LMFDB - Embedded newform 1638.2.p.k.991.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1638,2,Mod(919,1638)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1638, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1638.919"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.p (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [10,5,0,-5,2,0,0] 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:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.23207289578928.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 3x^{8} + 13x^{7} + x^{6} - 39x^{5} + 3x^{4} + 117x^{3} - 81x^{2} - 162x + 243 $ x^10 - 2x^9 - 3x^8 + 13x^7 + x^6 - 39x^5 + 3x^4 + 117x^3 - 81x^2 - 162x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			991.1
Root			$1.16412 - 1.28251i$ of defining polynomial
Character	$\chi$	$=$	1638.991
Dual form			1638.2.p.k.919.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.69274 - 2.93192i) q^{5} +(-2.60522 - 0.461340i) q^{7} -1.00000 q^{8} -3.38549 q^{10} -3.81165 q^{11} +(-3.24071 - 1.58045i) q^{13} +(-1.70214 + 2.02552i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.02198 + 3.50217i) q^{17} +6.15867 q^{19} +(-1.69274 + 2.93192i) q^{20} +(-1.90582 + 3.30098i) q^{22} +(0.528629 - 0.915612i) q^{23} +(-3.23077 + 5.59586i) q^{25} +(-2.98906 + 2.01631i) q^{26} +(0.903077 + 2.48686i) q^{28} +(1.15418 + 1.99910i) q^{29} +(-1.99060 + 3.44783i) q^{31} +(0.500000 + 0.866025i) q^{32} +4.04396 q^{34} +(3.05736 + 8.41923i) q^{35} +(2.71208 - 4.69745i) q^{37} +(3.07934 - 5.33357i) q^{38} +(1.69274 + 2.93192i) q^{40} +(2.26094 + 3.91606i) q^{41} +(3.46973 - 6.00975i) q^{43} +(1.90582 + 3.30098i) q^{44} +(-0.528629 - 0.915612i) q^{46} +(2.77034 + 4.79836i) q^{47} +(6.57433 + 2.40379i) q^{49} +(3.23077 + 5.59586i) q^{50} +(0.251642 + 3.59676i) q^{52} +(-3.81720 + 6.61158i) q^{53} +(6.45214 + 11.1754i) q^{55} +(2.60522 + 0.461340i) q^{56} +2.30836 q^{58} +(-3.74061 - 6.47892i) q^{59} -12.7931 q^{61} +(1.99060 + 3.44783i) q^{62} +1.00000 q^{64} +(0.851932 + 12.1768i) q^{65} -8.84811 q^{67} +(2.02198 - 3.50217i) q^{68} +(8.81994 + 1.56186i) q^{70} +(7.21308 - 12.4934i) q^{71} +(-3.61790 + 6.26639i) q^{73} +(-2.71208 - 4.69745i) q^{74} +(-3.07934 - 5.33357i) q^{76} +(9.93017 + 1.75847i) q^{77} +(0.222913 + 0.386097i) q^{79} +3.38549 q^{80} +4.52188 q^{82} -15.1718 q^{83} +(6.84539 - 11.8566i) q^{85} +(-3.46973 - 6.00975i) q^{86} +3.81165 q^{88} +(4.11790 - 7.13241i) q^{89} +(7.71362 + 5.61249i) q^{91} -1.05726 q^{92} +5.54067 q^{94} +(-10.4251 - 18.0567i) q^{95} +(-6.18181 + 10.7072i) q^{97} +(5.36890 - 4.49164i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 5 q^{2} - 5 q^{4} + 2 q^{5} - 10 q^{8} + 4 q^{10} - 8 q^{11} - 6 q^{13} + 3 q^{14} - 5 q^{16} + 3 q^{17} + 10 q^{19} + 2 q^{20} - 4 q^{22} - 4 q^{23} - 3 q^{25} - 6 q^{26} + 3 q^{28} - q^{29} - 21 q^{31}+ \cdots + 5 q^{98}+O(q^{100}) $ 10 * q + 5 * q^2 - 5 * q^4 + 2 * q^5 - 10 * q^8 + 4 * q^10 - 8 * q^11 - 6 * q^13 + 3 * q^14 - 5 * q^16 + 3 * q^17 + 10 * q^19 + 2 * q^20 - 4 * q^22 - 4 * q^23 - 3 * q^25 - 6 * q^26 + 3 * q^28 - q^29 - 21 * q^31 + 5 * q^32 + 6 * q^34 + 22 * q^35 + 10 * q^37 + 5 * q^38 - 2 * q^40 + 9 * q^41 + 9 * q^43 + 4 * q^44 + 4 * q^46 + 13 * q^47 - 8 * q^49 + 3 * q^50 + 15 * q^53 + 7 * q^55 - 2 * q^58 - q^59 + 30 * q^61 + 21 * q^62 + 10 * q^64 + 25 * q^65 + 3 * q^68 + 26 * q^70 + q^71 - 4 * q^73 - 10 * q^74 - 5 * q^76 - 16 * q^77 - q^79 - 4 * q^80 + 18 * q^82 - 96 * q^83 + 12 * q^85 - 9 * q^86 + 8 * q^88 + 9 * q^89 + 10 * q^91 + 8 * q^92 + 26 * q^94 - 6 * q^95 - 19 * q^97 + 5 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.69274	−	2.93192i	−0.757019	−	1.31119i	−0.944365	−	0.328901i	$-0.893322\pi$
$5$	−1.69274	−	2.93192i	−0.757019	−	1.31119i	0.187346	−	0.982294i	$-0.440011\pi$
$6$		0			0
$7$	−2.60522	−	0.461340i	−0.984680	−	0.174370i
$7$	−2.60522	−	0.461340i	−0.984680	−	0.174370i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−3.38549			−1.07059
$11$	−3.81165			−1.14925			−0.574627	−	0.818415i	$-0.694853\pi$
$11$	−3.81165			−1.14925			−0.574627	+	0.818415i	$0.694853\pi$
$12$		0			0
$13$	−3.24071	−	1.58045i	−0.898810	−	0.438338i
$13$	−3.24071	−	1.58045i	−0.898810	−	0.438338i
$14$	−1.70214	+	2.02552i	−0.454917	+	0.541342i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.02198	+	3.50217i	0.490402	+	0.849401i	0.999939	−	0.0110479i	$-0.00351672\pi$
$17$	2.02198	+	3.50217i	0.490402	+	0.849401i	−0.509537	+	0.860449i	$0.670183\pi$
$18$		0			0
$19$	6.15867			1.41290			0.706448	−	0.707765i	$-0.250296\pi$
$19$	6.15867			1.41290			0.706448	+	0.707765i	$0.250296\pi$
$20$	−1.69274	+	2.93192i	−0.378509	+	0.655597i
$21$		0			0
$22$	−1.90582	+	3.30098i	−0.406323	+	0.703772i
$23$	0.528629	−	0.915612i	0.110227	−	0.190918i	−0.805635	−	0.592412i	$-0.798176\pi$
$23$	0.528629	−	0.915612i	0.110227	−	0.190918i	0.915862	+	0.401494i	$0.131509\pi$
$24$		0			0
$25$	−3.23077	+	5.59586i	−0.646154	+	1.11917i
$26$	−2.98906	+	2.01631i	−0.586204	+	0.395431i
$27$		0			0
$28$	0.903077	+	2.48686i	0.170665	+	0.469972i
$29$	1.15418	+	1.99910i	0.214326	+	0.371224i	0.953064	−	0.302769i	$-0.0979112\pi$
$29$	1.15418	+	1.99910i	0.214326	+	0.371224i	−0.738738	+	0.673993i	$0.764578\pi$
$30$		0			0
$31$	−1.99060	+	3.44783i	−0.357523	+	0.619248i	−0.987546	−	0.157328i	$-0.949712\pi$
$31$	−1.99060	+	3.44783i	−0.357523	+	0.619248i	0.630023	+	0.776576i	$0.283045\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	4.04396			0.693533
$35$	3.05736	+	8.41923i	0.516788	+	1.42311i
$36$		0			0
$37$	2.71208	−	4.69745i	0.445863	−	0.772257i	−0.552249	−	0.833679i	$-0.686230\pi$
$37$	2.71208	−	4.69745i	0.445863	−	0.772257i	0.998112	+	0.0614223i	$0.0195636\pi$
$38$	3.07934	−	5.33357i	0.499534	−	0.865219i
$39$		0			0
$40$	1.69274	+	2.93192i	0.267646	+	0.463577i
$41$	2.26094	+	3.91606i	0.353099	+	0.611586i	0.986791	−	0.162000i	$-0.0517944\pi$
$41$	2.26094	+	3.91606i	0.353099	+	0.611586i	−0.633691	+	0.773586i	$0.718461\pi$
$42$		0			0
$43$	3.46973	−	6.00975i	0.529129	−	0.916479i	−0.470294	−	0.882510i	$-0.655852\pi$
$43$	3.46973	−	6.00975i	0.529129	−	0.916479i	0.999423	−	0.0339686i	$-0.0108146\pi$
$44$	1.90582	+	3.30098i	0.287314	+	0.497642i
$45$		0			0
$46$	−0.528629	−	0.915612i	−0.0779421	−	0.135000i
$47$	2.77034	+	4.79836i	0.404095	+	0.699913i	0.994216	−	0.107402i	$-0.0342532\pi$
$47$	2.77034	+	4.79836i	0.404095	+	0.699913i	−0.590121	+	0.807315i	$0.700920\pi$
$48$		0			0
$49$	6.57433	+	2.40379i	0.939190	+	0.343398i
$50$	3.23077	+	5.59586i	0.456900	+	0.791374i
$51$		0			0
$52$	0.251642	+	3.59676i	0.0348965	+	0.498781i
$53$	−3.81720	+	6.61158i	−0.524332	+	0.908170i	0.475267	+	0.879842i	$0.342352\pi$
$53$	−3.81720	+	6.61158i	−0.524332	+	0.908170i	−0.999599	+	0.0283281i	$0.990982\pi$
$54$		0			0
$55$	6.45214	+	11.1754i	0.870007	+	1.50690i
$56$	2.60522	+	0.461340i	0.348137	+	0.0616492i
$57$		0			0
$58$	2.30836			0.303103
$59$	−3.74061	−	6.47892i	−0.486985	−	0.843483i	0.512903	−	0.858447i	$-0.328570\pi$
$59$	−3.74061	−	6.47892i	−0.486985	−	0.843483i	−0.999888	+	0.0149633i	$0.995237\pi$
$60$		0			0
$61$	−12.7931			−1.63798			−0.818992	−	0.573805i	$-0.805467\pi$
$61$	−12.7931			−1.63798			−0.818992	+	0.573805i	$0.805467\pi$
$62$	1.99060	+	3.44783i	0.252807	+	0.437874i
$63$		0			0
$64$	1.00000			0.125000
$65$	0.851932	+	12.1768i	0.105669	+	1.51035i
$66$		0			0
