LMFDB - Embedded newform 1197.2.j.d.856.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1197,2,Mod(172,1197)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1197.172"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1197, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1197 = 3^{2} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1197.j (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,-2,0,-2,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$9.55809312195$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 399)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			856.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1197.856
Dual form			1197.2.j.d.172.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.20711 + 2.09077i) q^{2} +(-1.91421 - 3.31552i) q^{4} +(-1.91421 + 3.31552i) q^{5} +(-2.50000 + 0.866025i) q^{7} +4.41421 q^{8} +(-4.62132 - 8.00436i) q^{10} +(-1.91421 - 3.31552i) q^{11} +2.82843 q^{13} +(1.20711 - 6.27231i) q^{14} +(-1.50000 + 2.59808i) q^{16} +(-1.82843 - 3.16693i) q^{17} +(0.500000 - 0.866025i) q^{19} +14.6569 q^{20} +9.24264 q^{22} +(-0.914214 + 1.58346i) q^{23} +(-4.82843 - 8.36308i) q^{25} +(-3.41421 + 5.91359i) q^{26} +(7.65685 + 6.63103i) q^{28} +4.82843 q^{29} +(1.58579 + 2.74666i) q^{31} +(0.792893 + 1.37333i) q^{32} +8.82843 q^{34} +(1.91421 - 9.94655i) q^{35} +(-0.585786 + 1.01461i) q^{37} +(1.20711 + 2.09077i) q^{38} +(-8.44975 + 14.6354i) q^{40} -7.65685 q^{41} -12.6569 q^{43} +(-7.32843 + 12.6932i) q^{44} +(-2.20711 - 3.82282i) q^{46} +(3.08579 - 5.34474i) q^{47} +(5.50000 - 4.33013i) q^{49} +23.3137 q^{50} +(-5.41421 - 9.37769i) q^{52} +(-1.00000 - 1.73205i) q^{53} +14.6569 q^{55} +(-11.0355 + 3.82282i) q^{56} +(-5.82843 + 10.0951i) q^{58} +(5.41421 + 9.37769i) q^{59} +(7.32843 - 12.6932i) q^{61} -7.65685 q^{62} -9.82843 q^{64} +(-5.41421 + 9.37769i) q^{65} +(6.00000 + 10.3923i) q^{67} +(-7.00000 + 12.1244i) q^{68} +(18.4853 + 16.0087i) q^{70} -4.34315 q^{71} +(5.15685 + 8.93193i) q^{73} +(-1.41421 - 2.44949i) q^{74} -3.82843 q^{76} +(7.65685 + 6.63103i) q^{77} +(-1.17157 + 2.02922i) q^{79} +(-5.74264 - 9.94655i) q^{80} +(9.24264 - 16.0087i) q^{82} -4.17157 q^{83} +14.0000 q^{85} +(15.2782 - 26.4626i) q^{86} +(-8.44975 - 14.6354i) q^{88} +(5.41421 - 9.37769i) q^{89} +(-7.07107 + 2.44949i) q^{91} +7.00000 q^{92} +(7.44975 + 12.9033i) q^{94} +(1.91421 + 3.31552i) q^{95} +16.8284 q^{97} +(2.41421 + 16.7262i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} - 2 q^{5} - 10 q^{7} + 12 q^{8} - 10 q^{10} - 2 q^{11} + 2 q^{14} - 6 q^{16} + 4 q^{17} + 2 q^{19} + 36 q^{20} + 20 q^{22} + 2 q^{23} - 8 q^{25} - 8 q^{26} + 8 q^{28} + 8 q^{29}+ \cdots + 4 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 - 10 * q^7 + 12 * q^8 - 10 * q^10 - 2 * q^11 + 2 * q^14 - 6 * q^16 + 4 * q^17 + 2 * q^19 + 36 * q^20 + 20 * q^22 + 2 * q^23 - 8 * q^25 - 8 * q^26 + 8 * q^28 + 8 * q^29 + 12 * q^31 + 6 * q^32 + 24 * q^34 + 2 * q^35 - 8 * q^37 + 2 * q^38 - 14 * q^40 - 8 * q^41 - 28 * q^43 - 18 * q^44 - 6 * q^46 + 18 * q^47 + 22 * q^49 + 48 * q^50 - 16 * q^52 - 4 * q^53 + 36 * q^55 - 30 * q^56 - 12 * q^58 + 16 * q^59 + 18 * q^61 - 8 * q^62 - 28 * q^64 - 16 * q^65 + 24 * q^67 - 28 * q^68 + 40 * q^70 - 40 * q^71 - 2 * q^73 - 4 * q^76 + 8 * q^77 - 16 * q^79 - 6 * q^80 + 20 * q^82 - 28 * q^83 + 56 * q^85 + 30 * q^86 - 14 * q^88 + 16 * q^89 + 28 * q^92 + 10 * q^94 + 2 * q^95 + 56 * q^97 + 4 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1197\mathbb{Z}\right)^\times$.

$n$	$514$	$533$	$1009$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$	−1.20711	+	2.09077i	−0.853553	+	1.47840i	0.0244272	+	0.999702i	$0.492224\pi$
$2$	−1.20711	+	2.09077i	−0.853553	+	1.47840i	−0.877981	+	0.478696i	$0.841110\pi$
$3$		0			0
$3$		0			0
$4$	−1.91421	−	3.31552i	−0.957107	−	1.65776i
$5$	−1.91421	+	3.31552i	−0.856062	+	1.48274i	0.0195936	+	0.999808i	$0.493763\pi$
$5$	−1.91421	+	3.31552i	−0.856062	+	1.48274i	−0.875656	+	0.482935i	$0.839571\pi$
$6$		0			0
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$8$	4.41421			1.56066
$9$		0			0
$10$	−4.62132	−	8.00436i	−1.46139	−	2.53120i
$11$	−1.91421	−	3.31552i	−0.577157	−	0.999665i	−0.995804	−	0.0915161i	$-0.970829\pi$
$11$	−1.91421	−	3.31552i	−0.577157	−	0.999665i	0.418646	−	0.908149i	$-0.362505\pi$
$12$		0			0
$13$	2.82843			0.784465			0.392232	−	0.919866i	$-0.371703\pi$
$13$	2.82843			0.784465			0.392232	+	0.919866i	$0.371703\pi$
$14$	1.20711	−	6.27231i	0.322613	−	1.67635i
$15$		0			0
$16$	−1.50000	+	2.59808i	−0.375000	+	0.649519i
$17$	−1.82843	−	3.16693i	−0.443459	−	0.768093i	0.554485	−	0.832194i	$-0.312915\pi$
$17$	−1.82843	−	3.16693i	−0.443459	−	0.768093i	−0.997943	+	0.0641009i	$0.979582\pi$
$18$		0			0
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i
$20$	14.6569			3.27737
$21$		0			0
$22$	9.24264			1.97054
$23$	−0.914214	+	1.58346i	−0.190627	+	0.330175i	−0.945458	−	0.325744i	$-0.894385\pi$
$23$	−0.914214	+	1.58346i	−0.190627	+	0.330175i	0.754831	+	0.655919i	$0.227719\pi$
$24$		0			0
$25$	−4.82843	−	8.36308i	−0.965685	−	1.67262i
$26$	−3.41421	+	5.91359i	−0.669582	+	1.15975i
$27$		0			0
$28$	7.65685	+	6.63103i	1.44701	+	1.25315i
$29$	4.82843			0.896616			0.448308	−	0.893879i	$-0.352027\pi$
$29$	4.82843			0.896616			0.448308	+	0.893879i	$0.352027\pi$
$30$		0			0
$31$	1.58579	+	2.74666i	0.284816	+	0.493315i	0.972564	−	0.232634i	$-0.0747343\pi$
$31$	1.58579	+	2.74666i	0.284816	+	0.493315i	−0.687749	+	0.725949i	$0.741401\pi$
$32$	0.792893	+	1.37333i	0.140165	+	0.242773i
$33$		0			0
$34$	8.82843			1.51406
$35$	1.91421	−	9.94655i	0.323561	−	1.68127i
$36$		0			0
$37$	−0.585786	+	1.01461i	−0.0963027	+	0.166801i	−0.910152	−	0.414275i	$-0.864035\pi$
$37$	−0.585786	+	1.01461i	−0.0963027	+	0.166801i	0.813849	+	0.581077i	$0.197368\pi$
$38$	1.20711	+	2.09077i	0.195819	+	0.339168i
$39$		0			0
$40$	−8.44975	+	14.6354i	−1.33602	+	2.31406i
$41$	−7.65685			−1.19580			−0.597900	−	0.801571i	$-0.703998\pi$
$41$	−7.65685			−1.19580			−0.597900	+	0.801571i	$0.703998\pi$
$42$		0			0
$43$	−12.6569			−1.93015			−0.965076	−	0.261970i	$-0.915628\pi$
$43$	−12.6569			−1.93015			−0.965076	+	0.261970i	$0.915628\pi$
$44$	−7.32843	+	12.6932i	−1.10480	+	1.91357i
$45$		0			0
$46$	−2.20711	−	3.82282i	−0.325420	−	0.563644i
$47$	3.08579	−	5.34474i	0.450108	−	0.779610i	−0.548284	−	0.836292i	$-0.684719\pi$
$47$	3.08579	−	5.34474i	0.450108	−	0.779610i	0.998392	+	0.0566819i	$0.0180521\pi$
$48$		0			0
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$	23.3137			3.29706
$51$		0			0
$52$	−5.41421	−	9.37769i	−0.750816	−	1.30045i
$53$	−1.00000	−	1.73205i	−0.137361	−	0.237915i	0.789136	−	0.614218i	$-0.210529\pi$
$53$	−1.00000	−	1.73205i	−0.137361	−	0.237915i	−0.926497	+	0.376303i	$0.877195\pi$
$54$		0			0
$55$	14.6569			1.97633
$56$	−11.0355	+	3.82282i	−1.47469	+	0.510846i
$57$		0			0
$58$	−5.82843	+	10.0951i	−0.765310	+	1.32556i
$59$	5.41421	+	9.37769i	0.704871	+	1.22087i	0.966738	+	0.255768i	$0.0823283\pi$
$59$	5.41421	+	9.37769i	0.704871	+	1.22087i	−0.261868	+	0.965104i	$0.584338\pi$
$60$		0			0
$61$	7.32843	−	12.6932i	0.938309	−	1.62520i	0.169685	−	0.985498i	$-0.445725\pi$
$61$	7.32843	−	12.6932i	0.938309	−	1.62520i	0.768624	−	0.639700i	$-0.220942\pi$
