LMFDB - Embedded newform 495.2.n.b.91.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [495,2,Mod(91,495)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(495, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("495.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	495.n (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:	$3.95259490005$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.819390625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 10x^{6} - 13x^{5} + 29x^{4} - 7x^{3} + 80x^{2} + 143x + 121 $ x^8 - 3x^7 + 10x^6 - 13x^5 + 29x^4 - 7x^3 + 80x^2 + 143*x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.1
Root			$0.766388 - 2.35870i$ of defining polynomial
Character	$\chi$	$=$	495.91
Dual form			495.2.n.b.136.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00643 + 1.45776i) q^{2} +(1.28267 - 3.94765i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-1.35808 + 4.17973i) q^{7} +(1.64835 + 5.07311i) q^{8} +O(q^{10})$	\(q+(-2.00643 + 1.45776i) q^{2} +(1.28267 - 3.94765i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-1.35808 + 4.17973i) q^{7} +(1.64835 + 5.07311i) q^{8} +2.48008 q^{10} +(3.08183 - 1.22568i) q^{11} +(1.72964 - 1.25666i) q^{13} +(-3.36814 - 10.3661i) q^{14} +(-3.98651 - 2.89637i) q^{16} +(3.20384 + 2.32773i) q^{17} +(-0.664637 - 2.04554i) q^{19} +(-3.35808 + 2.43978i) q^{20} +(-4.39673 + 6.95181i) q^{22} -5.16367 q^{23} +(0.309017 + 0.951057i) q^{25} +(-1.63850 + 5.04278i) q^{26} +(14.7581 + 10.7224i) q^{28} +(-2.45340 + 7.55078i) q^{29} +(-5.00888 + 3.63917i) q^{31} +1.55248 q^{32} -9.82154 q^{34} +(3.55549 - 2.58321i) q^{35} +(-2.64835 + 8.15079i) q^{37} +(4.31545 + 3.13535i) q^{38} +(1.64835 - 5.07311i) q^{40} +(2.35808 + 7.25741i) q^{41} -2.22321 q^{43} +(-0.885601 - 13.7382i) q^{44} +(10.3605 - 7.52737i) q^{46} +(-2.12692 - 6.54598i) q^{47} +(-9.96262 - 7.23827i) q^{49} +(-2.00643 - 1.45776i) q^{50} +(-2.74229 - 8.43989i) q^{52} +(-4.60852 + 3.34828i) q^{53} +(-3.21369 - 0.819857i) q^{55} -23.4428 q^{56} +(-6.08463 - 18.7266i) q^{58} +(-1.16861 + 3.59661i) q^{59} +(-3.91111 - 2.84159i) q^{61} +(4.74495 - 14.6035i) q^{62} +(4.85808 - 3.52960i) q^{64} -2.13795 q^{65} +9.57025 q^{67} +(13.2985 - 9.66195i) q^{68} +(-3.36814 + 10.3661i) q^{70} +(-1.70727 - 1.24040i) q^{71} +(-4.52728 + 13.9335i) q^{73} +(-6.56814 - 20.2146i) q^{74} -8.92760 q^{76} +(0.937663 + 14.5458i) q^{77} +(-2.63829 + 1.91683i) q^{79} +(1.52271 + 4.68643i) q^{80} +(-15.3108 - 11.1240i) q^{82} +(8.62692 + 6.26782i) q^{83} +(-1.22376 - 3.76634i) q^{85} +(4.46071 - 3.24090i) q^{86} +(11.2980 + 13.6141i) q^{88} +7.64375 q^{89} +(2.90350 + 8.93605i) q^{91} +(-6.62328 + 20.3844i) q^{92} +(13.8100 + 10.0335i) q^{94} +(-0.664637 + 2.04554i) q^{95} +(4.58771 - 3.33317i) q^{97} +30.5409 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 2 q^{4} - 2 q^{5} + 9 q^{7} + 19 q^{8}+O(q^{10}) $ 8 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 + 9 * q^7 + 19 * q^8	$ 8 q - 2 q^{2} - 2 q^{4} - 2 q^{5} + 9 q^{7} + 19 q^{8} - 2 q^{10} + 3 q^{11} + 10 q^{13} - 24 q^{14} + 4 q^{16} + 2 q^{17} - 2 q^{19} - 7 q^{20} - 7 q^{22} + 2 q^{23} - 2 q^{25} - 14 q^{26} + 13 q^{28} - 14 q^{29} - 5 q^{31} + 16 q^{32} - 70 q^{34} - q^{35} - 27 q^{37} + 16 q^{38} + 19 q^{40} - q^{41} - 28 q^{43} - 47 q^{44} + 42 q^{46} + 27 q^{47} - 15 q^{49} - 2 q^{50} + 22 q^{52} + q^{53} - 7 q^{55} + 24 q^{56} + 18 q^{58} - 13 q^{59} - 3 q^{61} - 15 q^{62} + 19 q^{64} - 30 q^{65} + 10 q^{67} + 33 q^{68} - 24 q^{70} - 9 q^{71} + 5 q^{73} + 17 q^{74} - 46 q^{76} - q^{77} - 10 q^{79} - 11 q^{80} - 33 q^{82} + 25 q^{83} - 8 q^{85} - 20 q^{86} + 29 q^{88} - 4 q^{89} - 43 q^{91} + 22 q^{92} + 57 q^{94} - 2 q^{95} + 13 q^{97} + 2 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 + 9 * q^7 + 19 * q^8 - 2 * q^10 + 3 * q^11 + 10 * q^13 - 24 * q^14 + 4 * q^16 + 2 * q^17 - 2 * q^19 - 7 * q^20 - 7 * q^22 + 2 * q^23 - 2 * q^25 - 14 * q^26 + 13 * q^28 - 14 * q^29 - 5 * q^31 + 16 * q^32 - 70 * q^34 - q^35 - 27 * q^37 + 16 * q^38 + 19 * q^40 - q^41 - 28 * q^43 - 47 * q^44 + 42 * q^46 + 27 * q^47 - 15 * q^49 - 2 * q^50 + 22 * q^52 + q^53 - 7 * q^55 + 24 * q^56 + 18 * q^58 - 13 * q^59 - 3 * q^61 - 15 * q^62 + 19 * q^64 - 30 * q^65 + 10 * q^67 + 33 * q^68 - 24 * q^70 - 9 * q^71 + 5 * q^73 + 17 * q^74 - 46 * q^76 - q^77 - 10 * q^79 - 11 * q^80 - 33 * q^82 + 25 * q^83 - 8 * q^85 - 20 * q^86 + 29 * q^88 - 4 * q^89 - 43 * q^91 + 22 * q^92 + 57 * q^94 - 2 * q^95 + 13 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

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 $

$2$	−2.00643	+	1.45776i	−1.41876	+	1.03079i	−0.426785	+	0.904353i	$0.640354\pi$
$2$	−2.00643	+	1.45776i	−1.41876	+	1.03079i	−0.991975	+	0.126436i	$0.959646\pi$
$3$		0			0
$3$		0			0
$4$	1.28267	−	3.94765i	0.641335	−	1.97383i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$6$		0			0
$7$	−1.35808	+	4.17973i	−0.513304	+	1.57979i	0.273042	+	0.962002i	$0.411970\pi$
$7$	−1.35808	+	4.17973i	−0.513304	+	1.57979i	−0.786346	+	0.617786i	$0.788030\pi$
$8$	1.64835	+	5.07311i	0.582781	+	1.79362i
$9$		0			0
$10$	2.48008			0.784271
$11$	3.08183	−	1.22568i	0.929208	−	0.369558i
$11$	3.08183	−	1.22568i	0.929208	−	0.369558i
$12$		0			0
$13$	1.72964	−	1.25666i	0.479716	−	0.348534i	−0.321500	−	0.946910i	$-0.604187\pi$
$13$	1.72964	−	1.25666i	0.479716	−	0.348534i	0.801216	+	0.598376i	$0.204187\pi$
$14$	−3.36814	−	10.3661i	−0.900173	−	2.77045i
$15$		0			0
$16$	−3.98651	−	2.89637i	−0.996628	−	0.724093i
$17$	3.20384	+	2.32773i	0.777046	+	0.564557i	0.904091	−	0.427340i	$-0.140549\pi$
$17$	3.20384	+	2.32773i	0.777046	+	0.564557i	−0.127045	+	0.991897i	$0.540549\pi$
$18$		0			0
$19$	−0.664637	−	2.04554i	−0.152478	−	0.469279i	0.845419	−	0.534104i	$-0.179351\pi$
$19$	−0.664637	−	2.04554i	−0.152478	−	0.469279i	−0.997897	+	0.0648250i	$0.979351\pi$
$20$	−3.35808	+	2.43978i	−0.750888	+	0.545552i
$21$		0			0
$22$	−4.39673	+	6.95181i	−0.937386	+	1.48213i
$23$	−5.16367			−1.07670			−0.538350	−	0.842722i	$-0.680952\pi$
$23$	−5.16367			−1.07670			−0.538350	+	0.842722i	$0.680952\pi$
$24$		0			0
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	−1.63850	+	5.04278i	−0.321336	+	0.988971i
$27$		0			0
$28$	14.7581	+	10.7224i	2.78903	+	2.02635i
$29$	−2.45340	+	7.55078i	−0.455584	+	1.40214i	0.414863	+	0.909884i	$0.363829\pi$
$29$	−2.45340	+	7.55078i	−0.455584	+	1.40214i	−0.870448	+	0.492261i	$0.836171\pi$
$30$		0			0
$31$	−5.00888	+	3.63917i	−0.899622	+	0.653614i	−0.938369	−	0.345635i	$-0.887663\pi$
$31$	−5.00888	+	3.63917i	−0.899622	+	0.653614i	0.0387467	+	0.999249i	$0.487663\pi$
$32$	1.55248			0.274443
$33$		0			0
$34$	−9.82154			−1.68438
$35$	3.55549	−	2.58321i	0.600987	−	0.436643i
$36$		0			0
$37$	−2.64835	+	8.15079i	−0.435387	+	1.33998i	0.457303	+	0.889311i	$0.348815\pi$
$37$	−2.64835	+	8.15079i	−0.435387	+	1.33998i	−0.892690	+	0.450672i	$0.851185\pi$
$38$	4.31545	+	3.13535i	0.700058	+	0.508622i
$39$		0			0
$40$	1.64835	−	5.07311i	0.260628	−	0.802129i
$41$	2.35808	+	7.25741i	0.368269	+	1.13342i	0.947908	+	0.318543i	$0.103194\pi$
$41$	2.35808	+	7.25741i	0.368269	+	1.13342i	−0.579639	+	0.814874i	$0.696806\pi$
$42$		0			0
$43$	−2.22321			−0.339036			−0.169518	−	0.985527i	$-0.554221\pi$
$43$	−2.22321			−0.339036			−0.169518	+	0.985527i	$0.554221\pi$
$44$	−0.885601	−	13.7382i	−0.133509	−	2.07111i
$45$		0			0
$46$	10.3605	−	7.52737i	1.52758	−	1.10985i
$47$	−2.12692	−	6.54598i	−0.310243	−	0.954830i	−0.977668	−	0.210153i	$-0.932604\pi$
$47$	−2.12692	−	6.54598i	−0.310243	−	0.954830i	0.667426	−	0.744677i	$-0.267396\pi$
$48$		0			0
$49$	−9.96262	−	7.23827i	−1.42323	−	1.03404i
$50$	−2.00643	−	1.45776i	−0.283752	−	0.206158i
$51$		0			0
$52$	−2.74229	−	8.43989i	−0.380287	−	1.17040i
$53$	−4.60852	+	3.34828i	−0.633029	+	0.459922i	−0.857448	−	0.514570i	$-0.827951\pi$