$67$	−8.84811			−1.08097			−0.540484	−	0.841354i	$-0.681759\pi$
$67$	−8.84811			−1.08097			−0.540484	+	0.841354i	$0.681759\pi$
$68$	2.02198	−	3.50217i	0.245201	−	0.424700i
$69$		0			0
$70$	8.81994	+	1.56186i	1.05418	+	0.186678i
$71$	7.21308	−	12.4934i	0.856036	−	1.48270i	−0.0196454	−	0.999807i	$-0.506254\pi$
$71$	7.21308	−	12.4934i	0.856036	−	1.48270i	0.875681	−	0.482890i	$-0.160413\pi$
$72$		0			0
$73$	−3.61790	+	6.26639i	−0.423443	+	0.733425i	−0.996274	−	0.0862488i	$-0.972512\pi$
$73$	−3.61790	+	6.26639i	−0.423443	+	0.733425i	0.572830	+	0.819674i	$0.305845\pi$
$74$	−2.71208	−	4.69745i	−0.315273	−	0.546068i
$75$		0			0
$76$	−3.07934	−	5.33357i	−0.353224	−	0.611802i
$77$	9.93017	+	1.75847i	1.13165	+	0.200396i
$78$		0			0
$79$	0.222913	+	0.386097i	0.0250797	+	0.0434393i	0.878293	−	0.478123i	$-0.158683\pi$
$79$	0.222913	+	0.386097i	0.0250797	+	0.0434393i	−0.853213	+	0.521562i	$0.825349\pi$
$80$	3.38549			0.378509
$81$		0			0
$82$	4.52188			0.499358
$83$	−15.1718			−1.66532			−0.832659	−	0.553786i	$-0.813183\pi$
$83$	−15.1718			−1.66532			−0.832659	+	0.553786i	$0.813183\pi$
$84$		0			0
$85$	6.84539	−	11.8566i	0.742486	−	1.28602i
$86$	−3.46973	−	6.00975i	−0.374151	−	0.648048i
$87$		0			0
$88$	3.81165			0.406323
$89$	4.11790	−	7.13241i	0.436497	−	0.756034i	−0.560920	−	0.827870i	$-0.689552\pi$
$89$	4.11790	−	7.13241i	0.436497	−	0.756034i	0.997416	+	0.0718359i	$0.0228858\pi$
$90$		0			0
$91$	7.71362	+	5.61249i	0.808607	+	0.588349i
$92$	−1.05726			−0.110227
$93$		0			0
$94$	5.54067			0.571477
$95$	−10.4251	−	18.0567i	−1.06959	−	1.85258i
$96$		0			0
$97$	−6.18181	+	10.7072i	−0.627668	+	1.08715i	0.360351	+	0.932817i	$0.382657\pi$
$97$	−6.18181	+	10.7072i	−0.627668	+	1.08715i	−0.988019	+	0.154335i	$0.950676\pi$
$98$	5.36890	−	4.49164i	0.542341	−	0.453725i
$99$		0			0
$100$	6.46154			0.646154
$101$	−12.2347			−1.21740			−0.608700	−	0.793400i	$-0.708309\pi$
$101$	−12.2347			−1.21740			−0.608700	+	0.793400i	$0.708309\pi$
$102$		0			0
$103$	5.59528	+	9.69132i	0.551320	+	0.954914i	0.998180	+	0.0603098i	$0.0192089\pi$
$103$	5.59528	+	9.69132i	0.551320	+	0.954914i	−0.446860	+	0.894604i	$0.647458\pi$
$104$	3.24071	+	1.58045i	0.317777	+	0.154976i
$105$		0			0
$106$	3.81720	+	6.61158i	0.370759	+	0.642173i
$107$	0.681703	−	1.18074i	0.0659027	−	0.114147i	−0.831191	−	0.555986i	$-0.812341\pi$
$107$	0.681703	−	1.18074i	0.0659027	−	0.114147i	0.897094	+	0.441840i	$0.145674\pi$
$108$		0			0
$109$	−1.56445	+	2.70970i	−0.149847	+	0.259542i	−0.931171	−	0.364583i	$-0.881211\pi$
$109$	−1.56445	+	2.70970i	−0.149847	+	0.259542i	0.781324	+	0.624126i	$0.214545\pi$
$110$	12.9043			1.23038
$111$		0			0
$112$	1.70214	−	2.02552i	0.160837	−	0.191393i
$113$	−6.53202	+	11.3138i	−0.614481	+	1.06431i	0.375995	+	0.926622i	$0.377301\pi$
$113$	−6.53202	+	11.3138i	−0.614481	+	1.06431i	−0.990475	+	0.137690i	$0.956032\pi$
$114$		0			0
$115$	−3.57934			−0.333775
$116$	1.15418	−	1.99910i	0.107163	−	0.185612i
$117$		0			0
$118$	−7.48121			−0.688701
$119$	−3.65200	−	10.0567i	−0.334779	−	0.921900i
$120$		0			0
$121$	3.52865			0.320786
$122$	−6.39653	+	11.0791i	−0.579115	+	1.00306i
$123$		0			0
$124$	3.98121			0.357523
$125$	4.94803			0.442566
$126$		0			0
$127$	1.67077	+	2.89385i	0.148257	+	0.256788i	0.930583	−	0.366081i	$-0.119301\pi$
$127$	1.67077	+	2.89385i	0.148257	+	0.256788i	−0.782327	+	0.622868i	$0.785967\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	10.9714	+	5.35060i	0.962253	+	0.469279i
$131$	1.26769	+	2.19570i	0.110759	+	0.191839i	0.916076	−	0.401004i	$-0.131339\pi$
$131$	1.26769	+	2.19570i	0.110759	+	0.191839i	−0.805318	+	0.592843i	$0.798005\pi$
$132$		0			0
$133$	−16.0447	−	2.84124i	−1.39125	−	0.246367i
$134$	−4.42405	+	7.66269i	−0.382180	+	0.661955i
$135$		0			0
$136$	−2.02198	−	3.50217i	−0.173383	−	0.300309i
$137$	6.30346	+	10.9179i	0.538541	+	0.932780i	0.998983	+	0.0450901i	$0.0143575\pi$
$137$	6.30346	+	10.9179i	0.538541	+	0.932780i	−0.460442	+	0.887690i	$0.652309\pi$
$138$		0			0
$139$	−9.41422	+	16.3059i	−0.798504	+	1.38305i	0.122086	+	0.992520i	$0.461042\pi$
$139$	−9.41422	+	16.3059i	−0.798504	+	1.38305i	−0.920590	+	0.390530i	$0.872292\pi$
$140$	5.76258	−	6.85736i	0.487027	−	0.579553i
$141$		0			0
$142$	−7.21308	−	12.4934i	−0.605309	−	1.04843i
$143$	12.3524	+	6.02412i	1.03296	+	0.503762i
$144$		0			0
$145$	3.90747	−	6.76793i	0.324498	−	0.562046i
$146$	3.61790	+	6.26639i	0.299420	+	0.518610i
$147$		0			0
$148$	−5.42415			−0.445863
$149$	−0.900600			−0.0737800			−0.0368900	−	0.999319i	$-0.511745\pi$
$149$	−0.900600			−0.0737800			−0.0368900	+	0.999319i	$0.511745\pi$
$150$		0			0
$151$	4.25984	−	7.37826i	0.346661	−	0.600434i	−0.638993	−	0.769212i	$-0.720649\pi$
$151$	4.25984	−	7.37826i	0.346661	−	0.600434i	0.985654	+	0.168778i	$0.0539822\pi$
$152$	−6.15867			−0.499534
$153$		0			0
$154$	6.48796	−	7.72055i	0.522815	−	0.622140i
$155$	13.4783			1.08261
$156$		0			0
$157$	−8.58044	+	14.8618i	−0.684794	+	1.18610i	0.288708	+	0.957417i	$0.406774\pi$
$157$	−8.58044	+	14.8618i	−0.684794	+	1.18610i	−0.973502	+	0.228681i	$0.926559\pi$
$158$	0.445826			0.0354680
$159$		0			0
$160$	1.69274	−	2.93192i	0.133823	−	0.231789i
$161$	−1.79960	+	2.14149i	−0.141829	+	0.168773i
$162$		0			0
$163$	15.3363			1.20123			0.600614	−	0.799539i	$-0.294923\pi$
$163$	15.3363			1.20123			0.600614	+	0.799539i	$0.294923\pi$
$164$	2.26094	−	3.91606i	0.176550	−	0.305793i
$165$		0			0
$166$	−7.58589	+	13.1391i	−0.588779	+	1.01980i
$167$	−8.86135	−	15.3483i	−0.685712	−	1.18769i	−0.973212	−	0.229908i	$-0.926158\pi$
$167$	−8.86135	−	15.3483i	−0.685712	−	1.18769i	0.287500	−	0.957780i	$-0.407176\pi$
$168$		0			0
$169$	8.00435	+	10.2436i	0.615719	+	0.787966i
$170$	−6.84539	−	11.8566i	−0.525017	−	0.909356i
$171$		0			0
$172$	−6.93946			−0.529129
$173$	−1.13351			−0.0861791			−0.0430896	−	0.999071i	$-0.513720\pi$
$173$	−1.13351			−0.0861791			−0.0430896	+	0.999071i	$0.513720\pi$
$174$		0			0
$175$	10.9985	−	13.0880i	0.831405	−	0.989356i
$176$	1.90582	−	3.30098i	0.143657	−	0.248821i
$177$		0			0
$178$	−4.11790	−	7.13241i	−0.308650	−	0.534597i
$179$	−12.6667			−0.946753			−0.473376	−	0.880860i	$-0.656965\pi$
$179$	−12.6667			−0.946753			−0.473376	+	0.880860i	$0.656965\pi$
$180$		0			0
$181$	0.919394			0.0683380			0.0341690	−	0.999416i	$-0.489122\pi$
$181$	0.919394			0.0683380			0.0341690	+	0.999416i	$0.489122\pi$
$182$	8.71737	−	3.87395i	0.646174	−	0.287156i
$183$		0			0
$184$	−0.528629	+	0.915612i	−0.0389710	+	0.0674998i
$185$	−18.3634			−1.35011
$186$		0			0
$187$	−7.70707	−	13.3490i	−0.563596	−	0.976178i
$188$	2.77034	−	4.79836i	0.202048	−	0.349957i
$189$		0			0
$190$	−20.8501			−1.51263
$191$	−3.08586			−0.223285			−0.111643	−	0.993748i	$-0.535611\pi$
$191$	−3.08586			−0.223285			−0.111643	+	0.993748i	$0.535611\pi$
$192$		0			0
$193$	−20.9098			−1.50512			−0.752560	−	0.658524i	$-0.771181\pi$
$193$	−20.9098			−1.50512			−0.752560	+	0.658524i	$0.771181\pi$
$194$	6.18181	+	10.7072i	0.443828	+	0.768733i
$195$		0			0
$196$	−1.20543	−	6.89543i	−0.0861019	−	0.492531i
$197$	−1.71308	−	2.96714i	−0.122052	−	0.211400i	0.798525	−	0.601962i	$-0.205614\pi$
$197$	−1.71308	−	2.96714i	−0.122052	−	0.211400i	−0.920577	+	0.390562i	$0.872281\pi$
$198$		0			0
$199$	−6.44121	−	11.1565i	−0.456605	−	0.790863i	0.542174	−	0.840266i	$-0.317601\pi$
$199$	−6.44121	−	11.1565i	−0.456605	−	0.790863i	−0.998779	+	0.0494031i	$0.984268\pi$
