LMFDB - Embedded newform 136.3.p.a.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [136,3,Mod(19,136)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(136, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 4, 7]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("136.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	136.p (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.70573159530$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{8}]$

Embedding invariants

Embedding label			19.1
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	136.19
Dual form			136.3.p.a.43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41421 + 1.41421i) q^{2} +(-5.53553 + 2.29289i) q^{3} +4.00000i q^{4} +(-11.0711 - 4.58579i) q^{6} +(-5.65685 + 5.65685i) q^{8} +(19.0208 - 19.0208i) q^{9} +O(q^{10})$	\(q+(1.41421 + 1.41421i) q^{2} +(-5.53553 + 2.29289i) q^{3} +4.00000i q^{4} +(-11.0711 - 4.58579i) q^{6} +(-5.65685 + 5.65685i) q^{8} +(19.0208 - 19.0208i) q^{9} +(-17.9497 - 7.43503i) q^{11} +(-9.17157 - 22.1421i) q^{12} -16.0000 q^{16} +(-11.2929 + 12.7071i) q^{17} +53.7990 q^{18} +(12.0000 + 12.0000i) q^{19} +(-14.8701 - 35.8995i) q^{22} +(18.3431 - 44.2843i) q^{24} +(-17.6777 + 17.6777i) q^{25} +(-41.0416 + 99.0833i) q^{27} +(-22.6274 - 22.6274i) q^{32} +116.409 q^{33} +(-33.9411 + 2.00000i) q^{34} +(76.0833 + 76.0833i) q^{36} +33.9411i q^{38} +(-6.32233 + 15.2635i) q^{41} +(-35.4264 + 35.4264i) q^{43} +(29.7401 - 71.7990i) q^{44} +(88.5685 - 36.6863i) q^{48} +(-34.6482 - 34.6482i) q^{49} -50.0000 q^{50} +(33.3762 - 96.2340i) q^{51} +(-198.167 + 82.0833i) q^{54} +(-93.9411 - 38.9117i) q^{57} +(-1.42641 + 1.42641i) q^{59} -64.0000i q^{64} +(164.627 + 164.627i) q^{66} +127.841 q^{67} +(-50.8284 - 45.1716i) q^{68} +215.196i q^{72} +(45.2340 + 109.205i) q^{73} +(57.3223 - 138.388i) q^{75} +(-48.0000 + 48.0000i) q^{76} -400.487i q^{81} +(-30.5269 + 12.6447i) q^{82} +(53.5442 + 53.5442i) q^{83} -100.201 q^{86} +(143.598 - 59.4802i) q^{88} +31.2376i q^{89} +(177.137 + 73.3726i) q^{96} +(73.7660 + 178.087i) q^{97} -98.0000i q^{98} +(-482.839 + 199.999i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{3} - 16 q^{6} + 28 q^{9}+O(q^{10}) $ 4 * q - 8 * q^3 - 16 * q^6 + 28 * q^9	$ 4 q - 8 q^{3} - 16 q^{6} + 28 q^{9} - 52 q^{11} - 48 q^{12} - 64 q^{16} - 48 q^{17} + 136 q^{18} + 48 q^{19} + 48 q^{22} + 96 q^{24} - 68 q^{27} + 64 q^{33} + 112 q^{36} - 96 q^{41} + 28 q^{43} - 96 q^{44} + 128 q^{48} - 200 q^{50} - 56 q^{51} - 408 q^{54} - 240 q^{57} + 164 q^{59} + 568 q^{66} + 336 q^{67} - 192 q^{68} + 48 q^{73} + 300 q^{75} - 192 q^{76} + 8 q^{82} + 316 q^{83} - 480 q^{86} + 416 q^{88} + 256 q^{96} + 428 q^{97} - 1080 q^{99}+O(q^{100}) $ 4 * q - 8 * q^3 - 16 * q^6 + 28 * q^9 - 52 * q^11 - 48 * q^12 - 64 * q^16 - 48 * q^17 + 136 * q^18 + 48 * q^19 + 48 * q^22 + 96 * q^24 - 68 * q^27 + 64 * q^33 + 112 * q^36 - 96 * q^41 + 28 * q^43 - 96 * q^44 + 128 * q^48 - 200 * q^50 - 56 * q^51 - 408 * q^54 - 240 * q^57 + 164 * q^59 + 568 * q^66 + 336 * q^67 - 192 * q^68 + 48 * q^73 + 300 * q^75 - 192 * q^76 + 8 * q^82 + 316 * q^83 - 480 * q^86 + 416 * q^88 + 256 * q^96 + 428 * q^97 - 1080 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

$n$	$69$	$103$	$105$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{7}{8}\right)$

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 $

$2$	1.41421	+	1.41421i	0.707107	+	0.707107i
$2$	1.41421	+	1.41421i	0.707107	+	0.707107i
$3$	−5.53553	+	2.29289i	−1.84518	+	0.764298i	−0.902369	+	0.430964i	$0.858173\pi$
$3$	−5.53553	+	2.29289i	−1.84518	+	0.764298i	−0.942809	+	0.333333i	$0.891827\pi$
$4$			4.00000i			1.00000i
$5$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$5$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$6$	−11.0711	−	4.58579i	−1.84518	−	0.764298i
$7$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$7$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$8$	−5.65685	+	5.65685i	−0.707107	+	0.707107i
$9$	19.0208	−	19.0208i	2.11342	−	2.11342i
$10$		0			0
$11$	−17.9497	−	7.43503i	−1.63180	−	0.675912i	−0.636364	−	0.771389i	$-0.719562\pi$
$11$	−17.9497	−	7.43503i	−1.63180	−	0.675912i	−0.995432	+	0.0954775i	$0.969562\pi$
$12$	−9.17157	−	22.1421i	−0.764298	−	1.84518i
$13$		0			0			−	1.00000i	$-0.5\pi$
$13$		0			0				1.00000i	$0.5\pi$
$14$		0			0
$15$		0			0
$16$	−16.0000			−1.00000
$17$	−11.2929	+	12.7071i	−0.664288	+	0.747477i
$17$	−11.2929	+	12.7071i	−0.664288	+	0.747477i
$18$	53.7990			2.98883
$19$	12.0000	+	12.0000i	0.631579	+	0.631579i	0.948464	−	0.316885i	$-0.102637\pi$
$19$	12.0000	+	12.0000i	0.631579	+	0.631579i	−0.316885	+	0.948464i	$0.602637\pi$
$20$		0			0
$21$		0			0
$22$	−14.8701	−	35.8995i	−0.675912	−	1.63180i
$23$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$23$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$24$	18.3431	−	44.2843i	0.764298	−	1.84518i
$25$	−17.6777	+	17.6777i	−0.707107	+	0.707107i
$26$		0			0
$27$	−41.0416	+	99.0833i	−1.52006	+	3.66975i
$28$		0			0
$29$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$29$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$30$		0			0
$31$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$31$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$32$	−22.6274	−	22.6274i	−0.707107	−	0.707107i
$33$	116.409			3.52755
$34$	−33.9411	+	2.00000i	−0.998268	+	0.0588235i
$35$		0			0
$36$	76.0833	+	76.0833i	2.11342	+	2.11342i
$37$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$37$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$38$			33.9411i			0.893188i
$39$		0			0
$40$		0			0
$41$	−6.32233	+	15.2635i	−0.154203	+	0.372279i	−0.982036	−	0.188696i	$-0.939574\pi$
$41$	−6.32233	+	15.2635i	−0.154203	+	0.372279i	0.827832	+	0.560976i	$0.189574\pi$
$42$		0			0
