LMFDB - Embedded newform 819.2.bm.f.550.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(478,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 5]))

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

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

chi := DirichletCharacter("819.478");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.bm (of order $6$, degree $2$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.2346760387617129.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + \cdots + 64 $ x^12 - 3x^11 + x^10 + 10x^9 - 15x^8 - 10x^7 + 45x^6 - 20x^5 - 60x^4 + 80x^3 + 16x^2 - 96x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			550.3
Root			$-1.18541 - 0.771231i$ of defining polynomial
Character	$\chi$	$=$	819.550
Dual form			819.2.bm.f.478.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.499987i q^{2} +1.75001 q^{4} +(0.902810 - 0.521238i) q^{5} +(2.63491 - 0.239300i) q^{7} -1.87496i q^{8} +O(q^{10})$	\(q-0.499987i q^{2} +1.75001 q^{4} +(0.902810 - 0.521238i) q^{5} +(2.63491 - 0.239300i) q^{7} -1.87496i q^{8} +(-0.260612 - 0.451393i) q^{10} +(3.43579 - 1.98365i) q^{11} +(-3.57504 + 0.468096i) q^{13} +(-0.119647 - 1.31742i) q^{14} +2.56257 q^{16} -0.142035 q^{17} +(-4.77160 - 2.75488i) q^{19} +(1.57993 - 0.912173i) q^{20} +(-0.991800 - 1.71785i) q^{22} +4.39098 q^{23} +(-1.95662 + 3.38897i) q^{25} +(0.234042 + 1.78747i) q^{26} +(4.61112 - 0.418779i) q^{28} +(-4.19880 + 7.27253i) q^{29} +(2.46516 + 1.42326i) q^{31} -5.03117i q^{32} +0.0710158i q^{34} +(2.25409 - 1.58946i) q^{35} -0.843187i q^{37} +(-1.37740 + 2.38574i) q^{38} +(-0.977298 - 1.69273i) q^{40} +(-10.4766 - 6.04869i) q^{41} +(2.41161 + 4.17704i) q^{43} +(6.01267 - 3.47142i) q^{44} -2.19543i q^{46} +(3.94602 - 2.27824i) q^{47} +(6.88547 - 1.26107i) q^{49} +(1.69444 + 0.978285i) q^{50} +(-6.25636 + 0.819175i) q^{52} +(-0.139800 + 0.242141i) q^{53} +(2.06791 - 3.58172i) q^{55} +(-0.448678 - 4.94034i) q^{56} +(3.63617 + 2.09934i) q^{58} +10.7815i q^{59} +(2.93177 - 5.07797i) q^{61} +(0.711612 - 1.23255i) q^{62} +2.60963 q^{64} +(-2.98359 + 2.28605i) q^{65} +(-4.45524 + 2.57223i) q^{67} -0.248564 q^{68} +(-0.794706 - 1.12701i) q^{70} +(3.20326 - 1.84940i) q^{71} +(5.72686 + 3.30640i) q^{73} -0.421582 q^{74} +(-8.35036 - 4.82108i) q^{76} +(8.57829 - 6.04892i) q^{77} +(-5.96135 - 10.3254i) q^{79} +(2.31352 - 1.33571i) q^{80} +(-3.02426 + 5.23818i) q^{82} +2.87321i q^{83} +(-0.128231 + 0.0740342i) q^{85} +(2.08846 - 1.20578i) q^{86} +(-3.71926 - 6.44195i) q^{88} -1.74765i q^{89} +(-9.30787 + 2.08890i) q^{91} +7.68427 q^{92} +(-1.13909 - 1.97296i) q^{94} -5.74379 q^{95} +(2.34079 - 1.35145i) q^{97} +(-0.630517 - 3.44264i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 8 q^{4} + 3 q^{5} - 3 q^{7}+O(q^{10}) $ 12 * q - 8 * q^4 + 3 * q^5 - 3 * q^7	$ 12 q - 8 q^{4} + 3 q^{5} - 3 q^{7} + 12 q^{10} - 12 q^{11} - 2 q^{13} - 4 q^{14} + 16 q^{16} + 34 q^{17} + 9 q^{19} + 3 q^{20} - 15 q^{22} + 6 q^{23} - 5 q^{25} + 6 q^{26} - 9 q^{28} + q^{29} + 18 q^{31} + 6 q^{35} - 19 q^{38} - q^{40} + 6 q^{41} + 11 q^{43} + 33 q^{44} + 15 q^{47} - 3 q^{49} - 18 q^{50} - 7 q^{52} + 8 q^{53} - 15 q^{55} - 27 q^{56} - 24 q^{58} + 5 q^{61} - 41 q^{62} + 2 q^{64} - 21 q^{65} + 15 q^{67} - 22 q^{68} + 3 q^{70} - 30 q^{71} + 42 q^{73} - 66 q^{74} - 45 q^{76} + 19 q^{77} - 35 q^{79} + 63 q^{80} + 5 q^{82} - 21 q^{85} + 57 q^{86} - 14 q^{88} - 7 q^{91} + 66 q^{92} + q^{94} + 4 q^{95} - 3 q^{97} + 18 q^{98}+O(q^{100}) $ 12 * q - 8 * q^4 + 3 * q^5 - 3 * q^7 + 12 * q^10 - 12 * q^11 - 2 * q^13 - 4 * q^14 + 16 * q^16 + 34 * q^17 + 9 * q^19 + 3 * q^20 - 15 * q^22 + 6 * q^23 - 5 * q^25 + 6 * q^26 - 9 * q^28 + q^29 + 18 * q^31 + 6 * q^35 - 19 * q^38 - q^40 + 6 * q^41 + 11 * q^43 + 33 * q^44 + 15 * q^47 - 3 * q^49 - 18 * q^50 - 7 * q^52 + 8 * q^53 - 15 * q^55 - 27 * q^56 - 24 * q^58 + 5 * q^61 - 41 * q^62 + 2 * q^64 - 21 * q^65 + 15 * q^67 - 22 * q^68 + 3 * q^70 - 30 * q^71 + 42 * q^73 - 66 * q^74 - 45 * q^76 + 19 * q^77 - 35 * q^79 + 63 * q^80 + 5 * q^82 - 21 * q^85 + 57 * q^86 - 14 * q^88 - 7 * q^91 + 66 * q^92 + q^94 + 4 * q^95 - 3 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		−	0.499987i		−	0.353544i	−0.984252	−	0.176772i	$-0.943434\pi$
$2$		−	0.499987i		−	0.353544i	0.984252	−	0.176772i	$-0.0565655\pi$
$3$		0			0
$3$		0			0
$4$	1.75001			0.875007
$5$	0.902810	−	0.521238i	0.403749	−	0.233105i	−0.284351	−	0.958720i	$-0.591778\pi$
$5$	0.902810	−	0.521238i	0.403749	−	0.233105i	0.688100	+	0.725616i	$0.258445\pi$
$6$		0			0
$7$	2.63491	−	0.239300i	0.995901	−	0.0904471i
$7$	2.63491	−	0.239300i	0.995901	−	0.0904471i
$8$		−	1.87496i		−	0.662897i
$9$		0			0
$10$	−0.260612	−	0.451393i	−0.0824127	−	0.142743i
$11$	3.43579	−	1.98365i	1.03593	−	0.598094i	0.117251	−	0.993102i	$-0.462592\pi$
$11$	3.43579	−	1.98365i	1.03593	−	0.598094i	0.918677	+	0.395009i	$0.129258\pi$
$12$		0			0
$13$	−3.57504	+	0.468096i	−0.991537	+	0.129827i
$13$	−3.57504	+	0.468096i	−0.991537	+	0.129827i
$14$	−0.119647	−	1.31742i	−0.0319770	−	0.352095i
$15$		0			0
$16$	2.56257			0.640643
$17$	−0.142035			−0.0344486			−0.0172243	−	0.999852i	$-0.505483\pi$
$17$	−0.142035			−0.0344486			−0.0172243	+	0.999852i	$0.505483\pi$
$18$		0			0
$19$	−4.77160	−	2.75488i	−1.09468	−	0.632014i	−0.159861	−	0.987140i	$-0.551105\pi$
$19$	−4.77160	−	2.75488i	−1.09468	−	0.632014i	−0.934818	+	0.355126i	$0.884438\pi$
$20$	1.57993	−	0.912173i	0.353283	−	0.203968i
$21$		0			0
$22$	−0.991800	−	1.71785i	−0.211452	−	0.366246i
$23$	4.39098			0.915582			0.457791	−	0.889060i	$-0.348641\pi$
$23$	4.39098			0.915582			0.457791	+	0.889060i	$0.348641\pi$
$24$		0			0
$25$	−1.95662	+	3.38897i	−0.391325	+	0.677794i
$26$	0.234042	+	1.78747i	0.0458994	+	0.350552i
$27$		0			0
$28$	4.61112	−	0.418779i	0.871420	−	0.0791418i
$29$	−4.19880	+	7.27253i	−0.779697	+	1.35047i	0.152419	+	0.988316i	$0.451294\pi$
$29$	−4.19880	+	7.27253i	−0.779697	+	1.35047i	−0.932116	+	0.362159i	$0.882040\pi$
$30$		0			0
$31$	2.46516	+	1.42326i	0.442756	+	0.255625i	0.704766	−	0.709440i	$-0.251052\pi$
$31$	2.46516	+	1.42326i	0.442756	+	0.255625i	−0.262010	+	0.965065i	$0.584385\pi$
$32$		−	5.03117i		−	0.889393i
$33$		0			0
$34$			0.0710158i			0.0121791i
$35$	2.25409	−	1.58946i	0.381010	−	0.268667i
$36$		0			0
$37$		−	0.843187i		−	0.138619i	−0.997595	−	0.0693095i	$-0.977920\pi$
$37$		−	0.843187i		−	0.138619i	0.997595	−	0.0693095i	$-0.0220796\pi$
$38$	−1.37740	+	2.38574i	−0.223445	+	0.387017i
$39$		0			0
$40$	−0.977298	−	1.69273i	−0.154524	−	0.267644i
$41$	−10.4766	−	6.04869i	−1.63618	−	0.944647i	−0.982133	−	0.188190i	$-0.939738\pi$
$41$	−10.4766	−	6.04869i	−1.63618	−	0.944647i	−0.654044	−	0.756457i	$-0.726929\pi$
$42$		0			0
$43$	2.41161	+	4.17704i	0.367768	+	0.636993i	0.989216	−	0.146463i	$-0.0467888\pi$
$43$	2.41161	+	4.17704i	0.367768	+	0.636993i	−0.621448	+	0.783455i	$0.713455\pi$
$44$	6.01267	−	3.47142i	0.906444	−	0.523336i
$45$		0			0
$46$		−	2.19543i		−	0.323699i
$47$	3.94602	−	2.27824i	0.575587	−	0.332315i	−0.183791	−	0.982965i	$-0.558837\pi$
$47$	3.94602	−	2.27824i	0.575587	−	0.332315i	0.759378	+	0.650650i	$0.225504\pi$
$48$		0			0
$49$	6.88547	−	1.26107i	0.983639	−	0.180153i
$50$	1.69444	+	0.978285i	0.239630	+	0.138350i
$51$		0			0
$52$	−6.25636	+	0.819175i	−0.867601	+	0.113599i
$53$	−0.139800	+	0.242141i	−0.0192030	+	0.0332606i	−0.875467	−	0.483278i	$-0.839446\pi$
$53$	−0.139800	+	0.242141i	−0.0192030	+	0.0332606i	0.856264	+	0.516538i	$0.172780\pi$
$54$		0			0
$55$	2.06791	−	3.58172i	0.278837	−	0.482959i
$56$	−0.448678	−	4.94034i	−0.0599571	−	0.660180i
$57$		0			0
$58$	3.63617	+	2.09934i	0.477452	+	0.275657i
$59$			10.7815i			1.40363i	0.712359	+	0.701815i	$0.247627\pi$
