LMFDB - Embedded newform 108.3.f.c.91.7

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			91.7
Root			$1.84233 - 0.778342i$ of defining polynomial
Character	$\chi$	$=$	108.91
Dual form			108.3.f.c.19.7

$q$-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 $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.84233	−	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	−0.954864	−	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	0.115917	−	0.993259i	$-0.463019\pi$
$7$	7.23844	−	4.17912i	1.03406	−	0.597017i	0.918146	+	0.396242i	$0.129686\pi$
$8$	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	−0.278835	−	0.960339i	$-0.589948\pi$
$11$	4.54769	−	2.62561i	0.413426	−	0.238692i	0.692261	+	0.721648i	$0.256615\pi$
$12$		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	$0.974566\pi$
$14$	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	$0.167999\pi$
$19$			19.1376i			1.00724i	−0.863925	+	0.503620i	$0.832001\pi$
$20$	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	0.429569	−	0.903034i	$-0.358665\pi$
$23$	−3.16702	−	1.82848i	−0.137696	−	0.0794990i	−0.567266	+	0.823535i	$0.691999\pi$
$24$		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	−0.137077	−	0.990560i	$-0.543771\pi$
$31$	−32.9674	−	19.0338i	−1.06347	−	0.613992i	−0.926389	+	0.376568i	$0.877104\pi$
$32$	−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	−0.719235	−	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	−0.246518	−	0.969138i	$-0.579286\pi$
$43$	20.1894	−	11.6564i	0.469521	−	0.271078i	0.716039	+	0.698060i	$0.245953\pi$
$44$	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	−0.749155	−	0.662395i	$-0.769540\pi$
$47$	−25.8538	+	14.9267i	−0.550082	+	0.317590i	0.199073	+	0.979985i	$0.436207\pi$
$48$		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	0.565951	−	0.824439i	$-0.308509\pi$
$59$	7.96159	+	4.59663i	0.134942	+	0.0779089i	−0.431009	+	0.902348i	$0.641842\pi$
$60$		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	0.550333	−	0.834946i	$-0.314501\pi$
$67$	6.86179	+	3.96166i	0.102415	+	0.0591292i	−0.447918	+	0.894075i	$0.647834\pi$
$68$	−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	$-0.853858\pi$
$71$		−	62.9286i		−	0.886318i	0.896443	−	0.443159i	$-0.146142\pi$
$72$		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	−0.119908	−	0.992785i	$-0.538260\pi$
$79$	53.7133	−	31.0114i	0.679916	−	0.392549i	0.799823	+	0.600236i	$0.204927\pi$
$80$	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	0.272212	−	0.962237i	$-0.412245\pi$
$83$	103.056	−	59.4995i	1.24164	−	0.716861i	0.969428	+	0.245376i	$0.0789114\pi$
$84$		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	0.875086	−	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	−0.160294	−	0.987069i	$-0.551244\pi$
$103$	−112.813	−	65.1324i	−1.09527	−	0.632353i	−0.934974	+	0.354716i	$0.884578\pi$
$104$	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	$0.0770146\pi$
$107$			51.2733i			0.479190i	−0.970873	+	0.239595i	$0.922985\pi$
$108$		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	0.302864	+	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
$122$	−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	$-0.802886\pi$
$127$		−	147.428i		−	1.16085i	0.814314	−	0.580425i	$-0.197114\pi$
$128$	−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	0.864598	−	0.502464i	$-0.167573\pi$
$131$	112.889	+	65.1766i	0.861750	+	0.497532i	−0.00284803	+	0.999996i	$0.500907\pi$
$132$		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	0.767293	−	0.641297i	$-0.221603\pi$
$139$	82.7828	+	47.7947i	0.595560	+	0.343847i	−0.171733	+	0.985144i	$0.554937\pi$
$140$	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	−0.957943	−	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	−0.770768	−	0.637116i	$-0.780127\pi$
$151$	−91.2633	+	52.6909i	−0.604393	+	0.348946i	0.166375	+	0.986063i	$0.446794\pi$
$152$	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	$0.926587\pi$
$158$	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	$0.0330071\pi$
$163$			33.7439i			0.207018i	−0.994629	+	0.103509i	$0.966993\pi$
$164$	−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	0.0513797	−	0.998679i	$-0.483638\pi$
$167$	−131.565	−	75.9589i	−0.787812	−	0.454843i	−0.839192	+	0.543836i	$0.816971\pi$
$168$		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
$176$	−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	$-0.791383\pi$
$179$		−	218.189i		−	1.21894i	0.792811	−	0.609468i	$-0.208617\pi$
$180$		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	0.185849	−	0.982578i	$-0.440497\pi$
$191$	215.775	−	124.578i	1.12971	−	0.652239i	0.943862	+	0.330339i	$0.107163\pi$
$192$		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	$-0.0577758\pi$
