LMFDB - Embedded newform 378.2.t.a.17.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(17,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 1]))

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

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

chi := DirichletCharacter("378.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.t (of order $6$, degree $2$, not 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + \cdots + 6561 $ x^16 - 8x^15 + 23x^14 - 8x^13 - 131x^12 + 380x^11 - 289x^10 - 880x^9 + 2785x^8 - 2640x^7 - 2601x^6 + 10260x^5 - 10611x^4 - 1944x^3 + 16767x^2 - 17496*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.3
Root			$0.320287 - 1.70218i$ of defining polynomial
Character	$\chi$	$=$	378.17
Dual form			378.2.t.a.89.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +0.0676069 q^{5} +(-2.64192 - 0.142361i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +0.0676069 q^{5} +(-2.64192 - 0.142361i) q^{7} -1.00000i q^{8} +(-0.0585493 - 0.0338034i) q^{10} -3.92924i q^{11} +(-3.32589 - 1.92020i) q^{13} +(2.21679 + 1.44425i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.775337 - 1.34292i) q^{17} +(5.06375 - 2.92356i) q^{19} +(0.0338034 + 0.0585493i) q^{20} +(-1.96462 + 3.40282i) q^{22} -5.52740i q^{23} -4.99543 q^{25} +(1.92020 + 3.32589i) q^{26} +(-1.19767 - 2.35915i) q^{28} +(-1.20840 + 0.697671i) q^{29} +(1.09635 - 0.632976i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.34292 + 0.775337i) q^{34} +(-0.178612 - 0.00962461i) q^{35} +(-4.35534 - 7.54368i) q^{37} -5.84711 q^{38} -0.0676069i q^{40} +(-5.17415 + 8.96188i) q^{41} +(0.735847 + 1.27452i) q^{43} +(3.40282 - 1.96462i) q^{44} +(-2.76370 + 4.78687i) q^{46} +(1.77132 - 3.06802i) q^{47} +(6.95947 + 0.752214i) q^{49} +(4.32617 + 2.49771i) q^{50} -3.84040i q^{52} +(-6.28910 - 3.63101i) q^{53} -0.265644i q^{55} +(-0.142361 + 2.64192i) q^{56} +1.39534 q^{58} +(-4.70043 - 8.14138i) q^{59} +(0.0705919 + 0.0407562i) q^{61} -1.26595 q^{62} -1.00000 q^{64} +(-0.224853 - 0.129819i) q^{65} +(7.67257 + 13.2893i) q^{67} +1.55067 q^{68} +(0.149870 + 0.0976411i) q^{70} +4.30975i q^{71} +(6.12768 + 3.53782i) q^{73} +8.71069i q^{74} +(5.06375 + 2.92356i) q^{76} +(-0.559372 + 10.3807i) q^{77} +(3.42320 - 5.92915i) q^{79} +(-0.0338034 + 0.0585493i) q^{80} +(8.96188 - 5.17415i) q^{82} +(3.93194 + 6.81032i) q^{83} +(0.0524181 - 0.0907908i) q^{85} -1.47169i q^{86} -3.92924 q^{88} +(5.84745 + 10.1281i) q^{89} +(8.51336 + 5.54650i) q^{91} +(4.78687 - 2.76370i) q^{92} +(-3.06802 + 1.77132i) q^{94} +(0.342344 - 0.197652i) q^{95} +(0.363295 - 0.209749i) q^{97} +(-5.65097 - 4.13117i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 2 q^{7}+O(q^{10}) $ 16 * q + 8 * q^4 + 2 * q^7	$ 16 q + 8 q^{4} + 2 q^{7} - 6 q^{13} + 6 q^{14} - 8 q^{16} - 18 q^{17} + 16 q^{25} + 12 q^{26} - 2 q^{28} - 6 q^{29} + 6 q^{31} + 30 q^{35} - 2 q^{37} - 6 q^{41} - 2 q^{43} - 12 q^{44} + 6 q^{46} + 18 q^{47} + 10 q^{49} + 12 q^{50} - 36 q^{53} - 12 q^{58} - 30 q^{59} - 60 q^{61} + 36 q^{62} - 16 q^{64} - 42 q^{65} + 14 q^{67} - 36 q^{68} + 18 q^{77} - 16 q^{79} - 12 q^{85} - 24 q^{89} - 12 q^{91} - 6 q^{92} + 66 q^{95} - 6 q^{97} - 24 q^{98}+O(q^{100}) $ 16 * q + 8 * q^4 + 2 * q^7 - 6 * q^13 + 6 * q^14 - 8 * q^16 - 18 * q^17 + 16 * q^25 + 12 * q^26 - 2 * q^28 - 6 * q^29 + 6 * q^31 + 30 * q^35 - 2 * q^37 - 6 * q^41 - 2 * q^43 - 12 * q^44 + 6 * q^46 + 18 * q^47 + 10 * q^49 + 12 * q^50 - 36 * q^53 - 12 * q^58 - 30 * q^59 - 60 * q^61 + 36 * q^62 - 16 * q^64 - 42 * q^65 + 14 * q^67 - 36 * q^68 + 18 * q^77 - 16 * q^79 - 12 * q^85 - 24 * q^89 - 12 * q^91 - 6 * q^92 + 66 * q^95 - 6 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.0676069			0.0302347			0.0151174	−	0.999886i	$-0.495188\pi$
$5$	0.0676069			0.0302347			0.0151174	+	0.999886i	$0.495188\pi$
$6$		0			0
$7$	−2.64192	−	0.142361i	−0.998551	−	0.0538075i
$7$	−2.64192	−	0.142361i	−0.998551	−	0.0538075i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−0.0585493	−	0.0338034i	−0.0185149	−	0.0106896i
$11$		−	3.92924i		−	1.18471i	−0.805677	−	0.592356i	$-0.798198\pi$
$11$		−	3.92924i		−	1.18471i	0.805677	−	0.592356i	$-0.201802\pi$
$12$		0			0
$13$	−3.32589	−	1.92020i	−0.922435	−	0.532568i	−0.0380241	−	0.999277i	$-0.512106\pi$
$13$	−3.32589	−	1.92020i	−0.922435	−	0.532568i	−0.884411	+	0.466709i	$0.845440\pi$
$14$	2.21679	+	1.44425i	0.592461	+	0.385991i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.775337	−	1.34292i	0.188047	−	0.325707i	−0.756552	−	0.653933i	$-0.773118\pi$
$17$	0.775337	−	1.34292i	0.188047	−	0.325707i	0.944599	+	0.328227i	$0.106451\pi$
$18$		0			0
$19$	5.06375	−	2.92356i	1.16170	−	0.670710i	0.209991	−	0.977703i	$-0.432656\pi$
$19$	5.06375	−	2.92356i	1.16170	−	0.670710i	0.951712	+	0.306994i	$0.0993230\pi$
$20$	0.0338034	+	0.0585493i	0.00755868	+	0.0130920i
$21$		0			0
$22$	−1.96462	+	3.40282i	−0.418859	+	0.725484i
$23$		−	5.52740i		−	1.15254i	−0.817258	−	0.576272i	$-0.804507\pi$
$23$		−	5.52740i		−	1.15254i	0.817258	−	0.576272i	$-0.195493\pi$
$24$		0			0
$25$	−4.99543			−0.999086
$26$	1.92020	+	3.32589i	0.376583	+	0.652260i
$27$		0			0
$28$	−1.19767	−	2.35915i	−0.226338	−	0.445837i
$29$	−1.20840	+	0.697671i	−0.224394	+	0.129554i	−0.607983	−	0.793950i	$-0.708021\pi$
$29$	−1.20840	+	0.697671i	−0.224394	+	0.129554i	0.383589	+	0.923504i	$0.374688\pi$
$30$		0			0
$31$	1.09635	−	0.632976i	0.196910	−	0.113686i	−0.398304	−	0.917254i	$-0.630401\pi$
$31$	1.09635	−	0.632976i	0.196910	−	0.113686i	0.595213	+	0.803568i	$0.297068\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$	−1.34292	+	0.775337i	−0.230309	+	0.132969i
$35$	−0.178612	−	0.00962461i	−0.0301909	−	0.00162686i
$36$		0			0
$37$	−4.35534	−	7.54368i	−0.716014	−	1.24017i	−0.962567	−	0.271044i	$-0.912631\pi$
$37$	−4.35534	−	7.54368i	−0.716014	−	1.24017i	0.246553	−	0.969129i	$-0.420702\pi$
$38$	−5.84711			−0.948527
$39$		0			0
$40$		−	0.0676069i		−	0.0106896i
$41$	−5.17415	+	8.96188i	−0.808066	+	1.39961i	0.106136	+	0.994352i	$0.466152\pi$
$41$	−5.17415	+	8.96188i	−0.808066	+	1.39961i	−0.914202	+	0.405260i	$0.867181\pi$
$42$		0			0
$43$	0.735847	+	1.27452i	0.112216	+	0.194363i	0.916663	−	0.399660i	$-0.130872\pi$
$43$	0.735847	+	1.27452i	0.112216	+	0.194363i	−0.804448	+	0.594023i	$0.797539\pi$
$44$	3.40282	−	1.96462i	0.512995	−	0.296178i
$45$		0			0
$46$	−2.76370	+	4.78687i	−0.407486	+	0.705786i
$47$	1.77132	−	3.06802i	0.258374	−	0.447517i	−0.707432	−	0.706781i	$-0.750147\pi$
$47$	1.77132	−	3.06802i	0.258374	−	0.447517i	0.965806	+	0.259264i	$0.0834800\pi$
$48$		0			0
$49$	6.95947	+	0.752214i	0.994209	+	0.107459i
$50$	4.32617	+	2.49771i	0.611813	+	0.353230i
$51$		0			0
$52$		−	3.84040i		−	0.532568i
$53$	−6.28910	−	3.63101i	−0.863874	−	0.498758i	0.00143340	−	0.999999i	$-0.499544\pi$
$53$	−6.28910	−	3.63101i	−0.863874	−	0.498758i	−0.865308	+	0.501241i	$0.832877\pi$
$54$		0			0
$55$		−	0.265644i		−	0.0358194i
$56$	−0.142361	+	2.64192i	−0.0190238	+	0.353041i
$57$		0			0
$58$	1.39534			0.183217
$59$	−4.70043	−	8.14138i	−0.611944	−	1.05992i	−0.990912	−	0.134508i	$-0.957055\pi$
$59$	−4.70043	−	8.14138i	−0.611944	−	1.05992i	0.378969	−	0.925409i	$-0.376279\pi$
$60$		0			0
$61$	0.0705919	+	0.0407562i	0.00903836	+	0.00521830i	0.504512	−	0.863404i	$-0.331672\pi$
$61$	0.0705919	+	0.0407562i	0.00903836	+	0.00521830i	−0.495474	+	0.868623i	$0.665006\pi$
$62$	−1.26595			−0.160776
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−0.224853	−	0.129819i	−0.0278896	−	0.0161020i
$66$		0			0
$67$	7.67257	+	13.2893i	0.937354	+	1.62354i	0.770382	+	0.637583i	$0.220066\pi$
$67$	7.67257	+	13.2893i	0.937354	+	1.62354i	0.166972	+	0.985962i	$0.446601\pi$
