LMFDB - Embedded newform 792.2.f.h.397.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [792,2,Mod(397,792)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(792, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("792.397"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 792 = 2^{3} \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	792.f (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,0,4,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$6.32415184009$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	20.0.74831334220841134637329678336.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2x^{18} + 5x^{16} - 8x^{14} + 28x^{12} - 64x^{10} + 112x^{8} - 128x^{6} + 320x^{4} - 512x^{2} + 1024 $ x^20 - 2x^18 + 5x^16 - 8x^14 + 28x^12 - 64x^10 + 112x^8 - 128x^6 + 320x^4 - 512*x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{17} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			397.16
Root			$-1.13849 + 0.838954i$ of defining polynomial
Character	$\chi$	$=$	792.397
Dual form			792.2.f.h.397.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.13849 + 0.838954i) q^{2} +(0.592314 + 1.91028i) q^{4} +3.89064i q^{5} -1.77496 q^{7} +(-0.928292 + 2.67175i) q^{8} +(-3.26407 + 4.42945i) q^{10} +1.00000i q^{11} -5.27974i q^{13} +(-2.02077 - 1.48911i) q^{14} +(-3.29833 + 2.26297i) q^{16} -2.76137 q^{17} +4.13356i q^{19} +(-7.43221 + 2.30448i) q^{20} +(-0.838954 + 1.13849i) q^{22} +6.91533 q^{23} -10.1371 q^{25} +(4.42945 - 6.01092i) q^{26} +(-1.05133 - 3.39067i) q^{28} -1.74643i q^{29} +5.35581 q^{31} +(-5.65364 - 0.190780i) q^{32} +(-3.14379 - 2.31666i) q^{34} -6.90573i q^{35} -3.18176i q^{37} +(-3.46787 + 4.70601i) q^{38} +(-10.3948 - 3.61165i) q^{40} -2.49796 q^{41} +2.49796i q^{43} +(-1.91028 + 0.592314i) q^{44} +(7.87303 + 5.80164i) q^{46} +11.5487 q^{47} -3.84952 q^{49} +(-11.5410 - 8.50456i) q^{50} +(10.0858 - 3.12726i) q^{52} +9.61571i q^{53} -3.89064 q^{55} +(1.64768 - 4.74226i) q^{56} +(1.46517 - 1.98829i) q^{58} +9.27499i q^{59} +13.8896i q^{61} +(6.09753 + 4.49328i) q^{62} +(-6.27655 - 4.96034i) q^{64} +20.5416 q^{65} +3.84858i q^{67} +(-1.63560 - 5.27499i) q^{68} +(5.79359 - 7.86210i) q^{70} +7.62071 q^{71} -10.7678 q^{73} +(2.66935 - 3.62240i) q^{74} +(-7.89626 + 2.44837i) q^{76} -1.77496i q^{77} -0.281256 q^{79} +(-8.80440 - 12.8326i) q^{80} +(-2.84390 - 2.09568i) q^{82} +0.313040i q^{83} -10.7435i q^{85} +(-2.09568 + 2.84390i) q^{86} +(-2.67175 - 0.928292i) q^{88} -2.47638 q^{89} +9.37132i q^{91} +(4.09605 + 13.2102i) q^{92} +(13.1480 + 9.68879i) q^{94} -16.0822 q^{95} +11.7005 q^{97} +(-4.38263 - 3.22957i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{4} + 8 q^{10} - 12 q^{16} - 12 q^{25} + 24 q^{28} + 40 q^{31} - 24 q^{34} - 32 q^{40} + 40 q^{46} + 36 q^{49} + 56 q^{52} - 16 q^{55} + 24 q^{58} + 4 q^{64} + 56 q^{70} - 56 q^{73} - 8 q^{76}+ \cdots + 8 q^{97}+O(q^{100}) $ 20 * q + 4 * q^4 + 8 * q^10 - 12 * q^16 - 12 * q^25 + 24 * q^28 + 40 * q^31 - 24 * q^34 - 32 * q^40 + 40 * q^46 + 36 * q^49 + 56 * q^52 - 16 * q^55 + 24 * q^58 + 4 * q^64 + 56 * q^70 - 56 * q^73 - 8 * q^76 - 16 * q^79 - 32 * q^82 + 12 * q^88 - 24 * q^94 + 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/792\mathbb{Z}\right)^\times$.

$n$	$145$	$199$	$353$	$397$
$\chi(n)$	$1$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$	1.13849	+	0.838954i	0.805033	+	0.593230i
$2$	1.13849	+	0.838954i	0.805033	+	0.593230i
$3$		0			0
$3$		0			0
$4$	0.592314	+	1.91028i	0.296157	+	0.955139i
$5$			3.89064i			1.73995i	0.493097	+	0.869974i	$0.335865\pi$
$5$			3.89064i			1.73995i	−0.493097	+	0.869974i	$0.664135\pi$
$6$		0			0
$7$	−1.77496			−0.670872			−0.335436	−	0.942063i	$-0.608884\pi$
$7$	−1.77496			−0.670872			−0.335436	+	0.942063i	$0.608884\pi$
$8$	−0.928292	+	2.67175i	−0.328201	+	0.944608i
$9$		0			0
$10$	−3.26407	+	4.42945i	−1.03219	+	1.40072i
$11$			1.00000i			0.301511i
$11$			1.00000i			0.301511i
$12$		0			0
$13$		−	5.27974i		−	1.46434i	−0.681124	−	0.732168i	$-0.738509\pi$
$13$		−	5.27974i		−	1.46434i	0.681124	−	0.732168i	$-0.261491\pi$
$14$	−2.02077	−	1.48911i	−0.540074	−	0.397981i
$15$		0			0
$16$	−3.29833	+	2.26297i	−0.824582	+	0.565742i
$17$	−2.76137			−0.669731			−0.334865	−	0.942266i	$-0.608691\pi$
$17$	−2.76137			−0.669731			−0.334865	+	0.942266i	$0.608691\pi$
$18$		0			0
$19$			4.13356i			0.948304i	0.880443	+	0.474152i	$0.157245\pi$
$19$			4.13356i			0.948304i	−0.880443	+	0.474152i	$0.842755\pi$
$20$	−7.43221	+	2.30448i	−1.66189	+	0.515298i
$21$		0			0
$22$	−0.838954	+	1.13849i	−0.178866	+	0.242727i
$23$	6.91533			1.44195			0.720973	−	0.692963i	$-0.243695\pi$
$23$	6.91533			1.44195			0.720973	+	0.692963i	$0.243695\pi$
$24$		0			0
$25$	−10.1371			−2.02742
$26$	4.42945	−	6.01092i	0.868687	−	1.17884i
$27$		0			0
$28$	−1.05133	−	3.39067i	−0.198683	−	0.640776i
$29$		−	1.74643i		−	0.324303i	−0.986766	−	0.162152i	$-0.948157\pi$
$29$		−	1.74643i		−	0.324303i	0.986766	−	0.162152i	$-0.0518434\pi$
$30$		0			0
$31$	5.35581			0.961933			0.480966	−	0.876739i	$-0.340286\pi$
$31$	5.35581			0.961933			0.480966	+	0.876739i	$0.340286\pi$
$32$	−5.65364	−	0.190780i	−0.999431	−	0.0337255i
$33$		0			0
$34$	−3.14379	−	2.31666i	−0.539156	−	0.397304i
$35$		−	6.90573i		−	1.16728i
$36$		0			0
$37$		−	3.18176i		−	0.523079i	−0.965193	−	0.261539i	$-0.915770\pi$
$37$		−	3.18176i		−	0.523079i	0.965193	−	0.261539i	$-0.0842301\pi$
$38$	−3.46787	+	4.70601i	−0.562562	+	0.763416i
$39$		0			0
$40$	−10.3948	−	3.61165i	−1.64357	−	0.571053i
$41$	−2.49796			−0.390116			−0.195058	−	0.980792i	$-0.562490\pi$
$41$	−2.49796			−0.390116			−0.195058	+	0.980792i	$0.562490\pi$
$42$		0			0
$43$			2.49796i			0.380936i	0.981693	+	0.190468i	$0.0610005\pi$
$43$			2.49796i			0.380936i	−0.981693	+	0.190468i	$0.938999\pi$
$44$	−1.91028	+	0.592314i	−0.287985	+	0.0892947i
$45$		0			0
$46$	7.87303	+	5.80164i	1.16082	+	0.855406i
$47$	11.5487			1.68455			0.842273	−	0.539052i	$-0.181217\pi$
$47$	11.5487			1.68455			0.842273	+	0.539052i	$0.181217\pi$
$48$		0			0
$49$	−3.84952			−0.549931
$50$	−11.5410	−	8.50456i	−1.63214	−	1.20273i
$51$		0			0
$52$	10.0858	−	3.12726i	1.39864	−	0.433673i
$53$			9.61571i			1.32082i	0.750905	+	0.660410i	$0.229617\pi$
$53$			9.61571i			1.32082i	−0.750905	+	0.660410i	$0.770383\pi$
$54$		0			0
$55$	−3.89064			−0.524614
$56$	1.64768	−	4.74226i	0.220181	−	0.633711i
$57$		0			0
$58$	1.46517	−	1.98829i	0.192386	−	0.261075i
$59$			9.27499i			1.20750i	0.797173	+	0.603750i	$0.206328\pi$
$59$			9.27499i			1.20750i	−0.797173	+	0.603750i	$0.793672\pi$
$60$		0			0
$61$			13.8896i			1.77839i	0.457532	+	0.889193i	$0.348733\pi$