$194$	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	$-0.716913\pi$
$199$		−	309.110i		−	1.55332i	0.629921	−	0.776659i	$-0.283087\pi$
$200$	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	0.987725	+	0.156205i	$0.0499261\pi$
$211$	341.158	+	196.968i	1.61686	+	0.933497i	0.629140	+	0.777292i	$0.283407\pi$
$212$	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	−0.686871	−	0.726779i	$-0.741016\pi$
$223$	−89.4002	+	51.6152i	−0.400898	+	0.231458i	0.285974	+	0.958238i	$0.407683\pi$
$224$	−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	−0.744418	−	0.667714i	$-0.767273\pi$
$227$	−122.210	+	70.5578i	−0.538369	+	0.310828i	0.206049	+	0.978542i	$0.433939\pi$
$228$		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	$0.0141532\pi$
$230$	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	−0.423583	−	0.905857i	$-0.639228\pi$
$239$	−339.349	−	195.923i	−1.41987	−	0.819762i	−0.996287	+	0.0860949i	$0.972561\pi$
$240$		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
$248$	−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	$0.282618\pi$
$251$			389.416i			1.55146i	−0.631065	+	0.775730i	$0.717382\pi$
$252$		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	−0.795746	−	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	−0.718089	−	0.695951i	$-0.754983\pi$
$263$	−124.773	+	72.0378i	−0.474423	+	0.273908i	0.243667	+	0.969859i	$0.421650\pi$
$264$		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	$0.0208457\pi$
$271$			35.4695i			0.130884i	−0.997856	+	0.0654419i	$0.979154\pi$
$272$	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	−0.992425	−	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	0.0613442	−	0.998117i	$-0.480461\pi$
$283$	−218.583	−	126.199i	−0.772378	−	0.445933i	−0.833722	+	0.552184i	$0.813795\pi$
$284$	−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	−0.898648	−	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
$302$	−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	$0.0715361\pi$
$307$			136.830i			0.445701i	−0.974853	+	0.222850i	$0.928464\pi$
$308$	−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	0.959158	−	0.282871i	$-0.0912869\pi$
$311$	371.260	+	214.347i	1.19376	+	0.689219i	0.234605	+	0.972091i	$0.424620\pi$
$312$		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
$320$	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	−0.606412	−	0.795151i	$-0.707392\pi$
$331$	−73.1501	+	42.2332i	−0.220997	+	0.127593i	0.385415	+	0.922743i	$0.374058\pi$
$332$	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	$0.896994\pi$
$338$	−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	−0.258284	−	0.966069i	$-0.583157\pi$
$347$	−424.751	−	245.230i	−1.22407	−	0.706715i	−0.965782	+	0.259354i	$0.916490\pi$
$348$		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
$356$	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	$0.193939\pi$
$359$			410.893i			1.14455i	−0.820062	+	0.572274i	$0.806061\pi$
$360$		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	0.295203	−	0.955435i	$-0.404613\pi$
$367$	466.176	−	269.147i	1.27023	−	0.733370i	0.975032	+	0.222064i	$0.0712795\pi$
$368$	−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	$0.231075\pi$
$374$	−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	$-0.921796\pi$
$379$		−	184.361i		−	0.486442i	0.969971	−	0.243221i	$-0.0782040\pi$
$380$	−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	0.716790	−	0.697289i	$-0.245611\pi$
$383$	180.514	+	104.220i	0.471315	+	0.272114i	−0.245475	+	0.969403i	$0.578944\pi$
$384$		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
$392$	−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	−0.178703	+	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	$0.0631067\pi$
$410$	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	0.847665	−	0.530532i	$-0.178008\pi$
$419$	340.246	+	196.441i	0.812043	+	0.468833i	−0.0356217	+	0.999365i	$0.511341\pi$
$420$		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
$428$	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	$-0.819632\pi$
$431$		−	462.725i		−	1.07361i	0.843707	−	0.536803i	$-0.180368\pi$
$432$		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	−0.865337	−	0.501190i	$-0.832896\pi$
$439$	−379.279	+	218.977i	−0.863962	+	0.498809i	0.00137479	+	0.999999i	$0.499562\pi$
$440$	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	$0.723402\pi$
$443$	−721.993	+	416.843i	−1.62978	+	0.940954i	−0.984157	+	0.177297i	$0.943265\pi$
$444$		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	0.960484	−	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	0.528477	−	0.848948i	$-0.322763\pi$
$463$	26.6250	+	15.3719i	0.0575053	+	0.0332007i	−0.470972	+	0.882148i	$0.656097\pi$