$62$	−7.65685			−0.972421
$63$		0			0
$64$	−9.82843			−1.22855
$65$	−5.41421	+	9.37769i	−0.671551	+	1.16316i
$66$		0			0
$67$	6.00000	+	10.3923i	0.733017	+	1.26962i	0.955588	+	0.294706i	$0.0952216\pi$
$67$	6.00000	+	10.3923i	0.733017	+	1.26962i	−0.222571	+	0.974916i	$0.571445\pi$
$68$	−7.00000	+	12.1244i	−0.848875	+	1.47029i
$69$		0			0
$70$	18.4853	+	16.0087i	2.20941	+	1.91341i
$71$	−4.34315			−0.515437			−0.257718	−	0.966220i	$-0.582971\pi$
$71$	−4.34315			−0.515437			−0.257718	+	0.966220i	$0.582971\pi$
$72$		0			0
$73$	5.15685	+	8.93193i	0.603564	+	1.04540i	0.992277	+	0.124045i	$0.0395866\pi$
$73$	5.15685	+	8.93193i	0.603564	+	1.04540i	−0.388712	+	0.921359i	$0.627080\pi$
$74$	−1.41421	−	2.44949i	−0.164399	−	0.284747i
$75$		0			0
$76$	−3.82843			−0.439151
$77$	7.65685	+	6.63103i	0.872580	+	0.755676i
$78$		0			0
$79$	−1.17157	+	2.02922i	−0.131812	+	0.228306i	−0.924375	−	0.381485i	$-0.875413\pi$
$79$	−1.17157	+	2.02922i	−0.131812	+	0.228306i	0.792563	+	0.609790i	$0.208746\pi$
$80$	−5.74264	−	9.94655i	−0.642047	−	1.11206i
$81$		0			0
$82$	9.24264	−	16.0087i	1.02068	−	1.76787i
$83$	−4.17157			−0.457890			−0.228945	−	0.973439i	$-0.573528\pi$
$83$	−4.17157			−0.457890			−0.228945	+	0.973439i	$0.573528\pi$
$84$		0			0
$85$	14.0000			1.51851
$86$	15.2782	−	26.4626i	1.64749	−	2.85353i
$87$		0			0
$88$	−8.44975	−	14.6354i	−0.900746	−	1.56014i
$89$	5.41421	−	9.37769i	0.573905	−	0.994033i	−0.422254	−	0.906478i	$-0.638761\pi$
$89$	5.41421	−	9.37769i	0.573905	−	0.994033i	0.996160	−	0.0875560i	$-0.0279057\pi$
$90$		0			0
$91$	−7.07107	+	2.44949i	−0.741249	+	0.256776i
$92$	7.00000			0.729800
$93$		0			0
$94$	7.44975	+	12.9033i	0.768383	+	1.33088i
$95$	1.91421	+	3.31552i	0.196394	+	0.340165i
$96$		0			0
$97$	16.8284			1.70867			0.854334	−	0.519724i	$-0.173965\pi$
$97$	16.8284			1.70867			0.854334	+	0.519724i	$0.173965\pi$
$98$	2.41421	+	16.7262i	0.243872	+	1.68960i
$99$		0			0
$100$	−18.4853	+	32.0174i	−1.84853	+	3.20174i
$101$	−1.74264	−	3.01834i	−0.173399	−	0.300336i	0.766207	−	0.642594i	$-0.222142\pi$
$101$	−1.74264	−	3.01834i	−0.173399	−	0.300336i	−0.939606	+	0.342258i	$0.888808\pi$
$102$		0			0
$103$	−1.82843	+	3.16693i	−0.180160	+	0.312047i	−0.941935	−	0.335795i	$-0.890995\pi$
$103$	−1.82843	+	3.16693i	−0.180160	+	0.312047i	0.761775	+	0.647842i	$0.224328\pi$
$104$	12.4853			1.22428
$105$		0			0
$106$	4.82843			0.468978
$107$	−1.41421	+	2.44949i	−0.136717	+	0.236801i	−0.926252	−	0.376905i	$-0.876988\pi$
$107$	−1.41421	+	2.44949i	−0.136717	+	0.236801i	0.789535	+	0.613706i	$0.210322\pi$
$108$		0			0
$109$	−9.07107	−	15.7116i	−0.868851	−	1.50489i	−0.863172	−	0.504910i	$-0.831526\pi$
$109$	−9.07107	−	15.7116i	−0.868851	−	1.50489i	−0.00567856	−	0.999984i	$-0.501808\pi$
$110$	−17.6924	+	30.6441i	−1.68690	+	2.92180i
$111$		0			0
$112$	1.50000	−	7.79423i	0.141737	−	0.736485i
$113$	12.8284			1.20680			0.603398	−	0.797440i	$-0.293813\pi$
$113$	12.8284			1.20680			0.603398	+	0.797440i	$0.293813\pi$
$114$		0			0
$115$	−3.50000	−	6.06218i	−0.326377	−	0.565301i
$116$	−9.24264	−	16.0087i	−0.858158	−	1.48637i
$117$		0			0
$118$	−26.1421			−2.40658
$119$	7.31371	+	6.33386i	0.670447	+	0.580624i
$120$		0			0
$121$	−1.82843	+	3.16693i	−0.166221	+	0.287903i
$122$	17.6924	+	30.6441i	1.60179	+	2.77439i
$123$		0			0
$124$	6.07107	−	10.5154i	0.545198	−	0.944311i
$125$	17.8284			1.59462
$126$		0			0
$127$	16.9706			1.50589			0.752947	−	0.658081i	$-0.228632\pi$
$127$	16.9706			1.50589			0.752947	+	0.658081i	$0.228632\pi$
$128$	10.2782	−	17.8023i	0.908471	−	1.57352i
$129$		0			0
$130$	−13.0711	−	22.6398i	−1.14641	−	1.98564i
$131$	5.17157	−	8.95743i	0.451842	−	0.782614i	−0.546658	−	0.837356i	$-0.684100\pi$
$131$	5.17157	−	8.95743i	0.451842	−	0.782614i	0.998501	+	0.0547419i	$0.0174336\pi$
$132$		0			0
$133$	−0.500000	+	2.59808i	−0.0433555	+	0.225282i
$134$	−28.9706			−2.50268
$135$		0			0
$136$	−8.07107	−	13.9795i	−0.692088	−	1.19873i
$137$	−6.91421	−	11.9758i	−0.590721	−	1.02316i	−0.994136	−	0.108142i	$-0.965510\pi$
$137$	−6.91421	−	11.9758i	−0.590721	−	1.02316i	0.403414	−	0.915017i	$-0.367823\pi$
$138$		0			0
$139$	−6.65685			−0.564627			−0.282314	−	0.959322i	$-0.591102\pi$
$139$	−6.65685			−0.564627			−0.282314	+	0.959322i	$0.591102\pi$
$140$	−36.6421	+	12.6932i	−3.09683	+	1.07277i
$141$		0			0
$142$	5.24264	−	9.08052i	0.439953	−	0.762020i
$143$	−5.41421	−	9.37769i	−0.452759	−	0.784202i
$144$		0			0
$145$	−9.24264	+	16.0087i	−0.767560	+	1.32945i
$146$	−24.8995			−2.06070
$147$		0			0
$148$	4.48528			0.368688
$149$	1.91421	−	3.31552i	0.156818	−	0.271618i	−0.776901	−	0.629623i	$-0.783210\pi$
$149$	1.91421	−	3.31552i	0.156818	−	0.271618i	0.933720	+	0.358005i	$0.116543\pi$
$150$		0			0
$151$	4.65685	+	8.06591i	0.378969	+	0.656394i	0.990913	−	0.134507i	$-0.0429452\pi$
$151$	4.65685	+	8.06591i	0.378969	+	0.656394i	−0.611943	+	0.790902i	$0.709612\pi$
$152$	2.20711	−	3.82282i	0.179020	−	0.310072i
$153$		0			0
$154$	−23.1066	+	8.00436i	−1.86198	+	0.645010i
$155$	−12.1421			−0.975280
$156$		0			0
$157$	−5.32843	−	9.22911i	−0.425255	−	0.736563i	0.571189	−	0.820818i	$-0.306482\pi$
$157$	−5.32843	−	9.22911i	−0.425255	−	0.736563i	−0.996444	+	0.0842554i	$0.973149\pi$
$158$	−2.82843	−	4.89898i	−0.225018	−	0.389742i
$159$		0			0
$160$	−6.07107			−0.479960
$161$	0.914214	−	4.75039i	0.0720501	−	0.374383i
$162$		0			0
$163$	−10.9853	+	19.0271i	−0.860434	+	1.49031i	0.0110773	+	0.999939i	$0.496474\pi$
$163$	−10.9853	+	19.0271i	−0.860434	+	1.49031i	−0.871511	+	0.490376i	$0.836859\pi$
$164$	14.6569	+	25.3864i	1.14451	+	1.98235i
$165$		0			0
$166$	5.03553	−	8.72180i	0.390833	−	0.676943i
$167$	−8.82843			−0.683164			−0.341582	−	0.939852i	$-0.610963\pi$
$167$	−8.82843			−0.683164			−0.341582	+	0.939852i	$0.610963\pi$
$168$		0			0
$169$	−5.00000			−0.384615
$170$	−16.8995	+	29.2708i	−1.29613	+	2.24497i
$171$		0			0
$172$	24.2279	+	41.9640i	1.84736	+	3.19972i
$173$	1.41421	−	2.44949i	0.107521	−	0.186231i	−0.807245	−	0.590217i	$-0.799042\pi$
$173$	1.41421	−	2.44949i	0.107521	−	0.186231i	0.914765	+	0.403986i	$0.132375\pi$
$174$		0			0
$175$	19.3137	+	16.7262i	1.45998	+	1.26438i
$176$	11.4853			0.865736
$177$		0			0
$178$	13.0711	+	22.6398i	0.979718	+	1.69692i
$179$	−5.24264	−	9.08052i	−0.391853	−	0.678710i	0.600841	−	0.799369i	$-0.294833\pi$
$179$	−5.24264	−	9.08052i	−0.391853	−	0.678710i	−0.992694	+	0.120659i	$0.961499\pi$
$180$		0			0
$181$	−11.6569			−0.866447			−0.433224	−	0.901286i	$-0.642624\pi$
$181$	−11.6569			−0.866447			−0.433224	+	0.901286i	$0.642624\pi$
$182$	3.41421	−	17.7408i	0.253078	−	1.31503i
$183$		0			0
$184$	−4.03553	+	6.98975i	−0.297504	+	0.515291i
$185$	−2.24264	−	3.88437i	−0.164882	−	0.285584i
$186$		0			0
$187$	−7.00000	+	12.1244i	−0.511891	+	0.886621i
$188$	−23.6274			−1.72321
$189$		0			0
$190$	−9.24264			−0.670532
$191$	5.91421	−	10.2437i	0.427937	−	0.741209i	−0.568752	−	0.822509i	$-0.692574\pi$
$191$	5.91421	−	10.2437i	0.427937	−	0.741209i	0.996690	+	0.0812994i	$0.0259070\pi$
$192$		0			0
$193$	−2.00000	−	3.46410i	−0.143963	−	0.249351i	0.785022	−	0.619467i	$-0.212651\pi$
$193$	−2.00000	−	3.46410i	−0.143963	−	0.249351i	−0.928986	+	0.370116i	$0.879318\pi$
$194$	−20.3137	+	35.1844i	−1.45844	+	2.52609i
$195$		0			0
$196$	−24.8848	−	9.94655i	−1.77748	−	0.710468i