$200$	3.23077	−	5.59586i	0.228450	−	0.395687i
$201$		0			0
$202$	−6.11736	+	10.5956i	−0.430416	+	0.745503i
$203$	−2.08463	−	5.74056i	−0.146312	−	0.402909i
$204$		0			0
$205$	7.65439	−	13.2578i	0.534606	−	0.925964i
$206$	11.1906			0.779684
$207$		0			0
$208$	2.98906	−	2.01631i	0.207254	−	0.139806i
$209$	−23.4747			−1.62378
$210$		0			0
$211$	2.06776	+	3.58146i	0.142350	+	0.246558i	0.928381	−	0.371629i	$-0.121201\pi$
$211$	2.06776	+	3.58146i	0.142350	+	0.246558i	−0.786031	+	0.618187i	$0.787867\pi$
$212$	7.63439			0.524332
$213$		0			0
$214$	−0.681703	−	1.18074i	−0.0466003	−	0.0807140i
$215$	−23.4935			−1.60224
$216$		0			0
$217$	6.77658	−	8.06399i	0.460024	−	0.547420i
$218$	1.56445	+	2.70970i	0.105958	+	0.183524i
$219$		0			0
$220$	6.45214	−	11.1754i	0.435004	−	0.753448i
$221$	−1.01763	−	14.5451i	−0.0684532	−	0.978412i
$222$		0			0
$223$	−1.07475	−	1.86151i	−0.0719703	−	0.124656i	0.827794	−	0.561031i	$-0.189595\pi$
$223$	−1.07475	−	1.86151i	−0.0719703	−	0.124656i	−0.899765	+	0.436375i	$0.856262\pi$
$224$	−0.903077	−	2.48686i	−0.0603394	−	0.166160i
$225$		0			0
$226$	6.53202	+	11.3138i	0.434503	+	0.752582i
$227$	3.91933	+	6.78848i	0.260135	+	0.450567i	0.966278	−	0.257503i	$-0.0828996\pi$
$227$	3.91933	+	6.78848i	0.260135	+	0.450567i	−0.706143	+	0.708070i	$0.749566\pi$
$228$		0			0
$229$	5.97741	+	10.3532i	0.394998	+	0.684157i	0.993101	−	0.117262i	$-0.0374119\pi$
$229$	5.97741	+	10.3532i	0.394998	+	0.684157i	−0.598103	+	0.801419i	$0.704079\pi$
$230$	−1.78967	+	3.09980i	−0.118007	+	0.204394i
$231$		0			0
$232$	−1.15418	−	1.99910i	−0.0757757	−	0.131247i
$233$	14.0340	+	24.3076i	0.919400	+	1.59245i	0.800329	+	0.599561i	$0.204658\pi$
$233$	14.0340	+	24.3076i	0.919400	+	1.59245i	0.119071	+	0.992886i	$0.462008\pi$
$234$		0			0
$235$	9.37894	−	16.2448i	0.611815	−	1.05969i
$236$	−3.74061	+	6.47892i	−0.243493	+	0.421742i
$237$		0			0
$238$	−10.5354	−	1.86564i	−0.682908	−	0.120931i
$239$	14.8144			0.958262			0.479131	−	0.877743i	$-0.340952\pi$
$239$	14.8144			0.958262			0.479131	+	0.877743i	$0.340952\pi$
$240$		0			0
$241$	0.473016	+	0.819288i	0.0304696	+	0.0527750i	0.880858	−	0.473380i	$-0.156966\pi$
$241$	0.473016	+	0.819288i	0.0304696	+	0.0527750i	−0.850388	+	0.526155i	$0.823633\pi$
$242$	1.76432	−	3.05590i	0.113415	−	0.196441i
$243$		0			0
$244$	6.39653	+	11.0791i	0.409496	+	0.709268i
$245$	−4.08096	−	23.3444i	−0.260723	−	1.49142i
$246$		0			0
$247$	−19.9584	−	9.73348i	−1.26993	−	0.619327i
$248$	1.99060	−	3.44783i	0.126403	−	0.218937i
$249$		0			0
$250$	2.47402	−	4.28512i	0.156471	−	0.271015i
$251$	−6.43291	+	11.1421i	−0.406042	+	0.703285i	−0.994442	−	0.105285i	$-0.966425\pi$
$251$	−6.43291	+	11.1421i	−0.406042	+	0.703285i	0.588400	+	0.808570i	$0.299758\pi$
$252$		0			0
$253$	−2.01495	+	3.48999i	−0.126679	+	0.219414i
$254$	3.34153			0.209666
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−1.70763	+	2.95771i	−0.106519	+	0.184497i	−0.914358	−	0.404907i	$-0.867304\pi$
$257$	−1.70763	+	2.95771i	−0.106519	+	0.184497i	0.807839	+	0.589404i	$0.200637\pi$
$258$		0			0
$259$	−9.23268	+	10.9867i	−0.573691	+	0.682681i
$260$	10.1194	−	6.82619i	0.627581	−	0.423342i
$261$		0			0
$262$	2.53538			0.156636
$263$	0.446191			0.0275133			0.0137567	−	0.999905i	$-0.495621\pi$
$263$	0.446191			0.0275133			0.0137567	+	0.999905i	$0.495621\pi$
$264$		0			0
$265$	25.8462			1.58772
$266$	−10.4829	+	12.4745i	−0.642750	+	0.764860i
$267$		0			0
$268$	4.42405	+	7.66269i	0.270242	+	0.468073i
$269$	2.05561	+	3.56043i	0.125333	+	0.217083i	0.921863	−	0.387516i	$-0.126667\pi$
$269$	2.05561	+	3.56043i	0.125333	+	0.217083i	−0.796530	+	0.604599i	$0.793333\pi$
$270$		0			0
$271$	6.67506	−	11.5615i	0.405481	−	0.702314i	−0.588896	−	0.808209i	$-0.700437\pi$
$271$	6.67506	−	11.5615i	0.405481	−	0.702314i	0.994377	+	0.105895i	$0.0337707\pi$
$272$	−4.04396			−0.245201
$273$		0			0
$274$	12.6069			0.761611
$275$	12.3146	−	21.3294i	0.742596	−	1.28621i
$276$		0			0
$277$	−9.47805	−	16.4165i	−0.569481	−	0.986369i	−0.996617	−	0.0821822i	$-0.973811\pi$
$277$	−9.47805	−	16.4165i	−0.569481	−	0.986369i	0.427137	−	0.904187i	$-0.359522\pi$
$278$	9.41422	+	16.3059i	0.564628	+	0.977964i
$279$		0			0
$280$	−3.05736	−	8.41923i	−0.182712	−	0.503145i
$281$	0.101414			0.00604986			0.00302493	−	0.999995i	$-0.499037\pi$
$281$	0.101414			0.00604986			0.00302493	+	0.999995i	$0.499037\pi$
$282$		0			0
$283$	4.87779			0.289954			0.144977	−	0.989435i	$-0.453689\pi$
$283$	4.87779			0.289954			0.144977	+	0.989435i	$0.453689\pi$
$284$	−14.4262			−0.856036
$285$		0			0
$286$	11.3933	−	7.68545i	0.673697	−	0.454450i
$287$	−4.08360	−	11.2453i	−0.241048	−	0.663787i
$288$		0			0
$289$	0.323209	−	0.559814i	0.0190123	−	0.0329302i
$290$	−3.90747	−	6.76793i	−0.229454	−	0.397427i
$291$		0			0
$292$	7.23580			0.423443
$293$	12.4185	−	21.5095i	0.725497	−	1.25660i	−0.233272	−	0.972412i	$-0.574943\pi$
$293$	12.4185	−	21.5095i	0.725497	−	1.25660i	0.958769	−	0.284186i	$-0.0917234\pi$
$294$		0			0
$295$	−12.6638	+	21.9343i	−0.737314	+	1.27707i
$296$	−2.71208	+	4.69745i	−0.157636	+	0.273034i
$297$		0			0
$298$	−0.450300	+	0.779942i	−0.0260852	+	0.0451809i
$299$	−3.16021	+	2.13176i	−0.182760	+	0.123283i
$300$		0			0
$301$	−11.8120	+	14.0560i	−0.680830	+	0.810174i
$302$	−4.25984	−	7.37826i	−0.245126	−	0.424571i
$303$		0			0
$304$	−3.07934	+	5.33357i	−0.176612	+	0.305901i
$305$	21.6554	+	37.5082i	1.23998	+	2.14772i
$306$		0			0
$307$	−11.9098			−0.679727			−0.339864	−	0.940475i	$-0.610381\pi$
$307$	−11.9098			−0.679727			−0.339864	+	0.940475i	$0.610381\pi$
$308$	−3.44221	−	9.47901i	−0.196138	−	0.540117i
$309$		0			0
$310$	6.73917	−	11.6726i	0.382759	−	0.662958i
$311$	−1.98193	+	3.43280i	−0.112385	+	0.194656i	−0.916731	−	0.399504i	$-0.869182\pi$
$311$	−1.98193	+	3.43280i	−0.112385	+	0.194656i	0.804347	+	0.594160i	$0.202516\pi$
$312$		0			0
$313$	−13.7241	−	23.7709i	−0.775733	−	1.34361i	−0.934381	−	0.356275i	$-0.884047\pi$
$313$	−13.7241	−	23.7709i	−0.775733	−	1.34361i	0.158648	−	0.987335i	$-0.449287\pi$
$314$	8.58044	+	14.8618i	0.484222	+	0.838698i
$315$		0			0
$316$	0.222913	−	0.386097i	0.0125398	−	0.0217197i
$317$	−12.2858	−	21.2796i	−0.690038	−	1.19518i	−0.971825	−	0.235703i	$-0.924261\pi$
$317$	−12.2858	−	21.2796i	−0.690038	−	1.19518i	0.281788	−	0.959477i	$-0.409073\pi$
$318$		0			0
$319$	−4.39933	−	7.61986i	−0.246315	−	0.426630i
$320$	−1.69274	−	2.93192i	−0.0946273	−	0.163899i
$321$		0			0
$322$	0.954785	+	2.62925i	0.0532081	+	0.146522i
$323$	12.4527	+	21.5687i	0.692887	+	1.20012i
$324$		0			0
$325$	19.3140	−	13.0285i	1.07135	−	0.722689i
$326$	7.66813	−	13.2816i	0.424698	−	0.735599i
$327$		0			0
$328$	−2.26094	−	3.91606i	−0.124839	−	0.216228i
$329$	−5.00365	−	13.7789i	−0.275860	−	0.759653i
$330$		0			0
$331$	28.6536			1.57494			0.787472	−	0.616350i	$-0.211389\pi$
$331$	28.6536			1.57494			0.787472	+	0.616350i	$0.211389\pi$
$332$	7.58589	+	13.1391i	0.416330	+	0.721104i
$333$		0			0
$334$	−17.7227			−0.969743
$335$	14.9776	+	25.9419i	0.818313	+	1.41736i
$336$		0			0
$337$	8.86295			0.482795			0.241398	−	0.970426i	$-0.422394\pi$
$337$	8.86295			0.482795			0.241398	+	0.970426i	$0.422394\pi$
$338$	12.8734	−	1.81019i	0.700218	−	0.0984615i
$339$		0			0
$340$	−13.6908			−0.742486
$341$	7.58747	−	13.1419i	0.410885	−	0.711673i
$342$		0			0
$343$	−16.0186	−	9.29539i	−0.864923	−	0.501904i
$344$	−3.46973	+	6.00975i	−0.187075	+	0.324024i
