LMFDB - Embedded newform 693.2.i.g.100.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(100,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("693.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.i (of order $3$, degree $2$, 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:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.1783323.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 5x^{4} - 2x^{3} + 19x^{2} - 12x + 9 $ x^6 - x^5 + 5x^4 - 2x^3 + 19x^2 - 12x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.3
Root			$1.09935 + 1.90412i$ of defining polynomial
Character	$\chi$	$=$	693.100
Dual form			693.2.i.g.298.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.917122 - 1.58850i) q^{2} +(-0.682224 - 1.18165i) q^{4} +(-0.317776 + 0.550404i) q^{5} +(0.317776 - 2.62660i) q^{7} +1.16576 q^{8} +O(q^{10})$	\(q+(0.917122 - 1.58850i) q^{2} +(-0.682224 - 1.18165i) q^{4} +(-0.317776 + 0.550404i) q^{5} +(0.317776 - 2.62660i) q^{7} +1.16576 q^{8} +(0.582878 + 1.00958i) q^{10} +(-0.500000 - 0.866025i) q^{11} -1.80131 q^{13} +(-3.88092 - 2.91370i) q^{14} +(2.43359 - 4.21510i) q^{16} +(-1.41712 - 2.45453i) q^{17} +(2.78157 - 4.81782i) q^{19} +0.867178 q^{20} -1.83424 q^{22} +(1.08288 - 1.87560i) q^{23} +(2.29804 + 3.98032i) q^{25} +(-1.65202 + 2.86138i) q^{26} +(-3.32051 + 1.41643i) q^{28} +10.4303 q^{29} +(-3.21516 - 5.56882i) q^{31} +(-3.29804 - 5.71237i) q^{32} -5.19869 q^{34} +(1.34471 + 1.00958i) q^{35} +(-3.03293 + 5.25320i) q^{37} +(-5.10208 - 8.83705i) q^{38} +(-0.370450 + 0.641637i) q^{40} -7.53566 q^{41} -4.86718 q^{43} +(-0.682224 + 1.18165i) q^{44} +(-1.98626 - 3.44031i) q^{46} +(-1.41712 + 2.45453i) q^{47} +(-6.79804 - 1.66934i) q^{49} +8.43032 q^{50} +(1.22890 + 2.12851i) q^{52} +(3.73490 + 6.46903i) q^{53} +0.635552 q^{55} +(0.370450 - 3.06197i) q^{56} +(9.56587 - 16.5686i) q^{58} +(5.90338 + 10.2250i) q^{59} +(2.16576 - 3.75120i) q^{61} -11.7948 q^{62} -2.36445 q^{64} +(0.572413 - 0.991448i) q^{65} +(0.801309 + 1.38791i) q^{67} +(-1.93359 + 3.34907i) q^{68} +(2.83697 - 1.21017i) q^{70} -4.29204 q^{71} +(7.99673 + 13.8507i) q^{73} +(5.56314 + 9.63564i) q^{74} -7.59061 q^{76} +(-2.43359 + 1.03810i) q^{77} +(-2.38092 + 4.12387i) q^{79} +(1.54667 + 2.67891i) q^{80} +(-6.91112 + 11.9704i) q^{82} +9.23163 q^{83} +1.80131 q^{85} +(-4.46379 + 7.73152i) q^{86} +(-0.582878 - 1.00958i) q^{88} +(0.182224 - 0.315621i) q^{89} +(-0.572413 + 4.73131i) q^{91} -2.95506 q^{92} +(2.59935 + 4.50220i) q^{94} +(1.76783 + 3.06197i) q^{95} -2.59607 q^{97} +(-8.88637 + 9.26770i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 4 q^{4} - 2 q^{5} + 2 q^{7} + 18 q^{8}+O(q^{10}) $ 6 * q - 4 * q^4 - 2 * q^5 + 2 * q^7 + 18 * q^8	$ 6 q - 4 q^{4} - 2 q^{5} + 2 q^{7} + 18 q^{8} + 9 q^{10} - 3 q^{11} - 22 q^{13} - 12 q^{14} - 2 q^{16} - 3 q^{17} + 11 q^{19} - 28 q^{20} + 12 q^{23} - 3 q^{25} + q^{26} + 13 q^{28} + 18 q^{29} + 3 q^{31} - 3 q^{32} - 20 q^{34} - 9 q^{35} + 4 q^{37} + 8 q^{38} + 3 q^{40} + 10 q^{41} + 4 q^{43} - 4 q^{44} + 10 q^{46} - 3 q^{47} - 24 q^{49} + 6 q^{50} + 7 q^{52} + 17 q^{53} + 4 q^{55} - 3 q^{56} + 13 q^{58} + 8 q^{59} + 24 q^{61} - 26 q^{62} - 14 q^{64} + 15 q^{65} + 16 q^{67} + 5 q^{68} - 27 q^{70} - 14 q^{71} + 20 q^{73} + 22 q^{74} - 78 q^{76} + 2 q^{77} - 3 q^{79} + 9 q^{80} - 41 q^{82} + 22 q^{83} + 22 q^{85} - 21 q^{86} - 9 q^{88} + q^{89} - 15 q^{91} - 50 q^{92} + 10 q^{94} - 17 q^{95} + 18 q^{97} + 24 q^{98}+O(q^{100}) $ 6 * q - 4 * q^4 - 2 * q^5 + 2 * q^7 + 18 * q^8 + 9 * q^10 - 3 * q^11 - 22 * q^13 - 12 * q^14 - 2 * q^16 - 3 * q^17 + 11 * q^19 - 28 * q^20 + 12 * q^23 - 3 * q^25 + q^26 + 13 * q^28 + 18 * q^29 + 3 * q^31 - 3 * q^32 - 20 * q^34 - 9 * q^35 + 4 * q^37 + 8 * q^38 + 3 * q^40 + 10 * q^41 + 4 * q^43 - 4 * q^44 + 10 * q^46 - 3 * q^47 - 24 * q^49 + 6 * q^50 + 7 * q^52 + 17 * q^53 + 4 * q^55 - 3 * q^56 + 13 * q^58 + 8 * q^59 + 24 * q^61 - 26 * q^62 - 14 * q^64 + 15 * q^65 + 16 * q^67 + 5 * q^68 - 27 * q^70 - 14 * q^71 + 20 * q^73 + 22 * q^74 - 78 * q^76 + 2 * q^77 - 3 * q^79 + 9 * q^80 - 41 * q^82 + 22 * q^83 + 22 * q^85 - 21 * q^86 - 9 * q^88 + q^89 - 15 * q^91 - 50 * q^92 + 10 * q^94 - 17 * q^95 + 18 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.917122	−	1.58850i	0.648503	−	1.12324i	−0.334978	−	0.942226i	$-0.608729\pi$
$2$	0.917122	−	1.58850i	0.648503	−	1.12324i	0.983481	−	0.181014i	$-0.0579379\pi$
$3$		0			0
$3$		0			0
$4$	−0.682224	−	1.18165i	−0.341112	−	0.590823i
$5$	−0.317776	+	0.550404i	−0.142114	+	0.246148i	−0.928292	−	0.371851i	$-0.878723\pi$
$5$	−0.317776	+	0.550404i	−0.142114	+	0.246148i	0.786179	+	0.617999i	$0.212057\pi$
$6$		0			0
$7$	0.317776	−	2.62660i	0.120108	−	0.992761i
$7$	0.317776	−	2.62660i	0.120108	−	0.992761i
$8$	1.16576			0.412157
$9$		0			0
$10$	0.582878	+	1.00958i	0.184322	+	0.319256i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$		0			0
$13$	−1.80131			−0.499593			−0.249797	−	0.968298i	$-0.580364\pi$
$13$	−1.80131			−0.499593			−0.249797	+	0.968298i	$0.580364\pi$
$14$	−3.88092	−	2.91370i	−1.03722	−	0.778718i
$15$		0			0
$16$	2.43359	−	4.21510i	0.608397	−	1.05377i
$17$	−1.41712	−	2.45453i	−0.343702	−	0.595310i	0.641415	−	0.767194i	$-0.278348\pi$
$17$	−1.41712	−	2.45453i	−0.343702	−	0.595310i	−0.985117	+	0.171884i	$0.945014\pi$
$18$		0			0
$19$	2.78157	−	4.81782i	0.638136	−	1.10528i	−0.347706	−	0.937604i	$-0.613039\pi$
$19$	2.78157	−	4.81782i	0.638136	−	1.10528i	0.985841	−	0.167680i	$-0.0536275\pi$
$20$	0.867178			0.193907
$21$		0			0
$22$	−1.83424			−0.391062
$23$	1.08288	−	1.87560i	0.225796	−	0.391090i	−0.730762	−	0.682632i	$-0.760835\pi$
$23$	1.08288	−	1.87560i	0.225796	−	0.391090i	0.956558	+	0.291542i	$0.0941685\pi$
$24$		0			0
$25$	2.29804	+	3.98032i	0.459607	+	0.796063i
$26$	−1.65202	+	2.86138i	−0.323988	+	0.561163i
$27$		0			0
$28$	−3.32051	+	1.41643i	−0.627517	+	0.267680i
$29$	10.4303			1.93686			0.968431	−	0.249283i	$-0.0801950\pi$
$29$	10.4303			1.93686			0.968431	+	0.249283i	$0.0801950\pi$
$30$		0			0
$31$	−3.21516	−	5.56882i	−0.577460	−	1.00019i	−0.995770	−	0.0918849i	$-0.970711\pi$
$31$	−3.21516	−	5.56882i	−0.577460	−	1.00019i	0.418310	−	0.908304i	$-0.362623\pi$
$32$	−3.29804	−	5.71237i	−0.583016	−	1.00981i
$33$		0			0
$34$	−5.19869			−0.891568
$35$	1.34471	+	1.00958i	0.227297	+	0.170649i
$36$		0			0
$37$	−3.03293	+	5.25320i	−0.498611	+	0.863620i	−0.999999	−	0.00160274i	$-0.999490\pi$
$37$	−3.03293	+	5.25320i	−0.498611	+	0.863620i	0.501387	+	0.865223i	$0.332823\pi$
$38$	−5.10208	−	8.83705i	−0.827666	−	1.43356i
$39$		0			0
$40$	−0.370450	+	0.641637i	−0.0585732	+	0.101452i
$41$	−7.53566			−1.17687			−0.588436	−	0.808543i	$-0.700256\pi$
$41$	−7.53566			−1.17687			−0.588436	+	0.808543i	$0.700256\pi$
$42$		0			0
$43$	−4.86718			−0.742238			−0.371119	−	0.928585i	$-0.621026\pi$
$43$	−4.86718			−0.742238			−0.371119	+	0.928585i	$0.621026\pi$
$44$	−0.682224	+	1.18165i	−0.102849	+	0.178140i
$45$		0			0
$46$	−1.98626	−	3.44031i	−0.292858	−	0.507246i
$47$	−1.41712	+	2.45453i	−0.206708	+	0.358030i	−0.950676	−	0.310187i	$-0.899608\pi$
$47$	−1.41712	+	2.45453i	−0.206708	+	0.358030i	0.743967	+	0.668216i	$0.232942\pi$
$48$		0			0
$49$	−6.79804	−	1.66934i	−0.971148	−	0.238477i
$50$	8.43032			1.19223
$51$		0			0
$52$	1.22890	+	2.12851i	0.170417	+	0.295171i
$53$	3.73490	+	6.46903i	0.513028	+	0.888590i	0.999886	+	0.0151089i	$0.00480950\pi$
$53$	3.73490	+	6.46903i	0.513028	+	0.888590i	−0.486858	+	0.873481i	$0.661857\pi$
$54$		0			0
$55$	0.635552			0.0856978
$56$	0.370450	−	3.06197i	0.0495034	−	0.409174i
$57$		0			0
$58$	9.56587	−	16.5686i	1.25606	−	2.17556i
$59$	5.90338	+	10.2250i	0.768555	+	1.33118i	0.938346	+	0.345696i	$0.112357\pi$