$68$	1.55067			0.188047
$69$		0			0
$70$	0.149870	+	0.0976411i	0.0179129	+	0.0116703i
$71$			4.30975i			0.511474i	0.966746	+	0.255737i	$0.0823181\pi$
$71$			4.30975i			0.511474i	−0.966746	+	0.255737i	$0.917682\pi$
$72$		0			0
$73$	6.12768	+	3.53782i	0.717191	+	0.414070i	0.813718	−	0.581260i	$-0.197440\pi$
$73$	6.12768	+	3.53782i	0.717191	+	0.414070i	−0.0965271	+	0.995330i	$0.530773\pi$
$74$			8.71069i			1.01260i
$75$		0			0
$76$	5.06375	+	2.92356i	0.580852	+	0.335355i
$77$	−0.559372	+	10.3807i	−0.0637464	+	1.18299i
$78$		0			0
$79$	3.42320	−	5.92915i	0.385140	−	0.667082i	−0.606649	−	0.794970i	$-0.707487\pi$
$79$	3.42320	−	5.92915i	0.385140	−	0.667082i	0.991789	+	0.127888i	$0.0408199\pi$
$80$	−0.0338034	+	0.0585493i	−0.00377934	+	0.00654601i
$81$		0			0
$82$	8.96188	−	5.17415i	0.989675	−	0.571389i
$83$	3.93194	+	6.81032i	0.431587	+	0.747530i	0.997010	−	0.0772707i	$-0.0246206\pi$
$83$	3.93194	+	6.81032i	0.431587	+	0.747530i	−0.565423	+	0.824801i	$0.691287\pi$
$84$		0			0
$85$	0.0524181	−	0.0907908i	0.00568554	−	0.00984765i
$86$		−	1.47169i		−	0.158697i
$87$		0			0
$88$	−3.92924			−0.418859
$89$	5.84745	+	10.1281i	0.619828	+	1.07357i	0.989517	+	0.144418i	$0.0461311\pi$
$89$	5.84745	+	10.1281i	0.619828	+	1.07357i	−0.369688	+	0.929156i	$0.620536\pi$
$90$		0			0
$91$	8.51336	+	5.54650i	0.892443	+	0.581431i
$92$	4.78687	−	2.76370i	0.499066	−	0.288136i
$93$		0			0
$94$	−3.06802	+	1.77132i	−0.316442	+	0.182698i
$95$	0.342344	−	0.197652i	0.0351238	−	0.0202787i
$96$		0			0
$97$	0.363295	−	0.209749i	0.0368870	−	0.0212967i	−0.481443	−	0.876477i	$-0.659887\pi$
$97$	0.363295	−	0.209749i	0.0368870	−	0.0212967i	0.518330	+	0.855181i	$0.326554\pi$
$98$	−5.65097	−	4.13117i	−0.570834	−	0.417311i
$99$		0			0
$100$	−2.49771	−	4.32617i	−0.249771	−	0.432617i
$101$	17.3924			1.73061			0.865305	−	0.501246i	$-0.167125\pi$
$101$	17.3924			1.73061			0.865305	+	0.501246i	$0.167125\pi$
$102$		0			0
$103$		−	1.00114i		−	0.0986449i	−0.998783	−	0.0493225i	$-0.984294\pi$
$103$		−	1.00114i		−	0.0986449i	0.998783	−	0.0493225i	$-0.0157062\pi$
$104$	−1.92020	+	3.32589i	−0.188291	+	0.326130i
$105$		0			0
$106$	3.63101	+	6.28910i	0.352675	+	0.610851i
$107$	8.02352	−	4.63238i	0.775663	−	0.447829i	−0.0592279	−	0.998244i	$-0.518864\pi$
$107$	8.02352	−	4.63238i	0.775663	−	0.447829i	0.834891	+	0.550415i	$0.185531\pi$
$108$		0			0
$109$	0.821501	−	1.42288i	0.0786855	−	0.136287i	−0.823998	−	0.566593i	$-0.808261\pi$
$109$	0.821501	−	1.42288i	0.0786855	−	0.136287i	0.902683	+	0.430306i	$0.141594\pi$
$110$	−0.132822	+	0.230054i	−0.0126641	+	0.0219348i
$111$		0			0
$112$	1.44425	−	2.21679i	0.136469	−	0.209467i
$113$	−13.6537	−	7.88296i	−1.28443	−	0.741567i	−0.306776	−	0.951782i	$-0.599250\pi$
$113$	−13.6537	−	7.88296i	−1.28443	−	0.741567i	−0.977655	+	0.210215i	$0.932584\pi$
$114$		0			0
$115$		−	0.373691i		−	0.0348468i
$116$	−1.20840	−	0.697671i	−0.112197	−	0.0647771i
$117$		0			0
$118$			9.40086i			0.865419i
$119$	−2.23956	+	3.43752i	−0.205300	+	0.315117i
$120$		0			0
$121$	−4.43894			−0.403540
$122$	−0.0407562	−	0.0705919i	−0.00368990	−	0.00639109i
$123$		0			0
$124$	1.09635	+	0.632976i	0.0984548	+	0.0568429i
$125$	−0.675760			−0.0604418
$126$		0			0
$127$	−19.0776			−1.69286			−0.846430	−	0.532501i	$-0.821252\pi$
$127$	−19.0776			−1.69286			−0.846430	+	0.532501i	$0.821252\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$	0.129819	+	0.224853i	0.0113859	+	0.0197209i
$131$	18.6681			1.63104			0.815519	−	0.578731i	$-0.196452\pi$
$131$	18.6681			1.63104			0.815519	+	0.578731i	$0.196452\pi$
$132$		0			0
$133$	−13.7942	+	7.00291i	−1.19611	+	0.607230i
$134$		−	15.3451i		−	1.32562i
$135$		0			0
$136$	−1.34292	−	0.775337i	−0.115155	−	0.0664846i
$137$			6.28537i			0.536995i	0.963280	+	0.268498i	$0.0865272\pi$
$137$			6.28537i			0.536995i	−0.963280	+	0.268498i	$0.913473\pi$
$138$		0			0
$139$	−5.49596	−	3.17309i	−0.466161	−	0.269138i	0.248470	−	0.968640i	$-0.420072\pi$
$139$	−5.49596	−	3.17309i	−0.466161	−	0.269138i	−0.714631	+	0.699501i	$0.753406\pi$
$140$	−0.0809708	−	0.159495i	−0.00684328	−	0.0134798i
$141$		0			0
$142$	2.15488	−	3.73236i	0.180833	−	0.313212i
$143$	−7.54494	+	13.0682i	−0.630939	+	1.09282i
$144$		0			0
$145$	−0.0816962	+	0.0471673i	−0.00678450	+	0.00391703i
$146$	−3.53782	−	6.12768i	−0.292792	−	0.507130i
$147$		0			0
$148$	4.35534	−	7.54368i	0.358007	−	0.620087i
$149$		−	8.33685i		−	0.682981i	−0.939885	−	0.341491i	$-0.889068\pi$
$149$		−	8.33685i		−	0.682981i	0.939885	−	0.341491i	$-0.110932\pi$
$150$		0			0
$151$	14.1544			1.15187			0.575935	−	0.817496i	$-0.304638\pi$
$151$	14.1544			1.15187			0.575935	+	0.817496i	$0.304638\pi$
$152$	−2.92356	−	5.06375i	−0.237132	−	0.410724i
$153$		0			0
$154$	5.67480	−	8.71030i	0.457288	−	0.701896i
$155$	0.0741205	−	0.0427935i	0.00595350	−	0.00343726i
$156$		0			0
$157$	−14.2542	+	8.22967i	−1.13761	+	0.656799i	−0.945838	−	0.324640i	$-0.894757\pi$
$157$	−14.2542	+	8.22967i	−1.13761	+	0.656799i	−0.191772	+	0.981439i	$0.561424\pi$
$158$	−5.92915	+	3.42320i	−0.471698	+	0.272335i
$159$		0			0
$160$	0.0585493	−	0.0338034i	0.00462873	−	0.00267240i
$161$	−0.786889	+	14.6030i	−0.0620155	+	1.15087i
$162$		0			0
$163$	−4.53345	−	7.85216i	−0.355087	−	0.615029i	0.632046	−	0.774931i	$-0.282215\pi$
$163$	−4.53345	−	7.85216i	−0.355087	−	0.615029i	−0.987133	+	0.159902i	$0.948882\pi$
$164$	−10.3483			−0.808066
$165$		0			0
$166$		−	7.86388i		−	0.610356i
$167$	7.64922	−	13.2488i	0.591914	−	1.02523i	−0.402060	−	0.915613i	$-0.631706\pi$
$167$	7.64922	−	13.2488i	0.591914	−	1.02523i	0.993974	−	0.109612i	$-0.0349608\pi$
$168$		0			0
$169$	0.874352	+	1.51442i	0.0672579	+	0.116494i
$170$	−0.0907908	+	0.0524181i	−0.00696334	+	0.00402029i
$171$		0			0
$172$	−0.735847	+	1.27452i	−0.0561078	+	0.0971815i
$173$	1.15062	−	1.99294i	0.0874804	−	0.151520i	−0.818965	−	0.573843i	$-0.805452\pi$
$173$	1.15062	−	1.99294i	0.0874804	−	0.151520i	0.906445	+	0.422323i	$0.138785\pi$
$174$		0			0
$175$	13.1975	+	0.711156i	0.997639	+	0.0537583i
$176$	3.40282	+	1.96462i	0.256497	+	0.148089i
$177$		0			0
$178$		−	11.6949i		−	0.876570i
$179$	−13.8077	−	7.97186i	−1.03203	−	0.595845i	−0.114467	−	0.993427i	$-0.536516\pi$
$179$	−13.8077	−	7.97186i	−1.03203	−	0.595845i	−0.917567	+	0.397582i	$0.869849\pi$
$180$		0			0
$181$			18.4526i			1.37157i	0.727804	+	0.685785i	$0.240541\pi$
$181$			18.4526i			1.37157i	−0.727804	+	0.685785i	$0.759459\pi$
$182$	−4.59954	−	9.06009i	−0.340941	−	0.671578i
$183$		0			0
$184$	−5.52740			−0.407486
$185$	−0.294451	−	0.510005i	−0.0216485	−	0.0374963i
$186$		0			0
$187$	−5.27667	−	3.04649i	−0.385868	−	0.222781i
$188$	3.54265			0.258374
$189$		0			0
$190$	−0.395305			−0.0286784
$191$	−20.2162	−	11.6719i	−1.46280	−	0.844546i	−0.463656	−	0.886015i	$-0.653463\pi$
$191$	−20.2162	−	11.6719i	−1.46280	−	0.844546i	−0.999140	+	0.0414695i	$0.986796\pi$
$192$		0			0
$193$	−10.6439	−	18.4357i	−0.766164	−	1.32703i	−0.939629	−	0.342194i	$-0.888830\pi$
$193$	−10.6439	−	18.4357i	−0.766164	−	1.32703i	0.173466	−	0.984840i	$-0.444503\pi$
$194$	−0.419497			−0.0301181
$195$		0			0
$196$	2.82830	+	6.40318i	0.202021	+	0.457370i
$197$			12.8467i			0.915288i	0.889136	+	0.457644i	$0.151307\pi$
$197$			12.8467i			0.915288i	−0.889136	+	0.457644i	$0.848693\pi$
$198$		0			0
$199$	−3.24154	−	1.87150i	−0.229787	−	0.132667i	0.380687	−	0.924704i	$-0.375688\pi$
$199$	−3.24154	−	1.87150i	−0.229787	−	0.132667i	−0.610474	+	0.792037i	$0.709021\pi$
$200$			4.99543i			0.353230i
$201$		0			0
$202$	−15.0623	−	8.69621i	−1.05978	−	0.611863i
$203$	3.29182	−	1.67116i	0.231040	−	0.117292i
$204$		0			0
$205$	−0.349808	+	0.605885i	−0.0244316	+	0.0423168i
$206$	−0.500568	+	0.867010i	−0.0348762	+	0.0604074i