$345$		0			0
$346$	−0.566755	+	0.981648i	−0.0304689	+	0.0527737i
$347$	0.628304	+	1.08825i	0.0337291	+	0.0584205i	0.882397	−	0.470505i	$-0.155928\pi$
$347$	0.628304	+	1.08825i	0.0337291	+	0.0584205i	−0.848668	+	0.528926i	$0.822595\pi$
$348$		0			0
$349$	−11.8310	−	20.4919i	−0.633298	−	1.09690i	−0.986873	−	0.161499i	$-0.948367\pi$
$349$	−11.8310	−	20.4919i	−0.633298	−	1.09690i	0.353575	−	0.935406i	$-0.384966\pi$
$350$	−5.83527	−	16.0689i	−0.311908	−	0.858920i
$351$		0			0
$352$	−1.90582	−	3.30098i	−0.101581	−	0.175943i
$353$	11.9262			0.634766			0.317383	−	0.948298i	$-0.397196\pi$
$353$	11.9262			0.634766			0.317383	+	0.948298i	$0.397196\pi$
$354$		0			0
$355$	−48.8396			−2.59214
$356$	−8.23580			−0.436497
$357$		0			0
$358$	−6.33334	+	10.9697i	−0.334728	+	0.579765i
$359$	−1.48413	−	2.57060i	−0.0783296	−	0.135671i	0.824200	−	0.566299i	$-0.191625\pi$
$359$	−1.48413	−	2.57060i	−0.0783296	−	0.135671i	−0.902529	+	0.430628i	$0.858292\pi$
$360$		0			0
$361$	18.9292			0.996276
$362$	0.459697	−	0.796218i	0.0241611	−	0.0418483i
$363$		0			0
$364$	1.00375	−	9.48644i	0.0526107	−	0.497224i
$365$	24.4967			1.28222
$366$		0			0
$367$	13.2847			0.693455			0.346728	−	0.937966i	$-0.387293\pi$
$367$	13.2847			0.693455			0.346728	+	0.937966i	$0.387293\pi$
$368$	0.528629	+	0.915612i	0.0275567	+	0.0477296i
$369$		0			0
$370$	−9.18171	+	15.9032i	−0.477334	+	0.826767i
$371$	12.9948	−	15.4636i	0.674657	−	0.802829i
$372$		0			0
$373$	19.6620			1.01806			0.509029	−	0.860750i	$-0.330005\pi$
$373$	19.6620			1.01806			0.509029	+	0.860750i	$0.330005\pi$
$374$	−15.4141			−0.797046
$375$		0			0
$376$	−2.77034	−	4.79836i	−0.142869	−	0.247457i
$377$	−0.580881	−	8.30262i	−0.0299169	−	0.427607i
$378$		0			0
$379$	−17.0038	−	29.4514i	−0.873425	−	1.51282i	−0.858431	−	0.512929i	$-0.828560\pi$
$379$	−17.0038	−	29.4514i	−0.873425	−	1.51282i	−0.0149946	−	0.999888i	$-0.504773\pi$
$380$	−10.4251	+	18.0567i	−0.534794	+	0.926291i
$381$		0			0
$382$	−1.54293	+	2.67244i	−0.0789433	+	0.136734i
$383$	−35.8064			−1.82962			−0.914810	−	0.403885i	$-0.867660\pi$
$383$	−35.8064			−1.82962			−0.914810	+	0.403885i	$0.867660\pi$
$384$		0			0
$385$	−11.6536	−	32.0911i	−0.593921	−	1.63551i
$386$	−10.4549	+	18.1084i	−0.532140	+	0.921693i
$387$		0			0
$388$	12.3636			0.627668
$389$	−7.37957	+	12.7818i	−0.374159	+	0.648062i	−0.990201	−	0.139651i	$-0.955402\pi$
$389$	−7.37957	+	12.7818i	−0.374159	+	0.648062i	0.616042	+	0.787713i	$0.288735\pi$
$390$		0			0
$391$	4.27550			0.216222
$392$	−6.57433	−	2.40379i	−0.332054	−	0.121409i
$393$		0			0
$394$	−3.42616			−0.172607
$395$	0.754670	−	1.30713i	0.0379716	−	0.0657687i
$396$		0			0
$397$	−28.4087			−1.42579			−0.712895	−	0.701271i	$-0.752616\pi$
$397$	−28.4087			−1.42579			−0.712895	+	0.701271i	$0.752616\pi$
$398$	−12.8824			−0.645737
$399$		0			0
$400$	−3.23077	−	5.59586i	−0.161539	−	0.279793i
$401$	10.3718	−	17.9645i	0.517944	−	0.897105i	−0.481839	−	0.876260i	$-0.660031\pi$
$401$	10.3718	−	17.9645i	0.517944	−	0.897105i	0.999783	−	0.0208450i	$-0.00663564\pi$
$402$		0			0
$403$	11.9001	−	8.02734i	0.592785	−	0.399870i
$404$	6.11736	+	10.5956i	0.304350	+	0.527150i
$405$		0			0
$406$	−6.01379	−	1.06494i	−0.298459	−	0.0528521i
$407$	−10.3375	+	17.9050i	−0.512410	+	0.887520i
$408$		0			0
$409$	7.88886	+	13.6639i	0.390079	+	0.675637i	0.992460	−	0.122572i	$-0.0391143\pi$
$409$	7.88886	+	13.6639i	0.390079	+	0.675637i	−0.602380	+	0.798209i	$0.705781\pi$
$410$	−7.65439	−	13.2578i	−0.378023	−	0.654755i
$411$		0			0
$412$	5.59528	−	9.69132i	0.275660	−	0.477457i
$413$	6.75611	+	18.6047i	0.332446	+	0.915477i
$414$		0			0
$415$	25.6819	+	44.4824i	1.26068	+	2.18356i
$416$	−0.251642	−	3.59676i	−0.0123378	−	0.176346i
$417$		0			0
$418$	−11.7373	+	20.3297i	−0.574092	+	0.994357i
$419$	−2.80653	−	4.86106i	−0.137108	−	0.237478i	0.789293	−	0.614017i	$-0.210447\pi$
$419$	−2.80653	−	4.86106i	−0.137108	−	0.237478i	−0.926401	+	0.376539i	$0.877114\pi$
$420$		0			0
$421$	15.1986			0.740736			0.370368	−	0.928885i	$-0.379232\pi$
$421$	15.1986			0.740736			0.370368	+	0.928885i	$0.379232\pi$
$422$	4.13551			0.201314
$423$		0			0
$424$	3.81720	−	6.61158i	0.185379	−	0.321087i
$425$	−26.1302			−1.26750
$426$		0			0
$427$	33.3287	+	5.90196i	1.61289	+	0.285616i
$428$	−1.36341			−0.0659027
$429$		0			0
$430$	−11.7467	+	20.3460i	−0.566478	+	0.981169i
$431$	−3.37143			−0.162396			−0.0811980	−	0.996698i	$-0.525875\pi$
$431$	−3.37143			−0.162396			−0.0811980	+	0.996698i	$0.525875\pi$
$432$		0			0
$433$	−8.11993	+	14.0641i	−0.390219	+	0.675879i	−0.992478	−	0.122421i	$-0.960934\pi$
$433$	−8.11993	+	14.0641i	−0.390219	+	0.675879i	0.602259	+	0.798301i	$0.294267\pi$
$434$	−3.59534	−	9.90069i	−0.172582	−	0.475248i
$435$		0			0
$436$	3.12889			0.149847
$437$	3.25565	−	5.63896i	0.155739	−	0.269748i
$438$		0			0
$439$	12.0552	−	20.8802i	0.575361	−	0.996555i	−0.420641	−	0.907227i	$-0.638195\pi$
$439$	12.0552	−	20.8802i	0.575361	−	0.996555i	0.996002	−	0.0893280i	$-0.0284719\pi$
$440$	−6.45214	−	11.1754i	−0.307594	−	0.532768i
$441$		0			0
$442$	−13.1053	−	6.39128i	−0.623354	−	0.304002i
$443$	−12.4929	−	21.6383i	−0.593554	−	1.02807i	−0.993749	−	0.111636i	$-0.964391\pi$
$443$	−12.4929	−	21.6383i	−0.593554	−	1.02807i	0.400195	−	0.916430i	$-0.368942\pi$
$444$		0			0
$445$	−27.8822			−1.32174
$446$	−2.14949			−0.101781
$447$		0			0
$448$	−2.60522	−	0.461340i	−0.123085	−	0.0217963i
$449$	−18.3685	+	31.8153i	−0.866865	+	1.50145i	−0.00168225	+	0.999999i	$0.500535\pi$
$449$	−18.3685	+	31.8153i	−0.866865	+	1.50145i	−0.865183	+	0.501456i	$0.832798\pi$
$450$		0			0
$451$	−8.61790	−	14.9266i	−0.405801	−	0.702868i
$452$	13.0640			0.614481
$453$		0			0
$454$	7.83866			0.367887
$455$	3.39818	−	32.1162i	0.159309	−	1.50563i
$456$		0			0
$457$	−0.583289	+	1.01029i	−0.0272851	+	0.0472592i	−0.879346	−	0.476184i	$-0.842020\pi$
$457$	−0.583289	+	1.01029i	−0.0272851	+	0.0472592i	0.852060	+	0.523443i	$0.175353\pi$
$458$	11.9548			0.558612
$459$		0			0
$460$	1.78967	+	3.09980i	0.0834437	+	0.144529i
$461$	6.97353	−	12.0785i	0.324790	−	0.562552i	−0.656680	−	0.754169i	$-0.728040\pi$
$461$	6.97353	−	12.0785i	0.324790	−	0.562552i	0.981470	+	0.191617i	$0.0613731\pi$
$462$		0			0
$463$	−14.0476			−0.652849			−0.326425	−	0.945223i	$-0.605844\pi$
$463$	−14.0476			−0.652849			−0.326425	+	0.945223i	$0.605844\pi$
$464$	−2.30836			−0.107163
$465$		0			0
$466$	28.0681			1.30023
$467$	−4.23028	−	7.32707i	−0.195754	−	0.339056i	0.751393	−	0.659855i	$-0.229382\pi$
$467$	−4.23028	−	7.32707i	−0.195754	−	0.339056i	−0.947148	+	0.320798i	$0.896049\pi$
$468$		0			0
$469$	23.0513	+	4.08199i	1.06441	+	0.188489i
$470$	−9.37894	−	16.2448i	−0.432618	−	0.749317i
$471$		0			0
$472$	3.74061	+	6.47892i	0.172175	+	0.298216i
$473$	−13.2254	+	22.9070i	−0.608104	+	1.05327i
$474$		0			0
$475$	−19.8973	+	34.4631i	−0.912949	+	1.58127i
$476$	−6.88339	+	8.19110i	−0.315500	+	0.375438i
$477$		0			0
$478$	7.40719	−	12.8296i	0.338797	−	0.586813i
$479$	1.81904			0.0831143			0.0415571	−	0.999136i	$-0.486768\pi$
$479$	1.81904			0.0831143			0.0415571	+	0.999136i	$0.486768\pi$
$480$		0			0
$481$	−16.2131	+	10.9368i	−0.739256	+	0.498674i
$482$	0.946032			0.0430906
$483$		0			0
$484$	−1.76432	−	3.05590i	−0.0801965	−	0.138904i
$485$	41.8569			1.90062
$486$		0			0
$487$	−11.0288	−	19.1025i	−0.499764	−	0.865617i	0.500236	−	0.865889i	$-0.333247\pi$