$59$	5.90338	+	10.2250i	0.768555	+	1.33118i	−0.169791	+	0.985480i	$0.554309\pi$
$60$		0			0
$61$	2.16576	−	3.75120i	0.277297	−	0.480292i	−0.693415	−	0.720538i	$-0.743895\pi$
$61$	2.16576	−	3.75120i	0.277297	−	0.480292i	0.970712	+	0.240246i	$0.0772282\pi$
$62$	−11.7948			−1.49794
$63$		0			0
$64$	−2.36445			−0.295556
$65$	0.572413	−	0.991448i	0.0709990	−	0.122974i
$66$		0			0
$67$	0.801309	+	1.38791i	0.0978954	+	0.169560i	0.910813	−	0.412818i	$-0.135456\pi$
$67$	0.801309	+	1.38791i	0.0978954	+	0.169560i	−0.812918	+	0.582378i	$0.802122\pi$
$68$	−1.93359	+	3.34907i	−0.234482	+	0.406135i
$69$		0			0
$70$	2.83697	−	1.21017i	0.339083	−	0.144643i
$71$	−4.29204			−0.509371			−0.254685	−	0.967024i	$-0.581972\pi$
$71$	−4.29204			−0.509371			−0.254685	+	0.967024i	$0.581972\pi$
$72$		0			0
$73$	7.99673	+	13.8507i	0.935946	+	1.62111i	0.772938	+	0.634482i	$0.218786\pi$
$73$	7.99673	+	13.8507i	0.935946	+	1.62111i	0.163008	+	0.986625i	$0.447880\pi$
$74$	5.56314	+	9.63564i	0.646702	+	1.12012i
$75$		0			0
$76$	−7.59061			−0.870703
$77$	−2.43359	+	1.03810i	−0.277333	+	0.118302i
$78$		0			0
$79$	−2.38092	+	4.12387i	−0.267874	+	0.463971i	−0.968313	−	0.249741i	$-0.919654\pi$
$79$	−2.38092	+	4.12387i	−0.267874	+	0.463971i	0.700439	+	0.713713i	$0.252988\pi$
$80$	1.54667	+	2.67891i	0.172923	+	0.299512i
$81$		0			0
$82$	−6.91112	+	11.9704i	−0.763206	+	1.32191i
$83$	9.23163			1.01330			0.506651	−	0.862151i	$-0.330883\pi$
$83$	9.23163			1.01330			0.506651	+	0.862151i	$0.330883\pi$
$84$		0			0
$85$	1.80131			0.195379
$86$	−4.46379	+	7.73152i	−0.481343	+	0.833711i
$87$		0			0
$88$	−0.582878	−	1.00958i	−0.0621350	−	0.107621i
$89$	0.182224	−	0.315621i	0.0193157	−	0.0334558i	−0.856206	−	0.516635i	$-0.827185\pi$
$89$	0.182224	−	0.315621i	0.0193157	−	0.0334558i	0.875522	+	0.483179i	$0.160518\pi$
$90$		0			0
$91$	−0.572413	+	4.73131i	−0.0600051	+	0.495977i
$92$	−2.95506			−0.308087
$93$		0			0
$94$	2.59935	+	4.50220i	0.268102	+	0.464366i
$95$	1.76783	+	3.06197i	0.181376	+	0.314152i
$96$		0			0
$97$	−2.59607			−0.263591			−0.131796	−	0.991277i	$-0.542074\pi$
$97$	−2.59607			−0.263591			−0.131796	+	0.991277i	$0.542074\pi$
$98$	−8.88637	+	9.26770i	−0.897659	+	0.936179i
$99$		0			0
$100$	3.13555	−	5.43094i	0.313555	−	0.543094i
$101$	−4.95006	−	8.57375i	−0.492549	−	0.853120i	0.507414	−	0.861702i	$-0.330601\pi$
$101$	−4.95006	−	8.57375i	−0.492549	−	0.853120i	−0.999963	+	0.00858243i	$0.997268\pi$
$102$		0			0
$103$	−3.11581	+	5.39675i	−0.307010	+	0.531757i	−0.977707	−	0.209975i	$-0.932662\pi$
$103$	−3.11581	+	5.39675i	−0.307010	+	0.531757i	0.670697	+	0.741732i	$0.265995\pi$
$104$	−2.09989			−0.205911
$105$		0			0
$106$	13.7014			1.33080
$107$	5.54940	−	9.61185i	0.536481	−	0.929212i	−0.462609	−	0.886562i	$-0.653087\pi$
$107$	5.54940	−	9.61185i	0.536481	−	0.929212i	0.999090	−	0.0426499i	$-0.0135800\pi$
$108$		0			0
$109$	7.15202	+	12.3877i	0.685039	+	1.18652i	0.973424	+	0.229008i	$0.0735483\pi$
$109$	7.15202	+	12.3877i	0.685039	+	1.18652i	−0.288385	+	0.957514i	$0.593118\pi$
$110$	0.582878	−	1.00958i	0.0555753	−	0.0962592i
$111$		0			0
$112$	−10.2980	−	7.73152i	−0.973073	−	0.730560i
$113$	8.68942			0.817432			0.408716	−	0.912662i	$-0.365977\pi$
$113$	8.68942			0.817432			0.408716	+	0.912662i	$0.365977\pi$
$114$		0			0
$115$	0.688225	+	1.19204i	0.0641774	+	0.111158i
$116$	−7.11581	−	12.3249i	−0.660687	−	1.14434i
$117$		0			0
$118$	21.6565			1.99364
$119$	−6.89738	+	2.94222i	−0.632282	+	0.269713i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−3.97252	−	6.88061i	−0.359655	−	0.622942i
$123$		0			0
$124$	−4.38692	+	7.59836i	−0.393957	+	0.682353i
$125$	−6.09880			−0.545494
$126$		0			0
$127$	20.9989			1.86335			0.931676	−	0.363290i	$-0.118346\pi$
$127$	20.9989			1.86335			0.931676	+	0.363290i	$0.118346\pi$
$128$	4.42759	−	7.66881i	0.391347	−	0.677833i
$129$		0			0
$130$	−1.04994	−	1.81856i	−0.0920862	−	0.159498i
$131$	−6.85071	+	11.8658i	−0.598549	+	1.03672i	0.394486	+	0.918902i	$0.370923\pi$
$131$	−6.85071	+	11.8658i	−0.598549	+	1.03672i	−0.993035	+	0.117816i	$0.962411\pi$
$132$		0			0
$133$	−11.7706	−	8.83705i	−1.02064	−	0.766270i
$134$	2.93959			0.253942
$135$		0			0
$136$	−1.65202	−	2.86138i	−0.141659	−	0.245361i
$137$	3.63228	+	6.29129i	0.310327	+	0.537501i	0.978433	−	0.206564i	$-0.0662282\pi$
$137$	3.63228	+	6.29129i	0.310327	+	0.537501i	−0.668106	+	0.744066i	$0.732895\pi$
$138$		0			0
$139$	−2.60262			−0.220751			−0.110376	−	0.993890i	$-0.535205\pi$
$139$	−2.60262			−0.220751			−0.110376	+	0.993890i	$0.535205\pi$
$140$	0.275568	−	2.27773i	0.0232898	−	0.192503i
$141$		0			0
$142$	−3.93632	+	6.81790i	−0.330328	+	0.572146i
$143$	0.900654	+	1.55998i	0.0753165	+	0.130452i
$144$		0			0
$145$	−3.31450	+	5.74089i	−0.275255	+	0.476755i
$146$	29.3359			2.42786
$147$		0			0
$148$	8.27656			0.680329
$149$	−0.500000	+	0.866025i	−0.0409616	+	0.0709476i	−0.885779	−	0.464107i	$-0.846375\pi$
$149$	−0.500000	+	0.866025i	−0.0409616	+	0.0709476i	0.844818	+	0.535054i	$0.179709\pi$
$150$		0			0
$151$	−0.867720	−	1.50294i	−0.0706140	−	0.122307i	0.828557	−	0.559905i	$-0.189163\pi$
$151$	−0.867720	−	1.50294i	−0.0706140	−	0.122307i	−0.899171	+	0.437598i	$0.855829\pi$
$152$	3.24263	−	5.61641i	0.263012	−	0.455551i
$153$		0			0
$154$	−0.582878	+	4.81782i	−0.0469697	+	0.388231i
$155$	4.08680			0.328260
$156$		0			0
$157$	3.96980	+	6.87589i	0.316824	+	0.548756i	0.979824	−	0.199864i	$-0.0640502\pi$
$157$	3.96980	+	6.87589i	0.316824	+	0.548756i	−0.662999	+	0.748620i	$0.730717\pi$
$158$	4.36718	+	7.56417i	0.347434	+	0.601773i
$159$		0			0
$160$	4.19215			0.331418
$161$	−4.58234	−	3.44031i	−0.361139	−	0.271134i
$162$		0			0
$163$	8.00273	−	13.8611i	0.626822	−	1.08569i	−0.361363	−	0.932425i	$-0.617689\pi$
$163$	8.00273	−	13.8611i	0.626822	−	1.08569i	0.988185	−	0.153263i	$-0.0489781\pi$
$164$	5.14101	+	8.90449i	0.401446	+	0.695324i
$165$		0			0
$166$	8.46652	−	14.6644i	0.657130	−	1.13818i
$167$	−1.15921			−0.0897026			−0.0448513	−	0.998994i	$-0.514281\pi$
$167$	−1.15921			−0.0897026			−0.0448513	+	0.998994i	$0.514281\pi$
$168$		0			0
$169$	−9.75529			−0.750407
$170$	1.65202	−	2.86138i	0.126704	−	0.219458i
$171$		0			0
$172$	3.32051	+	5.75128i	0.253186	+	0.438531i
$173$	−0.496728	+	0.860358i	−0.0377655	+	0.0654118i	−0.884290	−	0.466937i	$-0.845357\pi$
$173$	−0.496728	+	0.860358i	−0.0377655	+	0.0654118i	0.846525	+	0.532349i	$0.178691\pi$
$174$		0			0
$175$	11.1850	−	4.77117i	0.845503	−	0.360667i
$176$	−4.86718			−0.366877
$177$		0			0
$178$	−0.334243	−	0.578926i	−0.0250526	−	0.0433924i
$179$	−9.83097	−	17.0277i	−0.734801	−	1.27271i	−0.954810	−	0.297215i	$-0.903942\pi$
$179$	−9.83097	−	17.0277i	−0.734801	−	1.27271i	0.220009	−	0.975498i	$-0.429391\pi$
$180$		0			0
$181$	−23.8726			−1.77444			−0.887220	−	0.461347i	$-0.847366\pi$
$181$	−23.8726			−1.77444			−0.887220	+	0.461347i	$0.847366\pi$
$182$	6.99073	+	5.24847i	0.518187	+	0.389042i
$183$		0			0
$184$	1.26237	−	2.18649i	0.0930634	−	0.161190i
$185$	−1.92759	−	3.33868i	−0.141719	−	0.245465i
$186$		0			0
$187$	−1.41712	+	2.45453i	−0.103630	+	0.179493i
$188$	3.86718			0.282043
$189$		0			0
$190$	6.48527			0.470491
$191$	−5.56587	+	9.64037i	−0.402732	+	0.697553i	−0.994055	−	0.108883i	$-0.965273\pi$
$191$	−5.56587	+	9.64037i	−0.402732	+	0.697553i	0.591322	+	0.806435i	$0.298606\pi$
$192$		0			0
$193$	−1.80731	−	3.13035i	−0.130093	−	0.225328i	0.793619	−	0.608415i	$-0.208194\pi$
$193$	−1.80731	−	3.13035i	−0.130093	−	0.225328i	−0.923712	+	0.383087i	$0.874861\pi$
$194$	−2.38092	+	4.12387i	−0.170940	+	0.296076i
$195$		0			0
$196$	2.66521	+	9.17174i	0.190372	+	0.655124i
$197$	−2.41831			−0.172298			−0.0861489	−	0.996282i	$-0.527456\pi$
$197$	−2.41831			−0.172298			−0.0861489	+	0.996282i	$0.527456\pi$