$59$			10.7815i			1.40363i	−0.712359	+	0.701815i	$0.752373\pi$
$60$		0			0
$61$	2.93177	−	5.07797i	0.375374	−	0.650168i	−0.615009	−	0.788520i	$-0.710847\pi$
$61$	2.93177	−	5.07797i	0.375374	−	0.650168i	0.990383	+	0.138353i	$0.0441808\pi$
$62$	0.711612	−	1.23255i	0.0903748	−	0.156534i
$63$		0			0
$64$	2.60963			0.326204
$65$	−2.98359	+	2.28605i	−0.370069	+	0.283549i
$66$		0			0
$67$	−4.45524	+	2.57223i	−0.544294	+	0.314248i	−0.746818	−	0.665029i	$-0.768419\pi$
$67$	−4.45524	+	2.57223i	−0.544294	+	0.314248i	0.202523	+	0.979277i	$0.435086\pi$
$68$	−0.248564			−0.0301428
$69$		0			0
$70$	−0.794706	−	1.12701i	−0.0949856	−	0.134704i
$71$	3.20326	−	1.84940i	0.380157	−	0.219484i	−0.297730	−	0.954650i	$-0.596229\pi$
$71$	3.20326	−	1.84940i	0.380157	−	0.219484i	0.677887	+	0.735167i	$0.262896\pi$
$72$		0			0
$73$	5.72686	+	3.30640i	0.670278	+	0.386985i	0.796182	−	0.605057i	$-0.206850\pi$
$73$	5.72686	+	3.30640i	0.670278	+	0.386985i	−0.125904	+	0.992042i	$0.540183\pi$
$74$	−0.421582			−0.0490079
$75$		0			0
$76$	−8.35036	−	4.82108i	−0.957852	−	0.553016i
$77$	8.57829	−	6.04892i	0.977587	−	0.689339i
$78$		0			0
$79$	−5.96135	−	10.3254i	−0.670705	−	1.16169i	−0.977705	−	0.209985i	$-0.932658\pi$
$79$	−5.96135	−	10.3254i	−0.670705	−	1.16169i	0.307000	−	0.951710i	$-0.400675\pi$
$80$	2.31352	−	1.33571i	0.258659	−	0.149337i
$81$		0			0
$82$	−3.02426	+	5.23818i	−0.333974	+	0.578460i
$83$			2.87321i			0.315376i	0.987489	+	0.157688i	$0.0504040\pi$
$83$			2.87321i			0.315376i	−0.987489	+	0.157688i	$0.949596\pi$
$84$		0			0
$85$	−0.128231	+	0.0740342i	−0.0139086	+	0.00803013i
$86$	2.08846	−	1.20578i	0.225205	−	0.130022i
$87$		0			0
$88$	−3.71926	−	6.44195i	−0.396475	−	0.686714i
$89$		−	1.74765i		−	0.185250i	−0.995701	−	0.0926252i	$-0.970474\pi$
$89$		−	1.74765i		−	0.185250i	0.995701	−	0.0926252i	$-0.0295258\pi$
$90$		0			0
$91$	−9.30787	+	2.08890i	−0.975730	+	0.218976i
$92$	7.68427			0.801141
$93$		0			0
$94$	−1.13909	−	1.97296i	−0.117488	−	0.203495i
$95$	−5.74379			−0.589301
$96$		0			0
$97$	2.34079	−	1.35145i	0.237671	−	0.137219i	−0.376435	−	0.926443i	$-0.622850\pi$
$97$	2.34079	−	1.35145i	0.237671	−	0.137219i	0.614106	+	0.789224i	$0.289517\pi$
$98$	−0.630517	−	3.44264i	−0.0636919	−	0.347759i
$99$		0			0
$100$	−3.42412	+	5.93074i	−0.342412	+	0.593074i
$101$	−5.73612	−	9.93524i	−0.570765	−	0.988594i	−0.996488	−	0.0837401i	$-0.973313\pi$
$101$	−5.73612	−	9.93524i	−0.570765	−	0.988594i	0.425723	−	0.904854i	$-0.360020\pi$
$102$		0			0
$103$	2.08475	+	3.61090i	0.205417	+	0.355792i	0.950265	−	0.311441i	$-0.100812\pi$
$103$	2.08475	+	3.61090i	0.205417	+	0.355792i	−0.744849	+	0.667233i	$0.767478\pi$
$104$	0.877660	+	6.70304i	0.0860617	+	0.657287i
$105$		0			0
$106$	0.121067	+	0.0698982i	0.0117591	+	0.00678911i
$107$	−8.48742			−0.820510			−0.410255	−	0.911971i	$-0.634560\pi$
$107$	−8.48742			−0.820510			−0.410255	+	0.911971i	$0.634560\pi$
$108$		0			0
$109$	5.56886	+	3.21518i	0.533400	+	0.307958i	0.742400	−	0.669957i	$-0.233688\pi$
$109$	5.56886	+	3.21518i	0.533400	+	0.307958i	−0.209000	+	0.977916i	$0.567021\pi$
$110$	−1.79081	−	1.03393i	−0.170747	−	0.0985810i
$111$		0			0
$112$	6.75214	−	0.613225i	0.638018	−	0.0579443i
$113$	5.48164	+	9.49448i	0.515670	+	0.893166i	0.999835	+	0.0181892i	$0.00579012\pi$
$113$	5.48164	+	9.49448i	0.515670	+	0.893166i	−0.484165	+	0.874977i	$0.660877\pi$
$114$		0			0
$115$	3.96422	−	2.28874i	0.369665	−	0.213426i
$116$	−7.34795	+	12.7270i	−0.682240	+	1.18167i
$117$		0			0
$118$	5.39060			0.496245
$119$	−0.374250	+	0.0339891i	−0.0343074	+	0.00311578i
$120$		0			0
$121$	2.36975	−	4.10453i	0.215432	−	0.373139i
$122$	−2.53892	−	1.46584i	−0.229863	−	0.132711i
$123$		0			0
$124$	4.31406	+	2.49073i	0.387414	+	0.223674i
$125$			9.29184i			0.831087i
$126$		0			0
$127$	−1.00394	+	1.73887i	−0.0890849	+	0.154300i	−0.907125	−	0.420862i	$-0.861728\pi$
$127$	−1.00394	+	1.73887i	−0.0890849	+	0.154300i	0.818040	+	0.575162i	$0.195061\pi$
$128$		−	11.3671i		−	1.00472i
$129$		0			0
$130$	1.14299	+	1.49175i	0.100247	+	0.130836i
$131$	−6.22511	−	10.7822i	−0.543890	−	0.942046i	−0.998676	−	0.0514449i	$-0.983617\pi$
$131$	−6.22511	−	10.7822i	−0.543890	−	0.942046i	0.454785	−	0.890601i	$-0.349716\pi$
$132$		0			0
$133$	−13.2320	−	6.11702i	−1.14736	−	0.530413i
$134$	1.28608	+	2.22756i	0.111101	+	0.192432i
$135$		0			0
$136$			0.266310i			0.0228359i
$137$			5.24518i			0.448126i	0.974575	+	0.224063i	$0.0719321\pi$
$137$			5.24518i			0.448126i	−0.974575	+	0.224063i	$0.928068\pi$
$138$		0			0
$139$	10.3693	+	17.9601i	0.879510	+	1.52336i	0.851880	+	0.523737i	$0.175463\pi$
$139$	10.3693	+	17.9601i	0.879510	+	1.52336i	0.0276301	+	0.999618i	$0.491204\pi$
$140$	3.94468	−	2.78157i	0.333387	−	0.235085i
$141$		0			0
$142$	−0.924676	−	1.60159i	−0.0775971	−	0.134402i
$143$	−11.3545	+	8.69991i	−0.949513	+	0.727523i
$144$		0			0
$145$			8.75428i			0.727004i
$146$	1.65316	−	2.86335i	0.136816	−	0.236973i
$147$		0			0
$148$		−	1.47559i		−	0.121293i
$149$	−0.00985188	−	0.00568799i	−0.000807098	−	0.000465978i	0.499596	−	0.866258i	$-0.333482\pi$
$149$	−0.00985188	−	0.00568799i	−0.000807098	−	0.000465978i	−0.500403	+	0.865792i	$0.666815\pi$
$150$		0			0
$151$	−16.3726	−	9.45271i	−1.33238	−	0.769251i	−0.346717	−	0.937970i	$-0.612704\pi$
$151$	−16.3726	−	9.45271i	−1.33238	−	0.769251i	−0.985664	+	0.168719i	$0.946037\pi$
$152$	−5.16529	+	8.94654i	−0.418960	+	0.725660i
$153$		0			0
$154$	−3.02438	−	4.28903i	−0.243712	−	0.345620i
$155$	2.96743			0.238350
$156$		0			0
$157$	−9.89687	+	17.1419i	−0.789856	+	1.36807i	0.136198	+	0.990682i	$0.456512\pi$
$157$	−9.89687	+	17.1419i	−0.789856	+	1.36807i	−0.926054	+	0.377390i	$0.876822\pi$
$158$	−5.16255	+	2.98060i	−0.410710	+	0.237124i
$159$		0			0
$160$	−2.62243	−	4.54219i	−0.207321	−	0.359091i
$161$	11.5698	−	1.05076i	0.911830	−	0.0828117i
$162$		0			0
$163$	7.73581	+	4.46627i	0.605915	+	0.349825i	0.771365	−	0.636393i	$-0.219574\pi$
$163$	7.73581	+	4.46627i	0.605915	+	0.349825i	−0.165450	+	0.986218i	$0.552908\pi$
$164$	−18.3343	−	10.5853i	−1.43167	−	0.826572i
$165$		0			0
$166$	1.43657			0.111499
$167$	−5.31279	−	3.06734i	−0.411116	−	0.237358i	0.280153	−	0.959955i	$-0.409615\pi$
$167$	−5.31279	−	3.06734i	−0.411116	−	0.237358i	−0.691269	+	0.722597i	$0.742948\pi$
$168$		0			0
$169$	12.5618	−	3.34692i	0.966290	−	0.257456i
$170$	0.0370161	+	0.0641138i	0.00283900	+	0.00491730i
$171$		0			0
$172$	4.22036	+	7.30987i	0.321799	+	0.557373i
$173$	−12.1314	+	21.0122i	−0.922332	+	1.59753i	−0.126535	+	0.991962i	$0.540386\pi$
$173$	−12.1314	+	21.0122i	−0.922332	+	1.59753i	−0.795797	+	0.605563i	$0.792948\pi$
$174$		0			0
$175$	−4.34454	+	9.39784i	−0.328416	+	0.710410i
$176$	8.80446	−	5.08325i	0.663661	−	0.383165i
$177$		0			0
$178$	−0.873801			−0.0654942
$179$	2.06838	+	3.58253i	0.154598	+	0.267771i	0.932912	−	0.360103i	$-0.117259\pi$
$179$	2.06838	+	3.58253i	0.154598	+	0.267771i	−0.778315	+	0.627874i	$0.783925\pi$
$180$		0			0
$181$	−7.86568			−0.584651			−0.292326	−	0.956319i	$-0.594429\pi$
$181$	−7.86568			−0.584651			−0.292326	+	0.956319i	$0.594429\pi$
$182$	1.04442	+	4.65381i	0.0774176	+	0.344964i
$183$		0			0
$184$		−	8.23289i		−	0.606937i
$185$	−0.439501	−	0.761237i	−0.0323127	−	0.0559673i
$186$		0			0
$187$	−0.488003	+	0.281749i	−0.0356863	+	0.0206035i
$188$	6.90560	−	3.98695i	0.503642	−	0.290778i
$189$		0			0
$190$			2.87182i			0.208344i
$191$	−3.23933	+	5.61069i	−0.234390	+	0.405975i	−0.959095	−	0.283084i	$-0.908643\pi$
$191$	−3.23933	+	5.61069i	−0.234390	+	0.405975i	0.724705	+	0.689059i	$0.241976\pi$
$192$		0			0
$193$	4.18228	−	2.41464i	0.301047	−	0.173810i	−0.341866	−	0.939749i	$-0.611059\pi$
$193$	4.18228	−	2.41464i	0.301047	−	0.173810i	0.642913	+	0.765939i	$0.277726\pi$