$487$	−11.0288	−	19.1025i	−0.499764	−	0.865617i	−1.00000		0.000272262i	$0.999913\pi$
$488$	12.7931			0.579115
$489$		0			0
$490$	−22.2573	−	8.13799i	−1.00548	−	0.367637i
$491$	−9.99653	−	17.3145i	−0.451137	−	0.781393i	0.547320	−	0.836924i	$-0.315648\pi$
$491$	−9.99653	−	17.3145i	−0.451137	−	0.781393i	−0.998457	+	0.0555310i	$0.982315\pi$
$492$		0			0
$493$	−4.66746	+	8.08427i	−0.210212	+	0.364097i
$494$	−18.4087	+	12.4178i	−0.828245	+	0.558702i
$495$		0			0
$496$	−1.99060	−	3.44783i	−0.0893807	−	0.154812i
$497$	−24.5554	+	29.2204i	−1.10146	+	1.31072i
$498$		0			0
$499$	−18.3789	−	31.8331i	−0.822750	−	1.42505i	−0.903627	−	0.428321i	$-0.859105\pi$
$499$	−18.3789	−	31.8331i	−0.822750	−	1.42505i	0.0808762	−	0.996724i	$-0.474228\pi$
$500$	−2.47402	−	4.28512i	−0.110641	−	0.191637i
$501$		0			0
$502$	6.43291	+	11.1421i	0.287115	+	0.497298i
$503$	−16.7668	+	29.0409i	−0.747594	+	1.29487i	0.201378	+	0.979514i	$0.435458\pi$
$503$	−16.7668	+	29.0409i	−0.747594	+	1.29487i	−0.948973	+	0.315358i	$0.897875\pi$
$504$		0			0
$505$	20.7103	+	35.8712i	0.921595	+	1.59625i
$506$	2.01495	+	3.48999i	0.0895753	+	0.155149i
$507$		0			0
$508$	1.67077	−	2.89385i	0.0741283	−	0.128394i
$509$	−10.6267	+	18.4059i	−0.471018	+	0.815828i	−0.999450	−	0.0331478i	$-0.989447\pi$
$509$	−10.6267	+	18.4059i	−0.471018	+	0.815828i	0.528432	+	0.848976i	$0.322780\pi$
$510$		0			0
$511$	12.3164	−	14.6562i	0.544844	−	0.648353i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	1.70763	+	2.95771i	0.0753205	+	0.130459i
$515$	18.9428	−	32.8099i	0.834718	−	1.44577i
$516$		0			0
$517$	−10.5595	−	18.2897i	−0.464408	−	0.804378i
$518$	4.89843	+	13.4891i	0.215225	+	0.592677i
$519$		0			0
$520$	−0.851932	−	12.1768i	−0.0373597	−	0.533988i
$521$	−2.85368	+	4.94272i	−0.125022	+	0.216545i	−0.921742	−	0.387805i	$-0.873234\pi$
$521$	−2.85368	+	4.94272i	−0.125022	+	0.216545i	0.796719	+	0.604349i	$0.206567\pi$
$522$		0			0
$523$	−8.77764	+	15.2033i	−0.383819	+	0.664794i	−0.991605	−	0.129307i	$-0.958725\pi$
$523$	−8.77764	+	15.2033i	−0.383819	+	0.664794i	0.607785	+	0.794101i	$0.292058\pi$
$524$	1.26769	−	2.19570i	0.0553793	−	0.0959197i
$525$		0			0
$526$	0.223096	−	0.386413i	0.00972743	−	0.0168484i
$527$	−16.0998			−0.701319
$528$		0			0
$529$	10.9411	+	18.9505i	0.475700	+	0.823937i
$530$	12.9231	−	22.3834i	0.561343	−	0.972274i
$531$		0			0
$532$	5.56175	+	15.3157i	0.241133	+	0.664021i
$533$	−1.13789	−	16.2641i	−0.0492877	−	0.704477i
$534$		0			0
$535$	−4.61580			−0.199558
$536$	8.84811			0.382180
$537$		0			0
$538$	4.11123			0.177248
$539$	−25.0590	−	9.16238i	−1.07937	−	0.394652i
$540$		0			0
$541$	−10.3398	−	17.9091i	−0.444545	−	0.769974i	0.553476	−	0.832865i	$-0.313301\pi$
$541$	−10.3398	−	17.9091i	−0.444545	−	0.769974i	−0.998020	+	0.0628915i	$0.979968\pi$
$542$	−6.67506	−	11.5615i	−0.286718	−	0.496611i
$543$		0			0
$544$	−2.02198	+	3.50217i	−0.0866916	+	0.150154i
$545$	10.5928			0.453747
$546$		0			0
$547$	18.2669			0.781035			0.390517	−	0.920596i	$-0.372296\pi$
$547$	18.2669			0.781035			0.390517	+	0.920596i	$0.372296\pi$
$548$	6.30346	−	10.9179i	0.269270	−	0.466390i
$549$		0			0
$550$	−12.3146	−	21.3294i	−0.525094	−	0.909490i
$551$	7.10822	+	12.3118i	0.302820	+	0.524500i
$552$		0			0
$553$	−0.402616	−	1.10871i	−0.0171210	−	0.0471470i
$554$	−18.9561			−0.805367
$555$		0			0
$556$	18.8284			0.798504
$557$	−11.8309			−0.501289			−0.250645	−	0.968079i	$-0.580643\pi$
$557$	−11.8309			−0.501289			−0.250645	+	0.968079i	$0.580643\pi$
$558$		0			0
$559$	−20.7425	+	13.9921i	−0.877314	+	0.591803i
$560$	−8.81994	−	1.56186i	−0.372711	−	0.0660008i
$561$		0			0
$562$	0.0507070	−	0.0878272i	0.00213895	−	0.00370476i
$563$	6.48506	+	11.2325i	0.273313	+	0.473391i	0.969708	−	0.244267i	$-0.0785473\pi$
$563$	6.48506	+	11.2325i	0.273313	+	0.473391i	−0.696395	+	0.717658i	$0.745214\pi$
$564$		0			0
$565$	44.2282			1.86069
$566$	2.43889	−	4.22429i	0.102514	−	0.177560i
$567$		0			0
$568$	−7.21308	+	12.4934i	−0.302654	+	0.524213i
$569$	10.6978	−	18.5291i	0.448475	−	0.776782i	−0.549812	−	0.835289i	$-0.685301\pi$
$569$	10.6978	−	18.5291i	0.448475	−	0.776782i	0.998287	+	0.0585066i	$0.0186339\pi$
$570$		0			0
$571$	−2.43854	+	4.22367i	−0.102050	+	0.176755i	−0.912529	−	0.409012i	$-0.865873\pi$
$571$	−2.43854	+	4.22367i	−0.102050	+	0.176755i	0.810479	+	0.585767i	$0.199207\pi$
$572$	−0.959171	−	13.7096i	−0.0401049	−	0.573226i
$573$		0			0
$574$	−11.7805	−	2.08612i	−0.491708	−	0.0870732i
$575$	3.41576	+	5.91627i	0.142447	+	0.246725i
$576$		0			0
$577$	−21.3531	+	36.9847i	−0.888942	+	1.53969i	−0.0478142	+	0.998856i	$0.515226\pi$
$577$	−21.3531	+	36.9847i	−0.888942	+	1.53969i	−0.841128	+	0.540836i	$0.818108\pi$
$578$	−0.323209	−	0.559814i	−0.0134437	−	0.0232852i
$579$		0			0
$580$	−7.81494			−0.324498
$581$	39.5258	+	6.99935i	1.63981	+	0.290382i
$582$		0			0
$583$	14.5498	−	25.2010i	0.602591	−	1.04372i
$584$	3.61790	−	6.26639i	0.149710	−	0.259305i
$585$		0			0
$586$	−12.4185	−	21.5095i	−0.513004	−	0.888549i
$587$	−10.9345	−	18.9390i	−0.451313	−	0.781698i	0.547155	−	0.837032i	$-0.315711\pi$
$587$	−10.9345	−	18.9390i	−0.451313	−	0.781698i	−0.998468	+	0.0553339i	$0.982378\pi$
$588$		0			0
$589$	−12.2595	+	21.2340i	−0.505143	+	0.874933i
$590$	12.6638	+	21.9343i	0.521360	+	0.903022i
$591$		0			0
$592$	2.71208	+	4.69745i	0.111466	+	0.193064i
$593$	−8.14635	−	14.1099i	−0.334531	−	0.579424i	0.648864	−	0.760904i	$-0.275244\pi$
$593$	−8.14635	−	14.1099i	−0.334531	−	0.579424i	−0.983395	+	0.181480i	$0.941911\pi$
$594$		0			0
$595$	−23.3036	+	27.7309i	−0.955356	+	1.13685i
$596$	0.450300	+	0.779942i	0.0184450	+	0.0319477i
$597$		0			0
$598$	0.266051	+	3.80270i	0.0108796	+	0.155504i
$599$	−3.60763	+	6.24860i	−0.147404	+	0.255311i	−0.930267	−	0.366883i	$-0.880425\pi$
$599$	−3.60763	+	6.24860i	−0.147404	+	0.255311i	0.782863	+	0.622194i	$0.213758\pi$
$600$		0			0
$601$	8.29314	+	14.3641i	0.338284	+	0.585926i	0.984110	−	0.177559i	$-0.0568201\pi$
$601$	8.29314	+	14.3641i	0.338284	+	0.585926i	−0.645826	+	0.763485i	$0.723487\pi$
$602$	6.26687	+	17.2574i	0.255419	+	0.703361i
$603$		0			0
$604$	−8.51968			−0.346661
$605$	−5.97310	−	10.3457i	−0.242841	−	0.420613i
$606$		0			0
$607$	−4.00144			−0.162413			−0.0812067	−	0.996697i	$-0.525877\pi$
$607$	−4.00144			−0.162413			−0.0812067	+	0.996697i	$0.525877\pi$
$608$	3.07934	+	5.33357i	0.124884	+	0.216305i
$609$		0			0
$610$	43.3108			1.75360
$611$	−1.39427	−	19.9285i	−0.0564060	−	0.806219i
$612$		0			0
$613$	34.1729			1.38023			0.690115	−	0.723700i	$-0.257560\pi$
$613$	34.1729			1.38023			0.690115	+	0.723700i	$0.257560\pi$
$614$	−5.95489	+	10.3142i	−0.240320	+	0.416246i
$615$		0			0
$616$	−9.93017	−	1.75847i	−0.400098	−	0.0708506i
$617$	−15.0353	+	26.0419i	−0.605298	+	1.04841i	0.386707	+	0.922203i	$0.373613\pi$
$617$	−15.0353	+	26.0419i	−0.605298	+	1.04841i	−0.992004	+	0.126204i	$0.959721\pi$
$618$		0			0
$619$	−11.2801	+	19.5377i	−0.453386	+	0.785288i	−0.998594	−	0.0530130i	$-0.983118\pi$
$619$	−11.2801	+	19.5377i	−0.453386	+	0.785288i	0.545208	+	0.838301i	$0.316451\pi$
$620$	−6.73917	−	11.6726i	−0.270651	−	0.468782i
$621$		0			0
$622$	1.98193	+	3.43280i	0.0794680	+	0.137643i
$623$	−14.0185	+	16.6817i	−0.561639	+	0.668340i
$624$		0			0
$625$	7.77809	+	13.4721i	0.311124	+	0.538882i
$626$	−27.4483			−1.09705
$627$		0			0
$628$	17.1609			0.684794
$629$	21.9350			0.874607
$630$		0			0
