LMFDB - Embedded newform 819.2.bm.f.478.4

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			478.4
Root			$-1.18541 + 0.771231i$ of defining polynomial
Character	$\chi$	$=$	819.478
Dual form			819.2.bm.f.550.3

$q$-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 $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

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	$0.0565655\pi$
$2$			0.499987i			0.353544i	−0.984252	+	0.176772i	$0.943434\pi$
$3$		0			0
$3$		0			0
$4$	1.75001			0.875007
$5$	0.902810	+	0.521238i	0.403749	+	0.233105i	0.688100	−	0.725616i	$-0.258445\pi$
$5$	0.902810	+	0.521238i	0.403749	+	0.233105i	−0.284351	+	0.958720i	$0.591778\pi$
$6$		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	0.918677	−	0.395009i	$-0.129258\pi$
$11$	3.43579	+	1.98365i	1.03593	+	0.598094i	0.117251	+	0.993102i	$0.462592\pi$
$12$		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	−0.934818	−	0.355126i	$-0.884438\pi$
$19$	−4.77160	+	2.75488i	−1.09468	+	0.632014i	−0.159861	+	0.987140i	$0.551105\pi$
$20$	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	−0.932116	−	0.362159i	$-0.882040\pi$
$29$	−4.19880	−	7.27253i	−0.779697	−	1.35047i	0.152419	−	0.988316i	$-0.451294\pi$
$30$		0			0
$31$	2.46516	−	1.42326i	0.442756	−	0.255625i	−0.262010	−	0.965065i	$-0.584385\pi$
$31$	2.46516	−	1.42326i	0.442756	−	0.255625i	0.704766	+	0.709440i	$0.251052\pi$
$32$			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	$0.0220796\pi$
$37$			0.843187i			0.138619i	−0.997595	+	0.0693095i	$0.977920\pi$
$38$	−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	−0.654044	+	0.756457i	$0.726929\pi$
$41$	−10.4766	+	6.04869i	−1.63618	+	0.944647i	−0.982133	+	0.188190i	$0.939738\pi$
$42$		0			0
$43$	2.41161	−	4.17704i	0.367768	−	0.636993i	−0.621448	−	0.783455i	$-0.713455\pi$
$43$	2.41161	−	4.17704i	0.367768	−	0.636993i	0.989216	+	0.146463i	$0.0467888\pi$
$44$	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	0.759378	−	0.650650i	$-0.225504\pi$
$47$	3.94602	+	2.27824i	0.575587	+	0.332315i	−0.183791	+	0.982965i	$0.558837\pi$
$48$		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	0.856264	−	0.516538i	$-0.172780\pi$
$53$	−0.139800	−	0.242141i	−0.0192030	−	0.0332606i	−0.875467	+	0.483278i	$0.839446\pi$
$54$		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	$-0.752373\pi$
$59$		−	10.7815i		−	1.40363i	0.712359	−	0.701815i	$-0.247627\pi$
$60$		0			0
$61$	2.93177	+	5.07797i	0.375374	+	0.650168i	0.990383	−	0.138353i	$-0.0441808\pi$
$61$	2.93177	+	5.07797i	0.375374	+	0.650168i	−0.615009	+	0.788520i	$0.710847\pi$
$62$	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	0.202523	−	0.979277i	$-0.435086\pi$
$67$	−4.45524	−	2.57223i	−0.544294	−	0.314248i	−0.746818	+	0.665029i	$0.768419\pi$
$68$	−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	0.677887	−	0.735167i	$-0.262896\pi$
$71$	3.20326	+	1.84940i	0.380157	+	0.219484i	−0.297730	+	0.954650i	$0.596229\pi$
$72$		0			0
$73$	5.72686	−	3.30640i	0.670278	−	0.386985i	−0.125904	−	0.992042i	$-0.540183\pi$
$73$	5.72686	−	3.30640i	0.670278	−	0.386985i	0.796182	+	0.605057i	$0.206850\pi$
$74$	−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	0.307000	+	0.951710i	$0.400675\pi$
$79$	−5.96135	+	10.3254i	−0.670705	+	1.16169i	−0.977705	+	0.209985i	$0.932658\pi$