$53$	−4.60852	+	3.34828i	−0.633029	+	0.459922i	0.224419	+	0.974493i	$0.427951\pi$
$54$		0			0
$55$	−3.21369	−	0.819857i	−0.433335	−	0.110549i
$56$	−23.4428			−3.13268
$57$		0			0
$58$	−6.08463	−	18.7266i	−0.798951	−	2.45892i
$59$	−1.16861	+	3.59661i	−0.152140	+	0.468239i	−0.997860	−	0.0653882i	$-0.979171\pi$
$59$	−1.16861	+	3.59661i	−0.152140	+	0.468239i	0.845720	+	0.533627i	$0.179171\pi$
$60$		0			0
$61$	−3.91111	−	2.84159i	−0.500766	−	0.363828i	0.308544	−	0.951210i	$-0.400158\pi$
$61$	−3.91111	−	2.84159i	−0.500766	−	0.363828i	−0.809309	+	0.587382i	$0.800158\pi$
$62$	4.74495	−	14.6035i	0.602610	−	1.85464i
$63$		0			0
$64$	4.85808	−	3.52960i	0.607259	−	0.441200i
$65$	−2.13795			−0.265180
$66$		0			0
$67$	9.57025			1.16919			0.584596	−	0.811324i	$-0.301253\pi$
$67$	9.57025			1.16919			0.584596	+	0.811324i	$0.301253\pi$
$68$	13.2985	−	9.66195i	1.61268	−	1.17168i
$69$		0			0
$70$	−3.36814	+	10.3661i	−0.402570	+	1.23898i
$71$	−1.70727	−	1.24040i	−0.202615	−	0.147209i	0.481851	−	0.876253i	$-0.339965\pi$
$71$	−1.70727	−	1.24040i	−0.202615	−	0.147209i	−0.684466	+	0.729045i	$0.739965\pi$
$72$		0			0
$73$	−4.52728	+	13.9335i	−0.529879	+	1.63080i	0.224584	+	0.974455i	$0.427898\pi$
$73$	−4.52728	+	13.9335i	−0.529879	+	1.63080i	−0.754462	+	0.656344i	$0.772102\pi$
$74$	−6.56814	−	20.2146i	−0.763530	−	2.34990i
$75$		0			0
$76$	−8.92760			−1.02407
$77$	0.937663	+	14.5458i	0.106857	+	1.65765i
$78$		0			0
$79$	−2.63829	+	1.91683i	−0.296831	+	0.215660i	−0.726225	−	0.687457i	$-0.758727\pi$
$79$	−2.63829	+	1.91683i	−0.296831	+	0.215660i	0.429394	+	0.903117i	$0.358727\pi$
$80$	1.52271	+	4.68643i	0.170244	+	0.523958i
$81$		0			0
$82$	−15.3108	−	11.1240i	−1.69080	−	1.22844i
$83$	8.62692	+	6.26782i	0.946927	+	0.687983i	0.950078	−	0.312012i	$-0.101003\pi$
$83$	8.62692	+	6.26782i	0.946927	+	0.687983i	−0.00315081	+	0.999995i	$0.501003\pi$
$84$		0			0
$85$	−1.22376	−	3.76634i	−0.132735	−	0.408517i
$86$	4.46071	−	3.24090i	0.481011	−	0.349475i
$87$		0			0
$88$	11.2980	+	13.6141i	1.20437	+	1.45127i
$89$	7.64375			0.810236			0.405118	−	0.914264i	$-0.367230\pi$
$89$	7.64375			0.810236			0.405118	+	0.914264i	$0.367230\pi$
$90$		0			0
$91$	2.90350	+	8.93605i	0.304369	+	0.936753i
$92$	−6.62328	+	20.3844i	−0.690525	+	2.12522i
$93$		0			0
$94$	13.8100	+	10.0335i	1.42439	+	1.03488i
$95$	−0.664637	+	2.04554i	−0.0681903	+	0.209868i
$96$		0			0
$97$	4.58771	−	3.33317i	0.465812	−	0.338432i	−0.329995	−	0.943983i	$-0.607047\pi$
$97$	4.58771	−	3.33317i	0.465812	−	0.338432i	0.795807	+	0.605551i	$0.207047\pi$
$98$	30.5409			3.08510
$99$		0			0
$100$	4.15081			0.415081
$101$	−5.69035	+	4.13428i	−0.566211	+	0.411377i	−0.833727	−	0.552177i	$-0.813797\pi$
$101$	−5.69035	+	4.13428i	−0.566211	+	0.411377i	0.267516	+	0.963553i	$0.413797\pi$
$102$		0			0
$103$	0.192501	−	0.592456i	0.0189677	−	0.0583764i	−0.941125	−	0.338060i	$-0.890229\pi$
$103$	0.192501	−	0.592456i	0.0189677	−	0.0583764i	0.960092	+	0.279683i	$0.0902294\pi$
$104$	9.22621	+	6.70324i	0.904705	+	0.657306i
$105$		0			0
$106$	4.36568	−	13.4362i	0.424033	−	1.30504i
$107$	−5.52669	−	17.0094i	−0.534285	−	1.64436i	−0.745189	−	0.666853i	$-0.767641\pi$
$107$	−5.52669	−	17.0094i	−0.534285	−	1.64436i	0.210905	−	0.977507i	$-0.432359\pi$
$108$		0			0
$109$	13.1041			1.25515			0.627574	−	0.778557i	$-0.284048\pi$
$109$	13.1041			1.25515			0.627574	+	0.778557i	$0.284048\pi$
$110$	7.64320	−	3.03980i	0.728751	−	0.289833i
$111$		0			0
$112$	17.5200	−	12.7290i	1.65549	−	1.20278i
$113$	2.59190	+	7.97704i	0.243825	+	0.750417i	0.995827	+	0.0912562i	$0.0290882\pi$
$113$	2.59190	+	7.97704i	0.243825	+	0.750417i	−0.752002	+	0.659160i	$0.770912\pi$
$114$		0			0
$115$	4.17749	+	3.03513i	0.389553	+	0.283027i
$116$	26.6610	+	19.3703i	2.47541	+	1.79849i
$117$		0			0
$118$	−2.89825	−	8.91989i	−0.266805	−	0.821143i
$119$	−14.0803	+	10.2299i	−1.29074	+	0.937778i
$120$		0			0
$121$	7.99540	−	7.55471i	0.726854	−	0.686792i
$122$	11.9897			1.08550
$123$		0			0
$124$	7.94143	+	24.4412i	0.713161	+	2.19488i
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$		0			0
$127$	−8.88531	−	6.45555i	−0.788444	−	0.572838i	0.119058	−	0.992887i	$-0.462013\pi$
$127$	−8.88531	−	6.45555i	−0.788444	−	0.572838i	−0.907501	+	0.420050i	$0.862013\pi$
$128$	−5.56158	+	17.1168i	−0.491579	+	1.51292i
$129$		0			0
$130$	4.28965	−	3.11661i	0.376227	−	0.273345i
$131$	7.33115			0.640525			0.320263	−	0.947329i	$-0.396229\pi$
$131$	7.33115			0.640525			0.320263	+	0.947329i	$0.396229\pi$
$132$		0			0
$133$	9.45243			0.819629
$134$	−19.2020	+	13.9511i	−1.65880	+	1.20519i
$135$		0			0
$136$	−6.52775	+	20.0904i	−0.559750	+	1.72273i
$137$	−13.4923	−	9.80274i	−1.15273	−	0.837504i	−0.163885	−	0.986479i	$-0.552403\pi$
$137$	−13.4923	−	9.80274i	−1.15273	−	0.837504i	−0.988841	+	0.148975i	$0.952403\pi$
$138$		0			0
$139$	−3.41111	+	10.4983i	−0.289326	+	0.890455i	0.695742	+	0.718292i	$0.255076\pi$
$139$	−3.41111	+	10.4983i	−0.289326	+	0.890455i	−0.985068	+	0.172163i	$0.944924\pi$
$140$	−5.63711	−	17.3492i	−0.476423	−	1.46628i
$141$		0			0
$142$	5.23371			0.439203
$143$	3.79020	−	5.99280i	0.316952	−	0.501143i
$144$		0			0
$145$	6.42308	−	4.66664i	0.533408	−	0.387543i
$146$	−11.2280	−	34.5564i	−0.929239	−	2.85990i
$147$		0			0
$148$	28.7796	+	20.9096i	2.36566	+	1.71876i
$149$	3.73053	+	2.71039i	0.305617	+	0.222043i	0.730013	−	0.683433i	$-0.239514\pi$
$149$	3.73053	+	2.71039i	0.305617	+	0.222043i	−0.424397	+	0.905476i	$0.639514\pi$
$150$		0			0
$151$	−2.78398	−	8.56821i	−0.226557	−	0.697271i	−0.998130	−	0.0611297i	$-0.980530\pi$
$151$	−2.78398	−	8.56821i	−0.226557	−	0.697271i	0.771573	−	0.636141i	$-0.219470\pi$
$152$	9.28170	−	6.74355i	0.752845	−	0.546974i
$153$		0			0
$154$	−23.0856	−	27.8182i	−1.86029	−	2.24166i
$155$	6.19132			0.497299
$156$		0			0
$157$	0.923657	+	2.84273i	0.0737159	+	0.226874i	0.981125	−	0.193374i	$-0.0619430\pi$
$157$	0.923657	+	2.84273i	0.0737159	+	0.226874i	−0.907409	+	0.420248i	$0.861943\pi$
$158$	2.49927	−	7.69197i	0.198831	−	0.611940i
$159$		0			0
$160$	−1.25599	−	0.912527i	−0.0992944	−	0.0721416i
$161$	7.01265	−	21.5827i	0.552674	−	1.70096i
$162$		0			0
$163$	2.34268	−	1.70206i	0.183493	−	0.133315i	−0.492247	−	0.870456i	$-0.663824\pi$
$163$	2.34268	−	1.70206i	0.183493	−	0.133315i	0.675740	+	0.737140i	$0.263824\pi$
$164$	31.6744			2.47335
$165$		0			0
$166$	−26.4463			−2.05263
$167$	−3.07841	+	2.23659i	−0.238214	+	0.173073i	−0.700487	−	0.713665i	$-0.747034\pi$
$167$	−3.07841	+	2.23659i	−0.238214	+	0.173073i	0.462273	+	0.886738i	$0.347034\pi$
$168$		0			0
$169$	−2.60475	+	8.01661i	−0.200366	+	0.616662i
$170$	7.94579	+	5.77295i	0.609414	+	0.442765i
$171$		0			0
$172$	−2.85165	+	8.77647i	−0.217436	+	0.669199i
$173$	0.343909	+	1.05844i	0.0261469	+	0.0804720i	0.963278	−	0.268504i	$-0.0865294\pi$
$173$	0.343909	+	1.05844i	0.0261469	+	0.0804720i	−0.937132	+	0.348976i	$0.886529\pi$
$174$		0			0
$175$	−4.39482			−0.332217
$176$	−15.8358	−	4.03993i	−1.19367	−	0.304521i
$177$		0			0
$178$	−15.3366	+	11.1427i	−1.14953	+	0.835182i
$179$	1.48921	+	4.58331i	0.111309	+	0.342573i	0.991159	−	0.132678i	$-0.0423575\pi$
$179$	1.48921	+	4.58331i	0.111309	+	0.342573i	−0.879851	+	0.475250i	$0.842357\pi$
$180$		0			0
$181$	17.3633	+	12.6152i	1.29061	+	0.937680i	0.999817	−	0.0191074i	$-0.00608244\pi$
$181$	17.3633	+	12.6152i	1.29061	+	0.937680i	0.290788	+	0.956787i	$0.406082\pi$
$182$	−18.8522	−	13.6970i	−1.39742	−	1.01529i
$183$		0			0
$184$	−8.51155	−	26.1959i	−0.627480	−	1.93118i
$185$	6.93348	−	5.03747i	0.509760	−	0.370362i
$186$		0			0
$187$	12.7268	+	3.24677i	0.930673	+	0.237427i
$188$	−28.5694			−2.08364
$189$		0			0
$190$	−1.64835	−	5.07311i	−0.119584	−	0.368042i
$191$	2.89297	−	8.90364i	0.209328	−	0.644245i	−0.790180	−	0.612875i	$-0.790013\pi$