$631$	−2.69111	+	4.66114i	−0.107131	+	0.185557i	−0.914607	−	0.404344i	$-0.867500\pi$
$631$	−2.69111	+	4.66114i	−0.107131	+	0.185557i	0.807476	+	0.589901i	$0.200833\pi$
$632$	−0.222913	−	0.386097i	−0.00886701	−	0.0153581i
$633$		0			0
$634$	−24.5715			−0.975860
$635$	5.65636	−	9.79711i	0.224466	−	0.388786i
$636$		0			0
$637$	−17.5064	−	18.1804i	−0.693629	−	0.720332i
$638$	−8.79866			−0.348342
$639$		0			0
$640$	−3.38549			−0.133823
$641$	−21.4269	−	37.1125i	−0.846313	−	1.46586i	−0.884476	−	0.466586i	$-0.845484\pi$
$641$	−21.4269	−	37.1125i	−0.846313	−	1.46586i	0.0381629	−	0.999272i	$-0.487849\pi$
$642$		0			0
$643$	−11.5199	+	19.9530i	−0.454299	+	0.786870i	−0.998648	−	0.0519898i	$-0.983444\pi$
$643$	−11.5199	+	19.9530i	−0.454299	+	0.786870i	0.544348	+	0.838859i	$0.316777\pi$
$644$	2.75439	+	0.487756i	0.108538	+	0.0192203i
$645$		0			0
$646$	24.9054			0.979890
$647$	7.95096			0.312585			0.156292	−	0.987711i	$-0.450046\pi$
$647$	7.95096			0.312585			0.156292	+	0.987711i	$0.450046\pi$
$648$		0			0
$649$	14.2579	+	24.6953i	0.559670	+	0.969377i
$650$	−1.62600	−	23.2406i	−0.0637768	−	0.911572i
$651$		0			0
$652$	−7.66813	−	13.2816i	−0.300307	−	0.520147i
$653$	−11.7941	+	20.4280i	−0.461540	+	0.799410i	−0.999038	−	0.0438547i	$-0.986036\pi$
$653$	−11.7941	+	20.4280i	−0.461540	+	0.799410i	0.537498	+	0.843265i	$0.319369\pi$
$654$		0			0
$655$	4.29175	−	7.43353i	0.167693	−	0.290452i
$656$	−4.52188			−0.176550
$657$		0			0
$658$	−14.4347	−	2.55614i	−0.562722	−	0.0996485i
$659$	4.71901	−	8.17356i	0.183826	−	0.318397i	−0.759354	−	0.650678i	$-0.774485\pi$
$659$	4.71901	−	8.17356i	0.183826	−	0.318397i	0.943180	+	0.332281i	$0.107818\pi$
$660$		0			0
$661$	12.2600			0.476859			0.238429	−	0.971160i	$-0.423367\pi$
$661$	12.2600			0.476859			0.238429	+	0.971160i	$0.423367\pi$
$662$	14.3268	−	24.8148i	0.556827	−	0.964453i
$663$		0			0
$664$	15.1718			0.588779
$665$	18.8293	+	51.8512i	0.730168	+	2.01071i
$666$		0			0
$667$	2.44053			0.0944979
$668$	−8.86135	+	15.3483i	−0.342856	+	0.593844i
$669$		0			0
$670$	29.9552			1.15727
$671$	48.7626			1.88246
$672$		0			0
$673$	−4.64315	−	8.04217i	−0.178980	−	0.310003i	0.762551	−	0.646928i	$-0.223947\pi$
$673$	−4.64315	−	8.04217i	−0.178980	−	0.310003i	−0.941532	+	0.336925i	$0.890613\pi$
$674$	4.43147	−	7.67554i	0.170694	−	0.295651i
$675$		0			0
$676$	4.86900	−	12.0537i	0.187269	−	0.463606i
$677$	18.6823	+	32.3586i	0.718017	+	1.24364i	0.961784	+	0.273809i	$0.0882835\pi$
$677$	18.6823	+	32.3586i	0.718017	+	1.24364i	−0.243767	+	0.969834i	$0.578383\pi$
$678$		0			0
$679$	21.0446	−	25.0427i	0.807619	−	0.961051i
$680$	−6.84539	+	11.8566i	−0.262509	+	0.454678i
$681$		0			0
$682$	−7.58747	−	13.1419i	−0.290539	−	0.503229i
$683$	13.5875	+	23.5343i	0.519912	+	0.900514i	0.999732	+	0.0231468i	$0.00736853\pi$
$683$	13.5875	+	23.5343i	0.519912	+	0.900514i	−0.479820	+	0.877367i	$0.659298\pi$
$684$		0			0
$685$	21.3403	−	36.9625i	0.815370	−	1.41226i
$686$	−16.0593	+	9.22482i	−0.613149	+	0.352205i
$687$		0			0
$688$	3.46973	+	6.00975i	0.132282	+	0.229120i
$689$	22.8197	−	15.3933i	0.869361	−	0.586437i
$690$		0			0
$691$	−4.83835	+	8.38028i	−0.184060	+	0.318801i	−0.943259	−	0.332057i	$-0.892257\pi$
$691$	−4.83835	+	8.38028i	−0.184060	+	0.318801i	0.759200	+	0.650858i	$0.225591\pi$
$692$	0.566755	+	0.981648i	0.0215448	+	0.0373167i
$693$		0			0
$694$	1.25661			0.0477002
$695$	63.7435			2.41793
$696$		0			0
$697$	−9.14314	+	15.8364i	−0.346321	+	0.599846i
$698$	−23.6620			−0.895619
$699$		0			0
$700$	−16.8337	−	2.98097i	−0.636255	−	0.112670i
$701$	−1.68502			−0.0636423			−0.0318212	−	0.999494i	$-0.510131\pi$
$701$	−1.68502			−0.0636423			−0.0318212	+	0.999494i	$0.510131\pi$
$702$		0			0
$703$	16.7028	−	28.9301i	0.629958	−	1.09112i
$704$	−3.81165			−0.143657
$705$		0			0
$706$	5.96308	−	10.3284i	0.224424	−	0.388713i
$707$	31.8741	+	5.64437i	1.19875	+	0.212278i
$708$		0			0
$709$	−0.718253			−0.0269745			−0.0134873	−	0.999909i	$-0.504293\pi$
$709$	−0.718253			−0.0269745			−0.0134873	+	0.999909i	$0.504293\pi$
$710$	−24.4198	+	42.2964i	−0.916460	+	1.58735i
$711$		0			0
$712$	−4.11790	+	7.13241i	−0.154325	+	0.267298i
$713$	2.10458	+	3.64524i	0.0788172	+	0.136515i
$714$		0			0
$715$	−3.24726	−	46.4136i	−0.121441	−	1.73577i
$716$	6.33334	+	10.9697i	0.236688	+	0.409956i
$717$		0			0
$718$	−2.96827			−0.110775
$719$	−6.01827			−0.224443			−0.112222	−	0.993683i	$-0.535797\pi$
$719$	−6.01827			−0.224443			−0.112222	+	0.993683i	$0.535797\pi$
$720$		0			0
$721$	−10.1059	−	27.8293i	−0.376365	−	1.03642i
$722$	9.46462	−	16.3932i	0.352237	−	0.610092i
$723$		0			0
$724$	−0.459697	−	0.796218i	−0.0170845	−	0.0295912i
$725$	−14.9156			−0.553951
$726$		0			0
$727$	−14.2302			−0.527770			−0.263885	−	0.964554i	$-0.585004\pi$
$727$	−14.2302			−0.527770			−0.263885	+	0.964554i	$0.585004\pi$
$728$	−7.71362	−	5.61249i	−0.285886	−	0.208013i
$729$		0			0
$730$	12.2484	−	21.2148i	0.453332	−	0.785195i
$731$	28.0629			1.03794
$732$		0			0
$733$	23.6186	+	40.9085i	0.872371	+	1.51099i	0.859537	+	0.511074i	$0.170752\pi$
$733$	23.6186	+	40.9085i	0.872371	+	1.51099i	0.0128348	+	0.999918i	$0.495914\pi$
$734$	6.64234	−	11.5049i	0.245173	−	0.424653i
$735$		0			0
$736$	1.05726			0.0389710
$737$	33.7259			1.24231
$738$		0			0
$739$	−45.8535			−1.68675			−0.843374	−	0.537327i	$-0.819434\pi$
$739$	−45.8535			−1.68675			−0.843374	+	0.537327i	$0.819434\pi$
$740$	9.18171	+	15.9032i	0.337526	+	0.584613i
$741$		0			0
$742$	−6.89444	−	18.9856i	−0.253103	−	0.696984i
$743$	−18.5214	−	32.0801i	−0.679486	−	1.17690i	−0.975136	−	0.221608i	$-0.928870\pi$
$743$	−18.5214	−	32.0801i	−0.679486	−	1.17690i	0.295650	−	0.955296i	$-0.404464\pi$
$744$		0			0
$745$	1.52449	+	2.64049i	0.0558528	+	0.0967400i
$746$	9.83098	−	17.0278i	0.359938	−	0.623430i
$747$		0			0
$748$	−7.70707	+	13.3490i	−0.281798	+	0.488089i
$749$	−2.32071	+	2.76160i	−0.0847969	+	0.100907i
$750$		0			0
$751$	11.5864	−	20.0682i	0.422793	−	0.732298i	−0.573419	−	0.819262i	$-0.694383\pi$
$751$	11.5864	−	20.0682i	0.422793	−	0.732298i	0.996211	+	0.0869641i	$0.0277166\pi$
$752$	−5.54067			−0.202048
$753$		0			0
$754$	−7.48072	−	3.64825i	−0.272432	−	0.132862i
$755$	−28.8433			−1.04971
$756$		0			0
$757$	6.69747	+	11.6004i	0.243424	+	0.421622i	0.961687	−	0.274149i	$-0.0883961\pi$
$757$	6.69747	+	11.6004i	0.243424	+	0.421622i	−0.718264	+	0.695771i	$0.755063\pi$
$758$	−34.0076			−1.23521
$759$		0			0
$760$	10.4251	+	18.0567i	0.378157	+	0.654987i
$761$	14.0640			0.509821			0.254910	−	0.966965i	$-0.417954\pi$
$761$	14.0640			0.509821			0.254910	+	0.966965i	$0.417954\pi$
$762$		0			0
$763$	5.32582	−	6.33762i	0.192808	−	0.229437i
$764$	1.54293	+	2.67244i	0.0558213	+	0.0966854i
$765$		0			0
$766$	−17.9032	+	31.0092i	−0.646868	+	1.12041i
$767$	1.88259	+	26.9081i	0.0679763	+	0.971596i
$768$		0			0
$769$	−0.0250756	−	0.0434323i	−0.000904251	−	0.00156621i	0.865573	−	0.500783i	$-0.166954\pi$
$769$	−0.0250756	−	0.0434323i	−0.000904251	−	0.00156621i	−0.866477	+	0.499217i	$0.833621\pi$
$770$	−33.6185	−	5.95327i	−1.21153	−	0.214541i
$771$		0			0
$772$	10.4549	+	18.1084i	0.376280	+	0.651736i
$773$	9.09389	+	15.7511i	0.327085	+	0.566527i	0.981932	−	0.189234i	$-0.0606004\pi$
$773$	9.09389	+	15.7511i	0.327085	+	0.566527i	−0.654847	+	0.755761i	$0.727267\pi$
$774$		0			0
$775$	−12.8624	−	22.2783i	−0.462030	−	0.800259i
$776$	6.18181	−	10.7072i	0.221914	−	0.384366i
$777$		0			0