$198$		0			0
$199$	9.24809	+	16.0182i	0.655580	+	1.13550i	0.981748	+	0.190186i	$0.0609091\pi$
$199$	9.24809	+	16.0182i	0.655580	+	1.13550i	−0.326168	+	0.945312i	$0.605758\pi$
$200$	2.67895	+	4.64008i	0.189431	+	0.328103i
$201$		0			0
$202$	−18.1592			−1.27768
$203$	3.31450	−	27.3963i	0.232633	−	1.92284i
$204$		0			0
$205$	2.39465	−	4.14766i	0.167250	−	0.289685i
$206$	5.71516	+	9.89894i	0.398194	+	0.689692i
$207$		0			0
$208$	−4.38364	+	7.59270i	−0.303951	+	0.526459i
$209$	−5.56314			−0.384810
$210$		0			0
$211$	−7.85517			−0.540773			−0.270386	−	0.962752i	$-0.587151\pi$
$211$	−7.85517			−0.540773			−0.270386	+	0.962752i	$0.587151\pi$
$212$	5.09607	−	8.82666i	0.350000	−	0.606217i
$213$		0			0
$214$	−10.1790	−	17.6305i	−0.695819	−	1.20519i
$215$	1.54667	−	2.67891i	0.105482	−	0.182700i
$216$		0			0
$217$	−15.6487	+	6.67529i	−1.06231	+	0.453148i
$218$	26.2371			1.77700
$219$		0			0
$220$	−0.433589	−	0.750998i	−0.0292326	−	0.0506323i
$221$	2.55267	+	4.42136i	0.171711	+	0.297413i
$222$		0			0
$223$	20.3370			1.36186			0.680932	−	0.732346i	$-0.261575\pi$
$223$	20.3370			1.36186			0.680932	+	0.732346i	$0.261575\pi$
$224$	−16.0521	+	6.84736i	−1.07253	+	0.457509i
$225$		0			0
$226$	7.96925	−	13.8032i	0.530107	−	0.918172i
$227$	3.60981	+	6.25238i	0.239592	+	0.414985i	0.960597	−	0.277944i	$-0.0896531\pi$
$227$	3.60981	+	6.25238i	0.239592	+	0.414985i	−0.721006	+	0.692929i	$0.756320\pi$
$228$		0			0
$229$	−6.03566	+	10.4541i	−0.398848	+	0.690825i	−0.993584	−	0.113096i	$-0.963923\pi$
$229$	−6.03566	+	10.4541i	−0.398848	+	0.690825i	0.594736	+	0.803921i	$0.297257\pi$
$230$	2.52475			0.166477
$231$		0			0
$232$	12.1592			0.798291
$233$	−3.77110	+	6.53174i	−0.247053	+	0.427909i	−0.962707	−	0.270547i	$-0.912796\pi$
$233$	−3.77110	+	6.53174i	−0.247053	+	0.427909i	0.715654	+	0.698455i	$0.246129\pi$
$234$		0			0
$235$	−0.900654	−	1.55998i	−0.0587522	−	0.101762i
$236$	8.05486	−	13.9514i	0.524327	−	0.908161i
$237$		0			0
$238$	−1.65202	+	13.6549i	−0.107084	+	0.885114i
$239$	9.84625			0.636901			0.318450	−	0.947940i	$-0.396838\pi$
$239$	9.84625			0.636901			0.318450	+	0.947940i	$0.396838\pi$
$240$		0			0
$241$	0.837515	+	1.45062i	0.0539491	+	0.0934426i	0.891739	−	0.452551i	$-0.149486\pi$
$241$	0.837515	+	1.45062i	0.0539491	+	0.0934426i	−0.837790	+	0.545993i	$0.816152\pi$
$242$	0.917122	+	1.58850i	0.0589548	+	0.102113i
$243$		0			0
$244$	−5.91013			−0.378357
$245$	3.07906	−	3.21119i	0.196714	−	0.205156i
$246$		0			0
$247$	−5.01047	+	8.67838i	−0.318808	+	0.552192i
$248$	−3.74809	−	6.49189i	−0.238004	−	0.412235i
$249$		0			0
$250$	−5.59334	+	9.68796i	−0.353754	+	0.612720i
$251$	−19.7738			−1.24811			−0.624057	−	0.781379i	$-0.714517\pi$
$251$	−19.7738			−1.24811			−0.624057	+	0.781379i	$0.714517\pi$
$252$		0			0
$253$	−2.16576			−0.136160
$254$	19.2586	−	33.3568i	1.20839	−	2.09299i
$255$		0			0
$256$	−10.4857	−	18.1618i	−0.655358	−	1.13511i
$257$	1.35998	−	2.35556i	0.0848335	−	0.146936i	−0.820487	−	0.571665i	$-0.806298\pi$
$257$	1.35998	−	2.35556i	0.0848335	−	0.146936i	0.905320	+	0.424730i	$0.139631\pi$
$258$		0			0
$259$	12.8342	+	9.63564i	0.797481	+	0.598730i
$260$	−1.56205			−0.0968745
$261$		0			0
$262$	12.5659	+	21.7647i	0.776322	+	1.34463i
$263$	6.34744	+	10.9941i	0.391400	+	0.677924i	0.992634	−	0.121148i	$-0.0386576\pi$
$263$	6.34744	+	10.9941i	0.391400	+	0.677924i	−0.601235	+	0.799073i	$0.705324\pi$
$264$		0			0
$265$	−4.74744			−0.291633
$266$	−24.8327	+	10.5929i	−1.52259	+	0.649492i
$267$		0			0
$268$	1.09334	−	1.89373i	0.0667866	−	0.115678i
$269$	−3.54667	−	6.14302i	−0.216244	−	0.374546i	0.737412	−	0.675443i	$-0.236047\pi$
$269$	−3.54667	−	6.14302i	−0.216244	−	0.374546i	−0.953657	+	0.300896i	$0.902714\pi$
$270$		0			0
$271$	9.10808	−	15.7757i	0.553276	−	0.958303i	−0.444759	−	0.895650i	$-0.646711\pi$
$271$	9.10808	−	15.7757i	0.553276	−	0.958303i	0.998035	−	0.0626524i	$-0.0199559\pi$
$272$	−13.7948			−0.836430
$273$		0			0
$274$	13.3250			0.804991
$275$	2.29804	−	3.98032i	0.138577	−	0.240022i
$276$		0			0
$277$	−6.92432	−	11.9933i	−0.416042	−	0.720606i	0.579495	−	0.814976i	$-0.303250\pi$
$277$	−6.92432	−	11.9933i	−0.416042	−	0.720606i	−0.995537	+	0.0943700i	$0.969916\pi$
$278$	−2.38692	+	4.13426i	−0.143158	+	0.247956i
$279$		0			0
$280$	1.56760	+	1.17692i	0.0936822	+	0.0703344i
$281$	−21.0329			−1.25472			−0.627360	−	0.778730i	$-0.715864\pi$
$281$	−21.0329			−1.25472			−0.627360	+	0.778730i	$0.715864\pi$
$282$		0			0
$283$	−0.176223	−	0.305226i	−0.0104753	−	0.0181438i	0.860740	−	0.509044i	$-0.170001\pi$
$283$	−0.176223	−	0.305226i	−0.0104753	−	0.0181438i	−0.871216	+	0.490901i	$0.836668\pi$
$284$	2.92813	+	5.07167i	0.173753	+	0.300948i
$285$		0			0
$286$	3.30404			0.195372
$287$	−2.39465	+	19.7932i	−0.141352	+	1.16835i
$288$		0			0
$289$	4.48353	−	7.76571i	0.263737	−	0.456806i
$290$	6.07961	+	10.5302i	0.357007	+	0.618354i
$291$		0			0
$292$	10.9111	−	18.8986i	0.638525	−	1.10596i
$293$	3.46325			0.202325			0.101163	−	0.994870i	$-0.467744\pi$
$293$	3.46325			0.202325			0.101163	+	0.994870i	$0.467744\pi$
$294$		0			0
$295$	−7.50381			−0.436889
$296$	−3.53566	+	6.12395i	−0.205506	+	0.355947i
$297$		0			0
$298$	0.917122	+	1.58850i	0.0531274	+	0.0920194i
$299$	−1.95060	+	3.37854i	−0.112806	+	0.195386i
$300$		0			0
$301$	−1.54667	+	12.7841i	−0.0891487	+	0.736864i
$302$	−3.18322			−0.183174
$303$		0			0
$304$	−13.5384	−	23.4492i	−0.776480	−	1.34490i
$305$	1.37645	+	2.38408i	0.0788154	+	0.136512i
$306$		0			0
$307$	−6.51473			−0.371815			−0.185908	−	0.982567i	$-0.559523\pi$
$307$	−6.51473			−0.371815			−0.185908	+	0.982567i	$0.559523\pi$
$308$	2.88692	+	2.16743i	0.164497	+	0.123501i
$309$		0			0
$310$	3.74809	−	6.49189i	0.212877	−	0.368714i
$311$	5.81505	+	10.0720i	0.329741	+	0.571128i	0.982460	−	0.186472i	$-0.0597052\pi$
$311$	5.81505	+	10.0720i	0.329741	+	0.571128i	−0.652719	+	0.757600i	$0.726372\pi$
$312$		0			0
$313$	13.5489	−	23.4673i	0.765827	−	1.32645i	−0.173982	−	0.984749i	$-0.555663\pi$
$313$	13.5489	−	23.4673i	0.765827	−	1.32645i	0.939808	−	0.341702i	$-0.111003\pi$
$314$	14.5631			0.821845
$315$		0			0
$316$	6.49727			0.365500
$317$	1.93086	−	3.34435i	0.108448	−	0.187837i	−0.806694	−	0.590970i	$-0.798745\pi$
$317$	1.93086	−	3.34435i	0.108448	−	0.187837i	0.915142	+	0.403132i	$0.132079\pi$
$318$		0			0
$319$	−5.21516	−	9.03292i	−0.291993	−	0.505746i
$320$	0.751365	−	1.30140i	0.0420026	−	0.0727506i
$321$		0			0
$322$	−9.66749	+	4.12387i	−0.538748	+	0.229814i
$323$	−15.7673			−0.877315
$324$		0			0
$325$	−4.13947	−	7.16978i	−0.229617	−	0.397708i
$326$	−14.6790	−	25.4247i	−0.812992	−	1.40814i
$327$		0			0
$328$	−8.78475			−0.485057
$329$	5.99673	+	4.50220i	0.330610	+	0.248214i
$330$		0			0
$331$	−3.07514	+	5.32630i	−0.169025	+	0.292760i	−0.938077	−	0.346426i	$-0.887395\pi$
$331$	−3.07514	+	5.32630i	−0.169025	+	0.292760i	0.769052	+	0.639186i	$0.220729\pi$
$332$	−6.29804	−	10.9085i	−0.345650	−	0.598683i
$333$		0			0
$334$	−1.06314	+	1.84141i	−0.0581724	+	0.100758i
$335$	−1.01855			−0.0556491
$336$		0			0
$337$	−11.7607			−0.640649			−0.320324	−	0.947308i	$-0.603792\pi$
$337$	−11.7607			−0.640649			−0.320324	+	0.947308i	$0.603792\pi$
$338$	−8.94678	+	15.4963i	−0.486641	+	0.842887i
$339$		0			0
$340$	−1.22890	−	2.12851i	−0.0666462	−	0.115435i
$341$	−3.21516	+	5.56882i	−0.174111	+	0.301568i
$342$		0			0
$343$	−6.54494	+	17.3252i	−0.353393	+	0.935475i
$344$	−5.67395			−0.305919
$345$		0			0
$346$	0.911120	+	1.57811i	0.0489821	+	0.0848395i
$347$	−0.420393	−	0.728143i	−0.0225679	−	0.0390888i	0.854521	−	0.519417i	$-0.173851\pi$
$347$	−0.420393	−	0.728143i	−0.0225679	−	0.0390888i	−0.877089	+	0.480328i	$0.840518\pi$
$348$		0			0