$61$			13.8896i			1.77839i	−0.457532	+	0.889193i	$0.651267\pi$
$62$	6.09753	+	4.49328i	0.774388	+	0.570647i
$63$		0			0
$64$	−6.27655	−	4.96034i	−0.784568	−	0.620042i
$65$	20.5416			2.54787
$66$		0			0
$67$			3.84858i			0.470178i	0.971974	+	0.235089i	$0.0755382\pi$
$67$			3.84858i			0.470178i	−0.971974	+	0.235089i	$0.924462\pi$
$68$	−1.63560	−	5.27499i	−0.198345	−	0.639686i
$69$		0			0
$70$	5.79359	−	7.86210i	0.692466	−	0.939701i
$71$	7.62071			0.904412			0.452206	−	0.891913i	$-0.350637\pi$
$71$	7.62071			0.904412			0.452206	+	0.891913i	$0.350637\pi$
$72$		0			0
$73$	−10.7678			−1.26028			−0.630140	−	0.776481i	$-0.717003\pi$
$73$	−10.7678			−1.26028			−0.630140	+	0.776481i	$0.717003\pi$
$74$	2.66935	−	3.62240i	0.310306	−	0.421096i
$75$		0			0
$76$	−7.89626	+	2.44837i	−0.905763	+	0.280847i
$77$		−	1.77496i		−	0.202275i
$78$		0			0
$79$	−0.281256			−0.0316438			−0.0158219	−	0.999875i	$-0.505036\pi$
$79$	−0.281256			−0.0316438			−0.0158219	+	0.999875i	$0.505036\pi$
$80$	−8.80440	−	12.8326i	−0.984362	−	1.43473i
$81$		0			0
$82$	−2.84390	−	2.09568i	−0.314057	−	0.231429i
$83$			0.313040i			0.0343606i	0.999852	+	0.0171803i	$0.00546892\pi$
$83$			0.313040i			0.0343606i	−0.999852	+	0.0171803i	$0.994531\pi$
$84$		0			0
$85$		−	10.7435i		−	1.16530i
$86$	−2.09568	+	2.84390i	−0.225983	+	0.306666i
$87$		0			0
$88$	−2.67175	−	0.928292i	−0.284810	−	0.0989563i
$89$	−2.47638			−0.262496			−0.131248	−	0.991350i	$-0.541898\pi$
$89$	−2.47638			−0.262496			−0.131248	+	0.991350i	$0.541898\pi$
$90$		0			0
$91$			9.37132i			0.982381i
$92$	4.09605	+	13.2102i	0.427042	+	1.37726i
$93$		0			0
$94$	13.1480	+	9.68879i	1.35611	+	0.999322i
$95$	−16.0822			−1.65000
$96$		0			0
$97$	11.7005			1.18800			0.594001	−	0.804464i	$-0.297548\pi$
$97$	11.7005			1.18800			0.594001	+	0.804464i	$0.297548\pi$
$98$	−4.38263	−	3.22957i	−0.442713	−	0.326236i
$99$		0			0
$100$	−6.00434	−	19.3647i	−0.600434	−	1.93647i
$101$		−	1.52771i		−	0.152013i	−0.997107	−	0.0760066i	$-0.975783\pi$
$101$		−	1.52771i		−	0.152013i	0.997107	−	0.0760066i	$-0.0242170\pi$
$102$		0			0
$103$	11.6174			1.14469			0.572346	−	0.820012i	$-0.306033\pi$
$103$	11.6174			1.14469			0.572346	+	0.820012i	$0.306033\pi$
$104$	14.1062	+	4.90114i	1.38322	+	0.480596i
$105$		0			0
$106$	−8.06714	+	10.9474i	−0.783550	+	1.06330i
$107$		−	10.9430i		−	1.05790i	−0.848653	−	0.528950i	$-0.822586\pi$
$107$		−	10.9430i		−	1.05790i	0.848653	−	0.528950i	$-0.177414\pi$
$108$		0			0
$109$		−	9.39172i		−	0.899563i	−0.893139	−	0.449782i	$-0.851502\pi$
$109$		−	9.39172i		−	0.899563i	0.893139	−	0.449782i	$-0.148498\pi$
$110$	−4.42945	−	3.26407i	−0.422332	−	0.311217i
$111$		0			0
$112$	5.85440	−	4.01668i	0.553189	−	0.379540i
$113$	20.0102			1.88240			0.941199	−	0.337853i	$-0.109701\pi$
$113$	20.0102			1.88240			0.941199	+	0.337853i	$0.109701\pi$
$114$		0			0
$115$			26.9051i			2.50891i
$116$	3.33616	−	1.03443i	0.309755	−	0.0960447i
$117$		0			0
$118$	−7.78129	+	10.5595i	−0.716325	+	0.972078i
$119$	4.90132			0.449304
$120$		0			0
$121$	−1.00000			−0.0909091
$122$	−11.6528	+	15.8132i	−1.05499	+	1.43166i
$123$		0			0
$124$	3.17232	+	10.2311i	0.284883	+	0.918780i
$125$		−	19.9866i		−	1.78766i
$126$		0			0
$127$	−4.00717			−0.355579			−0.177790	−	0.984069i	$-0.556895\pi$
$127$	−4.00717			−0.355579			−0.177790	+	0.984069i	$0.556895\pi$
$128$	−2.98428	−	10.9130i	−0.263776	−	0.964584i
$129$		0			0
$130$	23.3863	+	17.2334i	2.05112	+	1.51147i
$131$			11.3685i			0.993267i	0.867960	+	0.496634i	$0.165431\pi$
$131$			11.3685i			0.993267i	−0.867960	+	0.496634i	$0.834569\pi$
$132$		0			0
$133$		−	7.33691i		−	0.636191i
$134$	−3.22878	+	4.38156i	−0.278924	+	0.378509i
$135$		0			0
$136$	2.56336	−	7.37771i	0.219806	−	0.632633i
$137$	1.63560			0.139739			0.0698693	−	0.997556i	$-0.477742\pi$
$137$	1.63560			0.139739			0.0698693	+	0.997556i	$0.477742\pi$
$138$		0			0
$139$		−	14.1950i		−	1.20401i	−0.798494	−	0.602003i	$-0.794369\pi$
$139$		−	14.1950i		−	1.20401i	0.798494	−	0.602003i	$-0.205631\pi$
$140$	13.1919	−	4.09036i	1.11492	−	0.345699i
$141$		0			0
$142$	8.67610	+	6.39343i	0.728082	+	0.536524i
$143$	5.27974			0.441514
$144$		0			0
$145$	6.79473			0.564271
$146$	−12.2591	−	9.03372i	−1.01457	−	0.747636i
$147$		0			0
$148$	6.07806	−	1.88460i	0.499613	−	0.154913i
$149$		−	12.2964i		−	1.00736i	−0.863890	−	0.503680i	$-0.831979\pi$
$149$		−	12.2964i		−	1.00736i	0.863890	−	0.503680i	$-0.168021\pi$
$150$		0			0
$151$	20.0492			1.63158			0.815789	−	0.578350i	$-0.196303\pi$
$151$	20.0492			1.63158			0.815789	+	0.578350i	$0.196303\pi$
$152$	−11.0439	−	3.83715i	−0.895776	−	0.311234i
$153$		0			0
$154$	1.48911	−	2.02077i	0.119996	−	0.162838i
$155$			20.8376i			1.67371i
$156$		0			0
$157$		−	24.3493i		−	1.94329i	−0.236447	−	0.971644i	$-0.575983\pi$
$157$		−	24.3493i		−	1.94329i	0.236447	−	0.971644i	$-0.424017\pi$
$158$	−0.320207	−	0.235961i	−0.0254743	−	0.0187720i
$159$		0			0
$160$	0.742257	−	21.9963i	0.0586806	−	1.73896i
$161$	−12.2744			−0.967361
$162$		0			0
$163$		−	20.8050i		−	1.62957i	−0.579762	−	0.814786i	$-0.696855\pi$
$163$		−	20.8050i		−	1.62957i	0.579762	−	0.814786i	$-0.303145\pi$
$164$	−1.47958	−	4.77181i	−0.115536	−	0.372616i
$165$		0			0
$166$	−0.262626	+	0.356392i	−0.0203837	+	0.0276614i
$167$	−24.9601			−1.93147			−0.965736	−	0.259527i	$-0.916433\pi$
$167$	−24.9601			−1.93147			−0.965736	+	0.259527i	$0.916433\pi$
$168$		0			0
$169$	−14.8756			−1.14428
$170$	9.01331	−	12.2314i	0.691289	−	0.938103i
$171$		0			0
$172$	−4.77181	+	1.47958i	−0.363847	+	0.112817i
$173$			5.19657i			0.395088i	0.980294	+	0.197544i	$0.0632965\pi$
$173$			5.19657i			0.395088i	−0.980294	+	0.197544i	$0.936704\pi$
$174$		0			0
$175$	17.9929			1.36014
$176$	−2.26297	−	3.29833i	−0.170578	−	0.248621i
$177$		0			0
$178$	−2.81934	−	2.07757i	−0.211318	−	0.155721i
$179$		−	3.83835i		−	0.286892i	−0.989658	−	0.143446i	$-0.954182\pi$
$179$		−	3.83835i		−	0.286892i	0.989658	−	0.143446i	$-0.0458183\pi$
$180$		0			0
$181$		−	9.10791i		−	0.676986i	−0.940969	−	0.338493i	$-0.890083\pi$
$181$		−	9.10791i		−	0.676986i	0.940969	−	0.338493i	$-0.109917\pi$
$182$	−7.86210	+	10.6691i	−0.582778	+	0.790849i
$183$		0			0
$184$	−6.41945	+	18.4761i	−0.473248	+	1.36207i
$185$	12.3791			0.910130
$186$		0			0
$187$		−	2.76137i		−	0.201931i
$188$	6.84043	+	22.0612i	0.498890	+	1.60898i
$189$		0			0
$190$	−18.3094	−	13.4922i	−1.32831	−	0.978829i
$191$	−9.57028			−0.692481			−0.346241	−	0.938146i	$-0.612542\pi$
$191$	−9.57028			−0.692481			−0.346241	+	0.938146i	$0.612542\pi$
$192$		0			0
$193$	18.7186			1.34740			0.673698	−	0.739007i	$-0.264705\pi$
$193$	18.7186			1.34740			0.673698	+	0.739007i	$0.264705\pi$
