LMFDB - Embedded newform 108.3.f.c.91.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,3,Mod(19,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("108.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	108.f (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.94278685509$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 7 x^{14} - 30 x^{13} + 76 x^{12} - 144 x^{11} + 424 x^{10} - 912 x^{9} + \cdots + 65536 $ x^16 - 3x^15 + 7x^14 - 30x^13 + 76x^12 - 144x^11 + 424x^10 - 912x^9 + 1552x^8 - 3648x^7 + 6784x^6 - 9216x^5 + 19456x^4 - 30720x^3 + 28672x^2 - 49152*x + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			91.1
Root			$-1.59523 + 1.20633i$ of defining polynomial
Character	$\chi$	$=$	108.91
Dual form			108.3.f.c.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.59523 + 1.20633i) q^{2} +(1.08951 - 3.84876i) q^{4} +(-1.10093 + 1.90686i) q^{5} +(-7.23844 + 4.17912i) q^{7} +(2.90487 + 7.45397i) q^{8} +O(q^{10})$	\(q+(-1.59523 + 1.20633i) q^{2} +(1.08951 - 3.84876i) q^{4} +(-1.10093 + 1.90686i) q^{5} +(-7.23844 + 4.17912i) q^{7} +(2.90487 + 7.45397i) q^{8} +(-0.544081 - 4.36996i) q^{10} +(-4.54769 + 2.62561i) q^{11} +(-7.37788 + 12.7789i) q^{13} +(6.50556 - 15.3986i) q^{14} +(-13.6259 - 8.38655i) q^{16} -28.2789 q^{17} -19.1376i q^{19} +(6.13957 + 6.31475i) q^{20} +(4.08724 - 9.67448i) q^{22} +(3.16702 + 1.82848i) q^{23} +(10.0759 + 17.4520i) q^{25} +(-3.64618 - 29.2854i) q^{26} +(8.19805 + 32.4122i) q^{28} +(12.3355 + 21.3657i) q^{29} +(32.9674 + 19.0338i) q^{31} +(31.8535 - 3.05895i) q^{32} +(45.1113 - 34.1138i) q^{34} -18.4036i q^{35} -4.21977 q^{37} +(23.0863 + 30.5288i) q^{38} +(-17.4117 - 2.66709i) q^{40} +(9.92483 - 17.1903i) q^{41} +(-20.1894 + 11.6564i) q^{43} +(5.15057 + 20.3636i) q^{44} +(-7.25787 + 0.903640i) q^{46} +(25.8538 - 14.9267i) q^{47} +(10.4300 - 18.0654i) q^{49} +(-37.1264 - 15.6850i) q^{50} +(41.1445 + 42.3184i) q^{52} +32.1118 q^{53} -11.5624i q^{55} +(-52.1778 - 41.8154i) q^{56} +(-45.4521 - 19.2025i) q^{58} +(-7.96159 - 4.59663i) q^{59} +(-40.8215 - 70.7049i) q^{61} +(-75.5517 + 9.40656i) q^{62} +(-47.1234 + 43.3057i) q^{64} +(-16.2450 - 28.1372i) q^{65} +(-6.86179 - 3.96166i) q^{67} +(-30.8102 + 108.839i) q^{68} +(22.2009 + 29.3579i) q^{70} +62.9286i q^{71} +33.3218 q^{73} +(6.73149 - 5.09045i) q^{74} +(-73.6560 - 20.8506i) q^{76} +(21.9454 - 38.0106i) q^{77} +(-53.7133 + 31.0114i) q^{79} +(30.9931 - 16.7497i) q^{80} +(4.90489 + 39.3951i) q^{82} +(-103.056 + 59.4995i) q^{83} +(31.1329 - 53.9238i) q^{85} +(18.1453 - 42.9498i) q^{86} +(-32.7816 - 26.2713i) q^{88} +107.361 q^{89} -123.332i q^{91} +(10.4879 - 10.1969i) q^{92} +(-23.2362 + 54.9999i) q^{94} +(36.4927 + 21.0690i) q^{95} +(1.78621 + 3.09380i) q^{97} +(5.15457 + 41.4005i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} - 5 q^{4} - 6 q^{5} + 54 q^{8}+O(q^{10}) $ 16 * q + 3 * q^2 - 5 * q^4 - 6 * q^5 + 54 * q^8	$ 16 q + 3 q^{2} - 5 q^{4} - 6 q^{5} + 54 q^{8} + 20 q^{10} - 46 q^{13} + 12 q^{14} - 17 q^{16} - 12 q^{17} - 36 q^{20} + 33 q^{22} - 30 q^{25} - 72 q^{26} + 12 q^{28} - 42 q^{29} - 87 q^{32} + 11 q^{34} + 56 q^{37} + 99 q^{38} + 68 q^{40} - 84 q^{41} + 222 q^{44} - 264 q^{46} + 58 q^{49} + 219 q^{50} + 110 q^{52} + 72 q^{53} - 270 q^{56} - 16 q^{58} - 34 q^{61} - 516 q^{62} - 254 q^{64} + 30 q^{65} - 375 q^{68} + 150 q^{70} + 116 q^{73} + 372 q^{74} - 15 q^{76} + 330 q^{77} + 720 q^{80} + 254 q^{82} - 140 q^{85} + 273 q^{86} + 75 q^{88} + 384 q^{89} - 258 q^{92} + 36 q^{94} - 148 q^{97} - 1170 q^{98}+O(q^{100}) $ 16 * q + 3 * q^2 - 5 * q^4 - 6 * q^5 + 54 * q^8 + 20 * q^10 - 46 * q^13 + 12 * q^14 - 17 * q^16 - 12 * q^17 - 36 * q^20 + 33 * q^22 - 30 * q^25 - 72 * q^26 + 12 * q^28 - 42 * q^29 - 87 * q^32 + 11 * q^34 + 56 * q^37 + 99 * q^38 + 68 * q^40 - 84 * q^41 + 222 * q^44 - 264 * q^46 + 58 * q^49 + 219 * q^50 + 110 * q^52 + 72 * q^53 - 270 * q^56 - 16 * q^58 - 34 * q^61 - 516 * q^62 - 254 * q^64 + 30 * q^65 - 375 * q^68 + 150 * q^70 + 116 * q^73 + 372 * q^74 - 15 * q^76 + 330 * q^77 + 720 * q^80 + 254 * q^82 - 140 * q^85 + 273 * q^86 + 75 * q^88 + 384 * q^89 - 258 * q^92 + 36 * q^94 - 148 * q^97 - 1170 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.59523	+	1.20633i	−0.797615	+	0.603167i
$2$	−1.59523	+	1.20633i	−0.797615	+	0.603167i
$3$		0			0
$3$		0			0
$4$	1.08951	−	3.84876i	0.272378	−	0.962190i
$5$	−1.10093	+	1.90686i	−0.220185	+	0.381372i	−0.954864	−	0.297043i	$-0.903999\pi$
$5$	−1.10093	+	1.90686i	−0.220185	+	0.381372i	0.734679	+	0.678415i	$0.237333\pi$
$6$		0			0
$7$	−7.23844	+	4.17912i	−1.03406	+	0.597017i	−0.918146	−	0.396242i	$-0.870314\pi$
$7$	−7.23844	+	4.17912i	−1.03406	+	0.597017i	−0.115917	+	0.993259i	$0.536981\pi$
$8$	2.90487	+	7.45397i	0.363109	+	0.931747i
$9$		0			0
$10$	−0.544081	−	4.36996i	−0.0544081	−	0.436996i
$11$	−4.54769	+	2.62561i	−0.413426	+	0.238692i	−0.692261	−	0.721648i	$-0.743385\pi$
$11$	−4.54769	+	2.62561i	−0.413426	+	0.238692i	0.278835	+	0.960339i	$0.410052\pi$
$12$		0			0
$13$	−7.37788	+	12.7789i	−0.567529	+	0.982990i	0.429280	+	0.903171i	$0.358767\pi$
$13$	−7.37788	+	12.7789i	−0.567529	+	0.982990i	−0.996809	+	0.0798182i	$0.974566\pi$
$14$	6.50556	−	15.3986i	0.464683	−	1.09990i
$15$		0			0
$16$	−13.6259	−	8.38655i	−0.851620	−	0.524159i
$17$	−28.2789			−1.66346			−0.831732	−	0.555178i	$-0.812650\pi$
$17$	−28.2789			−1.66346			−0.831732	+	0.555178i	$0.812650\pi$
$18$		0			0
$19$		−	19.1376i		−	1.00724i	−0.863925	−	0.503620i	$-0.832001\pi$
$19$		−	19.1376i		−	1.00724i	0.863925	−	0.503620i	$-0.167999\pi$
$20$	6.13957	+	6.31475i	0.306979	+	0.315737i
$21$		0			0
$22$	4.08724	−	9.67448i	0.185784	−	0.439749i
$23$	3.16702	+	1.82848i	0.137696	+	0.0794990i	0.567266	−	0.823535i	$-0.308001\pi$
$23$	3.16702	+	1.82848i	0.137696	+	0.0794990i	−0.429569	+	0.903034i	$0.641335\pi$
$24$		0			0
$25$	10.0759	+	17.4520i	0.403037	+	0.698081i
$26$	−3.64618	−	29.2854i	−0.140238	−	1.12636i
$27$		0			0
$28$	8.19805	+	32.4122i	0.292787	+	1.15758i
$29$	12.3355	+	21.3657i	0.425362	+	0.736748i	0.996454	−	0.0841375i	$-0.0268135\pi$
$29$	12.3355	+	21.3657i	0.425362	+	0.736748i	−0.571092	+	0.820886i	$0.693480\pi$
$30$		0			0
$31$	32.9674	+	19.0338i	1.06347	+	0.613992i	0.926389	−	0.376568i	$-0.122896\pi$
$31$	32.9674	+	19.0338i	1.06347	+	0.613992i	0.137077	+	0.990560i	$0.456229\pi$
$32$	31.8535	−	3.05895i	0.995421	−	0.0955923i
$33$		0			0
$34$	45.1113	−	34.1138i	1.32680	−	1.00335i
$35$		−	18.4036i		−	0.525817i
$36$		0			0
$37$	−4.21977			−0.114048			−0.0570239	−	0.998373i	$-0.518161\pi$
$37$	−4.21977			−0.114048			−0.0570239	+	0.998373i	$0.518161\pi$
$38$	23.0863	+	30.5288i	0.607535	+	0.803390i
$39$		0			0
$40$	−17.4117	−	2.66709i	−0.435293	−	0.0666773i
$41$	9.92483	−	17.1903i	0.242069	−	0.419276i	−0.719235	−	0.694767i	$-0.755507\pi$
$41$	9.92483	−	17.1903i	0.242069	−	0.419276i	0.961303	+	0.275492i	$0.0888406\pi$
$42$		0			0
$43$	−20.1894	+	11.6564i	−0.469521	+	0.271078i	−0.716039	−	0.698060i	$-0.754047\pi$
$43$	−20.1894	+	11.6564i	−0.469521	+	0.271078i	0.246518	+	0.969138i	$0.420714\pi$
$44$	5.15057	+	20.3636i	0.117058	+	0.462809i
$45$		0			0
$46$	−7.25787	+	0.903640i	−0.157780	+	0.0196444i
$47$	25.8538	−	14.9267i	0.550082	−	0.317590i	−0.199073	−	0.979985i	$-0.563793\pi$
$47$	25.8538	−	14.9267i	0.550082	−	0.317590i	0.749155	+	0.662395i	$0.230460\pi$
$48$		0			0
$49$	10.4300	−	18.0654i	0.212858	−	0.368681i
$50$	−37.1264	−	15.6850i	−0.742528	−	0.313701i
$51$		0			0
$52$	41.1445	+	42.3184i	0.791240	+	0.813816i
$53$	32.1118			0.605883			0.302942	−	0.953009i	$-0.402031\pi$
$53$	32.1118			0.605883			0.302942	+	0.953009i	$0.402031\pi$
$54$		0			0
$55$		−	11.5624i		−	0.210225i
$56$	−52.1778	−	41.8154i	−0.931746	−	0.746703i
$57$		0			0
$58$	−45.4521	−	19.2025i	−0.783657	−	0.331077i