$349$	9.13174			0.488811			0.244405	−	0.969673i	$-0.421407\pi$
$349$	9.13174			0.488811			0.244405	+	0.969673i	$0.421407\pi$
$350$	2.67895	−	22.1431i	0.143196	−	1.18360i
$351$		0			0
$352$	−3.29804	+	5.71237i	−0.175786	+	0.304470i
$353$	11.3639	+	19.6829i	0.604840	+	1.04761i	0.992077	+	0.125633i	$0.0400961\pi$
$353$	11.3639	+	19.6829i	0.604840	+	1.04761i	−0.387237	+	0.921980i	$0.626571\pi$
$354$		0			0
$355$	1.36391	−	2.36235i	0.0723886	−	0.125381i
$356$	−0.497270			−0.0263553
$357$		0			0
$358$	−36.0648			−1.90608
$359$	−13.1093	+	22.7059i	−0.691881	+	1.19837i	0.279340	+	0.960192i	$0.409884\pi$
$359$	−13.1093	+	22.7059i	−0.691881	+	1.19837i	−0.971221	+	0.238180i	$0.923449\pi$
$360$		0			0
$361$	−5.97426	−	10.3477i	−0.314435	−	0.544617i
$362$	−21.8941	+	37.9217i	−1.15073	+	1.99312i
$363$		0			0
$364$	5.98126	−	2.55143i	0.313503	−	0.133731i
$365$	−10.1647			−0.532043
$366$		0			0
$367$	1.91112	+	3.31016i	0.0997597	+	0.172789i	0.911585	−	0.411111i	$-0.134859\pi$
$367$	1.91112	+	3.31016i	0.0997597	+	0.172789i	−0.811825	+	0.583900i	$0.801526\pi$
$368$	−5.27056	−	9.12888i	−0.274747	−	0.475876i
$369$		0			0
$370$	−7.07133			−0.367621
$371$	18.1784	−	7.75437i	0.943776	−	0.402587i
$372$		0			0
$373$	−7.55387	+	13.0837i	−0.391124	+	0.677447i	−0.992598	−	0.121445i	$-0.961247\pi$
$373$	−7.55387	+	13.0837i	−0.391124	+	0.677447i	0.601474	+	0.798893i	$0.294580\pi$
$374$	2.59935	+	4.50220i	0.134409	+	0.232803i
$375$		0			0
$376$	−1.65202	+	2.86138i	−0.0851964	+	0.147564i
$377$	−18.7882			−0.967643
$378$		0			0
$379$	−11.3765			−0.584369			−0.292185	−	0.956362i	$-0.594382\pi$
$379$	−11.3765			−0.584369			−0.292185	+	0.956362i	$0.594382\pi$
$380$	2.41211	−	4.17791i	0.123739	−	0.214322i
$381$		0			0
$382$	10.2092	+	17.6828i	0.522346	+	0.904730i
$383$	4.44286	−	7.69526i	0.227020	−	0.393210i	−0.729904	−	0.683550i	$-0.760435\pi$
$383$	4.44286	−	7.69526i	0.227020	−	0.393210i	0.956923	+	0.290340i	$0.0937685\pi$
$384$		0			0
$385$	0.201963	−	1.66934i	0.0102930	−	0.0850774i
$386$	−6.63009			−0.337463
$387$		0			0
$388$	1.77110	+	3.06764i	0.0899142	+	0.155736i
$389$	−9.94951	−	17.2331i	−0.504460	−	0.873751i	−0.999987	−	0.00515807i	$-0.998358\pi$
$389$	−9.94951	−	17.2331i	−0.504460	−	0.873751i	0.495526	−	0.868593i	$-0.334975\pi$
$390$		0			0
$391$	−6.13828			−0.310426
$392$	−7.92486	−	1.94604i	−0.400266	−	0.0982901i
$393$		0			0
$394$	−2.21789	+	3.84149i	−0.111736	+	0.193532i
$395$	−1.51320	−	2.62093i	−0.0761371	−	0.131873i
$396$		0			0
$397$	17.4303	−	30.1902i	0.874803	−	1.51520i	0.0178296	−	0.999841i	$-0.494324\pi$
$397$	17.4303	−	30.1902i	0.874803	−	1.51520i	0.856973	−	0.515361i	$-0.172342\pi$
$398$	33.9265			1.70058
$399$		0			0
$400$	22.3699			1.11850
$401$	5.69815	−	9.86948i	0.284552	−	0.492858i	−0.687948	−	0.725760i	$-0.741489\pi$
$401$	5.69815	−	9.86948i	0.284552	−	0.492858i	0.972500	+	0.232901i	$0.0748218\pi$
$402$		0			0
$403$	5.79149	+	10.0312i	0.288495	+	0.499688i
$404$	−6.75409	+	11.6984i	−0.336029	+	0.582019i
$405$		0			0
$406$	−40.4792	−	30.3908i	−2.00895	−	1.50827i
$407$	6.06587			0.300674
$408$		0			0
$409$	2.04394	+	3.54021i	0.101066	+	0.175052i	0.912124	−	0.409914i	$-0.134441\pi$
$409$	2.04394	+	3.54021i	0.101066	+	0.175052i	−0.811058	+	0.584966i	$0.801108\pi$
$410$	−4.39238	−	7.60782i	−0.216924	−	0.375723i
$411$		0			0
$412$	8.50273			0.418899
$413$	28.7328	−	12.2566i	1.41385	−	0.603106i
$414$		0			0
$415$	−2.93359	+	5.08112i	−0.144004	+	0.249423i
$416$	5.94078	+	10.2897i	0.291271	+	0.504496i
$417$		0			0
$418$	−5.10208	+	8.83705i	−0.249551	+	0.432234i
$419$	−32.8002			−1.60240			−0.801198	−	0.598399i	$-0.795804\pi$
$419$	−32.8002			−1.60240			−0.801198	+	0.598399i	$0.795804\pi$
$420$		0			0
$421$	−8.52128			−0.415302			−0.207651	−	0.978203i	$-0.566582\pi$
$421$	−8.52128			−0.415302			−0.207651	+	0.978203i	$0.566582\pi$
$422$	−7.20415	+	12.4780i	−0.350693	+	0.607417i
$423$		0			0
$424$	4.35398	+	7.54132i	0.211448	+	0.366239i
$425$	6.51320	−	11.2812i	0.315936	−	0.547218i
$426$		0			0
$427$	−9.16467	−	6.88061i	−0.443510	−	0.332976i
$428$	−15.1437			−0.732000
$429$		0			0
$430$	−2.83697	−	4.91378i	−0.136811	−	0.236964i
$431$	−8.36718	−	14.4924i	−0.403033	−	0.698073i	0.591058	−	0.806629i	$-0.298711\pi$
$431$	−8.36718	−	14.4924i	−0.403033	−	0.698073i	−0.994090	+	0.108556i	$0.965377\pi$
$432$		0			0
$433$	−25.8661			−1.24305			−0.621523	−	0.783396i	$-0.713486\pi$
$433$	−25.8661			−1.24305			−0.621523	+	0.783396i	$0.713486\pi$
$434$	−3.74809	+	30.9801i	−0.179914	+	1.48709i
$435$		0			0
$436$	9.75856	−	16.9023i	0.467350	−	0.809474i
$437$	−6.02420	−	10.4342i	−0.288177	−	0.499137i
$438$		0			0
$439$	4.78430	−	8.28665i	0.228342	−	0.395500i	−0.728975	−	0.684541i	$-0.760003\pi$
$439$	4.78430	−	8.28665i	0.228342	−	0.395500i	0.957317	+	0.289040i	$0.0933362\pi$
$440$	0.740899			0.0353210
$441$		0			0
$442$	9.36445			0.445421
$443$	9.51647	−	16.4830i	0.452141	−	0.783131i	−0.546378	−	0.837539i	$-0.683994\pi$
$443$	9.51647	−	16.4830i	0.452141	−	0.783131i	0.998519	+	0.0544076i	$0.0173270\pi$
$444$		0			0
$445$	0.115813	+	0.200594i	0.00549005	+	0.00950905i
$446$	18.6515	−	32.3053i	0.883173	−	1.52970i
$447$		0			0
$448$	−0.751365	+	6.21046i	−0.0354986	+	0.293416i
$449$	−33.3424			−1.57353			−0.786763	−	0.617255i	$-0.788245\pi$
$449$	−33.3424			−1.57353			−0.786763	+	0.617255i	$0.788245\pi$
$450$		0			0
$451$	3.76783	+	6.52608i	0.177420	+	0.307301i
$452$	−5.92813	−	10.2678i	−0.278836	−	0.482958i
$453$		0			0
$454$	13.2425			0.621503
$455$	−2.42224	−	1.81856i	−0.113556	−	0.0852552i
$456$		0			0
$457$	−5.98026	+	10.3581i	−0.279745	+	0.484532i	−0.971321	−	0.237771i	$-0.923583\pi$
$457$	−5.98026	+	10.3581i	−0.279745	+	0.484532i	0.691576	+	0.722303i	$0.256917\pi$
$458$	11.0709	+	19.1753i	0.517308	+	0.896004i
$459$		0			0
$460$	0.939048	−	1.62648i	0.0437833	−	0.0758350i
$461$	−12.4896			−0.581701			−0.290850	−	0.956769i	$-0.593938\pi$
$461$	−12.4896			−0.581701			−0.290850	+	0.956769i	$0.593938\pi$
$462$		0			0
$463$	12.3095			0.572071			0.286035	−	0.958219i	$-0.407662\pi$
$463$	12.3095			0.572071			0.286035	+	0.958219i	$0.407662\pi$
$464$	25.3831	−	43.9648i	1.17838	−	2.04102i
$465$		0			0
$466$	6.91712	+	11.9808i	0.320429	+	0.555000i
$467$	16.3804	−	28.3716i	0.757993	−	1.31288i	−0.185879	−	0.982573i	$-0.559513\pi$
$467$	16.3804	−	28.3716i	0.757993	−	1.31288i	0.943872	−	0.330310i	$-0.107153\pi$
$468$		0			0
$469$	3.90011	−	1.66367i	0.180090	−	0.0768213i
$470$	−3.30404			−0.152404
$471$		0			0
$472$	6.88191	+	11.9198i	0.316766	+	0.548654i
$473$	2.43359	+	4.21510i	0.111897	+	0.193810i
$474$		0			0
$475$	25.5686			1.17317
$476$	8.18222	+	6.14302i	0.375032	+	0.281565i
$477$		0			0
$478$	9.03020	−	15.6408i	0.413032	−	0.715392i
$479$	12.9890	+	22.4976i	0.593482	+	1.02794i	0.993759	+	0.111547i	$0.0355806\pi$
$479$	12.9890	+	22.4976i	0.593482	+	1.02794i	−0.400277	+	0.916394i	$0.631086\pi$
$480$		0			0
$481$	5.46325	−	9.46263i	0.249103	−	0.431459i
$482$	3.07241			0.139945
$483$		0			0
$484$	1.36445			0.0620204
$485$	0.824970	−	1.42889i	0.0374600	−	0.0648825i
$486$		0			0
$487$	−7.26783	−	12.5883i	−0.329337	−	0.570428i	0.653044	−	0.757320i	$-0.273492\pi$
$487$	−7.26783	−	12.5883i	−0.329337	−	0.570428i	−0.982380	+	0.186892i	$0.940159\pi$
$488$	2.52475	−	4.37299i	0.114290	−	0.197956i
$489$		0			0
$490$	−2.27711	−	7.83615i	−0.102869	−	0.354001i
$491$	39.3952			1.77788			0.888941	−	0.458023i	$-0.151442\pi$
$491$	39.3952			1.77788			0.888941	+	0.458023i	$0.151442\pi$
$492$		0			0
$493$	−14.7810	−	25.6015i	−0.665704	−	1.15303i
$494$	9.19041	+	15.9183i	0.413496	+	0.716196i
$495$		0			0
$496$	−31.2975			−1.40530
$497$	−1.36391	+	11.2735i	−0.0611795	+	0.505683i
$498$		0			0