$197$	17.4853			1.24577			0.622887	−	0.782312i	$-0.285959\pi$
$197$	17.4853			1.24577			0.622887	+	0.782312i	$0.285959\pi$
$198$		0			0
$199$	−1.67157	−	2.89525i	−0.118495	−	0.205239i	0.800677	−	0.599097i	$-0.204474\pi$
$199$	−1.67157	−	2.89525i	−0.118495	−	0.205239i	−0.919171	+	0.393858i	$0.871140\pi$
$200$	−21.3137	−	36.9164i	−1.50711	−	2.61039i
$201$		0			0
$202$	8.41421			0.592022
$203$	−12.0711	+	4.18154i	−0.847223	+	0.293487i
$204$		0			0
$205$	14.6569	−	25.3864i	1.02368	−	1.77306i
$206$	−4.41421	−	7.64564i	−0.307553	−	0.532697i
$207$		0			0
$208$	−4.24264	+	7.34847i	−0.294174	+	0.509525i
$209$	−3.82843			−0.264818
$210$		0			0
$211$	16.4853			1.13489			0.567447	−	0.823410i	$-0.307931\pi$
$211$	16.4853			1.13489			0.567447	+	0.823410i	$0.307931\pi$
$212$	−3.82843	+	6.63103i	−0.262937	+	0.455421i
$213$		0			0
$214$	−3.41421	−	5.91359i	−0.233391	−	0.404245i
$215$	24.2279	−	41.9640i	1.65233	−	2.86192i
$216$		0			0
$217$	−6.34315	−	5.49333i	−0.430601	−	0.372911i
$218$	43.7990			2.96644
$219$		0			0
$220$	−28.0563	−	48.5950i	−1.89156	−	3.27628i
$221$	−5.17157	−	8.95743i	−0.347878	−	0.602542i
$222$		0			0
$223$	21.7990			1.45977			0.729884	−	0.683571i	$-0.239574\pi$
$223$	21.7990			1.45977			0.729884	+	0.683571i	$0.239574\pi$
$224$	−3.17157	−	2.74666i	−0.211910	−	0.183519i
$225$		0			0
$226$	−15.4853	+	26.8213i	−1.03007	+	1.78413i
$227$	−3.17157	−	5.49333i	−0.210505	−	0.364605i	0.741368	−	0.671099i	$-0.234177\pi$
$227$	−3.17157	−	5.49333i	−0.210505	−	0.364605i	−0.951873	+	0.306494i	$0.900844\pi$
$228$		0			0
$229$	7.82843	−	13.5592i	0.517317	−	0.896019i	−0.482481	−	0.875907i	$-0.660264\pi$
$229$	7.82843	−	13.5592i	0.517317	−	0.896019i	0.999798	−	0.0201128i	$-0.00640252\pi$
$230$	16.8995			1.11432
$231$		0			0
$232$	21.3137			1.39931
$233$	3.00000	−	5.19615i	0.196537	−	0.340411i	−0.750867	−	0.660454i	$-0.770364\pi$
$233$	3.00000	−	5.19615i	0.196537	−	0.340411i	0.947403	+	0.320043i	$0.103697\pi$
$234$		0			0
$235$	11.8137	+	20.4619i	0.770641	+	1.33479i
$236$	20.7279	−	35.9018i	1.34927	−	2.33701i
$237$		0			0
$238$	−22.0711	+	7.64564i	−1.43065	+	0.495593i
$239$	−2.34315			−0.151565			−0.0757827	−	0.997124i	$-0.524146\pi$
$239$	−2.34315			−0.151565			−0.0757827	+	0.997124i	$0.524146\pi$
$240$		0			0
$241$	−9.89949	−	17.1464i	−0.637683	−	1.10450i	−0.985940	−	0.167100i	$-0.946560\pi$
$241$	−9.89949	−	17.1464i	−0.637683	−	1.10450i	0.348257	−	0.937399i	$-0.386773\pi$
$242$	−4.41421	−	7.64564i	−0.283756	−	0.491480i
$243$		0			0
$244$	−56.1127			−3.59225
$245$	3.82843	+	26.5241i	0.244589	+	1.69456i
$246$		0			0
$247$	1.41421	−	2.44949i	0.0899843	−	0.155857i
$248$	7.00000	+	12.1244i	0.444500	+	0.769897i
$249$		0			0
$250$	−21.5208	+	37.2751i	−1.36110	+	2.35749i
$251$	13.4853			0.851183			0.425592	−	0.904915i	$-0.360066\pi$
$251$	13.4853			0.851183			0.425592	+	0.904915i	$0.360066\pi$
$252$		0			0
$253$	7.00000			0.440086
$254$	−20.4853	+	35.4815i	−1.28536	+	2.22631i
$255$		0			0
$256$	14.9853	+	25.9553i	0.936580	+	1.62220i
$257$	13.0000	−	22.5167i	0.810918	−	1.40455i	−0.101305	−	0.994855i	$-0.532302\pi$
$257$	13.0000	−	22.5167i	0.810918	−	1.40455i	0.912222	−	0.409695i	$-0.134365\pi$
$258$		0			0
$259$	0.585786	−	3.04384i	0.0363990	−	0.189135i
$260$	41.4558			2.57098
$261$		0			0
$262$	12.4853	+	21.6251i	0.771343	+	1.33601i
$263$	5.65685	+	9.79796i	0.348817	+	0.604168i	0.986040	−	0.166511i	$-0.0532503\pi$
$263$	5.65685	+	9.79796i	0.348817	+	0.604168i	−0.637223	+	0.770680i	$0.719917\pi$
$264$		0			0
$265$	7.65685			0.470357
$266$	−4.82843	−	4.18154i	−0.296050	−	0.256387i
$267$		0			0
$268$	22.9706	−	39.7862i	1.40315	−	2.43033i
$269$	−4.00000	−	6.92820i	−0.243884	−	0.422420i	0.717933	−	0.696112i	$-0.245088\pi$
$269$	−4.00000	−	6.92820i	−0.243884	−	0.422420i	−0.961817	+	0.273692i	$0.911755\pi$
$270$		0			0
$271$	9.81371	−	16.9978i	0.596140	−	1.03255i	−0.397245	−	0.917713i	$-0.630034\pi$
$271$	9.81371	−	16.9978i	0.596140	−	1.03255i	0.993385	−	0.114833i	$-0.0366331\pi$
$272$	10.9706			0.665188
$273$		0			0
$274$	33.3848			2.01685
$275$	−18.4853	+	32.0174i	−1.11470	+	1.93072i
$276$		0			0
$277$	−6.50000	−	11.2583i	−0.390547	−	0.676448i	0.601975	−	0.798515i	$-0.294381\pi$
$277$	−6.50000	−	11.2583i	−0.390547	−	0.676448i	−0.992522	+	0.122068i	$0.961047\pi$
$278$	8.03553	−	13.9180i	0.481939	−	0.834743i
$279$		0			0
$280$	8.44975	−	43.9062i	0.504969	−	2.62390i
$281$	−6.97056			−0.415829			−0.207914	−	0.978147i	$-0.566668\pi$
$281$	−6.97056			−0.415829			−0.207914	+	0.978147i	$0.566668\pi$
$282$		0			0
$283$	−15.8137	−	27.3901i	−0.940027	−	1.62818i	−0.765414	−	0.643538i	$-0.777466\pi$
$283$	−15.8137	−	27.3901i	−0.940027	−	1.62818i	−0.174613	−	0.984637i	$-0.555868\pi$
$284$	8.31371	+	14.3998i	0.493328	+	0.854469i
$285$		0			0
$286$	26.1421			1.54582
$287$	19.1421	−	6.63103i	1.12992	−	0.391417i
$288$		0			0
$289$	1.81371	−	3.14144i	0.106689	−	0.184790i
$290$	−22.3137	−	38.6485i	−1.31031	−	2.26952i
$291$		0			0
$292$	19.7426	−	34.1953i	1.15535	−	2.00113i
$293$	0.828427			0.0483972			0.0241986	−	0.999707i	$-0.492297\pi$
$293$	0.828427			0.0483972			0.0241986	+	0.999707i	$0.492297\pi$
$294$		0			0
$295$	−41.4558			−2.41365
$296$	−2.58579	+	4.47871i	−0.150296	+	0.260320i
$297$		0			0
$298$	4.62132	+	8.00436i	0.267706	+	0.463680i
$299$	−2.58579	+	4.47871i	−0.149540	+	0.259011i
$300$		0			0
$301$	31.6421	−	10.9612i	1.82382	−	0.631791i
$302$	−22.4853			−1.29388
$303$		0			0
$304$	1.50000	+	2.59808i	0.0860309	+	0.149010i
$305$	28.0563	+	48.5950i	1.60650	+	2.78254i
$306$		0			0
$307$	2.48528			0.141843			0.0709213	−	0.997482i	$-0.477406\pi$
$307$	2.48528			0.141843			0.0709213	+	0.997482i	$0.477406\pi$
$308$	7.32843	−	38.0796i	0.417576	−	2.16979i
$309$		0			0
$310$	14.6569	−	25.3864i	0.832453	−	1.44185i
$311$	11.3137	+	19.5959i	0.641542	+	1.11118i	0.985089	+	0.172047i	$0.0550381\pi$
$311$	11.3137	+	19.5959i	0.641542	+	1.11118i	−0.343547	+	0.939135i	$0.611629\pi$
$312$		0			0
$313$	−15.6421	+	27.0930i	−0.884146	+	1.53139i	−0.0374562	+	0.999298i	$0.511925\pi$
$313$	−15.6421	+	27.0930i	−0.884146	+	1.53139i	−0.846690	+	0.532087i	$0.821408\pi$
$314$	25.7279			1.45191
$315$		0			0
$316$	8.97056			0.504634
$317$	14.8995	−	25.8067i	0.836839	−	1.44945i	−0.0556853	−	0.998448i	$-0.517734\pi$
$317$	14.8995	−	25.8067i	0.836839	−	1.44945i	0.892524	−	0.450999i	$-0.148932\pi$
$318$		0			0
$319$	−9.24264	−	16.0087i	−0.517489	−	0.896316i
$320$	18.8137	−	32.5863i	1.05172	−	1.82163i
$321$		0			0
$322$	8.82843	+	7.64564i	0.491989	+	0.426075i
$323$	−3.65685			−0.203473
$324$		0			0
$325$	−13.6569	−	23.6544i	−0.757546	−	1.31211i
$326$	−26.5208	−	45.9354i	−1.46885	−	2.54413i
$327$		0			0
$328$	−33.7990			−1.86624
$329$	−3.08579	+	16.0342i	−0.170125	+	0.883995i
$330$		0			0
$331$	2.75736	−	4.77589i	0.151558	−	0.262506i	−0.780242	−	0.625477i	$-0.784904\pi$
$331$	2.75736	−	4.77589i	0.151558	−	0.262506i	0.931800	+	0.362971i	$0.118238\pi$
$332$	7.98528	+	13.8309i	0.438249	+	0.759070i
$333$		0			0
$334$	10.6569	−	18.4582i	0.583117	−	1.00999i
$335$	−45.9411			−2.51003
$336$		0			0
$337$	−6.48528			−0.353276			−0.176638	−	0.984276i	$-0.556522\pi$
$337$	−6.48528			−0.353276			−0.176638	+	0.984276i	$0.556522\pi$
$338$	6.03553	−	10.4539i	0.328290	−	0.568615i
$339$		0			0