$207$		0			0
$208$	3.32589	−	1.92020i	0.230609	−	0.133142i
$209$	−11.4874	−	19.8967i	−0.794597	−	1.37628i
$210$		0			0
$211$	4.69581	−	8.13339i	0.323273	−	0.559925i	−0.657888	−	0.753116i	$-0.728550\pi$
$211$	4.69581	−	8.13339i	0.323273	−	0.559925i	0.981161	+	0.193190i	$0.0618834\pi$
$212$		−	7.26203i		−	0.498758i
$213$		0			0
$214$	−9.26477			−0.633326
$215$	0.0497483	+	0.0861666i	0.00339281	+	0.00587651i
$216$		0			0
$217$	−2.98657	+	1.51619i	−0.202741	+	0.102926i
$218$	−1.42288	+	0.821501i	−0.0963697	+	0.0556391i
$219$		0			0
$220$	0.230054	−	0.132822i	0.0155103	−	0.00895485i
$221$	−5.15737	+	2.97761i	−0.346922	+	0.200296i
$222$		0			0
$223$	17.7695	−	10.2592i	1.18993	−	0.687008i	0.231642	−	0.972801i	$-0.425590\pi$
$223$	17.7695	−	10.2592i	1.18993	−	0.687008i	0.958291	+	0.285793i	$0.0922570\pi$
$224$	−2.35915	+	1.19767i	−0.157627	+	0.0800227i
$225$		0			0
$226$	7.88296	+	13.6537i	0.524367	+	0.908230i
$227$	18.7766			1.24624			0.623122	−	0.782124i	$-0.285864\pi$
$227$	18.7766			1.24624			0.623122	+	0.782124i	$0.285864\pi$
$228$		0			0
$229$			4.98531i			0.329438i	0.986341	+	0.164719i	$0.0526718\pi$
$229$			4.98531i			0.329438i	−0.986341	+	0.164719i	$0.947328\pi$
$230$	−0.186845	+	0.323625i	−0.0123202	+	0.0213392i
$231$		0			0
$232$	0.697671	+	1.20840i	0.0458043	+	0.0793354i
$233$	12.7747	−	7.37548i	0.836899	−	0.483184i	−0.0193101	−	0.999814i	$-0.506147\pi$
$233$	12.7747	−	7.37548i	0.836899	−	0.483184i	0.856209	+	0.516630i	$0.172814\pi$
$234$		0			0
$235$	0.119754	−	0.207419i	0.00781186	−	0.0135305i
$236$	4.70043	−	8.14138i	0.305972	−	0.529959i
$237$		0			0
$238$	3.65827	−	1.85720i	0.237131	−	0.120384i
$239$	0.155388	+	0.0897132i	0.0100512	+	0.00580307i	0.505017	−	0.863109i	$-0.331486\pi$
$239$	0.155388	+	0.0897132i	0.0100512	+	0.00580307i	−0.494966	+	0.868912i	$0.664819\pi$
$240$		0			0
$241$			6.13358i			0.395098i	0.980293	+	0.197549i	$0.0632982\pi$
$241$			6.13358i			0.395098i	−0.980293	+	0.197549i	$0.936702\pi$
$242$	3.84424	+	2.21947i	0.247117	+	0.142673i
$243$		0			0
$244$			0.0815124i			0.00521830i
$245$	0.470508	+	0.0508548i	0.0300596	+	0.00324900i
$246$		0			0
$247$	−22.4553			−1.42879
$248$	−0.632976	−	1.09635i	−0.0401940	−	0.0696181i
$249$		0			0
$250$	0.585225	+	0.337880i	0.0370129	+	0.0213694i
$251$	−1.11296			−0.0702495			−0.0351247	−	0.999383i	$-0.511183\pi$
$251$	−1.11296			−0.0702495			−0.0351247	+	0.999383i	$0.511183\pi$
$252$		0			0
$253$	−21.7185			−1.36543
$254$	16.5216	+	9.53878i	1.03666	+	0.598516i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−4.74732			−0.296129			−0.148065	−	0.988978i	$-0.547304\pi$
$257$	−4.74732			−0.296129			−0.148065	+	0.988978i	$0.547304\pi$
$258$		0			0
$259$	10.4325	+	20.5498i	0.648246	+	1.27690i
$260$		−	0.259638i		−	0.0161020i
$261$		0			0
$262$	−16.1670	−	9.33404i	−0.998803	−	0.576659i
$263$			4.21634i			0.259991i	0.991515	+	0.129995i	$0.0414962\pi$
$263$			4.21634i			0.259991i	−0.991515	+	0.129995i	$0.958504\pi$
$264$		0			0
$265$	−0.425186	−	0.245482i	−0.0261190	−	0.0150798i
$266$	15.4476	+	0.832402i	0.947152	+	0.0510379i
$267$		0			0
$268$	−7.67257	+	13.2893i	−0.468677	+	0.811772i
$269$	7.97265	−	13.8090i	0.486101	−	0.841952i	−0.513771	−	0.857927i	$-0.671752\pi$
$269$	7.97265	−	13.8090i	0.486101	−	0.841952i	0.999872	+	0.0159753i	$0.00508533\pi$
$270$		0			0
$271$	14.1913	−	8.19335i	0.862060	−	0.497710i	−0.00264173	−	0.999997i	$-0.500841\pi$
$271$	14.1913	−	8.19335i	0.862060	−	0.497710i	0.864702	+	0.502286i	$0.167508\pi$
$272$	0.775337	+	1.34292i	0.0470117	+	0.0814267i
$273$		0			0
$274$	3.14269	−	5.44329i	0.189857	−	0.328841i
$275$			19.6283i			1.18363i
$276$		0			0
$277$	−1.85601			−0.111517			−0.0557583	−	0.998444i	$-0.517758\pi$
$277$	−1.85601			−0.111517			−0.0557583	+	0.998444i	$0.517758\pi$
$278$	3.17309	+	5.49596i	0.190309	+	0.329626i
$279$		0			0
$280$	−0.00962461	+	0.178612i	−0.000575180	+	0.0106741i
$281$	0.628441	−	0.362830i	0.0374896	−	0.0216446i	−0.481138	−	0.876645i	$-0.659776\pi$
$281$	0.628441	−	0.362830i	0.0374896	−	0.0216446i	0.518628	+	0.855000i	$0.326443\pi$
$282$		0			0
$283$	10.0698	−	5.81382i	0.598590	−	0.345596i	−0.169897	−	0.985462i	$-0.554343\pi$
$283$	10.0698	−	5.81382i	0.598590	−	0.345596i	0.768487	+	0.639866i	$0.221010\pi$
$284$	−3.73236	+	2.15488i	−0.221475	+	0.127868i
$285$		0			0
$286$	13.0682	−	7.54494i	0.772740	−	0.446142i
$287$	14.9455	−	22.9400i	0.882205	−	1.35410i
$288$		0			0
$289$	7.29770	+	12.6400i	0.429277	+	0.743529i
$290$	0.0943347			0.00553952
$291$		0			0
$292$			7.07564i			0.414070i
$293$	−6.45034	+	11.1723i	−0.376833	+	0.652694i	−0.990600	−	0.136794i	$-0.956320\pi$
$293$	−6.45034	+	11.1723i	−0.376833	+	0.652694i	0.613766	+	0.789488i	$0.289654\pi$
$294$		0			0
$295$	−0.317781	−	0.550413i	−0.0185019	−	0.0320463i
$296$	−7.54368	+	4.35534i	−0.438467	+	0.253149i
$297$		0			0
$298$	−4.16842	+	7.21992i	−0.241470	+	0.418239i
$299$	−10.6137	+	18.3835i	−0.613808	+	1.06315i
$300$		0			0
$301$	−1.76260	−	3.47194i	−0.101595	−	0.200120i
$302$	−12.2581	−	7.07721i	−0.705373	−	0.407247i
$303$		0			0
$304$			5.84711i			0.335355i
$305$	0.00477249	+	0.00275540i	0.000273272	+	0.000157774i
$306$		0			0
$307$			20.5111i			1.17063i	0.810806	+	0.585315i	$0.199029\pi$
$307$			20.5111i			1.17063i	−0.810806	+	0.585315i	$0.800971\pi$
$308$	−9.26967	+	4.70594i	−0.528188	+	0.268146i
$309$		0			0
$310$	−0.0855870			−0.00486102
$311$	7.51441	+	13.0153i	0.426103	+	0.738032i	0.996523	−	0.0833212i	$-0.0265527\pi$
$311$	7.51441	+	13.0153i	0.426103	+	0.738032i	−0.570420	+	0.821353i	$0.693219\pi$
$312$		0			0
$313$	−0.965929	−	0.557679i	−0.0545975	−	0.0315219i	0.472453	−	0.881356i	$-0.343369\pi$
$313$	−0.965929	−	0.557679i	−0.0545975	−	0.0315219i	−0.527050	+	0.849834i	$0.676702\pi$
$314$	16.4593			0.928855
$315$		0			0
$316$	6.84639			0.385140
$317$	1.06819	+	0.616719i	0.0599955	+	0.0346384i	0.529698	−	0.848187i	$-0.322305\pi$
$317$	1.06819	+	0.616719i	0.0599955	+	0.0346384i	−0.469702	+	0.882825i	$0.655639\pi$
$318$		0			0
$319$	2.74132	+	4.74810i	0.153484	+	0.265843i
$320$	−0.0676069			−0.00377934
$321$		0			0
$322$	7.98294	−	12.2531i	0.444872	−	0.682838i
$323$		−	9.06696i		−	0.504499i
$324$		0			0
$325$	16.6142	+	9.59223i	0.921592	+	0.532081i
$326$			9.06690i			0.502169i
$327$		0			0
$328$	8.96188	+	5.17415i	0.494837	+	0.285694i
$329$	−5.11646	+	7.85329i	−0.282079	+	0.432966i
$330$		0			0
$331$	2.51231	−	4.35145i	0.138089	−	0.239177i	−0.788684	−	0.614799i	$-0.789237\pi$
$331$	2.51231	−	4.35145i	0.138089	−	0.239177i	0.926773	+	0.375621i	$0.122571\pi$
$332$	−3.93194	+	6.81032i	−0.215793	+	0.373765i
$333$		0			0
$334$	−13.2488	+	7.64922i	−0.724944	+	0.418546i
$335$	0.518719	+	0.898447i	0.0283406	+	0.0490874i
$336$		0			0
$337$	10.6356	−	18.4213i	0.579356	−	1.00347i	−0.416198	−	0.909274i	$-0.636638\pi$
$337$	10.6356	−	18.4213i	0.579356	−	1.00347i	0.995553	−	0.0941995i	$-0.0300292\pi$
$338$		−	1.74870i		−	0.0951170i
$339$		0			0
$340$	0.104836			0.00568554
$341$	−2.48712	−	4.30781i	−0.134685	−	0.233281i
$342$		0			0
$343$	−18.2793	−	2.97805i	−0.986987	−	0.160799i
$344$	1.27452	−	0.735847i	0.0687177	−	0.0396742i
$345$		0			0
$346$	−1.99294	+	1.15062i	−0.107141	+	0.0618580i
$347$	18.6832	−	10.7868i	1.00297	−	0.579063i	0.0938425	−	0.995587i	$-0.470085\pi$
$347$	18.6832	−	10.7868i	1.00297	−	0.579063i	0.909125	+	0.416524i	$0.136752\pi$
$348$		0			0
$349$	24.1105	−	13.9202i	1.29061	−	0.745132i	0.311845	−	0.950133i	$-0.399053\pi$
$349$	24.1105	−	13.9202i	1.29061	−	0.745132i	0.978762	+	0.205001i	$0.0657198\pi$
$350$	−11.0738	−	7.21464i	−0.591920	−	0.385639i
$351$		0			0
$352$	−1.96462	−	3.40282i	−0.104715	−	0.181371i
