LMFDB - Embedded newform 108.3.f.c.19.7

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			19.7
Root			$1.84233 + 0.778342i$ of defining polynomial
Character	$\chi$	$=$	108.19
Dual form			108.3.f.c.91.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.84233 + 0.778342i) q^{2} +(2.78837 + 2.86793i) q^{4} +(-1.10093 - 1.90686i) q^{5} +(7.23844 + 4.17912i) q^{7} +(2.90487 + 7.45397i) q^{8} +O(q^{10})$	\(q+(1.84233 + 0.778342i) q^{2} +(2.78837 + 2.86793i) q^{4} +(-1.10093 - 1.90686i) q^{5} +(7.23844 + 4.17912i) q^{7} +(2.90487 + 7.45397i) q^{8} +(-0.544081 - 4.36996i) q^{10} +(4.54769 + 2.62561i) q^{11} +(-7.37788 - 12.7789i) q^{13} +(10.0828 + 13.3333i) q^{14} +(-0.450004 + 15.9937i) q^{16} -28.2789 q^{17} -19.1376i q^{19} +(2.39894 - 8.47440i) q^{20} +(6.33472 + 8.37689i) q^{22} +(-3.16702 + 1.82848i) q^{23} +(10.0759 - 17.4520i) q^{25} +(-3.64618 - 29.2854i) q^{26} +(8.19805 + 32.4122i) q^{28} +(12.3355 - 21.3657i) q^{29} +(-32.9674 + 19.0338i) q^{31} +(-13.2776 + 29.1154i) q^{32} +(-52.0991 - 22.0106i) q^{34} -18.4036i q^{35} -4.21977 q^{37} +(14.8956 - 35.2578i) q^{38} +(11.0156 - 13.7454i) q^{40} +(9.92483 + 17.1903i) q^{41} +(20.1894 + 11.6564i) q^{43} +(5.15057 + 20.3636i) q^{44} +(-7.25787 + 0.903640i) q^{46} +(-25.8538 - 14.9267i) q^{47} +(10.4300 + 18.0654i) q^{49} +(32.1468 - 24.3099i) q^{50} +(16.0766 - 56.7914i) q^{52} +32.1118 q^{53} -11.5624i q^{55} +(-10.1243 + 66.0950i) q^{56} +(39.3559 - 29.7615i) q^{58} +(7.96159 - 4.59663i) q^{59} +(-40.8215 + 70.7049i) q^{61} +(-75.5517 + 9.40656i) q^{62} +(-47.1234 + 43.3057i) q^{64} +(-16.2450 + 28.1372i) q^{65} +(6.86179 - 3.96166i) q^{67} +(-78.8519 - 81.1017i) q^{68} +(14.3243 - 33.9055i) q^{70} +62.9286i q^{71} +33.3218 q^{73} +(-7.77421 - 3.28442i) q^{74} +(54.8852 - 53.3626i) q^{76} +(21.9454 + 38.0106i) q^{77} +(53.7133 + 31.0114i) q^{79} +(30.9931 - 16.7497i) q^{80} +(4.90489 + 39.3951i) q^{82} +(103.056 + 59.4995i) q^{83} +(31.1329 + 53.9238i) q^{85} +(28.1230 + 37.1892i) q^{86} +(-6.36077 + 41.5254i) q^{88} +107.361 q^{89} -123.332i q^{91} +(-14.0747 - 3.98430i) q^{92} +(-36.0132 - 47.6231i) q^{94} +(-36.4927 + 21.0690i) q^{95} +(1.78621 - 3.09380i) q^{97} +(5.15457 + 41.4005i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	1.84233	+	0.778342i	0.921166	+	0.389171i
$2$	1.84233	+	0.778342i	0.921166	+	0.389171i
$3$		0			0
$3$		0			0
$4$	2.78837	+	2.86793i	0.697092	+	0.716982i
$5$	−1.10093	−	1.90686i	−0.220185	−	0.381372i	0.734679	−	0.678415i	$-0.237333\pi$
$5$	−1.10093	−	1.90686i	−0.220185	−	0.381372i	−0.954864	+	0.297043i	$0.903999\pi$
$6$		0			0
$7$	7.23844	+	4.17912i	1.03406	+	0.597017i	0.918146	−	0.396242i	$-0.129686\pi$
$7$	7.23844	+	4.17912i	1.03406	+	0.597017i	0.115917	+	0.993259i	$0.463019\pi$
$8$	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	$-0.256615\pi$
$11$	4.54769	+	2.62561i	0.413426	+	0.238692i	−0.278835	+	0.960339i	$0.589948\pi$
$12$		0			0
$13$	−7.37788	−	12.7789i	−0.567529	−	0.982990i	−0.996809	−	0.0798182i	$-0.974566\pi$
$13$	−7.37788	−	12.7789i	−0.567529	−	0.982990i	0.429280	−	0.903171i	$-0.358767\pi$
$14$	10.0828	+	13.3333i	0.720202	+	0.952379i
$15$		0			0
$16$	−0.450004	+	15.9937i	−0.0281253	+	0.999604i
$17$	−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	$-0.167999\pi$
$20$	2.39894	−	8.47440i	0.119947	−	0.423720i
$21$		0			0
$22$	6.33472	+	8.37689i	0.287942	+	0.380768i
$23$	−3.16702	+	1.82848i	−0.137696	+	0.0794990i	−0.567266	−	0.823535i	$-0.691999\pi$
$23$	−3.16702	+	1.82848i	−0.137696	+	0.0794990i	0.429569	+	0.903034i	$0.358665\pi$
$24$		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	−0.571092	−	0.820886i	$-0.693480\pi$
$29$	12.3355	−	21.3657i	0.425362	−	0.736748i	0.996454	+	0.0841375i	$0.0268135\pi$
$30$		0			0
$31$	−32.9674	+	19.0338i	−1.06347	+	0.613992i	−0.926389	−	0.376568i	$-0.877104\pi$
$31$	−32.9674	+	19.0338i	−1.06347	+	0.613992i	−0.137077	+	0.990560i	$0.543771\pi$
$32$	−13.2776	+	29.1154i	−0.414925	+	0.909856i
$33$		0			0
$34$	−52.0991	−	22.0106i	−1.53233	−	0.647372i
$35$		−	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	$0.518161\pi$
$38$	14.8956	−	35.2578i	0.391989	−	0.927836i
$39$		0			0
$40$	11.0156	−	13.7454i	0.275391	−	0.343636i
$41$	9.92483	+	17.1903i	0.242069	+	0.419276i	0.961303	−	0.275492i	$-0.0888406\pi$
$41$	9.92483	+	17.1903i	0.242069	+	0.419276i	−0.719235	+	0.694767i	$0.755507\pi$
$42$		0			0
$43$	20.1894	+	11.6564i	0.469521	+	0.271078i	0.716039	−	0.698060i	$-0.245953\pi$
$43$	20.1894	+	11.6564i	0.469521	+	0.271078i	−0.246518	+	0.969138i	$0.579286\pi$
$44$	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	$-0.436207\pi$
$47$	−25.8538	−	14.9267i	−0.550082	−	0.317590i	−0.749155	+	0.662395i	$0.769540\pi$
$48$		0			0
$49$	10.4300	+	18.0654i	0.212858	+	0.368681i
$50$	32.1468	−	24.3099i	0.642937	−	0.486198i
$51$		0			0
$52$	16.0766	−	56.7914i	0.309165	−	1.09214i
$53$	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
$56$	−10.1243	+	66.0950i	−0.180791	+	1.18027i
$57$		0			0
$58$	39.3559	−	29.7615i	0.678550	−	0.513129i
$59$	7.96159	−	4.59663i	0.134942	−	0.0779089i	−0.431009	−	0.902348i	$-0.641842\pi$
$59$	7.96159	−	4.59663i	0.134942	−	0.0779089i	0.565951	+	0.824439i	$0.308509\pi$
$60$		0			0
$61$	−40.8215	+	70.7049i	−0.669205	+	1.15910i	0.308922	+	0.951087i	$0.400032\pi$
$61$	−40.8215	+	70.7049i	−0.669205	+	1.15910i	−0.978127	+	0.208009i	$0.933302\pi$
$62$	−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	$-0.647834\pi$