$191$	2.89297	−	8.90364i	0.209328	−	0.644245i	0.999508	−	0.0313699i	$-0.00998699\pi$
$192$		0			0
$193$	14.8930	+	10.8204i	1.07202	+	0.778870i	0.976275	−	0.216536i	$-0.0694757\pi$
$193$	14.8930	+	10.8204i	1.07202	+	0.778870i	0.0957479	+	0.995406i	$0.469476\pi$
$194$	−4.34597	+	13.3755i	−0.312023	+	0.960307i
$195$		0			0
$196$	−41.3529	+	30.0447i	−2.95378	+	2.14605i
$197$	4.67182			0.332854			0.166427	−	0.986054i	$-0.446777\pi$
$197$	4.67182			0.332854			0.166427	+	0.986054i	$0.446777\pi$
$198$		0			0
$199$	−16.2018			−1.14852			−0.574258	−	0.818674i	$-0.694710\pi$
$199$	−16.2018			−1.14852			−0.574258	+	0.818674i	$0.694710\pi$
$200$	−4.31545	+	3.13535i	−0.305148	+	0.221703i
$201$		0			0
$202$	5.39051	−	16.5903i	0.379275	−	1.16729i
$203$	−28.2283	−	20.5091i	−1.98124	−	1.43945i
$204$		0			0
$205$	2.35808	−	7.25741i	0.164695	−	0.506879i
$206$	0.477418	+	1.46934i	0.0332633	+	0.102374i
$207$		0			0
$208$	−10.5350			−0.730469
$209$	−4.55549	−	5.48938i	−0.315110	−	0.379709i
$210$		0			0
$211$	5.18147	−	3.76456i	0.356707	−	0.259163i	−0.394970	−	0.918694i	$-0.629245\pi$
$211$	5.18147	−	3.76456i	0.356707	−	0.259163i	0.751677	+	0.659531i	$0.229245\pi$
$212$	7.30666	+	22.4876i	0.501823	+	1.54445i
$213$		0			0
$214$	35.8844	+	26.0716i	2.45301	+	1.78222i
$215$	1.79861	+	1.30677i	0.122665	+	0.0891210i
$216$		0			0
$217$	−8.40828	−	25.8780i	−0.570791	−	1.75671i
$218$	−26.2925	+	19.1026i	−1.78075	+	1.29379i
$219$		0			0
$220$	−7.35862	+	11.6349i	−0.496118	+	0.784428i
$221$	8.46664			0.569528
$222$		0			0
$223$	−4.43500	−	13.6495i	−0.296989	−	0.914039i	−0.982546	−	0.186020i	$-0.940441\pi$
$223$	−4.43500	−	13.6495i	−0.296989	−	0.914039i	0.685557	−	0.728019i	$-0.259559\pi$
$224$	−2.10839	+	6.48896i	−0.140873	+	0.433562i
$225$		0			0
$226$	−16.8290	−	12.2270i	−1.11945	−	0.813328i
$227$	−5.65851	+	17.4151i	−0.375569	+	1.15588i	0.567525	+	0.823356i	$0.307901\pi$
$227$	−5.65851	+	17.4151i	−0.375569	+	1.15588i	−0.943094	+	0.332526i	$0.892099\pi$
$228$		0			0
$229$	15.3058	−	11.1203i	1.01144	−	0.734853i	0.0469285	−	0.998898i	$-0.485057\pi$
$229$	15.3058	−	11.1203i	1.01144	−	0.734853i	0.964510	+	0.264045i	$0.0850567\pi$
$230$	−12.8063			−0.844424
$231$		0			0
$232$	−42.3500			−2.78041
$233$	−5.14383	+	3.73721i	−0.336984	+	0.244833i	−0.743388	−	0.668860i	$-0.766782\pi$
$233$	−5.14383	+	3.73721i	−0.336984	+	0.244833i	0.406404	+	0.913693i	$0.366782\pi$
$234$		0			0
$235$	−2.12692	+	6.54598i	−0.138745	+	0.427013i
$236$	12.6992	+	9.22654i	0.826650	+	0.600596i
$237$		0			0
$238$	13.3384	−	41.0513i	0.864599	−	2.66096i
$239$	4.20727	+	12.9486i	0.272145	+	0.837577i	0.989961	+	0.141344i	$0.0451423\pi$
$239$	4.20727	+	12.9486i	0.272145	+	0.837577i	−0.717815	+	0.696234i	$0.754858\pi$
$240$		0			0
$241$	10.1564			0.654231			0.327116	−	0.944984i	$-0.393923\pi$
$241$	10.1564			0.654231			0.327116	+	0.944984i	$0.393923\pi$
$242$	−5.02927	+	26.8133i	−0.323294	+	1.72363i
$243$		0			0
$244$	−16.2343	+	11.7949i	−1.03929	+	0.755090i
$245$	3.80538	+	11.7118i	0.243117	+	0.748237i
$246$		0			0
$247$	−3.72012	−	2.70283i	−0.236706	−	0.171977i
$248$	−26.7183	−	19.4120i	−1.69661	−	1.23266i
$249$		0			0
$250$	0.766388	+	2.35870i	0.0484706	+	0.149177i
$251$	12.7484	−	9.26224i	0.804670	−	0.584627i	−0.107610	−	0.994193i	$-0.534320\pi$
$251$	12.7484	−	9.26224i	0.804670	−	0.584627i	0.912281	+	0.409566i	$0.134320\pi$
$252$		0			0
$253$	−15.9136	+	6.32903i	−1.00048	+	0.397902i
$254$	27.2384			1.70909
$255$		0			0
$256$	−10.0819	−	31.0290i	−0.630121	−	1.93931i
$257$	0.421300	−	1.29663i	0.0262799	−	0.0808814i	−0.937056	−	0.349178i	$-0.886461\pi$
$257$	0.421300	−	1.29663i	0.0262799	−	0.0808814i	0.963336	+	0.268297i	$0.0864608\pi$
$258$		0			0
$259$	−30.4714	−	22.1388i	−1.89340	−	1.37564i
$260$	−2.74229	+	8.43989i	−0.170069	+	0.523420i
$261$		0			0
$262$	−14.7094	+	10.6870i	−0.908752	+	0.660247i
$263$	8.12002			0.500702			0.250351	−	0.968155i	$-0.419454\pi$
$263$	8.12002			0.500702			0.250351	+	0.968155i	$0.419454\pi$
$264$		0			0
$265$	5.69644			0.349930
$266$	−18.9656	+	13.7793i	−1.16286	+	0.844865i
$267$		0			0
$268$	12.2755	−	37.7800i	0.749844	−	2.30778i
$269$	−9.47459	−	6.88369i	−0.577676	−	0.419706i	0.260209	−	0.965552i	$-0.416208\pi$
$269$	−9.47459	−	6.88369i	−0.577676	−	0.419706i	−0.837886	+	0.545846i	$0.816208\pi$
$270$		0			0
$271$	0.675670	−	2.07950i	0.0410440	−	0.126320i	−0.928435	−	0.371495i	$-0.878845\pi$
$271$	0.675670	−	2.07950i	0.0410440	−	0.126320i	0.969479	+	0.245175i	$0.0788453\pi$
$272$	−6.03019	−	18.5590i	−0.365634	−	1.12531i
$273$		0			0
$274$	41.3614			2.49873
$275$	2.11803	+	2.55224i	0.127722	+	0.153906i
$276$		0			0
$277$	−8.63487	+	6.27360i	−0.518819	+	0.376944i	−0.816159	−	0.577828i	$-0.803901\pi$
$277$	−8.63487	+	6.27360i	−0.518819	+	0.376944i	0.297340	+	0.954772i	$0.403901\pi$
$278$	−8.45983	−	26.0367i	−0.507387	−	1.56158i
$279$		0			0
$280$	18.9656	+	13.7793i	1.13341	+	0.823473i
$281$	4.39516	+	3.19327i	0.262193	+	0.190495i	0.711113	−	0.703077i	$-0.248191\pi$
$281$	4.39516	+	3.19327i	0.262193	+	0.190495i	−0.448920	+	0.893572i	$0.648191\pi$
$282$		0			0
$283$	5.63651	+	17.3474i	0.335056	+	1.03120i	0.966695	+	0.255933i	$0.0823826\pi$
$283$	5.63651	+	17.3474i	0.335056	+	1.03120i	−0.631639	+	0.775263i	$0.717617\pi$
$284$	−7.08654	+	5.14867i	−0.420509	+	0.305517i
$285$		0			0
$286$	1.13128	+	17.5493i	0.0668938	+	1.03771i
$287$	−33.5364			−1.97959
$288$		0			0
$289$	−0.407004	−	1.25263i	−0.0239414	−	0.0736841i
$290$	−6.08463	+	18.7266i	−0.357302	+	1.09966i
$291$		0			0
$292$	49.1978	+	35.7443i	2.87908	+	2.09178i
$293$	4.90083	−	15.0832i	0.286310	−	0.881171i	−0.699693	−	0.714443i	$-0.746680\pi$
$293$	4.90083	−	15.0832i	0.286310	−	0.881171i	0.986003	−	0.166727i	$-0.0533200\pi$
$294$		0			0
$295$	3.05946	−	2.22283i	0.178129	−	0.129418i
$296$	−45.7153			−2.65715
$297$		0			0
$298$	−11.4361			−0.662476
$299$	−8.93128	+	6.48896i	−0.516509	+	0.375266i
$300$		0			0
$301$	3.01929	−	9.29241i	0.174029	−	0.535606i
$302$	18.0762	+	13.1331i	1.04017	+	0.755727i
$303$		0			0
$304$	−3.27506	+	10.0796i	−0.187838	+	0.578105i
$305$	1.49391	+	4.59778i	0.0855410	+	0.263268i
$306$		0			0
$307$	−18.1026			−1.03317			−0.516585	−	0.856236i	$-0.672797\pi$
$307$	−18.1026			−1.03317			−0.516585	+	0.856236i	$0.672797\pi$
$308$	58.6245	+	14.9559i	3.34044	+	0.852191i
$309$		0			0
$310$	−12.4224	+	9.02544i	−0.705548	+	0.512610i
$311$	5.66709	+	17.4415i	0.321351	+	0.989018i	0.973061	+	0.230549i	$0.0740522\pi$
$311$	5.66709	+	17.4415i	0.321351	+	0.989018i	−0.651709	+	0.758469i	$0.725948\pi$
$312$		0			0
$313$	−24.4714	−	17.7795i	−1.38321	−	1.00496i	−0.996572	−	0.0827252i	$-0.973638\pi$
$313$	−24.4714	−	17.7795i	−1.38321	−	1.00496i	−0.386634	−	0.922233i	$-0.626362\pi$
$314$	−5.99725	−	4.35726i	−0.338445	−	0.245894i
$315$		0			0
$316$	4.18292	+	12.8737i	0.235308	+	0.724203i
$317$	24.7547	−	17.9854i	1.39036	−	1.01016i	0.394538	−	0.918879i	$-0.370904\pi$
$317$	24.7547	−	17.9854i	1.39036	−	1.01016i	0.995825	−	0.0912790i	$-0.0290955\pi$
$318$		0			0
$319$	1.69391	+	26.2773i	0.0948408	+	1.47125i
$320$	−6.00491			−0.335685
$321$		0			0
$322$	17.3919	+	53.5269i	0.969215	+	2.98294i
$323$	2.63207	−	8.10068i	0.146452	−	0.450734i
$324$		0			0
$325$	1.72964	+	1.25666i	0.0959431	+	0.0697068i
$326$	−2.21924	+	6.83011i	−0.122912	+	0.378285i
$327$		0			0
$328$	−32.9307	+	23.9256i	−1.81829	+	1.32107i
$329$	30.2489			1.66768
$330$		0			0
$331$	−1.09362			−0.0601110			−0.0300555	−	0.999548i	$-0.509568\pi$
$331$	−1.09362			−0.0601110			−0.0300555	+	0.999548i	$0.509568\pi$
$332$	35.8087	−	26.0165i	1.96526	−	1.42784i
$333$		0			0
$334$	2.91620	−	8.97514i	0.159567	−	0.491098i
$335$	−7.74250	−	5.62525i	−0.423018	−	0.307340i
$336$		0			0
$337$	5.02689	−	15.4712i	0.273832	−	0.842769i	−0.715694	−	0.698414i	$-0.753889\pi$