$80$	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	$-0.949596\pi$
$83$		−	2.87321i		−	0.315376i	0.987489	−	0.157688i	$-0.0504040\pi$
$84$		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	$0.0295258\pi$
$89$			1.74765i			0.185250i	−0.995701	+	0.0926252i	$0.970474\pi$
$90$		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	0.614106	−	0.789224i	$-0.289517\pi$
$97$	2.34079	+	1.35145i	0.237671	+	0.137219i	−0.376435	+	0.926443i	$0.622850\pi$
$98$	−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	0.425723	+	0.904854i	$0.360020\pi$
$101$	−5.73612	+	9.93524i	−0.570765	+	0.988594i	−0.996488	+	0.0837401i	$0.973313\pi$
$102$		0			0
$103$	2.08475	−	3.61090i	0.205417	−	0.355792i	−0.744849	−	0.667233i	$-0.767478\pi$
$103$	2.08475	−	3.61090i	0.205417	−	0.355792i	0.950265	+	0.311441i	$0.100812\pi$
$104$	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	−0.209000	−	0.977916i	$-0.567021\pi$
$109$	5.56886	−	3.21518i	0.533400	−	0.307958i	0.742400	+	0.669957i	$0.233688\pi$
$110$	−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	−0.484165	−	0.874977i	$-0.660877\pi$
$113$	5.48164	−	9.49448i	0.515670	−	0.893166i	0.999835	−	0.0181892i	$-0.00579012\pi$
$114$		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	0.818040	−	0.575162i	$-0.195061\pi$
$127$	−1.00394	−	1.73887i	−0.0890849	−	0.154300i	−0.907125	+	0.420862i	$0.861728\pi$
$128$			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	0.454785	+	0.890601i	$0.349716\pi$
$131$	−6.22511	+	10.7822i	−0.543890	+	0.942046i	−0.998676	+	0.0514449i	$0.983617\pi$
$132$		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	$-0.928068\pi$
$137$		−	5.24518i		−	0.448126i	0.974575	−	0.224063i	$-0.0719321\pi$
$138$		0			0
$139$	10.3693	−	17.9601i	0.879510	−	1.52336i	0.0276301	−	0.999618i	$-0.491204\pi$
$139$	10.3693	−	17.9601i	0.879510	−	1.52336i	0.851880	−	0.523737i	$-0.175463\pi$
$140$	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	−0.500403	−	0.865792i	$-0.666815\pi$
$149$	−0.00985188	+	0.00568799i	−0.000807098	+	0.000465978i	0.499596	+	0.866258i	$0.333482\pi$
$150$		0			0
$151$	−16.3726	+	9.45271i	−1.33238	+	0.769251i	−0.985664	−	0.168719i	$-0.946037\pi$
$151$	−16.3726	+	9.45271i	−1.33238	+	0.769251i	−0.346717	+	0.937970i	$0.612704\pi$
$152$	−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	−0.926054	−	0.377390i	$-0.876822\pi$
$157$	−9.89687	−	17.1419i	−0.789856	−	1.36807i	0.136198	−	0.990682i	$-0.456512\pi$
$158$	−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	−0.165450	−	0.986218i	$-0.552908\pi$
$163$	7.73581	−	4.46627i	0.605915	−	0.349825i	0.771365	+	0.636393i	$0.219574\pi$
$164$	−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	−0.691269	−	0.722597i	$-0.742948\pi$
$167$	−5.31279	+	3.06734i	−0.411116	+	0.237358i	0.280153	+	0.959955i	$0.409615\pi$
$168$		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	−0.795797	−	0.605563i	$-0.792948\pi$
$173$	−12.1314	−	21.0122i	−0.922332	−	1.59753i	−0.126535	−	0.991962i	$-0.540386\pi$
$174$		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	−0.778315	−	0.627874i	$-0.783925\pi$
$179$	2.06838	−	3.58253i	0.154598	−	0.267771i	0.932912	+	0.360103i	$0.117259\pi$
$180$		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	0.724705	−	0.689059i	$-0.241976\pi$