$67$	6.86179	−	3.96166i	0.102415	−	0.0591292i	0.550333	+	0.834946i	$0.314501\pi$
$68$	−78.8519	−	81.1017i	−1.15959	−	1.19267i
$69$		0			0
$70$	14.3243	−	33.9055i	0.204633	−	0.484364i
$71$			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	$0.426706\pi$
$74$	−7.77421	−	3.28442i	−0.105057	−	0.0443841i
$75$		0			0
$76$	54.8852	−	53.3626i	0.722173	−	0.702140i
$77$	21.9454	+	38.0106i	0.285006	+	0.493644i
$78$		0			0
$79$	53.7133	+	31.0114i	0.679916	+	0.392549i	0.799823	−	0.600236i	$-0.204927\pi$
$79$	53.7133	+	31.0114i	0.679916	+	0.392549i	−0.119908	+	0.992785i	$0.538260\pi$
$80$	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	$-0.0789114\pi$
$83$	103.056	+	59.4995i	1.24164	+	0.716861i	0.272212	+	0.962237i	$0.412245\pi$
$84$		0			0
$85$	31.1329	+	53.9238i	0.366270	+	0.634398i
$86$	28.1230	+	37.1892i	0.327011	+	0.432432i
$87$		0			0
$88$	−6.36077	+	41.5254i	−0.0722815	+	0.471879i
$89$	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
$92$	−14.0747	−	3.98430i	−0.152986	−	0.0433076i
$93$		0			0
$94$	−36.0132	−	47.6231i	−0.383120	−	0.506629i
$95$	−36.4927	+	21.0690i	−0.384133	+	0.221779i
$96$		0			0
$97$	1.78621	−	3.09380i	0.0184145	−	0.0318949i	−0.856671	−	0.515863i	$-0.827471\pi$
$97$	1.78621	−	3.09380i	0.0184145	−	0.0318949i	0.875086	+	0.483968i	$0.160805\pi$
$98$	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	−0.900965	−	0.433891i	$-0.857140\pi$
$101$	−7.54688	+	13.0716i	−0.0747216	+	0.129422i	0.826244	+	0.563313i	$0.190473\pi$
$102$		0			0
$103$	−112.813	+	65.1324i	−1.09527	+	0.632353i	−0.934974	−	0.354716i	$-0.884578\pi$
$103$	−112.813	+	65.1324i	−1.09527	+	0.632353i	−0.160294	+	0.987069i	$0.551244\pi$
$104$	73.8215	−	92.1155i	0.709822	−	0.885726i
$105$		0			0
$106$	59.1606	+	24.9940i	0.558119	+	0.235792i
$107$		−	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	$0.537280\pi$
$110$	8.99949	−	21.3018i	0.0818136	−	0.193652i
$111$		0			0
$112$	−70.0968	+	113.889i	−0.625864	+	1.01686i
$113$	−76.1529	−	131.901i	−0.673919	−	1.16726i	−0.976783	−	0.214229i	$-0.931276\pi$
$113$	−76.1529	−	131.901i	−0.673919	−	1.16726i	0.302864	−	0.953034i	$-0.402057\pi$
$114$		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
$122$	−130.239	+	98.4888i	−1.06754	+	0.807285i
$123$		0			0
$124$	−146.513	−	41.4751i	−1.18156	−	0.334476i
$125$	−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	$0.802886\pi$
$128$	−120.524	+	43.1052i	−0.941591	+	0.336760i
$129$		0			0
$130$	−51.8290	+	39.1938i	−0.398684	+	0.301491i
$131$	112.889	−	65.1766i	0.861750	−	0.497532i	−0.00284803	−	0.999996i	$-0.500907\pi$
$131$	112.889	−	65.1766i	0.861750	−	0.497532i	0.864598	+	0.502464i	$0.167573\pi$
$132$		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	−0.988674	−	0.150079i	$-0.952047\pi$
$137$	−49.9179	+	86.4604i	−0.364364	+	0.631098i	0.624310	+	0.781177i	$0.285380\pi$
$138$		0			0
$139$	82.7828	−	47.7947i	0.595560	−	0.343847i	−0.171733	−	0.985144i	$-0.554937\pi$
$139$	82.7828	−	47.7947i	0.595560	−	0.343847i	0.767293	+	0.641297i	$0.221603\pi$
$140$	52.7801	−	51.3160i	0.377001	−	0.366543i
$141$		0			0
$142$	−48.9799	+	115.935i	−0.344929	+	0.816445i
$143$		−	77.4857i		−	0.541858i
$144$		0			0
$145$	−54.3218			−0.374633
$146$	61.3898	+	25.9358i	0.420478	+	0.177642i
$147$		0			0
$148$	−11.7663	−	12.1020i	−0.0795018	−	0.0817701i
$149$	−34.3382	−	59.4755i	−0.230458	−	0.399164i	0.727485	−	0.686123i	$-0.240689\pi$
$149$	−34.3382	−	59.4755i	−0.230458	−	0.399164i	−0.957943	+	0.286959i	$0.907356\pi$
$150$		0			0
$151$	−91.2633	−	52.6909i	−0.604393	−	0.348946i	0.166375	−	0.986063i	$-0.446794\pi$
$151$	−91.2633	−	52.6909i	−0.604393	−	0.348946i	−0.770768	+	0.637116i	$0.780127\pi$
$152$	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	−0.973522	−	0.228593i	$-0.926587\pi$
$157$	−107.502	−	186.200i	−0.684729	−	1.18598i	0.288794	−	0.957391i	$-0.406746\pi$
$158$	74.8203	+	98.9406i	0.473546	+	0.626206i
$159$		0			0
$160$	70.1366	−	6.73536i	0.438353	−	0.0420960i
$161$	−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	$-0.0330071\pi$
$164$	−21.6265	+	76.3966i	−0.131869	+	0.465833i
$165$		0			0
$166$	143.553	+	189.831i	0.864775	+	1.14356i
$167$	−131.565	+	75.9589i	−0.787812	+	0.454843i	−0.839192	−	0.543836i	$-0.816971\pi$
$167$	−131.565	+	75.9589i	−0.787812	+	0.454843i	0.0513797	+	0.998679i	$0.483638\pi$
$168$		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	−0.641699	−	0.766957i	$-0.721770\pi$
$173$	59.4003	−	102.884i	0.343354	−	0.594707i	0.985053	+	0.172249i	$0.0551035\pi$
$174$		0			0
$175$	145.868	−	84.2170i	0.833532	−	0.481240i
$176$	−44.0396	+	71.5526i	−0.250225	+	0.406549i
$177$		0			0
$178$	197.795	+	83.5636i	1.11121	+	0.469458i
$179$			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	$0.330199\pi$
$182$	95.9945	−	227.219i	0.527443	−	1.24845i
$183$		0			0
$184$	−22.8292	−	18.2954i	−0.124072	−	0.0994313i
$185$	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	$-0.107163\pi$
$191$	215.775	+	124.578i	1.12971	+	0.652239i	0.185849	+	0.982578i	$0.440497\pi$
$192$		0			0
$193$	125.086	+	216.656i	0.648115	+	1.12257i	0.983573	+	0.180513i	$0.0577758\pi$
$193$	125.086	+	216.656i	0.648115	+	1.12257i	−0.335457	+	0.942055i	$0.608891\pi$
$194$	5.69882	−	4.30953i	0.0293754	−	0.0222141i
$195$		0			0
$196$	−22.7273	+	80.2855i	−0.115956	+	0.409620i
$197$	−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	$0.716913\pi$
$200$	159.356	+	24.4098i	0.796781	+	0.122049i
$201$		0			0