$194$	−0.675708	−	1.17036i	−0.0485130	−	0.0840270i
$195$		0			0
$196$	12.0497	−	2.20689i	0.860690	−	0.157635i
$197$	22.3748	+	12.9181i	1.59414	+	0.920377i	0.992586	+	0.121545i	$0.0387850\pi$
$197$	22.3748	+	12.9181i	1.59414	+	0.920377i	0.601554	+	0.798832i	$0.294548\pi$
$198$		0			0
$199$	−17.1146			−1.21322			−0.606612	−	0.794998i	$-0.707472\pi$
$199$	−17.1146			−1.21322			−0.606612	+	0.794998i	$0.707472\pi$
$200$	6.35417	+	3.66858i	0.449308	+	0.259408i
$201$		0			0
$202$	−4.96749	+	2.86798i	−0.349511	+	0.201790i
$203$	−9.32312	+	20.1672i	−0.654355	+	1.41546i
$204$		0			0
$205$	−12.6112			−0.880806
$206$	1.80540	−	1.04235i	0.125788	−	0.0726238i
$207$		0			0
$208$	−9.16129	+	1.19953i	−0.635221	+	0.0831725i
$209$	−21.8589			−1.51201
$210$		0			0
$211$	−9.14557	+	15.8406i	−0.629607	+	1.09051i	0.358024	+	0.933713i	$0.383451\pi$
$211$	−9.14557	+	15.8406i	−0.629607	+	1.09051i	−0.987631	+	0.156799i	$0.949883\pi$
$212$	−0.244652	+	0.423750i	−0.0168028	+	0.0291032i
$213$		0			0
$214$			4.24360i			0.290086i
$215$	4.35446	+	2.51405i	0.296972	+	0.171457i
$216$		0			0
$217$	6.83606	+	3.16025i	0.464062	+	0.214532i
$218$	1.60755	−	2.78435i	0.108877	−	0.188580i
$219$		0			0
$220$	3.61887	−	6.26806i	0.243984	−	0.422593i
$221$	0.507782	−	0.0664862i	0.0341571	−	0.00447235i
$222$		0			0
$223$	−9.96682	−	5.75435i	−0.667428	−	0.385340i	0.127674	−	0.991816i	$-0.459249\pi$
$223$	−9.96682	−	5.75435i	−0.667428	−	0.385340i	−0.795101	+	0.606477i	$0.792582\pi$
$224$	−1.20396	−	13.2567i	−0.0804430	−	0.885747i
$225$		0			0
$226$	4.74711	−	2.74075i	0.315773	−	0.182312i
$227$			17.9045i			1.18836i	0.804332	+	0.594181i	$0.202524\pi$
$227$			17.9045i			1.18836i	−0.804332	+	0.594181i	$0.797476\pi$
$228$		0			0
$229$	−3.34589	+	1.93175i	−0.221103	+	0.127654i	−0.606461	−	0.795113i	$-0.707411\pi$
$229$	−3.34589	+	1.93175i	−0.221103	+	0.127654i	0.385358	+	0.922767i	$0.374078\pi$
$230$	−1.14434	−	1.98206i	−0.0754556	−	0.130693i
$231$		0			0
$232$	13.6357	+	7.87256i	0.895226	+	0.516859i
$233$	−12.5321	−	21.7062i	−0.821004	−	1.42202i	−0.904935	−	0.425549i	$-0.860081\pi$
$233$	−12.5321	−	21.7062i	−0.821004	−	1.42202i	0.0839312	−	0.996472i	$-0.473252\pi$
$234$		0			0
$235$	2.37501	−	4.11363i	0.154928	−	0.268344i
$236$			18.8678i			1.22819i
$237$		0			0
$238$	0.0169941	+	0.187120i	0.00110156	+	0.0121292i
$239$			7.80462i			0.504839i	0.967618	+	0.252419i	$0.0812263\pi$
$239$			7.80462i			0.504839i	−0.967618	+	0.252419i	$0.918774\pi$
$240$		0			0
$241$		−	21.7653i		−	1.40202i	−0.713150	−	0.701012i	$-0.752732\pi$
$241$		−	21.7653i		−	1.40202i	0.713150	−	0.701012i	$-0.247268\pi$
$242$	−2.05221	−	1.18484i	−0.131921	−	0.0761647i
$243$		0			0
$244$	5.13063	−	8.88652i	0.328455	−	0.568901i
$245$	5.55895	−	4.72747i	0.355149	−	0.302027i
$246$		0			0
$247$	18.3482	+	7.61524i	1.16747	+	0.484546i
$248$	2.66855	−	4.62207i	0.169453	−	0.293502i
$249$		0			0
$250$	4.64579			0.293826
$251$	−3.83990	−	6.65090i	−0.242372	−	0.419801i	0.719017	−	0.694992i	$-0.244592\pi$
$251$	−3.83990	−	6.65090i	−0.242372	−	0.419801i	−0.961390	+	0.275191i	$0.911259\pi$
$252$		0			0
$253$	15.0865	−	8.71017i	0.948478	−	0.547604i
$254$	0.869411	+	0.501955i	0.0545517	+	0.0314954i
$255$		0			0
$256$	−0.464141			−0.0290088
$257$	13.6237			0.849826			0.424913	−	0.905234i	$-0.360305\pi$
$257$	13.6237			0.849826			0.424913	+	0.905234i	$0.360305\pi$
$258$		0			0
$259$	−0.201775	−	2.22172i	−0.0125377	−	0.138051i
$260$	−5.22132	+	4.00061i	−0.323813	+	0.248107i
$261$		0			0
$262$	−5.39096	+	3.11247i	−0.333055	+	0.192289i
$263$	−5.86158	−	10.1525i	−0.361440	−	0.626033i	0.626758	−	0.779214i	$-0.284382\pi$
$263$	−5.86158	−	10.1525i	−0.361440	−	0.626033i	−0.988198	+	0.153181i	$0.951048\pi$
$264$		0			0
$265$			0.291476i			0.0179052i
$266$	−3.05843	+	6.61580i	−0.187524	+	0.405641i
$267$		0			0
$268$	−7.79673	+	4.50144i	−0.476261	+	0.274970i
$269$	−9.19876			−0.560858			−0.280429	−	0.959875i	$-0.590477\pi$
$269$	−9.19876			−0.560858			−0.280429	+	0.959875i	$0.590477\pi$
$270$		0			0
$271$			2.56369i			0.155733i	0.996964	+	0.0778665i	$0.0248108\pi$
$271$			2.56369i			0.155733i	−0.996964	+	0.0778665i	$0.975189\pi$
$272$	−0.363976			−0.0220693
$273$		0			0
$274$	2.62252			0.158432
$275$			15.5250i			0.936195i
$276$		0			0
$277$	0.933882			0.0561115			0.0280558	−	0.999606i	$-0.491068\pi$
$277$	0.933882			0.0561115			0.0280558	+	0.999606i	$0.491068\pi$
$278$	8.97981	−	5.18450i	0.538573	−	0.310945i
$279$		0			0
$280$	−2.98016	−	4.22632i	−0.178099	−	0.252571i
$281$			6.45288i			0.384947i	0.981302	+	0.192473i	$0.0616509\pi$
$281$			6.45288i			0.384947i	−0.981302	+	0.192473i	$0.938349\pi$
$282$		0			0
$283$	11.0873	+	19.2037i	0.659071	+	1.14154i	0.980857	+	0.194731i	$0.0623835\pi$
$283$	11.0873	+	19.2037i	0.659071	+	1.14154i	−0.321786	+	0.946812i	$0.604283\pi$
$284$	5.60575	−	3.23648i	0.332640	−	0.192050i
$285$		0			0
$286$	4.34984	+	5.67711i	0.257211	+	0.335695i
$287$	−29.0524	−	13.4307i	−1.71491	−	0.792788i
$288$		0			0
$289$	−16.9798			−0.998813
$290$	4.37702			0.257028
$291$		0			0
$292$	10.0221	+	5.78625i	0.586498	+	0.338615i
$293$	20.9600	−	12.1013i	1.22450	−	0.706964i	0.258624	−	0.965978i	$-0.416731\pi$
$293$	20.9600	−	12.1013i	1.22450	−	0.706964i	0.965874	+	0.259014i	$0.0833976\pi$
$294$		0			0
$295$	5.61972	+	9.73364i	0.327193	+	0.566714i
$296$	−1.58094			−0.0918902
$297$		0			0
$298$	−0.00284392	+	0.00492581i	−0.000164744	+	0.000285345i
$299$	−15.6979	+	2.05540i	−0.907833	+	0.118867i
$300$		0			0
$301$	7.35395	+	10.4290i	0.423875	+	0.601118i
$302$	−4.72623	+	8.18607i	−0.271964	+	0.471055i
$303$		0			0
$304$	−12.2276	−	7.05959i	−0.701299	−	0.404895i
$305$		−	6.11259i		−	0.350006i
$306$		0			0
$307$		−	24.2924i		−	1.38644i	−0.720726	−	0.693220i	$-0.756191\pi$
$307$		−	24.2924i		−	1.38644i	0.720726	−	0.693220i	$-0.243809\pi$
$308$	15.0121	−	10.5857i	0.855395	−	0.603176i
$309$		0			0
$310$		−	1.48367i		−	0.0842671i
$311$	−1.99355	+	3.45294i	−0.113044	+	0.195798i	−0.916996	−	0.398896i	$-0.869393\pi$
$311$	−1.99355	+	3.45294i	−0.113044	+	0.195798i	0.803952	+	0.594694i	$0.202727\pi$
$312$		0			0
$313$	−14.2377	−	24.6604i	−0.804763	−	1.39389i	−0.916451	−	0.400147i	$-0.868959\pi$
$313$	−14.2377	−	24.6604i	−0.804763	−	1.39389i	0.111688	−	0.993743i	$-0.464374\pi$
$314$	8.57071	+	4.94830i	0.483673	+	0.279249i
$315$		0			0
$316$	−10.4324	−	18.0695i	−0.586871	−	1.01649i
$317$	14.5632	−	8.40806i	0.817950	−	0.472244i	−0.0317591	−	0.999496i	$-0.510111\pi$
$317$	14.5632	−	8.40806i	0.817950	−	0.472244i	0.849709	+	0.527252i	$0.176778\pi$
$318$		0			0
$319$			33.3158i			1.86533i
$320$	2.35600	−	1.36024i	0.131704	−	0.0760396i
$321$		0			0
$322$	−0.525367	−	5.78476i	−0.0292776	−	0.322372i
$323$	0.677736	+	0.391291i	0.0377102	+	0.0217720i
$324$		0			0
$325$	5.40863	−	13.0316i	0.300017	−	0.722862i
$326$	2.23308	−	3.86780i	0.123679	−	0.214218i
$327$		0			0
$328$	−11.3410	+	19.6432i	−0.626204	+	1.08462i
$329$	9.85222	−	6.94723i	0.543171	−	0.383013i
$330$		0			0
$331$	5.37730	+	3.10459i	0.295563	+	0.170644i	0.640448	−	0.768002i	$-0.278749\pi$
$331$	5.37730	+	3.10459i	0.295563	+	0.170644i	−0.344885	+	0.938645i	$0.612082\pi$
$332$			5.02816i			0.275956i
$333$		0			0
$334$	−1.53363	+	2.65633i	−0.0839165	+	0.145348i
$335$	−2.68149	+	4.64448i	−0.146505	+	0.253755i
$336$		0			0
$337$	7.69650			0.419255			0.209628	−	0.977781i	$-0.432775\pi$
$337$	7.69650			0.419255			0.209628	+	0.977781i	$0.432775\pi$
$338$	−1.67342	−	6.28072i	−0.0910219	−	0.341626i
$339$		0			0
$340$	−0.224406	+	0.129561i	−0.0121701	+	0.00702642i
$341$	11.2930			0.611552
$342$		0			0
$343$	17.8408	−	4.97049i	0.963313	−	0.268381i
$344$	7.83177	−	4.52167i	0.422261	−	0.243792i
$345$		0			0