$353$	−5.70249			−0.303513			−0.151756	−	0.988418i	$-0.548493\pi$
$353$	−5.70249			−0.303513			−0.151756	+	0.988418i	$0.548493\pi$
$354$		0			0
$355$			0.291369i			0.0154643i
$356$	−5.84745	+	10.1281i	−0.309914	+	0.536787i
$357$		0			0
$358$	7.97186	+	13.8077i	0.421326	+	0.729758i
$359$	−18.5815	+	10.7280i	−0.980693	+	0.566203i	−0.902479	−	0.430733i	$-0.858255\pi$
$359$	−18.5815	+	10.7280i	−0.980693	+	0.566203i	−0.0782137	+	0.996937i	$0.524922\pi$
$360$		0			0
$361$	7.59435	−	13.1538i	0.399703	−	0.692305i
$362$	9.22629	−	15.9804i	0.484923	−	0.839911i
$363$		0			0
$364$	−0.546725	+	10.1460i	−0.0286562	+	0.531797i
$365$	0.414273	+	0.239181i	0.0216841	+	0.0125193i
$366$		0			0
$367$		−	9.20855i		−	0.480682i	−0.970688	−	0.240341i	$-0.922741\pi$
$367$		−	9.20855i		−	0.480682i	0.970688	−	0.240341i	$-0.0772593\pi$
$368$	4.78687	+	2.76370i	0.249533	+	0.144068i
$369$		0			0
$370$			0.588903i			0.0306156i
$371$	16.0984	+	10.4882i	0.835786	+	0.544519i
$372$		0			0
$373$	28.2000			1.46014			0.730071	−	0.683371i	$-0.239487\pi$
$373$	28.2000			1.46014			0.730071	+	0.683371i	$0.239487\pi$
$374$	3.04649	+	5.27667i	0.157530	+	0.272850i
$375$		0			0
$376$	−3.06802	−	1.77132i	−0.158221	−	0.0913490i
$377$	5.35867			0.275986
$378$		0			0
$379$	−4.72569			−0.242742			−0.121371	−	0.992607i	$-0.538729\pi$
$379$	−4.72569			−0.242742			−0.121371	+	0.992607i	$0.538729\pi$
$380$	0.342344	+	0.197652i	0.0175619	+	0.0101394i
$381$		0			0
$382$	11.6719	+	20.2162i	0.597184	+	1.03435i
$383$	−34.2349			−1.74932			−0.874660	−	0.484737i	$-0.838915\pi$
$383$	−34.2349			−1.74932			−0.874660	+	0.484737i	$0.838915\pi$
$384$		0			0
$385$	−0.0378174	+	0.701809i	−0.00192735	+	0.0357675i
$386$			21.2878i			1.08352i
$387$		0			0
$388$	0.363295	+	0.209749i	0.0184435	+	0.0106484i
$389$		−	18.4945i		−	0.937710i	−0.883275	−	0.468855i	$-0.844667\pi$
$389$		−	18.4945i		−	0.937710i	0.883275	−	0.468855i	$-0.155333\pi$
$390$		0			0
$391$	−7.42288	−	4.28560i	−0.375391	−	0.216732i
$392$	0.752214	−	6.95947i	0.0379926	−	0.351506i
$393$		0			0
$394$	6.42334	−	11.1255i	0.323603	−	0.560497i
$395$	0.231432	−	0.400851i	0.0116446	−	0.0201690i
$396$		0			0
$397$	−1.76126	+	1.01687i	−0.0883952	+	0.0510350i	−0.543546	−	0.839379i	$-0.682919\pi$
$397$	−1.76126	+	1.01687i	−0.0883952	+	0.0510350i	0.455151	+	0.890414i	$0.349585\pi$
$398$	1.87150	+	3.24154i	0.0938100	+	0.162484i
$399$		0			0
$400$	2.49771	−	4.32617i	0.124886	−	0.216308i
$401$			31.4236i			1.56922i	0.619989	+	0.784611i	$0.287137\pi$
$401$			31.4236i			1.56922i	−0.619989	+	0.784611i	$0.712863\pi$
$402$		0			0
$403$	−4.86177			−0.242182
$404$	8.69621	+	15.0623i	0.432653	+	0.749376i
$405$		0			0
$406$	−3.68638	−	0.198643i	−0.182952	−	0.00985847i
$407$	−29.6409	+	17.1132i	−1.46925	+	0.848270i
$408$		0			0
$409$	−0.476819	+	0.275292i	−0.0235772	+	0.0136123i	−0.511742	−	0.859139i	$-0.671000\pi$
$409$	−0.476819	+	0.275292i	−0.0235772	+	0.0136123i	0.488165	+	0.872751i	$0.337666\pi$
$410$	0.605885	−	0.349808i	0.0299225	−	0.0172758i
$411$		0			0
$412$	0.867010	−	0.500568i	0.0427145	−	0.0246612i
$413$	11.2591	+	22.1780i	0.554026	+	1.09131i
$414$		0			0
$415$	0.265826	+	0.460425i	0.0130489	+	0.0226014i
$416$	−3.84040			−0.188291
$417$		0			0
$418$			22.9747i			1.12373i
$419$	11.5649	−	20.0310i	0.564984	−	0.978580i	−0.432068	−	0.901841i	$-0.642216\pi$
$419$	11.5649	−	20.0310i	0.564984	−	0.978580i	0.997051	−	0.0767392i	$-0.0244509\pi$
$420$		0			0
$421$	5.49773	+	9.52235i	0.267943	+	0.464091i	0.968330	−	0.249672i	$-0.0803228\pi$
$421$	5.49773	+	9.52235i	0.267943	+	0.464091i	−0.700387	+	0.713763i	$0.746989\pi$
$422$	−8.13339	+	4.69581i	−0.395927	+	0.228589i
$423$		0			0
$424$	−3.63101	+	6.28910i	−0.176338	+	0.305426i
$425$	−3.87314	+	6.70848i	−0.187875	+	0.325409i
$426$		0			0
$427$	−0.180696	−	0.117724i	−0.00874448	−	0.00569707i
$428$	8.02352	+	4.63238i	0.387832	+	0.223915i
$429$		0			0
$430$		−	0.0994966i		−	0.00479815i
$431$	−7.19720	−	4.15530i	−0.346677	−	0.200154i	0.316544	−	0.948578i	$-0.397478\pi$
$431$	−7.19720	−	4.15530i	−0.346677	−	0.200154i	−0.663221	+	0.748424i	$0.730811\pi$
$432$		0			0
$433$		−	26.1051i		−	1.25453i	−0.778806	−	0.627265i	$-0.784174\pi$
$433$		−	26.1051i		−	1.25453i	0.778806	−	0.627265i	$-0.215826\pi$
$434$	3.34454	+	0.180223i	0.160543	+	0.00865096i
$435$		0			0
$436$	1.64300			0.0786855
$437$	−16.1597	−	27.9894i	−0.773022	−	1.33891i
$438$		0			0
$439$	−35.3605	−	20.4154i	−1.68766	−	0.974373i	−0.956301	−	0.292383i	$-0.905552\pi$
$439$	−35.3605	−	20.4154i	−1.68766	−	0.974373i	−0.731362	−	0.681990i	$-0.761115\pi$
$440$	−0.265644			−0.0126641
$441$		0			0
$442$	5.95522			0.283261
$443$	15.8106	+	9.12824i	0.751183	+	0.433696i	0.826121	−	0.563492i	$-0.190543\pi$
$443$	15.8106	+	9.12824i	0.751183	+	0.433696i	−0.0749382	+	0.997188i	$0.523876\pi$
$444$		0			0
$445$	0.395328	+	0.684728i	0.0187403	+	0.0324592i
$446$	−20.5184			−0.971576
$447$		0			0
$448$	2.64192	+	0.142361i	0.124819	+	0.00672594i
$449$		−	26.0881i		−	1.23117i	−0.788070	−	0.615586i	$-0.788919\pi$
$449$		−	26.0881i		−	1.23117i	0.788070	−	0.615586i	$-0.211081\pi$
$450$		0			0
$451$	35.2134	+	20.3305i	1.65813	+	0.957325i
$452$		−	15.7659i		−	0.741567i
$453$		0			0
$454$	−16.2610	−	9.38828i	−0.763166	−	0.440614i
$455$	0.575562	+	0.374981i	0.0269828	+	0.0175794i
$456$		0			0
$457$	3.19987	−	5.54233i	0.149683	−	0.259259i	−0.781427	−	0.623997i	$-0.785508\pi$
$457$	3.19987	−	5.54233i	0.149683	−	0.259259i	0.931110	+	0.364737i	$0.118841\pi$
$458$	2.49265	−	4.31740i	0.116474	−	0.201739i
$459$		0			0
$460$	0.323625	−	0.186845i	0.0150891	−	0.00871170i
$461$	1.04099	+	1.80304i	0.0484836	+	0.0839761i	0.889249	−	0.457424i	$-0.151228\pi$
$461$	1.04099	+	1.80304i	0.0484836	+	0.0839761i	−0.840765	+	0.541400i	$0.817894\pi$
$462$		0			0
$463$	−0.959084	+	1.66118i	−0.0445724	+	0.0772017i	−0.887451	−	0.460902i	$-0.847526\pi$
$463$	−0.959084	+	1.66118i	−0.0445724	+	0.0772017i	0.842879	+	0.538104i	$0.180859\pi$
$464$		−	1.39534i		−	0.0647771i
$465$		0			0
$466$	−14.7510			−0.683325
$467$	−17.1178	−	29.6488i	−0.792116	−	1.37199i	−0.924654	−	0.380807i	$-0.875646\pi$
$467$	−17.1178	−	29.6488i	−0.792116	−	1.37199i	0.132539	−	0.991178i	$-0.457687\pi$
$468$		0			0
$469$	−18.3784	−	36.2015i	−0.848637	−	1.67163i
$470$	−0.207419	+	0.119754i	−0.00956754	+	0.00552382i
$471$		0			0
$472$	−8.14138	+	4.70043i	−0.374737	+	0.216355i
$473$	5.00791	−	2.89132i	0.230264	−	0.132943i
$474$		0			0
$475$	−25.2956	+	14.6044i	−1.16064	+	0.670096i
$476$	−4.09675	−	0.220756i	−0.187774	−	0.0101183i
$477$		0			0
$478$	−0.0897132	−	0.155388i	−0.00410339	−	0.00710728i
$479$	−10.5825			−0.483525			−0.241763	−	0.970335i	$-0.577726\pi$
$479$	−10.5825			−0.483525			−0.241763	+	0.970335i	$0.577726\pi$
$480$		0			0
$481$			33.4526i			1.52531i
$482$	3.06679	−	5.31183i	0.139688	−	0.241947i
$483$		0			0
$484$	−2.21947	−	3.84424i	−0.100885	−	0.174738i
$485$	0.0245613	−	0.0141804i	0.00111527	−	0.000643901i
$486$		0			0
$487$	5.95804	−	10.3196i	0.269985	−	0.467627i	−0.698873	−	0.715246i	$-0.746315\pi$
$487$	5.95804	−	10.3196i	0.269985	−	0.467627i	0.968858	+	0.247619i	$0.0796481\pi$
$488$	0.0407562	−	0.0705919i	0.00184495	−	0.00319554i
$489$		0			0
$490$	−0.382044	−	0.279295i	−0.0172590	−	0.0126173i
$491$	14.9826	+	8.65023i	0.676157	+	0.390379i	0.798406	−	0.602120i	$-0.205677\pi$
$491$	14.9826	+	8.65023i	0.676157	+	0.390379i	−0.122248	+	0.992500i	$0.539010\pi$
$492$		0			0
$493$			2.16372i			0.0974490i
$494$	19.4468	+	11.2276i	0.874954	+	0.505155i
$495$		0			0
$496$			1.26595i			0.0568429i
$497$	0.613542	−	11.3860i	0.0275211	−	0.510733i
$498$		0			0
$499$	−12.8297			−0.574335			−0.287168	−	0.957880i	$-0.592714\pi$
