
$267$		0			0
$268$	−14.8800			−0.908943
$269$	5.93945	+	18.2797i	0.362135	+	1.11454i	0.951756	+	0.306856i	$0.0992770\pi$
$269$	5.93945	+	18.2797i	0.362135	+	1.11454i	−0.589621	+	0.807680i	$0.700723\pi$
$270$		0			0
$271$	−7.18256	+	22.1057i	−0.436310	+	1.34282i	0.455429	+	0.890272i	$0.349486\pi$
$271$	−7.18256	+	22.1057i	−0.436310	+	1.34282i	−0.891739	+	0.452551i	$0.850514\pi$
$272$	7.22415	−	22.2337i	0.438029	−	1.34811i
$273$		0			0
$274$	−13.8460			−0.836470
$275$	15.0677	−	5.09996i	0.908616	−	0.307539i
$276$		0			0
$277$	−17.7102	+	12.8672i	−1.06410	+	0.773115i	−0.974843	−	0.222894i	$-0.928450\pi$
$277$	−17.7102	+	12.8672i	−1.06410	+	0.773115i	−0.0892586	+	0.996008i	$0.528450\pi$
$278$	6.88968	−	21.2043i	0.413216	−	1.27175i
$279$		0			0
$280$	9.33566	−	1.53709i	0.557912	−	0.0918587i
$281$	−8.37863	−	25.7868i	−0.499827	−	1.53831i	−0.809296	−	0.587401i	$-0.800151\pi$
$281$	−8.37863	−	25.7868i	−0.499827	−	1.53831i	0.309469	−	0.950910i	$-0.399849\pi$
$282$		0			0
$283$	5.03926	+	15.5093i	0.299553	+	0.921929i	0.981654	+	0.190671i	$0.0610664\pi$
$283$	5.03926	+	15.5093i	0.299553	+	0.921929i	−0.682101	+	0.731258i	$0.738934\pi$
$284$	69.1171	+	50.2165i	4.10134	+	2.97980i
$285$		0			0
$286$	3.92485	−	2.85157i	0.232081	−	0.168617i
$287$	0.560112	+	0.406945i	0.0330624	+	0.0240212i
$288$		0			0
$289$	11.3977	−	8.28091i	0.670453	−	0.487112i
$290$	49.7068	−	8.18408i	2.91888	−	0.480586i
$291$		0			0
$292$	−16.1057	−	49.5682i	−0.942514	−	2.90076i
$293$	−5.46407			−0.319214			−0.159607	−	0.987181i	$-0.551023\pi$
$293$	−5.46407			−0.319214			−0.159607	+	0.987181i	$0.551023\pi$
$294$		0			0
$295$	20.2278	−	20.4762i	1.17771	−	1.19217i
$296$	−2.83820	+	8.73509i	−0.164967	+	0.507717i
$297$		0			0
$298$	22.0231	−	16.0007i	1.27576	−	0.926897i
$299$	1.27891			0.0739612
$300$		0			0
$301$	3.16377			0.182357
$302$	−26.2323	+	19.0589i	−1.50950	+	1.09672i
$303$		0			0
$304$	15.8343	−	48.7330i	0.908160	−	2.79503i
$305$	−0.130352	−	0.252015i	−0.00746392	−	0.0144304i
$306$		0			0
$307$	−21.4194			−1.22247			−0.611235	−	0.791450i	$-0.709327\pi$
$307$	−21.4194			−1.22247			−0.611235	+	0.791450i	$0.709327\pi$
$308$	2.46179	+	7.57662i	0.140274	+	0.431718i
$309$		0			0
$310$	−23.1213	+	23.4053i	−1.31320	+	1.32933i
$311$	−2.30731	+	1.67636i	−0.130836	+	0.0950578i	−0.651278	−	0.758839i	$-0.725767\pi$
$311$	−2.30731	+	1.67636i	−0.130836	+	0.0950578i	0.520443	+	0.853897i	$0.325767\pi$
$312$		0			0
$313$	−11.6802	−	8.48616i	−0.660204	−	0.479666i	0.206528	−	0.978441i	$-0.433784\pi$
$313$	−11.6802	−	8.48616i	−0.660204	−	0.479666i	−0.866732	+	0.498774i	$0.833784\pi$
$314$	42.9054	−	31.1726i	2.42129	−	1.75917i
$315$		0			0
$316$	20.4823	+	14.8812i	1.15222	+	0.837135i
$317$	−6.98695	−	21.5036i	−0.392426	−	1.20776i	−0.930948	−	0.365152i	$-0.881017\pi$
$317$	−6.98695	−	21.5036i	−0.392426	−	1.20776i	0.538522	−	0.842611i	$-0.318983\pi$
$318$		0			0
$319$	8.18397	+	25.1877i	0.458214	+	1.41024i
$320$	−24.9098	−	48.1594i	−1.39250	−	2.69219i
$321$		0			0
$322$	−0.892743	+	2.74758i	−0.0497506	+	0.153117i
$323$	−5.16312	+	3.75123i	−0.287284	+	0.208724i
$324$		0			0
$325$	1.68362	+	2.25880i	0.0933904	+	0.125295i
$326$	−32.1859			−1.78261
$327$		0			0
$328$	4.09288	−	12.5966i	0.225991	−	0.695530i
$329$	0.644327	−	1.98303i	0.0355229	−	0.109328i
$330$		0			0
$331$	1.19480	+	3.67721i	0.0656720	+	0.202118i	0.978508	−	0.206209i	$-0.0661125\pi$
$331$	1.19480	+	3.67721i	0.0656720	+	0.202118i	−0.912836	+	0.408326i	$0.866113\pi$
$332$	−62.2448			−3.41613
$333$		0			0
$334$	13.1233	+	9.53466i	0.718077	+	0.521713i
$335$	6.16610	−	1.01523i	0.336890	−	0.0554680i
$336$		0			0
$337$	−14.1459	−	10.2776i	−0.770576	−	0.559856i	0.131560	−	0.991308i	$-0.458001\pi$
$337$	−14.1459	−	10.2776i	−0.770576	−	0.559856i	−0.902136	+	0.431452i	$0.858001\pi$
$338$	−27.7683	−	20.1749i	−1.51040	−	1.09737i
$339$		0			0
$340$	−3.05551	+	20.0844i	−0.165708	+	1.08923i
$341$	−13.9930	−	10.1665i	−0.757763	−	0.550547i
$342$		0			0
$343$	−6.48010			−0.349893
$344$	−18.7032	−	57.5626i	−1.00841	−	3.10357i
$345$		0			0
$346$	14.4886	−	44.5913i	0.778912	−	2.39724i
$347$	7.13647	−	21.9638i	0.383106	−	1.17908i	−0.554739	−	0.832024i	$-0.687182\pi$
$347$	7.13647	−	21.9638i	0.383106	−	1.17908i	0.937845	−	0.347055i	$-0.112818\pi$
$348$		0			0
$349$	−9.32650			−0.499236			−0.249618	−	0.968344i	$-0.580305\pi$
$349$	−9.32650			−0.499236			−0.249618	+	0.968344i	$0.580305\pi$
$350$	−6.02800	+	2.04030i	−0.322210	+	0.109058i
$351$		0			0
$352$	49.1203	−	35.6880i	2.61812	−	1.90218i
$353$	−9.87219	+	30.3835i	−0.525444	+	1.61715i	0.237993	+	0.971267i	$0.423510\pi$
$353$	−9.87219	+	30.3835i	−0.525444	+	1.61715i	−0.763437	+	0.645883i	$0.776490\pi$
$354$		0			0
$355$	−32.0674	−	16.0934i	−1.70196	−	0.854148i
$356$	10.2018	+	31.3980i	0.540697	+	1.66409i
$357$		0			0
$358$	8.84525	+	27.2229i	0.467486	+	1.43877i
$359$	−7.75810	−	5.63659i	−0.409457	−	0.297488i	0.363925	−	0.931428i	$-0.381436\pi$
$359$	−7.75810	−	5.63659i	−0.409457	−	0.297488i	−0.773382	+	0.633940i	$0.781436\pi$
$360$		0			0
$361$	4.05451	−	2.94577i	0.213395	−	0.155041i
$362$	26.2298	+	19.0571i	1.37861	+	1.00162i
$363$		0			0
$364$	−1.14143	+	0.829296i	−0.0598271	+	0.0434669i
$365$	10.0559	+	19.4416i	0.526351	+	1.01762i
$366$		0			0
$367$	0.328866	+	1.01215i	0.0171667	+	0.0528336i	0.959273	−	0.282481i	$-0.0911574\pi$