$202$	−24.0780	+	18.2081i	−0.119198	+	0.0901392i
$203$	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	0.629140	−	0.777292i	$-0.283407\pi$
$211$	341.158	−	196.968i	1.61686	−	0.933497i	0.987725	−	0.156205i	$-0.0499261\pi$
$212$	89.5395	+	92.0943i	0.422356	+	0.434407i
$213$		0			0
$214$	39.9082	−	94.4624i	0.186487	−	0.441413i
$215$		−	51.3311i		−	0.238750i
$216$		0			0
$217$	−318.177			−1.46626
$218$	−46.9310	−	19.8272i	−0.215280	−	0.0909506i
$219$		0			0
$220$	33.1601	−	32.2402i	0.150728	−	0.146546i
$221$	208.638	+	361.372i	0.944064	+	1.63517i
$222$		0			0
$223$	−89.4002	−	51.6152i	−0.400898	−	0.231458i	0.285974	−	0.958238i	$-0.407683\pi$
$223$	−89.4002	−	51.6152i	−0.400898	−	0.231458i	−0.686871	+	0.726779i	$0.741016\pi$
$224$	−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	$-0.433939\pi$
$227$	−122.210	−	70.5578i	−0.538369	−	0.310828i	−0.744418	+	0.667714i	$0.767273\pi$
$228$		0			0
$229$	105.572	+	182.856i	0.461012	+	0.798496i	0.999012	−	0.0444490i	$-0.0141532\pi$
$229$	105.572	+	182.856i	0.461012	+	0.798496i	−0.538000	+	0.842945i	$0.680820\pi$
$230$	9.71349	+	12.8449i	0.0422326	+	0.0558474i
$231$		0			0
$232$	195.092	+	29.8838i	0.840916	+	0.128810i
$233$	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
$236$	35.3826	+	10.0162i	0.149926	+	0.0424414i
$237$		0			0
$238$	−285.131	−	377.051i	−1.19803	−	1.58425i
$239$	−339.349	+	195.923i	−1.41987	+	0.819762i	−0.996287	−	0.0860949i	$-0.972561\pi$
$239$	−339.349	+	195.923i	−1.41987	+	0.819762i	−0.423583	+	0.905857i	$0.639228\pi$
$240$		0			0
$241$	−23.6786	+	41.0125i	−0.0982514	+	0.170176i	−0.910961	−	0.412493i	$-0.864658\pi$
$241$	−23.6786	+	41.0125i	−0.0982514	+	0.170176i	0.812710	+	0.582669i	$0.197992\pi$
$242$	−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
$248$	−237.643	−	190.448i	−0.958239	−	0.767935i
$249$		0			0
$250$	−183.160	−	77.3809i	−0.732641	−	0.309524i
$251$		−	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
$254$	−114.749	+	271.611i	−0.451769	+	1.06933i
$255$		0			0
$256$	−255.595	−	14.3944i	−0.998418	−	0.0562283i
$257$	32.5409	+	56.3625i	0.126618	+	0.219310i	0.922364	−	0.386321i	$-0.126254\pi$
$257$	32.5409	+	56.3625i	0.126618	+	0.219310i	−0.795746	+	0.605631i	$0.792921\pi$
$258$		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	$-0.421650\pi$
$263$	−124.773	−	72.0378i	−0.474423	−	0.273908i	−0.718089	+	0.695951i	$0.754983\pi$
$264$		0			0
$265$	−35.3527	−	61.2327i	−0.133406	−	0.231067i
$266$	255.167	−	192.961i	0.959275	−	0.725417i
$267$		0			0
$268$	30.4949	+	8.63255i	0.113787	+	0.0322110i
$269$	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	$-0.0208457\pi$
$272$	12.7256	−	452.283i	0.0467854	−	1.66281i
$273$		0			0
$274$	−159.261	+	120.435i	−0.581245	+	0.439545i
$275$	91.6443	−	52.9109i	0.333252	−	0.192403i
$276$		0			0
$277$	−166.922	+	289.118i	−0.602607	+	1.04375i	0.389818	+	0.920892i	$0.372538\pi$
$277$	−166.922	+	289.118i	−0.602607	+	1.04375i	−0.992425	+	0.122854i	$0.960795\pi$
$278$	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	−0.827164	−	0.561961i	$-0.810047\pi$
$281$	20.5385	−	35.5737i	0.0730906	−	0.126597i	0.900254	+	0.435364i	$0.143380\pi$
$282$		0			0
$283$	−218.583	+	126.199i	−0.772378	+	0.445933i	−0.833722	−	0.552184i	$-0.813795\pi$
$283$	−218.583	+	126.199i	−0.772378	+	0.445933i	0.0613442	+	0.998117i	$0.480461\pi$
$284$	−180.474	+	175.468i	−0.635474	+	0.617845i
$285$		0			0
$286$	60.3103	−	142.754i	0.210875	−	0.499141i
$287$			165.908i			0.578077i
$288$		0			0
$289$	510.695			1.76711
$290$	−100.079	−	42.2809i	−0.345099	−	0.145796i
$291$		0			0
$292$	92.9135	+	95.5646i	0.318197	+	0.327276i
$293$	−20.3415	−	35.2325i	−0.0694248	−	0.120247i	0.829223	−	0.558917i	$-0.188783\pi$
$293$	−20.3415	−	35.2325i	−0.0694248	−	0.120247i	−0.898648	+	0.438670i	$0.855450\pi$
$294$		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
$302$	−127.126	−	168.108i	−0.420946	−	0.556650i
$303$		0			0
$304$	306.080	+	8.61199i	1.00684	+	0.0283289i
$305$	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	$-0.0715361\pi$
$308$	−47.8197	+	168.926i	−0.155259	+	0.548460i
$309$		0			0
$310$	101.114	+	133.711i	0.326174	+	0.431324i
$311$	371.260	−	214.347i	1.19376	−	0.689219i	0.234605	−	0.972091i	$-0.424620\pi$
$311$	371.260	−	214.347i	1.19376	−	0.689219i	0.959158	+	0.282871i	$0.0912869\pi$
$312$		0			0
$313$	5.98705	−	10.3699i	0.0191280	−	0.0331306i	−0.856303	−	0.516474i	$-0.827244\pi$
$313$	5.98705	−	10.3699i	0.0191280	−	0.0331306i	0.875431	+	0.483343i	$0.160578\pi$
$314$	−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	−0.826529	−	0.562894i	$-0.809688\pi$
$317$	23.5266	−	40.7493i	0.0742164	−	0.128547i	0.900745	+	0.434348i	$0.143021\pi$
$318$		0			0
$319$	112.196	−	64.7763i	0.351711	−	0.203061i
$320$	134.457	+	42.1814i	0.420179	+	0.131817i
$321$		0			0
$322$	−56.3121	−	23.7906i	−0.174882	−	0.0738837i
$323$			541.189i			1.67551i
$324$		0			0
$325$	−297.356			−0.914941
$326$	26.2643	−	62.1675i	0.0805654	−	0.190698i
$327$		0			0
$328$	−99.3057	+	123.915i	−0.302761	+	0.377790i
$329$	−124.761	−	216.092i	−0.379213	−	0.656816i
$330$		0			0
$331$	−73.1501	−	42.2332i	−0.220997	−	0.127593i	0.385415	−	0.922743i	$-0.374058\pi$
$331$	−73.1501	−	42.2332i	−0.220997	−	0.127593i	−0.606412	+	0.795151i	$0.707392\pi$
$332$	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	−0.948096	−	0.317983i	$-0.896994\pi$
$337$	−252.558	−	437.443i	−0.749430	−	1.29805i	0.198667	−	0.980067i	$-0.436339\pi$