$499$	13.1153	−	22.7163i	0.587120	−	1.01692i	−0.407487	−	0.913211i	$-0.633595\pi$
$499$	13.1153	−	22.7163i	0.587120	−	1.01692i	0.994607	−	0.103711i	$-0.0330717\pi$
$500$	4.16075	+	7.20663i	0.186074	+	0.322290i
$501$		0			0
$502$	−18.1350	+	31.4108i	−0.809405	+	1.40193i
$503$	−3.94613			−0.175949			−0.0879747	−	0.996123i	$-0.528039\pi$
$503$	−3.94613			−0.175949			−0.0879747	+	0.996123i	$0.528039\pi$
$504$		0			0
$505$	6.29204			0.279992
$506$	−1.98626	+	3.44031i	−0.0883001	+	0.152940i
$507$		0			0
$508$	−14.3260	−	24.8133i	−0.635612	−	1.10091i
$509$	8.45279	−	14.6407i	0.374663	−	0.648936i	−0.615613	−	0.788048i	$-0.711092\pi$
$509$	8.45279	−	14.6407i	0.374663	−	0.648936i	0.990277	+	0.139113i	$0.0444250\pi$
$510$		0			0
$511$	38.9215	−	16.6028i	1.72179	−	0.734463i
$512$	−20.7564			−0.917311
$513$		0			0
$514$	−2.49454	−	4.32067i	−0.110029	−	0.190577i
$515$	−1.98026	−	3.42991i	−0.0872607	−	0.151140i
$516$		0			0
$517$	2.83424			0.124650
$518$	27.0768	−	11.5502i	1.18969	−	0.507485i
$519$		0			0
$520$	0.667294	−	1.15579i	0.0292628	−	0.0506846i
$521$	0.778840	+	1.34899i	0.0341216	+	0.0591004i	0.882582	−	0.470159i	$-0.155803\pi$
$521$	0.778840	+	1.34899i	0.0341216	+	0.0591004i	−0.848460	+	0.529259i	$0.822470\pi$
$522$		0			0
$523$	6.25136	−	10.8277i	0.273353	−	0.473461i	−0.696365	−	0.717688i	$-0.745201\pi$
$523$	6.25136	−	10.8277i	0.273353	−	0.473461i	0.969718	+	0.244226i	$0.0785339\pi$
$524$	18.6949			0.816689
$525$		0			0
$526$	23.2855			1.01530
$527$	−9.11254	+	15.7834i	−0.396949	+	0.687535i
$528$		0			0
$529$	9.15475	+	15.8565i	0.398033	+	0.689413i
$530$	−4.35398	+	7.54132i	−0.189125	+	0.327574i
$531$		0			0
$532$	−2.41211	+	19.9375i	−0.104578	+	0.864400i
$533$	13.5741			0.587958
$534$		0			0
$535$	3.52693	+	6.10883i	0.152483	+	0.264108i
$536$	0.934131	+	1.61796i	0.0403483	+	0.0698853i
$537$		0			0
$538$	−13.0109			−0.560941
$539$	1.95333	+	6.72194i	0.0841358	+	0.289535i
$540$		0			0
$541$	8.28103	−	14.3432i	0.356029	−	0.616661i	−0.631264	−	0.775568i	$-0.717464\pi$
$541$	8.28103	−	14.3432i	0.356029	−	0.616661i	0.987294	+	0.158907i	$0.0507970\pi$
$542$	−16.7064	−	28.9364i	−0.717603	−	1.24292i
$543$		0			0
$544$	−9.34744	+	16.1902i	−0.400768	+	0.694151i
$545$	−9.09096			−0.389414
$546$		0			0
$547$	−6.64448			−0.284097			−0.142049	−	0.989860i	$-0.545369\pi$
$547$	−6.64448			−0.284097			−0.142049	+	0.989860i	$0.545369\pi$
$548$	4.95606	−	8.58414i	0.211712	−	0.366696i
$549$		0			0
$550$	−4.21516	−	7.30087i	−0.179735	−	0.311310i
$551$	29.0127	−	50.2514i	1.23598	−	2.14078i
$552$		0			0
$553$	10.0751	+	7.56417i	0.428439	+	0.321661i
$554$	−25.4018			−1.07922
$555$		0			0
$556$	1.77557	+	3.07537i	0.0753009	+	0.130425i
$557$	6.55595	+	11.3552i	0.277784	+	0.481137i	0.970834	−	0.239753i	$-0.0770666\pi$
$557$	6.55595	+	11.3552i	0.277784	+	0.481137i	−0.693049	+	0.720890i	$0.743733\pi$
$558$		0			0
$559$	8.76729			0.370817
$560$	7.52793	−	3.21119i	0.318113	−	0.135698i
$561$		0			0
$562$	−19.2898	+	33.4108i	−0.813689	+	1.40935i
$563$	15.2443	+	26.4039i	0.642470	+	1.11279i	0.984880	+	0.173240i	$0.0554235\pi$
$563$	15.2443	+	26.4039i	0.642470	+	1.11279i	−0.342410	+	0.939551i	$0.611243\pi$
$564$		0			0
$565$	−2.76129	+	4.78269i	−0.116168	+	0.201209i
$566$	−0.646470			−0.0271732
$567$		0			0
$568$	−5.00347			−0.209941
$569$	−17.6790	+	30.6208i	−0.741140	+	1.28369i	0.210836	+	0.977521i	$0.432381\pi$
$569$	−17.6790	+	30.6208i	−0.741140	+	1.28369i	−0.951976	+	0.306171i	$0.900952\pi$
$570$		0			0
$571$	20.6422	+	35.7533i	0.863849	+	1.49623i	0.868185	+	0.496240i	$0.165287\pi$
$571$	20.6422	+	35.7533i	0.863849	+	1.49623i	−0.00433587	+	0.999991i	$0.501380\pi$
$572$	1.22890	−	2.12851i	0.0513827	−	0.0889975i
$573$		0			0
$574$	29.2453	+	21.9566i	1.22067	+	0.916453i
$575$	9.95398			0.415110
$576$		0			0
$577$	−4.35125	−	7.53659i	−0.181145	−	0.313752i	0.761126	−	0.648604i	$-0.224647\pi$
$577$	−4.35125	−	7.53659i	−0.181145	−	0.313752i	−0.942271	+	0.334852i	$0.891314\pi$
$578$	−8.22389	−	14.2442i	−0.342069	−	0.592480i
$579$		0			0
$580$	9.04494			0.375571
$581$	2.93359	−	24.2478i	0.121706	−	1.00597i
$582$		0			0
$583$	3.73490	−	6.46903i	0.154684	−	0.267920i
$584$	9.32224	+	16.1466i	0.385757	+	0.668151i
$585$		0			0
$586$	3.17622	−	5.50138i	0.131209	−	0.227260i
$587$	23.0539			0.951535			0.475767	−	0.879571i	$-0.342170\pi$
$587$	23.0539			0.951535			0.475767	+	0.879571i	$0.342170\pi$
$588$		0			0
$589$	−35.7727			−1.47399
$590$	−6.88191	+	11.9198i	−0.283324	+	0.490731i
$591$		0			0
$592$	14.7618	+	25.5682i	0.606707	+	1.05085i
$593$	15.0494	−	26.0663i	0.618005	−	1.07042i	−0.371844	−	0.928295i	$-0.621275\pi$
$593$	15.0494	−	26.0663i	0.618005	−	1.07042i	0.989849	−	0.142121i	$-0.0453921\pi$
$594$		0			0
$595$	0.572413	−	4.73131i	0.0234666	−	0.193965i
$596$	1.36445			0.0558900
$597$		0			0
$598$	3.57787	+	6.19706i	0.146310	+	0.253416i
$599$	14.6257	+	25.3325i	0.597591	+	1.03506i	0.993176	+	0.116629i	$0.0372088\pi$
$599$	14.6257	+	25.3325i	0.597591	+	1.03506i	−0.395584	+	0.918430i	$0.629458\pi$
$600$		0			0
$601$	−26.8222			−1.09410			−0.547051	−	0.837099i	$-0.684250\pi$
$601$	−26.8222			−1.09410			−0.547051	+	0.837099i	$0.684250\pi$
$602$	18.8891	+	14.1815i	0.769862	+	0.577994i
$603$		0			0
$604$	−1.18396	+	2.05068i	−0.0481746	+	0.0834409i
$605$	−0.317776	−	0.550404i	−0.0129194	−	0.0223771i
$606$		0			0
$607$	−16.1048	+	27.8943i	−0.653674	+	1.13220i	0.328551	+	0.944486i	$0.393440\pi$
$607$	−16.1048	+	27.8943i	−0.653674	+	1.13220i	−0.982224	+	0.187710i	$0.939893\pi$
$608$	−36.6949			−1.48817
$609$		0			0
$610$	5.04949			0.204448
$611$	2.55267	−	4.42136i	0.103270	−	0.178869i
$612$		0			0
$613$	−22.2975	−	38.6204i	−0.900587	−	1.55986i	−0.826733	−	0.562594i	$-0.809803\pi$
$613$	−22.2975	−	38.6204i	−0.900587	−	1.55986i	−0.0738539	−	0.997269i	$-0.523530\pi$
$614$	−5.97480	+	10.3487i	−0.241123	+	0.417638i
$615$		0			0
$616$	−2.83697	+	1.21017i	−0.114305	+	0.0487591i
$617$	0.531290			0.0213889			0.0106945	−	0.999943i	$-0.496596\pi$
$617$	0.531290			0.0213889			0.0106945	+	0.999943i	$0.496596\pi$
$618$		0			0
$619$	−20.8726	−	36.1525i	−0.838942	−	1.45309i	−0.890780	−	0.454435i	$-0.849841\pi$
$619$	−20.8726	−	36.1525i	−0.838942	−	1.45309i	0.0518379	−	0.998656i	$-0.483492\pi$
$620$	−2.78811	−	4.82915i	−0.111973	−	0.193943i
$621$		0			0
$622$	21.3324			0.855352
$623$	−0.771104	−	0.578926i	−0.0308936	−	0.0231942i
$624$		0			0
$625$	−9.55213	+	16.5448i	−0.382085	+	0.661791i
$626$	−24.8519	−	43.0448i	−0.993282	−	1.72041i
$627$		0			0
$628$	5.41658	−	9.38179i	0.216145	−	0.374374i
$629$	17.1921			0.685496
$630$		0			0
$631$	−0.217238			−0.00864810			−0.00432405	−	0.999991i	$-0.501376\pi$
$631$	−0.217238			−0.00864810			−0.00432405	+	0.999991i	$0.501376\pi$
$632$	−2.77557	+	4.80743i	−0.110406	+	0.191229i
$633$		0			0
$634$	−3.54167	−	6.13434i	−0.140658	−	0.243626i
$635$	−6.67295	+	11.5579i	−0.264808	+	0.458661i
$636$		0			0
$637$	12.2454	+	3.00700i	0.485179	+	0.119142i
$638$	−19.1317			−0.757433
$639$		0			0
$640$	2.81396	+	4.87392i	0.111232	+	0.192659i
$641$	−4.84525	−	8.39222i	−0.191376	−	0.331473i	0.754331	−	0.656495i	$-0.227962\pi$
$641$	−4.84525	−	8.39222i	−0.191376	−	0.331473i	−0.945706	+	0.325022i	$0.894628\pi$
$642$		0			0
$643$	16.4633			0.649247			0.324624	−	0.945843i	$-0.394762\pi$
$643$	16.4633			0.649247			0.324624	+	0.945843i	$0.394762\pi$
$644$	−0.939048	+	7.76176i	−0.0370037	+	0.305856i
$645$		0			0
$646$	−14.4605	+	25.0464i	−0.568942	+	0.985436i
$647$	0.436861	+	0.756665i	0.0171748	+	0.0297476i	0.874485	−	0.485052i	$-0.161199\pi$
$647$	0.436861	+	0.756665i	0.0171748	+	0.0297476i	−0.857310	+	0.514800i	$0.827866\pi$
$648$		0			0
$649$	5.90338	−	10.2250i	0.231728	−	0.401365i