$499$	−12.8297			−0.574335			−0.287168	+	0.957880i	$0.592714\pi$
$500$	−0.337880	−	0.585225i	−0.0151104	−	0.0261721i
$501$		0			0
$502$	0.963852	+	0.556480i	0.0430188	+	0.0248369i
$503$	−10.9868			−0.489878			−0.244939	−	0.969539i	$-0.578768\pi$
$503$	−10.9868			−0.489878			−0.244939	+	0.969539i	$0.578768\pi$
$504$		0			0
$505$	1.17585			0.0523245
$506$	18.8088	+	10.8593i	0.836152	+	0.482753i
$507$		0			0
$508$	−9.53878	−	16.5216i	−0.423215	−	0.733030i
$509$	28.9677			1.28397			0.641985	−	0.766717i	$-0.278111\pi$
$509$	28.9677			1.28397			0.641985	+	0.766717i	$0.278111\pi$
$510$		0			0
$511$	−15.6852	−	10.2190i	−0.693872	−	0.452061i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	4.11130	+	2.37366i	0.181342	+	0.104698i
$515$		−	0.0676837i		−	0.00298250i
$516$		0			0
$517$	−12.0550	−	6.95996i	−0.530178	−	0.306099i
$518$	1.24007	−	23.0129i	0.0544854	−	1.01113i
$519$		0			0
$520$	−0.129819	+	0.224853i	−0.00569293	+	0.00986045i
$521$	−5.72133	+	9.90963i	−0.250656	+	0.434149i	−0.963707	−	0.266964i	$-0.913980\pi$
$521$	−5.72133	+	9.90963i	−0.250656	+	0.434149i	0.713051	+	0.701113i	$0.247313\pi$
$522$		0			0
$523$	14.1536	−	8.17161i	0.618896	−	0.357320i	−0.157543	−	0.987512i	$-0.550357\pi$
$523$	14.1536	−	8.17161i	0.618896	−	0.357320i	0.776439	+	0.630192i	$0.217024\pi$
$524$	9.33404	+	16.1670i	0.407759	+	0.706260i
$525$		0			0
$526$	2.10817	−	3.65146i	0.0919206	−	0.159211i
$527$		−	1.96308i		−	0.0855130i
$528$		0			0
$529$	−7.55220			−0.328356
$530$	0.245482	+	0.425186i	0.0106630	+	0.0184689i
$531$		0			0
$532$	−12.9618	−	8.44468i	−0.561965	−	0.366123i
$533$	34.4173	−	19.8708i	1.49078	−	0.860700i
$534$		0			0
$535$	0.542445	−	0.313181i	0.0234520	−	0.0135400i
$536$	13.2893	−	7.67257i	0.574010	−	0.331405i
$537$		0			0
$538$	−13.8090	+	7.97265i	−0.595350	+	0.343725i
$539$	2.95563	−	27.3454i	0.127308	−	1.17785i
$540$		0			0
$541$	15.9752	+	27.6699i	0.686830	+	1.18962i	0.972858	+	0.231403i	$0.0743314\pi$
$541$	15.9752	+	27.6699i	0.686830	+	1.18962i	−0.286029	+	0.958221i	$0.592335\pi$
$542$	−16.3867			−0.703869
$543$		0			0
$544$		−	1.55067i		−	0.0664846i
$545$	0.0555391	−	0.0961966i	0.00237903	−	0.00412061i
$546$		0			0
$547$	15.4351	+	26.7344i	0.659958	+	1.14308i	0.980626	+	0.195889i	$0.0627591\pi$
$547$	15.4351	+	26.7344i	0.659958	+	1.14308i	−0.320668	+	0.947192i	$0.603908\pi$
$548$	−5.44329	+	3.14269i	−0.232526	+	0.134249i
$549$		0			0
$550$	9.81413	−	16.9986i	0.418476	−	0.724821i
$551$	−4.07936	+	7.06565i	−0.173786	+	0.301007i
$552$		0			0
$553$	−9.88789	+	15.1770i	−0.420476	+	0.645392i
$554$	1.60735	+	0.928004i	0.0682897	+	0.0394271i
$555$		0			0
$556$		−	6.34619i		−	0.269138i
$557$	12.2398	+	7.06667i	0.518618	+	0.299424i	0.736369	−	0.676580i	$-0.236539\pi$
$557$	12.2398	+	7.06667i	0.518618	+	0.299424i	−0.217751	+	0.976004i	$0.569872\pi$
$558$		0			0
$559$		−	5.65190i		−	0.239050i
$560$	0.0976411	−	0.149870i	0.00412609	−	0.00633317i
$561$		0			0
$562$	−0.725661			−0.0306102
$563$	2.55718	+	4.42916i	0.107772	+	0.186667i	0.914867	−	0.403754i	$-0.132295\pi$
$563$	2.55718	+	4.42916i	0.107772	+	0.186667i	−0.807095	+	0.590421i	$0.798962\pi$
$564$		0			0
$565$	−0.923083	−	0.532942i	−0.0388344	−	0.0224211i
$566$	−11.6276			−0.488746
$567$		0			0
$568$	4.30975			0.180833
$569$	−32.2337	−	18.6101i	−1.35131	−	0.780177i	−0.362874	−	0.931838i	$-0.618204\pi$
$569$	−32.2337	−	18.6101i	−1.35131	−	0.780177i	−0.988433	+	0.151661i	$0.951538\pi$
$570$		0			0
$571$	−2.63869	−	4.57035i	−0.110426	−	0.191263i	0.805516	−	0.592574i	$-0.201888\pi$
$571$	−2.63869	−	4.57035i	−0.110426	−	0.191263i	−0.915942	+	0.401311i	$0.868555\pi$
$572$	−15.0899			−0.630939
$573$		0			0
$574$	−24.4132	+	12.3938i	−1.01899	+	0.517309i
$575$			27.6118i			1.15149i
$576$		0			0
$577$	−9.72172	−	5.61284i	−0.404721	−	0.233666i	0.283798	−	0.958884i	$-0.408405\pi$
$577$	−9.72172	−	5.61284i	−0.404721	−	0.233666i	−0.688519	+	0.725218i	$0.741739\pi$
$578$		−	14.5954i		−	0.607089i
$579$		0			0
$580$	−0.0816962	−	0.0471673i	−0.00339225	−	0.00195852i
$581$	−9.41834	−	18.5521i	−0.390739	−	0.769670i
$582$		0			0
$583$	−14.2671	+	24.7114i	−0.590884	+	1.02344i
$584$	3.53782	−	6.12768i	0.146396	−	0.253565i
$585$		0			0
$586$	11.1723	−	6.45034i	0.461524	−	0.266461i
$587$	12.4037	+	21.4838i	0.511955	+	0.886732i	0.999904	+	0.0138602i	$0.00441196\pi$
$587$	12.4037	+	21.4838i	0.511955	+	0.886732i	−0.487949	+	0.872872i	$0.662255\pi$
$588$		0			0
$589$	3.70108	−	6.41046i	0.152500	−	0.264138i
$590$			0.635563i			0.0261657i
$591$		0			0
$592$	8.71069			0.358007
$593$	−6.47382	−	11.2130i	−0.265848	−	0.460462i	0.701938	−	0.712238i	$-0.252319\pi$
$593$	−6.47382	−	11.2130i	−0.265848	−	0.460462i	−0.967785	+	0.251777i	$0.918985\pi$
$594$		0			0
$595$	−0.151410	+	0.232400i	−0.00620718	+	0.00952746i
$596$	7.21992	−	4.16842i	0.295739	−	0.170745i
$597$		0			0
$598$	18.3835	−	10.6137i	0.751758	−	0.434028i
$599$	20.9209	−	12.0787i	0.854804	−	0.493522i	−0.00746462	−	0.999972i	$-0.502376\pi$
$599$	20.9209	−	12.0787i	0.854804	−	0.493522i	0.862269	+	0.506451i	$0.169043\pi$
$600$		0			0
$601$	15.3377	−	8.85525i	0.625640	−	0.361213i	−0.153422	−	0.988161i	$-0.549029\pi$
$601$	15.3377	−	8.85525i	0.625640	−	0.361213i	0.779061	+	0.626948i	$0.215696\pi$
$602$	−0.209512	+	3.88809i	−0.00853908	+	0.158467i
$603$		0			0
$604$	7.07721	+	12.2581i	0.287967	+	0.498774i
$605$	−0.300103			−0.0122009
$606$		0			0
$607$			6.08758i			0.247087i	0.992339	+	0.123544i	$0.0394259\pi$
$607$			6.08758i			0.247087i	−0.992339	+	0.123544i	$0.960574\pi$
$608$	2.92356	−	5.06375i	0.118566	−	0.205362i
$609$		0			0
$610$	−0.00275540	−	0.00477249i	−0.000111563	−	0.000193233i
$611$	−11.7824	+	6.80260i	−0.476667	+	0.275204i
$612$		0			0
$613$	16.5026	−	28.5834i	0.666535	−	1.15447i	−0.312332	−	0.949973i	$-0.601110\pi$
$613$	16.5026	−	28.5834i	0.666535	−	1.15447i	0.978867	−	0.204499i	$-0.0655566\pi$
$614$	10.2555	−	17.7631i	0.413880	−	0.716861i
$615$		0			0
$616$	10.3807	+	0.559372i	0.418252	+	0.0225377i
$617$	8.36942	+	4.83209i	0.336940	+	0.194533i	0.658918	−	0.752215i	$-0.271014\pi$
$617$	8.36942	+	4.83209i	0.336940	+	0.194533i	−0.321978	+	0.946747i	$0.604348\pi$
$618$		0			0
$619$			18.1007i			0.727528i	0.931491	+	0.363764i	$0.118508\pi$
$619$			18.1007i			0.727528i	−0.931491	+	0.363764i	$0.881492\pi$
$620$	0.0741205	+	0.0427935i	0.00297675	+	0.00171863i
$621$		0			0
$622$		−	15.0288i		−	0.602601i
$623$	−14.0066	−	27.5900i	−0.561164	−	1.10537i
$624$		0			0
$625$	24.9315			0.997258
$626$	0.557679	+	0.965929i	0.0222893	+	0.0386063i
$627$		0			0
$628$	−14.2542	−	8.22967i	−0.568805	−	0.328400i
$629$	−13.5074			−0.538577
$630$		0			0
$631$	−5.07079			−0.201865			−0.100932	−	0.994893i	$-0.532183\pi$
$631$	−5.07079			−0.201865			−0.100932	+	0.994893i	$0.532183\pi$
$632$	−5.92915	−	3.42320i	−0.235849	−	0.136167i
$633$		0			0
$634$	−0.616719	−	1.06819i	−0.0244931	−	0.0424232i
$635$	−1.28977			−0.0511831
$636$		0			0
$637$	−21.7020	−	15.8654i	−0.859865	−	0.628609i
$638$		−	5.48263i		−	0.217060i
$639$		0			0
$640$	0.0585493	+	0.0338034i	0.00231436	+	0.00133620i
$641$		−	8.80698i		−	0.347855i	−0.984758	−	0.173927i	$-0.944354\pi$
$641$		−	8.80698i		−	0.347855i	0.984758	−	0.173927i	$-0.0556458\pi$
$642$		0			0
$643$	2.52364	+	1.45702i	0.0995227	+	0.0574594i	0.548935	−	0.835865i	$-0.315033\pi$
$643$	2.52364	+	1.45702i	0.0995227	+	0.0574594i	−0.449413	+	0.893324i	$0.648367\pi$
$644$	−13.0400	+	6.62001i	−0.513847	+	0.260865i
$645$		0			0
$646$	−4.53348	+	7.85222i	−0.178367	+	0.308941i
$647$	−5.15173	+	8.92306i	−0.202535	+	0.350802i	−0.949345	−	0.314237i	$-0.898251\pi$
$647$	−5.15173	+	8.92306i	−0.202535	+	0.350802i	0.746809	+	0.665038i	$0.231585\pi$