$338$	−77.7396	+	58.7877i	−0.229999	+	0.173928i
$339$		0			0
$340$	−67.8395	+	239.646i	−0.199528	+	0.704842i
$341$	−199.901			−0.586219
$342$		0			0
$343$		−	235.200i		−	0.685714i
$344$	−28.2386	+	184.352i	−0.0820889	+	0.535906i
$345$		0			0
$346$	189.514	−	143.313i	0.547729	−	0.414200i
$347$	−424.751	+	245.230i	−1.22407	+	0.706715i	−0.965782	−	0.259354i	$-0.916490\pi$
$347$	−424.751	+	245.230i	−1.22407	+	0.706715i	−0.258284	+	0.966069i	$0.583157\pi$
$348$		0			0
$349$	186.972	−	323.845i	0.535736	−	0.927923i	−0.463391	−	0.886154i	$-0.653367\pi$
$349$	186.972	−	323.845i	0.535736	−	0.927923i	0.999127	−	0.0417686i	$-0.0132992\pi$
$350$	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	0.0472483	+	0.998883i	$0.484955\pi$
$353$	−297.026	+	514.465i	−0.841434	+	1.45741i	−0.888682	+	0.458523i	$0.848379\pi$
$354$		0			0
$355$	119.996	−	69.2796i	0.338016	−	0.195154i
$356$	299.362	+	307.904i	0.840905	+	0.864898i
$357$		0			0
$358$	−169.826	+	401.977i	−0.474374	+	1.12284i
$359$		−	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
$362$	339.133	+	143.276i	0.936832	+	0.395789i
$363$		0			0
$364$	353.707	−	343.895i	0.971724	−	0.944768i
$365$	−36.6848	−	63.5400i	−0.100506	−	0.174082i
$366$		0			0
$367$	466.176	+	269.147i	1.27023	+	0.733370i	0.975032	−	0.222064i	$-0.0712795\pi$
$367$	466.176	+	269.147i	1.27023	+	0.733370i	0.295203	+	0.955435i	$0.404613\pi$
$368$	−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	0.747873	−	0.663841i	$-0.231075\pi$
$373$	−74.9606	−	129.836i	−0.200967	−	0.348085i	−0.948840	+	0.315757i	$0.897742\pi$
$374$	−179.139	−	236.889i	−0.478981	−	0.633393i
$375$		0			0
$376$	36.1613	−	236.074i	0.0961737	−	0.627857i
$377$	−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	$0.921796\pi$
$380$	−162.179	−	45.9100i	−0.426788	−	0.120816i
$381$		0			0
$382$	300.565	+	397.460i	0.786818	+	1.04047i
$383$	180.514	−	104.220i	0.471315	−	0.272114i	−0.245475	−	0.969403i	$-0.578944\pi$
$383$	180.514	−	104.220i	0.471315	−	0.272114i	0.716790	+	0.697289i	$0.245611\pi$
$384$		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	−0.604221	−	0.796816i	$-0.706516\pi$
$389$	150.914	−	261.390i	0.387953	−	0.671954i	0.992174	+	0.124863i	$0.0398491\pi$
$390$		0			0
$391$	89.5597	−	51.7073i	0.229053	−	0.132244i
$392$	−104.361	+	130.223i	−0.266227	+	0.332201i
$393$		0			0
$394$	−471.036	−	199.002i	−1.19552	−	0.505081i
$395$		−	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	$0.600553\pi$
$398$	−240.593	+	569.483i	−0.604506	+	1.43086i
$399$		0			0
$400$	274.588	+	169.005i	0.686469	+	0.422511i
$401$	−377.516	−	653.877i	−0.941437	−	1.63062i	−0.762734	−	0.646713i	$-0.776143\pi$
$401$	−377.516	−	653.877i	−0.941437	−	1.63062i	−0.178703	−	0.983903i	$-0.557190\pi$
$402$		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	0.980412	−	0.196959i	$-0.0631067\pi$
$409$	130.730	+	226.432i	0.319634	+	0.553622i	−0.660778	+	0.750582i	$0.729773\pi$
$410$	69.7210	−	52.7240i	0.170051	−	0.128595i
$411$		0			0
$412$	−501.358	−	141.925i	−1.21689	−	0.344479i
$413$	76.8394			0.186052
$414$		0			0
$415$		−	262.018i		−	0.631369i
$416$	470.022	−	45.1372i	1.12986	−	0.108503i
$417$		0			0
$418$	160.313	−	121.231i	0.383525	−	0.290027i
$419$	340.246	−	196.441i	0.812043	−	0.468833i	−0.0356217	−	0.999365i	$-0.511341\pi$
$419$	340.246	−	196.441i	0.812043	−	0.468833i	0.847665	+	0.530532i	$0.178008\pi$
$420$		0			0
$421$	102.451	−	177.450i	0.243351	−	0.421496i	−0.718316	−	0.695717i	$-0.755087\pi$
$421$	102.451	−	177.450i	0.243351	−	0.421496i	0.961667	+	0.274221i	$0.0884200\pi$
$422$	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
$428$	147.048	−	142.969i	0.343570	−	0.334039i
$429$		0			0
$430$	39.9532	−	94.5690i	0.0929144	−	0.219928i
$431$			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	$0.429374\pi$
$434$	−586.188	−	247.651i	−1.35066	−	0.570624i
$435$		0			0
$436$	−71.0300	−	73.0567i	−0.162913	−	0.167561i
$437$	34.9926	+	60.6090i	0.0800747	+	0.138693i
$438$		0			0
$439$	−379.279	−	218.977i	−0.863962	−	0.498809i	0.00137479	−	0.999999i	$-0.499562\pi$
$439$	−379.279	−	218.977i	−0.863962	−	0.498809i	−0.865337	+	0.501190i	$0.832896\pi$
$440$	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	−0.984157	−	0.177297i	$-0.943265\pi$
$443$	−721.993	−	416.843i	−1.62978	−	0.940954i	−0.645623	−	0.763657i	$-0.723402\pi$
$444$		0			0
$445$	−118.196	−	204.722i	−0.265610	−	0.460050i
$446$	−124.530	−	164.676i	−0.279216	−	0.369229i
$447$		0			0
$448$	−522.080	+	116.531i	−1.16536	+	0.260114i
$449$	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
$452$	165.939	−	586.189i	0.367122	−	1.29688i
$453$		0			0
$454$	−170.233	−	225.112i	−0.374962	−	0.495841i
$455$	−235.177	+	135.779i	−0.516872	+	0.298416i
$456$		0			0
$457$	109.313	−	189.336i	0.239197	−	0.414302i	−0.721287	−	0.692636i	$-0.756449\pi$
$457$	109.313	−	189.336i	0.239197	−	0.414302i	0.960484	+	0.278334i	$0.0897824\pi$
$458$	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	−0.155722	−	0.987801i	$-0.549770\pi$
$461$	358.474	−	620.894i	0.777600	−	1.34684i	0.933322	−	0.359042i	$-0.116896\pi$
$462$		0			0
$463$	26.6250	−	15.3719i	0.0575053	−	0.0332007i	−0.470972	−	0.882148i	$-0.656097\pi$
$463$	26.6250	−	15.3719i	0.0575053	−	0.0332007i	0.528477	+	0.848948i	$0.322763\pi$
$464$	336.165	+	206.904i	0.724494	+	0.445915i
$465$		0			0
$466$	516.054	+	218.021i	1.10741	+	0.467856i
$467$		−	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