$340$	−26.7990	−	46.4172i	−1.45338	−	2.51733i
$341$	6.07107	−	10.5154i	0.328767	−	0.569441i
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$	−55.8701			−3.01231
$345$		0			0
$346$	3.41421	+	5.91359i	0.183549	+	0.317917i
$347$	10.2279	+	17.7153i	0.549064	+	0.951006i	0.998339	+	0.0576128i	$0.0183489\pi$
$347$	10.2279	+	17.7153i	0.549064	+	0.951006i	−0.449275	+	0.893393i	$0.648318\pi$
$348$		0			0
$349$	14.0000			0.749403			0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000			0.749403			0.374701	+	0.927146i	$0.377745\pi$
$350$	−58.2843	+	20.1903i	−3.11543	+	1.07921i
$351$		0			0
$352$	3.03553	−	5.25770i	0.161795	−	0.280236i
$353$	−0.656854	−	1.13770i	−0.0349608	−	0.0605539i	0.848016	−	0.529971i	$-0.177797\pi$
$353$	−0.656854	−	1.13770i	−0.0349608	−	0.0605539i	−0.882976	+	0.469417i	$0.844464\pi$
$354$		0			0
$355$	8.31371	−	14.3998i	0.441246	−	0.764260i
$356$	−41.4558			−2.19716
$357$		0			0
$358$	25.3137			1.33787
$359$	−3.08579	+	5.34474i	−0.162862	+	0.282085i	−0.935894	−	0.352282i	$-0.885406\pi$
$359$	−3.08579	+	5.34474i	−0.162862	+	0.282085i	0.773032	+	0.634367i	$0.218739\pi$
$360$		0			0
$361$	−0.500000	−	0.866025i	−0.0263158	−	0.0455803i
$362$	14.0711	−	24.3718i	0.739559	−	1.28095i
$363$		0			0
$364$	21.6569	+	18.7554i	1.13513	+	0.983049i
$365$	−39.4853			−2.06675
$366$		0			0
$367$	−14.8284	−	25.6836i	−0.774038	−	1.34067i	−0.935334	−	0.353766i	$-0.884901\pi$
$367$	−14.8284	−	25.6836i	−0.774038	−	1.34067i	0.161296	−	0.986906i	$-0.448433\pi$
$368$	−2.74264	−	4.75039i	−0.142970	−	0.247631i
$369$		0			0
$370$	10.8284			0.562943
$371$	4.00000	+	3.46410i	0.207670	+	0.179847i
$372$		0			0
$373$	−10.1421	+	17.5667i	−0.525140	+	0.909569i	0.474431	+	0.880292i	$0.342654\pi$
$373$	−10.1421	+	17.5667i	−0.525140	+	0.909569i	−0.999571	+	0.0292765i	$0.990680\pi$
$374$	−16.8995	−	29.2708i	−0.873852	−	1.51356i
$375$		0			0
$376$	13.6213	−	23.5928i	0.702466	−	1.21671i
$377$	13.6569			0.703364
$378$		0			0
$379$	−16.4853			−0.846792			−0.423396	−	0.905945i	$-0.639162\pi$
$379$	−16.4853			−0.846792			−0.423396	+	0.905945i	$0.639162\pi$
$380$	7.32843	−	12.6932i	0.375940	−	0.651148i
$381$		0			0
$382$	14.2782	+	24.7305i	0.730535	+	1.26532i
$383$	8.00000	−	13.8564i	0.408781	−	0.708029i	−0.585973	−	0.810331i	$-0.699287\pi$
$383$	8.00000	−	13.8564i	0.408781	−	0.708029i	0.994753	+	0.102302i	$0.0326207\pi$
$384$		0			0
$385$	−36.6421	+	12.6932i	−1.86746	+	0.646906i
$386$	9.65685			0.491521
$387$		0			0
$388$	−32.2132	−	55.7949i	−1.63538	−	2.83256i
$389$	2.17157	+	3.76127i	0.110103	+	0.190704i	0.915812	−	0.401608i	$-0.131549\pi$
$389$	2.17157	+	3.76127i	0.110103	+	0.190704i	−0.805709	+	0.592312i	$0.798215\pi$
$390$		0			0
$391$	6.68629			0.338140
$392$	24.2782	−	19.1141i	1.22623	−	0.965408i
$393$		0			0
$394$	−21.1066	+	36.5577i	−1.06334	+	1.84175i
$395$	−4.48528	−	7.76874i	−0.225679	−	0.390887i
$396$		0			0
$397$	−2.65685	+	4.60181i	−0.133344	+	0.230958i	−0.924964	−	0.380056i	$-0.875905\pi$
$397$	−2.65685	+	4.60181i	−0.133344	+	0.230958i	0.791620	+	0.611014i	$0.209238\pi$
$398$	8.07107			0.404566
$399$		0			0
$400$	28.9706			1.44853
$401$	−0.343146	+	0.594346i	−0.0171359	+	0.0296802i	−0.874466	−	0.485086i	$-0.838788\pi$
$401$	−0.343146	+	0.594346i	−0.0171359	+	0.0296802i	0.857330	+	0.514767i	$0.172121\pi$
$402$		0			0
$403$	4.48528	+	7.76874i	0.223428	+	0.386988i
$404$	−6.67157	+	11.5555i	−0.331923	+	0.574908i
$405$		0			0
$406$	5.82843	−	30.2854i	0.289260	−	1.50304i
$407$	4.48528			0.222327
$408$		0			0
$409$	−2.65685	−	4.60181i	−0.131373	−	0.227545i	0.792833	−	0.609439i	$-0.208605\pi$
$409$	−2.65685	−	4.60181i	−0.131373	−	0.227545i	−0.924206	+	0.381894i	$0.875272\pi$
$410$	35.3848	+	61.2882i	1.74753	+	3.02681i
$411$		0			0
$412$	14.0000			0.689730
$413$	−21.6569	−	18.7554i	−1.06566	−	0.922892i
$414$		0			0
$415$	7.98528	−	13.8309i	0.391982	−	0.678933i
$416$	2.24264	+	3.88437i	0.109955	+	0.190447i
$417$		0			0
$418$	4.62132	−	8.00436i	0.226036	−	0.391506i
$419$	10.1716			0.496914			0.248457	−	0.968643i	$-0.420077\pi$
$419$	10.1716			0.496914			0.248457	+	0.968643i	$0.420077\pi$
$420$		0			0
$421$	19.1716			0.934365			0.467183	−	0.884161i	$-0.345269\pi$
$421$	19.1716			0.934365			0.467183	+	0.884161i	$0.345269\pi$
$422$	−19.8995	+	34.4669i	−0.968692	+	1.67782i
$423$		0			0
$424$	−4.41421	−	7.64564i	−0.214373	−	0.371305i
$425$	−17.6569	+	30.5826i	−0.856483	+	1.48347i
$426$		0			0
$427$	−7.32843	+	38.0796i	−0.354647	+	1.84280i
$428$	10.8284			0.523412
$429$		0			0
$430$	58.4914	+	101.310i	2.82070	+	4.88560i
$431$	−11.5858	−	20.0672i	−0.558068	−	0.966602i	−0.997658	−	0.0684031i	$-0.978210\pi$
$431$	−11.5858	−	20.0672i	−0.558068	−	0.966602i	0.439590	−	0.898199i	$-0.355124\pi$
$432$		0			0
$433$	8.48528			0.407777			0.203888	−	0.978994i	$-0.434642\pi$
$433$	8.48528			0.407777			0.203888	+	0.978994i	$0.434642\pi$
$434$	19.1421	−	6.63103i	0.918852	−	0.318300i
$435$		0			0
$436$	−34.7279	+	60.1505i	−1.66317	+	2.88069i
$437$	0.914214	+	1.58346i	0.0437328	+	0.0757474i
$438$		0			0
$439$	9.89949	−	17.1464i	0.472477	−	0.818354i	−0.527027	−	0.849849i	$-0.676693\pi$
$439$	9.89949	−	17.1464i	0.472477	−	0.818354i	0.999504	+	0.0314943i	$0.0100266\pi$
$440$	64.6985			3.08438
$441$		0			0
$442$	24.9706			1.18773
$443$	−16.8284	+	29.1477i	−0.799543	+	1.38485i	0.120372	+	0.992729i	$0.461591\pi$
$443$	−16.8284	+	29.1477i	−0.799543	+	1.38485i	−0.919914	+	0.392120i	$0.871742\pi$
$444$		0			0
$445$	20.7279	+	35.9018i	0.982598	+	1.70191i
$446$	−26.3137	+	45.5767i	−1.24599	+	2.15812i
$447$		0			0
$448$	24.5711	−	8.51167i	1.16087	−	0.402138i
$449$	−26.1421			−1.23372			−0.616862	−	0.787071i	$-0.711596\pi$
$449$	−26.1421			−1.23372			−0.616862	+	0.787071i	$0.711596\pi$
$450$		0			0
$451$	14.6569	+	25.3864i	0.690164	+	1.19540i
$452$	−24.5563	−	42.5328i	−1.15503	−	2.00058i
$453$		0			0
$454$	15.3137			0.718708
$455$	5.41421	−	28.1331i	0.253822	−	1.31890i
$456$		0			0
$457$	7.32843	−	12.6932i	0.342809	−	0.593763i	−0.642144	−	0.766584i	$-0.721955\pi$
$457$	7.32843	−	12.6932i	0.342809	−	0.593763i	0.984953	+	0.172821i	$0.0552882\pi$
$458$	18.8995	+	32.7349i	0.883115	+	1.52960i
$459$		0			0
$460$	−13.3995	+	23.2086i	−0.624755	+	1.08211i
$461$	−22.4558			−1.04587			−0.522936	−	0.852372i	$-0.675164\pi$
$461$	−22.4558			−1.04587			−0.522936	+	0.852372i	$0.675164\pi$
$462$		0			0
$463$	−20.6569			−0.960005			−0.480003	−	0.877267i	$-0.659364\pi$
$463$	−20.6569			−0.960005			−0.480003	+	0.877267i	$0.659364\pi$
$464$	−7.24264	+	12.5446i	−0.336231	+	0.582369i
$465$		0			0
$466$	7.24264	+	12.5446i	0.335509	+	0.581118i
$467$	12.7426	−	22.0709i	0.589659	−	1.02132i	−0.404618	−	0.914486i	$-0.632595\pi$
$467$	12.7426	−	22.0709i	0.589659	−	1.02132i	0.994277	−	0.106834i	$-0.0340712\pi$
$468$		0			0
$469$	−24.0000	−	20.7846i	−1.10822	−	0.959744i
$470$	−57.0416			−2.63113
$471$		0			0
$472$	23.8995	+	41.3951i	1.10006	+	1.90537i
$473$	24.2279	+	41.9640i	1.11400	+	1.92951i
$474$		0			0
$475$	−9.65685			−0.443087
$476$	7.00000	−	36.3731i	0.320844	−	1.66716i
$477$		0			0
$478$	2.82843	−	4.89898i	0.129369	−	0.224074i
$479$	6.08579	+	10.5409i	0.278067	+	0.481626i	0.970904	−	0.239468i	$-0.0769730\pi$
$479$	6.08579	+	10.5409i	0.278067	+	0.481626i	−0.692838	+	0.721094i	$0.743640\pi$