$346$	10.5058	+	6.06553i	0.564795	+	0.326085i
$347$	−30.4094			−1.63246			−0.816231	−	0.577725i	$-0.803941\pi$
$347$	−30.4094			−1.63246			−0.816231	+	0.577725i	$0.803941\pi$
$348$		0			0
$349$	−13.9933	−	8.07906i	−0.749046	−	0.432462i	0.0763028	−	0.997085i	$-0.475688\pi$
$349$	−13.9933	−	8.07906i	−0.749046	−	0.432462i	−0.825349	+	0.564623i	$0.809022\pi$
$350$	4.69880	+	2.17221i	0.251161	+	0.116110i
$351$		0			0
$352$	−9.98008	−	17.2860i	−0.531940	−	0.921347i
$353$	10.2558	−	5.92119i	0.545861	−	0.315153i	−0.201590	−	0.979470i	$-0.564611\pi$
$353$	10.2558	−	5.92119i	0.545861	−	0.315153i	0.747451	+	0.664317i	$0.231277\pi$
$354$		0			0
$355$	1.92796	−	3.33932i	0.102325	−	0.177233i
$356$		−	3.05841i		−	0.162095i
$357$		0			0
$358$	1.79122	−	1.03416i	0.0946688	−	0.0546571i
$359$	27.1631	−	15.6826i	1.43362	−	0.827698i	0.436221	−	0.899840i	$-0.356317\pi$
$359$	27.1631	−	15.6826i	1.43362	−	0.827698i	0.997394	+	0.0721417i	$0.0229834\pi$
$360$		0			0
$361$	5.67876	+	9.83591i	0.298882	+	0.517679i
$362$			3.93273i			0.206700i
$363$		0			0
$364$	−16.2889	+	3.65560i	−0.853770	+	0.191605i
$365$	6.89369			0.360832
$366$		0			0
$367$	−12.0387	−	20.8517i	−0.628415	−	1.08845i	−0.987870	−	0.155285i	$-0.950370\pi$
$367$	−12.0387	−	20.8517i	−0.628415	−	1.08845i	0.359454	−	0.933163i	$-0.382963\pi$
$368$	11.2522			0.586562
$369$		0			0
$370$	−0.380608	+	0.219744i	−0.0197869	+	0.0114240i
$371$	−0.310416	+	0.671473i	−0.0161160	+	0.0348611i
$372$		0			0
$373$	9.19612	−	15.9281i	0.476157	−	0.824728i	−0.523470	−	0.852044i	$-0.675363\pi$
$373$	9.19612	−	15.9281i	0.476157	−	0.824728i	0.999627	+	0.0273160i	$0.00869604\pi$
$374$	0.140871	+	0.243995i	0.00728425	+	0.0126167i
$375$		0			0
$376$	−4.27160	−	7.39862i	−0.220291	−	0.381555i
$377$	11.6066	−	27.9650i	0.597771	−	1.44027i
$378$		0			0
$379$	−7.04719	−	4.06870i	−0.361990	−	0.208995i	0.307963	−	0.951398i	$-0.400353\pi$
$379$	−7.04719	−	4.06870i	−0.361990	−	0.208995i	−0.669953	+	0.742403i	$0.733686\pi$
$380$	−10.0517			−0.515642
$381$		0			0
$382$	2.80527	+	1.61962i	0.143530	+	0.0828671i
$383$	19.3739	+	11.1856i	0.989962	+	0.571555i	0.905263	−	0.424852i	$-0.139674\pi$
$383$	19.3739	+	11.1856i	0.989962	+	0.571555i	0.0846992	+	0.996407i	$0.473007\pi$
$384$		0			0
$385$	4.59164	−	9.93236i	0.234012	−	0.506200i
$386$	−1.20729	−	2.09108i	−0.0614493	−	0.106433i
$387$		0			0
$388$	4.09641	−	2.36506i	0.207963	−	0.120068i
$389$	10.6973	−	18.5283i	0.542374	−	0.939420i	−0.456393	−	0.889778i	$-0.650859\pi$
$389$	10.6973	−	18.5283i	0.542374	−	0.939420i	0.998767	−	0.0496415i	$-0.0158079\pi$
$390$		0			0
$391$	−0.623674			−0.0315406
$392$	−2.36445	−	12.9100i	−0.119423	−	0.652051i
$393$		0			0
$394$	6.45888	−	11.1871i	0.325394	−	0.563599i
$395$	−10.7639	−	6.21456i	−0.541592	−	0.312689i
$396$		0			0
$397$	1.03640	+	0.598365i	0.0520154	+	0.0300311i	0.525782	−	0.850619i	$-0.323773\pi$
$397$	1.03640	+	0.598365i	0.0520154	+	0.0300311i	−0.473767	+	0.880650i	$0.657106\pi$
$398$			8.55708i			0.428928i
$399$		0			0
$400$	−5.01399	+	8.68449i	−0.250699	+	0.434224i
$401$		−	36.2749i		−	1.81148i	−0.423831	−	0.905741i	$-0.639315\pi$
$401$		−	36.2749i		−	1.81148i	0.423831	−	0.905741i	$-0.360685\pi$
$402$		0			0
$403$	−9.47926	−	3.93428i	−0.472196	−	0.195980i
$404$	−10.0383	−	17.3868i	−0.499423	−	0.865026i
$405$		0			0
$406$	10.0833	+	4.66144i	0.500428	+	0.231343i
$407$	−1.67259	−	2.89701i	−0.0829072	−	0.143599i
$408$		0			0
$409$			14.6723i			0.725500i	0.931887	+	0.362750i	$0.118162\pi$
$409$			14.6723i			0.725500i	−0.931887	+	0.362750i	$0.881838\pi$
$410$			6.30544i			0.311404i
$411$		0			0
$412$	3.64834	+	6.31912i	0.179741	+	0.311321i
$413$	2.58002	+	28.4082i	0.126954	+	1.39788i
$414$		0			0
$415$	1.49763	+	2.59397i	0.0735156	+	0.127333i
$416$	2.35507	+	17.9866i	0.115467	+	0.881866i
$417$		0			0
$418$			10.9292i			0.534563i
$419$	−2.96674	+	5.13855i	−0.144935	+	0.251034i	−0.929349	−	0.369203i	$-0.879631\pi$
$419$	−2.96674	+	5.13855i	−0.144935	+	0.251034i	0.784414	+	0.620238i	$0.212964\pi$
$420$		0			0
$421$			2.63174i			0.128263i	0.997941	+	0.0641317i	$0.0204278\pi$
$421$			2.63174i			0.128263i	−0.997941	+	0.0641317i	$0.979572\pi$
$422$	7.92008	+	4.57266i	0.385544	+	0.222594i
$423$		0			0
$424$	0.454004	+	0.262119i	0.0220484	+	0.0127296i
$425$	0.277910	−	0.481354i	0.0134806	−	0.0233491i
$426$		0			0
$427$	6.50978	−	14.0816i	0.315030	−	0.681454i
$428$	−14.8531			−0.717952
$429$		0			0
$430$	1.25699	−	2.17717i	0.0606175	−	0.104993i
$431$	−16.3139	+	9.41883i	−0.785812	+	0.453689i	−0.838486	−	0.544923i	$-0.816559\pi$
$431$	−16.3139	+	9.41883i	−0.785812	+	0.453689i	0.0526738	+	0.998612i	$0.483226\pi$
$432$		0			0
$433$	9.56773	+	16.5718i	0.459796	+	0.796389i	0.998950	−	0.0458176i	$-0.0145893\pi$
$433$	9.56773	+	16.5718i	0.459796	+	0.796389i	−0.539154	+	0.842207i	$0.681256\pi$
$434$	1.58008	−	3.41794i	0.0758463	−	0.164066i
$435$		0			0
$436$	9.74557	+	5.62661i	0.466728	+	0.269466i
$437$	−20.9520	−	12.0966i	−1.00227	−	0.578660i
$438$		0			0
$439$	1.26511			0.0603803			0.0301901	−	0.999544i	$-0.490389\pi$
$439$	1.26511			0.0603803			0.0301901	+	0.999544i	$0.490389\pi$
$440$	−6.71557	−	3.87724i	−0.320152	−	0.184840i
$441$		0			0
$442$	−0.0332422	−	0.253884i	−0.00158117	−	0.0120760i
$443$	−10.4696	−	18.1339i	−0.497426	−	0.861568i	0.502569	−	0.864537i	$-0.332388\pi$
$443$	−10.4696	−	18.1339i	−0.497426	−	0.861568i	−0.999996	+	0.00296930i	$0.999055\pi$
$444$		0			0
$445$	−0.910940	−	1.57779i	−0.0431827	−	0.0747946i
$446$	−2.87710	+	4.98328i	−0.136234	+	0.235965i
$447$		0			0
$448$	6.87614	−	0.624486i	0.324867	−	0.0295042i
$449$	−15.4700	+	8.93162i	−0.730075	+	0.421509i	−0.818450	−	0.574578i	$-0.805166\pi$
$449$	−15.4700	+	8.93162i	−0.730075	+	0.421509i	0.0883746	+	0.996087i	$0.471833\pi$
$450$		0			0
$451$	−47.9940			−2.25995
$452$	9.59295	+	16.6155i	0.451214	+	0.781526i
$453$		0			0
$454$	8.95199			0.420138
$455$	−7.31443	+	6.73749i	−0.342906	+	0.315858i
$456$		0			0
$457$		−	6.56597i		−	0.307143i	−0.988138	−	0.153571i	$-0.950922\pi$
$457$		−	6.56597i		−	0.307143i	0.988138	−	0.153571i	$-0.0490775\pi$
$458$	0.965850	+	1.67290i	0.0451312	+	0.0781695i
$459$		0			0
$460$	6.93744	−	4.00533i	0.323460	−	0.186749i
$461$	4.42854	−	2.55682i	0.206258	−	0.119083i	−0.393313	−	0.919404i	$-0.628671\pi$
$461$	4.42854	−	2.55682i	0.206258	−	0.119083i	0.599571	+	0.800322i	$0.295338\pi$
$462$		0			0
$463$			33.3239i			1.54869i	0.632761	+	0.774347i	$0.281921\pi$
$463$			33.3239i			1.54869i	−0.632761	+	0.774347i	$0.718079\pi$
$464$	−10.7597	+	18.6364i	−0.499508	+	0.865173i
$465$		0			0
$466$	−10.8528	+	6.26587i	−0.502747	+	0.290261i
$467$	6.47472	+	11.2145i	0.299614	+	0.518947i	0.976048	−	0.217557i	$-0.0698087\pi$
$467$	6.47472	+	11.2145i	0.299614	+	0.518947i	−0.676433	+	0.736504i	$0.736475\pi$
$468$		0			0
$469$	−11.1236	+	7.84374i	−0.513641	+	0.362190i
$470$	−2.05676	−	1.18747i	−0.0948713	−	0.0547740i
$471$		0			0
$472$	20.2148			0.930463
$473$	16.5716	+	9.56761i	0.761962	+	0.439919i
$474$		0			0
$475$	18.6724	−	10.7805i	0.856750	−	0.494645i
$476$	−0.654942	+	0.0594814i	−0.0300192	+	0.00272633i
$477$		0			0
$478$	3.90221			0.178483
$479$	−23.3930	+	13.5060i	−1.06885	+	0.617104i	−0.927868	−	0.372908i	$-0.878361\pi$
$479$	−23.3930	+	13.5060i	−1.06885	+	0.617104i	−0.140987	+	0.990012i	$0.545027\pi$
$480$		0			0
$481$	0.394692	+	3.01442i	0.0179964	+	0.137446i
$482$	−10.8823			−0.495677
$483$		0			0
$484$	4.14710	−	7.18299i	0.188505	−	0.326499i
$485$	1.40886	−	2.44021i	0.0639729	−	0.110804i
$486$		0			0
$487$		−	32.0838i		−	1.45386i	−0.686713	−	0.726928i	$-0.740947\pi$
$487$		−	32.0838i		−	1.45386i	0.686713	−	0.726928i	$-0.259053\pi$
$488$	−9.52097	−	5.49694i	−0.430994	−	0.248835i
