LMFDB - Embedded newform 1170.2.cu.f.1151.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1170,2,Mod(71,1170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1170, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 5]))

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

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

chi := DirichletCharacter("1170.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.cu (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
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} - 12x^{14} + 49x^{12} - 12x^{10} - 600x^{8} + 108x^{6} + 4057x^{4} + 18252x^{2} + 28561 $ x^16 - 12x^14 + 49x^12 - 12x^10 - 600x^8 + 108x^6 + 4057x^4 + 18252*x^2 + 28561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			1151.3
Root			$0.115299 - 1.50155i$ of defining polynomial
Character	$\chi$	$=$	1170.1151
Dual form			1170.2.cu.f.431.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-1.03475 - 0.277260i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-1.03475 - 0.277260i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{10} +(0.105325 - 0.0282216i) q^{11} +(1.19781 - 3.40077i) q^{13} -1.07125i q^{14} +(0.500000 - 0.866025i) q^{16} +(-1.09921 - 1.90389i) q^{17} +(0.578305 - 2.15826i) q^{19} +(-0.258819 + 0.965926i) q^{20} +(0.0545200 + 0.0944314i) q^{22} +(1.34004 - 2.32102i) q^{23} -1.00000i q^{25} +(3.59491 + 0.276806i) q^{26} +(1.03475 - 0.277260i) q^{28} +(0.745303 + 0.430301i) q^{29} +(-0.123514 - 0.123514i) q^{31} +(0.965926 + 0.258819i) q^{32} +(1.55452 - 1.55452i) q^{34} +(-0.927730 + 0.535625i) q^{35} +(-2.82648 - 10.5486i) q^{37} +2.23440 q^{38} -1.00000 q^{40} +(1.03528 + 3.86370i) q^{41} +(10.5279 - 6.07830i) q^{43} +(-0.0771029 + 0.0771029i) q^{44} +(2.58877 + 0.693658i) q^{46} +(8.91173 + 8.91173i) q^{47} +(-5.06835 - 2.92621i) q^{49} +(0.965926 - 0.258819i) q^{50} +(0.663057 + 3.54406i) q^{52} +3.57666i q^{53} +(0.0545200 - 0.0944314i) q^{55} +(0.535625 + 0.927730i) q^{56} +(-0.222740 + 0.831277i) q^{58} +(2.10359 - 7.85072i) q^{59} +(-4.30104 - 7.44963i) q^{61} +(0.0873374 - 0.151273i) q^{62} +1.00000i q^{64} +(-1.55773 - 3.25169i) q^{65} +(-3.67803 + 0.985526i) q^{67} +(1.90389 + 1.09921i) q^{68} +(-0.757488 - 0.757488i) q^{70} +(3.12935 + 0.838506i) q^{71} +(9.26565 - 9.26565i) q^{73} +(9.45759 - 5.46034i) q^{74} +(0.578305 + 2.15826i) q^{76} -0.116809 q^{77} +3.58347 q^{79} +(-0.258819 - 0.965926i) q^{80} +(-3.46410 + 2.00000i) q^{82} +(-6.23094 + 6.23094i) q^{83} +(-2.12351 - 0.568994i) q^{85} +(8.59602 + 8.59602i) q^{86} +(-0.0944314 - 0.0545200i) q^{88} +(0.486484 - 0.130353i) q^{89} +(-2.18233 + 3.18684i) q^{91} +2.68009i q^{92} +(-6.30155 + 10.9146i) q^{94} +(-1.11720 - 1.93504i) q^{95} +(-1.35837 + 5.06950i) q^{97} +(1.51472 - 5.65301i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{7}+O(q^{10}) $ 16 * q + 12 * q^7	$ 16 q + 12 q^{7} - 8 q^{13} + 8 q^{16} - 52 q^{19} - 8 q^{22} - 12 q^{28} + 36 q^{31} + 16 q^{34} + 8 q^{37} - 16 q^{40} + 72 q^{43} + 32 q^{46} + 60 q^{49} + 12 q^{52} - 8 q^{55} - 8 q^{58} - 12 q^{61} - 12 q^{67} + 12 q^{70} + 8 q^{73} - 52 q^{76} + 8 q^{79} + 4 q^{85} + 24 q^{88} - 84 q^{91} - 16 q^{94} - 96 q^{97}+O(q^{100}) $ 16 * q + 12 * q^7 - 8 * q^13 + 8 * q^16 - 52 * q^19 - 8 * q^22 - 12 * q^28 + 36 * q^31 + 16 * q^34 + 8 * q^37 - 16 * q^40 + 72 * q^43 + 32 * q^46 + 60 * q^49 + 12 * q^52 - 8 * q^55 - 8 * q^58 - 12 * q^61 - 12 * q^67 + 12 * q^70 + 8 * q^73 - 52 * q^76 + 8 * q^79 + 4 * q^85 + 24 * q^88 - 84 * q^91 - 16 * q^94 - 96 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$-1$	$1$	$e\left(\frac{11}{12}\right)$

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 $

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$		0			0
$3$		0			0
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$		0			0
$7$	−1.03475	−	0.277260i	−0.391098	−	0.104794i	0.0579107	−	0.998322i	$-0.481556\pi$
$7$	−1.03475	−	0.277260i	−0.391098	−	0.104794i	−0.449009	+	0.893527i	$0.648223\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	0.866025	+	0.500000i	0.273861	+	0.158114i
$11$	0.105325	−	0.0282216i	0.0317565	−	0.00850914i	−0.242906	−	0.970050i	$-0.578101\pi$
$11$	0.105325	−	0.0282216i	0.0317565	−	0.00850914i	0.274662	+	0.961541i	$0.411434\pi$
$12$		0			0
$13$	1.19781	−	3.40077i	0.332211	−	0.943205i
$13$	1.19781	−	3.40077i	0.332211	−	0.943205i
$14$		−	1.07125i		−	0.286304i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−1.09921	−	1.90389i	−0.266598	−	0.461761i	0.701383	−	0.712785i	$-0.252566\pi$
$17$	−1.09921	−	1.90389i	−0.266598	−	0.461761i	−0.967981	+	0.251023i	$0.919233\pi$
$18$		0			0
$19$	0.578305	−	2.15826i	0.132672	−	0.495139i	−0.867324	−	0.497743i	$-0.834162\pi$
$19$	0.578305	−	2.15826i	0.132672	−	0.495139i	0.999997	+	0.00260393i	$0.000828859\pi$
$20$	−0.258819	+	0.965926i	−0.0578737	+	0.215988i
$21$		0			0
$22$	0.0545200	+	0.0944314i	0.0116237	+	0.0201328i
$23$	1.34004	−	2.32102i	0.279418	−	0.483967i	−0.691822	−	0.722068i	$-0.743192\pi$
$23$	1.34004	−	2.32102i	0.279418	−	0.483967i	0.971240	+	0.238101i	$0.0765250\pi$
$24$		0			0
$25$		−	1.00000i		−	0.200000i
$26$	3.59491	+	0.276806i	0.705020	+	0.0542861i
$27$		0			0
$28$	1.03475	−	0.277260i	0.195549	−	0.0523972i
$29$	0.745303	+	0.430301i	0.138399	+	0.0799048i	0.567601	−	0.823304i	$-0.307872\pi$
$29$	0.745303	+	0.430301i	0.138399	+	0.0799048i	−0.429202	+	0.903209i	$0.641205\pi$
$30$		0			0
$31$	−0.123514	−	0.123514i	−0.0221837	−	0.0221837i	0.695928	−	0.718112i	$-0.254993\pi$
$31$	−0.123514	−	0.123514i	−0.0221837	−	0.0221837i	−0.718112	+	0.695928i	$0.754993\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$		0			0
$34$	1.55452	−	1.55452i	0.266598	−	0.266598i
$35$	−0.927730	+	0.535625i	−0.156815	+	0.0905372i
$36$		0			0
$37$	−2.82648	−	10.5486i	−0.464671	−	1.73418i	−0.657978	−	0.753037i	$-0.728588\pi$
$37$	−2.82648	−	10.5486i	−0.464671	−	1.73418i	0.193308	−	0.981138i	$-0.438078\pi$
$38$	2.23440			0.362467
$39$		0			0
$40$	−1.00000			−0.158114
$41$	1.03528	+	3.86370i	0.161683	+	0.603409i	0.998440	+	0.0558348i	$0.0177820\pi$
$41$	1.03528	+	3.86370i	0.161683	+	0.603409i	−0.836757	+	0.547574i	$0.815551\pi$
$42$		0			0
$43$	10.5279	−	6.07830i	1.60549	−	0.926933i	0.615134	−	0.788423i	$-0.289102\pi$
$43$	10.5279	−	6.07830i	1.60549	−	0.926933i	0.990361	−	0.138510i	$-0.0442313\pi$
$44$	−0.0771029	+	0.0771029i	−0.0116237	+	0.0116237i
$45$		0			0
$46$	2.58877	+	0.693658i	0.381693	+	0.102274i
$47$	8.91173	+	8.91173i	1.29991	+	1.29991i	0.928448	+	0.371462i	$0.121143\pi$
$47$	8.91173	+	8.91173i	1.29991	+	1.29991i	0.371462	+	0.928448i	$0.378857\pi$
$48$		0			0
$49$	−5.06835	−	2.92621i	−0.724050	−	0.418030i
$50$	0.965926	−	0.258819i	0.136603	−	0.0366025i
$51$		0			0
$52$	0.663057	+	3.54406i	0.0919495	+	0.491473i
$53$			3.57666i			0.491292i	0.969360	+	0.245646i	$0.0790001\pi$
$53$			3.57666i			0.491292i	−0.969360	+	0.245646i	$0.921000\pi$
$54$		0			0
$55$	0.0545200	−	0.0944314i	0.00735147	−	0.0127331i
$56$	0.535625	+	0.927730i	0.0715759	+	0.123973i
$57$		0			0
$58$	−0.222740	+	0.831277i	−0.0292472	+	0.109152i
$59$	2.10359	−	7.85072i	0.273865	−	1.02208i	−0.682734	−	0.730667i	$-0.739209\pi$
$59$	2.10359	−	7.85072i	0.273865	−	1.02208i	0.956598	−	0.291409i	$-0.0941242\pi$
$60$		0			0
$61$	−4.30104	−	7.44963i	−0.550692	−	0.953827i	−0.998225	−	0.0595594i	$-0.981030\pi$
$61$	−4.30104	−	7.44963i	−0.550692	−	0.953827i	0.447532	−	0.894268i	$-0.352303\pi$
$62$	0.0873374	−	0.151273i	0.0110919	−	0.0192117i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−1.55773	−	3.25169i	−0.193213	−	0.403322i
$66$		0			0
$67$	−3.67803	+	0.985526i	−0.449343	+	0.120401i	−0.476392	−	0.879233i	$-0.658056\pi$