$191$	−3.23933	−	5.61069i	−0.234390	−	0.405975i	−0.959095	+	0.283084i	$0.908643\pi$
$192$		0			0
$193$	4.18228	+	2.41464i	0.301047	+	0.173810i	0.642913	−	0.765939i	$-0.277726\pi$
$193$	4.18228	+	2.41464i	0.301047	+	0.173810i	−0.341866	+	0.939749i	$0.611059\pi$
$194$	−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	0.601554	−	0.798832i	$-0.294548\pi$
$197$	22.3748	−	12.9181i	1.59414	−	0.920377i	0.992586	−	0.121545i	$-0.0387850\pi$
$198$		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	−0.987631	−	0.156799i	$-0.949883\pi$
$211$	−9.14557	−	15.8406i	−0.629607	−	1.09051i	0.358024	−	0.933713i	$-0.383451\pi$
$212$	−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	−0.795101	−	0.606477i	$-0.792582\pi$
$223$	−9.96682	+	5.75435i	−0.667428	+	0.385340i	0.127674	+	0.991816i	$0.459249\pi$
$224$	−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	$-0.797476\pi$
$227$		−	17.9045i		−	1.18836i	0.804332	−	0.594181i	$-0.202524\pi$
$228$		0			0
$229$	−3.34589	−	1.93175i	−0.221103	−	0.127654i	0.385358	−	0.922767i	$-0.374078\pi$
$229$	−3.34589	−	1.93175i	−0.221103	−	0.127654i	−0.606461	+	0.795113i	$0.707411\pi$
$230$	−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	0.0839312	+	0.996472i	$0.473252\pi$
$233$	−12.5321	+	21.7062i	−0.821004	+	1.42202i	−0.904935	+	0.425549i	$0.860081\pi$
$234$		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	$-0.918774\pi$
$239$		−	7.80462i		−	0.504839i	0.967618	−	0.252419i	$-0.0812263\pi$
$240$		0			0
$241$			21.7653i			1.40202i	0.713150	+	0.701012i	$0.247268\pi$
$241$			21.7653i			1.40202i	−0.713150	+	0.701012i	$0.752732\pi$
$242$	−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	−0.961390	−	0.275191i	$-0.911259\pi$
$251$	−3.83990	+	6.65090i	−0.242372	+	0.419801i	0.719017	+	0.694992i	$0.244592\pi$
$252$		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	−0.988198	−	0.153181i	$-0.951048\pi$
$263$	−5.86158	+	10.1525i	−0.361440	+	0.626033i	0.626758	+	0.779214i	$0.284382\pi$
$264$		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	$-0.975189\pi$
$271$		−	2.56369i		−	0.155733i	0.996964	−	0.0778665i	$-0.0248108\pi$
$272$	−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	$-0.938349\pi$
$281$		−	6.45288i		−	0.384947i	0.981302	−	0.192473i	$-0.0616509\pi$
$282$		0			0
$283$	11.0873	−	19.2037i	0.659071	−	1.14154i	−0.321786	−	0.946812i	$-0.604283\pi$
$283$	11.0873	−	19.2037i	0.659071	−	1.14154i	0.980857	−	0.194731i	$-0.0623835\pi$
$284$	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	0.965874	−	0.259014i	$-0.0833976\pi$
$293$	20.9600	+	12.1013i	1.22450	+	0.706964i	0.258624	+	0.965978i	$0.416731\pi$
$294$		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	$0.243809\pi$
$307$			24.2924i			1.38644i	−0.720726	+	0.693220i	$0.756191\pi$
$308$	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	0.803952	−	0.594694i	$-0.202727\pi$
$311$	−1.99355	−	3.45294i	−0.113044	−	0.195798i	−0.916996	+	0.398896i	$0.869393\pi$
$312$		0			0
$313$	−14.2377	+	24.6604i	−0.804763	+	1.39389i	0.111688	+	0.993743i	$0.464374\pi$
$313$	−14.2377	+	24.6604i	−0.804763	+	1.39389i	−0.916451	+	0.400147i	$0.868959\pi$
$314$	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	0.849709	−	0.527252i	$-0.176778\pi$
$317$	14.5632	+	8.40806i	0.817950	+	0.472244i	−0.0317591	+	0.999496i	$0.510111\pi$