$59$	−7.96159	−	4.59663i	−0.134942	−	0.0779089i	0.431009	−	0.902348i	$-0.358158\pi$
$59$	−7.96159	−	4.59663i	−0.134942	−	0.0779089i	−0.565951	+	0.824439i	$0.691491\pi$
$60$		0			0
$61$	−40.8215	−	70.7049i	−0.669205	−	1.15910i	−0.978127	−	0.208009i	$-0.933302\pi$
$61$	−40.8215	−	70.7049i	−0.669205	−	1.15910i	0.308922	−	0.951087i	$-0.400032\pi$
$62$	−75.5517	+	9.40656i	−1.21858	+	0.151719i
$63$		0			0
$64$	−47.1234	+	43.3057i	−0.736304	+	0.676651i
$65$	−16.2450	−	28.1372i	−0.249923	−	0.432879i
$66$		0			0
$67$	−6.86179	−	3.96166i	−0.102415	−	0.0591292i	0.447918	−	0.894075i	$-0.352166\pi$
$67$	−6.86179	−	3.96166i	−0.102415	−	0.0591292i	−0.550333	+	0.834946i	$0.685499\pi$
$68$	−30.8102	+	108.839i	−0.453091	+	1.60057i
$69$		0			0
$70$	22.2009	+	29.3579i	0.317155	+	0.419399i
$71$			62.9286i			0.886318i	0.896443	+	0.443159i	$0.146142\pi$
$71$			62.9286i			0.886318i	−0.896443	+	0.443159i	$0.853858\pi$
$72$		0			0
$73$	33.3218			0.456463			0.228232	−	0.973607i	$-0.426706\pi$
$73$	33.3218			0.456463			0.228232	+	0.973607i	$0.426706\pi$
$74$	6.73149	−	5.09045i	0.0909661	−	0.0687899i
$75$		0			0
$76$	−73.6560	−	20.8506i	−0.969157	−	0.274351i
$77$	21.9454	−	38.0106i	0.285006	−	0.493644i
$78$		0			0
$79$	−53.7133	+	31.0114i	−0.679916	+	0.392549i	−0.799823	−	0.600236i	$-0.795073\pi$
$79$	−53.7133	+	31.0114i	−0.679916	+	0.392549i	0.119908	+	0.992785i	$0.461740\pi$
$80$	30.9931	−	16.7497i	0.387414	−	0.209372i
$81$		0			0
$82$	4.90489	+	39.3951i	0.0598157	+	0.480429i
$83$	−103.056	+	59.4995i	−1.24164	+	0.716861i	−0.969428	−	0.245376i	$-0.921089\pi$
$83$	−103.056	+	59.4995i	−1.24164	+	0.716861i	−0.272212	+	0.962237i	$0.587755\pi$
$84$		0			0
$85$	31.1329	−	53.9238i	0.366270	−	0.634398i
$86$	18.1453	−	42.9498i	0.210992	−	0.499416i
$87$		0			0
$88$	−32.7816	−	26.2713i	−0.372519	−	0.298537i
$89$	107.361			1.20630			0.603152	−	0.797626i	$-0.293911\pi$
$89$	107.361			1.20630			0.603152	+	0.797626i	$0.293911\pi$
$90$		0			0
$91$		−	123.332i		−	1.35530i
$92$	10.4879	−	10.1969i	0.113999	−	0.110836i
$93$		0			0
$94$	−23.2362	+	54.9999i	−0.247193	+	0.585106i
$95$	36.4927	+	21.0690i	0.384133	+	0.221779i
$96$		0			0
$97$	1.78621	+	3.09380i	0.0184145	+	0.0318949i	0.875086	−	0.483968i	$-0.160805\pi$
$97$	1.78621	+	3.09380i	0.0184145	+	0.0318949i	−0.856671	+	0.515863i	$0.827471\pi$
$98$	5.15457	+	41.4005i	0.0525976	+	0.422454i
$99$		0			0
$100$	78.1465	−	19.7656i	0.781465	−	0.197656i
$101$	−7.54688	−	13.0716i	−0.0747216	−	0.129422i	0.826244	−	0.563313i	$-0.190473\pi$
$101$	−7.54688	−	13.0716i	−0.0747216	−	0.129422i	−0.900965	+	0.433891i	$0.857140\pi$
$102$		0			0
$103$	112.813	+	65.1324i	1.09527	+	0.632353i	0.934974	−	0.354716i	$-0.115422\pi$
$103$	112.813	+	65.1324i	1.09527	+	0.632353i	0.160294	+	0.987069i	$0.448756\pi$
$104$	−116.685	−	17.8736i	−1.12197	−	0.171861i
$105$		0			0
$106$	−51.2257	+	38.7376i	−0.483261	+	0.365449i
$107$		−	51.2733i		−	0.479190i	−0.970873	−	0.239595i	$-0.922985\pi$
$107$		−	51.2733i		−	0.479190i	0.970873	−	0.239595i	$-0.0770146\pi$
$108$		0			0
$109$	−25.4737			−0.233704			−0.116852	−	0.993149i	$-0.537280\pi$
$109$	−25.4737			−0.233704			−0.116852	+	0.993149i	$0.537280\pi$
$110$	13.9481	+	18.4447i	0.126801	+	0.167679i
$111$		0			0
$112$	133.679	+	3.76124i	1.19356	+	0.0335825i
$113$	−76.1529	+	131.901i	−0.673919	+	1.16726i	0.302864	+	0.953034i	$0.402057\pi$
$113$	−76.1529	+	131.901i	−0.673919	+	1.16726i	−0.976783	+	0.214229i	$0.931276\pi$
$114$		0			0
$115$	−6.97330	+	4.02603i	−0.0606374	+	0.0350090i
$116$	95.6712	−	24.1982i	0.824751	−	0.208605i
$117$		0			0
$118$	18.2456	−	2.27167i	0.154624	−	0.0192514i
$119$	204.695	−	118.181i	1.72013	−	0.993116i
$120$		0			0
$121$	−46.7124	+	80.9082i	−0.386053	+	0.668663i
$122$	150.413	+	63.5461i	1.23290	+	0.520870i
$123$		0			0
$124$	109.175	−	106.146i	0.880443	−	0.856019i
$125$	−99.4176			−0.795341
$126$		0			0
$127$			147.428i			1.16085i	0.814314	+	0.580425i	$0.197114\pi$
$127$			147.428i			1.16085i	−0.814314	+	0.580425i	$0.802886\pi$
$128$	22.9316	−	125.929i	0.179153	−	0.983821i
$129$		0			0
$130$	59.8573	+	25.2883i	0.460441	+	0.194525i
$131$	−112.889	−	65.1766i	−0.861750	−	0.497532i	0.00284803	−	0.999996i	$-0.499093\pi$
$131$	−112.889	−	65.1766i	−0.861750	−	0.497532i	−0.864598	+	0.502464i	$0.832427\pi$
$132$		0			0
$133$	79.9782	+	138.526i	0.601340	+	1.04155i
$134$	15.7252	−	1.95787i	0.117352	−	0.0146109i
$135$		0			0
$136$	−82.1465	−	210.790i	−0.604018	−	1.54993i
$137$	−49.9179	−	86.4604i	−0.364364	−	0.631098i	0.624310	−	0.781177i	$-0.285380\pi$
$137$	−49.9179	−	86.4604i	−0.364364	−	0.631098i	−0.988674	+	0.150079i	$0.952047\pi$
$138$		0			0
$139$	−82.7828	−	47.7947i	−0.595560	−	0.343847i	0.171733	−	0.985144i	$-0.445063\pi$
$139$	−82.7828	−	47.7947i	−0.595560	−	0.343847i	−0.767293	+	0.641297i	$0.778397\pi$
$140$	−70.8310	−	20.0509i	−0.505936	−	0.143221i
$141$		0			0
$142$	−75.9129	−	100.385i	−0.534598	−	0.706940i
$143$		−	77.4857i		−	0.541858i
$144$		0			0
$145$	−54.3218			−0.374633
$146$	−53.1560	+	40.1973i	−0.364082	+	0.275324i
$147$		0			0
$148$	−4.59749	+	16.2409i	−0.0310641	+	0.109736i
$149$	−34.3382	+	59.4755i	−0.230458	+	0.399164i	−0.957943	−	0.286959i	$-0.907356\pi$
$149$	−34.3382	+	59.4755i	−0.230458	+	0.399164i	0.727485	+	0.686123i	$0.240689\pi$
$150$		0			0
$151$	91.2633	−	52.6909i	0.604393	−	0.348946i	−0.166375	−	0.986063i	$-0.553206\pi$
$151$	91.2633	−	52.6909i	0.604393	−	0.348946i	0.770768	+	0.637116i	$0.219873\pi$
$152$	142.651	−	55.5922i	0.938493	−	0.365738i
$153$		0			0
$154$	10.8455	+	87.1092i	0.0704255	+	0.565644i
$155$	−72.5894	+	41.9095i	−0.468319	+	0.270384i
$156$		0			0
$157$	−107.502	+	186.200i	−0.684729	+	1.18598i	0.288794	+	0.957391i	$0.406746\pi$
$157$	−107.502	+	186.200i	−0.684729	+	1.18598i	−0.973522	+	0.228593i	$0.926587\pi$
$158$	48.2749	−	114.267i	0.305538	−	0.723206i
$159$		0			0
$160$	−29.2353	+	64.1077i	−0.182721	+	0.400673i
$161$	−30.5657			−0.189849
$162$		0			0
$163$		−	33.7439i		−	0.207018i	−0.994629	−	0.103509i	$-0.966993\pi$
$163$		−	33.7439i		−	0.207018i	0.994629	−	0.103509i	$-0.0330071\pi$
$164$	−55.3481	−	56.9273i	−0.337489	−	0.347118i
$165$		0			0
$166$	92.6219	−	219.236i	0.557963	−	1.32070i
$167$	131.565	+	75.9589i	0.787812	+	0.454843i	0.839192	−	0.543836i	$-0.183029\pi$
$167$	131.565	+	75.9589i	0.787812	+	0.454843i	−0.0513797	+	0.998679i	$0.516362\pi$
$168$		0			0
$169$	−24.3663	−	42.2036i	−0.144179	−	0.249726i
$170$	15.3860	+	123.578i	0.0905060	+	0.726927i
$171$		0			0
$172$	22.8659	+	90.4040i	0.132941	+	0.525605i
$173$	59.4003	+	102.884i	0.343354	+	0.594707i	0.985053	−	0.172249i	$-0.0551035\pi$
$173$	59.4003	+	102.884i	0.343354	+	0.594707i	−0.641699	+	0.766957i	$0.721770\pi$
$174$		0			0
$175$	−145.868	−	84.2170i	−0.833532	−	0.481240i
$176$	83.9862	+	2.36307i	0.477194	+	0.0134265i
$177$		0			0
$178$	−171.265	+	129.513i	−0.962166	+	0.727603i
$179$			218.189i			1.21894i	0.792811	+	0.609468i	$0.208617\pi$
$179$			218.189i			1.21894i	−0.792811	+	0.609468i	$0.791383\pi$
$180$		0			0
$181$	184.078			1.01701			0.508503	−	0.861060i	$-0.330199\pi$
$181$	184.078			1.01701			0.508503	+	0.861060i	$0.330199\pi$
$182$	148.780	+	196.743i	0.817472	+	1.08101i
$183$		0			0
$184$	−4.42965	+	28.9183i	−0.0240742	+	0.157165i
$185$	4.64565	−	8.04650i	0.0251116	−	0.0434946i
$186$		0			0
$187$	128.603	−	74.2492i	0.687719	−	0.397055i
$188$	−29.2813	−	115.768i	−0.155752	−	0.615788i
$189$		0			0
$190$	−83.6305	+	10.4124i	−0.440160	+	0.0548021i
$191$	−215.775	+	124.578i	−1.12971	+	0.652239i	−0.943862	−	0.330339i	$-0.892837\pi$
$191$	−215.775	+	124.578i	−1.12971	+	0.652239i	−0.185849	+	0.982578i	$0.559503\pi$
$192$		0			0
$193$	125.086	−	216.656i	0.648115	−	1.12257i	−0.335457	−	0.942055i	$-0.608891\pi$
$193$	125.086	−	216.656i	0.648115	−	1.12257i	0.983573	−	0.180513i	$-0.0577758\pi$