$43$	−35.4264	+	35.4264i	−0.823870	+	0.823870i	−0.986661	−	0.162791i	$-0.947950\pi$
$43$	−35.4264	+	35.4264i	−0.823870	+	0.823870i	0.162791	+	0.986661i	$0.447950\pi$
$44$	29.7401	−	71.7990i	0.675912	−	1.63180i
$45$		0			0
$46$		0			0
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$	88.5685	−	36.6863i	1.84518	−	0.764298i
$49$	−34.6482	−	34.6482i	−0.707107	−	0.707107i
$50$	−50.0000			−1.00000
$51$	33.3762	−	96.2340i	0.654434	−	1.88694i
$52$		0			0
$53$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$53$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$54$	−198.167	+	82.0833i	−3.66975	+	1.52006i
$55$		0			0
$56$		0			0
$57$	−93.9411	−	38.9117i	−1.64809	−	0.682661i
$58$		0			0
$59$	−1.42641	+	1.42641i	−0.0241764	+	0.0241764i	−0.719092	−	0.694915i	$-0.755442\pi$
$59$	−1.42641	+	1.42641i	−0.0241764	+	0.0241764i	0.694915	+	0.719092i	$0.255442\pi$
$60$		0			0
$61$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$61$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$62$		0			0
$63$		0			0
$64$		−	64.0000i		−	1.00000i
$65$		0			0
$66$	164.627	+	164.627i	2.49435	+	2.49435i
$67$	127.841			1.90807			0.954034	−	0.299697i	$-0.0968855\pi$
$67$	127.841			1.90807			0.954034	+	0.299697i	$0.0968855\pi$
$68$	−50.8284	−	45.1716i	−0.747477	−	0.664288i
$69$		0			0
$70$		0			0
$71$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$71$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$72$			215.196i			2.98883i
$73$	45.2340	+	109.205i	0.619644	+	1.49595i	0.852118	+	0.523350i	$0.175318\pi$
$73$	45.2340	+	109.205i	0.619644	+	1.49595i	−0.232473	+	0.972603i	$0.574682\pi$
$74$		0			0
$75$	57.3223	−	138.388i	0.764298	−	1.84518i
$76$	−48.0000	+	48.0000i	−0.631579	+	0.631579i
$77$		0			0
$78$		0			0
$79$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$79$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$80$		0			0
$81$		−	400.487i		−	4.94429i
$82$	−30.5269	+	12.6447i	−0.372279	+	0.154203i
$83$	53.5442	+	53.5442i	0.645110	+	0.645110i	0.951807	−	0.306697i	$-0.0992238\pi$
$83$	53.5442	+	53.5442i	0.645110	+	0.645110i	−0.306697	+	0.951807i	$0.599224\pi$
$84$		0			0
$85$		0			0
$86$	−100.201			−1.16513
$87$		0			0
$88$	143.598	−	59.4802i	1.63180	−	0.675912i
$89$			31.2376i			0.350984i	0.984481	+	0.175492i	$0.0561516\pi$
$89$			31.2376i			0.350984i	−0.984481	+	0.175492i	$0.943848\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	177.137	+	73.3726i	1.84518	+	0.764298i
$97$	73.7660	+	178.087i	0.760474	+	1.83595i	0.484536	+	0.874771i	$0.338988\pi$
$97$	73.7660	+	178.087i	0.760474	+	1.83595i	0.275938	+	0.961175i	$0.411012\pi$
$98$		−	98.0000i		−	1.00000i
$99$	−482.839	+	199.999i	−4.87716	+	2.02019i
$100$	−70.7107	−	70.7107i	−0.707107	−	0.707107i
$101$		0			0		1.00000			$0$
$101$		0			0		−1.00000			$\pi$
$102$	183.296	−	88.8944i	1.79702	−	0.871514i
$103$		0			0		1.00000			$0$
$103$		0			0		−1.00000			$\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−68.0675	−	164.329i	−0.636145	−	1.53579i	−0.831776	−	0.555112i	$-0.812675\pi$
$107$	−68.0675	−	164.329i	−0.636145	−	1.53579i	0.195631	−	0.980678i	$-0.437325\pi$
$108$	−396.333	−	164.167i	−3.66975	−	1.52006i
$109$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$109$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−139.175	−	57.6482i	−1.23164	−	0.510161i	−0.330547	−	0.943790i	$-0.607233\pi$
$113$	−139.175	−	57.6482i	−1.23164	−	0.510161i	−0.901092	+	0.433628i	$0.857233\pi$
$114$	−77.8234	−	187.882i	−0.682661	−	1.64809i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−4.03449			−0.0341906
$119$		0			0
$120$		0			0
$121$	181.354	+	181.354i	1.49879	+	1.49879i
$122$		0			0
$123$		−	98.9878i		−	0.804779i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$127$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$128$	90.5097	−	90.5097i	0.707107	−	0.707107i
$129$	114.875	−	277.333i	0.890505	−	2.14987i
$130$		0			0
$131$	15.3589	+	37.0797i	0.117244	+	0.283051i	0.971597	−	0.236641i	$-0.0760466\pi$
$131$	15.3589	+	37.0797i	0.117244	+	0.283051i	−0.854354	+	0.519692i	$0.826047\pi$
$132$			465.637i			3.52755i
$133$		0			0
$134$	180.794	+	180.794i	1.34921	+	1.34921i
$135$		0			0
$136$	−8.00000	−	135.765i	−0.0588235	−	0.998268i
$137$	−135.765			−0.990982			−0.495491	−	0.868613i	$-0.665012\pi$
$137$	−135.765			−0.990982			−0.495491	+	0.868613i	$0.665012\pi$
$138$		0			0
$139$	86.5061	−	35.8320i	0.622346	−	0.257784i	−0.0491511	−	0.998791i	$-0.515652\pi$
$139$	86.5061	−	35.8320i	0.622346	−	0.257784i	0.671497	+	0.741007i	$0.265652\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−304.333	+	304.333i	−2.11342	+	2.11342i
$145$		0			0
$146$	−90.4680	+	218.409i	−0.619644	+	1.49595i
$147$	271.241	+	112.352i	1.84518	+	0.764298i
$148$		0			0
$149$		0			0			−	1.00000i	$-0.5\pi$
$149$		0			0				1.00000i	$0.5\pi$
$150$	276.777	−	114.645i	1.84518	−	0.764298i
$151$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$151$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$152$	−135.765			−0.893188
$153$	26.8995	+	456.500i	0.175814	+	2.98366i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0			−	1.00000i	$-0.5\pi$
$157$		0			0				1.00000i	$0.5\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	566.375	−	566.375i	3.49614	−	3.49614i
$163$	29.1558	−	70.3883i	0.178870	−	0.431830i	−0.808860	−	0.588001i	$-0.799915\pi$
$163$	29.1558	−	70.3883i	0.178870	−	0.431830i	0.987730	+	0.156171i	$0.0499150\pi$
$164$	−61.0538	−	25.2893i	−0.372279	−	0.154203i
$165$		0			0
$166$			151.446i			0.912324i
$167$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$167$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$168$		0			0
$169$	−169.000			−1.00000
$170$		0			0
$171$	456.500			2.66959
$172$	−141.706	−	141.706i	−0.823870	−	0.823870i