$489$		0			0
$490$	−2.36367	−	2.77940i	−0.106780	−	0.125561i
$491$	14.3020	−	24.7718i	0.645440	−	1.11793i	−0.338760	−	0.940873i	$-0.610008\pi$
$491$	14.3020	−	24.7718i	0.645440	−	1.11793i	0.984200	−	0.177061i	$-0.0566591\pi$
$492$		0			0
$493$	0.596378	−	1.03296i	0.0268595	−	0.0465220i
$494$	3.80752	−	9.17385i	0.171308	−	0.412751i
$495$		0			0
$496$	6.31716	+	3.64721i	0.283649	+	0.163765i
$497$	7.99773	−	5.63954i	0.358747	−	0.252968i
$498$		0			0
$499$	1.55726	−	0.899082i	0.0697123	−	0.0402484i	−0.464739	−	0.885448i	$-0.653852\pi$
$499$	1.55726	−	0.899082i	0.0697123	−	0.0402484i	0.534451	+	0.845199i	$0.320518\pi$
$500$			16.2608i			0.727207i
$501$		0			0
$502$	−3.32536	+	1.91990i	−0.148418	+	0.0856893i
$503$	14.5386	+	25.1816i	0.648245	+	1.12279i	0.983542	+	0.180681i	$0.0578300\pi$
$503$	14.5386	+	25.1816i	0.648245	+	1.12279i	−0.335297	+	0.942112i	$0.608837\pi$
$504$		0			0
$505$	−10.3572	−	5.97976i	−0.460891	−	0.266096i
$506$	−4.35497	−	7.54303i	−0.193602	−	0.335329i
$507$		0			0
$508$	−1.75690	+	3.04304i	−0.0779499	+	0.135013i
$509$		−	23.1913i		−	1.02794i	−0.857809	−	0.513969i	$-0.828175\pi$
$509$		−	23.1913i		−	1.02794i	0.857809	−	0.513969i	$-0.171825\pi$
$510$		0			0
$511$	15.8810	+	7.34163i	0.702532	+	0.324774i
$512$		−	22.5022i		−	0.994464i
$513$		0			0
$514$		−	6.81169i		−	0.300451i
$515$	3.76427	+	2.17330i	0.165874	+	0.0957671i
$516$		0			0
$517$	9.03847	−	15.6551i	0.397511	−	0.688510i
$518$	−1.11083	+	0.100885i	−0.0488070	+	0.00443262i
$519$		0			0
$520$	4.28624	+	5.59410i	0.187964	+	0.245318i
$521$	16.6255	−	28.7962i	0.728376	−	1.26158i	−0.229193	−	0.973381i	$-0.573609\pi$
$521$	16.6255	−	28.7962i	0.728376	−	1.26158i	0.957569	−	0.288203i	$-0.0930579\pi$
$522$		0			0
$523$	38.7121			1.69276			0.846380	−	0.532579i	$-0.178777\pi$
$523$	38.7121			1.69276			0.846380	+	0.532579i	$0.178777\pi$
$524$	−10.8940	−	18.8690i	−0.475908	−	0.824296i
$525$		0			0
$526$	−5.07614	+	2.93071i	−0.221330	+	0.127785i
$527$	−0.350140	−	0.202153i	−0.0152523	−	0.00880594i
$528$		0			0
$529$	−3.71931			−0.161709
$530$	0.145734			0.00633029
$531$		0			0
$532$	−23.1561	−	10.7049i	−1.00394	−	0.464115i
$533$	40.2857	+	16.7202i	1.74497	+	0.724233i
$534$		0			0
$535$	−7.66253	+	4.42396i	−0.331280	+	0.191265i
$536$	4.82283	+	8.35338i	0.208314	+	0.360811i
$537$		0			0
$538$			4.59926i			0.198288i
$539$	21.1555	−	17.9911i	0.911231	−	0.774933i
$540$		0			0
$541$	−19.6306	+	11.3337i	−0.843986	+	0.487275i	−0.858617	−	0.512618i	$-0.828676\pi$
$541$	−19.6306	+	11.3337i	−0.843986	+	0.487275i	0.0146313	+	0.999893i	$0.495343\pi$
$542$	1.28181			0.0550585
$543$		0			0
$544$			0.714603i			0.0306384i
$545$	6.70349			0.287146
$546$		0			0
$547$	−9.21134			−0.393848			−0.196924	−	0.980419i	$-0.563095\pi$
$547$	−9.21134			−0.393848			−0.196924	+	0.980419i	$0.563095\pi$
$548$			9.17913i			0.392113i
$549$		0			0
$550$	7.76231			0.330986
$551$	40.0699	−	23.1344i	1.70704	−	0.985558i
$552$		0			0
$553$	−18.1785	−	25.7798i	−0.773027	−	1.09627i
$554$		−	0.466928i		−	0.0198379i
$555$		0			0
$556$	18.1464	+	31.4304i	0.769577	+	1.33295i
$557$	−9.81039	+	5.66403i	−0.415680	+	0.239993i	−0.693227	−	0.720719i	$-0.743812\pi$
$557$	−9.81039	+	5.66403i	−0.415680	+	0.239993i	0.277547	+	0.960712i	$0.410478\pi$
$558$		0			0
$559$	−10.5769	−	13.8042i	−0.447354	−	0.583855i
$560$	5.77627	−	4.07310i	0.244092	−	0.172120i
$561$		0			0
$562$	3.22636			0.136096
$563$	32.6386			1.37555			0.687777	−	0.725922i	$-0.258586\pi$
$563$	32.6386			1.37555			0.687777	+	0.725922i	$0.258586\pi$
$564$		0			0
$565$	9.89776	+	5.71448i	0.416402	+	0.240410i
$566$	9.60161	−	5.54349i	0.403586	−	0.233010i
$567$		0			0
$568$	−3.46755	−	6.00597i	−0.145495	−	0.252005i
$569$	35.0091			1.46766			0.733829	−	0.679335i	$-0.237731\pi$
$569$	35.0091			1.46766			0.733829	+	0.679335i	$0.237731\pi$
$570$		0			0
$571$	13.1273	−	22.7371i	0.549360	−	0.951519i	−0.448959	−	0.893552i	$-0.648205\pi$
$571$	13.1273	−	22.7371i	0.549360	−	0.951519i	0.998319	−	0.0579663i	$-0.0184616\pi$
$572$	−19.8706	+	15.2250i	−0.830830	+	0.636587i
$573$		0			0
$574$	−6.71516	+	14.5258i	−0.280285	+	0.606296i
$575$	−8.59149	+	14.8809i	−0.358290	+	0.620576i
$576$		0			0
$577$	21.2806	+	12.2863i	0.885922	+	0.511487i	0.872606	−	0.488424i	$-0.162428\pi$
$577$	21.2806	+	12.2863i	0.885922	+	0.511487i	0.0133154	+	0.999911i	$0.495761\pi$
$578$			8.48969i			0.353124i
$579$		0			0
$580$			15.3201i			0.636133i
$581$	0.687561	+	7.57065i	0.0285248	+	0.314083i
$582$		0			0
$583$			1.10926i			0.0459408i
$584$	6.19936	−	10.7376i	0.256531	−	0.444325i
$585$		0			0
$586$	−6.05048	−	10.4797i	−0.249943	−	0.432914i
$587$	−17.7777	−	10.2640i	−0.733765	−	0.423639i	0.0860331	−	0.996292i	$-0.472581\pi$
$587$	−17.7777	−	10.2640i	−0.733765	−	0.423639i	−0.819798	+	0.572653i	$0.805914\pi$
$588$		0			0
$589$	−7.84184	−	13.5825i	−0.323117	−	0.559656i
$590$	4.86669	−	2.80978i	0.200358	−	0.115677i
$591$		0			0
$592$		−	2.16073i		−	0.0888054i
$593$	−33.1545	+	19.1417i	−1.36149	+	0.786057i	−0.989822	−	0.142308i	$-0.954548\pi$
$593$	−33.1545	+	19.1417i	−1.36149	+	0.786057i	−0.371669	+	0.928365i	$0.621214\pi$
$594$		0			0
$595$	−0.320160	+	0.225759i	−0.0131253	+	0.00925521i
$596$	−0.0172409	−	0.00995405i	−0.000706216	−	0.000407734i
$597$		0			0
$598$	1.02767	+	7.84874i	0.0420247	+	0.320959i
$599$	7.03567	−	12.1861i	0.287470	−	0.497912i	−0.685735	−	0.727851i	$-0.740519\pi$
$599$	7.03567	−	12.1861i	0.287470	−	0.497912i	0.973205	+	0.229939i	$0.0738526\pi$
$600$		0			0
$601$	10.1171	−	17.5233i	0.412685	−	0.714791i	−0.582498	−	0.812832i	$-0.697925\pi$
$601$	10.1171	−	17.5233i	0.412685	−	0.714791i	0.995182	+	0.0980417i	$0.0312579\pi$
$602$	5.21437	−	3.67688i	0.212522	−	0.149858i
$603$		0			0
$604$	−28.6522	−	16.5424i	−1.16584	−	0.673099i
$605$		−	4.94082i		−	0.200873i
$606$		0			0
$607$	−3.27563	+	5.67356i	−0.132954	+	0.230283i	−0.924814	−	0.380420i	$-0.875780\pi$
$607$	−3.27563	+	5.67356i	−0.132954	+	0.230283i	0.791860	+	0.610703i	$0.209113\pi$
$608$	−13.8603	+	24.0067i	−0.562108	+	0.973600i
$609$		0			0
$610$	−3.05621			−0.123742
$611$	−13.0407	+	9.99190i	−0.527572	+	0.404229i
$612$		0			0
$613$	28.8598	−	16.6622i	1.16564	−	0.672980i	0.212988	−	0.977055i	$-0.431681\pi$
$613$	28.8598	−	16.6622i	1.16564	−	0.672980i	0.952648	+	0.304075i	$0.0983472\pi$
$614$	−12.1459			−0.490168
$615$		0			0
$616$	−11.3415	−	16.0839i	−0.456961	−	0.648040i
$617$	−5.85466	+	3.38019i	−0.235700	+	0.136081i	−0.613199	−	0.789929i	$-0.710117\pi$
$617$	−5.85466	+	3.38019i	−0.235700	+	0.136081i	0.377499	+	0.926010i	$0.376784\pi$
$618$		0			0
$619$	15.2582	+	8.80931i	0.613278	+	0.354076i	0.774247	−	0.632883i	$-0.218129\pi$
$619$	15.2582	+	8.80931i	0.613278	+	0.354076i	−0.160970	+	0.986959i	$0.551462\pi$
$620$	5.19304			0.208558
$621$		0			0
$622$	1.72642	+	0.996751i	0.0692233	+	0.0399661i
$623$	−0.418213	−	4.60489i	−0.0167554	−	0.184491i
$624$		0			0
$625$	−4.93986	−	8.55609i	−0.197594	−	0.342244i
$626$	−12.3299	+	7.11866i	−0.492801	+	0.284519i
$627$		0			0
$628$	−17.3197	+	29.9985i	−0.691130	+	1.19707i
$629$			0.119762i			0.00477524i
$630$		0			0
$631$	13.6416	−	7.87596i	0.543062	−	0.313537i	−0.203257	−	0.979125i	$-0.565153\pi$
$631$	13.6416	−	7.87596i	0.543062	−	0.313537i	0.746319	+	0.665588i	$0.231819\pi$
$632$	−19.3596	+	11.1773i	−0.770084	+	0.444608i
$633$		0			0
$634$	−4.20392	−	7.28140i	−0.166959	−	0.289181i
$635$			2.09316i			0.0830644i
$636$		0			0
$637$	−24.0255	+	7.73143i	−0.951925	+	0.306330i
$638$	16.6575			0.659475
$639$		0			0
$640$	−5.92497	−	10.2623i	−0.234205	−	0.405655i
$641$	−20.9405			−0.827099			−0.413550	−	0.910482i	$-0.635711\pi$
$641$	−20.9405			−0.827099			−0.413550	+	0.910482i	$0.635711\pi$
$642$		0			0