$480$		0			0
$481$	−1.65685	+	2.86976i	−0.0755461	+	0.130850i
$482$	47.7990			2.17718
$483$		0			0
$484$	14.0000			0.636364
$485$	−32.2132	+	55.7949i	−1.46273	+	2.53352i
$486$		0			0
$487$	0.171573	+	0.297173i	0.00777471	+	0.0134662i	0.869887	−	0.493252i	$-0.164192\pi$
$487$	0.171573	+	0.297173i	0.00777471	+	0.0134662i	−0.862112	+	0.506718i	$0.830859\pi$
$488$	32.3492	−	56.0305i	1.46438	−	2.53638i
$489$		0			0
$490$	−60.0772	−	24.0131i	−2.71401	−	1.08480i
$491$	8.51472			0.384264			0.192132	−	0.981369i	$-0.438460\pi$
$491$	8.51472			0.384264			0.192132	+	0.981369i	$0.438460\pi$
$492$		0			0
$493$	−8.82843	−	15.2913i	−0.397612	−	0.688685i
$494$	3.41421	+	5.91359i	0.153613	+	0.266065i
$495$		0			0
$496$	−9.51472			−0.427223
$497$	10.8579	−	3.76127i	0.487042	−	0.168716i
$498$		0			0
$499$	−9.98528	+	17.2950i	−0.447003	+	0.774231i	−0.998189	−	0.0601507i	$-0.980842\pi$
$499$	−9.98528	+	17.2950i	−0.447003	+	0.774231i	0.551187	+	0.834382i	$0.314175\pi$
$500$	−34.1274	−	59.1104i	−1.52622	−	2.64350i
$501$		0			0
$502$	−16.2782	+	28.1946i	−0.726530	+	1.25839i
$503$	−20.1127			−0.896781			−0.448390	−	0.893838i	$-0.648003\pi$
$503$	−20.1127			−0.896781			−0.448390	+	0.893838i	$0.648003\pi$
$504$		0			0
$505$	13.3431			0.593762
$506$	−8.44975	+	14.6354i	−0.375637	+	0.650623i
$507$		0			0
$508$	−32.4853	−	56.2662i	−1.44130	−	2.49641i
$509$	−5.24264	+	9.08052i	−0.232376	+	0.402487i	−0.958507	−	0.285070i	$-0.907983\pi$
$509$	−5.24264	+	9.08052i	−0.232376	+	0.402487i	0.726131	+	0.687557i	$0.241317\pi$
$510$		0			0
$511$	−20.6274	−	17.8639i	−0.912503	−	0.790251i
$512$	−31.2426			−1.38074
$513$		0			0
$514$	31.3848	+	54.3600i	1.38432	+	2.39772i
$515$	−7.00000	−	12.1244i	−0.308457	−	0.534263i
$516$		0			0
$517$	−23.6274			−1.03913
$518$	5.65685	+	4.89898i	0.248548	+	0.215249i
$519$		0			0
$520$	−23.8995	+	41.3951i	−1.04806	+	1.81530i
$521$	−20.4853	−	35.4815i	−0.897476	−	1.55447i	−0.830709	−	0.556706i	$-0.812065\pi$
$521$	−20.4853	−	35.4815i	−0.897476	−	1.55447i	−0.0667670	−	0.997769i	$-0.521268\pi$
$522$		0			0
$523$	18.8995	−	32.7349i	0.826417	−	1.43140i	−0.0744141	−	0.997227i	$-0.523709\pi$
$523$	18.8995	−	32.7349i	0.826417	−	1.43140i	0.900831	−	0.434169i	$-0.142958\pi$
$524$	−39.5980			−1.72985
$525$		0			0
$526$	−27.3137			−1.19093
$527$	5.79899	−	10.0441i	0.252608	−	0.437530i
$528$		0			0
$529$	9.82843	+	17.0233i	0.427323	+	0.740145i
$530$	−9.24264	+	16.0087i	−0.401475	+	0.695375i
$531$		0			0
$532$	9.57107	−	3.31552i	0.414958	−	0.143746i
$533$	−21.6569			−0.938062
$534$		0			0
$535$	−5.41421	−	9.37769i	−0.234077	−	0.405433i
$536$	26.4853	+	45.8739i	1.14399	+	1.98145i
$537$		0			0
$538$	19.3137			0.832673
$539$	−24.8848	−	9.94655i	−1.07186	−	0.428428i
$540$		0			0
$541$	−11.5000	+	19.9186i	−0.494424	+	0.856367i	−0.999979	−	0.00642713i	$-0.997954\pi$
$541$	−11.5000	+	19.9186i	−0.494424	+	0.856367i	0.505556	+	0.862794i	$0.331288\pi$
$542$	23.6924	+	41.0364i	1.01768	+	1.76267i
$543$		0			0
$544$	2.89949	−	5.02207i	0.124315	−	0.215320i
$545$	69.4558			2.97516
$546$		0			0
$547$	−5.79899			−0.247947			−0.123973	−	0.992286i	$-0.539564\pi$
$547$	−5.79899			−0.247947			−0.123973	+	0.992286i	$0.539564\pi$
$548$	−26.4706	+	45.8484i	−1.13077	+	1.95854i
$549$		0			0
$550$	−44.6274	−	77.2970i	−1.90292	−	3.29595i
$551$	2.41421	−	4.18154i	0.102849	−	0.178140i
$552$		0			0
$553$	1.17157	−	6.08767i	0.0498203	−	0.258874i
$554$	31.3848			1.33341
$555$		0			0
$556$	12.7426	+	22.0709i	0.540408	+	0.936015i
$557$	7.22792	+	12.5191i	0.306257	+	0.530452i	0.977540	−	0.210748i	$-0.0675900\pi$
$557$	7.22792	+	12.5191i	0.306257	+	0.530452i	−0.671283	+	0.741201i	$0.734257\pi$
$558$		0			0
$559$	−35.7990			−1.51414
$560$	22.9706	+	19.8931i	0.970683	+	0.840637i
$561$		0			0
$562$	8.41421	−	14.5738i	0.354932	−	0.614761i
$563$	0.242641	+	0.420266i	0.0102261	+	0.0177121i	0.871093	−	0.491118i	$-0.163412\pi$
$563$	0.242641	+	0.420266i	0.0102261	+	0.0177121i	−0.860867	+	0.508830i	$0.830078\pi$
$564$		0			0
$565$	−24.5563	+	42.5328i	−1.03309	+	1.78937i
$566$	76.3553			3.20945
$567$		0			0
$568$	−19.1716			−0.804421
$569$	−22.8995	+	39.6631i	−0.959997	+	1.66276i	−0.237502	+	0.971387i	$0.576329\pi$
$569$	−22.8995	+	39.6631i	−0.959997	+	1.66276i	−0.722495	+	0.691376i	$0.757005\pi$
$570$		0			0
$571$	−13.6421	−	23.6289i	−0.570906	−	0.988838i	−0.996473	−	0.0839109i	$-0.973259\pi$
$571$	−13.6421	−	23.6289i	−0.570906	−	0.988838i	0.425568	−	0.904927i	$-0.360074\pi$
$572$	−20.7279	+	35.9018i	−0.866678	+	1.50113i
$573$		0			0
$574$	−9.24264	+	48.0262i	−0.385780	+	2.00457i
$575$	17.6569			0.736342
$576$		0			0
$577$	−9.15685	−	15.8601i	−0.381205	−	0.660266i	0.610030	−	0.792378i	$-0.291157\pi$
$577$	−9.15685	−	15.8601i	−0.381205	−	0.660266i	−0.991235	+	0.132112i	$0.957824\pi$
$578$	4.37868	+	7.58410i	0.182129	+	0.315457i
$579$		0			0
$580$	70.7696			2.93855
$581$	10.4289	−	3.61269i	0.432665	−	0.149880i
$582$		0			0
$583$	−3.82843	+	6.63103i	−0.158557	+	0.274629i
$584$	22.7635	+	39.4275i	0.941959	+	1.63152i
$585$		0			0
$586$	−1.00000	+	1.73205i	−0.0413096	+	0.0715504i
$587$	26.6274			1.09903			0.549516	−	0.835483i	$-0.314812\pi$
$587$	26.6274			1.09903			0.549516	+	0.835483i	$0.314812\pi$
$588$		0			0
$589$	3.17157			0.130682
$590$	50.0416	−	86.6746i	2.06018	−	3.56834i
$591$		0			0
$592$	−1.75736	−	3.04384i	−0.0722270	−	0.125101i
$593$	13.7426	−	23.8030i	0.564343	−	0.977470i	−0.432768	−	0.901505i	$-0.642463\pi$
$593$	13.7426	−	23.8030i	0.564343	−	0.977470i	0.997111	−	0.0759647i	$-0.0242036\pi$
$594$		0			0
$595$	−35.0000	+	12.1244i	−1.43486	+	0.497050i
$596$	−14.6569			−0.600368
$597$		0			0
$598$	−6.24264	−	10.8126i	−0.255281	−	0.442159i
$599$	−14.5563	−	25.2123i	−0.594756	−	1.03015i	−0.993581	−	0.113121i	$-0.963915\pi$
$599$	−14.5563	−	25.2123i	−0.594756	−	1.03015i	0.398825	−	0.917027i	$-0.369418\pi$
$600$		0			0
$601$	−8.68629			−0.354321			−0.177161	−	0.984182i	$-0.556691\pi$
$601$	−8.68629			−0.354321			−0.177161	+	0.984182i	$0.556691\pi$
$602$	−15.2782	+	79.3877i	−0.622692	+	3.23560i
$603$		0			0
$604$	17.8284	−	30.8797i	0.725428	−	1.25648i
$605$	−7.00000	−	12.1244i	−0.284590	−	0.492925i
$606$		0			0
$607$	−6.92893	+	12.0013i	−0.281237	+	0.487116i	−0.971690	−	0.236261i	$-0.924078\pi$
$607$	−6.92893	+	12.0013i	−0.281237	+	0.487116i	0.690453	+	0.723377i	$0.257411\pi$
$608$	1.58579			0.0643121
$609$		0			0
$610$	−135.468			−5.48494
$611$	8.72792	−	15.1172i	0.353094	−	0.611577i
$612$		0			0
$613$	18.3137	+	31.7203i	0.739684	+	1.28117i	0.952638	+	0.304108i	$0.0983582\pi$
$613$	18.3137	+	31.7203i	0.739684	+	1.28117i	−0.212954	+	0.977062i	$0.568308\pi$
$614$	−3.00000	+	5.19615i	−0.121070	+	0.209700i
$615$		0			0
$616$	33.7990	+	29.2708i	1.36180	+	1.17935i
$617$	32.1716			1.29518			0.647589	−	0.761989i	$-0.275777\pi$
$617$	32.1716			1.29518			0.647589	+	0.761989i	$0.275777\pi$
$618$		0			0
$619$	−4.67157	−	8.09140i	−0.187766	−	0.325221i	0.756739	−	0.653717i	$-0.226791\pi$
$619$	−4.67157	−	8.09140i	−0.187766	−	0.325221i	−0.944505	+	0.328496i	$0.893458\pi$
$620$	23.2426	+	40.2574i	0.933447	+	1.61678i
$621$		0			0
$622$	−54.6274			−2.19036
$623$	−5.41421	+	28.1331i	−0.216916	+	1.12713i
$624$		0			0
$625$	−9.98528	+	17.2950i	−0.399411	+	0.691801i