$194$	−6.58158	−	2.78056i	−0.0339256	−	0.0143328i
$195$		0			0
$196$	−58.1656	−	59.8252i	−0.296763	−	0.305231i
$197$	−255.674			−1.29784			−0.648919	−	0.760858i	$-0.724779\pi$
$197$	−255.674			−1.29784			−0.648919	+	0.760858i	$0.724779\pi$
$198$		0			0
$199$			309.110i			1.55332i	0.629921	+	0.776659i	$0.283087\pi$
$199$			309.110i			1.55332i	−0.629921	+	0.776659i	$0.716913\pi$
$200$	−100.818	+	125.802i	−0.504088	+	0.629008i
$201$		0			0
$202$	27.8077	+	11.7481i	0.137662	+	0.0581589i
$203$	−178.580	−	103.103i	−0.879702	−	0.507896i
$204$		0			0
$205$	21.8530	+	37.8505i	0.106600	+	0.184636i
$206$	−258.533	+	32.1887i	−1.25502	+	0.156256i
$207$		0			0
$208$	207.701	−	112.249i	0.998563	−	0.539658i
$209$	50.2478	+	87.0317i	0.240420	+	0.416420i
$210$		0			0
$211$	−341.158	−	196.968i	−1.61686	−	0.933497i	−0.987725	−	0.156205i	$-0.950074\pi$
$211$	−341.158	−	196.968i	−1.61686	−	0.933497i	−0.629140	−	0.777292i	$-0.716593\pi$
$212$	34.9862	−	123.591i	0.165029	−	0.582975i
$213$		0			0
$214$	61.8528	+	81.7927i	0.289032	+	0.382209i
$215$		−	51.3311i		−	0.238750i
$216$		0			0
$217$	−318.177			−1.46626
$218$	40.6364	−	30.7298i	0.186405	−	0.140962i
$219$		0			0
$220$	−44.5009	−	12.5974i	−0.202277	−	0.0572608i
$221$	208.638	−	361.372i	0.944064	−	1.63517i
$222$		0			0
$223$	89.4002	−	51.6152i	0.400898	−	0.231458i	−0.285974	−	0.958238i	$-0.592317\pi$
$223$	89.4002	−	51.6152i	0.400898	−	0.231458i	0.686871	+	0.726779i	$0.258984\pi$
$224$	−217.786	+	155.261i	−0.972258	+	0.693131i
$225$		0			0
$226$	−37.6350	−	302.278i	−0.166527	−	1.33751i
$227$	122.210	−	70.5578i	0.538369	−	0.310828i	−0.206049	−	0.978542i	$-0.566061\pi$
$227$	122.210	−	70.5578i	0.538369	−	0.310828i	0.744418	+	0.667714i	$0.232727\pi$
$228$		0			0
$229$	105.572	−	182.856i	0.461012	−	0.798496i	−0.538000	−	0.842945i	$-0.680820\pi$
$229$	105.572	−	182.856i	0.461012	−	0.798496i	0.999012	+	0.0444490i	$0.0141532\pi$
$230$	6.26726	−	14.8346i	0.0272490	−	0.0644982i
$231$		0			0
$232$	−123.426	+	154.013i	−0.532010	+	0.663849i
$233$	280.109			1.20219			0.601093	−	0.799179i	$-0.294732\pi$
$233$	280.109			1.20219			0.601093	+	0.799179i	$0.294732\pi$
$234$		0			0
$235$			65.7328i			0.279714i
$236$	−26.3656	+	25.6342i	−0.111719	+	0.108619i
$237$		0			0
$238$	−183.970	+	435.456i	−0.772983	+	1.82965i
$239$	339.349	+	195.923i	1.41987	+	0.819762i	0.996287	−	0.0860949i	$-0.0274388\pi$
$239$	339.349	+	195.923i	1.41987	+	0.819762i	0.423583	+	0.905857i	$0.360772\pi$
$240$		0			0
$241$	−23.6786	−	41.0125i	−0.0982514	−	0.170176i	0.812710	−	0.582669i	$-0.197992\pi$
$241$	−23.6786	−	41.0125i	−0.0982514	−	0.170176i	−0.910961	+	0.412493i	$0.864658\pi$
$242$	−23.0854	−	185.418i	−0.0953943	−	0.766190i
$243$		0			0
$244$	−316.602	+	80.0783i	−1.29755	+	0.328190i
$245$	22.9654	+	39.7772i	0.0937363	+	0.162356i
$246$		0			0
$247$	244.557	+	141.195i	0.990107	+	0.571639i
$248$	−46.1110	+	301.029i	−0.185931	+	1.21383i
$249$		0			0
$250$	158.594	−	119.931i	0.634376	−	0.479724i
$251$		−	389.416i		−	1.55146i	−0.631065	−	0.775730i	$-0.717382\pi$
$251$		−	389.416i		−	1.55146i	0.631065	−	0.775730i	$-0.282618\pi$
$252$		0			0
$253$	−19.2035			−0.0759030
$254$	−177.847	−	235.181i	−0.700187	−	0.925911i
$255$		0			0
$256$	115.332	+	228.549i	0.450514	+	0.892769i
$257$	32.5409	−	56.3625i	0.126618	−	0.219310i	−0.795746	−	0.605631i	$-0.792921\pi$
$257$	32.5409	−	56.3625i	0.126618	−	0.219310i	0.922364	+	0.386321i	$0.126254\pi$
$258$		0			0
$259$	30.5445	−	17.6349i	0.117933	−	0.0680884i
$260$	−125.992	+	31.8673i	−0.484586	+	0.122567i
$261$		0			0
$262$	258.709	−	32.2105i	0.987439	−	0.122941i
$263$	124.773	−	72.0378i	0.474423	−	0.273908i	−0.243667	−	0.969859i	$-0.578350\pi$
$263$	124.773	−	72.0378i	0.474423	−	0.273908i	0.718089	+	0.695951i	$0.245017\pi$
$264$		0			0
$265$	−35.3527	+	61.2327i	−0.133406	+	0.231067i
$266$	−294.693	−	124.501i	−1.10787	−	0.468048i
$267$		0			0
$268$	−22.7235	+	22.0931i	−0.0847891	+	0.0824370i
$269$	72.4113			0.269187			0.134593	−	0.990901i	$-0.457027\pi$
$269$	72.4113			0.269187			0.134593	+	0.990901i	$0.457027\pi$
$270$		0			0
$271$		−	35.4695i		−	0.130884i	−0.997856	−	0.0654419i	$-0.979154\pi$
$271$		−	35.4695i		−	0.130884i	0.997856	−	0.0654419i	$-0.0208457\pi$
$272$	385.326	+	237.162i	1.41664	+	0.871920i
$273$		0			0
$274$	183.931	+	77.7064i	0.671280	+	0.283600i
$275$	−91.6443	−	52.9109i	−0.333252	−	0.192403i
$276$		0			0
$277$	−166.922	−	289.118i	−0.602607	−	1.04375i	−0.992425	−	0.122854i	$-0.960795\pi$
$277$	−166.922	−	289.118i	−0.602607	−	1.04375i	0.389818	−	0.920892i	$-0.372538\pi$
$278$	189.714	−	23.6203i	0.682424	−	0.0849651i
$279$		0			0
$280$	137.180	−	53.4600i	0.489928	−	0.190929i
$281$	20.5385	+	35.5737i	0.0730906	+	0.126597i	0.900254	−	0.435364i	$-0.143380\pi$
$281$	20.5385	+	35.5737i	0.0730906	+	0.126597i	−0.827164	+	0.561961i	$0.810047\pi$
$282$		0			0
$283$	218.583	+	126.199i	0.772378	+	0.445933i	0.833722	−	0.552184i	$-0.186205\pi$
$283$	218.583	+	126.199i	0.772378	+	0.445933i	−0.0613442	+	0.998117i	$0.519539\pi$
$284$	242.197	+	68.5615i	0.852806	+	0.241414i
$285$		0			0
$286$	93.4737	+	123.607i	0.326831	+	0.432194i
$287$			165.908i			0.578077i
$288$		0			0
$289$	510.695			1.76711
$290$	86.6558	−	65.5303i	0.298813	−	0.225967i
$291$		0			0
$292$	36.3046	−	128.248i	0.124331	−	0.439205i
$293$	−20.3415	+	35.2325i	−0.0694248	+	0.120247i	−0.898648	−	0.438670i	$-0.855450\pi$
$293$	−20.3415	+	35.2325i	−0.0694248	+	0.120247i	0.829223	+	0.558917i	$0.188783\pi$
$294$		0			0
$295$	17.5302	−	10.1211i	0.0594245	−	0.0343088i
$296$	−12.2579	−	31.4540i	−0.0414117	−	0.106264i
$297$		0			0
$298$	−16.9701	−	136.300i	−0.0569465	−	0.457384i
$299$	−46.7317	+	26.9806i	−0.156293	+	0.0902361i
$300$		0			0
$301$	97.4266	−	168.748i	0.323677	−	0.560624i
$302$	−82.0231	+	194.148i	−0.271600	+	0.642875i
$303$		0			0
$304$	−160.498	+	260.767i	−0.527955	+	0.857787i
$305$	179.766			0.589396
$306$		0			0
$307$		−	136.830i		−	0.445701i	−0.974853	−	0.222850i	$-0.928464\pi$
$307$		−	136.830i		−	0.445701i	0.974853	−	0.222850i	$-0.0715361\pi$
$308$	−122.384	−	125.876i	−0.397351	−	0.408688i
$309$		0			0
$310$	65.2398	−	154.422i	0.210451	−	0.498137i
$311$	−371.260	−	214.347i	−1.19376	−	0.689219i	−0.234605	−	0.972091i	$-0.575380\pi$
$311$	−371.260	−	214.347i	−1.19376	−	0.689219i	−0.959158	+	0.282871i	$0.908713\pi$
$312$		0			0
$313$	5.98705	+	10.3699i	0.0191280	+	0.0331306i	0.875431	−	0.483343i	$-0.160578\pi$
$313$	5.98705	+	10.3699i	0.0191280	+	0.0331306i	−0.856303	+	0.516474i	$0.827244\pi$
$314$	−53.1281	−	426.715i	−0.169198	−	1.35896i
$315$		0			0
$316$	60.8341	+	240.517i	0.192513	+	0.761130i
$317$	23.5266	+	40.7493i	0.0742164	+	0.128547i	0.900745	−	0.434348i	$-0.143021\pi$
$317$	23.5266	+	40.7493i	0.0742164	+	0.128547i	−0.826529	+	0.562894i	$0.809688\pi$
$318$		0			0
$319$	−112.196	−	64.7763i	−0.351711	−	0.203061i
$320$	−30.6984	−	137.534i	−0.0959324	−	0.429794i
$321$		0			0
$322$	48.7593	−	36.8725i	0.151426	−	0.114511i
$323$			541.189i			1.67551i
$324$		0			0
$325$	−297.356			−0.914941
$326$	40.7065	+	53.8293i	0.124867	+	0.165121i
$327$		0			0
$328$	156.966	+	24.0438i	0.478556	+	0.0733042i
$329$	−124.761	+	216.092i	−0.379213	+	0.656816i
$330$		0			0
$331$	73.1501	−	42.2332i	0.220997	−	0.127593i	−0.385415	−	0.922743i	$-0.625942\pi$
$331$	73.1501	−	42.2332i	0.220997	−	0.127593i	0.606412	+	0.795151i	$0.292608\pi$
$332$	116.718	+	461.464i	0.351561	+	1.38995i
$333$		0			0
$334$	−301.508	+	37.5392i	−0.902717	+	0.112393i
$335$	15.1086	−	8.72297i	0.0451004	−	0.0260387i
$336$		0			0
$337$	−252.558	+	437.443i	−0.749430	+	1.29805i	0.198667	+	0.980067i	$0.436339\pi$
$337$	−252.558	+	437.443i	−0.749430	+	1.29805i	−0.948096	+	0.317983i	$0.896994\pi$
$338$	89.7815	+	37.9306i	0.265626	+	0.112221i
$339$		0			0
$340$	−173.620	−	178.574i	−0.510648	−	0.525217i