$643$	−16.3952	+	9.46576i	−0.646563	+	0.373293i	−0.787138	−	0.616777i	$-0.788438\pi$
$643$	−16.3952	+	9.46576i	−0.646563	+	0.373293i	0.140575	+	0.990070i	$0.455105\pi$
$644$	20.2473	−	1.83885i	0.797857	−	0.0724608i
$645$		0			0
$646$	0.195640	−	0.338859i	0.00769736	−	0.0133322i
$647$	18.8384	+	32.6291i	0.740614	+	1.28278i	0.952216	+	0.305426i	$0.0987988\pi$
$647$	18.8384	+	32.6291i	0.740614	+	1.28278i	−0.211601	+	0.977356i	$0.567868\pi$
$648$		0			0
$649$	21.3867	+	37.0429i	0.839503	+	1.45406i
$650$	−6.51562	−	2.70424i	−0.255563	−	0.106069i
$651$		0			0
$652$	13.5378	+	7.81604i	0.530180	+	0.306100i
$653$	−29.0326			−1.13613			−0.568066	−	0.822983i	$-0.692308\pi$
$653$	−29.0326			−1.13613			−0.568066	+	0.822983i	$0.692308\pi$
$654$		0			0
$655$	−11.2402	−	6.48952i	−0.439190	−	0.253567i
$656$	−26.8472	−	15.5002i	−1.04821	−	0.605182i
$657$		0			0
$658$	−3.47352	−	4.92598i	−0.135412	−	0.192035i
$659$	−0.709152	−	1.22829i	−0.0276247	−	0.0478473i	0.851883	−	0.523733i	$-0.175461\pi$
$659$	−0.709152	−	1.22829i	−0.0276247	−	0.0478473i	−0.879507	+	0.475886i	$0.842128\pi$
$660$		0			0
$661$	−3.97764	+	2.29649i	−0.154712	+	0.0893231i	−0.575357	−	0.817902i	$-0.695137\pi$
$661$	−3.97764	+	2.29649i	−0.154712	+	0.0893231i	0.420645	+	0.907225i	$0.361804\pi$
$662$	1.55225	−	2.68858i	0.0603300	−	0.104495i
$663$		0			0
$664$	5.38715			0.209062
$665$	−15.1344	+	1.37449i	−0.586885	+	0.0533005i
$666$		0			0
$667$	−18.4368	+	31.9335i	−0.713877	+	1.23647i
$668$	−9.29746	−	5.36789i	−0.359730	−	0.207690i
$669$		0			0
$670$	2.32218	+	1.34071i	0.0897135	+	0.0517961i
$671$		−	23.2624i		−	0.898036i
$672$		0			0
$673$	−2.10111	+	3.63924i	−0.0809920	+	0.140282i	−0.903676	−	0.428216i	$-0.859142\pi$
$673$	−2.10111	+	3.63924i	−0.0809920	+	0.140282i	0.822684	+	0.568499i	$0.192475\pi$
$674$		−	3.84815i		−	0.148225i
$675$		0			0
$676$	21.9833	−	5.85716i	0.845510	−	0.225275i
$677$	4.04354	+	7.00361i	0.155406	+	0.269171i	0.933207	−	0.359340i	$-0.116998\pi$
$677$	4.04354	+	7.00361i	0.155406	+	0.269171i	−0.777801	+	0.628511i	$0.783665\pi$
$678$		0			0
$679$	5.84435	−	4.12110i	0.224285	−	0.158153i
$680$	0.138811	+	0.240427i	0.00532315	+	0.00921997i
$681$		0			0
$682$		−	5.64636i		−	0.216210i
$683$			24.6865i			0.944604i	0.881437	+	0.472302i	$0.156577\pi$
$683$			24.6865i			0.944604i	−0.881437	+	0.472302i	$0.843423\pi$
$684$		0			0
$685$	2.73398	+	4.73540i	0.104460	+	0.180930i
$686$	−2.48518	−	8.92016i	−0.0948846	−	0.340573i
$687$		0			0
$688$	6.17994	+	10.7040i	0.235608	+	0.408085i
$689$	0.386445	−	0.931102i	0.0147224	−	0.0354722i
$690$		0			0
$691$		−	11.2567i		−	0.428225i	−0.976809	−	0.214113i	$-0.931314\pi$
$691$		−	11.2567i		−	0.428225i	0.976809	−	0.214113i	$-0.0686859\pi$
$692$	−21.2301	+	36.7716i	−0.807047	+	1.39785i
$693$		0			0
$694$			15.2043i			0.577147i
$695$	18.7230	+	10.8097i	0.710202	+	0.410035i
$696$		0			0
$697$	1.48805	+	0.859128i	0.0563640	+	0.0325418i
$698$	−4.03942	+	6.99648i	−0.152894	+	0.264821i
$699$		0			0
$700$	−7.60300	+	16.4463i	−0.287366	+	0.621614i
$701$	−22.2305			−0.839635			−0.419818	−	0.907608i	$-0.637906\pi$
$701$	−22.2305			−0.839635			−0.419818	+	0.907608i	$0.637906\pi$
$702$		0			0
$703$	−2.32288	+	4.02335i	−0.0876091	+	0.151743i
$704$	8.96614	−	5.17660i	0.337924	−	0.195101i
$705$		0			0
$706$	−2.96052	−	5.12776i	−0.111420	−	0.192986i
$707$	−17.4916	−	24.8058i	−0.657841	−	0.932918i
$708$		0			0
$709$	20.5889	+	11.8870i	0.773234	+	0.446427i	0.834027	−	0.551723i	$-0.186030\pi$
$709$	20.5889	+	11.8870i	0.773234	+	0.446427i	−0.0607929	+	0.998150i	$0.519363\pi$
$710$	−1.66961	−	0.963952i	−0.0626595	−	0.0361765i
$711$		0			0
$712$	−3.27677			−0.122802
$713$	10.8245	+	6.24951i	0.405380	+	0.234046i
$714$		0			0
$715$	−5.71626	+	13.7728i	−0.213776	+	0.515072i
$716$	3.61969	+	6.26948i	0.135274	+	0.234301i
$717$		0			0
$718$	−7.84111	−	13.5812i	−0.292628	−	0.506846i
$719$	−10.3904	+	17.9967i	−0.387496	+	0.671163i	−0.992112	−	0.125354i	$-0.959993\pi$
$719$	−10.3904	+	17.9967i	−0.387496	+	0.671163i	0.604616	+	0.796517i	$0.293327\pi$
$720$		0			0
$721$	6.35722	+	9.01550i	0.236755	+	0.335755i
$722$	4.91782	−	2.83931i	0.183022	−	0.105668i
$723$		0			0
$724$	−13.7650			−0.511574
$725$	−16.4309	−	28.4592i	−0.610229	−	1.05695i
$726$		0			0
$727$	−26.7719			−0.992915			−0.496457	−	0.868061i	$-0.665366\pi$
$727$	−26.7719			−0.992915			−0.496457	+	0.868061i	$0.665366\pi$
$728$	3.91659	+	17.4519i	0.145159	+	0.646809i
$729$		0			0
$730$		−	3.44675i		−	0.127570i
$731$	−0.342535	−	0.593287i	−0.0126691	−	0.0219435i
$732$		0			0
$733$	4.55224	−	2.62824i	0.168141	−	0.0970761i	−0.413568	−	0.910473i	$-0.635718\pi$
$733$	4.55224	−	2.62824i	0.168141	−	0.0970761i	0.581709	+	0.813397i	$0.302384\pi$
$734$	−10.4255	+	6.01919i	−0.384814	+	0.222172i
$735$		0			0
$736$		−	22.0917i		−	0.814312i
$737$	−10.2048	+	17.6753i	−0.375900	+	0.651078i
$738$		0			0
$739$	6.19209	−	3.57501i	0.227780	−	0.131509i	−0.381768	−	0.924258i	$-0.624685\pi$
$739$	6.19209	−	3.57501i	0.227780	−	0.131509i	0.609547	+	0.792750i	$0.291351\pi$
$740$	−0.769132	−	1.33218i	−0.0282738	−	0.0489717i
$741$		0			0
$742$	0.335727	+	0.155204i	0.0123249	+	0.00569771i
$743$	0.618032	+	0.356821i	0.0226734	+	0.0130905i	0.511294	−	0.859406i	$-0.329166\pi$
$743$	0.618032	+	0.356821i	0.0226734	+	0.0130905i	−0.488620	+	0.872496i	$0.662500\pi$
$744$		0			0
$745$	−0.0118592			−0.000434486
$746$	−7.96386	−	4.59794i	−0.291578	−	0.168342i
$747$		0			0
$748$	−0.854012	+	0.493064i	−0.0312258	+	0.0180282i
$749$	−22.3636	+	2.03104i	−0.817147	+	0.0742127i
$750$		0			0
$751$	25.7013			0.937854			0.468927	−	0.883237i	$-0.344641\pi$
$751$	25.7013			0.937854			0.468927	+	0.883237i	$0.344641\pi$
$752$	10.1120	−	5.83815i	0.368746	−	0.212896i
$753$		0			0
$754$	−13.9821	−	5.80315i	−0.509199	−	0.211338i
$755$	−19.7084			−0.717263
$756$		0			0
$757$	−8.19425	+	14.1928i	−0.297825	+	0.515848i	−0.975638	−	0.219386i	$-0.929594\pi$
$757$	−8.19425	+	14.1928i	−0.297825	+	0.515848i	0.677813	+	0.735234i	$0.262928\pi$
$758$	−2.03430	+	3.52350i	−0.0738889	+	0.127979i
$759$		0			0
$760$			10.7694i			0.390646i
$761$	−7.20531	−	4.15999i	−0.261192	−	0.150800i	0.363686	−	0.931522i	$-0.381518\pi$
$761$	−7.20531	−	4.15999i	−0.261192	−	0.150800i	−0.624878	+	0.780722i	$0.714851\pi$
$762$		0			0
$763$	15.4428	+	7.13907i	0.559067	+	0.258452i
$764$	−5.66888	+	9.81878i	−0.205093	+	0.355231i
$765$		0			0
$766$	5.59263	−	9.68671i	0.202070	−	0.349995i
$767$	−5.04678	−	38.5442i	−0.182229	−	1.39175i
$768$		0			0
$769$	22.1346	+	12.7794i	0.798194	+	0.460838i	0.842839	−	0.538165i	$-0.180882\pi$
$769$	22.1346	+	12.7794i	0.798194	+	0.460838i	−0.0446452	+	0.999003i	$0.514216\pi$
$770$	−4.96605	−	2.29576i	−0.178964	−	0.0827334i
$771$		0			0
$772$	7.31905	−	4.22565i	0.263418	−	0.152085i
$773$			8.40077i			0.302155i	0.988522	+	0.151077i	$0.0482742\pi$
$773$			8.40077i			0.302155i	−0.988522	+	0.151077i	$0.951726\pi$
$774$		0			0
$775$	−9.64678	+	5.56957i	−0.346523	+	0.200065i
$776$	−2.53392	−	4.38887i	−0.0909623	−	0.157551i
$777$		0			0
$778$	−9.26388	−	5.34850i	−0.332126	−	0.191753i
$779$	33.3269	+	57.7238i	1.19406	+	2.06817i
$780$		0			0
$781$	7.33714	−	12.7083i	0.262544	−	0.454739i
$782$			0.311829i			0.0111510i
$783$		0			0
$784$	17.6445	−	3.23158i	0.630162	−	0.115414i
$785$			20.6345i			0.736476i
$786$		0			0
$787$			35.0644i			1.24991i	0.780660	+	0.624956i	$0.214883\pi$
$787$			35.0644i			1.24991i	−0.780660	+	0.624956i	$0.785117\pi$
$788$	39.1562	+	22.6069i	1.39488	+	0.805336i
$789$		0			0
$790$	−3.10720	+	5.38182i	−0.110549	+	0.191477i
$791$	16.7157	+	23.7053i	0.594340	+	0.842864i
$792$		0			0
$793$	−8.10420	+	19.5263i	−0.287788	+	0.693399i
$794$	0.299175	−	0.518186i	0.0106173	−	0.0183897i