$173$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$173$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$174$		0			0
$175$		0			0
$176$	287.196	+	118.960i	1.63180	+	0.675912i
$177$	4.62532	−	11.1665i	0.0261318	−	0.0630877i
$178$	−44.1766	+	44.1766i	−0.248183	+	0.248183i
$179$	−252.000	+	252.000i	−1.40782	+	1.40782i	−0.636755	+	0.771066i	$0.719724\pi$
$179$	−252.000	+	252.000i	−1.40782	+	1.40782i	−0.771066	+	0.636755i	$0.780276\pi$
$180$		0			0
$181$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$181$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	297.182	−	144.126i	1.58921	−	0.770729i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0			−	1.00000i	$-0.5\pi$
$191$		0			0				1.00000i	$0.5\pi$
$192$	146.745	+	354.274i	0.764298	+	1.84518i
$193$	353.324	+	146.352i	1.83070	+	0.758299i	0.967234	+	0.253886i	$0.0817088\pi$
$193$	353.324	+	146.352i	1.83070	+	0.758299i	0.863462	+	0.504413i	$0.168291\pi$
$194$	−147.532	+	356.174i	−0.760474	+	1.83595i
$195$		0			0
$196$	138.593	−	138.593i	0.707107	−	0.707107i
$197$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$197$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$198$	−965.678	−	399.997i	−4.87716	−	2.02019i
$199$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$199$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$200$		−	200.000i		−	1.00000i
$201$	−707.666	+	293.125i	−3.52073	+	1.45833i
$202$		0			0
$203$		0			0
$204$	384.936	+	133.505i	1.88694	+	0.654434i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−126.177	−	304.617i	−0.603716	−	1.45750i
$210$		0			0
$211$	132.094	−	318.903i	0.626038	−	1.51139i	−0.218469	−	0.975844i	$-0.570106\pi$
$211$	132.094	−	318.903i	0.626038	−	1.51139i	0.844507	−	0.535545i	$-0.179894\pi$
$212$		0			0
$213$		0			0
$214$	136.135	−	328.659i	0.636145	−	1.53579i
$215$		0			0
$216$	−328.333	−	792.666i	−1.52006	−	3.66975i
$217$		0			0
$218$		0			0
$219$	−500.789	−	500.789i	−2.28671	−	2.28671i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$223$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$224$		0			0
$225$			672.487i			2.98883i
$226$	−115.296	−	278.350i	−0.510161	−	1.23164i
$227$	−85.2584	−	35.3152i	−0.375588	−	0.155574i	0.186900	−	0.982379i	$-0.440156\pi$
$227$	−85.2584	−	35.3152i	−0.375588	−	0.155574i	−0.562488	+	0.826805i	$0.690156\pi$
$228$	155.647	−	375.765i	0.682661	−	1.64809i
$229$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$229$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	123.558	+	298.295i	0.530291	+	1.28024i	0.931330	+	0.364175i	$0.118649\pi$
$233$	123.558	+	298.295i	0.530291	+	1.28024i	−0.401039	+	0.916061i	$0.631351\pi$
$234$		0			0
$235$		0			0
$236$	−5.70563	−	5.70563i	−0.0241764	−	0.0241764i
$237$		0			0
$238$		0			0
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$		0			0
$241$	−321.589	+	133.207i	−1.33440	+	0.552725i	−0.931906	−	0.362700i	$-0.881855\pi$
$241$	−321.589	+	133.207i	−1.33440	+	0.552725i	−0.402490	+	0.915425i	$0.631855\pi$
$242$			512.946i			2.11961i
$243$	548.900	+	1325.16i	2.25885	+	5.45334i
$244$		0			0
$245$		0			0
$246$	139.990	−	139.990i	0.569065	−	0.569065i
$247$		0			0
$248$		0			0
$249$	−419.167	−	173.624i	−1.68340	−	0.697287i
$250$		0			0
$251$		−	197.512i		−	0.786899i	−0.919346	−	0.393450i	$-0.871282\pi$
$251$		−	197.512i		−	0.786899i	0.919346	−	0.393450i	$-0.128718\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	256.000			1.00000
$257$	−362.706	−	362.706i	−1.41131	−	1.41131i	−0.750973	−	0.660333i	$-0.770415\pi$
$257$	−362.706	−	362.706i	−1.41131	−	1.41131i	−0.660333	−	0.750973i	$-0.729585\pi$
$258$	554.666	−	229.750i	2.14987	−	0.890505i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−30.7178	+	74.1594i	−0.117244	+	0.283051i
$263$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$263$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$264$	−658.510	+	658.510i	−2.49435	+	2.49435i
$265$		0			0
$266$		0			0
$267$	−71.6245	−	172.917i	−0.268256	−	0.647628i
$268$			511.362i			1.90807i
$269$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$269$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$270$		0			0
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$	180.686	−	203.314i	0.664288	−	0.747477i
$273$		0			0
$274$	−192.000	−	192.000i	−0.700730	−	0.700730i
$275$	448.744	−	185.876i	1.63180	−	0.675912i
$276$		0			0
$277$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$277$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$278$	173.012	+	71.6640i	0.622346	+	0.257784i
$279$		0			0
$280$		0			0
$281$	360.000	−	360.000i	1.28114	−	1.28114i	0.341118	−	0.940020i	$-0.389194\pi$
$281$	360.000	−	360.000i	1.28114	−	1.28114i	0.940020	−	0.341118i	$-0.110806\pi$
$282$		0			0
$283$	128.009	+	53.0229i	0.452327	+	0.187360i	0.597204	−	0.802090i	$-0.296278\pi$
$283$	128.009	+	53.0229i	0.452327	+	0.187360i	−0.144876	+	0.989450i	$0.546278\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−860.784			−2.98883
$289$	−33.9411	−	287.000i	−0.117443	−	0.993080i
$290$		0			0
$291$	−816.668	−	816.668i	−2.80642	−	2.80642i
$292$	−436.818	+	180.936i	−1.49595	+	0.619644i
$293$		0			0			−	1.00000i	$-0.5\pi$
$293$		0			0				1.00000i	$0.5\pi$
$294$	224.704	+	542.482i	0.764298	+	1.84518i
$295$		0			0
$296$		0			0
$297$	1473.37	−	1473.37i	4.96085	−	4.96085i
$298$		0			0
$299$		0			0
$300$	553.553	+	229.289i	1.84518	+	0.764298i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−192.000	−	192.000i	−0.631579	−	0.631579i
$305$		0			0
$306$	−607.546	+	683.630i	−1.98545	+	2.23408i
$307$	−542.000			−1.76547			−0.882736	−	0.469869i	$-0.844301\pi$
$307$	−542.000			−1.76547			−0.882736	+	0.469869i	$0.844301\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$311$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$312$		0			0