$778$	7.37957	+	12.7818i	0.264570	+	0.458249i
$779$	13.9244	+	24.1177i	0.498893	+	0.864108i
$780$		0			0
$781$	−27.4937	+	47.6205i	−0.983803	+	1.70400i
$782$	2.13775	−	3.70270i	0.0764459	−	0.132408i
$783$		0			0
$784$	−5.36890	+	4.49164i	−0.191747	+	0.160416i
$785$	58.0980			2.07361
$786$		0			0
$787$	−3.68104	−	6.37575i	−0.131215	−	0.227271i	0.792930	−	0.609312i	$-0.208554\pi$
$787$	−3.68104	−	6.37575i	−0.131215	−	0.227271i	−0.924145	+	0.382042i	$0.875221\pi$
$788$	−1.71308	+	2.96714i	−0.0610259	+	0.105700i
$789$		0			0
$790$	−0.754670	−	1.30713i	−0.0268500	−	0.0465055i
$791$	22.2368	−	26.4614i	0.790651	−	0.940859i
$792$		0			0
$793$	41.4586	+	20.2188i	1.47224	+	0.717991i
$794$	−14.2043	+	24.6026i	−0.504093	+	0.873114i
$795$		0			0
$796$	−6.44121	+	11.1565i	−0.228303	+	0.395432i
$797$	16.3412	−	28.3038i	0.578834	−	1.00257i	−0.416779	−	0.909008i	$-0.636841\pi$
$797$	16.3412	−	28.3038i	0.578834	−	1.00257i	0.995613	−	0.0935627i	$-0.0298256\pi$
$798$		0			0
$799$	−11.2031	+	19.4044i	−0.396338	+	0.686477i
$800$	−6.46154			−0.228450
$801$		0			0
$802$	−10.3718	−	17.9645i	−0.366241	−	0.634349i
$803$	13.7902	−	23.8852i	0.486644	−	0.842892i
$804$		0			0
$805$	9.32495	+	1.65129i	0.328661	+	0.0582004i
$806$	−1.00184	−	14.3194i	−0.0352883	−	0.504381i
$807$		0			0
$808$	12.2347			0.430416
$809$	43.4872			1.52893			0.764465	−	0.644666i	$-0.223003\pi$
$809$	43.4872			1.52893			0.764465	+	0.644666i	$0.223003\pi$
$810$		0			0
$811$	52.1463			1.83110			0.915552	−	0.402199i	$-0.131754\pi$
$811$	52.1463			1.83110			0.915552	+	0.402199i	$0.131754\pi$
$812$	−3.92916	+	4.67562i	−0.137886	+	0.164082i
$813$		0			0
$814$	10.3375	+	17.9050i	0.362328	+	0.627571i
$815$	−25.9604	−	44.9647i	−0.909352	−	1.57504i
$816$		0			0
$817$	21.3689	−	37.0121i	0.747605	−	1.29489i
$818$	15.7777			0.551655
$819$		0			0
$820$	−15.3088			−0.534606
$821$	−20.8070	+	36.0388i	−0.726171	+	1.25776i	0.232320	+	0.972639i	$0.425368\pi$
$821$	−20.8070	+	36.0388i	−0.726171	+	1.25776i	−0.958490	+	0.285125i	$0.907965\pi$
$822$		0			0
$823$	−17.7643	−	30.7686i	−0.619223	−	1.07253i	−0.989628	−	0.143655i	$-0.954114\pi$
$823$	−17.7643	−	30.7686i	−0.619223	−	1.07253i	0.370405	−	0.928870i	$-0.379219\pi$
$824$	−5.59528	−	9.69132i	−0.194921	−	0.337613i
$825$		0			0
$826$	19.4902	+	3.45138i	0.678151	+	0.120089i
$827$	−28.5697			−0.993467			−0.496734	−	0.867903i	$-0.665467\pi$
$827$	−28.5697			−0.993467			−0.496734	+	0.867903i	$0.665467\pi$
$828$		0			0
$829$	1.52449			0.0529478			0.0264739	−	0.999650i	$-0.491572\pi$
$829$	1.52449			0.0529478			0.0264739	+	0.999650i	$0.491572\pi$
$830$	51.3639			1.78287
$831$		0			0
$832$	−3.24071	−	1.58045i	−0.112351	−	0.0547923i
$833$	4.87469	+	27.8848i	0.168898	+	0.966152i
$834$		0			0
$835$	−30.0000	+	51.9616i	−1.03819	+	1.79820i
$836$	11.7373	+	20.3297i	0.405944	+	0.703116i
$837$		0			0
$838$	−5.61307			−0.193900
$839$	−13.9446	+	24.1527i	−0.481420	+	0.833844i	−0.999773	−	0.0213231i	$-0.993212\pi$
$839$	−13.9446	+	24.1527i	−0.481420	+	0.833844i	0.518353	+	0.855167i	$0.326545\pi$
$840$		0			0
$841$	11.8357	−	20.5001i	0.408129	−	0.706900i
$842$	7.59931	−	13.1624i	0.261890	−	0.453606i
$843$		0			0
$844$	2.06776	−	3.58146i	0.0711751	−	0.123279i
$845$	16.4840	−	40.8078i	0.567066	−	1.40383i
$846$		0			0
$847$	−9.19290	−	1.62791i	−0.315872	−	0.0559355i
$848$	−3.81720	−	6.61158i	−0.131083	−	0.227042i
$849$		0			0
$850$	−13.0651	+	22.6294i	−0.448129	+	0.776182i
$851$	−2.86736	−	4.96642i	−0.0982920	−	0.170247i
$852$		0			0
$853$	18.2171			0.623741			0.311871	−	0.950125i	$-0.399044\pi$
$853$	18.2171			0.623741			0.311871	+	0.950125i	$0.399044\pi$
$854$	21.7756	−	25.9125i	0.745146	−	0.886709i
$855$		0			0
$856$	−0.681703	+	1.18074i	−0.0233001	+	0.0403570i
$857$	0.512149	−	0.887068i	0.0174947	−	0.0303017i	−0.857146	−	0.515074i	$-0.827764\pi$
$857$	0.512149	−	0.887068i	0.0174947	−	0.0303017i	0.874640	+	0.484773i	$0.161098\pi$
$858$		0			0
$859$	25.0847	+	43.4480i	0.855880	+	1.48243i	0.875826	+	0.482627i	$0.160317\pi$
$859$	25.0847	+	43.4480i	0.855880	+	1.48243i	−0.0199461	+	0.999801i	$0.506349\pi$
$860$	11.7467	+	20.3460i	0.400561	+	0.693791i
$861$		0			0
$862$	−1.68571	+	2.91974i	−0.0574156	+	0.0994468i
$863$	−17.4645	−	30.2494i	−0.594499	−	1.02970i	−0.993617	−	0.112803i	$-0.964017\pi$
$863$	−17.4645	−	30.2494i	−0.594499	−	1.02970i	0.399119	−	0.916899i	$-0.369316\pi$
$864$		0			0
$865$	1.91874	+	3.32336i	0.0652392	+	0.112998i
$866$	8.11993	+	14.0641i	0.275927	+	0.477919i
$867$		0			0
$868$	−10.3719	−	1.83669i	−0.352046	−	0.0623414i
$869$	−0.849666	−	1.47167i	−0.0288230	−	0.0499228i
$870$		0			0
$871$	28.6741	+	13.9840i	0.971585	+	0.473830i
$872$	1.56445	−	2.70970i	0.0529789	−	0.0917621i
$873$		0			0
$874$	−3.25565	−	5.63896i	−0.110124	−	0.190741i
$875$	−12.8907	−	2.28273i	−0.435786	−	0.0771703i
$876$		0			0
$877$	−20.3263			−0.686370			−0.343185	−	0.939268i	$-0.611506\pi$
$877$	−20.3263			−0.686370			−0.343185	+	0.939268i	$0.611506\pi$
$878$	−12.0552	−	20.8802i	−0.406842	−	0.704671i
$879$		0			0
$880$	−12.9043			−0.435004
$881$	−0.505117	−	0.874889i	−0.0170178	−	0.0294757i	0.857391	−	0.514665i	$-0.172084\pi$
$881$	−0.505117	−	0.874889i	−0.0170178	−	0.0294757i	−0.874409	+	0.485190i	$0.838751\pi$
$882$		0			0
$883$	18.3609			0.617894			0.308947	−	0.951079i	$-0.400024\pi$
$883$	18.3609			0.617894			0.308947	+	0.951079i	$0.400024\pi$
$884$	−12.0876	+	8.15386i	−0.406551	+	0.274244i
$885$		0			0
$886$	−24.9857			−0.839413
$887$	9.59364	−	16.6167i	0.322123	−	0.557933i	−0.658803	−	0.752315i	$-0.728937\pi$
$887$	9.59364	−	16.6167i	0.322123	−	0.557933i	0.980926	+	0.194382i	$0.0622703\pi$
$888$		0			0
$889$	−3.01766	−	8.30991i	−0.101209	−	0.278706i
$890$	−13.9411	+	24.1467i	−0.467307	+	0.809400i
$891$		0			0
$892$	−1.07475	+	1.86151i	−0.0359851	+	0.0623281i
$893$	17.0616	+	29.5515i	0.570944	+	0.988905i
$894$		0			0
$895$	21.4415	+	37.1377i	0.716709	+	1.24138i
$896$	−1.70214	+	2.02552i	−0.0568646	+	0.0676677i
$897$		0			0
$898$	18.3685	+	31.8153i	0.612966	+	1.06169i
$899$	−9.19006			−0.306506
$900$		0			0
$901$	−30.8731			−1.02853
$902$	−17.2358			−0.573889
$903$		0			0
$904$	6.53202	−	11.3138i	0.217252	−	0.376291i
$905$	−1.55630	−	2.69559i	−0.0517331	−	0.0896044i
$906$		0			0
$907$	24.2061			0.803749			0.401875	−	0.915695i	$-0.368359\pi$
$907$	24.2061			0.803749			0.401875	+	0.915695i	$0.368359\pi$
$908$	3.91933	−	6.78848i	0.130068	−	0.225284i
$909$		0			0
$910$	−26.1144	−	19.0010i	−0.865684	−	0.629878i
$911$	7.43708			0.246401			0.123201	−	0.992382i	$-0.460684\pi$
$911$	7.43708			0.246401			0.123201	+	0.992382i	$0.460684\pi$
$912$		0			0
$913$	57.8294			1.91387
$914$	0.583289	+	1.01029i	0.0192935	+	0.0334173i
$915$		0			0
$916$	5.97741	−	10.3532i	0.197499	−	0.342078i
$917$	−2.28964	−	6.30512i	−0.0756107	−	0.208214i
$918$		0			0
$919$	−24.3286			−0.802527			−0.401263	−	0.915963i	$-0.631429\pi$
$919$	−24.3286			−0.802527			−0.401263	+	0.915963i	$0.631429\pi$
$920$	3.57934			0.118007
$921$		0			0
$922$	−6.97353	−	12.0785i	−0.229661	−	0.397785i
$923$	−43.1207	+	29.0876i	−1.41934	+	0.957430i
$924$		0			0
$925$	17.5242	+	30.3528i	0.576192	+	0.997994i
$926$	−7.02382	+	12.1656i	−0.230817	+	0.399787i
$927$		0			0
$928$	−1.15418	+	1.99910i	−0.0378878	+	0.0656237i
$929$	−22.6335			−0.742581			−0.371291	−	0.928517i	$-0.621085\pi$
$929$	−22.6335			−0.742581			−0.371291	+	0.928517i	$0.621085\pi$