$795$		0			0
$796$	−29.9508			−1.06158
$797$	12.2876	+	21.2828i	0.435250	+	0.753875i	0.997316	−	0.0732173i	$-0.0233267\pi$
$797$	12.2876	+	21.2828i	0.435250	+	0.753875i	−0.562066	+	0.827092i	$0.689993\pi$
$798$		0			0
$799$	−0.560475	+	0.323590i	−0.0198282	+	0.0114478i
$800$	17.0505	+	9.84409i	0.602825	+	0.348041i
$801$		0			0
$802$	−18.1370			−0.640439
$803$	26.2350			0.925814
$804$		0			0
$805$	9.89765	−	6.97926i	0.348846	−	0.245987i
$806$	−1.96709	+	4.73951i	−0.0692877	+	0.166942i
$807$		0			0
$808$	−18.6282	+	10.7550i	−0.655336	+	0.378358i
$809$	−15.9006	−	27.5406i	−0.559035	−	0.968277i	−0.997577	−	0.0695667i	$-0.977838\pi$
$809$	−15.9006	−	27.5406i	−0.559035	−	0.968277i	0.438542	−	0.898711i	$-0.355495\pi$
$810$		0			0
$811$		−	10.3633i		−	0.363905i	−0.983307	−	0.181953i	$-0.941758\pi$
$811$		−	10.3633i		−	0.363905i	0.983307	−	0.181953i	$-0.0582418\pi$
$812$	−16.3156	+	35.2929i	−0.572565	+	1.23854i
$813$		0			0
$814$	−1.44847	+	0.836272i	−0.0507687	+	0.0293113i
$815$	9.31196			0.326184
$816$		0			0
$817$		−	26.5749i		−	0.929737i
$818$	7.33597			0.256496
$819$		0			0
$820$	−22.0698			−0.770711
$821$		−	4.05592i		−	0.141552i	−0.997492	−	0.0707762i	$-0.977452\pi$
$821$		−	4.05592i		−	0.141552i	0.997492	−	0.0707762i	$-0.0225476\pi$
$822$		0			0
$823$	−8.71697			−0.303854			−0.151927	−	0.988392i	$-0.548548\pi$
$823$	−8.71697			−0.303854			−0.151927	+	0.988392i	$0.548548\pi$
$824$	6.77027	−	3.90882i	0.235854	−	0.136170i
$825$		0			0
$826$	14.2037	−	1.28997i	0.494211	−	0.0448839i
$827$		−	23.5788i		−	0.819915i	−0.912105	−	0.409957i	$-0.865544\pi$
$827$		−	23.5788i		−	0.819915i	0.912105	−	0.409957i	$-0.134456\pi$
$828$		0			0
$829$	−14.5203	−	25.1499i	−0.504311	−	0.873492i	−0.999988	−	0.00498467i	$-0.998413\pi$
$829$	−14.5203	−	25.1499i	−0.504311	−	0.873492i	0.495677	−	0.868507i	$-0.334920\pi$
$830$	1.29695	−	0.748793i	0.0450177	−	0.0259910i
$831$		0			0
$832$	−9.32953	+	1.22156i	−0.323443	+	0.0423499i
$833$	−0.977980	+	0.179116i	−0.0338850	+	0.00620601i
$834$		0			0
$835$	−6.39526			−0.221317
$836$	−38.2534			−1.32302
$837$		0			0
$838$	2.56921	+	1.48333i	0.0887517	+	0.0512408i
$839$	10.0090	−	5.77871i	0.345550	−	0.199503i	−0.317174	−	0.948367i	$-0.602734\pi$
$839$	10.0090	−	5.77871i	0.345550	−	0.199503i	0.662723	+	0.748864i	$0.269400\pi$
$840$		0			0
$841$	−20.7598	−	35.9570i	−0.715855	−	1.23990i
$842$	1.31584			0.0453467
$843$		0			0
$844$	−16.0049	+	27.7212i	−0.550910	+	0.954205i
$845$	9.59635	−	9.56930i	0.330124	−	0.329194i
$846$		0			0
$847$	5.26186	−	11.3821i	0.180800	−	0.391095i
$848$	−0.358248	+	0.620504i	−0.0123023	+	0.0213082i
$849$		0			0
$850$	−0.240670	−	0.138951i	−0.00825493	−	0.00476598i
$851$		−	3.70241i		−	0.126917i
$852$		0			0
$853$			1.51845i			0.0519906i	0.999662	+	0.0259953i	$0.00827550\pi$
$853$			1.51845i			0.0519906i	−0.999662	+	0.0259953i	$0.991725\pi$
$854$	−7.04059	−	3.25480i	−0.240924	−	0.111377i
$855$		0			0
$856$			15.9136i			0.543914i
$857$	3.00060	−	5.19718i	0.102498	−	0.177532i	−0.810215	−	0.586133i	$-0.800650\pi$
$857$	3.00060	−	5.19718i	0.102498	−	0.177532i	0.912713	+	0.408600i	$0.133983\pi$
$858$		0			0
$859$	−0.838021	−	1.45150i	−0.0285929	−	0.0495244i	0.851375	−	0.524558i	$-0.175769\pi$
$859$	−0.838021	−	1.45150i	−0.0285929	−	0.0495244i	−0.879968	+	0.475033i	$0.842436\pi$
$860$	7.62036	+	4.39962i	0.259852	+	0.150026i
$861$		0			0
$862$	4.70929	+	8.15673i	0.160399	+	0.277819i
$863$	−36.4167	+	21.0252i	−1.23964	+	0.715706i	−0.969021	−	0.246980i	$-0.920562\pi$
$863$	−36.4167	+	21.0252i	−1.23964	+	0.715706i	−0.270619	+	0.962687i	$0.587228\pi$
$864$		0			0
$865$			25.2933i			0.859999i
$866$	8.28567	−	4.78374i	0.281559	−	0.162558i
$867$		0			0
$868$	11.9632	+	5.53048i	0.406057	+	0.187717i
$869$	−40.9639	−	23.6505i	−1.38960	−	0.802288i
$870$		0			0
$871$	14.7236	−	11.2813i	0.498890	−	0.382253i
$872$	6.02832	−	10.4414i	0.204145	−	0.353589i
$873$		0			0
$874$	−6.04815	+	10.4757i	−0.204582	+	0.354346i
$875$	2.22354	+	24.4831i	0.0751694	+	0.827681i
$876$		0			0
$877$	26.7281	+	15.4315i	0.902545	+	0.521084i	0.878025	−	0.478615i	$-0.158861\pi$
$877$	26.7281	+	15.4315i	0.902545	+	0.521084i	0.0245198	+	0.999699i	$0.492194\pi$
$878$		−	0.632537i		−	0.0213471i
$879$		0			0
$880$	5.29917	−	9.17843i	0.178635	−	0.309405i
$881$	27.8669	−	48.2669i	0.938860	−	1.62615i	0.171260	−	0.985226i	$-0.445216\pi$
$881$	27.8669	−	48.2669i	0.938860	−	1.62615i	0.767601	−	0.640928i	$-0.221450\pi$
$882$		0			0
$883$	−2.92007			−0.0982681			−0.0491341	−	0.998792i	$-0.515646\pi$
$883$	−2.92007			−0.0982681			−0.0491341	+	0.998792i	$0.515646\pi$
$884$	0.888625	−	0.116352i	0.0298877	−	0.00391333i
$885$		0			0
$886$	−9.06671	+	5.23467i	−0.304602	+	0.175862i
$887$	−1.87909			−0.0630937			−0.0315468	−	0.999502i	$-0.510043\pi$
$887$	−1.87909			−0.0630937			−0.0315468	+	0.999502i	$0.510043\pi$
$888$		0			0
$889$	−2.22917	+	4.82200i	−0.0747639	+	0.161725i
$890$	−0.788876	+	0.455458i	−0.0264432	+	0.0152670i
$891$		0			0
$892$	−17.4421	−	10.0702i	−0.584004	−	0.337175i
$893$	−25.1051			−0.840111
$894$		0			0
$895$	3.73470	+	2.15623i	0.124837	+	0.0720748i
$896$	−2.72015	−	29.9513i	−0.0908740	−	1.00060i
$897$		0			0
$898$	4.46569	+	7.73480i	0.149022	+	0.258114i
$899$	−20.7014	+	11.9520i	−0.690431	+	0.398621i
$900$		0			0
$901$	0.0198566	−	0.0343926i	0.000661518	−	0.00114578i
$902$			23.9964i			0.798991i
$903$		0			0
$904$	17.8017	−	10.2778i	0.592077	−	0.341836i
$905$	−7.10121	+	4.09989i	−0.236052	+	0.136285i
$906$		0			0
$907$	−17.8082	−	30.8447i	−0.591311	−	1.02418i	−0.994056	−	0.108868i	$-0.965277\pi$
$907$	−17.8082	−	30.8447i	−0.591311	−	1.02418i	0.402745	−	0.915312i	$-0.368056\pi$
$908$			31.3331i			1.03982i
$909$		0			0
$910$	3.36866	+	3.65712i	0.111670	+	0.121232i
$911$	−44.2844			−1.46721			−0.733604	−	0.679577i	$-0.762163\pi$
$911$	−44.2844			−1.46721			−0.733604	+	0.679577i	$0.762163\pi$
$912$		0			0
$913$	5.69946	+	9.87175i	0.188624	+	0.326707i
$914$	−3.28290			−0.108589
$915$		0			0
$916$	−5.85535	+	3.38059i	−0.193466	+	0.111698i
$917$	−18.9828	−	26.9204i	−0.626866	−	0.888991i
$918$		0			0
$919$	−13.0564	+	22.6144i	−0.430691	+	0.745979i	−0.996933	−	0.0782603i	$-0.975063\pi$
$919$	−13.0564	+	22.6144i	−0.430691	+	0.745979i	0.566242	+	0.824239i	$0.308397\pi$
$920$	−4.29129	−	7.43274i	−0.141480	−	0.245050i
$921$		0			0
$922$	−1.27838	−	2.21421i	−0.0421010	−	0.0729211i
$923$	−10.5861	+	8.11111i	−0.348445	+	0.266981i
$924$		0			0
$925$	2.85753	+	1.64980i	0.0939551	+	0.0542450i
$926$	16.6615			0.547531
$927$		0			0
$928$	36.5893	+	21.1248i	1.20110	+	0.693457i
$929$	8.68030	+	5.01157i	0.284791	+	0.164424i	0.635591	−	0.772026i	$-0.280757\pi$
$929$	8.68030	+	5.01157i	0.284791	+	0.164424i	−0.350799	+	0.936451i	$0.614090\pi$
$930$		0			0
$931$	−36.3288	−	12.9514i	−1.19063	−	0.424464i
$932$	−21.9313	−	37.9861i	−0.718384	−	1.24428i
$933$		0			0
$934$	5.60712	−	3.23727i	0.183471	−	0.105927i
$935$	−0.293716	+	0.508731i	−0.00960554	+	0.0166373i
$936$		0			0
$937$	−0.916838			−0.0299518			−0.0149759	−	0.999888i	$-0.504767\pi$
$937$	−0.916838			−0.0299518			−0.0149759	+	0.999888i	$0.504767\pi$
$938$	3.92177	+	5.56166i	0.128050	+	0.181595i
$939$		0			0
$940$	4.15629	−	7.19891i	0.135563	−	0.234803i
$941$	14.8001	+	8.54482i	0.482468	+	0.278553i	0.721445	−	0.692472i	$-0.243478\pi$
$941$	14.8001	+	8.54482i	0.482468	+	0.278553i	−0.238976	+	0.971025i	$0.576812\pi$
$942$		0			0
$943$	−46.0027	−	26.5597i	−1.49805	−	0.864902i
$944$			27.6284i			0.899227i
$945$		0			0
$946$	4.78368	−	8.28557i	0.155531	−	0.269387i
$947$		−	21.7555i		−	0.706957i	−0.935443	−	0.353479i	$-0.884999\pi$
$947$		−	21.7555i		−	0.706957i	0.935443	−	0.353479i	$-0.115001\pi$
$948$		0			0