$337$	5.02689	−	15.4712i	0.273832	−	0.842769i	0.989526	−	0.144355i	$-0.0461107\pi$
$338$	−6.46001	−	19.8819i	−0.351378	−	1.08143i
$339$		0			0
$340$	−16.4379			−0.891470
$341$	−10.9761	+	17.3546i	−0.594388	+	0.939805i
$342$		0			0
$343$	18.8956	−	13.7284i	1.02026	−	0.741265i
$344$	−3.66464	−	11.2786i	−0.197584	−	0.608101i
$345$		0			0
$346$	−2.23298	−	1.62236i	−0.120046	−	0.0872184i
$347$	6.37990	+	4.63527i	0.342491	+	0.248834i	0.745712	−	0.666268i	$-0.232109\pi$
$347$	6.37990	+	4.63527i	0.342491	+	0.248834i	−0.403221	+	0.915103i	$0.632109\pi$
$348$		0			0
$349$	−3.83549	−	11.8044i	−0.205309	−	0.631877i	−0.999701	−	0.0244705i	$-0.992210\pi$
$349$	−3.83549	−	11.8044i	−0.205309	−	0.631877i	0.794391	−	0.607406i	$-0.207790\pi$
$350$	8.81790	−	6.40658i	0.471337	−	0.342446i
$351$		0			0
$352$	4.78450	−	1.90285i	0.255014	−	0.101422i
$353$	13.7984			0.734413			0.367207	−	0.930139i	$-0.380314\pi$
$353$	13.7984			0.734413			0.367207	+	0.930139i	$0.380314\pi$
$354$		0			0
$355$	0.652118	+	2.00701i	0.0346108	+	0.106521i
$356$	9.80441	−	30.1749i	0.519633	−	1.59927i
$357$		0			0
$358$	−9.66934	−	7.02519i	−0.511040	−	0.371293i
$359$	6.68244	−	20.5664i	0.352686	−	1.08545i	−0.604654	−	0.796488i	$-0.706689\pi$
$359$	6.68244	−	20.5664i	0.352686	−	1.08545i	0.957339	−	0.288966i	$-0.0933115\pi$
$360$		0			0
$361$	11.6288	−	8.44884i	0.612043	−	0.444676i
$362$	−53.2282			−2.79761
$363$		0			0
$364$	39.0007			2.04419
$365$	11.8526	−	8.61141i	0.620393	−	0.450742i
$366$		0			0
$367$	7.14705	−	21.9963i	0.373073	−	1.14820i	−0.571697	−	0.820465i	$-0.693715\pi$
$367$	7.14705	−	21.9963i	0.373073	−	1.14820i	0.944770	−	0.327735i	$-0.106285\pi$
$368$	20.5850	+	14.9559i	1.07307	+	0.779630i
$369$		0			0
$370$	−6.56814	+	20.2146i	−0.341461	+	1.05091i
$371$	−7.73620	−	23.8096i	−0.401643	−	1.23613i
$372$		0			0
$373$	−23.7304			−1.22871			−0.614356	−	0.789029i	$-0.710584\pi$
$373$	−23.7304			−1.22871			−0.614356	+	0.789029i	$0.710584\pi$
$374$	−30.2683	+	12.0381i	−1.56514	+	0.622475i
$375$		0			0
$376$	29.7026	−	21.5802i	1.53179	−	1.11291i
$377$	5.24524	+	16.1432i	0.270144	+	0.831417i
$378$		0			0
$379$	26.7367	+	19.4254i	1.37337	+	0.997814i	0.997465	+	0.0711565i	$0.0226690\pi$
$379$	26.7367	+	19.4254i	1.37337	+	0.997814i	0.375908	+	0.926657i	$0.377331\pi$
$380$	7.22258	+	5.24751i	0.370511	+	0.269192i
$381$		0			0
$382$	7.17480	+	22.0818i	0.367095	+	1.12980i
$383$	−6.45086	+	4.68682i	−0.329624	+	0.239485i	−0.740271	−	0.672309i	$-0.765303\pi$
$383$	−6.45086	+	4.68682i	−0.329624	+	0.239485i	0.410647	+	0.911794i	$0.365303\pi$
$384$		0			0
$385$	7.79122	−	12.3189i	0.397077	−	0.627831i
$386$	−45.6553			−2.32379
$387$		0			0
$388$	−7.27367	−	22.3861i	−0.369265	−	1.13648i
$389$	−1.32496	+	4.07781i	−0.0671782	+	0.206753i	−0.979011	−	0.203809i	$-0.934668\pi$
$389$	−1.32496	+	4.07781i	−0.0671782	+	0.206753i	0.911832	+	0.410563i	$0.134668\pi$
$390$		0			0
$391$	−16.5436	−	12.0196i	−0.836644	−	0.607858i
$392$	20.2986	−	62.4727i	1.02523	−	3.15535i
$393$		0			0
$394$	−9.37368	+	6.81038i	−0.472239	+	0.343102i
$395$	3.26111			0.164084
$396$		0			0
$397$	−2.21087			−0.110961			−0.0554803	−	0.998460i	$-0.517669\pi$
$397$	−2.21087			−0.110961			−0.0554803	+	0.998460i	$0.517669\pi$
$398$	32.5078	−	23.6183i	1.62947	−	1.18388i
$399$		0			0
$400$	1.52271	−	4.68643i	0.0761356	−	0.234321i
$401$	9.82776	+	7.14028i	0.490775	+	0.356569i	0.805482	−	0.592620i	$-0.201906\pi$
$401$	9.82776	+	7.14028i	0.490775	+	0.356569i	−0.314707	+	0.949189i	$0.601906\pi$
$402$		0			0
$403$	−4.09038	+	12.5889i	−0.203756	+	0.627097i
$404$	9.02187	+	27.7665i	0.448855	+	1.38143i
$405$		0			0
$406$	86.5353			4.29467
$407$	1.82852	+	28.3654i	0.0906362	+	1.40602i
$408$		0			0
$409$	−27.3936	+	19.9026i	−1.35452	+	0.984120i	−0.355752	+	0.934580i	$0.615775\pi$
$409$	−27.3936	+	19.9026i	−1.35452	+	0.984120i	−0.998772	+	0.0495394i	$0.984225\pi$
$410$	5.84822	+	17.9990i	0.288823	+	0.888906i
$411$		0			0
$412$	−2.09190	−	1.51985i	−0.103060	−	0.0748777i
$413$	−13.4458	−	9.76894i	−0.661624	−	0.480698i
$414$		0			0
$415$	−3.29519	−	10.1416i	−0.161754	−	0.497829i
$416$	2.68524	−	1.95094i	0.131655	−	0.0956526i
$417$		0			0
$418$	17.1424	+	4.37327i	0.838464	+	0.213904i
$419$	−18.1583			−0.887093			−0.443546	−	0.896251i	$-0.646280\pi$
$419$	−18.1583			−0.887093			−0.443546	+	0.896251i	$0.646280\pi$
$420$		0			0
$421$	12.0998	+	37.2394i	0.589709	+	1.81494i	0.579476	+	0.814989i	$0.303257\pi$
$421$	12.0998	+	37.2394i	0.589709	+	1.81494i	0.0102327	+	0.999948i	$0.496743\pi$
$422$	−4.90844	+	15.1066i	−0.238939	+	0.735379i
$423$		0			0
$424$	−24.5827	−	17.8604i	−1.19384	−	0.867376i
$425$	−1.22376	+	3.76634i	−0.0593610	+	0.182694i
$426$		0			0
$427$	17.1886	−	12.4883i	0.831816	−	0.604350i
$428$	−74.2361			−3.58834
$429$		0			0
$430$	−5.51374			−0.265896
$431$	18.4714	−	13.4203i	0.889737	−	0.646432i	−0.0460723	−	0.998938i	$-0.514670\pi$
$431$	18.4714	−	13.4203i	0.889737	−	0.646432i	0.935809	+	0.352506i	$0.114670\pi$
$432$		0			0
$433$	1.82070	−	5.60353i	0.0874971	−	0.269288i	−0.897729	−	0.440549i	$-0.854784\pi$
$433$	1.82070	−	5.60353i	0.0874971	−	0.269288i	0.985226	+	0.171260i	$0.0547839\pi$
$434$	54.5945	+	39.6652i	2.62062	+	1.90399i
$435$		0			0
$436$	16.8083	−	51.7306i	0.804970	−	2.47744i
$437$	3.43196	+	10.5625i	0.164173	+	0.505273i
$438$		0			0
$439$	5.46570			0.260864			0.130432	−	0.991457i	$-0.458364\pi$
$439$	5.46570			0.260864			0.130432	+	0.991457i	$0.458364\pi$
$440$	−1.13808	−	17.6548i	−0.0542559	−	0.841662i
$441$		0			0
$442$	−16.9877	+	12.3423i	−0.808023	+	0.587063i
$443$	−7.79180	−	23.9807i	−0.370199	−	1.13936i	−0.946661	−	0.322232i	$-0.895567\pi$
$443$	−7.79180	−	23.9807i	−0.370199	−	1.13936i	0.576461	−	0.817124i	$-0.304433\pi$
$444$		0			0
$445$	−6.18392	−	4.49288i	−0.293146	−	0.212983i
$446$	28.7962	+	20.9216i	1.36354	+	0.990669i
$447$		0			0
$448$	8.15512	+	25.0989i	0.385293	+	1.18581i
$449$	12.0230	−	8.73520i	0.567399	−	0.412239i	−0.266760	−	0.963763i	$-0.585953\pi$
$449$	12.0230	−	8.73520i	0.567399	−	0.412239i	0.834159	+	0.551523i	$0.185953\pi$
$450$		0			0
$451$	16.1625	+	19.4759i	0.761062	+	0.917083i
$452$	34.8151			1.63757
$453$		0			0
$454$	−14.0336	−	43.1909i	−0.658629	−	2.02705i
$455$	2.90350	−	8.93605i	0.136118	−	0.418929i
$456$		0			0
$457$	31.2953	+	22.7374i	1.46393	+	1.06361i	0.982317	+	0.187226i	$0.0599496\pi$
$457$	31.2953	+	22.7374i	1.46393	+	1.06361i	0.481615	+	0.876383i	$0.340050\pi$
$458$	−14.4993	+	44.6244i	−0.677510	+	2.08516i
$459$		0			0
$460$	17.3400	−	12.5982i	0.808481	−	0.587396i
$461$	4.32624			0.201493			0.100746	−	0.994912i	$-0.467877\pi$
$461$	4.32624			0.201493			0.100746	+	0.994912i	$0.467877\pi$
$462$		0			0
$463$	0.723001			0.0336007			0.0168003	−	0.999859i	$-0.494652\pi$
$463$	0.723001			0.0336007			0.0168003	+	0.999859i	$0.494652\pi$
$464$	31.6504	−	22.9953i	1.46933	−	1.06753i
$465$		0			0
$466$	4.87279	−	14.9969i	0.225728	−	0.694718i
$467$	−16.0966	−	11.6949i	−0.744862	−	0.541174i	0.149368	−	0.988782i	$-0.452276\pi$
$467$	−16.0966	−	11.6949i	−0.744862	−	0.541174i	−0.894230	+	0.447608i	$0.852276\pi$
$468$		0			0
$469$	−12.9971	+	40.0010i	−0.600151	+	1.84708i
$470$	−5.27493	−	16.2346i	−0.243315	−	0.748845i
$471$		0			0
$472$	−20.1723			−0.928505
$473$	−6.85156	+	2.72495i	−0.315035	+	0.125294i
$474$		0			0
$475$	1.74004	−	1.26421i	0.0798386	−	0.0580061i
$476$	22.3239	+	68.7059i	1.02321	+	3.14913i
$477$		0			0
$478$	−27.3175	−	19.8473i	−1.24947	−	0.907796i
$479$	−15.1606	−	11.0148i	−0.692705	−	0.503279i	0.184843	−	0.982768i	$-0.440822\pi$
$479$	−15.1606	−	11.0148i	−0.692705	−	0.503279i	−0.877548	+	0.479489i	$0.840822\pi$
$480$		0			0
$481$	5.66205	+	17.4260i	0.258167	+	0.794557i
$482$	−20.3781	+	14.8055i	−0.928197	+	0.674374i
$483$		0			0
$484$	−19.5679	−	41.2533i	−0.889451	−	1.87515i