$367$	0.328866	+	1.01215i	0.0171667	+	0.0528336i	−0.942106	+	0.335315i	$0.891157\pi$
$368$	31.0973			1.62106
$369$		0			0
$370$	0.929160	−	6.10752i	0.0483047	−	0.317515i
$371$	1.02480	−	3.15402i	0.0532051	−	0.163748i
$372$		0			0
$373$	3.33333	−	2.42181i	0.172593	−	0.125396i	−0.498135	−	0.867099i	$-0.665982\pi$
$373$	3.33333	−	2.42181i	0.172593	−	0.125396i	0.670728	+	0.741703i	$0.265982\pi$
$374$	−14.6922			−0.759714
$375$		0			0
$376$	−39.8890			−2.05712
$377$	−3.79456	+	2.75691i	−0.195430	+	0.141988i
$378$		0			0
$379$	3.20027	−	9.84942i	0.164387	−	0.505931i	−0.834604	−	0.550851i	$-0.814303\pi$
$379$	3.20027	−	9.84942i	0.164387	−	0.505931i	0.998991	+	0.0449201i	$0.0143033\pi$
$380$	−6.69724	+	44.0220i	−0.343561	+	2.25828i
$381$		0			0
$382$	49.4336			2.52924
$383$	−0.370619	−	1.14065i	−0.0189378	−	0.0582845i	0.941141	−	0.338014i	$-0.109755\pi$
$383$	−0.370619	−	1.14065i	−0.0189378	−	0.0582845i	−0.960079	+	0.279730i	$0.909755\pi$
$384$		0			0
$385$	−1.53707	−	2.97169i	−0.0783363	−	0.151451i
$386$	55.1890	−	40.0971i	2.80904	−	2.04089i
$387$		0			0
$388$	−36.4177	−	26.4590i	−1.84883	−	1.34325i
$389$	10.1971	−	7.40861i	0.517012	−	0.375631i	−0.298465	−	0.954421i	$-0.596475\pi$
$389$	10.1971	−	7.40861i	0.517012	−	0.375631i	0.815477	+	0.578789i	$0.196475\pi$
$390$		0			0
$391$	−3.13341	−	2.27656i	−0.158464	−	0.115130i
$392$	18.8467	+	58.0042i	0.951902	+	2.92965i
$393$		0			0
$394$	10.1129	+	31.1243i	0.509481	+	1.56802i
$395$	−9.50290	−	4.76914i	−0.478143	−	0.239961i
$396$		0			0
$397$	−0.405848	+	1.24907i	−0.0203689	+	0.0626891i	−0.960724	−	0.277505i	$-0.910493\pi$
$397$	−0.405848	+	1.24907i	−0.0203689	+	0.0626891i	0.940355	+	0.340194i	$0.110493\pi$
$398$	−1.19204	+	0.866064i	−0.0597513	+	0.0434119i
$399$		0			0
$400$	40.9380	+	54.9237i	2.04690	+	2.74618i
$401$	−16.1042			−0.804205			−0.402102	−	0.915595i	$-0.631720\pi$
$401$	−16.1042			−0.804205			−0.402102	+	0.915595i	$0.631720\pi$
$402$		0			0
$403$	0.946580	−	2.91327i	0.0471525	−	0.145120i
$404$	9.59762	−	29.5384i	0.477499	−	1.46959i
$405$		0			0
$406$	−3.27409	−	10.0766i	−0.162490	−	0.500094i
$407$	3.24782			0.160988
$408$		0			0
$409$	−17.1188	−	12.4375i	−0.846471	−	0.614997i	0.0776999	−	0.996977i	$-0.475242\pi$
$409$	−17.1188	−	12.4375i	−0.846471	−	0.614997i	−0.924171	+	0.381980i	$0.875242\pi$
$410$	−1.33991	+	8.80745i	−0.0661735	+	0.434969i
$411$		0			0
$412$	60.6473	+	44.0629i	2.98788	+	2.17082i
$413$	−4.89748	−	3.55823i	−0.240989	−	0.175089i
$414$		0			0
$415$	25.7935	−	4.24682i	1.26615	−	0.208468i
$416$	8.69927	+	6.32039i	0.426517	+	0.309883i
$417$		0			0
$418$	−32.2031			−1.57511
$419$	2.06144	+	6.34445i	0.100708	+	0.309946i	0.988699	−	0.149914i	$-0.0478996\pi$
$419$	2.06144	+	6.34445i	0.100708	+	0.309946i	−0.887991	+	0.459860i	$0.847900\pi$
$420$		0			0
$421$	8.43555	−	25.9620i	0.411124	−	1.26531i	−0.504549	−	0.863383i	$-0.668341\pi$
$421$	8.43555	−	25.9620i	0.411124	−	1.26531i	0.915673	−	0.401925i	$-0.131659\pi$
$422$	2.61102	−	8.03590i	0.127103	−	0.391181i
$423$		0			0
$424$	−63.4435			−3.08109
$425$	−0.104145	−	8.53118i	−0.00505177	−	0.413823i
$426$		0			0
$427$	−0.0482780	+	0.0350760i	−0.00233633	+	0.00169745i
$428$	14.1697	−	43.6098i	0.684918	−	2.10796i
$429$		0			0
$430$	18.7032	+	36.1598i	0.901949	+	1.74378i
$431$	−3.80011	−	11.6955i	−0.183045	−	0.563354i	0.816864	−	0.576830i	$-0.195710\pi$
$431$	−3.80011	−	11.6955i	−0.183045	−	0.563354i	−0.999909	+	0.0134755i	$0.995710\pi$
$432$		0			0
$433$	−10.4587	−	32.1887i	−0.502614	−	1.54689i	−0.804744	−	0.593622i	$-0.797698\pi$
$433$	−10.4587	−	32.1887i	−0.502614	−	1.54689i	0.302130	−	0.953267i	$-0.402302\pi$
$434$	5.59805	+	4.06722i	0.268715	+	0.195233i
$435$		0			0
$436$	−71.8819	+	52.2253i	−3.44252	+	2.50114i
$437$	−6.86799	−	4.98989i	−0.328541	−	0.238699i
$438$		0			0
$439$	16.9614	−	12.3231i	0.809521	−	0.588152i	−0.104171	−	0.994559i	$-0.533219\pi$
$439$	16.9614	−	12.3231i	0.809521	−	0.588152i	0.913692	+	0.406408i	$0.133219\pi$
$440$	−44.9812	+	45.5336i	−2.14439	+	2.17073i
$441$		0			0
$442$	−0.804064	−	2.47465i	−0.0382454	−	0.117707i
$443$	−6.04847			−0.287371			−0.143686	−	0.989623i	$-0.545895\pi$
$443$	−6.04847			−0.287371			−0.143686	+	0.989623i	$0.545895\pi$
$444$		0			0
$445$	−6.36973	−	12.3149i	−0.301954	−	0.583782i
$446$	−0.283614	+	0.872875i	−0.0134295	+	0.0413318i
$447$		0			0
$448$	−9.22577	+	6.70292i	−0.435877	+	0.316683i
$449$	−15.5896			−0.735721			−0.367860	−	0.929881i	$-0.619910\pi$
$449$	−15.5896			−0.735721			−0.367860	+	0.929881i	$0.619910\pi$
$450$		0			0
$451$	−4.68357			−0.220541
$452$	50.7248	−	36.8537i	2.38589	−	1.73345i
$453$		0			0
$454$	−1.49572	+	4.60334i	−0.0701974	+	0.216046i
$455$	0.416412	−	0.421527i	0.0195217	−	0.0197615i
$456$		0			0
$457$	−2.50193			−0.117035			−0.0585176	−	0.998286i	$-0.518637\pi$
$457$	−2.50193			−0.117035			−0.0585176	+	0.998286i	$0.518637\pi$
$458$	23.4027	+	72.0262i	1.09354	+	3.36556i
$459$		0			0
$460$	−26.6647	+	4.39026i	−1.24325	+	0.204697i
$461$	−0.124559	+	0.0904973i	−0.00580128	+	0.00421488i	−0.590682	−	0.806904i	$-0.701141\pi$
$461$	−0.124559	+	0.0904973i	−0.00580128	+	0.00421488i	0.584881	+	0.811119i	$0.301141\pi$
$462$		0			0
$463$	9.41102	+	6.83751i	0.437367	+	0.317766i	0.784588	−	0.620018i	$-0.212875\pi$
$463$	9.41102	+	6.83751i	0.437367	+	0.317766i	−0.347221	+	0.937783i	$0.612875\pi$
$464$	−92.2664	+	67.0355i	−4.28336	+	3.11204i