$318$		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	−0.344885	−	0.938645i	$-0.612082\pi$
$331$	5.37730	−	3.10459i	0.295563	−	0.170644i	0.640448	+	0.768002i	$0.278749\pi$
$332$		−	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	−0.825349	−	0.564623i	$-0.809022\pi$
$349$	−13.9933	+	8.07906i	−0.749046	+	0.432462i	0.0763028	+	0.997085i	$0.475688\pi$
$350$	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	0.747451	−	0.664317i	$-0.231277\pi$
$353$	10.2558	+	5.92119i	0.545861	+	0.315153i	−0.201590	+	0.979470i	$0.564611\pi$
$354$		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	0.997394	−	0.0721417i	$-0.0229834\pi$
$359$	27.1631	+	15.6826i	1.43362	+	0.827698i	0.436221	+	0.899840i	$0.356317\pi$
$360$		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	0.359454	+	0.933163i	$0.382963\pi$
$367$	−12.0387	+	20.8517i	−0.628415	+	1.08845i	−0.987870	+	0.155285i	$0.950370\pi$
$368$	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	0.999627	−	0.0273160i	$-0.00869604\pi$
$373$	9.19612	+	15.9281i	0.476157	+	0.824728i	−0.523470	+	0.852044i	$0.675363\pi$
$374$	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	−0.669953	−	0.742403i	$-0.733686\pi$
$379$	−7.04719	+	4.06870i	−0.361990	+	0.208995i	0.307963	+	0.951398i	$0.400353\pi$
$380$	−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	0.0846992	−	0.996407i	$-0.473007\pi$
$383$	19.3739	−	11.1856i	0.989962	−	0.571555i	0.905263	+	0.424852i	$0.139674\pi$
$384$		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	0.998767	+	0.0496415i	$0.0158079\pi$
$389$	10.6973	+	18.5283i	0.542374	+	0.939420i	−0.456393	+	0.889778i	$0.650859\pi$
$390$		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	−0.473767	−	0.880650i	$-0.657106\pi$
$397$	1.03640	−	0.598365i	0.0520154	−	0.0300311i	0.525782	+	0.850619i	$0.323773\pi$
$398$		−	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	$0.360685\pi$
$401$			36.2749i			1.81148i	−0.423831	+	0.905741i	$0.639315\pi$
$402$		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	$-0.881838\pi$
$409$		−	14.6723i		−	0.725500i	0.931887	−	0.362750i	$-0.118162\pi$
$410$		−	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	0.784414	−	0.620238i	$-0.212964\pi$
$419$	−2.96674	−	5.13855i	−0.144935	−	0.251034i	−0.929349	+	0.369203i	$0.879631\pi$
$420$		0			0
$421$		−	2.63174i		−	0.128263i	−0.997941	−	0.0641317i	$-0.979572\pi$
$421$		−	2.63174i		−	0.128263i	0.997941	−	0.0641317i	$-0.0204278\pi$
$422$	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	0.0526738	−	0.998612i	$-0.483226\pi$
$431$	−16.3139	−	9.41883i	−0.785812	−	0.453689i	−0.838486	+	0.544923i	$0.816559\pi$
$432$		0			0
$433$	9.56773	−	16.5718i	0.459796	−	0.796389i	−0.539154	−	0.842207i	$-0.681256\pi$
$433$	9.56773	−	16.5718i	0.459796	−	0.796389i	0.998950	+	0.0458176i	$0.0145893\pi$
$434$	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	−0.999996	−	0.00296930i	$-0.999055\pi$
$443$	−10.4696	+	18.1339i	−0.497426	+	0.861568i	0.502569	+	0.864537i	$0.332388\pi$
$444$		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	0.0883746	−	0.996087i	$-0.471833\pi$
$449$	−15.4700	−	8.93162i	−0.730075	−	0.421509i	−0.818450	+	0.574578i	$0.805166\pi$
$450$		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	$0.0490775\pi$
$457$			6.56597i			0.307143i	−0.988138	+	0.153571i	$0.950922\pi$