$67$	−3.67803	+	0.985526i	−0.449343	+	0.120401i	0.0270488	+	0.999634i	$0.491389\pi$
$68$	1.90389	+	1.09921i	0.230881	+	0.133299i
$69$		0			0
$70$	−0.757488	−	0.757488i	−0.0905372	−	0.0905372i
$71$	3.12935	+	0.838506i	0.371385	+	0.0995123i	0.439684	−	0.898153i	$-0.355090\pi$
$71$	3.12935	+	0.838506i	0.371385	+	0.0995123i	−0.0682988	+	0.997665i	$0.521757\pi$
$72$		0			0
$73$	9.26565	−	9.26565i	1.08446	−	1.08446i	0.0883749	−	0.996087i	$-0.471833\pi$
$73$	9.26565	−	9.26565i	1.08446	−	1.08446i	0.996087	−	0.0883749i	$-0.0281674\pi$
$74$	9.45759	−	5.46034i	1.09942	−	0.634752i
$75$		0			0
$76$	0.578305	+	2.15826i	0.0663361	+	0.247570i
$77$	−0.116809			−0.0133116
$78$		0			0
$79$	3.58347			0.403172			0.201586	−	0.979471i	$-0.435391\pi$
$79$	3.58347			0.403172			0.201586	+	0.979471i	$0.435391\pi$
$80$	−0.258819	−	0.965926i	−0.0289368	−	0.107994i
$81$		0			0
$82$	−3.46410	+	2.00000i	−0.382546	+	0.220863i
$83$	−6.23094	+	6.23094i	−0.683934	+	0.683934i	−0.960884	−	0.276950i	$-0.910676\pi$
$83$	−6.23094	+	6.23094i	−0.683934	+	0.683934i	0.276950	+	0.960884i	$0.410676\pi$
$84$		0			0
$85$	−2.12351	−	0.568994i	−0.230327	−	0.0617160i
$86$	8.59602	+	8.59602i	0.926933	+	0.926933i
$87$		0			0
$88$	−0.0944314	−	0.0545200i	−0.0100664	−	0.00581185i
$89$	0.486484	−	0.130353i	0.0515672	−	0.0138174i	−0.232943	−	0.972490i	$-0.574836\pi$
$89$	0.486484	−	0.130353i	0.0515672	−	0.0138174i	0.284510	+	0.958673i	$0.408169\pi$
$90$		0			0
$91$	−2.18233	+	3.18684i	−0.228770	+	0.334072i
$92$			2.68009i			0.279418i
$93$		0			0
$94$	−6.30155	+	10.9146i	−0.649955	+	1.12576i
$95$	−1.11720	−	1.93504i	−0.114622	−	0.198531i
$96$		0			0
$97$	−1.35837	+	5.06950i	−0.137921	+	0.514729i	0.862047	+	0.506828i	$0.169182\pi$
$97$	−1.35837	+	5.06950i	−0.137921	+	0.514729i	−0.999969	+	0.00790183i	$0.997485\pi$
$98$	1.51472	−	5.65301i	0.153010	−	0.571040i
$99$		0			0
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−4.35338	+	7.54028i	−0.433178	+	0.750285i	−0.997145	−	0.0755116i	$-0.975941\pi$
$101$	−4.35338	+	7.54028i	−0.433178	+	0.750285i	0.563967	+	0.825797i	$0.309274\pi$
$102$		0			0
$103$		−	3.66430i		−	0.361054i	−0.983570	−	0.180527i	$-0.942220\pi$
$103$		−	3.66430i		−	0.361054i	0.983570	−	0.180527i	$-0.0577803\pi$
$104$	−3.25169	+	1.55773i	−0.318854	+	0.152748i
$105$		0			0
$106$	−3.45479	+	0.925708i	−0.335559	+	0.0899127i
$107$	1.44217	+	0.832640i	0.139420	+	0.0804944i	0.568088	−	0.822968i	$-0.307683\pi$
$107$	1.44217	+	0.832640i	0.139420	+	0.0804944i	−0.428667	+	0.903462i	$0.641017\pi$
$108$		0			0
$109$	3.39561	+	3.39561i	0.325241	+	0.325241i	0.850773	−	0.525533i	$-0.176134\pi$
$109$	3.39561	+	3.39561i	0.325241	+	0.325241i	−0.525533	+	0.850773i	$0.676134\pi$
$110$	0.105325	+	0.0282216i	0.0100423	+	0.00269083i
$111$		0			0
$112$	−0.757488	+	0.757488i	−0.0715759	+	0.0715759i
$113$	8.54251	−	4.93202i	0.803612	−	0.463965i	−0.0411207	−	0.999154i	$-0.513093\pi$
$113$	8.54251	−	4.93202i	0.803612	−	0.463965i	0.844733	+	0.535189i	$0.179759\pi$
$114$		0			0
$115$	−0.693658	−	2.58877i	−0.0646839	−	0.241404i
$116$	−0.860601			−0.0799048
$117$		0			0
$118$	8.12766			0.748212
$119$	0.609535	+	2.27481i	0.0558760	+	0.208532i
$120$		0			0
$121$	−9.51598	+	5.49406i	−0.865089	+	0.499460i
$122$	6.08260	−	6.08260i	0.550692	−	0.550692i
$123$		0			0
$124$	0.168723	+	0.0452092i	0.0151518	+	0.00405990i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$		0			0
$127$	9.27412	+	5.35441i	0.822945	+	0.475127i	0.851431	−	0.524467i	$-0.175735\pi$
$127$	9.27412	+	5.35441i	0.822945	+	0.475127i	−0.0284860	+	0.999594i	$0.509069\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$		0			0
$130$	2.73772	−	2.34625i	0.240114	−	0.205780i
$131$		−	2.94079i		−	0.256938i	−0.991714	−	0.128469i	$-0.958994\pi$
$131$		−	2.94079i		−	0.256938i	0.991714	−	0.128469i	$-0.0410063\pi$
$132$		0			0
$133$	−1.19680	+	2.07292i	−0.103776	+	0.179745i
$134$	−1.90389	−	3.29763i	−0.164471	−	0.284872i
$135$		0			0
$136$	−0.568994	+	2.12351i	−0.0487908	+	0.182090i
$137$	−1.11178	+	4.14923i	−0.0949861	+	0.354493i	−0.997017	−	0.0771778i	$-0.975409\pi$
$137$	−1.11178	+	4.14923i	−0.0949861	+	0.354493i	0.902031	+	0.431671i	$0.142076\pi$
$138$		0			0
$139$	−1.45442	−	2.51913i	−0.123363	−	0.213670i	0.797729	−	0.603016i	$-0.206034\pi$
$139$	−1.45442	−	2.51913i	−0.123363	−	0.213670i	−0.921092	+	0.389346i	$0.872701\pi$
$140$	0.535625	−	0.927730i	0.0452686	−	0.0784075i
$141$		0			0
$142$			3.23974i			0.271873i
$143$	0.0301829	−	0.391989i	0.00252402	−	0.0327798i
$144$		0			0
$145$	0.831277	−	0.222740i	0.0690338	−	0.0184976i
$146$	11.3481	+	6.55180i	0.939172	+	0.542231i
$147$		0			0
$148$	7.72209	+	7.72209i	0.634752	+	0.634752i
$149$	−14.4305	−	3.86664i	−1.18219	−	0.316767i	−0.386396	−	0.922333i	$-0.626280\pi$
$149$	−14.4305	−	3.86664i	−1.18219	−	0.316767i	−0.795795	+	0.605566i	$0.792947\pi$
$150$		0			0
$151$	−8.78063	+	8.78063i	−0.714557	+	0.714557i	−0.967485	−	0.252928i	$-0.918606\pi$
$151$	−8.78063	+	8.78063i	−0.714557	+	0.714557i	0.252928	+	0.967485i	$0.418606\pi$
$152$	−1.93504	+	1.11720i	−0.156953	+	0.0906168i
$153$		0			0
$154$	−0.0302324	−	0.112829i	−0.00243620	−	0.00909201i
$155$	−0.174675			−0.0140302
$156$		0			0
$157$	−6.19716			−0.494587			−0.247294	−	0.968941i	$-0.579541\pi$
$157$	−6.19716			−0.494587			−0.247294	+	0.968941i	$0.579541\pi$
$158$	0.927470	+	3.46136i	0.0737855	+	0.275371i
$159$		0			0
$160$	0.866025	−	0.500000i	0.0684653	−	0.0395285i
$161$	−2.03013	+	2.03013i	−0.159997	+	0.159997i
$162$		0			0
$163$	13.6514	+	3.65789i	1.06926	+	0.286508i	0.750191	−	0.661222i	$-0.229962\pi$
$163$	13.6514	+	3.65789i	1.06926	+	0.286508i	0.319073	+	0.947730i	$0.396628\pi$
$164$	−2.82843	−	2.82843i	−0.220863	−	0.220863i
$165$		0			0
$166$	−7.63131	−	4.40594i	−0.592304	−	0.341967i
$167$	−1.84771	+	0.495092i	−0.142980	+	0.0383113i	−0.329599	−	0.944121i	$-0.606914\pi$
$167$	−1.84771	+	0.495092i	−0.142980	+	0.0383113i	0.186619	+	0.982432i	$0.440247\pi$
$168$		0			0
$169$	−10.1305	−	8.14693i	−0.779271	−	0.626687i
$170$		−	2.19842i		−	0.168611i
$171$		0			0
$172$	−6.07830	+	10.5279i	−0.463466	+	0.802747i
$173$	−5.66735	−	9.81614i	−0.430881	−	0.746307i	0.566069	−	0.824358i	$-0.308464\pi$
$173$	−5.66735	−	9.81614i	−0.430881	−	0.746307i	−0.996949	+	0.0780510i	$0.975130\pi$
$174$		0			0
$175$	−0.277260	+	1.03475i	−0.0209589	+	0.0782196i
$176$	0.0282216	−	0.105325i	0.00212728	−	0.00793913i
$177$		0			0
$178$	0.251822	+	0.436169i	0.0188749	+	0.0326923i
$179$	4.03616	−	6.99083i	0.301677	−	0.522519i	−0.674839	−	0.737965i	$-0.735787\pi$
$179$	4.03616	−	6.99083i	0.301677	−	0.522519i	0.976516	+	0.215446i	$0.0691204\pi$
$180$		0			0
$181$			5.34777i			0.397497i	0.980051	+	0.198748i	$0.0636877\pi$
$181$			5.34777i			0.397497i	−0.980051	+	0.198748i	$0.936312\pi$
$182$	−3.64308	−	1.28315i	−0.270043	−	0.0951134i
$183$		0			0
$184$	−2.58877	+	0.693658i	−0.190846	+	0.0511371i
$185$	−9.45759	−	5.46034i	−0.695336	−	0.401452i
$186$		0			0
$187$	−0.169505	−	0.169505i	−0.0123954	−	0.0123954i
$188$	−12.1737	−	3.26192i	−0.887855	−	0.237900i
$189$		0			0
$190$	1.57996	−	1.57996i	0.114622	−	0.114622i
$191$	0.740223	−	0.427368i	0.0535606	−	0.0309232i	−0.472981	−	0.881073i	$-0.656822\pi$
$191$	0.740223	−	0.427368i	0.0535606	−	0.0309232i	0.526541	+	0.850150i	$0.323489\pi$
$192$		0			0
$193$	−4.33330	−	16.1721i	−0.311918	−	1.16409i	−0.926825	−	0.375493i	$-0.877473\pi$
$193$	−4.33330	−	16.1721i	−0.311918	−	1.16409i	0.614908	−	0.788599i	$-0.289193\pi$
$194$	−5.24833			−0.376808
$195$		0			0
$196$	5.85242			0.418030
$197$	5.60341	+	20.9122i	0.399227	+	1.48993i	0.814460	+	0.580219i	$0.197033\pi$