$930$		0			0
$931$	40.4891	+	14.8041i	1.32698	+	0.485186i
$932$	14.0340	−	24.3076i	0.459700	−	0.796223i
$933$		0			0
$934$	−8.46057			−0.276838
$935$	−26.0922	+	45.1930i	−0.853306	+	1.47797i
$936$		0			0
$937$	−49.8108			−1.62725			−0.813623	−	0.581393i	$-0.802508\pi$
$937$	−49.8108			−1.62725			−0.813623	+	0.581393i	$0.802508\pi$
$938$	15.0607	−	17.9220i	0.491750	−	0.585173i
$939$		0			0
$940$	−18.7579			−0.611815
$941$	−17.5367	+	30.3745i	−0.571681	+	0.990180i	0.424713	+	0.905328i	$0.360375\pi$
$941$	−17.5367	+	30.3745i	−0.571681	+	0.990180i	−0.996394	+	0.0848518i	$0.972958\pi$
$942$		0			0
$943$	4.78079			0.155684
$944$	7.48121			0.243493
$945$		0			0
$946$	13.2254	+	22.9070i	0.429995	+	0.744772i
$947$	−17.4151	+	30.1638i	−0.565914	+	0.980191i	0.431050	+	0.902328i	$0.358143\pi$
$947$	−17.4151	+	30.1638i	−0.565914	+	0.980191i	−0.996964	+	0.0778634i	$0.975190\pi$
$948$		0			0
$949$	21.6283	−	14.5896i	0.702083	−	0.473598i
$950$	19.8973	+	34.4631i	0.645552	+	1.11813i
$951$		0			0
$952$	3.65200	+	10.0567i	0.118362	+	0.325941i
$953$	9.11097	−	15.7807i	0.295133	−	0.511186i	−0.679883	−	0.733321i	$-0.737969\pi$
$953$	9.11097	−	15.7807i	0.295133	−	0.511186i	0.975016	+	0.222135i	$0.0713026\pi$
$954$		0			0
$955$	5.22358	+	9.04751i	0.169031	+	0.292770i
$956$	−7.40719	−	12.8296i	−0.239566	−	0.414940i
$957$		0			0
$958$	0.909522	−	1.57534i	0.0293853	−	0.0508969i
$959$	−11.3850	−	31.3516i	−0.367641	−	1.01240i
$960$		0			0
$961$	7.57500	+	13.1203i	0.244355	+	0.423235i
$962$	1.36495	+	19.5094i	0.0440076	+	0.629007i
$963$		0			0
$964$	0.473016	−	0.819288i	0.0152348	−	0.0263875i
$965$	35.3949	+	61.3058i	1.13940	+	1.97350i
$966$		0			0
$967$	−16.6734			−0.536181			−0.268090	−	0.963394i	$-0.586393\pi$
$967$	−16.6734			−0.536181			−0.268090	+	0.963394i	$0.586393\pi$
$968$	−3.52865			−0.113415
$969$		0			0
$970$	20.9285	−	36.2491i	0.671972	−	1.16389i
$971$	5.78735			0.185725			0.0928624	−	0.995679i	$-0.470398\pi$
$971$	5.78735			0.185725			0.0928624	+	0.995679i	$0.470398\pi$
$972$		0			0
$973$	32.0487	−	38.1373i	1.02743	−	1.22263i
$974$	−22.0577			−0.706773
$975$		0			0
$976$	6.39653	−	11.0791i	0.204748	−	0.354634i
$977$	13.1451			0.420551			0.210275	−	0.977642i	$-0.432564\pi$
$977$	13.1451			0.420551			0.210275	+	0.977642i	$0.432564\pi$
$978$		0			0
$979$	−15.6960	+	27.1862i	−0.501646	+	0.868876i
$980$	−18.1764	+	15.2064i	−0.580623	+	0.485751i
$981$		0			0
$982$	−19.9931			−0.638004
$983$	18.5921	−	32.2025i	0.592997	−	1.02710i	−0.400829	−	0.916153i	$-0.631278\pi$
$983$	18.5921	−	32.2025i	0.592997	−	1.02710i	0.993826	−	0.110948i	$-0.0353887\pi$
$984$		0			0
$985$	−5.79961	+	10.0452i	−0.184791	+	0.320067i
$986$	4.66746	+	8.08427i	0.148642	+	0.257456i
$987$		0			0
$988$	1.54978	+	22.1513i	0.0493051	+	0.704725i
$989$	−3.66840	−	6.35386i	−0.116648	−	0.202041i
$990$		0			0
$991$	2.85803			0.0907882			0.0453941	−	0.998969i	$-0.485546\pi$
$991$	2.85803			0.0907882			0.0453941	+	0.998969i	$0.485546\pi$
$992$	−3.98121			−0.126403
$993$		0			0
$994$	13.0279	+	35.8758i	0.413221	+	1.13791i
$995$	−21.8066	+	37.7702i	−0.691317	+	1.19740i
$996$		0			0
$997$	−19.0032	−	32.9145i	−0.601837	−	1.04241i	−0.992543	−	0.121897i	$-0.961102\pi$
$997$	−19.0032	−	32.9145i	−0.601837	−	1.04241i	0.390706	−	0.920516i	$-0.372231\pi$
$998$	−36.7577			−1.16354
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.p.k.991.1		10
3.2	odd	2		182.2.h.d.81.4	yes	10
7.2	even	3		1638.2.m.j.289.1		10
13.9	even	3		1638.2.m.j.1621.1		10
21.2	odd	6		182.2.e.d.107.2	✓	10
21.5	even	6		1274.2.e.s.471.4		10
21.11	odd	6		1274.2.g.p.393.2		10
21.17	even	6		1274.2.g.q.393.4		10
21.20	even	2		1274.2.h.s.263.2		10
39.35	odd	6		182.2.e.d.165.2	yes	10
91.9	even	3	inner	1638.2.p.k.919.1		10
273.74	odd	6		1274.2.g.p.295.2		10
273.152	even	6		1274.2.h.s.373.2		10
273.191	odd	6		182.2.h.d.9.4	yes	10
273.230	even	6		1274.2.e.s.165.4		10
273.269	even	6		1274.2.g.q.295.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.e.d.107.2	✓	10	21.2	odd	6
182.2.e.d.165.2	yes	10	39.35	odd	6
182.2.h.d.9.4	yes	10	273.191	odd	6
182.2.h.d.81.4	yes	10	3.2	odd	2
1274.2.e.s.165.4		10	273.230	even	6
1274.2.e.s.471.4		10	21.5	even	6
1274.2.g.p.295.2		10	273.74	odd	6
1274.2.g.p.393.2		10	21.11	odd	6
1274.2.g.q.295.4		10	273.269	even	6
1274.2.g.q.393.4		10	21.17	even	6
1274.2.h.s.263.2		10	21.20	even	2
1274.2.h.s.373.2		10	273.152	even	6
1638.2.m.j.289.1		10	7.2	even	3
1638.2.m.j.1621.1		10	13.9	even	3
1638.2.p.k.919.1		10	91.9	even	3	inner
1638.2.p.k.991.1		10	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.p (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.69274 - 2.93192i) q^{5} +(-2.60522 - 0.461340i) q^{7} -1.00000 q^{8} -3.38549 q^{10} -3.81165 q^{11} +(-3.24071 - 1.58045i) q^{13} +(-1.70214 + 2.02552i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.02198 + 3.50217i) q^{17} +6.15867 q^{19} +(-1.69274 + 2.93192i) q^{20} +(-1.90582 + 3.30098i) q^{22} +(0.528629 - 0.915612i) q^{23} +(-3.23077 + 5.59586i) q^{25} +(-2.98906 + 2.01631i) q^{26} +(0.903077 + 2.48686i) q^{28} +(1.15418 + 1.99910i) q^{29} +(-1.99060 + 3.44783i) q^{31} +(0.500000 + 0.866025i) q^{32} +4.04396 q^{34} +(3.05736 + 8.41923i) q^{35} +(2.71208 - 4.69745i) q^{37} +(3.07934 - 5.33357i) q^{38} +(1.69274 + 2.93192i) q^{40} +(2.26094 + 3.91606i) q^{41} +(3.46973 - 6.00975i) q^{43} +(1.90582 + 3.30098i) q^{44} +(-0.528629 - 0.915612i) q^{46} +(2.77034 + 4.79836i) q^{47} +(6.57433 + 2.40379i) q^{49} +(3.23077 + 5.59586i) q^{50} +(0.251642 + 3.59676i) q^{52} +(-3.81720 + 6.61158i) q^{53} +(6.45214 + 11.1754i) q^{55} +(2.60522 + 0.461340i) q^{56} +2.30836 q^{58} +(-3.74061 - 6.47892i) q^{59} -12.7931 q^{61} +(1.99060 + 3.44783i) q^{62} +1.00000 q^{64} +(0.851932 + 12.1768i) q^{65} -8.84811 q^{67} +(2.02198 - 3.50217i) q^{68} +(8.81994 + 1.56186i) q^{70} +(7.21308 - 12.4934i) q^{71} +(-3.61790 + 6.26639i) q^{73} +(-2.71208 - 4.69745i) q^{74} +(-3.07934 - 5.33357i) q^{76} +(9.93017 + 1.75847i) q^{77} +(0.222913 + 0.386097i) q^{79} +3.38549 q^{80} +4.52188 q^{82} -15.1718 q^{83} +(6.84539 - 11.8566i) q^{85} +(-3.46973 - 6.00975i) q^{86} +3.81165 q^{88} +(4.11790 - 7.13241i) q^{89} +(7.71362 + 5.61249i) q^{91} -1.05726 q^{92} +5.54067 q^{94} +(-10.4251 - 18.0567i) q^{95} +(-6.18181 + 10.7072i) q^{97} +(5.36890 - 4.49164i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 5 q^{2} - 5 q^{4} + 2 q^{5} - 10 q^{8} + 4 q^{10} - 8 q^{11} - 6 q^{13} + 3 q^{14} - 5 q^{16} + 3 q^{17} + 10 q^{19} + 2 q^{20} - 4 q^{22} - 4 q^{23} - 3 q^{25} - 6 q^{26} + 3 q^{28} - q^{29} - 21 q^{31}+ \cdots + 5 q^{98}+O(q^{100}) \) 10 * q + 5 * q^2 - 5 * q^4 + 2 * q^5 - 10 * q^8 + 4 * q^10 - 8 * q^11 - 6 * q^13 + 3 * q^14 - 5 * q^16 + 3 * q^17 + 10 * q^19 + 2 * q^20 - 4 * q^22 - 4 * q^23 - 3 * q^25 - 6 * q^26 + 3 * q^28 - q^29 - 21 * q^31 + 5 * q^32 + 6 * q^34 + 22 * q^35 + 10 * q^37 + 5 * q^38 - 2 * q^40 + 9 * q^41 + 9 * q^43 + 4 * q^44 + 4 * q^46 + 13 * q^47 - 8 * q^49 + 3 * q^50 + 15 * q^53 + 7 * q^55 - 2 * q^58 - q^59 + 30 * q^61 + 21 * q^62 + 10 * q^64 + 25 * q^65 + 3 * q^68 + 26 * q^70 + q^71 - 4 * q^73 - 10 * q^74 - 5 * q^76 - 16 * q^77 - q^79 - 4 * q^80 + 18 * q^82 - 96 * q^83 + 12 * q^85 - 9 * q^86 + 8 * q^88 + 9 * q^89 + 10 * q^91 + 8 * q^92 + 26 * q^94 - 6 * q^95 - 19 * q^97 + 5 * q^98

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