$470$	−51.1626	+	121.102i	−0.108857	+	0.257663i
$471$		0			0
$472$	57.3905	+	45.9929i	0.121590	+	0.0974426i
$473$	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	$-0.0919932\pi$
$479$	570.477	+	329.365i	1.19098	+	0.687610i	0.232448	+	0.972609i	$0.425326\pi$
$480$		0			0
$481$	31.1329	+	53.9238i	0.0647254	+	0.112108i
$482$	−75.5456	+	57.1286i	−0.156734	+	0.118524i
$483$		0			0
$484$	101.787	−	359.570i	0.210305	−	0.742912i
$485$	−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	$-0.262673\pi$
$488$	−645.614	−	98.8937i	−1.32298	−	0.202651i
$489$		0			0
$490$	73.2702	−	55.4079i	0.149531	−	0.113077i
$491$	−574.179	+	331.502i	−1.16941	+	0.675157i	−0.953540	−	0.301266i	$-0.902591\pi$
$491$	−574.179	+	331.502i	−1.16941	+	0.675157i	−0.215866	+	0.976423i	$0.569258\pi$
$492$		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	$-0.844749\pi$
$499$	−458.706	+	264.834i	−0.919251	+	0.530730i	−0.0358546	+	0.999357i	$0.511415\pi$
$500$	−277.213	−	285.122i	−0.554426	−	0.570245i
$501$		0			0
$502$	303.099	−	717.434i	0.603783	−	1.42915i
$503$		−	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
$506$	−35.3791	−	14.9469i	−0.0699192	−	0.0295392i
$507$		0			0
$508$	−422.812	+	411.083i	−0.832308	+	0.809219i
$509$	400.473	+	693.640i	0.786784	+	1.36275i	0.927927	+	0.372761i	$0.121589\pi$
$509$	400.473	+	693.640i	0.786784	+	1.36275i	−0.141143	+	0.989989i	$0.545078\pi$
$510$		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
$518$	−42.5472	−	56.2634i	−0.0821374	−	0.108617i
$519$		0			0
$520$	−256.923	−	39.3549i	−0.494083	−	0.0756826i
$521$	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	$-0.00929347\pi$
$524$	501.699	+	142.022i	0.957440	+	0.271034i
$525$		0			0
$526$	−173.803	−	229.834i	−0.330425	−	0.436946i
$527$	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
$536$	49.4627	+	39.6395i	0.0922811	+	0.0739543i
$537$		0			0
$538$	133.406	+	56.3607i	0.247966	+	0.104760i
$539$			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	$0.338375\pi$
$542$	27.6074	−	65.3466i	0.0509361	−	0.120566i
$543$		0			0
$544$	375.476	−	823.350i	0.690213	−	1.51351i
$545$	28.0446	+	48.5747i	0.0514580	+	0.0891279i
$546$		0			0
$547$	823.276	+	475.318i	1.50507	+	0.868955i	0.999983	+	0.00588962i	$0.00187474\pi$
$547$	823.276	+	475.318i	1.50507	+	0.868955i	0.505092	+	0.863066i	$0.331459\pi$
$548$	−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
$554$	−532.558	+	402.728i	−0.961297	+	0.726946i
$555$		0			0
$556$	367.901	+	104.146i	0.661692	+	0.187313i
$557$	−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
$560$	294.341	+	8.28169i	0.525609	+	0.0147887i
$561$		0			0
$562$	65.5271	−	49.5525i	0.116596	−	0.0881718i
$563$	−925.131	+	534.125i	−1.64322	+	0.948712i	−0.663538	+	0.748143i	$0.730946\pi$
$563$	−925.131	+	534.125i	−1.64322	+	0.948712i	−0.979680	+	0.200569i	$0.935721\pi$
$564$		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	−0.0374271	−	0.999299i	$-0.511916\pi$
$569$	481.775	−	834.459i	0.846705	−	1.46654i	0.884132	−	0.467237i	$-0.154750\pi$
$570$		0			0
$571$	−243.132	+	140.372i	−0.425800	+	0.245836i	−0.697556	−	0.716531i	$-0.745729\pi$
$571$	−243.132	+	140.372i	−0.425800	+	0.245836i	0.271756	+	0.962366i	$0.412396\pi$
$572$	222.223	−	216.059i	0.388502	−	0.377725i
$573$		0			0
$574$	−129.133	+	305.658i	−0.224971	+	0.532505i
$575$			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	$0.658832\pi$
$578$	940.869	+	397.495i	1.62780	+	0.687708i
$579$		0			0
$580$	−151.469	−	155.791i	−0.261154	−	0.268605i
$581$	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	$-0.377770\pi$
$587$	−141.476	−	81.6811i	−0.241015	−	0.139150i	−0.615643	+	0.788025i	$0.711104\pi$
$588$		0			0
$589$	364.260	+	630.917i	0.618438	+	1.07117i
$590$	−24.4188	−	32.2909i	−0.0413879	−	0.0547304i
$591$		0			0
$592$	1.89891	−	67.4895i	0.00320762	−	0.114003i
$593$	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
$596$	74.8238	−	264.319i	0.125543	−	0.443488i
$597$		0			0
$598$	65.0952	+	86.0804i	0.108855	+	0.143947i
$599$	398.849	−	230.275i	0.665857	−	0.384433i	−0.128648	−	0.991690i	$-0.541064\pi$
$599$	398.849	−	230.275i	0.665857	−	0.384433i	0.794505	+	0.607257i	$0.207730\pi$
$600$		0			0
$601$	162.324	−	281.153i	0.270090	−	0.467809i	−0.698795	−	0.715322i	$-0.746280\pi$
$601$	162.324	−	281.153i	0.270090	−	0.467809i	0.968885	+	0.247513i	$0.0796132\pi$
$602$	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	$-0.407705\pi$
$607$	764.054	−	441.127i	1.25874	−	0.726733i	0.972829	+	0.231524i	$0.0743712\pi$
$608$	557.198	+	254.101i	0.916444	+	0.417929i
$609$		0			0
$610$	331.188	+	139.919i	0.542931	+	0.229376i
$611$			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	$0.494940\pi$
$614$	106.501	−	252.086i	0.173454	−	0.410564i
$615$		0			0
$616$	−219.582	+	273.997i	−0.356464	+	0.444800i
$617$	48.3314	+	83.7124i	0.0783329	+	0.135677i	0.902531	−	0.430625i	$-0.141707\pi$
$617$	48.3314	+	83.7124i	0.0783329	+	0.135677i	−0.824198	+	0.566302i	$0.808374\pi$
$618$		0			0
$619$	−363.937	−	210.119i	−0.587944	−	0.339449i	0.176340	−	0.984329i	$-0.443574\pi$
$619$	−363.937	−	210.119i	−0.587944	−	0.339449i	−0.764284	+	0.644880i	$0.776907\pi$
$620$	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
$626$	19.1014	−	14.4448i	0.0305135	−	0.0230747i
$627$		0			0
$628$	234.250	−	827.502i	0.373010	−	1.31768i
$629$	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	$0.874923\pi$
$632$	−75.1279	+	490.462i	−0.118873	+	0.776047i
$633$		0			0