$458$	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	0.599571	−	0.800322i	$-0.295338\pi$
$461$	4.42854	+	2.55682i	0.206258	+	0.119083i	−0.393313	+	0.919404i	$0.628671\pi$
$462$		0			0
$463$		−	33.3239i		−	1.54869i	−0.632761	−	0.774347i	$-0.718079\pi$
$463$		−	33.3239i		−	1.54869i	0.632761	−	0.774347i	$-0.281921\pi$
$464$	−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	−0.676433	−	0.736504i	$-0.736475\pi$
$467$	6.47472	−	11.2145i	0.299614	−	0.518947i	0.976048	+	0.217557i	$0.0698087\pi$
$468$		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	−0.140987	−	0.990012i	$-0.545027\pi$
$479$	−23.3930	−	13.5060i	−1.06885	−	0.617104i	−0.927868	+	0.372908i	$0.878361\pi$
$480$		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	$0.259053\pi$
$487$			32.0838i			1.45386i	−0.686713	+	0.726928i	$0.740947\pi$
$488$	−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	0.984200	+	0.177061i	$0.0566591\pi$
$491$	14.3020	+	24.7718i	0.645440	+	1.11793i	−0.338760	+	0.940873i	$0.610008\pi$
$492$		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	0.534451	−	0.845199i	$-0.320518\pi$
$499$	1.55726	+	0.899082i	0.0697123	+	0.0402484i	−0.464739	+	0.885448i	$0.653852\pi$
$500$		−	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	−0.335297	−	0.942112i	$-0.608837\pi$
$503$	14.5386	−	25.1816i	0.648245	−	1.12279i	0.983542	−	0.180681i	$-0.0578300\pi$
$504$		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	$0.171825\pi$
$509$			23.1913i			1.02794i	−0.857809	+	0.513969i	$0.828175\pi$
$510$		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	0.957569	+	0.288203i	$0.0930579\pi$
$521$	16.6255	+	28.7962i	0.728376	+	1.26158i	−0.229193	+	0.973381i	$0.573609\pi$
$522$		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	0.0146313	−	0.999893i	$-0.495343\pi$
$541$	−19.6306	−	11.3337i	−0.843986	−	0.487275i	−0.858617	+	0.512618i	$0.828676\pi$
$542$	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	0.277547	−	0.960712i	$-0.410478\pi$
$557$	−9.81039	−	5.66403i	−0.415680	−	0.239993i	−0.693227	+	0.720719i	$0.743812\pi$
$558$		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	0.998319	+	0.0579663i	$0.0184616\pi$
$571$	13.1273	+	22.7371i	0.549360	+	0.951519i	−0.448959	+	0.893552i	$0.648205\pi$
$572$	−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	0.0133154	−	0.999911i	$-0.495761\pi$
$577$	21.2806	−	12.2863i	0.885922	−	0.511487i	0.872606	+	0.488424i	$0.162428\pi$
$578$		−	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	−0.819798	−	0.572653i	$-0.805914\pi$
$587$	−17.7777	+	10.2640i	−0.733765	+	0.423639i	0.0860331	+	0.996292i	$0.472581\pi$
$588$		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	−0.371669	−	0.928365i	$-0.621214\pi$
$593$	−33.1545	−	19.1417i	−1.36149	−	0.786057i	−0.989822	+	0.142308i	$0.954548\pi$
$594$		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	0.973205	−	0.229939i	$-0.0738526\pi$
$599$	7.03567	+	12.1861i	0.287470	+	0.497912i	−0.685735	+	0.727851i	$0.740519\pi$
$600$		0			0
$601$	10.1171	+	17.5233i	0.412685	+	0.714791i	0.995182	−	0.0980417i	$-0.0312579\pi$
$601$	10.1171	+	17.5233i	0.412685	+	0.714791i	−0.582498	+	0.812832i	$0.697925\pi$
$602$	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	0.791860	−	0.610703i	$-0.209113\pi$
$607$	−3.27563	−	5.67356i	−0.132954	−	0.230283i	−0.924814	+	0.380420i	$0.875780\pi$