$626$	−37.7635	−	65.4082i	−1.50933	−	2.61424i
$627$		0			0
$628$	−20.3995	+	35.3330i	−0.814028	+	1.40994i
$629$	4.28427			0.170825
$630$		0			0
$631$	−16.6569			−0.663099			−0.331549	−	0.943438i	$-0.607571\pi$
$631$	−16.6569			−0.663099			−0.331549	+	0.943438i	$0.607571\pi$
$632$	−5.17157	+	8.95743i	−0.205714	+	0.356307i
$633$		0			0
$634$	35.9706	+	62.3028i	1.42857	+	2.47436i
$635$	−32.4853	+	56.2662i	−1.28914	+	2.23285i
$636$		0			0
$637$	15.5563	−	12.2474i	0.616365	−	0.485262i
$638$	44.6274			1.76682
$639$		0			0
$640$	39.3492	+	68.1549i	1.55542	+	2.69406i
$641$	−2.58579	−	4.47871i	−0.102132	−	0.176899i	0.810431	−	0.585835i	$-0.199233\pi$
$641$	−2.58579	−	4.47871i	−0.102132	−	0.176899i	−0.912563	+	0.408936i	$0.865900\pi$
$642$		0			0
$643$	1.37258			0.0541294			0.0270647	−	0.999634i	$-0.491384\pi$
$643$	1.37258			0.0541294			0.0270647	+	0.999634i	$0.491384\pi$
$644$	−17.5000	+	6.06218i	−0.689597	+	0.238883i
$645$		0			0
$646$	4.41421	−	7.64564i	0.173675	−	0.300814i
$647$	3.42893	+	5.93908i	0.134805	+	0.233490i	0.925523	−	0.378691i	$-0.123626\pi$
$647$	3.42893	+	5.93908i	0.134805	+	0.233490i	−0.790718	+	0.612181i	$0.790292\pi$
$648$		0			0
$649$	20.7279	−	35.9018i	0.813642	−	1.40927i
$650$	65.9411			2.58642
$651$		0			0
$652$	84.1127			3.29411
$653$	19.9706	−	34.5900i	0.781509	−	1.35361i	−0.149554	−	0.988754i	$-0.547784\pi$
$653$	19.9706	−	34.5900i	0.781509	−	1.35361i	0.931063	−	0.364859i	$-0.118883\pi$
$654$		0			0
$655$	19.7990	+	34.2929i	0.773611	+	1.33993i
$656$	11.4853	−	19.8931i	0.448425	−	0.776695i
$657$		0			0
$658$	−29.7990	−	25.8067i	−1.16169	−	1.00605i
$659$	21.5147			0.838094			0.419047	−	0.907964i	$-0.362364\pi$
$659$	21.5147			0.838094			0.419047	+	0.907964i	$0.362364\pi$
$660$		0			0
$661$	−6.14214	−	10.6385i	−0.238901	−	0.413789i	0.721498	−	0.692417i	$-0.243454\pi$
$661$	−6.14214	−	10.6385i	−0.238901	−	0.413789i	−0.960399	+	0.278627i	$0.910121\pi$
$662$	6.65685	+	11.5300i	0.258726	+	0.448127i
$663$		0			0
$664$	−18.4142			−0.714610
$665$	−7.65685	−	6.63103i	−0.296920	−	0.257140i
$666$		0			0
$667$	−4.41421	+	7.64564i	−0.170919	+	0.296040i
$668$	16.8995	+	29.2708i	0.653861	+	1.13252i
$669$		0			0
$670$	55.4558	−	96.0523i	2.14245	−	3.71083i
$671$	−56.1127			−2.16621
$672$		0			0
$673$	2.82843			0.109028			0.0545139	−	0.998513i	$-0.482639\pi$
$673$	2.82843			0.109028			0.0545139	+	0.998513i	$0.482639\pi$
$674$	7.82843	−	13.5592i	0.301540	−	0.522282i
$675$		0			0
$676$	9.57107	+	16.5776i	0.368118	+	0.637599i
$677$	−8.00000	+	13.8564i	−0.307465	+	0.532545i	−0.977807	−	0.209507i	$-0.932814\pi$
$677$	−8.00000	+	13.8564i	−0.307465	+	0.532545i	0.670342	+	0.742052i	$0.266147\pi$
$678$		0			0
$679$	−42.0711	+	14.5738i	−1.61454	+	0.559293i
$680$	61.7990			2.36988
$681$		0			0
$682$	14.6569	+	25.3864i	0.561240	+	0.972096i
$683$	2.51472	+	4.35562i	0.0962230	+	0.166663i	0.910118	−	0.414348i	$-0.135990\pi$
$683$	2.51472	+	4.35562i	0.0962230	+	0.166663i	−0.813895	+	0.581011i	$0.802657\pi$
$684$		0			0
$685$	52.9411			2.02278
$686$	−20.5208	−	39.7246i	−0.783488	−	1.51669i
$687$		0			0
$688$	18.9853	−	32.8835i	0.723807	−	1.25367i
$689$	−2.82843	−	4.89898i	−0.107754	−	0.186636i
$690$		0			0
$691$	−6.00000	+	10.3923i	−0.228251	+	0.395342i	−0.957290	−	0.289130i	$-0.906634\pi$
$691$	−6.00000	+	10.3923i	−0.228251	+	0.395342i	0.729039	+	0.684472i	$0.239967\pi$
$692$	−10.8284			−0.411635
$693$		0			0
$694$	−49.3848			−1.87462
$695$	12.7426	−	22.0709i	0.483356	−	0.837197i
$696$		0			0
$697$	14.0000	+	24.2487i	0.530288	+	0.918485i
$698$	−16.8995	+	29.2708i	−0.639655	+	1.10792i
$699$		0			0
$700$	18.4853	−	96.0523i	0.698678	−	3.63044i
$701$	−2.45584			−0.0927560			−0.0463780	−	0.998924i	$-0.514768\pi$
$701$	−2.45584			−0.0927560			−0.0463780	+	0.998924i	$0.514768\pi$
$702$		0			0
$703$	0.585786	+	1.01461i	0.0220934	+	0.0382668i
$704$	18.8137	+	32.5863i	0.709068	+	1.22814i
$705$		0			0
$706$	3.17157			0.119364
$707$	6.97056	+	6.03668i	0.262155	+	0.227033i
$708$		0			0
$709$	7.98528	−	13.8309i	0.299894	−	0.519431i	−0.676218	−	0.736702i	$-0.736382\pi$
$709$	7.98528	−	13.8309i	0.299894	−	0.519431i	0.976111	+	0.217271i	$0.0697155\pi$
$710$	20.0711	+	34.7641i	0.753254	+	1.30467i
$711$		0			0
$712$	23.8995	−	41.3951i	0.895671	−	1.55135i
$713$	−5.79899			−0.217174
$714$		0			0
$715$	41.4558			1.55036
$716$	−20.0711	+	34.7641i	−0.750091	+	1.29920i
$717$		0			0
$718$	−7.44975	−	12.9033i	−0.278022	−	0.481548i
$719$	−0.485281	+	0.840532i	−0.0180979	+	0.0313466i	−0.874933	−	0.484245i	$-0.839094\pi$
$719$	−0.485281	+	0.840532i	−0.0180979	+	0.0313466i	0.856835	+	0.515591i	$0.172428\pi$
$720$		0			0
$721$	1.82843	−	9.50079i	0.0680942	−	0.353828i
$722$	2.41421			0.0898477
$723$		0			0
$724$	22.3137	+	38.6485i	0.829282	+	1.43636i
$725$	−23.3137	−	40.3805i	−0.865849	−	1.49970i
$726$		0			0
$727$	−13.0000			−0.482143			−0.241072	−	0.970507i	$-0.577499\pi$
$727$	−13.0000			−0.482143			−0.241072	+	0.970507i	$0.577499\pi$
$728$	−31.2132	+	10.8126i	−1.15684	+	0.400741i
$729$		0			0
$730$	47.6630	−	82.5547i	1.76408	−	3.05548i
$731$	23.1421	+	40.0834i	0.855943	+	1.48254i
$732$		0			0
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	−0.588177	−	0.808732i	$-0.700154\pi$
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	0.994471	+	0.105010i	$0.0334875\pi$
$734$	71.5980			2.64273
$735$		0			0
$736$	−2.89949			−0.106877
$737$	22.9706	−	39.7862i	0.846132	−	1.46554i
$738$		0			0
$739$	4.00000	+	6.92820i	0.147142	+	0.254858i	0.930170	−	0.367129i	$-0.119659\pi$
$739$	4.00000	+	6.92820i	0.147142	+	0.254858i	−0.783028	+	0.621987i	$0.786326\pi$
$740$	−8.58579	+	14.8710i	−0.315620	+	0.546670i
$741$		0			0
$742$	−12.0711	+	4.18154i	−0.443143	+	0.153509i
$743$	−33.1716			−1.21695			−0.608473	−	0.793574i	$-0.708218\pi$
$743$	−33.1716			−1.21695			−0.608473	+	0.793574i	$0.708218\pi$
$744$		0			0
$745$	7.32843	+	12.6932i	0.268493	+	0.465043i
$746$	−24.4853	−	42.4098i	−0.896470	−	1.55273i
$747$		0			0
$748$	53.5980			1.95974
$749$	1.41421	−	7.34847i	0.0516742	−	0.268507i
$750$		0			0
$751$	−17.3137	+	29.9882i	−0.631786	+	1.09429i	0.355400	+	0.934714i	$0.384345\pi$
$751$	−17.3137	+	29.9882i	−0.631786	+	1.09429i	−0.987186	+	0.159572i	$0.948989\pi$
$752$	9.25736	+	16.0342i	0.337581	+	0.584708i
$753$		0			0
$754$	−16.4853	+	28.5533i	−0.600359	+	1.03985i
$755$	−35.6569			−1.29769
$756$		0			0
$757$	9.34315			0.339582			0.169791	−	0.985480i	$-0.445691\pi$
$757$	9.34315			0.339582			0.169791	+	0.985480i	$0.445691\pi$
$758$	19.8995	−	34.4669i	0.722782	−	1.25190i
$759$		0			0
$760$	8.44975	+	14.6354i	0.306505	+	0.530881i
$761$	−9.39949	+	16.2804i	−0.340731	+	0.590164i	−0.984569	−	0.174998i	$-0.944008\pi$
$761$	−9.39949	+	16.2804i	−0.340731	+	0.590164i	0.643837	+	0.765162i	$0.277341\pi$
$762$		0			0
$763$	36.2843	+	31.4231i	1.31358	+	1.13759i
$764$	−45.2843			−1.63833
$765$		0			0
$766$	19.3137	+	33.4523i	0.697833	+	1.20868i
$767$	15.3137	+	26.5241i	0.552946	+	0.957731i
$768$		0			0
$769$	14.3137			0.516166			0.258083	−	0.966123i	$-0.416909\pi$
$769$	14.3137			0.516166			0.258083	+	0.966123i	$0.416909\pi$
$770$	17.6924	−	91.9323i	0.637589	−	3.31301i
$771$		0			0
$772$	−7.65685	+	13.2621i	−0.275576	+	0.477312i
$773$	1.41421	+	2.44949i	0.0508657	+	0.0881020i	0.890337	−	0.455302i	$-0.150469\pi$