$650$	−15.1856			−0.595628
$651$		0			0
$652$	−21.8386			−0.855266
$653$	−19.9665	+	34.5830i	−0.781350	+	1.35334i	0.149805	+	0.988716i	$0.452135\pi$
$653$	−19.9665	+	34.5830i	−0.781350	+	1.35334i	−0.931155	+	0.364623i	$0.881198\pi$
$654$		0			0
$655$	−4.35398	−	7.54132i	−0.170124	−	0.294664i
$656$	−18.3387	+	31.7636i	−0.716006	+	1.24016i
$657$		0			0
$658$	12.6515	−	5.39675i	0.493206	−	0.210387i
$659$	6.89465			0.268578			0.134289	−	0.990942i	$-0.457125\pi$
$659$	6.89465			0.268578			0.134289	+	0.990942i	$0.457125\pi$
$660$		0			0
$661$	20.0072	+	34.6535i	0.778190	+	1.34786i	0.932984	+	0.359917i	$0.117195\pi$
$661$	20.0072	+	34.6535i	0.778190	+	1.34786i	−0.154795	+	0.987947i	$0.549472\pi$
$662$	5.64056	+	9.76973i	0.219227	+	0.379711i
$663$		0			0
$664$	10.7618			0.417640
$665$	8.60435	−	3.67036i	0.333662	−	0.142331i
$666$		0			0
$667$	11.2948	−	19.5631i	0.437335	−	0.757487i
$668$	0.790843	+	1.36978i	0.0305986	+	0.0529984i
$669$		0			0
$670$	−0.934131	+	1.61796i	−0.0360886	+	0.0625073i
$671$	−4.33151			−0.167216
$672$		0			0
$673$	31.3788			1.20957			0.604783	−	0.796391i	$-0.293260\pi$
$673$	31.3788			1.20957			0.604783	+	0.796391i	$0.293260\pi$
$674$	−10.7860	+	18.6820i	−0.415463	+	0.719602i
$675$		0			0
$676$	6.65529	+	11.5273i	0.255973	+	0.443358i
$677$	−18.2658	+	31.6372i	−0.702010	+	1.21592i	0.265750	+	0.964042i	$0.414380\pi$
$677$	−18.2658	+	31.6372i	−0.702010	+	1.21592i	−0.967760	+	0.251875i	$0.918953\pi$
$678$		0			0
$679$	−0.824970	+	6.81884i	−0.0316594	+	0.261683i
$680$	2.09989			0.0805270
$681$		0			0
$682$	5.89738	+	10.2146i	0.225822	+	0.391136i
$683$	−7.63501	−	13.2242i	−0.292146	−	0.506011i	0.682171	−	0.731192i	$-0.261036\pi$
$683$	−7.63501	−	13.2242i	−0.292146	−	0.506011i	−0.974317	+	0.225181i	$0.927702\pi$
$684$		0			0
$685$	−4.61701			−0.176407
$686$	21.5187	+	26.2860i	0.821586	+	1.00360i
$687$		0			0
$688$	−11.8447	+	20.5156i	−0.451575	+	0.782151i
$689$	−6.72770	−	11.6527i	−0.256305	−	0.443933i
$690$		0			0
$691$	19.1921	−	33.2418i	0.730104	−	1.26458i	−0.226735	−	0.973957i	$-0.572805\pi$
$691$	19.1921	−	33.2418i	0.730104	−	1.26458i	0.956839	−	0.290620i	$-0.0938616\pi$
$692$	1.35552			0.0515291
$693$		0			0
$694$	−1.54221			−0.0585414
$695$	0.827049	−	1.43249i	0.0313718	−	0.0543375i
$696$		0			0
$697$	10.6790	+	18.4965i	0.404494	+	0.700604i
$698$	8.37491	−	14.5058i	0.316995	−	0.549052i
$699$		0			0
$700$	−13.2685	−	9.96166i	−0.501501	−	0.376515i
$701$	−17.9056			−0.676284			−0.338142	−	0.941095i	$-0.609798\pi$
$701$	−17.9056			−0.676284			−0.338142	+	0.941095i	$0.609798\pi$
$702$		0			0
$703$	16.8726	+	29.2243i	0.636364	+	1.10221i
$704$	1.18222	+	2.04767i	0.0445567	+	0.0771745i
$705$		0			0
$706$	41.6883			1.56896
$707$	−24.0928	+	10.2773i	−0.906103	+	0.386517i
$708$		0			0
$709$	−17.1997	+	29.7907i	−0.645948	+	1.11881i	0.338134	+	0.941098i	$0.390204\pi$
$709$	−17.1997	+	29.7907i	−0.645948	+	1.11881i	−0.984082	+	0.177716i	$0.943129\pi$
$710$	−2.50173	−	4.33313i	−0.0938884	−	0.162620i
$711$		0			0
$712$	0.212429	−	0.367938i	0.00796111	−	0.0137890i
$713$	−13.9265			−0.521552
$714$		0			0
$715$	−1.14483			−0.0428140
$716$	−13.4138	+	23.2335i	−0.501299	+	0.868276i
$717$		0			0
$718$	24.0456	+	41.6482i	0.897373	+	1.55430i
$719$	24.7086	−	42.7966i	0.921476	−	1.59604i	0.124343	−	0.992239i	$-0.460318\pi$
$719$	24.7086	−	42.7966i	0.921476	−	1.59604i	0.797133	−	0.603804i	$-0.206349\pi$
$720$		0			0
$721$	13.1850	+	9.89894i	0.491033	+	0.368656i
$722$	−21.9165			−0.815647
$723$		0			0
$724$	16.2865	+	28.2090i	0.605283	+	1.04838i
$725$	23.9693	+	41.5160i	0.890196	+	1.54186i
$726$		0			0
$727$	−19.8201			−0.735086			−0.367543	−	0.930007i	$-0.619801\pi$
$727$	−19.8201			−0.735086			−0.367543	+	0.930007i	$0.619801\pi$
$728$	−0.667294	+	5.51556i	−0.0247316	+	0.204420i
$729$		0			0
$730$	−9.32224	+	16.1466i	−0.345032	+	0.597612i
$731$	6.89738	+	11.9466i	0.255109	+	0.441862i
$732$		0			0
$733$	15.3238	−	26.5416i	0.565997	−	0.980335i	−0.430960	−	0.902371i	$-0.641825\pi$
$733$	15.3238	−	26.5416i	0.565997	−	0.980335i	0.996956	−	0.0779637i	$-0.0248418\pi$
$734$	7.01092			0.258778
$735$		0			0
$736$	−14.2855			−0.526570
$737$	0.801309	−	1.38791i	0.0295166	−	0.0511242i
$738$		0			0
$739$	−8.55094	−	14.8107i	−0.314551	−	0.544819i	0.664791	−	0.747030i	$-0.268521\pi$
$739$	−8.55094	−	14.8107i	−0.314551	−	0.544819i	−0.979342	+	0.202211i	$0.935187\pi$
$740$	−2.63009	+	4.55545i	−0.0966841	+	0.167462i
$741$		0			0
$742$	4.35398	−	35.9881i	0.159840	−	1.32117i
$743$	6.97252			0.255797			0.127899	−	0.991787i	$-0.459177\pi$
$743$	6.97252			0.255797			0.127899	+	0.991787i	$0.459177\pi$
$744$		0			0
$745$	−0.317776	−	0.550404i	−0.0116424	−	0.0201652i
$746$	13.8556	+	23.9987i	0.507291	+	0.878653i
$747$		0			0
$748$	3.86718			0.141398
$749$	−23.4830	−	17.6305i	−0.858050	−	0.644203i
$750$		0			0
$751$	−7.61636	+	13.1919i	−0.277925	+	0.481380i	−0.970869	−	0.239612i	$-0.922980\pi$
$751$	−7.61636	+	13.1919i	−0.277925	+	0.481380i	0.692944	+	0.720991i	$0.256313\pi$
$752$	6.89738	+	11.9466i	0.251522	+	0.435648i
$753$		0			0
$754$	−17.2311	+	29.8451i	−0.627519	+	1.08689i
$755$	1.10296			0.0401409
$756$		0			0
$757$	−14.5326			−0.528196			−0.264098	−	0.964496i	$-0.585074\pi$
$757$	−14.5326			−0.528196			−0.264098	+	0.964496i	$0.585074\pi$
$758$	−10.4336	+	18.0715i	−0.378965	+	0.656387i
$759$		0			0
$760$	2.06086	+	3.56952i	0.0747553	+	0.129480i
$761$	−0.856712	+	1.48387i	−0.0310558	+	0.0537902i	−0.881136	−	0.472864i	$-0.843220\pi$
$761$	−0.856712	+	1.48387i	−0.0310558	+	0.0537902i	0.850080	+	0.526654i	$0.176554\pi$
$762$		0			0
$763$	34.8101	−	14.8490i	1.26021	−	0.537569i
$764$	15.1887			0.549507
$765$		0			0
$766$	−8.14929	−	14.1150i	−0.294446	−	0.509995i
$767$	−10.6338	−	18.4183i	−0.383965	−	0.665047i
$768$		0			0
$769$	−36.5874			−1.31937			−0.659687	−	0.751540i	$-0.729311\pi$
$769$	−36.5874			−1.31937			−0.659687	+	0.751540i	$0.729311\pi$
$770$	−2.46652	−	1.85181i	−0.0888873	−	0.0667345i
$771$		0			0
$772$	−2.46598	+	4.27120i	−0.0887526	+	0.153724i
$773$	13.4106	+	23.2278i	0.482345	+	0.835446i	0.999795	−	0.0202677i	$-0.00645185\pi$
$773$	13.4106	+	23.2278i	0.482345	+	0.835446i	−0.517450	+	0.855714i	$0.673119\pi$
$774$		0			0
$775$	14.7771	−	25.5947i	0.530809	−	0.919389i
$776$	−3.02639			−0.108641
$777$		0			0
$778$	−36.4997			−1.30858
$779$	−20.9610	+	36.3055i	−0.751005	+	1.30078i
$780$		0			0
$781$	2.14602	+	3.71701i	0.0767906	+	0.133005i
$782$	−5.62955	+	9.75067i	−0.201312	+	0.348683i
$783$		0			0
$784$	−23.5801	+	24.5919i	−0.842145	+	0.878283i
$785$	−5.04602			−0.180100
$786$		0			0
$787$	−2.47580	−	4.28821i	−0.0882526	−	0.152858i	0.818520	−	0.574478i	$-0.194795\pi$
$787$	−2.47580	−	4.28821i	−0.0882526	−	0.152858i	−0.906773	+	0.421620i	$0.861462\pi$
$788$	1.64983	+	2.85759i	0.0587728	+	0.101798i
$789$		0			0
$790$	−5.55114			−0.197501
$791$	2.76129	−	22.8236i	0.0981801	−	0.811514i
$792$		0			0
$793$	−3.90120	+	6.75707i	−0.138536	+	0.239951i
$794$	−31.9714	−	55.3762i	−1.13462	−	1.96523i
$795$		0			0
$796$	12.6185	−	21.8560i	0.447252	−	0.774664i
$797$	26.6818			0.945117			0.472559	−	0.881299i	$-0.343330\pi$
$797$	26.6818			0.945117			0.472559	+	0.881299i	$0.343330\pi$
$798$		0			0
$799$	8.03293			0.284185
$800$	15.1580	−	26.2545i	0.535917	−	0.928235i
$801$		0			0
$802$	−10.4518	−	18.1030i	−0.369066	−	0.639240i
$803$	7.99673	−	13.8507i	0.282198	−	0.488782i
$804$		0			0
$805$	3.34972	−	1.42889i	0.118062	−	0.0503617i
$806$	21.2460			0.748359
$807$		0			0
$808$	−5.77056	−	9.99491i	−0.203008	−	0.351620i
$809$	−19.7700	−	34.2427i	−0.695077	−	1.20391i	−0.970155	−	0.242487i	$-0.922037\pi$
$809$	−19.7700	−	34.2427i	−0.695077	−	1.20391i	0.275078	−	0.961422i	$-0.411296\pi$