$465$		0			0
$466$	14.8316	+	10.7758i	0.687062	+	0.499180i
$467$	−0.145329	−	0.447276i	−0.00672502	−	0.0206975i	0.947638	−	0.319347i	$-0.103464\pi$
$467$	−0.145329	−	0.447276i	−0.00672502	−	0.0206975i	−0.954363	+	0.298650i	$0.903464\pi$
$468$		0			0
$469$	−0.406149	−	1.25000i	−0.0187542	−	0.0577196i
$470$	26.4738	−	4.35884i	1.22115	−	0.201058i
$471$		0			0
$472$	−35.7871	+	110.141i	−1.64723	+	5.06966i
$473$	−17.3150	+	12.5801i	−0.796143	+	0.578432i
$474$		0			0
$475$	−0.228271	−	18.6991i	−0.0104738	−	0.857974i
$476$	4.27279			0.195843
$477$		0			0
$478$	−5.42210	+	16.6875i	−0.248001	+	0.763269i
$479$	−3.83534	+	11.8040i	−0.175241	+	0.539337i	−0.999644	−	0.0266660i	$-0.991511\pi$
$479$	−3.83534	+	11.8040i	−0.175241	+	0.539337i	0.824403	+	0.566003i	$0.191511\pi$
$480$		0			0
$481$	0.177744	+	0.547041i	0.00810444	+	0.0249429i
$482$	20.1585			0.918196
$483$		0			0
$484$	3.78286	+	2.74841i	0.171948	+	0.124928i
$485$	16.8963	+	8.47958i	0.767220	+	0.385038i
$486$		0			0
$487$	−27.9633	−	20.3165i	−1.26714	−	0.920631i	−0.268055	−	0.963404i	$-0.586381\pi$
$487$	−27.9633	−	20.3165i	−1.26714	−	0.920631i	−0.999085	+	0.0427731i	$0.986381\pi$
$488$	0.923588	+	0.671026i	0.0418088	+	0.0303759i
$489$		0			0
$490$	−18.8467	−	36.4372i	−0.851407	−	1.64607i
$491$	−20.1168	−	14.6157i	−0.907859	−	0.659598i	0.0326134	−	0.999468i	$-0.489617\pi$
$491$	−20.1168	−	14.6157i	−0.907859	−	0.659598i	−0.940473	+	0.339870i	$0.889617\pi$
$492$		0			0
$493$	14.2044			0.639736
$494$	−1.76239	−	5.42408i	−0.0792938	−	0.244041i
$495$		0			0
$496$	23.0165	−	70.8375i	1.03347	−	3.18070i
$497$	−2.33190	+	7.17684i	−0.104600	+	0.321925i
$498$		0			0
$499$	12.6037			0.564220			0.282110	−	0.959382i	$-0.408966\pi$
$499$	12.6037			0.564220			0.282110	+	0.959382i	$0.408966\pi$
$500$	−42.8567	−	41.3153i	−1.91661	−	1.84768i
$501$		0			0
$502$	10.0764	−	7.32094i	0.449732	−	0.326750i
$503$	−9.26827	+	28.5248i	−0.413252	+	1.27186i	0.500554	+	0.865705i	$0.333130\pi$
$503$	−9.26827	+	28.5248i	−0.413252	+	1.27186i	−0.913805	+	0.406152i	$0.866870\pi$
$504$		0			0
$505$	−1.96179	+	12.8952i	−0.0872986	+	0.573828i
$506$	−6.03929	−	18.5870i	−0.268479	−	0.826294i
$507$		0			0
$508$	2.92675	+	9.00761i	0.129854	+	0.399648i
$509$	−0.377802	−	0.274489i	−0.0167458	−	0.0121665i	0.579381	−	0.815057i	$-0.303294\pi$
$509$	−0.377802	−	0.274489i	−0.0167458	−	0.0121665i	−0.596127	+	0.802890i	$0.703294\pi$
$510$		0			0
$511$	3.72438	−	2.70592i	0.164757	−	0.119703i
$512$	12.0833	+	8.77902i	0.534011	+	0.387982i
$513$		0			0
$514$	12.6878	−	9.21822i	0.559634	−	0.406598i
$515$	−28.1378	−	14.1213i	−1.23990	−	0.622257i
$516$		0			0
$517$	4.35878	+	13.4150i	0.191699	+	0.589989i
$518$	−1.29933			−0.0570891
$519$		0			0
$520$	−10.1311	−	5.08440i	−0.444277	−	0.222966i
$521$	5.34039	−	16.4360i	0.233967	−	0.720076i	−0.763290	−	0.646056i	$-0.776417\pi$
$521$	5.34039	−	16.4360i	0.233967	−	0.720076i	0.997257	−	0.0740200i	$-0.0235829\pi$
$522$		0			0
$523$	−32.8849	+	23.8922i	−1.43795	+	1.04473i	−0.449489	+	0.893286i	$0.648394\pi$
$523$	−32.8849	+	23.8922i	−1.43795	+	1.04473i	−0.988465	+	0.151449i	$0.951606\pi$
$524$	31.5130			1.37665
$525$		0			0
$526$	38.6980			1.68731
$527$	−7.50503	+	5.45273i	−0.326924	+	0.237525i
$528$		0			0
$529$	−5.51533	+	16.9744i	−0.239797	+	0.738019i
$530$	42.1067	−	6.93275i	1.82900	−	0.301139i
$531$		0			0
$532$	9.36533			0.406039
$533$	−0.256319	−	0.788869i	−0.0111024	−	0.0341697i
$534$		0			0
$535$	−2.89634	+	19.0381i	−0.125220	+	0.823090i
$536$	−20.3418	+	14.7792i	−0.878633	+	0.638364i
$537$		0			0
$538$	42.0831	+	30.5751i	1.81433	+	1.31819i
$539$	17.4478	−	12.6766i	0.751530	−	0.546019i
$540$		0			0
$541$	1.60265	+	1.16440i	0.0689035	+	0.0500613i	0.621704	−	0.783252i	$-0.286441\pi$
$541$	1.60265	+	1.16440i	0.0689035	+	0.0500613i	−0.552800	+	0.833314i	$0.686441\pi$
$542$	19.4386	+	59.8259i	0.834960	+	2.56974i
$543$		0			0
$544$	−10.0630	−	30.9707i	−0.431448	−	1.32786i
$545$	26.2237	−	26.5458i	1.12330	−	1.13710i
$546$		0			0
$547$	10.8324	−	33.3386i	0.463158	−	1.42545i	−0.398126	−	0.917331i	$-0.630339\pi$
$547$	10.8324	−	33.3386i	0.463158	−	1.42545i	0.861284	−	0.508124i	$-0.169661\pi$
$548$	−22.0378	+	16.0114i	−0.941407	+	0.683972i
$549$		0			0
$550$	24.8778	−	35.1354i	1.06079	−	1.49818i
$551$	31.1341			1.32636
$552$		0			0
$553$	−0.691038	+	2.12680i	−0.0293859	+	0.0904405i
$554$	−18.3077	+	56.3453i	−0.777819	+	2.39388i
$555$		0			0
$556$	−13.5545	−	41.7165i	−0.574839	−	1.76917i
$557$	−19.2383			−0.815154			−0.407577	−	0.913171i	$-0.633626\pi$
$557$	−19.2383			−0.815154			−0.407577	+	0.913171i	$0.633626\pi$
$558$		0			0
$559$	−3.06651	−	2.22795i	−0.129699	−	0.0942321i
$560$	10.1253	−	10.2496i	0.427870	−	0.433125i
$561$		0			0
$562$	−59.3655	−	43.1316i	−2.50418	−	1.81940i
$563$	−23.6023	−	17.1481i	−0.994720	−	0.722707i	−0.0337705	−	0.999430i	$-0.510752\pi$
$563$	−23.6023	−	17.1481i	−0.994720	−	0.722707i	−0.960950	+	0.276723i	$0.910752\pi$
$564$		0			0
$565$	−18.5053	+	18.7325i	−0.778522	+	0.788084i
$566$	35.7049	+	25.9411i	1.50079	+	1.09039i
$567$		0			0
$568$	144.363			6.05734
$569$	10.1701	+	31.3004i	0.426354	+	1.31218i	0.901692	+	0.432380i	$0.142326\pi$
$569$	10.1701	+	31.3004i	0.426354	+	1.31218i	−0.475338	+	0.879803i	$0.657674\pi$
$570$		0			0
$571$	8.23065	−	25.3313i	0.344442	−	1.06008i	−0.617440	−	0.786618i	$-0.711830\pi$