$313$	−42.9691	+	103.737i	−0.137281	+	0.331427i	−0.977537	−	0.210764i	$-0.932405\pi$
$313$	−42.9691	+	103.737i	−0.137281	+	0.331427i	0.840256	+	0.542191i	$0.182405\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$317$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	753.580	+	753.580i	2.34760	+	2.34760i
$322$		0			0
$323$	−288.000	+	16.9706i	−0.891641	+	0.0525404i
$324$	1601.95			4.94429
$325$		0			0
$326$	140.777	−	58.3116i	0.431830	−	0.178870i
$327$		0			0
$328$	−50.5786	−	122.108i	−0.154203	−	0.372279i
$329$		0			0
$330$		0			0
$331$	−323.926	+	323.926i	−0.978628	+	0.978628i	−0.999776	−	0.0211480i	$-0.993268\pi$
$331$	−323.926	+	323.926i	−0.978628	+	0.978628i	0.0211480	+	0.999776i	$0.493268\pi$
$332$	−214.177	+	214.177i	−0.645110	+	0.645110i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	236.589	−	97.9985i	0.702046	−	0.290797i	−0.00296297	−	0.999996i	$-0.500943\pi$
$337$	236.589	−	97.9985i	0.702046	−	0.290797i	0.705009	+	0.709199i	$0.250943\pi$
$338$	−239.002	−	239.002i	−0.707107	−	0.707107i
$339$	902.590			2.66251
$340$		0			0
$341$		0			0
$342$	645.588	+	645.588i	1.88768	+	1.88768i
$343$		0			0
$344$		−	400.804i		−	1.16513i
$345$		0			0
$346$		0			0
$347$	−264.947	+	639.638i	−0.763535	+	1.84334i	−0.317892	+	0.948127i	$0.602975\pi$
$347$	−264.947	+	639.638i	−0.763535	+	1.84334i	−0.445643	+	0.895211i	$0.647025\pi$
$348$		0			0
$349$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$349$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$350$		0			0
$351$		0			0
$352$	237.921	+	574.392i	0.675912	+	1.63180i
$353$		−	617.179i		−	1.74838i	−0.485583	−	0.874191i	$-0.661392\pi$
$353$		−	617.179i		−	1.74838i	0.485583	−	0.874191i	$-0.338608\pi$
$354$	22.3330	−	9.25065i	0.0630877	−	0.0261318i
$355$		0			0
$356$	−124.950			−0.350984
$357$		0			0
$358$	−712.764			−1.99096
$359$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$359$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$360$		0			0
$361$		−	73.0000i		−	0.202216i
$362$		0			0
$363$	−1419.72	−	588.065i	−3.91106	−	1.62001i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$367$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$368$		0			0
$369$	170.067	+	410.579i	0.460888	+	1.11268i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		1.00000			$0$
$373$		0			0		−1.00000			$\pi$
$374$	624.105	+	216.454i	1.66873	+	0.578753i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	195.317	+	471.538i	0.515349	+	1.24416i	0.940733	+	0.339149i	$0.110139\pi$
$379$	195.317	+	471.538i	0.515349	+	1.24416i	−0.425383	+	0.905013i	$0.639861\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$383$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$384$	−293.490	+	708.548i	−0.764298	+	1.84518i
$385$		0			0
$386$	292.704	+	706.649i	0.758299	+	1.83070i
$387$			1347.68i			3.48237i
$388$	−712.347	+	295.064i	−1.83595	+	0.760474i
$389$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$389$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$390$		0			0
$391$		0			0
$392$	392.000			1.00000
$393$	−170.040	−	170.040i	−0.432671	−	0.432671i
$394$		0			0
$395$		0			0
$396$	−799.994	−	1931.36i	−2.02019	−	4.87716i
$397$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$397$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$398$		0			0
$399$		0			0
$400$	282.843	−	282.843i	0.707107	−	0.707107i
$401$	−28.1781	+	68.0280i	−0.0702696	+	0.169646i	−0.955112	−	0.296244i	$-0.904266\pi$
$401$	−28.1781	+	68.0280i	−0.0702696	+	0.169646i	0.884843	+	0.465890i	$0.154266\pi$
$402$	−1415.33	−	586.250i	−3.52073	−	1.45833i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	355.578	+	733.186i	0.871514	+	1.79702i
$409$	−291.826			−0.713512			−0.356756	−	0.934198i	$-0.616117\pi$
$409$	−291.826			−0.713512			−0.356756	+	0.934198i	$0.616117\pi$
$410$		0			0
$411$	751.529	−	311.294i	1.82854	−	0.757405i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−396.698	+	396.698i	−0.951315	+	0.951315i
$418$	252.353	−	609.235i	0.603716	−	1.45750i
$419$	383.200	+	158.726i	0.914557	+	0.378822i	0.789799	−	0.613365i	$-0.210185\pi$
$419$	383.200	+	158.726i	0.914557	+	0.378822i	0.124758	+	0.992187i	$0.460185\pi$
$420$		0			0
$421$		0			0			−	1.00000i	$-0.5\pi$
$421$		0			0				1.00000i	$0.5\pi$
$422$	637.806	−	264.188i	1.51139	−	0.626038i
$423$		0			0
$424$		0			0
$425$	−25.0000	−	424.264i	−0.0588235	−	0.998268i
$426$		0			0
$427$		0			0
$428$	657.318	−	272.270i	1.53579	−	0.636145i
$429$		0			0
$430$		0			0
$431$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$431$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$432$	656.666	−	1585.33i	1.52006	−	3.66975i
$433$	−456.000	+	456.000i	−1.05312	+	1.05312i	−0.0546100	+	0.998508i	$0.517392\pi$
$433$	−456.000	+	456.000i	−1.05312	+	1.05312i	−0.998508	+	0.0546100i	$0.982608\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		−	1416.44i		−	3.23389i
$439$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$439$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$440$		0			0
$441$	−1318.08			−2.98883
$442$		0			0
$443$	704.840			1.59106			0.795530	−	0.605914i	$-0.207192\pi$
$443$	704.840			1.59106			0.795530	+	0.605914i	$0.207192\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	210.823	−	508.971i	0.469538	−	1.13357i	−0.494827	−	0.868992i	$-0.664769\pi$
$449$	210.823	−	508.971i	0.469538	−	1.13357i	0.964365	−	0.264574i	$-0.0852315\pi$
$450$	−951.041	+	951.041i	−2.11342	+	2.11342i
$451$	226.968	−	226.968i	0.503256	−	0.503256i
$452$	230.593	−	556.701i	0.510161	−	1.23164i
$453$		0			0
$454$	−70.6304	−	170.517i	−0.155574	−	0.375588i
$455$		0			0
$456$	751.529	−	311.294i	1.64809	−	0.682661i
$457$	624.000	+	624.000i	1.36543	+	1.36543i	0.866840	+	0.498587i	$0.166148\pi$
$457$	624.000	+	624.000i	1.36543	+	1.36543i	0.498587	+	0.866840i	$0.333852\pi$