$194$	13.3208	+	9.81614i	0.956381	+	0.704758i
$195$		0			0
$196$	−2.28012	−	7.35365i	−0.162866	−	0.525261i
$197$			23.1078i			1.64636i	0.567778	+	0.823182i	$0.307803\pi$
$197$			23.1078i			1.64636i	−0.567778	+	0.823182i	$0.692197\pi$
$198$		0			0
$199$	−10.2068			−0.723538			−0.361769	−	0.932268i	$-0.617827\pi$
$199$	−10.2068			−0.723538			−0.361769	+	0.932268i	$0.617827\pi$
$200$	9.41019	−	27.0838i	0.665401	−	1.91512i
$201$		0			0
$202$	1.28168	−	1.73928i	0.0901787	−	0.122376i
$203$			3.09984i			0.217566i
$204$		0			0
$205$		−	9.71869i		−	0.678782i
$206$	13.2262	+	9.74643i	0.921516	+	0.679066i
$207$		0			0
$208$	11.9479	+	17.4143i	0.828436	+	1.20746i
$209$	−4.13356			−0.285925
$210$		0			0
$211$		−	10.3079i		−	0.709624i	−0.934938	−	0.354812i	$-0.884545\pi$
$211$		−	10.3079i		−	0.709624i	0.934938	−	0.354812i	$-0.115455\pi$
$212$	−18.3687	+	5.69552i	−1.26157	+	0.391170i
$213$		0			0
$214$	9.18066	−	12.4585i	0.627577	−	0.851644i
$215$	−9.71869			−0.662809
$216$		0			0
$217$	−9.50635			−0.645333
$218$	7.87922	−	10.6924i	0.533648	−	0.724178i
$219$		0			0
$220$	−2.30448	−	7.43221i	−0.155368	−	0.501080i
$221$			14.5793i			0.980711i
$222$		0			0
$223$	27.9184			1.86956			0.934779	−	0.355231i	$-0.115598\pi$
$223$	27.9184			1.86956			0.934779	+	0.355231i	$0.115598\pi$
$224$	10.0350	+	0.338627i	0.670490	+	0.0226255i
$225$		0			0
$226$	22.7813	+	16.7876i	1.51539	+	1.11669i
$227$		−	4.00000i		−	0.265489i	−0.991150	−	0.132745i	$-0.957621\pi$
$227$		−	4.00000i		−	0.265489i	0.991150	−	0.132745i	$-0.0423790\pi$
$228$		0			0
$229$			7.86372i			0.519649i	0.965656	+	0.259825i	$0.0836648\pi$
$229$			7.86372i			0.519649i	−0.965656	+	0.259825i	$0.916335\pi$
$230$	−22.5721	+	30.6311i	−1.48836	+	2.01976i
$231$		0			0
$232$	4.66603	+	1.62120i	0.306340	+	0.106437i
$233$	−14.0363			−0.919548			−0.459774	−	0.888036i	$-0.652070\pi$
$233$	−14.0363			−0.919548			−0.459774	+	0.888036i	$0.652070\pi$
$234$		0			0
$235$			44.9317i			2.93102i
$236$	−17.7178	+	5.49370i	−1.15333	+	0.357610i
$237$		0			0
$238$	5.58010	+	4.11198i	0.361704	+	0.266540i
$239$	14.1038			0.912302			0.456151	−	0.889903i	$-0.349228\pi$
$239$	14.1038			0.912302			0.456151	+	0.889903i	$0.349228\pi$
$240$		0			0
$241$	4.79473			0.308855			0.154428	−	0.988004i	$-0.450647\pi$
$241$	4.79473			0.308855			0.154428	+	0.988004i	$0.450647\pi$
$242$	−1.13849	−	0.838954i	−0.0731848	−	0.0539300i
$243$		0			0
$244$	−26.5331	+	8.22702i	−1.69861	+	0.526681i
$245$		−	14.9771i		−	0.956852i
$246$		0			0
$247$	21.8241			1.38864
$248$	−4.97176	+	14.3094i	−0.315707	+	0.908649i
$249$		0			0
$250$	16.7678	−	22.7545i	1.06049	−	1.43912i
$251$			3.79797i			0.239726i	0.992790	+	0.119863i	$0.0382455\pi$
$251$			3.79797i			0.239726i	−0.992790	+	0.119863i	$0.961755\pi$
$252$		0			0
$253$			6.91533i			0.434763i
$254$	−4.56212	−	3.36183i	−0.286253	−	0.210940i
$255$		0			0
$256$	5.75795	−	14.9280i	0.359872	−	0.933002i
$257$	−10.0615			−0.627617			−0.313808	−	0.949486i	$-0.601605\pi$
$257$	−10.0615			−0.627617			−0.313808	+	0.949486i	$0.601605\pi$
$258$		0			0
$259$			5.64750i			0.350919i
$260$	12.1671	+	39.2401i	0.754569	+	2.43357i
$261$		0			0
$262$	−9.53761	+	12.9429i	−0.589236	+	0.799613i
$263$	19.3534			1.19338			0.596691	−	0.802471i	$-0.296482\pi$
$263$	19.3534			1.19338			0.596691	+	0.802471i	$0.296482\pi$
$264$		0			0
$265$	−37.4113			−2.29816
$266$	6.15532	−	8.35299i	0.377407	−	0.512154i
$267$		0			0
$268$	−7.35185	+	2.27956i	−0.449086	+	0.139247i
$269$			2.15219i			0.131221i	0.997845	+	0.0656107i	$0.0208995\pi$
$269$			2.15219i			0.131221i	−0.997845	+	0.0656107i	$0.979100\pi$
$270$		0			0
$271$	−20.6117			−1.25207			−0.626035	−	0.779795i	$-0.715323\pi$
$271$	−20.6117			−1.25207			−0.626035	+	0.779795i	$0.715323\pi$
$272$	9.10791	−	6.24890i	0.552248	−	0.378895i
$273$		0			0
$274$	1.86211	+	1.37219i	0.112494	+	0.0828971i
$275$		−	10.1371i		−	0.611290i
$276$		0			0
$277$		−	11.6381i		−	0.699265i	−0.936887	−	0.349633i	$-0.886306\pi$
$277$		−	11.6381i		−	0.699265i	0.936887	−	0.349633i	$-0.113694\pi$
$278$	11.9090	−	16.1609i	0.714252	−	0.969265i
$279$		0			0
$280$	18.4504	+	6.41054i	1.10262	+	0.383103i
$281$	−0.509825			−0.0304136			−0.0152068	−	0.999884i	$-0.504841\pi$
$281$	−0.509825			−0.0304136			−0.0152068	+	0.999884i	$0.504841\pi$
$282$		0			0
$283$			28.0309i			1.66626i	0.553076	+	0.833131i	$0.313454\pi$
$283$			28.0309i			1.66626i	−0.553076	+	0.833131i	$0.686546\pi$
$284$	4.51385	+	14.5577i	0.267848	+	0.863840i
$285$		0			0
$286$	6.01092	+	4.42945i	0.355433	+	0.261919i
$287$	4.43379			0.261718
$288$		0			0
$289$	−9.37483			−0.551460
$290$	7.73572	+	5.70046i	0.454257	+	0.334743i
$291$		0			0
$292$	−6.37794	−	20.5696i	−0.373241	−	1.20374i
$293$			2.58472i			0.151001i	0.997146	+	0.0755004i	$0.0240554\pi$
$293$			2.58472i			0.151001i	−0.997146	+	0.0755004i	$0.975945\pi$
$294$		0			0
$295$	−36.0857			−2.10099
$296$	8.50089	+	2.95361i	0.494104	+	0.171675i
$297$		0			0
$298$	10.3161	−	13.9993i	0.597596	−	0.810959i
$299$		−	36.5111i		−	2.11149i
$300$		0			0
$301$		−	4.43379i		−	0.255559i
$302$	22.8257	+	16.8203i	1.31347	+	0.967900i
$303$		0			0
$304$	−9.35412	−	13.6338i	−0.536496	−	0.781955i
$305$	−54.0396			−3.09430
$306$		0			0
$307$		−	13.0982i		−	0.747556i	−0.927518	−	0.373778i	$-0.878062\pi$
$307$		−	13.0982i		−	0.747556i	0.927518	−	0.373778i	$-0.121938\pi$
$308$	3.39067	−	1.05133i	0.193201	−	0.0599053i
$309$		0			0
$310$	−17.4817	+	23.7233i	−0.992896	+	1.34739i
$311$	−16.8181			−0.953665			−0.476832	−	0.878994i	$-0.658215\pi$
$311$	−16.8181			−0.953665			−0.476832	+	0.878994i	$0.658215\pi$
$312$		0			0
$313$	−5.02609			−0.284091			−0.142046	−	0.989860i	$-0.545368\pi$
$313$	−5.02609			−0.284091			−0.142046	+	0.989860i	$0.545368\pi$
$314$	20.4280	−	27.7215i	1.15282	−	1.56441i
$315$		0			0
$316$	−0.166592	−	0.537277i	−0.00937152	−	0.0302242i
$317$			3.45321i			0.193952i	0.995287	+	0.0969759i	$0.0309170\pi$
$317$			3.45321i			0.193952i	−0.995287	+	0.0969759i	$0.969083\pi$
$318$		0			0
$319$	1.74643			0.0977812
$320$	19.2989	−	24.4198i	1.07884	−	1.36511i
$321$		0			0
$322$	−13.9743	−	10.2977i	−0.778758	−	0.573868i
$323$		−	11.4143i		−	0.635109i
$324$		0			0
$325$			53.5212i			2.96882i
$326$	17.4544	−	23.6862i	0.966710	−	1.31186i
$327$		0			0
$328$	2.31884	−	6.67395i	0.128037	−	0.368507i
$329$	−20.4984			−1.13011
$330$		0			0
$331$		−	4.99593i		−	0.274601i	−0.990529	−	0.137301i	$-0.956157\pi$
$331$		−	4.99593i		−	0.274601i	0.990529	−	0.137301i	$-0.0438426\pi$
$332$	−0.597993	+	0.185418i	−0.0328191	+	0.0101761i
$333$		0			0
$334$	−28.4168	−	20.9404i	−1.55490	−	1.14581i
$335$	−14.9734			−0.818086
$336$		0			0