$571$	8.23065	−	25.3313i	0.344442	−	1.06008i	0.961882	−	0.273465i	$-0.0881698\pi$
$572$	2.94939	−	9.07730i	0.123320	−	0.379541i
$573$		0			0
$574$	1.87371			0.0782073
$575$	10.7500	−	3.63854i	0.448304	−	0.151737i
$576$		0			0
$577$	−27.9237	+	20.2878i	−1.16248	+	0.844591i	−0.990089	−	0.140438i	$-0.955149\pi$
$577$	−27.9237	+	20.2878i	−1.16248	+	0.844591i	−0.172390	+	0.985029i	$0.555149\pi$
$578$	11.7822	−	36.2620i	0.490076	−	1.50830i
$579$		0			0
$580$	69.6508	−	70.5063i	2.89209	−	2.92761i
$581$	−1.69897	−	5.22888i	−0.0704850	−	0.216931i
$582$		0			0
$583$	6.93265	+	21.3365i	0.287121	+	0.883668i
$584$	−71.2496	−	51.7659i	−2.94833	−	2.14209i
$585$		0			0
$586$	−11.9635	+	8.69202i	−0.494209	+	0.359064i
$587$	−18.0213	−	13.0932i	−0.743817	−	0.540414i	0.150087	−	0.988673i	$-0.452045\pi$
$587$	−18.0213	−	13.0932i	−0.743817	−	0.540414i	−0.893904	+	0.448258i	$0.852045\pi$
$588$		0			0
$589$	−16.4500	+	11.9516i	−0.677809	+	0.492457i
$590$	11.7158	−	77.0101i	0.482333	−	3.17045i
$591$		0			0
$592$	4.32193	+	13.3015i	0.177630	+	0.546690i
$593$	30.9158			1.26956			0.634779	−	0.772693i	$-0.281091\pi$
$593$	30.9158			1.26956			0.634779	+	0.772693i	$0.281091\pi$
$594$		0			0
$595$	−1.77059	+	0.291522i	−0.0725870	+	0.0119513i
$596$	16.5496	−	50.9344i	0.677898	−	2.08636i
$597$		0			0
$598$	2.80016	−	2.03444i	0.114507	−	0.0831943i
$599$	24.0276			0.981742			0.490871	−	0.871232i	$-0.336679\pi$
$599$	24.0276			0.981742			0.490871	+	0.871232i	$0.336679\pi$
$600$		0			0
$601$	−32.0387			−1.30688			−0.653442	−	0.756977i	$-0.726676\pi$
$601$	−32.0387			−1.30688			−0.653442	+	0.756977i	$0.726676\pi$
$602$	6.92705	−	5.03280i	0.282326	−	0.205121i
$603$		0			0
$604$	−19.7127	+	60.6694i	−0.802097	+	2.46860i
$605$	−1.75508	−	0.880809i	−0.0713543	−	0.0358100i
$606$		0			0
$607$	45.5915			1.85050			0.925251	−	0.379356i	$-0.123855\pi$
$607$	45.5915			1.85050			0.925251	+	0.379356i	$0.123855\pi$
$608$	−22.0567	−	67.8834i	−0.894516	−	2.75304i
$609$		0			0
$610$	−0.686300	−	0.344427i	−0.0277875	−	0.0139455i
$611$	−2.02098	+	1.46833i	−0.0817602	+	0.0594023i
$612$		0			0
$613$	8.78299	+	6.38121i	0.354742	+	0.257735i	0.750855	−	0.660467i	$-0.229641\pi$
$613$	8.78299	+	6.38121i	0.354742	+	0.257735i	−0.396114	+	0.918201i	$0.629641\pi$
$614$	−46.8976	+	34.0731i	−1.89263	+	1.37508i
$615$		0			0
$616$	10.8907	+	7.91254i	0.438798	+	0.318805i
$617$	4.97685	+	15.3172i	0.200360	+	0.616646i	0.999872	+	0.0159954i	$0.00509171\pi$
$617$	4.97685	+	15.3172i	0.200360	+	0.616646i	−0.799512	+	0.600651i	$0.794908\pi$
$618$		0			0
$619$	11.8533	+	36.4807i	0.476425	+	1.46628i	0.844026	+	0.536302i	$0.180179\pi$
$619$	11.8533	+	36.4807i	0.476425	+	1.46628i	−0.367602	+	0.929983i	$0.619821\pi$
$620$	−9.73501	+	63.9898i	−0.390967	+	2.56989i
$621$		0			0
$622$	−2.38516	+	7.34076i	−0.0956362	+	0.294338i
$623$	−2.35914	+	1.71401i	−0.0945168	+	0.0686705i
$624$		0			0
$625$	20.5781	+	14.1965i	0.823125	+	0.567861i
$626$	−39.0732			−1.56168
$627$		0			0
$628$	32.2419	−	99.2305i	1.28659	−	3.95973i
$629$	0.538290	−	1.65669i	0.0214630	−	0.0660564i
$630$		0			0
$631$	7.02370	+	21.6167i	0.279609	+	0.860548i	0.987963	+	0.154690i	$0.0494380\pi$
$631$	7.02370	+	21.6167i	0.279609	+	0.860548i	−0.708354	+	0.705857i	$0.750562\pi$
$632$	42.7808			1.70173
$633$		0			0
$634$	−49.5049	−	35.9674i	−1.96609	−	1.42845i
$635$	−1.82738	−	3.53295i	−0.0725172	−	0.140201i
$636$		0			0
$637$	3.09003	+	2.24504i	0.122431	+	0.0889517i
$638$	57.9863	+	42.1295i	2.29570	+	1.66792i
$639$		0			0
$640$	−54.8699	−	27.5371i	−2.16892	−	1.08850i
$641$	21.8378	+	15.8661i	0.862541	+	0.626673i	0.928575	−	0.371145i	$-0.121035\pi$
$641$	21.8378	+	15.8661i	0.862541	+	0.626673i	−0.0660340	+	0.997817i	$0.521035\pi$
$642$		0			0
$643$	−25.9062			−1.02164			−0.510821	−	0.859687i	$-0.670659\pi$
$643$	−25.9062			−1.02164			−0.510821	+	0.859687i	$0.670659\pi$
$644$	1.75635	+	5.40549i	0.0692099	+	0.213006i
$645$		0			0
$646$	−5.33731	+	16.4266i	−0.209994	+	0.646295i
$647$	6.69401	−	20.6021i	0.263169	−	0.809950i	−0.728941	−	0.684577i	$-0.759987\pi$
$647$	6.69401	−	20.6021i	0.263169	−	0.809950i	0.992110	−	0.125374i	$-0.0400129\pi$
$648$		0			0
$649$	40.9519			1.60750
$650$	7.27947	+	2.26739i	0.285524	+	0.0889342i
$651$		0			0
$652$	−51.2280	+	37.2193i	−2.00624	+	1.45762i
$653$	−3.45405	+	10.6305i	−0.135167	+	0.416002i	−0.995616	−	0.0935349i	$-0.970183\pi$
$653$	−3.45405	+	10.6305i	−0.135167	+	0.416002i	0.860449	+	0.509537i	$0.170183\pi$
$654$		0			0
$655$	−13.0586	+	2.15006i	−0.510241	+	0.0840097i
$656$	−6.23252	−	19.1817i	−0.243339	−	0.748920i
$657$		0			0
$658$	−1.74378	−	5.36681i	−0.0679797	−	0.209220i
$659$	10.9010	+	7.92006i	0.424644	+	0.308522i	0.779503	−	0.626398i	$-0.215471\pi$
$659$	10.9010	+	7.92006i	0.424644	+	0.308522i	−0.354860	+	0.934919i	$0.615471\pi$
$660$		0			0
$661$	18.8195	−	13.6732i	0.731993	−	0.531824i	−0.158200	−	0.987407i	$-0.550569\pi$
$661$	18.8195	−	13.6732i	0.731993	−	0.531824i	0.890193	+	0.455583i	$0.150569\pi$
$662$	8.46556	+	6.15059i	0.329023	+	0.239049i
$663$		0			0
$664$	−85.0921	+	61.8230i	−3.30221	+	2.39920i
$665$	−3.88088	+	0.638975i	−0.150494	+	0.0247784i
$666$		0			0
$667$	5.83880	+	17.9700i	0.226079	+	0.695801i
$668$	31.9132			1.23476
$669$		0			0
$670$	11.8856	−	12.0316i	0.459182	−	0.464822i
$671$	0.124748	−	0.383934i	0.00481584	−	0.0148216i
$672$		0			0