$458$		0			0
$459$	−795.583	−	1640.46i	−1.73330	−	3.57398i
$460$		0			0
$461$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$461$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$462$		0			0
$463$		0			0			−	1.00000i	$-0.5\pi$
$463$		0			0				1.00000i	$0.5\pi$
$464$		0			0
$465$		0			0
$466$	−247.116	+	596.590i	−0.530291	+	1.28024i
$467$	−660.000	+	660.000i	−1.41328	+	1.41328i	−0.680898	+	0.732379i	$0.738410\pi$
$467$	−660.000	+	660.000i	−1.41328	+	1.41328i	−0.732379	+	0.680898i	$0.761590\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		−	16.1380i		−	0.0341906i
$473$	899.291	−	372.499i	1.90125	−	0.787524i
$474$		0			0
$475$	−424.264			−0.893188
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$479$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$480$		0			0
$481$		0			0
$482$	−643.179	−	266.413i	−1.33440	−	0.552725i
$483$		0			0
$484$	−725.415	+	725.415i	−1.49879	+	1.49879i
$485$		0			0
$486$	−1097.80	+	2650.32i	−2.25885	+	5.45334i
$487$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$487$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$488$		0			0
$489$			456.488i			0.933514i
$490$		0			0
$491$	420.000	+	420.000i	0.855397	+	0.855397i	0.990792	−	0.135395i	$-0.0432302\pi$
$491$	420.000	+	420.000i	0.855397	+	0.855397i	−0.135395	+	0.990792i	$0.543230\pi$
$492$	395.951			0.804779
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−347.249	−	838.333i	−0.697287	−	1.68340i
$499$	474.550	+	196.565i	0.951002	+	0.393918i	0.803607	−	0.595160i	$-0.202911\pi$
$499$	474.550	+	196.565i	0.951002	+	0.393918i	0.147394	+	0.989078i	$0.452911\pi$
$500$		0			0
$501$		0			0
$502$	279.324	−	279.324i	0.556422	−	0.556422i
$503$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$503$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	935.505	−	387.499i	1.84518	−	0.764298i
$508$		0			0
$509$		0			0		1.00000			$0$
$509$		0			0		−1.00000			$\pi$
$510$		0			0
$511$		0			0
$512$	362.039	+	362.039i	0.707107	+	0.707107i
$513$	−1681.50	+	696.500i	−3.27778	+	1.35770i
$514$		−	1025.89i		−	1.99589i
$515$		0			0
$516$	1109.33	+	459.500i	2.14987	+	0.890505i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	954.675	+	395.439i	1.83239	+	0.759000i	0.965451	+	0.260584i	$0.0839152\pi$
$521$	954.675	+	395.439i	1.83239	+	0.759000i	0.866938	+	0.498416i	$0.166085\pi$
$522$		0			0
$523$		−	965.428i		−	1.84594i	−0.384868	−	0.922972i	$-0.625753\pi$
$523$		−	965.428i		−	1.84594i	0.384868	−	0.922972i	$-0.374247\pi$
$524$	−148.319	+	61.4356i	−0.283051	+	0.117244i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−1862.55			−3.52755
$529$	374.059	+	374.059i	0.707107	+	0.707107i
$530$		0			0
$531$			54.2628i			0.102190i
$532$		0			0
$533$		0			0
$534$	143.249	−	345.833i	0.268256	−	0.647628i
$535$		0			0
$536$	−723.176	+	723.176i	−1.34921	+	1.34921i
$537$	817.145	−	1972.76i	1.52169	−	3.67368i
$538$		0			0
$539$	364.316	+	879.538i	0.675912	+	1.63180i
$540$		0			0
$541$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$541$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$542$		0			0
$543$		0			0
$544$	543.058	−	32.0000i	0.998268	−	0.0588235i
$545$		0			0
$546$		0			0
$547$	−694.493	+	287.668i	−1.26964	+	0.525902i	−0.912855	−	0.408284i	$-0.866127\pi$
$547$	−694.493	+	287.668i	−1.26964	+	0.525902i	−0.356785	+	0.934186i	$0.616127\pi$
$548$		−	543.058i		−	0.990982i
$549$		0			0
$550$	897.487	+	371.751i	1.63180	+	0.675912i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	143.328	+	346.024i	0.257784	+	0.622346i
$557$		0			0			−	1.00000i	$-0.5\pi$
$557$		0			0				1.00000i	$0.5\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−1314.60	+	1479.22i	−2.34331	+	2.63676i
$562$	1018.23			1.81180
$563$	664.543	+	664.543i	1.18036	+	1.18036i	0.979651	+	0.200710i	$0.0643251\pi$
$563$	664.543	+	664.543i	1.18036	+	1.18036i	0.200710	+	0.979651i	$0.435675\pi$
$564$		0			0
$565$		0			0
$566$	106.046	+	256.017i	0.187360	+	0.452327i
$567$		0			0
$568$		0			0
$569$	−162.176	+	162.176i	−0.285019	+	0.285019i	−0.835107	−	0.550088i	$-0.814594\pi$
$569$	−162.176	+	162.176i	−0.285019	+	0.285019i	0.550088	+	0.835107i	$0.314594\pi$
$570$		0			0
$571$	−95.9477	+	231.638i	−0.168034	+	0.405671i	−0.985356	−	0.170511i	$-0.945458\pi$
$571$	−95.9477	+	231.638i	−0.168034	+	0.405671i	0.817321	+	0.576182i	$0.195458\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−1217.33	−	1217.33i	−2.11342	−	2.11342i
$577$	2.00000			0.00346620			0.00173310	−	0.999998i	$-0.499448\pi$
$577$	2.00000			0.00346620			0.00173310	+	0.999998i	$0.499448\pi$
$578$	357.879	−	453.879i	0.619168	−	0.785258i
$579$	−2291.41			−3.95753
$580$		0			0
$581$		0			0
$582$		−	2309.89i		−	3.96888i
$583$		0			0
$584$	−873.637	−	361.872i	−1.49595	−	0.619644i
$585$		0			0
$586$		0			0
$587$	−804.688	+	804.688i	−1.37085	+	1.37085i	−0.511659	+	0.859189i	$0.670969\pi$
$587$	−804.688	+	804.688i	−1.37085	+	1.37085i	−0.859189	+	0.511659i	$0.829031\pi$
$588$	−449.407	+	1084.96i	−0.764298	+	1.84518i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−23.7065	−	23.7065i	−0.0399772	−	0.0399772i	0.686836	−	0.726813i	$-0.258999\pi$
$593$	−23.7065	−	23.7065i	−0.0399772	−	0.0399772i	−0.726813	+	0.686836i	$0.758999\pi$
$594$	4167.33			7.01571
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$	458.579	+	1107.11i	0.764298	+	1.84518i
$601$	−343.175	−	142.148i	−0.571007	−	0.236519i	0.0784489	−	0.996918i	$-0.475003\pi$
$601$	−343.175	−	142.148i	−0.571007	−	0.236519i	−0.649456	+	0.760399i	$0.725003\pi$
$602$		0			0
$603$	2431.63	−	2431.63i	4.03256	−	4.03256i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$607$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$608$		−	543.058i		−	0.893188i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−1826.00	+	107.598i	−2.98366	+	0.175814i