$341$	−199.901			−0.586219
$342$		0			0
$343$		−	235.200i		−	0.685714i
$344$	−145.534	−	116.631i	−0.423064	−	0.339044i
$345$		0			0
$346$	−218.870	−	92.4675i	−0.632572	−	0.267247i
$347$	424.751	+	245.230i	1.22407	+	0.706715i	0.965782	−	0.259354i	$-0.0835097\pi$
$347$	424.751	+	245.230i	1.22407	+	0.706715i	0.258284	+	0.966069i	$0.416843\pi$
$348$		0			0
$349$	186.972	+	323.845i	0.535736	+	0.927923i	0.999127	+	0.0417686i	$0.0132992\pi$
$349$	186.972	+	323.845i	0.535736	+	0.927923i	−0.463391	+	0.886154i	$0.653367\pi$
$350$	334.287	−	41.6203i	0.955105	−	0.118915i
$351$		0			0
$352$	−136.828	+	97.5458i	−0.388716	+	0.277119i
$353$	−297.026	−	514.465i	−0.841434	−	1.45741i	−0.888682	−	0.458523i	$-0.848379\pi$
$353$	−297.026	−	514.465i	−0.841434	−	1.45741i	0.0472483	−	0.998883i	$-0.484955\pi$
$354$		0			0
$355$	−119.996	−	69.2796i	−0.338016	−	0.195154i
$356$	116.971	−	413.207i	0.328571	−	1.16069i
$357$		0			0
$358$	−263.209	−	348.062i	−0.735222	−	0.972241i
$359$		−	410.893i		−	1.14455i	−0.820062	−	0.572274i	$-0.806061\pi$
$359$		−	410.893i		−	1.14455i	0.820062	−	0.572274i	$-0.193939\pi$
$360$		0			0
$361$	−5.24690			−0.0145343
$362$	−293.647	+	222.060i	−0.811180	+	0.613425i
$363$		0			0
$364$	−474.676	−	134.372i	−1.30405	−	0.369154i
$365$	−36.6848	+	63.5400i	−0.100506	+	0.174082i
$366$		0			0
$367$	−466.176	+	269.147i	−1.27023	+	0.733370i	−0.975032	−	0.222064i	$-0.928721\pi$
$367$	−466.176	+	269.147i	−1.27023	+	0.733370i	−0.295203	+	0.955435i	$0.595387\pi$
$368$	−27.8189	−	51.4750i	−0.0755948	−	0.139878i
$369$		0			0
$370$	2.29590	+	18.4402i	0.00620512	+	0.0498384i
$371$	−232.440	+	134.199i	−0.626522	+	0.361722i
$372$		0			0
$373$	−74.9606	+	129.836i	−0.200967	+	0.348085i	−0.948840	−	0.315757i	$-0.897742\pi$
$373$	−74.9606	+	129.836i	−0.200967	+	0.348085i	0.747873	+	0.663841i	$0.231075\pi$
$374$	−115.583	+	273.583i	−0.309044	+	0.731506i
$375$		0			0
$376$	186.365	+	149.354i	0.495653	+	0.397217i
$377$	−364.039			−0.965621
$378$		0			0
$379$			184.361i			0.486442i	0.969971	+	0.243221i	$0.0782040\pi$
$379$			184.361i			0.486442i	−0.969971	+	0.243221i	$0.921796\pi$
$380$	120.849	−	117.497i	0.318024	−	0.309201i
$381$		0			0
$382$	193.928	−	459.027i	0.507665	−	1.20164i
$383$	−180.514	−	104.220i	−0.471315	−	0.272114i	0.245475	−	0.969403i	$-0.421056\pi$
$383$	−180.514	−	104.220i	−0.471315	−	0.272114i	−0.716790	+	0.697289i	$0.754389\pi$
$384$		0			0
$385$	48.3206	+	83.6937i	0.125508	+	0.217386i
$386$	61.8181	+	496.511i	0.160150	+	1.28630i
$387$		0			0
$388$	13.8534	−	3.50395i	0.0357047	−	0.00903080i
$389$	150.914	+	261.390i	0.387953	+	0.671954i	0.992174	−	0.124863i	$-0.0398491\pi$
$389$	150.914	+	261.390i	0.387953	+	0.671954i	−0.604221	+	0.796816i	$0.706516\pi$
$390$		0			0
$391$	−89.5597	−	51.7073i	−0.229053	−	0.132244i
$392$	164.957	+	25.2677i	0.420808	+	0.0644585i
$393$		0			0
$394$	407.859	−	308.428i	1.03517	−	0.782813i
$395$		−	136.565i		−	0.345734i
$396$		0			0
$397$	−246.672			−0.621341			−0.310670	−	0.950518i	$-0.600553\pi$
$397$	−246.672			−0.621341			−0.310670	+	0.950518i	$0.600553\pi$
$398$	−372.890	−	493.102i	−0.936911	−	1.23895i
$399$		0			0
$400$	9.06842	−	322.302i	0.0226711	−	0.805755i
$401$	−377.516	+	653.877i	−0.941437	+	1.63062i	−0.178703	+	0.983903i	$0.557190\pi$
$401$	−377.516	+	653.877i	−0.941437	+	1.63062i	−0.762734	+	0.646713i	$0.776143\pi$
$402$		0			0
$403$	−486.460	+	280.858i	−1.20710	+	0.696917i
$404$	−58.5318	+	14.8045i	−0.144881	+	0.0366447i
$405$		0			0
$406$	409.252	−	50.9539i	1.00801	−	0.125502i
$407$	19.1902	−	11.0794i	0.0471503	−	0.0272222i
$408$		0			0
$409$	130.730	−	226.432i	0.319634	−	0.553622i	−0.660778	−	0.750582i	$-0.729773\pi$
$409$	130.730	−	226.432i	0.319634	−	0.553622i	0.980412	+	0.196959i	$0.0631067\pi$
$410$	−80.5209	−	34.0182i	−0.196392	−	0.0829712i
$411$		0			0
$412$	373.590	−	363.226i	0.906771	−	0.881617i
$413$	76.8394			0.186052
$414$		0			0
$415$		−	262.018i		−	0.631369i
$416$	−195.921	+	429.620i	−0.470964	+	1.03274i
$417$		0			0
$418$	−185.146	−	78.2199i	−0.442933	−	0.187129i
$419$	−340.246	−	196.441i	−0.812043	−	0.468833i	0.0356217	−	0.999365i	$-0.488659\pi$
$419$	−340.246	−	196.441i	−0.812043	−	0.468833i	−0.847665	+	0.530532i	$0.821992\pi$
$420$		0			0
$421$	102.451	+	177.450i	0.243351	+	0.421496i	0.961667	−	0.274221i	$-0.0884200\pi$
$421$	102.451	+	177.450i	0.243351	+	0.421496i	−0.718316	+	0.695717i	$0.755087\pi$
$422$	781.835	−	97.3423i	1.85269	−	0.230669i
$423$		0			0
$424$	93.2807	+	239.361i	0.220002	+	0.564530i
$425$	−284.936	−	493.524i	−0.670438	−	1.16123i
$426$		0			0
$427$	590.968	+	341.196i	1.38400	+	0.799053i
$428$	−197.339	−	55.8629i	−0.461072	−	0.130521i
$429$		0			0
$430$	61.9225	+	81.8850i	0.144006	+	0.190430i
$431$			462.725i			1.07361i	0.843707	+	0.536803i	$0.180368\pi$
$431$			462.725i			1.07361i	−0.843707	+	0.536803i	$0.819632\pi$
$432$		0			0
$433$	190.574			0.440126			0.220063	−	0.975486i	$-0.429374\pi$
$433$	190.574			0.440126			0.220063	+	0.975486i	$0.429374\pi$
$434$	507.566	−	383.828i	1.16951	−	0.884397i
$435$		0			0
$436$	−27.7539	+	98.0421i	−0.0636558	+	0.224867i
$437$	34.9926	−	60.6090i	0.0800747	−	0.138693i
$438$		0			0
$439$	379.279	−	218.977i	0.863962	−	0.498809i	−0.00137479	−	0.999999i	$-0.500438\pi$
$439$	379.279	−	218.977i	0.863962	−	0.498809i	0.865337	+	0.501190i	$0.167104\pi$
$440$	86.1858	−	33.5873i	0.195877	−	0.0763347i
$441$		0			0
$442$	103.110	+	828.159i	0.233280	+	1.87366i
$443$	721.993	−	416.843i	1.62978	−	0.940954i	0.645623	−	0.763657i	$-0.276598\pi$
$443$	721.993	−	416.843i	1.62978	−	0.940954i	0.984157	−	0.177297i	$-0.0567354\pi$
$444$		0			0
$445$	−118.196	+	204.722i	−0.265610	+	0.460050i
$446$	−80.3486	+	190.185i	−0.180154	+	0.426423i
$447$		0			0
$448$	160.121	−	510.400i	0.357413	−	1.13929i
$449$	480.789			1.07080			0.535399	−	0.844599i	$-0.320161\pi$
$449$	480.789			1.07080			0.535399	+	0.844599i	$0.320161\pi$
$450$		0			0
$451$			104.235i			0.231119i
$452$	424.685	+	436.802i	0.939568	+	0.966376i
$453$		0			0
$454$	−109.836	+	259.982i	−0.241930	+	0.572647i
$455$	235.177	+	135.779i	0.516872	+	0.298416i
$456$		0			0
$457$	109.313	+	189.336i	0.239197	+	0.414302i	0.960484	−	0.278334i	$-0.0897824\pi$
$457$	109.313	+	189.336i	0.239197	+	0.414302i	−0.721287	+	0.692636i	$0.756449\pi$
$458$	52.1739	+	419.051i	0.113917	+	0.914959i
$459$		0			0
$460$	7.89775	+	31.2250i	0.0171690	+	0.0678804i
$461$	358.474	+	620.894i	0.777600	+	1.34684i	0.933322	+	0.359042i	$0.116896\pi$
$461$	358.474	+	620.894i	0.777600	+	1.34684i	−0.155722	+	0.987801i	$0.549770\pi$
$462$		0			0
$463$	−26.6250	−	15.3719i	−0.0575053	−	0.0332007i	0.470972	−	0.882148i	$-0.343903\pi$
$463$	−26.6250	−	15.3719i	−0.0575053	−	0.0332007i	−0.528477	+	0.848948i	$0.677237\pi$
$464$	11.1021	−	394.580i	0.0239268	−	0.850387i
$465$		0			0
$466$	−446.838	+	337.905i	−0.958881	+	0.725119i
$467$		−	458.639i		−	0.982096i	−0.871133	−	0.491048i	$-0.836614\pi$
$467$		−	458.639i		−	0.982096i	0.871133	−	0.491048i	$-0.163386\pi$
$468$		0			0
$469$	66.2249			0.141204
$470$	−79.2958	−	104.859i	−0.168714	−	0.223104i
$471$		0			0
$472$	11.1357	−	72.6981i	0.0235927	−	0.154021i
$473$	61.2101	−	106.019i	0.129408	−	0.224142i
$474$		0			0
$475$	333.989	−	192.829i	0.703135	−	0.405955i
$476$	−231.832	−	916.582i	−0.487041	−	1.92559i
$477$		0			0
$478$	−777.688	+	96.8260i	−1.62696	+	0.202565i
$479$	−570.477	+	329.365i	−1.19098	+	0.687610i	−0.958528	−	0.284999i	$-0.908007\pi$
$479$	−570.477	+	329.365i	−1.19098	+	0.687610i	−0.232448	+	0.972609i	$0.574674\pi$
$480$		0			0
$481$	31.1329	−	53.9238i	0.0647254	−	0.112108i
$482$	87.2476	+	36.8601i	0.181012	+	0.0764732i
$483$		0			0
$484$	260.503	+	267.935i	0.538228	+	0.553585i
$485$	−7.86593			−0.0162184
$486$		0			0
$487$		−	715.589i		−	1.46938i	−0.678402	−	0.734691i	$-0.737327\pi$