$673$	−15.2412	+	11.0734i	−0.587507	+	0.426849i	−0.841423	−	0.540378i	$-0.818281\pi$
$673$	−15.2412	+	11.0734i	−0.587507	+	0.426849i	0.253916	+	0.967226i	$0.418281\pi$
$674$	−47.3215			−1.82276
$675$		0			0
$676$	−67.5268			−2.59719
$677$	−34.1761	+	24.8304i	−1.31350	+	0.954310i	−0.313507	+	0.949586i	$0.601504\pi$
$677$	−34.1761	+	24.8304i	−1.31350	+	0.954310i	−0.999989	+	0.00472433i	$0.998496\pi$
$678$		0			0
$679$	1.22867	−	3.78147i	0.0471521	−	0.145119i
$680$	15.7712	+	30.4912i	0.604798	+	1.16929i
$681$		0			0
$682$	−46.8100			−1.79245
$683$	−15.1264	−	46.5544i	−0.578797	−	1.78135i	−0.622870	−	0.782325i	$-0.714034\pi$
$683$	−15.1264	−	46.5544i	−0.578797	−	1.78135i	0.0440734	−	0.999028i	$-0.485966\pi$
$684$		0			0
$685$	8.03975	−	8.13850i	0.307183	−	0.310956i
$686$	−14.1881	+	10.3083i	−0.541705	+	0.393572i
$687$		0			0
$688$	−74.5635	−	54.1735i	−2.84271	−	2.06535i
$689$	−3.21438	+	2.33538i	−0.122458	+	0.0889710i
$690$		0			0
$691$	11.4813	+	8.34168i	0.436771	+	0.317332i	0.784350	−	0.620318i	$-0.212996\pi$
$691$	11.4813	+	8.34168i	0.436771	+	0.317332i	−0.347580	+	0.937650i	$0.612996\pi$
$692$	−28.5043	−	87.7273i	−1.08357	−	3.33489i
$693$		0			0
$694$	−19.3139	−	59.4420i	−0.733145	−	2.25639i
$695$	8.46303	+	16.3620i	0.321021	+	0.620645i
$696$		0			0
$697$	−0.776250	+	2.38905i	−0.0294026	+	0.0904918i
$698$	−20.4203	+	14.8362i	−0.772920	+	0.561559i
$699$		0			0
$700$	−7.23498	+	10.2181i	−0.273456	+	0.386208i
$701$	9.00786			0.340222			0.170111	−	0.985425i	$-0.445587\pi$
$701$	9.00786			0.340222			0.170111	+	0.985425i	$0.445587\pi$
$702$		0			0
$703$	1.17985	−	3.63122i	0.0444990	−	0.136954i
$704$	23.8389	−	73.3687i	0.898464	−	2.76519i
$705$		0			0
$706$	26.7177	+	82.2287i	1.00553	+	3.09472i
$707$	2.74334			0.103174
$708$		0			0
$709$	−40.2076	−	29.2126i	−1.51003	−	1.09710i	−0.966164	−	0.257928i	$-0.916960\pi$
$709$	−40.2076	−	29.2126i	−1.51003	−	1.09710i	−0.543865	−	0.839173i	$-0.683040\pi$
$710$	−95.8120	+	15.7752i	−3.59576	+	0.592032i
$711$		0			0
$712$	45.1318	+	32.7901i	1.69138	+	1.22886i
$713$	−9.98321	−	7.25323i	−0.373874	−	0.271636i
$714$		0			0
$715$	−0.602868	+	3.96275i	−0.0225460	+	0.148198i
$716$	45.5585	+	33.1002i	1.70260	+	1.23701i
$717$		0			0
$718$	−25.9528			−0.968549
$719$	0.660387	+	2.03246i	0.0246283	+	0.0757981i	0.962615	−	0.270872i	$-0.0873122\pi$
$719$	0.660387	+	2.03246i	0.0246283	+	0.0757981i	−0.937987	+	0.346671i	$0.887312\pi$
$720$		0			0
$721$	−2.04614	+	6.29738i	−0.0762023	+	0.234527i
$722$	4.19130	−	12.8995i	0.155984	−	0.480070i
$723$		0			0
$724$	63.7855			2.37057
$725$	−24.0519	+	33.9690i	−0.893266	+	1.26158i
$726$		0			0
$727$	33.5446	−	24.3716i	1.24410	−	0.903891i	0.246235	−	0.969210i	$-0.420807\pi$
$727$	33.5446	−	24.3716i	1.24410	−	0.903891i	0.997864	+	0.0653195i	$0.0208067\pi$
$728$	−0.736718	+	2.26739i	−0.0273046	+	0.0840349i
$729$		0			0
$730$	52.9442	+	26.5706i	1.95955	+	0.983424i
$731$	3.54723	+	10.9172i	0.131199	+	0.403789i
$732$		0			0
$733$	10.0496	+	30.9293i	0.371189	+	1.14240i	0.946014	+	0.324125i	$0.105070\pi$
$733$	10.0496	+	30.9293i	0.371189	+	1.14240i	−0.574826	+	0.818276i	$0.694930\pi$
$734$	2.33013	+	1.69294i	0.0860067	+	0.0624875i
$735$		0			0
$736$	35.0446	−	25.4614i	1.29176	−	0.938518i
$737$	7.19317	+	5.22614i	0.264964	+	0.192507i
$738$		0			0
$739$	28.5724	−	20.7591i	1.05105	−	0.763635i	0.0786411	−	0.996903i	$-0.474942\pi$
$739$	28.5724	−	20.7591i	1.05105	−	0.763635i	0.972413	+	0.233268i	$0.0749419\pi$
$740$	−5.58378	−	10.7954i	−0.205264	−	0.396846i
$741$		0			0
$742$	−2.77349	−	8.53592i	−0.101818	−	0.313363i
$743$	36.0897			1.32400			0.662001	−	0.749503i	$-0.269708\pi$
$743$	36.0897			1.32400			0.662001	+	0.749503i	$0.269708\pi$
$744$		0			0
$745$	−3.38281	+	22.2357i	−0.123936	+	0.814654i
$746$	3.44579	−	10.6051i	0.126159	−	0.388279i
$747$		0			0
$748$	−23.3845	+	16.9898i	−0.855022	+	0.621210i
$749$	4.05021			0.147991
$750$		0			0
$751$	−4.62810			−0.168882			−0.0844409	−	0.996428i	$-0.526910\pi$
$751$	−4.62810			−0.168882			−0.0844409	+	0.996428i	$0.526910\pi$
$752$	−49.1411	+	35.7031i	−1.79199	+	1.30196i
$753$		0			0
$754$	−3.92258	+	12.0725i	−0.142852	+	0.439653i
$755$	4.02935	−	26.4856i	0.146643	−	0.963908i
$756$		0			0
$757$	14.6243			0.531530			0.265765	−	0.964038i	$-0.414375\pi$
$757$	14.6243			0.531530			0.265765	+	0.964038i	$0.414375\pi$
$758$	−8.66109	−	26.6561i	−0.314585	−	0.968193i
$759$		0			0
$760$	34.5682	+	66.8324i	1.25392	+	2.42427i
$761$	9.86133	−	7.16467i	0.357473	−	0.259719i	−0.394524	−	0.918885i	$-0.629091\pi$
$761$	9.86133	−	7.16467i	0.357473	−	0.259719i	0.751997	+	0.659166i	$0.229091\pi$
$762$		0			0
$763$	−6.34920	−	4.61296i	−0.229856	−	0.167000i
$764$	78.6799	−	57.1643i	2.84654	−	2.06813i
$765$		0			0
$766$	−2.62597	−	1.90788i	−0.0948801	−	0.0689344i
$767$	2.24119	+	6.89767i	0.0809246	+	0.249060i
$768$		0			0
$769$	4.26323	+	13.1209i	0.153736	+	0.473150i	0.998031	−	0.0627287i	$-0.0199803\pi$
$769$	4.26323	+	13.1209i	0.153736	+	0.473150i	−0.844295	+	0.535879i	$0.819980\pi$
$770$	−8.09265	−	4.06139i	−0.291639	−	0.146362i
$771$		0			0
$772$	41.4726	−	127.640i	1.49263	−	4.59385i
$773$	18.3274	−	13.3156i	0.659190	−	0.478929i	−0.207199	−	0.978299i	$-0.566435\pi$
$773$	18.3274	−	13.3156i	0.659190	−	0.478929i	0.866389	+	0.499369i	$0.166435\pi$
$774$		0			0
$775$	−0.331811	−	27.1808i	−0.0119190	−	0.976362i
$776$	−76.0647			−2.73056
$777$		0			0