$608$	−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	0.952648	−	0.304075i	$-0.0983472\pi$
$613$	28.8598	+	16.6622i	1.16564	+	0.672980i	0.212988	+	0.977055i	$0.431681\pi$
$614$	−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	0.377499	−	0.926010i	$-0.376784\pi$
$617$	−5.85466	−	3.38019i	−0.235700	−	0.136081i	−0.613199	+	0.789929i	$0.710117\pi$
$618$		0			0
$619$	15.2582	−	8.80931i	0.613278	−	0.354076i	−0.160970	−	0.986959i	$-0.551462\pi$
$619$	15.2582	−	8.80931i	0.613278	−	0.354076i	0.774247	+	0.632883i	$0.218129\pi$
$620$	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	0.746319	−	0.665588i	$-0.231819\pi$
$631$	13.6416	+	7.87596i	0.543062	+	0.313537i	−0.203257	+	0.979125i	$0.565153\pi$
$632$	−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	0.140575	−	0.990070i	$-0.455105\pi$
$643$	−16.3952	−	9.46576i	−0.646563	−	0.373293i	−0.787138	+	0.616777i	$0.788438\pi$
$644$	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	−0.211601	−	0.977356i	$-0.567868\pi$
$647$	18.8384	−	32.6291i	0.740614	−	1.28278i	0.952216	−	0.305426i	$-0.0987988\pi$
$648$		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	−0.879507	−	0.475886i	$-0.842128\pi$
$659$	−0.709152	+	1.22829i	−0.0276247	+	0.0478473i	0.851883	+	0.523733i	$0.175461\pi$
$660$		0			0
$661$	−3.97764	−	2.29649i	−0.154712	−	0.0893231i	0.420645	−	0.907225i	$-0.361804\pi$
$661$	−3.97764	−	2.29649i	−0.154712	−	0.0893231i	−0.575357	+	0.817902i	$0.695137\pi$
$662$	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	0.822684	−	0.568499i	$-0.192475\pi$
$673$	−2.10111	−	3.63924i	−0.0809920	−	0.140282i	−0.903676	+	0.428216i	$0.859142\pi$
$674$			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	−0.777801	−	0.628511i	$-0.783665\pi$
$677$	4.04354	−	7.00361i	0.155406	−	0.269171i	0.933207	+	0.359340i	$0.116998\pi$
$678$		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	$-0.843423\pi$
$683$		−	24.6865i		−	0.944604i	0.881437	−	0.472302i	$-0.156577\pi$
$684$		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	$0.0686859\pi$
$691$			11.2567i			0.428225i	−0.976809	+	0.214113i	$0.931314\pi$
$692$	−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	−0.0607929	−	0.998150i	$-0.519363\pi$
$709$	20.5889	−	11.8870i	0.773234	−	0.446427i	0.834027	+	0.551723i	$0.186030\pi$
$710$	−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	0.604616	−	0.796517i	$-0.293327\pi$
$719$	−10.3904	−	17.9967i	−0.387496	−	0.671163i	−0.992112	+	0.125354i	$0.959993\pi$
$720$		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	0.581709	−	0.813397i	$-0.302384\pi$
$733$	4.55224	+	2.62824i	0.168141	+	0.0970761i	−0.413568	+	0.910473i	$0.635718\pi$
$734$	−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	0.609547	−	0.792750i	$-0.291351\pi$
$739$	6.19209	+	3.57501i	0.227780	+	0.131509i	−0.381768	+	0.924258i	$0.624685\pi$
$740$	−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	−0.488620	−	0.872496i	$-0.662500\pi$
$743$	0.618032	−	0.356821i	0.0226734	−	0.0130905i	0.511294	+	0.859406i	$0.329166\pi$
$744$		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	0.677813	−	0.735234i	$-0.262928\pi$
$757$	−8.19425	−	14.1928i	−0.297825	−	0.515848i	−0.975638	+	0.219386i	$0.929594\pi$
$758$	−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	−0.624878	−	0.780722i	$-0.714851\pi$