$464$	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	$0.163386\pi$
$467$			458.639i			0.982096i	−0.871133	+	0.491048i	$0.836614\pi$
$468$		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	0.232448	−	0.972609i	$-0.425326\pi$
$479$	570.477	−	329.365i	1.19098	−	0.687610i	0.958528	+	0.284999i	$0.0919932\pi$
$480$		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	$0.262673\pi$
$487$			715.589i			1.46938i	−0.678402	+	0.734691i	$0.737327\pi$
$488$	−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	−0.215866	−	0.976423i	$-0.569258\pi$
$491$	−574.179	−	331.502i	−1.16941	−	0.675157i	−0.953540	+	0.301266i	$0.902591\pi$
$492$		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	−0.0358546	−	0.999357i	$-0.511415\pi$
$499$	−458.706	−	264.834i	−0.919251	−	0.530730i	−0.883396	+	0.468627i	$0.844749\pi$
$500$	−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	$0.0216446\pi$
$503$			68.3537i			0.135892i	−0.997689	+	0.0679460i	$0.978355\pi$
$504$		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	−0.141143	−	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
$518$	−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	$0.00929347\pi$
$523$			30.5350i			0.0583843i	−0.999574	+	0.0291921i	$0.990707\pi$
$524$	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	0.505092	−	0.863066i	$-0.331459\pi$
$547$	823.276	−	475.318i	1.50507	−	0.868955i	0.999983	−	0.00588962i	$-0.00187474\pi$
$548$	−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	−0.979680	−	0.200569i	$-0.935721\pi$
$563$	−925.131	−	534.125i	−1.64322	−	0.948712i	−0.663538	−	0.748143i	$-0.730946\pi$
$564$		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	0.271756	−	0.962366i	$-0.412396\pi$
$571$	−243.132	−	140.372i	−0.425800	−	0.245836i	−0.697556	+	0.716531i	$0.745729\pi$
$572$	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	−0.615643	−	0.788025i	$-0.711104\pi$
$587$	−141.476	+	81.6811i	−0.241015	+	0.139150i	0.374628	+	0.927175i	$0.377770\pi$
$588$		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	0.794505	−	0.607257i	$-0.207730\pi$
$599$	398.849	+	230.275i	0.665857	+	0.384433i	−0.128648	+	0.991690i	$0.541064\pi$
$600$		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	0.972829	−	0.231524i	$-0.0743712\pi$
$607$	764.054	+	441.127i	1.25874	+	0.726733i	0.285909	+	0.958257i	$0.407705\pi$
$608$	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	−0.824198	−	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	−0.764284	−	0.644880i	$-0.776907\pi$
$619$	−363.937	+	210.119i	−0.587944	+	0.339449i	0.176340	+	0.984329i	$0.443574\pi$
$620$	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	$-0.874923\pi$
$631$		−	483.230i		−	0.765816i	0.923787	−	0.382908i	$-0.125077\pi$
$632$	−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	0.899193	−	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	0.809472	−	0.587159i	$-0.199754\pi$
$643$	453.773	+	261.986i	0.705713	+	0.407444i	−0.103759	+	0.994602i	$0.533087\pi$
$644$	−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	$-0.992299\pi$
$647$		−	31.3018i		−	0.0483799i	0.999707	−	0.0241900i	$-0.00770066\pi$
$648$		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	0.292833	+	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	−0.530918	−	0.847423i	$-0.678153\pi$
$659$	−41.1783	+	23.7743i	−0.0624860	+	0.0360763i	0.468432	+	0.883500i	$0.344819\pi$
$660$		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	$0.178632\pi$
$662$	−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	0.853556	−	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
$680$	−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	$0.219977\pi$
$683$			870.646i			1.27474i	−0.770559	+	0.637369i	$0.780023\pi$
$684$		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	−0.950827	−	0.309722i	$-0.899764\pi$
$691$	−800.188	+	461.988i	−1.15801	+	0.668580i	−0.207187	+	0.978301i	$0.566431\pi$
$692$	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	0.791268	+	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
$716$	−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	$-0.945330\pi$
$719$		−	245.763i		−	0.341813i	0.985287	−	0.170906i	$-0.0546695\pi$
$720$		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	−0.997365	−	0.0725411i	$-0.976889\pi$
$727$	−1041.96	+	601.573i	−1.43323	+	0.827473i	−0.435860	+	0.900014i	$0.643556\pi$
$728$	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	$0.921310\pi$
$734$	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	$-0.943865\pi$
$739$		−	259.300i		−	0.350879i	0.984490	−	0.175439i	$-0.0561346\pi$
$740$	−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	0.565956	−	0.824435i	$-0.308507\pi$
$743$	100.270	+	57.8907i	0.134953	+	0.0779149i	−0.431004	+	0.902350i	$0.641840\pi$