$197$	5.60341	+	20.9122i	0.399227	+	1.48993i	−0.415233	+	0.909715i	$0.636300\pi$
$198$		0			0
$199$	−6.12037	+	3.53360i	−0.433862	+	0.250490i	−0.700990	−	0.713171i	$-0.747258\pi$
$199$	−6.12037	+	3.53360i	−0.433862	+	0.250490i	0.267129	+	0.963661i	$0.413925\pi$
$200$	−0.707107	+	0.707107i	−0.0500000	+	0.0500000i
$201$		0			0
$202$	−8.41008	−	2.25348i	−0.591731	−	0.158554i
$203$	−0.651895	−	0.651895i	−0.0457541	−	0.0457541i
$204$		0			0
$205$	3.46410	+	2.00000i	0.241943	+	0.139686i
$206$	3.53944	−	0.948390i	0.246604	−	0.0660774i
$207$		0			0
$208$	−2.34625	−	2.73772i	−0.162683	−	0.189827i
$209$		−	0.243639i		−	0.0168528i
$210$		0			0
$211$	−11.3840	+	19.7177i	−0.783707	+	1.35742i	0.146062	+	0.989275i	$0.453340\pi$
$211$	−11.3840	+	19.7177i	−0.783707	+	1.35742i	−0.929769	+	0.368145i	$0.879993\pi$
$212$	−1.78833	−	3.09748i	−0.122823	−	0.212736i
$213$		0			0
$214$	−0.431006	+	1.60854i	−0.0294630	+	0.109957i
$215$	3.14636	−	11.7424i	0.214580	−	0.800824i
$216$		0			0
$217$	0.0935603	+	0.162051i	0.00635128	+	0.0110007i
$218$	−2.40106	+	4.15876i	−0.162620	+	0.281667i
$219$		0			0
$220$			0.109040i			0.00735147i
$221$	−7.79134	+	1.45768i	−0.524102	+	0.0980542i
$222$		0			0
$223$	14.5443	−	3.89713i	0.973957	−	0.260971i	0.263459	−	0.964670i	$-0.415136\pi$
$223$	14.5443	−	3.89713i	0.973957	−	0.260971i	0.710498	+	0.703699i	$0.248470\pi$
$224$	−0.927730	−	0.535625i	−0.0619866	−	0.0357880i
$225$		0			0
$226$	6.97493	+	6.97493i	0.463965	+	0.463965i
$227$	−4.96291	−	1.32981i	−0.329400	−	0.0882625i	0.0903288	−	0.995912i	$-0.471208\pi$
$227$	−4.96291	−	1.32981i	−0.329400	−	0.0882625i	−0.419729	+	0.907649i	$0.637875\pi$
$228$		0			0
$229$	−9.10674	+	9.10674i	−0.601790	+	0.601790i	−0.940787	−	0.338997i	$-0.889912\pi$
$229$	−9.10674	+	9.10674i	−0.601790	+	0.601790i	0.338997	+	0.940787i	$0.389912\pi$
$230$	2.32102	−	1.34004i	0.153044	−	0.0883599i
$231$		0			0
$232$	−0.222740	−	0.831277i	−0.0146236	−	0.0545760i
$233$	−24.0147			−1.57325			−0.786626	−	0.617430i	$-0.788174\pi$
$233$	−24.0147			−1.57325			−0.786626	+	0.617430i	$0.788174\pi$
$234$		0			0
$235$	12.6031			0.822135
$236$	2.10359	+	7.85072i	0.136932	+	0.511038i
$237$		0			0
$238$	−2.03954	+	1.17753i	−0.132204	+	0.0763280i
$239$	−9.02287	+	9.02287i	−0.583641	+	0.583641i	−0.935902	−	0.352261i	$-0.885413\pi$
$239$	−9.02287	+	9.02287i	−0.583641	+	0.583641i	0.352261	+	0.935902i	$0.385413\pi$
$240$		0			0
$241$	−5.76565	−	1.54490i	−0.371398	−	0.0995158i	0.0682920	−	0.997665i	$-0.478245\pi$
$241$	−5.76565	−	1.54490i	−0.371398	−	0.0995158i	−0.439690	+	0.898150i	$0.644912\pi$
$242$	−7.76977	−	7.76977i	−0.499460	−	0.499460i
$243$		0			0
$244$	7.44963	+	4.30104i	0.476914	+	0.275346i
$245$	−5.65301	+	1.51472i	−0.361157	+	0.0967718i
$246$		0			0
$247$	−6.64706	−	4.55186i	−0.422943	−	0.289628i
$248$			0.174675i			0.0110919i
$249$		0			0
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	−8.89831	−	15.4123i	−0.561656	−	0.972817i	−0.997352	−	0.0727231i	$-0.976831\pi$
$251$	−8.89831	−	15.4123i	−0.561656	−	0.972817i	0.435696	−	0.900094i	$-0.356502\pi$
$252$		0			0
$253$	0.0756364	−	0.282279i	0.00475522	−	0.0177467i
$254$	−2.77165	+	10.3439i	−0.173909	+	0.649036i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−5.30881	+	9.19513i	−0.331155	+	0.573576i	−0.982739	−	0.185000i	$-0.940771\pi$
$257$	−5.30881	+	9.19513i	−0.331155	+	0.573576i	0.651584	+	0.758577i	$0.274105\pi$
$258$		0			0
$259$			11.6988i			0.726928i
$260$	2.97488	+	2.03718i	0.184494	+	0.126340i
$261$		0			0
$262$	2.84059	−	0.761133i	0.175492	−	0.0470230i
$263$	−7.65056	−	4.41706i	−0.471754	−	0.272367i	0.245220	−	0.969468i	$-0.421140\pi$
$263$	−7.65056	−	4.41706i	−0.471754	−	0.272367i	−0.716974	+	0.697100i	$0.754473\pi$
$264$		0			0
$265$	2.52908	+	2.52908i	0.155360	+	0.155360i
$266$	−2.31204	−	0.619509i	−0.141760	−	0.0379845i
$267$		0			0
$268$	2.69251	−	2.69251i	0.164471	−	0.164471i
$269$	5.68391	−	3.28161i	0.346554	−	0.200083i	−0.316612	−	0.948555i	$-0.602545\pi$
$269$	5.68391	−	3.28161i	0.346554	−	0.200083i	0.663167	+	0.748472i	$0.269212\pi$
$270$		0			0
$271$	−2.18661	−	8.16053i	−0.132827	−	0.495717i	0.867170	−	0.498012i	$-0.165936\pi$
$271$	−2.18661	−	8.16053i	−0.132827	−	0.495717i	−0.999997	+	0.00229451i	$0.999270\pi$
$272$	−2.19842			−0.133299
$273$		0			0
$274$	−4.29560			−0.259507
$275$	−0.0282216	−	0.105325i	−0.00170183	−	0.00635131i
$276$		0			0
$277$	14.3496	−	8.28477i	0.862187	−	0.497784i	−0.00255715	−	0.999997i	$-0.500814\pi$
$277$	14.3496	−	8.28477i	0.862187	−	0.497784i	0.864744	+	0.502213i	$0.167481\pi$
$278$	2.05686	−	2.05686i	0.123363	−	0.123363i
$279$		0			0
$280$	1.03475	+	0.277260i	0.0618380	+	0.0165695i
$281$	13.5794	+	13.5794i	0.810079	+	0.810079i	0.984645	−	0.174566i	$-0.0558523\pi$
$281$	13.5794	+	13.5794i	0.810079	+	0.810079i	−0.174566	+	0.984645i	$0.555852\pi$
$282$		0			0
$283$	9.69503	+	5.59743i	0.576310	+	0.332733i	0.759666	−	0.650314i	$-0.225363\pi$
$283$	9.69503	+	5.59743i	0.576310	+	0.332733i	−0.183356	+	0.983047i	$0.558696\pi$
$284$	−3.12935	+	0.838506i	−0.185693	+	0.0497562i
$285$		0			0
$286$	0.386444	−	0.0722997i	0.0228509	−	0.00427517i
$287$		−	4.28500i		−	0.252936i
$288$		0			0
$289$	6.08347	−	10.5369i	0.357851	−	0.619816i
$290$	0.430301	+	0.745303i	0.0252681	+	0.0437657i
$291$		0			0
$292$	−3.39146	+	12.6571i	−0.198470	+	0.740701i
$293$	3.44063	−	12.8406i	0.201004	−	0.750157i	−0.789626	−	0.613588i	$-0.789726\pi$
$293$	3.44063	−	12.8406i	0.201004	−	0.750157i	0.990631	−	0.136569i	$-0.0436077\pi$
$294$		0			0
$295$	−4.06383	−	7.03876i	−0.236605	−	0.409813i
$296$	−5.46034	+	9.45759i	−0.317376	+	0.549711i
$297$		0			0
$298$		−	14.9395i		−	0.865424i
$299$	−6.28816	−	7.33732i	−0.363654	−	0.424328i
$300$		0			0
$301$	−12.5790	+	3.37054i	−0.725043	+	0.194275i
$302$	−10.7540	−	6.20884i	−0.618825	−	0.357279i
$303$		0			0
$304$	−1.57996	−	1.57996i	−0.0906168	−	0.0906168i
$305$	−8.30898	−	2.22638i	−0.475771	−	0.127482i
$306$		0			0
$307$	10.6353	−	10.6353i	0.606991	−	0.606991i	−0.335167	−	0.942159i	$-0.608793\pi$
$307$	10.6353	−	10.6353i	0.606991	−	0.606991i	0.942159	+	0.335167i	$0.108793\pi$
$308$	0.101160	−	0.0584045i	0.00576411	−	0.00332791i
$309$		0			0
$310$	−0.0452092	−	0.168723i	−0.00256771	−	0.00958282i
$311$	−14.2635			−0.808809			−0.404404	−	0.914580i	$-0.632521\pi$
$311$	−14.2635			−0.808809			−0.404404	+	0.914580i	$0.632521\pi$
$312$		0			0
$313$	15.1236			0.854838			0.427419	−	0.904054i	$-0.359423\pi$
$313$	15.1236			0.854838			0.427419	+	0.904054i	$0.359423\pi$
$314$	−1.60394	−	5.98600i	−0.0905157	−	0.337809i
$315$		0			0
$316$	−3.10337	+	1.79173i	−0.174578	+	0.100793i
$317$	−5.54215	+	5.54215i	−0.311278	+	0.311278i	−0.845405	−	0.534126i	$-0.820641\pi$
$317$	−5.54215	+	5.54215i	−0.311278	+	0.311278i	0.534126	+	0.845405i	$0.320641\pi$
$318$		0			0
$319$	0.0906424	+	0.0242876i	0.00507500	+	0.00135984i
$320$	0.707107	+	0.707107i	0.0395285	+	0.0395285i
$321$		0			0
$322$	−2.48640	−	1.43552i	−0.138562	−	0.0799985i
$323$	−4.74477	+	1.27136i	−0.264006	+	0.0707403i
$324$		0			0
$325$	−3.40077	−	1.19781i	−0.188641	−	0.0664423i
$326$			14.1330i			0.782755i
$327$		0			0
$328$	2.00000	−	3.46410i	0.110432	−	0.191273i
$329$	−6.75053	−	11.6923i	−0.372169	−	0.644616i
$330$		0			0
$331$	−8.27247	+	30.8733i	−0.454696	+	1.69695i	0.234285	+	0.972168i	$0.424725\pi$
$331$	−8.27247	+	30.8733i	−0.454696	+	1.69695i	−0.688981	+	0.724780i	$0.741941\pi$
$332$	2.28068	−	8.51162i	0.125169	−	0.467136i
$333$		0			0
$334$	−0.956444	−	1.65661i	−0.0523343	−	0.0906456i
$335$	−1.90389	+	3.29763i	−0.104021	+	0.180169i
$336$		0			0
$337$			10.3442i			0.563483i	0.959490	+	0.281742i	$0.0909121\pi$