$773$	1.41421	+	2.44949i	0.0508657	+	0.0881020i	−0.839471	+	0.543404i	$0.817135\pi$
$774$		0			0
$775$	15.3137	−	26.5241i	0.550085	−	0.952775i
$776$	74.2843			2.66665
$777$		0			0
$778$	−10.4853			−0.375916
$779$	−3.82843	+	6.63103i	−0.137168	+	0.237581i
$780$		0			0
$781$	8.31371	+	14.3998i	0.297488	+	0.515264i
$782$	−8.07107	+	13.9795i	−0.288621	+	0.499906i
$783$		0			0
$784$	3.00000	+	20.7846i	0.107143	+	0.742307i
$785$	40.7990			1.45618
$786$		0			0
$787$	−8.14214	−	14.1026i	−0.290236	−	0.502703i	0.683630	−	0.729829i	$-0.260400\pi$
$787$	−8.14214	−	14.1026i	−0.290236	−	0.502703i	−0.973865	+	0.227126i	$0.927067\pi$
$788$	−33.4706	−	57.9727i	−1.19234	−	2.06519i
$789$		0			0
$790$	21.6569			0.770516
$791$	−32.0711	+	11.1097i	−1.14032	+	0.395017i
$792$		0			0
$793$	20.7279	−	35.9018i	0.736070	−	1.27491i
$794$	−6.41421	−	11.1097i	−0.227632	−	0.394270i
$795$		0			0
$796$	−6.39949	+	11.0843i	−0.226824	+	0.392871i
$797$	−7.51472			−0.266185			−0.133092	−	0.991104i	$-0.542491\pi$
$797$	−7.51472			−0.266185			−0.133092	+	0.991104i	$0.542491\pi$
$798$		0			0
$799$	−22.5685			−0.798418
$800$	7.65685	−	13.2621i	0.270711	−	0.468885i
$801$		0			0
$802$	−0.828427	−	1.43488i	−0.0292528	−	0.0506673i
$803$	19.7426	−	34.1953i	0.696703	−	1.20672i
$804$		0			0
$805$	14.0000	+	12.1244i	0.493435	+	0.427327i
$806$	−21.6569			−0.762830
$807$		0			0
$808$	−7.69239	−	13.3236i	−0.270617	−	0.468723i
$809$	−12.3995	−	21.4766i	−0.435943	−	0.755075i	0.561429	−	0.827525i	$-0.310252\pi$
$809$	−12.3995	−	21.4766i	−0.435943	−	0.755075i	−0.997372	+	0.0724494i	$0.976918\pi$
$810$		0			0
$811$	−12.1421			−0.426368			−0.213184	−	0.977012i	$-0.568383\pi$
$811$	−12.1421			−0.426368			−0.213184	+	0.977012i	$0.568383\pi$
$812$	36.9706	+	32.0174i	1.29741	+	1.12359i
$813$		0			0
$814$	−5.41421	+	9.37769i	−0.189768	+	0.328688i
$815$	−42.0563	−	72.8437i	−1.47317	−	2.55160i
$816$		0			0
$817$	−6.32843	+	10.9612i	−0.221404	+	0.383482i
$818$	12.8284			0.448535
$819$		0			0
$820$	−112.225			−3.91908
$821$	3.42893	−	5.93908i	0.119671	−	0.207275i	−0.799967	−	0.600045i	$-0.795150\pi$
$821$	3.42893	−	5.93908i	0.119671	−	0.207275i	0.919637	+	0.392769i	$0.128483\pi$
$822$		0			0
$823$	−15.9853	−	27.6873i	−0.557212	−	0.965119i	−0.997728	−	0.0673745i	$-0.978538\pi$
$823$	−15.9853	−	27.6873i	−0.557212	−	0.965119i	0.440516	−	0.897745i	$-0.354796\pi$
$824$	−8.07107	+	13.9795i	−0.281169	+	0.486999i
$825$		0			0
$826$	65.3553	−	22.6398i	2.27400	−	0.787738i
$827$	15.1127			0.525520			0.262760	−	0.964861i	$-0.415367\pi$
$827$	15.1127			0.525520			0.262760	+	0.964861i	$0.415367\pi$
$828$		0			0
$829$	19.0711	+	33.0321i	0.662366	+	1.14725i	0.979992	+	0.199035i	$0.0637807\pi$
$829$	19.0711	+	33.0321i	0.662366	+	1.14725i	−0.317627	+	0.948216i	$0.602886\pi$
$830$	19.2782	+	33.3908i	0.669155	+	1.15901i
$831$		0			0
$832$	−27.7990			−0.963757
$833$	−23.7696	−	9.50079i	−0.823566	−	0.329183i
$834$		0			0
$835$	16.8995	−	29.2708i	0.584831	−	1.01296i
$836$	7.32843	+	12.6932i	0.253459	+	0.439004i
$837$		0			0
$838$	−12.2782	+	21.2664i	−0.424143	+	0.734636i
$839$	45.2548			1.56237			0.781185	−	0.624299i	$-0.214615\pi$
$839$	45.2548			1.56237			0.781185	+	0.624299i	$0.214615\pi$
$840$		0			0
$841$	−5.68629			−0.196079
$842$	−23.1421	+	40.0834i	−0.797531	+	1.38136i
$843$		0			0
$844$	−31.5563	−	54.6572i	−1.08621	−	1.88138i
$845$	9.57107	−	16.5776i	0.329255	−	0.570286i
$846$		0			0
$847$	1.82843	−	9.50079i	0.0628255	−	0.326451i
$848$	6.00000			0.206041
$849$		0			0
$850$	−42.6274	−	73.8329i	−1.46211	−	2.53245i
$851$	−1.07107	−	1.85514i	−0.0367157	−	0.0635935i
$852$		0			0
$853$	−6.37258			−0.218193			−0.109097	−	0.994031i	$-0.534796\pi$
$853$	−6.37258			−0.218193			−0.109097	+	0.994031i	$0.534796\pi$
$854$	−70.7696	−	61.2882i	−2.42168	−	2.09724i
$855$		0			0
$856$	−6.24264	+	10.8126i	−0.213369	+	0.369566i
$857$	−13.4142	−	23.2341i	−0.458221	−	0.793662i	0.540646	−	0.841250i	$-0.318180\pi$
$857$	−13.4142	−	23.2341i	−0.458221	−	0.793662i	−0.998867	+	0.0475883i	$0.984846\pi$
$858$		0			0
$859$	−15.4706	+	26.7958i	−0.527849	+	0.914261i	0.471624	+	0.881800i	$0.343668\pi$
$859$	−15.4706	+	26.7958i	−0.527849	+	0.914261i	−0.999473	+	0.0324613i	$0.989665\pi$
$860$	−185.510			−6.32583
$861$		0			0
$862$	55.9411			1.90536
$863$	3.58579	−	6.21076i	0.122062	−	0.211417i	−0.798519	−	0.601970i	$-0.794383\pi$
$863$	3.58579	−	6.21076i	0.122062	−	0.211417i	0.920581	+	0.390553i	$0.127716\pi$
$864$		0			0
$865$	5.41421	+	9.37769i	0.184089	+	0.318851i
$866$	−10.2426	+	17.7408i	−0.348059	+	0.602856i
$867$		0			0
$868$	−6.07107	+	31.5462i	−0.206065	+	1.07075i
$869$	8.97056			0.304305
$870$		0			0
$871$	16.9706	+	29.3939i	0.575026	+	0.995974i
$872$	−40.0416	−	69.3541i	−1.35598	−	2.34863i
$873$		0			0
$874$	−4.41421			−0.149313
$875$	−44.5711	+	15.4399i	−1.50678	+	0.521963i
$876$		0			0
$877$	−10.8284	+	18.7554i	−0.365650	+	0.633324i	−0.988880	−	0.148714i	$-0.952487\pi$
$877$	−10.8284	+	18.7554i	−0.365650	+	0.633324i	0.623230	+	0.782038i	$0.285820\pi$
$878$	23.8995	+	41.3951i	0.806569	+	1.39702i
$879$		0			0
$880$	−21.9853	+	38.0796i	−0.741124	+	1.28366i
$881$	4.62742			0.155902			0.0779508	−	0.996957i	$-0.475162\pi$
$881$	4.62742			0.155902			0.0779508	+	0.996957i	$0.475162\pi$
$882$		0			0
$883$	−44.9706			−1.51338			−0.756690	−	0.653774i	$-0.773185\pi$
$883$	−44.9706			−1.51338			−0.756690	+	0.653774i	$0.773185\pi$
$884$	−19.7990	+	34.2929i	−0.665912	+	1.15339i
$885$		0			0
$886$	−40.6274	−	70.3688i	−1.36490	−	2.36408i
$887$	−7.72792	+	13.3852i	−0.259478	+	0.449429i	−0.966102	−	0.258160i	$-0.916884\pi$
$887$	−7.72792	+	13.3852i	−0.259478	+	0.449429i	0.706624	+	0.707589i	$0.250217\pi$
$888$		0			0
$889$	−42.4264	+	14.6969i	−1.42294	+	0.492919i
$890$	−100.083			−3.35480
$891$		0			0
$892$	−41.7279	−	72.2749i	−1.39715	−	2.41994i
$893$	−3.08579	−	5.34474i	−0.103262	−	0.178855i
$894$		0			0
$895$	40.1421			1.34180
$896$	−10.2782	+	53.4070i	−0.343370	+	1.78420i
$897$		0			0
$898$	31.5563	−	54.6572i	1.05305	−	1.82393i
$899$	7.65685	+	13.2621i	0.255370	+	0.442314i
$900$		0			0
$901$	−3.65685	+	6.33386i	−0.121827	+	0.211011i
$902$	−70.7696			−2.35637
$903$		0			0
$904$	56.6274			1.88340
$905$	22.3137	−	38.6485i	0.741733	−	1.28472i
$906$		0			0
$907$	9.82843	+	17.0233i	0.326348	+	0.565251i	0.981784	−	0.190000i	$-0.0608487\pi$
$907$	9.82843	+	17.0233i	0.326348	+	0.565251i	−0.655437	+	0.755250i	$0.727515\pi$
$908$	−12.1421	+	21.0308i	−0.402951	+	0.697931i
$909$		0			0
$910$	52.2843	+	45.2795i	1.73321	+	1.50100i
$911$	−18.0000			−0.596367			−0.298183	−	0.954509i	$-0.596381\pi$
$911$	−18.0000			−0.596367			−0.298183	+	0.954509i	$0.596381\pi$
$912$		0			0
$913$	7.98528	+	13.8309i	0.264274	+	0.457736i
$914$	17.6924	+	30.6441i	0.585212	+	1.01362i
$915$		0			0
$916$	−59.9411			−1.98051
$917$	−5.17157	+	26.8723i	−0.170780	+	0.887401i
$918$		0			0
$919$	21.6716	−	37.5363i	0.714879	−	1.23821i	−0.248127	−	0.968728i	$-0.579815\pi$
$919$	21.6716	−	37.5363i	0.714879	−	1.23821i	0.963006	−	0.269480i	$-0.0868517\pi$
$920$	−15.4497	−	26.7597i	−0.509363	−	0.882243i
$921$		0			0
$922$	27.1066	−	46.9500i	0.892708	−	1.54622i
$923$	−12.2843			−0.404342
$924$		0			0
$925$	11.3137			0.371992
$926$	24.9350	−	43.1887i	0.819416	−	1.41927i