$613$		0			0		1.00000			$0$
$613$		0			0		−1.00000			$\pi$
$614$	−766.504	−	766.504i	−1.24838	−	1.24838i
$615$		0			0
$616$		0			0
$617$	−292.057	−	705.087i	−0.473349	−	1.14277i	−0.962674	−	0.270665i	$-0.912757\pi$
$617$	−292.057	−	705.087i	−0.473349	−	1.14277i	0.489324	−	0.872102i	$-0.337243\pi$
$618$		0			0
$619$	307.697	−	742.846i	0.497087	−	1.20007i	−0.453958	−	0.891023i	$-0.649988\pi$
$619$	307.697	−	742.846i	0.497087	−	1.20007i	0.951045	−	0.309052i	$-0.100012\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$		−	625.000i		−	1.00000i
$626$	−207.473	+	85.9382i	−0.331427	+	0.137281i
$627$	1396.91	+	1396.91i	2.22793	+	2.22793i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$631$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$632$		0			0
$633$			2068.18i			3.26726i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−3.55696	−	8.58727i	−0.00554908	−	0.0133967i	0.921081	−	0.389372i	$-0.127308\pi$
$641$	−3.55696	−	8.58727i	−0.00554908	−	0.0133967i	−0.926630	+	0.375975i	$0.877308\pi$
$642$			2131.45i			3.32001i
$643$	−886.214	+	367.082i	−1.37825	+	0.570889i	−0.944012	−	0.329910i	$-0.892982\pi$
$643$	−886.214	+	367.082i	−1.37825	+	0.570889i	−0.434236	+	0.900799i	$0.642982\pi$
$644$		0			0
$645$		0			0
$646$	−431.294	−	383.294i	−0.667637	−	0.593334i
$647$		0			0		1.00000			$0$
$647$		0			0		−1.00000			$\pi$
$648$	2265.50	+	2265.50i	3.49614	+	3.49614i
$649$	36.2090	−	14.9983i	0.0557920	−	0.0231098i
$650$		0			0
$651$		0			0
$652$	281.553	+	116.623i	0.431830	+	0.178870i
$653$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$653$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$654$		0			0
$655$		0			0
$656$	101.157	−	244.215i	0.154203	−	0.372279i
$657$	2937.55	+	1216.77i	4.47115	+	1.85201i
$658$		0			0
$659$			994.000i			1.50835i	0.656676	+	0.754173i	$0.271962\pi$
$659$			994.000i			1.50835i	−0.656676	+	0.754173i	$0.728038\pi$
$660$		0			0
$661$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$661$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$662$	−916.201			−1.38399
$663$		0			0
$664$	−605.783			−0.912324
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	365.969	−	883.528i	0.543788	−	1.31282i	−0.378244	−	0.925706i	$-0.623472\pi$
$673$	365.969	−	883.528i	0.543788	−	1.31282i	0.922032	−	0.387114i	$-0.126528\pi$
$674$	473.179	+	195.997i	0.702046	+	0.290797i
$675$	−1026.04	−	2477.08i	−1.52006	−	3.66975i
$676$		−	676.000i		−	1.00000i
$677$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$677$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$678$	1276.45	+	1276.45i	1.88268	+	1.88268i
$679$		0			0
$680$		0			0
$681$	552.925			0.811931
$682$		0			0
$683$	−801.714	+	332.081i	−1.17381	+	0.486209i	−0.882451	−	0.470404i	$-0.844108\pi$
$683$	−801.714	+	332.081i	−1.17381	+	0.486209i	−0.291362	+	0.956613i	$0.594108\pi$
$684$			1826.00i			2.66959i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	566.823	−	566.823i	0.823870	−	0.823870i
$689$		0			0
$690$		0			0
$691$	212.508	+	88.0238i	0.307537	+	0.127386i	0.531114	−	0.847300i	$-0.321773\pi$
$691$	212.508	+	88.0238i	0.307537	+	0.127386i	−0.223577	+	0.974686i	$0.571773\pi$
$692$		0			0
$693$		0			0
$694$	−1279.28	+	529.894i	−1.84334	+	0.763535i
$695$		0			0
$696$		0			0
$697$	−122.557	−	252.707i	−0.175835	−	0.362564i
$698$		0			0
$699$	−1367.92	−	1367.92i	−1.95696	−	1.95696i
$700$		0			0
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$		0			0
$703$		0			0
$704$	−475.842	+	1148.78i	−0.675912	+	1.63180i
$705$		0			0
$706$	872.823	−	872.823i	1.23629	−	1.23629i
$707$		0			0
$708$	44.6661	+	18.5013i	0.0630877	+	0.0261318i
$709$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$709$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$710$		0			0
$711$		0			0
$712$	−176.706	−	176.706i	−0.248183	−	0.248183i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−1008.00	−	1008.00i	−1.40782	−	1.40782i
$717$		0			0
$718$		0			0
$719$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$719$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$720$		0			0
$721$		0			0
$722$	103.238	−	103.238i	0.142988	−	0.142988i
$723$	1474.74	−	1474.74i	2.03975	−	2.03975i
$724$		0			0
$725$		0			0
$726$	−1176.13	−	2839.43i	−1.62001	−	3.91106i
$727$		0			0			−	1.00000i	$-0.5\pi$
$727$		0			0				1.00000i	$0.5\pi$
$728$		0			0
$729$	−3528.22	−	3528.22i	−4.83981	−	4.83981i
$730$		0			0
$731$	−50.1005	−	850.234i	−0.0685369	−	1.16311i
$732$		0			0
$733$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$733$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−2294.71	−	950.499i	−3.11358	−	1.28969i
$738$	−340.135	+	821.159i	−0.460888	+	1.11268i
$739$	−227.688	+	227.688i	−0.308103	+	0.308103i	−0.844173	−	0.536070i	$-0.819908\pi$
$739$	−227.688	+	227.688i	−0.308103	+	0.308103i	0.536070	+	0.844173i	$0.319908\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$743$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	2036.91			2.72678
$748$	576.505	+	1188.73i	0.770729	+	1.58921i
$749$		0			0
$750$		0			0
$751$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$751$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$752$		0			0
$753$	452.873	+	1093.33i	0.601425	+	1.45197i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$757$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$758$	−390.635	+	943.075i	−0.515349	+	1.24416i
$759$		0			0
$760$		0			0
$761$			610.940i			0.802812i	0.915900	+	0.401406i	$0.131478\pi$
$761$			610.940i			0.802812i	−0.915900	+	0.401406i	$0.868522\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−1417.10	+	586.981i	−1.84518	+	0.764298i
$769$		−	1120.06i		−	1.45651i	−0.685306	−	0.728256i	$-0.740331\pi$
$769$		−	1120.06i		−	1.45651i	0.685306	−	0.728256i	$-0.259669\pi$