$337$			10.3442i			0.563483i	−0.959490	+	0.281742i	$0.909088\pi$
$338$	5.24736	−	11.8939i	0.285419	−	0.646944i
$339$		0			0
$340$	2.12351	−	0.568994i	0.115164	−	0.0308580i
$341$	−0.0164948	−	0.00952327i	−0.000893243	−	0.000515714i
$342$		0			0
$343$	9.73556	+	9.73556i	0.525671	+	0.525671i
$344$	−11.7424	−	3.14636i	−0.633107	−	0.169640i
$345$		0			0
$346$	8.01484	−	8.01484i	0.430881	−	0.430881i
$347$	27.4249	−	15.8338i	1.47224	−	0.850000i	0.472731	−	0.881207i	$-0.343268\pi$
$347$	27.4249	−	15.8338i	1.47224	−	0.850000i	0.999513	+	0.0312067i	$0.00993501\pi$
$348$		0			0
$349$	−4.22925	−	15.7838i	−0.226386	−	0.844886i	−0.981844	−	0.189689i	$-0.939252\pi$
$349$	−4.22925	−	15.7838i	−0.226386	−	0.844886i	0.755458	−	0.655197i	$-0.227414\pi$
$350$	−1.07125			−0.0572607
$351$		0			0
$352$	0.109040			0.00581185
$353$	−0.337999	−	1.26143i	−0.0179899	−	0.0671392i	0.956347	−	0.292232i	$-0.0943980\pi$
$353$	−0.337999	−	1.26143i	−0.0179899	−	0.0671392i	−0.974337	+	0.225093i	$0.927731\pi$
$354$		0			0
$355$	2.80570	−	1.61987i	0.148911	−	0.0859737i
$356$	−0.356131	+	0.356131i	−0.0188749	+	0.0188749i
$357$		0			0
$358$	7.79726	+	2.08927i	0.412098	+	0.110421i
$359$	23.5889	+	23.5889i	1.24498	+	1.24498i	0.957911	+	0.287064i	$0.0926792\pi$
$359$	23.5889	+	23.5889i	1.24498	+	1.24498i	0.287064	+	0.957911i	$0.407321\pi$
$360$		0			0
$361$	12.1308	+	7.00373i	0.638464	+	0.368618i
$362$	−5.16555	+	1.38411i	−0.271495	+	0.0727470i
$363$		0			0
$364$	0.296529	−	3.85105i	0.0155423	−	0.201850i
$365$		−	13.1036i		−	0.685874i
$366$		0			0
$367$	−12.3778	+	21.4390i	−0.646118	+	1.11911i	0.337925	+	0.941173i	$0.390275\pi$
$367$	−12.3778	+	21.4390i	−0.646118	+	1.11911i	−0.984042	+	0.177935i	$0.943058\pi$
$368$	−1.34004	−	2.32102i	−0.0698546	−	0.120992i
$369$		0			0
$370$	2.82648	−	10.5486i	0.146942	−	0.548394i
$371$	0.991665	−	3.70095i	0.0514847	−	0.192144i
$372$		0			0
$373$	−11.4375	−	19.8104i	−0.592212	−	1.02574i	−0.993934	−	0.109980i	$-0.964921\pi$
$373$	−11.4375	−	19.8104i	−0.592212	−	1.02574i	0.401722	−	0.915762i	$-0.368412\pi$
$374$	0.119858	−	0.207600i	0.00619771	−	0.0107347i
$375$		0			0
$376$		−	12.6031i		−	0.649955i
$377$	2.35608	−	2.01919i	0.121344	−	0.103994i
$378$		0			0
$379$	−7.83077	+	2.09825i	−0.402240	+	0.107780i	−0.454266	−	0.890866i	$-0.650099\pi$
$379$	−7.83077	+	2.09825i	−0.402240	+	0.107780i	0.0520266	+	0.998646i	$0.483432\pi$
$380$	1.93504	+	1.11720i	0.0992657	+	0.0573111i
$381$		0			0
$382$	0.604389	+	0.604389i	0.0309232	+	0.0309232i
$383$	−9.70618	−	2.60076i	−0.495963	−	0.132893i	0.00216304	−	0.999998i	$-0.499311\pi$
$383$	−9.70618	−	2.60076i	−0.495963	−	0.132893i	−0.498126	+	0.867105i	$0.665978\pi$
$384$		0			0
$385$	−0.0825965	+	0.0825965i	−0.00420951	+	0.00420951i
$386$	14.4995	−	8.37129i	0.738005	−	0.426087i
$387$		0			0
$388$	−1.35837	−	5.06950i	−0.0689607	−	0.257365i
$389$	−0.817452			−0.0414465			−0.0207232	−	0.999785i	$-0.506597\pi$
$389$	−0.817452			−0.0414465			−0.0207232	+	0.999785i	$0.506597\pi$
$390$		0			0
$391$	−5.89197			−0.297970
$392$	1.51472	+	5.65301i	0.0765048	+	0.285520i
$393$		0			0
$394$	−18.7494	+	10.8250i	−0.944581	+	0.545354i
$395$	2.53389	−	2.53389i	0.127494	−	0.127494i
$396$		0			0
$397$	−10.8506	−	2.90742i	−0.544577	−	0.145919i	−0.0239659	−	0.999713i	$-0.507629\pi$
$397$	−10.8506	−	2.90742i	−0.544577	−	0.145919i	−0.520611	+	0.853794i	$0.674296\pi$
$398$	−4.99726	−	4.99726i	−0.250490	−	0.250490i
$399$		0			0
$400$	−0.866025	−	0.500000i	−0.0433013	−	0.0250000i
$401$	−2.69200	+	0.721320i	−0.134432	+	0.0360210i	−0.325408	−	0.945574i	$-0.605502\pi$
$401$	−2.69200	+	0.721320i	−0.134432	+	0.0360210i	0.190975	+	0.981595i	$0.438835\pi$
$402$		0			0
$403$	−0.567988	+	0.272097i	−0.0282935	+	0.0135541i
$404$		−	8.70676i		−	0.433178i
$405$		0			0
$406$	0.460960	−	0.798406i	0.0228770	−	0.0396242i
$407$	−0.595396	−	1.03126i	−0.0295127	−	0.0511174i
$408$		0			0
$409$	−4.03354	+	15.0534i	−0.199446	+	0.744341i	0.791625	+	0.611007i	$0.209235\pi$
$409$	−4.03354	+	15.0534i	−0.199446	+	0.744341i	−0.991071	+	0.133335i	$0.957432\pi$
$410$	−1.03528	+	3.86370i	−0.0511286	+	0.190815i
$411$		0			0
$412$	1.83215	+	3.17337i	0.0902635	+	0.156341i
$413$	−4.35338	+	7.54028i	−0.214216	+	0.371033i
$414$		0			0
$415$			8.81187i			0.432558i
$416$	2.03718	−	2.97488i	0.0998808	−	0.145856i
$417$		0			0
$418$	0.235337	−	0.0630583i	0.0115107	−	0.00308428i
$419$	16.5157	+	9.53535i	0.806845	+	0.465832i	0.845859	−	0.533406i	$-0.179088\pi$
$419$	16.5157	+	9.53535i	0.806845	+	0.465832i	−0.0390138	+	0.999239i	$0.512422\pi$
$420$		0			0
$421$	−1.84339	−	1.84339i	−0.0898414	−	0.0898414i	0.660758	−	0.750599i	$-0.270235\pi$
$421$	−1.84339	−	1.84339i	−0.0898414	−	0.0898414i	−0.750599	+	0.660758i	$0.770235\pi$
$422$	−21.9922	−	5.89279i	−1.07056	−	0.286857i
$423$		0			0
$424$	2.52908	−	2.52908i	0.122823	−	0.122823i
$425$	−1.90389	+	1.09921i	−0.0923522	+	0.0533196i
$426$		0			0
$427$	2.38502	+	8.90100i	0.115419	+	0.430749i
$428$	−1.66528			−0.0804944
$429$		0			0
$430$	12.1566			0.586244
$431$	5.92299	+	22.1049i	0.285300	+	1.06476i	0.948620	+	0.316419i	$0.102481\pi$
$431$	5.92299	+	22.1049i	0.285300	+	1.06476i	−0.663319	+	0.748337i	$0.730853\pi$
$432$		0			0
$433$	18.0124	−	10.3995i	0.865623	−	0.499768i	−0.000268392	−	1.00000i	$-0.500085\pi$
$433$	18.0124	−	10.3995i	0.865623	−	0.499768i	0.865891	+	0.500232i	$0.166752\pi$
$434$	−0.132314	+	0.132314i	−0.00635128	+	0.00635128i
$435$		0			0
$436$	−4.63849	−	1.24288i	−0.222143	−	0.0595231i
$437$	−4.23442	−	4.23442i	−0.202560	−	0.202560i
$438$		0			0
$439$	26.8169	+	15.4827i	1.27990	+	0.738950i	0.976830	−	0.214018i	$-0.0686553\pi$
$439$	26.8169	+	15.4827i	1.27990	+	0.738950i	0.303069	+	0.952968i	$0.401989\pi$
$440$	−0.105325	+	0.0282216i	−0.00502115	+	0.00134541i
$441$		0			0
$442$	−3.42456	−	7.14858i	−0.162890	−	0.340023i
$443$		−	24.8913i		−	1.18262i	−0.806444	−	0.591310i	$-0.798611\pi$
$443$		−	24.8913i		−	1.18262i	0.806444	−	0.591310i	$-0.201389\pi$
$444$		0			0
$445$	0.251822	−	0.436169i	0.0119375	−	0.0206764i
$446$	7.52867	+	13.0400i	0.356493	+	0.617464i
$447$		0			0
$448$	0.277260	−	1.03475i	0.0130993	−	0.0488873i
$449$	−10.3261	+	38.5375i	−0.487318	+	1.81870i	0.0820676	+	0.996627i	$0.473848\pi$
$449$	−10.3261	+	38.5375i	−0.487318	+	1.81870i	−0.569386	+	0.822070i	$0.692819\pi$
$450$		0			0
$451$	0.218080	+	0.377726i	0.0102690	+	0.0177864i
$452$	−4.93202	+	8.54251i	−0.231983	+	0.401806i
$453$		0			0
$454$		−	5.13799i		−	0.241138i
$455$	0.710300	+	3.79657i	0.0332994	+	0.177986i
$456$		0			0
$457$	17.8773	−	4.79022i	0.836266	−	0.224077i	0.184821	−	0.982772i	$-0.440830\pi$
$457$	17.8773	−	4.79022i	0.836266	−	0.224077i	0.651445	+	0.758695i	$0.274163\pi$
$458$	−11.1534	−	6.43944i	−0.521166	−	0.300895i
$459$		0			0
$460$	1.89511	+	1.89511i	0.0883599	+	0.0883599i
$461$	−12.6049	−	3.37748i	−0.587070	−	0.157305i	−0.0469562	−	0.998897i	$-0.514952\pi$
$461$	−12.6049	−	3.37748i	−0.587070	−	0.157305i	−0.540114	+	0.841592i	$0.681619\pi$
$462$		0			0
$463$	−17.8003	+	17.8003i	−0.827248	+	0.827248i	−0.987135	−	0.159887i	$-0.948887\pi$
$463$	−17.8003	+	17.8003i	−0.827248	+	0.827248i	0.159887	+	0.987135i	$0.448887\pi$
$464$	0.745303	−	0.430301i	0.0345998	−	0.0199762i
$465$		0			0
$466$	−6.21545	−	23.1964i	−0.287925	−	1.07455i
$467$	42.5798			1.97036			0.985180	−	0.171526i	$-0.0548697\pi$
$467$	42.5798			1.97036			0.985180	+	0.171526i	$0.0548697\pi$
$468$		0			0
$469$	4.07909			0.188355
$470$	3.26192	+	12.1737i	0.150461	+	0.561529i
$471$		0			0
$472$	−7.03876	+	4.06383i	−0.323985	+	0.187053i
$473$	0.937310	−	0.937310i	0.0430976	−	0.0430976i
$474$		0			0
$475$	−2.15826	−	0.578305i	−0.0990279	−	0.0265344i