$648$		0			0
$649$	−31.9895	+	18.4691i	−1.25570	+	0.724976i
$650$	−9.59223	−	16.6142i	−0.376238	−	0.651664i
$651$		0			0
$652$	4.53345	−	7.85216i	0.177544	−	0.307515i
$653$		−	17.7439i		−	0.694371i	−0.937796	−	0.347186i	$-0.887137\pi$
$653$		−	17.7439i		−	0.694371i	0.937796	−	0.347186i	$-0.112863\pi$
$654$		0			0
$655$	1.26209			0.0493140
$656$	−5.17415	−	8.96188i	−0.202016	−	0.349903i
$657$		0			0
$658$	8.35763	−	4.24292i	0.325814	−	0.165406i
$659$	4.08467	−	2.35828i	0.159116	−	0.0918657i	−0.418328	−	0.908296i	$-0.637384\pi$
$659$	4.08467	−	2.35828i	0.159116	−	0.0918657i	0.577444	+	0.816430i	$0.304050\pi$
$660$		0			0
$661$	8.16557	−	4.71439i	0.317604	−	0.183369i	−0.332720	−	0.943026i	$-0.607966\pi$
$661$	8.16557	−	4.71439i	0.317604	−	0.183369i	0.650324	+	0.759657i	$0.274633\pi$
$662$	−4.35145	+	2.51231i	−0.169124	+	0.0976438i
$663$		0			0
$664$	6.81032	−	3.93194i	0.264292	−	0.152589i
$665$	−0.932583	+	0.473445i	−0.0361640	+	0.0183594i
$666$		0			0
$667$	3.85631	+	6.67932i	0.149317	+	0.258624i
$668$	15.2984			0.591914
$669$		0			0
$670$		−	1.03744i		−	0.0400797i
$671$	0.160141	−	0.277372i	0.00618218	−	0.0107078i
$672$		0			0
$673$	−6.42728	−	11.1324i	−0.247753	−	0.429122i	0.715149	−	0.698972i	$-0.246359\pi$
$673$	−6.42728	−	11.1324i	−0.247753	−	0.429122i	−0.962902	+	0.269851i	$0.913026\pi$
$674$	−18.4213	+	10.6356i	−0.709563	+	0.409666i
$675$		0			0
$676$	−0.874352	+	1.51442i	−0.0336289	+	0.0582470i
$677$	−24.5946	+	42.5991i	−0.945248	+	1.63722i	−0.189995	+	0.981785i	$0.560847\pi$
$677$	−24.5946	+	42.5991i	−0.945248	+	1.63722i	−0.755253	+	0.655433i	$0.772486\pi$
$678$		0			0
$679$	−0.989657	+	0.502420i	−0.0379795	+	0.0192811i
$680$	−0.0907908	−	0.0524181i	−0.00348167	−	0.00201014i
$681$		0			0
$682$			4.97423i			0.190473i
$683$	36.2732	+	20.9424i	1.38796	+	0.801337i	0.993085	−	0.117399i	$-0.0374556\pi$
$683$	36.2732	+	20.9424i	1.38796	+	0.801337i	0.394872	+	0.918736i	$0.370789\pi$
$684$		0			0
$685$			0.424934i			0.0162359i
$686$	14.3413	+	11.7187i	0.547553	+	0.447422i
$687$		0			0
$688$	−1.47169			−0.0561078
$689$	13.9446	+	24.1527i	0.531245	+	0.920144i
$690$		0			0
$691$	−5.56780	−	3.21457i	−0.211809	−	0.122288i	0.390343	−	0.920670i	$-0.372356\pi$
$691$	−5.56780	−	3.21457i	−0.211809	−	0.122288i	−0.602152	+	0.798382i	$0.705690\pi$
$692$	2.30125			0.0874804
$693$		0			0
$694$	−21.5735			−0.818919
$695$	−0.371565	−	0.214523i	−0.0140942	−	0.00813732i
$696$		0			0
$697$	8.02342	+	13.8970i	0.303909	+	0.526385i
$698$	−27.8404			−1.05378
$699$		0			0
$700$	5.98288	+	11.7850i	0.226132	+	0.445430i
$701$			33.7907i			1.27626i	0.769930	+	0.638129i	$0.220291\pi$
$701$			33.7907i			1.27626i	−0.769930	+	0.638129i	$0.779709\pi$
$702$		0			0
$703$	−44.1087	−	25.4662i	−1.66359	−	0.960475i
$704$			3.92924i			0.148089i
$705$		0			0
$706$	4.93850	+	2.85124i	0.185863	+	0.107308i
$707$	−45.9493	−	2.47601i	−1.72810	−	0.0931199i
$708$		0			0
$709$	14.8416	−	25.7065i	0.557390	−	0.965427i	−0.440324	−	0.897839i	$-0.645136\pi$
$709$	14.8416	−	25.7065i	0.557390	−	0.965427i	0.997713	−	0.0675879i	$-0.0215303\pi$
$710$	0.145685	−	0.252333i	0.00546744	−	0.00946989i
$711$		0			0
$712$	10.1281	−	5.84745i	0.379566	−	0.219142i
$713$	−3.49871	−	6.05995i	−0.131028	−	0.226947i
$714$		0			0
$715$	−0.510090	+	0.883501i	−0.0190763	+	0.0330411i
$716$		−	15.9437i		−	0.595845i
$717$		0			0
$718$	21.4560			0.800733
$719$	−18.1588	−	31.4519i	−0.677207	−	1.17296i	−0.975818	−	0.218583i	$-0.929857\pi$
$719$	−18.1588	−	31.4519i	−0.677207	−	1.17296i	0.298611	−	0.954375i	$-0.403477\pi$
$720$		0			0
$721$	−0.142523	+	2.64492i	−0.00530784	+	0.0985020i
$722$	−13.1538	+	7.59435i	−0.489534	+	0.282632i
$723$		0			0
$724$	−15.9804	+	9.22629i	−0.593907	+	0.342892i
$725$	6.03648	−	3.48516i	0.224189	−	0.129436i
$726$		0			0
$727$	−14.9225	+	8.61552i	−0.553446	+	0.319532i	−0.750511	−	0.660858i	$-0.770192\pi$
$727$	−14.9225	+	8.61552i	−0.553446	+	0.319532i	0.197065	+	0.980390i	$0.436859\pi$
$728$	5.54650	−	8.51336i	0.205567	−	0.315526i
$729$		0			0
$730$	−0.239181	−	0.414273i	−0.00885248	−	0.0153329i
$731$	2.28212			0.0844071
$732$		0			0
$733$			43.0596i			1.59044i	0.606319	+	0.795222i	$0.292646\pi$
$733$			43.0596i			1.59044i	−0.606319	+	0.795222i	$0.707354\pi$
$734$	−4.60428	+	7.97484i	−0.169947	+	0.294357i
$735$		0			0
$736$	−2.76370	−	4.78687i	−0.101871	−	0.176446i
$737$	52.2168	−	30.1474i	1.92343	−	1.11049i
$738$		0			0
$739$	−1.87511	+	3.24778i	−0.0689770	+	0.119472i	−0.898451	−	0.439073i	$-0.855307\pi$
$739$	−1.87511	+	3.24778i	−0.0689770	+	0.119472i	0.829474	+	0.558545i	$0.188640\pi$
$740$	0.294451	−	0.510005i	0.0108242	−	0.0187481i
$741$		0			0
$742$	−8.69752	−	17.1322i	−0.319296	−	0.628943i
$743$	23.9862	+	13.8484i	0.879967	+	0.508049i	0.870648	−	0.491907i	$-0.163700\pi$
$743$	23.9862	+	13.8484i	0.879967	+	0.508049i	0.00931965	+	0.999957i	$0.497033\pi$
$744$		0			0
$745$		−	0.563628i		−	0.0206497i
$746$	−24.4219	−	14.1000i	−0.894151	−	0.516238i
$747$		0			0
$748$		−	6.09297i		−	0.222781i
$749$	−21.8570	+	11.0961i	−0.798636	+	0.405444i
$750$		0			0
$751$	−4.17712			−0.152425			−0.0762127	−	0.997092i	$-0.524283\pi$
$751$	−4.17712			−0.152425			−0.0762127	+	0.997092i	$0.524283\pi$
$752$	1.77132	+	3.06802i	0.0645935	+	0.111879i
$753$		0			0
$754$	−4.64075	−	2.67934i	−0.169006	−	0.0975757i
$755$	0.956936			0.0348264
$756$		0			0
$757$	35.9359			1.30611			0.653057	−	0.757309i	$-0.273486\pi$
$757$	35.9359			1.30611			0.653057	+	0.757309i	$0.273486\pi$
$758$	4.09257	+	2.36284i	0.148649	+	0.0858224i
$759$		0			0
$760$	−0.197652	−	0.342344i	−0.00716961	−	0.0124181i
$761$	29.1430			1.05643			0.528216	−	0.849110i	$-0.322861\pi$
$761$	29.1430			1.05643			0.528216	+	0.849110i	$0.322861\pi$
$762$		0			0
$763$	−2.37290	+	3.64219i	−0.0859048	+	0.131856i
$764$		−	23.3437i		−	0.844546i
$765$		0			0
$766$	29.6483	+	17.1174i	1.07124	+	0.618478i
$767$			36.1031i			1.30361i
$768$		0			0
$769$	−0.795911	−	0.459519i	−0.0287013	−	0.0165707i	0.485581	−	0.874192i	$-0.338608\pi$
$769$	−0.795911	−	0.459519i	−0.0287013	−	0.0165707i	−0.514282	+	0.857621i	$0.671942\pi$
$770$	0.383655	−	0.588876i	0.0138260	−	0.0212216i
$771$		0			0
$772$	10.6439	−	18.4357i	0.383082	−	0.663517i
$773$	−4.69708	+	8.13558i	−0.168942	+	0.292616i	−0.938048	−	0.346505i	$-0.887368\pi$
$773$	−4.69708	+	8.13558i	−0.168942	+	0.292616i	0.769106	+	0.639121i	$0.220702\pi$
$774$		0			0
$775$	−5.47672	+	3.16199i	−0.196730	+	0.113582i
$776$	−0.209749	−	0.363295i	−0.00752954	−	0.0130415i
$777$		0			0
$778$	−9.24726	+	16.0167i	−0.331530	+	0.574228i
$779$			60.5076i			2.16791i
$780$		0			0
$781$	16.9341			0.605949
$782$	4.28560	+	7.42288i	0.153253	+	0.265442i
$783$		0			0
$784$	−4.13117	+	5.65097i	−0.147542	+	0.201820i
$785$	−0.963683	+	0.556383i	−0.0343953	+	0.0198581i
$786$		0			0
$787$	−26.4969	+	15.2980i	−0.944513	+	0.545315i	−0.891372	−	0.453272i	$-0.850257\pi$
$787$	−26.4969	+	15.2980i	−0.944513	+	0.545315i	−0.0531407	+	0.998587i	$0.516923\pi$
$788$	−11.1255	+	6.42334i	−0.396331	+	0.228822i
$789$		0			0
$790$	−0.400851	+	0.231432i	−0.0142617	+	0.00823397i
$791$	34.9497	+	22.7699i	1.24267	+	0.809604i
$792$		0			0
$793$	−0.156520	−	0.271101i	−0.00555820	−	0.00962709i
$794$	2.03373			0.0721744
$795$		0			0
$796$		−	3.74301i		−	0.132667i
$797$	−1.64717	+	2.85299i	−0.0583459	+	0.101058i	−0.893723	−	0.448619i	$-0.851916\pi$
$797$	−1.64717	+	2.85299i	−0.0583459	+	0.101058i	0.835377	+	0.549677i	$0.185249\pi$
$798$		0			0
$799$	−2.74674	−	4.75750i	−0.0971728	−	0.168308i
$800$	−4.32617	+	2.49771i	−0.152953	+	0.0883075i
$801$		0			0
$802$	15.7118	−	27.2137i	0.554804	−	0.960948i
$803$	13.9009	−	24.0771i	0.490554	−	0.849664i