$927$		0			0
$928$	3.82843	+	6.63103i	0.125674	+	0.217674i
$929$	8.22792	−	14.2512i	0.269949	−	0.467566i	−0.698899	−	0.715220i	$-0.746326\pi$
$929$	8.22792	−	14.2512i	0.269949	−	0.467566i	0.968848	+	0.247654i	$0.0796597\pi$
$930$		0			0
$931$	−1.00000	−	6.92820i	−0.0327737	−	0.227063i
$932$	−22.9706			−0.752426
$933$		0			0
$934$	30.7635	+	53.2839i	1.00661	+	1.74350i
$935$	−26.7990	−	46.4172i	−0.876421	−	1.51801i
$936$		0			0
$937$	−27.0000			−0.882052			−0.441026	−	0.897494i	$-0.645385\pi$
$937$	−27.0000			−0.882052			−0.441026	+	0.897494i	$0.645385\pi$
$938$	72.4264	−	25.0892i	2.36481	−	0.819193i
$939$		0			0
$940$	45.2279	−	78.3371i	1.47517	−	2.55507i
$941$	29.9706	+	51.9105i	0.977012	+	1.69224i	0.673128	+	0.739526i	$0.264950\pi$
$941$	29.9706	+	51.9105i	0.977012	+	1.69224i	0.303885	+	0.952709i	$0.401716\pi$
$942$		0			0
$943$	7.00000	−	12.1244i	0.227951	−	0.394823i
$944$	−32.4853			−1.05731
$945$		0			0
$946$	−116.983			−3.80344
$947$	−8.34315	+	14.4508i	−0.271116	+	0.469586i	−0.969148	−	0.246480i	$-0.920726\pi$
$947$	−8.34315	+	14.4508i	−0.271116	+	0.469586i	0.698032	+	0.716067i	$0.254059\pi$
$948$		0			0
$949$	14.5858	+	25.2633i	0.473475	+	0.820082i
$950$	11.6569	−	20.1903i	0.378198	−	0.655059i
$951$		0			0
$952$	32.2843	+	27.9590i	1.04634	+	0.906156i
$953$	26.6274			0.862547			0.431273	−	0.902221i	$-0.358064\pi$
$953$	26.6274			0.862547			0.431273	+	0.902221i	$0.358064\pi$
$954$		0			0
$955$	22.6421	+	39.2173i	0.732682	+	1.26904i
$956$	4.48528	+	7.76874i	0.145064	+	0.251259i
$957$		0			0
$958$	−29.3848			−0.949379
$959$	27.6569	+	23.9515i	0.893086	+	0.773436i
$960$		0			0
$961$	10.4706	−	18.1355i	0.337760	−	0.585018i
$962$	−4.00000	−	6.92820i	−0.128965	−	0.223374i
$963$		0			0
$964$	−37.8995	+	65.6439i	−1.22066	+	2.11425i
$965$	15.3137			0.492966
$966$		0			0
$967$	−16.0000			−0.514525			−0.257263	−	0.966342i	$-0.582821\pi$
$967$	−16.0000			−0.514525			−0.257263	+	0.966342i	$0.582821\pi$
$968$	−8.07107	+	13.9795i	−0.259414	+	0.449318i
$969$		0			0
$970$	−77.7696	−	134.701i	−2.49703	−	4.32498i
$971$	−19.8995	+	34.4669i	−0.638605	+	1.10610i	0.347134	+	0.937816i	$0.387155\pi$
$971$	−19.8995	+	34.4669i	−0.638605	+	1.10610i	−0.985739	+	0.168281i	$0.946178\pi$
$972$		0			0
$973$	16.6421	−	5.76500i	0.533522	−	0.184818i
$974$	−0.828427			−0.0265445
$975$		0			0
$976$	21.9853	+	38.0796i	0.703732	+	1.21890i
$977$	11.5563	+	20.0162i	0.369720	+	0.640374i	0.989522	−	0.144384i	$-0.0461202\pi$
$977$	11.5563	+	20.0162i	0.369720	+	0.640374i	−0.619801	+	0.784759i	$0.712787\pi$
$978$		0			0
$979$	−41.4558			−1.32493
$980$	80.6127	−	63.4660i	2.57508	−	2.02735i
$981$		0			0
$982$	−10.2782	+	17.8023i	−0.327990	+	0.568095i
$983$	1.72792	+	2.99285i	0.0551122	+	0.0954571i	0.892265	−	0.451512i	$-0.149115\pi$
$983$	1.72792	+	2.99285i	0.0551122	+	0.0954571i	−0.837153	+	0.546969i	$0.815782\pi$
$984$		0			0
$985$	−33.4706	+	57.9727i	−1.06646	+	1.84716i
$986$	42.6274			1.35753
$987$		0			0
$988$	−10.8284			−0.344498
$989$	11.5711	−	20.0417i	0.367939	−	0.637288i
$990$		0			0
$991$	−26.6274	−	46.1200i	−0.845848	−	1.46505i	−0.884883	−	0.465813i	$-0.845762\pi$
$991$	−26.6274	−	46.1200i	−0.845848	−	1.46505i	0.0390352	−	0.999238i	$-0.487572\pi$
$992$	−2.51472	+	4.35562i	−0.0798424	+	0.138291i
$993$		0			0
$994$	−5.24264	+	27.2416i	−0.166286	+	0.864050i
$995$	12.7990			0.405755
$996$		0			0
$997$	15.0000	+	25.9808i	0.475055	+	0.822819i	0.999592	−	0.0285686i	$-0.00909491\pi$
$997$	15.0000	+	25.9808i	0.475055	+	0.822819i	−0.524537	+	0.851388i	$0.675762\pi$
$998$	−24.1066	−	41.7539i	−0.763081	−	1.32170i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1197.2.j.d.856.1		4
3.2	odd	2		399.2.j.c.58.2	✓	4
7.2	even	3		8379.2.a.bm.1.2		2
7.4	even	3	inner	1197.2.j.d.172.1		4
7.5	odd	6		8379.2.a.bh.1.2		2
21.2	odd	6		2793.2.a.o.1.1		2
21.5	even	6		2793.2.a.n.1.1		2
21.11	odd	6		399.2.j.c.172.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
399.2.j.c.58.2	✓	4	3.2	odd	2
399.2.j.c.172.2	yes	4	21.11	odd	6
1197.2.j.d.172.1		4	7.4	even	3	inner
1197.2.j.d.856.1		4	1.1	even	1	trivial
2793.2.a.n.1.1		2	21.5	even	6
2793.2.a.o.1.1		2	21.2	odd	6
8379.2.a.bh.1.2		2	7.5	odd	6
8379.2.a.bm.1.2		2	7.2	even	3

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:	\( N \)	\(=\)	\( 1197 = 3^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1197.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.20711 + 2.09077i) q^{2} +(-1.91421 - 3.31552i) q^{4} +(-1.91421 + 3.31552i) q^{5} +(-2.50000 + 0.866025i) q^{7} +4.41421 q^{8} +(-4.62132 - 8.00436i) q^{10} +(-1.91421 - 3.31552i) q^{11} +2.82843 q^{13} +(1.20711 - 6.27231i) q^{14} +(-1.50000 + 2.59808i) q^{16} +(-1.82843 - 3.16693i) q^{17} +(0.500000 - 0.866025i) q^{19} +14.6569 q^{20} +9.24264 q^{22} +(-0.914214 + 1.58346i) q^{23} +(-4.82843 - 8.36308i) q^{25} +(-3.41421 + 5.91359i) q^{26} +(7.65685 + 6.63103i) q^{28} +4.82843 q^{29} +(1.58579 + 2.74666i) q^{31} +(0.792893 + 1.37333i) q^{32} +8.82843 q^{34} +(1.91421 - 9.94655i) q^{35} +(-0.585786 + 1.01461i) q^{37} +(1.20711 + 2.09077i) q^{38} +(-8.44975 + 14.6354i) q^{40} -7.65685 q^{41} -12.6569 q^{43} +(-7.32843 + 12.6932i) q^{44} +(-2.20711 - 3.82282i) q^{46} +(3.08579 - 5.34474i) q^{47} +(5.50000 - 4.33013i) q^{49} +23.3137 q^{50} +(-5.41421 - 9.37769i) q^{52} +(-1.00000 - 1.73205i) q^{53} +14.6569 q^{55} +(-11.0355 + 3.82282i) q^{56} +(-5.82843 + 10.0951i) q^{58} +(5.41421 + 9.37769i) q^{59} +(7.32843 - 12.6932i) q^{61} -7.65685 q^{62} -9.82843 q^{64} +(-5.41421 + 9.37769i) q^{65} +(6.00000 + 10.3923i) q^{67} +(-7.00000 + 12.1244i) q^{68} +(18.4853 + 16.0087i) q^{70} -4.34315 q^{71} +(5.15685 + 8.93193i) q^{73} +(-1.41421 - 2.44949i) q^{74} -3.82843 q^{76} +(7.65685 + 6.63103i) q^{77} +(-1.17157 + 2.02922i) q^{79} +(-5.74264 - 9.94655i) q^{80} +(9.24264 - 16.0087i) q^{82} -4.17157 q^{83} +14.0000 q^{85} +(15.2782 - 26.4626i) q^{86} +(-8.44975 - 14.6354i) q^{88} +(5.41421 - 9.37769i) q^{89} +(-7.07107 + 2.44949i) q^{91} +7.00000 q^{92} +(7.44975 + 12.9033i) q^{94} +(1.91421 + 3.31552i) q^{95} +16.8284 q^{97} +(2.41421 + 16.7262i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} - 2 q^{5} - 10 q^{7} + 12 q^{8} - 10 q^{10} - 2 q^{11} + 2 q^{14} - 6 q^{16} + 4 q^{17} + 2 q^{19} + 36 q^{20} + 20 q^{22} + 2 q^{23} - 8 q^{25} - 8 q^{26} + 8 q^{28} + 8 q^{29}+ \cdots + 4 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 - 10 * q^7 + 12 * q^8 - 10 * q^10 - 2 * q^11 + 2 * q^14 - 6 * q^16 + 4 * q^17 + 2 * q^19 + 36 * q^20 + 20 * q^22 + 2 * q^23 - 8 * q^25 - 8 * q^26 + 8 * q^28 + 8 * q^29 + 12 * q^31 + 6 * q^32 + 24 * q^34 + 2 * q^35 - 8 * q^37 + 2 * q^38 - 14 * q^40 - 8 * q^41 - 28 * q^43 - 18 * q^44 - 6 * q^46 + 18 * q^47 + 22 * q^49 + 48 * q^50 - 16 * q^52 - 4 * q^53 + 36 * q^55 - 30 * q^56 - 12 * q^58 + 16 * q^59 + 18 * q^61 - 8 * q^62 - 28 * q^64 - 16 * q^65 + 24 * q^67 - 28 * q^68 + 40 * q^70 - 40 * q^71 - 2 * q^73 - 4 * q^76 + 8 * q^77 - 16 * q^79 - 6 * q^80 + 20 * q^82 - 28 * q^83 + 56 * q^85 + 30 * q^86 - 14 * q^88 + 16 * q^89 + 28 * q^92 + 10 * q^94 + 2 * q^95 + 56 * q^97 + 4 * q^98

Introduction

L-functions

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Database

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