$810$		0			0
$811$	−33.4543			−1.17474			−0.587370	−	0.809318i	$-0.699837\pi$
$811$	−33.4543			−1.17474			−0.587370	+	0.809318i	$0.699837\pi$
$812$	−34.6339	+	14.7738i	−1.21541	+	0.518459i
$813$		0			0
$814$	5.56314	−	9.63564i	0.194988	−	0.337729i
$815$	5.08615	+	8.80947i	0.178160	+	0.308582i
$816$		0			0
$817$	−13.5384	+	23.4492i	−0.473648	+	0.820383i
$818$	7.49818			0.262168
$819$		0			0
$820$	−6.53476			−0.228204
$821$	28.4310	−	49.2439i	0.992248	−	1.71862i	0.388497	−	0.921450i	$-0.372994\pi$
$821$	28.4310	−	49.2439i	0.992248	−	1.71862i	0.603751	−	0.797173i	$-0.293672\pi$
$822$		0			0
$823$	20.0878	+	34.7931i	0.700217	+	1.21281i	0.968390	+	0.249440i	$0.0802465\pi$
$823$	20.0878	+	34.7931i	0.700217	+	1.21281i	−0.268174	+	0.963371i	$0.586420\pi$
$824$	−3.63228	+	6.29129i	−0.126536	+	0.219168i
$825$		0			0
$826$	6.88191	−	56.8829i	0.239452	−	1.97921i
$827$	5.73544			0.199441			0.0997204	−	0.995015i	$-0.468205\pi$
$827$	5.73544			0.199441			0.0997204	+	0.995015i	$0.468205\pi$
$828$		0			0
$829$	17.7980	+	30.8271i	0.618151	+	1.07067i	0.989823	+	0.142305i	$0.0454515\pi$
$829$	17.7980	+	30.8271i	0.618151	+	1.07067i	−0.371671	+	0.928364i	$0.621215\pi$
$830$	5.38092	+	9.32002i	0.186774	+	0.323503i
$831$		0			0
$832$	4.25910			0.147658
$833$	5.53621	+	19.0516i	0.191818	+	0.660099i
$834$		0			0
$835$	0.368370	−	0.638036i	0.0127480	−	0.0220801i
$836$	3.79531	+	6.57367i	0.131263	+	0.227355i
$837$		0			0
$838$	−30.0818	+	52.1032i	−1.03916	+	1.79988i
$839$	41.7727			1.44216			0.721078	−	0.692854i	$-0.243647\pi$
$839$	41.7727			1.44216			0.721078	+	0.692854i	$0.243647\pi$
$840$		0			0
$841$	79.7915			2.75143
$842$	−7.81505	+	13.5361i	−0.269324	+	0.466483i
$843$		0			0
$844$	5.35899	+	9.28204i	0.184464	+	0.319501i
$845$	3.10000	−	5.36935i	0.106643	−	0.184711i
$846$		0			0
$847$	2.11581	+	1.58850i	0.0727002	+	0.0545815i
$848$	36.3568			1.24850
$849$		0			0
$850$	−11.9468	−	20.6924i	−0.409771	−	0.709745i
$851$	6.56860	+	11.3771i	0.225169	+	0.390004i
$852$		0			0
$853$	49.7871			1.70468			0.852340	−	0.522989i	$-0.175183\pi$
$853$	49.7871			1.70468			0.852340	+	0.522989i	$0.175183\pi$
$854$	−19.3350	+	8.24773i	−0.661630	+	0.282232i
$855$		0			0
$856$	6.46925	−	11.2051i	0.221115	−	0.382982i
$857$	12.7394	+	22.0652i	0.435168	+	0.753734i	0.997309	−	0.0733077i	$-0.0233555\pi$
$857$	12.7394	+	22.0652i	0.435168	+	0.753734i	−0.562141	+	0.827041i	$0.690022\pi$
$858$		0			0
$859$	−8.08080	+	13.9964i	−0.275713	+	0.477549i	−0.970315	−	0.241845i	$-0.922247\pi$
$859$	−8.08080	+	13.9964i	−0.275713	+	0.477549i	0.694602	+	0.719395i	$0.255581\pi$
$860$	−4.22071			−0.143925
$861$		0			0
$862$	−30.6949			−1.04547
$863$	1.44951	−	2.51063i	0.0493420	−	0.0854629i	−0.840300	−	0.542122i	$-0.817621\pi$
$863$	1.44951	−	2.51063i	0.0493420	−	0.0854629i	0.889642	+	0.456660i	$0.150954\pi$
$864$		0			0
$865$	−0.315697	−	0.546802i	−0.0107340	−	0.0185918i
$866$	−23.7224	+	41.0883i	−0.806118	+	1.39624i
$867$		0			0
$868$	18.5638	+	13.9372i	0.630096	+	0.473061i
$869$	4.76183			0.161534
$870$		0			0
$871$	−1.44340	−	2.50005i	−0.0489079	−	0.0847110i
$872$	8.33752	+	14.4410i	0.282344	+	0.489034i
$873$		0			0
$874$	−22.0997			−0.747534
$875$	−1.93805	+	16.0191i	−0.0655182	+	0.541545i
$876$		0			0
$877$	4.20742	−	7.28747i	0.142075	−	0.246080i	−0.786203	−	0.617968i	$-0.787956\pi$
$877$	4.20742	−	7.28747i	0.142075	−	0.246080i	0.928278	+	0.371888i	$0.121289\pi$
$878$	−8.77557	−	15.1997i	−0.296161	−	0.512966i
$879$		0			0
$880$	1.54667	−	2.67891i	0.0521383	−	0.0903062i
$881$	−41.5335			−1.39930			−0.699649	−	0.714486i	$-0.746660\pi$
$881$	−41.5335			−1.39930			−0.699649	+	0.714486i	$0.746660\pi$
$882$		0			0
$883$	−56.4753			−1.90054			−0.950272	−	0.311422i	$-0.899195\pi$
$883$	−56.4753			−1.90054			−0.950272	+	0.311422i	$0.899195\pi$
$884$	3.48299	−	6.03272i	0.117146	−	0.202902i
$885$		0			0
$886$	−17.4555	−	30.2338i	−0.586429	−	1.01573i
$887$	−17.2898	+	29.9467i	−0.580533	+	1.00551i	0.414883	+	0.909875i	$0.363823\pi$
$887$	−17.2898	+	29.9467i	−0.580533	+	1.00551i	−0.995416	+	0.0956383i	$0.969511\pi$
$888$		0			0
$889$	6.67295	−	55.1557i	0.223804	−	1.84986i
$890$	0.424858			0.0142413
$891$		0			0
$892$	−13.8744	−	24.0311i	−0.464548	−	0.804621i
$893$	7.88364	+	13.6549i	0.263816	+	0.456943i
$894$		0			0
$895$	12.4962			0.417701
$896$	−18.7359	−	14.0665i	−0.625922	−	0.469927i
$897$		0			0
$898$	−30.5791	+	52.9645i	−1.02044	+	1.76745i
$899$	−33.5351	−	58.0845i	−1.11846	−	1.93723i
$900$		0			0
$901$	10.5856	−	18.3348i	0.352658	−	0.610821i
$902$	13.8222			0.460230
$903$		0			0
$904$	10.1297			0.336910
$905$	7.58615	−	13.1396i	0.252172	−	0.436775i
$906$		0			0
$907$	−4.20142	−	7.27707i	−0.139506	−	0.241631i	0.787804	−	0.615926i	$-0.211218\pi$
$907$	−4.20142	−	7.27707i	−0.139506	−	0.241631i	−0.927310	+	0.374295i	$0.877885\pi$
$908$	4.92540	−	8.53104i	0.163455	−	0.283113i
$909$		0			0
$910$	−5.11026	+	2.17989i	−0.169404	+	0.0722626i
$911$	0.593689			0.0196698			0.00983489	−	0.999952i	$-0.496869\pi$
$911$	0.593689			0.0196698			0.00983489	+	0.999952i	$0.496869\pi$
$912$		0			0
$913$	−4.61581	−	7.99482i	−0.152761	−	0.264590i
$914$	10.9693	+	18.9993i	0.362831	+	0.628441i
$915$		0			0
$916$	16.4707			0.544207
$917$	28.9896	+	21.7647i	0.957322	+	0.718734i
$918$		0			0
$919$	8.16849	−	14.1482i	0.269454	−	0.466707i	−0.699267	−	0.714860i	$-0.746490\pi$
$919$	8.16849	−	14.1482i	0.269454	−	0.466707i	0.968721	+	0.248153i	$0.0798236\pi$
$920$	0.802304	+	1.38963i	0.0264512	+	0.0458148i
$921$		0			0
$922$	−11.4545	+	19.8398i	−0.377235	+	0.653389i
$923$	7.73128			0.254478
$924$		0			0
$925$	−27.8792			−0.916662
$926$	11.2893	−	19.5537i	0.370990	−	0.642573i
$927$		0			0
$928$	−34.3996	−	59.5818i	−1.12922	−	1.95587i
$929$	4.45060	−	7.70866i	0.146019	−	0.252913i	−0.783733	−	0.621097i	$-0.786687\pi$
$929$	4.45060	−	7.70866i	0.146019	−	0.252913i	0.929753	+	0.368184i	$0.120020\pi$
$930$		0			0
$931$	−26.9518	+	28.1083i	−0.883309	+	0.921213i
$932$	10.2910			0.337091
$933$		0			0
$934$	−30.0456	−	52.0405i	−0.983122	−	1.70282i
$935$	−0.900654	−	1.55998i	−0.0294545	−	0.0510168i
$936$		0			0
$937$	45.2360			1.47780			0.738898	−	0.673817i	$-0.235347\pi$
$937$	45.2360			1.47780			0.738898	+	0.673817i	$0.235347\pi$
$938$	0.934131	−	7.72112i	0.0305005	−	0.252104i
$939$		0			0
$940$	−1.22890	+	2.12851i	−0.0400822	+	0.0694244i
$941$	−3.46652	−	6.00419i	−0.113005	−	0.195731i	0.803975	−	0.594663i	$-0.202714\pi$
$941$	−3.46652	−	6.00419i	−0.113005	−	0.195731i	−0.916981	+	0.398932i	$0.869381\pi$
$942$		0			0
$943$	−8.16021	+	14.1339i	−0.265733	+	0.460263i
$944$	57.4656			1.87035
$945$		0			0
$946$	8.92759			0.290261
$947$	10.3716	−	17.9642i	0.337033	−	0.583758i	−0.646840	−	0.762626i	$-0.723910\pi$
$947$	10.3716	−	17.9642i	0.337033	−	0.583758i	0.983873	+	0.178867i	$0.0572432\pi$
$948$		0			0
$949$	−14.4046	−	24.9495i	−0.467592	−	0.809894i
$950$	23.4495	−	40.6157i	0.760803	−	1.31775i
$951$		0			0
$952$	−8.04067	+	3.42991i	−0.260600	+	0.111164i
$953$	−20.2076			−0.654589			−0.327295	−	0.944922i	$-0.606137\pi$
$953$	−20.2076			−0.654589			−0.327295	+	0.944922i	$0.606137\pi$
$954$		0			0
$955$	−3.53740	−	6.12695i	−0.114468	−	0.198264i
$956$	−6.71735	−	11.6348i	−0.217254	−	0.376296i
$957$		0			0
$958$	47.6499			1.53950
$959$	17.6790	−	7.54132i	0.570883	−	0.243522i
$960$		0			0
$961$	−5.17449	+	8.96248i	−0.166919	+	0.289112i
$962$	−10.0209	−	17.3568i	−0.323088	−	0.559604i
$963$		0			0
$964$	1.14275	−	1.97929i	0.0368054	−	0.0637488i
$965$	2.29728			0.0739520
$966$		0			0
$967$	−7.98254			−0.256701			−0.128351	−	0.991729i	$-0.540968\pi$
$967$	−7.98254			−0.256701			−0.128351	+	0.991729i	$0.540968\pi$