$487$		−	715.589i		−	1.46938i	0.678402	−	0.734691i	$-0.262673\pi$
$488$	408.451	−	509.671i	0.836990	−	1.04441i
$489$		0			0
$490$	−84.6198	−	35.7499i	−0.172693	−	0.0729589i
$491$	574.179	+	331.502i	1.16941	+	0.675157i	0.953540	−	0.301266i	$-0.0974091\pi$
$491$	574.179	+	331.502i	1.16941	+	0.675157i	0.215866	+	0.976423i	$0.430742\pi$
$492$		0			0
$493$	−348.834	−	604.198i	−0.707574	−	1.22555i
$494$	−560.452	+	69.7790i	−1.13452	+	0.141253i
$495$		0			0
$496$	−289.584	−	535.836i	−0.583839	−	1.08031i
$497$	−262.986	−	455.505i	−0.529147	−	0.916509i
$498$		0			0
$499$	458.706	+	264.834i	0.919251	+	0.530730i	0.883396	−	0.468627i	$-0.155251\pi$
$499$	458.706	+	264.834i	0.919251	+	0.530730i	0.0358546	+	0.999357i	$0.488585\pi$
$500$	−108.317	+	382.635i	−0.216634	+	0.765269i
$501$		0			0
$502$	469.766	+	621.208i	0.935790	+	1.23747i
$503$		−	68.3537i		−	0.135892i	−0.997689	−	0.0679460i	$-0.978355\pi$
$503$		−	68.3537i		−	0.135892i	0.997689	−	0.0679460i	$-0.0216446\pi$
$504$		0			0
$505$	33.2342			0.0658103
$506$	30.6339	−	23.1658i	0.0605413	−	0.0457822i
$507$		0			0
$508$	567.415	+	160.625i	1.11696	+	0.316190i
$509$	400.473	−	693.640i	0.786784	−	1.36275i	−0.141143	−	0.989989i	$-0.545078\pi$
$509$	400.473	−	693.640i	0.786784	−	1.36275i	0.927927	−	0.372761i	$-0.121589\pi$
$510$		0			0
$511$	−241.198	+	139.256i	−0.472012	+	0.272516i
$512$	−459.687	−	225.460i	−0.897826	−	0.440351i
$513$		0			0
$514$	16.0818	+	129.166i	0.0312876	+	0.251297i
$515$	−248.396	+	143.412i	−0.482323	+	0.278469i
$516$		0			0
$517$	−78.3834	+	135.764i	−0.151612	+	0.262600i
$518$	−27.4520	+	64.9786i	−0.0529961	+	0.125441i
$519$		0			0
$520$	162.544	−	202.825i	0.312585	−	0.390047i
$521$	208.227			0.399668			0.199834	−	0.979830i	$-0.435960\pi$
$521$	208.227			0.399668			0.199834	+	0.979830i	$0.435960\pi$
$522$		0			0
$523$		−	30.5350i		−	0.0583843i	−0.999574	−	0.0291921i	$-0.990707\pi$
$523$		−	30.5350i		−	0.0583843i	0.999574	−	0.0291921i	$-0.00929347\pi$
$524$	−373.844	+	363.473i	−0.713442	+	0.693651i
$525$		0			0
$526$	−112.140	+	265.435i	−0.213194	+	0.504629i
$527$	−932.283	−	538.254i	−1.76904	−	1.02135i
$528$		0			0
$529$	−257.813	−	446.546i	−0.487360	−	0.844132i
$530$	−17.4714	−	140.327i	−0.0329650	−	0.264769i
$531$		0			0
$532$	620.292	−	156.891i	1.16596	−	0.294907i
$533$	146.448	+	253.656i	0.274762	+	0.475903i
$534$		0			0
$535$	97.7710	+	56.4481i	0.182749	+	0.105510i
$536$	9.59747	−	62.6557i	0.0179057	−	0.116895i
$537$		0			0
$538$	−115.513	+	87.3522i	−0.214707	+	0.162365i
$539$			109.541i			0.203230i
$540$		0			0
$541$	526.091			0.972442			0.486221	−	0.873836i	$-0.338375\pi$
$541$	526.091			0.972442			0.486221	+	0.873836i	$0.338375\pi$
$542$	42.7881	+	56.5820i	0.0789448	+	0.104395i
$543$		0			0
$544$	−900.780	+	86.5038i	−1.65585	+	0.159014i
$545$	28.0446	−	48.5747i	0.0514580	−	0.0891279i
$546$		0			0
$547$	−823.276	+	475.318i	−1.50507	+	0.868955i	−0.505092	+	0.863066i	$0.668541\pi$
$547$	−823.276	+	475.318i	−1.50507	+	0.868955i	−0.999983	+	0.00588962i	$0.998125\pi$
$548$	−387.151	+	97.9224i	−0.706481	+	0.178691i
$549$		0			0
$550$	210.022	−	26.1487i	0.381858	−	0.0475432i
$551$	408.888	−	236.071i	0.742083	−	0.428442i
$552$		0			0
$553$	259.201	−	448.949i	0.468717	−	0.811842i
$554$	615.052	+	259.845i	1.11020	+	0.469034i
$555$		0			0
$556$	−274.143	+	266.538i	−0.493063	+	0.479385i
$557$	−978.257			−1.75630			−0.878148	−	0.478390i	$-0.841221\pi$
$557$	−978.257			−1.75630			−0.878148	+	0.478390i	$0.841221\pi$
$558$		0			0
$559$		−	343.997i		−	0.615379i
$560$	−154.343	+	250.766i	−0.275612	+	0.447796i
$561$		0			0
$562$	−75.6773	−	31.9719i	−0.134657	−	0.0568895i
$563$	925.131	+	534.125i	1.64322	+	0.948712i	0.979680	+	0.200569i	$0.0642792\pi$
$563$	925.131	+	534.125i	1.64322	+	0.948712i	0.663538	+	0.748143i	$0.269054\pi$
$564$		0			0
$565$	−167.677	−	290.426i	−0.296774	−	0.514028i
$566$	−500.928	+	62.3680i	−0.885032	+	0.110191i
$567$		0			0
$568$	−469.068	+	182.799i	−0.825824	+	0.321830i
$569$	481.775	+	834.459i	0.846705	+	1.46654i	0.884132	+	0.467237i	$0.154750\pi$
$569$	481.775	+	834.459i	0.846705	+	1.46654i	−0.0374271	+	0.999299i	$0.511916\pi$
$570$		0			0
$571$	243.132	+	140.372i	0.425800	+	0.245836i	0.697556	−	0.716531i	$-0.254271\pi$
$571$	243.132	+	140.372i	0.425800	+	0.245836i	−0.271756	+	0.962366i	$0.587604\pi$
$572$	−298.224	−	84.4217i	−0.521370	−	0.147590i
$573$		0			0
$574$	−200.141	−	264.661i	−0.348677	−	0.461083i
$575$			73.6944i			0.128164i
$576$		0			0
$577$	−552.228			−0.957068			−0.478534	−	0.878069i	$-0.658832\pi$
$577$	−552.228			−0.957068			−0.478534	+	0.878069i	$0.658832\pi$
$578$	−814.676	+	616.069i	−1.40947	+	1.06586i
$579$		0			0
$580$	−59.1843	+	209.072i	−0.102042	+	0.360469i
$581$	497.311	−	861.367i	0.855956	−	1.48256i
$582$		0			0
$583$	−146.034	+	84.3130i	−0.250488	+	0.144619i
$584$	96.7956	+	248.380i	0.165746	+	0.425308i
$585$		0			0
$586$	−10.0528	−	80.7425i	−0.0171550	−	0.137786i
$587$	141.476	−	81.6811i	0.241015	−	0.139150i	−0.374628	−	0.927175i	$-0.622230\pi$
$587$	141.476	−	81.6811i	0.241015	−	0.139150i	0.615643	+	0.788025i	$0.288896\pi$
$588$		0			0
$589$	364.260	−	630.917i	0.618438	−	1.07117i
$590$	−15.7553	+	37.2928i	−0.0267039	+	0.0632081i
$591$		0			0
$592$	57.4982	+	35.3893i	0.0971253	+	0.0597792i
$593$	818.460			1.38020			0.690101	−	0.723713i	$-0.257566\pi$
$593$	818.460			1.38020			0.690101	+	0.723713i	$0.257566\pi$
$594$		0			0
$595$			520.433i			0.874677i
$596$	191.495	+	196.959i	0.321300	+	0.330468i
$597$		0			0
$598$	42.0002	−	99.4143i	0.0702345	−	0.166245i
$599$	−398.849	−	230.275i	−0.665857	−	0.384433i	0.128648	−	0.991690i	$-0.458936\pi$
$599$	−398.849	−	230.275i	−0.665857	−	0.384433i	−0.794505	+	0.607257i	$0.792270\pi$
$600$		0			0
$601$	162.324	+	281.153i	0.270090	+	0.467809i	0.968885	−	0.247513i	$-0.0796132\pi$
$601$	162.324	+	281.153i	0.270090	+	0.467809i	−0.698795	+	0.715322i	$0.746280\pi$
$602$	48.1486	+	386.721i	0.0799811	+	0.642393i
$603$		0			0
$604$	−103.362	−	408.658i	−0.171129	−	0.676587i
$605$	−102.854	−	178.148i	−0.170006	−	0.294459i
$606$		0			0
$607$	−764.054	−	441.127i	−1.25874	−	0.726733i	−0.285909	−	0.958257i	$-0.592295\pi$
$607$	−764.054	−	441.127i	−1.25874	−	0.726733i	−0.972829	+	0.231524i	$0.925629\pi$
$608$	−58.5409	−	609.598i	−0.0962845	−	1.00263i
$609$		0			0
$610$	−286.767	+	216.858i	−0.470111	+	0.355504i
$611$			440.510i			0.720966i
$612$		0			0
$613$	19.4869			0.0317895			0.0158947	−	0.999874i	$-0.494940\pi$
$613$	19.4869			0.0317895			0.0158947	+	0.999874i	$0.494940\pi$
$614$	165.063	+	218.275i	0.268832	+	0.355497i
$615$		0			0
$616$	347.079	+	53.1648i	0.563440	+	0.0863065i
$617$	48.3314	−	83.7124i	0.0783329	−	0.135677i	−0.824198	−	0.566302i	$-0.808374\pi$
$617$	48.3314	−	83.7124i	0.0783329	−	0.135677i	0.902531	+	0.430625i	$0.141707\pi$
$618$		0			0
$619$	363.937	−	210.119i	0.587944	−	0.339449i	−0.176340	−	0.984329i	$-0.556426\pi$
$619$	363.937	−	210.119i	0.587944	−	0.339449i	0.764284	+	0.644880i	$0.223093\pi$
$620$	82.2126	+	325.040i	0.132601	+	0.524258i
$621$		0			0
$622$	850.820	−	105.931i	1.36788	−	0.170307i
$623$	−777.127	+	448.674i	−1.24739	+	0.720184i
$624$		0			0
$625$	−142.447	+	246.725i	−0.227915	+	0.394760i
$626$	−22.0603	−	9.31995i	−0.0352401	−	0.0148881i
$627$		0			0
$628$	599.512	+	616.618i	0.954638	+	0.981875i
$629$	119.330			0.189714
$630$		0			0
$631$			483.230i			0.765816i	0.923787	+	0.382908i	$0.125077\pi$
$631$			483.230i			0.765816i	−0.923787	+	0.382908i	$0.874923\pi$
$632$	−387.188	−	310.294i	−0.612640	−	0.490971i
$633$		0			0
$634$	−86.6876	−	36.6235i	−0.136731	−	0.0577658i
$635$	−281.124	−	162.307i	−0.442715	−	0.255602i
$636$		0			0
$637$	153.903	+	266.568i	0.241606	+	0.418475i
$638$	257.120	−	32.0127i	0.403010	−	0.0501767i
$639$		0			0