$476$	−1.66528	−	1.66528i	−0.0763280	−	0.0763280i
$477$		0			0
$478$	−11.0507	−	6.38013i	−0.505448	−	0.291820i
$479$	28.3109	−	7.58589i	1.29356	−	0.346608i	0.454548	−	0.890722i	$-0.349801\pi$
$479$	28.3109	−	7.58589i	1.29356	−	0.346608i	0.839011	+	0.544114i	$0.183134\pi$
$480$		0			0
$481$	−39.2589	−	3.02291i	−1.79005	−	0.137833i
$482$		−	5.96904i		−	0.271882i
$483$		0			0
$484$	5.49406	−	9.51598i	0.249730	−	0.432545i
$485$	2.62416	+	4.54519i	0.119157	+	0.206386i
$486$		0			0
$487$	−1.16056	+	4.33128i	−0.0525901	+	0.196269i	−0.987223	−	0.159345i	$-0.949062\pi$
$487$	−1.16056	+	4.33128i	−0.0525901	+	0.196269i	0.934633	+	0.355614i	$0.115728\pi$
$488$	−2.22638	+	8.30898i	−0.100784	+	0.376130i
$489$		0			0
$490$	−2.92621	−	5.06835i	−0.132193	−	0.228965i
$491$	−0.676664	+	1.17202i	−0.0305374	+	0.0528923i	−0.880890	−	0.473321i	$-0.843055\pi$
$491$	−0.676664	+	1.17202i	−0.0305374	+	0.0528923i	0.850353	+	0.526213i	$0.176389\pi$
$492$		0			0
$493$		−	1.89197i		−	0.0852099i
$494$	2.67637	−	7.59868i	0.120416	−	0.341881i
$495$		0			0
$496$	−0.168723	+	0.0452092i	−0.00757588	+	0.00202995i
$497$	−3.00560	−	1.73529i	−0.134820	−	0.0778382i
$498$		0			0
$499$	13.0655	+	13.0655i	0.584890	+	0.584890i	0.936243	−	0.351353i	$-0.114278\pi$
$499$	13.0655	+	13.0655i	0.584890	+	0.584890i	−0.351353	+	0.936243i	$0.614278\pi$
$500$	0.965926	+	0.258819i	0.0431975	+	0.0115747i
$501$		0			0
$502$	12.5841	−	12.5841i	0.561656	−	0.561656i
$503$	21.6756	−	12.5144i	0.966466	−	0.557989i	0.0683089	−	0.997664i	$-0.478240\pi$
$503$	21.6756	−	12.5144i	0.966466	−	0.557989i	0.898157	+	0.439675i	$0.144906\pi$
$504$		0			0
$505$	2.25348	+	8.41008i	0.100278	+	0.374244i
$506$	0.292237			0.0129915
$507$		0			0
$508$	−10.7088			−0.475127
$509$	9.53269	+	35.5765i	0.422529	+	1.57690i	0.769260	+	0.638936i	$0.220625\pi$
$509$	9.53269	+	35.5765i	0.422529	+	1.57690i	−0.346731	+	0.937965i	$0.612708\pi$
$510$		0			0
$511$	−12.1566	+	7.01862i	−0.537777	+	0.310486i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$	−10.2558	−	2.74804i	−0.452366	−	0.121211i
$515$	−2.59105	−	2.59105i	−0.114175	−	0.114175i
$516$		0			0
$517$	1.19013	+	0.687121i	0.0523418	+	0.0302195i
$518$	−11.3002	+	3.02787i	−0.496501	+	0.133037i
$519$		0			0
$520$	−1.19781	+	3.40077i	−0.0525272	+	0.149134i
$521$		−	20.3941i		−	0.893480i	−0.894664	−	0.446740i	$-0.852585\pi$
$521$		−	20.3941i		−	0.893480i	0.894664	−	0.446740i	$-0.147415\pi$
$522$		0			0
$523$	2.63613	−	4.56591i	0.115270	−	0.199653i	−0.802618	−	0.596494i	$-0.796560\pi$
$523$	2.63613	−	4.56591i	0.115270	−	0.199653i	0.917888	+	0.396840i	$0.129893\pi$
$524$	1.47040	+	2.54680i	0.0642346	+	0.111258i
$525$		0			0
$526$	2.28644	−	8.53310i	0.0996933	−	0.372061i
$527$	−0.0993889	+	0.370924i	−0.00432945	+	0.0161577i
$528$		0			0
$529$	7.90857	+	13.6980i	0.343851	+	0.595567i
$530$	−1.78833	+	3.09748i	−0.0776801	+	0.134546i
$531$		0			0
$532$		−	2.39360i		−	0.103776i
$533$	14.3796	+	1.10722i	0.622851	+	0.0479592i
$534$		0			0
$535$	1.60854	−	0.431006i	0.0695431	−	0.0186340i
$536$	3.29763	+	1.90389i	0.142436	+	0.0822355i
$537$		0			0
$538$	4.64090	+	4.64090i	0.200083	+	0.200083i
$539$	−0.616404	−	0.165165i	−0.0265504	−	0.00711415i
$540$		0			0
$541$	−17.3568	+	17.3568i	−0.746227	+	0.746227i	−0.973768	−	0.227541i	$-0.926931\pi$
$541$	−17.3568	+	17.3568i	−0.746227	+	0.746227i	0.227541	+	0.973768i	$0.426931\pi$
$542$	7.31653	−	4.22420i	0.314272	−	0.181445i
$543$		0			0
$544$	−0.568994	−	2.12351i	−0.0243954	−	0.0910449i
$545$	4.80212			0.205700
$546$		0			0
$547$	23.4243			1.00155			0.500775	−	0.865578i	$-0.333049\pi$
$547$	23.4243			1.00155			0.500775	+	0.865578i	$0.333049\pi$
$548$	−1.11178	−	4.14923i	−0.0474930	−	0.177246i
$549$		0			0
$550$	0.0944314	−	0.0545200i	0.00402657	−	0.00232474i
$551$	1.35971	−	1.35971i	0.0579257	−	0.0579257i
$552$		0			0
$553$	−3.70799	−	0.993552i	−0.157680	−	0.0422501i
$554$	11.7164	+	11.7164i	0.497784	+	0.497784i
$555$		0			0
$556$	2.51913	+	1.45442i	0.106835	+	0.0616813i
$557$	21.2427	−	5.69197i	0.900083	−	0.241177i	0.221031	−	0.975267i	$-0.429058\pi$
$557$	21.2427	−	5.69197i	0.900083	−	0.241177i	0.679052	+	0.734090i	$0.262391\pi$
$558$		0			0
$559$	−8.06052	−	43.0837i	−0.340924	−	1.82225i
$560$			1.07125i			0.0452686i
$561$		0			0
$562$	−9.60209	+	16.6313i	−0.405040	+	0.701549i
$563$	−18.3176	−	31.7270i	−0.771994	−	1.33713i	−0.936468	−	0.350752i	$-0.885926\pi$
$563$	−18.3176	−	31.7270i	−0.771994	−	1.33713i	0.164474	−	0.986381i	$-0.447407\pi$
$564$		0			0
$565$	2.55300	−	9.52793i	0.107406	−	0.400843i
$566$	−2.89744	+	10.8134i	−0.121789	+	0.454521i
$567$		0			0
$568$	−1.61987	−	2.80570i	−0.0679682	−	0.117724i
$569$	8.76469	−	15.1809i	0.367435	−	0.636416i	−0.621729	−	0.783232i	$-0.713569\pi$
$569$	8.76469	−	15.1809i	0.367435	−	0.636416i	0.989164	+	0.146817i	$0.0469028\pi$
$570$		0			0
$571$			16.1460i			0.675689i	0.941202	+	0.337844i	$0.109698\pi$
$571$			16.1460i			0.675689i	−0.941202	+	0.337844i	$0.890302\pi$
$572$	0.169855	+	0.354564i	0.00710200	+	0.0148251i
$573$		0			0
$574$	4.13899	−	1.10904i	0.172758	−	0.0462904i
$575$	−2.32102	−	1.34004i	−0.0967934	−	0.0558837i
$576$		0			0
$577$	−25.0194	−	25.0194i	−1.04157	−	1.04157i	−0.999098	−	0.0424718i	$-0.986477\pi$
$577$	−25.0194	−	25.0194i	−1.04157	−	1.04157i	−0.0424718	−	0.999098i	$-0.513523\pi$
$578$	11.7524	+	3.14903i	0.488834	+	0.130983i
$579$		0			0
$580$	−0.608537	+	0.608537i	−0.0252681	+	0.0252681i
$581$	8.17504	−	4.71986i	0.339158	−	0.195813i
$582$		0			0
$583$	0.100939	+	0.376710i	0.00418047	+	0.0156017i
$584$	−13.1036			−0.542231
$585$		0			0
$586$	13.2936			0.549153
$587$	11.5222	+	43.0015i	0.475573	+	1.77486i	0.619205	+	0.785230i	$0.287455\pi$
$587$	11.5222	+	43.0015i	0.475573	+	1.77486i	−0.143632	+	0.989631i	$0.545878\pi$
$588$		0			0
$589$	−0.338004	+	0.195147i	−0.0139272	+	0.00804087i
$590$	5.74712	−	5.74712i	0.236605	−	0.236605i
$591$		0			0
$592$	−10.5486	−	2.82648i	−0.433544	−	0.116168i
$593$	31.2099	+	31.2099i	1.28164	+	1.28164i	0.939737	+	0.341899i	$0.111070\pi$
$593$	31.2099	+	31.2099i	1.28164	+	1.28164i	0.341899	+	0.939737i	$0.388930\pi$
$594$		0			0
$595$	2.03954	+	1.17753i	0.0836131	+	0.0482741i
$596$	14.4305	−	3.86664i	0.591096	−	0.158384i
$597$		0			0
$598$	5.45981	−	7.97294i	0.223268	−	0.326038i
$599$			6.90043i			0.281944i	0.990014	+	0.140972i	$0.0450227\pi$
$599$			6.90043i			0.281944i	−0.990014	+	0.140972i	$0.954977\pi$
$600$		0			0
$601$	6.69946	−	11.6038i	0.273277	−	0.473329i	−0.696422	−	0.717632i	$-0.745226\pi$
$601$	6.69946	−	11.6038i	0.273277	−	0.473329i	0.969699	+	0.244303i	$0.0785592\pi$
$602$	−6.51139	−	11.2781i	−0.265384	−	0.459659i
$603$		0			0
$604$	3.21393	−	11.9946i	0.130773	−	0.488052i
$605$	−2.84393	+	10.6137i	−0.115622	+	0.431508i
$606$		0			0
$607$	−5.48852	−	9.50640i	−0.222772	−	0.385853i	0.732876	−	0.680362i	$-0.238177\pi$
$607$	−5.48852	−	9.50640i	−0.222772	−	0.385853i	−0.955649	+	0.294509i	$0.904844\pi$
$608$	1.11720	−	1.93504i	0.0453084	−	0.0784764i
$609$		0			0
$610$		−	8.60209i		−	0.348288i
$611$	40.9813	−	19.6323i	1.65793	−	0.794237i
$612$		0			0
$613$	23.5858	−	6.31980i	0.952622	−	0.255254i	0.251148	−	0.967949i	$-0.419192\pi$
$613$	23.5858	−	6.31980i	0.952622	−	0.255254i	0.701475	+	0.712694i	$0.252525\pi$
$614$	13.0256	+	7.52033i	0.525670	+	0.303496i
$615$		0			0
$616$	0.0825965	+	0.0825965i	0.00332791	+	0.00332791i
$617$	36.8960	+	9.88625i	1.48538	+	0.398006i	0.908173	−	0.418595i	$-0.137477\pi$
$617$	36.8960	+	9.88625i	1.48538	+	0.398006i	0.577204	+	0.816600i	$0.304144\pi$
$618$		0			0
$619$	19.6963	−	19.6963i	0.791661	−	0.791661i	−0.190103	−	0.981764i	$-0.560882\pi$