$949$	−22.0214	−	9.13979i	−0.714846	−	0.296690i
$950$	−5.39012	−	9.33597i	−0.174879	−	0.302899i
$951$		0			0
$952$	0.0637281	+	0.701702i	0.00206544	+	0.0227423i
$953$	8.90406	+	15.4223i	0.288431	+	0.499577i	0.973435	−	0.228962i	$-0.0735331\pi$
$953$	8.90406	+	15.4223i	0.288431	+	0.499577i	−0.685005	+	0.728539i	$0.740200\pi$
$954$		0			0
$955$			6.75385i			0.218549i
$956$			13.6582i			0.441737i
$957$		0			0
$958$	6.75281	+	11.6962i	0.218173	+	0.377887i
$959$	1.25517	+	13.8206i	0.0405317	+	0.446289i
$960$		0			0
$961$	−11.4487	−	19.8297i	−0.369311	−	0.639666i
$962$	1.50717	−	0.197341i	0.0485931	−	0.00636253i
$963$		0			0
$964$		−	38.0895i		−	1.22678i
$965$	2.51720	−	4.35992i	0.0810316	−	0.140351i
$966$		0			0
$967$		−	35.3813i		−	1.13779i	−0.822412	−	0.568893i	$-0.807372\pi$
$967$		−	35.3813i		−	1.13779i	0.822412	−	0.568893i	$-0.192628\pi$
$968$	−7.69582	−	4.44318i	−0.247353	−	0.142809i
$969$		0			0
$970$	−1.22007	−	0.704409i	−0.0391742	−	0.0226172i
$971$	24.8533	−	43.0472i	0.797582	−	1.38145i	−0.123605	−	0.992331i	$-0.539446\pi$
$971$	24.8533	−	43.0472i	0.797582	−	1.38145i	0.921187	−	0.389120i	$-0.127221\pi$
$972$		0			0
$973$	31.6199	+	44.8418i	1.01369	+	1.43756i
$974$	−16.0415			−0.514002
$975$		0			0
$976$	7.51287	−	13.0127i	0.240481	−	0.416526i
$977$	53.0701	−	30.6401i	1.69786	−	0.980262i	0.750081	−	0.661346i	$-0.230014\pi$
$977$	53.0701	−	30.6401i	1.69786	−	0.980262i	0.947783	−	0.318917i	$-0.103319\pi$
$978$		0			0
$979$	−3.46673	−	6.00455i	−0.110797	−	0.191906i
$980$	9.72825	−	8.27314i	0.310757	−	0.264276i
$981$		0			0
$982$	−12.3856	−	7.15080i	−0.395239	−	0.228191i
$983$	6.05318	+	3.49481i	0.193067	+	0.111467i	0.593417	−	0.804895i	$-0.297778\pi$
$983$	6.05318	+	3.49481i	0.193067	+	0.111467i	−0.400351	+	0.916362i	$0.631112\pi$
$984$		0			0
$985$	26.9336			0.858176
$986$	−0.516464	−	0.298181i	−0.0164476	−	0.00949601i
$987$		0			0
$988$	32.1096	+	13.3268i	1.02154	+	0.423981i
$989$	10.5893	+	18.3413i	0.336722	+	0.583219i
$990$		0			0
$991$	16.3671	+	28.3486i	0.519917	+	0.900522i	0.999732	+	0.0231525i	$0.00737033\pi$
$991$	16.3671	+	28.3486i	0.519917	+	0.900522i	−0.479815	+	0.877370i	$0.659296\pi$
$992$	7.16066	−	12.4026i	0.227351	−	0.393784i
$993$		0			0
$994$	−2.81970	−	3.99876i	−0.0894353	−	0.126833i
$995$	−15.4512	+	8.92078i	−0.489838	+	0.282808i
$996$		0			0
$997$	57.7897			1.83022			0.915109	−	0.403207i	$-0.132104\pi$
$997$	57.7897			1.83022			0.915109	+	0.403207i	$0.132104\pi$
$998$	−0.449529	−	0.778607i	−0.0142296	−	0.0246464i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.bm.f.550.3		12
3.2	odd	2		91.2.k.b.4.4	✓	12
7.2	even	3		819.2.do.e.667.3		12
13.10	even	6		819.2.do.e.361.3		12
21.2	odd	6		91.2.u.b.30.4	yes	12
21.5	even	6		637.2.u.g.30.4		12
21.11	odd	6		637.2.q.g.589.3		12
21.17	even	6		637.2.q.i.589.3		12
21.20	even	2		637.2.k.i.459.4		12
39.20	even	12		1183.2.e.j.508.8		24
39.23	odd	6		91.2.u.b.88.4	yes	12
39.32	even	12		1183.2.e.j.508.5		24
91.23	even	6	inner	819.2.bm.f.478.4		12
273.23	odd	6		91.2.k.b.23.3	yes	12
273.32	even	12		8281.2.a.cp.1.8		12
273.59	odd	12		8281.2.a.co.1.5		12
273.62	even	6		637.2.u.g.361.4		12
273.101	even	6		637.2.q.i.491.3		12
273.137	even	12		8281.2.a.cp.1.5		12
273.149	even	12		1183.2.e.j.170.5		24
273.179	odd	6		637.2.q.g.491.3		12
273.227	odd	12		8281.2.a.co.1.8		12
273.254	even	12		1183.2.e.j.170.8		24
273.257	even	6		637.2.k.i.569.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.k.b.4.4	✓	12	3.2	odd	2
91.2.k.b.23.3	yes	12	273.23	odd	6
91.2.u.b.30.4	yes	12	21.2	odd	6
91.2.u.b.88.4	yes	12	39.23	odd	6
637.2.k.i.459.4		12	21.20	even	2
637.2.k.i.569.3		12	273.257	even	6
637.2.q.g.491.3		12	273.179	odd	6
637.2.q.g.589.3		12	21.11	odd	6
637.2.q.i.491.3		12	273.101	even	6
637.2.q.i.589.3		12	21.17	even	6
637.2.u.g.30.4		12	21.5	even	6
637.2.u.g.361.4		12	273.62	even	6
819.2.bm.f.478.4		12	91.23	even	6	inner
819.2.bm.f.550.3		12	1.1	even	1	trivial
819.2.do.e.361.3		12	13.10	even	6
819.2.do.e.667.3		12	7.2	even	3
1183.2.e.j.170.5		24	273.149	even	12
1183.2.e.j.170.8		24	273.254	even	12
1183.2.e.j.508.5		24	39.32	even	12
1183.2.e.j.508.8		24	39.20	even	12
8281.2.a.co.1.5		12	273.59	odd	12
8281.2.a.co.1.8		12	273.227	odd	12
8281.2.a.cp.1.5		12	273.137	even	12
8281.2.a.cp.1.8		12	273.32	even	12

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.499987i q^{2} +1.75001 q^{4} +(0.902810 - 0.521238i) q^{5} +(2.63491 - 0.239300i) q^{7} -1.87496i q^{8} +O(q^{10})\)	\(q-0.499987i q^{2} +1.75001 q^{4} +(0.902810 - 0.521238i) q^{5} +(2.63491 - 0.239300i) q^{7} -1.87496i q^{8} +(-0.260612 - 0.451393i) q^{10} +(3.43579 - 1.98365i) q^{11} +(-3.57504 + 0.468096i) q^{13} +(-0.119647 - 1.31742i) q^{14} +2.56257 q^{16} -0.142035 q^{17} +(-4.77160 - 2.75488i) q^{19} +(1.57993 - 0.912173i) q^{20} +(-0.991800 - 1.71785i) q^{22} +4.39098 q^{23} +(-1.95662 + 3.38897i) q^{25} +(0.234042 + 1.78747i) q^{26} +(4.61112 - 0.418779i) q^{28} +(-4.19880 + 7.27253i) q^{29} +(2.46516 + 1.42326i) q^{31} -5.03117i q^{32} +0.0710158i q^{34} +(2.25409 - 1.58946i) q^{35} -0.843187i q^{37} +(-1.37740 + 2.38574i) q^{38} +(-0.977298 - 1.69273i) q^{40} +(-10.4766 - 6.04869i) q^{41} +(2.41161 + 4.17704i) q^{43} +(6.01267 - 3.47142i) q^{44} -2.19543i q^{46} +(3.94602 - 2.27824i) q^{47} +(6.88547 - 1.26107i) q^{49} +(1.69444 + 0.978285i) q^{50} +(-6.25636 + 0.819175i) q^{52} +(-0.139800 + 0.242141i) q^{53} +(2.06791 - 3.58172i) q^{55} +(-0.448678 - 4.94034i) q^{56} +(3.63617 + 2.09934i) q^{58} +10.7815i q^{59} +(2.93177 - 5.07797i) q^{61} +(0.711612 - 1.23255i) q^{62} +2.60963 q^{64} +(-2.98359 + 2.28605i) q^{65} +(-4.45524 + 2.57223i) q^{67} -0.248564 q^{68} +(-0.794706 - 1.12701i) q^{70} +(3.20326 - 1.84940i) q^{71} +(5.72686 + 3.30640i) q^{73} -0.421582 q^{74} +(-8.35036 - 4.82108i) q^{76} +(8.57829 - 6.04892i) q^{77} +(-5.96135 - 10.3254i) q^{79} +(2.31352 - 1.33571i) q^{80} +(-3.02426 + 5.23818i) q^{82} +2.87321i q^{83} +(-0.128231 + 0.0740342i) q^{85} +(2.08846 - 1.20578i) q^{86} +(-3.71926 - 6.44195i) q^{88} -1.74765i q^{89} +(-9.30787 + 2.08890i) q^{91} +7.68427 q^{92} +(-1.13909 - 1.97296i) q^{94} -5.74379 q^{95} +(2.34079 - 1.35145i) q^{97} +(-0.630517 - 3.44264i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 8 q^{4} + 3 q^{5} - 3 q^{7}+O(q^{10}) \) 12 * q - 8 * q^4 + 3 * q^5 - 3 * q^7	\( 12 q - 8 q^{4} + 3 q^{5} - 3 q^{7} + 12 q^{10} - 12 q^{11} - 2 q^{13} - 4 q^{14} + 16 q^{16} + 34 q^{17} + 9 q^{19} + 3 q^{20} - 15 q^{22} + 6 q^{23} - 5 q^{25} + 6 q^{26} - 9 q^{28} + q^{29} + 18 q^{31} + 6 q^{35} - 19 q^{38} - q^{40} + 6 q^{41} + 11 q^{43} + 33 q^{44} + 15 q^{47} - 3 q^{49} - 18 q^{50} - 7 q^{52} + 8 q^{53} - 15 q^{55} - 27 q^{56} - 24 q^{58} + 5 q^{61} - 41 q^{62} + 2 q^{64} - 21 q^{65} + 15 q^{67} - 22 q^{68} + 3 q^{70} - 30 q^{71} + 42 q^{73} - 66 q^{74} - 45 q^{76} + 19 q^{77} - 35 q^{79} + 63 q^{80} + 5 q^{82} - 21 q^{85} + 57 q^{86} - 14 q^{88} - 7 q^{91} + 66 q^{92} + q^{94} + 4 q^{95} - 3 q^{97} + 18 q^{98}+O(q^{100}) \) 12 * q - 8 * q^4 + 3 * q^5 - 3 * q^7 + 12 * q^10 - 12 * q^11 - 2 * q^13 - 4 * q^14 + 16 * q^16 + 34 * q^17 + 9 * q^19 + 3 * q^20 - 15 * q^22 + 6 * q^23 - 5 * q^25 + 6 * q^26 - 9 * q^28 + q^29 + 18 * q^31 + 6 * q^35 - 19 * q^38 - q^40 + 6 * q^41 + 11 * q^43 + 33 * q^44 + 15 * q^47 - 3 * q^49 - 18 * q^50 - 7 * q^52 + 8 * q^53 - 15 * q^55 - 27 * q^56 - 24 * q^58 + 5 * q^61 - 41 * q^62 + 2 * q^64 - 21 * q^65 + 15 * q^67 - 22 * q^68 + 3 * q^70 - 30 * q^71 + 42 * q^73 - 66 * q^74 - 45 * q^76 + 19 * q^77 - 35 * q^79 + 63 * q^80 + 5 * q^82 - 21 * q^85 + 57 * q^86 - 14 * q^88 - 7 * q^91 + 66 * q^92 + q^94 + 4 * q^95 - 3 * q^97 + 18 * q^98

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