$640$	214.883	+	182.366i	0.335755	+	0.284947i
$641$	45.2967	+	78.4562i	0.0706657	+	0.122397i	0.899193	−	0.437552i	$-0.144154\pi$
$641$	45.2967	+	78.4562i	0.0706657	+	0.122397i	−0.828528	+	0.559948i	$0.810821\pi$
$642$		0			0
$643$	−453.773	−	261.986i	−0.705713	−	0.407444i	0.103759	−	0.994602i	$-0.466913\pi$
$643$	−453.773	−	261.986i	−0.705713	−	0.407444i	−0.809472	+	0.587159i	$0.800246\pi$
$644$	−33.3017	+	117.640i	−0.0517107	+	0.182671i
$645$		0			0
$646$	−652.855	−	863.321i	−1.01061	−	1.33641i
$647$			31.3018i			0.0483799i	0.999707	+	0.0241900i	$0.00770066\pi$
$647$			31.3018i			0.0483799i	−0.999707	+	0.0241900i	$0.992299\pi$
$648$		0			0
$649$	48.2758			0.0743848
$650$	474.351	−	358.711i	0.729771	−	0.551863i
$651$		0			0
$652$	−129.872	−	36.7645i	−0.199191	−	0.0563872i
$653$	−445.115	+	770.961i	−0.681646	+	1.18065i	0.292833	+	0.956164i	$0.405402\pi$
$653$	−445.115	+	770.961i	−0.681646	+	1.18065i	−0.974478	+	0.224481i	$0.927931\pi$
$654$		0			0
$655$	248.565	−	143.509i	0.379489	−	0.219098i
$656$	−279.402	+	150.999i	−0.425918	+	0.230181i
$657$		0			0
$658$	−61.6574	−	495.221i	−0.0937042	−	0.752615i
$659$	41.1783	−	23.7743i	0.0624860	−	0.0360763i	−0.468432	−	0.883500i	$-0.655181\pi$
$659$	41.1783	−	23.7743i	0.0624860	−	0.0360763i	0.530918	+	0.847423i	$0.321847\pi$
$660$		0			0
$661$	−24.8421	+	43.0278i	−0.0375826	+	0.0650950i	−0.884205	−	0.467099i	$-0.845299\pi$
$661$	−24.8421	+	43.0278i	−0.0375826	+	0.0650950i	0.846622	+	0.532194i	$0.178632\pi$
$662$	−65.7437	+	155.615i	−0.0993108	+	0.235068i
$663$		0			0
$664$	−742.872	−	595.339i	−1.11878	−	0.896595i
$665$	−352.200			−0.529624
$666$		0			0
$667$			90.2207i			0.135263i
$668$	435.689	−	423.603i	0.652229	−	0.634136i
$669$		0			0
$670$	−13.5789	+	32.1412i	−0.0202670	+	0.0479720i
$671$	371.287	+	214.362i	0.553333	+	0.319467i
$672$		0			0
$673$	−16.4365	−	28.4688i	−0.0244227	−	0.0423013i	0.853556	−	0.521002i	$-0.174441\pi$
$673$	−16.4365	−	28.4688i	−0.0244227	−	0.0423013i	−0.877978	+	0.478700i	$0.841108\pi$
$674$	−124.815	−	1002.49i	−0.185185	−	1.48738i
$675$		0			0
$676$	−188.979	+	47.7986i	−0.279555	+	0.0707079i
$677$	−457.417	−	792.269i	−0.675653	−	1.17026i	−0.976278	−	0.216522i	$-0.930529\pi$
$677$	−457.417	−	792.269i	−0.675653	−	1.17026i	0.300625	−	0.953742i	$-0.402805\pi$
$678$		0			0
$679$	−25.8587	−	14.9296i	−0.0380836	−	0.0219876i
$680$	492.384	+	75.4223i	0.724094	+	0.110915i
$681$		0			0
$682$	318.888	−	241.147i	0.467577	−	0.353588i
$683$		−	870.646i		−	1.27474i	−0.770559	−	0.637369i	$-0.780023\pi$
$683$		−	870.646i		−	1.27474i	0.770559	−	0.637369i	$-0.219977\pi$
$684$		0			0
$685$	219.824			0.320910
$686$	283.730	+	375.198i	0.413600	+	0.546936i
$687$		0			0
$688$	372.856	+	10.4908i	0.541942	+	0.0152483i
$689$	−236.917	+	410.352i	−0.343856	+	0.595577i
$690$		0			0
$691$	800.188	−	461.988i	1.15801	−	0.668580i	0.207187	−	0.978301i	$-0.433569\pi$
$691$	800.188	−	461.988i	1.15801	−	0.668580i	0.950827	+	0.309722i	$0.100236\pi$
$692$	460.695	−	116.524i	0.665744	−	0.168387i
$693$		0			0
$694$	−973.405	+	121.194i	−1.40260	+	0.174631i
$695$	182.275	−	105.237i	0.262267	−	0.151420i
$696$		0			0
$697$	−280.663	+	486.123i	−0.402673	+	0.697450i
$698$	−688.929	−	291.056i	−0.987004	−	0.416986i
$699$		0			0
$700$	−483.056	+	469.656i	−0.690080	+	0.670937i
$701$	−1191.44			−1.69963			−0.849815	−	0.527082i	$-0.823286\pi$
$701$	−1191.44			−1.69963			−0.849815	+	0.527082i	$0.823286\pi$
$702$		0			0
$703$			80.7561i			0.114874i
$704$	100.599	−	320.668i	0.142896	−	0.455495i
$705$		0			0
$706$	1094.44	+	462.376i	1.55020	+	0.654923i
$707$	109.255	+	63.0786i	0.154534	+	0.0892201i
$708$		0			0
$709$	655.954	+	1136.15i	0.925182	+	1.60246i	0.791268	+	0.611469i	$0.209421\pi$
$709$	655.954	+	1136.15i	0.925182	+	1.60246i	0.133914	+	0.990993i	$0.457246\pi$
$710$	274.995	−	34.2383i	0.387317	−	0.0482229i
$711$		0			0
$712$	311.870	+	800.266i	0.438020	+	1.12397i
$713$	69.6056	+	120.560i	0.0976236	+	0.169089i
$714$		0			0
$715$	147.754	+	85.3059i	0.206649	+	0.119309i
$716$	839.759	+	237.720i	1.17285	+	0.332011i
$717$		0			0
$718$	495.674	+	655.468i	0.690354	+	0.912909i
$719$			245.763i			0.341813i	0.985287	+	0.170906i	$0.0546695\pi$
$719$			245.763i			0.341813i	−0.985287	+	0.170906i	$0.945330\pi$
$720$		0			0
$721$	−1088.78			−1.51010
$722$	8.37001	−	6.32952i	0.0115928	−	0.00876664i
$723$		0			0
$724$	200.556	−	708.473i	0.277011	−	0.978554i
$725$	−248.583	+	430.559i	−0.342873	+	0.593874i
$726$		0			0
$727$	1041.96	−	601.573i	1.43323	−	0.827473i	0.435860	−	0.900014i	$-0.356444\pi$
$727$	1041.96	−	601.573i	1.43323	−	0.827473i	0.997365	+	0.0725411i	$0.0231108\pi$
$728$	919.314	−	358.264i	1.26279	−	0.492121i
$729$		0			0
$730$	−18.1298	−	145.615i	−0.0248353	−	0.199473i
$731$	570.934	−	329.629i	0.781032	−	0.450929i
$732$		0			0
$733$	−510.693	+	884.546i	−0.696716	+	1.20675i	0.272883	+	0.962047i	$0.412023\pi$
$733$	−510.693	+	884.546i	−0.696716	+	1.20675i	−0.969599	+	0.244700i	$0.921310\pi$
$734$	418.977	−	991.716i	0.570813	−	1.35111i
$735$		0			0
$736$	106.474	+	48.5556i	0.144665	+	0.0659723i
$737$	41.6070			0.0564546
$738$		0			0
$739$			259.300i			0.350879i	0.984490	+	0.175439i	$0.0561346\pi$
$739$			259.300i			0.350879i	−0.984490	+	0.175439i	$0.943865\pi$
$740$	−25.9076	−	26.6467i	−0.0350102	−	0.0360091i
$741$		0			0
$742$	208.905	−	494.478i	0.281544	−	0.666412i
$743$	−100.270	−	57.8907i	−0.134953	−	0.0779149i	0.431004	−	0.902350i	$-0.358160\pi$
$743$	−100.270	−	57.8907i	−0.134953	−	0.0779149i	−0.565956	+	0.824435i	$0.691493\pi$
$744$		0			0
$745$	−75.6076	−	130.956i	−0.101487	−	0.175780i
$746$	−37.0458	−	297.545i	−0.0496593	−	0.398854i
$747$		0			0
$748$	−145.652	−	575.859i	−0.194723	−	0.769866i
$749$	214.277	+	371.139i	0.286084	+	0.495513i
$750$		0			0
$751$	−543.581	−	313.837i	−0.723809	−	0.417891i	0.0923438	−	0.995727i	$-0.470564\pi$
$751$	−543.581	−	313.837i	−0.723809	−	0.417891i	−0.816153	+	0.577836i	$0.803897\pi$
$752$	−477.466	−	13.4342i	−0.634928	−	0.0178646i
$753$		0			0
$754$	580.726	−	439.153i	0.770194	−	0.582431i
$755$			232.035i			0.307331i
$756$		0			0
$757$	49.5546			0.0654618			0.0327309	−	0.999464i	$-0.489580\pi$
$757$	49.5546			0.0654618			0.0327309	+	0.999464i	$0.489580\pi$
$758$	−222.402	−	294.099i	−0.293406	−	0.387993i
$759$		0			0
$760$	−51.0416	+	333.218i	−0.0671601	+	0.438445i
$761$	13.0738	−	22.6446i	0.0171798	−	0.0297563i	−0.857308	−	0.514804i	$-0.827865\pi$
$761$	13.0738	−	22.6446i	0.0171798	−	0.0297563i	0.874488	+	0.485048i	$0.161198\pi$
$762$		0			0
$763$	184.390	−	106.458i	0.241664	−	0.139525i
$764$	244.380	+	966.195i	0.319869	+	1.26465i
$765$		0			0
$766$	413.684	−	51.5057i	0.540058	−	0.0672398i
$767$	117.479	−	67.8267i	0.153167	−	0.0884312i
$768$		0			0
$769$	93.5875	−	162.098i	0.121700	−	0.210791i	−0.798738	−	0.601679i	$-0.794499\pi$
$769$	93.5875	−	162.098i	0.121700	−	0.210791i	0.920438	+	0.390888i	$0.127832\pi$
$770$	−178.045	−	75.2199i	−0.231227	−	0.0976881i
$771$		0			0
$772$	−697.573	−	717.476i	−0.903592	−	0.929373i
$773$	877.069			1.13463			0.567315	−	0.823501i	$-0.307982\pi$
$773$	877.069			1.13463			0.567315	+	0.823501i	$0.307982\pi$
$774$		0			0
$775$			767.131i			0.989847i
$776$	−17.8724	+	22.3015i	−0.0230315	+	0.0287390i
$777$		0			0
$778$	−556.066	−	234.925i	−0.714737	−	0.301960i
$779$	−328.981	−	189.937i	−0.422312	−	0.243822i
$780$		0			0
$781$	−165.226	−	286.179i	−0.211557	−	0.366427i
$782$	205.245	−	25.5539i	0.262461	−	0.0326777i
$783$		0			0
$784$	−293.625	+	158.685i	−0.374522	+	0.202405i
$785$	−236.704	−	409.984i	−0.301534	−	0.522272i
$786$		0			0
$787$	−577.106	−	333.192i	−0.733298	−	0.423370i	0.0863293	−	0.996267i	$-0.472486\pi$
$787$	−577.106	−	333.192i	−0.733298	−	0.423370i	−0.819628	+	0.572897i	$0.805820\pi$
$788$	−278.560	+	984.028i	−0.353503	+	1.24877i