$619$	19.6963	−	19.6963i	0.791661	−	0.791661i	0.981764	+	0.190103i	$0.0608823\pi$
$620$	0.151273	−	0.0873374i	0.00607526	−	0.00350756i
$621$		0			0
$622$	−3.69167	−	13.7775i	−0.148022	−	0.552427i
$623$	−0.539530			−0.0216158
$624$		0			0
$625$	−1.00000			−0.0400000
$626$	3.91428	+	14.6083i	0.156446	+	0.583865i
$627$		0			0
$628$	5.36690	−	3.09858i	0.214162	−	0.123647i
$629$	−16.9764	+	16.9764i	−0.676895	+	0.676895i
$630$		0			0
$631$	37.5943	+	10.0734i	1.49661	+	0.401015i	0.911962	−	0.410274i	$-0.134567\pi$
$631$	37.5943	+	10.0734i	1.49661	+	0.401015i	0.584645	+	0.811289i	$0.301234\pi$
$632$	−2.53389	−	2.53389i	−0.100793	−	0.100793i
$633$		0			0
$634$	−6.78772	−	3.91889i	−0.269575	−	0.155639i
$635$	10.3439	−	2.77165i	0.410487	−	0.109990i
$636$		0			0
$637$	−16.0223	+	13.7313i	−0.634826	+	0.544053i
$638$			0.0938399i			0.00371516i
$639$		0			0
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	−16.5081	−	28.5928i	−0.652030	−	1.12935i	−0.982630	−	0.185578i	$-0.940584\pi$
$641$	−16.5081	−	28.5928i	−0.652030	−	1.12935i	0.330600	−	0.943771i	$-0.392749\pi$
$642$		0			0
$643$	−12.6305	+	47.1375i	−0.498097	+	1.85892i	0.0138471	+	0.999904i	$0.495592\pi$
$643$	−12.6305	+	47.1375i	−0.498097	+	1.85892i	−0.511944	+	0.859019i	$0.671074\pi$
$644$	0.743081	−	2.77322i	0.0292815	−	0.109280i
$645$		0			0
$646$	−2.45608	−	4.25405i	−0.0966330	−	0.167373i
$647$	−12.2654	+	21.2444i	−0.482204	+	0.835202i	−0.999791	−	0.0204285i	$-0.993497\pi$
$647$	−12.2654	+	21.2444i	−0.482204	+	0.835202i	0.517587	+	0.855630i	$0.326830\pi$
$648$		0			0
$649$		−	0.886240i		−	0.0347880i
$650$	0.276806	−	3.59491i	0.0108572	−	0.141004i
$651$		0			0
$652$	−13.6514	+	3.65789i	−0.534632	+	0.143254i
$653$	18.8702	+	10.8947i	0.738446	+	0.426342i	0.821504	−	0.570203i	$-0.193135\pi$
$653$	18.8702	+	10.8947i	0.738446	+	0.426342i	−0.0830579	+	0.996545i	$0.526469\pi$
$654$		0			0
$655$	−2.07945	−	2.07945i	−0.0812510	−	0.0812510i
$656$	3.86370	+	1.03528i	0.150852	+	0.0404207i
$657$		0			0
$658$	9.54670	−	9.54670i	0.372169	−	0.372169i
$659$	41.2109	−	23.7931i	1.60535	−	0.926848i	0.614955	−	0.788562i	$-0.289174\pi$
$659$	41.2109	−	23.7931i	1.60535	−	0.926848i	0.990392	−	0.138285i	$-0.0441591\pi$
$660$		0			0
$661$	−0.133840	−	0.499497i	−0.00520577	−	0.0194282i	0.963274	−	0.268520i	$-0.0865346\pi$
$661$	−0.133840	−	0.499497i	−0.00520577	−	0.0194282i	−0.968480	+	0.249092i	$0.919868\pi$
$662$	−31.9624			−1.24225
$663$		0			0
$664$	8.81187			0.341967
$665$	0.619509	+	2.31204i	0.0240235	+	0.0896570i
$666$		0			0
$667$	1.99748	−	1.15324i	0.0773426	−	0.0446538i
$668$	1.35262	−	1.35262i	0.0523343	−	0.0523343i
$669$		0			0
$670$	−3.67803	−	0.985526i	−0.142095	−	0.0380742i
$671$	−0.663246	−	0.663246i	−0.0256043	−	0.0256043i
$672$		0			0
$673$	−17.7680	−	10.2584i	−0.684906	−	0.395431i	0.116795	−	0.993156i	$-0.462738\pi$
$673$	−17.7680	−	10.2584i	−0.684906	−	0.395431i	−0.801701	+	0.597725i	$0.796071\pi$
$674$	−9.99171	+	2.67727i	−0.384866	+	0.103125i
$675$		0			0
$676$	12.8468	+	1.99019i	0.494106	+	0.0765456i
$677$			32.3765i			1.24433i	0.782886	+	0.622165i	$0.213747\pi$
$677$			32.3765i			1.24433i	−0.782886	+	0.622165i	$0.786253\pi$
$678$		0			0
$679$	2.81114	−	4.86903i	0.107882	−	0.186856i
$680$	1.09921	+	1.90389i	0.0421528	+	0.0730109i
$681$		0			0
$682$	0.00492961	−	0.0183975i	0.000188764	−	0.000704478i
$683$	6.54431	−	24.4237i	0.250411	−	0.934547i	−0.720175	−	0.693793i	$-0.755938\pi$
$683$	6.54431	−	24.4237i	0.250411	−	0.934547i	0.970586	−	0.240754i	$-0.0773949\pi$
$684$		0			0
$685$	2.14780	+	3.72010i	0.0820633	+	0.142138i
$686$	−6.88408	+	11.9236i	−0.262835	+	0.455244i
$687$		0			0
$688$		−	12.1566i		−	0.463466i
$689$	12.1634	+	4.28415i	0.463389	+	0.163213i
$690$		0			0
$691$	30.8925	−	8.27763i	1.17521	−	0.314896i	0.382183	−	0.924086i	$-0.375172\pi$
$691$	30.8925	−	8.27763i	1.17521	−	0.314896i	0.793024	+	0.609191i	$0.208506\pi$
$692$	9.81614	+	5.66735i	0.373154	+	0.215440i
$693$		0			0
$694$	22.3923	+	22.3923i	0.850000	+	0.850000i
$695$	−2.80973	−	0.752865i	−0.106579	−	0.0285578i
$696$		0			0
$697$	6.21808	−	6.21808i	0.235527	−	0.235527i
$698$	14.1513	−	8.17028i	0.535636	−	0.309250i
$699$		0			0
$700$	−0.277260	−	1.03475i	−0.0104794	−	0.0391098i
$701$	18.5210			0.699528			0.349764	−	0.936838i	$-0.386262\pi$
$701$	18.5210			0.699528			0.349764	+	0.936838i	$0.386262\pi$
$702$		0			0
$703$	−24.4012			−0.920307
$704$	0.0282216	+	0.105325i	0.00106364	+	0.00396957i
$705$		0			0
$706$	1.13097	−	0.652964i	0.0425645	−	0.0245746i
$707$	6.59527	−	6.59527i	0.248041	−	0.248041i
$708$		0			0
$709$	8.77434	+	2.35108i	0.329527	+	0.0882966i	0.419790	−	0.907621i	$-0.362104\pi$
$709$	8.77434	+	2.35108i	0.329527	+	0.0882966i	−0.0902623	+	0.995918i	$0.528771\pi$
$710$	2.29084	+	2.29084i	0.0859737	+	0.0859737i
$711$		0			0
$712$	−0.436169	−	0.251822i	−0.0163461	−	0.00943744i
$713$	−0.452192	+	0.121165i	−0.0169347	+	0.00453765i
$714$		0			0
$715$	−0.255835	−	0.298521i	−0.00956770	−	0.0111640i
$716$			8.07231i			0.301677i
$717$		0			0
$718$	−16.6799	+	28.8904i	−0.622488	+	1.07818i
$719$	17.0038	+	29.4515i	0.634135	+	1.09835i	0.986698	+	0.162566i	$0.0519770\pi$
$719$	17.0038	+	29.4515i	0.634135	+	1.09835i	−0.352563	+	0.935788i	$0.614690\pi$
$720$		0			0
$721$	−1.01596	+	3.79162i	−0.0378364	+	0.141207i
$722$	−3.62540	+	13.5302i	−0.134923	+	0.503541i
$723$		0			0
$724$	−2.67389	−	4.63131i	−0.0993742	−	0.172121i
$725$	0.430301	−	0.745303i	0.0159810	−	0.0276798i
$726$		0			0
$727$		−	21.7524i		−	0.806752i	−0.915034	−	0.403376i	$-0.867837\pi$
$727$		−	21.7524i		−	0.806752i	0.915034	−	0.403376i	$-0.132163\pi$
$728$	3.79657	−	0.710300i	0.140710	−	0.0263255i
$729$		0			0
$730$	12.6571	−	3.39146i	0.468461	−	0.125524i
$731$	−23.1449	−	13.3627i	−0.856043	−	0.494237i
$732$		0			0
$733$	−11.3306	−	11.3306i	−0.418506	−	0.418506i	0.466182	−	0.884689i	$-0.345629\pi$
$733$	−11.3306	−	11.3306i	−0.418506	−	0.418506i	−0.884689	+	0.466182i	$0.845629\pi$
$734$	−23.9121	−	6.40724i	−0.882613	−	0.236495i
$735$		0			0
$736$	1.89511	−	1.89511i	0.0698546	−	0.0698546i
$737$	−0.359574	+	0.207600i	−0.0132451	+	0.00764705i
$738$		0			0
$739$	4.06627	+	15.1755i	0.149580	+	0.558240i	0.999509	+	0.0313424i	$0.00997824\pi$
$739$	4.06627	+	15.1755i	0.149580	+	0.558240i	−0.849929	+	0.526898i	$0.823355\pi$
$740$	10.9207			0.401452
$741$		0			0
$742$	3.83150			0.140659
$743$	5.97479	+	22.2982i	0.219194	+	0.818042i	0.984648	+	0.174552i	$0.0558477\pi$
$743$	5.97479	+	22.2982i	0.219194	+	0.818042i	−0.765454	+	0.643490i	$0.777486\pi$
$744$		0			0
$745$	−12.9380	+	7.46977i	−0.474012	+	0.273671i
$746$	16.1751	−	16.1751i	0.592212	−	0.592212i
$747$		0			0
$748$	0.231548	+	0.0620431i	0.00846623	+	0.00226852i
$749$	−1.26143	−	1.26143i	−0.0460917	−	0.0460917i
$750$		0			0
$751$	−40.5841	−	23.4312i	−1.48093	−	0.855018i	−0.481168	−	0.876629i	$-0.659787\pi$
$751$	−40.5841	−	23.4312i	−1.48093	−	0.855018i	−0.999766	+	0.0216108i	$0.993121\pi$
$752$	12.1737	−	3.26192i	0.443928	−	0.118950i
$753$		0			0
$754$	2.56019	+	1.75320i	0.0932365	+	0.0638476i
$755$			12.4177i			0.451926i
$756$		0			0
$757$	2.79868	−	4.84746i	0.101720	−	0.176184i	−0.810673	−	0.585499i	$-0.800899\pi$
$757$	2.79868	−	4.84746i	0.101720	−	0.176184i	0.912393	+	0.409315i	$0.134232\pi$
$758$	−4.05351	−	7.02088i	−0.147230	−	0.255010i
$759$		0			0
$760$	−0.578305	+	2.15826i	−0.0209773	+	0.0782884i
$761$	0.436236	−	1.62806i	0.0158136	−	0.0590170i	−0.957568	−	0.288207i	$-0.906941\pi$
$761$	0.436236	−	1.62806i	0.0158136	−	0.0590170i	0.973382	+	0.229190i	$0.0736076\pi$
$762$		0			0
$763$	−2.57214	−	4.45507i	−0.0931176	−	0.161284i
$764$	−0.427368	+	0.740223i	−0.0154616	+	0.0267803i
$765$		0			0