$761$	−7.20531	+	4.15999i	−0.261192	+	0.150800i	0.363686	+	0.931522i	$0.381518\pi$
$762$		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	−0.0446452	−	0.999003i	$-0.514216\pi$
$769$	22.1346	−	12.7794i	0.798194	−	0.460838i	0.842839	+	0.538165i	$0.180882\pi$
$770$	−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	$-0.951726\pi$
$773$		−	8.40077i		−	0.302155i	0.988522	−	0.151077i	$-0.0482742\pi$
$774$		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	$-0.785117\pi$
$787$		−	35.0644i		−	1.24991i	0.780660	−	0.624956i	$-0.214883\pi$
$788$	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	−0.562066	−	0.827092i	$-0.689993\pi$
$797$	12.2876	−	21.2828i	0.435250	−	0.753875i	0.997316	+	0.0732173i	$0.0233267\pi$
$798$		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	0.438542	+	0.898711i	$0.355495\pi$
$809$	−15.9006	+	27.5406i	−0.559035	+	0.968277i	−0.997577	+	0.0695667i	$0.977838\pi$
$810$		0			0
$811$			10.3633i			0.363905i	0.983307	+	0.181953i	$0.0582418\pi$
$811$			10.3633i			0.363905i	−0.983307	+	0.181953i	$0.941758\pi$
$812$	−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	$0.0225476\pi$
$821$			4.05592i			0.141552i	−0.997492	+	0.0707762i	$0.977452\pi$
$822$		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	$0.134456\pi$
$827$			23.5788i			0.819915i	−0.912105	+	0.409957i	$0.865544\pi$
$828$		0			0
$829$	−14.5203	+	25.1499i	−0.504311	+	0.873492i	0.495677	+	0.868507i	$0.334920\pi$
$829$	−14.5203	+	25.1499i	−0.504311	+	0.873492i	−0.999988	+	0.00498467i	$0.998413\pi$
$830$	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	0.662723	−	0.748864i	$-0.269400\pi$
$839$	10.0090	+	5.77871i	0.345550	+	0.199503i	−0.317174	+	0.948367i	$0.602734\pi$
$840$		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	$-0.991725\pi$
$853$		−	1.51845i		−	0.0519906i	0.999662	−	0.0259953i	$-0.00827550\pi$
$854$	−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	0.912713	−	0.408600i	$-0.133983\pi$
$857$	3.00060	+	5.19718i	0.102498	+	0.177532i	−0.810215	+	0.586133i	$0.800650\pi$
$858$		0			0
$859$	−0.838021	+	1.45150i	−0.0285929	+	0.0495244i	−0.879968	−	0.475033i	$-0.842436\pi$
$859$	−0.838021	+	1.45150i	−0.0285929	+	0.0495244i	0.851375	+	0.524558i	$0.175769\pi$
$860$	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	−0.270619	−	0.962687i	$-0.587228\pi$
$863$	−36.4167	−	21.0252i	−1.23964	−	0.715706i	−0.969021	+	0.246980i	$0.920562\pi$
$864$		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	0.0245198	−	0.999699i	$-0.492194\pi$
$877$	26.7281	−	15.4315i	0.902545	−	0.521084i	0.878025	+	0.478615i	$0.158861\pi$
$878$			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	0.767601	+	0.640928i	$0.221450\pi$
$881$	27.8669	+	48.2669i	0.938860	+	1.62615i	0.171260	+	0.985226i	$0.445216\pi$
$882$		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	0.402745	+	0.915312i	$0.368056\pi$
$907$	−17.8082	+	30.8447i	−0.591311	+	1.02418i	−0.994056	+	0.108868i	$0.965277\pi$
$908$		−	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	0.566242	−	0.824239i	$-0.308397\pi$
$919$	−13.0564	−	22.6144i	−0.430691	−	0.745979i	−0.996933	+	0.0782603i	$0.975063\pi$
$920$	−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	−0.350799	−	0.936451i	$-0.614090\pi$