$770$		0			0
$771$	2839.41	+	1176.12i	3.68277	+	1.52545i
$772$	−585.407	+	1413.30i	−0.758299	+	1.83070i
$773$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$773$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$774$	−1905.90	+	1905.90i	−2.46241	+	2.46241i
$775$		0			0
$776$	−1424.69	−	590.128i	−1.83595	−	0.760474i
$777$		0			0
$778$		0			0
$779$	−259.029	+	107.294i	−0.332515	+	0.137732i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	554.372	+	554.372i	0.707107	+	0.707107i
$785$		0			0
$786$		−	480.944i		−	0.611889i
$787$	−585.610	−	1413.79i	−0.744104	−	1.79643i	−0.588310	−	0.808635i	$-0.700207\pi$
$787$	−585.610	−	1413.79i	−0.744104	−	1.79643i	−0.155794	−	0.987790i	$-0.549793\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	1599.99	−	3862.71i	2.02019	−	4.87716i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$797$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$798$		0			0
$799$		0			0
$800$	800.000			1.00000
$801$	594.164	+	594.164i	0.741778	+	0.741778i
$802$	−136.056	+	56.3562i	−0.169646	+	0.0702696i
$803$		−	2296.51i		−	2.85991i
$804$	−1172.50	−	2830.66i	−1.45833	−	3.52073i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−351.679	+	849.027i	−0.434708	+	1.04948i	0.543043	+	0.839705i	$0.317272\pi$
$809$	−351.679	+	849.027i	−0.434708	+	1.04948i	−0.977750	+	0.209772i	$0.932728\pi$
$810$		0			0
$811$	543.933	+	1313.17i	0.670694	+	1.61920i	0.780435	+	0.625237i	$0.214998\pi$
$811$	543.933	+	1313.17i	0.670694	+	1.61920i	−0.109741	+	0.993960i	$0.535002\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−534.018	+	1539.74i	−0.654434	+	1.88694i
$817$	−850.234			−1.04068
$818$	−412.705	−	412.705i	−0.504529	−	0.504529i
$819$		0			0
$820$		0			0
$821$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$821$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$822$	1503.06	+	622.587i	1.82854	+	0.757405i
$823$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$823$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$824$		0			0
$825$	−2057.84	+	2057.84i	−2.49435	+	2.49435i
$826$		0			0
$827$	−1358.76	−	562.816i	−1.64300	−	0.680551i	−0.646400	−	0.762999i	$-0.723726\pi$
$827$	−1358.76	−	562.816i	−1.64300	−	0.680551i	−0.996595	+	0.0824479i	$0.973726\pi$
$828$		0			0
$829$		0			0			−	1.00000i	$-0.5\pi$
$829$		0			0				1.00000i	$0.5\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	831.558	−	49.0000i	0.998268	−	0.0588235i
$834$	−1122.03			−1.34536
$835$		0			0
$836$	1218.47	−	504.706i	1.45750	−	0.603716i
$837$		0			0
$838$	317.453	+	766.399i	0.378822	+	0.914557i
$839$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$839$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$840$		0			0
$841$	−594.677	+	594.677i	−0.707107	+	0.707107i
$842$		0			0
$843$	−1167.35	+	2818.23i	−1.38476	+	3.34310i
$844$	1275.61	+	528.376i	1.51139	+	0.626038i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−830.172			−0.977823
$850$	564.645	−	635.355i	0.664288	−	0.747477i
$851$		0			0
$852$		0			0
$853$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$853$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$854$		0			0
$855$		0			0
$856$	1314.64	+	544.540i	1.53579	+	0.636145i
$857$	−246.031	+	593.971i	−0.287084	+	0.693082i	−0.999966	−	0.00820166i	$-0.997389\pi$
$857$	−246.031	+	593.971i	−0.287084	+	0.693082i	0.712882	+	0.701284i	$0.247389\pi$
$858$		0			0
$859$	1069.07	−	1069.07i	1.24456	−	1.24456i	0.286465	−	0.958091i	$-0.407520\pi$
$859$	1069.07	−	1069.07i	1.24456	−	1.24456i	0.958091	−	0.286465i	$-0.0924801\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0			−	1.00000i	$-0.5\pi$
$863$		0			0				1.00000i	$0.5\pi$
$864$	3170.66	−	1313.33i	3.66975	−	1.52006i
$865$		0			0
$866$	−1289.76			−1.48933
$867$	845.943	+	1510.87i	0.975712	+	1.74265i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	4790.45	+	1984.27i	5.48734	+	2.27293i
$874$		0			0
$875$		0			0
$876$	2003.16	−	2003.16i	2.28671	−	2.28671i
$877$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$877$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	867.410	−	359.293i	0.984574	−	0.407824i	0.168456	−	0.985709i	$-0.446122\pi$
$881$	867.410	−	359.293i	0.984574	−	0.407824i	0.816118	+	0.577885i	$0.196122\pi$
$882$	−1864.04	−	1864.04i	−2.11342	−	2.11342i
$883$	1329.92			1.50614			0.753070	−	0.657940i	$-0.228572\pi$
$883$	1329.92			1.50614			0.753070	+	0.657940i	$0.228572\pi$
$884$		0			0
$885$		0			0
$886$	996.794	+	996.794i	1.12505	+	1.12505i
$887$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$887$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−2977.64	+	7188.65i	−3.34190	+	8.06807i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	1017.94	−	421.646i	1.13357	−	0.469538i
$899$		0			0
$900$	−2689.95			−2.98883
$901$		0			0
$902$	641.964			0.711712
$903$		0			0
$904$	1113.40	−	461.186i	1.23164	−	0.510161i
$905$		0			0
$906$		0			0
$907$	−1672.99	−	692.975i	−1.84453	−	0.764030i	−0.944873	−	0.327436i	$-0.893815\pi$
$907$	−1672.99	−	692.975i	−1.84453	−	0.764030i	−0.899659	−	0.436594i	$-0.856185\pi$
$908$	141.261	−	341.034i	0.155574	−	0.375588i
$909$		0			0
$910$		0			0
$911$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$911$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$912$	1503.06	+	622.587i	1.64809	+	0.682661i
$913$	−563.002	−	1359.21i	−0.616650	−	1.48873i
$914$			1764.94i			1.93100i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	1194.83	−	3445.08i	1.30156	−	3.75281i
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$		0			0
$921$	3000.26	−	1242.75i	3.25761	−	1.34935i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	929.616	+	385.059i	1.00066	+	0.414488i	0.822040	−	0.569429i	$-0.192836\pi$
$929$	929.616	+	385.059i	1.00066	+	0.414488i	0.178623	+	0.983918i	$0.442836\pi$