$968$	−0.582878	+	1.00958i	−0.0187344	+	0.0324490i
$969$		0			0
$970$	−1.51320	−	2.62093i	−0.0485858	−	0.0841530i
$971$	−6.88965	+	11.9332i	−0.221099	+	0.382955i	−0.955142	−	0.296148i	$-0.904298\pi$
$971$	−6.88965	+	11.9332i	−0.221099	+	0.382955i	0.734043	+	0.679103i	$0.237631\pi$
$972$		0			0
$973$	−0.827049	+	6.83603i	−0.0265140	+	0.219153i
$974$	−26.6619			−0.854304
$975$		0			0
$976$	−10.5411	−	18.2578i	−0.337413	−	0.584417i
$977$	6.01047	+	10.4104i	0.192292	+	0.333059i	0.946009	−	0.324139i	$-0.105075\pi$
$977$	6.01047	+	10.4104i	0.192292	+	0.333059i	−0.753718	+	0.657199i	$0.771741\pi$
$978$		0			0
$979$	−0.364448			−0.0116478
$980$	−5.89511	−	1.44761i	−0.188312	−	0.0462423i
$981$		0			0
$982$	36.1302	−	62.5793i	1.15296	−	1.99699i
$983$	−22.3272	−	38.6718i	−0.712126	−	1.23344i	−0.964058	−	0.265693i	$-0.914399\pi$
$983$	−22.3272	−	38.6718i	−0.712126	−	1.23344i	0.251932	−	0.967745i	$-0.418934\pi$
$984$		0			0
$985$	0.768482	−	1.33105i	0.0244859	−	0.0424108i
$986$	−54.2240			−1.72684
$987$		0			0
$988$	13.6730			0.434997
$989$	−5.27056	+	9.12888i	−0.167594	+	0.290282i
$990$		0			0
$991$	11.4830	+	19.8891i	0.364769	+	0.631799i	0.988739	−	0.149650i	$-0.0478146\pi$
$991$	11.4830	+	19.8891i	0.364769	+	0.631799i	−0.623970	+	0.781448i	$0.714481\pi$
$992$	−21.2074	+	36.7323i	−0.673336	+	1.16625i
$993$		0			0
$994$	16.6570	+	12.5057i	0.528329	+	0.396656i
$995$	−11.7553			−0.372668
$996$		0			0
$997$	−0.674488	−	1.16825i	−0.0213612	−	0.0369988i	0.855147	−	0.518385i	$-0.173467\pi$
$997$	−0.674488	−	1.16825i	−0.0213612	−	0.0369988i	−0.876508	+	0.481387i	$0.840133\pi$
$998$	−24.0566	−	41.6672i	−0.761498	−	1.31895i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.i.g.100.3		6
3.2	odd	2		77.2.e.b.23.1	✓	6
7.2	even	3		4851.2.a.bo.1.1		3
7.4	even	3	inner	693.2.i.g.298.3		6
7.5	odd	6		4851.2.a.bn.1.1		3
12.11	even	2		1232.2.q.k.177.1		6
21.2	odd	6		539.2.a.h.1.3		3
21.5	even	6		539.2.a.i.1.3		3
21.11	odd	6		77.2.e.b.67.1	yes	6
21.17	even	6		539.2.e.l.67.1		6
21.20	even	2		539.2.e.l.177.1		6
33.2	even	10		847.2.n.d.807.1		24
33.5	odd	10		847.2.n.e.366.1		24
33.8	even	10		847.2.n.d.9.1		24
33.14	odd	10		847.2.n.e.9.3		24
33.17	even	10		847.2.n.d.366.3		24
33.20	odd	10		847.2.n.e.807.3		24
33.26	odd	10		847.2.n.e.632.1		24
33.29	even	10		847.2.n.d.632.3		24
33.32	even	2		847.2.e.d.485.3		6
84.11	even	6		1232.2.q.k.529.1		6
84.23	even	6		8624.2.a.cl.1.3		3
84.47	odd	6		8624.2.a.ck.1.1		3
231.32	even	6		847.2.e.d.606.3		6
231.53	odd	30		847.2.n.e.81.1		24
231.65	even	6		5929.2.a.v.1.1		3
231.74	even	30		847.2.n.d.130.3		24
231.95	even	30		847.2.n.d.753.1		24
231.116	even	30		847.2.n.d.487.1		24
231.131	odd	6		5929.2.a.w.1.1		3
231.137	odd	30		847.2.n.e.487.3		24
231.158	odd	30		847.2.n.e.753.3		24
231.179	odd	30		847.2.n.e.130.1		24
231.200	even	30		847.2.n.d.81.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.e.b.23.1	✓	6	3.2	odd	2
77.2.e.b.67.1	yes	6	21.11	odd	6
539.2.a.h.1.3		3	21.2	odd	6
539.2.a.i.1.3		3	21.5	even	6
539.2.e.l.67.1		6	21.17	even	6
539.2.e.l.177.1		6	21.20	even	2
693.2.i.g.100.3		6	1.1	even	1	trivial
693.2.i.g.298.3		6	7.4	even	3	inner
847.2.e.d.485.3		6	33.32	even	2
847.2.e.d.606.3		6	231.32	even	6
847.2.n.d.9.1		24	33.8	even	10
847.2.n.d.81.3		24	231.200	even	30
847.2.n.d.130.3		24	231.74	even	30
847.2.n.d.366.3		24	33.17	even	10
847.2.n.d.487.1		24	231.116	even	30
847.2.n.d.632.3		24	33.29	even	10
847.2.n.d.753.1		24	231.95	even	30
847.2.n.d.807.1		24	33.2	even	10
847.2.n.e.9.3		24	33.14	odd	10
847.2.n.e.81.1		24	231.53	odd	30
847.2.n.e.130.1		24	231.179	odd	30
847.2.n.e.366.1		24	33.5	odd	10
847.2.n.e.487.3		24	231.137	odd	30
847.2.n.e.632.1		24	33.26	odd	10
847.2.n.e.753.3		24	231.158	odd	30
847.2.n.e.807.3		24	33.20	odd	10
1232.2.q.k.177.1		6	12.11	even	2
1232.2.q.k.529.1		6	84.11	even	6
4851.2.a.bn.1.1		3	7.5	odd	6
4851.2.a.bo.1.1		3	7.2	even	3
5929.2.a.v.1.1		3	231.65	even	6
5929.2.a.w.1.1		3	231.131	odd	6
8624.2.a.ck.1.1		3	84.47	odd	6
8624.2.a.cl.1.3		3	84.23	even	6

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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.917122 - 1.58850i) q^{2} +(-0.682224 - 1.18165i) q^{4} +(-0.317776 + 0.550404i) q^{5} +(0.317776 - 2.62660i) q^{7} +1.16576 q^{8} +O(q^{10})\)	\(q+(0.917122 - 1.58850i) q^{2} +(-0.682224 - 1.18165i) q^{4} +(-0.317776 + 0.550404i) q^{5} +(0.317776 - 2.62660i) q^{7} +1.16576 q^{8} +(0.582878 + 1.00958i) q^{10} +(-0.500000 - 0.866025i) q^{11} -1.80131 q^{13} +(-3.88092 - 2.91370i) q^{14} +(2.43359 - 4.21510i) q^{16} +(-1.41712 - 2.45453i) q^{17} +(2.78157 - 4.81782i) q^{19} +0.867178 q^{20} -1.83424 q^{22} +(1.08288 - 1.87560i) q^{23} +(2.29804 + 3.98032i) q^{25} +(-1.65202 + 2.86138i) q^{26} +(-3.32051 + 1.41643i) q^{28} +10.4303 q^{29} +(-3.21516 - 5.56882i) q^{31} +(-3.29804 - 5.71237i) q^{32} -5.19869 q^{34} +(1.34471 + 1.00958i) q^{35} +(-3.03293 + 5.25320i) q^{37} +(-5.10208 - 8.83705i) q^{38} +(-0.370450 + 0.641637i) q^{40} -7.53566 q^{41} -4.86718 q^{43} +(-0.682224 + 1.18165i) q^{44} +(-1.98626 - 3.44031i) q^{46} +(-1.41712 + 2.45453i) q^{47} +(-6.79804 - 1.66934i) q^{49} +8.43032 q^{50} +(1.22890 + 2.12851i) q^{52} +(3.73490 + 6.46903i) q^{53} +0.635552 q^{55} +(0.370450 - 3.06197i) q^{56} +(9.56587 - 16.5686i) q^{58} +(5.90338 + 10.2250i) q^{59} +(2.16576 - 3.75120i) q^{61} -11.7948 q^{62} -2.36445 q^{64} +(0.572413 - 0.991448i) q^{65} +(0.801309 + 1.38791i) q^{67} +(-1.93359 + 3.34907i) q^{68} +(2.83697 - 1.21017i) q^{70} -4.29204 q^{71} +(7.99673 + 13.8507i) q^{73} +(5.56314 + 9.63564i) q^{74} -7.59061 q^{76} +(-2.43359 + 1.03810i) q^{77} +(-2.38092 + 4.12387i) q^{79} +(1.54667 + 2.67891i) q^{80} +(-6.91112 + 11.9704i) q^{82} +9.23163 q^{83} +1.80131 q^{85} +(-4.46379 + 7.73152i) q^{86} +(-0.582878 - 1.00958i) q^{88} +(0.182224 - 0.315621i) q^{89} +(-0.572413 + 4.73131i) q^{91} -2.95506 q^{92} +(2.59935 + 4.50220i) q^{94} +(1.76783 + 3.06197i) q^{95} -2.59607 q^{97} +(-8.88637 + 9.26770i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 4 q^{4} - 2 q^{5} + 2 q^{7} + 18 q^{8}+O(q^{10}) \) 6 * q - 4 * q^4 - 2 * q^5 + 2 * q^7 + 18 * q^8	\( 6 q - 4 q^{4} - 2 q^{5} + 2 q^{7} + 18 q^{8} + 9 q^{10} - 3 q^{11} - 22 q^{13} - 12 q^{14} - 2 q^{16} - 3 q^{17} + 11 q^{19} - 28 q^{20} + 12 q^{23} - 3 q^{25} + q^{26} + 13 q^{28} + 18 q^{29} + 3 q^{31} - 3 q^{32} - 20 q^{34} - 9 q^{35} + 4 q^{37} + 8 q^{38} + 3 q^{40} + 10 q^{41} + 4 q^{43} - 4 q^{44} + 10 q^{46} - 3 q^{47} - 24 q^{49} + 6 q^{50} + 7 q^{52} + 17 q^{53} + 4 q^{55} - 3 q^{56} + 13 q^{58} + 8 q^{59} + 24 q^{61} - 26 q^{62} - 14 q^{64} + 15 q^{65} + 16 q^{67} + 5 q^{68} - 27 q^{70} - 14 q^{71} + 20 q^{73} + 22 q^{74} - 78 q^{76} + 2 q^{77} - 3 q^{79} + 9 q^{80} - 41 q^{82} + 22 q^{83} + 22 q^{85} - 21 q^{86} - 9 q^{88} + q^{89} - 15 q^{91} - 50 q^{92} + 10 q^{94} - 17 q^{95} + 18 q^{97} + 24 q^{98}+O(q^{100}) \) 6 * q - 4 * q^4 - 2 * q^5 + 2 * q^7 + 18 * q^8 + 9 * q^10 - 3 * q^11 - 22 * q^13 - 12 * q^14 - 2 * q^16 - 3 * q^17 + 11 * q^19 - 28 * q^20 + 12 * q^23 - 3 * q^25 + q^26 + 13 * q^28 + 18 * q^29 + 3 * q^31 - 3 * q^32 - 20 * q^34 - 9 * q^35 + 4 * q^37 + 8 * q^38 + 3 * q^40 + 10 * q^41 + 4 * q^43 - 4 * q^44 + 10 * q^46 - 3 * q^47 - 24 * q^49 + 6 * q^50 + 7 * q^52 + 17 * q^53 + 4 * q^55 - 3 * q^56 + 13 * q^58 + 8 * q^59 + 24 * q^61 - 26 * q^62 - 14 * q^64 + 15 * q^65 + 16 * q^67 + 5 * q^68 - 27 * q^70 - 14 * q^71 + 20 * q^73 + 22 * q^74 - 78 * q^76 + 2 * q^77 - 3 * q^79 + 9 * q^80 - 41 * q^82 + 22 * q^83 + 22 * q^85 - 21 * q^86 - 9 * q^88 + q^89 - 15 * q^91 - 50 * q^92 + 10 * q^94 - 17 * q^95 + 18 * q^97 + 24 * q^98

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