$337$	34.0563			1.85517			0.927583	−	0.373616i	$-0.121882\pi$
$337$	34.0563			1.85517			0.927583	+	0.373616i	$0.121882\pi$
$338$	−16.9357	−	12.4799i	−0.921182	−	0.678820i
$339$		0			0
$340$	20.5231	−	6.36353i	1.11302	−	0.345111i
$341$			5.35581i			0.290034i
$342$		0			0
$343$	19.2575			1.03980
$344$	−6.67395	−	2.31884i	−0.359835	−	0.125024i
$345$		0			0
$346$	−4.35968	+	5.91623i	−0.234378	+	0.318059i
$347$			11.4112i			0.612584i	0.951938	+	0.306292i	$0.0990884\pi$
$347$			11.4112i			0.612584i	−0.951938	+	0.306292i	$0.900912\pi$
$348$		0			0
$349$			5.73177i			0.306815i	0.988163	+	0.153407i	$0.0490247\pi$
$349$			5.73177i			0.306815i	−0.988163	+	0.153407i	$0.950975\pi$
$350$	20.4848	+	15.0952i	1.09496	+	0.806875i
$351$		0			0
$352$	0.190780	−	5.65364i	0.0101686	−	0.301340i
$353$	13.6007			0.723890			0.361945	−	0.932199i	$-0.382113\pi$
$353$	13.6007			0.723890			0.361945	+	0.932199i	$0.382113\pi$
$354$		0			0
$355$			29.6495i			1.57363i
$356$	−1.46680	−	4.73058i	−0.0777401	−	0.250720i
$357$		0			0
$358$	3.22020	−	4.36992i	0.170193	−	0.230957i
$359$	−3.62597			−0.191371			−0.0956856	−	0.995412i	$-0.530504\pi$
$359$	−3.62597			−0.191371			−0.0956856	+	0.995412i	$0.530504\pi$
$360$		0			0
$361$	1.91366			0.100719
$362$	7.64111	−	10.3693i	0.401608	−	0.544996i
$363$		0			0
$364$	−17.9018	+	5.55076i	−0.938311	+	0.290939i
$365$		−	41.8938i		−	2.19282i
$366$		0			0
$367$	−31.8060			−1.66026			−0.830130	−	0.557570i	$-0.811734\pi$
$367$	−31.8060			−1.66026			−0.830130	+	0.557570i	$0.811734\pi$
$368$	−22.8090	+	15.6492i	−1.18900	+	0.815770i
$369$		0			0
$370$	14.0935	+	10.3855i	0.732685	+	0.539916i
$371$		−	17.0675i		−	0.886101i
$372$		0			0
$373$		−	14.9984i		−	0.776589i	−0.921535	−	0.388294i	$-0.873064\pi$
$373$		−	14.9984i		−	0.776589i	0.921535	−	0.388294i	$-0.126936\pi$
$374$	2.31666	−	3.14379i	0.119792	−	0.162562i
$375$		0			0
$376$	−10.7205	+	30.8552i	−0.552869	+	1.59123i
$377$	−9.22068			−0.474889
$378$		0			0
$379$		−	19.2153i		−	0.987026i	−0.869738	−	0.493513i	$-0.835713\pi$
$379$		−	19.2153i		−	0.987026i	0.869738	−	0.493513i	$-0.164287\pi$
$380$	−9.52572	−	30.7215i	−0.488659	−	1.57598i
$381$		0			0
$382$	−10.8957	−	8.02902i	−0.557471	−	0.410801i
$383$	6.37652			0.325825			0.162913	−	0.986641i	$-0.447911\pi$
$383$	6.37652			0.325825			0.162913	+	0.986641i	$0.447911\pi$
$384$		0			0
$385$	6.90573			0.351949
$386$	21.3109	+	15.7041i	1.08470	+	0.799315i
$387$		0			0
$388$	6.93034	+	22.3511i	0.351835	+	1.13471i
$389$			17.7726i			0.901104i	0.892750	+	0.450552i	$0.148773\pi$
$389$			17.7726i			0.901104i	−0.892750	+	0.450552i	$0.851227\pi$
$390$		0			0
$391$	−19.0958			−0.965716
$392$	3.57348	−	10.2850i	0.180488	−	0.519469i
$393$		0			0
$394$	−19.3864	+	26.3080i	−0.976672	+	1.32538i
$395$		−	1.09427i		−	0.0550585i
$396$		0			0
$397$			23.9120i			1.20011i	0.799960	+	0.600053i	$0.204854\pi$
$397$			23.9120i			1.20011i	−0.799960	+	0.600053i	$0.795146\pi$
$398$	−11.6203	−	8.56299i	−0.582472	−	0.429224i
$399$		0			0
$400$	33.4355	−	22.9399i	1.67177	−	1.14700i
$401$	−16.1230			−0.805145			−0.402572	−	0.915388i	$-0.631884\pi$
$401$	−16.1230			−0.805145			−0.402572	+	0.915388i	$0.631884\pi$
$402$		0			0
$403$		−	28.2773i		−	1.40859i
$404$	2.91836	−	0.904885i	0.145194	−	0.0450197i
$405$		0			0
$406$	−2.60062	+	3.52913i	−0.129067	+	0.175148i
$407$	3.18176			0.157714
$408$		0			0
$409$	−8.08555			−0.399805			−0.199902	−	0.979816i	$-0.564062\pi$
$409$	−8.08555			−0.399805			−0.199902	+	0.979816i	$0.564062\pi$
$410$	8.15353	−	11.0646i	0.402674	−	0.546442i
$411$		0			0
$412$	6.88112	+	22.1924i	0.339009	+	1.09334i
$413$		−	16.4627i		−	0.810078i
$414$		0			0
$415$	−1.21792			−0.0597856
$416$	−1.00727	+	29.8497i	−0.0493854	+	1.46350i
$417$		0			0
$418$	−4.70601	−	3.46787i	−0.230179	−	0.169619i
$419$		−	20.8868i		−	1.02039i	−0.860060	−	0.510193i	$-0.829574\pi$
$419$		−	20.8868i		−	1.02039i	0.860060	−	0.510193i	$-0.170426\pi$
$420$		0			0
$421$		−	23.6241i		−	1.15137i	−0.817672	−	0.575685i	$-0.804736\pi$
$421$		−	23.6241i		−	1.15137i	0.817672	−	0.575685i	$-0.195264\pi$
$422$	8.64783	−	11.7354i	0.420970	−	0.571271i
$423$		0			0
$424$	−25.6908	−	8.92619i	−1.24766	−	0.433494i
$425$	27.9923			1.35783
$426$		0			0
$427$		−	24.6535i		−	1.19307i
$428$	20.9042	−	6.48169i	1.01044	−	0.313304i
$429$		0			0
$430$	−11.0646	−	8.15353i	−0.533583	−	0.393198i
$431$	23.2865			1.12167			0.560836	−	0.827927i	$-0.310480\pi$
$431$	23.2865			1.12167			0.560836	+	0.827927i	$0.310480\pi$
$432$		0			0
$433$	−19.8518			−0.954019			−0.477009	−	0.878898i	$-0.658279\pi$
$433$	−19.8518			−0.954019			−0.477009	+	0.878898i	$0.658279\pi$
$434$	−10.8229	−	7.97539i	−0.519515	−	0.382831i
$435$		0			0
$436$	17.9408	−	5.56284i	0.859208	−	0.266412i
$437$			28.5850i			1.36740i
$438$		0			0
$439$	−11.9661			−0.571109			−0.285554	−	0.958362i	$-0.592178\pi$
$439$	−11.9661			−0.571109			−0.285554	+	0.958362i	$0.592178\pi$
$440$	3.61165	−	10.3948i	0.172179	−	0.495555i
$441$		0			0
$442$	−12.2314	+	16.5984i	−0.581787	+	0.789505i
$443$		−	10.9365i		−	0.519608i	−0.965661	−	0.259804i	$-0.916342\pi$
$443$		−	10.9365i		−	0.519608i	0.965661	−	0.259804i	$-0.0836580\pi$
$444$		0			0
$445$		−	9.63473i		−	0.456730i
$446$	31.7848	+	23.4223i	1.50506	+	1.10908i
$447$		0			0
$448$	11.1406	+	8.80440i	0.526345	+	0.415969i
$449$	−11.3951			−0.537767			−0.268884	−	0.963173i	$-0.586655\pi$
$449$	−11.3951			−0.537767			−0.268884	+	0.963173i	$0.586655\pi$
$450$		0			0
$451$		−	2.49796i		−	0.117625i
$452$	11.8523	+	38.2250i	0.557485	+	1.79795i
$453$		0			0
$454$	3.35581	−	4.55396i	0.157496	−	0.213728i
$455$	−36.4604			−1.70929
$456$		0			0
$457$	21.8591			1.02253			0.511263	−	0.859424i	$-0.329178\pi$
$457$	21.8591			1.02253			0.511263	+	0.859424i	$0.329178\pi$
$458$	−6.59730	+	8.95276i	−0.308271	+	0.418335i
$459$		0			0
$460$	−51.3962	+	15.9363i	−2.39636	+	0.743032i
$461$		−	28.5151i		−	1.32808i	−0.747696	−	0.664041i	$-0.768840\pi$
$461$		−	28.5151i		−	1.32808i	0.747696	−	0.664041i	$-0.231160\pi$
$462$		0			0
$463$	−17.6442			−0.819998			−0.409999	−	0.912086i	$-0.634471\pi$
$463$	−17.6442			−0.819998			−0.409999	+	0.912086i	$0.634471\pi$
$464$	3.95211	+	5.76029i	0.183472	+	0.267415i
$465$		0			0
$466$	−15.9802	−	11.7758i	−0.740266	−	0.545503i
$467$			21.5357i			0.996553i	0.867018	+	0.498276i	$0.166034\pi$
$467$			21.5357i			0.996553i	−0.867018	+	0.498276i	$0.833966\pi$
$468$		0			0
$469$		−	6.83107i		−	0.315429i
$470$	−37.6956	+	51.1542i	−1.73877	+	2.35957i
$471$		0			0
$472$	−24.7805	−	8.60990i	−1.14061	−	0.396303i
$473$	−2.49796			−0.114857
$474$		0			0
$475$		−	41.9023i		−	1.92261i