$634$	75.0607	−	56.7619i	0.118392	−	0.0895299i
$635$	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	−0.828528	−	0.559948i	$-0.810821\pi$
$641$	45.2967	−	78.4562i	0.0706657	−	0.122397i	0.899193	+	0.437552i	$0.144154\pi$
$642$		0			0
$643$	453.773	−	261.986i	0.705713	−	0.407444i	−0.103759	−	0.994602i	$-0.533087\pi$
$643$	453.773	−	261.986i	0.705713	−	0.407444i	0.809472	+	0.587159i	$0.199754\pi$
$644$	−85.2284	−	87.6602i	−0.132342	−	0.136118i
$645$		0			0
$646$	−421.230	+	997.050i	−0.652059	+	1.54342i
$647$			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
$650$	−547.828	−	231.445i	−0.842813	−	0.356069i
$651$		0			0
$652$	96.7752	−	94.0906i	0.148428	−	0.144311i
$653$	−445.115	−	770.961i	−0.681646	−	1.18065i	−0.974478	−	0.224481i	$-0.927931\pi$
$653$	−445.115	−	770.961i	−0.681646	−	1.18065i	0.292833	−	0.956164i	$-0.405402\pi$
$654$		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	$-0.344819\pi$
$659$	−41.1783	−	23.7743i	−0.0624860	−	0.0360763i	−0.530918	+	0.847423i	$0.678153\pi$
$660$		0			0
$661$	−24.8421	−	43.0278i	−0.0375826	−	0.0650950i	0.846622	−	0.532194i	$-0.178632\pi$
$661$	−24.8421	−	43.0278i	−0.0375826	−	0.0650950i	−0.884205	+	0.467099i	$0.845299\pi$
$662$	−101.895	−	134.743i	−0.153920	−	0.203540i
$663$		0			0
$664$	−144.143	+	941.016i	−0.217083	+	1.41719i
$665$	−352.200			−0.529624
$666$		0			0
$667$			90.2207i			0.135263i
$668$	−584.695	−	165.516i	−0.875292	−	0.247779i
$669$		0			0
$670$	−21.0457	−	27.8303i	−0.0314114	−	0.0415377i
$671$	−371.287	+	214.362i	−0.553333	+	0.319467i
$672$		0			0
$673$	−16.4365	+	28.4688i	−0.0244227	+	0.0423013i	−0.877978	−	0.478700i	$-0.841108\pi$
$673$	−16.4365	+	28.4688i	−0.0244227	+	0.0423013i	0.853556	+	0.521002i	$0.174441\pi$
$674$	−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	0.300625	+	0.953742i	$0.402805\pi$
$677$	−457.417	+	792.269i	−0.675653	+	1.17026i	−0.976278	+	0.216522i	$0.930529\pi$
$678$		0			0
$679$	25.8587	−	14.9296i	0.0380836	−	0.0219876i
$680$	−311.510	+	388.706i	−0.458102	+	0.571626i
$681$		0			0
$682$	−368.283	−	155.591i	−0.540005	−	0.228139i
$683$		−	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
$686$	183.066	−	433.316i	0.266860	−	0.631656i
$687$		0			0
$688$	−195.513	+	317.657i	−0.284176	+	0.461711i
$689$	−236.917	−	410.352i	−0.343856	−	0.595577i
$690$		0			0
$691$	−800.188	−	461.988i	−1.15801	−	0.668580i	−0.207187	−	0.978301i	$-0.566431\pi$
$691$	−800.188	−	461.988i	−1.15801	−	0.668580i	−0.950827	+	0.309722i	$0.899764\pi$
$692$	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
$698$	596.526	−	451.102i	0.854622	−	0.646277i
$699$		0			0
$700$	648.262	+	183.511i	0.926089	+	0.262159i
$701$	−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
$704$	−328.006	+	73.2129i	−0.465918	+	0.103996i
$705$		0			0
$706$	−947.650	+	716.626i	−1.34228	+	1.01505i
$707$	−109.255	+	63.0786i	−0.154534	+	0.0892201i
$708$		0			0
$709$	655.954	−	1136.15i	0.925182	−	1.60246i	0.133914	−	0.990993i	$-0.457246\pi$
$709$	655.954	−	1136.15i	0.925182	−	1.60246i	0.791268	−	0.611469i	$-0.209421\pi$
$710$	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
$716$	−625.751	+	608.392i	−0.873954	+	0.849710i
$717$		0			0
$718$	319.815	−	757.001i	0.445425	−	1.05432i
$719$			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
$722$	−9.66652	−	4.08388i	−0.0133885	−	0.00565634i
$723$		0			0
$724$	513.278	+	527.923i	0.708947	+	0.729175i
$725$	−248.583	−	430.559i	−0.342873	−	0.593874i
$726$		0			0
$727$	−1041.96	−	601.573i	−1.43323	−	0.827473i	−0.435860	−	0.900014i	$-0.643556\pi$
$727$	−1041.96	−	601.573i	−1.43323	−	0.827473i	−0.997365	+	0.0725411i	$0.976889\pi$
$728$	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	−0.969599	−	0.244700i	$-0.921310\pi$
$733$	−510.693	−	884.546i	−0.696716	−	1.20675i	0.272883	−	0.962047i	$-0.412023\pi$
$734$	649.363	+	858.702i	0.884690	+	1.16989i
$735$		0			0
$736$	−11.1865	−	116.487i	−0.0151990	−	0.158270i
$737$	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	$0.943865\pi$
$740$	−10.1230	+	35.7600i	−0.0136797	+	0.0483243i
$741$		0			0
$742$	323.778	+	428.156i	0.436358	+	0.577030i
$743$	100.270	−	57.8907i	0.134953	−	0.0779149i	−0.431004	−	0.902350i	$-0.641840\pi$
$743$	100.270	−	57.8907i	0.134953	−	0.0779149i	0.565956	+	0.824435i	$0.308507\pi$
$744$		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	$-0.529436\pi$
$751$	543.581	−	313.837i	0.723809	−	0.417891i	0.816153	+	0.577836i	$0.196103\pi$
$752$	250.367	−	406.781i	0.332935	−	0.540932i
$753$		0			0
$754$	−670.681	−	283.347i	−0.889497	−	0.375792i
$755$			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	$0.489580\pi$
$758$	−143.496	+	339.655i	−0.189309	+	0.448093i
$759$		0			0
$760$	−263.055	−	210.812i	−0.346124	−	0.277385i
$761$	13.0738	+	22.6446i	0.0171798	+	0.0297563i	0.874488	−	0.485048i	$-0.161198\pi$
$761$	13.0738	+	22.6446i	0.0171798	+	0.0297563i	−0.857308	+	0.514804i	$0.827865\pi$
$762$		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	0.920438	−	0.390888i	$-0.127832\pi$
$769$	93.5875	+	162.098i	0.121700	+	0.210791i	−0.798738	+	0.601679i	$0.794499\pi$
$770$	154.165	−	116.582i	0.200214	−	0.151405i
$771$		0			0
$772$	−272.566	+	962.854i	−0.353065	+	1.24722i
$773$	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
$776$	28.2498	+	4.32725i	0.0364044	+	0.00557635i
$777$		0			0
$778$	481.483	−	364.105i	0.618873	−	0.468001i
$779$	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	$-0.527514\pi$