$485$	−5.67073			−0.257494
$486$		0			0
$487$	−0.162001	−	0.498586i	−0.00734094	−	0.0225931i	0.947319	−	0.320292i	$-0.103781\pi$
$487$	−0.162001	−	0.498586i	−0.00734094	−	0.0225931i	−0.954660	+	0.297699i	$0.903781\pi$
$488$	7.96879	−	24.5254i	0.360730	−	1.11021i
$489$		0			0
$490$	−24.7081	−	17.9515i	−1.11620	−	0.810966i
$491$	−6.32585	+	19.4690i	−0.285482	+	0.878622i	0.700772	+	0.713385i	$0.252839\pi$
$491$	−6.32585	+	19.4690i	−0.285482	+	0.878622i	−0.986254	+	0.165237i	$0.947161\pi$
$492$		0			0
$493$	−25.4364	+	18.4807i	−1.14560	+	0.832327i
$494$	11.4042			0.513100
$495$		0			0
$496$	30.5084			1.36987
$497$	7.50313	−	5.45135i	0.336562	−	0.244526i
$498$		0			0
$499$	−1.40985	+	4.33907i	−0.0631135	+	0.194243i	−0.977641	−	0.210280i	$-0.932563\pi$
$499$	−1.40985	+	4.33907i	−0.0631135	+	0.194243i	0.914528	+	0.404523i	$0.132563\pi$
$500$	−3.35808	−	2.43978i	−0.150178	−	0.109110i
$501$		0			0
$502$	−12.0766	+	37.1680i	−0.539006	+	1.65889i
$503$	7.25209	+	22.3196i	0.323355	+	0.995184i	0.972178	+	0.234244i	$0.0752615\pi$
$503$	7.25209	+	22.3196i	0.323355	+	0.995184i	−0.648823	+	0.760939i	$0.724738\pi$
$504$		0			0
$505$	7.03366			0.312994
$506$	22.7033	−	35.8968i	1.00928	−	1.59581i
$507$		0			0
$508$	−36.8812	+	26.7958i	−1.63634	+	1.18887i
$509$	−1.46511	−	4.50914i	−0.0649398	−	0.199864i	0.913322	−	0.407238i	$-0.133508\pi$
$509$	−1.46511	−	4.50914i	−0.0649398	−	0.199864i	−0.978262	+	0.207374i	$0.933508\pi$
$510$		0			0
$511$	−52.0900	−	37.8456i	−2.30433	−	1.67419i
$512$	36.3406	+	26.4030i	1.60604	+	1.16686i
$513$		0			0
$514$	1.04486	+	3.21574i	0.0460867	+	0.141840i
$515$	−0.503973	+	0.366158i	−0.0222077	+	0.0161349i
$516$		0			0
$517$	−14.5781	−	17.5667i	−0.641145	−	0.772582i
$518$	93.4117			4.10427
$519$		0			0
$520$	−3.52410	−	10.8461i	−0.154542	−	0.475631i
$521$	10.4476	−	32.1545i	0.457718	−	1.40871i	−0.410196	−	0.911998i	$-0.634540\pi$
$521$	10.4476	−	32.1545i	0.457718	−	1.40871i	0.867914	−	0.496715i	$-0.165460\pi$
$522$		0			0
$523$	22.7425	+	16.5234i	0.994459	+	0.722516i	0.960893	−	0.276920i	$-0.0893137\pi$
$523$	22.7425	+	16.5234i	0.994459	+	0.722516i	0.0335656	+	0.999437i	$0.489314\pi$
$524$	9.40345	−	28.9408i	0.410792	−	1.26429i
$525$		0			0
$526$	−16.2922	+	11.8370i	−0.710375	+	0.516118i
$527$	−24.5187			−1.06805
$528$		0			0
$529$	3.66346			0.159281
$530$	−11.4295	+	8.30402i	−0.496466	+	0.360704i
$531$		0			0
$532$	12.1244	−	37.3149i	0.525657	−	1.61781i
$533$	13.1987	+	9.58941i	0.571699	+	0.415363i
$534$		0			0
$535$	−5.52669	+	17.0094i	−0.238939	+	0.735380i
$536$	15.7752	+	48.5510i	0.681383	+	2.09708i
$537$		0			0
$538$	29.0448			1.25221
$539$	−39.5750	−	10.0961i	−1.70461	−	0.434870i
$540$		0			0
$541$	−11.4455	+	8.31561i	−0.492078	+	0.357516i	−0.805983	−	0.591939i	$-0.798363\pi$
$541$	−11.4455	+	8.31561i	−0.492078	+	0.357516i	0.313905	+	0.949455i	$0.398363\pi$
$542$	1.67572	+	5.15732i	0.0719782	+	0.221526i
$543$		0			0
$544$	4.97391	+	3.61376i	0.213255	+	0.154939i
$545$	−10.6015	−	7.70241i	−0.454117	−	0.329935i
$546$		0			0
$547$	−9.78204	−	30.1060i	−0.418250	−	1.28724i	−0.909312	−	0.416116i	$-0.863391\pi$
$547$	−9.78204	−	30.1060i	−0.418250	−	1.28724i	0.491062	−	0.871125i	$-0.336609\pi$
$548$	−56.0040	+	40.6893i	−2.39237	+	1.73816i
$549$		0			0
$550$	−7.97023	−	2.03331i	−0.339852	−	0.0867007i
$551$	17.0761			0.727464
$552$		0			0
$553$	−4.42883	−	13.6305i	−0.188333	−	0.579629i
$554$	8.17987	−	25.1751i	0.347529	−	1.06959i
$555$		0			0
$556$	37.0684	+	26.9317i	1.57205	+	1.14216i
$557$	8.37820	−	25.7855i	0.354996	−	1.09256i	−0.601016	−	0.799237i	$-0.705237\pi$
$557$	8.37820	−	25.7855i	0.354996	−	1.09256i	0.956012	−	0.293328i	$-0.0947628\pi$
$558$		0			0
$559$	−3.84535	+	2.79381i	−0.162641	+	0.118166i
$560$	−21.6559			−0.915130
$561$		0			0
$562$	−13.4736			−0.568349
$563$	−19.4614	+	14.1395i	−0.820198	+	0.595909i	−0.916769	−	0.399417i	$-0.869213\pi$
$563$	−19.4614	+	14.1395i	−0.820198	+	0.595909i	0.0965709	+	0.995326i	$0.469213\pi$
$564$		0			0
$565$	2.59190	−	7.97704i	0.109042	−	0.335597i
$566$	−36.5975	−	26.5897i	−1.53831	−	1.11765i
$567$		0			0
$568$	3.47852	−	10.7058i	0.145955	−	0.449204i
$569$	−8.60322	−	26.4780i	−0.360666	−	1.11001i	−0.952651	−	0.304066i	$-0.901656\pi$
$569$	−8.60322	−	26.4780i	−0.360666	−	1.11001i	0.591985	−	0.805949i	$-0.298344\pi$
$570$		0			0
$571$	−33.5792			−1.40525			−0.702624	−	0.711562i	$-0.747988\pi$
$571$	−33.5792			−1.40525			−0.702624	+	0.711562i	$0.747988\pi$
$572$	−18.7959	−	22.6492i	−0.785897	−	0.947009i
$573$		0			0
$574$	67.2885	−	48.8879i	2.80857	−	2.04054i
$575$	−1.59566	−	4.91094i	−0.0665437	−	0.204800i
$576$		0			0
$577$	15.4532	+	11.2274i	0.643323	+	0.467402i	0.860990	−	0.508621i	$-0.169845\pi$
$577$	15.4532	+	11.2274i	0.643323	+	0.467402i	−0.217667	+	0.976023i	$0.569845\pi$
$578$	2.64265	+	1.92000i	0.109920	+	0.0798615i
$579$		0			0
$580$	−10.1836	−	31.3419i	−0.422850	−	1.30140i
$581$	−37.9138	+	27.5460i	−1.57293	+	1.14280i
$582$		0			0
$583$	−10.0987	+	15.9674i	−0.418247	+	0.661304i
$584$	−78.1490			−3.23383
$585$		0			0
$586$	12.1545	+	37.4076i	0.502097	+	1.54529i
$587$	6.60209	−	20.3191i	0.272497	−	0.838661i	−0.717373	−	0.696689i	$-0.754656\pi$
$587$	6.60209	−	20.3191i	0.272497	−	0.838661i	0.989871	−	0.141972i	$-0.0453442\pi$
$588$		0			0
$589$	10.7732	+	7.82716i	0.443900	+	0.322512i
$590$	−2.89825	+	8.91989i	−0.119319	+	0.367226i
$591$		0			0
$592$	34.1654	−	24.8226i	1.40419	−	1.02020i
$593$	9.16002			0.376157			0.188078	−	0.982154i	$-0.439774\pi$
$593$	9.16002			0.376157			0.188078	+	0.982154i	$0.439774\pi$
$594$		0			0
$595$	17.4042			0.713504
$596$	15.4847	−	11.2503i	0.634278	−	0.460830i
$597$		0			0
$598$	8.46067	−	26.0393i	0.345982	−	1.06482i
$599$	−2.74715	−	1.99592i	−0.112246	−	0.0815512i	0.530246	−	0.847844i	$-0.322099\pi$
$599$	−2.74715	−	1.99592i	−0.112246	−	0.0815512i	−0.642492	+	0.766292i	$0.722099\pi$
$600$		0			0
$601$	−4.46173	+	13.7318i	−0.181998	+	0.560132i	−0.999884	−	0.0152486i	$-0.995146\pi$
$601$	−4.46173	+	13.7318i	−0.181998	+	0.560132i	0.817886	+	0.575381i	$0.195146\pi$
$602$	7.48808	+	23.0459i	0.305191	+	0.939282i
$603$		0			0
$604$	−37.3952			−1.52159
$605$	−10.9090	+	1.41231i	−0.443512	+	0.0574187i
$606$		0			0
$607$	−1.11393	+	0.809315i	−0.0452129	+	0.0328491i	−0.610162	−	0.792277i	$-0.708896\pi$
$607$	−1.11393	+	0.809315i	−0.0452129	+	0.0328491i	0.564949	+	0.825126i	$0.308896\pi$
$608$	−1.03184	−	3.17567i	−0.0418465	−	0.128790i
$609$		0			0
$610$	−9.69987	−	7.04737i	−0.392736	−	0.285340i
$611$	−11.9049	−	8.64938i	−0.481619	−	0.349916i
$612$		0			0
$613$	0.367958	+	1.13246i	0.0148617	+	0.0457396i	0.958212	−	0.286058i	$-0.0923450\pi$
$613$	0.367958	+	1.13246i	0.0148617	+	0.0457396i	−0.943351	+	0.331797i	$0.892345\pi$
$614$	36.3216	−	26.3892i	1.46582	−	1.06498i
$615$		0			0
$616$	−72.2468	+	28.7335i	−2.91091	+	1.15770i
$617$	10.9076			0.439122			0.219561	−	0.975599i	$-0.429537\pi$
$617$	10.9076			0.439122			0.219561	+	0.975599i	$0.429537\pi$
$618$		0			0
$619$	−8.87927	−	27.3276i	−0.356888	−	1.09839i	−0.954907	−	0.296906i	$-0.904045\pi$
$619$	−8.87927	−	27.3276i	−0.356888	−	1.09839i	0.598019	−	0.801482i	$-0.295955\pi$
$620$	7.94143	−	24.4412i	0.318935	−	0.981582i
$621$		0			0
$622$	−36.7961	−	26.7339i	−1.47539	−	1.07193i
$623$	−10.3808	+	31.9488i	−0.415897	+	1.28000i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	75.0184			2.99834
$627$		0			0
$628$	12.4068			0.495087
$629$	−27.4577	+	19.9492i	−1.09481	+	0.795427i
$630$		0			0
$631$	10.4255	−	32.0863i	0.415032	−	1.27734i	−0.497190	−	0.867641i	$-0.665635\pi$
$631$	10.4255	−	32.0863i	0.415032	−	1.27734i	0.912222	−	0.409695i	$-0.134365\pi$
$632$	−14.0731	−	10.2247i	−0.559799	−	0.406718i
$633$		0			0
$634$	−23.4503	+	72.1727i	−0.931332	+	2.86634i
$635$	3.39389	+	10.4453i	0.134682	+	0.414509i
$636$		0			0