$766$		−	10.0486i		−	0.363070i
$767$	−24.1788	−	16.5575i	−0.873047	−	0.597856i
$768$		0			0
$769$	8.70684	−	2.33299i	0.313977	−	0.0841298i	−0.0983896	−	0.995148i	$-0.531369\pi$
$769$	8.70684	−	2.33299i	0.313977	−	0.0841298i	0.412366	+	0.911018i	$0.364702\pi$
$770$	−0.101160	−	0.0584045i	−0.00364554	−	0.00210475i
$771$		0			0
$772$	11.8388	+	11.8388i	0.426087	+	0.426087i
$773$	−11.2273	−	3.00836i	−0.403819	−	0.108203i	0.0511917	−	0.998689i	$-0.483698\pi$
$773$	−11.2273	−	3.00836i	−0.403819	−	0.108203i	−0.455011	+	0.890486i	$0.650365\pi$
$774$		0			0
$775$	−0.123514	+	0.123514i	−0.00443675	+	0.00443675i
$776$	4.54519	−	2.62416i	0.163163	−	0.0942020i
$777$		0			0
$778$	−0.211572	−	0.789598i	−0.00758523	−	0.0283085i
$779$	8.93759			0.320222
$780$		0			0
$781$	0.353261			0.0126407
$782$	−1.52495	−	5.69120i	−0.0545322	−	0.203517i
$783$		0			0
$784$	−5.06835	+	2.92621i	−0.181012	+	0.104508i
$785$	−4.38205	+	4.38205i	−0.156402	+	0.156402i
$786$		0			0
$787$	8.36173	+	2.24052i	0.298064	+	0.0798659i	0.404752	−	0.914427i	$-0.367358\pi$
$787$	8.36173	+	2.24052i	0.298064	+	0.0798659i	−0.106688	+	0.994293i	$0.534025\pi$
$788$	−15.3088	−	15.3088i	−0.545354	−	0.545354i
$789$		0			0
$790$	3.10337	+	1.79173i	0.110413	+	0.0637470i
$791$	−10.2068	+	2.73490i	−0.362912	+	0.0972420i
$792$		0			0
$793$	−30.4863	+	5.70368i	−1.08260	+	0.202543i
$794$		−	11.2334i		−	0.398658i
$795$		0			0
$796$	3.53360	−	6.12037i	0.125245	−	0.216931i
$797$	−20.2024	−	34.9917i	−0.715607	−	1.23947i	−0.962725	−	0.270483i	$-0.912817\pi$
$797$	−20.2024	−	34.9917i	−0.715607	−	1.23947i	0.247118	−	0.968986i	$-0.420517\pi$
$798$		0			0
$799$	7.17108	−	26.7628i	0.253695	−	0.946801i
$800$	0.258819	−	0.965926i	0.00915064	−	0.0341506i
$801$		0			0
$802$	−1.39348	−	2.41359i	−0.0492056	−	0.0852267i
$803$	0.714408	−	1.23739i	0.0252109	−	0.0436666i
$804$		0			0
$805$			2.87104i			0.101191i
$806$	−0.409832	−	0.478210i	−0.0144357	−	0.0168442i
$807$		0			0
$808$	8.41008	−	2.25348i	0.295866	−	0.0792770i
$809$	−40.9883	−	23.6646i	−1.44107	−	0.832003i	−0.443150	−	0.896448i	$-0.646139\pi$
$809$	−40.9883	−	23.6646i	−1.44107	−	0.832003i	−0.997921	+	0.0644447i	$0.979472\pi$
$810$		0			0
$811$	21.7947	+	21.7947i	0.765317	+	0.765317i	0.977278	−	0.211961i	$-0.0679851\pi$
$811$	21.7947	+	21.7947i	0.765317	+	0.765317i	−0.211961	+	0.977278i	$0.567985\pi$
$812$	0.890506	+	0.238610i	0.0312506	+	0.00837358i
$813$		0			0
$814$	0.842017	−	0.842017i	0.0295127	−	0.0295127i
$815$	12.2396	−	7.06651i	0.428733	−	0.247529i
$816$		0			0
$817$	−7.03022	−	26.2371i	−0.245956	−	0.917922i
$818$	−15.5844			−0.544896
$819$		0			0
$820$	−4.00000			−0.139686
$821$	−11.6235	−	43.3794i	−0.405662	−	1.51395i	−0.802831	−	0.596207i	$-0.796674\pi$
$821$	−11.6235	−	43.3794i	−0.405662	−	1.51395i	0.397169	−	0.917746i	$-0.369993\pi$
$822$		0			0
$823$	−3.74668	+	2.16315i	−0.130601	+	0.0754025i	−0.563877	−	0.825859i	$-0.690691\pi$
$823$	−3.74668	+	2.16315i	−0.130601	+	0.0754025i	0.433276	+	0.901261i	$0.357358\pi$
$824$	−2.59105	+	2.59105i	−0.0902635	+	0.0902635i
$825$		0			0
$826$	−8.41008	−	2.25348i	−0.292624	−	0.0784084i
$827$	6.56307	+	6.56307i	0.228220	+	0.228220i	0.811949	−	0.583729i	$-0.198407\pi$
$827$	6.56307	+	6.56307i	0.228220	+	0.228220i	−0.583729	+	0.811949i	$0.698407\pi$
$828$		0			0
$829$	30.4626	+	17.5876i	1.05801	+	0.610843i	0.924881	−	0.380255i	$-0.124164\pi$
$829$	30.4626	+	17.5876i	1.05801	+	0.610843i	0.133130	+	0.991099i	$0.457497\pi$
$830$	−8.51162	+	2.28068i	−0.295443	+	0.0791636i
$831$		0			0
$832$	3.40077	+	1.19781i	0.117901	+	0.0415264i
$833$			12.8661i			0.445784i
$834$		0			0
$835$	−0.956444	+	1.65661i	−0.0330991	+	0.0573293i
$836$	0.121819	+	0.210997i	0.00421321	+	0.00729749i
$837$		0			0
$838$	−4.93586	+	18.4209i	−0.170506	+	0.636339i
$839$	2.40907	−	8.99078i	0.0831704	−	0.310396i	−0.911791	−	0.410654i	$-0.865300\pi$
$839$	2.40907	−	8.99078i	0.0831704	−	0.310396i	0.994961	+	0.100258i	$0.0319669\pi$
$840$		0			0
$841$	−14.1297	−	24.4733i	−0.487230	−	0.843908i
$842$	1.30347	−	2.25768i	0.0449207	−	0.0778049i
$843$		0			0
$844$		−	22.7680i		−	0.783707i
$845$	−12.9241	+	1.40261i	−0.444603	+	0.0482514i
$846$		0			0
$847$	11.3699	−	3.04656i	0.390675	−	0.104681i
$848$	3.09748	+	1.78833i	0.106368	+	0.0614115i
$849$		0			0
$850$	−1.55452	−	1.55452i	−0.0533196	−	0.0533196i
$851$	−28.2711	−	7.57522i	−0.969121	−	0.259675i
$852$		0			0
$853$	23.6039	−	23.6039i	0.808183	−	0.808183i	−0.176175	−	0.984359i	$-0.556373\pi$
$853$	23.6039	−	23.6039i	0.808183	−	0.808183i	0.984359	+	0.176175i	$0.0563726\pi$
$854$	−7.98042	+	4.60750i	−0.273084	+	0.157665i
$855$		0			0
$856$	−0.431006	−	1.60854i	−0.0147315	−	0.0549787i
$857$	4.43651			0.151548			0.0757742	−	0.997125i	$-0.475857\pi$
$857$	4.43651			0.151548			0.0757742	+	0.997125i	$0.475857\pi$
$858$		0			0
$859$	16.6789			0.569078			0.284539	−	0.958664i	$-0.408159\pi$
$859$	16.6789			0.569078			0.284539	+	0.958664i	$0.408159\pi$
$860$	3.14636	+	11.7424i	0.107290	+	0.400412i
$861$		0			0
$862$	−19.8187	+	11.4423i	−0.675028	+	0.389728i
$863$	−35.0616	+	35.0616i	−1.19351	+	1.19351i	−0.217436	+	0.976075i	$0.569769\pi$
$863$	−35.0616	+	35.0616i	−1.19351	+	1.19351i	−0.976075	+	0.217436i	$0.930231\pi$
$864$		0			0
$865$	−10.9485	−	2.93364i	−0.372259	−	0.0997466i
$866$	14.7071	+	14.7071i	0.499768	+	0.499768i
$867$		0			0
$868$	−0.162051	−	0.0935603i	−0.00550037	−	0.00317564i
$869$	0.377427	−	0.101131i	0.0128033	−	0.00343064i
$870$		0			0
$871$	−1.05402	+	13.6886i	−0.0357140	+	0.463822i
$872$		−	4.80212i		−	0.162620i
$873$		0			0
$874$	2.99419	−	5.18609i	0.101280	−	0.175422i
$875$	0.535625	+	0.927730i	0.0181074	+	0.0313630i
$876$		0			0
$877$	−6.14801	+	22.9447i	−0.207603	+	0.774786i	0.781037	+	0.624485i	$0.214691\pi$
$877$	−6.14801	+	22.9447i	−0.207603	+	0.774786i	−0.988640	+	0.150301i	$0.951976\pi$
$878$	−8.01445	+	29.9103i	−0.270474	+	1.00942i
$879$		0			0
$880$	−0.0545200	−	0.0944314i	−0.00183787	−	0.00318328i
$881$	−8.12877	+	14.0795i	−0.273865	+	0.474349i	−0.969848	−	0.243710i	$-0.921636\pi$
$881$	−8.12877	+	14.0795i	−0.273865	+	0.474349i	0.695983	+	0.718058i	$0.254969\pi$
$882$		0			0
$883$			23.3980i			0.787406i	0.919238	+	0.393703i	$0.128806\pi$
$883$			23.3980i			0.787406i	−0.919238	+	0.393703i	$0.871194\pi$
$884$	6.01866	−	5.15806i	0.202429	−	0.173484i
$885$		0			0
$886$	24.0431	−	6.44234i	0.807745	−	0.216435i
$887$	−35.3067	−	20.3844i	−1.18548	−	0.684440i	−0.228207	−	0.973613i	$-0.573286\pi$
$887$	−35.3067	−	20.3844i	−1.18548	−	0.684440i	−0.957277	+	0.289173i	$0.906620\pi$
$888$		0			0
$889$	−8.11181	−	8.11181i	−0.272061	−	0.272061i
$890$	0.486484	+	0.130353i	0.0163070	+	0.00436944i
$891$		0			0
$892$	−10.6472	+	10.6472i	−0.356493	+	0.356493i
$893$	24.3876	−	14.0802i	0.816098	−	0.471175i
$894$		0			0
$895$	−2.08927	−	7.79726i	−0.0698365	−	0.260634i
$896$	1.07125			0.0357880
$897$		0			0
$898$	−39.8970			−1.33138
$899$	−0.0389071	−	0.145203i	−0.00129762	−	0.00484280i
$900$		0			0
$901$	6.80957	−	3.93151i	0.226860	−	0.130978i
$902$	−0.308412	+	0.308412i	−0.0102690	+	0.0102690i
$903$		0			0
$904$	−9.52793	−	2.55300i	−0.316894	−	0.0849116i
$905$	3.78145	+	3.78145i	0.125700	+	0.125700i
$906$		0			0
$907$	47.3499	+	27.3375i	1.57223	+	0.907727i	0.995895	+	0.0905127i	$0.0288506\pi$
$907$	47.3499	+	27.3375i	1.57223	+	0.907727i	0.576334	+	0.817214i	$0.304483\pi$
$908$	4.96291	−	1.32981i	0.164700	−	0.0441313i
$909$		0			0
$910$	−3.48337	+	1.66872i	−0.115473	+	0.0553176i
$911$		−	19.4958i		−	0.645925i	−0.946412	−	0.322962i	$-0.895321\pi$
$911$		−	19.4958i		−	0.645925i	0.946412	−	0.322962i	$-0.104679\pi$
$912$		0			0
$913$	−0.480423	+	0.832117i	−0.0158997	+	0.0275391i