$778$	10.5411	−	32.4422i	0.377917	−	1.16311i
$779$	−1.70143	+	5.23646i	−0.0609600	+	0.187616i
$780$		0			0
$781$	−15.7750	−	48.5504i	−0.564473	−	1.73727i
$782$	−10.4820			−0.374837
$783$		0			0
$784$	75.1355	+	54.5891i	2.68341	+	1.94961i
$785$	−6.59038	+	43.3196i	−0.235221	+	1.54614i
$786$		0			0
$787$	38.5785	+	28.0289i	1.37518	+	0.999123i	0.997313	+	0.0732618i	$0.0233409\pi$
$787$	38.5785	+	28.0289i	1.37518	+	0.999123i	0.377863	+	0.925862i	$0.376659\pi$
$788$	52.0878	+	37.8440i	1.85555	+	1.34814i
$789$		0			0
$790$	−28.3931	+	4.67484i	−1.01018	+	0.166323i
$791$	4.48043	+	3.25522i	0.159306	+	0.115742i
$792$		0			0
$793$	0.0714945			0.00253884
$794$	1.09837	+	3.38044i	0.0389797	+	0.119967i
$795$		0			0
$796$	−0.895774	+	2.75691i	−0.0317499	+	0.0977160i
$797$	−8.40931	+	25.8812i	−0.297873	+	0.916759i	0.684368	+	0.729137i	$0.260078\pi$
$797$	−8.40931	+	25.8812i	−0.297873	+	0.916759i	−0.982241	+	0.187622i	$0.939922\pi$
$798$		0			0
$799$	7.56529			0.267641
$800$	91.1040	+	28.3768i	3.22101	+	1.00327i
$801$		0			0
$802$	−35.2600	+	25.6179i	−1.24507	+	0.904599i
$803$	−9.62360	+	29.6184i	−0.339610	+	1.04521i
$804$		0			0
$805$	−1.09661	−	2.12013i	−0.0386505	−	0.0747249i
$806$	−2.56179	−	7.88437i	−0.0902351	−	0.277715i
$807$		0			0
$808$	−16.2178	−	49.9132i	−0.570540	−	1.75594i
$809$	−15.8693	−	11.5297i	−0.557933	−	0.405362i	0.272769	−	0.962080i	$-0.412061\pi$
$809$	−15.8693	−	11.5297i	−0.557933	−	0.405362i	−0.830702	+	0.556717i	$0.812061\pi$
$810$		0			0
$811$	−17.0468	+	12.3852i	−0.598594	+	0.434904i	−0.845380	−	0.534166i	$-0.820626\pi$
$811$	−17.0468	+	12.3852i	−0.598594	+	0.434904i	0.246786	+	0.969070i	$0.420626\pi$
$812$	−16.8636	−	12.2521i	−0.591796	−	0.429965i
$813$		0			0
$814$	7.11107	−	5.16650i	0.249243	−	0.181086i
$815$	18.6888	−	18.9184i	0.654641	−	0.662682i
$816$		0			0
$817$	7.77501	+	23.9290i	0.272013	+	0.837170i
$818$	−57.2667			−2.00228
$819$		0			0
$820$	8.05218	+	15.5677i	0.281194	+	0.543646i
$821$	−12.8039	+	39.4062i	−0.446858	+	1.37529i	0.433575	+	0.901117i	$0.357252\pi$
$821$	−12.8039	+	39.4062i	−0.446858	+	1.37529i	−0.880433	+	0.474170i	$0.842748\pi$
$822$		0			0
$823$	−4.88721	+	3.55077i	−0.170358	+	0.123772i	−0.669697	−	0.742634i	$-0.733576\pi$
$823$	−4.88721	+	3.55077i	−0.170358	+	0.123772i	0.499340	+	0.866406i	$0.333576\pi$
$824$	126.673			4.41285
$825$		0			0
$826$	−16.3833			−0.570047
$827$	−2.42188	+	1.75960i	−0.0842172	+	0.0611874i	−0.629097	−	0.777327i	$-0.716575\pi$
$827$	−2.42188	+	1.75960i	−0.0842172	+	0.0611874i	0.544880	+	0.838514i	$0.316575\pi$
$828$		0			0
$829$	8.29802	−	25.5387i	0.288202	−	0.886995i	−0.697218	−	0.716859i	$-0.745579\pi$
$829$	8.29802	−	25.5387i	0.288202	−	0.886995i	0.985421	−	0.170136i	$-0.0544208\pi$
$830$	49.7189	−	50.3296i	1.72577	−	1.74697i
$831$		0			0
$832$	13.6624			0.473658
$833$	−3.57444	−	11.0010i	−0.123847	−	0.381162i
$834$		0			0
$835$	−13.2244	+	2.17737i	−0.457651	+	0.0753509i
$836$	−51.2555	+	37.2393i	−1.77271	+	1.28795i
$837$		0			0
$838$	14.6060	+	10.6119i	0.504555	+	0.366581i
$839$	10.0800	−	7.32352i	0.347999	−	0.252836i	−0.400030	−	0.916502i	$-0.631000\pi$
$839$	10.0800	−	7.32352i	0.347999	−	0.252836i	0.748029	+	0.663666i	$0.231000\pi$
$840$		0			0
$841$	−32.5998	−	23.6851i	−1.12413	−	0.816729i
$842$	−22.8297	−	70.2624i	−0.786762	−	2.42140i
$843$		0			0
$844$	−5.13683	−	15.8095i	−0.176817	−	0.544186i
$845$	27.9823	−	4.60720i	0.962619	−	0.158492i
$846$		0			0
$847$	−0.127627	+	0.392797i	−0.00438533	+	0.0134967i
$848$	−78.1590	+	56.7859i	−2.68399	+	1.95003i
$849$		0			0
$850$	−13.7991	−	18.5133i	−0.473304	−	0.635000i
$851$	2.31714			0.0794304
$852$		0			0
$853$	−1.76058	+	5.41851i	−0.0602811	+	0.185526i	−0.976662	−	0.214780i	$-0.931096\pi$
$853$	−1.76058	+	5.41851i	−0.0602811	+	0.185526i	0.916381	+	0.400307i	$0.131096\pi$
$854$	−0.0499068	+	0.153597i	−0.00170778	+	0.00525599i
$855$		0			0
$856$	−23.9436	−	73.6907i	−0.818374	−	2.51870i
$857$	7.41982			0.253456			0.126728	−	0.991937i	$-0.459552\pi$
$857$	7.41982			0.253456			0.126728	+	0.991937i	$0.459552\pi$
$858$		0			0
$859$	4.59726	+	3.34011i	0.156857	+	0.113963i	0.663445	−	0.748225i	$-0.269094\pi$
$859$	4.59726	+	3.34011i	0.156857	+	0.113963i	−0.506588	+	0.862188i	$0.669094\pi$
$860$	71.5833	+	35.9249i	2.44097	+	1.22503i
$861$		0			0
$862$	−26.9251	−	19.5622i	−0.917073	−	0.666293i
$863$	−27.9715	−	20.3225i	−0.952160	−	0.691785i	−0.000843465	−	1.00000i	$-0.500268\pi$
$863$	−27.9715	−	20.3225i	−0.952160	−	0.691785i	−0.951317	+	0.308215i	$0.900268\pi$
$864$		0			0
$865$	17.7973	+	34.4083i	0.605125	+	1.16992i
$866$	−74.1037	−	53.8395i	−2.51815	−	1.82954i
$867$		0			0
$868$	13.6133			0.462066
$869$	−4.67478	−	14.3875i	−0.158581	−	0.488062i
$870$		0			0
$871$	−0.486594	+	1.49758i	−0.0164876	+	0.0507437i
$872$	−46.3952	+	142.790i	−1.57114	+	4.83547i
$873$		0			0
$874$	−22.9751			−0.777145
$875$	2.30093	−	4.72788i	0.0777855	−	0.159831i
$876$		0			0
$877$	4.28790	−	3.11534i	0.144792	−	0.105197i	−0.513031	−	0.858370i	$-0.671477\pi$
$877$	4.28790	−	3.11534i	0.144792	−	0.105197i	0.657823	+	0.753173i	$0.271477\pi$
$878$	17.5336	−	53.9629i	0.591730	−	1.82116i
$879$		0			0
$880$	−14.6590	+	96.3560i	−0.494155	+	3.24816i
$881$	−2.35251	−	7.24028i	−0.0792580	−	0.243931i	0.903575	−	0.428431i	$-0.140933\pi$
$881$	−2.35251	−	7.24028i	−0.0792580	−	0.243931i	−0.982833	+	0.184500i	$0.940933\pi$