$637$	−26.3278			−1.04314
$638$	−41.7047	−	50.2543i	−1.65110	−	1.98959i
$639$		0			0
$640$	14.5604	−	10.5787i	0.575550	−	0.418162i
$641$	5.41427	+	16.6634i	0.213851	+	0.658165i	0.999233	+	0.0391543i	$0.0124664\pi$
$641$	5.41427	+	16.6634i	0.213851	+	0.658165i	−0.785382	+	0.619011i	$0.787534\pi$
$642$		0			0
$643$	0.565551	+	0.410897i	0.0223031	+	0.0162042i	0.598881	−	0.800838i	$-0.295612\pi$
$643$	0.565551	+	0.410897i	0.0223031	+	0.0162042i	−0.576578	+	0.817042i	$0.695612\pi$
$644$	−76.2062	−	55.3670i	−3.00294	−	2.18177i
$645$		0			0
$646$	6.52775	+	20.0904i	0.256831	+	0.790445i
$647$	36.7489	−	26.6997i	1.44475	−	1.04967i	0.457727	−	0.889093i	$-0.348664\pi$
$647$	36.7489	−	26.6997i	1.44475	−	1.04967i	0.987023	−	0.160580i	$-0.0513363\pi$
$648$		0			0
$649$	0.806849	+	12.5165i	0.0316716	+	0.491316i
$650$	−5.30230			−0.207973
$651$		0			0
$652$	−3.71424	−	11.4313i	−0.145461	−	0.447683i
$653$	−11.4664	+	35.2900i	−0.448715	+	1.38100i	0.429643	+	0.902999i	$0.358640\pi$
$653$	−11.4664	+	35.2900i	−0.448715	+	1.38100i	−0.878358	+	0.478004i	$0.841360\pi$
$654$		0			0
$655$	−5.93102	−	4.30914i	−0.231744	−	0.168372i
$656$	11.6196	−	35.7616i	0.453671	−	1.39626i
$657$		0			0
$658$	−60.6923	+	44.0956i	−2.36603	+	1.71902i
$659$	−16.0716			−0.626061			−0.313031	−	0.949743i	$-0.601344\pi$
$659$	−16.0716			−0.626061			−0.313031	+	0.949743i	$0.601344\pi$
$660$		0			0
$661$	42.1478			1.63936			0.819680	−	0.572822i	$-0.194151\pi$
$661$	42.1478			1.63936			0.819680	+	0.572822i	$0.194151\pi$
$662$	2.19428	−	1.59424i	0.0852831	−	0.0619618i
$663$		0			0
$664$	−17.5771	+	54.0969i	−0.682126	+	2.09937i
$665$	−7.64717	−	5.55600i	−0.296545	−	0.215452i
$666$		0			0
$667$	12.6685	−	38.9897i	0.490527	−	1.50969i
$668$	4.88072	+	15.0213i	0.188841	+	0.581192i
$669$		0			0
$670$	23.7350			0.916964
$671$	−15.5363	−	3.96351i	−0.599771	−	0.153010i
$672$		0			0
$673$	31.5240	−	22.9035i	1.21516	−	0.882865i	0.219470	−	0.975619i	$-0.429567\pi$
$673$	31.5240	−	22.9035i	1.21516	−	0.882865i	0.995689	+	0.0927543i	$0.0295671\pi$
$674$	12.4671	+	38.3698i	0.480215	+	1.47795i
$675$		0			0
$676$	28.3058	+	20.5653i	1.08868	+	0.790975i
$677$	−1.15293	−	0.837650i	−0.0443106	−	0.0321935i	0.565410	−	0.824810i	$-0.308718\pi$
$677$	−1.15293	−	0.837650i	−0.0443106	−	0.0321935i	−0.609720	+	0.792617i	$0.708718\pi$
$678$		0			0
$679$	7.70127	+	23.7021i	0.295548	+	0.909602i
$680$	17.0899	−	12.4165i	0.655367	−	0.476152i
$681$		0			0
$682$	−3.27608	−	50.8213i	−0.125448	−	1.94605i
$683$	21.1490			0.809245			0.404623	−	0.914484i	$-0.367403\pi$
$683$	21.1490			0.809245			0.404623	+	0.914484i	$0.367403\pi$
$684$		0			0
$685$	5.15360	+	15.8612i	0.196909	+	0.606024i
$686$	−17.8999	+	55.0902i	−0.683421	+	2.10335i
$687$		0			0
$688$	8.86285	+	6.43924i	0.337893	+	0.245494i
$689$	−3.76343	+	11.5826i	−0.143375	+	0.441264i
$690$		0			0
$691$	−22.5066	+	16.3520i	−0.856192	+	0.622060i	−0.926846	−	0.375441i	$-0.877491\pi$
$691$	−22.5066	+	16.3520i	−0.856192	+	0.622060i	0.0706547	+	0.997501i	$0.477491\pi$
$692$	4.61949			0.175607
$693$		0			0
$694$	−19.5579			−0.742408
$695$	8.93039	−	6.48831i	0.338749	−	0.246116i
$696$		0			0
$697$	−9.33837	+	28.7405i	−0.353716	+	1.08863i
$698$	24.9036	+	18.0935i	0.942616	+	0.684851i
$699$		0			0
$700$	−5.63711	+	17.3492i	−0.213063	+	0.655740i
$701$	−0.449424	−	1.38319i	−0.0169745	−	0.0522422i	0.942210	−	0.335022i	$-0.108744\pi$
$701$	−0.449424	−	1.38319i	−0.0169745	−	0.0522422i	−0.959185	+	0.282779i	$0.908744\pi$
$702$		0			0
$703$	18.4330			0.695213
$704$	10.6456	−	16.8321i	0.401221	−	0.634384i
$705$		0			0
$706$	−27.6855	+	20.1147i	−1.04196	+	0.757025i
$707$	−9.55224	−	29.3988i	−0.359249	−	1.10565i
$708$		0			0
$709$	10.0072	+	7.27068i	0.375830	+	0.273056i	0.759624	−	0.650362i	$-0.225383\pi$
$709$	10.0072	+	7.27068i	0.375830	+	0.273056i	−0.383795	+	0.923418i	$0.625383\pi$
$710$	−4.23416	−	3.07630i	−0.158905	−	0.115451i
$711$		0			0
$712$	12.5996	+	38.7776i	0.472190	+	1.45325i
$713$	25.8642	−	18.7915i	0.968622	−	0.703745i
$714$		0			0
$715$	−6.58881	+	2.62045i	−0.246408	+	0.0979994i
$716$	20.0035			0.747566
$717$		0			0
$718$	16.5730	+	51.0064i	0.618499	+	1.90354i
$719$	−9.39618	+	28.9185i	−0.350418	+	1.07848i	0.608200	+	0.793784i	$0.291892\pi$
$719$	−9.39618	+	28.9185i	−0.350418	+	1.07848i	−0.958619	+	0.284693i	$0.908108\pi$
$720$		0			0
$721$	2.21487	+	1.60920i	0.0824862	+	0.0599297i
$722$	−11.0161	+	33.9040i	−0.409976	+	1.26178i
$723$		0			0
$724$	72.0719	−	52.3633i	2.67853	−	1.94607i
$725$	−7.93936			−0.294860
$726$		0			0
$727$	36.7184			1.36181			0.680906	−	0.732371i	$-0.261586\pi$
$727$	36.7184			1.36181			0.680906	+	0.732371i	$0.261586\pi$
$728$	−40.5476	+	29.4595i	−1.50279	+	1.09184i
$729$		0			0
$730$	−11.2280	+	34.5564i	−0.415568	+	1.27899i
$731$	−7.12281	−	5.17503i	−0.263447	−	0.191405i
$732$		0			0
$733$	13.2260	−	40.7053i	0.488512	−	1.50348i	−0.338318	−	0.941032i	$-0.609858\pi$
$733$	13.2260	−	40.7053i	0.488512	−	1.50348i	0.826830	−	0.562453i	$-0.190142\pi$
$734$	17.7253	+	54.5527i	0.654251	+	2.01358i
$735$		0			0
$736$	−8.01651			−0.295492
$737$	29.4939	−	11.7301i	1.08642	−	0.432084i
$738$		0			0
$739$	26.1002	−	18.9629i	0.960111	−	0.697562i	0.00693470	−	0.999976i	$-0.497793\pi$
$739$	26.1002	−	18.9629i	0.960111	−	0.697562i	0.953177	+	0.302414i	$0.0977926\pi$
$740$	−10.9928	−	33.8324i	−0.404104	−	1.24370i
$741$		0			0
$742$	50.2307	+	36.4947i	1.84403	+	1.33976i
$743$	32.8034	+	23.8331i	1.20344	+	0.874351i	0.994619	−	0.103603i	$-0.0330372\pi$
$743$	32.8034	+	23.8331i	1.20344	+	0.874351i	0.208822	+	0.977954i	$0.433037\pi$
$744$		0			0
$745$	−1.42493	−	4.38550i	−0.0522055	−	0.160672i
$746$	47.6133	−	34.5931i	1.74325	−	1.26654i
$747$		0			0
$748$	29.1414	−	46.0763i	1.06551	−	1.68472i
$749$	78.6002			2.87199
$750$		0			0
$751$	−10.3606	−	31.8867i	−0.378064	−	1.16356i	−0.941388	−	0.337325i	$-0.890478\pi$
$751$	−10.3606	−	31.8867i	−0.378064	−	1.16356i	0.563324	−	0.826236i	$-0.309522\pi$
$752$	−10.4806	+	32.2560i	−0.382188	+	1.17625i
$753$		0			0
$754$	−34.0571	−	24.7439i	−1.24028	−	0.901120i
$755$	−2.78398	+	8.56821i	−0.101319	+	0.311829i
$756$		0			0
$757$	−8.80742	+	6.39896i	−0.320111	+	0.232574i	−0.736223	−	0.676739i	$-0.763392\pi$
$757$	−8.80742	+	6.39896i	−0.320111	+	0.232574i	0.416112	+	0.909313i	$0.363392\pi$
$758$	−81.9627			−2.97702
$759$		0			0
$760$	−11.4728			−0.416163
$761$	−17.5840	+	12.7756i	−0.637421	+	0.463114i	−0.858963	−	0.512037i	$-0.828891\pi$
$761$	−17.5840	+	12.7756i	−0.637421	+	0.463114i	0.221542	+	0.975151i	$0.428891\pi$
$762$		0			0
$763$	−17.7964	+	54.7716i	−0.644272	+	1.98287i
$764$	−31.4378	−	22.8409i	−1.13738	−	0.826354i
$765$		0			0
$766$	6.11095	−	18.8076i	0.220797	−	0.679545i
$767$	2.49843	+	7.68938i	0.0902131	+	0.277647i
$768$		0			0
$769$	−38.6384			−1.39333			−0.696667	−	0.717394i	$-0.745335\pi$
$769$	−38.6384			−1.39333			−0.696667	+	0.717394i	$0.745335\pi$
$770$	2.32548	+	36.0748i	0.0838045	+	1.30004i
$771$		0			0
$772$	61.8181	−	44.9135i	2.22488	−	1.61647i
$773$	2.32044	+	7.14157i	0.0834603	+	0.256864i	0.984075	−	0.177754i	$-0.0568832\pi$
$773$	2.32044	+	7.14157i	0.0834603	+	0.256864i	−0.900615	+	0.434619i	$0.856883\pi$
$774$		0			0
$775$	−5.00888	−	3.63917i	−0.179924	−	0.130723i
$776$	24.4717	+	17.7797i	0.878483	+	0.638256i
$777$		0			0
$778$	−3.28601	−	10.1133i	−0.117809	−	0.362580i
$779$	13.2781	−	9.64708i	0.475736	−	0.345643i
$780$		0			0
$781$	−6.78185	−	1.73014i	−0.242674	−	0.0619093i
$782$	50.7151			1.81357
$783$		0			0
$784$	18.7514	+	57.7109i	0.669693	+	2.06110i
$785$	0.923657	−	2.84273i	0.0329667	−	0.101461i
$786$		0			0
$787$	30.2657	+	21.9893i	1.07886	+	0.783835i	0.977483	−	0.211013i	$-0.0676764\pi$
$787$	30.2657	+	21.9893i	1.07886	+	0.783835i	0.101373	+	0.994848i	$0.467676\pi$
$788$	5.99241	−	18.4427i	0.213471	−	0.656995i