$914$	9.25399	+	16.0284i	0.306095	+	0.530171i
$915$		0			0
$916$	3.33330	−	12.4400i	0.110135	−	0.411030i
$917$	−0.815364	+	3.04298i	−0.0269257	+	0.100488i
$918$		0			0
$919$	−15.0266	−	26.0269i	−0.495683	−	0.858549i	0.504304	−	0.863526i	$-0.331749\pi$
$919$	−15.0266	−	26.0269i	−0.495683	−	0.858549i	−0.999988	+	0.00497727i	$0.998416\pi$
$920$	−1.34004	+	2.32102i	−0.0441799	+	0.0765219i
$921$		0			0
$922$		−	13.0496i		−	0.429765i
$923$	6.59992	−	9.63783i	0.217239	−	0.317233i
$924$		0			0
$925$	−10.5486	+	2.82648i	−0.346835	+	0.0929342i
$926$	−21.8008	−	12.5867i	−0.716418	−	0.413624i
$927$		0			0
$928$	0.608537	+	0.608537i	0.0199762	+	0.0199762i
$929$	−34.5256	−	9.25111i	−1.13275	−	0.303519i	−0.356717	−	0.934213i	$-0.616104\pi$
$929$	−34.5256	−	9.25111i	−1.13275	−	0.303519i	−0.776032	+	0.630693i	$0.782771\pi$
$930$		0			0
$931$	−9.24658	+	9.24658i	−0.303044	+	0.303044i
$932$	20.7973	−	12.0073i	0.681238	−	0.393313i
$933$		0			0
$934$	11.0205	+	41.1290i	0.360601	+	1.34578i
$935$	−0.239716			−0.00783955
$936$		0			0
$937$	9.51941			0.310986			0.155493	−	0.987837i	$-0.450303\pi$
$937$	9.51941			0.310986			0.155493	+	0.987837i	$0.450303\pi$
$938$	1.05575	+	3.94009i	0.0344713	+	0.128649i
$939$		0			0
$940$	−10.9146	+	6.30155i	−0.355995	+	0.205534i
$941$	−23.7474	+	23.7474i	−0.774144	+	0.774144i	−0.978828	−	0.204684i	$-0.934383\pi$
$941$	−23.7474	+	23.7474i	−0.774144	+	0.774144i	0.204684	+	0.978828i	$0.434383\pi$
$942$		0			0
$943$	10.3551	+	2.77463i	0.337207	+	0.0903544i
$944$	−5.74712	−	5.74712i	−0.187053	−	0.187053i
$945$		0			0
$946$	1.14797	+	0.662778i	0.0373236	+	0.0215488i
$947$	−15.7557	+	4.22174i	−0.511993	+	0.137188i	−0.505560	−	0.862791i	$-0.668714\pi$
$947$	−15.7557	+	4.22174i	−0.511993	+	0.137188i	−0.00643231	+	0.999979i	$0.502047\pi$
$948$		0			0
$949$	−20.4119	−	42.6088i	−0.662599	−	1.38314i
$950$		−	2.23440i		−	0.0724934i
$951$		0			0
$952$	1.17753	−	2.03954i	0.0381640	−	0.0661020i
$953$	0.0598968	+	0.103744i	0.00194025	+	0.00336061i	0.866994	−	0.498319i	$-0.166049\pi$
$953$	0.0598968	+	0.103744i	0.00194025	+	0.00336061i	−0.865054	+	0.501679i	$0.832716\pi$
$954$		0			0
$955$	0.221222	−	0.825611i	0.00715857	−	0.0267161i
$956$	3.30260	−	12.3255i	0.106814	−	0.398634i
$957$		0			0
$958$	14.6548	+	25.3829i	0.473475	+	0.820084i
$959$	2.30083	−	3.98516i	0.0742978	−	0.128688i
$960$		0			0
$961$		−	30.9695i		−	0.999016i
$962$	−7.24104	−	38.7036i	−0.233460	−	1.24785i
$963$		0			0
$964$	5.76565	−	1.54490i	0.185699	−	0.0497579i
$965$	−14.4995	−	8.37129i	−0.466755	−	0.269481i
$966$		0			0
$967$	−12.1095	−	12.1095i	−0.389416	−	0.389416i	0.485063	−	0.874479i	$-0.338797\pi$
$967$	−12.1095	−	12.1095i	−0.389416	−	0.389416i	−0.874479	+	0.485063i	$0.838797\pi$
$968$	10.6137	+	2.84393i	0.341137	+	0.0914074i
$969$		0			0
$970$	−3.71113	+	3.71113i	−0.119157	+	0.119157i
$971$	−46.2626	+	26.7097i	−1.48464	+	0.857156i	−0.999847	−	0.0174747i	$-0.994437\pi$
$971$	−46.2626	+	26.7097i	−1.48464	+	0.857156i	−0.484790	+	0.874631i	$0.661104\pi$
$972$		0			0
$973$	0.806506	+	3.00992i	0.0258554	+	0.0964937i
$974$	−4.48407			−0.143679
$975$		0			0
$976$	−8.60209			−0.275346
$977$	4.45733	+	16.6350i	0.142603	+	0.532200i	0.999850	+	0.0172960i	$0.00550577\pi$
$977$	4.45733	+	16.6350i	0.142603	+	0.532200i	−0.857248	+	0.514904i	$0.827828\pi$
$978$		0			0
$979$	0.0475599	−	0.0274587i	0.00152002	−	0.000877584i
$980$	4.13829	−	4.13829i	0.132193	−	0.132193i
$981$		0			0
$982$	−1.30721	−	0.350267i	−0.0417149	−	0.0111775i
$983$	−7.63036	−	7.63036i	−0.243371	−	0.243371i	0.574872	−	0.818243i	$-0.305052\pi$
$983$	−7.63036	−	7.63036i	−0.243371	−	0.243371i	−0.818243	+	0.574872i	$0.805052\pi$
$984$		0			0
$985$	18.7494	+	10.8250i	0.597405	+	0.344912i
$986$	1.82750	−	0.489677i	0.0581994	−	0.0155945i
$987$		0			0
$988$	8.03246	+	0.618495i	0.255547	+	0.0196769i
$989$		−	32.5808i		−	1.03601i
$990$		0			0
$991$	5.66822	−	9.81765i	0.180057	−	0.311868i	−0.761843	−	0.647762i	$-0.775705\pi$
$991$	5.66822	−	9.81765i	0.180057	−	0.311868i	0.941900	+	0.335894i	$0.109038\pi$
$992$	−0.0873374	−	0.151273i	−0.00277297	−	0.00480292i
$993$		0			0
$994$	0.898250	−	3.35231i	0.0284908	−	0.106329i
$995$	−1.82913	+	6.82639i	−0.0579872	+	0.216411i
$996$		0			0
$997$	−3.23856	−	5.60935i	−0.102566	−	0.177650i	0.810175	−	0.586188i	$-0.199372\pi$
$997$	−3.23856	−	5.60935i	−0.102566	−	0.177650i	−0.912741	+	0.408538i	$0.866039\pi$
$998$	−9.23867	+	16.0018i	−0.292445	+	0.506530i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.cu.f.1151.3	yes	16
3.2	odd	2	inner	1170.2.cu.f.1151.1	yes	16
13.2	odd	12	inner	1170.2.cu.f.431.1	✓	16
39.2	even	12	inner	1170.2.cu.f.431.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1170.2.cu.f.431.1	✓	16	13.2	odd	12	inner
1170.2.cu.f.431.3	yes	16	39.2	even	12	inner
1170.2.cu.f.1151.1	yes	16	3.2	odd	2	inner
1170.2.cu.f.1151.3	yes	16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.cu (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-1.03475 - 0.277260i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-1.03475 - 0.277260i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{10} +(0.105325 - 0.0282216i) q^{11} +(1.19781 - 3.40077i) q^{13} -1.07125i q^{14} +(0.500000 - 0.866025i) q^{16} +(-1.09921 - 1.90389i) q^{17} +(0.578305 - 2.15826i) q^{19} +(-0.258819 + 0.965926i) q^{20} +(0.0545200 + 0.0944314i) q^{22} +(1.34004 - 2.32102i) q^{23} -1.00000i q^{25} +(3.59491 + 0.276806i) q^{26} +(1.03475 - 0.277260i) q^{28} +(0.745303 + 0.430301i) q^{29} +(-0.123514 - 0.123514i) q^{31} +(0.965926 + 0.258819i) q^{32} +(1.55452 - 1.55452i) q^{34} +(-0.927730 + 0.535625i) q^{35} +(-2.82648 - 10.5486i) q^{37} +2.23440 q^{38} -1.00000 q^{40} +(1.03528 + 3.86370i) q^{41} +(10.5279 - 6.07830i) q^{43} +(-0.0771029 + 0.0771029i) q^{44} +(2.58877 + 0.693658i) q^{46} +(8.91173 + 8.91173i) q^{47} +(-5.06835 - 2.92621i) q^{49} +(0.965926 - 0.258819i) q^{50} +(0.663057 + 3.54406i) q^{52} +3.57666i q^{53} +(0.0545200 - 0.0944314i) q^{55} +(0.535625 + 0.927730i) q^{56} +(-0.222740 + 0.831277i) q^{58} +(2.10359 - 7.85072i) q^{59} +(-4.30104 - 7.44963i) q^{61} +(0.0873374 - 0.151273i) q^{62} +1.00000i q^{64} +(-1.55773 - 3.25169i) q^{65} +(-3.67803 + 0.985526i) q^{67} +(1.90389 + 1.09921i) q^{68} +(-0.757488 - 0.757488i) q^{70} +(3.12935 + 0.838506i) q^{71} +(9.26565 - 9.26565i) q^{73} +(9.45759 - 5.46034i) q^{74} +(0.578305 + 2.15826i) q^{76} -0.116809 q^{77} +3.58347 q^{79} +(-0.258819 - 0.965926i) q^{80} +(-3.46410 + 2.00000i) q^{82} +(-6.23094 + 6.23094i) q^{83} +(-2.12351 - 0.568994i) q^{85} +(8.59602 + 8.59602i) q^{86} +(-0.0944314 - 0.0545200i) q^{88} +(0.486484 - 0.130353i) q^{89} +(-2.18233 + 3.18684i) q^{91} +2.68009i q^{92} +(-6.30155 + 10.9146i) q^{94} +(-1.11720 - 1.93504i) q^{95} +(-1.35837 + 5.06950i) q^{97} +(1.51472 - 5.65301i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{7}+O(q^{10}) \) 16 * q + 12 * q^7	\( 16 q + 12 q^{7} - 8 q^{13} + 8 q^{16} - 52 q^{19} - 8 q^{22} - 12 q^{28} + 36 q^{31} + 16 q^{34} + 8 q^{37} - 16 q^{40} + 72 q^{43} + 32 q^{46} + 60 q^{49} + 12 q^{52} - 8 q^{55} - 8 q^{58} - 12 q^{61} - 12 q^{67} + 12 q^{70} + 8 q^{73} - 52 q^{76} + 8 q^{79} + 4 q^{85} + 24 q^{88} - 84 q^{91} - 16 q^{94} - 96 q^{97}+O(q^{100}) \) 16 * q + 12 * q^7 - 8 * q^13 + 8 * q^16 - 52 * q^19 - 8 * q^22 - 12 * q^28 + 36 * q^31 + 16 * q^34 + 8 * q^37 - 16 * q^40 + 72 * q^43 + 32 * q^46 + 60 * q^49 + 12 * q^52 - 8 * q^55 - 8 * q^58 - 12 * q^61 - 12 * q^67 + 12 * q^70 + 8 * q^73 - 52 * q^76 + 8 * q^79 + 4 * q^85 + 24 * q^88 - 84 * q^91 - 16 * q^94 - 96 * q^97

Introduction

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