$476$	2.90312	+	9.36289i	0.133064	+	0.429147i
$477$		0			0
$478$	16.0571	+	11.8325i	0.734433	+	0.541204i
$479$	−2.70358			−0.123530			−0.0617649	−	0.998091i	$-0.519673\pi$
$479$	−2.70358			−0.123530			−0.0617649	+	0.998091i	$0.519673\pi$
$480$		0			0
$481$	−16.7989			−0.765963
$482$	5.45874	+	4.02255i	0.248639	+	0.183222i
$483$		0			0
$484$	−0.592314	−	1.91028i	−0.0269234	−	0.0868308i
$485$			45.5223i			2.06706i
$486$		0			0
$487$	−31.3542			−1.42080			−0.710398	−	0.703800i	$-0.751485\pi$
$487$	−31.3542			−1.42080			−0.710398	+	0.703800i	$0.751485\pi$
$488$	−37.1097	−	12.8936i	−1.67988	−	0.583668i
$489$		0			0
$490$	12.5651	−	17.0513i	0.567633	−	0.770297i
$491$			15.9035i			0.717716i	0.933392	+	0.358858i	$0.116834\pi$
$491$			15.9035i			0.717716i	−0.933392	+	0.358858i	$0.883166\pi$
$492$		0			0
$493$			4.82254i			0.217196i
$494$	24.8465	+	18.3094i	1.11790	+	0.823780i
$495$		0			0
$496$	−17.6652	+	12.1200i	−0.793193	+	0.544206i
$497$	−13.5265			−0.606745
$498$		0			0
$499$			19.0802i			0.854149i	0.904216	+	0.427074i	$0.140456\pi$
$499$			19.0802i			0.854149i	−0.904216	+	0.427074i	$0.859544\pi$
$500$	38.1800	−	11.8383i	1.70746	−	0.529427i
$501$		0			0
$502$	−3.18632	+	4.32394i	−0.142212	+	0.192987i
$503$	16.8051			0.749301			0.374650	−	0.927166i	$-0.377763\pi$
$503$	16.8051			0.749301			0.374650	+	0.927166i	$0.377763\pi$
$504$		0			0
$505$	5.94378			0.264495
$506$	−5.80164	+	7.87303i	−0.257915	+	0.349999i
$507$		0			0
$508$	−2.37350	−	7.65482i	−0.105307	−	0.339628i
$509$		−	35.1514i		−	1.55806i	−0.626988	−	0.779029i	$-0.715712\pi$
$509$		−	35.1514i		−	1.55806i	0.626988	−	0.779029i	$-0.284288\pi$
$510$		0			0
$511$	19.1125			0.845487
$512$	19.0793	−	12.1647i	0.843193	−	0.537611i
$513$		0			0
$514$	−11.4549	−	8.44110i	−0.505252	−	0.372321i
$515$			45.1990i			1.99171i
$516$		0			0
$517$			11.5487i			0.507909i
$518$	−4.73799	+	6.42962i	−0.208175	+	0.282501i
$519$		0			0
$520$	−19.0686	+	54.8820i	−0.836213	+	2.40674i
$521$	44.8575			1.96524			0.982622	−	0.185620i	$-0.0594294\pi$
$521$	44.8575			1.96524			0.982622	+	0.185620i	$0.0594294\pi$
$522$		0			0
$523$		−	26.2365i		−	1.14724i	−0.819120	−	0.573622i	$-0.805538\pi$
$523$		−	26.2365i		−	1.14724i	0.819120	−	0.573622i	$-0.194462\pi$
$524$	−21.7169	+	6.73370i	−0.948709	+	0.294163i
$525$		0			0
$526$	22.0336	+	16.2366i	0.960712	+	0.707950i
$527$	−14.7894			−0.644236
$528$		0			0
$529$	24.8218			1.07921
$530$	−42.5923	−	31.3863i	−1.85009	−	1.36334i
$531$		0			0
$532$	14.0155	−	4.34575i	0.607651	−	0.188412i
$533$			13.1886i			0.571261i
$534$		0			0
$535$	42.5753			1.84069
$536$	−10.2824	−	3.57260i	−0.444134	−	0.154313i
$537$		0			0
$538$	−1.80559	+	2.45024i	−0.0778444	+	0.105638i
$539$		−	3.84952i		−	0.165810i
$540$		0			0
$541$		−	5.93131i		−	0.255007i	−0.991838	−	0.127503i	$-0.959304\pi$
$541$		−	5.93131i		−	0.255007i	0.991838	−	0.127503i	$-0.0406964\pi$
$542$	−23.4662	−	17.2922i	−1.00796	−	0.742765i
$543$		0			0
$544$	15.6118	+	0.526815i	0.669350	+	0.0225870i
$545$	36.5398			1.56519
$546$		0			0
$547$		−	19.0782i		−	0.815724i	−0.913043	−	0.407862i	$-0.866274\pi$
$547$		−	19.0782i		−	0.815724i	0.913043	−	0.407862i	$-0.133726\pi$
$548$	0.968787	+	3.12445i	0.0413845	+	0.133470i
$549$		0			0
$550$	8.50456	−	11.5410i	0.362635	−	0.492109i
$551$	7.21897			0.307538
$552$		0			0
$553$	0.499218			0.0212289
$554$	9.76382	−	13.2498i	0.414825	−	0.562932i
$555$		0			0
$556$	27.1165	−	8.40791i	1.14999	−	0.356575i
$557$		−	24.4027i		−	1.03398i	−0.855993	−	0.516988i	$-0.827053\pi$
$557$		−	24.4027i		−	1.03398i	0.855993	−	0.516988i	$-0.172947\pi$
$558$		0			0
$559$	13.1886			0.557818
$560$	15.6275	+	22.7774i	0.660381	+	0.962520i
$561$		0			0
$562$	−0.580430	−	0.427720i	−0.0244840	−	0.0180423i
$563$			25.5895i			1.07847i	0.842156	+	0.539233i	$0.181286\pi$
$563$			25.5895i			1.07847i	−0.842156	+	0.539233i	$0.818714\pi$
$564$		0			0
$565$			77.8524i			3.27527i
$566$	−23.5166	+	31.9128i	−0.988476	+	1.34140i
$567$		0			0
$568$	−7.07425	+	20.3607i	−0.296829	+	0.854315i
$569$	15.1100			0.633444			0.316722	−	0.948518i	$-0.397418\pi$
$569$	15.1100			0.633444			0.316722	+	0.948518i	$0.397418\pi$
$570$		0			0
$571$			20.3026i			0.849635i	0.905279	+	0.424818i	$0.139662\pi$
$571$			20.3026i			0.849635i	−0.905279	+	0.424818i	$0.860338\pi$
$572$	3.12726	+	10.0858i	0.130757	+	0.421707i
$573$		0			0
$574$	5.04782	+	3.71974i	0.210692	+	0.155259i
$575$	−70.1014			−2.92343
$576$		0			0
$577$	−7.82627			−0.325812			−0.162906	−	0.986642i	$-0.552087\pi$
$577$	−7.82627			−0.325812			−0.162906	+	0.986642i	$0.552087\pi$
$578$	−10.6731	−	7.86505i	−0.443944	−	0.327143i
$579$		0			0
$580$	4.02461	+	12.9798i	0.167113	+	0.538958i
$581$		−	0.555633i		−	0.0230515i
$582$		0			0
$583$	−9.61571			−0.398242
$584$	9.99571	−	28.7690i	0.413625	−	1.19047i
$585$		0			0
$586$	−2.16846	+	2.94267i	−0.0895782	+	0.121561i
$587$			35.7361i			1.47499i	0.675353	+	0.737494i	$0.263991\pi$
$587$			35.7361i			1.47499i	−0.675353	+	0.737494i	$0.736009\pi$
$588$		0			0
$589$			22.1386i			0.912205i
$590$	−41.0831	−	30.2742i	−1.69137	−	1.24637i
$591$		0			0
$592$	7.20023	+	10.4945i	0.295928	+	0.431321i
$593$	3.78102			0.155268			0.0776340	−	0.996982i	$-0.475263\pi$
$593$	3.78102			0.155268			0.0776340	+	0.996982i	$0.475263\pi$
$594$		0			0
$595$			19.0693i			0.781765i
$596$	23.4896	−	7.28333i	0.962170	−	0.298337i
$597$		0			0
$598$	30.6311	−	41.5675i	1.25260	−	1.69982i
$599$	14.0329			0.573368			0.286684	−	0.958025i	$-0.407447\pi$
$599$	14.0329			0.573368			0.286684	+	0.958025i	$0.407447\pi$
$600$		0			0
$601$	15.9691			0.651393			0.325696	−	0.945474i	$-0.394401\pi$
$601$	15.9691			0.651393			0.325696	+	0.945474i	$0.394401\pi$
$602$	3.71974	−	5.04782i	0.151605	−	0.205734i
$603$		0			0
$604$	11.8754	+	38.2995i	0.483203	+	1.55838i
$605$		−	3.89064i		−	0.158177i
$606$		0			0
$607$	−29.2838			−1.18859			−0.594296	−	0.804247i	$-0.702569\pi$
$607$	−29.2838			−1.18859			−0.594296	+	0.804247i	$0.702569\pi$
$608$	0.788601	−	23.3697i	0.0319820	−	0.947765i
$609$		0			0
$610$	−61.5235	−	45.3367i	−2.49101	−	1.83563i
$611$		−	60.9739i		−	2.46674i
$612$		0			0
$613$		−	25.4711i		−	1.02877i	−0.857560	−	0.514384i	$-0.828020\pi$
$613$		−	25.4711i		−	1.02877i	0.857560	−	0.514384i	$-0.171980\pi$
$614$	10.9888	−	14.9122i	0.443472	−	0.601807i
$615$		0			0
$616$	4.74226	+	1.64768i	0.191071	+	0.0663870i
$617$	−40.9704			−1.64940			−0.824702	−	0.565567i	$-0.808657\pi$
$617$	−40.9704			−1.64940			−0.824702	+	0.565567i	$0.808657\pi$
$618$		0			0
$619$		−	31.8239i		−	1.27911i	−0.768745	−	0.639555i	$-0.779119\pi$
$619$		−	31.8239i		−	1.27911i	0.768745	−	0.639555i	$-0.220881\pi$