$744$		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	0.816153	−	0.577836i	$-0.196103\pi$
$751$	543.581	+	313.837i	0.723809	+	0.417891i	−0.0923438	+	0.995727i	$0.529436\pi$
$752$	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	−0.857308	−	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	$0.127832\pi$
$770$	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	0.819628	−	0.572897i	$-0.194180\pi$
$787$	577.106	+	333.192i	0.733298	+	0.423370i	−0.0863293	+	0.996267i	$0.527514\pi$
$788$	−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	−0.917391	−	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
$806$	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	$-0.676682\pi$
$811$		−	1378.48i		−	1.69973i	0.526997	−	0.849867i	$-0.323318\pi$
$812$	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	0.947184	−	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	0.465169	−	0.885222i	$-0.345993\pi$
$823$	−56.6805	−	32.7245i	−0.0688706	−	0.0397625i	−0.534040	+	0.845459i	$0.679327\pi$
$824$	−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	$-0.844030\pi$
$827$		−	778.406i		−	0.941240i	0.882336	−	0.470620i	$-0.155970\pi$
$828$		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	−0.132282	−	0.991212i	$-0.542231\pi$
$839$	553.733	−	319.698i	0.659992	−	0.381046i	0.792274	+	0.610166i	$0.208897\pi$
$840$		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	0.842381	−	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	0.418188	−	0.908361i	$-0.362665\pi$
$859$	−136.909	−	79.0444i	−0.159382	−	0.0920191i	−0.577570	+	0.816342i	$0.695999\pi$
$860$	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	$-0.869902\pi$
$863$		−	685.963i		−	0.794859i	0.917633	−	0.397429i	$-0.130098\pi$
$864$		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	−0.476366	−	0.879247i	$-0.658046\pi$
$877$	458.905	−	794.847i	0.523267	−	0.906325i	0.999633	−	0.0270780i	$-0.00862025\pi$
$878$	−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	$0.113968\pi$
$883$			618.879i			0.700882i	−0.936585	+	0.350441i	$0.886032\pi$
$884$	−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	0.436214	−	0.899843i	$-0.356319\pi$
$887$	−110.844	−	63.9959i	−0.124965	−	0.0721487i	−0.561180	+	0.827694i	$0.689652\pi$
$888$		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	−0.492376	−	0.870382i	$-0.663872\pi$
$907$	13.7946	−	7.96431i	0.0152090	−	0.00878094i	0.507585	+	0.861602i	$0.330538\pi$
$908$	−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	−0.475698	−	0.879609i	$-0.657804\pi$
$911$	43.9255	−	25.3604i	0.0482168	−	0.0278380i	0.523915	+	0.851771i	$0.324471\pi$
$912$		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	$0.196736\pi$
$919$			1065.04i			1.15892i	−0.815002	+	0.579458i	$0.803264\pi$
$920$	−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	0.758695	−	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
$932$	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	−0.335130	−	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	0.474390	−	0.880315i	$-0.342669\pi$
$947$	1395.84	−	805.888i	1.47396	−	0.850991i	0.999570	+	0.0293240i	$0.00933547\pi$
$948$		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	−0.992155	−	0.125011i	$-0.960103\pi$
$967$	−1543.81	−	891.320i	−1.59650	−	0.921737i	−0.604340	−	0.796726i	$-0.706563\pi$
$968$	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	$0.107792\pi$
$971$			645.136i			0.664404i	−0.943208	+	0.332202i	$0.892208\pi$
$972$		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	−0.260306	−	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	−0.788789	−	0.614664i	$-0.789292\pi$
$983$	−639.804	+	369.391i	−0.650869	+	0.375779i	0.137920	+	0.990443i	$0.455958\pi$
$984$		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	$-0.718348\pi$
$991$		−	1533.69i		−	1.54762i	0.633416	−	0.773811i	$-0.281652\pi$
$992$	−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	−0.857934	−	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.91.7		16
3.2	odd	2		36.3.f.c.31.2	yes	16
4.3	odd	2	inner	108.3.f.c.91.1		16
8.3	odd	2		1728.3.o.g.1279.3		16
8.5	even	2		1728.3.o.g.1279.4		16
9.2	odd	6		36.3.f.c.7.8	yes	16
9.4	even	3		324.3.d.g.163.6		8
9.5	odd	6		324.3.d.i.163.3		8
9.7	even	3	inner	108.3.f.c.19.1		16
12.11	even	2		36.3.f.c.31.8	yes	16
24.5	odd	2		576.3.o.g.319.4		16
24.11	even	2		576.3.o.g.319.5		16
36.7	odd	6	inner	108.3.f.c.19.7		16
36.11	even	6		36.3.f.c.7.2	✓	16
36.23	even	6		324.3.d.i.163.4		8
36.31	odd	6		324.3.d.g.163.5		8
72.11	even	6		576.3.o.g.511.4		16
72.29	odd	6		576.3.o.g.511.5		16
72.43	odd	6		1728.3.o.g.127.4		16
72.61	even	6		1728.3.o.g.127.3		16

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

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