$882$		0			0
$883$	−16.3264	−	50.2476i	−0.549428	−	1.69096i	−0.710223	−	0.703977i	$-0.751406\pi$
$883$	−16.3264	−	50.2476i	−0.549428	−	1.69096i	0.160795	−	0.986988i	$-0.448594\pi$
$884$	−4.14143	−	3.00892i	−0.139291	−	0.101201i
$885$		0			0
$886$	−13.2431	+	9.62166i	−0.444910	+	0.323246i
$887$	6.23572	+	4.53052i	0.209375	+	0.152120i	0.687531	−	0.726155i	$-0.258695\pi$
$887$	6.23572	+	4.53052i	0.209375	+	0.152120i	−0.478156	+	0.878275i	$0.658695\pi$
$888$		0			0
$889$	−0.676800	+	0.491724i	−0.0226991	+	0.0164919i
$890$	−33.5365	−	16.8307i	−1.12415	−	0.564166i
$891$		0			0
$892$	0.557972	+	1.71726i	0.0186823	+	0.0574981i
$893$	16.5820			0.554896
$894$		0			0
$895$	−21.1372	−	10.6080i	−0.706540	−	0.354585i
$896$	−3.99006	+	12.2801i	−0.133299	+	0.410251i
$897$		0			0
$898$	−34.1334	+	24.7994i	−1.13905	+	0.827566i
$899$	45.2560			1.50937
$900$		0			0
$901$	12.0326			0.400864
$902$	−10.2546	+	7.45043i	−0.341442	+	0.248072i
$903$		0			0
$904$	32.7396	−	100.762i	1.08890	−	3.35130i
$905$	−26.4319	+	4.35194i	−0.878626	+	0.144663i
$906$		0			0
$907$	−11.3735			−0.377650			−0.188825	−	0.982011i	$-0.560468\pi$
$907$	−11.3735			−0.377650			−0.188825	+	0.982011i	$0.560468\pi$
$908$	2.94262	+	9.05644i	0.0976542	+	0.300549i
$909$		0			0
$910$	0.241184	−	1.58534i	0.00799517	−	0.0525536i
$911$	−15.0393	+	10.9267i	−0.498275	+	0.362018i	−0.808358	−	0.588691i	$-0.799643\pi$
$911$	−15.0393	+	10.9267i	−0.498275	+	0.362018i	0.310082	+	0.950710i	$0.399643\pi$
$912$		0			0
$913$	30.0898	+	21.8615i	0.995827	+	0.723511i
$914$	−5.47795	+	3.97997i	−0.181195	+	0.131646i
$915$		0			0
$916$	120.539	+	87.5764i	3.98271	+	2.89361i
$917$	0.860143	+	2.64725i	0.0284044	+	0.0874199i
$918$		0			0
$919$	2.36336	+	7.27367i	0.0779600	+	0.239936i	0.982440	−	0.186581i	$-0.0597405\pi$
$919$	2.36336	+	7.27367i	0.0779600	+	0.239936i	−0.904480	+	0.426517i	$0.859741\pi$
$920$	−32.0915	+	32.4857i	−1.05803	+	1.07102i
$921$		0			0
$922$	−0.128761	+	0.396286i	−0.00424052	+	0.0130510i
$923$	7.31418	−	5.31407i	0.240749	−	0.174915i
$924$		0			0
$925$	3.05039	+	4.09250i	0.100296	+	0.134561i
$926$	31.4822			1.03457
$927$		0			0
$928$	−49.0918	+	151.089i	−1.61152	+	4.95974i
$929$	9.56366	−	29.4339i	0.313774	−	0.965696i	−0.662483	−	0.749077i	$-0.730497\pi$
$929$	9.56366	−	29.4339i	0.313774	−	0.965696i	0.976256	−	0.216619i	$-0.0695028\pi$
$930$		0			0
$931$	−7.83466	−	24.1126i	−0.256770	−	0.790258i
$932$	36.0675			1.18143
$933$		0			0
$934$	−1.02971	−	0.748125i	−0.0336930	−	0.0244794i
$935$	8.53106	−	8.63584i	0.278996	−	0.282422i
$936$		0			0
$937$	−25.3784	−	18.4385i	−0.829077	−	0.602360i	0.0902212	−	0.995922i	$-0.471243\pi$
$937$	−25.3784	−	18.4385i	−0.829077	−	0.602360i	−0.919298	+	0.393562i	$0.871243\pi$
$938$	−2.87771	−	2.09078i	−0.0939605	−	0.0682663i
$939$		0			0
$940$	37.0960	−	37.5517i	1.20994	−	1.22480i
$941$	−2.92710	−	2.12666i	−0.0954208	−	0.0693273i	0.539052	−	0.842273i	$-0.318783\pi$
$941$	−2.92710	−	2.12666i	−0.0954208	−	0.0693273i	−0.634473	+	0.772945i	$0.718783\pi$
$942$		0			0
$943$	−3.34146			−0.108813
$944$	54.4955	+	167.720i	1.77368	+	5.45882i
$945$		0			0
$946$	−17.8992	+	55.0879i	−0.581952	+	1.79106i
$947$	3.49856	−	10.7675i	0.113688	−	0.349896i	−0.877983	−	0.478692i	$-0.841111\pi$
$947$	3.49856	−	10.7675i	0.113688	−	0.349896i	0.991671	+	0.128796i	$0.0411112\pi$
$948$		0			0
$949$	−5.51540			−0.179038
$950$	−30.2456	−	40.5784i	−0.981296	−	1.31654i
$951$		0			0
$952$	5.84113	−	4.24383i	0.189312	−	0.137543i
$953$	5.32071	−	16.3755i	0.172355	−	0.530453i	−0.827148	−	0.561984i	$-0.810038\pi$
$953$	5.32071	−	16.3755i	0.172355	−	0.530453i	0.999503	+	0.0315307i	$0.0100382\pi$
$954$		0			0
$955$	−28.7038	+	29.0563i	−0.928832	+	0.940240i
$956$	10.6672	+	32.8304i	0.345003	+	1.06181i
$957$		0			0
$958$	10.3798	+	31.9458i	0.335357	+	1.03212i
$959$	−1.94656	−	1.41426i	−0.0628576	−	0.0456687i
$960$		0			0
$961$	1.16811	−	0.848680i	0.0376809	−	0.0273768i
$962$	1.25938	+	0.914994i	0.0406041	+	0.0295006i
$963$		0			0
$964$	32.0849	−	23.3110i	1.03339	−	0.750798i
$965$	−8.47717	+	55.7218i	−0.272890	+	1.79375i
$966$		0			0
$967$	−9.24157	−	28.4426i	−0.297189	−	0.914653i	−0.982477	−	0.186382i	$-0.940324\pi$
$967$	−9.24157	−	28.4426i	−0.297189	−	0.914653i	0.685289	−	0.728272i	$-0.259676\pi$
$968$	7.90115			0.253953
$969$		0			0
$970$	50.4832	−	8.31192i	1.62092	−	0.266880i
$971$	7.78497	−	23.9597i	0.249832	−	0.768902i	−0.744973	−	0.667095i	$-0.767537\pi$
$971$	7.78497	−	23.9597i	0.249832	−	0.768902i	0.994804	−	0.101807i	$-0.0324625\pi$
$972$		0			0
$973$	3.13443	−	2.27729i	0.100485	−	0.0730067i
$974$	−93.5443			−2.99735
$975$		0			0
$976$	1.73842			0.0556455
$977$	46.1907	−	33.5595i	1.47777	−	1.07366i	0.499504	−	0.866311i	$-0.333515\pi$
$977$	46.1907	−	33.5595i	1.47777	−	1.07366i	0.978266	−	0.207352i	$-0.0664845\pi$
$978$		0			0
$979$	6.09589	−	18.7612i	0.194826	−	0.599611i
$980$	−72.1325	−	36.2005i	−2.30419	−	1.15638i
$981$		0			0
$982$	−67.2957			−2.14749
$983$	8.16325	+	25.1239i	0.260367	+	0.801328i	0.992725	+	0.120407i	$0.0384201\pi$
$983$	8.16325	+	25.1239i	0.260367	+	0.801328i	−0.732357	+	0.680921i	$0.761580\pi$
$984$		0			0
$985$	−24.1665	−	12.1282i	−0.770010	−	0.386438i
$986$	31.1005	−	22.5958i	0.990442	−	0.719598i
$987$		0			0
$988$	−9.07741	−	6.59513i	−0.288791	−	0.209819i
$989$	−12.3533	+	8.97517i	−0.392811	+	0.285394i
$990$		0			0