$787$	577.106	−	333.192i	0.733298	−	0.423370i	0.819628	+	0.572897i	$0.194180\pi$
$788$	−712.913	−	733.254i	−0.904712	−	0.930526i
$789$		0			0
$790$	106.294	−	251.598i	0.134550	−	0.318478i
$791$		−	1273.01i		−	1.60936i
$792$		0			0
$793$	1204.70			1.51917
$794$	−454.452	−	191.995i	−0.572358	−	0.241808i
$795$		0			0
$796$	−886.505	+	861.913i	−1.11370	+	1.08281i
$797$	−90.8816	−	157.412i	−0.114030	−	0.197505i	0.803362	−	0.595491i	$-0.203043\pi$
$797$	−90.8816	−	157.412i	−0.114030	−	0.197505i	−0.917391	+	0.397986i	$0.869709\pi$
$798$		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
$806$	677.617	+	896.065i	0.840716	+	1.11174i
$807$		0			0
$808$	−119.358	−	18.2830i	−0.147720	−	0.0226275i
$809$	−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	$0.676682\pi$
$812$	793.637	+	224.664i	0.977386	+	0.276680i
$813$		0			0
$814$	−26.7310	−	35.3485i	−0.0328391	−	0.0434257i
$815$	−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	−0.751317	−	0.659941i	$-0.770581\pi$
$821$	160.807	−	278.526i	0.195867	−	0.339252i	0.947184	+	0.320689i	$0.103915\pi$
$822$		0			0
$823$	−56.6805	+	32.7245i	−0.0688706	+	0.0397625i	−0.534040	−	0.845459i	$-0.679327\pi$
$823$	−56.6805	+	32.7245i	−0.0688706	+	0.0397625i	0.465169	+	0.885222i	$0.345993\pi$
$824$	−813.201	−	651.701i	−0.986895	−	0.790899i
$825$		0			0
$826$	141.564	+	59.8073i	0.171385	+	0.0724059i
$827$			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	$0.515623\pi$
$830$	203.940	−	482.724i	0.245710	−	0.581595i
$831$		0			0
$832$	901.068	+	282.680i	1.08301	+	0.339760i
$833$	−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	$-0.208897\pi$
$839$	553.733	+	319.698i	0.659992	+	0.381046i	−0.132282	+	0.991212i	$0.542231\pi$
$840$		0			0
$841$	116.171	+	201.214i	0.138135	+	0.239256i
$842$	326.865	−	247.180i	0.388200	−	0.293563i
$843$		0			0
$844$	1516.16	+	429.198i	1.79640	+	0.508529i
$845$	107.302			0.126984
$846$		0			0
$847$		−	780.866i		−	0.921920i
$848$	−14.4505	+	513.586i	−0.0170406	+	0.605643i
$849$		0			0
$850$	−909.076	+	687.456i	−1.06950	+	0.808772i
$851$	13.3641	−	7.71575i	0.0157040	−	0.00906668i
$852$		0			0
$853$	−38.8069	+	67.2155i	−0.0454946	+	0.0787989i	−0.887876	−	0.460083i	$-0.847820\pi$
$853$	−38.8069	+	67.2155i	−0.0454946	+	0.0787989i	0.842381	+	0.538882i	$0.181153\pi$
$854$	−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	0.491185	+	0.871055i	$0.336564\pi$
$857$	−436.010	+	755.192i	−0.508763	+	0.881204i	−0.999948	+	0.0101489i	$0.996769\pi$
$858$		0			0
$859$	−136.909	+	79.0444i	−0.159382	+	0.0920191i	−0.577570	−	0.816342i	$-0.695999\pi$
$859$	−136.909	+	79.0444i	−0.159382	+	0.0920191i	0.418188	+	0.908361i	$0.362665\pi$
$860$	147.214	−	143.130i	0.171179	−	0.166430i
$861$		0			0
$862$	−360.158	+	852.492i	−0.417816	+	0.988970i
$863$			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
$866$	351.101	+	148.332i	0.405429	+	0.171284i
$867$		0			0
$868$	−887.196	−	912.509i	−1.02211	−	1.05128i
$869$	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	0.999633	+	0.0270780i	$0.00862025\pi$
$877$	458.905	+	794.847i	0.523267	+	0.906325i	−0.476366	+	0.879247i	$0.658046\pi$
$878$	−528.319	−	698.637i	−0.601731	−	0.795715i
$879$		0			0
$880$	184.925	+	5.20313i	0.210142	+	0.00591264i
$881$	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	$-0.113968\pi$
$884$	−454.628	+	1606.00i	−0.514285	+	1.81674i
$885$		0			0
$886$	−1005.70	−	1329.92i	−1.13511	−	1.50104i
$887$	−110.844	+	63.9959i	−0.124965	+	0.0721487i	−0.561180	−	0.827694i	$-0.689652\pi$
$887$	−110.844	+	63.9959i	−0.124965	+	0.0721487i	0.436214	+	0.899843i	$0.356319\pi$
$888$		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
$896$	−1052.55	−	191.668i	−1.17472	−	0.213915i
$897$		0			0
$898$	885.772	+	374.218i	0.986383	+	0.416724i
$899$			939.164i			1.04468i
$900$		0			0
$901$	−908.086			−1.00786
$902$	−81.1303	+	192.035i	−0.0899449	+	0.212899i
$903$		0			0
$904$	761.970	−	950.796i	0.842887	−	1.05177i
$905$	−202.656	−	351.011i	−0.223930	−	0.387858i
$906$		0			0
$907$	13.7946	+	7.96431i	0.0152090	+	0.00878094i	0.507585	−	0.861602i	$-0.330538\pi$
$907$	13.7946	+	7.96431i	0.0152090	+	0.00878094i	−0.492376	+	0.870382i	$0.663872\pi$
$908$	−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	$-0.324471\pi$
$911$	43.9255	+	25.3604i	0.0482168	+	0.0278380i	−0.475698	+	0.879609i	$0.657804\pi$
$912$		0			0
$913$	312.445	+	541.170i	0.342218	+	0.592738i
$914$	348.759	−	263.737i	0.381575	−	0.288552i
$915$		0			0
$916$	−230.043	+	812.641i	−0.251139	+	0.887162i
$917$	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	$-0.196736\pi$
$920$	−9.75343	+	63.6739i	−0.0106016	+	0.0692107i
$921$		0			0
$922$	1143.70	−	864.878i	1.24045	−	0.938046i
$923$	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	−0.943516	−	0.331326i	$-0.892504\pi$
$929$	−171.699	+	297.392i	−0.184822	+	0.320121i	0.758695	+	0.651446i	$0.225837\pi$
$930$		0			0
$931$	345.727	−	199.606i	0.371351	−	0.214399i
$932$	781.048	+	803.333i	0.838034	+	0.861945i
$933$		0			0
$934$	356.978	−	844.964i	0.382203	−	0.904673i
$935$			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	$0.545634\pi$
$938$	122.008	+	51.5456i	0.130073	+	0.0549527i
$939$		0			0
$940$	−188.517	+	183.287i	−0.200550	+	0.194987i
$941$	610.126	+	1056.77i	0.648380	+	1.12303i	0.983510	+	0.180855i	$0.0578865\pi$
$941$	610.126	+	1056.77i	0.648380	+	1.12303i	−0.335130	+	0.942172i	$0.608780\pi$
$942$		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	$-0.00933547\pi$