$620$	−39.8055	+	12.3424i	−1.59863	+	0.495682i
$621$		0			0
$622$	−19.1472	−	14.1096i	−0.767732	−	0.565742i
$623$	4.39548			0.176101
$624$		0			0
$625$	27.0753			1.08301
$626$	−5.72215	−	4.21666i	−0.228703	−	0.168532i
$627$		0			0
$628$	46.5140	−	14.4224i	1.85611	−	0.575518i
$629$			8.78603i			0.350322i
$630$		0			0
$631$	16.2923			0.648586			0.324293	−	0.945957i	$-0.394874\pi$
$631$	16.2923			0.648586			0.324293	+	0.945957i	$0.394874\pi$
$632$	0.261088	−	0.751447i	0.0103855	−	0.0298910i
$633$		0			0
$634$	−2.89709	+	3.93144i	−0.115058	+	0.156138i
$635$		−	15.5905i		−	0.618689i
$636$		0			0
$637$			20.3244i			0.805284i
$638$	1.98829	+	1.46517i	0.0787171	+	0.0580067i
$639$		0			0
$640$	42.4587	−	11.6108i	1.67833	−	0.458956i
$641$	−43.0207			−1.69922			−0.849608	−	0.527415i	$-0.823161\pi$
$641$	−43.0207			−1.69922			−0.849608	+	0.527415i	$0.823161\pi$
$642$		0			0
$643$			20.8555i			0.822462i	0.911531	+	0.411231i	$0.134901\pi$
$643$			20.8555i			0.822462i	−0.911531	+	0.411231i	$0.865099\pi$
$644$	−7.27032	−	23.4476i	−0.286491	−	0.923965i
$645$		0			0
$646$	9.57607	−	12.9951i	0.376765	−	0.511284i
$647$	−21.3212			−0.838221			−0.419110	−	0.907935i	$-0.637658\pi$
$647$	−21.3212			−0.838221			−0.419110	+	0.907935i	$0.637658\pi$
$648$		0			0
$649$	−9.27499			−0.364075
$650$	−44.9018	+	60.9333i	−1.76119	+	2.39000i
$651$		0			0
$652$	39.7433	−	12.3231i	1.55647	−	0.482609i
$653$		−	16.6752i		−	0.652550i	−0.945275	−	0.326275i	$-0.894206\pi$
$653$		−	16.6752i		−	0.652550i	0.945275	−	0.326275i	$-0.105794\pi$
$654$		0			0
$655$	−44.2306			−1.72823
$656$	8.23911	−	5.65281i	0.321683	−	0.220705i
$657$		0			0
$658$	−23.3372	−	17.1972i	−0.909779	−	0.670417i
$659$			38.2694i			1.49076i	0.666638	+	0.745382i	$0.267733\pi$
$659$			38.2694i			1.49076i	−0.666638	+	0.745382i	$0.732267\pi$
$660$		0			0
$661$			10.7182i			0.416890i	0.978034	+	0.208445i	$0.0668402\pi$
$661$			10.7182i			0.416890i	−0.978034	+	0.208445i	$0.933160\pi$
$662$	4.19135	−	5.68781i	0.162902	−	0.221063i
$663$		0			0
$664$	−0.836365	−	0.290592i	−0.0324572	−	0.0112772i
$665$	28.5453			1.10694
$666$		0			0
$667$		−	12.0771i		−	0.467628i
$668$	−14.7842	−	47.6808i	−0.572019	−	1.84482i
$669$		0			0
$670$	−17.0471	−	12.5620i	−0.658586	−	0.485313i
$671$	−13.8896			−0.536204
$672$		0			0
$673$	19.1492			0.738146			0.369073	−	0.929400i	$-0.379675\pi$
$673$	19.1492			0.738146			0.369073	+	0.929400i	$0.379675\pi$
$674$	38.7728	+	28.5717i	1.49347	+	1.10054i
$675$		0			0
$676$	−8.81103	−	28.4166i	−0.338886	−	1.09294i
$677$			26.5420i			1.02009i	0.860147	+	0.510046i	$0.170372\pi$
$677$			26.5420i			1.02009i	−0.860147	+	0.510046i	$0.829628\pi$
$678$		0			0
$679$	−20.7678			−0.796997
$680$	28.7040	+	9.97312i	1.10075	+	0.382452i
$681$		0			0
$682$	−4.49328	+	6.09753i	−0.172057	+	0.233487i
$683$		−	17.8473i		−	0.682908i	−0.939898	−	0.341454i	$-0.889081\pi$
$683$		−	17.8473i		−	0.682908i	0.939898	−	0.341454i	$-0.110919\pi$
$684$		0			0
$685$			6.36353i			0.243138i
$686$	21.9244	+	16.1561i	0.837078	+	0.616843i
$687$		0			0
$688$	−5.65281	−	8.23911i	−0.215512	−	0.314113i
$689$	50.7684			1.93412
$690$		0			0
$691$		−	24.1267i		−	0.917824i	−0.888482	−	0.458912i	$-0.848239\pi$
$691$		−	24.1267i		−	0.917824i	0.888482	−	0.458912i	$-0.151761\pi$
$692$	−9.92689	+	3.07800i	−0.377364	+	0.117008i
$693$		0			0
$694$	−9.57345	+	12.9915i	−0.363403	+	0.493151i
$695$	55.2278			2.09491
$696$		0			0
$697$	6.89781			0.261273
$698$	−4.80869	+	6.52556i	−0.182012	+	0.246996i
$699$		0			0
$700$	10.6575	+	34.3715i	0.402814	+	1.29912i
$701$		−	24.1742i		−	0.913046i	−0.889712	−	0.456523i	$-0.849095\pi$
$701$		−	24.1742i		−	0.913046i	0.889712	−	0.456523i	$-0.150905\pi$
$702$		0			0
$703$	13.1520			0.496038
$704$	4.96034	−	6.27655i	0.186950	−	0.236556i
$705$		0			0
$706$	15.4842	+	11.4103i	0.582755	+	0.429433i
$707$			2.71163i			0.101981i
$708$		0			0
$709$			10.3521i			0.388781i	0.980924	+	0.194391i	$0.0622729\pi$
$709$			10.3521i			0.388781i	−0.980924	+	0.194391i	$0.937727\pi$
$710$	−24.8745	+	33.7556i	−0.933525	+	1.26683i
$711$		0			0
$712$	2.29881	−	6.61629i	0.0861515	−	0.247956i
$713$	37.0372			1.38706
$714$		0			0
$715$			20.5416i			0.768211i
$716$	7.33232	−	2.27351i	0.274022	−	0.0849649i
$717$		0			0
$718$	−4.12812	−	3.04202i	−0.154060	−	0.113527i
$719$	−11.8879			−0.443345			−0.221672	−	0.975121i	$-0.571152\pi$
$719$	−11.8879			−0.443345			−0.221672	+	0.975121i	$0.571152\pi$
$720$		0			0
$721$	−20.6203			−0.767942
$722$	2.17868	+	1.60547i	0.0810821	+	0.0597495i
$723$		0			0
$724$	17.3986	−	5.39474i	0.646616	−	0.200494i
$725$			17.7037i			0.657499i
$726$		0			0
$727$	29.4190			1.09109			0.545546	−	0.838081i	$-0.316322\pi$
$727$	29.4190			1.09109			0.545546	+	0.838081i	$0.316322\pi$
$728$	−25.0379	−	8.69932i	−0.927965	−	0.322418i
$729$		0			0
$730$	35.1470	−	47.6957i	1.30085	−	1.76530i
$731$		−	6.89781i		−	0.255125i
$732$		0			0
$733$		−	6.29939i		−	0.232673i	−0.993210	−	0.116337i	$-0.962885\pi$
$733$		−	6.29939i		−	0.232673i	0.993210	−	0.116337i	$-0.0371151\pi$
$734$	−36.2108	−	26.6838i	−1.33656	−	0.984916i
$735$		0			0
$736$	−39.0968	−	1.31931i	−1.44113	−	0.0486303i
$737$	−3.84858			−0.141764
$738$		0			0
$739$		−	23.0010i		−	0.846104i	−0.906105	−	0.423052i	$-0.860959\pi$
$739$		−	23.0010i		−	0.846104i	0.906105	−	0.423052i	$-0.139041\pi$
$740$	7.33232	+	23.6475i	0.269541	+	0.869301i
$741$		0			0
$742$	14.3188	−	19.4312i	0.525661	−	0.713340i
$743$	18.1445			0.665659			0.332829	−	0.942987i	$-0.391997\pi$
$743$	18.1445			0.665659			0.332829	+	0.942987i	$0.391997\pi$
$744$		0			0
$745$	47.8409			1.75276
$746$	12.5830	−	17.0755i	0.460696	−	0.625180i
$747$		0			0
$748$	5.27499	−	1.63560i	0.192873	−	0.0598034i
$749$			19.4234i			0.709715i
$750$		0			0
$751$	38.4541			1.40321			0.701605	−	0.712567i	$-0.252467\pi$
$751$	38.4541			1.40321			0.701605	+	0.712567i	$0.252467\pi$
$752$	−38.0913	+	26.1343i	−1.38905	+	0.953018i
$753$		0			0
$754$	−10.4976	−	7.73572i	−0.382301	−	0.281718i
$755$			78.0041i			2.83886i
$756$		0			0
$757$		−	6.81907i		−	0.247843i	−0.992292	−	0.123922i	$-0.960453\pi$
$757$		−	6.81907i		−	0.247843i	0.992292	−	0.123922i	$-0.0395472\pi$
$758$	16.1208	−	21.8765i	0.585533	−	0.794589i
$759$		0			0
$760$	14.9290	−	42.9677i	0.541532	−	1.55860i
$761$	−18.7256			−0.678804			−0.339402	−	0.940641i	$-0.610225\pi$
$761$	−18.7256			−0.678804			−0.339402	+	0.940641i	$0.610225\pi$
$762$		0			0
$763$			16.6699i			0.603492i
$764$	−5.66861	−	18.2819i	−0.205083	−	0.661416i
$765$		0			0
$766$	7.25960	+	5.34961i	0.262300	+	0.193289i
$767$	48.9695			1.76819
$768$		0			0
$769$	−13.8677			−0.500081			−0.250041	−	0.968235i	$-0.580444\pi$