$804$		0			0
$805$	−0.0531991	+	0.987260i	−0.00187502	+	0.0347963i
$806$	4.21041	+	2.43088i	0.148305	+	0.0856242i
$807$		0			0
$808$		−	17.3924i		−	0.611863i
$809$	19.7833	+	11.4219i	0.695542	+	0.401572i	0.805685	−	0.592344i	$-0.201797\pi$
$809$	19.7833	+	11.4219i	0.695542	+	0.401572i	−0.110143	+	0.993916i	$0.535131\pi$
$810$		0			0
$811$			23.9412i			0.840691i	0.907364	+	0.420345i	$0.138091\pi$
$811$			23.9412i			0.840691i	−0.907364	+	0.420345i	$0.861909\pi$
$812$	3.09318	+	2.01522i	0.108549	+	0.0707203i
$813$		0			0
$814$	34.2264			1.19964
$815$	−0.306492	−	0.530860i	−0.0107360	−	0.0185952i
$816$		0			0
$817$	7.45228	+	4.30258i	0.260722	+	0.150528i
$818$	0.550583			0.0192507
$819$		0			0
$820$	−0.699616			−0.0244316
$821$	−1.97936	−	1.14278i	−0.0690802	−	0.0398834i	0.465062	−	0.885278i	$-0.346032\pi$
$821$	−1.97936	−	1.14278i	−0.0690802	−	0.0398834i	−0.534142	+	0.845395i	$0.679365\pi$
$822$		0			0
$823$	11.4851	+	19.8928i	0.400347	+	0.693421i	0.993768	−	0.111471i	$-0.0355563\pi$
$823$	11.4851	+	19.8928i	0.400347	+	0.693421i	−0.593421	+	0.804892i	$0.702223\pi$
$824$	−1.00114			−0.0348762
$825$		0			0
$826$	1.33832	−	24.8363i	0.0465661	−	0.864165i
$827$		−	15.1679i		−	0.527438i	−0.964600	−	0.263719i	$-0.915051\pi$
$827$		−	15.1679i		−	0.527438i	0.964600	−	0.263719i	$-0.0849492\pi$
$828$		0			0
$829$	−5.73806	−	3.31287i	−0.199291	−	0.115061i	0.397034	−	0.917804i	$-0.370040\pi$
$829$	−5.73806	−	3.31287i	−0.199291	−	0.115061i	−0.596325	+	0.802743i	$0.703373\pi$
$830$		−	0.531653i		−	0.0184539i
$831$		0			0
$832$	3.32589	+	1.92020i	0.115304	+	0.0665710i
$833$	6.40610	−	8.76281i	0.221958	−	0.303613i
$834$		0			0
$835$	0.517140	−	0.895712i	0.0178964	−	0.0309974i
$836$	11.4874	−	19.8967i	0.397299	−	0.688141i
$837$		0			0
$838$	−20.0310	+	11.5649i	−0.691961	+	0.399504i
$839$	23.8462	+	41.3029i	0.823264	+	1.42593i	0.903239	+	0.429138i	$0.141182\pi$
$839$	23.8462	+	41.3029i	0.823264	+	1.42593i	−0.0799756	+	0.996797i	$0.525484\pi$
$840$		0			0
$841$	−13.5265	+	23.4286i	−0.466431	+	0.807883i
$842$		−	10.9955i		−	0.378929i
$843$		0			0
$844$	9.39162			0.323273
$845$	0.0591122	+	0.102385i	0.00203352	+	0.00352216i
$846$		0			0
$847$	11.7273	+	0.631934i	0.402956	+	0.0217135i
$848$	6.28910	−	3.63101i	0.215969	−	0.124690i
$849$		0			0
$850$	6.70848	−	3.87314i	0.230099	−	0.132848i
$851$	−41.6970	+	24.0738i	−1.42935	+	0.825238i
$852$		0			0
$853$	−22.0983	+	12.7585i	−0.756632	+	0.436842i	−0.828085	−	0.560602i	$-0.810570\pi$
$853$	−22.0983	+	12.7585i	−0.756632	+	0.436842i	0.0714529	+	0.997444i	$0.477236\pi$
$854$	0.0976251	+	0.192300i	0.00334066	+	0.00658037i
$855$		0			0
$856$	−4.63238	−	8.02352i	−0.158332	−	0.274238i
$857$	6.38085			0.217966			0.108983	−	0.994044i	$-0.465241\pi$
$857$	6.38085			0.217966			0.108983	+	0.994044i	$0.465241\pi$
$858$		0			0
$859$		−	34.3486i		−	1.17196i	−0.810326	−	0.585980i	$-0.800710\pi$
$859$		−	34.3486i		−	1.17196i	0.810326	−	0.585980i	$-0.199290\pi$
$860$	−0.0497483	+	0.0861666i	−0.00169640	+	0.00293826i
$861$		0			0
$862$	4.15530	+	7.19720i	0.141530	+	0.245137i
$863$	−31.3380	+	18.0930i	−1.06676	+	0.615893i	−0.927294	−	0.374334i	$-0.877871\pi$
$863$	−31.3380	+	18.0930i	−1.06676	+	0.615893i	−0.139464	+	0.990227i	$0.544538\pi$
$864$		0			0
$865$	0.0777901	−	0.134736i	0.00264494	−	0.00458118i
$866$	−13.0525	+	22.6077i	−0.443543	+	0.768240i
$867$		0			0
$868$	−2.80635	−	1.82835i	−0.0952536	−	0.0620582i
$869$	−23.2971	−	13.4506i	−0.790299	−	0.456279i
$870$		0			0
$871$		−	58.9315i		−	1.99682i
$872$	−1.42288	−	0.821501i	−0.0481849	−	0.0278195i
$873$		0			0
$874$			32.3193i			1.09322i
$875$	1.78530	+	0.0962021i	0.0603542	+	0.00325222i
$876$		0			0
$877$	34.0309			1.14914			0.574571	−	0.818455i	$-0.305169\pi$
$877$	34.0309			1.14914			0.574571	+	0.818455i	$0.305169\pi$
$878$	20.4154	+	35.3605i	0.688986	+	1.19336i
$879$		0			0
$880$	0.230054	+	0.132822i	0.00775513	+	0.00447742i
$881$	26.6961			0.899416			0.449708	−	0.893176i	$-0.351528\pi$
$881$	26.6961			0.899416			0.449708	+	0.893176i	$0.351528\pi$
$882$		0			0
$883$	11.2126			0.377333			0.188667	−	0.982041i	$-0.439583\pi$
$883$	11.2126			0.377333			0.188667	+	0.982041i	$0.439583\pi$
$884$	−5.15737	−	2.97761i	−0.173461	−	0.100148i
$885$		0			0
$886$	−9.12824	−	15.8106i	−0.306669	−	0.531167i
$887$	−10.1871			−0.342048			−0.171024	−	0.985267i	$-0.554708\pi$
$887$	−10.1871			−0.342048			−0.171024	+	0.985267i	$0.554708\pi$
$888$		0			0
$889$	50.4013	+	2.71591i	1.69041	+	0.0910886i
$890$		−	0.790656i		−	0.0265028i
$891$		0			0
$892$	17.7695	+	10.2592i	0.594966	+	0.343504i
$893$		−	20.7142i		−	0.693176i
$894$		0			0
$895$	−0.933494	−	0.538953i	−0.0312033	−	0.0180152i
$896$	−2.21679	−	1.44425i	−0.0740577	−	0.0482489i
$897$		0			0
$898$	−13.0440	+	22.5929i	−0.435285	+	0.753936i
$899$	−0.883217	+	1.52978i	−0.0294569	+	0.0510209i
$900$		0			0
$901$	−9.75235	+	5.63052i	−0.324898	+	0.187580i
$902$	−20.3305	−	35.2134i	−0.676931	−	1.17248i
$903$		0			0
$904$	−7.88296	+	13.6537i	−0.262183	+	0.454115i
$905$			1.24752i			0.0414690i
$906$		0			0
$907$	−15.1486			−0.503000			−0.251500	−	0.967857i	$-0.580924\pi$
$907$	−15.1486			−0.503000			−0.251500	+	0.967857i	$0.580924\pi$
$908$	9.38828	+	16.2610i	0.311561	+	0.539640i
$909$		0			0
$910$	−0.310960	−	0.612524i	−0.0103082	−	0.0203050i
$911$	8.43020	−	4.86718i	0.279305	−	0.161257i	−0.353804	−	0.935320i	$-0.615112\pi$
$911$	8.43020	−	4.86718i	0.279305	−	0.161257i	0.633109	+	0.774063i	$0.281779\pi$
$912$		0			0
$913$	26.7594	−	15.4496i	0.885607	−	0.511306i
$914$	−5.54233	+	3.19987i	−0.183324	+	0.105842i
$915$		0			0
$916$	−4.31740	+	2.49265i	−0.142651	+	0.0823596i
$917$	−49.3195	−	2.65761i	−1.62867	−	0.0877621i
$918$		0			0
$919$	−4.01638	−	6.95658i	−0.132488	−	0.229476i	0.792147	−	0.610330i	$-0.208963\pi$
$919$	−4.01638	−	6.95658i	−0.132488	−	0.229476i	−0.924635	+	0.380854i	$0.875630\pi$
$920$	−0.373691			−0.0123202
$921$		0			0
$922$		−	2.08197i		−	0.0685662i
$923$	8.27560	−	14.3338i	0.272395	−	0.471801i
$924$		0			0
$925$	21.7568	+	37.6839i	0.715360	+	1.23904i
$926$	1.66118	−	0.959084i	0.0545898	−	0.0315175i
$927$		0			0
$928$	−0.697671	+	1.20840i	−0.0229022	+	0.0396677i
$929$	13.1064	−	22.7010i	0.430007	−	0.744794i	−0.566866	−	0.823810i	$-0.691844\pi$
$929$	13.1064	−	22.7010i	0.430007	−	0.744794i	0.996873	+	0.0790158i	$0.0251777\pi$
$930$		0			0
$931$	37.4401	−	16.5374i	1.22705	−	0.541990i
$932$	12.7747	+	7.37548i	0.418449	+	0.241592i
$933$		0			0
$934$			34.2355i			1.12022i
$935$	−0.356739	−	0.205963i	−0.0116666	−	0.00673573i
$936$		0			0
$937$			37.5797i			1.22768i	0.789432	+	0.613838i	$0.210375\pi$
$937$			37.5797i			1.22768i	−0.789432	+	0.613838i	$0.789625\pi$
$938$	−2.18456	+	40.5406i	−0.0713283	+	1.32370i
$939$		0			0
$940$	0.239507			0.00781186
$941$	−4.63655	−	8.03074i	−0.151147	−	0.261794i	0.780502	−	0.625153i	$-0.214963\pi$
$941$	−4.63655	−	8.03074i	−0.151147	−	0.261794i	−0.931649	+	0.363358i	$0.881630\pi$
$942$		0			0
$943$	49.5360	+	28.5996i	1.61311	+	0.931331i
$944$	9.40086			0.305972
$945$		0			0
$946$	−5.78264			−0.188010
$947$	12.0019	+	6.92928i	0.390008	+	0.225171i	0.682164	−	0.731199i	$-0.261039\pi$
$947$	12.0019	+	6.92928i	0.390008	+	0.225171i	−0.292155	+	0.956371i	$0.594372\pi$
$948$		0			0
$949$	−13.5866	−	23.5328i	−0.441041	−	0.763906i
$950$	29.2088			0.947659
$951$		0			0
$952$	3.43752	+	2.23956i	0.111411	+	0.0725845i
$953$			2.65523i			0.0860115i	0.999075	+	0.0430057i	$0.0136934\pi$
$953$			2.65523i			0.0860115i	−0.999075	+	0.0430057i	$0.986307\pi$
$954$		0			0
$955$	−1.36676	−	0.789097i	−0.0442272	−	0.0255346i
$956$			0.179426i			0.00580307i
$957$		0			0
$958$	9.16468	+	5.29123i	0.296098	+	0.170952i