$789$		0			0
$790$	164.743	+	217.852i	0.208536	+	0.275763i
$791$		−	1273.01i		−	1.60936i
$792$		0			0
$793$	1204.70			1.51917
$794$	393.499	−	297.569i	0.495590	−	0.374772i
$795$		0			0
$796$	1189.69	+	336.780i	1.49459	+	0.423090i
$797$	−90.8816	+	157.412i	−0.114030	+	0.197505i	−0.917391	−	0.397986i	$-0.869709\pi$
$797$	−90.8816	+	157.412i	−0.114030	+	0.197505i	0.803362	+	0.595491i	$0.203043\pi$
$798$		0			0
$799$	−731.118	+	422.111i	−0.915041	+	0.528299i
$800$	374.338	+	525.085i	0.467923	+	0.656357i
$801$		0			0
$802$	−186.570	−	1498.49i	−0.232631	−	1.86845i
$803$	−151.537	+	87.4900i	−0.188714	+	0.108954i
$804$		0			0
$805$	33.6505	−	58.2844i	0.0418019	−	0.0724030i
$806$	437.207	−	1034.87i	0.542440	−	1.28395i
$807$		0			0
$808$	75.5125	−	94.2255i	0.0934560	−	0.116616i
$809$	−114.921			−0.142053			−0.0710266	−	0.997474i	$-0.522628\pi$
$809$	−114.921			−0.142053			−0.0710266	+	0.997474i	$0.522628\pi$
$810$		0			0
$811$			1378.48i			1.69973i	0.526997	+	0.849867i	$0.323318\pi$
$811$			1378.48i			1.69973i	−0.526997	+	0.849867i	$0.676682\pi$
$812$	−591.383	+	574.978i	−0.728305	+	0.708101i
$813$		0			0
$814$	−17.2472	+	40.8240i	−0.0211882	+	0.0501524i
$815$	64.3449	+	37.1496i	0.0789508	+	0.0455823i
$816$		0			0
$817$	223.075	+	386.377i	0.273041	+	0.472921i
$818$	64.6074	+	518.915i	0.0789822	+	0.634370i
$819$		0			0
$820$	169.487	−	42.8683i	0.206691	−	0.0522784i
$821$	160.807	+	278.526i	0.195867	+	0.339252i	0.947184	−	0.320689i	$-0.103915\pi$
$821$	160.807	+	278.526i	0.195867	+	0.339252i	−0.751317	+	0.659941i	$0.770581\pi$
$822$		0			0
$823$	56.6805	+	32.7245i	0.0688706	+	0.0397625i	0.534040	−	0.845459i	$-0.320673\pi$
$823$	56.6805	+	32.7245i	0.0688706	+	0.0397625i	−0.465169	+	0.885222i	$0.654007\pi$
$824$	−157.789	+	1030.10i	−0.191492	+	1.25013i
$825$		0			0
$826$	−122.576	+	92.6940i	−0.148398	+	0.112220i
$827$			778.406i			0.941240i	0.882336	+	0.470620i	$0.155970\pi$
$827$			778.406i			0.941240i	−0.882336	+	0.470620i	$0.844030\pi$
$828$		0			0
$829$	−81.3426			−0.0981214			−0.0490607	−	0.998796i	$-0.515623\pi$
$829$	−81.3426			−0.0981214			−0.0490607	+	0.998796i	$0.515623\pi$
$830$	316.081	+	417.979i	0.380821	+	0.503589i
$831$		0			0
$832$	−205.726	−	921.688i	−0.247267	−	1.10780i
$833$	−294.950	+	510.869i	−0.354082	+	0.613288i
$834$		0			0
$835$	−289.686	+	167.250i	−0.346929	+	0.200299i
$836$	389.710	−	98.5695i	0.466160	−	0.117906i
$837$		0			0
$838$	779.744	−	97.0820i	0.930483	−	0.115850i
$839$	−553.733	+	319.698i	−0.659992	+	0.381046i	−0.792274	−	0.610166i	$-0.791103\pi$
$839$	−553.733	+	319.698i	−0.659992	+	0.381046i	0.132282	+	0.991212i	$0.457769\pi$
$840$		0			0
$841$	116.171	−	201.214i	0.138135	−	0.239256i
$842$	−377.496	−	159.483i	−0.448333	−	0.189410i
$843$		0			0
$844$	−1129.78	+	1098.44i	−1.33860	+	1.30147i
$845$	107.302			0.126984
$846$		0			0
$847$		−	780.866i		−	0.921920i
$848$	−437.553	−	269.307i	−0.515982	−	0.317579i
$849$		0			0
$850$	1049.89	+	443.555i	1.23517	+	0.521829i
$851$	−13.3641	−	7.71575i	−0.0157040	−	0.00906668i
$852$		0			0
$853$	−38.8069	−	67.2155i	−0.0454946	−	0.0787989i	0.842381	−	0.538882i	$-0.181153\pi$
$853$	−38.8069	−	67.2155i	−0.0454946	−	0.0787989i	−0.887876	+	0.460083i	$0.847820\pi$
$854$	−1354.33	+	168.620i	−1.58586	+	0.197448i
$855$		0			0
$856$	382.190	−	148.942i	0.446484	−	0.173998i
$857$	−436.010	−	755.192i	−0.508763	−	0.881204i	−0.999948	−	0.0101489i	$-0.996769\pi$
$857$	−436.010	−	755.192i	−0.508763	−	0.881204i	0.491185	−	0.871055i	$-0.336564\pi$
$858$		0			0
$859$	136.909	+	79.0444i	0.159382	+	0.0920191i	0.577570	−	0.816342i	$-0.304001\pi$
$859$	136.909	+	79.0444i	0.159382	+	0.0920191i	−0.418188	+	0.908361i	$0.637335\pi$
$860$	−197.561	−	55.9260i	−0.229722	−	0.0650302i
$861$		0			0
$862$	−558.201	−	738.152i	−0.647565	−	0.856324i
$863$			685.963i			0.794859i	0.917633	+	0.397429i	$0.130098\pi$
$863$			685.963i			0.794859i	−0.917633	+	0.397429i	$0.869902\pi$
$864$		0			0
$865$	−261.581			−0.302406
$866$	−304.010	+	229.897i	−0.351051	+	0.265469i
$867$		0			0
$868$	−346.658	+	1224.59i	−0.399376	+	1.41082i
$869$	162.848	−	282.060i	0.187396	−	0.324580i
$870$		0			0
$871$	101.251	−	58.4573i	0.116247	−	0.0671151i
$872$	−73.9978	−	189.880i	−0.0848598	−	0.217752i
$873$		0			0
$874$	17.2935	+	138.898i	0.0197866	+	0.158922i
$875$	719.629	−	415.478i	0.822433	−	0.474832i
$876$		0			0
$877$	458.905	−	794.847i	0.523267	−	0.906325i	−0.476366	−	0.879247i	$-0.658046\pi$
$877$	458.905	−	794.847i	0.523267	−	0.906325i	0.999633	−	0.0270780i	$-0.00862025\pi$
$878$	−340.878	+	806.857i	−0.388244	+	0.918971i
$879$		0			0
$880$	−96.9686	+	157.548i	−0.110192	+	0.179032i
$881$	657.430			0.746231			0.373116	−	0.927785i	$-0.378289\pi$
$881$	657.430			0.746231			0.373116	+	0.927785i	$0.378289\pi$
$882$		0			0
$883$		−	618.879i		−	0.700882i	−0.936585	−	0.350441i	$-0.886032\pi$
$883$		−	618.879i		−	0.700882i	0.936585	−	0.350441i	$-0.113968\pi$
$884$	−1163.52	−	1196.72i	−1.31620	−	1.35375i
$885$		0			0
$886$	−648.892	+	1535.92i	−0.732384	+	1.73355i
$887$	110.844	+	63.9959i	0.124965	+	0.0721487i	0.561180	−	0.827694i	$-0.310348\pi$
$887$	110.844	+	63.9959i	0.124965	+	0.0721487i	−0.436214	+	0.899843i	$0.643681\pi$
$888$		0			0
$889$	−616.119	−	1067.15i	−0.693047	−	1.20039i
$890$	−58.4131	−	469.164i	−0.0656327	−	0.527150i
$891$		0			0
$892$	−101.252	−	400.315i	−0.113511	−	0.448784i
$893$	−285.661	−	494.780i	−0.319890	−	0.554065i
$894$		0			0
$895$	−416.056	−	240.210i	−0.464867	−	0.268391i
$896$	360.284	+	1007.36i	0.402102	+	1.12429i
$897$		0			0
$898$	−766.968	+	579.992i	−0.854085	+	0.645871i
$899$			939.164i			1.04468i
$900$		0			0
$901$	−908.086			−1.00786
$902$	−125.742	−	166.278i	−0.139404	−	0.184344i
$903$		0			0
$904$	−1204.40	−	184.487i	−1.33230	−	0.204079i
$905$	−202.656	+	351.011i	−0.223930	+	0.387858i
$906$		0			0
$907$	−13.7946	+	7.96431i	−0.0152090	+	0.00878094i	−0.507585	−	0.861602i	$-0.669462\pi$
$907$	−13.7946	+	7.96431i	−0.0152090	+	0.00878094i	0.492376	+	0.870382i	$0.336128\pi$
$908$	−138.411	−	547.230i	−0.152435	−	0.602676i
$909$		0			0
$910$	−538.957	+	67.1027i	−0.592260	+	0.0737393i
$911$	−43.9255	+	25.3604i	−0.0482168	+	0.0278380i	−0.523915	−	0.851771i	$-0.675529\pi$
$911$	−43.9255	+	25.3604i	−0.0482168	+	0.0278380i	0.475698	+	0.879609i	$0.342196\pi$
$912$		0			0
$913$	312.445	−	541.170i	0.342218	−	0.592738i
$914$	−402.782	−	170.166i	−0.440681	−	0.186177i
$915$		0			0
$916$	−588.746	−	605.544i	−0.642735	−	0.661074i
$917$	1089.52			1.18814
$918$		0			0
$919$		−	1065.04i		−	1.15892i	−0.815002	−	0.579458i	$-0.803264\pi$
$919$		−	1065.04i		−	1.15892i	0.815002	−	0.579458i	$-0.196736\pi$
$920$	−50.2665	−	40.2837i	−0.0546375	−	0.0437866i
$921$		0			0
$922$	−1320.85	−	558.030i	−1.43260	−	0.605239i
$923$	−804.156	−	464.279i	−0.871241	−	0.503011i
$924$		0			0
$925$	−42.5181	−	73.6434i	−0.0459655	−	0.0796145i
$926$	61.0166	−	7.59686i	0.0658927	−	0.00820396i
$927$		0			0
$928$	458.285	+	642.838i	0.493841	+	0.692713i
$929$	−171.699	−	297.392i	−0.184822	−	0.320121i	0.758695	−	0.651446i	$-0.225837\pi$
$929$	−171.699	−	297.392i	−0.184822	−	0.320121i	−0.943516	+	0.331326i	$0.892504\pi$
$930$		0			0
$931$	−345.727	−	199.606i	−0.371351	−	0.214399i
$932$	305.183	−	1078.07i	0.327449	−	1.15673i
$933$		0			0
$934$	553.272	+	731.634i	0.592368	+	0.783334i
$935$			326.971i			0.349702i
$936$		0			0
$937$	−267.742			−0.285744			−0.142872	−	0.989741i	$-0.545634\pi$
$937$	−267.742			−0.285744			−0.142872	+	0.989741i	$0.545634\pi$
$938$	−105.644	+	79.8894i	−0.112627	+	0.0851699i
$939$		0			0
$940$	252.990	+	71.6168i	0.269138	+	0.0761881i
$941$	610.126	−	1056.77i	0.648380	−	1.12303i	−0.335130	−	0.942172i	$-0.608780\pi$
$941$	610.126	−	1056.77i	0.648380	−	1.12303i	0.983510	−	0.180855i	$-0.0578865\pi$
$942$		0			0