$991$	18.2252	+	13.2414i	0.578943	+	0.420626i	0.838343	−	0.545144i	$-0.183525\pi$
$991$	18.2252	+	13.2414i	0.578943	+	0.420626i	−0.259400	+	0.965770i	$0.583525\pi$
$992$	−32.0612	−	98.6744i	−1.01795	−	3.13291i
$993$		0			0
$994$	6.31096	+	19.4231i	0.200171	+	0.616064i
$995$	0.183100	−	1.20354i	0.00580465	−	0.0381549i
$996$		0			0
$997$	−7.44865	+	22.9246i	−0.235901	+	0.726029i	0.761099	+	0.648635i	$0.224660\pi$
$997$	−7.44865	+	22.9246i	−0.235901	+	0.726029i	−0.997001	+	0.0773940i	$0.975340\pi$
$998$	27.5958	−	20.0495i	0.873529	−	0.634656i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.h.c.136.2		8
3.2	odd	2		75.2.g.b.61.1	yes	8
15.2	even	4		375.2.i.b.199.1		16
15.8	even	4		375.2.i.b.199.4		16
15.14	odd	2		375.2.g.b.301.2		8
25.4	even	10		5625.2.a.n.1.4		4
25.16	even	5	inner	225.2.h.c.91.2		8
25.21	even	5		5625.2.a.i.1.1		4
75.29	odd	10		1875.2.a.e.1.1		4
75.38	even	20		375.2.i.b.49.1		16
75.41	odd	10		75.2.g.b.16.1	✓	8
75.47	even	20		1875.2.b.c.1249.8		8
75.53	even	20		1875.2.b.c.1249.1		8
75.59	odd	10		375.2.g.b.76.2		8
75.62	even	20		375.2.i.b.49.4		16
75.71	odd	10		1875.2.a.h.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.b.16.1	✓	8	75.41	odd	10
75.2.g.b.61.1	yes	8	3.2	odd	2
225.2.h.c.91.2		8	25.16	even	5	inner
225.2.h.c.136.2		8	1.1	even	1	trivial
375.2.g.b.76.2		8	75.59	odd	10
375.2.g.b.301.2		8	15.14	odd	2
375.2.i.b.49.1		16	75.38	even	20
375.2.i.b.49.4		16	75.62	even	20
375.2.i.b.199.1		16	15.2	even	4
375.2.i.b.199.4		16	15.8	even	4
1875.2.a.e.1.1		4	75.29	odd	10
1875.2.a.h.1.4		4	75.71	odd	10
1875.2.b.c.1249.1		8	75.53	even	20
1875.2.b.c.1249.8		8	75.47	even	20
5625.2.a.i.1.1		4	25.21	even	5
5625.2.a.n.1.4		4	25.4	even	10

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.18949 - 1.59076i) q^{2} +(1.64533 - 5.06380i) q^{4} +(-0.336312 + 2.21063i) q^{5} +0.470294 q^{7} +(-2.78023 - 8.55667i) q^{8} +O(q^{10})\)	\(q+(2.18949 - 1.59076i) q^{2} +(1.64533 - 5.06380i) q^{4} +(-0.336312 + 2.21063i) q^{5} +0.470294 q^{7} +(-2.78023 - 8.55667i) q^{8} +(2.78023 + 5.37515i) q^{10} +(-2.57387 + 1.87003i) q^{11} +(-0.455836 - 0.331184i) q^{13} +(1.02971 - 0.748125i) q^{14} +(-11.0839 - 8.05289i) q^{16} +(0.527295 + 1.62285i) q^{17} +(1.15575 + 3.55705i) q^{19} +(10.6409 + 5.34023i) q^{20} +(-2.66071 + 8.18882i) q^{22} +(-1.83631 + 1.33416i) q^{23} +(-4.77379 - 1.48692i) q^{25} -1.52488 q^{26} +(0.773789 - 2.38148i) q^{28} +(2.57238 - 7.91697i) q^{29} +(1.67999 + 5.17047i) q^{31} -19.0842 q^{32} +(3.73607 + 2.71441i) q^{34} +(-0.158166 + 1.03965i) q^{35} +(-0.825886 - 0.600041i) q^{37} +(8.18892 + 5.94960i) q^{38} +(19.8507 - 3.26836i) q^{40} +(1.19098 + 0.865300i) q^{41} +6.72721 q^{43} +(5.23458 + 16.1104i) q^{44} +(-1.89827 + 5.84226i) q^{46} +(1.37005 - 4.21658i) q^{47} -6.77882 q^{49} +(-12.8175 + 4.33834i) q^{50} +(-2.42705 + 1.76336i) q^{52} +(2.17907 - 6.70648i) q^{53} +(-3.26832 - 6.31879i) q^{55} +(-1.30753 - 4.02415i) q^{56} +(-6.96179 - 21.4262i) q^{58} +(-10.4136 - 7.56596i) q^{59} +(-0.102655 + 0.0745831i) q^{61} +(11.9033 + 8.64825i) q^{62} +(-19.6170 + 14.2526i) q^{64} +(0.885429 - 0.896304i) q^{65} +(-0.863607 - 2.65791i) q^{67} +9.08535 q^{68} +(1.30753 + 2.52790i) q^{70} +(-4.95838 + 15.2603i) q^{71} +(7.91925 - 5.75367i) q^{73} -2.76279 q^{74} +19.9138 q^{76} +(-1.21048 + 0.879462i) q^{77} +(-1.46937 + 4.52227i) q^{79} +(21.5296 - 21.7940i) q^{80} +3.98413 q^{82} +(-3.61256 - 11.1183i) q^{83} +(-3.76485 + 0.619872i) q^{85} +(14.7292 - 10.7014i) q^{86} +(23.1572 + 16.8247i) q^{88} +(-5.01630 + 3.64456i) q^{89} +(-0.214377 - 0.155754i) q^{91} +(3.73458 + 11.4938i) q^{92} +(-3.70785 - 11.4116i) q^{94} +(-8.25202 + 1.35867i) q^{95} +(2.61256 - 8.04064i) q^{97} +(-14.8422 + 10.7835i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + q^{4} + 5 q^{5} + 4 q^{7}+O(q^{10}) \) 8 * q + q^2 + q^4 + 5 * q^5 + 4 * q^7	\( 8 q + q^{2} + q^{4} + 5 q^{5} + 4 q^{7} - 16 q^{11} - 8 q^{13} + 8 q^{14} - 17 q^{16} + q^{17} - 5 q^{19} + 10 q^{20} + 13 q^{22} - 7 q^{23} - 15 q^{25} - 6 q^{26} - 17 q^{28} - 5 q^{29} - 19 q^{31} - 24 q^{32} + 12 q^{34} + 10 q^{35} - q^{37} + 10 q^{38} + 25 q^{40} + 14 q^{41} + 32 q^{43} + 3 q^{44} + 16 q^{46} + q^{47} + 16 q^{49} - 10 q^{50} - 6 q^{52} + 3 q^{53} + 15 q^{55} + 15 q^{56} + 5 q^{58} - 30 q^{59} - 14 q^{61} + 17 q^{62} - 44 q^{64} - 25 q^{65} + 4 q^{67} + 22 q^{68} - 15 q^{70} - 21 q^{71} + 2 q^{73} + 38 q^{74} + 80 q^{76} + 37 q^{77} - 30 q^{79} + 50 q^{80} - 12 q^{82} - 2 q^{83} - 30 q^{85} + 34 q^{86} + 70 q^{88} + 21 q^{91} - 9 q^{92} - 33 q^{94} - 65 q^{95} - 6 q^{97} - 73 q^{98}+O(q^{100}) \) 8 * q + q^2 + q^4 + 5 * q^5 + 4 * q^7 - 16 * q^11 - 8 * q^13 + 8 * q^14 - 17 * q^16 + q^17 - 5 * q^19 + 10 * q^20 + 13 * q^22 - 7 * q^23 - 15 * q^25 - 6 * q^26 - 17 * q^28 - 5 * q^29 - 19 * q^31 - 24 * q^32 + 12 * q^34 + 10 * q^35 - q^37 + 10 * q^38 + 25 * q^40 + 14 * q^41 + 32 * q^43 + 3 * q^44 + 16 * q^46 + q^47 + 16 * q^49 - 10 * q^50 - 6 * q^52 + 3 * q^53 + 15 * q^55 + 15 * q^56 + 5 * q^58 - 30 * q^59 - 14 * q^61 + 17 * q^62 - 44 * q^64 - 25 * q^65 + 4 * q^67 + 22 * q^68 - 15 * q^70 - 21 * q^71 + 2 * q^73 + 38 * q^74 + 80 * q^76 + 37 * q^77 - 30 * q^79 + 50 * q^80 - 12 * q^82 - 2 * q^83 - 30 * q^85 + 34 * q^86 + 70 * q^88 + 21 * q^91 - 9 * q^92 - 33 * q^94 - 65 * q^95 - 6 * q^97 - 73 * q^98

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