$930$		0			0
$931$		−	831.558i		−	0.893188i
$932$	−1193.18	+	494.231i	−1.28024	+	0.530291i
$933$		0			0
$934$	−1866.76			−1.99867
$935$		0			0
$936$		0			0
$937$	507.703	+	507.703i	0.541838	+	0.541838i	0.924068	−	0.382229i	$-0.124843\pi$
$937$	507.703	+	507.703i	0.541838	+	0.541838i	−0.382229	+	0.924068i	$0.624843\pi$
$938$		0			0
$939$		−	672.761i		−	0.716465i
$940$		0			0
$941$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$941$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$942$		0			0
$943$		0			0
$944$	22.8225	−	22.8225i	0.0241764	−	0.0241764i
$945$		0			0
$946$	1798.58	+	744.997i	1.90125	+	0.787524i
$947$	424.432	+	1024.67i	0.448186	+	1.08202i	0.973001	+	0.230800i	$0.0741344\pi$
$947$	424.432	+	1024.67i	0.448186	+	1.08202i	−0.524815	+	0.851216i	$0.675866\pi$
$948$		0			0
$949$		0			0
$950$	−600.000	−	600.000i	−0.631579	−	0.631579i
$951$		0			0
$952$		0			0
$953$	−1444.41			−1.51564			−0.757822	−	0.652461i	$-0.773737\pi$
$953$	−1444.41			−1.51564			−0.757822	+	0.652461i	$0.773737\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	679.530	−	679.530i	0.707107	−	0.707107i
$962$		0			0
$963$	−4420.38	−	1830.98i	−4.59022	−	1.90133i
$964$	−532.827	−	1286.36i	−0.552725	−	1.33440i
$965$		0			0
$966$		0			0
$967$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$967$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$968$	−2051.78			−2.11961
$969$	1555.32	−	754.294i	1.60508	−	0.778426i
$970$		0			0
$971$	1327.04	+	1327.04i	1.36668	+	1.36668i	0.865132	+	0.501545i	$0.167235\pi$
$971$	1327.04	+	1327.04i	1.36668	+	1.36668i	0.501545	+	0.865132i	$0.332765\pi$
$972$	−5300.65	+	2195.60i	−5.45334	+	2.25885i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	772.324	−	772.324i	0.790505	−	0.790505i	−0.191071	−	0.981576i	$-0.561196\pi$
$977$	772.324	−	772.324i	0.790505	−	0.790505i	0.981576	+	0.191071i	$0.0611960\pi$
$978$	−645.572	+	645.572i	−0.660094	+	0.660094i
$979$	232.252	−	560.707i	0.237234	−	0.572734i
$980$		0			0
$981$		0			0
$982$			1187.94i			1.20971i
$983$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$983$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$984$	559.960	+	559.960i	0.569065	+	0.569065i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$991$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$992$		0			0
$993$	1050.38	−	2535.83i	1.05778	−	2.55371i
$994$		0			0
$995$		0			0
$996$	694.498	−	1676.67i	0.697287	−	1.68340i
$997$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$997$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$998$	393.130	+	949.100i	0.393918	+	0.951002i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.3.p.a.19.1	✓	4
8.3	odd	2	CM	136.3.p.a.19.1	✓	4
17.9	even	8	inner	136.3.p.a.43.1	yes	4
136.43	odd	8	inner	136.3.p.a.43.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.3.p.a.19.1	✓	4	1.1	even	1	trivial
136.3.p.a.19.1	✓	4	8.3	odd	2	CM
136.3.p.a.43.1	yes	4	17.9	even	8	inner
136.3.p.a.43.1	yes	4	136.43	odd	8	inner

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:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	136.p (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41421 + 1.41421i) q^{2} +(-5.53553 + 2.29289i) q^{3} +4.00000i q^{4} +(-11.0711 - 4.58579i) q^{6} +(-5.65685 + 5.65685i) q^{8} +(19.0208 - 19.0208i) q^{9} +O(q^{10})\)	\(q+(1.41421 + 1.41421i) q^{2} +(-5.53553 + 2.29289i) q^{3} +4.00000i q^{4} +(-11.0711 - 4.58579i) q^{6} +(-5.65685 + 5.65685i) q^{8} +(19.0208 - 19.0208i) q^{9} +(-17.9497 - 7.43503i) q^{11} +(-9.17157 - 22.1421i) q^{12} -16.0000 q^{16} +(-11.2929 + 12.7071i) q^{17} +53.7990 q^{18} +(12.0000 + 12.0000i) q^{19} +(-14.8701 - 35.8995i) q^{22} +(18.3431 - 44.2843i) q^{24} +(-17.6777 + 17.6777i) q^{25} +(-41.0416 + 99.0833i) q^{27} +(-22.6274 - 22.6274i) q^{32} +116.409 q^{33} +(-33.9411 + 2.00000i) q^{34} +(76.0833 + 76.0833i) q^{36} +33.9411i q^{38} +(-6.32233 + 15.2635i) q^{41} +(-35.4264 + 35.4264i) q^{43} +(29.7401 - 71.7990i) q^{44} +(88.5685 - 36.6863i) q^{48} +(-34.6482 - 34.6482i) q^{49} -50.0000 q^{50} +(33.3762 - 96.2340i) q^{51} +(-198.167 + 82.0833i) q^{54} +(-93.9411 - 38.9117i) q^{57} +(-1.42641 + 1.42641i) q^{59} -64.0000i q^{64} +(164.627 + 164.627i) q^{66} +127.841 q^{67} +(-50.8284 - 45.1716i) q^{68} +215.196i q^{72} +(45.2340 + 109.205i) q^{73} +(57.3223 - 138.388i) q^{75} +(-48.0000 + 48.0000i) q^{76} -400.487i q^{81} +(-30.5269 + 12.6447i) q^{82} +(53.5442 + 53.5442i) q^{83} -100.201 q^{86} +(143.598 - 59.4802i) q^{88} +31.2376i q^{89} +(177.137 + 73.3726i) q^{96} +(73.7660 + 178.087i) q^{97} -98.0000i q^{98} +(-482.839 + 199.999i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{3} - 16 q^{6} + 28 q^{9}+O(q^{10}) \) 4 * q - 8 * q^3 - 16 * q^6 + 28 * q^9	\( 4 q - 8 q^{3} - 16 q^{6} + 28 q^{9} - 52 q^{11} - 48 q^{12} - 64 q^{16} - 48 q^{17} + 136 q^{18} + 48 q^{19} + 48 q^{22} + 96 q^{24} - 68 q^{27} + 64 q^{33} + 112 q^{36} - 96 q^{41} + 28 q^{43} - 96 q^{44} + 128 q^{48} - 200 q^{50} - 56 q^{51} - 408 q^{54} - 240 q^{57} + 164 q^{59} + 568 q^{66} + 336 q^{67} - 192 q^{68} + 48 q^{73} + 300 q^{75} - 192 q^{76} + 8 q^{82} + 316 q^{83} - 480 q^{86} + 416 q^{88} + 256 q^{96} + 428 q^{97} - 1080 q^{99}+O(q^{100}) \) 4 * q - 8 * q^3 - 16 * q^6 + 28 * q^9 - 52 * q^11 - 48 * q^12 - 64 * q^16 - 48 * q^17 + 136 * q^18 + 48 * q^19 + 48 * q^22 + 96 * q^24 - 68 * q^27 + 64 * q^33 + 112 * q^36 - 96 * q^41 + 28 * q^43 - 96 * q^44 + 128 * q^48 - 200 * q^50 - 56 * q^51 - 408 * q^54 - 240 * q^57 + 164 * q^59 + 568 * q^66 + 336 * q^67 - 192 * q^68 + 48 * q^73 + 300 * q^75 - 192 * q^76 + 8 * q^82 + 316 * q^83 - 480 * q^86 + 416 * q^88 + 256 * q^96 + 428 * q^97 - 1080 * q^99

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