$789$		0			0
$790$	−6.54318	+	4.75390i	−0.232796	+	0.169136i
$791$	−36.8618			−1.31066
$792$		0			0
$793$	−10.3357			−0.367031
$794$	4.43596	−	3.22291i	0.157426	−	0.114377i
$795$		0			0
$796$	−20.7816	+	63.9592i	−0.736584	+	2.26697i
$797$	8.71273	+	6.33017i	0.308621	+	0.224226i	0.731304	−	0.682051i	$-0.238912\pi$
$797$	8.71273	+	6.33017i	0.308621	+	0.224226i	−0.422684	+	0.906277i	$0.638912\pi$
$798$		0			0
$799$	8.42295	−	25.9232i	0.297982	−	0.917096i
$800$	0.479744	+	1.47650i	0.0169615	+	0.0522021i
$801$		0			0
$802$	−30.1275			−1.06384
$803$	3.12580	+	48.4899i	0.110307	+	1.71117i
$804$		0			0
$805$	−18.3594	+	13.3388i	−0.647082	+	0.470133i
$806$	−10.1445	−	31.2215i	−0.357324	−	1.09973i
$807$		0			0
$808$	−30.3534	−	22.0530i	−1.06783	−	0.775823i
$809$	16.3182	+	11.8559i	0.573719	+	0.416831i	0.836454	−	0.548037i	$-0.184625\pi$
$809$	16.3182	+	11.8559i	0.573719	+	0.416831i	−0.262735	+	0.964868i	$0.584625\pi$
$810$		0			0
$811$	1.34009	+	4.12439i	0.0470571	+	0.144827i	0.971824	−	0.235707i	$-0.0757404\pi$
$811$	1.34009	+	4.12439i	0.0470571	+	0.144827i	−0.924767	+	0.380533i	$0.875740\pi$
$812$	−117.170	+	85.1292i	−4.11187	+	2.98745i
$813$		0			0
$814$	−45.0187	−	54.2477i	−1.57790	−	1.90138i
$815$	−2.89571			−0.101432
$816$		0			0
$817$	1.47763	+	4.54767i	0.0516956	+	0.159103i
$818$	25.9501	−	79.8663i	0.907325	−	2.79246i
$819$		0			0
$820$	−25.6251	−	18.6177i	−0.894868	−	0.650159i
$821$	−13.8171	+	42.5245i	−0.482219	+	1.48412i	0.353750	+	0.935340i	$0.384906\pi$
$821$	−13.8171	+	42.5245i	−0.482219	+	1.48412i	−0.835969	+	0.548777i	$0.815094\pi$
$822$		0			0
$823$	19.3130	−	14.0317i	0.673207	−	0.489114i	−0.197890	−	0.980224i	$-0.563409\pi$
$823$	19.3130	−	14.0317i	0.673207	−	0.489114i	0.871097	+	0.491110i	$0.163409\pi$
$824$	3.32290			0.115759
$825$		0			0
$826$	41.2187			1.43418
$827$	2.77718	−	2.01774i	0.0965720	−	0.0701637i	−0.538451	−	0.842657i	$-0.680990\pi$
$827$	2.77718	−	2.01774i	0.0965720	−	0.0701637i	0.635023	+	0.772493i	$0.280990\pi$
$828$		0			0
$829$	7.36785	−	22.6759i	0.255896	−	0.787567i	−0.737756	−	0.675068i	$-0.764114\pi$
$829$	7.36785	−	22.6759i	0.255896	−	0.787567i	0.993652	−	0.112499i	$-0.0358856\pi$
$830$	21.3955	+	15.5447i	0.742648	+	0.539565i
$831$		0			0
$832$	3.96722	−	12.2099i	0.137539	−	0.423301i
$833$	−15.0699	−	46.3805i	−0.522143	−	1.60699i
$834$		0			0
$835$	3.80512			0.131682
$836$	−27.5134	+	10.9424i	−0.951570	+	0.378451i
$837$		0			0
$838$	36.4334	−	26.4704i	1.25857	−	0.914406i
$839$	5.14341	+	15.8298i	0.177570	+	0.546505i	0.999742	−	0.0227351i	$-0.00723744\pi$
$839$	5.14341	+	15.8298i	0.177570	+	0.546505i	−0.822171	+	0.569240i	$0.807237\pi$
$840$		0			0
$841$	−27.5336	−	20.0044i	−0.949436	−	0.689805i
$842$	−78.5634	−	57.0796i	−2.70747	−	1.96709i
$843$		0			0
$844$	−8.21505	−	25.2833i	−0.282774	−	0.870288i
$845$	6.81934	−	4.95454i	0.234592	−	0.170441i
$846$		0			0
$847$	20.7183	+	43.6784i	0.711888	+	1.50081i
$848$	28.0698			0.963920
$849$		0			0
$850$	−3.03502	−	9.34084i	−0.104100	−	0.320388i
$851$	13.6752	−	42.0880i	0.468780	−	1.44276i
$852$		0			0
$853$	−3.85739	−	2.80256i	−0.132075	−	0.0959578i	0.519786	−	0.854296i	$-0.326011\pi$
$853$	−3.85739	−	2.80256i	−0.132075	−	0.0959578i	−0.651861	+	0.758338i	$0.726011\pi$
$854$	−16.2829	+	50.1136i	−0.557190	+	1.71485i
$855$		0			0
$856$	77.1806	−	56.0750i	2.63798	−	1.91660i
$857$	27.8195			0.950296			0.475148	−	0.879906i	$-0.342395\pi$
$857$	27.8195			0.950296			0.475148	+	0.879906i	$0.342395\pi$
$858$		0			0
$859$	−25.1802			−0.859139			−0.429569	−	0.903034i	$-0.641335\pi$
$859$	−25.1802			−0.859139			−0.429569	+	0.903034i	$0.641335\pi$
$860$	7.46571	−	5.42415i	0.254578	−	0.184962i
$861$		0			0
$862$	−17.4981	+	53.8537i	−0.595988	+	1.83426i
$863$	17.7728	+	12.9127i	0.604993	+	0.439553i	0.847648	−	0.530560i	$-0.178018\pi$
$863$	17.7728	+	12.9127i	0.604993	+	0.439553i	−0.242655	+	0.970113i	$0.578018\pi$
$864$		0			0
$865$	0.343909	−	1.05844i	0.0116933	−	0.0359882i
$866$	4.51548	+	13.8972i	0.153442	+	0.472246i
$867$		0			0
$868$	−112.943			−3.83352
$869$	−5.78134	+	9.14106i	−0.196119	+	0.310089i
$870$		0			0
$871$	16.5531	−	12.0265i	0.560880	−	0.407503i
$872$	21.6002	+	66.4787i	0.731476	+	2.25125i
$873$		0			0
$874$	−22.2835	−	16.1899i	−0.753752	−	0.547633i
$875$	3.55549	+	2.58321i	0.120197	+	0.0873285i
$876$		0			0
$877$	10.2028	+	31.4010i	0.344524	+	1.06034i	0.961838	+	0.273619i	$0.0882206\pi$
$877$	10.2028	+	31.4010i	0.344524	+	1.06034i	−0.617314	+	0.786716i	$0.711779\pi$
$878$	−10.9665	+	7.96766i	−0.370103	+	0.268896i
$879$		0			0
$880$	10.4368	+	12.5764i	0.351825	+	0.423951i
$881$	−2.26357			−0.0762615			−0.0381307	−	0.999273i	$-0.512140\pi$
$881$	−2.26357			−0.0762615			−0.0381307	+	0.999273i	$0.512140\pi$
$882$		0			0
$883$	−8.94710	−	27.5363i	−0.301094	−	0.926671i	−0.981106	−	0.193471i	$-0.938026\pi$
$883$	−8.94710	−	27.5363i	−0.301094	−	0.926671i	0.680012	−	0.733201i	$-0.261974\pi$
$884$	10.8599	−	33.4234i	0.365258	−	1.12415i
$885$		0			0
$886$	50.5917	+	36.7570i	1.69966	+	1.23488i
$887$	−11.3115	+	34.8131i	−0.379802	+	1.16891i	0.560379	+	0.828236i	$0.310655\pi$
$887$	−11.3115	+	34.8131i	−0.379802	+	1.16891i	−0.940181	+	0.340674i	$0.889345\pi$
$888$		0			0
$889$	39.0494	−	28.3710i	1.30967	−	0.951534i
$890$	18.9571			0.635444
$891$		0			0
$892$	−59.5722			−1.99463
$893$	−11.9764	+	8.70140i	−0.400777	+	0.291181i
$894$		0			0
$895$	1.48921	−	4.58331i	0.0497787	−	0.153203i
$896$	−63.9904	−	46.4917i	−2.13777	−	1.55318i
$897$		0			0
$898$	−11.3894	+	35.0531i	−0.380071	+	1.16974i
$899$	−15.1898	−	46.7493i	−0.506607	−	1.55918i
$900$		0			0
$901$	−22.5589			−0.751544
$902$	−60.8200	−	15.5160i	−2.02508	−	0.516626i
$903$		0			0
$904$	−36.1960	+	26.2980i	−1.20386	+	0.874657i
$905$	−6.63220	−	20.4118i	−0.220462	−	0.678512i
$906$		0			0
$907$	−18.8219	−	13.6749i	−0.624970	−	0.454067i	0.229684	−	0.973265i	$-0.426231\pi$
$907$	−18.8219	−	13.6749i	−0.624970	−	0.454067i	−0.854654	+	0.519198i	$0.826231\pi$
$908$	61.4909	+	44.6757i	2.04065	+	1.48262i
$909$		0			0
$910$	7.20092	+	22.1621i	0.238708	+	0.734668i
$911$	26.3619	−	19.1530i	0.873408	−	0.634568i	−0.0580911	−	0.998311i	$-0.518501\pi$
$911$	26.3619	−	19.1530i	0.873408	−	0.634568i	0.931499	+	0.363743i	$0.118501\pi$
$912$		0			0
$913$	34.2691	+	8.74251i	1.13414	+	0.289335i
$914$	−95.9373			−3.17332
$915$		0			0
$916$	−24.2669	−	74.6859i	−0.801802	−	2.46769i
$917$	−9.95625	+	30.6422i	−0.328784	+	1.01189i
$918$		0			0
$919$	−3.39681	−	2.46793i	−0.112051	−	0.0814095i	0.530349	−	0.847780i	$-0.322061\pi$
$919$	−3.39681	−	2.46793i	−0.112051	−	0.0814095i	−0.642399	+	0.766370i	$0.722061\pi$
$920$	−8.51155	+	26.1959i	−0.280617	+	0.863652i
$921$		0			0
$922$	−8.68029	+	6.30660i	−0.285870	+	0.207697i
$923$	−4.51171			−0.148505
$924$		0			0
$925$	−8.57025			−0.281788
$926$	−1.45065	+	1.05396i	−0.0476713	+	0.0346352i
$927$		0			0
$928$	−3.80886	+	11.7225i	−0.125032	+	0.384809i
$929$	−29.1063	−	21.1470i	−0.954946	−	0.693809i	−0.00297476	−	0.999996i	$-0.500947\pi$
$929$	−29.1063	−	21.1470i	−0.954946	−	0.693809i	−0.951972	+	0.306186i	$0.900947\pi$
$930$		0			0
$931$	−8.18465	+	25.1898i	−0.268241	+	0.825561i
$932$	8.15538	+	25.0997i	0.267138	+	0.822167i
$933$		0			0
$934$	49.3449			1.61462
$935$	−8.38776	−	10.1073i	−0.274309	−	0.330544i
$936$		0			0
$937$	−16.6835	+	12.1213i	−0.545026	+	0.395985i	−0.825948	−	0.563746i	$-0.809360\pi$
$937$	−16.6835	+	12.1213i	−0.545026	+	0.395985i	0.280922	+	0.959731i	$0.409360\pi$
$938$	−32.2339	−	99.2059i	−1.05248	−	3.23919i
$939$		0			0
$940$	23.1131	+	16.7927i	0.753867	+	0.547717i
$941$	−30.2927	−	22.0090i	−0.987515	−	0.717472i	−0.0281398	−	0.999604i	$-0.508958\pi$
$941$	−30.2927	−	22.0090i	−0.987515	−	0.717472i	−0.959376	+	0.282132i	$0.908958\pi$
$942$		0			0