$929$	8.68030	−	5.01157i	0.284791	−	0.164424i	0.635591	+	0.772026i	$0.280757\pi$
$930$		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	−0.238976	−	0.971025i	$-0.576812\pi$
$941$	14.8001	−	8.54482i	0.482468	−	0.278553i	0.721445	+	0.692472i	$0.243478\pi$
$942$		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	$0.115001\pi$
$947$			21.7555i			0.706957i	−0.935443	+	0.353479i	$0.884999\pi$
$948$		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	−0.685005	−	0.728539i	$-0.740200\pi$
$953$	8.90406	−	15.4223i	0.288431	−	0.499577i	0.973435	+	0.228962i	$0.0735331\pi$
$954$		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	$0.192628\pi$
$967$			35.3813i			1.13779i	−0.822412	+	0.568893i	$0.807372\pi$
$968$	−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	0.921187	+	0.389120i	$0.127221\pi$
$971$	24.8533	+	43.0472i	0.797582	+	1.38145i	−0.123605	+	0.992331i	$0.539446\pi$
$972$		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	0.947783	+	0.318917i	$0.103319\pi$
$977$	53.0701	+	30.6401i	1.69786	+	0.980262i	0.750081	+	0.661346i	$0.230014\pi$
$978$		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	−0.400351	−	0.916362i	$-0.631112\pi$
$983$	6.05318	−	3.49481i	0.193067	−	0.111467i	0.593417	+	0.804895i	$0.297778\pi$
$984$		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	−0.479815	−	0.877370i	$-0.659296\pi$
$991$	16.3671	−	28.3486i	0.519917	−	0.900522i	0.999732	−	0.0231525i	$-0.00737033\pi$
$992$	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.478.4		12
3.2	odd	2		91.2.k.b.23.3	yes	12
7.4	even	3		819.2.do.e.361.3		12
13.4	even	6		819.2.do.e.667.3		12
21.2	odd	6		637.2.q.g.491.3		12
21.5	even	6		637.2.q.i.491.3		12
21.11	odd	6		91.2.u.b.88.4	yes	12
21.17	even	6		637.2.u.g.361.4		12
21.20	even	2		637.2.k.i.569.3		12
39.2	even	12		1183.2.e.j.170.8		24
39.11	even	12		1183.2.e.j.170.5		24
39.17	odd	6		91.2.u.b.30.4	yes	12
91.4	even	6	inner	819.2.bm.f.550.3		12
273.2	even	12		8281.2.a.cp.1.5		12
273.11	even	12		1183.2.e.j.508.5		24
273.17	even	6		637.2.k.i.459.4		12
273.89	odd	12		8281.2.a.co.1.8		12
273.95	odd	6		91.2.k.b.4.4	✓	12
273.128	even	12		8281.2.a.cp.1.8		12
273.158	even	12		1183.2.e.j.508.8		24
273.173	even	6		637.2.q.i.589.3		12
273.212	odd	6		637.2.q.g.589.3		12
273.236	odd	12		8281.2.a.co.1.5		12
273.251	even	6		637.2.u.g.30.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.k.b.4.4	✓	12	273.95	odd	6
91.2.k.b.23.3	yes	12	3.2	odd	2
91.2.u.b.30.4	yes	12	39.17	odd	6
91.2.u.b.88.4	yes	12	21.11	odd	6
637.2.k.i.459.4		12	273.17	even	6
637.2.k.i.569.3		12	21.20	even	2
637.2.q.g.491.3		12	21.2	odd	6
637.2.q.g.589.3		12	273.212	odd	6
637.2.q.i.491.3		12	21.5	even	6
637.2.q.i.589.3		12	273.173	even	6
637.2.u.g.30.4		12	273.251	even	6
637.2.u.g.361.4		12	21.17	even	6
819.2.bm.f.478.4		12	1.1	even	1	trivial
819.2.bm.f.550.3		12	91.4	even	6	inner
819.2.do.e.361.3		12	7.4	even	3
819.2.do.e.667.3		12	13.4	even	6
1183.2.e.j.170.5		24	39.11	even	12
1183.2.e.j.170.8		24	39.2	even	12
1183.2.e.j.508.5		24	273.11	even	12
1183.2.e.j.508.8		24	273.158	even	12
8281.2.a.co.1.5		12	273.236	odd	12
8281.2.a.co.1.8		12	273.89	odd	12
8281.2.a.cp.1.5		12	273.2	even	12
8281.2.a.cp.1.8		12	273.128	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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more