$943$	62.8642	−	36.2946i	0.0666640	−	0.0384885i
$944$	69.9342	+	129.404i	0.0740828	+	0.137080i
$945$		0			0
$946$	30.2503	+	242.964i	0.0319770	+	0.256833i
$947$	−1395.84	+	805.888i	−1.47396	+	0.850991i	−0.999570	−	0.0293240i	$-0.990665\pi$
$947$	−1395.84	+	805.888i	−1.47396	+	0.850991i	−0.474390	+	0.880315i	$0.657331\pi$
$948$		0			0
$949$	−245.845	+	425.815i	−0.259056	+	0.448699i
$950$	−300.173	+	710.509i	−0.315972	+	0.747904i
$951$		0			0
$952$	1475.53	+	1182.49i	1.54993	+	1.24211i
$953$	−242.459			−0.254416			−0.127208	−	0.991876i	$-0.540602\pi$
$953$	−242.459			−0.254416			−0.127208	+	0.991876i	$0.540602\pi$
$954$		0			0
$955$		−	548.603i		−	0.574453i
$956$	1123.79	−	1092.61i	1.17551	−	1.14290i
$957$		0			0
$958$	512.717	−	1213.60i	0.535196	−	1.26681i
$959$	722.656	+	417.226i	0.753552	+	0.435063i
$960$		0			0
$961$	244.068	+	422.739i	0.253973	+	0.439895i
$962$	15.3860	+	123.578i	0.0159938	+	0.128459i
$963$		0			0
$964$	−183.646	+	46.4496i	−0.190504	+	0.0481842i
$965$	275.421	+	477.043i	0.285411	+	0.494346i
$966$		0			0
$967$	1543.81	+	891.320i	1.59650	+	0.921737i	0.992155	+	0.125011i	$0.0398966\pi$
$967$	1543.81	+	891.320i	1.59650	+	0.921737i	0.604340	+	0.796726i	$0.293437\pi$
$968$	−738.781	−	113.165i	−0.763204	−	0.116906i
$969$		0			0
$970$	12.5480	−	9.48894i	0.0129360	−	0.00978242i
$971$		−	645.136i		−	0.664404i	−0.943208	−	0.332202i	$-0.892208\pi$
$971$		−	645.136i		−	0.664404i	0.943208	−	0.332202i	$-0.107792\pi$
$972$		0			0
$973$	798.958			0.821129
$974$	863.240	+	1141.53i	0.886283	+	1.17200i
$975$		0			0
$976$	−36.7397	+	1305.77i	−0.0376431	+	1.33788i
$977$	689.779	−	1194.73i	0.706017	−	1.22286i	−0.260306	−	0.965526i	$-0.583824\pi$
$977$	689.779	−	1194.73i	0.706017	−	1.22286i	0.966323	−	0.257331i	$-0.0828431\pi$
$978$		0			0
$979$	−488.244	+	281.888i	−0.498717	+	0.287935i
$980$	178.114	−	45.0505i	0.181749	−	0.0459699i
$981$		0			0
$982$	−1315.85	+	163.830i	−1.33997	+	0.166833i
$983$	639.804	−	369.391i	0.650869	−	0.375779i	−0.137920	−	0.990443i	$-0.544042\pi$
$983$	639.804	−	369.391i	0.650869	−	0.375779i	0.788789	+	0.614664i	$0.210708\pi$
$984$		0			0
$985$	281.478	−	487.534i	0.285764	−	0.494959i
$986$	1285.34	+	543.024i	1.30359	+	0.550734i
$987$		0			0
$988$	809.872	−	787.406i	0.819709	−	0.796970i
$989$	−85.2536			−0.0862018
$990$		0			0
$991$			1533.69i			1.54762i	0.633416	+	0.773811i	$0.281652\pi$
$991$			1533.69i			1.54762i	−0.633416	+	0.773811i	$0.718348\pi$
$992$	1108.35	+	505.445i	1.11729	+	0.509522i
$993$		0			0
$994$	969.014	+	409.386i	0.974863	+	0.411857i
$995$	−589.430	−	340.307i	−0.592391	−	0.342017i
$996$		0			0
$997$	−871.274	−	1509.09i	−0.873896	−	1.51363i	−0.857934	−	0.513760i	$-0.828252\pi$
$997$	−871.274	−	1509.09i	−0.873896	−	1.51363i	−0.0159621	−	0.999873i	$-0.505081\pi$
$998$	−1051.22	+	130.882i	−1.05333	+	0.131144i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.3.f.c.91.1		16
3.2	odd	2		36.3.f.c.31.8	yes	16
4.3	odd	2	inner	108.3.f.c.91.7		16
8.3	odd	2		1728.3.o.g.1279.4		16
8.5	even	2		1728.3.o.g.1279.3		16
9.2	odd	6		36.3.f.c.7.2	✓	16
9.4	even	3		324.3.d.g.163.5		8
9.5	odd	6		324.3.d.i.163.4		8
9.7	even	3	inner	108.3.f.c.19.7		16
12.11	even	2		36.3.f.c.31.2	yes	16
24.5	odd	2		576.3.o.g.319.5		16
24.11	even	2		576.3.o.g.319.4		16
36.7	odd	6	inner	108.3.f.c.19.1		16
36.11	even	6		36.3.f.c.7.8	yes	16
36.23	even	6		324.3.d.i.163.3		8
36.31	odd	6		324.3.d.g.163.6		8
72.11	even	6		576.3.o.g.511.5		16
72.29	odd	6		576.3.o.g.511.4		16
72.43	odd	6		1728.3.o.g.127.3		16
72.61	even	6		1728.3.o.g.127.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.3.f.c.7.2	✓	16	9.2	odd	6
36.3.f.c.7.8	yes	16	36.11	even	6
36.3.f.c.31.2	yes	16	12.11	even	2
36.3.f.c.31.8	yes	16	3.2	odd	2
108.3.f.c.19.1		16	36.7	odd	6	inner
108.3.f.c.19.7		16	9.7	even	3	inner
108.3.f.c.91.1		16	1.1	even	1	trivial
108.3.f.c.91.7		16	4.3	odd	2	inner
324.3.d.g.163.5		8	9.4	even	3
324.3.d.g.163.6		8	36.31	odd	6
324.3.d.i.163.3		8	36.23	even	6
324.3.d.i.163.4		8	9.5	odd	6
576.3.o.g.319.4		16	24.11	even	2
576.3.o.g.319.5		16	24.5	odd	2
576.3.o.g.511.4		16	72.29	odd	6
576.3.o.g.511.5		16	72.11	even	6
1728.3.o.g.127.3		16	72.43	odd	6
1728.3.o.g.127.4		16	72.61	even	6
1728.3.o.g.1279.3		16	8.5	even	2
1728.3.o.g.1279.4		16	8.3	odd	2

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	108.f (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.59523 + 1.20633i) q^{2} +(1.08951 - 3.84876i) q^{4} +(-1.10093 + 1.90686i) q^{5} +(-7.23844 + 4.17912i) q^{7} +(2.90487 + 7.45397i) q^{8} +O(q^{10})\)	\(q+(-1.59523 + 1.20633i) q^{2} +(1.08951 - 3.84876i) q^{4} +(-1.10093 + 1.90686i) q^{5} +(-7.23844 + 4.17912i) q^{7} +(2.90487 + 7.45397i) q^{8} +(-0.544081 - 4.36996i) q^{10} +(-4.54769 + 2.62561i) q^{11} +(-7.37788 + 12.7789i) q^{13} +(6.50556 - 15.3986i) q^{14} +(-13.6259 - 8.38655i) q^{16} -28.2789 q^{17} -19.1376i q^{19} +(6.13957 + 6.31475i) q^{20} +(4.08724 - 9.67448i) q^{22} +(3.16702 + 1.82848i) q^{23} +(10.0759 + 17.4520i) q^{25} +(-3.64618 - 29.2854i) q^{26} +(8.19805 + 32.4122i) q^{28} +(12.3355 + 21.3657i) q^{29} +(32.9674 + 19.0338i) q^{31} +(31.8535 - 3.05895i) q^{32} +(45.1113 - 34.1138i) q^{34} -18.4036i q^{35} -4.21977 q^{37} +(23.0863 + 30.5288i) q^{38} +(-17.4117 - 2.66709i) q^{40} +(9.92483 - 17.1903i) q^{41} +(-20.1894 + 11.6564i) q^{43} +(5.15057 + 20.3636i) q^{44} +(-7.25787 + 0.903640i) q^{46} +(25.8538 - 14.9267i) q^{47} +(10.4300 - 18.0654i) q^{49} +(-37.1264 - 15.6850i) q^{50} +(41.1445 + 42.3184i) q^{52} +32.1118 q^{53} -11.5624i q^{55} +(-52.1778 - 41.8154i) q^{56} +(-45.4521 - 19.2025i) q^{58} +(-7.96159 - 4.59663i) q^{59} +(-40.8215 - 70.7049i) q^{61} +(-75.5517 + 9.40656i) q^{62} +(-47.1234 + 43.3057i) q^{64} +(-16.2450 - 28.1372i) q^{65} +(-6.86179 - 3.96166i) q^{67} +(-30.8102 + 108.839i) q^{68} +(22.2009 + 29.3579i) q^{70} +62.9286i q^{71} +33.3218 q^{73} +(6.73149 - 5.09045i) q^{74} +(-73.6560 - 20.8506i) q^{76} +(21.9454 - 38.0106i) q^{77} +(-53.7133 + 31.0114i) q^{79} +(30.9931 - 16.7497i) q^{80} +(4.90489 + 39.3951i) q^{82} +(-103.056 + 59.4995i) q^{83} +(31.1329 - 53.9238i) q^{85} +(18.1453 - 42.9498i) q^{86} +(-32.7816 - 26.2713i) q^{88} +107.361 q^{89} -123.332i q^{91} +(10.4879 - 10.1969i) q^{92} +(-23.2362 + 54.9999i) q^{94} +(36.4927 + 21.0690i) q^{95} +(1.78621 + 3.09380i) q^{97} +(5.15457 + 41.4005i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} - 5 q^{4} - 6 q^{5} + 54 q^{8}+O(q^{10}) \) 16 * q + 3 * q^2 - 5 * q^4 - 6 * q^5 + 54 * q^8	\( 16 q + 3 q^{2} - 5 q^{4} - 6 q^{5} + 54 q^{8} + 20 q^{10} - 46 q^{13} + 12 q^{14} - 17 q^{16} - 12 q^{17} - 36 q^{20} + 33 q^{22} - 30 q^{25} - 72 q^{26} + 12 q^{28} - 42 q^{29} - 87 q^{32} + 11 q^{34} + 56 q^{37} + 99 q^{38} + 68 q^{40} - 84 q^{41} + 222 q^{44} - 264 q^{46} + 58 q^{49} + 219 q^{50} + 110 q^{52} + 72 q^{53} - 270 q^{56} - 16 q^{58} - 34 q^{61} - 516 q^{62} - 254 q^{64} + 30 q^{65} - 375 q^{68} + 150 q^{70} + 116 q^{73} + 372 q^{74} - 15 q^{76} + 330 q^{77} + 720 q^{80} + 254 q^{82} - 140 q^{85} + 273 q^{86} + 75 q^{88} + 384 q^{89} - 258 q^{92} + 36 q^{94} - 148 q^{97} - 1170 q^{98}+O(q^{100}) \) 16 * q + 3 * q^2 - 5 * q^4 - 6 * q^5 + 54 * q^8 + 20 * q^10 - 46 * q^13 + 12 * q^14 - 17 * q^16 - 12 * q^17 - 36 * q^20 + 33 * q^22 - 30 * q^25 - 72 * q^26 + 12 * q^28 - 42 * q^29 - 87 * q^32 + 11 * q^34 + 56 * q^37 + 99 * q^38 + 68 * q^40 - 84 * q^41 + 222 * q^44 - 264 * q^46 + 58 * q^49 + 219 * q^50 + 110 * q^52 + 72 * q^53 - 270 * q^56 - 16 * q^58 - 34 * q^61 - 516 * q^62 - 254 * q^64 + 30 * q^65 - 375 * q^68 + 150 * q^70 + 116 * q^73 + 372 * q^74 - 15 * q^76 + 330 * q^77 + 720 * q^80 + 254 * q^82 - 140 * q^85 + 273 * q^86 + 75 * q^88 + 384 * q^89 - 258 * q^92 + 36 * q^94 - 148 * q^97 - 1170 * q^98

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