$769$	−13.8677			−0.500081			−0.250041	+	0.968235i	$0.580444\pi$
$770$	7.86210	+	5.79359i	0.283330	+	0.208786i
$771$		0			0
$772$	11.0873	+	35.7578i	0.399041	+	1.28695i
$773$		−	7.46132i		−	0.268365i	−0.990957	−	0.134183i	$-0.957159\pi$
$773$		−	7.46132i		−	0.268365i	0.990957	−	0.134183i	$-0.0428408\pi$
$774$		0			0
$775$	−54.2924			−1.95024
$776$	−10.8614	+	31.2608i	−0.389903	+	1.12220i
$777$		0			0
$778$	−14.9103	+	20.2339i	−0.534562	+	0.725419i
$779$		−	10.3255i		−	0.369949i
$780$		0			0
$781$			7.62071i			0.272691i
$782$	−21.7404	−	16.0205i	−0.777434	−	0.572892i
$783$		0			0
$784$	12.6970	−	8.71134i	0.453463	−	0.311119i
$785$	94.7346			3.38122
$786$		0			0
$787$			32.4924i			1.15823i	0.815246	+	0.579115i	$0.196602\pi$
$787$			32.4924i			1.15823i	−0.815246	+	0.579115i	$0.803398\pi$
$788$	−44.1424	+	13.6871i	−1.57251	+	0.487582i
$789$		0			0
$790$	0.918039	−	1.24581i	0.0326623	−	0.0443239i
$791$	−35.5172			−1.26285
$792$		0			0
$793$	73.3336			2.60415
$794$	−20.0610	+	27.2235i	−0.711939	+	0.966126i
$795$		0			0
$796$	−6.04560	−	19.4977i	−0.214281	−	0.691079i
$797$			19.0895i			0.676186i	0.941113	+	0.338093i	$0.109782\pi$
$797$			19.0895i			0.676186i	−0.941113	+	0.338093i	$0.890218\pi$
$798$		0			0
$799$	−31.8901			−1.12819
$800$	57.3115	+	1.93396i	2.02627	+	0.0683757i
$801$		0			0
$802$	−18.3559	−	13.5265i	−0.648168	−	0.477636i
$803$		−	10.7678i		−	0.379989i
$804$		0			0
$805$		−	47.7555i		−	1.68316i
$806$	23.7233	−	32.1934i	0.835619	−	1.13396i
$807$		0			0
$808$	4.08167	+	1.41816i	0.143593	+	0.0498908i
$809$	−33.8216			−1.18910			−0.594552	−	0.804057i	$-0.702671\pi$
$809$	−33.8216			−1.18910			−0.594552	+	0.804057i	$0.702671\pi$
$810$		0			0
$811$			7.94357i			0.278936i	0.990227	+	0.139468i	$0.0445393\pi$
$811$			7.94357i			0.278936i	−0.990227	+	0.139468i	$0.955461\pi$
$812$	−5.92156	+	1.83608i	−0.207806	+	0.0644337i
$813$		0			0
$814$	3.62240	+	2.66935i	0.126965	+	0.0935608i
$815$	80.9447			2.83537
$816$		0			0
$817$	−10.3255			−0.361243
$818$	−9.20531	−	6.78340i	−0.321856	−	0.237176i
$819$		0			0
$820$	18.5654	−	5.75651i	0.648332	−	0.201026i
$821$			5.39933i			0.188438i	0.995551	+	0.0942190i	$0.0300354\pi$
$821$			5.39933i			0.188438i	−0.995551	+	0.0942190i	$0.969965\pi$
$822$		0			0
$823$	27.0183			0.941798			0.470899	−	0.882187i	$-0.343930\pi$
$823$	27.0183			0.941798			0.470899	+	0.882187i	$0.343930\pi$
$824$	−10.7843	+	31.0387i	−0.375689	+	1.08129i
$825$		0			0
$826$	13.8115	−	18.7426i	0.480562	−	0.652140i
$827$		−	34.4936i		−	1.19946i	−0.800202	−	0.599730i	$-0.795275\pi$
$827$		−	34.4936i		−	1.19946i	0.800202	−	0.599730i	$-0.204725\pi$
$828$		0			0
$829$			18.5048i			0.642698i	0.946961	+	0.321349i	$0.104136\pi$
$829$			18.5048i			0.642698i	−0.946961	+	0.321349i	$0.895864\pi$
$830$	−1.38659	−	1.02178i	−0.0481294	−	0.0354666i
$831$		0			0
$832$	−26.1893	+	33.1385i	−0.907950	+	1.14887i
$833$	10.6299			0.368306
$834$		0			0
$835$		−	97.1109i		−	3.36066i
$836$	−2.44837	−	7.89626i	−0.0846785	−	0.273098i
$837$		0			0
$838$	17.5230	−	23.7794i	0.605323	−	0.821445i
$839$	5.80138			0.200286			0.100143	−	0.994973i	$-0.468070\pi$
$839$	5.80138			0.200286			0.100143	+	0.994973i	$0.468070\pi$
$840$		0			0
$841$	25.9500			0.894827
$842$	19.8196	−	26.8958i	0.683027	−	0.926891i
$843$		0			0
$844$	19.6909	−	6.10550i	0.677790	−	0.210160i
$845$		−	57.8757i		−	1.99098i
$846$		0			0
$847$	1.77496			0.0609883
$848$	−21.7601	−	31.7158i	−0.747243	−	1.08912i
$849$		0			0
$850$	31.8689	+	23.4842i	1.09309	+	0.805503i
$851$		−	22.0030i		−	0.754252i
$852$		0			0
$853$		−	20.8231i		−	0.712971i	−0.934301	−	0.356485i	$-0.883975\pi$
$853$		−	20.8231i		−	0.712971i	0.934301	−	0.356485i	$-0.116025\pi$
$854$	20.6832	−	28.0678i	0.707764	−	0.960460i
$855$		0			0
$856$	29.2370	+	10.1583i	0.999300	+	0.347204i
$857$	−36.0392			−1.23107			−0.615537	−	0.788108i	$-0.711061\pi$
$857$	−36.0392			−1.23107			−0.615537	+	0.788108i	$0.711061\pi$
$858$		0			0
$859$			6.58555i			0.224696i	0.993669	+	0.112348i	$0.0358372\pi$
$859$			6.58555i			0.224696i	−0.993669	+	0.112348i	$0.964163\pi$
$860$	−5.75651	−	18.5654i	−0.196295	−	0.633075i
$861$		0			0
$862$	26.5115	+	19.5363i	0.902984	+	0.665410i
$863$	34.2086			1.16447			0.582237	−	0.813019i	$-0.302178\pi$
$863$	34.2086			1.16447			0.582237	+	0.813019i	$0.302178\pi$
$864$		0			0
$865$	−20.2180			−0.687432
$866$	−22.6011	−	16.6548i	−0.768017	−	0.565952i
$867$		0			0
$868$	−5.63074	−	18.1598i	−0.191120	−	0.616383i
$869$		−	0.281256i		−	0.00954095i
$870$		0			0
$871$	20.3195			0.688499
$872$	25.0924	+	8.71826i	0.849735	+	0.295238i
$873$		0			0
$874$	−23.9815	+	32.5437i	−0.811185	+	1.10081i
$875$			35.4754i			1.19929i
$876$		0			0
$877$			22.9567i			0.775194i	0.921829	+	0.387597i	$0.126695\pi$
$877$			22.9567i			0.775194i	−0.921829	+	0.387597i	$0.873305\pi$
$878$	−13.6232	−	10.0390i	−0.459762	−	0.338799i
$879$		0			0
$880$	12.8326	−	8.80440i	0.432587	−	0.296796i
$881$	−38.4940			−1.29690			−0.648448	−	0.761259i	$-0.724581\pi$
$881$	−38.4940			−1.29690			−0.648448	+	0.761259i	$0.724581\pi$
$882$		0			0
$883$		−	17.6384i		−	0.593581i	−0.954943	−	0.296790i	$-0.904084\pi$
$883$		−	17.6384i		−	0.593581i	0.954943	−	0.296790i	$-0.0959163\pi$
$884$	−27.8505	+	8.63553i	−0.936715	+	0.290444i
$885$		0			0
$886$	9.17521	−	12.4511i	0.308247	−	0.418302i
$887$	43.5883			1.46355			0.731776	−	0.681545i	$-0.238692\pi$
$887$	43.5883			1.46355			0.731776	+	0.681545i	$0.238692\pi$
$888$		0			0
$889$	7.11257			0.238548
$890$	8.08309	−	10.9690i	0.270946	−	0.367683i
$891$		0			0
$892$	16.5365	+	53.3320i	0.553682	+	1.78569i
$893$			47.7371i			1.59746i
$894$		0			0
$895$	14.9336			0.499177
$896$	5.29698	+	19.3702i	0.176960	+	0.647112i
$897$		0			0
$898$	−12.9732	−	9.55995i	−0.432921	−	0.319020i
$899$		−	9.35354i		−	0.311958i
$900$		0			0
$901$		−	26.5526i		−	0.884594i
$902$	2.09568	−	2.84390i	0.0697784	−	0.0946917i
$903$		0			0
$904$	−18.5753	+	53.4622i	−0.617805	+	1.77813i
$905$	35.4356			1.17792
$906$		0			0
$907$		−	24.8519i		−	0.825195i	−0.910913	−	0.412598i	$-0.864622\pi$
$907$		−	24.8519i		−	0.825195i	0.910913	−	0.412598i	$-0.135378\pi$
$908$	7.64111	−	2.36926i	0.253579	−	0.0786265i
$909$		0			0
$910$	−41.5098	−	30.5886i	−1.37604	−	1.01400i
$911$	−15.4478			−0.511808			−0.255904	−	0.966702i	$-0.582373\pi$
$911$	−15.4478			−0.511808			−0.255904	+	0.966702i	$0.582373\pi$
$912$		0			0
$913$	−0.313040			−0.0103601
$914$	24.8863	+	18.3388i	0.823167	+	0.606593i
$915$		0			0
$916$	−15.0219	+	4.65779i	−0.496338	+	0.153898i
$917$		−	20.1786i		−	0.666355i
$918$		0			0
$919$	7.35006			0.242456			0.121228	−	0.992625i	$-0.461317\pi$