$947$	1395.84	+	805.888i	1.47396	+	0.850991i	0.474390	+	0.880315i	$0.342669\pi$
$948$		0			0
$949$	−245.845	−	425.815i	−0.259056	−	0.448699i
$950$	−465.232	−	615.212i	−0.489718	−	0.647592i
$951$		0			0
$952$	286.303	−	1869.09i	0.300739	−	1.96333i
$953$	−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
$956$	−1508.12	−	426.922i	−1.57753	−	0.446571i
$957$		0			0
$958$	794.650	+	1050.83i	0.829488	+	1.09690i
$959$	−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	−0.604340	+	0.796726i	$0.706563\pi$
$967$	−1543.81	+	891.320i	−1.59650	+	0.921737i	−0.992155	+	0.125011i	$0.960103\pi$
$968$	467.394	−	583.221i	0.482845	−	0.602501i
$969$		0			0
$970$	−14.4916	−	6.12238i	−0.0149398	−	0.00631173i
$971$		−	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
$974$	556.973	−	1318.35i	0.571841	−	1.35354i
$975$		0			0
$976$	−1112.46	−	684.703i	−1.13982	−	0.701540i
$977$	689.779	+	1194.73i	0.706017	+	1.22286i	0.966323	+	0.257331i	$0.0828431\pi$
$977$	689.779	+	1194.73i	0.706017	+	1.22286i	−0.260306	+	0.965526i	$0.583824\pi$
$978$		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	$-0.455958\pi$
$983$	−639.804	−	369.391i	−0.650869	−	0.375779i	−0.788789	+	0.614664i	$0.789292\pi$
$984$		0			0
$985$	281.478	+	487.534i	0.285764	+	0.494959i
$986$	−1112.94	+	841.621i	−1.12874	+	0.853571i
$987$		0			0
$988$	−1086.85	−	307.667i	−1.10005	−	0.311404i
$989$	−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	$0.718348\pi$
$992$	−116.447	−	1212.58i	−0.117386	−	1.22236i
$993$		0			0
$994$	−839.045	+	634.498i	−0.844110	+	0.638328i
$995$	589.430	−	340.307i	0.592391	−	0.342017i
$996$		0			0
$997$	−871.274	+	1509.09i	−0.873896	+	1.51363i	−0.0159621	+	0.999873i	$0.505081\pi$
$997$	−871.274	+	1509.09i	−0.873896	+	1.51363i	−0.857934	+	0.513760i	$0.828252\pi$
$998$	−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.19.7		16
3.2	odd	2		36.3.f.c.7.2	✓	16
4.3	odd	2	inner	108.3.f.c.19.1		16
8.3	odd	2		1728.3.o.g.127.3		16
8.5	even	2		1728.3.o.g.127.4		16
9.2	odd	6		324.3.d.i.163.4		8
9.4	even	3	inner	108.3.f.c.91.1		16
9.5	odd	6		36.3.f.c.31.8	yes	16
9.7	even	3		324.3.d.g.163.5		8
12.11	even	2		36.3.f.c.7.8	yes	16
24.5	odd	2		576.3.o.g.511.4		16
24.11	even	2		576.3.o.g.511.5		16
36.7	odd	6		324.3.d.g.163.6		8
36.11	even	6		324.3.d.i.163.3		8
36.23	even	6		36.3.f.c.31.2	yes	16
36.31	odd	6	inner	108.3.f.c.91.7		16
72.5	odd	6		576.3.o.g.319.5		16
72.13	even	6		1728.3.o.g.1279.3		16
72.59	even	6		576.3.o.g.319.4		16
72.67	odd	6		1728.3.o.g.1279.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.3.f.c.7.2	✓	16	3.2	odd	2
36.3.f.c.7.8	yes	16	12.11	even	2
36.3.f.c.31.2	yes	16	36.23	even	6
36.3.f.c.31.8	yes	16	9.5	odd	6
108.3.f.c.19.1		16	4.3	odd	2	inner
108.3.f.c.19.7		16	1.1	even	1	trivial
108.3.f.c.91.1		16	9.4	even	3	inner
108.3.f.c.91.7		16	36.31	odd	6	inner
324.3.d.g.163.5		8	9.7	even	3
324.3.d.g.163.6		8	36.7	odd	6
324.3.d.i.163.3		8	36.11	even	6
324.3.d.i.163.4		8	9.2	odd	6
576.3.o.g.319.4		16	72.59	even	6
576.3.o.g.319.5		16	72.5	odd	6
576.3.o.g.511.4		16	24.5	odd	2
576.3.o.g.511.5		16	24.11	even	2
1728.3.o.g.127.3		16	8.3	odd	2
1728.3.o.g.127.4		16	8.5	even	2
1728.3.o.g.1279.3		16	72.13	even	6
1728.3.o.g.1279.4		16	72.67	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.84233 + 0.778342i) q^{2} +(2.78837 + 2.86793i) q^{4} +(-1.10093 - 1.90686i) q^{5} +(7.23844 + 4.17912i) q^{7} +(2.90487 + 7.45397i) q^{8} +O(q^{10})\)	\(q+(1.84233 + 0.778342i) q^{2} +(2.78837 + 2.86793i) q^{4} +(-1.10093 - 1.90686i) q^{5} +(7.23844 + 4.17912i) q^{7} +(2.90487 + 7.45397i) q^{8} +(-0.544081 - 4.36996i) q^{10} +(4.54769 + 2.62561i) q^{11} +(-7.37788 - 12.7789i) q^{13} +(10.0828 + 13.3333i) q^{14} +(-0.450004 + 15.9937i) q^{16} -28.2789 q^{17} -19.1376i q^{19} +(2.39894 - 8.47440i) q^{20} +(6.33472 + 8.37689i) q^{22} +(-3.16702 + 1.82848i) q^{23} +(10.0759 - 17.4520i) q^{25} +(-3.64618 - 29.2854i) q^{26} +(8.19805 + 32.4122i) q^{28} +(12.3355 - 21.3657i) q^{29} +(-32.9674 + 19.0338i) q^{31} +(-13.2776 + 29.1154i) q^{32} +(-52.0991 - 22.0106i) q^{34} -18.4036i q^{35} -4.21977 q^{37} +(14.8956 - 35.2578i) q^{38} +(11.0156 - 13.7454i) q^{40} +(9.92483 + 17.1903i) q^{41} +(20.1894 + 11.6564i) q^{43} +(5.15057 + 20.3636i) q^{44} +(-7.25787 + 0.903640i) q^{46} +(-25.8538 - 14.9267i) q^{47} +(10.4300 + 18.0654i) q^{49} +(32.1468 - 24.3099i) q^{50} +(16.0766 - 56.7914i) q^{52} +32.1118 q^{53} -11.5624i q^{55} +(-10.1243 + 66.0950i) q^{56} +(39.3559 - 29.7615i) q^{58} +(7.96159 - 4.59663i) q^{59} +(-40.8215 + 70.7049i) q^{61} +(-75.5517 + 9.40656i) q^{62} +(-47.1234 + 43.3057i) q^{64} +(-16.2450 + 28.1372i) q^{65} +(6.86179 - 3.96166i) q^{67} +(-78.8519 - 81.1017i) q^{68} +(14.3243 - 33.9055i) q^{70} +62.9286i q^{71} +33.3218 q^{73} +(-7.77421 - 3.28442i) q^{74} +(54.8852 - 53.3626i) q^{76} +(21.9454 + 38.0106i) q^{77} +(53.7133 + 31.0114i) q^{79} +(30.9931 - 16.7497i) q^{80} +(4.90489 + 39.3951i) q^{82} +(103.056 + 59.4995i) q^{83} +(31.1329 + 53.9238i) q^{85} +(28.1230 + 37.1892i) q^{86} +(-6.36077 + 41.5254i) q^{88} +107.361 q^{89} -123.332i q^{91} +(-14.0747 - 3.98430i) q^{92} +(-36.0132 - 47.6231i) q^{94} +(-36.4927 + 21.0690i) q^{95} +(1.78621 - 3.09380i) q^{97} +(5.15457 + 41.4005i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} - 5 q^{4} - 6 q^{5} + 54 q^{8}+O(q^{10}) \) 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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