$943$	−12.1763	−	37.4748i	−0.396515	−	1.22035i
$944$	15.0758	−	10.9532i	0.490675	−	0.356496i
$945$		0			0
$946$	9.77486	−	15.4553i	0.317808	−	0.502496i
$947$	−46.3928			−1.50756			−0.753781	−	0.657126i	$-0.771772\pi$
$947$	−46.3928			−1.50756			−0.753781	+	0.657126i	$0.771772\pi$
$948$		0			0
$949$	9.67911	+	29.7893i	0.314197	+	0.967000i
$950$	−1.64835	+	5.07311i	−0.0534797	+	0.164593i
$951$		0			0
$952$	−75.1070	−	54.5684i	−2.43423	−	1.76857i
$953$	13.6231	−	41.9277i	0.441296	−	1.35817i	−0.445199	−	0.895432i	$-0.646867\pi$
$953$	13.6231	−	41.9277i	0.441296	−	1.35817i	0.886495	−	0.462738i	$-0.153133\pi$
$954$		0			0
$955$	−7.57389	+	5.50275i	−0.245085	+	0.178065i
$956$	56.5133			1.82777
$957$		0			0
$958$	46.4755			1.50156
$959$	59.2963	−	43.0813i	1.91478	−	1.39117i
$960$		0			0
$961$	2.26586	−	6.97359i	0.0730921	−	0.224954i
$962$	−36.7634	−	26.7101i	−1.18530	−	0.861170i
$963$		0			0
$964$	13.0273	−	40.0939i	0.419582	−	1.29134i
$965$	−5.68863	−	17.5078i	−0.183123	−	0.563596i
$966$		0			0
$967$	18.7661			0.603476			0.301738	−	0.953391i	$-0.402433\pi$
$967$	18.7661			0.603476			0.301738	+	0.953391i	$0.402433\pi$
$968$	51.5051	+	28.1087i	1.65544	+	0.903448i
$969$		0			0
$970$	11.3779	−	8.26654i	0.365323	−	0.265422i
$971$	15.0705	+	46.3821i	0.483634	+	1.48847i	0.833949	+	0.551841i	$0.186074\pi$
$971$	15.0705	+	46.3821i	0.483634	+	1.48847i	−0.350315	+	0.936632i	$0.613926\pi$
$972$		0			0
$973$	−39.2475	−	28.5150i	−1.25822	−	0.914148i
$974$	1.05186	+	0.764221i	0.0337038	+	0.0244872i
$975$		0			0
$976$	7.36139	+	22.6560i	0.235632	+	0.725202i
$977$	15.1263	−	10.9899i	0.483933	−	0.351598i	−0.318913	−	0.947784i	$-0.603318\pi$
$977$	15.1263	−	10.9899i	0.483933	−	0.351598i	0.802846	+	0.596186i	$0.203318\pi$
$978$		0			0
$979$	23.5568	−	9.36882i	0.752877	−	0.299429i
$980$	51.1150			1.63281
$981$		0			0
$982$	−15.6886	−	48.2846i	−0.500644	−	1.54082i
$983$	12.2534	−	37.7120i	0.390822	−	1.20283i	−0.541346	−	0.840800i	$-0.682085\pi$
$983$	12.2534	−	37.7120i	0.390822	−	1.20283i	0.932168	−	0.362026i	$-0.117915\pi$
$984$		0			0
$985$	−3.77958	−	2.74603i	−0.120428	−	0.0874957i
$986$	24.0961	−	74.1603i	0.767377	−	2.36174i
$987$		0			0
$988$	−15.4415	+	11.2189i	−0.491260	+	0.356922i
$989$	11.4799			0.365040
$990$		0			0
$991$	−15.4204			−0.489846			−0.244923	−	0.969542i	$-0.578763\pi$
$991$	−15.4204			−0.489846			−0.244923	+	0.969542i	$0.578763\pi$
$992$	−7.77621	+	5.64975i	−0.246895	+	0.179380i
$993$		0			0
$994$	−7.10777	+	21.8755i	−0.225445	+	0.693848i
$995$	13.1075	+	9.52319i	0.415537	+	0.301905i
$996$		0			0
$997$	4.74077	−	14.5906i	0.150142	−	0.462089i	−0.847495	−	0.530804i	$-0.821890\pi$
$997$	4.74077	−	14.5906i	0.150142	−	0.462089i	0.997636	+	0.0687154i	$0.0218900\pi$
$998$	−3.49654	−	10.7613i	−0.110681	−	0.340642i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.n.b.91.1		8
3.2	odd	2		165.2.m.b.91.2	✓	8
11.2	odd	10		5445.2.a.br.1.1		4
11.4	even	5	inner	495.2.n.b.136.1		8
11.9	even	5		5445.2.a.bk.1.4		4
15.2	even	4		825.2.bx.g.124.4		16
15.8	even	4		825.2.bx.g.124.1		16
15.14	odd	2		825.2.n.i.751.1		8
33.2	even	10		1815.2.a.r.1.4		4
33.20	odd	10		1815.2.a.v.1.1		4
33.26	odd	10		165.2.m.b.136.2	yes	8
165.59	odd	10		825.2.n.i.301.1		8
165.92	even	20		825.2.bx.g.499.1		16
165.119	odd	10		9075.2.a.cq.1.4		4
165.134	even	10		9075.2.a.dg.1.1		4
165.158	even	20		825.2.bx.g.499.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.m.b.91.2	✓	8	3.2	odd	2
165.2.m.b.136.2	yes	8	33.26	odd	10
495.2.n.b.91.1		8	1.1	even	1	trivial
495.2.n.b.136.1		8	11.4	even	5	inner
825.2.n.i.301.1		8	165.59	odd	10
825.2.n.i.751.1		8	15.14	odd	2
825.2.bx.g.124.1		16	15.8	even	4
825.2.bx.g.124.4		16	15.2	even	4
825.2.bx.g.499.1		16	165.92	even	20
825.2.bx.g.499.4		16	165.158	even	20
1815.2.a.r.1.4		4	33.2	even	10
1815.2.a.v.1.1		4	33.20	odd	10
5445.2.a.bk.1.4		4	11.9	even	5
5445.2.a.br.1.1		4	11.2	odd	10
9075.2.a.cq.1.4		4	165.119	odd	10
9075.2.a.dg.1.1		4	165.134	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:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00643 + 1.45776i) q^{2} +(1.28267 - 3.94765i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-1.35808 + 4.17973i) q^{7} +(1.64835 + 5.07311i) q^{8} +O(q^{10})\)	\(q+(-2.00643 + 1.45776i) q^{2} +(1.28267 - 3.94765i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-1.35808 + 4.17973i) q^{7} +(1.64835 + 5.07311i) q^{8} +2.48008 q^{10} +(3.08183 - 1.22568i) q^{11} +(1.72964 - 1.25666i) q^{13} +(-3.36814 - 10.3661i) q^{14} +(-3.98651 - 2.89637i) q^{16} +(3.20384 + 2.32773i) q^{17} +(-0.664637 - 2.04554i) q^{19} +(-3.35808 + 2.43978i) q^{20} +(-4.39673 + 6.95181i) q^{22} -5.16367 q^{23} +(0.309017 + 0.951057i) q^{25} +(-1.63850 + 5.04278i) q^{26} +(14.7581 + 10.7224i) q^{28} +(-2.45340 + 7.55078i) q^{29} +(-5.00888 + 3.63917i) q^{31} +1.55248 q^{32} -9.82154 q^{34} +(3.55549 - 2.58321i) q^{35} +(-2.64835 + 8.15079i) q^{37} +(4.31545 + 3.13535i) q^{38} +(1.64835 - 5.07311i) q^{40} +(2.35808 + 7.25741i) q^{41} -2.22321 q^{43} +(-0.885601 - 13.7382i) q^{44} +(10.3605 - 7.52737i) q^{46} +(-2.12692 - 6.54598i) q^{47} +(-9.96262 - 7.23827i) q^{49} +(-2.00643 - 1.45776i) q^{50} +(-2.74229 - 8.43989i) q^{52} +(-4.60852 + 3.34828i) q^{53} +(-3.21369 - 0.819857i) q^{55} -23.4428 q^{56} +(-6.08463 - 18.7266i) q^{58} +(-1.16861 + 3.59661i) q^{59} +(-3.91111 - 2.84159i) q^{61} +(4.74495 - 14.6035i) q^{62} +(4.85808 - 3.52960i) q^{64} -2.13795 q^{65} +9.57025 q^{67} +(13.2985 - 9.66195i) q^{68} +(-3.36814 + 10.3661i) q^{70} +(-1.70727 - 1.24040i) q^{71} +(-4.52728 + 13.9335i) q^{73} +(-6.56814 - 20.2146i) q^{74} -8.92760 q^{76} +(0.937663 + 14.5458i) q^{77} +(-2.63829 + 1.91683i) q^{79} +(1.52271 + 4.68643i) q^{80} +(-15.3108 - 11.1240i) q^{82} +(8.62692 + 6.26782i) q^{83} +(-1.22376 - 3.76634i) q^{85} +(4.46071 - 3.24090i) q^{86} +(11.2980 + 13.6141i) q^{88} +7.64375 q^{89} +(2.90350 + 8.93605i) q^{91} +(-6.62328 + 20.3844i) q^{92} +(13.8100 + 10.0335i) q^{94} +(-0.664637 + 2.04554i) q^{95} +(4.58771 - 3.33317i) q^{97} +30.5409 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 2 q^{4} - 2 q^{5} + 9 q^{7} + 19 q^{8}+O(q^{10}) \) 8 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 + 9 * q^7 + 19 * q^8	\( 8 q - 2 q^{2} - 2 q^{4} - 2 q^{5} + 9 q^{7} + 19 q^{8} - 2 q^{10} + 3 q^{11} + 10 q^{13} - 24 q^{14} + 4 q^{16} + 2 q^{17} - 2 q^{19} - 7 q^{20} - 7 q^{22} + 2 q^{23} - 2 q^{25} - 14 q^{26} + 13 q^{28} - 14 q^{29} - 5 q^{31} + 16 q^{32} - 70 q^{34} - q^{35} - 27 q^{37} + 16 q^{38} + 19 q^{40} - q^{41} - 28 q^{43} - 47 q^{44} + 42 q^{46} + 27 q^{47} - 15 q^{49} - 2 q^{50} + 22 q^{52} + q^{53} - 7 q^{55} + 24 q^{56} + 18 q^{58} - 13 q^{59} - 3 q^{61} - 15 q^{62} + 19 q^{64} - 30 q^{65} + 10 q^{67} + 33 q^{68} - 24 q^{70} - 9 q^{71} + 5 q^{73} + 17 q^{74} - 46 q^{76} - q^{77} - 10 q^{79} - 11 q^{80} - 33 q^{82} + 25 q^{83} - 8 q^{85} - 20 q^{86} + 29 q^{88} - 4 q^{89} - 43 q^{91} + 22 q^{92} + 57 q^{94} - 2 q^{95} + 13 q^{97} + 2 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 + 9 * q^7 + 19 * q^8 - 2 * q^10 + 3 * q^11 + 10 * q^13 - 24 * q^14 + 4 * q^16 + 2 * q^17 - 2 * q^19 - 7 * q^20 - 7 * q^22 + 2 * q^23 - 2 * q^25 - 14 * q^26 + 13 * q^28 - 14 * q^29 - 5 * q^31 + 16 * q^32 - 70 * q^34 - q^35 - 27 * q^37 + 16 * q^38 + 19 * q^40 - q^41 - 28 * q^43 - 47 * q^44 + 42 * q^46 + 27 * q^47 - 15 * q^49 - 2 * q^50 + 22 * q^52 + q^53 - 7 * q^55 + 24 * q^56 + 18 * q^58 - 13 * q^59 - 3 * q^61 - 15 * q^62 + 19 * q^64 - 30 * q^65 + 10 * q^67 + 33 * q^68 - 24 * q^70 - 9 * q^71 + 5 * q^73 + 17 * q^74 - 46 * q^76 - q^77 - 10 * q^79 - 11 * q^80 - 33 * q^82 + 25 * q^83 - 8 * q^85 - 20 * q^86 + 29 * q^88 - 4 * q^89 - 43 * q^91 + 22 * q^92 + 57 * q^94 - 2 * q^95 + 13 * q^97 + 2 * q^98

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