$919$	7.35006			0.242456			0.121228	+	0.992625i	$0.461317\pi$
$920$	−71.8838	−	24.9758i	−2.36994	−	0.823428i
$921$		0			0
$922$	23.9229	−	32.4641i	0.787858	−	1.06915i
$923$		−	40.2354i		−	1.32436i
$924$		0			0
$925$			32.2539i			1.06050i
$926$	−20.0878	−	14.8027i	−0.660125	−	0.486447i
$927$		0			0
$928$	−0.333184	+	9.87367i	−0.0109373	+	0.324119i
$929$	−0.143238			−0.00469947			−0.00234974	−	0.999997i	$-0.500748\pi$
$929$	−0.143238			−0.00469947			−0.00234974	+	0.999997i	$0.500748\pi$
$930$		0			0
$931$		−	15.9122i		−	0.521502i
$932$	−8.31389	−	26.8132i	−0.272330	−	0.878296i
$933$		0			0
$934$	−18.0674	+	24.5181i	−0.591185	+	0.802258i
$935$	10.7435			0.351350
$936$		0			0
$937$	45.5879			1.48929			0.744645	−	0.667460i	$-0.232619\pi$
$937$	45.5879			1.48929			0.744645	+	0.667460i	$0.232619\pi$
$938$	5.73095	−	7.77709i	0.187122	−	0.253931i
$939$		0			0
$940$	−85.8321	+	26.6137i	−2.79953	+	0.868042i
$941$			6.96032i			0.226900i	0.993544	+	0.113450i	$0.0361902\pi$
$941$			6.96032i			0.226900i	−0.993544	+	0.113450i	$0.963810\pi$
$942$		0			0
$943$	−17.2743			−0.562527
$944$	−20.9890	−	30.5920i	−0.683134	−	0.995684i
$945$		0			0
$946$	−2.84390	−	2.09568i	−0.0924633	−	0.0681363i
$947$		−	1.14748i		−	0.0372880i	−0.999826	−	0.0186440i	$-0.994065\pi$
$947$		−	1.14748i		−	0.0372880i	0.999826	−	0.0186440i	$-0.00593492\pi$
$948$		0			0
$949$			56.8514i			1.84547i
$950$	35.1541	−	47.7053i	1.14055	−	1.54777i
$951$		0			0
$952$	−4.54986	+	13.0951i	−0.147462	+	0.424416i
$953$	3.74999			0.121474			0.0607370	−	0.998154i	$-0.480655\pi$
$953$	3.74999			0.121474			0.0607370	+	0.998154i	$0.480655\pi$
$954$		0			0
$955$		−	37.2346i		−	1.20488i
$956$	8.35390	+	26.9423i	0.270184	+	0.871375i
$957$		0			0
$958$	−3.07800	−	2.26818i	−0.0994456	−	0.0732816i
$959$	−2.90312			−0.0937467
$960$		0			0
$961$	−2.31525			−0.0746856
$962$	−19.1253	−	14.0935i	−0.616625	−	0.454392i
$963$		0			0
$964$	2.83998	+	9.15926i	0.0914697	+	0.295000i
$965$			72.8275i			2.34440i
$966$		0			0
$967$	−33.7804			−1.08630			−0.543152	−	0.839635i	$-0.682769\pi$
$967$	−33.7804			−1.08630			−0.543152	+	0.839635i	$0.682769\pi$
$968$	0.928292	−	2.67175i	0.0298364	−	0.0858734i
$969$		0			0
$970$	−38.1911	+	51.8266i	−1.22624	+	1.66405i
$971$		−	10.0269i		−	0.321778i	−0.986973	−	0.160889i	$-0.948564\pi$
$971$		−	10.0269i		−	0.321778i	0.986973	−	0.160889i	$-0.0514361\pi$
$972$		0			0
$973$			25.1956i			0.807734i
$974$	−35.6964	−	26.3047i	−1.14379	−	0.842858i
$975$		0			0
$976$	−31.4318	−	45.8126i	−1.00611	−	1.46643i
$977$	2.53154			0.0809911			0.0404956	−	0.999180i	$-0.487106\pi$
$977$	2.53154			0.0809911			0.0404956	+	0.999180i	$0.487106\pi$
$978$		0			0
$979$		−	2.47638i		−	0.0791456i
$980$	28.6104	−	8.87114i	0.913927	−	0.283378i
$981$		0			0
$982$	−13.3423	+	18.1060i	−0.425770	+	0.577785i
$983$	2.07297			0.0661175			0.0330588	−	0.999453i	$-0.489475\pi$
$983$	2.07297			0.0661175			0.0330588	+	0.999453i	$0.489475\pi$
$984$		0			0
$985$	−89.9042			−2.86459
$986$	−4.04588	+	5.49040i	−0.128847	+	0.174850i
$987$		0			0
$988$	12.9267	+	41.6901i	0.411254	+	1.32634i
$989$			17.2743i			0.549289i
$990$		0			0
$991$	21.9913			0.698578			0.349289	−	0.937015i	$-0.386423\pi$
$991$	21.9913			0.698578			0.349289	+	0.937015i	$0.386423\pi$
$992$	−30.2798	−	1.02178i	−0.961385	−	0.0324416i
$993$		0			0
$994$	−15.3997	−	11.3481i	−0.488450	−	0.359939i
$995$		−	39.7108i		−	1.25892i
$996$		0			0
$997$			50.5232i			1.60009i	0.599943	+	0.800043i	$0.295190\pi$
$997$			50.5232i			1.60009i	−0.599943	+	0.800043i	$0.704810\pi$
$998$	−16.0074	+	21.7226i	−0.506707	+	0.687618i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	792.2.f.h.397.16	yes	20
3.2	odd	2	inner	792.2.f.h.397.5	✓	20
4.3	odd	2		3168.2.f.h.1585.19		20
8.3	odd	2		3168.2.f.h.1585.2		20
8.5	even	2	inner	792.2.f.h.397.15	yes	20
12.11	even	2		3168.2.f.h.1585.1		20
24.5	odd	2	inner	792.2.f.h.397.6	yes	20
24.11	even	2		3168.2.f.h.1585.20		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
792.2.f.h.397.5	✓	20	3.2	odd	2	inner
792.2.f.h.397.6	yes	20	24.5	odd	2	inner
792.2.f.h.397.15	yes	20	8.5	even	2	inner
792.2.f.h.397.16	yes	20	1.1	even	1	trivial
3168.2.f.h.1585.1		20	12.11	even	2
3168.2.f.h.1585.2		20	8.3	odd	2
3168.2.f.h.1585.19		20	4.3	odd	2
3168.2.f.h.1585.20		20	24.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 792 = 2^{3} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	792.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.13849 + 0.838954i) q^{2} +(0.592314 + 1.91028i) q^{4} +3.89064i q^{5} -1.77496 q^{7} +(-0.928292 + 2.67175i) q^{8} +(-3.26407 + 4.42945i) q^{10} +1.00000i q^{11} -5.27974i q^{13} +(-2.02077 - 1.48911i) q^{14} +(-3.29833 + 2.26297i) q^{16} -2.76137 q^{17} +4.13356i q^{19} +(-7.43221 + 2.30448i) q^{20} +(-0.838954 + 1.13849i) q^{22} +6.91533 q^{23} -10.1371 q^{25} +(4.42945 - 6.01092i) q^{26} +(-1.05133 - 3.39067i) q^{28} -1.74643i q^{29} +5.35581 q^{31} +(-5.65364 - 0.190780i) q^{32} +(-3.14379 - 2.31666i) q^{34} -6.90573i q^{35} -3.18176i q^{37} +(-3.46787 + 4.70601i) q^{38} +(-10.3948 - 3.61165i) q^{40} -2.49796 q^{41} +2.49796i q^{43} +(-1.91028 + 0.592314i) q^{44} +(7.87303 + 5.80164i) q^{46} +11.5487 q^{47} -3.84952 q^{49} +(-11.5410 - 8.50456i) q^{50} +(10.0858 - 3.12726i) q^{52} +9.61571i q^{53} -3.89064 q^{55} +(1.64768 - 4.74226i) q^{56} +(1.46517 - 1.98829i) q^{58} +9.27499i q^{59} +13.8896i q^{61} +(6.09753 + 4.49328i) q^{62} +(-6.27655 - 4.96034i) q^{64} +20.5416 q^{65} +3.84858i q^{67} +(-1.63560 - 5.27499i) q^{68} +(5.79359 - 7.86210i) q^{70} +7.62071 q^{71} -10.7678 q^{73} +(2.66935 - 3.62240i) q^{74} +(-7.89626 + 2.44837i) q^{76} -1.77496i q^{77} -0.281256 q^{79} +(-8.80440 - 12.8326i) q^{80} +(-2.84390 - 2.09568i) q^{82} +0.313040i q^{83} -10.7435i q^{85} +(-2.09568 + 2.84390i) q^{86} +(-2.67175 - 0.928292i) q^{88} -2.47638 q^{89} +9.37132i q^{91} +(4.09605 + 13.2102i) q^{92} +(13.1480 + 9.68879i) q^{94} -16.0822 q^{95} +11.7005 q^{97} +(-4.38263 - 3.22957i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{4} + 8 q^{10} - 12 q^{16} - 12 q^{25} + 24 q^{28} + 40 q^{31} - 24 q^{34} - 32 q^{40} + 40 q^{46} + 36 q^{49} + 56 q^{52} - 16 q^{55} + 24 q^{58} + 4 q^{64} + 56 q^{70} - 56 q^{73} - 8 q^{76}+ \cdots + 8 q^{97}+O(q^{100}) \) 20 * q + 4 * q^4 + 8 * q^10 - 12 * q^16 - 12 * q^25 + 24 * q^28 + 40 * q^31 - 24 * q^34 - 32 * q^40 + 40 * q^46 + 36 * q^49 + 56 * q^52 - 16 * q^55 + 24 * q^58 + 4 * q^64 + 56 * q^70 - 56 * q^73 - 8 * q^76 - 16 * q^79 - 32 * q^82 + 12 * q^88 - 24 * q^94 + 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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