$959$	0.894794	−	16.6054i	0.0288944	−	0.536218i
$960$		0			0
$961$	−14.6987	+	25.4589i	−0.474151	+	0.821254i
$962$	16.7263	−	28.9708i	0.539277	−	0.934055i
$963$		0			0
$964$	−5.31183	+	3.06679i	−0.171083	+	0.0987746i
$965$	−0.719600	−	1.24638i	−0.0231647	−	0.0401225i
$966$		0			0
$967$	7.14946	−	12.3832i	0.229911	−	0.398218i	−0.727870	−	0.685715i	$-0.759490\pi$
$967$	7.14946	−	12.3832i	0.229911	−	0.398218i	0.957782	+	0.287497i	$0.0928231\pi$
$968$			4.43894i			0.142673i
$969$		0			0
$970$	−0.0283609			−0.000910613
$971$	0.130666	+	0.226320i	0.00419326	+	0.00726295i	0.868114	−	0.496364i	$-0.165332\pi$
$971$	0.130666	+	0.226320i	0.00419326	+	0.00726295i	−0.863921	+	0.503627i	$0.831999\pi$
$972$		0			0
$973$	14.0681	+	9.16546i	0.451004	+	0.293831i
$974$	−10.3196	+	5.95804i	−0.330662	+	0.190908i
$975$		0			0
$976$	−0.0705919	+	0.0407562i	−0.00225959	+	0.00130457i
$977$	−33.9113	+	19.5787i	−1.08492	+	0.626378i	−0.932219	−	0.361894i	$-0.882130\pi$
$977$	−33.9113	+	19.5787i	−1.08492	+	0.626378i	−0.152700	+	0.988273i	$0.548797\pi$
$978$		0			0
$979$	39.7957	−	22.9760i	1.27188	−	0.734318i
$980$	0.191212	+	0.432899i	0.00610805	+	0.0138285i
$981$		0			0
$982$	−8.65023	−	14.9826i	−0.276040	−	0.478115i
$983$	−26.3688			−0.841035			−0.420517	−	0.907285i	$-0.638151\pi$
$983$	−26.3688			−0.841035			−0.420517	+	0.907285i	$0.638151\pi$
$984$		0			0
$985$			0.868524i			0.0276735i
$986$	1.08186	−	1.87384i	0.0344534	−	0.0596751i
$987$		0			0
$988$	−11.2276	−	19.4468i	−0.357199	−	0.618686i
$989$	7.04481	−	4.06732i	0.224012	−	0.129333i
$990$		0			0
$991$	−22.9516	+	39.7534i	−0.729082	+	1.26281i	0.228189	+	0.973617i	$0.426720\pi$
$991$	−22.9516	+	39.7534i	−0.729082	+	1.26281i	−0.957271	+	0.289191i	$0.906614\pi$
$992$	0.632976	−	1.09635i	0.0200970	−	0.0348090i
$993$		0			0
$994$	−6.22435	+	9.55381i	−0.197424	+	0.303028i
$995$	−0.219150	−	0.126526i	−0.00694753	−	0.00401116i
$996$		0			0
$997$		−	21.4693i		−	0.679939i	−0.940437	−	0.339969i	$-0.889583\pi$
$997$		−	21.4693i		−	0.679939i	0.940437	−	0.339969i	$-0.110417\pi$
$998$	11.1108	+	6.41484i	0.351707	+	0.203058i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.t.a.17.3		16
3.2	odd	2		126.2.t.a.59.7	yes	16
4.3	odd	2		3024.2.df.c.17.5		16
7.2	even	3		2646.2.l.a.1097.6		16
7.3	odd	6		2646.2.m.b.881.7		16
7.4	even	3		2646.2.m.a.881.6		16
7.5	odd	6		378.2.l.a.341.7		16
7.6	odd	2		2646.2.t.b.2285.2		16
9.2	odd	6		378.2.l.a.143.3		16
9.4	even	3		1134.2.k.a.647.6		16
9.5	odd	6		1134.2.k.b.647.3		16
9.7	even	3		126.2.l.a.101.6	yes	16
12.11	even	2		1008.2.df.c.689.2		16
21.2	odd	6		882.2.l.b.509.3		16
21.5	even	6		126.2.l.a.5.2	✓	16
21.11	odd	6		882.2.m.a.293.1		16
21.17	even	6		882.2.m.b.293.4		16
21.20	even	2		882.2.t.a.815.6		16
28.19	even	6		3024.2.ca.c.2609.5		16
36.7	odd	6		1008.2.ca.c.353.4		16
36.11	even	6		3024.2.ca.c.2033.5		16
63.2	odd	6		2646.2.t.b.1979.2		16
63.5	even	6		1134.2.k.a.971.6		16
63.11	odd	6		2646.2.m.b.1763.7		16
63.16	even	3		882.2.t.a.803.6		16
63.20	even	6		2646.2.l.a.521.2		16
63.25	even	3		882.2.m.b.587.4		16
63.34	odd	6		882.2.l.b.227.7		16
63.38	even	6		2646.2.m.a.1763.6		16
63.40	odd	6		1134.2.k.b.971.3		16
63.47	even	6	inner	378.2.t.a.89.3		16
63.52	odd	6		882.2.m.a.587.1		16
63.61	odd	6		126.2.t.a.47.7	yes	16
84.47	odd	6		1008.2.ca.c.257.4		16
252.47	odd	6		3024.2.df.c.1601.5		16
252.187	even	6		1008.2.df.c.929.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.2	✓	16	21.5	even	6
126.2.l.a.101.6	yes	16	9.7	even	3
126.2.t.a.47.7	yes	16	63.61	odd	6
126.2.t.a.59.7	yes	16	3.2	odd	2
378.2.l.a.143.3		16	9.2	odd	6
378.2.l.a.341.7		16	7.5	odd	6
378.2.t.a.17.3		16	1.1	even	1	trivial
378.2.t.a.89.3		16	63.47	even	6	inner
882.2.l.b.227.7		16	63.34	odd	6
882.2.l.b.509.3		16	21.2	odd	6
882.2.m.a.293.1		16	21.11	odd	6
882.2.m.a.587.1		16	63.52	odd	6
882.2.m.b.293.4		16	21.17	even	6
882.2.m.b.587.4		16	63.25	even	3
882.2.t.a.803.6		16	63.16	even	3
882.2.t.a.815.6		16	21.20	even	2
1008.2.ca.c.257.4		16	84.47	odd	6
1008.2.ca.c.353.4		16	36.7	odd	6
1008.2.df.c.689.2		16	12.11	even	2
1008.2.df.c.929.2		16	252.187	even	6
1134.2.k.a.647.6		16	9.4	even	3
1134.2.k.a.971.6		16	63.5	even	6
1134.2.k.b.647.3		16	9.5	odd	6
1134.2.k.b.971.3		16	63.40	odd	6
2646.2.l.a.521.2		16	63.20	even	6
2646.2.l.a.1097.6		16	7.2	even	3
2646.2.m.a.881.6		16	7.4	even	3
2646.2.m.a.1763.6		16	63.38	even	6
2646.2.m.b.881.7		16	7.3	odd	6
2646.2.m.b.1763.7		16	63.11	odd	6
2646.2.t.b.1979.2		16	63.2	odd	6
2646.2.t.b.2285.2		16	7.6	odd	2
3024.2.ca.c.2033.5		16	36.11	even	6
3024.2.ca.c.2609.5		16	28.19	even	6
3024.2.df.c.17.5		16	4.3	odd	2
3024.2.df.c.1601.5		16	252.47	odd	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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +0.0676069 q^{5} +(-2.64192 - 0.142361i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +0.0676069 q^{5} +(-2.64192 - 0.142361i) q^{7} -1.00000i q^{8} +(-0.0585493 - 0.0338034i) q^{10} -3.92924i q^{11} +(-3.32589 - 1.92020i) q^{13} +(2.21679 + 1.44425i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.775337 - 1.34292i) q^{17} +(5.06375 - 2.92356i) q^{19} +(0.0338034 + 0.0585493i) q^{20} +(-1.96462 + 3.40282i) q^{22} -5.52740i q^{23} -4.99543 q^{25} +(1.92020 + 3.32589i) q^{26} +(-1.19767 - 2.35915i) q^{28} +(-1.20840 + 0.697671i) q^{29} +(1.09635 - 0.632976i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.34292 + 0.775337i) q^{34} +(-0.178612 - 0.00962461i) q^{35} +(-4.35534 - 7.54368i) q^{37} -5.84711 q^{38} -0.0676069i q^{40} +(-5.17415 + 8.96188i) q^{41} +(0.735847 + 1.27452i) q^{43} +(3.40282 - 1.96462i) q^{44} +(-2.76370 + 4.78687i) q^{46} +(1.77132 - 3.06802i) q^{47} +(6.95947 + 0.752214i) q^{49} +(4.32617 + 2.49771i) q^{50} -3.84040i q^{52} +(-6.28910 - 3.63101i) q^{53} -0.265644i q^{55} +(-0.142361 + 2.64192i) q^{56} +1.39534 q^{58} +(-4.70043 - 8.14138i) q^{59} +(0.0705919 + 0.0407562i) q^{61} -1.26595 q^{62} -1.00000 q^{64} +(-0.224853 - 0.129819i) q^{65} +(7.67257 + 13.2893i) q^{67} +1.55067 q^{68} +(0.149870 + 0.0976411i) q^{70} +4.30975i q^{71} +(6.12768 + 3.53782i) q^{73} +8.71069i q^{74} +(5.06375 + 2.92356i) q^{76} +(-0.559372 + 10.3807i) q^{77} +(3.42320 - 5.92915i) q^{79} +(-0.0338034 + 0.0585493i) q^{80} +(8.96188 - 5.17415i) q^{82} +(3.93194 + 6.81032i) q^{83} +(0.0524181 - 0.0907908i) q^{85} -1.47169i q^{86} -3.92924 q^{88} +(5.84745 + 10.1281i) q^{89} +(8.51336 + 5.54650i) q^{91} +(4.78687 - 2.76370i) q^{92} +(-3.06802 + 1.77132i) q^{94} +(0.342344 - 0.197652i) q^{95} +(0.363295 - 0.209749i) q^{97} +(-5.65097 - 4.13117i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 2 q^{7}+O(q^{10}) \) 16 * q + 8 * q^4 + 2 * q^7	\( 16 q + 8 q^{4} + 2 q^{7} - 6 q^{13} + 6 q^{14} - 8 q^{16} - 18 q^{17} + 16 q^{25} + 12 q^{26} - 2 q^{28} - 6 q^{29} + 6 q^{31} + 30 q^{35} - 2 q^{37} - 6 q^{41} - 2 q^{43} - 12 q^{44} + 6 q^{46} + 18 q^{47} + 10 q^{49} + 12 q^{50} - 36 q^{53} - 12 q^{58} - 30 q^{59} - 60 q^{61} + 36 q^{62} - 16 q^{64} - 42 q^{65} + 14 q^{67} - 36 q^{68} + 18 q^{77} - 16 q^{79} - 12 q^{85} - 24 q^{89} - 12 q^{91} - 6 q^{92} + 66 q^{95} - 6 q^{97} - 24 q^{98}+O(q^{100}) \) 16 * q + 8 * q^4 + 2 * q^7 - 6 * q^13 + 6 * q^14 - 8 * q^16 - 18 * q^17 + 16 * q^25 + 12 * q^26 - 2 * q^28 - 6 * q^29 + 6 * q^31 + 30 * q^35 - 2 * q^37 - 6 * q^41 - 2 * q^43 - 12 * q^44 + 6 * q^46 + 18 * q^47 + 10 * q^49 + 12 * q^50 - 36 * q^53 - 12 * q^58 - 30 * q^59 - 60 * q^61 + 36 * q^62 - 16 * q^64 - 42 * q^65 + 14 * q^67 - 36 * q^68 + 18 * q^77 - 16 * q^79 - 12 * q^85 - 24 * q^89 - 12 * q^91 - 6 * q^92 + 66 * q^95 - 6 * q^97 - 24 * q^98

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